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git-svn-id: https://llvm.org/svn/llvm-project/llvm/trunk@17214 91177308-0d34-0410-b5e6-96231b3b80d8
2367 lines
94 KiB
C++
2367 lines
94 KiB
C++
//===- ScalarEvolution.cpp - Scalar Evolution Analysis ----------*- C++ -*-===//
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//
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// The LLVM Compiler Infrastructure
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//
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// This file was developed by the LLVM research group and is distributed under
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// the University of Illinois Open Source License. See LICENSE.TXT for details.
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//
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//===----------------------------------------------------------------------===//
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//
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// This file contains the implementation of the scalar evolution analysis
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// engine, which is used primarily to analyze expressions involving induction
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// variables in loops.
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//
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// There are several aspects to this library. First is the representation of
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// scalar expressions, which are represented as subclasses of the SCEV class.
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// These classes are used to represent certain types of subexpressions that we
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// can handle. These classes are reference counted, managed by the SCEVHandle
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// class. We only create one SCEV of a particular shape, so pointer-comparisons
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// for equality are legal.
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//
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// One important aspect of the SCEV objects is that they are never cyclic, even
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// if there is a cycle in the dataflow for an expression (ie, a PHI node). If
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// the PHI node is one of the idioms that we can represent (e.g., a polynomial
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// recurrence) then we represent it directly as a recurrence node, otherwise we
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// represent it as a SCEVUnknown node.
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//
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// In addition to being able to represent expressions of various types, we also
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// have folders that are used to build the *canonical* representation for a
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// particular expression. These folders are capable of using a variety of
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// rewrite rules to simplify the expressions.
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//
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// Once the folders are defined, we can implement the more interesting
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// higher-level code, such as the code that recognizes PHI nodes of various
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// types, computes the execution count of a loop, etc.
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//
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// TODO: We should use these routines and value representations to implement
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// dependence analysis!
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//
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//===----------------------------------------------------------------------===//
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//
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// There are several good references for the techniques used in this analysis.
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//
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// Chains of recurrences -- a method to expedite the evaluation
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// of closed-form functions
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// Olaf Bachmann, Paul S. Wang, Eugene V. Zima
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//
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// On computational properties of chains of recurrences
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// Eugene V. Zima
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//
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// Symbolic Evaluation of Chains of Recurrences for Loop Optimization
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// Robert A. van Engelen
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//
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// Efficient Symbolic Analysis for Optimizing Compilers
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// Robert A. van Engelen
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//
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// Using the chains of recurrences algebra for data dependence testing and
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// induction variable substitution
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// MS Thesis, Johnie Birch
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//
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//===----------------------------------------------------------------------===//
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#include "llvm/Analysis/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/Instructions.h"
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#include "llvm/Analysis/LoopInfo.h"
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#include "llvm/Assembly/Writer.h"
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#include "llvm/Transforms/Scalar.h"
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#include "llvm/Transforms/Utils/Local.h"
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#include "llvm/Support/CFG.h"
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#include "llvm/Support/ConstantRange.h"
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#include "llvm/Support/InstIterator.h"
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#include "llvm/Support/CommandLine.h"
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#include "llvm/ADT/Statistic.h"
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#include <cmath>
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#include <algorithm>
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using namespace llvm;
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namespace {
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RegisterAnalysis<ScalarEvolution>
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R("scalar-evolution", "Scalar Evolution Analysis");
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Statistic<>
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NumBruteForceEvaluations("scalar-evolution",
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"Number of brute force evaluations needed to "
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"calculate high-order polynomial exit values");
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Statistic<>
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NumArrayLenItCounts("scalar-evolution",
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"Number of trip counts computed with array length");
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Statistic<>
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NumTripCountsComputed("scalar-evolution",
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"Number of loops with predictable loop counts");
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Statistic<>
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NumTripCountsNotComputed("scalar-evolution",
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"Number of loops without predictable loop counts");
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Statistic<>
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NumBruteForceTripCountsComputed("scalar-evolution",
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"Number of loops with trip counts computed by force");
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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 symbolically execute a constant derived loop"),
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cl::init(100));
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}
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//===----------------------------------------------------------------------===//
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// SCEV class definitions
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//===----------------------------------------------------------------------===//
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//===----------------------------------------------------------------------===//
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// Implementation of the SCEV class.
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//
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SCEV::~SCEV() {}
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void SCEV::dump() const {
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print(std::cerr);
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}
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/// getValueRange - Return the tightest constant bounds that this value is
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/// known to have. This method is only valid on integer SCEV objects.
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ConstantRange SCEV::getValueRange() const {
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const Type *Ty = getType();
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assert(Ty->isInteger() && "Can't get range for a non-integer SCEV!");
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Ty = Ty->getUnsignedVersion();
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// Default to a full range if no better information is available.
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return ConstantRange(getType());
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}
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SCEVCouldNotCompute::SCEVCouldNotCompute() : SCEV(scCouldNotCompute) {}
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bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const {
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assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
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return false;
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}
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const Type *SCEVCouldNotCompute::getType() const {
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assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
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return 0;
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}
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bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const {
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assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
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return false;
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}
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void SCEVCouldNotCompute::print(std::ostream &OS) const {
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OS << "***COULDNOTCOMPUTE***";
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}
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bool SCEVCouldNotCompute::classof(const SCEV *S) {
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return S->getSCEVType() == scCouldNotCompute;
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}
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// SCEVConstants - Only allow the creation of one SCEVConstant for any
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// particular value. Don't use a SCEVHandle here, or else the object will
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// never be deleted!
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static std::map<ConstantInt*, SCEVConstant*> SCEVConstants;
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SCEVConstant::~SCEVConstant() {
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SCEVConstants.erase(V);
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}
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SCEVHandle SCEVConstant::get(ConstantInt *V) {
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// Make sure that SCEVConstant instances are all unsigned.
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if (V->getType()->isSigned()) {
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const Type *NewTy = V->getType()->getUnsignedVersion();
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V = cast<ConstantUInt>(ConstantExpr::getCast(V, NewTy));
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}
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SCEVConstant *&R = SCEVConstants[V];
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if (R == 0) R = new SCEVConstant(V);
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return R;
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}
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ConstantRange SCEVConstant::getValueRange() const {
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return ConstantRange(V);
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}
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const Type *SCEVConstant::getType() const { return V->getType(); }
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void SCEVConstant::print(std::ostream &OS) const {
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WriteAsOperand(OS, V, false);
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}
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// SCEVTruncates - Only allow the creation of one SCEVTruncateExpr for any
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// particular input. Don't use a SCEVHandle here, or else the object will
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// never be deleted!
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static std::map<std::pair<SCEV*, const Type*>, SCEVTruncateExpr*> SCEVTruncates;
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SCEVTruncateExpr::SCEVTruncateExpr(const SCEVHandle &op, const Type *ty)
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: SCEV(scTruncate), Op(op), Ty(ty) {
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assert(Op->getType()->isInteger() && Ty->isInteger() &&
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Ty->isUnsigned() &&
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"Cannot truncate non-integer value!");
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assert(Op->getType()->getPrimitiveSize() > Ty->getPrimitiveSize() &&
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"This is not a truncating conversion!");
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}
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SCEVTruncateExpr::~SCEVTruncateExpr() {
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SCEVTruncates.erase(std::make_pair(Op, Ty));
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}
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ConstantRange SCEVTruncateExpr::getValueRange() const {
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return getOperand()->getValueRange().truncate(getType());
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}
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void SCEVTruncateExpr::print(std::ostream &OS) const {
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OS << "(truncate " << *Op << " to " << *Ty << ")";
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}
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// SCEVZeroExtends - Only allow the creation of one SCEVZeroExtendExpr for any
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// particular input. Don't use a SCEVHandle here, or else the object will never
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// be deleted!
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static std::map<std::pair<SCEV*, const Type*>,
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SCEVZeroExtendExpr*> SCEVZeroExtends;
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SCEVZeroExtendExpr::SCEVZeroExtendExpr(const SCEVHandle &op, const Type *ty)
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: SCEV(scTruncate), Op(Op), Ty(ty) {
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assert(Op->getType()->isInteger() && Ty->isInteger() &&
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Ty->isUnsigned() &&
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"Cannot zero extend non-integer value!");
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assert(Op->getType()->getPrimitiveSize() < Ty->getPrimitiveSize() &&
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"This is not an extending conversion!");
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}
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SCEVZeroExtendExpr::~SCEVZeroExtendExpr() {
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SCEVZeroExtends.erase(std::make_pair(Op, Ty));
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}
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ConstantRange SCEVZeroExtendExpr::getValueRange() const {
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return getOperand()->getValueRange().zeroExtend(getType());
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}
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void SCEVZeroExtendExpr::print(std::ostream &OS) const {
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OS << "(zeroextend " << *Op << " to " << *Ty << ")";
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}
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// SCEVCommExprs - Only allow the creation of one SCEVCommutativeExpr for any
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// particular input. Don't use a SCEVHandle here, or else the object will never
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// be deleted!
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static std::map<std::pair<unsigned, std::vector<SCEV*> >,
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SCEVCommutativeExpr*> SCEVCommExprs;
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SCEVCommutativeExpr::~SCEVCommutativeExpr() {
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SCEVCommExprs.erase(std::make_pair(getSCEVType(),
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std::vector<SCEV*>(Operands.begin(),
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Operands.end())));
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}
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void SCEVCommutativeExpr::print(std::ostream &OS) const {
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assert(Operands.size() > 1 && "This plus expr shouldn't exist!");
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const char *OpStr = getOperationStr();
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OS << "(" << *Operands[0];
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for (unsigned i = 1, e = Operands.size(); i != e; ++i)
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OS << OpStr << *Operands[i];
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OS << ")";
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}
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// SCEVUDivs - Only allow the creation of one SCEVUDivExpr for any particular
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// input. Don't use a SCEVHandle here, or else the object will never be
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// deleted!
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static std::map<std::pair<SCEV*, SCEV*>, SCEVUDivExpr*> SCEVUDivs;
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SCEVUDivExpr::~SCEVUDivExpr() {
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SCEVUDivs.erase(std::make_pair(LHS, RHS));
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}
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void SCEVUDivExpr::print(std::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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const Type *Ty = LHS->getType();
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if (Ty->isSigned()) Ty = Ty->getUnsignedVersion();
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return Ty;
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}
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// SCEVAddRecExprs - Only allow the creation of one SCEVAddRecExpr for any
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// particular input. Don't use a SCEVHandle here, or else the object will never
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// be deleted!
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static std::map<std::pair<const Loop *, std::vector<SCEV*> >,
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SCEVAddRecExpr*> SCEVAddRecExprs;
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SCEVAddRecExpr::~SCEVAddRecExpr() {
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SCEVAddRecExprs.erase(std::make_pair(L,
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std::vector<SCEV*>(Operands.begin(),
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Operands.end())));
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}
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bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const {
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// This recurrence is invariant w.r.t to QueryLoop iff QueryLoop doesn't
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// contain L.
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return !QueryLoop->contains(L->getHeader());
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}
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void SCEVAddRecExpr::print(std::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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// SCEVUnknowns - Only allow the creation of one SCEVUnknown for any particular
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// value. Don't use a SCEVHandle here, or else the object will never be
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// deleted!
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static std::map<Value*, SCEVUnknown*> SCEVUnknowns;
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SCEVUnknown::~SCEVUnknown() { SCEVUnknowns.erase(V); }
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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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if (Instruction *I = dyn_cast<Instruction>(V))
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return !L->contains(I->getParent());
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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(std::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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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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struct SCEVComplexityCompare {
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bool operator()(SCEV *LHS, SCEV *RHS) {
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return LHS->getSCEVType() < RHS->getSCEVType();
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}
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};
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}
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/// GroupByComplexity - Given a list of SCEV objects, order them by their
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/// complexity, and group objects of the same complexity together by value.
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/// When this routine is finished, we know that any duplicates in the vector are
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/// consecutive and that complexity is monotonically increasing.
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///
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/// Note that we go take special precautions to ensure that we get determinstic
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/// results from this routine. In other words, we don't want the results of
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/// this to depend on where the addresses of various SCEV objects happened to
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/// land in memory.
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///
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static void GroupByComplexity(std::vector<SCEVHandle> &Ops) {
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if (Ops.size() < 2) return; // Noop
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if (Ops.size() == 2) {
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// This is the common case, which also happens to be trivially simple.
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// Special case it.
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if (Ops[0]->getSCEVType() > Ops[1]->getSCEVType())
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std::swap(Ops[0], Ops[1]);
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return;
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}
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// Do the rough sort by complexity.
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std::sort(Ops.begin(), Ops.end(), SCEVComplexityCompare());
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// Now that we are sorted by complexity, group elements of the same
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// complexity. Note that this is, at worst, N^2, but the vector is likely to
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// be extremely short in practice. Note that we take this approach because we
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// do not want to depend on the addresses of the objects we are grouping.
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for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
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SCEV *S = Ops[i];
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unsigned Complexity = S->getSCEVType();
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// If there are any objects of the same complexity and same value as this
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// one, group them.
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for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
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if (Ops[j] == S) { // Found a duplicate.
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// Move it to immediately after i'th element.
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std::swap(Ops[i+1], Ops[j]);
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++i; // no need to rescan it.
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if (i == e-2) return; // Done!
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}
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}
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}
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}
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//===----------------------------------------------------------------------===//
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// Simple SCEV method implementations
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//===----------------------------------------------------------------------===//
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/// getIntegerSCEV - Given an integer or FP type, create a constant for the
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/// specified signed integer value and return a SCEV for the constant.
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SCEVHandle SCEVUnknown::getIntegerSCEV(int Val, const Type *Ty) {
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Constant *C;
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if (Val == 0)
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C = Constant::getNullValue(Ty);
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else if (Ty->isFloatingPoint())
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C = ConstantFP::get(Ty, Val);
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else if (Ty->isSigned())
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C = ConstantSInt::get(Ty, Val);
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else {
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C = ConstantSInt::get(Ty->getSignedVersion(), Val);
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C = ConstantExpr::getCast(C, Ty);
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}
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return SCEVUnknown::get(C);
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}
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/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
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/// input value to the specified type. If the type must be extended, it is zero
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/// extended.
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static SCEVHandle getTruncateOrZeroExtend(const SCEVHandle &V, const Type *Ty) {
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const Type *SrcTy = V->getType();
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assert(SrcTy->isInteger() && Ty->isInteger() &&
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"Cannot truncate or zero extend with non-integer arguments!");
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if (SrcTy->getPrimitiveSize() == Ty->getPrimitiveSize())
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return V; // No conversion
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if (SrcTy->getPrimitiveSize() > Ty->getPrimitiveSize())
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return SCEVTruncateExpr::get(V, Ty);
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return SCEVZeroExtendExpr::get(V, Ty);
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}
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/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
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///
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static SCEVHandle getNegativeSCEV(const SCEVHandle &V) {
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if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
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return SCEVUnknown::get(ConstantExpr::getNeg(VC->getValue()));
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return SCEVMulExpr::get(V, SCEVUnknown::getIntegerSCEV(-1, V->getType()));
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}
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/// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
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///
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static SCEVHandle getMinusSCEV(const SCEVHandle &LHS, const SCEVHandle &RHS) {
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// X - Y --> X + -Y
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return SCEVAddExpr::get(LHS, getNegativeSCEV(RHS));
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}
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/// Binomial - Evaluate N!/((N-M)!*M!) . Note that N is often large and M is
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/// often very small, so we try to reduce the number of N! terms we need to
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/// evaluate by evaluating this as (N!/(N-M)!)/M!
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static ConstantInt *Binomial(ConstantInt *N, unsigned M) {
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uint64_t NVal = N->getRawValue();
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uint64_t FirstTerm = 1;
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for (unsigned i = 0; i != M; ++i)
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FirstTerm *= NVal-i;
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unsigned MFactorial = 1;
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for (; M; --M)
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MFactorial *= M;
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Constant *Result = ConstantUInt::get(Type::ULongTy, FirstTerm/MFactorial);
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Result = ConstantExpr::getCast(Result, N->getType());
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assert(isa<ConstantInt>(Result) && "Cast of integer not folded??");
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return cast<ConstantInt>(Result);
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}
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/// PartialFact - Compute V!/(V-NumSteps)!
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static SCEVHandle PartialFact(SCEVHandle V, unsigned NumSteps) {
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// Handle this case efficiently, it is common to have constant iteration
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// counts while computing loop exit values.
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if (SCEVConstant *SC = dyn_cast<SCEVConstant>(V)) {
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|
uint64_t Val = SC->getValue()->getRawValue();
|
|
uint64_t Result = 1;
|
|
for (; NumSteps; --NumSteps)
|
|
Result *= Val-(NumSteps-1);
|
|
Constant *Res = ConstantUInt::get(Type::ULongTy, Result);
|
|
return SCEVUnknown::get(ConstantExpr::getCast(Res, V->getType()));
|
|
}
|
|
|
|
const Type *Ty = V->getType();
|
|
if (NumSteps == 0)
|
|
return SCEVUnknown::getIntegerSCEV(1, Ty);
|
|
|
|
SCEVHandle Result = V;
|
|
for (unsigned i = 1; i != NumSteps; ++i)
|
|
Result = SCEVMulExpr::get(Result, getMinusSCEV(V,
|
|
SCEVUnknown::getIntegerSCEV(i, Ty)));
|
|
return Result;
|
|
}
|
|
|
|
|
|
/// evaluateAtIteration - Return the value of this chain of recurrences at
|
|
/// the specified iteration number. We can evaluate this recurrence by
|
|
/// multiplying each element in the chain by the binomial coefficient
|
|
/// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
|
|
///
|
|
/// A*choose(It, 0) + B*choose(It, 1) + C*choose(It, 2) + D*choose(It, 3)
|
|
///
|
|
/// FIXME/VERIFY: I don't trust that this is correct in the face of overflow.
|
|
/// Is the binomial equation safe using modular arithmetic??
|
|
///
|
|
SCEVHandle SCEVAddRecExpr::evaluateAtIteration(SCEVHandle It) const {
|
|
SCEVHandle Result = getStart();
|
|
int Divisor = 1;
|
|
const Type *Ty = It->getType();
|
|
for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
|
|
SCEVHandle BC = PartialFact(It, i);
|
|
Divisor *= i;
|
|
SCEVHandle Val = SCEVUDivExpr::get(SCEVMulExpr::get(BC, getOperand(i)),
|
|
SCEVUnknown::getIntegerSCEV(Divisor,Ty));
|
|
Result = SCEVAddExpr::get(Result, Val);
|
|
}
|
|
return Result;
|
|
}
|
|
|
|
|
|
//===----------------------------------------------------------------------===//
|
|
// SCEV Expression folder implementations
|
|
//===----------------------------------------------------------------------===//
|
|
|
|
SCEVHandle SCEVTruncateExpr::get(const SCEVHandle &Op, const Type *Ty) {
|
|
if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
|
|
return SCEVUnknown::get(ConstantExpr::getCast(SC->getValue(), Ty));
|
|
|
|
// If the input value is a chrec scev made out of constants, truncate
|
|
// all of the constants.
|
|
if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
|
|
std::vector<SCEVHandle> Operands;
|
|
for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
|
|
// FIXME: This should allow truncation of other expression types!
|
|
if (isa<SCEVConstant>(AddRec->getOperand(i)))
|
|
Operands.push_back(get(AddRec->getOperand(i), Ty));
|
|
else
|
|
break;
|
|
if (Operands.size() == AddRec->getNumOperands())
|
|
return SCEVAddRecExpr::get(Operands, AddRec->getLoop());
|
|
}
|
|
|
|
SCEVTruncateExpr *&Result = SCEVTruncates[std::make_pair(Op, Ty)];
|
|
if (Result == 0) Result = new SCEVTruncateExpr(Op, Ty);
|
|
return Result;
|
|
}
|
|
|
|
SCEVHandle SCEVZeroExtendExpr::get(const SCEVHandle &Op, const Type *Ty) {
|
|
if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
|
|
return SCEVUnknown::get(ConstantExpr::getCast(SC->getValue(), Ty));
|
|
|
|
// FIXME: If the input value is a chrec scev, and we can prove that the value
|
|
// did not overflow the old, smaller, value, we can zero extend all of the
|
|
// operands (often constants). This would allow analysis of something like
|
|
// this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
|
|
|
|
SCEVZeroExtendExpr *&Result = SCEVZeroExtends[std::make_pair(Op, Ty)];
|
|
if (Result == 0) Result = new SCEVZeroExtendExpr(Op, Ty);
|
|
return Result;
|
|
}
|
|
|
|
// get - Get a canonical add expression, or something simpler if possible.
|
|
SCEVHandle SCEVAddExpr::get(std::vector<SCEVHandle> &Ops) {
|
|
assert(!Ops.empty() && "Cannot get empty add!");
|
|
if (Ops.size() == 1) return Ops[0];
|
|
|
|
// Sort by complexity, this groups all similar expression types together.
|
|
GroupByComplexity(Ops);
|
|
|
|
// If there are any constants, fold them together.
|
|
unsigned Idx = 0;
|
|
if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
|
|
++Idx;
|
|
assert(Idx < Ops.size());
|
|
while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
|
|
// We found two constants, fold them together!
|
|
Constant *Fold = ConstantExpr::getAdd(LHSC->getValue(), RHSC->getValue());
|
|
if (ConstantInt *CI = dyn_cast<ConstantInt>(Fold)) {
|
|
Ops[0] = SCEVConstant::get(CI);
|
|
Ops.erase(Ops.begin()+1); // Erase the folded element
|
|
if (Ops.size() == 1) return Ops[0];
|
|
} else {
|
|
// If we couldn't fold the expression, move to the next constant. Note
|
|
// that this is impossible to happen in practice because we always
|
|
// constant fold constant ints to constant ints.
|
|
++Idx;
|
|
}
|
|
}
|
|
|
|
// If we are left with a constant zero being added, strip it off.
|
|
if (cast<SCEVConstant>(Ops[0])->getValue()->isNullValue()) {
|
|
Ops.erase(Ops.begin());
|
|
--Idx;
|
|
}
|
|
}
|
|
|
|
if (Ops.size() == 1) return Ops[0];
|
|
|
|
// Okay, check to see if the same value occurs in the operand list twice. If
|
|
// so, merge them together into an multiply expression. Since we sorted the
|
|
// list, these values are required to be adjacent.
|
|
const Type *Ty = Ops[0]->getType();
|
|
for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
|
|
if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
|
|
// Found a match, merge the two values into a multiply, and add any
|
|
// remaining values to the result.
|
|
SCEVHandle Two = SCEVUnknown::getIntegerSCEV(2, Ty);
|
|
SCEVHandle Mul = SCEVMulExpr::get(Ops[i], Two);
|
|
if (Ops.size() == 2)
|
|
return Mul;
|
|
Ops.erase(Ops.begin()+i, Ops.begin()+i+2);
|
|
Ops.push_back(Mul);
|
|
return SCEVAddExpr::get(Ops);
|
|
}
|
|
|
|
// Okay, now we know the first non-constant operand. If there are add
|
|
// operands they would be next.
|
|
if (Idx < Ops.size()) {
|
|
bool DeletedAdd = false;
|
|
while (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
|
|
// If we have an add, expand the add operands onto the end of the operands
|
|
// list.
|
|
Ops.insert(Ops.end(), Add->op_begin(), Add->op_end());
|
|
Ops.erase(Ops.begin()+Idx);
|
|
DeletedAdd = true;
|
|
}
|
|
|
|
// If we deleted at least one add, we added operands to the end of the list,
|
|
// and they are not necessarily sorted. Recurse to resort and resimplify
|
|
// any operands we just aquired.
|
|
if (DeletedAdd)
|
|
return get(Ops);
|
|
}
|
|
|
|
// Skip over the add expression until we get to a multiply.
|
|
while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
|
|
++Idx;
|
|
|
|
// If we are adding something to a multiply expression, make sure the
|
|
// something is not already an operand of the multiply. If so, merge it into
|
|
// the multiply.
|
|
for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
|
|
SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
|
|
for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
|
|
SCEV *MulOpSCEV = Mul->getOperand(MulOp);
|
|
for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
|
|
if (MulOpSCEV == Ops[AddOp] &&
|
|
(Mul->getNumOperands() != 2 || !isa<SCEVConstant>(MulOpSCEV))) {
|
|
// Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
|
|
SCEVHandle InnerMul = Mul->getOperand(MulOp == 0);
|
|
if (Mul->getNumOperands() != 2) {
|
|
// If the multiply has more than two operands, we must get the
|
|
// Y*Z term.
|
|
std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end());
|
|
MulOps.erase(MulOps.begin()+MulOp);
|
|
InnerMul = SCEVMulExpr::get(MulOps);
|
|
}
|
|
SCEVHandle One = SCEVUnknown::getIntegerSCEV(1, Ty);
|
|
SCEVHandle AddOne = SCEVAddExpr::get(InnerMul, One);
|
|
SCEVHandle OuterMul = SCEVMulExpr::get(AddOne, Ops[AddOp]);
|
|
if (Ops.size() == 2) return OuterMul;
|
|
if (AddOp < Idx) {
|
|
Ops.erase(Ops.begin()+AddOp);
|
|
Ops.erase(Ops.begin()+Idx-1);
|
|
} else {
|
|
Ops.erase(Ops.begin()+Idx);
|
|
Ops.erase(Ops.begin()+AddOp-1);
|
|
}
|
|
Ops.push_back(OuterMul);
|
|
return SCEVAddExpr::get(Ops);
|
|
}
|
|
|
|
// Check this multiply against other multiplies being added together.
|
|
for (unsigned OtherMulIdx = Idx+1;
|
|
OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
|
|
++OtherMulIdx) {
|
|
SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
|
|
// If MulOp occurs in OtherMul, we can fold the two multiplies
|
|
// together.
|
|
for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
|
|
OMulOp != e; ++OMulOp)
|
|
if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
|
|
// Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
|
|
SCEVHandle InnerMul1 = Mul->getOperand(MulOp == 0);
|
|
if (Mul->getNumOperands() != 2) {
|
|
std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end());
|
|
MulOps.erase(MulOps.begin()+MulOp);
|
|
InnerMul1 = SCEVMulExpr::get(MulOps);
|
|
}
|
|
SCEVHandle InnerMul2 = OtherMul->getOperand(OMulOp == 0);
|
|
if (OtherMul->getNumOperands() != 2) {
|
|
std::vector<SCEVHandle> MulOps(OtherMul->op_begin(),
|
|
OtherMul->op_end());
|
|
MulOps.erase(MulOps.begin()+OMulOp);
|
|
InnerMul2 = SCEVMulExpr::get(MulOps);
|
|
}
|
|
SCEVHandle InnerMulSum = SCEVAddExpr::get(InnerMul1,InnerMul2);
|
|
SCEVHandle OuterMul = SCEVMulExpr::get(MulOpSCEV, InnerMulSum);
|
|
if (Ops.size() == 2) return OuterMul;
|
|
Ops.erase(Ops.begin()+Idx);
|
|
Ops.erase(Ops.begin()+OtherMulIdx-1);
|
|
Ops.push_back(OuterMul);
|
|
return SCEVAddExpr::get(Ops);
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
// If there are any add recurrences in the operands list, see if any other
|
|
// added values are loop invariant. If so, we can fold them into the
|
|
// recurrence.
|
|
while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
|
|
++Idx;
|
|
|
|
// Scan over all recurrences, trying to fold loop invariants into them.
|
|
for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
|
|
// Scan all of the other operands to this add and add them to the vector if
|
|
// they are loop invariant w.r.t. the recurrence.
|
|
std::vector<SCEVHandle> LIOps;
|
|
SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
|
|
for (unsigned i = 0, e = Ops.size(); i != e; ++i)
|
|
if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
|
|
LIOps.push_back(Ops[i]);
|
|
Ops.erase(Ops.begin()+i);
|
|
--i; --e;
|
|
}
|
|
|
|
// If we found some loop invariants, fold them into the recurrence.
|
|
if (!LIOps.empty()) {
|
|
// NLI + LI + { Start,+,Step} --> NLI + { LI+Start,+,Step }
|
|
LIOps.push_back(AddRec->getStart());
|
|
|
|
std::vector<SCEVHandle> AddRecOps(AddRec->op_begin(), AddRec->op_end());
|
|
AddRecOps[0] = SCEVAddExpr::get(LIOps);
|
|
|
|
SCEVHandle NewRec = SCEVAddRecExpr::get(AddRecOps, AddRec->getLoop());
|
|
// If all of the other operands were loop invariant, we are done.
|
|
if (Ops.size() == 1) return NewRec;
|
|
|
|
// Otherwise, add the folded AddRec by the non-liv parts.
|
|
for (unsigned i = 0;; ++i)
|
|
if (Ops[i] == AddRec) {
|
|
Ops[i] = NewRec;
|
|
break;
|
|
}
|
|
return SCEVAddExpr::get(Ops);
|
|
}
|
|
|
|
// Okay, if there weren't any loop invariants to be folded, check to see if
|
|
// there are multiple AddRec's with the same loop induction variable being
|
|
// added together. If so, we can fold them.
|
|
for (unsigned OtherIdx = Idx+1;
|
|
OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
|
|
if (OtherIdx != Idx) {
|
|
SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
|
|
if (AddRec->getLoop() == OtherAddRec->getLoop()) {
|
|
// Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D}
|
|
std::vector<SCEVHandle> NewOps(AddRec->op_begin(), AddRec->op_end());
|
|
for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) {
|
|
if (i >= NewOps.size()) {
|
|
NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i,
|
|
OtherAddRec->op_end());
|
|
break;
|
|
}
|
|
NewOps[i] = SCEVAddExpr::get(NewOps[i], OtherAddRec->getOperand(i));
|
|
}
|
|
SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewOps, AddRec->getLoop());
|
|
|
|
if (Ops.size() == 2) return NewAddRec;
|
|
|
|
Ops.erase(Ops.begin()+Idx);
|
|
Ops.erase(Ops.begin()+OtherIdx-1);
|
|
Ops.push_back(NewAddRec);
|
|
return SCEVAddExpr::get(Ops);
|
|
}
|
|
}
|
|
|
|
// Otherwise couldn't fold anything into this recurrence. Move onto the
|
|
// next one.
|
|
}
|
|
|
|
// Okay, it looks like we really DO need an add expr. Check to see if we
|
|
// already have one, otherwise create a new one.
|
|
std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end());
|
|
SCEVCommutativeExpr *&Result = SCEVCommExprs[std::make_pair(scAddExpr,
|
|
SCEVOps)];
|
|
if (Result == 0) Result = new SCEVAddExpr(Ops);
|
|
return Result;
|
|
}
|
|
|
|
|
|
SCEVHandle SCEVMulExpr::get(std::vector<SCEVHandle> &Ops) {
|
|
assert(!Ops.empty() && "Cannot get empty mul!");
|
|
|
|
// Sort by complexity, this groups all similar expression types together.
|
|
GroupByComplexity(Ops);
|
|
|
|
// If there are any constants, fold them together.
|
|
unsigned Idx = 0;
|
|
if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
|
|
|
|
// C1*(C2+V) -> C1*C2 + C1*V
|
|
if (Ops.size() == 2)
|
|
if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
|
|
if (Add->getNumOperands() == 2 &&
|
|
isa<SCEVConstant>(Add->getOperand(0)))
|
|
return SCEVAddExpr::get(SCEVMulExpr::get(LHSC, Add->getOperand(0)),
|
|
SCEVMulExpr::get(LHSC, Add->getOperand(1)));
|
|
|
|
|
|
++Idx;
|
|
while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
|
|
// We found two constants, fold them together!
|
|
Constant *Fold = ConstantExpr::getMul(LHSC->getValue(), RHSC->getValue());
|
|
if (ConstantInt *CI = dyn_cast<ConstantInt>(Fold)) {
|
|
Ops[0] = SCEVConstant::get(CI);
|
|
Ops.erase(Ops.begin()+1); // Erase the folded element
|
|
if (Ops.size() == 1) return Ops[0];
|
|
} else {
|
|
// If we couldn't fold the expression, move to the next constant. Note
|
|
// that this is impossible to happen in practice because we always
|
|
// constant fold constant ints to constant ints.
|
|
++Idx;
|
|
}
|
|
}
|
|
|
|
// If we are left with a constant one being multiplied, strip it off.
|
|
if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
|
|
Ops.erase(Ops.begin());
|
|
--Idx;
|
|
} else if (cast<SCEVConstant>(Ops[0])->getValue()->isNullValue()) {
|
|
// If we have a multiply of zero, it will always be zero.
|
|
return Ops[0];
|
|
}
|
|
}
|
|
|
|
// Skip over the add expression until we get to a multiply.
|
|
while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
|
|
++Idx;
|
|
|
|
if (Ops.size() == 1)
|
|
return Ops[0];
|
|
|
|
// If there are mul operands inline them all into this expression.
|
|
if (Idx < Ops.size()) {
|
|
bool DeletedMul = false;
|
|
while (SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
|
|
// If we have an mul, expand the mul operands onto the end of the operands
|
|
// list.
|
|
Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end());
|
|
Ops.erase(Ops.begin()+Idx);
|
|
DeletedMul = true;
|
|
}
|
|
|
|
// If we deleted at least one mul, we added operands to the end of the list,
|
|
// and they are not necessarily sorted. Recurse to resort and resimplify
|
|
// any operands we just aquired.
|
|
if (DeletedMul)
|
|
return get(Ops);
|
|
}
|
|
|
|
// If there are any add recurrences in the operands list, see if any other
|
|
// added values are loop invariant. If so, we can fold them into the
|
|
// recurrence.
|
|
while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
|
|
++Idx;
|
|
|
|
// Scan over all recurrences, trying to fold loop invariants into them.
|
|
for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
|
|
// Scan all of the other operands to this mul and add them to the vector if
|
|
// they are loop invariant w.r.t. the recurrence.
|
|
std::vector<SCEVHandle> LIOps;
|
|
SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
|
|
for (unsigned i = 0, e = Ops.size(); i != e; ++i)
|
|
if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
|
|
LIOps.push_back(Ops[i]);
|
|
Ops.erase(Ops.begin()+i);
|
|
--i; --e;
|
|
}
|
|
|
|
// If we found some loop invariants, fold them into the recurrence.
|
|
if (!LIOps.empty()) {
|
|
// NLI * LI * { Start,+,Step} --> NLI * { LI*Start,+,LI*Step }
|
|
std::vector<SCEVHandle> NewOps;
|
|
NewOps.reserve(AddRec->getNumOperands());
|
|
if (LIOps.size() == 1) {
|
|
SCEV *Scale = LIOps[0];
|
|
for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
|
|
NewOps.push_back(SCEVMulExpr::get(Scale, AddRec->getOperand(i)));
|
|
} else {
|
|
for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
|
|
std::vector<SCEVHandle> MulOps(LIOps);
|
|
MulOps.push_back(AddRec->getOperand(i));
|
|
NewOps.push_back(SCEVMulExpr::get(MulOps));
|
|
}
|
|
}
|
|
|
|
SCEVHandle NewRec = SCEVAddRecExpr::get(NewOps, AddRec->getLoop());
|
|
|
|
// If all of the other operands were loop invariant, we are done.
|
|
if (Ops.size() == 1) return NewRec;
|
|
|
|
// Otherwise, multiply the folded AddRec by the non-liv parts.
|
|
for (unsigned i = 0;; ++i)
|
|
if (Ops[i] == AddRec) {
|
|
Ops[i] = NewRec;
|
|
break;
|
|
}
|
|
return SCEVMulExpr::get(Ops);
|
|
}
|
|
|
|
// Okay, if there weren't any loop invariants to be folded, check to see if
|
|
// there are multiple AddRec's with the same loop induction variable being
|
|
// multiplied together. If so, we can fold them.
|
|
for (unsigned OtherIdx = Idx+1;
|
|
OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
|
|
if (OtherIdx != Idx) {
|
|
SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
|
|
if (AddRec->getLoop() == OtherAddRec->getLoop()) {
|
|
// F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D}
|
|
SCEVAddRecExpr *F = AddRec, *G = OtherAddRec;
|
|
SCEVHandle NewStart = SCEVMulExpr::get(F->getStart(),
|
|
G->getStart());
|
|
SCEVHandle B = F->getStepRecurrence();
|
|
SCEVHandle D = G->getStepRecurrence();
|
|
SCEVHandle NewStep = SCEVAddExpr::get(SCEVMulExpr::get(F, D),
|
|
SCEVMulExpr::get(G, B),
|
|
SCEVMulExpr::get(B, D));
|
|
SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewStart, NewStep,
|
|
F->getLoop());
|
|
if (Ops.size() == 2) return NewAddRec;
|
|
|
|
Ops.erase(Ops.begin()+Idx);
|
|
Ops.erase(Ops.begin()+OtherIdx-1);
|
|
Ops.push_back(NewAddRec);
|
|
return SCEVMulExpr::get(Ops);
|
|
}
|
|
}
|
|
|
|
// Otherwise couldn't fold anything into this recurrence. Move onto the
|
|
// next one.
|
|
}
|
|
|
|
// Okay, it looks like we really DO need an mul expr. Check to see if we
|
|
// already have one, otherwise create a new one.
|
|
std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end());
|
|
SCEVCommutativeExpr *&Result = SCEVCommExprs[std::make_pair(scMulExpr,
|
|
SCEVOps)];
|
|
if (Result == 0) Result = new SCEVMulExpr(Ops);
|
|
return Result;
|
|
}
|
|
|
|
SCEVHandle SCEVUDivExpr::get(const SCEVHandle &LHS, const SCEVHandle &RHS) {
|
|
if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
|
|
if (RHSC->getValue()->equalsInt(1))
|
|
return LHS; // X /u 1 --> x
|
|
if (RHSC->getValue()->isAllOnesValue())
|
|
return getNegativeSCEV(LHS); // X /u -1 --> -x
|
|
|
|
if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
|
|
Constant *LHSCV = LHSC->getValue();
|
|
Constant *RHSCV = RHSC->getValue();
|
|
if (LHSCV->getType()->isSigned())
|
|
LHSCV = ConstantExpr::getCast(LHSCV,
|
|
LHSCV->getType()->getUnsignedVersion());
|
|
if (RHSCV->getType()->isSigned())
|
|
RHSCV = ConstantExpr::getCast(RHSCV, LHSCV->getType());
|
|
return SCEVUnknown::get(ConstantExpr::getDiv(LHSCV, RHSCV));
|
|
}
|
|
}
|
|
|
|
// FIXME: implement folding of (X*4)/4 when we know X*4 doesn't overflow.
|
|
|
|
SCEVUDivExpr *&Result = SCEVUDivs[std::make_pair(LHS, RHS)];
|
|
if (Result == 0) Result = new SCEVUDivExpr(LHS, RHS);
|
|
return Result;
|
|
}
|
|
|
|
|
|
/// SCEVAddRecExpr::get - Get a add recurrence expression for the
|
|
/// specified loop. Simplify the expression as much as possible.
|
|
SCEVHandle SCEVAddRecExpr::get(const SCEVHandle &Start,
|
|
const SCEVHandle &Step, const Loop *L) {
|
|
std::vector<SCEVHandle> Operands;
|
|
Operands.push_back(Start);
|
|
if (SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
|
|
if (StepChrec->getLoop() == L) {
|
|
Operands.insert(Operands.end(), StepChrec->op_begin(),
|
|
StepChrec->op_end());
|
|
return get(Operands, L);
|
|
}
|
|
|
|
Operands.push_back(Step);
|
|
return get(Operands, L);
|
|
}
|
|
|
|
/// SCEVAddRecExpr::get - Get a add recurrence expression for the
|
|
/// specified loop. Simplify the expression as much as possible.
|
|
SCEVHandle SCEVAddRecExpr::get(std::vector<SCEVHandle> &Operands,
|
|
const Loop *L) {
|
|
if (Operands.size() == 1) return Operands[0];
|
|
|
|
if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Operands.back()))
|
|
if (StepC->getValue()->isNullValue()) {
|
|
Operands.pop_back();
|
|
return get(Operands, L); // { X,+,0 } --> X
|
|
}
|
|
|
|
SCEVAddRecExpr *&Result =
|
|
SCEVAddRecExprs[std::make_pair(L, std::vector<SCEV*>(Operands.begin(),
|
|
Operands.end()))];
|
|
if (Result == 0) Result = new SCEVAddRecExpr(Operands, L);
|
|
return Result;
|
|
}
|
|
|
|
SCEVHandle SCEVUnknown::get(Value *V) {
|
|
if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
|
|
return SCEVConstant::get(CI);
|
|
SCEVUnknown *&Result = SCEVUnknowns[V];
|
|
if (Result == 0) Result = new SCEVUnknown(V);
|
|
return Result;
|
|
}
|
|
|
|
|
|
//===----------------------------------------------------------------------===//
|
|
// ScalarEvolutionsImpl Definition and Implementation
|
|
//===----------------------------------------------------------------------===//
|
|
//
|
|
/// ScalarEvolutionsImpl - This class implements the main driver for the scalar
|
|
/// evolution code.
|
|
///
|
|
namespace {
|
|
struct ScalarEvolutionsImpl {
|
|
/// F - The function we are analyzing.
|
|
///
|
|
Function &F;
|
|
|
|
/// LI - The loop information for the function we are currently analyzing.
|
|
///
|
|
LoopInfo &LI;
|
|
|
|
/// UnknownValue - This SCEV is used to represent unknown trip counts and
|
|
/// things.
|
|
SCEVHandle UnknownValue;
|
|
|
|
/// Scalars - This is a cache of the scalars we have analyzed so far.
|
|
///
|
|
std::map<Value*, SCEVHandle> Scalars;
|
|
|
|
/// IterationCounts - Cache the iteration count of the loops for this
|
|
/// function as they are computed.
|
|
std::map<const Loop*, SCEVHandle> IterationCounts;
|
|
|
|
/// ConstantEvolutionLoopExitValue - This map contains entries for all of
|
|
/// the PHI instructions that we attempt to compute constant evolutions for.
|
|
/// This allows us to avoid potentially expensive recomputation of these
|
|
/// properties. An instruction maps to null if we are unable to compute its
|
|
/// exit value.
|
|
std::map<PHINode*, Constant*> ConstantEvolutionLoopExitValue;
|
|
|
|
public:
|
|
ScalarEvolutionsImpl(Function &f, LoopInfo &li)
|
|
: F(f), LI(li), UnknownValue(new SCEVCouldNotCompute()) {}
|
|
|
|
/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
|
|
/// expression and create a new one.
|
|
SCEVHandle getSCEV(Value *V);
|
|
|
|
/// getSCEVAtScope - Compute the value of the specified expression within
|
|
/// the indicated loop (which may be null to indicate in no loop). If the
|
|
/// expression cannot be evaluated, return UnknownValue itself.
|
|
SCEVHandle getSCEVAtScope(SCEV *V, const Loop *L);
|
|
|
|
|
|
/// hasLoopInvariantIterationCount - Return true if the specified loop has
|
|
/// an analyzable loop-invariant iteration count.
|
|
bool hasLoopInvariantIterationCount(const Loop *L);
|
|
|
|
/// getIterationCount - If the specified loop has a predictable iteration
|
|
/// count, return it. Note that it is not valid to call this method on a
|
|
/// loop without a loop-invariant iteration count.
|
|
SCEVHandle getIterationCount(const Loop *L);
|
|
|
|
/// deleteInstructionFromRecords - This method should be called by the
|
|
/// client before it removes an instruction from the program, to make sure
|
|
/// that no dangling references are left around.
|
|
void deleteInstructionFromRecords(Instruction *I);
|
|
|
|
private:
|
|
/// createSCEV - We know that there is no SCEV for the specified value.
|
|
/// Analyze the expression.
|
|
SCEVHandle createSCEV(Value *V);
|
|
SCEVHandle createNodeForCast(CastInst *CI);
|
|
|
|
/// createNodeForPHI - Provide the special handling we need to analyze PHI
|
|
/// SCEVs.
|
|
SCEVHandle createNodeForPHI(PHINode *PN);
|
|
void UpdatePHIUserScalarEntries(Instruction *I, PHINode *PN,
|
|
std::set<Instruction*> &UpdatedInsts);
|
|
|
|
/// ComputeIterationCount - Compute the number of times the specified loop
|
|
/// will iterate.
|
|
SCEVHandle ComputeIterationCount(const Loop *L);
|
|
|
|
/// ComputeLoadConstantCompareIterationCount - Given an exit condition of
|
|
/// 'setcc load X, cst', try to se if we can compute the trip count.
|
|
SCEVHandle ComputeLoadConstantCompareIterationCount(LoadInst *LI,
|
|
Constant *RHS,
|
|
const Loop *L,
|
|
unsigned SetCCOpcode);
|
|
|
|
/// ComputeIterationCountExhaustively - If the trip 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 UnknownValue.
|
|
SCEVHandle ComputeIterationCountExhaustively(const Loop *L, Value *Cond,
|
|
bool ExitWhen);
|
|
|
|
/// HowFarToZero - Return the number of times a backedge comparing the
|
|
/// specified value to zero will execute. If not computable, return
|
|
/// UnknownValue
|
|
SCEVHandle HowFarToZero(SCEV *V, const Loop *L);
|
|
|
|
/// HowFarToNonZero - Return the number of times a backedge checking the
|
|
/// specified value for nonzero will execute. If not computable, return
|
|
/// UnknownValue
|
|
SCEVHandle HowFarToNonZero(SCEV *V, const Loop *L);
|
|
|
|
/// 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 *getConstantEvolutionLoopExitValue(PHINode *PN, uint64_t Its,
|
|
const Loop *L);
|
|
};
|
|
}
|
|
|
|
//===----------------------------------------------------------------------===//
|
|
// Basic SCEV Analysis and PHI Idiom Recognition Code
|
|
//
|
|
|
|
/// deleteInstructionFromRecords - This method should be called by the
|
|
/// client before it removes an instruction from the program, to make sure
|
|
/// that no dangling references are left around.
|
|
void ScalarEvolutionsImpl::deleteInstructionFromRecords(Instruction *I) {
|
|
Scalars.erase(I);
|
|
if (PHINode *PN = dyn_cast<PHINode>(I))
|
|
ConstantEvolutionLoopExitValue.erase(PN);
|
|
}
|
|
|
|
|
|
/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
|
|
/// expression and create a new one.
|
|
SCEVHandle ScalarEvolutionsImpl::getSCEV(Value *V) {
|
|
assert(V->getType() != Type::VoidTy && "Can't analyze void expressions!");
|
|
|
|
std::map<Value*, SCEVHandle>::iterator I = Scalars.find(V);
|
|
if (I != Scalars.end()) return I->second;
|
|
SCEVHandle S = createSCEV(V);
|
|
Scalars.insert(std::make_pair(V, S));
|
|
return S;
|
|
}
|
|
|
|
|
|
/// UpdatePHIUserScalarEntries - After PHI node analysis, we have a bunch of
|
|
/// entries in the scalar map that refer to the "symbolic" PHI value instead of
|
|
/// the recurrence value. After we resolve the PHI we must loop over all of the
|
|
/// using instructions that have scalar map entries and update them.
|
|
void ScalarEvolutionsImpl::UpdatePHIUserScalarEntries(Instruction *I,
|
|
PHINode *PN,
|
|
std::set<Instruction*> &UpdatedInsts) {
|
|
std::map<Value*, SCEVHandle>::iterator SI = Scalars.find(I);
|
|
if (SI == Scalars.end()) return; // This scalar wasn't previous processed.
|
|
if (UpdatedInsts.insert(I).second) {
|
|
Scalars.erase(SI); // Remove the old entry
|
|
getSCEV(I); // Calculate the new entry
|
|
|
|
for (Value::use_iterator UI = I->use_begin(), E = I->use_end();
|
|
UI != E; ++UI)
|
|
UpdatePHIUserScalarEntries(cast<Instruction>(*UI), PN, UpdatedInsts);
|
|
}
|
|
}
|
|
|
|
|
|
/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
|
|
/// a loop header, making it a potential recurrence, or it doesn't.
|
|
///
|
|
SCEVHandle ScalarEvolutionsImpl::createNodeForPHI(PHINode *PN) {
|
|
if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized.
|
|
if (const Loop *L = LI.getLoopFor(PN->getParent()))
|
|
if (L->getHeader() == PN->getParent()) {
|
|
// If it lives in the loop header, it has two incoming values, one
|
|
// from outside the loop, and one from inside.
|
|
unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0));
|
|
unsigned BackEdge = IncomingEdge^1;
|
|
|
|
// While we are analyzing this PHI node, handle its value symbolically.
|
|
SCEVHandle SymbolicName = SCEVUnknown::get(PN);
|
|
assert(Scalars.find(PN) == Scalars.end() &&
|
|
"PHI node already processed?");
|
|
Scalars.insert(std::make_pair(PN, SymbolicName));
|
|
|
|
// Using this symbolic name for the PHI, analyze the value coming around
|
|
// the back-edge.
|
|
SCEVHandle BEValue = getSCEV(PN->getIncomingValue(BackEdge));
|
|
|
|
// NOTE: If BEValue is loop invariant, we know that the PHI node just
|
|
// has a special value for the first iteration of the loop.
|
|
|
|
// If the value coming around the backedge is an add with the symbolic
|
|
// value we just inserted, then we found a simple induction variable!
|
|
if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
|
|
// If there is a single occurrence of the symbolic value, replace it
|
|
// with a recurrence.
|
|
unsigned FoundIndex = Add->getNumOperands();
|
|
for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
|
|
if (Add->getOperand(i) == SymbolicName)
|
|
if (FoundIndex == e) {
|
|
FoundIndex = i;
|
|
break;
|
|
}
|
|
|
|
if (FoundIndex != Add->getNumOperands()) {
|
|
// Create an add with everything but the specified operand.
|
|
std::vector<SCEVHandle> Ops;
|
|
for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
|
|
if (i != FoundIndex)
|
|
Ops.push_back(Add->getOperand(i));
|
|
SCEVHandle Accum = SCEVAddExpr::get(Ops);
|
|
|
|
// This is not a valid addrec if the step amount is varying each
|
|
// loop iteration, but is not itself an addrec in this loop.
|
|
if (Accum->isLoopInvariant(L) ||
|
|
(isa<SCEVAddRecExpr>(Accum) &&
|
|
cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
|
|
SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
|
|
SCEVHandle PHISCEV = SCEVAddRecExpr::get(StartVal, Accum, L);
|
|
|
|
// Okay, for the entire analysis of this edge we assumed the PHI
|
|
// to be symbolic. We now need to go back and update all of the
|
|
// entries for the scalars that use the PHI (except for the PHI
|
|
// itself) to use the new analyzed value instead of the "symbolic"
|
|
// value.
|
|
Scalars.find(PN)->second = PHISCEV; // Update the PHI value
|
|
std::set<Instruction*> UpdatedInsts;
|
|
UpdatedInsts.insert(PN);
|
|
for (Value::use_iterator UI = PN->use_begin(), E = PN->use_end();
|
|
UI != E; ++UI)
|
|
UpdatePHIUserScalarEntries(cast<Instruction>(*UI), PN,
|
|
UpdatedInsts);
|
|
return PHISCEV;
|
|
}
|
|
}
|
|
}
|
|
|
|
return SymbolicName;
|
|
}
|
|
|
|
// If it's not a loop phi, we can't handle it yet.
|
|
return SCEVUnknown::get(PN);
|
|
}
|
|
|
|
/// createNodeForCast - Handle the various forms of casts that we support.
|
|
///
|
|
SCEVHandle ScalarEvolutionsImpl::createNodeForCast(CastInst *CI) {
|
|
const Type *SrcTy = CI->getOperand(0)->getType();
|
|
const Type *DestTy = CI->getType();
|
|
|
|
// If this is a noop cast (ie, conversion from int to uint), ignore it.
|
|
if (SrcTy->isLosslesslyConvertibleTo(DestTy))
|
|
return getSCEV(CI->getOperand(0));
|
|
|
|
if (SrcTy->isInteger() && DestTy->isInteger()) {
|
|
// Otherwise, if this is a truncating integer cast, we can represent this
|
|
// cast.
|
|
if (SrcTy->getPrimitiveSize() > DestTy->getPrimitiveSize())
|
|
return SCEVTruncateExpr::get(getSCEV(CI->getOperand(0)),
|
|
CI->getType()->getUnsignedVersion());
|
|
if (SrcTy->isUnsigned() &&
|
|
SrcTy->getPrimitiveSize() > DestTy->getPrimitiveSize())
|
|
return SCEVZeroExtendExpr::get(getSCEV(CI->getOperand(0)),
|
|
CI->getType()->getUnsignedVersion());
|
|
}
|
|
|
|
// If this is an sign or zero extending cast and we can prove that the value
|
|
// will never overflow, we could do similar transformations.
|
|
|
|
// Otherwise, we can't handle this cast!
|
|
return SCEVUnknown::get(CI);
|
|
}
|
|
|
|
|
|
/// createSCEV - We know that there is no SCEV for the specified value.
|
|
/// Analyze the expression.
|
|
///
|
|
SCEVHandle ScalarEvolutionsImpl::createSCEV(Value *V) {
|
|
if (Instruction *I = dyn_cast<Instruction>(V)) {
|
|
switch (I->getOpcode()) {
|
|
case Instruction::Add:
|
|
return SCEVAddExpr::get(getSCEV(I->getOperand(0)),
|
|
getSCEV(I->getOperand(1)));
|
|
case Instruction::Mul:
|
|
return SCEVMulExpr::get(getSCEV(I->getOperand(0)),
|
|
getSCEV(I->getOperand(1)));
|
|
case Instruction::Div:
|
|
if (V->getType()->isInteger() && V->getType()->isUnsigned())
|
|
return SCEVUDivExpr::get(getSCEV(I->getOperand(0)),
|
|
getSCEV(I->getOperand(1)));
|
|
break;
|
|
|
|
case Instruction::Sub:
|
|
return getMinusSCEV(getSCEV(I->getOperand(0)), getSCEV(I->getOperand(1)));
|
|
|
|
case Instruction::Shl:
|
|
// Turn shift left of a constant amount into a multiply.
|
|
if (ConstantInt *SA = dyn_cast<ConstantInt>(I->getOperand(1))) {
|
|
Constant *X = ConstantInt::get(V->getType(), 1);
|
|
X = ConstantExpr::getShl(X, SA);
|
|
return SCEVMulExpr::get(getSCEV(I->getOperand(0)), getSCEV(X));
|
|
}
|
|
break;
|
|
|
|
case Instruction::Shr:
|
|
if (ConstantUInt *SA = dyn_cast<ConstantUInt>(I->getOperand(1)))
|
|
if (V->getType()->isUnsigned()) {
|
|
Constant *X = ConstantInt::get(V->getType(), 1);
|
|
X = ConstantExpr::getShl(X, SA);
|
|
return SCEVUDivExpr::get(getSCEV(I->getOperand(0)), getSCEV(X));
|
|
}
|
|
break;
|
|
|
|
case Instruction::Cast:
|
|
return createNodeForCast(cast<CastInst>(I));
|
|
|
|
case Instruction::PHI:
|
|
return createNodeForPHI(cast<PHINode>(I));
|
|
|
|
default: // We cannot analyze this expression.
|
|
break;
|
|
}
|
|
}
|
|
|
|
return SCEVUnknown::get(V);
|
|
}
|
|
|
|
|
|
|
|
//===----------------------------------------------------------------------===//
|
|
// Iteration Count Computation Code
|
|
//
|
|
|
|
/// getIterationCount - If the specified loop has a predictable iteration
|
|
/// count, return it. Note that it is not valid to call this method on a
|
|
/// loop without a loop-invariant iteration count.
|
|
SCEVHandle ScalarEvolutionsImpl::getIterationCount(const Loop *L) {
|
|
std::map<const Loop*, SCEVHandle>::iterator I = IterationCounts.find(L);
|
|
if (I == IterationCounts.end()) {
|
|
SCEVHandle ItCount = ComputeIterationCount(L);
|
|
I = IterationCounts.insert(std::make_pair(L, ItCount)).first;
|
|
if (ItCount != UnknownValue) {
|
|
assert(ItCount->isLoopInvariant(L) &&
|
|
"Computed trip count isn't loop invariant for loop!");
|
|
++NumTripCountsComputed;
|
|
} else if (isa<PHINode>(L->getHeader()->begin())) {
|
|
// Only count loops that have phi nodes as not being computable.
|
|
++NumTripCountsNotComputed;
|
|
}
|
|
}
|
|
return I->second;
|
|
}
|
|
|
|
/// ComputeIterationCount - Compute the number of times the specified loop
|
|
/// will iterate.
|
|
SCEVHandle ScalarEvolutionsImpl::ComputeIterationCount(const Loop *L) {
|
|
// If the loop has a non-one exit block count, we can't analyze it.
|
|
std::vector<BasicBlock*> ExitBlocks;
|
|
L->getExitBlocks(ExitBlocks);
|
|
if (ExitBlocks.size() != 1) return UnknownValue;
|
|
|
|
// Okay, there is one exit block. Try to find the condition that causes the
|
|
// loop to be exited.
|
|
BasicBlock *ExitBlock = ExitBlocks[0];
|
|
|
|
BasicBlock *ExitingBlock = 0;
|
|
for (pred_iterator PI = pred_begin(ExitBlock), E = pred_end(ExitBlock);
|
|
PI != E; ++PI)
|
|
if (L->contains(*PI)) {
|
|
if (ExitingBlock == 0)
|
|
ExitingBlock = *PI;
|
|
else
|
|
return UnknownValue; // More than one block exiting!
|
|
}
|
|
assert(ExitingBlock && "No exits from loop, something is broken!");
|
|
|
|
// Okay, we've computed the exiting block. See what condition causes us to
|
|
// exit.
|
|
//
|
|
// FIXME: we should be able to handle switch instructions (with a single exit)
|
|
// FIXME: We should handle cast of int to bool as well
|
|
BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
|
|
if (ExitBr == 0) return UnknownValue;
|
|
assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
|
|
SetCondInst *ExitCond = dyn_cast<SetCondInst>(ExitBr->getCondition());
|
|
if (ExitCond == 0) // Not a setcc
|
|
return ComputeIterationCountExhaustively(L, ExitBr->getCondition(),
|
|
ExitBr->getSuccessor(0) == ExitBlock);
|
|
|
|
// If the condition was exit on true, convert the condition to exit on false.
|
|
Instruction::BinaryOps Cond;
|
|
if (ExitBr->getSuccessor(1) == ExitBlock)
|
|
Cond = ExitCond->getOpcode();
|
|
else
|
|
Cond = ExitCond->getInverseCondition();
|
|
|
|
// 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))) {
|
|
SCEVHandle ItCnt =
|
|
ComputeLoadConstantCompareIterationCount(LI, RHS, L, Cond);
|
|
if (!isa<SCEVCouldNotCompute>(ItCnt)) return ItCnt;
|
|
}
|
|
|
|
SCEVHandle LHS = getSCEV(ExitCond->getOperand(0));
|
|
SCEVHandle RHS = getSCEV(ExitCond->getOperand(1));
|
|
|
|
// Try to evaluate any dependencies out of the loop.
|
|
SCEVHandle Tmp = getSCEVAtScope(LHS, L);
|
|
if (!isa<SCEVCouldNotCompute>(Tmp)) LHS = Tmp;
|
|
Tmp = getSCEVAtScope(RHS, L);
|
|
if (!isa<SCEVCouldNotCompute>(Tmp)) RHS = Tmp;
|
|
|
|
// At this point, we would like to compute how many iterations of the loop the
|
|
// predicate will return true for these inputs.
|
|
if (isa<SCEVConstant>(LHS) && !isa<SCEVConstant>(RHS)) {
|
|
// If there is a constant, force it into the RHS.
|
|
std::swap(LHS, RHS);
|
|
Cond = SetCondInst::getSwappedCondition(Cond);
|
|
}
|
|
|
|
// FIXME: think about handling pointer comparisons! i.e.:
|
|
// while (P != P+100) ++P;
|
|
|
|
// If we have a comparison of a chrec against a constant, try to use value
|
|
// ranges to answer this query.
|
|
if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
|
|
if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
|
|
if (AddRec->getLoop() == L) {
|
|
// Form the comparison range using the constant of the correct type so
|
|
// that the ConstantRange class knows to do a signed or unsigned
|
|
// comparison.
|
|
ConstantInt *CompVal = RHSC->getValue();
|
|
const Type *RealTy = ExitCond->getOperand(0)->getType();
|
|
CompVal = dyn_cast<ConstantInt>(ConstantExpr::getCast(CompVal, RealTy));
|
|
if (CompVal) {
|
|
// Form the constant range.
|
|
ConstantRange CompRange(Cond, CompVal);
|
|
|
|
// Now that we have it, if it's signed, convert it to an unsigned
|
|
// range.
|
|
if (CompRange.getLower()->getType()->isSigned()) {
|
|
const Type *NewTy = RHSC->getValue()->getType();
|
|
Constant *NewL = ConstantExpr::getCast(CompRange.getLower(), NewTy);
|
|
Constant *NewU = ConstantExpr::getCast(CompRange.getUpper(), NewTy);
|
|
CompRange = ConstantRange(NewL, NewU);
|
|
}
|
|
|
|
SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange);
|
|
if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
|
|
}
|
|
}
|
|
|
|
switch (Cond) {
|
|
case Instruction::SetNE: // while (X != Y)
|
|
// Convert to: while (X-Y != 0)
|
|
if (LHS->getType()->isInteger()) {
|
|
SCEVHandle TC = HowFarToZero(getMinusSCEV(LHS, RHS), L);
|
|
if (!isa<SCEVCouldNotCompute>(TC)) return TC;
|
|
}
|
|
break;
|
|
case Instruction::SetEQ:
|
|
// Convert to: while (X-Y == 0) // while (X == Y)
|
|
if (LHS->getType()->isInteger()) {
|
|
SCEVHandle TC = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
|
|
if (!isa<SCEVCouldNotCompute>(TC)) return TC;
|
|
}
|
|
break;
|
|
default:
|
|
#if 0
|
|
std::cerr << "ComputeIterationCount ";
|
|
if (ExitCond->getOperand(0)->getType()->isUnsigned())
|
|
std::cerr << "[unsigned] ";
|
|
std::cerr << *LHS << " "
|
|
<< Instruction::getOpcodeName(Cond) << " " << *RHS << "\n";
|
|
#endif
|
|
break;
|
|
}
|
|
|
|
return ComputeIterationCountExhaustively(L, ExitCond,
|
|
ExitBr->getSuccessor(0) == ExitBlock);
|
|
}
|
|
|
|
static ConstantInt *
|
|
EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, Constant *C) {
|
|
SCEVHandle InVal = SCEVConstant::get(cast<ConstantInt>(C));
|
|
SCEVHandle Val = AddRec->evaluateAtIteration(InVal);
|
|
assert(isa<SCEVConstant>(Val) &&
|
|
"Evaluation of SCEV at constant didn't fold correctly?");
|
|
return cast<SCEVConstant>(Val)->getValue();
|
|
}
|
|
|
|
/// 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(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]->getRawValue();
|
|
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 {
|
|
assert(0 && "Unknown constant aggregate type!");
|
|
}
|
|
return 0;
|
|
} else {
|
|
return 0; // Unknown initializer type
|
|
}
|
|
}
|
|
return Init;
|
|
}
|
|
|
|
/// ComputeLoadConstantCompareIterationCount - Given an exit condition of
|
|
/// 'setcc load X, cst', try to se if we can compute the trip count.
|
|
SCEVHandle ScalarEvolutionsImpl::
|
|
ComputeLoadConstantCompareIterationCount(LoadInst *LI, Constant *RHS,
|
|
const Loop *L, unsigned SetCCOpcode) {
|
|
if (LI->isVolatile()) return UnknownValue;
|
|
|
|
// Check to see if the loaded pointer is a getelementptr of a global.
|
|
GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
|
|
if (!GEP) return UnknownValue;
|
|
|
|
// 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->hasInitializer() ||
|
|
GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
|
|
!cast<Constant>(GEP->getOperand(1))->isNullValue())
|
|
return UnknownValue;
|
|
|
|
// 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 UnknownValue; // 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.
|
|
SCEVHandle Idx = getSCEV(VarIdx);
|
|
SCEVHandle Tmp = getSCEVAtScope(Idx, L);
|
|
if (!isa<SCEVCouldNotCompute>(Tmp)) Idx = Tmp;
|
|
|
|
// We can only recognize very limited forms of loop index expressions, in
|
|
// particular, only affine AddRec's like {C1,+,C2}.
|
|
SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
|
|
if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) ||
|
|
!isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
|
|
!isa<SCEVConstant>(IdxExpr->getOperand(1)))
|
|
return UnknownValue;
|
|
|
|
unsigned MaxSteps = MaxBruteForceIterations;
|
|
for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
|
|
ConstantUInt *ItCst =
|
|
ConstantUInt::get(IdxExpr->getType()->getUnsignedVersion(), IterationNum);
|
|
ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst);
|
|
|
|
// Form the GEP offset.
|
|
Indexes[VarIdxNum] = Val;
|
|
|
|
Constant *Result = GetAddressedElementFromGlobal(GV, Indexes);
|
|
if (Result == 0) break; // Cannot compute!
|
|
|
|
// Evaluate the condition for this iteration.
|
|
Result = ConstantExpr::get(SetCCOpcode, Result, RHS);
|
|
if (!isa<ConstantBool>(Result)) break; // Couldn't decide for sure
|
|
if (Result == ConstantBool::False) {
|
|
#if 0
|
|
std::cerr << "\n***\n*** Computed loop count " << *ItCst
|
|
<< "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
|
|
<< "***\n";
|
|
#endif
|
|
++NumArrayLenItCounts;
|
|
return SCEVConstant::get(ItCst); // Found terminating iteration!
|
|
}
|
|
}
|
|
return UnknownValue;
|
|
}
|
|
|
|
|
|
/// 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<ShiftInst>(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((Function*)F); // FIXME: elim cast
|
|
return false;
|
|
}
|
|
|
|
/// ConstantFold - Constant fold an instruction of the specified type with the
|
|
/// specified constant operands. This function may modify the operands vector.
|
|
static Constant *ConstantFold(const Instruction *I,
|
|
std::vector<Constant*> &Operands) {
|
|
if (isa<BinaryOperator>(I) || isa<ShiftInst>(I))
|
|
return ConstantExpr::get(I->getOpcode(), Operands[0], Operands[1]);
|
|
|
|
switch (I->getOpcode()) {
|
|
case Instruction::Cast:
|
|
return ConstantExpr::getCast(Operands[0], I->getType());
|
|
case Instruction::Select:
|
|
return ConstantExpr::getSelect(Operands[0], Operands[1], Operands[2]);
|
|
case Instruction::Call:
|
|
if (Function *GV = dyn_cast<Function>(Operands[0])) {
|
|
Operands.erase(Operands.begin());
|
|
return ConstantFoldCall(cast<Function>(GV), Operands);
|
|
}
|
|
|
|
return 0;
|
|
case Instruction::GetElementPtr:
|
|
Constant *Base = Operands[0];
|
|
Operands.erase(Operands.begin());
|
|
return ConstantExpr::getGetElementPtr(Base, Operands);
|
|
}
|
|
return 0;
|
|
}
|
|
|
|
|
|
/// 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 (GlobalValue *GV = dyn_cast<GlobalValue>(V))
|
|
return GV;
|
|
if (Constant *C = dyn_cast<Constant>(V)) return C;
|
|
Instruction *I = cast<Instruction>(V);
|
|
|
|
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;
|
|
}
|
|
|
|
return ConstantFold(I, Operands);
|
|
}
|
|
|
|
/// 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 *ScalarEvolutionsImpl::
|
|
getConstantEvolutionLoopExitValue(PHINode *PN, uint64_t Its, const Loop *L) {
|
|
std::map<PHINode*, Constant*>::iterator I =
|
|
ConstantEvolutionLoopExitValue.find(PN);
|
|
if (I != ConstantEvolutionLoopExitValue.end())
|
|
return I->second;
|
|
|
|
if (Its > 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.
|
|
unsigned IterationNum = 0;
|
|
unsigned NumIterations = Its;
|
|
if (NumIterations != Its)
|
|
return RetVal = 0; // More than 2^32 iterations??
|
|
|
|
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;
|
|
}
|
|
}
|
|
|
|
/// ComputeIterationCountExhaustively - If the trip 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 UnknownValue.
|
|
SCEVHandle ScalarEvolutionsImpl::
|
|
ComputeIterationCountExhaustively(const Loop *L, Value *Cond, bool ExitWhen) {
|
|
PHINode *PN = getConstantEvolvingPHI(Cond, L);
|
|
if (PN == 0) return UnknownValue;
|
|
|
|
// 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 UnknownValue; // Must be a constant.
|
|
|
|
Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
|
|
PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
|
|
if (PN2 != PN) return UnknownValue; // 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) {
|
|
ConstantBool *CondVal =
|
|
dyn_cast_or_null<ConstantBool>(EvaluateExpression(Cond, PHIVal));
|
|
if (!CondVal) return UnknownValue; // Couldn't symbolically evaluate.
|
|
|
|
if (CondVal->getValue() == ExitWhen) {
|
|
ConstantEvolutionLoopExitValue[PN] = PHIVal;
|
|
++NumBruteForceTripCountsComputed;
|
|
return SCEVConstant::get(ConstantUInt::get(Type::UIntTy, IterationNum));
|
|
}
|
|
|
|
// Compute the value of the PHI node for the next iteration.
|
|
Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
|
|
if (NextPHI == 0 || NextPHI == PHIVal)
|
|
return UnknownValue; // Couldn't evaluate or not making progress...
|
|
PHIVal = NextPHI;
|
|
}
|
|
|
|
// Too many iterations were needed to evaluate.
|
|
return UnknownValue;
|
|
}
|
|
|
|
/// getSCEVAtScope - Compute the value of the specified expression within the
|
|
/// indicated loop (which may be null to indicate in no loop). If the
|
|
/// expression cannot be evaluated, return UnknownValue.
|
|
SCEVHandle ScalarEvolutionsImpl::getSCEVAtScope(SCEV *V, const Loop *L) {
|
|
// FIXME: this should be turned into a virtual method on SCEV!
|
|
|
|
if (isa<SCEVConstant>(V)) return V;
|
|
|
|
// If this instruction is evolves from a constant-evolving PHI, compute the
|
|
// exit value from the loop without using SCEVs.
|
|
if (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 iteration count.
|
|
// If so, we may be able to force computation of the exit value.
|
|
SCEVHandle IterationCount = getIterationCount(LI);
|
|
if (SCEVConstant *ICC = dyn_cast<SCEVConstant>(IterationCount)) {
|
|
// 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,
|
|
ICC->getValue()->getRawValue(),
|
|
LI);
|
|
if (RV) return SCEVUnknown::get(RV);
|
|
}
|
|
}
|
|
|
|
// Okay, this is a some 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 see, 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 {
|
|
SCEVHandle OpV = getSCEVAtScope(getSCEV(Op), L);
|
|
if (SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV))
|
|
Operands.push_back(ConstantExpr::getCast(SC->getValue(),
|
|
Op->getType()));
|
|
else if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) {
|
|
if (Constant *C = dyn_cast<Constant>(SU->getValue()))
|
|
Operands.push_back(ConstantExpr::getCast(C, Op->getType()));
|
|
else
|
|
return V;
|
|
} else {
|
|
return V;
|
|
}
|
|
}
|
|
}
|
|
return SCEVUnknown::get(ConstantFold(I, Operands));
|
|
}
|
|
}
|
|
|
|
// This is some other type of SCEVUnknown, just return it.
|
|
return V;
|
|
}
|
|
|
|
if (SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
|
|
// Avoid performing the look-up in the common case where the specified
|
|
// expression has no loop-variant portions.
|
|
for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
|
|
SCEVHandle OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
|
|
if (OpAtScope != Comm->getOperand(i)) {
|
|
if (OpAtScope == UnknownValue) return UnknownValue;
|
|
// Okay, at least one of these operands is loop variant but might be
|
|
// foldable. Build a new instance of the folded commutative expression.
|
|
std::vector<SCEVHandle> NewOps(Comm->op_begin(), Comm->op_begin()+i);
|
|
NewOps.push_back(OpAtScope);
|
|
|
|
for (++i; i != e; ++i) {
|
|
OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
|
|
if (OpAtScope == UnknownValue) return UnknownValue;
|
|
NewOps.push_back(OpAtScope);
|
|
}
|
|
if (isa<SCEVAddExpr>(Comm))
|
|
return SCEVAddExpr::get(NewOps);
|
|
assert(isa<SCEVMulExpr>(Comm) && "Only know about add and mul!");
|
|
return SCEVMulExpr::get(NewOps);
|
|
}
|
|
}
|
|
// If we got here, all operands are loop invariant.
|
|
return Comm;
|
|
}
|
|
|
|
if (SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(V)) {
|
|
SCEVHandle LHS = getSCEVAtScope(UDiv->getLHS(), L);
|
|
if (LHS == UnknownValue) return LHS;
|
|
SCEVHandle RHS = getSCEVAtScope(UDiv->getRHS(), L);
|
|
if (RHS == UnknownValue) return RHS;
|
|
if (LHS == UDiv->getLHS() && RHS == UDiv->getRHS())
|
|
return UDiv; // must be loop invariant
|
|
return SCEVUDivExpr::get(LHS, RHS);
|
|
}
|
|
|
|
// If this is a loop recurrence for a loop that does not contain L, then we
|
|
// are dealing with the final value computed by the loop.
|
|
if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
|
|
if (!L || !AddRec->getLoop()->contains(L->getHeader())) {
|
|
// To evaluate this recurrence, we need to know how many times the AddRec
|
|
// loop iterates. Compute this now.
|
|
SCEVHandle IterationCount = getIterationCount(AddRec->getLoop());
|
|
if (IterationCount == UnknownValue) return UnknownValue;
|
|
IterationCount = getTruncateOrZeroExtend(IterationCount,
|
|
AddRec->getType());
|
|
|
|
// If the value is affine, simplify the expression evaluation to just
|
|
// Start + Step*IterationCount.
|
|
if (AddRec->isAffine())
|
|
return SCEVAddExpr::get(AddRec->getStart(),
|
|
SCEVMulExpr::get(IterationCount,
|
|
AddRec->getOperand(1)));
|
|
|
|
// Otherwise, evaluate it the hard way.
|
|
return AddRec->evaluateAtIteration(IterationCount);
|
|
}
|
|
return UnknownValue;
|
|
}
|
|
|
|
//assert(0 && "Unknown SCEV type!");
|
|
return UnknownValue;
|
|
}
|
|
|
|
|
|
/// SolveQuadraticEquation - Find the roots of the quadratic equation for the
|
|
/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
|
|
/// might be the same) or two SCEVCouldNotCompute objects.
|
|
///
|
|
static std::pair<SCEVHandle,SCEVHandle>
|
|
SolveQuadraticEquation(const SCEVAddRecExpr *AddRec) {
|
|
assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
|
|
SCEVConstant *L = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
|
|
SCEVConstant *M = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
|
|
SCEVConstant *N = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
|
|
|
|
// We currently can only solve this if the coefficients are constants.
|
|
if (!L || !M || !N) {
|
|
SCEV *CNC = new SCEVCouldNotCompute();
|
|
return std::make_pair(CNC, CNC);
|
|
}
|
|
|
|
Constant *Two = ConstantInt::get(L->getValue()->getType(), 2);
|
|
|
|
// Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
|
|
Constant *C = L->getValue();
|
|
// The B coefficient is M-N/2
|
|
Constant *B = ConstantExpr::getSub(M->getValue(),
|
|
ConstantExpr::getDiv(N->getValue(),
|
|
Two));
|
|
// The A coefficient is N/2
|
|
Constant *A = ConstantExpr::getDiv(N->getValue(), Two);
|
|
|
|
// Compute the B^2-4ac term.
|
|
Constant *SqrtTerm =
|
|
ConstantExpr::getMul(ConstantInt::get(C->getType(), 4),
|
|
ConstantExpr::getMul(A, C));
|
|
SqrtTerm = ConstantExpr::getSub(ConstantExpr::getMul(B, B), SqrtTerm);
|
|
|
|
// Compute floor(sqrt(B^2-4ac))
|
|
ConstantUInt *SqrtVal =
|
|
cast<ConstantUInt>(ConstantExpr::getCast(SqrtTerm,
|
|
SqrtTerm->getType()->getUnsignedVersion()));
|
|
uint64_t SqrtValV = SqrtVal->getValue();
|
|
uint64_t SqrtValV2 = (uint64_t)sqrt((double)SqrtValV);
|
|
// The square root might not be precise for arbitrary 64-bit integer
|
|
// values. Do some sanity checks to ensure it's correct.
|
|
if (SqrtValV2*SqrtValV2 > SqrtValV ||
|
|
(SqrtValV2+1)*(SqrtValV2+1) <= SqrtValV) {
|
|
SCEV *CNC = new SCEVCouldNotCompute();
|
|
return std::make_pair(CNC, CNC);
|
|
}
|
|
|
|
SqrtVal = ConstantUInt::get(Type::ULongTy, SqrtValV2);
|
|
SqrtTerm = ConstantExpr::getCast(SqrtVal, SqrtTerm->getType());
|
|
|
|
Constant *NegB = ConstantExpr::getNeg(B);
|
|
Constant *TwoA = ConstantExpr::getMul(A, Two);
|
|
|
|
// The divisions must be performed as signed divisions.
|
|
const Type *SignedTy = NegB->getType()->getSignedVersion();
|
|
NegB = ConstantExpr::getCast(NegB, SignedTy);
|
|
TwoA = ConstantExpr::getCast(TwoA, SignedTy);
|
|
SqrtTerm = ConstantExpr::getCast(SqrtTerm, SignedTy);
|
|
|
|
Constant *Solution1 =
|
|
ConstantExpr::getDiv(ConstantExpr::getAdd(NegB, SqrtTerm), TwoA);
|
|
Constant *Solution2 =
|
|
ConstantExpr::getDiv(ConstantExpr::getSub(NegB, SqrtTerm), TwoA);
|
|
return std::make_pair(SCEVUnknown::get(Solution1),
|
|
SCEVUnknown::get(Solution2));
|
|
}
|
|
|
|
/// HowFarToZero - Return the number of times a backedge comparing the specified
|
|
/// value to zero will execute. If not computable, return UnknownValue
|
|
SCEVHandle ScalarEvolutionsImpl::HowFarToZero(SCEV *V, const Loop *L) {
|
|
// If the value is a constant
|
|
if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
|
|
// If the value is already zero, the branch will execute zero times.
|
|
if (C->getValue()->isNullValue()) return C;
|
|
return UnknownValue; // Otherwise it will loop infinitely.
|
|
}
|
|
|
|
SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
|
|
if (!AddRec || AddRec->getLoop() != L)
|
|
return UnknownValue;
|
|
|
|
if (AddRec->isAffine()) {
|
|
// If this is an affine expression the execution count of this branch is
|
|
// equal to:
|
|
//
|
|
// (0 - Start/Step) iff Start % Step == 0
|
|
//
|
|
// Get the initial value for the loop.
|
|
SCEVHandle Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
|
|
if (isa<SCEVCouldNotCompute>(Start)) return UnknownValue;
|
|
SCEVHandle Step = AddRec->getOperand(1);
|
|
|
|
Step = getSCEVAtScope(Step, L->getParentLoop());
|
|
|
|
// Figure out if Start % Step == 0.
|
|
// FIXME: We should add DivExpr and RemExpr operations to our AST.
|
|
if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) {
|
|
if (StepC->getValue()->equalsInt(1)) // N % 1 == 0
|
|
return getNegativeSCEV(Start); // 0 - Start/1 == -Start
|
|
if (StepC->getValue()->isAllOnesValue()) // N % -1 == 0
|
|
return Start; // 0 - Start/-1 == Start
|
|
|
|
// Check to see if Start is divisible by SC with no remainder.
|
|
if (SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) {
|
|
ConstantInt *StartCC = StartC->getValue();
|
|
Constant *StartNegC = ConstantExpr::getNeg(StartCC);
|
|
Constant *Rem = ConstantExpr::getRem(StartNegC, StepC->getValue());
|
|
if (Rem->isNullValue()) {
|
|
Constant *Result =ConstantExpr::getDiv(StartNegC,StepC->getValue());
|
|
return SCEVUnknown::get(Result);
|
|
}
|
|
}
|
|
}
|
|
} else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) {
|
|
// If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
|
|
// the quadratic equation to solve it.
|
|
std::pair<SCEVHandle,SCEVHandle> Roots = SolveQuadraticEquation(AddRec);
|
|
SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
|
|
SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
|
|
if (R1) {
|
|
#if 0
|
|
std::cerr << "HFTZ: " << *V << " - sol#1: " << *R1
|
|
<< " sol#2: " << *R2 << "\n";
|
|
#endif
|
|
// Pick the smallest positive root value.
|
|
assert(R1->getType()->isUnsigned()&&"Didn't canonicalize to unsigned?");
|
|
if (ConstantBool *CB =
|
|
dyn_cast<ConstantBool>(ConstantExpr::getSetLT(R1->getValue(),
|
|
R2->getValue()))) {
|
|
if (CB != ConstantBool::True)
|
|
std::swap(R1, R2); // R1 is the minimum root now.
|
|
|
|
// We can only use this value if the chrec ends up with an exact zero
|
|
// value at this index. When solving for "X*X != 5", for example, we
|
|
// should not accept a root of 2.
|
|
SCEVHandle Val = AddRec->evaluateAtIteration(R1);
|
|
if (SCEVConstant *EvalVal = dyn_cast<SCEVConstant>(Val))
|
|
if (EvalVal->getValue()->isNullValue())
|
|
return R1; // We found a quadratic root!
|
|
}
|
|
}
|
|
}
|
|
|
|
return UnknownValue;
|
|
}
|
|
|
|
/// HowFarToNonZero - Return the number of times a backedge checking the
|
|
/// specified value for nonzero will execute. If not computable, return
|
|
/// UnknownValue
|
|
SCEVHandle ScalarEvolutionsImpl::HowFarToNonZero(SCEV *V, const Loop *L) {
|
|
// Loops that look like: while (X == 0) are very strange indeed. We don't
|
|
// handle them yet except for the trivial case. This could be expanded in the
|
|
// future as needed.
|
|
|
|
// If the value is a constant, check to see if it is known to be non-zero
|
|
// already. If so, the backedge will execute zero times.
|
|
if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
|
|
Constant *Zero = Constant::getNullValue(C->getValue()->getType());
|
|
Constant *NonZero = ConstantExpr::getSetNE(C->getValue(), Zero);
|
|
if (NonZero == ConstantBool::True)
|
|
return getSCEV(Zero);
|
|
return UnknownValue; // Otherwise it will loop infinitely.
|
|
}
|
|
|
|
// We could implement others, but I really doubt anyone writes loops like
|
|
// this, and if they did, they would already be constant folded.
|
|
return UnknownValue;
|
|
}
|
|
|
|
/// getNumIterationsInRange - Return the number of iterations of this loop that
|
|
/// produce values in the specified constant range. Another way of looking at
|
|
/// this is that it returns the first iteration number where the value is not in
|
|
/// the condition, thus computing the exit count. If the iteration count can't
|
|
/// be computed, an instance of SCEVCouldNotCompute is returned.
|
|
SCEVHandle SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range) const {
|
|
if (Range.isFullSet()) // Infinite loop.
|
|
return new SCEVCouldNotCompute();
|
|
|
|
// If the start is a non-zero constant, shift the range to simplify things.
|
|
if (SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
|
|
if (!SC->getValue()->isNullValue()) {
|
|
std::vector<SCEVHandle> Operands(op_begin(), op_end());
|
|
Operands[0] = SCEVUnknown::getIntegerSCEV(0, SC->getType());
|
|
SCEVHandle Shifted = SCEVAddRecExpr::get(Operands, getLoop());
|
|
if (SCEVAddRecExpr *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted))
|
|
return ShiftedAddRec->getNumIterationsInRange(
|
|
Range.subtract(SC->getValue()));
|
|
// This is strange and shouldn't happen.
|
|
return new SCEVCouldNotCompute();
|
|
}
|
|
|
|
// The only time we can solve this is when we have all constant indices.
|
|
// Otherwise, we cannot determine the overflow conditions.
|
|
for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
|
|
if (!isa<SCEVConstant>(getOperand(i)))
|
|
return new SCEVCouldNotCompute();
|
|
|
|
|
|
// Okay at this point we know that all elements of the chrec are constants and
|
|
// that the start element is zero.
|
|
|
|
// First check to see if the range contains zero. If not, the first
|
|
// iteration exits.
|
|
ConstantInt *Zero = ConstantInt::get(getType(), 0);
|
|
if (!Range.contains(Zero)) return SCEVConstant::get(Zero);
|
|
|
|
if (isAffine()) {
|
|
// If this is an affine expression then we have this situation:
|
|
// Solve {0,+,A} in Range === Ax in Range
|
|
|
|
// Since we know that zero is in the range, we know that the upper value of
|
|
// the range must be the first possible exit value. Also note that we
|
|
// already checked for a full range.
|
|
ConstantInt *Upper = cast<ConstantInt>(Range.getUpper());
|
|
ConstantInt *A = cast<SCEVConstant>(getOperand(1))->getValue();
|
|
ConstantInt *One = ConstantInt::get(getType(), 1);
|
|
|
|
// The exit value should be (Upper+A-1)/A.
|
|
Constant *ExitValue = Upper;
|
|
if (A != One) {
|
|
ExitValue = ConstantExpr::getSub(ConstantExpr::getAdd(Upper, A), One);
|
|
ExitValue = ConstantExpr::getDiv(ExitValue, A);
|
|
}
|
|
assert(isa<ConstantInt>(ExitValue) &&
|
|
"Constant folding of integers not implemented?");
|
|
|
|
// Evaluate at the exit value. If we really did fall out of the valid
|
|
// range, then we computed our trip count, otherwise wrap around or other
|
|
// things must have happened.
|
|
ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue);
|
|
if (Range.contains(Val))
|
|
return new SCEVCouldNotCompute(); // Something strange happened
|
|
|
|
// Ensure that the previous value is in the range. This is a sanity check.
|
|
assert(Range.contains(EvaluateConstantChrecAtConstant(this,
|
|
ConstantExpr::getSub(ExitValue, One))) &&
|
|
"Linear scev computation is off in a bad way!");
|
|
return SCEVConstant::get(cast<ConstantInt>(ExitValue));
|
|
} else if (isQuadratic()) {
|
|
// If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
|
|
// quadratic equation to solve it. To do this, we must frame our problem in
|
|
// terms of figuring out when zero is crossed, instead of when
|
|
// Range.getUpper() is crossed.
|
|
std::vector<SCEVHandle> NewOps(op_begin(), op_end());
|
|
NewOps[0] = getNegativeSCEV(SCEVUnknown::get(Range.getUpper()));
|
|
SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewOps, getLoop());
|
|
|
|
// Next, solve the constructed addrec
|
|
std::pair<SCEVHandle,SCEVHandle> Roots =
|
|
SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec));
|
|
SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
|
|
SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
|
|
if (R1) {
|
|
// Pick the smallest positive root value.
|
|
assert(R1->getType()->isUnsigned() && "Didn't canonicalize to unsigned?");
|
|
if (ConstantBool *CB =
|
|
dyn_cast<ConstantBool>(ConstantExpr::getSetLT(R1->getValue(),
|
|
R2->getValue()))) {
|
|
if (CB != ConstantBool::True)
|
|
std::swap(R1, R2); // R1 is the minimum root now.
|
|
|
|
// Make sure the root is not off by one. The returned iteration should
|
|
// not be in the range, but the previous one should be. When solving
|
|
// for "X*X < 5", for example, we should not return a root of 2.
|
|
ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
|
|
R1->getValue());
|
|
if (Range.contains(R1Val)) {
|
|
// The next iteration must be out of the range...
|
|
Constant *NextVal =
|
|
ConstantExpr::getAdd(R1->getValue(),
|
|
ConstantInt::get(R1->getType(), 1));
|
|
|
|
R1Val = EvaluateConstantChrecAtConstant(this, NextVal);
|
|
if (!Range.contains(R1Val))
|
|
return SCEVUnknown::get(NextVal);
|
|
return new SCEVCouldNotCompute(); // Something strange happened
|
|
}
|
|
|
|
// If R1 was not in the range, then it is a good return value. Make
|
|
// sure that R1-1 WAS in the range though, just in case.
|
|
Constant *NextVal =
|
|
ConstantExpr::getSub(R1->getValue(),
|
|
ConstantInt::get(R1->getType(), 1));
|
|
R1Val = EvaluateConstantChrecAtConstant(this, NextVal);
|
|
if (Range.contains(R1Val))
|
|
return R1;
|
|
return new SCEVCouldNotCompute(); // Something strange happened
|
|
}
|
|
}
|
|
}
|
|
|
|
// Fallback, if this is a general polynomial, figure out the progression
|
|
// through brute force: evaluate until we find an iteration that fails the
|
|
// test. This is likely to be slow, but getting an accurate trip count is
|
|
// incredibly important, we will be able to simplify the exit test a lot, and
|
|
// we are almost guaranteed to get a trip count in this case.
|
|
ConstantInt *TestVal = ConstantInt::get(getType(), 0);
|
|
ConstantInt *One = ConstantInt::get(getType(), 1);
|
|
ConstantInt *EndVal = TestVal; // Stop when we wrap around.
|
|
do {
|
|
++NumBruteForceEvaluations;
|
|
SCEVHandle Val = evaluateAtIteration(SCEVConstant::get(TestVal));
|
|
if (!isa<SCEVConstant>(Val)) // This shouldn't happen.
|
|
return new SCEVCouldNotCompute();
|
|
|
|
// Check to see if we found the value!
|
|
if (!Range.contains(cast<SCEVConstant>(Val)->getValue()))
|
|
return SCEVConstant::get(TestVal);
|
|
|
|
// Increment to test the next index.
|
|
TestVal = cast<ConstantInt>(ConstantExpr::getAdd(TestVal, One));
|
|
} while (TestVal != EndVal);
|
|
|
|
return new SCEVCouldNotCompute();
|
|
}
|
|
|
|
|
|
|
|
//===----------------------------------------------------------------------===//
|
|
// ScalarEvolution Class Implementation
|
|
//===----------------------------------------------------------------------===//
|
|
|
|
bool ScalarEvolution::runOnFunction(Function &F) {
|
|
Impl = new ScalarEvolutionsImpl(F, getAnalysis<LoopInfo>());
|
|
return false;
|
|
}
|
|
|
|
void ScalarEvolution::releaseMemory() {
|
|
delete (ScalarEvolutionsImpl*)Impl;
|
|
Impl = 0;
|
|
}
|
|
|
|
void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
|
|
AU.setPreservesAll();
|
|
AU.addRequiredID(LoopSimplifyID);
|
|
AU.addRequiredTransitive<LoopInfo>();
|
|
}
|
|
|
|
SCEVHandle ScalarEvolution::getSCEV(Value *V) const {
|
|
return ((ScalarEvolutionsImpl*)Impl)->getSCEV(V);
|
|
}
|
|
|
|
SCEVHandle ScalarEvolution::getIterationCount(const Loop *L) const {
|
|
return ((ScalarEvolutionsImpl*)Impl)->getIterationCount(L);
|
|
}
|
|
|
|
bool ScalarEvolution::hasLoopInvariantIterationCount(const Loop *L) const {
|
|
return !isa<SCEVCouldNotCompute>(getIterationCount(L));
|
|
}
|
|
|
|
SCEVHandle ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) const {
|
|
return ((ScalarEvolutionsImpl*)Impl)->getSCEVAtScope(getSCEV(V), L);
|
|
}
|
|
|
|
void ScalarEvolution::deleteInstructionFromRecords(Instruction *I) const {
|
|
return ((ScalarEvolutionsImpl*)Impl)->deleteInstructionFromRecords(I);
|
|
}
|
|
|
|
static void PrintLoopInfo(std::ostream &OS, const ScalarEvolution *SE,
|
|
const Loop *L) {
|
|
// Print all inner loops first
|
|
for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
|
|
PrintLoopInfo(OS, SE, *I);
|
|
|
|
std::cerr << "Loop " << L->getHeader()->getName() << ": ";
|
|
|
|
std::vector<BasicBlock*> ExitBlocks;
|
|
L->getExitBlocks(ExitBlocks);
|
|
if (ExitBlocks.size() != 1)
|
|
std::cerr << "<multiple exits> ";
|
|
|
|
if (SE->hasLoopInvariantIterationCount(L)) {
|
|
std::cerr << *SE->getIterationCount(L) << " iterations! ";
|
|
} else {
|
|
std::cerr << "Unpredictable iteration count. ";
|
|
}
|
|
|
|
std::cerr << "\n";
|
|
}
|
|
|
|
void ScalarEvolution::print(std::ostream &OS) const {
|
|
Function &F = ((ScalarEvolutionsImpl*)Impl)->F;
|
|
LoopInfo &LI = ((ScalarEvolutionsImpl*)Impl)->LI;
|
|
|
|
OS << "Classifying expressions for: " << F.getName() << "\n";
|
|
for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
|
|
if (I->getType()->isInteger()) {
|
|
OS << *I;
|
|
OS << " --> ";
|
|
SCEVHandle SV = getSCEV(&*I);
|
|
SV->print(OS);
|
|
OS << "\t\t";
|
|
|
|
if ((*I).getType()->isIntegral()) {
|
|
ConstantRange Bounds = SV->getValueRange();
|
|
if (!Bounds.isFullSet())
|
|
OS << "Bounds: " << Bounds << " ";
|
|
}
|
|
|
|
if (const Loop *L = LI.getLoopFor((*I).getParent())) {
|
|
OS << "Exits: ";
|
|
SCEVHandle ExitValue = getSCEVAtScope(&*I, L->getParentLoop());
|
|
if (isa<SCEVCouldNotCompute>(ExitValue)) {
|
|
OS << "<<Unknown>>";
|
|
} else {
|
|
OS << *ExitValue;
|
|
}
|
|
}
|
|
|
|
|
|
OS << "\n";
|
|
}
|
|
|
|
OS << "Determining loop execution counts for: " << F.getName() << "\n";
|
|
for (LoopInfo::iterator I = LI.begin(), E = LI.end(); I != E; ++I)
|
|
PrintLoopInfo(OS, this, *I);
|
|
}
|
|
|