//
// The LLVM Compiler Infrastructure
//
-// This file was developed by the LLVM research group and is distributed under
-// the University of Illinois Open Source License. See LICENSE.TXT for details.
+// This file is distributed under the University of Illinois Open Source
+// License. See LICENSE.TXT for details.
//
//===----------------------------------------------------------------------===//
//
#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/Streams.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(NumBruteForceEvaluations,
- "Number of brute force evaluations needed to "
- "calculate high-order polynomial exit values");
STATISTIC(NumArrayLenItCounts,
"Number of trip counts computed with array length");
STATISTIC(NumTripCountsComputed,
STATISTIC(NumBruteForceTripCountsComputed,
"Number of loops with trip counts computed by force");
-cl::opt<unsigned>
+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));
-namespace {
- RegisterPass<ScalarEvolution>
- R("scalar-evolution", "Scalar Evolution Analysis");
-}
+static RegisterPass<ScalarEvolution>
+R("scalar-evolution", "Scalar Evolution Analysis", false, true);
char ScalarEvolution::ID = 0;
//===----------------------------------------------------------------------===//
//
SCEV::~SCEV() {}
void SCEV::dump() const {
- print(cerr);
+ print(errs());
+ errs() << '\n';
}
-/// getValueRange - Return the tightest constant bounds that this value is
-/// known to have. This method is only valid on integer SCEV objects.
-ConstantRange SCEV::getValueRange() const {
- const Type *Ty = getType();
- assert(Ty->isInteger() && "Can't get range for a non-integer SCEV!");
- // Default to a full range if no better information is available.
- return ConstantRange(getBitWidth());
+void SCEV::print(std::ostream &o) const {
+ raw_os_ostream OS(o);
+ print(OS);
}
-uint32_t SCEV::getBitWidth() const {
- if (const IntegerType* ITy = dyn_cast<IntegerType>(getType()))
- return ITy->getBitWidth();
- return 0;
+bool SCEV::isZero() const {
+ if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
+ return SC->getValue()->isZero();
+ return false;
}
SCEVHandle SCEVCouldNotCompute::
replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
- const SCEVHandle &Conc) const {
+ const SCEVHandle &Conc,
+ ScalarEvolution &SE) const {
return this;
}
-void SCEVCouldNotCompute::print(std::ostream &OS) const {
+void SCEVCouldNotCompute::print(raw_ostream &OS) const {
OS << "***COULDNOTCOMPUTE***";
}
SCEVConstants->erase(V);
}
-SCEVHandle SCEVConstant::get(ConstantInt *V) {
+SCEVHandle ScalarEvolution::getConstant(ConstantInt *V) {
SCEVConstant *&R = (*SCEVConstants)[V];
if (R == 0) R = new SCEVConstant(V);
return R;
}
-ConstantRange SCEVConstant::getValueRange() const {
- return ConstantRange(V->getValue());
+SCEVHandle ScalarEvolution::getConstant(const APInt& Val) {
+ return getConstant(ConstantInt::get(Val));
}
const Type *SCEVConstant::getType() const { return V->getType(); }
-void SCEVConstant::print(std::ostream &OS) const {
+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!
SCEVTruncateExpr*> > SCEVTruncates;
SCEVTruncateExpr::SCEVTruncateExpr(const SCEVHandle &op, const Type *ty)
- : SCEV(scTruncate), Op(op), Ty(ty) {
- assert(Op->getType()->isInteger() && Ty->isInteger() &&
+ : SCEVCastExpr(scTruncate, op, ty) {
+ assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
+ (Ty->isInteger() || isa<PointerType>(Ty)) &&
"Cannot truncate non-integer value!");
- assert(Op->getType()->getPrimitiveSizeInBits() > Ty->getPrimitiveSizeInBits()
- && "This is not a truncating conversion!");
}
SCEVTruncateExpr::~SCEVTruncateExpr() {
SCEVTruncates->erase(std::make_pair(Op, Ty));
}
-ConstantRange SCEVTruncateExpr::getValueRange() const {
- return getOperand()->getValueRange().truncate(getBitWidth());
-}
-
-void SCEVTruncateExpr::print(std::ostream &OS) const {
+void SCEVTruncateExpr::print(raw_ostream &OS) const {
OS << "(truncate " << *Op << " to " << *Ty << ")";
}
SCEVZeroExtendExpr*> > SCEVZeroExtends;
SCEVZeroExtendExpr::SCEVZeroExtendExpr(const SCEVHandle &op, const Type *ty)
- : SCEV(scZeroExtend), Op(op), Ty(ty) {
- assert(Op->getType()->isInteger() && Ty->isInteger() &&
+ : SCEVCastExpr(scZeroExtend, op, ty) {
+ assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
+ (Ty->isInteger() || isa<PointerType>(Ty)) &&
"Cannot zero extend non-integer value!");
- assert(Op->getType()->getPrimitiveSizeInBits() < Ty->getPrimitiveSizeInBits()
- && "This is not an extending conversion!");
}
SCEVZeroExtendExpr::~SCEVZeroExtendExpr() {
SCEVZeroExtends->erase(std::make_pair(Op, Ty));
}
-ConstantRange SCEVZeroExtendExpr::getValueRange() const {
- return getOperand()->getValueRange().zeroExtend(getBitWidth());
-}
-
-void SCEVZeroExtendExpr::print(std::ostream &OS) const {
+void SCEVZeroExtendExpr::print(raw_ostream &OS) const {
OS << "(zeroextend " << *Op << " to " << *Ty << ")";
}
SCEVSignExtendExpr*> > SCEVSignExtends;
SCEVSignExtendExpr::SCEVSignExtendExpr(const SCEVHandle &op, const Type *ty)
- : SCEV(scSignExtend), Op(op), Ty(ty) {
- assert(Op->getType()->isInteger() && Ty->isInteger() &&
+ : SCEVCastExpr(scSignExtend, op, ty) {
+ assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
+ (Ty->isInteger() || isa<PointerType>(Ty)) &&
"Cannot sign extend non-integer value!");
- assert(Op->getType()->getPrimitiveSizeInBits() < Ty->getPrimitiveSizeInBits()
- && "This is not an extending conversion!");
}
SCEVSignExtendExpr::~SCEVSignExtendExpr() {
SCEVSignExtends->erase(std::make_pair(Op, Ty));
}
-ConstantRange SCEVSignExtendExpr::getValueRange() const {
- return getOperand()->getValueRange().signExtend(getBitWidth());
-}
-
-void SCEVSignExtendExpr::print(std::ostream &OS) const {
+void SCEVSignExtendExpr::print(raw_ostream &OS) const {
OS << "(signextend " << *Op << " to " << *Ty << ")";
}
Operands.end())));
}
-void SCEVCommutativeExpr::print(std::ostream &OS) const {
+void SCEVCommutativeExpr::print(raw_ostream &OS) const {
assert(Operands.size() > 1 && "This plus expr shouldn't exist!");
const char *OpStr = getOperationStr();
OS << "(" << *Operands[0];
SCEVHandle SCEVCommutativeExpr::
replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
- const SCEVHandle &Conc) const {
+ const SCEVHandle &Conc,
+ ScalarEvolution &SE) const {
for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
- SCEVHandle H = getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc);
+ SCEVHandle H =
+ getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE);
if (H != getOperand(i)) {
std::vector<SCEVHandle> NewOps;
NewOps.reserve(getNumOperands());
NewOps.push_back(H);
for (++i; i != e; ++i)
NewOps.push_back(getOperand(i)->
- replaceSymbolicValuesWithConcrete(Sym, Conc));
+ replaceSymbolicValuesWithConcrete(Sym, Conc, SE));
if (isa<SCEVAddExpr>(this))
- return SCEVAddExpr::get(NewOps);
+ return SE.getAddExpr(NewOps);
else if (isa<SCEVMulExpr>(this))
- return SCEVMulExpr::get(NewOps);
+ 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;
+}
-// SCEVSDivs - Only allow the creation of one SCEVSDivExpr for any particular
+
+// 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<SCEV*, SCEV*>,
- SCEVSDivExpr*> > SCEVSDivs;
+ SCEVUDivExpr*> > SCEVUDivs;
+
+SCEVUDivExpr::~SCEVUDivExpr() {
+ SCEVUDivs->erase(std::make_pair(LHS, RHS));
+}
-SCEVSDivExpr::~SCEVSDivExpr() {
- SCEVSDivs->erase(std::make_pair(LHS, RHS));
+bool SCEVUDivExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
+ return LHS->dominates(BB, DT) && RHS->dominates(BB, DT);
}
-void SCEVSDivExpr::print(std::ostream &OS) const {
- OS << "(" << *LHS << " /s " << *RHS << ")";
+void SCEVUDivExpr::print(raw_ostream &OS) const {
+ OS << "(" << *LHS << " /u " << *RHS << ")";
}
-const Type *SCEVSDivExpr::getType() const {
+const Type *SCEVUDivExpr::getType() const {
return LHS->getType();
}
Operands.end())));
}
+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) const {
+ const SCEVHandle &Conc,
+ ScalarEvolution &SE) const {
for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
- SCEVHandle H = getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc);
+ SCEVHandle H =
+ getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE);
if (H != getOperand(i)) {
std::vector<SCEVHandle> NewOps;
NewOps.reserve(getNumOperands());
NewOps.push_back(H);
for (++i; i != e; ++i)
NewOps.push_back(getOperand(i)->
- replaceSymbolicValuesWithConcrete(Sym, Conc));
+ replaceSymbolicValuesWithConcrete(Sym, Conc, SE));
- return get(NewOps, L);
+ return SE.getAddRecExpr(NewOps, L);
}
}
return this;
}
-void SCEVAddRecExpr::print(std::ostream &OS) const {
+void SCEVAddRecExpr::print(raw_ostream &OS) const {
OS << "{" << *Operands[0];
for (unsigned i = 1, e = Operands.size(); i != e; ++i)
OS << ",+," << *Operands[i];
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(std::ostream &OS) const {
+void SCEVUnknown::print(raw_ostream &OS) const {
+ if (isa<PointerType>(V->getType()))
+ OS << "(ptrtoint " << *V->getType() << " ";
WriteAsOperand(OS, V, false);
+ if (isa<PointerType>(V->getType()))
+ OS << " to iPTR)";
}
//===----------------------------------------------------------------------===//
/// than the complexity of the RHS. This comparator is used to canonicalize
/// expressions.
struct VISIBILITY_HIDDEN SCEVComplexityCompare {
- bool operator()(SCEV *LHS, SCEV *RHS) {
+ bool operator()(const SCEV *LHS, const SCEV *RHS) const {
return LHS->getSCEVType() < RHS->getSCEVType();
}
};
if (Ops.size() == 2) {
// This is the common case, which also happens to be trivially simple.
// Special case it.
- if (Ops[0]->getSCEVType() > Ops[1]->getSCEVType())
+ if (SCEVComplexityCompare()(Ops[1], Ops[0]))
std::swap(Ops[0], Ops[1]);
return;
}
// Simple SCEV method implementations
//===----------------------------------------------------------------------===//
-/// getIntegerSCEV - Given an integer or FP type, create a constant for the
-/// specified signed integer value and return a SCEV for the constant.
-SCEVHandle SCEVUnknown::getIntegerSCEV(int Val, const Type *Ty) {
- Constant *C;
- if (Val == 0)
- C = Constant::getNullValue(Ty);
- else if (Ty->isFloatingPoint())
- C = ConstantFP::get(Ty, Val);
- else
- C = ConstantInt::get(Ty, Val);
- return SCEVUnknown::get(C);
-}
-
-SCEVHandle SCEVUnknown::getIntegerSCEV(const APInt& Val) {
- return SCEVUnknown::get(ConstantInt::get(Val));
-}
-
-/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
-/// input value to the specified type. If the type must be extended, it is zero
-/// extended.
-static SCEVHandle getTruncateOrZeroExtend(const SCEVHandle &V, const Type *Ty) {
- const Type *SrcTy = V->getType();
- assert(SrcTy->isInteger() && Ty->isInteger() &&
- "Cannot truncate or zero extend with non-integer arguments!");
- if (SrcTy->getPrimitiveSizeInBits() == Ty->getPrimitiveSizeInBits())
- return V; // No conversion
- if (SrcTy->getPrimitiveSizeInBits() > Ty->getPrimitiveSizeInBits())
- return SCEVTruncateExpr::get(V, Ty);
- return SCEVZeroExtendExpr::get(V, Ty);
-}
-
-/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
-///
-SCEVHandle SCEV::getNegativeSCEV(const SCEVHandle &V) {
- if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
- return SCEVUnknown::get(ConstantExpr::getNeg(VC->getValue()));
-
- return SCEVMulExpr::get(V, SCEVUnknown::getIntegerSCEV(-1, V->getType()));
-}
-
-/// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
-///
-SCEVHandle SCEV::getMinusSCEV(const SCEVHandle &LHS, const SCEVHandle &RHS) {
- // X - Y --> X + -Y
- return SCEVAddExpr::get(LHS, SCEV::getNegativeSCEV(RHS));
-}
+/// 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;
+ }
-/// PartialFact - Compute V!/(V-NumSteps)!
-static SCEVHandle PartialFact(SCEVHandle V, unsigned NumSteps) {
- // Handle this case efficiently, it is common to have constant iteration
- // counts while computing loop exit values.
- if (SCEVConstant *SC = dyn_cast<SCEVConstant>(V)) {
- const APInt& Val = SC->getValue()->getValue();
- APInt Result(Val.getBitWidth(), 1);
- for (; NumSteps; --NumSteps)
- Result *= Val-(NumSteps-1);
- return SCEVUnknown::get(ConstantInt::get(Result));
+ // 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));
}
- const Type *Ty = V->getType();
- if (NumSteps == 0)
- return SCEVUnknown::getIntegerSCEV(1, Ty);
+ // Divide by 2^T
+ SCEVHandle DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
- SCEVHandle Result = V;
- for (unsigned i = 1; i != NumSteps; ++i)
- Result = SCEVMulExpr::get(Result, SCEV::getMinusSCEV(V,
- SCEVUnknown::getIntegerSCEV(i, Ty)));
- return Result;
-}
+ // 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*choose(It, 0) + B*choose(It, 1) + C*choose(It, 2) + D*choose(It, 3)
+/// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
///
-/// FIXME/VERIFY: I don't trust that this is correct in the face of overflow.
-/// Is the binomial equation safe using modular arithmetic??
+/// where BC(It, k) stands for binomial coefficient.
///
-SCEVHandle SCEVAddRecExpr::evaluateAtIteration(SCEVHandle It) const {
+SCEVHandle SCEVAddRecExpr::evaluateAtIteration(SCEVHandle It,
+ ScalarEvolution &SE) const {
SCEVHandle Result = getStart();
- int Divisor = 1;
- const Type *Ty = It->getType();
for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
- SCEVHandle BC = PartialFact(It, i);
- Divisor *= i;
- SCEVHandle Val = SCEVSDivExpr::get(SCEVMulExpr::get(BC, getOperand(i)),
- SCEVUnknown::getIntegerSCEV(Divisor,Ty));
- Result = SCEVAddExpr::get(Result, Val);
+ // 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 SCEVTruncateExpr::get(const SCEVHandle &Op, const Type *Ty) {
+SCEVHandle ScalarEvolution::getTruncateExpr(const SCEVHandle &Op, const Type *Ty) {
+ assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
+ "This is not a truncating conversion!");
+
if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
- return SCEVUnknown::get(
+ return getUnknown(
ConstantExpr::getTrunc(SC->getValue(), Ty));
// If the input value is a chrec scev made out of constants, truncate
for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
// FIXME: This should allow truncation of other expression types!
if (isa<SCEVConstant>(AddRec->getOperand(i)))
- Operands.push_back(get(AddRec->getOperand(i), Ty));
+ Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty));
else
break;
if (Operands.size() == AddRec->getNumOperands())
- return SCEVAddRecExpr::get(Operands, AddRec->getLoop());
+ return getAddRecExpr(Operands, AddRec->getLoop());
}
SCEVTruncateExpr *&Result = (*SCEVTruncates)[std::make_pair(Op, Ty)];
return Result;
}
-SCEVHandle SCEVZeroExtendExpr::get(const SCEVHandle &Op, const Type *Ty) {
- if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
- return SCEVUnknown::get(
- ConstantExpr::getZExt(SC->getValue(), Ty));
+SCEVHandle ScalarEvolution::getZeroExtendExpr(const SCEVHandle &Op,
+ const Type *Ty) {
+ assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
+ "This is not an extending conversion!");
+
+ if (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);
+ }
// FIXME: If the input value is a chrec scev, and we can prove that the value
// did not overflow the old, smaller, value, we can zero extend all of the
return Result;
}
-SCEVHandle SCEVSignExtendExpr::get(const SCEVHandle &Op, const Type *Ty) {
- if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
- return SCEVUnknown::get(
- ConstantExpr::getSExt(SC->getValue(), Ty));
+SCEVHandle ScalarEvolution::getSignExtendExpr(const SCEVHandle &Op, const Type *Ty) {
+ assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
+ "This is not an extending conversion!");
+
+ if (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);
+ }
// FIXME: If the input value is a chrec scev, and we can prove that the value
// did not overflow the old, smaller, value, we can sign extend all of the
}
// get - Get a canonical add expression, or something simpler if possible.
-SCEVHandle SCEVAddExpr::get(std::vector<SCEVHandle> &Ops) {
+SCEVHandle ScalarEvolution::getAddExpr(std::vector<SCEVHandle> &Ops) {
assert(!Ops.empty() && "Cannot get empty add!");
if (Ops.size() == 1) return Ops[0];
assert(Idx < Ops.size());
while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
// We found two constants, fold them together!
- Constant *Fold = ConstantInt::get(LHSC->getValue()->getValue() +
- RHSC->getValue()->getValue());
- if (ConstantInt *CI = dyn_cast<ConstantInt>(Fold)) {
- Ops[0] = SCEVConstant::get(CI);
- Ops.erase(Ops.begin()+1); // Erase the folded element
- if (Ops.size() == 1) return Ops[0];
- LHSC = cast<SCEVConstant>(Ops[0]);
- } else {
- // If we couldn't fold the expression, move to the next constant. Note
- // that this is impossible to happen in practice because we always
- // constant fold constant ints to constant ints.
- ++Idx;
- }
+ 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 (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
// Found a match, merge the two values into a multiply, and add any
// remaining values to the result.
- SCEVHandle Two = SCEVUnknown::getIntegerSCEV(2, Ty);
- SCEVHandle Mul = SCEVMulExpr::get(Ops[i], Two);
+ 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 SCEVAddExpr::get(Ops);
+ return getAddExpr(Ops);
}
- // Okay, now we know the first non-constant operand. If there are add
- // operands they would be next.
+ // 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 (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
// and they are not necessarily sorted. Recurse to resort and resimplify
// any operands we just aquired.
if (DeletedAdd)
- return get(Ops);
+ return getAddExpr(Ops);
}
// Skip over the add expression until we get to a multiply.
// Y*Z term.
std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end());
MulOps.erase(MulOps.begin()+MulOp);
- InnerMul = SCEVMulExpr::get(MulOps);
+ InnerMul = getMulExpr(MulOps);
}
- SCEVHandle One = SCEVUnknown::getIntegerSCEV(1, Ty);
- SCEVHandle AddOne = SCEVAddExpr::get(InnerMul, One);
- SCEVHandle OuterMul = SCEVMulExpr::get(AddOne, Ops[AddOp]);
+ 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()+AddOp-1);
}
Ops.push_back(OuterMul);
- return SCEVAddExpr::get(Ops);
+ return getAddExpr(Ops);
}
// Check this multiply against other multiplies being added together.
if (Mul->getNumOperands() != 2) {
std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end());
MulOps.erase(MulOps.begin()+MulOp);
- InnerMul1 = SCEVMulExpr::get(MulOps);
+ 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 = SCEVMulExpr::get(MulOps);
+ InnerMul2 = getMulExpr(MulOps);
}
- SCEVHandle InnerMulSum = SCEVAddExpr::get(InnerMul1,InnerMul2);
- SCEVHandle OuterMul = SCEVMulExpr::get(MulOpSCEV, InnerMulSum);
+ 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 SCEVAddExpr::get(Ops);
+ return getAddExpr(Ops);
}
}
}
// If we found some loop invariants, fold them into the recurrence.
if (!LIOps.empty()) {
- // NLI + LI + { Start,+,Step} --> NLI + { LI+Start,+,Step }
+ // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
LIOps.push_back(AddRec->getStart());
std::vector<SCEVHandle> AddRecOps(AddRec->op_begin(), AddRec->op_end());
- AddRecOps[0] = SCEVAddExpr::get(LIOps);
+ AddRecOps[0] = getAddExpr(LIOps);
- SCEVHandle NewRec = SCEVAddRecExpr::get(AddRecOps, AddRec->getLoop());
+ SCEVHandle NewRec = getAddRecExpr(AddRecOps, AddRec->getLoop());
// If all of the other operands were loop invariant, we are done.
if (Ops.size() == 1) return NewRec;
Ops[i] = NewRec;
break;
}
- return SCEVAddExpr::get(Ops);
+ return getAddExpr(Ops);
}
// Okay, if there weren't any loop invariants to be folded, check to see if
OtherAddRec->op_end());
break;
}
- NewOps[i] = SCEVAddExpr::get(NewOps[i], OtherAddRec->getOperand(i));
+ NewOps[i] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i));
}
- SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewOps, AddRec->getLoop());
+ 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 SCEVAddExpr::get(Ops);
+ return getAddExpr(Ops);
}
}
}
-SCEVHandle SCEVMulExpr::get(std::vector<SCEVHandle> &Ops) {
+SCEVHandle ScalarEvolution::getMulExpr(std::vector<SCEVHandle> &Ops) {
assert(!Ops.empty() && "Cannot get empty mul!");
// Sort by complexity, this groups all similar expression types together.
if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
if (Add->getNumOperands() == 2 &&
isa<SCEVConstant>(Add->getOperand(0)))
- return SCEVAddExpr::get(SCEVMulExpr::get(LHSC, Add->getOperand(0)),
- SCEVMulExpr::get(LHSC, Add->getOperand(1)));
+ return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
+ getMulExpr(LHSC, Add->getOperand(1)));
++Idx;
while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
// We found two constants, fold them together!
- Constant *Fold = ConstantInt::get(LHSC->getValue()->getValue() *
- RHSC->getValue()->getValue());
- if (ConstantInt *CI = dyn_cast<ConstantInt>(Fold)) {
- Ops[0] = SCEVConstant::get(CI);
- Ops.erase(Ops.begin()+1); // Erase the folded element
- if (Ops.size() == 1) return Ops[0];
- LHSC = cast<SCEVConstant>(Ops[0]);
- } else {
- // If we couldn't fold the expression, move to the next constant. Note
- // that this is impossible to happen in practice because we always
- // constant fold constant ints to constant ints.
- ++Idx;
- }
+ 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.
// and they are not necessarily sorted. Recurse to resort and resimplify
// any operands we just aquired.
if (DeletedMul)
- return get(Ops);
+ return getMulExpr(Ops);
}
// If there are any add recurrences in the operands list, see if any other
// If we found some loop invariants, fold them into the recurrence.
if (!LIOps.empty()) {
- // NLI * LI * { Start,+,Step} --> NLI * { LI*Start,+,LI*Step }
+ // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
std::vector<SCEVHandle> NewOps;
NewOps.reserve(AddRec->getNumOperands());
if (LIOps.size() == 1) {
SCEV *Scale = LIOps[0];
for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
- NewOps.push_back(SCEVMulExpr::get(Scale, AddRec->getOperand(i)));
+ 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(SCEVMulExpr::get(MulOps));
+ NewOps.push_back(getMulExpr(MulOps));
}
}
- SCEVHandle NewRec = SCEVAddRecExpr::get(NewOps, AddRec->getLoop());
+ SCEVHandle NewRec = getAddRecExpr(NewOps, AddRec->getLoop());
// If all of the other operands were loop invariant, we are done.
if (Ops.size() == 1) return NewRec;
Ops[i] = NewRec;
break;
}
- return SCEVMulExpr::get(Ops);
+ return getMulExpr(Ops);
}
// Okay, if there weren't any loop invariants to be folded, check to see if
if (AddRec->getLoop() == OtherAddRec->getLoop()) {
// F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D}
SCEVAddRecExpr *F = AddRec, *G = OtherAddRec;
- SCEVHandle NewStart = SCEVMulExpr::get(F->getStart(),
+ SCEVHandle NewStart = getMulExpr(F->getStart(),
G->getStart());
- SCEVHandle B = F->getStepRecurrence();
- SCEVHandle D = G->getStepRecurrence();
- SCEVHandle NewStep = SCEVAddExpr::get(SCEVMulExpr::get(F, D),
- SCEVMulExpr::get(G, B),
- SCEVMulExpr::get(B, D));
- SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewStart, NewStep,
- F->getLoop());
+ 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 SCEVMulExpr::get(Ops);
+ return getMulExpr(Ops);
}
}
return Result;
}
-SCEVHandle SCEVSDivExpr::get(const SCEVHandle &LHS, const SCEVHandle &RHS) {
+SCEVHandle ScalarEvolution::getUDivExpr(const SCEVHandle &LHS, const SCEVHandle &RHS) {
if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
if (RHSC->getValue()->equalsInt(1))
- return LHS; // X sdiv 1 --> x
- if (RHSC->getValue()->isAllOnesValue())
- return SCEV::getNegativeSCEV(LHS); // X sdiv -1 --> -x
+ return LHS; // X udiv 1 --> x
if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
Constant *LHSCV = LHSC->getValue();
Constant *RHSCV = RHSC->getValue();
- return SCEVUnknown::get(ConstantExpr::getSDiv(LHSCV, RHSCV));
+ return getUnknown(ConstantExpr::getUDiv(LHSCV, RHSCV));
}
}
// FIXME: implement folding of (X*4)/4 when we know X*4 doesn't overflow.
- SCEVSDivExpr *&Result = (*SCEVSDivs)[std::make_pair(LHS, RHS)];
- if (Result == 0) Result = new SCEVSDivExpr(LHS, RHS);
+ SCEVUDivExpr *&Result = (*SCEVUDivs)[std::make_pair(LHS, RHS)];
+ if (Result == 0) Result = new SCEVUDivExpr(LHS, RHS);
return Result;
}
/// SCEVAddRecExpr::get - Get a add recurrence expression for the
/// specified loop. Simplify the expression as much as possible.
-SCEVHandle SCEVAddRecExpr::get(const SCEVHandle &Start,
+SCEVHandle ScalarEvolution::getAddRecExpr(const SCEVHandle &Start,
const SCEVHandle &Step, const Loop *L) {
std::vector<SCEVHandle> Operands;
Operands.push_back(Start);
if (StepChrec->getLoop() == L) {
Operands.insert(Operands.end(), StepChrec->op_begin(),
StepChrec->op_end());
- return get(Operands, L);
+ return getAddRecExpr(Operands, L);
}
Operands.push_back(Step);
- return get(Operands, L);
+ return getAddRecExpr(Operands, L);
}
/// SCEVAddRecExpr::get - Get a add recurrence expression for the
/// specified loop. Simplify the expression as much as possible.
-SCEVHandle SCEVAddRecExpr::get(std::vector<SCEVHandle> &Operands,
+SCEVHandle ScalarEvolution::getAddRecExpr(std::vector<SCEVHandle> &Operands,
const Loop *L) {
if (Operands.size() == 1) return Operands[0];
- if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Operands.back()))
- if (StepC->getValue()->isZero()) {
- Operands.pop_back();
- return get(Operands, L); // { X,+,0 } --> X
+ 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 (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);
}
+ }
SCEVAddRecExpr *&Result =
(*SCEVAddRecExprs)[std::make_pair(L, std::vector<SCEV*>(Operands.begin(),
return Result;
}
-SCEVHandle SCEVUnknown::get(Value *V) {
+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 (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
+ ++Idx;
+ assert(Idx < Ops.size());
+ while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
+ // We found two constants, fold them together!
+ 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 (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<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 (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
+ ++Idx;
+ assert(Idx < Ops.size());
+ while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
+ // We found two constants, fold them together!
+ 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 (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<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 SCEVConstant::get(CI);
+ 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;
}
-
//===----------------------------------------------------------------------===//
// ScalarEvolutionsImpl Definition and Implementation
//===----------------------------------------------------------------------===//
///
namespace {
struct VISIBILITY_HIDDEN ScalarEvolutionsImpl {
+ /// SE - A reference to the public ScalarEvolution object.
+ ScalarEvolution &SE;
+
/// F - The function we are analyzing.
///
Function &F;
///
LoopInfo &LI;
+ /// TD - The target data information for the target we are targetting.
+ ///
+ TargetData *TD;
+
/// UnknownValue - This SCEV is used to represent unknown trip counts and
/// things.
SCEVHandle UnknownValue;
///
std::map<Value*, SCEVHandle> Scalars;
- /// IterationCounts - Cache the iteration count of the loops for this
- /// function as they are computed.
- std::map<const Loop*, SCEVHandle> IterationCounts;
+ /// BackedgeTakenCounts - Cache the backedge-taken count of the loops for
+ /// this function as they are computed.
+ std::map<const Loop*, SCEVHandle> BackedgeTakenCounts;
/// ConstantEvolutionLoopExitValue - This map contains entries for all of
/// the PHI instructions that we attempt to compute constant evolutions for.
std::map<PHINode*, Constant*> ConstantEvolutionLoopExitValue;
public:
- ScalarEvolutionsImpl(Function &f, LoopInfo &li)
- : F(f), LI(li), UnknownValue(new SCEVCouldNotCompute()) {}
+ ScalarEvolutionsImpl(ScalarEvolution &se, Function &f, LoopInfo &li,
+ TargetData *td)
+ : SE(se), F(f), LI(li), TD(td), UnknownValue(new SCEVCouldNotCompute()) {}
+
+ /// 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 isSCEVable(const Type *Ty) const;
+
+ /// getTypeSizeInBits - Return the size in bits of the specified type,
+ /// for which isSCEVable must return true.
+ uint64_t getTypeSizeInBits(const Type *Ty) const;
+
+ /// 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 *getEffectiveSCEVType(const Type *Ty) const;
+
+ SCEVHandle getCouldNotCompute();
+
+ /// getIntegerSCEV - Given an integer or FP type, create a constant for the
+ /// specified signed integer value and return a SCEV for the constant.
+ SCEVHandle getIntegerSCEV(int Val, const Type *Ty);
+
+ /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
+ ///
+ SCEVHandle getNegativeSCEV(const SCEVHandle &V);
+
+ /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
+ ///
+ SCEVHandle getNotSCEV(const SCEVHandle &V);
+
+ /// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
+ ///
+ SCEVHandle getMinusSCEV(const SCEVHandle &LHS, const SCEVHandle &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 getTruncateOrZeroExtend(const SCEVHandle &V, const Type *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 getTruncateOrSignExtend(const SCEVHandle &V, const Type *Ty);
/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
/// expression and create a new one.
void setSCEV(Value *V, const SCEVHandle &H) {
bool isNew = Scalars.insert(std::make_pair(V, H)).second;
assert(isNew && "This entry already existed!");
+ isNew = false;
}
SCEVHandle getSCEVAtScope(SCEV *V, const Loop *L);
- /// hasLoopInvariantIterationCount - Return true if the specified loop has
- /// an analyzable loop-invariant iteration count.
- bool hasLoopInvariantIterationCount(const Loop *L);
+ /// isLoopGuardedByCond - Test whether entry to the loop is protected by
+ /// a conditional between LHS and RHS.
+ bool isLoopGuardedByCond(const Loop *L, ICmpInst::Predicate Pred,
+ SCEV *LHS, SCEV *RHS);
+
+ /// hasLoopInvariantBackedgeTakenCount - Return true if the specified loop
+ /// has an analyzable loop-invariant backedge-taken count.
+ bool hasLoopInvariantBackedgeTakenCount(const Loop *L);
- /// getIterationCount - If the specified loop has a predictable iteration
- /// count, return it. Note that it is not valid to call this method on a
- /// loop without a loop-invariant iteration count.
- SCEVHandle getIterationCount(const Loop *L);
+ /// 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 forgetLoopBackedgeTakenCount(const Loop *L);
- /// deleteInstructionFromRecords - This method should be called by the
- /// client before it removes an instruction from the program, to make sure
+ /// 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 getBackedgeTakenCount(const Loop *L);
+
+ /// deleteValueFromRecords - This method should be called by the
+ /// client before it removes a value from the program, to make sure
/// that no dangling references are left around.
- void deleteInstructionFromRecords(Instruction *I);
+ void deleteValueFromRecords(Value *V);
private:
/// createSCEV - We know that there is no SCEV for the specified value.
const SCEVHandle &SymName,
const SCEVHandle &NewVal);
- /// ComputeIterationCount - Compute the number of times the specified loop
- /// will iterate.
- SCEVHandle ComputeIterationCount(const Loop *L);
+ /// ComputeBackedgeTakenCount - Compute the number of times the specified
+ /// loop will iterate.
+ SCEVHandle ComputeBackedgeTakenCount(const Loop *L);
- /// ComputeLoadConstantCompareIterationCount - Given an exit condition of
- /// 'setcc load X, cst', try to see if we can compute the trip count.
- SCEVHandle ComputeLoadConstantCompareIterationCount(LoadInst *LI,
- Constant *RHS,
- const Loop *L,
- ICmpInst::Predicate p);
+ /// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition
+ /// of 'icmp op load X, cst', try to see if we can compute the trip count.
+ SCEVHandle
+ ComputeLoadConstantCompareBackedgeTakenCount(LoadInst *LI,
+ Constant *RHS,
+ const Loop *L,
+ ICmpInst::Predicate p);
- /// ComputeIterationCountExhaustively - If the trip is known to execute a
- /// constant number of times (the condition evolves only from constants),
+ /// 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 ComputeIterationCountExhaustively(const Loop *L, Value *Cond,
- bool ExitWhen);
+ SCEVHandle ComputeBackedgeTakenCountExhaustively(const Loop *L, Value *Cond,
+ bool ExitWhen);
/// HowFarToZero - Return the number of times a backedge comparing the
/// specified value to zero will execute. If not computable, return
/// HowManyLessThans - Return the number of times a backedge containing the
/// specified less-than comparison will execute. If not computable, return
- /// UnknownValue.
- SCEVHandle HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L);
+ /// UnknownValue. isSigned specifies whether the less-than is signed.
+ SCEVHandle HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L,
+ bool isSigned);
+
+ /// 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* getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB);
/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
/// in the header of its containing loop, we know the loop executes a
/// constant number of times, and the PHI node is just a recurrence
/// involving constants, fold it.
- Constant *getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& Its,
+ Constant *getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& BEs,
const Loop *L);
};
}
// Basic SCEV Analysis and PHI Idiom Recognition Code
//
-/// deleteInstructionFromRecords - This method should be called by the
+/// deleteValueFromRecords - This method should be called by the
/// client before it removes an instruction from the program, to make sure
/// that no dangling references are left around.
-void ScalarEvolutionsImpl::deleteInstructionFromRecords(Instruction *I) {
- SmallVector<Instruction *, 16> Worklist;
+void ScalarEvolutionsImpl::deleteValueFromRecords(Value *V) {
+ SmallVector<Value *, 16> Worklist;
- if (Scalars.erase(I)) {
- if (PHINode *PN = dyn_cast<PHINode>(I))
+ if (Scalars.erase(V)) {
+ if (PHINode *PN = dyn_cast<PHINode>(V))
ConstantEvolutionLoopExitValue.erase(PN);
- Worklist.push_back(I);
+ Worklist.push_back(V);
}
while (!Worklist.empty()) {
- Instruction *II = Worklist.back();
+ Value *VV = Worklist.back();
Worklist.pop_back();
- for (Instruction::use_iterator UI = II->use_begin(), UE = II->use_end();
+ for (Instruction::use_iterator UI = VV->use_begin(), UE = VV->use_end();
UI != UE; ++UI) {
Instruction *Inst = cast<Instruction>(*UI);
if (Scalars.erase(Inst)) {
- if (PHINode *PN = dyn_cast<PHINode>(II))
+ if (PHINode *PN = dyn_cast<PHINode>(VV))
ConstantEvolutionLoopExitValue.erase(PN);
Worklist.push_back(Inst);
}
}
}
+/// 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 ScalarEvolutionsImpl::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 ScalarEvolutionsImpl::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 *ScalarEvolutionsImpl::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 ScalarEvolutionsImpl::getCouldNotCompute() {
+ return UnknownValue;
+}
/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
/// expression and create a new one.
SCEVHandle ScalarEvolutionsImpl::getSCEV(Value *V) {
- assert(V->getType() != Type::VoidTy && "Can't analyze void expressions!");
+ assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
std::map<Value*, SCEVHandle>::iterator I = Scalars.find(V);
if (I != Scalars.end()) return I->second;
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 ScalarEvolutionsImpl::getIntegerSCEV(int Val, const Type *Ty) {
+ Ty = SE.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 SE.getUnknown(C);
+}
+
+/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
+///
+SCEVHandle ScalarEvolutionsImpl::getNegativeSCEV(const SCEVHandle &V) {
+ if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
+ return SE.getUnknown(ConstantExpr::getNeg(VC->getValue()));
+
+ const Type *Ty = V->getType();
+ Ty = SE.getEffectiveSCEVType(Ty);
+ return SE.getMulExpr(V, SE.getConstant(ConstantInt::getAllOnesValue(Ty)));
+}
+
+/// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
+SCEVHandle ScalarEvolutionsImpl::getNotSCEV(const SCEVHandle &V) {
+ if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
+ return SE.getUnknown(ConstantExpr::getNot(VC->getValue()));
+
+ const Type *Ty = V->getType();
+ Ty = SE.getEffectiveSCEVType(Ty);
+ SCEVHandle AllOnes = SE.getConstant(ConstantInt::getAllOnesValue(Ty));
+ return getMinusSCEV(AllOnes, V);
+}
+
+/// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
+///
+SCEVHandle ScalarEvolutionsImpl::getMinusSCEV(const SCEVHandle &LHS,
+ const SCEVHandle &RHS) {
+ // X - Y --> X + -Y
+ return SE.getAddExpr(LHS, SE.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
+ScalarEvolutionsImpl::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 SE.getTruncateExpr(V, Ty);
+ return SE.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
+ScalarEvolutionsImpl::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 SE.getTruncateExpr(V, Ty);
+ return SE.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.
if (SI == Scalars.end()) return;
SCEVHandle NV =
- SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal);
+ SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal, SE);
if (NV == SI->second) return; // No change.
SI->second = NV; // Update the scalars map!
unsigned BackEdge = IncomingEdge^1;
// While we are analyzing this PHI node, handle its value symbolically.
- SCEVHandle SymbolicName = SCEVUnknown::get(PN);
+ SCEVHandle SymbolicName = SE.getUnknown(PN);
assert(Scalars.find(PN) == Scalars.end() &&
"PHI node already processed?");
Scalars.insert(std::make_pair(PN, SymbolicName));
for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
if (i != FoundIndex)
Ops.push_back(Add->getOperand(i));
- SCEVHandle Accum = SCEVAddExpr::get(Ops);
+ SCEVHandle Accum = SE.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.
(isa<SCEVAddRecExpr>(Accum) &&
cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
- SCEVHandle PHISCEV = SCEVAddRecExpr::get(StartVal, Accum, L);
+ SCEVHandle PHISCEV = SE.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
// If StartVal = j.start - j.stride, we can use StartVal as the
// initial step of the addrec evolution.
- if (StartVal == SCEV::getMinusSCEV(AddRec->getOperand(0),
- AddRec->getOperand(1))) {
+ if (StartVal == SE.getMinusSCEV(AddRec->getOperand(0),
+ AddRec->getOperand(1))) {
SCEVHandle PHISCEV =
- SCEVAddRecExpr::get(StartVal, AddRec->getOperand(1), L);
+ SE.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
}
// If it's not a loop phi, we can't handle it yet.
- return SCEVUnknown::get(PN);
-}
-
-/// GetConstantFactor - Determine the largest constant factor that S has. For
-/// example, turn {4,+,8} -> 4. (S umod result) should always equal zero.
-static APInt GetConstantFactor(SCEVHandle S) {
- if (SCEVConstant *C = dyn_cast<SCEVConstant>(S)) {
- const APInt& V = C->getValue()->getValue();
- if (!V.isMinValue())
- return V;
- else // Zero is a multiple of everything.
- return APInt(C->getBitWidth(), 1).shl(C->getBitWidth()-1);
- }
-
- if (SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S)) {
- return GetConstantFactor(T->getOperand()).trunc(
- cast<IntegerType>(T->getType())->getBitWidth());
- }
- if (SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S))
- return GetConstantFactor(E->getOperand()).zext(
- cast<IntegerType>(E->getType())->getBitWidth());
- if (SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S))
- return GetConstantFactor(E->getOperand()).sext(
- cast<IntegerType>(E->getType())->getBitWidth());
-
+ return SE.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 (SCEVConstant *C = dyn_cast<SCEVConstant>(S))
+ return C->getValue()->getValue().countTrailingZeros();
+
+ if (SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
+ return std::min(GetMinTrailingZeros(T->getOperand(), SE),
+ (uint32_t)SE.getTypeSizeInBits(T->getType()));
+
+ if (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 (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 (SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
- // The result is the min of all operands.
- APInt Res(GetConstantFactor(A->getOperand(0)));
- for (unsigned i = 1, e = A->getNumOperands();
- i != e && Res.ugt(APInt(Res.getBitWidth(),1)); ++i) {
- APInt Tmp(GetConstantFactor(A->getOperand(i)));
- Res = APIntOps::umin(Res, Tmp);
- }
- return Res;
+ // 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 (SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
- // The result is the product of all the operands.
- APInt Res(GetConstantFactor(M->getOperand(0)));
- for (unsigned i = 1, e = M->getNumOperands(); i != e; ++i) {
- APInt Tmp(GetConstantFactor(M->getOperand(i)));
- Res *= Tmp;
- }
- return Res;
+ // 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 (SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
- // For now, we just handle linear expressions.
- if (A->getNumOperands() == 2) {
- // We want the GCD between the start and the stride value.
- APInt Start(GetConstantFactor(A->getOperand(0)));
- if (Start == 1)
- return Start;
- APInt Stride(GetConstantFactor(A->getOperand(1)));
- return APIntOps::GreatestCommonDivisor(Start, Stride);
- }
+ // 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;
}
-
- // SCEVSDivExpr, SCEVUnknown.
- return APInt(S->getBitWidth(), 1);
+
+ if (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 (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 ScalarEvolutionsImpl::createSCEV(Value *V) {
- if (Instruction *I = dyn_cast<Instruction>(V)) {
- switch (I->getOpcode()) {
- case Instruction::Add:
- return SCEVAddExpr::get(getSCEV(I->getOperand(0)),
- getSCEV(I->getOperand(1)));
- case Instruction::Mul:
- return SCEVMulExpr::get(getSCEV(I->getOperand(0)),
- getSCEV(I->getOperand(1)));
- case Instruction::SDiv:
- return SCEVSDivExpr::get(getSCEV(I->getOperand(0)),
- getSCEV(I->getOperand(1)));
- break;
-
- case Instruction::Sub:
- return SCEV::getMinusSCEV(getSCEV(I->getOperand(0)),
- getSCEV(I->getOperand(1)));
- 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.
- if (ConstantInt *CI = dyn_cast<ConstantInt>(I->getOperand(1))) {
- SCEVHandle LHS = getSCEV(I->getOperand(0));
- APInt CommonFact(GetConstantFactor(LHS));
- assert(!CommonFact.isMinValue() &&
- "Common factor should at least be 1!");
- if (CommonFact.ugt(CI->getValue())) {
- // If the LHS is a multiple that is larger than the RHS, use +.
- return SCEVAddExpr::get(LHS,
- getSCEV(I->getOperand(1)));
- }
- }
- break;
- case Instruction::Xor:
+ if (!isSCEVable(V->getType()))
+ return SE.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 SE.getUnknown(V);
+
+ User *U = cast<User>(V);
+ switch (Opcode) {
+ case Instruction::Add:
+ return SE.getAddExpr(getSCEV(U->getOperand(0)),
+ getSCEV(U->getOperand(1)));
+ case Instruction::Mul:
+ return SE.getMulExpr(getSCEV(U->getOperand(0)),
+ getSCEV(U->getOperand(1)));
+ case Instruction::UDiv:
+ return SE.getUDivExpr(getSCEV(U->getOperand(0)),
+ getSCEV(U->getOperand(1)));
+ case Instruction::Sub:
+ return SE.getMinusSCEV(getSCEV(U->getOperand(0)),
+ getSCEV(U->getOperand(1)));
+ 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, SE) >=
+ (CIVal.getBitWidth() - CIVal.countLeadingZeros()))
+ return SE.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 (ConstantInt *CI = dyn_cast<ConstantInt>(I->getOperand(1))) {
- if (CI->getValue().isSignBit())
- return SCEVAddExpr::get(getSCEV(I->getOperand(0)),
- getSCEV(I->getOperand(1)));
- }
- break;
-
- case Instruction::Shl:
- // Turn shift left of a constant amount into a multiply.
- if (ConstantInt *SA = dyn_cast<ConstantInt>(I->getOperand(1))) {
- uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth();
- Constant *X = ConstantInt::get(
- APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
- return SCEVMulExpr::get(getSCEV(I->getOperand(0)), getSCEV(X));
- }
- break;
+ if (CI->getValue().isSignBit())
+ return SE.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 SE.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 SE.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 SE.getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
+ }
+ break;
- case Instruction::Trunc:
- return SCEVTruncateExpr::get(getSCEV(I->getOperand(0)), I->getType());
+ case Instruction::Trunc:
+ return SE.getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
- case Instruction::ZExt:
- return SCEVZeroExtendExpr::get(getSCEV(I->getOperand(0)), I->getType());
+ case Instruction::ZExt:
+ return SE.getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
- case Instruction::SExt:
- return SCEVSignExtendExpr::get(getSCEV(I->getOperand(0)), I->getType());
+ case Instruction::SExt:
+ return SE.getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
- case Instruction::BitCast:
- // BitCasts are no-op casts so we just eliminate the cast.
- if (I->getType()->isInteger() &&
- I->getOperand(0)->getType()->isInteger())
- return getSCEV(I->getOperand(0));
- break;
+ 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::PHI:
- return createNodeForPHI(cast<PHINode>(I));
+ 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 = SE.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 = SE.getAddExpr(TotalOffset,
+ SE.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 =
+ SE.getMulExpr(LocalOffset,
+ SE.getIntegerSCEV(TD->getTypePaddedSize(*GTI),
+ IntPtrTy));
+ TotalOffset = SE.getAddExpr(TotalOffset, LocalOffset);
+ }
+ }
+ return SE.getAddExpr(getSCEV(Base), TotalOffset);
+ }
- default: // We cannot analyze this expression.
- break;
+ 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 SE.getSMaxExpr(getSCEV(LHS), getSCEV(RHS));
+ else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
+ // ~smax(~x, ~y) == smin(x, y).
+ return SE.getNotSCEV(SE.getSMaxExpr(
+ SE.getNotSCEV(getSCEV(LHS)),
+ SE.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 SE.getUMaxExpr(getSCEV(LHS), getSCEV(RHS));
+ else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
+ // ~umax(~x, ~y) == umin(x, y)
+ return SE.getNotSCEV(SE.getUMaxExpr(SE.getNotSCEV(getSCEV(LHS)),
+ SE.getNotSCEV(getSCEV(RHS))));
+ break;
+ default:
+ break;
+ }
}
+
+ default: // We cannot analyze this expression.
+ break;
}
- return SCEVUnknown::get(V);
+ return SE.getUnknown(V);
}
// Iteration Count Computation Code
//
-/// getIterationCount - If the specified loop has a predictable iteration
-/// count, return it. Note that it is not valid to call this method on a
-/// loop without a loop-invariant iteration count.
-SCEVHandle ScalarEvolutionsImpl::getIterationCount(const Loop *L) {
- std::map<const Loop*, SCEVHandle>::iterator I = IterationCounts.find(L);
- if (I == IterationCounts.end()) {
- SCEVHandle ItCount = ComputeIterationCount(L);
- I = IterationCounts.insert(std::make_pair(L, ItCount)).first;
+/// 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 ScalarEvolutionsImpl::getBackedgeTakenCount(const Loop *L) {
+ std::map<const Loop*, SCEVHandle>::iterator I = BackedgeTakenCounts.find(L);
+ if (I == BackedgeTakenCounts.end()) {
+ SCEVHandle ItCount = ComputeBackedgeTakenCount(L);
+ I = BackedgeTakenCounts.insert(std::make_pair(L, ItCount)).first;
if (ItCount != UnknownValue) {
assert(ItCount->isLoopInvariant(L) &&
"Computed trip count isn't loop invariant for loop!");
return I->second;
}
-/// ComputeIterationCount - Compute the number of times the specified loop
-/// will iterate.
-SCEVHandle ScalarEvolutionsImpl::ComputeIterationCount(const Loop *L) {
+/// 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 ScalarEvolutionsImpl::forgetLoopBackedgeTakenCount(const Loop *L) {
+ BackedgeTakenCounts.erase(L);
+}
+
+/// ComputeBackedgeTakenCount - Compute the number of times the backedge
+/// of the specified loop will execute.
+SCEVHandle ScalarEvolutionsImpl::ComputeBackedgeTakenCount(const Loop *L) {
// If the loop has a non-one exit block count, we can't analyze it.
- std::vector<BasicBlock*> ExitBlocks;
+ SmallVector<BasicBlock*, 8> ExitBlocks;
L->getExitBlocks(ExitBlocks);
if (ExitBlocks.size() != 1) return UnknownValue;
ICmpInst *ExitCond = dyn_cast<ICmpInst>(ExitBr->getCondition());
- // If its not an integer comparison then compute it the hard way.
+ // 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 ComputeIterationCountExhaustively(L, ExitBr->getCondition(),
+ return ComputeBackedgeTakenCountExhaustively(L, ExitBr->getCondition(),
ExitBr->getSuccessor(0) == ExitBlock);
// If the condition was exit on true, convert the condition to exit on false
if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
SCEVHandle ItCnt =
- ComputeLoadConstantCompareIterationCount(LI, RHS, L, Cond);
+ ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond);
if (!isa<SCEVCouldNotCompute>(ItCnt)) return ItCnt;
}
// At this point, we would like to compute how many iterations of the
// loop the predicate will return true for these inputs.
- if (isa<SCEVConstant>(LHS) && !isa<SCEVConstant>(RHS)) {
- // If there is a constant, force it into the RHS.
+ 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);
}
ConstantRange CompRange(
ICmpInst::makeConstantRange(Cond, CompVal->getValue()));
- SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange,
- false /*Always treat as unsigned range*/);
+ SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange, SE);
if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
}
}
switch (Cond) {
case ICmpInst::ICMP_NE: { // while (X != Y)
// Convert to: while (X-Y != 0)
- SCEVHandle TC = HowFarToZero(SCEV::getMinusSCEV(LHS, RHS), L);
+ SCEVHandle TC = HowFarToZero(SE.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(SCEV::getMinusSCEV(LHS, RHS), L);
+ SCEVHandle TC = HowFarToNonZero(SE.getMinusSCEV(LHS, RHS), L);
if (!isa<SCEVCouldNotCompute>(TC)) return TC;
break;
}
case ICmpInst::ICMP_SLT: {
- SCEVHandle TC = HowManyLessThans(LHS, RHS, L);
+ SCEVHandle TC = HowManyLessThans(LHS, RHS, L, true);
if (!isa<SCEVCouldNotCompute>(TC)) return TC;
break;
}
case ICmpInst::ICMP_SGT: {
- SCEVHandle TC = HowManyLessThans(RHS, LHS, L);
+ SCEVHandle TC = HowManyLessThans(SE.getNotSCEV(LHS),
+ SE.getNotSCEV(RHS), L, true);
+ if (!isa<SCEVCouldNotCompute>(TC)) return TC;
+ break;
+ }
+ case ICmpInst::ICMP_ULT: {
+ SCEVHandle TC = HowManyLessThans(LHS, RHS, L, false);
+ if (!isa<SCEVCouldNotCompute>(TC)) return TC;
+ break;
+ }
+ case ICmpInst::ICMP_UGT: {
+ SCEVHandle TC = HowManyLessThans(SE.getNotSCEV(LHS),
+ SE.getNotSCEV(RHS), L, false);
if (!isa<SCEVCouldNotCompute>(TC)) return TC;
break;
}
default:
#if 0
- cerr << "ComputeIterationCount ";
+ errs() << "ComputeBackedgeTakenCount ";
if (ExitCond->getOperand(0)->getType()->isUnsigned())
- cerr << "[unsigned] ";
- cerr << *LHS << " "
+ errs() << "[unsigned] ";
+ errs() << *LHS << " "
<< Instruction::getOpcodeName(Instruction::ICmp)
<< " " << *RHS << "\n";
#endif
break;
}
- return ComputeIterationCountExhaustively(L, ExitCond,
- ExitBr->getSuccessor(0) == ExitBlock);
+ return
+ ComputeBackedgeTakenCountExhaustively(L, ExitCond,
+ ExitBr->getSuccessor(0) == ExitBlock);
}
static ConstantInt *
-EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, Constant *C) {
- SCEVHandle InVal = SCEVConstant::get(cast<ConstantInt>(C));
- SCEVHandle Val = AddRec->evaluateAtIteration(InVal);
+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();
return Init;
}
-/// ComputeLoadConstantCompareIterationCount - Given an exit condition of
-/// 'setcc load X, cst', try to se if we can compute the trip count.
+/// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of
+/// 'icmp op load X, cst', try to see if we can compute the backedge
+/// execution count.
SCEVHandle ScalarEvolutionsImpl::
-ComputeLoadConstantCompareIterationCount(LoadInst *LI, Constant *RHS,
- const Loop *L,
- ICmpInst::Predicate predicate) {
+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.
for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
ConstantInt *ItCst =
ConstantInt::get(IdxExpr->getType(), IterationNum);
- ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst);
+ ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, SE);
// Form the GEP offset.
Indexes[VarIdxNum] = Val;
if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
#if 0
- cerr << "\n***\n*** Computed loop count " << *ItCst
- << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
- << "***\n";
+ errs() << "\n***\n*** Computed loop count " << *ItCst
+ << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
+ << "***\n";
#endif
++NumArrayLenItCounts;
- return SCEVConstant::get(ItCst); // Found terminating iteration!
+ return SE.getConstant(ItCst); // Found terminating iteration!
}
}
return UnknownValue;
if (const CallInst *CI = dyn_cast<CallInst>(I))
if (const Function *F = CI->getCalledFunction())
- return canConstantFoldCallTo((Function*)F); // FIXME: elim cast
+ return canConstantFoldCallTo(F);
return false;
}
Instruction *I = dyn_cast<Instruction>(V);
if (I == 0 || !L->contains(I->getParent())) return 0;
- if (PHINode *PN = dyn_cast<PHINode>(I))
+ 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.
/// reason, return null.
static Constant *EvaluateExpression(Value *V, Constant *PHIVal) {
if (isa<PHINode>(V)) return PHIVal;
- if (GlobalValue *GV = dyn_cast<GlobalValue>(V))
- return GV;
if (Constant *C = dyn_cast<Constant>(V)) return C;
+ if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) return GV;
Instruction *I = cast<Instruction>(V);
std::vector<Constant*> Operands;
if (Operands[i] == 0) return 0;
}
- return ConstantFoldInstOperands(I, &Operands[0], Operands.size());
+ 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
/// constant number of times, and the PHI node is just a recurrence
/// involving constants, fold it.
Constant *ScalarEvolutionsImpl::
-getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& Its, const Loop *L){
+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 (Its.ugt(APInt(Its.getBitWidth(),MaxBruteForceIterations)))
+ if (BEs.ugt(APInt(BEs.getBitWidth(),MaxBruteForceIterations)))
return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
return RetVal = 0; // Not derived from same PHI.
// Execute the loop symbolically to determine the exit value.
- if (Its.getActiveBits() >= 32)
+ if (BEs.getActiveBits() >= 32)
return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
- unsigned NumIterations = Its.getZExtValue(); // must be in range
+ unsigned NumIterations = BEs.getZExtValue(); // must be in range
unsigned IterationNum = 0;
for (Constant *PHIVal = StartCST; ; ++IterationNum) {
if (IterationNum == NumIterations)
}
}
-/// ComputeIterationCountExhaustively - If the trip is known to execute a
+/// 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 ScalarEvolutionsImpl::
-ComputeIterationCountExhaustively(const Loop *L, Value *Cond, bool ExitWhen) {
+ComputeBackedgeTakenCountExhaustively(const Loop *L, Value *Cond, bool ExitWhen) {
PHINode *PN = getConstantEvolvingPHI(Cond, L);
if (PN == 0) return UnknownValue;
if (CondVal->getValue() == uint64_t(ExitWhen)) {
ConstantEvolutionLoopExitValue[PN] = PHIVal;
++NumBruteForceTripCountsComputed;
- return SCEVConstant::get(ConstantInt::get(Type::Int32Ty, IterationNum));
+ return SE.getConstant(ConstantInt::get(Type::Int32Ty, IterationNum));
}
// Compute the value of the PHI node for the next iteration.
if (isa<SCEVConstant>(V)) return V;
- // If this instruction is evolves from a constant-evolving PHI, compute the
+ // If this instruction is evolved from a constant-evolving PHI, compute the
// exit value from the loop without using SCEVs.
if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
if (PHINode *PN = dyn_cast<PHINode>(I))
if (PN->getParent() == LI->getHeader()) {
// Okay, there is no closed form solution for the PHI node. Check
- // to see if the loop that contains it has a known iteration count.
- // If so, we may be able to force computation of the exit value.
- SCEVHandle IterationCount = getIterationCount(LI);
- if (SCEVConstant *ICC = dyn_cast<SCEVConstant>(IterationCount)) {
+ // 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 (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,
- ICC->getValue()->getValue(),
+ BTCC->getValue()->getValue(),
LI);
- if (RV) return SCEVUnknown::get(RV);
+ if (RV) return SE.getUnknown(RV);
}
}
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 (!isa<IntegerType>(Op->getType()) &&
+ !isa<PointerType>(Op->getType()))
+ return V;
+
SCEVHandle OpV = getSCEVAtScope(getSCEV(Op), L);
if (SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV))
Operands.push_back(ConstantExpr::getIntegerCast(SC->getValue(),
}
}
}
- Constant *C =ConstantFoldInstOperands(I, &Operands[0], Operands.size());
- return SCEVUnknown::get(C);
+
+ 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 SE.getUnknown(C);
}
}
NewOps.push_back(OpAtScope);
}
if (isa<SCEVAddExpr>(Comm))
- return SCEVAddExpr::get(NewOps);
- assert(isa<SCEVMulExpr>(Comm) && "Only know about add and mul!");
- return SCEVMulExpr::get(NewOps);
+ return SE.getAddExpr(NewOps);
+ if (isa<SCEVMulExpr>(Comm))
+ return SE.getMulExpr(NewOps);
+ if (isa<SCEVSMaxExpr>(Comm))
+ return SE.getSMaxExpr(NewOps);
+ if (isa<SCEVUMaxExpr>(Comm))
+ return SE.getUMaxExpr(NewOps);
+ assert(0 && "Unknown commutative SCEV type!");
}
}
// If we got here, all operands are loop invariant.
return Comm;
}
- if (SCEVSDivExpr *Div = dyn_cast<SCEVSDivExpr>(V)) {
+ if (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 SCEVSDivExpr::get(LHS, RHS);
+ return SE.getUDivExpr(LHS, RHS);
}
// If this is a loop recurrence for a loop that does not contain L, then we
if (!L || !AddRec->getLoop()->contains(L->getHeader())) {
// To evaluate this recurrence, we need to know how many times the AddRec
// loop iterates. Compute this now.
- SCEVHandle IterationCount = getIterationCount(AddRec->getLoop());
- if (IterationCount == UnknownValue) return UnknownValue;
- IterationCount = getTruncateOrZeroExtend(IterationCount,
- AddRec->getType());
-
- // If the value is affine, simplify the expression evaluation to just
- // Start + Step*IterationCount.
- if (AddRec->isAffine())
- return SCEVAddExpr::get(AddRec->getStart(),
- SCEVMulExpr::get(IterationCount,
- AddRec->getOperand(1)));
-
- // Otherwise, evaluate it the hard way.
- return AddRec->evaluateAtIteration(IterationCount);
+ SCEVHandle BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
+ if (BackedgeTakenCount == UnknownValue) return UnknownValue;
+
+ // Then, evaluate the AddRec.
+ return AddRec->evaluateAtIteration(BackedgeTakenCount, SE);
}
return UnknownValue;
}
return UnknownValue;
}
+/// 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) {
+SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
// We currently can only solve this if the coefficients are constants.
if (!LC || !MC || !NC) {
- SCEV *CNC = new SCEVCouldNotCompute();
+ SCEV *CNC = SE.getCouldNotCompute();
return std::make_pair(CNC, CNC);
}
// The divisions must be performed as signed divisions.
APInt NegB(-B);
APInt TwoA( A << 1 );
+ if (TwoA.isMinValue()) {
+ 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(SCEVUnknown::get(Solution1),
- SCEVUnknown::get(Solution2));
+ return std::make_pair(SE.getConstant(Solution1),
+ SE.getConstant(Solution2));
} // end APIntOps namespace
}
return UnknownValue;
if (AddRec->isAffine()) {
- // If this is an affine expression the execution count of this branch is
- // equal to:
+ // 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)
//
- // (0 - Start/Step) iff Start % Step == 0
+ // 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 = AddRec->getOperand(1);
- Step = getSCEVAtScope(Step, L->getParentLoop());
+ SCEVHandle Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
- // Figure out if Start % Step == 0.
- // FIXME: We should add DivExpr and RemExpr operations to our AST.
if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) {
- if (StepC->getValue()->equalsInt(1)) // N % 1 == 0
- return SCEV::getNegativeSCEV(Start); // 0 - Start/1 == -Start
- if (StepC->getValue()->isAllOnesValue()) // N % -1 == 0
- return Start; // 0 - Start/-1 == Start
-
- // Check to see if Start is divisible by SC with no remainder.
- if (SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) {
- ConstantInt *StartCC = StartC->getValue();
- Constant *StartNegC = ConstantExpr::getNeg(StartCC);
- Constant *Rem = ConstantExpr::getSRem(StartNegC, StepC->getValue());
- if (Rem->isNullValue()) {
- Constant *Result =ConstantExpr::getSDiv(StartNegC,StepC->getValue());
- return SCEVUnknown::get(Result);
- }
- }
+ // For now we handle only constant steps.
+
+ // First, handle unitary steps.
+ if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so:
+ return SE.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 (SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
+ return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
+ -StartC->getValue()->getValue(),SE);
}
} 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);
+ std::pair<SCEVHandle,SCEVHandle> Roots = SolveQuadraticEquation(AddRec, SE);
SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
if (R1) {
#if 0
- cerr << "HFTZ: " << *V << " - sol#1: " << *R1
- << " sol#2: " << *R2 << "\n";
+ errs() << "HFTZ: " << *V << " - sol#1: " << *R1
+ << " sol#2: " << *R2 << "\n";
#endif
// Pick the smallest positive root value.
if (ConstantInt *CB =
// We can only use this value if the chrec ends up with an exact zero
// value at this index. When solving for "X*X != 5", for example, we
// should not accept a root of 2.
- SCEVHandle Val = AddRec->evaluateAtIteration(R1);
- if (SCEVConstant *EvalVal = dyn_cast<SCEVConstant>(Val))
- if (EvalVal->getValue()->isZero())
- return R1; // We found a quadratic root!
+ SCEVHandle Val = AddRec->evaluateAtIteration(R1, SE);
+ if (Val->isZero())
+ return R1; // We found a quadratic root!
}
}
}
// If the value is a constant, check to see if it is known to be non-zero
// already. If so, the backedge will execute zero times.
if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
- Constant *Zero = Constant::getNullValue(C->getValue()->getType());
- Constant *NonZero =
- ConstantExpr::getICmp(ICmpInst::ICMP_NE, C->getValue(), Zero);
- if (NonZero == ConstantInt::getTrue())
- return getSCEV(Zero);
+ if (!C->getValue()->isNullValue())
+ return SE.getIntegerSCEV(0, C->getType());
return UnknownValue; // Otherwise it will loop infinitely.
}
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 *
+ScalarEvolutionsImpl::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
+ // If the block has a unique predecessor, the predecessor must have
+ // no other successors from which BB is reachable.
+ 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.
+bool ScalarEvolutionsImpl::isLoopGuardedByCond(const Loop *L,
+ ICmpInst::Predicate Pred,
+ SCEV *LHS, 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 == SE.getNotSCEV(PreCondRHSSCEV) &&
+ RHS == SE.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.
SCEVHandle ScalarEvolutionsImpl::
-HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L) {
+HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L, bool isSigned) {
// Only handle: "ADDREC < LoopInvariant".
if (!RHS->isLoopInvariant(L)) return UnknownValue;
if (AddRec->isAffine()) {
// FORNOW: We only support unit strides.
- SCEVHandle One = SCEVUnknown::getIntegerSCEV(1, RHS->getType());
+ SCEVHandle One = SE.getIntegerSCEV(1, RHS->getType());
if (AddRec->getOperand(1) != One)
return UnknownValue;
- // The number of iterations for "[n,+,1] < m", is m-n. However, we don't
- // know that m is >= n on input to the loop. If it is, the condition return
- // true zero times. What we really should return, for full generality, is
- // SMAX(0, m-n). Since we cannot check this, we will instead check for a
- // canonical loop form: most do-loops will have a check that dominates the
- // loop, that only enters the loop if [n-1]<m. If we can find this check,
- // we know that the SMAX will evaluate to m-n, because we know that m >= n.
+ // We know the LHS is of the form {n,+,1} and the RHS is some loop-invariant
+ // m. So, we count the number of iterations in which {n,+,1} < m is true.
+ // Note that we cannot simply return max(m-n,0) because it's not safe to
+ // treat m-n as signed nor unsigned due to overflow possibility.
- // Search for the check.
- BasicBlock *Preheader = L->getLoopPreheader();
- BasicBlock *PreheaderDest = L->getHeader();
- if (Preheader == 0) return UnknownValue;
+ // First, we get the value of the LHS in the first iteration: n
+ SCEVHandle Start = AddRec->getOperand(0);
- BranchInst *LoopEntryPredicate =
- dyn_cast<BranchInst>(Preheader->getTerminator());
- if (!LoopEntryPredicate) return UnknownValue;
-
- // This might be a critical edge broken out. If the loop preheader ends in
- // an unconditional branch to the loop, check to see if the preheader has a
- // single predecessor, and if so, look for its terminator.
- while (LoopEntryPredicate->isUnconditional()) {
- PreheaderDest = Preheader;
- Preheader = Preheader->getSinglePredecessor();
- if (!Preheader) return UnknownValue; // Multiple preds.
-
- LoopEntryPredicate =
- dyn_cast<BranchInst>(Preheader->getTerminator());
- if (!LoopEntryPredicate) return UnknownValue;
- }
-
- // Now that we found a conditional branch that dominates the loop, check to
- // see if it is the comparison we are looking for.
- if (ICmpInst *ICI = dyn_cast<ICmpInst>(LoopEntryPredicate->getCondition())){
- 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();
-
- switch (Cond) {
- case ICmpInst::ICMP_UGT:
- std::swap(PreCondLHS, PreCondRHS);
- Cond = ICmpInst::ICMP_ULT;
- break;
- case ICmpInst::ICMP_SGT:
- std::swap(PreCondLHS, PreCondRHS);
- Cond = ICmpInst::ICMP_SLT;
- break;
- default: break;
- }
-
- if (Cond == ICmpInst::ICMP_SLT) {
- if (PreCondLHS->getType()->isInteger()) {
- if (RHS != getSCEV(PreCondRHS))
- return UnknownValue; // Not a comparison against 'm'.
-
- if (SCEV::getMinusSCEV(AddRec->getOperand(0), One)
- != getSCEV(PreCondLHS))
- return UnknownValue; // Not a comparison against 'n-1'.
- }
- else return UnknownValue;
- } else if (Cond == ICmpInst::ICMP_ULT)
- return UnknownValue;
-
- // cerr << "Computed Loop Trip Count as: "
- // << // *SCEV::getMinusSCEV(RHS, AddRec->getOperand(0)) << "\n";
- return SCEV::getMinusSCEV(RHS, AddRec->getOperand(0));
+ if (isLoopGuardedByCond(L,
+ isSigned ? ICmpInst::ICMP_SLT : ICmpInst::ICMP_ULT,
+ SE.getMinusSCEV(AddRec->getOperand(0), One), RHS)) {
+ // Since we know that the condition is true in order to enter the loop,
+ // we know that it will run exactly m-n times.
+ return SE.getMinusSCEV(RHS, Start);
+ } else {
+ // Then, we get the value of the LHS in the first iteration in which the
+ // above condition doesn't hold. This equals to max(m,n).
+ SCEVHandle End = isSigned ? SE.getSMaxExpr(RHS, Start)
+ : SE.getUMaxExpr(RHS, Start);
+
+ // Finally, we subtract these two values to get the number of times the
+ // backedge is executed: max(m,n)-n.
+ return SE.getMinusSCEV(End, Start);
}
- else
- return UnknownValue;
}
return UnknownValue;
/// 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,
- bool isSigned) const {
+SCEVHandle SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
+ ScalarEvolution &SE) const {
if (Range.isFullSet()) // Infinite loop.
- return new SCEVCouldNotCompute();
+ return SE.getCouldNotCompute();
// If the start is a non-zero constant, shift the range to simplify things.
if (SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
if (!SC->getValue()->isZero()) {
std::vector<SCEVHandle> Operands(op_begin(), op_end());
- Operands[0] = SCEVUnknown::getIntegerSCEV(0, SC->getType());
- SCEVHandle Shifted = SCEVAddRecExpr::get(Operands, getLoop());
+ Operands[0] = SE.getIntegerSCEV(0, SC->getType());
+ SCEVHandle Shifted = SE.getAddRecExpr(Operands, getLoop());
if (SCEVAddRecExpr *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted))
return ShiftedAddRec->getNumIterationsInRange(
- Range.subtract(SC->getValue()->getValue()),isSigned);
+ Range.subtract(SC->getValue()->getValue()), SE);
// This is strange and shouldn't happen.
- return new SCEVCouldNotCompute();
+ 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 new SCEVCouldNotCompute();
+ return SE.getCouldNotCompute();
// Okay at this point we know that all elements of the chrec are constants and
// First check to see if the range contains zero. If not, the first
// iteration exits.
- if (!Range.contains(APInt(getBitWidth(),0)))
- return SCEVConstant::get(ConstantInt::get(getType(),0));
+ 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
- // Since we know that zero is in the range, we know that the upper value of
- // the range must be the first possible exit value. Also note that we
- // already checked for a full range.
- const APInt &Upper = Range.getUpper();
+ // 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 One(getBitWidth(),1);
+ APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
- // The exit value should be (Upper+A-1)/A.
- APInt ExitVal(Upper);
- if (A != One)
- ExitVal = (Upper + A - One).sdiv(A);
+ // 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);
+ ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
if (Range.contains(Val->getValue()))
- return new SCEVCouldNotCompute(); // Something strange happened
+ 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))->getValue()) &&
+ ConstantInt::get(ExitVal - One), SE)->getValue()) &&
"Linear scev computation is off in a bad way!");
- return SCEVConstant::get(cast<ConstantInt>(ExitValue));
+ 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] = SCEV::getNegativeSCEV(SCEVUnknown::get(
- ConstantInt::get(Range.getUpper())));
- SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewOps, getLoop());
+ 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));
+ SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
if (R1) {
// 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());
+ R1->getValue(),
+ SE);
if (Range.contains(R1Val->getValue())) {
// The next iteration must be out of the range...
- Constant *NextVal = ConstantInt::get(R1->getValue()->getValue()+1);
+ ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()+1);
- R1Val = EvaluateConstantChrecAtConstant(this, NextVal);
+ R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
if (!Range.contains(R1Val->getValue()))
- return SCEVUnknown::get(NextVal);
- return new SCEVCouldNotCompute(); // Something strange happened
+ 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.
- Constant *NextVal = ConstantInt::get(R1->getValue()->getValue()-1);
- R1Val = EvaluateConstantChrecAtConstant(this, NextVal);
+ ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()-1);
+ R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
if (Range.contains(R1Val->getValue()))
return R1;
- return new SCEVCouldNotCompute(); // Something strange happened
+ return SE.getCouldNotCompute(); // Something strange happened
}
}
}
- // Fallback, if this is a general polynomial, figure out the progression
- // through brute force: evaluate until we find an iteration that fails the
- // test. This is likely to be slow, but getting an accurate trip count is
- // incredibly important, we will be able to simplify the exit test a lot, and
- // we are almost guaranteed to get a trip count in this case.
- ConstantInt *TestVal = ConstantInt::get(getType(), 0);
- ConstantInt *EndVal = TestVal; // Stop when we wrap around.
- do {
- ++NumBruteForceEvaluations;
- SCEVHandle Val = evaluateAtIteration(SCEVConstant::get(TestVal));
- if (!isa<SCEVConstant>(Val)) // This shouldn't happen.
- return new SCEVCouldNotCompute();
-
- // Check to see if we found the value!
- if (!Range.contains(cast<SCEVConstant>(Val)->getValue()->getValue()))
- return SCEVConstant::get(TestVal);
-
- // Increment to test the next index.
- TestVal = ConstantInt::get(TestVal->getValue()+1);
- } while (TestVal != EndVal);
-
- return new SCEVCouldNotCompute();
+ return SE.getCouldNotCompute();
}
//===----------------------------------------------------------------------===//
bool ScalarEvolution::runOnFunction(Function &F) {
- Impl = new ScalarEvolutionsImpl(F, getAnalysis<LoopInfo>());
+ Impl = new ScalarEvolutionsImpl(*this, F,
+ getAnalysis<LoopInfo>(),
+ getAnalysisIfAvailable<TargetData>());
return false;
}
AU.addRequiredTransitive<LoopInfo>();
}
+bool ScalarEvolution::isSCEVable(const Type *Ty) const {
+ return ((ScalarEvolutionsImpl*)Impl)->isSCEVable(Ty);
+}
+
+uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const {
+ return ((ScalarEvolutionsImpl*)Impl)->getTypeSizeInBits(Ty);
+}
+
+const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const {
+ return ((ScalarEvolutionsImpl*)Impl)->getEffectiveSCEVType(Ty);
+}
+
+SCEVHandle ScalarEvolution::getCouldNotCompute() {
+ return ((ScalarEvolutionsImpl*)Impl)->getCouldNotCompute();
+}
+
+SCEVHandle ScalarEvolution::getIntegerSCEV(int Val, const Type *Ty) {
+ return ((ScalarEvolutionsImpl*)Impl)->getIntegerSCEV(Val, Ty);
+}
+
SCEVHandle ScalarEvolution::getSCEV(Value *V) const {
return ((ScalarEvolutionsImpl*)Impl)->getSCEV(V);
}
((ScalarEvolutionsImpl*)Impl)->setSCEV(V, H);
}
+/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
+///
+SCEVHandle ScalarEvolution::getNegativeSCEV(const SCEVHandle &V) {
+ return ((ScalarEvolutionsImpl*)Impl)->getNegativeSCEV(V);
+}
+
+/// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
+///
+SCEVHandle ScalarEvolution::getNotSCEV(const SCEVHandle &V) {
+ return ((ScalarEvolutionsImpl*)Impl)->getNotSCEV(V);
+}
+
+/// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
+///
+SCEVHandle ScalarEvolution::getMinusSCEV(const SCEVHandle &LHS,
+ const SCEVHandle &RHS) {
+ return ((ScalarEvolutionsImpl*)Impl)->getMinusSCEV(LHS, 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) {
+ return ((ScalarEvolutionsImpl*)Impl)->getTruncateOrZeroExtend(V, Ty);
+}
-SCEVHandle ScalarEvolution::getIterationCount(const Loop *L) const {
- return ((ScalarEvolutionsImpl*)Impl)->getIterationCount(L);
+/// 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) {
+ return ((ScalarEvolutionsImpl*)Impl)->getTruncateOrSignExtend(V, Ty);
}
-bool ScalarEvolution::hasLoopInvariantIterationCount(const Loop *L) const {
- return !isa<SCEVCouldNotCompute>(getIterationCount(L));
+
+bool ScalarEvolution::isLoopGuardedByCond(const Loop *L,
+ ICmpInst::Predicate Pred,
+ SCEV *LHS, SCEV *RHS) {
+ return ((ScalarEvolutionsImpl*)Impl)->isLoopGuardedByCond(L, Pred,
+ LHS, RHS);
+}
+
+SCEVHandle ScalarEvolution::getBackedgeTakenCount(const Loop *L) const {
+ return ((ScalarEvolutionsImpl*)Impl)->getBackedgeTakenCount(L);
+}
+
+bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) const {
+ return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
+}
+
+void ScalarEvolution::forgetLoopBackedgeTakenCount(const Loop *L) {
+ return ((ScalarEvolutionsImpl*)Impl)->forgetLoopBackedgeTakenCount(L);
}
SCEVHandle ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) const {
return ((ScalarEvolutionsImpl*)Impl)->getSCEVAtScope(getSCEV(V), L);
}
-void ScalarEvolution::deleteInstructionFromRecords(Instruction *I) const {
- return ((ScalarEvolutionsImpl*)Impl)->deleteInstructionFromRecords(I);
+void ScalarEvolution::deleteValueFromRecords(Value *V) const {
+ return ((ScalarEvolutionsImpl*)Impl)->deleteValueFromRecords(V);
}
-static void PrintLoopInfo(std::ostream &OS, const ScalarEvolution *SE,
+static void PrintLoopInfo(raw_ostream &OS, const ScalarEvolution *SE,
const Loop *L) {
// Print all inner loops first
for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
PrintLoopInfo(OS, SE, *I);
- cerr << "Loop " << L->getHeader()->getName() << ": ";
+ OS << "Loop " << L->getHeader()->getName() << ": ";
- std::vector<BasicBlock*> ExitBlocks;
+ SmallVector<BasicBlock*, 8> ExitBlocks;
L->getExitBlocks(ExitBlocks);
if (ExitBlocks.size() != 1)
- cerr << "<multiple exits> ";
+ OS << "<multiple exits> ";
- if (SE->hasLoopInvariantIterationCount(L)) {
- cerr << *SE->getIterationCount(L) << " iterations! ";
+ if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
+ OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
} else {
- cerr << "Unpredictable iteration count. ";
+ OS << "Unpredictable backedge-taken count. ";
}
- cerr << "\n";
+ OS << "\n";
}
-void ScalarEvolution::print(std::ostream &OS, const Module* ) const {
+void ScalarEvolution::print(raw_ostream &OS, const Module* ) const {
Function &F = ((ScalarEvolutionsImpl*)Impl)->F;
LoopInfo &LI = ((ScalarEvolutionsImpl*)Impl)->LI;
for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
if (I->getType()->isInteger()) {
OS << *I;
- OS << " --> ";
+ OS << " --> ";
SCEVHandle SV = getSCEV(&*I);
SV->print(OS);
OS << "\t\t";
- if ((*I).getType()->isInteger()) {
- ConstantRange Bounds = SV->getValueRange();
- if (!Bounds.isFullSet())
- OS << "Bounds: " << Bounds << " ";
- }
-
if (const Loop *L = LI.getLoopFor((*I).getParent())) {
OS << "Exits: ";
SCEVHandle ExitValue = getSCEVAtScope(&*I, L->getParentLoop());
PrintLoopInfo(OS, this, *I);
}
+void ScalarEvolution::print(std::ostream &o, const Module *M) const {
+ raw_os_ostream OS(o);
+ print(OS, M);
+}
projects / oota-llvm.git / blobdiff