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https://github.com/c64scene-ar/llvm-6502.git
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git-svn-id: https://llvm.org/svn/llvm-project/llvm/trunk@12670 91177308-0d34-0410-b5e6-96231b3b80d8
2492 lines
96 KiB
C++
2492 lines
96 KiB
C++
//===- ScalarEvolution.cpp - Scalar Evolution Analysis ----------*- C++ -*-===//
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//
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// The LLVM Compiler Infrastructure
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//
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// This file was developed by the LLVM research group and is distributed under
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// the University of Illinois Open Source License. See LICENSE.TXT for details.
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//
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//===----------------------------------------------------------------------===//
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//
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// This file contains the implementation of the scalar evolution analysis
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// engine, which is used primarily to analyze expressions involving induction
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// variables in loops.
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//
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// There are several aspects to this library. First is the representation of
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// scalar expressions, which are represented as subclasses of the SCEV class.
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// These classes are used to represent certain types of subexpressions that we
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// can handle. These classes are reference counted, managed by the SCEVHandle
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// class. We only create one SCEV of a particular shape, so pointer-comparisons
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// for equality are legal.
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//
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// One important aspect of the SCEV objects is that they are never cyclic, even
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// if there is a cycle in the dataflow for an expression (ie, a PHI node). If
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// the PHI node is one of the idioms that we can represent (e.g., a polynomial
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// recurrence) then we represent it directly as a recurrence node, otherwise we
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// represent it as a SCEVUnknown node.
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//
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// In addition to being able to represent expressions of various types, we also
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// have folders that are used to build the *canonical* representation for a
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// particular expression. These folders are capable of using a variety of
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// rewrite rules to simplify the expressions.
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//
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// Once the folders are defined, we can implement the more interesting
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// higher-level code, such as the code that recognizes PHI nodes of various
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// types, computes the execution count of a loop, etc.
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//
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// Orthogonal to the analysis of code above, this file also implements the
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// ScalarEvolutionRewriter class, which is used to emit code that represents the
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// various recurrences present in a loop, in canonical forms.
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//
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// TODO: We should use these routines and value representations to implement
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// dependence analysis!
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//
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//===----------------------------------------------------------------------===//
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//
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// There are several good references for the techniques used in this analysis.
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//
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// Chains of recurrences -- a method to expedite the evaluation
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// of closed-form functions
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// Olaf Bachmann, Paul S. Wang, Eugene V. Zima
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//
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// On computational properties of chains of recurrences
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// Eugene V. Zima
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//
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// Symbolic Evaluation of Chains of Recurrences for Loop Optimization
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// Robert A. van Engelen
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//
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// Efficient Symbolic Analysis for Optimizing Compilers
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// Robert A. van Engelen
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//
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// Using the chains of recurrences algebra for data dependence testing and
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// induction variable substitution
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// MS Thesis, Johnie Birch
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//
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//===----------------------------------------------------------------------===//
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#include "llvm/Analysis/ScalarEvolution.h"
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#include "llvm/Constants.h"
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#include "llvm/DerivedTypes.h"
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#include "llvm/Instructions.h"
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#include "llvm/Type.h"
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#include "llvm/Value.h"
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#include "llvm/Analysis/LoopInfo.h"
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#include "llvm/Assembly/Writer.h"
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#include "llvm/Transforms/Scalar.h"
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#include "llvm/Support/CFG.h"
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#include "llvm/Support/ConstantRange.h"
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#include "llvm/Support/InstIterator.h"
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#include "Support/Statistic.h"
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using namespace llvm;
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namespace {
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RegisterAnalysis<ScalarEvolution>
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R("scalar-evolution", "Scalar Evolution Analysis Printer");
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Statistic<>
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NumBruteForceEvaluations("scalar-evolution",
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"Number of brute force evaluations needed to calculate high-order polynomial exit values");
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Statistic<>
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NumTripCountsComputed("scalar-evolution",
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"Number of loops with predictable loop counts");
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Statistic<>
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NumTripCountsNotComputed("scalar-evolution",
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"Number of loops without predictable loop counts");
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}
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//===----------------------------------------------------------------------===//
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// SCEV class definitions
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//===----------------------------------------------------------------------===//
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//===----------------------------------------------------------------------===//
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// Implementation of the SCEV class.
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//
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namespace {
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enum SCEVTypes {
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// These should be ordered in terms of increasing complexity to make the
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// folders simpler.
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scConstant, scTruncate, scZeroExtend, scAddExpr, scMulExpr, scUDivExpr,
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scAddRecExpr, scUnknown, scCouldNotCompute
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};
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/// SCEVComplexityCompare - Return true if the complexity of the LHS is less
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/// than the complexity of the RHS. If the SCEVs have identical complexity,
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/// order them by their addresses. This comparator is used to canonicalize
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/// expressions.
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struct SCEVComplexityCompare {
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bool operator()(SCEV *LHS, SCEV *RHS) {
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if (LHS->getSCEVType() < RHS->getSCEVType())
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return true;
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if (LHS->getSCEVType() == RHS->getSCEVType())
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return LHS < RHS;
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return false;
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}
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};
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}
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SCEV::~SCEV() {}
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void SCEV::dump() const {
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print(std::cerr);
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}
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/// getValueRange - Return the tightest constant bounds that this value is
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/// known to have. This method is only valid on integer SCEV objects.
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ConstantRange SCEV::getValueRange() const {
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const Type *Ty = getType();
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assert(Ty->isInteger() && "Can't get range for a non-integer SCEV!");
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Ty = Ty->getUnsignedVersion();
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// Default to a full range if no better information is available.
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return ConstantRange(getType());
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}
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SCEVCouldNotCompute::SCEVCouldNotCompute() : SCEV(scCouldNotCompute) {}
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bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const {
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assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
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return false;
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}
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const Type *SCEVCouldNotCompute::getType() const {
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assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
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return 0;
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}
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bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const {
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assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
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return false;
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}
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Value *SCEVCouldNotCompute::expandCodeFor(ScalarEvolutionRewriter &SER,
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Instruction *InsertPt) {
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assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
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return 0;
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}
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void SCEVCouldNotCompute::print(std::ostream &OS) const {
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OS << "***COULDNOTCOMPUTE***";
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}
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bool SCEVCouldNotCompute::classof(const SCEV *S) {
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return S->getSCEVType() == scCouldNotCompute;
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}
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//===----------------------------------------------------------------------===//
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// SCEVConstant - This class represents a constant integer value.
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//
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namespace {
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class SCEVConstant;
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// SCEVConstants - Only allow the creation of one SCEVConstant for any
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// particular value. Don't use a SCEVHandle here, or else the object will
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// never be deleted!
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std::map<ConstantInt*, SCEVConstant*> SCEVConstants;
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class SCEVConstant : public SCEV {
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ConstantInt *V;
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SCEVConstant(ConstantInt *v) : SCEV(scConstant), V(v) {}
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virtual ~SCEVConstant() {
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SCEVConstants.erase(V);
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}
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public:
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/// get method - This just gets and returns a new SCEVConstant object.
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///
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static SCEVHandle get(ConstantInt *V) {
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// Make sure that SCEVConstant instances are all unsigned.
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if (V->getType()->isSigned()) {
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const Type *NewTy = V->getType()->getUnsignedVersion();
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V = cast<ConstantUInt>(ConstantExpr::getCast(V, NewTy));
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}
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SCEVConstant *&R = SCEVConstants[V];
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if (R == 0) R = new SCEVConstant(V);
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return R;
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}
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ConstantInt *getValue() const { return V; }
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/// getValueRange - Return the tightest constant bounds that this value is
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/// known to have. This method is only valid on integer SCEV objects.
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virtual ConstantRange getValueRange() const {
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return ConstantRange(V);
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}
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virtual bool isLoopInvariant(const Loop *L) const {
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return true;
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}
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virtual bool hasComputableLoopEvolution(const Loop *L) const {
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return false; // Not loop variant
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}
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virtual const Type *getType() const { return V->getType(); }
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Value *expandCodeFor(ScalarEvolutionRewriter &SER,
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Instruction *InsertPt) {
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return getValue();
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}
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virtual void print(std::ostream &OS) const {
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WriteAsOperand(OS, V, false);
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}
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/// Methods for support type inquiry through isa, cast, and dyn_cast:
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static inline bool classof(const SCEVConstant *S) { return true; }
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static inline bool classof(const SCEV *S) {
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return S->getSCEVType() == scConstant;
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}
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};
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}
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//===----------------------------------------------------------------------===//
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// SCEVTruncateExpr - This class represents a truncation of an integer value to
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// a smaller integer value.
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//
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namespace {
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class SCEVTruncateExpr;
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// SCEVTruncates - Only allow the creation of one SCEVTruncateExpr for any
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// particular input. Don't use a SCEVHandle here, or else the object will
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// never be deleted!
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std::map<std::pair<SCEV*, const Type*>, SCEVTruncateExpr*> SCEVTruncates;
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class SCEVTruncateExpr : public SCEV {
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SCEVHandle Op;
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const Type *Ty;
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SCEVTruncateExpr(const SCEVHandle &op, const Type *ty)
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: SCEV(scTruncate), Op(op), Ty(ty) {
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assert(Op->getType()->isInteger() && Ty->isInteger() &&
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Ty->isUnsigned() &&
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"Cannot truncate non-integer value!");
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assert(Op->getType()->getPrimitiveSize() > Ty->getPrimitiveSize() &&
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"This is not a truncating conversion!");
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}
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virtual ~SCEVTruncateExpr() {
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SCEVTruncates.erase(std::make_pair(Op, Ty));
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}
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public:
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/// get method - This just gets and returns a new SCEVTruncate object
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///
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static SCEVHandle get(const SCEVHandle &Op, const Type *Ty);
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const SCEVHandle &getOperand() const { return Op; }
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virtual const Type *getType() const { return Ty; }
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virtual bool isLoopInvariant(const Loop *L) const {
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return Op->isLoopInvariant(L);
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}
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virtual bool hasComputableLoopEvolution(const Loop *L) const {
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return Op->hasComputableLoopEvolution(L);
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}
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/// getValueRange - Return the tightest constant bounds that this value is
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/// known to have. This method is only valid on integer SCEV objects.
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virtual ConstantRange getValueRange() const {
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return getOperand()->getValueRange().truncate(getType());
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}
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Value *expandCodeFor(ScalarEvolutionRewriter &SER,
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Instruction *InsertPt);
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virtual void print(std::ostream &OS) const {
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OS << "(truncate " << *Op << " to " << *Ty << ")";
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}
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/// Methods for support type inquiry through isa, cast, and dyn_cast:
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static inline bool classof(const SCEVTruncateExpr *S) { return true; }
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static inline bool classof(const SCEV *S) {
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return S->getSCEVType() == scTruncate;
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}
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};
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}
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//===----------------------------------------------------------------------===//
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// SCEVZeroExtendExpr - This class represents a zero extension of a small
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// integer value to a larger integer value.
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//
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namespace {
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class SCEVZeroExtendExpr;
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// SCEVZeroExtends - Only allow the creation of one SCEVZeroExtendExpr for any
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// particular input. Don't use a SCEVHandle here, or else the object will
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// never be deleted!
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std::map<std::pair<SCEV*, const Type*>, SCEVZeroExtendExpr*> SCEVZeroExtends;
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class SCEVZeroExtendExpr : public SCEV {
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SCEVHandle Op;
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const Type *Ty;
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SCEVZeroExtendExpr(const SCEVHandle &op, const Type *ty)
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: SCEV(scTruncate), Op(Op), Ty(ty) {
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assert(Op->getType()->isInteger() && Ty->isInteger() &&
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Ty->isUnsigned() &&
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"Cannot zero extend non-integer value!");
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assert(Op->getType()->getPrimitiveSize() < Ty->getPrimitiveSize() &&
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"This is not an extending conversion!");
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}
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virtual ~SCEVZeroExtendExpr() {
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SCEVZeroExtends.erase(std::make_pair(Op, Ty));
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}
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public:
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/// get method - This just gets and returns a new SCEVZeroExtend object
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///
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static SCEVHandle get(const SCEVHandle &Op, const Type *Ty);
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const SCEVHandle &getOperand() const { return Op; }
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virtual const Type *getType() const { return Ty; }
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virtual bool isLoopInvariant(const Loop *L) const {
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return Op->isLoopInvariant(L);
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}
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virtual bool hasComputableLoopEvolution(const Loop *L) const {
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return Op->hasComputableLoopEvolution(L);
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}
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/// getValueRange - Return the tightest constant bounds that this value is
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/// known to have. This method is only valid on integer SCEV objects.
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virtual ConstantRange getValueRange() const {
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return getOperand()->getValueRange().zeroExtend(getType());
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}
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Value *expandCodeFor(ScalarEvolutionRewriter &SER,
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Instruction *InsertPt);
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virtual void print(std::ostream &OS) const {
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OS << "(zeroextend " << *Op << " to " << *Ty << ")";
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}
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/// Methods for support type inquiry through isa, cast, and dyn_cast:
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static inline bool classof(const SCEVZeroExtendExpr *S) { return true; }
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static inline bool classof(const SCEV *S) {
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return S->getSCEVType() == scZeroExtend;
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}
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};
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}
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//===----------------------------------------------------------------------===//
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// SCEVCommutativeExpr - This node is the base class for n'ary commutative
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// operators.
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namespace {
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class SCEVCommutativeExpr;
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// SCEVCommExprs - Only allow the creation of one SCEVCommutativeExpr for any
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// particular input. Don't use a SCEVHandle here, or else the object will
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// never be deleted!
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std::map<std::pair<unsigned, std::vector<SCEV*> >,
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SCEVCommutativeExpr*> SCEVCommExprs;
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class SCEVCommutativeExpr : public SCEV {
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std::vector<SCEVHandle> Operands;
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protected:
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SCEVCommutativeExpr(enum SCEVTypes T, const std::vector<SCEVHandle> &ops)
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: SCEV(T) {
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Operands.reserve(ops.size());
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Operands.insert(Operands.end(), ops.begin(), ops.end());
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}
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~SCEVCommutativeExpr() {
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SCEVCommExprs.erase(std::make_pair(getSCEVType(),
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std::vector<SCEV*>(Operands.begin(),
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Operands.end())));
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}
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public:
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unsigned getNumOperands() const { return Operands.size(); }
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const SCEVHandle &getOperand(unsigned i) const {
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assert(i < Operands.size() && "Operand index out of range!");
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return Operands[i];
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}
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const std::vector<SCEVHandle> &getOperands() const { return Operands; }
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typedef std::vector<SCEVHandle>::const_iterator op_iterator;
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op_iterator op_begin() const { return Operands.begin(); }
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op_iterator op_end() const { return Operands.end(); }
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virtual bool isLoopInvariant(const Loop *L) const {
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for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
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if (!getOperand(i)->isLoopInvariant(L)) return false;
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return true;
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}
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virtual bool hasComputableLoopEvolution(const Loop *L) const {
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for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
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if (getOperand(i)->hasComputableLoopEvolution(L)) return true;
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return false;
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}
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virtual const Type *getType() const { return getOperand(0)->getType(); }
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virtual const char *getOperationStr() const = 0;
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virtual void print(std::ostream &OS) const {
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assert(Operands.size() > 1 && "This plus expr shouldn't exist!");
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const char *OpStr = getOperationStr();
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OS << "(" << *Operands[0];
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for (unsigned i = 1, e = Operands.size(); i != e; ++i)
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OS << OpStr << *Operands[i];
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OS << ")";
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}
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/// Methods for support type inquiry through isa, cast, and dyn_cast:
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static inline bool classof(const SCEVCommutativeExpr *S) { return true; }
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static inline bool classof(const SCEV *S) {
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return S->getSCEVType() == scAddExpr ||
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S->getSCEVType() == scMulExpr;
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}
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};
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}
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//===----------------------------------------------------------------------===//
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// SCEVAddExpr - This node represents an addition of some number of SCEV's.
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//
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namespace {
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class SCEVAddExpr : public SCEVCommutativeExpr {
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SCEVAddExpr(const std::vector<SCEVHandle> &ops)
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: SCEVCommutativeExpr(scAddExpr, ops) {
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}
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public:
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static SCEVHandle get(std::vector<SCEVHandle> &Ops);
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static SCEVHandle get(const SCEVHandle &LHS, const SCEVHandle &RHS) {
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std::vector<SCEVHandle> Ops;
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Ops.push_back(LHS);
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Ops.push_back(RHS);
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return get(Ops);
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}
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static SCEVHandle get(const SCEVHandle &Op0, const SCEVHandle &Op1,
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const SCEVHandle &Op2) {
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std::vector<SCEVHandle> Ops;
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Ops.push_back(Op0);
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Ops.push_back(Op1);
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Ops.push_back(Op2);
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return get(Ops);
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}
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virtual const char *getOperationStr() const { return " + "; }
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Value *expandCodeFor(ScalarEvolutionRewriter &SER,
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Instruction *InsertPt);
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/// Methods for support type inquiry through isa, cast, and dyn_cast:
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static inline bool classof(const SCEVAddExpr *S) { return true; }
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static inline bool classof(const SCEV *S) {
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return S->getSCEVType() == scAddExpr;
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}
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};
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}
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//===----------------------------------------------------------------------===//
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// SCEVMulExpr - This node represents multiplication of some number of SCEV's.
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//
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namespace {
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class SCEVMulExpr : public SCEVCommutativeExpr {
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SCEVMulExpr(const std::vector<SCEVHandle> &ops)
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: SCEVCommutativeExpr(scMulExpr, ops) {
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}
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|
|
|
public:
|
|
static SCEVHandle get(std::vector<SCEVHandle> &Ops);
|
|
|
|
static SCEVHandle get(const SCEVHandle &LHS, const SCEVHandle &RHS) {
|
|
std::vector<SCEVHandle> Ops;
|
|
Ops.push_back(LHS);
|
|
Ops.push_back(RHS);
|
|
return get(Ops);
|
|
}
|
|
|
|
virtual const char *getOperationStr() const { return " * "; }
|
|
|
|
Value *expandCodeFor(ScalarEvolutionRewriter &SER,
|
|
Instruction *InsertPt);
|
|
|
|
/// Methods for support type inquiry through isa, cast, and dyn_cast:
|
|
static inline bool classof(const SCEVMulExpr *S) { return true; }
|
|
static inline bool classof(const SCEV *S) {
|
|
return S->getSCEVType() == scMulExpr;
|
|
}
|
|
};
|
|
}
|
|
|
|
|
|
//===----------------------------------------------------------------------===//
|
|
// SCEVUDivExpr - This class represents a binary unsigned division operation.
|
|
//
|
|
namespace {
|
|
class SCEVUDivExpr;
|
|
// SCEVUDivs - Only allow the creation of one SCEVUDivExpr for any particular
|
|
// input. Don't use a SCEVHandle here, or else the object will never be
|
|
// deleted!
|
|
std::map<std::pair<SCEV*, SCEV*>, SCEVUDivExpr*> SCEVUDivs;
|
|
|
|
class SCEVUDivExpr : public SCEV {
|
|
SCEVHandle LHS, RHS;
|
|
SCEVUDivExpr(const SCEVHandle &lhs, const SCEVHandle &rhs)
|
|
: SCEV(scUDivExpr), LHS(lhs), RHS(rhs) {}
|
|
|
|
virtual ~SCEVUDivExpr() {
|
|
SCEVUDivs.erase(std::make_pair(LHS, RHS));
|
|
}
|
|
public:
|
|
/// get method - This just gets and returns a new SCEVUDiv object.
|
|
///
|
|
static SCEVHandle get(const SCEVHandle &LHS, const SCEVHandle &RHS);
|
|
|
|
const SCEVHandle &getLHS() const { return LHS; }
|
|
const SCEVHandle &getRHS() const { return RHS; }
|
|
|
|
virtual bool isLoopInvariant(const Loop *L) const {
|
|
return LHS->isLoopInvariant(L) && RHS->isLoopInvariant(L);
|
|
}
|
|
|
|
virtual bool hasComputableLoopEvolution(const Loop *L) const {
|
|
return LHS->hasComputableLoopEvolution(L) &&
|
|
RHS->hasComputableLoopEvolution(L);
|
|
}
|
|
|
|
virtual const Type *getType() const {
|
|
const Type *Ty = LHS->getType();
|
|
if (Ty->isSigned()) Ty = Ty->getUnsignedVersion();
|
|
return Ty;
|
|
}
|
|
|
|
Value *expandCodeFor(ScalarEvolutionRewriter &SER,
|
|
Instruction *InsertPt);
|
|
|
|
virtual void print(std::ostream &OS) const {
|
|
OS << "(" << *LHS << " /u " << *RHS << ")";
|
|
}
|
|
|
|
/// Methods for support type inquiry through isa, cast, and dyn_cast:
|
|
static inline bool classof(const SCEVUDivExpr *S) { return true; }
|
|
static inline bool classof(const SCEV *S) {
|
|
return S->getSCEVType() == scUDivExpr;
|
|
}
|
|
};
|
|
}
|
|
|
|
|
|
//===----------------------------------------------------------------------===//
|
|
|
|
// SCEVAddRecExpr - This node represents a polynomial recurrence on the trip
|
|
// count of the specified loop.
|
|
//
|
|
// All operands of an AddRec are required to be loop invariant.
|
|
//
|
|
namespace {
|
|
class SCEVAddRecExpr;
|
|
// SCEVAddRecExprs - Only allow the creation of one SCEVAddRecExpr for any
|
|
// particular input. Don't use a SCEVHandle here, or else the object will
|
|
// never be deleted!
|
|
std::map<std::pair<const Loop *, std::vector<SCEV*> >,
|
|
SCEVAddRecExpr*> SCEVAddRecExprs;
|
|
|
|
class SCEVAddRecExpr : public SCEV {
|
|
std::vector<SCEVHandle> Operands;
|
|
const Loop *L;
|
|
|
|
SCEVAddRecExpr(const std::vector<SCEVHandle> &ops, const Loop *l)
|
|
: SCEV(scAddRecExpr), Operands(ops), L(l) {
|
|
for (unsigned i = 0, e = Operands.size(); i != e; ++i)
|
|
assert(Operands[i]->isLoopInvariant(l) &&
|
|
"Operands of AddRec must be loop-invariant!");
|
|
}
|
|
~SCEVAddRecExpr() {
|
|
SCEVAddRecExprs.erase(std::make_pair(L,
|
|
std::vector<SCEV*>(Operands.begin(),
|
|
Operands.end())));
|
|
}
|
|
public:
|
|
static SCEVHandle get(const SCEVHandle &Start, const SCEVHandle &Step,
|
|
const Loop *);
|
|
static SCEVHandle get(std::vector<SCEVHandle> &Operands,
|
|
const Loop *);
|
|
static SCEVHandle get(const std::vector<SCEVHandle> &Operands,
|
|
const Loop *L) {
|
|
std::vector<SCEVHandle> NewOp(Operands);
|
|
return get(NewOp, L);
|
|
}
|
|
|
|
typedef std::vector<SCEVHandle>::const_iterator op_iterator;
|
|
op_iterator op_begin() const { return Operands.begin(); }
|
|
op_iterator op_end() const { return Operands.end(); }
|
|
|
|
unsigned getNumOperands() const { return Operands.size(); }
|
|
const SCEVHandle &getOperand(unsigned i) const { return Operands[i]; }
|
|
const SCEVHandle &getStart() const { return Operands[0]; }
|
|
const Loop *getLoop() const { return L; }
|
|
|
|
|
|
/// getStepRecurrence - This method constructs and returns the recurrence
|
|
/// indicating how much this expression steps by. If this is a polynomial
|
|
/// of degree N, it returns a chrec of degree N-1.
|
|
SCEVHandle getStepRecurrence() const {
|
|
if (getNumOperands() == 2) return getOperand(1);
|
|
return SCEVAddRecExpr::get(std::vector<SCEVHandle>(op_begin()+1,op_end()),
|
|
getLoop());
|
|
}
|
|
|
|
virtual bool hasComputableLoopEvolution(const Loop *QL) const {
|
|
if (L == QL) return true;
|
|
/// FIXME: What if the start or step value a recurrence for the specified
|
|
/// loop?
|
|
return false;
|
|
}
|
|
|
|
|
|
virtual bool isLoopInvariant(const Loop *QueryLoop) const {
|
|
// This recurrence is invariant w.r.t to QueryLoop iff QueryLoop doesn't
|
|
// contain L.
|
|
return !QueryLoop->contains(L->getHeader());
|
|
}
|
|
|
|
virtual const Type *getType() const { return Operands[0]->getType(); }
|
|
|
|
Value *expandCodeFor(ScalarEvolutionRewriter &SER,
|
|
Instruction *InsertPt);
|
|
|
|
|
|
/// isAffine - Return true if this is an affine AddRec (i.e., it represents
|
|
/// an expressions A+B*x where A and B are loop invariant values.
|
|
bool isAffine() const {
|
|
// We know that the start value is invariant. This expression is thus
|
|
// affine iff the step is also invariant.
|
|
return getNumOperands() == 2;
|
|
}
|
|
|
|
/// isQuadratic - Return true if this is an quadratic AddRec (i.e., it
|
|
/// represents an expressions A+B*x+C*x^2 where A, B and C are loop
|
|
/// invariant values. This corresponds to an addrec of the form {L,+,M,+,N}
|
|
bool isQuadratic() const {
|
|
return getNumOperands() == 3;
|
|
}
|
|
|
|
/// evaluateAtIteration - Return the value of this chain of recurrences at
|
|
/// the specified iteration number.
|
|
SCEVHandle evaluateAtIteration(SCEVHandle It) const;
|
|
|
|
/// getNumIterationsInRange - Return the number of iterations of this loop
|
|
/// that produce values in the specified constant range. Another way of
|
|
/// looking at this is that it returns the first iteration number where the
|
|
/// value is not in the condition, thus computing the exit count. If the
|
|
/// iteration count can't be computed, an instance of SCEVCouldNotCompute is
|
|
/// returned.
|
|
SCEVHandle getNumIterationsInRange(ConstantRange Range) const;
|
|
|
|
|
|
virtual void print(std::ostream &OS) const {
|
|
OS << "{" << *Operands[0];
|
|
for (unsigned i = 1, e = Operands.size(); i != e; ++i)
|
|
OS << ",+," << *Operands[i];
|
|
OS << "}<" << L->getHeader()->getName() + ">";
|
|
}
|
|
|
|
/// Methods for support type inquiry through isa, cast, and dyn_cast:
|
|
static inline bool classof(const SCEVAddRecExpr *S) { return true; }
|
|
static inline bool classof(const SCEV *S) {
|
|
return S->getSCEVType() == scAddRecExpr;
|
|
}
|
|
};
|
|
}
|
|
|
|
|
|
//===----------------------------------------------------------------------===//
|
|
// SCEVUnknown - This means that we are dealing with an entirely unknown SCEV
|
|
// value, and only represent it as it's LLVM Value. This is the "bottom" value
|
|
// for the analysis.
|
|
//
|
|
namespace {
|
|
class SCEVUnknown;
|
|
// SCEVUnknowns - Only allow the creation of one SCEVUnknown for any
|
|
// particular value. Don't use a SCEVHandle here, or else the object will
|
|
// never be deleted!
|
|
std::map<Value*, SCEVUnknown*> SCEVUnknowns;
|
|
|
|
class SCEVUnknown : public SCEV {
|
|
Value *V;
|
|
SCEVUnknown(Value *v) : SCEV(scUnknown), V(v) {}
|
|
|
|
protected:
|
|
~SCEVUnknown() { SCEVUnknowns.erase(V); }
|
|
public:
|
|
/// get method - For SCEVUnknown, this just gets and returns a new
|
|
/// SCEVUnknown.
|
|
static SCEVHandle get(Value *V) {
|
|
if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
|
|
return SCEVConstant::get(CI);
|
|
SCEVUnknown *&Result = SCEVUnknowns[V];
|
|
if (Result == 0) Result = new SCEVUnknown(V);
|
|
return Result;
|
|
}
|
|
|
|
Value *getValue() const { return V; }
|
|
|
|
Value *expandCodeFor(ScalarEvolutionRewriter &SER,
|
|
Instruction *InsertPt) {
|
|
return V;
|
|
}
|
|
|
|
virtual bool isLoopInvariant(const Loop *L) const {
|
|
// All non-instruction values are loop invariant. All instructions are
|
|
// loop invariant if they are not contained in the specified loop.
|
|
if (Instruction *I = dyn_cast<Instruction>(V))
|
|
return !L->contains(I->getParent());
|
|
return true;
|
|
}
|
|
|
|
virtual bool hasComputableLoopEvolution(const Loop *QL) const {
|
|
return false; // not computable
|
|
}
|
|
|
|
virtual const Type *getType() const { return V->getType(); }
|
|
|
|
virtual void print(std::ostream &OS) const {
|
|
WriteAsOperand(OS, V, false);
|
|
}
|
|
|
|
/// Methods for support type inquiry through isa, cast, and dyn_cast:
|
|
static inline bool classof(const SCEVUnknown *S) { return true; }
|
|
static inline bool classof(const SCEV *S) {
|
|
return S->getSCEVType() == scUnknown;
|
|
}
|
|
};
|
|
}
|
|
|
|
//===----------------------------------------------------------------------===//
|
|
// Simple SCEV method implementations
|
|
//===----------------------------------------------------------------------===//
|
|
|
|
/// getIntegerSCEV - Given an integer or FP type, create a constant for the
|
|
/// specified signed integer value and return a SCEV for the constant.
|
|
static SCEVHandle getIntegerSCEV(int Val, const Type *Ty) {
|
|
Constant *C;
|
|
if (Val == 0)
|
|
C = Constant::getNullValue(Ty);
|
|
else if (Ty->isFloatingPoint())
|
|
C = ConstantFP::get(Ty, Val);
|
|
else if (Ty->isSigned())
|
|
C = ConstantSInt::get(Ty, Val);
|
|
else {
|
|
C = ConstantSInt::get(Ty->getSignedVersion(), Val);
|
|
C = ConstantExpr::getCast(C, Ty);
|
|
}
|
|
return SCEVUnknown::get(C);
|
|
}
|
|
|
|
/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
|
|
/// input value to the specified type. If the type must be extended, it is zero
|
|
/// extended.
|
|
static SCEVHandle getTruncateOrZeroExtend(const SCEVHandle &V, const Type *Ty) {
|
|
const Type *SrcTy = V->getType();
|
|
assert(SrcTy->isInteger() && Ty->isInteger() &&
|
|
"Cannot truncate or zero extend with non-integer arguments!");
|
|
if (SrcTy->getPrimitiveSize() == Ty->getPrimitiveSize())
|
|
return V; // No conversion
|
|
if (SrcTy->getPrimitiveSize() > Ty->getPrimitiveSize())
|
|
return SCEVTruncateExpr::get(V, Ty);
|
|
return SCEVZeroExtendExpr::get(V, Ty);
|
|
}
|
|
|
|
/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
|
|
///
|
|
static SCEVHandle getNegativeSCEV(const SCEVHandle &V) {
|
|
if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
|
|
return SCEVUnknown::get(ConstantExpr::getNeg(VC->getValue()));
|
|
|
|
return SCEVMulExpr::get(V, getIntegerSCEV(-1, V->getType()));
|
|
}
|
|
|
|
/// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
|
|
///
|
|
static SCEVHandle getMinusSCEV(const SCEVHandle &LHS, const SCEVHandle &RHS) {
|
|
// X - Y --> X + -Y
|
|
return SCEVAddExpr::get(LHS, getNegativeSCEV(RHS));
|
|
}
|
|
|
|
|
|
/// Binomial - Evaluate N!/((N-M)!*M!) . Note that N is often large and M is
|
|
/// often very small, so we try to reduce the number of N! terms we need to
|
|
/// evaluate by evaluating this as (N!/(N-M)!)/M!
|
|
static ConstantInt *Binomial(ConstantInt *N, unsigned M) {
|
|
uint64_t NVal = N->getRawValue();
|
|
uint64_t FirstTerm = 1;
|
|
for (unsigned i = 0; i != M; ++i)
|
|
FirstTerm *= NVal-i;
|
|
|
|
unsigned MFactorial = 1;
|
|
for (; M; --M)
|
|
MFactorial *= M;
|
|
|
|
Constant *Result = ConstantUInt::get(Type::ULongTy, FirstTerm/MFactorial);
|
|
Result = ConstantExpr::getCast(Result, N->getType());
|
|
assert(isa<ConstantInt>(Result) && "Cast of integer not folded??");
|
|
return cast<ConstantInt>(Result);
|
|
}
|
|
|
|
/// PartialFact - Compute V!/(V-NumSteps)!
|
|
static SCEVHandle PartialFact(SCEVHandle V, unsigned NumSteps) {
|
|
// Handle this case efficiently, it is common to have constant iteration
|
|
// counts while computing loop exit values.
|
|
if (SCEVConstant *SC = dyn_cast<SCEVConstant>(V)) {
|
|
uint64_t Val = SC->getValue()->getRawValue();
|
|
uint64_t Result = 1;
|
|
for (; NumSteps; --NumSteps)
|
|
Result *= Val-(NumSteps-1);
|
|
Constant *Res = ConstantUInt::get(Type::ULongTy, Result);
|
|
return SCEVUnknown::get(ConstantExpr::getCast(Res, V->getType()));
|
|
}
|
|
|
|
const Type *Ty = V->getType();
|
|
if (NumSteps == 0)
|
|
return getIntegerSCEV(1, Ty);
|
|
|
|
SCEVHandle Result = V;
|
|
for (unsigned i = 1; i != NumSteps; ++i)
|
|
Result = SCEVMulExpr::get(Result, getMinusSCEV(V, getIntegerSCEV(i, Ty)));
|
|
return Result;
|
|
}
|
|
|
|
|
|
/// evaluateAtIteration - Return the value of this chain of recurrences at
|
|
/// the specified iteration number. We can evaluate this recurrence by
|
|
/// multiplying each element in the chain by the binomial coefficient
|
|
/// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
|
|
///
|
|
/// A*choose(It, 0) + B*choose(It, 1) + C*choose(It, 2) + D*choose(It, 3)
|
|
///
|
|
/// FIXME/VERIFY: I don't trust that this is correct in the face of overflow.
|
|
/// Is the binomial equation safe using modular arithmetic??
|
|
///
|
|
SCEVHandle SCEVAddRecExpr::evaluateAtIteration(SCEVHandle It) const {
|
|
SCEVHandle Result = getStart();
|
|
int Divisor = 1;
|
|
const Type *Ty = It->getType();
|
|
for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
|
|
SCEVHandle BC = PartialFact(It, i);
|
|
Divisor *= i;
|
|
SCEVHandle Val = SCEVUDivExpr::get(SCEVMulExpr::get(BC, getOperand(i)),
|
|
getIntegerSCEV(Divisor, Ty));
|
|
Result = SCEVAddExpr::get(Result, Val);
|
|
}
|
|
return Result;
|
|
}
|
|
|
|
|
|
//===----------------------------------------------------------------------===//
|
|
// SCEV Expression folder implementations
|
|
//===----------------------------------------------------------------------===//
|
|
|
|
SCEVHandle SCEVTruncateExpr::get(const SCEVHandle &Op, const Type *Ty) {
|
|
if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
|
|
return SCEVUnknown::get(ConstantExpr::getCast(SC->getValue(), Ty));
|
|
|
|
// If the input value is a chrec scev made out of constants, truncate
|
|
// all of the constants.
|
|
if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
|
|
std::vector<SCEVHandle> Operands;
|
|
for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
|
|
// FIXME: This should allow truncation of other expression types!
|
|
if (isa<SCEVConstant>(AddRec->getOperand(i)))
|
|
Operands.push_back(get(AddRec->getOperand(i), Ty));
|
|
else
|
|
break;
|
|
if (Operands.size() == AddRec->getNumOperands())
|
|
return SCEVAddRecExpr::get(Operands, AddRec->getLoop());
|
|
}
|
|
|
|
SCEVTruncateExpr *&Result = SCEVTruncates[std::make_pair(Op, Ty)];
|
|
if (Result == 0) Result = new SCEVTruncateExpr(Op, Ty);
|
|
return Result;
|
|
}
|
|
|
|
SCEVHandle SCEVZeroExtendExpr::get(const SCEVHandle &Op, const Type *Ty) {
|
|
if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
|
|
return SCEVUnknown::get(ConstantExpr::getCast(SC->getValue(), Ty));
|
|
|
|
// FIXME: If the input value is a chrec scev, and we can prove that the value
|
|
// did not overflow the old, smaller, value, we can zero extend all of the
|
|
// operands (often constants). This would allow analysis of something like
|
|
// this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
|
|
|
|
SCEVZeroExtendExpr *&Result = SCEVZeroExtends[std::make_pair(Op, Ty)];
|
|
if (Result == 0) Result = new SCEVZeroExtendExpr(Op, Ty);
|
|
return Result;
|
|
}
|
|
|
|
// get - Get a canonical add expression, or something simpler if possible.
|
|
SCEVHandle SCEVAddExpr::get(std::vector<SCEVHandle> &Ops) {
|
|
assert(!Ops.empty() && "Cannot get empty add!");
|
|
|
|
// Sort by complexity, this groups all similar expression types together.
|
|
std::sort(Ops.begin(), Ops.end(), SCEVComplexityCompare());
|
|
|
|
// If there are any constants, fold them together.
|
|
unsigned Idx = 0;
|
|
if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
|
|
++Idx;
|
|
while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
|
|
// We found two constants, fold them together!
|
|
Constant *Fold = ConstantExpr::getAdd(LHSC->getValue(), RHSC->getValue());
|
|
if (ConstantInt *CI = dyn_cast<ConstantInt>(Fold)) {
|
|
Ops[0] = SCEVConstant::get(CI);
|
|
Ops.erase(Ops.begin()+1); // Erase the folded element
|
|
if (Ops.size() == 1) return Ops[0];
|
|
} else {
|
|
// If we couldn't fold the expression, move to the next constant. Note
|
|
// that this is impossible to happen in practice because we always
|
|
// constant fold constant ints to constant ints.
|
|
++Idx;
|
|
}
|
|
}
|
|
|
|
// If we are left with a constant zero being added, strip it off.
|
|
if (cast<SCEVConstant>(Ops[0])->getValue()->isNullValue()) {
|
|
Ops.erase(Ops.begin());
|
|
--Idx;
|
|
}
|
|
}
|
|
|
|
if (Ops.size() == 1)
|
|
return Ops[0];
|
|
|
|
// Okay, check to see if the same value occurs in the operand list twice. If
|
|
// so, merge them together into an multiply expression. Since we sorted the
|
|
// list, these values are required to be adjacent.
|
|
const Type *Ty = Ops[0]->getType();
|
|
for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
|
|
if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
|
|
// Found a match, merge the two values into a multiply, and add any
|
|
// remaining values to the result.
|
|
SCEVHandle Two = getIntegerSCEV(2, Ty);
|
|
SCEVHandle Mul = SCEVMulExpr::get(Ops[i], Two);
|
|
if (Ops.size() == 2)
|
|
return Mul;
|
|
Ops.erase(Ops.begin()+i, Ops.begin()+i+2);
|
|
Ops.push_back(Mul);
|
|
return SCEVAddExpr::get(Ops);
|
|
}
|
|
|
|
// Okay, now we know the first non-constant operand. If there are add
|
|
// operands they would be next.
|
|
if (Idx < Ops.size()) {
|
|
bool DeletedAdd = false;
|
|
while (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
|
|
// If we have an add, expand the add operands onto the end of the operands
|
|
// list.
|
|
Ops.insert(Ops.end(), Add->op_begin(), Add->op_end());
|
|
Ops.erase(Ops.begin()+Idx);
|
|
DeletedAdd = true;
|
|
}
|
|
|
|
// If we deleted at least one add, we added operands to the end of the list,
|
|
// and they are not necessarily sorted. Recurse to resort and resimplify
|
|
// any operands we just aquired.
|
|
if (DeletedAdd)
|
|
return get(Ops);
|
|
}
|
|
|
|
// Skip over the add expression until we get to a multiply.
|
|
while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
|
|
++Idx;
|
|
|
|
// If we are adding something to a multiply expression, make sure the
|
|
// something is not already an operand of the multiply. If so, merge it into
|
|
// the multiply.
|
|
for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
|
|
SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
|
|
for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
|
|
SCEV *MulOpSCEV = Mul->getOperand(MulOp);
|
|
for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
|
|
if (MulOpSCEV == Ops[AddOp] &&
|
|
(Mul->getNumOperands() != 2 || !isa<SCEVConstant>(MulOpSCEV))) {
|
|
// Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
|
|
SCEVHandle InnerMul = Mul->getOperand(MulOp == 0);
|
|
if (Mul->getNumOperands() != 2) {
|
|
// If the multiply has more than two operands, we must get the
|
|
// Y*Z term.
|
|
std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end());
|
|
MulOps.erase(MulOps.begin()+MulOp);
|
|
InnerMul = SCEVMulExpr::get(MulOps);
|
|
}
|
|
SCEVHandle One = getIntegerSCEV(1, Ty);
|
|
SCEVHandle AddOne = SCEVAddExpr::get(InnerMul, One);
|
|
SCEVHandle OuterMul = SCEVMulExpr::get(AddOne, Ops[AddOp]);
|
|
if (Ops.size() == 2) return OuterMul;
|
|
if (AddOp < Idx) {
|
|
Ops.erase(Ops.begin()+AddOp);
|
|
Ops.erase(Ops.begin()+Idx-1);
|
|
} else {
|
|
Ops.erase(Ops.begin()+Idx);
|
|
Ops.erase(Ops.begin()+AddOp-1);
|
|
}
|
|
Ops.push_back(OuterMul);
|
|
return SCEVAddExpr::get(Ops);
|
|
}
|
|
|
|
// Check this multiply against other multiplies being added together.
|
|
for (unsigned OtherMulIdx = Idx+1;
|
|
OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
|
|
++OtherMulIdx) {
|
|
SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
|
|
// If MulOp occurs in OtherMul, we can fold the two multiplies
|
|
// together.
|
|
for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
|
|
OMulOp != e; ++OMulOp)
|
|
if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
|
|
// Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
|
|
SCEVHandle InnerMul1 = Mul->getOperand(MulOp == 0);
|
|
if (Mul->getNumOperands() != 2) {
|
|
std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end());
|
|
MulOps.erase(MulOps.begin()+MulOp);
|
|
InnerMul1 = SCEVMulExpr::get(MulOps);
|
|
}
|
|
SCEVHandle InnerMul2 = OtherMul->getOperand(OMulOp == 0);
|
|
if (OtherMul->getNumOperands() != 2) {
|
|
std::vector<SCEVHandle> MulOps(OtherMul->op_begin(),
|
|
OtherMul->op_end());
|
|
MulOps.erase(MulOps.begin()+OMulOp);
|
|
InnerMul2 = SCEVMulExpr::get(MulOps);
|
|
}
|
|
SCEVHandle InnerMulSum = SCEVAddExpr::get(InnerMul1,InnerMul2);
|
|
SCEVHandle OuterMul = SCEVMulExpr::get(MulOpSCEV, InnerMulSum);
|
|
if (Ops.size() == 2) return OuterMul;
|
|
Ops.erase(Ops.begin()+Idx);
|
|
Ops.erase(Ops.begin()+OtherMulIdx-1);
|
|
Ops.push_back(OuterMul);
|
|
return SCEVAddExpr::get(Ops);
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
// If there are any add recurrences in the operands list, see if any other
|
|
// added values are loop invariant. If so, we can fold them into the
|
|
// recurrence.
|
|
while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
|
|
++Idx;
|
|
|
|
// Scan over all recurrences, trying to fold loop invariants into them.
|
|
for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
|
|
// Scan all of the other operands to this add and add them to the vector if
|
|
// they are loop invariant w.r.t. the recurrence.
|
|
std::vector<SCEVHandle> LIOps;
|
|
SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
|
|
for (unsigned i = 0, e = Ops.size(); i != e; ++i)
|
|
if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
|
|
LIOps.push_back(Ops[i]);
|
|
Ops.erase(Ops.begin()+i);
|
|
--i; --e;
|
|
}
|
|
|
|
// If we found some loop invariants, fold them into the recurrence.
|
|
if (!LIOps.empty()) {
|
|
// NLI + LI + { Start,+,Step} --> NLI + { LI+Start,+,Step }
|
|
LIOps.push_back(AddRec->getStart());
|
|
|
|
std::vector<SCEVHandle> AddRecOps(AddRec->op_begin(), AddRec->op_end());
|
|
AddRecOps[0] = SCEVAddExpr::get(LIOps);
|
|
|
|
SCEVHandle NewRec = SCEVAddRecExpr::get(AddRecOps, AddRec->getLoop());
|
|
// If all of the other operands were loop invariant, we are done.
|
|
if (Ops.size() == 1) return NewRec;
|
|
|
|
// Otherwise, add the folded AddRec by the non-liv parts.
|
|
for (unsigned i = 0;; ++i)
|
|
if (Ops[i] == AddRec) {
|
|
Ops[i] = NewRec;
|
|
break;
|
|
}
|
|
return SCEVAddExpr::get(Ops);
|
|
}
|
|
|
|
// Okay, if there weren't any loop invariants to be folded, check to see if
|
|
// there are multiple AddRec's with the same loop induction variable being
|
|
// added together. If so, we can fold them.
|
|
for (unsigned OtherIdx = Idx+1;
|
|
OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
|
|
if (OtherIdx != Idx) {
|
|
SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
|
|
if (AddRec->getLoop() == OtherAddRec->getLoop()) {
|
|
// Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D}
|
|
std::vector<SCEVHandle> NewOps(AddRec->op_begin(), AddRec->op_end());
|
|
for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) {
|
|
if (i >= NewOps.size()) {
|
|
NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i,
|
|
OtherAddRec->op_end());
|
|
break;
|
|
}
|
|
NewOps[i] = SCEVAddExpr::get(NewOps[i], OtherAddRec->getOperand(i));
|
|
}
|
|
SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewOps, AddRec->getLoop());
|
|
|
|
if (Ops.size() == 2) return NewAddRec;
|
|
|
|
Ops.erase(Ops.begin()+Idx);
|
|
Ops.erase(Ops.begin()+OtherIdx-1);
|
|
Ops.push_back(NewAddRec);
|
|
return SCEVAddExpr::get(Ops);
|
|
}
|
|
}
|
|
|
|
// Otherwise couldn't fold anything into this recurrence. Move onto the
|
|
// next one.
|
|
}
|
|
|
|
// Okay, it looks like we really DO need an add expr. Check to see if we
|
|
// already have one, otherwise create a new one.
|
|
std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end());
|
|
SCEVCommutativeExpr *&Result = SCEVCommExprs[std::make_pair(scAddExpr,
|
|
SCEVOps)];
|
|
if (Result == 0) Result = new SCEVAddExpr(Ops);
|
|
return Result;
|
|
}
|
|
|
|
|
|
SCEVHandle SCEVMulExpr::get(std::vector<SCEVHandle> &Ops) {
|
|
assert(!Ops.empty() && "Cannot get empty mul!");
|
|
|
|
// Sort by complexity, this groups all similar expression types together.
|
|
std::sort(Ops.begin(), Ops.end(), SCEVComplexityCompare());
|
|
|
|
// If there are any constants, fold them together.
|
|
unsigned Idx = 0;
|
|
if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
|
|
|
|
// C1*(C2+V) -> C1*C2 + C1*V
|
|
if (Ops.size() == 2)
|
|
if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
|
|
if (Add->getNumOperands() == 2 &&
|
|
isa<SCEVConstant>(Add->getOperand(0)))
|
|
return SCEVAddExpr::get(SCEVMulExpr::get(LHSC, Add->getOperand(0)),
|
|
SCEVMulExpr::get(LHSC, Add->getOperand(1)));
|
|
|
|
|
|
++Idx;
|
|
while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
|
|
// We found two constants, fold them together!
|
|
Constant *Fold = ConstantExpr::getMul(LHSC->getValue(), RHSC->getValue());
|
|
if (ConstantInt *CI = dyn_cast<ConstantInt>(Fold)) {
|
|
Ops[0] = SCEVConstant::get(CI);
|
|
Ops.erase(Ops.begin()+1); // Erase the folded element
|
|
if (Ops.size() == 1) return Ops[0];
|
|
} else {
|
|
// If we couldn't fold the expression, move to the next constant. Note
|
|
// that this is impossible to happen in practice because we always
|
|
// constant fold constant ints to constant ints.
|
|
++Idx;
|
|
}
|
|
}
|
|
|
|
// If we are left with a constant one being multiplied, strip it off.
|
|
if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
|
|
Ops.erase(Ops.begin());
|
|
--Idx;
|
|
} else if (cast<SCEVConstant>(Ops[0])->getValue()->isNullValue()) {
|
|
// If we have a multiply of zero, it will always be zero.
|
|
return Ops[0];
|
|
}
|
|
}
|
|
|
|
// Skip over the add expression until we get to a multiply.
|
|
while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
|
|
++Idx;
|
|
|
|
if (Ops.size() == 1)
|
|
return Ops[0];
|
|
|
|
// If there are mul operands inline them all into this expression.
|
|
if (Idx < Ops.size()) {
|
|
bool DeletedMul = false;
|
|
while (SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
|
|
// If we have an mul, expand the mul operands onto the end of the operands
|
|
// list.
|
|
Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end());
|
|
Ops.erase(Ops.begin()+Idx);
|
|
DeletedMul = true;
|
|
}
|
|
|
|
// If we deleted at least one mul, we added operands to the end of the list,
|
|
// and they are not necessarily sorted. Recurse to resort and resimplify
|
|
// any operands we just aquired.
|
|
if (DeletedMul)
|
|
return get(Ops);
|
|
}
|
|
|
|
// If there are any add recurrences in the operands list, see if any other
|
|
// added values are loop invariant. If so, we can fold them into the
|
|
// recurrence.
|
|
while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
|
|
++Idx;
|
|
|
|
// Scan over all recurrences, trying to fold loop invariants into them.
|
|
for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
|
|
// Scan all of the other operands to this mul and add them to the vector if
|
|
// they are loop invariant w.r.t. the recurrence.
|
|
std::vector<SCEVHandle> LIOps;
|
|
SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
|
|
for (unsigned i = 0, e = Ops.size(); i != e; ++i)
|
|
if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
|
|
LIOps.push_back(Ops[i]);
|
|
Ops.erase(Ops.begin()+i);
|
|
--i; --e;
|
|
}
|
|
|
|
// If we found some loop invariants, fold them into the recurrence.
|
|
if (!LIOps.empty()) {
|
|
// NLI * LI * { Start,+,Step} --> NLI * { LI*Start,+,LI*Step }
|
|
std::vector<SCEVHandle> NewOps;
|
|
NewOps.reserve(AddRec->getNumOperands());
|
|
if (LIOps.size() == 1) {
|
|
SCEV *Scale = LIOps[0];
|
|
for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
|
|
NewOps.push_back(SCEVMulExpr::get(Scale, AddRec->getOperand(i)));
|
|
} else {
|
|
for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
|
|
std::vector<SCEVHandle> MulOps(LIOps);
|
|
MulOps.push_back(AddRec->getOperand(i));
|
|
NewOps.push_back(SCEVMulExpr::get(MulOps));
|
|
}
|
|
}
|
|
|
|
SCEVHandle NewRec = SCEVAddRecExpr::get(NewOps, AddRec->getLoop());
|
|
|
|
// If all of the other operands were loop invariant, we are done.
|
|
if (Ops.size() == 1) return NewRec;
|
|
|
|
// Otherwise, multiply the folded AddRec by the non-liv parts.
|
|
for (unsigned i = 0;; ++i)
|
|
if (Ops[i] == AddRec) {
|
|
Ops[i] = NewRec;
|
|
break;
|
|
}
|
|
return SCEVMulExpr::get(Ops);
|
|
}
|
|
|
|
// Okay, if there weren't any loop invariants to be folded, check to see if
|
|
// there are multiple AddRec's with the same loop induction variable being
|
|
// multiplied together. If so, we can fold them.
|
|
for (unsigned OtherIdx = Idx+1;
|
|
OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
|
|
if (OtherIdx != Idx) {
|
|
SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
|
|
if (AddRec->getLoop() == OtherAddRec->getLoop()) {
|
|
// F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D}
|
|
SCEVAddRecExpr *F = AddRec, *G = OtherAddRec;
|
|
SCEVHandle NewStart = SCEVMulExpr::get(F->getStart(),
|
|
G->getStart());
|
|
SCEVHandle B = F->getStepRecurrence();
|
|
SCEVHandle D = G->getStepRecurrence();
|
|
SCEVHandle NewStep = SCEVAddExpr::get(SCEVMulExpr::get(F, D),
|
|
SCEVMulExpr::get(G, B),
|
|
SCEVMulExpr::get(B, D));
|
|
SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewStart, NewStep,
|
|
F->getLoop());
|
|
if (Ops.size() == 2) return NewAddRec;
|
|
|
|
Ops.erase(Ops.begin()+Idx);
|
|
Ops.erase(Ops.begin()+OtherIdx-1);
|
|
Ops.push_back(NewAddRec);
|
|
return SCEVMulExpr::get(Ops);
|
|
}
|
|
}
|
|
|
|
// Otherwise couldn't fold anything into this recurrence. Move onto the
|
|
// next one.
|
|
}
|
|
|
|
// Okay, it looks like we really DO need an mul expr. Check to see if we
|
|
// already have one, otherwise create a new one.
|
|
std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end());
|
|
SCEVCommutativeExpr *&Result = SCEVCommExprs[std::make_pair(scMulExpr,
|
|
SCEVOps)];
|
|
if (Result == 0) Result = new SCEVMulExpr(Ops);
|
|
return Result;
|
|
}
|
|
|
|
SCEVHandle SCEVUDivExpr::get(const SCEVHandle &LHS, const SCEVHandle &RHS) {
|
|
if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
|
|
if (RHSC->getValue()->equalsInt(1))
|
|
return LHS; // X /u 1 --> x
|
|
if (RHSC->getValue()->isAllOnesValue())
|
|
return getNegativeSCEV(LHS); // X /u -1 --> -x
|
|
|
|
if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
|
|
Constant *LHSCV = LHSC->getValue();
|
|
Constant *RHSCV = RHSC->getValue();
|
|
if (LHSCV->getType()->isSigned())
|
|
LHSCV = ConstantExpr::getCast(LHSCV,
|
|
LHSCV->getType()->getUnsignedVersion());
|
|
if (RHSCV->getType()->isSigned())
|
|
RHSCV = ConstantExpr::getCast(RHSCV, LHSCV->getType());
|
|
return SCEVUnknown::get(ConstantExpr::getDiv(LHSCV, RHSCV));
|
|
}
|
|
}
|
|
|
|
// FIXME: implement folding of (X*4)/4 when we know X*4 doesn't overflow.
|
|
|
|
SCEVUDivExpr *&Result = SCEVUDivs[std::make_pair(LHS, RHS)];
|
|
if (Result == 0) Result = new SCEVUDivExpr(LHS, RHS);
|
|
return Result;
|
|
}
|
|
|
|
|
|
/// SCEVAddRecExpr::get - Get a add recurrence expression for the
|
|
/// specified loop. Simplify the expression as much as possible.
|
|
SCEVHandle SCEVAddRecExpr::get(const SCEVHandle &Start,
|
|
const SCEVHandle &Step, const Loop *L) {
|
|
std::vector<SCEVHandle> Operands;
|
|
Operands.push_back(Start);
|
|
if (SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
|
|
if (StepChrec->getLoop() == L) {
|
|
Operands.insert(Operands.end(), StepChrec->op_begin(),
|
|
StepChrec->op_end());
|
|
return get(Operands, L);
|
|
}
|
|
|
|
Operands.push_back(Step);
|
|
return get(Operands, L);
|
|
}
|
|
|
|
/// SCEVAddRecExpr::get - Get a add recurrence expression for the
|
|
/// specified loop. Simplify the expression as much as possible.
|
|
SCEVHandle SCEVAddRecExpr::get(std::vector<SCEVHandle> &Operands,
|
|
const Loop *L) {
|
|
if (Operands.size() == 1) return Operands[0];
|
|
|
|
if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Operands.back()))
|
|
if (StepC->getValue()->isNullValue()) {
|
|
Operands.pop_back();
|
|
return get(Operands, L); // { X,+,0 } --> X
|
|
}
|
|
|
|
SCEVAddRecExpr *&Result =
|
|
SCEVAddRecExprs[std::make_pair(L, std::vector<SCEV*>(Operands.begin(),
|
|
Operands.end()))];
|
|
if (Result == 0) Result = new SCEVAddRecExpr(Operands, L);
|
|
return Result;
|
|
}
|
|
|
|
|
|
//===----------------------------------------------------------------------===//
|
|
// Non-trivial closed-form SCEV Expanders
|
|
//===----------------------------------------------------------------------===//
|
|
|
|
Value *SCEVTruncateExpr::expandCodeFor(ScalarEvolutionRewriter &SER,
|
|
Instruction *InsertPt) {
|
|
Value *V = SER.ExpandCodeFor(getOperand(), InsertPt);
|
|
return new CastInst(V, getType(), "tmp.", InsertPt);
|
|
}
|
|
|
|
Value *SCEVZeroExtendExpr::expandCodeFor(ScalarEvolutionRewriter &SER,
|
|
Instruction *InsertPt) {
|
|
Value *V = SER.ExpandCodeFor(getOperand(), InsertPt,
|
|
getOperand()->getType()->getUnsignedVersion());
|
|
return new CastInst(V, getType(), "tmp.", InsertPt);
|
|
}
|
|
|
|
Value *SCEVAddExpr::expandCodeFor(ScalarEvolutionRewriter &SER,
|
|
Instruction *InsertPt) {
|
|
const Type *Ty = getType();
|
|
Value *V = SER.ExpandCodeFor(getOperand(getNumOperands()-1), InsertPt, Ty);
|
|
|
|
// Emit a bunch of add instructions
|
|
for (int i = getNumOperands()-2; i >= 0; --i)
|
|
V = BinaryOperator::create(Instruction::Add, V,
|
|
SER.ExpandCodeFor(getOperand(i), InsertPt, Ty),
|
|
"tmp.", InsertPt);
|
|
return V;
|
|
}
|
|
|
|
Value *SCEVMulExpr::expandCodeFor(ScalarEvolutionRewriter &SER,
|
|
Instruction *InsertPt) {
|
|
const Type *Ty = getType();
|
|
int FirstOp = 0; // Set if we should emit a subtract.
|
|
if (SCEVConstant *SC = dyn_cast<SCEVConstant>(getOperand(0)))
|
|
if (SC->getValue()->isAllOnesValue())
|
|
FirstOp = 1;
|
|
|
|
int i = getNumOperands()-2;
|
|
Value *V = SER.ExpandCodeFor(getOperand(i+1), InsertPt, Ty);
|
|
|
|
// Emit a bunch of multiply instructions
|
|
for (; i >= FirstOp; --i)
|
|
V = BinaryOperator::create(Instruction::Mul, V,
|
|
SER.ExpandCodeFor(getOperand(i), InsertPt, Ty),
|
|
"tmp.", InsertPt);
|
|
// -1 * ... ---> 0 - ...
|
|
if (FirstOp == 1)
|
|
V = BinaryOperator::create(Instruction::Sub, Constant::getNullValue(Ty), V,
|
|
"tmp.", InsertPt);
|
|
return V;
|
|
}
|
|
|
|
Value *SCEVUDivExpr::expandCodeFor(ScalarEvolutionRewriter &SER,
|
|
Instruction *InsertPt) {
|
|
const Type *Ty = getType();
|
|
Value *LHS = SER.ExpandCodeFor(getLHS(), InsertPt, Ty);
|
|
Value *RHS = SER.ExpandCodeFor(getRHS(), InsertPt, Ty);
|
|
return BinaryOperator::create(Instruction::Div, LHS, RHS, "tmp.", InsertPt);
|
|
}
|
|
|
|
Value *SCEVAddRecExpr::expandCodeFor(ScalarEvolutionRewriter &SER,
|
|
Instruction *InsertPt) {
|
|
const Type *Ty = getType();
|
|
// We cannot yet do fp recurrences, e.g. the xform of {X,+,F} --> X+{0,+,F}
|
|
assert(Ty->isIntegral() && "Cannot expand fp recurrences yet!");
|
|
|
|
// {X,+,F} --> X + {0,+,F}
|
|
if (!isa<SCEVConstant>(getStart()) ||
|
|
!cast<SCEVConstant>(getStart())->getValue()->isNullValue()) {
|
|
Value *Start = SER.ExpandCodeFor(getStart(), InsertPt, Ty);
|
|
std::vector<SCEVHandle> NewOps(op_begin(), op_end());
|
|
NewOps[0] = getIntegerSCEV(0, getType());
|
|
Value *Rest = SER.ExpandCodeFor(SCEVAddRecExpr::get(NewOps, getLoop()),
|
|
InsertPt, getType());
|
|
|
|
// FIXME: look for an existing add to use.
|
|
return BinaryOperator::create(Instruction::Add, Rest, Start, "tmp.",
|
|
InsertPt);
|
|
}
|
|
|
|
// {0,+,1} --> Insert a canonical induction variable into the loop!
|
|
if (getNumOperands() == 2 && getOperand(1) == getIntegerSCEV(1, getType())) {
|
|
// Create and insert the PHI node for the induction variable in the
|
|
// specified loop.
|
|
BasicBlock *Header = getLoop()->getHeader();
|
|
PHINode *PN = new PHINode(Ty, "indvar", Header->begin());
|
|
PN->addIncoming(Constant::getNullValue(Ty), L->getLoopPreheader());
|
|
|
|
// Insert a unit add instruction after the PHI nodes in the header block.
|
|
BasicBlock::iterator I = PN;
|
|
while (isa<PHINode>(I)) ++I;
|
|
|
|
Constant *One = Ty->isFloatingPoint() ?(Constant*)ConstantFP::get(Ty, 1.0)
|
|
:(Constant*)ConstantInt::get(Ty, 1);
|
|
Instruction *Add = BinaryOperator::create(Instruction::Add, PN, One,
|
|
"indvar.next", I);
|
|
|
|
pred_iterator PI = pred_begin(Header);
|
|
if (*PI == L->getLoopPreheader())
|
|
++PI;
|
|
PN->addIncoming(Add, *PI);
|
|
return PN;
|
|
}
|
|
|
|
// Get the canonical induction variable I for this loop.
|
|
Value *I = SER.GetOrInsertCanonicalInductionVariable(getLoop(), Ty);
|
|
|
|
if (getNumOperands() == 2) { // {0,+,F} --> i*F
|
|
Value *F = SER.ExpandCodeFor(getOperand(1), InsertPt, Ty);
|
|
return BinaryOperator::create(Instruction::Mul, I, F, "tmp.", InsertPt);
|
|
}
|
|
|
|
// If this is a chain of recurrences, turn it into a closed form, using the
|
|
// folders, then expandCodeFor the closed form. This allows the folders to
|
|
// simplify the expression without having to build a bunch of special code
|
|
// into this folder.
|
|
SCEVHandle IH = SCEVUnknown::get(I); // Get I as a "symbolic" SCEV.
|
|
|
|
SCEVHandle V = evaluateAtIteration(IH);
|
|
//std::cerr << "Evaluated: " << *this << "\n to: " << *V << "\n";
|
|
|
|
return SER.ExpandCodeFor(V, InsertPt, Ty);
|
|
}
|
|
|
|
|
|
//===----------------------------------------------------------------------===//
|
|
// ScalarEvolutionsImpl Definition and Implementation
|
|
//===----------------------------------------------------------------------===//
|
|
//
|
|
/// ScalarEvolutionsImpl - This class implements the main driver for the scalar
|
|
/// evolution code.
|
|
///
|
|
namespace {
|
|
struct ScalarEvolutionsImpl {
|
|
/// F - The function we are analyzing.
|
|
///
|
|
Function &F;
|
|
|
|
/// LI - The loop information for the function we are currently analyzing.
|
|
///
|
|
LoopInfo &LI;
|
|
|
|
/// UnknownValue - This SCEV is used to represent unknown trip counts and
|
|
/// things.
|
|
SCEVHandle UnknownValue;
|
|
|
|
/// Scalars - This is a cache of the scalars we have analyzed so far.
|
|
///
|
|
std::map<Value*, SCEVHandle> Scalars;
|
|
|
|
/// IterationCounts - Cache the iteration count of the loops for this
|
|
/// function as they are computed.
|
|
std::map<const Loop*, SCEVHandle> IterationCounts;
|
|
|
|
public:
|
|
ScalarEvolutionsImpl(Function &f, LoopInfo &li)
|
|
: F(f), LI(li), UnknownValue(new SCEVCouldNotCompute()) {}
|
|
|
|
/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
|
|
/// expression and create a new one.
|
|
SCEVHandle getSCEV(Value *V);
|
|
|
|
/// getSCEVAtScope - Compute the value of the specified expression within
|
|
/// the indicated loop (which may be null to indicate in no loop). If the
|
|
/// expression cannot be evaluated, return UnknownValue itself.
|
|
SCEVHandle getSCEVAtScope(SCEV *V, const Loop *L);
|
|
|
|
|
|
/// hasLoopInvariantIterationCount - Return true if the specified loop has
|
|
/// an analyzable loop-invariant iteration count.
|
|
bool hasLoopInvariantIterationCount(const Loop *L);
|
|
|
|
/// getIterationCount - If the specified loop has a predictable iteration
|
|
/// count, return it. Note that it is not valid to call this method on a
|
|
/// loop without a loop-invariant iteration count.
|
|
SCEVHandle getIterationCount(const Loop *L);
|
|
|
|
/// deleteInstructionFromRecords - This method should be called by the
|
|
/// client before it removes an instruction from the program, to make sure
|
|
/// that no dangling references are left around.
|
|
void deleteInstructionFromRecords(Instruction *I);
|
|
|
|
private:
|
|
/// createSCEV - We know that there is no SCEV for the specified value.
|
|
/// Analyze the expression.
|
|
SCEVHandle createSCEV(Value *V);
|
|
SCEVHandle createNodeForCast(CastInst *CI);
|
|
|
|
/// createNodeForPHI - Provide the special handling we need to analyze PHI
|
|
/// SCEVs.
|
|
SCEVHandle createNodeForPHI(PHINode *PN);
|
|
void UpdatePHIUserScalarEntries(Instruction *I, PHINode *PN,
|
|
std::set<Instruction*> &UpdatedInsts);
|
|
|
|
/// ComputeIterationCount - Compute the number of times the specified loop
|
|
/// will iterate.
|
|
SCEVHandle ComputeIterationCount(const Loop *L);
|
|
|
|
/// HowFarToZero - Return the number of times a backedge comparing the
|
|
/// specified value to zero will execute. If not computable, return
|
|
/// UnknownValue
|
|
SCEVHandle HowFarToZero(SCEV *V, const Loop *L);
|
|
|
|
/// HowFarToNonZero - Return the number of times a backedge checking the
|
|
/// specified value for nonzero will execute. If not computable, return
|
|
/// UnknownValue
|
|
SCEVHandle HowFarToNonZero(SCEV *V, const Loop *L);
|
|
};
|
|
}
|
|
|
|
//===----------------------------------------------------------------------===//
|
|
// Basic SCEV Analysis and PHI Idiom Recognition Code
|
|
//
|
|
|
|
/// deleteInstructionFromRecords - This method should be called by the
|
|
/// client before it removes an instruction from the program, to make sure
|
|
/// that no dangling references are left around.
|
|
void ScalarEvolutionsImpl::deleteInstructionFromRecords(Instruction *I) {
|
|
Scalars.erase(I);
|
|
}
|
|
|
|
|
|
/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
|
|
/// expression and create a new one.
|
|
SCEVHandle ScalarEvolutionsImpl::getSCEV(Value *V) {
|
|
assert(V->getType() != Type::VoidTy && "Can't analyze void expressions!");
|
|
|
|
std::map<Value*, SCEVHandle>::iterator I = Scalars.find(V);
|
|
if (I != Scalars.end()) return I->second;
|
|
SCEVHandle S = createSCEV(V);
|
|
Scalars.insert(std::make_pair(V, S));
|
|
return S;
|
|
}
|
|
|
|
|
|
/// UpdatePHIUserScalarEntries - After PHI node analysis, we have a bunch of
|
|
/// entries in the scalar map that refer to the "symbolic" PHI value instead of
|
|
/// the recurrence value. After we resolve the PHI we must loop over all of the
|
|
/// using instructions that have scalar map entries and update them.
|
|
void ScalarEvolutionsImpl::UpdatePHIUserScalarEntries(Instruction *I,
|
|
PHINode *PN,
|
|
std::set<Instruction*> &UpdatedInsts) {
|
|
std::map<Value*, SCEVHandle>::iterator SI = Scalars.find(I);
|
|
if (SI == Scalars.end()) return; // This scalar wasn't previous processed.
|
|
if (UpdatedInsts.insert(I).second) {
|
|
Scalars.erase(SI); // Remove the old entry
|
|
getSCEV(I); // Calculate the new entry
|
|
|
|
for (Value::use_iterator UI = I->use_begin(), E = I->use_end();
|
|
UI != E; ++UI)
|
|
UpdatePHIUserScalarEntries(cast<Instruction>(*UI), PN, UpdatedInsts);
|
|
}
|
|
}
|
|
|
|
|
|
/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
|
|
/// a loop header, making it a potential recurrence, or it doesn't.
|
|
///
|
|
SCEVHandle ScalarEvolutionsImpl::createNodeForPHI(PHINode *PN) {
|
|
if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized.
|
|
if (const Loop *L = LI.getLoopFor(PN->getParent()))
|
|
if (L->getHeader() == PN->getParent()) {
|
|
// If it lives in the loop header, it has two incoming values, one
|
|
// from outside the loop, and one from inside.
|
|
unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0));
|
|
unsigned BackEdge = IncomingEdge^1;
|
|
|
|
// While we are analyzing this PHI node, handle its value symbolically.
|
|
SCEVHandle SymbolicName = SCEVUnknown::get(PN);
|
|
assert(Scalars.find(PN) == Scalars.end() &&
|
|
"PHI node already processed?");
|
|
Scalars.insert(std::make_pair(PN, SymbolicName));
|
|
|
|
// Using this symbolic name for the PHI, analyze the value coming around
|
|
// the back-edge.
|
|
SCEVHandle BEValue = getSCEV(PN->getIncomingValue(BackEdge));
|
|
|
|
// NOTE: If BEValue is loop invariant, we know that the PHI node just
|
|
// has a special value for the first iteration of the loop.
|
|
|
|
// If the value coming around the backedge is an add with the symbolic
|
|
// value we just inserted, then we found a simple induction variable!
|
|
if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
|
|
// If there is a single occurrence of the symbolic value, replace it
|
|
// with a recurrence.
|
|
unsigned FoundIndex = Add->getNumOperands();
|
|
for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
|
|
if (Add->getOperand(i) == SymbolicName)
|
|
if (FoundIndex == e) {
|
|
FoundIndex = i;
|
|
break;
|
|
}
|
|
|
|
if (FoundIndex != Add->getNumOperands()) {
|
|
// Create an add with everything but the specified operand.
|
|
std::vector<SCEVHandle> Ops;
|
|
for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
|
|
if (i != FoundIndex)
|
|
Ops.push_back(Add->getOperand(i));
|
|
SCEVHandle Accum = SCEVAddExpr::get(Ops);
|
|
|
|
// This is not a valid addrec if the step amount is varying each
|
|
// loop iteration, but is not itself an addrec in this loop.
|
|
if (Accum->isLoopInvariant(L) ||
|
|
(isa<SCEVAddRecExpr>(Accum) &&
|
|
cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
|
|
SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
|
|
SCEVHandle PHISCEV = SCEVAddRecExpr::get(StartVal, Accum, L);
|
|
|
|
// Okay, for the entire analysis of this edge we assumed the PHI
|
|
// to be symbolic. We now need to go back and update all of the
|
|
// entries for the scalars that use the PHI (except for the PHI
|
|
// itself) to use the new analyzed value instead of the "symbolic"
|
|
// value.
|
|
Scalars.find(PN)->second = PHISCEV; // Update the PHI value
|
|
std::set<Instruction*> UpdatedInsts;
|
|
UpdatedInsts.insert(PN);
|
|
for (Value::use_iterator UI = PN->use_begin(), E = PN->use_end();
|
|
UI != E; ++UI)
|
|
UpdatePHIUserScalarEntries(cast<Instruction>(*UI), PN,
|
|
UpdatedInsts);
|
|
return PHISCEV;
|
|
}
|
|
}
|
|
}
|
|
|
|
return SymbolicName;
|
|
}
|
|
|
|
// If it's not a loop phi, we can't handle it yet.
|
|
return SCEVUnknown::get(PN);
|
|
}
|
|
|
|
/// createNodeForCast - Handle the various forms of casts that we support.
|
|
///
|
|
SCEVHandle ScalarEvolutionsImpl::createNodeForCast(CastInst *CI) {
|
|
const Type *SrcTy = CI->getOperand(0)->getType();
|
|
const Type *DestTy = CI->getType();
|
|
|
|
// If this is a noop cast (ie, conversion from int to uint), ignore it.
|
|
if (SrcTy->isLosslesslyConvertibleTo(DestTy))
|
|
return getSCEV(CI->getOperand(0));
|
|
|
|
if (SrcTy->isInteger() && DestTy->isInteger()) {
|
|
// Otherwise, if this is a truncating integer cast, we can represent this
|
|
// cast.
|
|
if (SrcTy->getPrimitiveSize() > DestTy->getPrimitiveSize())
|
|
return SCEVTruncateExpr::get(getSCEV(CI->getOperand(0)),
|
|
CI->getType()->getUnsignedVersion());
|
|
if (SrcTy->isUnsigned() &&
|
|
SrcTy->getPrimitiveSize() > DestTy->getPrimitiveSize())
|
|
return SCEVZeroExtendExpr::get(getSCEV(CI->getOperand(0)),
|
|
CI->getType()->getUnsignedVersion());
|
|
}
|
|
|
|
// If this is an sign or zero extending cast and we can prove that the value
|
|
// will never overflow, we could do similar transformations.
|
|
|
|
// Otherwise, we can't handle this cast!
|
|
return SCEVUnknown::get(CI);
|
|
}
|
|
|
|
|
|
/// createSCEV - We know that there is no SCEV for the specified value.
|
|
/// Analyze the expression.
|
|
///
|
|
SCEVHandle ScalarEvolutionsImpl::createSCEV(Value *V) {
|
|
if (Instruction *I = dyn_cast<Instruction>(V)) {
|
|
switch (I->getOpcode()) {
|
|
case Instruction::Add:
|
|
return SCEVAddExpr::get(getSCEV(I->getOperand(0)),
|
|
getSCEV(I->getOperand(1)));
|
|
case Instruction::Mul:
|
|
return SCEVMulExpr::get(getSCEV(I->getOperand(0)),
|
|
getSCEV(I->getOperand(1)));
|
|
case Instruction::Div:
|
|
if (V->getType()->isInteger() && V->getType()->isUnsigned())
|
|
return SCEVUDivExpr::get(getSCEV(I->getOperand(0)),
|
|
getSCEV(I->getOperand(1)));
|
|
break;
|
|
|
|
case Instruction::Sub:
|
|
return getMinusSCEV(getSCEV(I->getOperand(0)), getSCEV(I->getOperand(1)));
|
|
|
|
case Instruction::Shl:
|
|
// Turn shift left of a constant amount into a multiply.
|
|
if (ConstantInt *SA = dyn_cast<ConstantInt>(I->getOperand(1))) {
|
|
Constant *X = ConstantInt::get(V->getType(), 1);
|
|
X = ConstantExpr::getShl(X, SA);
|
|
return SCEVMulExpr::get(getSCEV(I->getOperand(0)), getSCEV(X));
|
|
}
|
|
break;
|
|
|
|
case Instruction::Shr:
|
|
if (ConstantUInt *SA = dyn_cast<ConstantUInt>(I->getOperand(1)))
|
|
if (V->getType()->isUnsigned()) {
|
|
Constant *X = ConstantInt::get(V->getType(), 1);
|
|
X = ConstantExpr::getShl(X, SA);
|
|
return SCEVUDivExpr::get(getSCEV(I->getOperand(0)), getSCEV(X));
|
|
}
|
|
break;
|
|
|
|
case Instruction::Cast:
|
|
return createNodeForCast(cast<CastInst>(I));
|
|
|
|
case Instruction::PHI:
|
|
return createNodeForPHI(cast<PHINode>(I));
|
|
|
|
default: // We cannot analyze this expression.
|
|
break;
|
|
}
|
|
}
|
|
|
|
return SCEVUnknown::get(V);
|
|
}
|
|
|
|
|
|
|
|
//===----------------------------------------------------------------------===//
|
|
// Iteration Count Computation Code
|
|
//
|
|
|
|
/// getIterationCount - If the specified loop has a predictable iteration
|
|
/// count, return it. Note that it is not valid to call this method on a
|
|
/// loop without a loop-invariant iteration count.
|
|
SCEVHandle ScalarEvolutionsImpl::getIterationCount(const Loop *L) {
|
|
std::map<const Loop*, SCEVHandle>::iterator I = IterationCounts.find(L);
|
|
if (I == IterationCounts.end()) {
|
|
SCEVHandle ItCount = ComputeIterationCount(L);
|
|
I = IterationCounts.insert(std::make_pair(L, ItCount)).first;
|
|
if (ItCount != UnknownValue) {
|
|
assert(ItCount->isLoopInvariant(L) &&
|
|
"Computed trip count isn't loop invariant for loop!");
|
|
++NumTripCountsComputed;
|
|
} else if (isa<PHINode>(L->getHeader()->begin())) {
|
|
// Only count loops that have phi nodes as not being computable.
|
|
++NumTripCountsNotComputed;
|
|
}
|
|
}
|
|
return I->second;
|
|
}
|
|
|
|
/// ComputeIterationCount - Compute the number of times the specified loop
|
|
/// will iterate.
|
|
SCEVHandle ScalarEvolutionsImpl::ComputeIterationCount(const Loop *L) {
|
|
// If the loop has a non-one exit block count, we can't analyze it.
|
|
if (L->getExitBlocks().size() != 1) return UnknownValue;
|
|
|
|
// Okay, there is one exit block. Try to find the condition that causes the
|
|
// loop to be exited.
|
|
BasicBlock *ExitBlock = L->getExitBlocks()[0];
|
|
|
|
BasicBlock *ExitingBlock = 0;
|
|
for (pred_iterator PI = pred_begin(ExitBlock), E = pred_end(ExitBlock);
|
|
PI != E; ++PI)
|
|
if (L->contains(*PI)) {
|
|
if (ExitingBlock == 0)
|
|
ExitingBlock = *PI;
|
|
else
|
|
return UnknownValue; // More than one block exiting!
|
|
}
|
|
assert(ExitingBlock && "No exits from loop, something is broken!");
|
|
|
|
// Okay, we've computed the exiting block. See what condition causes us to
|
|
// exit.
|
|
//
|
|
// FIXME: we should be able to handle switch instructions (with a single exit)
|
|
// FIXME: We should handle cast of int to bool as well
|
|
BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
|
|
if (ExitBr == 0) return UnknownValue;
|
|
assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
|
|
SetCondInst *ExitCond = dyn_cast<SetCondInst>(ExitBr->getCondition());
|
|
if (ExitCond == 0) return UnknownValue;
|
|
|
|
SCEVHandle LHS = getSCEV(ExitCond->getOperand(0));
|
|
SCEVHandle RHS = getSCEV(ExitCond->getOperand(1));
|
|
|
|
// Try to evaluate any dependencies out of the loop.
|
|
SCEVHandle Tmp = getSCEVAtScope(LHS, L);
|
|
if (!isa<SCEVCouldNotCompute>(Tmp)) LHS = Tmp;
|
|
Tmp = getSCEVAtScope(RHS, L);
|
|
if (!isa<SCEVCouldNotCompute>(Tmp)) RHS = Tmp;
|
|
|
|
// If the condition was exit on true, convert the condition to exit on false.
|
|
Instruction::BinaryOps Cond;
|
|
if (ExitBr->getSuccessor(1) == ExitBlock)
|
|
Cond = ExitCond->getOpcode();
|
|
else
|
|
Cond = ExitCond->getInverseCondition();
|
|
|
|
// At this point, we would like to compute how many iterations of the loop the
|
|
// predicate will return true for these inputs.
|
|
if (isa<SCEVConstant>(LHS) && !isa<SCEVConstant>(RHS)) {
|
|
// If there is a constant, force it into the RHS.
|
|
std::swap(LHS, RHS);
|
|
Cond = SetCondInst::getSwappedCondition(Cond);
|
|
}
|
|
|
|
// FIXME: think about handling pointer comparisons! i.e.:
|
|
// while (P != P+100) ++P;
|
|
|
|
// If we have a comparison of a chrec against a constant, try to use value
|
|
// ranges to answer this query.
|
|
if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
|
|
if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
|
|
if (AddRec->getLoop() == L) {
|
|
// Form the comparison range using the constant of the correct type so
|
|
// that the ConstantRange class knows to do a signed or unsigned
|
|
// comparison.
|
|
ConstantInt *CompVal = RHSC->getValue();
|
|
const Type *RealTy = ExitCond->getOperand(0)->getType();
|
|
CompVal = dyn_cast<ConstantInt>(ConstantExpr::getCast(CompVal, RealTy));
|
|
if (CompVal) {
|
|
// Form the constant range.
|
|
ConstantRange CompRange(Cond, CompVal);
|
|
|
|
// Now that we have it, if it's signed, convert it to an unsigned
|
|
// range.
|
|
if (CompRange.getLower()->getType()->isSigned()) {
|
|
const Type *NewTy = RHSC->getValue()->getType();
|
|
Constant *NewL = ConstantExpr::getCast(CompRange.getLower(), NewTy);
|
|
Constant *NewU = ConstantExpr::getCast(CompRange.getUpper(), NewTy);
|
|
CompRange = ConstantRange(NewL, NewU);
|
|
}
|
|
|
|
SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange);
|
|
if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
|
|
}
|
|
}
|
|
|
|
switch (Cond) {
|
|
case Instruction::SetNE: // while (X != Y)
|
|
// Convert to: while (X-Y != 0)
|
|
if (LHS->getType()->isInteger())
|
|
return HowFarToZero(getMinusSCEV(LHS, RHS), L);
|
|
break;
|
|
case Instruction::SetEQ:
|
|
// Convert to: while (X-Y == 0) // while (X == Y)
|
|
if (LHS->getType()->isInteger())
|
|
return HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
|
|
break;
|
|
default:
|
|
#if 0
|
|
std::cerr << "ComputeIterationCount ";
|
|
if (ExitCond->getOperand(0)->getType()->isUnsigned())
|
|
std::cerr << "[unsigned] ";
|
|
std::cerr << *LHS << " "
|
|
<< Instruction::getOpcodeName(Cond) << " " << *RHS << "\n";
|
|
#endif
|
|
break;
|
|
}
|
|
return UnknownValue;
|
|
}
|
|
|
|
/// getSCEVAtScope - Compute the value of the specified expression within the
|
|
/// indicated loop (which may be null to indicate in no loop). If the
|
|
/// expression cannot be evaluated, return UnknownValue.
|
|
SCEVHandle ScalarEvolutionsImpl::getSCEVAtScope(SCEV *V, const Loop *L) {
|
|
// FIXME: this should be turned into a virtual method on SCEV!
|
|
|
|
if (isa<SCEVConstant>(V) || isa<SCEVUnknown>(V)) return V;
|
|
if (SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
|
|
// Avoid performing the look-up in the common case where the specified
|
|
// expression has no loop-variant portions.
|
|
for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
|
|
SCEVHandle OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
|
|
if (OpAtScope != Comm->getOperand(i)) {
|
|
if (OpAtScope == UnknownValue) return UnknownValue;
|
|
// Okay, at least one of these operands is loop variant but might be
|
|
// foldable. Build a new instance of the folded commutative expression.
|
|
std::vector<SCEVHandle> NewOps(Comm->op_begin(), Comm->op_begin()+i-1);
|
|
NewOps.push_back(OpAtScope);
|
|
|
|
for (++i; i != e; ++i) {
|
|
OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
|
|
if (OpAtScope == UnknownValue) return UnknownValue;
|
|
NewOps.push_back(OpAtScope);
|
|
}
|
|
if (isa<SCEVAddExpr>(Comm))
|
|
return SCEVAddExpr::get(NewOps);
|
|
assert(isa<SCEVMulExpr>(Comm) && "Only know about add and mul!");
|
|
return SCEVMulExpr::get(NewOps);
|
|
}
|
|
}
|
|
// If we got here, all operands are loop invariant.
|
|
return Comm;
|
|
}
|
|
|
|
if (SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(V)) {
|
|
SCEVHandle LHS = getSCEVAtScope(UDiv->getLHS(), L);
|
|
if (LHS == UnknownValue) return LHS;
|
|
SCEVHandle RHS = getSCEVAtScope(UDiv->getRHS(), L);
|
|
if (RHS == UnknownValue) return RHS;
|
|
if (LHS == UDiv->getLHS() && RHS == UDiv->getRHS())
|
|
return UDiv; // must be loop invariant
|
|
return SCEVUDivExpr::get(LHS, RHS);
|
|
}
|
|
|
|
// If this is a loop recurrence for a loop that does not contain L, then we
|
|
// are dealing with the final value computed by the loop.
|
|
if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
|
|
if (!L || !AddRec->getLoop()->contains(L->getHeader())) {
|
|
// To evaluate this recurrence, we need to know how many times the AddRec
|
|
// loop iterates. Compute this now.
|
|
SCEVHandle IterationCount = getIterationCount(AddRec->getLoop());
|
|
if (IterationCount == UnknownValue) return UnknownValue;
|
|
IterationCount = getTruncateOrZeroExtend(IterationCount,
|
|
AddRec->getType());
|
|
|
|
// If the value is affine, simplify the expression evaluation to just
|
|
// Start + Step*IterationCount.
|
|
if (AddRec->isAffine())
|
|
return SCEVAddExpr::get(AddRec->getStart(),
|
|
SCEVMulExpr::get(IterationCount,
|
|
AddRec->getOperand(1)));
|
|
|
|
// Otherwise, evaluate it the hard way.
|
|
return AddRec->evaluateAtIteration(IterationCount);
|
|
}
|
|
return UnknownValue;
|
|
}
|
|
|
|
//assert(0 && "Unknown SCEV type!");
|
|
return UnknownValue;
|
|
}
|
|
|
|
|
|
/// SolveQuadraticEquation - Find the roots of the quadratic equation for the
|
|
/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
|
|
/// might be the same) or two SCEVCouldNotCompute objects.
|
|
///
|
|
static std::pair<SCEVHandle,SCEVHandle>
|
|
SolveQuadraticEquation(const SCEVAddRecExpr *AddRec) {
|
|
assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
|
|
SCEVConstant *L = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
|
|
SCEVConstant *M = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
|
|
SCEVConstant *N = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
|
|
|
|
// We currently can only solve this if the coefficients are constants.
|
|
if (!L || !M || !N) {
|
|
SCEV *CNC = new SCEVCouldNotCompute();
|
|
return std::make_pair(CNC, CNC);
|
|
}
|
|
|
|
Constant *Two = ConstantInt::get(L->getValue()->getType(), 2);
|
|
|
|
// Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
|
|
Constant *C = L->getValue();
|
|
// The B coefficient is M-N/2
|
|
Constant *B = ConstantExpr::getSub(M->getValue(),
|
|
ConstantExpr::getDiv(N->getValue(),
|
|
Two));
|
|
// The A coefficient is N/2
|
|
Constant *A = ConstantExpr::getDiv(N->getValue(), Two);
|
|
|
|
// Compute the B^2-4ac term.
|
|
Constant *SqrtTerm =
|
|
ConstantExpr::getMul(ConstantInt::get(C->getType(), 4),
|
|
ConstantExpr::getMul(A, C));
|
|
SqrtTerm = ConstantExpr::getSub(ConstantExpr::getMul(B, B), SqrtTerm);
|
|
|
|
// Compute floor(sqrt(B^2-4ac))
|
|
ConstantUInt *SqrtVal =
|
|
cast<ConstantUInt>(ConstantExpr::getCast(SqrtTerm,
|
|
SqrtTerm->getType()->getUnsignedVersion()));
|
|
uint64_t SqrtValV = SqrtVal->getValue();
|
|
uint64_t SqrtValV2 = (uint64_t)sqrt(SqrtValV);
|
|
// The square root might not be precise for arbitrary 64-bit integer
|
|
// values. Do some sanity checks to ensure it's correct.
|
|
if (SqrtValV2*SqrtValV2 > SqrtValV ||
|
|
(SqrtValV2+1)*(SqrtValV2+1) <= SqrtValV) {
|
|
SCEV *CNC = new SCEVCouldNotCompute();
|
|
return std::make_pair(CNC, CNC);
|
|
}
|
|
|
|
SqrtVal = ConstantUInt::get(Type::ULongTy, SqrtValV2);
|
|
SqrtTerm = ConstantExpr::getCast(SqrtVal, SqrtTerm->getType());
|
|
|
|
Constant *NegB = ConstantExpr::getNeg(B);
|
|
Constant *TwoA = ConstantExpr::getMul(A, Two);
|
|
|
|
// The divisions must be performed as signed divisions.
|
|
const Type *SignedTy = NegB->getType()->getSignedVersion();
|
|
NegB = ConstantExpr::getCast(NegB, SignedTy);
|
|
TwoA = ConstantExpr::getCast(TwoA, SignedTy);
|
|
SqrtTerm = ConstantExpr::getCast(SqrtTerm, SignedTy);
|
|
|
|
Constant *Solution1 =
|
|
ConstantExpr::getDiv(ConstantExpr::getAdd(NegB, SqrtTerm), TwoA);
|
|
Constant *Solution2 =
|
|
ConstantExpr::getDiv(ConstantExpr::getSub(NegB, SqrtTerm), TwoA);
|
|
return std::make_pair(SCEVUnknown::get(Solution1),
|
|
SCEVUnknown::get(Solution2));
|
|
}
|
|
|
|
/// HowFarToZero - Return the number of times a backedge comparing the specified
|
|
/// value to zero will execute. If not computable, return UnknownValue
|
|
SCEVHandle ScalarEvolutionsImpl::HowFarToZero(SCEV *V, const Loop *L) {
|
|
// If the value is a constant
|
|
if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
|
|
// If the value is already zero, the branch will execute zero times.
|
|
if (C->getValue()->isNullValue()) return C;
|
|
return UnknownValue; // Otherwise it will loop infinitely.
|
|
}
|
|
|
|
SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
|
|
if (!AddRec || AddRec->getLoop() != L)
|
|
return UnknownValue;
|
|
|
|
if (AddRec->isAffine()) {
|
|
// If this is an affine expression the execution count of this branch is
|
|
// equal to:
|
|
//
|
|
// (0 - Start/Step) iff Start % Step == 0
|
|
//
|
|
// Get the initial value for the loop.
|
|
SCEVHandle Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
|
|
SCEVHandle Step = AddRec->getOperand(1);
|
|
|
|
Step = getSCEVAtScope(Step, L->getParentLoop());
|
|
|
|
// Figure out if Start % Step == 0.
|
|
// FIXME: We should add DivExpr and RemExpr operations to our AST.
|
|
if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) {
|
|
if (StepC->getValue()->equalsInt(1)) // N % 1 == 0
|
|
return getNegativeSCEV(Start); // 0 - Start/1 == -Start
|
|
if (StepC->getValue()->isAllOnesValue()) // N % -1 == 0
|
|
return Start; // 0 - Start/-1 == Start
|
|
|
|
// Check to see if Start is divisible by SC with no remainder.
|
|
if (SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) {
|
|
ConstantInt *StartCC = StartC->getValue();
|
|
Constant *StartNegC = ConstantExpr::getNeg(StartCC);
|
|
Constant *Rem = ConstantExpr::getRem(StartNegC, StepC->getValue());
|
|
if (Rem->isNullValue()) {
|
|
Constant *Result =ConstantExpr::getDiv(StartNegC,StepC->getValue());
|
|
return SCEVUnknown::get(Result);
|
|
}
|
|
}
|
|
}
|
|
} else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) {
|
|
// If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
|
|
// the quadratic equation to solve it.
|
|
std::pair<SCEVHandle,SCEVHandle> Roots = SolveQuadraticEquation(AddRec);
|
|
SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
|
|
SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
|
|
if (R1) {
|
|
#if 0
|
|
std::cerr << "HFTZ: " << *V << " - sol#1: " << *R1
|
|
<< " sol#2: " << *R2 << "\n";
|
|
#endif
|
|
// Pick the smallest positive root value.
|
|
assert(R1->getType()->isUnsigned()&&"Didn't canonicalize to unsigned?");
|
|
if (ConstantBool *CB =
|
|
dyn_cast<ConstantBool>(ConstantExpr::getSetLT(R1->getValue(),
|
|
R2->getValue()))) {
|
|
if (CB != ConstantBool::True)
|
|
std::swap(R1, R2); // R1 is the minimum root now.
|
|
|
|
// We can only use this value if the chrec ends up with an exact zero
|
|
// value at this index. When solving for "X*X != 5", for example, we
|
|
// should not accept a root of 2.
|
|
SCEVHandle Val = AddRec->evaluateAtIteration(R1);
|
|
if (SCEVConstant *EvalVal = dyn_cast<SCEVConstant>(Val))
|
|
if (EvalVal->getValue()->isNullValue())
|
|
return R1; // We found a quadratic root!
|
|
}
|
|
}
|
|
}
|
|
|
|
return UnknownValue;
|
|
}
|
|
|
|
/// HowFarToNonZero - Return the number of times a backedge checking the
|
|
/// specified value for nonzero will execute. If not computable, return
|
|
/// UnknownValue
|
|
SCEVHandle ScalarEvolutionsImpl::HowFarToNonZero(SCEV *V, const Loop *L) {
|
|
// Loops that look like: while (X == 0) are very strange indeed. We don't
|
|
// handle them yet except for the trivial case. This could be expanded in the
|
|
// future as needed.
|
|
|
|
// If the value is a constant, check to see if it is known to be non-zero
|
|
// already. If so, the backedge will execute zero times.
|
|
if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
|
|
Constant *Zero = Constant::getNullValue(C->getValue()->getType());
|
|
Constant *NonZero = ConstantExpr::getSetNE(C->getValue(), Zero);
|
|
if (NonZero == ConstantBool::True)
|
|
return getSCEV(Zero);
|
|
return UnknownValue; // Otherwise it will loop infinitely.
|
|
}
|
|
|
|
// We could implement others, but I really doubt anyone writes loops like
|
|
// this, and if they did, they would already be constant folded.
|
|
return UnknownValue;
|
|
}
|
|
|
|
static ConstantInt *
|
|
EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, Constant *C) {
|
|
SCEVHandle InVal = SCEVConstant::get(cast<ConstantInt>(C));
|
|
SCEVHandle Val = AddRec->evaluateAtIteration(InVal);
|
|
assert(isa<SCEVConstant>(Val) &&
|
|
"Evaluation of SCEV at constant didn't fold correctly?");
|
|
return cast<SCEVConstant>(Val)->getValue();
|
|
}
|
|
|
|
|
|
/// getNumIterationsInRange - Return the number of iterations of this loop that
|
|
/// produce values in the specified constant range. Another way of looking at
|
|
/// this is that it returns the first iteration number where the value is not in
|
|
/// the condition, thus computing the exit count. If the iteration count can't
|
|
/// be computed, an instance of SCEVCouldNotCompute is returned.
|
|
SCEVHandle SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range) const {
|
|
if (Range.isFullSet()) // Infinite loop.
|
|
return new SCEVCouldNotCompute();
|
|
|
|
// If the start is a non-zero constant, shift the range to simplify things.
|
|
if (SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
|
|
if (!SC->getValue()->isNullValue()) {
|
|
std::vector<SCEVHandle> Operands(op_begin(), op_end());
|
|
Operands[0] = getIntegerSCEV(0, SC->getType());
|
|
SCEVHandle Shifted = SCEVAddRecExpr::get(Operands, getLoop());
|
|
if (SCEVAddRecExpr *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted))
|
|
return ShiftedAddRec->getNumIterationsInRange(
|
|
Range.subtract(SC->getValue()));
|
|
// This is strange and shouldn't happen.
|
|
return new SCEVCouldNotCompute();
|
|
}
|
|
|
|
// The only time we can solve this is when we have all constant indices.
|
|
// Otherwise, we cannot determine the overflow conditions.
|
|
for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
|
|
if (!isa<SCEVConstant>(getOperand(i)))
|
|
return new SCEVCouldNotCompute();
|
|
|
|
|
|
// Okay at this point we know that all elements of the chrec are constants and
|
|
// that the start element is zero.
|
|
|
|
// First check to see if the range contains zero. If not, the first
|
|
// iteration exits.
|
|
ConstantInt *Zero = ConstantInt::get(getType(), 0);
|
|
if (!Range.contains(Zero)) return SCEVConstant::get(Zero);
|
|
|
|
if (isAffine()) {
|
|
// If this is an affine expression then we have this situation:
|
|
// Solve {0,+,A} in Range === Ax in Range
|
|
|
|
// Since we know that zero is in the range, we know that the upper value of
|
|
// the range must be the first possible exit value. Also note that we
|
|
// already checked for a full range.
|
|
ConstantInt *Upper = cast<ConstantInt>(Range.getUpper());
|
|
ConstantInt *A = cast<SCEVConstant>(getOperand(1))->getValue();
|
|
ConstantInt *One = ConstantInt::get(getType(), 1);
|
|
|
|
// The exit value should be (Upper+A-1)/A.
|
|
Constant *ExitValue = Upper;
|
|
if (A != One) {
|
|
ExitValue = ConstantExpr::getSub(ConstantExpr::getAdd(Upper, A), One);
|
|
ExitValue = ConstantExpr::getDiv(ExitValue, A);
|
|
}
|
|
assert(isa<ConstantInt>(ExitValue) &&
|
|
"Constant folding of integers not implemented?");
|
|
|
|
// Evaluate at the exit value. If we really did fall out of the valid
|
|
// range, then we computed our trip count, otherwise wrap around or other
|
|
// things must have happened.
|
|
ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue);
|
|
if (Range.contains(Val))
|
|
return new SCEVCouldNotCompute(); // Something strange happened
|
|
|
|
// Ensure that the previous value is in the range. This is a sanity check.
|
|
assert(Range.contains(EvaluateConstantChrecAtConstant(this,
|
|
ConstantExpr::getSub(ExitValue, One))) &&
|
|
"Linear scev computation is off in a bad way!");
|
|
return SCEVConstant::get(cast<ConstantInt>(ExitValue));
|
|
} else if (isQuadratic()) {
|
|
// If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
|
|
// quadratic equation to solve it. To do this, we must frame our problem in
|
|
// terms of figuring out when zero is crossed, instead of when
|
|
// Range.getUpper() is crossed.
|
|
std::vector<SCEVHandle> NewOps(op_begin(), op_end());
|
|
NewOps[0] = getNegativeSCEV(SCEVUnknown::get(Range.getUpper()));
|
|
SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewOps, getLoop());
|
|
|
|
// Next, solve the constructed addrec
|
|
std::pair<SCEVHandle,SCEVHandle> Roots =
|
|
SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec));
|
|
SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
|
|
SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
|
|
if (R1) {
|
|
// Pick the smallest positive root value.
|
|
assert(R1->getType()->isUnsigned() && "Didn't canonicalize to unsigned?");
|
|
if (ConstantBool *CB =
|
|
dyn_cast<ConstantBool>(ConstantExpr::getSetLT(R1->getValue(),
|
|
R2->getValue()))) {
|
|
if (CB != ConstantBool::True)
|
|
std::swap(R1, R2); // R1 is the minimum root now.
|
|
|
|
// Make sure the root is not off by one. The returned iteration should
|
|
// not be in the range, but the previous one should be. When solving
|
|
// for "X*X < 5", for example, we should not return a root of 2.
|
|
ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
|
|
R1->getValue());
|
|
if (Range.contains(R1Val)) {
|
|
// The next iteration must be out of the range...
|
|
Constant *NextVal =
|
|
ConstantExpr::getAdd(R1->getValue(),
|
|
ConstantInt::get(R1->getType(), 1));
|
|
|
|
R1Val = EvaluateConstantChrecAtConstant(this, NextVal);
|
|
if (!Range.contains(R1Val))
|
|
return SCEVUnknown::get(NextVal);
|
|
return new SCEVCouldNotCompute(); // Something strange happened
|
|
}
|
|
|
|
// If R1 was not in the range, then it is a good return value. Make
|
|
// sure that R1-1 WAS in the range though, just in case.
|
|
Constant *NextVal =
|
|
ConstantExpr::getSub(R1->getValue(),
|
|
ConstantInt::get(R1->getType(), 1));
|
|
R1Val = EvaluateConstantChrecAtConstant(this, NextVal);
|
|
if (Range.contains(R1Val))
|
|
return R1;
|
|
return new SCEVCouldNotCompute(); // Something strange happened
|
|
}
|
|
}
|
|
}
|
|
|
|
// Fallback, if this is a general polynomial, figure out the progression
|
|
// through brute force: evaluate until we find an iteration that fails the
|
|
// test. This is likely to be slow, but getting an accurate trip count is
|
|
// incredibly important, we will be able to simplify the exit test a lot, and
|
|
// we are almost guaranteed to get a trip count in this case.
|
|
ConstantInt *TestVal = ConstantInt::get(getType(), 0);
|
|
ConstantInt *One = ConstantInt::get(getType(), 1);
|
|
ConstantInt *EndVal = TestVal; // Stop when we wrap around.
|
|
do {
|
|
++NumBruteForceEvaluations;
|
|
SCEVHandle Val = evaluateAtIteration(SCEVConstant::get(TestVal));
|
|
if (!isa<SCEVConstant>(Val)) // This shouldn't happen.
|
|
return new SCEVCouldNotCompute();
|
|
|
|
// Check to see if we found the value!
|
|
if (!Range.contains(cast<SCEVConstant>(Val)->getValue()))
|
|
return SCEVConstant::get(TestVal);
|
|
|
|
// Increment to test the next index.
|
|
TestVal = cast<ConstantInt>(ConstantExpr::getAdd(TestVal, One));
|
|
} while (TestVal != EndVal);
|
|
|
|
return new SCEVCouldNotCompute();
|
|
}
|
|
|
|
|
|
|
|
//===----------------------------------------------------------------------===//
|
|
// ScalarEvolution Class Implementation
|
|
//===----------------------------------------------------------------------===//
|
|
|
|
bool ScalarEvolution::runOnFunction(Function &F) {
|
|
Impl = new ScalarEvolutionsImpl(F, getAnalysis<LoopInfo>());
|
|
return false;
|
|
}
|
|
|
|
void ScalarEvolution::releaseMemory() {
|
|
delete (ScalarEvolutionsImpl*)Impl;
|
|
Impl = 0;
|
|
}
|
|
|
|
void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
|
|
AU.setPreservesAll();
|
|
AU.addRequiredID(LoopSimplifyID);
|
|
AU.addRequiredTransitive<LoopInfo>();
|
|
}
|
|
|
|
SCEVHandle ScalarEvolution::getSCEV(Value *V) const {
|
|
return ((ScalarEvolutionsImpl*)Impl)->getSCEV(V);
|
|
}
|
|
|
|
SCEVHandle ScalarEvolution::getIterationCount(const Loop *L) const {
|
|
return ((ScalarEvolutionsImpl*)Impl)->getIterationCount(L);
|
|
}
|
|
|
|
bool ScalarEvolution::hasLoopInvariantIterationCount(const Loop *L) const {
|
|
return !isa<SCEVCouldNotCompute>(getIterationCount(L));
|
|
}
|
|
|
|
SCEVHandle ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) const {
|
|
return ((ScalarEvolutionsImpl*)Impl)->getSCEVAtScope(getSCEV(V), L);
|
|
}
|
|
|
|
void ScalarEvolution::deleteInstructionFromRecords(Instruction *I) const {
|
|
return ((ScalarEvolutionsImpl*)Impl)->deleteInstructionFromRecords(I);
|
|
}
|
|
|
|
|
|
/// shouldSubstituteIndVar - Return true if we should perform induction variable
|
|
/// substitution for this variable. This is a hack because we don't have a
|
|
/// strength reduction pass yet. When we do we will promote all vars, because
|
|
/// we can strength reduce them later as desired.
|
|
bool ScalarEvolution::shouldSubstituteIndVar(const SCEV *S) const {
|
|
// Don't substitute high degree polynomials.
|
|
if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S))
|
|
if (AddRec->getNumOperands() > 3) return false;
|
|
return true;
|
|
}
|
|
|
|
|
|
static void PrintLoopInfo(std::ostream &OS, const ScalarEvolution *SE,
|
|
const Loop *L) {
|
|
// Print all inner loops first
|
|
for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
|
|
PrintLoopInfo(OS, SE, *I);
|
|
|
|
std::cerr << "Loop " << L->getHeader()->getName() << ": ";
|
|
if (L->getExitBlocks().size() != 1)
|
|
std::cerr << "<multiple exits> ";
|
|
|
|
if (SE->hasLoopInvariantIterationCount(L)) {
|
|
std::cerr << *SE->getIterationCount(L) << " iterations! ";
|
|
} else {
|
|
std::cerr << "Unpredictable iteration count. ";
|
|
}
|
|
|
|
std::cerr << "\n";
|
|
}
|
|
|
|
void ScalarEvolution::print(std::ostream &OS) const {
|
|
Function &F = ((ScalarEvolutionsImpl*)Impl)->F;
|
|
LoopInfo &LI = ((ScalarEvolutionsImpl*)Impl)->LI;
|
|
|
|
OS << "Classifying expressions for: " << F.getName() << "\n";
|
|
for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
|
|
if ((*I)->getType()->isInteger()) {
|
|
OS << **I;
|
|
OS << " --> ";
|
|
SCEVHandle SV = getSCEV(*I);
|
|
SV->print(OS);
|
|
OS << "\t\t";
|
|
|
|
if ((*I)->getType()->isIntegral()) {
|
|
ConstantRange Bounds = SV->getValueRange();
|
|
if (!Bounds.isFullSet())
|
|
OS << "Bounds: " << Bounds << " ";
|
|
}
|
|
|
|
if (const Loop *L = LI.getLoopFor((*I)->getParent())) {
|
|
OS << "Exits: ";
|
|
SCEVHandle ExitValue = getSCEVAtScope(*I, L->getParentLoop());
|
|
if (isa<SCEVCouldNotCompute>(ExitValue)) {
|
|
OS << "<<Unknown>>";
|
|
} else {
|
|
OS << *ExitValue;
|
|
}
|
|
}
|
|
|
|
|
|
OS << "\n";
|
|
}
|
|
|
|
OS << "Determining loop execution counts for: " << F.getName() << "\n";
|
|
for (LoopInfo::iterator I = LI.begin(), E = LI.end(); I != E; ++I)
|
|
PrintLoopInfo(OS, this, *I);
|
|
}
|
|
|
|
//===----------------------------------------------------------------------===//
|
|
// ScalarEvolutionRewriter Class Implementation
|
|
//===----------------------------------------------------------------------===//
|
|
|
|
Value *ScalarEvolutionRewriter::
|
|
GetOrInsertCanonicalInductionVariable(const Loop *L, const Type *Ty) {
|
|
assert((Ty->isInteger() || Ty->isFloatingPoint()) &&
|
|
"Can only insert integer or floating point induction variables!");
|
|
|
|
// Check to see if we already inserted one.
|
|
SCEVHandle H = SCEVAddRecExpr::get(getIntegerSCEV(0, Ty),
|
|
getIntegerSCEV(1, Ty), L);
|
|
return ExpandCodeFor(H, 0, Ty);
|
|
}
|
|
|
|
/// ExpandCodeFor - Insert code to directly compute the specified SCEV
|
|
/// expression into the program. The inserted code is inserted into the
|
|
/// specified block.
|
|
Value *ScalarEvolutionRewriter::ExpandCodeFor(SCEVHandle SH,
|
|
Instruction *InsertPt,
|
|
const Type *Ty) {
|
|
std::map<SCEVHandle, Value*>::iterator ExistVal =InsertedExpressions.find(SH);
|
|
Value *V;
|
|
if (ExistVal != InsertedExpressions.end()) {
|
|
V = ExistVal->second;
|
|
} else {
|
|
// Ask the recurrence object to expand the code for itself.
|
|
V = SH->expandCodeFor(*this, InsertPt);
|
|
// Cache the generated result.
|
|
InsertedExpressions.insert(std::make_pair(SH, V));
|
|
}
|
|
|
|
if (Ty == 0 || V->getType() == Ty)
|
|
return V;
|
|
if (Constant *C = dyn_cast<Constant>(V))
|
|
return ConstantExpr::getCast(C, Ty);
|
|
else if (Instruction *I = dyn_cast<Instruction>(V)) {
|
|
// FIXME: check to see if there is already a cast!
|
|
BasicBlock::iterator IP = I; ++IP;
|
|
if (InvokeInst *II = dyn_cast<InvokeInst>(I))
|
|
IP = II->getNormalDest()->begin();
|
|
while (isa<PHINode>(IP)) ++IP;
|
|
return new CastInst(V, Ty, V->getName(), IP);
|
|
} else {
|
|
// FIXME: check to see if there is already a cast!
|
|
return new CastInst(V, Ty, V->getName(), InsertPt);
|
|
}
|
|
}
|