import collections
import contextlib
import dataclasses
import functools
import itertools
import logging
import re
import textwrap
import traceback
from contextlib import nullcontext
from enum import Enum
from functools import partial
from inspect import signature
from typing import (
    Any,
    Callable,
    ClassVar,
    Dict,
    List,
    Optional,
    Sequence,
    Set,
    Tuple,
    Union,
)
from unittest.mock import patch

import sympy
from sympy import Expr, Integer

import torch._logging

import torch.fx
import torch.utils._pytree as pytree
from torch._dynamo.utils import identity
from torch._prims_common import (
    compute_required_storage_length,
    is_boolean_dtype,
    is_float_dtype,
    make_channels_last_strides_for,
    make_contiguous_strides_for,
)
from torch.fx.operator_schemas import get_signature_for_torch_op
from torch.utils._sympy.functions import CleanDiv, FloorDiv, ModularIndexing

from . import config, dependencies
from .codegen.common import index_prevent_reordering
from .cuda_properties import get_device_properties
from .dependencies import extract_read_writes, var_builder
from .utils import (
    argsort,
    cache_on_self,
    convert_shape_to_inductor,
    convert_shape_to_symint,
    developer_warning,
    get_kernel_metadata,
    pad_listlike,
    sympy_dot,
    sympy_product,
    sympy_subs,
    sympy_symbol,
    try_find_schema,
)
from .virtualized import ops, V

log = logging.getLogger(__name__)
indent = functools.partial(textwrap.indent, prefix="  ")
aten = torch.ops.aten

""" [Note: Inductor IR]

Inductor's IR is produced by executing 'lowering' code (see lowering.py).  Each
lowering is registered to a particular aten operator, and expects inputs that
correspond to the aten schema.  However, in place of torch Tensor inputs, lowerings
expect Inductor TensorBox inputs.

TensorBox IR represents torch tensors.  Tensors are sometimes single objects owning
storage, and sometimes views of another Tensor's storage.  Mutating tensor operations
(such as add_()) affect the underlying storage and any associated views.  Other operations
(such as .t_()) update metadata about the current view but don't modify the underlying storage.

To model this in Inductor, the IR distinguishes between TensorBox, View, StorageBox and Buffer.

TensorBox is the top level IR construct that any lowering should produce and maps to a torch.Tensor
output from an operation.  But just as torch.Tensors take different forms, TensorBox IR can
reference View IR or directly reference StorageBox IRs.

Some Inductor lowerings produce new sets of 'Box'es, while others (such as .t() or other view ops)
may take an existing TensorBox and point it to a new underlying View IR.

Tensors that directly own storage are represented as a chain of:
TensorBox -> StorageBox -> Buffer
where Buffer is a simple (1D) allocation, and StorageBox introduces the concept of a Layout.

If you mutate the data of such a tensor, we swing the StorageBox pointer to point to a new buffer
(leaving the old buffer unmodified and functionalizing the operation).

Tensors backed by views add one more indirection to the IR.
TensorBox -> View -> StorageBox -> Buffer
In these cases, the underlying StorageBox/Buffer will be shared with the pre-view TensorBox.
"""


def validate_ir(node_or_nodes):
    def _check_tensorbox(nodes):
        # Could expand this to check deeper properties
        # (e.g. TensorBox points to View or StorageBox)
        if isinstance(nodes, (list, tuple)):
            for node in nodes:
                _check_tensorbox(node)
        else:
            assert isinstance(
                nodes,
                (
                    torch._inductor.ir.ExpandView,
                    DynamicScalar,
                    TensorBox,
                    sympy.Symbol,
                    sympy.logic.boolalg.Boolean,
                    Expr,
                    torch._inductor.ir.ExpandView,
                ),
            ), f"Found {type(nodes)}, which is not a supported top level IR node. See [Note: Inductor IR]"

    # Be picky about the accepted data structure (don't use pytree here)
    _check_tensorbox(node_or_nodes)


def ops_wrapper(name):
    assert isinstance(name, str)

    def fn(*args, **kwargs):
        return getattr(ops, name)(*args, **kwargs)

    return fn


def inverse_reorder(order):
    inv_order = dict(zip(order, range(len(order))))

    def reindex(index):
        assert len(index) == len(inv_order)
        return [index[inv_order[i]] for i in range(len(index))]

    return reindex


def same_reorder(order):
    def reindex(index):
        assert len(index) == len(order)
        return [index[order[i]] for i in range(len(index))]

    return reindex


def fuse_reindexing(reindex1, reindex2):
    def reindex(index):
        return reindex1(reindex2(index))

    return reindex


NHWC_STRIDE_ORDER = [3, 0, 2, 1]


def stride_order2fill_order(order):
    """
    Convert stride order to fill order
    For channel last format,
    stride order = [3, 0, 2, 1] and fill order = [1, 3, 2, 0]
    """
    lookup = {pos: idx for idx, pos in enumerate(order)}
    fill_order = [lookup[i] for i in range(len(order))]
    return fill_order


def get_stride_order(seq: Sequence[int]):
    """
    Convert strides to stride order
    """
    sorted_idx: List[int] = argsort(seq)
    out = [None for _ in range(len(seq))]
    for i, elem in enumerate(sorted_idx):
        out[elem] = i
    return out


def ir_node_to_tensor(x, guard_shape=True):
    if x is None:
        return None

    if not guard_shape:
        shape_fn = V.graph.sizevars.size_hint
    else:
        shape_fn = identity
    size = [shape_fn(s) for s in x.get_size()]
    if is_storage_and_layout(x):
        stride = [shape_fn(s) for s in x.get_layout().stride]
    else:
        stride = make_contiguous_strides_for(size)
    dtype = x.get_dtype()
    device = x.get_device()
    size = convert_shape_to_symint(size)
    stride = convert_shape_to_symint(stride)
    t = torch.empty_strided(
        size=size, stride=stride, dtype=dtype, device=device
    ).zero_()
    return t


class OptionalAttr:
    def __init__(self):
        self.name = "optional_attr"

    def __repr__(self):
        return self.name


class OptionalString(OptionalAttr):
    def __init__(self):
        self.name = "optional_string"


class OptionalList(OptionalAttr):
    def __init__(self):
        self.name = "optional_list"


class OptionalScalar(OptionalAttr):
    def __init__(self):
        self.name = "optional_scalar"


class OptionalLayout(OptionalAttr):
    def __init__(self):
        self.name = "optional_layout"


class OptionalTensor(OptionalAttr):
    def __init__(self):
        self.name = "optional_tensor"


default_value_map = {"Optional[Layout]": OptionalLayout}


def may_convert_to_optional(optional_value, value):
    return optional_value if not value and V.graph.cpp_wrapper else value


def get_device_type(x):
    if getattr(x, "get_device", None):
        return get_device_type(x.get_device())
    if isinstance(x, torch.device):
        return x.type
    return None


def is_triton(x):
    return get_device_type(x) == "cuda"


def is_cpu(x):
    return get_device_type(x) == "cpu"


@dataclasses.dataclass
class IRNode:
    _current_origins: ClassVar[Set[Any]] = set()

    @staticmethod
    @contextlib.contextmanager
    def current_origins(origins: Set[torch.fx.Node]):
        old = IRNode._current_origins
        IRNode._current_origins = old | origins
        try:
            yield
        finally:
            IRNode._current_origins = old

    def __post_init__(self):
        self.origins = set(self._current_origins)
        self.traceback = traceback.format_stack() if config.debug_ir_traceback else None

    def get_traceback(self):
        return self.traceback

    def common_repr(self):
        origins = f"origins={getattr(self, 'origins', '')}"
        if len(origins) > 64:
            # this can get *very* long
            origins = f"{origins[:61]}..."
        return [origins]

    def str_helper(self, lines):
        lines = lines + self.common_repr()
        lines = indent(",\n".join(map(str, lines)))
        return f"{type(self).__name__}(\n{lines}\n)"

    def is_user_of(self, name):
        return name in self.get_read_names()

    @cache_on_self
    def get_read_names(self):
        return {dep.name for dep in self.get_reads()}

    def get_numel(self):
        return sympy_product(self.get_size())

    def is_zero_elements(self):
        return V.graph.sizevars.is_expr_static_and_true(sympy.Eq(self.get_numel(), 0))

    def realize(self):
        """
        If the IRNode refers to data which has not been materialized (e.g.,
        it is a Pointwise/Reduction that could potentially have more
        compute fused into it), realize the IRNode into physical memory,
        ending the possibility of fusing into it, but allowing, e.g., multiple
        users to access the data without having to recompute.

        Check StorageBox.realize for a particularly notable implementation.

        TODO(ezyang): I think, in principle, every IRNode should have an
        implementation of this, and most of the time no-op is OK, but you
        really do have to audit each IRNode for this, so for now, raise
        an error if it's not implemented.  Note that some code in graph.py
        will catch this thrown error and suppress it with a warning.
        """
        raise NotImplementedError(f"realize NYI on {type(self)}")


@dataclasses.dataclass
class Loops(IRNode):
    device: torch.device
    dtype: torch.dtype
    inner_fn: Callable[..., Any]
    ranges: List[Expr]

    def __str__(self, names=("ranges",)):
        return self.str_helper(
            [
                f"'{self.device.type}'",
                str(self.dtype),
                self.inner_fn_str(),
            ]
            + [f"{name}={getattr(self, name)}" for name in names]
            + [f"origin_node={self.origin_node!r}"]
        )

    def __post_init__(self):
        super().__post_init__()
        self.origin_node = None

    __repr__ = __str__

    def get_dtype(self):
        return self.dtype

    def get_device(self):
        return self.device

    def get_origin_node(self):
        return self.origin_node

    def get_size(self):
        return self.ranges

    def is_extern(self):
        return False

    @classmethod
    def create(cls, *args, **kwargs):
        origin_node = kwargs.pop("origin_node", None)
        tb = kwargs.pop("traceback", None)
        r = cls(*args, **kwargs)
        r.origin_node = origin_node
        r.traceback = (
            tb or traceback.format_stack() if config.debug_ir_traceback else None
        )
        return TensorBox.create(r)

    @staticmethod
    def _index(ranges, prefix="i"):
        return [
            sympy.Integer(0) if s == 1 else sympy_symbol(f"{prefix}{n}")
            for n, s in enumerate(ranges)
        ]

    @cache_on_self
    def inner_fn_str_len(self):
        return len(self.inner_fn_str())

    def inner_fn_str(self):
        index = self._index(self.ranges)
        return V.KernelFormatterHandler.ir_to_string(self.inner_fn, index)

    def get_reads(self):
        with patch.object(FlexibleLayout, "allow_indexing", True):
            if self.get_reduction_type():
                return extract_read_writes(
                    self.make_loader(),
                    self.get_size(),
                    self.get_reduction_size(),
                ).reads
            else:
                return extract_read_writes(
                    self.make_loader(),
                    self.get_size(),
                ).reads


def nop_loader_fn(idx, *, dtype):
    if dtype.is_floating_point:
        return ops.constant(float("nan"), dtype)
    else:
        return ops.constant(0, dtype)


class Pointwise(Loops):
    def make_loader(self):
        # Make zero-element loops into a no-op
        if self.is_zero_elements():
            return partial(nop_loader_fn, dtype=self.dtype)

        return self.inner_fn

    def get_reduction_size(self):
        return []

    def get_reduction_type(self):
        return None

    def store_output(self, output_name, indexer, vars):
        loader = self.make_loader()
        return ops.store(output_name, indexer(vars), loader(vars))

    def constant_to_device(self, device):
        """Move this to a given device. Requires that all reads are to constants."""
        loader = self.make_loader()
        loader = patch.object(ConstantBuffer, "override_device", device)(loader)
        return Pointwise(device, self.dtype, loader, self.ranges)


@dataclasses.dataclass
class Scatter(Pointwise):
    output_indexer: Callable[[List[Expr]], Expr]
    scatter_mode: Optional[str] = None

    def constant_to_device(self, device):
        """Move this to a given device. Requires that all reads are to constants."""
        loader = self.make_loader()
        loader = patch.object(ConstantBuffer, "override_device", device)(loader)
        return Scatter(
            device,
            self.dtype,
            loader,
            self.ranges,
            self.output_indexer,
            self.scatter_mode,
        )

    def store_output(self, output_name, indexer, vars):
        loader = self.make_loader()
        return ops.store(
            output_name,
            indexer(self.output_indexer(vars)),
            loader(vars),
            mode=self.scatter_mode,
        )


class ReductionHint(Enum):
    INNER = 0
    OUTER = 1
    OUTER_TINY = 2
    DEFAULT = 3


class TileHint(Enum):
    SQUARE = 0
    DEFAULT = 1


REDUCTION_COMBINE_FN = {
    "any": ops_wrapper("logical_or"),
    "max": ops_wrapper("maximum"),
    "min": ops_wrapper("minimum"),
    "prod": ops_wrapper("mul"),
    "sum": ops_wrapper("add"),
    "xor_sum": ops_wrapper("bitwise_xor"),
}


def get_reduction_combine_fn(reduction_type, dtype):
    if reduction_type in REDUCTION_COMBINE_FN:
        combine_fn = REDUCTION_COMBINE_FN[reduction_type]
    elif reduction_type in {"argmax", "argmin"}:

        def combine_fn(a, b):
            a_value, a_index = a
            b_value, b_index = b

            if reduction_type == "argmin":
                mask = ops.lt(a_value, b_value)
            else:
                mask = ops.gt(a_value, b_value)

            equal = ops.eq(a_value, b_value)
            if is_float_dtype(dtype):
                a_isnan = ops.ne(a_value, a_value)
                b_isnan = ops.ne(b_value, b_value)
                mask = ops.logical_or(mask, ops.gt(a_isnan, b_isnan))
                equal = ops.logical_or(equal, ops.logical_and(a_isnan, b_isnan))

            mask = ops.logical_or(
                mask, ops.logical_and(equal, ops.lt(a_index, b_index))
            )
            return (
                ops.where(mask, a_value, b_value),
                ops.where(mask, a_index, b_index),
            )

    elif reduction_type == "welford_combine":

        def combine_fn(a, b):
            a_mean, a_m2, a_weight = a
            b_mean, b_m2, b_weight = b

            delta = b_mean - a_mean
            new_weight = a_weight + b_weight
            w2_over_w = b_weight / new_weight
            return (
                a_mean + delta * w2_over_w,
                a_m2 + b_m2 + delta * delta * a_weight * w2_over_w,
                new_weight,
            )

    else:
        raise NotImplementedError(f"unknown reduction_type={reduction_type}")

    return combine_fn


@dataclasses.dataclass
class Reduction(Loops):
    reduction_ranges: List[Expr]
    reduction_type: str
    # self.dtype represents the dst dtype
    src_dtype: torch.dtype
    reduction_hint: ReductionHint

    def __str__(self):
        return Loops.__str__(  # type: ignore[call-arg]
            self, names=("ranges", "reduction_ranges", "reduction_type")
        )

    def __repr__(self):
        return self.__str__()

    def get_reduction_size(self):
        return self.reduction_ranges

    def get_reduction_type(self):
        return self.reduction_type

    def store_reduction(self, output_name, indexer, vars, reduction_vars):
        value = ops.reduction(
            self.dtype,
            self.src_dtype,
            self.reduction_type,
            self.inner_fn(vars, reduction_vars),
        )
        return ops.store_reduction(output_name, indexer(vars), value)

    def index_length(self):
        return len(self.ranges) + len(self.reduction_ranges)

    def inner_fn_str(self):
        index = self._index(self.ranges)
        rindex = self._index(self.reduction_ranges, "r")
        return V.KernelFormatterHandler.ir_to_string(
            self.inner_fn,
            index,
            rindex,
        )

    def constant_to_device(self, device):
        """Move this to a given device. Requires that all reads are to constants."""
        loader = self.make_loader()
        loader = patch.object(ConstantBuffer, "override_device", device)(loader)
        return Reduction(
            device,
            self.dtype,
            loader,
            self.ranges,
            self.reduction_ranges,
            self.reduction_type,
            self.src_dtype,
            ReductionHint.DEFAULT,
        )

    @staticmethod
    def num_splits(
        device,
        dst_dtype,
        src_dtype,
        inner_fn,
        ranges,
        reduction_ranges,
        reduction_type,
        reduction_numel,
    ):
        def _is_static(x):
            return isinstance(x, (int, sympy.Integer))

        reduction_numel_hint = V.graph.sizevars.symbolic_hint(reduction_numel)
        numel_hint = V.graph.sizevars.symbolic_hint(sympy_product(ranges))

        should_split = (
            is_triton(device)
            and reduction_type
            not in {
                "argmax",
                "argmin",
            }
            and config.split_reductions
            # We don't support unbacked symints
            and _is_static(reduction_numel_hint)
            and _is_static(numel_hint)
        )
        if not should_split:
            return ReductionHint.DEFAULT, 1

        num_sm = get_device_properties(device).multi_processor_count
        min_elements_per_thread = 32
        max_elements_per_thread = 512
        threads_per_sm = 2048
        min_elements_per_device = min_elements_per_thread * num_sm * threads_per_sm
        max_elements_per_device = max_elements_per_thread * num_sm * threads_per_sm

        def inner_reduction_splits(reduction_numel_hint, numel_hint):
            # do heuristics that's close to eager mode for split inner reduction
            # we leak reduction autotune configs here, and will need to refactor to avoid this later
            num_warps = 8
            num_threads = 32 * num_warps
            if numel_hint >= 2 * num_sm:  # don't split if there are enough outputs
                return 1
            if reduction_numel_hint <= 8192:
                return 1
            if reduction_numel_hint * numel_hint <= min_elements_per_device:
                split_size = min_elements_per_thread
            elif reduction_numel_hint * numel_hint < max_elements_per_device:
                target_blocks = num_sm * threads_per_sm // (2 * num_threads)
                blocks_per_output = (target_blocks + numel_hint - 1) // numel_hint
                tmp_split_size = (
                    reduction_numel_hint + num_threads * blocks_per_output - 1
                ) // (num_threads * blocks_per_output)
                divisors = sympy.divisors(reduction_numel_hint)
                closest = min(divisors, key=lambda x: abs(x - tmp_split_size))
                if abs(closest - tmp_split_size) < 30:
                    # prefer even splits, but never smalle than min_elements_per_thread
                    split_size = max(closest, min_elements_per_thread)
                else:
                    split_size = tmp_split_size
            else:
                divisors = sympy.divisors(reduction_numel_hint)
                closest = min(divisors, key=lambda x: abs(x - max_elements_per_thread))
                if abs(closest - max_elements_per_thread) < 50:
                    # prefer even splits
                    split_size = closest
                else:
                    split_size = max_elements_per_thread
            return (reduction_numel_hint + split_size * num_threads - 1) // (
                split_size * num_threads
            )

        def outer_reduction_splits(reduction_numel_hint, numel_hint):
            # TODO the best heuristic currently has XBLOCK (corresponding to numel_hint) 128
            # extend to even smaller number of outputs
            num_warps = 8
            num_threads = num_warps * 32
            rvals_per_thread = 4  # comes from heuristics, refactor to not leak here
            xvals_per_block = 128
            xblocks = (numel_hint + xvals_per_block - 1) // xvals_per_block
            if reduction_numel_hint * numel_hint < min_elements_per_device:
                split_size = min_elements_per_thread
            elif reduction_numel_hint * numel_hint < max_elements_per_device:
                target_blocks = num_sm * threads_per_sm // (num_threads)
                target_blocks = (target_blocks + xblocks - 1) // xblocks
                tmp_split_size = (
                    reduction_numel_hint + rvals_per_thread * target_blocks - 1
                ) // (rvals_per_thread * target_blocks)
                divisors = sympy.divisors(reduction_numel_hint)
                closest = min(divisors, key=lambda x: abs(x - tmp_split_size))
                if abs(tmp_split_size - closest) < 20:
                    split_size = max(closest, min_elements_per_thread)
                else:
                    split_size = tmp_split_size
            else:
                divisors = sympy.divisors(reduction_numel_hint)
                closest = min(divisors, key=lambda x: abs(x - max_elements_per_thread))
                if abs(closest - max_elements_per_thread) < 50:
                    # prefer even splits
                    split_size = closest
                else:
                    split_size = max_elements_per_thread

            return (reduction_numel_hint + rvals_per_thread * split_size - 1) // (
                rvals_per_thread * split_size
            )

        # easy cases
        if numel_hint == 1:
            return ReductionHint.INNER, inner_reduction_splits(
                reduction_numel_hint, numel_hint
            )
        if (
            reduction_numel_hint <= min_elements_per_thread
            or numel_hint >= num_sm * 2 * 32
        ):
            return ReductionHint.DEFAULT, 1

        r = Reduction(
            device,
            dst_dtype,
            inner_fn,
            ranges,
            reduction_ranges,
            reduction_type,
            src_dtype,
            ReductionHint.DEFAULT,
        )

        def get_read_indices(r):
            cb = ComputedBuffer(
                name=None,
                layout=FlexibleLayout(
                    device=r.get_device(),
                    dtype=r.get_dtype(),
                    size=r.get_size(),
                ),
                data=r,
            )
            read_writes = cb.get_read_writes()
            # try finding the full size producer
            # TODO this will fail for something like ((1, N) * (N, 1)).sum()
            # this would also possibly be wrong for producers with the different contiguity but we hope those cases are rare
            range_vars = [
                r
                for r in read_writes.range_vars
                if isinstance(r, sympy.Expr) and not isinstance(r, sympy.Number)
            ]
            indices = []
            changed = False
            for md in sorted(read_writes.reads, key=lambda x: x.name):
                if all(r in md.index.free_symbols for r in range_vars):
                    indices.append(md.index)
                    if md.name in V.graph.name_to_buffer:
                        buf = V.graph.name_to_buffer[md.name]
                        original_stride = buf.layout.stride
                        buf.decide_layout()
                        if buf.layout.stride != original_stride:
                            changed = True
            return indices, changed

        indices, changed = get_read_indices(r)
        if changed:
            indices, _ = get_read_indices(r)

        if len(indices) == 0:
            # TODO determine splits when all inputs are broadcast
            return ReductionHint.DEFAULT, 1

        (_, reduction_vars), ranges = dependencies.index_vars_squeeze(
            r.get_size(), r.get_reduction_size()
        )
        num_outer = 0
        num_inner = 0
        for i in indices:
            i = V.graph.sizevars.simplify_with_ranges(i, ranges)
            strides = V.graph.sizevars.stride_hints(i, reduction_vars, ranges.keys())
            outer = all(s > 1 for s in strides)
            if outer:
                num_outer += 1
            else:
                num_inner += 1
        if num_inner > num_outer:
            return ReductionHint.INNER, inner_reduction_splits(
                reduction_numel_hint, numel_hint
            )
        else:
            return ReductionHint.OUTER, outer_reduction_splits(
                reduction_numel_hint, numel_hint
            )

    @staticmethod
    def _unroll_reduction_fn(inner_fn, reduction_ranges, reduction_type, src_dtype):
        """Convert inner_fn from a reduction to an pointwise"""
        reduction_ranges = [
            V.graph.sizevars.evaluate_static_shape(x) for x in reduction_ranges
        ]

        combine_fn = get_reduction_combine_fn(reduction_type, src_dtype)

        def fn(index):
            return functools.reduce(
                combine_fn,
                (
                    value_fn(index, rindex)
                    for rindex in itertools.product(
                        *[range(x) for x in reduction_ranges]
                    )
                ),
            )

        if reduction_type in ("argmin", "argmax"):
            flatten_index = FixedLayout(
                None,
                None,
                reduction_ranges,
                FlexibleLayout.contiguous_strides(reduction_ranges),
            ).make_indexer()

            def value_fn(index, rindex):
                rindex = [sympy.expand(i) for i in rindex]
                return (
                    inner_fn(index, rindex),
                    ops.index_expr(flatten_index(rindex), torch.int64),
                )

            return lambda index: fn(index)[1]
        else:
            value_fn = inner_fn
            return fn

    @classmethod
    def create(  # type: ignore[override]
        cls,
        device: torch.device,
        dst_dtype: torch.dtype,
        src_dtype: torch.dtype,
        inner_fn: Callable[..., Any],
        ranges: List[Expr],
        reduction_ranges: List[Expr],
        reduction_type: str,
        reduction_hint: ReductionHint = ReductionHint.DEFAULT,
    ):
        reduction_numel = V.graph.sizevars.simplify(sympy_product(reduction_ranges))

        if reduction_numel == 0:
            # N.B. This is a hack to generate the literal of the given type
            # Ideally, we should be fixing `def constant` in triton.py
            # but it breaks due to hardcoded dtypes in other places
            def py_cnst(val):
                return (
                    bool(val)
                    if dst_dtype == torch.bool
                    else float(val)
                    if dst_dtype.is_floating_point
                    else int(val)
                )

            rtypes_to_inits = {
                "sum": py_cnst(0),
                "xor_sum": py_cnst(0),
                "prod": py_cnst(1),
                "any": py_cnst(0),
                # "all" is desugared to `!any(!val)`
            }

            assert (
                reduction_type in rtypes_to_inits.keys()
            ), f"{reduction_type} not supported for zero-dimension tensors!"

            def const_fn(index):
                return ops.constant(rtypes_to_inits[reduction_type], dst_dtype)

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

        if reduction_numel == 1:
            # this reduction is actually a pointwise op
            if reduction_type in ("argmin", "argmax"):

                def fn(index):
                    return ops.constant(0, dst_dtype)

            else:

                def fn(index):
                    reduction_index = [sympy.Integer(0) for _ in reduction_ranges]
                    return inner_fn(index, reduction_index)

            return Pointwise.create(device, dst_dtype, fn, ranges)

        if (
            isinstance(reduction_numel, sympy.Integer)
            and V.graph.sizevars.size_hint(reduction_numel)
            < config.unroll_reductions_threshold
            and sympy_product(ranges) != 1
        ):
            return Pointwise.create(
                device,
                dst_dtype,
                cls._unroll_reduction_fn(
                    inner_fn, reduction_ranges, reduction_type, src_dtype
                ),
                ranges,
            )

        # triton doesn't support reduce to single element well, so break it up
        hint, split = cls.num_splits(
            device,
            dst_dtype,
            src_dtype,
            inner_fn,
            ranges,
            reduction_ranges,
            reduction_type,
            reduction_numel,
        )
        # intermediate reduction in split can contain complex indexing,
        # and num_splits will fail to correctly set the hint
        # reuse the passed hint if available
        if reduction_hint == ReductionHint.DEFAULT:
            reduction_hint = hint
        if split > 1:
            # triton doesn't support reduce to single element well, so break it up
            return cls.create_multilayer(
                device,
                dst_dtype,
                src_dtype,
                inner_fn,
                ranges,
                reduction_ranges,
                reduction_type,
                split,
                reduction_hint,
            )

        return TensorBox.create(
            Reduction(
                device,
                dst_dtype,
                inner_fn,
                ranges,
                reduction_ranges,
                reduction_type,
                src_dtype,
                reduction_hint,
            )
        )

    @staticmethod
    def default_accumulator(reduction_type, dtype):
        if reduction_type in {"max", "argmax"}:
            if is_float_dtype(dtype):
                return float("-inf")
            elif is_boolean_dtype(dtype):
                return 0
            else:
                return torch.iinfo(dtype).min
        if reduction_type in {"min", "argmin"}:
            if is_float_dtype(dtype):
                return float("inf")
            elif is_boolean_dtype(dtype):
                return 1
            else:
                return torch.iinfo(dtype).max

        return {
            "sum": 0,
            "prod": 1,
            "xor_sum": 0,
            "any": 0,
            "welford_reduce": (0, 0, 0),
            "welford_combine": (0, 0, 0),
        }[reduction_type]

    @staticmethod
    def default_value(reduction_type, dtype):
        if reduction_type == "welford_reduce":
            return 0
        return Reduction.default_accumulator(reduction_type, dtype)

    @staticmethod
    def _multilayer_second_step_hint(
        split: int, numel_hint: int, reduction_hint: ReductionHint
    ) -> ReductionHint:
        if split <= 512 and numel_hint <= 512 and reduction_hint == ReductionHint.OUTER:
            return ReductionHint.OUTER_TINY
        if (
            split <= 1024
            and numel_hint <= 256
            and reduction_hint == ReductionHint.OUTER
        ):
            return ReductionHint.OUTER_TINY

        return reduction_hint

    @classmethod
    def _multilayer_wrap_loader(
        cls,
        loader,
        reduction_ranges,
        reduction_numel,
        split,
        block_size,
        default,
    ):
        reindex = View.dynamic_reshape_indexer(reduction_ranges, [reduction_numel])
        need_mask = not V.graph.sizevars.is_expr_static_and_true(
            sympy.Eq(reduction_numel % split, 0)
        )

        def wrapper_fn(index, reduction_index):
            (reduction_index,) = reduction_index
            *new_index, reduction_block = index
            indices = block_size * reduction_block + reduction_index

            def body():
                return loader(new_index, reindex([indices]))

            if need_mask:
                mask = ops.lt(
                    ops.index_expr(indices, torch.int32),
                    ops.index_expr(reduction_numel, torch.int32),
                )
                return ops.masked(mask, body, default)
            else:
                return body()

        return wrapper_fn

    @classmethod
    def create_multilayer(
        cls,
        device: torch.device,
        dst_dtype: torch.dtype,
        src_dtype: torch.dtype,
        inner_fn: Callable[..., Any],
        ranges: List[Expr],
        reduction_ranges: List[Expr],
        reduction_type: str,
        split: int,
        reduction_hint: ReductionHint,
    ):
        """
        Break a large reduction up into multiple smaller reductions
        recursively
        """
        # TODO(jansel): realize the reduction so we can do dynamic indexing
        reduction_numel = sympy_product(reduction_ranges)
        block_size = FloorDiv(reduction_numel + (split - 1), split)
        default = cls.default_value(reduction_type, dst_dtype)
        wrapper_fn = cls._multilayer_wrap_loader(
            inner_fn, reduction_ranges, reduction_numel, split, block_size, default
        )

        # triton will automatically compute reductions in fp32 if reducing over fp16/bf16
        # within the kernel. keep the intermediate in fp32 so as to keep the whole reduction
        # in fp32 and not reduce precision by breaking up the kernel into multiple layers
        intermediate_dtype = (
            dst_dtype
            if dst_dtype not in (torch.float16, torch.bfloat16)
            else torch.float
        )
        intermediate = Reduction.create(
            device,
            intermediate_dtype,
            src_dtype,
            wrapper_fn,
            [*ranges, split],
            [block_size],
            reduction_type,
            reduction_hint,
        )
        intermediate.realize()
        intermediate_loader = intermediate.make_loader()

        def intermediate_fn(index, reduction_index):
            return intermediate_loader([*index, *reduction_index])

        numel_hint = V.graph.sizevars.size_hint(sympy_product(ranges))
        reduction_hint = cls._multilayer_second_step_hint(
            split, numel_hint, reduction_hint
        )
        return TensorBox.create(
            Reduction(
                device,
                dst_dtype,
                intermediate_fn,
                ranges,
                [split],
                reduction_type,
                src_dtype,
                reduction_hint,
            )
        )


def num_reduction_outputs(reduction_type):
    return 3 if "welford" in reduction_type else 1


class WelfordReduction(Reduction):
    output_index: int

    def __init__(
        self,
        device,
        dtype,
        inner_fns,
        ranges,
        reduction_ranges,
        reduction_type,
        reduction_hint,
        output_index,
    ):
        if len(inner_fns) == 1:
            loader = inner_fns[0]
        else:

            def loader(idx, reduction_idx):
                return tuple(fn(idx, reduction_idx) for fn in inner_fns)

        super().__init__(
            device,
            dtype,
            loader,
            ranges,
            reduction_ranges,
            reduction_type,
            dtype,
            reduction_hint,
        )
        self.output_index = output_index

    def store_reduction(self, output_name, indexer, vars, reduction_vars):
        values = ops.reduction(
            self.dtype,
            self.src_dtype,
            self.reduction_type,
            self.inner_fn(vars, reduction_vars),
        )
        value = values[self.output_index]
        return ops.store_reduction(output_name, indexer(vars), value)

    @classmethod
    def create(  # type: ignore[override]
        cls,
        device: torch.device,
        dtype: torch.dtype,
        inner_fns: Sequence[Callable[..., Any]],
        ranges: List[Expr],
        reduction_ranges: List[Expr],
        reduction_type: str,
        reduction_hint: ReductionHint = ReductionHint.DEFAULT,
    ):
        assert reduction_type in {"welford_reduce", "welford_combine"}

        reduction_numel = V.graph.sizevars.simplify(sympy_product(reduction_ranges))

        def const(idx, val):
            def inner_fn(idx):
                return ops.constant(val, dst_dtype)

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

        if reduction_numel == 0:
            mean = const(0)
            m2 = const(0)
            weight = const(0)
            return mean, m2, weight

        if reduction_numel == 1:

            def copy(loader):
                def inner_fn(idx):
                    reduction_index = [sympy.Integer(0) for _ in reduction_ranges]
                    return loader(idx, reduction_index)

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

            if reduction_type == "welford_reduce":
                return copy(inner_fns[0]), const(0), const(1)
            else:
                return tuple(copy(fn) for fn in inner_fns)

        # TODO: Unrolled reduction
        # if (
        #     isinstance(reduction_numel, sympy.Integer)
        #     and V.graph.sizevars.size_hint(reduction_numel)
        #     < config.unroll_reductions_threshold
        #     and sympy_product(ranges) != 1
        # ):
        #     return Pointwise.create(
        #         device,
        #         dst_dtype,
        #         cls._unroll_reduction_fn(
        #             inner_fn, reduction_ranges, reduction_type, src_dtype
        #         ),
        #         ranges,
        #     )

        # triton doesn't support reduce to single element well, so break it up
        hint, split = Reduction.num_splits(
            device,
            dtype,
            dtype,
            inner_fns[0],
            ranges,
            reduction_ranges,
            reduction_type=reduction_type,
            reduction_numel=reduction_numel,
        )
        # intermediate reduction in split can contain complex indexing,
        # and num_splits will fail to correctly set the hint
        # reuse the passed hint if available
        if reduction_hint == ReductionHint.DEFAULT:
            reduction_hint = hint
        if split > 1:
            # triton doesn't support reduce to single element well, so break it up
            return cls.create_multilayer(
                device,
                dtype,
                inner_fns,
                ranges,
                reduction_ranges,
                reduction_type,
                split,
                reduction_hint,
            )

        results = [
            TensorBox.create(
                WelfordReduction(
                    device,
                    dtype,
                    inner_fns,
                    ranges,
                    reduction_ranges,
                    reduction_type,
                    reduction_hint,
                    output_idx,
                )
            )
            for output_idx in range(3)
        ]
        for t in results:
            t.realize()
        return results

    @staticmethod
    def default_value(reduction_type, dtype):
        return (0, 0, 0)

    @classmethod
    def create_multilayer(
        cls,
        device: torch.device,
        dtype: torch.dtype,
        inner_fns: Sequence[Callable[..., Any]],
        ranges: List[Expr],
        reduction_ranges: List[Expr],
        reduction_type: str,
        split: int,
        reduction_hint: ReductionHint,
    ):
        """
        Break a large reduction up into multiple smaller reductions
        recursively
        """
        reduction_numel = sympy_product(reduction_ranges)
        need_mask = not V.graph.sizevars.is_expr_static_and_true(
            sympy.Eq(reduction_numel % split, 0)
        )

        if need_mask and reduction_type != "welford_combine":
            # If we need mask, then "welford_reduce" doesn't work because
            # masked inputs shouldn't count towards the welford weight

            def constant(idx, reduction_idx, value):
                return ops.constant(value, dtype)

            return cls.create_multilayer(
                device=device,
                dtype=dtype,
                inner_fns=(
                    inner_fns[0],
                    partial(constant, value=0),
                    partial(constant, value=1),
                ),
                ranges=ranges,
                reduction_ranges=reduction_ranges,
                reduction_type="welford_combine",
                split=split,
                reduction_hint=reduction_hint,
            )

        block_size = FloorDiv(reduction_numel + (split - 1), split)
        intermediates = WelfordReduction.create(
            device,
            dtype,
            tuple(
                cls._multilayer_wrap_loader(
                    loader,
                    reduction_ranges,
                    reduction_numel,
                    split,
                    block_size,
                    default=0,
                )
                for loader in inner_fns
            ),
            [*ranges, split],
            [block_size],
            reduction_type,
            reduction_hint,
        )
        for i in intermediates:
            i.realize()

        i_loaders = [i.make_loader() for i in intermediates]

        def intermediate_loader_fn(index, reduction_index, loader):
            return loader([*index, *reduction_index])

        numel_hint = V.graph.sizevars.size_hint(sympy_product(ranges))
        reduction_hint = cls._multilayer_second_step_hint(
            split, numel_hint, reduction_hint
        )
        return WelfordReduction.create(
            device,
            dtype,
            tuple(
                partial(intermediate_loader_fn, loader=i.make_loader())
                for i in intermediates
            ),
            ranges,
            [split],
            # welford_reduce turns one input into three outputs, which are combined with welford_combine
            "welford_combine",
            reduction_hint,
        )


def is_storage_and_layout(x):
    try:
        as_storage_and_layout(x, freeze=False)
        return True
    except NotImplementedError:
        return False


def is_contiguous_storage_and_layout(x):
    try:
        buffer, layout = as_storage_and_layout(x, freeze=False)
        return layout.is_contiguous()
    except NotImplementedError:
        return False


def as_storage_and_layout(x, freeze=True, want_contiguous=False, stride_order=None):
    """Try to simplify x into a StorageBox and a Layout"""
    if isinstance(x, TensorBox):
        return as_storage_and_layout(
            x.data,
            freeze=freeze,
            want_contiguous=want_contiguous,
            stride_order=stride_order,
        )
    if isinstance(x, StorageBox) and isinstance(x.data, Buffer):
        if freeze:
            if want_contiguous:
                x.data.freeze_layout()
                assert x.data.layout.is_contiguous()
            elif stride_order is not None:
                x.data.freeze_layout_with_stride_order(stride_order)
            else:
                x.data.decide_layout()
        return x, x.data.layout
    if isinstance(x, ReinterpretView):
        # making the base of x contiguous or stride_ordered will not necessarily make
        # the ReinterpretedView either, so dont pass along those arguments
        buffer, _ = as_storage_and_layout(
            x.data,
            freeze=freeze,
        )
        return buffer, x.layout
    raise NotImplementedError


as_contiguous_storage_and_layout = functools.partial(
    as_storage_and_layout, want_contiguous=True
)


def is_stride_order_storage_and_layout(x, stride_order):
    try:
        buffer, layout = as_storage_and_layout(x, freeze=False)
        return layout.is_stride_ordered(stride_order)
    except NotImplementedError:
        return False


@dataclasses.dataclass
class BaseView(IRNode):
    data: IRNode

    def make_reindexer(self):
        raise NotImplementedError(f"make_reindexer NYI on {self}")

    def make_indexer(self):
        inner = self.data.make_indexer()
        reindex = self.make_reindexer()

        def indexer(idx):
            return inner(reindex(idx))

        return indexer

    def make_loader(self):
        inner = self.data.make_loader()
        reindex = self.make_reindexer()

        def loader(idx):
            return inner(reindex(idx))

        return loader

    def get_dtype(self):
        return self.data.get_dtype()

    def get_device(self):
        return self.data.get_device()

    def get_origin_node(self):
        return None

    def get_name(self):
        return self.data.get_name()

    def mark_reuse(self, users):
        return self.data.mark_reuse(users)

    def has_exceeded_max_reads(self):
        return self.data.has_exceeded_max_reads()

    def realize(self):
        return self.data.realize()

    def realize_hint(self):
        return self.data.realize_hint()

    def get_storage_numel(self):
        return self.data.get_storage_numel()

    def is_extern(self):
        return self.data.is_extern()

    def get_reads(self):
        with patch.object(FlexibleLayout, "allow_indexing", True):
            return extract_read_writes(
                self.make_loader(),
                self.get_size(),
            ).reads

    def unwrap_view(self):
        x = self
        while isinstance(x, BaseView):
            x = x.data
        return x

    def constant_to_device(self, device):
        """Move this to a given device. Requires that all reads are to constants."""
        loader = self.make_loader()
        loader = patch.object(ConstantBuffer, "override_device", device)(loader)
        return Pointwise(device, self.get_dtype(), loader, self.get_size())


@dataclasses.dataclass
class ExpandView(BaseView):
    size: List[Expr]

    @staticmethod
    def _normalize_size(x, new_size):
        """Replace `-1` with correct sizes"""
        new_size = list(map(sympy.expand, new_size))
        old_size = x.get_size()
        old_size = [None] * (len(new_size) - len(old_size)) + list(old_size)
        assert len(new_size) == len(old_size)
        for i in range(len(new_size)):
            if new_size[i] == -1:
                assert old_size[i] is not None
                new_size[i] = old_size[i]
        return new_size

    @classmethod
    def create(cls, x, new_size):
        new_size = cls._normalize_size(x, new_size)

        if is_storage_and_layout(x):
            storage, old_layout = as_storage_and_layout(x)
            skip = len(new_size) - len(old_layout.size)
            assert skip >= 0
            new_stride = [sympy.Integer(0)] * skip
            for stride, size in zip(old_layout.stride, old_layout.size):
                new_stride.append(stride if size != 1 else sympy.Integer(0))
            new_layout = FixedLayout(
                old_layout.device,
                old_layout.dtype,
                list(new_size),
                new_stride,
                old_layout.offset,
            )
            return ReinterpretView(storage, new_layout)

        return ExpandView(x, new_size)

    def get_size(self):
        return self.size

    def make_reindexer(self):
        target = self.get_size()
        actual = self.data.get_size()
        skip = len(target) - len(actual)

        def reindex(index):
            index = list(index[skip:])
            assert len(index) == len(actual)
            for i in range(len(actual)):
                if actual[i] == 1:
                    # zero out broadcast dimension
                    index[i] = sympy.Integer(0)
            return index

        return reindex


@dataclasses.dataclass
class PermuteView(BaseView):
    dims: List[Expr]

    @classmethod
    def create(cls, x, dims):
        dims = cls._map_neg_dims(dims)
        assert set(dims) == set(range(len(dims)))

        if is_storage_and_layout(x):
            storage, old_layout = as_storage_and_layout(x)
            new_layout = FixedLayout(
                old_layout.device,
                old_layout.dtype,
                [old_layout.size[i] for i in dims],
                [old_layout.stride[i] for i in dims],
                old_layout.offset,
            )
            return ReinterpretView(storage, new_layout)

        return PermuteView(x, dims)

    @classmethod
    def _map_neg_dims(cls, dims):
        return [dim if dim >= 0 else len(dims) + dim for dim in dims]

    def get_size(self):
        assert set(self._map_neg_dims(self.dims)) == set(range(len(self.dims)))
        size = self.data.get_size()
        return [size[i] for i in self.dims]

    def make_reindexer(self):
        inv = {j: i for i, j in enumerate(self.dims)}
        inv = [inv[i] for i in range(len(self.dims))]
        assert set(inv) == set(range(len(self.dims)))

        def reindex(index):
            return [index[i] for i in inv]

        return reindex


class SqueezeView(BaseView):
    @classmethod
    def create(cls, x, *, dim=None):
        if is_storage_and_layout(x):
            storage, old_layout = as_storage_and_layout(x)
            new_size = []
            new_stride = []
            if dim is not None:
                assert isinstance(dim, int), "expected integer dim argument"
                assert 0 <= dim and dim < len(old_layout.size)

            for i, (size, stride) in enumerate(zip(old_layout.size, old_layout.stride)):
                if dim is None:
                    if size != 1:
                        new_size.append(size)
                        new_stride.append(stride)
                else:
                    if i != dim:
                        new_size.append(size)
                        new_stride.append(stride)
                    else:
                        assert size == 1, "expected squeezed size to be 1"

            new_layout = FixedLayout(
                old_layout.device,
                old_layout.dtype,
                new_size,
                new_stride,
                old_layout.offset,
            )
            return ReinterpretView(storage, new_layout)

        if dim is None:
            # redirect to a generic view
            return View.create(x, [s for s in x.get_size() if s != 1])
        else:
            assert x.get_size()[dim] == 1
            return View.create(x, [s for i, s in enumerate(x.get_size()) if i != dim])

    @staticmethod
    def squeezer(size: Tuple[sympy.Expr, ...]):
        new_size = [s for s in size if s != 1]
        not_one = [i for i, s in enumerate(size) if s != 1]
        length = len(size)

        def reindex(index: List[sympy.Expr]) -> Tuple[sympy.Expr, ...]:
            assert len(index) == len(not_one), f"{index} {not_one}"
            new_index = [sympy.Integer(0)] * length
            for idx, s in zip(not_one, index):
                new_index[idx] = s
            return tuple(new_index)

        return new_size, reindex

    def __init__(self, data):
        raise AssertionError("use SqueezeView.create()")


@dataclasses.dataclass
class GenericView(BaseView):
    size: List[Expr]
    reindex: Callable[..., Any]

    def make_reindexer(self):
        return self.reindex

    def reindex_str(self):
        index_old = [sympy_symbol(f"i{n}") for n in range(len(self.size))]
        index_new = list(self.reindex(index_old))
        return f"lambda {', '.join(map(str, index_old))}: {index_new}"

    def __str__(self):
        return self.str_helper(
            [self.data, f"size={self.size}", f"reindex={self.reindex_str()}"]
        )

    __repr__ = __str__

    @classmethod
    def create(cls, x, new_size, reindex):
        return cls(x, list(new_size), reindex)

    def get_size(self):
        return self.size


@dataclasses.dataclass
class View(GenericView):
    @staticmethod
    def handle_negative_index(idx, size):
        idx = sympy.expand(idx)
        size = sympy.expand(size)
        evaluate_expr = V.graph.sizevars.shape_env.evaluate_expr
        if evaluate_expr(sympy.Lt(idx, 0)):
            idx = idx + size
        return idx

    @classmethod
    def create(cls, x, new_size):
        assert isinstance(new_size, (tuple, list))
        old_size, new_size = cls.resolve_negative_size(x.get_size(), new_size)

        # Skip pointless views
        if V.graph.sizevars.statically_known_list_equals(old_size, new_size):
            return x

        if 0 in new_size:

            def fake_reindex(index):
                return tuple([0] * len(old_size))

            return cls(x, tuple(new_size), fake_reindex)
        # TODO: a new class for FixedTransferLayout that output layout is constrained by input layout
        elif is_contiguous_storage_and_layout(x) and not isinstance(
            x.data, ExternKernelAlloc
        ):
            storage, old_layout = as_contiguous_storage_and_layout(x)
            new_layout = FixedLayout(
                old_layout.device,
                old_layout.dtype,
                new_size,
                FlexibleLayout.contiguous_strides(new_size),
                old_layout.offset,
            )
            return ReinterpretView(storage, new_layout)

        reindex = cls.dynamic_reshape_indexer(old_size, new_size)
        return cls(x, list(new_size), reindex)

    @staticmethod
    def resolve_negative_size(old_size, new_size):
        new_size = [V.graph.sizevars.simplify(x) for x in new_size]
        old_size = [V.graph.sizevars.simplify(x) for x in old_size]

        new_size = list(new_size)
        for i in range(len(new_size)):
            if new_size[i] == -1:
                new_size[i] = sympy.Integer(1)
                new_size[i] = CleanDiv(sympy_product(old_size), sympy_product(new_size))
                break

        V.graph.sizevars.guard_equals(sympy_product(old_size), sympy_product(new_size))
        return old_size, new_size

    @classmethod
    def dynamic_reshape_indexer(cls, old_size, new_size):
        try:
            reindex = cls._dynamic_reshape_indexer(old_size, new_size)
        except (AssertionError, IndexError):
            # optimistic algorithm failed, lets do a fallback
            flat = [sympy_product(old_size)]
            reindex1 = cls._dynamic_reshape_indexer(old_size, flat)
            reindex2 = cls._dynamic_reshape_indexer(flat, new_size)
            reindex = fuse_reindexing(reindex1, reindex2)
        return reindex

    @staticmethod
    def _dynamic_reshape_indexer(old_size, new_size):
        """
        Perform a reshape entirely by modifying indexing math
        """
        size_hint = V.graph.sizevars.size_hint
        vars = [sympy_symbol(f"view{i}") for i in range(len(new_size))]

        stack_new = list(zip(vars, new_size))
        stack_old = list(old_size)

        view_expr = []
        while stack_new and stack_old:
            size_old = stack_old.pop()
            var, size_new = stack_new.pop()
            if size_old == 1:
                view_expr.append(sympy.Integer(0))
                stack_new.append((var, size_new))  # re-add
            elif size_new == 1:
                stack_old.append(size_old)  # re-add
            elif size_hint(size_new) == size_hint(size_old):
                view_expr.append(var)
                V.graph.sizevars.guard_equals(size_new, size_old)
            elif size_hint(size_new) < size_hint(size_old):
                while size_hint(size_new) < size_hint(size_old):
                    var2, size_new2 = stack_new.pop()
                    var = var2 * size_new + var
                    size_new = size_new * size_new2
                view_expr.append(var)
                V.graph.sizevars.guard_equals(size_new, size_old)
            elif size_hint(size_new) > size_hint(size_old):
                divisor = sympy.Integer(1)
                modulus = size_old
                view_expr.append(ModularIndexing(var, divisor, modulus))
                divisor = divisor * modulus
                while size_hint(size_new) > size_hint(size_old):
                    modulus = stack_old.pop()
                    view_expr.append(ModularIndexing(var, divisor, modulus))
                    divisor = divisor * modulus
                    size_old = size_old * modulus
                V.graph.sizevars.guard_equals(size_new, size_old)
            else:
                raise AssertionError()

        while stack_old:
            size_old = stack_old.pop()
            V.graph.sizevars.guard_equals(size_old, 1)
            view_expr.append(sympy.Integer(0))

        while stack_new:
            var, size_new = stack_new.pop()
            V.graph.sizevars.guard_equals(size_new, 1)

        view_expr = list(reversed(view_expr))
        assert len(view_expr) == len(old_size)

        def reindex(index):
            assert len(index) == len(vars), (len(index), len(vars))
            replacements = dict(zip(vars, index))
            return tuple(sympy_subs(x, replacements) for x in view_expr)

        return reindex


@dataclasses.dataclass
class ReinterpretView(BaseView):
    """Pretend our storage has a different layout"""

    layout: "Layout"

    def __post_init__(self):
        super().__post_init__()
        if isinstance(self.data, BaseView):
            self.data = self.data.unwrap_view()

    def __str__(self):
        return self.str_helper(
            [
                self.data,
                self.layout,
            ]
        )

    __repr__ = __str__

    def get_name(self):
        return self.data.get_name()

    def get_device(self):
        return self.layout.device

    def get_origin_node(self):
        return None

    def get_dtype(self):
        return self.layout.dtype

    def get_size(self):
        return list(self.layout.size)

    def get_stride(self):
        return list(self.layout.stride)

    def make_loader(self):
        def loader(index):
            indexer = self.layout.make_indexer()
            return ops.load(self.get_name(), indexer(index))

        return loader

    def make_indexer(self):
        return self.layout.make_indexer()

    def get_layout(self):
        return self.layout

    def freeze_layout(self):
        pass

    def codegen_reference(self):
        size = V.graph.wrapper_code.codegen_shape_tuple(self.layout.size)
        stride = V.graph.wrapper_code.codegen_shape_tuple(self.layout.stride)
        offset = V.graph.wrapper_code.codegen_sizevar(self.layout.offset)
        # reinterpret_tensor is similar to as_strided except:
        # - offset is added to the existing offset (rather than replacing it)
        # - view tracking is disabled similar to unsafe_view
        return f"reinterpret_tensor({self.get_name()}, {size}, {stride}, {offset})"


class SliceView(View):
    @classmethod
    def create(cls, x, dim, start, end, step=1):
        step = sympy.expand(step)
        assert step > 0
        try:
            if start == 0 and end >= 2**63 - 1 and step == 1:
                return x
        except TypeError:
            pass

        sizevars = V.graph.sizevars
        new_size = list(x.get_size())

        start = cls.handle_negative_index(start, new_size[dim])
        end = cls.handle_negative_index(end, new_size[dim])

        end = sizevars.evaluate_min(end, new_size[dim])
        start = sizevars.evaluate_min(sizevars.evaluate_min(start, new_size[dim]), end)
        if start == 0 and sizevars.size_hint(end - new_size[dim]) == 0 and step == 1:
            sizevars.guard_equals(end, new_size[dim])
            return x

        new_size[dim] = FloorDiv(end - start + (step - 1), step)

        if is_storage_and_layout(x):
            # Fast path
            storage, old_layout = as_storage_and_layout(x)
            new_stride = list(old_layout.stride)
            new_stride[dim] = new_stride[dim] * step
            new_layout = FixedLayout(
                old_layout.device,
                old_layout.dtype,
                new_size,
                new_stride,
                old_layout.offset + old_layout.stride[dim] * start,
            )
            return ReinterpretView(storage, new_layout)

        def reindex(index):
            assert len(index) == len(new_size), f"wrong ndim {index} {new_size}"
            index = list(index)
            index[dim] = index[dim] * step + start
            return index

        # redirect to a generic view
        return SliceView(x, size=new_size, reindex=reindex)


class BaseConstant(IRNode):
    def get_size(self):
        return ()

    def get_dtype(self):
        return self.dtype

    def get_device(self):
        return self.device

    def get_origin_node(self):
        return None

    def mark_reuse(self, users):
        pass

    def has_exceeded_max_reads(self):
        return False

    def get_reads(self):
        return ()

    def is_extern(self):
        return False


@dataclasses.dataclass
class Constant(BaseConstant):
    value: Any
    dtype: torch.dtype
    device: torch.device

    def make_loader(self):
        def loader(index):
            return ops.constant(self.value, self.dtype)

        return loader

    def realize(self):
        pass

    def constant_to_device(self, device):
        return Constant(self.value, self.dtype, device)


@dataclasses.dataclass
class IndexingConstant(BaseConstant):
    index: Any
    dtype: torch.dtype
    device: torch.device

    def make_loader(self):
        def loader(index):
            return ops.index_expr(self.index, self.dtype)

        return loader

    def constant_to_device(self, device):
        return IndexingConstant(self.index, self.dtype, device)


@dataclasses.dataclass
class Layout(IRNode):
    def __init__(
        self,
        device: torch.device,
        dtype: torch.dtype,
        size: List[Expr],
        stride: List[Expr],
        offset: Expr = Integer(0),
    ):
        assert stride is None or len(size) == len(
            stride
        ), f"size={size}, stride={stride}"
        self.device = device
        self.dtype = dtype
        assert all(isinstance(s, (Expr, int)) for s in size)
        self.size = size
        self._stride = stride
        self.offset = offset

    @property
    def stride(self):
        return self._stride

    def __str__(self):
        offset = ""
        if self.offset != 0:
            offset = f", offset={self.offset}"
        return (
            f"{type(self).__name__}('{self.device.type}', {self.dtype}, "
            f"size={self.size}, stride={self.stride}{offset})"
        )

    __repr__ = __str__

    def is_contiguous(self):
        for left, right, size in zip(
            self.stride, FlexibleLayout.contiguous_strides(self.size), self.size
        ):
            if size != 1 and left != right:
                return False
        return True

    def is_channels_last_contiguous(self):
        ndim = len(self.size)
        if ndim not in [4, 5]:
            return False
        for left, right, size in zip(
            self.stride, make_channels_last_strides_for(self.size), self.size
        ):
            if size != 1 and left != right:
                return False
        return True

    def is_transposed(self):
        for left, right, size in zip(
            self.stride,
            reversed(FlexibleLayout.contiguous_strides(self.size)),
            self.size,
        ):
            if size != 1 and left != right:
                return False
        return True

    def is_stride_ordered(self, order):
        assert len(self.stride) == len(order)
        # reorder the stride given order
        stride_ordered = [-1] * len(order)
        for i in range(len(order)):
            stride_ordered[order[i]] = V.graph.sizevars.size_hint(self.stride[i])
        # check if it is in ascending order
        for i in range(len(order) - 1):
            if stride_ordered[i] > stride_ordered[i + 1]:
                return False
        return True

    def is_channels_last_stride_ordered(self):
        # create channels_last order(NCHW, NCDHW, the C is the first order).
        order = [0] + list(reversed(range(1, len(self.stride) - 1)))
        order = [len(order)] + order
        return self.is_stride_ordered(order)

    def as_fixed(self):
        return FixedLayout(
            self.device,
            self.dtype,
            self.size,
            self.stride,
            self.offset,
        )

    def make_indexer(self):
        assert (
            FlexibleLayout.allow_indexing
        ), f"convert {type(self).__name__} to FixedLayout first"
        return self.as_fixed().make_indexer()

    def __eq__(self, other) -> bool:
        return (
            self.device == other.device
            and self.dtype == other.dtype
            and self.size == other.size
            and self.stride == other.stride
            and self.offset == other.offset
        )

    def storage_size(self) -> sympy.Expr:
        return compute_required_storage_length(self.size, self.stride, self.offset)


class FixedLayout(Layout):
    """A Tensor layout we cannot change"""

    def __init__(
        self,
        device: torch.device,
        dtype: torch.dtype,
        size: Union[List[Expr], List[int]],
        stride: Optional[Union[List[Expr], List[int]]] = None,
        offset: Union[Expr, int] = Integer(0),
    ):
        if stride is None:
            stride = FlexibleLayout.contiguous_strides(size)
        super().__init__(
            device,
            dtype,
            size,
            stride,
            offset,
        )

    def make_indexer(self):
        """A closure containing math to read a given element"""

        def indexer(index):
            assert len(index) == len(self.stride) == len(self.size)
            result = self.offset
            for idx, stride, sz in zip(index, self.stride, self.size):
                if sz != 1:
                    result = result + idx * stride
            return result

        return indexer


class FlexibleLayout(Layout):
    """A Tensor layout we are allowed to change"""

    allow_indexing = False

    @staticmethod
    def contiguous_strides(sizes):
        if len(sizes) == 0:
            return []
        reversed_strides = [sympy.Integer(1)]
        for size in reversed(sizes[1:]):
            reversed_strides.append(size * reversed_strides[-1])
        return list(reversed(reversed_strides))

    @staticmethod
    def fill_ordered(sizes, order):
        """
        Create a stride based on the order the dimensions should be filled in.

        In this format, channels last would be:
            [1, 3, 2, 0]
        """
        assert set(range(len(sizes))) == set(order)
        next_stride = sympy.Integer(1)
        strides = [None] * len(order)

        for i in order:
            strides[i] = next_stride
            next_stride = next_stride * sizes[i]
        return strides

    @staticmethod
    def stride_ordered(sizes, order):
        """
        Create a stride based on the sorted order of a permuted range.

        In this format, channels last would be:
            [3, 0, 2, 1]
        """
        assert set(range(len(sizes))) == set(order)
        fill_order = stride_order2fill_order(order)
        return FlexibleLayout.fill_ordered(sizes, fill_order)

    @staticmethod
    def same_ordered(sizes, stride):
        """
        Create a stride that has the same stride order as given stride

        For example, if given stride is [1000, 1, 100, 10],
        the fill order should be [1, 3, 2, 0]
        """
        assert len(sizes) == len(stride)
        stride = [V.graph.sizevars.size_hint(x) for x in stride]
        fill_order = sorted(range(len(stride)), key=stride.__getitem__)
        return FlexibleLayout.fill_ordered(sizes, fill_order)

    def as_stride_order(self, order):
        return FixedLayout(
            self.device,
            self.dtype,
            self.size,
            self.stride_ordered(self.size, order),
            self.offset,
        )

    def as_fill_order(self, order):
        return FixedLayout(
            self.device,
            self.dtype,
            self.size,
            self.fill_ordered(self.size, order),
            self.offset,
        )

    def as_same_order(self, stride):
        return FixedLayout(
            self.device,
            self.dtype,
            self.size,
            self.same_ordered(self.size, stride),
            self.offset,
        )

    def __init__(self, device, dtype, size, stride_order=None):
        if stride_order:
            strides = FlexibleLayout.fill_ordered(size, stride_order)
        else:
            strides = FlexibleLayout.contiguous_strides(size)
        super().__init__(device, dtype, size, strides)


class AliasedLayout(Layout):
    """Shares the same storage as another tensor"""

    def __init__(self, view: "ReinterpretView"):
        layout = view.get_layout()
        super().__init__(
            layout.device,
            layout.dtype,
            layout.size,
            layout.stride,
        )
        self.view = view

    def make_indexer(self):
        return self.as_fixed().make_indexer()

    def maybe_guard_aligned(self):
        offset = self.view.get_layout().offset
        if offset == 0:
            return True
        from .compile_fx import ALIGNMENT

        return V.graph.sizevars.statically_known_multiple_of(offset, ALIGNMENT)


class MutationLayout(Layout):
    def __init__(self, target: IRNode):
        super().__init__(
            target.get_device(),
            target.get_dtype(),
            target.get_size(),
            None,  # type: ignore[arg-type]
        )
        self.target = target
        name = self.get_buffer().get_name()
        V.graph.mark_buffer_mutated(name)

    @Layout.stride.getter
    def stride(self):
        return self.real_layout().stride

    def storage_size(self) -> sympy.Expr:
        return self.real_layout().storage_size()

    def get_buffer(self) -> "Buffer":
        def unwrap_views(target):
            if isinstance(target, MutationLayout):
                return unwrap_views(target.target)
            if isinstance(target, BaseView):
                return unwrap_views(target.unwrap_view())
            if isinstance(target, MutableBox):
                return unwrap_views(target.data)
            return target

        result = unwrap_views(self.target)
        assert isinstance(result, Buffer), "MutationLayout must refer to a buffer"
        return result

    def real_layout(self):
        return self.get_buffer().layout

    @classmethod
    def realize_into(cls, src, dst):
        dst.realize()

        if isinstance(src, TensorBox):
            src = src.data

        if not isinstance(src, StorageBox) or src.is_user_of(dst.get_name()):
            need_copy = True
        else:
            src.realize()
            need_copy = not isinstance(src.data.layout, FlexibleLayout)

        if need_copy:
            src = Pointwise.create(
                device=src.get_device(),
                dtype=src.get_dtype(),
                inner_fn=src.make_loader(),
                ranges=[
                    V.graph.sizevars.guard_equals(a, b)
                    for a, b in zip(src.get_size(), dst.get_size())
                ],
            ).data
            src.realize()

        assert isinstance(src.data.layout, FlexibleLayout)
        src.data.layout = MutationLayout(dst)
        return src.data

    def as_fixed(self):
        return self

    def make_indexer(self):
        return self.target.make_indexer()


@dataclasses.dataclass
class Buffer(IRNode):
    # Name is sometimes None; e.g., ForceInPlace, where there isn't
    # a meaningful name
    name: Optional[str]
    layout: Layout

    def __post_init__(self):
        super().__post_init__()
        self.origin_node = None

    def make_indexer(self):
        return self.layout.make_indexer()

    def get_name(self):
        assert self.name
        return self.name

    def get_device(self):
        return self.layout.device

    def get_origin_node(self):
        return self.origin_node

    def get_dtype(self):
        return getattr(self.layout, "dtype", None)

    def get_size(self):
        return list(self.layout.size)

    def get_stride(self):
        return list(self.layout.stride)

    def get_layout(self):
        return self.layout

    def get_storage_numel(self):
        return self.get_numel()

    def is_extern(self):
        return False

    def freeze_layout(self):
        if not isinstance(self.layout, (MultiOutputLayout, AliasedLayout)):
            self.layout = self.layout.as_fixed()

    def freeze_layout_with_stride_order(self, order):
        assert isinstance(self.layout, FlexibleLayout)
        self.layout = self.layout.as_stride_order(order)

    def freeze_layout_with_fill_order(self, order):
        assert isinstance(self.layout, FlexibleLayout)
        self.layout = self.layout.as_fill_order(order)

    def freeze_layout_with_same_order(self, stride):
        assert isinstance(self.layout, FlexibleLayout)
        self.layout = self.layout.as_same_order(stride)

    def is_zero_elements(self):
        return V.graph.sizevars.is_expr_static_and_true(sympy.Eq(self.get_numel(), 0))

    def make_loader(self):
        # Loading from a zero-element buffer is a no-op
        if self.is_zero_elements():
            return partial(nop_loader_fn, dtype=self.get_dtype())

        def loader(index):
            indexer = self.layout.make_indexer()
            return ops.load(self.name, indexer(index))

        return loader

    def is_no_op(self):
        return False

    def codegen_reference(self):
        return self.get_name()

    def decide_layout(self):
        pass

    def get_alias_names(self):
        if isinstance(self.layout, AliasedLayout):
            return [self.layout.view.get_name()]
        return ()

    def get_mutation_names(self):
        if isinstance(self.layout, MutationLayout):
            return [self.layout.target.get_name()]
        return ()

    def get_read_writes(self):
        with patch.object(FlexibleLayout, "allow_indexing", True):
            return extract_read_writes(
                self.make_loader(),
                self.get_size(),
            )

    def get_reads(self):
        return self.get_read_writes().reads

    def realize(self):
        pass


class InputBuffer(Buffer):
    pass


class ConstantBuffer(InputBuffer):
    override_device = None

    def make_loader(self):
        def loader(index):
            indexer = self.layout.make_indexer()
            return ops.load(
                V.graph.constant_name(self.name, self.override_device), indexer(index)
            )

        return loader

    def constant_to_device(self, device):
        return ConstantBuffer(V.graph.constant_name(self.name, device), self.layout)


class NoneAsConstantBuffer(IRNode):
    def codegen_reference(self):
        return V.graph.wrapper_code.none_str


class ShapeAsConstantBuffer(IRNode):
    def __init__(self, shape):
        super().__init__()
        self.shape = shape

    def codegen_reference(self):
        expr = V.graph.wrapper_code.expr_printer(V.graph.sizevars.simplify(self.shape))
        if V.graph.cpp_wrapper:
            # wrap scalar to 0-d tensor for cpp wrapper
            return f"torch::tensor({expr})"
        else:
            return expr


@dataclasses.dataclass
class ComputedBuffer(Buffer):
    data: Loops

    @cache_on_self
    def num_reads(self):
        return len(self.get_read_writes().reads)

    def get_read_writes(self):
        with patch.object(FlexibleLayout, "allow_indexing", True):
            if self.data.get_reduction_type():
                return extract_read_writes(
                    self.get_store_function(),
                    self.data.get_size(),
                    self.data.get_reduction_size(),
                )
            else:
                return extract_read_writes(
                    self.get_store_function(),
                    self.data.get_size(),
                )

    def make_loader(self):
        # Inline constants and index_expressions
        can_inline = (
            hasattr(self.data, "make_loader")
            and self.name not in V.graph.mutated_buffers
            and self.num_reads() == 0
        )
        if can_inline:
            return self.data.make_loader()
        return super().make_loader()

    def get_store_function(self):
        indexer = self.layout.as_fixed().make_indexer()
        if self.data.get_reduction_type():
            return partial(self.data.store_reduction, self.name, indexer)
        else:
            return partial(self.data.store_output, self.name, indexer)

    def get_fill_order(self):
        """
        If our layout is still flexible, try to determine the stride order based on stride orders of reads.

        TODO(jansel): A better algorithm here would look at downstream consumers of this
                      value and try to do global graph-level layout optimization.
                      This is also something just begging to be autotuned.
        """
        if isinstance(self.layout, FlexibleLayout):
            (index_vars, reduction_vars), _ = dependencies.index_vars_squeeze(
                self.data.get_size(), self.data.get_reduction_size()
            )
            reads = self.get_read_writes().reads
            reads_bufs = [
                V.graph.name_to_buffer[r.name]
                if r.name in V.graph.name_to_buffer.keys()
                else None
                for r in reads
            ]
            # only consider reads to buffer of same size
            # ignore StarDeps because they don't contribute stride information
            assert all(
                isinstance(r, (dependencies.StarDep, dependencies.MemoryDep))
                for r in reads
            )
            reads = [
                sympy_subs(
                    r.index, {v: sympy.Integer(0) for v in reduction_vars if v != 0}
                )
                for r in reads
                if isinstance(r, dependencies.MemoryDep)
            ]

            if reads:
                stride_lengths = [
                    V.graph.sizevars.stride_hints(expr, index_vars) for expr in reads
                ]
                from .scheduler import pick_loop_order

                return pick_loop_order(stride_lengths, self.get_size())

        return None

    def decide_layout(self):
        if isinstance(self.layout, FlexibleLayout):
            order = self.get_fill_order()
            if order:
                self.freeze_layout_with_fill_order(order)
            else:
                self.freeze_layout()

    def simplify_and_reorder(self):
        """
        This is a main place where we do loop transformations in a
        backend-agnostic way.

        Here we:
            1) Remove any 1 dimensions
            2) Fuse contiguous dimensions together
            3) Reorder dimensions based on stride orders
        """
        args, var_ranges = dependencies.index_vars_squeeze(
            self.data.get_size(), self.data.get_reduction_size(), prefix="q"
        )
        with patch.object(ConstantBuffer, "override_device", self.get_device()):
            body = LoopBody(
                self.get_store_function(),
                (args if self.get_reduction_type() else args[:1]),
                var_ranges,
            )
        index_formulas = [*body.indexing_exprs.values()]
        reads_bufs = [
            V.graph.name_to_buffer[reads_name]
            if reads_name in V.graph.name_to_buffer.keys()
            else None
            for reads_name in body.reads_name2expr.keys()
        ]
        memory_addrs = [
            *body.reads_name2expr.values(),
            *body.writes_name2expr.values(),
        ]
        index_vars = []
        reduce_vars: List[Any] = []
        index_size = []
        reduce_size = []
        for v, s in var_ranges.items():
            if v in args[0]:
                assert not reduce_vars
                index_vars.append(v)
                index_size.append(s)
            else:
                assert v in args[1]
                reduce_vars.append(v)
                reduce_size.append(s)

        # the reordering_reindex in reads' simplify_reorder_and_tile
        reordering_reindex = [same_reorder(range(len(index_vars)))] * len(memory_addrs)
        for i, reads_buf in enumerate(reads_bufs):
            if isinstance(reads_buf, ComputedBuffer) and hasattr(
                reads_buf, "iter_reordering_reindex"
            ):
                reordering_reindex[i] = reads_buf.iter_reordering_reindex  # type: ignore[has-type]

        def simplify_and_reorder(x_vars, support_vars, sizes, reordering_reindex=None):
            sizes, reindex0, reindex1 = self._apply_loop_reordering(
                x_vars, support_vars, sizes, memory_addrs, reordering_reindex
            )
            # for NHWC: reindex0([0,1,2,3]) = [0,2,3,1], reindex1([0,1,2,3]) = [0,3,2,1]
            x_vars = reindex0(x_vars)
            sizes, reindex2, prune = V.graph.sizevars._simplify_loops(
                x_vars,
                sizes,
                index_prevent_reordering(index_formulas, x_vars, sizes),
            )
            x_vars = prune(x_vars)
            # sizes, reindex1, prune = _simplify_loops(x_vars, sizes, index_formulas)
            # x_vars = prune(x_vars)
            # sizes, reindex2 = self._apply_loop_reordering(x_vars, sizes, memory_addrs)
            reindex = fuse_reindexing(reindex1, reindex2)
            return sizes, reindex, reindex1

        support_vars = index_vars + reduce_vars
        iter_ranges, iter_reindex, iter_reordering_reindex = simplify_and_reorder(
            index_vars, support_vars, index_size, reordering_reindex
        )
        reduce_ranges, reduce_reindex, _ = simplify_and_reorder(
            reduce_vars, support_vars, reduce_size
        )

        # remember the reordering if not have loop collapse.
        if len(iter_ranges) == len(index_vars):
            self.iter_reordering_reindex = iter_reordering_reindex
        # retrace the loop body with simplification and reordering applied
        (iter_vars, reduce_vars), var_ranges = dependencies.index_vars_no_squeeze(
            iter_ranges, reduce_ranges, prefix="z"
        )
        body = LoopBody(
            body, [iter_reindex(iter_vars), reduce_reindex(reduce_vars)], var_ranges
        )
        return (iter_ranges, reduce_ranges), body

    @staticmethod
    def _apply_loop_reordering(
        index_vars,
        support_vars,
        sizes,
        memory_addrs,
        reordering_reindex=None,
        priority_idx=None,
    ):
        """
        Shuffle the order of loops around to hopefully improve performance.
        """
        from .scheduler import pick_loop_order

        if priority_idx is None:
            priority_idx = []

        try:
            strides = [
                V.graph.sizevars.stride_hints(expr, index_vars, support_vars)
                for expr in memory_addrs
            ]
            assert len(strides) == len(memory_addrs) and len(strides[0]) == len(
                index_vars
            )
            # consider both layout(strides) and reordering(reordering_reindex)
            if reordering_reindex is not None:
                for i in range(len(memory_addrs)):
                    try:
                        strides[i] = reordering_reindex[i](strides[i])
                    # if len(order) != len(strides), do not reorder
                    except AssertionError:
                        pass
            order = list(reversed(pick_loop_order(strides, sizes, priority_idx)))
        except Exception:
            if config.debug:
                log.warning(
                    "Did not simplify complex index:\n%s\n%s",
                    dict(zip(index_vars, sizes)),
                    memory_addrs,
                )
            order = list(range(len(sizes)))
        sizes = [sizes[i] for i in order]
        return sizes, same_reorder(order), inverse_reorder(order)

    def get_reduction_size(self):
        return self.data.get_reduction_size()

    def get_reduction_type(self):
        return self.data.get_reduction_type()

    def is_no_op(self):
        return self.data.is_zero_elements()

    def should_allocate(self):
        return True

    def constant_to_device(self, device):
        """Move this to a given device. Requires that all reads are to constants."""
        return self.data.constant_to_device(device)


class TemplateBuffer(Buffer):
    """
    Represents a Triton (in the future other type) of template operator
    that we can fuse an epilogue onto.
    """

    def __init__(self, layout, inputs, make_kernel_render):
        super().__init__(name=None, layout=layout)
        self.inputs = InputsKernel.unwrap_storage(inputs)
        self.make_kernel_render = make_kernel_render
        self.name = V.graph.register_buffer(self)

    def get_read_writes(self):
        return self.normalized_read_writes()

    def normalized_read_writes(self):
        name = self.get_name()
        indexer = self.layout.make_indexer()

        def dummy(index, rindex):
            assert len(rindex) == 0
            return ops.store(name, indexer(index), "fake")

        deps = dependencies.extract_read_writes(
            dummy, self.get_size(), (), normalize=True
        )
        deps.reads = {dependencies.StarDep(x.get_name()) for x in self.inputs}
        return deps

    def get_reduction_size(self):
        return 1

    def get_reduction_type(self):
        return None

    def is_no_op(self):
        return False

    def should_allocate(self):
        return True

    def simplify_and_reorder(self):
        return (
            (
                self.get_size(),
                (),
            ),
            None,
        )


@dataclasses.dataclass
class InputsKernel(Buffer):
    inputs: List[Buffer]

    def get_read_writes_input(self, x):
        return dependencies.StarDep(x.get_name())

    def get_read_writes(self):
        star_dep = []
        for input in self.inputs:
            if isinstance(input, list):
                star_dep.extend([self.get_read_writes_input(x) for x in input])
            else:
                star_dep.append(self.get_read_writes_input(input))

        return dependencies.ReadWrites(
            set(star_dep),
            {dependencies.StarDep(self.get_name())},
            set(),
            [],
            None,
            op_counts=collections.Counter(),
        )

    @staticmethod
    def unwrap_storage_for_input(x):
        if isinstance(x, TensorBox):
            x = x.data
        if isinstance(x, StorageBox):
            x = x.data
        if isinstance(x, BaseView) and not isinstance(x, ReinterpretView):
            x = ExternKernel.realize_input(x)
        assert isinstance(x, (Buffer, ReinterpretView)), x
        return x

    @staticmethod
    def unwrap_storage(inputs):
        inputs_new = []
        for x in inputs:
            if isinstance(x, list):
                x = [InputsKernel.unwrap_storage_for_input(i) for i in x]
            else:
                x = InputsKernel.unwrap_storage_for_input(x)
            inputs_new.append(x)
        return inputs_new

    def is_extern(self):
        return True


class NopKernel(InputsKernel):
    def is_no_op(self):
        return True


class ConcatKernel(NopKernel):
    """
    There isn't actually a real kernel for concat, we just change the
    storage for the upstream data.
    """

    @classmethod
    def create(cls, inputs, dim):
        device = inputs[0].get_device()
        dtype = inputs[0].get_dtype()
        new_size = list(inputs[0].get_size())
        offsets_start = [0]
        offsets_end = [new_size[dim]]
        assert 0 <= dim < len(new_size)
        for i in range(1, len(inputs)):
            input_size = inputs[i].get_size()
            offsets_start.append(new_size[dim])
            assert len(input_size) == len(new_size)
            assert inputs[i].get_dtype() == dtype
            assert inputs[i].get_device() == device
            for j in range(len(new_size)):
                if j == dim:
                    new_size[j] = new_size[j] + input_size[j]
                else:
                    new_size[j] = V.graph.sizevars.guard_equals(
                        new_size[j], input_size[j]
                    )
            offsets_end.append(new_size[dim])

        output_stride = FlexibleLayout.contiguous_strides(new_size)
        # If any of the inputs is in CL format, use CL format for the output
        for i in range(len(inputs)):
            x = inputs[i]
            if is_storage_and_layout(x):
                layout = x.get_layout()
                if (
                    isinstance(layout, FixedLayout)
                    and layout.is_channels_last_contiguous()
                ):
                    # use CL stride for the output
                    output_stride = make_channels_last_strides_for(new_size)
                    break

        concat_kernel = ConcatKernel(
            name=None,
            layout=FixedLayout(
                device=device,
                dtype=dtype,
                size=new_size,
                stride=output_stride,
            ),
            inputs=[],
        )
        kernel = StorageBox(concat_kernel)
        for i in range(len(inputs)):
            kernel.data.inputs.append(
                cls.realize_into(
                    inputs[i],
                    SliceView.create(kernel, dim, offsets_start[i], offsets_end[i]),
                )
            )
        kernel.data.name = V.graph.register_buffer(kernel.data)
        kernel.data.inputs = cls.unwrap_storage(kernel.data.inputs)

        return kernel

    @classmethod
    def realize_into(cls, src, dst):
        # Attempt to turn this into a ReinterpretView rather than assert.
        # This has concessions around layout, as as_storage_and_layout
        # can cause us to go from flexible to fixed layout.
        if not isinstance(dst, ReinterpretView):
            if is_storage_and_layout(dst):
                storage, layout = as_storage_and_layout(dst)
                dst = ReinterpretView(storage, layout)
        assert isinstance(dst, ReinterpretView), dst
        if isinstance(src, TensorBox):
            # unwrap a TensorBox
            return cls.realize_into(src.data, dst)
        if isinstance(src, StorageBox):
            src.realize()
            # ExternKernelAlloc has specific requirements for output layout, should create a copy
            if isinstance(src.data.layout, FlexibleLayout) and not isinstance(
                src.data, ExternKernelAlloc
            ):
                src.data.layout = AliasedLayout(dst)
                return src.data
        # introduce a copy
        pw = Pointwise.create(
            device=src.get_device(),
            dtype=src.get_dtype(),
            inner_fn=src.make_loader(),
            ranges=[
                V.graph.sizevars.guard_equals(a, b)
                for a, b in zip(src.get_size(), dst.get_size())
            ],
        )
        return cls.realize_into(pw, dst)

    def should_allocate(self):
        return True


@dataclasses.dataclass
class ExternKernel(InputsKernel):
    constant_args: Tuple[Any, ...] = ()
    kwargs: Dict[str, Any] = dataclasses.field(default_factory=dict)
    output_view: Optional[ReinterpretView] = None

    def decide_layout(self):
        if isinstance(self.layout, FlexibleLayout):
            self.apply_constraint()
            self.freeze_layout()

    def codegen_comment(self, wrapper):
        origin_str, detailed_origin_str = get_kernel_metadata(self, wrapper)
        if origin_str:
            wrapper.writeline(origin_str)

    def codegen(self, wrapper):
        raise NotImplementedError()

    @staticmethod
    def copy_input(x):
        pw = Pointwise.create(
            device=x.get_device(),
            dtype=x.get_dtype(),
            inner_fn=x.make_loader(),
            ranges=x.get_size(),
            origin_node=x.get_origin_node(),
            traceback=x.get_traceback(),
        )
        pw.realize()
        return pw

    @classmethod
    def process_kernel(cls, kernel, *args, **kwargs):
        binded_args = signature(kernel).bind(*args, **kwargs).arguments

        _, schemas = get_signature_for_torch_op(kernel, return_schemas=True)

        schema = None
        # For cpp wrapper, when kwargs is not empty, for OpOverloadPacket kernel, we need to
        # know the exact overload schema to handle the kwargs properly when calling the cpp kernel.
        if (
            V.graph.cpp_wrapper
            and kwargs
            and isinstance(kernel, torch._ops.OpOverloadPacket)
        ):
            schema = try_find_schema(schemas, args, kwargs)

        args_flat, args_spec = pytree.tree_flatten(binded_args)

        is_arg_tensor = []
        tensor_args = []
        non_tensor_args = []
        for arg in args_flat:
            is_arg_tensor.append(isinstance(arg, IRNode))
            if is_arg_tensor[-1]:
                tensor_args.append(arg)
            else:
                if isinstance(arg, sympy.Expr):
                    arg = V.graph.sizevars.shape_env.create_symintnode(arg, hint=None)
                non_tensor_args.append(arg)

        def unflatten_args(new_tensor_args, new_non_tensor_args):
            result = []
            it_tensors = iter(new_tensor_args)
            it_non_tensors = iter(new_non_tensor_args)
            for is_tensor in is_arg_tensor:
                if is_tensor:
                    result.append(next(it_tensors))
                else:
                    result.append(next(it_non_tensors))
            r = pytree.tree_unflatten(result, args_spec)
            return r.get("args", []), r.get("kwargs", {})

        tensor_args = [cls.realize_input(x) for x in tensor_args]

        # freeze layout otherwise our output stride calculation might
        # become incorrect
        for x in tensor_args:
            if is_storage_and_layout(x):
                as_storage_and_layout(x, freeze=True)

        # We don't have generic shape formulas, so just burn in the
        # shapes and run an example input.
        # TODO(jansel): replace this with dynamic shape formulas
        example_args = []

        # We need to retain the constant values of fake tensors that we originally
        # propagated the graph with, because for some operators running without a
        # constant would trigger an error / DataDependentException
        for x in tensor_args:
            if x.get_name() in V.graph.constants:
                example_args.append(V.graph.constants[x.get_name()])
            else:
                example_args.append(ir_node_to_tensor(x, guard_shape=True))

        new_args, new_kwargs = unflatten_args(example_args, non_tensor_args)
        example_output = kernel(*new_args, **new_kwargs)

        return example_output, tensor_args, non_tensor_args, unflatten_args, schema

    @classmethod
    def convert_to_reinterpret_view(cls, x):
        """
        In order to pass this to an extern kernel we need a
        ReinterpretView not a View.  This allows us to avoid some
        unneeded copies.
        """
        assert isinstance(x, BaseView)
        if isinstance(x, ReinterpretView):
            return x

        # NOTE: Don't use extract_read_writes here as it fails when
        # make_loader() inlines the computation
        x.unwrap_view().freeze_layout()
        index_args, var_ranges = dependencies.index_vars_squeeze(
            x.get_size(), prefix="r"
        )
        range_vars = index_args[0]
        index = x.make_indexer()(range_vars)

        index = V.graph.sizevars.simplify_with_ranges(index, var_ranges)
        strides = V.graph.sizevars.stride_vars(index, range_vars)
        offset = V.graph.sizevars.offset_var(index, range_vars)
        expected = sympy_dot(range_vars, strides) + offset

        if index != expected:
            log.debug(
                "convert_to_reinterpret_view failed: stride=%s offset=%s index=%s",
                strides,
                offset,
                index,
            )
            raise NotImplementedError()

        return ReinterpretView(
            data=x.data,
            layout=FixedLayout(
                device=x.get_device(),
                dtype=x.get_dtype(),
                size=x.get_size(),
                stride=strides,
                offset=offset,
            ),
        )

    @classmethod
    def realize_input(cls, x):
        if x is None:
            return NoneAsConstantBuffer()
        if isinstance(x, (sympy.Expr, sympy.logic.boolalg.Boolean, int)):
            return ShapeAsConstantBuffer(x)
        if isinstance(x, Constant):
            return V.graph.add_tensor_constant(
                torch.tensor(x.value, dtype=x.get_dtype(), device=x.get_device())
            )
        if isinstance(x, ConstantBuffer):
            return x
        if isinstance(x, TensorBox):
            return cls.realize_input(x.data)
        if isinstance(x, ReinterpretView):
            return x
        if isinstance(x, BaseView):
            x.realize()
            if is_storage_and_layout(x.unwrap_view()) and not isinstance(
                x.unwrap_view().data, ExternKernelAlloc
            ):
                try:
                    return cls.convert_to_reinterpret_view(x)
                except NotImplementedError:
                    pass
        if isinstance(x, StorageBox):
            # TODO(jansel): impose layout preference on realized buffer
            x.realize()
            return x
        return cls.copy_input(x)

    @classmethod
    def require_stride1(cls, x):
        if is_storage_and_layout(x):
            if len(x.get_stride()) == 0:
                return x
            for stride in x.get_stride():
                if stride == 1:
                    return x
        return cls.copy_input(x)

    @classmethod
    def require_stride_order(cls, x, order):
        if x.get_numel() == 0:  # Layout doesn't matter
            return x

        # require x to have the layout as strided_ordered as order
        if is_storage_and_layout(x):
            if isinstance(x.get_layout(), FlexibleLayout):
                # fix flexiblelayout to be FixedLayout with stride_order
                as_storage_and_layout(
                    x, freeze=True, want_contiguous=False, stride_order=order
                )
                return x
            elif isinstance(
                x.get_layout(), FixedLayout
            ) and x.get_layout().is_stride_ordered(order):
                return x
            elif isinstance(x.get_layout(), MutationLayout):
                if isinstance(x.get_layout().real_layout(), FlexibleLayout):
                    raise AssertionError(
                        "the MutationLayout's real layout shouldn't be FlexibleLayout"
                    )
                elif isinstance(
                    x.get_layout().real_layout(), FixedLayout
                ) and x.get_layout().real_layout().is_stride_ordered(order):
                    return x

        # TODO - Storage to InputBuffer
        if isinstance(x, InputBuffer) and x.get_layout().is_stride_ordered(order):
            return x
        if (
            isinstance(x, TensorBox)
            and isinstance(x.data, BaseView)
            and not isinstance(x.data, ReinterpretView)
            and is_storage_and_layout(x.unwrap_view())
            and not isinstance(x.unwrap_view().data, ExternKernelAlloc)
        ):
            try:
                x.data = cls.convert_to_reinterpret_view(x.data)
                return cls.require_stride_order(x, order)
            except NotImplementedError:
                pass
        x = cls.copy_input(x)
        as_storage_and_layout(x, freeze=True, want_contiguous=False, stride_order=order)
        assert is_stride_order_storage_and_layout(x, order)
        return x

    @classmethod
    def require_channels_last(cls, x):
        return cls.require_stride_order(x, NHWC_STRIDE_ORDER)

    @classmethod
    def require_contiguous(cls, x):
        return cls.require_stride_order(x, list(reversed(range(len(x.get_size())))))

    def apply_constraint(self):
        pass

    def codegen_const_args(self):
        return map(V.graph.wrapper_code.val_to_arg_str, self.constant_args)

    def codegen_args(self):
        args = []
        for x in self.inputs:
            if isinstance(x, list):
                names = [i.codegen_reference() for i in x]
                codegen_reference = f'[{", ".join(names)}]'
                args.append(codegen_reference)
            else:
                args.append(x.codegen_reference())
        args.extend(self.codegen_const_args())
        return args

    def get_kwargs_value(self, arg_name):
        if arg_name in self.kwargs:
            return self.kwargs.get(arg_name)
        if (
            hasattr(self, "kwargs_default_value")
            and arg_name in self.kwargs_default_value
        ):
            default_value = self.kwargs_default_value.get(arg_name).get("value")
            if default_value is None:
                arg_type = self.kwargs_default_value.get(arg_name).get("type")
                # TODO: extend the support here
                assert (
                    str(arg_type) in default_value_map
                ), f"unsupported default_value arg_type: {str(arg_type)}"
                return default_value_map[str(arg_type)]()
            else:
                return default_value
        raise AssertionError(
            f"arg {arg_name} not found in self.kwargs or self.kwargs_default_value"
        )

    def codegen_kwargs(self):
        kwargs = []
        if self.kwargs:
            if V.graph.cpp_wrapper:
                # TODO: use native_functions.yaml as the ground truth
                assert (
                    self.ordered_kwargs_for_cpp_kernel
                ), "ordered_kwargs_for_cpp_kernel has to be provided"
                for arg_name in self.ordered_kwargs_for_cpp_kernel:
                    v = self.get_kwargs_value(arg_name)
                    kwargs.append(V.graph.wrapper_code.val_to_arg_str(v))
            else:
                kwargs = [
                    f"{k}={V.graph.wrapper_code.val_to_arg_str(v)}"
                    for k, v in self.kwargs.items()
                ]
        return kwargs

    def codegen_size_asserts(self, wrapper):
        if config.size_asserts and not V.graph.cpp_wrapper:
            size = V.graph.wrapper_code.codegen_shape_tuple(self.get_size())
            stride = V.graph.wrapper_code.codegen_shape_tuple(self.get_stride())
            wrapper.writeline(
                f"assert_size_stride({self.get_name()}, {size}, {stride})"
            )

    def get_group_stride(self):
        """
        get output sizes and strides, for template_codegen
        """
        _size = self.get_size()
        _stride = self.get_stride()
        # iter_ranges = _size of output tensor, reduce_range = [] because no reduction
        return [_size, []], _stride

    def canonicalize(self):
        """
        Manually get canonicalization of the output index
        """
        # manually generate index formula for conv
        sizevars = V.graph.sizevars
        sizes = self.get_size()
        strides = self.get_stride()
        strides = [sizevars.size_hint(x) for x in strides]
        index_vars = [sympy_symbol(f"d{i}") for i in range(len(sizes))]
        # reorder index vars according to stride
        index_order = sorted(range(len(strides)), key=strides.__getitem__, reverse=True)
        lookup = {pos: idx for idx, pos in enumerate(index_order)}
        order = [lookup[i] for i in range(len(lookup))]
        index_vars = [index_vars[i] for i in order]
        indexer = self.make_indexer()
        index = indexer(index_vars)

        new_sizes, reindex, prune = V.graph.sizevars._simplify_loops(
            index_vars, sizes, [index]
        )

        # assign new variables each dimension to deal with numbering mismatches
        # d0, d1, d2 could become d0, d2 -- which won't match d0, d1
        _, add_var = var_builder("c")
        replacement = dict(zip(index_vars, reindex([add_var(x) for x in new_sizes])))

        index = sympy_subs(sympy.expand(index), replacement)
        return index, tuple(new_sizes)

    def __str__(self):
        kernel_name = getattr(self, "kernel", None)
        lines = [
            f"kernel={kernel_name!r}",
        ]
        lines += [
            f"{field.name}={getattr(self, field.name)}"
            for field in dataclasses.fields(self)
        ]
        lines.append(f"origin_node={self.origin_node!r}")
        return self.str_helper(lines)

    __repr__ = __str__


@dataclasses.dataclass
class ExternKernelOut(ExternKernel):
    output_view: Optional[ReinterpretView] = None

    def codegen(self, wrapper):
        self.codegen_comment(wrapper)
        args = [*self.codegen_args(), *self.codegen_kwargs()]
        wrapper.generate_extern_kernel_out(
            self.output_view,
            self.codegen_reference(),
            args,
            self.kernel,
        )

    def __init__(
        self,
        layout,
        inputs,
        constant_args=(),
        kwargs=None,
        output_view=None,
        kernel=None,
        cpp_kernel=None,
        ordered_kwargs_for_cpp_kernel=(),
    ):
        super().__init__(
            None, layout, self.unwrap_storage(inputs), constant_args, kwargs or {}
        )
        self.output_view = output_view
        self.name = V.graph.register_buffer(self)
        self.kernel = cpp_kernel if V.graph.cpp_wrapper else kernel
        self.ordered_kwargs_for_cpp_kernel = ordered_kwargs_for_cpp_kernel

    def should_allocate(self):
        return True


class RandomSeeds(ExternKernelOut):
    def __init__(self, count: int, device: torch.device):
        limits = torch.iinfo(torch.int64)
        super().__init__(
            layout=FixedLayout(
                device=device,
                dtype=torch.int64,
                size=[count],
            ),
            inputs=[],
            constant_args=[limits.min, limits.max, [count]],
            kernel="aten.randint.low_out",
            cpp_kernel="at::randint_out",
        )


class ExternKernelAlloc(ExternKernel):
    def codegen(self, wrapper):
        self.codegen_comment(wrapper)
        args = [*self.codegen_args(), *self.codegen_kwargs()]
        V.graph.wrapper_code.generate_extern_kernel_alloc(
            self.get_name(), self.kernel, args, self.get_origin_node()
        )
        if isinstance(self.layout, Layout):
            self.codegen_size_asserts(wrapper)

    def __init__(
        self,
        layout,
        inputs,
        constant_args=(),
        kwargs=None,
        kernel=None,
        cpp_kernel=None,
        ordered_kwargs_for_cpp_kernel=(),
    ):
        super().__init__(
            None, layout, self.unwrap_storage(inputs), constant_args, kwargs or {}
        )
        self.name = V.graph.register_buffer(self)
        self.kernel = cpp_kernel if V.graph.cpp_wrapper else kernel
        self.ordered_kwargs_for_cpp_kernel = ordered_kwargs_for_cpp_kernel

    def should_allocate(self):
        return False

    def apply_constraint(self):
        raise NotImplementedError


class InplaceBernoulliFallback(ExternKernel):
    """
    This needs to be a custom class to handle mutation properly
    """

    kernel = "aten.bernoulli_"

    def codegen(self, wrapper):
        (x,) = (t.codegen_reference() for t in self.inputs)
        wrapper.writeline(
            f"{self.kernel}({x}, {', '.join(map(repr, self.constant_args))})"
        )

    def should_allocate(self):
        return False

    def get_mutation_names(self):
        assert isinstance(self.layout, MutationLayout)
        return (self.layout.target.get_name(),)

    def __init__(self, x, *constant_args):
        super().__init__(
            None,
            MutationLayout(x),
            self.unwrap_storage([x]),
            constant_args,
        )
        self.name = V.graph.register_buffer(self)


class ScatterFallback(ExternKernel):
    """
    This needs to be a custom class to handle mutation properly.
    This class handles both aten.scatter_ and aten.scatter_reduce_.
    It also handle the case `src` being a scalar properly.
    """

    def codegen(self, wrapper):
        if self.src_is_tensor:
            (x, index, src) = (t.codegen_reference() for t in self.inputs)
        else:
            (x, index) = (t.codegen_reference() for t in self.inputs)
            src = self.constant_args[1]
        wrapper.generate_scatter_fallback(
            x,
            [x, self.constant_args[0], index, src],
            self.kernel,
            self.fn,
            self.src_is_tensor,
            self.kwargs["reduce"],
            self.codegen_kwargs(),
        )

    def should_allocate(self):
        return False

    def get_cpp_kernel(self, fn, reduce):
        if fn == "aten.scatter_":
            if self.src_is_tensor:
                kernel = (
                    "at::scatter_out" if reduce is None else "at::scatter_reduce_out"
                )
            else:
                assert (
                    reduce is None
                ), "Expect reduce to be None for aten.scatter_ with scalar src"
                kernel = "at::scatter_out"
        else:
            assert (
                reduce is not None
            ), "Expect reduce to be not None for aten.scatter_reduce_"
            kernel = "at::scatter_reduce_out"
        return kernel

    def __init__(
        self,
        fn,
        x,
        dim: int,
        index,
        src,
        *,
        reduce: Optional[str] = None,
        include_self: bool = True,
    ):
        assert fn in {"aten.scatter_", "aten.scatter_reduce_"}
        self.src_is_tensor = isinstance(src, TensorBox)

        if V.graph.cpp_wrapper:
            # Follow aten/src/ATen/native/ReductionType.h:get_operator_enum
            get_operator_enum = {"add": "sum", "multiply": "prod"}
            if reduce in get_operator_enum:
                reduce = get_operator_enum[reduce]
            self.kernel = self.get_cpp_kernel(fn, reduce)
        else:
            self.kernel = fn
        self.fn = fn

        constant_args: Tuple[Any, ...]
        if self.src_is_tensor:
            tensors = [self.realize_input(t) for t in [x, index, src]]
            constant_args = (dim,)
        else:
            tensors = [self.realize_input(t) for t in [x, index]]
            constant_args = (dim, src)
        super().__init__(
            None,
            MutationLayout(x),
            self.unwrap_storage(tensors),
            constant_args,
            {"reduce": reduce, "include_self": include_self},
        )
        self.ordered_kwargs_for_cpp_kernel = ["reduce", "include_self"]
        self.name = V.graph.register_buffer(self)


class IndexPutFallback(ExternKernel):
    """
    This needs to be a custom class to handle mutation and indices properly
    """

    def codegen(self, wrapper):
        (x, values, *valid_indices) = (t.codegen_reference() for t in self.inputs)
        indices = []
        iter_valid_indices = iter(valid_indices)
        for i, _ in enumerate(self.indices):
            if self.indices[i] is not None:
                indices.append(next(iter_valid_indices))
            else:
                indices.append(V.graph.wrapper_code.none_str)

        indices_str = f"{V.graph.wrapper_code.open_bracket}{', '.join(indices)}{V.graph.wrapper_code.closed_bracket}"
        args = [x, indices_str, values, *self.codegen_const_args()]
        wrapper.writeline(wrapper.wrap_kernel_call(self.kernel, args))

    def should_allocate(self):
        return False

    def __init__(self, x, indices, values, accumulate):
        self.indices = indices
        valid_indices = [i for i in indices if i is not None]
        tensors = [self.realize_input(x) for x in [x, values, *valid_indices]]
        super().__init__(
            None,
            MutationLayout(x),
            self.unwrap_storage(tensors),
            (accumulate,),
        )
        self.name = V.graph.register_buffer(self)
        self.kernel = "at::index_put_" if V.graph.cpp_wrapper else "aten.index_put_"


class DeviceCopy(ExternKernelOut):
    @classmethod
    def create(cls, x, device):
        if not x.is_extern() and all(
            (r.name in V.graph.constants and isinstance(r, dependencies.MemoryDep))
            for r in x.get_reads()
        ):
            return x.constant_to_device(device)

        V.graph.device_types.add(device.type)
        V.graph.add_device_idx(device.index)
        V.graph.device_types.add(x.get_device().type)
        V.graph.add_device_idx(x.get_device().index)

        developer_warning("DeviceCopy in input program")
        return DeviceCopy(
            FlexibleLayout(
                device=device,
                dtype=x.get_dtype(),
                size=x.get_size(),
            ),
            [cls.realize_input(x)],
        )

    def codegen(self, wrapper):
        args = self.codegen_args()
        assert len(args) == 1
        if self.output_view:
            wrapper.writeline(
                f"{self.output_view.codegen_reference()}.copy_({args[0]}){V.graph.wrapper_code.ending}"
            )
        else:
            wrapper.writeline(
                f"{self.codegen_reference()}.copy_({args[0]}){V.graph.wrapper_code.ending}"
            )


class DynamicScalar(IRNode):
    """
    The result of a call to aten._local_scalar_dense.

    This is not yet implemented.  The one model (so far) that calls this
    (fastNLP_Bert) does not actually use the result.  So we expect this
    node to get dead code eliminated.
    """

    def get_reads(self):
        return ()


@dataclasses.dataclass
class FallbackKernel(ExternKernelAlloc):
    def __init__(
        self,
        layout,
        kernel,
        tensor_args,
        nontensor_args,
        unflatten_args,
        kwargs=None,
        schema=None,
    ):
        super().__init__(
            layout,
            tuple(tensor_args),
            tuple(nontensor_args),
        )
        self.use_cpp_op_schema = False

        op_overload_packet = (
            kernel._overloadpacket
            if isinstance(kernel, torch._ops.OpOverload)
            else kernel
        )

        if (
            getattr(torch.ops.aten, op_overload_packet.__name__, None)
            is op_overload_packet
        ):
            self.kernel = (
                f"at::{op_overload_packet.__name__}"
                if V.graph.cpp_wrapper
                else f"aten.{kernel.__name__}"
            )
            if schema is not None:
                self.args_default_value = [
                    {"type": x.real_type, "value": x.default_value}
                    for x in schema.arguments
                    if not x.kwarg_only
                ]
                self.ordered_kwargs_for_cpp_kernel = [
                    x.name for x in schema.arguments if x.kwarg_only
                ]
                self.kwargs_default_value = {
                    x.name: {"type": x.real_type, "value": x.default_value}
                    for x in schema.arguments
                    if x.kwarg_only
                }
        elif isinstance(kernel, torch._ops.HigherOrderOperator):
            if getattr(torch._prims.rng_prims, kernel.__name__, None) is kernel:
                self.kernel = f"torch._prims.rng_prims.{kernel.__name__}"
            else:
                raise NotImplementedError(
                    "Unable to find HigherOrderOperator kernel name"
                )
        else:
            if V.graph.cpp_wrapper:
                self.use_cpp_op_schema = True
                self.set_cpp_kernel(kernel)
            else:
                self.kernel = (
                    f"{kernel.__module__.replace('._ops.', '.ops.')}.{kernel.__name__}"
                )
        self.unflatten_args = unflatten_args
        self.kwargs = {} if kwargs is None else kwargs
        V.graph.warn_fallback(self.kernel)

    def set_cpp_kernel(self, kernel):
        from .codegen.wrapper import get_cpp_op_schema

        assert (
            not kernel._schema.is_mutable
        ), f"mutable {kernel.__name__} is not supported with cpp_wrapper"

        # These checks are here because ops that return aliasing tensors will
        # return type Tensor& instead of Tensor, but codegen will always write
        # type Tensor on the LHS.
        def is_not_write(arg):
            return arg.alias_info is None or not arg.alias_info.is_write

        assert all(
            is_not_write(x) for x in kernel._schema.arguments
        ), f"{kernel.__name__} with alias_info arguments is not supported with cpp_wrapper"
        assert all(
            is_not_write(x) for x in kernel._schema.returns
        ), f"{kernel.__name__} with alias_info returns is not supported with cpp_wrapper"

        self.kernel = kernel._schema.name
        self.cpp_kernel_overlad_name = kernel._schema.overload_name
        self.cpp_kernel_key = (
            f"{self.kernel.replace('::', '_')}_{self.cpp_kernel_overlad_name}"
        )

        self.cpp_op_schema = get_cpp_op_schema(kernel)
        self.ordered_kwargs_for_cpp_kernel = [
            x.name for x in kernel._schema.arguments if x.kwarg_only
        ]

    def get_arg_default_value(self, pos):
        assert hasattr(
            self, "args_default_value"
        ), "self.args_default_value has to be provided"
        assert pos < len(
            self.args_default_value
        ), f"expected the index {pos} to be smaller than len(self.args_default_value): {len(self.args_default_value)}"
        v = self.args_default_value[pos]["value"]
        if v is None:
            arg_type = self.args_default_value[pos]["type"]
            # TODO: extend the support here
            assert (
                str(arg_type) in default_value_map
            ), f"unsupported default_value arg_type: {str(arg_type)}"
            return default_value_map[str(arg_type)]()
        else:
            return v

    def codegen_args(self):
        @dataclasses.dataclass
        class Shim:
            ref: Any

            def __repr__(self):
                return self.ref

        tensor_args = [Shim(x.codegen_reference()) for x in self.inputs]
        args, kwargs = self.unflatten_args(tensor_args, self.constant_args)
        args = [V.graph.wrapper_code.val_to_arg_str(x) for x in args]
        if V.graph.cpp_wrapper and hasattr(self, "args_default_value"):
            n_args = len(args)
            n_pos_args = len(self.args_default_value)
            # Some positional args are not provided, need to use their default value in cpp wrapper
            if n_args < n_pos_args:
                pos_args = [
                    self.get_arg_default_value(i) for i in range(n_args, n_pos_args)
                ]
                pos_args = [V.graph.wrapper_code.val_to_arg_str(x) for x in pos_args]
                args.extend(pos_args)

        # let self.codegen_kwargs handle kwargs
        self.kwargs.update(kwargs)
        return args

    @staticmethod
    def find_device(tensor_args, example_output):
        if tensor_args:
            return tensor_args[0].get_device()
        if isinstance(example_output, torch.Tensor):
            return example_output.device
        if isinstance(example_output, (list, tuple)):
            devices = {FallbackKernel.find_device(None, x) for x in example_output}
            # Remove None
            devices = [device for device in devices if device]
            if len(devices) == 1:
                return devices[0]
            for device in devices:
                if device.type == "cuda":
                    return device
            return devices[0]
        return None

    def codegen(self, wrapper):
        if self.use_cpp_op_schema:
            args = [*self.codegen_args(), *self.codegen_kwargs()]
            wrapper.generate_extern_kernel_alloc_and_find_schema_if_needed(
                self.get_name(),
                self.kernel,
                args,
                self.cpp_op_schema,
                self.cpp_kernel_key,
                self.cpp_kernel_overlad_name,
            )
        else:
            super().codegen(wrapper)

    @classmethod
    def create(cls, kernel, *args, **kwargs):
        fake_incorrect_kernels = (aten._fused_moving_avg_obs_fq_helper_functional,)
        context = (
            V.graph.fake_mode if kernel not in fake_incorrect_kernels else nullcontext()
        )
        with context:
            (
                example_output,
                tensor_args,
                non_tensor_args,
                unflatten_args,
                schema,
            ) = cls.process_kernel(kernel, *args, **kwargs)

        device = FallbackKernel.find_device(tensor_args, example_output)
        assert device, "Not sure where to find device info"
        packed = FallbackKernel(
            MultiOutputLayout(device),
            kernel,
            tensor_args,
            non_tensor_args,
            unflatten_args,
            schema=schema,
        )

        def generate_output(output, indices):
            if isinstance(output, (list, tuple)):
                return type(output)(
                    generate_output(output[i], indices + [(type(output), i)])
                    for i in range(len(output))
                )
            elif isinstance(output, torch.Tensor):
                return MultiOutput(
                    FixedLayout(
                        output.device,
                        output.dtype,
                        convert_shape_to_inductor(output.size()),
                        convert_shape_to_inductor(output.stride()),
                    ),
                    packed,
                    indices,
                )
            elif isinstance(output, int):
                return output
            else:
                assert output is None, "FallbackKernel output type is not supported"
                return None

        return generate_output(example_output, [])

    def apply_constraint(self):
        return super().apply_constraint()


@dataclasses.dataclass
class MultiOutputLayout(IRNode):
    device: torch.device


class MultiOutput(ExternKernel):
    def codegen_list_tuple_access(self, basename, indices):
        if len(indices) > 0:
            itype, i = indices[0]
            if itype == list:
                return self.codegen_list_tuple_access(f"{basename}[{i}]", indices[1:])
            elif itype == tuple:
                # cpp wrapper code needs to use std::get<> to access a tuple
                tuple_access = V.graph.wrapper_code.codegen_tuple_access(
                    basename, str(i)
                )
                return self.codegen_list_tuple_access(tuple_access, indices[1:])
            else:
                raise AssertionError("non supported index type")
        else:
            return basename

    def codegen(self, wrapper):
        line = V.graph.wrapper_code.declare
        line += f"{self.get_name()} = {self.codegen_list_tuple_access(self.inputs[0].get_name(), self.indices)}"
        line += V.graph.wrapper_code.ending
        V.graph.wrapper_code.writeline(line)
        self.codegen_size_asserts(V.graph.wrapper_code)

    def __init__(self, layout, input, indices: List[Tuple[Any, ...]]):
        super().__init__(None, layout, [input], ())
        self.name = V.graph.register_buffer(self)
        self.indices = indices

    def should_allocate(self):
        return False


def _prepare_convolution_fusion_create(
    cls,
    x: "TensorBox",
    weight: "TensorBox",
    bias: "TensorBox",
    padding: List[int],
    stride: List[int],
    dilation: List[int],
    groups: int,
    transposed: bool = False,
    output_padding: List[int] = None,
):
    """
    This function is a helper function to prepare inputs, layout and constant args
    for convolution post-op fusion's create function, including deciding the output
    layout (channels first or channels last), realizing inputs and make them etc. The
    function only supports the CPU device since conv post-op fusion kernel is only
    supported on CPU right now.
    """

    # Port from aten/src/ATen/native/ConvUtils.h: _conv_input_size
    def _conv_input_size(
        output_size, weight_size, padding, output_padding, stride, dilation, groups
    ):
        assert len(output_size) == len(weight_size), "Expect input dim == weight dim"
        dim = len(output_size)
        assert dim > 2, "Expect input dim > 2"

        BATCH_DIM = 0
        WEIGHT_INPUT_CHANNELS_DIM = 1
        input_size = []
        input_size.append(output_size[BATCH_DIM])
        input_size.append(weight_size[WEIGHT_INPUT_CHANNELS_DIM] * groups)
        for d in range(2, dim):
            kernel = (weight_size[d] - 1) * dilation[d - 2] + 1
            input_size_d = (
                (output_size[d] - 1) * stride[d - 2]
                - (padding[d - 2] * 2)
                + kernel
                + output_padding[d - 2]
            )
            input_size.append(input_size_d)
        return list(map(int, input_size))

    # The size of prepacked_weight is the prepacked weight size of deconv:
    #   Groups > 1:  [g*o, i/g, ...]
    #   Groups == 1: [o, i, ...]
    # Returns original weight size in [i, o, ...]
    def _original_deconv_weight_size(
        prepacked_weight,
        groups,
    ):
        prepacked_weight_size = prepacked_weight.size()
        dim = len(prepacked_weight_size)
        assert dim > 2, "Expect weight dim > 2"
        if groups > 1:
            weight_size = []
            weight_size.append(prepacked_weight_size[1] * groups)
            weight_size.append(prepacked_weight_size[0] / groups)
            for d in range(2, dim):
                weight_size.append(prepacked_weight_size[d])
        else:
            weight_size = prepacked_weight.transpose(0, 1).size()
        return weight_size

    x.realize()
    weight.realize()
    if bias is not None:
        bias.realize()
    with V.graph.fake_mode:
        x_fake = ir_node_to_tensor(x, guard_shape=True)
        weight_fake = ir_node_to_tensor(weight, guard_shape=True)
        dims = len(x_fake.size()) - 2
        assert 0 < len(padding) <= dims
        assert 0 < len(dilation) <= dims
        assert 0 < len(stride) <= dims
        padding = pad_listlike(padding, dims)
        dilation = pad_listlike(dilation, dims)
        stride = pad_listlike(stride, dims)
        if output_padding is None:
            output_padding = pad_listlike([0], dims)
        else:
            assert 0 < len(output_padding) <= dims
            output_padding = pad_listlike(output_padding, dims)
        assert isinstance(groups, int)
        if transposed:
            # When transposed, the size of the prepacked oneDNN weight is different
            # from the PyTorch weight. We're not able to run aten conv with such
            # size. We infer the output size from the input params here:
            weight_size = _original_deconv_weight_size(weight_fake, groups)
            input_size = x_fake.size()
            output_size = _conv_input_size(
                input_size,
                weight_size,
                padding,
                output_padding,
                stride,
                dilation,
                groups,
            )
        else:
            bias_fake = (
                ir_node_to_tensor(bias, guard_shape=True) if bias is not None else bias
            )
            output = torch.ops.aten.convolution(
                x_fake,
                weight_fake,
                bias_fake,
                stride,
                padding,
                dilation,
                transposed,
                output_padding,
                groups,
            )
            output_size = output.size()

        req_stride_order = [0] + list(reversed(range(1, len(stride) + 1)))
        req_stride_order = [len(req_stride_order)] + req_stride_order
        output_stride = make_channels_last_strides_for(output_size)

    x = cls.require_stride_order(x, req_stride_order)
    assert x.get_device().type == "cpu" and weight.get_device().type == "cpu"
    inputs = [x, weight]

    kernel_layout = FixedLayout(
        x.get_device(),
        x.get_dtype(),
        convert_shape_to_inductor(output_size),
        convert_shape_to_inductor(output_stride),
    )
    constant_args = [padding, stride, dilation, groups]
    if transposed:
        constant_args.insert(1, output_padding)

    if bias is not None:
        inputs.append(bias)
    else:
        constant_args.insert(0, bias)
    return inputs, constant_args, kernel_layout, req_stride_order


def _prepare_linear_fusion_create(
    cls,
    x: "TensorBox",
    weight: "TensorBox",
    bias: "TensorBox",
):
    """
    This function is a helper function to prepare inputs, layout and constant args
    for linear post-op fusion's create function. The function only supports the CPU device
    since linear post-op fusion kernel is only supported on CPU right now.
    """
    x.realize()
    weight.realize()
    if bias is not None:
        bias.realize()
    with V.graph.fake_mode:
        x_fake = ir_node_to_tensor(x, guard_shape=True)
        weight_fake = ir_node_to_tensor(weight, guard_shape=True)
        bias_fake = (
            ir_node_to_tensor(bias, guard_shape=True) if bias is not None else bias
        )
        if bias is not None:
            output = torch.ops.aten.addmm.default(
                bias_fake,
                x_fake,
                weight_fake,
            )
        else:
            output = torch.ops.aten.mm.default(
                x_fake,
                weight_fake,
            )
        output_size = output.size()

        req_stride_order = [1, 0]
        output_stride = make_contiguous_strides_for(output_size)

    x = cls.require_stride_order(x, req_stride_order)
    assert x.get_device().type == "cpu" and weight.get_device().type == "cpu"
    inputs = [x, weight]

    kernel_layout = FixedLayout(
        x.get_device(),
        x.get_dtype(),
        convert_shape_to_inductor(output_size),
        convert_shape_to_inductor(output_stride),
    )
    constant_args = []

    if bias is not None:
        inputs.append(bias)
    else:
        constant_args.insert(0, bias)
    return inputs, constant_args, kernel_layout, req_stride_order


class ConvolutionUnary(ExternKernelAlloc):
    def __init__(
        self,
        layout,
        inputs,
        constant_args=(),
        kernel="torch.ops.mkldnn._convolution_pointwise",
    ):
        super().__init__(
            layout,
            inputs,
            constant_args,
            None,
            kernel="torch.ops.mkldnn._convolution_pointwise",
            cpp_kernel="mkldnn::_convolution_pointwise",
        )
        self.cpp_kernel_key = "convolution_pointwise"
        self.cpp_op_schema = """
            at::Tensor(
                const at::Tensor& input_t,
                const at::Tensor& weight_t,
                const c10::optional<at::Tensor>& bias_opt,
                at::IntArrayRef padding,
                at::IntArrayRef stride,
                at::IntArrayRef dilation,
                int64_t groups,
                c10::string_view attr,
                torch::List<c10::optional<at::Scalar>> scalars,
                c10::optional<c10::string_view> algorithm)"""

    def codegen(self, wrapper):
        wrapper.generate_extern_kernel_alloc_and_find_schema_if_needed(
            self.get_name(),
            self.kernel,
            self.codegen_args(),
            self.cpp_op_schema,
            self.cpp_kernel_key,
        )
        if isinstance(self.layout, Layout):
            self.codegen_size_asserts(wrapper)

    @classmethod
    def create(
        cls,
        x: "TensorBox",
        weight: "TensorBox",
        bias: "TensorBox",
        padding_: List[int],
        stride_: List[int],
        dilation_: List[int],
        groups: int,
        attr,
        scalars,
        algorithm,
    ):
        (inputs, constant_args, kernel_layout, _) = _prepare_convolution_fusion_create(
            cls, x, weight, bias, padding_, stride_, dilation_, groups
        )
        optional_string = OptionalString()
        optional_list = OptionalList()
        constant_args = constant_args + [
            attr,
            may_convert_to_optional(optional_list, scalars),
            may_convert_to_optional(optional_string, algorithm),
        ]
        return ConvolutionUnary(
            layout=kernel_layout,
            inputs=inputs,
            constant_args=constant_args,
        )


class ConvolutionBinary(ExternKernelAlloc):
    def __init__(
        self,
        layout,
        inputs,
        constant_args=(),
        cpp_constant_args=(),
    ):
        super().__init__(
            layout,
            inputs,
            constant_args,
            None,
            kernel="torch.ops.mkldnn._convolution_pointwise.binary",
            cpp_kernel="mkldnn::_convolution_pointwise",
        )
        self.cpp_kernel_overlad_name = "binary"
        self.cpp_kernel_key = "convolution_pointwise_binary"
        self.cpp_op_schema = """
            at::Tensor(
                const at::Tensor& input_t,
                const at::Tensor& other_t,
                const at::Tensor& weight_t,
                const c10::optional<at::Tensor>& bias_opt,
                at::IntArrayRef padding,
                at::IntArrayRef stride,
                at::IntArrayRef dilation,
                int64_t groups,
                c10::string_view binary_attr,
                c10::optional<at::Scalar> alpha,
                c10::optional<c10::string_view> unary_attr,
                torch::List<c10::optional<at::Scalar>> unary_scalars,
                c10::optional<c10::string_view> unary_algorithm)"""
        self.cpp_constant_args = cpp_constant_args

    def codegen(self, wrapper):
        wrapper.generate_extern_kernel_alloc_and_find_schema_if_needed(
            self.get_name(),
            self.kernel,
            self.codegen_args(),
            self.cpp_op_schema,
            self.cpp_kernel_key,
            self.cpp_kernel_overlad_name,
        )
        if isinstance(self.layout, Layout):
            self.codegen_size_asserts(wrapper)

    @classmethod
    def create(
        cls,
        x: "TensorBox",
        other: "TensorBox",
        weight: "TensorBox",
        bias: "TensorBox",
        padding_: List[int],
        stride_: List[int],
        dilation_: List[int],
        groups: int,
        binary_attr: str,
        binary_alpha: Optional[float],
        unary_attr: Optional[str],
        unary_scalars: Optional[List[Any]],
        unary_algorithm: Optional[str],
    ):
        (
            inputs,
            constant_args,
            kernel_layout,
            req_stride_order,
        ) = _prepare_convolution_fusion_create(
            cls, x, weight, bias, padding_, stride_, dilation_, groups
        )
        other = cls.require_stride_order(other, req_stride_order)
        inputs.insert(1, other)
        optional_scalar = OptionalScalar()
        optional_string = OptionalString()
        optional_list = OptionalList()
        constant_args = constant_args + [
            binary_attr,
            may_convert_to_optional(optional_scalar, binary_alpha),
            may_convert_to_optional(optional_string, unary_attr),
            may_convert_to_optional(optional_list, unary_scalars),
            may_convert_to_optional(optional_string, unary_algorithm),
        ]
        return ConvolutionBinary(
            layout=kernel_layout,
            inputs=inputs,
            constant_args=constant_args,
        )


class ConvolutionBinaryInplace(ExternKernelAlloc):
    def __init__(
        self,
        kernel_layout,
        inputs,
        constant_args=(),
    ):
        # Due to constrain of op.call, other (Tensor&) should be at input[0]
        reordered_inputs = [inputs[1], inputs[0]] + inputs[2:]

        super().__init__(
            kernel_layout,
            reordered_inputs,
            constant_args,
            None,
            kernel="torch.ops.mkldnn._convolution_pointwise_.binary",
            cpp_kernel="mkldnn::_convolution_pointwise_",
        )
        self.cpp_kernel_overlad_name = "binary"
        self.cpp_kernel_key = "convolution_pointwise_binary_"
        # TODO: op.call: input[0] should be at::Tensor&
        self.cpp_op_schema = """
            at::Tensor&(
                at::Tensor& other_t,
                const at::Tensor& input_t,
                const at::Tensor& weight_t,
                const c10::optional<at::Tensor>& bias_opt,
                at::IntArrayRef padding,
                at::IntArrayRef stride,
                at::IntArrayRef dilation,
                int64_t groups,
                c10::string_view binary_attr,
                c10::optional<at::Scalar> alpha,
                c10::optional<c10::string_view> unary_attr,
                torch::List<c10::optional<at::Scalar>> unary_scalars,
                c10::optional<c10::string_view> unary_algorithm)"""

    def codegen(self, wrapper):
        wrapper.generate_extern_kernel_alloc_and_find_schema_if_needed(
            self.get_name(),
            self.kernel,
            self.codegen_args(),
            self.cpp_op_schema,
            self.cpp_kernel_key,
            self.cpp_kernel_overlad_name,
        )

    def get_mutation_names(self):
        assert isinstance(self.layout, MutationLayout)
        return (self.layout.target.get_name(),)

    @classmethod
    def create(
        cls,
        x: "TensorBox",
        other: "TensorBox",
        weight: "TensorBox",
        bias: "TensorBox",
        padding_: List[int],
        stride_: List[int],
        dilation_: List[int],
        groups: int,
        binary_attr: str,
        binary_alpha: Optional[float],
        unary_attr: Optional[str],
        unary_scalars: Optional[List[Any]],
        unary_algorithm: Optional[str],
    ):
        (
            inputs,
            constant_args,
            _,
            req_stride_order,
        ) = _prepare_convolution_fusion_create(
            cls, x, weight, bias, padding_, stride_, dilation_, groups
        )
        other = cls.require_stride_order(other, req_stride_order)
        inputs.insert(1, other)
        optional_scalar = OptionalScalar()
        optional_string = OptionalString()
        optional_list = OptionalList()
        constant_args = constant_args + [
            binary_attr,
            may_convert_to_optional(optional_scalar, binary_alpha),
            may_convert_to_optional(optional_string, unary_attr),
            may_convert_to_optional(optional_list, unary_scalars),
            may_convert_to_optional(optional_string, unary_algorithm),
        ]
        return ConvolutionBinaryInplace(
            kernel_layout=MutationLayout(inputs[1]),
            inputs=inputs,
            constant_args=constant_args,
        )


class MKLPackedLinear(ExternKernelAlloc):
    def __init__(
        self,
        layout,
        inputs,
        constant_args=(),
    ):
        super().__init__(
            layout,
            inputs,
            constant_args,
            None,
            kernel="torch.ops.mkl._mkl_linear",
            cpp_kernel="mkl::_mkl_linear",
        )
        self.cpp_kernel_key = "mkl_linear"
        self.cpp_op_schema = """
            at::Tensor(
                const at::Tensor& self,
                const at::Tensor& mkl_weight_t,
                const at::Tensor& origin_weight_t,
                const c10::optional<at::Tensor>& bias_opt,
                const int64_t prepack_batch_size)"""

    def codegen(self, wrapper):
        wrapper.generate_extern_kernel_alloc_and_find_schema_if_needed(
            self.get_name(),
            self.kernel,
            self.codegen_args(),
            self.cpp_op_schema,
            self.cpp_kernel_key,
        )

    @classmethod
    def create(cls, x, packed_w, orig_w, batch_size):
        x = cls.require_stride1(cls.realize_input(x))
        orig_w = cls.require_stride1(cls.realize_input(orig_w))
        *m, _ = x.get_size()
        oc, _ = orig_w.get_size()
        output_size = list(m) + [oc]
        output_stride = make_contiguous_strides_for(output_size)
        inputs = [x, packed_w, orig_w]
        constant_args = [None, batch_size]

        return MKLPackedLinear(
            layout=FixedLayout(
                x.get_device(), x.get_dtype(), output_size, output_stride
            ),
            inputs=inputs,
            constant_args=constant_args,
        )


class LinearUnary(ExternKernelAlloc):
    def __init__(
        self,
        layout,
        inputs,
        constant_args=(),
    ):
        super().__init__(
            layout,
            inputs,
            constant_args,
            None,
            kernel="torch.ops.mkldnn._linear_pointwise",
            cpp_kernel="mkldnn::_linear_pointwise",
        )
        self.cpp_kernel_key = "linear_pointwise"
        self.cpp_op_schema = """
            at::Tensor(
                const at::Tensor& input_t,
                const at::Tensor& weight_t,
                const c10::optional<at::Tensor>& bias_opt,
                c10::string_view attr,
                torch::List<c10::optional<at::Scalar>> scalars,
                c10::optional<c10::string_view> algorithm)"""

    def codegen(self, wrapper):
        wrapper.generate_extern_kernel_alloc_and_find_schema_if_needed(
            self.get_name(),
            self.kernel,
            self.codegen_args(),
            self.cpp_op_schema,
            self.cpp_kernel_key,
        )

    @classmethod
    def create(cls, x, w, b, attr, scalars, algorithm):
        x = cls.require_stride1(cls.realize_input(x))
        w = cls.require_stride1(cls.realize_input(w))

        *m, ic = x.get_size()
        oc, ic = w.get_size()

        inputs = [x, w]
        constant_args = [attr, scalars if scalars else [-1], algorithm]
        if b is not None:
            b = cls.require_stride1(cls.realize_input(b))
            inputs.append(b)
        else:
            constant_args.insert(0, None)

        return LinearUnary(
            layout=FlexibleLayout(
                device=x.get_device(),
                dtype=x.get_dtype(),
                size=list(m) + [oc],
            ),
            inputs=inputs,
            constant_args=constant_args,
        )

    def apply_constraint(self):
        pass


class LinearBinary(ExternKernelAlloc):
    kernel = "torch.ops.mkldnn._linear_pointwise.binary"

    def __init__(
        self,
        layout,
        inputs,
        constant_args=(),
    ):
        super().__init__(
            layout,
            inputs,
            constant_args,
            None,
            kernel="torch.ops.mkldnn._linear_pointwise.binary",
            cpp_kernel="mkldnn::_linear_pointwise",
        )
        self.cpp_kernel_overlad_name = "binary"
        self.cpp_kernel_key = "linear_pointwise_binary"
        self.cpp_op_schema = """
            at::Tensor(
                const at::Tensor& input_t,
                const at::Tensor& other_t,
                const at::Tensor& weight_t,
                const c10::optional<at::Tensor>& bias_opt,
                c10::string_view attr)
        """

    def codegen(self, wrapper):
        wrapper.generate_extern_kernel_alloc_and_find_schema_if_needed(
            self.get_name(),
            self.kernel,
            self.codegen_args(),
            self.cpp_op_schema,
            self.cpp_kernel_key,
            self.cpp_kernel_overlad_name,
        )

    @classmethod
    def create(cls, x, y, w, b, attr):
        x = cls.require_stride1(cls.realize_input(x))
        y = cls.require_stride1(cls.realize_input(y))
        w = cls.require_stride1(cls.realize_input(w))

        *m, ic = x.get_size()
        oc, ic = w.get_size()

        inputs = [x, y, w]
        constant_args = [attr]
        if b is not None:
            b = cls.require_stride1(cls.realize_input(b))
            inputs.append(b)
        else:
            constant_args.insert(0, b)

        return LinearBinary(
            layout=FlexibleLayout(
                device=x.get_device(),
                dtype=x.get_dtype(),
                size=list(m) + [oc],
            ),
            inputs=inputs,
            constant_args=constant_args,
        )

    def apply_constraint(self):
        pass


class ConvolutionTransposeUnary(ExternKernelAlloc):
    def __init__(
        self,
        layout,
        inputs,
        constant_args=(),
    ):
        super().__init__(
            layout,
            inputs,
            constant_args,
            None,
            kernel="torch.ops.mkldnn._convolution_transpose_pointwise",
            cpp_kernel="mkldnn::_convolution_transpose_pointwise",
        )
        self.cpp_kernel_key = "convolution_transpose_pointwise"
        self.cpp_op_schema = """
            at::Tensor(
                const at::Tensor& input_t,
                const at::Tensor& weight_t,
                const c10::optional<at::Tensor>& bias_opt,
                at::IntArrayRef padding,
                at::IntArrayRef output_padding,
                at::IntArrayRef stride,
                at::IntArrayRef dilation,
                int64_t groups,
                c10::string_view attr,
                torch::List<c10::optional<at::Scalar>> scalars,
                c10::optional<c10::string_view> algorithm)"""

    def codegen(self, wrapper):
        wrapper.generate_extern_kernel_alloc_and_find_schema_if_needed(
            self.get_name(),
            self.kernel,
            self.codegen_args(),
            self.cpp_op_schema,
            self.cpp_kernel_key,
        )

    @classmethod
    def create(
        cls,
        x: "TensorBox",
        weight: "TensorBox",
        bias: "TensorBox",
        padding_: List[int],
        output_padding_: List[int],
        stride_: List[int],
        dilation_: List[int],
        groups_: int,
        attr,
        scalars,
        algorithm,
    ):
        transposed = True
        (
            inputs,
            constant_args,
            kernel_layout,
            _,
        ) = _prepare_convolution_fusion_create(
            cls,
            x,
            weight,
            bias,
            padding_,
            stride_,
            dilation_,
            groups_,
            transposed,
            output_padding_,
        )
        optional_string = OptionalString()
        optional_list = OptionalList()
        constant_args = constant_args + [
            attr,
            may_convert_to_optional(optional_list, scalars),
            may_convert_to_optional(optional_string, algorithm),
        ]
        return ConvolutionTransposeUnary(
            layout=kernel_layout,
            inputs=inputs,
            constant_args=constant_args,
        )


class MkldnnRnnLayer(ExternKernelAlloc):
    def __init__(
        self, layout, inputs, constant_args=(), kernel="aten.mkldnn_rnn_layer"
    ):
        super().__init__(
            layout,
            inputs,
            constant_args,
        )
        self.kernel = kernel

    def codegen(self, wrapper):
        wrapper.writeline(
            f"{self.get_name()} = {self.kernel}({', '.join(self.codegen_args())})"
        )

    @classmethod
    def create(
        cls,
        x: "TensorBox",
        w0: "TensorBox",
        w1: "TensorBox",
        w2: "TensorBox",
        w3: "TensorBox",
        hx: "TensorBox",
        cx: "TensorBox",
        reverse: bool,
        batch_sizes: List[int],
        mode: int,
        hidden_size: int,
        num_layers: int,
        has_biases: bool,
        bidirectional: bool,
        batch_first: bool,
        train: bool,
    ):
        x = cls.require_stride1(cls.realize_input(x))
        # If batch_first, x has been permuted in lstm before entering the mkldnn_rnn_layer.
        # Make sure x is contiguous in batch_first case.
        x.freeze_layout()
        w0 = cls.require_stride1(cls.realize_input(w0))
        w1 = cls.require_stride1(cls.realize_input(w1))
        w2 = cls.require_stride1(cls.realize_input(w2))
        w3 = cls.require_stride1(cls.realize_input(w3))
        hx = cls.require_stride1(cls.realize_input(hx))
        hx.freeze_layout()
        cx = cls.require_stride1(cls.realize_input(cx))
        cx.freeze_layout()

        input_size = x.get_size()
        assert len(input_size) == 3, "Expect lstm input to be 3D"
        # batch_first is handled in the lstm OP. When entering
        # rnn_layer here, we'll always have batch_first = False
        seq_length, mini_batch, input_size = input_size
        output_shape = [seq_length, mini_batch, hidden_size]

        hy_shape = hx.get_size()
        cy_shape = cx.get_size()

        res: List[IRNode] = []

        inputs = [x, w0, w1, w2, w3, hx, cx]
        constant_args = [
            reverse,
            batch_sizes,
            mode,
            hidden_size,
            num_layers,
            has_biases,
            bidirectional,
            batch_first,
            train,
        ]

        packed = MkldnnRnnLayer(
            MultiOutputLayout(x.get_device()),
            inputs=inputs,
            constant_args=constant_args,
        )

        def get_strides_of_lstm_output(output_shape, batch_first):
            assert len(output_shape) == 3, "Expect output_shape to be 3D"
            return make_contiguous_strides_for(output_shape)

        indices = []
        output_sizes = [output_shape, hy_shape, cy_shape]
        output_strides = [
            get_strides_of_lstm_output(output_shape, batch_first),
            make_contiguous_strides_for(hy_shape),
            make_contiguous_strides_for(cy_shape),
        ]
        output_ir = [
            MultiOutput(
                FixedLayout(
                    x.get_device(),
                    x.get_dtype(),
                    output_size,
                    output_stride,
                ),
                packed,
                indices + [(list, i)],
            )
            for i, (output_size, output_stride) in enumerate(
                zip(output_sizes, output_strides)
            )
        ]

        return output_ir


class QConvPointWisePT2E(ExternKernelAlloc):
    def __init__(
        self,
        layout,
        inputs,
        constant_args=(),
    ):
        """
        if bias is not None
            - inputs = [x, w, b, weight_scale, weight_zp]
            - const_args is: [stride, padding, dilation, groups, x_scale, x_zp, o_inv_scale, o_zp,
              fp32_output, unary_attr, unary_scalars, unary_algorithm]
        else
            - inputs = [x, w, weight_scale, weight_zp]
            - const_args is: [bias, stride, padding, dilation, groups, x_scale, x_zp, o_inv_scale, o_zp,
              fp32_output, unary_attr, unary_scalars, unary_algorithm]
        """
        self.has_bias = len(inputs) == 5
        super().__init__(layout, inputs, constant_args)

    def codegen(self, wrapper):
        # Parser the inputs and constant
        args = [x.codegen_reference() for x in self.inputs]
        const_args = []
        const_args.extend(self.codegen_const_args())

        x = args[0]
        packed_weight = args[1]
        bias = args[2] if self.has_bias else const_args[0]
        w_scale, w_zp = args[-2], args[-1]
        (
            stride,
            padding,
            dilation,
            groups,
            x_scale,
            x_zp,
            o_inv_scale,
            o_zp,
            fp32_output,
            unary_attr,
            unary_scalars,
            unary_algorithm,
        ) = const_args[-12:]

        self.kernel = "torch.ops.onednn.qconv2d_pointwise"
        codegen_args = (
            f"{x}"
            + f", {x_scale}"
            + f", {x_zp}"
            + f", {packed_weight}"
            + f", {w_scale}"
            + f", {w_zp}"
            + f", {bias}"
            + f", {stride}"
            + f", {padding}"
            + f", {dilation}"
            + f", {groups}"
            + f", {o_inv_scale}"
            + f", {o_zp}"
            + f", {fp32_output}"
            + f", {unary_attr}"
            + f", {unary_scalars}"
            + f", {unary_algorithm}"
        )
        wrapper.writeline(f"{self.get_name()} = {self.kernel}({codegen_args})")
        if isinstance(self.layout, Layout):
            self.codegen_size_asserts(wrapper)

    @classmethod
    def create(
        cls,
        x: "TensorBox",
        x_scale: float,
        x_zp: int,
        weight: "TensorBox",  # packed_weight
        w_scale: "TensorBox",
        w_zp: "TensorBox",
        bias: "TensorBox",
        stride_: List[int],
        padding_: List[int],
        dilation_: List[int],
        groups: int,
        o_inv_scale: float,
        output_zero_point: int,
        fp32_output,
        unary_attr,
        unary_scalars,
        unary_algorithm,
    ):
        transposed = False
        output_padding = None
        (inputs, constant_args, kernel_layout, _) = _prepare_convolution_fusion_create(
            cls,
            x,
            weight,
            bias,
            padding_,
            stride_,
            dilation_,
            groups,
            transposed,
            output_padding,
        )
        # swap padding and stride to align with functional conv arg order
        if bias is None:
            constant_args[1], constant_args[2] = constant_args[2], constant_args[1]
        else:
            constant_args[0], constant_args[1] = constant_args[1], constant_args[0]

        w_scale.realize()
        w_zp.realize()
        inputs = inputs + [w_scale, w_zp]
        constant_args = constant_args + [
            x_scale,
            x_zp,
            o_inv_scale,
            output_zero_point,
            fp32_output,
            unary_attr,
            unary_scalars,
            unary_algorithm,
        ]

        if fp32_output:
            # in _prepare_convolution_fusion_create, we use x.dtype (uint8) to create kernel_layout
            # if we set fp32_output, the output buf should be dtype float32 instead of uint8.
            kernel_layout.dtype = torch.float32

        return QConvPointWisePT2E(
            layout=kernel_layout,
            inputs=inputs,
            constant_args=constant_args,
        )


class QConvPointWiseBinaryPT2E(ExternKernelAlloc):
    def __init__(
        self,
        layout,
        inputs,
        constant_args=(),
    ):
        """
        Needs input/weight/output qparams
        if bias is not None
            - inputs = [x, w, b, accum, w_scale, w_zp]
            - const_args = [stride, padding, dilation, groups, x_scale, x_zp, accum_scale, accum_zp, o_inv_scale, o_zp,
            fp32_output, binary_attr, aplha, unary_attr, unary_scalars, unary_algorithm]
        else
            - inputs = [x, w, accum, w_scale, w_zp]
            - const_args = const_args is: [bias, stride, padding, dilation, groups, x_scale, x_zp, accum_scale,
            accum_zp, o_inv_scale, o_zp, fp32_output, binary_attr, aplha, unary_attr, unary_scalars, unary_algorithm]
        """
        self.has_bias = len(inputs) == 6
        super().__init__(layout, inputs, constant_args)

    def codegen(self, wrapper):
        # Parser the inputs and constant
        args = [x.codegen_reference() for x in self.inputs]
        const_args = []
        const_args.extend(self.codegen_const_args())

        x = args[0]
        packed_weight = args[1]
        bias = args[2] if self.has_bias else const_args[0]
        accum, w_scale, w_zp = args[-3], args[-2], args[-1]
        (
            stride,
            padding,
            dilation,
            groups,
            x_scale,
            x_zp,
            accum_scale,
            accum_zp,
            o_inv_scale,
            o_zp,
            fp32_output,
            binary_attr,
            alpha,
            unary_attr,
            unary_scalars,
            unary_algorithm,
        ) = const_args[-16:]
        self.kernel = "torch.ops.onednn.qconv2d_pointwise.binary"
        conv_args = (
            f"{x}"
            + f", {x_scale}"
            + f", {x_zp}"
            + f", {accum}"
            + f", {accum_scale}"
            + f", {accum_zp}"
            + f", {packed_weight}"
            + f", {w_scale}"
            + f", {w_zp}"
            + f", {bias}"
            + f", {stride}"
            + f", {padding}"
            + f", {dilation}"
            + f", {groups}"
            + f", {o_inv_scale}"
            + f", {o_zp}"
            + f", {fp32_output}"
            + f", {binary_attr}"
            + f", {alpha}"
            + f", {unary_attr}"
            + f", {unary_scalars}"
            + f", {unary_algorithm}"
        )
        wrapper.writeline(f"{self.get_name()} = {self.kernel}({conv_args})")
        if isinstance(self.layout, Layout):
            self.codegen_size_asserts(wrapper)

    @classmethod
    def create(
        cls,
        x: "TensorBox",
        x_scale,
        x_zp,
        accum: "TensorBox",
        accum_scale,
        accum_zp,
        weight: "TensorBox",  # packed_weight
        w_scale,
        w_zp,
        bias: "TensorBox",
        stride_: List[int],
        padding_: List[int],
        dilation_: List[int],
        groups: int,
        o_inv_scale: "TensorBox",
        output_zero_point: "TensorBox",
        fp32_output,
        binary_attr,
        alpha,
        unary_attr,
        unary_scalars,
        unary_algorithm,
    ):
        transposed = False
        output_padding = None
        (
            inputs,
            constant_args,
            kernel_layout,
            req_stride_order,
        ) = _prepare_convolution_fusion_create(
            cls,
            x,
            weight,
            bias,
            padding_,
            stride_,
            dilation_,
            groups,
            transposed,
            output_padding,
        )

        accum = cls.require_stride_order(accum, req_stride_order)
        inputs.append(accum)

        # swap padding and stride to align with functional conv arg order
        if bias is None:
            constant_args[1], constant_args[2] = constant_args[2], constant_args[1]
        else:
            constant_args[0], constant_args[1] = constant_args[1], constant_args[0]

        w_scale.realize()
        w_zp.realize()
        inputs = inputs + [w_scale, w_zp]
        constant_args = constant_args + [
            x_scale,
            x_zp,
            accum_scale,
            accum_zp,
            o_inv_scale,
            output_zero_point,
            fp32_output,
            binary_attr,
            alpha,
            unary_attr,
            unary_scalars,
            unary_algorithm,
        ]
        if fp32_output:
            # in _prepare_convolution_fusion_create, we use x.dtype (uint8) to create kernel_layout
            # if we set fp32_output, the output buf should be dtype float32 instead of uint8.
            kernel_layout.dtype = torch.float32

        return QConvPointWiseBinaryPT2E(
            layout=kernel_layout,
            inputs=inputs,
            constant_args=constant_args,
        )


class QLinearPointwisePT2E(ExternKernelAlloc):
    def __init__(
        self,
        layout,
        inputs,
        constant_args=(),
    ):
        """
        if bias is not None
            - inputs = [x, w, b, weight_scale, weight_zp]
            - const_args is: [x_scale, x_zp, o_inv_scale, o_zp,
              fp32_output, unary_attr, unary_scalars, unary_algorithm]
        else
            - inputs = [x, w, weight_scale, weight_zp]
            - const_args is: [bias, x_scale, x_zp, o_inv_scale, o_zp,
              fp32_output, unary_attr, unary_scalars, unary_algorithm]
        """
        self.has_bias = len(inputs) == 5
        super().__init__(layout, inputs, constant_args)

    def codegen(self, wrapper):
        # Parser the inputs and constant
        args = [x.codegen_reference() for x in self.inputs]
        const_args = []
        const_args.extend(self.codegen_const_args())

        x = args[0]
        packed_weight = args[1]
        bias = args[2] if self.has_bias else const_args[0]
        w_scale, w_zp = args[-2], args[-1]
        (
            x_scale,
            x_zp,
            o_inv_scale,
            o_zp,
            fp32_output,
            unary_attr,
            unary_scalars,
            unary_algorithm,
        ) = const_args[-8:]

        self.kernel = "torch.ops.onednn.qlinear_pointwise"
        codegen_args = (
            f"{x}"
            + f", {x_scale}"
            + f", {x_zp}"
            + f", {packed_weight}"
            + f", {w_scale}"
            + f", {w_zp}"
            + f", {bias}"
            + f", {o_inv_scale}"
            + f", {o_zp}"
            + f", {fp32_output}"
            + f", {unary_attr}"
            + f", {unary_scalars}"
            + f", {unary_algorithm}"
        )
        wrapper.writeline(f"{self.get_name()} = {self.kernel}({codegen_args})")
        if isinstance(self.layout, Layout):
            self.codegen_size_asserts(wrapper)

    @classmethod
    def create(
        cls,
        x: "TensorBox",
        x_scale: float,
        x_zp: int,
        weight: "TensorBox",  # packed_weight
        w_scale: "TensorBox",
        w_zp: "TensorBox",
        bias: "TensorBox",
        o_inv_scale: float,
        output_zero_point: int,
        fp32_output,
        unary_attr,
        unary_scalars,
        unary_algorithm,
    ):
        (inputs, constant_args, kernel_layout, _) = _prepare_linear_fusion_create(
            cls,
            x,
            weight,
            bias,
        )

        w_scale.realize()
        w_zp.realize()
        inputs = inputs + [w_scale, w_zp]
        constant_args = constant_args + [
            x_scale,
            x_zp,
            o_inv_scale,
            output_zero_point,
            fp32_output,
            unary_attr,
            unary_scalars,
            unary_algorithm,
        ]

        if fp32_output:
            # in _prepare_linear_fusion_create, we use x.dtype (uint8) to create kernel_layout
            # if we set fp32_output, the output buf should be dtype float32 instead of uint8.
            kernel_layout.dtype = torch.float32

        return QLinearPointwisePT2E(
            layout=kernel_layout,
            inputs=inputs,
            constant_args=constant_args,
        )


@dataclasses.dataclass
class MutableBox(IRNode):
    """
    TensorBox / StorageBox allow in-place mutation of Tensors
    """

    data: IRNode

    def __getattr__(self, name):
        fn = getattr(self.data, name)
        if callable(fn):
            return fn
        raise AttributeError(f"{type(self.data).__name__}.{name} not callable")

    def realize(self):
        return self.data.realize()

    @property
    def layout(self):
        return self.data.layout

    def __str__(self):
        if isinstance(self.data, MutableBox):
            line0 = f"{type(self).__name__}({type(self.data).__name__}("
            endl = "))"
            inner = self.data.data
        else:
            line0 = f"{type(self).__name__}("
            inner = self.data
            endl = ")"

        lines = [
            line0,
            indent(str(inner)),
            endl,
        ]
        return "\n".join(lines)

    __repr__ = __str__


class TensorBox(MutableBox):
    @staticmethod
    def create(data):
        return TensorBox(StorageBox(data))


class StorageBox(MutableBox):
    def is_input_buffer(self):
        if isinstance(self.data, (InputBuffer, ReinterpretView)):
            return self.data.get_name() in V.graph.graph_inputs
        return False

    def realize(self):
        if isinstance(
            self.data,
            (
                ComputedBuffer,
                InputsKernel,
                InputBuffer,
                ReinterpretView,
                TemplateBuffer,
            ),
        ):
            return self.data.get_name()
        assert isinstance(self.data, (Pointwise, Reduction)), type(self.data)
        origin_node = self.data.get_origin_node()
        traceback = self.data.get_traceback()
        self.data = ComputedBuffer(
            name=None,
            layout=FlexibleLayout(
                device=self.data.get_device(),
                dtype=self.data.get_dtype(),
                size=self.data.get_size(),
            ),
            data=self.data,
        )
        self.data.name = V.graph.register_buffer(self.data)
        self.data.origins = self.origins
        self.data.origin_node = origin_node
        self.data.traceback = traceback
        return self.data.name

    def realize_hint(self):
        """
        Called on buffers we expect to be forced to realize later.
        """
        if (
            isinstance(self.data, (Pointwise, Reduction))
            and self.num_reads() > 1
            and self.is_pointwise_non_scalar_tensor_num_reads_larger_than_one()
        ):
            self.realize()

    def has_exceeded_max_reads(self):
        return isinstance(self.data, Pointwise) and (
            self.num_reads() > config.realize_acc_reads_threshold
            or self.inner_fn_str_len() > config.realize_bytes_threshold
        )

    def mark_reuse(self, users):
        """
        A heuristic to decide if we should realize a tensor
        that is used multiple times.
        """

        def should_realize_on_cpu(loops: Union[Pointwise, Reduction]):
            """
            The heuristic for realizing reused result of heavy ops on cpu
            """
            heavy_ops = ["exp"]  # a list of heavy ops
            fn_str = loops.inner_fn_str()
            return any((op + "(") in fn_str for op in heavy_ops)

        if (
            users > 1
            and isinstance(self.data, (Pointwise, Reduction))
            and (
                self.num_reads() > config.realize_reads_threshold
                or len(self.inner_fn_str()) > config.realize_bytes_threshold
                or (is_cpu(self.data) and should_realize_on_cpu(self.data))
            )
        ):
            self.realize()

    @cache_on_self
    def num_reads(self):
        data = self.data
        if isinstance(data, (InputsKernel, InputBuffer, ReinterpretView)):
            return 1
        if isinstance(data, ComputedBuffer):
            read_writes = data.get_read_writes()
        else:
            assert isinstance(data, (Pointwise, Reduction)), type(data)
            read_writes = ComputedBuffer(
                name=None,
                layout=FlexibleLayout(
                    device=data.get_device(),
                    dtype=data.get_dtype(),
                    size=data.get_size(),
                ),
                data=data,
            ).get_read_writes()
        return len(read_writes.reads)

    @cache_on_self
    def is_pointwise_non_scalar_tensor_num_reads_larger_than_one(self):
        # Skip the check for non Pointwise instances
        return (
            (sum(read.index != 0 for read in self.data.get_reads()) > 1)
            if isinstance(self.data, Pointwise)
            else True
        )


class InterpreterShim(torch.fx.Interpreter):
    @staticmethod
    @functools.lru_cache(None)
    def _dummy_gm():
        return torch.fx.symbolic_trace(identity)

    def __init__(self, graph, submodules):
        # call super() with a placeholder to avoid constructing a
        # GraphModule which is very expensive (it does codegen).
        super().__init__(self._dummy_gm(), garbage_collect_values=False)
        self.module = self
        self.graph = graph
        self.submodules = submodules
        self.extra_traceback = False
        self.fetch_attr = submodules.__getitem__
        self.current_node = None

    def run_node(self, n: torch.fx.Node) -> Any:
        self.current_node = n
        return super().run_node(n)

    def run(self, *args, **kwargs):
        with V.set_interpreter_handler(self):
            return super().run(*args, **kwargs)


class LoopBody:
    """
    Captures the body of a Loops subclass into an FX graph.  Persists any
    indexing simplifications and makes it easier to analyze loop bodies.
    """

    def __init__(self, fn, args, var_ranges):
        super().__init__()
        self.var_ranges = var_ranges
        self.indexing_exprs = {}
        self.indexing_exprs_name = {}
        self.reads = []
        self.writes = []
        self.reads_name2expr = {}
        self.writes_name2expr = {}
        self.other = []
        self.submodules = {"get_index": self.get_index}
        self.subblocks = {}
        self.indirect_vars = []
        self.root_block = LoopBodyBlock(self, fn, args)
        self.indexing = None

    @cache_on_self
    def get_nodes(self):
        all_graphs = itertools.chain(
            (self.root_block.graph,),
            (block.graph for block in self.subblocks.values()),
        )
        return [node for graph in all_graphs for node in graph.nodes]

    @cache_on_self
    def bounds(self):
        # Doing a local import to avoid dumping all the code here
        from .bounds import BoundVars

        return BoundVars(self)

    def debug_str(self):
        lines = [f"var_ranges = {dict(self.var_ranges)}"]
        lines.extend([f"{name} = {val}" for name, val in self.indexing_exprs.items()])
        lines.extend(
            [
                block.debug_str(name)
                for name, block in itertools.chain(
                    [("body", self.root_block)], self.subblocks.items()
                )
            ]
        )
        return "\n".join(lines)

    def add_index_expr(self, expr: sympy.Expr, category, buf_name):
        getattr(self, category).append(expr)
        if buf_name is not None:
            getattr(self, f"{category}_name2expr")[buf_name] = expr
        if expr not in self.indexing_exprs_name:
            name = f"index{len(self.indexing_exprs)}"
            self.indexing_exprs_name[expr] = name
            self.indexing_exprs[name] = expr
        return self.indexing_exprs_name[expr]

    def add_submodule(self, block, prefix):
        """Not actually for nn.Modules, but subblocks in generated code are mapped to FX call_module opcodes"""
        if prefix[-1].isnumeric() and prefix not in self.submodules:
            name = prefix
        else:
            name = f"{prefix}{len(self.submodules)}"
        self.submodules[name] = block
        return name

    def add_indirect(self, size):
        name = f"indirect{len(self.indirect_vars)}"
        var = sympy_symbol(name)
        self.indirect_vars.append(var)
        return var

    def replace_indirect(self, old, new):
        """Swap in a variable used in indirect indexing"""
        if str(old) == str(new):
            return
        assert self.indexing is not None
        self.indexing = {k: sympy_subs(v, {old: new}) for k, v in self.indexing.items()}

    def get_index(self, name):
        assert self.indexing is not None
        return self.indexing[name]

    def __call__(self, *indices):
        index = list(itertools.chain(*indices))
        assert len(index) == len(self.var_ranges), (index, self.var_ranges)
        assert all(v not in self.var_ranges for v in index)
        replacements = dict(zip(self.var_ranges.keys(), index))
        self.indexing = {
            name: sympy_subs(expr, replacements)
            for name, expr in self.indexing_exprs.items()
        }
        result = self.root_block()
        self.indexing = None
        return result


class LoopBodyBlock:
    """
    Captures the body of a Loops subclass into an FX graph.
    In normal cases there will be a 1:1 mapping between LoopBody and
    LoopBodyBlock, hower in the case of ops.masked() the masked out
    operations will manifest as an extra LoopBodyBlock.
    """

    def __init__(self, body: LoopBody, fn: Callable[..., Any], args: List[Any]):
        self.body = body

        def add_index(expr, category, buf_name=None):
            return tracer.create_proxy(
                "call_module",
                "get_index",
                (self.body.add_index_expr(expr, category, buf_name),),
                {},
            )

        class CaptureIndexing(V.WrapperHandler):
            self.name = "CaptureIndexing"

            def load(self, name: str, index: sympy.Expr):
                index = add_index(index, "reads", name)
                return self._inner.load(name, index)

            def store(self, name, index, value, mode=None):
                index = add_index(index, "writes", name)
                return self._inner.store(name, index, value, mode)

            def store_reduction(self, name, index, value):
                index = add_index(index, "writes", name)
                return self._inner.store_reduction(name, index, value)

            def reduction(self, dtype, src_dtype, reduction_type, value):
                result = self._inner.reduction(dtype, src_dtype, reduction_type, value)
                if "welford" in reduction_type:
                    return tuple(result[i] for i in range(3))
                return result

            def index_expr(self, index, dtype):
                if isinstance(index, (int, sympy.Integer)):
                    return self._inner.constant(int(index), dtype)
                index = add_index(index, "other")
                return self._inner.index_expr(index, dtype)

            def bucketize(
                self,
                values,
                offsets_name: str,
                offsets_size: sympy.Expr,
                indexing_dtype: torch.dtype,
                right: bool,
            ):
                offsets_size = add_index(offsets_size, "other")
                return self._inner.bucketize(
                    values, offsets_name, offsets_size, indexing_dtype, right
                )

            @staticmethod
            def masked(mask_proxy, masked_body: Callable[..., Any], other_proxy):
                """
                Recursively capture the masked out body in another LoopBodyBlock
                """

                def shim(mask, other):
                    return V.ops.masked(mask, subblock, other)

                name = self.body.add_submodule(shim, "masked_subblock")
                subblock = LoopBodyBlock(self.body, masked_body, [])
                self.body.subblocks[name] = subblock
                return tracer.create_proxy(
                    "call_module", name, (mask_proxy, other_proxy), {}
                )

            @staticmethod
            def indirect_indexing(index_proxy, size, check=True):
                """
                Flow data from tensors into indexing formulas.
                Introduce a call_module to update the indexing.
                """

                def set_indirect(new_var):
                    self.body.replace_indirect(
                        var, V.ops.indirect_indexing(new_var, size, check)
                    )

                var = self.body.add_indirect(size)
                tracer.create_proxy(
                    "call_module",
                    self.body.add_submodule(set_indirect, f"set_{var}"),
                    (index_proxy,),
                    {},
                )
                return var

            @staticmethod
            def output(result):
                tracer.create_proxy("output", "output", (result,), {})

        tracer = torch.fx.Tracer()
        tracer.graph = torch.fx.Graph(tracer_cls=tracer.__class__)
        proxy_ops = tracer.create_proxy("placeholder", "ops", (), {})

        from .index_propagation import IndexPropagation
        from .sizevars import SimplifyIndexing

        handler = SimplifyIndexing(CaptureIndexing(proxy_ops), self.body.var_ranges)
        if config.constant_and_index_propagation:
            handler = IndexPropagation(handler)

        with V.set_ops_handler(handler):
            # This indirection is just a cute way to get IndexPropagation to
            # unwrap the return value.
            ops.output(fn(*args))
        self.graph = tracer.graph

    def __call__(self):
        graph = self.graph
        submodules = self.body.submodules

        return InterpreterShim(graph, submodules).run(V.get_ops_handler())

    def debug_str(self, name="block"):
        code = torch.fx.GraphModule(self.body.submodules, self.graph).code
        return re.sub(
            # strip `; del var0` suffixes to make output prettier
            r";[^\n]*",
            "",
            code.strip().replace("def forward(", f"def {name}("),
        )


class Wait(ExternKernelAlloc):
    """
    Wait should not be used by itself.  It should always be constructed in tandem
    with a collective op that produces a work to wait on.
    """

    def __init__(
        self,
        layout,
        inputs,
        constant_args=(),
    ):
        super().__init__(layout, inputs, constant_args)

    def should_allocate(self):
        return False

    def codegen(self, wrapper):
        wrapper.add_import_once(
            "from torch.distributed._functional_collectives_impl import _wait_tensor"
        )
        (input_collective,) = (t.codegen_reference() for t in self.inputs)
        wrapper.writeline(f"{input_collective} = _wait_tensor({input_collective})")

        # wait op still needs to produce a 'buffer' that represents the tensor output.
        # this is a symbolic gesture, and it gets handled by WrapperCodegen.
        # codegen outputs a '# reuse' line that assigns the input buffer here ('input_collective')
        # to a new name (`self.get_name()`) and `del`s the old name.
        wrapper.writeline(f"{self.get_name()} = {input_collective}")

    @classmethod
    def create(cls, collective_op: "TensorBox"):
        # TODO(whc) i'm not sure what's going on here, this probably means I missed something upstream
        collective_op.decide_layout()
        return Wait(
            layout=collective_op.get_layout(),
            inputs=[collective_op],
        )

    def get_alias_names(self):
        # Signal to codegen that our output buffer isn't safe to reuse
        return [self.inputs[0].codegen_reference()]


class CollectiveKernel(ExternKernel):
    """
    Each collective should follow the pattern:
    - extend InPlaceCollectiveKernel or OutOfPlaceCollectiveKernel.
    - the kernel delegates into c10d processgroup, which returns a 'work' obj
    - the work obj is registered via _register_tensor_work so it can be waited on later
    """

    def __init__(self, layout, inputs, constant_args):
        super().__init__(None, layout, inputs, constant_args)
        self.name = V.graph.register_buffer(self)

    def codegen_collective(self, wrapper, output_name, input_names):
        # factor so the boilerplate can be handled in CollectiveKernel.codegen
        raise NotImplementedError("Must implement")

    def codegen_output(self, wrapper, output_name, input_names):
        # factor so the boilerplate can be handled in CollectiveKernel.codegen
        raise NotImplementedError("Must implement")

    @classmethod
    def wrap_inputs_as_inplace(cls, inputs):
        def wrap_input(var):
            op = InPlaceHint(
                FlexibleLayout(var.get_device(), var.get_dtype(), var.get_size()), var
            )
            return TensorBox.create(op)

        return list(map(wrap_input, inputs))

    def codegen(self, wrapper):
        wrapper.add_import_once("import torch.distributed as dist")
        wrapper.add_import_once("import torch.distributed.distributed_c10d as c10d")
        wrapper.add_import_once(
            "import torch.distributed._functional_collectives_impl as fun_col_impl"
        )
        # extract references to our args in string form for codegen output
        input_names = [t.codegen_reference() for t in self.inputs]
        output_name = self.get_name()
        tag, ranks, group_size = self.constant_args

        # TODO: avoid more than one ref of the same pg (even though they are cached inside the api)
        wrapper.writeline(
            f"{output_name}_pg = c10d._find_or_create_pg_by_ranks_and_tag('{tag}', {ranks}, {group_size})"
        )

        self.codegen_output(wrapper, output_name, input_names)
        self.codegen_collective(wrapper, output_name, input_names)
        wrapper.writeline(
            f"fun_col_impl._register_tensor_work({output_name}, {output_name}_work)"
        )


class InPlaceCollectiveKernel(CollectiveKernel):
    """
    InPlaceCollectiveKernel are those with in-out arguments such as all_reduce.
    Extend this kernel if your collective needs to modify its inputs in-place.
    """

    def __init__(self, layout, inputs, constant_args):
        super().__init__(layout, inputs, constant_args)

    def should_allocate(self):
        return False

    def has_side_effects(self):
        return True

    def codegen_output(self, wrapper, output_name, input_names):
        if len(input_names) > 1:
            wrapper.writeline(f"{output_name} = [{','.join(input_names)}] ")
        else:
            wrapper.writeline(f"{output_name} = {input_names[0]}")


class OutOfPlaceCollectiveKernel(CollectiveKernel):
    """
    OutOfPlaceCollectiveKernel are those that allocate their
    outputs and leave their inputs inplace, such as all_gather.
    """

    def __init__(self, layout, inputs, outputs, constant_args):
        super().__init__(layout, inputs + outputs, constant_args)
        self.outputs = outputs
        self.original_inputs = inputs

    def should_allocate(self):
        return False

    def has_side_effects(self):
        return True

    def codegen_output(self, wrapper, output_name, input_names):
        input_names = [t.codegen_reference() for t in self.original_inputs]
        wrapper.writeline(f"{output_name}_inputs = [{','.join(input_names)}]")
        wrapper.writeline(f"{output_name} = [{','.join(x.name for x in self.outputs)}]")

    @classmethod
    def create_output_buffers(cls, inputs, size_cb=None):
        outputs = []
        for input in inputs:
            new_size = input.get_size()
            if size_cb is not None:
                size_cb(new_size)
            # new_size[0] *= group_size

            buff = OutputBuffer(
                layout=FlexibleLayout(
                    device=input.get_device(),
                    dtype=input.get_dtype(),
                    size=new_size,
                ),
            )
            outputs.append(buff)
        return outputs

    @classmethod
    def create_output_nodes(cls, coll, output_buffers):
        return [
            MultiOutputNoSizeAssert(
                out_t.layout,
                coll,
                f"[{i}]",
            )
            for i, out_t in enumerate(output_buffers)
        ]


class InPlaceHint(ExternKernel):
    """
    Helper OP to encode an in/out argument that tries to make it inplace whenever possible.
    Wrap the input of your inplace op to enable this behavior.

    The design is based on two key decisions:
    - this node is resposible for allocating the in/out buffer used by the collective.
        This is controlled by the ``should_allocate`` method that returns True here and
        False for the collective node
    - The scheduler special-case this node and enable it to reuse its input.
    """

    def codegen(self, wrapper):
        input_name = self.inputs[0].codegen_reference()
        output_name = self.get_name()
        if not wrapper.did_reuse(self, self.inputs[0]):
            wrapper.writeline(f"{output_name}.copy_({input_name}) #no reuse")

    def __init__(self, layout, input):
        input = self.realize_input(input)
        super().__init__(None, layout, self.unwrap_storage([input]), ())
        self.name = V.graph.register_buffer(self)

    def should_allocate(self):
        return True


class OutputBuffer(ExternKernel):
    """
    Represent the output buffer used by ops that require multiple of them
    """

    def __init__(self, layout):
        super().__init__(name=None, layout=layout, inputs=[])
        self.name = V.graph.register_buffer(self)

    def should_allocate(self):
        return True

    def codegen(self, wrapper):
        wrapper.writeline(f"# collective out buffer {self.name}")


class MultiOutputNoSizeAssert(MultiOutput):
    """
    Extract partial output from a multi-output OP.
    Works like MultiOutput but doesn't assert size. This must be a property guaranteed by the op emiting this.
    """

    def __init__(self, layout, input, index):
        super().__init__(layout, input, [])
        self.index = index

    def codegen(self, wrapper):
        wrapper.writeline(
            f"{self.get_name()} = {self.inputs[0].get_name()}{self.index}"
        )


class AllReduceCoalesced(InPlaceCollectiveKernel):
    def __init__(self, layout, inputs, constant_args, reduce_op):
        super().__init__(layout, inputs, constant_args)
        self.reduce_op = reduce_op

    def should_allocate(self):
        return False

    @classmethod
    def create(
        cls,
        inputs: List["TensorBox"],
        reduce_op: str,
        tag: str,
        ranks: List[int],
        group_size: int,
    ):
        inplace_inputs = cls.wrap_inputs_as_inplace(inputs)
        layout = MultiOutputLayout(inputs[0].get_device())

        _ = AllReduceCoalesced(
            layout=layout,
            inputs=inplace_inputs,
            constant_args=[tag, ranks, group_size],
            reduce_op=reduce_op,
        )
        return inplace_inputs

    def codegen_collective(self, wrapper, output_name, input_names):
        wrapper.writeline(
            f"{output_name}_work = dist.all_reduce_coalesced("
            f"{output_name}, "
            f"op=fun_col_impl._str_to_reduce_op('{str(self.reduce_op)}'), "
            f"group={output_name}_pg, "
            "async_op=True)"
        )


class AllReduce(InPlaceCollectiveKernel):
    def __init__(self, layout, inputs, constant_args, reduce_op):
        super().__init__(layout, inputs, constant_args)
        self.reduce_op = reduce_op

    @classmethod
    def create(
        cls, x: "TensorBox", reduce_op: str, tag: str, ranks: List[int], group_size: int
    ):
        inplace_inputs = cls.wrap_inputs_as_inplace([x])
        layout = MultiOutputLayout(inplace_inputs[0].get_device())

        _ = AllReduce(
            layout=layout,
            inputs=inplace_inputs,
            constant_args=[tag, ranks, group_size],
            reduce_op=reduce_op,
        )
        return inplace_inputs[0]

    def codegen_collective(self, wrapper, output_name, input_names):
        wrapper.writeline(
            f"{output_name}_work = dist.all_reduce("
            f"{output_name}, async_op=True, group={output_name}_pg, op=fun_col_impl._str_to_reduce_op('{str(self.reduce_op)}'))"
        )


class AllGatherIntoTensor(OutOfPlaceCollectiveKernel):
    def __init__(self, layout, inputs, outputs, constant_args):
        super().__init__(layout, inputs, outputs, constant_args)

    @classmethod
    def create(cls, x: "TensorBox", tag: str, ranks: List[int], group_size: int):
        inputs = [cls.realize_input(x)]

        def compute_size(new_size):
            new_size[0] *= group_size

        outputs = cls.create_output_buffers(inputs, compute_size)

        layout = MultiOutputLayout(inputs[0].get_device())

        packed = AllGatherIntoTensor(
            layout=layout,
            inputs=inputs,
            outputs=outputs,
            constant_args=[tag, ranks, group_size],
        )
        return cls.create_output_nodes(packed, outputs)[0]

    def codegen_collective(self, wrapper, output_name, input_names):
        wrapper.writeline(
            f"{output_name}_work = dist.all_gather_into_tensor("
            f"{output_name}[0], {output_name}_inputs[0], async_op=True, group={output_name}_pg)"
        )


class ReduceScatterTensor(OutOfPlaceCollectiveKernel):
    def __init__(self, layout, inputs, outputs, constant_args, reduce_op):
        super().__init__(layout, inputs, outputs, constant_args)
        self.reduce_op = reduce_op

    @classmethod
    def create(
        cls,
        x: "TensorBox",
        reduce_op: str,
        tag: str,
        ranks: List[int],
        group_size: int,
    ):
        inputs = [cls.realize_input(x)]

        def compute_size(new_size):
            new_size[0] //= group_size

        outputs = cls.create_output_buffers(inputs, compute_size)

        layout = MultiOutputLayout(inputs[0].get_device())

        packed = ReduceScatterTensor(
            layout=layout,
            inputs=inputs,
            outputs=outputs,
            constant_args=[tag, ranks, group_size],
            reduce_op=reduce_op,
        )
        return cls.create_output_nodes(packed, outputs)[0]

    def codegen_collective(self, wrapper, output_name, input_names):
        wrapper.writeline(
            f"{output_name}_work = dist.reduce_scatter_tensor("
            f"{output_name}[0], {output_name}_inputs[0], "
            f"async_op=True, group={output_name}_pg, op=fun_col_impl._str_to_reduce_op('{str(self.reduce_op)}'))"
        )


class AllGatherIntoTensorCoalesced(OutOfPlaceCollectiveKernel):
    def __init__(self, layout, inputs, outputs, constant_args):
        super().__init__(layout, inputs, outputs, constant_args)

    @classmethod
    def create(
        cls,
        inputs: List["TensorBox"],
        tag: str,
        ranks: List[int],
        group_size: int,
    ):
        inputs = [cls.realize_input(x) for x in inputs]

        def compute_size(new_size):
            new_size[0] *= group_size

        outputs = cls.create_output_buffers(inputs, compute_size)

        layout = MultiOutputLayout(inputs[0].get_device())

        packed = AllGatherIntoTensorCoalesced(
            layout=layout,
            inputs=inputs,
            outputs=outputs,
            constant_args=[tag, ranks, group_size],
        )

        return outputs
        # return cls.create_output_nodes(packed, outputs)

    def codegen_collective(self, wrapper, output_name, input_names):
        wrapper.writeline(
            f"{output_name}_work = fun_col_impl._all_gather_into_tensor_coalesced_fallback("
            f"output_tensors={output_name}, "
            f"input_tensors={output_name}_inputs, "
            f"group={output_name}_pg, "
            "async_op=True)"
        )


class ReduceScatterTensorCoalesced(OutOfPlaceCollectiveKernel):
    def __init__(self, layout, inputs, outputs, constant_args, reduce_op):
        super().__init__(layout, inputs, outputs, constant_args)
        self.reduce_op = reduce_op

    @classmethod
    def create(
        cls,
        inputs: List["TensorBox"],
        reduce_op: str,
        tag: str,
        ranks: List[int],
        group_size: int,
    ):
        inputs = [cls.realize_input(x) for x in inputs]

        def compute_size(new_size):
            new_size[0] //= group_size

        outputs = cls.create_output_buffers(inputs, compute_size)

        layout = MultiOutputLayout(inputs[0].get_device())

        _ = ReduceScatterTensorCoalesced(
            layout=layout,
            inputs=inputs,
            outputs=outputs,
            constant_args=[tag, ranks, group_size],
            reduce_op=reduce_op,
        )

        return outputs

    def codegen_collective(self, wrapper, output_name, input_names):
        wrapper.writeline(
            f"{output_name}_work = fun_col_impl._reduce_scatter_tensor_coalesced_fallback("
            f"output_tensors={output_name}, "
            f"input_tensors={output_name}_inputs, "
            f"op=fun_col_impl._str_to_reduce_op('{str(self.reduce_op)}'), "
            f"group={output_name}_pg, "
            "async_op=True)"
        )