//===- ScalarEvolution.cpp - Scalar Evolution Analysis --------------------===// // // 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 // //===----------------------------------------------------------------------===// #include "llvm/Analysis/ScalarEvolution.h" #include "llvm/ADT/Optional.h" #include "llvm/ADT/STLExtras.h" #include "llvm/ADT/SmallPtrSet.h" #include "llvm/ADT/Statistic.h" #include "llvm/Analysis/AssumptionCache.h" #include "llvm/Analysis/ConstantFolding.h" #include "llvm/Analysis/InstructionSimplify.h" #include "llvm/Analysis/LoopInfo.h" #include "llvm/Analysis/ScalarEvolutionExpressions.h" #include "llvm/Analysis/TargetLibraryInfo.h" #include "llvm/Analysis/ValueTracking.h" #include "llvm/IR/ConstantRange.h" #include "llvm/IR/Constants.h" #include "llvm/IR/DataLayout.h" #include "llvm/IR/DerivedTypes.h" #include "llvm/IR/Dominators.h" #include "llvm/IR/GetElementPtrTypeIterator.h" #include "llvm/IR/GlobalAlias.h" #include "llvm/IR/GlobalVariable.h" #include "llvm/IR/InstIterator.h" #include "llvm/IR/Instructions.h" #include "llvm/IR/LLVMContext.h" #include "llvm/IR/Metadata.h" #include "llvm/IR/Operator.h" #include "llvm/Support/CommandLine.h" #include "llvm/Support/Debug.h" #include "llvm/Support/ErrorHandling.h" #include "llvm/Support/MathExtras.h" #include "llvm/Support/raw_ostream.h" #include using namespace llvm; #define DEBUG_TYPE "scalar-evolution" 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 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden, cl::desc("Maximum number of iterations SCEV will " "symbolically execute a constant " "derived loop"), cl::init(100)); // FIXME: Enable this with XDEBUG when the test suite is clean. static cl::opt VerifySCEV("verify-scev", cl::desc("Verify ScalarEvolution's backedge taken counts (slow)")); INITIALIZE_PASS_BEGIN(ScalarEvolution, "scalar-evolution", "Scalar Evolution Analysis", false, true) INITIALIZE_PASS_DEPENDENCY(AssumptionCacheTracker) INITIALIZE_PASS_DEPENDENCY(LoopInfoWrapperPass) INITIALIZE_PASS_DEPENDENCY(DominatorTreeWrapperPass) INITIALIZE_PASS_DEPENDENCY(TargetLibraryInfoWrapperPass) INITIALIZE_PASS_END(ScalarEvolution, "scalar-evolution", "Scalar Evolution Analysis", false, true) char ScalarEvolution::ID = 0; //===----------------------------------------------------------------------===// // SCEV class definitions //===----------------------------------------------------------------------===// //===----------------------------------------------------------------------===// // Implementation of the SCEV class. // #if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP) void SCEV::dump() const { print(dbgs()); dbgs() << '\n'; } #endif void SCEV::print(raw_ostream &OS) const { switch (static_cast(getSCEVType())) { case scConstant: cast(this)->getValue()->printAsOperand(OS, false); return; case scTruncate: { const SCEVTruncateExpr *Trunc = cast(this); const SCEV *Op = Trunc->getOperand(); OS << "(trunc " << *Op->getType() << " " << *Op << " to " << *Trunc->getType() << ")"; return; } case scZeroExtend: { const SCEVZeroExtendExpr *ZExt = cast(this); const SCEV *Op = ZExt->getOperand(); OS << "(zext " << *Op->getType() << " " << *Op << " to " << *ZExt->getType() << ")"; return; } case scSignExtend: { const SCEVSignExtendExpr *SExt = cast(this); const SCEV *Op = SExt->getOperand(); OS << "(sext " << *Op->getType() << " " << *Op << " to " << *SExt->getType() << ")"; return; } case scAddRecExpr: { const SCEVAddRecExpr *AR = cast(this); OS << "{" << *AR->getOperand(0); for (unsigned i = 1, e = AR->getNumOperands(); i != e; ++i) OS << ",+," << *AR->getOperand(i); OS << "}<"; if (AR->getNoWrapFlags(FlagNUW)) OS << "nuw><"; if (AR->getNoWrapFlags(FlagNSW)) OS << "nsw><"; if (AR->getNoWrapFlags(FlagNW) && !AR->getNoWrapFlags((NoWrapFlags)(FlagNUW | FlagNSW))) OS << "nw><"; AR->getLoop()->getHeader()->printAsOperand(OS, /*PrintType=*/false); OS << ">"; return; } case scAddExpr: case scMulExpr: case scUMaxExpr: case scSMaxExpr: { const SCEVNAryExpr *NAry = cast(this); const char *OpStr = nullptr; switch (NAry->getSCEVType()) { case scAddExpr: OpStr = " + "; break; case scMulExpr: OpStr = " * "; break; case scUMaxExpr: OpStr = " umax "; break; case scSMaxExpr: OpStr = " smax "; break; } OS << "("; for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end(); I != E; ++I) { OS << **I; if (std::next(I) != E) OS << OpStr; } OS << ")"; switch (NAry->getSCEVType()) { case scAddExpr: case scMulExpr: if (NAry->getNoWrapFlags(FlagNUW)) OS << ""; if (NAry->getNoWrapFlags(FlagNSW)) OS << ""; } return; } case scUDivExpr: { const SCEVUDivExpr *UDiv = cast(this); OS << "(" << *UDiv->getLHS() << " /u " << *UDiv->getRHS() << ")"; return; } case scUnknown: { const SCEVUnknown *U = cast(this); Type *AllocTy; if (U->isSizeOf(AllocTy)) { OS << "sizeof(" << *AllocTy << ")"; return; } if (U->isAlignOf(AllocTy)) { OS << "alignof(" << *AllocTy << ")"; return; } Type *CTy; Constant *FieldNo; if (U->isOffsetOf(CTy, FieldNo)) { OS << "offsetof(" << *CTy << ", "; FieldNo->printAsOperand(OS, false); OS << ")"; return; } // Otherwise just print it normally. U->getValue()->printAsOperand(OS, false); return; } case scCouldNotCompute: OS << "***COULDNOTCOMPUTE***"; return; } llvm_unreachable("Unknown SCEV kind!"); } Type *SCEV::getType() const { switch (static_cast(getSCEVType())) { case scConstant: return cast(this)->getType(); case scTruncate: case scZeroExtend: case scSignExtend: return cast(this)->getType(); case scAddRecExpr: case scMulExpr: case scUMaxExpr: case scSMaxExpr: return cast(this)->getType(); case scAddExpr: return cast(this)->getType(); case scUDivExpr: return cast(this)->getType(); case scUnknown: return cast(this)->getType(); case scCouldNotCompute: llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); } llvm_unreachable("Unknown SCEV kind!"); } bool SCEV::isZero() const { if (const SCEVConstant *SC = dyn_cast(this)) return SC->getValue()->isZero(); return false; } bool SCEV::isOne() const { if (const SCEVConstant *SC = dyn_cast(this)) return SC->getValue()->isOne(); return false; } bool SCEV::isAllOnesValue() const { if (const SCEVConstant *SC = dyn_cast(this)) return SC->getValue()->isAllOnesValue(); return false; } /// isNonConstantNegative - Return true if the specified scev is negated, but /// not a constant. bool SCEV::isNonConstantNegative() const { const SCEVMulExpr *Mul = dyn_cast(this); if (!Mul) return false; // If there is a constant factor, it will be first. const SCEVConstant *SC = dyn_cast(Mul->getOperand(0)); if (!SC) return false; // Return true if the value is negative, this matches things like (-42 * V). return SC->getValue()->getValue().isNegative(); } SCEVCouldNotCompute::SCEVCouldNotCompute() : SCEV(FoldingSetNodeIDRef(), scCouldNotCompute) {} 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 = nullptr; 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(Type *Ty, uint64_t V, bool isSigned) { IntegerType *ITy = cast(getEffectiveSCEVType(Ty)); return getConstant(ConstantInt::get(ITy, V, isSigned)); } SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID, unsigned SCEVTy, const SCEV *op, Type *ty) : SCEV(ID, SCEVTy), Op(op), Ty(ty) {} SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID, const SCEV *op, Type *ty) : SCEVCastExpr(ID, scTruncate, op, ty) { assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) && (Ty->isIntegerTy() || Ty->isPointerTy()) && "Cannot truncate non-integer value!"); } SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID, const SCEV *op, Type *ty) : SCEVCastExpr(ID, scZeroExtend, op, ty) { assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) && (Ty->isIntegerTy() || Ty->isPointerTy()) && "Cannot zero extend non-integer value!"); } SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID, const SCEV *op, 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 SCEVUnknown::deleted() { // Clear this SCEVUnknown from various maps. SE->forgetMemoizedResults(this); // Remove this SCEVUnknown from the uniquing map. SE->UniqueSCEVs.RemoveNode(this); // Release the value. setValPtr(nullptr); } void SCEVUnknown::allUsesReplacedWith(Value *New) { // Clear this SCEVUnknown from various maps. SE->forgetMemoizedResults(this); // Remove this SCEVUnknown from the uniquing map. SE->UniqueSCEVs.RemoveNode(this); // Update this SCEVUnknown to point to the new value. This is needed // because there may still be outstanding SCEVs which still point to // this SCEVUnknown. setValPtr(New); } bool SCEVUnknown::isSizeOf(Type *&AllocTy) const { if (ConstantExpr *VCE = dyn_cast(getValue())) if (VCE->getOpcode() == Instruction::PtrToInt) if (ConstantExpr *CE = dyn_cast(VCE->getOperand(0))) if (CE->getOpcode() == Instruction::GetElementPtr && CE->getOperand(0)->isNullValue() && CE->getNumOperands() == 2) if (ConstantInt *CI = dyn_cast(CE->getOperand(1))) if (CI->isOne()) { AllocTy = cast(CE->getOperand(0)->getType()) ->getElementType(); return true; } return false; } bool SCEVUnknown::isAlignOf(Type *&AllocTy) const { if (ConstantExpr *VCE = dyn_cast(getValue())) if (VCE->getOpcode() == Instruction::PtrToInt) if (ConstantExpr *CE = dyn_cast(VCE->getOperand(0))) if (CE->getOpcode() == Instruction::GetElementPtr && CE->getOperand(0)->isNullValue()) { Type *Ty = cast(CE->getOperand(0)->getType())->getElementType(); if (StructType *STy = dyn_cast(Ty)) if (!STy->isPacked() && CE->getNumOperands() == 3 && CE->getOperand(1)->isNullValue()) { if (ConstantInt *CI = dyn_cast(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(Type *&CTy, Constant *&FieldNo) const { if (ConstantExpr *VCE = dyn_cast(getValue())) if (VCE->getOpcode() == Instruction::PtrToInt) if (ConstantExpr *CE = dyn_cast(VCE->getOperand(0))) if (CE->getOpcode() == Instruction::GetElementPtr && CE->getNumOperands() == 3 && CE->getOperand(0)->isNullValue() && CE->getOperand(1)->isNullValue()) { Type *Ty = cast(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; } //===----------------------------------------------------------------------===// // SCEV Utilities //===----------------------------------------------------------------------===// namespace { /// SCEVComplexityCompare - Return true if the complexity of the LHS is less /// than the complexity of the RHS. This comparator is used to canonicalize /// expressions. class SCEVComplexityCompare { const LoopInfo *const LI; public: explicit SCEVComplexityCompare(const LoopInfo *li) : LI(li) {} // Return true or false if LHS is less than, or at least RHS, respectively. bool operator()(const SCEV *LHS, const SCEV *RHS) const { return compare(LHS, RHS) < 0; } // Return negative, zero, or positive, if LHS is less than, equal to, or // greater than RHS, respectively. A three-way result allows recursive // comparisons to be more efficient. int compare(const SCEV *LHS, const SCEV *RHS) const { // Fast-path: SCEVs are uniqued so we can do a quick equality check. if (LHS == RHS) return 0; // Primarily, sort the SCEVs by their getSCEVType(). unsigned LType = LHS->getSCEVType(), RType = RHS->getSCEVType(); if (LType != RType) return (int)LType - (int)RType; // 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. switch (static_cast(LType)) { case scUnknown: { const SCEVUnknown *LU = cast(LHS); const SCEVUnknown *RU = cast(RHS); // Sort SCEVUnknown values with some loose heuristics. TODO: This is // not as complete as it could be. const Value *LV = LU->getValue(), *RV = RU->getValue(); // Order pointer values after integer values. This helps SCEVExpander // form GEPs. bool LIsPointer = LV->getType()->isPointerTy(), RIsPointer = RV->getType()->isPointerTy(); if (LIsPointer != RIsPointer) return (int)LIsPointer - (int)RIsPointer; // Compare getValueID values. unsigned LID = LV->getValueID(), RID = RV->getValueID(); if (LID != RID) return (int)LID - (int)RID; // Sort arguments by their position. if (const Argument *LA = dyn_cast(LV)) { const Argument *RA = cast(RV); unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo(); return (int)LArgNo - (int)RArgNo; } // For instructions, compare their loop depth, and their operand // count. This is pretty loose. if (const Instruction *LInst = dyn_cast(LV)) { const Instruction *RInst = cast(RV); // Compare loop depths. const BasicBlock *LParent = LInst->getParent(), *RParent = RInst->getParent(); if (LParent != RParent) { unsigned LDepth = LI->getLoopDepth(LParent), RDepth = LI->getLoopDepth(RParent); if (LDepth != RDepth) return (int)LDepth - (int)RDepth; } // Compare the number of operands. unsigned LNumOps = LInst->getNumOperands(), RNumOps = RInst->getNumOperands(); return (int)LNumOps - (int)RNumOps; } return 0; } case scConstant: { const SCEVConstant *LC = cast(LHS); const SCEVConstant *RC = cast(RHS); // Compare constant values. const APInt &LA = LC->getValue()->getValue(); const APInt &RA = RC->getValue()->getValue(); unsigned LBitWidth = LA.getBitWidth(), RBitWidth = RA.getBitWidth(); if (LBitWidth != RBitWidth) return (int)LBitWidth - (int)RBitWidth; return LA.ult(RA) ? -1 : 1; } case scAddRecExpr: { const SCEVAddRecExpr *LA = cast(LHS); const SCEVAddRecExpr *RA = cast(RHS); // Compare addrec loop depths. const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop(); if (LLoop != RLoop) { unsigned LDepth = LLoop->getLoopDepth(), RDepth = RLoop->getLoopDepth(); if (LDepth != RDepth) return (int)LDepth - (int)RDepth; } // Addrec complexity grows with operand count. unsigned LNumOps = LA->getNumOperands(), RNumOps = RA->getNumOperands(); if (LNumOps != RNumOps) return (int)LNumOps - (int)RNumOps; // Lexicographically compare. for (unsigned i = 0; i != LNumOps; ++i) { long X = compare(LA->getOperand(i), RA->getOperand(i)); if (X != 0) return X; } return 0; } case scAddExpr: case scMulExpr: case scSMaxExpr: case scUMaxExpr: { const SCEVNAryExpr *LC = cast(LHS); const SCEVNAryExpr *RC = cast(RHS); // Lexicographically compare n-ary expressions. unsigned LNumOps = LC->getNumOperands(), RNumOps = RC->getNumOperands(); if (LNumOps != RNumOps) return (int)LNumOps - (int)RNumOps; for (unsigned i = 0; i != LNumOps; ++i) { if (i >= RNumOps) return 1; long X = compare(LC->getOperand(i), RC->getOperand(i)); if (X != 0) return X; } return (int)LNumOps - (int)RNumOps; } case scUDivExpr: { const SCEVUDivExpr *LC = cast(LHS); const SCEVUDivExpr *RC = cast(RHS); // Lexicographically compare udiv expressions. long X = compare(LC->getLHS(), RC->getLHS()); if (X != 0) return X; return compare(LC->getRHS(), RC->getRHS()); } case scTruncate: case scZeroExtend: case scSignExtend: { const SCEVCastExpr *LC = cast(LHS); const SCEVCastExpr *RC = cast(RHS); // Compare cast expressions by operand. return compare(LC->getOperand(), RC->getOperand()); } case scCouldNotCompute: llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); } llvm_unreachable("Unknown SCEV kind!"); } }; } /// 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 &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. const SCEV *&LHS = Ops[0], *&RHS = Ops[1]; if (SCEVComplexityCompare(LI)(RHS, LHS)) std::swap(LHS, RHS); 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! } } } } namespace { struct FindSCEVSize { int Size; FindSCEVSize() : Size(0) {} bool follow(const SCEV *S) { ++Size; // Keep looking at all operands of S. return true; } bool isDone() const { return false; } }; } // Returns the size of the SCEV S. static inline int sizeOfSCEV(const SCEV *S) { FindSCEVSize F; SCEVTraversal ST(F); ST.visitAll(S); return F.Size; } namespace { struct SCEVDivision : public SCEVVisitor { public: // Computes the Quotient and Remainder of the division of Numerator by // Denominator. static void divide(ScalarEvolution &SE, const SCEV *Numerator, const SCEV *Denominator, const SCEV **Quotient, const SCEV **Remainder) { assert(Numerator && Denominator && "Uninitialized SCEV"); SCEVDivision D(SE, Numerator, Denominator); // Check for the trivial case here to avoid having to check for it in the // rest of the code. if (Numerator == Denominator) { *Quotient = D.One; *Remainder = D.Zero; return; } if (Numerator->isZero()) { *Quotient = D.Zero; *Remainder = D.Zero; return; } // Split the Denominator when it is a product. if (const SCEVMulExpr *T = dyn_cast(Denominator)) { const SCEV *Q, *R; *Quotient = Numerator; for (const SCEV *Op : T->operands()) { divide(SE, *Quotient, Op, &Q, &R); *Quotient = Q; // Bail out when the Numerator is not divisible by one of the terms of // the Denominator. if (!R->isZero()) { *Quotient = D.Zero; *Remainder = Numerator; return; } } *Remainder = D.Zero; return; } D.visit(Numerator); *Quotient = D.Quotient; *Remainder = D.Remainder; } // Except in the trivial case described above, we do not know how to divide // Expr by Denominator for the following functions with empty implementation. void visitTruncateExpr(const SCEVTruncateExpr *Numerator) {} void visitZeroExtendExpr(const SCEVZeroExtendExpr *Numerator) {} void visitSignExtendExpr(const SCEVSignExtendExpr *Numerator) {} void visitUDivExpr(const SCEVUDivExpr *Numerator) {} void visitSMaxExpr(const SCEVSMaxExpr *Numerator) {} void visitUMaxExpr(const SCEVUMaxExpr *Numerator) {} void visitUnknown(const SCEVUnknown *Numerator) {} void visitCouldNotCompute(const SCEVCouldNotCompute *Numerator) {} void visitConstant(const SCEVConstant *Numerator) { if (const SCEVConstant *D = dyn_cast(Denominator)) { APInt NumeratorVal = Numerator->getValue()->getValue(); APInt DenominatorVal = D->getValue()->getValue(); uint32_t NumeratorBW = NumeratorVal.getBitWidth(); uint32_t DenominatorBW = DenominatorVal.getBitWidth(); if (NumeratorBW > DenominatorBW) DenominatorVal = DenominatorVal.sext(NumeratorBW); else if (NumeratorBW < DenominatorBW) NumeratorVal = NumeratorVal.sext(DenominatorBW); APInt QuotientVal(NumeratorVal.getBitWidth(), 0); APInt RemainderVal(NumeratorVal.getBitWidth(), 0); APInt::sdivrem(NumeratorVal, DenominatorVal, QuotientVal, RemainderVal); Quotient = SE.getConstant(QuotientVal); Remainder = SE.getConstant(RemainderVal); return; } } void visitAddRecExpr(const SCEVAddRecExpr *Numerator) { const SCEV *StartQ, *StartR, *StepQ, *StepR; assert(Numerator->isAffine() && "Numerator should be affine"); divide(SE, Numerator->getStart(), Denominator, &StartQ, &StartR); divide(SE, Numerator->getStepRecurrence(SE), Denominator, &StepQ, &StepR); Quotient = SE.getAddRecExpr(StartQ, StepQ, Numerator->getLoop(), Numerator->getNoWrapFlags()); Remainder = SE.getAddRecExpr(StartR, StepR, Numerator->getLoop(), Numerator->getNoWrapFlags()); } void visitAddExpr(const SCEVAddExpr *Numerator) { SmallVector Qs, Rs; Type *Ty = Denominator->getType(); for (const SCEV *Op : Numerator->operands()) { const SCEV *Q, *R; divide(SE, Op, Denominator, &Q, &R); // Bail out if types do not match. if (Ty != Q->getType() || Ty != R->getType()) { Quotient = Zero; Remainder = Numerator; return; } Qs.push_back(Q); Rs.push_back(R); } if (Qs.size() == 1) { Quotient = Qs[0]; Remainder = Rs[0]; return; } Quotient = SE.getAddExpr(Qs); Remainder = SE.getAddExpr(Rs); } void visitMulExpr(const SCEVMulExpr *Numerator) { SmallVector Qs; Type *Ty = Denominator->getType(); bool FoundDenominatorTerm = false; for (const SCEV *Op : Numerator->operands()) { // Bail out if types do not match. if (Ty != Op->getType()) { Quotient = Zero; Remainder = Numerator; return; } if (FoundDenominatorTerm) { Qs.push_back(Op); continue; } // Check whether Denominator divides one of the product operands. const SCEV *Q, *R; divide(SE, Op, Denominator, &Q, &R); if (!R->isZero()) { Qs.push_back(Op); continue; } // Bail out if types do not match. if (Ty != Q->getType()) { Quotient = Zero; Remainder = Numerator; return; } FoundDenominatorTerm = true; Qs.push_back(Q); } if (FoundDenominatorTerm) { Remainder = Zero; if (Qs.size() == 1) Quotient = Qs[0]; else Quotient = SE.getMulExpr(Qs); return; } if (!isa(Denominator)) { Quotient = Zero; Remainder = Numerator; return; } // The Remainder is obtained by replacing Denominator by 0 in Numerator. ValueToValueMap RewriteMap; RewriteMap[cast(Denominator)->getValue()] = cast(Zero)->getValue(); Remainder = SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true); if (Remainder->isZero()) { // The Quotient is obtained by replacing Denominator by 1 in Numerator. RewriteMap[cast(Denominator)->getValue()] = cast(One)->getValue(); Quotient = SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true); return; } // Quotient is (Numerator - Remainder) divided by Denominator. const SCEV *Q, *R; const SCEV *Diff = SE.getMinusSCEV(Numerator, Remainder); if (sizeOfSCEV(Diff) > sizeOfSCEV(Numerator)) { // This SCEV does not seem to simplify: fail the division here. Quotient = Zero; Remainder = Numerator; return; } divide(SE, Diff, Denominator, &Q, &R); assert(R == Zero && "(Numerator - Remainder) should evenly divide Denominator"); Quotient = Q; } private: SCEVDivision(ScalarEvolution &S, const SCEV *Numerator, const SCEV *Denominator) : SE(S), Denominator(Denominator) { Zero = SE.getConstant(Denominator->getType(), 0); One = SE.getConstant(Denominator->getType(), 1); // By default, we don't know how to divide Expr by Denominator. // Providing the default here simplifies the rest of the code. Quotient = Zero; Remainder = Numerator; } ScalarEvolution &SE; const SCEV *Denominator, *Quotient, *Remainder, *Zero, *One; }; } //===----------------------------------------------------------------------===// // 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, 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::getOneBitSet(CalculationBits, 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 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(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, 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 = nullptr; if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; // Fold if the operand is constant. if (const SCEVConstant *SC = dyn_cast(Op)) return getConstant( cast(ConstantExpr::getTrunc(SC->getValue(), Ty))); // trunc(trunc(x)) --> trunc(x) if (const SCEVTruncateExpr *ST = dyn_cast(Op)) return getTruncateExpr(ST->getOperand(), Ty); // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing if (const SCEVSignExtendExpr *SS = dyn_cast(Op)) return getTruncateOrSignExtend(SS->getOperand(), Ty); // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing if (const SCEVZeroExtendExpr *SZ = dyn_cast(Op)) return getTruncateOrZeroExtend(SZ->getOperand(), Ty); // trunc(x1+x2+...+xN) --> trunc(x1)+trunc(x2)+...+trunc(xN) if we can // eliminate all the truncates. if (const SCEVAddExpr *SA = dyn_cast(Op)) { SmallVector Operands; bool hasTrunc = false; for (unsigned i = 0, e = SA->getNumOperands(); i != e && !hasTrunc; ++i) { const SCEV *S = getTruncateExpr(SA->getOperand(i), Ty); hasTrunc = isa(S); Operands.push_back(S); } if (!hasTrunc) return getAddExpr(Operands); UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL. } // trunc(x1*x2*...*xN) --> trunc(x1)*trunc(x2)*...*trunc(xN) if we can // eliminate all the truncates. if (const SCEVMulExpr *SM = dyn_cast(Op)) { SmallVector Operands; bool hasTrunc = false; for (unsigned i = 0, e = SM->getNumOperands(); i != e && !hasTrunc; ++i) { const SCEV *S = getTruncateExpr(SM->getOperand(i), Ty); hasTrunc = isa(S); Operands.push_back(S); } if (!hasTrunc) return getMulExpr(Operands); UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL. } // If the input value is a chrec scev, truncate the chrec's operands. if (const SCEVAddRecExpr *AddRec = dyn_cast(Op)) { SmallVector Operands; for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty)); return getAddRecExpr(Operands, AddRec->getLoop(), SCEV::FlagAnyWrap); } // The cast wasn't folded; create an explicit cast node. We can reuse // the existing insert position since if we get here, we won't have // made any changes which would invalidate it. SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator), Op, Ty); UniqueSCEVs.InsertNode(S, IP); return S; } // Get the limit of a recurrence such that incrementing by Step cannot cause // signed overflow as long as the value of the recurrence within the // loop does not exceed this limit before incrementing. static const SCEV *getSignedOverflowLimitForStep(const SCEV *Step, ICmpInst::Predicate *Pred, ScalarEvolution *SE) { unsigned BitWidth = SE->getTypeSizeInBits(Step->getType()); if (SE->isKnownPositive(Step)) { *Pred = ICmpInst::ICMP_SLT; return SE->getConstant(APInt::getSignedMinValue(BitWidth) - SE->getSignedRange(Step).getSignedMax()); } if (SE->isKnownNegative(Step)) { *Pred = ICmpInst::ICMP_SGT; return SE->getConstant(APInt::getSignedMaxValue(BitWidth) - SE->getSignedRange(Step).getSignedMin()); } return nullptr; } // Get the limit of a recurrence such that incrementing by Step cannot cause // unsigned overflow as long as the value of the recurrence within the loop does // not exceed this limit before incrementing. static const SCEV *getUnsignedOverflowLimitForStep(const SCEV *Step, ICmpInst::Predicate *Pred, ScalarEvolution *SE) { unsigned BitWidth = SE->getTypeSizeInBits(Step->getType()); *Pred = ICmpInst::ICMP_ULT; return SE->getConstant(APInt::getMinValue(BitWidth) - SE->getUnsignedRange(Step).getUnsignedMax()); } namespace { struct ExtendOpTraitsBase { typedef const SCEV *(ScalarEvolution::*GetExtendExprTy)(const SCEV *, Type *); }; // Used to make code generic over signed and unsigned overflow. template struct ExtendOpTraits { // Members present: // // static const SCEV::NoWrapFlags WrapType; // // static const ExtendOpTraitsBase::GetExtendExprTy GetExtendExpr; // // static const SCEV *getOverflowLimitForStep(const SCEV *Step, // ICmpInst::Predicate *Pred, // ScalarEvolution *SE); }; template <> struct ExtendOpTraits : public ExtendOpTraitsBase { static const SCEV::NoWrapFlags WrapType = SCEV::FlagNSW; static const GetExtendExprTy GetExtendExpr; static const SCEV *getOverflowLimitForStep(const SCEV *Step, ICmpInst::Predicate *Pred, ScalarEvolution *SE) { return getSignedOverflowLimitForStep(Step, Pred, SE); } }; const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits< SCEVSignExtendExpr>::GetExtendExpr = &ScalarEvolution::getSignExtendExpr; template <> struct ExtendOpTraits : public ExtendOpTraitsBase { static const SCEV::NoWrapFlags WrapType = SCEV::FlagNUW; static const GetExtendExprTy GetExtendExpr; static const SCEV *getOverflowLimitForStep(const SCEV *Step, ICmpInst::Predicate *Pred, ScalarEvolution *SE) { return getUnsignedOverflowLimitForStep(Step, Pred, SE); } }; const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits< SCEVZeroExtendExpr>::GetExtendExpr = &ScalarEvolution::getZeroExtendExpr; } // The recurrence AR has been shown to have no signed/unsigned wrap or something // close to it. Typically, if we can prove NSW/NUW for AR, then we can just as // easily prove NSW/NUW for its preincrement or postincrement sibling. This // allows normalizing a sign/zero extended AddRec as such: {sext/zext(Step + // Start),+,Step} => {(Step + sext/zext(Start),+,Step} As a result, the // expression "Step + sext/zext(PreIncAR)" is congruent with // "sext/zext(PostIncAR)" template static const SCEV *getPreStartForExtend(const SCEVAddRecExpr *AR, Type *Ty, ScalarEvolution *SE) { auto WrapType = ExtendOpTraits::WrapType; auto GetExtendExpr = ExtendOpTraits::GetExtendExpr; const Loop *L = AR->getLoop(); const SCEV *Start = AR->getStart(); const SCEV *Step = AR->getStepRecurrence(*SE); // Check for a simple looking step prior to loop entry. const SCEVAddExpr *SA = dyn_cast(Start); if (!SA) return nullptr; // Create an AddExpr for "PreStart" after subtracting Step. Full SCEV // subtraction is expensive. For this purpose, perform a quick and dirty // difference, by checking for Step in the operand list. SmallVector DiffOps; for (const SCEV *Op : SA->operands()) if (Op != Step) DiffOps.push_back(Op); if (DiffOps.size() == SA->getNumOperands()) return nullptr; // Try to prove `WrapType` (SCEV::FlagNSW or SCEV::FlagNUW) on `PreStart` + // `Step`: // 1. NSW/NUW flags on the step increment. const SCEV *PreStart = SE->getAddExpr(DiffOps, SA->getNoWrapFlags()); const SCEVAddRecExpr *PreAR = dyn_cast( SE->getAddRecExpr(PreStart, Step, L, SCEV::FlagAnyWrap)); // "{S,+,X} is /" and "the backedge is taken at least once" implies // "S+X does not sign/unsign-overflow". // const SCEV *BECount = SE->getBackedgeTakenCount(L); if (PreAR && PreAR->getNoWrapFlags(WrapType) && !isa(BECount) && SE->isKnownPositive(BECount)) return PreStart; // 2. Direct overflow check on the step operation's expression. unsigned BitWidth = SE->getTypeSizeInBits(AR->getType()); Type *WideTy = IntegerType::get(SE->getContext(), BitWidth * 2); const SCEV *OperandExtendedStart = SE->getAddExpr((SE->*GetExtendExpr)(PreStart, WideTy), (SE->*GetExtendExpr)(Step, WideTy)); if ((SE->*GetExtendExpr)(Start, WideTy) == OperandExtendedStart) { if (PreAR && AR->getNoWrapFlags(WrapType)) { // If we know `AR` == {`PreStart`+`Step`,+,`Step`} is `WrapType` (FlagNSW // or FlagNUW) and that `PreStart` + `Step` is `WrapType` too, then // `PreAR` == {`PreStart`,+,`Step`} is also `WrapType`. Cache this fact. const_cast(PreAR)->setNoWrapFlags(WrapType); } return PreStart; } // 3. Loop precondition. ICmpInst::Predicate Pred; const SCEV *OverflowLimit = ExtendOpTraits::getOverflowLimitForStep(Step, &Pred, SE); if (OverflowLimit && SE->isLoopEntryGuardedByCond(L, Pred, PreStart, OverflowLimit)) { return PreStart; } return nullptr; } // Get the normalized zero or sign extended expression for this AddRec's Start. template static const SCEV *getExtendAddRecStart(const SCEVAddRecExpr *AR, Type *Ty, ScalarEvolution *SE) { auto GetExtendExpr = ExtendOpTraits::GetExtendExpr; const SCEV *PreStart = getPreStartForExtend(AR, Ty, SE); if (!PreStart) return (SE->*GetExtendExpr)(AR->getStart(), Ty); return SE->getAddExpr((SE->*GetExtendExpr)(AR->getStepRecurrence(*SE), Ty), (SE->*GetExtendExpr)(PreStart, Ty)); } // Try to prove away overflow by looking at "nearby" add recurrences. A // motivating example for this rule: if we know `{0,+,4}` is `ult` `-1` and it // does not itself wrap then we can conclude that `{1,+,4}` is `nuw`. // // Formally: // // {S,+,X} == {S-T,+,X} + T // => Ext({S,+,X}) == Ext({S-T,+,X} + T) // // If ({S-T,+,X} + T) does not overflow ... (1) // // RHS == Ext({S-T,+,X} + T) == Ext({S-T,+,X}) + Ext(T) // // If {S-T,+,X} does not overflow ... (2) // // RHS == Ext({S-T,+,X}) + Ext(T) == {Ext(S-T),+,Ext(X)} + Ext(T) // == {Ext(S-T)+Ext(T),+,Ext(X)} // // If (S-T)+T does not overflow ... (3) // // RHS == {Ext(S-T)+Ext(T),+,Ext(X)} == {Ext(S-T+T),+,Ext(X)} // == {Ext(S),+,Ext(X)} == LHS // // Thus, if (1), (2) and (3) are true for some T, then // Ext({S,+,X}) == {Ext(S),+,Ext(X)} // // (3) is implied by (1) -- "(S-T)+T does not overflow" is simply "({S-T,+,X}+T) // does not overflow" restricted to the 0th iteration. Therefore we only need // to check for (1) and (2). // // In the current context, S is `Start`, X is `Step`, Ext is `ExtendOpTy` and T // is `Delta` (defined below). // template bool ScalarEvolution::proveNoWrapByVaryingStart(const SCEV *Start, const SCEV *Step, const Loop *L) { auto WrapType = ExtendOpTraits::WrapType; // We restrict `Start` to a constant to prevent SCEV from spending too much // time here. It is correct (but more expensive) to continue with a // non-constant `Start` and do a general SCEV subtraction to compute // `PreStart` below. // const SCEVConstant *StartC = dyn_cast(Start); if (!StartC) return false; APInt StartAI = StartC->getValue()->getValue(); for (unsigned Delta : {-2, -1, 1, 2}) { const SCEV *PreStart = getConstant(StartAI - Delta); // Give up if we don't already have the add recurrence we need because // actually constructing an add recurrence is relatively expensive. const SCEVAddRecExpr *PreAR = [&]() { FoldingSetNodeID ID; ID.AddInteger(scAddRecExpr); ID.AddPointer(PreStart); ID.AddPointer(Step); ID.AddPointer(L); void *IP = nullptr; return static_cast( this->UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); }(); if (PreAR && PreAR->getNoWrapFlags(WrapType)) { // proves (2) const SCEV *DeltaS = getConstant(StartC->getType(), Delta); ICmpInst::Predicate Pred = ICmpInst::BAD_ICMP_PREDICATE; const SCEV *Limit = ExtendOpTraits::getOverflowLimitForStep( DeltaS, &Pred, this); if (Limit && isKnownPredicate(Pred, PreAR, Limit)) // proves (1) return true; } } return false; } const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op, 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(Op)) return getConstant( cast(ConstantExpr::getZExt(SC->getValue(), Ty))); // zext(zext(x)) --> zext(x) if (const SCEVZeroExtendExpr *SZ = dyn_cast(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 = nullptr; if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; // zext(trunc(x)) --> zext(x) or x or trunc(x) if (const SCEVTruncateExpr *ST = dyn_cast(Op)) { // It's possible the bits taken off by the truncate were all zero bits. If // so, we should be able to simplify this further. const SCEV *X = ST->getOperand(); ConstantRange CR = getUnsignedRange(X); unsigned TruncBits = getTypeSizeInBits(ST->getType()); unsigned NewBits = getTypeSizeInBits(Ty); if (CR.truncate(TruncBits).zeroExtend(NewBits).contains( CR.zextOrTrunc(NewBits))) return getTruncateOrZeroExtend(X, Ty); } // If the input value is a chrec scev, and we can prove that the value // did not overflow the old, smaller, value, we can zero extend all of the // operands (often constants). This allows analysis of something like // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; } if (const SCEVAddRecExpr *AR = dyn_cast(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->getNoWrapFlags(SCEV::FlagNUW)) return getAddRecExpr( getExtendAddRecStart(AR, Ty, this), getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags()); // 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(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) { Type *WideTy = IntegerType::get(getContext(), BitWidth * 2); // Check whether Start+Step*MaxBECount has no unsigned overflow. const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step); const SCEV *ZAdd = getZeroExtendExpr(getAddExpr(Start, ZMul), WideTy); const SCEV *WideStart = getZeroExtendExpr(Start, WideTy); const SCEV *WideMaxBECount = getZeroExtendExpr(CastedMaxBECount, WideTy); const SCEV *OperandExtendedAdd = getAddExpr(WideStart, getMulExpr(WideMaxBECount, getZeroExtendExpr(Step, WideTy))); if (ZAdd == OperandExtendedAdd) { // Cache knowledge of AR NUW, which is propagated to this AddRec. const_cast(AR)->setNoWrapFlags(SCEV::FlagNUW); // Return the expression with the addrec on the outside. return getAddRecExpr( getExtendAddRecStart(AR, Ty, this), getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags()); } // Similar to above, only this time treat the step value as signed. // This covers loops that count down. OperandExtendedAdd = getAddExpr(WideStart, getMulExpr(WideMaxBECount, getSignExtendExpr(Step, WideTy))); if (ZAdd == OperandExtendedAdd) { // Cache knowledge of AR NW, which is propagated to this AddRec. // Negative step causes unsigned wrap, but it still can't self-wrap. const_cast(AR)->setNoWrapFlags(SCEV::FlagNW); // Return the expression with the addrec on the outside. return getAddRecExpr( getExtendAddRecStart(AR, Ty, this), getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags()); } } // 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))) { // Cache knowledge of AR NUW, which is propagated to this AddRec. const_cast(AR)->setNoWrapFlags(SCEV::FlagNUW); // Return the expression with the addrec on the outside. return getAddRecExpr( getExtendAddRecStart(AR, Ty, this), getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags()); } } 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))) { // Cache knowledge of AR NW, which is propagated to this AddRec. // Negative step causes unsigned wrap, but it still can't self-wrap. const_cast(AR)->setNoWrapFlags(SCEV::FlagNW); // Return the expression with the addrec on the outside. return getAddRecExpr( getExtendAddRecStart(AR, Ty, this), getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags()); } } } if (proveNoWrapByVaryingStart(Start, Step, L)) { const_cast(AR)->setNoWrapFlags(SCEV::FlagNUW); return getAddRecExpr( getExtendAddRecStart(AR, Ty, this), getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags()); } } // 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, 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(Op)) return getConstant( cast(ConstantExpr::getSExt(SC->getValue(), Ty))); // sext(sext(x)) --> sext(x) if (const SCEVSignExtendExpr *SS = dyn_cast(Op)) return getSignExtendExpr(SS->getOperand(), Ty); // sext(zext(x)) --> zext(x) if (const SCEVZeroExtendExpr *SZ = dyn_cast(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(scSignExtend); ID.AddPointer(Op); ID.AddPointer(Ty); void *IP = nullptr; if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; // If the input value is provably positive, build a zext instead. if (isKnownNonNegative(Op)) return getZeroExtendExpr(Op, Ty); // sext(trunc(x)) --> sext(x) or x or trunc(x) if (const SCEVTruncateExpr *ST = dyn_cast(Op)) { // It's possible the bits taken off by the truncate were all sign bits. If // so, we should be able to simplify this further. const SCEV *X = ST->getOperand(); ConstantRange CR = getSignedRange(X); unsigned TruncBits = getTypeSizeInBits(ST->getType()); unsigned NewBits = getTypeSizeInBits(Ty); if (CR.truncate(TruncBits).signExtend(NewBits).contains( CR.sextOrTrunc(NewBits))) return getTruncateOrSignExtend(X, Ty); } // sext(C1 + (C2 * x)) --> C1 + sext(C2 * x) if C1 < C2 if (auto SA = dyn_cast(Op)) { if (SA->getNumOperands() == 2) { auto SC1 = dyn_cast(SA->getOperand(0)); auto SMul = dyn_cast(SA->getOperand(1)); if (SMul && SC1) { if (auto SC2 = dyn_cast(SMul->getOperand(0))) { const APInt &C1 = SC1->getValue()->getValue(); const APInt &C2 = SC2->getValue()->getValue(); if (C1.isStrictlyPositive() && C2.isStrictlyPositive() && C2.ugt(C1) && C2.isPowerOf2()) return getAddExpr(getSignExtendExpr(SC1, Ty), getSignExtendExpr(SMul, Ty)); } } } } // If the input value is a chrec scev, and we can prove that the value // did not overflow the old, smaller, value, we can sign extend all of the // operands (often constants). This allows analysis of something like // this: for (signed char X = 0; X < 100; ++X) { int Y = X; } if (const SCEVAddRecExpr *AR = dyn_cast(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->getNoWrapFlags(SCEV::FlagNSW)) return getAddRecExpr( getExtendAddRecStart(AR, Ty, this), getSignExtendExpr(Step, Ty), L, SCEV::FlagNSW); // 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(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) { Type *WideTy = IntegerType::get(getContext(), BitWidth * 2); // Check whether Start+Step*MaxBECount has no signed overflow. const SCEV *SMul = getMulExpr(CastedMaxBECount, Step); const SCEV *SAdd = getSignExtendExpr(getAddExpr(Start, SMul), WideTy); const SCEV *WideStart = getSignExtendExpr(Start, WideTy); const SCEV *WideMaxBECount = getZeroExtendExpr(CastedMaxBECount, WideTy); const SCEV *OperandExtendedAdd = getAddExpr(WideStart, getMulExpr(WideMaxBECount, getSignExtendExpr(Step, WideTy))); if (SAdd == OperandExtendedAdd) { // Cache knowledge of AR NSW, which is propagated to this AddRec. const_cast(AR)->setNoWrapFlags(SCEV::FlagNSW); // Return the expression with the addrec on the outside. return getAddRecExpr( getExtendAddRecStart(AR, Ty, this), getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags()); } // Similar to above, only this time treat the step value as unsigned. // This covers loops that count up with an unsigned step. OperandExtendedAdd = getAddExpr(WideStart, getMulExpr(WideMaxBECount, getZeroExtendExpr(Step, WideTy))); if (SAdd == OperandExtendedAdd) { // If AR wraps around then // // abs(Step) * MaxBECount > unsigned-max(AR->getType()) // => SAdd != OperandExtendedAdd // // Thus (AR is not NW => SAdd != OperandExtendedAdd) <=> // (SAdd == OperandExtendedAdd => AR is NW) const_cast(AR)->setNoWrapFlags(SCEV::FlagNW); // Return the expression with the addrec on the outside. return getAddRecExpr( getExtendAddRecStart(AR, Ty, this), getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags()); } } // 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. ICmpInst::Predicate Pred; const SCEV *OverflowLimit = getSignedOverflowLimitForStep(Step, &Pred, this); if (OverflowLimit && (isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) || (isLoopEntryGuardedByCond(L, Pred, Start, OverflowLimit) && isLoopBackedgeGuardedByCond(L, Pred, AR->getPostIncExpr(*this), OverflowLimit)))) { // Cache knowledge of AR NSW, then propagate NSW to the wide AddRec. const_cast(AR)->setNoWrapFlags(SCEV::FlagNSW); return getAddRecExpr( getExtendAddRecStart(AR, Ty, this), getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags()); } } // If Start and Step are constants, check if we can apply this // transformation: // sext{C1,+,C2} --> C1 + sext{0,+,C2} if C1 < C2 auto SC1 = dyn_cast(Start); auto SC2 = dyn_cast(Step); if (SC1 && SC2) { const APInt &C1 = SC1->getValue()->getValue(); const APInt &C2 = SC2->getValue()->getValue(); if (C1.isStrictlyPositive() && C2.isStrictlyPositive() && C2.ugt(C1) && C2.isPowerOf2()) { Start = getSignExtendExpr(Start, Ty); const SCEV *NewAR = getAddRecExpr(getConstant(AR->getType(), 0), Step, L, AR->getNoWrapFlags()); return getAddExpr(Start, getSignExtendExpr(NewAR, Ty)); } } if (proveNoWrapByVaryingStart(Start, Step, L)) { const_cast(AR)->setNoWrapFlags(SCEV::FlagNSW); return getAddRecExpr( getExtendAddRecStart(AR, Ty, this), getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags()); } } // 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, 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(Op)) if (SC->getValue()->getValue().isNegative()) return getSignExtendExpr(Op, Ty); // Peel off a truncate cast. if (const SCEVTruncateExpr *T = dyn_cast(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(ZExt)) return ZExt; // Next try a sext cast. If the cast is folded, use it. const SCEV *SExt = getSignExtendExpr(Op, Ty); if (!isa(SExt)) return SExt; // Force the cast to be folded into the operands of an addrec. if (const SCEVAddRecExpr *AR = dyn_cast(Op)) { SmallVector Ops; for (const SCEV *Op : AR->operands()) Ops.push_back(getAnyExtendExpr(Op, Ty)); return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW); } // If the expression is obviously signed, use the sext cast value. if (isa(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 &M, SmallVectorImpl &NewOps, APInt &AccumulatedConstant, const SCEV *const *Ops, size_t NumOperands, const APInt &Scale, ScalarEvolution &SE) { bool Interesting = false; // Iterate over the add operands. They are sorted, with constants first. unsigned i = 0; while (const SCEVConstant *C = dyn_cast(Ops[i])) { ++i; // Pull a buried constant out to the outside. if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero()) Interesting = true; AccumulatedConstant += Scale * C->getValue()->getValue(); } // Next comes everything else. We're especially interested in multiplies // here, but they're in the middle, so just visit the rest with one loop. for (; i != NumOperands; ++i) { const SCEVMulExpr *Mul = dyn_cast(Ops[i]); if (Mul && isa(Mul->getOperand(0))) { APInt NewScale = Scale * cast(Mul->getOperand(0))->getValue()->getValue(); if (Mul->getNumOperands() == 2 && isa(Mul->getOperand(1))) { // A multiplication of a constant with another add; recurse. const SCEVAddExpr *Add = cast(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 MulOps(Mul->op_begin()+1, Mul->op_end()); const SCEV *Key = SE.getMulExpr(MulOps); std::pair::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 { // An ordinary operand. Update the map. std::pair::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); } }; } // We're trying to construct a SCEV of type `Type' with `Ops' as operands and // `OldFlags' as can't-wrap behavior. Infer a more aggressive set of // can't-overflow flags for the operation if possible. static SCEV::NoWrapFlags StrengthenNoWrapFlags(ScalarEvolution *SE, SCEVTypes Type, const SmallVectorImpl &Ops, SCEV::NoWrapFlags OldFlags) { using namespace std::placeholders; bool CanAnalyze = Type == scAddExpr || Type == scAddRecExpr || Type == scMulExpr; (void)CanAnalyze; assert(CanAnalyze && "don't call from other places!"); int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW; SCEV::NoWrapFlags SignOrUnsignWrap = ScalarEvolution::maskFlags(OldFlags, SignOrUnsignMask); // If FlagNSW is true and all the operands are non-negative, infer FlagNUW. auto IsKnownNonNegative = std::bind(std::mem_fn(&ScalarEvolution::isKnownNonNegative), SE, _1); if (SignOrUnsignWrap == SCEV::FlagNSW && std::all_of(Ops.begin(), Ops.end(), IsKnownNonNegative)) return ScalarEvolution::setFlags(OldFlags, (SCEV::NoWrapFlags)SignOrUnsignMask); return OldFlags; } /// getAddExpr - Get a canonical add expression, or something simpler if /// possible. const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl &Ops, SCEV::NoWrapFlags Flags) { assert(!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) && "only nuw or nsw allowed"); assert(!Ops.empty() && "Cannot get empty add!"); if (Ops.size() == 1) return Ops[0]; #ifndef NDEBUG Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); for (unsigned i = 1, e = Ops.size(); i != e; ++i) assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && "SCEVAddExpr operand types don't match!"); #endif Flags = StrengthenNoWrapFlags(this, scAddExpr, Ops, Flags); // 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(Ops[0])) { ++Idx; assert(Idx < Ops.size()); while (const SCEVConstant *RHSC = dyn_cast(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(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 more than // once. If so, merge them together into an multiply expression. Since we // sorted the list, these values are required to be adjacent. Type *Ty = Ops[0]->getType(); bool FoundMatch = false; for (unsigned i = 0, e = Ops.size(); i != e-1; ++i) if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2 // Scan ahead to count how many equal operands there are. unsigned Count = 2; while (i+Count != e && Ops[i+Count] == Ops[i]) ++Count; // Merge the values into a multiply. const SCEV *Scale = getConstant(Ty, Count); const SCEV *Mul = getMulExpr(Scale, Ops[i]); if (Ops.size() == Count) return Mul; Ops[i] = Mul; Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count); --i; e -= Count - 1; FoundMatch = true; } if (FoundMatch) return getAddExpr(Ops, Flags); // 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(Ops[Idx]); ++Idx) { const SCEVTruncateExpr *Trunc = cast(Ops[Idx]); Type *DstType = Trunc->getType(); Type *SrcType = Trunc->getOperand()->getType(); SmallVector 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(Ops[i])) { if (T->getOperand()->getType() != SrcType) { Ok = false; break; } LargeOps.push_back(T->getOperand()); } else if (const SCEVConstant *C = dyn_cast(Ops[i])) { LargeOps.push_back(getAnyExtendExpr(C, SrcType)); } else if (const SCEVMulExpr *M = dyn_cast(Ops[i])) { SmallVector LargeMulOps; for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) { if (const SCEVTruncateExpr *T = dyn_cast(M->getOperand(j))) { if (T->getOperand()->getType() != SrcType) { Ok = false; break; } LargeMulOps.push_back(T->getOperand()); } else if (const SCEVConstant *C = dyn_cast(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, Flags); // If it folds to something simple, use it. Otherwise, don't. if (isa(Fold) || isa(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(Ops[Idx])) { // If we have an add, expand the add operands onto the end of the operands // list. Ops.erase(Ops.begin()+Idx); Ops.append(Add->op_begin(), Add->op_end()); 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(Ops[Idx])) { uint64_t BitWidth = getTypeSizeInBits(Ty); DenseMap M; SmallVector 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, APIntCompare> MulOpLists; for (SmallVectorImpl::const_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, 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(Ops[Idx]); ++Idx) { const SCEVMulExpr *Mul = cast(Ops[Idx]); for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) { const SCEV *MulOpSCEV = Mul->getOperand(MulOp); if (isa(MulOpSCEV)) continue; for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp) if (MulOpSCEV == 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 MulOps(Mul->op_begin(), Mul->op_begin()+MulOp); MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end()); InnerMul = getMulExpr(MulOps); } const SCEV *One = getConstant(Ty, 1); const SCEV *AddOne = getAddExpr(One, InnerMul); const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV); 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(Ops[OtherMulIdx]); ++OtherMulIdx) { const SCEVMulExpr *OtherMul = cast(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 MulOps(Mul->op_begin(), Mul->op_begin()+MulOp); MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end()); InnerMul1 = getMulExpr(MulOps); } const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0); if (OtherMul->getNumOperands() != 2) { SmallVector MulOps(OtherMul->op_begin(), OtherMul->op_begin()+OMulOp); MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end()); 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(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 LIOps; const SCEVAddRecExpr *AddRec = cast(Ops[Idx]); const Loop *AddRecLoop = AddRec->getLoop(); for (unsigned i = 0, e = Ops.size(); i != e; ++i) if (isLoopInvariant(Ops[i], 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 AddRecOps(AddRec->op_begin(), AddRec->op_end()); AddRecOps[0] = getAddExpr(LIOps); // Build the new addrec. Propagate the NUW and NSW flags if both the // outer add and the inner addrec are guaranteed to have no overflow. // Always propagate NW. Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW)); const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags); // 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-invariant 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(Ops[OtherIdx]); ++OtherIdx) if (AddRecLoop == cast(Ops[OtherIdx])->getLoop()) { // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D} SmallVector AddRecOps(AddRec->op_begin(), AddRec->op_end()); for (; OtherIdx != Ops.size() && isa(Ops[OtherIdx]); ++OtherIdx) if (const SCEVAddRecExpr *OtherAddRec = dyn_cast(Ops[OtherIdx])) if (OtherAddRec->getLoop() == AddRecLoop) { for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) { if (i >= AddRecOps.size()) { AddRecOps.append(OtherAddRec->op_begin()+i, OtherAddRec->op_end()); break; } AddRecOps[i] = getAddExpr(AddRecOps[i], OtherAddRec->getOperand(i)); } Ops.erase(Ops.begin() + OtherIdx); --OtherIdx; } // Step size has changed, so we cannot guarantee no self-wraparound. Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap); 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); for (unsigned i = 0, e = Ops.size(); i != e; ++i) ID.AddPointer(Ops[i]); void *IP = nullptr; SCEVAddExpr *S = static_cast(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); if (!S) { const SCEV **O = SCEVAllocator.Allocate(Ops.size()); std::uninitialized_copy(Ops.begin(), Ops.end(), O); S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator), O, Ops.size()); UniqueSCEVs.InsertNode(S, IP); } S->setNoWrapFlags(Flags); return S; } static uint64_t umul_ov(uint64_t i, uint64_t j, bool &Overflow) { uint64_t k = i*j; if (j > 1 && k / j != i) Overflow = true; return k; } /// Compute the result of "n choose k", the binomial coefficient. If an /// intermediate computation overflows, Overflow will be set and the return will /// be garbage. Overflow is not cleared on absence of overflow. static uint64_t Choose(uint64_t n, uint64_t k, bool &Overflow) { // We use the multiplicative formula: // n(n-1)(n-2)...(n-(k-1)) / k(k-1)(k-2)...1 . // At each iteration, we take the n-th term of the numeral and divide by the // (k-n)th term of the denominator. This division will always produce an // integral result, and helps reduce the chance of overflow in the // intermediate computations. However, we can still overflow even when the // final result would fit. if (n == 0 || n == k) return 1; if (k > n) return 0; if (k > n/2) k = n-k; uint64_t r = 1; for (uint64_t i = 1; i <= k; ++i) { r = umul_ov(r, n-(i-1), Overflow); r /= i; } return r; } /// Determine if any of the operands in this SCEV are a constant or if /// any of the add or multiply expressions in this SCEV contain a constant. static bool containsConstantSomewhere(const SCEV *StartExpr) { SmallVector Ops; Ops.push_back(StartExpr); while (!Ops.empty()) { const SCEV *CurrentExpr = Ops.pop_back_val(); if (isa(*CurrentExpr)) return true; if (isa(*CurrentExpr) || isa(*CurrentExpr)) { const auto *CurrentNAry = cast(CurrentExpr); Ops.append(CurrentNAry->op_begin(), CurrentNAry->op_end()); } } return false; } /// getMulExpr - Get a canonical multiply expression, or something simpler if /// possible. const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl &Ops, SCEV::NoWrapFlags Flags) { assert(Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) && "only nuw or nsw allowed"); assert(!Ops.empty() && "Cannot get empty mul!"); if (Ops.size() == 1) return Ops[0]; #ifndef NDEBUG Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); for (unsigned i = 1, e = Ops.size(); i != e; ++i) assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && "SCEVMulExpr operand types don't match!"); #endif Flags = StrengthenNoWrapFlags(this, scMulExpr, Ops, Flags); // 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(Ops[0])) { // C1*(C2+V) -> C1*C2 + C1*V if (Ops.size() == 2) if (const SCEVAddExpr *Add = dyn_cast(Ops[1])) // If any of Add's ops are Adds or Muls with a constant, // apply this transformation as well. if (Add->getNumOperands() == 2) if (containsConstantSomewhere(Add)) return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)), getMulExpr(LHSC, Add->getOperand(1))); ++Idx; while (const SCEVConstant *RHSC = dyn_cast(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(Ops[0]); } // If we are left with a constant one being multiplied, strip it off. if (cast(Ops[0])->getValue()->equalsInt(1)) { Ops.erase(Ops.begin()); --Idx; } else if (cast(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(Ops[1])) { SmallVector 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(Mul)) AnyFolded = true; NewOps.push_back(Mul); } if (AnyFolded) return getAddExpr(NewOps); } else if (const SCEVAddRecExpr * AddRec = dyn_cast(Ops[1])) { // Negation preserves a recurrence's no self-wrap property. SmallVector Operands; for (SCEVAddRecExpr::op_iterator I = AddRec->op_begin(), E = AddRec->op_end(); I != E; ++I) { Operands.push_back(getMulExpr(Ops[0], *I)); } return getAddRecExpr(Operands, AddRec->getLoop(), AddRec->getNoWrapFlags(SCEV::FlagNW)); } } } 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(Ops[Idx])) { // If we have an mul, expand the mul operands onto the end of the operands // list. Ops.erase(Ops.begin()+Idx); Ops.append(Mul->op_begin(), Mul->op_end()); 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(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 LIOps; const SCEVAddRecExpr *AddRec = cast(Ops[Idx]); const Loop *AddRecLoop = AddRec->getLoop(); for (unsigned i = 0, e = Ops.size(); i != e; ++i) if (isLoopInvariant(Ops[i], 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,+,LI*Step} SmallVector NewOps; NewOps.reserve(AddRec->getNumOperands()); const SCEV *Scale = getMulExpr(LIOps); for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i))); // Build the new addrec. Propagate the NUW and NSW flags if both the // outer mul and the inner addrec are guaranteed to have no overflow. // // No self-wrap cannot be guaranteed after changing the step size, but // will be inferred if either NUW or NSW is true. Flags = AddRec->getNoWrapFlags(clearFlags(Flags, SCEV::FlagNW)); const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, Flags); // 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-invariant 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. // {A1,+,A2,+,...,+,An} * {B1,+,B2,+,...,+,Bn} // = {x=1 in [ sum y=x..2x [ sum z=max(y-x, y-n)..min(x,n) [ // choose(x, 2x)*choose(2x-y, x-z)*A_{y-z}*B_z // ]]],+,...up to x=2n}. // Note that the arguments to choose() are always integers with values // known at compile time, never SCEV objects. // // The implementation avoids pointless extra computations when the two // addrec's are of different length (mathematically, it's equivalent to // an infinite stream of zeros on the right). bool OpsModified = false; for (unsigned OtherIdx = Idx+1; OtherIdx != Ops.size() && isa(Ops[OtherIdx]); ++OtherIdx) { const SCEVAddRecExpr *OtherAddRec = dyn_cast(Ops[OtherIdx]); if (!OtherAddRec || OtherAddRec->getLoop() != AddRecLoop) continue; bool Overflow = false; Type *Ty = AddRec->getType(); bool LargerThan64Bits = getTypeSizeInBits(Ty) > 64; SmallVector AddRecOps; for (int x = 0, xe = AddRec->getNumOperands() + OtherAddRec->getNumOperands() - 1; x != xe && !Overflow; ++x) { const SCEV *Term = getConstant(Ty, 0); for (int y = x, ye = 2*x+1; y != ye && !Overflow; ++y) { uint64_t Coeff1 = Choose(x, 2*x - y, Overflow); for (int z = std::max(y-x, y-(int)AddRec->getNumOperands()+1), ze = std::min(x+1, (int)OtherAddRec->getNumOperands()); z < ze && !Overflow; ++z) { uint64_t Coeff2 = Choose(2*x - y, x-z, Overflow); uint64_t Coeff; if (LargerThan64Bits) Coeff = umul_ov(Coeff1, Coeff2, Overflow); else Coeff = Coeff1*Coeff2; const SCEV *CoeffTerm = getConstant(Ty, Coeff); const SCEV *Term1 = AddRec->getOperand(y-z); const SCEV *Term2 = OtherAddRec->getOperand(z); Term = getAddExpr(Term, getMulExpr(CoeffTerm, Term1,Term2)); } } AddRecOps.push_back(Term); } if (!Overflow) { const SCEV *NewAddRec = getAddRecExpr(AddRecOps, AddRec->getLoop(), SCEV::FlagAnyWrap); if (Ops.size() == 2) return NewAddRec; Ops[Idx] = NewAddRec; Ops.erase(Ops.begin() + OtherIdx); --OtherIdx; OpsModified = true; AddRec = dyn_cast(NewAddRec); if (!AddRec) break; } } if (OpsModified) 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); for (unsigned i = 0, e = Ops.size(); i != e; ++i) ID.AddPointer(Ops[i]); void *IP = nullptr; SCEVMulExpr *S = static_cast(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); if (!S) { const SCEV **O = SCEVAllocator.Allocate(Ops.size()); std::uninitialized_copy(Ops.begin(), Ops.end(), O); S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator), O, Ops.size()); UniqueSCEVs.InsertNode(S, IP); } S->setNoWrapFlags(Flags); 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(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. Type *Ty = LHS->getType(); unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros(); unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1; // For non-power-of-two values, effectively round the value up to the // nearest power of two. if (!RHSC->getValue()->getValue().isPowerOf2()) ++MaxShiftAmt; IntegerType *ExtTy = IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt); if (const SCEVAddRecExpr *AR = dyn_cast(LHS)) if (const SCEVConstant *Step = dyn_cast(AR->getStepRecurrence(*this))) { // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded. const APInt &StepInt = Step->getValue()->getValue(); const APInt &DivInt = RHSC->getValue()->getValue(); if (!StepInt.urem(DivInt) && getZeroExtendExpr(AR, ExtTy) == getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy), getZeroExtendExpr(Step, ExtTy), AR->getLoop(), SCEV::FlagAnyWrap)) { SmallVector Operands; for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i) Operands.push_back(getUDivExpr(AR->getOperand(i), RHS)); return getAddRecExpr(Operands, AR->getLoop(), SCEV::FlagNW); } /// Get a canonical UDivExpr for a recurrence. /// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0. // We can currently only fold X%N if X is constant. const SCEVConstant *StartC = dyn_cast(AR->getStart()); if (StartC && !DivInt.urem(StepInt) && getZeroExtendExpr(AR, ExtTy) == getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy), getZeroExtendExpr(Step, ExtTy), AR->getLoop(), SCEV::FlagAnyWrap)) { const APInt &StartInt = StartC->getValue()->getValue(); const APInt &StartRem = StartInt.urem(StepInt); if (StartRem != 0) LHS = getAddRecExpr(getConstant(StartInt - StartRem), Step, AR->getLoop(), SCEV::FlagNW); } } // (A*B)/C --> A*(B/C) if safe and B/C can be folded. if (const SCEVMulExpr *M = dyn_cast(LHS)) { SmallVector 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(Div) && getMulExpr(Div, RHSC) == Op) { Operands = SmallVector(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 SCEVAddExpr *A = dyn_cast(LHS)) { SmallVector 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(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(LHS)) { Constant *LHSCV = LHSC->getValue(); Constant *RHSCV = RHSC->getValue(); return getConstant(cast(ConstantExpr::getUDiv(LHSCV, RHSCV))); } } } FoldingSetNodeID ID; ID.AddInteger(scUDivExpr); ID.AddPointer(LHS); ID.AddPointer(RHS); void *IP = nullptr; 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; } static const APInt gcd(const SCEVConstant *C1, const SCEVConstant *C2) { APInt A = C1->getValue()->getValue().abs(); APInt B = C2->getValue()->getValue().abs(); uint32_t ABW = A.getBitWidth(); uint32_t BBW = B.getBitWidth(); if (ABW > BBW) B = B.zext(ABW); else if (ABW < BBW) A = A.zext(BBW); return APIntOps::GreatestCommonDivisor(A, B); } /// getUDivExactExpr - Get a canonical unsigned division expression, or /// something simpler if possible. There is no representation for an exact udiv /// in SCEV IR, but we can attempt to remove factors from the LHS and RHS. /// We can't do this when it's not exact because the udiv may be clearing bits. const SCEV *ScalarEvolution::getUDivExactExpr(const SCEV *LHS, const SCEV *RHS) { // TODO: we could try to find factors in all sorts of things, but for now we // just deal with u/exact (multiply, constant). See SCEVDivision towards the // end of this file for inspiration. const SCEVMulExpr *Mul = dyn_cast(LHS); if (!Mul) return getUDivExpr(LHS, RHS); if (const SCEVConstant *RHSCst = dyn_cast(RHS)) { // If the mulexpr multiplies by a constant, then that constant must be the // first element of the mulexpr. if (const SCEVConstant *LHSCst = dyn_cast(Mul->getOperand(0))) { if (LHSCst == RHSCst) { SmallVector Operands; Operands.append(Mul->op_begin() + 1, Mul->op_end()); return getMulExpr(Operands); } // We can't just assume that LHSCst divides RHSCst cleanly, it could be // that there's a factor provided by one of the other terms. We need to // check. APInt Factor = gcd(LHSCst, RHSCst); if (!Factor.isIntN(1)) { LHSCst = cast( getConstant(LHSCst->getValue()->getValue().udiv(Factor))); RHSCst = cast( getConstant(RHSCst->getValue()->getValue().udiv(Factor))); SmallVector Operands; Operands.push_back(LHSCst); Operands.append(Mul->op_begin() + 1, Mul->op_end()); LHS = getMulExpr(Operands); RHS = RHSCst; Mul = dyn_cast(LHS); if (!Mul) return getUDivExactExpr(LHS, RHS); } } } for (int i = 0, e = Mul->getNumOperands(); i != e; ++i) { if (Mul->getOperand(i) == RHS) { SmallVector Operands; Operands.append(Mul->op_begin(), Mul->op_begin() + i); Operands.append(Mul->op_begin() + i + 1, Mul->op_end()); return getMulExpr(Operands); } } return getUDivExpr(LHS, RHS); } /// 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, SCEV::NoWrapFlags Flags) { SmallVector Operands; Operands.push_back(Start); if (const SCEVAddRecExpr *StepChrec = dyn_cast(Step)) if (StepChrec->getLoop() == L) { Operands.append(StepChrec->op_begin(), StepChrec->op_end()); return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW)); } Operands.push_back(Step); return getAddRecExpr(Operands, L, Flags); } /// getAddRecExpr - Get an add recurrence expression for the specified loop. /// Simplify the expression as much as possible. const SCEV * ScalarEvolution::getAddRecExpr(SmallVectorImpl &Operands, const Loop *L, SCEV::NoWrapFlags Flags) { if (Operands.size() == 1) return Operands[0]; #ifndef NDEBUG Type *ETy = getEffectiveSCEVType(Operands[0]->getType()); for (unsigned i = 1, e = Operands.size(); i != e; ++i) assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy && "SCEVAddRecExpr operand types don't match!"); for (unsigned i = 0, e = Operands.size(); i != e; ++i) assert(isLoopInvariant(Operands[i], L) && "SCEVAddRecExpr operand is not loop-invariant!"); #endif if (Operands.back()->isZero()) { Operands.pop_back(); return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {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). Flags = StrengthenNoWrapFlags(this, scAddRecExpr, Operands, Flags); // Canonicalize nested AddRecs in by nesting them in order of loop depth. if (const SCEVAddRecExpr *NestedAR = dyn_cast(Operands[0])) { const Loop *NestedLoop = NestedAR->getLoop(); if (L->contains(NestedLoop) ? (L->getLoopDepth() < NestedLoop->getLoopDepth()) : (!NestedLoop->contains(L) && DT->dominates(L->getHeader(), NestedLoop->getHeader()))) { SmallVector 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 (!isLoopInvariant(Operands[i], L)) { AllInvariant = false; break; } if (AllInvariant) { // Create a recurrence for the outer loop with the same step size. // // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the // inner recurrence has the same property. SCEV::NoWrapFlags OuterFlags = maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags()); NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags); AllInvariant = true; for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i) if (!isLoopInvariant(NestedOperands[i], NestedLoop)) { AllInvariant = false; break; } if (AllInvariant) { // Ok, both add recurrences are valid after the transformation. // // The inner recurrence keeps its NW flag but only keeps NUW/NSW if // the outer recurrence has the same property. SCEV::NoWrapFlags InnerFlags = maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags); return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags); } } // 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); for (unsigned i = 0, e = Operands.size(); i != e; ++i) ID.AddPointer(Operands[i]); ID.AddPointer(L); void *IP = nullptr; SCEVAddRecExpr *S = static_cast(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); if (!S) { const SCEV **O = SCEVAllocator.Allocate(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); } S->setNoWrapFlags(Flags); return S; } const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS, const SCEV *RHS) { SmallVector Ops; Ops.push_back(LHS); Ops.push_back(RHS); return getSMaxExpr(Ops); } const SCEV * ScalarEvolution::getSMaxExpr(SmallVectorImpl &Ops) { assert(!Ops.empty() && "Cannot get empty smax!"); if (Ops.size() == 1) return Ops[0]; #ifndef NDEBUG Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); for (unsigned i = 1, e = Ops.size(); i != e; ++i) assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && "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(Ops[0])) { ++Idx; assert(Idx < Ops.size()); while (const SCEVConstant *RHSC = dyn_cast(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(Ops[0]); } // If we are left with a constant minimum-int, strip it off. if (cast(Ops[0])->getValue()->isMinValue(true)) { Ops.erase(Ops.begin()); --Idx; } else if (cast(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(Ops[Idx])) { Ops.erase(Ops.begin()+Idx); Ops.append(SMax->op_begin(), SMax->op_end()); 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); for (unsigned i = 0, e = Ops.size(); i != e; ++i) ID.AddPointer(Ops[i]); void *IP = nullptr; if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; const SCEV **O = SCEVAllocator.Allocate(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 Ops; Ops.push_back(LHS); Ops.push_back(RHS); return getUMaxExpr(Ops); } const SCEV * ScalarEvolution::getUMaxExpr(SmallVectorImpl &Ops) { assert(!Ops.empty() && "Cannot get empty umax!"); if (Ops.size() == 1) return Ops[0]; #ifndef NDEBUG Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); for (unsigned i = 1, e = Ops.size(); i != e; ++i) assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && "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(Ops[0])) { ++Idx; assert(Idx < Ops.size()); while (const SCEVConstant *RHSC = dyn_cast(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(Ops[0]); } // If we are left with a constant minimum-int, strip it off. if (cast(Ops[0])->getValue()->isMinValue(false)) { Ops.erase(Ops.begin()); --Idx; } else if (cast(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(Ops[Idx])) { Ops.erase(Ops.begin()+Idx); Ops.append(UMax->op_begin(), UMax->op_end()); 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); for (unsigned i = 0, e = Ops.size(); i != e; ++i) ID.AddPointer(Ops[i]); void *IP = nullptr; if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; const SCEV **O = SCEVAllocator.Allocate(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(Type *IntTy, Type *AllocTy) { // If we have DataLayout, 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 (DL) return getConstant(IntTy, DL->getTypeAllocSize(AllocTy)); Constant *C = ConstantExpr::getSizeOf(AllocTy); if (ConstantExpr *CE = dyn_cast(C)) if (Constant *Folded = ConstantFoldConstantExpression(CE, DL, TLI)) C = Folded; Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy)); assert(Ty == IntTy && "Effective SCEV type doesn't match"); return getTruncateOrZeroExtend(getSCEV(C), Ty); } const SCEV *ScalarEvolution::getOffsetOfExpr(Type *IntTy, StructType *STy, unsigned FieldNo) { // If we have DataLayout, 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 (DL) { return getConstant(IntTy, DL->getStructLayout(STy)->getElementOffset(FieldNo)); } Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo); if (ConstantExpr *CE = dyn_cast(C)) if (Constant *Folded = ConstantFoldConstantExpression(CE, DL, TLI)) C = Folded; Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy)); 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 = nullptr; if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) { assert(cast(S)->getValue() == V && "Stale SCEVUnknown in uniquing map!"); return S; } SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this, FirstUnknown); FirstUnknown = cast(S); 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(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(Type *Ty) const { assert(isSCEVable(Ty) && "Type is not SCEVable!"); // If we have a DataLayout, use it! if (DL) return DL->getTypeSizeInBits(Ty); // Integer types have fixed sizes. if (Ty->isIntegerTy()) return Ty->getPrimitiveSizeInBits(); // The only other support type is pointer. Without DataLayout, 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. Type *ScalarEvolution::getEffectiveSCEVType(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 (DL) return DL->getIntPtrType(Ty); // Without DataLayout, conservatively assume pointers are 64-bit. return Type::getInt64Ty(getContext()); } const SCEV *ScalarEvolution::getCouldNotCompute() { return &CouldNotCompute; } namespace { // Helper class working with SCEVTraversal to figure out if a SCEV contains // a SCEVUnknown with null value-pointer. FindInvalidSCEVUnknown::FindOne // is set iff if find such SCEVUnknown. // struct FindInvalidSCEVUnknown { bool FindOne; FindInvalidSCEVUnknown() { FindOne = false; } bool follow(const SCEV *S) { switch (static_cast(S->getSCEVType())) { case scConstant: return false; case scUnknown: if (!cast(S)->getValue()) FindOne = true; return false; default: return true; } } bool isDone() const { return FindOne; } }; } bool ScalarEvolution::checkValidity(const SCEV *S) const { FindInvalidSCEVUnknown F; SCEVTraversal ST(F); ST.visitAll(S); return !F.FindOne; } /// 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!"); ValueExprMapType::iterator I = ValueExprMap.find_as(V); if (I != ValueExprMap.end()) { const SCEV *S = I->second; if (checkValidity(S)) return S; else ValueExprMap.erase(I); } const SCEV *S = createSCEV(V); // The process of creating a SCEV for V may have caused other SCEVs // to have been created, so it's necessary to insert the new entry // from scratch, rather than trying to remember the insert position // above. ValueExprMap.insert(std::make_pair(SCEVCallbackVH(V, this), S)); return S; } /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V /// const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) { if (const SCEVConstant *VC = dyn_cast(V)) return getConstant( cast(ConstantExpr::getNeg(VC->getValue()))); Type *Ty = V->getType(); Ty = getEffectiveSCEVType(Ty); return getMulExpr(V, getConstant(cast(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(V)) return getConstant( cast(ConstantExpr::getNot(VC->getValue()))); Type *Ty = V->getType(); Ty = getEffectiveSCEVType(Ty); const SCEV *AllOnes = getConstant(cast(Constant::getAllOnesValue(Ty))); return getMinusSCEV(AllOnes, V); } /// getMinusSCEV - Return LHS-RHS. Minus is represented in SCEV as A+B*-1. const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS, SCEV::NoWrapFlags Flags) { assert(!maskFlags(Flags, SCEV::FlagNUW) && "subtraction does not have NUW"); // Fast path: X - X --> 0. if (LHS == RHS) return getConstant(LHS->getType(), 0); // X - Y --> X + -Y. // X -(nsw || nuw) 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, Type *Ty) { 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, Type *Ty) { 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, Type *Ty) { 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, Type *Ty) { 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, Type *Ty) { 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, Type *Ty) { 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); } /// getPointerBase - Transitively follow the chain of pointer-type operands /// until reaching a SCEV that does not have a single pointer operand. This /// returns a SCEVUnknown pointer for well-formed pointer-type expressions, /// but corner cases do exist. const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) { // A pointer operand may evaluate to a nonpointer expression, such as null. if (!V->getType()->isPointerTy()) return V; if (const SCEVCastExpr *Cast = dyn_cast(V)) { return getPointerBase(Cast->getOperand()); } else if (const SCEVNAryExpr *NAry = dyn_cast(V)) { const SCEV *PtrOp = nullptr; for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end(); I != E; ++I) { if ((*I)->getType()->isPointerTy()) { // Cannot find the base of an expression with multiple pointer operands. if (PtrOp) return V; PtrOp = *I; } } if (!PtrOp) return V; return getPointerBase(PtrOp); } return V; } /// PushDefUseChildren - Push users of the given Instruction /// onto the given Worklist. static void PushDefUseChildren(Instruction *I, SmallVectorImpl &Worklist) { // Push the def-use children onto the Worklist stack. for (User *U : I->users()) Worklist.push_back(cast(U)); } /// ForgetSymbolicValue - This looks up computed SCEV values for all /// instructions that depend on the given instruction and removes them from /// the ValueExprMapType map if they reference SymName. This is used during PHI /// resolution. void ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) { SmallVector Worklist; PushDefUseChildren(PN, Worklist); SmallPtrSet Visited; Visited.insert(PN); while (!Worklist.empty()) { Instruction *I = Worklist.pop_back_val(); if (!Visited.insert(I).second) continue; ValueExprMapType::iterator It = ValueExprMap.find_as(static_cast(I)); if (It != ValueExprMap.end()) { const SCEV *Old = It->second; // Short-circuit the def-use traversal if the symbolic name // ceases to appear in expressions. if (Old != SymName && !hasOperand(Old, 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(I) || !isa(Old) || (I != PN && Old == SymName)) { forgetMemoizedResults(Old); ValueExprMap.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 = nullptr, *StartValueV = nullptr; 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 = nullptr; break; } } else if (!StartValueV) { StartValueV = V; } else if (StartValueV != V) { StartValueV = nullptr; break; } } if (BEValueV && StartValueV) { // While we are analyzing this PHI node, handle its value symbolically. const SCEV *SymbolicName = getUnknown(PN); assert(ValueExprMap.find_as(PN) == ValueExprMap.end() && "PHI node already processed?"); ValueExprMap.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(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 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 (isLoopInvariant(Accum, L) || (isa(Accum) && cast(Accum)->getLoop() == L)) { SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap; // If the increment doesn't overflow, then neither the addrec nor // the post-increment will overflow. if (const AddOperator *OBO = dyn_cast(BEValueV)) { if (OBO->hasNoUnsignedWrap()) Flags = setFlags(Flags, SCEV::FlagNUW); if (OBO->hasNoSignedWrap()) Flags = setFlags(Flags, SCEV::FlagNSW); } else if (GEPOperator *GEP = dyn_cast(BEValueV)) { // If the increment is an inbounds GEP, then we know the address // space cannot be wrapped around. We cannot make any guarantee // about signed or unsigned overflow because pointers are // unsigned but we may have a negative index from the base // pointer. We can guarantee that no unsigned wrap occurs if the // indices form a positive value. if (GEP->isInBounds()) { Flags = setFlags(Flags, SCEV::FlagNW); const SCEV *Ptr = getSCEV(GEP->getPointerOperand()); if (isKnownPositive(getMinusSCEV(getSCEV(GEP), Ptr))) Flags = setFlags(Flags, SCEV::FlagNUW); } // We cannot transfer nuw and nsw flags from subtraction // operations -- sub nuw X, Y is not the same as add nuw X, -Y // for instance. } const SCEV *StartVal = getSCEV(StartValueV); const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags); // Since the no-wrap flags are on the increment, they apply to the // post-incremented value as well. if (isLoopInvariant(Accum, L)) (void)getAddRecExpr(getAddExpr(StartVal, Accum), Accum, L, Flags); // 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); ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV; return PHISCEV; } } } else if (const SCEVAddRecExpr *AddRec = dyn_cast(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))) { // FIXME: For constant StartVal, we should be able to infer // no-wrap flags. const SCEV *PHISCEV = getAddRecExpr(StartVal, AddRec->getOperand(1), L, SCEV::FlagAnyWrap); // 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); ValueExprMap[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 = SimplifyInstruction(PN, DL, TLI, DT, AC)) if (LI->replacementPreservesLCSSAForm(PN, V)) 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) { Type *IntPtrTy = getEffectiveSCEVType(GEP->getType()); Value *Base = GEP->getOperand(0); // Don't attempt to analyze GEPs over unsized objects. if (!Base->getType()->getPointerElementType()->isSized()) return getUnknown(GEP); // Don't blindly transfer the inbounds flag from the GEP 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. SCEV::NoWrapFlags Wrap = GEP->isInBounds() ? SCEV::FlagNSW : SCEV::FlagAnyWrap; const SCEV *TotalOffset = getConstant(IntPtrTy, 0); gep_type_iterator GTI = gep_type_begin(GEP); for (GetElementPtrInst::op_iterator I = std::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 (StructType *STy = dyn_cast(*GTI++)) { // For a struct, add the member offset. unsigned FieldNo = cast(Index)->getZExtValue(); const SCEV *FieldOffset = getOffsetOfExpr(IntPtrTy, STy, FieldNo); // Add the field offset to the running total offset. TotalOffset = getAddExpr(TotalOffset, FieldOffset); } else { // For an array, add the element offset, explicitly scaled. const SCEV *ElementSize = getSizeOfExpr(IntPtrTy, *GTI); const SCEV *IndexS = getSCEV(Index); // Getelementptr indices are signed. IndexS = getTruncateOrSignExtend(IndexS, IntPtrTy); // Multiply the index by the element size to compute the element offset. const SCEV *LocalOffset = getMulExpr(IndexS, ElementSize, Wrap); // Add the element offset to the running total offset. TotalOffset = getAddExpr(TotalOffset, LocalOffset); } } // Get the SCEV for the GEP base. const SCEV *BaseS = getSCEV(Base); // Add the total offset from all the GEP indices to the base. return getAddExpr(BaseS, TotalOffset, Wrap); } /// 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(S)) return C->getValue()->getValue().countTrailingZeros(); if (const SCEVTruncateExpr *T = dyn_cast(S)) return std::min(GetMinTrailingZeros(T->getOperand()), (uint32_t)getTypeSizeInBits(T->getType())); if (const SCEVZeroExtendExpr *E = dyn_cast(S)) { uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? getTypeSizeInBits(E->getType()) : OpRes; } if (const SCEVSignExtendExpr *E = dyn_cast(S)) { uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ? getTypeSizeInBits(E->getType()) : OpRes; } if (const SCEVAddExpr *A = dyn_cast(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(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(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(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(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(S)) { // For a SCEVUnknown, ask ValueTracking. unsigned BitWidth = getTypeSizeInBits(U->getType()); APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); computeKnownBits(U->getValue(), Zeros, Ones, DL, 0, AC, nullptr, DT); return Zeros.countTrailingOnes(); } // SCEVUDivExpr return 0; } /// GetRangeFromMetadata - Helper method to assign a range to V from /// metadata present in the IR. static Optional GetRangeFromMetadata(Value *V) { if (Instruction *I = dyn_cast(V)) { if (MDNode *MD = I->getMetadata(LLVMContext::MD_range)) { ConstantRange TotalRange( cast(I->getType())->getBitWidth(), false); unsigned NumRanges = MD->getNumOperands() / 2; assert(NumRanges >= 1); for (unsigned i = 0; i < NumRanges; ++i) { ConstantInt *Lower = mdconst::extract(MD->getOperand(2 * i + 0)); ConstantInt *Upper = mdconst::extract(MD->getOperand(2 * i + 1)); ConstantRange Range(Lower->getValue(), Upper->getValue()); TotalRange = TotalRange.unionWith(Range); } return TotalRange; } } return None; } /// getUnsignedRange - Determine the unsigned range for a particular SCEV. /// ConstantRange ScalarEvolution::getUnsignedRange(const SCEV *S) { // See if we've computed this range already. DenseMap::iterator I = UnsignedRanges.find(S); if (I != UnsignedRanges.end()) return I->second; if (const SCEVConstant *C = dyn_cast(S)) return setUnsignedRange(C, 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(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 setUnsignedRange(Add, ConservativeResult.intersectWith(X)); } if (const SCEVMulExpr *Mul = dyn_cast(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 setUnsignedRange(Mul, ConservativeResult.intersectWith(X)); } if (const SCEVSMaxExpr *SMax = dyn_cast(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 setUnsignedRange(SMax, ConservativeResult.intersectWith(X)); } if (const SCEVUMaxExpr *UMax = dyn_cast(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 setUnsignedRange(UMax, ConservativeResult.intersectWith(X)); } if (const SCEVUDivExpr *UDiv = dyn_cast(S)) { ConstantRange X = getUnsignedRange(UDiv->getLHS()); ConstantRange Y = getUnsignedRange(UDiv->getRHS()); return setUnsignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y))); } if (const SCEVZeroExtendExpr *ZExt = dyn_cast(S)) { ConstantRange X = getUnsignedRange(ZExt->getOperand()); return setUnsignedRange(ZExt, ConservativeResult.intersectWith(X.zeroExtend(BitWidth))); } if (const SCEVSignExtendExpr *SExt = dyn_cast(S)) { ConstantRange X = getUnsignedRange(SExt->getOperand()); return setUnsignedRange(SExt, ConservativeResult.intersectWith(X.signExtend(BitWidth))); } if (const SCEVTruncateExpr *Trunc = dyn_cast(S)) { ConstantRange X = getUnsignedRange(Trunc->getOperand()); return setUnsignedRange(Trunc, ConservativeResult.intersectWith(X.truncate(BitWidth))); } if (const SCEVAddRecExpr *AddRec = dyn_cast(S)) { // If there's no unsigned wrap, the value will never be less than its // initial value. if (AddRec->getNoWrapFlags(SCEV::FlagNUW)) if (const SCEVConstant *C = dyn_cast(AddRec->getStart())) if (!C->getValue()->isZero()) ConservativeResult = ConservativeResult.intersectWith( ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0))); // TODO: non-affine addrec if (AddRec->isAffine()) { Type *Ty = AddRec->getType(); const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop()); if (!isa(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 setUnsignedRange(AddRec, ConservativeResult); APInt Min = APIntOps::umin(StartRange.getUnsignedMin(), EndRange.getUnsignedMin()); APInt Max = APIntOps::umax(StartRange.getUnsignedMax(), EndRange.getUnsignedMax()); if (Min.isMinValue() && Max.isMaxValue()) return setUnsignedRange(AddRec, ConservativeResult); return setUnsignedRange(AddRec, ConservativeResult.intersectWith(ConstantRange(Min, Max+1))); } } return setUnsignedRange(AddRec, ConservativeResult); } if (const SCEVUnknown *U = dyn_cast(S)) { // Check if the IR explicitly contains !range metadata. Optional MDRange = GetRangeFromMetadata(U->getValue()); if (MDRange.hasValue()) ConservativeResult = ConservativeResult.intersectWith(MDRange.getValue()); // For a SCEVUnknown, ask ValueTracking. APInt Zeros(BitWidth, 0), Ones(BitWidth, 0); computeKnownBits(U->getValue(), Zeros, Ones, DL, 0, AC, nullptr, DT); if (Ones == ~Zeros + 1) return setUnsignedRange(U, ConservativeResult); return setUnsignedRange(U, ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1))); } return setUnsignedRange(S, ConservativeResult); } /// getSignedRange - Determine the signed range for a particular SCEV. /// ConstantRange ScalarEvolution::getSignedRange(const SCEV *S) { // See if we've computed this range already. DenseMap::iterator I = SignedRanges.find(S); if (I != SignedRanges.end()) return I->second; if (const SCEVConstant *C = dyn_cast(S)) return setSignedRange(C, 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(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 setSignedRange(Add, ConservativeResult.intersectWith(X)); } if (const SCEVMulExpr *Mul = dyn_cast(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 setSignedRange(Mul, ConservativeResult.intersectWith(X)); } if (const SCEVSMaxExpr *SMax = dyn_cast(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 setSignedRange(SMax, ConservativeResult.intersectWith(X)); } if (const SCEVUMaxExpr *UMax = dyn_cast(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 setSignedRange(UMax, ConservativeResult.intersectWith(X)); } if (const SCEVUDivExpr *UDiv = dyn_cast(S)) { ConstantRange X = getSignedRange(UDiv->getLHS()); ConstantRange Y = getSignedRange(UDiv->getRHS()); return setSignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y))); } if (const SCEVZeroExtendExpr *ZExt = dyn_cast(S)) { ConstantRange X = getSignedRange(ZExt->getOperand()); return setSignedRange(ZExt, ConservativeResult.intersectWith(X.zeroExtend(BitWidth))); } if (const SCEVSignExtendExpr *SExt = dyn_cast(S)) { ConstantRange X = getSignedRange(SExt->getOperand()); return setSignedRange(SExt, ConservativeResult.intersectWith(X.signExtend(BitWidth))); } if (const SCEVTruncateExpr *Trunc = dyn_cast(S)) { ConstantRange X = getSignedRange(Trunc->getOperand()); return setSignedRange(Trunc, ConservativeResult.intersectWith(X.truncate(BitWidth))); } if (const SCEVAddRecExpr *AddRec = dyn_cast(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->getNoWrapFlags(SCEV::FlagNSW)) { 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()) { Type *Ty = AddRec->getType(); const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop()); if (!isa(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 setSignedRange(AddRec, ConservativeResult); APInt Min = APIntOps::smin(StartRange.getSignedMin(), EndRange.getSignedMin()); APInt Max = APIntOps::smax(StartRange.getSignedMax(), EndRange.getSignedMax()); if (Min.isMinSignedValue() && Max.isMaxSignedValue()) return setSignedRange(AddRec, ConservativeResult); return setSignedRange(AddRec, ConservativeResult.intersectWith(ConstantRange(Min, Max+1))); } } return setSignedRange(AddRec, ConservativeResult); } if (const SCEVUnknown *U = dyn_cast(S)) { // Check if the IR explicitly contains !range metadata. Optional MDRange = GetRangeFromMetadata(U->getValue()); if (MDRange.hasValue()) ConservativeResult = ConservativeResult.intersectWith(MDRange.getValue()); // For a SCEVUnknown, ask ValueTracking. if (!U->getValue()->getType()->isIntegerTy() && !DL) return setSignedRange(U, ConservativeResult); unsigned NS = ComputeNumSignBits(U->getValue(), DL, 0, AC, nullptr, DT); if (NS <= 1) return setSignedRange(U, ConservativeResult); return setSignedRange(U, ConservativeResult.intersectWith( ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1), APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1))); } return setSignedRange(S, 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(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(V)) Opcode = CE->getOpcode(); else if (ConstantInt *CI = dyn_cast(V)) return getConstant(CI); else if (isa(V)) return getConstant(V->getType(), 0); else if (GlobalAlias *GA = dyn_cast(V)) return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee()); else return getUnknown(V); Operator *U = cast(V); switch (Opcode) { case Instruction::Add: { // The simple thing to do would be to just call getSCEV on both operands // and call getAddExpr with the result. However if we're looking at a // bunch of things all added together, this can be quite inefficient, // because it leads to N-1 getAddExpr calls for N ultimate operands. // Instead, gather up all the operands and make a single getAddExpr call. // LLVM IR canonical form means we need only traverse the left operands. // // Don't apply this instruction's NSW or NUW flags to the new // expression. The instruction may be guarded by control flow that the // no-wrap behavior depends on. Non-control-equivalent instructions can be // mapped to the same SCEV expression, and it would be incorrect to transfer // NSW/NUW semantics to those operations. SmallVector AddOps; AddOps.push_back(getSCEV(U->getOperand(1))); for (Value *Op = U->getOperand(0); ; Op = U->getOperand(0)) { unsigned Opcode = Op->getValueID() - Value::InstructionVal; if (Opcode != Instruction::Add && Opcode != Instruction::Sub) break; U = cast(Op); const SCEV *Op1 = getSCEV(U->getOperand(1)); if (Opcode == Instruction::Sub) AddOps.push_back(getNegativeSCEV(Op1)); else AddOps.push_back(Op1); } AddOps.push_back(getSCEV(U->getOperand(0))); return getAddExpr(AddOps); } case Instruction::Mul: { // Don't transfer NSW/NUW for the same reason as AddExpr. SmallVector MulOps; MulOps.push_back(getSCEV(U->getOperand(1))); for (Value *Op = U->getOperand(0); Op->getValueID() == Instruction::Mul + Value::InstructionVal; Op = U->getOperand(0)) { U = cast(Op); MulOps.push_back(getSCEV(U->getOperand(1))); } MulOps.push_back(getSCEV(U->getOperand(0))); return getMulExpr(MulOps); } 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(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 computeKnownBits to compute what ShrinkDemandedConstant // knew about to reconstruct a low-bits mask value. unsigned LZ = A.countLeadingZeros(); unsigned TZ = A.countTrailingZeros(); unsigned BitWidth = A.getBitWidth(); APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0); computeKnownBits(U->getOperand(0), KnownZero, KnownOne, DL, 0, AC, nullptr, DT); APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ - TZ).shl(TZ); if ((LZ != 0 || TZ != 0) && !((~A & ~KnownZero) & EffectiveMask)) { const SCEV *MulCount = getConstant( ConstantInt::get(getContext(), APInt::getOneBitSet(BitWidth, TZ))); return getMulExpr( getZeroExtendExpr( getTruncateExpr( getUDivExactExpr(getSCEV(U->getOperand(0)), MulCount), IntegerType::get(getContext(), BitWidth - LZ - TZ)), U->getType()), MulCount); } } 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(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(S)) { const SCEVAddRecExpr *OldAR = cast(LHS); const_cast(NewAR)->setNoWrapFlags( OldAR->getNoWrapFlags()); } return S; } } break; case Instruction::Xor: if (ConstantInt *CI = dyn_cast(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(U->getOperand(0))) if (ConstantInt *LCI = dyn_cast(BO->getOperand(1))) if (BO->getOpcode() == Instruction::And && LCI->getValue() == CI->getValue()) if (const SCEVZeroExtendExpr *Z = dyn_cast(getSCEV(U->getOperand(0)))) { Type *UTy = U->getType(); const SCEV *Z0 = Z->getOperand(); 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 = CI->getValue().trunc(Z0TySize); if (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(U->getOperand(1))) { uint32_t BitWidth = cast(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::getOneBitSet(BitWidth, 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(U->getOperand(1))) { uint32_t BitWidth = cast(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::getOneBitSet(BitWidth, 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(U->getOperand(1))) if (Operator *L = dyn_cast(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(U)); case Instruction::PHI: return createNodeForPHI(cast(U)); case Instruction::Select: // This could be a smax or umax that was lowered earlier. // Try to recover it. if (ICmpInst *ICI = dyn_cast(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 (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(U->getType())) { const SCEV *LS = getNoopOrSignExtend(getSCEV(LHS), U->getType()); const SCEV *RS = getNoopOrSignExtend(getSCEV(RHS), U->getType()); 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 (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(U->getType())) { const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), U->getType()); const SCEV *RS = getNoopOrZeroExtend(getSCEV(RHS), U->getType()); 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 (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(U->getType()) && isa(RHS) && cast(RHS)->isZero()) { const SCEV *One = getConstant(U->getType(), 1); const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), U->getType()); 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(One, LS), LDiff); } break; case ICmpInst::ICMP_EQ: // n == 0 ? 1+x : n+x -> umax(n, 1)+x if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(U->getType()) && isa(RHS) && cast(RHS)->isZero()) { const SCEV *One = getConstant(U->getType(), 1); const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), U->getType()); 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(One, LS), LDiff); } break; default: break; } } default: // We cannot analyze this expression. break; } return getUnknown(V); } //===----------------------------------------------------------------------===// // Iteration Count Computation Code // unsigned ScalarEvolution::getSmallConstantTripCount(Loop *L) { if (BasicBlock *ExitingBB = L->getExitingBlock()) return getSmallConstantTripCount(L, ExitingBB); // No trip count information for multiple exits. return 0; } /// getSmallConstantTripCount - Returns the maximum trip count of this loop as a /// normal unsigned value. Returns 0 if the trip count is unknown or not /// constant. Will also return 0 if the maximum trip count is very large (>= /// 2^32). /// /// This "trip count" assumes that control exits via ExitingBlock. More /// precisely, it is the number of times that control may reach ExitingBlock /// before taking the branch. For loops with multiple exits, it may not be the /// number times that the loop header executes because the loop may exit /// prematurely via another branch. unsigned ScalarEvolution::getSmallConstantTripCount(Loop *L, BasicBlock *ExitingBlock) { assert(ExitingBlock && "Must pass a non-null exiting block!"); assert(L->isLoopExiting(ExitingBlock) && "Exiting block must actually branch out of the loop!"); const SCEVConstant *ExitCount = dyn_cast(getExitCount(L, ExitingBlock)); if (!ExitCount) return 0; ConstantInt *ExitConst = ExitCount->getValue(); // Guard against huge trip counts. if (ExitConst->getValue().getActiveBits() > 32) return 0; // In case of integer overflow, this returns 0, which is correct. return ((unsigned)ExitConst->getZExtValue()) + 1; } unsigned ScalarEvolution::getSmallConstantTripMultiple(Loop *L) { if (BasicBlock *ExitingBB = L->getExitingBlock()) return getSmallConstantTripMultiple(L, ExitingBB); // No trip multiple information for multiple exits. return 0; } /// getSmallConstantTripMultiple - Returns the largest constant divisor of the /// trip count of this loop as a normal unsigned value, if possible. This /// means that the actual trip count is always a multiple of the returned /// value (don't forget the trip count could very well be zero as well!). /// /// Returns 1 if the trip count is unknown or not guaranteed to be the /// multiple of a constant (which is also the case if the trip count is simply /// constant, use getSmallConstantTripCount for that case), Will also return 1 /// if the trip count is very large (>= 2^32). /// /// As explained in the comments for getSmallConstantTripCount, this assumes /// that control exits the loop via ExitingBlock. unsigned ScalarEvolution::getSmallConstantTripMultiple(Loop *L, BasicBlock *ExitingBlock) { assert(ExitingBlock && "Must pass a non-null exiting block!"); assert(L->isLoopExiting(ExitingBlock) && "Exiting block must actually branch out of the loop!"); const SCEV *ExitCount = getExitCount(L, ExitingBlock); if (ExitCount == getCouldNotCompute()) return 1; // Get the trip count from the BE count by adding 1. const SCEV *TCMul = getAddExpr(ExitCount, getConstant(ExitCount->getType(), 1)); // FIXME: SCEV distributes multiplication as V1*C1 + V2*C1. We could attempt // to factor simple cases. if (const SCEVMulExpr *Mul = dyn_cast(TCMul)) TCMul = Mul->getOperand(0); const SCEVConstant *MulC = dyn_cast(TCMul); if (!MulC) return 1; ConstantInt *Result = MulC->getValue(); // Guard against huge trip counts (this requires checking // for zero to handle the case where the trip count == -1 and the // addition wraps). if (!Result || Result->getValue().getActiveBits() > 32 || Result->getValue().getActiveBits() == 0) return 1; return (unsigned)Result->getZExtValue(); } // getExitCount - Get the expression for the number of loop iterations for which // this loop is guaranteed not to exit via ExitingBlock. Otherwise return // SCEVCouldNotCompute. const SCEV *ScalarEvolution::getExitCount(Loop *L, BasicBlock *ExitingBlock) { return getBackedgeTakenInfo(L).getExact(ExitingBlock, this); } /// 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).getExact(this); } /// 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).getMax(this); } /// PushLoopPHIs - Push PHI nodes in the header of the given loop /// onto the given Worklist. static void PushLoopPHIs(const Loop *L, SmallVectorImpl &Worklist) { BasicBlock *Header = L->getHeader(); // Push all Loop-header PHIs onto the Worklist stack. for (BasicBlock::iterator I = Header->begin(); PHINode *PN = dyn_cast(I); ++I) Worklist.push_back(PN); } const ScalarEvolution::BackedgeTakenInfo & ScalarEvolution::getBackedgeTakenInfo(const Loop *L) { // Initially insert an invalid entry 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::iterator, bool> Pair = BackedgeTakenCounts.insert(std::make_pair(L, BackedgeTakenInfo())); if (!Pair.second) return Pair.first->second; // ComputeBackedgeTakenCount may allocate memory for its result. Inserting it // into the BackedgeTakenCounts map transfers ownership. Otherwise, the result // must be cleared in this scope. BackedgeTakenInfo Result = ComputeBackedgeTakenCount(L); if (Result.getExact(this) != getCouldNotCompute()) { assert(isLoopInvariant(Result.getExact(this), L) && isLoopInvariant(Result.getMax(this), L) && "Computed backedge-taken count isn't loop invariant for loop!"); ++NumTripCountsComputed; } else if (Result.getMax(this) == getCouldNotCompute() && isa(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 (Result.hasAnyInfo()) { SmallVector Worklist; PushLoopPHIs(L, Worklist); SmallPtrSet Visited; while (!Worklist.empty()) { Instruction *I = Worklist.pop_back_val(); if (!Visited.insert(I).second) continue; ValueExprMapType::iterator It = ValueExprMap.find_as(static_cast(I)); if (It != ValueExprMap.end()) { const SCEV *Old = It->second; // 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(I) || !isa(Old)) { forgetMemoizedResults(Old); ValueExprMap.erase(It); } if (PHINode *PN = dyn_cast(I)) ConstantEvolutionLoopExitValue.erase(PN); } PushDefUseChildren(I, Worklist); } } // Re-lookup the insert position, since the call to // ComputeBackedgeTakenCount above could result in a // recusive call to getBackedgeTakenInfo (on a different // loop), which would invalidate the iterator computed // earlier. return BackedgeTakenCounts.find(L)->second = Result; } /// 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. DenseMap::iterator BTCPos = BackedgeTakenCounts.find(L); if (BTCPos != BackedgeTakenCounts.end()) { BTCPos->second.clear(); BackedgeTakenCounts.erase(BTCPos); } // Drop information about expressions based on loop-header PHIs. SmallVector Worklist; PushLoopPHIs(L, Worklist); SmallPtrSet Visited; while (!Worklist.empty()) { Instruction *I = Worklist.pop_back_val(); if (!Visited.insert(I).second) continue; ValueExprMapType::iterator It = ValueExprMap.find_as(static_cast(I)); if (It != ValueExprMap.end()) { forgetMemoizedResults(It->second); ValueExprMap.erase(It); if (PHINode *PN = dyn_cast(I)) ConstantEvolutionLoopExitValue.erase(PN); } PushDefUseChildren(I, Worklist); } // Forget all contained loops too, to avoid dangling entries in the // ValuesAtScopes map. for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) forgetLoop(*I); } /// 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(V); if (!I) return; // Drop information about expressions based on loop-header PHIs. SmallVector Worklist; Worklist.push_back(I); SmallPtrSet Visited; while (!Worklist.empty()) { I = Worklist.pop_back_val(); if (!Visited.insert(I).second) continue; ValueExprMapType::iterator It = ValueExprMap.find_as(static_cast(I)); if (It != ValueExprMap.end()) { forgetMemoizedResults(It->second); ValueExprMap.erase(It); if (PHINode *PN = dyn_cast(I)) ConstantEvolutionLoopExitValue.erase(PN); } PushDefUseChildren(I, Worklist); } } /// getExact - Get the exact loop backedge taken count considering all loop /// exits. A computable result can only be return for loops with a single exit. /// Returning the minimum taken count among all exits is incorrect because one /// of the loop's exit limit's may have been skipped. HowFarToZero assumes that /// the limit of each loop test is never skipped. This is a valid assumption as /// long as the loop exits via that test. For precise results, it is the /// caller's responsibility to specify the relevant loop exit using /// getExact(ExitingBlock, SE). const SCEV * ScalarEvolution::BackedgeTakenInfo::getExact(ScalarEvolution *SE) const { // If any exits were not computable, the loop is not computable. if (!ExitNotTaken.isCompleteList()) return SE->getCouldNotCompute(); // We need exactly one computable exit. if (!ExitNotTaken.ExitingBlock) return SE->getCouldNotCompute(); assert(ExitNotTaken.ExactNotTaken && "uninitialized not-taken info"); const SCEV *BECount = nullptr; for (const ExitNotTakenInfo *ENT = &ExitNotTaken; ENT != nullptr; ENT = ENT->getNextExit()) { assert(ENT->ExactNotTaken != SE->getCouldNotCompute() && "bad exit SCEV"); if (!BECount) BECount = ENT->ExactNotTaken; else if (BECount != ENT->ExactNotTaken) return SE->getCouldNotCompute(); } assert(BECount && "Invalid not taken count for loop exit"); return BECount; } /// getExact - Get the exact not taken count for this loop exit. const SCEV * ScalarEvolution::BackedgeTakenInfo::getExact(BasicBlock *ExitingBlock, ScalarEvolution *SE) const { for (const ExitNotTakenInfo *ENT = &ExitNotTaken; ENT != nullptr; ENT = ENT->getNextExit()) { if (ENT->ExitingBlock == ExitingBlock) return ENT->ExactNotTaken; } return SE->getCouldNotCompute(); } /// getMax - Get the max backedge taken count for the loop. const SCEV * ScalarEvolution::BackedgeTakenInfo::getMax(ScalarEvolution *SE) const { return Max ? Max : SE->getCouldNotCompute(); } bool ScalarEvolution::BackedgeTakenInfo::hasOperand(const SCEV *S, ScalarEvolution *SE) const { if (Max && Max != SE->getCouldNotCompute() && SE->hasOperand(Max, S)) return true; if (!ExitNotTaken.ExitingBlock) return false; for (const ExitNotTakenInfo *ENT = &ExitNotTaken; ENT != nullptr; ENT = ENT->getNextExit()) { if (ENT->ExactNotTaken != SE->getCouldNotCompute() && SE->hasOperand(ENT->ExactNotTaken, S)) { return true; } } return false; } /// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each /// computable exit into a persistent ExitNotTakenInfo array. ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo( SmallVectorImpl< std::pair > &ExitCounts, bool Complete, const SCEV *MaxCount) : Max(MaxCount) { if (!Complete) ExitNotTaken.setIncomplete(); unsigned NumExits = ExitCounts.size(); if (NumExits == 0) return; ExitNotTaken.ExitingBlock = ExitCounts[0].first; ExitNotTaken.ExactNotTaken = ExitCounts[0].second; if (NumExits == 1) return; // Handle the rare case of multiple computable exits. ExitNotTakenInfo *ENT = new ExitNotTakenInfo[NumExits-1]; ExitNotTakenInfo *PrevENT = &ExitNotTaken; for (unsigned i = 1; i < NumExits; ++i, PrevENT = ENT, ++ENT) { PrevENT->setNextExit(ENT); ENT->ExitingBlock = ExitCounts[i].first; ENT->ExactNotTaken = ExitCounts[i].second; } } /// clear - Invalidate this result and free the ExitNotTakenInfo array. void ScalarEvolution::BackedgeTakenInfo::clear() { ExitNotTaken.ExitingBlock = nullptr; ExitNotTaken.ExactNotTaken = nullptr; delete[] ExitNotTaken.getNextExit(); } /// ComputeBackedgeTakenCount - Compute the number of times the backedge /// of the specified loop will execute. ScalarEvolution::BackedgeTakenInfo ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) { SmallVector ExitingBlocks; L->getExitingBlocks(ExitingBlocks); SmallVector, 4> ExitCounts; bool CouldComputeBECount = true; BasicBlock *Latch = L->getLoopLatch(); // may be NULL. const SCEV *MustExitMaxBECount = nullptr; const SCEV *MayExitMaxBECount = nullptr; // Compute the ExitLimit for each loop exit. Use this to populate ExitCounts // and compute maxBECount. for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) { BasicBlock *ExitBB = ExitingBlocks[i]; ExitLimit EL = ComputeExitLimit(L, ExitBB); // 1. For each exit that can be computed, add an entry to ExitCounts. // CouldComputeBECount is true only if all exits can be computed. if (EL.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. CouldComputeBECount = false; else ExitCounts.push_back(std::make_pair(ExitBB, EL.Exact)); // 2. Derive the loop's MaxBECount from each exit's max number of // non-exiting iterations. Partition the loop exits into two kinds: // LoopMustExits and LoopMayExits. // // If the exit dominates the loop latch, it is a LoopMustExit otherwise it // is a LoopMayExit. If any computable LoopMustExit is found, then // MaxBECount is the minimum EL.Max of computable LoopMustExits. Otherwise, // MaxBECount is conservatively the maximum EL.Max, where CouldNotCompute is // considered greater than any computable EL.Max. if (EL.Max != getCouldNotCompute() && Latch && DT->dominates(ExitBB, Latch)) { if (!MustExitMaxBECount) MustExitMaxBECount = EL.Max; else { MustExitMaxBECount = getUMinFromMismatchedTypes(MustExitMaxBECount, EL.Max); } } else if (MayExitMaxBECount != getCouldNotCompute()) { if (!MayExitMaxBECount || EL.Max == getCouldNotCompute()) MayExitMaxBECount = EL.Max; else { MayExitMaxBECount = getUMaxFromMismatchedTypes(MayExitMaxBECount, EL.Max); } } } const SCEV *MaxBECount = MustExitMaxBECount ? MustExitMaxBECount : (MayExitMaxBECount ? MayExitMaxBECount : getCouldNotCompute()); return BackedgeTakenInfo(ExitCounts, CouldComputeBECount, MaxBECount); } /// ComputeExitLimit - Compute the number of times the backedge of the specified /// loop will execute if it exits via the specified block. ScalarEvolution::ExitLimit ScalarEvolution::ComputeExitLimit(const Loop *L, BasicBlock *ExitingBlock) { // Okay, we've chosen an exiting block. See what condition causes us to // exit at this block and remember the exit block and whether all other targets // lead to the loop header. bool MustExecuteLoopHeader = true; BasicBlock *Exit = nullptr; for (succ_iterator SI = succ_begin(ExitingBlock), SE = succ_end(ExitingBlock); SI != SE; ++SI) if (!L->contains(*SI)) { if (Exit) // Multiple exit successors. return getCouldNotCompute(); Exit = *SI; } else if (*SI != L->getHeader()) { MustExecuteLoopHeader = false; } // 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 (!MustExecuteLoopHeader && ExitingBlock != L->getHeader()) { // The simple checks failed, try climbing the unique predecessor chain // up to the header. bool Ok = false; for (BasicBlock *BB = ExitingBlock; 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(); } bool IsOnlyExit = (L->getExitingBlock() != nullptr); TerminatorInst *Term = ExitingBlock->getTerminator(); if (BranchInst *BI = dyn_cast(Term)) { assert(BI->isConditional() && "If unconditional, it can't be in loop!"); // Proceed to the next level to examine the exit condition expression. return ComputeExitLimitFromCond(L, BI->getCondition(), BI->getSuccessor(0), BI->getSuccessor(1), /*ControlsExit=*/IsOnlyExit); } if (SwitchInst *SI = dyn_cast(Term)) return ComputeExitLimitFromSingleExitSwitch(L, SI, Exit, /*ControlsExit=*/IsOnlyExit); return getCouldNotCompute(); } /// ComputeExitLimitFromCond - 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. /// /// @param ControlsExit is true if ExitCond directly controls the exit /// branch. In this case, we can assume that the loop exits only if the /// condition is true and can infer that failing to meet the condition prior to /// integer wraparound results in undefined behavior. ScalarEvolution::ExitLimit ScalarEvolution::ComputeExitLimitFromCond(const Loop *L, Value *ExitCond, BasicBlock *TBB, BasicBlock *FBB, bool ControlsExit) { // Check if the controlling expression for this loop is an And or Or. if (BinaryOperator *BO = dyn_cast(ExitCond)) { if (BO->getOpcode() == Instruction::And) { // Recurse on the operands of the and. bool EitherMayExit = L->contains(TBB); ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB, ControlsExit && !EitherMayExit); ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB, ControlsExit && !EitherMayExit); const SCEV *BECount = getCouldNotCompute(); const SCEV *MaxBECount = getCouldNotCompute(); if (EitherMayExit) { // Both conditions must be true for the loop to continue executing. // Choose the less conservative count. if (EL0.Exact == getCouldNotCompute() || EL1.Exact == getCouldNotCompute()) BECount = getCouldNotCompute(); else BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact); if (EL0.Max == getCouldNotCompute()) MaxBECount = EL1.Max; else if (EL1.Max == getCouldNotCompute()) MaxBECount = EL0.Max; else MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max); } else { // Both conditions must be true at the same time for the loop to exit. // For now, be conservative. assert(L->contains(FBB) && "Loop block has no successor in loop!"); if (EL0.Max == EL1.Max) MaxBECount = EL0.Max; if (EL0.Exact == EL1.Exact) BECount = EL0.Exact; } return ExitLimit(BECount, MaxBECount); } if (BO->getOpcode() == Instruction::Or) { // Recurse on the operands of the or. bool EitherMayExit = L->contains(FBB); ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB, ControlsExit && !EitherMayExit); ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB, ControlsExit && !EitherMayExit); const SCEV *BECount = getCouldNotCompute(); const SCEV *MaxBECount = getCouldNotCompute(); if (EitherMayExit) { // Both conditions must be false for the loop to continue executing. // Choose the less conservative count. if (EL0.Exact == getCouldNotCompute() || EL1.Exact == getCouldNotCompute()) BECount = getCouldNotCompute(); else BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact); if (EL0.Max == getCouldNotCompute()) MaxBECount = EL1.Max; else if (EL1.Max == getCouldNotCompute()) MaxBECount = EL0.Max; else MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max); } else { // Both conditions must be false at the same time for the loop to exit. // For now, be conservative. assert(L->contains(TBB) && "Loop block has no successor in loop!"); if (EL0.Max == EL1.Max) MaxBECount = EL0.Max; if (EL0.Exact == EL1.Exact) BECount = EL0.Exact; } return ExitLimit(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(ExitCond)) return ComputeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB, ControlsExit); // 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(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 ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB)); } /// ComputeExitLimitFromICmp - 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::ExitLimit ScalarEvolution::ComputeExitLimitFromICmp(const Loop *L, ICmpInst *ExitCond, BasicBlock *TBB, BasicBlock *FBB, bool ControlsExit) { // 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(ExitCond->getOperand(0))) if (Constant *RHS = dyn_cast(ExitCond->getOperand(1))) { ExitLimit ItCnt = ComputeLoadConstantCompareExitLimit(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 (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, 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(RHS)) if (const SCEVAddRecExpr *AddRec = dyn_cast(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(Ret)) return Ret; } switch (Cond) { case ICmpInst::ICMP_NE: { // while (X != Y) // Convert to: while (X-Y != 0) ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit); if (EL.hasAnyInfo()) return EL; break; } case ICmpInst::ICMP_EQ: { // while (X == Y) // Convert to: while (X-Y == 0) ExitLimit EL = HowFarToNonZero(getMinusSCEV(LHS, RHS), L); if (EL.hasAnyInfo()) return EL; break; } case ICmpInst::ICMP_SLT: case ICmpInst::ICMP_ULT: { // while (X < Y) bool IsSigned = Cond == ICmpInst::ICMP_SLT; ExitLimit EL = HowManyLessThans(LHS, RHS, L, IsSigned, ControlsExit); if (EL.hasAnyInfo()) return EL; break; } case ICmpInst::ICMP_SGT: case ICmpInst::ICMP_UGT: { // while (X > Y) bool IsSigned = Cond == ICmpInst::ICMP_SGT; ExitLimit EL = HowManyGreaterThans(LHS, RHS, L, IsSigned, ControlsExit); if (EL.hasAnyInfo()) return EL; 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 ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB)); } ScalarEvolution::ExitLimit ScalarEvolution::ComputeExitLimitFromSingleExitSwitch(const Loop *L, SwitchInst *Switch, BasicBlock *ExitingBlock, bool ControlsExit) { assert(!L->contains(ExitingBlock) && "Not an exiting block!"); // Give up if the exit is the default dest of a switch. if (Switch->getDefaultDest() == ExitingBlock) return getCouldNotCompute(); assert(L->contains(Switch->getDefaultDest()) && "Default case must not exit the loop!"); const SCEV *LHS = getSCEVAtScope(Switch->getCondition(), L); const SCEV *RHS = getConstant(Switch->findCaseDest(ExitingBlock)); // while (X != Y) --> while (X-Y != 0) ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit); if (EL.hasAnyInfo()) return EL; return getCouldNotCompute(); } 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(Val) && "Evaluation of SCEV at constant didn't fold correctly?"); return cast(Val)->getValue(); } /// ComputeLoadConstantCompareExitLimit - Given an exit condition of /// 'icmp op load X, cst', try to see if we can compute the backedge /// execution count. ScalarEvolution::ExitLimit ScalarEvolution::ComputeLoadConstantCompareExitLimit( 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(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(GEP->getOperand(0)); if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() || GEP->getNumOperands() < 3 || !isa(GEP->getOperand(1)) || !cast(GEP->getOperand(1))->isNullValue()) return getCouldNotCompute(); // Okay, we allow one non-constant index into the GEP instruction. Value *VarIdx = nullptr; std::vector Indexes; unsigned VarIdxNum = 0; for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i) if (ConstantInt *CI = dyn_cast(GEP->getOperand(i))) { Indexes.push_back(CI); } else if (!isa(GEP->getOperand(i))) { if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's. VarIdx = GEP->getOperand(i); VarIdxNum = i-2; Indexes.push_back(nullptr); } // Loop-invariant loads may be a byproduct of loop optimization. Skip them. if (!VarIdx) return getCouldNotCompute(); // 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(Idx); if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) || !isa(IdxExpr->getOperand(0)) || !isa(IdxExpr->getOperand(1))) return getCouldNotCompute(); unsigned MaxSteps = MaxBruteForceIterations; for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) { ConstantInt *ItCst = ConstantInt::get( cast(IdxExpr->getType()), IterationNum); ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this); // Form the GEP offset. Indexes[VarIdxNum] = Val; Constant *Result = ConstantFoldLoadThroughGEPIndices(GV->getInitializer(), Indexes); if (!Result) break; // Cannot compute! // Evaluate the condition for this iteration. Result = ConstantExpr::getICmp(predicate, Result, RHS); if (!isa(Result)) break; // Couldn't decide for sure if (cast(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(I) || isa(I) || isa(I) || isa(I) || isa(I) || isa(I)) return true; if (const CallInst *CI = dyn_cast(I)) if (const Function *F = CI->getCalledFunction()) return canConstantFoldCallTo(F); return false; } /// Determine whether this instruction can constant evolve within this loop /// assuming its operands can all constant evolve. static bool canConstantEvolve(Instruction *I, const Loop *L) { // An instruction outside of the loop can't be derived from a loop PHI. if (!L->contains(I)) return false; if (isa(I)) { if (L->getHeader() == I->getParent()) return true; else // We don't currently keep track of the control flow needed to evaluate // PHIs, so we cannot handle PHIs inside of loops. return false; } // If we won't be able to constant fold this expression even if the operands // are constants, bail early. return CanConstantFold(I); } /// getConstantEvolvingPHIOperands - Implement getConstantEvolvingPHI by /// recursing through each instruction operand until reaching a loop header phi. static PHINode * getConstantEvolvingPHIOperands(Instruction *UseInst, const Loop *L, DenseMap &PHIMap) { // Otherwise, we can evaluate this instruction if all of its operands are // constant or derived from a PHI node themselves. PHINode *PHI = nullptr; for (Instruction::op_iterator OpI = UseInst->op_begin(), OpE = UseInst->op_end(); OpI != OpE; ++OpI) { if (isa(*OpI)) continue; Instruction *OpInst = dyn_cast(*OpI); if (!OpInst || !canConstantEvolve(OpInst, L)) return nullptr; PHINode *P = dyn_cast(OpInst); if (!P) // If this operand is already visited, reuse the prior result. // We may have P != PHI if this is the deepest point at which the // inconsistent paths meet. P = PHIMap.lookup(OpInst); if (!P) { // Recurse and memoize the results, whether a phi is found or not. // This recursive call invalidates pointers into PHIMap. P = getConstantEvolvingPHIOperands(OpInst, L, PHIMap); PHIMap[OpInst] = P; } if (!P) return nullptr; // Not evolving from PHI if (PHI && PHI != P) return nullptr; // Evolving from multiple different PHIs. PHI = P; } // This is a expression evolving from a constant PHI! return PHI; } /// 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) { Instruction *I = dyn_cast(V); if (!I || !canConstantEvolve(I, L)) return nullptr; if (PHINode *PN = dyn_cast(I)) { return PN; } // Record non-constant instructions contained by the loop. DenseMap PHIMap; return getConstantEvolvingPHIOperands(I, L, PHIMap); } /// 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, const Loop *L, DenseMap &Vals, const DataLayout *DL, const TargetLibraryInfo *TLI) { // Convenient constant check, but redundant for recursive calls. if (Constant *C = dyn_cast(V)) return C; Instruction *I = dyn_cast(V); if (!I) return nullptr; if (Constant *C = Vals.lookup(I)) return C; // An instruction inside the loop depends on a value outside the loop that we // weren't given a mapping for, or a value such as a call inside the loop. if (!canConstantEvolve(I, L)) return nullptr; // An unmapped PHI can be due to a branch or another loop inside this loop, // or due to this not being the initial iteration through a loop where we // couldn't compute the evolution of this particular PHI last time. if (isa(I)) return nullptr; std::vector Operands(I->getNumOperands()); for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { Instruction *Operand = dyn_cast(I->getOperand(i)); if (!Operand) { Operands[i] = dyn_cast(I->getOperand(i)); if (!Operands[i]) return nullptr; continue; } Constant *C = EvaluateExpression(Operand, L, Vals, DL, TLI); Vals[Operand] = C; if (!C) return nullptr; Operands[i] = C; } if (CmpInst *CI = dyn_cast(I)) return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0], Operands[1], DL, TLI); if (LoadInst *LI = dyn_cast(I)) { if (!LI->isVolatile()) return ConstantFoldLoadFromConstPtr(Operands[0], DL); } return ConstantFoldInstOperands(I->getOpcode(), I->getType(), Operands, DL, TLI); } /// 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) { DenseMap::const_iterator I = ConstantEvolutionLoopExitValue.find(PN); if (I != ConstantEvolutionLoopExitValue.end()) return I->second; if (BEs.ugt(MaxBruteForceIterations)) return ConstantEvolutionLoopExitValue[PN] = nullptr; // Not going to evaluate it. Constant *&RetVal = ConstantEvolutionLoopExitValue[PN]; DenseMap CurrentIterVals; BasicBlock *Header = L->getHeader(); assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!"); // 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)); PHINode *PHI = nullptr; for (BasicBlock::iterator I = Header->begin(); (PHI = dyn_cast(I)); ++I) { Constant *StartCST = dyn_cast(PHI->getIncomingValue(!SecondIsBackedge)); if (!StartCST) continue; CurrentIterVals[PHI] = StartCST; } if (!CurrentIterVals.count(PN)) return RetVal = nullptr; Value *BEValue = PN->getIncomingValue(SecondIsBackedge); // Execute the loop symbolically to determine the exit value. if (BEs.getActiveBits() >= 32) return RetVal = nullptr; // More than 2^32-1 iterations?? Not doing it! unsigned NumIterations = BEs.getZExtValue(); // must be in range unsigned IterationNum = 0; for (; ; ++IterationNum) { if (IterationNum == NumIterations) return RetVal = CurrentIterVals[PN]; // Got exit value! // Compute the value of the PHIs for the next iteration. // EvaluateExpression adds non-phi values to the CurrentIterVals map. DenseMap NextIterVals; Constant *NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, TLI); if (!NextPHI) return nullptr; // Couldn't evaluate! NextIterVals[PN] = NextPHI; bool StoppedEvolving = NextPHI == CurrentIterVals[PN]; // Also evaluate the other PHI nodes. However, we don't get to stop if we // cease to be able to evaluate one of them or if they stop evolving, // because that doesn't necessarily prevent us from computing PN. SmallVector, 8> PHIsToCompute; for (DenseMap::const_iterator I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){ PHINode *PHI = dyn_cast(I->first); if (!PHI || PHI == PN || PHI->getParent() != Header) continue; PHIsToCompute.push_back(std::make_pair(PHI, I->second)); } // We use two distinct loops because EvaluateExpression may invalidate any // iterators into CurrentIterVals. for (SmallVectorImpl >::const_iterator I = PHIsToCompute.begin(), E = PHIsToCompute.end(); I != E; ++I) { PHINode *PHI = I->first; Constant *&NextPHI = NextIterVals[PHI]; if (!NextPHI) { // Not already computed. Value *BEValue = PHI->getIncomingValue(SecondIsBackedge); NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, TLI); } if (NextPHI != I->second) StoppedEvolving = false; } // If all entries in CurrentIterVals == NextIterVals then we can stop // iterating, the loop can't continue to change. if (StoppedEvolving) return RetVal = CurrentIterVals[PN]; CurrentIterVals.swap(NextIterVals); } } /// ComputeExitCountExhaustively - 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::ComputeExitCountExhaustively(const Loop *L, Value *Cond, bool ExitWhen) { PHINode *PN = getConstantEvolvingPHI(Cond, L); if (!PN) return getCouldNotCompute(); // If the loop is canonicalized, the PHI will have exactly two entries. // That's the only form we support here. if (PN->getNumIncomingValues() != 2) return getCouldNotCompute(); DenseMap CurrentIterVals; BasicBlock *Header = L->getHeader(); assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!"); // 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)); PHINode *PHI = nullptr; for (BasicBlock::iterator I = Header->begin(); (PHI = dyn_cast(I)); ++I) { Constant *StartCST = dyn_cast(PHI->getIncomingValue(!SecondIsBackedge)); if (!StartCST) continue; CurrentIterVals[PHI] = StartCST; } if (!CurrentIterVals.count(PN)) return getCouldNotCompute(); // 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 MaxIterations = MaxBruteForceIterations; // Limit analysis. for (unsigned IterationNum = 0; IterationNum != MaxIterations;++IterationNum){ ConstantInt *CondVal = dyn_cast_or_null(EvaluateExpression(Cond, L, CurrentIterVals, DL, TLI)); // Couldn't symbolically evaluate. if (!CondVal) return getCouldNotCompute(); if (CondVal->getValue() == uint64_t(ExitWhen)) { ++NumBruteForceTripCountsComputed; return getConstant(Type::getInt32Ty(getContext()), IterationNum); } // Update all the PHI nodes for the next iteration. DenseMap NextIterVals; // Create a list of which PHIs we need to compute. We want to do this before // calling EvaluateExpression on them because that may invalidate iterators // into CurrentIterVals. SmallVector PHIsToCompute; for (DenseMap::const_iterator I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){ PHINode *PHI = dyn_cast(I->first); if (!PHI || PHI->getParent() != Header) continue; PHIsToCompute.push_back(PHI); } for (SmallVectorImpl::const_iterator I = PHIsToCompute.begin(), E = PHIsToCompute.end(); I != E; ++I) { PHINode *PHI = *I; Constant *&NextPHI = NextIterVals[PHI]; if (NextPHI) continue; // Already computed! Value *BEValue = PHI->getIncomingValue(SecondIsBackedge); NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, TLI); } CurrentIterVals.swap(NextIterVals); } // 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. SmallVector, 2> &Values = ValuesAtScopes[V]; for (unsigned u = 0; u < Values.size(); u++) { if (Values[u].first == L) return Values[u].second ? Values[u].second : V; } Values.push_back(std::make_pair(L, static_cast(nullptr))); // Otherwise compute it. const SCEV *C = computeSCEVAtScope(V, L); SmallVector, 2> &Values2 = ValuesAtScopes[V]; for (unsigned u = Values2.size(); u > 0; u--) { if (Values2[u - 1].first == L) { Values2[u - 1].second = C; break; } } return C; } /// This builds up a Constant using the ConstantExpr interface. That way, we /// will return Constants for objects which aren't represented by a /// SCEVConstant, because SCEVConstant is restricted to ConstantInt. /// Returns NULL if the SCEV isn't representable as a Constant. static Constant *BuildConstantFromSCEV(const SCEV *V) { switch (static_cast(V->getSCEVType())) { case scCouldNotCompute: case scAddRecExpr: break; case scConstant: return cast(V)->getValue(); case scUnknown: return dyn_cast(cast(V)->getValue()); case scSignExtend: { const SCEVSignExtendExpr *SS = cast(V); if (Constant *CastOp = BuildConstantFromSCEV(SS->getOperand())) return ConstantExpr::getSExt(CastOp, SS->getType()); break; } case scZeroExtend: { const SCEVZeroExtendExpr *SZ = cast(V); if (Constant *CastOp = BuildConstantFromSCEV(SZ->getOperand())) return ConstantExpr::getZExt(CastOp, SZ->getType()); break; } case scTruncate: { const SCEVTruncateExpr *ST = cast(V); if (Constant *CastOp = BuildConstantFromSCEV(ST->getOperand())) return ConstantExpr::getTrunc(CastOp, ST->getType()); break; } case scAddExpr: { const SCEVAddExpr *SA = cast(V); if (Constant *C = BuildConstantFromSCEV(SA->getOperand(0))) { if (PointerType *PTy = dyn_cast(C->getType())) { unsigned AS = PTy->getAddressSpace(); Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS); C = ConstantExpr::getBitCast(C, DestPtrTy); } for (unsigned i = 1, e = SA->getNumOperands(); i != e; ++i) { Constant *C2 = BuildConstantFromSCEV(SA->getOperand(i)); if (!C2) return nullptr; // First pointer! if (!C->getType()->isPointerTy() && C2->getType()->isPointerTy()) { unsigned AS = C2->getType()->getPointerAddressSpace(); std::swap(C, C2); Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS); // The offsets have been converted to bytes. We can add bytes to an // i8* by GEP with the byte count in the first index. C = ConstantExpr::getBitCast(C, DestPtrTy); } // Don't bother trying to sum two pointers. We probably can't // statically compute a load that results from it anyway. if (C2->getType()->isPointerTy()) return nullptr; if (PointerType *PTy = dyn_cast(C->getType())) { if (PTy->getElementType()->isStructTy()) C2 = ConstantExpr::getIntegerCast( C2, Type::getInt32Ty(C->getContext()), true); C = ConstantExpr::getGetElementPtr(C, C2); } else C = ConstantExpr::getAdd(C, C2); } return C; } break; } case scMulExpr: { const SCEVMulExpr *SM = cast(V); if (Constant *C = BuildConstantFromSCEV(SM->getOperand(0))) { // Don't bother with pointers at all. if (C->getType()->isPointerTy()) return nullptr; for (unsigned i = 1, e = SM->getNumOperands(); i != e; ++i) { Constant *C2 = BuildConstantFromSCEV(SM->getOperand(i)); if (!C2 || C2->getType()->isPointerTy()) return nullptr; C = ConstantExpr::getMul(C, C2); } return C; } break; } case scUDivExpr: { const SCEVUDivExpr *SU = cast(V); if (Constant *LHS = BuildConstantFromSCEV(SU->getLHS())) if (Constant *RHS = BuildConstantFromSCEV(SU->getRHS())) if (LHS->getType() == RHS->getType()) return ConstantExpr::getUDiv(LHS, RHS); break; } case scSMaxExpr: case scUMaxExpr: break; // TODO: smax, umax. } return nullptr; } const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) { if (isa(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(V)) { if (Instruction *I = dyn_cast(SU->getValue())) { const Loop *LI = (*this->LI)[I->getParent()]; if (LI && LI->getParentLoop() == L) // Looking for loop exit value. if (PHINode *PN = dyn_cast(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(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)) { SmallVector Operands; bool MadeImprovement = false; for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { Value *Op = I->getOperand(i); if (Constant *C = dyn_cast(Op)) { Operands.push_back(C); continue; } // 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 *OrigV = getSCEV(Op); const SCEV *OpV = getSCEVAtScope(OrigV, L); MadeImprovement |= OrigV != OpV; Constant *C = BuildConstantFromSCEV(OpV); if (!C) return V; if (C->getType() != Op->getType()) C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false, Op->getType(), false), C, Op->getType()); Operands.push_back(C); } // Check to see if getSCEVAtScope actually made an improvement. if (MadeImprovement) { Constant *C = nullptr; if (const CmpInst *CI = dyn_cast(I)) C = ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0], Operands[1], DL, TLI); else if (const LoadInst *LI = dyn_cast(I)) { if (!LI->isVolatile()) C = ConstantFoldLoadFromConstPtr(Operands[0], DL); } else C = ConstantFoldInstOperands(I->getOpcode(), I->getType(), Operands, DL, TLI); if (!C) return V; return getSCEV(C); } } } // This is some other type of SCEVUnknown, just return it. return V; } if (const SCEVCommutativeExpr *Comm = dyn_cast(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 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(Comm)) return getAddExpr(NewOps); if (isa(Comm)) return getMulExpr(NewOps); if (isa(Comm)) return getSMaxExpr(NewOps); if (isa(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(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(V)) { // First, attempt to evaluate each operand. // Avoid performing the look-up in the common case where the specified // expression has no loop-variant portions. for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L); if (OpAtScope == AddRec->getOperand(i)) continue; // Okay, at least one of these operands is loop variant but might be // foldable. Build a new instance of the folded commutative expression. SmallVector NewOps(AddRec->op_begin(), AddRec->op_begin()+i); NewOps.push_back(OpAtScope); for (++i; i != e; ++i) NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L)); const SCEV *FoldedRec = getAddRecExpr(NewOps, AddRec->getLoop(), AddRec->getNoWrapFlags(SCEV::FlagNW)); AddRec = dyn_cast(FoldedRec); // The addrec may be folded to a nonrecurrence, for example, if the // induction variable is multiplied by zero after constant folding. Go // ahead and return the folded value. if (!AddRec) return FoldedRec; break; } // If the scope is outside the addrec's loop, evaluate it by using the // loop exit value of the addrec. if (!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(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(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(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!"); } /// 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.setBit(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 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) { assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!"); const SCEVConstant *LC = dyn_cast(AddRec->getOperand(0)); const SCEVConstant *MC = dyn_cast(AddRec->getOperand(1)); const SCEVConstant *NC = dyn_cast(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); if (SqrtTerm.isNegative()) { // The loop is provably infinite. const SCEV *CNC = SE.getCouldNotCompute(); return std::make_pair(CNC, CNC); } // 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. /// /// This is only used for loops with a "x != y" exit test. The exit condition is /// now expressed as a single expression, V = x-y. So the exit test is /// effectively V != 0. We know and take advantage of the fact that this /// expression only being used in a comparison by zero context. ScalarEvolution::ExitLimit ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L, bool ControlsExit) { // If the value is a constant if (const SCEVConstant *C = dyn_cast(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(V); if (!AddRec || AddRec->getLoop() != L) return getCouldNotCompute(); // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of // the quadratic equation to solve it. if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) { std::pair Roots = SolveQuadraticEquation(AddRec, *this); const SCEVConstant *R1 = dyn_cast(Roots.first); const SCEVConstant *R2 = dyn_cast(Roots.second); if (R1 && R2) { #if 0 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1 << " sol#2: " << *R2 << "\n"; #endif // Pick the smallest positive root value. if (ConstantInt *CB = dyn_cast(ConstantExpr::getICmp(CmpInst::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(); } // Otherwise we can only handle this if it is affine. if (!AddRec->isAffine()) return getCouldNotCompute(); // 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()); // For now we handle only constant steps. // // TODO: Handle a nonconstant Step given AddRec. If the // AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap // to 0, it must be counting down to equal 0. Consequently, N = Start / -Step. // We have not yet seen any such cases. const SCEVConstant *StepC = dyn_cast(Step); if (!StepC || StepC->getValue()->equalsInt(0)) return getCouldNotCompute(); // For positive steps (counting up until unsigned overflow): // N = -Start/Step (as unsigned) // For negative steps (counting down to zero): // N = Start/-Step // First compute the unsigned distance from zero in the direction of Step. bool CountDown = StepC->getValue()->getValue().isNegative(); const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start); // Handle unitary steps, which cannot wraparound. // 1*N = -Start; -1*N = Start (mod 2^BW), so: // N = Distance (as unsigned) if (StepC->getValue()->equalsInt(1) || StepC->getValue()->isAllOnesValue()) { ConstantRange CR = getUnsignedRange(Start); const SCEV *MaxBECount; if (!CountDown && CR.getUnsignedMin().isMinValue()) // When counting up, the worst starting value is 1, not 0. MaxBECount = CR.getUnsignedMax().isMinValue() ? getConstant(APInt::getMinValue(CR.getBitWidth())) : getConstant(APInt::getMaxValue(CR.getBitWidth())); else MaxBECount = getConstant(CountDown ? CR.getUnsignedMax() : -CR.getUnsignedMin()); return ExitLimit(Distance, MaxBECount); } // As a special case, handle the instance where Step is a positive power of // two. In this case, determining whether Step divides Distance evenly can be // done by counting and comparing the number of trailing zeros of Step and // Distance. if (!CountDown) { const APInt &StepV = StepC->getValue()->getValue(); // StepV.isPowerOf2() returns true if StepV is an positive power of two. It // also returns true if StepV is maximally negative (eg, INT_MIN), but that // case is not handled as this code is guarded by !CountDown. if (StepV.isPowerOf2() && GetMinTrailingZeros(Distance) >= StepV.countTrailingZeros()) return getUDivExactExpr(Distance, Step); } // If the condition controls loop exit (the loop exits only if the expression // is true) and the addition is no-wrap we can use unsigned divide to // compute the backedge count. In this case, the step may not divide the // distance, but we don't care because if the condition is "missed" the loop // will have undefined behavior due to wrapping. if (ControlsExit && AddRec->getNoWrapFlags(SCEV::FlagNW)) { const SCEV *Exact = getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step); return ExitLimit(Exact, Exact); } // Then, try to solve the above equation provided that Start is constant. if (const SCEVConstant *StartC = dyn_cast(Start)) return SolveLinEquationWithOverflow(StepC->getValue()->getValue(), -StartC->getValue()->getValue(), *this); return getCouldNotCompute(); } /// HowFarToNonZero - Return the number of times a backedge checking the /// specified value for nonzero will execute. If not computable, return /// CouldNotCompute ScalarEvolution::ExitLimit 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(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(); } /// 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 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(L->getLoopPredecessor(), L->getHeader()); return std::pair(); } /// 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(A)) if (const SCEVUnknown *BU = dyn_cast(B)) if (const Instruction *AI = dyn_cast(AU->getValue())) if (const Instruction *BI = dyn_cast(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, unsigned Depth) { bool Changed = false; // If we hit the max recursion limit bail out. if (Depth >= 3) return false; // Canonicalize a constant to the right side. if (const SCEVConstant *LHSC = dyn_cast(LHS)) { // Check for both operands constant. if (const SCEVConstant *RHSC = dyn_cast(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(RHS)) { const Loop *L = AR->getLoop(); if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) { 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(RHS)) { const APInt &RA = RC->getValue()->getValue(); switch (Pred) { default: llvm_unreachable("Unexpected ICmpInst::Predicate value!"); case ICmpInst::ICMP_EQ: case ICmpInst::ICMP_NE: // Fold ((-1) * %a) + %b == 0 (equivalent to %b-%a == 0) into %a == %b. if (!RA) if (const SCEVAddExpr *AE = dyn_cast(LHS)) if (const SCEVMulExpr *ME = dyn_cast(AE->getOperand(0))) if (AE->getNumOperands() == 2 && ME->getNumOperands() == 2 && ME->getOperand(0)->isAllOnesValue()) { RHS = AE->getOperand(1); LHS = ME->getOperand(1); Changed = true; } 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, SCEV::FlagNSW); Pred = ICmpInst::ICMP_SLT; Changed = true; } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) { LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS, SCEV::FlagNSW); 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, SCEV::FlagNSW); Pred = ICmpInst::ICMP_SGT; Changed = true; } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) { LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS, SCEV::FlagNSW); Pred = ICmpInst::ICMP_SGT; Changed = true; } break; case ICmpInst::ICMP_ULE: if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) { RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS, SCEV::FlagNUW); Pred = ICmpInst::ICMP_ULT; Changed = true; } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) { LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS, SCEV::FlagNUW); 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, SCEV::FlagNUW); Pred = ICmpInst::ICMP_UGT; Changed = true; } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) { LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS, SCEV::FlagNUW); Pred = ICmpInst::ICMP_UGT; Changed = true; } break; default: break; } // TODO: More simplifications are possible here. // Recursively simplify until we either hit a recursion limit or nothing // changes. if (Changed) return SimplifyICmpOperands(Pred, LHS, RHS, Depth+1); return Changed; trivially_true: // Return 0 == 0. LHS = RHS = getConstant(ConstantInt::getFalse(getContext())); Pred = ICmpInst::ICMP_EQ; return true; trivially_false: // Return 0 != 0. LHS = RHS = getConstant(ConstantInt::getFalse(getContext())); 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 LHS and RHS are both addrec, both conditions must be true in // every iteration of the loop. const SCEVAddRecExpr *LAR = dyn_cast(LHS); const SCEVAddRecExpr *RAR = dyn_cast(RHS); bool LeftGuarded = false; bool RightGuarded = false; if (LAR) { const Loop *L = LAR->getLoop(); if (isLoopEntryGuardedByCond(L, Pred, LAR->getStart(), RHS) && isLoopBackedgeGuardedByCond(L, Pred, LAR->getPostIncExpr(*this), RHS)) { if (!RAR) return true; LeftGuarded = true; } } if (RAR) { const Loop *L = RAR->getLoop(); if (isLoopEntryGuardedByCond(L, Pred, LHS, RAR->getStart()) && isLoopBackedgeGuardedByCond(L, Pred, LHS, RAR->getPostIncExpr(*this))) { if (!LAR) return true; RightGuarded = true; } } if (LeftGuarded && RightGuarded) 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!"); case ICmpInst::ICMP_SGT: 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: 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: 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: 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; if (isKnownPredicateWithRanges(Pred, LHS, RHS)) return true; BasicBlock *Latch = L->getLoopLatch(); if (!Latch) return false; BranchInst *LoopContinuePredicate = dyn_cast(Latch->getTerminator()); if (LoopContinuePredicate && LoopContinuePredicate->isConditional() && isImpliedCond(Pred, LHS, RHS, LoopContinuePredicate->getCondition(), LoopContinuePredicate->getSuccessor(0) != L->getHeader())) return true; // Check conditions due to any @llvm.assume intrinsics. for (auto &AssumeVH : AC->assumptions()) { if (!AssumeVH) continue; auto *CI = cast(AssumeVH); if (!DT->dominates(CI, Latch->getTerminator())) continue; if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false)) return true; } return false; } /// 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; if (isKnownPredicateWithRanges(Pred, LHS, RHS)) return true; // 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 Pair(L->getLoopPredecessor(), L->getHeader()); Pair.first; Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) { BranchInst *LoopEntryPredicate = dyn_cast(Pair.first->getTerminator()); if (!LoopEntryPredicate || LoopEntryPredicate->isUnconditional()) continue; if (isImpliedCond(Pred, LHS, RHS, LoopEntryPredicate->getCondition(), LoopEntryPredicate->getSuccessor(0) != Pair.second)) return true; } // Check conditions due to any @llvm.assume intrinsics. for (auto &AssumeVH : AC->assumptions()) { if (!AssumeVH) continue; auto *CI = cast(AssumeVH); if (!DT->dominates(CI, L->getHeader())) continue; if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false)) return true; } return false; } /// RAII wrapper to prevent recursive application of isImpliedCond. /// ScalarEvolution's PendingLoopPredicates set must be empty unless we are /// currently evaluating isImpliedCond. struct MarkPendingLoopPredicate { Value *Cond; DenseSet &LoopPreds; bool Pending; MarkPendingLoopPredicate(Value *C, DenseSet &LP) : Cond(C), LoopPreds(LP) { Pending = !LoopPreds.insert(Cond).second; } ~MarkPendingLoopPredicate() { if (!Pending) LoopPreds.erase(Cond); } }; /// isImpliedCond - Test whether the condition described by Pred, LHS, /// and RHS is true whenever the given Cond value evaluates to true. bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS, Value *FoundCondValue, bool Inverse) { MarkPendingLoopPredicate Mark(FoundCondValue, PendingLoopPredicates); if (Mark.Pending) return false; // Recursively handle And and Or conditions. if (BinaryOperator *BO = dyn_cast(FoundCondValue)) { if (BO->getOpcode() == Instruction::And) { if (!Inverse) return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) || isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse); } else if (BO->getOpcode() == Instruction::Or) { if (Inverse) return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) || isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse); } } ICmpInst *ICI = dyn_cast(FoundCondValue); 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 or controls // the loop latch. 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(FoundPred)) { 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(FoundPred); // Check to see if we can make the LHS or RHS match. if (LHS == FoundRHS || RHS == FoundLHS) { if (isa(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(RHS)) return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS); else return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred), RHS, LHS, FoundLHS, FoundRHS); } // Check if we can make progress by sharpening ranges. if (FoundPred == ICmpInst::ICMP_NE && (isa(FoundLHS) || isa(FoundRHS))) { const SCEVConstant *C = nullptr; const SCEV *V = nullptr; if (isa(FoundLHS)) { C = cast(FoundLHS); V = FoundRHS; } else { C = cast(FoundRHS); V = FoundLHS; } // The guarding predicate tells us that C != V. If the known range // of V is [C, t), we can sharpen the range to [C + 1, t). The // range we consider has to correspond to same signedness as the // predicate we're interested in folding. APInt Min = ICmpInst::isSigned(Pred) ? getSignedRange(V).getSignedMin() : getUnsignedRange(V).getUnsignedMin(); if (Min == C->getValue()->getValue()) { // Given (V >= Min && V != Min) we conclude V >= (Min + 1). // This is true even if (Min + 1) wraps around -- in case of // wraparound, (Min + 1) < Min, so (V >= Min => V >= (Min + 1)). APInt SharperMin = Min + 1; switch (Pred) { case ICmpInst::ICMP_SGE: case ICmpInst::ICMP_UGE: // We know V `Pred` SharperMin. If this implies LHS `Pred` // RHS, we're done. if (isImpliedCondOperands(Pred, LHS, RHS, V, getConstant(SharperMin))) return true; case ICmpInst::ICMP_SGT: case ICmpInst::ICMP_UGT: // We know from the range information that (V `Pred` Min || // V == Min). We know from the guarding condition that !(V // == Min). This gives us // // V `Pred` Min || V == Min && !(V == Min) // => V `Pred` Min // // If V `Pred` Min implies LHS `Pred` RHS, we're done. if (isImpliedCondOperands(Pred, LHS, RHS, V, getConstant(Min))) return true; default: // No change break; } } } // 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)); } /// If Expr computes ~A, return A else return nullptr static const SCEV *MatchNotExpr(const SCEV *Expr) { const SCEVAddExpr *Add = dyn_cast(Expr); if (!Add || Add->getNumOperands() != 2) return nullptr; const SCEVConstant *AddLHS = dyn_cast(Add->getOperand(0)); if (!(AddLHS && AddLHS->getValue()->getValue().isAllOnesValue())) return nullptr; const SCEVMulExpr *AddRHS = dyn_cast(Add->getOperand(1)); if (!AddRHS || AddRHS->getNumOperands() != 2) return nullptr; const SCEVConstant *MulLHS = dyn_cast(AddRHS->getOperand(0)); if (!(MulLHS && MulLHS->getValue()->getValue().isAllOnesValue())) return nullptr; return AddRHS->getOperand(1); } /// Is MaybeMaxExpr an SMax or UMax of Candidate and some other values? template static bool IsMaxConsistingOf(const SCEV *MaybeMaxExpr, const SCEV *Candidate) { const MaxExprType *MaxExpr = dyn_cast(MaybeMaxExpr); if (!MaxExpr) return false; auto It = std::find(MaxExpr->op_begin(), MaxExpr->op_end(), Candidate); return It != MaxExpr->op_end(); } /// Is MaybeMinExpr an SMin or UMin of Candidate and some other values? template static bool IsMinConsistingOf(ScalarEvolution &SE, const SCEV *MaybeMinExpr, const SCEV *Candidate) { const SCEV *MaybeMaxExpr = MatchNotExpr(MaybeMinExpr); if (!MaybeMaxExpr) return false; return IsMaxConsistingOf(MaybeMaxExpr, SE.getNotSCEV(Candidate)); } /// Is LHS `Pred` RHS true on the virtue of LHS or RHS being a Min or Max /// expression? static bool IsKnownPredicateViaMinOrMax(ScalarEvolution &SE, ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS) { switch (Pred) { default: return false; case ICmpInst::ICMP_SGE: std::swap(LHS, RHS); // fall through case ICmpInst::ICMP_SLE: return // min(A, ...) <= A IsMinConsistingOf(SE, LHS, RHS) || // A <= max(A, ...) IsMaxConsistingOf(RHS, LHS); case ICmpInst::ICMP_UGE: std::swap(LHS, RHS); // fall through case ICmpInst::ICMP_ULE: return // min(A, ...) <= A IsMinConsistingOf(SE, LHS, RHS) || // A <= max(A, ...) IsMaxConsistingOf(RHS, LHS); } llvm_unreachable("covered switch fell through?!"); } /// 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) { auto IsKnownPredicateFull = [this](ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS) { return isKnownPredicateWithRanges(Pred, LHS, RHS) || IsKnownPredicateViaMinOrMax(*this, Pred, LHS, RHS); }; 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 (IsKnownPredicateFull(ICmpInst::ICMP_SLE, LHS, FoundLHS) && IsKnownPredicateFull(ICmpInst::ICMP_SGE, RHS, FoundRHS)) return true; break; case ICmpInst::ICMP_SGT: case ICmpInst::ICMP_SGE: if (IsKnownPredicateFull(ICmpInst::ICMP_SGE, LHS, FoundLHS) && IsKnownPredicateFull(ICmpInst::ICMP_SLE, RHS, FoundRHS)) return true; break; case ICmpInst::ICMP_ULT: case ICmpInst::ICMP_ULE: if (IsKnownPredicateFull(ICmpInst::ICMP_ULE, LHS, FoundLHS) && IsKnownPredicateFull(ICmpInst::ICMP_UGE, RHS, FoundRHS)) return true; break; case ICmpInst::ICMP_UGT: case ICmpInst::ICMP_UGE: if (IsKnownPredicateFull(ICmpInst::ICMP_UGE, LHS, FoundLHS) && IsKnownPredicateFull(ICmpInst::ICMP_ULE, RHS, FoundRHS)) return true; break; } return false; } // Verify if an linear IV with positive stride can overflow when in a // less-than comparison, knowing the invariant term of the comparison, the // stride and the knowledge of NSW/NUW flags on the recurrence. bool ScalarEvolution::doesIVOverflowOnLT(const SCEV *RHS, const SCEV *Stride, bool IsSigned, bool NoWrap) { if (NoWrap) return false; unsigned BitWidth = getTypeSizeInBits(RHS->getType()); const SCEV *One = getConstant(Stride->getType(), 1); if (IsSigned) { APInt MaxRHS = getSignedRange(RHS).getSignedMax(); APInt MaxValue = APInt::getSignedMaxValue(BitWidth); APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One)) .getSignedMax(); // SMaxRHS + SMaxStrideMinusOne > SMaxValue => overflow! return (MaxValue - MaxStrideMinusOne).slt(MaxRHS); } APInt MaxRHS = getUnsignedRange(RHS).getUnsignedMax(); APInt MaxValue = APInt::getMaxValue(BitWidth); APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One)) .getUnsignedMax(); // UMaxRHS + UMaxStrideMinusOne > UMaxValue => overflow! return (MaxValue - MaxStrideMinusOne).ult(MaxRHS); } // Verify if an linear IV with negative stride can overflow when in a // greater-than comparison, knowing the invariant term of the comparison, // the stride and the knowledge of NSW/NUW flags on the recurrence. bool ScalarEvolution::doesIVOverflowOnGT(const SCEV *RHS, const SCEV *Stride, bool IsSigned, bool NoWrap) { if (NoWrap) return false; unsigned BitWidth = getTypeSizeInBits(RHS->getType()); const SCEV *One = getConstant(Stride->getType(), 1); if (IsSigned) { APInt MinRHS = getSignedRange(RHS).getSignedMin(); APInt MinValue = APInt::getSignedMinValue(BitWidth); APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One)) .getSignedMax(); // SMinRHS - SMaxStrideMinusOne < SMinValue => overflow! return (MinValue + MaxStrideMinusOne).sgt(MinRHS); } APInt MinRHS = getUnsignedRange(RHS).getUnsignedMin(); APInt MinValue = APInt::getMinValue(BitWidth); APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One)) .getUnsignedMax(); // UMinRHS - UMaxStrideMinusOne < UMinValue => overflow! return (MinValue + MaxStrideMinusOne).ugt(MinRHS); } // Compute the backedge taken count knowing the interval difference, the // stride and presence of the equality in the comparison. const SCEV *ScalarEvolution::computeBECount(const SCEV *Delta, const SCEV *Step, bool Equality) { const SCEV *One = getConstant(Step->getType(), 1); Delta = Equality ? getAddExpr(Delta, Step) : getAddExpr(Delta, getMinusSCEV(Step, One)); return getUDivExpr(Delta, Step); } /// HowManyLessThans - Return the number of times a backedge containing the /// specified less-than comparison will execute. If not computable, return /// CouldNotCompute. /// /// @param ControlsExit is true when the LHS < RHS condition directly controls /// the branch (loops exits only if condition is true). In this case, we can use /// NoWrapFlags to skip overflow checks. ScalarEvolution::ExitLimit ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS, const Loop *L, bool IsSigned, bool ControlsExit) { // We handle only IV < Invariant if (!isLoopInvariant(RHS, L)) return getCouldNotCompute(); const SCEVAddRecExpr *IV = dyn_cast(LHS); // Avoid weird loops if (!IV || IV->getLoop() != L || !IV->isAffine()) return getCouldNotCompute(); bool NoWrap = ControlsExit && IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW); const SCEV *Stride = IV->getStepRecurrence(*this); // Avoid negative or zero stride values if (!isKnownPositive(Stride)) return getCouldNotCompute(); // Avoid proven overflow cases: this will ensure that the backedge taken count // will not generate any unsigned overflow. Relaxed no-overflow conditions // exploit NoWrapFlags, allowing to optimize in presence of undefined // behaviors like the case of C language. if (!Stride->isOne() && doesIVOverflowOnLT(RHS, Stride, IsSigned, NoWrap)) return getCouldNotCompute(); ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SLT : ICmpInst::ICMP_ULT; const SCEV *Start = IV->getStart(); const SCEV *End = RHS; if (!isLoopEntryGuardedByCond(L, Cond, getMinusSCEV(Start, Stride), RHS)) { const SCEV *Diff = getMinusSCEV(RHS, Start); // If we have NoWrap set, then we can assume that the increment won't // overflow, in which case if RHS - Start is a constant, we don't need to // do a max operation since we can just figure it out statically if (NoWrap && isa(Diff)) { APInt D = dyn_cast(Diff)->getValue()->getValue(); if (D.isNegative()) End = Start; } else End = IsSigned ? getSMaxExpr(RHS, Start) : getUMaxExpr(RHS, Start); } const SCEV *BECount = computeBECount(getMinusSCEV(End, Start), Stride, false); APInt MinStart = IsSigned ? getSignedRange(Start).getSignedMin() : getUnsignedRange(Start).getUnsignedMin(); APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin() : getUnsignedRange(Stride).getUnsignedMin(); unsigned BitWidth = getTypeSizeInBits(LHS->getType()); APInt Limit = IsSigned ? APInt::getSignedMaxValue(BitWidth) - (MinStride - 1) : APInt::getMaxValue(BitWidth) - (MinStride - 1); // Although End can be a MAX expression we estimate MaxEnd considering only // the case End = RHS. This is safe because in the other case (End - Start) // is zero, leading to a zero maximum backedge taken count. APInt MaxEnd = IsSigned ? APIntOps::smin(getSignedRange(RHS).getSignedMax(), Limit) : APIntOps::umin(getUnsignedRange(RHS).getUnsignedMax(), Limit); const SCEV *MaxBECount; if (isa(BECount)) MaxBECount = BECount; else MaxBECount = computeBECount(getConstant(MaxEnd - MinStart), getConstant(MinStride), false); if (isa(MaxBECount)) MaxBECount = BECount; return ExitLimit(BECount, MaxBECount); } ScalarEvolution::ExitLimit ScalarEvolution::HowManyGreaterThans(const SCEV *LHS, const SCEV *RHS, const Loop *L, bool IsSigned, bool ControlsExit) { // We handle only IV > Invariant if (!isLoopInvariant(RHS, L)) return getCouldNotCompute(); const SCEVAddRecExpr *IV = dyn_cast(LHS); // Avoid weird loops if (!IV || IV->getLoop() != L || !IV->isAffine()) return getCouldNotCompute(); bool NoWrap = ControlsExit && IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW); const SCEV *Stride = getNegativeSCEV(IV->getStepRecurrence(*this)); // Avoid negative or zero stride values if (!isKnownPositive(Stride)) return getCouldNotCompute(); // Avoid proven overflow cases: this will ensure that the backedge taken count // will not generate any unsigned overflow. Relaxed no-overflow conditions // exploit NoWrapFlags, allowing to optimize in presence of undefined // behaviors like the case of C language. if (!Stride->isOne() && doesIVOverflowOnGT(RHS, Stride, IsSigned, NoWrap)) return getCouldNotCompute(); ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SGT : ICmpInst::ICMP_UGT; const SCEV *Start = IV->getStart(); const SCEV *End = RHS; if (!isLoopEntryGuardedByCond(L, Cond, getAddExpr(Start, Stride), RHS)) { const SCEV *Diff = getMinusSCEV(RHS, Start); // If we have NoWrap set, then we can assume that the increment won't // overflow, in which case if RHS - Start is a constant, we don't need to // do a max operation since we can just figure it out statically if (NoWrap && isa(Diff)) { APInt D = dyn_cast(Diff)->getValue()->getValue(); if (!D.isNegative()) End = Start; } else End = IsSigned ? getSMinExpr(RHS, Start) : getUMinExpr(RHS, Start); } const SCEV *BECount = computeBECount(getMinusSCEV(Start, End), Stride, false); APInt MaxStart = IsSigned ? getSignedRange(Start).getSignedMax() : getUnsignedRange(Start).getUnsignedMax(); APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin() : getUnsignedRange(Stride).getUnsignedMin(); unsigned BitWidth = getTypeSizeInBits(LHS->getType()); APInt Limit = IsSigned ? APInt::getSignedMinValue(BitWidth) + (MinStride - 1) : APInt::getMinValue(BitWidth) + (MinStride - 1); // Although End can be a MIN expression we estimate MinEnd considering only // the case End = RHS. This is safe because in the other case (Start - End) // is zero, leading to a zero maximum backedge taken count. APInt MinEnd = IsSigned ? APIntOps::smax(getSignedRange(RHS).getSignedMin(), Limit) : APIntOps::umax(getUnsignedRange(RHS).getUnsignedMin(), Limit); const SCEV *MaxBECount = getCouldNotCompute(); if (isa(BECount)) MaxBECount = BECount; else MaxBECount = computeBECount(getConstant(MaxStart - MinEnd), getConstant(MinStride), false); if (isa(MaxBECount)) MaxBECount = BECount; return ExitLimit(BECount, MaxBECount); } /// 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(getStart())) if (!SC->getValue()->isZero()) { SmallVector Operands(op_begin(), op_end()); Operands[0] = SE.getConstant(SC->getType(), 0); const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(), getNoWrapFlags(FlagNW)); if (const SCEVAddRecExpr *ShiftedAddRec = dyn_cast(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(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(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 NewOps(op_begin(), op_end()); NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper())); const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop(), // getNoWrapFlags(FlagNW) FlagAnyWrap); // Next, solve the constructed addrec std::pair Roots = SolveQuadraticEquation(cast(NewAddRec), SE); const SCEVConstant *R1 = dyn_cast(Roots.first); const SCEVConstant *R2 = dyn_cast(Roots.second); if (R1) { // Pick the smallest positive root value. if (ConstantInt *CB = dyn_cast(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(); } namespace { struct FindUndefs { bool Found; FindUndefs() : Found(false) {} bool follow(const SCEV *S) { if (const SCEVUnknown *C = dyn_cast(S)) { if (isa(C->getValue())) Found = true; } else if (const SCEVConstant *C = dyn_cast(S)) { if (isa(C->getValue())) Found = true; } // Keep looking if we haven't found it yet. return !Found; } bool isDone() const { // Stop recursion if we have found an undef. return Found; } }; } // Return true when S contains at least an undef value. static inline bool containsUndefs(const SCEV *S) { FindUndefs F; SCEVTraversal ST(F); ST.visitAll(S); return F.Found; } namespace { // Collect all steps of SCEV expressions. struct SCEVCollectStrides { ScalarEvolution &SE; SmallVectorImpl &Strides; SCEVCollectStrides(ScalarEvolution &SE, SmallVectorImpl &S) : SE(SE), Strides(S) {} bool follow(const SCEV *S) { if (const SCEVAddRecExpr *AR = dyn_cast(S)) Strides.push_back(AR->getStepRecurrence(SE)); return true; } bool isDone() const { return false; } }; // Collect all SCEVUnknown and SCEVMulExpr expressions. struct SCEVCollectTerms { SmallVectorImpl &Terms; SCEVCollectTerms(SmallVectorImpl &T) : Terms(T) {} bool follow(const SCEV *S) { if (isa(S) || isa(S)) { if (!containsUndefs(S)) Terms.push_back(S); // Stop recursion: once we collected a term, do not walk its operands. return false; } // Keep looking. return true; } bool isDone() const { return false; } }; } /// Find parametric terms in this SCEVAddRecExpr. void SCEVAddRecExpr::collectParametricTerms( ScalarEvolution &SE, SmallVectorImpl &Terms) const { SmallVector Strides; SCEVCollectStrides StrideCollector(SE, Strides); visitAll(this, StrideCollector); DEBUG({ dbgs() << "Strides:\n"; for (const SCEV *S : Strides) dbgs() << *S << "\n"; }); for (const SCEV *S : Strides) { SCEVCollectTerms TermCollector(Terms); visitAll(S, TermCollector); } DEBUG({ dbgs() << "Terms:\n"; for (const SCEV *T : Terms) dbgs() << *T << "\n"; }); } static bool findArrayDimensionsRec(ScalarEvolution &SE, SmallVectorImpl &Terms, SmallVectorImpl &Sizes) { int Last = Terms.size() - 1; const SCEV *Step = Terms[Last]; // End of recursion. if (Last == 0) { if (const SCEVMulExpr *M = dyn_cast(Step)) { SmallVector Qs; for (const SCEV *Op : M->operands()) if (!isa(Op)) Qs.push_back(Op); Step = SE.getMulExpr(Qs); } Sizes.push_back(Step); return true; } for (const SCEV *&Term : Terms) { // Normalize the terms before the next call to findArrayDimensionsRec. const SCEV *Q, *R; SCEVDivision::divide(SE, Term, Step, &Q, &R); // Bail out when GCD does not evenly divide one of the terms. if (!R->isZero()) return false; Term = Q; } // Remove all SCEVConstants. Terms.erase(std::remove_if(Terms.begin(), Terms.end(), [](const SCEV *E) { return isa(E); }), Terms.end()); if (Terms.size() > 0) if (!findArrayDimensionsRec(SE, Terms, Sizes)) return false; Sizes.push_back(Step); return true; } namespace { struct FindParameter { bool FoundParameter; FindParameter() : FoundParameter(false) {} bool follow(const SCEV *S) { if (isa(S)) { FoundParameter = true; // Stop recursion: we found a parameter. return false; } // Keep looking. return true; } bool isDone() const { // Stop recursion if we have found a parameter. return FoundParameter; } }; } // Returns true when S contains at least a SCEVUnknown parameter. static inline bool containsParameters(const SCEV *S) { FindParameter F; SCEVTraversal ST(F); ST.visitAll(S); return F.FoundParameter; } // Returns true when one of the SCEVs of Terms contains a SCEVUnknown parameter. static inline bool containsParameters(SmallVectorImpl &Terms) { for (const SCEV *T : Terms) if (containsParameters(T)) return true; return false; } // Return the number of product terms in S. static inline int numberOfTerms(const SCEV *S) { if (const SCEVMulExpr *Expr = dyn_cast(S)) return Expr->getNumOperands(); return 1; } static const SCEV *removeConstantFactors(ScalarEvolution &SE, const SCEV *T) { if (isa(T)) return nullptr; if (isa(T)) return T; if (const SCEVMulExpr *M = dyn_cast(T)) { SmallVector Factors; for (const SCEV *Op : M->operands()) if (!isa(Op)) Factors.push_back(Op); return SE.getMulExpr(Factors); } return T; } /// Return the size of an element read or written by Inst. const SCEV *ScalarEvolution::getElementSize(Instruction *Inst) { Type *Ty; if (StoreInst *Store = dyn_cast(Inst)) Ty = Store->getValueOperand()->getType(); else if (LoadInst *Load = dyn_cast(Inst)) Ty = Load->getType(); else return nullptr; Type *ETy = getEffectiveSCEVType(PointerType::getUnqual(Ty)); return getSizeOfExpr(ETy, Ty); } /// Second step of delinearization: compute the array dimensions Sizes from the /// set of Terms extracted from the memory access function of this SCEVAddRec. void ScalarEvolution::findArrayDimensions(SmallVectorImpl &Terms, SmallVectorImpl &Sizes, const SCEV *ElementSize) const { if (Terms.size() < 1 || !ElementSize) return; // Early return when Terms do not contain parameters: we do not delinearize // non parametric SCEVs. if (!containsParameters(Terms)) return; DEBUG({ dbgs() << "Terms:\n"; for (const SCEV *T : Terms) dbgs() << *T << "\n"; }); // Remove duplicates. std::sort(Terms.begin(), Terms.end()); Terms.erase(std::unique(Terms.begin(), Terms.end()), Terms.end()); // Put larger terms first. std::sort(Terms.begin(), Terms.end(), [](const SCEV *LHS, const SCEV *RHS) { return numberOfTerms(LHS) > numberOfTerms(RHS); }); ScalarEvolution &SE = *const_cast(this); // Divide all terms by the element size. for (const SCEV *&Term : Terms) { const SCEV *Q, *R; SCEVDivision::divide(SE, Term, ElementSize, &Q, &R); Term = Q; } SmallVector NewTerms; // Remove constant factors. for (const SCEV *T : Terms) if (const SCEV *NewT = removeConstantFactors(SE, T)) NewTerms.push_back(NewT); DEBUG({ dbgs() << "Terms after sorting:\n"; for (const SCEV *T : NewTerms) dbgs() << *T << "\n"; }); if (NewTerms.empty() || !findArrayDimensionsRec(SE, NewTerms, Sizes)) { Sizes.clear(); return; } // The last element to be pushed into Sizes is the size of an element. Sizes.push_back(ElementSize); DEBUG({ dbgs() << "Sizes:\n"; for (const SCEV *S : Sizes) dbgs() << *S << "\n"; }); } /// Third step of delinearization: compute the access functions for the /// Subscripts based on the dimensions in Sizes. void SCEVAddRecExpr::computeAccessFunctions( ScalarEvolution &SE, SmallVectorImpl &Subscripts, SmallVectorImpl &Sizes) const { // Early exit in case this SCEV is not an affine multivariate function. if (Sizes.empty() || !this->isAffine()) return; const SCEV *Res = this; int Last = Sizes.size() - 1; for (int i = Last; i >= 0; i--) { const SCEV *Q, *R; SCEVDivision::divide(SE, Res, Sizes[i], &Q, &R); DEBUG({ dbgs() << "Res: " << *Res << "\n"; dbgs() << "Sizes[i]: " << *Sizes[i] << "\n"; dbgs() << "Res divided by Sizes[i]:\n"; dbgs() << "Quotient: " << *Q << "\n"; dbgs() << "Remainder: " << *R << "\n"; }); Res = Q; // Do not record the last subscript corresponding to the size of elements in // the array. if (i == Last) { // Bail out if the remainder is too complex. if (isa(R)) { Subscripts.clear(); Sizes.clear(); return; } continue; } // Record the access function for the current subscript. Subscripts.push_back(R); } // Also push in last position the remainder of the last division: it will be // the access function of the innermost dimension. Subscripts.push_back(Res); std::reverse(Subscripts.begin(), Subscripts.end()); DEBUG({ dbgs() << "Subscripts:\n"; for (const SCEV *S : Subscripts) dbgs() << *S << "\n"; }); } /// Splits the SCEV into two vectors of SCEVs representing the subscripts and /// sizes of an array access. Returns the remainder of the delinearization that /// is the offset start of the array. The SCEV->delinearize algorithm computes /// the multiples of SCEV coefficients: that is a pattern matching of sub /// expressions in the stride and base of a SCEV corresponding to the /// computation of a GCD (greatest common divisor) of base and stride. When /// SCEV->delinearize fails, it returns the SCEV unchanged. /// /// For example: when analyzing the memory access A[i][j][k] in this loop nest /// /// void foo(long n, long m, long o, double A[n][m][o]) { /// /// for (long i = 0; i < n; i++) /// for (long j = 0; j < m; j++) /// for (long k = 0; k < o; k++) /// A[i][j][k] = 1.0; /// } /// /// the delinearization input is the following AddRec SCEV: /// /// AddRec: {{{%A,+,(8 * %m * %o)}<%for.i>,+,(8 * %o)}<%for.j>,+,8}<%for.k> /// /// From this SCEV, we are able to say that the base offset of the access is %A /// because it appears as an offset that does not divide any of the strides in /// the loops: /// /// CHECK: Base offset: %A /// /// and then SCEV->delinearize determines the size of some of the dimensions of /// the array as these are the multiples by which the strides are happening: /// /// CHECK: ArrayDecl[UnknownSize][%m][%o] with elements of sizeof(double) bytes. /// /// Note that the outermost dimension remains of UnknownSize because there are /// no strides that would help identifying the size of the last dimension: when /// the array has been statically allocated, one could compute the size of that /// dimension by dividing the overall size of the array by the size of the known /// dimensions: %m * %o * 8. /// /// Finally delinearize provides the access functions for the array reference /// that does correspond to A[i][j][k] of the above C testcase: /// /// CHECK: ArrayRef[{0,+,1}<%for.i>][{0,+,1}<%for.j>][{0,+,1}<%for.k>] /// /// The testcases are checking the output of a function pass: /// DelinearizationPass that walks through all loads and stores of a function /// asking for the SCEV of the memory access with respect to all enclosing /// loops, calling SCEV->delinearize on that and printing the results. void SCEVAddRecExpr::delinearize(ScalarEvolution &SE, SmallVectorImpl &Subscripts, SmallVectorImpl &Sizes, const SCEV *ElementSize) const { // First step: collect parametric terms. SmallVector Terms; collectParametricTerms(SE, Terms); if (Terms.empty()) return; // Second step: find subscript sizes. SE.findArrayDimensions(Terms, Sizes, ElementSize); if (Sizes.empty()) return; // Third step: compute the access functions for each subscript. computeAccessFunctions(SE, Subscripts, Sizes); if (Subscripts.empty()) return; DEBUG({ dbgs() << "succeeded to delinearize " << *this << "\n"; dbgs() << "ArrayDecl[UnknownSize]"; for (const SCEV *S : Sizes) dbgs() << "[" << *S << "]"; dbgs() << "\nArrayRef"; for (const SCEV *S : Subscripts) dbgs() << "[" << *S << "]"; dbgs() << "\n"; }); } //===----------------------------------------------------------------------===// // SCEVCallbackVH Class Implementation //===----------------------------------------------------------------------===// void ScalarEvolution::SCEVCallbackVH::deleted() { assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!"); if (PHINode *PN = dyn_cast(getValPtr())) SE->ConstantEvolutionLoopExitValue.erase(PN); SE->ValueExprMap.erase(getValPtr()); // this now dangles! } void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) { 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. Value *Old = getValPtr(); SmallVector Worklist(Old->user_begin(), Old->user_end()); SmallPtrSet Visited; 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) continue; if (!Visited.insert(U).second) continue; if (PHINode *PN = dyn_cast(U)) SE->ConstantEvolutionLoopExitValue.erase(PN); SE->ValueExprMap.erase(U); Worklist.insert(Worklist.end(), U->user_begin(), U->user_end()); } // Delete the Old value. if (PHINode *PN = dyn_cast(Old)) SE->ConstantEvolutionLoopExitValue.erase(PN); SE->ValueExprMap.erase(Old); // this now dangles! } ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se) : CallbackVH(V), SE(se) {} //===----------------------------------------------------------------------===// // ScalarEvolution Class Implementation //===----------------------------------------------------------------------===// ScalarEvolution::ScalarEvolution() : FunctionPass(ID), ValuesAtScopes(64), LoopDispositions(64), BlockDispositions(64), FirstUnknown(nullptr) { initializeScalarEvolutionPass(*PassRegistry::getPassRegistry()); } bool ScalarEvolution::runOnFunction(Function &F) { this->F = &F; AC = &getAnalysis().getAssumptionCache(F); LI = &getAnalysis().getLoopInfo(); DL = &F.getParent()->getDataLayout(); TLI = &getAnalysis().getTLI(); DT = &getAnalysis().getDomTree(); return false; } void ScalarEvolution::releaseMemory() { // Iterate through all the SCEVUnknown instances and call their // destructors, so that they release their references to their values. for (SCEVUnknown *U = FirstUnknown; U; U = U->Next) U->~SCEVUnknown(); FirstUnknown = nullptr; ValueExprMap.clear(); // Free any extra memory created for ExitNotTakenInfo in the unlikely event // that a loop had multiple computable exits. for (DenseMap::iterator I = BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end(); I != E; ++I) { I->second.clear(); } assert(PendingLoopPredicates.empty() && "isImpliedCond garbage"); BackedgeTakenCounts.clear(); ConstantEvolutionLoopExitValue.clear(); ValuesAtScopes.clear(); LoopDispositions.clear(); BlockDispositions.clear(); UnsignedRanges.clear(); SignedRanges.clear(); UniqueSCEVs.clear(); SCEVAllocator.Reset(); } void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const { AU.setPreservesAll(); AU.addRequired(); AU.addRequiredTransitive(); AU.addRequiredTransitive(); AU.addRequired(); } bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) { return !isa(getBackedgeTakenCount(L)); } static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE, const Loop *L) { // Print all inner loops first for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I) PrintLoopInfo(OS, SE, *I); OS << "Loop "; L->getHeader()->printAsOperand(OS, /*PrintType=*/false); OS << ": "; SmallVector ExitBlocks; L->getExitBlocks(ExitBlocks); if (ExitBlocks.size() != 1) OS << " "; if (SE->hasLoopInvariantBackedgeTakenCount(L)) { OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L); } else { OS << "Unpredictable backedge-taken count. "; } OS << "\n" "Loop "; L->getHeader()->printAsOperand(OS, /*PrintType=*/false); OS << ": "; if (!isa(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(this); OS << "Classifying expressions for: "; F->printAsOperand(OS, /*PrintType=*/false); OS << "\n"; for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I) if (isSCEVable(I->getType()) && !isa(*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 (!SE.isLoopInvariant(ExitValue, L)) { OS << "<>"; } else { OS << *ExitValue; } } OS << "\n"; } OS << "Determining loop execution counts for: "; F->printAsOperand(OS, /*PrintType=*/false); OS << "\n"; for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I) PrintLoopInfo(OS, &SE, *I); } ScalarEvolution::LoopDisposition ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) { auto &Values = LoopDispositions[S]; for (auto &V : Values) { if (V.getPointer() == L) return V.getInt(); } Values.emplace_back(L, LoopVariant); LoopDisposition D = computeLoopDisposition(S, L); auto &Values2 = LoopDispositions[S]; for (auto &V : make_range(Values2.rbegin(), Values2.rend())) { if (V.getPointer() == L) { V.setInt(D); break; } } return D; } ScalarEvolution::LoopDisposition ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) { switch (static_cast(S->getSCEVType())) { case scConstant: return LoopInvariant; case scTruncate: case scZeroExtend: case scSignExtend: return getLoopDisposition(cast(S)->getOperand(), L); case scAddRecExpr: { const SCEVAddRecExpr *AR = cast(S); // If L is the addrec's loop, it's computable. if (AR->getLoop() == L) return LoopComputable; // Add recurrences are never invariant in the function-body (null loop). if (!L) return LoopVariant; // This recurrence is variant w.r.t. L if L contains AR's loop. if (L->contains(AR->getLoop())) return LoopVariant; // This recurrence is invariant w.r.t. L if AR's loop contains L. if (AR->getLoop()->contains(L)) return LoopInvariant; // This recurrence is variant w.r.t. L if any of its operands // are variant. for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end(); I != E; ++I) if (!isLoopInvariant(*I, L)) return LoopVariant; // Otherwise it's loop-invariant. return LoopInvariant; } case scAddExpr: case scMulExpr: case scUMaxExpr: case scSMaxExpr: { const SCEVNAryExpr *NAry = cast(S); bool HasVarying = false; for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end(); I != E; ++I) { LoopDisposition D = getLoopDisposition(*I, L); if (D == LoopVariant) return LoopVariant; if (D == LoopComputable) HasVarying = true; } return HasVarying ? LoopComputable : LoopInvariant; } case scUDivExpr: { const SCEVUDivExpr *UDiv = cast(S); LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L); if (LD == LoopVariant) return LoopVariant; LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L); if (RD == LoopVariant) return LoopVariant; return (LD == LoopInvariant && RD == LoopInvariant) ? LoopInvariant : LoopComputable; } case scUnknown: // 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(cast(S)->getValue())) return (L && !L->contains(I)) ? LoopInvariant : LoopVariant; return LoopInvariant; case scCouldNotCompute: llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); } llvm_unreachable("Unknown SCEV kind!"); } bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) { return getLoopDisposition(S, L) == LoopInvariant; } bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) { return getLoopDisposition(S, L) == LoopComputable; } ScalarEvolution::BlockDisposition ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) { auto &Values = BlockDispositions[S]; for (auto &V : Values) { if (V.getPointer() == BB) return V.getInt(); } Values.emplace_back(BB, DoesNotDominateBlock); BlockDisposition D = computeBlockDisposition(S, BB); auto &Values2 = BlockDispositions[S]; for (auto &V : make_range(Values2.rbegin(), Values2.rend())) { if (V.getPointer() == BB) { V.setInt(D); break; } } return D; } ScalarEvolution::BlockDisposition ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) { switch (static_cast(S->getSCEVType())) { case scConstant: return ProperlyDominatesBlock; case scTruncate: case scZeroExtend: case scSignExtend: return getBlockDisposition(cast(S)->getOperand(), BB); case scAddRecExpr: { // This uses a "dominates" query instead of "properly dominates" query // to test for proper dominance too, because the instruction which // produces the addrec's value is a PHI, and a PHI effectively properly // dominates its entire containing block. const SCEVAddRecExpr *AR = cast(S); if (!DT->dominates(AR->getLoop()->getHeader(), BB)) return DoesNotDominateBlock; } // FALL THROUGH into SCEVNAryExpr handling. case scAddExpr: case scMulExpr: case scUMaxExpr: case scSMaxExpr: { const SCEVNAryExpr *NAry = cast(S); bool Proper = true; for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end(); I != E; ++I) { BlockDisposition D = getBlockDisposition(*I, BB); if (D == DoesNotDominateBlock) return DoesNotDominateBlock; if (D == DominatesBlock) Proper = false; } return Proper ? ProperlyDominatesBlock : DominatesBlock; } case scUDivExpr: { const SCEVUDivExpr *UDiv = cast(S); const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS(); BlockDisposition LD = getBlockDisposition(LHS, BB); if (LD == DoesNotDominateBlock) return DoesNotDominateBlock; BlockDisposition RD = getBlockDisposition(RHS, BB); if (RD == DoesNotDominateBlock) return DoesNotDominateBlock; return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ? ProperlyDominatesBlock : DominatesBlock; } case scUnknown: if (Instruction *I = dyn_cast(cast(S)->getValue())) { if (I->getParent() == BB) return DominatesBlock; if (DT->properlyDominates(I->getParent(), BB)) return ProperlyDominatesBlock; return DoesNotDominateBlock; } return ProperlyDominatesBlock; case scCouldNotCompute: llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); } llvm_unreachable("Unknown SCEV kind!"); } bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) { return getBlockDisposition(S, BB) >= DominatesBlock; } bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) { return getBlockDisposition(S, BB) == ProperlyDominatesBlock; } namespace { // Search for a SCEV expression node within an expression tree. // Implements SCEVTraversal::Visitor. struct SCEVSearch { const SCEV *Node; bool IsFound; SCEVSearch(const SCEV *N): Node(N), IsFound(false) {} bool follow(const SCEV *S) { IsFound |= (S == Node); return !IsFound; } bool isDone() const { return IsFound; } }; } bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const { SCEVSearch Search(Op); visitAll(S, Search); return Search.IsFound; } void ScalarEvolution::forgetMemoizedResults(const SCEV *S) { ValuesAtScopes.erase(S); LoopDispositions.erase(S); BlockDispositions.erase(S); UnsignedRanges.erase(S); SignedRanges.erase(S); for (DenseMap::iterator I = BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end(); I != E; ) { BackedgeTakenInfo &BEInfo = I->second; if (BEInfo.hasOperand(S, this)) { BEInfo.clear(); BackedgeTakenCounts.erase(I++); } else ++I; } } typedef DenseMap VerifyMap; /// replaceSubString - Replaces all occurrences of From in Str with To. static void replaceSubString(std::string &Str, StringRef From, StringRef To) { size_t Pos = 0; while ((Pos = Str.find(From, Pos)) != std::string::npos) { Str.replace(Pos, From.size(), To.data(), To.size()); Pos += To.size(); } } /// getLoopBackedgeTakenCounts - Helper method for verifyAnalysis. static void getLoopBackedgeTakenCounts(Loop *L, VerifyMap &Map, ScalarEvolution &SE) { for (Loop::reverse_iterator I = L->rbegin(), E = L->rend(); I != E; ++I) { getLoopBackedgeTakenCounts(*I, Map, SE); // recurse. std::string &S = Map[L]; if (S.empty()) { raw_string_ostream OS(S); SE.getBackedgeTakenCount(L)->print(OS); // false and 0 are semantically equivalent. This can happen in dead loops. replaceSubString(OS.str(), "false", "0"); // Remove wrap flags, their use in SCEV is highly fragile. // FIXME: Remove this when SCEV gets smarter about them. replaceSubString(OS.str(), "", ""); replaceSubString(OS.str(), "", ""); replaceSubString(OS.str(), "", ""); } } } void ScalarEvolution::verifyAnalysis() const { if (!VerifySCEV) return; ScalarEvolution &SE = *const_cast(this); // Gather stringified backedge taken counts for all loops using SCEV's caches. // FIXME: It would be much better to store actual values instead of strings, // but SCEV pointers will change if we drop the caches. VerifyMap BackedgeDumpsOld, BackedgeDumpsNew; for (LoopInfo::reverse_iterator I = LI->rbegin(), E = LI->rend(); I != E; ++I) getLoopBackedgeTakenCounts(*I, BackedgeDumpsOld, SE); // Gather stringified backedge taken counts for all loops without using // SCEV's caches. SE.releaseMemory(); for (LoopInfo::reverse_iterator I = LI->rbegin(), E = LI->rend(); I != E; ++I) getLoopBackedgeTakenCounts(*I, BackedgeDumpsNew, SE); // Now compare whether they're the same with and without caches. This allows // verifying that no pass changed the cache. assert(BackedgeDumpsOld.size() == BackedgeDumpsNew.size() && "New loops suddenly appeared!"); for (VerifyMap::iterator OldI = BackedgeDumpsOld.begin(), OldE = BackedgeDumpsOld.end(), NewI = BackedgeDumpsNew.begin(); OldI != OldE; ++OldI, ++NewI) { assert(OldI->first == NewI->first && "Loop order changed!"); // Compare the stringified SCEVs. We don't care if undef backedgetaken count // changes. // FIXME: We currently ignore SCEV changes from/to CouldNotCompute. This // means that a pass is buggy or SCEV has to learn a new pattern but is // usually not harmful. if (OldI->second != NewI->second && OldI->second.find("undef") == std::string::npos && NewI->second.find("undef") == std::string::npos && OldI->second != "***COULDNOTCOMPUTE***" && NewI->second != "***COULDNOTCOMPUTE***") { dbgs() << "SCEVValidator: SCEV for loop '" << OldI->first->getHeader()->getName() << "' changed from '" << OldI->second << "' to '" << NewI->second << "'!\n"; std::abort(); } } // TODO: Verify more things. }