import operator from functools import partial from typing import Any, Callable, Dict from sympy import Expr import torch from torch.utils._sympy.value_ranges import bound_sympy, ValueRangeAnalysis, ValueRanges from .ir import InterpreterShim, LoopBody, LoopBodyBlock from .utils import cache_on_self, dominated_nodes from .virtualized import V class BoundVars: """ Performs Value Range Analysis on LoopBody's fx graph by calling BoundVars.run() It exposes the ranges of the nodes in the `bounds` variable Note. A current limitation of this analysis is that it just works on a per-loop basis. We should be able to propagate the bounds between across the whole graph. This may benefit the case a bounded variable is returned by a kernel and fed into another. """ def __init__(self, loop_body: LoopBody) -> None: self.loop_body = loop_body self.replacement_vals = { k: ValueRanges[Expr](0, v - 1) if (isinstance(v, int) or v.is_number) else bound_sympy(v) for k, v in loop_body.var_ranges.items() } # avoid computing these values, pessimistically assume that they are unbounded self.unbounded_vars = dominated_nodes( node for node in self.loop_body.get_nodes() if node.target in ["load", "reduction", operator.getitem] or "masked_subblock" in node.target ) # To access this variable call `get_bounds()` self._bounds: Dict[torch.fx.Node, ValueRanges[Expr]] = {} @cache_on_self def get_bounds(self) -> Dict[torch.fx.Node, ValueRanges[Expr]]: submodules = self.swap_submodules(self.loop_body.submodules) # Initialize the environment with the unbounded variables for node in self.unbounded_vars: # we need to evaluate masked_subblock to recurse, and we need to set indirect values if not isinstance(node.target, str) or ( "masked_subblock" not in node.target and "set_indirect" not in node.target ): self._bounds[node] = ValueRanges[Expr].unknown() with V.set_ops_handler(ValueRangeAnalysis()): interpreter = InterpreterShim(self.loop_body.root_block.graph, submodules) interpreter.run(V.get_ops_handler(), initial_env=self._bounds) return self._bounds def swap_submodules( self, submodules: Dict[str, Callable[..., Any]] ) -> Dict[str, Callable[..., ValueRanges[Expr]]]: result: Dict[str, Callable[..., ValueRanges[Expr]]] = {} for key in submodules.keys(): if key == "get_index": result[key] = self.get_index elif "masked_subblock" in key: subblock = self.loop_body.subblocks[key] # The result within the lambda will reference to the final # set of modules at the end of the for-loop as it stores a reference to it # bind subblock in a function because python lambdas close over by reference # moving the lambda out of make_fn would close over the reference to subblock, # so all lambdas would have the same subblock reference that is the final # subblock in the loop def make_fn(subblock): return lambda mask, value: self.masked_subblock( subblock, self._bounds, mask, value, result ) result[key] = make_fn(subblock) elif "set_indirect" in key: idx = int(key[len("set_indirect") :]) var = self.loop_body.indirect_vars[idx] indirect = partial(self.set_indirect, var) result[key] = indirect else: assert "scan" in key result[key] = submodules[key] return result def masked_subblock( self, subblock: LoopBodyBlock, env: Dict[torch.fx.Node, ValueRanges[Expr]], mask: Any, value: Any, submodules: Dict[str, Callable[..., Any]], ) -> ValueRanges[Expr]: interp = InterpreterShim(subblock.graph, submodules) interp.run(V.get_ops_handler(), initial_env=env) output = [node for node in subblock.graph.nodes if node.target == "output"] assert len(output) == 1 # dont bother unioning with value since the load from buffer will be # pessimistically assumed to be inf anyway return interp.env[output[0]] def set_indirect(self, old: Expr, new: ValueRanges[Expr]) -> ValueRanges[Expr]: assert isinstance(new, ValueRanges) self.replacement_vals[old] = new return new def get_index(self, name: Expr) -> ValueRanges[Expr]: expr = self.loop_body.indexing_exprs[name] bound = self.replacement_vals.get(expr) if bound is None: bound = bound_sympy(expr, self.replacement_vals) # The following assertion is true at the time of this writing # We don't assert is as to not execute bound_sympy when bound is not None # assert bound is None or bound == bound_sympy(expr, self.replacement_vals) self.replacement_vals[name] = bound return bound