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Diffstat (limited to 'contrib/llvm/lib/Analysis/ScalarEvolution.cpp')
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diff --git a/contrib/llvm/lib/Analysis/ScalarEvolution.cpp b/contrib/llvm/lib/Analysis/ScalarEvolution.cpp new file mode 100644 index 0000000..6870268 --- /dev/null +++ b/contrib/llvm/lib/Analysis/ScalarEvolution.cpp @@ -0,0 +1,5801 @@ +//===- ScalarEvolution.cpp - Scalar Evolution Analysis ----------*- C++ -*-===// +// +// The LLVM Compiler Infrastructure +// +// This file is distributed under the University of Illinois Open Source +// License. See LICENSE.TXT for details. +// +//===----------------------------------------------------------------------===// +// +// This file contains the implementation of the scalar evolution analysis +// engine, which is used primarily to analyze expressions involving induction +// variables in loops. +// +// There are several aspects to this library. First is the representation of +// scalar expressions, which are represented as subclasses of the SCEV class. +// These classes are used to represent certain types of subexpressions that we +// can handle. We only create one SCEV of a particular shape, so +// pointer-comparisons for equality are legal. +// +// One important aspect of the SCEV objects is that they are never cyclic, even +// if there is a cycle in the dataflow for an expression (ie, a PHI node). If +// the PHI node is one of the idioms that we can represent (e.g., a polynomial +// recurrence) then we represent it directly as a recurrence node, otherwise we +// represent it as a SCEVUnknown node. +// +// In addition to being able to represent expressions of various types, we also +// have folders that are used to build the *canonical* representation for a +// particular expression. These folders are capable of using a variety of +// rewrite rules to simplify the expressions. +// +// Once the folders are defined, we can implement the more interesting +// higher-level code, such as the code that recognizes PHI nodes of various +// types, computes the execution count of a loop, etc. +// +// TODO: We should use these routines and value representations to implement +// dependence analysis! +// +//===----------------------------------------------------------------------===// +// +// There are several good references for the techniques used in this analysis. +// +// Chains of recurrences -- a method to expedite the evaluation +// of closed-form functions +// Olaf Bachmann, Paul S. Wang, Eugene V. Zima +// +// On computational properties of chains of recurrences +// Eugene V. Zima +// +// Symbolic Evaluation of Chains of Recurrences for Loop Optimization +// Robert A. van Engelen +// +// Efficient Symbolic Analysis for Optimizing Compilers +// Robert A. van Engelen +// +// Using the chains of recurrences algebra for data dependence testing and +// induction variable substitution +// MS Thesis, Johnie Birch +// +//===----------------------------------------------------------------------===// + +#define DEBUG_TYPE "scalar-evolution" +#include "llvm/Analysis/ScalarEvolutionExpressions.h" +#include "llvm/Constants.h" +#include "llvm/DerivedTypes.h" +#include "llvm/GlobalVariable.h" +#include "llvm/GlobalAlias.h" +#include "llvm/Instructions.h" +#include "llvm/LLVMContext.h" +#include "llvm/Operator.h" +#include "llvm/Analysis/ConstantFolding.h" +#include "llvm/Analysis/Dominators.h" +#include "llvm/Analysis/LoopInfo.h" +#include "llvm/Analysis/ValueTracking.h" +#include "llvm/Assembly/Writer.h" +#include "llvm/Target/TargetData.h" +#include "llvm/Support/CommandLine.h" +#include "llvm/Support/ConstantRange.h" +#include "llvm/Support/Debug.h" +#include "llvm/Support/ErrorHandling.h" +#include "llvm/Support/GetElementPtrTypeIterator.h" +#include "llvm/Support/InstIterator.h" +#include "llvm/Support/MathExtras.h" +#include "llvm/Support/raw_ostream.h" +#include "llvm/ADT/Statistic.h" +#include "llvm/ADT/STLExtras.h" +#include "llvm/ADT/SmallPtrSet.h" +#include <algorithm> +using namespace llvm; + +STATISTIC(NumArrayLenItCounts, + "Number of trip counts computed with array length"); +STATISTIC(NumTripCountsComputed, + "Number of loops with predictable loop counts"); +STATISTIC(NumTripCountsNotComputed, + "Number of loops without predictable loop counts"); +STATISTIC(NumBruteForceTripCountsComputed, + "Number of loops with trip counts computed by force"); + +static cl::opt<unsigned> +MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden, + cl::desc("Maximum number of iterations SCEV will " + "symbolically execute a constant " + "derived loop"), + cl::init(100)); + +static RegisterPass<ScalarEvolution> +R("scalar-evolution", "Scalar Evolution Analysis", false, true); +char ScalarEvolution::ID = 0; + +//===----------------------------------------------------------------------===// +// SCEV class definitions +//===----------------------------------------------------------------------===// + +//===----------------------------------------------------------------------===// +// Implementation of the SCEV class. +// + +SCEV::~SCEV() {} + +void SCEV::dump() const { + print(dbgs()); + dbgs() << '\n'; +} + +bool SCEV::isZero() const { + if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) + return SC->getValue()->isZero(); + return false; +} + +bool SCEV::isOne() const { + if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) + return SC->getValue()->isOne(); + return false; +} + +bool SCEV::isAllOnesValue() const { + if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) + return SC->getValue()->isAllOnesValue(); + return false; +} + +SCEVCouldNotCompute::SCEVCouldNotCompute() : + SCEV(FoldingSetNodeIDRef(), scCouldNotCompute) {} + +bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const { + llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); + return false; +} + +const Type *SCEVCouldNotCompute::getType() const { + llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); + return 0; +} + +bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const { + llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); + return false; +} + +bool SCEVCouldNotCompute::hasOperand(const SCEV *) const { + llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); + return false; +} + +void SCEVCouldNotCompute::print(raw_ostream &OS) const { + OS << "***COULDNOTCOMPUTE***"; +} + +bool SCEVCouldNotCompute::classof(const SCEV *S) { + return S->getSCEVType() == scCouldNotCompute; +} + +const SCEV *ScalarEvolution::getConstant(ConstantInt *V) { + FoldingSetNodeID ID; + ID.AddInteger(scConstant); + ID.AddPointer(V); + void *IP = 0; + if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; + SCEV *S = new (SCEVAllocator) SCEVConstant(ID.Intern(SCEVAllocator), V); + UniqueSCEVs.InsertNode(S, IP); + return S; +} + +const SCEV *ScalarEvolution::getConstant(const APInt& Val) { + return getConstant(ConstantInt::get(getContext(), Val)); +} + +const SCEV * +ScalarEvolution::getConstant(const Type *Ty, uint64_t V, bool isSigned) { + const IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty)); + return getConstant(ConstantInt::get(ITy, V, isSigned)); +} + +const Type *SCEVConstant::getType() const { return V->getType(); } + +void SCEVConstant::print(raw_ostream &OS) const { + WriteAsOperand(OS, V, false); +} + +SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID, + unsigned SCEVTy, const SCEV *op, const Type *ty) + : SCEV(ID, SCEVTy), Op(op), Ty(ty) {} + +bool SCEVCastExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { + return Op->dominates(BB, DT); +} + +bool SCEVCastExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const { + return Op->properlyDominates(BB, DT); +} + +SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID, + const SCEV *op, const Type *ty) + : SCEVCastExpr(ID, scTruncate, op, ty) { + assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) && + (Ty->isIntegerTy() || Ty->isPointerTy()) && + "Cannot truncate non-integer value!"); +} + +void SCEVTruncateExpr::print(raw_ostream &OS) const { + OS << "(trunc " << *Op->getType() << " " << *Op << " to " << *Ty << ")"; +} + +SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID, + const SCEV *op, const Type *ty) + : SCEVCastExpr(ID, scZeroExtend, op, ty) { + assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) && + (Ty->isIntegerTy() || Ty->isPointerTy()) && + "Cannot zero extend non-integer value!"); +} + +void SCEVZeroExtendExpr::print(raw_ostream &OS) const { + OS << "(zext " << *Op->getType() << " " << *Op << " to " << *Ty << ")"; +} + +SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID, + const SCEV *op, const Type *ty) + : SCEVCastExpr(ID, scSignExtend, op, ty) { + assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) && + (Ty->isIntegerTy() || Ty->isPointerTy()) && + "Cannot sign extend non-integer value!"); +} + +void SCEVSignExtendExpr::print(raw_ostream &OS) const { + OS << "(sext " << *Op->getType() << " " << *Op << " to " << *Ty << ")"; +} + +void SCEVCommutativeExpr::print(raw_ostream &OS) const { + const char *OpStr = getOperationStr(); + OS << "("; + for (op_iterator I = op_begin(), E = op_end(); I != E; ++I) { + OS << **I; + if (next(I) != E) + OS << OpStr; + } + OS << ")"; +} + +bool SCEVNAryExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { + for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { + if (!getOperand(i)->dominates(BB, DT)) + return false; + } + return true; +} + +bool SCEVNAryExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const { + for (unsigned i = 0, e = getNumOperands(); i != e; ++i) { + if (!getOperand(i)->properlyDominates(BB, DT)) + return false; + } + return true; +} + +bool SCEVUDivExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { + return LHS->dominates(BB, DT) && RHS->dominates(BB, DT); +} + +bool SCEVUDivExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const { + return LHS->properlyDominates(BB, DT) && RHS->properlyDominates(BB, DT); +} + +void SCEVUDivExpr::print(raw_ostream &OS) const { + OS << "(" << *LHS << " /u " << *RHS << ")"; +} + +const Type *SCEVUDivExpr::getType() const { + // In most cases the types of LHS and RHS will be the same, but in some + // crazy cases one or the other may be a pointer. ScalarEvolution doesn't + // depend on the type for correctness, but handling types carefully can + // avoid extra casts in the SCEVExpander. The LHS is more likely to be + // a pointer type than the RHS, so use the RHS' type here. + return RHS->getType(); +} + +bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const { + // Add recurrences are never invariant in the function-body (null loop). + if (!QueryLoop) + return false; + + // This recurrence is variant w.r.t. QueryLoop if QueryLoop contains L. + if (QueryLoop->contains(L)) + return false; + + // This recurrence is variant w.r.t. QueryLoop if any of its operands + // are variant. + for (unsigned i = 0, e = getNumOperands(); i != e; ++i) + if (!getOperand(i)->isLoopInvariant(QueryLoop)) + return false; + + // Otherwise it's loop-invariant. + return true; +} + +bool +SCEVAddRecExpr::dominates(BasicBlock *BB, DominatorTree *DT) const { + return DT->dominates(L->getHeader(), BB) && + SCEVNAryExpr::dominates(BB, DT); +} + +bool +SCEVAddRecExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const { + // This uses a "dominates" query instead of "properly dominates" query because + // the instruction which produces the addrec's value is a PHI, and a PHI + // effectively properly dominates its entire containing block. + return DT->dominates(L->getHeader(), BB) && + SCEVNAryExpr::properlyDominates(BB, DT); +} + +void SCEVAddRecExpr::print(raw_ostream &OS) const { + OS << "{" << *Operands[0]; + for (unsigned i = 1, e = NumOperands; i != e; ++i) + OS << ",+," << *Operands[i]; + OS << "}<"; + WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false); + OS << ">"; +} + +bool SCEVUnknown::isLoopInvariant(const Loop *L) const { + // All non-instruction values are loop invariant. All instructions are loop + // invariant if they are not contained in the specified loop. + // Instructions are never considered invariant in the function body + // (null loop) because they are defined within the "loop". + if (Instruction *I = dyn_cast<Instruction>(V)) + return L && !L->contains(I); + return true; +} + +bool SCEVUnknown::dominates(BasicBlock *BB, DominatorTree *DT) const { + if (Instruction *I = dyn_cast<Instruction>(getValue())) + return DT->dominates(I->getParent(), BB); + return true; +} + +bool SCEVUnknown::properlyDominates(BasicBlock *BB, DominatorTree *DT) const { + if (Instruction *I = dyn_cast<Instruction>(getValue())) + return DT->properlyDominates(I->getParent(), BB); + return true; +} + +const Type *SCEVUnknown::getType() const { + return V->getType(); +} + +bool SCEVUnknown::isSizeOf(const Type *&AllocTy) const { + if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(V)) + if (VCE->getOpcode() == Instruction::PtrToInt) + if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) + if (CE->getOpcode() == Instruction::GetElementPtr && + CE->getOperand(0)->isNullValue() && + CE->getNumOperands() == 2) + if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1))) + if (CI->isOne()) { + AllocTy = cast<PointerType>(CE->getOperand(0)->getType()) + ->getElementType(); + return true; + } + + return false; +} + +bool SCEVUnknown::isAlignOf(const Type *&AllocTy) const { + if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(V)) + if (VCE->getOpcode() == Instruction::PtrToInt) + if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) + if (CE->getOpcode() == Instruction::GetElementPtr && + CE->getOperand(0)->isNullValue()) { + const Type *Ty = + cast<PointerType>(CE->getOperand(0)->getType())->getElementType(); + if (const StructType *STy = dyn_cast<StructType>(Ty)) + if (!STy->isPacked() && + CE->getNumOperands() == 3 && + CE->getOperand(1)->isNullValue()) { + if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2))) + if (CI->isOne() && + STy->getNumElements() == 2 && + STy->getElementType(0)->isIntegerTy(1)) { + AllocTy = STy->getElementType(1); + return true; + } + } + } + + return false; +} + +bool SCEVUnknown::isOffsetOf(const Type *&CTy, Constant *&FieldNo) const { + if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(V)) + if (VCE->getOpcode() == Instruction::PtrToInt) + if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) + if (CE->getOpcode() == Instruction::GetElementPtr && + CE->getNumOperands() == 3 && + CE->getOperand(0)->isNullValue() && + CE->getOperand(1)->isNullValue()) { + const Type *Ty = + cast<PointerType>(CE->getOperand(0)->getType())->getElementType(); + // Ignore vector types here so that ScalarEvolutionExpander doesn't + // emit getelementptrs that index into vectors. + if (Ty->isStructTy() || Ty->isArrayTy()) { + CTy = Ty; + FieldNo = CE->getOperand(2); + return true; + } + } + + return false; +} + +void SCEVUnknown::print(raw_ostream &OS) const { + const Type *AllocTy; + if (isSizeOf(AllocTy)) { + OS << "sizeof(" << *AllocTy << ")"; + return; + } + if (isAlignOf(AllocTy)) { + OS << "alignof(" << *AllocTy << ")"; + return; + } + + const Type *CTy; + Constant *FieldNo; + if (isOffsetOf(CTy, FieldNo)) { + OS << "offsetof(" << *CTy << ", "; + WriteAsOperand(OS, FieldNo, false); + OS << ")"; + return; + } + + // Otherwise just print it normally. + WriteAsOperand(OS, V, false); +} + +//===----------------------------------------------------------------------===// +// SCEV Utilities +//===----------------------------------------------------------------------===// + +static bool CompareTypes(const Type *A, const Type *B) { + if (A->getTypeID() != B->getTypeID()) + return A->getTypeID() < B->getTypeID(); + if (const IntegerType *AI = dyn_cast<IntegerType>(A)) { + const IntegerType *BI = cast<IntegerType>(B); + return AI->getBitWidth() < BI->getBitWidth(); + } + if (const PointerType *AI = dyn_cast<PointerType>(A)) { + const PointerType *BI = cast<PointerType>(B); + return CompareTypes(AI->getElementType(), BI->getElementType()); + } + if (const ArrayType *AI = dyn_cast<ArrayType>(A)) { + const ArrayType *BI = cast<ArrayType>(B); + if (AI->getNumElements() != BI->getNumElements()) + return AI->getNumElements() < BI->getNumElements(); + return CompareTypes(AI->getElementType(), BI->getElementType()); + } + if (const VectorType *AI = dyn_cast<VectorType>(A)) { + const VectorType *BI = cast<VectorType>(B); + if (AI->getNumElements() != BI->getNumElements()) + return AI->getNumElements() < BI->getNumElements(); + return CompareTypes(AI->getElementType(), BI->getElementType()); + } + if (const StructType *AI = dyn_cast<StructType>(A)) { + const StructType *BI = cast<StructType>(B); + if (AI->getNumElements() != BI->getNumElements()) + return AI->getNumElements() < BI->getNumElements(); + for (unsigned i = 0, e = AI->getNumElements(); i != e; ++i) + if (CompareTypes(AI->getElementType(i), BI->getElementType(i)) || + CompareTypes(BI->getElementType(i), AI->getElementType(i))) + return CompareTypes(AI->getElementType(i), BI->getElementType(i)); + } + return false; +} + +namespace { + /// SCEVComplexityCompare - Return true if the complexity of the LHS is less + /// than the complexity of the RHS. This comparator is used to canonicalize + /// expressions. + class SCEVComplexityCompare { + LoopInfo *LI; + public: + explicit SCEVComplexityCompare(LoopInfo *li) : LI(li) {} + + bool operator()(const SCEV *LHS, const SCEV *RHS) const { + // Fast-path: SCEVs are uniqued so we can do a quick equality check. + if (LHS == RHS) + return false; + + // Primarily, sort the SCEVs by their getSCEVType(). + if (LHS->getSCEVType() != RHS->getSCEVType()) + return LHS->getSCEVType() < RHS->getSCEVType(); + + // Aside from the getSCEVType() ordering, the particular ordering + // isn't very important except that it's beneficial to be consistent, + // so that (a + b) and (b + a) don't end up as different expressions. + + // Sort SCEVUnknown values with some loose heuristics. TODO: This is + // not as complete as it could be. + if (const SCEVUnknown *LU = dyn_cast<SCEVUnknown>(LHS)) { + const SCEVUnknown *RU = cast<SCEVUnknown>(RHS); + + // Order pointer values after integer values. This helps SCEVExpander + // form GEPs. + if (LU->getType()->isPointerTy() && !RU->getType()->isPointerTy()) + return false; + if (RU->getType()->isPointerTy() && !LU->getType()->isPointerTy()) + return true; + + // Compare getValueID values. + if (LU->getValue()->getValueID() != RU->getValue()->getValueID()) + return LU->getValue()->getValueID() < RU->getValue()->getValueID(); + + // Sort arguments by their position. + if (const Argument *LA = dyn_cast<Argument>(LU->getValue())) { + const Argument *RA = cast<Argument>(RU->getValue()); + return LA->getArgNo() < RA->getArgNo(); + } + + // For instructions, compare their loop depth, and their opcode. + // This is pretty loose. + if (Instruction *LV = dyn_cast<Instruction>(LU->getValue())) { + Instruction *RV = cast<Instruction>(RU->getValue()); + + // Compare loop depths. + if (LI->getLoopDepth(LV->getParent()) != + LI->getLoopDepth(RV->getParent())) + return LI->getLoopDepth(LV->getParent()) < + LI->getLoopDepth(RV->getParent()); + + // Compare opcodes. + if (LV->getOpcode() != RV->getOpcode()) + return LV->getOpcode() < RV->getOpcode(); + + // Compare the number of operands. + if (LV->getNumOperands() != RV->getNumOperands()) + return LV->getNumOperands() < RV->getNumOperands(); + } + + return false; + } + + // Compare constant values. + if (const SCEVConstant *LC = dyn_cast<SCEVConstant>(LHS)) { + const SCEVConstant *RC = cast<SCEVConstant>(RHS); + if (LC->getValue()->getBitWidth() != RC->getValue()->getBitWidth()) + return LC->getValue()->getBitWidth() < RC->getValue()->getBitWidth(); + return LC->getValue()->getValue().ult(RC->getValue()->getValue()); + } + + // Compare addrec loop depths. + if (const SCEVAddRecExpr *LA = dyn_cast<SCEVAddRecExpr>(LHS)) { + const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS); + if (LA->getLoop()->getLoopDepth() != RA->getLoop()->getLoopDepth()) + return LA->getLoop()->getLoopDepth() < RA->getLoop()->getLoopDepth(); + } + + // Lexicographically compare n-ary expressions. + if (const SCEVNAryExpr *LC = dyn_cast<SCEVNAryExpr>(LHS)) { + const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS); + for (unsigned i = 0, e = LC->getNumOperands(); i != e; ++i) { + if (i >= RC->getNumOperands()) + return false; + if (operator()(LC->getOperand(i), RC->getOperand(i))) + return true; + if (operator()(RC->getOperand(i), LC->getOperand(i))) + return false; + } + return LC->getNumOperands() < RC->getNumOperands(); + } + + // Lexicographically compare udiv expressions. + if (const SCEVUDivExpr *LC = dyn_cast<SCEVUDivExpr>(LHS)) { + const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS); + if (operator()(LC->getLHS(), RC->getLHS())) + return true; + if (operator()(RC->getLHS(), LC->getLHS())) + return false; + if (operator()(LC->getRHS(), RC->getRHS())) + return true; + if (operator()(RC->getRHS(), LC->getRHS())) + return false; + return false; + } + + // Compare cast expressions by operand. + if (const SCEVCastExpr *LC = dyn_cast<SCEVCastExpr>(LHS)) { + const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS); + return operator()(LC->getOperand(), RC->getOperand()); + } + + llvm_unreachable("Unknown SCEV kind!"); + return false; + } + }; +} + +/// GroupByComplexity - Given a list of SCEV objects, order them by their +/// complexity, and group objects of the same complexity together by value. +/// When this routine is finished, we know that any duplicates in the vector are +/// consecutive and that complexity is monotonically increasing. +/// +/// Note that we go take special precautions to ensure that we get deterministic +/// results from this routine. In other words, we don't want the results of +/// this to depend on where the addresses of various SCEV objects happened to +/// land in memory. +/// +static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops, + LoopInfo *LI) { + if (Ops.size() < 2) return; // Noop + if (Ops.size() == 2) { + // This is the common case, which also happens to be trivially simple. + // Special case it. + if (SCEVComplexityCompare(LI)(Ops[1], Ops[0])) + std::swap(Ops[0], Ops[1]); + return; + } + + // Do the rough sort by complexity. + std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI)); + + // Now that we are sorted by complexity, group elements of the same + // complexity. Note that this is, at worst, N^2, but the vector is likely to + // be extremely short in practice. Note that we take this approach because we + // do not want to depend on the addresses of the objects we are grouping. + for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) { + const SCEV *S = Ops[i]; + unsigned Complexity = S->getSCEVType(); + + // If there are any objects of the same complexity and same value as this + // one, group them. + for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) { + if (Ops[j] == S) { // Found a duplicate. + // Move it to immediately after i'th element. + std::swap(Ops[i+1], Ops[j]); + ++i; // no need to rescan it. + if (i == e-2) return; // Done! + } + } + } +} + + + +//===----------------------------------------------------------------------===// +// Simple SCEV method implementations +//===----------------------------------------------------------------------===// + +/// BinomialCoefficient - Compute BC(It, K). The result has width W. +/// Assume, K > 0. +static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K, + ScalarEvolution &SE, + const Type* ResultTy) { + // Handle the simplest case efficiently. + if (K == 1) + return SE.getTruncateOrZeroExtend(It, ResultTy); + + // We are using the following formula for BC(It, K): + // + // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K! + // + // Suppose, W is the bitwidth of the return value. We must be prepared for + // overflow. Hence, we must assure that the result of our computation is + // equal to the accurate one modulo 2^W. Unfortunately, division isn't + // safe in modular arithmetic. + // + // However, this code doesn't use exactly that formula; the formula it uses + // is something like the following, where T is the number of factors of 2 in + // K! (i.e. trailing zeros in the binary representation of K!), and ^ is + // exponentiation: + // + // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T) + // + // This formula is trivially equivalent to the previous formula. However, + // this formula can be implemented much more efficiently. The trick is that + // K! / 2^T is odd, and exact division by an odd number *is* safe in modular + // arithmetic. To do exact division in modular arithmetic, all we have + // to do is multiply by the inverse. Therefore, this step can be done at + // width W. + // + // The next issue is how to safely do the division by 2^T. The way this + // is done is by doing the multiplication step at a width of at least W + T + // bits. This way, the bottom W+T bits of the product are accurate. Then, + // when we perform the division by 2^T (which is equivalent to a right shift + // by T), the bottom W bits are accurate. Extra bits are okay; they'll get + // truncated out after the division by 2^T. + // + // In comparison to just directly using the first formula, this technique + // is much more efficient; using the first formula requires W * K bits, + // but this formula less than W + K bits. Also, the first formula requires + // a division step, whereas this formula only requires multiplies and shifts. + // + // It doesn't matter whether the subtraction step is done in the calculation + // width or the input iteration count's width; if the subtraction overflows, + // the result must be zero anyway. We prefer here to do it in the width of + // the induction variable because it helps a lot for certain cases; CodeGen + // isn't smart enough to ignore the overflow, which leads to much less + // efficient code if the width of the subtraction is wider than the native + // register width. + // + // (It's possible to not widen at all by pulling out factors of 2 before + // the multiplication; for example, K=2 can be calculated as + // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires + // extra arithmetic, so it's not an obvious win, and it gets + // much more complicated for K > 3.) + + // Protection from insane SCEVs; this bound is conservative, + // but it probably doesn't matter. + if (K > 1000) + return SE.getCouldNotCompute(); + + unsigned W = SE.getTypeSizeInBits(ResultTy); + + // Calculate K! / 2^T and T; we divide out the factors of two before + // multiplying for calculating K! / 2^T to avoid overflow. + // Other overflow doesn't matter because we only care about the bottom + // W bits of the result. + APInt OddFactorial(W, 1); + unsigned T = 1; + for (unsigned i = 3; i <= K; ++i) { + APInt Mult(W, i); + unsigned TwoFactors = Mult.countTrailingZeros(); + T += TwoFactors; + Mult = Mult.lshr(TwoFactors); + OddFactorial *= Mult; + } + + // We need at least W + T bits for the multiplication step + unsigned CalculationBits = W + T; + + // Calculate 2^T, at width T+W. + APInt DivFactor = APInt(CalculationBits, 1).shl(T); + + // Calculate the multiplicative inverse of K! / 2^T; + // this multiplication factor will perform the exact division by + // K! / 2^T. + APInt Mod = APInt::getSignedMinValue(W+1); + APInt MultiplyFactor = OddFactorial.zext(W+1); + MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod); + MultiplyFactor = MultiplyFactor.trunc(W); + + // Calculate the product, at width T+W + const IntegerType *CalculationTy = IntegerType::get(SE.getContext(), + CalculationBits); + const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy); + for (unsigned i = 1; i != K; ++i) { + const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i)); + Dividend = SE.getMulExpr(Dividend, + SE.getTruncateOrZeroExtend(S, CalculationTy)); + } + + // Divide by 2^T + const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor)); + + // Truncate the result, and divide by K! / 2^T. + + return SE.getMulExpr(SE.getConstant(MultiplyFactor), + SE.getTruncateOrZeroExtend(DivResult, ResultTy)); +} + +/// evaluateAtIteration - Return the value of this chain of recurrences at +/// the specified iteration number. We can evaluate this recurrence by +/// multiplying each element in the chain by the binomial coefficient +/// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as: +/// +/// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3) +/// +/// where BC(It, k) stands for binomial coefficient. +/// +const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It, + ScalarEvolution &SE) const { + const SCEV *Result = getStart(); + for (unsigned i = 1, e = getNumOperands(); i != e; ++i) { + // The computation is correct in the face of overflow provided that the + // multiplication is performed _after_ the evaluation of the binomial + // coefficient. + const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType()); + if (isa<SCEVCouldNotCompute>(Coeff)) + return Coeff; + + Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff)); + } + return Result; +} + +//===----------------------------------------------------------------------===// +// SCEV Expression folder implementations +//===----------------------------------------------------------------------===// + +const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op, + const Type *Ty) { + assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) && + "This is not a truncating conversion!"); + assert(isSCEVable(Ty) && + "This is not a conversion to a SCEVable type!"); + Ty = getEffectiveSCEVType(Ty); + + FoldingSetNodeID ID; + ID.AddInteger(scTruncate); + ID.AddPointer(Op); + ID.AddPointer(Ty); + void *IP = 0; + if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; + + // Fold if the operand is constant. + if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) + return getConstant( + cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty))); + + // trunc(trunc(x)) --> trunc(x) + if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) + return getTruncateExpr(ST->getOperand(), Ty); + + // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing + if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) + return getTruncateOrSignExtend(SS->getOperand(), Ty); + + // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing + if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) + return getTruncateOrZeroExtend(SZ->getOperand(), Ty); + + // If the input value is a chrec scev, truncate the chrec's operands. + if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) { + SmallVector<const SCEV *, 4> Operands; + for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) + Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty)); + return getAddRecExpr(Operands, AddRec->getLoop()); + } + + // The cast wasn't folded; create an explicit cast node. + // Recompute the insert position, as it may have been invalidated. + if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; + SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator), + Op, Ty); + UniqueSCEVs.InsertNode(S, IP); + return S; +} + +const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op, + const Type *Ty) { + assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && + "This is not an extending conversion!"); + assert(isSCEVable(Ty) && + "This is not a conversion to a SCEVable type!"); + Ty = getEffectiveSCEVType(Ty); + + // Fold if the operand is constant. + if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) { + const Type *IntTy = getEffectiveSCEVType(Ty); + Constant *C = ConstantExpr::getZExt(SC->getValue(), IntTy); + if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty); + return getConstant(cast<ConstantInt>(C)); + } + + // zext(zext(x)) --> zext(x) + if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) + return getZeroExtendExpr(SZ->getOperand(), Ty); + + // Before doing any expensive analysis, check to see if we've already + // computed a SCEV for this Op and Ty. + FoldingSetNodeID ID; + ID.AddInteger(scZeroExtend); + ID.AddPointer(Op); + ID.AddPointer(Ty); + void *IP = 0; + if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; + + // If the input value is a chrec scev, and we can prove that the value + // did not overflow the old, smaller, value, we can zero extend all of the + // operands (often constants). This allows analysis of something like + // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; } + if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) + if (AR->isAffine()) { + const SCEV *Start = AR->getStart(); + const SCEV *Step = AR->getStepRecurrence(*this); + unsigned BitWidth = getTypeSizeInBits(AR->getType()); + const Loop *L = AR->getLoop(); + + // If we have special knowledge that this addrec won't overflow, + // we don't need to do any further analysis. + if (AR->hasNoUnsignedWrap()) + return getAddRecExpr(getZeroExtendExpr(Start, Ty), + getZeroExtendExpr(Step, Ty), + L); + + // Check whether the backedge-taken count is SCEVCouldNotCompute. + // Note that this serves two purposes: It filters out loops that are + // simply not analyzable, and it covers the case where this code is + // being called from within backedge-taken count analysis, such that + // attempting to ask for the backedge-taken count would likely result + // in infinite recursion. In the later case, the analysis code will + // cope with a conservative value, and it will take care to purge + // that value once it has finished. + const SCEV *MaxBECount = getMaxBackedgeTakenCount(L); + if (!isa<SCEVCouldNotCompute>(MaxBECount)) { + // Manually compute the final value for AR, checking for + // overflow. + + // Check whether the backedge-taken count can be losslessly casted to + // the addrec's type. The count is always unsigned. + const SCEV *CastedMaxBECount = + getTruncateOrZeroExtend(MaxBECount, Start->getType()); + const SCEV *RecastedMaxBECount = + getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType()); + if (MaxBECount == RecastedMaxBECount) { + const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2); + // Check whether Start+Step*MaxBECount has no unsigned overflow. + const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step); + const SCEV *Add = getAddExpr(Start, ZMul); + const SCEV *OperandExtendedAdd = + getAddExpr(getZeroExtendExpr(Start, WideTy), + getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), + getZeroExtendExpr(Step, WideTy))); + if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) + // Return the expression with the addrec on the outside. + return getAddRecExpr(getZeroExtendExpr(Start, Ty), + getZeroExtendExpr(Step, Ty), + L); + + // Similar to above, only this time treat the step value as signed. + // This covers loops that count down. + const SCEV *SMul = getMulExpr(CastedMaxBECount, Step); + Add = getAddExpr(Start, SMul); + OperandExtendedAdd = + getAddExpr(getZeroExtendExpr(Start, WideTy), + getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), + getSignExtendExpr(Step, WideTy))); + if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) + // Return the expression with the addrec on the outside. + return getAddRecExpr(getZeroExtendExpr(Start, Ty), + getSignExtendExpr(Step, Ty), + L); + } + + // If the backedge is guarded by a comparison with the pre-inc value + // the addrec is safe. Also, if the entry is guarded by a comparison + // with the start value and the backedge is guarded by a comparison + // with the post-inc value, the addrec is safe. + if (isKnownPositive(Step)) { + const SCEV *N = getConstant(APInt::getMinValue(BitWidth) - + getUnsignedRange(Step).getUnsignedMax()); + if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) || + (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) && + isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, + AR->getPostIncExpr(*this), N))) + // Return the expression with the addrec on the outside. + return getAddRecExpr(getZeroExtendExpr(Start, Ty), + getZeroExtendExpr(Step, Ty), + L); + } else if (isKnownNegative(Step)) { + const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) - + getSignedRange(Step).getSignedMin()); + if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) || + (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) && + isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, + AR->getPostIncExpr(*this), N))) + // Return the expression with the addrec on the outside. + return getAddRecExpr(getZeroExtendExpr(Start, Ty), + getSignExtendExpr(Step, Ty), + L); + } + } + } + + // The cast wasn't folded; create an explicit cast node. + // Recompute the insert position, as it may have been invalidated. + if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; + SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator), + Op, Ty); + UniqueSCEVs.InsertNode(S, IP); + return S; +} + +const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op, + const Type *Ty) { + assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && + "This is not an extending conversion!"); + assert(isSCEVable(Ty) && + "This is not a conversion to a SCEVable type!"); + Ty = getEffectiveSCEVType(Ty); + + // Fold if the operand is constant. + if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) { + const Type *IntTy = getEffectiveSCEVType(Ty); + Constant *C = ConstantExpr::getSExt(SC->getValue(), IntTy); + if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty); + return getConstant(cast<ConstantInt>(C)); + } + + // sext(sext(x)) --> sext(x) + if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) + return getSignExtendExpr(SS->getOperand(), Ty); + + // Before doing any expensive analysis, check to see if we've already + // computed a SCEV for this Op and Ty. + FoldingSetNodeID ID; + ID.AddInteger(scSignExtend); + ID.AddPointer(Op); + ID.AddPointer(Ty); + void *IP = 0; + if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; + + // If the input value is a chrec scev, and we can prove that the value + // did not overflow the old, smaller, value, we can sign extend all of the + // operands (often constants). This allows analysis of something like + // this: for (signed char X = 0; X < 100; ++X) { int Y = X; } + if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) + if (AR->isAffine()) { + const SCEV *Start = AR->getStart(); + const SCEV *Step = AR->getStepRecurrence(*this); + unsigned BitWidth = getTypeSizeInBits(AR->getType()); + const Loop *L = AR->getLoop(); + + // If we have special knowledge that this addrec won't overflow, + // we don't need to do any further analysis. + if (AR->hasNoSignedWrap()) + return getAddRecExpr(getSignExtendExpr(Start, Ty), + getSignExtendExpr(Step, Ty), + L); + + // Check whether the backedge-taken count is SCEVCouldNotCompute. + // Note that this serves two purposes: It filters out loops that are + // simply not analyzable, and it covers the case where this code is + // being called from within backedge-taken count analysis, such that + // attempting to ask for the backedge-taken count would likely result + // in infinite recursion. In the later case, the analysis code will + // cope with a conservative value, and it will take care to purge + // that value once it has finished. + const SCEV *MaxBECount = getMaxBackedgeTakenCount(L); + if (!isa<SCEVCouldNotCompute>(MaxBECount)) { + // Manually compute the final value for AR, checking for + // overflow. + + // Check whether the backedge-taken count can be losslessly casted to + // the addrec's type. The count is always unsigned. + const SCEV *CastedMaxBECount = + getTruncateOrZeroExtend(MaxBECount, Start->getType()); + const SCEV *RecastedMaxBECount = + getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType()); + if (MaxBECount == RecastedMaxBECount) { + const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2); + // Check whether Start+Step*MaxBECount has no signed overflow. + const SCEV *SMul = getMulExpr(CastedMaxBECount, Step); + const SCEV *Add = getAddExpr(Start, SMul); + const SCEV *OperandExtendedAdd = + getAddExpr(getSignExtendExpr(Start, WideTy), + getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), + getSignExtendExpr(Step, WideTy))); + if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd) + // Return the expression with the addrec on the outside. + return getAddRecExpr(getSignExtendExpr(Start, Ty), + getSignExtendExpr(Step, Ty), + L); + + // Similar to above, only this time treat the step value as unsigned. + // This covers loops that count up with an unsigned step. + const SCEV *UMul = getMulExpr(CastedMaxBECount, Step); + Add = getAddExpr(Start, UMul); + OperandExtendedAdd = + getAddExpr(getSignExtendExpr(Start, WideTy), + getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy), + getZeroExtendExpr(Step, WideTy))); + if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd) + // Return the expression with the addrec on the outside. + return getAddRecExpr(getSignExtendExpr(Start, Ty), + getZeroExtendExpr(Step, Ty), + L); + } + + // If the backedge is guarded by a comparison with the pre-inc value + // the addrec is safe. Also, if the entry is guarded by a comparison + // with the start value and the backedge is guarded by a comparison + // with the post-inc value, the addrec is safe. + if (isKnownPositive(Step)) { + const SCEV *N = getConstant(APInt::getSignedMinValue(BitWidth) - + getSignedRange(Step).getSignedMax()); + if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT, AR, N) || + (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_SLT, Start, N) && + isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT, + AR->getPostIncExpr(*this), N))) + // Return the expression with the addrec on the outside. + return getAddRecExpr(getSignExtendExpr(Start, Ty), + getSignExtendExpr(Step, Ty), + L); + } else if (isKnownNegative(Step)) { + const SCEV *N = getConstant(APInt::getSignedMaxValue(BitWidth) - + getSignedRange(Step).getSignedMin()); + if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT, AR, N) || + (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_SGT, Start, N) && + isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT, + AR->getPostIncExpr(*this), N))) + // Return the expression with the addrec on the outside. + return getAddRecExpr(getSignExtendExpr(Start, Ty), + getSignExtendExpr(Step, Ty), + L); + } + } + } + + // The cast wasn't folded; create an explicit cast node. + // Recompute the insert position, as it may have been invalidated. + if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; + SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator), + Op, Ty); + UniqueSCEVs.InsertNode(S, IP); + return S; +} + +/// getAnyExtendExpr - Return a SCEV for the given operand extended with +/// unspecified bits out to the given type. +/// +const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op, + const Type *Ty) { + assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && + "This is not an extending conversion!"); + assert(isSCEVable(Ty) && + "This is not a conversion to a SCEVable type!"); + Ty = getEffectiveSCEVType(Ty); + + // Sign-extend negative constants. + if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) + if (SC->getValue()->getValue().isNegative()) + return getSignExtendExpr(Op, Ty); + + // Peel off a truncate cast. + if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) { + const SCEV *NewOp = T->getOperand(); + if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty)) + return getAnyExtendExpr(NewOp, Ty); + return getTruncateOrNoop(NewOp, Ty); + } + + // Next try a zext cast. If the cast is folded, use it. + const SCEV *ZExt = getZeroExtendExpr(Op, Ty); + if (!isa<SCEVZeroExtendExpr>(ZExt)) + return ZExt; + + // Next try a sext cast. If the cast is folded, use it. + const SCEV *SExt = getSignExtendExpr(Op, Ty); + if (!isa<SCEVSignExtendExpr>(SExt)) + return SExt; + + // Force the cast to be folded into the operands of an addrec. + if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) { + SmallVector<const SCEV *, 4> Ops; + for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end(); + I != E; ++I) + Ops.push_back(getAnyExtendExpr(*I, Ty)); + return getAddRecExpr(Ops, AR->getLoop()); + } + + // If the expression is obviously signed, use the sext cast value. + if (isa<SCEVSMaxExpr>(Op)) + return SExt; + + // Absent any other information, use the zext cast value. + return ZExt; +} + +/// CollectAddOperandsWithScales - Process the given Ops list, which is +/// a list of operands to be added under the given scale, update the given +/// map. This is a helper function for getAddRecExpr. As an example of +/// what it does, given a sequence of operands that would form an add +/// expression like this: +/// +/// m + n + 13 + (A * (o + p + (B * q + m + 29))) + r + (-1 * r) +/// +/// where A and B are constants, update the map with these values: +/// +/// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0) +/// +/// and add 13 + A*B*29 to AccumulatedConstant. +/// This will allow getAddRecExpr to produce this: +/// +/// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B) +/// +/// This form often exposes folding opportunities that are hidden in +/// the original operand list. +/// +/// Return true iff it appears that any interesting folding opportunities +/// may be exposed. This helps getAddRecExpr short-circuit extra work in +/// the common case where no interesting opportunities are present, and +/// is also used as a check to avoid infinite recursion. +/// +static bool +CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M, + SmallVector<const SCEV *, 8> &NewOps, + APInt &AccumulatedConstant, + const SCEV *const *Ops, size_t NumOperands, + const APInt &Scale, + ScalarEvolution &SE) { + bool Interesting = false; + + // Iterate over the add operands. + for (unsigned i = 0, e = NumOperands; i != e; ++i) { + const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]); + if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) { + APInt NewScale = + Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue(); + if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) { + // A multiplication of a constant with another add; recurse. + const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1)); + Interesting |= + CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, + Add->op_begin(), Add->getNumOperands(), + NewScale, SE); + } else { + // A multiplication of a constant with some other value. Update + // the map. + SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end()); + const SCEV *Key = SE.getMulExpr(MulOps); + std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair = + M.insert(std::make_pair(Key, NewScale)); + if (Pair.second) { + NewOps.push_back(Pair.first->first); + } else { + Pair.first->second += NewScale; + // The map already had an entry for this value, which may indicate + // a folding opportunity. + Interesting = true; + } + } + } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { + // Pull a buried constant out to the outside. + if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero()) + Interesting = true; + AccumulatedConstant += Scale * C->getValue()->getValue(); + } else { + // An ordinary operand. Update the map. + std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair = + M.insert(std::make_pair(Ops[i], Scale)); + if (Pair.second) { + NewOps.push_back(Pair.first->first); + } else { + Pair.first->second += Scale; + // The map already had an entry for this value, which may indicate + // a folding opportunity. + Interesting = true; + } + } + } + + return Interesting; +} + +namespace { + struct APIntCompare { + bool operator()(const APInt &LHS, const APInt &RHS) const { + return LHS.ult(RHS); + } + }; +} + +/// getAddExpr - Get a canonical add expression, or something simpler if +/// possible. +const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops, + bool HasNUW, bool HasNSW) { + assert(!Ops.empty() && "Cannot get empty add!"); + if (Ops.size() == 1) return Ops[0]; +#ifndef NDEBUG + for (unsigned i = 1, e = Ops.size(); i != e; ++i) + assert(getEffectiveSCEVType(Ops[i]->getType()) == + getEffectiveSCEVType(Ops[0]->getType()) && + "SCEVAddExpr operand types don't match!"); +#endif + + // If HasNSW is true and all the operands are non-negative, infer HasNUW. + if (!HasNUW && HasNSW) { + bool All = true; + for (unsigned i = 0, e = Ops.size(); i != e; ++i) + if (!isKnownNonNegative(Ops[i])) { + All = false; + break; + } + if (All) HasNUW = true; + } + + // Sort by complexity, this groups all similar expression types together. + GroupByComplexity(Ops, LI); + + // If there are any constants, fold them together. + unsigned Idx = 0; + if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { + ++Idx; + assert(Idx < Ops.size()); + while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { + // We found two constants, fold them together! + Ops[0] = getConstant(LHSC->getValue()->getValue() + + RHSC->getValue()->getValue()); + if (Ops.size() == 2) return Ops[0]; + Ops.erase(Ops.begin()+1); // Erase the folded element + LHSC = cast<SCEVConstant>(Ops[0]); + } + + // If we are left with a constant zero being added, strip it off. + if (LHSC->getValue()->isZero()) { + Ops.erase(Ops.begin()); + --Idx; + } + + if (Ops.size() == 1) return Ops[0]; + } + + // Okay, check to see if the same value occurs in the operand list twice. If + // so, merge them together into an multiply expression. Since we sorted the + // list, these values are required to be adjacent. + const Type *Ty = Ops[0]->getType(); + for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) + if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2 + // Found a match, merge the two values into a multiply, and add any + // remaining values to the result. + const SCEV *Two = getConstant(Ty, 2); + const SCEV *Mul = getMulExpr(Ops[i], Two); + if (Ops.size() == 2) + return Mul; + Ops.erase(Ops.begin()+i, Ops.begin()+i+2); + Ops.push_back(Mul); + return getAddExpr(Ops, HasNUW, HasNSW); + } + + // Check for truncates. If all the operands are truncated from the same + // type, see if factoring out the truncate would permit the result to be + // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n) + // if the contents of the resulting outer trunc fold to something simple. + for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) { + const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]); + const Type *DstType = Trunc->getType(); + const Type *SrcType = Trunc->getOperand()->getType(); + SmallVector<const SCEV *, 8> LargeOps; + bool Ok = true; + // Check all the operands to see if they can be represented in the + // source type of the truncate. + for (unsigned i = 0, e = Ops.size(); i != e; ++i) { + if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) { + if (T->getOperand()->getType() != SrcType) { + Ok = false; + break; + } + LargeOps.push_back(T->getOperand()); + } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { + LargeOps.push_back(getAnyExtendExpr(C, SrcType)); + } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) { + SmallVector<const SCEV *, 8> LargeMulOps; + for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) { + if (const SCEVTruncateExpr *T = + dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) { + if (T->getOperand()->getType() != SrcType) { + Ok = false; + break; + } + LargeMulOps.push_back(T->getOperand()); + } else if (const SCEVConstant *C = + dyn_cast<SCEVConstant>(M->getOperand(j))) { + LargeMulOps.push_back(getAnyExtendExpr(C, SrcType)); + } else { + Ok = false; + break; + } + } + if (Ok) + LargeOps.push_back(getMulExpr(LargeMulOps)); + } else { + Ok = false; + break; + } + } + if (Ok) { + // Evaluate the expression in the larger type. + const SCEV *Fold = getAddExpr(LargeOps, HasNUW, HasNSW); + // If it folds to something simple, use it. Otherwise, don't. + if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold)) + return getTruncateExpr(Fold, DstType); + } + } + + // Skip past any other cast SCEVs. + while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr) + ++Idx; + + // If there are add operands they would be next. + if (Idx < Ops.size()) { + bool DeletedAdd = false; + while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) { + // If we have an add, expand the add operands onto the end of the operands + // list. + Ops.insert(Ops.end(), Add->op_begin(), Add->op_end()); + Ops.erase(Ops.begin()+Idx); + DeletedAdd = true; + } + + // If we deleted at least one add, we added operands to the end of the list, + // and they are not necessarily sorted. Recurse to resort and resimplify + // any operands we just acquired. + if (DeletedAdd) + return getAddExpr(Ops); + } + + // Skip over the add expression until we get to a multiply. + while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) + ++Idx; + + // Check to see if there are any folding opportunities present with + // operands multiplied by constant values. + if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) { + uint64_t BitWidth = getTypeSizeInBits(Ty); + DenseMap<const SCEV *, APInt> M; + SmallVector<const SCEV *, 8> NewOps; + APInt AccumulatedConstant(BitWidth, 0); + if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, + Ops.data(), Ops.size(), + APInt(BitWidth, 1), *this)) { + // Some interesting folding opportunity is present, so its worthwhile to + // re-generate the operands list. Group the operands by constant scale, + // to avoid multiplying by the same constant scale multiple times. + std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists; + for (SmallVector<const SCEV *, 8>::iterator I = NewOps.begin(), + E = NewOps.end(); I != E; ++I) + MulOpLists[M.find(*I)->second].push_back(*I); + // Re-generate the operands list. + Ops.clear(); + if (AccumulatedConstant != 0) + Ops.push_back(getConstant(AccumulatedConstant)); + for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator + I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I) + if (I->first != 0) + Ops.push_back(getMulExpr(getConstant(I->first), + getAddExpr(I->second))); + if (Ops.empty()) + return getConstant(Ty, 0); + if (Ops.size() == 1) + return Ops[0]; + return getAddExpr(Ops); + } + } + + // If we are adding something to a multiply expression, make sure the + // something is not already an operand of the multiply. If so, merge it into + // the multiply. + for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) { + const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]); + for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) { + const SCEV *MulOpSCEV = Mul->getOperand(MulOp); + for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp) + if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(Ops[AddOp])) { + // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1)) + const SCEV *InnerMul = Mul->getOperand(MulOp == 0); + if (Mul->getNumOperands() != 2) { + // If the multiply has more than two operands, we must get the + // Y*Z term. + SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), Mul->op_end()); + MulOps.erase(MulOps.begin()+MulOp); + InnerMul = getMulExpr(MulOps); + } + const SCEV *One = getConstant(Ty, 1); + const SCEV *AddOne = getAddExpr(InnerMul, One); + const SCEV *OuterMul = getMulExpr(AddOne, Ops[AddOp]); + if (Ops.size() == 2) return OuterMul; + if (AddOp < Idx) { + Ops.erase(Ops.begin()+AddOp); + Ops.erase(Ops.begin()+Idx-1); + } else { + Ops.erase(Ops.begin()+Idx); + Ops.erase(Ops.begin()+AddOp-1); + } + Ops.push_back(OuterMul); + return getAddExpr(Ops); + } + + // Check this multiply against other multiplies being added together. + for (unsigned OtherMulIdx = Idx+1; + OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]); + ++OtherMulIdx) { + const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]); + // If MulOp occurs in OtherMul, we can fold the two multiplies + // together. + for (unsigned OMulOp = 0, e = OtherMul->getNumOperands(); + OMulOp != e; ++OMulOp) + if (OtherMul->getOperand(OMulOp) == MulOpSCEV) { + // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E)) + const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0); + if (Mul->getNumOperands() != 2) { + SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), + Mul->op_end()); + MulOps.erase(MulOps.begin()+MulOp); + InnerMul1 = getMulExpr(MulOps); + } + const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0); + if (OtherMul->getNumOperands() != 2) { + SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(), + OtherMul->op_end()); + MulOps.erase(MulOps.begin()+OMulOp); + InnerMul2 = getMulExpr(MulOps); + } + const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2); + const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum); + if (Ops.size() == 2) return OuterMul; + Ops.erase(Ops.begin()+Idx); + Ops.erase(Ops.begin()+OtherMulIdx-1); + Ops.push_back(OuterMul); + return getAddExpr(Ops); + } + } + } + } + + // If there are any add recurrences in the operands list, see if any other + // added values are loop invariant. If so, we can fold them into the + // recurrence. + while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) + ++Idx; + + // Scan over all recurrences, trying to fold loop invariants into them. + for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { + // Scan all of the other operands to this add and add them to the vector if + // they are loop invariant w.r.t. the recurrence. + SmallVector<const SCEV *, 8> LIOps; + const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); + const Loop *AddRecLoop = AddRec->getLoop(); + for (unsigned i = 0, e = Ops.size(); i != e; ++i) + if (Ops[i]->isLoopInvariant(AddRecLoop)) { + LIOps.push_back(Ops[i]); + Ops.erase(Ops.begin()+i); + --i; --e; + } + + // If we found some loop invariants, fold them into the recurrence. + if (!LIOps.empty()) { + // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step} + LIOps.push_back(AddRec->getStart()); + + SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(), + AddRec->op_end()); + AddRecOps[0] = getAddExpr(LIOps); + + // It's tempting to propagate NUW/NSW flags here, but nuw/nsw addition + // is not associative so this isn't necessarily safe. + const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop); + + // If all of the other operands were loop invariant, we are done. + if (Ops.size() == 1) return NewRec; + + // Otherwise, add the folded AddRec by the non-liv parts. + for (unsigned i = 0;; ++i) + if (Ops[i] == AddRec) { + Ops[i] = NewRec; + break; + } + return getAddExpr(Ops); + } + + // Okay, if there weren't any loop invariants to be folded, check to see if + // there are multiple AddRec's with the same loop induction variable being + // added together. If so, we can fold them. + for (unsigned OtherIdx = Idx+1; + OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) + if (OtherIdx != Idx) { + const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); + if (AddRecLoop == OtherAddRec->getLoop()) { + // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D} + SmallVector<const SCEV *, 4> NewOps(AddRec->op_begin(), + AddRec->op_end()); + for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) { + if (i >= NewOps.size()) { + NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i, + OtherAddRec->op_end()); + break; + } + NewOps[i] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i)); + } + const SCEV *NewAddRec = getAddRecExpr(NewOps, AddRecLoop); + + if (Ops.size() == 2) return NewAddRec; + + Ops.erase(Ops.begin()+Idx); + Ops.erase(Ops.begin()+OtherIdx-1); + Ops.push_back(NewAddRec); + return getAddExpr(Ops); + } + } + + // Otherwise couldn't fold anything into this recurrence. Move onto the + // next one. + } + + // Okay, it looks like we really DO need an add expr. Check to see if we + // already have one, otherwise create a new one. + FoldingSetNodeID ID; + ID.AddInteger(scAddExpr); + ID.AddInteger(Ops.size()); + for (unsigned i = 0, e = Ops.size(); i != e; ++i) + ID.AddPointer(Ops[i]); + void *IP = 0; + SCEVAddExpr *S = + static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); + if (!S) { + const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); + std::uninitialized_copy(Ops.begin(), Ops.end(), O); + S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator), + O, Ops.size()); + UniqueSCEVs.InsertNode(S, IP); + } + if (HasNUW) S->setHasNoUnsignedWrap(true); + if (HasNSW) S->setHasNoSignedWrap(true); + return S; +} + +/// getMulExpr - Get a canonical multiply expression, or something simpler if +/// possible. +const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops, + bool HasNUW, bool HasNSW) { + assert(!Ops.empty() && "Cannot get empty mul!"); + if (Ops.size() == 1) return Ops[0]; +#ifndef NDEBUG + for (unsigned i = 1, e = Ops.size(); i != e; ++i) + assert(getEffectiveSCEVType(Ops[i]->getType()) == + getEffectiveSCEVType(Ops[0]->getType()) && + "SCEVMulExpr operand types don't match!"); +#endif + + // If HasNSW is true and all the operands are non-negative, infer HasNUW. + if (!HasNUW && HasNSW) { + bool All = true; + for (unsigned i = 0, e = Ops.size(); i != e; ++i) + if (!isKnownNonNegative(Ops[i])) { + All = false; + break; + } + if (All) HasNUW = true; + } + + // Sort by complexity, this groups all similar expression types together. + GroupByComplexity(Ops, LI); + + // If there are any constants, fold them together. + unsigned Idx = 0; + if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { + + // C1*(C2+V) -> C1*C2 + C1*V + if (Ops.size() == 2) + if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) + if (Add->getNumOperands() == 2 && + isa<SCEVConstant>(Add->getOperand(0))) + return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)), + getMulExpr(LHSC, Add->getOperand(1))); + + ++Idx; + while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { + // We found two constants, fold them together! + ConstantInt *Fold = ConstantInt::get(getContext(), + LHSC->getValue()->getValue() * + RHSC->getValue()->getValue()); + Ops[0] = getConstant(Fold); + Ops.erase(Ops.begin()+1); // Erase the folded element + if (Ops.size() == 1) return Ops[0]; + LHSC = cast<SCEVConstant>(Ops[0]); + } + + // If we are left with a constant one being multiplied, strip it off. + if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) { + Ops.erase(Ops.begin()); + --Idx; + } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { + // If we have a multiply of zero, it will always be zero. + return Ops[0]; + } else if (Ops[0]->isAllOnesValue()) { + // If we have a mul by -1 of an add, try distributing the -1 among the + // add operands. + if (Ops.size() == 2) + if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) { + SmallVector<const SCEV *, 4> NewOps; + bool AnyFolded = false; + for (SCEVAddRecExpr::op_iterator I = Add->op_begin(), E = Add->op_end(); + I != E; ++I) { + const SCEV *Mul = getMulExpr(Ops[0], *I); + if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true; + NewOps.push_back(Mul); + } + if (AnyFolded) + return getAddExpr(NewOps); + } + } + + if (Ops.size() == 1) + return Ops[0]; + } + + // Skip over the add expression until we get to a multiply. + while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) + ++Idx; + + // If there are mul operands inline them all into this expression. + if (Idx < Ops.size()) { + bool DeletedMul = false; + while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) { + // If we have an mul, expand the mul operands onto the end of the operands + // list. + Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end()); + Ops.erase(Ops.begin()+Idx); + DeletedMul = true; + } + + // If we deleted at least one mul, we added operands to the end of the list, + // and they are not necessarily sorted. Recurse to resort and resimplify + // any operands we just acquired. + if (DeletedMul) + return getMulExpr(Ops); + } + + // If there are any add recurrences in the operands list, see if any other + // added values are loop invariant. If so, we can fold them into the + // recurrence. + while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr) + ++Idx; + + // Scan over all recurrences, trying to fold loop invariants into them. + for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { + // Scan all of the other operands to this mul and add them to the vector if + // they are loop invariant w.r.t. the recurrence. + SmallVector<const SCEV *, 8> LIOps; + const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); + for (unsigned i = 0, e = Ops.size(); i != e; ++i) + if (Ops[i]->isLoopInvariant(AddRec->getLoop())) { + LIOps.push_back(Ops[i]); + Ops.erase(Ops.begin()+i); + --i; --e; + } + + // If we found some loop invariants, fold them into the recurrence. + if (!LIOps.empty()) { + // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step} + SmallVector<const SCEV *, 4> NewOps; + NewOps.reserve(AddRec->getNumOperands()); + if (LIOps.size() == 1) { + const SCEV *Scale = LIOps[0]; + for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) + NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i))); + } else { + for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { + SmallVector<const SCEV *, 4> MulOps(LIOps.begin(), LIOps.end()); + MulOps.push_back(AddRec->getOperand(i)); + NewOps.push_back(getMulExpr(MulOps)); + } + } + + // It's tempting to propagate the NSW flag here, but nsw multiplication + // is not associative so this isn't necessarily safe. + const SCEV *NewRec = getAddRecExpr(NewOps, AddRec->getLoop(), + HasNUW && AddRec->hasNoUnsignedWrap(), + /*HasNSW=*/false); + + // If all of the other operands were loop invariant, we are done. + if (Ops.size() == 1) return NewRec; + + // Otherwise, multiply the folded AddRec by the non-liv parts. + for (unsigned i = 0;; ++i) + if (Ops[i] == AddRec) { + Ops[i] = NewRec; + break; + } + return getMulExpr(Ops); + } + + // Okay, if there weren't any loop invariants to be folded, check to see if + // there are multiple AddRec's with the same loop induction variable being + // multiplied together. If so, we can fold them. + for (unsigned OtherIdx = Idx+1; + OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx) + if (OtherIdx != Idx) { + const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]); + if (AddRec->getLoop() == OtherAddRec->getLoop()) { + // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D} + const SCEVAddRecExpr *F = AddRec, *G = OtherAddRec; + const SCEV *NewStart = getMulExpr(F->getStart(), + G->getStart()); + const SCEV *B = F->getStepRecurrence(*this); + const SCEV *D = G->getStepRecurrence(*this); + const SCEV *NewStep = getAddExpr(getMulExpr(F, D), + getMulExpr(G, B), + getMulExpr(B, D)); + const SCEV *NewAddRec = getAddRecExpr(NewStart, NewStep, + F->getLoop()); + if (Ops.size() == 2) return NewAddRec; + + Ops.erase(Ops.begin()+Idx); + Ops.erase(Ops.begin()+OtherIdx-1); + Ops.push_back(NewAddRec); + return getMulExpr(Ops); + } + } + + // Otherwise couldn't fold anything into this recurrence. Move onto the + // next one. + } + + // Okay, it looks like we really DO need an mul expr. Check to see if we + // already have one, otherwise create a new one. + FoldingSetNodeID ID; + ID.AddInteger(scMulExpr); + ID.AddInteger(Ops.size()); + for (unsigned i = 0, e = Ops.size(); i != e; ++i) + ID.AddPointer(Ops[i]); + void *IP = 0; + SCEVMulExpr *S = + static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); + if (!S) { + const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); + std::uninitialized_copy(Ops.begin(), Ops.end(), O); + S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator), + O, Ops.size()); + UniqueSCEVs.InsertNode(S, IP); + } + if (HasNUW) S->setHasNoUnsignedWrap(true); + if (HasNSW) S->setHasNoSignedWrap(true); + return S; +} + +/// getUDivExpr - Get a canonical unsigned division expression, or something +/// simpler if possible. +const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS, + const SCEV *RHS) { + assert(getEffectiveSCEVType(LHS->getType()) == + getEffectiveSCEVType(RHS->getType()) && + "SCEVUDivExpr operand types don't match!"); + + if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { + if (RHSC->getValue()->equalsInt(1)) + return LHS; // X udiv 1 --> x + // If the denominator is zero, the result of the udiv is undefined. Don't + // try to analyze it, because the resolution chosen here may differ from + // the resolution chosen in other parts of the compiler. + if (!RHSC->getValue()->isZero()) { + // Determine if the division can be folded into the operands of + // its operands. + // TODO: Generalize this to non-constants by using known-bits information. + const Type *Ty = LHS->getType(); + unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros(); + unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ; + // For non-power-of-two values, effectively round the value up to the + // nearest power of two. + if (!RHSC->getValue()->getValue().isPowerOf2()) + ++MaxShiftAmt; + const IntegerType *ExtTy = + IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt); + // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded. + if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS)) + if (const SCEVConstant *Step = + dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) + if (!Step->getValue()->getValue() + .urem(RHSC->getValue()->getValue()) && + getZeroExtendExpr(AR, ExtTy) == + getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy), + getZeroExtendExpr(Step, ExtTy), + AR->getLoop())) { + SmallVector<const SCEV *, 4> Operands; + for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i) + Operands.push_back(getUDivExpr(AR->getOperand(i), RHS)); + return getAddRecExpr(Operands, AR->getLoop()); + } + // (A*B)/C --> A*(B/C) if safe and B/C can be folded. + if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) { + SmallVector<const SCEV *, 4> Operands; + for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) + Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy)); + if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands)) + // Find an operand that's safely divisible. + for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) { + const SCEV *Op = M->getOperand(i); + const SCEV *Div = getUDivExpr(Op, RHSC); + if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) { + Operands = SmallVector<const SCEV *, 4>(M->op_begin(), + M->op_end()); + Operands[i] = Div; + return getMulExpr(Operands); + } + } + } + // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded. + if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(LHS)) { + SmallVector<const SCEV *, 4> Operands; + for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) + Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy)); + if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) { + Operands.clear(); + for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) { + const SCEV *Op = getUDivExpr(A->getOperand(i), RHS); + if (isa<SCEVUDivExpr>(Op) || + getMulExpr(Op, RHS) != A->getOperand(i)) + break; + Operands.push_back(Op); + } + if (Operands.size() == A->getNumOperands()) + return getAddExpr(Operands); + } + } + + // Fold if both operands are constant. + if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { + Constant *LHSCV = LHSC->getValue(); + Constant *RHSCV = RHSC->getValue(); + return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV, + RHSCV))); + } + } + } + + FoldingSetNodeID ID; + ID.AddInteger(scUDivExpr); + ID.AddPointer(LHS); + ID.AddPointer(RHS); + void *IP = 0; + if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; + SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator), + LHS, RHS); + UniqueSCEVs.InsertNode(S, IP); + return S; +} + + +/// getAddRecExpr - Get an add recurrence expression for the specified loop. +/// Simplify the expression as much as possible. +const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, + const SCEV *Step, const Loop *L, + bool HasNUW, bool HasNSW) { + SmallVector<const SCEV *, 4> Operands; + Operands.push_back(Start); + if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step)) + if (StepChrec->getLoop() == L) { + Operands.insert(Operands.end(), StepChrec->op_begin(), + StepChrec->op_end()); + return getAddRecExpr(Operands, L); + } + + Operands.push_back(Step); + return getAddRecExpr(Operands, L, HasNUW, HasNSW); +} + +/// getAddRecExpr - Get an add recurrence expression for the specified loop. +/// Simplify the expression as much as possible. +const SCEV * +ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands, + const Loop *L, + bool HasNUW, bool HasNSW) { + if (Operands.size() == 1) return Operands[0]; +#ifndef NDEBUG + for (unsigned i = 1, e = Operands.size(); i != e; ++i) + assert(getEffectiveSCEVType(Operands[i]->getType()) == + getEffectiveSCEVType(Operands[0]->getType()) && + "SCEVAddRecExpr operand types don't match!"); +#endif + + if (Operands.back()->isZero()) { + Operands.pop_back(); + return getAddRecExpr(Operands, L, HasNUW, HasNSW); // {X,+,0} --> X + } + + // It's tempting to want to call getMaxBackedgeTakenCount count here and + // use that information to infer NUW and NSW flags. However, computing a + // BE count requires calling getAddRecExpr, so we may not yet have a + // meaningful BE count at this point (and if we don't, we'd be stuck + // with a SCEVCouldNotCompute as the cached BE count). + + // If HasNSW is true and all the operands are non-negative, infer HasNUW. + if (!HasNUW && HasNSW) { + bool All = true; + for (unsigned i = 0, e = Operands.size(); i != e; ++i) + if (!isKnownNonNegative(Operands[i])) { + All = false; + break; + } + if (All) HasNUW = true; + } + + // Canonicalize nested AddRecs in by nesting them in order of loop depth. + if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) { + const Loop *NestedLoop = NestedAR->getLoop(); + if (L->contains(NestedLoop->getHeader()) ? + (L->getLoopDepth() < NestedLoop->getLoopDepth()) : + (!NestedLoop->contains(L->getHeader()) && + DT->dominates(L->getHeader(), NestedLoop->getHeader()))) { + SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(), + NestedAR->op_end()); + Operands[0] = NestedAR->getStart(); + // AddRecs require their operands be loop-invariant with respect to their + // loops. Don't perform this transformation if it would break this + // requirement. + bool AllInvariant = true; + for (unsigned i = 0, e = Operands.size(); i != e; ++i) + if (!Operands[i]->isLoopInvariant(L)) { + AllInvariant = false; + break; + } + if (AllInvariant) { + NestedOperands[0] = getAddRecExpr(Operands, L); + AllInvariant = true; + for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i) + if (!NestedOperands[i]->isLoopInvariant(NestedLoop)) { + AllInvariant = false; + break; + } + if (AllInvariant) + // Ok, both add recurrences are valid after the transformation. + return getAddRecExpr(NestedOperands, NestedLoop, HasNUW, HasNSW); + } + // Reset Operands to its original state. + Operands[0] = NestedAR; + } + } + + // Okay, it looks like we really DO need an addrec expr. Check to see if we + // already have one, otherwise create a new one. + FoldingSetNodeID ID; + ID.AddInteger(scAddRecExpr); + ID.AddInteger(Operands.size()); + for (unsigned i = 0, e = Operands.size(); i != e; ++i) + ID.AddPointer(Operands[i]); + ID.AddPointer(L); + void *IP = 0; + SCEVAddRecExpr *S = + static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); + if (!S) { + const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size()); + std::uninitialized_copy(Operands.begin(), Operands.end(), O); + S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator), + O, Operands.size(), L); + UniqueSCEVs.InsertNode(S, IP); + } + if (HasNUW) S->setHasNoUnsignedWrap(true); + if (HasNSW) S->setHasNoSignedWrap(true); + return S; +} + +const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS, + const SCEV *RHS) { + SmallVector<const SCEV *, 2> Ops; + Ops.push_back(LHS); + Ops.push_back(RHS); + return getSMaxExpr(Ops); +} + +const SCEV * +ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { + assert(!Ops.empty() && "Cannot get empty smax!"); + if (Ops.size() == 1) return Ops[0]; +#ifndef NDEBUG + for (unsigned i = 1, e = Ops.size(); i != e; ++i) + assert(getEffectiveSCEVType(Ops[i]->getType()) == + getEffectiveSCEVType(Ops[0]->getType()) && + "SCEVSMaxExpr operand types don't match!"); +#endif + + // Sort by complexity, this groups all similar expression types together. + GroupByComplexity(Ops, LI); + + // If there are any constants, fold them together. + unsigned Idx = 0; + if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { + ++Idx; + assert(Idx < Ops.size()); + while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { + // We found two constants, fold them together! + ConstantInt *Fold = ConstantInt::get(getContext(), + APIntOps::smax(LHSC->getValue()->getValue(), + RHSC->getValue()->getValue())); + Ops[0] = getConstant(Fold); + Ops.erase(Ops.begin()+1); // Erase the folded element + if (Ops.size() == 1) return Ops[0]; + LHSC = cast<SCEVConstant>(Ops[0]); + } + + // If we are left with a constant minimum-int, strip it off. + if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) { + Ops.erase(Ops.begin()); + --Idx; + } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) { + // If we have an smax with a constant maximum-int, it will always be + // maximum-int. + return Ops[0]; + } + + if (Ops.size() == 1) return Ops[0]; + } + + // Find the first SMax + while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr) + ++Idx; + + // Check to see if one of the operands is an SMax. If so, expand its operands + // onto our operand list, and recurse to simplify. + if (Idx < Ops.size()) { + bool DeletedSMax = false; + while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) { + Ops.insert(Ops.end(), SMax->op_begin(), SMax->op_end()); + Ops.erase(Ops.begin()+Idx); + DeletedSMax = true; + } + + if (DeletedSMax) + return getSMaxExpr(Ops); + } + + // Okay, check to see if the same value occurs in the operand list twice. If + // so, delete one. Since we sorted the list, these values are required to + // be adjacent. + for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) + // X smax Y smax Y --> X smax Y + // X smax Y --> X, if X is always greater than Y + if (Ops[i] == Ops[i+1] || + isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) { + Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2); + --i; --e; + } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) { + Ops.erase(Ops.begin()+i, Ops.begin()+i+1); + --i; --e; + } + + if (Ops.size() == 1) return Ops[0]; + + assert(!Ops.empty() && "Reduced smax down to nothing!"); + + // Okay, it looks like we really DO need an smax expr. Check to see if we + // already have one, otherwise create a new one. + FoldingSetNodeID ID; + ID.AddInteger(scSMaxExpr); + ID.AddInteger(Ops.size()); + for (unsigned i = 0, e = Ops.size(); i != e; ++i) + ID.AddPointer(Ops[i]); + void *IP = 0; + if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; + const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); + std::uninitialized_copy(Ops.begin(), Ops.end(), O); + SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator), + O, Ops.size()); + UniqueSCEVs.InsertNode(S, IP); + return S; +} + +const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS, + const SCEV *RHS) { + SmallVector<const SCEV *, 2> Ops; + Ops.push_back(LHS); + Ops.push_back(RHS); + return getUMaxExpr(Ops); +} + +const SCEV * +ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { + assert(!Ops.empty() && "Cannot get empty umax!"); + if (Ops.size() == 1) return Ops[0]; +#ifndef NDEBUG + for (unsigned i = 1, e = Ops.size(); i != e; ++i) + assert(getEffectiveSCEVType(Ops[i]->getType()) == + getEffectiveSCEVType(Ops[0]->getType()) && + "SCEVUMaxExpr operand types don't match!"); +#endif + + // Sort by complexity, this groups all similar expression types together. + GroupByComplexity(Ops, LI); + + // If there are any constants, fold them together. + unsigned Idx = 0; + if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { + ++Idx; + assert(Idx < Ops.size()); + while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { + // We found two constants, fold them together! + ConstantInt *Fold = ConstantInt::get(getContext(), + APIntOps::umax(LHSC->getValue()->getValue(), + RHSC->getValue()->getValue())); + Ops[0] = getConstant(Fold); + Ops.erase(Ops.begin()+1); // Erase the folded element + if (Ops.size() == 1) return Ops[0]; + LHSC = cast<SCEVConstant>(Ops[0]); + } + + // If we are left with a constant minimum-int, strip it off. + if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) { + Ops.erase(Ops.begin()); + --Idx; + } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) { + // If we have an umax with a constant maximum-int, it will always be + // maximum-int. + return Ops[0]; + } + + if (Ops.size() == 1) return Ops[0]; + } + + // Find the first UMax + while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr) + ++Idx; + + // Check to see if one of the operands is a UMax. If so, expand its operands + // onto our operand list, and recurse to simplify. + if (Idx < Ops.size()) { + bool DeletedUMax = false; + while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) { + Ops.insert(Ops.end(), UMax->op_begin(), UMax->op_end()); + Ops.erase(Ops.begin()+Idx); + DeletedUMax = true; + } + + if (DeletedUMax) + return getUMaxExpr(Ops); + } + + // Okay, check to see if the same value occurs in the operand list twice. If + // so, delete one. Since we sorted the list, these values are required to + // be adjacent. + for (unsigned i = 0, e = Ops.size()-1; i != e; ++i) + // X umax Y umax Y --> X umax Y + // X umax Y --> X, if X is always greater than Y + if (Ops[i] == Ops[i+1] || + isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) { + Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2); + --i; --e; + } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) { + Ops.erase(Ops.begin()+i, Ops.begin()+i+1); + --i; --e; + } + + if (Ops.size() == 1) return Ops[0]; + + assert(!Ops.empty() && "Reduced umax down to nothing!"); + + // Okay, it looks like we really DO need a umax expr. Check to see if we + // already have one, otherwise create a new one. + FoldingSetNodeID ID; + ID.AddInteger(scUMaxExpr); + ID.AddInteger(Ops.size()); + for (unsigned i = 0, e = Ops.size(); i != e; ++i) + ID.AddPointer(Ops[i]); + void *IP = 0; + if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; + const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); + std::uninitialized_copy(Ops.begin(), Ops.end(), O); + SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator), + O, Ops.size()); + UniqueSCEVs.InsertNode(S, IP); + return S; +} + +const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS, + const SCEV *RHS) { + // ~smax(~x, ~y) == smin(x, y). + return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); +} + +const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS, + const SCEV *RHS) { + // ~umax(~x, ~y) == umin(x, y) + return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS))); +} + +const SCEV *ScalarEvolution::getSizeOfExpr(const Type *AllocTy) { + // If we have TargetData, we can bypass creating a target-independent + // constant expression and then folding it back into a ConstantInt. + // This is just a compile-time optimization. + if (TD) + return getConstant(TD->getIntPtrType(getContext()), + TD->getTypeAllocSize(AllocTy)); + + Constant *C = ConstantExpr::getSizeOf(AllocTy); + if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) + C = ConstantFoldConstantExpression(CE, TD); + const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy)); + return getTruncateOrZeroExtend(getSCEV(C), Ty); +} + +const SCEV *ScalarEvolution::getAlignOfExpr(const Type *AllocTy) { + Constant *C = ConstantExpr::getAlignOf(AllocTy); + if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) + C = ConstantFoldConstantExpression(CE, TD); + const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy)); + return getTruncateOrZeroExtend(getSCEV(C), Ty); +} + +const SCEV *ScalarEvolution::getOffsetOfExpr(const StructType *STy, + unsigned FieldNo) { + // If we have TargetData, we can bypass creating a target-independent + // constant expression and then folding it back into a ConstantInt. + // This is just a compile-time optimization. + if (TD) + return getConstant(TD->getIntPtrType(getContext()), + TD->getStructLayout(STy)->getElementOffset(FieldNo)); + + Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo); + if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) + C = ConstantFoldConstantExpression(CE, TD); + const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy)); + return getTruncateOrZeroExtend(getSCEV(C), Ty); +} + +const SCEV *ScalarEvolution::getOffsetOfExpr(const Type *CTy, + Constant *FieldNo) { + Constant *C = ConstantExpr::getOffsetOf(CTy, FieldNo); + if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C)) + C = ConstantFoldConstantExpression(CE, TD); + const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(CTy)); + return getTruncateOrZeroExtend(getSCEV(C), Ty); +} + +const SCEV *ScalarEvolution::getUnknown(Value *V) { + // Don't attempt to do anything other than create a SCEVUnknown object + // here. createSCEV only calls getUnknown after checking for all other + // interesting possibilities, and any other code that calls getUnknown + // is doing so in order to hide a value from SCEV canonicalization. + + FoldingSetNodeID ID; + ID.AddInteger(scUnknown); + ID.AddPointer(V); + void *IP = 0; + if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; + SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V); + UniqueSCEVs.InsertNode(S, IP); + return S; +} + +//===----------------------------------------------------------------------===// +// Basic SCEV Analysis and PHI Idiom Recognition Code +// + +/// isSCEVable - Test if values of the given type are analyzable within +/// the SCEV framework. This primarily includes integer types, and it +/// can optionally include pointer types if the ScalarEvolution class +/// has access to target-specific information. +bool ScalarEvolution::isSCEVable(const Type *Ty) const { + // Integers and pointers are always SCEVable. + return Ty->isIntegerTy() || Ty->isPointerTy(); +} + +/// getTypeSizeInBits - Return the size in bits of the specified type, +/// for which isSCEVable must return true. +uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const { + assert(isSCEVable(Ty) && "Type is not SCEVable!"); + + // If we have a TargetData, use it! + if (TD) + return TD->getTypeSizeInBits(Ty); + + // Integer types have fixed sizes. + if (Ty->isIntegerTy()) + return Ty->getPrimitiveSizeInBits(); + + // The only other support type is pointer. Without TargetData, conservatively + // assume pointers are 64-bit. + assert(Ty->isPointerTy() && "isSCEVable permitted a non-SCEVable type!"); + return 64; +} + +/// getEffectiveSCEVType - Return a type with the same bitwidth as +/// the given type and which represents how SCEV will treat the given +/// type, for which isSCEVable must return true. For pointer types, +/// this is the pointer-sized integer type. +const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const { + assert(isSCEVable(Ty) && "Type is not SCEVable!"); + + if (Ty->isIntegerTy()) + return Ty; + + // The only other support type is pointer. + assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!"); + if (TD) return TD->getIntPtrType(getContext()); + + // Without TargetData, conservatively assume pointers are 64-bit. + return Type::getInt64Ty(getContext()); +} + +const SCEV *ScalarEvolution::getCouldNotCompute() { + return &CouldNotCompute; +} + +/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the +/// expression and create a new one. +const SCEV *ScalarEvolution::getSCEV(Value *V) { + assert(isSCEVable(V->getType()) && "Value is not SCEVable!"); + + std::map<SCEVCallbackVH, const SCEV *>::iterator I = Scalars.find(V); + if (I != Scalars.end()) return I->second; + const SCEV *S = createSCEV(V); + Scalars.insert(std::make_pair(SCEVCallbackVH(V, this), S)); + return S; +} + +/// getIntegerSCEV - Given a SCEVable type, create a constant for the +/// specified signed integer value and return a SCEV for the constant. +const SCEV *ScalarEvolution::getIntegerSCEV(int64_t Val, const Type *Ty) { + const IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty)); + return getConstant(ConstantInt::get(ITy, Val)); +} + +/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V +/// +const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) { + if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) + return getConstant( + cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue()))); + + const Type *Ty = V->getType(); + Ty = getEffectiveSCEVType(Ty); + return getMulExpr(V, + getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)))); +} + +/// getNotSCEV - Return a SCEV corresponding to ~V = -1-V +const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) { + if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V)) + return getConstant( + cast<ConstantInt>(ConstantExpr::getNot(VC->getValue()))); + + const Type *Ty = V->getType(); + Ty = getEffectiveSCEVType(Ty); + const SCEV *AllOnes = + getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))); + return getMinusSCEV(AllOnes, V); +} + +/// getMinusSCEV - Return a SCEV corresponding to LHS - RHS. +/// +const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, + const SCEV *RHS) { + // X - Y --> X + -Y + return getAddExpr(LHS, getNegativeSCEV(RHS)); +} + +/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the +/// input value to the specified type. If the type must be extended, it is zero +/// extended. +const SCEV * +ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, + const Type *Ty) { + const Type *SrcTy = V->getType(); + assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && + (Ty->isIntegerTy() || Ty->isPointerTy()) && + "Cannot truncate or zero extend with non-integer arguments!"); + if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) + return V; // No conversion + if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) + return getTruncateExpr(V, Ty); + return getZeroExtendExpr(V, Ty); +} + +/// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the +/// input value to the specified type. If the type must be extended, it is sign +/// extended. +const SCEV * +ScalarEvolution::getTruncateOrSignExtend(const SCEV *V, + const Type *Ty) { + const Type *SrcTy = V->getType(); + assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && + (Ty->isIntegerTy() || Ty->isPointerTy()) && + "Cannot truncate or zero extend with non-integer arguments!"); + if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) + return V; // No conversion + if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty)) + return getTruncateExpr(V, Ty); + return getSignExtendExpr(V, Ty); +} + +/// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the +/// input value to the specified type. If the type must be extended, it is zero +/// extended. The conversion must not be narrowing. +const SCEV * +ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, const Type *Ty) { + const Type *SrcTy = V->getType(); + assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && + (Ty->isIntegerTy() || Ty->isPointerTy()) && + "Cannot noop or zero extend with non-integer arguments!"); + assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && + "getNoopOrZeroExtend cannot truncate!"); + if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) + return V; // No conversion + return getZeroExtendExpr(V, Ty); +} + +/// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the +/// input value to the specified type. If the type must be extended, it is sign +/// extended. The conversion must not be narrowing. +const SCEV * +ScalarEvolution::getNoopOrSignExtend(const SCEV *V, const Type *Ty) { + const Type *SrcTy = V->getType(); + assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && + (Ty->isIntegerTy() || Ty->isPointerTy()) && + "Cannot noop or sign extend with non-integer arguments!"); + assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && + "getNoopOrSignExtend cannot truncate!"); + if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) + return V; // No conversion + return getSignExtendExpr(V, Ty); +} + +/// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of +/// the input value to the specified type. If the type must be extended, +/// it is extended with unspecified bits. The conversion must not be +/// narrowing. +const SCEV * +ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, const Type *Ty) { + const Type *SrcTy = V->getType(); + assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && + (Ty->isIntegerTy() || Ty->isPointerTy()) && + "Cannot noop or any extend with non-integer arguments!"); + assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) && + "getNoopOrAnyExtend cannot truncate!"); + if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) + return V; // No conversion + return getAnyExtendExpr(V, Ty); +} + +/// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the +/// input value to the specified type. The conversion must not be widening. +const SCEV * +ScalarEvolution::getTruncateOrNoop(const SCEV *V, const Type *Ty) { + const Type *SrcTy = V->getType(); + assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) && + (Ty->isIntegerTy() || Ty->isPointerTy()) && + "Cannot truncate or noop with non-integer arguments!"); + assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) && + "getTruncateOrNoop cannot extend!"); + if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty)) + return V; // No conversion + return getTruncateExpr(V, Ty); +} + +/// getUMaxFromMismatchedTypes - Promote the operands to the wider of +/// the types using zero-extension, and then perform a umax operation +/// with them. +const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS, + const SCEV *RHS) { + const SCEV *PromotedLHS = LHS; + const SCEV *PromotedRHS = RHS; + + if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) + PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); + else + PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); + + return getUMaxExpr(PromotedLHS, PromotedRHS); +} + +/// getUMinFromMismatchedTypes - Promote the operands to the wider of +/// the types using zero-extension, and then perform a umin operation +/// with them. +const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS, + const SCEV *RHS) { + const SCEV *PromotedLHS = LHS; + const SCEV *PromotedRHS = RHS; + + if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType())) + PromotedRHS = getZeroExtendExpr(RHS, LHS->getType()); + else + PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType()); + + return getUMinExpr(PromotedLHS, PromotedRHS); +} + +/// PushDefUseChildren - Push users of the given Instruction +/// onto the given Worklist. +static void +PushDefUseChildren(Instruction *I, + SmallVectorImpl<Instruction *> &Worklist) { + // Push the def-use children onto the Worklist stack. + for (Value::use_iterator UI = I->use_begin(), UE = I->use_end(); + UI != UE; ++UI) + Worklist.push_back(cast<Instruction>(UI)); +} + +/// ForgetSymbolicValue - This looks up computed SCEV values for all +/// instructions that depend on the given instruction and removes them from +/// the Scalars map if they reference SymName. This is used during PHI +/// resolution. +void +ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) { + SmallVector<Instruction *, 16> Worklist; + PushDefUseChildren(PN, Worklist); + + SmallPtrSet<Instruction *, 8> Visited; + Visited.insert(PN); + while (!Worklist.empty()) { + Instruction *I = Worklist.pop_back_val(); + if (!Visited.insert(I)) continue; + + std::map<SCEVCallbackVH, const SCEV *>::iterator It = + Scalars.find(static_cast<Value *>(I)); + if (It != Scalars.end()) { + // Short-circuit the def-use traversal if the symbolic name + // ceases to appear in expressions. + if (It->second != SymName && !It->second->hasOperand(SymName)) + continue; + + // SCEVUnknown for a PHI either means that it has an unrecognized + // structure, it's a PHI that's in the progress of being computed + // by createNodeForPHI, or it's a single-value PHI. In the first case, + // additional loop trip count information isn't going to change anything. + // In the second case, createNodeForPHI will perform the necessary + // updates on its own when it gets to that point. In the third, we do + // want to forget the SCEVUnknown. + if (!isa<PHINode>(I) || + !isa<SCEVUnknown>(It->second) || + (I != PN && It->second == SymName)) { + ValuesAtScopes.erase(It->second); + Scalars.erase(It); + } + } + + PushDefUseChildren(I, Worklist); + } +} + +/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in +/// a loop header, making it a potential recurrence, or it doesn't. +/// +const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) { + if (const Loop *L = LI->getLoopFor(PN->getParent())) + if (L->getHeader() == PN->getParent()) { + // The loop may have multiple entrances or multiple exits; we can analyze + // this phi as an addrec if it has a unique entry value and a unique + // backedge value. + Value *BEValueV = 0, *StartValueV = 0; + for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) { + Value *V = PN->getIncomingValue(i); + if (L->contains(PN->getIncomingBlock(i))) { + if (!BEValueV) { + BEValueV = V; + } else if (BEValueV != V) { + BEValueV = 0; + break; + } + } else if (!StartValueV) { + StartValueV = V; + } else if (StartValueV != V) { + StartValueV = 0; + break; + } + } + if (BEValueV && StartValueV) { + // While we are analyzing this PHI node, handle its value symbolically. + const SCEV *SymbolicName = getUnknown(PN); + assert(Scalars.find(PN) == Scalars.end() && + "PHI node already processed?"); + Scalars.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName)); + + // Using this symbolic name for the PHI, analyze the value coming around + // the back-edge. + const SCEV *BEValue = getSCEV(BEValueV); + + // NOTE: If BEValue is loop invariant, we know that the PHI node just + // has a special value for the first iteration of the loop. + + // If the value coming around the backedge is an add with the symbolic + // value we just inserted, then we found a simple induction variable! + if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) { + // If there is a single occurrence of the symbolic value, replace it + // with a recurrence. + unsigned FoundIndex = Add->getNumOperands(); + for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) + if (Add->getOperand(i) == SymbolicName) + if (FoundIndex == e) { + FoundIndex = i; + break; + } + + if (FoundIndex != Add->getNumOperands()) { + // Create an add with everything but the specified operand. + SmallVector<const SCEV *, 8> Ops; + for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) + if (i != FoundIndex) + Ops.push_back(Add->getOperand(i)); + const SCEV *Accum = getAddExpr(Ops); + + // This is not a valid addrec if the step amount is varying each + // loop iteration, but is not itself an addrec in this loop. + if (Accum->isLoopInvariant(L) || + (isa<SCEVAddRecExpr>(Accum) && + cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) { + bool HasNUW = false; + bool HasNSW = false; + + // If the increment doesn't overflow, then neither the addrec nor + // the post-increment will overflow. + if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) { + if (OBO->hasNoUnsignedWrap()) + HasNUW = true; + if (OBO->hasNoSignedWrap()) + HasNSW = true; + } + + const SCEV *StartVal = getSCEV(StartValueV); + const SCEV *PHISCEV = + getAddRecExpr(StartVal, Accum, L, HasNUW, HasNSW); + + // Since the no-wrap flags are on the increment, they apply to the + // post-incremented value as well. + if (Accum->isLoopInvariant(L)) + (void)getAddRecExpr(getAddExpr(StartVal, Accum), + Accum, L, HasNUW, HasNSW); + + // Okay, for the entire analysis of this edge we assumed the PHI + // to be symbolic. We now need to go back and purge all of the + // entries for the scalars that use the symbolic expression. + ForgetSymbolicName(PN, SymbolicName); + Scalars[SCEVCallbackVH(PN, this)] = PHISCEV; + return PHISCEV; + } + } + } else if (const SCEVAddRecExpr *AddRec = + dyn_cast<SCEVAddRecExpr>(BEValue)) { + // Otherwise, this could be a loop like this: + // i = 0; for (j = 1; ..; ++j) { .... i = j; } + // In this case, j = {1,+,1} and BEValue is j. + // Because the other in-value of i (0) fits the evolution of BEValue + // i really is an addrec evolution. + if (AddRec->getLoop() == L && AddRec->isAffine()) { + const SCEV *StartVal = getSCEV(StartValueV); + + // If StartVal = j.start - j.stride, we can use StartVal as the + // initial step of the addrec evolution. + if (StartVal == getMinusSCEV(AddRec->getOperand(0), + AddRec->getOperand(1))) { + const SCEV *PHISCEV = + getAddRecExpr(StartVal, AddRec->getOperand(1), L); + + // Okay, for the entire analysis of this edge we assumed the PHI + // to be symbolic. We now need to go back and purge all of the + // entries for the scalars that use the symbolic expression. + ForgetSymbolicName(PN, SymbolicName); + Scalars[SCEVCallbackVH(PN, this)] = PHISCEV; + return PHISCEV; + } + } + } + } + } + + // If the PHI has a single incoming value, follow that value, unless the + // PHI's incoming blocks are in a different loop, in which case doing so + // risks breaking LCSSA form. Instcombine would normally zap these, but + // it doesn't have DominatorTree information, so it may miss cases. + if (Value *V = PN->hasConstantValue(DT)) { + bool AllSameLoop = true; + Loop *PNLoop = LI->getLoopFor(PN->getParent()); + for (size_t i = 0, e = PN->getNumIncomingValues(); i != e; ++i) + if (LI->getLoopFor(PN->getIncomingBlock(i)) != PNLoop) { + AllSameLoop = false; + break; + } + if (AllSameLoop) + return getSCEV(V); + } + + // If it's not a loop phi, we can't handle it yet. + return getUnknown(PN); +} + +/// createNodeForGEP - Expand GEP instructions into add and multiply +/// operations. This allows them to be analyzed by regular SCEV code. +/// +const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) { + + bool InBounds = GEP->isInBounds(); + const Type *IntPtrTy = getEffectiveSCEVType(GEP->getType()); + Value *Base = GEP->getOperand(0); + // Don't attempt to analyze GEPs over unsized objects. + if (!cast<PointerType>(Base->getType())->getElementType()->isSized()) + return getUnknown(GEP); + const SCEV *TotalOffset = getConstant(IntPtrTy, 0); + gep_type_iterator GTI = gep_type_begin(GEP); + for (GetElementPtrInst::op_iterator I = next(GEP->op_begin()), + E = GEP->op_end(); + I != E; ++I) { + Value *Index = *I; + // Compute the (potentially symbolic) offset in bytes for this index. + if (const StructType *STy = dyn_cast<StructType>(*GTI++)) { + // For a struct, add the member offset. + unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue(); + TotalOffset = getAddExpr(TotalOffset, + getOffsetOfExpr(STy, FieldNo), + /*HasNUW=*/false, /*HasNSW=*/InBounds); + } else { + // For an array, add the element offset, explicitly scaled. + const SCEV *LocalOffset = getSCEV(Index); + // Getelementptr indices are signed. + LocalOffset = getTruncateOrSignExtend(LocalOffset, IntPtrTy); + // Lower "inbounds" GEPs to NSW arithmetic. + LocalOffset = getMulExpr(LocalOffset, getSizeOfExpr(*GTI), + /*HasNUW=*/false, /*HasNSW=*/InBounds); + TotalOffset = getAddExpr(TotalOffset, LocalOffset, + /*HasNUW=*/false, /*HasNSW=*/InBounds); + } + } + return getAddExpr(getSCEV(Base), TotalOffset, + /*HasNUW=*/false, /*HasNSW=*/InBounds); +} + +/// GetMinTrailingZeros - Determine the minimum number of zero bits that S is +/// guaranteed to end in (at every loop iteration). It is, at the same time, +/// the minimum number of times S is divisible by 2. For example, given {4,+,8} +/// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S. +uint32_t +ScalarEvolution::GetMinTrailingZeros(const SCEV *S) { + if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) + return C->getValue()->getValue().countTrailingZeros(); + + if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S)) + return std::min(GetMinTrailingZeros(T->getOperand()), + (uint32_t)getTypeSizeInBits(T->getType())); + + if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) { + uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); + return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? + getTypeSizeInBits(E->getType()) : OpRes; + } + + if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) { + uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); + return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? + getTypeSizeInBits(E->getType()) : OpRes; + } + + if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) { + // The result is the min of all operands results. + uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); + for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) + MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); + return MinOpRes; + } + + if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) { + // The result is the sum of all operands results. + uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0)); + uint32_t BitWidth = getTypeSizeInBits(M->getType()); + for (unsigned i = 1, e = M->getNumOperands(); + SumOpRes != BitWidth && i != e; ++i) + SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)), + BitWidth); + return SumOpRes; + } + + if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) { + // The result is the min of all operands results. + uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); + for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) + MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); + return MinOpRes; + } + + if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) { + // The result is the min of all operands results. + uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); + for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) + MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); + return MinOpRes; + } + + if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) { + // The result is the min of all operands results. + uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); + for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) + MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); + return MinOpRes; + } + + if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { + // For a SCEVUnknown, ask ValueTracking. + unsigned BitWidth = getTypeSizeInBits(U->getType()); + APInt Mask = APInt::getAllOnesValue(BitWidth); + APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); + ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones); + return Zeros.countTrailingOnes(); + } + + // SCEVUDivExpr + return 0; +} + +/// getUnsignedRange - Determine the unsigned range for a particular SCEV. +/// +ConstantRange +ScalarEvolution::getUnsignedRange(const SCEV *S) { + + if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) + return ConstantRange(C->getValue()->getValue()); + + unsigned BitWidth = getTypeSizeInBits(S->getType()); + ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true); + + // If the value has known zeros, the maximum unsigned value will have those + // known zeros as well. + uint32_t TZ = GetMinTrailingZeros(S); + if (TZ != 0) + ConservativeResult = + ConstantRange(APInt::getMinValue(BitWidth), + APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1); + + if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) { + ConstantRange X = getUnsignedRange(Add->getOperand(0)); + for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i) + X = X.add(getUnsignedRange(Add->getOperand(i))); + return ConservativeResult.intersectWith(X); + } + + if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) { + ConstantRange X = getUnsignedRange(Mul->getOperand(0)); + for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i) + X = X.multiply(getUnsignedRange(Mul->getOperand(i))); + return ConservativeResult.intersectWith(X); + } + + if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) { + ConstantRange X = getUnsignedRange(SMax->getOperand(0)); + for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i) + X = X.smax(getUnsignedRange(SMax->getOperand(i))); + return ConservativeResult.intersectWith(X); + } + + if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) { + ConstantRange X = getUnsignedRange(UMax->getOperand(0)); + for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i) + X = X.umax(getUnsignedRange(UMax->getOperand(i))); + return ConservativeResult.intersectWith(X); + } + + if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) { + ConstantRange X = getUnsignedRange(UDiv->getLHS()); + ConstantRange Y = getUnsignedRange(UDiv->getRHS()); + return ConservativeResult.intersectWith(X.udiv(Y)); + } + + if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) { + ConstantRange X = getUnsignedRange(ZExt->getOperand()); + return ConservativeResult.intersectWith(X.zeroExtend(BitWidth)); + } + + if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) { + ConstantRange X = getUnsignedRange(SExt->getOperand()); + return ConservativeResult.intersectWith(X.signExtend(BitWidth)); + } + + if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) { + ConstantRange X = getUnsignedRange(Trunc->getOperand()); + return ConservativeResult.intersectWith(X.truncate(BitWidth)); + } + + if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) { + // If there's no unsigned wrap, the value will never be less than its + // initial value. + if (AddRec->hasNoUnsignedWrap()) + if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart())) + if (!C->getValue()->isZero()) + ConservativeResult = + ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0)); + + // TODO: non-affine addrec + if (AddRec->isAffine()) { + const Type *Ty = AddRec->getType(); + const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop()); + if (!isa<SCEVCouldNotCompute>(MaxBECount) && + getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) { + MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty); + + const SCEV *Start = AddRec->getStart(); + const SCEV *Step = AddRec->getStepRecurrence(*this); + + ConstantRange StartRange = getUnsignedRange(Start); + ConstantRange StepRange = getSignedRange(Step); + ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount); + ConstantRange EndRange = + StartRange.add(MaxBECountRange.multiply(StepRange)); + + // Check for overflow. This must be done with ConstantRange arithmetic + // because we could be called from within the ScalarEvolution overflow + // checking code. + ConstantRange ExtStartRange = StartRange.zextOrTrunc(BitWidth*2+1); + ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1); + ConstantRange ExtMaxBECountRange = + MaxBECountRange.zextOrTrunc(BitWidth*2+1); + ConstantRange ExtEndRange = EndRange.zextOrTrunc(BitWidth*2+1); + if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) != + ExtEndRange) + return ConservativeResult; + + APInt Min = APIntOps::umin(StartRange.getUnsignedMin(), + EndRange.getUnsignedMin()); + APInt Max = APIntOps::umax(StartRange.getUnsignedMax(), + EndRange.getUnsignedMax()); + if (Min.isMinValue() && Max.isMaxValue()) + return ConservativeResult; + return ConservativeResult.intersectWith(ConstantRange(Min, Max+1)); + } + } + + return ConservativeResult; + } + + if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { + // For a SCEVUnknown, ask ValueTracking. + APInt Mask = APInt::getAllOnesValue(BitWidth); + APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); + ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones, TD); + if (Ones == ~Zeros + 1) + return ConservativeResult; + return ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1)); + } + + return ConservativeResult; +} + +/// getSignedRange - Determine the signed range for a particular SCEV. +/// +ConstantRange +ScalarEvolution::getSignedRange(const SCEV *S) { + + if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) + return ConstantRange(C->getValue()->getValue()); + + unsigned BitWidth = getTypeSizeInBits(S->getType()); + ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true); + + // If the value has known zeros, the maximum signed value will have those + // known zeros as well. + uint32_t TZ = GetMinTrailingZeros(S); + if (TZ != 0) + ConservativeResult = + ConstantRange(APInt::getSignedMinValue(BitWidth), + APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1); + + if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) { + ConstantRange X = getSignedRange(Add->getOperand(0)); + for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i) + X = X.add(getSignedRange(Add->getOperand(i))); + return ConservativeResult.intersectWith(X); + } + + if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) { + ConstantRange X = getSignedRange(Mul->getOperand(0)); + for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i) + X = X.multiply(getSignedRange(Mul->getOperand(i))); + return ConservativeResult.intersectWith(X); + } + + if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) { + ConstantRange X = getSignedRange(SMax->getOperand(0)); + for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i) + X = X.smax(getSignedRange(SMax->getOperand(i))); + return ConservativeResult.intersectWith(X); + } + + if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) { + ConstantRange X = getSignedRange(UMax->getOperand(0)); + for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i) + X = X.umax(getSignedRange(UMax->getOperand(i))); + return ConservativeResult.intersectWith(X); + } + + if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) { + ConstantRange X = getSignedRange(UDiv->getLHS()); + ConstantRange Y = getSignedRange(UDiv->getRHS()); + return ConservativeResult.intersectWith(X.udiv(Y)); + } + + if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) { + ConstantRange X = getSignedRange(ZExt->getOperand()); + return ConservativeResult.intersectWith(X.zeroExtend(BitWidth)); + } + + if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) { + ConstantRange X = getSignedRange(SExt->getOperand()); + return ConservativeResult.intersectWith(X.signExtend(BitWidth)); + } + + if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) { + ConstantRange X = getSignedRange(Trunc->getOperand()); + return ConservativeResult.intersectWith(X.truncate(BitWidth)); + } + + if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) { + // If there's no signed wrap, and all the operands have the same sign or + // zero, the value won't ever change sign. + if (AddRec->hasNoSignedWrap()) { + bool AllNonNeg = true; + bool AllNonPos = true; + for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { + if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false; + if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false; + } + if (AllNonNeg) + ConservativeResult = ConservativeResult.intersectWith( + ConstantRange(APInt(BitWidth, 0), + APInt::getSignedMinValue(BitWidth))); + else if (AllNonPos) + ConservativeResult = ConservativeResult.intersectWith( + ConstantRange(APInt::getSignedMinValue(BitWidth), + APInt(BitWidth, 1))); + } + + // TODO: non-affine addrec + if (AddRec->isAffine()) { + const Type *Ty = AddRec->getType(); + const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop()); + if (!isa<SCEVCouldNotCompute>(MaxBECount) && + getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) { + MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty); + + const SCEV *Start = AddRec->getStart(); + const SCEV *Step = AddRec->getStepRecurrence(*this); + + ConstantRange StartRange = getSignedRange(Start); + ConstantRange StepRange = getSignedRange(Step); + ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount); + ConstantRange EndRange = + StartRange.add(MaxBECountRange.multiply(StepRange)); + + // Check for overflow. This must be done with ConstantRange arithmetic + // because we could be called from within the ScalarEvolution overflow + // checking code. + ConstantRange ExtStartRange = StartRange.sextOrTrunc(BitWidth*2+1); + ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1); + ConstantRange ExtMaxBECountRange = + MaxBECountRange.zextOrTrunc(BitWidth*2+1); + ConstantRange ExtEndRange = EndRange.sextOrTrunc(BitWidth*2+1); + if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) != + ExtEndRange) + return ConservativeResult; + + APInt Min = APIntOps::smin(StartRange.getSignedMin(), + EndRange.getSignedMin()); + APInt Max = APIntOps::smax(StartRange.getSignedMax(), + EndRange.getSignedMax()); + if (Min.isMinSignedValue() && Max.isMaxSignedValue()) + return ConservativeResult; + return ConservativeResult.intersectWith(ConstantRange(Min, Max+1)); + } + } + + return ConservativeResult; + } + + if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { + // For a SCEVUnknown, ask ValueTracking. + if (!U->getValue()->getType()->isIntegerTy() && !TD) + return ConservativeResult; + unsigned NS = ComputeNumSignBits(U->getValue(), TD); + if (NS == 1) + return ConservativeResult; + return ConservativeResult.intersectWith( + ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1), + APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1)); + } + + return ConservativeResult; +} + +/// createSCEV - We know that there is no SCEV for the specified value. +/// Analyze the expression. +/// +const SCEV *ScalarEvolution::createSCEV(Value *V) { + if (!isSCEVable(V->getType())) + return getUnknown(V); + + unsigned Opcode = Instruction::UserOp1; + if (Instruction *I = dyn_cast<Instruction>(V)) { + Opcode = I->getOpcode(); + + // Don't attempt to analyze instructions in blocks that aren't + // reachable. Such instructions don't matter, and they aren't required + // to obey basic rules for definitions dominating uses which this + // analysis depends on. + if (!DT->isReachableFromEntry(I->getParent())) + return getUnknown(V); + } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V)) + Opcode = CE->getOpcode(); + else if (ConstantInt *CI = dyn_cast<ConstantInt>(V)) + return getConstant(CI); + else if (isa<ConstantPointerNull>(V)) + return getConstant(V->getType(), 0); + else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V)) + return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee()); + else + return getUnknown(V); + + Operator *U = cast<Operator>(V); + switch (Opcode) { + case Instruction::Add: + // Don't transfer the NSW and NUW bits from the Add instruction to the + // Add expression, because the Instruction may be guarded by control + // flow and the no-overflow bits may not be valid for the expression in + // any context. + return getAddExpr(getSCEV(U->getOperand(0)), + getSCEV(U->getOperand(1))); + case Instruction::Mul: + // Don't transfer the NSW and NUW bits from the Mul instruction to the + // Mul expression, as with Add. + return getMulExpr(getSCEV(U->getOperand(0)), + getSCEV(U->getOperand(1))); + case Instruction::UDiv: + return getUDivExpr(getSCEV(U->getOperand(0)), + getSCEV(U->getOperand(1))); + case Instruction::Sub: + return getMinusSCEV(getSCEV(U->getOperand(0)), + getSCEV(U->getOperand(1))); + case Instruction::And: + // For an expression like x&255 that merely masks off the high bits, + // use zext(trunc(x)) as the SCEV expression. + if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { + if (CI->isNullValue()) + return getSCEV(U->getOperand(1)); + if (CI->isAllOnesValue()) + return getSCEV(U->getOperand(0)); + const APInt &A = CI->getValue(); + + // Instcombine's ShrinkDemandedConstant may strip bits out of + // constants, obscuring what would otherwise be a low-bits mask. + // Use ComputeMaskedBits to compute what ShrinkDemandedConstant + // knew about to reconstruct a low-bits mask value. + unsigned LZ = A.countLeadingZeros(); + unsigned BitWidth = A.getBitWidth(); + APInt AllOnes = APInt::getAllOnesValue(BitWidth); + APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0); + ComputeMaskedBits(U->getOperand(0), AllOnes, KnownZero, KnownOne, TD); + + APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ); + + if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask)) + return + getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)), + IntegerType::get(getContext(), BitWidth - LZ)), + U->getType()); + } + break; + + case Instruction::Or: + // If the RHS of the Or is a constant, we may have something like: + // X*4+1 which got turned into X*4|1. Handle this as an Add so loop + // optimizations will transparently handle this case. + // + // In order for this transformation to be safe, the LHS must be of the + // form X*(2^n) and the Or constant must be less than 2^n. + if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { + const SCEV *LHS = getSCEV(U->getOperand(0)); + const APInt &CIVal = CI->getValue(); + if (GetMinTrailingZeros(LHS) >= + (CIVal.getBitWidth() - CIVal.countLeadingZeros())) { + // Build a plain add SCEV. + const SCEV *S = getAddExpr(LHS, getSCEV(CI)); + // If the LHS of the add was an addrec and it has no-wrap flags, + // transfer the no-wrap flags, since an or won't introduce a wrap. + if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) { + const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS); + if (OldAR->hasNoUnsignedWrap()) + const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoUnsignedWrap(true); + if (OldAR->hasNoSignedWrap()) + const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoSignedWrap(true); + } + return S; + } + } + break; + case Instruction::Xor: + if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) { + // If the RHS of the xor is a signbit, then this is just an add. + // Instcombine turns add of signbit into xor as a strength reduction step. + if (CI->getValue().isSignBit()) + return getAddExpr(getSCEV(U->getOperand(0)), + getSCEV(U->getOperand(1))); + + // If the RHS of xor is -1, then this is a not operation. + if (CI->isAllOnesValue()) + return getNotSCEV(getSCEV(U->getOperand(0))); + + // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask. + // This is a variant of the check for xor with -1, and it handles + // the case where instcombine has trimmed non-demanded bits out + // of an xor with -1. + if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0))) + if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1))) + if (BO->getOpcode() == Instruction::And && + LCI->getValue() == CI->getValue()) + if (const SCEVZeroExtendExpr *Z = + dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) { + const Type *UTy = U->getType(); + const SCEV *Z0 = Z->getOperand(); + const Type *Z0Ty = Z0->getType(); + unsigned Z0TySize = getTypeSizeInBits(Z0Ty); + + // If C is a low-bits mask, the zero extend is serving to + // mask off the high bits. Complement the operand and + // re-apply the zext. + if (APIntOps::isMask(Z0TySize, CI->getValue())) + return getZeroExtendExpr(getNotSCEV(Z0), UTy); + + // If C is a single bit, it may be in the sign-bit position + // before the zero-extend. In this case, represent the xor + // using an add, which is equivalent, and re-apply the zext. + APInt Trunc = APInt(CI->getValue()).trunc(Z0TySize); + if (APInt(Trunc).zext(getTypeSizeInBits(UTy)) == CI->getValue() && + Trunc.isSignBit()) + return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)), + UTy); + } + } + break; + + case Instruction::Shl: + // Turn shift left of a constant amount into a multiply. + if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { + uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth(); + + // If the shift count is not less than the bitwidth, the result of + // the shift is undefined. Don't try to analyze it, because the + // resolution chosen here may differ from the resolution chosen in + // other parts of the compiler. + if (SA->getValue().uge(BitWidth)) + break; + + Constant *X = ConstantInt::get(getContext(), + APInt(BitWidth, 1).shl(SA->getZExtValue())); + return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X)); + } + break; + + case Instruction::LShr: + // Turn logical shift right of a constant into a unsigned divide. + if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) { + uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth(); + + // If the shift count is not less than the bitwidth, the result of + // the shift is undefined. Don't try to analyze it, because the + // resolution chosen here may differ from the resolution chosen in + // other parts of the compiler. + if (SA->getValue().uge(BitWidth)) + break; + + Constant *X = ConstantInt::get(getContext(), + APInt(BitWidth, 1).shl(SA->getZExtValue())); + return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X)); + } + break; + + case Instruction::AShr: + // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression. + if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) + if (Operator *L = dyn_cast<Operator>(U->getOperand(0))) + if (L->getOpcode() == Instruction::Shl && + L->getOperand(1) == U->getOperand(1)) { + uint64_t BitWidth = getTypeSizeInBits(U->getType()); + + // If the shift count is not less than the bitwidth, the result of + // the shift is undefined. Don't try to analyze it, because the + // resolution chosen here may differ from the resolution chosen in + // other parts of the compiler. + if (CI->getValue().uge(BitWidth)) + break; + + uint64_t Amt = BitWidth - CI->getZExtValue(); + if (Amt == BitWidth) + return getSCEV(L->getOperand(0)); // shift by zero --> noop + return + getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)), + IntegerType::get(getContext(), + Amt)), + U->getType()); + } + break; + + case Instruction::Trunc: + return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType()); + + case Instruction::ZExt: + return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType()); + + case Instruction::SExt: + return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType()); + + case Instruction::BitCast: + // BitCasts are no-op casts so we just eliminate the cast. + if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType())) + return getSCEV(U->getOperand(0)); + break; + + // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can + // lead to pointer expressions which cannot safely be expanded to GEPs, + // because ScalarEvolution doesn't respect the GEP aliasing rules when + // simplifying integer expressions. + + case Instruction::GetElementPtr: + return createNodeForGEP(cast<GEPOperator>(U)); + + case Instruction::PHI: + return createNodeForPHI(cast<PHINode>(U)); + + case Instruction::Select: + // This could be a smax or umax that was lowered earlier. + // Try to recover it. + if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) { + Value *LHS = ICI->getOperand(0); + Value *RHS = ICI->getOperand(1); + switch (ICI->getPredicate()) { + case ICmpInst::ICMP_SLT: + case ICmpInst::ICMP_SLE: + std::swap(LHS, RHS); + // fall through + case ICmpInst::ICMP_SGT: + case ICmpInst::ICMP_SGE: + // a >s b ? a+x : b+x -> smax(a, b)+x + // a >s b ? b+x : a+x -> smin(a, b)+x + if (LHS->getType() == U->getType()) { + const SCEV *LS = getSCEV(LHS); + const SCEV *RS = getSCEV(RHS); + const SCEV *LA = getSCEV(U->getOperand(1)); + const SCEV *RA = getSCEV(U->getOperand(2)); + const SCEV *LDiff = getMinusSCEV(LA, LS); + const SCEV *RDiff = getMinusSCEV(RA, RS); + if (LDiff == RDiff) + return getAddExpr(getSMaxExpr(LS, RS), LDiff); + LDiff = getMinusSCEV(LA, RS); + RDiff = getMinusSCEV(RA, LS); + if (LDiff == RDiff) + return getAddExpr(getSMinExpr(LS, RS), LDiff); + } + break; + case ICmpInst::ICMP_ULT: + case ICmpInst::ICMP_ULE: + std::swap(LHS, RHS); + // fall through + case ICmpInst::ICMP_UGT: + case ICmpInst::ICMP_UGE: + // a >u b ? a+x : b+x -> umax(a, b)+x + // a >u b ? b+x : a+x -> umin(a, b)+x + if (LHS->getType() == U->getType()) { + const SCEV *LS = getSCEV(LHS); + const SCEV *RS = getSCEV(RHS); + const SCEV *LA = getSCEV(U->getOperand(1)); + const SCEV *RA = getSCEV(U->getOperand(2)); + const SCEV *LDiff = getMinusSCEV(LA, LS); + const SCEV *RDiff = getMinusSCEV(RA, RS); + if (LDiff == RDiff) + return getAddExpr(getUMaxExpr(LS, RS), LDiff); + LDiff = getMinusSCEV(LA, RS); + RDiff = getMinusSCEV(RA, LS); + if (LDiff == RDiff) + return getAddExpr(getUMinExpr(LS, RS), LDiff); + } + break; + case ICmpInst::ICMP_NE: + // n != 0 ? n+x : 1+x -> umax(n, 1)+x + if (LHS->getType() == U->getType() && + isa<ConstantInt>(RHS) && + cast<ConstantInt>(RHS)->isZero()) { + const SCEV *One = getConstant(LHS->getType(), 1); + const SCEV *LS = getSCEV(LHS); + const SCEV *LA = getSCEV(U->getOperand(1)); + const SCEV *RA = getSCEV(U->getOperand(2)); + const SCEV *LDiff = getMinusSCEV(LA, LS); + const SCEV *RDiff = getMinusSCEV(RA, One); + if (LDiff == RDiff) + return getAddExpr(getUMaxExpr(LS, One), LDiff); + } + break; + case ICmpInst::ICMP_EQ: + // n == 0 ? 1+x : n+x -> umax(n, 1)+x + if (LHS->getType() == U->getType() && + isa<ConstantInt>(RHS) && + cast<ConstantInt>(RHS)->isZero()) { + const SCEV *One = getConstant(LHS->getType(), 1); + const SCEV *LS = getSCEV(LHS); + const SCEV *LA = getSCEV(U->getOperand(1)); + const SCEV *RA = getSCEV(U->getOperand(2)); + const SCEV *LDiff = getMinusSCEV(LA, One); + const SCEV *RDiff = getMinusSCEV(RA, LS); + if (LDiff == RDiff) + return getAddExpr(getUMaxExpr(LS, One), LDiff); + } + break; + default: + break; + } + } + + default: // We cannot analyze this expression. + break; + } + + return getUnknown(V); +} + + + +//===----------------------------------------------------------------------===// +// Iteration Count Computation Code +// + +/// getBackedgeTakenCount - If the specified loop has a predictable +/// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute +/// object. The backedge-taken count is the number of times the loop header +/// will be branched to from within the loop. This is one less than the +/// trip count of the loop, since it doesn't count the first iteration, +/// when the header is branched to from outside the loop. +/// +/// Note that it is not valid to call this method on a loop without a +/// loop-invariant backedge-taken count (see +/// hasLoopInvariantBackedgeTakenCount). +/// +const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) { + return getBackedgeTakenInfo(L).Exact; +} + +/// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except +/// return the least SCEV value that is known never to be less than the +/// actual backedge taken count. +const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) { + return getBackedgeTakenInfo(L).Max; +} + +/// PushLoopPHIs - Push PHI nodes in the header of the given loop +/// onto the given Worklist. +static void +PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) { + BasicBlock *Header = L->getHeader(); + + // Push all Loop-header PHIs onto the Worklist stack. + for (BasicBlock::iterator I = Header->begin(); + PHINode *PN = dyn_cast<PHINode>(I); ++I) + Worklist.push_back(PN); +} + +const ScalarEvolution::BackedgeTakenInfo & +ScalarEvolution::getBackedgeTakenInfo(const Loop *L) { + // Initially insert a CouldNotCompute for this loop. If the insertion + // succeeds, proceed to actually compute a backedge-taken count and + // update the value. The temporary CouldNotCompute value tells SCEV + // code elsewhere that it shouldn't attempt to request a new + // backedge-taken count, which could result in infinite recursion. + std::pair<std::map<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair = + BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute())); + if (Pair.second) { + BackedgeTakenInfo BECount = ComputeBackedgeTakenCount(L); + if (BECount.Exact != getCouldNotCompute()) { + assert(BECount.Exact->isLoopInvariant(L) && + BECount.Max->isLoopInvariant(L) && + "Computed backedge-taken count isn't loop invariant for loop!"); + ++NumTripCountsComputed; + + // Update the value in the map. + Pair.first->second = BECount; + } else { + if (BECount.Max != getCouldNotCompute()) + // Update the value in the map. + Pair.first->second = BECount; + if (isa<PHINode>(L->getHeader()->begin())) + // Only count loops that have phi nodes as not being computable. + ++NumTripCountsNotComputed; + } + + // Now that we know more about the trip count for this loop, forget any + // existing SCEV values for PHI nodes in this loop since they are only + // conservative estimates made without the benefit of trip count + // information. This is similar to the code in forgetLoop, except that + // it handles SCEVUnknown PHI nodes specially. + if (BECount.hasAnyInfo()) { + SmallVector<Instruction *, 16> Worklist; + PushLoopPHIs(L, Worklist); + + SmallPtrSet<Instruction *, 8> Visited; + while (!Worklist.empty()) { + Instruction *I = Worklist.pop_back_val(); + if (!Visited.insert(I)) continue; + + std::map<SCEVCallbackVH, const SCEV *>::iterator It = + Scalars.find(static_cast<Value *>(I)); + if (It != Scalars.end()) { + // SCEVUnknown for a PHI either means that it has an unrecognized + // structure, or it's a PHI that's in the progress of being computed + // by createNodeForPHI. In the former case, additional loop trip + // count information isn't going to change anything. In the later + // case, createNodeForPHI will perform the necessary updates on its + // own when it gets to that point. + if (!isa<PHINode>(I) || !isa<SCEVUnknown>(It->second)) { + ValuesAtScopes.erase(It->second); + Scalars.erase(It); + } + if (PHINode *PN = dyn_cast<PHINode>(I)) + ConstantEvolutionLoopExitValue.erase(PN); + } + + PushDefUseChildren(I, Worklist); + } + } + } + return Pair.first->second; +} + +/// forgetLoop - This method should be called by the client when it has +/// changed a loop in a way that may effect ScalarEvolution's ability to +/// compute a trip count, or if the loop is deleted. +void ScalarEvolution::forgetLoop(const Loop *L) { + // Drop any stored trip count value. + BackedgeTakenCounts.erase(L); + + // Drop information about expressions based on loop-header PHIs. + SmallVector<Instruction *, 16> Worklist; + PushLoopPHIs(L, Worklist); + + SmallPtrSet<Instruction *, 8> Visited; + while (!Worklist.empty()) { + Instruction *I = Worklist.pop_back_val(); + if (!Visited.insert(I)) continue; + + std::map<SCEVCallbackVH, const SCEV *>::iterator It = + Scalars.find(static_cast<Value *>(I)); + if (It != Scalars.end()) { + ValuesAtScopes.erase(It->second); + Scalars.erase(It); + if (PHINode *PN = dyn_cast<PHINode>(I)) + ConstantEvolutionLoopExitValue.erase(PN); + } + + PushDefUseChildren(I, Worklist); + } +} + +/// forgetValue - This method should be called by the client when it has +/// changed a value in a way that may effect its value, or which may +/// disconnect it from a def-use chain linking it to a loop. +void ScalarEvolution::forgetValue(Value *V) { + Instruction *I = dyn_cast<Instruction>(V); + if (!I) return; + + // Drop information about expressions based on loop-header PHIs. + SmallVector<Instruction *, 16> Worklist; + Worklist.push_back(I); + + SmallPtrSet<Instruction *, 8> Visited; + while (!Worklist.empty()) { + I = Worklist.pop_back_val(); + if (!Visited.insert(I)) continue; + + std::map<SCEVCallbackVH, const SCEV *>::iterator It = + Scalars.find(static_cast<Value *>(I)); + if (It != Scalars.end()) { + ValuesAtScopes.erase(It->second); + Scalars.erase(It); + if (PHINode *PN = dyn_cast<PHINode>(I)) + ConstantEvolutionLoopExitValue.erase(PN); + } + + PushDefUseChildren(I, Worklist); + } +} + +/// ComputeBackedgeTakenCount - Compute the number of times the backedge +/// of the specified loop will execute. +ScalarEvolution::BackedgeTakenInfo +ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) { + SmallVector<BasicBlock *, 8> ExitingBlocks; + L->getExitingBlocks(ExitingBlocks); + + // Examine all exits and pick the most conservative values. + const SCEV *BECount = getCouldNotCompute(); + const SCEV *MaxBECount = getCouldNotCompute(); + bool CouldNotComputeBECount = false; + for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) { + BackedgeTakenInfo NewBTI = + ComputeBackedgeTakenCountFromExit(L, ExitingBlocks[i]); + + if (NewBTI.Exact == getCouldNotCompute()) { + // We couldn't compute an exact value for this exit, so + // we won't be able to compute an exact value for the loop. + CouldNotComputeBECount = true; + BECount = getCouldNotCompute(); + } else if (!CouldNotComputeBECount) { + if (BECount == getCouldNotCompute()) + BECount = NewBTI.Exact; + else + BECount = getUMinFromMismatchedTypes(BECount, NewBTI.Exact); + } + if (MaxBECount == getCouldNotCompute()) + MaxBECount = NewBTI.Max; + else if (NewBTI.Max != getCouldNotCompute()) + MaxBECount = getUMinFromMismatchedTypes(MaxBECount, NewBTI.Max); + } + + return BackedgeTakenInfo(BECount, MaxBECount); +} + +/// ComputeBackedgeTakenCountFromExit - Compute the number of times the backedge +/// of the specified loop will execute if it exits via the specified block. +ScalarEvolution::BackedgeTakenInfo +ScalarEvolution::ComputeBackedgeTakenCountFromExit(const Loop *L, + BasicBlock *ExitingBlock) { + + // Okay, we've chosen an exiting block. See what condition causes us to + // exit at this block. + // + // FIXME: we should be able to handle switch instructions (with a single exit) + BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator()); + if (ExitBr == 0) return getCouldNotCompute(); + assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!"); + + // At this point, we know we have a conditional branch that determines whether + // the loop is exited. However, we don't know if the branch is executed each + // time through the loop. If not, then the execution count of the branch will + // not be equal to the trip count of the loop. + // + // Currently we check for this by checking to see if the Exit branch goes to + // the loop header. If so, we know it will always execute the same number of + // times as the loop. We also handle the case where the exit block *is* the + // loop header. This is common for un-rotated loops. + // + // If both of those tests fail, walk up the unique predecessor chain to the + // header, stopping if there is an edge that doesn't exit the loop. If the + // header is reached, the execution count of the branch will be equal to the + // trip count of the loop. + // + // More extensive analysis could be done to handle more cases here. + // + if (ExitBr->getSuccessor(0) != L->getHeader() && + ExitBr->getSuccessor(1) != L->getHeader() && + ExitBr->getParent() != L->getHeader()) { + // The simple checks failed, try climbing the unique predecessor chain + // up to the header. + bool Ok = false; + for (BasicBlock *BB = ExitBr->getParent(); BB; ) { + BasicBlock *Pred = BB->getUniquePredecessor(); + if (!Pred) + return getCouldNotCompute(); + TerminatorInst *PredTerm = Pred->getTerminator(); + for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) { + BasicBlock *PredSucc = PredTerm->getSuccessor(i); + if (PredSucc == BB) + continue; + // If the predecessor has a successor that isn't BB and isn't + // outside the loop, assume the worst. + if (L->contains(PredSucc)) + return getCouldNotCompute(); + } + if (Pred == L->getHeader()) { + Ok = true; + break; + } + BB = Pred; + } + if (!Ok) + return getCouldNotCompute(); + } + + // Proceed to the next level to examine the exit condition expression. + return ComputeBackedgeTakenCountFromExitCond(L, ExitBr->getCondition(), + ExitBr->getSuccessor(0), + ExitBr->getSuccessor(1)); +} + +/// ComputeBackedgeTakenCountFromExitCond - Compute the number of times the +/// backedge of the specified loop will execute if its exit condition +/// were a conditional branch of ExitCond, TBB, and FBB. +ScalarEvolution::BackedgeTakenInfo +ScalarEvolution::ComputeBackedgeTakenCountFromExitCond(const Loop *L, + Value *ExitCond, + BasicBlock *TBB, + BasicBlock *FBB) { + // Check if the controlling expression for this loop is an And or Or. + if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) { + if (BO->getOpcode() == Instruction::And) { + // Recurse on the operands of the and. + BackedgeTakenInfo BTI0 = + ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB); + BackedgeTakenInfo BTI1 = + ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB); + const SCEV *BECount = getCouldNotCompute(); + const SCEV *MaxBECount = getCouldNotCompute(); + if (L->contains(TBB)) { + // Both conditions must be true for the loop to continue executing. + // Choose the less conservative count. + if (BTI0.Exact == getCouldNotCompute() || + BTI1.Exact == getCouldNotCompute()) + BECount = getCouldNotCompute(); + else + BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact); + if (BTI0.Max == getCouldNotCompute()) + MaxBECount = BTI1.Max; + else if (BTI1.Max == getCouldNotCompute()) + MaxBECount = BTI0.Max; + else + MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max); + } else { + // Both conditions must be true for the loop to exit. + assert(L->contains(FBB) && "Loop block has no successor in loop!"); + if (BTI0.Exact != getCouldNotCompute() && + BTI1.Exact != getCouldNotCompute()) + BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact); + if (BTI0.Max != getCouldNotCompute() && + BTI1.Max != getCouldNotCompute()) + MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max); + } + + return BackedgeTakenInfo(BECount, MaxBECount); + } + if (BO->getOpcode() == Instruction::Or) { + // Recurse on the operands of the or. + BackedgeTakenInfo BTI0 = + ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB); + BackedgeTakenInfo BTI1 = + ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB); + const SCEV *BECount = getCouldNotCompute(); + const SCEV *MaxBECount = getCouldNotCompute(); + if (L->contains(FBB)) { + // Both conditions must be false for the loop to continue executing. + // Choose the less conservative count. + if (BTI0.Exact == getCouldNotCompute() || + BTI1.Exact == getCouldNotCompute()) + BECount = getCouldNotCompute(); + else + BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact); + if (BTI0.Max == getCouldNotCompute()) + MaxBECount = BTI1.Max; + else if (BTI1.Max == getCouldNotCompute()) + MaxBECount = BTI0.Max; + else + MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max); + } else { + // Both conditions must be false for the loop to exit. + assert(L->contains(TBB) && "Loop block has no successor in loop!"); + if (BTI0.Exact != getCouldNotCompute() && + BTI1.Exact != getCouldNotCompute()) + BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact); + if (BTI0.Max != getCouldNotCompute() && + BTI1.Max != getCouldNotCompute()) + MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max); + } + + return BackedgeTakenInfo(BECount, MaxBECount); + } + } + + // With an icmp, it may be feasible to compute an exact backedge-taken count. + // Proceed to the next level to examine the icmp. + if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond)) + return ComputeBackedgeTakenCountFromExitCondICmp(L, ExitCondICmp, TBB, FBB); + + // Check for a constant condition. These are normally stripped out by + // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to + // preserve the CFG and is temporarily leaving constant conditions + // in place. + if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) { + if (L->contains(FBB) == !CI->getZExtValue()) + // The backedge is always taken. + return getCouldNotCompute(); + else + // The backedge is never taken. + return getConstant(CI->getType(), 0); + } + + // If it's not an integer or pointer comparison then compute it the hard way. + return ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB)); +} + +/// ComputeBackedgeTakenCountFromExitCondICmp - Compute the number of times the +/// backedge of the specified loop will execute if its exit condition +/// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB. +ScalarEvolution::BackedgeTakenInfo +ScalarEvolution::ComputeBackedgeTakenCountFromExitCondICmp(const Loop *L, + ICmpInst *ExitCond, + BasicBlock *TBB, + BasicBlock *FBB) { + + // If the condition was exit on true, convert the condition to exit on false + ICmpInst::Predicate Cond; + if (!L->contains(FBB)) + Cond = ExitCond->getPredicate(); + else + Cond = ExitCond->getInversePredicate(); + + // Handle common loops like: for (X = "string"; *X; ++X) + if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0))) + if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) { + BackedgeTakenInfo ItCnt = + ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond); + if (ItCnt.hasAnyInfo()) + return ItCnt; + } + + const SCEV *LHS = getSCEV(ExitCond->getOperand(0)); + const SCEV *RHS = getSCEV(ExitCond->getOperand(1)); + + // Try to evaluate any dependencies out of the loop. + LHS = getSCEVAtScope(LHS, L); + RHS = getSCEVAtScope(RHS, L); + + // At this point, we would like to compute how many iterations of the + // loop the predicate will return true for these inputs. + if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) { + // If there is a loop-invariant, force it into the RHS. + std::swap(LHS, RHS); + Cond = ICmpInst::getSwappedPredicate(Cond); + } + + // Simplify the operands before analyzing them. + (void)SimplifyICmpOperands(Cond, LHS, RHS); + + // If we have a comparison of a chrec against a constant, try to use value + // ranges to answer this query. + if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) + if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS)) + if (AddRec->getLoop() == L) { + // Form the constant range. + ConstantRange CompRange( + ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue())); + + const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this); + if (!isa<SCEVCouldNotCompute>(Ret)) return Ret; + } + + switch (Cond) { + case ICmpInst::ICMP_NE: { // while (X != Y) + // Convert to: while (X-Y != 0) + BackedgeTakenInfo BTI = HowFarToZero(getMinusSCEV(LHS, RHS), L); + if (BTI.hasAnyInfo()) return BTI; + break; + } + case ICmpInst::ICMP_EQ: { // while (X == Y) + // Convert to: while (X-Y == 0) + BackedgeTakenInfo BTI = HowFarToNonZero(getMinusSCEV(LHS, RHS), L); + if (BTI.hasAnyInfo()) return BTI; + break; + } + case ICmpInst::ICMP_SLT: { + BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true); + if (BTI.hasAnyInfo()) return BTI; + break; + } + case ICmpInst::ICMP_SGT: { + BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS), + getNotSCEV(RHS), L, true); + if (BTI.hasAnyInfo()) return BTI; + break; + } + case ICmpInst::ICMP_ULT: { + BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false); + if (BTI.hasAnyInfo()) return BTI; + break; + } + case ICmpInst::ICMP_UGT: { + BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS), + getNotSCEV(RHS), L, false); + if (BTI.hasAnyInfo()) return BTI; + break; + } + default: +#if 0 + dbgs() << "ComputeBackedgeTakenCount "; + if (ExitCond->getOperand(0)->getType()->isUnsigned()) + dbgs() << "[unsigned] "; + dbgs() << *LHS << " " + << Instruction::getOpcodeName(Instruction::ICmp) + << " " << *RHS << "\n"; +#endif + break; + } + return + ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB)); +} + +static ConstantInt * +EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C, + ScalarEvolution &SE) { + const SCEV *InVal = SE.getConstant(C); + const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE); + assert(isa<SCEVConstant>(Val) && + "Evaluation of SCEV at constant didn't fold correctly?"); + return cast<SCEVConstant>(Val)->getValue(); +} + +/// GetAddressedElementFromGlobal - Given a global variable with an initializer +/// and a GEP expression (missing the pointer index) indexing into it, return +/// the addressed element of the initializer or null if the index expression is +/// invalid. +static Constant * +GetAddressedElementFromGlobal(GlobalVariable *GV, + const std::vector<ConstantInt*> &Indices) { + Constant *Init = GV->getInitializer(); + for (unsigned i = 0, e = Indices.size(); i != e; ++i) { + uint64_t Idx = Indices[i]->getZExtValue(); + if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) { + assert(Idx < CS->getNumOperands() && "Bad struct index!"); + Init = cast<Constant>(CS->getOperand(Idx)); + } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) { + if (Idx >= CA->getNumOperands()) return 0; // Bogus program + Init = cast<Constant>(CA->getOperand(Idx)); + } else if (isa<ConstantAggregateZero>(Init)) { + if (const StructType *STy = dyn_cast<StructType>(Init->getType())) { + assert(Idx < STy->getNumElements() && "Bad struct index!"); + Init = Constant::getNullValue(STy->getElementType(Idx)); + } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) { + if (Idx >= ATy->getNumElements()) return 0; // Bogus program + Init = Constant::getNullValue(ATy->getElementType()); + } else { + llvm_unreachable("Unknown constant aggregate type!"); + } + return 0; + } else { + return 0; // Unknown initializer type + } + } + return Init; +} + +/// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of +/// 'icmp op load X, cst', try to see if we can compute the backedge +/// execution count. +ScalarEvolution::BackedgeTakenInfo +ScalarEvolution::ComputeLoadConstantCompareBackedgeTakenCount( + LoadInst *LI, + Constant *RHS, + const Loop *L, + ICmpInst::Predicate predicate) { + if (LI->isVolatile()) return getCouldNotCompute(); + + // Check to see if the loaded pointer is a getelementptr of a global. + // TODO: Use SCEV instead of manually grubbing with GEPs. + GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0)); + if (!GEP) return getCouldNotCompute(); + + // Make sure that it is really a constant global we are gepping, with an + // initializer, and make sure the first IDX is really 0. + GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0)); + if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() || + GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) || + !cast<Constant>(GEP->getOperand(1))->isNullValue()) + return getCouldNotCompute(); + + // Okay, we allow one non-constant index into the GEP instruction. + Value *VarIdx = 0; + std::vector<ConstantInt*> Indexes; + unsigned VarIdxNum = 0; + for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i) + if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) { + Indexes.push_back(CI); + } else if (!isa<ConstantInt>(GEP->getOperand(i))) { + if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's. + VarIdx = GEP->getOperand(i); + VarIdxNum = i-2; + Indexes.push_back(0); + } + + // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant. + // Check to see if X is a loop variant variable value now. + const SCEV *Idx = getSCEV(VarIdx); + Idx = getSCEVAtScope(Idx, L); + + // We can only recognize very limited forms of loop index expressions, in + // particular, only affine AddRec's like {C1,+,C2}. + const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx); + if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) || + !isa<SCEVConstant>(IdxExpr->getOperand(0)) || + !isa<SCEVConstant>(IdxExpr->getOperand(1))) + return getCouldNotCompute(); + + unsigned MaxSteps = MaxBruteForceIterations; + for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) { + ConstantInt *ItCst = ConstantInt::get( + cast<IntegerType>(IdxExpr->getType()), IterationNum); + ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this); + + // Form the GEP offset. + Indexes[VarIdxNum] = Val; + + Constant *Result = GetAddressedElementFromGlobal(GV, Indexes); + if (Result == 0) break; // Cannot compute! + + // Evaluate the condition for this iteration. + Result = ConstantExpr::getICmp(predicate, Result, RHS); + if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure + if (cast<ConstantInt>(Result)->getValue().isMinValue()) { +#if 0 + dbgs() << "\n***\n*** Computed loop count " << *ItCst + << "\n*** From global " << *GV << "*** BB: " << *L->getHeader() + << "***\n"; +#endif + ++NumArrayLenItCounts; + return getConstant(ItCst); // Found terminating iteration! + } + } + return getCouldNotCompute(); +} + + +/// CanConstantFold - Return true if we can constant fold an instruction of the +/// specified type, assuming that all operands were constants. +static bool CanConstantFold(const Instruction *I) { + if (isa<BinaryOperator>(I) || isa<CmpInst>(I) || + isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I)) + return true; + + if (const CallInst *CI = dyn_cast<CallInst>(I)) + if (const Function *F = CI->getCalledFunction()) + return canConstantFoldCallTo(F); + return false; +} + +/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node +/// in the loop that V is derived from. We allow arbitrary operations along the +/// way, but the operands of an operation must either be constants or a value +/// derived from a constant PHI. If this expression does not fit with these +/// constraints, return null. +static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) { + // If this is not an instruction, or if this is an instruction outside of the + // loop, it can't be derived from a loop PHI. + Instruction *I = dyn_cast<Instruction>(V); + if (I == 0 || !L->contains(I)) return 0; + + if (PHINode *PN = dyn_cast<PHINode>(I)) { + if (L->getHeader() == I->getParent()) + return PN; + else + // We don't currently keep track of the control flow needed to evaluate + // PHIs, so we cannot handle PHIs inside of loops. + return 0; + } + + // If we won't be able to constant fold this expression even if the operands + // are constants, return early. + if (!CanConstantFold(I)) return 0; + + // Otherwise, we can evaluate this instruction if all of its operands are + // constant or derived from a PHI node themselves. + PHINode *PHI = 0; + for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op) + if (!(isa<Constant>(I->getOperand(Op)) || + isa<GlobalValue>(I->getOperand(Op)))) { + PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L); + if (P == 0) return 0; // Not evolving from PHI + if (PHI == 0) + PHI = P; + else if (PHI != P) + return 0; // Evolving from multiple different PHIs. + } + + // This is a expression evolving from a constant PHI! + return PHI; +} + +/// EvaluateExpression - Given an expression that passes the +/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node +/// in the loop has the value PHIVal. If we can't fold this expression for some +/// reason, return null. +static Constant *EvaluateExpression(Value *V, Constant *PHIVal, + const TargetData *TD) { + if (isa<PHINode>(V)) return PHIVal; + if (Constant *C = dyn_cast<Constant>(V)) return C; + if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) return GV; + Instruction *I = cast<Instruction>(V); + + std::vector<Constant*> Operands; + Operands.resize(I->getNumOperands()); + + for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { + Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal, TD); + if (Operands[i] == 0) return 0; + } + + if (const CmpInst *CI = dyn_cast<CmpInst>(I)) + return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0], + Operands[1], TD); + return ConstantFoldInstOperands(I->getOpcode(), I->getType(), + &Operands[0], Operands.size(), TD); +} + +/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is +/// in the header of its containing loop, we know the loop executes a +/// constant number of times, and the PHI node is just a recurrence +/// involving constants, fold it. +Constant * +ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN, + const APInt &BEs, + const Loop *L) { + std::map<PHINode*, Constant*>::iterator I = + ConstantEvolutionLoopExitValue.find(PN); + if (I != ConstantEvolutionLoopExitValue.end()) + return I->second; + + if (BEs.ugt(MaxBruteForceIterations)) + return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it. + + Constant *&RetVal = ConstantEvolutionLoopExitValue[PN]; + + // Since the loop is canonicalized, the PHI node must have two entries. One + // entry must be a constant (coming in from outside of the loop), and the + // second must be derived from the same PHI. + bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); + Constant *StartCST = + dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); + if (StartCST == 0) + return RetVal = 0; // Must be a constant. + + Value *BEValue = PN->getIncomingValue(SecondIsBackedge); + PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); + if (PN2 != PN) + return RetVal = 0; // Not derived from same PHI. + + // Execute the loop symbolically to determine the exit value. + if (BEs.getActiveBits() >= 32) + return RetVal = 0; // More than 2^32-1 iterations?? Not doing it! + + unsigned NumIterations = BEs.getZExtValue(); // must be in range + unsigned IterationNum = 0; + for (Constant *PHIVal = StartCST; ; ++IterationNum) { + if (IterationNum == NumIterations) + return RetVal = PHIVal; // Got exit value! + + // Compute the value of the PHI node for the next iteration. + Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD); + if (NextPHI == PHIVal) + return RetVal = NextPHI; // Stopped evolving! + if (NextPHI == 0) + return 0; // Couldn't evaluate! + PHIVal = NextPHI; + } +} + +/// ComputeBackedgeTakenCountExhaustively - If the loop is known to execute a +/// constant number of times (the condition evolves only from constants), +/// try to evaluate a few iterations of the loop until we get the exit +/// condition gets a value of ExitWhen (true or false). If we cannot +/// evaluate the trip count of the loop, return getCouldNotCompute(). +const SCEV * +ScalarEvolution::ComputeBackedgeTakenCountExhaustively(const Loop *L, + Value *Cond, + bool ExitWhen) { + PHINode *PN = getConstantEvolvingPHI(Cond, L); + if (PN == 0) return getCouldNotCompute(); + + // Since the loop is canonicalized, the PHI node must have two entries. One + // entry must be a constant (coming in from outside of the loop), and the + // second must be derived from the same PHI. + bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1)); + Constant *StartCST = + dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge)); + if (StartCST == 0) return getCouldNotCompute(); // Must be a constant. + + Value *BEValue = PN->getIncomingValue(SecondIsBackedge); + PHINode *PN2 = getConstantEvolvingPHI(BEValue, L); + if (PN2 != PN) return getCouldNotCompute(); // Not derived from same PHI. + + // Okay, we find a PHI node that defines the trip count of this loop. Execute + // the loop symbolically to determine when the condition gets a value of + // "ExitWhen". + unsigned IterationNum = 0; + unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis. + for (Constant *PHIVal = StartCST; + IterationNum != MaxIterations; ++IterationNum) { + ConstantInt *CondVal = + dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal, TD)); + + // Couldn't symbolically evaluate. + if (!CondVal) return getCouldNotCompute(); + + if (CondVal->getValue() == uint64_t(ExitWhen)) { + ++NumBruteForceTripCountsComputed; + return getConstant(Type::getInt32Ty(getContext()), IterationNum); + } + + // Compute the value of the PHI node for the next iteration. + Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD); + if (NextPHI == 0 || NextPHI == PHIVal) + return getCouldNotCompute();// Couldn't evaluate or not making progress... + PHIVal = NextPHI; + } + + // Too many iterations were needed to evaluate. + return getCouldNotCompute(); +} + +/// getSCEVAtScope - Return a SCEV expression for the specified value +/// at the specified scope in the program. The L value specifies a loop +/// nest to evaluate the expression at, where null is the top-level or a +/// specified loop is immediately inside of the loop. +/// +/// This method can be used to compute the exit value for a variable defined +/// in a loop by querying what the value will hold in the parent loop. +/// +/// In the case that a relevant loop exit value cannot be computed, the +/// original value V is returned. +const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) { + // Check to see if we've folded this expression at this loop before. + std::map<const Loop *, const SCEV *> &Values = ValuesAtScopes[V]; + std::pair<std::map<const Loop *, const SCEV *>::iterator, bool> Pair = + Values.insert(std::make_pair(L, static_cast<const SCEV *>(0))); + if (!Pair.second) + return Pair.first->second ? Pair.first->second : V; + + // Otherwise compute it. + const SCEV *C = computeSCEVAtScope(V, L); + ValuesAtScopes[V][L] = C; + return C; +} + +const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) { + if (isa<SCEVConstant>(V)) return V; + + // If this instruction is evolved from a constant-evolving PHI, compute the + // exit value from the loop without using SCEVs. + if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) { + if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) { + const Loop *LI = (*this->LI)[I->getParent()]; + if (LI && LI->getParentLoop() == L) // Looking for loop exit value. + if (PHINode *PN = dyn_cast<PHINode>(I)) + if (PN->getParent() == LI->getHeader()) { + // Okay, there is no closed form solution for the PHI node. Check + // to see if the loop that contains it has a known backedge-taken + // count. If so, we may be able to force computation of the exit + // value. + const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI); + if (const SCEVConstant *BTCC = + dyn_cast<SCEVConstant>(BackedgeTakenCount)) { + // Okay, we know how many times the containing loop executes. If + // this is a constant evolving PHI node, get the final value at + // the specified iteration number. + Constant *RV = getConstantEvolutionLoopExitValue(PN, + BTCC->getValue()->getValue(), + LI); + if (RV) return getSCEV(RV); + } + } + + // Okay, this is an expression that we cannot symbolically evaluate + // into a SCEV. Check to see if it's possible to symbolically evaluate + // the arguments into constants, and if so, try to constant propagate the + // result. This is particularly useful for computing loop exit values. + if (CanConstantFold(I)) { + std::vector<Constant*> Operands; + Operands.reserve(I->getNumOperands()); + for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { + Value *Op = I->getOperand(i); + if (Constant *C = dyn_cast<Constant>(Op)) { + Operands.push_back(C); + } else { + // If any of the operands is non-constant and if they are + // non-integer and non-pointer, don't even try to analyze them + // with scev techniques. + if (!isSCEVable(Op->getType())) + return V; + + const SCEV *OpV = getSCEVAtScope(Op, L); + if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) { + Constant *C = SC->getValue(); + if (C->getType() != Op->getType()) + C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false, + Op->getType(), + false), + C, Op->getType()); + Operands.push_back(C); + } else if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) { + if (Constant *C = dyn_cast<Constant>(SU->getValue())) { + if (C->getType() != Op->getType()) + C = + ConstantExpr::getCast(CastInst::getCastOpcode(C, false, + Op->getType(), + false), + C, Op->getType()); + Operands.push_back(C); + } else + return V; + } else { + return V; + } + } + } + + Constant *C = 0; + if (const CmpInst *CI = dyn_cast<CmpInst>(I)) + C = ConstantFoldCompareInstOperands(CI->getPredicate(), + Operands[0], Operands[1], TD); + else + C = ConstantFoldInstOperands(I->getOpcode(), I->getType(), + &Operands[0], Operands.size(), TD); + if (C) + return getSCEV(C); + } + } + + // This is some other type of SCEVUnknown, just return it. + return V; + } + + if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) { + // Avoid performing the look-up in the common case where the specified + // expression has no loop-variant portions. + for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) { + const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); + if (OpAtScope != Comm->getOperand(i)) { + // Okay, at least one of these operands is loop variant but might be + // foldable. Build a new instance of the folded commutative expression. + SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(), + Comm->op_begin()+i); + NewOps.push_back(OpAtScope); + + for (++i; i != e; ++i) { + OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); + NewOps.push_back(OpAtScope); + } + if (isa<SCEVAddExpr>(Comm)) + return getAddExpr(NewOps); + if (isa<SCEVMulExpr>(Comm)) + return getMulExpr(NewOps); + if (isa<SCEVSMaxExpr>(Comm)) + return getSMaxExpr(NewOps); + if (isa<SCEVUMaxExpr>(Comm)) + return getUMaxExpr(NewOps); + llvm_unreachable("Unknown commutative SCEV type!"); + } + } + // If we got here, all operands are loop invariant. + return Comm; + } + + if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) { + const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L); + const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L); + if (LHS == Div->getLHS() && RHS == Div->getRHS()) + return Div; // must be loop invariant + return getUDivExpr(LHS, RHS); + } + + // If this is a loop recurrence for a loop that does not contain L, then we + // are dealing with the final value computed by the loop. + if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) { + if (!L || !AddRec->getLoop()->contains(L)) { + // To evaluate this recurrence, we need to know how many times the AddRec + // loop iterates. Compute this now. + const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop()); + if (BackedgeTakenCount == getCouldNotCompute()) return AddRec; + + // Then, evaluate the AddRec. + return AddRec->evaluateAtIteration(BackedgeTakenCount, *this); + } + return AddRec; + } + + if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) { + const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); + if (Op == Cast->getOperand()) + return Cast; // must be loop invariant + return getZeroExtendExpr(Op, Cast->getType()); + } + + if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) { + const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); + if (Op == Cast->getOperand()) + return Cast; // must be loop invariant + return getSignExtendExpr(Op, Cast->getType()); + } + + if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) { + const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); + if (Op == Cast->getOperand()) + return Cast; // must be loop invariant + return getTruncateExpr(Op, Cast->getType()); + } + + llvm_unreachable("Unknown SCEV type!"); + return 0; +} + +/// getSCEVAtScope - This is a convenience function which does +/// getSCEVAtScope(getSCEV(V), L). +const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) { + return getSCEVAtScope(getSCEV(V), L); +} + +/// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the +/// following equation: +/// +/// A * X = B (mod N) +/// +/// where N = 2^BW and BW is the common bit width of A and B. The signedness of +/// A and B isn't important. +/// +/// If the equation does not have a solution, SCEVCouldNotCompute is returned. +static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B, + ScalarEvolution &SE) { + uint32_t BW = A.getBitWidth(); + assert(BW == B.getBitWidth() && "Bit widths must be the same."); + assert(A != 0 && "A must be non-zero."); + + // 1. D = gcd(A, N) + // + // The gcd of A and N may have only one prime factor: 2. The number of + // trailing zeros in A is its multiplicity + uint32_t Mult2 = A.countTrailingZeros(); + // D = 2^Mult2 + + // 2. Check if B is divisible by D. + // + // B is divisible by D if and only if the multiplicity of prime factor 2 for B + // is not less than multiplicity of this prime factor for D. + if (B.countTrailingZeros() < Mult2) + return SE.getCouldNotCompute(); + + // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic + // modulo (N / D). + // + // (N / D) may need BW+1 bits in its representation. Hence, we'll use this + // bit width during computations. + APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D + APInt Mod(BW + 1, 0); + Mod.set(BW - Mult2); // Mod = N / D + APInt I = AD.multiplicativeInverse(Mod); + + // 4. Compute the minimum unsigned root of the equation: + // I * (B / D) mod (N / D) + APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod); + + // The result is guaranteed to be less than 2^BW so we may truncate it to BW + // bits. + return SE.getConstant(Result.trunc(BW)); +} + +/// SolveQuadraticEquation - Find the roots of the quadratic equation for the +/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which +/// might be the same) or two SCEVCouldNotCompute objects. +/// +static std::pair<const SCEV *,const SCEV *> +SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) { + assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!"); + const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0)); + const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1)); + const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2)); + + // We currently can only solve this if the coefficients are constants. + if (!LC || !MC || !NC) { + const SCEV *CNC = SE.getCouldNotCompute(); + return std::make_pair(CNC, CNC); + } + + uint32_t BitWidth = LC->getValue()->getValue().getBitWidth(); + const APInt &L = LC->getValue()->getValue(); + const APInt &M = MC->getValue()->getValue(); + const APInt &N = NC->getValue()->getValue(); + APInt Two(BitWidth, 2); + APInt Four(BitWidth, 4); + + { + using namespace APIntOps; + const APInt& C = L; + // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C + // The B coefficient is M-N/2 + APInt B(M); + B -= sdiv(N,Two); + + // The A coefficient is N/2 + APInt A(N.sdiv(Two)); + + // Compute the B^2-4ac term. + APInt SqrtTerm(B); + SqrtTerm *= B; + SqrtTerm -= Four * (A * C); + + // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest + // integer value or else APInt::sqrt() will assert. + APInt SqrtVal(SqrtTerm.sqrt()); + + // Compute the two solutions for the quadratic formula. + // The divisions must be performed as signed divisions. + APInt NegB(-B); + APInt TwoA( A << 1 ); + if (TwoA.isMinValue()) { + const SCEV *CNC = SE.getCouldNotCompute(); + return std::make_pair(CNC, CNC); + } + + LLVMContext &Context = SE.getContext(); + + ConstantInt *Solution1 = + ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA)); + ConstantInt *Solution2 = + ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA)); + + return std::make_pair(SE.getConstant(Solution1), + SE.getConstant(Solution2)); + } // end APIntOps namespace +} + +/// HowFarToZero - Return the number of times a backedge comparing the specified +/// value to zero will execute. If not computable, return CouldNotCompute. +ScalarEvolution::BackedgeTakenInfo +ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) { + // If the value is a constant + if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { + // If the value is already zero, the branch will execute zero times. + if (C->getValue()->isZero()) return C; + return getCouldNotCompute(); // Otherwise it will loop infinitely. + } + + const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V); + if (!AddRec || AddRec->getLoop() != L) + return getCouldNotCompute(); + + if (AddRec->isAffine()) { + // If this is an affine expression, the execution count of this branch is + // the minimum unsigned root of the following equation: + // + // Start + Step*N = 0 (mod 2^BW) + // + // equivalent to: + // + // Step*N = -Start (mod 2^BW) + // + // where BW is the common bit width of Start and Step. + + // Get the initial value for the loop. + const SCEV *Start = getSCEVAtScope(AddRec->getStart(), + L->getParentLoop()); + const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), + L->getParentLoop()); + + if (const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) { + // For now we handle only constant steps. + + // First, handle unitary steps. + if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so: + return getNegativeSCEV(Start); // N = -Start (as unsigned) + if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so: + return Start; // N = Start (as unsigned) + + // Then, try to solve the above equation provided that Start is constant. + if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) + return SolveLinEquationWithOverflow(StepC->getValue()->getValue(), + -StartC->getValue()->getValue(), + *this); + } + } else if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) { + // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of + // the quadratic equation to solve it. + std::pair<const SCEV *,const SCEV *> Roots = SolveQuadraticEquation(AddRec, + *this); + const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); + const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); + if (R1) { +#if 0 + dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1 + << " sol#2: " << *R2 << "\n"; +#endif + // Pick the smallest positive root value. + if (ConstantInt *CB = + dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, + R1->getValue(), R2->getValue()))) { + if (CB->getZExtValue() == false) + std::swap(R1, R2); // R1 is the minimum root now. + + // We can only use this value if the chrec ends up with an exact zero + // value at this index. When solving for "X*X != 5", for example, we + // should not accept a root of 2. + const SCEV *Val = AddRec->evaluateAtIteration(R1, *this); + if (Val->isZero()) + return R1; // We found a quadratic root! + } + } + } + + return getCouldNotCompute(); +} + +/// HowFarToNonZero - Return the number of times a backedge checking the +/// specified value for nonzero will execute. If not computable, return +/// CouldNotCompute +ScalarEvolution::BackedgeTakenInfo +ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) { + // Loops that look like: while (X == 0) are very strange indeed. We don't + // handle them yet except for the trivial case. This could be expanded in the + // future as needed. + + // If the value is a constant, check to see if it is known to be non-zero + // already. If so, the backedge will execute zero times. + if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { + if (!C->getValue()->isNullValue()) + return getConstant(C->getType(), 0); + return getCouldNotCompute(); // Otherwise it will loop infinitely. + } + + // We could implement others, but I really doubt anyone writes loops like + // this, and if they did, they would already be constant folded. + return getCouldNotCompute(); +} + +/// getLoopPredecessor - If the given loop's header has exactly one unique +/// predecessor outside the loop, return it. Otherwise return null. +/// This is less strict that the loop "preheader" concept, which requires +/// the predecessor to have only one single successor. +/// +BasicBlock *ScalarEvolution::getLoopPredecessor(const Loop *L) { + BasicBlock *Header = L->getHeader(); + BasicBlock *Pred = 0; + for (pred_iterator PI = pred_begin(Header), E = pred_end(Header); + PI != E; ++PI) + if (!L->contains(*PI)) { + if (Pred && Pred != *PI) return 0; // Multiple predecessors. + Pred = *PI; + } + return Pred; +} + +/// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB +/// (which may not be an immediate predecessor) which has exactly one +/// successor from which BB is reachable, or null if no such block is +/// found. +/// +std::pair<BasicBlock *, BasicBlock *> +ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) { + // If the block has a unique predecessor, then there is no path from the + // predecessor to the block that does not go through the direct edge + // from the predecessor to the block. + if (BasicBlock *Pred = BB->getSinglePredecessor()) + return std::make_pair(Pred, BB); + + // A loop's header is defined to be a block that dominates the loop. + // If the header has a unique predecessor outside the loop, it must be + // a block that has exactly one successor that can reach the loop. + if (Loop *L = LI->getLoopFor(BB)) + return std::make_pair(getLoopPredecessor(L), L->getHeader()); + + return std::pair<BasicBlock *, BasicBlock *>(); +} + +/// HasSameValue - SCEV structural equivalence is usually sufficient for +/// testing whether two expressions are equal, however for the purposes of +/// looking for a condition guarding a loop, it can be useful to be a little +/// more general, since a front-end may have replicated the controlling +/// expression. +/// +static bool HasSameValue(const SCEV *A, const SCEV *B) { + // Quick check to see if they are the same SCEV. + if (A == B) return true; + + // Otherwise, if they're both SCEVUnknown, it's possible that they hold + // two different instructions with the same value. Check for this case. + if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A)) + if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B)) + if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue())) + if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue())) + if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory()) + return true; + + // Otherwise assume they may have a different value. + return false; +} + +/// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with +/// predicate Pred. Return true iff any changes were made. +/// +bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred, + const SCEV *&LHS, const SCEV *&RHS) { + bool Changed = false; + + // Canonicalize a constant to the right side. + if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { + // Check for both operands constant. + if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) { + if (ConstantExpr::getICmp(Pred, + LHSC->getValue(), + RHSC->getValue())->isNullValue()) + goto trivially_false; + else + goto trivially_true; + } + // Otherwise swap the operands to put the constant on the right. + std::swap(LHS, RHS); + Pred = ICmpInst::getSwappedPredicate(Pred); + Changed = true; + } + + // If we're comparing an addrec with a value which is loop-invariant in the + // addrec's loop, put the addrec on the left. Also make a dominance check, + // as both operands could be addrecs loop-invariant in each other's loop. + if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) { + const Loop *L = AR->getLoop(); + if (LHS->isLoopInvariant(L) && LHS->properlyDominates(L->getHeader(), DT)) { + std::swap(LHS, RHS); + Pred = ICmpInst::getSwappedPredicate(Pred); + Changed = true; + } + } + + // If there's a constant operand, canonicalize comparisons with boundary + // cases, and canonicalize *-or-equal comparisons to regular comparisons. + if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) { + const APInt &RA = RC->getValue()->getValue(); + switch (Pred) { + default: llvm_unreachable("Unexpected ICmpInst::Predicate value!"); + case ICmpInst::ICMP_EQ: + case ICmpInst::ICMP_NE: + break; + case ICmpInst::ICMP_UGE: + if ((RA - 1).isMinValue()) { + Pred = ICmpInst::ICMP_NE; + RHS = getConstant(RA - 1); + Changed = true; + break; + } + if (RA.isMaxValue()) { + Pred = ICmpInst::ICMP_EQ; + Changed = true; + break; + } + if (RA.isMinValue()) goto trivially_true; + + Pred = ICmpInst::ICMP_UGT; + RHS = getConstant(RA - 1); + Changed = true; + break; + case ICmpInst::ICMP_ULE: + if ((RA + 1).isMaxValue()) { + Pred = ICmpInst::ICMP_NE; + RHS = getConstant(RA + 1); + Changed = true; + break; + } + if (RA.isMinValue()) { + Pred = ICmpInst::ICMP_EQ; + Changed = true; + break; + } + if (RA.isMaxValue()) goto trivially_true; + + Pred = ICmpInst::ICMP_ULT; + RHS = getConstant(RA + 1); + Changed = true; + break; + case ICmpInst::ICMP_SGE: + if ((RA - 1).isMinSignedValue()) { + Pred = ICmpInst::ICMP_NE; + RHS = getConstant(RA - 1); + Changed = true; + break; + } + if (RA.isMaxSignedValue()) { + Pred = ICmpInst::ICMP_EQ; + Changed = true; + break; + } + if (RA.isMinSignedValue()) goto trivially_true; + + Pred = ICmpInst::ICMP_SGT; + RHS = getConstant(RA - 1); + Changed = true; + break; + case ICmpInst::ICMP_SLE: + if ((RA + 1).isMaxSignedValue()) { + Pred = ICmpInst::ICMP_NE; + RHS = getConstant(RA + 1); + Changed = true; + break; + } + if (RA.isMinSignedValue()) { + Pred = ICmpInst::ICMP_EQ; + Changed = true; + break; + } + if (RA.isMaxSignedValue()) goto trivially_true; + + Pred = ICmpInst::ICMP_SLT; + RHS = getConstant(RA + 1); + Changed = true; + break; + case ICmpInst::ICMP_UGT: + if (RA.isMinValue()) { + Pred = ICmpInst::ICMP_NE; + Changed = true; + break; + } + if ((RA + 1).isMaxValue()) { + Pred = ICmpInst::ICMP_EQ; + RHS = getConstant(RA + 1); + Changed = true; + break; + } + if (RA.isMaxValue()) goto trivially_false; + break; + case ICmpInst::ICMP_ULT: + if (RA.isMaxValue()) { + Pred = ICmpInst::ICMP_NE; + Changed = true; + break; + } + if ((RA - 1).isMinValue()) { + Pred = ICmpInst::ICMP_EQ; + RHS = getConstant(RA - 1); + Changed = true; + break; + } + if (RA.isMinValue()) goto trivially_false; + break; + case ICmpInst::ICMP_SGT: + if (RA.isMinSignedValue()) { + Pred = ICmpInst::ICMP_NE; + Changed = true; + break; + } + if ((RA + 1).isMaxSignedValue()) { + Pred = ICmpInst::ICMP_EQ; + RHS = getConstant(RA + 1); + Changed = true; + break; + } + if (RA.isMaxSignedValue()) goto trivially_false; + break; + case ICmpInst::ICMP_SLT: + if (RA.isMaxSignedValue()) { + Pred = ICmpInst::ICMP_NE; + Changed = true; + break; + } + if ((RA - 1).isMinSignedValue()) { + Pred = ICmpInst::ICMP_EQ; + RHS = getConstant(RA - 1); + Changed = true; + break; + } + if (RA.isMinSignedValue()) goto trivially_false; + break; + } + } + + // Check for obvious equality. + if (HasSameValue(LHS, RHS)) { + if (ICmpInst::isTrueWhenEqual(Pred)) + goto trivially_true; + if (ICmpInst::isFalseWhenEqual(Pred)) + goto trivially_false; + } + + // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by + // adding or subtracting 1 from one of the operands. + switch (Pred) { + case ICmpInst::ICMP_SLE: + if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) { + RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS, + /*HasNUW=*/false, /*HasNSW=*/true); + Pred = ICmpInst::ICMP_SLT; + Changed = true; + } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) { + LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS, + /*HasNUW=*/false, /*HasNSW=*/true); + Pred = ICmpInst::ICMP_SLT; + Changed = true; + } + break; + case ICmpInst::ICMP_SGE: + if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) { + RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS, + /*HasNUW=*/false, /*HasNSW=*/true); + Pred = ICmpInst::ICMP_SGT; + Changed = true; + } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) { + LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS, + /*HasNUW=*/false, /*HasNSW=*/true); + Pred = ICmpInst::ICMP_SGT; + Changed = true; + } + break; + case ICmpInst::ICMP_ULE: + if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) { + RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS, + /*HasNUW=*/true, /*HasNSW=*/false); + Pred = ICmpInst::ICMP_ULT; + Changed = true; + } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) { + LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS, + /*HasNUW=*/true, /*HasNSW=*/false); + Pred = ICmpInst::ICMP_ULT; + Changed = true; + } + break; + case ICmpInst::ICMP_UGE: + if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) { + RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS, + /*HasNUW=*/true, /*HasNSW=*/false); + Pred = ICmpInst::ICMP_UGT; + Changed = true; + } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) { + LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS, + /*HasNUW=*/true, /*HasNSW=*/false); + Pred = ICmpInst::ICMP_UGT; + Changed = true; + } + break; + default: + break; + } + + // TODO: More simplifications are possible here. + + return Changed; + +trivially_true: + // Return 0 == 0. + LHS = RHS = getConstant(Type::getInt1Ty(getContext()), 0); + Pred = ICmpInst::ICMP_EQ; + return true; + +trivially_false: + // Return 0 != 0. + LHS = RHS = getConstant(Type::getInt1Ty(getContext()), 0); + Pred = ICmpInst::ICMP_NE; + return true; +} + +bool ScalarEvolution::isKnownNegative(const SCEV *S) { + return getSignedRange(S).getSignedMax().isNegative(); +} + +bool ScalarEvolution::isKnownPositive(const SCEV *S) { + return getSignedRange(S).getSignedMin().isStrictlyPositive(); +} + +bool ScalarEvolution::isKnownNonNegative(const SCEV *S) { + return !getSignedRange(S).getSignedMin().isNegative(); +} + +bool ScalarEvolution::isKnownNonPositive(const SCEV *S) { + return !getSignedRange(S).getSignedMax().isStrictlyPositive(); +} + +bool ScalarEvolution::isKnownNonZero(const SCEV *S) { + return isKnownNegative(S) || isKnownPositive(S); +} + +bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred, + const SCEV *LHS, const SCEV *RHS) { + // Canonicalize the inputs first. + (void)SimplifyICmpOperands(Pred, LHS, RHS); + + // If LHS or RHS is an addrec, check to see if the condition is true in + // every iteration of the loop. + if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS)) + if (isLoopEntryGuardedByCond( + AR->getLoop(), Pred, AR->getStart(), RHS) && + isLoopBackedgeGuardedByCond( + AR->getLoop(), Pred, AR->getPostIncExpr(*this), RHS)) + return true; + if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) + if (isLoopEntryGuardedByCond( + AR->getLoop(), Pred, LHS, AR->getStart()) && + isLoopBackedgeGuardedByCond( + AR->getLoop(), Pred, LHS, AR->getPostIncExpr(*this))) + return true; + + // Otherwise see what can be done with known constant ranges. + return isKnownPredicateWithRanges(Pred, LHS, RHS); +} + +bool +ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred, + const SCEV *LHS, const SCEV *RHS) { + if (HasSameValue(LHS, RHS)) + return ICmpInst::isTrueWhenEqual(Pred); + + // This code is split out from isKnownPredicate because it is called from + // within isLoopEntryGuardedByCond. + switch (Pred) { + default: + llvm_unreachable("Unexpected ICmpInst::Predicate value!"); + break; + case ICmpInst::ICMP_SGT: + Pred = ICmpInst::ICMP_SLT; + std::swap(LHS, RHS); + case ICmpInst::ICMP_SLT: { + ConstantRange LHSRange = getSignedRange(LHS); + ConstantRange RHSRange = getSignedRange(RHS); + if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin())) + return true; + if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax())) + return false; + break; + } + case ICmpInst::ICMP_SGE: + Pred = ICmpInst::ICMP_SLE; + std::swap(LHS, RHS); + case ICmpInst::ICMP_SLE: { + ConstantRange LHSRange = getSignedRange(LHS); + ConstantRange RHSRange = getSignedRange(RHS); + if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin())) + return true; + if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax())) + return false; + break; + } + case ICmpInst::ICMP_UGT: + Pred = ICmpInst::ICMP_ULT; + std::swap(LHS, RHS); + case ICmpInst::ICMP_ULT: { + ConstantRange LHSRange = getUnsignedRange(LHS); + ConstantRange RHSRange = getUnsignedRange(RHS); + if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin())) + return true; + if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax())) + return false; + break; + } + case ICmpInst::ICMP_UGE: + Pred = ICmpInst::ICMP_ULE; + std::swap(LHS, RHS); + case ICmpInst::ICMP_ULE: { + ConstantRange LHSRange = getUnsignedRange(LHS); + ConstantRange RHSRange = getUnsignedRange(RHS); + if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin())) + return true; + if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax())) + return false; + break; + } + case ICmpInst::ICMP_NE: { + if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet()) + return true; + if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet()) + return true; + + const SCEV *Diff = getMinusSCEV(LHS, RHS); + if (isKnownNonZero(Diff)) + return true; + break; + } + case ICmpInst::ICMP_EQ: + // The check at the top of the function catches the case where + // the values are known to be equal. + break; + } + return false; +} + +/// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is +/// protected by a conditional between LHS and RHS. This is used to +/// to eliminate casts. +bool +ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L, + ICmpInst::Predicate Pred, + const SCEV *LHS, const SCEV *RHS) { + // Interpret a null as meaning no loop, where there is obviously no guard + // (interprocedural conditions notwithstanding). + if (!L) return true; + + BasicBlock *Latch = L->getLoopLatch(); + if (!Latch) + return false; + + BranchInst *LoopContinuePredicate = + dyn_cast<BranchInst>(Latch->getTerminator()); + if (!LoopContinuePredicate || + LoopContinuePredicate->isUnconditional()) + return false; + + return isImpliedCond(LoopContinuePredicate->getCondition(), Pred, LHS, RHS, + LoopContinuePredicate->getSuccessor(0) != L->getHeader()); +} + +/// isLoopEntryGuardedByCond - Test whether entry to the loop is protected +/// by a conditional between LHS and RHS. This is used to help avoid max +/// expressions in loop trip counts, and to eliminate casts. +bool +ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L, + ICmpInst::Predicate Pred, + const SCEV *LHS, const SCEV *RHS) { + // Interpret a null as meaning no loop, where there is obviously no guard + // (interprocedural conditions notwithstanding). + if (!L) return false; + + // Starting at the loop predecessor, climb up the predecessor chain, as long + // as there are predecessors that can be found that have unique successors + // leading to the original header. + for (std::pair<BasicBlock *, BasicBlock *> + Pair(getLoopPredecessor(L), L->getHeader()); + Pair.first; + Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) { + + BranchInst *LoopEntryPredicate = + dyn_cast<BranchInst>(Pair.first->getTerminator()); + if (!LoopEntryPredicate || + LoopEntryPredicate->isUnconditional()) + continue; + + if (isImpliedCond(LoopEntryPredicate->getCondition(), Pred, LHS, RHS, + LoopEntryPredicate->getSuccessor(0) != Pair.second)) + return true; + } + + return false; +} + +/// isImpliedCond - Test whether the condition described by Pred, LHS, +/// and RHS is true whenever the given Cond value evaluates to true. +bool ScalarEvolution::isImpliedCond(Value *CondValue, + ICmpInst::Predicate Pred, + const SCEV *LHS, const SCEV *RHS, + bool Inverse) { + // Recursively handle And and Or conditions. + if (BinaryOperator *BO = dyn_cast<BinaryOperator>(CondValue)) { + if (BO->getOpcode() == Instruction::And) { + if (!Inverse) + return isImpliedCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) || + isImpliedCond(BO->getOperand(1), Pred, LHS, RHS, Inverse); + } else if (BO->getOpcode() == Instruction::Or) { + if (Inverse) + return isImpliedCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) || + isImpliedCond(BO->getOperand(1), Pred, LHS, RHS, Inverse); + } + } + + ICmpInst *ICI = dyn_cast<ICmpInst>(CondValue); + if (!ICI) return false; + + // Bail if the ICmp's operands' types are wider than the needed type + // before attempting to call getSCEV on them. This avoids infinite + // recursion, since the analysis of widening casts can require loop + // exit condition information for overflow checking, which would + // lead back here. + if (getTypeSizeInBits(LHS->getType()) < + getTypeSizeInBits(ICI->getOperand(0)->getType())) + return false; + + // Now that we found a conditional branch that dominates the loop, check to + // see if it is the comparison we are looking for. + ICmpInst::Predicate FoundPred; + if (Inverse) + FoundPred = ICI->getInversePredicate(); + else + FoundPred = ICI->getPredicate(); + + const SCEV *FoundLHS = getSCEV(ICI->getOperand(0)); + const SCEV *FoundRHS = getSCEV(ICI->getOperand(1)); + + // Balance the types. The case where FoundLHS' type is wider than + // LHS' type is checked for above. + if (getTypeSizeInBits(LHS->getType()) > + getTypeSizeInBits(FoundLHS->getType())) { + if (CmpInst::isSigned(Pred)) { + FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType()); + FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType()); + } else { + FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType()); + FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType()); + } + } + + // Canonicalize the query to match the way instcombine will have + // canonicalized the comparison. + if (SimplifyICmpOperands(Pred, LHS, RHS)) + if (LHS == RHS) + return CmpInst::isTrueWhenEqual(Pred); + if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS)) + if (FoundLHS == FoundRHS) + return CmpInst::isFalseWhenEqual(Pred); + + // Check to see if we can make the LHS or RHS match. + if (LHS == FoundRHS || RHS == FoundLHS) { + if (isa<SCEVConstant>(RHS)) { + std::swap(FoundLHS, FoundRHS); + FoundPred = ICmpInst::getSwappedPredicate(FoundPred); + } else { + std::swap(LHS, RHS); + Pred = ICmpInst::getSwappedPredicate(Pred); + } + } + + // Check whether the found predicate is the same as the desired predicate. + if (FoundPred == Pred) + return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS); + + // Check whether swapping the found predicate makes it the same as the + // desired predicate. + if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) { + if (isa<SCEVConstant>(RHS)) + return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS); + else + return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred), + RHS, LHS, FoundLHS, FoundRHS); + } + + // Check whether the actual condition is beyond sufficient. + if (FoundPred == ICmpInst::ICMP_EQ) + if (ICmpInst::isTrueWhenEqual(Pred)) + if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS)) + return true; + if (Pred == ICmpInst::ICMP_NE) + if (!ICmpInst::isTrueWhenEqual(FoundPred)) + if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS)) + return true; + + // Otherwise assume the worst. + return false; +} + +/// isImpliedCondOperands - Test whether the condition described by Pred, +/// LHS, and RHS is true whenever the condition described by Pred, FoundLHS, +/// and FoundRHS is true. +bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred, + const SCEV *LHS, const SCEV *RHS, + const SCEV *FoundLHS, + const SCEV *FoundRHS) { + return isImpliedCondOperandsHelper(Pred, LHS, RHS, + FoundLHS, FoundRHS) || + // ~x < ~y --> x > y + isImpliedCondOperandsHelper(Pred, LHS, RHS, + getNotSCEV(FoundRHS), + getNotSCEV(FoundLHS)); +} + +/// isImpliedCondOperandsHelper - Test whether the condition described by +/// Pred, LHS, and RHS is true whenever the condition described by Pred, +/// FoundLHS, and FoundRHS is true. +bool +ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred, + const SCEV *LHS, const SCEV *RHS, + const SCEV *FoundLHS, + const SCEV *FoundRHS) { + switch (Pred) { + default: llvm_unreachable("Unexpected ICmpInst::Predicate value!"); + case ICmpInst::ICMP_EQ: + case ICmpInst::ICMP_NE: + if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS)) + return true; + break; + case ICmpInst::ICMP_SLT: + case ICmpInst::ICMP_SLE: + if (isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, LHS, FoundLHS) && + isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, RHS, FoundRHS)) + return true; + break; + case ICmpInst::ICMP_SGT: + case ICmpInst::ICMP_SGE: + if (isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, LHS, FoundLHS) && + isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, RHS, FoundRHS)) + return true; + break; + case ICmpInst::ICMP_ULT: + case ICmpInst::ICMP_ULE: + if (isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, LHS, FoundLHS) && + isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, RHS, FoundRHS)) + return true; + break; + case ICmpInst::ICMP_UGT: + case ICmpInst::ICMP_UGE: + if (isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, LHS, FoundLHS) && + isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, RHS, FoundRHS)) + return true; + break; + } + + return false; +} + +/// getBECount - Subtract the end and start values and divide by the step, +/// rounding up, to get the number of times the backedge is executed. Return +/// CouldNotCompute if an intermediate computation overflows. +const SCEV *ScalarEvolution::getBECount(const SCEV *Start, + const SCEV *End, + const SCEV *Step, + bool NoWrap) { + assert(!isKnownNegative(Step) && + "This code doesn't handle negative strides yet!"); + + const Type *Ty = Start->getType(); + const SCEV *NegOne = getConstant(Ty, (uint64_t)-1); + const SCEV *Diff = getMinusSCEV(End, Start); + const SCEV *RoundUp = getAddExpr(Step, NegOne); + + // Add an adjustment to the difference between End and Start so that + // the division will effectively round up. + const SCEV *Add = getAddExpr(Diff, RoundUp); + + if (!NoWrap) { + // Check Add for unsigned overflow. + // TODO: More sophisticated things could be done here. + const Type *WideTy = IntegerType::get(getContext(), + getTypeSizeInBits(Ty) + 1); + const SCEV *EDiff = getZeroExtendExpr(Diff, WideTy); + const SCEV *ERoundUp = getZeroExtendExpr(RoundUp, WideTy); + const SCEV *OperandExtendedAdd = getAddExpr(EDiff, ERoundUp); + if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd) + return getCouldNotCompute(); + } + + return getUDivExpr(Add, Step); +} + +/// HowManyLessThans - Return the number of times a backedge containing the +/// specified less-than comparison will execute. If not computable, return +/// CouldNotCompute. +ScalarEvolution::BackedgeTakenInfo +ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS, + const Loop *L, bool isSigned) { + // Only handle: "ADDREC < LoopInvariant". + if (!RHS->isLoopInvariant(L)) return getCouldNotCompute(); + + const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS); + if (!AddRec || AddRec->getLoop() != L) + return getCouldNotCompute(); + + // Check to see if we have a flag which makes analysis easy. + bool NoWrap = isSigned ? AddRec->hasNoSignedWrap() : + AddRec->hasNoUnsignedWrap(); + + if (AddRec->isAffine()) { + unsigned BitWidth = getTypeSizeInBits(AddRec->getType()); + const SCEV *Step = AddRec->getStepRecurrence(*this); + + if (Step->isZero()) + return getCouldNotCompute(); + if (Step->isOne()) { + // With unit stride, the iteration never steps past the limit value. + } else if (isKnownPositive(Step)) { + // Test whether a positive iteration can step past the limit + // value and past the maximum value for its type in a single step. + // Note that it's not sufficient to check NoWrap here, because even + // though the value after a wrap is undefined, it's not undefined + // behavior, so if wrap does occur, the loop could either terminate or + // loop infinitely, but in either case, the loop is guaranteed to + // iterate at least until the iteration where the wrapping occurs. + const SCEV *One = getConstant(Step->getType(), 1); + if (isSigned) { + APInt Max = APInt::getSignedMaxValue(BitWidth); + if ((Max - getSignedRange(getMinusSCEV(Step, One)).getSignedMax()) + .slt(getSignedRange(RHS).getSignedMax())) + return getCouldNotCompute(); + } else { + APInt Max = APInt::getMaxValue(BitWidth); + if ((Max - getUnsignedRange(getMinusSCEV(Step, One)).getUnsignedMax()) + .ult(getUnsignedRange(RHS).getUnsignedMax())) + return getCouldNotCompute(); + } + } else + // TODO: Handle negative strides here and below. + return getCouldNotCompute(); + + // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant + // m. So, we count the number of iterations in which {n,+,s} < m is true. + // Note that we cannot simply return max(m-n,0)/s because it's not safe to + // treat m-n as signed nor unsigned due to overflow possibility. + + // First, we get the value of the LHS in the first iteration: n + const SCEV *Start = AddRec->getOperand(0); + + // Determine the minimum constant start value. + const SCEV *MinStart = getConstant(isSigned ? + getSignedRange(Start).getSignedMin() : + getUnsignedRange(Start).getUnsignedMin()); + + // If we know that the condition is true in order to enter the loop, + // then we know that it will run exactly (m-n)/s times. Otherwise, we + // only know that it will execute (max(m,n)-n)/s times. In both cases, + // the division must round up. + const SCEV *End = RHS; + if (!isLoopEntryGuardedByCond(L, + isSigned ? ICmpInst::ICMP_SLT : + ICmpInst::ICMP_ULT, + getMinusSCEV(Start, Step), RHS)) + End = isSigned ? getSMaxExpr(RHS, Start) + : getUMaxExpr(RHS, Start); + + // Determine the maximum constant end value. + const SCEV *MaxEnd = getConstant(isSigned ? + getSignedRange(End).getSignedMax() : + getUnsignedRange(End).getUnsignedMax()); + + // If MaxEnd is within a step of the maximum integer value in its type, + // adjust it down to the minimum value which would produce the same effect. + // This allows the subsequent ceiling division of (N+(step-1))/step to + // compute the correct value. + const SCEV *StepMinusOne = getMinusSCEV(Step, + getConstant(Step->getType(), 1)); + MaxEnd = isSigned ? + getSMinExpr(MaxEnd, + getMinusSCEV(getConstant(APInt::getSignedMaxValue(BitWidth)), + StepMinusOne)) : + getUMinExpr(MaxEnd, + getMinusSCEV(getConstant(APInt::getMaxValue(BitWidth)), + StepMinusOne)); + + // Finally, we subtract these two values and divide, rounding up, to get + // the number of times the backedge is executed. + const SCEV *BECount = getBECount(Start, End, Step, NoWrap); + + // The maximum backedge count is similar, except using the minimum start + // value and the maximum end value. + const SCEV *MaxBECount = getBECount(MinStart, MaxEnd, Step, NoWrap); + + return BackedgeTakenInfo(BECount, MaxBECount); + } + + return getCouldNotCompute(); +} + +/// getNumIterationsInRange - Return the number of iterations of this loop that +/// produce values in the specified constant range. Another way of looking at +/// this is that it returns the first iteration number where the value is not in +/// the condition, thus computing the exit count. If the iteration count can't +/// be computed, an instance of SCEVCouldNotCompute is returned. +const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range, + ScalarEvolution &SE) const { + if (Range.isFullSet()) // Infinite loop. + return SE.getCouldNotCompute(); + + // If the start is a non-zero constant, shift the range to simplify things. + if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart())) + if (!SC->getValue()->isZero()) { + SmallVector<const SCEV *, 4> Operands(op_begin(), op_end()); + Operands[0] = SE.getConstant(SC->getType(), 0); + const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop()); + if (const SCEVAddRecExpr *ShiftedAddRec = + dyn_cast<SCEVAddRecExpr>(Shifted)) + return ShiftedAddRec->getNumIterationsInRange( + Range.subtract(SC->getValue()->getValue()), SE); + // This is strange and shouldn't happen. + return SE.getCouldNotCompute(); + } + + // The only time we can solve this is when we have all constant indices. + // Otherwise, we cannot determine the overflow conditions. + for (unsigned i = 0, e = getNumOperands(); i != e; ++i) + if (!isa<SCEVConstant>(getOperand(i))) + return SE.getCouldNotCompute(); + + + // Okay at this point we know that all elements of the chrec are constants and + // that the start element is zero. + + // First check to see if the range contains zero. If not, the first + // iteration exits. + unsigned BitWidth = SE.getTypeSizeInBits(getType()); + if (!Range.contains(APInt(BitWidth, 0))) + return SE.getConstant(getType(), 0); + + if (isAffine()) { + // If this is an affine expression then we have this situation: + // Solve {0,+,A} in Range === Ax in Range + + // We know that zero is in the range. If A is positive then we know that + // the upper value of the range must be the first possible exit value. + // If A is negative then the lower of the range is the last possible loop + // value. Also note that we already checked for a full range. + APInt One(BitWidth,1); + APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue(); + APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower(); + + // The exit value should be (End+A)/A. + APInt ExitVal = (End + A).udiv(A); + ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal); + + // Evaluate at the exit value. If we really did fall out of the valid + // range, then we computed our trip count, otherwise wrap around or other + // things must have happened. + ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE); + if (Range.contains(Val->getValue())) + return SE.getCouldNotCompute(); // Something strange happened + + // Ensure that the previous value is in the range. This is a sanity check. + assert(Range.contains( + EvaluateConstantChrecAtConstant(this, + ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) && + "Linear scev computation is off in a bad way!"); + return SE.getConstant(ExitValue); + } else if (isQuadratic()) { + // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the + // quadratic equation to solve it. To do this, we must frame our problem in + // terms of figuring out when zero is crossed, instead of when + // Range.getUpper() is crossed. + SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end()); + NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper())); + const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop()); + + // Next, solve the constructed addrec + std::pair<const SCEV *,const SCEV *> Roots = + SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE); + const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first); + const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second); + if (R1) { + // Pick the smallest positive root value. + if (ConstantInt *CB = + dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT, + R1->getValue(), R2->getValue()))) { + if (CB->getZExtValue() == false) + std::swap(R1, R2); // R1 is the minimum root now. + + // Make sure the root is not off by one. The returned iteration should + // not be in the range, but the previous one should be. When solving + // for "X*X < 5", for example, we should not return a root of 2. + ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this, + R1->getValue(), + SE); + if (Range.contains(R1Val->getValue())) { + // The next iteration must be out of the range... + ConstantInt *NextVal = + ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1); + + R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); + if (!Range.contains(R1Val->getValue())) + return SE.getConstant(NextVal); + return SE.getCouldNotCompute(); // Something strange happened + } + + // If R1 was not in the range, then it is a good return value. Make + // sure that R1-1 WAS in the range though, just in case. + ConstantInt *NextVal = + ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1); + R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE); + if (Range.contains(R1Val->getValue())) + return R1; + return SE.getCouldNotCompute(); // Something strange happened + } + } + } + + return SE.getCouldNotCompute(); +} + + + +//===----------------------------------------------------------------------===// +// SCEVCallbackVH Class Implementation +//===----------------------------------------------------------------------===// + +void ScalarEvolution::SCEVCallbackVH::deleted() { + assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!"); + if (PHINode *PN = dyn_cast<PHINode>(getValPtr())) + SE->ConstantEvolutionLoopExitValue.erase(PN); + SE->Scalars.erase(getValPtr()); + // this now dangles! +} + +void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *) { + assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!"); + + // Forget all the expressions associated with users of the old value, + // so that future queries will recompute the expressions using the new + // value. + SmallVector<User *, 16> Worklist; + SmallPtrSet<User *, 8> Visited; + Value *Old = getValPtr(); + bool DeleteOld = false; + for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end(); + UI != UE; ++UI) + Worklist.push_back(*UI); + while (!Worklist.empty()) { + User *U = Worklist.pop_back_val(); + // Deleting the Old value will cause this to dangle. Postpone + // that until everything else is done. + if (U == Old) { + DeleteOld = true; + continue; + } + if (!Visited.insert(U)) + continue; + if (PHINode *PN = dyn_cast<PHINode>(U)) + SE->ConstantEvolutionLoopExitValue.erase(PN); + SE->Scalars.erase(U); + for (Value::use_iterator UI = U->use_begin(), UE = U->use_end(); + UI != UE; ++UI) + Worklist.push_back(*UI); + } + // Delete the Old value if it (indirectly) references itself. + if (DeleteOld) { + if (PHINode *PN = dyn_cast<PHINode>(Old)) + SE->ConstantEvolutionLoopExitValue.erase(PN); + SE->Scalars.erase(Old); + // this now dangles! + } + // this may dangle! +} + +ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se) + : CallbackVH(V), SE(se) {} + +//===----------------------------------------------------------------------===// +// ScalarEvolution Class Implementation +//===----------------------------------------------------------------------===// + +ScalarEvolution::ScalarEvolution() + : FunctionPass(&ID) { +} + +bool ScalarEvolution::runOnFunction(Function &F) { + this->F = &F; + LI = &getAnalysis<LoopInfo>(); + TD = getAnalysisIfAvailable<TargetData>(); + DT = &getAnalysis<DominatorTree>(); + return false; +} + +void ScalarEvolution::releaseMemory() { + Scalars.clear(); + BackedgeTakenCounts.clear(); + ConstantEvolutionLoopExitValue.clear(); + ValuesAtScopes.clear(); + UniqueSCEVs.clear(); + SCEVAllocator.Reset(); +} + +void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const { + AU.setPreservesAll(); + AU.addRequiredTransitive<LoopInfo>(); + AU.addRequiredTransitive<DominatorTree>(); +} + +bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) { + return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L)); +} + +static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE, + const Loop *L) { + // Print all inner loops first + for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) + PrintLoopInfo(OS, SE, *I); + + OS << "Loop "; + WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false); + OS << ": "; + + SmallVector<BasicBlock *, 8> ExitBlocks; + L->getExitBlocks(ExitBlocks); + if (ExitBlocks.size() != 1) + OS << "<multiple exits> "; + + if (SE->hasLoopInvariantBackedgeTakenCount(L)) { + OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L); + } else { + OS << "Unpredictable backedge-taken count. "; + } + + OS << "\n" + "Loop "; + WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false); + OS << ": "; + + if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) { + OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L); + } else { + OS << "Unpredictable max backedge-taken count. "; + } + + OS << "\n"; +} + +void ScalarEvolution::print(raw_ostream &OS, const Module *) const { + // ScalarEvolution's implementation of the print method is to print + // out SCEV values of all instructions that are interesting. Doing + // this potentially causes it to create new SCEV objects though, + // which technically conflicts with the const qualifier. This isn't + // observable from outside the class though, so casting away the + // const isn't dangerous. + ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this); + + OS << "Classifying expressions for: "; + WriteAsOperand(OS, F, /*PrintType=*/false); + OS << "\n"; + for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I) + if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) { + OS << *I << '\n'; + OS << " --> "; + const SCEV *SV = SE.getSCEV(&*I); + SV->print(OS); + + const Loop *L = LI->getLoopFor((*I).getParent()); + + const SCEV *AtUse = SE.getSCEVAtScope(SV, L); + if (AtUse != SV) { + OS << " --> "; + AtUse->print(OS); + } + + if (L) { + OS << "\t\t" "Exits: "; + const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop()); + if (!ExitValue->isLoopInvariant(L)) { + OS << "<<Unknown>>"; + } else { + OS << *ExitValue; + } + } + + OS << "\n"; + } + + OS << "Determining loop execution counts for: "; + WriteAsOperand(OS, F, /*PrintType=*/false); + OS << "\n"; + for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I) + PrintLoopInfo(OS, &SE, *I); +} + |
