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//===- ScalarEvolution.cpp - Scalar Evolution Analysis ----------*- C++ -*-===//
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// The LLVM Compiler Infrastructure
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// This file is distributed under the University of Illinois Open Source
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// License. See LICENSE.TXT for details.
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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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// 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. We only create one SCEV of a particular shape, so
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// pointer-comparisons for equality are legal.
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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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// 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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// 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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// 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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// There are several good references for the techniques used in this analysis.
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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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// On computational properties of chains of recurrences
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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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// Efficient Symbolic Analysis for Optimizing Compilers
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// Robert A. van Engelen
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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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#define DEBUG_TYPE "scalar-evolution"
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#include "llvm/Analysis/ScalarEvolutionExpressions.h"
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#include "llvm/Constants.h"
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#include "llvm/DerivedTypes.h"
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#include "llvm/GlobalVariable.h"
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#include "llvm/GlobalAlias.h"
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#include "llvm/Instructions.h"
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#include "llvm/LLVMContext.h"
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#include "llvm/Operator.h"
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#include "llvm/Analysis/ConstantFolding.h"
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#include "llvm/Analysis/Dominators.h"
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#include "llvm/Analysis/LoopInfo.h"
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#include "llvm/Analysis/ValueTracking.h"
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#include "llvm/Assembly/Writer.h"
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#include "llvm/Target/TargetData.h"
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#include "llvm/Support/CommandLine.h"
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#include "llvm/Support/ConstantRange.h"
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#include "llvm/Support/Debug.h"
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#include "llvm/Support/ErrorHandling.h"
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#include "llvm/Support/GetElementPtrTypeIterator.h"
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#include "llvm/Support/InstIterator.h"
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#include "llvm/Support/MathExtras.h"
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#include "llvm/Support/raw_ostream.h"
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#include "llvm/ADT/Statistic.h"
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#include "llvm/ADT/STLExtras.h"
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#include "llvm/ADT/SmallPtrSet.h"
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STATISTIC(NumArrayLenItCounts,
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"Number of trip counts computed with array length");
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STATISTIC(NumTripCountsComputed,
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"Number of loops with predictable loop counts");
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STATISTIC(NumTripCountsNotComputed,
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"Number of loops without predictable loop counts");
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STATISTIC(NumBruteForceTripCountsComputed,
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"Number of loops with trip counts computed by force");
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static cl::opt<unsigned>
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MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
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cl::desc("Maximum number of iterations SCEV will "
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"symbolically execute a constant "
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static RegisterPass<ScalarEvolution>
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R("scalar-evolution", "Scalar Evolution Analysis", false, true);
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char ScalarEvolution::ID = 0;
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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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void SCEV::dump() const {
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bool SCEV::isZero() const {
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if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
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return SC->getValue()->isZero();
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bool SCEV::isOne() const {
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if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
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return SC->getValue()->isOne();
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bool SCEV::isAllOnesValue() const {
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if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
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return SC->getValue()->isAllOnesValue();
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SCEVCouldNotCompute::SCEVCouldNotCompute() :
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SCEV(FoldingSetNodeID(), scCouldNotCompute) {}
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bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const {
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llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
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const Type *SCEVCouldNotCompute::getType() const {
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llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
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bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const {
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llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
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bool SCEVCouldNotCompute::hasOperand(const SCEV *) const {
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llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
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void SCEVCouldNotCompute::print(raw_ostream &OS) const {
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OS << "***COULDNOTCOMPUTE***";
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bool SCEVCouldNotCompute::classof(const SCEV *S) {
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return S->getSCEVType() == scCouldNotCompute;
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const SCEV *ScalarEvolution::getConstant(ConstantInt *V) {
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ID.AddInteger(scConstant);
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if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
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SCEV *S = SCEVAllocator.Allocate<SCEVConstant>();
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new (S) SCEVConstant(ID, V);
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UniqueSCEVs.InsertNode(S, IP);
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const SCEV *ScalarEvolution::getConstant(const APInt& Val) {
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return getConstant(ConstantInt::get(getContext(), Val));
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ScalarEvolution::getConstant(const Type *Ty, uint64_t V, bool isSigned) {
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ConstantInt::get(cast<IntegerType>(Ty), V, isSigned));
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const Type *SCEVConstant::getType() const { return V->getType(); }
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void SCEVConstant::print(raw_ostream &OS) const {
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WriteAsOperand(OS, V, false);
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SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeID &ID,
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unsigned SCEVTy, const SCEV *op, const Type *ty)
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: SCEV(ID, SCEVTy), Op(op), Ty(ty) {}
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bool SCEVCastExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
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return Op->dominates(BB, DT);
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bool SCEVCastExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const {
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return Op->properlyDominates(BB, DT);
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SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeID &ID,
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const SCEV *op, const Type *ty)
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: SCEVCastExpr(ID, scTruncate, op, ty) {
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assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
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(Ty->isIntegerTy() || Ty->isPointerTy()) &&
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"Cannot truncate non-integer value!");
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void SCEVTruncateExpr::print(raw_ostream &OS) const {
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OS << "(trunc " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
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SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeID &ID,
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const SCEV *op, const Type *ty)
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: SCEVCastExpr(ID, scZeroExtend, op, ty) {
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assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
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(Ty->isIntegerTy() || Ty->isPointerTy()) &&
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"Cannot zero extend non-integer value!");
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void SCEVZeroExtendExpr::print(raw_ostream &OS) const {
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OS << "(zext " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
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SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeID &ID,
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const SCEV *op, const Type *ty)
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: SCEVCastExpr(ID, scSignExtend, op, ty) {
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assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
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(Ty->isIntegerTy() || Ty->isPointerTy()) &&
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"Cannot sign extend non-integer value!");
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void SCEVSignExtendExpr::print(raw_ostream &OS) const {
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OS << "(sext " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
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void SCEVCommutativeExpr::print(raw_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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bool SCEVNAryExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
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for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
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if (!getOperand(i)->dominates(BB, DT))
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bool SCEVNAryExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const {
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for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
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if (!getOperand(i)->properlyDominates(BB, DT))
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bool SCEVUDivExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
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return LHS->dominates(BB, DT) && RHS->dominates(BB, DT);
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bool SCEVUDivExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const {
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return LHS->properlyDominates(BB, DT) && RHS->properlyDominates(BB, DT);
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void SCEVUDivExpr::print(raw_ostream &OS) const {
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OS << "(" << *LHS << " /u " << *RHS << ")";
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const Type *SCEVUDivExpr::getType() const {
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// In most cases the types of LHS and RHS will be the same, but in some
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// crazy cases one or the other may be a pointer. ScalarEvolution doesn't
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// depend on the type for correctness, but handling types carefully can
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// avoid extra casts in the SCEVExpander. The LHS is more likely to be
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// a pointer type than the RHS, so use the RHS' type here.
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return RHS->getType();
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bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const {
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// Add recurrences are never invariant in the function-body (null loop).
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// This recurrence is variant w.r.t. QueryLoop if QueryLoop contains L.
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if (QueryLoop->contains(L))
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// This recurrence is variant w.r.t. QueryLoop if any of its operands
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for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
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if (!getOperand(i)->isLoopInvariant(QueryLoop))
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// Otherwise it's loop-invariant.
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SCEVAddRecExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
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return DT->dominates(L->getHeader(), BB) &&
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SCEVNAryExpr::dominates(BB, DT);
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SCEVAddRecExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const {
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// This uses a "dominates" query instead of "properly dominates" query because
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// the instruction which produces the addrec's value is a PHI, and a PHI
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// effectively properly dominates its entire containing block.
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return DT->dominates(L->getHeader(), BB) &&
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SCEVNAryExpr::properlyDominates(BB, DT);
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void SCEVAddRecExpr::print(raw_ostream &OS) const {
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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 << ",+," << *Operands[i];
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WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
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bool SCEVUnknown::isLoopInvariant(const Loop *L) const {
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// All non-instruction values are loop invariant. All instructions are loop
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// invariant if they are not contained in the specified loop.
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// Instructions are never considered invariant in the function body
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// (null loop) because they are defined within the "loop".
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if (Instruction *I = dyn_cast<Instruction>(V))
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return L && !L->contains(I);
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bool SCEVUnknown::dominates(BasicBlock *BB, DominatorTree *DT) const {
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if (Instruction *I = dyn_cast<Instruction>(getValue()))
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return DT->dominates(I->getParent(), BB);
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bool SCEVUnknown::properlyDominates(BasicBlock *BB, DominatorTree *DT) const {
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if (Instruction *I = dyn_cast<Instruction>(getValue()))
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return DT->properlyDominates(I->getParent(), BB);
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const Type *SCEVUnknown::getType() const {
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bool SCEVUnknown::isSizeOf(const Type *&AllocTy) const {
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if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(V))
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if (VCE->getOpcode() == Instruction::PtrToInt)
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if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
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if (CE->getOpcode() == Instruction::GetElementPtr &&
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CE->getOperand(0)->isNullValue() &&
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CE->getNumOperands() == 2)
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if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1)))
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AllocTy = cast<PointerType>(CE->getOperand(0)->getType())
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bool SCEVUnknown::isAlignOf(const Type *&AllocTy) const {
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if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(V))
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if (VCE->getOpcode() == Instruction::PtrToInt)
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if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
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if (CE->getOpcode() == Instruction::GetElementPtr &&
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CE->getOperand(0)->isNullValue()) {
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cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
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if (const StructType *STy = dyn_cast<StructType>(Ty))
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if (!STy->isPacked() &&
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CE->getNumOperands() == 3 &&
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CE->getOperand(1)->isNullValue()) {
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if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2)))
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STy->getNumElements() == 2 &&
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STy->getElementType(0)->isIntegerTy(1)) {
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AllocTy = STy->getElementType(1);
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bool SCEVUnknown::isOffsetOf(const Type *&CTy, Constant *&FieldNo) const {
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if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(V))
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if (VCE->getOpcode() == Instruction::PtrToInt)
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if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
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if (CE->getOpcode() == Instruction::GetElementPtr &&
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CE->getNumOperands() == 3 &&
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CE->getOperand(0)->isNullValue() &&
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CE->getOperand(1)->isNullValue()) {
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cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
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// Ignore vector types here so that ScalarEvolutionExpander doesn't
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// emit getelementptrs that index into vectors.
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if (Ty->isStructTy() || Ty->isArrayTy()) {
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FieldNo = CE->getOperand(2);
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void SCEVUnknown::print(raw_ostream &OS) const {
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if (isSizeOf(AllocTy)) {
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OS << "sizeof(" << *AllocTy << ")";
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if (isAlignOf(AllocTy)) {
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OS << "alignof(" << *AllocTy << ")";
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if (isOffsetOf(CTy, FieldNo)) {
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OS << "offsetof(" << *CTy << ", ";
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WriteAsOperand(OS, FieldNo, false);
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// Otherwise just print it normally.
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WriteAsOperand(OS, V, false);
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//===----------------------------------------------------------------------===//
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//===----------------------------------------------------------------------===//
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static bool CompareTypes(const Type *A, const Type *B) {
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if (A->getTypeID() != B->getTypeID())
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return A->getTypeID() < B->getTypeID();
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if (const IntegerType *AI = dyn_cast<IntegerType>(A)) {
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const IntegerType *BI = cast<IntegerType>(B);
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return AI->getBitWidth() < BI->getBitWidth();
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if (const PointerType *AI = dyn_cast<PointerType>(A)) {
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const PointerType *BI = cast<PointerType>(B);
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return CompareTypes(AI->getElementType(), BI->getElementType());
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if (const ArrayType *AI = dyn_cast<ArrayType>(A)) {
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const ArrayType *BI = cast<ArrayType>(B);
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if (AI->getNumElements() != BI->getNumElements())
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return AI->getNumElements() < BI->getNumElements();
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return CompareTypes(AI->getElementType(), BI->getElementType());
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if (const VectorType *AI = dyn_cast<VectorType>(A)) {
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const VectorType *BI = cast<VectorType>(B);
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if (AI->getNumElements() != BI->getNumElements())
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return AI->getNumElements() < BI->getNumElements();
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return CompareTypes(AI->getElementType(), BI->getElementType());
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if (const StructType *AI = dyn_cast<StructType>(A)) {
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const StructType *BI = cast<StructType>(B);
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if (AI->getNumElements() != BI->getNumElements())
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return AI->getNumElements() < BI->getNumElements();
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for (unsigned i = 0, e = AI->getNumElements(); i != e; ++i)
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if (CompareTypes(AI->getElementType(i), BI->getElementType(i)) ||
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CompareTypes(BI->getElementType(i), AI->getElementType(i)))
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return CompareTypes(AI->getElementType(i), BI->getElementType(i));
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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. This comparator is used to canonicalize
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class SCEVComplexityCompare {
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explicit SCEVComplexityCompare(LoopInfo *li) : LI(li) {}
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bool operator()(const SCEV *LHS, const SCEV *RHS) const {
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// Fast-path: SCEVs are uniqued so we can do a quick equality check.
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// Primarily, sort the SCEVs by their getSCEVType().
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if (LHS->getSCEVType() != RHS->getSCEVType())
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return LHS->getSCEVType() < RHS->getSCEVType();
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// Aside from the getSCEVType() ordering, the particular ordering
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// isn't very important except that it's beneficial to be consistent,
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// so that (a + b) and (b + a) don't end up as different expressions.
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// Sort SCEVUnknown values with some loose heuristics. TODO: This is
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// not as complete as it could be.
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if (const SCEVUnknown *LU = dyn_cast<SCEVUnknown>(LHS)) {
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const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
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// Order pointer values after integer values. This helps SCEVExpander
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if (LU->getType()->isPointerTy() && !RU->getType()->isPointerTy())
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if (RU->getType()->isPointerTy() && !LU->getType()->isPointerTy())
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// Compare getValueID values.
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if (LU->getValue()->getValueID() != RU->getValue()->getValueID())
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return LU->getValue()->getValueID() < RU->getValue()->getValueID();
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// Sort arguments by their position.
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if (const Argument *LA = dyn_cast<Argument>(LU->getValue())) {
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const Argument *RA = cast<Argument>(RU->getValue());
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return LA->getArgNo() < RA->getArgNo();
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// For instructions, compare their loop depth, and their opcode.
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// This is pretty loose.
538
if (Instruction *LV = dyn_cast<Instruction>(LU->getValue())) {
539
Instruction *RV = cast<Instruction>(RU->getValue());
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// Compare loop depths.
542
if (LI->getLoopDepth(LV->getParent()) !=
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LI->getLoopDepth(RV->getParent()))
544
return LI->getLoopDepth(LV->getParent()) <
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LI->getLoopDepth(RV->getParent());
548
if (LV->getOpcode() != RV->getOpcode())
549
return LV->getOpcode() < RV->getOpcode();
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// Compare the number of operands.
552
if (LV->getNumOperands() != RV->getNumOperands())
553
return LV->getNumOperands() < RV->getNumOperands();
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// Compare constant values.
560
if (const SCEVConstant *LC = dyn_cast<SCEVConstant>(LHS)) {
561
const SCEVConstant *RC = cast<SCEVConstant>(RHS);
562
if (LC->getValue()->getBitWidth() != RC->getValue()->getBitWidth())
563
return LC->getValue()->getBitWidth() < RC->getValue()->getBitWidth();
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return LC->getValue()->getValue().ult(RC->getValue()->getValue());
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// Compare addrec loop depths.
568
if (const SCEVAddRecExpr *LA = dyn_cast<SCEVAddRecExpr>(LHS)) {
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const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS);
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if (LA->getLoop()->getLoopDepth() != RA->getLoop()->getLoopDepth())
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return LA->getLoop()->getLoopDepth() < RA->getLoop()->getLoopDepth();
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// Lexicographically compare n-ary expressions.
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if (const SCEVNAryExpr *LC = dyn_cast<SCEVNAryExpr>(LHS)) {
576
const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
577
for (unsigned i = 0, e = LC->getNumOperands(); i != e; ++i) {
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if (i >= RC->getNumOperands())
580
if (operator()(LC->getOperand(i), RC->getOperand(i)))
582
if (operator()(RC->getOperand(i), LC->getOperand(i)))
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return LC->getNumOperands() < RC->getNumOperands();
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// Lexicographically compare udiv expressions.
589
if (const SCEVUDivExpr *LC = dyn_cast<SCEVUDivExpr>(LHS)) {
590
const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
591
if (operator()(LC->getLHS(), RC->getLHS()))
593
if (operator()(RC->getLHS(), LC->getLHS()))
595
if (operator()(LC->getRHS(), RC->getRHS()))
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if (operator()(RC->getRHS(), LC->getRHS()))
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// Compare cast expressions by operand.
603
if (const SCEVCastExpr *LC = dyn_cast<SCEVCastExpr>(LHS)) {
604
const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
605
return operator()(LC->getOperand(), RC->getOperand());
608
llvm_unreachable("Unknown SCEV kind!");
614
/// GroupByComplexity - Given a list of SCEV objects, order them by their
615
/// complexity, and group objects of the same complexity together by value.
616
/// When this routine is finished, we know that any duplicates in the vector are
617
/// consecutive and that complexity is monotonically increasing.
619
/// Note that we go take special precautions to ensure that we get deterministic
620
/// results from this routine. In other words, we don't want the results of
621
/// this to depend on where the addresses of various SCEV objects happened to
624
static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops,
626
if (Ops.size() < 2) return; // Noop
627
if (Ops.size() == 2) {
628
// This is the common case, which also happens to be trivially simple.
630
if (SCEVComplexityCompare(LI)(Ops[1], Ops[0]))
631
std::swap(Ops[0], Ops[1]);
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// Do the rough sort by complexity.
636
std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI));
638
// Now that we are sorted by complexity, group elements of the same
639
// complexity. Note that this is, at worst, N^2, but the vector is likely to
640
// be extremely short in practice. Note that we take this approach because we
641
// do not want to depend on the addresses of the objects we are grouping.
642
for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
643
const SCEV *S = Ops[i];
644
unsigned Complexity = S->getSCEVType();
646
// If there are any objects of the same complexity and same value as this
648
for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
649
if (Ops[j] == S) { // Found a duplicate.
650
// Move it to immediately after i'th element.
651
std::swap(Ops[i+1], Ops[j]);
652
++i; // no need to rescan it.
653
if (i == e-2) return; // Done!
661
//===----------------------------------------------------------------------===//
662
// Simple SCEV method implementations
663
//===----------------------------------------------------------------------===//
665
/// BinomialCoefficient - Compute BC(It, K). The result has width W.
667
static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K,
669
const Type* ResultTy) {
670
// Handle the simplest case efficiently.
672
return SE.getTruncateOrZeroExtend(It, ResultTy);
674
// We are using the following formula for BC(It, K):
676
// BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
678
// Suppose, W is the bitwidth of the return value. We must be prepared for
679
// overflow. Hence, we must assure that the result of our computation is
680
// equal to the accurate one modulo 2^W. Unfortunately, division isn't
681
// safe in modular arithmetic.
683
// However, this code doesn't use exactly that formula; the formula it uses
684
// is something like the following, where T is the number of factors of 2 in
685
// K! (i.e. trailing zeros in the binary representation of K!), and ^ is
688
// BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
690
// This formula is trivially equivalent to the previous formula. However,
691
// this formula can be implemented much more efficiently. The trick is that
692
// K! / 2^T is odd, and exact division by an odd number *is* safe in modular
693
// arithmetic. To do exact division in modular arithmetic, all we have
694
// to do is multiply by the inverse. Therefore, this step can be done at
697
// The next issue is how to safely do the division by 2^T. The way this
698
// is done is by doing the multiplication step at a width of at least W + T
699
// bits. This way, the bottom W+T bits of the product are accurate. Then,
700
// when we perform the division by 2^T (which is equivalent to a right shift
701
// by T), the bottom W bits are accurate. Extra bits are okay; they'll get
702
// truncated out after the division by 2^T.
704
// In comparison to just directly using the first formula, this technique
705
// is much more efficient; using the first formula requires W * K bits,
706
// but this formula less than W + K bits. Also, the first formula requires
707
// a division step, whereas this formula only requires multiplies and shifts.
709
// It doesn't matter whether the subtraction step is done in the calculation
710
// width or the input iteration count's width; if the subtraction overflows,
711
// the result must be zero anyway. We prefer here to do it in the width of
712
// the induction variable because it helps a lot for certain cases; CodeGen
713
// isn't smart enough to ignore the overflow, which leads to much less
714
// efficient code if the width of the subtraction is wider than the native
717
// (It's possible to not widen at all by pulling out factors of 2 before
718
// the multiplication; for example, K=2 can be calculated as
719
// It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
720
// extra arithmetic, so it's not an obvious win, and it gets
721
// much more complicated for K > 3.)
723
// Protection from insane SCEVs; this bound is conservative,
724
// but it probably doesn't matter.
726
return SE.getCouldNotCompute();
728
unsigned W = SE.getTypeSizeInBits(ResultTy);
730
// Calculate K! / 2^T and T; we divide out the factors of two before
731
// multiplying for calculating K! / 2^T to avoid overflow.
732
// Other overflow doesn't matter because we only care about the bottom
733
// W bits of the result.
734
APInt OddFactorial(W, 1);
736
for (unsigned i = 3; i <= K; ++i) {
738
unsigned TwoFactors = Mult.countTrailingZeros();
740
Mult = Mult.lshr(TwoFactors);
741
OddFactorial *= Mult;
744
// We need at least W + T bits for the multiplication step
745
unsigned CalculationBits = W + T;
747
// Calculate 2^T, at width T+W.
748
APInt DivFactor = APInt(CalculationBits, 1).shl(T);
750
// Calculate the multiplicative inverse of K! / 2^T;
751
// this multiplication factor will perform the exact division by
753
APInt Mod = APInt::getSignedMinValue(W+1);
754
APInt MultiplyFactor = OddFactorial.zext(W+1);
755
MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
756
MultiplyFactor = MultiplyFactor.trunc(W);
758
// Calculate the product, at width T+W
759
const IntegerType *CalculationTy = IntegerType::get(SE.getContext(),
761
const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
762
for (unsigned i = 1; i != K; ++i) {
763
const SCEV *S = SE.getMinusSCEV(It, SE.getIntegerSCEV(i, It->getType()));
764
Dividend = SE.getMulExpr(Dividend,
765
SE.getTruncateOrZeroExtend(S, CalculationTy));
769
const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
771
// Truncate the result, and divide by K! / 2^T.
773
return SE.getMulExpr(SE.getConstant(MultiplyFactor),
774
SE.getTruncateOrZeroExtend(DivResult, ResultTy));
777
/// evaluateAtIteration - Return the value of this chain of recurrences at
778
/// the specified iteration number. We can evaluate this recurrence by
779
/// multiplying each element in the chain by the binomial coefficient
780
/// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
782
/// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
784
/// where BC(It, k) stands for binomial coefficient.
786
const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It,
787
ScalarEvolution &SE) const {
788
const SCEV *Result = getStart();
789
for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
790
// The computation is correct in the face of overflow provided that the
791
// multiplication is performed _after_ the evaluation of the binomial
793
const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType());
794
if (isa<SCEVCouldNotCompute>(Coeff))
797
Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
802
//===----------------------------------------------------------------------===//
803
// SCEV Expression folder implementations
804
//===----------------------------------------------------------------------===//
806
const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op,
808
assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
809
"This is not a truncating conversion!");
810
assert(isSCEVable(Ty) &&
811
"This is not a conversion to a SCEVable type!");
812
Ty = getEffectiveSCEVType(Ty);
815
ID.AddInteger(scTruncate);
819
if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
821
// Fold if the operand is constant.
822
if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
824
cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty)));
826
// trunc(trunc(x)) --> trunc(x)
827
if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
828
return getTruncateExpr(ST->getOperand(), Ty);
830
// trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
831
if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
832
return getTruncateOrSignExtend(SS->getOperand(), Ty);
834
// trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
835
if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
836
return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
838
// If the input value is a chrec scev, truncate the chrec's operands.
839
if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
840
SmallVector<const SCEV *, 4> Operands;
841
for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
842
Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty));
843
return getAddRecExpr(Operands, AddRec->getLoop());
846
// The cast wasn't folded; create an explicit cast node.
847
// Recompute the insert position, as it may have been invalidated.
848
if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
849
SCEV *S = SCEVAllocator.Allocate<SCEVTruncateExpr>();
850
new (S) SCEVTruncateExpr(ID, Op, Ty);
851
UniqueSCEVs.InsertNode(S, IP);
855
const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op,
857
assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
858
"This is not an extending conversion!");
859
assert(isSCEVable(Ty) &&
860
"This is not a conversion to a SCEVable type!");
861
Ty = getEffectiveSCEVType(Ty);
863
// Fold if the operand is constant.
864
if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) {
865
const Type *IntTy = getEffectiveSCEVType(Ty);
866
Constant *C = ConstantExpr::getZExt(SC->getValue(), IntTy);
867
if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty);
868
return getConstant(cast<ConstantInt>(C));
871
// zext(zext(x)) --> zext(x)
872
if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
873
return getZeroExtendExpr(SZ->getOperand(), Ty);
875
// Before doing any expensive analysis, check to see if we've already
876
// computed a SCEV for this Op and Ty.
878
ID.AddInteger(scZeroExtend);
882
if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
884
// If the input value is a chrec scev, and we can prove that the value
885
// did not overflow the old, smaller, value, we can zero extend all of the
886
// operands (often constants). This allows analysis of something like
887
// this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
888
if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
889
if (AR->isAffine()) {
890
const SCEV *Start = AR->getStart();
891
const SCEV *Step = AR->getStepRecurrence(*this);
892
unsigned BitWidth = getTypeSizeInBits(AR->getType());
893
const Loop *L = AR->getLoop();
895
// If we have special knowledge that this addrec won't overflow,
896
// we don't need to do any further analysis.
897
if (AR->hasNoUnsignedWrap())
898
return getAddRecExpr(getZeroExtendExpr(Start, Ty),
899
getZeroExtendExpr(Step, Ty),
902
// Check whether the backedge-taken count is SCEVCouldNotCompute.
903
// Note that this serves two purposes: It filters out loops that are
904
// simply not analyzable, and it covers the case where this code is
905
// being called from within backedge-taken count analysis, such that
906
// attempting to ask for the backedge-taken count would likely result
907
// in infinite recursion. In the later case, the analysis code will
908
// cope with a conservative value, and it will take care to purge
909
// that value once it has finished.
910
const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
911
if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
912
// Manually compute the final value for AR, checking for
915
// Check whether the backedge-taken count can be losslessly casted to
916
// the addrec's type. The count is always unsigned.
917
const SCEV *CastedMaxBECount =
918
getTruncateOrZeroExtend(MaxBECount, Start->getType());
919
const SCEV *RecastedMaxBECount =
920
getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
921
if (MaxBECount == RecastedMaxBECount) {
922
const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
923
// Check whether Start+Step*MaxBECount has no unsigned overflow.
924
const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step);
925
const SCEV *Add = getAddExpr(Start, ZMul);
926
const SCEV *OperandExtendedAdd =
927
getAddExpr(getZeroExtendExpr(Start, WideTy),
928
getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
929
getZeroExtendExpr(Step, WideTy)));
930
if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd)
931
// Return the expression with the addrec on the outside.
932
return getAddRecExpr(getZeroExtendExpr(Start, Ty),
933
getZeroExtendExpr(Step, Ty),
936
// Similar to above, only this time treat the step value as signed.
937
// This covers loops that count down.
938
const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
939
Add = getAddExpr(Start, SMul);
941
getAddExpr(getZeroExtendExpr(Start, WideTy),
942
getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
943
getSignExtendExpr(Step, WideTy)));
944
if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd)
945
// Return the expression with the addrec on the outside.
946
return getAddRecExpr(getZeroExtendExpr(Start, Ty),
947
getSignExtendExpr(Step, Ty),
951
// If the backedge is guarded by a comparison with the pre-inc value
952
// the addrec is safe. Also, if the entry is guarded by a comparison
953
// with the start value and the backedge is guarded by a comparison
954
// with the post-inc value, the addrec is safe.
955
if (isKnownPositive(Step)) {
956
const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
957
getUnsignedRange(Step).getUnsignedMax());
958
if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
959
(isLoopGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) &&
960
isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT,
961
AR->getPostIncExpr(*this), N)))
962
// Return the expression with the addrec on the outside.
963
return getAddRecExpr(getZeroExtendExpr(Start, Ty),
964
getZeroExtendExpr(Step, Ty),
966
} else if (isKnownNegative(Step)) {
967
const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
968
getSignedRange(Step).getSignedMin());
969
if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) &&
970
(isLoopGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) ||
971
isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT,
972
AR->getPostIncExpr(*this), N)))
973
// Return the expression with the addrec on the outside.
974
return getAddRecExpr(getZeroExtendExpr(Start, Ty),
975
getSignExtendExpr(Step, Ty),
981
// The cast wasn't folded; create an explicit cast node.
982
// Recompute the insert position, as it may have been invalidated.
983
if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
984
SCEV *S = SCEVAllocator.Allocate<SCEVZeroExtendExpr>();
985
new (S) SCEVZeroExtendExpr(ID, Op, Ty);
986
UniqueSCEVs.InsertNode(S, IP);
990
const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op,
992
assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
993
"This is not an extending conversion!");
994
assert(isSCEVable(Ty) &&
995
"This is not a conversion to a SCEVable type!");
996
Ty = getEffectiveSCEVType(Ty);
998
// Fold if the operand is constant.
999
if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) {
1000
const Type *IntTy = getEffectiveSCEVType(Ty);
1001
Constant *C = ConstantExpr::getSExt(SC->getValue(), IntTy);
1002
if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty);
1003
return getConstant(cast<ConstantInt>(C));
1006
// sext(sext(x)) --> sext(x)
1007
if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1008
return getSignExtendExpr(SS->getOperand(), Ty);
1010
// Before doing any expensive analysis, check to see if we've already
1011
// computed a SCEV for this Op and Ty.
1012
FoldingSetNodeID ID;
1013
ID.AddInteger(scSignExtend);
1017
if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1019
// If the input value is a chrec scev, and we can prove that the value
1020
// did not overflow the old, smaller, value, we can sign extend all of the
1021
// operands (often constants). This allows analysis of something like
1022
// this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
1023
if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1024
if (AR->isAffine()) {
1025
const SCEV *Start = AR->getStart();
1026
const SCEV *Step = AR->getStepRecurrence(*this);
1027
unsigned BitWidth = getTypeSizeInBits(AR->getType());
1028
const Loop *L = AR->getLoop();
1030
// If we have special knowledge that this addrec won't overflow,
1031
// we don't need to do any further analysis.
1032
if (AR->hasNoSignedWrap())
1033
return getAddRecExpr(getSignExtendExpr(Start, Ty),
1034
getSignExtendExpr(Step, Ty),
1037
// Check whether the backedge-taken count is SCEVCouldNotCompute.
1038
// Note that this serves two purposes: It filters out loops that are
1039
// simply not analyzable, and it covers the case where this code is
1040
// being called from within backedge-taken count analysis, such that
1041
// attempting to ask for the backedge-taken count would likely result
1042
// in infinite recursion. In the later case, the analysis code will
1043
// cope with a conservative value, and it will take care to purge
1044
// that value once it has finished.
1045
const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1046
if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1047
// Manually compute the final value for AR, checking for
1050
// Check whether the backedge-taken count can be losslessly casted to
1051
// the addrec's type. The count is always unsigned.
1052
const SCEV *CastedMaxBECount =
1053
getTruncateOrZeroExtend(MaxBECount, Start->getType());
1054
const SCEV *RecastedMaxBECount =
1055
getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1056
if (MaxBECount == RecastedMaxBECount) {
1057
const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1058
// Check whether Start+Step*MaxBECount has no signed overflow.
1059
const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
1060
const SCEV *Add = getAddExpr(Start, SMul);
1061
const SCEV *OperandExtendedAdd =
1062
getAddExpr(getSignExtendExpr(Start, WideTy),
1063
getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
1064
getSignExtendExpr(Step, WideTy)));
1065
if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd)
1066
// Return the expression with the addrec on the outside.
1067
return getAddRecExpr(getSignExtendExpr(Start, Ty),
1068
getSignExtendExpr(Step, Ty),
1071
// Similar to above, only this time treat the step value as unsigned.
1072
// This covers loops that count up with an unsigned step.
1073
const SCEV *UMul = getMulExpr(CastedMaxBECount, Step);
1074
Add = getAddExpr(Start, UMul);
1075
OperandExtendedAdd =
1076
getAddExpr(getSignExtendExpr(Start, WideTy),
1077
getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
1078
getZeroExtendExpr(Step, WideTy)));
1079
if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd)
1080
// Return the expression with the addrec on the outside.
1081
return getAddRecExpr(getSignExtendExpr(Start, Ty),
1082
getZeroExtendExpr(Step, Ty),
1086
// If the backedge is guarded by a comparison with the pre-inc value
1087
// the addrec is safe. Also, if the entry is guarded by a comparison
1088
// with the start value and the backedge is guarded by a comparison
1089
// with the post-inc value, the addrec is safe.
1090
if (isKnownPositive(Step)) {
1091
const SCEV *N = getConstant(APInt::getSignedMinValue(BitWidth) -
1092
getSignedRange(Step).getSignedMax());
1093
if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT, AR, N) ||
1094
(isLoopGuardedByCond(L, ICmpInst::ICMP_SLT, Start, N) &&
1095
isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT,
1096
AR->getPostIncExpr(*this), N)))
1097
// Return the expression with the addrec on the outside.
1098
return getAddRecExpr(getSignExtendExpr(Start, Ty),
1099
getSignExtendExpr(Step, Ty),
1101
} else if (isKnownNegative(Step)) {
1102
const SCEV *N = getConstant(APInt::getSignedMaxValue(BitWidth) -
1103
getSignedRange(Step).getSignedMin());
1104
if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT, AR, N) ||
1105
(isLoopGuardedByCond(L, ICmpInst::ICMP_SGT, Start, N) &&
1106
isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT,
1107
AR->getPostIncExpr(*this), N)))
1108
// Return the expression with the addrec on the outside.
1109
return getAddRecExpr(getSignExtendExpr(Start, Ty),
1110
getSignExtendExpr(Step, Ty),
1116
// The cast wasn't folded; create an explicit cast node.
1117
// Recompute the insert position, as it may have been invalidated.
1118
if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1119
SCEV *S = SCEVAllocator.Allocate<SCEVSignExtendExpr>();
1120
new (S) SCEVSignExtendExpr(ID, Op, Ty);
1121
UniqueSCEVs.InsertNode(S, IP);
1125
/// getAnyExtendExpr - Return a SCEV for the given operand extended with
1126
/// unspecified bits out to the given type.
1128
const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
1130
assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1131
"This is not an extending conversion!");
1132
assert(isSCEVable(Ty) &&
1133
"This is not a conversion to a SCEVable type!");
1134
Ty = getEffectiveSCEVType(Ty);
1136
// Sign-extend negative constants.
1137
if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1138
if (SC->getValue()->getValue().isNegative())
1139
return getSignExtendExpr(Op, Ty);
1141
// Peel off a truncate cast.
1142
if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
1143
const SCEV *NewOp = T->getOperand();
1144
if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
1145
return getAnyExtendExpr(NewOp, Ty);
1146
return getTruncateOrNoop(NewOp, Ty);
1149
// Next try a zext cast. If the cast is folded, use it.
1150
const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
1151
if (!isa<SCEVZeroExtendExpr>(ZExt))
1154
// Next try a sext cast. If the cast is folded, use it.
1155
const SCEV *SExt = getSignExtendExpr(Op, Ty);
1156
if (!isa<SCEVSignExtendExpr>(SExt))
1159
// Force the cast to be folded into the operands of an addrec.
1160
if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
1161
SmallVector<const SCEV *, 4> Ops;
1162
for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
1164
Ops.push_back(getAnyExtendExpr(*I, Ty));
1165
return getAddRecExpr(Ops, AR->getLoop());
1168
// If the expression is obviously signed, use the sext cast value.
1169
if (isa<SCEVSMaxExpr>(Op))
1172
// Absent any other information, use the zext cast value.
1176
/// CollectAddOperandsWithScales - Process the given Ops list, which is
1177
/// a list of operands to be added under the given scale, update the given
1178
/// map. This is a helper function for getAddRecExpr. As an example of
1179
/// what it does, given a sequence of operands that would form an add
1180
/// expression like this:
1182
/// m + n + 13 + (A * (o + p + (B * q + m + 29))) + r + (-1 * r)
1184
/// where A and B are constants, update the map with these values:
1186
/// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
1188
/// and add 13 + A*B*29 to AccumulatedConstant.
1189
/// This will allow getAddRecExpr to produce this:
1191
/// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
1193
/// This form often exposes folding opportunities that are hidden in
1194
/// the original operand list.
1196
/// Return true iff it appears that any interesting folding opportunities
1197
/// may be exposed. This helps getAddRecExpr short-circuit extra work in
1198
/// the common case where no interesting opportunities are present, and
1199
/// is also used as a check to avoid infinite recursion.
1202
CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
1203
SmallVector<const SCEV *, 8> &NewOps,
1204
APInt &AccumulatedConstant,
1205
const SmallVectorImpl<const SCEV *> &Ops,
1207
ScalarEvolution &SE) {
1208
bool Interesting = false;
1210
// Iterate over the add operands.
1211
for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1212
const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
1213
if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
1215
Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue();
1216
if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
1217
// A multiplication of a constant with another add; recurse.
1219
CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1220
cast<SCEVAddExpr>(Mul->getOperand(1))
1224
// A multiplication of a constant with some other value. Update
1226
SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
1227
const SCEV *Key = SE.getMulExpr(MulOps);
1228
std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1229
M.insert(std::make_pair(Key, NewScale));
1231
NewOps.push_back(Pair.first->first);
1233
Pair.first->second += NewScale;
1234
// The map already had an entry for this value, which may indicate
1235
// a folding opportunity.
1239
} else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1240
// Pull a buried constant out to the outside.
1241
if (Scale != 1 || AccumulatedConstant != 0 || C->isZero())
1243
AccumulatedConstant += Scale * C->getValue()->getValue();
1245
// An ordinary operand. Update the map.
1246
std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1247
M.insert(std::make_pair(Ops[i], Scale));
1249
NewOps.push_back(Pair.first->first);
1251
Pair.first->second += Scale;
1252
// The map already had an entry for this value, which may indicate
1253
// a folding opportunity.
1263
struct APIntCompare {
1264
bool operator()(const APInt &LHS, const APInt &RHS) const {
1265
return LHS.ult(RHS);
1270
/// getAddExpr - Get a canonical add expression, or something simpler if
1272
const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
1273
bool HasNUW, bool HasNSW) {
1274
assert(!Ops.empty() && "Cannot get empty add!");
1275
if (Ops.size() == 1) return Ops[0];
1277
for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1278
assert(getEffectiveSCEVType(Ops[i]->getType()) ==
1279
getEffectiveSCEVType(Ops[0]->getType()) &&
1280
"SCEVAddExpr operand types don't match!");
1283
// If HasNSW is true and all the operands are non-negative, infer HasNUW.
1284
if (!HasNUW && HasNSW) {
1286
for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1287
if (!isKnownNonNegative(Ops[i])) {
1291
if (All) HasNUW = true;
1294
// Sort by complexity, this groups all similar expression types together.
1295
GroupByComplexity(Ops, LI);
1297
// If there are any constants, fold them together.
1299
if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1301
assert(Idx < Ops.size());
1302
while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1303
// We found two constants, fold them together!
1304
Ops[0] = getConstant(LHSC->getValue()->getValue() +
1305
RHSC->getValue()->getValue());
1306
if (Ops.size() == 2) return Ops[0];
1307
Ops.erase(Ops.begin()+1); // Erase the folded element
1308
LHSC = cast<SCEVConstant>(Ops[0]);
1311
// If we are left with a constant zero being added, strip it off.
1312
if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
1313
Ops.erase(Ops.begin());
1318
if (Ops.size() == 1) return Ops[0];
1320
// Okay, check to see if the same value occurs in the operand list twice. If
1321
// so, merge them together into an multiply expression. Since we sorted the
1322
// list, these values are required to be adjacent.
1323
const Type *Ty = Ops[0]->getType();
1324
for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
1325
if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
1326
// Found a match, merge the two values into a multiply, and add any
1327
// remaining values to the result.
1328
const SCEV *Two = getIntegerSCEV(2, Ty);
1329
const SCEV *Mul = getMulExpr(Ops[i], Two);
1330
if (Ops.size() == 2)
1332
Ops.erase(Ops.begin()+i, Ops.begin()+i+2);
1334
return getAddExpr(Ops, HasNUW, HasNSW);
1337
// Check for truncates. If all the operands are truncated from the same
1338
// type, see if factoring out the truncate would permit the result to be
1339
// folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
1340
// if the contents of the resulting outer trunc fold to something simple.
1341
for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
1342
const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
1343
const Type *DstType = Trunc->getType();
1344
const Type *SrcType = Trunc->getOperand()->getType();
1345
SmallVector<const SCEV *, 8> LargeOps;
1347
// Check all the operands to see if they can be represented in the
1348
// source type of the truncate.
1349
for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1350
if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
1351
if (T->getOperand()->getType() != SrcType) {
1355
LargeOps.push_back(T->getOperand());
1356
} else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1357
// This could be either sign or zero extension, but sign extension
1358
// is much more likely to be foldable here.
1359
LargeOps.push_back(getSignExtendExpr(C, SrcType));
1360
} else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
1361
SmallVector<const SCEV *, 8> LargeMulOps;
1362
for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
1363
if (const SCEVTruncateExpr *T =
1364
dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
1365
if (T->getOperand()->getType() != SrcType) {
1369
LargeMulOps.push_back(T->getOperand());
1370
} else if (const SCEVConstant *C =
1371
dyn_cast<SCEVConstant>(M->getOperand(j))) {
1372
// This could be either sign or zero extension, but sign extension
1373
// is much more likely to be foldable here.
1374
LargeMulOps.push_back(getSignExtendExpr(C, SrcType));
1381
LargeOps.push_back(getMulExpr(LargeMulOps));
1388
// Evaluate the expression in the larger type.
1389
const SCEV *Fold = getAddExpr(LargeOps, HasNUW, HasNSW);
1390
// If it folds to something simple, use it. Otherwise, don't.
1391
if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
1392
return getTruncateExpr(Fold, DstType);
1396
// Skip past any other cast SCEVs.
1397
while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
1400
// If there are add operands they would be next.
1401
if (Idx < Ops.size()) {
1402
bool DeletedAdd = false;
1403
while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
1404
// If we have an add, expand the add operands onto the end of the operands
1406
Ops.insert(Ops.end(), Add->op_begin(), Add->op_end());
1407
Ops.erase(Ops.begin()+Idx);
1411
// If we deleted at least one add, we added operands to the end of the list,
1412
// and they are not necessarily sorted. Recurse to resort and resimplify
1413
// any operands we just acquired.
1415
return getAddExpr(Ops);
1418
// Skip over the add expression until we get to a multiply.
1419
while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1422
// Check to see if there are any folding opportunities present with
1423
// operands multiplied by constant values.
1424
if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
1425
uint64_t BitWidth = getTypeSizeInBits(Ty);
1426
DenseMap<const SCEV *, APInt> M;
1427
SmallVector<const SCEV *, 8> NewOps;
1428
APInt AccumulatedConstant(BitWidth, 0);
1429
if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1430
Ops, APInt(BitWidth, 1), *this)) {
1431
// Some interesting folding opportunity is present, so its worthwhile to
1432
// re-generate the operands list. Group the operands by constant scale,
1433
// to avoid multiplying by the same constant scale multiple times.
1434
std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
1435
for (SmallVector<const SCEV *, 8>::iterator I = NewOps.begin(),
1436
E = NewOps.end(); I != E; ++I)
1437
MulOpLists[M.find(*I)->second].push_back(*I);
1438
// Re-generate the operands list.
1440
if (AccumulatedConstant != 0)
1441
Ops.push_back(getConstant(AccumulatedConstant));
1442
for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator
1443
I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I)
1445
Ops.push_back(getMulExpr(getConstant(I->first),
1446
getAddExpr(I->second)));
1448
return getIntegerSCEV(0, Ty);
1449
if (Ops.size() == 1)
1451
return getAddExpr(Ops);
1455
// If we are adding something to a multiply expression, make sure the
1456
// something is not already an operand of the multiply. If so, merge it into
1458
for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
1459
const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
1460
for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
1461
const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
1462
for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
1463
if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(Ops[AddOp])) {
1464
// Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
1465
const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
1466
if (Mul->getNumOperands() != 2) {
1467
// If the multiply has more than two operands, we must get the
1469
SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), Mul->op_end());
1470
MulOps.erase(MulOps.begin()+MulOp);
1471
InnerMul = getMulExpr(MulOps);
1473
const SCEV *One = getIntegerSCEV(1, Ty);
1474
const SCEV *AddOne = getAddExpr(InnerMul, One);
1475
const SCEV *OuterMul = getMulExpr(AddOne, Ops[AddOp]);
1476
if (Ops.size() == 2) return OuterMul;
1478
Ops.erase(Ops.begin()+AddOp);
1479
Ops.erase(Ops.begin()+Idx-1);
1481
Ops.erase(Ops.begin()+Idx);
1482
Ops.erase(Ops.begin()+AddOp-1);
1484
Ops.push_back(OuterMul);
1485
return getAddExpr(Ops);
1488
// Check this multiply against other multiplies being added together.
1489
for (unsigned OtherMulIdx = Idx+1;
1490
OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
1492
const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
1493
// If MulOp occurs in OtherMul, we can fold the two multiplies
1495
for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
1496
OMulOp != e; ++OMulOp)
1497
if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
1498
// Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
1499
const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
1500
if (Mul->getNumOperands() != 2) {
1501
SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
1503
MulOps.erase(MulOps.begin()+MulOp);
1504
InnerMul1 = getMulExpr(MulOps);
1506
const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
1507
if (OtherMul->getNumOperands() != 2) {
1508
SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
1509
OtherMul->op_end());
1510
MulOps.erase(MulOps.begin()+OMulOp);
1511
InnerMul2 = getMulExpr(MulOps);
1513
const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
1514
const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
1515
if (Ops.size() == 2) return OuterMul;
1516
Ops.erase(Ops.begin()+Idx);
1517
Ops.erase(Ops.begin()+OtherMulIdx-1);
1518
Ops.push_back(OuterMul);
1519
return getAddExpr(Ops);
1525
// If there are any add recurrences in the operands list, see if any other
1526
// added values are loop invariant. If so, we can fold them into the
1528
while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1531
// Scan over all recurrences, trying to fold loop invariants into them.
1532
for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1533
// Scan all of the other operands to this add and add them to the vector if
1534
// they are loop invariant w.r.t. the recurrence.
1535
SmallVector<const SCEV *, 8> LIOps;
1536
const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1537
for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1538
if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
1539
LIOps.push_back(Ops[i]);
1540
Ops.erase(Ops.begin()+i);
1544
// If we found some loop invariants, fold them into the recurrence.
1545
if (!LIOps.empty()) {
1546
// NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
1547
LIOps.push_back(AddRec->getStart());
1549
SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
1551
AddRecOps[0] = getAddExpr(LIOps);
1553
// It's tempting to propagate NUW/NSW flags here, but nuw/nsw addition
1554
// is not associative so this isn't necessarily safe.
1555
const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRec->getLoop());
1557
// If all of the other operands were loop invariant, we are done.
1558
if (Ops.size() == 1) return NewRec;
1560
// Otherwise, add the folded AddRec by the non-liv parts.
1561
for (unsigned i = 0;; ++i)
1562
if (Ops[i] == AddRec) {
1566
return getAddExpr(Ops);
1569
// Okay, if there weren't any loop invariants to be folded, check to see if
1570
// there are multiple AddRec's with the same loop induction variable being
1571
// added together. If so, we can fold them.
1572
for (unsigned OtherIdx = Idx+1;
1573
OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
1574
if (OtherIdx != Idx) {
1575
const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
1576
if (AddRec->getLoop() == OtherAddRec->getLoop()) {
1577
// Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D}
1578
SmallVector<const SCEV *, 4> NewOps(AddRec->op_begin(),
1580
for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) {
1581
if (i >= NewOps.size()) {
1582
NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i,
1583
OtherAddRec->op_end());
1586
NewOps[i] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i));
1588
const SCEV *NewAddRec = getAddRecExpr(NewOps, AddRec->getLoop());
1590
if (Ops.size() == 2) return NewAddRec;
1592
Ops.erase(Ops.begin()+Idx);
1593
Ops.erase(Ops.begin()+OtherIdx-1);
1594
Ops.push_back(NewAddRec);
1595
return getAddExpr(Ops);
1599
// Otherwise couldn't fold anything into this recurrence. Move onto the
1603
// Okay, it looks like we really DO need an add expr. Check to see if we
1604
// already have one, otherwise create a new one.
1605
FoldingSetNodeID ID;
1606
ID.AddInteger(scAddExpr);
1607
ID.AddInteger(Ops.size());
1608
for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1609
ID.AddPointer(Ops[i]);
1612
static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1614
S = SCEVAllocator.Allocate<SCEVAddExpr>();
1615
new (S) SCEVAddExpr(ID, Ops);
1616
UniqueSCEVs.InsertNode(S, IP);
1618
if (HasNUW) S->setHasNoUnsignedWrap(true);
1619
if (HasNSW) S->setHasNoSignedWrap(true);
1623
/// getMulExpr - Get a canonical multiply expression, or something simpler if
1625
const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
1626
bool HasNUW, bool HasNSW) {
1627
assert(!Ops.empty() && "Cannot get empty mul!");
1628
if (Ops.size() == 1) return Ops[0];
1630
for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1631
assert(getEffectiveSCEVType(Ops[i]->getType()) ==
1632
getEffectiveSCEVType(Ops[0]->getType()) &&
1633
"SCEVMulExpr operand types don't match!");
1636
// If HasNSW is true and all the operands are non-negative, infer HasNUW.
1637
if (!HasNUW && HasNSW) {
1639
for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1640
if (!isKnownNonNegative(Ops[i])) {
1644
if (All) HasNUW = true;
1647
// Sort by complexity, this groups all similar expression types together.
1648
GroupByComplexity(Ops, LI);
1650
// If there are any constants, fold them together.
1652
if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1654
// C1*(C2+V) -> C1*C2 + C1*V
1655
if (Ops.size() == 2)
1656
if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
1657
if (Add->getNumOperands() == 2 &&
1658
isa<SCEVConstant>(Add->getOperand(0)))
1659
return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
1660
getMulExpr(LHSC, Add->getOperand(1)));
1663
while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1664
// We found two constants, fold them together!
1665
ConstantInt *Fold = ConstantInt::get(getContext(),
1666
LHSC->getValue()->getValue() *
1667
RHSC->getValue()->getValue());
1668
Ops[0] = getConstant(Fold);
1669
Ops.erase(Ops.begin()+1); // Erase the folded element
1670
if (Ops.size() == 1) return Ops[0];
1671
LHSC = cast<SCEVConstant>(Ops[0]);
1674
// If we are left with a constant one being multiplied, strip it off.
1675
if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
1676
Ops.erase(Ops.begin());
1678
} else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
1679
// If we have a multiply of zero, it will always be zero.
1681
} else if (Ops[0]->isAllOnesValue()) {
1682
// If we have a mul by -1 of an add, try distributing the -1 among the
1684
if (Ops.size() == 2)
1685
if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
1686
SmallVector<const SCEV *, 4> NewOps;
1687
bool AnyFolded = false;
1688
for (SCEVAddRecExpr::op_iterator I = Add->op_begin(), E = Add->op_end();
1690
const SCEV *Mul = getMulExpr(Ops[0], *I);
1691
if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
1692
NewOps.push_back(Mul);
1695
return getAddExpr(NewOps);
1700
// Skip over the add expression until we get to a multiply.
1701
while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1704
if (Ops.size() == 1)
1707
// If there are mul operands inline them all into this expression.
1708
if (Idx < Ops.size()) {
1709
bool DeletedMul = false;
1710
while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
1711
// If we have an mul, expand the mul operands onto the end of the operands
1713
Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end());
1714
Ops.erase(Ops.begin()+Idx);
1718
// If we deleted at least one mul, we added operands to the end of the list,
1719
// and they are not necessarily sorted. Recurse to resort and resimplify
1720
// any operands we just acquired.
1722
return getMulExpr(Ops);
1725
// If there are any add recurrences in the operands list, see if any other
1726
// added values are loop invariant. If so, we can fold them into the
1728
while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1731
// Scan over all recurrences, trying to fold loop invariants into them.
1732
for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1733
// Scan all of the other operands to this mul and add them to the vector if
1734
// they are loop invariant w.r.t. the recurrence.
1735
SmallVector<const SCEV *, 8> LIOps;
1736
const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1737
for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1738
if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
1739
LIOps.push_back(Ops[i]);
1740
Ops.erase(Ops.begin()+i);
1744
// If we found some loop invariants, fold them into the recurrence.
1745
if (!LIOps.empty()) {
1746
// NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
1747
SmallVector<const SCEV *, 4> NewOps;
1748
NewOps.reserve(AddRec->getNumOperands());
1749
if (LIOps.size() == 1) {
1750
const SCEV *Scale = LIOps[0];
1751
for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
1752
NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
1754
for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
1755
SmallVector<const SCEV *, 4> MulOps(LIOps.begin(), LIOps.end());
1756
MulOps.push_back(AddRec->getOperand(i));
1757
NewOps.push_back(getMulExpr(MulOps));
1761
// It's tempting to propagate the NSW flag here, but nsw multiplication
1762
// is not associative so this isn't necessarily safe.
1763
const SCEV *NewRec = getAddRecExpr(NewOps, AddRec->getLoop(),
1764
HasNUW && AddRec->hasNoUnsignedWrap(),
1767
// If all of the other operands were loop invariant, we are done.
1768
if (Ops.size() == 1) return NewRec;
1770
// Otherwise, multiply the folded AddRec by the non-liv parts.
1771
for (unsigned i = 0;; ++i)
1772
if (Ops[i] == AddRec) {
1776
return getMulExpr(Ops);
1779
// Okay, if there weren't any loop invariants to be folded, check to see if
1780
// there are multiple AddRec's with the same loop induction variable being
1781
// multiplied together. If so, we can fold them.
1782
for (unsigned OtherIdx = Idx+1;
1783
OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
1784
if (OtherIdx != Idx) {
1785
const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
1786
if (AddRec->getLoop() == OtherAddRec->getLoop()) {
1787
// F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D}
1788
const SCEVAddRecExpr *F = AddRec, *G = OtherAddRec;
1789
const SCEV *NewStart = getMulExpr(F->getStart(),
1791
const SCEV *B = F->getStepRecurrence(*this);
1792
const SCEV *D = G->getStepRecurrence(*this);
1793
const SCEV *NewStep = getAddExpr(getMulExpr(F, D),
1796
const SCEV *NewAddRec = getAddRecExpr(NewStart, NewStep,
1798
if (Ops.size() == 2) return NewAddRec;
1800
Ops.erase(Ops.begin()+Idx);
1801
Ops.erase(Ops.begin()+OtherIdx-1);
1802
Ops.push_back(NewAddRec);
1803
return getMulExpr(Ops);
1807
// Otherwise couldn't fold anything into this recurrence. Move onto the
1811
// Okay, it looks like we really DO need an mul expr. Check to see if we
1812
// already have one, otherwise create a new one.
1813
FoldingSetNodeID ID;
1814
ID.AddInteger(scMulExpr);
1815
ID.AddInteger(Ops.size());
1816
for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1817
ID.AddPointer(Ops[i]);
1820
static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1822
S = SCEVAllocator.Allocate<SCEVMulExpr>();
1823
new (S) SCEVMulExpr(ID, Ops);
1824
UniqueSCEVs.InsertNode(S, IP);
1826
if (HasNUW) S->setHasNoUnsignedWrap(true);
1827
if (HasNSW) S->setHasNoSignedWrap(true);
1831
/// getUDivExpr - Get a canonical unsigned division expression, or something
1832
/// simpler if possible.
1833
const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
1835
assert(getEffectiveSCEVType(LHS->getType()) ==
1836
getEffectiveSCEVType(RHS->getType()) &&
1837
"SCEVUDivExpr operand types don't match!");
1839
if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
1840
if (RHSC->getValue()->equalsInt(1))
1841
return LHS; // X udiv 1 --> x
1843
return getIntegerSCEV(0, LHS->getType()); // value is undefined
1845
// Determine if the division can be folded into the operands of
1847
// TODO: Generalize this to non-constants by using known-bits information.
1848
const Type *Ty = LHS->getType();
1849
unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
1850
unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ;
1851
// For non-power-of-two values, effectively round the value up to the
1852
// nearest power of two.
1853
if (!RHSC->getValue()->getValue().isPowerOf2())
1855
const IntegerType *ExtTy =
1856
IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
1857
// {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
1858
if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
1859
if (const SCEVConstant *Step =
1860
dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this)))
1861
if (!Step->getValue()->getValue()
1862
.urem(RHSC->getValue()->getValue()) &&
1863
getZeroExtendExpr(AR, ExtTy) ==
1864
getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
1865
getZeroExtendExpr(Step, ExtTy),
1867
SmallVector<const SCEV *, 4> Operands;
1868
for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i)
1869
Operands.push_back(getUDivExpr(AR->getOperand(i), RHS));
1870
return getAddRecExpr(Operands, AR->getLoop());
1872
// (A*B)/C --> A*(B/C) if safe and B/C can be folded.
1873
if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
1874
SmallVector<const SCEV *, 4> Operands;
1875
for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i)
1876
Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy));
1877
if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
1878
// Find an operand that's safely divisible.
1879
for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
1880
const SCEV *Op = M->getOperand(i);
1881
const SCEV *Div = getUDivExpr(Op, RHSC);
1882
if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
1883
const SmallVectorImpl<const SCEV *> &MOperands = M->getOperands();
1884
Operands = SmallVector<const SCEV *, 4>(MOperands.begin(),
1887
return getMulExpr(Operands);
1891
// (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
1892
if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(LHS)) {
1893
SmallVector<const SCEV *, 4> Operands;
1894
for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i)
1895
Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy));
1896
if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
1898
for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
1899
const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
1900
if (isa<SCEVUDivExpr>(Op) || getMulExpr(Op, RHS) != A->getOperand(i))
1902
Operands.push_back(Op);
1904
if (Operands.size() == A->getNumOperands())
1905
return getAddExpr(Operands);
1909
// Fold if both operands are constant.
1910
if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
1911
Constant *LHSCV = LHSC->getValue();
1912
Constant *RHSCV = RHSC->getValue();
1913
return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
1918
FoldingSetNodeID ID;
1919
ID.AddInteger(scUDivExpr);
1923
if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1924
SCEV *S = SCEVAllocator.Allocate<SCEVUDivExpr>();
1925
new (S) SCEVUDivExpr(ID, LHS, RHS);
1926
UniqueSCEVs.InsertNode(S, IP);
1931
/// getAddRecExpr - Get an add recurrence expression for the specified loop.
1932
/// Simplify the expression as much as possible.
1933
const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start,
1934
const SCEV *Step, const Loop *L,
1935
bool HasNUW, bool HasNSW) {
1936
SmallVector<const SCEV *, 4> Operands;
1937
Operands.push_back(Start);
1938
if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
1939
if (StepChrec->getLoop() == L) {
1940
Operands.insert(Operands.end(), StepChrec->op_begin(),
1941
StepChrec->op_end());
1942
return getAddRecExpr(Operands, L);
1945
Operands.push_back(Step);
1946
return getAddRecExpr(Operands, L, HasNUW, HasNSW);
1949
/// getAddRecExpr - Get an add recurrence expression for the specified loop.
1950
/// Simplify the expression as much as possible.
1952
ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
1954
bool HasNUW, bool HasNSW) {
1955
if (Operands.size() == 1) return Operands[0];
1957
for (unsigned i = 1, e = Operands.size(); i != e; ++i)
1958
assert(getEffectiveSCEVType(Operands[i]->getType()) ==
1959
getEffectiveSCEVType(Operands[0]->getType()) &&
1960
"SCEVAddRecExpr operand types don't match!");
1963
if (Operands.back()->isZero()) {
1964
Operands.pop_back();
1965
return getAddRecExpr(Operands, L, HasNUW, HasNSW); // {X,+,0} --> X
1968
// It's tempting to want to call getMaxBackedgeTakenCount count here and
1969
// use that information to infer NUW and NSW flags. However, computing a
1970
// BE count requires calling getAddRecExpr, so we may not yet have a
1971
// meaningful BE count at this point (and if we don't, we'd be stuck
1972
// with a SCEVCouldNotCompute as the cached BE count).
1974
// If HasNSW is true and all the operands are non-negative, infer HasNUW.
1975
if (!HasNUW && HasNSW) {
1977
for (unsigned i = 0, e = Operands.size(); i != e; ++i)
1978
if (!isKnownNonNegative(Operands[i])) {
1982
if (All) HasNUW = true;
1985
// Canonicalize nested AddRecs in by nesting them in order of loop depth.
1986
if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
1987
const Loop *NestedLoop = NestedAR->getLoop();
1988
if (L->contains(NestedLoop->getHeader()) ?
1989
(L->getLoopDepth() < NestedLoop->getLoopDepth()) :
1990
(!NestedLoop->contains(L->getHeader()) &&
1991
DT->dominates(L->getHeader(), NestedLoop->getHeader()))) {
1992
SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
1993
NestedAR->op_end());
1994
Operands[0] = NestedAR->getStart();
1995
// AddRecs require their operands be loop-invariant with respect to their
1996
// loops. Don't perform this transformation if it would break this
1998
bool AllInvariant = true;
1999
for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2000
if (!Operands[i]->isLoopInvariant(L)) {
2001
AllInvariant = false;
2005
NestedOperands[0] = getAddRecExpr(Operands, L);
2006
AllInvariant = true;
2007
for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i)
2008
if (!NestedOperands[i]->isLoopInvariant(NestedLoop)) {
2009
AllInvariant = false;
2013
// Ok, both add recurrences are valid after the transformation.
2014
return getAddRecExpr(NestedOperands, NestedLoop, HasNUW, HasNSW);
2016
// Reset Operands to its original state.
2017
Operands[0] = NestedAR;
2021
// Okay, it looks like we really DO need an addrec expr. Check to see if we
2022
// already have one, otherwise create a new one.
2023
FoldingSetNodeID ID;
2024
ID.AddInteger(scAddRecExpr);
2025
ID.AddInteger(Operands.size());
2026
for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2027
ID.AddPointer(Operands[i]);
2031
static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2033
S = SCEVAllocator.Allocate<SCEVAddRecExpr>();
2034
new (S) SCEVAddRecExpr(ID, Operands, L);
2035
UniqueSCEVs.InsertNode(S, IP);
2037
if (HasNUW) S->setHasNoUnsignedWrap(true);
2038
if (HasNSW) S->setHasNoSignedWrap(true);
2042
const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
2044
SmallVector<const SCEV *, 2> Ops;
2047
return getSMaxExpr(Ops);
2051
ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2052
assert(!Ops.empty() && "Cannot get empty smax!");
2053
if (Ops.size() == 1) return Ops[0];
2055
for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2056
assert(getEffectiveSCEVType(Ops[i]->getType()) ==
2057
getEffectiveSCEVType(Ops[0]->getType()) &&
2058
"SCEVSMaxExpr operand types don't match!");
2061
// Sort by complexity, this groups all similar expression types together.
2062
GroupByComplexity(Ops, LI);
2064
// If there are any constants, fold them together.
2066
if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2068
assert(Idx < Ops.size());
2069
while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2070
// We found two constants, fold them together!
2071
ConstantInt *Fold = ConstantInt::get(getContext(),
2072
APIntOps::smax(LHSC->getValue()->getValue(),
2073
RHSC->getValue()->getValue()));
2074
Ops[0] = getConstant(Fold);
2075
Ops.erase(Ops.begin()+1); // Erase the folded element
2076
if (Ops.size() == 1) return Ops[0];
2077
LHSC = cast<SCEVConstant>(Ops[0]);
2080
// If we are left with a constant minimum-int, strip it off.
2081
if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
2082
Ops.erase(Ops.begin());
2084
} else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
2085
// If we have an smax with a constant maximum-int, it will always be
2091
if (Ops.size() == 1) return Ops[0];
2093
// Find the first SMax
2094
while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
2097
// Check to see if one of the operands is an SMax. If so, expand its operands
2098
// onto our operand list, and recurse to simplify.
2099
if (Idx < Ops.size()) {
2100
bool DeletedSMax = false;
2101
while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
2102
Ops.insert(Ops.end(), SMax->op_begin(), SMax->op_end());
2103
Ops.erase(Ops.begin()+Idx);
2108
return getSMaxExpr(Ops);
2111
// Okay, check to see if the same value occurs in the operand list twice. If
2112
// so, delete one. Since we sorted the list, these values are required to
2114
for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2115
if (Ops[i] == Ops[i+1]) { // X smax Y smax Y --> X smax Y
2116
Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2120
if (Ops.size() == 1) return Ops[0];
2122
assert(!Ops.empty() && "Reduced smax down to nothing!");
2124
// Okay, it looks like we really DO need an smax expr. Check to see if we
2125
// already have one, otherwise create a new one.
2126
FoldingSetNodeID ID;
2127
ID.AddInteger(scSMaxExpr);
2128
ID.AddInteger(Ops.size());
2129
for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2130
ID.AddPointer(Ops[i]);
2132
if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2133
SCEV *S = SCEVAllocator.Allocate<SCEVSMaxExpr>();
2134
new (S) SCEVSMaxExpr(ID, Ops);
2135
UniqueSCEVs.InsertNode(S, IP);
2139
const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
2141
SmallVector<const SCEV *, 2> Ops;
2144
return getUMaxExpr(Ops);
2148
ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2149
assert(!Ops.empty() && "Cannot get empty umax!");
2150
if (Ops.size() == 1) return Ops[0];
2152
for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2153
assert(getEffectiveSCEVType(Ops[i]->getType()) ==
2154
getEffectiveSCEVType(Ops[0]->getType()) &&
2155
"SCEVUMaxExpr operand types don't match!");
2158
// Sort by complexity, this groups all similar expression types together.
2159
GroupByComplexity(Ops, LI);
2161
// If there are any constants, fold them together.
2163
if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2165
assert(Idx < Ops.size());
2166
while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2167
// We found two constants, fold them together!
2168
ConstantInt *Fold = ConstantInt::get(getContext(),
2169
APIntOps::umax(LHSC->getValue()->getValue(),
2170
RHSC->getValue()->getValue()));
2171
Ops[0] = getConstant(Fold);
2172
Ops.erase(Ops.begin()+1); // Erase the folded element
2173
if (Ops.size() == 1) return Ops[0];
2174
LHSC = cast<SCEVConstant>(Ops[0]);
2177
// If we are left with a constant minimum-int, strip it off.
2178
if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
2179
Ops.erase(Ops.begin());
2181
} else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
2182
// If we have an umax with a constant maximum-int, it will always be
2188
if (Ops.size() == 1) return Ops[0];
2190
// Find the first UMax
2191
while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
2194
// Check to see if one of the operands is a UMax. If so, expand its operands
2195
// onto our operand list, and recurse to simplify.
2196
if (Idx < Ops.size()) {
2197
bool DeletedUMax = false;
2198
while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
2199
Ops.insert(Ops.end(), UMax->op_begin(), UMax->op_end());
2200
Ops.erase(Ops.begin()+Idx);
2205
return getUMaxExpr(Ops);
2208
// Okay, check to see if the same value occurs in the operand list twice. If
2209
// so, delete one. Since we sorted the list, these values are required to
2211
for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2212
if (Ops[i] == Ops[i+1]) { // X umax Y umax Y --> X umax Y
2213
Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2217
if (Ops.size() == 1) return Ops[0];
2219
assert(!Ops.empty() && "Reduced umax down to nothing!");
2221
// Okay, it looks like we really DO need a umax expr. Check to see if we
2222
// already have one, otherwise create a new one.
2223
FoldingSetNodeID ID;
2224
ID.AddInteger(scUMaxExpr);
2225
ID.AddInteger(Ops.size());
2226
for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2227
ID.AddPointer(Ops[i]);
2229
if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2230
SCEV *S = SCEVAllocator.Allocate<SCEVUMaxExpr>();
2231
new (S) SCEVUMaxExpr(ID, Ops);
2232
UniqueSCEVs.InsertNode(S, IP);
2236
const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
2238
// ~smax(~x, ~y) == smin(x, y).
2239
return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2242
const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
2244
// ~umax(~x, ~y) == umin(x, y)
2245
return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2248
const SCEV *ScalarEvolution::getSizeOfExpr(const Type *AllocTy) {
2249
Constant *C = ConstantExpr::getSizeOf(AllocTy);
2250
if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2251
C = ConstantFoldConstantExpression(CE, TD);
2252
const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2253
return getTruncateOrZeroExtend(getSCEV(C), Ty);
2256
const SCEV *ScalarEvolution::getAlignOfExpr(const Type *AllocTy) {
2257
Constant *C = ConstantExpr::getAlignOf(AllocTy);
2258
if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2259
C = ConstantFoldConstantExpression(CE, TD);
2260
const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2261
return getTruncateOrZeroExtend(getSCEV(C), Ty);
2264
const SCEV *ScalarEvolution::getOffsetOfExpr(const StructType *STy,
2266
Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo);
2267
if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2268
C = ConstantFoldConstantExpression(CE, TD);
2269
const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy));
2270
return getTruncateOrZeroExtend(getSCEV(C), Ty);
2273
const SCEV *ScalarEvolution::getOffsetOfExpr(const Type *CTy,
2274
Constant *FieldNo) {
2275
Constant *C = ConstantExpr::getOffsetOf(CTy, FieldNo);
2276
if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2277
C = ConstantFoldConstantExpression(CE, TD);
2278
const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(CTy));
2279
return getTruncateOrZeroExtend(getSCEV(C), Ty);
2282
const SCEV *ScalarEvolution::getUnknown(Value *V) {
2283
// Don't attempt to do anything other than create a SCEVUnknown object
2284
// here. createSCEV only calls getUnknown after checking for all other
2285
// interesting possibilities, and any other code that calls getUnknown
2286
// is doing so in order to hide a value from SCEV canonicalization.
2288
FoldingSetNodeID ID;
2289
ID.AddInteger(scUnknown);
2292
if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2293
SCEV *S = SCEVAllocator.Allocate<SCEVUnknown>();
2294
new (S) SCEVUnknown(ID, V);
2295
UniqueSCEVs.InsertNode(S, IP);
2299
//===----------------------------------------------------------------------===//
2300
// Basic SCEV Analysis and PHI Idiom Recognition Code
2303
/// isSCEVable - Test if values of the given type are analyzable within
2304
/// the SCEV framework. This primarily includes integer types, and it
2305
/// can optionally include pointer types if the ScalarEvolution class
2306
/// has access to target-specific information.
2307
bool ScalarEvolution::isSCEVable(const Type *Ty) const {
2308
// Integers and pointers are always SCEVable.
2309
return Ty->isIntegerTy() || Ty->isPointerTy();
2312
/// getTypeSizeInBits - Return the size in bits of the specified type,
2313
/// for which isSCEVable must return true.
2314
uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const {
2315
assert(isSCEVable(Ty) && "Type is not SCEVable!");
2317
// If we have a TargetData, use it!
2319
return TD->getTypeSizeInBits(Ty);
2321
// Integer types have fixed sizes.
2322
if (Ty->isIntegerTy())
2323
return Ty->getPrimitiveSizeInBits();
2325
// The only other support type is pointer. Without TargetData, conservatively
2326
// assume pointers are 64-bit.
2327
assert(Ty->isPointerTy() && "isSCEVable permitted a non-SCEVable type!");
2331
/// getEffectiveSCEVType - Return a type with the same bitwidth as
2332
/// the given type and which represents how SCEV will treat the given
2333
/// type, for which isSCEVable must return true. For pointer types,
2334
/// this is the pointer-sized integer type.
2335
const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const {
2336
assert(isSCEVable(Ty) && "Type is not SCEVable!");
2338
if (Ty->isIntegerTy())
2341
// The only other support type is pointer.
2342
assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
2343
if (TD) return TD->getIntPtrType(getContext());
2345
// Without TargetData, conservatively assume pointers are 64-bit.
2346
return Type::getInt64Ty(getContext());
2349
const SCEV *ScalarEvolution::getCouldNotCompute() {
2350
return &CouldNotCompute;
2353
/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
2354
/// expression and create a new one.
2355
const SCEV *ScalarEvolution::getSCEV(Value *V) {
2356
assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
2358
std::map<SCEVCallbackVH, const SCEV *>::iterator I = Scalars.find(V);
2359
if (I != Scalars.end()) return I->second;
2360
const SCEV *S = createSCEV(V);
2361
Scalars.insert(std::make_pair(SCEVCallbackVH(V, this), S));
2365
/// getIntegerSCEV - Given a SCEVable type, create a constant for the
2366
/// specified signed integer value and return a SCEV for the constant.
2367
const SCEV *ScalarEvolution::getIntegerSCEV(int64_t Val, const Type *Ty) {
2368
const IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty));
2369
return getConstant(ConstantInt::get(ITy, Val));
2372
/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
2374
const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) {
2375
if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2377
cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
2379
const Type *Ty = V->getType();
2380
Ty = getEffectiveSCEVType(Ty);
2381
return getMulExpr(V,
2382
getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))));
2385
/// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
2386
const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
2387
if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2389
cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
2391
const Type *Ty = V->getType();
2392
Ty = getEffectiveSCEVType(Ty);
2393
const SCEV *AllOnes =
2394
getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
2395
return getMinusSCEV(AllOnes, V);
2398
/// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
2400
const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS,
2403
return getAddExpr(LHS, getNegativeSCEV(RHS));
2406
/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
2407
/// input value to the specified type. If the type must be extended, it is zero
2410
ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V,
2412
const Type *SrcTy = V->getType();
2413
assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2414
(Ty->isIntegerTy() || Ty->isPointerTy()) &&
2415
"Cannot truncate or zero extend with non-integer arguments!");
2416
if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2417
return V; // No conversion
2418
if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2419
return getTruncateExpr(V, Ty);
2420
return getZeroExtendExpr(V, Ty);
2423
/// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
2424
/// input value to the specified type. If the type must be extended, it is sign
2427
ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
2429
const Type *SrcTy = V->getType();
2430
assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2431
(Ty->isIntegerTy() || Ty->isPointerTy()) &&
2432
"Cannot truncate or zero extend with non-integer arguments!");
2433
if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2434
return V; // No conversion
2435
if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2436
return getTruncateExpr(V, Ty);
2437
return getSignExtendExpr(V, Ty);
2440
/// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
2441
/// input value to the specified type. If the type must be extended, it is zero
2442
/// extended. The conversion must not be narrowing.
2444
ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, const Type *Ty) {
2445
const Type *SrcTy = V->getType();
2446
assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2447
(Ty->isIntegerTy() || Ty->isPointerTy()) &&
2448
"Cannot noop or zero extend with non-integer arguments!");
2449
assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2450
"getNoopOrZeroExtend cannot truncate!");
2451
if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2452
return V; // No conversion
2453
return getZeroExtendExpr(V, Ty);
2456
/// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
2457
/// input value to the specified type. If the type must be extended, it is sign
2458
/// extended. The conversion must not be narrowing.
2460
ScalarEvolution::getNoopOrSignExtend(const SCEV *V, const Type *Ty) {
2461
const Type *SrcTy = V->getType();
2462
assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2463
(Ty->isIntegerTy() || Ty->isPointerTy()) &&
2464
"Cannot noop or sign extend with non-integer arguments!");
2465
assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2466
"getNoopOrSignExtend cannot truncate!");
2467
if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2468
return V; // No conversion
2469
return getSignExtendExpr(V, Ty);
2472
/// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
2473
/// the input value to the specified type. If the type must be extended,
2474
/// it is extended with unspecified bits. The conversion must not be
2477
ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, const Type *Ty) {
2478
const Type *SrcTy = V->getType();
2479
assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2480
(Ty->isIntegerTy() || Ty->isPointerTy()) &&
2481
"Cannot noop or any extend with non-integer arguments!");
2482
assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2483
"getNoopOrAnyExtend cannot truncate!");
2484
if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2485
return V; // No conversion
2486
return getAnyExtendExpr(V, Ty);
2489
/// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
2490
/// input value to the specified type. The conversion must not be widening.
2492
ScalarEvolution::getTruncateOrNoop(const SCEV *V, const Type *Ty) {
2493
const Type *SrcTy = V->getType();
2494
assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2495
(Ty->isIntegerTy() || Ty->isPointerTy()) &&
2496
"Cannot truncate or noop with non-integer arguments!");
2497
assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
2498
"getTruncateOrNoop cannot extend!");
2499
if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2500
return V; // No conversion
2501
return getTruncateExpr(V, Ty);
2504
/// getUMaxFromMismatchedTypes - Promote the operands to the wider of
2505
/// the types using zero-extension, and then perform a umax operation
2507
const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
2509
const SCEV *PromotedLHS = LHS;
2510
const SCEV *PromotedRHS = RHS;
2512
if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2513
PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2515
PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2517
return getUMaxExpr(PromotedLHS, PromotedRHS);
2520
/// getUMinFromMismatchedTypes - Promote the operands to the wider of
2521
/// the types using zero-extension, and then perform a umin operation
2523
const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
2525
const SCEV *PromotedLHS = LHS;
2526
const SCEV *PromotedRHS = RHS;
2528
if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2529
PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2531
PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2533
return getUMinExpr(PromotedLHS, PromotedRHS);
2536
/// PushDefUseChildren - Push users of the given Instruction
2537
/// onto the given Worklist.
2539
PushDefUseChildren(Instruction *I,
2540
SmallVectorImpl<Instruction *> &Worklist) {
2541
// Push the def-use children onto the Worklist stack.
2542
for (Value::use_iterator UI = I->use_begin(), UE = I->use_end();
2544
Worklist.push_back(cast<Instruction>(UI));
2547
/// ForgetSymbolicValue - This looks up computed SCEV values for all
2548
/// instructions that depend on the given instruction and removes them from
2549
/// the Scalars map if they reference SymName. This is used during PHI
2552
ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) {
2553
SmallVector<Instruction *, 16> Worklist;
2554
PushDefUseChildren(PN, Worklist);
2556
SmallPtrSet<Instruction *, 8> Visited;
2558
while (!Worklist.empty()) {
2559
Instruction *I = Worklist.pop_back_val();
2560
if (!Visited.insert(I)) continue;
2562
std::map<SCEVCallbackVH, const SCEV *>::iterator It =
2563
Scalars.find(static_cast<Value *>(I));
2564
if (It != Scalars.end()) {
2565
// Short-circuit the def-use traversal if the symbolic name
2566
// ceases to appear in expressions.
2567
if (It->second != SymName && !It->second->hasOperand(SymName))
2570
// SCEVUnknown for a PHI either means that it has an unrecognized
2571
// structure, it's a PHI that's in the progress of being computed
2572
// by createNodeForPHI, or it's a single-value PHI. In the first case,
2573
// additional loop trip count information isn't going to change anything.
2574
// In the second case, createNodeForPHI will perform the necessary
2575
// updates on its own when it gets to that point. In the third, we do
2576
// want to forget the SCEVUnknown.
2577
if (!isa<PHINode>(I) ||
2578
!isa<SCEVUnknown>(It->second) ||
2579
(I != PN && It->second == SymName)) {
2580
ValuesAtScopes.erase(It->second);
2585
PushDefUseChildren(I, Worklist);
2589
/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
2590
/// a loop header, making it a potential recurrence, or it doesn't.
2592
const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
2593
if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized.
2594
if (const Loop *L = LI->getLoopFor(PN->getParent()))
2595
if (L->getHeader() == PN->getParent()) {
2596
// If it lives in the loop header, it has two incoming values, one
2597
// from outside the loop, and one from inside.
2598
unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0));
2599
unsigned BackEdge = IncomingEdge^1;
2601
// While we are analyzing this PHI node, handle its value symbolically.
2602
const SCEV *SymbolicName = getUnknown(PN);
2603
assert(Scalars.find(PN) == Scalars.end() &&
2604
"PHI node already processed?");
2605
Scalars.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
2607
// Using this symbolic name for the PHI, analyze the value coming around
2609
Value *BEValueV = PN->getIncomingValue(BackEdge);
2610
const SCEV *BEValue = getSCEV(BEValueV);
2612
// NOTE: If BEValue is loop invariant, we know that the PHI node just
2613
// has a special value for the first iteration of the loop.
2615
// If the value coming around the backedge is an add with the symbolic
2616
// value we just inserted, then we found a simple induction variable!
2617
if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
2618
// If there is a single occurrence of the symbolic value, replace it
2619
// with a recurrence.
2620
unsigned FoundIndex = Add->getNumOperands();
2621
for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
2622
if (Add->getOperand(i) == SymbolicName)
2623
if (FoundIndex == e) {
2628
if (FoundIndex != Add->getNumOperands()) {
2629
// Create an add with everything but the specified operand.
2630
SmallVector<const SCEV *, 8> Ops;
2631
for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
2632
if (i != FoundIndex)
2633
Ops.push_back(Add->getOperand(i));
2634
const SCEV *Accum = getAddExpr(Ops);
2636
// This is not a valid addrec if the step amount is varying each
2637
// loop iteration, but is not itself an addrec in this loop.
2638
if (Accum->isLoopInvariant(L) ||
2639
(isa<SCEVAddRecExpr>(Accum) &&
2640
cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
2641
bool HasNUW = false;
2642
bool HasNSW = false;
2644
// If the increment doesn't overflow, then neither the addrec nor
2645
// the post-increment will overflow.
2646
if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) {
2647
if (OBO->hasNoUnsignedWrap())
2649
if (OBO->hasNoSignedWrap())
2653
const SCEV *StartVal =
2654
getSCEV(PN->getIncomingValue(IncomingEdge));
2655
const SCEV *PHISCEV =
2656
getAddRecExpr(StartVal, Accum, L, HasNUW, HasNSW);
2658
// Since the no-wrap flags are on the increment, they apply to the
2659
// post-incremented value as well.
2660
if (Accum->isLoopInvariant(L))
2661
(void)getAddRecExpr(getAddExpr(StartVal, Accum),
2662
Accum, L, HasNUW, HasNSW);
2664
// Okay, for the entire analysis of this edge we assumed the PHI
2665
// to be symbolic. We now need to go back and purge all of the
2666
// entries for the scalars that use the symbolic expression.
2667
ForgetSymbolicName(PN, SymbolicName);
2668
Scalars[SCEVCallbackVH(PN, this)] = PHISCEV;
2672
} else if (const SCEVAddRecExpr *AddRec =
2673
dyn_cast<SCEVAddRecExpr>(BEValue)) {
2674
// Otherwise, this could be a loop like this:
2675
// i = 0; for (j = 1; ..; ++j) { .... i = j; }
2676
// In this case, j = {1,+,1} and BEValue is j.
2677
// Because the other in-value of i (0) fits the evolution of BEValue
2678
// i really is an addrec evolution.
2679
if (AddRec->getLoop() == L && AddRec->isAffine()) {
2680
const SCEV *StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
2682
// If StartVal = j.start - j.stride, we can use StartVal as the
2683
// initial step of the addrec evolution.
2684
if (StartVal == getMinusSCEV(AddRec->getOperand(0),
2685
AddRec->getOperand(1))) {
2686
const SCEV *PHISCEV =
2687
getAddRecExpr(StartVal, AddRec->getOperand(1), L);
2689
// Okay, for the entire analysis of this edge we assumed the PHI
2690
// to be symbolic. We now need to go back and purge all of the
2691
// entries for the scalars that use the symbolic expression.
2692
ForgetSymbolicName(PN, SymbolicName);
2693
Scalars[SCEVCallbackVH(PN, this)] = PHISCEV;
2699
return SymbolicName;
2702
// If the PHI has a single incoming value, follow that value, unless the
2703
// PHI's incoming blocks are in a different loop, in which case doing so
2704
// risks breaking LCSSA form. Instcombine would normally zap these, but
2705
// it doesn't have DominatorTree information, so it may miss cases.
2706
if (Value *V = PN->hasConstantValue(DT)) {
2707
bool AllSameLoop = true;
2708
Loop *PNLoop = LI->getLoopFor(PN->getParent());
2709
for (size_t i = 0, e = PN->getNumIncomingValues(); i != e; ++i)
2710
if (LI->getLoopFor(PN->getIncomingBlock(i)) != PNLoop) {
2711
AllSameLoop = false;
2718
// If it's not a loop phi, we can't handle it yet.
2719
return getUnknown(PN);
2722
/// createNodeForGEP - Expand GEP instructions into add and multiply
2723
/// operations. This allows them to be analyzed by regular SCEV code.
2725
const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
2727
bool InBounds = GEP->isInBounds();
2728
const Type *IntPtrTy = getEffectiveSCEVType(GEP->getType());
2729
Value *Base = GEP->getOperand(0);
2730
// Don't attempt to analyze GEPs over unsized objects.
2731
if (!cast<PointerType>(Base->getType())->getElementType()->isSized())
2732
return getUnknown(GEP);
2733
const SCEV *TotalOffset = getIntegerSCEV(0, IntPtrTy);
2734
gep_type_iterator GTI = gep_type_begin(GEP);
2735
for (GetElementPtrInst::op_iterator I = next(GEP->op_begin()),
2739
// Compute the (potentially symbolic) offset in bytes for this index.
2740
if (const StructType *STy = dyn_cast<StructType>(*GTI++)) {
2741
// For a struct, add the member offset.
2742
unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
2743
TotalOffset = getAddExpr(TotalOffset,
2744
getOffsetOfExpr(STy, FieldNo),
2745
/*HasNUW=*/false, /*HasNSW=*/InBounds);
2747
// For an array, add the element offset, explicitly scaled.
2748
const SCEV *LocalOffset = getSCEV(Index);
2749
// Getelementptr indices are signed.
2750
LocalOffset = getTruncateOrSignExtend(LocalOffset, IntPtrTy);
2751
// Lower "inbounds" GEPs to NSW arithmetic.
2752
LocalOffset = getMulExpr(LocalOffset, getSizeOfExpr(*GTI),
2753
/*HasNUW=*/false, /*HasNSW=*/InBounds);
2754
TotalOffset = getAddExpr(TotalOffset, LocalOffset,
2755
/*HasNUW=*/false, /*HasNSW=*/InBounds);
2758
return getAddExpr(getSCEV(Base), TotalOffset,
2759
/*HasNUW=*/false, /*HasNSW=*/InBounds);
2762
/// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
2763
/// guaranteed to end in (at every loop iteration). It is, at the same time,
2764
/// the minimum number of times S is divisible by 2. For example, given {4,+,8}
2765
/// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
2767
ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
2768
if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
2769
return C->getValue()->getValue().countTrailingZeros();
2771
if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
2772
return std::min(GetMinTrailingZeros(T->getOperand()),
2773
(uint32_t)getTypeSizeInBits(T->getType()));
2775
if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
2776
uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
2777
return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
2778
getTypeSizeInBits(E->getType()) : OpRes;
2781
if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
2782
uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
2783
return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
2784
getTypeSizeInBits(E->getType()) : OpRes;
2787
if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
2788
// The result is the min of all operands results.
2789
uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
2790
for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
2791
MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
2795
if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
2796
// The result is the sum of all operands results.
2797
uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
2798
uint32_t BitWidth = getTypeSizeInBits(M->getType());
2799
for (unsigned i = 1, e = M->getNumOperands();
2800
SumOpRes != BitWidth && i != e; ++i)
2801
SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
2806
if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
2807
// The result is the min of all operands results.
2808
uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
2809
for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
2810
MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
2814
if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
2815
// The result is the min of all operands results.
2816
uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
2817
for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
2818
MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
2822
if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
2823
// The result is the min of all operands results.
2824
uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
2825
for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
2826
MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
2830
if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
2831
// For a SCEVUnknown, ask ValueTracking.
2832
unsigned BitWidth = getTypeSizeInBits(U->getType());
2833
APInt Mask = APInt::getAllOnesValue(BitWidth);
2834
APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
2835
ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones);
2836
return Zeros.countTrailingOnes();
2843
/// getUnsignedRange - Determine the unsigned range for a particular SCEV.
2846
ScalarEvolution::getUnsignedRange(const SCEV *S) {
2848
if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
2849
return ConstantRange(C->getValue()->getValue());
2851
unsigned BitWidth = getTypeSizeInBits(S->getType());
2852
ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
2854
// If the value has known zeros, the maximum unsigned value will have those
2855
// known zeros as well.
2856
uint32_t TZ = GetMinTrailingZeros(S);
2858
ConservativeResult =
2859
ConstantRange(APInt::getMinValue(BitWidth),
2860
APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
2862
if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
2863
ConstantRange X = getUnsignedRange(Add->getOperand(0));
2864
for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
2865
X = X.add(getUnsignedRange(Add->getOperand(i)));
2866
return ConservativeResult.intersectWith(X);
2869
if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
2870
ConstantRange X = getUnsignedRange(Mul->getOperand(0));
2871
for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
2872
X = X.multiply(getUnsignedRange(Mul->getOperand(i)));
2873
return ConservativeResult.intersectWith(X);
2876
if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
2877
ConstantRange X = getUnsignedRange(SMax->getOperand(0));
2878
for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
2879
X = X.smax(getUnsignedRange(SMax->getOperand(i)));
2880
return ConservativeResult.intersectWith(X);
2883
if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
2884
ConstantRange X = getUnsignedRange(UMax->getOperand(0));
2885
for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
2886
X = X.umax(getUnsignedRange(UMax->getOperand(i)));
2887
return ConservativeResult.intersectWith(X);
2890
if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
2891
ConstantRange X = getUnsignedRange(UDiv->getLHS());
2892
ConstantRange Y = getUnsignedRange(UDiv->getRHS());
2893
return ConservativeResult.intersectWith(X.udiv(Y));
2896
if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
2897
ConstantRange X = getUnsignedRange(ZExt->getOperand());
2898
return ConservativeResult.intersectWith(X.zeroExtend(BitWidth));
2901
if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
2902
ConstantRange X = getUnsignedRange(SExt->getOperand());
2903
return ConservativeResult.intersectWith(X.signExtend(BitWidth));
2906
if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
2907
ConstantRange X = getUnsignedRange(Trunc->getOperand());
2908
return ConservativeResult.intersectWith(X.truncate(BitWidth));
2911
if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
2912
// If there's no unsigned wrap, the value will never be less than its
2914
if (AddRec->hasNoUnsignedWrap())
2915
if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
2916
ConservativeResult =
2917
ConstantRange(C->getValue()->getValue(),
2918
APInt(getTypeSizeInBits(C->getType()), 0));
2920
// TODO: non-affine addrec
2921
if (AddRec->isAffine()) {
2922
const Type *Ty = AddRec->getType();
2923
const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
2924
if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
2925
getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
2926
MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
2928
const SCEV *Start = AddRec->getStart();
2929
const SCEV *End = AddRec->evaluateAtIteration(MaxBECount, *this);
2931
// Check for overflow.
2932
if (!AddRec->hasNoUnsignedWrap())
2933
return ConservativeResult;
2935
ConstantRange StartRange = getUnsignedRange(Start);
2936
ConstantRange EndRange = getUnsignedRange(End);
2937
APInt Min = APIntOps::umin(StartRange.getUnsignedMin(),
2938
EndRange.getUnsignedMin());
2939
APInt Max = APIntOps::umax(StartRange.getUnsignedMax(),
2940
EndRange.getUnsignedMax());
2941
if (Min.isMinValue() && Max.isMaxValue())
2942
return ConservativeResult;
2943
return ConservativeResult.intersectWith(ConstantRange(Min, Max+1));
2947
return ConservativeResult;
2950
if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
2951
// For a SCEVUnknown, ask ValueTracking.
2952
APInt Mask = APInt::getAllOnesValue(BitWidth);
2953
APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
2954
ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones, TD);
2955
if (Ones == ~Zeros + 1)
2956
return ConservativeResult;
2957
return ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1));
2960
return ConservativeResult;
2963
/// getSignedRange - Determine the signed range for a particular SCEV.
2966
ScalarEvolution::getSignedRange(const SCEV *S) {
2968
if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
2969
return ConstantRange(C->getValue()->getValue());
2971
unsigned BitWidth = getTypeSizeInBits(S->getType());
2972
ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
2974
// If the value has known zeros, the maximum signed value will have those
2975
// known zeros as well.
2976
uint32_t TZ = GetMinTrailingZeros(S);
2978
ConservativeResult =
2979
ConstantRange(APInt::getSignedMinValue(BitWidth),
2980
APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
2982
if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
2983
ConstantRange X = getSignedRange(Add->getOperand(0));
2984
for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
2985
X = X.add(getSignedRange(Add->getOperand(i)));
2986
return ConservativeResult.intersectWith(X);
2989
if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
2990
ConstantRange X = getSignedRange(Mul->getOperand(0));
2991
for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
2992
X = X.multiply(getSignedRange(Mul->getOperand(i)));
2993
return ConservativeResult.intersectWith(X);
2996
if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
2997
ConstantRange X = getSignedRange(SMax->getOperand(0));
2998
for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
2999
X = X.smax(getSignedRange(SMax->getOperand(i)));
3000
return ConservativeResult.intersectWith(X);
3003
if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3004
ConstantRange X = getSignedRange(UMax->getOperand(0));
3005
for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3006
X = X.umax(getSignedRange(UMax->getOperand(i)));
3007
return ConservativeResult.intersectWith(X);
3010
if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3011
ConstantRange X = getSignedRange(UDiv->getLHS());
3012
ConstantRange Y = getSignedRange(UDiv->getRHS());
3013
return ConservativeResult.intersectWith(X.udiv(Y));
3016
if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3017
ConstantRange X = getSignedRange(ZExt->getOperand());
3018
return ConservativeResult.intersectWith(X.zeroExtend(BitWidth));
3021
if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3022
ConstantRange X = getSignedRange(SExt->getOperand());
3023
return ConservativeResult.intersectWith(X.signExtend(BitWidth));
3026
if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3027
ConstantRange X = getSignedRange(Trunc->getOperand());
3028
return ConservativeResult.intersectWith(X.truncate(BitWidth));
3031
if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3032
// If there's no signed wrap, and all the operands have the same sign or
3033
// zero, the value won't ever change sign.
3034
if (AddRec->hasNoSignedWrap()) {
3035
bool AllNonNeg = true;
3036
bool AllNonPos = true;
3037
for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
3038
if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
3039
if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
3042
ConservativeResult = ConservativeResult.intersectWith(
3043
ConstantRange(APInt(BitWidth, 0),
3044
APInt::getSignedMinValue(BitWidth)));
3046
ConservativeResult = ConservativeResult.intersectWith(
3047
ConstantRange(APInt::getSignedMinValue(BitWidth),
3048
APInt(BitWidth, 1)));
3051
// TODO: non-affine addrec
3052
if (AddRec->isAffine()) {
3053
const Type *Ty = AddRec->getType();
3054
const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3055
if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3056
getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3057
MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3059
const SCEV *Start = AddRec->getStart();
3060
const SCEV *End = AddRec->evaluateAtIteration(MaxBECount, *this);
3062
// Check for overflow.
3063
if (!AddRec->hasNoSignedWrap())
3064
return ConservativeResult;
3066
ConstantRange StartRange = getSignedRange(Start);
3067
ConstantRange EndRange = getSignedRange(End);
3068
APInt Min = APIntOps::smin(StartRange.getSignedMin(),
3069
EndRange.getSignedMin());
3070
APInt Max = APIntOps::smax(StartRange.getSignedMax(),
3071
EndRange.getSignedMax());
3072
if (Min.isMinSignedValue() && Max.isMaxSignedValue())
3073
return ConservativeResult;
3074
return ConservativeResult.intersectWith(ConstantRange(Min, Max+1));
3078
return ConservativeResult;
3081
if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3082
// For a SCEVUnknown, ask ValueTracking.
3083
if (!U->getValue()->getType()->isIntegerTy() && !TD)
3084
return ConservativeResult;
3085
unsigned NS = ComputeNumSignBits(U->getValue(), TD);
3087
return ConservativeResult;
3088
return ConservativeResult.intersectWith(
3089
ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
3090
APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1));
3093
return ConservativeResult;
3096
/// createSCEV - We know that there is no SCEV for the specified value.
3097
/// Analyze the expression.
3099
const SCEV *ScalarEvolution::createSCEV(Value *V) {
3100
if (!isSCEVable(V->getType()))
3101
return getUnknown(V);
3103
unsigned Opcode = Instruction::UserOp1;
3104
if (Instruction *I = dyn_cast<Instruction>(V))
3105
Opcode = I->getOpcode();
3106
else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
3107
Opcode = CE->getOpcode();
3108
else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
3109
return getConstant(CI);
3110
else if (isa<ConstantPointerNull>(V))
3111
return getIntegerSCEV(0, V->getType());
3112
else if (isa<UndefValue>(V))
3113
return getIntegerSCEV(0, V->getType());
3114
else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
3115
return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee());
3117
return getUnknown(V);
3119
Operator *U = cast<Operator>(V);
3121
case Instruction::Add:
3122
// Don't transfer the NSW and NUW bits from the Add instruction to the
3123
// Add expression, because the Instruction may be guarded by control
3124
// flow and the no-overflow bits may not be valid for the expression in
3126
return getAddExpr(getSCEV(U->getOperand(0)),
3127
getSCEV(U->getOperand(1)));
3128
case Instruction::Mul:
3129
// Don't transfer the NSW and NUW bits from the Mul instruction to the
3130
// Mul expression, as with Add.
3131
return getMulExpr(getSCEV(U->getOperand(0)),
3132
getSCEV(U->getOperand(1)));
3133
case Instruction::UDiv:
3134
return getUDivExpr(getSCEV(U->getOperand(0)),
3135
getSCEV(U->getOperand(1)));
3136
case Instruction::Sub:
3137
return getMinusSCEV(getSCEV(U->getOperand(0)),
3138
getSCEV(U->getOperand(1)));
3139
case Instruction::And:
3140
// For an expression like x&255 that merely masks off the high bits,
3141
// use zext(trunc(x)) as the SCEV expression.
3142
if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3143
if (CI->isNullValue())
3144
return getSCEV(U->getOperand(1));
3145
if (CI->isAllOnesValue())
3146
return getSCEV(U->getOperand(0));
3147
const APInt &A = CI->getValue();
3149
// Instcombine's ShrinkDemandedConstant may strip bits out of
3150
// constants, obscuring what would otherwise be a low-bits mask.
3151
// Use ComputeMaskedBits to compute what ShrinkDemandedConstant
3152
// knew about to reconstruct a low-bits mask value.
3153
unsigned LZ = A.countLeadingZeros();
3154
unsigned BitWidth = A.getBitWidth();
3155
APInt AllOnes = APInt::getAllOnesValue(BitWidth);
3156
APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
3157
ComputeMaskedBits(U->getOperand(0), AllOnes, KnownZero, KnownOne, TD);
3159
APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ);
3161
if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask))
3163
getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)),
3164
IntegerType::get(getContext(), BitWidth - LZ)),
3169
case Instruction::Or:
3170
// If the RHS of the Or is a constant, we may have something like:
3171
// X*4+1 which got turned into X*4|1. Handle this as an Add so loop
3172
// optimizations will transparently handle this case.
3174
// In order for this transformation to be safe, the LHS must be of the
3175
// form X*(2^n) and the Or constant must be less than 2^n.
3176
if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3177
const SCEV *LHS = getSCEV(U->getOperand(0));
3178
const APInt &CIVal = CI->getValue();
3179
if (GetMinTrailingZeros(LHS) >=
3180
(CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
3181
// Build a plain add SCEV.
3182
const SCEV *S = getAddExpr(LHS, getSCEV(CI));
3183
// If the LHS of the add was an addrec and it has no-wrap flags,
3184
// transfer the no-wrap flags, since an or won't introduce a wrap.
3185
if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
3186
const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
3187
if (OldAR->hasNoUnsignedWrap())
3188
const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoUnsignedWrap(true);
3189
if (OldAR->hasNoSignedWrap())
3190
const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoSignedWrap(true);
3196
case Instruction::Xor:
3197
if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3198
// If the RHS of the xor is a signbit, then this is just an add.
3199
// Instcombine turns add of signbit into xor as a strength reduction step.
3200
if (CI->getValue().isSignBit())
3201
return getAddExpr(getSCEV(U->getOperand(0)),
3202
getSCEV(U->getOperand(1)));
3204
// If the RHS of xor is -1, then this is a not operation.
3205
if (CI->isAllOnesValue())
3206
return getNotSCEV(getSCEV(U->getOperand(0)));
3208
// Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
3209
// This is a variant of the check for xor with -1, and it handles
3210
// the case where instcombine has trimmed non-demanded bits out
3211
// of an xor with -1.
3212
if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
3213
if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
3214
if (BO->getOpcode() == Instruction::And &&
3215
LCI->getValue() == CI->getValue())
3216
if (const SCEVZeroExtendExpr *Z =
3217
dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
3218
const Type *UTy = U->getType();
3219
const SCEV *Z0 = Z->getOperand();
3220
const Type *Z0Ty = Z0->getType();
3221
unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
3223
// If C is a low-bits mask, the zero extend is serving to
3224
// mask off the high bits. Complement the operand and
3225
// re-apply the zext.
3226
if (APIntOps::isMask(Z0TySize, CI->getValue()))
3227
return getZeroExtendExpr(getNotSCEV(Z0), UTy);
3229
// If C is a single bit, it may be in the sign-bit position
3230
// before the zero-extend. In this case, represent the xor
3231
// using an add, which is equivalent, and re-apply the zext.
3232
APInt Trunc = APInt(CI->getValue()).trunc(Z0TySize);
3233
if (APInt(Trunc).zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
3235
return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
3241
case Instruction::Shl:
3242
// Turn shift left of a constant amount into a multiply.
3243
if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3244
uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3245
Constant *X = ConstantInt::get(getContext(),
3246
APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
3247
return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3251
case Instruction::LShr:
3252
// Turn logical shift right of a constant into a unsigned divide.
3253
if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3254
uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3255
Constant *X = ConstantInt::get(getContext(),
3256
APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
3257
return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3261
case Instruction::AShr:
3262
// For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
3263
if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
3264
if (Instruction *L = dyn_cast<Instruction>(U->getOperand(0)))
3265
if (L->getOpcode() == Instruction::Shl &&
3266
L->getOperand(1) == U->getOperand(1)) {
3267
unsigned BitWidth = getTypeSizeInBits(U->getType());
3268
uint64_t Amt = BitWidth - CI->getZExtValue();
3269
if (Amt == BitWidth)
3270
return getSCEV(L->getOperand(0)); // shift by zero --> noop
3272
return getIntegerSCEV(0, U->getType()); // value is undefined
3274
getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
3275
IntegerType::get(getContext(), Amt)),
3280
case Instruction::Trunc:
3281
return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
3283
case Instruction::ZExt:
3284
return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3286
case Instruction::SExt:
3287
return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3289
case Instruction::BitCast:
3290
// BitCasts are no-op casts so we just eliminate the cast.
3291
if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
3292
return getSCEV(U->getOperand(0));
3295
// It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
3296
// lead to pointer expressions which cannot safely be expanded to GEPs,
3297
// because ScalarEvolution doesn't respect the GEP aliasing rules when
3298
// simplifying integer expressions.
3300
case Instruction::GetElementPtr:
3301
return createNodeForGEP(cast<GEPOperator>(U));
3303
case Instruction::PHI:
3304
return createNodeForPHI(cast<PHINode>(U));
3306
case Instruction::Select:
3307
// This could be a smax or umax that was lowered earlier.
3308
// Try to recover it.
3309
if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
3310
Value *LHS = ICI->getOperand(0);
3311
Value *RHS = ICI->getOperand(1);
3312
switch (ICI->getPredicate()) {
3313
case ICmpInst::ICMP_SLT:
3314
case ICmpInst::ICMP_SLE:
3315
std::swap(LHS, RHS);
3317
case ICmpInst::ICMP_SGT:
3318
case ICmpInst::ICMP_SGE:
3319
if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
3320
return getSMaxExpr(getSCEV(LHS), getSCEV(RHS));
3321
else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
3322
return getSMinExpr(getSCEV(LHS), getSCEV(RHS));
3324
case ICmpInst::ICMP_ULT:
3325
case ICmpInst::ICMP_ULE:
3326
std::swap(LHS, RHS);
3328
case ICmpInst::ICMP_UGT:
3329
case ICmpInst::ICMP_UGE:
3330
if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
3331
return getUMaxExpr(getSCEV(LHS), getSCEV(RHS));
3332
else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
3333
return getUMinExpr(getSCEV(LHS), getSCEV(RHS));
3335
case ICmpInst::ICMP_NE:
3336
// n != 0 ? n : 1 -> umax(n, 1)
3337
if (LHS == U->getOperand(1) &&
3338
isa<ConstantInt>(U->getOperand(2)) &&
3339
cast<ConstantInt>(U->getOperand(2))->isOne() &&
3340
isa<ConstantInt>(RHS) &&
3341
cast<ConstantInt>(RHS)->isZero())
3342
return getUMaxExpr(getSCEV(LHS), getSCEV(U->getOperand(2)));
3344
case ICmpInst::ICMP_EQ:
3345
// n == 0 ? 1 : n -> umax(n, 1)
3346
if (LHS == U->getOperand(2) &&
3347
isa<ConstantInt>(U->getOperand(1)) &&
3348
cast<ConstantInt>(U->getOperand(1))->isOne() &&
3349
isa<ConstantInt>(RHS) &&
3350
cast<ConstantInt>(RHS)->isZero())
3351
return getUMaxExpr(getSCEV(LHS), getSCEV(U->getOperand(1)));
3358
default: // We cannot analyze this expression.
3362
return getUnknown(V);
3367
//===----------------------------------------------------------------------===//
3368
// Iteration Count Computation Code
3371
/// getBackedgeTakenCount - If the specified loop has a predictable
3372
/// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
3373
/// object. The backedge-taken count is the number of times the loop header
3374
/// will be branched to from within the loop. This is one less than the
3375
/// trip count of the loop, since it doesn't count the first iteration,
3376
/// when the header is branched to from outside the loop.
3378
/// Note that it is not valid to call this method on a loop without a
3379
/// loop-invariant backedge-taken count (see
3380
/// hasLoopInvariantBackedgeTakenCount).
3382
const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
3383
return getBackedgeTakenInfo(L).Exact;
3386
/// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
3387
/// return the least SCEV value that is known never to be less than the
3388
/// actual backedge taken count.
3389
const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
3390
return getBackedgeTakenInfo(L).Max;
3393
/// PushLoopPHIs - Push PHI nodes in the header of the given loop
3394
/// onto the given Worklist.
3396
PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
3397
BasicBlock *Header = L->getHeader();
3399
// Push all Loop-header PHIs onto the Worklist stack.
3400
for (BasicBlock::iterator I = Header->begin();
3401
PHINode *PN = dyn_cast<PHINode>(I); ++I)
3402
Worklist.push_back(PN);
3405
const ScalarEvolution::BackedgeTakenInfo &
3406
ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
3407
// Initially insert a CouldNotCompute for this loop. If the insertion
3408
// succeeds, proceed to actually compute a backedge-taken count and
3409
// update the value. The temporary CouldNotCompute value tells SCEV
3410
// code elsewhere that it shouldn't attempt to request a new
3411
// backedge-taken count, which could result in infinite recursion.
3412
std::pair<std::map<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
3413
BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute()));
3415
BackedgeTakenInfo BECount = ComputeBackedgeTakenCount(L);
3416
if (BECount.Exact != getCouldNotCompute()) {
3417
assert(BECount.Exact->isLoopInvariant(L) &&
3418
BECount.Max->isLoopInvariant(L) &&
3419
"Computed backedge-taken count isn't loop invariant for loop!");
3420
++NumTripCountsComputed;
3422
// Update the value in the map.
3423
Pair.first->second = BECount;
3425
if (BECount.Max != getCouldNotCompute())
3426
// Update the value in the map.
3427
Pair.first->second = BECount;
3428
if (isa<PHINode>(L->getHeader()->begin()))
3429
// Only count loops that have phi nodes as not being computable.
3430
++NumTripCountsNotComputed;
3433
// Now that we know more about the trip count for this loop, forget any
3434
// existing SCEV values for PHI nodes in this loop since they are only
3435
// conservative estimates made without the benefit of trip count
3436
// information. This is similar to the code in forgetLoop, except that
3437
// it handles SCEVUnknown PHI nodes specially.
3438
if (BECount.hasAnyInfo()) {
3439
SmallVector<Instruction *, 16> Worklist;
3440
PushLoopPHIs(L, Worklist);
3442
SmallPtrSet<Instruction *, 8> Visited;
3443
while (!Worklist.empty()) {
3444
Instruction *I = Worklist.pop_back_val();
3445
if (!Visited.insert(I)) continue;
3447
std::map<SCEVCallbackVH, const SCEV *>::iterator It =
3448
Scalars.find(static_cast<Value *>(I));
3449
if (It != Scalars.end()) {
3450
// SCEVUnknown for a PHI either means that it has an unrecognized
3451
// structure, or it's a PHI that's in the progress of being computed
3452
// by createNodeForPHI. In the former case, additional loop trip
3453
// count information isn't going to change anything. In the later
3454
// case, createNodeForPHI will perform the necessary updates on its
3455
// own when it gets to that point.
3456
if (!isa<PHINode>(I) || !isa<SCEVUnknown>(It->second)) {
3457
ValuesAtScopes.erase(It->second);
3460
if (PHINode *PN = dyn_cast<PHINode>(I))
3461
ConstantEvolutionLoopExitValue.erase(PN);
3464
PushDefUseChildren(I, Worklist);
3468
return Pair.first->second;
3471
/// forgetLoop - This method should be called by the client when it has
3472
/// changed a loop in a way that may effect ScalarEvolution's ability to
3473
/// compute a trip count, or if the loop is deleted.
3474
void ScalarEvolution::forgetLoop(const Loop *L) {
3475
// Drop any stored trip count value.
3476
BackedgeTakenCounts.erase(L);
3478
// Drop information about expressions based on loop-header PHIs.
3479
SmallVector<Instruction *, 16> Worklist;
3480
PushLoopPHIs(L, Worklist);
3482
SmallPtrSet<Instruction *, 8> Visited;
3483
while (!Worklist.empty()) {
3484
Instruction *I = Worklist.pop_back_val();
3485
if (!Visited.insert(I)) continue;
3487
std::map<SCEVCallbackVH, const SCEV *>::iterator It =
3488
Scalars.find(static_cast<Value *>(I));
3489
if (It != Scalars.end()) {
3490
ValuesAtScopes.erase(It->second);
3492
if (PHINode *PN = dyn_cast<PHINode>(I))
3493
ConstantEvolutionLoopExitValue.erase(PN);
3496
PushDefUseChildren(I, Worklist);
3500
/// forgetValue - This method should be called by the client when it has
3501
/// changed a value in a way that may effect its value, or which may
3502
/// disconnect it from a def-use chain linking it to a loop.
3503
void ScalarEvolution::forgetValue(Value *V) {
3504
Instruction *I = dyn_cast<Instruction>(V);
3507
// Drop information about expressions based on loop-header PHIs.
3508
SmallVector<Instruction *, 16> Worklist;
3509
Worklist.push_back(I);
3511
SmallPtrSet<Instruction *, 8> Visited;
3512
while (!Worklist.empty()) {
3513
I = Worklist.pop_back_val();
3514
if (!Visited.insert(I)) continue;
3516
std::map<SCEVCallbackVH, const SCEV *>::iterator It =
3517
Scalars.find(static_cast<Value *>(I));
3518
if (It != Scalars.end()) {
3519
ValuesAtScopes.erase(It->second);
3521
if (PHINode *PN = dyn_cast<PHINode>(I))
3522
ConstantEvolutionLoopExitValue.erase(PN);
3525
PushDefUseChildren(I, Worklist);
3529
/// ComputeBackedgeTakenCount - Compute the number of times the backedge
3530
/// of the specified loop will execute.
3531
ScalarEvolution::BackedgeTakenInfo
3532
ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
3533
SmallVector<BasicBlock *, 8> ExitingBlocks;
3534
L->getExitingBlocks(ExitingBlocks);
3536
// Examine all exits and pick the most conservative values.
3537
const SCEV *BECount = getCouldNotCompute();
3538
const SCEV *MaxBECount = getCouldNotCompute();
3539
bool CouldNotComputeBECount = false;
3540
for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
3541
BackedgeTakenInfo NewBTI =
3542
ComputeBackedgeTakenCountFromExit(L, ExitingBlocks[i]);
3544
if (NewBTI.Exact == getCouldNotCompute()) {
3545
// We couldn't compute an exact value for this exit, so
3546
// we won't be able to compute an exact value for the loop.
3547
CouldNotComputeBECount = true;
3548
BECount = getCouldNotCompute();
3549
} else if (!CouldNotComputeBECount) {
3550
if (BECount == getCouldNotCompute())
3551
BECount = NewBTI.Exact;
3553
BECount = getUMinFromMismatchedTypes(BECount, NewBTI.Exact);
3555
if (MaxBECount == getCouldNotCompute())
3556
MaxBECount = NewBTI.Max;
3557
else if (NewBTI.Max != getCouldNotCompute())
3558
MaxBECount = getUMinFromMismatchedTypes(MaxBECount, NewBTI.Max);
3561
return BackedgeTakenInfo(BECount, MaxBECount);
3564
/// ComputeBackedgeTakenCountFromExit - Compute the number of times the backedge
3565
/// of the specified loop will execute if it exits via the specified block.
3566
ScalarEvolution::BackedgeTakenInfo
3567
ScalarEvolution::ComputeBackedgeTakenCountFromExit(const Loop *L,
3568
BasicBlock *ExitingBlock) {
3570
// Okay, we've chosen an exiting block. See what condition causes us to
3571
// exit at this block.
3573
// FIXME: we should be able to handle switch instructions (with a single exit)
3574
BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
3575
if (ExitBr == 0) return getCouldNotCompute();
3576
assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
3578
// At this point, we know we have a conditional branch that determines whether
3579
// the loop is exited. However, we don't know if the branch is executed each
3580
// time through the loop. If not, then the execution count of the branch will
3581
// not be equal to the trip count of the loop.
3583
// Currently we check for this by checking to see if the Exit branch goes to
3584
// the loop header. If so, we know it will always execute the same number of
3585
// times as the loop. We also handle the case where the exit block *is* the
3586
// loop header. This is common for un-rotated loops.
3588
// If both of those tests fail, walk up the unique predecessor chain to the
3589
// header, stopping if there is an edge that doesn't exit the loop. If the
3590
// header is reached, the execution count of the branch will be equal to the
3591
// trip count of the loop.
3593
// More extensive analysis could be done to handle more cases here.
3595
if (ExitBr->getSuccessor(0) != L->getHeader() &&
3596
ExitBr->getSuccessor(1) != L->getHeader() &&
3597
ExitBr->getParent() != L->getHeader()) {
3598
// The simple checks failed, try climbing the unique predecessor chain
3599
// up to the header.
3601
for (BasicBlock *BB = ExitBr->getParent(); BB; ) {
3602
BasicBlock *Pred = BB->getUniquePredecessor();
3604
return getCouldNotCompute();
3605
TerminatorInst *PredTerm = Pred->getTerminator();
3606
for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) {
3607
BasicBlock *PredSucc = PredTerm->getSuccessor(i);
3610
// If the predecessor has a successor that isn't BB and isn't
3611
// outside the loop, assume the worst.
3612
if (L->contains(PredSucc))
3613
return getCouldNotCompute();
3615
if (Pred == L->getHeader()) {
3622
return getCouldNotCompute();
3625
// Proceed to the next level to examine the exit condition expression.
3626
return ComputeBackedgeTakenCountFromExitCond(L, ExitBr->getCondition(),
3627
ExitBr->getSuccessor(0),
3628
ExitBr->getSuccessor(1));
3631
/// ComputeBackedgeTakenCountFromExitCond - Compute the number of times the
3632
/// backedge of the specified loop will execute if its exit condition
3633
/// were a conditional branch of ExitCond, TBB, and FBB.
3634
ScalarEvolution::BackedgeTakenInfo
3635
ScalarEvolution::ComputeBackedgeTakenCountFromExitCond(const Loop *L,
3639
// Check if the controlling expression for this loop is an And or Or.
3640
if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
3641
if (BO->getOpcode() == Instruction::And) {
3642
// Recurse on the operands of the and.
3643
BackedgeTakenInfo BTI0 =
3644
ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB);
3645
BackedgeTakenInfo BTI1 =
3646
ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB);
3647
const SCEV *BECount = getCouldNotCompute();
3648
const SCEV *MaxBECount = getCouldNotCompute();
3649
if (L->contains(TBB)) {
3650
// Both conditions must be true for the loop to continue executing.
3651
// Choose the less conservative count.
3652
if (BTI0.Exact == getCouldNotCompute() ||
3653
BTI1.Exact == getCouldNotCompute())
3654
BECount = getCouldNotCompute();
3656
BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3657
if (BTI0.Max == getCouldNotCompute())
3658
MaxBECount = BTI1.Max;
3659
else if (BTI1.Max == getCouldNotCompute())
3660
MaxBECount = BTI0.Max;
3662
MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max);
3664
// Both conditions must be true for the loop to exit.
3665
assert(L->contains(FBB) && "Loop block has no successor in loop!");
3666
if (BTI0.Exact != getCouldNotCompute() &&
3667
BTI1.Exact != getCouldNotCompute())
3668
BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3669
if (BTI0.Max != getCouldNotCompute() &&
3670
BTI1.Max != getCouldNotCompute())
3671
MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max);
3674
return BackedgeTakenInfo(BECount, MaxBECount);
3676
if (BO->getOpcode() == Instruction::Or) {
3677
// Recurse on the operands of the or.
3678
BackedgeTakenInfo BTI0 =
3679
ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB);
3680
BackedgeTakenInfo BTI1 =
3681
ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB);
3682
const SCEV *BECount = getCouldNotCompute();
3683
const SCEV *MaxBECount = getCouldNotCompute();
3684
if (L->contains(FBB)) {
3685
// Both conditions must be false for the loop to continue executing.
3686
// Choose the less conservative count.
3687
if (BTI0.Exact == getCouldNotCompute() ||
3688
BTI1.Exact == getCouldNotCompute())
3689
BECount = getCouldNotCompute();
3691
BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3692
if (BTI0.Max == getCouldNotCompute())
3693
MaxBECount = BTI1.Max;
3694
else if (BTI1.Max == getCouldNotCompute())
3695
MaxBECount = BTI0.Max;
3697
MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max);
3699
// Both conditions must be false for the loop to exit.
3700
assert(L->contains(TBB) && "Loop block has no successor in loop!");
3701
if (BTI0.Exact != getCouldNotCompute() &&
3702
BTI1.Exact != getCouldNotCompute())
3703
BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3704
if (BTI0.Max != getCouldNotCompute() &&
3705
BTI1.Max != getCouldNotCompute())
3706
MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max);
3709
return BackedgeTakenInfo(BECount, MaxBECount);
3713
// With an icmp, it may be feasible to compute an exact backedge-taken count.
3714
// Proceed to the next level to examine the icmp.
3715
if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
3716
return ComputeBackedgeTakenCountFromExitCondICmp(L, ExitCondICmp, TBB, FBB);
3718
// Check for a constant condition. These are normally stripped out by
3719
// SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
3720
// preserve the CFG and is temporarily leaving constant conditions
3722
if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
3723
if (L->contains(FBB) == !CI->getZExtValue())
3724
// The backedge is always taken.
3725
return getCouldNotCompute();
3727
// The backedge is never taken.
3728
return getIntegerSCEV(0, CI->getType());
3731
// If it's not an integer or pointer comparison then compute it the hard way.
3732
return ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB));
3735
/// ComputeBackedgeTakenCountFromExitCondICmp - Compute the number of times the
3736
/// backedge of the specified loop will execute if its exit condition
3737
/// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB.
3738
ScalarEvolution::BackedgeTakenInfo
3739
ScalarEvolution::ComputeBackedgeTakenCountFromExitCondICmp(const Loop *L,
3744
// If the condition was exit on true, convert the condition to exit on false
3745
ICmpInst::Predicate Cond;
3746
if (!L->contains(FBB))
3747
Cond = ExitCond->getPredicate();
3749
Cond = ExitCond->getInversePredicate();
3751
// Handle common loops like: for (X = "string"; *X; ++X)
3752
if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
3753
if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
3754
BackedgeTakenInfo ItCnt =
3755
ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond);
3756
if (ItCnt.hasAnyInfo())
3760
const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
3761
const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
3763
// Try to evaluate any dependencies out of the loop.
3764
LHS = getSCEVAtScope(LHS, L);
3765
RHS = getSCEVAtScope(RHS, L);
3767
// At this point, we would like to compute how many iterations of the
3768
// loop the predicate will return true for these inputs.
3769
if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) {
3770
// If there is a loop-invariant, force it into the RHS.
3771
std::swap(LHS, RHS);
3772
Cond = ICmpInst::getSwappedPredicate(Cond);
3775
// If we have a comparison of a chrec against a constant, try to use value
3776
// ranges to answer this query.
3777
if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
3778
if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
3779
if (AddRec->getLoop() == L) {
3780
// Form the constant range.
3781
ConstantRange CompRange(
3782
ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
3784
const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
3785
if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
3789
case ICmpInst::ICMP_NE: { // while (X != Y)
3790
// Convert to: while (X-Y != 0)
3791
BackedgeTakenInfo BTI = HowFarToZero(getMinusSCEV(LHS, RHS), L);
3792
if (BTI.hasAnyInfo()) return BTI;
3795
case ICmpInst::ICMP_EQ: { // while (X == Y)
3796
// Convert to: while (X-Y == 0)
3797
BackedgeTakenInfo BTI = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
3798
if (BTI.hasAnyInfo()) return BTI;
3801
case ICmpInst::ICMP_SLT: {
3802
BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true);
3803
if (BTI.hasAnyInfo()) return BTI;
3806
case ICmpInst::ICMP_SGT: {
3807
BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
3808
getNotSCEV(RHS), L, true);
3809
if (BTI.hasAnyInfo()) return BTI;
3812
case ICmpInst::ICMP_ULT: {
3813
BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false);
3814
if (BTI.hasAnyInfo()) return BTI;
3817
case ICmpInst::ICMP_UGT: {
3818
BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
3819
getNotSCEV(RHS), L, false);
3820
if (BTI.hasAnyInfo()) return BTI;
3825
dbgs() << "ComputeBackedgeTakenCount ";
3826
if (ExitCond->getOperand(0)->getType()->isUnsigned())
3827
dbgs() << "[unsigned] ";
3828
dbgs() << *LHS << " "
3829
<< Instruction::getOpcodeName(Instruction::ICmp)
3830
<< " " << *RHS << "\n";
3835
ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB));
3838
static ConstantInt *
3839
EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
3840
ScalarEvolution &SE) {
3841
const SCEV *InVal = SE.getConstant(C);
3842
const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
3843
assert(isa<SCEVConstant>(Val) &&
3844
"Evaluation of SCEV at constant didn't fold correctly?");
3845
return cast<SCEVConstant>(Val)->getValue();
3848
/// GetAddressedElementFromGlobal - Given a global variable with an initializer
3849
/// and a GEP expression (missing the pointer index) indexing into it, return
3850
/// the addressed element of the initializer or null if the index expression is
3853
GetAddressedElementFromGlobal(GlobalVariable *GV,
3854
const std::vector<ConstantInt*> &Indices) {
3855
Constant *Init = GV->getInitializer();
3856
for (unsigned i = 0, e = Indices.size(); i != e; ++i) {
3857
uint64_t Idx = Indices[i]->getZExtValue();
3858
if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) {
3859
assert(Idx < CS->getNumOperands() && "Bad struct index!");
3860
Init = cast<Constant>(CS->getOperand(Idx));
3861
} else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) {
3862
if (Idx >= CA->getNumOperands()) return 0; // Bogus program
3863
Init = cast<Constant>(CA->getOperand(Idx));
3864
} else if (isa<ConstantAggregateZero>(Init)) {
3865
if (const StructType *STy = dyn_cast<StructType>(Init->getType())) {
3866
assert(Idx < STy->getNumElements() && "Bad struct index!");
3867
Init = Constant::getNullValue(STy->getElementType(Idx));
3868
} else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) {
3869
if (Idx >= ATy->getNumElements()) return 0; // Bogus program
3870
Init = Constant::getNullValue(ATy->getElementType());
3872
llvm_unreachable("Unknown constant aggregate type!");
3876
return 0; // Unknown initializer type
3882
/// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of
3883
/// 'icmp op load X, cst', try to see if we can compute the backedge
3884
/// execution count.
3885
ScalarEvolution::BackedgeTakenInfo
3886
ScalarEvolution::ComputeLoadConstantCompareBackedgeTakenCount(
3890
ICmpInst::Predicate predicate) {
3891
if (LI->isVolatile()) return getCouldNotCompute();
3893
// Check to see if the loaded pointer is a getelementptr of a global.
3894
// TODO: Use SCEV instead of manually grubbing with GEPs.
3895
GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
3896
if (!GEP) return getCouldNotCompute();
3898
// Make sure that it is really a constant global we are gepping, with an
3899
// initializer, and make sure the first IDX is really 0.
3900
GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
3901
if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
3902
GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
3903
!cast<Constant>(GEP->getOperand(1))->isNullValue())
3904
return getCouldNotCompute();
3906
// Okay, we allow one non-constant index into the GEP instruction.
3908
std::vector<ConstantInt*> Indexes;
3909
unsigned VarIdxNum = 0;
3910
for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
3911
if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
3912
Indexes.push_back(CI);
3913
} else if (!isa<ConstantInt>(GEP->getOperand(i))) {
3914
if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
3915
VarIdx = GEP->getOperand(i);
3917
Indexes.push_back(0);
3920
// Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
3921
// Check to see if X is a loop variant variable value now.
3922
const SCEV *Idx = getSCEV(VarIdx);
3923
Idx = getSCEVAtScope(Idx, L);
3925
// We can only recognize very limited forms of loop index expressions, in
3926
// particular, only affine AddRec's like {C1,+,C2}.
3927
const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
3928
if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) ||
3929
!isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
3930
!isa<SCEVConstant>(IdxExpr->getOperand(1)))
3931
return getCouldNotCompute();
3933
unsigned MaxSteps = MaxBruteForceIterations;
3934
for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
3935
ConstantInt *ItCst = ConstantInt::get(
3936
cast<IntegerType>(IdxExpr->getType()), IterationNum);
3937
ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
3939
// Form the GEP offset.
3940
Indexes[VarIdxNum] = Val;
3942
Constant *Result = GetAddressedElementFromGlobal(GV, Indexes);
3943
if (Result == 0) break; // Cannot compute!
3945
// Evaluate the condition for this iteration.
3946
Result = ConstantExpr::getICmp(predicate, Result, RHS);
3947
if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
3948
if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
3950
dbgs() << "\n***\n*** Computed loop count " << *ItCst
3951
<< "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
3954
++NumArrayLenItCounts;
3955
return getConstant(ItCst); // Found terminating iteration!
3958
return getCouldNotCompute();
3962
/// CanConstantFold - Return true if we can constant fold an instruction of the
3963
/// specified type, assuming that all operands were constants.
3964
static bool CanConstantFold(const Instruction *I) {
3965
if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
3966
isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I))
3969
if (const CallInst *CI = dyn_cast<CallInst>(I))
3970
if (const Function *F = CI->getCalledFunction())
3971
return canConstantFoldCallTo(F);
3975
/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
3976
/// in the loop that V is derived from. We allow arbitrary operations along the
3977
/// way, but the operands of an operation must either be constants or a value
3978
/// derived from a constant PHI. If this expression does not fit with these
3979
/// constraints, return null.
3980
static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
3981
// If this is not an instruction, or if this is an instruction outside of the
3982
// loop, it can't be derived from a loop PHI.
3983
Instruction *I = dyn_cast<Instruction>(V);
3984
if (I == 0 || !L->contains(I)) return 0;
3986
if (PHINode *PN = dyn_cast<PHINode>(I)) {
3987
if (L->getHeader() == I->getParent())
3990
// We don't currently keep track of the control flow needed to evaluate
3991
// PHIs, so we cannot handle PHIs inside of loops.
3995
// If we won't be able to constant fold this expression even if the operands
3996
// are constants, return early.
3997
if (!CanConstantFold(I)) return 0;
3999
// Otherwise, we can evaluate this instruction if all of its operands are
4000
// constant or derived from a PHI node themselves.
4002
for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op)
4003
if (!(isa<Constant>(I->getOperand(Op)) ||
4004
isa<GlobalValue>(I->getOperand(Op)))) {
4005
PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L);
4006
if (P == 0) return 0; // Not evolving from PHI
4010
return 0; // Evolving from multiple different PHIs.
4013
// This is a expression evolving from a constant PHI!
4017
/// EvaluateExpression - Given an expression that passes the
4018
/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
4019
/// in the loop has the value PHIVal. If we can't fold this expression for some
4020
/// reason, return null.
4021
static Constant *EvaluateExpression(Value *V, Constant *PHIVal,
4022
const TargetData *TD) {
4023
if (isa<PHINode>(V)) return PHIVal;
4024
if (Constant *C = dyn_cast<Constant>(V)) return C;
4025
if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) return GV;
4026
Instruction *I = cast<Instruction>(V);
4028
std::vector<Constant*> Operands;
4029
Operands.resize(I->getNumOperands());
4031
for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
4032
Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal, TD);
4033
if (Operands[i] == 0) return 0;
4036
if (const CmpInst *CI = dyn_cast<CmpInst>(I))
4037
return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
4039
return ConstantFoldInstOperands(I->getOpcode(), I->getType(),
4040
&Operands[0], Operands.size(), TD);
4043
/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
4044
/// in the header of its containing loop, we know the loop executes a
4045
/// constant number of times, and the PHI node is just a recurrence
4046
/// involving constants, fold it.
4048
ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
4051
std::map<PHINode*, Constant*>::iterator I =
4052
ConstantEvolutionLoopExitValue.find(PN);
4053
if (I != ConstantEvolutionLoopExitValue.end())
4056
if (BEs.ugt(APInt(BEs.getBitWidth(),MaxBruteForceIterations)))
4057
return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
4059
Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
4061
// Since the loop is canonicalized, the PHI node must have two entries. One
4062
// entry must be a constant (coming in from outside of the loop), and the
4063
// second must be derived from the same PHI.
4064
bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
4065
Constant *StartCST =
4066
dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
4068
return RetVal = 0; // Must be a constant.
4070
Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
4071
PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
4073
return RetVal = 0; // Not derived from same PHI.
4075
// Execute the loop symbolically to determine the exit value.
4076
if (BEs.getActiveBits() >= 32)
4077
return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
4079
unsigned NumIterations = BEs.getZExtValue(); // must be in range
4080
unsigned IterationNum = 0;
4081
for (Constant *PHIVal = StartCST; ; ++IterationNum) {
4082
if (IterationNum == NumIterations)
4083
return RetVal = PHIVal; // Got exit value!
4085
// Compute the value of the PHI node for the next iteration.
4086
Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD);
4087
if (NextPHI == PHIVal)
4088
return RetVal = NextPHI; // Stopped evolving!
4090
return 0; // Couldn't evaluate!
4095
/// ComputeBackedgeTakenCountExhaustively - If the loop is known to execute a
4096
/// constant number of times (the condition evolves only from constants),
4097
/// try to evaluate a few iterations of the loop until we get the exit
4098
/// condition gets a value of ExitWhen (true or false). If we cannot
4099
/// evaluate the trip count of the loop, return getCouldNotCompute().
4101
ScalarEvolution::ComputeBackedgeTakenCountExhaustively(const Loop *L,
4104
PHINode *PN = getConstantEvolvingPHI(Cond, L);
4105
if (PN == 0) return getCouldNotCompute();
4107
// Since the loop is canonicalized, the PHI node must have two entries. One
4108
// entry must be a constant (coming in from outside of the loop), and the
4109
// second must be derived from the same PHI.
4110
bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
4111
Constant *StartCST =
4112
dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
4113
if (StartCST == 0) return getCouldNotCompute(); // Must be a constant.
4115
Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
4116
PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
4117
if (PN2 != PN) return getCouldNotCompute(); // Not derived from same PHI.
4119
// Okay, we find a PHI node that defines the trip count of this loop. Execute
4120
// the loop symbolically to determine when the condition gets a value of
4122
unsigned IterationNum = 0;
4123
unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
4124
for (Constant *PHIVal = StartCST;
4125
IterationNum != MaxIterations; ++IterationNum) {
4126
ConstantInt *CondVal =
4127
dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal, TD));
4129
// Couldn't symbolically evaluate.
4130
if (!CondVal) return getCouldNotCompute();
4132
if (CondVal->getValue() == uint64_t(ExitWhen)) {
4133
++NumBruteForceTripCountsComputed;
4134
return getConstant(Type::getInt32Ty(getContext()), IterationNum);
4137
// Compute the value of the PHI node for the next iteration.
4138
Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD);
4139
if (NextPHI == 0 || NextPHI == PHIVal)
4140
return getCouldNotCompute();// Couldn't evaluate or not making progress...
4144
// Too many iterations were needed to evaluate.
4145
return getCouldNotCompute();
4148
/// getSCEVAtScope - Return a SCEV expression for the specified value
4149
/// at the specified scope in the program. The L value specifies a loop
4150
/// nest to evaluate the expression at, where null is the top-level or a
4151
/// specified loop is immediately inside of the loop.
4153
/// This method can be used to compute the exit value for a variable defined
4154
/// in a loop by querying what the value will hold in the parent loop.
4156
/// In the case that a relevant loop exit value cannot be computed, the
4157
/// original value V is returned.
4158
const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
4159
// Check to see if we've folded this expression at this loop before.
4160
std::map<const Loop *, const SCEV *> &Values = ValuesAtScopes[V];
4161
std::pair<std::map<const Loop *, const SCEV *>::iterator, bool> Pair =
4162
Values.insert(std::make_pair(L, static_cast<const SCEV *>(0)));
4164
return Pair.first->second ? Pair.first->second : V;
4166
// Otherwise compute it.
4167
const SCEV *C = computeSCEVAtScope(V, L);
4168
ValuesAtScopes[V][L] = C;
4172
const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
4173
if (isa<SCEVConstant>(V)) return V;
4175
// If this instruction is evolved from a constant-evolving PHI, compute the
4176
// exit value from the loop without using SCEVs.
4177
if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
4178
if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
4179
const Loop *LI = (*this->LI)[I->getParent()];
4180
if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
4181
if (PHINode *PN = dyn_cast<PHINode>(I))
4182
if (PN->getParent() == LI->getHeader()) {
4183
// Okay, there is no closed form solution for the PHI node. Check
4184
// to see if the loop that contains it has a known backedge-taken
4185
// count. If so, we may be able to force computation of the exit
4187
const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
4188
if (const SCEVConstant *BTCC =
4189
dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
4190
// Okay, we know how many times the containing loop executes. If
4191
// this is a constant evolving PHI node, get the final value at
4192
// the specified iteration number.
4193
Constant *RV = getConstantEvolutionLoopExitValue(PN,
4194
BTCC->getValue()->getValue(),
4196
if (RV) return getSCEV(RV);
4200
// Okay, this is an expression that we cannot symbolically evaluate
4201
// into a SCEV. Check to see if it's possible to symbolically evaluate
4202
// the arguments into constants, and if so, try to constant propagate the
4203
// result. This is particularly useful for computing loop exit values.
4204
if (CanConstantFold(I)) {
4205
std::vector<Constant*> Operands;
4206
Operands.reserve(I->getNumOperands());
4207
for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
4208
Value *Op = I->getOperand(i);
4209
if (Constant *C = dyn_cast<Constant>(Op)) {
4210
Operands.push_back(C);
4212
// If any of the operands is non-constant and if they are
4213
// non-integer and non-pointer, don't even try to analyze them
4214
// with scev techniques.
4215
if (!isSCEVable(Op->getType()))
4218
const SCEV *OpV = getSCEVAtScope(Op, L);
4219
if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) {
4220
Constant *C = SC->getValue();
4221
if (C->getType() != Op->getType())
4222
C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
4226
Operands.push_back(C);
4227
} else if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) {
4228
if (Constant *C = dyn_cast<Constant>(SU->getValue())) {
4229
if (C->getType() != Op->getType())
4231
ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
4235
Operands.push_back(C);
4245
if (const CmpInst *CI = dyn_cast<CmpInst>(I))
4246
C = ConstantFoldCompareInstOperands(CI->getPredicate(),
4247
Operands[0], Operands[1], TD);
4249
C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
4250
&Operands[0], Operands.size(), TD);
4256
// This is some other type of SCEVUnknown, just return it.
4260
if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
4261
// Avoid performing the look-up in the common case where the specified
4262
// expression has no loop-variant portions.
4263
for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
4264
const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
4265
if (OpAtScope != Comm->getOperand(i)) {
4266
// Okay, at least one of these operands is loop variant but might be
4267
// foldable. Build a new instance of the folded commutative expression.
4268
SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
4269
Comm->op_begin()+i);
4270
NewOps.push_back(OpAtScope);
4272
for (++i; i != e; ++i) {
4273
OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
4274
NewOps.push_back(OpAtScope);
4276
if (isa<SCEVAddExpr>(Comm))
4277
return getAddExpr(NewOps);
4278
if (isa<SCEVMulExpr>(Comm))
4279
return getMulExpr(NewOps);
4280
if (isa<SCEVSMaxExpr>(Comm))
4281
return getSMaxExpr(NewOps);
4282
if (isa<SCEVUMaxExpr>(Comm))
4283
return getUMaxExpr(NewOps);
4284
llvm_unreachable("Unknown commutative SCEV type!");
4287
// If we got here, all operands are loop invariant.
4291
if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
4292
const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
4293
const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
4294
if (LHS == Div->getLHS() && RHS == Div->getRHS())
4295
return Div; // must be loop invariant
4296
return getUDivExpr(LHS, RHS);
4299
// If this is a loop recurrence for a loop that does not contain L, then we
4300
// are dealing with the final value computed by the loop.
4301
if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
4302
if (!L || !AddRec->getLoop()->contains(L)) {
4303
// To evaluate this recurrence, we need to know how many times the AddRec
4304
// loop iterates. Compute this now.
4305
const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
4306
if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
4308
// Then, evaluate the AddRec.
4309
return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
4314
if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
4315
const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
4316
if (Op == Cast->getOperand())
4317
return Cast; // must be loop invariant
4318
return getZeroExtendExpr(Op, Cast->getType());
4321
if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
4322
const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
4323
if (Op == Cast->getOperand())
4324
return Cast; // must be loop invariant
4325
return getSignExtendExpr(Op, Cast->getType());
4328
if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
4329
const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
4330
if (Op == Cast->getOperand())
4331
return Cast; // must be loop invariant
4332
return getTruncateExpr(Op, Cast->getType());
4335
llvm_unreachable("Unknown SCEV type!");
4339
/// getSCEVAtScope - This is a convenience function which does
4340
/// getSCEVAtScope(getSCEV(V), L).
4341
const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
4342
return getSCEVAtScope(getSCEV(V), L);
4345
/// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
4346
/// following equation:
4348
/// A * X = B (mod N)
4350
/// where N = 2^BW and BW is the common bit width of A and B. The signedness of
4351
/// A and B isn't important.
4353
/// If the equation does not have a solution, SCEVCouldNotCompute is returned.
4354
static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
4355
ScalarEvolution &SE) {
4356
uint32_t BW = A.getBitWidth();
4357
assert(BW == B.getBitWidth() && "Bit widths must be the same.");
4358
assert(A != 0 && "A must be non-zero.");
4362
// The gcd of A and N may have only one prime factor: 2. The number of
4363
// trailing zeros in A is its multiplicity
4364
uint32_t Mult2 = A.countTrailingZeros();
4367
// 2. Check if B is divisible by D.
4369
// B is divisible by D if and only if the multiplicity of prime factor 2 for B
4370
// is not less than multiplicity of this prime factor for D.
4371
if (B.countTrailingZeros() < Mult2)
4372
return SE.getCouldNotCompute();
4374
// 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
4377
// (N / D) may need BW+1 bits in its representation. Hence, we'll use this
4378
// bit width during computations.
4379
APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
4380
APInt Mod(BW + 1, 0);
4381
Mod.set(BW - Mult2); // Mod = N / D
4382
APInt I = AD.multiplicativeInverse(Mod);
4384
// 4. Compute the minimum unsigned root of the equation:
4385
// I * (B / D) mod (N / D)
4386
APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
4388
// The result is guaranteed to be less than 2^BW so we may truncate it to BW
4390
return SE.getConstant(Result.trunc(BW));
4393
/// SolveQuadraticEquation - Find the roots of the quadratic equation for the
4394
/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
4395
/// might be the same) or two SCEVCouldNotCompute objects.
4397
static std::pair<const SCEV *,const SCEV *>
4398
SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
4399
assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
4400
const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
4401
const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
4402
const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
4404
// We currently can only solve this if the coefficients are constants.
4405
if (!LC || !MC || !NC) {
4406
const SCEV *CNC = SE.getCouldNotCompute();
4407
return std::make_pair(CNC, CNC);
4410
uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
4411
const APInt &L = LC->getValue()->getValue();
4412
const APInt &M = MC->getValue()->getValue();
4413
const APInt &N = NC->getValue()->getValue();
4414
APInt Two(BitWidth, 2);
4415
APInt Four(BitWidth, 4);
4418
using namespace APIntOps;
4420
// Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
4421
// The B coefficient is M-N/2
4425
// The A coefficient is N/2
4426
APInt A(N.sdiv(Two));
4428
// Compute the B^2-4ac term.
4431
SqrtTerm -= Four * (A * C);
4433
// Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
4434
// integer value or else APInt::sqrt() will assert.
4435
APInt SqrtVal(SqrtTerm.sqrt());
4437
// Compute the two solutions for the quadratic formula.
4438
// The divisions must be performed as signed divisions.
4440
APInt TwoA( A << 1 );
4441
if (TwoA.isMinValue()) {
4442
const SCEV *CNC = SE.getCouldNotCompute();
4443
return std::make_pair(CNC, CNC);
4446
LLVMContext &Context = SE.getContext();
4448
ConstantInt *Solution1 =
4449
ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
4450
ConstantInt *Solution2 =
4451
ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
4453
return std::make_pair(SE.getConstant(Solution1),
4454
SE.getConstant(Solution2));
4455
} // end APIntOps namespace
4458
/// HowFarToZero - Return the number of times a backedge comparing the specified
4459
/// value to zero will execute. If not computable, return CouldNotCompute.
4460
ScalarEvolution::BackedgeTakenInfo
4461
ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) {
4462
// If the value is a constant
4463
if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
4464
// If the value is already zero, the branch will execute zero times.
4465
if (C->getValue()->isZero()) return C;
4466
return getCouldNotCompute(); // Otherwise it will loop infinitely.
4469
const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
4470
if (!AddRec || AddRec->getLoop() != L)
4471
return getCouldNotCompute();
4473
if (AddRec->isAffine()) {
4474
// If this is an affine expression, the execution count of this branch is
4475
// the minimum unsigned root of the following equation:
4477
// Start + Step*N = 0 (mod 2^BW)
4481
// Step*N = -Start (mod 2^BW)
4483
// where BW is the common bit width of Start and Step.
4485
// Get the initial value for the loop.
4486
const SCEV *Start = getSCEVAtScope(AddRec->getStart(),
4487
L->getParentLoop());
4488
const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1),
4489
L->getParentLoop());
4491
if (const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) {
4492
// For now we handle only constant steps.
4494
// First, handle unitary steps.
4495
if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so:
4496
return getNegativeSCEV(Start); // N = -Start (as unsigned)
4497
if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so:
4498
return Start; // N = Start (as unsigned)
4500
// Then, try to solve the above equation provided that Start is constant.
4501
if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
4502
return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
4503
-StartC->getValue()->getValue(),
4506
} else if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
4507
// If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
4508
// the quadratic equation to solve it.
4509
std::pair<const SCEV *,const SCEV *> Roots = SolveQuadraticEquation(AddRec,
4511
const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
4512
const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
4515
dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1
4516
<< " sol#2: " << *R2 << "\n";
4518
// Pick the smallest positive root value.
4519
if (ConstantInt *CB =
4520
dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
4521
R1->getValue(), R2->getValue()))) {
4522
if (CB->getZExtValue() == false)
4523
std::swap(R1, R2); // R1 is the minimum root now.
4525
// We can only use this value if the chrec ends up with an exact zero
4526
// value at this index. When solving for "X*X != 5", for example, we
4527
// should not accept a root of 2.
4528
const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
4530
return R1; // We found a quadratic root!
4535
return getCouldNotCompute();
4538
/// HowFarToNonZero - Return the number of times a backedge checking the
4539
/// specified value for nonzero will execute. If not computable, return
4541
ScalarEvolution::BackedgeTakenInfo
4542
ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
4543
// Loops that look like: while (X == 0) are very strange indeed. We don't
4544
// handle them yet except for the trivial case. This could be expanded in the
4545
// future as needed.
4547
// If the value is a constant, check to see if it is known to be non-zero
4548
// already. If so, the backedge will execute zero times.
4549
if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
4550
if (!C->getValue()->isNullValue())
4551
return getIntegerSCEV(0, C->getType());
4552
return getCouldNotCompute(); // Otherwise it will loop infinitely.
4555
// We could implement others, but I really doubt anyone writes loops like
4556
// this, and if they did, they would already be constant folded.
4557
return getCouldNotCompute();
4560
/// getLoopPredecessor - If the given loop's header has exactly one unique
4561
/// predecessor outside the loop, return it. Otherwise return null.
4563
BasicBlock *ScalarEvolution::getLoopPredecessor(const Loop *L) {
4564
BasicBlock *Header = L->getHeader();
4565
BasicBlock *Pred = 0;
4566
for (pred_iterator PI = pred_begin(Header), E = pred_end(Header);
4568
if (!L->contains(*PI)) {
4569
if (Pred && Pred != *PI) return 0; // Multiple predecessors.
4575
/// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
4576
/// (which may not be an immediate predecessor) which has exactly one
4577
/// successor from which BB is reachable, or null if no such block is
4581
ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
4582
// If the block has a unique predecessor, then there is no path from the
4583
// predecessor to the block that does not go through the direct edge
4584
// from the predecessor to the block.
4585
if (BasicBlock *Pred = BB->getSinglePredecessor())
4588
// A loop's header is defined to be a block that dominates the loop.
4589
// If the header has a unique predecessor outside the loop, it must be
4590
// a block that has exactly one successor that can reach the loop.
4591
if (Loop *L = LI->getLoopFor(BB))
4592
return getLoopPredecessor(L);
4597
/// HasSameValue - SCEV structural equivalence is usually sufficient for
4598
/// testing whether two expressions are equal, however for the purposes of
4599
/// looking for a condition guarding a loop, it can be useful to be a little
4600
/// more general, since a front-end may have replicated the controlling
4603
static bool HasSameValue(const SCEV *A, const SCEV *B) {
4604
// Quick check to see if they are the same SCEV.
4605
if (A == B) return true;
4607
// Otherwise, if they're both SCEVUnknown, it's possible that they hold
4608
// two different instructions with the same value. Check for this case.
4609
if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
4610
if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
4611
if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
4612
if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
4613
if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory())
4616
// Otherwise assume they may have a different value.
4620
bool ScalarEvolution::isKnownNegative(const SCEV *S) {
4621
return getSignedRange(S).getSignedMax().isNegative();
4624
bool ScalarEvolution::isKnownPositive(const SCEV *S) {
4625
return getSignedRange(S).getSignedMin().isStrictlyPositive();
4628
bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
4629
return !getSignedRange(S).getSignedMin().isNegative();
4632
bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
4633
return !getSignedRange(S).getSignedMax().isStrictlyPositive();
4636
bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
4637
return isKnownNegative(S) || isKnownPositive(S);
4640
bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
4641
const SCEV *LHS, const SCEV *RHS) {
4643
if (HasSameValue(LHS, RHS))
4644
return ICmpInst::isTrueWhenEqual(Pred);
4648
llvm_unreachable("Unexpected ICmpInst::Predicate value!");
4650
case ICmpInst::ICMP_SGT:
4651
Pred = ICmpInst::ICMP_SLT;
4652
std::swap(LHS, RHS);
4653
case ICmpInst::ICMP_SLT: {
4654
ConstantRange LHSRange = getSignedRange(LHS);
4655
ConstantRange RHSRange = getSignedRange(RHS);
4656
if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
4658
if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
4662
case ICmpInst::ICMP_SGE:
4663
Pred = ICmpInst::ICMP_SLE;
4664
std::swap(LHS, RHS);
4665
case ICmpInst::ICMP_SLE: {
4666
ConstantRange LHSRange = getSignedRange(LHS);
4667
ConstantRange RHSRange = getSignedRange(RHS);
4668
if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
4670
if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
4674
case ICmpInst::ICMP_UGT:
4675
Pred = ICmpInst::ICMP_ULT;
4676
std::swap(LHS, RHS);
4677
case ICmpInst::ICMP_ULT: {
4678
ConstantRange LHSRange = getUnsignedRange(LHS);
4679
ConstantRange RHSRange = getUnsignedRange(RHS);
4680
if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
4682
if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
4686
case ICmpInst::ICMP_UGE:
4687
Pred = ICmpInst::ICMP_ULE;
4688
std::swap(LHS, RHS);
4689
case ICmpInst::ICMP_ULE: {
4690
ConstantRange LHSRange = getUnsignedRange(LHS);
4691
ConstantRange RHSRange = getUnsignedRange(RHS);
4692
if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
4694
if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
4698
case ICmpInst::ICMP_NE: {
4699
if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
4701
if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
4704
const SCEV *Diff = getMinusSCEV(LHS, RHS);
4705
if (isKnownNonZero(Diff))
4709
case ICmpInst::ICMP_EQ:
4710
// The check at the top of the function catches the case where
4711
// the values are known to be equal.
4717
/// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
4718
/// protected by a conditional between LHS and RHS. This is used to
4719
/// to eliminate casts.
4721
ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
4722
ICmpInst::Predicate Pred,
4723
const SCEV *LHS, const SCEV *RHS) {
4724
// Interpret a null as meaning no loop, where there is obviously no guard
4725
// (interprocedural conditions notwithstanding).
4726
if (!L) return true;
4728
BasicBlock *Latch = L->getLoopLatch();
4732
BranchInst *LoopContinuePredicate =
4733
dyn_cast<BranchInst>(Latch->getTerminator());
4734
if (!LoopContinuePredicate ||
4735
LoopContinuePredicate->isUnconditional())
4738
return isImpliedCond(LoopContinuePredicate->getCondition(), Pred, LHS, RHS,
4739
LoopContinuePredicate->getSuccessor(0) != L->getHeader());
4742
/// isLoopGuardedByCond - Test whether entry to the loop is protected
4743
/// by a conditional between LHS and RHS. This is used to help avoid max
4744
/// expressions in loop trip counts, and to eliminate casts.
4746
ScalarEvolution::isLoopGuardedByCond(const Loop *L,
4747
ICmpInst::Predicate Pred,
4748
const SCEV *LHS, const SCEV *RHS) {
4749
// Interpret a null as meaning no loop, where there is obviously no guard
4750
// (interprocedural conditions notwithstanding).
4751
if (!L) return false;
4753
BasicBlock *Predecessor = getLoopPredecessor(L);
4754
BasicBlock *PredecessorDest = L->getHeader();
4756
// Starting at the loop predecessor, climb up the predecessor chain, as long
4757
// as there are predecessors that can be found that have unique successors
4758
// leading to the original header.
4760
PredecessorDest = Predecessor,
4761
Predecessor = getPredecessorWithUniqueSuccessorForBB(Predecessor)) {
4763
BranchInst *LoopEntryPredicate =
4764
dyn_cast<BranchInst>(Predecessor->getTerminator());
4765
if (!LoopEntryPredicate ||
4766
LoopEntryPredicate->isUnconditional())
4769
if (isImpliedCond(LoopEntryPredicate->getCondition(), Pred, LHS, RHS,
4770
LoopEntryPredicate->getSuccessor(0) != PredecessorDest))
4777
/// isImpliedCond - Test whether the condition described by Pred, LHS,
4778
/// and RHS is true whenever the given Cond value evaluates to true.
4779
bool ScalarEvolution::isImpliedCond(Value *CondValue,
4780
ICmpInst::Predicate Pred,
4781
const SCEV *LHS, const SCEV *RHS,
4783
// Recursively handle And and Or conditions.
4784
if (BinaryOperator *BO = dyn_cast<BinaryOperator>(CondValue)) {
4785
if (BO->getOpcode() == Instruction::And) {
4787
return isImpliedCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) ||
4788
isImpliedCond(BO->getOperand(1), Pred, LHS, RHS, Inverse);
4789
} else if (BO->getOpcode() == Instruction::Or) {
4791
return isImpliedCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) ||
4792
isImpliedCond(BO->getOperand(1), Pred, LHS, RHS, Inverse);
4796
ICmpInst *ICI = dyn_cast<ICmpInst>(CondValue);
4797
if (!ICI) return false;
4799
// Bail if the ICmp's operands' types are wider than the needed type
4800
// before attempting to call getSCEV on them. This avoids infinite
4801
// recursion, since the analysis of widening casts can require loop
4802
// exit condition information for overflow checking, which would
4804
if (getTypeSizeInBits(LHS->getType()) <
4805
getTypeSizeInBits(ICI->getOperand(0)->getType()))
4808
// Now that we found a conditional branch that dominates the loop, check to
4809
// see if it is the comparison we are looking for.
4810
ICmpInst::Predicate FoundPred;
4812
FoundPred = ICI->getInversePredicate();
4814
FoundPred = ICI->getPredicate();
4816
const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
4817
const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
4819
// Balance the types. The case where FoundLHS' type is wider than
4820
// LHS' type is checked for above.
4821
if (getTypeSizeInBits(LHS->getType()) >
4822
getTypeSizeInBits(FoundLHS->getType())) {
4823
if (CmpInst::isSigned(Pred)) {
4824
FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
4825
FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
4827
FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
4828
FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
4832
// Canonicalize the query to match the way instcombine will have
4833
// canonicalized the comparison.
4834
// First, put a constant operand on the right.
4835
if (isa<SCEVConstant>(LHS)) {
4836
std::swap(LHS, RHS);
4837
Pred = ICmpInst::getSwappedPredicate(Pred);
4839
// Then, canonicalize comparisons with boundary cases.
4840
if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
4841
const APInt &RA = RC->getValue()->getValue();
4843
default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
4844
case ICmpInst::ICMP_EQ:
4845
case ICmpInst::ICMP_NE:
4847
case ICmpInst::ICMP_UGE:
4848
if ((RA - 1).isMinValue()) {
4849
Pred = ICmpInst::ICMP_NE;
4850
RHS = getConstant(RA - 1);
4853
if (RA.isMaxValue()) {
4854
Pred = ICmpInst::ICMP_EQ;
4857
if (RA.isMinValue()) return true;
4859
case ICmpInst::ICMP_ULE:
4860
if ((RA + 1).isMaxValue()) {
4861
Pred = ICmpInst::ICMP_NE;
4862
RHS = getConstant(RA + 1);
4865
if (RA.isMinValue()) {
4866
Pred = ICmpInst::ICMP_EQ;
4869
if (RA.isMaxValue()) return true;
4871
case ICmpInst::ICMP_SGE:
4872
if ((RA - 1).isMinSignedValue()) {
4873
Pred = ICmpInst::ICMP_NE;
4874
RHS = getConstant(RA - 1);
4877
if (RA.isMaxSignedValue()) {
4878
Pred = ICmpInst::ICMP_EQ;
4881
if (RA.isMinSignedValue()) return true;
4883
case ICmpInst::ICMP_SLE:
4884
if ((RA + 1).isMaxSignedValue()) {
4885
Pred = ICmpInst::ICMP_NE;
4886
RHS = getConstant(RA + 1);
4889
if (RA.isMinSignedValue()) {
4890
Pred = ICmpInst::ICMP_EQ;
4893
if (RA.isMaxSignedValue()) return true;
4895
case ICmpInst::ICMP_UGT:
4896
if (RA.isMinValue()) {
4897
Pred = ICmpInst::ICMP_NE;
4900
if ((RA + 1).isMaxValue()) {
4901
Pred = ICmpInst::ICMP_EQ;
4902
RHS = getConstant(RA + 1);
4905
if (RA.isMaxValue()) return false;
4907
case ICmpInst::ICMP_ULT:
4908
if (RA.isMaxValue()) {
4909
Pred = ICmpInst::ICMP_NE;
4912
if ((RA - 1).isMinValue()) {
4913
Pred = ICmpInst::ICMP_EQ;
4914
RHS = getConstant(RA - 1);
4917
if (RA.isMinValue()) return false;
4919
case ICmpInst::ICMP_SGT:
4920
if (RA.isMinSignedValue()) {
4921
Pred = ICmpInst::ICMP_NE;
4924
if ((RA + 1).isMaxSignedValue()) {
4925
Pred = ICmpInst::ICMP_EQ;
4926
RHS = getConstant(RA + 1);
4929
if (RA.isMaxSignedValue()) return false;
4931
case ICmpInst::ICMP_SLT:
4932
if (RA.isMaxSignedValue()) {
4933
Pred = ICmpInst::ICMP_NE;
4936
if ((RA - 1).isMinSignedValue()) {
4937
Pred = ICmpInst::ICMP_EQ;
4938
RHS = getConstant(RA - 1);
4941
if (RA.isMinSignedValue()) return false;
4946
// Check to see if we can make the LHS or RHS match.
4947
if (LHS == FoundRHS || RHS == FoundLHS) {
4948
if (isa<SCEVConstant>(RHS)) {
4949
std::swap(FoundLHS, FoundRHS);
4950
FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
4952
std::swap(LHS, RHS);
4953
Pred = ICmpInst::getSwappedPredicate(Pred);
4957
// Check whether the found predicate is the same as the desired predicate.
4958
if (FoundPred == Pred)
4959
return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
4961
// Check whether swapping the found predicate makes it the same as the
4962
// desired predicate.
4963
if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
4964
if (isa<SCEVConstant>(RHS))
4965
return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
4967
return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
4968
RHS, LHS, FoundLHS, FoundRHS);
4971
// Check whether the actual condition is beyond sufficient.
4972
if (FoundPred == ICmpInst::ICMP_EQ)
4973
if (ICmpInst::isTrueWhenEqual(Pred))
4974
if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
4976
if (Pred == ICmpInst::ICMP_NE)
4977
if (!ICmpInst::isTrueWhenEqual(FoundPred))
4978
if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
4981
// Otherwise assume the worst.
4985
/// isImpliedCondOperands - Test whether the condition described by Pred,
4986
/// LHS, and RHS is true whenever the condition described by Pred, FoundLHS,
4987
/// and FoundRHS is true.
4988
bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
4989
const SCEV *LHS, const SCEV *RHS,
4990
const SCEV *FoundLHS,
4991
const SCEV *FoundRHS) {
4992
return isImpliedCondOperandsHelper(Pred, LHS, RHS,
4993
FoundLHS, FoundRHS) ||
4994
// ~x < ~y --> x > y
4995
isImpliedCondOperandsHelper(Pred, LHS, RHS,
4996
getNotSCEV(FoundRHS),
4997
getNotSCEV(FoundLHS));
5000
/// isImpliedCondOperandsHelper - Test whether the condition described by
5001
/// Pred, LHS, and RHS is true whenever the condition described by Pred,
5002
/// FoundLHS, and FoundRHS is true.
5004
ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
5005
const SCEV *LHS, const SCEV *RHS,
5006
const SCEV *FoundLHS,
5007
const SCEV *FoundRHS) {
5009
default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
5010
case ICmpInst::ICMP_EQ:
5011
case ICmpInst::ICMP_NE:
5012
if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
5015
case ICmpInst::ICMP_SLT:
5016
case ICmpInst::ICMP_SLE:
5017
if (isKnownPredicate(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
5018
isKnownPredicate(ICmpInst::ICMP_SGE, RHS, FoundRHS))
5021
case ICmpInst::ICMP_SGT:
5022
case ICmpInst::ICMP_SGE:
5023
if (isKnownPredicate(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
5024
isKnownPredicate(ICmpInst::ICMP_SLE, RHS, FoundRHS))
5027
case ICmpInst::ICMP_ULT:
5028
case ICmpInst::ICMP_ULE:
5029
if (isKnownPredicate(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
5030
isKnownPredicate(ICmpInst::ICMP_UGE, RHS, FoundRHS))
5033
case ICmpInst::ICMP_UGT:
5034
case ICmpInst::ICMP_UGE:
5035
if (isKnownPredicate(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
5036
isKnownPredicate(ICmpInst::ICMP_ULE, RHS, FoundRHS))
5044
/// getBECount - Subtract the end and start values and divide by the step,
5045
/// rounding up, to get the number of times the backedge is executed. Return
5046
/// CouldNotCompute if an intermediate computation overflows.
5047
const SCEV *ScalarEvolution::getBECount(const SCEV *Start,
5051
assert(!isKnownNegative(Step) &&
5052
"This code doesn't handle negative strides yet!");
5054
const Type *Ty = Start->getType();
5055
const SCEV *NegOne = getIntegerSCEV(-1, Ty);
5056
const SCEV *Diff = getMinusSCEV(End, Start);
5057
const SCEV *RoundUp = getAddExpr(Step, NegOne);
5059
// Add an adjustment to the difference between End and Start so that
5060
// the division will effectively round up.
5061
const SCEV *Add = getAddExpr(Diff, RoundUp);
5064
// Check Add for unsigned overflow.
5065
// TODO: More sophisticated things could be done here.
5066
const Type *WideTy = IntegerType::get(getContext(),
5067
getTypeSizeInBits(Ty) + 1);
5068
const SCEV *EDiff = getZeroExtendExpr(Diff, WideTy);
5069
const SCEV *ERoundUp = getZeroExtendExpr(RoundUp, WideTy);
5070
const SCEV *OperandExtendedAdd = getAddExpr(EDiff, ERoundUp);
5071
if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd)
5072
return getCouldNotCompute();
5075
return getUDivExpr(Add, Step);
5078
/// HowManyLessThans - Return the number of times a backedge containing the
5079
/// specified less-than comparison will execute. If not computable, return
5080
/// CouldNotCompute.
5081
ScalarEvolution::BackedgeTakenInfo
5082
ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
5083
const Loop *L, bool isSigned) {
5084
// Only handle: "ADDREC < LoopInvariant".
5085
if (!RHS->isLoopInvariant(L)) return getCouldNotCompute();
5087
const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
5088
if (!AddRec || AddRec->getLoop() != L)
5089
return getCouldNotCompute();
5091
// Check to see if we have a flag which makes analysis easy.
5092
bool NoWrap = isSigned ? AddRec->hasNoSignedWrap() :
5093
AddRec->hasNoUnsignedWrap();
5095
if (AddRec->isAffine()) {
5096
unsigned BitWidth = getTypeSizeInBits(AddRec->getType());
5097
const SCEV *Step = AddRec->getStepRecurrence(*this);
5100
return getCouldNotCompute();
5101
if (Step->isOne()) {
5102
// With unit stride, the iteration never steps past the limit value.
5103
} else if (isKnownPositive(Step)) {
5104
// Test whether a positive iteration can step past the limit
5105
// value and past the maximum value for its type in a single step.
5106
// Note that it's not sufficient to check NoWrap here, because even
5107
// though the value after a wrap is undefined, it's not undefined
5108
// behavior, so if wrap does occur, the loop could either terminate or
5109
// loop infinitely, but in either case, the loop is guaranteed to
5110
// iterate at least until the iteration where the wrapping occurs.
5111
const SCEV *One = getIntegerSCEV(1, Step->getType());
5113
APInt Max = APInt::getSignedMaxValue(BitWidth);
5114
if ((Max - getSignedRange(getMinusSCEV(Step, One)).getSignedMax())
5115
.slt(getSignedRange(RHS).getSignedMax()))
5116
return getCouldNotCompute();
5118
APInt Max = APInt::getMaxValue(BitWidth);
5119
if ((Max - getUnsignedRange(getMinusSCEV(Step, One)).getUnsignedMax())
5120
.ult(getUnsignedRange(RHS).getUnsignedMax()))
5121
return getCouldNotCompute();
5124
// TODO: Handle negative strides here and below.
5125
return getCouldNotCompute();
5127
// We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant
5128
// m. So, we count the number of iterations in which {n,+,s} < m is true.
5129
// Note that we cannot simply return max(m-n,0)/s because it's not safe to
5130
// treat m-n as signed nor unsigned due to overflow possibility.
5132
// First, we get the value of the LHS in the first iteration: n
5133
const SCEV *Start = AddRec->getOperand(0);
5135
// Determine the minimum constant start value.
5136
const SCEV *MinStart = getConstant(isSigned ?
5137
getSignedRange(Start).getSignedMin() :
5138
getUnsignedRange(Start).getUnsignedMin());
5140
// If we know that the condition is true in order to enter the loop,
5141
// then we know that it will run exactly (m-n)/s times. Otherwise, we
5142
// only know that it will execute (max(m,n)-n)/s times. In both cases,
5143
// the division must round up.
5144
const SCEV *End = RHS;
5145
if (!isLoopGuardedByCond(L,
5146
isSigned ? ICmpInst::ICMP_SLT :
5148
getMinusSCEV(Start, Step), RHS))
5149
End = isSigned ? getSMaxExpr(RHS, Start)
5150
: getUMaxExpr(RHS, Start);
5152
// Determine the maximum constant end value.
5153
const SCEV *MaxEnd = getConstant(isSigned ?
5154
getSignedRange(End).getSignedMax() :
5155
getUnsignedRange(End).getUnsignedMax());
5157
// If MaxEnd is within a step of the maximum integer value in its type,
5158
// adjust it down to the minimum value which would produce the same effect.
5159
// This allows the subsequent ceiling division of (N+(step-1))/step to
5160
// compute the correct value.
5161
const SCEV *StepMinusOne = getMinusSCEV(Step,
5162
getIntegerSCEV(1, Step->getType()));
5165
getMinusSCEV(getConstant(APInt::getSignedMaxValue(BitWidth)),
5168
getMinusSCEV(getConstant(APInt::getMaxValue(BitWidth)),
5171
// Finally, we subtract these two values and divide, rounding up, to get
5172
// the number of times the backedge is executed.
5173
const SCEV *BECount = getBECount(Start, End, Step, NoWrap);
5175
// The maximum backedge count is similar, except using the minimum start
5176
// value and the maximum end value.
5177
const SCEV *MaxBECount = getBECount(MinStart, MaxEnd, Step, NoWrap);
5179
return BackedgeTakenInfo(BECount, MaxBECount);
5182
return getCouldNotCompute();
5185
/// getNumIterationsInRange - Return the number of iterations of this loop that
5186
/// produce values in the specified constant range. Another way of looking at
5187
/// this is that it returns the first iteration number where the value is not in
5188
/// the condition, thus computing the exit count. If the iteration count can't
5189
/// be computed, an instance of SCEVCouldNotCompute is returned.
5190
const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
5191
ScalarEvolution &SE) const {
5192
if (Range.isFullSet()) // Infinite loop.
5193
return SE.getCouldNotCompute();
5195
// If the start is a non-zero constant, shift the range to simplify things.
5196
if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
5197
if (!SC->getValue()->isZero()) {
5198
SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
5199
Operands[0] = SE.getIntegerSCEV(0, SC->getType());
5200
const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop());
5201
if (const SCEVAddRecExpr *ShiftedAddRec =
5202
dyn_cast<SCEVAddRecExpr>(Shifted))
5203
return ShiftedAddRec->getNumIterationsInRange(
5204
Range.subtract(SC->getValue()->getValue()), SE);
5205
// This is strange and shouldn't happen.
5206
return SE.getCouldNotCompute();
5209
// The only time we can solve this is when we have all constant indices.
5210
// Otherwise, we cannot determine the overflow conditions.
5211
for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
5212
if (!isa<SCEVConstant>(getOperand(i)))
5213
return SE.getCouldNotCompute();
5216
// Okay at this point we know that all elements of the chrec are constants and
5217
// that the start element is zero.
5219
// First check to see if the range contains zero. If not, the first
5221
unsigned BitWidth = SE.getTypeSizeInBits(getType());
5222
if (!Range.contains(APInt(BitWidth, 0)))
5223
return SE.getIntegerSCEV(0, getType());
5226
// If this is an affine expression then we have this situation:
5227
// Solve {0,+,A} in Range === Ax in Range
5229
// We know that zero is in the range. If A is positive then we know that
5230
// the upper value of the range must be the first possible exit value.
5231
// If A is negative then the lower of the range is the last possible loop
5232
// value. Also note that we already checked for a full range.
5233
APInt One(BitWidth,1);
5234
APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
5235
APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
5237
// The exit value should be (End+A)/A.
5238
APInt ExitVal = (End + A).udiv(A);
5239
ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
5241
// Evaluate at the exit value. If we really did fall out of the valid
5242
// range, then we computed our trip count, otherwise wrap around or other
5243
// things must have happened.
5244
ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
5245
if (Range.contains(Val->getValue()))
5246
return SE.getCouldNotCompute(); // Something strange happened
5248
// Ensure that the previous value is in the range. This is a sanity check.
5249
assert(Range.contains(
5250
EvaluateConstantChrecAtConstant(this,
5251
ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
5252
"Linear scev computation is off in a bad way!");
5253
return SE.getConstant(ExitValue);
5254
} else if (isQuadratic()) {
5255
// If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
5256
// quadratic equation to solve it. To do this, we must frame our problem in
5257
// terms of figuring out when zero is crossed, instead of when
5258
// Range.getUpper() is crossed.
5259
SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
5260
NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
5261
const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop());
5263
// Next, solve the constructed addrec
5264
std::pair<const SCEV *,const SCEV *> Roots =
5265
SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
5266
const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
5267
const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
5269
// Pick the smallest positive root value.
5270
if (ConstantInt *CB =
5271
dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
5272
R1->getValue(), R2->getValue()))) {
5273
if (CB->getZExtValue() == false)
5274
std::swap(R1, R2); // R1 is the minimum root now.
5276
// Make sure the root is not off by one. The returned iteration should
5277
// not be in the range, but the previous one should be. When solving
5278
// for "X*X < 5", for example, we should not return a root of 2.
5279
ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
5282
if (Range.contains(R1Val->getValue())) {
5283
// The next iteration must be out of the range...
5284
ConstantInt *NextVal =
5285
ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1);
5287
R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
5288
if (!Range.contains(R1Val->getValue()))
5289
return SE.getConstant(NextVal);
5290
return SE.getCouldNotCompute(); // Something strange happened
5293
// If R1 was not in the range, then it is a good return value. Make
5294
// sure that R1-1 WAS in the range though, just in case.
5295
ConstantInt *NextVal =
5296
ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1);
5297
R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
5298
if (Range.contains(R1Val->getValue()))
5300
return SE.getCouldNotCompute(); // Something strange happened
5305
return SE.getCouldNotCompute();
5310
//===----------------------------------------------------------------------===//
5311
// SCEVCallbackVH Class Implementation
5312
//===----------------------------------------------------------------------===//
5314
void ScalarEvolution::SCEVCallbackVH::deleted() {
5315
assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
5316
if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
5317
SE->ConstantEvolutionLoopExitValue.erase(PN);
5318
SE->Scalars.erase(getValPtr());
5319
// this now dangles!
5322
void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *) {
5323
assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
5325
// Forget all the expressions associated with users of the old value,
5326
// so that future queries will recompute the expressions using the new
5328
SmallVector<User *, 16> Worklist;
5329
SmallPtrSet<User *, 8> Visited;
5330
Value *Old = getValPtr();
5331
bool DeleteOld = false;
5332
for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end();
5334
Worklist.push_back(*UI);
5335
while (!Worklist.empty()) {
5336
User *U = Worklist.pop_back_val();
5337
// Deleting the Old value will cause this to dangle. Postpone
5338
// that until everything else is done.
5343
if (!Visited.insert(U))
5345
if (PHINode *PN = dyn_cast<PHINode>(U))
5346
SE->ConstantEvolutionLoopExitValue.erase(PN);
5347
SE->Scalars.erase(U);
5348
for (Value::use_iterator UI = U->use_begin(), UE = U->use_end();
5350
Worklist.push_back(*UI);
5352
// Delete the Old value if it (indirectly) references itself.
5354
if (PHINode *PN = dyn_cast<PHINode>(Old))
5355
SE->ConstantEvolutionLoopExitValue.erase(PN);
5356
SE->Scalars.erase(Old);
5357
// this now dangles!
5362
ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
5363
: CallbackVH(V), SE(se) {}
5365
//===----------------------------------------------------------------------===//
5366
// ScalarEvolution Class Implementation
5367
//===----------------------------------------------------------------------===//
5369
ScalarEvolution::ScalarEvolution()
5370
: FunctionPass(&ID) {
5373
bool ScalarEvolution::runOnFunction(Function &F) {
5375
LI = &getAnalysis<LoopInfo>();
5376
TD = getAnalysisIfAvailable<TargetData>();
5377
DT = &getAnalysis<DominatorTree>();
5381
void ScalarEvolution::releaseMemory() {
5383
BackedgeTakenCounts.clear();
5384
ConstantEvolutionLoopExitValue.clear();
5385
ValuesAtScopes.clear();
5386
UniqueSCEVs.clear();
5387
SCEVAllocator.Reset();
5390
void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
5391
AU.setPreservesAll();
5392
AU.addRequiredTransitive<LoopInfo>();
5393
AU.addRequiredTransitive<DominatorTree>();
5396
bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
5397
return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
5400
static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
5402
// Print all inner loops first
5403
for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
5404
PrintLoopInfo(OS, SE, *I);
5407
WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
5410
SmallVector<BasicBlock *, 8> ExitBlocks;
5411
L->getExitBlocks(ExitBlocks);
5412
if (ExitBlocks.size() != 1)
5413
OS << "<multiple exits> ";
5415
if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
5416
OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
5418
OS << "Unpredictable backedge-taken count. ";
5423
WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
5426
if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
5427
OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
5429
OS << "Unpredictable max backedge-taken count. ";
5435
void ScalarEvolution::print(raw_ostream &OS, const Module *) const {
5436
// ScalarEvolution's implementation of the print method is to print
5437
// out SCEV values of all instructions that are interesting. Doing
5438
// this potentially causes it to create new SCEV objects though,
5439
// which technically conflicts with the const qualifier. This isn't
5440
// observable from outside the class though, so casting away the
5441
// const isn't dangerous.
5442
ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
5444
OS << "Classifying expressions for: ";
5445
WriteAsOperand(OS, F, /*PrintType=*/false);
5447
for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
5448
if (isSCEVable(I->getType())) {
5451
const SCEV *SV = SE.getSCEV(&*I);
5454
const Loop *L = LI->getLoopFor((*I).getParent());
5456
const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
5463
OS << "\t\t" "Exits: ";
5464
const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
5465
if (!ExitValue->isLoopInvariant(L)) {
5466
OS << "<<Unknown>>";
5475
OS << "Determining loop execution counts for: ";
5476
WriteAsOperand(OS, F, /*PrintType=*/false);
5478
for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
5479
PrintLoopInfo(OS, &SE, *I);
added
removed
libclamav/c++/llvm/lib/Analysis/ScalarEvolution.cpp
