pytorch/torch/_inductor/lowering.py

import functools
import itertools
import logging
import os
import warnings
from collections import defaultdict
from collections.abc import Iterable
from typing import Any, Callable, Dict, List, Optional, Tuple, Union

import sympy

import torch
import torch.fx
import torch.utils._pytree as pytree
from torch._higher_order_ops.triton_kernel_wrap import (
    triton_kernel_wrapper_functional,
    triton_kernel_wrapper_mutation,
)
from torch._prims_common import (
    canonicalize_dim,
    canonicalize_dims,
    check,
    dtype_to_type,
    elementwise_dtypes,
    ELEMENTWISE_TYPE_PROMOTION_KIND,
    get_computation_dtype,
    is_boolean_dtype,
    is_float_dtype,
    is_integer_dtype,
    Number,
)
from torch.fx.experimental.sym_node import magic_methods, method_to_operator
from torch.utils._sympy.functions import CeilDiv, FloorDiv, ModularIndexing
from .._dynamo.utils import import_submodule

from . import config, inductor_prims, ir, test_operators  # NOQA: F401
from .decomposition import decompositions, get_decompositions
from .ir import (
    ExpandView,
    IndexingConstant,
    is_triton,
    ops_wrapper,
    PermuteView,
    Pointwise,
    Reduction,
    SqueezeView,
    TensorBox,
    validate_ir,
    View,
)
from .utils import (
    ceildiv,
    decode_device,
    is_dynamic,
    is_pointwise_use,
    pad_listlike,
    sympy_product,
)
from .virtualized import ops, V

log = logging.getLogger(__name__)
lowerings = {}
layout_constraints = {}
fallbacks = set()
aten = torch.ops.aten
tr_c10d = torch.ops.tr_c10d
prims = torch.ops.prims
needs_realized_inputs = set()
foreach_ops = set()
inplace_foreach_ops = set()
inplaceable_foreach_ops = dict()


def assert_nyi(cond, msg):
    if not cond:
        raise NotImplementedError(f"inductor does not support {msg}")


def add_needs_realized_inputs(fn):
    if isinstance(fn, (list, tuple, set)):
        return [add_needs_realized_inputs(x) for x in fn]
    needs_realized_inputs.add(fn)
    if isinstance(fn, torch._ops.OpOverloadPacket):
        for overload in fn.overloads():
            needs_realized_inputs.add(getattr(fn, overload))


def add_layout_constraint(fn, constraint):
    if isinstance(fn, torch._ops.OpOverloadPacket):
        for overload in fn.overloads():
            layout_constraints[getattr(fn, overload)] = constraint
    else:
        layout_constraints[fn] = constraint


add_needs_realized_inputs(
    [
        aten.as_strided,
        aten.avg_pool2d,
        aten.avg_pool2d_backward,
        aten.bmm,
        aten.convolution,
        aten.convolution_backward,
        aten.max_pool2d_with_indices,
        aten.max_pool2d_with_indices_backward,
        aten.mm,
        aten.upsample_nearest2d,
        aten._upsample_nearest_exact2d,
        aten.upsample_bicubic2d,
        aten._int_mm,
    ]
)

# TODO(jansel): ezyang says we won't need this in the future, try removing it
# based on https://github.com/pytorch/pytorch/blob/9e3eb329df8f701/c10/core/ScalarType.h#L28
DTYPE_ID_LOOKUP = {
    0: torch.uint8,
    1: torch.int8,
    2: torch.int16,
    3: torch.int32,
    4: torch.int64,
    5: torch.float16,
    6: torch.float32,
    7: torch.float64,
    8: torch.complex32,
    9: torch.complex64,
    10: torch.complex32,
    11: torch.bool,
    15: torch.bfloat16,
    # TODO(jansel): add quantized types?
    #  _(c10::qint8, QInt8) /* 12 */
    # _(c10::quint8, QUInt8) /* 13 */
    # _(c10::qint32, QInt32) /* 14 */
    # _(c10::quint4x2, QUInt4x2) /* 16 */
    # _(c10::quint2x4, QUInt2x4) /* 17 */
}


def decode_dtype(dtype: int):
    if not isinstance(dtype, int):
        return dtype
    assert dtype in DTYPE_ID_LOOKUP, f"id {dtype} missing from DTYPE_ID_LOOKUP"
    dtype = DTYPE_ID_LOOKUP[dtype]
    return dtype


def is_integer_type(x):
    if isinstance(x, TensorBox):
        return is_integer_dtype(x.get_dtype()) or is_boolean_dtype(x.get_dtype())
    elif isinstance(x, sympy.Expr):
        return x.is_integer is True  # type: ignore[attr-defined]
    else:
        return isinstance(x, int)


def is_boolean_type(x):
    if isinstance(x, TensorBox):
        return is_boolean_dtype(x.get_dtype())
    else:
        return isinstance(x, bool)


def get_promoted_dtype(*args, type_promotion_kind: ELEMENTWISE_TYPE_PROMOTION_KIND):
    def construct_input(inp):
        if isinstance(inp, (Number, sympy.Expr)):
            return inp
        else:
            assert hasattr(inp, "get_dtype")
            dim = len(inp.get_size())
            # construct a tmp tensor to feed into torch.result_type
            return torch.zeros([1] * dim, dtype=inp.get_dtype())

    inps = [construct_input(arg) for arg in args]
    _, dtype = elementwise_dtypes(*inps, type_promotion_kind=type_promotion_kind)
    return dtype


def get_overloads(aten_fn):
    if not isinstance(aten_fn, (list, tuple)):
        aten_fn = [aten_fn]
    else:
        aten_fn = list(aten_fn)

    for fn in list(aten_fn):
        if isinstance(fn, torch._ops.OpOverloadPacket):
            for overload in fn.overloads():
                other_fn = getattr(fn, overload)
                if other_fn not in lowerings:
                    aten_fn.append(other_fn)

    return aten_fn


def transform_args(args, broadcast, type_promotion_kind, convert_input_to_bool):
    indices = [i for i, x in enumerate(args) if isinstance(x, TensorBox)]
    if (type_promotion_kind or convert_input_to_bool) and indices:
        if convert_input_to_bool:
            dtype = torch.bool
        else:
            # FIXME that's a crude approximation for promoting args
            promoting_args = [
                a
                for a in args
                if isinstance(a, (Number, sympy.Expr)) or hasattr(a, "get_dtype")
            ]
            dtype = get_promoted_dtype(
                *promoting_args, type_promotion_kind=type_promotion_kind
            )

        # sometimes args are an immutable list so we can't mutate them
        def promote(arg):
            if isinstance(arg, TensorBox):
                return to_dtype(arg, dtype)
            elif isinstance(arg, ir.Constant):
                return ir.Constant(arg.value, dtype, args[indices[0]].get_device())
            else:
                return arg

        args = [promote(a) for a in args]
    if broadcast and indices:
        for i, x in zip(indices, broadcast_tensors(*[args[i] for i in indices])):
            args[i] = x
        for i in range(len(args)):
            if isinstance(args[i], ir.Constant):
                args[i] = ExpandView.create(args[i], list(args[indices[0]].get_size()))

    return args


def _register_foreach_lowering(aten_fn, decomp_fn):
    """
    Add a foreach lowering to lowerings dict.

    Arguments:
        aten_fn: torch.ops.aten.* fn we are lowering
        decomp_fn: alternate implementation on our IR
        broadcast: True to apply broadcasting to tensor inputs
        type_promotion_kind: kind of type promotion applied to tensor inputs, `None` means no type promotion
        convert_input_to_bool: some logical ops require inputs are converted to bool
    """

    @functools.wraps(decomp_fn)
    def wrapped(*args, **kwargs):
        assert len(args) <= 2
        out = decomp_fn(*args, **kwargs)
        validate_ir(out)
        return out

    aten_fns = get_overloads(aten_fn)
    foreach_ops.update(aten_fns)
    lowerings.update({fn: wrapped for fn in aten_fns})
    return wrapped


def _register_lowering(
    aten_fn, decomp_fn, broadcast, type_promotion_kind, convert_input_to_bool
):
    """
    Add a lowering to lowerings dict

    Arguments:
        aten_fn: torch.ops.aten.* fn we are lowering
        decomp_fn: alternate implementation on our IR
        broadcast: True to apply broadcasting to tensor inputs
        type_promotion_kind: kind of type promotion applied to tensor inputs, `None` means no type promotion
        convert_input_to_bool: some logical ops require inputs are converted to bool
    """

    @functools.wraps(decomp_fn)
    def wrapped(*args, **kwargs):
        args: Union[List[Any], Tuple[Any, ...], Dict[Any, Any]] = list(args)
        unpacked = False
        # TODO maybe we need to use pytrees here
        if len(args) == 1 and isinstance(args[0], (list, tuple)):
            unpacked = True
            args = args[0]

        # explicitly assert for "out=" ops for better error messages
        assert not any(
            x == "out" for x in kwargs.keys()
        ), "out= ops aren't yet supported"
        # kwargs tensors not supported yet unless it's a fallback op
        assert not any(isinstance(x, TensorBox) for x in kwargs.values()) or all(
            fn in fallbacks for fn in aten_fn
        )

        args = transform_args(
            args, broadcast, type_promotion_kind, convert_input_to_bool
        )

        if unpacked:
            args = [args]

        out = decomp_fn(*args, **kwargs)
        validate_ir(out)

        return out

    aten_fn = get_overloads(aten_fn)

    lowerings.update({fn: wrapped for fn in aten_fn})
    return wrapped


def register_lowering(
    aten_fn,
    broadcast=False,
    type_promotion_kind=ELEMENTWISE_TYPE_PROMOTION_KIND.DEFAULT,
    convert_input_to_bool=False,
):
    """
    Shim to support decorator syntax.
    """
    return functools.partial(
        _register_lowering,
        aten_fn,
        broadcast=broadcast,
        type_promotion_kind=type_promotion_kind,
        convert_input_to_bool=convert_input_to_bool,
    )


def broadcast_symbolic_shapes(a, b):
    """
    Broadcasting logic based on symbolic shapes.

    We give the shapes 0 and 1 concrete values, while all other shapes
    are symbolic sympy formulas.
    """
    output = []
    for x, y in itertools.zip_longest(
        reversed(a), reversed(b), fillvalue=sympy.Integer(1)
    ):
        if y == 1:
            output.append(x)
        elif x == 1:
            output.append(y)
        else:
            V.graph.sizevars.guard_equals(x, y)
            if len(sympy.expand(y).free_symbols) < len(sympy.expand(x).free_symbols):
                output.append(y)  # prefer shorter formula
            else:
                output.append(x)
    return tuple(reversed(output))


def promote_constants(inputs, override_return_dtype=None, type_promotion_kind=None):
    assert (
        override_return_dtype is None or type_promotion_kind is None
    ), "only one of override_return_dtype or type_promotion_kind may be given"

    if override_return_dtype is None and type_promotion_kind is None:
        type_promotion_kind = ELEMENTWISE_TYPE_PROMOTION_KIND.DEFAULT

    if not any(isinstance(x, (sympy.Expr, int, float)) for x in inputs):
        return inputs
    if all(isinstance(x, (int, float, sympy.Expr)) for x in inputs):
        dtype = override_return_dtype or get_promoted_dtype(
            *inputs, type_promotion_kind=type_promotion_kind
        )

        def const_func(x):
            if isinstance(x, sympy.Expr):
                return ir.IndexingConstant(x, dtype, decode_device(None))
            else:
                return ir.Constant(x, dtype, decode_device(None))

        return [const_func(x) for x in inputs]
    ex = next(x for x in inputs if isinstance(x, (TensorBox, ExpandView)))
    out = []
    for x in inputs:
        if isinstance(x, (int, float)):
            out.append(
                ExpandView.create(
                    ir.Constant(x, ex.get_dtype(), ex.get_device()), list(ex.get_size())
                )
            )
        elif isinstance(x, sympy.Expr):
            out.append(
                ExpandView.create(
                    IndexingConstant(x, ex.get_dtype(), ex.get_device()),
                    list(ex.get_size()),
                )
            )
        else:
            out.append(x)

    return out


def make_pointwise(
    fn,
    override_return_dtype=None,
    override_device=None,
    override_fn_when_input_bool=None,
    override_fn_when_cuda_float64=None,
    allow_alpha=False,
):
    def inner(*inputs: List[TensorBox], alpha=None):
        inputs = promote_constants(inputs, override_return_dtype)
        if allow_alpha:
            if alpha is not None and alpha != 1:
                inputs = list(inputs)
                inputs[-1] = mul(inputs[-1], alpha)
        else:
            assert alpha is None
        loaders = [x.make_loader() for x in inputs]
        ranges = inputs[0].get_size()
        dtype = override_return_dtype or inputs[0].get_dtype()
        is_cuda = decode_device(inputs[0].get_device()).type == "cuda"

        for other in inputs[1:]:
            assert isinstance(other, ir.BaseConstant) or len(ranges) == len(
                other.get_size()
            ), f"ndim mismatch {fn} {ranges} {other.get_size()}"

        def inner_fn(index):
            assert len(index) == len(ranges), f"wrong ndim {index} {ranges}"
            if dtype == torch.bool and override_fn_when_input_bool is not None:
                return override_fn_when_input_bool(*[load(index) for load in loaders])
            elif override_fn_when_cuda_float64 and is_cuda and dtype == torch.float64:
                return override_fn_when_cuda_float64(*[load(index) for load in loaders])
            else:
                return fn(*[load(index) for load in loaders])

        if not override_device:
            device = None
            for i in inputs:
                if i.get_device().type == "cuda":
                    device = i.get_device()
                    break
            if not device:
                device = inputs[0].get_device()

        device = override_device or device

        return Pointwise.create(
            device=device,
            dtype=dtype,
            inner_fn=inner_fn,
            ranges=ranges,
        )

    return inner


def make_foreach_pointwise(pw_fn, allow_alpha=False):
    def inner(*inputs: List[List[TensorBox]], alpha=1):
        # group by device, whether any of the inputs are dynamic, and whether their types match
        # (proxy for type promotion)
        def group_args(arg_pairs):
            out = defaultdict(list)
            for i, args in enumerate(arg_pairs):
                use_foreach = not is_dynamic(*args)
                device = None
                for t in args:
                    if isinstance(t, TensorBox):
                        device = t.data.get_device()
                        break
                assert (
                    device is not None
                ), "foreach op should have at least one tensor arg"
                out[(device, use_foreach)].append((i, args))
            return out

        realize_outputs = (
            len(V.graph.current_node.users) == 0
            or V.graph.current_node.target in inplace_foreach_ops
        )
        for node in V.graph.current_node.users:
            for user in node.users:
                if not (user.op == "call_function" and (user.target in foreach_ops)):
                    realize_outputs = True

        a_list_input = None
        for input in inputs:
            if isinstance(input, (list, tuple)):
                a_list_input = input
                break
        assert (
            a_list_input is not None
        ), "at least one input must be a list to a foreach op"

        # broadcast scalar inputs to match length of list inputs
        broadcast_inputs = []
        for input in inputs:
            if not isinstance(input, (list, tuple)):
                broadcast_inputs.append([input] * len(a_list_input))
            else:
                broadcast_inputs.append(input)

        groups = group_args(zip(*broadcast_inputs))

        outputs = [None] * len(a_list_input)
        for (device, use_foreach), group in groups.items():
            buffer_list = []
            for (
                output_ind,
                args,
            ) in group:
                if allow_alpha:
                    output = pw_fn(*args, alpha=alpha)
                else:
                    output = pw_fn(*args)

                outputs[output_ind] = output

                if device.type == "cuda" and use_foreach and realize_outputs:
                    buffer_list.append(output.realize())

            if buffer_list:
                V.graph.register_list(buffer_list)

        assert all(x is not None for x in outputs)
        return outputs

    return inner


def to_dtype(x: TensorBox, dtype: torch.dtype, copy=False):
    src_dtype = x.get_dtype()
    if src_dtype == dtype:
        return clone(x) if copy else x

    def _to_dtype(x):
        return ops.to_dtype(x, dtype, src_dtype=src_dtype)

    return make_pointwise(_to_dtype, override_return_dtype=dtype)(x)


@register_lowering(prims.convert_element_type, type_promotion_kind=None)
def _convert_element_type(x: TensorBox, dtype: torch.dtype):
    return to_dtype(x, dtype, copy=True)


def to_dtype_bitcast(x: TensorBox, dtype: torch.dtype, *, copy=False):
    x_dtype = x.get_dtype()
    if x_dtype == dtype:
        return clone(x) if copy else x

    def _get_primitive_bitwidth(dtype):
        if dtype.is_floating_point:
            return torch.finfo(dtype).bits
        else:
            return torch.iinfo(dtype).bits

    src_bits = _get_primitive_bitwidth(x_dtype)
    dst_bits = _get_primitive_bitwidth(dtype)
    if src_bits != dst_bits:
        raise NotImplementedError(
            f"bitcast {x_dtype} to different bitwidth type {dtype} is not supported yet."
        )

    def _to_dtype_bitcast(x):
        # Because we may promote tensor type from float16 or bfloat16
        # to float, we will need to pass the original src dtype (i.e. x_dtype),
        # which is used for correctly constructing type conversion before bitcast,
        # which requires the bitwidth of the input tensor type is the same as the
        # target type.
        return ops.to_dtype_bitcast(x, dtype, x_dtype)

    return make_pointwise(_to_dtype_bitcast, override_return_dtype=dtype)(x)


@register_lowering(aten.view.dtype, type_promotion_kind=None)
def _view_dtype(x: TensorBox, dtype: torch.dtype):
    if dtype.is_complex or x.get_dtype().is_complex:
        return TensorBox.create(
            ir.ComplexView.create(torch.ops.aten.view.dtype, x, dtype)
        )
    return to_dtype_bitcast(x, dtype, copy=True)


def to_device(x: TensorBox, device: torch.device, *, copy=False):
    device = decode_device(device)
    if x.get_device() == device:
        return clone(x) if copy else x
    return TensorBox.create(ir.DeviceCopy.create(x, device))


@register_lowering(prims.device_put, type_promotion_kind=None)
def _device_put(x: TensorBox, device: torch.device):
    return to_device(x, device, copy=True)


def register_pointwise(
    aten_fn,
    name=None,
    broadcast=True,
    type_promotion_kind=ELEMENTWISE_TYPE_PROMOTION_KIND.DEFAULT,
    convert_input_to_bool=False,
    override_return_dtype=None,
    override_fn_when_input_bool=None,
    allow_alpha=False,
    use_libdevice_for_f64=False,
):
    """A pointwise function that maps ops.{name} to inputs"""
    name = name or aten_fn.__name__
    fn = ops_wrapper(name)
    if use_libdevice_for_f64:
        fn_libdevice = ops_wrapper("libdevice_" + name)
    if override_fn_when_input_bool is not None:
        override_fn_when_input_bool = ops_wrapper(override_fn_when_input_bool)

    fn = make_pointwise(
        fn,
        override_return_dtype=override_return_dtype,
        override_fn_when_input_bool=override_fn_when_input_bool,
        override_fn_when_cuda_float64=fn_libdevice if use_libdevice_for_f64 else None,
        allow_alpha=allow_alpha,
    )
    fn = register_lowering(
        aten_fn,
        broadcast=broadcast,
        type_promotion_kind=type_promotion_kind,
        convert_input_to_bool=convert_input_to_bool,
    )(fn)

    if hasattr(prims, name):
        register_lowering(
            getattr(prims, name),
            type_promotion_kind=None,
            convert_input_to_bool=convert_input_to_bool,
        )(fn)
    return fn


def register_foreach_pointwise(
    aten_fn,
    pointwise_lowering_fn,
    allow_alpha=False,
):
    fn = make_foreach_pointwise(pointwise_lowering_fn, allow_alpha=allow_alpha)
    fn = _register_foreach_lowering(aten_fn, fn)
    return fn


@register_lowering(aten.where, broadcast=False, type_promotion_kind=None)
def where(cond, a, b):
    def fn(*args):
        return ops.where(*args)

    if isinstance(a, (float, int)):
        a = constant_like(a)(b)
    if isinstance(b, (float, int)):
        b = constant_like(b)(a)

    args = [cond, a, b]
    dtype = get_promoted_dtype(
        args[1], args[2], type_promotion_kind=ELEMENTWISE_TYPE_PROMOTION_KIND.DEFAULT
    )
    indices = [i for i, x in enumerate(args) if isinstance(x, TensorBox)]
    for i, x in zip(indices, broadcast_tensors(*[args[i] for i in indices])):
        args[i] = x
    for i in range(len(args)):
        if isinstance(args[i], ir.Constant):
            args[i] = ExpandView.create(args[i], list(args[indices[0]].get_size()))
    return make_pointwise(fn, override_return_dtype=dtype)(
        args[0], to_dtype(args[1], dtype), to_dtype(args[2], dtype)
    )


@register_lowering(aten.broadcast_tensors, broadcast=False, type_promotion_kind=None)
def broadcast_tensors(*inputs):
    if len(inputs) == 1 and isinstance(inputs[0], (list, tuple)):
        return broadcast_tensors(*inputs[0])
    target: List[sympy.Expr] = functools.reduce(
        broadcast_symbolic_shapes, [x.get_size() for x in inputs], []
    )
    outputs = []
    for x in inputs:
        sizes = x.get_size()
        if len(sizes) != len(target) or any(
            ((a == 1 and b != 1) or (a != 1 and b == 1)) for a, b in zip(sizes, target)
        ):
            x = expand(x, target)
        outputs.append(x)
    return outputs


@register_lowering([aten.alias, aten.detach, aten.detach_, aten.lift, prims.view_of])
def nop(x):
    return x  # AOT autograd handles this for us


if hasattr(aten, "lift_fresh"):
    register_lowering(aten.lift_fresh)(nop)


@register_lowering(aten.squeeze, type_promotion_kind=None)
def squeeze(x, dim=None):
    assert isinstance(x, TensorBox)
    if dim is None:
        return TensorBox(SqueezeView.create(x.data))

    dim = canonicalize_dims(len(x.get_size()), dim)
    dims = set((dim,) if not isinstance(dim, tuple) else dim)

    new_shape = []
    for d, s in enumerate(x.get_size()):
        if not (d in dims and V.graph.sizevars.evaluate_expr(sympy.Eq(s, 1))):
            new_shape.append(s)

    # squeeze does nothing if the size isn't 1
    return view(x, new_shape) if new_shape != x.get_size() else x


@register_lowering(aten.squeeze_copy, type_promotion_kind=None)
def squeeze_copy(x, dim=None):
    return clone(squeeze(x, dim))


@register_lowering([aten.squeeze_])
def squeeze_(x, dim=None):
    val = squeeze(x, dim)
    assert isinstance(x, TensorBox)
    assert isinstance(val, TensorBox)
    x.data = val.data
    return x


@register_lowering(aten.isinf)
def isinf(x):
    if is_integer_type(x):
        return full_like(x, False, dtype=torch.bool)
    fn = ops_wrapper("isinf")
    return make_pointwise(fn, override_return_dtype=torch.bool)(x)


@register_lowering(aten.isnan)
def isnan(x):
    if is_integer_type(x):
        return full_like(x, False, dtype=torch.bool)
    fn = ops_wrapper("isnan")
    return make_pointwise(fn, override_return_dtype=torch.bool)(x)


@register_lowering(aten.ceil)
def ceil(x):
    if is_integer_type(x):
        return clone(x)
    fn = ops_wrapper("ceil")
    return make_pointwise(fn)(x)


@register_lowering(aten.floor)
def floor(x):
    if is_integer_type(x):
        return clone(x)
    fn = ops_wrapper("floor")
    return make_pointwise(fn)(x)


@register_lowering(aten.round)
def round(x):
    if is_integer_type(x):
        return clone(x)
    fn = ops_wrapper("round")
    return make_pointwise(fn)(x)


@register_lowering(aten.trunc)
def trunc(x):
    if is_integer_type(x):
        return clone(x)
    fn = ops_wrapper("trunc")
    return make_pointwise(fn)(x)


@register_lowering(aten.expand, type_promotion_kind=None)
def expand(x, sizes):
    (x,) = promote_constants([x])
    if isinstance(x, ir.BaseConstant):
        return ExpandView.create(x, tuple(sizes))
    assert isinstance(x, TensorBox)
    assert isinstance(sizes, (list, tuple))
    if tuple(x.get_size()) == tuple(sizes):
        return x

    if not any(V.graph.sizevars.shape_env.is_unbacked_symint(s) for s in x.get_size()):
        x_size_product = V.graph.sizevars.size_hint(sympy_product(x.get_size()))
        # TODO: It would be better to realize the input if any of its sizes
        # are unbacked, because typically the size will be non-zero.  However,
        # this cannot be done directly as below as we'll choke on the size_hint
        # here
        if x_size_product > 0 and not any(
            V.graph.sizevars.shape_env.is_unbacked_symint(s) for s in sizes
        ):
            # maybe realize input before broadcasting it
            x.mark_reuse(
                V.graph.sizevars.size_hint(sympy_product(sizes)) // x_size_product
            )
    return TensorBox(ExpandView.create(x.data, tuple(sizes)))


@register_lowering(prims.broadcast_in_dim, type_promotion_kind=None)
def broadcast_in_dim(a, shape, broadcast_dimensions):
    s = list(shape)
    for broadcast_dimension in broadcast_dimensions:
        s[broadcast_dimension] = -1

    v = a
    for idx, x in enumerate(s):
        if x != -1:
            v = unsqueeze(v, idx)

    return expand(v, shape)


@register_lowering(aten.expand_as, type_promotion_kind=None)
def expand_as(x, y):
    return expand(x, y.get_size())


@register_lowering(aten.repeat)
def repeat(x, repeats):
    old_size = list(x.get_size())
    if len(repeats) > len(old_size):
        old_size = [sympy.Integer(1)] * (len(repeats) - len(old_size)) + old_size
        x = view(x, list(old_size))
    assert len(repeats) == len(x.get_size())

    new_size = list(x.get_size())

    zero_tensor = False
    for i in range(len(repeats)):
        if repeats[i] == 0:
            zero_tensor = True
        new_size[i] = new_size[i] * repeats[i]

    if zero_tensor:
        return empty(new_size, dtype=x.get_dtype(), device=x.get_device())
    if all((a == 1 or b == 1) for a, b in zip(repeats, old_size)):
        return expand(x, new_size)

    x_loader: Callable[[Any], Any]

    def inner_fn(index):
        assert len(index) == len(repeats)
        index = list(index)
        for i in range(len(repeats)):
            if repeats[i] != 1:
                if old_size[i] == 1:
                    index[i] = sympy.Integer(0)
                else:
                    index[i] = ModularIndexing(index[i], 1, old_size[i])
        return x_loader(index)

    old_size_product = V.graph.sizevars.size_hint(sympy_product(old_size))
    if old_size_product > 0:
        # maybe realize the input
        x.mark_reuse(
            V.graph.sizevars.size_hint(sympy_product(new_size)) // old_size_product
        )

    x_loader = x.make_loader()
    return Pointwise.create(
        device=x.get_device(),
        dtype=x.get_dtype(),
        inner_fn=inner_fn,
        ranges=list(new_size),
    )


@register_lowering(aten._unsafe_view, type_promotion_kind=None)
@register_lowering(aten.view, type_promotion_kind=None)
@register_lowering(aten.reshape, type_promotion_kind=None)
def view(x, sizes):
    assert isinstance(x, TensorBox)
    assert isinstance(sizes, (list, tuple))
    return TensorBox(View.create(x.data, sizes))


@register_lowering(aten.permute, type_promotion_kind=None)
def permute(x, dims):
    assert isinstance(x, TensorBox)
    assert isinstance(dims, (list, tuple))
    return TensorBox(PermuteView.create(x.data, tuple(dims)))


@register_lowering(aten.slice, type_promotion_kind=None)
def slice_(x, dim=0, start=0, end=2**63, step=1):
    assert isinstance(x, TensorBox)
    dim = _validate_dim(x, dim, 0)
    dim_size = x.get_size()[dim]
    if V.graph.sizevars.evaluate_expr(sympy.Lt(start + dim_size, 0)):
        start = 0
    if V.graph.sizevars.evaluate_expr(sympy.Lt(end + dim_size, 0)):
        end = 0
    return TensorBox(ir.SliceView.create(x.data, dim, start, end, step))


@register_lowering(aten.roll, type_promotion_kind=None)
def roll(a, shifts, dims=tuple()):
    """
    This is based on torch._refs.roll(), but uses ModularIndexing().

    We can't use the ref here because it is based on multiple calls to
    torch.cat() that this will result in terrible code.
    """
    # ATen specifies int[1] type for shifts and dims which expands integers to tuples of length 1
    if not isinstance(shifts, Iterable):
        shifts = (shifts,)
    if not isinstance(dims, Iterable):
        dims = (dims,)
    dims = [_validate_dim(a, d) for d in dims]

    if sympy_product(a.get_size()) == 0:
        return clone(a)

    len_shifts = len(shifts)
    len_dims = len(dims)
    if len_shifts != 1 or len_dims != 1:
        if len_shifts == 0:
            raise RuntimeError("`shifts` required")
        # Takes care of the case when dims is not specified (default)
        # By default, the tensor is flattened before shifting, after which the original shape is restored
        if len_dims == 0 and len_shifts == 1:
            flat = view(a, [sympy_product(a.get_size())])
            rolled = roll(flat, shifts, 0)
            return view(rolled, list(a.get_size()))
        if len_shifts != len_dims:
            raise RuntimeError(
                f"shifts and dimensions must align. shifts: {len_shifts}, dims: {len_dims}"
            )
        tail_shifts = shifts[1:]
        tail_dims = dims[1:]
        first_dim_rolled = roll(a, shifts[0], dims[0])
        return roll(first_dim_rolled, tail_shifts, tail_dims)

    (dim,) = dims
    # TODO: Avoid guarding on shape here
    size = V.graph.sizevars.evaluate_static_shape(a.get_size()[dim])
    start = (size - shifts[0]) % size
    a_loader = a.make_loader()

    def fn(index):
        index = list(index)
        index[dim] = ModularIndexing(
            index[dim] + start, sympy.Integer(1), sympy.expand(size)
        )
        return a_loader(index)

    return Pointwise.create(
        device=a.get_device(),
        dtype=a.get_dtype(),
        inner_fn=fn,
        ranges=a.get_size(),
    )


@register_lowering(aten.as_strided, type_promotion_kind=None)
def as_strided(x, size, stride, storage_offset=None):
    if isinstance(x, TensorBox) and isinstance(x.data, ir.BaseView):
        # as_strided ignores views
        x = x.data.unwrap_view()
    x.realize()
    if not ir.is_storage_and_layout(x):
        raise NotImplementedError(f"unrealized as_strided({x}, ...)")
    storage, old_layout = ir.as_storage_and_layout(x)
    new_layout = ir.FixedLayout(
        old_layout.device,
        old_layout.dtype,
        [sympy.expand(s) for s in size],
        [sympy.expand(s) for s in stride],
        sympy.expand(storage_offset or 0),
    )
    return TensorBox(ir.ReinterpretView(storage, new_layout))


@register_lowering(aten.as_strided_, type_promotion_kind=None)
def as_strided_(x, size, stride, storage_offset=None):
    assert isinstance(x, TensorBox)
    x.data = as_strided(x, size, stride, storage_offset).data
    return x


@register_lowering(aten.as_strided_copy, type_promotion_kind=None)
def as_strided_copy(x, size, stride, storage_offset=None):
    result = as_strided(x, size, stride, storage_offset)
    return clone(result)


def pointwise_cat(inputs, dim=0):
    # (inclusive, exclusive)
    inputs_ranges: List[Tuple[sympy.Expr, sympy.Expr]] = []
    prev_end = 0
    for inp in inputs:
        inputs_ranges.append((prev_end, prev_end + inp.get_size()[dim]))
        prev_end = inputs_ranges[-1][-1]

    inputs_loaders = [inp.make_loader() for inp in inputs]

    def inner_fn(idx):
        idx_dim = ops.index_expr(idx[dim], torch.int64)

        masks = []
        masked_loads = []
        for i in range(len(inputs)):
            start = (
                ops.constant(0, torch.int64)
                if i == 0
                else ops.index_expr(inputs_ranges[i][0], torch.int64)
            )
            end = ops.index_expr(inputs_ranges[i][1], torch.int64)

            start_cond = ops.ge(idx_dim, start)
            end_cond = ops.lt(idx_dim, end)
            if i == 0:
                mask = end_cond
            elif i == len(inputs) - 1:
                mask = start_cond
            else:
                mask = ops.and_(start_cond, end_cond)

            masks.append(mask)
            idx_load = list(idx)

            # if we're concatting [4], [2]
            # when we index the second tensor for 5 we want to index 5 - 4
            idx_load[dim] -= inputs_ranges[i][0]

            masked_loads.append(
                ops.masked(
                    mask,
                    lambda: inputs_loaders[i](idx_load),
                    0.0,  # this value should be unused
                ),
            )

        def get_masked_val(i):
            if i != len(inputs) - 1:
                return ops.where(
                    masks[i],
                    masked_loads[i],
                    get_masked_val(i + 1),
                )
            else:
                return masked_loads[-1]

        return get_masked_val(0)

    new_size = list(inputs[0].get_size())
    new_size[dim] = inputs_ranges[-1][-1]

    return Pointwise.create(
        device=inputs[0].get_device(),
        dtype=inputs[0].get_dtype(),
        inner_fn=inner_fn,
        ranges=new_size,
    )


@register_lowering(aten.cat)
def cat(inputs, dim=0):
    if all(input.get_dtype() is torch.uint8 for input in inputs):
        # TODO <leslie> Remove this fallback when we support vectorization
        # code gen with uint8 data type directly.
        for input in inputs:
            input.realize()
        if all(len(input.get_size()) == 4 for input in inputs):
            inputs, _ = require_channels_last(aten.cat, *inputs)
        return fallback_handler(aten.cat.default)(inputs, dim)

    if len(inputs) == 1:
        return clone(inputs[0])

    dim = _validate_dim(inputs[0], dim, 0)
    dtype = get_promoted_dtype(
        *inputs, type_promotion_kind=ELEMENTWISE_TYPE_PROMOTION_KIND.DEFAULT
    )
    inputs = [to_dtype(inp, dtype) for inp in inputs]

    def should_lower_cat_input(x) -> bool:
        # Unrealized inputs will not be storage and layouts, and we dont want to realize
        # them in case we want to fuse
        if ir.is_storage_and_layout(x):
            storage, _ = ir.as_storage_and_layout(x, freeze=False)
            return not ir.ConcatKernel.can_realize_into_without_copy(storage)

        if isinstance(x, TensorBox):
            if isinstance(x.data, ir.BaseView):
                return should_lower_cat_input(x.data.unwrap_view())
            else:
                return should_lower_cat_input(x.data)

        if isinstance(x, ir.StorageBox):
            return should_lower_cat_input(x.data)

        if isinstance(x, ir.Pointwise):
            return True

        return False

    # TODO: We observed negative performance impact of pointwise_cat optimization on CPU so disabled it.
    #             We will revisit this later after enabling vectorization on index_expr.
    if (
        len(inputs) <= config.max_pointwise_cat_inputs
        and inputs[0].get_device().type != "cpu"
    ):
        pointwise_uses = all(is_pointwise_use(use) for use in V.current_node.users)
        all_pointwise_inputs = all(should_lower_cat_input(inp) for inp in inputs)
        any_pointwise_inputs = any(should_lower_cat_input(inp) for inp in inputs)

        if all_pointwise_inputs or (any_pointwise_inputs and pointwise_uses):
            return pointwise_cat(inputs, dim)

    return TensorBox(ir.ConcatKernel.create(inputs, dim))


@register_lowering(aten.diagonal, type_promotion_kind=None)
def diagonal(input, offset: int = 0, dim1: int = 0, dim2: int = 1):
    original_shape = input.get_size()
    num_dims = len(original_shape)
    dim1 = canonicalize_dim(idx=dim1, rank=num_dims)
    dim2 = canonicalize_dim(idx=dim2, rank=num_dims)

    check(
        dim1 != dim2, lambda: f"diagonal dimensions cannot be identical {dim1}, {dim2}"
    )

    offset_negative = V.graph.sizevars.evaluate_expr(sympy.Lt(offset, 0))
    if offset_negative:
        diag_size = max(min(original_shape[dim1] + offset, original_shape[dim2]), 0)
    else:
        diag_size = max(min(original_shape[dim1], original_shape[dim2] - offset), 0)

    base_idx = (0, 0)
    if offset_negative:
        base_idx = (-offset, 0)
    else:
        base_idx = (0, offset)

    sizes = [s for i, s in enumerate(original_shape) if i not in (dim1, dim2)]
    sizes.append(diag_size)

    def reindexer(idx):
        diag_idx = idx[-1]
        original_idx = [0] * len(original_shape)
        cur_dim = 0
        for d in range(num_dims):
            if d == dim1:
                original_idx[d] = diag_idx + base_idx[0]
            elif d == dim2:
                original_idx[d] = diag_idx + base_idx[1]
            else:
                original_idx[d] = idx[cur_dim]
                cur_dim += 1

        assert cur_dim == len(original_shape) - 2
        return original_idx

    return TensorBox(ir.GenericView.create(input, sizes, reindexer))


@register_lowering(aten.diagonal_copy, type_promotion_kind=None)
def diagonal_copy(input, offset: int = 0, dim1: int = 0, dim2: int = 1):
    return clone(diagonal(input, offset, dim1, dim2))


@register_lowering(aten.diagonal_scatter, type_promotion_kind=None)
def diagonal_scatter(input, src, offset: int = 0, dim1: int = 0, dim2: int = 1):
    output = clone(input)
    target = diagonal(output, offset, dim1, dim2)
    mutate_to(target, src)
    return output


@register_lowering(aten.select, type_promotion_kind=None)
def select(x, dim, idx):
    idx = View.handle_negative_index(idx, x.get_size()[dim])
    return squeeze(slice_(x, dim, idx, idx + 1), dim)


@register_lowering(aten.split, type_promotion_kind=None)
def split(x, sizes, dim=0):
    dim = _validate_dim(x, dim, 0)
    x_size = V.graph.sizevars.evaluate_static_shape(x.get_size()[dim])
    if isinstance(sizes, sympy.Expr):
        # TODO: We don't have to guard on sizes per se, but the number
        # of splits must stay constant
        sizes = V.graph.sizevars.evaluate_static_shape(sizes)
    if isinstance(sizes, (int, sympy.Integer)):
        sizes = [sizes] * ((x_size + sizes - 1) // sizes)
    result = []
    start = 0
    for size in sizes:
        end = start + size
        result.append(slice_(x, dim, start, end))
        start = end
    return result


@register_lowering(aten.split_with_sizes, type_promotion_kind=None)
def split_with_sizes(x, sizes, dim=0):
    return split(x, sizes, dim)


@register_lowering(aten.unbind, type_promotion_kind=None)
def unbind(x, dim=0):
    dim = _validate_dim(x, dim, 0)
    x_size = V.graph.sizevars.evaluate_static_shape(x.get_size()[dim])
    result = []
    for i in range(x_size):
        result.append(select(x, dim, i))
    return result


@register_lowering(aten.unfold, type_promotion_kind=None)
def unfold(x, dimension, size, step):
    sizes = x.get_size()
    ndim = len(sizes)
    dim = canonicalize_dim(ndim, dimension)

    if ndim == 0:
        return slice_(unsqueeze(x, 0), end=size)

    dim_size = sizes[dim]
    sizevars = V.graph.sizevars
    sizevars.guard_leq(size, dim_size)
    sizevars.guard_lt(0, step)

    new_dim_size = FloorDiv(dim_size - size, step) + 1
    if sizevars.size_hint(dim_size) > 0:
        x.mark_reuse(sizevars.size_hint(CeilDiv(new_dim_size * size, dim_size)))

    out_size = [*sizes[:dim], new_dim_size, *sizes[dim + 1 :], size]

    def reindexer(idx):
        dim_idx = idx[-1] + idx[dim] * step
        return (*idx[:dim], dim_idx, *idx[dim + 1 : -1])

    return TensorBox(ir.GenericView.create(x, out_size, reindexer))


@register_lowering(aten.unsqueeze, type_promotion_kind=None)
def unsqueeze(x, dim):
    dim = _validate_dim(x, dim, 1)
    new_shape = list(x.get_size())
    new_shape.insert(dim, sympy.Integer(1))
    return view(x, new_shape)


@register_lowering(aten.unsqueeze_, type_promotion_kind=None)
def unsqueeze_(x, dim):
    val = unsqueeze(x, dim)
    assert isinstance(x, TensorBox)
    assert isinstance(val, TensorBox)
    x.data = val.data
    return x


def _validate_dim(x, dim, offset=0):
    assert isinstance(dim, int)
    ndim = len(x.get_size())
    if dim < 0:
        dim += ndim + offset
    assert 0 <= dim < ndim + offset
    return dim


@register_lowering(aten.glu)
def glu(x, dim=-1):
    dim = _validate_dim(x, dim, 0)
    # TODO: don't guard on static shape here
    new_len = V.graph.sizevars.evaluate_static_shape(x.get_size()[dim]) // 2
    a = slice_(x, dim, 0, new_len)
    b = slice_(x, dim, new_len, new_len * 2)
    return mul(a, sigmoid(b))


def register_onednn_fusion_ops():
    if torch._C._has_mkldnn:
        cpu_needs_realized_inputs = [
            torch.ops.mkldnn._convolution_pointwise,
            torch.ops.mkldnn._convolution_pointwise_,
            torch.ops.mkldnn._convolution_transpose_pointwise,
            torch.ops.mkldnn._linear_pointwise,
            aten.mkldnn_rnn_layer.default,
            torch.ops.onednn.qconv2d_pointwise,
        ]

        @register_lowering(torch.ops.mkldnn._convolution_pointwise)
        def convolution_unary(
            x: TensorBox,
            weight: TensorBox,
            bias: TensorBox,
            padding,
            stride,
            dilation,
            groups,
            attr,
            scalars,
            algorithm,
        ):
            return TensorBox.create(
                ir.ConvolutionUnary.create(
                    x,
                    weight,
                    bias,
                    padding,
                    stride,
                    dilation,
                    groups,
                    attr,
                    scalars,
                    algorithm,
                )
            )

        @register_lowering(torch.ops.mkldnn._convolution_pointwise.binary)
        def convolution_binary(
            x: TensorBox,
            other: TensorBox,
            weight: TensorBox,
            bias: TensorBox,
            padding,
            stride,
            dilation,
            groups,
            binary_attr,
            binary_alpha,
            unary_attr,
            unary_scalars,
            unary_algorithm,
        ):
            return TensorBox.create(
                ir.ConvolutionBinary.create(
                    x,
                    other,
                    weight,
                    bias,
                    padding,
                    stride,
                    dilation,
                    groups,
                    binary_attr,
                    binary_alpha,
                    unary_attr,
                    unary_scalars,
                    unary_algorithm,
                )
            )

        @register_lowering(torch.ops.mkldnn._convolution_pointwise_.binary)
        def convolution_binary_inplace(
            x: TensorBox,
            other: TensorBox,
            weight: TensorBox,
            bias: TensorBox,
            padding,
            stride,
            dilation,
            groups,
            binary_attr,
            binary_alpha,
            unary_attr,
            unary_scalars,
            unary_algorithm,
        ):
            return TensorBox.create(
                ir.ConvolutionBinaryInplace.create(
                    x,
                    other,
                    weight,
                    bias,
                    padding,
                    stride,
                    dilation,
                    groups,
                    binary_attr,
                    binary_alpha,
                    unary_attr,
                    unary_scalars,
                    unary_algorithm,
                )
            )

        @register_lowering(torch.ops.mkldnn._linear_pointwise)
        def linear_unary(
            x: TensorBox, w: TensorBox, b: TensorBox, attr, scalars, algorithm
        ):
            return TensorBox.create(
                ir.LinearUnary.create(x, w, b, attr, scalars, algorithm)
            )

        @register_lowering(torch.ops.mkldnn._linear_pointwise.binary)
        def linear_binary(x: TensorBox, y: TensorBox, w: TensorBox, b: TensorBox, attr):
            return TensorBox.create(ir.LinearBinary.create(x, y, w, b, attr))

        @register_lowering(torch.ops.mkldnn._convolution_transpose_pointwise)
        def convolution_transpose_unary(
            x: TensorBox,
            weight: TensorBox,
            bias: TensorBox,
            padding,
            output_padding,
            stride,
            dilation,
            groups,
            attr,
            scalars,
            algorithm,
        ):
            return TensorBox.create(
                ir.ConvolutionTransposeUnary.create(
                    x,
                    weight,
                    bias,
                    padding,
                    output_padding,
                    stride,
                    dilation,
                    groups,
                    attr,
                    scalars,
                    algorithm,
                )
            )

        @register_lowering(aten.mkldnn_rnn_layer.default)
        def mkldnn_rnn_layer(
            x: TensorBox,
            w0: TensorBox,
            w1: TensorBox,
            w2: TensorBox,
            w3: TensorBox,
            hx: TensorBox,
            cx: TensorBox,
            reverse: bool,
            batch_sizes: List[int],
            mode: int,
            hidden_size: int,
            num_layers: int,
            has_biases: bool,
            bidirectional: bool,
            batch_first: bool,
            train: bool,
        ):
            return pytree.tree_map(
                TensorBox.create,
                ir.MkldnnRnnLayer.create(
                    x,
                    w0,
                    w1,
                    w2,
                    w3,
                    hx,
                    cx,
                    reverse,
                    batch_sizes,
                    mode,
                    hidden_size,
                    num_layers,
                    has_biases,
                    bidirectional,
                    batch_first,
                    train,
                ),
            )

        @register_lowering(torch.ops.onednn.qconv2d_pointwise, type_promotion_kind=None)
        def qconvolution_unary(
            x: TensorBox,
            x_scale,
            x_zp,
            packed_weight: TensorBox,
            w_scale: TensorBox,
            w_zp: TensorBox,
            bias: TensorBox,
            stride,
            padding,
            dilation,
            groups,
            o_inv_scale,
            o_zero_point,
            output_dtype,
            attr,
            scalars,
            algorithm,
        ):
            return TensorBox.create(
                ir.QConvPointWisePT2E.create(
                    x,
                    x_scale,
                    x_zp,
                    packed_weight,
                    w_scale,
                    w_zp,
                    bias,
                    stride,
                    padding,
                    dilation,
                    groups,
                    o_inv_scale,
                    o_zero_point,
                    output_dtype,
                    attr,
                    scalars,
                    algorithm,
                )
            )

        @register_lowering(
            torch.ops.onednn.qconv2d_pointwise.binary, type_promotion_kind=None
        )
        def qconvolution_binary(
            x: TensorBox,
            x_scale,
            x_zp,
            accum: TensorBox,
            accum_scale,
            accum_zp,
            packed_weight: TensorBox,
            w_scale: TensorBox,
            w_zp: TensorBox,
            bias: TensorBox,
            stride,
            padding,
            dilation,
            groups,
            o_inv_scale,
            o_zero_point,
            output_dtype,
            binary_attr,
            alpha,
            unary_attr,
            unary_scalars,
            unary_algorithmm,
        ):
            if (
                binary_attr == "sum"
                and output_dtype in [torch.float32, torch.bfloat16]
                and accum.get_dtype() in [torch.float32, torch.bfloat16]
                and accum.get_dtype() != output_dtype
            ):
                # For int8-mixed-bf16 quantization and inplace add,
                # there is case when accum dtype is float32 but output dtype is bfloat16.
                # Since the accum will be inplaced changed with post op sum,
                # we will do accum dtype convertion here.
                accum = to_dtype(accum, output_dtype)
            return TensorBox.create(
                ir.QConvPointWiseBinaryPT2E.create(
                    x,
                    x_scale,
                    x_zp,
                    accum,
                    accum_scale,
                    accum_zp,
                    packed_weight,
                    w_scale,
                    w_zp,
                    bias,
                    stride,
                    padding,
                    dilation,
                    groups,
                    o_inv_scale,
                    o_zero_point,
                    output_dtype,
                    binary_attr,
                    alpha,
                    unary_attr,
                    unary_scalars,
                    unary_algorithmm,
                )
            )

        @register_lowering(torch.ops.onednn.qlinear_pointwise, type_promotion_kind=None)
        def qlinear_unary(
            x: TensorBox,
            x_scale,
            x_zp,
            packed_weight: TensorBox,
            w_scale: TensorBox,
            w_zp: TensorBox,
            bias: TensorBox,
            o_inv_scale,
            o_zero_point,
            output_dtype,
            attr,
            scalars,
            algorithm,
        ):
            return TensorBox.create(
                ir.QLinearPointwisePT2E.create(
                    x,
                    x_scale,
                    x_zp,
                    packed_weight,
                    w_scale,
                    w_zp,
                    bias,
                    o_inv_scale,
                    o_zero_point,
                    output_dtype,
                    attr,
                    scalars,
                    algorithm,
                )
            )

        if torch._C.has_mkl:
            cpu_needs_realized_inputs.append(torch.ops.mkl._mkl_linear)

            @register_lowering(torch.ops.mkl._mkl_linear)
            def mkl_packed_linear(
                x: TensorBox,
                packed_w: TensorBox,
                orig_w: TensorBox,
                b: TensorBox,
                batch_size,
            ):
                result = TensorBox.create(
                    ir.MKLPackedLinear.create(x, packed_w, orig_w, batch_size)
                )
                if b is not None:
                    result = add(result, b)
                return result

        add_needs_realized_inputs(cpu_needs_realized_inputs)
    else:
        pass


register_onednn_fusion_ops()


def fallback_handler(kernel, add_to_fallback_set=True):
    if add_to_fallback_set:
        fallbacks.add(kernel)

    def handler(*args, **kwargs):
        return pytree.tree_map(
            TensorBox.create, ir.FallbackKernel.create(kernel, *args, **kwargs)
        )

    return handler


@functools.lru_cache(None)
def _warn_complex_not_supported():
    warnings.warn(
        "Torchinductor does not support code generation for complex operators. Performance may be worse than eager."
    )


# There are some types (CPU) which we accept as input but not as
# output.
def unsupported_input_tensor(t: torch._subclasses.FakeTensor, parent=None):
    "Do not support reading or writing to this tensor"
    if t.is_complex():
        # Complex views are supported with IR ComplexView
        if parent and parent.target == torch.ops.aten.view.dtype:
            return False
        _warn_complex_not_supported()
        return True
    return False


def unsupported_output_tensor(t: torch._subclasses.FakeTensor, parent=None):
    "Do not support writing tensor but can read from it"
    if unsupported_input_tensor(t, parent):
        return True
    return t.is_cpu and config.disable_cpp_codegen


def fallback_node_due_to_unsupported_type(node: torch.fx.Node, allow_cpu_inputs=True):
    # Custom fallback lowering
    if node.target is aten.view_as_complex.default:
        return False

    # We should be able to remove this special case once `disable_cpp_codegen` is killed.
    if node.target is aten.lift_fresh_copy.default:
        return False

    def check_skip_condition(node, parent, is_output):
        if not isinstance(node, torch.fx.Node):
            return False

        if "val" not in node.meta:
            return False

        for meta in pytree.tree_leaves(node.meta["val"]):
            if not isinstance(meta, torch._subclasses.FakeTensor):
                continue

            if is_output:
                if unsupported_output_tensor(meta, parent):
                    return True
            else:
                if unsupported_input_tensor(meta, parent):
                    return True

        return False

    # only skip codegen if there is a cpu output, not input
    for arg in pytree.arg_tree_leaves(*node.args, **node.kwargs):
        if check_skip_condition(arg, node, is_output=False):
            return True

    return check_skip_condition(node, node, is_output=True)


def make_fallback(op, layout_constraint=None, warn=True):
    assert op not in decompositions, f"both a fallback and a decomp for same op: {op}"
    if (
        warn
        and bool(os.getenv("CI"))
        and get_decompositions([op])
        # if fallback_random, we allow not decomposing random
        and not (
            config.fallback_random
            and op in torch._decomp.decompositions_for_rng.extra_random_decomps
        )
    ):
        # Note: 'warn' is holdover from when this was a warning, but for ops that previously
        # set warn=False we do not want a CI error.
        # Ignore the 'suppress errors' configs in CI, as this particular warning happens on startup anyway and is not
        # likely to be triggered preferentially on one CI config over another.
        if torch._dynamo.config.suppress_errors:
            torch._dynamo.config.suppress_errors = False
            log.warning(
                "A make_fallback error occurred in suppress_errors config,"
                " and suppress_errors is being disabled to surface it."
            )
        raise AssertionError(
            f"make_fallback({op}): a decomposition exists, we should switch to it."
            " To fix this error, either add a decomposition to core_aten_decompositions (preferred)"
            " or inductor_decompositions, and delete the corresponding `make_fallback` line."
            " Get help from the inductor team if unsure, don't pick arbitrarily to unblock yourself.",
        )

    def register_fallback(op_overload):
        add_needs_realized_inputs(op_overload)
        if layout_constraint is not None:
            add_layout_constraint(op_overload, layout_constraint)
        return register_lowering(op_overload, type_promotion_kind=None)(
            fallback_handler(op_overload)
        )

    if isinstance(op, torch._ops.OpOverloadPacket):
        for ol in op.overloads():
            op_overload = getattr(op, ol)
            register_fallback(op_overload)
    elif isinstance(op, (torch._ops.OpOverload, torch._ops.HigherOrderOperator)):
        register_fallback(op)
    else:
        raise RuntimeError(f"Unsupported fallback {op} with type {type(op)}")


def philox_rand_offset(shape):
    """
    TorchInductor offset calculation differs from PyTorch eager offset
    calculation for random ops (tl.rand vs torch.rand). In future, we should
    strive for same impl for tl.rand and torch.rand.
    """
    numel = 1
    for s in shape:
        numel = numel * s
    return tensor(numel, dtype=torch.int64)


@register_lowering(torch.ops.rngprims.philox_rand, type_promotion_kind=None)
def philox_rand(size, seed, offset, stride, device, dtype):
    # stride arg is optional and will be used in future for distributed random
    # ops. Currently, its unused.
    random_pos = ir.FixedLayout(
        device,
        dtype,
        size,
        ir.FlexibleLayout.contiguous_strides(size),
    ).make_indexer()
    seed_loader = seed.make_loader()
    offset_loader = offset.make_loader()

    def inner_fn(index):
        # Both seed and offset in the philox_rand op are tensors.
        # torch seed and offsets are of type int64, but tl.rand accepts int32
        seed_index_expr = ops.to_dtype(seed_loader([]), torch.int32)
        offset_index_expr = ops.to_dtype(offset_loader([]), torch.int32)
        # Get the offset'd position
        rand_index_expr = ops.add(
            ops.index_expr(random_pos(index), torch.int32), offset_index_expr
        )
        result = ops.rand(
            seed_index_expr,
            rand_index_expr,
        )
        return ops.to_dtype(result, dtype)

    random_values_node = Pointwise.create(
        device=device,
        dtype=dtype,
        inner_fn=inner_fn,
        ranges=list(size),
    )

    offset_node = philox_rand_offset(size)
    return random_values_node, offset_node


@register_lowering(aten.native_dropout, type_promotion_kind=None)
def native_dropout(x, p, train):
    if config.fallback_random:
        return pytree.tree_map(
            TensorBox.create,
            ir.FallbackKernel.create(aten.native_dropout.default, x, p, train),
        )
    else:
        raise AssertionError("should be handled in replace_random.py")


@register_lowering(aten.bernoulli_, type_promotion_kind=None)
def bernoulli_(x, *args):
    assert config.fallback_random or x.get_device() == torch.device(
        "cpu"
    ), "this should be handled in decomps unless config.fallback_random or the device is CPU"
    x.realize()
    ir.InplaceBernoulliFallback(x, *args)
    return x


@register_lowering(aten.bernoulli.p, type_promotion_kind=None)
def bernoulli_p(x, *args):
    assert config.fallback_random or x.get_device() == torch.device(
        "cpu"
    ), "this should be handled in decomps unless config.fallback_random or the device is CPU"
    return bernoulli_(clone(x), *args)


# This shouldn't be called in general
@register_lowering(aten._foobar)
def _foobar(_):
    raise AssertionError()


@functools.lru_cache(1)
def _warn_triton_random(salt):
    log.info("using triton random, expect difference from eager")


def warn_triton_random():
    # only warn once per graph
    _warn_triton_random(V.graph.creation_time)


fallback_rand_default = fallback_handler(aten.rand.default)
fallback_rand_generator = fallback_handler(aten.rand.generator)
fallback_randn_default = fallback_handler(aten.randn.default)
fallback_randn_generator = fallback_handler(aten.randn.generator)
make_fallback(aten.randint)


@register_lowering(aten.rand)
def rand(*args, **kwargs):
    if kwargs.get("generator", None) is not None:
        return fallback_rand_generator(*args, **kwargs)
    elif config.fallback_random:
        kwargs.pop("generator", None)
        return fallback_rand_default(*args, **kwargs)
    raise AssertionError("should have been handled in replace_random.py")


@register_lowering(aten.randn)
def randn(*args, **kwargs):
    if kwargs.get("generator", None) is not None:
        return fallback_randn_generator(*args, **kwargs)
    elif config.fallback_random:
        kwargs.pop("generator", None)
        return fallback_randn_default(*args, **kwargs)
    raise AssertionError("should have been handled in replace_random.py")


@register_lowering(inductor_prims.force_stride_order, type_promotion_kind=None)
def inductor_force_stride_order(input_tensor, stride):
    stride_order = ir.get_stride_order(stride)
    return ir.ExternKernel.require_stride_order(input_tensor, stride_order)


@register_lowering(inductor_prims.seed, type_promotion_kind=None)
def inductor_seed(device: torch.device):
    raise AssertionError("should be handled in fuse_seed_creation_pass()")


@register_lowering(inductor_prims.seeds, type_promotion_kind=None)
def inductor_seeds(count, device):
    warn_triton_random()
    return TensorBox.create(ir.RandomSeeds(count, decode_device(device)))


@register_lowering(inductor_prims.lookup_seed, type_promotion_kind=None)
def inductor_lookup_seed(seeds, index):
    def inner_fn(_):
        return ops.load_seed(seeds.get_name(), index)

    return Pointwise.create(
        device=seeds.get_device(),
        dtype=seeds.get_dtype(),
        inner_fn=inner_fn,
        ranges=[],
    )


@register_lowering(inductor_prims.random, type_promotion_kind=None)
def inductor_random(size: List[int], seed: TensorBox, mode: str, *, offset: int = 0):
    assert not config.fallback_random
    assert mode in ("rand", "randn")
    size = [*size]
    dtype = torch.float32
    device = seed.get_device()
    random_pos = ir.FixedLayout(
        device, dtype, size, ir.FlexibleLayout.contiguous_strides(size), offset=offset
    ).make_indexer()
    seed_loader = seed.make_loader()

    def inner_fn(index):
        return getattr(ops, mode)(
            seed_loader([]),
            ops.index_expr(random_pos(index), torch.int32),
        )

    result = Pointwise.create(
        device=device,
        dtype=dtype,
        inner_fn=inner_fn,
        ranges=[*size],
    )
    result.realize()
    return result


@register_lowering(inductor_prims.randint, type_promotion_kind=None)
def inductor_randint(
    low: int, high: int, size: List[int], seed: TensorBox, *, offset: int = 0
):
    assert not config.fallback_random
    size = [*size]
    dtype = torch.int64
    device = seed.get_device()
    random_pos = ir.FixedLayout(
        device, dtype, size, ir.FlexibleLayout.contiguous_strides(size), offset=offset
    ).make_indexer()
    seed_loader = seed.make_loader()

    def inner_fn(index):
        return ops.randint64(
            seed_loader([]),
            ops.index_expr(random_pos(index), torch.int32),
            low,
            high,
        )

    return Pointwise.create(
        device=device,
        dtype=dtype,
        inner_fn=inner_fn,
        ranges=[*size],
    )


@register_lowering(aten.bucketize, type_promotion_kind=None)
def bucketize(
    input: TensorBox,
    boundaries: TensorBox,
    *,
    out_int32: bool = False,
    right: bool = False,
):
    assert len(boundaries.get_size()) == 1

    if not (is_triton(input) and is_triton(boundaries)):
        return fallback_handler(aten.bucketize.Tensor, add_to_fallback_set=False)(
            input, boundaries, out_int32=out_int32, right=right
        )

    # The entire boundaries tensor needs to be used by ops.bucketize, so we
    # need to realize it into global memory; or in other words, we can't
    # guarantee that boundaries.get_name() (used below) will exist unless
    # we call boundaries.realize().
    boundaries.realize()
    boundaries_size = boundaries.get_size()[0]
    boundaries_loader = boundaries.make_loader()
    device = input.get_device()
    input_loader = input.make_loader()

    index_dtype = torch.int32 if out_int32 else torch.int64

    def inner_fn(index):
        val = input_loader(index)
        indices = ops.bucketize(
            val,
            boundaries.get_name(),
            boundaries_size,
            index_dtype,
            right,
        )

        return indices

    return Pointwise.create(
        device=device,
        dtype=index_dtype,
        inner_fn=inner_fn,
        ranges=input.get_size(),
    )


def require_dense(_, *args, **kwargs):
    args, kwargs = pytree.tree_map_only(
        ir.IRNode, ir.ExternKernel.require_stride1, (args, kwargs)
    )
    return args, kwargs


def require_contiguous(_, *args, **kwargs):
    args, kwargs = pytree.tree_map_only(
        ir.IRNode, ir.ExternKernel.require_contiguous, (args, kwargs)
    )
    return args, kwargs


def require_channels_last(_, *args, **kwargs):
    args, kwargs = pytree.tree_map_only(
        ir.IRNode, ir.ExternKernel.require_channels_last, (args, kwargs)
    )
    return args, kwargs


def constrain_to_fx_strides(fx_node, *args, **kwargs):
    def apply_constraint(arg, fx_arg):
        if isinstance(arg, ir.IRNode):
            stride_order = ir.get_stride_order(fx_arg.meta["val"].stride())
            return ir.ExternKernel.require_stride_order(arg, stride_order)
        return arg

    args = tuple(
        apply_constraint(arg, fx_arg) for arg, fx_arg in zip(args, fx_node.args)
    )
    kwargs = {k: apply_constraint(v, fx_node.kwargs[k]) for k, v in kwargs.items()}
    return args, kwargs


# TODO(jansel): we should implement decomps or lowerings for these
# https://github.com/pytorch/torchdynamo/issues/327
FALLBACK_ALLOW_LIST = {
    "torchvision::roi_align",
}
make_fallback(aten._adaptive_avg_pool2d_backward, require_dense)
make_fallback(aten.convolution_backward, constrain_to_fx_strides)
make_fallback(aten._cudnn_rnn, require_dense)
make_fallback(aten._cudnn_rnn_backward, require_contiguous)
make_fallback(aten._embedding_bag, require_contiguous)
make_fallback(aten._embedding_bag_forward_only, require_contiguous)
make_fallback(aten._fused_moving_avg_obs_fq_helper)
make_fallback(aten._fused_moving_avg_obs_fq_helper_functional)
make_fallback(aten.grid_sampler_2d_backward, require_dense)
make_fallback(aten.randperm)


def sdpa_constraint(fx_node, *args, **kwargs):
    # sdpa requires dense last dimension]

    def apply_constraint(arg, fx_arg):
        if not isinstance(arg, ir.IRNode):
            return arg

        meta_val = fx_arg.meta["val"]
        if not meta_val.is_cuda:
            return arg

        stride_order = ir.get_stride_order(meta_val.stride())
        if stride_order and stride_order[-1] != 0:
            # contiguous stride order
            stride_order = list(reversed(range(len(arg.get_size()))))

        # This is the minimum alignment required by SDPA kernels for attention_bias.
        # This value can be found in pytorch/aten/src/ATen/native/transformers/attention.cpp preprocess_mask
        ALIGNMENT = 8

        assert isinstance(arg, TensorBox)
        if len(arg.get_size()) not in (3, 4):
            return arg

        def is_aligned_realized_tensor(x):
            aligned_strides = all(
                (V.graph.sizevars.size_hint(x.get_stride()[i]) % ALIGNMENT) == 0
                for i in range(len(x.get_stride()) - 1)
            )
            return (
                V.graph.sizevars.size_hint(x.get_stride()[-1])
            ) == 1 and aligned_strides

        try:
            arg.get_stride()
            if is_aligned_realized_tensor(arg):
                return arg
        except AttributeError:
            pass

        def is_aligned(x):
            return (V.graph.sizevars.size_hint(x.get_size()[-1]) % ALIGNMENT) == 0

        if isinstance(arg.data, ir.BaseView):
            if not is_aligned(arg):
                if is_aligned(arg.unwrap_view()):
                    return arg

        return ir.ExternKernel.require_stride_order(arg, stride_order)

    args = tuple(
        apply_constraint(arg, fx_arg) for arg, fx_arg in zip(args, fx_node.args)
    )
    kwargs = {k: apply_constraint(v, fx_node.kwargs[k]) for k, v in kwargs.items()}
    return args, kwargs


make_fallback(
    aten._scaled_dot_product_efficient_attention.default,
    sdpa_constraint,
    warn=False,
)
make_fallback(
    aten._scaled_dot_product_efficient_attention_backward.default,
    sdpa_constraint,
    warn=False,
)
make_fallback(
    aten._scaled_dot_product_flash_attention.default,
    sdpa_constraint,
    warn=False,
)
make_fallback(
    aten._scaled_dot_product_flash_attention_backward.default,
    sdpa_constraint,
    warn=False,
)
make_fallback(
    aten._scaled_dot_product_flash_attention_for_cpu.default,
    sdpa_constraint,
    warn=False,
)
make_fallback(
    aten._scaled_dot_product_flash_attention_for_cpu_backward.default,
    sdpa_constraint,
    warn=False,
)
make_fallback(aten._flash_attention_forward.default, sdpa_constraint)
make_fallback(aten._flash_attention_backward.default, sdpa_constraint)
make_fallback(aten._efficient_attention_forward.default, sdpa_constraint)
make_fallback(aten._efficient_attention_backward.default, sdpa_constraint)
make_fallback(aten.sort)
make_fallback(aten.sort.stable)
make_fallback(aten._sparse_coo_tensor_with_dims_and_tensors)
make_fallback(aten._thnn_fused_lstm_cell, require_dense)
make_fallback(aten.topk)
make_fallback(aten.upsample_bicubic2d_backward, require_contiguous)
make_fallback(aten._scaled_mm.default, constrain_to_fx_strides)

# TODO: This is done, just need to enable support in TorchInductor for complex types.
make_fallback(aten.view_as_complex, require_contiguous)

# The following were added as a result of https://github.com/pytorch/pytorch/pull/94039 to pass tests
# It's not necessarily a priority to implement these
make_fallback(aten.upsample_linear1d)
make_fallback(aten.upsample_trilinear3d)
make_fallback(aten.upsample_linear1d_backward)
make_fallback(aten.upsample_trilinear3d_backward)
make_fallback(aten._adaptive_avg_pool3d)
make_fallback(aten.adaptive_max_pool2d)
make_fallback(aten.adaptive_max_pool3d)
make_fallback(aten.addbmm)
make_fallback(aten.addmv, warn=False)
make_fallback(aten._addmm_activation, warn=False)
make_fallback(aten.avg_pool3d)
make_fallback(aten._cdist_forward)
make_fallback(aten.cummax)
make_fallback(aten.cummin)
make_fallback(aten.digamma, warn=False)
make_fallback(aten._efficientzerotensor)
make_fallback(aten._embedding_bag_per_sample_weights_backward)
make_fallback(aten._efficientzerotensor)
make_fallback(aten._embedding_bag_per_sample_weights_backward)
make_fallback(aten.fractional_max_pool2d)
make_fallback(aten.fractional_max_pool3d)
make_fallback(aten.frexp)
make_fallback(aten.geqrf)
make_fallback(aten.histc)
make_fallback(aten.i0)
make_fallback(aten.igamma, warn=False)
make_fallback(aten.igammac, warn=False)
make_fallback(aten.isin)
make_fallback(aten.kthvalue)
make_fallback(aten.linalg_cholesky_ex)
make_fallback(aten.linalg_cross)
make_fallback(aten._linalg_det)
make_fallback(aten.linalg_householder_product)
make_fallback(aten.linalg_inv_ex)
make_fallback(aten.linalg_ldl_factor_ex)
make_fallback(aten.linalg_ldl_solve)
make_fallback(aten.linalg_lu)
make_fallback(aten.linalg_lu_factor_ex)
make_fallback(aten.linalg_lu_solve)
make_fallback(aten.linalg_matrix_exp)
make_fallback(aten.linalg_qr)
make_fallback(aten._linalg_slogdet)
make_fallback(aten._linalg_solve_ex)
make_fallback(aten.linalg_solve_triangular)
make_fallback(aten._linalg_svd)
make_fallback(aten.logcumsumexp)
make_fallback(aten.lu_unpack)
make_fallback(aten.max_pool3d_with_indices)
make_fallback(aten.max_unpool2d)
make_fallback(aten.max_unpool3d)
make_fallback(aten.median)
make_fallback(aten.mode)
make_fallback(aten.nanmedian)
make_fallback(aten.ormqr)
make_fallback(aten._pdist_forward)
make_fallback(aten.pixel_shuffle)
make_fallback(aten.pixel_unshuffle)
make_fallback(aten.polygamma)
make_fallback(aten.put)
make_fallback(aten.resize)
make_fallback(aten.resize_)
make_fallback(aten.resize_as)
make_fallback(aten.resize_as_)
make_fallback(aten.searchsorted)
make_fallback(aten.special_airy_ai)
make_fallback(aten.special_bessel_j0, warn=False)
make_fallback(aten.special_bessel_j1, warn=False)
make_fallback(aten.special_bessel_y0, warn=False)
make_fallback(aten.special_bessel_y1)
make_fallback(aten.special_chebyshev_polynomial_t)
make_fallback(aten.special_chebyshev_polynomial_u)
make_fallback(aten.special_erfcx, warn=False)
make_fallback(aten.special_hermite_polynomial_h)
make_fallback(aten.special_hermite_polynomial_he)
make_fallback(aten.special_i0e, warn=False)
make_fallback(aten.special_i1, warn=False)
make_fallback(aten.special_i1e, warn=False)
make_fallback(aten.special_laguerre_polynomial_l)
make_fallback(aten.special_modified_bessel_i0)
make_fallback(aten.special_modified_bessel_i1)
make_fallback(aten.special_modified_bessel_k0)
make_fallback(aten.special_modified_bessel_k1)
make_fallback(aten.special_ndtri, warn=False)
make_fallback(aten.special_scaled_modified_bessel_k0)
make_fallback(aten.special_scaled_modified_bessel_k1)
make_fallback(aten.special_spherical_bessel_j0, warn=False)
make_fallback(aten.special_zeta, warn=False)
make_fallback(aten._trilinear)
make_fallback(aten.uniform, warn=False)
make_fallback(aten._adaptive_avg_pool3d_backward)
make_fallback(aten.adaptive_max_pool2d_backward)
make_fallback(aten.adaptive_max_pool3d_backward)
make_fallback(aten.avg_pool3d_backward)
make_fallback(aten._cdist_backward)
make_fallback(aten._embedding_bag_dense_backward)
make_fallback(aten.fractional_max_pool2d_backward)
make_fallback(aten.fractional_max_pool3d_backward)
make_fallback(aten._linalg_check_errors)
make_fallback(aten.max_pool3d_with_indices_backward)
make_fallback(aten._pdist_backward)
make_fallback(aten.replication_pad1d_backward)
make_fallback(aten.replication_pad2d_backward)
make_fallback(aten.soft_margin_loss_backward, warn=False)
make_fallback(aten.linalg_pinv.atol_rtol_tensor)
make_fallback(aten.segment_reduce.default)
make_fallback(aten._segment_reduce_backward.default)
make_fallback(aten.angle)
make_fallback(aten.cholesky_inverse)
make_fallback(aten.cholesky_solve)
make_fallback(aten._fft_r2c)
make_fallback(aten.histogram.bin_ct)
make_fallback(aten._histogramdd_bin_edges.default)
make_fallback(aten._histogramdd_from_bin_cts.default)
make_fallback(aten.index_reduce)
make_fallback(aten.masked_scatter)
make_fallback(aten.masked_scatter_backward)
make_fallback(aten.to_sparse)
make_fallback(aten._to_sparse)
make_fallback(aten.triangular_solve)
make_fallback(aten.gcd.default, warn=False)
make_fallback(aten._linalg_eigh)
make_fallback(aten.zeros.names)

# these are data-dependent, highly unlikely you can write a lowering
make_fallback(aten.nonzero.default)

make_fallback(torch._prims.rng_prims.run_and_save_rng_state)
make_fallback(torch._prims.rng_prims.run_with_rng_state)

# fails accuracy on test_torch.py, and explicit fallback required to avoid warn=True on implicit
make_fallback(aten.exponential.default, warn=False)


# Register with type_promotion_kind None.
# For example, fp16.copy_(fp32) should **not** promote the first input's dtype.
@register_lowering(aten.copy, type_promotion_kind=None)
def copy(self, src, non_blocking=False):
    x = src
    if self.get_device() != src.get_device():
        x = to_device(x, self.get_device())
    if self.get_dtype() != src.get_dtype():
        x = to_dtype(x, self.get_dtype())

    if self.get_size() != src.get_size():
        out = expand(x, self.get_size())
        return clone(out)
    return clone(x)


@register_lowering(aten.clone)
def clone(x, *, memory_format=None):
    # TODO(jansel): memory format
    return Pointwise.create(
        device=x.get_device(),
        dtype=x.get_dtype(),
        inner_fn=x.make_loader(),
        ranges=list(x.get_size()),
    )


def clone_preserve_reinterpret_view(x):
    reinterpret_view_layouts = []
    if isinstance(x, TensorBox) and isinstance(x.data, ir.ReinterpretView):
        x = x.data  # unwrap TensorBox
        while isinstance(x, ir.ReinterpretView):
            reinterpret_view_layouts.append(x.get_layout())
            x = x.data
        x = TensorBox(x)

    x = clone(x)

    if reinterpret_view_layouts:
        x = x.data  # unwrap TensorBox
        for layout in reinterpret_view_layouts[::-1]:
            x = ir.ReinterpretView(x, layout)
        x = TensorBox(x)

    return x


if hasattr(aten, "lift_fresh_copy"):
    register_lowering(aten.lift_fresh_copy)(clone)


@register_lowering(prims.iota)
def iota(
    length,
    *,
    start,
    step,
    dtype,
    device,
    requires_grad,
):
    def fn(index):
        return ops.index_expr(step * index[0] + start, dtype=dtype)

    return Pointwise.create(
        device=decode_device(device),
        dtype=dtype,
        inner_fn=fn,
        ranges=[length],
    )


@register_lowering(aten.select_scatter, type_promotion_kind=None)
def select_scatter(x, src, dim: int, index: int):
    assert x.get_dtype() == src.get_dtype()
    x_loader = x.make_loader()
    dim = _validate_dim(x, dim, 0)
    if V.graph.sizevars.evaluate_expr(sympy.Lt(index, 0)):
        index = index + x.get_size()[dim]
    V.graph.sizevars.guard_leq(0, index)
    V.graph.sizevars.guard_lt(index, x.get_size()[dim])
    src = expand(unsqueeze(src, dim), x.get_size())
    src_loader = src.make_loader()

    def inner_fn(idx):
        return ops.where(
            ops.eq(
                ops.index_expr(idx[dim], torch.int32),
                ops.index_expr(index, torch.int32),
            ),
            src_loader(idx),
            x_loader(idx),
        )

    return Pointwise.create(
        device=x.get_device(),
        dtype=x.get_dtype(),
        inner_fn=inner_fn,
        ranges=list(x.get_size()),
    )


@register_lowering(aten.slice_scatter, type_promotion_kind=None)
def slice_scatter(x, src, dim=0, start=None, end=None, step=1):
    assert x.get_dtype() == src.get_dtype()
    x_loader = x.make_loader()
    dim = _validate_dim(x, dim, 0)
    dim_size = x.get_size()[dim]
    if start is not None and V.graph.sizevars.evaluate_expr(sympy.Lt(start, 0)):
        start = start + dim_size
    if end is not None and V.graph.sizevars.evaluate_expr(sympy.Lt(end, 0)):
        end = end + dim_size
    if start is None:
        start = 0
    if end is None or V.graph.sizevars.statically_known_leq(x.get_size()[dim], end):
        end = dim_size

    src_size = list(x.get_size())
    src_size[dim] = FloorDiv(end - start + (step - 1), step)
    src = expand(src, src_size)
    src_loader = src.make_loader()

    def inner_fn(idx):
        if start == 0 and end == dim_size and step == 1:
            # selecting every element is the same as just src.clone()
            return src_loader(idx)

        idx_dim = ops.index_expr(idx[dim], torch.int64)
        src_idx = list(idx)
        src_idx[dim] = FloorDiv(idx[dim] - start, step)

        mask = []
        if start != 0:
            mask.append(
                ops.ge(
                    idx_dim,
                    ops.index_expr(sympy.expand(start), torch.int64),
                )
            )
        if end != dim_size:
            mask.append(
                ops.lt(
                    idx_dim,
                    ops.index_expr(sympy.expand(end), torch.int64),
                )
            )
        if step != 1:
            mask.append(
                ops.eq(
                    ops.index_expr(
                        ModularIndexing(idx[dim] - start, 1, step), torch.int64
                    ),
                    ops.constant(0, torch.torch.int64),
                )
            )
        assert mask
        mask = functools.reduce(ops.and_, mask)
        src_val = ops.masked(
            mask,
            lambda: src_loader(src_idx),
            0 if is_integer_type(x) else 0.0,
        )
        return ops.where(
            mask,
            src_val,
            x_loader(idx),
        )

    return Pointwise.create(
        device=x.get_device(),
        dtype=x.get_dtype(),
        inner_fn=inner_fn,
        ranges=list(x.get_size()),
    )


def _unwrap(x):
    if isinstance(x, (list, tuple)) and len(x) > 0:
        return _unwrap(x[0])
    return x


@register_lowering([torch.tensor, aten.scalar_tensor])
def tensor(data, *, dtype=None, device=None, layout=None, pin_memory=False):
    assert_nyi(layout in (None, torch.strided), f"layout={layout}")
    assert_nyi(not pin_memory, "pin_memory")
    if isinstance(_unwrap(data), int):
        dtype = dtype or torch.int64
    else:
        dtype = dtype or torch.get_default_dtype()

    ranges: List[sympy.Expr] = []

    if isinstance(data, sympy.Expr):

        def inner_fn(index):
            return ops.index_expr(data, dtype)

    elif isinstance(data, (float, int)):

        def inner_fn(index):
            return ops.constant(data, dtype)

    elif len(data) == 0 or isinstance(data[0], (float, int)) and len(data) <= 8:
        # inline small tensors
        ranges.append(sympy.Integer(len(data)))

        def inner_fn(index):
            def binary_search(start, end):
                assert start < end
                if end - start == 1:
                    return ops.constant(data[start], dtype)
                mid = (end - start) // 2 + start
                return ops.where(
                    ops.lt(
                        ops.index_expr(index[0], torch.int64),
                        ops.constant(mid, torch.int64),
                    ),
                    binary_search(start, mid),
                    binary_search(mid, end),
                )

            if len(data) == 0:
                return ops.constant(0, dtype)
            return binary_search(0, len(data))

    else:
        return V.graph.add_tensor_constant(
            torch.tensor(data, dtype=dtype, device=device)
        )

    return Pointwise.create(
        device=decode_device(device),
        dtype=dtype,
        inner_fn=inner_fn,
        ranges=ranges,
    )


@register_lowering(torch.as_tensor)
def as_tensor(data, dtype=None, device=None):
    if isinstance(data, TensorBox):
        if dtype is not None:
            data = to_dtype(data, dtype)
        if device is not None:
            data = to_device(data, device)
        return data
    return tensor(data, dtype=dtype, device=device)


@register_lowering(torch.LongTensor)
def long_tensor(data):
    return tensor(data, dtype=torch.int64)


@register_lowering(aten._local_scalar_dense)
def _local_scalar_dense(data):
    # This is interesting!  Most lowerings return tensors, so you can just
    # return the buffer you allocated and it will get used (or not used, if
    # it's dead.)  But _local_scalar_dense (aka item) returns an int,
    # not a Tensor, so you would have a type mismatch if you return a buffer;
    # we are obligated to return a sympy expression instead.  However,
    # we need to actually codegen the .item() call somehow.  We do this
    # by registering a faux buffer for the DynamicScalar IR node, which is
    # solely responsible for generating this .item().  The buffer is
    # not used for anything (notice we discard it); at codegen time,
    # the "buffer" just gets assigned None.
    sym = V.graph.current_node.meta["val"].node.expr
    buffer = ir.DynamicScalar(sym, data)
    buffer.name = V.graph.register_buffer(buffer)
    return sym


def _full(fill_value, device, dtype, size):
    value = fill_value
    if not isinstance(fill_value, (int, float)) and hasattr(value, "value"):
        value = value.value

    if isinstance(value, (int, float)):

        def inner_fn(index):
            return ops.constant(value, dtype)

    elif isinstance(value, sympy.Expr):

        def inner_fn(index):
            return ops.index_expr(value, dtype)

    else:
        assert len(value.get_size()) == 0
        value_loader = value.make_loader()

        def inner_fn(index):
            return value_loader([])

    return Pointwise.create(
        device=device,
        dtype=dtype,
        inner_fn=inner_fn,
        ranges=list(size),
    )


@register_lowering(aten.full_like, type_promotion_kind=None)
def full_like(x, fill_value, **kwargs):
    return create_tensor_like(tensor_constructor(fill_value))(x, **kwargs)


def tensor_constructor(fill_value):
    # torch.zeros, torch.ones, etc
    def inner(
        *size,
        names=None,
        dtype=None,
        device=None,
        layout=None,
        pin_memory=False,
        memory_format=None,
    ):
        assert_nyi(names is None, "named tensors")
        assert_nyi(layout in (None, torch.strided), f"layout={layout}")
        assert_nyi(not pin_memory, "pin_memory")
        device = decode_device(device)
        dtype = dtype or torch.get_default_dtype()
        if len(size) == 1 and isinstance(size[0], (list, tuple, torch.Size)):
            size = tuple(size[0])
        size = [sympy.expand(s) for s in size]
        return _full(fill_value, device, dtype, size)

    return inner


@register_lowering([torch.empty, aten.empty])
def empty(
    *size,
    names=None,
    dtype=None,
    layout=None,
    device=None,
    pin_memory=None,
    memory_format=None,
):
    assert_nyi(names is None, "named tensors")
    device = decode_device(device)
    if len(size) == 1 and isinstance(size[0], (list, tuple, torch.Size)):
        size = tuple(size[0])
    return empty_strided(
        size, None, dtype=dtype, layout=layout, device=device, pin_memory=pin_memory
    )


def create_tensor_like(creation_fn):
    """
    Shim to convert X_like(...) into X(...).  For example zeros_like() into zeros().
    """

    def _constant_like(
        x, *, dtype=None, device=None, layout=None, pin_memory=False, memory_format=None
    ):
        assert_nyi(not pin_memory, "pin_memory")
        assert_nyi(layout in (None, torch.strided), f"layout={layout}")
        if dtype is None:
            dtype = x.get_dtype()
        else:
            dtype = decode_dtype(dtype)
        device = device or x.get_device()
        size = list(x.get_size())
        return creation_fn(
            size, dtype=dtype, device=device, layout=layout, pin_memory=pin_memory
        )

    return _constant_like


def constant_like(fill_value):
    return create_tensor_like(tensor_constructor(fill_value))


empty_like = register_lowering(aten.empty_like)(create_tensor_like(empty))
ones_like = create_tensor_like(tensor_constructor(1))
zeros_like = create_tensor_like(tensor_constructor(0))


def new_constant(fill_value):
    def _new_constant(
        x, size, *, dtype=None, layout=None, device=None, pin_memory=None
    ):
        assert isinstance(size, (list, tuple))
        assert_nyi(not pin_memory, "pin_memory")
        assert_nyi(layout in (None, torch.strided), f"layout={layout}")
        dtype = decode_dtype(dtype) or x.get_dtype()
        device = device or x.get_device()
        size = [sympy.Integer(s) for s in size]
        return _full(fill_value, device, dtype, size)

    return _new_constant


@register_lowering(aten.new_empty)
def new_empty(x, size, *, dtype=None, layout=None, device=None, pin_memory=None):
    if dtype is None:
        dtype = x.get_dtype()
    if device is None:
        device = x.get_device()
    return empty_strided(
        size, None, dtype=dtype, layout=layout, device=device, pin_memory=pin_memory
    )


@register_lowering(aten.empty_strided)
def empty_strided(
    size, stride, *, dtype=None, layout=None, device=None, pin_memory=None
):
    assert isinstance(size, (list, tuple))
    assert isinstance(stride, (list, tuple, type(None)))
    assert_nyi(not pin_memory, "pin_memory")
    assert_nyi(layout in (None, torch.strided), f"layout={layout}")
    dtype = decode_dtype(dtype) or torch.get_default_dtype()
    device = device or torch.tensor(0.0).device
    pointwise = _full(fill_value=0, device=device, dtype=dtype, size=size)
    pointwise.realize()
    buffer = pointwise.data.data
    # explicitly set ranges to zeros in order to make a NopKernelSchedulerNode
    buffer.data.ranges = [0] * len(size)
    assert isinstance(buffer, ir.ComputedBuffer)
    size = [sympy.expand(s) for s in size]
    stride = (
        [sympy.expand(s) for s in stride]
        if stride
        else ir.FlexibleLayout.contiguous_strides(size)
    )
    buffer.layout = ir.FixedLayout(
        device=device,
        dtype=dtype,
        size=size,
        stride=stride,
    )
    return pointwise


@register_lowering(aten.new_empty_strided)
def new_empty_strided(
    x, size, stride, *, dtype=None, layout=None, device=None, pin_memory=None
):
    if dtype is None:
        dtype = x.get_dtype()
    if device is None:
        device = x.get_device()
    return empty_strided(
        size, stride, dtype=dtype, layout=layout, device=device, pin_memory=pin_memory
    )


@register_lowering(prims.copy_strided.default)
def copy_strided(x, stride):
    stride = [V.graph.sizevars.size_hint(s) for s in stride]
    stride_order = sorted(range(len(stride)), key=stride.__getitem__)
    return ir.ExternKernel.require_stride_order(x, stride_order)


@register_lowering([torch.full, aten.full])
def full(size, fill_value, **kwargs):
    assert kwargs.get("dtype") is not None, "dtype should be handled by decomposition"
    return tensor_constructor(fill_value)(size, **kwargs)


@register_lowering(aten.gather, type_promotion_kind=None)
def gather(x, dim, index, sparse_grad=False):
    # sparse_grad doesn't affect forward computation,
    # and backward tracing is taken care of by AOT Autograd
    assert isinstance(x, TensorBox)
    assert index.get_dtype() == torch.int64
    size = x.get_size()
    offset = len(size) == 0
    dim = _validate_dim(x, dim, offset)

    x_loader = x.make_loader()
    index_loader = index.make_loader()

    def fn(idx):
        idx = list(idx)
        if len(idx) != 0:
            idx[dim] = ops.indirect_indexing(index_loader(idx), size[dim])
        return x_loader(idx)

    return Pointwise.create(
        device=x.get_device(),
        dtype=x.get_dtype(),
        inner_fn=fn,
        ranges=index.get_size(),
    )


@register_lowering(aten.embedding, type_promotion_kind=None)
def embedding(weight, indices, padding_idx=-1, scale_grad_by_freq=False, sparse=False):
    assert not sparse
    assert isinstance(weight, TensorBox)
    assert isinstance(indices, TensorBox)
    assert "int" in str(indices.get_dtype())

    weight_loader = weight.make_loader()
    indices_loader = indices.make_loader()
    indices_ndim = len(indices.get_size())
    weight_size = weight.get_size()
    new_size = [*indices.get_size(), *weight_size[1:]]

    def fn(idx):
        assert len(idx) == len(new_size), f"{idx} != {new_size}"
        var_index = indices_loader(idx[:indices_ndim])
        weight_idx = [ops.indirect_indexing(var_index, weight_size[0])] + [
            *idx[indices_ndim:]
        ]
        return weight_loader(weight_idx)

    return Pointwise.create(
        device=weight.get_device(),
        dtype=weight.get_dtype(),
        inner_fn=fn,
        ranges=new_size,
    )


def check_and_broadcast_indices(indices, device):
    assert all(
        i.get_dtype() in (torch.int64, torch.int32, torch.bool, torch.uint8)
        for i in indices
        if i is not None
    ), f"indices must be int64, byte or bool. Got {[i.get_dtype() for i in indices if i is not None]}"
    if any(
        i.get_dtype() in (torch.bool, torch.uint8) for i in indices if i is not None
    ):
        raise NotImplementedError("Fallback for bool indices")

    valid_idxs = [i for i, x in enumerate(indices) if isinstance(x, TensorBox)]
    assert len(valid_idxs) > 0, "requires at least 1 non-None index"
    new_indices = [None] * len(indices)
    for i, x in zip(valid_idxs, broadcast_tensors(*[indices[i] for i in valid_idxs])):
        # Eager allows indices to be CPU tensor when running on CUDA
        # FIXME: Calling to_device(x, device) should work but
        # test_advancedindex_mixed_cpu_devices still fails
        if x.get_device() != device:
            raise NotImplementedError("Fallback when indices is on a different device")
        new_indices[i] = x
    return new_indices, valid_idxs


def index_output_size_and_inner_fn(
    x_size,
    indices,
    tensor_indices,
    tensor_size,
    indices_loaders,
    indexed_size,
    x_loader,
    check,
):
    # Note that behavior of indexing differs when there are non consecutive
    # tensors. In this case, the tensor index is pulled to the beginning.
    #
    # Suppose a = torch.arange(3 * 4 * 5 * 6 * 7).view(3, 4, 5, 6, 7)
    #         x = torch.tensor[1,2]
    # Then, a[:,x,:,x,:] will have shape 2,3,5,7 as due to x,:,x then 2 will
    # be pulled to the front.
    non_consecutive_tensors = False
    for previous, current in zip(tensor_indices, tensor_indices[1:]):
        if current - previous != 1:
            non_consecutive_tensors = True

    output_size = [x_size[i] for i, val in enumerate(indices) if val is None]
    output_size = [*output_size, *x_size[len(output_size) + len(tensor_indices) :]]

    first_tensor_index = tensor_indices[0]
    if non_consecutive_tensors:
        output_size = tensor_size + output_size
    else:
        output_size = (
            output_size[:first_tensor_index]
            + tensor_size
            + output_size[first_tensor_index:]
        )

    def fn(idx):
        assert len(idx) == len(output_size)
        assert len(indices_loaders) == len(indexed_size)

        rank = len(tensor_size)
        new_index = []
        first_tensor_index = tensor_indices[0]
        start_offset = 0 if non_consecutive_tensors else first_tensor_index
        next_idx = 0
        for i in range(tensor_indices[-1] + 1):
            if i == start_offset:
                next_idx += rank
            if indices[i] is None:
                assert next_idx < len(idx)
                new_index.append(idx[next_idx])
                next_idx += 1
            else:
                loader = indices_loaders[i]
                assert loader is not None
                size = indexed_size[i]
                new_index.append(
                    ops.indirect_indexing(
                        loader(idx[start_offset : start_offset + rank]),
                        size,
                        check=check,
                    )
                )
        new_index = [
            *new_index,
            *idx[next_idx:],
        ]
        return new_index if x_loader is None else x_loader(new_index)

    return output_size, fn


def index_impl(x, indices, check):
    assert isinstance(indices, (list, tuple))
    x_loader = x.make_loader()
    indices, tensor_indices = check_and_broadcast_indices(indices, x.get_device())
    assert len(tensor_indices) > 0, "Must have at least one valid idx"

    indices_loaders = [i.make_loader() if i is not None else None for i in indices]
    # no guards on output size, all the guards are set in broadcast_tensors

    # We can use the first one since they are all required to be the same size
    tensor_size = list(indices[tensor_indices[0]].get_size())

    x_size = x.get_size()

    indexed_size = [x_size[i] for i in range(len(indices)) if indices[i] is not None]
    if 0 in indexed_size and 0 not in tensor_size:
        raise IndexError("index is out of bounds for dimension with size 0")

    indexed_size = [x_size[i] for i in range(len(indices))]
    output_size, inner_fn = index_output_size_and_inner_fn(
        x_size,
        indices,
        tensor_indices,
        tensor_size,
        indices_loaders,
        indexed_size,
        x_loader,
        check=check,
    )

    return Pointwise.create(
        device=x.get_device(),
        dtype=x.get_dtype(),
        inner_fn=inner_fn,
        ranges=output_size,
    )


@register_lowering(aten.index, type_promotion_kind=None)
def index(x, indices):
    try:
        return index_impl(x, indices, check=True)
    except NotImplementedError:
        # Fallback to ATen for boolean indexing
        x.realize()
        return fallback_handler(aten.index.Tensor, add_to_fallback_set=False)(
            x, indices
        )


@register_lowering(aten._unsafe_index, type_promotion_kind=None)
def _unsafe_index(x, indices):
    return index_impl(x, indices, check=False)


# All the indexing decompositions are written in terms of index, index_put, and index_put_
# We cannot have this lowering as a decomposition as it introduces
# mutation in the graph, which is bad for Aot Autograd. Aot Autograd runs dead
# code elimination and common subexpression elimination optimizations, which
# assume graphs to be side-effect free. More details at
# https://github.com/pytorch/torchdynamo/issues/1235
# and
# https://github.com/pytorch/torchdynamo/issues/1863
@register_lowering(aten.index_put)
def index_put(x, indices, values, accumulate=False):
    return index_put_(clone(x), indices, values, accumulate)


@register_lowering(aten._unsafe_index_put)
def _unsafe_index_put(x, indices, values, accumulate=False):
    return index_put_impl_(clone(x), indices, values, accumulate, check=False)


def index_put_as_masked_fill(self, indices, value, accumulate):
    if value.get_device() != self.get_device():
        value = to_device(value, self.get_device())
    if accumulate:
        value = add(self, value)
    return mutate_to(self, where(indices[0], value, self))


def index_put_fallback(self, indices, values, accumulate):
    deterministic = torch.are_deterministic_algorithms_enabled()
    if is_triton(values) and (accumulate or deterministic):
        V.graph.disable_cudagraphs = True
        msg = (
            "index put with accumulate."
            if not deterministic
            else "deterministic index put."
        )
        if stack_trace := V.graph.current_node.meta.get("stack_trace", None):
            msg = f"{msg} Found from : \n {stack_trace}"
        V.graph.disable_cudagraphs_reason = msg

    ir.IndexPutFallback(self, indices, values, accumulate)
    return self


@register_lowering(aten.index_put_, type_promotion_kind=None)
def index_put_(self, indices, values, accumulate=False):
    return index_put_impl_(self, indices, values, accumulate, check=True)


@register_lowering(inductor_prims._unsafe_index_put_, type_promotion_kind=None)
def _unsafe_index_put_(self, indices, values, accumulate=False):
    return index_put_impl_(self, indices, values, accumulate, check=False)


def needs_fallback_due_to_atomic_add_limitations(dtype):
    # tl.atomic_add does NOT support the following types
    return dtype in {torch.int64, torch.bool, torch.bfloat16}


def index_put_impl_(self, indices, values, accumulate, check):
    # Dispatch to masked fill for single boolean index with single value
    if (
        values.get_numel() == 1
        and len(indices) == 1
        and indices[0].get_dtype() in {torch.bool, torch.uint8}
    ):
        mask = indices[0]
        for _ in range(len(mask.get_size()), len(self.get_size())):
            mask = unsqueeze(mask, -1)
        return index_put_as_masked_fill(self, [mask], values, accumulate)

    # Fallback in torch deterministic mode
    if torch.are_deterministic_algorithms_enabled():
        return index_put_fallback(self, indices, values, accumulate)

    # Fallback if there is a boolean index
    for index in indices:
        if index is not None and index.get_dtype() in {torch.bool, torch.uint8}:
            return index_put_fallback(self, indices, values, accumulate)

    x_size = self.get_size()
    x_ndim = len(x_size)

    if accumulate and needs_fallback_due_to_atomic_add_limitations(self.get_dtype()):
        # self is an scalar Tensor
        if x_ndim == 0:
            self = view(self, [1])
        self = index_put_fallback(self, indices, values, accumulate)
        if x_ndim == 0:
            self = view(self, [])
        return self

    values = to_dtype(values, self.get_dtype())

    try:
        # Note that code will only get here when dtype is uint32
        indices, tensor_indices = check_and_broadcast_indices(
            indices, self.get_device()
        )
    except NotImplementedError:
        return index_put_fallback(self, indices, values, accumulate)

    indices_loaders = [i.make_loader() if i is not None else None for i in indices]

    assert isinstance(self, TensorBox)
    self.realize()

    # self is an scalar Tensor
    if x_ndim == 0:
        self = view(self, [1])

    # We can use the first one since they are all required to be the same size
    tensor_size = list(indices[tensor_indices[0]].get_size())
    indexed_size = [x_size[i] for i in range(len(indices))]

    expected_vals_size, inner_fn = index_output_size_and_inner_fn(
        x_size,
        indices,
        tensor_indices,
        tensor_size,
        indices_loaders,
        indexed_size,
        None,
        check=check,
    )

    values = expand(values, expected_vals_size)
    # all guards are set above during broadcast_tensors and expand

    scatter = ir.Scatter(
        device=self.get_device(),
        dtype=self.get_dtype(),
        inner_fn=values.make_loader(),
        ranges=expected_vals_size,  # iter_ranges,
        output_indexer=inner_fn,
        scatter_mode="atomic_add" if accumulate else None,
    )
    buffer = ir.ComputedBuffer(
        None,
        ir.MutationLayout(self),
        scatter,
    )
    buffer.name = V.graph.register_buffer(buffer)

    if x_ndim == 0:
        self = view(self, [])
    return self


@register_lowering(
    inductor_prims.masked_scatter_with_index, type_promotion_kind=None, broadcast=False
)
def masked_scatter_with_index(self, mask, source_idx, source):
    self_flat, mask_flat, source_flat = (view(x, (-1,)) for x in (self, mask, source))

    assert self.get_size() == mask.get_size()
    assert mask.get_dtype() in {torch.bool, torch.uint8}

    self_loader = self_flat.make_loader()
    mask_loader = mask_flat.make_loader()
    source_idx_loader = source_idx.make_loader()
    source_loader = source_flat.make_loader()
    source_numel = source.get_numel()

    def inner_fn(idx):
        self_val = self_loader(idx)
        mask_val = ops.to_dtype(mask_loader(idx), torch.bool)

        def load_source_val():
            source_idx_val = source_idx_loader(idx)
            i = ops.indirect_indexing(source_idx_val, source_numel)
            return source_loader([i])

        source_val = ops.masked(mask_val, load_source_val, 0)
        return ops.where(mask_val, source_val, self_val)

    result_flat = Pointwise.create(
        device=self.get_device(),
        dtype=self.get_dtype(),
        inner_fn=inner_fn,
        ranges=self_flat.get_size(),
    )
    return view(result_flat, self.get_size())


@register_lowering(aten.as_strided_scatter, type_promotion_kind=None)
def as_strided_scatter(self, src, size, stride, storage_offset=None):
    output = clone(self)
    output_view = as_strided(output, size, stride, storage_offset)
    copy_(output_view, src)
    return output


@register_lowering(aten.scatter, type_promotion_kind=None)
def scatter(x, dim: int, index, src, **kwargs):
    return scatter_(clone(x), dim, index, src, **kwargs)


def scatter_fallback(
    fn,
    self,
    dim: int,
    index,
    src,
    *,
    reduce: Optional[str] = None,
    include_self: bool = True,
):
    reduce_ty = "add" if fn == "aten.scatter_" else "sum"
    if (
        reduce not in {None, reduce_ty}
        or (
            isinstance(src, TensorBox)
            and src.get_device().type == torch.device("cuda").type
            and needs_fallback_due_to_atomic_add_limitations(src.get_dtype())
        )
        or (
            fn == "aten.scatter_reduce_"
            and reduce == "sum"
            and isinstance(src, TensorBox)
            and src.get_device() == torch.device("cpu")
            and config.cpp.fallback_scatter_reduce_sum
        )
        or (reduce == reduce_ty and self.get_dtype() in {torch.bool, torch.int64})
        or torch.are_deterministic_algorithms_enabled()
    ):
        ir.ScatterFallback(
            fn, self, dim, index, src, reduce=reduce, include_self=include_self
        )
        return self

    return None


@register_lowering(aten.scatter_, type_promotion_kind=None)
def scatter_(self, dim: int, index, src, *, reduce: Optional[str] = None):
    assert reduce in {None, "add", "multiply"}

    fallback_result = scatter_fallback(
        "aten.scatter_", self, dim, index, src, reduce=reduce
    )

    if fallback_result:
        return fallback_result

    if reduce == "add":
        reduce = "sum"
    elif reduce == "multiply":
        reduce = "prod"

    return scatter_reduce_(self, dim, index, src, reduce)


@register_lowering(aten.scatter_add, type_promotion_kind=None)
def scatter_add(x, dim: int, index, src):
    return scatter_add_(clone(x), dim, index, src)


@register_lowering(aten.scatter_add_, type_promotion_kind=None)
def scatter_add_(x, dim: int, index, src):
    return scatter_reduce_(x, dim, index, src, "sum")


@register_lowering(aten.scatter_reduce, type_promotion_kind=None)
def scatter_reduce(x, dim: int, index, src, reduction_type, **kwargs):
    return scatter_reduce_(clone(x), dim, index, src, reduction_type, **kwargs)


@register_lowering(aten.scatter_reduce_, type_promotion_kind=None)
def scatter_reduce_(self, dim: int, index, src, reduce, *, include_self: bool = True):
    assert reduce in {None, "sum", "prod", "mean", "amax", "amin"}

    fallback_result = scatter_fallback(
        "aten.scatter_reduce_",
        self,
        dim,
        index,
        src,
        reduce=reduce,
        include_self=include_self,
    )

    if fallback_result:
        return fallback_result

    assert isinstance(self, TensorBox)
    assert "int" in str(index.get_dtype())

    ndim = len(self.get_size())
    if ndim == 0:
        self = view(self, [1])

    if isinstance(src, TensorBox) and len(src.get_size()) == 0:
        src = view(src, [1])

    if isinstance(index, TensorBox) and len(index.get_size()) == 0:
        index = view(index, [1])

    dim = _validate_dim(self, dim)

    self.realize()
    index_loader = index.make_loader()
    src_loader = src.make_loader() if isinstance(src, TensorBox) else None

    def output_indexer(idx):
        # self is captured from the end of the function, so it may have 0 dim
        shape = self.get_size()
        ndim = len(shape)
        indirect_idx = list(idx)
        indirect_idx[dim] = ops.indirect_indexing(
            index_loader(idx), 1 if ndim == 0 else shape[dim]
        )
        return indirect_idx

    def fn(idx):
        if src_loader:
            return src_loader(idx)
        else:
            # src is a scalar
            return ops.constant(src, self.get_dtype())

    def backend_reduce_str(reduce):
        if reduce == "sum":
            return "atomic_add"
        else:
            # TODO: Need to support more reduction type
            assert reduce is None
            return None

    if not include_self:
        # zero out the corresponding elements first
        zero_out = ir.Scatter(
            device=self.get_device(),
            dtype=self.get_dtype(),
            inner_fn=lambda index: ops.constant(0, self.get_dtype()),
            ranges=index.get_size(),
            output_indexer=output_indexer,
            scatter_mode=None,
        )
        buffer = ir.ComputedBuffer(
            None,
            ir.MutationLayout(self),
            zero_out,
        )
        buffer.name = V.graph.register_buffer(buffer)

    # self[index[i][j][k]][j][k] += src[i][j][k]  # if dim == 0
    # self[i][index[i][j][k]][k] += src[i][j][k]  # if dim == 1
    # self[i][j][index[i][j][k]] += src[i][j][k]  # if dim == 2
    scatter = ir.Scatter(
        device=self.get_device(),
        dtype=self.get_dtype(),
        inner_fn=fn,
        ranges=index.get_size(),
        output_indexer=output_indexer,
        scatter_mode=backend_reduce_str(reduce),
    )
    buffer = ir.ComputedBuffer(
        None,
        ir.MutationLayout(self),
        scatter,
    )
    buffer.name = V.graph.register_buffer(buffer)

    if ndim == 0:
        self = view(self, [])
    return self


def upsample_nearestnd(
    x,
    output_size,
    scales_x: Tuple[Optional[float], ...],
    n: int = 2,
    exact: bool = False,
):
    x.realize_hint()  # elements are reused
    x_loader = x.make_loader()
    i_sizes = x.get_size()[-n:]
    batch = x.get_size()[:-n]
    i_sizes = [V.graph.sizevars.evaluate_static_shape(i) for i in i_sizes]

    assert len(scales_x) == n
    o_sizes = output_size

    scales = [i / o for i, o in zip(i_sizes, o_sizes)]
    for i, scale in enumerate(scales_x):
        if scale:
            scales[i] = scale

    def scale_fn(x, scale, size):
        # Nearest Exact: input_index = round(scale * (output_index + 0.5) - 0.5)
        #                            = floor(scale * (output_index + 0.5))
        # Nearest: input_index = floor(scale * output_index)
        x = ops.index_expr(x, torch.float32)
        if exact:
            x = ops.add(x, ops.constant(0.5, torch.float32))
        x = ops.mul(x, ops.constant(scale, torch.float32))
        x = ops.to_dtype(x, torch.int32)
        return ops.indirect_indexing(x, size, check=False)

    def fn(idx):
        x = idx[-n:]
        b = idx[:-n]
        return x_loader(
            [*b, *[scale_fn(i, s, size) for i, s, size in zip(x, scales, i_sizes)]]
        )

    return Pointwise.create(
        device=x.get_device(),
        dtype=x.get_dtype(),
        inner_fn=fn,
        ranges=[*batch, *o_sizes],
    )


@register_lowering(aten.upsample_nearest1d.default)
def upsample_nearest1d(x, output_size, scales: Optional[float] = None):
    return upsample_nearestnd(x, output_size, (scales,), n=1)


@register_lowering(aten._upsample_nearest_exact1d.default)
def _upsample_nearest_exact1d(x, output_size, scales: Optional[float] = None):
    return upsample_nearestnd(x, output_size, (scales,), n=1, exact=True)


@register_lowering(aten.upsample_nearest2d.default)
def upsample_nearest2d(
    x, output_size, scales_h: Optional[float] = None, scales_w: Optional[float] = None
):
    return upsample_nearestnd(x, output_size, (scales_h, scales_w), n=2)


@register_lowering(aten._upsample_nearest_exact2d.default)
def _upsample_nearest_exact2d(
    x, output_size, scales_h: Optional[float] = None, scales_w: Optional[float] = None
):
    return upsample_nearestnd(x, output_size, (scales_h, scales_w), n=2, exact=True)


@register_lowering(aten.upsample_nearest3d.default)
def upsample_nearest3d(
    x,
    output_size,
    scales_d: Optional[float] = None,
    scales_h: Optional[float] = None,
    scales_w: Optional[float] = None,
):
    return upsample_nearestnd(x, output_size, (scales_d, scales_h, scales_w), n=3)


@register_lowering(aten._upsample_nearest_exact3d.default)
def _upsample_nearest_exact3d(
    x,
    output_size,
    scales_d: Optional[float] = None,
    scales_h: Optional[float] = None,
    scales_w: Optional[float] = None,
):
    return upsample_nearestnd(
        x, output_size, (scales_d, scales_h, scales_w), n=3, exact=True
    )


def _create_constants(*args, dtype):
    return tuple(ops.constant(a, dtype) for a in args)


@register_lowering(aten.upsample_bicubic2d.default)
def upsample_bicubic2d_default(
    x,
    output_size,
    align_corners: bool,
    scales_h: Optional[float] = None,
    scales_w: Optional[float] = None,
):
    x.realize_hint()
    x_loader = x.make_loader()

    N, C, iH, iW = x.get_size()
    oH, oW = output_size

    iH = V.graph.sizevars.evaluate_static_shape(iH)
    iW = V.graph.sizevars.evaluate_static_shape(iW)

    def get_int_dtype(maxval):
        if maxval > torch.iinfo(torch.int32).max:
            return torch.int64
        return torch.int32

    def compute_scale(in_size, out_size, align_corners, scale=None):
        if align_corners:
            return (in_size - 1) / (out_size - 1) if out_size > 1 else 0
        else:
            return 1 / scale if scale is not None and scale > 0 else in_size / out_size

    def compute_source_index(scale, dst_index, align_corners):
        dst_index_ie = ops.index_expr(dst_index, torch.float32)
        scale = ops.constant(scale, torch.float32)
        if align_corners:
            return ops.mul(scale, dst_index_ie)
        else:
            half = ops.constant(0.5, torch.float32)
            return scale * (dst_index_ie + half) - half

    def cubic_convolution1(x, A):
        _Ap2, _Ap3, _1 = _create_constants(A + 2, A + 3, 1, dtype=torch.float32)
        return (_Ap2 * x - _Ap3) * x * x + _1

    def cubic_convolution2(x, A):
        _A, _4A, _5A, _8A = _create_constants(
            A, 4 * A, 5 * A, 8 * A, dtype=torch.float32
        )
        return ((_A * x - _5A) * x + _8A) * x - _4A

    def get_cubic_upsample_coefficients(t):
        A = -0.75
        _1 = ops.constant(1.0, torch.float32)
        c0 = cubic_convolution2(ops.add(t, _1), A)
        c1 = cubic_convolution1(t, A)

        x2 = ops.sub(_1, t)
        c2 = cubic_convolution1(x2, A)
        c3 = cubic_convolution2(ops.add(x2, _1), A)
        return (c0, c1, c2, c3)

    def cubic_interp1d(xs, t):
        cs = get_cubic_upsample_coefficients(t)
        # dot product between xs and cs
        return xs[0] * cs[0] + xs[1] * cs[1] + xs[2] * cs[2] + xs[3] * cs[3]

    height_scale = compute_scale(iH, oH, align_corners, scales_h)
    width_scale = compute_scale(iW, oW, align_corners, scales_h)

    def clamp(v, min, max):
        return ops.maximum(min, ops.minimum(max, v))

    def fn(idx):
        n, c, oy, ox = idx

        real_x = compute_source_index(width_scale, ox, align_corners)
        in_x = ops.floor(real_x)
        t_x = ops.sub(real_x, in_x)

        real_y = compute_source_index(height_scale, oy, align_corners)
        in_y = ops.floor(real_y)
        t_y = ops.sub(real_y, in_y)

        def load_bounded(fy, fx):
            # TODO(Lezcano) Here we may not need to set-up a device_size
            _0 = ops.constant(0, torch.int32)
            iHm1 = ops.constant(iH - 1, torch.int32)
            iWm1 = ops.constant(iW - 1, torch.int32)
            iy = ops.indirect_indexing(clamp(fy, _0, iHm1), iH, check=False)
            ix = ops.indirect_indexing(clamp(fx, _0, iWm1), iW, check=False)
            return x_loader([n, c, iy, ix])

        iy = ops.to_dtype(in_y, get_int_dtype(iH + 1))
        ix = ops.to_dtype(in_x, get_int_dtype(iW + 1))
        iys_ofs = tuple(ops.add(iy, ofs) for ofs in (-1, 0, 1, 2))
        ixs_ofs = tuple(ops.add(ix, ofs) for ofs in (-1, 0, 1, 2))

        def get_x_interp(y):
            coeffs_x = tuple(load_bounded(y, x) for x in ixs_ofs)
            return cubic_interp1d(coeffs_x, t_x)

        coeffs_y = tuple(get_x_interp(y) for y in iys_ofs)
        return cubic_interp1d(coeffs_y, t_y)

    return Pointwise.create(
        device=x.get_device(),
        dtype=x.get_dtype(),
        inner_fn=fn,
        ranges=[N, C, sympy.Integer(oH), sympy.Integer(oW)],
    )


@register_lowering(aten.reflection_pad1d_backward)
@register_lowering(aten.reflection_pad2d_backward)
@register_lowering(aten.reflection_pad3d_backward)
def _reflection_padnd_backward(grad_output, x, padding):
    dim = len(padding) // 2

    dhw = [h - 1 for h in x.get_size()[-dim:]]
    grad_loader = grad_output.make_loader()

    padding_left = [padding[2 * (dim - 1 - i)] for i in range(dim)]
    padding_right = [padding[2 * (dim - 1 - i) + 1] for i in range(dim)]

    def fn(idx):
        b = idx[:-dim]
        xyz = idx[-dim:]

        def load_from_output(x):
            return grad_loader([*b, *x])

        def index_range_condition(index_range):
            i, lb, ub = index_range
            i = ops.index_expr(i, torch.int32)
            lb = ops.index_expr(lb, torch.int64)
            ub = ops.index_expr(ub, torch.int64)
            return ops.and_(ops.ge(i, lb), ops.le(i, ub))

        # Areas after reflection:
        #
        #   top-left    |   top     |   top-right
        # -----------------------------------------
        #   left        |   center  |   right
        # -----------------------------------------
        #   bottom-left |   bottom  |   bottom-right
        #
        # The center area is the original matrix. Other areas are reflections.

        center = [xyz[i] + padding_left[i] for i in range(dim)]
        left_reflect = [padding_left[i] - xyz[i] for i in range(dim)]
        right_reflect = [2 * dhw[i] + padding_left[i] - xyz[i] for i in range(dim)]

        # Accumulate gradients from different areas
        # If some of the padding is negative, center load is not always valid
        range_c = [
            (center[i], 0, dhw[i] + padding_left[i] + padding_right[i])
            for i in range(dim)
        ]
        cond = functools.reduce(
            ops.and_, [index_range_condition(range_c[i]) for i in range(dim)]
        )
        grad = ops.masked(cond, lambda: load_from_output(center), 0.0)

        def accumulate(grad, out, index_ranges):
            # If the upper bound is less than the lower bound, we can get rid of one accumulation.
            # This happens when the padding size is zero.
            for i in range(dim):
                upper_less_than_lower = index_ranges[i][2] < index_ranges[i][1]
                if isinstance(upper_less_than_lower, bool) and upper_less_than_lower:
                    return grad
            cond = functools.reduce(
                ops.and_,
                [index_range_condition(index_range) for index_range in index_ranges],
            )
            g = ops.masked(cond, lambda: load_from_output(out), 0.0)
            return ops.add(grad, g)

        for area in itertools.product(*[[-1, 0, 1] for _ in range(dim)]):
            if area == tuple([0] * dim):
                # center, this is already done.
                continue

            outs = []
            index_ranges = []

            for i in range(dim):
                if area[i] == 0:
                    out = center[i]
                    index_range = range_c[i]
                elif area[i] == -1:
                    out = left_reflect[i]
                    index_range = (xyz[i], 1, padding_left[i])
                elif area[i] == 1:
                    out = right_reflect[i]
                    index_range = (xyz[i], dhw[i] - padding_right[i], dhw[i] - 1)

                outs.append(out)
                index_ranges.append(index_range)

            grad = accumulate(grad, outs, index_ranges)

        return grad

    return Pointwise.create(
        device=grad_output.get_device(),
        dtype=grad_output.get_dtype(),
        inner_fn=fn,
        ranges=list(x.get_size()),
    )


@register_lowering(prims.rev.default)
def rev(x, dims):
    # note - dims pre-canonicalized
    x_loader = x.make_loader()
    sizes = x.get_size()

    def loader(idx):
        idx = list(idx)
        assert len(idx) == len(sizes)
        for dim in dims:
            idx[dim] = (sizes[dim] - 1) - idx[dim]

        return x_loader(idx)

    return Pointwise.create(
        device=x.get_device(),
        dtype=x.get_dtype(),
        inner_fn=loader,
        ranges=sizes,
    )


@register_lowering(aten.constant_pad_nd, type_promotion_kind=None)
def constant_pad_nd(x, padding, fill_value=0):
    assert (len(padding) % 2) == 0
    if all(p == 0 for p in padding):
        return clone(x)

    sizes = x.get_size()

    bounds = list(reversed(list(zip(padding[::2], padding[1::2]))))
    n = len(sizes) - len(bounds)

    # if padding is a complicated expression, hoist it
    bounds_precomp: List[Tuple[sympy.Symbol, Any]] = []
    for l, h in bounds:
        bounds_precomp.append((V.graph.sizevars.lookup_precomputed_size(l), h))

    output_size = list(sizes[:n])
    mask_sizes = []
    for (low, high), size in zip(bounds, sizes[n:]):
        mask_sizes.append(size)
        output_size.append(sympy.expand(size + low + high))
    assert len(output_size) == len(sizes)
    fill_value = dtype_to_type(x.get_dtype())(fill_value)

    def mask(index):
        mask = []
        for idx, (low, high), length in zip(index[n:], bounds, mask_sizes):
            if low != 0:
                mask.append(range_mask_low(idx, 0))
            if high != 0:
                mask.append(range_mask_high(idx, length))
        mask = functools.reduce(ops.and_, mask)
        return ops.masked(mask, lambda: x_loader(index), fill_value)

    def offset_fn(index):
        new_index = list(index[:n])
        for idx, (low, high) in zip(index[n:], bounds_precomp):
            new_index.append(idx - low)
        assert len(new_index) == len(index)
        return mask(new_index)

    x_loader = x.make_loader()
    return Pointwise.create(
        device=x.get_device(),
        dtype=x.get_dtype(),
        inner_fn=offset_fn,
        ranges=output_size,
    )


def range_mask_low(i: sympy.Expr, low: Union[sympy.Expr, int]):
    return ops.ge(
        ops.index_expr(i, torch.int64),
        ops.index_expr(sympy.Integer(low), torch.int64),
    )


def range_mask_high(i: sympy.Expr, high: sympy.Expr):
    return ops.lt(
        ops.index_expr(i, torch.int64),
        ops.index_expr(high, torch.int64),
    )


def range_mask(i: sympy.Expr, high: sympy.Expr, low: sympy.Expr):
    return ops.and_(
        range_mask_low(i, low),
        range_mask_high(i, high),
    )


def constant_boundary_condition_2d(x, fill_value, padding=None, pad_fill_value=1.0):
    *_, h, w = x.get_size()
    x_loader = x.make_loader()
    padding_h = padding[0] if padding else 0
    padding_w = padding[1] if padding else 0

    def load(index):
        *prefix, ih, iw = index

        mask = ops.and_(
            range_mask(ih, h + padding_h, -padding_h),
            range_mask(iw, w + padding_w, -padding_w),
        )
        return (
            ops.masked(
                mask,
                lambda: constant_boundary_condition_2d(x, pad_fill_value)(
                    [*prefix, ih, iw]
                ),
                fill_value,
            )
            if padding
            else ops.masked(mask, lambda: x_loader([*prefix, ih, iw]), fill_value)
        )

    return load


def pooling_size(x, i, kernel_size, stride, padding, ceil_mode):
    x_out = FloorDiv(
        x + 2 * padding[i] - (kernel_size[i] - 1) + (stride[i] - 1), stride[i]
    )

    if ceil_mode:
        x_alt = FloorDiv(
            x + 2 * padding[i] - (kernel_size[i] - 1) + 2 * (stride[i] - 1), stride[i]
        )
        if V.graph.sizevars.size_hint((x_alt - 1) * stride[i] - x - padding[i]) >= 0:
            # Sliding windows must start within the input or left padding
            x_alt -= 1
            V.graph.sizevars.guard_leq(0, x_alt * stride[i] - x - padding[i])
        if V.graph.sizevars.size_hint(x_out - x_alt) == 0:
            # ceil mode is actually a no-op, lets guard on that
            V.graph.sizevars.guard_equals(x_out, x_alt)
            ceil_mode = False
        else:
            x_out = x_alt
    return x_out, ceil_mode


fallback_max_pool2d_with_indices = fallback_handler(
    aten.max_pool2d_with_indices.default,
    add_to_fallback_set=False,
)


@register_lowering(aten.max_pool2d_with_indices, type_promotion_kind=None)
def max_pool2d_with_indices(
    x, kernel_size, stride=None, padding=0, dilation=1, ceil_mode=False
):
    if padding == 0:
        padding = [0, 0]
    if dilation == 1:
        dilation = [1, 1]
    if not stride:
        stride = kernel_size
    kernel_size = pad_listlike(kernel_size, 2)
    stride = pad_listlike(stride, 2)
    padding = pad_listlike(padding, 2)
    dilation = pad_listlike(dilation, 2)

    assert isinstance(x, TensorBox)
    assert len(kernel_size) == 2
    assert len(stride) == 2
    assert len(padding) == 2
    assert len(dilation) == 2
    assert len(x.get_size()) in (3, 4)

    x.realize_hint()
    *batch, h, w = x.get_size()

    h_out, ceil_mode1 = pooling_size(h, 0, kernel_size, stride, padding, ceil_mode)
    w_out, ceil_mode2 = pooling_size(w, 1, kernel_size, stride, padding, ceil_mode)

    if padding[0] or padding[1] or ceil_mode1 or ceil_mode2:
        x_loader = constant_boundary_condition_2d(x, float("-inf"))
    else:
        x_loader = x.make_loader()

    new_size = list(batch) + [h_out, w_out]
    window_size = kernel_size[0] * kernel_size[1]

    if window_size > 25 or any(d != 1 for d in dilation):
        # Kernel size too big. Results in hard-to-optimize Triton code. Use fallback.
        return fallback_max_pool2d_with_indices(
            x, kernel_size, stride, padding, dilation, ceil_mode
        )

    def fn(idx, return_index):
        *prefix, bh, bw = idx
        maxval = None
        maxindex = None
        for ih, iw in itertools.product(range(kernel_size[0]), range(kernel_size[1])):
            ih = bh * stride[0] + ih - padding[0]
            iw = bw * stride[1] + iw - padding[1]
            val = x_loader([*prefix, ih, iw])
            if return_index:
                index = ops.index_expr(ih * w + iw, torch.int64)
                if maxindex is None:
                    maxindex = index
                else:
                    maxindex = ops.where(ops.gt(val, maxval), index, maxindex)
            if maxval is None:
                maxval = val
            else:
                maxval = ops.maximum(val, maxval)
        if return_index:
            return maxindex
        else:
            return maxval

    r1 = Pointwise.create(
        device=x.get_device(),
        dtype=x.get_dtype(),
        inner_fn=functools.partial(fn, return_index=False),
        ranges=new_size,
    )
    r2 = Pointwise.create(
        device=x.get_device(),
        dtype=torch.int64,
        inner_fn=functools.partial(fn, return_index=True),
        ranges=new_size,
    )
    # TODO(jansel): should we force these to be realized?
    return r1, r2


fallback_max_pool2d_with_indices_backward = fallback_handler(
    aten.max_pool2d_with_indices_backward.default,
    add_to_fallback_set=False,
)


@register_lowering(aten.max_pool2d_with_indices_backward, type_promotion_kind=None)
def max_pool2d_with_indices_backward(
    grad_output, x, kernel_size, stride, padding, dilation, ceil_mode, indices
):
    if padding == 0:
        padding = [0, 0]
    if dilation == 1:
        dilation = [1, 1]
    if not stride:
        stride = kernel_size

    assert isinstance(x, TensorBox)
    assert len(kernel_size) == 2
    assert len(stride) == 2
    assert len(padding) == 2
    assert len(dilation) == 2
    assert len(x.get_size()) in (3, 4)

    # we will read this many times, so make sure it is computed
    grad_output.realize_hint()
    try:
        gO_stride = grad_output.get_stride()
    except AttributeError:
        # some classes don't have `get_stride`
        # TODO will need a better way of determining if inputs are channels-last
        gO_stride = None
    if isinstance(x, TensorBox) and isinstance(x.data.data, Pointwise):  # type: ignore[attr-defined]
        data = x.data.data  # type: ignore[attr-defined]
        x_buffer = ir.ComputedBuffer(
            name=None,
            layout=ir.FlexibleLayout(
                device=data.get_device(),
                dtype=data.get_dtype(),
                size=data.get_size(),
            ),
            data=data,
        )
        x_buffer.decide_layout()
        x_stride = x_buffer.get_stride()
    else:
        try:
            x_stride = x.get_stride()
        except AttributeError:
            x_stride = None

    is_channels_last = (x_stride is not None and x_stride[1] == 1) or (
        gO_stride is not None and gO_stride[1] == 1
    )
    autotune = (
        config.coordinate_descent_tuning
        or config.max_autotune
        or config.max_autotune_pointwise
    )
    if any(d != 1 for d in dilation) or (is_channels_last and not autotune):
        # don't codegen channels-last when autotune is not enabled, it's very slow
        return fallback_max_pool2d_with_indices_backward(
            grad_output, x, kernel_size, stride, padding, dilation, ceil_mode, indices
        )

    indices.realize_hint()

    *batch, height, width = x.get_size()
    *_, pooled_height, pooled_width = grad_output.get_size()

    indices_loader = indices.make_loader()
    grad_loader = grad_output.make_loader()
    new_size = list(x.get_size())

    h_window_size = max(
        [
            max(h // stride[0] - max(0, (h - kernel_size[0]) // stride[0]), 1)
            for h in range(kernel_size[0] * 2)
        ]
    )
    w_window_size = max(
        [
            max(w // stride[1] - max(0, (w - kernel_size[1]) // stride[1]), 1)
            for w in range(kernel_size[1] * 2)
        ]
    )

    window_size = h_window_size * w_window_size

    if window_size > 25:
        # Kernel size too big. Results in hard-to-optimize Triton code. Use fallback.
        return fallback_max_pool2d_with_indices_backward(
            grad_output, x, kernel_size, stride, padding, dilation, ceil_mode, indices
        )

    indices_size = indices.get_size()

    def fn(idx):
        *prefix, h, w = idx
        index_test = ops.index_expr(h * width + w, torch.int32)
        h = h + padding[0]
        w = w + padding[1]
        phstart = ops.index_expr(
            FloorDiv(h - kernel_size[0] + stride[0], stride[0]), torch.int32
        )
        pwstart = ops.index_expr(
            FloorDiv(w - kernel_size[1] + stride[1], stride[1]), torch.int32
        )
        phend = ops.index_expr(FloorDiv(h, stride[0]) + 1, torch.int32)
        pwend = ops.index_expr(FloorDiv(w, stride[1]) + 1, torch.int32)

        phstart = ops.maximum(phstart, ops.constant(0, torch.int32))
        pwstart = ops.maximum(pwstart, ops.constant(0, torch.int32))
        phend = ops.minimum(phend, ops.index_expr(pooled_height, torch.int32))
        pwend = ops.minimum(pwend, ops.index_expr(pooled_width, torch.int32))

        gradient = None
        for ph_ in range(h_window_size):
            for pw_ in range(w_window_size):
                ph = ops.add(phstart, ops.constant(ph_, torch.int32))
                pw = ops.add(pwstart, ops.constant(pw_, torch.int32))
                grad_index = [
                    *prefix,
                    ops.indirect_indexing(
                        ops.minimum(ph, ops.sub(phend, ops.constant(1, torch.int32))),
                        indices_size[-2],
                        check=False,
                    ),
                    ops.indirect_indexing(
                        ops.minimum(pw, ops.sub(pwend, ops.constant(1, torch.int32))),
                        indices_size[-1],
                        check=False,
                    ),
                ]

                index_actual = indices_loader(grad_index)
                grad_part = grad_loader(grad_index)
                check = ops.eq(index_actual, index_test)

                if gradient is None:
                    # don't need mask for 0, 0
                    gradient = ops.where(
                        check, grad_part, ops.constant(0.0, torch.float32)
                    )
                else:
                    mask = ops.and_(
                        ops.and_(
                            ops.lt(ph, phend),
                            ops.lt(pw, pwend),
                        ),
                        check,
                    )
                    gradient = ops.where(mask, ops.add(gradient, grad_part), gradient)
        assert gradient is not None
        return gradient

    return Pointwise.create(
        device=grad_output.get_device(),
        dtype=grad_output.get_dtype(),
        inner_fn=fn,
        ranges=new_size,
    )


def pad_adaptive_loader(x):
    *_, h, w = x.get_size()
    x_loader = x.make_loader()

    def load(prefix, increments, start_indices, end_indices):
        ih, iw = increments
        h_start_index, w_start_index = start_indices
        h_end_index, w_end_index = end_indices

        mask = ops.and_(
            ops.lt(
                ops.index_expr(h_start_index + ih, torch.int64),
                ops.index_expr(h_end_index, torch.int64),
            ),
            ops.lt(
                ops.index_expr(w_start_index + iw, torch.int64),
                ops.index_expr(w_end_index, torch.int64),
            ),
        )

        return ops.masked(
            mask,
            lambda: x_loader([*prefix, h_start_index + ih, w_start_index + iw]),
            0.0,
        )

    return load


def _adaptive_pooling_idx_sum(kernel_maxes, start_index_fns, end_index_fns):
    h_start_index_fn, w_start_index_fn = start_index_fns
    h_end_index_fn, w_end_index_fn = end_index_fns

    def fn_sum(idx, loader):
        *prefix, bh, bw = idx

        h_start_index = h_start_index_fn(bh)
        h_end_index = h_end_index_fn(bh)

        w_start_index = w_start_index_fn(bw)
        w_end_index = w_end_index_fn(bw)

        total = None
        for ih, iw in itertools.product(range(kernel_maxes[0]), range(kernel_maxes[1])):
            val = loader(
                prefix,
                [ih, iw],
                [h_start_index, w_start_index],
                [h_end_index, w_end_index],
            )
            if total is None:
                total = val
            else:
                total = ops.add(val, total)
        return total

    return fn_sum


fallback_adaptive_avg_pool2d = fallback_handler(
    aten._adaptive_avg_pool2d.default, add_to_fallback_set=False
)


@register_lowering(aten._adaptive_avg_pool2d)
def _adaptive_avg_pool2d(x, output_size):
    assert isinstance(x, TensorBox)
    assert len(output_size) == 2
    x.realize_hint()

    *batch, h_in, w_in = x.get_size()

    h_in = V.graph.sizevars.evaluate_static_shape(h_in)
    w_in = V.graph.sizevars.evaluate_static_shape(w_in)

    h_out, w_out = output_size

    # no-op if the same input and output
    if h_in == h_out and w_in == w_out:
        return clone(x)

    if h_out == 0 or w_out == 0:
        o_size = [*batch, h_out, w_out]
        return empty(o_size, dtype=x.get_dtype(), device=x.get_device())
    if h_in % h_out == 0 and w_in % w_out == 0:
        kernel_size = [h_in // h_out, w_in // w_out]
        return avg_pool2d(x, kernel_size)

    h_kernel_max = ceildiv((h_in + h_out - 1), h_out)
    w_kernel_max = ceildiv((w_in + w_out - 1), w_out)

    new_size = list(batch) + [h_out, w_out]
    dtype = x.get_dtype()

    def start_index(index, out_dim, inp_dim):
        return FloorDiv((index * inp_dim), out_dim)

    def end_index(index, out_dim, inp_dim):
        return FloorDiv((index + 1) * inp_dim + out_dim - 1, out_dim)

    h_start_index = functools.partial(start_index, out_dim=h_out, inp_dim=h_in)
    h_end_index = functools.partial(end_index, out_dim=h_out, inp_dim=h_in)

    w_start_index = functools.partial(start_index, out_dim=w_out, inp_dim=w_in)
    w_end_index = functools.partial(end_index, out_dim=w_out, inp_dim=w_in)

    window_size = h_kernel_max * w_kernel_max
    if window_size > 25:
        # Kernel size too big. Results in hard-to-optimize Triton code. Use fallback.
        return fallback_adaptive_avg_pool2d(x, output_size)

    fn_sum = _adaptive_pooling_idx_sum(
        [h_kernel_max, w_kernel_max],
        [h_start_index, w_start_index],
        [h_end_index, w_end_index],
    )

    ones_loader = pad_adaptive_loader(ones_like(x))

    def fn(idx):
        return ops.truediv(
            fn_sum(idx, pad_adaptive_loader(x)), fn_sum(idx, ones_loader)
        )

    rv = Pointwise.create(
        device=x.get_device(),
        dtype=dtype,
        inner_fn=fn,
        ranges=new_size,
    )
    # TODO: should we force these to be realized?
    return rv


@register_lowering(aten.upsample_nearest2d_backward.default)
def upsample_nearest2d_backward(
    x, output_size=None, input_size=None, scales_h=None, scales_w=None
):
    x.realize_hint()

    *batch, inp_h, inp_w = x.get_size()
    inp_h = V.graph.sizevars.evaluate_static_shape(inp_h)
    inp_w = V.graph.sizevars.evaluate_static_shape(inp_w)

    *batch, out_h, out_w = input_size

    if inp_h % out_h == 0 and inp_w % out_w == 0:
        return avg_pool2d(x, [inp_h // out_h, inp_w // out_w], divisor_override=1)

    h_kernel_max = ceildiv(inp_h, out_h)
    w_kernel_max = ceildiv(inp_w, out_w)

    def start_index(index, out_dim, inp_dim):
        return CeilDiv(index * inp_dim, out_dim)

    def end_index(index, out_dim, inp_dim):
        return start_index((index + 1), out_dim, inp_dim)

    h_start_index = functools.partial(start_index, out_dim=out_h, inp_dim=inp_h)
    h_end_index = functools.partial(end_index, out_dim=out_h, inp_dim=inp_h)

    w_start_index = functools.partial(start_index, out_dim=out_w, inp_dim=inp_w)
    w_end_index = functools.partial(end_index, out_dim=out_w, inp_dim=inp_w)

    fn_sum = _adaptive_pooling_idx_sum(
        [h_kernel_max, w_kernel_max],
        [h_start_index, w_start_index],
        [h_end_index, w_end_index],
    )

    def fn(idx):
        return fn_sum(idx, pad_adaptive_loader(x))

    rv = Pointwise.create(
        device=x.get_device(),
        dtype=x.get_dtype(),
        inner_fn=fn,
        ranges=list(input_size),
    )

    return rv


fallback_avg_pool2d = fallback_handler(
    aten.avg_pool2d.default, add_to_fallback_set=False
)


@register_lowering(aten.avg_pool2d, type_promotion_kind=None)
def avg_pool2d(
    x,
    kernel_size,
    stride=(),
    padding=0,
    ceil_mode=False,
    count_include_pad=True,
    divisor_override=None,
):
    if not stride:
        stride = kernel_size
    if not padding:
        padding = [0, 0]
    kernel_size = pad_listlike(kernel_size, 2)
    stride = pad_listlike(stride, 2)
    padding = pad_listlike(padding, 2)

    assert isinstance(x, TensorBox)
    assert len(kernel_size) == 2
    assert len(stride) == 2
    assert len(padding) == 2
    assert len(x.get_size()) in (3, 4)

    x.realize_hint()
    *batch, h, w = x.get_size()

    h_out, ceil_mode1 = pooling_size(h, 0, kernel_size, stride, padding, ceil_mode)
    w_out, ceil_mode2 = pooling_size(w, 1, kernel_size, stride, padding, ceil_mode)

    if padding[0] or padding[1] or ceil_mode1 or ceil_mode2:
        x_loader = constant_boundary_condition_2d(x, 0.0)
        had_padding = True
    else:
        x_loader = x.make_loader()
        had_padding = False

    new_size = list(batch) + [h_out, w_out]
    dtype = x.get_dtype()

    window_size = kernel_size[0] * kernel_size[1]
    if window_size > 25:
        # Kernel size too big. Results in hard-to-optimize Triton code. Use fallback.
        return fallback_avg_pool2d(
            x,
            kernel_size,
            stride,
            padding,
            ceil_mode,
            count_include_pad,
            divisor_override,
        )

    def fn_sum(idx, loader):
        *prefix, bh, bw = idx
        total = None
        for ih, iw in itertools.product(range(kernel_size[0]), range(kernel_size[1])):
            ih = bh * stride[0] + ih - padding[0]
            iw = bw * stride[1] + iw - padding[1]
            val = loader([*prefix, ih, iw])
            if total is None:
                total = val
            else:
                total = ops.add(val, total)
        return total

    if not had_padding or divisor_override:
        if divisor_override:
            scale = 1 / divisor_override
        else:
            scale = 1.0 / (kernel_size[0] * kernel_size[1])

        def fn(idx):
            return ops.mul(fn_sum(idx, x_loader), ops.constant(scale, dtype))

    else:
        ones_loader = constant_boundary_condition_2d(
            ones_like(x), 0.0, padding if count_include_pad else None
        )

        def fn(idx):
            # TODO(jansel): optimize to do `int(x<h)` rather than `x<h?1:0`
            return ops.truediv(fn_sum(idx, x_loader), fn_sum(idx, ones_loader))

    rv = Pointwise.create(
        device=x.get_device(),
        dtype=dtype,
        inner_fn=fn,
        ranges=new_size,
    )
    # TODO(jansel): should we force these to be realized?
    return rv


fallback_avg_pool2d_backward = fallback_handler(
    aten.avg_pool2d_backward.default, add_to_fallback_set=False
)


@register_lowering(aten.avg_pool2d_backward, type_promotion_kind=None)
def avg_pool2d_backward(
    grad_output,
    x,
    kernel_size,
    stride,
    padding,
    ceil_mode,
    count_include_pad,
    divisor_override=None,
):
    assert divisor_override is None or divisor_override != 0, "divisor must be not zero"
    if not stride:
        stride = kernel_size
    if not padding:
        padding = [0, 0]

    assert isinstance(grad_output, TensorBox)
    assert isinstance(x, TensorBox)
    assert len(kernel_size) == 2
    assert len(stride) == 2
    assert len(padding) == 2
    assert len(x.get_size()) in (3, 4)

    grad_output.realize_hint()  # we will read this many times, so make sure it is computed

    *batch, height, width = x.get_size()

    h_out, ceil_mode1 = pooling_size(height, 0, kernel_size, stride, padding, ceil_mode)
    w_out, ceil_mode2 = pooling_size(width, 1, kernel_size, stride, padding, ceil_mode)

    grad_loader = grad_output.make_loader()

    had_padding = padding[0] or padding[1] or ceil_mode1 or ceil_mode2

    *_, pooled_height, pooled_width = grad_output.get_size()
    new_size = list(x.get_size())
    dtype = x.get_dtype()

    h_window_size = max(
        [
            max(h // stride[0] - max(0, (h - kernel_size[0]) // stride[0]), 1)
            for h in range(kernel_size[0] * 2)
        ]
    )
    w_window_size = max(
        [
            max(w // stride[1] - max(0, (w - kernel_size[1]) // stride[1]), 1)
            for w in range(kernel_size[1] * 2)
        ]
    )

    window_size = h_window_size * w_window_size
    if window_size > 25:
        # Kernel size too big. Results in hard-to-optimize Triton code. Use fallback.
        return fallback_avg_pool2d_backward(
            grad_output,
            x,
            kernel_size,
            stride,
            padding,
            ceil_mode,
            count_include_pad,
            divisor_override,
        )

    def compute_pool_size_without_padding(ph, pw):
        """
        This computes the scaling factor that we will divide an element
        by when `count_include_pad=False`
        """
        stride_h = ops.constant(stride[0], torch.int32)
        stride_w = ops.constant(stride[1], torch.int32)
        pad_h = ops.constant(padding[0], torch.int32)
        pad_w = ops.constant(padding[1], torch.int32)
        kernel_h = ops.constant(kernel_size[0], torch.int32)
        kernel_w = ops.constant(kernel_size[1], torch.int32)
        hstart = ops.sub(ops.mul(ph, stride_h), pad_h)
        wstart = ops.sub(ops.mul(pw, stride_w), pad_w)
        hend = ops.minimum(
            ops.add(hstart, kernel_h),
            ops.add(ops.index_expr(height, torch.int32), pad_h),
        )
        wend = ops.minimum(
            ops.add(wstart, kernel_w),
            ops.add(ops.index_expr(width, torch.int32), pad_w),
        )
        hstart = ops.maximum(hstart, ops.constant(0, torch.int32))
        wstart = ops.maximum(wstart, ops.constant(0, torch.int32))
        hend = ops.minimum(hend, ops.index_expr(height, torch.int32))
        wend = ops.minimum(wend, ops.index_expr(width, torch.int32))
        divide_factor = ops.mul(ops.sub(hend, hstart), ops.sub(wend, wstart))
        return divide_factor

    def fn(idx):
        *prefix, h, w = idx
        h = h + padding[0]
        w = w + padding[1]
        phstart = ops.index_expr(
            FloorDiv(h - kernel_size[0] + stride[0], stride[0]), torch.int32
        )
        pwstart = ops.index_expr(
            FloorDiv(w - kernel_size[1] + stride[1], stride[1]), torch.int32
        )
        phend = ops.index_expr(FloorDiv(h, stride[0]) + 1, torch.int32)
        pwend = ops.index_expr(FloorDiv(w, stride[1]) + 1, torch.int32)

        phstart = ops.maximum(phstart, ops.constant(0, torch.int32))
        pwstart = ops.maximum(pwstart, ops.constant(0, torch.int32))
        phend = ops.minimum(phend, ops.index_expr(pooled_height, torch.int32))
        pwend = ops.minimum(pwend, ops.index_expr(pooled_width, torch.int32))

        gradient = None
        for ph_ in range(h_window_size):
            for pw_ in range(w_window_size):
                ph = ops.add(phstart, ops.constant(ph_, torch.int32))
                pw = ops.add(pwstart, ops.constant(pw_, torch.int32))

                if divisor_override is not None:
                    scale = divisor_override
                elif count_include_pad or not had_padding:
                    scale = kernel_size[0] * kernel_size[1]
                else:
                    scale = compute_pool_size_without_padding(ph, pw)

                part = ops.truediv(
                    grad_loader(
                        [
                            *prefix,
                            ops.indirect_indexing(
                                ops.minimum(
                                    ph, ops.sub(phend, ops.constant(1, torch.int32))
                                ),
                                pooled_height,
                                check=False,
                            ),
                            ops.indirect_indexing(
                                ops.minimum(
                                    pw, ops.sub(pwend, ops.constant(1, torch.int32))
                                ),
                                pooled_width,
                                check=False,
                            ),
                        ]
                    ),
                    scale,
                )

                mask = ops.and_(
                    ops.lt(ph, phend),
                    ops.lt(pw, pwend),
                )
                if gradient is None:
                    gradient = ops.where(mask, part, ops.constant(0.0, torch.float32))
                else:
                    gradient = ops.where(mask, ops.add(gradient, part), gradient)
        assert gradient is not None
        return gradient

    rv = Pointwise.create(
        device=grad_output.get_device(),
        dtype=dtype,
        inner_fn=fn,
        ranges=new_size,
    )
    return rv


def _validate_reduction_axis(x, axis):
    size = x.get_size()
    if isinstance(axis, int):
        axis = [axis]
    elif not axis:
        axis = range(len(size))
    if len(size) == 0:
        assert tuple(axis) in [(), (0,), (-1,)], f"invalid axis: {axis}"
        return []
    axis = list(axis)
    for i in range(len(axis)):
        if axis[i] < 0:
            axis[i] += len(size) if len(size) else 1
        assert 0 <= axis[i] < len(size) or (len(size) == 0 and axis[i] == 0)
    assert len(set(axis)) == len(axis), "reduction axis not unique"
    return axis


def _make_reduction_inner(x, *, axis, keepdims, dtype, override_return_dtype):
    if dtype is not None:
        x = to_dtype(x, dtype)
    size = x.get_size()
    axis = set(_validate_reduction_axis(x, axis))

    kept_sizes = []
    kept_idx = []
    reduced_sizes = []
    reduced_idx = []
    for i in range(len(size)):
        if i in axis:
            reduced_idx.append(i)
            reduced_sizes.append(size[i])
        else:
            kept_idx.append(i)
            kept_sizes.append(size[i])

    def loader(index, reduction_index):
        assert len(reduction_index) == len(reduced_idx)
        if keepdims:
            assert len(index) == len(size)
            index = [index[i] for i in kept_idx]
        assert len(index) == len(kept_idx)
        new_index = [None] * (len(index) + len(reduction_index))
        for idx, var in itertools.chain(
            zip(kept_idx, index), zip(reduced_idx, reduction_index)
        ):
            new_index[idx] = var
        return inner_loader(new_index)

    if keepdims:
        new_size = list(size)
        for i in reduced_idx:
            new_size[i] = sympy.Integer(1)
    else:
        new_size = kept_sizes

    inner_loader = x.make_loader()
    return dict(
        device=x.get_device(),
        dst_dtype=override_return_dtype or x.get_dtype(),
        src_dtype=x.get_dtype(),
        inner_fn=loader,
        ranges=new_size,
        reduction_ranges=reduced_sizes,
    )


def make_reduction(reduction_type: str, override_return_dtype=None):
    def inner(x, axis=None, keepdims=False, *, dtype=None):
        kwargs = _make_reduction_inner(
            x,
            axis=axis,
            keepdims=keepdims,
            dtype=dtype,
            override_return_dtype=override_return_dtype,
        )
        result = Reduction.create(reduction_type=reduction_type, input_node=x, **kwargs)
        if isinstance(
            result.data.data, Reduction
        ):  # Only realize if reduction isn't unrolled
            result.realize()
        return result

    return inner


def _make_scan_inner(x, *, axis, dtype):
    if dtype is not None:
        x = to_dtype(x, dtype)
    size = x.get_size()
    axis = _validate_reduction_axis(x, axis)[0]

    return dict(
        device=x.get_device(),
        dtype=x.get_dtype(),
        inner_fn=x.make_loader(),
        size=x.get_size(),
        axis=axis,
    )


@register_lowering(aten.mean)
def mean(x, axis=None, keepdim=False, *, dtype=None):
    if dtype is not None:
        x = to_dtype(x, dtype)
    size = x.get_size()
    axis = _validate_reduction_axis(x, axis)
    # compute in higher-precision until end of mean lowering
    output_dtype = x.get_dtype()
    if output_dtype in (torch.float16, torch.bfloat16):
        x = to_dtype(x, torch.float)
    sum_result = sum_(x, axis, keepdim)
    denom = sympy_product(size[i] for i in axis)
    denom = ir.IndexingConstant(denom, x.get_dtype(), x.get_device())
    denom = ExpandView.create(denom, list(sum_result.get_size()))
    return to_dtype(div(sum_result, denom), output_dtype)


def var_mean_sum_(x, axis, correction, keepdim, return_mean):
    if correction is None:
        correction = 1

    size = x.get_size()
    axis = _validate_reduction_axis(x, axis)
    x_mean = mean(x, axis, keepdim=True)
    if return_mean:
        x_mean.realize()

    diffs = square(sub(x, x_mean))
    sum_result = sum_(diffs, axis, keepdim)

    denom = sympy_product(size[i] for i in axis)
    if correction:
        denom = sympy.Max(denom - correction, 0)
    denom = ir.IndexingConstant(denom, x.get_dtype(), x.get_device())
    denom = ExpandView.create(denom, list(sum_result.get_size()))
    x_var = div(sum_result, denom)
    if not return_mean:
        return (x_var,)

    x_mean = x_mean if keepdim else squeeze(x_mean, axis)
    return x_var, x_mean


def use_two_step_variance(x, axis, keepdim):
    # Instead of unrolling welford, just unroll the simpler two-step var
    axis = _validate_reduction_axis(x, axis)
    kwargs = _make_reduction_inner(
        x, axis=axis, keepdims=keepdim, dtype=None, override_return_dtype=None
    )

    ranges = kwargs["ranges"]
    reduction_numel = sympy_product(kwargs["reduction_ranges"])
    return (
        isinstance(reduction_numel, sympy.Integer)
        and int(reduction_numel) < config.unroll_reductions_threshold
        and sympy_product(ranges) != 1
    )


def var_mean_welford_(x, axis, *, correction, keepdim, return_mean):
    if correction is None:
        correction = 1

    kwargs = _make_reduction_inner(
        x, axis=axis, keepdims=keepdim, dtype=None, override_return_dtype=None
    )
    loader = kwargs.pop("inner_fn")
    kwargs.pop("dst_dtype")
    kwargs.pop("src_dtype")

    mean, m2, _ = ir.WelfordReduction.create(
        inner_fns=(loader,),
        reduction_type="welford_reduce",
        dtype=x.get_dtype(),
        **kwargs,
    )
    m2.realize()

    dtype = x.get_dtype()
    size = x.get_size()
    axis = _validate_reduction_axis(x, axis)
    rnumel = sympy_product(size[i] for i in axis)

    def get_constant_or_index_expr(x, dtype):
        if isinstance(x, sympy.Expr) and not x.is_number:
            return ops.to_dtype(ops.index_expr(x, torch.int64), dtype)
        return ops.constant(x, dtype)

    def scale_fn(data):
        c = get_constant_or_index_expr(correction, dtype)
        N = get_constant_or_index_expr(rnumel, dtype)
        zero = ops.constant(0, dtype)
        return data / ops.maximum(zero, N - c)

    var = make_pointwise(scale_fn)(m2)

    if return_mean:
        mean.realize()
        return var, mean
    return (var,)


def var_mean_helper_(x, *, axis, correction, keepdim, return_mean):
    out_dtype = x.get_dtype()
    compute_dtype = get_computation_dtype(out_dtype)
    x = to_dtype(x, compute_dtype, copy=False)
    kwargs = dict(
        x=x,
        axis=axis,
        correction=correction,
        keepdim=keepdim,
        return_mean=return_mean,
    )
    output = (
        var_mean_sum_(**kwargs)
        if use_two_step_variance(x, axis=axis, keepdim=keepdim)
        else var_mean_welford_(**kwargs)
    )
    output = tuple(to_dtype(x, out_dtype, copy=False) for x in output)
    return output[0] if not return_mean else output


@register_lowering([aten.var, prims.var])
def var_(x, axis=None, *, correction=None, keepdim=False):
    return var_mean_helper_(
        x, axis=axis, correction=correction, keepdim=keepdim, return_mean=False
    )


@register_lowering(aten.var_mean)
def var_mean(x, axis=None, *, correction=None, keepdim=False):
    return var_mean_helper_(
        x, axis=axis, correction=correction, keepdim=keepdim, return_mean=True
    )


def pow_recursive(x, y, dtype):
    if y < 0:
        return pow_recursive(ops.reciprocal(x), -y, dtype)
    if y == 0:
        return ops.constant(1, dtype)
    if y == 1:
        return x

    result = pow_recursive(x, y // 2, dtype)
    result = ops.mul(result, result)
    if (y % 2) == 1:
        result = ops.mul(result, x)
    return result


@make_pointwise
def pow_native(a, b):
    return ops.pow(a, b)


fallback_pow_tensor_tensor = fallback_handler(
    aten.pow.Tensor_Tensor, add_to_fallback_set=False
)
fallback_pow_scalar = fallback_handler(aten.pow.Scalar, add_to_fallback_set=False)
fallback_pow_tensor_scalar = fallback_handler(
    aten.pow.Tensor_Scalar, add_to_fallback_set=False
)


@register_lowering(aten.pow, broadcast=True)
def pow(a, b):
    if isinstance(b, float) and b == int(b):
        return pow(a, int(b))
    elif isinstance(b, float) and b == 0.5:
        return sqrt(a)
    elif isinstance(b, int) and b == 1:
        return clone(a)

    # Type promotion ensures all tensor arguments have the same type
    dtype = next(x.get_dtype() for x in (a, b) if isinstance(x, ir.TensorBox))
    is_integer_pow = is_integer_dtype(dtype)

    # Optimize away small fixed powers, or for integers avoid falling back to ATen
    embed_exponent = isinstance(b, int) and (
        -32 < b < 32 or (is_integer_pow and b >= 0)
    )
    if embed_exponent:
        loader = a.make_loader()

        def fn(idx):
            return pow_recursive(loader(idx), b, a.get_dtype())

        return Pointwise.create(
            device=a.get_device(),
            dtype=a.get_dtype(),
            inner_fn=fn,
            ranges=a.get_size(),
        )

    if isinstance(a, Number):
        if a == 1:
            return full_like(b, 1)
        if a == 2 and is_float_dtype(b.get_dtype()):
            return exp2(b)

    if is_integer_pow:
        # ops.pow doesn't work for integers
        if isinstance(a, Number):
            return fallback_pow_scalar(a, b)
        elif isinstance(b, Number):
            return fallback_pow_tensor_scalar(a, b)
        else:
            return fallback_pow_tensor_tensor(a, b)

    return pow_native(a, b)


def mutate_to(changed, val, unsafe_alias=False):
    if isinstance(changed, TensorBox):
        changed_data = changed.data
    else:
        changed_data = changed
    if isinstance(val, TensorBox):
        val = val.data

    if not isinstance(val, ir.StorageBox):
        # introduce a copy to handle views
        val = Pointwise.create(
            device=changed.get_device(),
            dtype=changed.get_dtype(),
            inner_fn=val.make_loader(),
            ranges=changed.get_size(),
        ).data
        assert isinstance(val, ir.StorageBox)

    if isinstance(changed_data, ir.StorageBox) and not (
        changed_data.is_input_buffer() or isinstance(changed_data.data, ir.NopKernel)
    ):
        # Fast path, just swing the data pointer
        val.realize()
        changed_data.data = val.data
        return changed

    ir.MutationLayout.realize_into(val, changed_data, unsafe_alias=unsafe_alias)
    return changed


@register_lowering(aten.fill_)
def fill_(x, fill_value):
    return mutate_to(x, full_like(x, fill_value))


@register_lowering(aten.copy_, type_promotion_kind=None)
def copy_(dst, src, non_blocking=False):
    src = to_device(src, dst.get_device())
    src = to_dtype(src, dst.get_dtype())
    src = expand(src, dst.get_size())
    return mutate_to(dst, src)


@make_pointwise
def floordiv(a, b):
    return ops.floordiv(a, b)


@make_pointwise
def truncdiv(a, b):
    return ops.truncdiv(a, b)


@register_lowering(aten.div, broadcast=True)
def div_mode(a, b, rounding_mode=None):
    both_integer = is_integer_type(a) and is_integer_type(b)
    both_boolean = is_boolean_type(a) and is_boolean_type(b)

    # floordiv and truncdiv need special handling for integer tensors on Triton,
    # see the discussion at https://github.com/openai/triton/issues/605
    if rounding_mode == "floor":
        assert not both_boolean, "floordiv operands can not be boolean at the same time"
        return floordiv(a, b) if both_integer else floor(div(a, b))
    if rounding_mode == "trunc":
        assert not both_boolean, "truncdiv operands can not be boolean at the same time"
        return truncdiv(a, b) if both_integer else trunc(div(a, b))
    return div(a, b)


@register_lowering([aten.mul], broadcast=True)
def mul(a, b):
    both_bool = is_boolean_type(a) and is_boolean_type(b)
    if both_bool:
        return logical_and(a, b)
    else:
        fn = ops_wrapper(aten.mul.__name__)
        return make_pointwise(fn)(a, b)


# NOTE: prims.div maps to a / b in C, so performs truncation division on
#   integer inputs and true division for floating and complex inputs.
@register_lowering([prims.div], broadcast=True)
def div_prim(a, b):
    is_integral = all(is_boolean_type(x) or is_integer_type(x) for x in [a, b])

    if is_integral:
        return truncdiv(a, b)

    def fn(*args):
        return ops.truediv(*args)

    return make_pointwise(fn)(a, b)


@register_lowering(
    [aten.true_divide, aten.div.Tensor],
    broadcast=True,
    type_promotion_kind=ELEMENTWISE_TYPE_PROMOTION_KIND.INT_TO_FLOAT,
)
def div(a, b):
    a, b = promote_constants(
        (a, b), type_promotion_kind=ELEMENTWISE_TYPE_PROMOTION_KIND.INT_TO_FLOAT
    )
    return div_prim(a, b)


@register_lowering([aten.fmod, prims.fmod], broadcast=True)
def fmod(a, b):
    is_integral = is_boolean_type(a) or is_integer_type(a)

    if is_integral:

        def fn(a, b):
            return ops.mod(a, b)

    else:

        def fn(a, b):
            return ops.fmod(a, b)

    return make_pointwise(fn)(a, b)


@register_lowering(aten.rsqrt)
def rsqrt(x):
    dtype = x.get_dtype()
    if is_integer_dtype(dtype) or is_boolean_dtype(dtype):
        x = to_dtype(x, torch.get_default_dtype())

    def _rsqrt(x):
        return ops.rsqrt(x)

    return make_pointwise(_rsqrt)(x)


@register_lowering([aten.sum, prims.sum])
def sum_(x, axis=None, keepdims=False, *, dtype=None):
    if (
        is_integer_dtype(x.get_dtype()) or is_boolean_dtype(x.get_dtype())
    ) and dtype is None:
        dtype = torch.int64

    fn = make_reduction("sum", override_return_dtype=dtype)
    return fn(x, axis, keepdims, dtype=dtype)


fallback_cumsum = fallback_handler(aten.cumsum.default)
fallback_cumprod = fallback_handler(aten.cumprod.default)


@register_lowering(aten.cumsum)
def cumsum(x, axis=None, dtype=None):
    if (
        is_integer_dtype(x.get_dtype()) or is_boolean_dtype(x.get_dtype())
    ) and dtype is None:
        dtype = torch.int64

    kwargs = _make_scan_inner(x, axis=axis, dtype=dtype)
    result = ir.Scan.create(**kwargs, combine_fn=ops.add, init=0)
    if result is None:
        return fallback_cumsum(x, dim=axis, dtype=dtype)
    return result


@register_lowering(aten.cumprod)
def cumprod(x, axis=None, dtype=None):
    if (
        is_integer_dtype(x.get_dtype()) or is_boolean_dtype(x.get_dtype())
    ) and dtype is None:
        dtype = torch.int64

    kwargs = _make_scan_inner(x, axis=axis, dtype=dtype)
    result = ir.Scan.create(**kwargs, combine_fn=ops.mul, init=1)
    if result is None:
        return fallback_cumprod(x, dim=axis, dtype=dtype)
    return result


@register_lowering(aten.prod)
def prod(x, axis=None, keepdims=False, *, dtype=None):
    if (
        is_integer_dtype(x.get_dtype()) or is_boolean_dtype(x.get_dtype())
    ) and dtype is None:
        dtype = torch.int64

    fn = make_reduction("prod", override_return_dtype=dtype)
    return fn(x, axis, keepdims, dtype=dtype)


@register_lowering(aten.any)
def reduce_any(x, dim=None, keepdim=False):
    x = to_dtype(x, torch.bool)
    return make_reduction("any")(x, axis=dim, keepdims=keepdim)


@register_lowering(aten.max, type_promotion_kind=None)
def reduce_max(x, dim=None, keepdim=False):
    if dim is not None:
        return (
            reduce_amax(x, axis=dim, keepdims=keepdim),
            reduce_argmax(x, axis=dim, keepdims=keepdim),
        )

    return reduce_amax(x, axis=None, keepdims=keepdim)


@register_lowering(aten.min, type_promotion_kind=None)
def reduce_min(x, dim=None, keepdim=False):
    if dim is not None:
        return (
            reduce_amin(x, axis=dim, keepdims=keepdim),
            reduce_argmin(x, axis=dim, keepdims=keepdim),
        )

    return reduce_amin(x, axis=None, keepdims=keepdim)


register_lowering(prims.xor_sum)(make_reduction("xor_sum"))
reduce_amax = register_lowering(aten.amax)(make_reduction("max"))
reduce_amin = register_lowering(aten.amin)(make_reduction("min"))
reduce_argmax = register_lowering(aten.argmax)(
    make_reduction("argmax", override_return_dtype=torch.int64)
)
reduce_argmin = register_lowering(aten.argmin)(
    make_reduction("argmin", override_return_dtype=torch.int64)
)

add = register_pointwise(
    aten.add, allow_alpha=True, override_fn_when_input_bool="logical_or"
)


def register_pointwise_numeric(op):
    return register_pointwise(
        op, type_promotion_kind=ELEMENTWISE_TYPE_PROMOTION_KIND.INT_TO_FLOAT
    )


def register_pointwise_numeric_ldf64(op):
    return register_pointwise(
        op,
        type_promotion_kind=ELEMENTWISE_TYPE_PROMOTION_KIND.INT_TO_FLOAT,
        use_libdevice_for_f64=True,
    )


exp = register_pointwise_numeric_ldf64(aten.exp)
exp2 = register_pointwise_numeric(aten.exp2)
expm1 = register_pointwise_numeric(aten.expm1)
relu = register_pointwise(aten.relu)
sigmoid = register_pointwise_numeric_ldf64(aten.sigmoid)
sqrt = register_pointwise_numeric_ldf64(aten.sqrt)
square = register_pointwise(aten.square)
sub = register_pointwise(aten.sub, allow_alpha=True)
register_pointwise_numeric_ldf64(aten.cos)
register_pointwise_numeric_ldf64(aten.sin)
abs = register_pointwise(aten.abs)
bitwise_and = register_pointwise(aten.bitwise_and)
bitwise_left_shift = register_pointwise(aten.bitwise_left_shift)
bitwise_not = register_pointwise(
    aten.bitwise_not, override_fn_when_input_bool="logical_not"
)
bitwise_or = register_pointwise(aten.bitwise_or)
bitwise_right_shift = register_pointwise(aten.bitwise_right_shift)
bitwise_xor = register_pointwise(aten.bitwise_xor)
register_pointwise_numeric(aten.lgamma)
erf = register_pointwise_numeric(aten.erf)
register_lowering(
    aten.special_erf, type_promotion_kind=ELEMENTWISE_TYPE_PROMOTION_KIND.INT_TO_FLOAT
)(erf)

register_pointwise_numeric(aten.log1p)
register_pointwise_numeric(aten.tan)
register_pointwise_numeric(aten.tanh)
register_pointwise_numeric_ldf64(aten.log)
logical_and = register_pointwise(
    aten.logical_and,
    type_promotion_kind=None,
    convert_input_to_bool=True,
    override_return_dtype=torch.bool,
)
logical_not = register_pointwise(
    aten.logical_not,
    type_promotion_kind=None,
    convert_input_to_bool=True,
    override_return_dtype=torch.bool,
)
logical_or = register_pointwise(
    aten.logical_or,
    type_promotion_kind=None,
    convert_input_to_bool=True,
    override_return_dtype=torch.bool,
)
logical_xor = register_pointwise(
    aten.logical_xor,
    type_promotion_kind=None,
    convert_input_to_bool=True,
    override_return_dtype=torch.bool,
)
maximum = register_pointwise(aten.maximum)
minimum = register_pointwise(aten.minimum)
register_lowering(aten.clamp_min)(maximum)
register_lowering(aten.clamp_max)(minimum)
neg = register_pointwise(aten.neg)
reciprocal = register_pointwise_numeric(aten.reciprocal)
register_pointwise(aten.remainder)
sign = register_pointwise(aten.sign, override_fn_when_input_bool="identity")
register_pointwise(aten.ceil)
register_pointwise(aten.signbit, override_return_dtype=torch.bool)

register_lowering(aten._neg_view)(neg)

register_pointwise(aten.le, override_return_dtype=torch.bool)
register_pointwise(aten.lt, override_return_dtype=torch.bool)
register_pointwise(aten.ge, override_return_dtype=torch.bool)
gt = register_pointwise(aten.gt, override_return_dtype=torch.bool)
register_pointwise(aten.eq, override_return_dtype=torch.bool)
register_pointwise(aten.ne, override_return_dtype=torch.bool)

register_pointwise_numeric(aten.cosh)
register_pointwise_numeric(aten.sinh)
register_pointwise_numeric(aten.acos)
register_pointwise_numeric(aten.acosh)
register_pointwise_numeric(aten.asin)
register_pointwise_numeric(aten.asinh)
register_pointwise_numeric(aten.atan2)
register_pointwise_numeric(aten.atan)
register_pointwise_numeric(aten.atanh)
register_pointwise_numeric(aten.copysign)
register_pointwise_numeric(aten.erfc)
register_pointwise_numeric(aten.erfinv)
register_pointwise_numeric(aten.hypot)
register_pointwise_numeric(aten.log10)
register_pointwise_numeric(aten.nextafter)

foreach_add_list = register_foreach_pointwise(
    aten._foreach_add.List, add, allow_alpha=True
)
foreach_add_scalar = register_foreach_pointwise(
    aten._foreach_add.Scalar, add, allow_alpha=True
)
register_foreach_pointwise(aten._foreach_add.Tensor, add, allow_alpha=True)
foreach_mul_list = register_foreach_pointwise(aten._foreach_mul.List, mul)
foreach_mul_scalar = register_foreach_pointwise(aten._foreach_mul.Scalar, mul)
register_foreach_pointwise(aten._foreach_sub.List, sub)
register_foreach_pointwise(aten._foreach_sub.Scalar, sub)
register_foreach_pointwise(aten._foreach_neg.default, neg)
register_foreach_pointwise(aten._foreach_abs.default, abs)
register_foreach_pointwise(aten._foreach_pow.Scalar, pow)
register_foreach_pointwise(aten._foreach_pow.ScalarAndTensor, pow)
foreach_div_list = register_foreach_pointwise(aten._foreach_div.List, div)
foreach_div_scalar = register_foreach_pointwise(aten._foreach_div.Scalar, div)
register_foreach_pointwise(aten._foreach_sqrt, sqrt)
register_foreach_pointwise(aten._foreach_maximum.List, maximum)
register_foreach_pointwise(aten._foreach_maximum.Scalar, maximum)
register_foreach_pointwise(aten._foreach_minimum.List, minimum)
register_foreach_pointwise(aten._foreach_minimum.Scalar, minimum)
register_foreach_pointwise(aten._foreach_clamp_min.List, maximum)
register_foreach_pointwise(aten._foreach_clamp_min.Scalar, maximum)
register_foreach_pointwise(aten._foreach_clamp_max.List, minimum)
register_foreach_pointwise(aten._foreach_clamp_max.Scalar, minimum)
register_foreach_pointwise(aten._foreach_reciprocal, reciprocal)
register_foreach_pointwise(aten._foreach_sign, sign)
register_foreach_pointwise(aten._foreach_copy, copy)


# these are only encountered as outputs of the graph
# reinplacing epilogue copies improves compile time
# by removing extra buffers sent to the scheduler.
def register_foreach_inplace(aten_op, outplace_aten_op, outplace_op):
    inplaceable_foreach_ops[outplace_aten_op] = aten_op
    inplace_foreach_ops.add(aten_op)

    def fn(*args, **kwargs):
        results = outplace_op(*args, **kwargs)
        mut_results = []
        for arg, result in zip(args[0], results):
            mut_results.append(mutate_to(arg, result, unsafe_alias=True))

        return mut_results

    _register_foreach_lowering(aten_op, fn)


register_foreach_inplace(
    aten._foreach_add_.List, aten._foreach_add.List, foreach_add_list
)
register_foreach_inplace(
    aten._foreach_add_.Scalar, aten._foreach_add.Scalar, foreach_add_scalar
)
register_foreach_inplace(
    aten._foreach_mul_.List, aten._foreach_mul.List, foreach_mul_list
)
register_foreach_inplace(
    aten._foreach_mul_.Scalar, aten._foreach_mul.Scalar, foreach_mul_scalar
)
register_foreach_inplace(
    aten._foreach_div_.List, aten._foreach_div.List, foreach_div_list
)
register_foreach_inplace(
    aten._foreach_div_.Scalar, aten._foreach_div.Scalar, foreach_div_scalar
)


def register_inplace(aten_op, outplace_op):
    @register_lowering(aten_op, type_promotion_kind=None)
    def fn(*args, **kwargs):
        result = outplace_op(*args, **kwargs)
        result = to_dtype(result, args[0].get_dtype())
        return mutate_to(args[0], result)

    return fn


register_inplace(aten.add_, add)
register_inplace(aten.bitwise_and_, bitwise_and)
register_inplace(aten.bitwise_left_shift_, bitwise_left_shift)
register_inplace(aten.bitwise_not_, bitwise_not)
register_inplace(aten.bitwise_or_, bitwise_or)
register_inplace(aten.bitwise_right_shift_, bitwise_right_shift)
register_inplace(aten.bitwise_xor_, bitwise_xor)
register_inplace(aten.mul_, mul)
register_inplace(aten.div_.Tensor, div)
register_inplace(aten.div_.Tensor_mode, div_mode)
register_inplace(aten.logical_and_, logical_and)
register_inplace(aten.logical_not_, logical_not)
register_inplace(aten.logical_or_, logical_or)
register_inplace(aten.logical_xor_, logical_xor)
register_inplace(aten.sub_, sub)
register_inplace(aten.relu_, relu)
register_inplace(aten.sigmoid_, sigmoid)


register_lowering(aten.__and__)(bitwise_and)
register_lowering(aten.__lshift__)(bitwise_left_shift)
register_lowering(aten.__or__)(bitwise_or)
register_lowering(aten.__rshift__)(bitwise_right_shift)
register_lowering(aten.__xor__)(bitwise_xor)

register_inplace(aten.__iand__, aten.__and__)
register_inplace(aten.__ilshift__, aten.__lshift__)
register_inplace(aten.__ior__, aten.__or__)
register_inplace(aten.__irshift__, aten.__rshift__)
register_inplace(aten.__ixor__, aten.__xor__)


@register_lowering(aten.sym_constrain_range)
def sym_constrain_range(a, min, max):
    tracing_context = torch._guards.TracingContext.get()
    assert a in tracing_context.fake_mode.shape_env.var_to_range
    return a


@register_lowering(aten.sym_size.int)
def sym_size(a, dim):
    val = V.graph.current_node.meta["val"]
    # Note [Can val be an int?]
    # ~~~~~~~~~~~~~~~~~~~~~~~~~
    # In principle, someone could construct an FX graph where
    # a call to size/stride has a val that is a plain int (not
    # SymInt).  However, we will maintain the invariant that
    # this is not possible: if you are constructing an FX graph
    # where there is a call to size/stride that returns an
    # int, but you KNOW that int must always be a constant,
    # then you do not need trace that call at all (and just
    # constant propagate the integer as is.)
    assert isinstance(val, torch.SymInt)
    return val.node.expr


@register_lowering(aten.sym_stride.int)
def sym_stride(a, dim):
    val = V.graph.current_node.meta["val"]
    # See Note [Can val be an int?]
    assert isinstance(val, torch.SymInt)
    return val.node.expr


@register_lowering(aten.sym_numel)
def sym_numel(a):
    return a.get_numel()


for method, func in magic_methods.items():
    register_lowering(method_to_operator(method))(func)


@register_lowering(aten._foobar)
def foobar(self, *args, **kwargs):
    raise NotImplementedError("Helpful for debugging")


@register_lowering(torch.ops._inductor_test.realize)
def _realize(x):
    x.realize()
    return clone(x)


@register_lowering(torch.ops.inductor.accumulate_grad_)
def accumulate_grad_(variable, new_grad):
    # TODO(jansel): decompose into `variable.grad += new_grad` when variable.grad is defined
    variable.realize()
    new_grad.realize()
    ir.AccumulateGrad(variable, new_grad)
    return variable


from torch._higher_order_ops.auto_functionalize import auto_functionalized

make_fallback(auto_functionalized)


@register_lowering(triton_kernel_wrapper_mutation)
def triton_kernel_wrap_(*, kernel_idx, grid, kwargs):
    ir.UserDefinedTritonKernel(kernel_idx=kernel_idx, grid=grid, kernel_args=kwargs)
    return {key: val for key, val in kwargs.items() if isinstance(val, TensorBox)}


@register_lowering(triton_kernel_wrapper_functional)
def triton_kernel_wrap(*, kernel_idx, grid, kwargs, tensors_to_clone):
    new_kwargs = {}
    for name, value in kwargs.items():
        if isinstance(value, ir.TensorBox):
            x = value.data
            has_non_rv_views = False
            while isinstance(x, ir.BaseView):
                if not isinstance(x, ir.ReinterpretView):
                    has_non_rv_views = True
                    break
                x = x.data
            if has_non_rv_views:
                # we realize the inputs wrapped into any view which is not
                # ReinterpretView to convert them into ReinterpretView during
                # realization; all views being ReinterpretView is assumed by
                # the downstream code (e.g., preserving ReinterpretView in
                # cloning; layout should be available in mutation marking)
                value = ir.TensorBox(ir.ExternKernel.realize_input(value))
            if name in tensors_to_clone:
                value = clone_preserve_reinterpret_view(value)
        new_kwargs[name] = value

    return triton_kernel_wrap_(kernel_idx=kernel_idx, grid=grid, kwargs=new_kwargs)


try:
    import torch.distributed._functional_collectives

    c10d_functional = torch.ops.c10d_functional

    @register_lowering(c10d_functional.wait_tensor)
    def wait(input):
        return TensorBox.create(ir.Wait.create(input))

    @register_lowering(c10d_functional.broadcast)
    def broadcast(input, src, tag, ranks, group_size):
        return ir.Broadcast.create(input, src, tag, ranks, group_size)

    @register_lowering(c10d_functional.all_reduce)
    def allreduce(input, reduce_op, tag, ranks, group_size):
        return ir.AllReduce.create(input, reduce_op, tag, ranks, group_size)

    @register_lowering(c10d_functional.all_gather_into_tensor)
    def all_gather_into_tensor(shard, tag, ranks, group_size):
        return TensorBox.create(
            ir.AllGatherIntoTensor.create(
                ir.ExternKernel.require_contiguous(shard), tag, ranks, group_size
            )
        )

    @register_lowering(c10d_functional.reduce_scatter_tensor)
    def reduce_scatter_tensor(input, reduce_op, tag, ranks, group_size):
        return TensorBox.create(
            ir.ReduceScatterTensor.create(input, reduce_op, tag, ranks, group_size)
        )

    @register_lowering(c10d_functional.all_reduce_coalesced)
    def all_reduce_coalesced(input, reduce_op, tag, ranks, group_size):
        return ir.AllReduceCoalesced.create(input, reduce_op, tag, ranks, group_size)

    @register_lowering(c10d_functional.all_gather_into_tensor_coalesced)
    def all_gather_into_tensor_coalesced(self, tag, ranks, group_size):
        result = ir.AllGatherIntoTensorCoalesced.create(self, tag, ranks, group_size)
        return list(map(TensorBox.create, result))

    @register_lowering(c10d_functional.reduce_scatter_tensor_coalesced)
    def reduce_scatter_tensor_coalesced(self, reduceOp, tag, ranks, group_size):
        result = ir.ReduceScatterTensorCoalesced.create(
            self, reduceOp, tag, ranks, group_size
        )
        return list(map(TensorBox.create, result))

    @register_lowering(c10d_functional.all_to_all_single)
    def all_to_all_single(
        self, output_split_sizes, input_split_sizes, tag, ranks, group_size
    ):
        return TensorBox.create(
            ir.AllToAllSingle.create(
                self, output_split_sizes, input_split_sizes, tag, ranks, group_size
            )
        )

    _c10d_functional = torch.ops._c10d_functional

    @register_lowering(_c10d_functional.all_reduce)
    def _all_reduce(inp, reduce_op, group_name):
        inp = clone(inp)
        ir._CollectiveKernel.create_inplace(
            _c10d_functional.all_reduce_.default, inp, reduce_op, group_name
        )
        return inp

    @register_lowering(_c10d_functional.all_reduce_)
    def _all_reduce_(inp, reduce_op, group_name):
        ir._CollectiveKernel.create_inplace(
            _c10d_functional.all_reduce_.default, inp, reduce_op, group_name
        )
        return inp

    @register_lowering(_c10d_functional.all_reduce_coalesced)
    def _all_reduce_coalesced(inputs, reduce_op, group_name):
        inputs = [clone(inp) for inp in inputs]
        ir._CollectiveKernel.create_inplace(
            _c10d_functional.all_reduce_coalesced_.default,
            inputs,
            reduce_op,
            group_name,
        )
        return inputs

    @register_lowering(_c10d_functional.all_reduce_coalesced_)
    def _all_reduce_coalesced_(inputs, reduce_op, group_name):
        ir._CollectiveKernel.create_inplace(
            _c10d_functional.all_reduce_coalesced_.default,
            inputs,
            reduce_op,
            group_name,
        )
        return inputs

    @register_lowering(_c10d_functional.all_gather_into_tensor)
    def _all_gather_into_tensor(inp, group_size, group_name):
        return ir.TensorBox.create(
            ir._CollectiveKernel.create_out_of_place(
                _c10d_functional.all_gather_into_tensor.default,
                inp,
                group_size,
                group_name,
            )
        )

    @register_lowering(_c10d_functional.all_gather_into_tensor_coalesced)
    def _all_gather_into_tensor_coalesced(inputs, group_size, group_name):
        return pytree.tree_map(
            ir.TensorBox.create,
            ir._CollectiveKernel.create_out_of_place(
                _c10d_functional.all_gather_into_tensor_coalesced.default,
                inputs,
                group_size,
                group_name,
            ),
        )

    @register_lowering(_c10d_functional.reduce_scatter_tensor)
    def _reduce_scatter_tensor(inp, reduce_op, group_size, group_name):
        return ir.TensorBox.create(
            ir._CollectiveKernel.create_out_of_place(
                _c10d_functional.reduce_scatter_tensor.default,
                inp,
                reduce_op,
                group_size,
                group_name,
            )
        )

    @register_lowering(_c10d_functional.reduce_scatter_tensor_coalesced)
    def _reduce_scatter_tensor_coalesced(inputs, reduce_op, group_size, group_name):
        return pytree.tree_map(
            ir.TensorBox.create,
            ir._CollectiveKernel.create_out_of_place(
                _c10d_functional.reduce_scatter_tensor_coalesced.default,
                inputs,
                reduce_op,
                group_size,
                group_name,
            ),
        )

    @register_lowering(_c10d_functional.all_to_all_single)
    def _all_to_all_single(inp, output_split_sizes, input_split_sizes, group_name):
        return ir.TensorBox.create(
            ir._CollectiveKernel.create_out_of_place(
                _c10d_functional.all_to_all_single.default,
                inp,
                output_split_sizes,
                input_split_sizes,
                group_name,
            )
        )

    @register_lowering(_c10d_functional.wait_tensor)
    def _wait_tensor(inp):
        ir._WaitKernel.create_wait(_c10d_functional.wait_tensor.default, inp)
        return inp

except ImportError:
    log.info(
        "Inductor support for distributed collectives depends on building torch.distributed"
    )

# populate lowerings defined in kernel/*
from . import kernel

import_submodule(kernel)

from . import quantized_lowerings

quantized_lowerings.register_quantized_ops()