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a1bfb39a31
pytorch/torch/utils/_sympy/functions.py
Blaine Burton Rister a1bfb39a31 [Inductor] Expand Identity ops prior to block pattern matching (#146000) 
# Feature

Inductor sometimes uses `Identity` functions to group various terms of an expression. While this is convenient in some scenarios, it can frustrate pattern matching. For example, when we're matching an indexing expression to tell if it can be represented as a block pointer, that analysis should be invariant to `Identity`'s.

This PR adds a few features to achieve this invariance.
 - Create a new expansion mode `expr.expand(identity=True)`, which removes all `Identity` functions from the expression.
 -  Preprocess the expression with this expansion prior to pattern matching.
 - Bonus: create a new test utility function called `dummy_graph()`, which creates a simple `GraphLowering`. This is useful for testing the pattern matcher, as we need to initialize `V.graph` before we can access `V.graph.sizevars`.

# Test plan
This PR adds a few new unit tests:
 - Added a unit test specifically for `expr.expand(identity=True)`.
 - Added a new unit test module for the block pattern matcher. Tested that we can correctly match some example patterns containing Identity ops.

I originally intended to add an end to end test compiling pointwise cat, and mapping the corresponding memory accesses to block pointers. However, it looks like that will take more work, since the [relevant code path](https://github.com/pytorch/pytorch/blob/main/torch/_inductor/codegen/triton.py#L1306) disables block pointer analysis. It might be better to defer that to a future PR.

Pull Request resolved: https://github.com/pytorch/pytorch/pull/146000
Approved by: https://github.com/eellison, https://github.com/jansel
2025-02-08 18:11:53 +00:00

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# mypy: allow-untyped-defs
import functools
import math
import operator
import sys
from typing import Callable, Optional, SupportsFloat, TYPE_CHECKING, TypeVar, Union
from typing_extensions import TypeVarTuple, Unpack
import sympy
from sympy import S
from sympy.core import sympify
from sympy.core.expr import Expr
from sympy.core.function import Application
from sympy.core.logic import _torf, fuzzy_and, fuzzy_or
from sympy.core.numbers import equal_valued
from sympy.core.operations import LatticeOp, ShortCircuit
from sympy.core.sorting import ordered
from sympy.core.traversal import walk
from sympy.printing.precedence import PRECEDENCE
from sympy.utilities.iterables import sift
from .numbers import int_oo
if TYPE_CHECKING:
from collections.abc import Iterable
_T = TypeVar("_T", bound=SupportsFloat)
_Ts = TypeVarTuple("_Ts")
# Portions of this file are adapted from the Sympy codebase, which was
# licensed as follows:
#
# Copyright (c) 2006-2023 SymPy Development Team
#
# All rights reserved.
#
# Redistribution and use in source and binary forms, with or without
# modification, are permitted provided that the following conditions are met:
#
# a. Redistributions of source code must retain the above copyright notice,
# this list of conditions and the following disclaimer.
# b. Redistributions in binary form must reproduce the above copyright
# notice, this list of conditions and the following disclaimer in the
# documentation and/or other materials provided with the distribution.
# c. Neither the name of SymPy nor the names of its contributors
# may be used to endorse or promote products derived from this software
# without specific prior written permission.
#
# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
# AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
# IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
# ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE FOR
# ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
# DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
# SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
# CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
# LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
# OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH
# DAMAGE.
__all__ = [
"FloorDiv",
"ModularIndexing",
"Where",
"PythonMod",
"Mod",
"CleanDiv",
"CeilToInt",
"FloorToInt",
"CeilDiv",
"IntTrueDiv",
"FloatTrueDiv",
"LShift",
"RShift",
"IsNonOverlappingAndDenseIndicator",
"TruncToFloat",
"TruncToInt",
"RoundToInt",
"RoundDecimal",
"ToFloat",
"FloatPow",
"PowByNatural",
"Identity",
]
def _is_symbols_binary_summation(expr: sympy.Expr) -> bool:
# No need to check that two args are not the same, since expr is pr-optimized but we do it anyway.
return (
expr.is_Add
and len(expr._args) == 2
and expr._args[0].is_symbol
and expr._args[1].is_symbol
and expr._args[0] is not expr._args[1]
)
def _keep_float(
f: Callable[[Unpack[_Ts]], _T]
) -> Callable[[Unpack[_Ts]], Union[_T, sympy.Float]]:
@functools.wraps(f)
def inner(*args: Unpack[_Ts]) -> Union[_T, sympy.Float]:
r: Union[_T, sympy.Float] = f(*args)
if any(isinstance(a, sympy.Float) for a in args) and not isinstance(
r, sympy.Float
):
r = sympy.Float(float(r))
return r
return inner
def fuzzy_eq(x: Optional[bool], y: Optional[bool]) -> Optional[bool]:
if None in (x, y):
return None
return x == y
def simple_floordiv_gcd(p: sympy.Basic, q: sympy.Basic) -> sympy.Basic:
"""
Fast path for sympy.gcd, using a simple factoring strategy.
We try to rewrite p and q in the form n*e*p1 + n*e*p2 and n*e*q0,
where n is the greatest common integer factor and e is the largest
syntactic common factor (i.e., common sub-expression) in p and q.
Then the gcd returned is n*e, cancelling which we would be left with
p1 + p2 and q0.
Note that further factoring of p1 + p2 and q0 might be possible with
sympy.factor (which uses domain-specific theories). E.g., we are unable
to find that x*y + x + y + 1 is divisible by x + 1. More generally,
when q is of the form q1 + q2 (instead of being already factored) it
might be necessary to fall back on sympy.gcd.
"""
def integer_coefficient(x: sympy.Basic) -> int:
integer_coefficients: list[int] = [
abs(int(arg))
for arg in sympy.Mul.make_args(x)
if isinstance(arg, (int, sympy.Integer))
]
return math.prod(integer_coefficients)
def integer_factor(expr: sympy.Basic) -> int:
integer_factors: Iterable[int] = map(
integer_coefficient, sympy.Add.make_args(expr)
)
return functools.reduce(math.gcd, integer_factors)
gcd: int = math.gcd(integer_factor(p), integer_factor(q))
p, q = p / gcd, q / gcd # type: ignore[operator, assignment] # remove in py3.12
base_splits: list[tuple[sympy.Basic, ...]] = list(
map(sympy.Mul.make_args, sympy.Add.make_args(p))
)
divisor_split: tuple[sympy.Basic, ...] = sympy.Mul.make_args(q)
for x in divisor_split:
if all(x in base_split for base_split in base_splits):
gcd = gcd * x # type: ignore[operator] # remove in py3.12
return gcd # type: ignore[return-value] # remove in py3.12
# It would be nice to have assertions on whether or not inputs is_integer
# However, with bugs like https://github.com/sympy/sympy/issues/26620 sympy
# sometimes inconsistently reports floats an integers.
#
# What we can assume from sympy is that if something is an int, it
# definitely is is_integer, but if it is a float it may or may not
# be is_integer. So we are unable to do strong asserts that things
# are NOT integers.
# TODO: In Triton, // rounds to zero, but in Python, it is floor division.
# When we can prove both arguments are non-negative, we should just have a
# GenericFloorDiv (name pending) which can codegen efficiently in Python/C,
# and then PythonFloorDiv and CIntDiv which have the appropriate rounding
# semantics.
#
# Right now, FloorDiv de facto changes behavior if arguments are negative or
# not, this can potentially cause correctness issues.
class FloorDiv(sympy.Function):
"""
We maintain this so that:
1. We can use divisibility guards to simplify FloorDiv(a, b) to a / b.
2. Printing out the expression is nicer (compared to say, representing a//b as (a - a % b) / b)
NB: This is Python-style floor division, round to -Inf
"""
nargs: tuple[int, ...] = (2,)
precedence: int = 35 # lower precedence than add
is_integer: bool = True
@property
def base(self) -> sympy.Basic:
return self.args[0]
@property
def divisor(self) -> sympy.Basic:
return self.args[1]
def _sympystr(self, printer: sympy.printing.StrPrinter) -> str:
base = printer.parenthesize(self.base, PRECEDENCE["Atom"] - 0.5)
divisor = printer.parenthesize(self.divisor, PRECEDENCE["Atom"] - 0.5)
return f"({base}//{divisor})"
# Automatic evaluation.
# https://docs.sympy.org/latest/guides/custom-functions.html#best-practices-for-eval
@classmethod
def eval(
cls, base: sympy.Integer, divisor: sympy.Integer
) -> Union[sympy.Basic, None]:
# python test/test_dynamic_shapes.py -k TestDimConstraints.test_dim_constraints_solve_full
# Assert triggered by inequality solver
# assert base.is_integer, base
# assert divisor.is_integer, divisor
# We don't provide the same error message as in Python because SymPy
# makes it difficult to check the types.
if divisor.is_zero:
raise ZeroDivisionError("division by zero")
if base in (int_oo, -int_oo, sympy.oo, -sympy.oo) and divisor in (
int_oo,
-int_oo,
sympy.oo,
-sympy.oo,
):
return sympy.nan
if base is sympy.nan or divisor is sympy.nan:
return sympy.nan
if base.is_zero:
return sympy.S.Zero
if base.is_integer and equal_valued(divisor, 1):
return base
if base.is_integer and equal_valued(divisor, -1):
return sympy.Mul(base, -1)
if (
isinstance(base, sympy.Number)
and isinstance(divisor, sympy.Number)
and (
base in (int_oo, -int_oo, sympy.oo, -sympy.oo)
or divisor in (int_oo, -int_oo, sympy.oo, -sympy.oo)
)
):
r = float(base) / float(divisor)
if r == math.inf:
return int_oo
elif r == -math.inf:
return -int_oo
elif math.isnan(r):
return sympy.nan
else:
return sympy.Integer(math.floor(r))
if isinstance(base, sympy.Integer) and isinstance(divisor, sympy.Integer):
return sympy.Integer(int(base) // int(divisor))
if isinstance(base, FloorDiv):
return FloorDiv(base.args[0], base.args[1] * divisor)
# Expands (x + y) // b into x // b + y // b.
# This only works if floor is an identity, i.e. x / b is an integer.
if isinstance(divisor, sympy.Integer):
quotients = 0
terms = []
for term in sympy.Add.make_args(base):
quotient = term / divisor
if quotient.is_integer:
terms.append(term)
quotients += quotient
if len(terms) != 0:
# Passing evaluate = False since expression will be optimized during the subtraction post its construction.
return (
FloorDiv(base - sympy.Add(*terms, evaluate=False), divisor)
+ quotients
)
try:
gcd = simple_floordiv_gcd(base, divisor)
if equal_valued(gcd, 1) and isinstance(divisor, sympy.Add):
gcd = sympy.gcd(base, divisor)
if not equal_valued(gcd, 1):
return FloorDiv(
sympy.simplify(base / gcd), sympy.simplify(divisor / gcd)
)
except sympy.PolynomialError:
pass # https://github.com/pytorch/pytorch/issues/108276
return None
class ModularIndexing(sympy.Function):
"""
ModularIndexing(a, b, c) => (a // b) % c where % is the C modulus
"""
nargs: tuple[int, ...] = (3,)
is_integer: bool = True
precedence: int = 35 # lower precedence than add
@classmethod
def eval(
cls, base: sympy.Integer, divisor: sympy.Integer, modulus: sympy.Integer
) -> Optional[sympy.Basic]:
if base == 0 or modulus == 1:
return sympy.S.Zero
if (
isinstance(base, sympy.Integer)
and isinstance(divisor, sympy.Integer)
and isinstance(modulus, sympy.Integer)
):
return (base // divisor) % modulus
try:
if divisor != 1:
gcd = sympy.gcd(base, divisor)
if gcd != 1:
return ModularIndexing(
sympy.simplify(base / gcd),
sympy.simplify(divisor / gcd),
modulus,
)
except sympy.PolynomialError:
pass # https://github.com/pytorch/pytorch/issues/108276
if isinstance(base, sympy.Add):
new_terms: list[sympy.Integer] = []
all_positive: bool = True
for term in base.args:
if sympy.gcd(term, modulus * divisor) != modulus * divisor:
if (isinstance(term, sympy.Integer) and term < 0) or (
isinstance(term, sympy.Mul)
and isinstance(term.args[0], sympy.Integer)
and term.args[0] < 0
):
# workaround for https://github.com/openai/triton/issues/619,
# if there are negative terms, // produces wrong result
# TODO if https://github.com/openai/triton/issues/619 is fixed
# this optimization would become valid
all_positive = False
break
else:
new_terms.append(term)
if len(new_terms) != len(base.args) and all_positive:
return ModularIndexing(sum(new_terms), divisor, modulus)
if isinstance(base, FloorDiv):
return ModularIndexing(base.args[0], base.args[1] * divisor, modulus)
return None
def _eval_is_nonnegative(self) -> Optional[bool]:
p, q = self.args[:2]
return fuzzy_eq(p.is_nonnegative, q.is_nonnegative) # type: ignore[attr-defined]
def _eval_is_positive(self) -> Optional[bool]:
p, q = self.args[:2]
return fuzzy_eq(p.is_positive, q.is_positive) # type: ignore[attr-defined]
class Where(sympy.Function):
"""
Good ol' ternary operator
"""
nargs: tuple[int, ...] = (3,)
precedence: int = 35 # lower precedence than add
def _eval_is_integer(self) -> Optional[bool]:
return True if self.args[1].is_integer and self.args[2].is_integer else None # type: ignore[attr-defined]
def _eval_is_nonnegative(self) -> Optional[bool]:
return (
True
if self.args[1].is_nonnegative and self.args[2].is_nonnegative # type: ignore[attr-defined]
else None
)
def _eval_is_positive(self) -> Optional[bool]:
return True if self.args[1].is_positive and self.args[2].is_positive else None # type: ignore[attr-defined]
@classmethod
def eval(
cls, c: sympy.Basic, p: sympy.Basic, q: sympy.Basic
) -> Optional[sympy.Basic]:
if c == sympy.true:
return p
elif c == sympy.false:
return q
return None
# Python-style modulus: take sign from RHS
class PythonMod(sympy.Function):
nargs: tuple[int, ...] = (2,)
precedence: int = 35 # lower precedence than add
is_integer: bool = True
@classmethod
def eval(cls, p: sympy.Expr, q: sympy.Expr) -> Optional[sympy.Expr]:
# python test/dynamo/test_export.py -k ExportTests.test_trivial_constraint
# Triggered by sympy.solvers.inequalities.reduce_inequalities
# assert p.is_integer, p
# assert q.is_integer, q
if q.is_zero:
raise ZeroDivisionError("Modulo by zero")
# Three cases:
# 1. p == 0
# 2. p is either q or -q
# 3. p is integer and q == 1
if p is S.Zero or p in (q, -q) or q == 1:
return S.Zero
# Evaluate if they are both literals.
if q.is_Number and p.is_Number:
return p % q
# If q == 2, it's a matter of whether p is odd or even.
if q.is_Number and q == 2:
if p.is_even:
return S.Zero
if p.is_odd:
return S.One
# If p is a multiple of q.
r = p / q
if r.is_integer:
return S.Zero
# If p < q and its ratio is positive, then:
# - floor(p / q) = 0
# - p % q = p - floor(p / q) * q = p
less = p < q
if less.is_Boolean and bool(less) and r.is_positive:
return p
if sympy.Mod(p, q) == 0:
return S.Zero
return None
# NB: args[1] for PythonMod
def _eval_is_nonnegative(self) -> Optional[bool]:
return True if self.args[1].is_positive else None # type: ignore[attr-defined]
def _eval_is_nonpositive(self) -> Optional[bool]:
return True if self.args[1].is_negative else None # type: ignore[attr-defined]
# Generic modulus: only defined on non-negative arguments
class Mod(sympy.Function):
nargs = (2,)
precedence: int = 35 # lower precedence than add
is_integer = True
is_nonnegative = True
@classmethod
def eval(cls, p, q):
# This was adapted from: sympy/core/mod.py
# Triggered by
# python test/test_dynamic_shapes.py -k TestDimConstraints.test_dim_constraints_solve_full
# assert p.is_integer, p
# assert q.is_integer, q
if q.is_zero:
raise ZeroDivisionError("Modulo by zero")
# Three cases:
# 1. p == 0
# 2. p is either q or -q
# 3. p is integer and q == 1
if p is S.Zero or p in (q, -q) or q == 1:
return S.Zero
# Evaluate if they are both literals.
if q.is_Number and p.is_Number:
assert p >= 0, p
assert q >= 1, q
return p % q
# If q == 2, it's a matter of whether p is odd or even.
if q.is_Number and q == 2:
if p.is_even:
return S.Zero
if p.is_odd:
return S.One
# If p is a multiple of q.
r = p / q
if r.is_integer:
return S.Zero
# If p < q and its ratio is positive, then:
# - floor(p / q) = 0
# - p % q = p - floor(p / q) * q = p
less = p < q
if less.is_Boolean and bool(less) and r.is_positive:
return p
class CleanDiv(FloorDiv):
"""
Div where we can assume no rounding.
This is to enable future optimizations.
"""
# Don't use sympy ceiling/floor as they will attempt simplifications involving
# frac
class CeilToInt(sympy.Function):
is_integer = True
@classmethod
def eval(cls, number):
# assert number.is_integer is not True, number
if number in (sympy.oo, int_oo):
return int_oo
if number in (-sympy.oo, -int_oo):
return -int_oo
if isinstance(number, sympy.Number):
return sympy.Integer(math.ceil(float(number)))
class FloorToInt(sympy.Function):
is_integer = True
@classmethod
def eval(cls, number):
if number in (sympy.oo, int_oo):
return int_oo
if number in (-sympy.oo, int_oo):
return -int_oo
if isinstance(number, sympy.Integer):
return number
if isinstance(number, sympy.Number):
return sympy.Integer(math.floor(float(number)))
class CeilDiv(sympy.Function):
"""
Div used in indexing that rounds up.
"""
is_integer = True
def __new__(cls, base, divisor):
base = sympy.sympify(base)
divisor = sympy.sympify(divisor)
if sympy.gcd(base, divisor) == divisor:
return CleanDiv(base, divisor)
else:
return FloorDiv(base + (divisor - 1), divisor)
class LShift(sympy.Function):
is_integer = True
@classmethod
def eval(cls, base, shift):
if shift < 0:
raise ValueError("negative shift count")
return base * 2**shift
class RShift(sympy.Function):
is_integer = True
@classmethod
def eval(cls, base, shift):
if shift < 0:
raise ValueError("negative shift count")
return FloorDiv(base, 2**shift)
class MinMaxBase(Expr, LatticeOp): # type: ignore[misc]
def __new__(cls, *original_args, **assumptions):
from sympy.core.parameters import global_parameters
evaluate = assumptions.pop("evaluate", global_parameters.evaluate)
args = (sympify(arg) for arg in original_args)
# See the comment in _satisfy_unique_summations_symbols.
unique_summations_symbols = (
None
if not evaluate
else cls._satisfy_unique_summations_symbols(original_args)
)
if evaluate:
try:
# first standard filter, for cls.zero and cls.identity
# also reshape Max(a, Max(b, c)) to Max(a, b, c)
args = frozenset(cls._new_args_filter(args)) # type: ignore[assignment]
except ShortCircuit:
return cls.zero # type: ignore[attr-defined]
# No need to run _collapse_arguments and _find_localzeros, see the comment
# in _satisfy_unique_summations_symbols.
if unique_summations_symbols is None:
# remove redundant args that are easily identified
args = cls._collapse_arguments(args, **assumptions)
# find local zeros
args = cls._find_localzeros(args, **assumptions)
args = frozenset(args)
if not args:
return cls.identity # type: ignore[attr-defined]
if len(args) == 1:
return list(args).pop()
# base creation
obj = Expr.__new__(cls, *ordered(args), **assumptions)
obj._argset = args
obj.unique_summations_symbols = unique_summations_symbols
return obj
@classmethod
def _satisfy_unique_summations_symbols(
cls, args
) -> Optional[set[sympy.core.symbol.Symbol]]:
"""
One common case in some models is building expressions of the form
max(max(max(a+b...), c+d), e+f) which is simplified to max(a+b, c+d, e+f, ...).
For such expressions, we call the Max constructor X times (once for each nested
max) and the expression gets flattened.
An expensive cost in constructing those expressions is running _collapse_arguments
and _find_localzeros. However, those two optimizations are unnecessary when the args
to max are all of the form a+b, c+d, ..etc where each term uses a unique set of symbols.
This function is used to detect such properties of the expressions we are building
and if so inform that we do not need to run those optimizations. To detect those,
we store a property in the expression that tells that this expression is a min/max
operation over terms that use unique symbols "unique_summations_symbols". This property
also memoize the set of symbols used in all the terms to make it faster to detect this
property inductively.
When we apply max to add a new term, all we need to do is check if the new term uses
unique symbols (with respect to existing terms and itself).
Example:
t = Max(a+b, c+d) ==> satisfies the property
Max(t, h+j) ==> h,j not in [a,b,c,d] => satisfy the property.
The function returns None if the new expression does not satisfy the unique_summations_symbols
property. Otherwise, it returns a new set of unique symbols.
"""
if len(args) != 2:
return None
(lhs, rhs) = (
(args[1], args[0])
if isinstance(args[1], MinMaxBase)
else (args[0], args[1])
)
if not _is_symbols_binary_summation(rhs):
return None
# base case max(a+b, c+d) ==> satisfies the property if a+b and c+d use unique symbols.
if _is_symbols_binary_summation(lhs):
return cls._unique_symbols(args)
# inductive case max(t, h+j) ==> satisfies the property if h, j not in t.unique_summations_symbols
if isinstance(lhs, MinMaxBase):
lhs_unique_summations_symbols = getattr(
lhs, "unique_summations_symbols", None
)
if lhs_unique_summations_symbols is not None:
return cls._unique_symbols([rhs], lhs_unique_summations_symbols)
return None
@classmethod
def _unique_symbols(
cls, args, initial_set: Optional[set[sympy.core.symbol.Symbol]] = None
) -> Optional[set[sympy.core.symbol.Symbol]]:
"""
Return seen_symbols if all atoms in all args are all unique symbols,
else returns None. initial_set can be used to represent initial value for seen_symbols
"""
seen_symbols = set() if initial_set is None else initial_set
for arg in args:
for element in arg.atoms():
if not isinstance(element, sympy.core.symbol.Symbol):
return None
elif element in seen_symbols:
return None
else:
seen_symbols.add(element)
return seen_symbols
@classmethod
def _collapse_arguments(cls, args, **assumptions):
"""Remove redundant args.
Examples
========
>>> from sympy import Min, Max
>>> from sympy.abc import a, b, c, d, e
Any arg in parent that appears in any
parent-like function in any of the flat args
of parent can be removed from that sub-arg:
>>> Min(a, Max(b, Min(a, c, d)))
Min(a, Max(b, Min(c, d)))
If the arg of parent appears in an opposite-than parent
function in any of the flat args of parent that function
can be replaced with the arg:
>>> Min(a, Max(b, Min(c, d, Max(a, e))))
Min(a, Max(b, Min(a, c, d)))
"""
if not args:
return args
args = list(ordered(args))
if cls is Min:
other = Max
else:
other = Min # type: ignore[assignment]
# find global comparable max of Max and min of Min if a new
# value is being introduced in these args at position 0 of
# the ordered args
if args[0].is_number:
sifted = mins, maxs = [], [] # type: ignore[var-annotated]
for i in args:
for v in walk(i, Min, Max):
if v.args[0].is_comparable:
sifted[isinstance(v, Max)].append(v)
small = Min.identity
for i in mins:
v = i.args[0]
if v.is_number and (v < small) == True: # noqa: E712
small = v
big = Max.identity
for i in maxs:
v = i.args[0]
if v.is_number and (v > big) == True: # noqa: E712
big = v
# at the point when this function is called from __new__,
# there may be more than one numeric arg present since
# local zeros have not been handled yet, so look through
# more than the first arg
if cls is Min:
for arg in args:
if not arg.is_number:
break
if (arg < small) == True: # noqa: E712
small = arg
elif cls == Max:
for arg in args:
if not arg.is_number:
break
if (arg > big) == True: # noqa: E712
big = arg
T = None
if cls is Min:
if small != Min.identity:
other = Max
T = small
elif big != Max.identity:
other = Min # type: ignore[assignment]
T = big
if T is not None:
# remove numerical redundancy
for i in range(len(args)):
a = args[i]
if isinstance(a, other):
a0 = a.args[0]
if ( # noqa: E712
(a0 > T) if other == Max else (a0 < T) # noqa: E712
) == True: # noqa: E712
args[i] = cls.identity # type: ignore[attr-defined]
# remove redundant symbolic args
def do(ai, a):
if not isinstance(ai, (Min, Max)):
return ai
cond = a in ai.args
if not cond:
return ai.func(*[do(i, a) for i in ai.args], evaluate=False)
if isinstance(ai, cls):
return ai.func(*[do(i, a) for i in ai.args if i != a], evaluate=False)
return a
for i, a in enumerate(args):
args[i + 1 :] = [do(ai, a) for ai in args[i + 1 :]]
# factor out common elements as for
# Min(Max(x, y), Max(x, z)) -> Max(x, Min(y, z))
# and vice versa when swapping Min/Max -- do this only for the
# easy case where all functions contain something in common;
# trying to find some optimal subset of args to modify takes
# too long
def factor_minmax(args):
is_other = lambda arg: isinstance(arg, other) # noqa: E731
other_args, remaining_args = sift(args, is_other, binary=True)
if not other_args:
return args
# Min(Max(x, y, z), Max(x, y, u, v)) -> {x,y}, ({z}, {u,v})
arg_sets = [set(arg.args) for arg in other_args]
common = set.intersection(*arg_sets)
if not common:
return args
new_other_args = list(common)
arg_sets_diff = [arg_set - common for arg_set in arg_sets]
# If any set is empty after removing common then all can be
# discarded e.g. Min(Max(a, b, c), Max(a, b)) -> Max(a, b)
if all(arg_sets_diff):
other_args_diff = [other(*s, evaluate=False) for s in arg_sets_diff]
new_other_args.append(cls(*other_args_diff, evaluate=False))
other_args_factored = other(*new_other_args, evaluate=False)
return remaining_args + [other_args_factored]
if len(args) > 1:
args = factor_minmax(args)
return args
@classmethod
def _new_args_filter(cls, arg_sequence):
"""
Generator filtering args.
first standard filter, for cls.zero and cls.identity.
Also reshape ``Max(a, Max(b, c))`` to ``Max(a, b, c)``,
and check arguments for comparability
"""
for arg in arg_sequence:
# pre-filter, checking comparability of arguments
if (
not isinstance(arg, Expr)
or arg.is_extended_real is False
or (arg.is_number and not arg.is_comparable)
):
raise ValueError(f"The argument '{arg}' is not comparable.")
if arg == cls.zero: # type: ignore[attr-defined]
raise ShortCircuit(arg)
elif arg == cls.identity: # type: ignore[attr-defined]
continue
elif arg.func == cls:
yield from arg.args
else:
yield arg
@classmethod
def _find_localzeros(cls, values, **options):
"""
Sequentially allocate values to localzeros.
When a value is identified as being more extreme than another member it
replaces that member; if this is never true, then the value is simply
appended to the localzeros.
Unlike the sympy implementation, we only look for zero and one, we don't
do generic is connected test pairwise which is slow
"""
# First, collapse all numeric arguments
other_values = set()
num_value = None
for arg in values:
if arg.is_Number:
if num_value is None:
num_value = arg
else:
if cls is Max:
num_value = max(num_value, arg)
elif cls is Min:
num_value = min(num_value, arg)
else:
raise AssertionError(f"impossible {cls}")
else:
other_values.add(arg)
# Special cases when there is only one symbolic value
if num_value is None:
return other_values
if len(other_values) == 0:
return {num_value}
if len(other_values) == 1:
other_value = next(iter(other_values))
if num_value in (0.0, 0) and other_value.is_nonnegative:
return other_values if cls is Max else {num_value}
if num_value == 1 and other_value.is_positive:
return other_values if cls is Max else {num_value}
other_values.add(num_value)
return other_values
_eval_is_algebraic = lambda s: _torf(i.is_algebraic for i in s.args) # noqa: E731
_eval_is_antihermitian = lambda s: _torf( # noqa: E731
i.is_antihermitian for i in s.args # noqa: E731
) # noqa: E731
_eval_is_commutative = lambda s: _torf( # noqa: E731
i.is_commutative for i in s.args # noqa: E731
) # noqa: E731
_eval_is_complex = lambda s: _torf(i.is_complex for i in s.args) # noqa: E731
_eval_is_composite = lambda s: _torf(i.is_composite for i in s.args) # noqa: E731
_eval_is_even = lambda s: _torf(i.is_even for i in s.args) # noqa: E731
_eval_is_finite = lambda s: _torf(i.is_finite for i in s.args) # noqa: E731
_eval_is_hermitian = lambda s: _torf(i.is_hermitian for i in s.args) # noqa: E731
_eval_is_imaginary = lambda s: _torf(i.is_imaginary for i in s.args) # noqa: E731
_eval_is_infinite = lambda s: _torf(i.is_infinite for i in s.args) # noqa: E731
_eval_is_integer = lambda s: _torf(i.is_integer for i in s.args) # noqa: E731
_eval_is_irrational = lambda s: _torf(i.is_irrational for i in s.args) # noqa: E731
_eval_is_negative = lambda s: _torf(i.is_negative for i in s.args) # noqa: E731
_eval_is_noninteger = lambda s: _torf(i.is_noninteger for i in s.args) # noqa: E731
_eval_is_nonnegative = lambda s: _torf( # noqa: E731
i.is_nonnegative for i in s.args # noqa: E731
) # noqa: E731
_eval_is_nonpositive = lambda s: _torf( # noqa: E731
i.is_nonpositive for i in s.args # noqa: E731
) # noqa: E731
_eval_is_nonzero = lambda s: _torf(i.is_nonzero for i in s.args) # noqa: E731
_eval_is_odd = lambda s: _torf(i.is_odd for i in s.args) # noqa: E731
_eval_is_polar = lambda s: _torf(i.is_polar for i in s.args) # noqa: E731
_eval_is_positive = lambda s: _torf(i.is_positive for i in s.args) # noqa: E731
_eval_is_prime = lambda s: _torf(i.is_prime for i in s.args) # noqa: E731
_eval_is_rational = lambda s: _torf(i.is_rational for i in s.args) # noqa: E731
_eval_is_real = lambda s: _torf(i.is_real for i in s.args) # noqa: E731
_eval_is_extended_real = lambda s: _torf( # noqa: E731
i.is_extended_real for i in s.args # noqa: E731
) # noqa: E731
_eval_is_transcendental = lambda s: _torf( # noqa: E731
i.is_transcendental for i in s.args # noqa: E731
) # noqa: E731
_eval_is_zero = lambda s: _torf(i.is_zero for i in s.args) # noqa: E731
class Max(MinMaxBase, Application): # type: ignore[misc]
r"""
Return, if possible, the maximum value of the list.
"""
zero = S.Infinity
identity = S.NegativeInfinity
def _eval_is_positive(self): # type:ignore[override]
return fuzzy_or(a.is_positive for a in self.args) # type: ignore[attr-defined]
def _eval_is_nonnegative(self): # type:ignore[override]
return fuzzy_or(a.is_nonnegative for a in self.args) # type: ignore[attr-defined]
def _eval_is_negative(self): # type:ignore[override]
return fuzzy_and(a.is_negative for a in self.args)
class Min(MinMaxBase, Application): # type: ignore[misc]
"""
Return, if possible, the minimum value of the list.
"""
zero = S.NegativeInfinity
identity = S.Infinity
def _eval_is_positive(self): # type:ignore[override]
return fuzzy_and(a.is_positive for a in self.args) # type: ignore[attr-defined]
def _eval_is_nonnegative(self): # type:ignore[override]
return fuzzy_and(a.is_nonnegative for a in self.args) # type: ignore[attr-defined]
def _eval_is_negative(self): # type:ignore[override]
return fuzzy_or(a.is_negative for a in self.args)
def safe_pow(base, exp):
sign = 1
if base < 0:
base = -base
sign = 1 if exp % 2 == 0 else -1
return sign * _safe_pow(base, exp)
# Prevent people from overflowing pow
def _safe_pow(base, exponent):
if exponent < 0:
raise ValueError("Exponent must be non-negative.")
if exponent == 0:
return 1
half_exp = safe_pow(base, exponent // 2)
if half_exp is int_oo:
return int_oo
# TODO: microoptimization is to avoid overflowing into arbitrary precision
# and detect overflow prior to doing operations
result = half_exp * half_exp
if result > sys.maxsize:
return int_oo
if exponent % 2 == 1:
result *= base
if result > sys.maxsize:
return int_oo
return result
class PowByNatural(sympy.Function):
is_integer = True
precedence: int = 50 # precedence of mul
@classmethod
def eval(cls, base, exp):
if isinstance(base, sympy.Integer) and isinstance(exp, sympy.Integer):
r = safe_pow(base, exp)
if r in (-int_oo, int_oo):
return r
return sympy.Integer(r)
if isinstance(exp, sympy.Integer):
# Rely on regular sympy Pow for this (note that iterated
# multiplication turns into a Pow anyway, you can't escape!!)
return sympy.Pow(base, exp)
if exp in (int_oo, sympy.oo):
if base.is_nonnegative:
return int_oo
elif base.is_negative:
return sympy.zoo # this is apparently what (-2)**sympy.oo does
# NB: do NOT translate into sympy.Pow, we will lose knowledge that exp
# is a natural number if we do
# base is assumed to be nonnegative, thereby prevent complex numbers from
# occuring
class FloatPow(sympy.Function):
is_real = True
precedence: int = 60 # precedence of pow
@classmethod
def eval(cls, base, exp):
# NB: These test sympy.Number, not sympy.Float, because:
# - Sometimes we may have sympy.oo or int_oo, and that's not a Float
# (but coerces to math.Inf)
# - Sometimes Float(0.0) will unpredictably decay to Integer(0),
# but we should still accept it in floatey contexts
if isinstance(base, sympy.Number) and isinstance(exp, sympy.Number):
return sympy.Float(float(base) ** float(exp))
# NB: do not do any nontrivial reasoning
# Overloaded to be compatible with regular Python.
# https://github.com/pytorch/pytorch/issues/90900
#
# In particular, sympy division is willing to simplify x/x == 1
# where 1 is an integer, but this must be a float if x was float.
class FloatTrueDiv(sympy.Function):
is_real = True
precedence: int = 35 # lower precedence than add
@classmethod
def eval(cls, base, divisor):
# assert base.is_integer is not True, base
# assert divisor.is_integer is not True, divisor
if divisor.is_zero:
raise ZeroDivisionError("division by zero")
if isinstance(base, sympy.Number) and isinstance(divisor, sympy.Number):
return sympy.Float(float(base) / float(divisor))
# Overloaded to be compatible with regular Python. We distinguish this from
# FloatTrueDiv, because the code generation has to be different for this case:
# Python has a fancy algorithm for integer true division that isn't just
# "promote both arguments to float and use float division", so you need to
# codegen it differently. While technically you can work it out from the
# types of the input, this is often inconvenient to do in Inductor codegen,
# so just have a different operator
# NB: Right now, Inductor codegen doesn't implement this correctly lol
class IntTrueDiv(sympy.Function):
is_real = True
precedence: int = 35 # lower precedence than add
@classmethod
def eval(cls, base, divisor):
if divisor.is_zero:
raise ZeroDivisionError("division by zero")
if (
isinstance(base, sympy.Number)
and isinstance(divisor, sympy.Number)
and (
base in (int_oo, -int_oo, sympy.oo, -sympy.oo)
or divisor in (int_oo, -int_oo, sympy.oo, -sympy.oo)
)
):
# Don't have to worry about precision here, you're getting zero or
# inf from the division
return sympy.Float(float(base) / float(divisor))
if isinstance(base, sympy.Integer) and isinstance(divisor, sympy.Integer):
return sympy.Float(int(base) / int(divisor))
# TODO: As an indicator, this != 0 implies == 1 (and vice versa).
# Because we do not have the ability to guard on the stride permutation
# at the moment, it is hard to make further inferences when this is true,
# as although we know the tensor is contiguous in *some* layout, we don't
# know which one (however, you could, for example, make the inference that
# reshaping this to a 1D tensor can be guard-free.)
class IsNonOverlappingAndDenseIndicator(sympy.Function):
is_integer = True
@classmethod
def eval(cls, *args):
assert len(args) % 2 == 0
dim = len(args) // 2
sizes = args[0:dim]
strides = args[dim:]
# sym_node imported in torch.__init__. Local import to avoid an import cycle
from torch.fx.experimental.symbolic_shapes import (
eval_is_non_overlapping_and_dense,
)
if all(isinstance(a, sympy.Integer) for a in args):
return eval_is_non_overlapping_and_dense(
[int(a) for a in sizes], [int(a) for a in strides]
)
if dim == 1:
# Manually implement the rank one short circuit
if strides[0].is_Number and strides[0] == 1:
return 1
if sizes[0].is_Number and sizes[0] < 2:
return 1
# return 0 case covered by case above
# TODO: Inability to access size-obliviousness sucks: if we have a
# size oblivious test on a size-like unbacked SymInt, we could
# confidently return zero when we have a size-like u0 stride
# and a size-like u1 size. Maybe a fancy ValueRanges analysis for
# this function could help figure this out.
if all(isinstance(a, sympy.Integer) for a in strides):
assert dim != 0
# When all strides are integral, we can sort, and the size for the
# largest stride doesn't matter and can be arbitrarily symbolic
s_sizes, s_strides = zip(
*sorted(zip(sizes, strides), key=operator.itemgetter(1))
)
# Put something arbitrary in the max size spot, it'll be ignored
if all(isinstance(a, sympy.Integer) for a in s_sizes[:-1]):
s_sizes = s_sizes[:-1] + (42,)
# We can reuse the regular eval, because it is invariant to
# permutation of dimensions
return eval_is_non_overlapping_and_dense(
[int(a) for a in s_sizes], [int(a) for a in s_strides]
)
return None
# NB: this is inconsistent with math.trunc in Python
class TruncToFloat(sympy.Function):
is_real = True
@classmethod
def eval(cls, number):
# assert number.is_integer is not True, number
if isinstance(number, sympy.Number):
# NB: It is safe to use truncation to integer, which is what
# math.trunc does, as Python integers are arbitrary precision and
# so we are guaranteed not to lose precision when we do this
return sympy.Float(math.trunc(float(number)))
class TruncToInt(sympy.Function):
is_integer = True
@classmethod
def eval(cls, number):
# assert number.is_integer is not True, number
if number in (sympy.oo, int_oo):
return int_oo
if number in (-sympy.oo, -int_oo):
return -int_oo
if isinstance(number, sympy.Number):
return sympy.Integer(math.trunc(float(number)))
# This is float -> int
class RoundToInt(sympy.Function):
is_integer = True
@classmethod
def eval(cls, number):
# assert number.is_integer is not True, number
if number is sympy.oo:
return int_oo
if number is -sympy.oo:
return -int_oo
if isinstance(number, sympy.Number):
return sympy.Integer(round(float(number), 0))
# To get float -> int, Python style round semantics.
#
# x = PyFloat_AsDouble(self);
# if (o_ndigits == Py_None) {
# /* single-argument round or with None ndigits:
# * round to nearest integer */
# rounded = round(x);
# if (fabs(x-rounded) == 0.5)
# /* halfway case: round to even */
# rounded = 2.0*round(x/2.0);
# return PyLong_FromDouble(rounded);
# }
# NB: Like Round, this only ever returns floats. ndigits cannot be None
class RoundDecimal(sympy.Function):
is_real = True
@classmethod
def eval(cls, number, ndigits):
# assert number.is_integer is not True, number
if isinstance(number, sympy.Number) and isinstance(ndigits, sympy.Integer):
return sympy.Float(round(float(number), int(ndigits)))
class ToFloat(sympy.Function):
is_real = True
@classmethod
def eval(cls, number):
if number in [sympy.oo, -sympy.oo]:
return number
if isinstance(number, sympy.Integer):
return sympy.Float(int(number))
if number is int_oo:
return sympy.oo
if number is -int_oo:
return -sympy.oo
class Identity(sympy.Function):
"""
Prevents expansion and other optimizations
"""
precedence = 10
def __repr__(self): # type: ignore[override]
return f"Identity({self.args[0]})"
def _eval_is_real(self):
return self.args[0].is_real
def _eval_is_integer(self):
return self.args[0].is_integer # type: ignore[attr-defined]
def _eval_expand_identity(self, **hints):
# Removes the identity op.
return self.args[0]
def make_opaque_unary_fn(name):
class OpaqueUnaryFn(sympy.Function):
"""
Unlike the builtin sympy functions on real numbers like sympy.sqrt,
these equivalents do not do any nontrivial reasoning besides
constant propagation. This helps avoid performing transformations
that are valid for real numbers but are invalid for floating point;
in particular, while we are willing to make optimizations that change
numerics for Tensor compute, we are NOT willing to make optimziations
that change numerics for size compute.
"""
_torch_handler_name = name
@classmethod
def eval(cls, a):
if isinstance(a, (sympy.Integer, sympy.Float)):
# Python converts to float64 before computing, c.f.
# >>> math.sin(2**53+1)
# -0.848925964814655
# >>> math.sin(float(2**53+1))
# -0.848925964814655
try:
return sympy.Float(getattr(math, name)(float(a)))
# Just use sympy semantics for infinity/overflow, you might get some
# weird objects but ask silly questions, get silly answers
except OverflowError:
return getattr(sympy, name)(a)
elif a in [sympy.oo, -sympy.oo, sympy.zoo, -sympy.zoo, int_oo, -int_oo]:
if a is int_oo:
a = sympy.oo
if a is -int_oo:
a = -sympy.oo
if name == "log2":
return sympy.log(a, 2)
return getattr(sympy, name)(a)
return None
nm = "OpaqueUnaryFn_" + name
OpaqueUnaryFn.__name__ = nm
OpaqueUnaryFn.__qualname__ = nm
return OpaqueUnaryFn
# Keep in sync with math_op_names in torch/fx/experimental/sym_node.py
OpaqueUnaryFn_sqrt = make_opaque_unary_fn("sqrt")
OpaqueUnaryFn_cos = make_opaque_unary_fn("cos")
OpaqueUnaryFn_cosh = make_opaque_unary_fn("cosh")
OpaqueUnaryFn_sin = make_opaque_unary_fn("sin")
OpaqueUnaryFn_sinh = make_opaque_unary_fn("sinh")
OpaqueUnaryFn_tan = make_opaque_unary_fn("tan")
OpaqueUnaryFn_tanh = make_opaque_unary_fn("tanh")
OpaqueUnaryFn_asin = make_opaque_unary_fn("asin")
OpaqueUnaryFn_acos = make_opaque_unary_fn("acos")
OpaqueUnaryFn_atan = make_opaque_unary_fn("atan")
OpaqueUnaryFn_exp = make_opaque_unary_fn("exp")
OpaqueUnaryFn_log = make_opaque_unary_fn("log")
OpaqueUnaryFn_asinh = make_opaque_unary_fn("asinh")
OpaqueUnaryFn_log2 = make_opaque_unary_fn("log2")
def make_opaque_bitwise_fn(name, real_op_name):
if name == "bitwise_and":
prec = PRECEDENCE["BitwiseAnd"]
elif name == "bitwise_or":
prec = PRECEDENCE["BitwiseOr"]
else:
raise AssertionError(f"unrecognized {name}")
class BitwiseFn(sympy.Function):
_torch_handler_name = name
precedence: int = prec
@classmethod
def eval(cls, a, b):
if a.is_Boolean and b.is_Boolean:
return getattr(operator, real_op_name)(a, b)
if a.is_Boolean:
a = sympy.Integer(1 if a else 0)
if b.is_Boolean:
b = sympy.Integer(1 if b else 0)
if isinstance(a, (sympy.Integer, int)) and isinstance(
b, (sympy.Integer, int)
):
return sympy.Integer(getattr(operator, real_op_name)(int(a), int(b)))
return None
BitwiseFn.__name__ = "BitwiseFn_" + name
return BitwiseFn
BitwiseFn_bitwise_and = make_opaque_bitwise_fn("bitwise_and", "and_")
BitwiseFn_bitwise_or = make_opaque_bitwise_fn("bitwise_or", "or_")
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