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# mypy: allow-untyped-defs
import contextlib
import dataclasses
import functools
import math
import sys
from collections import namedtuple
from typing import Any, Callable, Dict, List, Optional, Sequence, Set, Tuple
from unittest.mock import patch
import sympy
import torch
from torch._prims_common import is_integer_dtype
from torch.utils._ordered_set import OrderedSet
from torch.utils._sympy.printers import CppPrinter as _CppPrinter
from torch.utils._sympy.symbol import symbol_is_type, SymT
from torch.utils._sympy.value_ranges import ValueRanges
from .. import ir
from ..dependencies import Dep
from ..loop_body import LoopBody
from ..scheduler import BaseSchedulerNode, SchedulerBuffer
from ..utils import IndentedBuffer, sympy_index_symbol_with_prefix, sympy_subs
from ..virtualized import ops, OpsValue, V
from .common import (
CSEVariable,
deduce_output_dtype_by_name,
Kernel,
KernelArgs,
OptimizationContext,
)
DTYPE_TO_CPP = {
torch.float32: "float",
torch.float64: "double",
torch.float16: "half",
torch.int64: "int64_t",
torch.int32: "int32_t",
torch.int16: "int16_t",
torch.int8: "int8_t",
torch.uint64: "uint64_t",
torch.uint32: "uint32_t",
torch.uint16: "uint16_t",
torch.uint8: "uint8_t",
torch.bool: "bool",
torch.bfloat16: "bfloat16",
torch.complex64: "c10::complex<float>",
torch.float8_e4m3fn: "float8_e4m3fn",
torch.float8_e5m2: "float8_e5m2",
torch.float8_e4m3fnuz: "float8_e4m3fnuz",
torch.float8_e5m2fnuz: "float8_e5m2fnuz",
}
DTYPE_TO_ATEN = {
torch.float32: "at::kFloat",
torch.float64: "at::kDouble",
torch.float16: "at::kHalf",
torch.int64: "at::kLong",
torch.int32: "at::kInt",
torch.int16: "at::kShort",
torch.int8: "at::kChar",
torch.uint64: "at::kUInt64",
torch.uint32: "at::kUInt32",
torch.uint16: "at::kUInt16",
torch.uint8: "at::kByte",
torch.uint32: "at::kUInt32",
torch.uint64: "at::kUInt64",
torch.bool: "at::kBool",
torch.bfloat16: "at::kBFloat16",
torch.complex32: "at::kComplexHalf",
torch.complex64: "at::kComplexFloat",
torch.complex128: "at::kComplexDouble",
torch.float8_e4m3fn: "at::kFloat8_e4m3fn",
torch.float8_e5m2: "at::kFloat8_e5m2",
torch.float8_e4m3fnuz: "at::kFloat8_e4m3fnuz",
torch.float8_e5m2fnuz: "at::kFloat8_e5m2fnuz",
}
DEVICE_TO_ATEN = {
"cpu": "at::kCPU",
"cuda": "at::kCUDA",
"xpu": "at::kXPU",
}
LAYOUT_TO_ATEN = {
torch.strided: "at::kStrided",
torch._mkldnn: "at::kMkldnn", # type: ignore[attr-defined]
}
_IS_WINDOWS = sys.platform == "win32"
INDEX_TYPE = "int64_t"
GemmBlocking = namedtuple("GemmBlocking", ["block_m", "block_n", "block_k"])
def get_promote_dtype(args):
return (
functools.reduce(
torch.promote_types, # type: ignore[arg-type]
[n.dtype for n in args if isinstance(n, CppCSEVariable)],
)
if all(n.dtype is not None for n in args if isinstance(n, CppCSEVariable))
else None # not enough info to calculate the promote dtype
)
def promote_args(new_args):
def promote_arg(arg, promote_type):
if (
isinstance(arg, CppCSEVariable)
and arg.dtype
and promote_type
and arg.dtype != promote_type
):
arg = ops.to_dtype(arg, promote_type)
arg = arg.value if isinstance(arg, OpsValue) else arg
arg.dtype = promote_type
return arg
promote_type = get_promote_dtype(new_args)
promote_fn = functools.partial(
promote_arg,
promote_type=promote_type,
)
if (
all(
new_arg.dtype is not None
for new_arg in new_args
if isinstance(new_arg, CppCSEVariable)
)
and promote_type
):
new_args = list(map(promote_fn, new_args))
return new_args
def get_opt_ctx(node: torch.fx.Node) -> OptimizationContext:
return node.meta.get(OptimizationContext.key, None)
def get_current_node_opt_ctx() -> OptimizationContext:
assert V.interpreter.current_node
return get_opt_ctx(V.interpreter.current_node)
def deduce_dtype_for_cpp_cse_variable(name, *args, **kwargs):
if (
output_dtype := deduce_output_dtype_by_name(
name,
*args,
**kwargs,
)
) is not None:
return output_dtype
elif name == "masked":
# <TODO> Leslie: perhaps we can also deduce the masked dtype by
# inputs' CppCseVariable like other. Let's check it if any
# unexpected failures.
assert (
hasattr(V.interpreter, "current_node")
and V.interpreter.current_node.target.startswith("masked_subblock")
and get_current_node_opt_ctx() is not None
)
return get_current_node_opt_ctx().dtype
else:
# deduce output dtype by inputs' dtype
assert all(
arg.dtype is not None for arg in args if isinstance(arg, CppCSEVariable)
)
return functools.reduce(
torch.promote_types, # type: ignore[arg-type]
[arg.dtype for arg in args if isinstance(arg, CppCSEVariable)],
)
class CppCSEVariable(CSEVariable):
def __init__(
self,
name,
bounds: ValueRanges[Any],
dtype: Optional[torch.dtype] = None,
) -> None:
super().__init__(name, bounds, dtype)
self.is_vec = False
self.dependent_itervars: Set[sympy.Symbol] = set()
def __repr__(self) -> str:
return (
f"CppCSEVariable(name: {self.name}, bounds: {self.bounds}, is_vec: {self.is_vec}, dtype: {self.dtype}, "
f"dependent_itervars: {self.dependent_itervars})"
)
def update_on_args(self, name, args, kwargs):
if name == "load":
# args[2] is index
self._set_dependent_itervars(args[2])
else:
# propagate relevant itervars and is_vec from args
self.dependent_itervars.update(
*[
arg.dependent_itervars
for arg in args
if isinstance(arg, CppCSEVariable)
]
)
if name == "index_expr":
self._set_dependent_itervars(args[0])
if any(arg.is_vec for arg in args if isinstance(arg, CppCSEVariable)):
self.is_vec = True
# NOTE [Deduce dtype of CppCSEVariable at runtime]
self.dtype = deduce_dtype_for_cpp_cse_variable(name, *args, **kwargs)
assert self.dtype is not None
def _set_dependent_itervars(self, index: sympy.Expr):
"""
Set the relevant itervars for this variable based on the `index` expression.
This includes the itervars directly used in the `index` as well as relevant itervars
of other cse variables used in the `index`.
"""
for s in index.free_symbols:
if s in V.kernel.itervars:
self.dependent_itervars.add(s) # type: ignore[arg-type]
elif s.name in V.kernel.cse.varname_map: # type: ignore[attr-defined]
self.dependent_itervars.update(
V.kernel.cse.varname_map[s.name].dependent_itervars # type: ignore[attr-defined]
)
def depends_on(self, itervar: sympy.Symbol):
return itervar in self.dependent_itervars
class CppPrinter(_CppPrinter):
def doprint(self, expr, *, simplify: bool = True, p=True):
# TODO: why are people passing strings to the printer here :think:
if simplify and isinstance(expr, sympy.Expr) and hasattr(V.graph, "sizevars"):
expr = V.graph.sizevars.simplify(expr)
return super().doprint(expr)
# A function to print, useful for printing sympy symbols.
cexpr = CppPrinter().doprint
def cexpr_index(index):
return f"static_cast<{INDEX_TYPE}>({cexpr(index)})"
def value_to_cpp(value, cpp_type):
if value == float("-inf"):
return f"-std::numeric_limits<{cpp_type}>::infinity()"
elif value == float("inf"):
return f"std::numeric_limits<{cpp_type}>::infinity()"
elif isinstance(value, bool):
return f"static_cast<{cpp_type}>({str(value).lower()})"
elif math.isnan(value):
return f"std::numeric_limits<{cpp_type}>::quiet_NaN()"
else:
return f"static_cast<{cpp_type}>({repr(value)})"
def rewrite_index_for_function(
localize_buffer_handler: "LocalizeBufferHandler",
index: sympy.Expr,
global_buf_name: str,
):
# Local buffer at the inner dimensions
snode = V.graph.scheduler.name_to_buf[global_buf_name].defining_op
local_buf = localize_buffer_handler.global_to_local[global_buf_name]
scheduler_nodes = snode.get_nodes()
_, (group, reduction_group) = max(
scheduler_nodes, key=lambda x: int(x.is_reduction())
).group
call_ranges = tuple(group) + tuple(reduction_group)
indices_to_keep = [
f"x{len(call_ranges) - (idx + 1)}"
for idx in range(len(local_buf.get_layout().size))
]
sorted_symbols = sorted(index.free_symbols, key=lambda s: s.name) # type: ignore[attr-defined]
replacements = {}
for x in sorted_symbols:
if x.name.startswith("x") and x.name not in indices_to_keep: # type: ignore[attr-defined]
# Only keep index used by local buffer
replacements[x] = sympy.core.numbers.Zero()
index = sympy_subs(index, replacements) # type: ignore[arg-type]
return index
def rewrite_index_for_nodes(
localize_buffer_handler: "LocalizeBufferHandler",
index: sympy.Expr,
global_buf_name: str,
):
used_vars = {s for s in index.free_symbols if symbol_is_type(s, SymT.INDEX)}
index_vars = []
local_buf = localize_buffer_handler.global_to_local[global_buf_name]
for i in range(len(local_buf.get_size())):
var = sympy_index_symbol_with_prefix(SymT.INDEX, i)
index_vars.append(var if var in used_vars else 0)
index = local_buf.get_layout().make_indexer()(index_vars)
return index
class LocalizeBufferHandler(V.WrapperHandler): # type: ignore[name-defined]
def __init__(
self,
inner,
global_to_local: Dict[str, ir.Buffer],
rewrite_index: Callable[["LocalizeBufferHandler", sympy.Expr, str], sympy.Expr],
) -> None:
super().__init__(inner)
self.global_to_local = global_to_local
self.rewrite_index = rewrite_index
def localize(self, name: str, index: sympy.Expr):
if self.global_to_local and name in self.global_to_local:
assert self.rewrite_index is not None
index = self.rewrite_index(self, index, name)
name = self.global_to_local[name].get_name()
return name, index
def load(self, name: str, index: sympy.Expr):
return self._inner.load(*self.localize(name, index))
def store(self, name, index, value, mode=None):
local_buffer_name, local_buffer_index = self.localize(name, index)
res = self._inner.store(local_buffer_name, local_buffer_index, value, mode)
if (
self.global_to_local
and name in self.global_to_local
and isinstance(V.kernel, Kernel)
):
# Remove name of local buffer from Kernel.store_buffer_names
# local_buffer_name is added to Kernel.store_buffer_names in Kernel.CSEProxy.store.
V.kernel.store_buffer_names.discard(local_buffer_name)
return res
def store_reduction(self, name, index, value):
return self._inner.store_reduction(*self.localize(name, index), value)
class LocalBufferContext:
"""
This class creates a context that helps to generate code involving Inductor IR with
function local buffers. These buffers are constructed during the codegen process and
are used to store intermediate results such as local accumulators. We do not want to
add them to `V.graph` since they are not global and we do not want to add them as
function arguments either. So we patch the codegen processes under this scope to support
these buffers without exposure to the outside world.
"""
def __init__(self, kernel_args: KernelArgs) -> None:
self.kernel_args = kernel_args
self.exit_stack = contextlib.ExitStack()
# map local buffer name to local buffer
self.local_buffers: Dict[str, ir.Buffer] = {}
# map global buffer name to global buffer
self.global_buffers: Dict[str, ir.Buffer] = {}
# map global buffer name to local buffer
self.global_to_local: Dict[str, ir.Buffer] = {}
def __enter__(self):
self.exit_stack.__enter__()
original_get_dtype = V.graph.get_dtype
def get_dtype(name):
if name in self.local_buffers:
return self.local_buffers[name].get_dtype()
return original_get_dtype(name)
self.exit_stack.enter_context(patch.object(V.graph, "get_dtype", get_dtype))
original_input = self.kernel_args.input
def input(name):
if name in self.local_buffers:
return name
return original_input(name)
self.exit_stack.enter_context(patch.object(self.kernel_args, "input", input))
original_output = self.kernel_args.output
def output(name):
if name in self.local_buffers:
return name
return original_output(name)
self.exit_stack.enter_context(patch.object(self.kernel_args, "output", output))
# Set current LocalBufferContext into V
self.exit_stack.enter_context(V.set_local_buffer_context(self))
return self
def __exit__(self, exc_type, exc_val, exc_tb):
self.local_buffers.clear()
self.exit_stack.__exit__(exc_type, exc_val, exc_tb)
def add_local_buffer(
self, local_buffer: ir.Buffer, global_buffers: Optional[List[ir.Buffer]] = None
):
assert local_buffer.get_name() not in self.local_buffers
self.local_buffers[local_buffer.get_name()] = local_buffer
if global_buffers:
for global_buffer in global_buffers:
global_buffer_name = global_buffer.get_name()
assert (
global_buffer_name not in self.global_buffers
and global_buffer_name not in self.global_to_local
)
self.global_buffers[global_buffer_name] = global_buffer
self.global_to_local[global_buffer_name] = local_buffer
V.graph.removed_buffers.add(global_buffer_name)
def localize_function(
self,
fn: Callable[..., Any],
rewrite_index: Callable[
["LocalizeBufferHandler", sympy.Expr, str], sympy.Expr
] = rewrite_index_for_function,
):
def inner(*args, **kwargs):
with V.set_ops_handler(
LocalizeBufferHandler(
V.get_ops_handler(),
global_to_local=self.global_to_local,
rewrite_index=rewrite_index,
)
):
return fn(*args, **kwargs)
return inner
def localize_nodes(
self,
nodes: List[ir.IRNode],
rewrite_index: Callable[
["LocalizeBufferHandler", sympy.Expr, str], sympy.Expr
] = rewrite_index_for_nodes,
) -> List[ir.IRNode]:
"""
Given `local_buf` and `global_buf` registered in current `LocalBufferContext`
though the method of `add_local_buffer`, localizes the `global_buf` to `local_buf`
for the given `nodes` and returns a new list of IR nodes that work on `local_buf`
instead of `global_buf`, i.e., all the loads and stores are redirected to
`local_buf`. This helps the fused loops to work on smaller-sized local buffers
for better data locality.
The the data access of `local_buf` is assumed to be contiguous with the
same order as the `global_buf`.
"""
assert len(nodes) > 0
def wrap_inner_fn_for_node(node: ir.IRNode):
loops = node.data if isinstance(node, ir.ComputedBuffer) else node
assert isinstance(loops, ir.Loops)
new_inner_fn = self.localize_function(
loops.inner_fn,
rewrite_index,
)
new_loops = dataclasses.replace(loops, inner_fn=new_inner_fn)
if isinstance(node, ir.ComputedBuffer):
new_node = ir.ComputedBuffer(
name=node.get_name(), layout=node.get_layout(), data=new_loops
)
else:
new_node = new_loops # type: ignore[assignment]
return new_node
return [wrap_inner_fn_for_node(node) for node in nodes]
def unify_mask_base_type(
buffer: IndentedBuffer,
vars: Tuple[CSEVariable, ...],
dtype=torch.float,
):
"""
Given list of cse variables,
Cast each to new mask base dtype and return casted cse variable.
"""
new_vars = (
V.kernel.cse.generate(
buffer,
f"{V.kernel._get_mask_cast(var, dtype)}",
)
for var in vars
)
return new_vars
def codegen_rand(offset, code, rand_function, dst_dtype=torch.float32):
assert is_integer_dtype(offset.dtype)
code.writeline("[&]()")
with code.indent():
code.writeline(
f"{DTYPE_TO_CPP[offset.dtype]} offset[{V.kernel.tiling_factor}];"
)
code.writeline(f"{DTYPE_TO_CPP[dst_dtype]} result[{V.kernel.tiling_factor}];")
code.writeline(f"{offset}.store(offset);")
code.writeline(
f"for( {DTYPE_TO_CPP[offset.dtype]} offset_idx = 0; offset_idx < {V.kernel.tiling_factor}; offset_idx++ )"
)
with code.indent():
code.writeline(rand_function)
num_vectors = V.kernel._get_num_vectors(dtype=dst_dtype)
if num_vectors == 1:
code.writeline(
f"return at::vec::Vectorized<{DTYPE_TO_CPP[dst_dtype]}>::loadu(result);"
)
else:
code.writeline(
f"return at::vec::VectorizedN<{DTYPE_TO_CPP[dst_dtype]}, {num_vectors}>::loadu(result);"
)
code.writeline("()")
return code
def get_gemm_template_output_and_compute_dtype(input_dtype):
if input_dtype == torch.uint8:
return (torch.int32, torch.int32)
else:
return (torch.float32, torch.float32)
def create_epilogue_with_attr(input_buffer, attr, **kwargs):
input_loader = input_buffer.make_loader()
dtype = input_buffer.get_dtype()
if attr == "relu":
def inner_fn(index):
input = input_loader(index)
zero = ops.constant(0, dtype)
return ops.maximum(input, zero)
elif attr == "gelu":
assert "algorithm" in kwargs
if kwargs["algorithm"] == "none":
def inner_fn(index):
input = input_loader(index)
if dtype != torch.float:
input = ops.to_dtype(input, torch.float)
half = ops.constant(0.5, torch.float)
one = ops.constant(1.0, torch.float)
const = ops.constant(0.7071067811865476, torch.float)
result = input * half * (ops.erf(input * const) + one)
if dtype != torch.float:
result = ops.to_dtype(result, dtype)
return result
else:
assert kwargs["algorithm"] == "tanh"
def inner_fn(index):
input = input_loader(index)
if dtype != torch.float:
input = ops.to_dtype(input, torch.float)
half = ops.constant(0.5, torch.float)
one = ops.constant(1.0, torch.float)
const1 = ops.constant(0.7978845608028654, torch.float)
const2 = ops.constant(0.044715, torch.float)
result = (
half
* input
* (
one
+ ops.tanh(const1 * (input + const2 * input * input * input))
)
)
if dtype != torch.float:
result = ops.to_dtype(result, dtype)
return result
elif attr == "swish":
def inner_fn(index):
input = input_loader(index)
result = input * ops.sigmoid(input)
return result
elif attr == "sigmoid":
def inner_fn(index):
return ops.sigmoid(input_loader(index))
elif attr == "tanh":
def inner_fn(index):
return ops.tanh(input_loader(index))
elif attr == "hardswish" or attr == "hardsigmoid":
def hardsigmoid_float(input):
zero = ops.constant(0, torch.float)
six = ops.constant(6, torch.float)
three = ops.constant(3, torch.float)
one_over_six = ops.constant(0.16666666666666666, torch.float)
max = ops.maximum(input + three, zero)
min = ops.minimum(max, six)
return min * one_over_six
def inner_fn(index):
input = input_loader(index)
if dtype != torch.float:
input = ops.to_dtype(input, torch.float)
result = hardsigmoid_float(input)
if attr == "hardswish":
result = input * result
if dtype != torch.float:
result = ops.to_dtype(result, dtype)
return result
elif attr == "leaky_relu":
assert "scalars" in kwargs
assert len(kwargs["scalars"]) == 1
negative_slope = kwargs["scalars"][0]
def inner_fn(index):
input = input_loader(index)
if dtype != torch.float:
input = ops.to_dtype(input, torch.float)
zero = ops.constant(0, torch.float)
result = ops.where(
input > zero, input, input * ops.constant(negative_slope, torch.float)
)
if dtype != torch.float:
result = ops.to_dtype(result, dtype)
return result
elif attr == "hardtanh":
assert "scalars" in kwargs
assert len(kwargs["scalars"]) == 2
min_value = kwargs["scalars"][0]
max_value = kwargs["scalars"][1]
def inner_fn(index):
input = input_loader(index)
if dtype != torch.float:
input = ops.to_dtype(input, torch.float)
result = ops.minimum(
ops.maximum(input, ops.constant(min_value, torch.float)),
ops.constant(max_value, torch.float),
)
if dtype != torch.float:
result = ops.to_dtype(result, dtype)
return result
elif attr in ["add", "sub", "mul"]:
assert "other" in kwargs
other = kwargs["other"]
num_input_dims = len(input_buffer.get_size())
num_other_dims = len(other.get_size())
dims_diff = num_input_dims - num_other_dims
other_loader = other.make_loader()
def inner_fn(index):
op = getattr(ops, attr)
if dims_diff != 0:
return op(input_loader(index), other_loader(index[dims_diff:]))
else:
return op(input_loader(index), other_loader(index))
elif attr == "bias_add":
assert "other" in kwargs
assert "beta" in kwargs
assert "dtype" in kwargs
beta = kwargs["beta"]
other = kwargs["other"]
dtype = kwargs["dtype"]
bias_loader = other.make_loader()
def inner_fn(index):
bias = bias_loader(index)
input = input_loader(index)
if beta != 1:
result = ops.constant(beta, torch.float) * bias + input
else:
result = bias + input
return result
else:
raise ValueError(f"Unsupported epilogue attribute: {attr}")
return ir.Pointwise(
device=input_buffer.get_device(),
dtype=dtype,
inner_fn=inner_fn,
ranges=input_buffer.get_size(),
)
def _get_loop_body(fn_list):
if all(isinstance(fn, LoopBody) for fn in fn_list):
loop_bodies = fn_list
else:
if hasattr(fn_list[0], "original_fn"):
# For the case of local buffer, we wrap the fn with localize_function
assert all(hasattr(fn, "original_fn") for fn in fn_list)
assert all(
isinstance(fn.original_fn.args[0]._body, LoopBody) for fn in fn_list
)
loop_bodies = [fn.original_fn.args[0]._body for fn in fn_list]
else:
assert all(isinstance(fn, functools.partial) for fn in fn_list)
assert all(isinstance(fn.args[0]._body, LoopBody) for fn in fn_list)
loop_bodies = [fn.args[0]._body for fn in fn_list]
assert loop_bodies is not None
return loop_bodies
def _get_dtype_from_loopbodies(loop_bodies):
dtypes = set()
for loop_body in loop_bodies:
graphs = [loop_body.root_block.graph] + [
body.graph for body in list(loop_body.subblocks.values())
]
for graph in graphs:
for node in graph.nodes:
if node.op != "call_method":
continue
dtypes.add(node.meta[OptimizationContext.key].dtype)
return dtypes
def template_fusion_with_epilogues_supported(
template: BaseSchedulerNode, epilogues: List[BaseSchedulerNode]
) -> Tuple[bool, bool]:
def _get_indexes_of_template_buf_read(
epilogue_node: ir.Operation, template_buf_names: List[str]
) -> List[sympy.Expr]:
return [
read.index
for read in epilogue_node.get_reads()
if read.name in template_buf_names
]
def _check_supported_and_same_indexes(
index_of_template_buf_read: Sequence[sympy.Expr],
epilogue_writes: OrderedSet[Dep],
) -> Tuple[bool, bool]:
num_indexes = len(set(index_of_template_buf_read))
if num_indexes > 1:
same_index = False
supported = False # Different read indexes not supported
elif num_indexes == 0:
same_index = True
supported = True # No reads, automatically supported
elif num_indexes == 1:
iotbr = index_of_template_buf_read[0]
same_index = all(write.index == iotbr for write in epilogue_writes)
# TODO: Add support of fusion when the read of template buffer and the write of epilogue output
# in the epilogue node don't have the same index and change supported to True
supported = same_index
else:
raise AssertionError("Should not reach here")
return supported, same_index
def _template_fusion_supported(
template_outputs: Sequence[SchedulerBuffer], epilogue_nodes: List[ir.Operation]
) -> Tuple[bool, bool]:
template_buf_names = [x.get_name() for x in template_outputs]
indexes_of_template_buf_reads = [
_get_indexes_of_template_buf_read(epilogue_node, template_buf_names)
for epilogue_node in epilogue_nodes
]
epilogue_nodes_writes = [
epilogue_node.get_read_writes().writes for epilogue_node in epilogue_nodes
]
results = [
_check_supported_and_same_indexes(reads, writes)
for reads, writes in zip(
indexes_of_template_buf_reads, epilogue_nodes_writes
)
]
supported, same_indexes = zip(*results)
return all(supported), all(same_indexes)
assert template.is_template()
template_outputs = template.get_outputs()
epilogue_nodes = [
n.node
for epilogue in epilogues
for n in epilogue.get_nodes()
if n.node is not None
]
return _template_fusion_supported(template_outputs, epilogue_nodes)
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