team-10/env/Lib/site-packages/torch/_inductor/lowering.py

# mypy: allow-untyped-defs
from __future__ import annotations

import contextlib
import dataclasses
import functools
import itertools
import logging
import math
import operator
import os
import textwrap
import warnings
from collections import defaultdict
from collections.abc import Iterable, Sequence
from typing import Any, Callable, cast, Optional, TYPE_CHECKING, TypeVar, Union
from typing_extensions import ParamSpec
from unittest.mock import patch

import sympy

import torch
import torch.ao.quantization.fx._decomposed
import torch.fx
import torch.utils._pytree as pytree
from torch._dynamo.utils import counters
from torch._higher_order_ops.associative_scan import associative_scan_op
from torch._higher_order_ops.triton_kernel_wrap import 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._ordered_set import OrderedSet
from torch.utils._sympy.functions import (
    CeilDiv,
    FloorDiv,
    Identity,
    IntTrueDiv,
    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 (
    DtypeView,
    ExpandView,
    IndexingConstant,
    IRNode,
    is_triton,
    OnlineSoftmaxReduction,
    ops_wrapper,
    PermuteView,
    Pointwise,
    Reduction,
    SqueezeView,
    TensorBox,
    validate_ir,
    View,
)
from .utils import (
    ceildiv,
    decode_device,
    is_dynamic,
    is_gpu,
    is_pointwise_use,
    is_view,
    needs_fallback_due_to_atomic_add_limitations,
    pad_listlike,
    register_op_dtype_propagation_rules,
    sympy_product,
    use_scatter_fallback,
)
from .virtualized import ops, V


if TYPE_CHECKING:
    from .ops_handler import ReductionType


_T = TypeVar("_T")
_P = ParamSpec("_P")

# TODO(jansel): we should implement decomps or lowerings for these
# https://github.com/pytorch/torchdynamo/issues/327
FALLBACK_ALLOW_LIST = OrderedSet(
    [
        "torchvision::roi_align",
        "aten::index_add",
    ]
)

log = logging.getLogger(__name__)
lowerings: dict[Union[Callable[..., Any], str], Callable[..., Any]] = {}
# Use maybe_layout_constraints to access this dict, we lazily register tag-based layout constraints
_maybe_layout_constraints: dict[
    torch._ops.OpOverload, Optional[Callable[..., Any]]
] = {}
fallbacks = OrderedSet[torch._ops.OpOverload]()
aten = torch.ops.aten
tr_c10d = torch.ops.tr_c10d
prims = torch.ops.prims
needs_realized_inputs = OrderedSet[torch._ops.OpOverload]()
foreach_ops = OrderedSet[torch._ops.OpOverload](
    [torch._higher_order_ops._foreach_map]  # type: ignore[list-item]
)
# TODO(rec): torch._higher_order_ops._foreach_map is not an OpOverload
# so why is it in foreach_ops?
inplace_foreach_ops = OrderedSet[torch._ops.OpOverload]()
inplaceable_foreach_ops: dict[torch._ops.OpOverload, torch._ops.OpOverload] = {}
quantized_decomposed = torch.ops.quantized_decomposed


def cur_node_has_non_foreach_users():
    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)):
                return True

    return False


# group by device, whether any of the inputs are dynamic
# note arg_pairs may or may not be a pair
# foreach_map for example just passes output buffers here
def group_foreach_args(arg_pairs: Iterable[Union[tuple[Any, Any], Any]]):
    out = defaultdict(list)
    unpack_args = False
    for i, args in enumerate(arg_pairs):
        if not isinstance(args, Iterable):
            unpack_args = True
            args = (args,)
        use_foreach = (
            not is_dynamic(*args) or config.combo_kernel_foreach_dynamic_shapes
        )
        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"
        if unpack_args:
            (args,) = args
        out[(device, use_foreach)].append((i, args))
    return out


def maybe_layout_constraints(fn: Callable[..., Any]) -> Optional[Callable[..., Any]]:
    """Get layout constraints. Returns None if there are no layout constraints."""
    if not isinstance(fn, torch._ops.OpOverload):
        # Only OpOverloads have layout constraints.
        return None
    if fn in _maybe_layout_constraints:
        return _maybe_layout_constraints[fn]
    # OpOverload with custom lowerings override tag-based layout constraints
    if fn in lowerings:
        _maybe_layout_constraints[fn] = None
        return None
    # We lazily register tag-based layout constraints.

    def handle_layout_constraint_tag(tag):
        if tag is torch._C.Tag.needs_fixed_stride_order:
            _maybe_layout_constraints[fn] = constrain_to_fx_strides
            return _maybe_layout_constraints[fn]
        elif tag is torch._C.Tag.flexible_layout:
            _maybe_layout_constraints[fn] = None
            return None
        else:
            raise AssertionError(f"Unknown layout constraint tag: {tag}")

    tag = get_layout_constraint_tag(fn)
    return handle_layout_constraint_tag(tag)


def get_layout_constraint_tag(fn):
    tags_by_priority = [
        torch._C.Tag.needs_fixed_stride_order,
        torch._C.Tag.flexible_layout,
    ]
    for tag in tags_by_priority:
        if tag in fn.tags:
            return tag
    if torch._library.utils.is_builtin(fn):
        return torch._C.Tag.flexible_layout
    return getattr(torch._C.Tag, config.custom_op_default_layout_constraint)


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, set, tuple, OrderedSet)):  # noqa: set_linter
        return [add_needs_realized_inputs(x) for x in fn]
    needs_realized_inputs.add(fn)
    if isinstance(fn, torch._ops.OpOverloadPacket):
        needs_realized_inputs.update(
            getattr(fn, overload) for overload in fn.overloads()
        )


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


add_needs_realized_inputs(
    [
        aten.as_strided,
        aten.as_strided_copy,
        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._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.Basic)):
            return inp
        else:
            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 in_namespace(op, namespace):
    if isinstance(op, torch._ops.OpOverloadPacket):
        return namespace in op._qualified_op_name
    elif isinstance(op, torch._ops.OpOverload):
        return namespace in op.name()
    return False


def transform_args(
    args: list[Any],
    kwargs: dict[str, Any],
    broadcast: bool,
    type_promotion_kind: Optional[ELEMENTWISE_TYPE_PROMOTION_KIND],
    convert_input_to_bool: bool,
) -> tuple[list[Any], dict[str, Any]]:
    args_indices = [i for i, x in enumerate(args) if isinstance(x, TensorBox)]
    kwargs_indices = [k for k, v in kwargs.items() if isinstance(v, TensorBox)]
    # check that there's something to transform
    if not args_indices and not kwargs_indices:
        return args, kwargs

    if type_promotion_kind or convert_input_to_bool:
        if convert_input_to_bool:
            dtype = torch.bool
        else:
            # FIXME this is a crude approximation for promoting args
            promoting_args = [
                a
                for a in args
                if isinstance(a, (Number, sympy.Basic)) or hasattr(a, "dtype")
            ]
            # only consider tensor kwargs for promotion, for now
            promoting_args.extend(a for a in kwargs.values() if hasattr(a, "dtype"))
            dtype = get_promoted_dtype(
                *promoting_args,
                type_promotion_kind=type_promotion_kind,  # type: ignore[arg-type]
            )

        device = (
            args[args_indices[0]] if args_indices else kwargs[kwargs_indices[0]]
        ).get_device()

        # 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(value=arg.value, dtype=dtype, device=device)
            else:
                return arg

        args = [promote(a) for a in args]
        kwargs = {k: promote(v) for k, v in kwargs.items()}

    if broadcast:
        broadcasted = broadcast_tensors(
            *list(
                itertools.chain(
                    (args[i] for i in args_indices),
                    (kwargs[k] for k in kwargs_indices),
                )
            )
        )
        size = list(broadcasted[0].get_size())

        for i, x in zip(args_indices, broadcasted[: len(args_indices)]):
            args[i] = x
        for k, x in zip(kwargs_indices, broadcasted[len(args_indices) :]):
            kwargs[k] = x

        for i in range(len(args)):
            if isinstance(args[i], ir.Constant):
                args[i] = ExpandView.create(args[i], size)
        for k in kwargs:
            if isinstance(kwargs[k], ir.Constant):
                kwargs[k] = ExpandView.create(kwargs[k], size)

    return args, kwargs


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(dict.fromkeys(aten_fns, wrapped))
    return wrapped


def _register_lowering(
    aten_fn,
    decomp_fn,
    broadcast,
    type_promotion_kind: Optional[ELEMENTWISE_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: list[Any] = list(args)
        kwargs: dict[str, Any] = dict(kwargs)
        unpacked = False
        # TODO maybe we need to use pytrees here
        if len(args) == 1 and isinstance(args[0], (list, tuple)):
            unpacked = True
            args = list(args[0])

        if not all(
            (fn in fallbacks or in_namespace(fn, "_c10d_functional")) for fn in aten_fn
        ):
            # 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"
            )

        args, kwargs = transform_args(
            args, kwargs, 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(dict.fromkeys(aten_fn, wrapped))
    return wrapped


def register_lowering(
    aten_fn,
    broadcast=False,
    type_promotion_kind: Optional[
        ELEMENTWISE_TYPE_PROMOTION_KIND
    ] = ELEMENTWISE_TYPE_PROMOTION_KIND.DEFAULT,
    convert_input_to_bool=False,
) -> Callable[[Callable[_P, _T]], Callable[_P, _T]]:
    """
    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.S.One):
        if V.graph.sizevars.shape_env.evaluate_expr(
            sympy.Eq(y, 1), size_oblivious=True
        ):
            output.append(x)
        elif V.graph.sizevars.shape_env.evaluate_expr(
            sympy.Eq(x, 1), size_oblivious=True
        ):
            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.Basic, int, float)) for x in inputs):
        return inputs
    if all(isinstance(x, (int, float, sympy.Basic)) 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.Basic):
                return ir.IndexingConstant(
                    index=x, dtype=dtype, device=decode_device(None)
                )
            else:
                return ir.Constant(value=x, dtype=dtype, device=decode_device(None))

        return [const_func(x) for x in inputs]
    ex = next(x for x in inputs if isinstance(x, (TensorBox, ExpandView, ir.Constant)))
    out = []
    for x in inputs:
        if isinstance(x, (int, float)):
            out.append(
                ExpandView.create(
                    ir.Constant(
                        value=x, dtype=ex.get_dtype(), device=ex.get_device_or_error()
                    ),
                    list(ex.get_size()),
                )
            )
        elif isinstance(x, sympy.Basic):
            out.append(
                ExpandView.create(
                    IndexingConstant(
                        index=x, dtype=ex.get_dtype(), device=ex.get_device_or_error()
                    ),
                    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_gpu_float64=None,
    allow_alpha=False,
    triton_fallback=None,
):
    def inner(*inputs: TensorBox, alpha=None):
        if triton_fallback is not None and any(
            isinstance(inp, IRNode) and is_triton(inp) for inp in inputs
        ):
            assert not allow_alpha  # not implemented
            return triton_fallback(*inputs)

        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_gpu_device = is_gpu(decode_device(inputs[0].get_device()).type)

        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()}"

        # in tracing, we will annotate pointwise nodes that correspond to the output of
        # a pointwise node that would have been run in eager. intermediary pointwise nodes
        # during decompositions are not annotated.
        low_pr_fp = (torch.bfloat16, torch.float16)
        emulate_precision_casts = (
            V.graph is not None
            and getattr(V.graph, "current_node", None) is not None
            and V.graph.current_node.meta is not None
            and V.graph.current_node.meta.get("low_precision_pointwise_barrier", False)
            and dtype in low_pr_fp
        )

        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_gpu_float64
                and is_gpu_device
                and dtype == torch.float64
            ):
                return override_fn_when_gpu_float64(*[load(index) for load in loaders])
            else:
                inputs_loaded = []
                for inp_index, load in enumerate(loaders):
                    out = load(index)
                    inp_dtype = inputs[inp_index].get_dtype()
                    if emulate_precision_casts and inp_dtype in low_pr_fp:
                        downcast = ops.to_dtype(out, inp_dtype, use_compute_types=False)
                        out = ops.to_dtype(downcast, inp_dtype)
                    inputs_loaded.append(out)

                out = fn(*inputs_loaded)
                if emulate_precision_casts:
                    # fp16/bf16 kernels are computed in fp32. Casting down to fp16/bf16 here,
                    # then upcasting again, to emulate casts that eager would do.
                    downcast = ops.to_dtype(out, dtype, use_compute_types=False)
                    return ops.to_dtype(downcast, dtype)
                return out

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

        device = override_device or device

        return Pointwise.create(
            device=device,  # type: ignore[arg-type]
            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):
        realize_outputs = (
            len(V.graph.current_node.users) == 0
            or V.graph.current_node.target in inplace_foreach_ops
            or cur_node_has_non_foreach_users()
        )

        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_foreach_args(zip(*broadcast_inputs))

        outputs = [None] * len(a_list_input)
        for (device, use_foreach), group in groups.items():
            operation_list: list[str] = []
            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 (
                    V.graph.has_feature(device, BackendFeature.FOREACH)
                    and use_foreach
                    and realize_outputs
                ):
                    output.realize()
                    operation_list.append(output.get_operation_name())

            if operation_list:
                V.graph.register_operation_list(operation_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(torch._higher_order_ops._foreach_map, type_promotion_kind=None)
def _foreach_map(subgraph, *args, **kwargs):
    """
    This lowers an invocation of foreach_map
    The way this works is that an arbitrary N-arg func is provided by the user, looped over by the
    polyfill with the same semantics as a foreach op (a loop applying an n-ary function to n args)
    and then traced into a subgraph by dynamo.
    This code allows us to inline the subgraph into the main graph lowering using the PontwiseSubgraphLowering.
    The graph outputs represent the vertically fused sequence of ops, and then register_operation_list
    below registers the buffers as horizontally fuseable in the scheduler.
    """
    from .subgraph_lowering import PointwiseSubgraphLowering

    inputs = args

    gm = subgraph.graph_module
    pw_subgraph = PointwiseSubgraphLowering(gm, root_graph_lowering=V.graph)
    with V.set_graph_handler(pw_subgraph):  # type: ignore[arg-type]
        pw_subgraph.run(*inputs)

    sub_outputs = pw_subgraph.graph_outputs
    # group outputs by device and register as foreach
    assert sub_outputs  # mypy lol
    groups = group_foreach_args(sub_outputs)

    outputs = [None] * len(sub_outputs)
    for (device, use_foreach), group in groups.items():
        operation_list: list[str] = []
        for (
            output_ind,
            output,
        ) in group:
            outputs[output_ind] = output

            if V.graph.has_feature(device, BackendFeature.FOREACH) and use_foreach:
                output.realize()
                operation_list.append(output.get_operation_name())

        if operation_list:
            V.graph.register_operation_list(operation_list)

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


@register_lowering(prims.convert_element_type, type_promotion_kind=None)
def _convert_element_type(x: TensorBox, dtype: torch.dtype):
    if dtype.is_complex or x.get_dtype().is_complex:
        if x.get_size():
            # Decompose since aa aten fallback is more friendly for c++ codegen.
            # This decomposition doesn't work for empty tensor, which needs more investigation.
            dst = empty_like(x, dtype=dtype)
            ir.InplaceCopyFallback.create(dst, x)
            return dst
        else:
            return fallback_handler(
                prims.convert_element_type.default, add_to_fallback_set=False
            )(x, 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:
        # fallback to aten eager implementation for differing bitwidths
        return fallback_handler(aten.view.dtype)(x, dtype)
    else:
        return TensorBox(DtypeView.create(x, dtype))


@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)


def to_device(x: TensorBox, device: torch.device, *, copy=False, non_blocking=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, non_blocking))


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


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,
    triton_fallback=None,
):
    """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)
        register_op_dtype_propagation_rules(
            "libdevice_" + name, type_promotion_kind, override_return_dtype
        )

    register_op_dtype_propagation_rules(
        name, type_promotion_kind, override_return_dtype
    )

    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_gpu_float64=fn_libdevice if use_libdevice_for_f64 else None,  # type: ignore[possibly-undefined]
        allow_alpha=allow_alpha,
        triton_fallback=triton_fallback,
    )
    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_frexp():
    """A pointwise function that maps ops.frexp to inputs"""
    name = "frexp"
    frexp = ops_wrapper("frexp")

    def frexp0(*args, **kwargs):
        return frexp(*args, **kwargs)[0]  # type: ignore[index]

    def frexp1(*args, **kwargs):
        return frexp(*args, **kwargs)[1]  # type: ignore[index]

    pw_fns = [
        make_pointwise(frexp0),
        make_pointwise(frexp1, override_return_dtype=torch.int32),
    ]

    def fn(*args, **kwargs):
        return pw_fns[0](*args, **kwargs), pw_fns[1](*args, **kwargs)

    fn = register_lowering(
        aten.frexp,
    )(fn)

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


register_frexp()


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(
            (
                (
                    V.graph.sizevars.shape_env.evaluate_expr(
                        sympy.Eq(a, 1), size_oblivious=True
                    )
                    and not V.graph.sizevars.shape_env.evaluate_expr(
                        sympy.Eq(b, 1), size_oblivious=True
                    )
                )
                or (
                    not V.graph.sizevars.shape_env.evaluate_expr(
                        sympy.Eq(a, 1), size_oblivious=True
                    )
                    and V.graph.sizevars.shape_env.evaluate_expr(
                        sympy.Eq(b, 1), size_oblivious=True
                    )
                )
            )
            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 = (
        V.graph.sizevars.evaluate_static_shape(dim)
        if isinstance(dim, (int, sympy.Expr))
        else tuple(V.graph.sizevars.evaluate_static_shape(d) for d in dim)
    )
    dim = canonicalize_dims(len(x.get_size()), dim)  # type: ignore[call-overload]
    dims = OrderedSet((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), size_oblivious=True)
        ):
            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.default)
def round(x):
    if is_integer_type(x):
        return clone(x)
    else:
        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):
    from torch.fx.experimental.symbolic_shapes import free_unbacked_symbols

    (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 free_unbacked_symbols(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 free_unbacked_symbols(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.S.One] * (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 clone(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.S.Zero
                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, clamp=True):
    assert isinstance(x, TensorBox)
    dim = _validate_dim(x, dim, 0)
    return TensorBox(ir.SliceView.create(x.data, dim, start, end, step, clamp=clamp))


@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(data=storage, layout=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]))  # type: ignore[arg-type]
        prev_end = inputs_ranges[-1][-1]  # type: ignore[assignment]

    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
            # Use Identity to prevent expansion of index * stride to keep expression
            # in same int bitwidth as shape
            idx_load[dim] = Identity(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
                ),
            )

        next_val = masked_loads[-1]
        for i in range((len(inputs)) - 2, -1, -1):
            next_val = ops.where(
                masks[i],
                masked_loads[i],
                next_val,
            )
        return next_val

    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(quantized_decomposed.quantize_per_channel, type_promotion_kind=None)
def quantized_decomposed_quantize_per_channel(
    input: TensorBox,
    scales: TensorBox,
    zero_points: TensorBox,
    axis: int,
    quant_min: int,
    quant_max: int,
    dtype: torch.dtype,
) -> TensorBox:
    assert len(scales.get_size()) == 1, "expect scales 1 dim"
    assert len(zero_points.get_size()) == 1, "expect zero_points 1 dim"

    if input.get_dtype() == torch.bfloat16:
        input = to_dtype(input, torch.float32)
    assert input.get_dtype() == torch.float32, (
        f"Expecting input to have dtype torch.float32, but got dtype: {input.get_dtype()}"
    )
    assert axis < len(input.get_size()), (
        f"Expecting axis to be < {len(input.get_size())}"
    )

    input_loader = input.make_loader()
    scales_loader = scales.make_loader()
    zero_points_loader = zero_points.make_loader()

    def inner_fn(idx):
        channel_idx = (idx[axis],)

        input = input_loader(idx)
        scale = scales_loader(channel_idx)
        zero_point = zero_points_loader(channel_idx)
        qmin, qmax = _create_constants(quant_min, quant_max, dtype=torch.float32)

        if scales.dtype != torch.float32:
            scale = ops.to_dtype(scale, torch.float32)
        if zero_points.dtype != torch.int32:
            zero_point = ops.to_dtype(zero_point, torch.int32)
        inv_scale = ops.reciprocal(scale)
        val = ops.round(input * inv_scale) + zero_point
        clamped = ops.maximum(qmin, ops.minimum(qmax, val))
        return ops.to_dtype(clamped, dtype)

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


@register_lowering(
    quantized_decomposed.dequantize_per_channel, type_promotion_kind=None
)
def quantized_decomposed_dequantize_per_channel(
    input: TensorBox,
    scales: TensorBox,
    zero_points: TensorBox,
    axis: int,
    quant_min: int,
    quant_max: int,
    dtype: torch.dtype,
    *,
    out_dtype: Optional[torch.dtype] = None,
) -> TensorBox:
    assert len(scales.get_size()) == 1, "expect scales 1 dim"
    assert len(zero_points.get_size()) == 1, "expect zero_points 1 dim"
    assert input.get_dtype() == dtype, (
        f"Expecting input to have dtype {dtype}, but got dtype: {input.get_dtype()}"
    )
    assert axis < len(input.get_size()), (
        f"Expecting axis to be < {len(input.get_size())}"
    )

    if out_dtype is None:
        out_dtype = torch.float32

    input_loader = input.make_loader()
    scales_loader = scales.make_loader()
    zero_points_loader = zero_points.make_loader()

    def inner_fn(idx):
        channel_idx = (idx[axis],)

        input = input_loader(idx)
        scale = scales_loader(channel_idx)
        zero_point = zero_points_loader(channel_idx)

        if scales.dtype != torch.float32:
            scale = ops.to_dtype(scale, torch.float32)
        if zero_points.dtype != torch.float32:
            zero_point = ops.to_dtype(zero_point, torch.float32)
        val = ops.sub(ops.to_dtype(input, torch.float32), zero_point) * scale
        val = ops.to_dtype(val, out_dtype)
        return val

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


@register_lowering(
    quantized_decomposed.quantize_per_tensor.default, type_promotion_kind=None
)
def quantized_decomposed_quantize_per_tensor_default(
    input: TensorBox,
    scale: float,
    zero_point: int,
    quant_min: int,
    quant_max: int,
    dtype: torch.dtype,
) -> TensorBox:
    if input.get_dtype() == torch.bfloat16:
        input = to_dtype(input, torch.float32)
    assert input.get_dtype() == torch.float32, (
        f"Expecting input to have dtype torch.float32, but got dtype: {input.get_dtype()}"
    )

    input_loader = input.make_loader()

    def inner_fn(idx, scale, zero_point):
        input = input_loader(idx)
        inv_scale, zero_point = _create_constants(
            1.0 / scale, zero_point, dtype=torch.float32
        )
        val = ops.round(input * inv_scale) + zero_point
        qmin, qmax = _create_constants(quant_min, quant_max, dtype=torch.float32)
        clamped = ops.minimum(ops.maximum(val, qmin), qmax)
        return ops.to_dtype(clamped, dtype)

    return Pointwise.create(
        device=input.get_device(),
        dtype=dtype,
        inner_fn=functools.partial(
            inner_fn, scale=float(scale), zero_point=int(zero_point)
        ),
        ranges=input.get_size(),
    )


@register_lowering(
    quantized_decomposed.dequantize_per_tensor.default, type_promotion_kind=None
)
def quantized_decomposed_dequantize_per_tensor_default(
    input: TensorBox,
    scale: float,
    zero_point: int,
    quant_min: int,
    quant_max: int,
    dtype: torch.dtype,
    *,
    out_dtype: Optional[torch.dtype] = None,
) -> TensorBox:
    assert input.get_dtype() == dtype, (
        f"Expecting input to have dtype {dtype}, but got dtype: {input.get_dtype()}"
    )

    if out_dtype is None:
        out_dtype = torch.float32

    input_loader = input.make_loader()

    def inner_fn(idx, scale, zero_point):
        input = input_loader(idx)
        scale, zero_point = _create_constants(scale, zero_point, dtype=torch.float32)
        val = ops.sub(ops.to_dtype(input, torch.float32), zero_point) * scale
        val = ops.to_dtype(val, out_dtype)
        return val

    return Pointwise.create(
        device=input.get_device(),
        dtype=out_dtype,
        inner_fn=functools.partial(
            inner_fn, scale=float(scale), zero_point=int(zero_point)
        ),
        ranges=input.get_size(),
    )


@register_lowering(
    quantized_decomposed.quantize_per_tensor.tensor, type_promotion_kind=None
)
def quantized_decomposed_quantize_per_tensor_tensor(
    input: TensorBox,
    scale: TensorBox,
    zero_point: TensorBox,
    quant_min: int,
    quant_max: int,
    dtype: torch.dtype,
) -> TensorBox:
    if input.get_dtype() == torch.bfloat16:
        input = to_dtype(input, torch.float32)
    assert input.get_dtype() == torch.float32, (
        f"Expecting input to have dtype torch.float32, but got dtype: {input.get_dtype()}"
    )
    assert len(scale.get_size()) == 0 or (
        len(scale.get_size()) == 1 and scale.get_size()[0] == 1
    ), "expect scale as scalar tensor"
    assert len(zero_point.get_size()) == 0 or (
        len(zero_point.get_size()) == 1 and zero_point.get_size()[0] == 1
    ), "expect zero_point as scalar tensor"

    input_loader = input.make_loader()
    scale_loader = scale.make_loader()
    zero_point_loader = zero_point.make_loader()

    def inner_fn(idx):
        input = input_loader(idx)
        _scale = scale_loader((0,) if len(scale.get_size()) == 1 else ())
        _zero_point = zero_point_loader((0,) if len(scale.get_size()) == 1 else ())
        if scale.dtype != torch.float32:
            _scale = ops.to_dtype(_scale, torch.float32)
        if zero_point.dtype != torch.float32:
            _zero_point = ops.to_dtype(_zero_point, torch.float32)
        val = ops.round(input * ops.reciprocal(_scale)) + _zero_point
        qmin, qmax = _create_constants(quant_min, quant_max, dtype=torch.float32)
        clamped = ops.minimum(ops.maximum(val, qmin), qmax)
        return ops.to_dtype(clamped, dtype)

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


@register_lowering(
    quantized_decomposed.dequantize_per_tensor.tensor, type_promotion_kind=None
)
def quantized_decomposed_dequantize_per_tensor_tensor(
    input: TensorBox,
    scale: TensorBox,
    zero_point: TensorBox,
    quant_min: int,
    quant_max: int,
    dtype: torch.dtype,
    *,
    out_dtype: Optional[torch.dtype] = None,
) -> TensorBox:
    assert len(scale.get_size()) == 0 or (
        len(scale.get_size()) == 1 and scale.get_size()[0] == 1
    ), "expect scale as scalar tensor"
    assert len(zero_point.get_size()) == 0 or (
        len(zero_point.get_size()) == 1 and zero_point.get_size()[0] == 1
    ), "expect zero_point as scalar tensor"
    assert input.get_dtype() == dtype, (
        f"Expecting input to have dtype {dtype}, but got dtype: {input.get_dtype()}"
    )

    if out_dtype is None:
        out_dtype = torch.float32

    input_loader = input.make_loader()
    scale_loader = scale.make_loader()
    zero_point_loader = zero_point.make_loader()

    def inner_fn(idx):
        input = input_loader(idx)
        _scale = scale_loader((0,) if len(scale.get_size()) == 1 else ())
        _zero_point = zero_point_loader((0,) if len(scale.get_size()) == 1 else ())
        if scale.dtype != torch.float32:
            _scale = ops.to_dtype(_scale, torch.float32)
        if zero_point.dtype != torch.float32:
            _zero_point = ops.to_dtype(_zero_point, torch.float32)
        val = ops.sub(ops.to_dtype(input, torch.float32), _zero_point) * _scale
        val = ops.to_dtype(val, out_dtype)
        return val

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


@register_lowering(aten.cat)
def cat(inputs, dim=0):
    cpu_device = inputs[0].get_device().type == "cpu"
    if cpu_device and all(
        input.get_dtype() in [torch.int8, 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 unwrap_tensor(x: Union[TensorBox, ir.StorageBox]) -> ir.IRNode:
        if isinstance(x, TensorBox):
            if isinstance(x.data, ir.BaseView):
                return x.data.unwrap_view()
            else:
                return x.data

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

        return x

    def is_reduction(t):
        return isinstance(t, ir.ComputedBuffer) and isinstance(t.data, ir.Reduction)

    def can_fuse_reduction(t):
        if isinstance(t, (TensorBox, ir.StorageBox)):
            return can_fuse_reduction(unwrap_tensor(t))
        return (
            is_reduction(t)
            or isinstance(t, ir.Pointwise)
            and any(
                can_fuse_reduction(V.graph.get_buffer(read))
                for read in t.get_read_names()
            )
        )

    # fusing reducutions into computed concat buffer can cause regressions.
    fusable_reduction = any(can_fuse_reduction(t) for t 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, ir.StorageBox)):
            return should_lower_cat_input(unwrap_tensor(x))

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

        return False

    if config.force_pointwise_cat:
        return pointwise_cat(inputs, dim)

    # 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 cpu_device:
        return TensorBox(ir.ConcatKernel.create(inputs, dim))

    def op_count(x):
        if isinstance(x, (TensorBox, ir.StorageBox)):
            return op_count(unwrap_tensor(x))

        # this will correspond to a direct memory read
        if not isinstance(x, ir.Pointwise):
            return 0

        count = x.inner_fn_opcount().num_ops
        for read in x.get_read_names():
            count += op_count(V.graph.get_buffer(read))

        return count

    # as of inputs increase, possibility for register spilling also increases
    # past a certain threshold of inputs we only fuse if the if the input kernels
    # are simple
    # not sure if we want to expose to users via config since logic may change in future
    MAX_COMPLEX_POINTWISE_CAT = 8
    MAX_SIMPLE_OP_COUNT = 2

    def additional_pointwise_ops(op: torch._ops.OpOverload):
        return op in (aten.cat.default, aten.constant_pad_nd.default)

    if len(inputs) <= MAX_COMPLEX_POINTWISE_CAT or (
        (len(inputs) <= config.max_pointwise_cat_inputs)
        and all(op_count(t) <= MAX_SIMPLE_OP_COUNT for t in inputs)
    ):
        pointwise_uses = all(
            is_pointwise_use(use, additional_pointwise_ops)
            for use in V.current_node.users
        )
        # fuse in case we will be used in a pointwise node, and there are any inputs we
        # we can prevent materialization of.
        fuse_pointwise_use = (
            any(should_lower_cat_input(inp) for inp in inputs) and pointwise_uses
        )

        # horizontal fuse in case all inputs will require a copy kernel anyway.
        # only horizontally fuse pointwise kernels
        horizontal_fuse_cat = all(
            should_lower_cat_input(inp) for inp in inputs
        ) and not any(can_fuse_reduction(t) for t in inputs)
        if fuse_pointwise_use or (horizontal_fuse_cat and not fusable_reduction):
            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 = V.graph.sizevars.evaluate_max(
            V.graph.sizevars.evaluate_min(
                original_shape[dim1] + offset, original_shape[dim2]
            ),
            0,  # type: ignore[arg-type]
        )
    else:
        diag_size = V.graph.sizevars.evaluate_max(
            V.graph.sizevars.evaluate_min(
                original_shape[dim1], original_shape[dim2] - offset
            ),
            0,  # type: ignore[arg-type]
        )

    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)
    sizes_ = sizes

    # If sizes is an integer (or a SymInt), we turn it into a list of sizes
    # by computing what the actual size of each chunk should be.
    if not isinstance(sizes, (list, tuple)):
        x_size = x.get_size()[dim]
        chunks = V.graph.sizevars.evaluate_static_shape(
            FloorDiv(x_size + sizes - 1, sizes)
        )
        sizes_ = [sizes] * chunks
        # The last chunk might have a smaller size than the rest.
        sizes_[-1] = x_size - (chunks - 1) * sizes

    # From this point, we assume that the sum of the sizes of all chunks
    # equals the size of the base tensor.
    result = []
    start = 0
    for size in sizes_:
        end = start + size
        # No need for clamping here, since we compute the exact
        # start and end values.
        result.append(slice_(x, dim, start, end, clamp=False))
        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 = [select(x, dim, i) for i in range(x_size)]
    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)  # type: ignore[arg-type]

    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.S.One)
    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):
    dim = V.graph.sizevars.shape_env.evaluate_expr(sympy.sympify(dim))
    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 fallback_handler(kernel, add_to_fallback_set=True):
    if add_to_fallback_set:
        fallbacks.add(kernel)

    def handler(*args, **kwargs):
        def wrap_tensors(x):
            return TensorBox.create(x) if isinstance(x, ir.IRNode) else x

        return pytree.tree_map(
            wrap_tensors, ir.FallbackKernel.create(kernel, *args, **kwargs)
        )

    # This lets us detect that a lowering is a fallback handler.
    handler._is_fallback_handler = True  # type: ignore[attr-defined]

    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.Tensor, parent=None, node=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 in (
            torch.ops.aten.view.dtype,
            torch.ops.prims.convert_element_type.default,
        ):
            return False
        _warn_complex_not_supported()
        return True

    if t.dtype == torch.float8_e8m0fnu:
        if not node:
            return True

        # allow bitcast, views, memory movement, but not arithmetic
        # TODO: delete once triton adds native support
        return not (
            node.target
            in (
                aten.view.dtype,
                aten.cat.default,
            )
            or is_view(node.target)
        )

    return False


def unsupported_output_tensor(t: torch.Tensor, parent=None, node=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, node):
                    return True
            else:
                if unsupported_input_tensor(meta, parent, node):
                    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, override_decomp=False):
    assert op not in decompositions or override_decomp, (
        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
        )
        and not override_decomp
    ):
        # 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()
    op_overload = (
        aten.bernoulli_.float
        if len(args) == 0 or isinstance(args[0], float)
        else aten.bernoulli_.Tensor
    )
    ir.InplaceBernoulliFallback(op_overload, 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_or_error()
    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_or_error()
    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),
            ops.index_expr(low, torch.int64),
            ops.index_expr(high, torch.int64),
        )

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


def _boundaries_helper(tb: TensorBox) -> tuple[str, sympy.Expr, sympy.Expr, sympy.Expr]:
    return (
        tb.get_name(),
        tb.get_size()[-1],
        tb.get_size()[0] * tb.get_stride()[0],
        tb.get_stride()[-1],
    )


def _sorter_helper(tb: TensorBox) -> tuple[str, sympy.Expr]:
    return tb.get_name(), tb.get_stride()[-1]


@register_lowering(aten.searchsorted.Tensor, type_promotion_kind=None)
def searchsorted(
    sorted_sequence: TensorBox,
    self: TensorBox,
    *,
    out_int32: bool = False,
    right: bool = False,
    side: Optional[str] = None,
    sorter: Optional[TensorBox] = None,
) -> TensorBox:
    validate_bucketize = lambda tb: V.graph.has_feature(  # noqa: E731
        tb, BackendFeature.BUCKETIZE
    )
    if (
        not validate_bucketize(sorted_sequence)
        or not validate_bucketize(self)
        or (sorter is not None and not validate_bucketize(sorter))
    ):
        return fallback_handler(aten.searchsorted.Tensor, add_to_fallback_set=False)(
            sorted_sequence,
            self,
            out_int32=out_int32,
            right=right,
            side=side,
            sorter=sorter,
        )

    # If side is present, override the value of right if needed.  This assumes that
    # validation of the two options being non-contradictory is already done by the
    # searchsorted meta-function.
    if side is not None and side == "right":
        right = True

    index_dtype = torch.int32 if out_int32 else torch.int64
    values_loader = self.make_loader()

    # The entire sorted_sequence 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
    # sorted_sequence.get_name() (used below) will exist unless we call
    # sorted_sequence.realize().
    sorted_sequence.realize()

    if sorter is not None:
        sorter.realize()

    if len(sorted_sequence.get_size()) == 1:

        def inner_fn(idx):
            val = values_loader(idx)
            return ops.bucketize(
                val,
                _boundaries_helper(sorted_sequence),
                0,
                index_dtype,
                right,
                sorter=None if sorter is None else _sorter_helper(sorter),
                sorter_indices=None if sorter is None else 0,
            )

    else:

        def inner_fn(idx):
            val = values_loader(idx)

            # Get index to the beginning of the sorted sequence within a flattened
            # version of the array.
            def get_flattened_index(tb: TensorBox):
                strides = tb.get_stride()
                return ops.index_expr(
                    functools.reduce(
                        operator.add, (s * i for s, i in zip(strides[:-1], idx[:-1]))
                    ),
                    index_dtype,
                )

            return ops.bucketize(
                val,
                _boundaries_helper(sorted_sequence),
                get_flattened_index(sorted_sequence),
                index_dtype,
                right,
                sorter=None if sorter is None else _sorter_helper(sorter),
                sorter_indices=None if sorter is None else get_flattened_index(sorter),
            )

    device = self.get_device()
    return Pointwise.create(
        device=device,
        dtype=index_dtype,
        inner_fn=inner_fn,
        ranges=self.shape,
    )


@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 (
        V.graph.has_feature(input, BackendFeature.BUCKETIZE)
        and V.graph.has_feature(boundaries, BackendFeature.BUCKETIZE)
    ):
        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()
    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_helper(boundaries),
            0,
            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_fake_tensors(args, kwargs, fake_args, fake_kwargs):
    def apply_constraint(arg, fake_arg):
        if isinstance(arg, ir.IRNode):
            meta_stride_expr = [
                s.node.expr if isinstance(s, torch.SymInt) else s
                for s in fake_arg.stride()
            ]
            return ir.ExternKernel.require_exact_strides(arg, meta_stride_expr)
        if isinstance(arg, dict):
            return {
                key: apply_constraint(arg[key], fake_arg[key]) for key in arg.keys()
            }
        elif isinstance(arg, (tuple, list)):
            return type(arg)(
                apply_constraint(a, f_a) for (a, f_a) in zip(arg, fake_arg)
            )
        return arg

    args = tuple(
        apply_constraint(arg, fake_arg) for arg, fake_arg in zip(args, fake_args)
    )
    kwargs = {k: apply_constraint(v, fake_kwargs[k]) for k, v in kwargs.items()}
    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(), V.graph.sizevars.shape_env
            )
            return ir.ExternKernel.require_stride_order(arg, stride_order)
        if isinstance(arg, dict):
            return {key: apply_constraint(arg[key], fx_arg[key]) for key in arg.keys()}
        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


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

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

        meta_val = fx_arg.meta["val"]
        meta_stride_expr = [
            s.node.expr if isinstance(s, torch.SymInt) else s for s in meta_val.stride()
        ]

        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()))))

        if (
            fx_node.target
            == aten._scaled_dot_product_efficient_attention_backward.default
            and idx in (0, 5)
        ):
            assert len(stride_order) == 4
            # The 0 and 5th arguments for aten._scaled_dot_product_efficient_attention_backward.default
            # are for out and gradient_out. They have to be in
            # (3, 1, 2, 0) stride order. Otherwise the kernel will crash.
            # Check https://github.com/pytorch/pytorch/issues/138772
            stride_order = (3, 1, 2, 0)

        if not meta_val.is_cuda:
            return ir.ExternKernel.require_stride_order(arg, stride_order)

        # 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

        # effn_attn_fwd does requires dense last dim, not just alignment
        effn_attn_fwd_bias = (
            fx_node.target
            == torch.ops.aten._scaled_dot_product_efficient_attention.default
            and idx == 3
        )

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

        if ir.is_aligned_realized_tensor(arg, ALIGNMENT):
            return ir.try_match_insignificant_strides(
                ir.ExternKernel.realize_input(arg), meta_stride_expr
            )

        if (
            isinstance(arg, IRNode)
            and arg.maybe_get_stride() is not None
            and ir.is_aligned_realized_tensor(arg, ALIGNMENT)
        ):
            return ir.try_match_insignificant_strides(
                ir.ExternKernel.realize_input(arg), meta_stride_expr
            )

        if effn_attn_fwd_bias:
            out_size = list(arg.get_size())

            expanded_dims = []
            # We require a dense last dimension, but the other strides
            # can be expanded, which results in a smaller tensor
            maybe_stride = arg.maybe_get_stride()
            for i in range(len(arg.get_size()) - 1):
                if V.graph.sizevars.statically_known_equals(meta_stride_expr[i], 0) or (
                    maybe_stride is not None
                    and V.graph.sizevars.statically_known_equals(maybe_stride[i], 0)
                ):
                    expanded_dims.append(i)

            # Now, pad strides to alignment
            out_strides = [-1] * len(out_size)
            out_strides[-1] = 1
            stride = 1
            for i in range(len(out_size) - 2, -1, -1):
                if out_strides[i + 1] != 0:
                    stride = stride * out_size[i + 1]

                # the expanded dims still need to be aligned, if they are,
                # we can make them expanded by setting the stride equal to 0
                if i in expanded_dims:
                    if V.graph.sizevars.statically_known_equals(
                        out_strides[i + 1] % ALIGNMENT, 0
                    ):
                        out_strides[i] = 0
                        continue

                if not V.graph.sizevars.statically_known_equals(stride % ALIGNMENT, 0):
                    stride = ceildiv(stride, ALIGNMENT) * ALIGNMENT

                out_strides[i] = stride

            return ir.ExternKernel.require_exact_strides(arg, out_strides)

        if ir.is_aligned_realized_tensor(arg, ALIGNMENT):
            return ir.try_match_insignificant_strides(
                ir.ExternKernel.realize_input(arg), meta_stride_expr
            )

        if (
            isinstance(arg, IRNode)
            and arg.maybe_get_stride() is not None
            and ir.is_aligned_realized_tensor(arg, ALIGNMENT)
        ):
            return ir.try_match_insignificant_strides(
                ir.ExternKernel.realize_input(arg), meta_stride_expr
            )

        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 ir.try_match_insignificant_strides(
                        ir.ExternKernel.realize_input(arg), meta_stride_expr
                    )

        return ir.ExternKernel.require_stride_order(arg, stride_order)

    args = tuple(
        apply_constraint(idx, arg, fx_arg)
        for idx, (arg, fx_arg) in enumerate(zip(args, fx_node.args))
    )
    kwargs = {k: apply_constraint(-1, v, fx_node.kwargs[k]) for k, v in kwargs.items()}
    return args, kwargs


# WIP
make_fallback(aten._adaptive_avg_pool3d)  # @isuruf
make_fallback(aten.adaptive_max_pool3d)  # @isuruf
make_fallback(aten.fractional_max_pool3d)  # @isuruf
make_fallback(aten.max_pool3d_with_indices)  # @isuruf (can this one be implemented?)


# 1) Easy
make_fallback(aten.uniform, warn=False)
make_fallback(aten.exponential.default, warn=False)  # (fails accuracy on test_torch.py)
make_fallback(aten._pdist_forward)  # Has decomp. Needs benchmarks
make_fallback(aten.soft_margin_loss_backward, warn=False)  # py_impl?


# 1.5) Easy or Impossible
make_fallback(aten._cdist_forward)  # p=2 should be feasible
make_fallback(aten._cdist_backward)

# 2) Medium
make_fallback(aten._trilinear)


# 3) Difficult
# Scans
# See the discussion at
# https://dev-discuss.pytorch.org/t/pytorch-sparse-gnn-compiler-rfc/1644/19
make_fallback(aten.segment_reduce.default)
make_fallback(aten._segment_reduce_backward.default)

# Histogram (need to implement Histogram IR)
make_fallback(aten.histc)
make_fallback(aten.histogram.bin_ct)
make_fallback(aten._histogramdd_bin_edges.default)
make_fallback(aten._histogramdd_from_bin_cts.default)

# Need templated kernel
make_fallback(aten.addbmm)
make_fallback(aten._addmm_activation, warn=False)

# Need templated kernel. Probably impossible to write efficiently
make_fallback(aten.convolution_backward, constrain_to_fx_strides)
make_fallback(aten._cudnn_rnn, require_dense)
make_fallback(aten._cudnn_rnn_backward, require_contiguous)

# Haven't checked but sound difficult / impossible
make_fallback(aten._embedding_bag, require_contiguous)
make_fallback(aten._embedding_bag_forward_only, require_contiguous)
make_fallback(aten._embedding_bag_backward)
make_fallback(aten._embedding_bag_per_sample_weights_backward)
make_fallback(aten._embedding_bag_per_sample_weights_backward)
make_fallback(aten._fused_moving_avg_obs_fq_helper)
make_fallback(aten._fused_moving_avg_obs_fq_helper_functional)


# 4) Backwards (try py_impl'ing them) when fwd is written as a decomp
make_fallback(aten.max_pool3d_with_indices_backward)
make_fallback(aten._adaptive_avg_pool2d_backward, require_dense)
make_fallback(aten._adaptive_avg_pool3d_backward)
make_fallback(aten.adaptive_max_pool2d_backward)
make_fallback(aten.adaptive_max_pool3d_backward)
make_fallback(aten.fractional_max_pool2d_backward)
make_fallback(aten.fractional_max_pool3d_backward)
make_fallback(aten.replication_pad1d_backward)
make_fallback(aten.replication_pad2d_backward)
make_fallback(aten.upsample_linear1d_backward)
make_fallback(aten.upsample_bicubic2d_backward, require_contiguous)
make_fallback(aten.upsample_trilinear3d_backward)
make_fallback(aten.grid_sampler_2d_backward, require_dense)
make_fallback(aten._pdist_backward)


# 5) Impossible (missing triton/CPU features)

# Sorting / Sorting-like
make_fallback(aten.sort)
make_fallback(aten.sort.stable)
make_fallback(aten.kthvalue)
make_fallback(aten.topk)
make_fallback(aten.mode)
make_fallback(aten.median)
make_fallback(aten.nanmedian)
make_fallback(aten.randperm)
# see: https://github.com/pytorch/pytorch/pull/121354
make_fallback(aten.resize_)
make_fallback(aten.resize_as_)

# Linalg
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.lu_unpack)
make_fallback(aten.ormqr)
make_fallback(aten._linalg_check_errors)
make_fallback(aten.linalg_pinv.atol_rtol_tensor)
make_fallback(aten._linalg_eigh)
make_fallback(aten.triangular_solve)
make_fallback(aten.linalg_cholesky_ex)
make_fallback(aten.cholesky_inverse)
make_fallback(aten.cholesky_solve)
make_fallback(aten.geqrf)
make_fallback(aten._fft_r2c)  # needs complex as well

# Data dependent (are these necessary?)
make_fallback(aten.nonzero.default)

# Misc
make_fallback(aten.gcd.default, warn=False)
make_fallback(aten._thnn_fused_lstm_cell, require_dense)
make_fallback(torch._prims.rng_prims.run_and_save_rng_state)
make_fallback(torch._prims.rng_prims.run_with_rng_state)
make_fallback(torch._prims.rng_prims.graphsafe_run_with_rng_state)


# Implmented / Half implemented
# Scans. Implemented for CUDA, missing CPU
make_fallback(aten.masked_scatter)
make_fallback(aten.masked_scatter_backward)

# Complex number support
make_fallback(aten.view_as_complex, require_contiguous)
make_fallback(aten.angle)  # needs complex

# Needs efficentzerotensor
make_fallback(aten._efficientzerotensor)

# Needs Sparse
make_fallback(aten._sparse_coo_tensor_with_dims_and_tensors)
make_fallback(aten.to_sparse)
make_fallback(aten._to_sparse)

# Needs dimname support
make_fallback(aten.zeros.names)

# 6) Pattern-matched
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_cudnn_attention.default,
    sdpa_constraint,
    warn=False,
)
make_fallback(
    aten._scaled_dot_product_cudnn_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._scaled_dot_product_fused_attention_overrideable.default,
    sdpa_constraint,
    warn=False,
)
make_fallback(
    aten._scaled_dot_product_fused_attention_overrideable_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)

# index_reduce requires fallback when use_scatter_fallback(...) returns True
make_fallback(aten.index_reduce)


# 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(data=x, layout=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)  # type: ignore[arg-type]
    V.graph.sizevars.guard_lt(index, x.get_size()[dim])  # type: ignore[arg-type]
    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]

    start, end = ir.SliceView.normalize_start_end(x, dim, start, end)

    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.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.Basic):

        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):
    from torch.fx.experimental.symbolic_shapes import resolve_unbacked_bindings

    # 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.
    unbacked_bindings = resolve_unbacked_bindings(
        V.graph.sizevars.shape_env, V.graph.current_node.meta["unbacked_bindings"]
    )
    assert unbacked_bindings is not None
    assert len(unbacked_bindings) == 1, unbacked_bindings
    # NB: Have to be very careful here.  V.graph.current_node.meta["val"]
    # seemingly also contains a symbol which you want to do binding for,
    # but it actually isn't.  In particular, if we have later performed
    # a deferred runtime assert saying that u0 == s0, you will actually
    # see s0 from expr!  This is bad because we need to actually generate
    # the assert that says u0 == s0, so we need to know where to get u0
    # from (this call).  In particular, we must use unbacked_bindings, which
    # is guaranteed to have the original, unreplaced symbol in question.
    #
    # NB2: Another thing we have to be very careful about are symbol bindings
    # that require nontrivial refinement, e.g., when you have a binding site
    # x: Sym(u0 * 4) = y.item().  Here, the code generation must do a division
    # in order to appropriately bind u0.  This is communicated via the keypath
    # in unbacked_bindings, and we need to hold onto it in order to generate
    # code appropriately for this case.
    binding_sym, keypath = next(iter(unbacked_bindings.items()))
    buffer = ir.DynamicScalar(binding_sym, keypath, data)
    buffer.name = V.graph.register_buffer(buffer)
    V.graph.register_operation(buffer)
    # NB: the replaced expr is OK to use directly downstream, we want
    # simplifications in this case!
    val = V.graph.current_node.meta["val"]
    if isinstance(val, (torch.SymInt, torch.SymFloat, torch.SymBool)):
        return val.node.expr
    else:
        return sympy.sympify(val)


@register_lowering(aten._assert_scalar)
def _assert_scalar(data, msg):
    # NB: These will be handled at codegen time
    # Not sure if we are guaranteed to be able to serve out truth from the
    # deferred_runtime_asserts, TODO: try this assert out
    # assert bool(data.scalar), data
    return None


@register_lowering(aten._assert_tensor_metadata)
def _assert_tensor_metadata(
    a, size=None, stride=None, dtype=None, *, device=None, layout=None
):
    return None


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.Basic):

        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])
        # See https://github.com/pytorch/pytorch/issues/118102
        # All sizes at lowering time should be sympy.Symbol, not SymInt!
        for s in size:
            assert not isinstance(s, torch.SymInt)
        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, decode_device(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=decode_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
    device = decode_device(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 = dataclasses.replace(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=decode_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)
    if index.get_numel() == 0:
        # Empty index case. Return an empty array with the same shape
        return new_empty(x, index.get_size())

    assert index.get_dtype() == torch.int64
    size = x.get_size()
    offset = len(size) == 0
    dim = _validate_dim(x, dim, offset)

    if offset:
        x = expand(x, [1])
        size = [1]

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

    def fn(idx):
        idx = list(idx)
        gather_idx = ops.indirect_indexing(index_loader(idx), size[dim])
        if len(idx) == 0:
            idx = [gather_idx]
        else:
            idx[dim] = gather_idx
        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,
    wrap_neg=True,
):
    # 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,
                        wrap_neg=wrap_neg,
                    )
                )
        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):
    output_size, inner_fn, _ = index_impl_helper(x, indices, check)

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


def index_impl_helper(x, indices, check, wrap_neg=True):
    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 check and 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, index_inner_fn = index_output_size_and_inner_fn(
        x_size,
        indices,
        tensor_indices,
        tensor_size,
        indices_loaders,
        indexed_size,
        None,
        check=check,
        wrap_neg=wrap_neg,
    )

    def inner_fn(idx):
        return x_loader(index_inner_fn(idx))

    return output_size, inner_fn, index_inner_fn


@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_impl_(
        clone(x), indices, values, accumulate, check=True, may_realize=False
    )


@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, may_realize=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):
        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(V.graph.current_node.target, 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, may_realize=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, may_realize=True
    )


def index_put_impl_(self, indices, values, accumulate, check, may_realize=False):
    if may_realize:

        def try_get_name(x):
            if isinstance(x, ir.TensorBox):
                x = x.data
            if isinstance(x, ir.BaseView):
                x = x.unwrap_view()
            if isinstance(x, ir.StorageBox):
                x = x.data
            return x.get_name() if isinstance(x, ir.Buffer) else None

        def indice_slice_from_randperm(indice):
            # Refer to: https://github.com/pytorch/pytorch/pull/139366#discussion_r1825424660
            # For this specific pattern, indices is unique as coming from torch.randperm.
            # However, as the content of the indices is unknown, we have to check this specific pattern.
            if isinstance(indice, TensorBox) and isinstance(indice.data, ir.BaseView):
                indice = indice.data.unwrap_view()
                return (
                    isinstance(indice, ir.StorageBox)
                    and isinstance(indice.data, ir.ExternKernel)
                    and getattr(indice.data, "fx_node", None)
                    and indice.data.fx_node.target == torch.ops.aten.randperm.default
                )
            return False

        if try_get_name(self) in values.get_read_names() and not all(
            indice_slice_from_randperm(indice) for indice in indices
        ):
            # Fix issue: https://github.com/pytorch/pytorch/issues/138908
            # When self and values have memory overlapping, indices may
            # contain duplicate values, potentially causing incorrect results since
            # the load of `values` might contain modified value from the store of `self`.
            # To address this, store values in a temporary buffer in such cases.
            values.realize()

    # 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(
        name=None,
        layout=ir.MutationLayoutSHOULDREMOVE(self),
        data=scatter,
    )
    buffer.name = V.graph.register_buffer(buffer)
    V.graph.register_operation(buffer)

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


fallback__unsafe_masked_index = fallback_handler(
    aten._unsafe_masked_index.default, add_to_fallback_set=False
)

fallback__unsafe_masked_index_put_accumulate = fallback_handler(
    aten._unsafe_masked_index_put_accumulate.default, add_to_fallback_set=False
)


@register_lowering(aten._unsafe_masked_index, type_promotion_kind=None)
def _unsafe_masked_index(self, mask, indices, fill):
    ranges, _, _unsafe_index_fn = index_impl_helper(
        self, indices, check=False, wrap_neg=False
    )
    mask_loader = mask.make_loader()
    self_loader = self.make_loader()

    def inner_fn(idx):
        if mask.dtype != torch.bool:
            mask_val = ops.to_dtype(mask_loader(idx), torch.bool)
        else:
            mask_val = mask_loader(idx)
        return ops.masked(mask_val, lambda: self_loader(_unsafe_index_fn(idx)), fill)

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


@register_lowering(aten._unsafe_masked_index_put_accumulate, type_promotion_kind=None)
def _unsafe_masked_index_put_accumulate(x, mask, indices, values):
    masked_value = where(mask, values, 0)
    shape = x.get_size()
    clamped_indices = [
        clamp(indices[i], -shape[i], shape[i] - 1) if indices[i] else None
        for i in range(len(indices))
    ]
    # TODO: use a masked store for this. currently only triton
    # supports masked stores and cpp backend does not.
    return _unsafe_index_put(x, clamped_indices, masked_value, accumulate=True)


@make_pointwise
def clamp(a, min, max):
    return ops.maximum(min, ops.minimum(max, a))


@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(
    op_overload: torch._ops.OpOverload,
    self,
    dim: int,
    index,
    src,
    *,
    reduce: Optional[str] = None,
    include_self: bool = True,
):
    src_is_tensor = isinstance(src, TensorBox)
    if use_scatter_fallback(
        op_overload,
        reduce,
        self.get_dtype(),
        cast(torch.dtype, src.get_dtype() if src_is_tensor else type(src)),
        src.get_device().type if src_is_tensor else "not impl",
        src_is_tensor,
    ):
        ir.ScatterFallback(
            op_overload,
            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")
    if reduce is None:
        op_overload = getattr(aten.scatter_, V.graph.current_node.target._overloadname)  # type: ignore[union-attr]
        fallback_result = scatter_fallback(
            op_overload, self, dim, index, src, reduce=reduce
        )
        if fallback_result is not None:
            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")
    assert (
        len(aten.scatter_reduce_.overloads()) == 1
        and "two" in aten.scatter_reduce_.overloads()
    ), "aten.scatter_reduce_.two is not the unique overload of aten.scatter_reduce_"

    if isinstance(src, Number):
        src = full_like(self, src)

    fallback_result = scatter_fallback(
        aten.scatter_reduce_.two,
        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])

    if index.get_numel() == 0:
        return self

    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], wrap_neg=False
        )
        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(
            name=None,
            layout=ir.MutationLayoutSHOULDREMOVE(self),
            data=zero_out,
        )
        buffer.name = V.graph.register_buffer(buffer)
        V.graph.register_operation(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(
        name=None,
        layout=ir.MutationLayoutSHOULDREMOVE(self),
        data=scatter,
    )
    buffer.name = V.graph.register_buffer(buffer)
    V.graph.register_operation(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

    inv_scales = [i / o for i, o in zip(i_sizes, o_sizes)]
    for i, scale in enumerate(scales_x):
        if scale is not None:
            inv_scales[i] = 1.0 / 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, inv_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(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,
    )


def inplace_constant_pad_nd(
    x: TensorBox, padding: Sequence[int], fill_value: float
) -> Optional[TensorBox]:
    """
    This optimization changes the semantics of padding from 'clone'
    style to 'view' style.

    Thanks to functionalization, this change can still maintain numerical
    correctness.
    """

    def _padding_can_be_fused():
        """
        Conservatively check if padding can be fused with downstream op.
        1. if the downstream op is a sum, then there is little benefit to
           do inplace padding
        2. if the downstream op is a matmul, doing inplace padding can
           save membw.
        """
        current_node = V.graph.current_node
        if current_node is None:
            return True  # be conservative
        users = tuple(current_node.users)
        if len(users) == 1 and users[0].target in (
            aten.mm.default,
            aten.addmm.default,
        ):
            return False

        return True  # be conservative

    if _padding_can_be_fused():
        return None

    # Only handle 2D case for now
    if len(padding) != 4 or len(x.get_size()) != 2:
        return None

    # No harm to realize since we already know that
    # the op can not be fused into the single user.
    # It need to be realized later anyways.
    x.realize()

    # If x is a view (e.g. a SliceView), realizing it just realizing the
    # underlying storage. x itself is still a view.
    if (
        not isinstance(x, ir.TensorBox)
        or not isinstance(x.data, ir.StorageBox)
        or not (
            isinstance(x.data.data, ir.ComputedBuffer)
            or (
                config.can_inplace_pad_graph_input
                and isinstance(x.data.data, ir.InputBuffer)
            )
        )
        or not x.data.data.name
    ):
        return None
    x.freeze_layout()

    _, layout = ir.as_storage_and_layout(x)
    strides = layout.stride
    if strides[1] != 1:
        return None

    if padding[0] != 0 or padding[2] != 0 or padding[3] != 0:
        return None

    npad = padding[1]
    if npad == 0:
        return None

    stride0 = strides[0]
    rowsize = layout.size[1]

    if stride0 < rowsize + npad:
        return None

    bufname = x.data.data.name
    padded_size = [layout.size[0], layout.size[1] + npad]
    V.graph.buffer_to_padded_size[bufname] = padded_size
    resized_x = as_strided(
        x,
        padded_size,
        layout.stride,
        layout.offset,
    )

    sliced_x = slice_(resized_x, dim=1, start=rowsize, end=rowsize + npad)
    fill_(sliced_x, fill_value)

    counters["inductor"]["inplace_padding"] += 1
    return resized_x


@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)

    if config.inplace_padding:
        out = inplace_constant_pad_nd(x, padding, fill_value)
        if out:
            return out
            # fall through if can not inplace the padding

    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))  # type: ignore[arg-type]

    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(
    x, fill_value, padding=None, pad_fill_value=1.0, dim=None
):
    h = x.get_size()[-dim:]
    x_loader = x.make_loader()
    padding_h = padding or [0] * dim

    def load(index):
        prefix = index[:-dim]
        ih = index[-dim:]

        mask = functools.reduce(
            ops.and_,
            [range_mask(ih[i], h[i] + padding_h[i], -padding_h[i]) for i in range(dim)],
        )
        return (
            ops.masked(
                mask,
                lambda: constant_boundary_condition(x, pad_fill_value, dim=dim)(
                    [*prefix, *ih]
                ),
                fill_value,
            )
            if padding
            else ops.masked(mask, lambda: x_loader([*prefix, *ih]), 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  # type: ignore[assignment]
            V.graph.sizevars.guard_leq(0, x_alt * stride[i] - x - padding[i])  # type: ignore[arg-type]
        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


def should_fallback_max_pool2d_with_indices(kernel_size, dilation):
    kernel_size = pad_listlike(kernel_size, 2)
    window_size = kernel_size[0] * kernel_size[1]
    return (window_size > 25) or any(d > 1 for d in dilation)


def max_pool2d_checks(
    x, kernel_size, stride, padding, dilation, *, assert_fallback=None
):
    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)

    use_fallback = should_fallback_max_pool2d_with_indices(kernel_size, dilation)
    if assert_fallback is not None:
        assert use_fallback == assert_fallback

    return kernel_size, stride, padding, dilation, use_fallback


def _max_pool2d_with_offsets(
    x,
    kernel_size,
    stride,
    padding,
    dilation,
    ceil_mode=False,
):
    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)

    dtype = x.dtype
    min_value = (
        False
        if dtype is torch.bool
        else (float("-inf") if dtype.is_floating_point else torch.iinfo(dtype).min)
    )

    new_size = list(batch) + [h_out, w_out]
    if padding[0] or padding[1] or ceil_mode1 or ceil_mode2:
        x_loader = constant_boundary_condition(x, min_value, dim=2)
    else:
        x_loader = x.make_loader()

    dim = 2

    def fn_inner(idx, reduction_idx):
        prefix = idx[:-dim]
        bh = idx[-dim:]
        ih = [bh[i] * stride[i] + reduction_idx[i] - padding[i] for i in range(dim)]
        return x_loader([*prefix, *ih])

    result = Reduction.create(
        reduction_type="max",
        input_node=x,
        device=x.get_device(),
        dst_dtype=dtype,
        src_dtype=dtype,
        inner_fn=fn_inner,
        ranges=new_size,
        reduction_ranges=kernel_size,
    )
    offsets = Reduction.create(
        reduction_type="argmax",
        input_node=x,
        device=x.get_device(),
        dst_dtype=torch.int64,
        src_dtype=dtype,
        inner_fn=fn_inner,
        ranges=new_size,
        reduction_ranges=kernel_size,
    )
    if isinstance(result.data.data, Reduction):  # type: ignore[attr-defined]
        # Only realize if reduction isn't unrolled
        result.realize()
    if isinstance(offsets.data.data, Reduction):  # type: ignore[attr-defined]
        # Only realize if reduction isn't unrolled
        offsets.realize()

    return result, offsets


@register_lowering(prims._low_memory_max_pool2d_with_offsets, type_promotion_kind=None)
def _low_memory_max_pool2d_with_offsets(
    x,
    kernel_size,
    stride,
    padding,
    dilation,
    ceil_mode=False,
):
    # assert we are not on a fallback path, the inductor decomp should have guaranteed this
    kernel_size, stride, padding, dilation, _ = max_pool2d_checks(
        x,
        kernel_size,
        stride,
        padding,
        dilation,
        assert_fallback=False,
    )

    with config.patch(unroll_reductions_threshold=25):
        result, offsets = _max_pool2d_with_offsets(
            x,
            kernel_size,
            stride,
            padding,
            dilation,
            ceil_mode,
        )
        return result, to_dtype(offsets, torch.int8)


@register_lowering(
    prims._low_memory_max_pool2d_offsets_to_indices, type_promotion_kind=None
)
def _low_memory_max_pool2d_offsets_to_indices(
    offsets, kernel_width, input_width, stride, padding
):
    # TODO: Generalize to other max pooling flavors, and arbitrary dim

    offsets_loader = offsets.make_loader()

    def increments_to_index(h_inc, w_inc, bh, bw):
        w_in = ops.index_expr(input_width, torch.int64)
        hbase = ops.index_expr(bh * stride[0] - padding[0], torch.int64)
        wbase = ops.index_expr(bw * stride[1] - padding[1], torch.int64)
        ih = hbase + h_inc
        iw = wbase + w_inc
        return ih * w_in + iw

    def offsets_to_indices(idx):
        *prefix, bh, bw = idx
        offset = offsets_loader([*prefix, bh, bw])
        kw_const = ops.constant(kernel_width, torch.int32)
        h_inc = offset // kw_const
        w_inc = offset - (h_inc * kw_const)
        return increments_to_index(h_inc, w_inc, bh, bw)

    indices = Pointwise.create(
        device=offsets.get_device(),
        dtype=torch.int64,
        inner_fn=offsets_to_indices,
        ranges=offsets.get_size(),
    )
    return indices


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


# Fallback when we do not decompose to the low-memory path.
@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,
):
    kernel_size, stride, padding, dilation, _ = max_pool2d_checks(
        x, kernel_size, stride, padding, dilation
    )

    if any(d > 1 for d in dilation):
        return fallback_max_pool2d_with_indices(
            x, kernel_size, stride, padding, dilation, ceil_mode=ceil_mode
        )

    out, offsets = _max_pool2d_with_offsets(
        x, kernel_size, stride, padding, dilation, ceil_mode
    )

    indices = _low_memory_max_pool2d_offsets_to_indices(
        offsets, kernel_size[-1], x.shape[-1], stride, padding
    )

    return out, indices


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()
    gO_stride = grad_output.maybe_get_stride()
    x_stride: Optional[Sequence[Any]]
    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:
        x_stride = x.maybe_get_stride()

    is_channels_last = (x_stride is not None and x_stride[1] == 1) or (
        gO_stride is not None and gO_stride[1] == 1
    )
    if any(d != 1 for d in dilation):
        # dilation NYI
        return fallback_max_pool2d_with_indices_backward(
            grad_output, x, kernel_size, stride, padding, dilation, ceil_mode, indices
        )

    *_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

    out = Pointwise.create(
        device=grad_output.get_device(),
        dtype=grad_output.get_dtype(),
        inner_fn=fn,
        ranges=new_size,
    )
    if is_channels_last:
        return ir.ExternKernel.require_channels_last(out)
    else:
        return out


def pad_adaptive_loader(x, pad_val=0.0):
    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]),
            pad_val,
        )

    return load


def compute_indices_adaptive_pooling(start_index, end_index, h_in, w_in, h_out, w_out):
    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)

    return h_start_index, h_end_index, w_start_index, w_end_index


def _adaptive_pooling_fn(
    start_index, end_index, kernel_maxes, in_sizes, out_sizes, pooling_fn
):
    h_in, w_in = in_sizes
    h_out, w_out = out_sizes

    (
        h_start_index_fn,
        h_end_index_fn,
        w_start_index_fn,
        w_end_index_fn,
    ) = compute_indices_adaptive_pooling(
        start_index, end_index, h_in, w_in, h_out, w_out
    )

    def fn(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)

        result = 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 result is None:
                result = val
            else:
                result = pooling_fn(val, result)
        return result

    return fn


def _adaptive_pooling_fn_with_idx(
    start_index, end_index, kernel_maxes, in_sizes, out_sizes, pooling_fn
):
    h_in, w_in = in_sizes
    h_out, w_out = out_sizes

    (
        h_start_index_fn,
        h_end_index_fn,
        w_start_index_fn,
        w_end_index_fn,
    ) = compute_indices_adaptive_pooling(
        start_index, end_index, h_in, w_in, h_out, w_out
    )

    def fn(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)

        maxval = None
        maxindex = 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],
            )

            index = ops.index_expr(
                (h_start_index + ih) * w_in + w_start_index + 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 = pooling_fn(val, maxval)

        return maxindex

    return fn


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):
    if x.get_dtype() == torch.int64:
        # not supported in eager
        raise RuntimeError("'adaptive_avg_pool2d' not implemented for 'Long'")
    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()

    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)

    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)

    fn_sum = _adaptive_pooling_fn(
        start_index=start_index,
        end_index=end_index,
        kernel_maxes=[h_kernel_max, w_kernel_max],
        in_sizes=[h_in, w_in],
        out_sizes=[h_out, w_out],
        pooling_fn=ops.add,
    )

    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


fallback_adaptive_max_pool2d = fallback_handler(
    aten.adaptive_max_pool2d.default, add_to_fallback_set=False
)


@register_lowering(aten.adaptive_max_pool2d)
def adaptive_max_pool2d(x, output_size):
    if x.get_dtype() == torch.int64:
        # not supported in eager
        raise RuntimeError("adaptive_max_pool2d not implemented for Long")
    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

    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()), empty(
            o_size, dtype=torch.int64, device=x.get_device()
        )

    if h_in % h_out == 0 and w_in % w_out == 0:
        # This is handled by a decomposition
        raise ValueError

    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()

    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_max_pool2d(x, output_size)

    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)

    inner_func_max_val = _adaptive_pooling_fn(
        start_index=start_index,
        end_index=end_index,
        kernel_maxes=[h_kernel_max, w_kernel_max],
        in_sizes=[h_in, w_in],
        out_sizes=[h_out, w_out],
        pooling_fn=ops.maximum,
    )

    inner_func_max_idx = _adaptive_pooling_fn_with_idx(
        start_index=start_index,
        end_index=end_index,
        kernel_maxes=[h_kernel_max, w_kernel_max],
        in_sizes=[h_in, w_in],
        out_sizes=[h_out, w_out],
        pooling_fn=ops.maximum,
    )

    def inner_fn_max_val(idx):
        return inner_func_max_val(idx, pad_adaptive_loader(x, float("-inf")))

    def inner_fn_max_idx(idx):
        return inner_func_max_idx(idx, pad_adaptive_loader(x, float("-inf")))

    rv = Pointwise.create(
        device=x.get_device(),
        dtype=dtype,
        inner_fn=inner_fn_max_val,
        ranges=new_size,
    )
    ri = Pointwise.create(
        device=x.get_device(),
        dtype=torch.int64,
        inner_fn=inner_fn_max_idx,
        ranges=new_size,
    )
    return rv, ri


fallback_fractional_max_pool2d = fallback_handler(
    aten.fractional_max_pool2d.default, add_to_fallback_set=False
)


def _fractional_pooling_offsets(samples, in_sz, out_sz, kernel_sz, dim, ndims):
    out_sz = out_sz[dim]
    in_sz = in_sz[dim]
    kernel_sz = kernel_sz[dim]
    alpha = IntTrueDiv(in_sz - kernel_sz, out_sz - 1)
    samples_loader = samples.make_loader()

    def load(prefix, i):
        sample = samples_loader([*prefix, ndims - 1 - dim])
        i_expr = ops.index_expr(i, samples.get_dtype())
        alpha_expr = ops.index_expr(alpha, samples.get_dtype())
        seq_i = ops.trunc((i_expr + sample) * alpha_expr) - ops.trunc(
            sample * alpha_expr
        )
        seq_i = ops.to_dtype(seq_i, torch.int64)

        mask = ops.lt(
            i_expr,
            ops.index_expr(out_sz - 1, torch.int64),
        )
        return ops.where(mask, seq_i, ops.index_expr(in_sz - kernel_sz, torch.int64))

    return load


@register_lowering(aten.fractional_max_pool2d)
def fractional_max_pool2d(x, kernel_size, output_size, random_samples):
    x.realize_hint()
    *batch, inp_h, inp_w = x.get_size()
    kernel_h, kernel_w = kernel_size
    h_out, w_out = output_size

    if kernel_h * kernel_w >= 25:
        return fallback_fractional_max_pool2d(
            x, kernel_size, output_size, random_samples
        )

    gen_offsets_for_dim = functools.partial(
        _fractional_pooling_offsets,
        samples=random_samples,
        in_sz=[inp_h, inp_w],
        out_sz=output_size,
        kernel_sz=kernel_size,
        ndims=2,
    )

    h_index_fn = gen_offsets_for_dim(dim=0)
    w_index_fn = gen_offsets_for_dim(dim=1)
    x_loader = x.make_loader()

    def fn(idx, return_index):
        *prefix, bh, bw = idx

        h_start_index = ops.indirect_indexing(h_index_fn(prefix, bh), inp_h)
        w_start_index = ops.indirect_indexing(w_index_fn(prefix, bw), inp_w)

        maxval = None
        maxindex = None
        for ih, iw in itertools.product(range(kernel_size[0]), range(kernel_size[1])):
            val = x_loader([*prefix, h_start_index + ih, w_start_index + iw])
            if return_index:
                index = ops.index_expr(
                    (h_start_index + ih) * inp_w + w_start_index + iw, torch.int64
                )
                if maxindex is None:
                    maxindex = index
                else:
                    maxindex = ops.where(
                        ops.or_(ops.gt(val, maxval), ops.isnan(val)), index, maxindex
                    )
            if maxval is None:
                maxval = val
            else:
                maxval = ops.maximum(val, maxval)
        if return_index:
            return maxindex
        else:
            return maxval

    new_size = list(batch) + [h_out, w_out]
    rv = Pointwise.create(
        device=x.get_device(),
        dtype=x.get_dtype(),
        inner_fn=functools.partial(fn, return_index=False),
        ranges=new_size,
    )

    ri = Pointwise.create(
        device=x.get_device(),
        dtype=torch.int64,
        inner_fn=functools.partial(fn, return_index=True),
        ranges=new_size,
    )
    return rv, ri


@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, sympy.sympify(out_dim))

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

    fn_sum = _adaptive_pooling_fn(
        start_index=start_index,
        end_index=end_index,
        kernel_maxes=[h_kernel_max, w_kernel_max],
        in_sizes=[inp_h, inp_w],
        out_sizes=[out_h, out_w],
        pooling_fn=ops.add,
    )

    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
)
fallback_avg_pool3d = fallback_handler(
    aten.avg_pool3d.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,
):
    return _avg_poolnd(
        x,
        kernel_size,
        stride,
        padding,
        ceil_mode,
        count_include_pad,
        divisor_override,
        dim=2,
    )


@register_lowering(aten.avg_pool3d, type_promotion_kind=None)
def avg_pool3d(
    x,
    kernel_size,
    stride=(),
    padding=0,
    ceil_mode=False,
    count_include_pad=True,
    divisor_override=None,
):
    return _avg_poolnd(
        x,
        kernel_size,
        stride,
        padding,
        ceil_mode,
        count_include_pad,
        divisor_override,
        dim=3,
    )


def _avg_poolnd(
    x,
    kernel_size,
    stride,
    padding,
    ceil_mode,
    count_include_pad,
    divisor_override,
    dim,
):
    if not stride:
        stride = kernel_size
    if not padding:
        padding = [0] * dim
    kernel_size = pad_listlike(kernel_size, dim)
    stride = pad_listlike(stride, dim)
    padding = pad_listlike(padding, dim)

    assert isinstance(x, TensorBox)
    assert len(kernel_size) == dim
    assert len(stride) == dim
    assert len(padding) == dim
    assert len(x.get_size()) in (dim + 1, dim + 2)

    x.realize_hint()
    batch = x.get_size()[:-dim]
    h = x.get_size()[-dim:]

    h_out, ceil_modes = zip(
        *[
            pooling_size(h[i], i, kernel_size, stride, padding, ceil_mode)
            for i in range(dim)
        ]
    )

    if any(padding) or any(ceil_modes):
        x_loader = constant_boundary_condition(x, 0.0, dim=dim)
        had_padding = True
    else:
        x_loader = x.make_loader()
        had_padding = False

    new_size = list(batch) + list(h_out)
    dtype = x.get_dtype()

    window_size = functools.reduce(operator.mul, kernel_size)
    if window_size > 25:
        # Kernel size too big. Results in hard-to-optimize Triton code. Use fallback.
        if dim == 2:
            fallback = fallback_avg_pool2d
        elif dim == 3:
            fallback = fallback_avg_pool3d
        else:
            raise ValueError(f"Unknown dim: {dim}")

        return fallback(
            x,
            kernel_size,
            stride,
            padding,
            ceil_mode,
            count_include_pad,
            divisor_override,
        )

    def fn_sum(idx, loader):
        prefix = idx[:-dim]
        b = idx[-dim:]
        total = None
        for ih in itertools.product(*[range(kernel_size[i]) for i in range(dim)]):
            inp = [b[i] * stride[i] + ih[i] - padding[i] for i in range(dim)]
            val = loader([*prefix, *inp])
            if total is None:
                total = val
            else:
                total = ops.add(val, total)
        return total

    if not had_padding or divisor_override:
        divisor = divisor_override if divisor_override else window_size
        if dtype.is_floating_point:
            scale = 1 / divisor

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

        else:

            def fn(idx):
                # C style integer division as done in native/cpu/AvgPoolKernel.cpp
                return ops.truncdiv(fn_sum(idx, x_loader), ops.constant(divisor, dtype))

    else:

        def fn(idx):
            bh = idx[-dim:]

            divide_factors = []
            for i in range(dim):
                hstart = bh[i] * stride[i] - padding[i]
                hend = sympy.Min(hstart + kernel_size[i], h[i] + padding[i])
                if not count_include_pad:
                    hstart = sympy.Max(hstart, 0)
                    hend = sympy.Min(hend, h[i])
                factor = ops.index_expr(hend - hstart, torch.int32)
                divide_factors.append(factor)
            divide_factor = functools.reduce(ops.mul, divide_factors)
            if dtype.is_floating_point:
                return ops.truediv(fn_sum(idx, x_loader), divide_factor)
            # C style integer division as done in native/cpu/AvgPoolKernel.cpp
            return ops.truncdiv(fn_sum(idx, x_loader), divide_factor)

    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

    *_, 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


fallback_avg_pool3d_backward = fallback_handler(
    aten.avg_pool3d_backward.default, add_to_fallback_set=False
)


@register_lowering(aten.avg_pool3d_backward, type_promotion_kind=None)
def avg_pool3d_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, 0]

    assert isinstance(grad_output, TensorBox)
    assert isinstance(x, TensorBox)
    assert len(kernel_size) == 3
    assert len(stride) == 3
    assert len(padding) == 3
    assert len(x.get_size()) in (4, 5)

    grad_output.realize_hint()

    *_batch, depth, height, width = x.get_size()

    _d_out, ceil_mode_d = pooling_size(
        depth, 0, kernel_size, stride, padding, ceil_mode
    )
    _h_out, ceil_mode_h = pooling_size(
        height, 1, kernel_size, stride, padding, ceil_mode
    )
    _w_out, ceil_mode_w = pooling_size(
        width, 2, kernel_size, stride, padding, ceil_mode
    )

    grad_loader = grad_output.make_loader()
    had_padding = any(padding) or ceil_mode_d or ceil_mode_h or ceil_mode_w

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

    d_window_size, h_window_size, w_window_size = (
        max(
            max(d // stride[i] - max(0, (d - kernel_size[i]) // stride[i]), 1)
            for d in range(kernel_size[i] * 2)
        )
        for i in range(3)
    )

    window_size = d_window_size * h_window_size * w_window_size
    if window_size > 125:
        # Kernel size too big. Results in hard-to-optimize Triton code.
        return fallback_avg_pool3d_backward(
            grad_output,
            x,
            kernel_size,
            stride,
            padding,
            ceil_mode,
            count_include_pad,
            divisor_override,
        )

    def compute_pool_size_without_padding(pd, ph, pw):
        stride_d, stride_h, stride_w = (ops.constant(s, torch.int32) for s in stride)
        pad_d, pad_h, pad_w = (ops.constant(p, torch.int32) for p in padding)
        kernel_d, kernel_h, kernel_w = (
            ops.constant(k, torch.int32) for k in kernel_size
        )

        dstart, hstart, wstart = (
            ops.sub(ops.mul(p, s), pad)
            for p, s, pad in zip(
                [pd, ph, pw], [stride_d, stride_h, stride_w], [pad_d, pad_h, pad_w]
            )
        )
        dend, hend, wend = (
            ops.minimum(
                ops.add(start, k), ops.add(ops.index_expr(dim, torch.int32), pad)
            )
            for start, k, dim, pad in zip(
                [dstart, hstart, wstart],
                [kernel_d, kernel_h, kernel_w],
                [depth, height, width],
                [pad_d, pad_h, pad_w],
            )
        )
        dstart, hstart, wstart = (
            ops.maximum(start, ops.constant(0, torch.int32))
            for start in [dstart, hstart, wstart]
        )
        dend, hend, wend = (
            ops.minimum(end, ops.index_expr(dim, torch.int32))
            for end, dim in zip([dend, hend, wend], [depth, height, width])
        )
        divide_factor = ops.mul(
            ops.mul(ops.sub(dend, dstart), ops.sub(hend, hstart)), ops.sub(wend, wstart)
        )
        return divide_factor

    def fn(idx):
        *prefix, d, h, w = idx
        d, h, w = (v + pad for v, pad in zip([d, h, w], padding))

        pdstart, phstart, pwstart = (
            ops.index_expr(FloorDiv(v - k + s, s), torch.int32)
            for v, k, s in zip([d, h, w], kernel_size, stride)
        )

        pdend, phend, pwend = (
            ops.index_expr(FloorDiv(v, s) + 1, torch.int32)
            for v, s in zip([d, h, w], stride)
        )

        pdstart, phstart, pwstart = (
            ops.maximum(pstart, ops.constant(0, torch.int32))
            for pstart in [pdstart, phstart, pwstart]
        )
        pdend, phend, pwend = (
            ops.minimum(pend, ops.index_expr(pooled_dim, torch.int32))
            for pend, pooled_dim in zip(
                [pdend, phend, pwend], [pooled_depth, pooled_height, pooled_width]
            )
        )

        gradient = None
        # Iterate over the 3D region to accumulate gradients
        for pd_ in range(d_window_size):
            for ph_ in range(h_window_size):
                for pw_ in range(w_window_size):
                    pd, ph, pw = (
                        ops.add(pstart, ops.constant(p_, torch.int32))
                        for pstart, p_ in zip(
                            [pdstart, phstart, pwstart], [pd_, ph_, pw_]
                        )
                    )

                    if divisor_override is not None:
                        scale = divisor_override
                    elif count_include_pad or not had_padding:
                        scale = kernel_size[0] * kernel_size[1] * kernel_size[2]
                    else:
                        scale = compute_pool_size_without_padding(pd, ph, pw)

                    part = ops.truediv(
                        grad_loader(
                            [
                                *prefix,
                                ops.indirect_indexing(
                                    ops.minimum(
                                        pd, ops.sub(pdend, ops.constant(1, torch.int32))
                                    ),
                                    pooled_depth,
                                    check=False,
                                ),
                                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.and_(ops.lt(pd, pdend), 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(OrderedSet(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 = OrderedSet[int](_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.S.One
    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: ReductionType, 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,  # type: ignore[attr-defined]
            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)
    axis = _validate_dim(x, axis)

    return dict(
        device=x.get_device(),
        dtypes=(x.get_dtype(),),
        inner_fns=(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(index=denom, dtype=x.get_dtype(), device=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(index=denom, dtype=x.get_dtype(), device=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()
        # In AOTI, module parameters and buffers are not lifted as graph inputs
        or changed_data.is_module_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.MutationLayoutSHOULDREMOVE.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):
    if dst is src:
        # dst.copy_(dst) can happen from the reinplacing pass
        return dst
    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)


def get_constant_value(x: ir.IRNode) -> Optional[ir.Constant]:
    """Try convert an arbitrary IR node into an ir.Constant value"""

    # First try unwrapping the IRNode to see if it is already an ir.Constant
    # Optional step, but avoids unnecessary inner_fn evaluation.
    if isinstance(x, ir.MutableBox):
        return get_constant_value(x.data)
    if isinstance(x, ir.BaseView):
        return get_constant_value(x.unwrap_view())
    if isinstance(x, ir.Constant):
        return x

    # If the unwrapped node is not an ir.Constant, try evaluating inner_fn
    # to see if the returned value is from an `ops.constant` call
    if not isinstance(x, ir.Loops):
        return None

    handler = torch._inductor.ops_handler.ExtractConstantsHandler(x.get_device())
    with (
        V.set_ops_handler(handler),
        patch.object(ir.FlexibleLayout, "allow_indexing", True),
    ):
        out = x.inner_fn(*x.inner_fn_args())

    assert isinstance(out, torch._inductor.virtualized.OpsValue)
    if isinstance(out.value, ir.Constant):
        return out.value
    return None


# 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)

    if (divisor := get_constant_value(b)) is not None:
        # Replace divide by constant with multiply by reciprocal
        if divisor.value == 0:
            reciprocal = math.copysign(float("inf"), divisor.value)
        else:
            reciprocal = 1.0 / divisor.value
        return mul(a, reciprocal)

    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.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)
fallback_logcumsumexp = fallback_handler(aten.logcumsumexp.default)
fallback_cummax = fallback_handler(aten.cummax.default)
fallback_cummin = fallback_handler(aten.cummin.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

    if len(x.get_size()) == 0:
        assert axis in [0, -1]
        dtype = dtype or x.get_dtype()
        return to_dtype(x, dtype, copy=True)

    def combine_fn(a_tuple, b_tuple):
        (a,) = a_tuple
        (b,) = b_tuple
        return (ops.add(a, b),)

    kwargs = _make_scan_inner(x, axis=axis, dtype=dtype)
    (result,) = ir.Scan.create(**kwargs, combine_fn=combine_fn)
    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

    if len(x.get_size()) == 0:
        assert axis in [0, -1]
        dtype = dtype or x.get_dtype()
        return to_dtype(x, dtype, copy=True)

    def combine_fn(a_tuple, b_tuple):
        (a,) = a_tuple
        (b,) = b_tuple
        return (ops.mul(a, b),)

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


@register_lowering(aten.logcumsumexp)
def logcumsumexp(x, dim):
    def log_add_exp_helper(a_tuple, b_tuple):
        (a,) = a_tuple
        (b,) = b_tuple
        min_v = ops.minimum(a, b)
        max_v = ops.maximum(a, b)
        mask = (min_v != max_v) | (~ops.isinf(min_v))
        return (ops.where(mask, ops.log1p(ops.exp(min_v - max_v)) + max_v, a),)

    dtype = x.get_dtype()
    if len(x.get_size()) == 0:
        assert dim in [0, -1]
        return clone(x)

    kwargs = _make_scan_inner(x, axis=dim, dtype=dtype)
    (result,) = ir.Scan.create(**kwargs, combine_fn=log_add_exp_helper)
    if result is None:
        return fallback_logcumsumexp(x, dim=dim)
    return result


@register_lowering(aten.cummax, type_promotion_kind=None)
def cummax(x, axis=None):
    if len(x.get_size()) == 0:
        assert axis in [0, -1]
        return clone(x), empty_like(x, dtype=torch.int64)

    dtype = x.get_dtype()
    combine_fn = ir.get_reduction_combine_fn(
        "argmax", dtype=dtype, arg_break_ties_left=False
    )

    kwargs = _make_scan_inner(x, axis=axis, dtype=dtype)
    kwargs["dtypes"] = (dtype, torch.int64)
    kwargs["inner_fns"] = (x.make_loader(), lambda _: "rindex")
    values, indices = ir.Scan.create(**kwargs, combine_fn=combine_fn)  # type: ignore[arg-type]
    if values is None:
        return fallback_cummax(x, dim=axis)
    return values, indices


@register_lowering(aten.cummin, type_promotion_kind=None)
def cummin(x, axis=None):
    if len(x.get_size()) == 0:
        assert axis in [0, -1]
        return clone(x), empty_like(x, dtype=torch.int64)

    dtype = x.get_dtype()
    combine_fn = ir.get_reduction_combine_fn(
        "argmin", dtype=dtype, arg_break_ties_left=False
    )

    kwargs = _make_scan_inner(x, axis=axis, dtype=dtype)
    kwargs["dtypes"] = (dtype, torch.int64)
    kwargs["inner_fns"] = (x.make_loader(), lambda _: "rindex")
    values, indices = ir.Scan.create(**kwargs, combine_fn=combine_fn)  # type: ignore[arg-type]
    if values is None:
        return fallback_cummin(x, dim=axis)
    return values, indices


@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"
)

sort_fallback = fallback_handler(aten.sort.stable, add_to_fallback_set=False)


@register_lowering(aten.sort.stable, type_promotion_kind=None)
def sort_stable(x, *, stable=None, dim=-1, descending=False):
    if stable is None:
        stable = False

    shape = x.get_size()
    device = x.get_device()
    dim = canonicalize_dim(len(shape), dim)
    if len(shape) == 0:
        return clone(x), _full(0, device, torch.int64, shape)

    dim_size = shape[dim] if len(shape) else 1
    if not V.graph.sizevars.statically_known_lt(dim_size, torch.iinfo(torch.int16).max):
        return sort_fallback(x, stable=stable, dim=dim, descending=descending)

    indices = iota(
        dim_size, start=0, step=1, dtype=torch.int16, device=device, requires_grad=False
    )
    view_shape = [1] * len(shape)
    if len(shape):
        view_shape[dim] = dim_size
    indices = view(indices, view_shape)
    indices = expand(indices, shape)

    values, indices = ir.Sort.create(
        device=device,
        dtypes=(x.dtype, indices.dtype),
        inner_fns=(x.make_loader(), indices.make_loader()),
        size=shape,
        axis=dim,
        stable=stable,
        descending=descending,
    )
    if values is None:
        return sort_fallback(x, stable=stable, dim=dim, descending=descending)

    assert indices is not None
    return values, to_dtype(indices, torch.int64)


@register_lowering(aten.sort.default, type_promotion_kind=None)
def sort(x, dim=-1, descending=False):
    return sort_stable(x, stable=False, dim=dim, descending=descending)


def register_pointwise_numeric(op, name=None, triton_fallback=None):
    return register_pointwise(
        op,
        name=name,
        type_promotion_kind=ELEMENTWISE_TYPE_PROMOTION_KIND.INT_TO_FLOAT,
        triton_fallback=triton_fallback,
    )


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,
    )


rsqrt = register_pointwise_numeric(aten.rsqrt)
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)
abs = register_pointwise(aten.abs)
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.log2)
register_pointwise_numeric(aten.nextafter)

from .codegen.common import BackendFeature, pointwise_overrides_data


def _get_pointwise_overrides(ns, name):
    data = pointwise_overrides_data[name]
    op = getattr(ns, data.name, None)
    if op is None:
        return

    def make_triton_fallback(op):
        if data.triton is None:
            return fallback_handler(op)

    if isinstance(op, torch._ops.OpOverloadPacket):
        for olname in op.overloads():
            ol = getattr(op, olname)
            yield ol, data.type_promotion_kind, make_triton_fallback(ol)
    else:
        yield op, data.type_promotion_kind, make_triton_fallback(op)


for name in pointwise_overrides_data:
    for op, type_promotion_kind, triton_fallback in _get_pointwise_overrides(
        aten, name
    ):
        register_pointwise(
            op,
            name=name,
            type_promotion_kind=type_promotion_kind,
            triton_fallback=triton_fallback,
        )

    for op, type_promotion_kind, triton_fallback in _get_pointwise_overrides(
        prims, name
    ):
        register_pointwise(
            op,
            name=name,
            type_promotion_kind=type_promotion_kind,
            triton_fallback=triton_fallback,
        )


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)
register_foreach_pointwise(aten._foreach_mul.Tensor, 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.List, pow)
register_foreach_pointwise(aten._foreach_pow.ScalarAndTensor, pow)
foreach_div_list = register_foreach_pointwise(aten._foreach_div.List, div)
register_foreach_pointwise(aten._foreach_div.Tensor, div)
foreach_div_scalar = register_foreach_pointwise(aten._foreach_div.Scalar, div)
register_foreach_pointwise(aten._foreach_sqrt, sqrt)
register_foreach_pointwise(aten._foreach_rsqrt, rsqrt)
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=None, max=None):
    return None


@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)  # type: ignore[arg-type]


@register_lowering(torch.sym_sum)
def sym_sum(args):
    return sympy.Add(*args)


@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.resize_storage_bytes_)
def resize_storage_bytes_(variable, new_size):
    variable.realize()
    ir.ResizeStorageBytes(variable, new_size)
    return variable


@register_lowering(torch.ops.aten.set_.source_Tensor)
def set__source_tensor(self, source_tensor):
    self.realize()
    source_tensor.realize()
    return TensorBox.create(ir.SetSourceTensorKernel(self, source_tensor))


if hasattr(torch.ops.fsdp, "copy_"):

    @register_lowering(torch.ops.fsdp.copy_.default)
    def fsdp_copy_(dst, src):
        if dst is src:
            # dst.copy_(dst) can happen from the reinplacing pass
            return dst
        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)


@register_lowering(torch.ops.aten.resize)
def resize(x, size, *, memory_format=None):
    assert isinstance(x, TensorBox)
    assert isinstance(size, (list, tuple))

    if memory_format is None:
        memory_format = torch.contiguous_format
    if memory_format == torch.preserve_format:
        raise RuntimeError(f"unsupported memory format: {memory_format}")

    if memory_format == torch.channels_last:
        assert len(size) == 4
    if memory_format == torch.channels_last_3d:
        assert len(size) == 5

    old_numel = x.get_numel()
    dtype = x.get_dtype()
    device = x.get_device_or_error()

    if isinstance(x.data, ir.BaseView):
        x.data = x.data.unwrap_view()

    if (
        torch.are_deterministic_algorithms_enabled()
        and torch.utils.deterministic.fill_uninitialized_memory  # type: ignore[attr-defined]
    ):
        if is_float_dtype(dtype):
            uninitalized_val = float("nan")
        elif is_integer_dtype(dtype):
            uninitalized_val = torch.iinfo(dtype).max
        else:
            uninitalized_val = True
    else:
        # using zero as that is what empty does
        uninitalized_val = 0.0

    if V.graph.sizevars.statically_known_equals(old_numel, 0):  # type: ignore[arg-type]
        return full(size, uninitalized_val, dtype=dtype, device=device)

    x_flat = as_strided(
        x,
        [
            old_numel,
        ],
        [
            1,
        ],
    )
    flat_loader = x_flat.make_loader()
    out_stride = ir.FlexibleLayout.stride_ordered_for_memory_format(size, memory_format)
    out_indexer = ir.FixedLayout(device, dtype, size, out_stride).make_indexer()

    def inner_fn(idx):
        flat_index = out_indexer(idx)
        flat_index_expr = ops.index_expr(flat_index, torch.int64)
        limit = ops.index_expr(old_numel, torch.int64)
        mask = ops.lt(flat_index_expr, limit)
        return ops.masked(mask, lambda: flat_loader([flat_index]), uninitalized_val)

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


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,
    constant_args_idx,
    grid,
    tma_descriptor_metadata,
    kwargs,
):
    from torch._higher_order_ops.triton_kernel_wrap import kernel_side_table

    constant_args = kernel_side_table.get_constant_args(constant_args_idx)
    ir.UserDefinedTritonKernel(
        kernel_idx=kernel_idx,
        grid=grid,
        tma_descriptor_metadata=tma_descriptor_metadata,
        kernel_args={**kwargs, **constant_args},
    )
    return {key: val for key, val in kwargs.items() if isinstance(val, TensorBox)}


@register_lowering(torch.ops.higher_order.cond, type_promotion_kind=None)
def cond(pred, true_fn, false_fn, operands):
    if any(isinstance(x, IRNode) and is_triton(x) for x in [pred, *operands]):
        msg = "control flow operator: torch.cond."
        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

    result = ir.Conditional.create(pred, true_fn, false_fn, operands)
    return list(map(TensorBox.create, result))


@register_lowering(torch.ops.higher_order.while_loop, type_promotion_kind=None)
def while_loop(cond_fn, body_fn, carried_inputs, additional_inputs):
    if any(
        isinstance(x, IRNode) and is_triton(x)
        for x in carried_inputs + additional_inputs
    ):
        msg = "control flow operator: torch.while_loop."
        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

    result = ir.WhileLoop.create(cond_fn, body_fn, carried_inputs, additional_inputs)
    return list(map(TensorBox.create, result))


@register_lowering(torch.ops.higher_order.invoke_subgraph, type_promotion_kind=None)
def invoke_subgraph(subgraph_fn: ir.Subgraph, identifier: str, operands):
    result = ir.InvokeSubgraph.create(subgraph_fn, operands)
    return list(map(TensorBox.create, result))


@register_lowering(torch._higher_order_ops.invoke_quant, type_promotion_kind=None)
def invoke_quant_tracer(subgraph_fn: ir.Subgraph, *operands, scheme=None):
    output = None
    quant_options = V.graph.current_node.meta.get("quant_options", None)
    assert quant_options is not None

    for i, node in enumerate(subgraph_fn.graph_module.graph.nodes):
        if node.op == "placeholder":
            V.graph.env[node] = operands[i]
            continue
        # todo getattr
        elif node.op == "output":
            args, kwargs = V.graph.fetch_args_kwargs_from_env(node)

            for v in itertools.chain(args, kwargs.values()):
                v.realize()

                if quant_options.codegen_low_precision:
                    V.graph.low_precision_codegen_ops.add(v.get_operation_name())

                V.graph.invoke_quant_ops.add(v.get_operation_name())

            output = torch.fx.Interpreter.output(V.graph, node, args, kwargs)
        else:
            V.graph.env[node] = V.graph.run_node(node)

    return output


@register_lowering(associative_scan_op, type_promotion_kind=None)
def associative_scan(
    combine_fn: ir.Subgraph, xs, additional_inputs: tuple[torch.Tensor]
):
    from .subgraph_lowering import InputDescriptor, lower_pointwise_subgraph

    if len(additional_inputs) > 0:
        raise RuntimeError(
            "Unable to generate code for associative_scan op, because there are lifted arguments"
        )

    subgraph_inputs = [
        InputDescriptor(dtype=x.get_dtype(), device=x.get_device())
        for x in itertools.chain(xs, xs)
    ]
    lowered_combine_fn = lower_pointwise_subgraph(combine_fn, subgraph_inputs)  # type: ignore[var-annotated]

    def wrapped_combine_fn(lhs, rhs):
        return lowered_combine_fn(
            *pytree.tree_leaves(lhs),
            *pytree.tree_leaves(rhs),
        )

    kwargs = _make_scan_inner(xs[0], axis=0, dtype=None)
    kwargs["dtypes"] = tuple(x.get_dtype() for x in xs)
    kwargs["inner_fns"] = tuple(x.make_loader() for x in xs)
    result = ir.Scan.create(
        combine_fn=wrapped_combine_fn,
        can_fallback_to_aten=False,
        **kwargs,
    )
    if result[0] is None:
        raise RuntimeError("Unable to generate code for associative_scan op")
    return result


@register_lowering(torch.ops.prims._sink_tokens.default)
def _sink_tokens(tokens):
    return None


@register_lowering(torch.ops.higher_order.with_effects, type_promotion_kind=None)
def with_effects(token, op, *args, **kwargs):
    result = ir.EffectfulKernel.create(op, *args, **kwargs)

    from torch._higher_order_ops.effects import get_effect_key

    effect_type = get_effect_key(op, args, kwargs)
    assert effect_type is not None
    effectful_kernel = V.graph.effectful_ops[effect_type]

    if result is None:
        return (effectful_kernel,)

    result = pytree.tree_map_only(ir.MultiOutput, TensorBox.create, result)
    if not isinstance(result, (list, tuple)):
        return (effectful_kernel, result)
    else:
        return (effectful_kernel, *result)


from .comm_lowering import register_comm_lowerings


register_comm_lowerings()


@register_lowering(inductor_prims.prepare_softmax_online, type_promotion_kind=None)
def prepare_softmax_online(x, dim):
    """
    Lowering inductor_prims.prepare_softmax_online to compute max/sum in one pass if no split is needed.
    """
    kwargs = _make_reduction_inner(
        x, axis=dim, keepdims=True, dtype=None, override_return_dtype=None
    )

    reduction_ranges = kwargs["reduction_ranges"]
    rnumel = V.graph.sizevars.simplify(sympy_product(reduction_ranges))
    hint, num_split = ir.Reduction.num_splits(
        **kwargs,
        reduction_type="online_softmax_reduce",  # type: ignore[arg-type]
        reduction_numel=rnumel,
    )

    if (
        num_split == 1
        and V.graph.sizevars.size_hint(rnumel) >= config.unroll_reductions_threshold
    ):
        max_tensor, sum_tensor = OnlineSoftmaxReduction.create(
            input_node=x, num_output=2, reduction_hint=hint, **kwargs
        )
        return max_tensor, sum_tensor
    else:
        # Note: [Split online_softmax_reduce]
        # We don't split reduction for online_softmax_reduce for now.
        # On one hand, supporting split reduction makes things complex since
        # the splitted out reuctions requires 2 inputs rather than one.
        # On the other hand, during training the online_softmax_reduce should
        # usually don't requires a split due to large batch size
        # (more specifically batch size times sequence length).
        # We should support split reduction if we find legit use cases to
        # motivate the work.
        #
        # TODO: does inference need split online_softmax_reduce?

        warnings.warn(
            textwrap.dedent(
                """
            Online softmax is disabled on the fly since Inductor decides to
            split the reduction. Cut an issue to PyTorch if this is an
            important use case and you want to speed it up with online
            softmax.
            """
            )
        )
        amax = reduce_amax(x, dim, keepdims=True)
        exp = lowerings[aten.exp](sub(x, amax))
        xsum = sum_(exp, dim, keepdims=True)
        return amax, xsum


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


import_submodule(kernel)

from . import quantized_lowerings


quantized_lowerings.register_quantized_ops()
quantized_lowerings.register_woq_mm_ops()

from . import mkldnn_lowerings


mkldnn_lowerings.register_onednn_fusion_ops()

from . import jagged_lowerings


jagged_lowerings.register_jagged_ops()


@contextlib.contextmanager
def force_fallback(op: torch._ops.OpOverload):
    """
    A context manager to force fallback an op. Used in unit test
    for FallbackKernel.
    """
    assert isinstance(op, torch._ops.OpOverload), (
        "Only OpOverload to make the clean up easier"
    )
    old_handler = lowerings.get(op)
    try:
        register_lowering(op)(fallback_handler(op))
        yield
    finally:
        if old_handler:
            lowerings[op] = old_handler
        else:
            lowerings.pop(op)