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2229884102
pytorch/torch/utils/_sympy/functions.py
Edward Z. Yang 2229884102 Introduce int_oo (#127693) 
In a previous life, we used sympy.oo to represent the lower/upper bounds of integer ranges. Later, we changed this to be sys.maxsize - 1 for a few reasons: (1) sometimes we do tests on a value being exactly sys.maxsize, and we wanted to avoid a data dependent guard in this case, (2) sympy.oo corresponds to floating point infinity, so you get incorrect types for value ranges with oo, and (3) you can do slightly better reasoning if you assume that input sizes fall within representable 64-bit integer range.

After working in the sys.maxsize regime for a bit, I've concluded that this was actually a bad idea. Specifically, the problem is that you end up with sys.maxsize in your upper bound, and then whenever you do any sort of size-increasing computation like size * 2, you end up with 2 * sys.maxsize, and you end up doing a ton of arbitrary precision int computation that is totally unnecessary. A symbolic bound is better.

But especially after #126905, we can't go back to using sympy.oo, because that advertises that it's not an integer, and now your ValueRanges is typed incorrectly. So what do we do? We define a new numeric constant `int_oo`, which is like `sympy.oo` but it advertises `is_integer`. **test/test_sympy_utils.py** describes some basic properties of the number, and **torch/utils/_sympy/numbers.py** has the actual implementation.

The rest of the changes of the PR are working out the implications of this change. I'll give more commentary as inline comments.

Fixes https://github.com/pytorch/pytorch/issues/127396

Signed-off-by: Edward Z. Yang <ezyang@meta.com>

Pull Request resolved: https://github.com/pytorch/pytorch/pull/127693
Approved by: https://github.com/lezcano
ghstack dependencies: #126905
2024-06-13 04:08:20 +00:00

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# mypy: allow-untyped-defs
import functools
import math
import operator
import sys
import sympy
from sympy import S
from .numbers import int_oo
__all__ = [
"FloorDiv",
"ModularIndexing",
"CleanDiv",
"CeilDiv",
"IntTrueDiv",
"FloatTrueDiv",
"LShift",
"RShift",
"IsNonOverlappingAndDenseIndicator",
"RoundToInt",
"RoundDecimal",
"ToFloat",
"FloatPow",
"PowByNatural",
]
def _keep_float(f):
@functools.wraps(f)
def inner(*args):
r = 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, y):
if None in (x, y):
return None
return x == y
# 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 = (2,)
precedence = 50 # precedence of mul # noqa: F811
is_integer = True
@property
def base(self):
return self.args[0]
@property
def divisor(self):
return self.args[1]
def _sympystr(self, printer):
base = printer.parenthesize(self.base, self.precedence)
divisor = printer.parenthesize(self.divisor, self.precedence)
return f"({base}//{divisor})"
# Automatic evaluation.
# https://docs.sympy.org/latest/guides/custom-functions.html#best-practices-for-eval
@classmethod
def eval(cls, base, divisor):
# 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 divisor == 1:
return base
if base.is_integer and 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)
# gcd in sympy is over polynomials, so you'll end up with rationals if
# you do this. Don't.
"""
if isinstance(base, sympy.Add):
for a in base.args:
gcd = sympy.gcd(a, divisor)
if gcd == divisor:
return FloorDiv(base - a, divisor) + a / gcd
"""
try:
gcd = sympy.gcd(base, divisor)
if gcd != 1:
return FloorDiv(
sympy.simplify(base / gcd), sympy.simplify(divisor / gcd)
)
except sympy.PolynomialError:
pass # https://github.com/pytorch/pytorch/issues/108276
class ModularIndexing(sympy.Function):
"""
ModularIndexing(a, b, c) => (a // b) % c where % is the C modulus
"""
nargs = (3,)
is_integer = True
@classmethod
def eval(cls, base, divisor, modulus):
if base == 0 or modulus == 1:
return sympy.Integer(0)
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 = []
all_positive = 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)
def _eval_is_nonnegative(self):
p, q = self.args[:2]
return fuzzy_eq(p.is_nonnegative, q.is_nonnegative) # type: ignore[attr-defined]
def _eval_is_positive(self):
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 = (3,)
def _eval_is_integer(self):
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):
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):
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, p, q):
if c == sympy.true:
return p
elif c == sympy.false:
return q
# Python-style modulus: take sign from RHS
class PythonMod(sympy.Function):
nargs = (2,)
is_integer = True
@classmethod
def eval(cls, p, q):
# 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
# NB: args[1] for PythonMod
def _eval_is_nonnegative(self):
return True if self.args[1].is_positive else None # type: ignore[attr-defined]
def _eval_is_nonpositive(self):
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,)
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.
"""
pass
# 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):
# 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.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 base // 2**shift
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
@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_integer = False
is_real = True
@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_integer = False
is_real = True
@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_integer = False
is_real = True
@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_integer = False
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_integer = False
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_integer = False
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
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
return getattr(sympy, name)(a)
return None
OpaqueUnaryFn.__name__ = "OpaqueUnaryFn_" + name
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")
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