//
// 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 <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 class definitions
print(cerr);
}
-/// 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(getType());
+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;
}
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);
+SCEVHandle ScalarEvolution::getConstant(const APInt& Val) {
+ return getConstant(ConstantInt::get(Val));
}
const Type *SCEVConstant::getType() const { return V->getType(); }
SCEVTruncates->erase(std::make_pair(Op, Ty));
}
-ConstantRange SCEVTruncateExpr::getValueRange() const {
- return getOperand()->getValueRange().truncate(getType());
-}
-
void SCEVTruncateExpr::print(std::ostream &OS) const {
OS << "(truncate " << *Op << " to " << *Ty << ")";
}
SCEVZeroExtends->erase(std::make_pair(Op, Ty));
}
-ConstantRange SCEVZeroExtendExpr::getValueRange() const {
- return getOperand()->getValueRange().zeroExtend(getType());
-}
-
void SCEVZeroExtendExpr::print(std::ostream &OS) const {
OS << "(zeroextend " << *Op << " to " << *Ty << ")";
}
+// SCEVSignExtends - Only allow the creation of one SCEVSignExtendExpr for any
+// particular input. Don't use a SCEVHandle here, or else the object will never
+// be deleted!
+static ManagedStatic<std::map<std::pair<SCEV*, const Type*>,
+ SCEVSignExtendExpr*> > SCEVSignExtends;
+
+SCEVSignExtendExpr::SCEVSignExtendExpr(const SCEVHandle &op, const Type *ty)
+ : SCEV(scSignExtend), Op(op), Ty(ty) {
+ assert(Op->getType()->isInteger() && Ty->isInteger() &&
+ "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));
+}
+
+void SCEVSignExtendExpr::print(std::ostream &OS) const {
+ OS << "(signextend " << *Op << " to " << *Ty << ")";
+}
+
// SCEVCommExprs - Only allow the creation of one SCEVCommutativeExpr for any
// particular input. Don't use a SCEVHandle here, or else the object will never
// be deleted!
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!");
}
}
-// 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;
-SCEVSDivExpr::~SCEVSDivExpr() {
- SCEVSDivs->erase(std::make_pair(LHS, RHS));
+SCEVUDivExpr::~SCEVUDivExpr() {
+ SCEVUDivs->erase(std::make_pair(LHS, RHS));
}
-void SCEVSDivExpr::print(std::ostream &OS) const {
- OS << "(" << *LHS << " /s " << *RHS << ")";
+void SCEVUDivExpr::print(std::ostream &OS) const {
+ OS << "(" << *LHS << " /u " << *RHS << ")";
}
-const Type *SCEVSDivExpr::getType() const {
+const Type *SCEVUDivExpr::getType() const {
return LHS->getType();
}
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;
/// 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;
}
/// 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) {
+SCEVHandle ScalarEvolution::getIntegerSCEV(int Val, const Type *Ty) {
Constant *C;
if (Val == 0)
C = Constant::getNullValue(Ty);
else if (Ty->isFloatingPoint())
- C = ConstantFP::get(Ty, Val);
+ C = ConstantFP::get(APFloat(Ty==Type::FloatTy ? APFloat::IEEEsingle :
+ APFloat::IEEEdouble, Val));
else
C = ConstantInt::get(Ty, Val);
- return SCEVUnknown::get(C);
-}
-
-/// 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);
+ return getUnknown(C);
}
/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
///
-SCEVHandle SCEV::getNegativeSCEV(const SCEVHandle &V) {
+SCEVHandle ScalarEvolution::getNegativeSCEV(const SCEVHandle &V) {
+ if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
+ return getUnknown(ConstantExpr::getNeg(VC->getValue()));
+
+ return getMulExpr(V, getConstant(ConstantInt::getAllOnesValue(V->getType())));
+}
+
+/// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
+SCEVHandle ScalarEvolution::getNotSCEV(const SCEVHandle &V) {
if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
- return SCEVUnknown::get(ConstantExpr::getNeg(VC->getValue()));
+ return getUnknown(ConstantExpr::getNot(VC->getValue()));
- return SCEVMulExpr::get(V, SCEVUnknown::getIntegerSCEV(-1, V->getType()));
+ SCEVHandle AllOnes = getConstant(ConstantInt::getAllOnesValue(V->getType()));
+ return getMinusSCEV(AllOnes, V);
}
/// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
///
-SCEVHandle SCEV::getMinusSCEV(const SCEVHandle &LHS, const SCEVHandle &RHS) {
+SCEVHandle ScalarEvolution::getMinusSCEV(const SCEVHandle &LHS,
+ const SCEVHandle &RHS) {
// X - Y --> X + -Y
- return SCEVAddExpr::get(LHS, SCEV::getNegativeSCEV(RHS));
+ return getAddExpr(LHS, getNegativeSCEV(RHS));
}
-/// 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)) {
- uint64_t Val = SC->getValue()->getZExtValue();
- uint64_t Result = 1;
- for (; NumSteps; --NumSteps)
- Result *= Val-(NumSteps-1);
- Constant *Res = ConstantInt::get(Type::Int64Ty, Result);
- return SCEVUnknown::get(ConstantExpr::getTruncOrBitCast(Res, V->getType()));
+/// BinomialCoefficient - Compute BC(It, K). The result has width W.
+// Assume, K > 0.
+static SCEVHandle BinomialCoefficient(SCEVHandle It, unsigned K,
+ ScalarEvolution &SE,
+ const IntegerType* 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 new SCEVCouldNotCompute();
+
+ unsigned W = ResultTy->getBitWidth();
+
+ // Calculate K! / 2^T and T; we divide out the factors of two before
+ // multiplying for calculating K! / 2^T to avoid overflow.
+ // Other overflow doesn't matter because we only care about the bottom
+ // W bits of the result.
+ APInt OddFactorial(W, 1);
+ unsigned T = 1;
+ for (unsigned i = 3; i <= K; ++i) {
+ APInt Mult(W, i);
+ unsigned TwoFactors = Mult.countTrailingZeros();
+ T += TwoFactors;
+ Mult = Mult.lshr(TwoFactors);
+ OddFactorial *= Mult;
+ }
+
+ // We need at least W + T bits for the multiplication step
+ // FIXME: A temporary hack; we round up the bitwidths
+ // to the nearest power of 2 to be nice to the code generator.
+ unsigned CalculationBits = 1U << Log2_32_Ceil(W + T);
+ // FIXME: Temporary hack to avoid generating integers that are too wide.
+ // Although, it's not completely clear how to determine how much
+ // widening is safe; for example, on X86, we can't really widen
+ // beyond 64 because we need to be able to do multiplication
+ // that's CalculationBits wide, but on X86-64, we can safely widen up to
+ // 128 bits.
+ if (CalculationBits > 64)
+ return new SCEVCouldNotCompute();
+
+ // 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,
+ cast<IntegerType>(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) {
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) {
+SCEVHandle ScalarEvolution::getZeroExtendExpr(const SCEVHandle &Op, const Type *Ty) {
if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
- return SCEVUnknown::get(
+ return getUnknown(
ConstantExpr::getZExt(SC->getValue(), Ty));
// FIXME: If the input value is a chrec scev, and we can prove that the value
return Result;
}
+SCEVHandle ScalarEvolution::getSignExtendExpr(const SCEVHandle &Op, const Type *Ty) {
+ if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
+ return getUnknown(
+ ConstantExpr::getSExt(SC->getValue(), Ty));
+
+ // FIXME: If the input value is a chrec scev, and we can prove that the value
+ // did not overflow the old, smaller, value, we can sign extend all of the
+ // operands (often constants). This would allow analysis of something like
+ // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
+
+ SCEVSignExtendExpr *&Result = (*SCEVSignExtends)[std::make_pair(Op, Ty)];
+ if (Result == 0) Result = new SCEVSignExtendExpr(Op, Ty);
+ return Result;
+}
+
+/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion
+/// of the input value to the specified type. If the type must be
+/// extended, it is zero extended.
+SCEVHandle ScalarEvolution::getTruncateOrZeroExtend(const SCEVHandle &V,
+ const Type *Ty) {
+ const Type *SrcTy = V->getType();
+ assert(SrcTy->isInteger() && 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 getTruncateExpr(V, Ty);
+ return getZeroExtendExpr(V, Ty);
+}
+
// 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 = ConstantExpr::getAdd(LHSC->getValue(), RHSC->getValue());
- if (ConstantInt *CI = dyn_cast<ConstantInt>(Fold)) {
- Ops[0] = SCEVConstant::get(CI);
- Ops.erase(Ops.begin()+1); // Erase the folded element
- if (Ops.size() == 1) return Ops[0];
- 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 (cast<SCEVConstant>(Ops[0])->getValue()->isNullValue()) {
+ if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
Ops.erase(Ops.begin());
--Idx;
}
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 = ConstantExpr::getMul(LHSC->getValue(), RHSC->getValue());
- if (ConstantInt *CI = dyn_cast<ConstantInt>(Fold)) {
- Ops[0] = SCEVConstant::get(CI);
- Ops.erase(Ops.begin()+1); // Erase the folded element
- if (Ops.size() == 1) return Ops[0];
- 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.
if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
Ops.erase(Ops.begin());
--Idx;
- } else if (cast<SCEVConstant>(Ops[0])->getValue()->isNullValue()) {
+ } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
// If we have a multiply of zero, it will always be zero.
return Ops[0];
}
// 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()->isNullValue()) {
- 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);
SCEVUnknown *&Result = (*SCEVUnknowns)[V];
if (Result == 0) Result = new SCEVUnknown(V);
return Result;
///
namespace {
struct VISIBILITY_HIDDEN ScalarEvolutionsImpl {
+ /// SE - A reference to the public ScalarEvolution object.
+ ScalarEvolution &SE;
+
/// F - The function we are analyzing.
///
Function &F;
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)
+ : SE(se), F(f), LI(li), UnknownValue(new SCEVCouldNotCompute()) {}
/// 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;
}
/// loop without a loop-invariant iteration count.
SCEVHandle getIterationCount(const Loop *L);
- /// deleteInstructionFromRecords - This method should be called by the
- /// client before it removes an instruction from the program, to make sure
+ /// 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.
SCEVHandle ComputeIterationCount(const Loop *L);
/// ComputeLoadConstantCompareIterationCount - Given an exit condition of
- /// 'setcc load X, cst', try to se if we can compute the trip count.
+ /// 'icmp op load X, cst', try to see if we can compute the trip count.
SCEVHandle ComputeLoadConstantCompareIterationCount(LoadInst *LI,
Constant *RHS,
const Loop *L,
/// 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, bool trueWhenEqual);
+
+ /// 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);
+
+ /// executesAtLeastOnce - Test whether entry to the loop is protected by
+ /// a conditional between LHS and RHS.
+ bool executesAtLeastOnce(const Loop *L, bool isSigned, bool trueWhenEqual,
+ SCEV *LHS, SCEV *RHS);
+
+ /// potentialInfiniteLoop - Test whether the loop might jump over the exit value
+ /// due to wrapping.
+ bool potentialInfiniteLoop(SCEV *Stride, SCEV *RHS, bool isSigned,
+ bool trueWhenEqual);
/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
/// in the header of its containing loop, we know the loop executes a
/// constant number of times, and the PHI node is just a recurrence
/// involving constants, fold it.
- Constant *getConstantEvolutionLoopExitValue(PHINode *PN, uint64_t Its,
+ Constant *getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& Its,
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) {
- Scalars.erase(I);
- if (PHINode *PN = dyn_cast<PHINode>(I))
- ConstantEvolutionLoopExitValue.erase(PN);
+void ScalarEvolutionsImpl::deleteValueFromRecords(Value *V) {
+ SmallVector<Value *, 16> Worklist;
+
+ if (Scalars.erase(V)) {
+ if (PHINode *PN = dyn_cast<PHINode>(V))
+ ConstantEvolutionLoopExitValue.erase(PN);
+ Worklist.push_back(V);
+ }
+
+ while (!Worklist.empty()) {
+ Value *VV = Worklist.back();
+ Worklist.pop_back();
+
+ 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>(VV))
+ ConstantEvolutionLoopExitValue.erase(PN);
+ Worklist.push_back(Inst);
+ }
+ }
+ }
}
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);
+ return SE.getUnknown(PN);
}
-/// GetConstantFactor - Determine the largest constant factor that S has. For
-/// example, turn {4,+,8} -> 4. (S umod result) should always equal zero.
-static uint64_t GetConstantFactor(SCEVHandle S) {
- if (SCEVConstant *C = dyn_cast<SCEVConstant>(S)) {
- if (uint64_t V = C->getValue()->getZExtValue())
- return V;
- else // Zero is a multiple of everything.
- return 1ULL << (S->getType()->getPrimitiveSizeInBits()-1);
- }
+/// 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) {
+ if (SCEVConstant *C = dyn_cast<SCEVConstant>(S))
+ return C->getValue()->getValue().countTrailingZeros();
if (SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
- return GetConstantFactor(T->getOperand()) &
- cast<IntegerType>(T->getType())->getBitMask();
- if (SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S))
- return GetConstantFactor(E->getOperand());
-
+ return std::min(GetMinTrailingZeros(T->getOperand()), T->getBitWidth());
+
+ if (SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
+ uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
+ return OpRes == E->getOperand()->getBitWidth() ? E->getBitWidth() : OpRes;
+ }
+
+ if (SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
+ uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
+ return OpRes == E->getOperand()->getBitWidth() ? E->getBitWidth() : OpRes;
+ }
+
if (SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
- // The result is the min of all operands.
- uint64_t Res = GetConstantFactor(A->getOperand(0));
- for (unsigned i = 1, e = A->getNumOperands(); i != e && Res > 1; ++i)
- Res = std::min(Res, GetConstantFactor(A->getOperand(i)));
- return Res;
+ // The result is the min of all operands results.
+ uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
+ for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
+ MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
+ return MinOpRes;
}
if (SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
- // The result is the product of all the operands.
- uint64_t Res = GetConstantFactor(M->getOperand(0));
- for (unsigned i = 1, e = M->getNumOperands(); i != e; ++i)
- Res *= GetConstantFactor(M->getOperand(i));
- return Res;
+ // The result is the sum of all operands results.
+ uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
+ uint32_t BitWidth = M->getBitWidth();
+ for (unsigned i = 1, e = M->getNumOperands();
+ SumOpRes != BitWidth && i != e; ++i)
+ SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
+ 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.
- uint64_t Start = GetConstantFactor(A->getOperand(0));
- if (Start == 1) return 1;
- uint64_t Stride = GetConstantFactor(A->getOperand(1));
- return GreatestCommonDivisor64(Start, Stride);
- }
+ // The result is the min of all operands results.
+ uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
+ for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
+ MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
+ return MinOpRes;
}
-
- // SCEVSDivExpr, SCEVUnknown.
- return 1;
+
+ if (SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
+ // The result is the min of all operands results.
+ uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
+ for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
+ MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
+ return MinOpRes;
+ }
+
+ if (SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
+ // The result is the min of all operands results.
+ uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
+ for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
+ MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
+ return MinOpRes;
+ }
+
+ // 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;
+ if (!isa<IntegerType>(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) >=
+ (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 (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::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));
- uint64_t CommonFact = GetConstantFactor(LHS);
- assert(CommonFact && "Common factor should at least be 1!");
- if (CommonFact > CI->getZExtValue()) {
- // If the LHS is a multiple that is larger than the RHS, use +.
- return SCEVAddExpr::get(LHS,
- 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))) {
- Constant *X = ConstantInt::get(V->getType(), 1);
- X = ConstantExpr::getShl(X, SA);
- return SCEVMulExpr::get(getSCEV(I->getOperand(0)), getSCEV(X));
- }
- 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::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::SExt:
+ return SE.getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
- case Instruction::PHI:
- return createNodeForPHI(cast<PHINode>(I));
+ case Instruction::BitCast:
+ // BitCasts are no-op casts so we just eliminate the cast.
+ if (U->getType()->isInteger() &&
+ U->getOperand(0)->getType()->isInteger())
+ return getSCEV(U->getOperand(0));
+ break;
- 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);
}
/// will iterate.
SCEVHandle ScalarEvolutionsImpl::ComputeIterationCount(const Loop *L) {
// If the loop has a non-one exit block count, we can't analyze it.
- std::vector<BasicBlock*> ExitBlocks;
+ 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()))
// 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);
}
ConstantExpr::getBitCast(CompVal, RealTy));
if (CompVal) {
// Form the constant range.
- ConstantRange CompRange(Cond, CompVal);
+ 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, false);
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, false);
+ if (!isa<SCEVCouldNotCompute>(TC)) return TC;
+ break;
+ }
+ case ICmpInst::ICMP_ULT: {
+ SCEVHandle TC = HowManyLessThans(LHS, RHS, L, false, false);
+ if (!isa<SCEVCouldNotCompute>(TC)) return TC;
+ break;
+ }
+ case ICmpInst::ICMP_UGT: {
+ SCEVHandle TC = HowManyLessThans(SE.getNotSCEV(LHS),
+ SE.getNotSCEV(RHS), L, false, false);
+ if (!isa<SCEVCouldNotCompute>(TC)) return TC;
+ break;
+ }
+ case ICmpInst::ICMP_SLE: {
+ SCEVHandle TC = HowManyLessThans(LHS, RHS, L, true, true);
+ if (!isa<SCEVCouldNotCompute>(TC)) return TC;
+ break;
+ }
+ case ICmpInst::ICMP_SGE: {
+ SCEVHandle TC = HowManyLessThans(SE.getNotSCEV(LHS),
+ SE.getNotSCEV(RHS), L, true, true);
+ if (!isa<SCEVCouldNotCompute>(TC)) return TC;
+ break;
+ }
+ case ICmpInst::ICMP_ULE: {
+ SCEVHandle TC = HowManyLessThans(LHS, RHS, L, false, true);
+ if (!isa<SCEVCouldNotCompute>(TC)) return TC;
+ break;
+ }
+ case ICmpInst::ICMP_UGE: {
+ SCEVHandle TC = HowManyLessThans(SE.getNotSCEV(LHS),
+ SE.getNotSCEV(RHS), L, false, true);
if (!isa<SCEVCouldNotCompute>(TC)) return TC;
break;
}
}
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();
}
/// ComputeLoadConstantCompareIterationCount - Given an exit condition of
-/// 'setcc load X, cst', try to se if we can compute the trip count.
+/// 'icmp op load X, cst', try to see if we can compute the trip count.
SCEVHandle ScalarEvolutionsImpl::
ComputeLoadConstantCompareIterationCount(LoadInst *LI, Constant *RHS,
const Loop *L,
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;
// Evaluate the condition for this iteration.
Result = ConstantExpr::getICmp(predicate, Result, RHS);
if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
- if (cast<ConstantInt>(Result)->getZExtValue() == false) {
+ if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
#if 0
cerr << "\n***\n*** Computed loop count " << *ItCst
<< "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
<< "***\n";
#endif
++NumArrayLenItCounts;
- return SCEVConstant::get(ItCst); // Found terminating iteration!
+ return SE.getConstant(ItCst); // Found terminating iteration!
}
}
return UnknownValue;
/// CanConstantFold - Return true if we can constant fold an instruction of the
/// specified type, assuming that all operands were constants.
static bool CanConstantFold(const Instruction *I) {
- if (isa<BinaryOperator>(I) || isa<ShiftInst>(I) || isa<CmpInst>(I) ||
+ if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I))
return true;
if (const CallInst *CI = dyn_cast<CallInst>(I))
if (const Function *F = CI->getCalledFunction())
- return canConstantFoldCallTo((Function*)F); // FIXME: elim cast
+ return canConstantFoldCallTo(F);
return false;
}
-/// ConstantFold - Constant fold an instruction of the specified type with the
-/// specified constant operands. This function may modify the operands vector.
-static Constant *ConstantFold(const Instruction *I,
- std::vector<Constant*> &Operands) {
- if (isa<BinaryOperator>(I) || isa<ShiftInst>(I))
- return ConstantExpr::get(I->getOpcode(), Operands[0], Operands[1]);
-
- if (isa<CastInst>(I))
- return ConstantExpr::getCast(I->getOpcode(), Operands[0], I->getType());
-
- switch (I->getOpcode()) {
- case Instruction::Select:
- return ConstantExpr::getSelect(Operands[0], Operands[1], Operands[2]);
- case Instruction::Call:
- if (Function *GV = dyn_cast<Function>(Operands[0])) {
- return ConstantFoldCall(cast<Function>(GV), &Operands[1],
- Operands.size()-1);
- }
- return 0;
- case Instruction::GetElementPtr: {
- Constant *Base = Operands[0];
- Operands.erase(Operands.begin());
- return ConstantExpr::getGetElementPtr(Base, Operands);
- }
- case Instruction::ICmp:
- return ConstantExpr::getICmp(
- cast<ICmpInst>(I)->getPredicate(), Operands[0], Operands[1]);
- case Instruction::FCmp:
- return ConstantExpr::getFCmp(
- cast<FCmpInst>(I)->getPredicate(), Operands[0], Operands[1]);
- }
- return 0;
-}
-
-
/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
/// in the loop that V is derived from. We allow arbitrary operations along the
/// way, but the operands of an operation must either be constants or a value
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;
Instruction *I = cast<Instruction>(V);
if (Operands[i] == 0) return 0;
}
- return ConstantFold(I, Operands);
+ 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, uint64_t Its, const Loop *L) {
+getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& Its, const Loop *L){
std::map<PHINode*, Constant*>::iterator I =
ConstantEvolutionLoopExitValue.find(PN);
if (I != ConstantEvolutionLoopExitValue.end())
return I->second;
- if (Its > MaxBruteForceIterations)
+ if (Its.ugt(APInt(Its.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.
- unsigned IterationNum = 0;
- unsigned NumIterations = Its;
- if (NumIterations != Its)
- return RetVal = 0; // More than 2^32 iterations??
+ if (Its.getActiveBits() >= 32)
+ return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
+ unsigned NumIterations = Its.getZExtValue(); // must be in range
+ unsigned IterationNum = 0;
for (Constant *PHIVal = StartCST; ; ++IterationNum) {
if (IterationNum == NumIterations)
return RetVal = PHIVal; // Got exit value!
// Couldn't symbolically evaluate.
if (!CondVal) return UnknownValue;
- if (CondVal->getZExtValue() == uint64_t(ExitWhen)) {
+ 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())) {
// this is a constant evolving PHI node, get the final value at
// the specified iteration number.
Constant *RV = getConstantEvolutionLoopExitValue(PN,
- ICC->getValue()->getZExtValue(),
+ ICC->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, don't even try to analyze them with scev techniques.
+ if (!isa<IntegerType>(Op->getType()))
+ return V;
+
SCEVHandle OpV = getSCEVAtScope(getSCEV(Op), L);
if (SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV))
Operands.push_back(ConstantExpr::getIntegerCast(SC->getValue(),
}
}
}
- return SCEVUnknown::get(ConstantFold(I, Operands));
+
+ 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
// 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);
+
+ // Then, evaluate the AddRec.
+ return AddRec->evaluateAtIteration(IterationCount, 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 new SCEVCouldNotCompute();
+
+ // 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 *L = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
- SCEVConstant *M = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
- SCEVConstant *N = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
+ SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
+ SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
+ SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
// We currently can only solve this if the coefficients are constants.
- if (!L || !M || !N) {
+ if (!LC || !MC || !NC) {
SCEV *CNC = new SCEVCouldNotCompute();
return std::make_pair(CNC, CNC);
}
- Constant *C = L->getValue();
- Constant *Two = ConstantInt::get(C->getType(), 2);
-
- // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
- // The B coefficient is M-N/2
- Constant *B = ConstantExpr::getSub(M->getValue(),
- ConstantExpr::getSDiv(N->getValue(),
- Two));
- // The A coefficient is N/2
- Constant *A = ConstantExpr::getSDiv(N->getValue(), Two);
-
- // Compute the B^2-4ac term.
- Constant *SqrtTerm =
- ConstantExpr::getMul(ConstantInt::get(C->getType(), 4),
- ConstantExpr::getMul(A, C));
- SqrtTerm = ConstantExpr::getSub(ConstantExpr::getMul(B, B), SqrtTerm);
-
- // Compute floor(sqrt(B^2-4ac))
- uint64_t SqrtValV = cast<ConstantInt>(SqrtTerm)->getZExtValue();
- uint64_t SqrtValV2 = (uint64_t)sqrt((double)SqrtValV);
- // The square root might not be precise for arbitrary 64-bit integer
- // values. Do some sanity checks to ensure it's correct.
- if (SqrtValV2*SqrtValV2 > SqrtValV ||
- (SqrtValV2+1)*(SqrtValV2+1) <= SqrtValV) {
- SCEV *CNC = new SCEVCouldNotCompute();
- return std::make_pair(CNC, CNC);
- }
-
- ConstantInt *SqrtVal = ConstantInt::get(Type::Int64Ty, SqrtValV2);
- SqrtTerm = ConstantExpr::getTruncOrBitCast(SqrtVal, SqrtTerm->getType());
+ uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
+ const APInt &L = LC->getValue()->getValue();
+ const APInt &M = MC->getValue()->getValue();
+ const APInt &N = NC->getValue()->getValue();
+ APInt Two(BitWidth, 2);
+ APInt Four(BitWidth, 4);
+
+ {
+ using namespace APIntOps;
+ const APInt& C = L;
+ // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
+ // The B coefficient is M-N/2
+ APInt B(M);
+ B -= sdiv(N,Two);
+
+ // The A coefficient is N/2
+ APInt A(N.sdiv(Two));
+
+ // Compute the B^2-4ac term.
+ APInt SqrtTerm(B);
+ SqrtTerm *= B;
+ SqrtTerm -= Four * (A * C);
+
+ // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
+ // integer value or else APInt::sqrt() will assert.
+ APInt SqrtVal(SqrtTerm.sqrt());
+
+ // Compute the two solutions for the quadratic formula.
+ // The divisions must be performed as signed divisions.
+ APInt NegB(-B);
+ APInt TwoA( A << 1 );
+ if (TwoA.isMinValue()) {
+ SCEV *CNC = new SCEVCouldNotCompute();
+ return std::make_pair(CNC, CNC);
+ }
- Constant *NegB = ConstantExpr::getNeg(B);
- Constant *TwoA = ConstantExpr::getMul(A, Two);
+ ConstantInt *Solution1 = ConstantInt::get((NegB + SqrtVal).sdiv(TwoA));
+ ConstantInt *Solution2 = ConstantInt::get((NegB - SqrtVal).sdiv(TwoA));
- // The divisions must be performed as signed divisions.
- Constant *Solution1 =
- ConstantExpr::getSDiv(ConstantExpr::getAdd(NegB, SqrtTerm), TwoA);
- Constant *Solution2 =
- ConstantExpr::getSDiv(ConstantExpr::getSub(NegB, SqrtTerm), TwoA);
- return std::make_pair(SCEVUnknown::get(Solution1),
- SCEVUnknown::get(Solution2));
+ return std::make_pair(SE.getConstant(Solution1),
+ SE.getConstant(Solution2));
+ } // end APIntOps namespace
}
/// HowFarToZero - Return the number of times a backedge comparing the specified
// If the value is a constant
if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
// If the value is already zero, the branch will execute zero times.
- if (C->getValue()->isNullValue()) return C;
+ if (C->getValue()->isZero()) return C;
return UnknownValue; // Otherwise it will loop infinitely.
}
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:
//
- // (0 - Start/Step) iff Start % Step == 0
+ // Start + Step*N = 0 (mod 2^BW)
//
+ // equivalent to:
+ //
+ // Step*N = -Start (mod 2^BW)
+ //
+ // where BW is the common bit width of Start and Step.
+
// Get the initial value for the loop.
SCEVHandle Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
if (isa<SCEVCouldNotCompute>(Start)) return UnknownValue;
- SCEVHandle Step = 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) {
// We can only use this value if the chrec ends up with an exact zero
// value at this index. When solving for "X*X != 5", for example, we
// should not accept a root of 2.
- SCEVHandle Val = AddRec->evaluateAtIteration(R1);
- if (SCEVConstant *EvalVal = dyn_cast<SCEVConstant>(Val))
- if (EvalVal->getValue()->isNullValue())
- return R1; // We found a quadratic root!
+ 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;
+}
+
+/// executesAtLeastOnce - Test whether entry to the loop is protected by
+/// a conditional between LHS and RHS.
+bool ScalarEvolutionsImpl::executesAtLeastOnce(const Loop *L, bool isSigned,
+ bool trueWhenEqual,
+ 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();
+
+ switch (Cond) {
+ case ICmpInst::ICMP_UGT:
+ if (isSigned || trueWhenEqual) continue;
+ std::swap(PreCondLHS, PreCondRHS);
+ Cond = ICmpInst::ICMP_ULT;
+ break;
+ case ICmpInst::ICMP_SGT:
+ if (!isSigned || trueWhenEqual) continue;
+ std::swap(PreCondLHS, PreCondRHS);
+ Cond = ICmpInst::ICMP_SLT;
+ break;
+ case ICmpInst::ICMP_ULT:
+ if (isSigned || trueWhenEqual) continue;
+ break;
+ case ICmpInst::ICMP_SLT:
+ if (!isSigned || trueWhenEqual) continue;
+ break;
+ case ICmpInst::ICMP_UGE:
+ if (isSigned || !trueWhenEqual) continue;
+ std::swap(PreCondLHS, PreCondRHS);
+ Cond = ICmpInst::ICMP_ULE;
+ break;
+ case ICmpInst::ICMP_SGE:
+ if (!isSigned || !trueWhenEqual) continue;
+ std::swap(PreCondLHS, PreCondRHS);
+ Cond = ICmpInst::ICMP_SLE;
+ break;
+ case ICmpInst::ICMP_ULE:
+ if (isSigned || !trueWhenEqual) continue;
+ break;
+ case ICmpInst::ICMP_SLE:
+ if (!isSigned || !trueWhenEqual) continue;
+ break;
+ default:
+ 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;
+}
+
+/// potentialInfiniteLoop - Test whether the loop might jump over the exit value
+/// due to wrapping around 2^n.
+bool ScalarEvolutionsImpl::potentialInfiniteLoop(SCEV *Stride, SCEV *RHS,
+ bool isSigned, bool trueWhenEqual) {
+ // Return true when the distance from RHS to maxint > Stride.
+
+ if (!isa<SCEVConstant>(Stride))
+ return true;
+ SCEVConstant *SC = cast<SCEVConstant>(Stride);
+
+ if (SC->getValue()->isZero())
+ return true;
+ if (!trueWhenEqual && SC->getValue()->isOne())
+ return false;
+
+ if (!isa<SCEVConstant>(RHS))
+ return true;
+ SCEVConstant *R = cast<SCEVConstant>(RHS);
+
+ if (isSigned)
+ return true; // XXX: because we don't have an sdiv scev.
+
+ // If negative, it wraps around every iteration, but we don't care about that.
+ APInt S = SC->getValue()->getValue().abs();
+
+ APInt Dist = APInt::getMaxValue(R->getValue()->getBitWidth()) -
+ R->getValue()->getValue();
+
+ if (trueWhenEqual)
+ return !S.ult(Dist);
+ else
+ return !S.ule(Dist);
+}
+
/// 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, bool trueWhenEqual) {
// Only handle: "ADDREC < LoopInvariant".
if (!RHS->isLoopInvariant(L)) return UnknownValue;
return UnknownValue;
if (AddRec->isAffine()) {
- // FORNOW: We only support unit strides.
- SCEVHandle One = SCEVUnknown::getIntegerSCEV(1, RHS->getType());
- if (AddRec->getOperand(1) != One)
+ SCEVHandle Stride = AddRec->getOperand(1);
+ if (potentialInfiniteLoop(Stride, RHS, isSigned, trueWhenEqual))
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,+,s} and the RHS is some loop-invariant
+ // m. So, we count the number of iterations in which {n,+,s} < m is true.
+ // Note that we cannot simply return max(m-n,0)/s because it's not safe to
+ // treat m-n as signed nor unsigned due to overflow possibility.
- // 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;
- }
+ SCEVHandle One = SE.getIntegerSCEV(1, RHS->getType());
- // 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;
- }
+ // Assuming that the loop will run at least once, we know that it will
+ // run (m-n)/s times.
+ SCEVHandle End = RHS;
- if (Cond == ICmpInst::ICMP_SLT) {
- if (PreCondLHS->getType()->isInteger()) {
- if (RHS != getSCEV(PreCondRHS))
- return UnknownValue; // Not a comparison against 'm'.
+ if (!executesAtLeastOnce(L, isSigned, trueWhenEqual,
+ SE.getMinusSCEV(Start, One), RHS)) {
+ // If not, 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).
+ End = isSigned ? SE.getSMaxExpr(RHS, Start)
+ : SE.getUMaxExpr(RHS, Start);
+ }
- 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;
+ // If the expression is less-than-or-equal to, we need to extend the
+ // loop by one iteration.
+ //
+ // The loop won't actually run (m-n)/s times because the loop iterations
+ // won't divide evenly. For example, if you have {2,+,5} u< 10 the
+ // division would equal one, but the loop runs twice putting the
+ // induction variable at 12.
+
+ if (!trueWhenEqual)
+ // (Stride - 1) is correct only because we know it's unsigned.
+ // What we really want is to decrease the magnitude of Stride by one.
+ Start = SE.getMinusSCEV(Start, SE.getMinusSCEV(Stride, One));
+ else
+ Start = SE.getMinusSCEV(Start, Stride);
- // cerr << "Computed Loop Trip Count as: "
- // << // *SCEV::getMinusSCEV(RHS, AddRec->getOperand(0)) << "\n";
- return SCEV::getMinusSCEV(RHS, AddRec->getOperand(0));
- }
- else
- return UnknownValue;
+ // Finally, we subtract these two values to get the number of times the
+ // backedge is executed: max(m,n)-n.
+ return SE.getUDivExpr(SE.getMinusSCEV(End, Start), Stride);
}
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();
// If the start is a non-zero constant, shift the range to simplify things.
if (SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
- if (!SC->getValue()->isNullValue()) {
+ 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()),isSigned);
+ Range.subtract(SC->getValue()->getValue()), SE);
// This is strange and shouldn't happen.
return new SCEVCouldNotCompute();
}
// First check to see if the range contains zero. If not, the first
// iteration exits.
- ConstantInt *Zero = ConstantInt::get(getType(), 0);
- if (!Range.contains(Zero, isSigned)) return SCEVConstant::get(Zero);
+ if (!Range.contains(APInt(getBitWidth(),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.
- ConstantInt *Upper = cast<ConstantInt>(Range.getUpper());
- ConstantInt *A = cast<SCEVConstant>(getOperand(1))->getValue();
- ConstantInt *One = ConstantInt::get(getType(), 1);
-
- // The exit value should be (Upper+A-1)/A.
- Constant *ExitValue = Upper;
- if (A != One) {
- ExitValue = ConstantExpr::getSub(ConstantExpr::getAdd(Upper, A), One);
- ExitValue = ConstantExpr::getSDiv(ExitValue, A);
- }
- assert(isa<ConstantInt>(ExitValue) &&
- "Constant folding of integers not implemented?");
+ // 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(getBitWidth(),1);
+ APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
+ APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
+
+ // The exit value should be (End+A)/A.
+ APInt ExitVal = (End + A).udiv(A);
+ ConstantInt *ExitValue = ConstantInt::get(ExitVal);
// Evaluate at the exit value. If we really did fall out of the valid
// range, then we computed our trip count, otherwise wrap around or other
// things must have happened.
- ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue);
- if (Range.contains(Val, isSigned))
+ ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
+ if (Range.contains(Val->getValue()))
return new SCEVCouldNotCompute(); // Something strange happened
// Ensure that the previous value is in the range. This is a sanity check.
- assert(Range.contains(EvaluateConstantChrecAtConstant(this,
- ConstantExpr::getSub(ExitValue, One)), isSigned) &&
+ assert(Range.contains(
+ EvaluateConstantChrecAtConstant(this,
+ 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(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());
- if (Range.contains(R1Val, isSigned)) {
+ R1->getValue(),
+ SE);
+ if (Range.contains(R1Val->getValue())) {
// The next iteration must be out of the range...
- Constant *NextVal =
- ConstantExpr::getAdd(R1->getValue(),
- ConstantInt::get(R1->getType(), 1));
+ ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()+1);
- R1Val = EvaluateConstantChrecAtConstant(this, NextVal);
- if (!Range.contains(R1Val, isSigned))
- return SCEVUnknown::get(NextVal);
+ R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
+ if (!Range.contains(R1Val->getValue()))
+ return SE.getConstant(NextVal);
return new SCEVCouldNotCompute(); // Something strange happened
}
// If R1 was not in the range, then it is a good return value. Make
// sure that R1-1 WAS in the range though, just in case.
- Constant *NextVal =
- ConstantExpr::getSub(R1->getValue(),
- ConstantInt::get(R1->getType(), 1));
- R1Val = EvaluateConstantChrecAtConstant(this, NextVal);
- if (Range.contains(R1Val, isSigned))
+ 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
}
}
}
- // Fallback, if this is a general polynomial, figure out the progression
- // through brute force: evaluate until we find an iteration that fails the
- // test. This is likely to be slow, but getting an accurate trip count is
- // incredibly important, we will be able to simplify the exit test a lot, and
- // we are almost guaranteed to get a trip count in this case.
- ConstantInt *TestVal = ConstantInt::get(getType(), 0);
- ConstantInt *One = ConstantInt::get(getType(), 1);
- ConstantInt *EndVal = TestVal; // Stop when we wrap around.
- do {
- ++NumBruteForceEvaluations;
- SCEVHandle Val = evaluateAtIteration(SCEVConstant::get(TestVal));
- if (!isa<SCEVConstant>(Val)) // This shouldn't happen.
- return new SCEVCouldNotCompute();
-
- // Check to see if we found the value!
- if (!Range.contains(cast<SCEVConstant>(Val)->getValue(), isSigned))
- return SCEVConstant::get(TestVal);
-
- // Increment to test the next index.
- TestVal = cast<ConstantInt>(ConstantExpr::getAdd(TestVal, One));
- } while (TestVal != EndVal);
-
return new SCEVCouldNotCompute();
}
//===----------------------------------------------------------------------===//
bool ScalarEvolution::runOnFunction(Function &F) {
- Impl = new ScalarEvolutionsImpl(F, getAnalysis<LoopInfo>());
+ Impl = new ScalarEvolutionsImpl(*this, F, getAnalysis<LoopInfo>());
return false;
}
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,
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! ";
+ OS << *SE->getIterationCount(L) << " iterations! ";
} else {
- cerr << "Unpredictable iteration count. ";
+ OS << "Unpredictable iteration count. ";
}
- cerr << "\n";
+ OS << "\n";
}
void ScalarEvolution::print(std::ostream &OS, const Module* ) const {
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());
for (LoopInfo::iterator I = LI.begin(), E = LI.end(); I != E; ++I)
PrintLoopInfo(OS, this, *I);
}
-
projects / oota-llvm.git / blobdiff