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https://github.com/c64scene-ar/llvm-6502.git
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git-svn-id: https://llvm.org/svn/llvm-project/llvm/trunk@80918 91177308-0d34-0410-b5e6-96231b3b80d8
5198 lines
206 KiB
C++
5198 lines
206 KiB
C++
//===- ScalarEvolution.cpp - Scalar Evolution Analysis ----------*- C++ -*-===//
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//
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// The LLVM Compiler Infrastructure
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//
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// This file 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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//===----------------------------------------------------------------------===//
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//
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// This file contains the implementation of the scalar evolution analysis
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// engine, which is used primarily to analyze expressions involving induction
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// variables in loops.
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//
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// There are several aspects to this library. First is the representation of
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// scalar expressions, which are represented as subclasses of the SCEV class.
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// These classes are used to represent certain types of subexpressions that we
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// can handle. We only create one SCEV of a particular shape, so
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// pointer-comparisons for equality are legal.
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//
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// One important aspect of the SCEV objects is that they are never cyclic, even
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// if there is a cycle in the dataflow for an expression (ie, a PHI node). If
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// the PHI node is one of the idioms that we can represent (e.g., a polynomial
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// recurrence) then we represent it directly as a recurrence node, otherwise we
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// represent it as a SCEVUnknown node.
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//
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// In addition to being able to represent expressions of various types, we also
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// have folders that are used to build the *canonical* representation for a
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// particular expression. These folders are capable of using a variety of
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// rewrite rules to simplify the expressions.
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//
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// Once the folders are defined, we can implement the more interesting
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// higher-level code, such as the code that recognizes PHI nodes of various
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// types, computes the execution count of a loop, etc.
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//
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// TODO: We should use these routines and value representations to implement
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// dependence analysis!
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//
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//===----------------------------------------------------------------------===//
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//
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// There are several good references for the techniques used in this analysis.
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//
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// Chains of recurrences -- a method to expedite the evaluation
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// of closed-form functions
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// Olaf Bachmann, Paul S. Wang, Eugene V. Zima
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//
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// On computational properties of chains of recurrences
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// Eugene V. Zima
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//
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// Symbolic Evaluation of Chains of Recurrences for Loop Optimization
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// Robert A. van Engelen
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//
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// Efficient Symbolic Analysis for Optimizing Compilers
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// Robert A. van Engelen
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//
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// Using the chains of recurrences algebra for data dependence testing and
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// induction variable substitution
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// MS Thesis, Johnie Birch
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//
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//===----------------------------------------------------------------------===//
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#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/Compiler.h"
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#include "llvm/Support/ConstantRange.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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#include <algorithm>
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using namespace llvm;
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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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"derived loop"),
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cl::init(100));
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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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//
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SCEV::~SCEV() {}
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void SCEV::dump() const {
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print(errs());
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errs() << '\n';
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}
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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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return false;
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}
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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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return false;
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}
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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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return false;
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}
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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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return false;
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}
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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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return 0;
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}
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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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return false;
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}
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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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return false;
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}
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void SCEVCouldNotCompute::print(raw_ostream &OS) const {
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OS << "***COULDNOTCOMPUTE***";
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}
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bool SCEVCouldNotCompute::classof(const SCEV *S) {
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return S->getSCEVType() == scCouldNotCompute;
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}
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const SCEV *ScalarEvolution::getConstant(ConstantInt *V) {
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FoldingSetNodeID ID;
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ID.AddInteger(scConstant);
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ID.AddPointer(V);
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void *IP = 0;
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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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return S;
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}
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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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}
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const SCEV *
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ScalarEvolution::getConstant(const Type *Ty, uint64_t V, bool isSigned) {
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return getConstant(
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ConstantInt::get(cast<IntegerType>(Ty), V, isSigned));
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}
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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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}
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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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}
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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()->isInteger() || isa<PointerType>(Op->getType())) &&
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(Ty->isInteger() || isa<PointerType>(Ty)) &&
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"Cannot truncate non-integer value!");
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}
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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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}
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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()->isInteger() || isa<PointerType>(Op->getType())) &&
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(Ty->isInteger() || isa<PointerType>(Ty)) &&
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"Cannot zero extend non-integer value!");
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}
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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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}
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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()->isInteger() || isa<PointerType>(Op->getType())) &&
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(Ty->isInteger() || isa<PointerType>(Ty)) &&
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"Cannot sign extend non-integer value!");
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}
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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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}
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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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OS << ")";
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}
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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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return false;
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}
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return true;
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}
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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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}
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void SCEVUDivExpr::print(raw_ostream &OS) const {
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OS << "(" << *LHS << " /u " << *RHS << ")";
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}
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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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}
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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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if (!QueryLoop)
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return false;
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// This recurrence is variant w.r.t. QueryLoop if QueryLoop contains L.
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if (QueryLoop->contains(L->getHeader()))
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return false;
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// This recurrence is variant w.r.t. QueryLoop if any of its operands
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// are variant.
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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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return false;
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// Otherwise it's loop-invariant.
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return true;
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}
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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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OS << "}<" << L->getHeader()->getName() + ">";
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}
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void SCEVFieldOffsetExpr::print(raw_ostream &OS) const {
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// LLVM struct fields don't have names, so just print the field number.
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OS << "offsetof(" << *STy << ", " << FieldNo << ")";
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}
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void SCEVAllocSizeExpr::print(raw_ostream &OS) const {
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OS << "sizeof(" << *AllocTy << ")";
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}
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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->getParent());
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return true;
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}
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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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return true;
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}
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const Type *SCEVUnknown::getType() const {
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return V->getType();
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}
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void SCEVUnknown::print(raw_ostream &OS) const {
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WriteAsOperand(OS, V, false);
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}
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//===----------------------------------------------------------------------===//
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// SCEV Utilities
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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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}
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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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}
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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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}
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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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}
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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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}
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return false;
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}
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namespace {
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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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/// expressions.
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class VISIBILITY_HIDDEN SCEVComplexityCompare {
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LoopInfo *LI;
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public:
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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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if (LHS == RHS)
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return false;
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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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// form GEPs.
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if (isa<PointerType>(LU->getType()) && !isa<PointerType>(RU->getType()))
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return false;
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if (isa<PointerType>(RU->getType()) && !isa<PointerType>(LU->getType()))
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return true;
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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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}
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// For instructions, compare their loop depth, and their opcode.
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// This is pretty loose.
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if (Instruction *LV = dyn_cast<Instruction>(LU->getValue())) {
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Instruction *RV = cast<Instruction>(RU->getValue());
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// Compare loop depths.
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if (LI->getLoopDepth(LV->getParent()) !=
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LI->getLoopDepth(RV->getParent()))
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return LI->getLoopDepth(LV->getParent()) <
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LI->getLoopDepth(RV->getParent());
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// Compare opcodes.
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if (LV->getOpcode() != RV->getOpcode())
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return LV->getOpcode() < RV->getOpcode();
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// Compare the number of operands.
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if (LV->getNumOperands() != RV->getNumOperands())
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return LV->getNumOperands() < RV->getNumOperands();
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}
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return false;
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}
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// Compare constant values.
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if (const SCEVConstant *LC = dyn_cast<SCEVConstant>(LHS)) {
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const SCEVConstant *RC = cast<SCEVConstant>(RHS);
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if (LC->getValue()->getBitWidth() != RC->getValue()->getBitWidth())
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return LC->getValue()->getBitWidth() < RC->getValue()->getBitWidth();
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return LC->getValue()->getValue().ult(RC->getValue()->getValue());
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}
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// Compare addrec loop depths.
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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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}
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// Lexicographically compare n-ary expressions.
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if (const SCEVNAryExpr *LC = dyn_cast<SCEVNAryExpr>(LHS)) {
|
|
const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
|
|
for (unsigned i = 0, e = LC->getNumOperands(); i != e; ++i) {
|
|
if (i >= RC->getNumOperands())
|
|
return false;
|
|
if (operator()(LC->getOperand(i), RC->getOperand(i)))
|
|
return true;
|
|
if (operator()(RC->getOperand(i), LC->getOperand(i)))
|
|
return false;
|
|
}
|
|
return LC->getNumOperands() < RC->getNumOperands();
|
|
}
|
|
|
|
// Lexicographically compare udiv expressions.
|
|
if (const SCEVUDivExpr *LC = dyn_cast<SCEVUDivExpr>(LHS)) {
|
|
const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
|
|
if (operator()(LC->getLHS(), RC->getLHS()))
|
|
return true;
|
|
if (operator()(RC->getLHS(), LC->getLHS()))
|
|
return false;
|
|
if (operator()(LC->getRHS(), RC->getRHS()))
|
|
return true;
|
|
if (operator()(RC->getRHS(), LC->getRHS()))
|
|
return false;
|
|
return false;
|
|
}
|
|
|
|
// Compare cast expressions by operand.
|
|
if (const SCEVCastExpr *LC = dyn_cast<SCEVCastExpr>(LHS)) {
|
|
const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
|
|
return operator()(LC->getOperand(), RC->getOperand());
|
|
}
|
|
|
|
// Compare offsetof expressions.
|
|
if (const SCEVFieldOffsetExpr *LA = dyn_cast<SCEVFieldOffsetExpr>(LHS)) {
|
|
const SCEVFieldOffsetExpr *RA = cast<SCEVFieldOffsetExpr>(RHS);
|
|
if (CompareTypes(LA->getStructType(), RA->getStructType()) ||
|
|
CompareTypes(RA->getStructType(), LA->getStructType()))
|
|
return CompareTypes(LA->getStructType(), RA->getStructType());
|
|
return LA->getFieldNo() < RA->getFieldNo();
|
|
}
|
|
|
|
// Compare sizeof expressions by the allocation type.
|
|
if (const SCEVAllocSizeExpr *LA = dyn_cast<SCEVAllocSizeExpr>(LHS)) {
|
|
const SCEVAllocSizeExpr *RA = cast<SCEVAllocSizeExpr>(RHS);
|
|
return CompareTypes(LA->getAllocType(), RA->getAllocType());
|
|
}
|
|
|
|
llvm_unreachable("Unknown SCEV kind!");
|
|
return false;
|
|
}
|
|
};
|
|
}
|
|
|
|
/// GroupByComplexity - Given a list of SCEV objects, order them by their
|
|
/// complexity, and group objects of the same complexity together by value.
|
|
/// When this routine is finished, we know that any duplicates in the vector are
|
|
/// consecutive and that complexity is monotonically increasing.
|
|
///
|
|
/// Note that we go take special precautions to ensure that we get determinstic
|
|
/// results from this routine. In other words, we don't want the results of
|
|
/// this to depend on where the addresses of various SCEV objects happened to
|
|
/// land in memory.
|
|
///
|
|
static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops,
|
|
LoopInfo *LI) {
|
|
if (Ops.size() < 2) return; // Noop
|
|
if (Ops.size() == 2) {
|
|
// This is the common case, which also happens to be trivially simple.
|
|
// Special case it.
|
|
if (SCEVComplexityCompare(LI)(Ops[1], Ops[0]))
|
|
std::swap(Ops[0], Ops[1]);
|
|
return;
|
|
}
|
|
|
|
// Do the rough sort by complexity.
|
|
std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI));
|
|
|
|
// Now that we are sorted by complexity, group elements of the same
|
|
// complexity. Note that this is, at worst, N^2, but the vector is likely to
|
|
// be extremely short in practice. Note that we take this approach because we
|
|
// do not want to depend on the addresses of the objects we are grouping.
|
|
for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
|
|
const SCEV *S = Ops[i];
|
|
unsigned Complexity = S->getSCEVType();
|
|
|
|
// If there are any objects of the same complexity and same value as this
|
|
// one, group them.
|
|
for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
|
|
if (Ops[j] == S) { // Found a duplicate.
|
|
// Move it to immediately after i'th element.
|
|
std::swap(Ops[i+1], Ops[j]);
|
|
++i; // no need to rescan it.
|
|
if (i == e-2) return; // Done!
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
|
|
//===----------------------------------------------------------------------===//
|
|
// Simple SCEV method implementations
|
|
//===----------------------------------------------------------------------===//
|
|
|
|
/// BinomialCoefficient - Compute BC(It, K). The result has width W.
|
|
/// Assume, K > 0.
|
|
static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K,
|
|
ScalarEvolution &SE,
|
|
const Type* ResultTy) {
|
|
// Handle the simplest case efficiently.
|
|
if (K == 1)
|
|
return SE.getTruncateOrZeroExtend(It, ResultTy);
|
|
|
|
// We are using the following formula for BC(It, K):
|
|
//
|
|
// BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
|
|
//
|
|
// Suppose, W is the bitwidth of the return value. We must be prepared for
|
|
// overflow. Hence, we must assure that the result of our computation is
|
|
// equal to the accurate one modulo 2^W. Unfortunately, division isn't
|
|
// safe in modular arithmetic.
|
|
//
|
|
// However, this code doesn't use exactly that formula; the formula it uses
|
|
// is something like the following, where T is the number of factors of 2 in
|
|
// K! (i.e. trailing zeros in the binary representation of K!), and ^ is
|
|
// exponentiation:
|
|
//
|
|
// BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
|
|
//
|
|
// This formula is trivially equivalent to the previous formula. However,
|
|
// this formula can be implemented much more efficiently. The trick is that
|
|
// K! / 2^T is odd, and exact division by an odd number *is* safe in modular
|
|
// arithmetic. To do exact division in modular arithmetic, all we have
|
|
// to do is multiply by the inverse. Therefore, this step can be done at
|
|
// width W.
|
|
//
|
|
// The next issue is how to safely do the division by 2^T. The way this
|
|
// is done is by doing the multiplication step at a width of at least W + T
|
|
// bits. This way, the bottom W+T bits of the product are accurate. Then,
|
|
// when we perform the division by 2^T (which is equivalent to a right shift
|
|
// by T), the bottom W bits are accurate. Extra bits are okay; they'll get
|
|
// truncated out after the division by 2^T.
|
|
//
|
|
// In comparison to just directly using the first formula, this technique
|
|
// is much more efficient; using the first formula requires W * K bits,
|
|
// but this formula less than W + K bits. Also, the first formula requires
|
|
// a division step, whereas this formula only requires multiplies and shifts.
|
|
//
|
|
// It doesn't matter whether the subtraction step is done in the calculation
|
|
// width or the input iteration count's width; if the subtraction overflows,
|
|
// the result must be zero anyway. We prefer here to do it in the width of
|
|
// the induction variable because it helps a lot for certain cases; CodeGen
|
|
// isn't smart enough to ignore the overflow, which leads to much less
|
|
// efficient code if the width of the subtraction is wider than the native
|
|
// register width.
|
|
//
|
|
// (It's possible to not widen at all by pulling out factors of 2 before
|
|
// the multiplication; for example, K=2 can be calculated as
|
|
// It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
|
|
// extra arithmetic, so it's not an obvious win, and it gets
|
|
// much more complicated for K > 3.)
|
|
|
|
// Protection from insane SCEVs; this bound is conservative,
|
|
// but it probably doesn't matter.
|
|
if (K > 1000)
|
|
return SE.getCouldNotCompute();
|
|
|
|
unsigned W = SE.getTypeSizeInBits(ResultTy);
|
|
|
|
// Calculate K! / 2^T and T; we divide out the factors of two before
|
|
// multiplying for calculating K! / 2^T to avoid overflow.
|
|
// Other overflow doesn't matter because we only care about the bottom
|
|
// W bits of the result.
|
|
APInt OddFactorial(W, 1);
|
|
unsigned T = 1;
|
|
for (unsigned i = 3; i <= K; ++i) {
|
|
APInt Mult(W, i);
|
|
unsigned TwoFactors = Mult.countTrailingZeros();
|
|
T += TwoFactors;
|
|
Mult = Mult.lshr(TwoFactors);
|
|
OddFactorial *= Mult;
|
|
}
|
|
|
|
// We need at least W + T bits for the multiplication step
|
|
unsigned CalculationBits = W + T;
|
|
|
|
// Calcuate 2^T, at width T+W.
|
|
APInt DivFactor = APInt(CalculationBits, 1).shl(T);
|
|
|
|
// Calculate the multiplicative inverse of K! / 2^T;
|
|
// this multiplication factor will perform the exact division by
|
|
// K! / 2^T.
|
|
APInt Mod = APInt::getSignedMinValue(W+1);
|
|
APInt MultiplyFactor = OddFactorial.zext(W+1);
|
|
MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
|
|
MultiplyFactor = MultiplyFactor.trunc(W);
|
|
|
|
// Calculate the product, at width T+W
|
|
const IntegerType *CalculationTy = IntegerType::get(SE.getContext(),
|
|
CalculationBits);
|
|
const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
|
|
for (unsigned i = 1; i != K; ++i) {
|
|
const SCEV *S = SE.getMinusSCEV(It, SE.getIntegerSCEV(i, It->getType()));
|
|
Dividend = SE.getMulExpr(Dividend,
|
|
SE.getTruncateOrZeroExtend(S, CalculationTy));
|
|
}
|
|
|
|
// Divide by 2^T
|
|
const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
|
|
|
|
// Truncate the result, and divide by K! / 2^T.
|
|
|
|
return SE.getMulExpr(SE.getConstant(MultiplyFactor),
|
|
SE.getTruncateOrZeroExtend(DivResult, ResultTy));
|
|
}
|
|
|
|
/// evaluateAtIteration - Return the value of this chain of recurrences at
|
|
/// the specified iteration number. We can evaluate this recurrence by
|
|
/// multiplying each element in the chain by the binomial coefficient
|
|
/// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
|
|
///
|
|
/// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
|
|
///
|
|
/// where BC(It, k) stands for binomial coefficient.
|
|
///
|
|
const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It,
|
|
ScalarEvolution &SE) const {
|
|
const SCEV *Result = getStart();
|
|
for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
|
|
// The computation is correct in the face of overflow provided that the
|
|
// multiplication is performed _after_ the evaluation of the binomial
|
|
// coefficient.
|
|
const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType());
|
|
if (isa<SCEVCouldNotCompute>(Coeff))
|
|
return Coeff;
|
|
|
|
Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
|
|
}
|
|
return Result;
|
|
}
|
|
|
|
//===----------------------------------------------------------------------===//
|
|
// SCEV Expression folder implementations
|
|
//===----------------------------------------------------------------------===//
|
|
|
|
const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op,
|
|
const Type *Ty) {
|
|
assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
|
|
"This is not a truncating conversion!");
|
|
assert(isSCEVable(Ty) &&
|
|
"This is not a conversion to a SCEVable type!");
|
|
Ty = getEffectiveSCEVType(Ty);
|
|
|
|
FoldingSetNodeID ID;
|
|
ID.AddInteger(scTruncate);
|
|
ID.AddPointer(Op);
|
|
ID.AddPointer(Ty);
|
|
void *IP = 0;
|
|
if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
|
|
|
|
// Fold if the operand is constant.
|
|
if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
|
|
return getConstant(
|
|
cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty)));
|
|
|
|
// trunc(trunc(x)) --> trunc(x)
|
|
if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
|
|
return getTruncateExpr(ST->getOperand(), Ty);
|
|
|
|
// trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
|
|
if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
|
|
return getTruncateOrSignExtend(SS->getOperand(), Ty);
|
|
|
|
// trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
|
|
if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
|
|
return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
|
|
|
|
// If the input value is a chrec scev, truncate the chrec's operands.
|
|
if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
|
|
SmallVector<const SCEV *, 4> Operands;
|
|
for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
|
|
Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty));
|
|
return getAddRecExpr(Operands, AddRec->getLoop());
|
|
}
|
|
|
|
// The cast wasn't folded; create an explicit cast node.
|
|
// Recompute the insert position, as it may have been invalidated.
|
|
if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
|
|
SCEV *S = SCEVAllocator.Allocate<SCEVTruncateExpr>();
|
|
new (S) SCEVTruncateExpr(ID, Op, Ty);
|
|
UniqueSCEVs.InsertNode(S, IP);
|
|
return S;
|
|
}
|
|
|
|
const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op,
|
|
const Type *Ty) {
|
|
assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
|
|
"This is not an extending conversion!");
|
|
assert(isSCEVable(Ty) &&
|
|
"This is not a conversion to a SCEVable type!");
|
|
Ty = getEffectiveSCEVType(Ty);
|
|
|
|
// Fold if the operand is constant.
|
|
if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) {
|
|
const Type *IntTy = getEffectiveSCEVType(Ty);
|
|
Constant *C = ConstantExpr::getZExt(SC->getValue(), IntTy);
|
|
if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty);
|
|
return getConstant(cast<ConstantInt>(C));
|
|
}
|
|
|
|
// zext(zext(x)) --> zext(x)
|
|
if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
|
|
return getZeroExtendExpr(SZ->getOperand(), Ty);
|
|
|
|
// Before doing any expensive analysis, check to see if we've already
|
|
// computed a SCEV for this Op and Ty.
|
|
FoldingSetNodeID ID;
|
|
ID.AddInteger(scZeroExtend);
|
|
ID.AddPointer(Op);
|
|
ID.AddPointer(Ty);
|
|
void *IP = 0;
|
|
if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
|
|
|
|
// If the input value is a chrec scev, and we can prove that the value
|
|
// did not overflow the old, smaller, value, we can zero extend all of the
|
|
// operands (often constants). This allows analysis of something like
|
|
// this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
|
|
if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
|
|
if (AR->isAffine()) {
|
|
const SCEV *Start = AR->getStart();
|
|
const SCEV *Step = AR->getStepRecurrence(*this);
|
|
unsigned BitWidth = getTypeSizeInBits(AR->getType());
|
|
const Loop *L = AR->getLoop();
|
|
|
|
// If we have special knowledge that this addrec won't overflow,
|
|
// we don't need to do any further analysis.
|
|
if (AR->hasNoUnsignedWrap())
|
|
return getAddRecExpr(getZeroExtendExpr(Start, Ty),
|
|
getZeroExtendExpr(Step, Ty),
|
|
L);
|
|
|
|
// Check whether the backedge-taken count is SCEVCouldNotCompute.
|
|
// Note that this serves two purposes: It filters out loops that are
|
|
// simply not analyzable, and it covers the case where this code is
|
|
// being called from within backedge-taken count analysis, such that
|
|
// attempting to ask for the backedge-taken count would likely result
|
|
// in infinite recursion. In the later case, the analysis code will
|
|
// cope with a conservative value, and it will take care to purge
|
|
// that value once it has finished.
|
|
const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
|
|
if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
|
|
// Manually compute the final value for AR, checking for
|
|
// overflow.
|
|
|
|
// Check whether the backedge-taken count can be losslessly casted to
|
|
// the addrec's type. The count is always unsigned.
|
|
const SCEV *CastedMaxBECount =
|
|
getTruncateOrZeroExtend(MaxBECount, Start->getType());
|
|
const SCEV *RecastedMaxBECount =
|
|
getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
|
|
if (MaxBECount == RecastedMaxBECount) {
|
|
const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
|
|
// Check whether Start+Step*MaxBECount has no unsigned overflow.
|
|
const SCEV *ZMul =
|
|
getMulExpr(CastedMaxBECount,
|
|
getTruncateOrZeroExtend(Step, Start->getType()));
|
|
const SCEV *Add = getAddExpr(Start, ZMul);
|
|
const SCEV *OperandExtendedAdd =
|
|
getAddExpr(getZeroExtendExpr(Start, WideTy),
|
|
getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
|
|
getZeroExtendExpr(Step, WideTy)));
|
|
if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd)
|
|
// Return the expression with the addrec on the outside.
|
|
return getAddRecExpr(getZeroExtendExpr(Start, Ty),
|
|
getZeroExtendExpr(Step, Ty),
|
|
L);
|
|
|
|
// Similar to above, only this time treat the step value as signed.
|
|
// This covers loops that count down.
|
|
const SCEV *SMul =
|
|
getMulExpr(CastedMaxBECount,
|
|
getTruncateOrSignExtend(Step, Start->getType()));
|
|
Add = getAddExpr(Start, SMul);
|
|
OperandExtendedAdd =
|
|
getAddExpr(getZeroExtendExpr(Start, WideTy),
|
|
getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
|
|
getSignExtendExpr(Step, WideTy)));
|
|
if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd)
|
|
// Return the expression with the addrec on the outside.
|
|
return getAddRecExpr(getZeroExtendExpr(Start, Ty),
|
|
getSignExtendExpr(Step, Ty),
|
|
L);
|
|
}
|
|
|
|
// If the backedge is guarded by a comparison with the pre-inc value
|
|
// the addrec is safe. Also, if the entry is guarded by a comparison
|
|
// with the start value and the backedge is guarded by a comparison
|
|
// with the post-inc value, the addrec is safe.
|
|
if (isKnownPositive(Step)) {
|
|
const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
|
|
getUnsignedRange(Step).getUnsignedMax());
|
|
if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
|
|
(isLoopGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) &&
|
|
isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT,
|
|
AR->getPostIncExpr(*this), N)))
|
|
// Return the expression with the addrec on the outside.
|
|
return getAddRecExpr(getZeroExtendExpr(Start, Ty),
|
|
getZeroExtendExpr(Step, Ty),
|
|
L);
|
|
} else if (isKnownNegative(Step)) {
|
|
const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
|
|
getSignedRange(Step).getSignedMin());
|
|
if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) &&
|
|
(isLoopGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) ||
|
|
isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT,
|
|
AR->getPostIncExpr(*this), N)))
|
|
// Return the expression with the addrec on the outside.
|
|
return getAddRecExpr(getZeroExtendExpr(Start, Ty),
|
|
getSignExtendExpr(Step, Ty),
|
|
L);
|
|
}
|
|
}
|
|
}
|
|
|
|
// The cast wasn't folded; create an explicit cast node.
|
|
// Recompute the insert position, as it may have been invalidated.
|
|
if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
|
|
SCEV *S = SCEVAllocator.Allocate<SCEVZeroExtendExpr>();
|
|
new (S) SCEVZeroExtendExpr(ID, Op, Ty);
|
|
UniqueSCEVs.InsertNode(S, IP);
|
|
return S;
|
|
}
|
|
|
|
const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op,
|
|
const Type *Ty) {
|
|
assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
|
|
"This is not an extending conversion!");
|
|
assert(isSCEVable(Ty) &&
|
|
"This is not a conversion to a SCEVable type!");
|
|
Ty = getEffectiveSCEVType(Ty);
|
|
|
|
// Fold if the operand is constant.
|
|
if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) {
|
|
const Type *IntTy = getEffectiveSCEVType(Ty);
|
|
Constant *C = ConstantExpr::getSExt(SC->getValue(), IntTy);
|
|
if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty);
|
|
return getConstant(cast<ConstantInt>(C));
|
|
}
|
|
|
|
// sext(sext(x)) --> sext(x)
|
|
if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
|
|
return getSignExtendExpr(SS->getOperand(), Ty);
|
|
|
|
// Before doing any expensive analysis, check to see if we've already
|
|
// computed a SCEV for this Op and Ty.
|
|
FoldingSetNodeID ID;
|
|
ID.AddInteger(scSignExtend);
|
|
ID.AddPointer(Op);
|
|
ID.AddPointer(Ty);
|
|
void *IP = 0;
|
|
if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
|
|
|
|
// If the input value is a chrec scev, and we can prove that the value
|
|
// did not overflow the old, smaller, value, we can sign extend all of the
|
|
// operands (often constants). This allows analysis of something like
|
|
// this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
|
|
if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
|
|
if (AR->isAffine()) {
|
|
const SCEV *Start = AR->getStart();
|
|
const SCEV *Step = AR->getStepRecurrence(*this);
|
|
unsigned BitWidth = getTypeSizeInBits(AR->getType());
|
|
const Loop *L = AR->getLoop();
|
|
|
|
// If we have special knowledge that this addrec won't overflow,
|
|
// we don't need to do any further analysis.
|
|
if (AR->hasNoSignedWrap())
|
|
return getAddRecExpr(getSignExtendExpr(Start, Ty),
|
|
getSignExtendExpr(Step, Ty),
|
|
L);
|
|
|
|
// Check whether the backedge-taken count is SCEVCouldNotCompute.
|
|
// Note that this serves two purposes: It filters out loops that are
|
|
// simply not analyzable, and it covers the case where this code is
|
|
// being called from within backedge-taken count analysis, such that
|
|
// attempting to ask for the backedge-taken count would likely result
|
|
// in infinite recursion. In the later case, the analysis code will
|
|
// cope with a conservative value, and it will take care to purge
|
|
// that value once it has finished.
|
|
const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
|
|
if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
|
|
// Manually compute the final value for AR, checking for
|
|
// overflow.
|
|
|
|
// Check whether the backedge-taken count can be losslessly casted to
|
|
// the addrec's type. The count is always unsigned.
|
|
const SCEV *CastedMaxBECount =
|
|
getTruncateOrZeroExtend(MaxBECount, Start->getType());
|
|
const SCEV *RecastedMaxBECount =
|
|
getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
|
|
if (MaxBECount == RecastedMaxBECount) {
|
|
const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
|
|
// Check whether Start+Step*MaxBECount has no signed overflow.
|
|
const SCEV *SMul =
|
|
getMulExpr(CastedMaxBECount,
|
|
getTruncateOrSignExtend(Step, Start->getType()));
|
|
const SCEV *Add = getAddExpr(Start, SMul);
|
|
const SCEV *OperandExtendedAdd =
|
|
getAddExpr(getSignExtendExpr(Start, WideTy),
|
|
getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
|
|
getSignExtendExpr(Step, WideTy)));
|
|
if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd)
|
|
// Return the expression with the addrec on the outside.
|
|
return getAddRecExpr(getSignExtendExpr(Start, Ty),
|
|
getSignExtendExpr(Step, Ty),
|
|
L);
|
|
|
|
// Similar to above, only this time treat the step value as unsigned.
|
|
// This covers loops that count up with an unsigned step.
|
|
const SCEV *UMul =
|
|
getMulExpr(CastedMaxBECount,
|
|
getTruncateOrZeroExtend(Step, Start->getType()));
|
|
Add = getAddExpr(Start, UMul);
|
|
OperandExtendedAdd =
|
|
getAddExpr(getSignExtendExpr(Start, WideTy),
|
|
getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
|
|
getZeroExtendExpr(Step, WideTy)));
|
|
if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd)
|
|
// Return the expression with the addrec on the outside.
|
|
return getAddRecExpr(getSignExtendExpr(Start, Ty),
|
|
getZeroExtendExpr(Step, Ty),
|
|
L);
|
|
}
|
|
|
|
// If the backedge is guarded by a comparison with the pre-inc value
|
|
// the addrec is safe. Also, if the entry is guarded by a comparison
|
|
// with the start value and the backedge is guarded by a comparison
|
|
// with the post-inc value, the addrec is safe.
|
|
if (isKnownPositive(Step)) {
|
|
const SCEV *N = getConstant(APInt::getSignedMinValue(BitWidth) -
|
|
getSignedRange(Step).getSignedMax());
|
|
if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT, AR, N) ||
|
|
(isLoopGuardedByCond(L, ICmpInst::ICMP_SLT, Start, N) &&
|
|
isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT,
|
|
AR->getPostIncExpr(*this), N)))
|
|
// Return the expression with the addrec on the outside.
|
|
return getAddRecExpr(getSignExtendExpr(Start, Ty),
|
|
getSignExtendExpr(Step, Ty),
|
|
L);
|
|
} else if (isKnownNegative(Step)) {
|
|
const SCEV *N = getConstant(APInt::getSignedMaxValue(BitWidth) -
|
|
getSignedRange(Step).getSignedMin());
|
|
if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT, AR, N) ||
|
|
(isLoopGuardedByCond(L, ICmpInst::ICMP_SGT, Start, N) &&
|
|
isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT,
|
|
AR->getPostIncExpr(*this), N)))
|
|
// Return the expression with the addrec on the outside.
|
|
return getAddRecExpr(getSignExtendExpr(Start, Ty),
|
|
getSignExtendExpr(Step, Ty),
|
|
L);
|
|
}
|
|
}
|
|
}
|
|
|
|
// The cast wasn't folded; create an explicit cast node.
|
|
// Recompute the insert position, as it may have been invalidated.
|
|
if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
|
|
SCEV *S = SCEVAllocator.Allocate<SCEVSignExtendExpr>();
|
|
new (S) SCEVSignExtendExpr(ID, Op, Ty);
|
|
UniqueSCEVs.InsertNode(S, IP);
|
|
return S;
|
|
}
|
|
|
|
/// getAnyExtendExpr - Return a SCEV for the given operand extended with
|
|
/// unspecified bits out to the given type.
|
|
///
|
|
const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
|
|
const Type *Ty) {
|
|
assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
|
|
"This is not an extending conversion!");
|
|
assert(isSCEVable(Ty) &&
|
|
"This is not a conversion to a SCEVable type!");
|
|
Ty = getEffectiveSCEVType(Ty);
|
|
|
|
// Sign-extend negative constants.
|
|
if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
|
|
if (SC->getValue()->getValue().isNegative())
|
|
return getSignExtendExpr(Op, Ty);
|
|
|
|
// Peel off a truncate cast.
|
|
if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
|
|
const SCEV *NewOp = T->getOperand();
|
|
if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
|
|
return getAnyExtendExpr(NewOp, Ty);
|
|
return getTruncateOrNoop(NewOp, Ty);
|
|
}
|
|
|
|
// Next try a zext cast. If the cast is folded, use it.
|
|
const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
|
|
if (!isa<SCEVZeroExtendExpr>(ZExt))
|
|
return ZExt;
|
|
|
|
// Next try a sext cast. If the cast is folded, use it.
|
|
const SCEV *SExt = getSignExtendExpr(Op, Ty);
|
|
if (!isa<SCEVSignExtendExpr>(SExt))
|
|
return SExt;
|
|
|
|
// If the expression is obviously signed, use the sext cast value.
|
|
if (isa<SCEVSMaxExpr>(Op))
|
|
return SExt;
|
|
|
|
// Absent any other information, use the zext cast value.
|
|
return ZExt;
|
|
}
|
|
|
|
/// CollectAddOperandsWithScales - Process the given Ops list, which is
|
|
/// a list of operands to be added under the given scale, update the given
|
|
/// map. This is a helper function for getAddRecExpr. As an example of
|
|
/// what it does, given a sequence of operands that would form an add
|
|
/// expression like this:
|
|
///
|
|
/// m + n + 13 + (A * (o + p + (B * q + m + 29))) + r + (-1 * r)
|
|
///
|
|
/// where A and B are constants, update the map with these values:
|
|
///
|
|
/// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
|
|
///
|
|
/// and add 13 + A*B*29 to AccumulatedConstant.
|
|
/// This will allow getAddRecExpr to produce this:
|
|
///
|
|
/// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
|
|
///
|
|
/// This form often exposes folding opportunities that are hidden in
|
|
/// the original operand list.
|
|
///
|
|
/// Return true iff it appears that any interesting folding opportunities
|
|
/// may be exposed. This helps getAddRecExpr short-circuit extra work in
|
|
/// the common case where no interesting opportunities are present, and
|
|
/// is also used as a check to avoid infinite recursion.
|
|
///
|
|
static bool
|
|
CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
|
|
SmallVector<const SCEV *, 8> &NewOps,
|
|
APInt &AccumulatedConstant,
|
|
const SmallVectorImpl<const SCEV *> &Ops,
|
|
const APInt &Scale,
|
|
ScalarEvolution &SE) {
|
|
bool Interesting = false;
|
|
|
|
// Iterate over the add operands.
|
|
for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
|
|
const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
|
|
if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
|
|
APInt NewScale =
|
|
Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue();
|
|
if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
|
|
// A multiplication of a constant with another add; recurse.
|
|
Interesting |=
|
|
CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
|
|
cast<SCEVAddExpr>(Mul->getOperand(1))
|
|
->getOperands(),
|
|
NewScale, SE);
|
|
} else {
|
|
// A multiplication of a constant with some other value. Update
|
|
// the map.
|
|
SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
|
|
const SCEV *Key = SE.getMulExpr(MulOps);
|
|
std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
|
|
M.insert(std::make_pair(Key, NewScale));
|
|
if (Pair.second) {
|
|
NewOps.push_back(Pair.first->first);
|
|
} else {
|
|
Pair.first->second += NewScale;
|
|
// The map already had an entry for this value, which may indicate
|
|
// a folding opportunity.
|
|
Interesting = true;
|
|
}
|
|
}
|
|
} else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
|
|
// Pull a buried constant out to the outside.
|
|
if (Scale != 1 || AccumulatedConstant != 0 || C->isZero())
|
|
Interesting = true;
|
|
AccumulatedConstant += Scale * C->getValue()->getValue();
|
|
} else {
|
|
// An ordinary operand. Update the map.
|
|
std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
|
|
M.insert(std::make_pair(Ops[i], Scale));
|
|
if (Pair.second) {
|
|
NewOps.push_back(Pair.first->first);
|
|
} else {
|
|
Pair.first->second += Scale;
|
|
// The map already had an entry for this value, which may indicate
|
|
// a folding opportunity.
|
|
Interesting = true;
|
|
}
|
|
}
|
|
}
|
|
|
|
return Interesting;
|
|
}
|
|
|
|
namespace {
|
|
struct APIntCompare {
|
|
bool operator()(const APInt &LHS, const APInt &RHS) const {
|
|
return LHS.ult(RHS);
|
|
}
|
|
};
|
|
}
|
|
|
|
/// getAddExpr - Get a canonical add expression, or something simpler if
|
|
/// possible.
|
|
const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops) {
|
|
assert(!Ops.empty() && "Cannot get empty add!");
|
|
if (Ops.size() == 1) return Ops[0];
|
|
#ifndef NDEBUG
|
|
for (unsigned i = 1, e = Ops.size(); i != e; ++i)
|
|
assert(getEffectiveSCEVType(Ops[i]->getType()) ==
|
|
getEffectiveSCEVType(Ops[0]->getType()) &&
|
|
"SCEVAddExpr operand types don't match!");
|
|
#endif
|
|
|
|
// Sort by complexity, this groups all similar expression types together.
|
|
GroupByComplexity(Ops, LI);
|
|
|
|
// If there are any constants, fold them together.
|
|
unsigned Idx = 0;
|
|
if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
|
|
++Idx;
|
|
assert(Idx < Ops.size());
|
|
while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
|
|
// We found two constants, fold them together!
|
|
Ops[0] = getConstant(LHSC->getValue()->getValue() +
|
|
RHSC->getValue()->getValue());
|
|
if (Ops.size() == 2) return Ops[0];
|
|
Ops.erase(Ops.begin()+1); // Erase the folded element
|
|
LHSC = cast<SCEVConstant>(Ops[0]);
|
|
}
|
|
|
|
// If we are left with a constant zero being added, strip it off.
|
|
if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
|
|
Ops.erase(Ops.begin());
|
|
--Idx;
|
|
}
|
|
}
|
|
|
|
if (Ops.size() == 1) return Ops[0];
|
|
|
|
// Okay, check to see if the same value occurs in the operand list twice. If
|
|
// so, merge them together into an multiply expression. Since we sorted the
|
|
// list, these values are required to be adjacent.
|
|
const Type *Ty = Ops[0]->getType();
|
|
for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
|
|
if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
|
|
// Found a match, merge the two values into a multiply, and add any
|
|
// remaining values to the result.
|
|
const SCEV *Two = getIntegerSCEV(2, Ty);
|
|
const SCEV *Mul = getMulExpr(Ops[i], Two);
|
|
if (Ops.size() == 2)
|
|
return Mul;
|
|
Ops.erase(Ops.begin()+i, Ops.begin()+i+2);
|
|
Ops.push_back(Mul);
|
|
return getAddExpr(Ops);
|
|
}
|
|
|
|
// Check for truncates. If all the operands are truncated from the same
|
|
// type, see if factoring out the truncate would permit the result to be
|
|
// folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
|
|
// if the contents of the resulting outer trunc fold to something simple.
|
|
for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
|
|
const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
|
|
const Type *DstType = Trunc->getType();
|
|
const Type *SrcType = Trunc->getOperand()->getType();
|
|
SmallVector<const SCEV *, 8> LargeOps;
|
|
bool Ok = true;
|
|
// Check all the operands to see if they can be represented in the
|
|
// source type of the truncate.
|
|
for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
|
|
if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
|
|
if (T->getOperand()->getType() != SrcType) {
|
|
Ok = false;
|
|
break;
|
|
}
|
|
LargeOps.push_back(T->getOperand());
|
|
} else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
|
|
// This could be either sign or zero extension, but sign extension
|
|
// is much more likely to be foldable here.
|
|
LargeOps.push_back(getSignExtendExpr(C, SrcType));
|
|
} else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
|
|
SmallVector<const SCEV *, 8> LargeMulOps;
|
|
for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
|
|
if (const SCEVTruncateExpr *T =
|
|
dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
|
|
if (T->getOperand()->getType() != SrcType) {
|
|
Ok = false;
|
|
break;
|
|
}
|
|
LargeMulOps.push_back(T->getOperand());
|
|
} else if (const SCEVConstant *C =
|
|
dyn_cast<SCEVConstant>(M->getOperand(j))) {
|
|
// This could be either sign or zero extension, but sign extension
|
|
// is much more likely to be foldable here.
|
|
LargeMulOps.push_back(getSignExtendExpr(C, SrcType));
|
|
} else {
|
|
Ok = false;
|
|
break;
|
|
}
|
|
}
|
|
if (Ok)
|
|
LargeOps.push_back(getMulExpr(LargeMulOps));
|
|
} else {
|
|
Ok = false;
|
|
break;
|
|
}
|
|
}
|
|
if (Ok) {
|
|
// Evaluate the expression in the larger type.
|
|
const SCEV *Fold = getAddExpr(LargeOps);
|
|
// If it folds to something simple, use it. Otherwise, don't.
|
|
if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
|
|
return getTruncateExpr(Fold, DstType);
|
|
}
|
|
}
|
|
|
|
// Skip past any other cast SCEVs.
|
|
while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
|
|
++Idx;
|
|
|
|
// If there are add operands they would be next.
|
|
if (Idx < Ops.size()) {
|
|
bool DeletedAdd = false;
|
|
while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
|
|
// If we have an add, expand the add operands onto the end of the operands
|
|
// list.
|
|
Ops.insert(Ops.end(), Add->op_begin(), Add->op_end());
|
|
Ops.erase(Ops.begin()+Idx);
|
|
DeletedAdd = true;
|
|
}
|
|
|
|
// If we deleted at least one add, we added operands to the end of the list,
|
|
// and they are not necessarily sorted. Recurse to resort and resimplify
|
|
// any operands we just aquired.
|
|
if (DeletedAdd)
|
|
return getAddExpr(Ops);
|
|
}
|
|
|
|
// Skip over the add expression until we get to a multiply.
|
|
while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
|
|
++Idx;
|
|
|
|
// Check to see if there are any folding opportunities present with
|
|
// operands multiplied by constant values.
|
|
if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
|
|
uint64_t BitWidth = getTypeSizeInBits(Ty);
|
|
DenseMap<const SCEV *, APInt> M;
|
|
SmallVector<const SCEV *, 8> NewOps;
|
|
APInt AccumulatedConstant(BitWidth, 0);
|
|
if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
|
|
Ops, APInt(BitWidth, 1), *this)) {
|
|
// Some interesting folding opportunity is present, so its worthwhile to
|
|
// re-generate the operands list. Group the operands by constant scale,
|
|
// to avoid multiplying by the same constant scale multiple times.
|
|
std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
|
|
for (SmallVector<const SCEV *, 8>::iterator I = NewOps.begin(),
|
|
E = NewOps.end(); I != E; ++I)
|
|
MulOpLists[M.find(*I)->second].push_back(*I);
|
|
// Re-generate the operands list.
|
|
Ops.clear();
|
|
if (AccumulatedConstant != 0)
|
|
Ops.push_back(getConstant(AccumulatedConstant));
|
|
for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator
|
|
I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I)
|
|
if (I->first != 0)
|
|
Ops.push_back(getMulExpr(getConstant(I->first),
|
|
getAddExpr(I->second)));
|
|
if (Ops.empty())
|
|
return getIntegerSCEV(0, Ty);
|
|
if (Ops.size() == 1)
|
|
return Ops[0];
|
|
return getAddExpr(Ops);
|
|
}
|
|
}
|
|
|
|
// If we are adding something to a multiply expression, make sure the
|
|
// something is not already an operand of the multiply. If so, merge it into
|
|
// the multiply.
|
|
for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
|
|
const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
|
|
for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
|
|
const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
|
|
for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
|
|
if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(Ops[AddOp])) {
|
|
// Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
|
|
const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
|
|
if (Mul->getNumOperands() != 2) {
|
|
// If the multiply has more than two operands, we must get the
|
|
// Y*Z term.
|
|
SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), Mul->op_end());
|
|
MulOps.erase(MulOps.begin()+MulOp);
|
|
InnerMul = getMulExpr(MulOps);
|
|
}
|
|
const SCEV *One = getIntegerSCEV(1, Ty);
|
|
const SCEV *AddOne = getAddExpr(InnerMul, One);
|
|
const SCEV *OuterMul = getMulExpr(AddOne, Ops[AddOp]);
|
|
if (Ops.size() == 2) return OuterMul;
|
|
if (AddOp < Idx) {
|
|
Ops.erase(Ops.begin()+AddOp);
|
|
Ops.erase(Ops.begin()+Idx-1);
|
|
} else {
|
|
Ops.erase(Ops.begin()+Idx);
|
|
Ops.erase(Ops.begin()+AddOp-1);
|
|
}
|
|
Ops.push_back(OuterMul);
|
|
return getAddExpr(Ops);
|
|
}
|
|
|
|
// Check this multiply against other multiplies being added together.
|
|
for (unsigned OtherMulIdx = Idx+1;
|
|
OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
|
|
++OtherMulIdx) {
|
|
const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
|
|
// If MulOp occurs in OtherMul, we can fold the two multiplies
|
|
// together.
|
|
for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
|
|
OMulOp != e; ++OMulOp)
|
|
if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
|
|
// Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
|
|
const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
|
|
if (Mul->getNumOperands() != 2) {
|
|
SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
|
|
Mul->op_end());
|
|
MulOps.erase(MulOps.begin()+MulOp);
|
|
InnerMul1 = getMulExpr(MulOps);
|
|
}
|
|
const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
|
|
if (OtherMul->getNumOperands() != 2) {
|
|
SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
|
|
OtherMul->op_end());
|
|
MulOps.erase(MulOps.begin()+OMulOp);
|
|
InnerMul2 = getMulExpr(MulOps);
|
|
}
|
|
const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
|
|
const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
|
|
if (Ops.size() == 2) return OuterMul;
|
|
Ops.erase(Ops.begin()+Idx);
|
|
Ops.erase(Ops.begin()+OtherMulIdx-1);
|
|
Ops.push_back(OuterMul);
|
|
return getAddExpr(Ops);
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
// If there are any add recurrences in the operands list, see if any other
|
|
// added values are loop invariant. If so, we can fold them into the
|
|
// recurrence.
|
|
while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
|
|
++Idx;
|
|
|
|
// Scan over all recurrences, trying to fold loop invariants into them.
|
|
for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
|
|
// Scan all of the other operands to this add and add them to the vector if
|
|
// they are loop invariant w.r.t. the recurrence.
|
|
SmallVector<const SCEV *, 8> LIOps;
|
|
const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
|
|
for (unsigned i = 0, e = Ops.size(); i != e; ++i)
|
|
if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
|
|
LIOps.push_back(Ops[i]);
|
|
Ops.erase(Ops.begin()+i);
|
|
--i; --e;
|
|
}
|
|
|
|
// If we found some loop invariants, fold them into the recurrence.
|
|
if (!LIOps.empty()) {
|
|
// NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
|
|
LIOps.push_back(AddRec->getStart());
|
|
|
|
SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
|
|
AddRec->op_end());
|
|
AddRecOps[0] = getAddExpr(LIOps);
|
|
|
|
const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRec->getLoop());
|
|
// If all of the other operands were loop invariant, we are done.
|
|
if (Ops.size() == 1) return NewRec;
|
|
|
|
// Otherwise, add the folded AddRec by the non-liv parts.
|
|
for (unsigned i = 0;; ++i)
|
|
if (Ops[i] == AddRec) {
|
|
Ops[i] = NewRec;
|
|
break;
|
|
}
|
|
return getAddExpr(Ops);
|
|
}
|
|
|
|
// Okay, if there weren't any loop invariants to be folded, check to see if
|
|
// there are multiple AddRec's with the same loop induction variable being
|
|
// added together. If so, we can fold them.
|
|
for (unsigned OtherIdx = Idx+1;
|
|
OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
|
|
if (OtherIdx != Idx) {
|
|
const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
|
|
if (AddRec->getLoop() == OtherAddRec->getLoop()) {
|
|
// Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D}
|
|
SmallVector<const SCEV *, 4> NewOps(AddRec->op_begin(),
|
|
AddRec->op_end());
|
|
for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) {
|
|
if (i >= NewOps.size()) {
|
|
NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i,
|
|
OtherAddRec->op_end());
|
|
break;
|
|
}
|
|
NewOps[i] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i));
|
|
}
|
|
const SCEV *NewAddRec = getAddRecExpr(NewOps, AddRec->getLoop());
|
|
|
|
if (Ops.size() == 2) return NewAddRec;
|
|
|
|
Ops.erase(Ops.begin()+Idx);
|
|
Ops.erase(Ops.begin()+OtherIdx-1);
|
|
Ops.push_back(NewAddRec);
|
|
return getAddExpr(Ops);
|
|
}
|
|
}
|
|
|
|
// Otherwise couldn't fold anything into this recurrence. Move onto the
|
|
// next one.
|
|
}
|
|
|
|
// Okay, it looks like we really DO need an add expr. Check to see if we
|
|
// already have one, otherwise create a new one.
|
|
FoldingSetNodeID ID;
|
|
ID.AddInteger(scAddExpr);
|
|
ID.AddInteger(Ops.size());
|
|
for (unsigned i = 0, e = Ops.size(); i != e; ++i)
|
|
ID.AddPointer(Ops[i]);
|
|
void *IP = 0;
|
|
if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
|
|
SCEV *S = SCEVAllocator.Allocate<SCEVAddExpr>();
|
|
new (S) SCEVAddExpr(ID, Ops);
|
|
UniqueSCEVs.InsertNode(S, IP);
|
|
return S;
|
|
}
|
|
|
|
|
|
/// getMulExpr - Get a canonical multiply expression, or something simpler if
|
|
/// possible.
|
|
const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops) {
|
|
assert(!Ops.empty() && "Cannot get empty mul!");
|
|
#ifndef NDEBUG
|
|
for (unsigned i = 1, e = Ops.size(); i != e; ++i)
|
|
assert(getEffectiveSCEVType(Ops[i]->getType()) ==
|
|
getEffectiveSCEVType(Ops[0]->getType()) &&
|
|
"SCEVMulExpr operand types don't match!");
|
|
#endif
|
|
|
|
// Sort by complexity, this groups all similar expression types together.
|
|
GroupByComplexity(Ops, LI);
|
|
|
|
// If there are any constants, fold them together.
|
|
unsigned Idx = 0;
|
|
if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
|
|
|
|
// C1*(C2+V) -> C1*C2 + C1*V
|
|
if (Ops.size() == 2)
|
|
if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
|
|
if (Add->getNumOperands() == 2 &&
|
|
isa<SCEVConstant>(Add->getOperand(0)))
|
|
return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
|
|
getMulExpr(LHSC, Add->getOperand(1)));
|
|
|
|
|
|
++Idx;
|
|
while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
|
|
// We found two constants, fold them together!
|
|
ConstantInt *Fold = ConstantInt::get(getContext(),
|
|
LHSC->getValue()->getValue() *
|
|
RHSC->getValue()->getValue());
|
|
Ops[0] = getConstant(Fold);
|
|
Ops.erase(Ops.begin()+1); // Erase the folded element
|
|
if (Ops.size() == 1) return Ops[0];
|
|
LHSC = cast<SCEVConstant>(Ops[0]);
|
|
}
|
|
|
|
// If we are left with a constant one being multiplied, strip it off.
|
|
if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
|
|
Ops.erase(Ops.begin());
|
|
--Idx;
|
|
} else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
|
|
// If we have a multiply of zero, it will always be zero.
|
|
return Ops[0];
|
|
}
|
|
}
|
|
|
|
// Skip over the add expression until we get to a multiply.
|
|
while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
|
|
++Idx;
|
|
|
|
if (Ops.size() == 1)
|
|
return Ops[0];
|
|
|
|
// If there are mul operands inline them all into this expression.
|
|
if (Idx < Ops.size()) {
|
|
bool DeletedMul = false;
|
|
while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
|
|
// If we have an mul, expand the mul operands onto the end of the operands
|
|
// list.
|
|
Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end());
|
|
Ops.erase(Ops.begin()+Idx);
|
|
DeletedMul = true;
|
|
}
|
|
|
|
// If we deleted at least one mul, we added operands to the end of the list,
|
|
// and they are not necessarily sorted. Recurse to resort and resimplify
|
|
// any operands we just aquired.
|
|
if (DeletedMul)
|
|
return getMulExpr(Ops);
|
|
}
|
|
|
|
// If there are any add recurrences in the operands list, see if any other
|
|
// added values are loop invariant. If so, we can fold them into the
|
|
// recurrence.
|
|
while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
|
|
++Idx;
|
|
|
|
// Scan over all recurrences, trying to fold loop invariants into them.
|
|
for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
|
|
// Scan all of the other operands to this mul and add them to the vector if
|
|
// they are loop invariant w.r.t. the recurrence.
|
|
SmallVector<const SCEV *, 8> LIOps;
|
|
const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
|
|
for (unsigned i = 0, e = Ops.size(); i != e; ++i)
|
|
if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
|
|
LIOps.push_back(Ops[i]);
|
|
Ops.erase(Ops.begin()+i);
|
|
--i; --e;
|
|
}
|
|
|
|
// If we found some loop invariants, fold them into the recurrence.
|
|
if (!LIOps.empty()) {
|
|
// NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
|
|
SmallVector<const SCEV *, 4> NewOps;
|
|
NewOps.reserve(AddRec->getNumOperands());
|
|
if (LIOps.size() == 1) {
|
|
const SCEV *Scale = LIOps[0];
|
|
for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
|
|
NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
|
|
} else {
|
|
for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
|
|
SmallVector<const SCEV *, 4> MulOps(LIOps.begin(), LIOps.end());
|
|
MulOps.push_back(AddRec->getOperand(i));
|
|
NewOps.push_back(getMulExpr(MulOps));
|
|
}
|
|
}
|
|
|
|
const SCEV *NewRec = getAddRecExpr(NewOps, AddRec->getLoop());
|
|
|
|
// If all of the other operands were loop invariant, we are done.
|
|
if (Ops.size() == 1) return NewRec;
|
|
|
|
// Otherwise, multiply the folded AddRec by the non-liv parts.
|
|
for (unsigned i = 0;; ++i)
|
|
if (Ops[i] == AddRec) {
|
|
Ops[i] = NewRec;
|
|
break;
|
|
}
|
|
return getMulExpr(Ops);
|
|
}
|
|
|
|
// Okay, if there weren't any loop invariants to be folded, check to see if
|
|
// there are multiple AddRec's with the same loop induction variable being
|
|
// multiplied together. If so, we can fold them.
|
|
for (unsigned OtherIdx = Idx+1;
|
|
OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
|
|
if (OtherIdx != Idx) {
|
|
const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
|
|
if (AddRec->getLoop() == OtherAddRec->getLoop()) {
|
|
// F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D}
|
|
const SCEVAddRecExpr *F = AddRec, *G = OtherAddRec;
|
|
const SCEV *NewStart = getMulExpr(F->getStart(),
|
|
G->getStart());
|
|
const SCEV *B = F->getStepRecurrence(*this);
|
|
const SCEV *D = G->getStepRecurrence(*this);
|
|
const SCEV *NewStep = getAddExpr(getMulExpr(F, D),
|
|
getMulExpr(G, B),
|
|
getMulExpr(B, D));
|
|
const SCEV *NewAddRec = getAddRecExpr(NewStart, NewStep,
|
|
F->getLoop());
|
|
if (Ops.size() == 2) return NewAddRec;
|
|
|
|
Ops.erase(Ops.begin()+Idx);
|
|
Ops.erase(Ops.begin()+OtherIdx-1);
|
|
Ops.push_back(NewAddRec);
|
|
return getMulExpr(Ops);
|
|
}
|
|
}
|
|
|
|
// Otherwise couldn't fold anything into this recurrence. Move onto the
|
|
// next one.
|
|
}
|
|
|
|
// Okay, it looks like we really DO need an mul expr. Check to see if we
|
|
// already have one, otherwise create a new one.
|
|
FoldingSetNodeID ID;
|
|
ID.AddInteger(scMulExpr);
|
|
ID.AddInteger(Ops.size());
|
|
for (unsigned i = 0, e = Ops.size(); i != e; ++i)
|
|
ID.AddPointer(Ops[i]);
|
|
void *IP = 0;
|
|
if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
|
|
SCEV *S = SCEVAllocator.Allocate<SCEVMulExpr>();
|
|
new (S) SCEVMulExpr(ID, Ops);
|
|
UniqueSCEVs.InsertNode(S, IP);
|
|
return S;
|
|
}
|
|
|
|
/// getUDivExpr - Get a canonical unsigned division expression, or something
|
|
/// simpler if possible.
|
|
const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
|
|
const SCEV *RHS) {
|
|
assert(getEffectiveSCEVType(LHS->getType()) ==
|
|
getEffectiveSCEVType(RHS->getType()) &&
|
|
"SCEVUDivExpr operand types don't match!");
|
|
|
|
if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
|
|
if (RHSC->getValue()->equalsInt(1))
|
|
return LHS; // X udiv 1 --> x
|
|
if (RHSC->isZero())
|
|
return getIntegerSCEV(0, LHS->getType()); // value is undefined
|
|
|
|
// Determine if the division can be folded into the operands of
|
|
// its operands.
|
|
// TODO: Generalize this to non-constants by using known-bits information.
|
|
const Type *Ty = LHS->getType();
|
|
unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
|
|
unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ;
|
|
// For non-power-of-two values, effectively round the value up to the
|
|
// nearest power of two.
|
|
if (!RHSC->getValue()->getValue().isPowerOf2())
|
|
++MaxShiftAmt;
|
|
const IntegerType *ExtTy =
|
|
IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
|
|
// {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
|
|
if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
|
|
if (const SCEVConstant *Step =
|
|
dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this)))
|
|
if (!Step->getValue()->getValue()
|
|
.urem(RHSC->getValue()->getValue()) &&
|
|
getZeroExtendExpr(AR, ExtTy) ==
|
|
getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
|
|
getZeroExtendExpr(Step, ExtTy),
|
|
AR->getLoop())) {
|
|
SmallVector<const SCEV *, 4> Operands;
|
|
for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i)
|
|
Operands.push_back(getUDivExpr(AR->getOperand(i), RHS));
|
|
return getAddRecExpr(Operands, AR->getLoop());
|
|
}
|
|
// (A*B)/C --> A*(B/C) if safe and B/C can be folded.
|
|
if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
|
|
SmallVector<const SCEV *, 4> Operands;
|
|
for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i)
|
|
Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy));
|
|
if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
|
|
// Find an operand that's safely divisible.
|
|
for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
|
|
const SCEV *Op = M->getOperand(i);
|
|
const SCEV *Div = getUDivExpr(Op, RHSC);
|
|
if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
|
|
const SmallVectorImpl<const SCEV *> &MOperands = M->getOperands();
|
|
Operands = SmallVector<const SCEV *, 4>(MOperands.begin(),
|
|
MOperands.end());
|
|
Operands[i] = Div;
|
|
return getMulExpr(Operands);
|
|
}
|
|
}
|
|
}
|
|
// (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
|
|
if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(LHS)) {
|
|
SmallVector<const SCEV *, 4> Operands;
|
|
for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i)
|
|
Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy));
|
|
if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
|
|
Operands.clear();
|
|
for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
|
|
const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
|
|
if (isa<SCEVUDivExpr>(Op) || getMulExpr(Op, RHS) != A->getOperand(i))
|
|
break;
|
|
Operands.push_back(Op);
|
|
}
|
|
if (Operands.size() == A->getNumOperands())
|
|
return getAddExpr(Operands);
|
|
}
|
|
}
|
|
|
|
// Fold if both operands are constant.
|
|
if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
|
|
Constant *LHSCV = LHSC->getValue();
|
|
Constant *RHSCV = RHSC->getValue();
|
|
return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
|
|
RHSCV)));
|
|
}
|
|
}
|
|
|
|
FoldingSetNodeID ID;
|
|
ID.AddInteger(scUDivExpr);
|
|
ID.AddPointer(LHS);
|
|
ID.AddPointer(RHS);
|
|
void *IP = 0;
|
|
if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
|
|
SCEV *S = SCEVAllocator.Allocate<SCEVUDivExpr>();
|
|
new (S) SCEVUDivExpr(ID, LHS, RHS);
|
|
UniqueSCEVs.InsertNode(S, IP);
|
|
return S;
|
|
}
|
|
|
|
|
|
/// getAddRecExpr - Get an add recurrence expression for the specified loop.
|
|
/// Simplify the expression as much as possible.
|
|
const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start,
|
|
const SCEV *Step, const Loop *L) {
|
|
SmallVector<const SCEV *, 4> Operands;
|
|
Operands.push_back(Start);
|
|
if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
|
|
if (StepChrec->getLoop() == L) {
|
|
Operands.insert(Operands.end(), StepChrec->op_begin(),
|
|
StepChrec->op_end());
|
|
return getAddRecExpr(Operands, L);
|
|
}
|
|
|
|
Operands.push_back(Step);
|
|
return getAddRecExpr(Operands, L);
|
|
}
|
|
|
|
/// getAddRecExpr - Get an add recurrence expression for the specified loop.
|
|
/// Simplify the expression as much as possible.
|
|
const SCEV *
|
|
ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
|
|
const Loop *L) {
|
|
if (Operands.size() == 1) return Operands[0];
|
|
#ifndef NDEBUG
|
|
for (unsigned i = 1, e = Operands.size(); i != e; ++i)
|
|
assert(getEffectiveSCEVType(Operands[i]->getType()) ==
|
|
getEffectiveSCEVType(Operands[0]->getType()) &&
|
|
"SCEVAddRecExpr operand types don't match!");
|
|
#endif
|
|
|
|
if (Operands.back()->isZero()) {
|
|
Operands.pop_back();
|
|
return getAddRecExpr(Operands, L); // {X,+,0} --> X
|
|
}
|
|
|
|
// Canonicalize nested AddRecs in by nesting them in order of loop depth.
|
|
if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
|
|
const Loop* NestedLoop = NestedAR->getLoop();
|
|
if (L->getLoopDepth() < NestedLoop->getLoopDepth()) {
|
|
SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
|
|
NestedAR->op_end());
|
|
Operands[0] = NestedAR->getStart();
|
|
// AddRecs require their operands be loop-invariant with respect to their
|
|
// loops. Don't perform this transformation if it would break this
|
|
// requirement.
|
|
bool AllInvariant = true;
|
|
for (unsigned i = 0, e = Operands.size(); i != e; ++i)
|
|
if (!Operands[i]->isLoopInvariant(L)) {
|
|
AllInvariant = false;
|
|
break;
|
|
}
|
|
if (AllInvariant) {
|
|
NestedOperands[0] = getAddRecExpr(Operands, L);
|
|
AllInvariant = true;
|
|
for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i)
|
|
if (!NestedOperands[i]->isLoopInvariant(NestedLoop)) {
|
|
AllInvariant = false;
|
|
break;
|
|
}
|
|
if (AllInvariant)
|
|
// Ok, both add recurrences are valid after the transformation.
|
|
return getAddRecExpr(NestedOperands, NestedLoop);
|
|
}
|
|
// Reset Operands to its original state.
|
|
Operands[0] = NestedAR;
|
|
}
|
|
}
|
|
|
|
FoldingSetNodeID ID;
|
|
ID.AddInteger(scAddRecExpr);
|
|
ID.AddInteger(Operands.size());
|
|
for (unsigned i = 0, e = Operands.size(); i != e; ++i)
|
|
ID.AddPointer(Operands[i]);
|
|
ID.AddPointer(L);
|
|
void *IP = 0;
|
|
if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
|
|
SCEV *S = SCEVAllocator.Allocate<SCEVAddRecExpr>();
|
|
new (S) SCEVAddRecExpr(ID, Operands, L);
|
|
UniqueSCEVs.InsertNode(S, IP);
|
|
return S;
|
|
}
|
|
|
|
const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
|
|
const SCEV *RHS) {
|
|
SmallVector<const SCEV *, 2> Ops;
|
|
Ops.push_back(LHS);
|
|
Ops.push_back(RHS);
|
|
return getSMaxExpr(Ops);
|
|
}
|
|
|
|
const SCEV *
|
|
ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
|
|
assert(!Ops.empty() && "Cannot get empty smax!");
|
|
if (Ops.size() == 1) return Ops[0];
|
|
#ifndef NDEBUG
|
|
for (unsigned i = 1, e = Ops.size(); i != e; ++i)
|
|
assert(getEffectiveSCEVType(Ops[i]->getType()) ==
|
|
getEffectiveSCEVType(Ops[0]->getType()) &&
|
|
"SCEVSMaxExpr operand types don't match!");
|
|
#endif
|
|
|
|
// Sort by complexity, this groups all similar expression types together.
|
|
GroupByComplexity(Ops, LI);
|
|
|
|
// If there are any constants, fold them together.
|
|
unsigned Idx = 0;
|
|
if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
|
|
++Idx;
|
|
assert(Idx < Ops.size());
|
|
while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
|
|
// We found two constants, fold them together!
|
|
ConstantInt *Fold = ConstantInt::get(getContext(),
|
|
APIntOps::smax(LHSC->getValue()->getValue(),
|
|
RHSC->getValue()->getValue()));
|
|
Ops[0] = getConstant(Fold);
|
|
Ops.erase(Ops.begin()+1); // Erase the folded element
|
|
if (Ops.size() == 1) return Ops[0];
|
|
LHSC = cast<SCEVConstant>(Ops[0]);
|
|
}
|
|
|
|
// If we are left with a constant minimum-int, strip it off.
|
|
if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
|
|
Ops.erase(Ops.begin());
|
|
--Idx;
|
|
} else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
|
|
// If we have an smax with a constant maximum-int, it will always be
|
|
// maximum-int.
|
|
return Ops[0];
|
|
}
|
|
}
|
|
|
|
if (Ops.size() == 1) return Ops[0];
|
|
|
|
// Find the first SMax
|
|
while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
|
|
++Idx;
|
|
|
|
// Check to see if one of the operands is an SMax. If so, expand its operands
|
|
// onto our operand list, and recurse to simplify.
|
|
if (Idx < Ops.size()) {
|
|
bool DeletedSMax = false;
|
|
while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
|
|
Ops.insert(Ops.end(), SMax->op_begin(), SMax->op_end());
|
|
Ops.erase(Ops.begin()+Idx);
|
|
DeletedSMax = true;
|
|
}
|
|
|
|
if (DeletedSMax)
|
|
return getSMaxExpr(Ops);
|
|
}
|
|
|
|
// Okay, check to see if the same value occurs in the operand list twice. If
|
|
// so, delete one. Since we sorted the list, these values are required to
|
|
// be adjacent.
|
|
for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
|
|
if (Ops[i] == Ops[i+1]) { // X smax Y smax Y --> X smax Y
|
|
Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
|
|
--i; --e;
|
|
}
|
|
|
|
if (Ops.size() == 1) return Ops[0];
|
|
|
|
assert(!Ops.empty() && "Reduced smax down to nothing!");
|
|
|
|
// Okay, it looks like we really DO need an smax expr. Check to see if we
|
|
// already have one, otherwise create a new one.
|
|
FoldingSetNodeID ID;
|
|
ID.AddInteger(scSMaxExpr);
|
|
ID.AddInteger(Ops.size());
|
|
for (unsigned i = 0, e = Ops.size(); i != e; ++i)
|
|
ID.AddPointer(Ops[i]);
|
|
void *IP = 0;
|
|
if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
|
|
SCEV *S = SCEVAllocator.Allocate<SCEVSMaxExpr>();
|
|
new (S) SCEVSMaxExpr(ID, Ops);
|
|
UniqueSCEVs.InsertNode(S, IP);
|
|
return S;
|
|
}
|
|
|
|
const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
|
|
const SCEV *RHS) {
|
|
SmallVector<const SCEV *, 2> Ops;
|
|
Ops.push_back(LHS);
|
|
Ops.push_back(RHS);
|
|
return getUMaxExpr(Ops);
|
|
}
|
|
|
|
const SCEV *
|
|
ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
|
|
assert(!Ops.empty() && "Cannot get empty umax!");
|
|
if (Ops.size() == 1) return Ops[0];
|
|
#ifndef NDEBUG
|
|
for (unsigned i = 1, e = Ops.size(); i != e; ++i)
|
|
assert(getEffectiveSCEVType(Ops[i]->getType()) ==
|
|
getEffectiveSCEVType(Ops[0]->getType()) &&
|
|
"SCEVUMaxExpr operand types don't match!");
|
|
#endif
|
|
|
|
// Sort by complexity, this groups all similar expression types together.
|
|
GroupByComplexity(Ops, LI);
|
|
|
|
// If there are any constants, fold them together.
|
|
unsigned Idx = 0;
|
|
if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
|
|
++Idx;
|
|
assert(Idx < Ops.size());
|
|
while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
|
|
// We found two constants, fold them together!
|
|
ConstantInt *Fold = ConstantInt::get(getContext(),
|
|
APIntOps::umax(LHSC->getValue()->getValue(),
|
|
RHSC->getValue()->getValue()));
|
|
Ops[0] = getConstant(Fold);
|
|
Ops.erase(Ops.begin()+1); // Erase the folded element
|
|
if (Ops.size() == 1) return Ops[0];
|
|
LHSC = cast<SCEVConstant>(Ops[0]);
|
|
}
|
|
|
|
// If we are left with a constant minimum-int, strip it off.
|
|
if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
|
|
Ops.erase(Ops.begin());
|
|
--Idx;
|
|
} else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
|
|
// If we have an umax with a constant maximum-int, it will always be
|
|
// maximum-int.
|
|
return Ops[0];
|
|
}
|
|
}
|
|
|
|
if (Ops.size() == 1) return Ops[0];
|
|
|
|
// Find the first UMax
|
|
while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
|
|
++Idx;
|
|
|
|
// Check to see if one of the operands is a UMax. If so, expand its operands
|
|
// onto our operand list, and recurse to simplify.
|
|
if (Idx < Ops.size()) {
|
|
bool DeletedUMax = false;
|
|
while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
|
|
Ops.insert(Ops.end(), UMax->op_begin(), UMax->op_end());
|
|
Ops.erase(Ops.begin()+Idx);
|
|
DeletedUMax = true;
|
|
}
|
|
|
|
if (DeletedUMax)
|
|
return getUMaxExpr(Ops);
|
|
}
|
|
|
|
// Okay, check to see if the same value occurs in the operand list twice. If
|
|
// so, delete one. Since we sorted the list, these values are required to
|
|
// be adjacent.
|
|
for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
|
|
if (Ops[i] == Ops[i+1]) { // X umax Y umax Y --> X umax Y
|
|
Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
|
|
--i; --e;
|
|
}
|
|
|
|
if (Ops.size() == 1) return Ops[0];
|
|
|
|
assert(!Ops.empty() && "Reduced umax down to nothing!");
|
|
|
|
// Okay, it looks like we really DO need a umax expr. Check to see if we
|
|
// already have one, otherwise create a new one.
|
|
FoldingSetNodeID ID;
|
|
ID.AddInteger(scUMaxExpr);
|
|
ID.AddInteger(Ops.size());
|
|
for (unsigned i = 0, e = Ops.size(); i != e; ++i)
|
|
ID.AddPointer(Ops[i]);
|
|
void *IP = 0;
|
|
if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
|
|
SCEV *S = SCEVAllocator.Allocate<SCEVUMaxExpr>();
|
|
new (S) SCEVUMaxExpr(ID, Ops);
|
|
UniqueSCEVs.InsertNode(S, IP);
|
|
return S;
|
|
}
|
|
|
|
const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
|
|
const SCEV *RHS) {
|
|
// ~smax(~x, ~y) == smin(x, y).
|
|
return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
|
|
}
|
|
|
|
const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
|
|
const SCEV *RHS) {
|
|
// ~umax(~x, ~y) == umin(x, y)
|
|
return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
|
|
}
|
|
|
|
const SCEV *ScalarEvolution::getFieldOffsetExpr(const StructType *STy,
|
|
unsigned FieldNo) {
|
|
// If we have TargetData we can determine the constant offset.
|
|
if (TD) {
|
|
const Type *IntPtrTy = TD->getIntPtrType(getContext());
|
|
const StructLayout &SL = *TD->getStructLayout(STy);
|
|
uint64_t Offset = SL.getElementOffset(FieldNo);
|
|
return getIntegerSCEV(Offset, IntPtrTy);
|
|
}
|
|
|
|
// Field 0 is always at offset 0.
|
|
if (FieldNo == 0) {
|
|
const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy));
|
|
return getIntegerSCEV(0, Ty);
|
|
}
|
|
|
|
// Okay, it looks like we really DO need an offsetof expr. Check to see if we
|
|
// already have one, otherwise create a new one.
|
|
FoldingSetNodeID ID;
|
|
ID.AddInteger(scFieldOffset);
|
|
ID.AddPointer(STy);
|
|
ID.AddInteger(FieldNo);
|
|
void *IP = 0;
|
|
if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
|
|
SCEV *S = SCEVAllocator.Allocate<SCEVFieldOffsetExpr>();
|
|
const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy));
|
|
new (S) SCEVFieldOffsetExpr(ID, Ty, STy, FieldNo);
|
|
UniqueSCEVs.InsertNode(S, IP);
|
|
return S;
|
|
}
|
|
|
|
const SCEV *ScalarEvolution::getAllocSizeExpr(const Type *AllocTy) {
|
|
// If we have TargetData we can determine the constant size.
|
|
if (TD && AllocTy->isSized()) {
|
|
const Type *IntPtrTy = TD->getIntPtrType(getContext());
|
|
return getIntegerSCEV(TD->getTypeAllocSize(AllocTy), IntPtrTy);
|
|
}
|
|
|
|
// Expand an array size into the element size times the number
|
|
// of elements.
|
|
if (const ArrayType *ATy = dyn_cast<ArrayType>(AllocTy)) {
|
|
const SCEV *E = getAllocSizeExpr(ATy->getElementType());
|
|
return getMulExpr(
|
|
E, getConstant(ConstantInt::get(cast<IntegerType>(E->getType()),
|
|
ATy->getNumElements())));
|
|
}
|
|
|
|
// Expand a vector size into the element size times the number
|
|
// of elements.
|
|
if (const VectorType *VTy = dyn_cast<VectorType>(AllocTy)) {
|
|
const SCEV *E = getAllocSizeExpr(VTy->getElementType());
|
|
return getMulExpr(
|
|
E, getConstant(ConstantInt::get(cast<IntegerType>(E->getType()),
|
|
VTy->getNumElements())));
|
|
}
|
|
|
|
// Okay, it looks like we really DO need a sizeof expr. Check to see if we
|
|
// already have one, otherwise create a new one.
|
|
FoldingSetNodeID ID;
|
|
ID.AddInteger(scAllocSize);
|
|
ID.AddPointer(AllocTy);
|
|
void *IP = 0;
|
|
if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
|
|
SCEV *S = SCEVAllocator.Allocate<SCEVAllocSizeExpr>();
|
|
const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
|
|
new (S) SCEVAllocSizeExpr(ID, Ty, AllocTy);
|
|
UniqueSCEVs.InsertNode(S, IP);
|
|
return S;
|
|
}
|
|
|
|
const SCEV *ScalarEvolution::getUnknown(Value *V) {
|
|
// Don't attempt to do anything other than create a SCEVUnknown object
|
|
// here. createSCEV only calls getUnknown after checking for all other
|
|
// interesting possibilities, and any other code that calls getUnknown
|
|
// is doing so in order to hide a value from SCEV canonicalization.
|
|
|
|
FoldingSetNodeID ID;
|
|
ID.AddInteger(scUnknown);
|
|
ID.AddPointer(V);
|
|
void *IP = 0;
|
|
if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
|
|
SCEV *S = SCEVAllocator.Allocate<SCEVUnknown>();
|
|
new (S) SCEVUnknown(ID, V);
|
|
UniqueSCEVs.InsertNode(S, IP);
|
|
return S;
|
|
}
|
|
|
|
//===----------------------------------------------------------------------===//
|
|
// Basic SCEV Analysis and PHI Idiom Recognition Code
|
|
//
|
|
|
|
/// isSCEVable - Test if values of the given type are analyzable within
|
|
/// the SCEV framework. This primarily includes integer types, and it
|
|
/// can optionally include pointer types if the ScalarEvolution class
|
|
/// has access to target-specific information.
|
|
bool ScalarEvolution::isSCEVable(const Type *Ty) const {
|
|
// Integers and pointers are always SCEVable.
|
|
return Ty->isInteger() || isa<PointerType>(Ty);
|
|
}
|
|
|
|
/// getTypeSizeInBits - Return the size in bits of the specified type,
|
|
/// for which isSCEVable must return true.
|
|
uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const {
|
|
assert(isSCEVable(Ty) && "Type is not SCEVable!");
|
|
|
|
// If we have a TargetData, use it!
|
|
if (TD)
|
|
return TD->getTypeSizeInBits(Ty);
|
|
|
|
// Integer types have fixed sizes.
|
|
if (Ty->isInteger())
|
|
return Ty->getPrimitiveSizeInBits();
|
|
|
|
// The only other support type is pointer. Without TargetData, conservatively
|
|
// assume pointers are 64-bit.
|
|
assert(isa<PointerType>(Ty) && "isSCEVable permitted a non-SCEVable type!");
|
|
return 64;
|
|
}
|
|
|
|
/// getEffectiveSCEVType - Return a type with the same bitwidth as
|
|
/// the given type and which represents how SCEV will treat the given
|
|
/// type, for which isSCEVable must return true. For pointer types,
|
|
/// this is the pointer-sized integer type.
|
|
const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const {
|
|
assert(isSCEVable(Ty) && "Type is not SCEVable!");
|
|
|
|
if (Ty->isInteger())
|
|
return Ty;
|
|
|
|
// The only other support type is pointer.
|
|
assert(isa<PointerType>(Ty) && "Unexpected non-pointer non-integer type!");
|
|
if (TD) return TD->getIntPtrType(getContext());
|
|
|
|
// Without TargetData, conservatively assume pointers are 64-bit.
|
|
return Type::getInt64Ty(getContext());
|
|
}
|
|
|
|
const SCEV *ScalarEvolution::getCouldNotCompute() {
|
|
return &CouldNotCompute;
|
|
}
|
|
|
|
/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
|
|
/// expression and create a new one.
|
|
const SCEV *ScalarEvolution::getSCEV(Value *V) {
|
|
assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
|
|
|
|
std::map<SCEVCallbackVH, const SCEV *>::iterator I = Scalars.find(V);
|
|
if (I != Scalars.end()) return I->second;
|
|
const SCEV *S = createSCEV(V);
|
|
Scalars.insert(std::make_pair(SCEVCallbackVH(V, this), S));
|
|
return S;
|
|
}
|
|
|
|
/// getIntegerSCEV - Given a SCEVable type, create a constant for the
|
|
/// specified signed integer value and return a SCEV for the constant.
|
|
const SCEV *ScalarEvolution::getIntegerSCEV(int Val, const Type *Ty) {
|
|
const IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty));
|
|
return getConstant(ConstantInt::get(ITy, Val));
|
|
}
|
|
|
|
/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
|
|
///
|
|
const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) {
|
|
if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
|
|
return getConstant(
|
|
cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
|
|
|
|
const Type *Ty = V->getType();
|
|
Ty = getEffectiveSCEVType(Ty);
|
|
return getMulExpr(V,
|
|
getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))));
|
|
}
|
|
|
|
/// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
|
|
const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
|
|
if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
|
|
return getConstant(
|
|
cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
|
|
|
|
const Type *Ty = V->getType();
|
|
Ty = getEffectiveSCEVType(Ty);
|
|
const SCEV *AllOnes =
|
|
getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
|
|
return getMinusSCEV(AllOnes, V);
|
|
}
|
|
|
|
/// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
|
|
///
|
|
const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS,
|
|
const SCEV *RHS) {
|
|
// X - Y --> X + -Y
|
|
return getAddExpr(LHS, getNegativeSCEV(RHS));
|
|
}
|
|
|
|
/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
|
|
/// input value to the specified type. If the type must be extended, it is zero
|
|
/// extended.
|
|
const SCEV *
|
|
ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V,
|
|
const Type *Ty) {
|
|
const Type *SrcTy = V->getType();
|
|
assert((SrcTy->isInteger() || isa<PointerType>(SrcTy)) &&
|
|
(Ty->isInteger() || isa<PointerType>(Ty)) &&
|
|
"Cannot truncate or zero extend with non-integer arguments!");
|
|
if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
|
|
return V; // No conversion
|
|
if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
|
|
return getTruncateExpr(V, Ty);
|
|
return getZeroExtendExpr(V, Ty);
|
|
}
|
|
|
|
/// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
|
|
/// input value to the specified type. If the type must be extended, it is sign
|
|
/// extended.
|
|
const SCEV *
|
|
ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
|
|
const Type *Ty) {
|
|
const Type *SrcTy = V->getType();
|
|
assert((SrcTy->isInteger() || isa<PointerType>(SrcTy)) &&
|
|
(Ty->isInteger() || isa<PointerType>(Ty)) &&
|
|
"Cannot truncate or zero extend with non-integer arguments!");
|
|
if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
|
|
return V; // No conversion
|
|
if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
|
|
return getTruncateExpr(V, Ty);
|
|
return getSignExtendExpr(V, Ty);
|
|
}
|
|
|
|
/// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
|
|
/// input value to the specified type. If the type must be extended, it is zero
|
|
/// extended. The conversion must not be narrowing.
|
|
const SCEV *
|
|
ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, const Type *Ty) {
|
|
const Type *SrcTy = V->getType();
|
|
assert((SrcTy->isInteger() || isa<PointerType>(SrcTy)) &&
|
|
(Ty->isInteger() || isa<PointerType>(Ty)) &&
|
|
"Cannot noop or zero extend with non-integer arguments!");
|
|
assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
|
|
"getNoopOrZeroExtend cannot truncate!");
|
|
if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
|
|
return V; // No conversion
|
|
return getZeroExtendExpr(V, Ty);
|
|
}
|
|
|
|
/// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
|
|
/// input value to the specified type. If the type must be extended, it is sign
|
|
/// extended. The conversion must not be narrowing.
|
|
const SCEV *
|
|
ScalarEvolution::getNoopOrSignExtend(const SCEV *V, const Type *Ty) {
|
|
const Type *SrcTy = V->getType();
|
|
assert((SrcTy->isInteger() || isa<PointerType>(SrcTy)) &&
|
|
(Ty->isInteger() || isa<PointerType>(Ty)) &&
|
|
"Cannot noop or sign extend with non-integer arguments!");
|
|
assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
|
|
"getNoopOrSignExtend cannot truncate!");
|
|
if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
|
|
return V; // No conversion
|
|
return getSignExtendExpr(V, Ty);
|
|
}
|
|
|
|
/// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
|
|
/// the input value to the specified type. If the type must be extended,
|
|
/// it is extended with unspecified bits. The conversion must not be
|
|
/// narrowing.
|
|
const SCEV *
|
|
ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, const Type *Ty) {
|
|
const Type *SrcTy = V->getType();
|
|
assert((SrcTy->isInteger() || isa<PointerType>(SrcTy)) &&
|
|
(Ty->isInteger() || isa<PointerType>(Ty)) &&
|
|
"Cannot noop or any extend with non-integer arguments!");
|
|
assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
|
|
"getNoopOrAnyExtend cannot truncate!");
|
|
if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
|
|
return V; // No conversion
|
|
return getAnyExtendExpr(V, Ty);
|
|
}
|
|
|
|
/// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
|
|
/// input value to the specified type. The conversion must not be widening.
|
|
const SCEV *
|
|
ScalarEvolution::getTruncateOrNoop(const SCEV *V, const Type *Ty) {
|
|
const Type *SrcTy = V->getType();
|
|
assert((SrcTy->isInteger() || isa<PointerType>(SrcTy)) &&
|
|
(Ty->isInteger() || isa<PointerType>(Ty)) &&
|
|
"Cannot truncate or noop with non-integer arguments!");
|
|
assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
|
|
"getTruncateOrNoop cannot extend!");
|
|
if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
|
|
return V; // No conversion
|
|
return getTruncateExpr(V, Ty);
|
|
}
|
|
|
|
/// getUMaxFromMismatchedTypes - Promote the operands to the wider of
|
|
/// the types using zero-extension, and then perform a umax operation
|
|
/// with them.
|
|
const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
|
|
const SCEV *RHS) {
|
|
const SCEV *PromotedLHS = LHS;
|
|
const SCEV *PromotedRHS = RHS;
|
|
|
|
if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
|
|
PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
|
|
else
|
|
PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
|
|
|
|
return getUMaxExpr(PromotedLHS, PromotedRHS);
|
|
}
|
|
|
|
/// getUMinFromMismatchedTypes - Promote the operands to the wider of
|
|
/// the types using zero-extension, and then perform a umin operation
|
|
/// with them.
|
|
const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
|
|
const SCEV *RHS) {
|
|
const SCEV *PromotedLHS = LHS;
|
|
const SCEV *PromotedRHS = RHS;
|
|
|
|
if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
|
|
PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
|
|
else
|
|
PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
|
|
|
|
return getUMinExpr(PromotedLHS, PromotedRHS);
|
|
}
|
|
|
|
/// PushDefUseChildren - Push users of the given Instruction
|
|
/// onto the given Worklist.
|
|
static void
|
|
PushDefUseChildren(Instruction *I,
|
|
SmallVectorImpl<Instruction *> &Worklist) {
|
|
// Push the def-use children onto the Worklist stack.
|
|
for (Value::use_iterator UI = I->use_begin(), UE = I->use_end();
|
|
UI != UE; ++UI)
|
|
Worklist.push_back(cast<Instruction>(UI));
|
|
}
|
|
|
|
/// ForgetSymbolicValue - This looks up computed SCEV values for all
|
|
/// instructions that depend on the given instruction and removes them from
|
|
/// the Scalars map if they reference SymName. This is used during PHI
|
|
/// resolution.
|
|
void
|
|
ScalarEvolution::ForgetSymbolicName(Instruction *I, const SCEV *SymName) {
|
|
SmallVector<Instruction *, 16> Worklist;
|
|
PushDefUseChildren(I, Worklist);
|
|
|
|
SmallPtrSet<Instruction *, 8> Visited;
|
|
Visited.insert(I);
|
|
while (!Worklist.empty()) {
|
|
Instruction *I = Worklist.pop_back_val();
|
|
if (!Visited.insert(I)) continue;
|
|
|
|
std::map<SCEVCallbackVH, const SCEV*>::iterator It =
|
|
Scalars.find(static_cast<Value *>(I));
|
|
if (It != Scalars.end()) {
|
|
// Short-circuit the def-use traversal if the symbolic name
|
|
// ceases to appear in expressions.
|
|
if (!It->second->hasOperand(SymName))
|
|
continue;
|
|
|
|
// SCEVUnknown for a PHI either means that it has an unrecognized
|
|
// structure, or it's a PHI that's in the progress of being computed
|
|
// by createNodeForPHI. In the former case, additional loop trip
|
|
// count information isn't going to change anything. In the later
|
|
// case, createNodeForPHI will perform the necessary updates on its
|
|
// own when it gets to that point.
|
|
if (!isa<PHINode>(I) || !isa<SCEVUnknown>(It->second)) {
|
|
ValuesAtScopes.erase(It->second);
|
|
Scalars.erase(It);
|
|
}
|
|
}
|
|
|
|
PushDefUseChildren(I, Worklist);
|
|
}
|
|
}
|
|
|
|
/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
|
|
/// a loop header, making it a potential recurrence, or it doesn't.
|
|
///
|
|
const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
|
|
if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized.
|
|
if (const Loop *L = LI->getLoopFor(PN->getParent()))
|
|
if (L->getHeader() == PN->getParent()) {
|
|
// If it lives in the loop header, it has two incoming values, one
|
|
// from outside the loop, and one from inside.
|
|
unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0));
|
|
unsigned BackEdge = IncomingEdge^1;
|
|
|
|
// While we are analyzing this PHI node, handle its value symbolically.
|
|
const SCEV *SymbolicName = getUnknown(PN);
|
|
assert(Scalars.find(PN) == Scalars.end() &&
|
|
"PHI node already processed?");
|
|
Scalars.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
|
|
|
|
// Using this symbolic name for the PHI, analyze the value coming around
|
|
// the back-edge.
|
|
Value *BEValueV = PN->getIncomingValue(BackEdge);
|
|
const SCEV *BEValue = getSCEV(BEValueV);
|
|
|
|
// NOTE: If BEValue is loop invariant, we know that the PHI node just
|
|
// has a special value for the first iteration of the loop.
|
|
|
|
// If the value coming around the backedge is an add with the symbolic
|
|
// value we just inserted, then we found a simple induction variable!
|
|
if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
|
|
// If there is a single occurrence of the symbolic value, replace it
|
|
// with a recurrence.
|
|
unsigned FoundIndex = Add->getNumOperands();
|
|
for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
|
|
if (Add->getOperand(i) == SymbolicName)
|
|
if (FoundIndex == e) {
|
|
FoundIndex = i;
|
|
break;
|
|
}
|
|
|
|
if (FoundIndex != Add->getNumOperands()) {
|
|
// Create an add with everything but the specified operand.
|
|
SmallVector<const SCEV *, 8> Ops;
|
|
for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
|
|
if (i != FoundIndex)
|
|
Ops.push_back(Add->getOperand(i));
|
|
const SCEV *Accum = getAddExpr(Ops);
|
|
|
|
// This is not a valid addrec if the step amount is varying each
|
|
// loop iteration, but is not itself an addrec in this loop.
|
|
if (Accum->isLoopInvariant(L) ||
|
|
(isa<SCEVAddRecExpr>(Accum) &&
|
|
cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
|
|
const SCEV *StartVal =
|
|
getSCEV(PN->getIncomingValue(IncomingEdge));
|
|
const SCEVAddRecExpr *PHISCEV =
|
|
cast<SCEVAddRecExpr>(getAddRecExpr(StartVal, Accum, L));
|
|
|
|
// If the increment doesn't overflow, then neither the addrec nor the
|
|
// post-increment will overflow.
|
|
if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV))
|
|
if (OBO->getOperand(0) == PN &&
|
|
getSCEV(OBO->getOperand(1)) ==
|
|
PHISCEV->getStepRecurrence(*this)) {
|
|
const SCEVAddRecExpr *PostInc = PHISCEV->getPostIncExpr(*this);
|
|
if (OBO->hasNoUnsignedWrap()) {
|
|
const_cast<SCEVAddRecExpr *>(PHISCEV)
|
|
->setHasNoUnsignedWrap(true);
|
|
const_cast<SCEVAddRecExpr *>(PostInc)
|
|
->setHasNoUnsignedWrap(true);
|
|
}
|
|
if (OBO->hasNoSignedWrap()) {
|
|
const_cast<SCEVAddRecExpr *>(PHISCEV)
|
|
->setHasNoSignedWrap(true);
|
|
const_cast<SCEVAddRecExpr *>(PostInc)
|
|
->setHasNoSignedWrap(true);
|
|
}
|
|
}
|
|
|
|
// Okay, for the entire analysis of this edge we assumed the PHI
|
|
// to be symbolic. We now need to go back and purge all of the
|
|
// entries for the scalars that use the symbolic expression.
|
|
ForgetSymbolicName(PN, SymbolicName);
|
|
Scalars[SCEVCallbackVH(PN, this)] = PHISCEV;
|
|
return PHISCEV;
|
|
}
|
|
}
|
|
} else if (const SCEVAddRecExpr *AddRec =
|
|
dyn_cast<SCEVAddRecExpr>(BEValue)) {
|
|
// Otherwise, this could be a loop like this:
|
|
// i = 0; for (j = 1; ..; ++j) { .... i = j; }
|
|
// In this case, j = {1,+,1} and BEValue is j.
|
|
// Because the other in-value of i (0) fits the evolution of BEValue
|
|
// i really is an addrec evolution.
|
|
if (AddRec->getLoop() == L && AddRec->isAffine()) {
|
|
const SCEV *StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
|
|
|
|
// If StartVal = j.start - j.stride, we can use StartVal as the
|
|
// initial step of the addrec evolution.
|
|
if (StartVal == getMinusSCEV(AddRec->getOperand(0),
|
|
AddRec->getOperand(1))) {
|
|
const SCEV *PHISCEV =
|
|
getAddRecExpr(StartVal, AddRec->getOperand(1), L);
|
|
|
|
// Okay, for the entire analysis of this edge we assumed the PHI
|
|
// to be symbolic. We now need to go back and purge all of the
|
|
// entries for the scalars that use the symbolic expression.
|
|
ForgetSymbolicName(PN, SymbolicName);
|
|
Scalars[SCEVCallbackVH(PN, this)] = PHISCEV;
|
|
return PHISCEV;
|
|
}
|
|
}
|
|
}
|
|
|
|
return SymbolicName;
|
|
}
|
|
|
|
// It's tempting to recognize PHIs with a unique incoming value, however
|
|
// this leads passes like indvars to break LCSSA form. Fortunately, such
|
|
// PHIs are rare, as instcombine zaps them.
|
|
|
|
// If it's not a loop phi, we can't handle it yet.
|
|
return getUnknown(PN);
|
|
}
|
|
|
|
/// createNodeForGEP - Expand GEP instructions into add and multiply
|
|
/// operations. This allows them to be analyzed by regular SCEV code.
|
|
///
|
|
const SCEV *ScalarEvolution::createNodeForGEP(Operator *GEP) {
|
|
|
|
const Type *IntPtrTy = getEffectiveSCEVType(GEP->getType());
|
|
Value *Base = GEP->getOperand(0);
|
|
// Don't attempt to analyze GEPs over unsized objects.
|
|
if (!cast<PointerType>(Base->getType())->getElementType()->isSized())
|
|
return getUnknown(GEP);
|
|
const SCEV *TotalOffset = getIntegerSCEV(0, IntPtrTy);
|
|
gep_type_iterator GTI = gep_type_begin(GEP);
|
|
for (GetElementPtrInst::op_iterator I = next(GEP->op_begin()),
|
|
E = GEP->op_end();
|
|
I != E; ++I) {
|
|
Value *Index = *I;
|
|
// Compute the (potentially symbolic) offset in bytes for this index.
|
|
if (const StructType *STy = dyn_cast<StructType>(*GTI++)) {
|
|
// For a struct, add the member offset.
|
|
unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
|
|
TotalOffset = getAddExpr(TotalOffset,
|
|
getFieldOffsetExpr(STy, FieldNo));
|
|
} else {
|
|
// For an array, add the element offset, explicitly scaled.
|
|
const SCEV *LocalOffset = getSCEV(Index);
|
|
if (!isa<PointerType>(LocalOffset->getType()))
|
|
// Getelementptr indicies are signed.
|
|
LocalOffset = getTruncateOrSignExtend(LocalOffset, IntPtrTy);
|
|
LocalOffset = getMulExpr(LocalOffset, getAllocSizeExpr(*GTI));
|
|
TotalOffset = getAddExpr(TotalOffset, LocalOffset);
|
|
}
|
|
}
|
|
return getAddExpr(getSCEV(Base), TotalOffset);
|
|
}
|
|
|
|
/// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
|
|
/// guaranteed to end in (at every loop iteration). It is, at the same time,
|
|
/// the minimum number of times S is divisible by 2. For example, given {4,+,8}
|
|
/// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
|
|
uint32_t
|
|
ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
|
|
if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
|
|
return C->getValue()->getValue().countTrailingZeros();
|
|
|
|
if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
|
|
return std::min(GetMinTrailingZeros(T->getOperand()),
|
|
(uint32_t)getTypeSizeInBits(T->getType()));
|
|
|
|
if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
|
|
uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
|
|
return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
|
|
getTypeSizeInBits(E->getType()) : OpRes;
|
|
}
|
|
|
|
if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
|
|
uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
|
|
return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
|
|
getTypeSizeInBits(E->getType()) : OpRes;
|
|
}
|
|
|
|
if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
|
|
// The result is the min of all operands results.
|
|
uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
|
|
for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
|
|
MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
|
|
return MinOpRes;
|
|
}
|
|
|
|
if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
|
|
// The result is the sum of all operands results.
|
|
uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
|
|
uint32_t BitWidth = getTypeSizeInBits(M->getType());
|
|
for (unsigned i = 1, e = M->getNumOperands();
|
|
SumOpRes != BitWidth && i != e; ++i)
|
|
SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
|
|
BitWidth);
|
|
return SumOpRes;
|
|
}
|
|
|
|
if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
|
|
// The result is the min of all operands results.
|
|
uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
|
|
for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
|
|
MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
|
|
return MinOpRes;
|
|
}
|
|
|
|
if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
|
|
// The result is the min of all operands results.
|
|
uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
|
|
for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
|
|
MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
|
|
return MinOpRes;
|
|
}
|
|
|
|
if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
|
|
// The result is the min of all operands results.
|
|
uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
|
|
for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
|
|
MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
|
|
return MinOpRes;
|
|
}
|
|
|
|
if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
|
|
// For a SCEVUnknown, ask ValueTracking.
|
|
unsigned BitWidth = getTypeSizeInBits(U->getType());
|
|
APInt Mask = APInt::getAllOnesValue(BitWidth);
|
|
APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
|
|
ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones);
|
|
return Zeros.countTrailingOnes();
|
|
}
|
|
|
|
// SCEVUDivExpr
|
|
return 0;
|
|
}
|
|
|
|
/// getUnsignedRange - Determine the unsigned range for a particular SCEV.
|
|
///
|
|
ConstantRange
|
|
ScalarEvolution::getUnsignedRange(const SCEV *S) {
|
|
|
|
if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
|
|
return ConstantRange(C->getValue()->getValue());
|
|
|
|
if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
|
|
ConstantRange X = getUnsignedRange(Add->getOperand(0));
|
|
for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
|
|
X = X.add(getUnsignedRange(Add->getOperand(i)));
|
|
return X;
|
|
}
|
|
|
|
if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
|
|
ConstantRange X = getUnsignedRange(Mul->getOperand(0));
|
|
for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
|
|
X = X.multiply(getUnsignedRange(Mul->getOperand(i)));
|
|
return X;
|
|
}
|
|
|
|
if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
|
|
ConstantRange X = getUnsignedRange(SMax->getOperand(0));
|
|
for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
|
|
X = X.smax(getUnsignedRange(SMax->getOperand(i)));
|
|
return X;
|
|
}
|
|
|
|
if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
|
|
ConstantRange X = getUnsignedRange(UMax->getOperand(0));
|
|
for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
|
|
X = X.umax(getUnsignedRange(UMax->getOperand(i)));
|
|
return X;
|
|
}
|
|
|
|
if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
|
|
ConstantRange X = getUnsignedRange(UDiv->getLHS());
|
|
ConstantRange Y = getUnsignedRange(UDiv->getRHS());
|
|
return X.udiv(Y);
|
|
}
|
|
|
|
if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
|
|
ConstantRange X = getUnsignedRange(ZExt->getOperand());
|
|
return X.zeroExtend(cast<IntegerType>(ZExt->getType())->getBitWidth());
|
|
}
|
|
|
|
if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
|
|
ConstantRange X = getUnsignedRange(SExt->getOperand());
|
|
return X.signExtend(cast<IntegerType>(SExt->getType())->getBitWidth());
|
|
}
|
|
|
|
if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
|
|
ConstantRange X = getUnsignedRange(Trunc->getOperand());
|
|
return X.truncate(cast<IntegerType>(Trunc->getType())->getBitWidth());
|
|
}
|
|
|
|
ConstantRange FullSet(getTypeSizeInBits(S->getType()), true);
|
|
|
|
if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
|
|
const SCEV *T = getBackedgeTakenCount(AddRec->getLoop());
|
|
const SCEVConstant *Trip = dyn_cast<SCEVConstant>(T);
|
|
if (!Trip) return FullSet;
|
|
|
|
// TODO: non-affine addrec
|
|
if (AddRec->isAffine()) {
|
|
const Type *Ty = AddRec->getType();
|
|
const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
|
|
if (getTypeSizeInBits(MaxBECount->getType()) <= getTypeSizeInBits(Ty)) {
|
|
MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
|
|
|
|
const SCEV *Start = AddRec->getStart();
|
|
const SCEV *Step = AddRec->getStepRecurrence(*this);
|
|
const SCEV *End = AddRec->evaluateAtIteration(MaxBECount, *this);
|
|
|
|
// Check for overflow.
|
|
// TODO: This is very conservative.
|
|
if (!(Step->isOne() &&
|
|
isKnownPredicate(ICmpInst::ICMP_ULT, Start, End)) &&
|
|
!(Step->isAllOnesValue() &&
|
|
isKnownPredicate(ICmpInst::ICMP_UGT, Start, End)))
|
|
return FullSet;
|
|
|
|
ConstantRange StartRange = getUnsignedRange(Start);
|
|
ConstantRange EndRange = getUnsignedRange(End);
|
|
APInt Min = APIntOps::umin(StartRange.getUnsignedMin(),
|
|
EndRange.getUnsignedMin());
|
|
APInt Max = APIntOps::umax(StartRange.getUnsignedMax(),
|
|
EndRange.getUnsignedMax());
|
|
if (Min.isMinValue() && Max.isMaxValue())
|
|
return FullSet;
|
|
return ConstantRange(Min, Max+1);
|
|
}
|
|
}
|
|
}
|
|
|
|
if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
|
|
// For a SCEVUnknown, ask ValueTracking.
|
|
unsigned BitWidth = getTypeSizeInBits(U->getType());
|
|
APInt Mask = APInt::getAllOnesValue(BitWidth);
|
|
APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
|
|
ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones, TD);
|
|
if (Ones == ~Zeros + 1)
|
|
return FullSet;
|
|
return ConstantRange(Ones, ~Zeros + 1);
|
|
}
|
|
|
|
return FullSet;
|
|
}
|
|
|
|
/// getSignedRange - Determine the signed range for a particular SCEV.
|
|
///
|
|
ConstantRange
|
|
ScalarEvolution::getSignedRange(const SCEV *S) {
|
|
|
|
if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
|
|
return ConstantRange(C->getValue()->getValue());
|
|
|
|
if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
|
|
ConstantRange X = getSignedRange(Add->getOperand(0));
|
|
for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
|
|
X = X.add(getSignedRange(Add->getOperand(i)));
|
|
return X;
|
|
}
|
|
|
|
if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
|
|
ConstantRange X = getSignedRange(Mul->getOperand(0));
|
|
for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
|
|
X = X.multiply(getSignedRange(Mul->getOperand(i)));
|
|
return X;
|
|
}
|
|
|
|
if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
|
|
ConstantRange X = getSignedRange(SMax->getOperand(0));
|
|
for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
|
|
X = X.smax(getSignedRange(SMax->getOperand(i)));
|
|
return X;
|
|
}
|
|
|
|
if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
|
|
ConstantRange X = getSignedRange(UMax->getOperand(0));
|
|
for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
|
|
X = X.umax(getSignedRange(UMax->getOperand(i)));
|
|
return X;
|
|
}
|
|
|
|
if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
|
|
ConstantRange X = getSignedRange(UDiv->getLHS());
|
|
ConstantRange Y = getSignedRange(UDiv->getRHS());
|
|
return X.udiv(Y);
|
|
}
|
|
|
|
if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
|
|
ConstantRange X = getSignedRange(ZExt->getOperand());
|
|
return X.zeroExtend(cast<IntegerType>(ZExt->getType())->getBitWidth());
|
|
}
|
|
|
|
if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
|
|
ConstantRange X = getSignedRange(SExt->getOperand());
|
|
return X.signExtend(cast<IntegerType>(SExt->getType())->getBitWidth());
|
|
}
|
|
|
|
if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
|
|
ConstantRange X = getSignedRange(Trunc->getOperand());
|
|
return X.truncate(cast<IntegerType>(Trunc->getType())->getBitWidth());
|
|
}
|
|
|
|
ConstantRange FullSet(getTypeSizeInBits(S->getType()), true);
|
|
|
|
if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
|
|
const SCEV *T = getBackedgeTakenCount(AddRec->getLoop());
|
|
const SCEVConstant *Trip = dyn_cast<SCEVConstant>(T);
|
|
if (!Trip) return FullSet;
|
|
|
|
// TODO: non-affine addrec
|
|
if (AddRec->isAffine()) {
|
|
const Type *Ty = AddRec->getType();
|
|
const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
|
|
if (getTypeSizeInBits(MaxBECount->getType()) <= getTypeSizeInBits(Ty)) {
|
|
MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
|
|
|
|
const SCEV *Start = AddRec->getStart();
|
|
const SCEV *Step = AddRec->getStepRecurrence(*this);
|
|
const SCEV *End = AddRec->evaluateAtIteration(MaxBECount, *this);
|
|
|
|
// Check for overflow.
|
|
// TODO: This is very conservative.
|
|
if (!(Step->isOne() &&
|
|
isKnownPredicate(ICmpInst::ICMP_SLT, Start, End)) &&
|
|
!(Step->isAllOnesValue() &&
|
|
isKnownPredicate(ICmpInst::ICMP_SGT, Start, End)))
|
|
return FullSet;
|
|
|
|
ConstantRange StartRange = getSignedRange(Start);
|
|
ConstantRange EndRange = getSignedRange(End);
|
|
APInt Min = APIntOps::smin(StartRange.getSignedMin(),
|
|
EndRange.getSignedMin());
|
|
APInt Max = APIntOps::smax(StartRange.getSignedMax(),
|
|
EndRange.getSignedMax());
|
|
if (Min.isMinSignedValue() && Max.isMaxSignedValue())
|
|
return FullSet;
|
|
return ConstantRange(Min, Max+1);
|
|
}
|
|
}
|
|
}
|
|
|
|
if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
|
|
// For a SCEVUnknown, ask ValueTracking.
|
|
unsigned BitWidth = getTypeSizeInBits(U->getType());
|
|
unsigned NS = ComputeNumSignBits(U->getValue(), TD);
|
|
if (NS == 1)
|
|
return FullSet;
|
|
return
|
|
ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
|
|
APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1);
|
|
}
|
|
|
|
return FullSet;
|
|
}
|
|
|
|
/// createSCEV - We know that there is no SCEV for the specified value.
|
|
/// Analyze the expression.
|
|
///
|
|
const SCEV *ScalarEvolution::createSCEV(Value *V) {
|
|
if (!isSCEVable(V->getType()))
|
|
return getUnknown(V);
|
|
|
|
unsigned Opcode = Instruction::UserOp1;
|
|
if (Instruction *I = dyn_cast<Instruction>(V))
|
|
Opcode = I->getOpcode();
|
|
else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
|
|
Opcode = CE->getOpcode();
|
|
else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
|
|
return getConstant(CI);
|
|
else if (isa<ConstantPointerNull>(V))
|
|
return getIntegerSCEV(0, V->getType());
|
|
else if (isa<UndefValue>(V))
|
|
return getIntegerSCEV(0, V->getType());
|
|
else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
|
|
return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee());
|
|
else
|
|
return getUnknown(V);
|
|
|
|
Operator *U = cast<Operator>(V);
|
|
switch (Opcode) {
|
|
case Instruction::Add:
|
|
return getAddExpr(getSCEV(U->getOperand(0)),
|
|
getSCEV(U->getOperand(1)));
|
|
case Instruction::Mul:
|
|
return getMulExpr(getSCEV(U->getOperand(0)),
|
|
getSCEV(U->getOperand(1)));
|
|
case Instruction::UDiv:
|
|
return getUDivExpr(getSCEV(U->getOperand(0)),
|
|
getSCEV(U->getOperand(1)));
|
|
case Instruction::Sub:
|
|
return getMinusSCEV(getSCEV(U->getOperand(0)),
|
|
getSCEV(U->getOperand(1)));
|
|
case Instruction::And:
|
|
// For an expression like x&255 that merely masks off the high bits,
|
|
// use zext(trunc(x)) as the SCEV expression.
|
|
if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
|
|
if (CI->isNullValue())
|
|
return getSCEV(U->getOperand(1));
|
|
if (CI->isAllOnesValue())
|
|
return getSCEV(U->getOperand(0));
|
|
const APInt &A = CI->getValue();
|
|
|
|
// Instcombine's ShrinkDemandedConstant may strip bits out of
|
|
// constants, obscuring what would otherwise be a low-bits mask.
|
|
// Use ComputeMaskedBits to compute what ShrinkDemandedConstant
|
|
// knew about to reconstruct a low-bits mask value.
|
|
unsigned LZ = A.countLeadingZeros();
|
|
unsigned BitWidth = A.getBitWidth();
|
|
APInt AllOnes = APInt::getAllOnesValue(BitWidth);
|
|
APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
|
|
ComputeMaskedBits(U->getOperand(0), AllOnes, KnownZero, KnownOne, TD);
|
|
|
|
APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ);
|
|
|
|
if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask))
|
|
return
|
|
getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)),
|
|
IntegerType::get(getContext(), BitWidth - LZ)),
|
|
U->getType());
|
|
}
|
|
break;
|
|
|
|
case Instruction::Or:
|
|
// If the RHS of the Or is a constant, we may have something like:
|
|
// X*4+1 which got turned into X*4|1. Handle this as an Add so loop
|
|
// optimizations will transparently handle this case.
|
|
//
|
|
// In order for this transformation to be safe, the LHS must be of the
|
|
// form X*(2^n) and the Or constant must be less than 2^n.
|
|
if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
|
|
const SCEV *LHS = getSCEV(U->getOperand(0));
|
|
const APInt &CIVal = CI->getValue();
|
|
if (GetMinTrailingZeros(LHS) >=
|
|
(CIVal.getBitWidth() - CIVal.countLeadingZeros()))
|
|
return getAddExpr(LHS, getSCEV(U->getOperand(1)));
|
|
}
|
|
break;
|
|
case Instruction::Xor:
|
|
if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
|
|
// If the RHS of the xor is a signbit, then this is just an add.
|
|
// Instcombine turns add of signbit into xor as a strength reduction step.
|
|
if (CI->getValue().isSignBit())
|
|
return getAddExpr(getSCEV(U->getOperand(0)),
|
|
getSCEV(U->getOperand(1)));
|
|
|
|
// If the RHS of xor is -1, then this is a not operation.
|
|
if (CI->isAllOnesValue())
|
|
return getNotSCEV(getSCEV(U->getOperand(0)));
|
|
|
|
// Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
|
|
// This is a variant of the check for xor with -1, and it handles
|
|
// the case where instcombine has trimmed non-demanded bits out
|
|
// of an xor with -1.
|
|
if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
|
|
if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
|
|
if (BO->getOpcode() == Instruction::And &&
|
|
LCI->getValue() == CI->getValue())
|
|
if (const SCEVZeroExtendExpr *Z =
|
|
dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
|
|
const Type *UTy = U->getType();
|
|
const SCEV *Z0 = Z->getOperand();
|
|
const Type *Z0Ty = Z0->getType();
|
|
unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
|
|
|
|
// If C is a low-bits mask, the zero extend is zerving to
|
|
// mask off the high bits. Complement the operand and
|
|
// re-apply the zext.
|
|
if (APIntOps::isMask(Z0TySize, CI->getValue()))
|
|
return getZeroExtendExpr(getNotSCEV(Z0), UTy);
|
|
|
|
// If C is a single bit, it may be in the sign-bit position
|
|
// before the zero-extend. In this case, represent the xor
|
|
// using an add, which is equivalent, and re-apply the zext.
|
|
APInt Trunc = APInt(CI->getValue()).trunc(Z0TySize);
|
|
if (APInt(Trunc).zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
|
|
Trunc.isSignBit())
|
|
return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
|
|
UTy);
|
|
}
|
|
}
|
|
break;
|
|
|
|
case Instruction::Shl:
|
|
// Turn shift left of a constant amount into a multiply.
|
|
if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
|
|
uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth();
|
|
Constant *X = ConstantInt::get(getContext(),
|
|
APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
|
|
return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
|
|
}
|
|
break;
|
|
|
|
case Instruction::LShr:
|
|
// Turn logical shift right of a constant into a unsigned divide.
|
|
if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
|
|
uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth();
|
|
Constant *X = ConstantInt::get(getContext(),
|
|
APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
|
|
return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
|
|
}
|
|
break;
|
|
|
|
case Instruction::AShr:
|
|
// For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
|
|
if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
|
|
if (Instruction *L = dyn_cast<Instruction>(U->getOperand(0)))
|
|
if (L->getOpcode() == Instruction::Shl &&
|
|
L->getOperand(1) == U->getOperand(1)) {
|
|
unsigned BitWidth = getTypeSizeInBits(U->getType());
|
|
uint64_t Amt = BitWidth - CI->getZExtValue();
|
|
if (Amt == BitWidth)
|
|
return getSCEV(L->getOperand(0)); // shift by zero --> noop
|
|
if (Amt > BitWidth)
|
|
return getIntegerSCEV(0, U->getType()); // value is undefined
|
|
return
|
|
getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
|
|
IntegerType::get(getContext(), Amt)),
|
|
U->getType());
|
|
}
|
|
break;
|
|
|
|
case Instruction::Trunc:
|
|
return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
|
|
|
|
case Instruction::ZExt:
|
|
return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
|
|
|
|
case Instruction::SExt:
|
|
return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
|
|
|
|
case Instruction::BitCast:
|
|
// BitCasts are no-op casts so we just eliminate the cast.
|
|
if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
|
|
return getSCEV(U->getOperand(0));
|
|
break;
|
|
|
|
// It's tempting to handle inttoptr and ptrtoint, however this can
|
|
// lead to pointer expressions which cannot be expanded to GEPs
|
|
// (because they may overflow). For now, the only pointer-typed
|
|
// expressions we handle are GEPs and address literals.
|
|
|
|
case Instruction::GetElementPtr:
|
|
return createNodeForGEP(U);
|
|
|
|
case Instruction::PHI:
|
|
return createNodeForPHI(cast<PHINode>(U));
|
|
|
|
case Instruction::Select:
|
|
// This could be a smax or umax that was lowered earlier.
|
|
// Try to recover it.
|
|
if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
|
|
Value *LHS = ICI->getOperand(0);
|
|
Value *RHS = ICI->getOperand(1);
|
|
switch (ICI->getPredicate()) {
|
|
case ICmpInst::ICMP_SLT:
|
|
case ICmpInst::ICMP_SLE:
|
|
std::swap(LHS, RHS);
|
|
// fall through
|
|
case ICmpInst::ICMP_SGT:
|
|
case ICmpInst::ICMP_SGE:
|
|
if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
|
|
return getSMaxExpr(getSCEV(LHS), getSCEV(RHS));
|
|
else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
|
|
return getSMinExpr(getSCEV(LHS), getSCEV(RHS));
|
|
break;
|
|
case ICmpInst::ICMP_ULT:
|
|
case ICmpInst::ICMP_ULE:
|
|
std::swap(LHS, RHS);
|
|
// fall through
|
|
case ICmpInst::ICMP_UGT:
|
|
case ICmpInst::ICMP_UGE:
|
|
if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
|
|
return getUMaxExpr(getSCEV(LHS), getSCEV(RHS));
|
|
else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
|
|
return getUMinExpr(getSCEV(LHS), getSCEV(RHS));
|
|
break;
|
|
case ICmpInst::ICMP_NE:
|
|
// n != 0 ? n : 1 -> umax(n, 1)
|
|
if (LHS == U->getOperand(1) &&
|
|
isa<ConstantInt>(U->getOperand(2)) &&
|
|
cast<ConstantInt>(U->getOperand(2))->isOne() &&
|
|
isa<ConstantInt>(RHS) &&
|
|
cast<ConstantInt>(RHS)->isZero())
|
|
return getUMaxExpr(getSCEV(LHS), getSCEV(U->getOperand(2)));
|
|
break;
|
|
case ICmpInst::ICMP_EQ:
|
|
// n == 0 ? 1 : n -> umax(n, 1)
|
|
if (LHS == U->getOperand(2) &&
|
|
isa<ConstantInt>(U->getOperand(1)) &&
|
|
cast<ConstantInt>(U->getOperand(1))->isOne() &&
|
|
isa<ConstantInt>(RHS) &&
|
|
cast<ConstantInt>(RHS)->isZero())
|
|
return getUMaxExpr(getSCEV(LHS), getSCEV(U->getOperand(1)));
|
|
break;
|
|
default:
|
|
break;
|
|
}
|
|
}
|
|
|
|
default: // We cannot analyze this expression.
|
|
break;
|
|
}
|
|
|
|
return getUnknown(V);
|
|
}
|
|
|
|
|
|
|
|
//===----------------------------------------------------------------------===//
|
|
// Iteration Count Computation Code
|
|
//
|
|
|
|
/// getBackedgeTakenCount - If the specified loop has a predictable
|
|
/// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
|
|
/// object. The backedge-taken count is the number of times the loop header
|
|
/// will be branched to from within the loop. This is one less than the
|
|
/// trip count of the loop, since it doesn't count the first iteration,
|
|
/// when the header is branched to from outside the loop.
|
|
///
|
|
/// Note that it is not valid to call this method on a loop without a
|
|
/// loop-invariant backedge-taken count (see
|
|
/// hasLoopInvariantBackedgeTakenCount).
|
|
///
|
|
const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
|
|
return getBackedgeTakenInfo(L).Exact;
|
|
}
|
|
|
|
/// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
|
|
/// return the least SCEV value that is known never to be less than the
|
|
/// actual backedge taken count.
|
|
const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
|
|
return getBackedgeTakenInfo(L).Max;
|
|
}
|
|
|
|
/// PushLoopPHIs - Push PHI nodes in the header of the given loop
|
|
/// onto the given Worklist.
|
|
static void
|
|
PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
|
|
BasicBlock *Header = L->getHeader();
|
|
|
|
// Push all Loop-header PHIs onto the Worklist stack.
|
|
for (BasicBlock::iterator I = Header->begin();
|
|
PHINode *PN = dyn_cast<PHINode>(I); ++I)
|
|
Worklist.push_back(PN);
|
|
}
|
|
|
|
const ScalarEvolution::BackedgeTakenInfo &
|
|
ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
|
|
// Initially insert a CouldNotCompute for this loop. If the insertion
|
|
// succeeds, procede to actually compute a backedge-taken count and
|
|
// update the value. The temporary CouldNotCompute value tells SCEV
|
|
// code elsewhere that it shouldn't attempt to request a new
|
|
// backedge-taken count, which could result in infinite recursion.
|
|
std::pair<std::map<const Loop*, BackedgeTakenInfo>::iterator, bool> Pair =
|
|
BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute()));
|
|
if (Pair.second) {
|
|
BackedgeTakenInfo ItCount = ComputeBackedgeTakenCount(L);
|
|
if (ItCount.Exact != getCouldNotCompute()) {
|
|
assert(ItCount.Exact->isLoopInvariant(L) &&
|
|
ItCount.Max->isLoopInvariant(L) &&
|
|
"Computed trip count isn't loop invariant for loop!");
|
|
++NumTripCountsComputed;
|
|
|
|
// Update the value in the map.
|
|
Pair.first->second = ItCount;
|
|
} else {
|
|
if (ItCount.Max != getCouldNotCompute())
|
|
// Update the value in the map.
|
|
Pair.first->second = ItCount;
|
|
if (isa<PHINode>(L->getHeader()->begin()))
|
|
// Only count loops that have phi nodes as not being computable.
|
|
++NumTripCountsNotComputed;
|
|
}
|
|
|
|
// Now that we know more about the trip count for this loop, forget any
|
|
// existing SCEV values for PHI nodes in this loop since they are only
|
|
// conservative estimates made without the benefit of trip count
|
|
// information. This is similar to the code in
|
|
// forgetLoopBackedgeTakenCount, except that it handles SCEVUnknown PHI
|
|
// nodes specially.
|
|
if (ItCount.hasAnyInfo()) {
|
|
SmallVector<Instruction *, 16> Worklist;
|
|
PushLoopPHIs(L, Worklist);
|
|
|
|
SmallPtrSet<Instruction *, 8> Visited;
|
|
while (!Worklist.empty()) {
|
|
Instruction *I = Worklist.pop_back_val();
|
|
if (!Visited.insert(I)) continue;
|
|
|
|
std::map<SCEVCallbackVH, const SCEV*>::iterator It =
|
|
Scalars.find(static_cast<Value *>(I));
|
|
if (It != Scalars.end()) {
|
|
// SCEVUnknown for a PHI either means that it has an unrecognized
|
|
// structure, or it's a PHI that's in the progress of being computed
|
|
// by createNodeForPHI. In the former case, additional loop trip
|
|
// count information isn't going to change anything. In the later
|
|
// case, createNodeForPHI will perform the necessary updates on its
|
|
// own when it gets to that point.
|
|
if (!isa<PHINode>(I) || !isa<SCEVUnknown>(It->second)) {
|
|
ValuesAtScopes.erase(It->second);
|
|
Scalars.erase(It);
|
|
}
|
|
if (PHINode *PN = dyn_cast<PHINode>(I))
|
|
ConstantEvolutionLoopExitValue.erase(PN);
|
|
}
|
|
|
|
PushDefUseChildren(I, Worklist);
|
|
}
|
|
}
|
|
}
|
|
return Pair.first->second;
|
|
}
|
|
|
|
/// forgetLoopBackedgeTakenCount - This method should be called by the
|
|
/// client when it has changed a loop in a way that may effect
|
|
/// ScalarEvolution's ability to compute a trip count, or if the loop
|
|
/// is deleted.
|
|
void ScalarEvolution::forgetLoopBackedgeTakenCount(const Loop *L) {
|
|
BackedgeTakenCounts.erase(L);
|
|
|
|
SmallVector<Instruction *, 16> Worklist;
|
|
PushLoopPHIs(L, Worklist);
|
|
|
|
SmallPtrSet<Instruction *, 8> Visited;
|
|
while (!Worklist.empty()) {
|
|
Instruction *I = Worklist.pop_back_val();
|
|
if (!Visited.insert(I)) continue;
|
|
|
|
std::map<SCEVCallbackVH, const SCEV*>::iterator It =
|
|
Scalars.find(static_cast<Value *>(I));
|
|
if (It != Scalars.end()) {
|
|
ValuesAtScopes.erase(It->second);
|
|
Scalars.erase(It);
|
|
if (PHINode *PN = dyn_cast<PHINode>(I))
|
|
ConstantEvolutionLoopExitValue.erase(PN);
|
|
}
|
|
|
|
PushDefUseChildren(I, Worklist);
|
|
}
|
|
}
|
|
|
|
/// ComputeBackedgeTakenCount - Compute the number of times the backedge
|
|
/// of the specified loop will execute.
|
|
ScalarEvolution::BackedgeTakenInfo
|
|
ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
|
|
SmallVector<BasicBlock*, 8> ExitingBlocks;
|
|
L->getExitingBlocks(ExitingBlocks);
|
|
|
|
// Examine all exits and pick the most conservative values.
|
|
const SCEV *BECount = getCouldNotCompute();
|
|
const SCEV *MaxBECount = getCouldNotCompute();
|
|
bool CouldNotComputeBECount = false;
|
|
for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
|
|
BackedgeTakenInfo NewBTI =
|
|
ComputeBackedgeTakenCountFromExit(L, ExitingBlocks[i]);
|
|
|
|
if (NewBTI.Exact == getCouldNotCompute()) {
|
|
// We couldn't compute an exact value for this exit, so
|
|
// we won't be able to compute an exact value for the loop.
|
|
CouldNotComputeBECount = true;
|
|
BECount = getCouldNotCompute();
|
|
} else if (!CouldNotComputeBECount) {
|
|
if (BECount == getCouldNotCompute())
|
|
BECount = NewBTI.Exact;
|
|
else
|
|
BECount = getUMinFromMismatchedTypes(BECount, NewBTI.Exact);
|
|
}
|
|
if (MaxBECount == getCouldNotCompute())
|
|
MaxBECount = NewBTI.Max;
|
|
else if (NewBTI.Max != getCouldNotCompute())
|
|
MaxBECount = getUMinFromMismatchedTypes(MaxBECount, NewBTI.Max);
|
|
}
|
|
|
|
return BackedgeTakenInfo(BECount, MaxBECount);
|
|
}
|
|
|
|
/// ComputeBackedgeTakenCountFromExit - Compute the number of times the backedge
|
|
/// of the specified loop will execute if it exits via the specified block.
|
|
ScalarEvolution::BackedgeTakenInfo
|
|
ScalarEvolution::ComputeBackedgeTakenCountFromExit(const Loop *L,
|
|
BasicBlock *ExitingBlock) {
|
|
|
|
// Okay, we've chosen an exiting block. See what condition causes us to
|
|
// exit at this block.
|
|
//
|
|
// FIXME: we should be able to handle switch instructions (with a single exit)
|
|
BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
|
|
if (ExitBr == 0) return getCouldNotCompute();
|
|
assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
|
|
|
|
// At this point, we know we have a conditional branch that determines whether
|
|
// the loop is exited. However, we don't know if the branch is executed each
|
|
// time through the loop. If not, then the execution count of the branch will
|
|
// not be equal to the trip count of the loop.
|
|
//
|
|
// Currently we check for this by checking to see if the Exit branch goes to
|
|
// the loop header. If so, we know it will always execute the same number of
|
|
// times as the loop. We also handle the case where the exit block *is* the
|
|
// loop header. This is common for un-rotated loops.
|
|
//
|
|
// If both of those tests fail, walk up the unique predecessor chain to the
|
|
// header, stopping if there is an edge that doesn't exit the loop. If the
|
|
// header is reached, the execution count of the branch will be equal to the
|
|
// trip count of the loop.
|
|
//
|
|
// More extensive analysis could be done to handle more cases here.
|
|
//
|
|
if (ExitBr->getSuccessor(0) != L->getHeader() &&
|
|
ExitBr->getSuccessor(1) != L->getHeader() &&
|
|
ExitBr->getParent() != L->getHeader()) {
|
|
// The simple checks failed, try climbing the unique predecessor chain
|
|
// up to the header.
|
|
bool Ok = false;
|
|
for (BasicBlock *BB = ExitBr->getParent(); BB; ) {
|
|
BasicBlock *Pred = BB->getUniquePredecessor();
|
|
if (!Pred)
|
|
return getCouldNotCompute();
|
|
TerminatorInst *PredTerm = Pred->getTerminator();
|
|
for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) {
|
|
BasicBlock *PredSucc = PredTerm->getSuccessor(i);
|
|
if (PredSucc == BB)
|
|
continue;
|
|
// If the predecessor has a successor that isn't BB and isn't
|
|
// outside the loop, assume the worst.
|
|
if (L->contains(PredSucc))
|
|
return getCouldNotCompute();
|
|
}
|
|
if (Pred == L->getHeader()) {
|
|
Ok = true;
|
|
break;
|
|
}
|
|
BB = Pred;
|
|
}
|
|
if (!Ok)
|
|
return getCouldNotCompute();
|
|
}
|
|
|
|
// Procede to the next level to examine the exit condition expression.
|
|
return ComputeBackedgeTakenCountFromExitCond(L, ExitBr->getCondition(),
|
|
ExitBr->getSuccessor(0),
|
|
ExitBr->getSuccessor(1));
|
|
}
|
|
|
|
/// ComputeBackedgeTakenCountFromExitCond - Compute the number of times the
|
|
/// backedge of the specified loop will execute if its exit condition
|
|
/// were a conditional branch of ExitCond, TBB, and FBB.
|
|
ScalarEvolution::BackedgeTakenInfo
|
|
ScalarEvolution::ComputeBackedgeTakenCountFromExitCond(const Loop *L,
|
|
Value *ExitCond,
|
|
BasicBlock *TBB,
|
|
BasicBlock *FBB) {
|
|
// Check if the controlling expression for this loop is an And or Or.
|
|
if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
|
|
if (BO->getOpcode() == Instruction::And) {
|
|
// Recurse on the operands of the and.
|
|
BackedgeTakenInfo BTI0 =
|
|
ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB);
|
|
BackedgeTakenInfo BTI1 =
|
|
ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB);
|
|
const SCEV *BECount = getCouldNotCompute();
|
|
const SCEV *MaxBECount = getCouldNotCompute();
|
|
if (L->contains(TBB)) {
|
|
// Both conditions must be true for the loop to continue executing.
|
|
// Choose the less conservative count.
|
|
if (BTI0.Exact == getCouldNotCompute() ||
|
|
BTI1.Exact == getCouldNotCompute())
|
|
BECount = getCouldNotCompute();
|
|
else
|
|
BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
|
|
if (BTI0.Max == getCouldNotCompute())
|
|
MaxBECount = BTI1.Max;
|
|
else if (BTI1.Max == getCouldNotCompute())
|
|
MaxBECount = BTI0.Max;
|
|
else
|
|
MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max);
|
|
} else {
|
|
// Both conditions must be true for the loop to exit.
|
|
assert(L->contains(FBB) && "Loop block has no successor in loop!");
|
|
if (BTI0.Exact != getCouldNotCompute() &&
|
|
BTI1.Exact != getCouldNotCompute())
|
|
BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
|
|
if (BTI0.Max != getCouldNotCompute() &&
|
|
BTI1.Max != getCouldNotCompute())
|
|
MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max);
|
|
}
|
|
|
|
return BackedgeTakenInfo(BECount, MaxBECount);
|
|
}
|
|
if (BO->getOpcode() == Instruction::Or) {
|
|
// Recurse on the operands of the or.
|
|
BackedgeTakenInfo BTI0 =
|
|
ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB);
|
|
BackedgeTakenInfo BTI1 =
|
|
ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB);
|
|
const SCEV *BECount = getCouldNotCompute();
|
|
const SCEV *MaxBECount = getCouldNotCompute();
|
|
if (L->contains(FBB)) {
|
|
// Both conditions must be false for the loop to continue executing.
|
|
// Choose the less conservative count.
|
|
if (BTI0.Exact == getCouldNotCompute() ||
|
|
BTI1.Exact == getCouldNotCompute())
|
|
BECount = getCouldNotCompute();
|
|
else
|
|
BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
|
|
if (BTI0.Max == getCouldNotCompute())
|
|
MaxBECount = BTI1.Max;
|
|
else if (BTI1.Max == getCouldNotCompute())
|
|
MaxBECount = BTI0.Max;
|
|
else
|
|
MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max);
|
|
} else {
|
|
// Both conditions must be false for the loop to exit.
|
|
assert(L->contains(TBB) && "Loop block has no successor in loop!");
|
|
if (BTI0.Exact != getCouldNotCompute() &&
|
|
BTI1.Exact != getCouldNotCompute())
|
|
BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
|
|
if (BTI0.Max != getCouldNotCompute() &&
|
|
BTI1.Max != getCouldNotCompute())
|
|
MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max);
|
|
}
|
|
|
|
return BackedgeTakenInfo(BECount, MaxBECount);
|
|
}
|
|
}
|
|
|
|
// With an icmp, it may be feasible to compute an exact backedge-taken count.
|
|
// Procede to the next level to examine the icmp.
|
|
if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
|
|
return ComputeBackedgeTakenCountFromExitCondICmp(L, ExitCondICmp, TBB, FBB);
|
|
|
|
// If it's not an integer or pointer comparison then compute it the hard way.
|
|
return ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB));
|
|
}
|
|
|
|
/// ComputeBackedgeTakenCountFromExitCondICmp - Compute the number of times the
|
|
/// backedge of the specified loop will execute if its exit condition
|
|
/// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB.
|
|
ScalarEvolution::BackedgeTakenInfo
|
|
ScalarEvolution::ComputeBackedgeTakenCountFromExitCondICmp(const Loop *L,
|
|
ICmpInst *ExitCond,
|
|
BasicBlock *TBB,
|
|
BasicBlock *FBB) {
|
|
|
|
// If the condition was exit on true, convert the condition to exit on false
|
|
ICmpInst::Predicate Cond;
|
|
if (!L->contains(FBB))
|
|
Cond = ExitCond->getPredicate();
|
|
else
|
|
Cond = ExitCond->getInversePredicate();
|
|
|
|
// Handle common loops like: for (X = "string"; *X; ++X)
|
|
if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
|
|
if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
|
|
const SCEV *ItCnt =
|
|
ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond);
|
|
if (!isa<SCEVCouldNotCompute>(ItCnt)) {
|
|
unsigned BitWidth = getTypeSizeInBits(ItCnt->getType());
|
|
return BackedgeTakenInfo(ItCnt,
|
|
isa<SCEVConstant>(ItCnt) ? ItCnt :
|
|
getConstant(APInt::getMaxValue(BitWidth)-1));
|
|
}
|
|
}
|
|
|
|
const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
|
|
const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
|
|
|
|
// Try to evaluate any dependencies out of the loop.
|
|
LHS = getSCEVAtScope(LHS, L);
|
|
RHS = getSCEVAtScope(RHS, L);
|
|
|
|
// At this point, we would like to compute how many iterations of the
|
|
// loop the predicate will return true for these inputs.
|
|
if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) {
|
|
// If there is a loop-invariant, force it into the RHS.
|
|
std::swap(LHS, RHS);
|
|
Cond = ICmpInst::getSwappedPredicate(Cond);
|
|
}
|
|
|
|
// If we have a comparison of a chrec against a constant, try to use value
|
|
// ranges to answer this query.
|
|
if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
|
|
if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
|
|
if (AddRec->getLoop() == L) {
|
|
// Form the constant range.
|
|
ConstantRange CompRange(
|
|
ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
|
|
|
|
const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
|
|
if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
|
|
}
|
|
|
|
switch (Cond) {
|
|
case ICmpInst::ICMP_NE: { // while (X != Y)
|
|
// Convert to: while (X-Y != 0)
|
|
const SCEV *TC = HowFarToZero(getMinusSCEV(LHS, RHS), L);
|
|
if (!isa<SCEVCouldNotCompute>(TC)) return TC;
|
|
break;
|
|
}
|
|
case ICmpInst::ICMP_EQ: { // while (X == Y)
|
|
// Convert to: while (X-Y == 0)
|
|
const SCEV *TC = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
|
|
if (!isa<SCEVCouldNotCompute>(TC)) return TC;
|
|
break;
|
|
}
|
|
case ICmpInst::ICMP_SLT: {
|
|
BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true);
|
|
if (BTI.hasAnyInfo()) return BTI;
|
|
break;
|
|
}
|
|
case ICmpInst::ICMP_SGT: {
|
|
BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
|
|
getNotSCEV(RHS), L, true);
|
|
if (BTI.hasAnyInfo()) return BTI;
|
|
break;
|
|
}
|
|
case ICmpInst::ICMP_ULT: {
|
|
BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false);
|
|
if (BTI.hasAnyInfo()) return BTI;
|
|
break;
|
|
}
|
|
case ICmpInst::ICMP_UGT: {
|
|
BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
|
|
getNotSCEV(RHS), L, false);
|
|
if (BTI.hasAnyInfo()) return BTI;
|
|
break;
|
|
}
|
|
default:
|
|
#if 0
|
|
errs() << "ComputeBackedgeTakenCount ";
|
|
if (ExitCond->getOperand(0)->getType()->isUnsigned())
|
|
errs() << "[unsigned] ";
|
|
errs() << *LHS << " "
|
|
<< Instruction::getOpcodeName(Instruction::ICmp)
|
|
<< " " << *RHS << "\n";
|
|
#endif
|
|
break;
|
|
}
|
|
return
|
|
ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB));
|
|
}
|
|
|
|
static ConstantInt *
|
|
EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
|
|
ScalarEvolution &SE) {
|
|
const SCEV *InVal = SE.getConstant(C);
|
|
const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
|
|
assert(isa<SCEVConstant>(Val) &&
|
|
"Evaluation of SCEV at constant didn't fold correctly?");
|
|
return cast<SCEVConstant>(Val)->getValue();
|
|
}
|
|
|
|
/// GetAddressedElementFromGlobal - Given a global variable with an initializer
|
|
/// and a GEP expression (missing the pointer index) indexing into it, return
|
|
/// the addressed element of the initializer or null if the index expression is
|
|
/// invalid.
|
|
static Constant *
|
|
GetAddressedElementFromGlobal(LLVMContext &Context, GlobalVariable *GV,
|
|
const std::vector<ConstantInt*> &Indices) {
|
|
Constant *Init = GV->getInitializer();
|
|
for (unsigned i = 0, e = Indices.size(); i != e; ++i) {
|
|
uint64_t Idx = Indices[i]->getZExtValue();
|
|
if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) {
|
|
assert(Idx < CS->getNumOperands() && "Bad struct index!");
|
|
Init = cast<Constant>(CS->getOperand(Idx));
|
|
} else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) {
|
|
if (Idx >= CA->getNumOperands()) return 0; // Bogus program
|
|
Init = cast<Constant>(CA->getOperand(Idx));
|
|
} else if (isa<ConstantAggregateZero>(Init)) {
|
|
if (const StructType *STy = dyn_cast<StructType>(Init->getType())) {
|
|
assert(Idx < STy->getNumElements() && "Bad struct index!");
|
|
Init = Constant::getNullValue(STy->getElementType(Idx));
|
|
} else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) {
|
|
if (Idx >= ATy->getNumElements()) return 0; // Bogus program
|
|
Init = Constant::getNullValue(ATy->getElementType());
|
|
} else {
|
|
llvm_unreachable("Unknown constant aggregate type!");
|
|
}
|
|
return 0;
|
|
} else {
|
|
return 0; // Unknown initializer type
|
|
}
|
|
}
|
|
return Init;
|
|
}
|
|
|
|
/// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of
|
|
/// 'icmp op load X, cst', try to see if we can compute the backedge
|
|
/// execution count.
|
|
const SCEV *
|
|
ScalarEvolution::ComputeLoadConstantCompareBackedgeTakenCount(
|
|
LoadInst *LI,
|
|
Constant *RHS,
|
|
const Loop *L,
|
|
ICmpInst::Predicate predicate) {
|
|
if (LI->isVolatile()) return getCouldNotCompute();
|
|
|
|
// Check to see if the loaded pointer is a getelementptr of a global.
|
|
GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
|
|
if (!GEP) return getCouldNotCompute();
|
|
|
|
// Make sure that it is really a constant global we are gepping, with an
|
|
// initializer, and make sure the first IDX is really 0.
|
|
GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
|
|
if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
|
|
GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
|
|
!cast<Constant>(GEP->getOperand(1))->isNullValue())
|
|
return getCouldNotCompute();
|
|
|
|
// Okay, we allow one non-constant index into the GEP instruction.
|
|
Value *VarIdx = 0;
|
|
std::vector<ConstantInt*> Indexes;
|
|
unsigned VarIdxNum = 0;
|
|
for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
|
|
if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
|
|
Indexes.push_back(CI);
|
|
} else if (!isa<ConstantInt>(GEP->getOperand(i))) {
|
|
if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
|
|
VarIdx = GEP->getOperand(i);
|
|
VarIdxNum = i-2;
|
|
Indexes.push_back(0);
|
|
}
|
|
|
|
// Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
|
|
// Check to see if X is a loop variant variable value now.
|
|
const SCEV *Idx = getSCEV(VarIdx);
|
|
Idx = getSCEVAtScope(Idx, L);
|
|
|
|
// We can only recognize very limited forms of loop index expressions, in
|
|
// particular, only affine AddRec's like {C1,+,C2}.
|
|
const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
|
|
if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) ||
|
|
!isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
|
|
!isa<SCEVConstant>(IdxExpr->getOperand(1)))
|
|
return getCouldNotCompute();
|
|
|
|
unsigned MaxSteps = MaxBruteForceIterations;
|
|
for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
|
|
ConstantInt *ItCst = ConstantInt::get(
|
|
cast<IntegerType>(IdxExpr->getType()), IterationNum);
|
|
ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
|
|
|
|
// Form the GEP offset.
|
|
Indexes[VarIdxNum] = Val;
|
|
|
|
Constant *Result = GetAddressedElementFromGlobal(getContext(), GV, Indexes);
|
|
if (Result == 0) break; // Cannot compute!
|
|
|
|
// Evaluate the condition for this iteration.
|
|
Result = ConstantExpr::getICmp(predicate, Result, RHS);
|
|
if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
|
|
if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
|
|
#if 0
|
|
errs() << "\n***\n*** Computed loop count " << *ItCst
|
|
<< "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
|
|
<< "***\n";
|
|
#endif
|
|
++NumArrayLenItCounts;
|
|
return getConstant(ItCst); // Found terminating iteration!
|
|
}
|
|
}
|
|
return getCouldNotCompute();
|
|
}
|
|
|
|
|
|
/// CanConstantFold - Return true if we can constant fold an instruction of the
|
|
/// specified type, assuming that all operands were constants.
|
|
static bool CanConstantFold(const Instruction *I) {
|
|
if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
|
|
isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I))
|
|
return true;
|
|
|
|
if (const CallInst *CI = dyn_cast<CallInst>(I))
|
|
if (const Function *F = CI->getCalledFunction())
|
|
return canConstantFoldCallTo(F);
|
|
return false;
|
|
}
|
|
|
|
/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
|
|
/// in the loop that V is derived from. We allow arbitrary operations along the
|
|
/// way, but the operands of an operation must either be constants or a value
|
|
/// derived from a constant PHI. If this expression does not fit with these
|
|
/// constraints, return null.
|
|
static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
|
|
// If this is not an instruction, or if this is an instruction outside of the
|
|
// loop, it can't be derived from a loop PHI.
|
|
Instruction *I = dyn_cast<Instruction>(V);
|
|
if (I == 0 || !L->contains(I->getParent())) return 0;
|
|
|
|
if (PHINode *PN = dyn_cast<PHINode>(I)) {
|
|
if (L->getHeader() == I->getParent())
|
|
return PN;
|
|
else
|
|
// We don't currently keep track of the control flow needed to evaluate
|
|
// PHIs, so we cannot handle PHIs inside of loops.
|
|
return 0;
|
|
}
|
|
|
|
// If we won't be able to constant fold this expression even if the operands
|
|
// are constants, return early.
|
|
if (!CanConstantFold(I)) return 0;
|
|
|
|
// Otherwise, we can evaluate this instruction if all of its operands are
|
|
// constant or derived from a PHI node themselves.
|
|
PHINode *PHI = 0;
|
|
for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op)
|
|
if (!(isa<Constant>(I->getOperand(Op)) ||
|
|
isa<GlobalValue>(I->getOperand(Op)))) {
|
|
PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L);
|
|
if (P == 0) return 0; // Not evolving from PHI
|
|
if (PHI == 0)
|
|
PHI = P;
|
|
else if (PHI != P)
|
|
return 0; // Evolving from multiple different PHIs.
|
|
}
|
|
|
|
// This is a expression evolving from a constant PHI!
|
|
return PHI;
|
|
}
|
|
|
|
/// EvaluateExpression - Given an expression that passes the
|
|
/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
|
|
/// in the loop has the value PHIVal. If we can't fold this expression for some
|
|
/// reason, return null.
|
|
static Constant *EvaluateExpression(Value *V, Constant *PHIVal) {
|
|
if (isa<PHINode>(V)) return PHIVal;
|
|
if (Constant *C = dyn_cast<Constant>(V)) return C;
|
|
if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) return GV;
|
|
Instruction *I = cast<Instruction>(V);
|
|
LLVMContext &Context = I->getParent()->getContext();
|
|
|
|
std::vector<Constant*> Operands;
|
|
Operands.resize(I->getNumOperands());
|
|
|
|
for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
|
|
Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal);
|
|
if (Operands[i] == 0) return 0;
|
|
}
|
|
|
|
if (const CmpInst *CI = dyn_cast<CmpInst>(I))
|
|
return ConstantFoldCompareInstOperands(CI->getPredicate(),
|
|
&Operands[0], Operands.size(),
|
|
Context);
|
|
else
|
|
return ConstantFoldInstOperands(I->getOpcode(), I->getType(),
|
|
&Operands[0], Operands.size(),
|
|
Context);
|
|
}
|
|
|
|
/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
|
|
/// in the header of its containing loop, we know the loop executes a
|
|
/// constant number of times, and the PHI node is just a recurrence
|
|
/// involving constants, fold it.
|
|
Constant *
|
|
ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
|
|
const APInt& BEs,
|
|
const Loop *L) {
|
|
std::map<PHINode*, Constant*>::iterator I =
|
|
ConstantEvolutionLoopExitValue.find(PN);
|
|
if (I != ConstantEvolutionLoopExitValue.end())
|
|
return I->second;
|
|
|
|
if (BEs.ugt(APInt(BEs.getBitWidth(),MaxBruteForceIterations)))
|
|
return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
|
|
|
|
Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
|
|
|
|
// Since the loop is canonicalized, the PHI node must have two entries. One
|
|
// entry must be a constant (coming in from outside of the loop), and the
|
|
// second must be derived from the same PHI.
|
|
bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
|
|
Constant *StartCST =
|
|
dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
|
|
if (StartCST == 0)
|
|
return RetVal = 0; // Must be a constant.
|
|
|
|
Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
|
|
PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
|
|
if (PN2 != PN)
|
|
return RetVal = 0; // Not derived from same PHI.
|
|
|
|
// Execute the loop symbolically to determine the exit value.
|
|
if (BEs.getActiveBits() >= 32)
|
|
return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
|
|
|
|
unsigned NumIterations = BEs.getZExtValue(); // must be in range
|
|
unsigned IterationNum = 0;
|
|
for (Constant *PHIVal = StartCST; ; ++IterationNum) {
|
|
if (IterationNum == NumIterations)
|
|
return RetVal = PHIVal; // Got exit value!
|
|
|
|
// Compute the value of the PHI node for the next iteration.
|
|
Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
|
|
if (NextPHI == PHIVal)
|
|
return RetVal = NextPHI; // Stopped evolving!
|
|
if (NextPHI == 0)
|
|
return 0; // Couldn't evaluate!
|
|
PHIVal = NextPHI;
|
|
}
|
|
}
|
|
|
|
/// ComputeBackedgeTakenCountExhaustively - If the loop is known to execute a
|
|
/// constant number of times (the condition evolves only from constants),
|
|
/// try to evaluate a few iterations of the loop until we get the exit
|
|
/// condition gets a value of ExitWhen (true or false). If we cannot
|
|
/// evaluate the trip count of the loop, return getCouldNotCompute().
|
|
const SCEV *
|
|
ScalarEvolution::ComputeBackedgeTakenCountExhaustively(const Loop *L,
|
|
Value *Cond,
|
|
bool ExitWhen) {
|
|
PHINode *PN = getConstantEvolvingPHI(Cond, L);
|
|
if (PN == 0) return getCouldNotCompute();
|
|
|
|
// Since the loop is canonicalized, the PHI node must have two entries. One
|
|
// entry must be a constant (coming in from outside of the loop), and the
|
|
// second must be derived from the same PHI.
|
|
bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
|
|
Constant *StartCST =
|
|
dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
|
|
if (StartCST == 0) return getCouldNotCompute(); // Must be a constant.
|
|
|
|
Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
|
|
PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
|
|
if (PN2 != PN) return getCouldNotCompute(); // Not derived from same PHI.
|
|
|
|
// Okay, we find a PHI node that defines the trip count of this loop. Execute
|
|
// the loop symbolically to determine when the condition gets a value of
|
|
// "ExitWhen".
|
|
unsigned IterationNum = 0;
|
|
unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
|
|
for (Constant *PHIVal = StartCST;
|
|
IterationNum != MaxIterations; ++IterationNum) {
|
|
ConstantInt *CondVal =
|
|
dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal));
|
|
|
|
// Couldn't symbolically evaluate.
|
|
if (!CondVal) return getCouldNotCompute();
|
|
|
|
if (CondVal->getValue() == uint64_t(ExitWhen)) {
|
|
++NumBruteForceTripCountsComputed;
|
|
return getConstant(Type::getInt32Ty(getContext()), IterationNum);
|
|
}
|
|
|
|
// Compute the value of the PHI node for the next iteration.
|
|
Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
|
|
if (NextPHI == 0 || NextPHI == PHIVal)
|
|
return getCouldNotCompute();// Couldn't evaluate or not making progress...
|
|
PHIVal = NextPHI;
|
|
}
|
|
|
|
// Too many iterations were needed to evaluate.
|
|
return getCouldNotCompute();
|
|
}
|
|
|
|
/// getSCEVAtScope - Return a SCEV expression for the specified value
|
|
/// at the specified scope in the program. The L value specifies a loop
|
|
/// nest to evaluate the expression at, where null is the top-level or a
|
|
/// specified loop is immediately inside of the loop.
|
|
///
|
|
/// This method can be used to compute the exit value for a variable defined
|
|
/// in a loop by querying what the value will hold in the parent loop.
|
|
///
|
|
/// In the case that a relevant loop exit value cannot be computed, the
|
|
/// original value V is returned.
|
|
const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
|
|
// Check to see if we've folded this expression at this loop before.
|
|
std::map<const Loop *, const SCEV *> &Values = ValuesAtScopes[V];
|
|
std::pair<std::map<const Loop *, const SCEV *>::iterator, bool> Pair =
|
|
Values.insert(std::make_pair(L, static_cast<const SCEV *>(0)));
|
|
if (!Pair.second)
|
|
return Pair.first->second ? Pair.first->second : V;
|
|
|
|
// Otherwise compute it.
|
|
const SCEV *C = computeSCEVAtScope(V, L);
|
|
ValuesAtScopes[V][L] = C;
|
|
return C;
|
|
}
|
|
|
|
const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
|
|
if (isa<SCEVConstant>(V)) return V;
|
|
|
|
// If this instruction is evolved from a constant-evolving PHI, compute the
|
|
// exit value from the loop without using SCEVs.
|
|
if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
|
|
if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
|
|
const Loop *LI = (*this->LI)[I->getParent()];
|
|
if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
|
|
if (PHINode *PN = dyn_cast<PHINode>(I))
|
|
if (PN->getParent() == LI->getHeader()) {
|
|
// Okay, there is no closed form solution for the PHI node. Check
|
|
// to see if the loop that contains it has a known backedge-taken
|
|
// count. If so, we may be able to force computation of the exit
|
|
// value.
|
|
const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
|
|
if (const SCEVConstant *BTCC =
|
|
dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
|
|
// Okay, we know how many times the containing loop executes. If
|
|
// this is a constant evolving PHI node, get the final value at
|
|
// the specified iteration number.
|
|
Constant *RV = getConstantEvolutionLoopExitValue(PN,
|
|
BTCC->getValue()->getValue(),
|
|
LI);
|
|
if (RV) return getSCEV(RV);
|
|
}
|
|
}
|
|
|
|
// Okay, this is an expression that we cannot symbolically evaluate
|
|
// into a SCEV. Check to see if it's possible to symbolically evaluate
|
|
// the arguments into constants, and if so, try to constant propagate the
|
|
// result. This is particularly useful for computing loop exit values.
|
|
if (CanConstantFold(I)) {
|
|
std::vector<Constant*> Operands;
|
|
Operands.reserve(I->getNumOperands());
|
|
for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
|
|
Value *Op = I->getOperand(i);
|
|
if (Constant *C = dyn_cast<Constant>(Op)) {
|
|
Operands.push_back(C);
|
|
} else {
|
|
// If any of the operands is non-constant and if they are
|
|
// non-integer and non-pointer, don't even try to analyze them
|
|
// with scev techniques.
|
|
if (!isSCEVable(Op->getType()))
|
|
return V;
|
|
|
|
const SCEV* OpV = getSCEVAtScope(Op, L);
|
|
if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) {
|
|
Constant *C = SC->getValue();
|
|
if (C->getType() != Op->getType())
|
|
C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
|
|
Op->getType(),
|
|
false),
|
|
C, Op->getType());
|
|
Operands.push_back(C);
|
|
} else if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) {
|
|
if (Constant *C = dyn_cast<Constant>(SU->getValue())) {
|
|
if (C->getType() != Op->getType())
|
|
C =
|
|
ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
|
|
Op->getType(),
|
|
false),
|
|
C, Op->getType());
|
|
Operands.push_back(C);
|
|
} else
|
|
return V;
|
|
} else {
|
|
return V;
|
|
}
|
|
}
|
|
}
|
|
|
|
Constant *C;
|
|
if (const CmpInst *CI = dyn_cast<CmpInst>(I))
|
|
C = ConstantFoldCompareInstOperands(CI->getPredicate(),
|
|
&Operands[0], Operands.size(),
|
|
getContext());
|
|
else
|
|
C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
|
|
&Operands[0], Operands.size(),
|
|
getContext());
|
|
return getSCEV(C);
|
|
}
|
|
}
|
|
|
|
// This is some other type of SCEVUnknown, just return it.
|
|
return V;
|
|
}
|
|
|
|
if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
|
|
// Avoid performing the look-up in the common case where the specified
|
|
// expression has no loop-variant portions.
|
|
for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
|
|
const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
|
|
if (OpAtScope != Comm->getOperand(i)) {
|
|
// Okay, at least one of these operands is loop variant but might be
|
|
// foldable. Build a new instance of the folded commutative expression.
|
|
SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
|
|
Comm->op_begin()+i);
|
|
NewOps.push_back(OpAtScope);
|
|
|
|
for (++i; i != e; ++i) {
|
|
OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
|
|
NewOps.push_back(OpAtScope);
|
|
}
|
|
if (isa<SCEVAddExpr>(Comm))
|
|
return getAddExpr(NewOps);
|
|
if (isa<SCEVMulExpr>(Comm))
|
|
return getMulExpr(NewOps);
|
|
if (isa<SCEVSMaxExpr>(Comm))
|
|
return getSMaxExpr(NewOps);
|
|
if (isa<SCEVUMaxExpr>(Comm))
|
|
return getUMaxExpr(NewOps);
|
|
llvm_unreachable("Unknown commutative SCEV type!");
|
|
}
|
|
}
|
|
// If we got here, all operands are loop invariant.
|
|
return Comm;
|
|
}
|
|
|
|
if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
|
|
const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
|
|
const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
|
|
if (LHS == Div->getLHS() && RHS == Div->getRHS())
|
|
return Div; // must be loop invariant
|
|
return getUDivExpr(LHS, RHS);
|
|
}
|
|
|
|
// If this is a loop recurrence for a loop that does not contain L, then we
|
|
// are dealing with the final value computed by the loop.
|
|
if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
|
|
if (!L || !AddRec->getLoop()->contains(L->getHeader())) {
|
|
// To evaluate this recurrence, we need to know how many times the AddRec
|
|
// loop iterates. Compute this now.
|
|
const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
|
|
if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
|
|
|
|
// Then, evaluate the AddRec.
|
|
return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
|
|
}
|
|
return AddRec;
|
|
}
|
|
|
|
if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
|
|
const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
|
|
if (Op == Cast->getOperand())
|
|
return Cast; // must be loop invariant
|
|
return getZeroExtendExpr(Op, Cast->getType());
|
|
}
|
|
|
|
if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
|
|
const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
|
|
if (Op == Cast->getOperand())
|
|
return Cast; // must be loop invariant
|
|
return getSignExtendExpr(Op, Cast->getType());
|
|
}
|
|
|
|
if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
|
|
const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
|
|
if (Op == Cast->getOperand())
|
|
return Cast; // must be loop invariant
|
|
return getTruncateExpr(Op, Cast->getType());
|
|
}
|
|
|
|
if (isa<SCEVTargetDataConstant>(V))
|
|
return V;
|
|
|
|
llvm_unreachable("Unknown SCEV type!");
|
|
return 0;
|
|
}
|
|
|
|
/// getSCEVAtScope - This is a convenience function which does
|
|
/// getSCEVAtScope(getSCEV(V), L).
|
|
const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
|
|
return getSCEVAtScope(getSCEV(V), L);
|
|
}
|
|
|
|
/// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
|
|
/// following equation:
|
|
///
|
|
/// A * X = B (mod N)
|
|
///
|
|
/// where N = 2^BW and BW is the common bit width of A and B. The signedness of
|
|
/// A and B isn't important.
|
|
///
|
|
/// If the equation does not have a solution, SCEVCouldNotCompute is returned.
|
|
static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
|
|
ScalarEvolution &SE) {
|
|
uint32_t BW = A.getBitWidth();
|
|
assert(BW == B.getBitWidth() && "Bit widths must be the same.");
|
|
assert(A != 0 && "A must be non-zero.");
|
|
|
|
// 1. D = gcd(A, N)
|
|
//
|
|
// The gcd of A and N may have only one prime factor: 2. The number of
|
|
// trailing zeros in A is its multiplicity
|
|
uint32_t Mult2 = A.countTrailingZeros();
|
|
// D = 2^Mult2
|
|
|
|
// 2. Check if B is divisible by D.
|
|
//
|
|
// B is divisible by D if and only if the multiplicity of prime factor 2 for B
|
|
// is not less than multiplicity of this prime factor for D.
|
|
if (B.countTrailingZeros() < Mult2)
|
|
return SE.getCouldNotCompute();
|
|
|
|
// 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
|
|
// modulo (N / D).
|
|
//
|
|
// (N / D) may need BW+1 bits in its representation. Hence, we'll use this
|
|
// bit width during computations.
|
|
APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
|
|
APInt Mod(BW + 1, 0);
|
|
Mod.set(BW - Mult2); // Mod = N / D
|
|
APInt I = AD.multiplicativeInverse(Mod);
|
|
|
|
// 4. Compute the minimum unsigned root of the equation:
|
|
// I * (B / D) mod (N / D)
|
|
APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
|
|
|
|
// The result is guaranteed to be less than 2^BW so we may truncate it to BW
|
|
// bits.
|
|
return SE.getConstant(Result.trunc(BW));
|
|
}
|
|
|
|
/// SolveQuadraticEquation - Find the roots of the quadratic equation for the
|
|
/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
|
|
/// might be the same) or two SCEVCouldNotCompute objects.
|
|
///
|
|
static std::pair<const SCEV *,const SCEV *>
|
|
SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
|
|
assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
|
|
const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
|
|
const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
|
|
const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
|
|
|
|
// We currently can only solve this if the coefficients are constants.
|
|
if (!LC || !MC || !NC) {
|
|
const SCEV *CNC = SE.getCouldNotCompute();
|
|
return std::make_pair(CNC, CNC);
|
|
}
|
|
|
|
uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
|
|
const APInt &L = LC->getValue()->getValue();
|
|
const APInt &M = MC->getValue()->getValue();
|
|
const APInt &N = NC->getValue()->getValue();
|
|
APInt Two(BitWidth, 2);
|
|
APInt Four(BitWidth, 4);
|
|
|
|
{
|
|
using namespace APIntOps;
|
|
const APInt& C = L;
|
|
// Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
|
|
// The B coefficient is M-N/2
|
|
APInt B(M);
|
|
B -= sdiv(N,Two);
|
|
|
|
// The A coefficient is N/2
|
|
APInt A(N.sdiv(Two));
|
|
|
|
// Compute the B^2-4ac term.
|
|
APInt SqrtTerm(B);
|
|
SqrtTerm *= B;
|
|
SqrtTerm -= Four * (A * C);
|
|
|
|
// Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
|
|
// integer value or else APInt::sqrt() will assert.
|
|
APInt SqrtVal(SqrtTerm.sqrt());
|
|
|
|
// Compute the two solutions for the quadratic formula.
|
|
// The divisions must be performed as signed divisions.
|
|
APInt NegB(-B);
|
|
APInt TwoA( A << 1 );
|
|
if (TwoA.isMinValue()) {
|
|
const SCEV *CNC = SE.getCouldNotCompute();
|
|
return std::make_pair(CNC, CNC);
|
|
}
|
|
|
|
LLVMContext &Context = SE.getContext();
|
|
|
|
ConstantInt *Solution1 =
|
|
ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
|
|
ConstantInt *Solution2 =
|
|
ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
|
|
|
|
return std::make_pair(SE.getConstant(Solution1),
|
|
SE.getConstant(Solution2));
|
|
} // end APIntOps namespace
|
|
}
|
|
|
|
/// HowFarToZero - Return the number of times a backedge comparing the specified
|
|
/// value to zero will execute. If not computable, return CouldNotCompute.
|
|
const SCEV *ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) {
|
|
// If the value is a constant
|
|
if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
|
|
// If the value is already zero, the branch will execute zero times.
|
|
if (C->getValue()->isZero()) return C;
|
|
return getCouldNotCompute(); // Otherwise it will loop infinitely.
|
|
}
|
|
|
|
const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
|
|
if (!AddRec || AddRec->getLoop() != L)
|
|
return getCouldNotCompute();
|
|
|
|
if (AddRec->isAffine()) {
|
|
// If this is an affine expression, the execution count of this branch is
|
|
// the minimum unsigned root of the following equation:
|
|
//
|
|
// Start + Step*N = 0 (mod 2^BW)
|
|
//
|
|
// equivalent to:
|
|
//
|
|
// Step*N = -Start (mod 2^BW)
|
|
//
|
|
// where BW is the common bit width of Start and Step.
|
|
|
|
// Get the initial value for the loop.
|
|
const SCEV *Start = getSCEVAtScope(AddRec->getStart(),
|
|
L->getParentLoop());
|
|
const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1),
|
|
L->getParentLoop());
|
|
|
|
if (const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) {
|
|
// For now we handle only constant steps.
|
|
|
|
// First, handle unitary steps.
|
|
if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so:
|
|
return getNegativeSCEV(Start); // N = -Start (as unsigned)
|
|
if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so:
|
|
return Start; // N = Start (as unsigned)
|
|
|
|
// Then, try to solve the above equation provided that Start is constant.
|
|
if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
|
|
return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
|
|
-StartC->getValue()->getValue(),
|
|
*this);
|
|
}
|
|
} else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) {
|
|
// If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
|
|
// the quadratic equation to solve it.
|
|
std::pair<const SCEV *,const SCEV *> Roots = SolveQuadraticEquation(AddRec,
|
|
*this);
|
|
const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
|
|
const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
|
|
if (R1) {
|
|
#if 0
|
|
errs() << "HFTZ: " << *V << " - sol#1: " << *R1
|
|
<< " sol#2: " << *R2 << "\n";
|
|
#endif
|
|
// Pick the smallest positive root value.
|
|
if (ConstantInt *CB =
|
|
dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
|
|
R1->getValue(), R2->getValue()))) {
|
|
if (CB->getZExtValue() == false)
|
|
std::swap(R1, R2); // R1 is the minimum root now.
|
|
|
|
// We can only use this value if the chrec ends up with an exact zero
|
|
// value at this index. When solving for "X*X != 5", for example, we
|
|
// should not accept a root of 2.
|
|
const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
|
|
if (Val->isZero())
|
|
return R1; // We found a quadratic root!
|
|
}
|
|
}
|
|
}
|
|
|
|
return getCouldNotCompute();
|
|
}
|
|
|
|
/// HowFarToNonZero - Return the number of times a backedge checking the
|
|
/// specified value for nonzero will execute. If not computable, return
|
|
/// CouldNotCompute
|
|
const SCEV *ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
|
|
// Loops that look like: while (X == 0) are very strange indeed. We don't
|
|
// handle them yet except for the trivial case. This could be expanded in the
|
|
// future as needed.
|
|
|
|
// If the value is a constant, check to see if it is known to be non-zero
|
|
// already. If so, the backedge will execute zero times.
|
|
if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
|
|
if (!C->getValue()->isNullValue())
|
|
return getIntegerSCEV(0, C->getType());
|
|
return getCouldNotCompute(); // Otherwise it will loop infinitely.
|
|
}
|
|
|
|
// We could implement others, but I really doubt anyone writes loops like
|
|
// this, and if they did, they would already be constant folded.
|
|
return getCouldNotCompute();
|
|
}
|
|
|
|
/// getLoopPredecessor - If the given loop's header has exactly one unique
|
|
/// predecessor outside the loop, return it. Otherwise return null.
|
|
///
|
|
BasicBlock *ScalarEvolution::getLoopPredecessor(const Loop *L) {
|
|
BasicBlock *Header = L->getHeader();
|
|
BasicBlock *Pred = 0;
|
|
for (pred_iterator PI = pred_begin(Header), E = pred_end(Header);
|
|
PI != E; ++PI)
|
|
if (!L->contains(*PI)) {
|
|
if (Pred && Pred != *PI) return 0; // Multiple predecessors.
|
|
Pred = *PI;
|
|
}
|
|
return Pred;
|
|
}
|
|
|
|
/// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
|
|
/// (which may not be an immediate predecessor) which has exactly one
|
|
/// successor from which BB is reachable, or null if no such block is
|
|
/// found.
|
|
///
|
|
BasicBlock *
|
|
ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
|
|
// If the block has a unique predecessor, then there is no path from the
|
|
// predecessor to the block that does not go through the direct edge
|
|
// from the predecessor to the block.
|
|
if (BasicBlock *Pred = BB->getSinglePredecessor())
|
|
return Pred;
|
|
|
|
// A loop's header is defined to be a block that dominates the loop.
|
|
// If the header has a unique predecessor outside the loop, it must be
|
|
// a block that has exactly one successor that can reach the loop.
|
|
if (Loop *L = LI->getLoopFor(BB))
|
|
return getLoopPredecessor(L);
|
|
|
|
return 0;
|
|
}
|
|
|
|
/// HasSameValue - SCEV structural equivalence is usually sufficient for
|
|
/// testing whether two expressions are equal, however for the purposes of
|
|
/// looking for a condition guarding a loop, it can be useful to be a little
|
|
/// more general, since a front-end may have replicated the controlling
|
|
/// expression.
|
|
///
|
|
static bool HasSameValue(const SCEV *A, const SCEV *B) {
|
|
// Quick check to see if they are the same SCEV.
|
|
if (A == B) return true;
|
|
|
|
// Otherwise, if they're both SCEVUnknown, it's possible that they hold
|
|
// two different instructions with the same value. Check for this case.
|
|
if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
|
|
if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
|
|
if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
|
|
if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
|
|
if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory())
|
|
return true;
|
|
|
|
// Otherwise assume they may have a different value.
|
|
return false;
|
|
}
|
|
|
|
bool ScalarEvolution::isKnownNegative(const SCEV *S) {
|
|
return getSignedRange(S).getSignedMax().isNegative();
|
|
}
|
|
|
|
bool ScalarEvolution::isKnownPositive(const SCEV *S) {
|
|
return getSignedRange(S).getSignedMin().isStrictlyPositive();
|
|
}
|
|
|
|
bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
|
|
return !getSignedRange(S).getSignedMin().isNegative();
|
|
}
|
|
|
|
bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
|
|
return !getSignedRange(S).getSignedMax().isStrictlyPositive();
|
|
}
|
|
|
|
bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
|
|
return isKnownNegative(S) || isKnownPositive(S);
|
|
}
|
|
|
|
bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
|
|
const SCEV *LHS, const SCEV *RHS) {
|
|
|
|
if (HasSameValue(LHS, RHS))
|
|
return ICmpInst::isTrueWhenEqual(Pred);
|
|
|
|
switch (Pred) {
|
|
default:
|
|
llvm_unreachable("Unexpected ICmpInst::Predicate value!");
|
|
break;
|
|
case ICmpInst::ICMP_SGT:
|
|
Pred = ICmpInst::ICMP_SLT;
|
|
std::swap(LHS, RHS);
|
|
case ICmpInst::ICMP_SLT: {
|
|
ConstantRange LHSRange = getSignedRange(LHS);
|
|
ConstantRange RHSRange = getSignedRange(RHS);
|
|
if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
|
|
return true;
|
|
if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
|
|
return false;
|
|
break;
|
|
}
|
|
case ICmpInst::ICMP_SGE:
|
|
Pred = ICmpInst::ICMP_SLE;
|
|
std::swap(LHS, RHS);
|
|
case ICmpInst::ICMP_SLE: {
|
|
ConstantRange LHSRange = getSignedRange(LHS);
|
|
ConstantRange RHSRange = getSignedRange(RHS);
|
|
if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
|
|
return true;
|
|
if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
|
|
return false;
|
|
break;
|
|
}
|
|
case ICmpInst::ICMP_UGT:
|
|
Pred = ICmpInst::ICMP_ULT;
|
|
std::swap(LHS, RHS);
|
|
case ICmpInst::ICMP_ULT: {
|
|
ConstantRange LHSRange = getUnsignedRange(LHS);
|
|
ConstantRange RHSRange = getUnsignedRange(RHS);
|
|
if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
|
|
return true;
|
|
if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
|
|
return false;
|
|
break;
|
|
}
|
|
case ICmpInst::ICMP_UGE:
|
|
Pred = ICmpInst::ICMP_ULE;
|
|
std::swap(LHS, RHS);
|
|
case ICmpInst::ICMP_ULE: {
|
|
ConstantRange LHSRange = getUnsignedRange(LHS);
|
|
ConstantRange RHSRange = getUnsignedRange(RHS);
|
|
if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
|
|
return true;
|
|
if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
|
|
return false;
|
|
break;
|
|
}
|
|
case ICmpInst::ICMP_NE: {
|
|
if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
|
|
return true;
|
|
if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
|
|
return true;
|
|
|
|
const SCEV *Diff = getMinusSCEV(LHS, RHS);
|
|
if (isKnownNonZero(Diff))
|
|
return true;
|
|
break;
|
|
}
|
|
case ICmpInst::ICMP_EQ:
|
|
// The check at the top of the function catches the case where
|
|
// the values are known to be equal.
|
|
break;
|
|
}
|
|
return false;
|
|
}
|
|
|
|
/// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
|
|
/// protected by a conditional between LHS and RHS. This is used to
|
|
/// to eliminate casts.
|
|
bool
|
|
ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
|
|
ICmpInst::Predicate Pred,
|
|
const SCEV *LHS, const SCEV *RHS) {
|
|
// Interpret a null as meaning no loop, where there is obviously no guard
|
|
// (interprocedural conditions notwithstanding).
|
|
if (!L) return true;
|
|
|
|
BasicBlock *Latch = L->getLoopLatch();
|
|
if (!Latch)
|
|
return false;
|
|
|
|
BranchInst *LoopContinuePredicate =
|
|
dyn_cast<BranchInst>(Latch->getTerminator());
|
|
if (!LoopContinuePredicate ||
|
|
LoopContinuePredicate->isUnconditional())
|
|
return false;
|
|
|
|
return isImpliedCond(LoopContinuePredicate->getCondition(), Pred, LHS, RHS,
|
|
LoopContinuePredicate->getSuccessor(0) != L->getHeader());
|
|
}
|
|
|
|
/// isLoopGuardedByCond - Test whether entry to the loop is protected
|
|
/// by a conditional between LHS and RHS. This is used to help avoid max
|
|
/// expressions in loop trip counts, and to eliminate casts.
|
|
bool
|
|
ScalarEvolution::isLoopGuardedByCond(const Loop *L,
|
|
ICmpInst::Predicate Pred,
|
|
const SCEV *LHS, const SCEV *RHS) {
|
|
// Interpret a null as meaning no loop, where there is obviously no guard
|
|
// (interprocedural conditions notwithstanding).
|
|
if (!L) return false;
|
|
|
|
BasicBlock *Predecessor = getLoopPredecessor(L);
|
|
BasicBlock *PredecessorDest = L->getHeader();
|
|
|
|
// Starting at the loop predecessor, climb up the predecessor chain, as long
|
|
// as there are predecessors that can be found that have unique successors
|
|
// leading to the original header.
|
|
for (; Predecessor;
|
|
PredecessorDest = Predecessor,
|
|
Predecessor = getPredecessorWithUniqueSuccessorForBB(Predecessor)) {
|
|
|
|
BranchInst *LoopEntryPredicate =
|
|
dyn_cast<BranchInst>(Predecessor->getTerminator());
|
|
if (!LoopEntryPredicate ||
|
|
LoopEntryPredicate->isUnconditional())
|
|
continue;
|
|
|
|
if (isImpliedCond(LoopEntryPredicate->getCondition(), Pred, LHS, RHS,
|
|
LoopEntryPredicate->getSuccessor(0) != PredecessorDest))
|
|
return true;
|
|
}
|
|
|
|
return false;
|
|
}
|
|
|
|
/// isImpliedCond - Test whether the condition described by Pred, LHS,
|
|
/// and RHS is true whenever the given Cond value evaluates to true.
|
|
bool ScalarEvolution::isImpliedCond(Value *CondValue,
|
|
ICmpInst::Predicate Pred,
|
|
const SCEV *LHS, const SCEV *RHS,
|
|
bool Inverse) {
|
|
// Recursivly handle And and Or conditions.
|
|
if (BinaryOperator *BO = dyn_cast<BinaryOperator>(CondValue)) {
|
|
if (BO->getOpcode() == Instruction::And) {
|
|
if (!Inverse)
|
|
return isImpliedCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) ||
|
|
isImpliedCond(BO->getOperand(1), Pred, LHS, RHS, Inverse);
|
|
} else if (BO->getOpcode() == Instruction::Or) {
|
|
if (Inverse)
|
|
return isImpliedCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) ||
|
|
isImpliedCond(BO->getOperand(1), Pred, LHS, RHS, Inverse);
|
|
}
|
|
}
|
|
|
|
ICmpInst *ICI = dyn_cast<ICmpInst>(CondValue);
|
|
if (!ICI) return false;
|
|
|
|
// Bail if the ICmp's operands' types are wider than the needed type
|
|
// before attempting to call getSCEV on them. This avoids infinite
|
|
// recursion, since the analysis of widening casts can require loop
|
|
// exit condition information for overflow checking, which would
|
|
// lead back here.
|
|
if (getTypeSizeInBits(LHS->getType()) <
|
|
getTypeSizeInBits(ICI->getOperand(0)->getType()))
|
|
return false;
|
|
|
|
// Now that we found a conditional branch that dominates the loop, check to
|
|
// see if it is the comparison we are looking for.
|
|
ICmpInst::Predicate FoundPred;
|
|
if (Inverse)
|
|
FoundPred = ICI->getInversePredicate();
|
|
else
|
|
FoundPred = ICI->getPredicate();
|
|
|
|
const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
|
|
const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
|
|
|
|
// Balance the types. The case where FoundLHS' type is wider than
|
|
// LHS' type is checked for above.
|
|
if (getTypeSizeInBits(LHS->getType()) >
|
|
getTypeSizeInBits(FoundLHS->getType())) {
|
|
if (CmpInst::isSigned(Pred)) {
|
|
FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
|
|
FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
|
|
} else {
|
|
FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
|
|
FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
|
|
}
|
|
}
|
|
|
|
// Canonicalize the query to match the way instcombine will have
|
|
// canonicalized the comparison.
|
|
// First, put a constant operand on the right.
|
|
if (isa<SCEVConstant>(LHS)) {
|
|
std::swap(LHS, RHS);
|
|
Pred = ICmpInst::getSwappedPredicate(Pred);
|
|
}
|
|
// Then, canonicalize comparisons with boundary cases.
|
|
if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
|
|
const APInt &RA = RC->getValue()->getValue();
|
|
switch (Pred) {
|
|
default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
|
|
case ICmpInst::ICMP_EQ:
|
|
case ICmpInst::ICMP_NE:
|
|
break;
|
|
case ICmpInst::ICMP_UGE:
|
|
if ((RA - 1).isMinValue()) {
|
|
Pred = ICmpInst::ICMP_NE;
|
|
RHS = getConstant(RA - 1);
|
|
break;
|
|
}
|
|
if (RA.isMaxValue()) {
|
|
Pred = ICmpInst::ICMP_EQ;
|
|
break;
|
|
}
|
|
if (RA.isMinValue()) return true;
|
|
break;
|
|
case ICmpInst::ICMP_ULE:
|
|
if ((RA + 1).isMaxValue()) {
|
|
Pred = ICmpInst::ICMP_NE;
|
|
RHS = getConstant(RA + 1);
|
|
break;
|
|
}
|
|
if (RA.isMinValue()) {
|
|
Pred = ICmpInst::ICMP_EQ;
|
|
break;
|
|
}
|
|
if (RA.isMaxValue()) return true;
|
|
break;
|
|
case ICmpInst::ICMP_SGE:
|
|
if ((RA - 1).isMinSignedValue()) {
|
|
Pred = ICmpInst::ICMP_NE;
|
|
RHS = getConstant(RA - 1);
|
|
break;
|
|
}
|
|
if (RA.isMaxSignedValue()) {
|
|
Pred = ICmpInst::ICMP_EQ;
|
|
break;
|
|
}
|
|
if (RA.isMinSignedValue()) return true;
|
|
break;
|
|
case ICmpInst::ICMP_SLE:
|
|
if ((RA + 1).isMaxSignedValue()) {
|
|
Pred = ICmpInst::ICMP_NE;
|
|
RHS = getConstant(RA + 1);
|
|
break;
|
|
}
|
|
if (RA.isMinSignedValue()) {
|
|
Pred = ICmpInst::ICMP_EQ;
|
|
break;
|
|
}
|
|
if (RA.isMaxSignedValue()) return true;
|
|
break;
|
|
case ICmpInst::ICMP_UGT:
|
|
if (RA.isMinValue()) {
|
|
Pred = ICmpInst::ICMP_NE;
|
|
break;
|
|
}
|
|
if ((RA + 1).isMaxValue()) {
|
|
Pred = ICmpInst::ICMP_EQ;
|
|
RHS = getConstant(RA + 1);
|
|
break;
|
|
}
|
|
if (RA.isMaxValue()) return false;
|
|
break;
|
|
case ICmpInst::ICMP_ULT:
|
|
if (RA.isMaxValue()) {
|
|
Pred = ICmpInst::ICMP_NE;
|
|
break;
|
|
}
|
|
if ((RA - 1).isMinValue()) {
|
|
Pred = ICmpInst::ICMP_EQ;
|
|
RHS = getConstant(RA - 1);
|
|
break;
|
|
}
|
|
if (RA.isMinValue()) return false;
|
|
break;
|
|
case ICmpInst::ICMP_SGT:
|
|
if (RA.isMinSignedValue()) {
|
|
Pred = ICmpInst::ICMP_NE;
|
|
break;
|
|
}
|
|
if ((RA + 1).isMaxSignedValue()) {
|
|
Pred = ICmpInst::ICMP_EQ;
|
|
RHS = getConstant(RA + 1);
|
|
break;
|
|
}
|
|
if (RA.isMaxSignedValue()) return false;
|
|
break;
|
|
case ICmpInst::ICMP_SLT:
|
|
if (RA.isMaxSignedValue()) {
|
|
Pred = ICmpInst::ICMP_NE;
|
|
break;
|
|
}
|
|
if ((RA - 1).isMinSignedValue()) {
|
|
Pred = ICmpInst::ICMP_EQ;
|
|
RHS = getConstant(RA - 1);
|
|
break;
|
|
}
|
|
if (RA.isMinSignedValue()) return false;
|
|
break;
|
|
}
|
|
}
|
|
|
|
// Check to see if we can make the LHS or RHS match.
|
|
if (LHS == FoundRHS || RHS == FoundLHS) {
|
|
if (isa<SCEVConstant>(RHS)) {
|
|
std::swap(FoundLHS, FoundRHS);
|
|
FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
|
|
} else {
|
|
std::swap(LHS, RHS);
|
|
Pred = ICmpInst::getSwappedPredicate(Pred);
|
|
}
|
|
}
|
|
|
|
// Check whether the found predicate is the same as the desired predicate.
|
|
if (FoundPred == Pred)
|
|
return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
|
|
|
|
// Check whether swapping the found predicate makes it the same as the
|
|
// desired predicate.
|
|
if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
|
|
if (isa<SCEVConstant>(RHS))
|
|
return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
|
|
else
|
|
return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
|
|
RHS, LHS, FoundLHS, FoundRHS);
|
|
}
|
|
|
|
// Check whether the actual condition is beyond sufficient.
|
|
if (FoundPred == ICmpInst::ICMP_EQ)
|
|
if (ICmpInst::isTrueWhenEqual(Pred))
|
|
if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
|
|
return true;
|
|
if (Pred == ICmpInst::ICMP_NE)
|
|
if (!ICmpInst::isTrueWhenEqual(FoundPred))
|
|
if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
|
|
return true;
|
|
|
|
// Otherwise assume the worst.
|
|
return false;
|
|
}
|
|
|
|
/// isImpliedCondOperands - Test whether the condition described by Pred,
|
|
/// LHS, and RHS is true whenever the condition desribed by Pred, FoundLHS,
|
|
/// and FoundRHS is true.
|
|
bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
|
|
const SCEV *LHS, const SCEV *RHS,
|
|
const SCEV *FoundLHS,
|
|
const SCEV *FoundRHS) {
|
|
return isImpliedCondOperandsHelper(Pred, LHS, RHS,
|
|
FoundLHS, FoundRHS) ||
|
|
// ~x < ~y --> x > y
|
|
isImpliedCondOperandsHelper(Pred, LHS, RHS,
|
|
getNotSCEV(FoundRHS),
|
|
getNotSCEV(FoundLHS));
|
|
}
|
|
|
|
/// isImpliedCondOperandsHelper - Test whether the condition described by
|
|
/// Pred, LHS, and RHS is true whenever the condition desribed by Pred,
|
|
/// FoundLHS, and FoundRHS is true.
|
|
bool
|
|
ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
|
|
const SCEV *LHS, const SCEV *RHS,
|
|
const SCEV *FoundLHS,
|
|
const SCEV *FoundRHS) {
|
|
switch (Pred) {
|
|
default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
|
|
case ICmpInst::ICMP_EQ:
|
|
case ICmpInst::ICMP_NE:
|
|
if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
|
|
return true;
|
|
break;
|
|
case ICmpInst::ICMP_SLT:
|
|
case ICmpInst::ICMP_SLE:
|
|
if (isKnownPredicate(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
|
|
isKnownPredicate(ICmpInst::ICMP_SGE, RHS, FoundRHS))
|
|
return true;
|
|
break;
|
|
case ICmpInst::ICMP_SGT:
|
|
case ICmpInst::ICMP_SGE:
|
|
if (isKnownPredicate(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
|
|
isKnownPredicate(ICmpInst::ICMP_SLE, RHS, FoundRHS))
|
|
return true;
|
|
break;
|
|
case ICmpInst::ICMP_ULT:
|
|
case ICmpInst::ICMP_ULE:
|
|
if (isKnownPredicate(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
|
|
isKnownPredicate(ICmpInst::ICMP_UGE, RHS, FoundRHS))
|
|
return true;
|
|
break;
|
|
case ICmpInst::ICMP_UGT:
|
|
case ICmpInst::ICMP_UGE:
|
|
if (isKnownPredicate(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
|
|
isKnownPredicate(ICmpInst::ICMP_ULE, RHS, FoundRHS))
|
|
return true;
|
|
break;
|
|
}
|
|
|
|
return false;
|
|
}
|
|
|
|
/// getBECount - Subtract the end and start values and divide by the step,
|
|
/// rounding up, to get the number of times the backedge is executed. Return
|
|
/// CouldNotCompute if an intermediate computation overflows.
|
|
const SCEV *ScalarEvolution::getBECount(const SCEV *Start,
|
|
const SCEV *End,
|
|
const SCEV *Step) {
|
|
const Type *Ty = Start->getType();
|
|
const SCEV *NegOne = getIntegerSCEV(-1, Ty);
|
|
const SCEV *Diff = getMinusSCEV(End, Start);
|
|
const SCEV *RoundUp = getAddExpr(Step, NegOne);
|
|
|
|
// Add an adjustment to the difference between End and Start so that
|
|
// the division will effectively round up.
|
|
const SCEV *Add = getAddExpr(Diff, RoundUp);
|
|
|
|
// Check Add for unsigned overflow.
|
|
// TODO: More sophisticated things could be done here.
|
|
const Type *WideTy = IntegerType::get(getContext(),
|
|
getTypeSizeInBits(Ty) + 1);
|
|
const SCEV *EDiff = getZeroExtendExpr(Diff, WideTy);
|
|
const SCEV *ERoundUp = getZeroExtendExpr(RoundUp, WideTy);
|
|
const SCEV *OperandExtendedAdd = getAddExpr(EDiff, ERoundUp);
|
|
if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd)
|
|
return getCouldNotCompute();
|
|
|
|
return getUDivExpr(Add, Step);
|
|
}
|
|
|
|
/// HowManyLessThans - Return the number of times a backedge containing the
|
|
/// specified less-than comparison will execute. If not computable, return
|
|
/// CouldNotCompute.
|
|
ScalarEvolution::BackedgeTakenInfo
|
|
ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
|
|
const Loop *L, bool isSigned) {
|
|
// Only handle: "ADDREC < LoopInvariant".
|
|
if (!RHS->isLoopInvariant(L)) return getCouldNotCompute();
|
|
|
|
const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
|
|
if (!AddRec || AddRec->getLoop() != L)
|
|
return getCouldNotCompute();
|
|
|
|
if (AddRec->isAffine()) {
|
|
// FORNOW: We only support unit strides.
|
|
unsigned BitWidth = getTypeSizeInBits(AddRec->getType());
|
|
const SCEV *Step = AddRec->getStepRecurrence(*this);
|
|
|
|
// TODO: handle non-constant strides.
|
|
const SCEVConstant *CStep = dyn_cast<SCEVConstant>(Step);
|
|
if (!CStep || CStep->isZero())
|
|
return getCouldNotCompute();
|
|
if (CStep->isOne()) {
|
|
// With unit stride, the iteration never steps past the limit value.
|
|
} else if (CStep->getValue()->getValue().isStrictlyPositive()) {
|
|
if (const SCEVConstant *CLimit = dyn_cast<SCEVConstant>(RHS)) {
|
|
// Test whether a positive iteration iteration can step past the limit
|
|
// value and past the maximum value for its type in a single step.
|
|
if (isSigned) {
|
|
APInt Max = APInt::getSignedMaxValue(BitWidth);
|
|
if ((Max - CStep->getValue()->getValue())
|
|
.slt(CLimit->getValue()->getValue()))
|
|
return getCouldNotCompute();
|
|
} else {
|
|
APInt Max = APInt::getMaxValue(BitWidth);
|
|
if ((Max - CStep->getValue()->getValue())
|
|
.ult(CLimit->getValue()->getValue()))
|
|
return getCouldNotCompute();
|
|
}
|
|
} else
|
|
// TODO: handle non-constant limit values below.
|
|
return getCouldNotCompute();
|
|
} else
|
|
// TODO: handle negative strides below.
|
|
return getCouldNotCompute();
|
|
|
|
// We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant
|
|
// m. So, we count the number of iterations in which {n,+,s} < m is true.
|
|
// Note that we cannot simply return max(m-n,0)/s because it's not safe to
|
|
// treat m-n as signed nor unsigned due to overflow possibility.
|
|
|
|
// First, we get the value of the LHS in the first iteration: n
|
|
const SCEV *Start = AddRec->getOperand(0);
|
|
|
|
// Determine the minimum constant start value.
|
|
const SCEV *MinStart = getConstant(isSigned ?
|
|
getSignedRange(Start).getSignedMin() :
|
|
getUnsignedRange(Start).getUnsignedMin());
|
|
|
|
// If we know that the condition is true in order to enter the loop,
|
|
// then we know that it will run exactly (m-n)/s times. Otherwise, we
|
|
// only know that it will execute (max(m,n)-n)/s times. In both cases,
|
|
// the division must round up.
|
|
const SCEV *End = RHS;
|
|
if (!isLoopGuardedByCond(L,
|
|
isSigned ? ICmpInst::ICMP_SLT :
|
|
ICmpInst::ICMP_ULT,
|
|
getMinusSCEV(Start, Step), RHS))
|
|
End = isSigned ? getSMaxExpr(RHS, Start)
|
|
: getUMaxExpr(RHS, Start);
|
|
|
|
// Determine the maximum constant end value.
|
|
const SCEV *MaxEnd = getConstant(isSigned ?
|
|
getSignedRange(End).getSignedMax() :
|
|
getUnsignedRange(End).getUnsignedMax());
|
|
|
|
// Finally, we subtract these two values and divide, rounding up, to get
|
|
// the number of times the backedge is executed.
|
|
const SCEV *BECount = getBECount(Start, End, Step);
|
|
|
|
// The maximum backedge count is similar, except using the minimum start
|
|
// value and the maximum end value.
|
|
const SCEV *MaxBECount = getBECount(MinStart, MaxEnd, Step);
|
|
|
|
return BackedgeTakenInfo(BECount, MaxBECount);
|
|
}
|
|
|
|
return getCouldNotCompute();
|
|
}
|
|
|
|
/// getNumIterationsInRange - Return the number of iterations of this loop that
|
|
/// produce values in the specified constant range. Another way of looking at
|
|
/// this is that it returns the first iteration number where the value is not in
|
|
/// the condition, thus computing the exit count. If the iteration count can't
|
|
/// be computed, an instance of SCEVCouldNotCompute is returned.
|
|
const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
|
|
ScalarEvolution &SE) const {
|
|
if (Range.isFullSet()) // Infinite loop.
|
|
return SE.getCouldNotCompute();
|
|
|
|
// If the start is a non-zero constant, shift the range to simplify things.
|
|
if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
|
|
if (!SC->getValue()->isZero()) {
|
|
SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
|
|
Operands[0] = SE.getIntegerSCEV(0, SC->getType());
|
|
const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop());
|
|
if (const SCEVAddRecExpr *ShiftedAddRec =
|
|
dyn_cast<SCEVAddRecExpr>(Shifted))
|
|
return ShiftedAddRec->getNumIterationsInRange(
|
|
Range.subtract(SC->getValue()->getValue()), SE);
|
|
// This is strange and shouldn't happen.
|
|
return SE.getCouldNotCompute();
|
|
}
|
|
|
|
// The only time we can solve this is when we have all constant indices.
|
|
// Otherwise, we cannot determine the overflow conditions.
|
|
for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
|
|
if (!isa<SCEVConstant>(getOperand(i)))
|
|
return SE.getCouldNotCompute();
|
|
|
|
|
|
// Okay at this point we know that all elements of the chrec are constants and
|
|
// that the start element is zero.
|
|
|
|
// First check to see if the range contains zero. If not, the first
|
|
// iteration exits.
|
|
unsigned BitWidth = SE.getTypeSizeInBits(getType());
|
|
if (!Range.contains(APInt(BitWidth, 0)))
|
|
return SE.getIntegerSCEV(0, getType());
|
|
|
|
if (isAffine()) {
|
|
// If this is an affine expression then we have this situation:
|
|
// Solve {0,+,A} in Range === Ax in Range
|
|
|
|
// We know that zero is in the range. If A is positive then we know that
|
|
// the upper value of the range must be the first possible exit value.
|
|
// If A is negative then the lower of the range is the last possible loop
|
|
// value. Also note that we already checked for a full range.
|
|
APInt One(BitWidth,1);
|
|
APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
|
|
APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
|
|
|
|
// The exit value should be (End+A)/A.
|
|
APInt ExitVal = (End + A).udiv(A);
|
|
ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
|
|
|
|
// Evaluate at the exit value. If we really did fall out of the valid
|
|
// range, then we computed our trip count, otherwise wrap around or other
|
|
// things must have happened.
|
|
ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
|
|
if (Range.contains(Val->getValue()))
|
|
return SE.getCouldNotCompute(); // Something strange happened
|
|
|
|
// Ensure that the previous value is in the range. This is a sanity check.
|
|
assert(Range.contains(
|
|
EvaluateConstantChrecAtConstant(this,
|
|
ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
|
|
"Linear scev computation is off in a bad way!");
|
|
return SE.getConstant(ExitValue);
|
|
} else if (isQuadratic()) {
|
|
// If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
|
|
// quadratic equation to solve it. To do this, we must frame our problem in
|
|
// terms of figuring out when zero is crossed, instead of when
|
|
// Range.getUpper() is crossed.
|
|
SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
|
|
NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
|
|
const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop());
|
|
|
|
// Next, solve the constructed addrec
|
|
std::pair<const SCEV *,const SCEV *> Roots =
|
|
SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
|
|
const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
|
|
const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
|
|
if (R1) {
|
|
// Pick the smallest positive root value.
|
|
if (ConstantInt *CB =
|
|
dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
|
|
R1->getValue(), R2->getValue()))) {
|
|
if (CB->getZExtValue() == false)
|
|
std::swap(R1, R2); // R1 is the minimum root now.
|
|
|
|
// Make sure the root is not off by one. The returned iteration should
|
|
// not be in the range, but the previous one should be. When solving
|
|
// for "X*X < 5", for example, we should not return a root of 2.
|
|
ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
|
|
R1->getValue(),
|
|
SE);
|
|
if (Range.contains(R1Val->getValue())) {
|
|
// The next iteration must be out of the range...
|
|
ConstantInt *NextVal =
|
|
ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1);
|
|
|
|
R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
|
|
if (!Range.contains(R1Val->getValue()))
|
|
return SE.getConstant(NextVal);
|
|
return SE.getCouldNotCompute(); // Something strange happened
|
|
}
|
|
|
|
// If R1 was not in the range, then it is a good return value. Make
|
|
// sure that R1-1 WAS in the range though, just in case.
|
|
ConstantInt *NextVal =
|
|
ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1);
|
|
R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
|
|
if (Range.contains(R1Val->getValue()))
|
|
return R1;
|
|
return SE.getCouldNotCompute(); // Something strange happened
|
|
}
|
|
}
|
|
}
|
|
|
|
return SE.getCouldNotCompute();
|
|
}
|
|
|
|
|
|
|
|
//===----------------------------------------------------------------------===//
|
|
// SCEVCallbackVH Class Implementation
|
|
//===----------------------------------------------------------------------===//
|
|
|
|
void ScalarEvolution::SCEVCallbackVH::deleted() {
|
|
assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
|
|
if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
|
|
SE->ConstantEvolutionLoopExitValue.erase(PN);
|
|
SE->Scalars.erase(getValPtr());
|
|
// this now dangles!
|
|
}
|
|
|
|
void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *) {
|
|
assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
|
|
|
|
// Forget all the expressions associated with users of the old value,
|
|
// so that future queries will recompute the expressions using the new
|
|
// value.
|
|
SmallVector<User *, 16> Worklist;
|
|
SmallPtrSet<User *, 8> Visited;
|
|
Value *Old = getValPtr();
|
|
bool DeleteOld = false;
|
|
for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end();
|
|
UI != UE; ++UI)
|
|
Worklist.push_back(*UI);
|
|
while (!Worklist.empty()) {
|
|
User *U = Worklist.pop_back_val();
|
|
// Deleting the Old value will cause this to dangle. Postpone
|
|
// that until everything else is done.
|
|
if (U == Old) {
|
|
DeleteOld = true;
|
|
continue;
|
|
}
|
|
if (!Visited.insert(U))
|
|
continue;
|
|
if (PHINode *PN = dyn_cast<PHINode>(U))
|
|
SE->ConstantEvolutionLoopExitValue.erase(PN);
|
|
SE->Scalars.erase(U);
|
|
for (Value::use_iterator UI = U->use_begin(), UE = U->use_end();
|
|
UI != UE; ++UI)
|
|
Worklist.push_back(*UI);
|
|
}
|
|
// Delete the Old value if it (indirectly) references itself.
|
|
if (DeleteOld) {
|
|
if (PHINode *PN = dyn_cast<PHINode>(Old))
|
|
SE->ConstantEvolutionLoopExitValue.erase(PN);
|
|
SE->Scalars.erase(Old);
|
|
// this now dangles!
|
|
}
|
|
// this may dangle!
|
|
}
|
|
|
|
ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
|
|
: CallbackVH(V), SE(se) {}
|
|
|
|
//===----------------------------------------------------------------------===//
|
|
// ScalarEvolution Class Implementation
|
|
//===----------------------------------------------------------------------===//
|
|
|
|
ScalarEvolution::ScalarEvolution()
|
|
: FunctionPass(&ID) {
|
|
}
|
|
|
|
bool ScalarEvolution::runOnFunction(Function &F) {
|
|
this->F = &F;
|
|
LI = &getAnalysis<LoopInfo>();
|
|
TD = getAnalysisIfAvailable<TargetData>();
|
|
return false;
|
|
}
|
|
|
|
void ScalarEvolution::releaseMemory() {
|
|
Scalars.clear();
|
|
BackedgeTakenCounts.clear();
|
|
ConstantEvolutionLoopExitValue.clear();
|
|
ValuesAtScopes.clear();
|
|
UniqueSCEVs.clear();
|
|
SCEVAllocator.Reset();
|
|
}
|
|
|
|
void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
|
|
AU.setPreservesAll();
|
|
AU.addRequiredTransitive<LoopInfo>();
|
|
}
|
|
|
|
bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
|
|
return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
|
|
}
|
|
|
|
static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
|
|
const Loop *L) {
|
|
// Print all inner loops first
|
|
for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
|
|
PrintLoopInfo(OS, SE, *I);
|
|
|
|
OS << "Loop " << L->getHeader()->getName() << ": ";
|
|
|
|
SmallVector<BasicBlock*, 8> ExitBlocks;
|
|
L->getExitBlocks(ExitBlocks);
|
|
if (ExitBlocks.size() != 1)
|
|
OS << "<multiple exits> ";
|
|
|
|
if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
|
|
OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
|
|
} else {
|
|
OS << "Unpredictable backedge-taken count. ";
|
|
}
|
|
|
|
OS << "\n";
|
|
OS << "Loop " << L->getHeader()->getName() << ": ";
|
|
|
|
if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
|
|
OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
|
|
} else {
|
|
OS << "Unpredictable max backedge-taken count. ";
|
|
}
|
|
|
|
OS << "\n";
|
|
}
|
|
|
|
void ScalarEvolution::print(raw_ostream &OS, const Module* ) const {
|
|
// ScalarEvolution's implementaiton of the print method is to print
|
|
// out SCEV values of all instructions that are interesting. Doing
|
|
// this potentially causes it to create new SCEV objects though,
|
|
// which technically conflicts with the const qualifier. This isn't
|
|
// observable from outside the class though, so casting away the
|
|
// const isn't dangerous.
|
|
ScalarEvolution &SE = *const_cast<ScalarEvolution*>(this);
|
|
|
|
OS << "Classifying expressions for: " << F->getName() << "\n";
|
|
for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
|
|
if (isSCEVable(I->getType())) {
|
|
OS << *I << '\n';
|
|
OS << " --> ";
|
|
const SCEV *SV = SE.getSCEV(&*I);
|
|
SV->print(OS);
|
|
|
|
const Loop *L = LI->getLoopFor((*I).getParent());
|
|
|
|
const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
|
|
if (AtUse != SV) {
|
|
OS << " --> ";
|
|
AtUse->print(OS);
|
|
}
|
|
|
|
if (L) {
|
|
OS << "\t\t" "Exits: ";
|
|
const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
|
|
if (!ExitValue->isLoopInvariant(L)) {
|
|
OS << "<<Unknown>>";
|
|
} else {
|
|
OS << *ExitValue;
|
|
}
|
|
}
|
|
|
|
OS << "\n";
|
|
}
|
|
|
|
OS << "Determining loop execution counts for: " << F->getName() << "\n";
|
|
for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
|
|
PrintLoopInfo(OS, &SE, *I);
|
|
}
|
|
|