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llvm-project/llvm/lib/Analysis/ScalarEvolution.cpp

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//===- ScalarEvolution.cpp - Scalar Evolution Analysis ----------*- C++ -*-===//
//
// The LLVM Compiler Infrastructure
//
// This file is distributed under the University of Illinois Open Source
// License. See LICENSE.TXT for details.
//
//===----------------------------------------------------------------------===//
//
// This file contains the implementation of the scalar evolution analysis
// engine, which is used primarily to analyze expressions involving induction
// variables in loops.
//
// There are several aspects to this library. First is the representation of
// scalar expressions, which are represented as subclasses of the SCEV class.
// These classes are used to represent certain types of subexpressions that we
// can handle. These classes are reference counted, managed by the SCEVHandle
// class. We only create one SCEV of a particular shape, so pointer-comparisons
// for equality are legal.
//
// One important aspect of the SCEV objects is that they are never cyclic, even
// if there is a cycle in the dataflow for an expression (ie, a PHI node). If
// the PHI node is one of the idioms that we can represent (e.g., a polynomial
// recurrence) then we represent it directly as a recurrence node, otherwise we
// represent it as a SCEVUnknown node.
//
// In addition to being able to represent expressions of various types, we also
// have folders that are used to build the *canonical* representation for a
// particular expression. These folders are capable of using a variety of
// rewrite rules to simplify the expressions.
//
// Once the folders are defined, we can implement the more interesting
// higher-level code, such as the code that recognizes PHI nodes of various
// types, computes the execution count of a loop, etc.
//
// TODO: We should use these routines and value representations to implement
// dependence analysis!
//
//===----------------------------------------------------------------------===//
//
// There are several good references for the techniques used in this analysis.
//
// Chains of recurrences -- a method to expedite the evaluation
// of closed-form functions
// Olaf Bachmann, Paul S. Wang, Eugene V. Zima
//
// On computational properties of chains of recurrences
// Eugene V. Zima
//
// Symbolic Evaluation of Chains of Recurrences for Loop Optimization
// Robert A. van Engelen
//
// Efficient Symbolic Analysis for Optimizing Compilers
// Robert A. van Engelen
//
// Using the chains of recurrences algebra for data dependence testing and
// induction variable substitution
// MS Thesis, Johnie Birch
//
//===----------------------------------------------------------------------===//
#define DEBUG_TYPE "scalar-evolution"
#include "llvm/Analysis/ScalarEvolutionExpressions.h"
#include "llvm/Constants.h"
#include "llvm/DerivedTypes.h"
#include "llvm/GlobalVariable.h"
#include "llvm/Instructions.h"
#include "llvm/Analysis/ConstantFolding.h"
#include "llvm/Analysis/Dominators.h"
#include "llvm/Analysis/LoopInfo.h"
#include "llvm/Assembly/Writer.h"
#include "llvm/Target/TargetData.h"
#include "llvm/Transforms/Scalar.h"
#include "llvm/Support/CFG.h"
#include "llvm/Support/CommandLine.h"
#include "llvm/Support/Compiler.h"
#include "llvm/Support/ConstantRange.h"
#include "llvm/Support/GetElementPtrTypeIterator.h"
#include "llvm/Support/InstIterator.h"
#include "llvm/Support/ManagedStatic.h"
#include "llvm/Support/MathExtras.h"
#include "llvm/Support/raw_ostream.h"
#include "llvm/ADT/Statistic.h"
#include "llvm/ADT/STLExtras.h"
#include <ostream>
#include <algorithm>
#include <cmath>
using namespace llvm;
STATISTIC(NumArrayLenItCounts,
"Number of trip counts computed with array length");
STATISTIC(NumTripCountsComputed,
"Number of loops with predictable loop counts");
STATISTIC(NumTripCountsNotComputed,
"Number of loops without predictable loop counts");
STATISTIC(NumBruteForceTripCountsComputed,
"Number of loops with trip counts computed by force");
static cl::opt<unsigned>
MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
cl::desc("Maximum number of iterations SCEV will "
"symbolically execute a constant derived loop"),
cl::init(100));
static RegisterPass<ScalarEvolution>
R("scalar-evolution", "Scalar Evolution Analysis", false, true);
char ScalarEvolution::ID = 0;
//===----------------------------------------------------------------------===//
// SCEV class definitions
//===----------------------------------------------------------------------===//
//===----------------------------------------------------------------------===//
// Implementation of the SCEV class.
//
SCEV::~SCEV() {}
void SCEV::dump() const {
print(errs());
errs() << '\n';
}
void SCEV::print(std::ostream &o) const {
raw_os_ostream OS(o);
print(OS);
}
bool SCEV::isZero() const {
if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
return SC->getValue()->isZero();
return false;
}
SCEVCouldNotCompute::SCEVCouldNotCompute() : SCEV(scCouldNotCompute) {}
SCEVCouldNotCompute::~SCEVCouldNotCompute() {}
bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const {
assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
return false;
}
const Type *SCEVCouldNotCompute::getType() const {
assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
return 0;
}
bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const {
assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
return false;
}
SCEVHandle SCEVCouldNotCompute::
replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
const SCEVHandle &Conc,
ScalarEvolution &SE) const {
return this;
}
void SCEVCouldNotCompute::print(raw_ostream &OS) const {
OS << "***COULDNOTCOMPUTE***";
}
bool SCEVCouldNotCompute::classof(const SCEV *S) {
return S->getSCEVType() == scCouldNotCompute;
}
// SCEVConstants - Only allow the creation of one SCEVConstant for any
// particular value. Don't use a SCEVHandle here, or else the object will
// never be deleted!
static ManagedStatic<std::map<ConstantInt*, SCEVConstant*> > SCEVConstants;
SCEVConstant::~SCEVConstant() {
SCEVConstants->erase(V);
}
SCEVHandle ScalarEvolution::getConstant(ConstantInt *V) {
SCEVConstant *&R = (*SCEVConstants)[V];
if (R == 0) R = new SCEVConstant(V);
return R;
}
SCEVHandle ScalarEvolution::getConstant(const APInt& Val) {
return getConstant(ConstantInt::get(Val));
}
const Type *SCEVConstant::getType() const { return V->getType(); }
void SCEVConstant::print(raw_ostream &OS) const {
WriteAsOperand(OS, V, false);
}
SCEVCastExpr::SCEVCastExpr(unsigned SCEVTy,
const SCEVHandle &op, const Type *ty)
: SCEV(SCEVTy), Op(op), Ty(ty) {}
SCEVCastExpr::~SCEVCastExpr() {}
bool SCEVCastExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
return Op->dominates(BB, DT);
}
// SCEVTruncates - Only allow the creation of one SCEVTruncateExpr for any
// particular input. Don't use a SCEVHandle here, or else the object will
// never be deleted!
static ManagedStatic<std::map<std::pair<const SCEV*, const Type*>,
SCEVTruncateExpr*> > SCEVTruncates;
SCEVTruncateExpr::SCEVTruncateExpr(const SCEVHandle &op, const Type *ty)
: SCEVCastExpr(scTruncate, op, ty) {
assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
(Ty->isInteger() || isa<PointerType>(Ty)) &&
"Cannot truncate non-integer value!");
}
SCEVTruncateExpr::~SCEVTruncateExpr() {
SCEVTruncates->erase(std::make_pair(Op, Ty));
}
void SCEVTruncateExpr::print(raw_ostream &OS) const {
OS << "(trunc " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
}
// SCEVZeroExtends - Only allow the creation of one SCEVZeroExtendExpr for any
// particular input. Don't use a SCEVHandle here, or else the object will never
// be deleted!
static ManagedStatic<std::map<std::pair<const SCEV*, const Type*>,
SCEVZeroExtendExpr*> > SCEVZeroExtends;
SCEVZeroExtendExpr::SCEVZeroExtendExpr(const SCEVHandle &op, const Type *ty)
: SCEVCastExpr(scZeroExtend, op, ty) {
assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
(Ty->isInteger() || isa<PointerType>(Ty)) &&
"Cannot zero extend non-integer value!");
}
SCEVZeroExtendExpr::~SCEVZeroExtendExpr() {
SCEVZeroExtends->erase(std::make_pair(Op, Ty));
}
void SCEVZeroExtendExpr::print(raw_ostream &OS) const {
OS << "(zext " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
}
// SCEVSignExtends - Only allow the creation of one SCEVSignExtendExpr for any
// particular input. Don't use a SCEVHandle here, or else the object will never
// be deleted!
static ManagedStatic<std::map<std::pair<const SCEV*, const Type*>,
SCEVSignExtendExpr*> > SCEVSignExtends;
SCEVSignExtendExpr::SCEVSignExtendExpr(const SCEVHandle &op, const Type *ty)
: SCEVCastExpr(scSignExtend, op, ty) {
assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
(Ty->isInteger() || isa<PointerType>(Ty)) &&
"Cannot sign extend non-integer value!");
}
SCEVSignExtendExpr::~SCEVSignExtendExpr() {
SCEVSignExtends->erase(std::make_pair(Op, Ty));
}
void SCEVSignExtendExpr::print(raw_ostream &OS) const {
OS << "(sext " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
}
// SCEVCommExprs - Only allow the creation of one SCEVCommutativeExpr for any
// particular input. Don't use a SCEVHandle here, or else the object will never
// be deleted!
static ManagedStatic<std::map<std::pair<unsigned, std::vector<const SCEV*> >,
SCEVCommutativeExpr*> > SCEVCommExprs;
SCEVCommutativeExpr::~SCEVCommutativeExpr() {
std::vector<const SCEV*> SCEVOps(Operands.begin(), Operands.end());
SCEVCommExprs->erase(std::make_pair(getSCEVType(), SCEVOps));
}
void SCEVCommutativeExpr::print(raw_ostream &OS) const {
assert(Operands.size() > 1 && "This plus expr shouldn't exist!");
const char *OpStr = getOperationStr();
OS << "(" << *Operands[0];
for (unsigned i = 1, e = Operands.size(); i != e; ++i)
OS << OpStr << *Operands[i];
OS << ")";
}
SCEVHandle SCEVCommutativeExpr::
replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
const SCEVHandle &Conc,
ScalarEvolution &SE) const {
for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
SCEVHandle H =
getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE);
if (H != getOperand(i)) {
std::vector<SCEVHandle> NewOps;
NewOps.reserve(getNumOperands());
for (unsigned j = 0; j != i; ++j)
NewOps.push_back(getOperand(j));
NewOps.push_back(H);
for (++i; i != e; ++i)
NewOps.push_back(getOperand(i)->
replaceSymbolicValuesWithConcrete(Sym, Conc, SE));
if (isa<SCEVAddExpr>(this))
return SE.getAddExpr(NewOps);
else if (isa<SCEVMulExpr>(this))
return SE.getMulExpr(NewOps);
else if (isa<SCEVSMaxExpr>(this))
return SE.getSMaxExpr(NewOps);
else if (isa<SCEVUMaxExpr>(this))
return SE.getUMaxExpr(NewOps);
else
assert(0 && "Unknown commutative expr!");
}
}
return this;
}
bool SCEVCommutativeExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
if (!getOperand(i)->dominates(BB, DT))
return false;
}
return true;
}
// SCEVUDivs - Only allow the creation of one SCEVUDivExpr for any particular
// input. Don't use a SCEVHandle here, or else the object will never be
// deleted!
static ManagedStatic<std::map<std::pair<const SCEV*, const SCEV*>,
SCEVUDivExpr*> > SCEVUDivs;
SCEVUDivExpr::~SCEVUDivExpr() {
SCEVUDivs->erase(std::make_pair(LHS, RHS));
}
bool SCEVUDivExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
return LHS->dominates(BB, DT) && RHS->dominates(BB, DT);
}
void SCEVUDivExpr::print(raw_ostream &OS) const {
OS << "(" << *LHS << " /u " << *RHS << ")";
}
const Type *SCEVUDivExpr::getType() const {
return LHS->getType();
}
// SCEVAddRecExprs - Only allow the creation of one SCEVAddRecExpr for any
// particular input. Don't use a SCEVHandle here, or else the object will never
// be deleted!
static ManagedStatic<std::map<std::pair<const Loop *,
std::vector<const SCEV*> >,
SCEVAddRecExpr*> > SCEVAddRecExprs;
SCEVAddRecExpr::~SCEVAddRecExpr() {
std::vector<const SCEV*> SCEVOps(Operands.begin(), Operands.end());
SCEVAddRecExprs->erase(std::make_pair(L, SCEVOps));
}
bool SCEVAddRecExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
if (!getOperand(i)->dominates(BB, DT))
return false;
}
return true;
}
SCEVHandle SCEVAddRecExpr::
replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
const SCEVHandle &Conc,
ScalarEvolution &SE) const {
for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
SCEVHandle H =
getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE);
if (H != getOperand(i)) {
std::vector<SCEVHandle> NewOps;
NewOps.reserve(getNumOperands());
for (unsigned j = 0; j != i; ++j)
NewOps.push_back(getOperand(j));
NewOps.push_back(H);
for (++i; i != e; ++i)
NewOps.push_back(getOperand(i)->
replaceSymbolicValuesWithConcrete(Sym, Conc, SE));
return SE.getAddRecExpr(NewOps, L);
}
}
return this;
}
bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const {
// This recurrence is invariant w.r.t to QueryLoop iff QueryLoop doesn't
// contain L and if the start is invariant.
return !QueryLoop->contains(L->getHeader()) &&
getOperand(0)->isLoopInvariant(QueryLoop);
}
void SCEVAddRecExpr::print(raw_ostream &OS) const {
OS << "{" << *Operands[0];
for (unsigned i = 1, e = Operands.size(); i != e; ++i)
OS << ",+," << *Operands[i];
OS << "}<" << L->getHeader()->getName() + ">";
}
// SCEVUnknowns - Only allow the creation of one SCEVUnknown for any particular
// value. Don't use a SCEVHandle here, or else the object will never be
// deleted!
static ManagedStatic<std::map<Value*, SCEVUnknown*> > SCEVUnknowns;
SCEVUnknown::~SCEVUnknown() { SCEVUnknowns->erase(V); }
bool SCEVUnknown::isLoopInvariant(const Loop *L) const {
// All non-instruction values are loop invariant. All instructions are loop
// invariant if they are not contained in the specified loop.
if (Instruction *I = dyn_cast<Instruction>(V))
return !L->contains(I->getParent());
return true;
}
bool SCEVUnknown::dominates(BasicBlock *BB, DominatorTree *DT) const {
if (Instruction *I = dyn_cast<Instruction>(getValue()))
return DT->dominates(I->getParent(), BB);
return true;
}
const Type *SCEVUnknown::getType() const {
return V->getType();
}
void SCEVUnknown::print(raw_ostream &OS) const {
WriteAsOperand(OS, V, false);
}
//===----------------------------------------------------------------------===//
// SCEV Utilities
//===----------------------------------------------------------------------===//
namespace {
/// SCEVComplexityCompare - Return true if the complexity of the LHS is less
/// than the complexity of the RHS. This comparator is used to canonicalize
/// expressions.
struct VISIBILITY_HIDDEN SCEVComplexityCompare {
bool operator()(const SCEV *LHS, const SCEV *RHS) const {
return LHS->getSCEVType() < RHS->getSCEVType();
}
};
}
/// GroupByComplexity - Given a list of SCEV objects, order them by their
/// complexity, and group objects of the same complexity together by value.
/// When this routine is finished, we know that any duplicates in the vector are
/// consecutive and that complexity is monotonically increasing.
///
/// Note that we go take special precautions to ensure that we get determinstic
/// results from this routine. In other words, we don't want the results of
/// this to depend on where the addresses of various SCEV objects happened to
/// land in memory.
///
static void GroupByComplexity(std::vector<SCEVHandle> &Ops) {
if (Ops.size() < 2) return; // Noop
if (Ops.size() == 2) {
// This is the common case, which also happens to be trivially simple.
// Special case it.
if (SCEVComplexityCompare()(Ops[1], Ops[0]))
std::swap(Ops[0], Ops[1]);
return;
}
// Do the rough sort by complexity.
std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare());
// Now that we are sorted by complexity, group elements of the same
// complexity. Note that this is, at worst, N^2, but the vector is likely to
// be extremely short in practice. Note that we take this approach because we
// do not want to depend on the addresses of the objects we are grouping.
for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
const SCEV *S = Ops[i];
unsigned Complexity = S->getSCEVType();
// If there are any objects of the same complexity and same value as this
// one, group them.
for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
if (Ops[j] == S) { // Found a duplicate.
// Move it to immediately after i'th element.
std::swap(Ops[i+1], Ops[j]);
++i; // no need to rescan it.
if (i == e-2) return; // Done!
}
}
}
}
//===----------------------------------------------------------------------===//
// Simple SCEV method implementations
//===----------------------------------------------------------------------===//
/// BinomialCoefficient - Compute BC(It, K). The result has width W.
// Assume, K > 0.
static SCEVHandle BinomialCoefficient(SCEVHandle It, unsigned K,
ScalarEvolution &SE,
const Type* ResultTy) {
// Handle the simplest case efficiently.
if (K == 1)
return SE.getTruncateOrZeroExtend(It, ResultTy);
// We are using the following formula for BC(It, K):
//
// BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
//
// Suppose, W is the bitwidth of the return value. We must be prepared for
// overflow. Hence, we must assure that the result of our computation is
// equal to the accurate one modulo 2^W. Unfortunately, division isn't
// safe in modular arithmetic.
//
// However, this code doesn't use exactly that formula; the formula it uses
// is something like the following, where T is the number of factors of 2 in
// K! (i.e. trailing zeros in the binary representation of K!), and ^ is
// exponentiation:
//
// BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
//
// This formula is trivially equivalent to the previous formula. However,
// this formula can be implemented much more efficiently. The trick is that
// K! / 2^T is odd, and exact division by an odd number *is* safe in modular
// arithmetic. To do exact division in modular arithmetic, all we have
// to do is multiply by the inverse. Therefore, this step can be done at
// width W.
//
// The next issue is how to safely do the division by 2^T. The way this
// is done is by doing the multiplication step at a width of at least W + T
// bits. This way, the bottom W+T bits of the product are accurate. Then,
// when we perform the division by 2^T (which is equivalent to a right shift
// by T), the bottom W bits are accurate. Extra bits are okay; they'll get
// truncated out after the division by 2^T.
//
// In comparison to just directly using the first formula, this technique
// is much more efficient; using the first formula requires W * K bits,
// but this formula less than W + K bits. Also, the first formula requires
// a division step, whereas this formula only requires multiplies and shifts.
//
// It doesn't matter whether the subtraction step is done in the calculation
// width or the input iteration count's width; if the subtraction overflows,
// the result must be zero anyway. We prefer here to do it in the width of
// the induction variable because it helps a lot for certain cases; CodeGen
// isn't smart enough to ignore the overflow, which leads to much less
// efficient code if the width of the subtraction is wider than the native
// register width.
//
// (It's possible to not widen at all by pulling out factors of 2 before
// the multiplication; for example, K=2 can be calculated as
// It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
// extra arithmetic, so it's not an obvious win, and it gets
// much more complicated for K > 3.)
// Protection from insane SCEVs; this bound is conservative,
// but it probably doesn't matter.
if (K > 1000)
return SE.getCouldNotCompute();
unsigned W = SE.getTypeSizeInBits(ResultTy);
// Calculate K! / 2^T and T; we divide out the factors of two before
// multiplying for calculating K! / 2^T to avoid overflow.
// Other overflow doesn't matter because we only care about the bottom
// W bits of the result.
APInt OddFactorial(W, 1);
unsigned T = 1;
for (unsigned i = 3; i <= K; ++i) {
APInt Mult(W, i);
unsigned TwoFactors = Mult.countTrailingZeros();
T += TwoFactors;
Mult = Mult.lshr(TwoFactors);
OddFactorial *= Mult;
}
// We need at least W + T bits for the multiplication step
unsigned CalculationBits = W + T;
// Calcuate 2^T, at width T+W.
APInt DivFactor = APInt(CalculationBits, 1).shl(T);
// Calculate the multiplicative inverse of K! / 2^T;
// this multiplication factor will perform the exact division by
// K! / 2^T.
APInt Mod = APInt::getSignedMinValue(W+1);
APInt MultiplyFactor = OddFactorial.zext(W+1);
MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
MultiplyFactor = MultiplyFactor.trunc(W);
// Calculate the product, at width T+W
const IntegerType *CalculationTy = IntegerType::get(CalculationBits);
SCEVHandle Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
for (unsigned i = 1; i != K; ++i) {
SCEVHandle S = SE.getMinusSCEV(It, SE.getIntegerSCEV(i, It->getType()));
Dividend = SE.getMulExpr(Dividend,
SE.getTruncateOrZeroExtend(S, CalculationTy));
}
// Divide by 2^T
SCEVHandle DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
// Truncate the result, and divide by K! / 2^T.
return SE.getMulExpr(SE.getConstant(MultiplyFactor),
SE.getTruncateOrZeroExtend(DivResult, ResultTy));
}
/// evaluateAtIteration - Return the value of this chain of recurrences at
/// the specified iteration number. We can evaluate this recurrence by
/// multiplying each element in the chain by the binomial coefficient
/// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
///
/// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
///
/// where BC(It, k) stands for binomial coefficient.
///
SCEVHandle SCEVAddRecExpr::evaluateAtIteration(SCEVHandle It,
ScalarEvolution &SE) const {
SCEVHandle Result = getStart();
for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
// The computation is correct in the face of overflow provided that the
// multiplication is performed _after_ the evaluation of the binomial
// coefficient.
SCEVHandle Coeff = BinomialCoefficient(It, i, SE, getType());
if (isa<SCEVCouldNotCompute>(Coeff))
return Coeff;
Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
}
return Result;
}
//===----------------------------------------------------------------------===//
// SCEV Expression folder implementations
//===----------------------------------------------------------------------===//
SCEVHandle ScalarEvolution::getTruncateExpr(const SCEVHandle &Op,
const Type *Ty) {
assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
"This is not a truncating conversion!");
assert(isSCEVable(Ty) &&
"This is not a conversion to a SCEVable type!");
Ty = getEffectiveSCEVType(Ty);
if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
return getUnknown(
ConstantExpr::getTrunc(SC->getValue(), Ty));
// trunc(trunc(x)) --> trunc(x)
if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
return getTruncateExpr(ST->getOperand(), Ty);
// trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
return getTruncateOrSignExtend(SS->getOperand(), Ty);
// trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
// If the input value is a chrec scev made out of constants, truncate
// all of the constants.
if (const 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(getTruncateExpr(AddRec->getOperand(i), Ty));
else
break;
if (Operands.size() == AddRec->getNumOperands())
return getAddRecExpr(Operands, AddRec->getLoop());
}
SCEVTruncateExpr *&Result = (*SCEVTruncates)[std::make_pair(Op, Ty)];
if (Result == 0) Result = new SCEVTruncateExpr(Op, Ty);
return Result;
}
SCEVHandle ScalarEvolution::getZeroExtendExpr(const SCEVHandle &Op,
const Type *Ty) {
assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
"This is not an extending conversion!");
assert(isSCEVable(Ty) &&
"This is not a conversion to a SCEVable type!");
Ty = getEffectiveSCEVType(Ty);
if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) {
const Type *IntTy = getEffectiveSCEVType(Ty);
Constant *C = ConstantExpr::getZExt(SC->getValue(), IntTy);
if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty);
return getUnknown(C);
}
// zext(zext(x)) --> zext(x)
if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
return getZeroExtendExpr(SZ->getOperand(), Ty);
// If the input value is a chrec scev, and we can prove that the value
// did not overflow the old, smaller, value, we can zero extend all of the
// operands (often constants). This allows analysis of something like
// this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
if (AR->isAffine()) {
// Check whether the backedge-taken count is SCEVCouldNotCompute.
// Note that this serves two purposes: It filters out loops that are
// simply not analyzable, and it covers the case where this code is
// being called from within backedge-taken count analysis, such that
// attempting to ask for the backedge-taken count would likely result
// in infinite recursion. In the later case, the analysis code will
// cope with a conservative value, and it will take care to purge
// that value once it has finished.
SCEVHandle MaxBECount = getMaxBackedgeTakenCount(AR->getLoop());
if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
// Manually compute the final value for AR, checking for
// overflow.
SCEVHandle Start = AR->getStart();
SCEVHandle Step = AR->getStepRecurrence(*this);
// Check whether the backedge-taken count can be losslessly casted to
// the addrec's type. The count is always unsigned.
SCEVHandle CastedMaxBECount =
getTruncateOrZeroExtend(MaxBECount, Start->getType());
if (MaxBECount ==
getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType())) {
const Type *WideTy =
IntegerType::get(getTypeSizeInBits(Start->getType()) * 2);
// Check whether Start+Step*MaxBECount has no unsigned overflow.
SCEVHandle ZMul =
getMulExpr(CastedMaxBECount,
getTruncateOrZeroExtend(Step, Start->getType()));
SCEVHandle Add = getAddExpr(Start, ZMul);
if (getZeroExtendExpr(Add, WideTy) ==
getAddExpr(getZeroExtendExpr(Start, WideTy),
getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
getZeroExtendExpr(Step, WideTy))))
// Return the expression with the addrec on the outside.
return getAddRecExpr(getZeroExtendExpr(Start, Ty),
getZeroExtendExpr(Step, Ty),
AR->getLoop());
// Similar to above, only this time treat the step value as signed.
// This covers loops that count down.
SCEVHandle SMul =
getMulExpr(CastedMaxBECount,
getTruncateOrSignExtend(Step, Start->getType()));
Add = getAddExpr(Start, SMul);
if (getZeroExtendExpr(Add, WideTy) ==
getAddExpr(getZeroExtendExpr(Start, WideTy),
getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
getSignExtendExpr(Step, WideTy))))
// Return the expression with the addrec on the outside.
return getAddRecExpr(getZeroExtendExpr(Start, Ty),
getSignExtendExpr(Step, Ty),
AR->getLoop());
}
}
}
SCEVZeroExtendExpr *&Result = (*SCEVZeroExtends)[std::make_pair(Op, Ty)];
if (Result == 0) Result = new SCEVZeroExtendExpr(Op, Ty);
return Result;
}
SCEVHandle ScalarEvolution::getSignExtendExpr(const SCEVHandle &Op,
const Type *Ty) {
assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
"This is not an extending conversion!");
assert(isSCEVable(Ty) &&
"This is not a conversion to a SCEVable type!");
Ty = getEffectiveSCEVType(Ty);
if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) {
const Type *IntTy = getEffectiveSCEVType(Ty);
Constant *C = ConstantExpr::getSExt(SC->getValue(), IntTy);
if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty);
return getUnknown(C);
}
// sext(sext(x)) --> sext(x)
if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
return getSignExtendExpr(SS->getOperand(), Ty);
// If the input value is a chrec scev, and we can prove that the value
// did not overflow the old, smaller, value, we can sign extend all of the
// operands (often constants). This allows analysis of something like
// this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
if (AR->isAffine()) {
// Check whether the backedge-taken count is SCEVCouldNotCompute.
// Note that this serves two purposes: It filters out loops that are
// simply not analyzable, and it covers the case where this code is
// being called from within backedge-taken count analysis, such that
// attempting to ask for the backedge-taken count would likely result
// in infinite recursion. In the later case, the analysis code will
// cope with a conservative value, and it will take care to purge
// that value once it has finished.
SCEVHandle MaxBECount = getMaxBackedgeTakenCount(AR->getLoop());
if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
// Manually compute the final value for AR, checking for
// overflow.
SCEVHandle Start = AR->getStart();
SCEVHandle Step = AR->getStepRecurrence(*this);
// Check whether the backedge-taken count can be losslessly casted to
// the addrec's type. The count is always unsigned.
SCEVHandle CastedMaxBECount =
getTruncateOrZeroExtend(MaxBECount, Start->getType());
if (MaxBECount ==
getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType())) {
const Type *WideTy =
IntegerType::get(getTypeSizeInBits(Start->getType()) * 2);
// Check whether Start+Step*MaxBECount has no signed overflow.
SCEVHandle SMul =
getMulExpr(CastedMaxBECount,
getTruncateOrSignExtend(Step, Start->getType()));
SCEVHandle Add = getAddExpr(Start, SMul);
if (getSignExtendExpr(Add, WideTy) ==
getAddExpr(getSignExtendExpr(Start, WideTy),
getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
getSignExtendExpr(Step, WideTy))))
// Return the expression with the addrec on the outside.
return getAddRecExpr(getSignExtendExpr(Start, Ty),
getSignExtendExpr(Step, Ty),
AR->getLoop());
}
}
}
SCEVSignExtendExpr *&Result = (*SCEVSignExtends)[std::make_pair(Op, Ty)];
if (Result == 0) Result = new SCEVSignExtendExpr(Op, Ty);
return Result;
}
// get - Get a canonical add expression, or something simpler if possible.
SCEVHandle ScalarEvolution::getAddExpr(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 (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
++Idx;
assert(Idx < Ops.size());
while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
// We found two constants, fold them together!
ConstantInt *Fold = ConstantInt::get(LHSC->getValue()->getValue() +
RHSC->getValue()->getValue());
Ops[0] = getConstant(Fold);
Ops.erase(Ops.begin()+1); // Erase the folded element
if (Ops.size() == 1) return Ops[0];
LHSC = cast<SCEVConstant>(Ops[0]);
}
// If we are left with a constant zero being added, strip it off.
if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
Ops.erase(Ops.begin());
--Idx;
}
}
if (Ops.size() == 1) return Ops[0];
// Okay, check to see if the same value occurs in the operand list twice. If
// so, merge them together into an multiply expression. Since we sorted the
// list, these values are required to be adjacent.
const Type *Ty = Ops[0]->getType();
for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
// Found a match, merge the two values into a multiply, and add any
// remaining values to the result.
SCEVHandle Two = getIntegerSCEV(2, Ty);
SCEVHandle Mul = getMulExpr(Ops[i], Two);
if (Ops.size() == 2)
return Mul;
Ops.erase(Ops.begin()+i, Ops.begin()+i+2);
Ops.push_back(Mul);
return getAddExpr(Ops);
}
// Now we know the first non-constant operand. Skip past any cast SCEVs.
while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
++Idx;
// If there are add operands they would be next.
if (Idx < Ops.size()) {
bool DeletedAdd = false;
while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
// If we have an add, expand the add operands onto the end of the operands
// list.
Ops.insert(Ops.end(), Add->op_begin(), Add->op_end());
Ops.erase(Ops.begin()+Idx);
DeletedAdd = true;
}
// If we deleted at least one add, we added operands to the end of the list,
// and they are not necessarily sorted. Recurse to resort and resimplify
// any operands we just aquired.
if (DeletedAdd)
return getAddExpr(Ops);
}
// Skip over the add expression until we get to a multiply.
while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
++Idx;
// If we are adding something to a multiply expression, make sure the
// something is not already an operand of the multiply. If so, merge it into
// the multiply.
for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(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 = getMulExpr(MulOps);
}
SCEVHandle One = getIntegerSCEV(1, Ty);
SCEVHandle AddOne = getAddExpr(InnerMul, One);
SCEVHandle OuterMul = getMulExpr(AddOne, Ops[AddOp]);
if (Ops.size() == 2) return OuterMul;
if (AddOp < Idx) {
Ops.erase(Ops.begin()+AddOp);
Ops.erase(Ops.begin()+Idx-1);
} else {
Ops.erase(Ops.begin()+Idx);
Ops.erase(Ops.begin()+AddOp-1);
}
Ops.push_back(OuterMul);
return getAddExpr(Ops);
}
// Check this multiply against other multiplies being added together.
for (unsigned OtherMulIdx = Idx+1;
OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
++OtherMulIdx) {
const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
// If MulOp occurs in OtherMul, we can fold the two multiplies
// together.
for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
OMulOp != e; ++OMulOp)
if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
// Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
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 = getMulExpr(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 = getMulExpr(MulOps);
}
SCEVHandle InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
SCEVHandle OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
if (Ops.size() == 2) return OuterMul;
Ops.erase(Ops.begin()+Idx);
Ops.erase(Ops.begin()+OtherMulIdx-1);
Ops.push_back(OuterMul);
return getAddExpr(Ops);
}
}
}
}
// If there are any add recurrences in the operands list, see if any other
// added values are loop invariant. If so, we can fold them into the
// recurrence.
while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
++Idx;
// Scan over all recurrences, trying to fold loop invariants into them.
for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
// Scan all of the other operands to this add and add them to the vector if
// they are loop invariant w.r.t. the recurrence.
std::vector<SCEVHandle> LIOps;
const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
for (unsigned i = 0, e = Ops.size(); i != e; ++i)
if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
LIOps.push_back(Ops[i]);
Ops.erase(Ops.begin()+i);
--i; --e;
}
// If we found some loop invariants, fold them into the recurrence.
if (!LIOps.empty()) {
// NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
LIOps.push_back(AddRec->getStart());
std::vector<SCEVHandle> AddRecOps(AddRec->op_begin(), AddRec->op_end());
AddRecOps[0] = getAddExpr(LIOps);
SCEVHandle NewRec = getAddRecExpr(AddRecOps, AddRec->getLoop());
// If all of the other operands were loop invariant, we are done.
if (Ops.size() == 1) return NewRec;
// Otherwise, add the folded AddRec by the non-liv parts.
for (unsigned i = 0;; ++i)
if (Ops[i] == AddRec) {
Ops[i] = NewRec;
break;
}
return getAddExpr(Ops);
}
// Okay, if there weren't any loop invariants to be folded, check to see if
// there are multiple AddRec's with the same loop induction variable being
// added together. If so, we can fold them.
for (unsigned OtherIdx = Idx+1;
OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
if (OtherIdx != Idx) {
const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
if (AddRec->getLoop() == OtherAddRec->getLoop()) {
// Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D}
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] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i));
}
SCEVHandle NewAddRec = getAddRecExpr(NewOps, AddRec->getLoop());
if (Ops.size() == 2) return NewAddRec;
Ops.erase(Ops.begin()+Idx);
Ops.erase(Ops.begin()+OtherIdx-1);
Ops.push_back(NewAddRec);
return getAddExpr(Ops);
}
}
// Otherwise couldn't fold anything into this recurrence. Move onto the
// next one.
}
// Okay, it looks like we really DO need an add expr. Check to see if we
// already have one, otherwise create a new one.
std::vector<const SCEV*> SCEVOps(Ops.begin(), Ops.end());
SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scAddExpr,
SCEVOps)];
if (Result == 0) Result = new SCEVAddExpr(Ops);
return Result;
}
SCEVHandle ScalarEvolution::getMulExpr(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 (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
// C1*(C2+V) -> C1*C2 + C1*V
if (Ops.size() == 2)
if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
if (Add->getNumOperands() == 2 &&
isa<SCEVConstant>(Add->getOperand(0)))
return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
getMulExpr(LHSC, Add->getOperand(1)));
++Idx;
while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
// We found two constants, fold them together!
ConstantInt *Fold = ConstantInt::get(LHSC->getValue()->getValue() *
RHSC->getValue()->getValue());
Ops[0] = getConstant(Fold);
Ops.erase(Ops.begin()+1); // Erase the folded element
if (Ops.size() == 1) return Ops[0];
LHSC = cast<SCEVConstant>(Ops[0]);
}
// If we are left with a constant one being multiplied, strip it off.
if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
Ops.erase(Ops.begin());
--Idx;
} else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
// If we have a multiply of zero, it will always be zero.
return Ops[0];
}
}
// Skip over the add expression until we get to a multiply.
while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
++Idx;
if (Ops.size() == 1)
return Ops[0];
// If there are mul operands inline them all into this expression.
if (Idx < Ops.size()) {
bool DeletedMul = false;
while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
// If we have an mul, expand the mul operands onto the end of the operands
// list.
Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end());
Ops.erase(Ops.begin()+Idx);
DeletedMul = true;
}
// If we deleted at least one mul, we added operands to the end of the list,
// and they are not necessarily sorted. Recurse to resort and resimplify
// any operands we just aquired.
if (DeletedMul)
return getMulExpr(Ops);
}
// If there are any add recurrences in the operands list, see if any other
// added values are loop invariant. If so, we can fold them into the
// recurrence.
while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
++Idx;
// Scan over all recurrences, trying to fold loop invariants into them.
for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
// Scan all of the other operands to this mul and add them to the vector if
// they are loop invariant w.r.t. the recurrence.
std::vector<SCEVHandle> LIOps;
const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
for (unsigned i = 0, e = Ops.size(); i != e; ++i)
if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
LIOps.push_back(Ops[i]);
Ops.erase(Ops.begin()+i);
--i; --e;
}
// If we found some loop invariants, fold them into the recurrence.
if (!LIOps.empty()) {
// NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
std::vector<SCEVHandle> NewOps;
NewOps.reserve(AddRec->getNumOperands());
if (LIOps.size() == 1) {
const SCEV *Scale = LIOps[0];
for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
} else {
for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
std::vector<SCEVHandle> MulOps(LIOps);
MulOps.push_back(AddRec->getOperand(i));
NewOps.push_back(getMulExpr(MulOps));
}
}
SCEVHandle NewRec = getAddRecExpr(NewOps, AddRec->getLoop());
// If all of the other operands were loop invariant, we are done.
if (Ops.size() == 1) return NewRec;
// Otherwise, multiply the folded AddRec by the non-liv parts.
for (unsigned i = 0;; ++i)
if (Ops[i] == AddRec) {
Ops[i] = NewRec;
break;
}
return getMulExpr(Ops);
}
// Okay, if there weren't any loop invariants to be folded, check to see if
// there are multiple AddRec's with the same loop induction variable being
// multiplied together. If so, we can fold them.
for (unsigned OtherIdx = Idx+1;
OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
if (OtherIdx != Idx) {
const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
if (AddRec->getLoop() == OtherAddRec->getLoop()) {
// F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D}
const SCEVAddRecExpr *F = AddRec, *G = OtherAddRec;
SCEVHandle NewStart = getMulExpr(F->getStart(),
G->getStart());
SCEVHandle B = F->getStepRecurrence(*this);
SCEVHandle D = G->getStepRecurrence(*this);
SCEVHandle NewStep = getAddExpr(getMulExpr(F, D),
getMulExpr(G, B),
getMulExpr(B, D));
SCEVHandle NewAddRec = getAddRecExpr(NewStart, NewStep,
F->getLoop());
if (Ops.size() == 2) return NewAddRec;
Ops.erase(Ops.begin()+Idx);
Ops.erase(Ops.begin()+OtherIdx-1);
Ops.push_back(NewAddRec);
return getMulExpr(Ops);
}
}
// Otherwise couldn't fold anything into this recurrence. Move onto the
// next one.
}
// Okay, it looks like we really DO need an mul expr. Check to see if we
// already have one, otherwise create a new one.
std::vector<const SCEV*> SCEVOps(Ops.begin(), Ops.end());
SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scMulExpr,
SCEVOps)];
if (Result == 0)
Result = new SCEVMulExpr(Ops);
return Result;
}
SCEVHandle ScalarEvolution::getUDivExpr(const SCEVHandle &LHS,
const SCEVHandle &RHS) {
if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
if (RHSC->getValue()->equalsInt(1))
return LHS; // X udiv 1 --> x
if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
Constant *LHSCV = LHSC->getValue();
Constant *RHSCV = RHSC->getValue();
return getUnknown(ConstantExpr::getUDiv(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 ScalarEvolution::getAddRecExpr(const SCEVHandle &Start,
const SCEVHandle &Step, const Loop *L) {
std::vector<SCEVHandle> Operands;
Operands.push_back(Start);
if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
if (StepChrec->getLoop() == L) {
Operands.insert(Operands.end(), StepChrec->op_begin(),
StepChrec->op_end());
return getAddRecExpr(Operands, L);
}
Operands.push_back(Step);
return getAddRecExpr(Operands, L);
}
/// SCEVAddRecExpr::get - Get a add recurrence expression for the
/// specified loop. Simplify the expression as much as possible.
SCEVHandle ScalarEvolution::getAddRecExpr(std::vector<SCEVHandle> &Operands,
const Loop *L) {
if (Operands.size() == 1) return Operands[0];
if (Operands.back()->isZero()) {
Operands.pop_back();
return getAddRecExpr(Operands, L); // {X,+,0} --> X
}
// Canonicalize nested AddRecs in by nesting them in order of loop depth.
if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
const Loop* NestedLoop = NestedAR->getLoop();
if (L->getLoopDepth() < NestedLoop->getLoopDepth()) {
std::vector<SCEVHandle> NestedOperands(NestedAR->op_begin(),
NestedAR->op_end());
SCEVHandle NestedARHandle(NestedAR);
Operands[0] = NestedAR->getStart();
NestedOperands[0] = getAddRecExpr(Operands, L);
return getAddRecExpr(NestedOperands, NestedLoop);
}
}
std::vector<const SCEV*> SCEVOps(Operands.begin(), Operands.end());
SCEVAddRecExpr *&Result = (*SCEVAddRecExprs)[std::make_pair(L, SCEVOps)];
if (Result == 0) Result = new SCEVAddRecExpr(Operands, L);
return Result;
}
SCEVHandle ScalarEvolution::getSMaxExpr(const SCEVHandle &LHS,
const SCEVHandle &RHS) {
std::vector<SCEVHandle> Ops;
Ops.push_back(LHS);
Ops.push_back(RHS);
return getSMaxExpr(Ops);
}
SCEVHandle ScalarEvolution::getSMaxExpr(std::vector<SCEVHandle> Ops) {
assert(!Ops.empty() && "Cannot get empty smax!");
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 (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
++Idx;
assert(Idx < Ops.size());
while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
// We found two constants, fold them together!
ConstantInt *Fold = ConstantInt::get(
APIntOps::smax(LHSC->getValue()->getValue(),
RHSC->getValue()->getValue()));
Ops[0] = getConstant(Fold);
Ops.erase(Ops.begin()+1); // Erase the folded element
if (Ops.size() == 1) return Ops[0];
LHSC = cast<SCEVConstant>(Ops[0]);
}
// If we are left with a constant -inf, strip it off.
if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
Ops.erase(Ops.begin());
--Idx;
}
}
if (Ops.size() == 1) return Ops[0];
// Find the first SMax
while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
++Idx;
// Check to see if one of the operands is an SMax. If so, expand its operands
// onto our operand list, and recurse to simplify.
if (Idx < Ops.size()) {
bool DeletedSMax = false;
while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
Ops.insert(Ops.end(), SMax->op_begin(), SMax->op_end());
Ops.erase(Ops.begin()+Idx);
DeletedSMax = true;
}
if (DeletedSMax)
return getSMaxExpr(Ops);
}
// Okay, check to see if the same value occurs in the operand list twice. If
// so, delete one. Since we sorted the list, these values are required to
// be adjacent.
for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
if (Ops[i] == Ops[i+1]) { // X smax Y smax Y --> X smax Y
Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
--i; --e;
}
if (Ops.size() == 1) return Ops[0];
assert(!Ops.empty() && "Reduced smax down to nothing!");
// Okay, it looks like we really DO need an smax expr. Check to see if we
// already have one, otherwise create a new one.
std::vector<const SCEV*> SCEVOps(Ops.begin(), Ops.end());
SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scSMaxExpr,
SCEVOps)];
if (Result == 0) Result = new SCEVSMaxExpr(Ops);
return Result;
}
SCEVHandle ScalarEvolution::getUMaxExpr(const SCEVHandle &LHS,
const SCEVHandle &RHS) {
std::vector<SCEVHandle> Ops;
Ops.push_back(LHS);
Ops.push_back(RHS);
return getUMaxExpr(Ops);
}
SCEVHandle ScalarEvolution::getUMaxExpr(std::vector<SCEVHandle> Ops) {
assert(!Ops.empty() && "Cannot get empty umax!");
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 (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
++Idx;
assert(Idx < Ops.size());
while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
// We found two constants, fold them together!
ConstantInt *Fold = ConstantInt::get(
APIntOps::umax(LHSC->getValue()->getValue(),
RHSC->getValue()->getValue()));
Ops[0] = getConstant(Fold);
Ops.erase(Ops.begin()+1); // Erase the folded element
if (Ops.size() == 1) return Ops[0];
LHSC = cast<SCEVConstant>(Ops[0]);
}
// If we are left with a constant zero, strip it off.
if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
Ops.erase(Ops.begin());
--Idx;
}
}
if (Ops.size() == 1) return Ops[0];
// Find the first UMax
while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
++Idx;
// Check to see if one of the operands is a UMax. If so, expand its operands
// onto our operand list, and recurse to simplify.
if (Idx < Ops.size()) {
bool DeletedUMax = false;
while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
Ops.insert(Ops.end(), UMax->op_begin(), UMax->op_end());
Ops.erase(Ops.begin()+Idx);
DeletedUMax = true;
}
if (DeletedUMax)
return getUMaxExpr(Ops);
}
// Okay, check to see if the same value occurs in the operand list twice. If
// so, delete one. Since we sorted the list, these values are required to
// be adjacent.
for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
if (Ops[i] == Ops[i+1]) { // X umax Y umax Y --> X umax Y
Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
--i; --e;
}
if (Ops.size() == 1) return Ops[0];
assert(!Ops.empty() && "Reduced umax down to nothing!");
// Okay, it looks like we really DO need a umax expr. Check to see if we
// already have one, otherwise create a new one.
std::vector<const SCEV*> SCEVOps(Ops.begin(), Ops.end());
SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scUMaxExpr,
SCEVOps)];
if (Result == 0) Result = new SCEVUMaxExpr(Ops);
return Result;
}
SCEVHandle ScalarEvolution::getUnknown(Value *V) {
if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
return getConstant(CI);
if (isa<ConstantPointerNull>(V))
return getIntegerSCEV(0, V->getType());
SCEVUnknown *&Result = (*SCEVUnknowns)[V];
if (Result == 0) Result = new SCEVUnknown(V);
return Result;
}
//===----------------------------------------------------------------------===//
// Basic SCEV Analysis and PHI Idiom Recognition Code
//
/// isSCEVable - Test if values of the given type are analyzable within
/// the SCEV framework. This primarily includes integer types, and it
/// can optionally include pointer types if the ScalarEvolution class
/// has access to target-specific information.
bool ScalarEvolution::isSCEVable(const Type *Ty) const {
// Integers are always SCEVable.
if (Ty->isInteger())
return true;
// Pointers are SCEVable if TargetData information is available
// to provide pointer size information.
if (isa<PointerType>(Ty))
return TD != NULL;
// Otherwise it's not SCEVable.
return false;
}
/// getTypeSizeInBits - Return the size in bits of the specified type,
/// for which isSCEVable must return true.
uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const {
assert(isSCEVable(Ty) && "Type is not SCEVable!");
// If we have a TargetData, use it!
if (TD)
return TD->getTypeSizeInBits(Ty);
// Otherwise, we support only integer types.
assert(Ty->isInteger() && "isSCEVable permitted a non-SCEVable type!");
return Ty->getPrimitiveSizeInBits();
}
/// getEffectiveSCEVType - Return a type with the same bitwidth as
/// the given type and which represents how SCEV will treat the given
/// type, for which isSCEVable must return true. For pointer types,
/// this is the pointer-sized integer type.
const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const {
assert(isSCEVable(Ty) && "Type is not SCEVable!");
if (Ty->isInteger())
return Ty;
assert(isa<PointerType>(Ty) && "Unexpected non-pointer non-integer type!");
return TD->getIntPtrType();
}
SCEVHandle ScalarEvolution::getCouldNotCompute() {
return UnknownValue;
}
/// hasSCEV - Return true if the SCEV for this value has already been
/// computed.
bool ScalarEvolution::hasSCEV(Value *V) const {
return Scalars.count(V);
}
/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
/// expression and create a new one.
SCEVHandle ScalarEvolution::getSCEV(Value *V) {
assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
std::map<SCEVCallbackVH, SCEVHandle>::iterator I = Scalars.find(V);
if (I != Scalars.end()) return I->second;
SCEVHandle S = createSCEV(V);
Scalars.insert(std::make_pair(SCEVCallbackVH(V, this), S));
return S;
}
/// getIntegerSCEV - Given an integer or FP type, create a constant for the
/// specified signed integer value and return a SCEV for the constant.
SCEVHandle ScalarEvolution::getIntegerSCEV(int Val, const Type *Ty) {
Ty = getEffectiveSCEVType(Ty);
Constant *C;
if (Val == 0)
C = Constant::getNullValue(Ty);
else if (Ty->isFloatingPoint())
C = ConstantFP::get(APFloat(Ty==Type::FloatTy ? APFloat::IEEEsingle :
APFloat::IEEEdouble, Val));
else
C = ConstantInt::get(Ty, Val);
return getUnknown(C);
}
/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
///
SCEVHandle ScalarEvolution::getNegativeSCEV(const SCEVHandle &V) {
if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
return getUnknown(ConstantExpr::getNeg(VC->getValue()));
const Type *Ty = V->getType();
Ty = getEffectiveSCEVType(Ty);
return getMulExpr(V, getConstant(ConstantInt::getAllOnesValue(Ty)));
}
/// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
SCEVHandle ScalarEvolution::getNotSCEV(const SCEVHandle &V) {
if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
return getUnknown(ConstantExpr::getNot(VC->getValue()));
const Type *Ty = V->getType();
Ty = getEffectiveSCEVType(Ty);
SCEVHandle AllOnes = getConstant(ConstantInt::getAllOnesValue(Ty));
return getMinusSCEV(AllOnes, V);
}
/// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
///
SCEVHandle ScalarEvolution::getMinusSCEV(const SCEVHandle &LHS,
const SCEVHandle &RHS) {
// X - Y --> X + -Y
return getAddExpr(LHS, getNegativeSCEV(RHS));
}
/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
/// input value to the specified type. If the type must be extended, it is zero
/// extended.
SCEVHandle
ScalarEvolution::getTruncateOrZeroExtend(const SCEVHandle &V,
const Type *Ty) {
const Type *SrcTy = V->getType();
assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
(Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
"Cannot truncate or zero extend with non-integer arguments!");
if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
return V; // No conversion
if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
return getTruncateExpr(V, Ty);
return getZeroExtendExpr(V, Ty);
}
/// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
/// input value to the specified type. If the type must be extended, it is sign
/// extended.
SCEVHandle
ScalarEvolution::getTruncateOrSignExtend(const SCEVHandle &V,
const Type *Ty) {
const Type *SrcTy = V->getType();
assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
(Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
"Cannot truncate or zero extend with non-integer arguments!");
if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
return V; // No conversion
if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
return getTruncateExpr(V, Ty);
return getSignExtendExpr(V, Ty);
}
/// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value for
/// the specified instruction and replaces any references to the symbolic value
/// SymName with the specified value. This is used during PHI resolution.
void ScalarEvolution::
ReplaceSymbolicValueWithConcrete(Instruction *I, const SCEVHandle &SymName,
const SCEVHandle &NewVal) {
std::map<SCEVCallbackVH, SCEVHandle>::iterator SI =
Scalars.find(SCEVCallbackVH(I, this));
if (SI == Scalars.end()) return;
SCEVHandle NV =
SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal, *this);
if (NV == SI->second) return; // No change.
SI->second = NV; // Update the scalars map!
// Any instruction values that use this instruction might also need to be
// updated!
for (Value::use_iterator UI = I->use_begin(), E = I->use_end();
UI != E; ++UI)
ReplaceSymbolicValueWithConcrete(cast<Instruction>(*UI), SymName, NewVal);
}
/// 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 ScalarEvolution::createNodeForPHI(PHINode *PN) {
if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized.
if (const Loop *L = LI->getLoopFor(PN->getParent()))
if (L->getHeader() == PN->getParent()) {
// If it lives in the loop header, it has two incoming values, one
// from outside the loop, and one from inside.
unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0));
unsigned BackEdge = IncomingEdge^1;
// While we are analyzing this PHI node, handle its value symbolically.
SCEVHandle SymbolicName = getUnknown(PN);
assert(Scalars.find(PN) == Scalars.end() &&
"PHI node already processed?");
Scalars.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
// Using this symbolic name for the PHI, analyze the value coming around
// the back-edge.
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 (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
// If there is a single occurrence of the symbolic value, replace it
// with a recurrence.
unsigned FoundIndex = Add->getNumOperands();
for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
if (Add->getOperand(i) == SymbolicName)
if (FoundIndex == e) {
FoundIndex = i;
break;
}
if (FoundIndex != Add->getNumOperands()) {
// Create an add with everything but the specified operand.
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 = getAddExpr(Ops);
// This is not a valid addrec if the step amount is varying each
// loop iteration, but is not itself an addrec in this loop.
if (Accum->isLoopInvariant(L) ||
(isa<SCEVAddRecExpr>(Accum) &&
cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
SCEVHandle PHISCEV = getAddRecExpr(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.
ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
return PHISCEV;
}
}
} else if (const SCEVAddRecExpr *AddRec =
dyn_cast<SCEVAddRecExpr>(BEValue)) {
// Otherwise, this could be a loop like this:
// i = 0; for (j = 1; ..; ++j) { .... i = j; }
// In this case, j = {1,+,1} and BEValue is j.
// Because the other in-value of i (0) fits the evolution of BEValue
// i really is an addrec evolution.
if (AddRec->getLoop() == L && AddRec->isAffine()) {
SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
// If StartVal = j.start - j.stride, we can use StartVal as the
// initial step of the addrec evolution.
if (StartVal == getMinusSCEV(AddRec->getOperand(0),
AddRec->getOperand(1))) {
SCEVHandle PHISCEV =
getAddRecExpr(StartVal, AddRec->getOperand(1), L);
// Okay, for the entire analysis of this edge we assumed the PHI
// to be symbolic. We now need to go back and 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.
ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
return PHISCEV;
}
}
}
return SymbolicName;
}
// If it's not a loop phi, we can't handle it yet.
return getUnknown(PN);
}
/// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
/// guaranteed to end in (at every loop iteration). It is, at the same time,
/// the minimum number of times S is divisible by 2. For example, given {4,+,8}
/// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
static uint32_t GetMinTrailingZeros(SCEVHandle S, const ScalarEvolution &SE) {
if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
return C->getValue()->getValue().countTrailingZeros();
if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
return std::min(GetMinTrailingZeros(T->getOperand(), SE),
(uint32_t)SE.getTypeSizeInBits(T->getType()));
if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
uint32_t OpRes = GetMinTrailingZeros(E->getOperand(), SE);
return OpRes == SE.getTypeSizeInBits(E->getOperand()->getType()) ?
SE.getTypeSizeInBits(E->getOperand()->getType()) : OpRes;
}
if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
uint32_t OpRes = GetMinTrailingZeros(E->getOperand(), SE);
return OpRes == SE.getTypeSizeInBits(E->getOperand()->getType()) ?
SE.getTypeSizeInBits(E->getOperand()->getType()) : OpRes;
}
if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
// The result is the min of all operands results.
uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0), SE);
for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i), SE));
return MinOpRes;
}
if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
// The result is the sum of all operands results.
uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0), SE);
uint32_t BitWidth = SE.getTypeSizeInBits(M->getType());
for (unsigned i = 1, e = M->getNumOperands();
SumOpRes != BitWidth && i != e; ++i)
SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i), SE),
BitWidth);
return SumOpRes;
}
if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
// The result is the min of all operands results.
uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0), SE);
for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i), SE));
return MinOpRes;
}
if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
// The result is the min of all operands results.
uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0), SE);
for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i), SE));
return MinOpRes;
}
if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
// The result is the min of all operands results.
uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0), SE);
for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i), SE));
return MinOpRes;
}
// SCEVUDivExpr, SCEVUnknown
return 0;
}
/// createSCEV - We know that there is no SCEV for the specified value.
/// Analyze the expression.
///
SCEVHandle ScalarEvolution::createSCEV(Value *V) {
if (!isSCEVable(V->getType()))
return getUnknown(V);
unsigned Opcode = Instruction::UserOp1;
if (Instruction *I = dyn_cast<Instruction>(V))
Opcode = I->getOpcode();
else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
Opcode = CE->getOpcode();
else
return getUnknown(V);
User *U = cast<User>(V);
switch (Opcode) {
case Instruction::Add:
return getAddExpr(getSCEV(U->getOperand(0)),
getSCEV(U->getOperand(1)));
case Instruction::Mul:
return getMulExpr(getSCEV(U->getOperand(0)),
getSCEV(U->getOperand(1)));
case Instruction::UDiv:
return getUDivExpr(getSCEV(U->getOperand(0)),
getSCEV(U->getOperand(1)));
case Instruction::Sub:
return getMinusSCEV(getSCEV(U->getOperand(0)),
getSCEV(U->getOperand(1)));
case Instruction::And:
// For an expression like x&255 that merely masks off the high bits,
// use zext(trunc(x)) as the SCEV expression.
if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
if (CI->isNullValue())
return getSCEV(U->getOperand(1));
if (CI->isAllOnesValue())
return getSCEV(U->getOperand(0));
const APInt &A = CI->getValue();
unsigned Ones = A.countTrailingOnes();
if (APIntOps::isMask(Ones, A))
return
getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)),
IntegerType::get(Ones)),
U->getType());
}
break;
case Instruction::Or:
// If the RHS of the Or is a constant, we may have something like:
// X*4+1 which got turned into X*4|1. Handle this as an Add so loop
// optimizations will transparently handle this case.
//
// In order for this transformation to be safe, the LHS must be of the
// form X*(2^n) and the Or constant must be less than 2^n.
if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
SCEVHandle LHS = getSCEV(U->getOperand(0));
const APInt &CIVal = CI->getValue();
if (GetMinTrailingZeros(LHS, *this) >=
(CIVal.getBitWidth() - CIVal.countLeadingZeros()))
return getAddExpr(LHS, getSCEV(U->getOperand(1)));
}
break;
case Instruction::Xor:
if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
// If the RHS of the xor is a signbit, then this is just an add.
// Instcombine turns add of signbit into xor as a strength reduction step.
if (CI->getValue().isSignBit())
return getAddExpr(getSCEV(U->getOperand(0)),
getSCEV(U->getOperand(1)));
// If the RHS of xor is -1, then this is a not operation.
else if (CI->isAllOnesValue())
return getNotSCEV(getSCEV(U->getOperand(0)));
}
break;
case Instruction::Shl:
// Turn shift left of a constant amount into a multiply.
if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth();
Constant *X = ConstantInt::get(
APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
}
break;
case Instruction::LShr:
// Turn logical shift right of a constant into a unsigned divide.
if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth();
Constant *X = ConstantInt::get(
APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
}
break;
case Instruction::AShr:
// For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
if (Instruction *L = dyn_cast<Instruction>(U->getOperand(0)))
if (L->getOpcode() == Instruction::Shl &&
L->getOperand(1) == U->getOperand(1)) {
unsigned BitWidth = getTypeSizeInBits(U->getType());
uint64_t Amt = BitWidth - CI->getZExtValue();
if (Amt == BitWidth)
return getSCEV(L->getOperand(0)); // shift by zero --> noop
if (Amt > BitWidth)
return getIntegerSCEV(0, U->getType()); // value is undefined
return
getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
IntegerType::get(Amt)),
U->getType());
}
break;
case Instruction::Trunc:
return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
case Instruction::ZExt:
return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
case Instruction::SExt:
return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
case Instruction::BitCast:
// BitCasts are no-op casts so we just eliminate the cast.
if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
return getSCEV(U->getOperand(0));
break;
case Instruction::IntToPtr:
if (!TD) break; // Without TD we can't analyze pointers.
return getTruncateOrZeroExtend(getSCEV(U->getOperand(0)),
TD->getIntPtrType());
case Instruction::PtrToInt:
if (!TD) break; // Without TD we can't analyze pointers.
return getTruncateOrZeroExtend(getSCEV(U->getOperand(0)),
U->getType());
case Instruction::GetElementPtr: {
if (!TD) break; // Without TD we can't analyze pointers.
const Type *IntPtrTy = TD->getIntPtrType();
Value *Base = U->getOperand(0);
SCEVHandle TotalOffset = getIntegerSCEV(0, IntPtrTy);
gep_type_iterator GTI = gep_type_begin(U);
for (GetElementPtrInst::op_iterator I = next(U->op_begin()),
E = U->op_end();
I != E; ++I) {
Value *Index = *I;
// Compute the (potentially symbolic) offset in bytes for this index.
if (const StructType *STy = dyn_cast<StructType>(*GTI++)) {
// For a struct, add the member offset.
const StructLayout &SL = *TD->getStructLayout(STy);
unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
uint64_t Offset = SL.getElementOffset(FieldNo);
TotalOffset = getAddExpr(TotalOffset,
getIntegerSCEV(Offset, IntPtrTy));
} else {
// For an array, add the element offset, explicitly scaled.
SCEVHandle LocalOffset = getSCEV(Index);
if (!isa<PointerType>(LocalOffset->getType()))
// Getelementptr indicies are signed.
LocalOffset = getTruncateOrSignExtend(LocalOffset,
IntPtrTy);
LocalOffset =
getMulExpr(LocalOffset,
getIntegerSCEV(TD->getTypePaddedSize(*GTI),
IntPtrTy));
TotalOffset = getAddExpr(TotalOffset, LocalOffset);
}
}
return getAddExpr(getSCEV(Base), TotalOffset);
}
case Instruction::PHI:
return createNodeForPHI(cast<PHINode>(U));
case Instruction::Select:
// This could be a smax or umax that was lowered earlier.
// Try to recover it.
if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
Value *LHS = ICI->getOperand(0);
Value *RHS = ICI->getOperand(1);
switch (ICI->getPredicate()) {
case ICmpInst::ICMP_SLT:
case ICmpInst::ICMP_SLE:
std::swap(LHS, RHS);
// fall through
case ICmpInst::ICMP_SGT:
case ICmpInst::ICMP_SGE:
if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
return getSMaxExpr(getSCEV(LHS), getSCEV(RHS));
else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
// ~smax(~x, ~y) == smin(x, y).
return getNotSCEV(getSMaxExpr(
getNotSCEV(getSCEV(LHS)),
getNotSCEV(getSCEV(RHS))));
break;
case ICmpInst::ICMP_ULT:
case ICmpInst::ICMP_ULE:
std::swap(LHS, RHS);
// fall through
case ICmpInst::ICMP_UGT:
case ICmpInst::ICMP_UGE:
if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
return getUMaxExpr(getSCEV(LHS), getSCEV(RHS));
else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
// ~umax(~x, ~y) == umin(x, y)
return getNotSCEV(getUMaxExpr(getNotSCEV(getSCEV(LHS)),
getNotSCEV(getSCEV(RHS))));
break;
default:
break;
}
}
default: // We cannot analyze this expression.
break;
}
return getUnknown(V);
}
//===----------------------------------------------------------------------===//
// Iteration Count Computation Code
//
/// getBackedgeTakenCount - If the specified loop has a predictable
/// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
/// object. The backedge-taken count is the number of times the loop header
/// will be branched to from within the loop. This is one less than the
/// trip count of the loop, since it doesn't count the first iteration,
/// when the header is branched to from outside the loop.
///
/// Note that it is not valid to call this method on a loop without a
/// loop-invariant backedge-taken count (see
/// hasLoopInvariantBackedgeTakenCount).
///
SCEVHandle ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
return getBackedgeTakenInfo(L).Exact;
}
/// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
/// return the least SCEV value that is known never to be less than the
/// actual backedge taken count.
SCEVHandle ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
return getBackedgeTakenInfo(L).Max;
}
const ScalarEvolution::BackedgeTakenInfo &
ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
// Initially insert a CouldNotCompute for this loop. If the insertion
// succeeds, procede to actually compute a backedge-taken count and
// update the value. The temporary CouldNotCompute value tells SCEV
// code elsewhere that it shouldn't attempt to request a new
// backedge-taken count, which could result in infinite recursion.
std::pair<std::map<const Loop*, BackedgeTakenInfo>::iterator, bool> Pair =
BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute()));
if (Pair.second) {
BackedgeTakenInfo ItCount = ComputeBackedgeTakenCount(L);
if (ItCount.Exact != UnknownValue) {
assert(ItCount.Exact->isLoopInvariant(L) &&
ItCount.Max->isLoopInvariant(L) &&
"Computed trip count isn't loop invariant for loop!");
++NumTripCountsComputed;
// Update the value in the map.
Pair.first->second = ItCount;
} else if (isa<PHINode>(L->getHeader()->begin())) {
// Only count loops that have phi nodes as not being computable.
++NumTripCountsNotComputed;
}
// Now that we know more about the trip count for this loop, forget any
// existing SCEV values for PHI nodes in this loop since they are only
// conservative estimates made without the benefit
// of trip count information.
if (ItCount.hasAnyInfo())
forgetLoopPHIs(L);
}
return Pair.first->second;
}
/// forgetLoopBackedgeTakenCount - This method should be called by the
/// client when it has changed a loop in a way that may effect
/// ScalarEvolution's ability to compute a trip count, or if the loop
/// is deleted.
void ScalarEvolution::forgetLoopBackedgeTakenCount(const Loop *L) {
BackedgeTakenCounts.erase(L);
forgetLoopPHIs(L);
}
/// forgetLoopPHIs - Delete the memoized SCEVs associated with the
/// PHI nodes in the given loop. This is used when the trip count of
/// the loop may have changed.
void ScalarEvolution::forgetLoopPHIs(const Loop *L) {
BasicBlock *Header = L->getHeader();
SmallVector<Instruction *, 16> Worklist;
for (BasicBlock::iterator I = Header->begin();
PHINode *PN = dyn_cast<PHINode>(I); ++I)
Worklist.push_back(PN);
while (!Worklist.empty()) {
Instruction *I = Worklist.pop_back_val();
if (Scalars.erase(I))
for (Value::use_iterator UI = I->use_begin(), UE = I->use_end();
UI != UE; ++UI)
Worklist.push_back(cast<Instruction>(UI));
}
}
/// ComputeBackedgeTakenCount - Compute the number of times the backedge
/// of the specified loop will execute.
ScalarEvolution::BackedgeTakenInfo
ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
// If the loop has a non-one exit block count, we can't analyze it.
SmallVector<BasicBlock*, 8> 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)
BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
if (ExitBr == 0) return UnknownValue;
assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
// At this point, we know we have a conditional branch that determines whether
// the loop is exited. However, we don't know if the branch is executed each
// time through the loop. If not, then the execution count of the branch will
// not be equal to the trip count of the loop.
//
// Currently we check for this by checking to see if the Exit branch goes to
// the loop header. If so, we know it will always execute the same number of
// times as the loop. We also handle the case where the exit block *is* the
// loop header. This is common for un-rotated loops. More extensive analysis
// could be done to handle more cases here.
if (ExitBr->getSuccessor(0) != L->getHeader() &&
ExitBr->getSuccessor(1) != L->getHeader() &&
ExitBr->getParent() != L->getHeader())
return UnknownValue;
ICmpInst *ExitCond = dyn_cast<ICmpInst>(ExitBr->getCondition());
// If it's not an integer comparison then compute it the hard way.
// Note that ICmpInst deals with pointer comparisons too so we must check
// the type of the operand.
if (ExitCond == 0 || isa<PointerType>(ExitCond->getOperand(0)->getType()))
return ComputeBackedgeTakenCountExhaustively(L, ExitBr->getCondition(),
ExitBr->getSuccessor(0) == ExitBlock);
// If the condition was exit on true, convert the condition to exit on false
ICmpInst::Predicate Cond;
if (ExitBr->getSuccessor(1) == ExitBlock)
Cond = ExitCond->getPredicate();
else
Cond = ExitCond->getInversePredicate();
// Handle common loops like: for (X = "string"; *X; ++X)
if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
SCEVHandle ItCnt =
ComputeLoadConstantCompareBackedgeTakenCount(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 (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) {
// If there is a loop-invariant, force it into the RHS.
std::swap(LHS, RHS);
Cond = ICmpInst::getSwappedPredicate(Cond);
}
// If we have a comparison of a chrec against a constant, try to use value
// ranges to answer this query.
if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
if (AddRec->getLoop() == L) {
// Form the 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::getBitCast(CompVal, RealTy));
if (CompVal) {
// Form the constant range.
ConstantRange CompRange(
ICmpInst::makeConstantRange(Cond, CompVal->getValue()));
SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange, *this);
if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
}
}
switch (Cond) {
case ICmpInst::ICMP_NE: { // while (X != Y)
// Convert to: while (X-Y != 0)
SCEVHandle TC = HowFarToZero(getMinusSCEV(LHS, RHS), L);
if (!isa<SCEVCouldNotCompute>(TC)) return TC;
break;
}
case ICmpInst::ICMP_EQ: {
// Convert to: while (X-Y == 0) // while (X == Y)
SCEVHandle TC = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
if (!isa<SCEVCouldNotCompute>(TC)) return TC;
break;
}
case ICmpInst::ICMP_SLT: {
BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true);
if (BTI.hasAnyInfo()) return BTI;
break;
}
case ICmpInst::ICMP_SGT: {
BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
getNotSCEV(RHS), L, true);
if (BTI.hasAnyInfo()) return BTI;
break;
}
case ICmpInst::ICMP_ULT: {
BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false);
if (BTI.hasAnyInfo()) return BTI;
break;
}
case ICmpInst::ICMP_UGT: {
BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
getNotSCEV(RHS), L, false);
if (BTI.hasAnyInfo()) return BTI;
break;
}
default:
#if 0
errs() << "ComputeBackedgeTakenCount ";
if (ExitCond->getOperand(0)->getType()->isUnsigned())
errs() << "[unsigned] ";
errs() << *LHS << " "
<< Instruction::getOpcodeName(Instruction::ICmp)
<< " " << *RHS << "\n";
#endif
break;
}
return
ComputeBackedgeTakenCountExhaustively(L, ExitCond,
ExitBr->getSuccessor(0) == ExitBlock);
}
static ConstantInt *
EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
ScalarEvolution &SE) {
SCEVHandle InVal = SE.getConstant(C);
SCEVHandle Val = AddRec->evaluateAtIteration(InVal, SE);
assert(isa<SCEVConstant>(Val) &&
"Evaluation of SCEV at constant didn't fold correctly?");
return cast<SCEVConstant>(Val)->getValue();
}
/// GetAddressedElementFromGlobal - Given a global variable with an initializer
/// and a GEP expression (missing the pointer index) indexing into it, return
/// the addressed element of the initializer or null if the index expression is
/// invalid.
static Constant *
GetAddressedElementFromGlobal(GlobalVariable *GV,
const std::vector<ConstantInt*> &Indices) {
Constant *Init = GV->getInitializer();
for (unsigned i = 0, e = Indices.size(); i != e; ++i) {
uint64_t Idx = Indices[i]->getZExtValue();
if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) {
assert(Idx < CS->getNumOperands() && "Bad struct index!");
Init = cast<Constant>(CS->getOperand(Idx));
} else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) {
if (Idx >= CA->getNumOperands()) return 0; // Bogus program
Init = cast<Constant>(CA->getOperand(Idx));
} else if (isa<ConstantAggregateZero>(Init)) {
if (const StructType *STy = dyn_cast<StructType>(Init->getType())) {
assert(Idx < STy->getNumElements() && "Bad struct index!");
Init = Constant::getNullValue(STy->getElementType(Idx));
} else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) {
if (Idx >= ATy->getNumElements()) return 0; // Bogus program
Init = Constant::getNullValue(ATy->getElementType());
} else {
assert(0 && "Unknown constant aggregate type!");
}
return 0;
} else {
return 0; // Unknown initializer type
}
}
return Init;
}
/// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of
/// 'icmp op load X, cst', try to see if we can compute the backedge
/// execution count.
SCEVHandle ScalarEvolution::
ComputeLoadConstantCompareBackedgeTakenCount(LoadInst *LI, Constant *RHS,
const Loop *L,
ICmpInst::Predicate predicate) {
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}.
const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) ||
!isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
!isa<SCEVConstant>(IdxExpr->getOperand(1)))
return UnknownValue;
unsigned MaxSteps = MaxBruteForceIterations;
for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
ConstantInt *ItCst =
ConstantInt::get(IdxExpr->getType(), IterationNum);
ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
// 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::getICmp(predicate, Result, RHS);
if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
#if 0
errs() << "\n***\n*** Computed loop count " << *ItCst
<< "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
<< "***\n";
#endif
++NumArrayLenItCounts;
return getConstant(ItCst); // Found terminating iteration!
}
}
return 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<CmpInst>(I) ||
isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I))
return true;
if (const CallInst *CI = dyn_cast<CallInst>(I))
if (const Function *F = CI->getCalledFunction())
return canConstantFoldCallTo(F);
return false;
}
/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
/// in the loop that V is derived from. We allow arbitrary operations along the
/// way, but the operands of an operation must either be constants or a value
/// derived from a constant PHI. If this expression does not fit with these
/// constraints, return null.
static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
// If this is not an instruction, or if this is an instruction outside of the
// loop, it can't be derived from a loop PHI.
Instruction *I = dyn_cast<Instruction>(V);
if (I == 0 || !L->contains(I->getParent())) return 0;
if (PHINode *PN = dyn_cast<PHINode>(I)) {
if (L->getHeader() == I->getParent())
return PN;
else
// We don't currently keep track of the control flow needed to evaluate
// PHIs, so we cannot handle PHIs inside of loops.
return 0;
}
// If we won't be able to constant fold this expression even if the operands
// are constants, return early.
if (!CanConstantFold(I)) return 0;
// Otherwise, we can evaluate this instruction if all of its operands are
// constant or derived from a PHI node themselves.
PHINode *PHI = 0;
for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op)
if (!(isa<Constant>(I->getOperand(Op)) ||
isa<GlobalValue>(I->getOperand(Op)))) {
PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L);
if (P == 0) return 0; // Not evolving from PHI
if (PHI == 0)
PHI = P;
else if (PHI != P)
return 0; // Evolving from multiple different PHIs.
}
// This is a expression evolving from a constant PHI!
return PHI;
}
/// EvaluateExpression - Given an expression that passes the
/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
/// in the loop has the value PHIVal. If we can't fold this expression for some
/// reason, return null.
static Constant *EvaluateExpression(Value *V, Constant *PHIVal) {
if (isa<PHINode>(V)) return PHIVal;
if (Constant *C = dyn_cast<Constant>(V)) return C;
if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) return GV;
Instruction *I = cast<Instruction>(V);
std::vector<Constant*> Operands;
Operands.resize(I->getNumOperands());
for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal);
if (Operands[i] == 0) return 0;
}
if (const CmpInst *CI = dyn_cast<CmpInst>(I))
return ConstantFoldCompareInstOperands(CI->getPredicate(),
&Operands[0], Operands.size());
else
return ConstantFoldInstOperands(I->getOpcode(), I->getType(),
&Operands[0], Operands.size());
}
/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
/// in the header of its containing loop, we know the loop executes a
/// constant number of times, and the PHI node is just a recurrence
/// involving constants, fold it.
Constant *ScalarEvolution::
getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& BEs, const Loop *L){
std::map<PHINode*, Constant*>::iterator I =
ConstantEvolutionLoopExitValue.find(PN);
if (I != ConstantEvolutionLoopExitValue.end())
return I->second;
if (BEs.ugt(APInt(BEs.getBitWidth(),MaxBruteForceIterations)))
return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
// Since the loop is canonicalized, the PHI node must have two entries. One
// entry must be a constant (coming in from outside of the loop), and the
// second must be derived from the same PHI.
bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
Constant *StartCST =
dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
if (StartCST == 0)
return RetVal = 0; // Must be a constant.
Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
if (PN2 != PN)
return RetVal = 0; // Not derived from same PHI.
// Execute the loop symbolically to determine the exit value.
if (BEs.getActiveBits() >= 32)
return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
unsigned NumIterations = BEs.getZExtValue(); // must be in range
unsigned IterationNum = 0;
for (Constant *PHIVal = StartCST; ; ++IterationNum) {
if (IterationNum == NumIterations)
return RetVal = PHIVal; // Got exit value!
// Compute the value of the PHI node for the next iteration.
Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
if (NextPHI == PHIVal)
return RetVal = NextPHI; // Stopped evolving!
if (NextPHI == 0)
return 0; // Couldn't evaluate!
PHIVal = NextPHI;
}
}
/// ComputeBackedgeTakenCountExhaustively - If the 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 ScalarEvolution::
ComputeBackedgeTakenCountExhaustively(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) {
ConstantInt *CondVal =
dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal));
// Couldn't symbolically evaluate.
if (!CondVal) return UnknownValue;
if (CondVal->getValue() == uint64_t(ExitWhen)) {
ConstantEvolutionLoopExitValue[PN] = PHIVal;
++NumBruteForceTripCountsComputed;
return getConstant(ConstantInt::get(Type::Int32Ty, 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 ScalarEvolution::getSCEVAtScope(const 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 evolved from a constant-evolving PHI, compute the
// exit value from the loop without using SCEVs.
if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
const Loop *LI = (*this->LI)[I->getParent()];
if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
if (PHINode *PN = dyn_cast<PHINode>(I))
if (PN->getParent() == LI->getHeader()) {
// Okay, there is no closed form solution for the PHI node. Check
// to see if the loop that contains it has a known backedge-taken
// count. If so, we may be able to force computation of the exit
// value.
SCEVHandle BackedgeTakenCount = getBackedgeTakenCount(LI);
if (const SCEVConstant *BTCC =
dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
// Okay, we know how many times the containing loop executes. If
// this is a constant evolving PHI node, get the final value at
// the specified iteration number.
Constant *RV = getConstantEvolutionLoopExitValue(PN,
BTCC->getValue()->getValue(),
LI);
if (RV) return getUnknown(RV);
}
}
// Okay, this is an expression that we cannot symbolically evaluate
// into a SCEV. Check to see if it's possible to symbolically evaluate
// the arguments into constants, and if so, try to constant propagate the
// result. This is particularly useful for computing loop exit values.
if (CanConstantFold(I)) {
std::vector<Constant*> Operands;
Operands.reserve(I->getNumOperands());
for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
Value *Op = I->getOperand(i);
if (Constant *C = dyn_cast<Constant>(Op)) {
Operands.push_back(C);
} else {
// If any of the operands is non-constant and if they are
// non-integer and non-pointer, don't even try to analyze them
// with scev techniques.
if (!isSCEVable(Op->getType()))
return V;
SCEVHandle OpV = getSCEVAtScope(getSCEV(Op), L);
if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) {
Constant *C = SC->getValue();
if (C->getType() != Op->getType())
C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
Op->getType(),
false),
C, Op->getType());
Operands.push_back(C);
} else if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) {
if (Constant *C = dyn_cast<Constant>(SU->getValue())) {
if (C->getType() != Op->getType())
C =
ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
Op->getType(),
false),
C, Op->getType());
Operands.push_back(C);
} else
return V;
} else {
return V;
}
}
}
Constant *C;
if (const CmpInst *CI = dyn_cast<CmpInst>(I))
C = ConstantFoldCompareInstOperands(CI->getPredicate(),
&Operands[0], Operands.size());
else
C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
&Operands[0], Operands.size());
return getUnknown(C);
}
}
// This is some other type of SCEVUnknown, just return it.
return V;
}
if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
// Avoid performing the look-up in the common case where the specified
// expression has no loop-variant portions.
for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
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 getAddExpr(NewOps);
if (isa<SCEVMulExpr>(Comm))
return getMulExpr(NewOps);
if (isa<SCEVSMaxExpr>(Comm))
return getSMaxExpr(NewOps);
if (isa<SCEVUMaxExpr>(Comm))
return getUMaxExpr(NewOps);
assert(0 && "Unknown commutative SCEV type!");
}
}
// If we got here, all operands are loop invariant.
return Comm;
}
if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
SCEVHandle LHS = getSCEVAtScope(Div->getLHS(), L);
if (LHS == UnknownValue) return LHS;
SCEVHandle RHS = getSCEVAtScope(Div->getRHS(), L);
if (RHS == UnknownValue) return RHS;
if (LHS == Div->getLHS() && RHS == Div->getRHS())
return Div; // must be loop invariant
return getUDivExpr(LHS, RHS);
}
// If this is a loop recurrence for a loop that does not contain L, then we
// are dealing with the final value computed by the loop.
if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
if (!L || !AddRec->getLoop()->contains(L->getHeader())) {
// To evaluate this recurrence, we need to know how many times the AddRec
// loop iterates. Compute this now.
SCEVHandle BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
if (BackedgeTakenCount == UnknownValue) return UnknownValue;
// Then, evaluate the AddRec.
return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
}
return UnknownValue;
}
if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
SCEVHandle Op = getSCEVAtScope(Cast->getOperand(), L);
if (Op == UnknownValue) return Op;
if (Op == Cast->getOperand())
return Cast; // must be loop invariant
return getZeroExtendExpr(Op, Cast->getType());
}
if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
SCEVHandle Op = getSCEVAtScope(Cast->getOperand(), L);
if (Op == UnknownValue) return Op;
if (Op == Cast->getOperand())
return Cast; // must be loop invariant
return getSignExtendExpr(Op, Cast->getType());
}
if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
SCEVHandle Op = getSCEVAtScope(Cast->getOperand(), L);
if (Op == UnknownValue) return Op;
if (Op == Cast->getOperand())
return Cast; // must be loop invariant
return getTruncateExpr(Op, Cast->getType());
}
assert(0 && "Unknown SCEV type!");
}
/// getSCEVAtScope - Return a SCEV expression handle for the specified value
/// at the specified scope in the program. The L value specifies a loop
/// nest to evaluate the expression at, where null is the top-level or a
/// specified loop is immediately inside of the loop.
///
/// This method can be used to compute the exit value for a variable defined
/// in a loop by querying what the value will hold in the parent loop.
///
/// If this value is not computable at this scope, a SCEVCouldNotCompute
/// object is returned.
SCEVHandle ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
return getSCEVAtScope(getSCEV(V), L);
}
/// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
/// following equation:
///
/// A * X = B (mod N)
///
/// where N = 2^BW and BW is the common bit width of A and B. The signedness of
/// A and B isn't important.
///
/// If the equation does not have a solution, SCEVCouldNotCompute is returned.
static SCEVHandle SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
ScalarEvolution &SE) {
uint32_t BW = A.getBitWidth();
assert(BW == B.getBitWidth() && "Bit widths must be the same.");
assert(A != 0 && "A must be non-zero.");
// 1. D = gcd(A, N)
//
// The gcd of A and N may have only one prime factor: 2. The number of
// trailing zeros in A is its multiplicity
uint32_t Mult2 = A.countTrailingZeros();
// D = 2^Mult2
// 2. Check if B is divisible by D.
//
// B is divisible by D if and only if the multiplicity of prime factor 2 for B
// is not less than multiplicity of this prime factor for D.
if (B.countTrailingZeros() < Mult2)
return SE.getCouldNotCompute();
// 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
// modulo (N / D).
//
// (N / D) may need BW+1 bits in its representation. Hence, we'll use this
// bit width during computations.
APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
APInt Mod(BW + 1, 0);
Mod.set(BW - Mult2); // Mod = N / D
APInt I = AD.multiplicativeInverse(Mod);
// 4. Compute the minimum unsigned root of the equation:
// I * (B / D) mod (N / D)
APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
// The result is guaranteed to be less than 2^BW so we may truncate it to BW
// bits.
return SE.getConstant(Result.trunc(BW));
}
/// SolveQuadraticEquation - Find the roots of the quadratic equation for the
/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
/// might be the same) or two SCEVCouldNotCompute objects.
///
static std::pair<SCEVHandle,SCEVHandle>
SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
// We currently can only solve this if the coefficients are constants.
if (!LC || !MC || !NC) {
const SCEV *CNC = SE.getCouldNotCompute();
return std::make_pair(CNC, CNC);
}
uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
const APInt &L = LC->getValue()->getValue();
const APInt &M = MC->getValue()->getValue();
const APInt &N = NC->getValue()->getValue();
APInt Two(BitWidth, 2);
APInt Four(BitWidth, 4);
{
using namespace APIntOps;
const APInt& C = L;
// Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
// The B coefficient is M-N/2
APInt B(M);
B -= sdiv(N,Two);
// The A coefficient is N/2
APInt A(N.sdiv(Two));
// Compute the B^2-4ac term.
APInt SqrtTerm(B);
SqrtTerm *= B;
SqrtTerm -= Four * (A * C);
// Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
// integer value or else APInt::sqrt() will assert.
APInt SqrtVal(SqrtTerm.sqrt());
// Compute the two solutions for the quadratic formula.
// The divisions must be performed as signed divisions.
APInt NegB(-B);
APInt TwoA( A << 1 );
if (TwoA.isMinValue()) {
const SCEV *CNC = SE.getCouldNotCompute();
return std::make_pair(CNC, CNC);
}
ConstantInt *Solution1 = ConstantInt::get((NegB + SqrtVal).sdiv(TwoA));
ConstantInt *Solution2 = ConstantInt::get((NegB - SqrtVal).sdiv(TwoA));
return std::make_pair(SE.getConstant(Solution1),
SE.getConstant(Solution2));
} // end APIntOps namespace
}
/// HowFarToZero - Return the number of times a backedge comparing the specified
/// value to zero will execute. If not computable, return UnknownValue
SCEVHandle ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) {
// If the value is a constant
if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
// If the value is already zero, the branch will execute zero times.
if (C->getValue()->isZero()) return C;
return UnknownValue; // Otherwise it will loop infinitely.
}
const 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
// the minimum unsigned root of the following equation:
//
// Start + Step*N = 0 (mod 2^BW)
//
// equivalent to:
//
// Step*N = -Start (mod 2^BW)
//
// where BW is the common bit width of Start and Step.
// Get the initial value for the loop.
SCEVHandle Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
if (isa<SCEVCouldNotCompute>(Start)) return UnknownValue;
SCEVHandle Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
if (const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) {
// For now we handle only constant steps.
// First, handle unitary steps.
if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so:
return getNegativeSCEV(Start); // N = -Start (as unsigned)
if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so:
return Start; // N = Start (as unsigned)
// Then, try to solve the above equation provided that Start is constant.
if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
-StartC->getValue()->getValue(),
*this);
}
} else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) {
// If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
// the quadratic equation to solve it.
std::pair<SCEVHandle,SCEVHandle> Roots = SolveQuadraticEquation(AddRec,
*this);
const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
if (R1) {
#if 0
errs() << "HFTZ: " << *V << " - sol#1: " << *R1
<< " sol#2: " << *R2 << "\n";
#endif
// Pick the smallest positive root value.
if (ConstantInt *CB =
dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
R1->getValue(), R2->getValue()))) {
if (CB->getZExtValue() == false)
std::swap(R1, R2); // R1 is the minimum root now.
// We can only use this value if the chrec ends up with an exact zero
// value at this index. When solving for "X*X != 5", for example, we
// should not accept a root of 2.
SCEVHandle Val = AddRec->evaluateAtIteration(R1, *this);
if (Val->isZero())
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 ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
// Loops that look like: while (X == 0) are very strange indeed. We don't
// handle them yet except for the trivial case. This could be expanded in the
// future as needed.
// If the value is a constant, check to see if it is known to be non-zero
// already. If so, the backedge will execute zero times.
if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
if (!C->getValue()->isNullValue())
return getIntegerSCEV(0, C->getType());
return 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;
}
/// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
/// (which may not be an immediate predecessor) which has exactly one
/// successor from which BB is reachable, or null if no such block is
/// found.
///
BasicBlock *
ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
// If the block has a unique predecessor, then there is no path from the
// predecessor to the block that does not go through the direct edge
// from the predecessor to the block.
if (BasicBlock *Pred = BB->getSinglePredecessor())
return Pred;
// A loop's header is defined to be a block that dominates the loop.
// If the loop has a preheader, it must be a block that has exactly
// one successor that can reach BB. This is slightly more strict
// than necessary, but works if critical edges are split.
if (Loop *L = LI->getLoopFor(BB))
return L->getLoopPreheader();
return 0;
}
/// isLoopGuardedByCond - Test whether entry to the loop is protected by
/// a conditional between LHS and RHS. This is used to help avoid max
/// expressions in loop trip counts.
bool ScalarEvolution::isLoopGuardedByCond(const Loop *L,
ICmpInst::Predicate Pred,
const SCEV *LHS, const SCEV *RHS) {
BasicBlock *Preheader = L->getLoopPreheader();
BasicBlock *PreheaderDest = L->getHeader();
// Starting at the preheader, climb up the predecessor chain, as long as
// there are predecessors that can be found that have unique successors
// leading to the original header.
for (; Preheader;
PreheaderDest = Preheader,
Preheader = getPredecessorWithUniqueSuccessorForBB(Preheader)) {
BranchInst *LoopEntryPredicate =
dyn_cast<BranchInst>(Preheader->getTerminator());
if (!LoopEntryPredicate ||
LoopEntryPredicate->isUnconditional())
continue;
ICmpInst *ICI = dyn_cast<ICmpInst>(LoopEntryPredicate->getCondition());
if (!ICI) continue;
// Now that we found a conditional branch that dominates the loop, check to
// see if it is the comparison we are looking for.
Value *PreCondLHS = ICI->getOperand(0);
Value *PreCondRHS = ICI->getOperand(1);
ICmpInst::Predicate Cond;
if (LoopEntryPredicate->getSuccessor(0) == PreheaderDest)
Cond = ICI->getPredicate();
else
Cond = ICI->getInversePredicate();
if (Cond == Pred)
; // An exact match.
else if (!ICmpInst::isTrueWhenEqual(Cond) && Pred == ICmpInst::ICMP_NE)
; // The actual condition is beyond sufficient.
else
// Check a few special cases.
switch (Cond) {
case ICmpInst::ICMP_UGT:
if (Pred == ICmpInst::ICMP_ULT) {
std::swap(PreCondLHS, PreCondRHS);
Cond = ICmpInst::ICMP_ULT;
break;
}
continue;
case ICmpInst::ICMP_SGT:
if (Pred == ICmpInst::ICMP_SLT) {
std::swap(PreCondLHS, PreCondRHS);
Cond = ICmpInst::ICMP_SLT;
break;
}
continue;
case ICmpInst::ICMP_NE:
// Expressions like (x >u 0) are often canonicalized to (x != 0),
// so check for this case by checking if the NE is comparing against
// a minimum or maximum constant.
if (!ICmpInst::isTrueWhenEqual(Pred))
if (ConstantInt *CI = dyn_cast<ConstantInt>(PreCondRHS)) {
const APInt &A = CI->getValue();
switch (Pred) {
case ICmpInst::ICMP_SLT:
if (A.isMaxSignedValue()) break;
continue;
case ICmpInst::ICMP_SGT:
if (A.isMinSignedValue()) break;
continue;
case ICmpInst::ICMP_ULT:
if (A.isMaxValue()) break;
continue;
case ICmpInst::ICMP_UGT:
if (A.isMinValue()) break;
continue;
default:
continue;
}
Cond = ICmpInst::ICMP_NE;
// NE is symmetric but the original comparison may not be. Swap
// the operands if necessary so that they match below.
if (isa<SCEVConstant>(LHS))
std::swap(PreCondLHS, PreCondRHS);
break;
}
continue;
default:
// We weren't able to reconcile the condition.
continue;
}
if (!PreCondLHS->getType()->isInteger()) continue;
SCEVHandle PreCondLHSSCEV = getSCEV(PreCondLHS);
SCEVHandle PreCondRHSSCEV = getSCEV(PreCondRHS);
if ((LHS == PreCondLHSSCEV && RHS == PreCondRHSSCEV) ||
(LHS == getNotSCEV(PreCondRHSSCEV) &&
RHS == getNotSCEV(PreCondLHSSCEV)))
return true;
}
return false;
}
/// HowManyLessThans - Return the number of times a backedge containing the
/// specified less-than comparison will execute. If not computable, return
/// UnknownValue.
ScalarEvolution::BackedgeTakenInfo ScalarEvolution::
HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
const Loop *L, bool isSigned) {
// Only handle: "ADDREC < LoopInvariant".
if (!RHS->isLoopInvariant(L)) return UnknownValue;
const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
if (!AddRec || AddRec->getLoop() != L)
return UnknownValue;
if (AddRec->isAffine()) {
// FORNOW: We only support unit strides.
unsigned BitWidth = getTypeSizeInBits(AddRec->getType());
SCEVHandle Step = AddRec->getStepRecurrence(*this);
SCEVHandle NegOne = getIntegerSCEV(-1, AddRec->getType());
// TODO: handle non-constant strides.
const SCEVConstant *CStep = dyn_cast<SCEVConstant>(Step);
if (!CStep || CStep->isZero())
return UnknownValue;
if (CStep->getValue()->getValue() == 1) {
// With unit stride, the iteration never steps past the limit value.
} else if (CStep->getValue()->getValue().isStrictlyPositive()) {
if (const SCEVConstant *CLimit = dyn_cast<SCEVConstant>(RHS)) {
// Test whether a positive iteration iteration can step past the limit
// value and past the maximum value for its type in a single step.
if (isSigned) {
APInt Max = APInt::getSignedMaxValue(BitWidth);
if ((Max - CStep->getValue()->getValue())
.slt(CLimit->getValue()->getValue()))
return UnknownValue;
} else {
APInt Max = APInt::getMaxValue(BitWidth);
if ((Max - CStep->getValue()->getValue())
.ult(CLimit->getValue()->getValue()))
return UnknownValue;
}
} else
// TODO: handle non-constant limit values below.
return UnknownValue;
} else
// TODO: handle negative strides below.
return UnknownValue;
// We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant
// m. So, we count the number of iterations in which {n,+,s} < m is true.
// Note that we cannot simply return max(m-n,0)/s because it's not safe to
// treat m-n as signed nor unsigned due to overflow possibility.
// First, we get the value of the LHS in the first iteration: n
SCEVHandle Start = AddRec->getOperand(0);
// Determine the minimum constant start value.
SCEVHandle MinStart = isa<SCEVConstant>(Start) ? Start :
getConstant(isSigned ? APInt::getSignedMinValue(BitWidth) :
APInt::getMinValue(BitWidth));
// If we know that the condition is true in order to enter the loop,
// then we know that it will run exactly (m-n)/s times. Otherwise, we
// only know if will execute (max(m,n)-n)/s times. In both cases, the
// division must round up.
SCEVHandle End = RHS;
if (!isLoopGuardedByCond(L,
isSigned ? ICmpInst::ICMP_SLT : ICmpInst::ICMP_ULT,
getMinusSCEV(Start, Step), RHS))
End = isSigned ? getSMaxExpr(RHS, Start)
: getUMaxExpr(RHS, Start);
// Determine the maximum constant end value.
SCEVHandle MaxEnd = isa<SCEVConstant>(End) ? End :
getConstant(isSigned ? APInt::getSignedMaxValue(BitWidth) :
APInt::getMaxValue(BitWidth));
// Finally, we subtract these two values and divide, rounding up, to get
// the number of times the backedge is executed.
SCEVHandle BECount = getUDivExpr(getAddExpr(getMinusSCEV(End, Start),
getAddExpr(Step, NegOne)),
Step);
// The maximum backedge count is similar, except using the minimum start
// value and the maximum end value.
SCEVHandle MaxBECount = getUDivExpr(getAddExpr(getMinusSCEV(MaxEnd,
MinStart),
getAddExpr(Step, NegOne)),
Step);
return BackedgeTakenInfo(BECount, MaxBECount);
}
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,
ScalarEvolution &SE) const {
if (Range.isFullSet()) // Infinite loop.
return SE.getCouldNotCompute();
// If the start is a non-zero constant, shift the range to simplify things.
if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
if (!SC->getValue()->isZero()) {
std::vector<SCEVHandle> Operands(op_begin(), op_end());
Operands[0] = SE.getIntegerSCEV(0, SC->getType());
SCEVHandle Shifted = SE.getAddRecExpr(Operands, getLoop());
if (const SCEVAddRecExpr *ShiftedAddRec =
dyn_cast<SCEVAddRecExpr>(Shifted))
return ShiftedAddRec->getNumIterationsInRange(
Range.subtract(SC->getValue()->getValue()), SE);
// This is strange and shouldn't happen.
return SE.getCouldNotCompute();
}
// The only time we can solve this is when we have all constant indices.
// Otherwise, we cannot determine the overflow conditions.
for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
if (!isa<SCEVConstant>(getOperand(i)))
return SE.getCouldNotCompute();
// Okay at this point we know that all elements of the chrec are constants and
// that the start element is zero.
// First check to see if the range contains zero. If not, the first
// iteration exits.
unsigned BitWidth = SE.getTypeSizeInBits(getType());
if (!Range.contains(APInt(BitWidth, 0)))
return SE.getConstant(ConstantInt::get(getType(),0));
if (isAffine()) {
// If this is an affine expression then we have this situation:
// Solve {0,+,A} in Range === Ax in Range
// We know that zero is in the range. If A is positive then we know that
// the upper value of the range must be the first possible exit value.
// If A is negative then the lower of the range is the last possible loop
// value. Also note that we already checked for a full range.
APInt One(BitWidth,1);
APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
// The exit value should be (End+A)/A.
APInt ExitVal = (End + A).udiv(A);
ConstantInt *ExitValue = ConstantInt::get(ExitVal);
// Evaluate at the exit value. If we really did fall out of the valid
// range, then we computed our trip count, otherwise wrap around or other
// things must have happened.
ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
if (Range.contains(Val->getValue()))
return SE.getCouldNotCompute(); // Something strange happened
// Ensure that the previous value is in the range. This is a sanity check.
assert(Range.contains(
EvaluateConstantChrecAtConstant(this,
ConstantInt::get(ExitVal - One), SE)->getValue()) &&
"Linear scev computation is off in a bad way!");
return SE.getConstant(ExitValue);
} else if (isQuadratic()) {
// If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
// quadratic equation to solve it. To do this, we must frame our problem in
// terms of figuring out when zero is crossed, instead of when
// Range.getUpper() is crossed.
std::vector<SCEVHandle> NewOps(op_begin(), op_end());
NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
SCEVHandle NewAddRec = SE.getAddRecExpr(NewOps, getLoop());
// Next, solve the constructed addrec
std::pair<SCEVHandle,SCEVHandle> Roots =
SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
if (R1) {
// Pick the smallest positive root value.
if (ConstantInt *CB =
dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
R1->getValue(), R2->getValue()))) {
if (CB->getZExtValue() == false)
std::swap(R1, R2); // R1 is the minimum root now.
// Make sure the root is not off by one. The returned iteration should
// not be in the range, but the previous one should be. When solving
// for "X*X < 5", for example, we should not return a root of 2.
ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
R1->getValue(),
SE);
if (Range.contains(R1Val->getValue())) {
// The next iteration must be out of the range...
ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()+1);
R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
if (!Range.contains(R1Val->getValue()))
return SE.getConstant(NextVal);
return SE.getCouldNotCompute(); // Something strange happened
}
// If R1 was not in the range, then it is a good return value. Make
// sure that R1-1 WAS in the range though, just in case.
ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()-1);
R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
if (Range.contains(R1Val->getValue()))
return R1;
return SE.getCouldNotCompute(); // Something strange happened
}
}
}
return SE.getCouldNotCompute();
}
//===----------------------------------------------------------------------===//
// SCEVCallbackVH Class Implementation
//===----------------------------------------------------------------------===//
void SCEVCallbackVH::deleted() {
assert(SE && "SCEVCallbackVH called with a non-null ScalarEvolution!");
if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
SE->ConstantEvolutionLoopExitValue.erase(PN);
SE->Scalars.erase(getValPtr());
// this now dangles!
}
void SCEVCallbackVH::allUsesReplacedWith(Value *) {
assert(SE && "SCEVCallbackVH called with a non-null ScalarEvolution!");
// Forget all the expressions associated with users of the old value,
// so that future queries will recompute the expressions using the new
// value.
SmallVector<User *, 16> Worklist;
Value *Old = getValPtr();
bool DeleteOld = false;
for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end();
UI != UE; ++UI)
Worklist.push_back(*UI);
while (!Worklist.empty()) {
User *U = Worklist.pop_back_val();
// Deleting the Old value will cause this to dangle. Postpone
// that until everything else is done.
if (U == Old) {
DeleteOld = true;
continue;
}
if (PHINode *PN = dyn_cast<PHINode>(U))
SE->ConstantEvolutionLoopExitValue.erase(PN);
if (SE->Scalars.erase(U))
for (Value::use_iterator UI = U->use_begin(), UE = U->use_end();
UI != UE; ++UI)
Worklist.push_back(*UI);
}
if (DeleteOld) {
if (PHINode *PN = dyn_cast<PHINode>(Old))
SE->ConstantEvolutionLoopExitValue.erase(PN);
SE->Scalars.erase(Old);
// this now dangles!
}
// this may dangle!
}
SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
: CallbackVH(V), SE(se) {}
//===----------------------------------------------------------------------===//
// ScalarEvolution Class Implementation
//===----------------------------------------------------------------------===//
ScalarEvolution::ScalarEvolution()
: FunctionPass(&ID), UnknownValue(new SCEVCouldNotCompute()) {
}
bool ScalarEvolution::runOnFunction(Function &F) {
this->F = &F;
LI = &getAnalysis<LoopInfo>();
TD = getAnalysisIfAvailable<TargetData>();
return false;
}
void ScalarEvolution::releaseMemory() {
Scalars.clear();
BackedgeTakenCounts.clear();
ConstantEvolutionLoopExitValue.clear();
}
void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
AU.setPreservesAll();
AU.addRequiredTransitive<LoopInfo>();
}
bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
}
static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
const Loop *L) {
// Print all inner loops first
for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
PrintLoopInfo(OS, SE, *I);
OS << "Loop " << L->getHeader()->getName() << ": ";
SmallVector<BasicBlock*, 8> ExitBlocks;
L->getExitBlocks(ExitBlocks);
if (ExitBlocks.size() != 1)
OS << "<multiple exits> ";
if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
} else {
OS << "Unpredictable backedge-taken count. ";
}
OS << "\n";
}
void ScalarEvolution::print(raw_ostream &OS, const Module* ) const {
// ScalarEvolution's implementaiton of the print method is to print
// out SCEV values of all instructions that are interesting. Doing
// this potentially causes it to create new SCEV objects though,
// which technically conflicts with the const qualifier. This isn't
// observable from outside the class though (the hasSCEV function
// notwithstanding), so casting away the const isn't dangerous.
ScalarEvolution &SE = *const_cast<ScalarEvolution*>(this);
OS << "Classifying expressions for: " << F->getName() << "\n";
for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
if (isSCEVable(I->getType())) {
OS << *I;
OS << " --> ";
SCEVHandle SV = SE.getSCEV(&*I);
SV->print(OS);
OS << "\t\t";
if (const Loop *L = LI->getLoopFor((*I).getParent())) {
OS << "Exits: ";
SCEVHandle ExitValue = SE.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, &SE, *I);
}
void ScalarEvolution::print(std::ostream &o, const Module *M) const {
raw_os_ostream OS(o);
print(OS, M);
}
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