| import torch |
| from typing import Set, Dict, List, Type, Optional, cast, Union |
| import sys |
| import builtins |
| import itertools |
| import operator |
| import math |
| import functools |
| import threading |
| from contextlib import contextmanager |
| from functools import lru_cache |
| import traceback |
| import collections |
| import textwrap |
| import logging |
| |
| # NB: The sym_* functions are used via getattr() and must be imported here. |
| from torch import SymInt, SymFloat, SymBool, sym_not, sym_float, sym_max, sym_min # noqa: F401 |
| from torch._guards import ShapeGuard, Source |
| from torch.utils._sympy.value_ranges import ValueRanges, ValueRangeAnalysis |
| from torch.utils._sympy.interp import sympy_interp |
| |
| SymTypes = (SymInt, SymFloat, SymBool) |
| |
| log = logging.getLogger(__name__) |
| |
| class GuardOnDataDependentSymNode(RuntimeError): |
| pass |
| |
| import sympy |
| from sympy.printing.str import StrPrinter |
| from sympy.core.logic import fuzzy_and, fuzzy_or |
| |
| aten = torch._ops.ops.aten # type: ignore[has-type] |
| |
| __all__ = [ |
| "has_symbolic_sizes_strides", "create_contiguous", "ShapeEnv", |
| "SymDispatchMode", "FloorDiv", "guard_int", "guard_float", "guard_scalar", "wrap_node", |
| "method_to_operator", "hint_int", "SYMPY_INTERP", |
| ] |
| |
| SYM_FUNCTION_MODE = None |
| |
| # We don't bother with the metaclass as all of the dispatching logic happens |
| # entirely from Python |
| # |
| # Didn't bother with ancestors for now, unlikely to have multiple modes for |
| # symints right now |
| |
| |
| # SymDispatchMode gets invoked whenever an operation is processed on |
| # a PySymInt. When this occurs, you get called at __sym_dispatch__ |
| # with the operation in question. This is symmetric to TorchDispatchMode |
| # but with some caveats: |
| # |
| # - In TorchDispatchMode, you get the same arguments as what a user |
| # invoked your API with; e.g., if you call torch.ops.aten.foo(a, b), |
| # you get (a, b) as args to your call. In SymDispatchMode, if |
| # you call a + b (where a and b are SymInts), you will get |
| # (a.node, b.node) as your args (these are PySymInts) |
| # |
| # - SymInt/PySymInt don't have FX proxy support (unlike, e.g., Tensor). |
| # So you have to manually call Tracer/create_node to write into |
| # the graph. See ProxySymDispatchMode for an example |
| # |
| class SymDispatchMode: |
| def __sym_dispatch__(self, func, types, args, kwargs): |
| raise NotImplementedError() |
| |
| def __enter__(self): |
| global SYM_FUNCTION_MODE |
| old = SYM_FUNCTION_MODE |
| if hasattr(self, "inner"): |
| raise RuntimeError(f"{self} has already been used as a mode. Please use a fresh version") |
| else: |
| self.inner = old |
| SYM_FUNCTION_MODE = self |
| return self |
| |
| def __exit__(self, exc_type, exc_val, exc_tb): |
| global SYM_FUNCTION_MODE |
| SYM_FUNCTION_MODE = self.inner |
| |
| def has_symbolic_sizes_strides(elem): |
| return elem._has_symbolic_sizes_strides |
| |
| def create_contiguous(shape): |
| strides = [1] |
| for dim in reversed(shape[:-1]): |
| strides.append(dim * strides[-1]) |
| return list(reversed(strides)) |
| |
| def _handle_sym_dispatch(func, args, kwargs): |
| global SYM_FUNCTION_MODE |
| mode = SYM_FUNCTION_MODE |
| assert mode |
| SYM_FUNCTION_MODE = mode.inner |
| try: |
| # TODO: properly compute types |
| types: List[Type] = [] |
| return mode.__sym_dispatch__(func, types, args, kwargs) |
| finally: |
| SYM_FUNCTION_MODE = mode |
| |
| def hint_int(a): |
| if isinstance(a, torch.SymInt): |
| return a.node.require_hint() |
| assert type(a) is int, a |
| return a |
| |
| def has_hint(a): |
| if isinstance(a, SymTypes): |
| return a.node.has_hint() |
| return True |
| |
| # Returns True if every size dim on the tensor has a hint |
| # TODO: Should this include strides too? For now it doesn't matter, |
| # that's quite an obscure case |
| def tensor_has_hints(t): |
| return all(has_hint(s) for s in t.size()) |
| |
| def definitely_true(a): |
| """ |
| Returns True only if we can tell that a is True, possibly introducing |
| a guard in the process. If a depends on some unbacked SymInt, we may |
| return False even though there may exist a possible value of the SymInt |
| that would cause the expression to return True. |
| |
| When is it appropriate to use definitely_true? First, if you can use |
| a higher level combinator like parallel_or/parallel_and, prefer using |
| those instead, they are definitely safe (modulo short-circuiting). |
| Second, it can be used if the program would behave equivalently if |
| definitely_true always returned False (parallel_or/parallel_and are |
| examples of this pattern, modulo short-circuiting). Finally, it even |
| be OK if the program wouldn't behave equivalently, so long as the |
| change is semantics preserving. It can be semantics preserving if |
| the program errors in more cases than it did previously (but otherwise |
| behaves identically), or if it changes some quantity in a way that |
| doesn't matter (e.g., strides often fall in this bucket.) |
| """ |
| if isinstance(a, SymBool): |
| if a.node.has_hint(): |
| return guard_bool(a) |
| else: |
| return False |
| return bool(a) |
| |
| def definitely_false(a): |
| """ |
| Returns True only if we can tell that a is False, possibly introducing |
| a guard in the process. If a depends on some unbacked SymInt, we may |
| return False even though there may exist a possible value of the SymInt |
| that would cause the expression a to be False. See definitely_true |
| for more usage guidance. |
| """ |
| if isinstance(a, SymBool): |
| if a.node.has_hint(): |
| return not guard_bool(a) |
| else: |
| return False |
| return not bool(a) |
| |
| # TODO: could improve parallel_or/parallel_and by avoiding guards |
| # if there exists a quantity that can be handled un-guardedly. However, |
| # for backed SymInts, avoiding guards doesn't really matter in practice, |
| # so I chose not to do it. |
| |
| def parallel_or(*args): |
| """ |
| Evaluate the logical OR of several arguments, avoiding guarding on |
| unbacked SymInts if another argument is definitely True. |
| """ |
| if any(definitely_true(args) for a in args): |
| return True |
| return any(args) |
| |
| def parallel_and(*args): |
| """ |
| Evaluate the logical FALSE of several arguments, avoiding guarding on |
| unbacked SymInts if another argument is definitely False. |
| """ |
| if any(definitely_false(args) for a in args): |
| return False |
| return all(args) |
| |
| def guard_scalar(a): |
| if isinstance(a, (SymBool, bool)): |
| return guard_bool(a) |
| elif isinstance(a, (SymInt, int)): |
| return guard_int(a) |
| elif isinstance(a, (SymFloat, float)): |
| return guard_float(a) |
| else: |
| raise AssertionError(f"unrecognized scalar {a}") |
| |
| # inclusive both ways |
| def constrain_range(a, *, min: Optional[int], max: Optional[int] = None): |
| if min is None: |
| min = -sympy.oo |
| if max is None: |
| max = sympy.oo |
| if not isinstance(a, SymInt): |
| assert min <= a <= max |
| return |
| if isinstance(a.node.expr, sympy.Integer): |
| assert min <= int(a.node.expr) <= max |
| return |
| # TODO: Turn this into a runtime assert too |
| assert isinstance(a.node.expr, sympy.Symbol), "constraining non-Symbols NYI" |
| r = a.node.shape_env.var_to_range[a.node.expr] |
| a.node.shape_env.var_to_range[a.node.expr] = ValueRanges( |
| builtins.max(r.lower, min), builtins.min(r.upper, max) |
| ) |
| |
| |
| def constrain_unify(a, b): |
| """ |
| Given two SymInts, constrain them so that they must be equal. NB: |
| this will not work with SymInts that represent nontrivial expressions |
| (yet!) |
| """ |
| # TODO: Maybe dedupe this with _maybe_guard_eq? |
| if not isinstance(a, SymInt): |
| if not isinstance(b, SymInt): |
| assert a == b |
| else: |
| assert isinstance(b.node.expr, sympy.Symbol), "constraining non-Symbols NYI" |
| shape_env = b.node.shape_env |
| shape_env.replacements[b.node.expr] = sympy.Integer(a) |
| else: |
| # TODO: Actually, we can support this as long as one of them is a symbol. |
| # NB: We can't actually do "unification" as our operators are not |
| # injective |
| assert isinstance(a.node.expr, sympy.Symbol), "constraining non-Symbols NYI" |
| shape_env = a.node.shape_env |
| if not isinstance(b, SymInt): |
| shape_env.replacements[a.node.expr] = sympy.Integer(b) |
| else: |
| assert a.node.shape_env is b.node.shape_env |
| assert isinstance(b.node.expr, sympy.Symbol), "constraining non-Symbols NYI" |
| new_var = shape_env._find(a.node.expr) |
| shape_env.replacements[b.node.expr] = new_var |
| |
| def guard_bool(a): |
| if isinstance(a, SymBool): |
| return a.node.guard_bool("", 0) # NB: uses Python backtrace |
| assert type(a) is bool, a |
| return a |
| |
| def guard_int(a): |
| if isinstance(a, SymInt): |
| return a.node.guard_int("", 0) # NB: uses Python backtrace |
| assert type(a) is int, a |
| return a |
| |
| def guard_float(a): |
| if isinstance(a, SymFloat): |
| return a.node.guard_float("", 0) # NB: uses Python backtrace |
| assert isinstance(a, float), a |
| return a |
| |
| # Drop in replacement for math.sqrt |
| def sym_sqrt(a): |
| if hasattr(a, '__sym_sqrt__'): |
| return a.__sym_sqrt__() |
| return math.sqrt(a) |
| |
| def to_node(self, num): |
| if isinstance(num, SymTypes): |
| return num.node |
| elif type(num) is bool: |
| return self.wrap_bool(num) |
| elif type(num) is int: |
| return self.wrap_int(num) |
| elif type(num) is float: |
| return self.wrap_float(num) |
| else: |
| # NotImplemented is important so that Python tries the |
| # other magic method |
| return NotImplemented |
| |
| # Given a GraphModule, return all the FakeTensors for all the placeholders |
| def fx_placeholder_vals(gm): |
| return [n.meta['val'] for n in gm.graph.nodes if n.op == "placeholder"] |
| |
| def fx_placeholder_targets(gm): |
| return [n.target for n in gm.graph.nodes if n.op == "placeholder"] |
| |
| # Given a GraphModule and arguments to run it with, evaluate that the guards |
| # for its associated ShapeEnv are satisfied by the passed arguments. This |
| # WILL check for duck sizing. |
| def eval_guards(gm, *args): |
| return gm.shape_env.evaluate_guards_for_args(fx_placeholder_vals(gm), args) |
| |
| def bind_symbols(gm, *args): |
| return gm.shape_env.bind_symbols(fx_placeholder_vals(gm), args) |
| |
| # TODO: An incomplete list |
| # 1. Set variables to be equal when we do equality |
| # 2. Specialize on 0/1 when we do subtraction |
| class SymNode: |
| """ |
| This is a type erased SymInt/SymFloat which we use to do actual operations. |
| End users don't touch this. Magic methods are NOT defined on this object. |
| """ |
| def __init__(self, expr, shape_env, pytype, hint: Optional[Union[int, float]], constant=None): |
| self._expr = expr |
| self.shape_env = shape_env |
| self.pytype = pytype |
| # What's the difference between hint and constant? |
| # |
| # - A constant is known to be invariant across invocations of the model; |
| # it will always be this value. We only really know this when we |
| # encounter an honest-to-goodness literal (when wrapping it into |
| # a SymNode, we set constant.) Most of the time, constant is None |
| # |
| # - A hint is a *particular* value from the particular run we are |
| # tracing, but it may vary the next time around. It's useful to |
| # keep this around, as if we need a concrete value from a SymNode, |
| # we will return the hint and guard on the expression that produced |
| # it giving the same hint next time around. The hint is not |
| # guaranteed to be set either: if you have an unbacked SymNode, |
| # there won't be any hint; it was the result of some tensor-dependent |
| # computation, but we don't know what it actually is because we |
| # haven't actually run the tensor computation. |
| # |
| # hint_expr is only set if we don't have a hint. When it is set, it |
| # contains the expression which contains the unbacked symnodes that, |
| # if constrained, would allow this expression to be hinted again. |
| if hint is None: |
| self._hint_expr = self.expr.xreplace(shape_env.var_to_val) |
| self._hint = None |
| self._update_hint() # check if the replacement actually was enough |
| else: |
| self._hint_expr = None |
| self._hint = hint |
| self.constant: Optional[Union[int, float, bool]] = constant |
| |
| @property |
| def expr(self): |
| self._update_expr() |
| return self._expr |
| |
| # Check if we have replacements hint_expr that would allow us to |
| # simplify it into a hint |
| def _update_hint(self): |
| if self._hint_expr.free_symbols <= self.shape_env.replacements.keys(): |
| new_hint = self.shape_env.replace(self._hint_expr) |
| # NB: unification constraints could result in a replacement that |
| # doesn't actually solve the hint! Check for this. |
| if new_hint.free_symbols: |
| self._hint_expr = new_hint |
| return |
| self._hint = self.pytype(new_hint) |
| self._hint_expr = None |
| |
| @property |
| def hint(self): |
| if self._hint is None: |
| self._update_hint() |
| return self._hint |
| |
| def has_hint(self): |
| return self._hint is not None |
| |
| def require_hint(self): |
| if self._hint is None: |
| self._update_hint() |
| if self._hint is None: |
| raise self.shape_env._make_data_dependent_error(self._hint_expr, self.expr) |
| else: |
| return self._hint |
| else: |
| return self._hint |
| |
| def _update_expr(self): |
| self._expr = self.shape_env.replace(self._expr) |
| |
| def is_int(self): |
| return self.pytype is int |
| |
| def is_float(self): |
| return self.pytype is float |
| |
| def is_bool(self): |
| return self.pytype is bool |
| |
| def wrap_int(self, num): |
| assert type(num) is int |
| return SymNode(sympy.Integer(num), self.shape_env, int, num, constant=num) |
| |
| def wrap_float(self, num): |
| assert type(num) is float |
| return SymNode(sympy.Float(num), self.shape_env, float, num, constant=num) |
| |
| def wrap_bool(self, num): |
| assert type(num) is bool |
| return SymNode(sympy.true if num else sympy.false, self.shape_env, bool, num, constant=num) |
| |
| def clone(self): |
| return self |
| |
| def str(self): |
| return f"{self.expr}" |
| |
| def __str__(self): |
| return self.str() |
| |
| def __repr__(self): |
| return self.str() |
| |
| # These methods call the metaprogrammed methods, they're hand written |
| # here so we get good stack traces |
| def add(self, other) -> "SymNode": # noqa: F811 |
| return self._add(other) # type: ignore[attr-defined] |
| |
| def sub(self, other) -> "SymNode": # noqa: F811 |
| return self._sub(other) # type: ignore[attr-defined] |
| |
| def mul(self, other) -> "SymNode": # noqa: F811 |
| return self._mul(other) # type: ignore[attr-defined] |
| |
| def mod(self, other) -> "SymNode": # noqa: F811 |
| return self._mod(other) # type: ignore[attr-defined] |
| |
| def pow(self, other) -> "SymNode": # noqa: F811 |
| return self._pow(other) # type: ignore[attr-defined] |
| |
| def and_(self, other) -> "SymNode": # noqa: F811 |
| return self._and_(other) # type: ignore[attr-defined] |
| |
| def or_(self, other) -> "SymNode": # noqa: F811 |
| return self._or_(other) # type: ignore[attr-defined] |
| |
| def truediv(self, other) -> "SymNode": # noqa: F811 |
| return self._truediv(other) # type: ignore[attr-defined] |
| |
| def floordiv(self, other) -> "SymNode": # noqa: F811 |
| return self._floordiv(other) # type: ignore[attr-defined] |
| |
| def sym_not(self) -> "SymNode": # noqa: F811 |
| return self._sym_not() # type: ignore[attr-defined] |
| |
| def eq(self, other) -> "SymNode": # noqa: F811 |
| return self._eq(other) # type: ignore[attr-defined] |
| |
| def ne(self, other) -> "SymNode": # noqa: F811 |
| return self._ne(other) # type: ignore[attr-defined] |
| |
| def gt(self, other) -> "SymNode": # noqa: F811 |
| return self._gt(other) # type: ignore[attr-defined] |
| |
| def lt(self, other) -> "SymNode": # noqa: F811 |
| return self._lt(other) # type: ignore[attr-defined] |
| |
| def le(self, other) -> "SymNode": # noqa: F811 |
| return self._le(other) # type: ignore[attr-defined] |
| |
| def ge(self, other) -> "SymNode": # noqa: F811 |
| return self._ge(other) # type: ignore[attr-defined] |
| |
| def floor(self) -> "SymNode": # noqa: F811 |
| return self._floor() # type: ignore[attr-defined] |
| |
| def sym_float(self) -> "SymNode": # noqa: F811 |
| return self._sym_float() # type: ignore[attr-defined] |
| |
| def sym_int(self) -> "SymNode": # noqa: F811 |
| return self._sym_int() # type: ignore[attr-defined] |
| |
| def ceil(self) -> "SymNode": # noqa: F811 |
| return self._ceil() # type: ignore[attr-defined] |
| |
| def neg(self) -> "SymNode": # noqa: F811 |
| return self._neg() # type: ignore[attr-defined] |
| |
| def sym_min(self, other) -> "SymNode": # noqa: F811 |
| return self._sym_min(other) # type: ignore[attr-defined] |
| |
| def sym_max(self, other) -> "SymNode": # noqa: F811 |
| return self._sym_max(other) # type: ignore[attr-defined] |
| |
| def sym_sqrt(self) -> "SymNode": # noqa: F811 |
| return self._sym_sqrt() # type: ignore[attr-defined] |
| |
| def is_contiguous(self, sizes, strides) -> "SymNode": # noqa: F811 |
| return self._is_contiguous(sizes, strides) # type: ignore[attr-defined] |
| |
| def is_channels_last_contiguous_2d(self, sizes, strides) -> "SymNode": # noqa: F811 |
| return self._is_channels_last_contiguous_2d(sizes, strides) # type: ignore[attr-defined] |
| |
| def is_channels_last_contiguous_3d(self, sizes, strides) -> "SymNode": # noqa: F811 |
| return self._is_channels_last_contiguous_3d(sizes, strides) # type: ignore[attr-defined] |
| |
| def is_channels_last_strides_2d(self, sizes, strides) -> "SymNode": # noqa: F811 |
| return self._is_channels_last_strides_2d(sizes, strides) # type: ignore[attr-defined] |
| |
| def is_channels_last_strides_3d(self, sizes, strides) -> "SymNode": # noqa: F811 |
| return self._is_channels_last_strides_3d(sizes, strides) # type: ignore[attr-defined] |
| |
| def is_non_overlapping_and_dense_indicator(self, sizes, strides) -> "SymNode": # noqa: F811 |
| return self._is_non_overlapping_and_dense_indicator(sizes, strides) # type: ignore[attr-defined] |
| |
| # Make C++ happy |
| def sym_or(self, other): # noqa: F811 |
| return self.or_(other) |
| |
| def sym_and(self, other): # noqa: F811 |
| return self.and_(other) |
| |
| def is_non_overlapping_and_dense(self, sizes, strides): |
| return self.is_non_overlapping_and_dense_indicator(sizes, strides).eq(to_node(self, 1)) # type: ignore[attr-defined] |
| |
| def int_(self): |
| return self.guard_int("", 0) # NB: uses Python backtrace |
| |
| # You can manually trigger a guard with this function |
| def guard_int(self, file, line): |
| # TODO: use the file/line for some useful diagnostic on why a |
| # guard occurred |
| r = self.shape_env.evaluate_expr(self.expr, self.hint) |
| try: |
| return int(r) |
| except Exception: |
| log.warning(f"Failed to convert to int: {r}") |
| raise |
| |
| def guard_float(self, file, line): |
| # TODO: use the file/line for some useful diagnostic on why a |
| # guard occurred |
| r = self.shape_env.evaluate_expr(self.expr, self.hint) |
| try: |
| return float(r) |
| except Exception: |
| log.warning(f"Failed to convert to float: {r}") |
| raise |
| |
| def guard_bool(self, file, line): |
| # TODO: use the file/line for some useful diagnostic on why a |
| # guard occurred |
| r = self.shape_env.evaluate_expr(self.expr, self.hint) |
| try: |
| return bool(r) |
| except Exception: |
| log.warning(f"Failed to convert to bool: {r}") |
| raise |
| |
| def bool_(self): |
| return self.guard_bool("", 0) |
| |
| |
| # Overloaded to be compatible with regular Python. |
| # https://github.com/pytorch/pytorch/issues/90900 |
| class Pow(sympy.Function): |
| @classmethod |
| def eval(cls, base, exp): |
| if exp.is_zero: |
| return sympy.Integer(1) |
| elif base.is_zero and exp < 0: |
| raise ZeroDivisionError(f"{base} cannot be raised to a negative power") |
| else: |
| return base ** exp |
| |
| # Overloaded to be compatible with regular Python. |
| # https://github.com/pytorch/pytorch/issues/90900 |
| class TrueDiv(sympy.Function): |
| @classmethod |
| def eval(cls, base, divisor): |
| if divisor.is_zero: |
| raise ZeroDivisionError("division by zero") |
| else: |
| return base / divisor |
| |
| 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) |
| """ |
| nargs = (2,) |
| precedence = 50 # precedence of mul # noqa: F811 |
| |
| # Default return type for SymPy assumptions. |
| # https://docs.sympy.org/latest/guides/assumptions.html#implementing-assumptions-handlers |
| is_real = 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}" |
| |
| # SymPy assumptions based on argument types. |
| def _eval_is_real(self): |
| return fuzzy_or([self.base.is_real, self.divisor.is_real]) |
| |
| def _eval_is_integer(self): |
| return fuzzy_and([self.base.is_integer, self.divisor.is_integer]) |
| |
| # Automatic evaluation. |
| # https://docs.sympy.org/latest/guides/custom-functions.html#best-practices-for-eval |
| @classmethod |
| def eval(cls, base, divisor): |
| def check_supported_type(x): |
| if (x.is_integer is False and x.is_real is False and x.is_complex) or x.is_Boolean: |
| raise TypeError( |
| f"unsupported operand type(s) for //: " |
| f"'{type(base).__name__}' and '{type(divisor).__name__}'" |
| f", expected integer or real") |
| |
| check_supported_type(base) |
| check_supported_type(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.is_zero: |
| return sympy.S.Zero |
| if base.is_integer and divisor == 1: |
| return base |
| if base.is_real and divisor == 1: |
| return sympy.floor(base) |
| if isinstance(base, sympy.Integer) and isinstance(divisor, sympy.Integer): |
| return base // divisor |
| if isinstance(base, (sympy.Integer, sympy.Float)) and isinstance(divisor, (sympy.Integer, sympy.Float)): |
| return sympy.floor(base / divisor) |
| if isinstance(base, FloorDiv): |
| return FloorDiv(base.args[0], base.args[1] * divisor) |
| |
| 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 |
| |
| gcd = sympy.gcd(base, divisor) |
| if gcd != 1: |
| return FloorDiv( |
| sympy.simplify(base / gcd), sympy.simplify(divisor / gcd) |
| ) |
| |
| # 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 |
| # TODO: it is possible to make progress evaluating this guard |
| # even if not all of the inputs are known. For example, a 2D |
| # tensor with non-0/1 sizes but strides (0, 1) is definitely |
| # false, because we know its numel > 1 but it's broadcasted |
| # in dim 0. |
| if all(isinstance(a, sympy.Integer) for a in args): |
| size_args = args[0:dim] |
| stride_args = args[dim:] |
| return eval_is_non_overlapping_and_dense( |
| [int(a) for a in size_args], |
| [int(a) for a in stride_args] |
| ) |
| return None |
| |
| IndicatorTypes = (IsNonOverlappingAndDenseIndicator,) |
| |
| @lru_cache(256) |
| def safe_expand(r): |
| if hasattr(r, 'expand'): |
| try: |
| return sympy.expand(r) |
| except RecursionError: |
| log.warning(f"RecursionError in sympy.expand({r})") |
| return r |
| else: |
| return r |
| |
| # Methods that have a `__foo__` as well as `__rfoo__` |
| reflectable_magic_methods = { |
| 'add': lambda a, b: a + b, |
| 'sub': lambda a, b: a - b, |
| 'mul': lambda a, b: a * b, |
| 'mod': lambda a, b: a % b, |
| 'pow': lambda a, b: Pow(a, b), |
| 'and': lambda a, b: a & b, |
| 'or': lambda a, b: a | b, |
| 'truediv': lambda a, b: TrueDiv(a, b), |
| 'floordiv': lambda a, b: FloorDiv(a, b), |
| } |
| |
| |
| def error(): |
| raise AssertionError("shouldn't be hit") |
| |
| def floor_ceil_helper(a, fn): |
| if isinstance(a, sympy.Mul): |
| aa = a.args |
| if len(aa) == 2 and isinstance(aa[0], sympy.Float) and aa[1].is_integer: |
| coef = sympy.Integer(aa[0]) |
| if aa[0] == coef: # structural equality test |
| return coef * aa[1] |
| if isinstance(a, sympy.Float) and a == sympy.Integer(a) or isinstance(a, sympy.Integer): |
| return sympy.Integer(a) |
| return fn(a) |
| |
| def floor_impl(a): |
| return floor_ceil_helper(a, sympy.floor) |
| |
| def ceil_impl(a): |
| return floor_ceil_helper(a, sympy.ceiling) |
| |
| |
| magic_methods = { |
| **reflectable_magic_methods, |
| 'sym_not': lambda a: ~a, |
| 'eq': lambda a, b: sympy.Eq(a, b), |
| 'ne': lambda a, b: sympy.Ne(a, b), |
| 'gt': lambda a, b: sympy.Gt(a, b), |
| 'lt': lambda a, b: sympy.Lt(a, b), |
| 'le': lambda a, b: sympy.Le(a, b), |
| 'ge': lambda a, b: sympy.Ge(a, b), |
| 'floor': floor_impl, |
| 'sym_float': lambda a: a, # Cannot use sympy.Float(a) here, coz it expects python literals |
| 'ceil': ceil_impl, |
| 'neg': lambda a: -a, |
| 'sym_min': lambda a, b: sympy.Min(a, b), |
| 'sym_max': lambda a, b: sympy.Max(a, b), |
| 'sym_sqrt': lambda a: sympy.sqrt(a), |
| } |
| |
| sizes_strides_methods = { |
| # TODO: These could also be done with indicators, maybe it is better |
| # for reasoning to do it that way |
| 'is_contiguous': lambda sizes, strides: sympy_is_contiguous(sizes, strides), |
| 'is_channels_last_contiguous_2d': lambda sizes, strides: sympy_is_channels_last_contiguous_2d(sizes, strides), |
| 'is_channels_last_contiguous_3d': lambda sizes, strides: sympy_is_channels_last_contiguous_3d(sizes, strides), |
| 'is_channels_last_strides_2d': lambda sizes, strides: sympy_is_channels_last_strides_2d(sizes, strides), |
| 'is_channels_last_strides_3d': lambda sizes, strides: sympy_is_channels_last_strides_3d(sizes, strides), |
| 'is_non_overlapping_and_dense_indicator': lambda sizes, strides: IsNonOverlappingAndDenseIndicator(*sizes, *strides), |
| } |
| |
| alternate_impl_if_hinted_methods = { |
| "sym_min": builtins.min, |
| "sym_max": builtins.max, |
| } |
| |
| def sympy_is_contiguous_generic(sizes, strides, dim_order): |
| dim = len(sizes) |
| |
| if len(dim_order) != dim: |
| return sympy.false |
| |
| is_contiguous = sympy.true |
| z = sympy.Integer(1) |
| # Contiguous if the strides make sense (or the dim is size 1) |
| for d in dim_order: |
| is_contiguous &= sympy.Eq(sizes[d], sympy.Integer(1)) | sympy.Eq(strides[d], z) |
| z *= sizes[d] |
| # OR if any size is zero |
| for d in range(dim): |
| is_contiguous |= sympy.Eq(sizes[d], sympy.Integer(0)) |
| return is_contiguous |
| |
| def sympy_is_contiguous(sizes, strides): |
| dim = len(sizes) |
| return sympy_is_contiguous_generic(sizes, strides, list(range(dim - 1, -1, -1))) |
| |
| # NB: There is a TODO in C++ to allow omitting the batch dim. If that |
| # happens you will need to refactor this |
| |
| def sympy_is_channels_last_contiguous_2d(sizes, strides): |
| return sympy_is_contiguous_generic(sizes, strides, [1, 3, 2, 0]) |
| |
| def sympy_is_channels_last_contiguous_3d(sizes, strides): |
| return sympy_is_contiguous_generic(sizes, strides, [1, 4, 3, 2, 0]) |
| |
| def sympy_is_channels_last_strides_generic(sizes, strides, dim_order): |
| dim = len(sizes) |
| |
| if dim != len(dim_order): |
| return sympy.false |
| |
| m = sympy.Integer(0) |
| r = sympy.true |
| |
| # special case for trivial C dimension. default to NCHW |
| r &= sympy.Ne(strides[1], 0) |
| |
| for d in dim_order: |
| r &= sympy.Ne(sizes[d], 0) & (strides[d] >= m) |
| # Fallback to NCHW as default layout for ambiguous cases |
| # This is the flaw of implicit memory_format from strides. |
| # N111 tensor with identical strides for size 1 dimension; |
| # Two cases could lead us here: |
| # a. N111 contiguous Tensor ([N,1,1,1]@[1,1,1,1]) |
| # b. N11W contiguous Tensor sliced on the W-dimension. |
| # ([N,1,1,1]@[W,W,W,W]) |
| if d == 0: |
| r &= sympy.Ne(m, strides[1]) |
| # This is necessary to: |
| # 1. distinguish the memory_format of N1H1; |
| # [H, 1, 1, 1] channels_last stride |
| # [H, H, 1, 1] contiguous stride |
| # 2. permutation of 1C1W: |
| # [1, C, 1, H]@[HC, H, H, 1] transpose(1, 3) |
| # [1, H, 1, C]@[HC, 1, H, H] shouldn't be identified as |
| # channels_last |
| m = strides[d] * sympy.Max(sizes[d], 1) |
| |
| return r |
| |
| def sympy_is_channels_last_strides_2d(sizes, strides): |
| return sympy_is_channels_last_strides_generic(sizes, strides, [1, 3, 2, 0]) |
| |
| def sympy_is_channels_last_strides_3d(sizes, strides): |
| return sympy_is_channels_last_strides_generic(sizes, strides, [1, 4, 3, 2, 0]) |
| |
| # TODO: Deduplicate this with torch/_prims_common/__init__.py |
| def eval_is_non_overlapping_and_dense(sizes, strides): |
| return int(guard_bool(_eval_is_non_overlapping_and_dense(sizes, strides))) |
| |
| def _eval_is_non_overlapping_and_dense(sizes, strides): |
| dim = len(sizes) |
| |
| # Short-circuits for tensors of rank one, which are |
| # non-overlapping and "dense" if their stride is one |
| # or it is a 0/1 element tensor |
| if dim == 1: |
| return strides[0] == 1 or sizes[0] < 2 |
| |
| # Checks that there exists a permutation of the strides s.t. the tensor would be contiguous |
| # Sorts (length, stride) pairs by stride |
| lengths_and_strides = sorted( |
| zip(sizes, strides), key=operator.itemgetter(1) |
| ) |
| |
| # Unlike the C++ code, we don't move the 0/1 size dimensions to the |
| # end. So we have to keep going for this code. |
| expected_stride = 1 |
| for length, stride in lengths_and_strides: |
| |
| if length == 1: |
| continue |
| |
| if stride != expected_stride: |
| return False |
| |
| expected_stride *= length |
| |
| return True |
| |
| unary_magic_methods = { |
| 'sym_float', |
| 'ceil', |
| 'floor', |
| 'neg', |
| 'sym_sqrt', |
| 'sym_not', |
| } |
| |
| bool_magic_methods = {"and", "or", "sym_not"} |
| |
| magic_methods_on_math = {"ceil", "floor"} |
| magic_methods_on_submodule = {"sym_float", "sym_sqrt", "sym_min", "sym_max", "sym_not"} |
| magic_methods_on_operator_with_trailing_underscore = {"and", "or"} |
| |
| def method_to_operator(method): |
| if method in magic_methods_on_operator_with_trailing_underscore: |
| method_attr = f"{method}_" |
| else: |
| method_attr = method |
| if method in magic_methods_on_submodule: |
| op = getattr(torch.fx.experimental.symbolic_shapes, method_attr) |
| elif method in magic_methods_on_math: |
| op = getattr(math, method_attr) |
| else: |
| op = getattr(operator, method_attr) |
| return op |
| |
| SYMPY_INTERP = { |
| 'Eq': operator.eq, |
| 'Ne': operator.ne, |
| 'Gt': operator.gt, |
| 'Lt': operator.lt, |
| 'Le': operator.le, |
| 'Ge': operator.ge, |
| 'Min': min, |
| 'Max': max, |
| 'Mod': operator.mod, |
| 'FloorDiv': operator.floordiv, |
| 'TrueDiv': operator.truediv, |
| 'IsNonOverlappingAndDenseIndicator': eval_is_non_overlapping_and_dense, |
| 'floor': math.floor, |
| 'ceiling': math.ceil, |
| } |
| |
| always_float_magic_methods = {"truediv", "sym_float", "sym_sqrt", "pow"} |
| always_int_magic_methods = {"ceil", "floor"} |
| always_bool_magic_methods = {"eq", "ne", "gt", "lt", "le", "ge", "and", "or", "sym_not", "is_non_overlapping_and_dense"} |
| |
| def wrap_node(x): |
| # TODO: let C++ also take advantage of this |
| if isinstance(x, SymNode) and x.constant is not None: |
| return x.constant |
| if x.is_int(): |
| return SymInt(x) |
| elif x.is_float(): |
| return SymFloat(x) |
| elif x.is_bool(): |
| return SymBool(x) |
| else: |
| raise AssertionError(f"unrecognized return type {x}") |
| |
| def _make_node_magic(method, func): |
| func = lru_cache(256)(func) |
| |
| if method in magic_methods_on_operator_with_trailing_underscore: |
| method_attr = f"{method}_" |
| else: |
| method_attr = method |
| |
| def binary_magic_impl(self, other): |
| op = method_to_operator(method) |
| |
| out_hint = None |
| if self.hint is not None and other.hint is not None: |
| out_hint = op(self.hint, other.hint) |
| |
| alternate_impl = alternate_impl_if_hinted_methods.get(method) |
| if alternate_impl and out_hint is not None: |
| return to_node(self, alternate_impl(wrap_node(self), wrap_node(other))) |
| |
| if SYM_FUNCTION_MODE: |
| return to_node(self, _handle_sym_dispatch(op, (wrap_node(self), wrap_node(other)), {})) |
| assert isinstance(other, SymNode) |
| other_expr = other.expr |
| # TODO: consider constant prop here |
| expr = self.shape_env.replace(self.expr) |
| other_expr = self.shape_env.replace(other_expr) |
| try: |
| out = func(expr, other_expr) |
| except Exception: |
| log.warning(f"failed to eval {method}({expr}, {other_expr})") |
| raise |
| out = safe_expand(out) |
| pytype: Type |
| # This is not strictly correct. In Python, a**b may return complex when |
| # a < 0 and b is a float: (-1)**2.1. Same for sympy.sqrt(-3.14). This |
| # returns a float while both arguments are ints: 2**(-1). Also, max and |
| # min do not type promote. To avoid having data-dependent control flow |
| # here, we just set the type to float if one of the args is a float. In |
| # case of a type mismatch, we assume that it will be detected during |
| # evaluation. |
| if method in always_float_magic_methods: |
| pytype = float |
| elif method in always_bool_magic_methods: |
| pytype = bool |
| elif self.pytype is float or other.pytype is float: |
| pytype = float |
| else: |
| pytype = self.pytype |
| |
| return SymNode(out, self.shape_env, pytype, out_hint) |
| |
| def unary_magic_impl(self): |
| op = method_to_operator(method) |
| if SYM_FUNCTION_MODE: |
| return to_node(self, _handle_sym_dispatch(op, (wrap_node(self),), {})) |
| # TODO: consider constant prop here |
| expr = self.shape_env.replace(self.expr) |
| if method == "floor" or method == "ceiling": |
| expr = self.shape_env._simplify_floor_div(expr) |
| |
| try: |
| out = func(expr) |
| except Exception: |
| log.warning(f"failed to eval {method}({expr})") |
| raise |
| |
| out_hint = None |
| if self.hint is not None: |
| out_hint = op(self.hint) |
| out = safe_expand(out) |
| pytype: Type |
| if method in always_int_magic_methods: |
| pytype = int |
| elif method in always_float_magic_methods: |
| pytype = float |
| else: |
| pytype = self.pytype |
| |
| return SymNode(out, self.shape_env, pytype, out_hint) |
| |
| if method in unary_magic_methods: |
| setattr(SymNode, f"_{method_attr}", unary_magic_impl) |
| else: |
| setattr(SymNode, f"_{method_attr}", binary_magic_impl) |
| |
| def _make_node_sizes_strides(method, func): |
| # NB: don't LRU cache, lots of arguments |
| |
| def sizes_strides_impl(self, sizes, strides): |
| op = getattr(sys.modules[__name__], method) |
| if SYM_FUNCTION_MODE: |
| return to_node( |
| self, |
| _handle_sym_dispatch( |
| op, |
| ([wrap_node(s) for s in sizes], [wrap_node(s) for s in strides]), |
| {} |
| ) |
| ) |
| size_exprs = [s.expr for s in sizes] |
| stride_exprs = [s.expr for s in strides] |
| try: |
| out = func(size_exprs, stride_exprs) |
| except Exception: |
| log.warning(f"failed to eval {method}({size_exprs}, {stride_exprs})") |
| raise |
| # bool is never expandable |
| |
| size_hints = [] |
| out_hint = None |
| for s in sizes: |
| if s.hint is None: |
| break |
| size_hints.append(s.hint) |
| else: |
| stride_hints = [] |
| for s in strides: |
| if s.hint is None: |
| break |
| stride_hints.append(s.hint) |
| else: |
| out_hint = op(size_hints, stride_hints) |
| |
| # NB: This is the indicator function, not the actual bool! |
| pytype: Type |
| if method.endswith("_indicator"): |
| pytype = int |
| else: |
| pytype = bool |
| return SymNode(out, self.shape_env, pytype, out_hint) |
| |
| setattr(SymNode, f"_{method}", sizes_strides_impl) |
| |
| # TODO: This is technically hotpath, but in the ideal end state |
| # guards on this will resolve at a higher level so you never |
| # spend time in this code |
| def sizes_strides_user(sizes, strides): |
| for a in itertools.chain(sizes, strides): |
| if isinstance(a, SymInt): |
| return wrap_node(getattr(a.node, method)( |
| [to_node(a.node, b) for b in sizes], |
| [to_node(a.node, b) for b in strides], |
| )) |
| if method == "is_non_overlapping_and_dense_indicator": |
| return eval_is_non_overlapping_and_dense(sizes, strides) |
| else: |
| # TODO: this is an awful implementation |
| return bool(func( |
| [sympy.sympify(a) for a in sizes], |
| [sympy.sympify(a) for a in strides], |
| )) |
| |
| # Skip for is_non_overlapping_and_dense_indicator |
| if not hasattr(sys.modules[__name__], method): |
| setattr(sys.modules[__name__], method, sizes_strides_user) |
| |
| for method, func in magic_methods.items(): |
| _make_node_magic(method, func) |
| |
| for method, func in sizes_strides_methods.items(): |
| _make_node_sizes_strides(method, func) |
| |
| def _make_user_magic(method, user_type): |
| # User magic takes care of wrapping the other operand into a node, |
| # so that our internal logic can assume everything is nodes |
| |
| if method in magic_methods_on_operator_with_trailing_underscore: |
| method_attr = f"{method}_" |
| else: |
| method_attr = method |
| |
| def unary_magic_impl(self): |
| return wrap_node(getattr(self.node, method_attr)()) |
| |
| def binary_magic_impl(self, other): |
| other_node = to_node(self.node, other) |
| if other_node is NotImplemented: |
| return NotImplemented |
| return wrap_node(getattr(self.node, method_attr)(other_node)) |
| |
| def rbinary_magic_impl(self, other): |
| other_node = to_node(self.node, other) |
| if other_node is NotImplemented: |
| return NotImplemented |
| return wrap_node(getattr(other_node, method_attr)(self.node)) |
| |
| if method in unary_magic_methods: |
| setattr(user_type, f"__{method}__", unary_magic_impl) |
| else: |
| setattr(user_type, f"__{method}__", binary_magic_impl) |
| if method in reflectable_magic_methods: |
| setattr(user_type, f"__r{method}__", rbinary_magic_impl) |
| |
| for method, func in magic_methods.items(): |
| if method in bool_magic_methods: |
| _make_user_magic(method, SymBool) |
| else: |
| _make_user_magic(method, SymInt) |
| _make_user_magic(method, SymFloat) |
| |
| del method |
| del func |
| |
| def _lru_cache(fn, maxsize=None): |
| """ |
| Wrapper around lru_cache that clears when new info about shapes has been |
| updated. |
| |
| Use lru_cache if the output is always the same, regardless of the |
| constraints we know now (i.e. evaluate_expr) |
| |
| Use _lru_cache otherwise. |
| """ |
| fn_cache = lru_cache(maxsize)(fn) |
| prior_key = None |
| |
| @functools.wraps(fn) |
| def wrapper(self, *args, **kwargs): |
| nonlocal prior_key |
| if prior_key != self._get_key(): |
| prior_key = self._get_key() |
| fn_cache.cache_clear() |
| return fn_cache(self, *args, **kwargs) |
| |
| wrapper.cache_info = fn_cache.cache_info # type: ignore[attr-defined] |
| return wrapper |
| |
| |
| class ShapeGuardPrinter(StrPrinter): |
| def __init__( |
| self, |
| symbol_to_source, |
| source_ref, |
| var_to_sources, |
| ): |
| super().__init__() |
| self.symbol_to_source = symbol_to_source |
| self.source_ref = source_ref |
| self.var_to_sources = var_to_sources |
| |
| def _print_Symbol(self, expr) -> str: |
| assert isinstance(expr, sympy.Symbol), str(type(expr)) |
| |
| def repr_symbol_to_source(): |
| return repr({ |
| symbol: [s.name() for s in sources] |
| for symbol, sources in self.symbol_to_source |
| }) |
| |
| assert expr in self.symbol_to_source, ( |
| f"{expr} (could be from {[s.name() for s in self.var_to_sources[expr]]}) " |
| f"not in {repr_symbol_to_source()}. If this assert is failing, it could be " |
| "due to the issue described in https://github.com/pytorch/pytorch/pull/90665" |
| ) |
| return self.source_ref(self.symbol_to_source[expr][0]) |
| |
| |
| TLS = threading.local() |
| |
| |
| class ShapeEnv: |
| def __init__( |
| self, *, |
| allow_scalar_outputs=True, |
| allow_dynamic_output_shape_ops=True, |
| strict_mark_dyn=False, |
| assume_static_by_default=False, |
| # The following options affect decisions we make about eager |
| # specialization. Disabling them will increase trace time (as we do |
| # more symbolic reasoning) and can also harm the quality of generated |
| # code (because inductor may not be able to specialize for bounds |
| # being equal--although if we later respecialize because of a guard, |
| # your code may be just as good as it was before.) |
| # |
| # When True, eagerly specialize input sizes which have 0/1. |
| specialize_zero_one=True, |
| # When True, assume input sizes which have the same size are |
| # symbolically equal. |
| duck_shape=True, |
| ): |
| # Not directly used by ShapeEnv; indirectly used by FakeTensor |
| self.allow_scalar_outputs = allow_scalar_outputs |
| self.allow_dynamic_output_shape_ops = allow_dynamic_output_shape_ops |
| self.guards: List[ShapeGuard] = [] |
| # Maps symbolic ints to their original concrete values |
| # Currently populated from tensors |
| self.var_to_val: Dict["sympy.Symbol", "sympy.Integer"] = {} |
| # Maps symbolic ints to their min/max range. These ranges |
| # are conservative: the int MUST fall in the range, but the |
| # range may contain ints which may not actually appear in |
| # practice |
| self.var_to_range: Dict["sympy.Symbol", ValueRanges] = {} |
| self.var_to_sources: Dict["sympy.Symbol", List[Source]] = {} |
| self.var_to_stack: Dict["sympy.Symbol", str] = {} |
| # Maps from sympy ints to expressions representing them |
| # Populated from equality guards (i.e. a.shape[0] == b.shape[0]) |
| self.replacements: Dict["sympy.Symbol", "sympy.Expr"] = {} # |
| # Set holds a % b expressions that evaluate to 0. |
| self.divisible: Set["sympy.Expr"] = set() |
| # Duck-shaping says that if two input tensors have the same size, |
| # they get assigned the same symbolic variable |
| self.val_to_var: Dict[int, "sympy.Expr"] = {} |
| if specialize_zero_one: |
| self.val_to_var = {0: sympy.Integer(0), 1: sympy.Integer(1)} |
| self.unbacked_symfloat_counter = itertools.count() |
| self.unbacked_symint_counter = itertools.count() |
| self.strict_mark_dyn = strict_mark_dyn |
| self.assume_static_by_default = assume_static_by_default |
| self.specialize_zero_one = specialize_zero_one |
| self.duck_shape = duck_shape |
| |
| def _suppress_guards_tls(self): |
| return getattr(TLS, "suppress_guards", False) |
| |
| @contextmanager |
| def suppress_guards(self): |
| TLS.suppress_guards = True |
| try: |
| yield |
| finally: |
| TLS.suppress_guards = False |
| |
| def _get_key(self): |
| """ |
| Defines the current "state" of the guards we've accumulated in this ShapeEnv. |
| Determines when we need to invalidate our cache |
| """ |
| return (len(self.replacements), len(self.divisible)) |
| |
| def _produce_dyn_sizes(self, ex: torch.Tensor, source: Source) -> List[sympy.Expr]: |
| from torch._dynamo.source import TensorPropertySource, TensorProperty |
| size = [] |
| for i, val in enumerate(ex.size()): |
| is_dynamic = _is_dim_dynamic(ex, i) |
| if _should_allocate(is_dynamic, self.assume_static_by_default): |
| size.append(self.create_symbol( |
| val, TensorPropertySource(source, TensorProperty.SIZE, i), is_dynamic |
| )) |
| else: |
| size.append(sympy.Integer(val)) |
| return size |
| |
| def create_symbolic_sizes_strides_storage_offset(self, ex: torch.Tensor, source: Source): |
| """ |
| Returns a list of symbolic sizes and strides for the given tensor. |
| We try our best to express stride in terms of the sizes, so as to not |
| introduce new symbolic variables. |
| """ |
| from torch._dynamo.source import TensorPropertySource, TensorProperty |
| size: List[sympy.Expr] = self._produce_dyn_sizes(ex, source) |
| stride: List[Optional[sympy.Expr]] = [None] * len(size) |
| for i, val in enumerate(ex.stride()): |
| if val in (0, 1): |
| stride[i] = sympy.Integer(val) |
| while any(x is None for x in stride): |
| candidates = { |
| ex.size(i) * ex.stride()[i]: size[i] * stride[i] |
| for i in range(len(size)) |
| if stride[i] is not None and ex.stride()[i] >= 0 |
| } |
| # iterate over unbound strides in sorted order |
| val_list = sorted( |
| [(ex.stride()[i], i) for i in range(len(stride)) if stride[i] is None] |
| ) |
| for _, i in val_list: |
| if stride[i] is None and ex.stride()[i] in candidates: |
| stride[i] = candidates[ex.stride()[i]] |
| candidates[ex.size(i) * ex.stride()[i]] = size[i] * stride[i] |
| if any(x is None for x in stride): |
| # bind the smallest unbound stride to a new variable |
| val, i = min( |
| [ |
| (ex.stride()[i], i) |
| for i in range(len(stride)) |
| if stride[i] is None |
| ] |
| ) |
| stride[i] = self.create_symbol( |
| val, |
| TensorPropertySource(source, TensorProperty.STRIDE, i) |
| ) |
| assert all(x is not None for x in stride) |
| sym_size = [self.create_symintnode(i, hint=hint) for i, hint in zip(size, ex.size())] |
| sym_stride = [] |
| for i, stride_expr in enumerate(stride): |
| # NB: Don't duck size the stride; instead use the expression |
| # we computed |
| assert stride_expr is not None |
| sym_stride.append(self.create_symintnode(stride_expr, hint=ex.stride(i))) |
| sym_storage_offset = self.create_symintnode(self.create_symbol( |
| ex.storage_offset(), |
| TensorPropertySource(source, TensorProperty.STORAGE_OFFSET) |
| ), hint=ex.storage_offset()) |
| return sym_size, sym_stride, sym_storage_offset |
| |
| # If you know what the current hint value of the SymInt to be created |
| # is, pass it into hint. Otherwise, pass None and we will make our best |
| # guess |
| def create_symintnode(self, sym: "sympy.Expr", *, hint: Optional[int]): |
| return SymInt(SymNode(sym, self, int, hint)) |
| |
| def create_unbacked_symfloat(self): |
| symbol = sympy.Symbol(f"f{next(self.unbacked_symfloat_counter)}") |
| self.var_to_stack[symbol] = ''.join(traceback.format_list(traceback.extract_stack()[:-1])) |
| self.var_to_range[symbol] = ValueRanges.unknown() |
| return SymFloat(SymNode(symbol, self, float, None)) |
| |
| def create_unbacked_symint(self): |
| symbol = sympy.Symbol(f"i{next(self.unbacked_symint_counter)}", integer=True) |
| self.var_to_stack[symbol] = ''.join(traceback.format_list(traceback.extract_stack()[:-1])) |
| self.var_to_range[symbol] = ValueRanges.unknown() |
| return SymInt(SymNode(symbol, self, int, None)) |
| |
| # This is guaranteed to return a symbol or its negation is a sympy.Symbol, |
| # but there may be a replacement that allows it to be immediately |
| # simplified |
| def create_symbol(self, val: int, source: Source, dyn=False) -> "sympy.Expr": |
| assert isinstance(source, Source), f"{type(source)} {source}" |
| |
| if val < 0: |
| from torch._dynamo.source import NegateSource |
| return -self.create_symbol(-val, NegateSource(source), dyn) |
| |
| if dyn or val not in self.val_to_var or not self.duck_shape: |
| # If a value is never before seen, or dynamic, we want to create an expression |
| sympy_expr = sympy.Symbol(f"s{len(self.var_to_val)}", positive=True, integer=True) |
| # We always associate vars to vals |
| self.var_to_val[sympy_expr] = sympy.Integer(val) |
| # Do the appending later, because we always want to populate this |
| self.var_to_sources[sympy_expr] = [] |
| |
| if not dyn: |
| # Non explicitly marked dynamic dims register to val_to_var to get duck shaped |
| self.val_to_var[val] = sympy_expr |
| |
| # We also infer that it must be not 0/1 |
| lower = 2 if self.specialize_zero_one else 0 |
| self.var_to_range[sympy_expr] = ValueRanges(lower, sympy.oo) |
| |
| if not dyn and self.duck_shape: |
| # This implements duck-shaping: input sizes that match are assigned |
| # the same symint |
| r = self.duck_int(val) |
| else: |
| r = sympy_expr |
| |
| if isinstance(r, sympy.Symbol): |
| self.var_to_sources[r].append(source) |
| return r |
| |
| # Given a concrete integer value, return the duck sized symbol associated |
| # with it; e.g., suppose we already have a tensor of size 3 in scope, |
| # which was assigned s3, then shape_env.duck_int(3) we will get back s3. |
| # This has some pretty tricky preconditions associated with it, so if |
| # you are in a binding context, you probably wanted create_symbol instead. |
| def duck_int(self, val): |
| assert self.duck_shape |
| assert val in self.val_to_var, ( |
| "Direct call to duck_int MUST only duck size an integer values " |
| "that have already produced by inputs (allocated " |
| "by create_symbol), or we risk being unable to instantiate the " |
| "symbolic variable later. However, at time of this call " |
| f"val={val} was not duck sized. Bound duck sized integers: " |
| f"{list(self.val_to_var.keys())}" |
| ) |
| return self.val_to_var[val] |
| |
| # Generates a list of guards strings which, when evaluated in a context that |
| # defines tensors for all the sources, returns True or False depending |
| # on if the guards in the list evaluated to True or not. Primarily used by Dynamo, |
| # but this is also helpful for manual testing of guards (see |
| # evaluate_guards_for_args) |
| # |
| # For convenience in testing, a source is allowed to be a str, |
| # in which case we will assume it is a LocalSource |
| # |
| # simplified lets you omit duck sizing, equality and 0/1 guards. |
| # This is useful for testing when you don't care about the boilerplate |
| # guards, and it may be helpful for user output too (be careful though; |
| # some equality guards are nontrivial! It would be nice to get simplified |
| # output to print them too). It's private because it's not |
| # intended for normal use |
| def produce_guards(self, placeholders, sources, |
| source_ref=lambda n: n.name(), *, _simplified=False) -> List[str]: |
| # It took a lot of sweat to figure out the algorithm here. Let's |
| # explain how it works. |
| # |
| # The ShapeEnv lifecycle looks something like this: |
| # |
| # - For each input, you either generate a fresh Sympy symbol (s0) to |
| # represent its value (a binding site), or you reuse some |
| # preexisting symbol or expression, skipping the symbol allocation |
| # (e.g., duck sizing to a preexisting symbol, or expressing a |
| # stride as a multiplication of a separate stride and size.) |
| # Naively, you might expect to bind a fresh Sympy symbol for |
| # every input, but this is fairly wasteful as most of these |
| # symbols immediately simplify away, and if you don't eagerly |
| # specialize, e.g., 0/1 symbols, you end up with very complicated |
| # expressions that are not optimizable in practice. |
| # |
| # - You perform some compute on these symbols, occasionally |
| # introducing guards on boolean expressions on these symbols. |
| # In particular, whenever we guard on equality (_maybe_guard_eq), |
| # we can simplify shapes; e.g., when s0 == s1 * 2, we can now |
| # replace all occurrences of s0 with s1 * 2. Sometimes, a |
| # boolean expression evaluation doesn't introduce a guard, as |
| # the guard is already entailed by the simplifications we have |
| # applied. |
| # |
| # - In the end, you have a bunch of replacements (saying how to |
| # simplify shapes) and a bunch of guards (all the equality guards |
| # are trivial, because they're covered by the replacements). |
| # |
| # From the ShapeEnv, we must generate a Python expression that, when |
| # evaluated on a set of inputs, tells us whether or not these boolean |
| # expressions would have evaluated in the same way. However, |
| # we cannot easily compute this, as we elide recording boolean |
| # expressions when we think they are vacuously true. Thus, we seek |
| # an approximation: we must generate an expression, if true, would have |
| # produced an "equivalent" ShapeEnv, which would answer guard |
| # expressions in the same way. |
| # |
| # Our notion of equivalence is a bit subtle. For example, consider |
| # the ShapeEnv created from an input of size (5, 4) versus (4, 4) |
| # (no other guards.) Duck sizing would generate (s0, s1) in the first |
| # case but (s0, s0) in the second. We do NOT assume that size |
| # variables are disjoint; so in fact a graph that assumes the input |
| # could be (s0, s1) subsumes (s0, s0) (setting s0 == s1), but not |
| # vice versa. However, consider an analogous case (1,) versus (2,). |
| # Duck sizing generates (1,) and (s0,); the (s0,) graph does NOT |
| # subsume the (1,) graph because we assume that any size variables |
| # is NOT 0/1 (and make simplifications according to this; e.g., if |
| # we queried s0 == 0, we would immediately return False without |
| # returning a guard.) |
| # |
| # So, it is perhaps easier to flip things on their head: the guard |
| # expressions we generate here say what simplifications are valid, |
| # and what are not. Below, we explain each of the guard expressions |
| # we generate |
| |
| # TODO: Make this more efficient by binding all the size/stride/offsets |
| # to locals before performing tests on them. |
| |
| from torch._dynamo.source import NegateSource, TensorPropertySource, TensorProperty |
| |
| # Actual codegen must be delayed as we don't necessarily know what |
| # the symbol mapping is |
| input_guards = [] |
| |
| symbol_to_source = collections.defaultdict(list) |
| dynamic_sources = [] |
| |
| # How do we know what the value of s0 is? Fresh variables can only be |
| # bound by inputs, so there MUST be some other input which binds the |
| # variable. If there is no such input, this is an error in our |
| # system. We record where all symbols come from, to help you diagnose |
| # why those symbols didn't occur. |
| # |
| # In fact, generally speaking it is only possible for the "outermost" |
| # user of a ShapeEnv to evaluate the guards, because some inputs may |
| # not be available to inner levels. For example, Dynamo can guard on |
| # tensors that never actually become graph arguments (they are |
| # pruned). In this case, only Dynamo knows about these arguments. |
| def track_symint(source, val): |
| if isinstance(val, SymInt): |
| s = val.node.expr |
| |
| if isinstance(s, sympy.Symbol): |
| symbol_to_source[s].append(source) |
| elif isinstance(-s, sympy.Symbol): |
| symbol_to_source[-s].append(NegateSource(source)) |
| input_guards.append((source, s)) |
| else: |
| input_guards.append((source, sympy.Integer(val))) |
| |
| def _verify(expr, potential_expr): |
| # An expression of > 1 symbols is a relationship, |
| # and relationships can be ignored due to the nature of the |
| # constraint api explicitly not supporting relationships. |
| # |
| # In a future where we want to extend the constraint API to include |
| # user directives about relationships, we can remove this check from |
| # verification. |
| if len(expr.free_symbols) == 1: |
| srcs = symbol_to_source[expr.free_symbols.pop()] |
| for src in srcs: |
| if src in dynamic_sources: |
| raise RuntimeError(f"Attempting to introduce a guard {potential_expr} that violates user's mark_dynamic") |
| |
| for t, source in zip(placeholders, sources): |
| if isinstance(source, str): |
| from torch._dynamo.source import LocalSource |
| source = LocalSource(source) |
| assert isinstance(source, Source) |
| if t is None: |
| continue |
| if isinstance(t, SymInt): |
| track_symint(source, t) |
| continue |
| assert isinstance(t, torch.Tensor) |
| for i, ss in enumerate(t.size()): |
| property_source = TensorPropertySource(source, TensorProperty.SIZE, i) |
| track_symint(property_source, ss) |
| if _is_dim_dynamic(t, i): |
| # If this dim is marked dynamic, we need to do a test on it, to ensure that it has not bee |
| # constrained to an integer. |
| if _is_int(ss): |
| raise RuntimeError(f"Attempting to constrain dim {i} for {source}, which violates user's mark_dynamic") |
| dynamic_sources.append(property_source) |
| for i, ss in enumerate(t.stride()): |
| track_symint(TensorPropertySource(source, TensorProperty.STRIDE, i), ss) |
| track_symint(TensorPropertySource(source, TensorProperty.STORAGE_OFFSET), t.storage_offset()) |
| |
| # 1. Every input must equal the final simplified symbolic expression |
| # stored on the placeholder. Given a placeholder (s0*2, s1), |
| # if we have an input (2, 3), we must show s0*2 == 2 and s1 == 3. |
| # This does a lot of work: it covers duck sizing and equality guards. |
| exprs = [] |
| if not _simplified: |
| for source, expr in input_guards: |
| # Small optimization |
| if ( |
| isinstance(expr, sympy.Symbol) and |
| expr in symbol_to_source and |
| source == symbol_to_source[expr][0] |
| ): |
| continue |
| sexpr = ShapeGuardPrinter(symbol_to_source, source_ref, self.var_to_sources).doprint(expr) |
| exprs.append(f"{source_ref(source)} == {sexpr}") |
| |
| # 2. Every guard must evaluate to True (but remember many guards |
| # like s0 == s1*2 because trivial due to simplification) |
| for g, tb in self.guards: |
| if self._maybe_evaluate_static(g) is not None: |
| continue |
| g = self.simplify(g) |
| try: |
| guard_expr = ShapeGuardPrinter(symbol_to_source, source_ref, self.var_to_sources).doprint(g) |
| exprs.append(guard_expr) |
| if self.strict_mark_dyn: |
| _verify(g, guard_expr) |
| except Exception: |
| log.warning(f"Failing guard allocated at: \n{tb}") |
| raise |
| |
| # 3. Every symbol must be within its value range (this handles 0/1 |
| # specialization too). NB: because we never update value ranges |
| # except in case of explicit user annotation, these are not included |
| # in simplified. However, when we start updating value ranges |
| # these should probably get reported in tests too |
| if not _simplified: |
| for symbol, sources in symbol_to_source.items(): |
| assert sources |
| r = self.var_to_range[symbol] |
| bounds = [] |
| if r.lower != -sympy.oo: |
| bounds.append(str(r.lower)) |
| bounds.append(source_ref(sources[0])) |
| if r.upper != sympy.oo: |
| bounds.append(str(r.upper)) |
| if len(bounds) > 1: |
| exprs.append(" <= ".join(bounds)) |
| |
| return exprs |
| |
| def evaluate_guards_for_args(self, placeholders, args): |
| from torch._dynamo.source import GlobalSource |
| arg_names = [f"t{i}" for i in range(len(args))] |
| guards = self.produce_guards(placeholders, [GlobalSource(a) for a in arg_names]) |
| if guards: |
| code = " and ".join(guards) |
| return eval(code, SYMPY_INTERP, dict(zip(arg_names, args))) |
| return True |
| |
| def bind_symbols(self, placeholders, args): |
| # Given a paired list of placeholders (fake tensors with |
| # symbolic sizes) and concrete arguments (regular tensors |
| # with real sizes), returns a dictionary mapping each |
| # symbol to its real value. So for example, if you |
| # have a placeholder with size (s0, s1), binding |
| # (2, 4) to it will give you {s0: 2, s1: 4}. This is |
| # not guaranteed to bind ALL symbols in the ShapeEnv; |
| # we can't bind a symbol if it doesn't occur in any placeholder, |
| # and symbols that already have replacements won't get bindings. |
| |
| # This is a little duplicative with evaluate_guards but |
| # it's different enough that it seemed cleanest to make |
| # another copy. This assumes the guards are already checked, |
| # though if it's cheap we'll check for shenanigans |
| bindings: Dict[sympy.Symbol, int] = {} |
| |
| def bind_symint(arg, val): |
| if isinstance(val, SymInt): |
| s = val.node.expr |
| |
| if isinstance(s, sympy.Symbol): |
| if s in bindings: |
| assert bindings[s] == arg, f"{bindings[s]} != {arg}" |
| else: |
| bindings[s] = arg |
| elif isinstance(-s, sympy.Symbol): |
| if -s in bindings: |
| assert bindings[-s] == -arg, f"{bindings[-s]} != {-arg}" |
| else: |
| bindings[-s] = -arg |
| |
| for t, arg in zip(placeholders, args): |
| if t is None: |
| continue |
| if isinstance(t, SymInt): |
| bind_symint(arg, t) |
| continue |
| assert isinstance(t, torch.Tensor) |
| for i, s in enumerate(t.size()): |
| bind_symint(arg.size(i), s) |
| for i, s in enumerate(t.stride()): |
| bind_symint(arg.stride(i), s) |
| bind_symint(arg.storage_offset(), t.storage_offset()) |
| |
| return bindings |
| |
| def get_nontrivial_guards(self): |
| return [self.simplify(guard.expr) for guard in self.guards if self._maybe_evaluate_static(guard.expr) is None] |
| |
| def format_guards(self, verbose=False): |
| def format_tb(tb): |
| if not verbose: |
| return "" |
| return f"\n Guarded at:\n{textwrap.indent(tb, ' ')}" |
| |
| return '\n'.join(f" - {guard.expr}{format_tb(guard.stack)}" for guard in self.guards) |
| |
| def get_shape_groups(self): |
| shape_groups = collections.defaultdict(list) |
| for k, v in self.replacements.items(): |
| shape_groups[v].append(k) |
| return shape_groups |
| |
| @_lru_cache |
| def _maybe_evaluate_static(self, expr: "sympy.Expr", *, unbacked_only: bool = False) -> "Optional[sympy.Expr]": |
| """ |
| Tries to evaluate expr without introducing guards |
| """ |
| expr = self.simplify(expr) |
| |
| # Simplify making use of value range lower bound |
| symbols = list(expr.free_symbols) |
| new_shape_env = {} |
| new_range_env = {} |
| for idx, k in enumerate(symbols): |
| vr = self.var_to_range[k] |
| # Don't do anything if we don't have a nontrivial lower bound |
| # Also don't do anything if we asked only to simplify unbacked |
| # SymInt |
| if vr.lower == -sympy.oo or (unbacked_only and k in self.var_to_val): |
| new_range_env[k] = vr |
| continue |
| # Positive means >= 1 |
| # Positive - 1 means >= 0 |
| # Positive + lower - 1 means >= lower |
| # The new symbol 's' is "too low", so when we substitute it in |
| # we have to increase it by offset (and conversely, the new |
| # variables have to have their value range bounds adjusted as |
| # well) |
| s = sympy.Symbol(f"shape_{idx}", positive=True, integer=True) |
| offset = vr.lower - 1 |
| new_shape_env[k] = s + offset |
| new_range_env[s] = ValueRangeAnalysis.sub(vr, offset) |
| |
| new_expr = expr.xreplace(new_shape_env) |
| floor_div_replace = {} |
| for atom in new_expr.atoms(FloorDiv): |
| floor_div_replace[atom] = sympy.floor(atom.args[0] / atom.args[1]) |
| new_expr = safe_expand(new_expr.xreplace(floor_div_replace)) |
| # TODO: when unbacked_only, can sometimes early return even when there |
| # are still free symbols |
| if len(list(new_expr.free_symbols)) == 0: |
| return new_expr |
| |
| # Check if the range can solve it statically |
| out = sympy_interp(ValueRangeAnalysis, new_range_env, new_expr) |
| if out.is_singleton(): |
| return out.lower |
| |
| return new_expr if unbacked_only else None |
| |
| @_lru_cache |
| def replace(self, expr: "sympy.Expr") -> "sympy.Expr": |
| replacements = {s: self._find(cast(sympy.Symbol, s)) for s in expr.free_symbols} |
| return safe_expand(expr.xreplace(replacements)) |
| |
| @_lru_cache |
| def _update_divisible(self): |
| new_divisible = set() |
| for k in self.divisible: |
| res = self.replace(k) |
| if len(res.free_symbols) > 0: |
| new_divisible.add(k) |
| |
| self.divisible = new_divisible |
| |
| @_lru_cache |
| def simplify(self, expr: "sympy.Expr") -> "sympy.Expr": |
| expr = self.replace(expr) |
| # TODO it would seem that this pass is not necessary given the |
| # below replacement of // with /, but for nested FloorDivs |
| # the non-recursive replacement doesn't work, and |
| # recursive makes it hard to look up divisibility, |
| # because existing divisibility info has FloorDiv in it, not / |
| # for now just do a separate pass to catch common nested case |
| if expr.has(FloorDiv): |
| self._update_divisible() |
| div_replacements = {} |
| for atom in expr.atoms(FloorDiv): |
| base, divisor = atom.args |
| if isinstance(divisor, FloorDiv): |
| base1, divisor1 = divisor.args |
| if self.replace(base % divisor) in self.divisible and \ |
| base == base1 and self.replace(base1 % divisor1) in self.divisible: |
| div_replacements[atom] = divisor1 |
| expr = expr.xreplace(div_replacements) |
| expr = safe_expand(expr) |
| if expr.has(FloorDiv): |
| div_replacements = {} |
| pows = expr.atoms(sympy.Pow) |
| rationals = expr.atoms(sympy.Rational).difference(expr.atoms(sympy.Integer)) |
| for fd in expr.atoms(FloorDiv): |
| base, divisor = fd.args |
| if self.replace(base % divisor) in self.divisible: |
| div_replacements[fd] = base / divisor |
| new_expr = expr.xreplace(div_replacements) |
| new_expr = safe_expand(new_expr) |
| new_pows = new_expr.atoms(sympy.Pow) |
| new_rationals = new_expr.atoms(sympy.Rational).difference(new_expr.atoms(sympy.Integer)) |
| # divisions simplified away |
| if new_pows.issubset(pows) and new_rationals.issubset(rationals): |
| expr = new_expr |
| return expr |
| |
| @lru_cache(256) |
| def size_hint(self, expr: "sympy.Expr"): |
| """ |
| Gets a size hint for a given expression from the underlying shapes we had. |
| Does not introduce a guard, so only use this when you can guarantee that |
| your code is still valid for arbitrary shapes (such as optimization decisions) |
| """ |
| result_expr = safe_expand(expr).xreplace(self.var_to_val) |
| if len(result_expr.free_symbols) != 0: |
| r = self._maybe_evaluate_static(result_expr) |
| if r is not None: |
| return r |
| raise self._make_data_dependent_error(result_expr, expr) |
| return result_expr |
| |
| def _make_data_dependent_error(self, expr, unhinted_expr): |
| # TODO: in a Dynamo context, having user code, and having the |
| # name of the local, will be much better |
| for s in expr.free_symbols: |
| log.debug(f"Data dependent variable '{s}' allocated at:\n{self.var_to_stack[s]}") |
| return GuardOnDataDependentSymNode( |
| "It appears that you're trying to get a value out of symbolic int/float " |
| "whose value is data-dependent (and thus we do not know the true value.) " |
| f"The expression we were trying to evaluate is {expr} (unhinted: {unhinted_expr}). " |
| "Scroll up to see where each of these data-dependent accesses originally occurred." |
| # TODO: Help text about how to use our runtime tests to fix this |
| # problem |
| ) |
| |
| @_lru_cache |
| def _find(self, a: "sympy.Symbol") -> "sympy.Expr": |
| """ |
| Implements a DSU-like algorithm to find the variable that represents a |
| Also handles transitive non-identity replacements. |
| |
| a: b + c |
| c: d |
| """ |
| if a not in self.replacements: |
| return a |
| res = self.replacements[a] |
| cur_replace = {s: self._find(s) for s in res.free_symbols} |
| self.replacements[a] = self.replacements[a].xreplace(cur_replace) |
| return self.replacements[a] |
| |
| @lru_cache(256) |
| def _maybe_guard_eq(self, expr: Union["sympy.Eq", "sympy.Ne"], concrete_bool: bool) -> None: |
| """ |
| Evaluates the result of an eq call. If true, uses information to |
| simplify shapes (i.e. a == b or a % 5 == 0) |
| """ |
| assert type(concrete_bool) is bool |
| if isinstance(expr, sympy.Eq): |
| if not concrete_bool: |
| return |
| # NB: Apparently this is load bearing; to see what test fails if |
| # you comment it out run: |
| # python test/functorch/test_aotdispatch.py -k |
| # test_aot_autograd_symbolic_module_exhaustive_nn_LazyConv3d_cpu_float32 |
| elif isinstance(expr, sympy.Ne): |
| if concrete_bool: |
| return |
| free = list(expr.free_symbols) |
| |
| assert len(free) > 0, f"The expression should not be static by this point: {expr}" |
| # In case of really gnarly expression, we don't blow up |
| if len(free) > 5: |
| return |
| free = sorted(free, key=lambda x: (self.size_hint(x), x.name), reverse=True) # type: ignore[attr-defined] |
| lhs = expr.lhs |
| rhs = expr.rhs |
| if not expr.has(sympy.Mod): |
| try: |
| floor_div_atoms = lhs.atoms(FloorDiv).union(rhs.atoms(FloorDiv)) |
| if len(floor_div_atoms) > 0 and any([a.divisor != 1 for a in floor_div_atoms]): |
| raise NotImplementedError |
| solutions = sympy.solve(lhs - rhs, free[0], dict=True) |
| if len(solutions) != 1: |
| return |
| solution = solutions[0][free[0]] |
| if all(t.is_integer for t in sympy.preorder_traversal(solution)): |
| new_var = self._find(solution) |
| self.replacements[cast(sympy.Symbol, free[0])] = new_var |
| except NotImplementedError: |
| pass |
| except RecursionError: |
| log.warning(f"RecursionError in sympy.solve({lhs} - {rhs}, {free[0]})") |
| if expr.has(sympy.Mod): |
| mod_expr = tuple(expr.atoms(sympy.Mod))[0] |
| try: |
| solutions = sympy.solve(lhs - rhs, mod_expr, dict=True) |
| if len(solutions) == 1 and solutions[0][mod_expr] == 0: |
| self.divisible.add(mod_expr) |
| except NotImplementedError: |
| pass |
| return |
| |
| @_lru_cache |
| def _simplify_floor_div(self, expr): |
| floor_divs = tuple(expr.atoms(FloorDiv)) |
| # we expect floor_divs to be exact, |
| # and thus add the guards for the exact floordivs, |
| # even if tracing doesn't require them otherwise |
| for fd in reversed(floor_divs): |
| base, divisor = fd.args |
| mod_expr = sympy.Mod(base, divisor) |
| eq_expr = sympy.Eq(mod_expr, 0) |
| # add necessary mod guards |
| self.evaluate_expr(eq_expr) |
| return self.simplify(expr) |
| |
| @lru_cache(256) |
| def evaluate_expr(self, expr: "sympy.Expr", hint=None): |
| """ |
| Given an expression, evaluates it, adding guards if necessary |
| """ |
| if len(expr.free_symbols) == 0: |
| return expr |
| expr = self.simplify(expr) |
| |
| static_expr = self._maybe_evaluate_static(expr) |
| if static_expr is not None: |
| return static_expr |
| |
| if not (expr.free_symbols <= self.var_to_val.keys()): |
| # TODO: dedupe this with _maybe_evaluate_static |
| # Attempt to eliminate the unbacked SymInt |
| new_expr = self._maybe_evaluate_static(expr, unbacked_only=True) |
| if not (new_expr.free_symbols <= self.var_to_val.keys()): |
| raise self._make_data_dependent_error(expr.xreplace(self.var_to_val), expr) |
| expr = new_expr |
| |
| if hint is None: |
| concrete_val = self.size_hint(expr) |
| else: |
| concrete_val = sympy.sympify(hint) |
| |
| if isinstance(expr, (sympy.Eq, sympy.Ne)): |
| self._maybe_guard_eq(expr, bool(concrete_val)) |
| # TODO: If we successfully eliminate a symbol via equality, it |
| # is not actually necessary to save a guard for the equality, |
| # as we will implicitly generate a guard when we match that |
| # input against the symbol |
| elif isinstance(concrete_val, sympy.Integer): |
| # WARNING: we cannot actually do simplifications on guards |
| # on floating point values, because Sympy generally does not |
| # think expressions on integers can ever be equal to floating |
| # point (e.g., sympy.Eq(s0/6, 0.5) evaluates to False). Without |
| # very clear algebraic laws that hold for floating point, such |
| # simplifications are error prone anyway, so be sure not to |
| # maybe_guard_eq in those cases. |
| self._maybe_guard_eq(sympy.Eq(expr, concrete_val), True) |
| |
| # TODO: optimize this; avoid formatting traces until we need them |
| # NB: drop two frames; evaluate_expr and the Sym* function that |
| # actually called us |
| if not self._suppress_guards_tls(): |
| stack = ''.join(traceback.format_list(traceback.extract_stack()[:-2])) |
| if concrete_val is sympy.true: |
| self.guards.append(ShapeGuard(expr, stack)) |
| elif concrete_val is sympy.false: |
| self.guards.append(ShapeGuard(sympy.Not(expr), stack)) |
| else: |
| self.guards.append( |
| ShapeGuard(sympy.Eq(expr, concrete_val), stack)) # type: ignore[arg-type] |
| return concrete_val |
| |
| def _should_allocate(user_marked_dynamic, assume_static_by_default): |
| """ |
| Mainly here for readability, repurposes the flag name for the context |
| of shape_env, which cares about allocation. |
| """ |
| if user_marked_dynamic: |
| return True |
| # If we got here, the user did *NOT* mark this dim as dynamic, |
| # but BC behavior is to allocate a symbol anyway. |
| return not assume_static_by_default |
| |
| def _is_dim_dynamic(t, d): |
| return hasattr(t, "_dynamo_dynamic_indices") and d in t._dynamo_dynamic_indices |
| |
| def _is_int(expr): |
| if not isinstance(expr, SymInt): |
| return False |
| if len(expr.node.expr.free_symbols) > 0: |
| return False |
| return True |
