//===- ScalarEvolution.cpp - Scalar Evolution Analysis --------------------===// // // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. // See https://llvm.org/LICENSE.txt for license information. // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception // //===----------------------------------------------------------------------===// // // 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/APInt.h" #include "llvm/ADT/ArrayRef.h" #include "llvm/ADT/DenseMap.h" #include "llvm/ADT/DepthFirstIterator.h" #include "llvm/ADT/EquivalenceClasses.h" #include "llvm/ADT/FoldingSet.h" #include "llvm/ADT/None.h" #include "llvm/ADT/Optional.h" #include "llvm/ADT/STLExtras.h" #include "llvm/ADT/ScopeExit.h" #include "llvm/ADT/Sequence.h" #include "llvm/ADT/SetVector.h" #include "llvm/ADT/SmallPtrSet.h" #include "llvm/ADT/SmallSet.h" #include "llvm/ADT/SmallVector.h" #include "llvm/ADT/Statistic.h" #include "llvm/ADT/StringRef.h" #include "llvm/Analysis/AssumptionCache.h" #include "llvm/Analysis/ConstantFolding.h" #include "llvm/Analysis/InstructionSimplify.h" #include "llvm/Analysis/LoopInfo.h" #include "llvm/Analysis/ScalarEvolutionDivision.h" #include "llvm/Analysis/ScalarEvolutionExpressions.h" #include "llvm/Analysis/TargetLibraryInfo.h" #include "llvm/Analysis/ValueTracking.h" #include "llvm/Config/llvm-config.h" #include "llvm/IR/Argument.h" #include "llvm/IR/BasicBlock.h" #include "llvm/IR/CFG.h" #include "llvm/IR/Constant.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/Function.h" #include "llvm/IR/GlobalAlias.h" #include "llvm/IR/GlobalValue.h" #include "llvm/IR/GlobalVariable.h" #include "llvm/IR/InstIterator.h" #include "llvm/IR/InstrTypes.h" #include "llvm/IR/Instruction.h" #include "llvm/IR/Instructions.h" #include "llvm/IR/IntrinsicInst.h" #include "llvm/IR/Intrinsics.h" #include "llvm/IR/LLVMContext.h" #include "llvm/IR/Metadata.h" #include "llvm/IR/Operator.h" #include "llvm/IR/PatternMatch.h" #include "llvm/IR/Type.h" #include "llvm/IR/Use.h" #include "llvm/IR/User.h" #include "llvm/IR/Value.h" #include "llvm/IR/Verifier.h" #include "llvm/InitializePasses.h" #include "llvm/Pass.h" #include "llvm/Support/Casting.h" #include "llvm/Support/CommandLine.h" #include "llvm/Support/Compiler.h" #include "llvm/Support/Debug.h" #include "llvm/Support/ErrorHandling.h" #include "llvm/Support/KnownBits.h" #include "llvm/Support/SaveAndRestore.h" #include "llvm/Support/raw_ostream.h" #include #include #include #include #include #include #include #include #include #include #include using namespace llvm; using namespace PatternMatch; #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::ZeroOrMore, cl::desc("Maximum number of iterations SCEV will " "symbolically execute a constant " "derived loop"), cl::init(100)); // FIXME: Enable this with EXPENSIVE_CHECKS when the test suite is clean. static cl::opt VerifySCEV( "verify-scev", cl::Hidden, cl::desc("Verify ScalarEvolution's backedge taken counts (slow)")); static cl::opt VerifySCEVStrict( "verify-scev-strict", cl::Hidden, cl::desc("Enable stricter verification with -verify-scev is passed")); static cl::opt VerifySCEVMap("verify-scev-maps", cl::Hidden, cl::desc("Verify no dangling value in ScalarEvolution's " "ExprValueMap (slow)")); static cl::opt VerifyIR( "scev-verify-ir", cl::Hidden, cl::desc("Verify IR correctness when making sensitive SCEV queries (slow)"), cl::init(false)); static cl::opt MulOpsInlineThreshold( "scev-mulops-inline-threshold", cl::Hidden, cl::desc("Threshold for inlining multiplication operands into a SCEV"), cl::init(32)); static cl::opt AddOpsInlineThreshold( "scev-addops-inline-threshold", cl::Hidden, cl::desc("Threshold for inlining addition operands into a SCEV"), cl::init(500)); static cl::opt MaxSCEVCompareDepth( "scalar-evolution-max-scev-compare-depth", cl::Hidden, cl::desc("Maximum depth of recursive SCEV complexity comparisons"), cl::init(32)); static cl::opt MaxSCEVOperationsImplicationDepth( "scalar-evolution-max-scev-operations-implication-depth", cl::Hidden, cl::desc("Maximum depth of recursive SCEV operations implication analysis"), cl::init(2)); static cl::opt MaxValueCompareDepth( "scalar-evolution-max-value-compare-depth", cl::Hidden, cl::desc("Maximum depth of recursive value complexity comparisons"), cl::init(2)); static cl::opt MaxArithDepth("scalar-evolution-max-arith-depth", cl::Hidden, cl::desc("Maximum depth of recursive arithmetics"), cl::init(32)); static cl::opt MaxConstantEvolvingDepth( "scalar-evolution-max-constant-evolving-depth", cl::Hidden, cl::desc("Maximum depth of recursive constant evolving"), cl::init(32)); static cl::opt MaxCastDepth("scalar-evolution-max-cast-depth", cl::Hidden, cl::desc("Maximum depth of recursive SExt/ZExt/Trunc"), cl::init(8)); static cl::opt MaxAddRecSize("scalar-evolution-max-add-rec-size", cl::Hidden, cl::desc("Max coefficients in AddRec during evolving"), cl::init(8)); static cl::opt HugeExprThreshold("scalar-evolution-huge-expr-threshold", cl::Hidden, cl::desc("Size of the expression which is considered huge"), cl::init(4096)); static cl::opt ClassifyExpressions("scalar-evolution-classify-expressions", cl::Hidden, cl::init(true), cl::desc("When printing analysis, include information on every instruction")); static cl::opt UseExpensiveRangeSharpening( "scalar-evolution-use-expensive-range-sharpening", cl::Hidden, cl::init(false), cl::desc("Use more powerful methods of sharpening expression ranges. May " "be costly in terms of compile time")); //===----------------------------------------------------------------------===// // SCEV class definitions //===----------------------------------------------------------------------===// //===----------------------------------------------------------------------===// // Implementation of the SCEV class. // #if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP) LLVM_DUMP_METHOD void SCEV::dump() const { print(dbgs()); dbgs() << '\n'; } #endif void SCEV::print(raw_ostream &OS) const { switch (getSCEVType()) { case scConstant: cast(this)->getValue()->printAsOperand(OS, false); return; case scPtrToInt: { const SCEVPtrToIntExpr *PtrToInt = cast(this); const SCEV *Op = PtrToInt->getOperand(); OS << "(ptrtoint " << *Op->getType() << " " << *Op << " to " << *PtrToInt->getType() << ")"; 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->hasNoUnsignedWrap()) OS << "nuw><"; if (AR->hasNoSignedWrap()) OS << "nsw><"; if (AR->hasNoSelfWrap() && !AR->getNoWrapFlags((NoWrapFlags)(FlagNUW | FlagNSW))) OS << "nw><"; AR->getLoop()->getHeader()->printAsOperand(OS, /*PrintType=*/false); OS << ">"; return; } case scAddExpr: case scMulExpr: case scUMaxExpr: case scSMaxExpr: case scUMinExpr: case scSMinExpr: { 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; case scUMinExpr: OpStr = " umin "; break; case scSMinExpr: OpStr = " smin "; break; default: llvm_unreachable("There are no other nary expression types."); } OS << "("; ListSeparator LS(OpStr); for (const SCEV *Op : NAry->operands()) OS << LS << *Op; OS << ")"; switch (NAry->getSCEVType()) { case scAddExpr: case scMulExpr: if (NAry->hasNoUnsignedWrap()) OS << ""; if (NAry->hasNoSignedWrap()) OS << ""; break; default: // Nothing to print for other nary expressions. break; } 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 (getSCEVType()) { case scConstant: return cast(this)->getType(); case scPtrToInt: case scTruncate: case scZeroExtend: case scSignExtend: return cast(this)->getType(); case scAddRecExpr: return cast(this)->getType(); case scMulExpr: return cast(this)->getType(); case scUMaxExpr: case scSMaxExpr: case scUMinExpr: case scSMinExpr: 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()->isMinusOne(); return false; } 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->getAPInt().isNegative(); } SCEVCouldNotCompute::SCEVCouldNotCompute() : SCEV(FoldingSetNodeIDRef(), scCouldNotCompute, 0) {} 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, SCEVTypes SCEVTy, const SCEV *op, Type *ty) : SCEV(ID, SCEVTy, computeExpressionSize(op)), Ty(ty) { Operands[0] = op; } SCEVPtrToIntExpr::SCEVPtrToIntExpr(const FoldingSetNodeIDRef ID, const SCEV *Op, Type *ITy) : SCEVCastExpr(ID, scPtrToInt, Op, ITy) { assert(getOperand()->getType()->isPointerTy() && Ty->isIntegerTy() && "Must be a non-bit-width-changing pointer-to-integer cast!"); } SCEVIntegralCastExpr::SCEVIntegralCastExpr(const FoldingSetNodeIDRef ID, SCEVTypes SCEVTy, const SCEV *op, Type *ty) : SCEVCastExpr(ID, SCEVTy, op, ty) {} SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID, const SCEV *op, Type *ty) : SCEVIntegralCastExpr(ID, scTruncate, op, ty) { assert(getOperand()->getType()->isIntOrPtrTy() && Ty->isIntOrPtrTy() && "Cannot truncate non-integer value!"); } SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID, const SCEV *op, Type *ty) : SCEVIntegralCastExpr(ID, scZeroExtend, op, ty) { assert(getOperand()->getType()->isIntOrPtrTy() && Ty->isIntOrPtrTy() && "Cannot zero extend non-integer value!"); } SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID, const SCEV *op, Type *ty) : SCEVIntegralCastExpr(ID, scSignExtend, op, ty) { assert(getOperand()->getType()->isIntOrPtrTy() && Ty->isIntOrPtrTy() && "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) { // 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)->getSourceElementType(); 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)->getSourceElementType(); 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)->getSourceElementType(); // 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 //===----------------------------------------------------------------------===// /// Compare the two values \p LV and \p RV in terms of their "complexity" where /// "complexity" is a partial (and somewhat ad-hoc) relation used to order /// operands in SCEV expressions. \p EqCache is a set of pairs of values that /// have been previously deemed to be "equally complex" by this routine. It is /// intended to avoid exponential time complexity in cases like: /// /// %a = f(%x, %y) /// %b = f(%a, %a) /// %c = f(%b, %b) /// /// %d = f(%x, %y) /// %e = f(%d, %d) /// %f = f(%e, %e) /// /// CompareValueComplexity(%f, %c) /// /// Since we do not continue running this routine on expression trees once we /// have seen unequal values, there is no need to track them in the cache. static int CompareValueComplexity(EquivalenceClasses &EqCacheValue, const LoopInfo *const LI, Value *LV, Value *RV, unsigned Depth) { if (Depth > MaxValueCompareDepth || EqCacheValue.isEquivalent(LV, RV)) return 0; // 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 auto *LA = dyn_cast(LV)) { const auto *RA = cast(RV); unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo(); return (int)LArgNo - (int)RArgNo; } if (const auto *LGV = dyn_cast(LV)) { const auto *RGV = cast(RV); const auto IsGVNameSemantic = [&](const GlobalValue *GV) { auto LT = GV->getLinkage(); return !(GlobalValue::isPrivateLinkage(LT) || GlobalValue::isInternalLinkage(LT)); }; // Use the names to distinguish the two values, but only if the // names are semantically important. if (IsGVNameSemantic(LGV) && IsGVNameSemantic(RGV)) return LGV->getName().compare(RGV->getName()); } // For instructions, compare their loop depth, and their operand count. This // is pretty loose. if (const auto *LInst = dyn_cast(LV)) { const auto *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(); if (LNumOps != RNumOps) return (int)LNumOps - (int)RNumOps; for (unsigned Idx : seq(0u, LNumOps)) { int Result = CompareValueComplexity(EqCacheValue, LI, LInst->getOperand(Idx), RInst->getOperand(Idx), Depth + 1); if (Result != 0) return Result; } } EqCacheValue.unionSets(LV, RV); return 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. // If the max analysis depth was reached, return None, assuming we do not know // if they are equivalent for sure. static Optional CompareSCEVComplexity(EquivalenceClasses &EqCacheSCEV, EquivalenceClasses &EqCacheValue, const LoopInfo *const LI, const SCEV *LHS, const SCEV *RHS, DominatorTree &DT, unsigned Depth = 0) { // 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(). SCEVTypes LType = LHS->getSCEVType(), RType = RHS->getSCEVType(); if (LType != RType) return (int)LType - (int)RType; if (EqCacheSCEV.isEquivalent(LHS, RHS)) return 0; if (Depth > MaxSCEVCompareDepth) return None; // 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 (LType) { case scUnknown: { const SCEVUnknown *LU = cast(LHS); const SCEVUnknown *RU = cast(RHS); int X = CompareValueComplexity(EqCacheValue, LI, LU->getValue(), RU->getValue(), Depth + 1); if (X == 0) EqCacheSCEV.unionSets(LHS, RHS); return X; } case scConstant: { const SCEVConstant *LC = cast(LHS); const SCEVConstant *RC = cast(RHS); // Compare constant values. const APInt &LA = LC->getAPInt(); const APInt &RA = RC->getAPInt(); 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); // There is always a dominance between two recs that are used by one SCEV, // so we can safely sort recs by loop header dominance. We require such // order in getAddExpr. const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop(); if (LLoop != RLoop) { const BasicBlock *LHead = LLoop->getHeader(), *RHead = RLoop->getHeader(); assert(LHead != RHead && "Two loops share the same header?"); if (DT.dominates(LHead, RHead)) return 1; else assert(DT.dominates(RHead, LHead) && "No dominance between recurrences used by one SCEV?"); return -1; } // 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) { auto X = CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI, LA->getOperand(i), RA->getOperand(i), DT, Depth + 1); if (X != 0) return X; } EqCacheSCEV.unionSets(LHS, RHS); return 0; } case scAddExpr: case scMulExpr: case scSMaxExpr: case scUMaxExpr: case scSMinExpr: case scUMinExpr: { 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) { auto X = CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI, LC->getOperand(i), RC->getOperand(i), DT, Depth + 1); if (X != 0) return X; } EqCacheSCEV.unionSets(LHS, RHS); return 0; } case scUDivExpr: { const SCEVUDivExpr *LC = cast(LHS); const SCEVUDivExpr *RC = cast(RHS); // Lexicographically compare udiv expressions. auto X = CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI, LC->getLHS(), RC->getLHS(), DT, Depth + 1); if (X != 0) return X; X = CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI, LC->getRHS(), RC->getRHS(), DT, Depth + 1); if (X == 0) EqCacheSCEV.unionSets(LHS, RHS); return X; } case scPtrToInt: case scTruncate: case scZeroExtend: case scSignExtend: { const SCEVCastExpr *LC = cast(LHS); const SCEVCastExpr *RC = cast(RHS); // Compare cast expressions by operand. auto X = CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI, LC->getOperand(), RC->getOperand(), DT, Depth + 1); if (X == 0) EqCacheSCEV.unionSets(LHS, RHS); return X; } case scCouldNotCompute: llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); } llvm_unreachable("Unknown SCEV kind!"); } /// 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, DominatorTree &DT) { if (Ops.size() < 2) return; // Noop EquivalenceClasses EqCacheSCEV; EquivalenceClasses EqCacheValue; // Whether LHS has provably less complexity than RHS. auto IsLessComplex = [&](const SCEV *LHS, const SCEV *RHS) { auto Complexity = CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI, LHS, RHS, DT); return Complexity && *Complexity < 0; }; 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 (IsLessComplex(RHS, LHS)) std::swap(LHS, RHS); return; } // Do the rough sort by complexity. llvm::stable_sort(Ops, [&](const SCEV *LHS, const SCEV *RHS) { return IsLessComplex(LHS, RHS); }); // 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! } } } } /// Returns true if \p Ops contains a huge SCEV (the subtree of S contains at /// least HugeExprThreshold nodes). static bool hasHugeExpression(ArrayRef Ops) { return any_of(Ops, [](const SCEV *S) { return S->getExpressionSize() >= HugeExprThreshold; }); } //===----------------------------------------------------------------------===// // Simple SCEV method implementations //===----------------------------------------------------------------------===// /// 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.lshrInPlace(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)); } /// 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 { return evaluateAtIteration(makeArrayRef(op_begin(), op_end()), It, SE); } const SCEV * SCEVAddRecExpr::evaluateAtIteration(ArrayRef Operands, const SCEV *It, ScalarEvolution &SE) { assert(Operands.size() > 0); const SCEV *Result = Operands[0]; for (unsigned i = 1, e = Operands.size(); 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, Result->getType()); if (isa(Coeff)) return Coeff; Result = SE.getAddExpr(Result, SE.getMulExpr(Operands[i], Coeff)); } return Result; } //===----------------------------------------------------------------------===// // SCEV Expression folder implementations //===----------------------------------------------------------------------===// const SCEV *ScalarEvolution::getLosslessPtrToIntExpr(const SCEV *Op, unsigned Depth) { assert(Depth <= 1 && "getLosslessPtrToIntExpr() should self-recurse at most once."); // We could be called with an integer-typed operands during SCEV rewrites. // Since the operand is an integer already, just perform zext/trunc/self cast. if (!Op->getType()->isPointerTy()) return Op; // What would be an ID for such a SCEV cast expression? FoldingSetNodeID ID; ID.AddInteger(scPtrToInt); ID.AddPointer(Op); void *IP = nullptr; // Is there already an expression for such a cast? if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; // It isn't legal for optimizations to construct new ptrtoint expressions // for non-integral pointers. if (getDataLayout().isNonIntegralPointerType(Op->getType())) return getCouldNotCompute(); Type *IntPtrTy = getDataLayout().getIntPtrType(Op->getType()); // We can only trivially model ptrtoint if SCEV's effective (integer) type // is sufficiently wide to represent all possible pointer values. // We could theoretically teach SCEV to truncate wider pointers, but // that isn't implemented for now. if (getDataLayout().getTypeSizeInBits(getEffectiveSCEVType(Op->getType())) != getDataLayout().getTypeSizeInBits(IntPtrTy)) return getCouldNotCompute(); // If not, is this expression something we can't reduce any further? if (auto *U = dyn_cast(Op)) { // Perform some basic constant folding. If the operand of the ptr2int cast // is a null pointer, don't create a ptr2int SCEV expression (that will be // left as-is), but produce a zero constant. // NOTE: We could handle a more general case, but lack motivational cases. if (isa(U->getValue())) return getZero(IntPtrTy); // 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) SCEVPtrToIntExpr(ID.Intern(SCEVAllocator), Op, IntPtrTy); UniqueSCEVs.InsertNode(S, IP); addToLoopUseLists(S); return S; } assert(Depth == 0 && "getLosslessPtrToIntExpr() should not self-recurse for " "non-SCEVUnknown's."); // Otherwise, we've got some expression that is more complex than just a // single SCEVUnknown. But we don't want to have a SCEVPtrToIntExpr of an // arbitrary expression, we want to have SCEVPtrToIntExpr of an SCEVUnknown // only, and the expressions must otherwise be integer-typed. // So sink the cast down to the SCEVUnknown's. /// The SCEVPtrToIntSinkingRewriter takes a scalar evolution expression, /// which computes a pointer-typed value, and rewrites the whole expression /// tree so that *all* the computations are done on integers, and the only /// pointer-typed operands in the expression are SCEVUnknown. class SCEVPtrToIntSinkingRewriter : public SCEVRewriteVisitor { using Base = SCEVRewriteVisitor; public: SCEVPtrToIntSinkingRewriter(ScalarEvolution &SE) : SCEVRewriteVisitor(SE) {} static const SCEV *rewrite(const SCEV *Scev, ScalarEvolution &SE) { SCEVPtrToIntSinkingRewriter Rewriter(SE); return Rewriter.visit(Scev); } const SCEV *visit(const SCEV *S) { Type *STy = S->getType(); // If the expression is not pointer-typed, just keep it as-is. if (!STy->isPointerTy()) return S; // Else, recursively sink the cast down into it. return Base::visit(S); } const SCEV *visitAddExpr(const SCEVAddExpr *Expr) { SmallVector Operands; bool Changed = false; for (auto *Op : Expr->operands()) { Operands.push_back(visit(Op)); Changed |= Op != Operands.back(); } return !Changed ? Expr : SE.getAddExpr(Operands, Expr->getNoWrapFlags()); } const SCEV *visitMulExpr(const SCEVMulExpr *Expr) { SmallVector Operands; bool Changed = false; for (auto *Op : Expr->operands()) { Operands.push_back(visit(Op)); Changed |= Op != Operands.back(); } return !Changed ? Expr : SE.getMulExpr(Operands, Expr->getNoWrapFlags()); } const SCEV *visitUnknown(const SCEVUnknown *Expr) { assert(Expr->getType()->isPointerTy() && "Should only reach pointer-typed SCEVUnknown's."); return SE.getLosslessPtrToIntExpr(Expr, /*Depth=*/1); } }; // And actually perform the cast sinking. const SCEV *IntOp = SCEVPtrToIntSinkingRewriter::rewrite(Op, *this); assert(IntOp->getType()->isIntegerTy() && "We must have succeeded in sinking the cast, " "and ending up with an integer-typed expression!"); return IntOp; } const SCEV *ScalarEvolution::getPtrToIntExpr(const SCEV *Op, Type *Ty) { assert(Ty->isIntegerTy() && "Target type must be an integer type!"); const SCEV *IntOp = getLosslessPtrToIntExpr(Op); if (isa(IntOp)) return IntOp; return getTruncateOrZeroExtend(IntOp, Ty); } const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op, Type *Ty, unsigned Depth) { assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) && "This is not a truncating conversion!"); assert(isSCEVable(Ty) && "This is not a conversion to a SCEVable type!"); assert(!Op->getType()->isPointerTy() && "Can't truncate pointer!"); 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, Depth + 1); // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing if (const SCEVSignExtendExpr *SS = dyn_cast(Op)) return getTruncateOrSignExtend(SS->getOperand(), Ty, Depth + 1); // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing if (const SCEVZeroExtendExpr *SZ = dyn_cast(Op)) return getTruncateOrZeroExtend(SZ->getOperand(), Ty, Depth + 1); if (Depth > MaxCastDepth) { SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator), Op, Ty); UniqueSCEVs.InsertNode(S, IP); addToLoopUseLists(S); return S; } // trunc(x1 + ... + xN) --> trunc(x1) + ... + trunc(xN) and // trunc(x1 * ... * xN) --> trunc(x1) * ... * trunc(xN), // if after transforming we have at most one truncate, not counting truncates // that replace other casts. if (isa(Op) || isa(Op)) { auto *CommOp = cast(Op); SmallVector Operands; unsigned numTruncs = 0; for (unsigned i = 0, e = CommOp->getNumOperands(); i != e && numTruncs < 2; ++i) { const SCEV *S = getTruncateExpr(CommOp->getOperand(i), Ty, Depth + 1); if (!isa(CommOp->getOperand(i)) && isa(S)) numTruncs++; Operands.push_back(S); } if (numTruncs < 2) { if (isa(Op)) return getAddExpr(Operands); else if (isa(Op)) return getMulExpr(Operands); else llvm_unreachable("Unexpected SCEV type for Op."); } // Although we checked in the beginning that ID is not in the cache, it is // possible that during recursion and different modification ID was inserted // into the cache. So if we find it, just return it. if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; } // If the input value is a chrec scev, truncate the chrec's operands. if (const SCEVAddRecExpr *AddRec = dyn_cast(Op)) { SmallVector Operands; for (const SCEV *Op : AddRec->operands()) Operands.push_back(getTruncateExpr(Op, Ty, Depth + 1)); return getAddRecExpr(Operands, AddRec->getLoop(), SCEV::FlagAnyWrap); } // Return zero if truncating to known zeros. uint32_t MinTrailingZeros = GetMinTrailingZeros(Op); if (MinTrailingZeros >= getTypeSizeInBits(Ty)) return getZero(Ty); // 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); addToLoopUseLists(S); 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->getSignedRangeMax(Step)); } if (SE->isKnownNegative(Step)) { *Pred = ICmpInst::ICMP_SGT; return SE->getConstant(APInt::getSignedMaxValue(BitWidth) - SE->getSignedRangeMin(Step)); } 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->getUnsignedRangeMax(Step)); } namespace { struct ExtendOpTraitsBase { typedef const SCEV *(ScalarEvolution::*GetExtendExprTy)(const SCEV *, Type *, unsigned); }; // 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; } // end anonymous namespace // 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, unsigned Depth) { 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. auto PreStartFlags = ScalarEvolution::maskFlags(SA->getNoWrapFlags(), SCEV::FlagNUW); const SCEV *PreStart = SE->getAddExpr(DiffOps, PreStartFlags); 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, Depth), (SE->*GetExtendExpr)(Step, WideTy, Depth)); if ((SE->*GetExtendExpr)(Start, WideTy, Depth) == 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. SE->setNoWrapFlags(const_cast(PreAR), 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, unsigned Depth) { auto GetExtendExpr = ExtendOpTraits::GetExtendExpr; const SCEV *PreStart = getPreStartForExtend(AR, Ty, SE, Depth); if (!PreStart) return (SE->*GetExtendExpr)(AR->getStart(), Ty, Depth); return SE->getAddExpr((SE->*GetExtendExpr)(AR->getStepRecurrence(*SE), Ty, Depth), (SE->*GetExtendExpr)(PreStart, Ty, Depth)); } // 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->getAPInt(); for (unsigned Delta : {-2, -1, 1, 2}) { const SCEV *PreStart = getConstant(StartAI - Delta); FoldingSetNodeID ID; ID.AddInteger(scAddRecExpr); ID.AddPointer(PreStart); ID.AddPointer(Step); ID.AddPointer(L); void *IP = nullptr; const auto *PreAR = static_cast(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); // Give up if we don't already have the add recurrence we need because // actually constructing an add recurrence is relatively expensive. 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; } // Finds an integer D for an expression (C + x + y + ...) such that the top // level addition in (D + (C - D + x + y + ...)) would not wrap (signed or // unsigned) and the number of trailing zeros of (C - D + x + y + ...) is // maximized, where C is the \p ConstantTerm, x, y, ... are arbitrary SCEVs, and // the (C + x + y + ...) expression is \p WholeAddExpr. static APInt extractConstantWithoutWrapping(ScalarEvolution &SE, const SCEVConstant *ConstantTerm, const SCEVAddExpr *WholeAddExpr) { const APInt &C = ConstantTerm->getAPInt(); const unsigned BitWidth = C.getBitWidth(); // Find number of trailing zeros of (x + y + ...) w/o the C first: uint32_t TZ = BitWidth; for (unsigned I = 1, E = WholeAddExpr->getNumOperands(); I < E && TZ; ++I) TZ = std::min(TZ, SE.GetMinTrailingZeros(WholeAddExpr->getOperand(I))); if (TZ) { // Set D to be as many least significant bits of C as possible while still // guaranteeing that adding D to (C - D + x + y + ...) won't cause a wrap: return TZ < BitWidth ? C.trunc(TZ).zext(BitWidth) : C; } return APInt(BitWidth, 0); } // Finds an integer D for an affine AddRec expression {C,+,x} such that the top // level addition in (D + {C-D,+,x}) would not wrap (signed or unsigned) and the // number of trailing zeros of (C - D + x * n) is maximized, where C is the \p // ConstantStart, x is an arbitrary \p Step, and n is the loop trip count. static APInt extractConstantWithoutWrapping(ScalarEvolution &SE, const APInt &ConstantStart, const SCEV *Step) { const unsigned BitWidth = ConstantStart.getBitWidth(); const uint32_t TZ = SE.GetMinTrailingZeros(Step); if (TZ) return TZ < BitWidth ? ConstantStart.trunc(TZ).zext(BitWidth) : ConstantStart; return APInt(BitWidth, 0); } const SCEV * ScalarEvolution::getZeroExtendExpr(const SCEV *Op, Type *Ty, unsigned Depth) { assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && "This is not an extending conversion!"); assert(isSCEVable(Ty) && "This is not a conversion to a SCEVable type!"); assert(!Op->getType()->isPointerTy() && "Can't extend pointer!"); 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, Depth + 1); // 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; if (Depth > MaxCastDepth) { SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator), Op, Ty); UniqueSCEVs.InsertNode(S, IP); addToLoopUseLists(S); 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, Depth); } // 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 (!AR->hasNoUnsignedWrap()) { auto NewFlags = proveNoWrapViaConstantRanges(AR); setNoWrapFlags(const_cast(AR), NewFlags); } // If we have special knowledge that this addrec won't overflow, // we don't need to do any further analysis. if (AR->hasNoUnsignedWrap()) return getAddRecExpr( getExtendAddRecStart(AR, Ty, this, Depth + 1), getZeroExtendExpr(Step, Ty, Depth + 1), 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 = getConstantMaxBackedgeTakenCount(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(), Depth); const SCEV *RecastedMaxBECount = getTruncateOrZeroExtend( CastedMaxBECount, MaxBECount->getType(), Depth); 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, SCEV::FlagAnyWrap, Depth + 1); const SCEV *ZAdd = getZeroExtendExpr(getAddExpr(Start, ZMul, SCEV::FlagAnyWrap, Depth + 1), WideTy, Depth + 1); const SCEV *WideStart = getZeroExtendExpr(Start, WideTy, Depth + 1); const SCEV *WideMaxBECount = getZeroExtendExpr(CastedMaxBECount, WideTy, Depth + 1); const SCEV *OperandExtendedAdd = getAddExpr(WideStart, getMulExpr(WideMaxBECount, getZeroExtendExpr(Step, WideTy, Depth + 1), SCEV::FlagAnyWrap, Depth + 1), SCEV::FlagAnyWrap, Depth + 1); if (ZAdd == OperandExtendedAdd) { // Cache knowledge of AR NUW, which is propagated to this AddRec. setNoWrapFlags(const_cast(AR), SCEV::FlagNUW); // Return the expression with the addrec on the outside. return getAddRecExpr( getExtendAddRecStart(AR, Ty, this, Depth + 1), getZeroExtendExpr(Step, Ty, Depth + 1), 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, Depth + 1), SCEV::FlagAnyWrap, Depth + 1), SCEV::FlagAnyWrap, Depth + 1); 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. setNoWrapFlags(const_cast(AR), SCEV::FlagNW); // Return the expression with the addrec on the outside. return getAddRecExpr( getExtendAddRecStart(AR, Ty, this, Depth + 1), getSignExtendExpr(Step, Ty, Depth + 1), L, AR->getNoWrapFlags()); } } } // Normally, in the cases we can prove no-overflow via a // backedge guarding condition, we can also compute a backedge // taken count for the loop. The exceptions are assumptions and // guards present in the loop -- SCEV is not great at exploiting // these to compute max backedge taken counts, but can still use // these to prove lack of overflow. Use this fact to avoid // doing extra work that may not pay off. if (!isa(MaxBECount) || HasGuards || !AC.assumptions().empty()) { auto NewFlags = proveNoUnsignedWrapViaInduction(AR); setNoWrapFlags(const_cast(AR), NewFlags); if (AR->hasNoUnsignedWrap()) { // Same as nuw case above - duplicated here to avoid a compile time // issue. It's not clear that the order of checks does matter, but // it's one of two issue possible causes for a change which was // reverted. Be conservative for the moment. return getAddRecExpr( getExtendAddRecStart(AR, Ty, this, Depth + 1), getZeroExtendExpr(Step, Ty, Depth + 1), L, AR->getNoWrapFlags()); } // For a negative step, we can extend the operands iff doing so only // traverses values in the range zext([0,UINT_MAX]). if (isKnownNegative(Step)) { const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) - getSignedRangeMin(Step)); if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) || isKnownOnEveryIteration(ICmpInst::ICMP_UGT, AR, N)) { // Cache knowledge of AR NW, which is propagated to this // AddRec. Negative step causes unsigned wrap, but it // still can't self-wrap. setNoWrapFlags(const_cast(AR), SCEV::FlagNW); // Return the expression with the addrec on the outside. return getAddRecExpr( getExtendAddRecStart(AR, Ty, this, Depth + 1), getSignExtendExpr(Step, Ty, Depth + 1), L, AR->getNoWrapFlags()); } } } // zext({C,+,Step}) --> (zext(D) + zext({C-D,+,Step})) // if D + (C - D + Step * n) could be proven to not unsigned wrap // where D maximizes the number of trailing zeros of (C - D + Step * n) if (const auto *SC = dyn_cast(Start)) { const APInt &C = SC->getAPInt(); const APInt &D = extractConstantWithoutWrapping(*this, C, Step); if (D != 0) { const SCEV *SZExtD = getZeroExtendExpr(getConstant(D), Ty, Depth); const SCEV *SResidual = getAddRecExpr(getConstant(C - D), Step, L, AR->getNoWrapFlags()); const SCEV *SZExtR = getZeroExtendExpr(SResidual, Ty, Depth + 1); return getAddExpr(SZExtD, SZExtR, (SCEV::NoWrapFlags)(SCEV::FlagNSW | SCEV::FlagNUW), Depth + 1); } } if (proveNoWrapByVaryingStart(Start, Step, L)) { setNoWrapFlags(const_cast(AR), SCEV::FlagNUW); return getAddRecExpr( getExtendAddRecStart(AR, Ty, this, Depth + 1), getZeroExtendExpr(Step, Ty, Depth + 1), L, AR->getNoWrapFlags()); } } // zext(A % B) --> zext(A) % zext(B) { const SCEV *LHS; const SCEV *RHS; if (matchURem(Op, LHS, RHS)) return getURemExpr(getZeroExtendExpr(LHS, Ty, Depth + 1), getZeroExtendExpr(RHS, Ty, Depth + 1)); } // zext(A / B) --> zext(A) / zext(B). if (auto *Div = dyn_cast(Op)) return getUDivExpr(getZeroExtendExpr(Div->getLHS(), Ty, Depth + 1), getZeroExtendExpr(Div->getRHS(), Ty, Depth + 1)); if (auto *SA = dyn_cast(Op)) { // zext((A + B + ...)) --> (zext(A) + zext(B) + ...) if (SA->hasNoUnsignedWrap()) { // If the addition does not unsign overflow then we can, by definition, // commute the zero extension with the addition operation. SmallVector Ops; for (const auto *Op : SA->operands()) Ops.push_back(getZeroExtendExpr(Op, Ty, Depth + 1)); return getAddExpr(Ops, SCEV::FlagNUW, Depth + 1); } // zext(C + x + y + ...) --> (zext(D) + zext((C - D) + x + y + ...)) // if D + (C - D + x + y + ...) could be proven to not unsigned wrap // where D maximizes the number of trailing zeros of (C - D + x + y + ...) // // Often address arithmetics contain expressions like // (zext (add (shl X, C1), C2)), for instance, (zext (5 + (4 * X))). // This transformation is useful while proving that such expressions are // equal or differ by a small constant amount, see LoadStoreVectorizer pass. if (const auto *SC = dyn_cast(SA->getOperand(0))) { const APInt &D = extractConstantWithoutWrapping(*this, SC, SA); if (D != 0) { const SCEV *SZExtD = getZeroExtendExpr(getConstant(D), Ty, Depth); const SCEV *SResidual = getAddExpr(getConstant(-D), SA, SCEV::FlagAnyWrap, Depth); const SCEV *SZExtR = getZeroExtendExpr(SResidual, Ty, Depth + 1); return getAddExpr(SZExtD, SZExtR, (SCEV::NoWrapFlags)(SCEV::FlagNSW | SCEV::FlagNUW), Depth + 1); } } } if (auto *SM = dyn_cast(Op)) { // zext((A * B * ...)) --> (zext(A) * zext(B) * ...) if (SM->hasNoUnsignedWrap()) { // If the multiply does not unsign overflow then we can, by definition, // commute the zero extension with the multiply operation. SmallVector Ops; for (const auto *Op : SM->operands()) Ops.push_back(getZeroExtendExpr(Op, Ty, Depth + 1)); return getMulExpr(Ops, SCEV::FlagNUW, Depth + 1); } // zext(2^K * (trunc X to iN)) to iM -> // 2^K * (zext(trunc X to i{N-K}) to iM) // // Proof: // // zext(2^K * (trunc X to iN)) to iM // = zext((trunc X to iN) << K) to iM // = zext((trunc X to i{N-K}) << K) to iM // (because shl removes the top K bits) // = zext((2^K * (trunc X to i{N-K}))) to iM // = (2^K * (zext(trunc X to i{N-K}) to iM)). // if (SM->getNumOperands() == 2) if (auto *MulLHS = dyn_cast(SM->getOperand(0))) if (MulLHS->getAPInt().isPowerOf2()) if (auto *TruncRHS = dyn_cast(SM->getOperand(1))) { int NewTruncBits = getTypeSizeInBits(TruncRHS->getType()) - MulLHS->getAPInt().logBase2(); Type *NewTruncTy = IntegerType::get(getContext(), NewTruncBits); return getMulExpr( getZeroExtendExpr(MulLHS, Ty), getZeroExtendExpr( getTruncateExpr(TruncRHS->getOperand(), NewTruncTy), Ty), SCEV::FlagNUW, Depth + 1); } } // 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); addToLoopUseLists(S); return S; } const SCEV * ScalarEvolution::getSignExtendExpr(const SCEV *Op, Type *Ty, unsigned Depth) { assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) && "This is not an extending conversion!"); assert(isSCEVable(Ty) && "This is not a conversion to a SCEVable type!"); assert(!Op->getType()->isPointerTy() && "Can't extend pointer!"); 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, Depth + 1); // sext(zext(x)) --> zext(x) if (const SCEVZeroExtendExpr *SZ = dyn_cast(Op)) return getZeroExtendExpr(SZ->getOperand(), Ty, Depth + 1); // 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; // Limit recursion depth. if (Depth > MaxCastDepth) { SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator), Op, Ty); UniqueSCEVs.InsertNode(S, IP); addToLoopUseLists(S); return S; } // 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, Depth); } if (auto *SA = dyn_cast(Op)) { // sext((A + B + ...)) --> (sext(A) + sext(B) + ...) if (SA->hasNoSignedWrap()) { // If the addition does not sign overflow then we can, by definition, // commute the sign extension with the addition operation. SmallVector Ops; for (const auto *Op : SA->operands()) Ops.push_back(getSignExtendExpr(Op, Ty, Depth + 1)); return getAddExpr(Ops, SCEV::FlagNSW, Depth + 1); } // sext(C + x + y + ...) --> (sext(D) + sext((C - D) + x + y + ...)) // if D + (C - D + x + y + ...) could be proven to not signed wrap // where D maximizes the number of trailing zeros of (C - D + x + y + ...) // // For instance, this will bring two seemingly different expressions: // 1 + sext(5 + 20 * %x + 24 * %y) and // sext(6 + 20 * %x + 24 * %y) // to the same form: // 2 + sext(4 + 20 * %x + 24 * %y) if (const auto *SC = dyn_cast(SA->getOperand(0))) { const APInt &D = extractConstantWithoutWrapping(*this, SC, SA); if (D != 0) { const SCEV *SSExtD = getSignExtendExpr(getConstant(D), Ty, Depth); const SCEV *SResidual = getAddExpr(getConstant(-D), SA, SCEV::FlagAnyWrap, Depth); const SCEV *SSExtR = getSignExtendExpr(SResidual, Ty, Depth + 1); return getAddExpr(SSExtD, SSExtR, (SCEV::NoWrapFlags)(SCEV::FlagNSW | SCEV::FlagNUW), Depth + 1); } } } // 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 (!AR->hasNoSignedWrap()) { auto NewFlags = proveNoWrapViaConstantRanges(AR); setNoWrapFlags(const_cast(AR), NewFlags); } // If we have special knowledge that this addrec won't overflow, // we don't need to do any further analysis. if (AR->hasNoSignedWrap()) return getAddRecExpr( getExtendAddRecStart(AR, Ty, this, Depth + 1), getSignExtendExpr(Step, Ty, Depth + 1), 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 = getConstantMaxBackedgeTakenCount(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(), Depth); const SCEV *RecastedMaxBECount = getTruncateOrZeroExtend( CastedMaxBECount, MaxBECount->getType(), Depth); 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, SCEV::FlagAnyWrap, Depth + 1); const SCEV *SAdd = getSignExtendExpr(getAddExpr(Start, SMul, SCEV::FlagAnyWrap, Depth + 1), WideTy, Depth + 1); const SCEV *WideStart = getSignExtendExpr(Start, WideTy, Depth + 1); const SCEV *WideMaxBECount = getZeroExtendExpr(CastedMaxBECount, WideTy, Depth + 1); const SCEV *OperandExtendedAdd = getAddExpr(WideStart, getMulExpr(WideMaxBECount, getSignExtendExpr(Step, WideTy, Depth + 1), SCEV::FlagAnyWrap, Depth + 1), SCEV::FlagAnyWrap, Depth + 1); if (SAdd == OperandExtendedAdd) { // Cache knowledge of AR NSW, which is propagated to this AddRec. setNoWrapFlags(const_cast(AR), SCEV::FlagNSW); // Return the expression with the addrec on the outside. return getAddRecExpr( getExtendAddRecStart(AR, Ty, this, Depth + 1), getSignExtendExpr(Step, Ty, Depth + 1), 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, Depth + 1), SCEV::FlagAnyWrap, Depth + 1), SCEV::FlagAnyWrap, Depth + 1); 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) setNoWrapFlags(const_cast(AR), SCEV::FlagNW); // Return the expression with the addrec on the outside. return getAddRecExpr( getExtendAddRecStart(AR, Ty, this, Depth + 1), getZeroExtendExpr(Step, Ty, Depth + 1), L, AR->getNoWrapFlags()); } } } auto NewFlags = proveNoSignedWrapViaInduction(AR); setNoWrapFlags(const_cast(AR), NewFlags); if (AR->hasNoSignedWrap()) { // Same as nsw case above - duplicated here to avoid a compile time // issue. It's not clear that the order of checks does matter, but // it's one of two issue possible causes for a change which was // reverted. Be conservative for the moment. return getAddRecExpr( getExtendAddRecStart(AR, Ty, this, Depth + 1), getSignExtendExpr(Step, Ty, Depth + 1), L, AR->getNoWrapFlags()); } // sext({C,+,Step}) --> (sext(D) + sext({C-D,+,Step})) // if D + (C - D + Step * n) could be proven to not signed wrap // where D maximizes the number of trailing zeros of (C - D + Step * n) if (const auto *SC = dyn_cast(Start)) { const APInt &C = SC->getAPInt(); const APInt &D = extractConstantWithoutWrapping(*this, C, Step); if (D != 0) { const SCEV *SSExtD = getSignExtendExpr(getConstant(D), Ty, Depth); const SCEV *SResidual = getAddRecExpr(getConstant(C - D), Step, L, AR->getNoWrapFlags()); const SCEV *SSExtR = getSignExtendExpr(SResidual, Ty, Depth + 1); return getAddExpr(SSExtD, SSExtR, (SCEV::NoWrapFlags)(SCEV::FlagNSW | SCEV::FlagNUW), Depth + 1); } } if (proveNoWrapByVaryingStart(Start, Step, L)) { setNoWrapFlags(const_cast(AR), SCEV::FlagNSW); return getAddRecExpr( getExtendAddRecStart(AR, Ty, this, Depth + 1), getSignExtendExpr(Step, Ty, Depth + 1), L, AR->getNoWrapFlags()); } } // If the input value is provably positive and we could not simplify // away the sext build a zext instead. if (isKnownNonNegative(Op)) return getZeroExtendExpr(Op, Ty, Depth + 1); // 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); addToLoopUseLists(S); 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->getAPInt().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; } /// 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->getAPInt(); } // 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))->getAPInt(); 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(drop_begin(Mul->operands())); const SCEV *Key = SE.getMulExpr(MulOps); auto Pair = M.insert({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({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; } bool ScalarEvolution::willNotOverflow(Instruction::BinaryOps BinOp, bool Signed, const SCEV *LHS, const SCEV *RHS) { const SCEV *(ScalarEvolution::*Operation)(const SCEV *, const SCEV *, SCEV::NoWrapFlags, unsigned); switch (BinOp) { default: llvm_unreachable("Unsupported binary op"); case Instruction::Add: Operation = &ScalarEvolution::getAddExpr; break; case Instruction::Sub: Operation = &ScalarEvolution::getMinusSCEV; break; case Instruction::Mul: Operation = &ScalarEvolution::getMulExpr; break; } const SCEV *(ScalarEvolution::*Extension)(const SCEV *, Type *, unsigned) = Signed ? &ScalarEvolution::getSignExtendExpr : &ScalarEvolution::getZeroExtendExpr; // Check ext(LHS op RHS) == ext(LHS) op ext(RHS) auto *NarrowTy = cast(LHS->getType()); auto *WideTy = IntegerType::get(NarrowTy->getContext(), NarrowTy->getBitWidth() * 2); const SCEV *A = (this->*Extension)( (this->*Operation)(LHS, RHS, SCEV::FlagAnyWrap, 0), WideTy, 0); const SCEV *B = (this->*Operation)((this->*Extension)(LHS, WideTy, 0), (this->*Extension)(RHS, WideTy, 0), SCEV::FlagAnyWrap, 0); return A == B; } std::pair ScalarEvolution::getStrengthenedNoWrapFlagsFromBinOp( const OverflowingBinaryOperator *OBO) { SCEV::NoWrapFlags Flags = SCEV::NoWrapFlags::FlagAnyWrap; if (OBO->hasNoUnsignedWrap()) Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW); if (OBO->hasNoSignedWrap()) Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW); bool Deduced = false; if (OBO->hasNoUnsignedWrap() && OBO->hasNoSignedWrap()) return {Flags, Deduced}; if (OBO->getOpcode() != Instruction::Add && OBO->getOpcode() != Instruction::Sub && OBO->getOpcode() != Instruction::Mul) return {Flags, Deduced}; const SCEV *LHS = getSCEV(OBO->getOperand(0)); const SCEV *RHS = getSCEV(OBO->getOperand(1)); if (!OBO->hasNoUnsignedWrap() && willNotOverflow((Instruction::BinaryOps)OBO->getOpcode(), /* Signed */ false, LHS, RHS)) { Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW); Deduced = true; } if (!OBO->hasNoSignedWrap() && willNotOverflow((Instruction::BinaryOps)OBO->getOpcode(), /* Signed */ true, LHS, RHS)) { Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW); Deduced = true; } return {Flags, Deduced}; } // 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 ArrayRef Ops, SCEV::NoWrapFlags Flags) { using namespace std::placeholders; using OBO = OverflowingBinaryOperator; 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(Flags, SignOrUnsignMask); // If FlagNSW is true and all the operands are non-negative, infer FlagNUW. auto IsKnownNonNegative = [&](const SCEV *S) { return SE->isKnownNonNegative(S); }; if (SignOrUnsignWrap == SCEV::FlagNSW && all_of(Ops, IsKnownNonNegative)) Flags = ScalarEvolution::setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask); SignOrUnsignWrap = ScalarEvolution::maskFlags(Flags, SignOrUnsignMask); if (SignOrUnsignWrap != SignOrUnsignMask && (Type == scAddExpr || Type == scMulExpr) && Ops.size() == 2 && isa(Ops[0])) { auto Opcode = [&] { switch (Type) { case scAddExpr: return Instruction::Add; case scMulExpr: return Instruction::Mul; default: llvm_unreachable("Unexpected SCEV op."); } }(); const APInt &C = cast(Ops[0])->getAPInt(); // (A C) --> (A C) if the op doesn't sign overflow. if (!(SignOrUnsignWrap & SCEV::FlagNSW)) { auto NSWRegion = ConstantRange::makeGuaranteedNoWrapRegion( Opcode, C, OBO::NoSignedWrap); if (NSWRegion.contains(SE->getSignedRange(Ops[1]))) Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW); } // (A C) --> (A C) if the op doesn't unsign overflow. if (!(SignOrUnsignWrap & SCEV::FlagNUW)) { auto NUWRegion = ConstantRange::makeGuaranteedNoWrapRegion( Opcode, C, OBO::NoUnsignedWrap); if (NUWRegion.contains(SE->getUnsignedRange(Ops[1]))) Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW); } } return Flags; } bool ScalarEvolution::isAvailableAtLoopEntry(const SCEV *S, const Loop *L) { return isLoopInvariant(S, L) && properlyDominates(S, L->getHeader()); } /// Get a canonical add expression, or something simpler if possible. const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl &Ops, SCEV::NoWrapFlags OrigFlags, unsigned Depth) { assert(!(OrigFlags & ~(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!"); unsigned NumPtrs = count_if( Ops, [](const SCEV *Op) { return Op->getType()->isPointerTy(); }); assert(NumPtrs <= 1 && "add has at most one pointer operand"); #endif // Sort by complexity, this groups all similar expression types together. GroupByComplexity(Ops, &LI, DT); // 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->getAPInt() + RHSC->getAPInt()); 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]; } // Delay expensive flag strengthening until necessary. auto ComputeFlags = [this, OrigFlags](const ArrayRef Ops) { return StrengthenNoWrapFlags(this, scAddExpr, Ops, OrigFlags); }; // Limit recursion calls depth. if (Depth > MaxArithDepth || hasHugeExpression(Ops)) return getOrCreateAddExpr(Ops, ComputeFlags(Ops)); if (SCEV *S = std::get<0>(findExistingSCEVInCache(scAddExpr, Ops))) { // Don't strengthen flags if we have no new information. SCEVAddExpr *Add = static_cast(S); if (Add->getNoWrapFlags(OrigFlags) != OrigFlags) Add->setNoWrapFlags(ComputeFlags(Ops)); return S; } // 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], SCEV::FlagAnyWrap, Depth + 1); 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, OrigFlags, Depth + 1); // 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., n*trunc(x) + m*trunc(y) --> trunc(trunc(m)*x + trunc(n)*y) // if the contents of the resulting outer trunc fold to something simple. auto FindTruncSrcType = [&]() -> Type * { // We're ultimately looking to fold an addrec of truncs and muls of only // constants and truncs, so if we find any other types of SCEV // as operands of the addrec then we bail and return nullptr here. // Otherwise, we return the type of the operand of a trunc that we find. if (auto *T = dyn_cast(Ops[Idx])) return T->getOperand()->getType(); if (const auto *Mul = dyn_cast(Ops[Idx])) { const auto *LastOp = Mul->getOperand(Mul->getNumOperands() - 1); if (const auto *T = dyn_cast(LastOp)) return T->getOperand()->getType(); } return nullptr; }; if (auto *SrcType = FindTruncSrcType()) { 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 auto *C = dyn_cast(M->getOperand(j))) { LargeMulOps.push_back(getAnyExtendExpr(C, SrcType)); } else { Ok = false; break; } } if (Ok) LargeOps.push_back(getMulExpr(LargeMulOps, SCEV::FlagAnyWrap, Depth + 1)); } else { Ok = false; break; } } if (Ok) { // Evaluate the expression in the larger type. const SCEV *Fold = getAddExpr(LargeOps, SCEV::FlagAnyWrap, Depth + 1); // If it folds to something simple, use it. Otherwise, don't. if (isa(Fold) || isa(Fold)) return getTruncateExpr(Fold, Ty); } } if (Ops.size() == 2) { // Check if we have an expression of the form ((X + C1) - C2), where C1 and // C2 can be folded in a way that allows retaining wrapping flags of (X + // C1). const SCEV *A = Ops[0]; const SCEV *B = Ops[1]; auto *AddExpr = dyn_cast(B); auto *C = dyn_cast(A); if (AddExpr && C && isa(AddExpr->getOperand(0))) { auto C1 = cast(AddExpr->getOperand(0))->getAPInt(); auto C2 = C->getAPInt(); SCEV::NoWrapFlags PreservedFlags = SCEV::FlagAnyWrap; APInt ConstAdd = C1 + C2; auto AddFlags = AddExpr->getNoWrapFlags(); // Adding a smaller constant is NUW if the original AddExpr was NUW. if (ScalarEvolution::maskFlags(AddFlags, SCEV::FlagNUW) == SCEV::FlagNUW && ConstAdd.ule(C1)) { PreservedFlags = ScalarEvolution::setFlags(PreservedFlags, SCEV::FlagNUW); } // Adding a constant with the same sign and small magnitude is NSW, if the // original AddExpr was NSW. if (ScalarEvolution::maskFlags(AddFlags, SCEV::FlagNSW) == SCEV::FlagNSW && C1.isSignBitSet() == ConstAdd.isSignBitSet() && ConstAdd.abs().ule(C1.abs())) { PreservedFlags = ScalarEvolution::setFlags(PreservedFlags, SCEV::FlagNSW); } if (PreservedFlags != SCEV::FlagAnyWrap) { SmallVector NewOps(AddExpr->op_begin(), AddExpr->op_end()); NewOps[0] = getConstant(ConstAdd); return getAddExpr(NewOps, PreservedFlags); } } } // 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; // If the original flags and all inlined SCEVAddExprs are NUW, use the // common NUW flag for expression after inlining. Other flags cannot be // preserved, because they may depend on the original order of operations. SCEV::NoWrapFlags CommonFlags = maskFlags(OrigFlags, SCEV::FlagNUW); while (const SCEVAddExpr *Add = dyn_cast(Ops[Idx])) { if (Ops.size() > AddOpsInlineThreshold || Add->getNumOperands() > AddOpsInlineThreshold) break; // 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; CommonFlags = maskFlags(CommonFlags, Add->getNoWrapFlags()); } // 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, CommonFlags, Depth + 1); } // 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)) { struct APIntCompare { bool operator()(const APInt &LHS, const APInt &RHS) const { return LHS.ult(RHS); } }; // 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 (const SCEV *NewOp : NewOps) MulOpLists[M.find(NewOp)->second].push_back(NewOp); // Re-generate the operands list. Ops.clear(); if (AccumulatedConstant != 0) Ops.push_back(getConstant(AccumulatedConstant)); for (auto &MulOp : MulOpLists) { if (MulOp.first == 1) { Ops.push_back(getAddExpr(MulOp.second, SCEV::FlagAnyWrap, Depth + 1)); } else if (MulOp.first != 0) { Ops.push_back(getMulExpr( getConstant(MulOp.first), getAddExpr(MulOp.second, SCEV::FlagAnyWrap, Depth + 1), SCEV::FlagAnyWrap, Depth + 1)); } } if (Ops.empty()) return getZero(Ty); if (Ops.size() == 1) return Ops[0]; return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1); } } // 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, SCEV::FlagAnyWrap, Depth + 1); } SmallVector TwoOps = {getOne(Ty), InnerMul}; const SCEV *AddOne = getAddExpr(TwoOps, SCEV::FlagAnyWrap, Depth + 1); const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV, SCEV::FlagAnyWrap, Depth + 1); 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, SCEV::FlagAnyWrap, Depth + 1); } // 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, SCEV::FlagAnyWrap, Depth + 1); } 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, SCEV::FlagAnyWrap, Depth + 1); } SmallVector TwoOps = {InnerMul1, InnerMul2}; const SCEV *InnerMulSum = getAddExpr(TwoOps, SCEV::FlagAnyWrap, Depth + 1); const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum, SCEV::FlagAnyWrap, Depth + 1); if (Ops.size() == 2) return OuterMul; Ops.erase(Ops.begin()+Idx); Ops.erase(Ops.begin()+OtherMulIdx-1); Ops.push_back(OuterMul); return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1); } } } } // 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 (isAvailableAtLoopEntry(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()) { // Compute nowrap flags for the addition of the loop-invariant ops and // the addrec. Temporarily push it as an operand for that purpose. LIOps.push_back(AddRec); SCEV::NoWrapFlags Flags = ComputeFlags(LIOps); LIOps.pop_back(); // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step} LIOps.push_back(AddRec->getStart()); SmallVector AddRecOps(AddRec->operands()); // This follows from the fact that the no-wrap flags on the outer add // expression are applicable on the 0th iteration, when the add recurrence // will be equal to its start value. AddRecOps[0] = getAddExpr(LIOps, Flags, Depth + 1); // 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, SCEV::FlagAnyWrap, Depth + 1); } // 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) { // We expect the AddRecExpr's to be sorted in reverse dominance order, // so that the 1st found AddRecExpr is dominated by all others. assert(DT.dominates( cast(Ops[OtherIdx])->getLoop()->getHeader(), AddRec->getLoop()->getHeader()) && "AddRecExprs are not sorted in reverse dominance order?"); if (AddRecLoop == cast(Ops[OtherIdx])->getLoop()) { // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D} SmallVector AddRecOps(AddRec->operands()); for (; OtherIdx != Ops.size() && isa(Ops[OtherIdx]); ++OtherIdx) { const auto *OtherAddRec = 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; } SmallVector TwoOps = { AddRecOps[i], OtherAddRec->getOperand(i)}; AddRecOps[i] = getAddExpr(TwoOps, SCEV::FlagAnyWrap, Depth + 1); } 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, SCEV::FlagAnyWrap, Depth + 1); } } // 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. return getOrCreateAddExpr(Ops, ComputeFlags(Ops)); } const SCEV * ScalarEvolution::getOrCreateAddExpr(ArrayRef Ops, SCEV::NoWrapFlags Flags) { FoldingSetNodeID ID; ID.AddInteger(scAddExpr); for (const SCEV *Op : Ops) ID.AddPointer(Op); 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); addToLoopUseLists(S); } S->setNoWrapFlags(Flags); return S; } const SCEV * ScalarEvolution::getOrCreateAddRecExpr(ArrayRef Ops, const Loop *L, SCEV::NoWrapFlags Flags) { FoldingSetNodeID ID; ID.AddInteger(scAddRecExpr); for (unsigned i = 0, e = Ops.size(); i != e; ++i) ID.AddPointer(Ops[i]); ID.AddPointer(L); void *IP = nullptr; SCEVAddRecExpr *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) SCEVAddRecExpr(ID.Intern(SCEVAllocator), O, Ops.size(), L); UniqueSCEVs.InsertNode(S, IP); addToLoopUseLists(S); } setNoWrapFlags(S, Flags); return S; } const SCEV * ScalarEvolution::getOrCreateMulExpr(ArrayRef Ops, SCEV::NoWrapFlags Flags) { 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); addToLoopUseLists(S); } 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 containsConstantInAddMulChain(const SCEV *StartExpr) { struct FindConstantInAddMulChain { bool FoundConstant = false; bool follow(const SCEV *S) { FoundConstant |= isa(S); return isa(S) || isa(S); } bool isDone() const { return FoundConstant; } }; FindConstantInAddMulChain F; SCEVTraversal ST(F); ST.visitAll(StartExpr); return F.FoundConstant; } /// Get a canonical multiply expression, or something simpler if possible. const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl &Ops, SCEV::NoWrapFlags OrigFlags, unsigned Depth) { assert(OrigFlags == maskFlags(OrigFlags, 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 = Ops[0]->getType(); assert(!ETy->isPointerTy()); for (unsigned i = 1, e = Ops.size(); i != e; ++i) assert(Ops[i]->getType() == ETy && "SCEVMulExpr operand types don't match!"); #endif // Sort by complexity, this groups all similar expression types together. GroupByComplexity(Ops, &LI, DT); // 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->getAPInt() * RHSC->getAPInt()); if (Ops.size() == 2) return Ops[0]; Ops.erase(Ops.begin()+1); // Erase the folded element LHSC = cast(Ops[0]); } // If we have a multiply of zero, it will always be zero. if (LHSC->getValue()->isZero()) return LHSC; // If we are left with a constant one being multiplied, strip it off. if (LHSC->getValue()->isOne()) { Ops.erase(Ops.begin()); --Idx; } if (Ops.size() == 1) return Ops[0]; } // Delay expensive flag strengthening until necessary. auto ComputeFlags = [this, OrigFlags](const ArrayRef Ops) { return StrengthenNoWrapFlags(this, scMulExpr, Ops, OrigFlags); }; // Limit recursion calls depth. if (Depth > MaxArithDepth || hasHugeExpression(Ops)) return getOrCreateMulExpr(Ops, ComputeFlags(Ops)); if (SCEV *S = std::get<0>(findExistingSCEVInCache(scMulExpr, Ops))) { // Don't strengthen flags if we have no new information. SCEVMulExpr *Mul = static_cast(S); if (Mul->getNoWrapFlags(OrigFlags) != OrigFlags) Mul->setNoWrapFlags(ComputeFlags(Ops)); return S; } if (const SCEVConstant *LHSC = dyn_cast(Ops[0])) { if (Ops.size() == 2) { // C1*(C2+V) -> C1*C2 + C1*V 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. // // TODO: There are some cases where this transformation is not // profitable; for example, Add = (C0 + X) * Y + Z. Maybe the scope of // this transformation should be narrowed down. if (Add->getNumOperands() == 2 && containsConstantInAddMulChain(Add)) return getAddExpr(getMulExpr(LHSC, Add->getOperand(0), SCEV::FlagAnyWrap, Depth + 1), getMulExpr(LHSC, Add->getOperand(1), SCEV::FlagAnyWrap, Depth + 1), SCEV::FlagAnyWrap, Depth + 1); if (Ops[0]->isAllOnesValue()) { // If we have a mul by -1 of an add, try distributing the -1 among the // add operands. if (const SCEVAddExpr *Add = dyn_cast(Ops[1])) { SmallVector NewOps; bool AnyFolded = false; for (const SCEV *AddOp : Add->operands()) { const SCEV *Mul = getMulExpr(Ops[0], AddOp, SCEV::FlagAnyWrap, Depth + 1); if (!isa(Mul)) AnyFolded = true; NewOps.push_back(Mul); } if (AnyFolded) return getAddExpr(NewOps, SCEV::FlagAnyWrap, Depth + 1); } else if (const auto *AddRec = dyn_cast(Ops[1])) { // Negation preserves a recurrence's no self-wrap property. SmallVector Operands; for (const SCEV *AddRecOp : AddRec->operands()) Operands.push_back(getMulExpr(Ops[0], AddRecOp, SCEV::FlagAnyWrap, Depth + 1)); return getAddRecExpr(Operands, AddRec->getLoop(), AddRec->getNoWrapFlags(SCEV::FlagNW)); } } } } // 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 (Ops.size() > MulOpsInlineThreshold) break; // 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, SCEV::FlagAnyWrap, Depth + 1); } // 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 (isAvailableAtLoopEntry(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, SCEV::FlagAnyWrap, Depth + 1); for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i), SCEV::FlagAnyWrap, Depth + 1)); // 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. SCEV::NoWrapFlags Flags = ComputeFlags({Scale, AddRec}); const SCEV *NewRec = getAddRecExpr( NewOps, AddRecLoop, AddRec->getNoWrapFlags(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, SCEV::FlagAnyWrap, Depth + 1); } // 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; // Limit max number of arguments to avoid creation of unreasonably big // SCEVAddRecs with very complex operands. if (AddRec->getNumOperands() + OtherAddRec->getNumOperands() - 1 > MaxAddRecSize || hasHugeExpression({AddRec, OtherAddRec})) 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) { SmallVector SumOps; 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); SumOps.push_back(getMulExpr(CoeffTerm, Term1, Term2, SCEV::FlagAnyWrap, Depth + 1)); } } if (SumOps.empty()) SumOps.push_back(getZero(Ty)); AddRecOps.push_back(getAddExpr(SumOps, SCEV::FlagAnyWrap, Depth + 1)); } if (!Overflow) { const SCEV *NewAddRec = getAddRecExpr(AddRecOps, AddRecLoop, 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, SCEV::FlagAnyWrap, Depth + 1); // 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. return getOrCreateMulExpr(Ops, ComputeFlags(Ops)); } /// Represents an unsigned remainder expression based on unsigned division. const SCEV *ScalarEvolution::getURemExpr(const SCEV *LHS, const SCEV *RHS) { assert(getEffectiveSCEVType(LHS->getType()) == getEffectiveSCEVType(RHS->getType()) && "SCEVURemExpr operand types don't match!"); // Short-circuit easy cases if (const SCEVConstant *RHSC = dyn_cast(RHS)) { // If constant is one, the result is trivial if (RHSC->getValue()->isOne()) return getZero(LHS->getType()); // X urem 1 --> 0 // If constant is a power of two, fold into a zext(trunc(LHS)). if (RHSC->getAPInt().isPowerOf2()) { Type *FullTy = LHS->getType(); Type *TruncTy = IntegerType::get(getContext(), RHSC->getAPInt().logBase2()); return getZeroExtendExpr(getTruncateExpr(LHS, TruncTy), FullTy); } } // Fallback to %a == %x urem %y == %x - ((%x udiv %y) * %y) const SCEV *UDiv = getUDivExpr(LHS, RHS); const SCEV *Mult = getMulExpr(UDiv, RHS, SCEV::FlagNUW); return getMinusSCEV(LHS, Mult, SCEV::FlagNUW); } /// Get a canonical unsigned division expression, or something simpler if /// possible. const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS, const SCEV *RHS) { assert(!LHS->getType()->isPointerTy() && "SCEVUDivExpr operand can't be pointer!"); assert(LHS->getType() == RHS->getType() && "SCEVUDivExpr operand types don't match!"); FoldingSetNodeID ID; ID.AddInteger(scUDivExpr); ID.AddPointer(LHS); ID.AddPointer(RHS); void *IP = nullptr; if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; // 0 udiv Y == 0 if (const SCEVConstant *LHSC = dyn_cast(LHS)) if (LHSC->getValue()->isZero()) return LHS; if (const SCEVConstant *RHSC = dyn_cast(RHS)) { if (RHSC->getValue()->isOne()) 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->getAPInt().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->getAPInt().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->getAPInt(); const APInt &DivInt = RHSC->getAPInt(); if (!StepInt.urem(DivInt) && getZeroExtendExpr(AR, ExtTy) == getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy), getZeroExtendExpr(Step, ExtTy), AR->getLoop(), SCEV::FlagAnyWrap)) { SmallVector Operands; for (const SCEV *Op : AR->operands()) Operands.push_back(getUDivExpr(Op, 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->getAPInt(); const APInt &StartRem = StartInt.urem(StepInt); if (StartRem != 0) { const SCEV *NewLHS = getAddRecExpr(getConstant(StartInt - StartRem), Step, AR->getLoop(), SCEV::FlagNW); if (LHS != NewLHS) { LHS = NewLHS; // Reset the ID to include the new LHS, and check if it is // already cached. ID.clear(); ID.AddInteger(scUDivExpr); ID.AddPointer(LHS); ID.AddPointer(RHS); IP = nullptr; if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S; } } } } // (A*B)/C --> A*(B/C) if safe and B/C can be folded. if (const SCEVMulExpr *M = dyn_cast(LHS)) { SmallVector Operands; for (const SCEV *Op : M->operands()) Operands.push_back(getZeroExtendExpr(Op, 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->operands()); Operands[i] = Div; return getMulExpr(Operands); } } } // (A/B)/C --> A/(B*C) if safe and B*C can be folded. if (const SCEVUDivExpr *OtherDiv = dyn_cast(LHS)) { if (auto *DivisorConstant = dyn_cast(OtherDiv->getRHS())) { bool Overflow = false; APInt NewRHS = DivisorConstant->getAPInt().umul_ov(RHSC->getAPInt(), Overflow); if (Overflow) { return getConstant(RHSC->getType(), 0, false); } return getUDivExpr(OtherDiv->getLHS(), getConstant(NewRHS)); } } // (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 (const SCEV *Op : A->operands()) Operands.push_back(getZeroExtendExpr(Op, 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))); } } } // The Insertion Point (IP) might be invalid by now (due to UniqueSCEVs // changes). Make sure we get a new one. 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); addToLoopUseLists(S); return S; } static const APInt gcd(const SCEVConstant *C1, const SCEVConstant *C2) { APInt A = C1->getAPInt().abs(); APInt B = C2->getAPInt().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(std::move(A), std::move(B)); } /// 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 || !Mul->hasNoUnsignedWrap()) 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 auto *LHSCst = dyn_cast(Mul->getOperand(0))) { if (LHSCst == RHSCst) { SmallVector Operands(drop_begin(Mul->operands())); 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->getAPInt().udiv(Factor))); RHSCst = cast(getConstant(RHSCst->getAPInt().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); } /// 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); } /// 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!"); assert(!Operands[i]->getType()->isPointerTy() && "Step must be integer"); } 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 getConstantMaxBackedgeTakenCount 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->operands()); 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 = all_of( Operands, [&](const SCEV *Op) { return isLoopInvariant(Op, L); }); 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 = all_of(NestedOperands, [&](const SCEV *Op) { return isLoopInvariant(Op, NestedLoop); }); 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. return getOrCreateAddRecExpr(Operands, L, Flags); } const SCEV * ScalarEvolution::getGEPExpr(GEPOperator *GEP, const SmallVectorImpl &IndexExprs) { const SCEV *BaseExpr = getSCEV(GEP->getPointerOperand()); // getSCEV(Base)->getType() has the same address space as Base->getType() // because SCEV::getType() preserves the address space. Type *IntIdxTy = getEffectiveSCEVType(BaseExpr->getType()); // FIXME(PR23527): Don't blindly transfer the inbounds flag from the GEP // instruction to its SCEV, because the Instruction may be guarded by control // flow and the no-overflow bits may not be valid for the expression in any // context. This can be fixed similarly to how these flags are handled for // adds. SCEV::NoWrapFlags OffsetWrap = GEP->isInBounds() ? SCEV::FlagNSW : SCEV::FlagAnyWrap; Type *CurTy = GEP->getType(); bool FirstIter = true; SmallVector Offsets; for (const SCEV *IndexExpr : IndexExprs) { // Compute the (potentially symbolic) offset in bytes for this index. if (StructType *STy = dyn_cast(CurTy)) { // For a struct, add the member offset. ConstantInt *Index = cast(IndexExpr)->getValue(); unsigned FieldNo = Index->getZExtValue(); const SCEV *FieldOffset = getOffsetOfExpr(IntIdxTy, STy, FieldNo); Offsets.push_back(FieldOffset); // Update CurTy to the type of the field at Index. CurTy = STy->getTypeAtIndex(Index); } else { // Update CurTy to its element type. if (FirstIter) { assert(isa(CurTy) && "The first index of a GEP indexes a pointer"); CurTy = GEP->getSourceElementType(); FirstIter = false; } else { CurTy = GetElementPtrInst::getTypeAtIndex(CurTy, (uint64_t)0); } // For an array, add the element offset, explicitly scaled. const SCEV *ElementSize = getSizeOfExpr(IntIdxTy, CurTy); // Getelementptr indices are signed. IndexExpr = getTruncateOrSignExtend(IndexExpr, IntIdxTy); // Multiply the index by the element size to compute the element offset. const SCEV *LocalOffset = getMulExpr(IndexExpr, ElementSize, OffsetWrap); Offsets.push_back(LocalOffset); } } // Handle degenerate case of GEP without offsets. if (Offsets.empty()) return BaseExpr; // Add the offsets together, assuming nsw if inbounds. const SCEV *Offset = getAddExpr(Offsets, OffsetWrap); // Add the base address and the offset. We cannot use the nsw flag, as the // base address is unsigned. However, if we know that the offset is // non-negative, we can use nuw. SCEV::NoWrapFlags BaseWrap = GEP->isInBounds() && isKnownNonNegative(Offset) ? SCEV::FlagNUW : SCEV::FlagAnyWrap; return getAddExpr(BaseExpr, Offset, BaseWrap); } std::tuple ScalarEvolution::findExistingSCEVInCache(SCEVTypes SCEVType, ArrayRef Ops) { FoldingSetNodeID ID; void *IP = nullptr; ID.AddInteger(SCEVType); for (unsigned i = 0, e = Ops.size(); i != e; ++i) ID.AddPointer(Ops[i]); return std::tuple( UniqueSCEVs.FindNodeOrInsertPos(ID, IP), std::move(ID), IP); } const SCEV *ScalarEvolution::getAbsExpr(const SCEV *Op, bool IsNSW) { SCEV::NoWrapFlags Flags = IsNSW ? SCEV::FlagNSW : SCEV::FlagAnyWrap; return getSMaxExpr(Op, getNegativeSCEV(Op, Flags)); } const SCEV *ScalarEvolution::getMinMaxExpr(SCEVTypes Kind, SmallVectorImpl &Ops) { assert(!Ops.empty() && "Cannot get empty (u|s)(min|max)!"); 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 && "Operand types don't match!"); assert(Ops[0]->getType()->isPointerTy() == Ops[i]->getType()->isPointerTy() && "min/max should be consistently pointerish"); } #endif bool IsSigned = Kind == scSMaxExpr || Kind == scSMinExpr; bool IsMax = Kind == scSMaxExpr || Kind == scUMaxExpr; // Sort by complexity, this groups all similar expression types together. GroupByComplexity(Ops, &LI, DT); // Check if we have created the same expression before. if (const SCEV *S = std::get<0>(findExistingSCEVInCache(Kind, Ops))) { return S; } // If there are any constants, fold them together. unsigned Idx = 0; if (const SCEVConstant *LHSC = dyn_cast(Ops[0])) { ++Idx; assert(Idx < Ops.size()); auto FoldOp = [&](const APInt &LHS, const APInt &RHS) { if (Kind == scSMaxExpr) return APIntOps::smax(LHS, RHS); else if (Kind == scSMinExpr) return APIntOps::smin(LHS, RHS); else if (Kind == scUMaxExpr) return APIntOps::umax(LHS, RHS); else if (Kind == scUMinExpr) return APIntOps::umin(LHS, RHS); llvm_unreachable("Unknown SCEV min/max opcode"); }; while (const SCEVConstant *RHSC = dyn_cast(Ops[Idx])) { // We found two constants, fold them together! ConstantInt *Fold = ConstantInt::get( getContext(), FoldOp(LHSC->getAPInt(), RHSC->getAPInt())); Ops[0] = getConstant(Fold); Ops.erase(Ops.begin()+1); // Erase the folded element if (Ops.size() == 1) return Ops[0]; LHSC = cast(Ops[0]); } bool IsMinV = LHSC->getValue()->isMinValue(IsSigned); bool IsMaxV = LHSC->getValue()->isMaxValue(IsSigned); if (IsMax ? IsMinV : IsMaxV) { // If we are left with a constant minimum(/maximum)-int, strip it off. Ops.erase(Ops.begin()); --Idx; } else if (IsMax ? IsMaxV : IsMinV) { // If we have a max(/min) with a constant maximum(/minimum)-int, // it will always be the extremum. return LHSC; } if (Ops.size() == 1) return Ops[0]; } // Find the first operation of the same kind while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < Kind) ++Idx; // Check to see if one of the operands is of the same kind. If so, expand its // operands onto our operand list, and recurse to simplify. if (Idx < Ops.size()) { bool DeletedAny = false; while (Ops[Idx]->getSCEVType() == Kind) { const SCEVMinMaxExpr *SMME = cast(Ops[Idx]); Ops.erase(Ops.begin()+Idx); Ops.append(SMME->op_begin(), SMME->op_end()); DeletedAny = true; } if (DeletedAny) return getMinMaxExpr(Kind, 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. llvm::CmpInst::Predicate GEPred = IsSigned ? ICmpInst::ICMP_SGE : ICmpInst::ICMP_UGE; llvm::CmpInst::Predicate LEPred = IsSigned ? ICmpInst::ICMP_SLE : ICmpInst::ICMP_ULE; llvm::CmpInst::Predicate FirstPred = IsMax ? GEPred : LEPred; llvm::CmpInst::Predicate SecondPred = IsMax ? LEPred : GEPred; for (unsigned i = 0, e = Ops.size() - 1; i != e; ++i) { if (Ops[i] == Ops[i + 1] || isKnownViaNonRecursiveReasoning(FirstPred, Ops[i], Ops[i + 1])) { // X op Y op Y --> X op Y // X op Y --> X, if we know X, Y are ordered appropriately Ops.erase(Ops.begin() + i + 1, Ops.begin() + i + 2); --i; --e; } else if (isKnownViaNonRecursiveReasoning(SecondPred, Ops[i], Ops[i + 1])) { // X op Y --> Y, if we know X, Y are ordered appropriately 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 expr. Check to see if we // already have one, otherwise create a new one. const SCEV *ExistingSCEV; FoldingSetNodeID ID; void *IP; std::tie(ExistingSCEV, ID, IP) = findExistingSCEVInCache(Kind, Ops); if (ExistingSCEV) return ExistingSCEV; const SCEV **O = SCEVAllocator.Allocate(Ops.size()); std::uninitialized_copy(Ops.begin(), Ops.end(), O); SCEV *S = new (SCEVAllocator) SCEVMinMaxExpr(ID.Intern(SCEVAllocator), Kind, O, Ops.size()); UniqueSCEVs.InsertNode(S, IP); addToLoopUseLists(S); return S; } const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS, const SCEV *RHS) { SmallVector Ops = {LHS, RHS}; return getSMaxExpr(Ops); } const SCEV *ScalarEvolution::getSMaxExpr(SmallVectorImpl &Ops) { return getMinMaxExpr(scSMaxExpr, Ops); } const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS, const SCEV *RHS) { SmallVector Ops = {LHS, RHS}; return getUMaxExpr(Ops); } const SCEV *ScalarEvolution::getUMaxExpr(SmallVectorImpl &Ops) { return getMinMaxExpr(scUMaxExpr, Ops); } const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS, const SCEV *RHS) { SmallVector Ops = { LHS, RHS }; return getSMinExpr(Ops); } const SCEV *ScalarEvolution::getSMinExpr(SmallVectorImpl &Ops) { return getMinMaxExpr(scSMinExpr, Ops); } const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS, const SCEV *RHS) { SmallVector Ops = { LHS, RHS }; return getUMinExpr(Ops); } const SCEV *ScalarEvolution::getUMinExpr(SmallVectorImpl &Ops) { return getMinMaxExpr(scUMinExpr, Ops); } const SCEV * ScalarEvolution::getSizeOfScalableVectorExpr(Type *IntTy, ScalableVectorType *ScalableTy) { Constant *NullPtr = Constant::getNullValue(ScalableTy->getPointerTo()); Constant *One = ConstantInt::get(IntTy, 1); Constant *GEP = ConstantExpr::getGetElementPtr(ScalableTy, NullPtr, One); // Note that the expression we created is the final expression, we don't // want to simplify it any further Also, if we call a normal getSCEV(), // we'll end up in an endless recursion. So just create an SCEVUnknown. return getUnknown(ConstantExpr::getPtrToInt(GEP, IntTy)); } const SCEV *ScalarEvolution::getSizeOfExpr(Type *IntTy, Type *AllocTy) { if (auto *ScalableAllocTy = dyn_cast(AllocTy)) return getSizeOfScalableVectorExpr(IntTy, ScalableAllocTy); // We can bypass creating a target-independent constant expression and then // folding it back into a ConstantInt. This is just a compile-time // optimization. return getConstant(IntTy, getDataLayout().getTypeAllocSize(AllocTy)); } const SCEV *ScalarEvolution::getStoreSizeOfExpr(Type *IntTy, Type *StoreTy) { if (auto *ScalableStoreTy = dyn_cast(StoreTy)) return getSizeOfScalableVectorExpr(IntTy, ScalableStoreTy); // We can bypass creating a target-independent constant expression and then // folding it back into a ConstantInt. This is just a compile-time // optimization. return getConstant(IntTy, getDataLayout().getTypeStoreSize(StoreTy)); } const SCEV *ScalarEvolution::getOffsetOfExpr(Type *IntTy, StructType *STy, unsigned FieldNo) { // We can bypass creating a target-independent constant expression and then // folding it back into a ConstantInt. This is just a compile-time // optimization. return getConstant( IntTy, getDataLayout().getStructLayout(STy)->getElementOffset(FieldNo)); } 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 // /// 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->isIntOrPtrTy(); } /// 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 (Ty->isPointerTy()) return getDataLayout().getIndexTypeSizeInBits(Ty); return getDataLayout().getTypeSizeInBits(Ty); } /// 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 index 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!"); return getDataLayout().getIndexType(Ty); } Type *ScalarEvolution::getWiderType(Type *T1, Type *T2) const { return getTypeSizeInBits(T1) >= getTypeSizeInBits(T2) ? T1 : T2; } const SCEV *ScalarEvolution::getCouldNotCompute() { return CouldNotCompute.get(); } bool ScalarEvolution::checkValidity(const SCEV *S) const { bool ContainsNulls = SCEVExprContains(S, [](const SCEV *S) { auto *SU = dyn_cast(S); return SU && SU->getValue() == nullptr; }); return !ContainsNulls; } bool ScalarEvolution::containsAddRecurrence(const SCEV *S) { HasRecMapType::iterator I = HasRecMap.find(S); if (I != HasRecMap.end()) return I->second; bool FoundAddRec = SCEVExprContains(S, [](const SCEV *S) { return isa(S); }); HasRecMap.insert({S, FoundAddRec}); return FoundAddRec; } /// Try to split a SCEVAddExpr into a pair of {SCEV, ConstantInt}. /// If \p S is a SCEVAddExpr and is composed of a sub SCEV S' and an /// offset I, then return {S', I}, else return {\p S, nullptr}. static std::pair splitAddExpr(const SCEV *S) { const auto *Add = dyn_cast(S); if (!Add) return {S, nullptr}; if (Add->getNumOperands() != 2) return {S, nullptr}; auto *ConstOp = dyn_cast(Add->getOperand(0)); if (!ConstOp) return {S, nullptr}; return {Add->getOperand(1), ConstOp->getValue()}; } /// Return the ValueOffsetPair set for \p S. \p S can be represented /// by the value and offset from any ValueOffsetPair in the set. ScalarEvolution::ValueOffsetPairSetVector * ScalarEvolution::getSCEVValues(const SCEV *S) { ExprValueMapType::iterator SI = ExprValueMap.find_as(S); if (SI == ExprValueMap.end()) return nullptr; #ifndef NDEBUG if (VerifySCEVMap) { // Check there is no dangling Value in the set returned. for (const auto &VE : SI->second) assert(ValueExprMap.count(VE.first)); } #endif return &SI->second; } /// Erase Value from ValueExprMap and ExprValueMap. ValueExprMap.erase(V) /// cannot be used separately. eraseValueFromMap should be used to remove /// V from ValueExprMap and ExprValueMap at the same time. void ScalarEvolution::eraseValueFromMap(Value *V) { ValueExprMapType::iterator I = ValueExprMap.find_as(V); if (I != ValueExprMap.end()) { const SCEV *S = I->second; // Remove {V, 0} from the set of ExprValueMap[S] if (auto *SV = getSCEVValues(S)) SV->remove({V, nullptr}); // Remove {V, Offset} from the set of ExprValueMap[Stripped] const SCEV *Stripped; ConstantInt *Offset; std::tie(Stripped, Offset) = splitAddExpr(S); if (Offset != nullptr) { if (auto *SV = getSCEVValues(Stripped)) SV->remove({V, Offset}); } ValueExprMap.erase(V); } } /// Check whether value has nuw/nsw/exact set but SCEV does not. /// TODO: In reality it is better to check the poison recursively /// but this is better than nothing. static bool SCEVLostPoisonFlags(const SCEV *S, const Value *V) { if (auto *I = dyn_cast(V)) { if (isa(I)) { if (auto *NS = dyn_cast(S)) { if (I->hasNoSignedWrap() && !NS->hasNoSignedWrap()) return true; if (I->hasNoUnsignedWrap() && !NS->hasNoUnsignedWrap()) return true; } } else if (isa(I) && I->isExact()) return true; } return false; } /// 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!"); const SCEV *S = getExistingSCEV(V); if (S == nullptr) { S = createSCEV(V); // During PHI resolution, it is possible to create two SCEVs for the same // V, so it is needed to double check whether V->S is inserted into // ValueExprMap before insert S->{V, 0} into ExprValueMap. std::pair Pair = ValueExprMap.insert({SCEVCallbackVH(V, this), S}); if (Pair.second && !SCEVLostPoisonFlags(S, V)) { ExprValueMap[S].insert({V, nullptr}); // If S == Stripped + Offset, add Stripped -> {V, Offset} into // ExprValueMap. const SCEV *Stripped = S; ConstantInt *Offset = nullptr; std::tie(Stripped, Offset) = splitAddExpr(S); // If stripped is SCEVUnknown, don't bother to save // Stripped -> {V, offset}. It doesn't simplify and sometimes even // increase the complexity of the expansion code. // If V is GetElementPtrInst, don't save Stripped -> {V, offset} // because it may generate add/sub instead of GEP in SCEV expansion. if (Offset != nullptr && !isa(Stripped) && !isa(V)) ExprValueMap[Stripped].insert({V, Offset}); } } return S; } const SCEV *ScalarEvolution::getExistingSCEV(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; eraseValueFromMap(V); forgetMemoizedResults(S); } return nullptr; } /// Return a SCEV corresponding to -V = -1*V const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V, SCEV::NoWrapFlags Flags) { if (const SCEVConstant *VC = dyn_cast(V)) return getConstant( cast(ConstantExpr::getNeg(VC->getValue()))); Type *Ty = V->getType(); Ty = getEffectiveSCEVType(Ty); return getMulExpr(V, getMinusOne(Ty), Flags); } /// 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 || !Add->getOperand(0)->isAllOnesValue()) return nullptr; const SCEVMulExpr *AddRHS = dyn_cast(Add->getOperand(1)); if (!AddRHS || AddRHS->getNumOperands() != 2 || !AddRHS->getOperand(0)->isAllOnesValue()) return nullptr; return AddRHS->getOperand(1); } /// 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()))); // Fold ~(u|s)(min|max)(~x, ~y) to (u|s)(max|min)(x, y) if (const SCEVMinMaxExpr *MME = dyn_cast(V)) { auto MatchMinMaxNegation = [&](const SCEVMinMaxExpr *MME) { SmallVector MatchedOperands; for (const SCEV *Operand : MME->operands()) { const SCEV *Matched = MatchNotExpr(Operand); if (!Matched) return (const SCEV *)nullptr; MatchedOperands.push_back(Matched); } return getMinMaxExpr(SCEVMinMaxExpr::negate(MME->getSCEVType()), MatchedOperands); }; if (const SCEV *Replaced = MatchMinMaxNegation(MME)) return Replaced; } Type *Ty = V->getType(); Ty = getEffectiveSCEVType(Ty); return getMinusSCEV(getMinusOne(Ty), V); } /// Compute an expression equivalent to S - getPointerBase(S). static const SCEV *removePointerBase(ScalarEvolution *SE, const SCEV *P) { assert(P->getType()->isPointerTy()); if (auto *AddRec = dyn_cast(P)) { // The base of an AddRec is the first operand. SmallVector Ops{AddRec->operands()}; Ops[0] = removePointerBase(SE, Ops[0]); // Don't try to transfer nowrap flags for now. We could in some cases // (for example, if pointer operand of the AddRec is a SCEVUnknown). return SE->getAddRecExpr(Ops, AddRec->getLoop(), SCEV::FlagAnyWrap); } if (auto *Add = dyn_cast(P)) { // The base of an Add is the pointer operand. SmallVector Ops{Add->operands()}; const SCEV **PtrOp = nullptr; for (const SCEV *&AddOp : Ops) { if (AddOp->getType()->isPointerTy()) { // If we find an Add with multiple pointer operands, treat it as a // pointer base to be consistent with getPointerBase. Eventually // we should be able to assert this is impossible. if (PtrOp) return SE->getZero(P->getType()); PtrOp = &AddOp; } } *PtrOp = removePointerBase(SE, *PtrOp); // Don't try to transfer nowrap flags for now. We could in some cases // (for example, if the pointer operand of the Add is a SCEVUnknown). return SE->getAddExpr(Ops); } // Any other expression must be a pointer base. return SE->getZero(P->getType()); } const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS, SCEV::NoWrapFlags Flags, unsigned Depth) { // Fast path: X - X --> 0. if (LHS == RHS) return getZero(LHS->getType()); // If we subtract two pointers with different pointer bases, bail. // Eventually, we're going to add an assertion to getMulExpr that we // can't multiply by a pointer. if (RHS->getType()->isPointerTy()) { if (!LHS->getType()->isPointerTy() || getPointerBase(LHS) != getPointerBase(RHS)) return getCouldNotCompute(); LHS = removePointerBase(this, LHS); RHS = removePointerBase(this, RHS); } // We represent LHS - RHS as LHS + (-1)*RHS. This transformation // makes it so that we cannot make much use of NUW. auto AddFlags = SCEV::FlagAnyWrap; const bool RHSIsNotMinSigned = !getSignedRangeMin(RHS).isMinSignedValue(); if (maskFlags(Flags, SCEV::FlagNSW) == SCEV::FlagNSW) { // Let M be the minimum representable signed value. Then (-1)*RHS // signed-wraps if and only if RHS is M. That can happen even for // a NSW subtraction because e.g. (-1)*M signed-wraps even though // -1 - M does not. So to transfer NSW from LHS - RHS to LHS + // (-1)*RHS, we need to prove that RHS != M. // // If LHS is non-negative and we know that LHS - RHS does not // signed-wrap, then RHS cannot be M. So we can rule out signed-wrap // either by proving that RHS > M or that LHS >= 0. if (RHSIsNotMinSigned || isKnownNonNegative(LHS)) { AddFlags = SCEV::FlagNSW; } } // FIXME: Find a correct way to transfer NSW to (-1)*M when LHS - // RHS is NSW and LHS >= 0. // // The difficulty here is that the NSW flag may have been proven // relative to a loop that is to be found in a recurrence in LHS and // not in RHS. Applying NSW to (-1)*M may then let the NSW have a // larger scope than intended. auto NegFlags = RHSIsNotMinSigned ? SCEV::FlagNSW : SCEV::FlagAnyWrap; return getAddExpr(LHS, getNegativeSCEV(RHS, NegFlags), AddFlags, Depth); } const SCEV *ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty, unsigned Depth) { Type *SrcTy = V->getType(); assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() && "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, Depth); return getZeroExtendExpr(V, Ty, Depth); } const SCEV *ScalarEvolution::getTruncateOrSignExtend(const SCEV *V, Type *Ty, unsigned Depth) { Type *SrcTy = V->getType(); assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() && "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, Depth); return getSignExtendExpr(V, Ty, Depth); } const SCEV * ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) { Type *SrcTy = V->getType(); assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() && "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); } const SCEV * ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) { Type *SrcTy = V->getType(); assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() && "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); } const SCEV * ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) { Type *SrcTy = V->getType(); assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() && "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); } const SCEV * ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) { Type *SrcTy = V->getType(); assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() && "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); } 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); } const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS, const SCEV *RHS) { SmallVector Ops = { LHS, RHS }; return getUMinFromMismatchedTypes(Ops); } const SCEV *ScalarEvolution::getUMinFromMismatchedTypes( SmallVectorImpl &Ops) { assert(!Ops.empty() && "At least one operand must be!"); // Trivial case. if (Ops.size() == 1) return Ops[0]; // Find the max type first. Type *MaxType = nullptr; for (auto *S : Ops) if (MaxType) MaxType = getWiderType(MaxType, S->getType()); else MaxType = S->getType(); assert(MaxType && "Failed to find maximum type!"); // Extend all ops to max type. SmallVector PromotedOps; for (auto *S : Ops) PromotedOps.push_back(getNoopOrZeroExtend(S, MaxType)); // Generate umin. return getUMinExpr(PromotedOps); } 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; while (true) { if (auto *AddRec = dyn_cast(V)) { V = AddRec->getStart(); } else if (auto *Add = dyn_cast(V)) { const SCEV *PtrOp = nullptr; for (const SCEV *AddOp : Add->operands()) { if (AddOp->getType()->isPointerTy()) { // Cannot find the base of an expression with multiple pointer ops. if (PtrOp) return V; PtrOp = AddOp; } } if (!PtrOp) // All operands were non-pointer. return V; V = PtrOp; } else // Not something we can look further into. return V; } } /// 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)); } 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; auto 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)) { eraseValueFromMap(It->first); forgetMemoizedResults(Old); } } PushDefUseChildren(I, Worklist); } } namespace { /// Takes SCEV S and Loop L. For each AddRec sub-expression, use its start /// expression in case its Loop is L. If it is not L then /// if IgnoreOtherLoops is true then use AddRec itself /// otherwise rewrite cannot be done. /// If SCEV contains non-invariant unknown SCEV rewrite cannot be done. class SCEVInitRewriter : public SCEVRewriteVisitor { public: static const SCEV *rewrite(const SCEV *S, const Loop *L, ScalarEvolution &SE, bool IgnoreOtherLoops = true) { SCEVInitRewriter Rewriter(L, SE); const SCEV *Result = Rewriter.visit(S); if (Rewriter.hasSeenLoopVariantSCEVUnknown()) return SE.getCouldNotCompute(); return Rewriter.hasSeenOtherLoops() && !IgnoreOtherLoops ? SE.getCouldNotCompute() : Result; } const SCEV *visitUnknown(const SCEVUnknown *Expr) { if (!SE.isLoopInvariant(Expr, L)) SeenLoopVariantSCEVUnknown = true; return Expr; } const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) { // Only re-write AddRecExprs for this loop. if (Expr->getLoop() == L) return Expr->getStart(); SeenOtherLoops = true; return Expr; } bool hasSeenLoopVariantSCEVUnknown() { return SeenLoopVariantSCEVUnknown; } bool hasSeenOtherLoops() { return SeenOtherLoops; } private: explicit SCEVInitRewriter(const Loop *L, ScalarEvolution &SE) : SCEVRewriteVisitor(SE), L(L) {} const Loop *L; bool SeenLoopVariantSCEVUnknown = false; bool SeenOtherLoops = false; }; /// Takes SCEV S and Loop L. For each AddRec sub-expression, use its post /// increment expression in case its Loop is L. If it is not L then /// use AddRec itself. /// If SCEV contains non-invariant unknown SCEV rewrite cannot be done. class SCEVPostIncRewriter : public SCEVRewriteVisitor { public: static const SCEV *rewrite(const SCEV *S, const Loop *L, ScalarEvolution &SE) { SCEVPostIncRewriter Rewriter(L, SE); const SCEV *Result = Rewriter.visit(S); return Rewriter.hasSeenLoopVariantSCEVUnknown() ? SE.getCouldNotCompute() : Result; } const SCEV *visitUnknown(const SCEVUnknown *Expr) { if (!SE.isLoopInvariant(Expr, L)) SeenLoopVariantSCEVUnknown = true; return Expr; } const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) { // Only re-write AddRecExprs for this loop. if (Expr->getLoop() == L) return Expr->getPostIncExpr(SE); SeenOtherLoops = true; return Expr; } bool hasSeenLoopVariantSCEVUnknown() { return SeenLoopVariantSCEVUnknown; } bool hasSeenOtherLoops() { return SeenOtherLoops; } private: explicit SCEVPostIncRewriter(const Loop *L, ScalarEvolution &SE) : SCEVRewriteVisitor(SE), L(L) {} const Loop *L; bool SeenLoopVariantSCEVUnknown = false; bool SeenOtherLoops = false; }; /// This class evaluates the compare condition by matching it against the /// condition of loop latch. If there is a match we assume a true value /// for the condition while building SCEV nodes. class SCEVBackedgeConditionFolder : public SCEVRewriteVisitor { public: static const SCEV *rewrite(const SCEV *S, const Loop *L, ScalarEvolution &SE) { bool IsPosBECond = false; Value *BECond = nullptr; if (BasicBlock *Latch = L->getLoopLatch()) { BranchInst *BI = dyn_cast(Latch->getTerminator()); if (BI && BI->isConditional()) { assert(BI->getSuccessor(0) != BI->getSuccessor(1) && "Both outgoing branches should not target same header!"); BECond = BI->getCondition(); IsPosBECond = BI->getSuccessor(0) == L->getHeader(); } else { return S; } } SCEVBackedgeConditionFolder Rewriter(L, BECond, IsPosBECond, SE); return Rewriter.visit(S); } const SCEV *visitUnknown(const SCEVUnknown *Expr) { const SCEV *Result = Expr; bool InvariantF = SE.isLoopInvariant(Expr, L); if (!InvariantF) { Instruction *I = cast(Expr->getValue()); switch (I->getOpcode()) { case Instruction::Select: { SelectInst *SI = cast(I); Optional Res = compareWithBackedgeCondition(SI->getCondition()); if (Res.hasValue()) { bool IsOne = cast(Res.getValue())->getValue()->isOne(); Result = SE.getSCEV(IsOne ? SI->getTrueValue() : SI->getFalseValue()); } break; } default: { Optional Res = compareWithBackedgeCondition(I); if (Res.hasValue()) Result = Res.getValue(); break; } } } return Result; } private: explicit SCEVBackedgeConditionFolder(const Loop *L, Value *BECond, bool IsPosBECond, ScalarEvolution &SE) : SCEVRewriteVisitor(SE), L(L), BackedgeCond(BECond), IsPositiveBECond(IsPosBECond) {} Optional compareWithBackedgeCondition(Value *IC); const Loop *L; /// Loop back condition. Value *BackedgeCond = nullptr; /// Set to true if loop back is on positive branch condition. bool IsPositiveBECond; }; Optional SCEVBackedgeConditionFolder::compareWithBackedgeCondition(Value *IC) { // If value matches the backedge condition for loop latch, // then return a constant evolution node based on loopback // branch taken. if (BackedgeCond == IC) return IsPositiveBECond ? SE.getOne(Type::getInt1Ty(SE.getContext())) : SE.getZero(Type::getInt1Ty(SE.getContext())); return None; } class SCEVShiftRewriter : public SCEVRewriteVisitor { public: static const SCEV *rewrite(const SCEV *S, const Loop *L, ScalarEvolution &SE) { SCEVShiftRewriter Rewriter(L, SE); const SCEV *Result = Rewriter.visit(S); return Rewriter.isValid() ? Result : SE.getCouldNotCompute(); } const SCEV *visitUnknown(const SCEVUnknown *Expr) { // Only allow AddRecExprs for this loop. if (!SE.isLoopInvariant(Expr, L)) Valid = false; return Expr; } const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) { if (Expr->getLoop() == L && Expr->isAffine()) return SE.getMinusSCEV(Expr, Expr->getStepRecurrence(SE)); Valid = false; return Expr; } bool isValid() { return Valid; } private: explicit SCEVShiftRewriter(const Loop *L, ScalarEvolution &SE) : SCEVRewriteVisitor(SE), L(L) {} const Loop *L; bool Valid = true; }; } // end anonymous namespace SCEV::NoWrapFlags ScalarEvolution::proveNoWrapViaConstantRanges(const SCEVAddRecExpr *AR) { if (!AR->isAffine()) return SCEV::FlagAnyWrap; using OBO = OverflowingBinaryOperator; SCEV::NoWrapFlags Result = SCEV::FlagAnyWrap; if (!AR->hasNoSignedWrap()) { ConstantRange AddRecRange = getSignedRange(AR); ConstantRange IncRange = getSignedRange(AR->getStepRecurrence(*this)); auto NSWRegion = ConstantRange::makeGuaranteedNoWrapRegion( Instruction::Add, IncRange, OBO::NoSignedWrap); if (NSWRegion.contains(AddRecRange)) Result = ScalarEvolution::setFlags(Result, SCEV::FlagNSW); } if (!AR->hasNoUnsignedWrap()) { ConstantRange AddRecRange = getUnsignedRange(AR); ConstantRange IncRange = getUnsignedRange(AR->getStepRecurrence(*this)); auto NUWRegion = ConstantRange::makeGuaranteedNoWrapRegion( Instruction::Add, IncRange, OBO::NoUnsignedWrap); if (NUWRegion.contains(AddRecRange)) Result = ScalarEvolution::setFlags(Result, SCEV::FlagNUW); } return Result; } SCEV::NoWrapFlags ScalarEvolution::proveNoSignedWrapViaInduction(const SCEVAddRecExpr *AR) { SCEV::NoWrapFlags Result = AR->getNoWrapFlags(); if (AR->hasNoSignedWrap()) return Result; if (!AR->isAffine()) return Result; const SCEV *Step = AR->getStepRecurrence(*this); const Loop *L = AR->getLoop(); // 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 = getConstantMaxBackedgeTakenCount(L); // Normally, in the cases we can prove no-overflow via a // backedge guarding condition, we can also compute a backedge // taken count for the loop. The exceptions are assumptions and // guards present in the loop -- SCEV is not great at exploiting // these to compute max backedge taken counts, but can still use // these to prove lack of overflow. Use this fact to avoid // doing extra work that may not pay off. if (isa(MaxBECount) && !HasGuards && AC.assumptions().empty()) return Result; // 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) || isKnownOnEveryIteration(Pred, AR, OverflowLimit))) { Result = setFlags(Result, SCEV::FlagNSW); } return Result; } SCEV::NoWrapFlags ScalarEvolution::proveNoUnsignedWrapViaInduction(const SCEVAddRecExpr *AR) { SCEV::NoWrapFlags Result = AR->getNoWrapFlags(); if (AR->hasNoUnsignedWrap()) return Result; if (!AR->isAffine()) return Result; const SCEV *Step = AR->getStepRecurrence(*this); unsigned BitWidth = getTypeSizeInBits(AR->getType()); const Loop *L = AR->getLoop(); // 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 = getConstantMaxBackedgeTakenCount(L); // Normally, in the cases we can prove no-overflow via a // backedge guarding condition, we can also compute a backedge // taken count for the loop. The exceptions are assumptions and // guards present in the loop -- SCEV is not great at exploiting // these to compute max backedge taken counts, but can still use // these to prove lack of overflow. Use this fact to avoid // doing extra work that may not pay off. if (isa(MaxBECount) && !HasGuards && AC.assumptions().empty()) return Result; // 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) - getUnsignedRangeMax(Step)); if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) || isKnownOnEveryIteration(ICmpInst::ICMP_ULT, AR, N)) { Result = setFlags(Result, SCEV::FlagNUW); } } return Result; } namespace { /// Represents an abstract binary operation. This may exist as a /// normal instruction or constant expression, or may have been /// derived from an expression tree. struct BinaryOp { unsigned Opcode; Value *LHS; Value *RHS; bool IsNSW = false; bool IsNUW = false; /// Op is set if this BinaryOp corresponds to a concrete LLVM instruction or /// constant expression. Operator *Op = nullptr; explicit BinaryOp(Operator *Op) : Opcode(Op->getOpcode()), LHS(Op->getOperand(0)), RHS(Op->getOperand(1)), Op(Op) { if (auto *OBO = dyn_cast(Op)) { IsNSW = OBO->hasNoSignedWrap(); IsNUW = OBO->hasNoUnsignedWrap(); } } explicit BinaryOp(unsigned Opcode, Value *LHS, Value *RHS, bool IsNSW = false, bool IsNUW = false) : Opcode(Opcode), LHS(LHS), RHS(RHS), IsNSW(IsNSW), IsNUW(IsNUW) {} }; } // end anonymous namespace /// Try to map \p V into a BinaryOp, and return \c None on failure. static Optional MatchBinaryOp(Value *V, DominatorTree &DT) { auto *Op = dyn_cast(V); if (!Op) return None; // Implementation detail: all the cleverness here should happen without // creating new SCEV expressions -- our caller knowns tricks to avoid creating // SCEV expressions when possible, and we should not break that. switch (Op->getOpcode()) { case Instruction::Add: case Instruction::Sub: case Instruction::Mul: case Instruction::UDiv: case Instruction::URem: case Instruction::And: case Instruction::Or: case Instruction::AShr: case Instruction::Shl: return BinaryOp(Op); case Instruction::Xor: if (auto *RHSC = dyn_cast(Op->getOperand(1))) // If the RHS of the xor is a signmask, then this is just an add. // Instcombine turns add of signmask into xor as a strength reduction step. if (RHSC->getValue().isSignMask()) return BinaryOp(Instruction::Add, Op->getOperand(0), Op->getOperand(1)); return BinaryOp(Op); case Instruction::LShr: // Turn logical shift right of a constant into a unsigned divide. if (ConstantInt *SA = dyn_cast(Op->getOperand(1))) { uint32_t BitWidth = cast(Op->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().ult(BitWidth)) { Constant *X = ConstantInt::get(SA->getContext(), APInt::getOneBitSet(BitWidth, SA->getZExtValue())); return BinaryOp(Instruction::UDiv, Op->getOperand(0), X); } } return BinaryOp(Op); case Instruction::ExtractValue: { auto *EVI = cast(Op); if (EVI->getNumIndices() != 1 || EVI->getIndices()[0] != 0) break; auto *WO = dyn_cast(EVI->getAggregateOperand()); if (!WO) break; Instruction::BinaryOps BinOp = WO->getBinaryOp(); bool Signed = WO->isSigned(); // TODO: Should add nuw/nsw flags for mul as well. if (BinOp == Instruction::Mul || !isOverflowIntrinsicNoWrap(WO, DT)) return BinaryOp(BinOp, WO->getLHS(), WO->getRHS()); // Now that we know that all uses of the arithmetic-result component of // CI are guarded by the overflow check, we can go ahead and pretend // that the arithmetic is non-overflowing. return BinaryOp(BinOp, WO->getLHS(), WO->getRHS(), /* IsNSW = */ Signed, /* IsNUW = */ !Signed); } default: break; } // Recognise intrinsic loop.decrement.reg, and as this has exactly the same // semantics as a Sub, return a binary sub expression. if (auto *II = dyn_cast(V)) if (II->getIntrinsicID() == Intrinsic::loop_decrement_reg) return BinaryOp(Instruction::Sub, II->getOperand(0), II->getOperand(1)); return None; } /// Helper function to createAddRecFromPHIWithCasts. We have a phi /// node whose symbolic (unknown) SCEV is \p SymbolicPHI, which is updated via /// the loop backedge by a SCEVAddExpr, possibly also with a few casts on the /// way. This function checks if \p Op, an operand of this SCEVAddExpr, /// follows one of the following patterns: /// Op == (SExt ix (Trunc iy (%SymbolicPHI) to ix) to iy) /// Op == (ZExt ix (Trunc iy (%SymbolicPHI) to ix) to iy) /// If the SCEV expression of \p Op conforms with one of the expected patterns /// we return the type of the truncation operation, and indicate whether the /// truncated type should be treated as signed/unsigned by setting /// \p Signed to true/false, respectively. static Type *isSimpleCastedPHI(const SCEV *Op, const SCEVUnknown *SymbolicPHI, bool &Signed, ScalarEvolution &SE) { // The case where Op == SymbolicPHI (that is, with no type conversions on // the way) is handled by the regular add recurrence creating logic and // would have already been triggered in createAddRecForPHI. Reaching it here // means that createAddRecFromPHI had failed for this PHI before (e.g., // because one of the other operands of the SCEVAddExpr updating this PHI is // not invariant). // // Here we look for the case where Op = (ext(trunc(SymbolicPHI))), and in // this case predicates that allow us to prove that Op == SymbolicPHI will // be added. if (Op == SymbolicPHI) return nullptr; unsigned SourceBits = SE.getTypeSizeInBits(SymbolicPHI->getType()); unsigned NewBits = SE.getTypeSizeInBits(Op->getType()); if (SourceBits != NewBits) return nullptr; const SCEVSignExtendExpr *SExt = dyn_cast(Op); const SCEVZeroExtendExpr *ZExt = dyn_cast(Op); if (!SExt && !ZExt) return nullptr; const SCEVTruncateExpr *Trunc = SExt ? dyn_cast(SExt->getOperand()) : dyn_cast(ZExt->getOperand()); if (!Trunc) return nullptr; const SCEV *X = Trunc->getOperand(); if (X != SymbolicPHI) return nullptr; Signed = SExt != nullptr; return Trunc->getType(); } static const Loop *isIntegerLoopHeaderPHI(const PHINode *PN, LoopInfo &LI) { if (!PN->getType()->isIntegerTy()) return nullptr; const Loop *L = LI.getLoopFor(PN->getParent()); if (!L || L->getHeader() != PN->getParent()) return nullptr; return L; } // Analyze \p SymbolicPHI, a SCEV expression of a phi node, and check if the // computation that updates the phi follows the following pattern: // (SExt/ZExt ix (Trunc iy (%SymbolicPHI) to ix) to iy) + InvariantAccum // which correspond to a phi->trunc->sext/zext->add->phi update chain. // If so, try to see if it can be rewritten as an AddRecExpr under some // Predicates. If successful, return them as a pair. Also cache the results // of the analysis. // // Example usage scenario: // Say the Rewriter is called for the following SCEV: // 8 * ((sext i32 (trunc i64 %X to i32) to i64) + %Step) // where: // %X = phi i64 (%Start, %BEValue) // It will visitMul->visitAdd->visitSExt->visitTrunc->visitUnknown(%X), // and call this function with %SymbolicPHI = %X. // // The analysis will find that the value coming around the backedge has // the following SCEV: // BEValue = ((sext i32 (trunc i64 %X to i32) to i64) + %Step) // Upon concluding that this matches the desired pattern, the function // will return the pair {NewAddRec, SmallPredsVec} where: // NewAddRec = {%Start,+,%Step} // SmallPredsVec = {P1, P2, P3} as follows: // P1(WrapPred): AR: {trunc(%Start),+,(trunc %Step)} Flags: // P2(EqualPred): %Start == (sext i32 (trunc i64 %Start to i32) to i64) // P3(EqualPred): %Step == (sext i32 (trunc i64 %Step to i32) to i64) // The returned pair means that SymbolicPHI can be rewritten into NewAddRec // under the predicates {P1,P2,P3}. // This predicated rewrite will be cached in PredicatedSCEVRewrites: // PredicatedSCEVRewrites[{%X,L}] = {NewAddRec, {P1,P2,P3)} // // TODO's: // // 1) Extend the Induction descriptor to also support inductions that involve // casts: When needed (namely, when we are called in the context of the // vectorizer induction analysis), a Set of cast instructions will be // populated by this method, and provided back to isInductionPHI. This is // needed to allow the vectorizer to properly record them to be ignored by // the cost model and to avoid vectorizing them (otherwise these casts, // which are redundant under the runtime overflow checks, will be // vectorized, which can be costly). // // 2) Support additional induction/PHISCEV patterns: We also want to support // inductions where the sext-trunc / zext-trunc operations (partly) occur // after the induction update operation (the induction increment): // // (Trunc iy (SExt/ZExt ix (%SymbolicPHI + InvariantAccum) to iy) to ix) // which correspond to a phi->add->trunc->sext/zext->phi update chain. // // (Trunc iy ((SExt/ZExt ix (%SymbolicPhi) to iy) + InvariantAccum) to ix) // which correspond to a phi->trunc->add->sext/zext->phi update chain. // // 3) Outline common code with createAddRecFromPHI to avoid duplication. Optional>> ScalarEvolution::createAddRecFromPHIWithCastsImpl(const SCEVUnknown *SymbolicPHI) { SmallVector Predicates; // *** Part1: Analyze if we have a phi-with-cast pattern for which we can // return an AddRec expression under some predicate. auto *PN = cast(SymbolicPHI->getValue()); const Loop *L = isIntegerLoopHeaderPHI(PN, LI); assert(L && "Expecting an integer loop header phi"); // 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) return None; const SCEV *BEValue = getSCEV(BEValueV); // If the value coming around the backedge is an add with the symbolic // value we just inserted, possibly with casts that we can ignore under // an appropriate runtime guard, then we found a simple induction variable! const auto *Add = dyn_cast(BEValue); if (!Add) return None; // If there is a single occurrence of the symbolic value, possibly // casted, replace it with a recurrence. unsigned FoundIndex = Add->getNumOperands(); Type *TruncTy = nullptr; bool Signed; for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) if ((TruncTy = isSimpleCastedPHI(Add->getOperand(i), SymbolicPHI, Signed, *this))) if (FoundIndex == e) { FoundIndex = i; break; } if (FoundIndex == Add->getNumOperands()) return None; // 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); // The runtime checks will not be valid if the step amount is // varying inside the loop. if (!isLoopInvariant(Accum, L)) return None; // *** Part2: Create the predicates // Analysis was successful: we have a phi-with-cast pattern for which we // can return an AddRec expression under the following predicates: // // P1: A Wrap predicate that guarantees that Trunc(Start) + i*Trunc(Accum) // fits within the truncated type (does not overflow) for i = 0 to n-1. // P2: An Equal predicate that guarantees that // Start = (Ext ix (Trunc iy (Start) to ix) to iy) // P3: An Equal predicate that guarantees that // Accum = (Ext ix (Trunc iy (Accum) to ix) to iy) // // As we next prove, the above predicates guarantee that: // Start + i*Accum = (Ext ix (Trunc iy ( Start + i*Accum ) to ix) to iy) // // // More formally, we want to prove that: // Expr(i+1) = Start + (i+1) * Accum // = (Ext ix (Trunc iy (Expr(i)) to ix) to iy) + Accum // // Given that: // 1) Expr(0) = Start // 2) Expr(1) = Start + Accum // = (Ext ix (Trunc iy (Start) to ix) to iy) + Accum :: from P2 // 3) Induction hypothesis (step i): // Expr(i) = (Ext ix (Trunc iy (Expr(i-1)) to ix) to iy) + Accum // // Proof: // Expr(i+1) = // = Start + (i+1)*Accum // = (Start + i*Accum) + Accum // = Expr(i) + Accum // = (Ext ix (Trunc iy (Expr(i-1)) to ix) to iy) + Accum + Accum // :: from step i // // = (Ext ix (Trunc iy (Start + (i-1)*Accum) to ix) to iy) + Accum + Accum // // = (Ext ix (Trunc iy (Start + (i-1)*Accum) to ix) to iy) // + (Ext ix (Trunc iy (Accum) to ix) to iy) // + Accum :: from P3 // // = (Ext ix (Trunc iy ((Start + (i-1)*Accum) + Accum) to ix) to iy) // + Accum :: from P1: Ext(x)+Ext(y)=>Ext(x+y) // // = (Ext ix (Trunc iy (Start + i*Accum) to ix) to iy) + Accum // = (Ext ix (Trunc iy (Expr(i)) to ix) to iy) + Accum // // By induction, the same applies to all iterations 1<=i(PHISCEV)) { SCEVWrapPredicate::IncrementWrapFlags AddedFlags = Signed ? SCEVWrapPredicate::IncrementNSSW : SCEVWrapPredicate::IncrementNUSW; const SCEVPredicate *AddRecPred = getWrapPredicate(AR, AddedFlags); Predicates.push_back(AddRecPred); } // Create the Equal Predicates P2,P3: // It is possible that the predicates P2 and/or P3 are computable at // compile time due to StartVal and/or Accum being constants. // If either one is, then we can check that now and escape if either P2 // or P3 is false. // Construct the extended SCEV: (Ext ix (Trunc iy (Expr) to ix) to iy) // for each of StartVal and Accum auto getExtendedExpr = [&](const SCEV *Expr, bool CreateSignExtend) -> const SCEV * { assert(isLoopInvariant(Expr, L) && "Expr is expected to be invariant"); const SCEV *TruncatedExpr = getTruncateExpr(Expr, TruncTy); const SCEV *ExtendedExpr = CreateSignExtend ? getSignExtendExpr(TruncatedExpr, Expr->getType()) : getZeroExtendExpr(TruncatedExpr, Expr->getType()); return ExtendedExpr; }; // Given: // ExtendedExpr = (Ext ix (Trunc iy (Expr) to ix) to iy // = getExtendedExpr(Expr) // Determine whether the predicate P: Expr == ExtendedExpr // is known to be false at compile time auto PredIsKnownFalse = [&](const SCEV *Expr, const SCEV *ExtendedExpr) -> bool { return Expr != ExtendedExpr && isKnownPredicate(ICmpInst::ICMP_NE, Expr, ExtendedExpr); }; const SCEV *StartExtended = getExtendedExpr(StartVal, Signed); if (PredIsKnownFalse(StartVal, StartExtended)) { LLVM_DEBUG(dbgs() << "P2 is compile-time false\n";); return None; } // The Step is always Signed (because the overflow checks are either // NSSW or NUSW) const SCEV *AccumExtended = getExtendedExpr(Accum, /*CreateSignExtend=*/true); if (PredIsKnownFalse(Accum, AccumExtended)) { LLVM_DEBUG(dbgs() << "P3 is compile-time false\n";); return None; } auto AppendPredicate = [&](const SCEV *Expr, const SCEV *ExtendedExpr) -> void { if (Expr != ExtendedExpr && !isKnownPredicate(ICmpInst::ICMP_EQ, Expr, ExtendedExpr)) { const SCEVPredicate *Pred = getEqualPredicate(Expr, ExtendedExpr); LLVM_DEBUG(dbgs() << "Added Predicate: " << *Pred); Predicates.push_back(Pred); } }; AppendPredicate(StartVal, StartExtended); AppendPredicate(Accum, AccumExtended); // *** Part3: Predicates are ready. Now go ahead and create the new addrec in // which the casts had been folded away. The caller can rewrite SymbolicPHI // into NewAR if it will also add the runtime overflow checks specified in // Predicates. auto *NewAR = getAddRecExpr(StartVal, Accum, L, SCEV::FlagAnyWrap); std::pair> PredRewrite = std::make_pair(NewAR, Predicates); // Remember the result of the analysis for this SCEV at this locayyytion. PredicatedSCEVRewrites[{SymbolicPHI, L}] = PredRewrite; return PredRewrite; } Optional>> ScalarEvolution::createAddRecFromPHIWithCasts(const SCEVUnknown *SymbolicPHI) { auto *PN = cast(SymbolicPHI->getValue()); const Loop *L = isIntegerLoopHeaderPHI(PN, LI); if (!L) return None; // Check to see if we already analyzed this PHI. auto I = PredicatedSCEVRewrites.find({SymbolicPHI, L}); if (I != PredicatedSCEVRewrites.end()) { std::pair> Rewrite = I->second; // Analysis was done before and failed to create an AddRec: if (Rewrite.first == SymbolicPHI) return None; // Analysis was done before and succeeded to create an AddRec under // a predicate: assert(isa(Rewrite.first) && "Expected an AddRec"); assert(!(Rewrite.second).empty() && "Expected to find Predicates"); return Rewrite; } Optional>> Rewrite = createAddRecFromPHIWithCastsImpl(SymbolicPHI); // Record in the cache that the analysis failed if (!Rewrite) { SmallVector Predicates; PredicatedSCEVRewrites[{SymbolicPHI, L}] = {SymbolicPHI, Predicates}; return None; } return Rewrite; } // FIXME: This utility is currently required because the Rewriter currently // does not rewrite this expression: // {0, +, (sext ix (trunc iy to ix) to iy)} // into {0, +, %step}, // even when the following Equal predicate exists: // "%step == (sext ix (trunc iy to ix) to iy)". bool PredicatedScalarEvolution::areAddRecsEqualWithPreds( const SCEVAddRecExpr *AR1, const SCEVAddRecExpr *AR2) const { if (AR1 == AR2) return true; auto areExprsEqual = [&](const SCEV *Expr1, const SCEV *Expr2) -> bool { if (Expr1 != Expr2 && !Preds.implies(SE.getEqualPredicate(Expr1, Expr2)) && !Preds.implies(SE.getEqualPredicate(Expr2, Expr1))) return false; return true; }; if (!areExprsEqual(AR1->getStart(), AR2->getStart()) || !areExprsEqual(AR1->getStepRecurrence(SE), AR2->getStepRecurrence(SE))) return false; return true; } /// A helper function for createAddRecFromPHI to handle simple cases. /// /// This function tries to find an AddRec expression for the simplest (yet most /// common) cases: PN = PHI(Start, OP(Self, LoopInvariant)). /// If it fails, createAddRecFromPHI will use a more general, but slow, /// technique for finding the AddRec expression. const SCEV *ScalarEvolution::createSimpleAffineAddRec(PHINode *PN, Value *BEValueV, Value *StartValueV) { const Loop *L = LI.getLoopFor(PN->getParent()); assert(L && L->getHeader() == PN->getParent()); assert(BEValueV && StartValueV); auto BO = MatchBinaryOp(BEValueV, DT); if (!BO) return nullptr; if (BO->Opcode != Instruction::Add) return nullptr; const SCEV *Accum = nullptr; if (BO->LHS == PN && L->isLoopInvariant(BO->RHS)) Accum = getSCEV(BO->RHS); else if (BO->RHS == PN && L->isLoopInvariant(BO->LHS)) Accum = getSCEV(BO->LHS); if (!Accum) return nullptr; SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap; if (BO->IsNUW) Flags = setFlags(Flags, SCEV::FlagNUW); if (BO->IsNSW) Flags = setFlags(Flags, SCEV::FlagNSW); const SCEV *StartVal = getSCEV(StartValueV); const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags); ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV; // We can add Flags to the post-inc expression only if we // know that it is *undefined behavior* for BEValueV to // overflow. if (auto *BEInst = dyn_cast(BEValueV)) if (isLoopInvariant(Accum, L) && isAddRecNeverPoison(BEInst, L)) (void)getAddRecExpr(getAddExpr(StartVal, Accum), Accum, L, Flags); return PHISCEV; } const SCEV *ScalarEvolution::createAddRecFromPHI(PHINode *PN) { const Loop *L = LI.getLoopFor(PN->getParent()); if (!L || L->getHeader() != PN->getParent()) return nullptr; // 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) return nullptr; assert(ValueExprMap.find_as(PN) == ValueExprMap.end() && "PHI node already processed?"); // First, try to find AddRec expression without creating a fictituos symbolic // value for PN. if (auto *S = createSimpleAffineAddRec(PN, BEValueV, StartValueV)) return S; // Handle PHI node value symbolically. const SCEV *SymbolicName = getUnknown(PN); ValueExprMap.insert({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(SCEVBackedgeConditionFolder::rewrite(Add->getOperand(i), L, *this)); 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 (auto BO = MatchBinaryOp(BEValueV, DT)) { if (BO->Opcode == Instruction::Add && BO->LHS == PN) { if (BO->IsNUW) Flags = setFlags(Flags, SCEV::FlagNUW); if (BO->IsNSW) 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() && GEP->getOperand(0) == PN) { 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); // 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; // We can add Flags to the post-inc expression only if we // know that it is *undefined behavior* for BEValueV to // overflow. if (auto *BEInst = dyn_cast(BEValueV)) if (isLoopInvariant(Accum, L) && isAddRecNeverPoison(BEInst, L)) (void)getAddRecExpr(getAddExpr(StartVal, Accum), Accum, L, Flags); return PHISCEV; } } } else { // 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. // // We can generalize this saying that i is the shifted value of BEValue // by one iteration: // PHI(f(0), f({1,+,1})) --> f({0,+,1}) const SCEV *Shifted = SCEVShiftRewriter::rewrite(BEValue, L, *this); const SCEV *Start = SCEVInitRewriter::rewrite(Shifted, L, *this, false); if (Shifted != getCouldNotCompute() && Start != getCouldNotCompute()) { const SCEV *StartVal = getSCEV(StartValueV); if (Start == StartVal) { // 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)] = Shifted; return Shifted; } } } // Remove the temporary PHI node SCEV that has been inserted while intending // to create an AddRecExpr for this PHI node. We can not keep this temporary // as it will prevent later (possibly simpler) SCEV expressions to be added // to the ValueExprMap. eraseValueFromMap(PN); return nullptr; } // Checks if the SCEV S is available at BB. S is considered available at BB // if S can be materialized at BB without introducing a fault. static bool IsAvailableOnEntry(const Loop *L, DominatorTree &DT, const SCEV *S, BasicBlock *BB) { struct CheckAvailable { bool TraversalDone = false; bool Available = true; const Loop *L = nullptr; // The loop BB is in (can be nullptr) BasicBlock *BB = nullptr; DominatorTree &DT; CheckAvailable(const Loop *L, BasicBlock *BB, DominatorTree &DT) : L(L), BB(BB), DT(DT) {} bool setUnavailable() { TraversalDone = true; Available = false; return false; } bool follow(const SCEV *S) { switch (S->getSCEVType()) { case scConstant: case scPtrToInt: case scTruncate: case scZeroExtend: case scSignExtend: case scAddExpr: case scMulExpr: case scUMaxExpr: case scSMaxExpr: case scUMinExpr: case scSMinExpr: // These expressions are available if their operand(s) is/are. return true; case scAddRecExpr: { // We allow add recurrences that are on the loop BB is in, or some // outer loop. This guarantees availability because the value of the // add recurrence at BB is simply the "current" value of the induction // variable. We can relax this in the future; for instance an add // recurrence on a sibling dominating loop is also available at BB. const auto *ARLoop = cast(S)->getLoop(); if (L && (ARLoop == L || ARLoop->contains(L))) return true; return setUnavailable(); } case scUnknown: { // For SCEVUnknown, we check for simple dominance. const auto *SU = cast(S); Value *V = SU->getValue(); if (isa(V)) return false; if (isa(V) && DT.dominates(cast(V), BB)) return false; return setUnavailable(); } case scUDivExpr: case scCouldNotCompute: // We do not try to smart about these at all. return setUnavailable(); } llvm_unreachable("Unknown SCEV kind!"); } bool isDone() { return TraversalDone; } }; CheckAvailable CA(L, BB, DT); SCEVTraversal ST(CA); ST.visitAll(S); return CA.Available; } // Try to match a control flow sequence that branches out at BI and merges back // at Merge into a "C ? LHS : RHS" select pattern. Return true on a successful // match. static bool BrPHIToSelect(DominatorTree &DT, BranchInst *BI, PHINode *Merge, Value *&C, Value *&LHS, Value *&RHS) { C = BI->getCondition(); BasicBlockEdge LeftEdge(BI->getParent(), BI->getSuccessor(0)); BasicBlockEdge RightEdge(BI->getParent(), BI->getSuccessor(1)); if (!LeftEdge.isSingleEdge()) return false; assert(RightEdge.isSingleEdge() && "Follows from LeftEdge.isSingleEdge()"); Use &LeftUse = Merge->getOperandUse(0); Use &RightUse = Merge->getOperandUse(1); if (DT.dominates(LeftEdge, LeftUse) && DT.dominates(RightEdge, RightUse)) { LHS = LeftUse; RHS = RightUse; return true; } if (DT.dominates(LeftEdge, RightUse) && DT.dominates(RightEdge, LeftUse)) { LHS = RightUse; RHS = LeftUse; return true; } return false; } const SCEV *ScalarEvolution::createNodeFromSelectLikePHI(PHINode *PN) { auto IsReachable = [&](BasicBlock *BB) { return DT.isReachableFromEntry(BB); }; if (PN->getNumIncomingValues() == 2 && all_of(PN->blocks(), IsReachable)) { const Loop *L = LI.getLoopFor(PN->getParent()); // We don't want to break LCSSA, even in a SCEV expression tree. for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) if (LI.getLoopFor(PN->getIncomingBlock(i)) != L) return nullptr; // Try to match // // br %cond, label %left, label %right // left: // br label %merge // right: // br label %merge // merge: // V = phi [ %x, %left ], [ %y, %right ] // // as "select %cond, %x, %y" BasicBlock *IDom = DT[PN->getParent()]->getIDom()->getBlock(); assert(IDom && "At least the entry block should dominate PN"); auto *BI = dyn_cast(IDom->getTerminator()); Value *Cond = nullptr, *LHS = nullptr, *RHS = nullptr; if (BI && BI->isConditional() && BrPHIToSelect(DT, BI, PN, Cond, LHS, RHS) && IsAvailableOnEntry(L, DT, getSCEV(LHS), PN->getParent()) && IsAvailableOnEntry(L, DT, getSCEV(RHS), PN->getParent())) return createNodeForSelectOrPHI(PN, Cond, LHS, RHS); } return nullptr; } const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) { if (const SCEV *S = createAddRecFromPHI(PN)) return S; if (const SCEV *S = createNodeFromSelectLikePHI(PN)) return S; // 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, {getDataLayout(), &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); } const SCEV *ScalarEvolution::createNodeForSelectOrPHI(Instruction *I, Value *Cond, Value *TrueVal, Value *FalseVal) { // Handle "constant" branch or select. This can occur for instance when a // loop pass transforms an inner loop and moves on to process the outer loop. if (auto *CI = dyn_cast(Cond)) return getSCEV(CI->isOne() ? TrueVal : FalseVal); // Try to match some simple smax or umax patterns. auto *ICI = dyn_cast(Cond); if (!ICI) return getUnknown(I); Value *LHS = ICI->getOperand(0); Value *RHS = ICI->getOperand(1); switch (ICI->getPredicate()) { case ICmpInst::ICMP_SLT: case ICmpInst::ICMP_SLE: case ICmpInst::ICMP_ULT: case ICmpInst::ICMP_ULE: std::swap(LHS, RHS); LLVM_FALLTHROUGH; case ICmpInst::ICMP_SGT: case ICmpInst::ICMP_SGE: case ICmpInst::ICMP_UGT: case ICmpInst::ICMP_UGE: // a > b ? a+x : b+x -> max(a, b)+x // a > b ? b+x : a+x -> min(a, b)+x if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType())) { bool Signed = ICI->isSigned(); const SCEV *LA = getSCEV(TrueVal); const SCEV *RA = getSCEV(FalseVal); const SCEV *LS = getSCEV(LHS); const SCEV *RS = getSCEV(RHS); if (LA->getType()->isPointerTy()) { // FIXME: Handle cases where LS/RS are pointers not equal to LA/RA. // Need to make sure we can't produce weird expressions involving // negated pointers. if (LA == LS && RA == RS) return Signed ? getSMaxExpr(LS, RS) : getUMaxExpr(LS, RS); if (LA == RS && RA == LS) return Signed ? getSMinExpr(LS, RS) : getUMinExpr(LS, RS); } auto CoerceOperand = [&](const SCEV *Op) -> const SCEV * { if (Op->getType()->isPointerTy()) { Op = getLosslessPtrToIntExpr(Op); if (isa(Op)) return Op; } if (Signed) Op = getNoopOrSignExtend(Op, I->getType()); else Op = getNoopOrZeroExtend(Op, I->getType()); return Op; }; LS = CoerceOperand(LS); RS = CoerceOperand(RS); if (isa(LS) || isa(RS)) break; const SCEV *LDiff = getMinusSCEV(LA, LS); const SCEV *RDiff = getMinusSCEV(RA, RS); if (LDiff == RDiff) return getAddExpr(Signed ? getSMaxExpr(LS, RS) : getUMaxExpr(LS, RS), LDiff); LDiff = getMinusSCEV(LA, RS); RDiff = getMinusSCEV(RA, LS); if (LDiff == RDiff) return getAddExpr(Signed ? getSMinExpr(LS, RS) : getUMinExpr(LS, RS), LDiff); } break; case ICmpInst::ICMP_NE: // n != 0 ? n+x : 1+x -> umax(n, 1)+x if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType()) && isa(RHS) && cast(RHS)->isZero()) { const SCEV *One = getOne(I->getType()); const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType()); const SCEV *LA = getSCEV(TrueVal); const SCEV *RA = getSCEV(FalseVal); 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(I->getType()) && isa(RHS) && cast(RHS)->isZero()) { const SCEV *One = getOne(I->getType()); const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType()); const SCEV *LA = getSCEV(TrueVal); const SCEV *RA = getSCEV(FalseVal); const SCEV *LDiff = getMinusSCEV(LA, One); const SCEV *RDiff = getMinusSCEV(RA, LS); if (LDiff == RDiff) return getAddExpr(getUMaxExpr(One, LS), LDiff); } break; default: break; } return getUnknown(I); } /// Expand GEP instructions into add and multiply operations. This allows them /// to be analyzed by regular SCEV code. const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) { // Don't attempt to analyze GEPs over unsized objects. if (!GEP->getSourceElementType()->isSized()) return getUnknown(GEP); SmallVector IndexExprs; for (Value *Index : GEP->indices()) IndexExprs.push_back(getSCEV(Index)); return getGEPExpr(GEP, IndexExprs); } uint32_t ScalarEvolution::GetMinTrailingZerosImpl(const SCEV *S) { if (const SCEVConstant *C = dyn_cast(S)) return C->getAPInt().countTrailingZeros(); if (const SCEVPtrToIntExpr *I = dyn_cast(S)) return GetMinTrailingZeros(I->getOperand()); 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. KnownBits Known = computeKnownBits(U->getValue(), getDataLayout(), 0, &AC, nullptr, &DT); return Known.countMinTrailingZeros(); } // SCEVUDivExpr return 0; } uint32_t ScalarEvolution::GetMinTrailingZeros(const SCEV *S) { auto I = MinTrailingZerosCache.find(S); if (I != MinTrailingZerosCache.end()) return I->second; uint32_t Result = GetMinTrailingZerosImpl(S); auto InsertPair = MinTrailingZerosCache.insert({S, Result}); assert(InsertPair.second && "Should insert a new key"); return InsertPair.first->second; } /// 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)) return getConstantRangeFromMetadata(*MD); return None; } void ScalarEvolution::setNoWrapFlags(SCEVAddRecExpr *AddRec, SCEV::NoWrapFlags Flags) { if (AddRec->getNoWrapFlags(Flags) != Flags) { AddRec->setNoWrapFlags(Flags); UnsignedRanges.erase(AddRec); SignedRanges.erase(AddRec); } } ConstantRange ScalarEvolution:: getRangeForUnknownRecurrence(const SCEVUnknown *U) { const DataLayout &DL = getDataLayout(); unsigned BitWidth = getTypeSizeInBits(U->getType()); const ConstantRange FullSet(BitWidth, /*isFullSet=*/true); // Match a simple recurrence of the form: , and then // use information about the trip count to improve our available range. Note // that the trip count independent cases are already handled by known bits. // WARNING: The definition of recurrence used here is subtly different than // the one used by AddRec (and thus most of this file). Step is allowed to // be arbitrarily loop varying here, where AddRec allows only loop invariant // and other addrecs in the same loop (for non-affine addrecs). The code // below intentionally handles the case where step is not loop invariant. auto *P = dyn_cast(U->getValue()); if (!P) return FullSet; // Make sure that no Phi input comes from an unreachable block. Otherwise, // even the values that are not available in these blocks may come from them, // and this leads to false-positive recurrence test. for (auto *Pred : predecessors(P->getParent())) if (!DT.isReachableFromEntry(Pred)) return FullSet; BinaryOperator *BO; Value *Start, *Step; if (!matchSimpleRecurrence(P, BO, Start, Step)) return FullSet; // If we found a recurrence in reachable code, we must be in a loop. Note // that BO might be in some subloop of L, and that's completely okay. auto *L = LI.getLoopFor(P->getParent()); assert(L && L->getHeader() == P->getParent()); if (!L->contains(BO->getParent())) // NOTE: This bailout should be an assert instead. However, asserting // the condition here exposes a case where LoopFusion is querying SCEV // with malformed loop information during the midst of the transform. // There doesn't appear to be an obvious fix, so for the moment bailout // until the caller issue can be fixed. PR49566 tracks the bug. return FullSet; // TODO: Extend to other opcodes such as mul, and div switch (BO->getOpcode()) { default: return FullSet; case Instruction::AShr: case Instruction::LShr: case Instruction::Shl: break; }; if (BO->getOperand(0) != P) // TODO: Handle the power function forms some day. return FullSet; unsigned TC = getSmallConstantMaxTripCount(L); if (!TC || TC >= BitWidth) return FullSet; auto KnownStart = computeKnownBits(Start, DL, 0, &AC, nullptr, &DT); auto KnownStep = computeKnownBits(Step, DL, 0, &AC, nullptr, &DT); assert(KnownStart.getBitWidth() == BitWidth && KnownStep.getBitWidth() == BitWidth); // Compute total shift amount, being careful of overflow and bitwidths. auto MaxShiftAmt = KnownStep.getMaxValue(); APInt TCAP(BitWidth, TC-1); bool Overflow = false; auto TotalShift = MaxShiftAmt.umul_ov(TCAP, Overflow); if (Overflow) return FullSet; switch (BO->getOpcode()) { default: llvm_unreachable("filtered out above"); case Instruction::AShr: { // For each ashr, three cases: // shift = 0 => unchanged value // saturation => 0 or -1 // other => a value closer to zero (of the same sign) // Thus, the end value is closer to zero than the start. auto KnownEnd = KnownBits::ashr(KnownStart, KnownBits::makeConstant(TotalShift)); if (KnownStart.isNonNegative()) // Analogous to lshr (simply not yet canonicalized) return ConstantRange::getNonEmpty(KnownEnd.getMinValue(), KnownStart.getMaxValue() + 1); if (KnownStart.isNegative()) // End >=u Start && End <=s Start return ConstantRange::getNonEmpty(KnownStart.getMinValue(), KnownEnd.getMaxValue() + 1); break; } case Instruction::LShr: { // For each lshr, three cases: // shift = 0 => unchanged value // saturation => 0 // other => a smaller positive number // Thus, the low end of the unsigned range is the last value produced. auto KnownEnd = KnownBits::lshr(KnownStart, KnownBits::makeConstant(TotalShift)); return ConstantRange::getNonEmpty(KnownEnd.getMinValue(), KnownStart.getMaxValue() + 1); } case Instruction::Shl: { // Iff no bits are shifted out, value increases on every shift. auto KnownEnd = KnownBits::shl(KnownStart, KnownBits::makeConstant(TotalShift)); if (TotalShift.ult(KnownStart.countMinLeadingZeros())) return ConstantRange(KnownStart.getMinValue(), KnownEnd.getMaxValue() + 1); break; } }; return FullSet; } /// Determine the range for a particular SCEV. If SignHint is /// HINT_RANGE_UNSIGNED (resp. HINT_RANGE_SIGNED) then getRange prefers ranges /// with a "cleaner" unsigned (resp. signed) representation. const ConstantRange & ScalarEvolution::getRangeRef(const SCEV *S, ScalarEvolution::RangeSignHint SignHint) { DenseMap &Cache = SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED ? UnsignedRanges : SignedRanges; ConstantRange::PreferredRangeType RangeType = SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED ? ConstantRange::Unsigned : ConstantRange::Signed; // See if we've computed this range already. DenseMap::iterator I = Cache.find(S); if (I != Cache.end()) return I->second; if (const SCEVConstant *C = dyn_cast(S)) return setRange(C, SignHint, ConstantRange(C->getAPInt())); unsigned BitWidth = getTypeSizeInBits(S->getType()); ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true); using OBO = OverflowingBinaryOperator; // If the value has known zeros, the maximum value will have those known zeros // as well. uint32_t TZ = GetMinTrailingZeros(S); if (TZ != 0) { if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED) ConservativeResult = ConstantRange(APInt::getMinValue(BitWidth), APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1); else ConservativeResult = ConstantRange( APInt::getSignedMinValue(BitWidth), APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1); } if (const SCEVAddExpr *Add = dyn_cast(S)) { ConstantRange X = getRangeRef(Add->getOperand(0), SignHint); unsigned WrapType = OBO::AnyWrap; if (Add->hasNoSignedWrap()) WrapType |= OBO::NoSignedWrap; if (Add->hasNoUnsignedWrap()) WrapType |= OBO::NoUnsignedWrap; for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i) X = X.addWithNoWrap(getRangeRef(Add->getOperand(i), SignHint), WrapType, RangeType); return setRange(Add, SignHint, ConservativeResult.intersectWith(X, RangeType)); } if (const SCEVMulExpr *Mul = dyn_cast(S)) { ConstantRange X = getRangeRef(Mul->getOperand(0), SignHint); for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i) X = X.multiply(getRangeRef(Mul->getOperand(i), SignHint)); return setRange(Mul, SignHint, ConservativeResult.intersectWith(X, RangeType)); } if (const SCEVSMaxExpr *SMax = dyn_cast(S)) { ConstantRange X = getRangeRef(SMax->getOperand(0), SignHint); for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i) X = X.smax(getRangeRef(SMax->getOperand(i), SignHint)); return setRange(SMax, SignHint, ConservativeResult.intersectWith(X, RangeType)); } if (const SCEVUMaxExpr *UMax = dyn_cast(S)) { ConstantRange X = getRangeRef(UMax->getOperand(0), SignHint); for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i) X = X.umax(getRangeRef(UMax->getOperand(i), SignHint)); return setRange(UMax, SignHint, ConservativeResult.intersectWith(X, RangeType)); } if (const SCEVSMinExpr *SMin = dyn_cast(S)) { ConstantRange X = getRangeRef(SMin->getOperand(0), SignHint); for (unsigned i = 1, e = SMin->getNumOperands(); i != e; ++i) X = X.smin(getRangeRef(SMin->getOperand(i), SignHint)); return setRange(SMin, SignHint, ConservativeResult.intersectWith(X, RangeType)); } if (const SCEVUMinExpr *UMin = dyn_cast(S)) { ConstantRange X = getRangeRef(UMin->getOperand(0), SignHint); for (unsigned i = 1, e = UMin->getNumOperands(); i != e; ++i) X = X.umin(getRangeRef(UMin->getOperand(i), SignHint)); return setRange(UMin, SignHint, ConservativeResult.intersectWith(X, RangeType)); } if (const SCEVUDivExpr *UDiv = dyn_cast(S)) { ConstantRange X = getRangeRef(UDiv->getLHS(), SignHint); ConstantRange Y = getRangeRef(UDiv->getRHS(), SignHint); return setRange(UDiv, SignHint, ConservativeResult.intersectWith(X.udiv(Y), RangeType)); } if (const SCEVZeroExtendExpr *ZExt = dyn_cast(S)) { ConstantRange X = getRangeRef(ZExt->getOperand(), SignHint); return setRange(ZExt, SignHint, ConservativeResult.intersectWith(X.zeroExtend(BitWidth), RangeType)); } if (const SCEVSignExtendExpr *SExt = dyn_cast(S)) { ConstantRange X = getRangeRef(SExt->getOperand(), SignHint); return setRange(SExt, SignHint, ConservativeResult.intersectWith(X.signExtend(BitWidth), RangeType)); } if (const SCEVPtrToIntExpr *PtrToInt = dyn_cast(S)) { ConstantRange X = getRangeRef(PtrToInt->getOperand(), SignHint); return setRange(PtrToInt, SignHint, X); } if (const SCEVTruncateExpr *Trunc = dyn_cast(S)) { ConstantRange X = getRangeRef(Trunc->getOperand(), SignHint); return setRange(Trunc, SignHint, ConservativeResult.intersectWith(X.truncate(BitWidth), RangeType)); } 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->hasNoUnsignedWrap()) { APInt UnsignedMinValue = getUnsignedRangeMin(AddRec->getStart()); if (!UnsignedMinValue.isNullValue()) ConservativeResult = ConservativeResult.intersectWith( ConstantRange(UnsignedMinValue, APInt(BitWidth, 0)), RangeType); } // If there's no signed wrap, and all the operands except initial value have // the same sign or zero, the value won't ever be: // 1: smaller than initial value if operands are non negative, // 2: bigger than initial value if operands are non positive. // For both cases, value can not cross signed min/max boundary. if (AddRec->hasNoSignedWrap()) { bool AllNonNeg = true; bool AllNonPos = true; for (unsigned i = 1, 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::getNonEmpty(getSignedRangeMin(AddRec->getStart()), APInt::getSignedMinValue(BitWidth)), RangeType); else if (AllNonPos) ConservativeResult = ConservativeResult.intersectWith( ConstantRange::getNonEmpty( APInt::getSignedMinValue(BitWidth), getSignedRangeMax(AddRec->getStart()) + 1), RangeType); } // TODO: non-affine addrec if (AddRec->isAffine()) { const SCEV *MaxBECount = getConstantMaxBackedgeTakenCount(AddRec->getLoop()); if (!isa(MaxBECount) && getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) { auto RangeFromAffine = getRangeForAffineAR( AddRec->getStart(), AddRec->getStepRecurrence(*this), MaxBECount, BitWidth); ConservativeResult = ConservativeResult.intersectWith(RangeFromAffine, RangeType); auto RangeFromFactoring = getRangeViaFactoring( AddRec->getStart(), AddRec->getStepRecurrence(*this), MaxBECount, BitWidth); ConservativeResult = ConservativeResult.intersectWith(RangeFromFactoring, RangeType); } // Now try symbolic BE count and more powerful methods. if (UseExpensiveRangeSharpening) { const SCEV *SymbolicMaxBECount = getSymbolicMaxBackedgeTakenCount(AddRec->getLoop()); if (!isa(SymbolicMaxBECount) && getTypeSizeInBits(MaxBECount->getType()) <= BitWidth && AddRec->hasNoSelfWrap()) { auto RangeFromAffineNew = getRangeForAffineNoSelfWrappingAR( AddRec, SymbolicMaxBECount, BitWidth, SignHint); ConservativeResult = ConservativeResult.intersectWith(RangeFromAffineNew, RangeType); } } } return setRange(AddRec, SignHint, std::move(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(), RangeType); // Use facts about recurrences in the underlying IR. Note that add // recurrences are AddRecExprs and thus don't hit this path. This // primarily handles shift recurrences. auto CR = getRangeForUnknownRecurrence(U); ConservativeResult = ConservativeResult.intersectWith(CR); // See if ValueTracking can give us a useful range. const DataLayout &DL = getDataLayout(); KnownBits Known = computeKnownBits(U->getValue(), DL, 0, &AC, nullptr, &DT); if (Known.getBitWidth() != BitWidth) Known = Known.zextOrTrunc(BitWidth); // ValueTracking may be able to compute a tighter result for the number of // sign bits than for the value of those sign bits. unsigned NS = ComputeNumSignBits(U->getValue(), DL, 0, &AC, nullptr, &DT); if (U->getType()->isPointerTy()) { // If the pointer size is larger than the index size type, this can cause // NS to be larger than BitWidth. So compensate for this. unsigned ptrSize = DL.getPointerTypeSizeInBits(U->getType()); int ptrIdxDiff = ptrSize - BitWidth; if (ptrIdxDiff > 0 && ptrSize > BitWidth && NS > (unsigned)ptrIdxDiff) NS -= ptrIdxDiff; } if (NS > 1) { // If we know any of the sign bits, we know all of the sign bits. if (!Known.Zero.getHiBits(NS).isNullValue()) Known.Zero.setHighBits(NS); if (!Known.One.getHiBits(NS).isNullValue()) Known.One.setHighBits(NS); } if (Known.getMinValue() != Known.getMaxValue() + 1) ConservativeResult = ConservativeResult.intersectWith( ConstantRange(Known.getMinValue(), Known.getMaxValue() + 1), RangeType); if (NS > 1) ConservativeResult = ConservativeResult.intersectWith( ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1), APInt::getSignedMaxValue(BitWidth).ashr(NS - 1) + 1), RangeType); // A range of Phi is a subset of union of all ranges of its input. if (const PHINode *Phi = dyn_cast(U->getValue())) { // Make sure that we do not run over cycled Phis. if (PendingPhiRanges.insert(Phi).second) { ConstantRange RangeFromOps(BitWidth, /*isFullSet=*/false); for (auto &Op : Phi->operands()) { auto OpRange = getRangeRef(getSCEV(Op), SignHint); RangeFromOps = RangeFromOps.unionWith(OpRange); // No point to continue if we already have a full set. if (RangeFromOps.isFullSet()) break; } ConservativeResult = ConservativeResult.intersectWith(RangeFromOps, RangeType); bool Erased = PendingPhiRanges.erase(Phi); assert(Erased && "Failed to erase Phi properly?"); (void) Erased; } } return setRange(U, SignHint, std::move(ConservativeResult)); } return setRange(S, SignHint, std::move(ConservativeResult)); } // Given a StartRange, Step and MaxBECount for an expression compute a range of // values that the expression can take. Initially, the expression has a value // from StartRange and then is changed by Step up to MaxBECount times. Signed // argument defines if we treat Step as signed or unsigned. static ConstantRange getRangeForAffineARHelper(APInt Step, const ConstantRange &StartRange, const APInt &MaxBECount, unsigned BitWidth, bool Signed) { // If either Step or MaxBECount is 0, then the expression won't change, and we // just need to return the initial range. if (Step == 0 || MaxBECount == 0) return StartRange; // If we don't know anything about the initial value (i.e. StartRange is // FullRange), then we don't know anything about the final range either. // Return FullRange. if (StartRange.isFullSet()) return ConstantRange::getFull(BitWidth); // If Step is signed and negative, then we use its absolute value, but we also // note that we're moving in the opposite direction. bool Descending = Signed && Step.isNegative(); if (Signed) // This is correct even for INT_SMIN. Let's look at i8 to illustrate this: // abs(INT_SMIN) = abs(-128) = abs(0x80) = -0x80 = 0x80 = 128. // This equations hold true due to the well-defined wrap-around behavior of // APInt. Step = Step.abs(); // Check if Offset is more than full span of BitWidth. If it is, the // expression is guaranteed to overflow. if (APInt::getMaxValue(StartRange.getBitWidth()).udiv(Step).ult(MaxBECount)) return ConstantRange::getFull(BitWidth); // Offset is by how much the expression can change. Checks above guarantee no // overflow here. APInt Offset = Step * MaxBECount; // Minimum value of the final range will match the minimal value of StartRange // if the expression is increasing and will be decreased by Offset otherwise. // Maximum value of the final range will match the maximal value of StartRange // if the expression is decreasing and will be increased by Offset otherwise. APInt StartLower = StartRange.getLower(); APInt StartUpper = StartRange.getUpper() - 1; APInt MovedBoundary = Descending ? (StartLower - std::move(Offset)) : (StartUpper + std::move(Offset)); // It's possible that the new minimum/maximum value will fall into the initial // range (due to wrap around). This means that the expression can take any // value in this bitwidth, and we have to return full range. if (StartRange.contains(MovedBoundary)) return ConstantRange::getFull(BitWidth); APInt NewLower = Descending ? std::move(MovedBoundary) : std::move(StartLower); APInt NewUpper = Descending ? std::move(StartUpper) : std::move(MovedBoundary); NewUpper += 1; // No overflow detected, return [StartLower, StartUpper + Offset + 1) range. return ConstantRange::getNonEmpty(std::move(NewLower), std::move(NewUpper)); } ConstantRange ScalarEvolution::getRangeForAffineAR(const SCEV *Start, const SCEV *Step, const SCEV *MaxBECount, unsigned BitWidth) { assert(!isa(MaxBECount) && getTypeSizeInBits(MaxBECount->getType()) <= BitWidth && "Precondition!"); MaxBECount = getNoopOrZeroExtend(MaxBECount, Start->getType()); APInt MaxBECountValue = getUnsignedRangeMax(MaxBECount); // First, consider step signed. ConstantRange StartSRange = getSignedRange(Start); ConstantRange StepSRange = getSignedRange(Step); // If Step can be both positive and negative, we need to find ranges for the // maximum absolute step values in both directions and union them. ConstantRange SR = getRangeForAffineARHelper(StepSRange.getSignedMin(), StartSRange, MaxBECountValue, BitWidth, /* Signed = */ true); SR = SR.unionWith(getRangeForAffineARHelper(StepSRange.getSignedMax(), StartSRange, MaxBECountValue, BitWidth, /* Signed = */ true)); // Next, consider step unsigned. ConstantRange UR = getRangeForAffineARHelper( getUnsignedRangeMax(Step), getUnsignedRange(Start), MaxBECountValue, BitWidth, /* Signed = */ false); // Finally, intersect signed and unsigned ranges. return SR.intersectWith(UR, ConstantRange::Smallest); } ConstantRange ScalarEvolution::getRangeForAffineNoSelfWrappingAR( const SCEVAddRecExpr *AddRec, const SCEV *MaxBECount, unsigned BitWidth, ScalarEvolution::RangeSignHint SignHint) { assert(AddRec->isAffine() && "Non-affine AddRecs are not suppored!\n"); assert(AddRec->hasNoSelfWrap() && "This only works for non-self-wrapping AddRecs!"); const bool IsSigned = SignHint == HINT_RANGE_SIGNED; const SCEV *Step = AddRec->getStepRecurrence(*this); // Only deal with constant step to save compile time. if (!isa(Step)) return ConstantRange::getFull(BitWidth); // Let's make sure that we can prove that we do not self-wrap during // MaxBECount iterations. We need this because MaxBECount is a maximum // iteration count estimate, and we might infer nw from some exit for which we // do not know max exit count (or any other side reasoning). // TODO: Turn into assert at some point. if (getTypeSizeInBits(MaxBECount->getType()) > getTypeSizeInBits(AddRec->getType())) return ConstantRange::getFull(BitWidth); MaxBECount = getNoopOrZeroExtend(MaxBECount, AddRec->getType()); const SCEV *RangeWidth = getMinusOne(AddRec->getType()); const SCEV *StepAbs = getUMinExpr(Step, getNegativeSCEV(Step)); const SCEV *MaxItersWithoutWrap = getUDivExpr(RangeWidth, StepAbs); if (!isKnownPredicateViaConstantRanges(ICmpInst::ICMP_ULE, MaxBECount, MaxItersWithoutWrap)) return ConstantRange::getFull(BitWidth); ICmpInst::Predicate LEPred = IsSigned ? ICmpInst::ICMP_SLE : ICmpInst::ICMP_ULE; ICmpInst::Predicate GEPred = IsSigned ? ICmpInst::ICMP_SGE : ICmpInst::ICMP_UGE; const SCEV *End = AddRec->evaluateAtIteration(MaxBECount, *this); // We know that there is no self-wrap. Let's take Start and End values and // look at all intermediate values V1, V2, ..., Vn that IndVar takes during // the iteration. They either lie inside the range [Min(Start, End), // Max(Start, End)] or outside it: // // Case 1: RangeMin ... Start V1 ... VN End ... RangeMax; // Case 2: RangeMin Vk ... V1 Start ... End Vn ... Vk + 1 RangeMax; // // No self wrap flag guarantees that the intermediate values cannot be BOTH // outside and inside the range [Min(Start, End), Max(Start, End)]. Using that // knowledge, let's try to prove that we are dealing with Case 1. It is so if // Start <= End and step is positive, or Start >= End and step is negative. const SCEV *Start = AddRec->getStart(); ConstantRange StartRange = getRangeRef(Start, SignHint); ConstantRange EndRange = getRangeRef(End, SignHint); ConstantRange RangeBetween = StartRange.unionWith(EndRange); // If they already cover full iteration space, we will know nothing useful // even if we prove what we want to prove. if (RangeBetween.isFullSet()) return RangeBetween; // Only deal with ranges that do not wrap (i.e. RangeMin < RangeMax). bool IsWrappedSet = IsSigned ? RangeBetween.isSignWrappedSet() : RangeBetween.isWrappedSet(); if (IsWrappedSet) return ConstantRange::getFull(BitWidth); if (isKnownPositive(Step) && isKnownPredicateViaConstantRanges(LEPred, Start, End)) return RangeBetween; else if (isKnownNegative(Step) && isKnownPredicateViaConstantRanges(GEPred, Start, End)) return RangeBetween; return ConstantRange::getFull(BitWidth); } ConstantRange ScalarEvolution::getRangeViaFactoring(const SCEV *Start, const SCEV *Step, const SCEV *MaxBECount, unsigned BitWidth) { // RangeOf({C?A:B,+,C?P:Q}) == RangeOf(C?{A,+,P}:{B,+,Q}) // == RangeOf({A,+,P}) union RangeOf({B,+,Q}) struct SelectPattern { Value *Condition = nullptr; APInt TrueValue; APInt FalseValue; explicit SelectPattern(ScalarEvolution &SE, unsigned BitWidth, const SCEV *S) { Optional CastOp; APInt Offset(BitWidth, 0); assert(SE.getTypeSizeInBits(S->getType()) == BitWidth && "Should be!"); // Peel off a constant offset: if (auto *SA = dyn_cast(S)) { // In the future we could consider being smarter here and handle // {Start+Step,+,Step} too. if (SA->getNumOperands() != 2 || !isa(SA->getOperand(0))) return; Offset = cast(SA->getOperand(0))->getAPInt(); S = SA->getOperand(1); } // Peel off a cast operation if (auto *SCast = dyn_cast(S)) { CastOp = SCast->getSCEVType(); S = SCast->getOperand(); } using namespace llvm::PatternMatch; auto *SU = dyn_cast(S); const APInt *TrueVal, *FalseVal; if (!SU || !match(SU->getValue(), m_Select(m_Value(Condition), m_APInt(TrueVal), m_APInt(FalseVal)))) { Condition = nullptr; return; } TrueValue = *TrueVal; FalseValue = *FalseVal; // Re-apply the cast we peeled off earlier if (CastOp.hasValue()) switch (*CastOp) { default: llvm_unreachable("Unknown SCEV cast type!"); case scTruncate: TrueValue = TrueValue.trunc(BitWidth); FalseValue = FalseValue.trunc(BitWidth); break; case scZeroExtend: TrueValue = TrueValue.zext(BitWidth); FalseValue = FalseValue.zext(BitWidth); break; case scSignExtend: TrueValue = TrueValue.sext(BitWidth); FalseValue = FalseValue.sext(BitWidth); break; } // Re-apply the constant offset we peeled off earlier TrueValue += Offset; FalseValue += Offset; } bool isRecognized() { return Condition != nullptr; } }; SelectPattern StartPattern(*this, BitWidth, Start); if (!StartPattern.isRecognized()) return ConstantRange::getFull(BitWidth); SelectPattern StepPattern(*this, BitWidth, Step); if (!StepPattern.isRecognized()) return ConstantRange::getFull(BitWidth); if (StartPattern.Condition != StepPattern.Condition) { // We don't handle this case today; but we could, by considering four // possibilities below instead of two. I'm not sure if there are cases where // that will help over what getRange already does, though. return ConstantRange::getFull(BitWidth); } // NB! Calling ScalarEvolution::getConstant is fine, but we should not try to // construct arbitrary general SCEV expressions here. This function is called // from deep in the call stack, and calling getSCEV (on a sext instruction, // say) can end up caching a suboptimal value. // FIXME: without the explicit `this` receiver below, MSVC errors out with // C2352 and C2512 (otherwise it isn't needed). const SCEV *TrueStart = this->getConstant(StartPattern.TrueValue); const SCEV *TrueStep = this->getConstant(StepPattern.TrueValue); const SCEV *FalseStart = this->getConstant(StartPattern.FalseValue); const SCEV *FalseStep = this->getConstant(StepPattern.FalseValue); ConstantRange TrueRange = this->getRangeForAffineAR(TrueStart, TrueStep, MaxBECount, BitWidth); ConstantRange FalseRange = this->getRangeForAffineAR(FalseStart, FalseStep, MaxBECount, BitWidth); return TrueRange.unionWith(FalseRange); } SCEV::NoWrapFlags ScalarEvolution::getNoWrapFlagsFromUB(const Value *V) { if (isa(V)) return SCEV::FlagAnyWrap; const BinaryOperator *BinOp = cast(V); // Return early if there are no flags to propagate to the SCEV. SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap; if (BinOp->hasNoUnsignedWrap()) Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW); if (BinOp->hasNoSignedWrap()) Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW); if (Flags == SCEV::FlagAnyWrap) return SCEV::FlagAnyWrap; return isSCEVExprNeverPoison(BinOp) ? Flags : SCEV::FlagAnyWrap; } bool ScalarEvolution::isSCEVExprNeverPoison(const Instruction *I) { // Here we check that I is in the header of the innermost loop containing I, // since we only deal with instructions in the loop header. The actual loop we // need to check later will come from an add recurrence, but getting that // requires computing the SCEV of the operands, which can be expensive. This // check we can do cheaply to rule out some cases early. Loop *InnermostContainingLoop = LI.getLoopFor(I->getParent()); if (InnermostContainingLoop == nullptr || InnermostContainingLoop->getHeader() != I->getParent()) return false; // Only proceed if we can prove that I does not yield poison. if (!programUndefinedIfPoison(I)) return false; // At this point we know that if I is executed, then it does not wrap // according to at least one of NSW or NUW. If I is not executed, then we do // not know if the calculation that I represents would wrap. Multiple // instructions can map to the same SCEV. If we apply NSW or NUW from I to // the SCEV, we must guarantee no wrapping for that SCEV also when it is // derived from other instructions that map to the same SCEV. We cannot make // that guarantee for cases where I is not executed. So we need to find the // loop that I is considered in relation to and prove that I is executed for // every iteration of that loop. That implies that the value that I // calculates does not wrap anywhere in the loop, so then we can apply the // flags to the SCEV. // // We check isLoopInvariant to disambiguate in case we are adding recurrences // from different loops, so that we know which loop to prove that I is // executed in. for (unsigned OpIndex = 0; OpIndex < I->getNumOperands(); ++OpIndex) { // I could be an extractvalue from a call to an overflow intrinsic. // TODO: We can do better here in some cases. if (!isSCEVable(I->getOperand(OpIndex)->getType())) return false; const SCEV *Op = getSCEV(I->getOperand(OpIndex)); if (auto *AddRec = dyn_cast(Op)) { bool AllOtherOpsLoopInvariant = true; for (unsigned OtherOpIndex = 0; OtherOpIndex < I->getNumOperands(); ++OtherOpIndex) { if (OtherOpIndex != OpIndex) { const SCEV *OtherOp = getSCEV(I->getOperand(OtherOpIndex)); if (!isLoopInvariant(OtherOp, AddRec->getLoop())) { AllOtherOpsLoopInvariant = false; break; } } } if (AllOtherOpsLoopInvariant && isGuaranteedToExecuteForEveryIteration(I, AddRec->getLoop())) return true; } } return false; } bool ScalarEvolution::isAddRecNeverPoison(const Instruction *I, const Loop *L) { // If we know that \c I can never be poison period, then that's enough. if (isSCEVExprNeverPoison(I)) return true; // For an add recurrence specifically, we assume that infinite loops without // side effects are undefined behavior, and then reason as follows: // // If the add recurrence is poison in any iteration, it is poison on all // future iterations (since incrementing poison yields poison). If the result // of the add recurrence is fed into the loop latch condition and the loop // does not contain any throws or exiting blocks other than the latch, we now // have the ability to "choose" whether the backedge is taken or not (by // choosing a sufficiently evil value for the poison feeding into the branch) // for every iteration including and after the one in which \p I first became // poison. There are two possibilities (let's call the iteration in which \p // I first became poison as K): // // 1. In the set of iterations including and after K, the loop body executes // no side effects. In this case executing the backege an infinte number // of times will yield undefined behavior. // // 2. In the set of iterations including and after K, the loop body executes // at least one side effect. In this case, that specific instance of side // effect is control dependent on poison, which also yields undefined // behavior. auto *ExitingBB = L->getExitingBlock(); auto *LatchBB = L->getLoopLatch(); if (!ExitingBB || !LatchBB || ExitingBB != LatchBB) return false; SmallPtrSet Pushed; SmallVector PoisonStack; // We start by assuming \c I, the post-inc add recurrence, is poison. Only // things that are known to be poison under that assumption go on the // PoisonStack. Pushed.insert(I); PoisonStack.push_back(I); bool LatchControlDependentOnPoison = false; while (!PoisonStack.empty() && !LatchControlDependentOnPoison) { const Instruction *Poison = PoisonStack.pop_back_val(); for (auto *PoisonUser : Poison->users()) { if (propagatesPoison(cast(PoisonUser))) { if (Pushed.insert(cast(PoisonUser)).second) PoisonStack.push_back(cast(PoisonUser)); } else if (auto *BI = dyn_cast(PoisonUser)) { assert(BI->isConditional() && "Only possibility!"); if (BI->getParent() == LatchBB) { LatchControlDependentOnPoison = true; break; } } } } return LatchControlDependentOnPoison && loopHasNoAbnormalExits(L); } ScalarEvolution::LoopProperties ScalarEvolution::getLoopProperties(const Loop *L) { using LoopProperties = ScalarEvolution::LoopProperties; auto Itr = LoopPropertiesCache.find(L); if (Itr == LoopPropertiesCache.end()) { auto HasSideEffects = [](Instruction *I) { if (auto *SI = dyn_cast(I)) return !SI->isSimple(); return I->mayThrow() || I->mayWriteToMemory(); }; LoopProperties LP = {/* HasNoAbnormalExits */ true, /*HasNoSideEffects*/ true}; for (auto *BB : L->getBlocks()) for (auto &I : *BB) { if (!isGuaranteedToTransferExecutionToSuccessor(&I)) LP.HasNoAbnormalExits = false; if (HasSideEffects(&I)) LP.HasNoSideEffects = false; if (!LP.HasNoAbnormalExits && !LP.HasNoSideEffects) break; // We're already as pessimistic as we can get. } auto InsertPair = LoopPropertiesCache.insert({L, LP}); assert(InsertPair.second && "We just checked!"); Itr = InsertPair.first; } return Itr->second; } bool ScalarEvolution::loopIsFiniteByAssumption(const Loop *L) { // A mustprogress loop without side effects must be finite. // TODO: The check used here is very conservative. It's only *specific* // side effects which are well defined in infinite loops. return isMustProgress(L) && loopHasNoSideEffects(L); } const SCEV *ScalarEvolution::createSCEV(Value *V) { if (!isSCEVable(V->getType())) return getUnknown(V); if (Instruction *I = dyn_cast(V)) { // 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(UndefValue::get(V->getType())); } else if (ConstantInt *CI = dyn_cast(V)) return getConstant(CI); else if (GlobalAlias *GA = dyn_cast(V)) return GA->isInterposable() ? getUnknown(V) : getSCEV(GA->getAliasee()); else if (!isa(V)) return getUnknown(V); Operator *U = cast(V); if (auto BO = MatchBinaryOp(U, DT)) { switch (BO->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. SmallVector AddOps; do { if (BO->Op) { if (auto *OpSCEV = getExistingSCEV(BO->Op)) { AddOps.push_back(OpSCEV); break; } // If a NUW or NSW flag can be applied to the SCEV for this // addition, then compute the SCEV for this addition by itself // with a separate call to getAddExpr. We need to do that // instead of pushing the operands of the addition onto AddOps, // since the flags are only known to apply to this particular // addition - they may not apply to other additions that can be // formed with operands from AddOps. const SCEV *RHS = getSCEV(BO->RHS); SCEV::NoWrapFlags Flags = getNoWrapFlagsFromUB(BO->Op); if (Flags != SCEV::FlagAnyWrap) { const SCEV *LHS = getSCEV(BO->LHS); if (BO->Opcode == Instruction::Sub) AddOps.push_back(getMinusSCEV(LHS, RHS, Flags)); else AddOps.push_back(getAddExpr(LHS, RHS, Flags)); break; } } if (BO->Opcode == Instruction::Sub) AddOps.push_back(getNegativeSCEV(getSCEV(BO->RHS))); else AddOps.push_back(getSCEV(BO->RHS)); auto NewBO = MatchBinaryOp(BO->LHS, DT); if (!NewBO || (NewBO->Opcode != Instruction::Add && NewBO->Opcode != Instruction::Sub)) { AddOps.push_back(getSCEV(BO->LHS)); break; } BO = NewBO; } while (true); return getAddExpr(AddOps); } case Instruction::Mul: { SmallVector MulOps; do { if (BO->Op) { if (auto *OpSCEV = getExistingSCEV(BO->Op)) { MulOps.push_back(OpSCEV); break; } SCEV::NoWrapFlags Flags = getNoWrapFlagsFromUB(BO->Op); if (Flags != SCEV::FlagAnyWrap) { MulOps.push_back( getMulExpr(getSCEV(BO->LHS), getSCEV(BO->RHS), Flags)); break; } } MulOps.push_back(getSCEV(BO->RHS)); auto NewBO = MatchBinaryOp(BO->LHS, DT); if (!NewBO || NewBO->Opcode != Instruction::Mul) { MulOps.push_back(getSCEV(BO->LHS)); break; } BO = NewBO; } while (true); return getMulExpr(MulOps); } case Instruction::UDiv: return getUDivExpr(getSCEV(BO->LHS), getSCEV(BO->RHS)); case Instruction::URem: return getURemExpr(getSCEV(BO->LHS), getSCEV(BO->RHS)); case Instruction::Sub: { SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap; if (BO->Op) Flags = getNoWrapFlagsFromUB(BO->Op); return getMinusSCEV(getSCEV(BO->LHS), getSCEV(BO->RHS), Flags); } 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(BO->RHS)) { if (CI->isZero()) return getSCEV(BO->RHS); if (CI->isMinusOne()) return getSCEV(BO->LHS); 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(); KnownBits Known(BitWidth); computeKnownBits(BO->LHS, Known, getDataLayout(), 0, &AC, nullptr, &DT); APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ - TZ).shl(TZ); if ((LZ != 0 || TZ != 0) && !((~A & ~Known.Zero) & EffectiveMask)) { const SCEV *MulCount = getConstant(APInt::getOneBitSet(BitWidth, TZ)); const SCEV *LHS = getSCEV(BO->LHS); const SCEV *ShiftedLHS = nullptr; if (auto *LHSMul = dyn_cast(LHS)) { if (auto *OpC = dyn_cast(LHSMul->getOperand(0))) { // For an expression like (x * 8) & 8, simplify the multiply. unsigned MulZeros = OpC->getAPInt().countTrailingZeros(); unsigned GCD = std::min(MulZeros, TZ); APInt DivAmt = APInt::getOneBitSet(BitWidth, TZ - GCD); SmallVector MulOps; MulOps.push_back(getConstant(OpC->getAPInt().lshr(GCD))); MulOps.append(LHSMul->op_begin() + 1, LHSMul->op_end()); auto *NewMul = getMulExpr(MulOps, LHSMul->getNoWrapFlags()); ShiftedLHS = getUDivExpr(NewMul, getConstant(DivAmt)); } } if (!ShiftedLHS) ShiftedLHS = getUDivExpr(LHS, MulCount); return getMulExpr( getZeroExtendExpr( getTruncateExpr(ShiftedLHS, IntegerType::get(getContext(), BitWidth - LZ - TZ)), BO->LHS->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(BO->RHS)) { const SCEV *LHS = getSCEV(BO->LHS); const APInt &CIVal = CI->getValue(); if (GetMinTrailingZeros(LHS) >= (CIVal.getBitWidth() - CIVal.countLeadingZeros())) { // Build a plain add SCEV. return getAddExpr(LHS, getSCEV(CI), (SCEV::NoWrapFlags)(SCEV::FlagNUW | SCEV::FlagNSW)); } } break; case Instruction::Xor: if (ConstantInt *CI = dyn_cast(BO->RHS)) { // If the RHS of xor is -1, then this is a not operation. if (CI->isMinusOne()) return getNotSCEV(getSCEV(BO->LHS)); // 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 (auto *LBO = dyn_cast(BO->LHS)) if (ConstantInt *LCI = dyn_cast(LBO->getOperand(1))) if (LBO->getOpcode() == Instruction::And && LCI->getValue() == CI->getValue()) if (const SCEVZeroExtendExpr *Z = dyn_cast(getSCEV(BO->LHS))) { Type *UTy = BO->LHS->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 (CI->getValue().isMask(Z0TySize)) 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.isSignMask()) 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(BO->RHS)) { uint32_t BitWidth = cast(SA->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; // We can safely preserve the nuw flag in all cases. It's also safe to // turn a nuw nsw shl into a nuw nsw mul. However, nsw in isolation // requires special handling. It can be preserved as long as we're not // left shifting by bitwidth - 1. auto Flags = SCEV::FlagAnyWrap; if (BO->Op) { auto MulFlags = getNoWrapFlagsFromUB(BO->Op); if ((MulFlags & SCEV::FlagNSW) && ((MulFlags & SCEV::FlagNUW) || SA->getValue().ult(BitWidth - 1))) Flags = (SCEV::NoWrapFlags)(Flags | SCEV::FlagNSW); if (MulFlags & SCEV::FlagNUW) Flags = (SCEV::NoWrapFlags)(Flags | SCEV::FlagNUW); } Constant *X = ConstantInt::get( getContext(), APInt::getOneBitSet(BitWidth, SA->getZExtValue())); return getMulExpr(getSCEV(BO->LHS), getSCEV(X), Flags); } break; case Instruction::AShr: { // AShr X, C, where C is a constant. ConstantInt *CI = dyn_cast(BO->RHS); if (!CI) break; Type *OuterTy = BO->LHS->getType(); uint64_t BitWidth = getTypeSizeInBits(OuterTy); // 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; if (CI->isZero()) return getSCEV(BO->LHS); // shift by zero --> noop uint64_t AShrAmt = CI->getZExtValue(); Type *TruncTy = IntegerType::get(getContext(), BitWidth - AShrAmt); Operator *L = dyn_cast(BO->LHS); if (L && L->getOpcode() == Instruction::Shl) { // X = Shl A, n // Y = AShr X, m // Both n and m are constant. const SCEV *ShlOp0SCEV = getSCEV(L->getOperand(0)); if (L->getOperand(1) == BO->RHS) // For a two-shift sext-inreg, i.e. n = m, // use sext(trunc(x)) as the SCEV expression. return getSignExtendExpr( getTruncateExpr(ShlOp0SCEV, TruncTy), OuterTy); ConstantInt *ShlAmtCI = dyn_cast(L->getOperand(1)); if (ShlAmtCI && ShlAmtCI->getValue().ult(BitWidth)) { uint64_t ShlAmt = ShlAmtCI->getZExtValue(); if (ShlAmt > AShrAmt) { // When n > m, use sext(mul(trunc(x), 2^(n-m)))) as the SCEV // expression. We already checked that ShlAmt < BitWidth, so // the multiplier, 1 << (ShlAmt - AShrAmt), fits into TruncTy as // ShlAmt - AShrAmt < Amt. APInt Mul = APInt::getOneBitSet(BitWidth - AShrAmt, ShlAmt - AShrAmt); return getSignExtendExpr( getMulExpr(getTruncateExpr(ShlOp0SCEV, TruncTy), getConstant(Mul)), OuterTy); } } } break; } } } switch (U->getOpcode()) { 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: if (auto BO = MatchBinaryOp(U->getOperand(0), DT)) { // The NSW flag of a subtract does not always survive the conversion to // A + (-1)*B. By pushing sign extension onto its operands we are much // more likely to preserve NSW and allow later AddRec optimisations. // // NOTE: This is effectively duplicating this logic from getSignExtend: // sext((A + B + ...)) --> (sext(A) + sext(B) + ...) // but by that point the NSW information has potentially been lost. if (BO->Opcode == Instruction::Sub && BO->IsNSW) { Type *Ty = U->getType(); auto *V1 = getSignExtendExpr(getSCEV(BO->LHS), Ty); auto *V2 = getSignExtendExpr(getSCEV(BO->RHS), Ty); return getMinusSCEV(V1, V2, SCEV::FlagNSW); } } return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType()); case Instruction::BitCast: // BitCasts are no-op casts so we just eliminate the cast. if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType())) return getSCEV(U->getOperand(0)); break; case Instruction::PtrToInt: { // Pointer to integer cast is straight-forward, so do model it. const SCEV *Op = getSCEV(U->getOperand(0)); Type *DstIntTy = U->getType(); // But only if effective SCEV (integer) type is wide enough to represent // all possible pointer values. const SCEV *IntOp = getPtrToIntExpr(Op, DstIntTy); if (isa(IntOp)) return getUnknown(V); return IntOp; } case Instruction::IntToPtr: // Just don't deal with inttoptr casts. return getUnknown(V); case Instruction::SDiv: // If both operands are non-negative, this is just an udiv. if (isKnownNonNegative(getSCEV(U->getOperand(0))) && isKnownNonNegative(getSCEV(U->getOperand(1)))) return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(U->getOperand(1))); break; case Instruction::SRem: // If both operands are non-negative, this is just an urem. if (isKnownNonNegative(getSCEV(U->getOperand(0))) && isKnownNonNegative(getSCEV(U->getOperand(1)))) return getURemExpr(getSCEV(U->getOperand(0)), getSCEV(U->getOperand(1))); break; case Instruction::GetElementPtr: return createNodeForGEP(cast(U)); case Instruction::PHI: return createNodeForPHI(cast(U)); case Instruction::Select: // U can also be a select constant expr, which let fall through. Since // createNodeForSelect only works for a condition that is an `ICmpInst`, and // constant expressions cannot have instructions as operands, we'd have // returned getUnknown for a select constant expressions anyway. if (isa(U)) return createNodeForSelectOrPHI(cast(U), U->getOperand(0), U->getOperand(1), U->getOperand(2)); break; case Instruction::Call: case Instruction::Invoke: if (Value *RV = cast(U)->getReturnedArgOperand()) return getSCEV(RV); if (auto *II = dyn_cast(U)) { switch (II->getIntrinsicID()) { case Intrinsic::abs: return getAbsExpr( getSCEV(II->getArgOperand(0)), /*IsNSW=*/cast(II->getArgOperand(1))->isOne()); case Intrinsic::umax: return getUMaxExpr(getSCEV(II->getArgOperand(0)), getSCEV(II->getArgOperand(1))); case Intrinsic::umin: return getUMinExpr(getSCEV(II->getArgOperand(0)), getSCEV(II->getArgOperand(1))); case Intrinsic::smax: return getSMaxExpr(getSCEV(II->getArgOperand(0)), getSCEV(II->getArgOperand(1))); case Intrinsic::smin: return getSMinExpr(getSCEV(II->getArgOperand(0)), getSCEV(II->getArgOperand(1))); case Intrinsic::usub_sat: { const SCEV *X = getSCEV(II->getArgOperand(0)); const SCEV *Y = getSCEV(II->getArgOperand(1)); const SCEV *ClampedY = getUMinExpr(X, Y); return getMinusSCEV(X, ClampedY, SCEV::FlagNUW); } case Intrinsic::uadd_sat: { const SCEV *X = getSCEV(II->getArgOperand(0)); const SCEV *Y = getSCEV(II->getArgOperand(1)); const SCEV *ClampedX = getUMinExpr(X, getNotSCEV(Y)); return getAddExpr(ClampedX, Y, SCEV::FlagNUW); } case Intrinsic::start_loop_iterations: // A start_loop_iterations is just equivalent to the first operand for // SCEV purposes. return getSCEV(II->getArgOperand(0)); default: break; } } break; } return getUnknown(V); } //===----------------------------------------------------------------------===// // Iteration Count Computation Code // const SCEV *ScalarEvolution::getTripCountFromExitCount(const SCEV *ExitCount) { // Get the trip count from the BE count by adding 1. Overflow, results // in zero which means "unknown". return getAddExpr(ExitCount, getOne(ExitCount->getType())); } static unsigned getConstantTripCount(const SCEVConstant *ExitCount) { 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::getSmallConstantTripCount(const Loop *L) { auto *ExitCount = dyn_cast(getBackedgeTakenCount(L, Exact)); return getConstantTripCount(ExitCount); } unsigned ScalarEvolution::getSmallConstantTripCount(const Loop *L, const 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)); return getConstantTripCount(ExitCount); } unsigned ScalarEvolution::getSmallConstantMaxTripCount(const Loop *L) { const auto *MaxExitCount = dyn_cast(getConstantMaxBackedgeTakenCount(L)); return getConstantTripCount(MaxExitCount); } unsigned ScalarEvolution::getSmallConstantTripMultiple(const Loop *L) { SmallVector ExitingBlocks; L->getExitingBlocks(ExitingBlocks); Optional Res = None; for (auto *ExitingBB : ExitingBlocks) { unsigned Multiple = getSmallConstantTripMultiple(L, ExitingBB); if (!Res) Res = Multiple; Res = (unsigned)GreatestCommonDivisor64(*Res, Multiple); } return Res.getValueOr(1); } unsigned ScalarEvolution::getSmallConstantTripMultiple(const Loop *L, const SCEV *ExitCount) { if (ExitCount == getCouldNotCompute()) return 1; // Get the trip count const SCEV *TCExpr = getTripCountFromExitCount(ExitCount); const SCEVConstant *TC = dyn_cast(TCExpr); if (!TC) // Attempt to factor more general cases. Returns the greatest power of // two divisor. If overflow happens, the trip count expression is still // divisible by the greatest power of 2 divisor returned. return 1U << std::min((uint32_t)31, GetMinTrailingZeros(applyLoopGuards(TCExpr, L))); ConstantInt *Result = TC->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(); } /// 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(const Loop *L, const 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); return getSmallConstantTripMultiple(L, ExitCount); } const SCEV *ScalarEvolution::getExitCount(const Loop *L, const BasicBlock *ExitingBlock, ExitCountKind Kind) { switch (Kind) { case Exact: case SymbolicMaximum: return getBackedgeTakenInfo(L).getExact(ExitingBlock, this); case ConstantMaximum: return getBackedgeTakenInfo(L).getConstantMax(ExitingBlock, this); }; llvm_unreachable("Invalid ExitCountKind!"); } const SCEV * ScalarEvolution::getPredicatedBackedgeTakenCount(const Loop *L, SCEVUnionPredicate &Preds) { return getPredicatedBackedgeTakenInfo(L).getExact(L, this, &Preds); } const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L, ExitCountKind Kind) { switch (Kind) { case Exact: return getBackedgeTakenInfo(L).getExact(L, this); case ConstantMaximum: return getBackedgeTakenInfo(L).getConstantMax(this); case SymbolicMaximum: return getBackedgeTakenInfo(L).getSymbolicMax(L, this); }; llvm_unreachable("Invalid ExitCountKind!"); } bool ScalarEvolution::isBackedgeTakenCountMaxOrZero(const Loop *L) { return getBackedgeTakenInfo(L).isConstantMaxOrZero(this); } /// 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 (PHINode &PN : Header->phis()) Worklist.push_back(&PN); } const ScalarEvolution::BackedgeTakenInfo & ScalarEvolution::getPredicatedBackedgeTakenInfo(const Loop *L) { auto &BTI = getBackedgeTakenInfo(L); if (BTI.hasFullInfo()) return BTI; auto Pair = PredicatedBackedgeTakenCounts.insert({L, BackedgeTakenInfo()}); if (!Pair.second) return Pair.first->second; BackedgeTakenInfo Result = computeBackedgeTakenCount(L, /*AllowPredicates=*/true); return PredicatedBackedgeTakenCounts.find(L)->second = std::move(Result); } 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({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); // In product build, there are no usage of statistic. (void)NumTripCountsComputed; (void)NumTripCountsNotComputed; #if LLVM_ENABLE_STATS || !defined(NDEBUG) const SCEV *BEExact = Result.getExact(L, this); if (BEExact != getCouldNotCompute()) { assert(isLoopInvariant(BEExact, L) && isLoopInvariant(Result.getConstantMax(this), L) && "Computed backedge-taken count isn't loop invariant for loop!"); ++NumTripCountsComputed; } else if (Result.getConstantMax(this) == getCouldNotCompute() && isa(L->getHeader()->begin())) { // Only count loops that have phi nodes as not being computable. ++NumTripCountsNotComputed; } #endif // LLVM_ENABLE_STATS || !defined(NDEBUG) // 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 Discovered; while (!Worklist.empty()) { Instruction *I = Worklist.pop_back_val(); 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)) { eraseValueFromMap(It->first); forgetMemoizedResults(Old); } if (PHINode *PN = dyn_cast(I)) ConstantEvolutionLoopExitValue.erase(PN); } // Since we don't need to invalidate anything for correctness and we're // only invalidating to make SCEV's results more precise, we get to stop // early to avoid invalidating too much. This is especially important in // cases like: // // %v = f(pn0, pn1) // pn0 and pn1 used through some other phi node // loop0: // %pn0 = phi // ... // loop1: // %pn1 = phi // ... // // where both loop0 and loop1's backedge taken count uses the SCEV // expression for %v. If we don't have the early stop below then in cases // like the above, getBackedgeTakenInfo(loop1) will clear out the trip // count for loop0 and getBackedgeTakenInfo(loop0) will clear out the trip // count for loop1, effectively nullifying SCEV's trip count cache. for (auto *U : I->users()) if (auto *I = dyn_cast(U)) { auto *LoopForUser = LI.getLoopFor(I->getParent()); if (LoopForUser && L->contains(LoopForUser) && Discovered.insert(I).second) Worklist.push_back(I); } } } // 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 = std::move(Result); } void ScalarEvolution::forgetAllLoops() { // This method is intended to forget all info about loops. It should // invalidate caches as if the following happened: // - The trip counts of all loops have changed arbitrarily // - Every llvm::Value has been updated in place to produce a different // result. BackedgeTakenCounts.clear(); PredicatedBackedgeTakenCounts.clear(); LoopPropertiesCache.clear(); ConstantEvolutionLoopExitValue.clear(); ValueExprMap.clear(); ValuesAtScopes.clear(); LoopDispositions.clear(); BlockDispositions.clear(); UnsignedRanges.clear(); SignedRanges.clear(); ExprValueMap.clear(); HasRecMap.clear(); MinTrailingZerosCache.clear(); PredicatedSCEVRewrites.clear(); } void ScalarEvolution::forgetLoop(const Loop *L) { SmallVector LoopWorklist(1, L); SmallVector Worklist; SmallPtrSet Visited; // Iterate over all the loops and sub-loops to drop SCEV information. while (!LoopWorklist.empty()) { auto *CurrL = LoopWorklist.pop_back_val(); // Drop any stored trip count value. BackedgeTakenCounts.erase(CurrL); PredicatedBackedgeTakenCounts.erase(CurrL); // Drop information about predicated SCEV rewrites for this loop. for (auto I = PredicatedSCEVRewrites.begin(); I != PredicatedSCEVRewrites.end();) { std::pair Entry = I->first; if (Entry.second == CurrL) PredicatedSCEVRewrites.erase(I++); else ++I; } auto LoopUsersItr = LoopUsers.find(CurrL); if (LoopUsersItr != LoopUsers.end()) { for (auto *S : LoopUsersItr->second) forgetMemoizedResults(S); LoopUsers.erase(LoopUsersItr); } // Drop information about expressions based on loop-header PHIs. PushLoopPHIs(CurrL, Worklist); 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()) { eraseValueFromMap(It->first); forgetMemoizedResults(It->second); if (PHINode *PN = dyn_cast(I)) ConstantEvolutionLoopExitValue.erase(PN); } PushDefUseChildren(I, Worklist); } LoopPropertiesCache.erase(CurrL); // Forget all contained loops too, to avoid dangling entries in the // ValuesAtScopes map. LoopWorklist.append(CurrL->begin(), CurrL->end()); } } void ScalarEvolution::forgetTopmostLoop(const Loop *L) { while (Loop *Parent = L->getParentLoop()) L = Parent; forgetLoop(L); } 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()) { eraseValueFromMap(It->first); forgetMemoizedResults(It->second); if (PHINode *PN = dyn_cast(I)) ConstantEvolutionLoopExitValue.erase(PN); } PushDefUseChildren(I, Worklist); } } void ScalarEvolution::forgetLoopDispositions(const Loop *L) { LoopDispositions.clear(); } /// Get the exact loop backedge taken count considering all loop exits. A /// computable result can only be returned for loops with all exiting blocks /// dominating the latch. 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 exiting block using getExact(ExitingBlock, SE). const SCEV * ScalarEvolution::BackedgeTakenInfo::getExact(const Loop *L, ScalarEvolution *SE, SCEVUnionPredicate *Preds) const { // If any exits were not computable, the loop is not computable. if (!isComplete() || ExitNotTaken.empty()) return SE->getCouldNotCompute(); const BasicBlock *Latch = L->getLoopLatch(); // All exiting blocks we have collected must dominate the only backedge. if (!Latch) return SE->getCouldNotCompute(); // All exiting blocks we have gathered dominate loop's latch, so exact trip // count is simply a minimum out of all these calculated exit counts. SmallVector Ops; for (auto &ENT : ExitNotTaken) { const SCEV *BECount = ENT.ExactNotTaken; assert(BECount != SE->getCouldNotCompute() && "Bad exit SCEV!"); assert(SE->DT.dominates(ENT.ExitingBlock, Latch) && "We should only have known counts for exiting blocks that dominate " "latch!"); Ops.push_back(BECount); if (Preds && !ENT.hasAlwaysTruePredicate()) Preds->add(ENT.Predicate.get()); assert((Preds || ENT.hasAlwaysTruePredicate()) && "Predicate should be always true!"); } return SE->getUMinFromMismatchedTypes(Ops); } /// Get the exact not taken count for this loop exit. const SCEV * ScalarEvolution::BackedgeTakenInfo::getExact(const BasicBlock *ExitingBlock, ScalarEvolution *SE) const { for (auto &ENT : ExitNotTaken) if (ENT.ExitingBlock == ExitingBlock && ENT.hasAlwaysTruePredicate()) return ENT.ExactNotTaken; return SE->getCouldNotCompute(); } const SCEV *ScalarEvolution::BackedgeTakenInfo::getConstantMax( const BasicBlock *ExitingBlock, ScalarEvolution *SE) const { for (auto &ENT : ExitNotTaken) if (ENT.ExitingBlock == ExitingBlock && ENT.hasAlwaysTruePredicate()) return ENT.MaxNotTaken; return SE->getCouldNotCompute(); } /// getConstantMax - Get the constant max backedge taken count for the loop. const SCEV * ScalarEvolution::BackedgeTakenInfo::getConstantMax(ScalarEvolution *SE) const { auto PredicateNotAlwaysTrue = [](const ExitNotTakenInfo &ENT) { return !ENT.hasAlwaysTruePredicate(); }; if (any_of(ExitNotTaken, PredicateNotAlwaysTrue) || !getConstantMax()) return SE->getCouldNotCompute(); assert((isa(getConstantMax()) || isa(getConstantMax())) && "No point in having a non-constant max backedge taken count!"); return getConstantMax(); } const SCEV * ScalarEvolution::BackedgeTakenInfo::getSymbolicMax(const Loop *L, ScalarEvolution *SE) { if (!SymbolicMax) SymbolicMax = SE->computeSymbolicMaxBackedgeTakenCount(L); return SymbolicMax; } bool ScalarEvolution::BackedgeTakenInfo::isConstantMaxOrZero( ScalarEvolution *SE) const { auto PredicateNotAlwaysTrue = [](const ExitNotTakenInfo &ENT) { return !ENT.hasAlwaysTruePredicate(); }; return MaxOrZero && !any_of(ExitNotTaken, PredicateNotAlwaysTrue); } bool ScalarEvolution::BackedgeTakenInfo::hasOperand(const SCEV *S) const { return Operands.contains(S); } ScalarEvolution::ExitLimit::ExitLimit(const SCEV *E) : ExitLimit(E, E, false, None) { } ScalarEvolution::ExitLimit::ExitLimit( const SCEV *E, const SCEV *M, bool MaxOrZero, ArrayRef *> PredSetList) : ExactNotTaken(E), MaxNotTaken(M), MaxOrZero(MaxOrZero) { assert((isa(ExactNotTaken) || !isa(MaxNotTaken)) && "Exact is not allowed to be less precise than Max"); assert((isa(MaxNotTaken) || isa(MaxNotTaken)) && "No point in having a non-constant max backedge taken count!"); for (auto *PredSet : PredSetList) for (auto *P : *PredSet) addPredicate(P); assert((isa(E) || !E->getType()->isPointerTy()) && "Backedge count should be int"); assert((isa(M) || !M->getType()->isPointerTy()) && "Max backedge count should be int"); } ScalarEvolution::ExitLimit::ExitLimit( const SCEV *E, const SCEV *M, bool MaxOrZero, const SmallPtrSetImpl &PredSet) : ExitLimit(E, M, MaxOrZero, {&PredSet}) { } ScalarEvolution::ExitLimit::ExitLimit(const SCEV *E, const SCEV *M, bool MaxOrZero) : ExitLimit(E, M, MaxOrZero, None) { } class SCEVRecordOperands { SmallPtrSetImpl &Operands; public: SCEVRecordOperands(SmallPtrSetImpl &Operands) : Operands(Operands) {} bool follow(const SCEV *S) { Operands.insert(S); return true; } bool isDone() { return false; } }; /// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each /// computable exit into a persistent ExitNotTakenInfo array. ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo( ArrayRef ExitCounts, bool IsComplete, const SCEV *ConstantMax, bool MaxOrZero) : ConstantMax(ConstantMax), IsComplete(IsComplete), MaxOrZero(MaxOrZero) { using EdgeExitInfo = ScalarEvolution::BackedgeTakenInfo::EdgeExitInfo; ExitNotTaken.reserve(ExitCounts.size()); std::transform( ExitCounts.begin(), ExitCounts.end(), std::back_inserter(ExitNotTaken), [&](const EdgeExitInfo &EEI) { BasicBlock *ExitBB = EEI.first; const ExitLimit &EL = EEI.second; if (EL.Predicates.empty()) return ExitNotTakenInfo(ExitBB, EL.ExactNotTaken, EL.MaxNotTaken, nullptr); std::unique_ptr Predicate(new SCEVUnionPredicate); for (auto *Pred : EL.Predicates) Predicate->add(Pred); return ExitNotTakenInfo(ExitBB, EL.ExactNotTaken, EL.MaxNotTaken, std::move(Predicate)); }); assert((isa(ConstantMax) || isa(ConstantMax)) && "No point in having a non-constant max backedge taken count!"); SCEVRecordOperands RecordOperands(Operands); SCEVTraversal ST(RecordOperands); if (!isa(ConstantMax)) ST.visitAll(ConstantMax); for (auto &ENT : ExitNotTaken) if (!isa(ENT.ExactNotTaken)) ST.visitAll(ENT.ExactNotTaken); } /// Compute the number of times the backedge of the specified loop will execute. ScalarEvolution::BackedgeTakenInfo ScalarEvolution::computeBackedgeTakenCount(const Loop *L, bool AllowPredicates) { SmallVector ExitingBlocks; L->getExitingBlocks(ExitingBlocks); using EdgeExitInfo = ScalarEvolution::BackedgeTakenInfo::EdgeExitInfo; SmallVector ExitCounts; bool CouldComputeBECount = true; BasicBlock *Latch = L->getLoopLatch(); // may be NULL. const SCEV *MustExitMaxBECount = nullptr; const SCEV *MayExitMaxBECount = nullptr; bool MustExitMaxOrZero = false; // Compute the ExitLimit for each loop exit. Use this to populate ExitCounts // and compute maxBECount. // Do a union of all the predicates here. for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) { BasicBlock *ExitBB = ExitingBlocks[i]; // We canonicalize untaken exits to br (constant), ignore them so that // proving an exit untaken doesn't negatively impact our ability to reason // about the loop as whole. if (auto *BI = dyn_cast(ExitBB->getTerminator())) if (auto *CI = dyn_cast(BI->getCondition())) { bool ExitIfTrue = !L->contains(BI->getSuccessor(0)); if ((ExitIfTrue && CI->isZero()) || (!ExitIfTrue && CI->isOne())) continue; } ExitLimit EL = computeExitLimit(L, ExitBB, AllowPredicates); assert((AllowPredicates || EL.Predicates.empty()) && "Predicated exit limit when predicates are not allowed!"); // 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.ExactNotTaken == 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.emplace_back(ExitBB, EL); // 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.MaxNotTaken of computable // LoopMustExits. Otherwise, MaxBECount is conservatively the maximum // EL.MaxNotTaken, where CouldNotCompute is considered greater than any // computable EL.MaxNotTaken. if (EL.MaxNotTaken != getCouldNotCompute() && Latch && DT.dominates(ExitBB, Latch)) { if (!MustExitMaxBECount) { MustExitMaxBECount = EL.MaxNotTaken; MustExitMaxOrZero = EL.MaxOrZero; } else { MustExitMaxBECount = getUMinFromMismatchedTypes(MustExitMaxBECount, EL.MaxNotTaken); } } else if (MayExitMaxBECount != getCouldNotCompute()) { if (!MayExitMaxBECount || EL.MaxNotTaken == getCouldNotCompute()) MayExitMaxBECount = EL.MaxNotTaken; else { MayExitMaxBECount = getUMaxFromMismatchedTypes(MayExitMaxBECount, EL.MaxNotTaken); } } } const SCEV *MaxBECount = MustExitMaxBECount ? MustExitMaxBECount : (MayExitMaxBECount ? MayExitMaxBECount : getCouldNotCompute()); // The loop backedge will be taken the maximum or zero times if there's // a single exit that must be taken the maximum or zero times. bool MaxOrZero = (MustExitMaxOrZero && ExitingBlocks.size() == 1); return BackedgeTakenInfo(std::move(ExitCounts), CouldComputeBECount, MaxBECount, MaxOrZero); } ScalarEvolution::ExitLimit ScalarEvolution::computeExitLimit(const Loop *L, BasicBlock *ExitingBlock, bool AllowPredicates) { assert(L->contains(ExitingBlock) && "Exit count for non-loop block?"); // If our exiting block does not dominate the latch, then its connection with // loop's exit limit may be far from trivial. const BasicBlock *Latch = L->getLoopLatch(); if (!Latch || !DT.dominates(ExitingBlock, Latch)) return getCouldNotCompute(); bool IsOnlyExit = (L->getExitingBlock() != nullptr); Instruction *Term = ExitingBlock->getTerminator(); if (BranchInst *BI = dyn_cast(Term)) { assert(BI->isConditional() && "If unconditional, it can't be in loop!"); bool ExitIfTrue = !L->contains(BI->getSuccessor(0)); assert(ExitIfTrue == L->contains(BI->getSuccessor(1)) && "It should have one successor in loop and one exit block!"); // Proceed to the next level to examine the exit condition expression. return computeExitLimitFromCond( L, BI->getCondition(), ExitIfTrue, /*ControlsExit=*/IsOnlyExit, AllowPredicates); } if (SwitchInst *SI = dyn_cast(Term)) { // For switch, make sure that there is a single exit from the loop. BasicBlock *Exit = nullptr; for (auto *SBB : successors(ExitingBlock)) if (!L->contains(SBB)) { if (Exit) // Multiple exit successors. return getCouldNotCompute(); Exit = SBB; } assert(Exit && "Exiting block must have at least one exit"); return computeExitLimitFromSingleExitSwitch(L, SI, Exit, /*ControlsExit=*/IsOnlyExit); } return getCouldNotCompute(); } ScalarEvolution::ExitLimit ScalarEvolution::computeExitLimitFromCond( const Loop *L, Value *ExitCond, bool ExitIfTrue, bool ControlsExit, bool AllowPredicates) { ScalarEvolution::ExitLimitCacheTy Cache(L, ExitIfTrue, AllowPredicates); return computeExitLimitFromCondCached(Cache, L, ExitCond, ExitIfTrue, ControlsExit, AllowPredicates); } Optional ScalarEvolution::ExitLimitCache::find(const Loop *L, Value *ExitCond, bool ExitIfTrue, bool ControlsExit, bool AllowPredicates) { (void)this->L; (void)this->ExitIfTrue; (void)this->AllowPredicates; assert(this->L == L && this->ExitIfTrue == ExitIfTrue && this->AllowPredicates == AllowPredicates && "Variance in assumed invariant key components!"); auto Itr = TripCountMap.find({ExitCond, ControlsExit}); if (Itr == TripCountMap.end()) return None; return Itr->second; } void ScalarEvolution::ExitLimitCache::insert(const Loop *L, Value *ExitCond, bool ExitIfTrue, bool ControlsExit, bool AllowPredicates, const ExitLimit &EL) { assert(this->L == L && this->ExitIfTrue == ExitIfTrue && this->AllowPredicates == AllowPredicates && "Variance in assumed invariant key components!"); auto InsertResult = TripCountMap.insert({{ExitCond, ControlsExit}, EL}); assert(InsertResult.second && "Expected successful insertion!"); (void)InsertResult; (void)ExitIfTrue; } ScalarEvolution::ExitLimit ScalarEvolution::computeExitLimitFromCondCached( ExitLimitCacheTy &Cache, const Loop *L, Value *ExitCond, bool ExitIfTrue, bool ControlsExit, bool AllowPredicates) { if (auto MaybeEL = Cache.find(L, ExitCond, ExitIfTrue, ControlsExit, AllowPredicates)) return *MaybeEL; ExitLimit EL = computeExitLimitFromCondImpl(Cache, L, ExitCond, ExitIfTrue, ControlsExit, AllowPredicates); Cache.insert(L, ExitCond, ExitIfTrue, ControlsExit, AllowPredicates, EL); return EL; } ScalarEvolution::ExitLimit ScalarEvolution::computeExitLimitFromCondImpl( ExitLimitCacheTy &Cache, const Loop *L, Value *ExitCond, bool ExitIfTrue, bool ControlsExit, bool AllowPredicates) { // Handle BinOp conditions (And, Or). if (auto LimitFromBinOp = computeExitLimitFromCondFromBinOp( Cache, L, ExitCond, ExitIfTrue, ControlsExit, AllowPredicates)) return *LimitFromBinOp; // 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)) { ExitLimit EL = computeExitLimitFromICmp(L, ExitCondICmp, ExitIfTrue, ControlsExit); if (EL.hasFullInfo() || !AllowPredicates) return EL; // Try again, but use SCEV predicates this time. return computeExitLimitFromICmp(L, ExitCondICmp, ExitIfTrue, ControlsExit, /*AllowPredicates=*/true); } // 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 (ExitIfTrue == !CI->getZExtValue()) // The backedge is always taken. return getCouldNotCompute(); else // The backedge is never taken. return getZero(CI->getType()); } // If it's not an integer or pointer comparison then compute it the hard way. return computeExitCountExhaustively(L, ExitCond, ExitIfTrue); } Optional ScalarEvolution::computeExitLimitFromCondFromBinOp( ExitLimitCacheTy &Cache, const Loop *L, Value *ExitCond, bool ExitIfTrue, bool ControlsExit, bool AllowPredicates) { // Check if the controlling expression for this loop is an And or Or. Value *Op0, *Op1; bool IsAnd = false; if (match(ExitCond, m_LogicalAnd(m_Value(Op0), m_Value(Op1)))) IsAnd = true; else if (match(ExitCond, m_LogicalOr(m_Value(Op0), m_Value(Op1)))) IsAnd = false; else return None; // EitherMayExit is true in these two cases: // br (and Op0 Op1), loop, exit // br (or Op0 Op1), exit, loop bool EitherMayExit = IsAnd ^ ExitIfTrue; ExitLimit EL0 = computeExitLimitFromCondCached(Cache, L, Op0, ExitIfTrue, ControlsExit && !EitherMayExit, AllowPredicates); ExitLimit EL1 = computeExitLimitFromCondCached(Cache, L, Op1, ExitIfTrue, ControlsExit && !EitherMayExit, AllowPredicates); // Be robust against unsimplified IR for the form "op i1 X, NeutralElement" const Constant *NeutralElement = ConstantInt::get(ExitCond->getType(), IsAnd); if (isa(Op1)) return Op1 == NeutralElement ? EL0 : EL1; if (isa(Op0)) return Op0 == NeutralElement ? EL1 : EL0; const SCEV *BECount = getCouldNotCompute(); const SCEV *MaxBECount = getCouldNotCompute(); if (EitherMayExit) { // Both conditions must be same for the loop to continue executing. // Choose the less conservative count. // If ExitCond is a short-circuit form (select), using // umin(EL0.ExactNotTaken, EL1.ExactNotTaken) is unsafe in general. // To see the detailed examples, please see // test/Analysis/ScalarEvolution/exit-count-select.ll bool PoisonSafe = isa(ExitCond); if (!PoisonSafe) // Even if ExitCond is select, we can safely derive BECount using both // EL0 and EL1 in these cases: // (1) EL0.ExactNotTaken is non-zero // (2) EL1.ExactNotTaken is non-poison // (3) EL0.ExactNotTaken is zero (BECount should be simply zero and // it cannot be umin(0, ..)) // The PoisonSafe assignment below is simplified and the assertion after // BECount calculation fully guarantees the condition (3). PoisonSafe = isa(EL0.ExactNotTaken) || isa(EL1.ExactNotTaken); if (EL0.ExactNotTaken != getCouldNotCompute() && EL1.ExactNotTaken != getCouldNotCompute() && PoisonSafe) { BECount = getUMinFromMismatchedTypes(EL0.ExactNotTaken, EL1.ExactNotTaken); // If EL0.ExactNotTaken was zero and ExitCond was a short-circuit form, // it should have been simplified to zero (see the condition (3) above) assert(!isa(ExitCond) || !EL0.ExactNotTaken->isZero() || BECount->isZero()); } if (EL0.MaxNotTaken == getCouldNotCompute()) MaxBECount = EL1.MaxNotTaken; else if (EL1.MaxNotTaken == getCouldNotCompute()) MaxBECount = EL0.MaxNotTaken; else MaxBECount = getUMinFromMismatchedTypes(EL0.MaxNotTaken, EL1.MaxNotTaken); } else { // Both conditions must be same at the same time for the loop to exit. // For now, be conservative. if (EL0.ExactNotTaken == EL1.ExactNotTaken) BECount = EL0.ExactNotTaken; } // There are cases (e.g. PR26207) where computeExitLimitFromCond is able // to be more aggressive when computing BECount than when computing // MaxBECount. In these cases it is possible for EL0.ExactNotTaken and // EL1.ExactNotTaken to match, but for EL0.MaxNotTaken and EL1.MaxNotTaken // to not. if (isa(MaxBECount) && !isa(BECount)) MaxBECount = getConstant(getUnsignedRangeMax(BECount)); return ExitLimit(BECount, MaxBECount, false, { &EL0.Predicates, &EL1.Predicates }); } ScalarEvolution::ExitLimit ScalarEvolution::computeExitLimitFromICmp(const Loop *L, ICmpInst *ExitCond, bool ExitIfTrue, bool ControlsExit, bool AllowPredicates) { // If the condition was exit on true, convert the condition to exit on false ICmpInst::Predicate Pred; if (!ExitIfTrue) Pred = ExitCond->getPredicate(); else Pred = ExitCond->getInversePredicate(); const ICmpInst::Predicate OriginalPred = Pred; // 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, Pred); 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); Pred = ICmpInst::getSwappedPredicate(Pred); } // Simplify the operands before analyzing them. (void)SimplifyICmpOperands(Pred, 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 = ConstantRange::makeExactICmpRegion(Pred, RHSC->getAPInt()); const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this); if (!isa(Ret)) return Ret; } switch (Pred) { case ICmpInst::ICMP_NE: { // while (X != Y) // Convert to: while (X-Y != 0) if (LHS->getType()->isPointerTy()) { LHS = getLosslessPtrToIntExpr(LHS); if (isa(LHS)) return LHS; } if (RHS->getType()->isPointerTy()) { RHS = getLosslessPtrToIntExpr(RHS); if (isa(RHS)) return RHS; } ExitLimit EL = howFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit, AllowPredicates); if (EL.hasAnyInfo()) return EL; break; } case ICmpInst::ICMP_EQ: { // while (X == Y) // Convert to: while (X-Y == 0) if (LHS->getType()->isPointerTy()) { LHS = getLosslessPtrToIntExpr(LHS); if (isa(LHS)) return LHS; } if (RHS->getType()->isPointerTy()) { RHS = getLosslessPtrToIntExpr(RHS); if (isa(RHS)) return RHS; } 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 = Pred == ICmpInst::ICMP_SLT; ExitLimit EL = howManyLessThans(LHS, RHS, L, IsSigned, ControlsExit, AllowPredicates); if (EL.hasAnyInfo()) return EL; break; } case ICmpInst::ICMP_SGT: case ICmpInst::ICMP_UGT: { // while (X > Y) bool IsSigned = Pred == ICmpInst::ICMP_SGT; ExitLimit EL = howManyGreaterThans(LHS, RHS, L, IsSigned, ControlsExit, AllowPredicates); if (EL.hasAnyInfo()) return EL; break; } default: break; } auto *ExhaustiveCount = computeExitCountExhaustively(L, ExitCond, ExitIfTrue); if (!isa(ExhaustiveCount)) return ExhaustiveCount; return computeShiftCompareExitLimit(ExitCond->getOperand(0), ExitCond->getOperand(1), L, OriginalPred); } 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(); } /// 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->getLoop() != L || !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()) { ++NumArrayLenItCounts; return getConstant(ItCst); // Found terminating iteration! } } return getCouldNotCompute(); } ScalarEvolution::ExitLimit ScalarEvolution::computeShiftCompareExitLimit( Value *LHS, Value *RHSV, const Loop *L, ICmpInst::Predicate Pred) { ConstantInt *RHS = dyn_cast(RHSV); if (!RHS) return getCouldNotCompute(); const BasicBlock *Latch = L->getLoopLatch(); if (!Latch) return getCouldNotCompute(); const BasicBlock *Predecessor = L->getLoopPredecessor(); if (!Predecessor) return getCouldNotCompute(); // Return true if V is of the form "LHS `shift_op` ". // Return LHS in OutLHS and shift_opt in OutOpCode. auto MatchPositiveShift = [](Value *V, Value *&OutLHS, Instruction::BinaryOps &OutOpCode) { using namespace PatternMatch; ConstantInt *ShiftAmt; if (match(V, m_LShr(m_Value(OutLHS), m_ConstantInt(ShiftAmt)))) OutOpCode = Instruction::LShr; else if (match(V, m_AShr(m_Value(OutLHS), m_ConstantInt(ShiftAmt)))) OutOpCode = Instruction::AShr; else if (match(V, m_Shl(m_Value(OutLHS), m_ConstantInt(ShiftAmt)))) OutOpCode = Instruction::Shl; else return false; return ShiftAmt->getValue().isStrictlyPositive(); }; // Recognize a "shift recurrence" either of the form %iv or of %iv.shifted in // // loop: // %iv = phi i32 [ %iv.shifted, %loop ], [ %val, %preheader ] // %iv.shifted = lshr i32 %iv, // // Return true on a successful match. Return the corresponding PHI node (%iv // above) in PNOut and the opcode of the shift operation in OpCodeOut. auto MatchShiftRecurrence = [&](Value *V, PHINode *&PNOut, Instruction::BinaryOps &OpCodeOut) { Optional PostShiftOpCode; { Instruction::BinaryOps OpC; Value *V; // If we encounter a shift instruction, "peel off" the shift operation, // and remember that we did so. Later when we inspect %iv's backedge // value, we will make sure that the backedge value uses the same // operation. // // Note: the peeled shift operation does not have to be the same // instruction as the one feeding into the PHI's backedge value. We only // really care about it being the same *kind* of shift instruction -- // that's all that is required for our later inferences to hold. if (MatchPositiveShift(LHS, V, OpC)) { PostShiftOpCode = OpC; LHS = V; } } PNOut = dyn_cast(LHS); if (!PNOut || PNOut->getParent() != L->getHeader()) return false; Value *BEValue = PNOut->getIncomingValueForBlock(Latch); Value *OpLHS; return // The backedge value for the PHI node must be a shift by a positive // amount MatchPositiveShift(BEValue, OpLHS, OpCodeOut) && // of the PHI node itself OpLHS == PNOut && // and the kind of shift should be match the kind of shift we peeled // off, if any. (!PostShiftOpCode.hasValue() || *PostShiftOpCode == OpCodeOut); }; PHINode *PN; Instruction::BinaryOps OpCode; if (!MatchShiftRecurrence(LHS, PN, OpCode)) return getCouldNotCompute(); const DataLayout &DL = getDataLayout(); // The key rationale for this optimization is that for some kinds of shift // recurrences, the value of the recurrence "stabilizes" to either 0 or -1 // within a finite number of iterations. If the condition guarding the // backedge (in the sense that the backedge is taken if the condition is true) // is false for the value the shift recurrence stabilizes to, then we know // that the backedge is taken only a finite number of times. ConstantInt *StableValue = nullptr; switch (OpCode) { default: llvm_unreachable("Impossible case!"); case Instruction::AShr: { // {K,ashr,} stabilizes to signum(K) in at most // bitwidth(K) iterations. Value *FirstValue = PN->getIncomingValueForBlock(Predecessor); KnownBits Known = computeKnownBits(FirstValue, DL, 0, &AC, Predecessor->getTerminator(), &DT); auto *Ty = cast(RHS->getType()); if (Known.isNonNegative()) StableValue = ConstantInt::get(Ty, 0); else if (Known.isNegative()) StableValue = ConstantInt::get(Ty, -1, true); else return getCouldNotCompute(); break; } case Instruction::LShr: case Instruction::Shl: // Both {K,lshr,} and {K,shl,} // stabilize to 0 in at most bitwidth(K) iterations. StableValue = ConstantInt::get(cast(RHS->getType()), 0); break; } auto *Result = ConstantFoldCompareInstOperands(Pred, StableValue, RHS, DL, &TLI); assert(Result->getType()->isIntegerTy(1) && "Otherwise cannot be an operand to a branch instruction"); if (Result->isZeroValue()) { unsigned BitWidth = getTypeSizeInBits(RHS->getType()); const SCEV *UpperBound = getConstant(getEffectiveSCEVType(RHS->getType()), BitWidth); return ExitLimit(getCouldNotCompute(), UpperBound, false); } return getCouldNotCompute(); } /// 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) || isa(I)) return true; if (const CallInst *CI = dyn_cast(I)) if (const Function *F = CI->getCalledFunction()) return canConstantFoldCallTo(CI, 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)) { // We don't currently keep track of the control flow needed to evaluate // PHIs, so we cannot handle PHIs inside of loops. return L->getHeader() == I->getParent(); } // 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, unsigned Depth) { if (Depth > MaxConstantEvolvingDepth) return nullptr; // Otherwise, we can evaluate this instruction if all of its operands are // constant or derived from a PHI node themselves. PHINode *PHI = nullptr; for (Value *Op : UseInst->operands()) { if (isa(Op)) continue; Instruction *OpInst = dyn_cast(Op); 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, Depth + 1); 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, 0); } /// 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], LI->getType(), DL); } return ConstantFoldInstOperands(I, Operands, DL, TLI); } // If every incoming value to PN except the one for BB is a specific Constant, // return that, else return nullptr. static Constant *getOtherIncomingValue(PHINode *PN, BasicBlock *BB) { Constant *IncomingVal = nullptr; for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) { if (PN->getIncomingBlock(i) == BB) continue; auto *CurrentVal = dyn_cast(PN->getIncomingValue(i)); if (!CurrentVal) return nullptr; if (IncomingVal != CurrentVal) { if (IncomingVal) return nullptr; IncomingVal = CurrentVal; } } return IncomingVal; } /// 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) { auto 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!"); BasicBlock *Latch = L->getLoopLatch(); if (!Latch) return nullptr; for (PHINode &PHI : Header->phis()) { if (auto *StartCST = getOtherIncomingValue(&PHI, Latch)) CurrentIterVals[&PHI] = StartCST; } if (!CurrentIterVals.count(PN)) return RetVal = nullptr; Value *BEValue = PN->getIncomingValueForBlock(Latch); // Execute the loop symbolically to determine the exit value. assert(BEs.getActiveBits() < CHAR_BIT * sizeof(unsigned) && "BEs is <= MaxBruteForceIterations which is an 'unsigned'!"); unsigned NumIterations = BEs.getZExtValue(); // must be in range unsigned IterationNum = 0; const DataLayout &DL = getDataLayout(); 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 (const auto &I : CurrentIterVals) { PHINode *PHI = dyn_cast(I.first); if (!PHI || PHI == PN || PHI->getParent() != Header) continue; PHIsToCompute.emplace_back(PHI, I.second); } // We use two distinct loops because EvaluateExpression may invalidate any // iterators into CurrentIterVals. for (const auto &I : PHIsToCompute) { PHINode *PHI = I.first; Constant *&NextPHI = NextIterVals[PHI]; if (!NextPHI) { // Not already computed. Value *BEValue = PHI->getIncomingValueForBlock(Latch); 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); } } 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!"); BasicBlock *Latch = L->getLoopLatch(); assert(Latch && "Should follow from NumIncomingValues == 2!"); for (PHINode &PHI : Header->phis()) { if (auto *StartCST = getOtherIncomingValue(&PHI, Latch)) 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. const DataLayout &DL = getDataLayout(); for (unsigned IterationNum = 0; IterationNum != MaxIterations;++IterationNum){ auto *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 (const auto &I : CurrentIterVals) { PHINode *PHI = dyn_cast(I.first); if (!PHI || PHI->getParent() != Header) continue; PHIsToCompute.push_back(PHI); } for (PHINode *PHI : PHIsToCompute) { Constant *&NextPHI = NextIterVals[PHI]; if (NextPHI) continue; // Already computed! Value *BEValue = PHI->getIncomingValueForBlock(Latch); NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI); } CurrentIterVals.swap(NextIterVals); } // Too many iterations were needed to evaluate. return getCouldNotCompute(); } const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) { SmallVector, 2> &Values = ValuesAtScopes[V]; // Check to see if we've folded this expression at this loop before. for (auto &LS : Values) if (LS.first == L) return LS.second ? LS.second : V; Values.emplace_back(L, nullptr); // Otherwise compute it. const SCEV *C = computeSCEVAtScope(V, L); for (auto &LS : reverse(ValuesAtScopes[V])) if (LS.first == L) { LS.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 (V->getSCEVType()) { case scCouldNotCompute: case scAddRecExpr: return nullptr; 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()); return nullptr; } case scZeroExtend: { const SCEVZeroExtendExpr *SZ = cast(V); if (Constant *CastOp = BuildConstantFromSCEV(SZ->getOperand())) return ConstantExpr::getZExt(CastOp, SZ->getType()); return nullptr; } case scPtrToInt: { const SCEVPtrToIntExpr *P2I = cast(V); if (Constant *CastOp = BuildConstantFromSCEV(P2I->getOperand())) return ConstantExpr::getPtrToInt(CastOp, P2I->getType()); return nullptr; } case scTruncate: { const SCEVTruncateExpr *ST = cast(V); if (Constant *CastOp = BuildConstantFromSCEV(ST->getOperand())) return ConstantExpr::getTrunc(CastOp, ST->getType()); return nullptr; } 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 (C->getType()->isPointerTy()) { C = ConstantExpr::getGetElementPtr(Type::getInt8Ty(C->getContext()), C, C2); } else { C = ConstantExpr::getAdd(C, C2); } } return C; } return nullptr; } 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; } return nullptr; } 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); return nullptr; } case scSMaxExpr: case scUMaxExpr: case scSMinExpr: case scUMinExpr: return nullptr; // TODO: smax, umax, smin, umax. } llvm_unreachable("Unknown SCEV kind!"); } 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())) { if (PHINode *PN = dyn_cast(I)) { const Loop *CurrLoop = this->LI[I->getParent()]; // Looking for loop exit value. if (CurrLoop && CurrLoop->getParentLoop() == L && PN->getParent() == CurrLoop->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(CurrLoop); // This trivial case can show up in some degenerate cases where // the incoming IR has not yet been fully simplified. if (BackedgeTakenCount->isZero()) { Value *InitValue = nullptr; bool MultipleInitValues = false; for (unsigned i = 0; i < PN->getNumIncomingValues(); i++) { if (!CurrLoop->contains(PN->getIncomingBlock(i))) { if (!InitValue) InitValue = PN->getIncomingValue(i); else if (InitValue != PN->getIncomingValue(i)) { MultipleInitValues = true; break; } } } if (!MultipleInitValues && InitValue) return getSCEV(InitValue); } // Do we have a loop invariant value flowing around the backedge // for a loop which must execute the backedge? if (!isa(BackedgeTakenCount) && isKnownPositive(BackedgeTakenCount) && PN->getNumIncomingValues() == 2) { unsigned InLoopPred = CurrLoop->contains(PN->getIncomingBlock(0)) ? 0 : 1; Value *BackedgeVal = PN->getIncomingValue(InLoopPred); if (CurrLoop->isLoopInvariant(BackedgeVal)) return getSCEV(BackedgeVal); } if (auto *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->getAPInt(), CurrLoop); if (RV) return getSCEV(RV); } } // If there is a single-input Phi, evaluate it at our scope. If we can // prove that this replacement does not break LCSSA form, use new value. if (PN->getNumOperands() == 1) { const SCEV *Input = getSCEV(PN->getOperand(0)); const SCEV *InputAtScope = getSCEVAtScope(Input, L); // TODO: We can generalize it using LI.replacementPreservesLCSSAForm, // for the simplest case just support constants. if (isa(InputAtScope)) return InputAtScope; } } // 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 (Value *Op : I->operands()) { 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; const DataLayout &DL = getDataLayout(); if (const CmpInst *CI = dyn_cast(I)) C = ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0], Operands[1], DL, &TLI); else if (const LoadInst *Load = dyn_cast(I)) { if (!Load->isVolatile()) C = ConstantFoldLoadFromConstPtr(Operands[0], Load->getType(), DL); } else C = ConstantFoldInstOperands(I, 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, Comm->getNoWrapFlags()); if (isa(Comm)) return getMulExpr(NewOps, Comm->getNoWrapFlags()); if (isa(Comm)) return getMinMaxExpr(Comm->getSCEVType(), 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()); } if (const SCEVPtrToIntExpr *Cast = dyn_cast(V)) { const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); if (Op == Cast->getOperand()) return Cast; // must be loop invariant return getPtrToIntExpr(Op, Cast->getType()); } llvm_unreachable("Unknown SCEV type!"); } const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) { return getSCEVAtScope(getSCEV(V), L); } const SCEV *ScalarEvolution::stripInjectiveFunctions(const SCEV *S) const { if (const SCEVZeroExtendExpr *ZExt = dyn_cast(S)) return stripInjectiveFunctions(ZExt->getOperand()); if (const SCEVSignExtendExpr *SExt = dyn_cast(S)) return stripInjectiveFunctions(SExt->getOperand()); return S; } /// 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 SCEV *B, ScalarEvolution &SE) { uint32_t BW = A.getBitWidth(); assert(BW == SE.getTypeSizeInBits(B->getType())); 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 (SE.GetMinTrailingZeros(B) < Mult2) return SE.getCouldNotCompute(); // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic // modulo (N / D). // // If D == 1, (N / D) == N == 2^BW, so we need one extra bit to represent // (N / D) in general. The inverse itself always fits into BW bits, though, // so we immediately truncate it. 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).trunc(BW); // 4. Compute the minimum unsigned root of the equation: // I * (B / D) mod (N / D) // To simplify the computation, we factor out the divide by D: // (I * B mod N) / D const SCEV *D = SE.getConstant(APInt::getOneBitSet(BW, Mult2)); return SE.getUDivExactExpr(SE.getMulExpr(B, SE.getConstant(I)), D); } /// For a given quadratic addrec, generate coefficients of the corresponding /// quadratic equation, multiplied by a common value to ensure that they are /// integers. /// The returned value is a tuple { A, B, C, M, BitWidth }, where /// Ax^2 + Bx + C is the quadratic function, M is the value that A, B and C /// were multiplied by, and BitWidth is the bit width of the original addrec /// coefficients. /// This function returns None if the addrec coefficients are not compile- /// time constants. static Optional> GetQuadraticEquation(const SCEVAddRecExpr *AddRec) { 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)); LLVM_DEBUG(dbgs() << __func__ << ": analyzing quadratic addrec: " << *AddRec << '\n'); // We currently can only solve this if the coefficients are constants. if (!LC || !MC || !NC) { LLVM_DEBUG(dbgs() << __func__ << ": coefficients are not constant\n"); return None; } APInt L = LC->getAPInt(); APInt M = MC->getAPInt(); APInt N = NC->getAPInt(); assert(!N.isNullValue() && "This is not a quadratic addrec"); unsigned BitWidth = LC->getAPInt().getBitWidth(); unsigned NewWidth = BitWidth + 1; LLVM_DEBUG(dbgs() << __func__ << ": addrec coeff bw: " << BitWidth << '\n'); // The sign-extension (as opposed to a zero-extension) here matches the // extension used in SolveQuadraticEquationWrap (with the same motivation). N = N.sext(NewWidth); M = M.sext(NewWidth); L = L.sext(NewWidth); // The increments are M, M+N, M+2N, ..., so the accumulated values are // L+M, (L+M)+(M+N), (L+M)+(M+N)+(M+2N), ..., that is, // L+M, L+2M+N, L+3M+3N, ... // After n iterations the accumulated value Acc is L + nM + n(n-1)/2 N. // // The equation Acc = 0 is then // L + nM + n(n-1)/2 N = 0, or 2L + 2M n + n(n-1) N = 0. // In a quadratic form it becomes: // N n^2 + (2M-N) n + 2L = 0. APInt A = N; APInt B = 2 * M - A; APInt C = 2 * L; APInt T = APInt(NewWidth, 2); LLVM_DEBUG(dbgs() << __func__ << ": equation " << A << "x^2 + " << B << "x + " << C << ", coeff bw: " << NewWidth << ", multiplied by " << T << '\n'); return std::make_tuple(A, B, C, T, BitWidth); } /// Helper function to compare optional APInts: /// (a) if X and Y both exist, return min(X, Y), /// (b) if neither X nor Y exist, return None, /// (c) if exactly one of X and Y exists, return that value. static Optional MinOptional(Optional X, Optional Y) { if (X.hasValue() && Y.hasValue()) { unsigned W = std::max(X->getBitWidth(), Y->getBitWidth()); APInt XW = X->sextOrSelf(W); APInt YW = Y->sextOrSelf(W); return XW.slt(YW) ? *X : *Y; } if (!X.hasValue() && !Y.hasValue()) return None; return X.hasValue() ? *X : *Y; } /// Helper function to truncate an optional APInt to a given BitWidth. /// When solving addrec-related equations, it is preferable to return a value /// that has the same bit width as the original addrec's coefficients. If the /// solution fits in the original bit width, truncate it (except for i1). /// Returning a value of a different bit width may inhibit some optimizations. /// /// In general, a solution to a quadratic equation generated from an addrec /// may require BW+1 bits, where BW is the bit width of the addrec's /// coefficients. The reason is that the coefficients of the quadratic /// equation are BW+1 bits wide (to avoid truncation when converting from /// the addrec to the equation). static Optional TruncIfPossible(Optional X, unsigned BitWidth) { if (!X.hasValue()) return None; unsigned W = X->getBitWidth(); if (BitWidth > 1 && BitWidth < W && X->isIntN(BitWidth)) return X->trunc(BitWidth); return X; } /// Let c(n) be the value of the quadratic chrec {L,+,M,+,N} after n /// iterations. The values L, M, N are assumed to be signed, and they /// should all have the same bit widths. /// Find the least n >= 0 such that c(n) = 0 in the arithmetic modulo 2^BW, /// where BW is the bit width of the addrec's coefficients. /// If the calculated value is a BW-bit integer (for BW > 1), it will be /// returned as such, otherwise the bit width of the returned value may /// be greater than BW. /// /// This function returns None if /// (a) the addrec coefficients are not constant, or /// (b) SolveQuadraticEquationWrap was unable to find a solution. For cases /// like x^2 = 5, no integer solutions exist, in other cases an integer /// solution may exist, but SolveQuadraticEquationWrap may fail to find it. static Optional SolveQuadraticAddRecExact(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) { APInt A, B, C, M; unsigned BitWidth; auto T = GetQuadraticEquation(AddRec); if (!T.hasValue()) return None; std::tie(A, B, C, M, BitWidth) = *T; LLVM_DEBUG(dbgs() << __func__ << ": solving for unsigned overflow\n"); Optional X = APIntOps::SolveQuadraticEquationWrap(A, B, C, BitWidth+1); if (!X.hasValue()) return None; ConstantInt *CX = ConstantInt::get(SE.getContext(), *X); ConstantInt *V = EvaluateConstantChrecAtConstant(AddRec, CX, SE); if (!V->isZero()) return None; return TruncIfPossible(X, BitWidth); } /// Let c(n) be the value of the quadratic chrec {0,+,M,+,N} after n /// iterations. The values M, N are assumed to be signed, and they /// should all have the same bit widths. /// Find the least n such that c(n) does not belong to the given range, /// while c(n-1) does. /// /// This function returns None if /// (a) the addrec coefficients are not constant, or /// (b) SolveQuadraticEquationWrap was unable to find a solution for the /// bounds of the range. static Optional SolveQuadraticAddRecRange(const SCEVAddRecExpr *AddRec, const ConstantRange &Range, ScalarEvolution &SE) { assert(AddRec->getOperand(0)->isZero() && "Starting value of addrec should be 0"); LLVM_DEBUG(dbgs() << __func__ << ": solving boundary crossing for range " << Range << ", addrec " << *AddRec << '\n'); // This case is handled in getNumIterationsInRange. Here we can assume that // we start in the range. assert(Range.contains(APInt(SE.getTypeSizeInBits(AddRec->getType()), 0)) && "Addrec's initial value should be in range"); APInt A, B, C, M; unsigned BitWidth; auto T = GetQuadraticEquation(AddRec); if (!T.hasValue()) return None; // Be careful about the return value: there can be two reasons for not // returning an actual number. First, if no solutions to the equations // were found, and second, if the solutions don't leave the given range. // The first case means that the actual solution is "unknown", the second // means that it's known, but not valid. If the solution is unknown, we // cannot make any conclusions. // Return a pair: the optional solution and a flag indicating if the // solution was found. auto SolveForBoundary = [&](APInt Bound) -> std::pair,bool> { // Solve for signed overflow and unsigned overflow, pick the lower // solution. LLVM_DEBUG(dbgs() << "SolveQuadraticAddRecRange: checking boundary " << Bound << " (before multiplying by " << M << ")\n"); Bound *= M; // The quadratic equation multiplier. Optional SO = None; if (BitWidth > 1) { LLVM_DEBUG(dbgs() << "SolveQuadraticAddRecRange: solving for " "signed overflow\n"); SO = APIntOps::SolveQuadraticEquationWrap(A, B, -Bound, BitWidth); } LLVM_DEBUG(dbgs() << "SolveQuadraticAddRecRange: solving for " "unsigned overflow\n"); Optional UO = APIntOps::SolveQuadraticEquationWrap(A, B, -Bound, BitWidth+1); auto LeavesRange = [&] (const APInt &X) { ConstantInt *C0 = ConstantInt::get(SE.getContext(), X); ConstantInt *V0 = EvaluateConstantChrecAtConstant(AddRec, C0, SE); if (Range.contains(V0->getValue())) return false; // X should be at least 1, so X-1 is non-negative. ConstantInt *C1 = ConstantInt::get(SE.getContext(), X-1); ConstantInt *V1 = EvaluateConstantChrecAtConstant(AddRec, C1, SE); if (Range.contains(V1->getValue())) return true; return false; }; // If SolveQuadraticEquationWrap returns None, it means that there can // be a solution, but the function failed to find it. We cannot treat it // as "no solution". if (!SO.hasValue() || !UO.hasValue()) return { None, false }; // Check the smaller value first to see if it leaves the range. // At this point, both SO and UO must have values. Optional Min = MinOptional(SO, UO); if (LeavesRange(*Min)) return { Min, true }; Optional Max = Min == SO ? UO : SO; if (LeavesRange(*Max)) return { Max, true }; // Solutions were found, but were eliminated, hence the "true". return { None, true }; }; std::tie(A, B, C, M, BitWidth) = *T; // Lower bound is inclusive, subtract 1 to represent the exiting value. APInt Lower = Range.getLower().sextOrSelf(A.getBitWidth()) - 1; APInt Upper = Range.getUpper().sextOrSelf(A.getBitWidth()); auto SL = SolveForBoundary(Lower); auto SU = SolveForBoundary(Upper); // If any of the solutions was unknown, no meaninigful conclusions can // be made. if (!SL.second || !SU.second) return None; // Claim: The correct solution is not some value between Min and Max. // // Justification: Assuming that Min and Max are different values, one of // them is when the first signed overflow happens, the other is when the // first unsigned overflow happens. Crossing the range boundary is only // possible via an overflow (treating 0 as a special case of it, modeling // an overflow as crossing k*2^W for some k). // // The interesting case here is when Min was eliminated as an invalid // solution, but Max was not. The argument is that if there was another // overflow between Min and Max, it would also have been eliminated if // it was considered. // // For a given boundary, it is possible to have two overflows of the same // type (signed/unsigned) without having the other type in between: this // can happen when the vertex of the parabola is between the iterations // corresponding to the overflows. This is only possible when the two // overflows cross k*2^W for the same k. In such case, if the second one // left the range (and was the first one to do so), the first overflow // would have to enter the range, which would mean that either we had left // the range before or that we started outside of it. Both of these cases // are contradictions. // // Claim: In the case where SolveForBoundary returns None, the correct // solution is not some value between the Max for this boundary and the // Min of the other boundary. // // Justification: Assume that we had such Max_A and Min_B corresponding // to range boundaries A and B and such that Max_A < Min_B. If there was // a solution between Max_A and Min_B, it would have to be caused by an // overflow corresponding to either A or B. It cannot correspond to B, // since Min_B is the first occurrence of such an overflow. If it // corresponded to A, it would have to be either a signed or an unsigned // overflow that is larger than both eliminated overflows for A. But // between the eliminated overflows and this overflow, the values would // cover the entire value space, thus crossing the other boundary, which // is a contradiction. return TruncIfPossible(MinOptional(SL.first, SU.first), BitWidth); } ScalarEvolution::ExitLimit ScalarEvolution::howFarToZero(const SCEV *V, const Loop *L, bool ControlsExit, bool AllowPredicates) { // 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. SmallPtrSet Predicates; // 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(stripInjectiveFunctions(V)); if (!AddRec && AllowPredicates) // Try to make this an AddRec using runtime tests, in the first X // iterations of this loop, where X is the SCEV expression found by the // algorithm below. AddRec = convertSCEVToAddRecWithPredicates(V, L, Predicates); 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()) { // 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. if (auto S = SolveQuadraticAddRecExact(AddRec, *this)) { const auto *R = cast(getConstant(S.getValue())); return ExitLimit(R, R, false, Predicates); } 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()->isZero()) 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->getAPInt().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()->isOne() || StepC->getValue()->isMinusOne()) { APInt MaxBECount = getUnsignedRangeMax(applyLoopGuards(Distance, L)); APInt MaxBECountBase = getUnsignedRangeMax(Distance); if (MaxBECountBase.ult(MaxBECount)) MaxBECount = MaxBECountBase; // When a loop like "for (int i = 0; i != n; ++i) { /* body */ }" is rotated, // we end up with a loop whose backedge-taken count is n - 1. Detect this // case, and see if we can improve the bound. // // Explicitly handling this here is necessary because getUnsignedRange // isn't context-sensitive; it doesn't know that we only care about the // range inside the loop. const SCEV *Zero = getZero(Distance->getType()); const SCEV *One = getOne(Distance->getType()); const SCEV *DistancePlusOne = getAddExpr(Distance, One); if (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_NE, DistancePlusOne, Zero)) { // If Distance + 1 doesn't overflow, we can compute the maximum distance // as "unsigned_max(Distance + 1) - 1". ConstantRange CR = getUnsignedRange(DistancePlusOne); MaxBECount = APIntOps::umin(MaxBECount, CR.getUnsignedMax() - 1); } return ExitLimit(Distance, getConstant(MaxBECount), false, Predicates); } // 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->hasNoSelfWrap() && loopHasNoAbnormalExits(AddRec->getLoop())) { const SCEV *Exact = getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step); const SCEV *Max = getCouldNotCompute(); if (Exact != getCouldNotCompute()) { APInt MaxInt = getUnsignedRangeMax(applyLoopGuards(Exact, L)); APInt BaseMaxInt = getUnsignedRangeMax(Exact); if (BaseMaxInt.ult(MaxInt)) Max = getConstant(BaseMaxInt); else Max = getConstant(MaxInt); } return ExitLimit(Exact, Max, false, Predicates); } // Solve the general equation. const SCEV *E = SolveLinEquationWithOverflow(StepC->getAPInt(), getNegativeSCEV(Start), *this); const SCEV *M = E == getCouldNotCompute() ? E : getConstant(getUnsignedRangeMax(E)); return ExitLimit(E, M, false, Predicates); } 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()->isZero()) return getZero(C->getType()); 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(); } std::pair ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(const BasicBlock *BB) const { // 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 (const BasicBlock *Pred = BB->getSinglePredecessor()) return {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 (const Loop *L = LI.getLoopFor(BB)) return {L->getLoopPredecessor(), L->getHeader()}; return {nullptr, nullptr}; } /// 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; auto ComputesEqualValues = [](const Instruction *A, const Instruction *B) { // Not all instructions that are "identical" compute the same value. For // instance, two distinct alloca instructions allocating the same type are // identical and do not read memory; but compute distinct values. return A->isIdenticalTo(B) && (isa(A) || isa(A)); }; // 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 (ComputesEqualValues(AI, BI)) return true; // Otherwise assume they may have a different value. return false; } bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred, const SCEV *&LHS, const SCEV *&RHS, unsigned Depth) { bool Changed = false; // Simplifies ICMP to trivial true or false by turning it into '0 == 0' or // '0 != 0'. auto TrivialCase = [&](bool TriviallyTrue) { LHS = RHS = getConstant(ConstantInt::getFalse(getContext())); Pred = TriviallyTrue ? ICmpInst::ICMP_EQ : ICmpInst::ICMP_NE; return true; }; // 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()) return TrivialCase(false); else return TrivialCase(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->getAPInt(); bool SimplifiedByConstantRange = false; if (!ICmpInst::isEquality(Pred)) { ConstantRange ExactCR = ConstantRange::makeExactICmpRegion(Pred, RA); if (ExactCR.isFullSet()) return TrivialCase(true); else if (ExactCR.isEmptySet()) return TrivialCase(false); APInt NewRHS; CmpInst::Predicate NewPred; if (ExactCR.getEquivalentICmp(NewPred, NewRHS) && ICmpInst::isEquality(NewPred)) { // We were able to convert an inequality to an equality. Pred = NewPred; RHS = getConstant(NewRHS); Changed = SimplifiedByConstantRange = true; } } if (!SimplifiedByConstantRange) { switch (Pred) { default: break; 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; // The "Should have been caught earlier!" messages refer to the fact // that the ExactCR.isFullSet() or ExactCR.isEmptySet() check above // should have fired on the corresponding cases, and canonicalized the // check to trivial case. case ICmpInst::ICMP_UGE: assert(!RA.isMinValue() && "Should have been caught earlier!"); Pred = ICmpInst::ICMP_UGT; RHS = getConstant(RA - 1); Changed = true; break; case ICmpInst::ICMP_ULE: assert(!RA.isMaxValue() && "Should have been caught earlier!"); Pred = ICmpInst::ICMP_ULT; RHS = getConstant(RA + 1); Changed = true; break; case ICmpInst::ICMP_SGE: assert(!RA.isMinSignedValue() && "Should have been caught earlier!"); Pred = ICmpInst::ICMP_SGT; RHS = getConstant(RA - 1); Changed = true; break; case ICmpInst::ICMP_SLE: assert(!RA.isMaxSignedValue() && "Should have been caught earlier!"); Pred = ICmpInst::ICMP_SLT; RHS = getConstant(RA + 1); Changed = true; break; } } } // Check for obvious equality. if (HasSameValue(LHS, RHS)) { if (ICmpInst::isTrueWhenEqual(Pred)) return TrivialCase(true); if (ICmpInst::isFalseWhenEqual(Pred)) return TrivialCase(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 (!getSignedRangeMax(RHS).isMaxSignedValue()) { RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS, SCEV::FlagNSW); Pred = ICmpInst::ICMP_SLT; Changed = true; } else if (!getSignedRangeMin(LHS).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 (!getSignedRangeMin(RHS).isMinSignedValue()) { RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS, SCEV::FlagNSW); Pred = ICmpInst::ICMP_SGT; Changed = true; } else if (!getSignedRangeMax(LHS).isMaxSignedValue()) { LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS, SCEV::FlagNSW); Pred = ICmpInst::ICMP_SGT; Changed = true; } break; case ICmpInst::ICMP_ULE: if (!getUnsignedRangeMax(RHS).isMaxValue()) { RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS, SCEV::FlagNUW); Pred = ICmpInst::ICMP_ULT; Changed = true; } else if (!getUnsignedRangeMin(LHS).isMinValue()) { LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS); Pred = ICmpInst::ICMP_ULT; Changed = true; } break; case ICmpInst::ICMP_UGE: if (!getUnsignedRangeMin(RHS).isMinValue()) { RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS); Pred = ICmpInst::ICMP_UGT; Changed = true; } else if (!getUnsignedRangeMax(LHS).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; } bool ScalarEvolution::isKnownNegative(const SCEV *S) { return getSignedRangeMax(S).isNegative(); } bool ScalarEvolution::isKnownPositive(const SCEV *S) { return getSignedRangeMin(S).isStrictlyPositive(); } bool ScalarEvolution::isKnownNonNegative(const SCEV *S) { return !getSignedRangeMin(S).isNegative(); } bool ScalarEvolution::isKnownNonPositive(const SCEV *S) { return !getSignedRangeMax(S).isStrictlyPositive(); } bool ScalarEvolution::isKnownNonZero(const SCEV *S) { return getUnsignedRangeMin(S) != 0; } std::pair ScalarEvolution::SplitIntoInitAndPostInc(const Loop *L, const SCEV *S) { // Compute SCEV on entry of loop L. const SCEV *Start = SCEVInitRewriter::rewrite(S, L, *this); if (Start == getCouldNotCompute()) return { Start, Start }; // Compute post increment SCEV for loop L. const SCEV *PostInc = SCEVPostIncRewriter::rewrite(S, L, *this); assert(PostInc != getCouldNotCompute() && "Unexpected could not compute"); return { Start, PostInc }; } bool ScalarEvolution::isKnownViaInduction(ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS) { // First collect all loops. SmallPtrSet LoopsUsed; getUsedLoops(LHS, LoopsUsed); getUsedLoops(RHS, LoopsUsed); if (LoopsUsed.empty()) return false; // Domination relationship must be a linear order on collected loops. #ifndef NDEBUG for (auto *L1 : LoopsUsed) for (auto *L2 : LoopsUsed) assert((DT.dominates(L1->getHeader(), L2->getHeader()) || DT.dominates(L2->getHeader(), L1->getHeader())) && "Domination relationship is not a linear order"); #endif const Loop *MDL = *std::max_element(LoopsUsed.begin(), LoopsUsed.end(), [&](const Loop *L1, const Loop *L2) { return DT.properlyDominates(L1->getHeader(), L2->getHeader()); }); // Get init and post increment value for LHS. auto SplitLHS = SplitIntoInitAndPostInc(MDL, LHS); // if LHS contains unknown non-invariant SCEV then bail out. if (SplitLHS.first == getCouldNotCompute()) return false; assert (SplitLHS.second != getCouldNotCompute() && "Unexpected CNC"); // Get init and post increment value for RHS. auto SplitRHS = SplitIntoInitAndPostInc(MDL, RHS); // if RHS contains unknown non-invariant SCEV then bail out. if (SplitRHS.first == getCouldNotCompute()) return false; assert (SplitRHS.second != getCouldNotCompute() && "Unexpected CNC"); // It is possible that init SCEV contains an invariant load but it does // not dominate MDL and is not available at MDL loop entry, so we should // check it here. if (!isAvailableAtLoopEntry(SplitLHS.first, MDL) || !isAvailableAtLoopEntry(SplitRHS.first, MDL)) return false; // It seems backedge guard check is faster than entry one so in some cases // it can speed up whole estimation by short circuit return isLoopBackedgeGuardedByCond(MDL, Pred, SplitLHS.second, SplitRHS.second) && isLoopEntryGuardedByCond(MDL, Pred, SplitLHS.first, SplitRHS.first); } bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS) { // Canonicalize the inputs first. (void)SimplifyICmpOperands(Pred, LHS, RHS); if (isKnownViaInduction(Pred, LHS, RHS)) return true; if (isKnownPredicateViaSplitting(Pred, LHS, RHS)) return true; // Otherwise see what can be done with some simple reasoning. return isKnownViaNonRecursiveReasoning(Pred, LHS, RHS); } Optional ScalarEvolution::evaluatePredicate(ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS) { if (isKnownPredicate(Pred, LHS, RHS)) return true; else if (isKnownPredicate(ICmpInst::getInversePredicate(Pred), LHS, RHS)) return false; return None; } bool ScalarEvolution::isKnownPredicateAt(ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS, const Instruction *Context) { // TODO: Analyze guards and assumes from Context's block. return isKnownPredicate(Pred, LHS, RHS) || isBasicBlockEntryGuardedByCond(Context->getParent(), Pred, LHS, RHS); } Optional ScalarEvolution::evaluatePredicateAt(ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS, const Instruction *Context) { Optional KnownWithoutContext = evaluatePredicate(Pred, LHS, RHS); if (KnownWithoutContext) return KnownWithoutContext; if (isBasicBlockEntryGuardedByCond(Context->getParent(), Pred, LHS, RHS)) return true; else if (isBasicBlockEntryGuardedByCond(Context->getParent(), ICmpInst::getInversePredicate(Pred), LHS, RHS)) return false; return None; } bool ScalarEvolution::isKnownOnEveryIteration(ICmpInst::Predicate Pred, const SCEVAddRecExpr *LHS, const SCEV *RHS) { const Loop *L = LHS->getLoop(); return isLoopEntryGuardedByCond(L, Pred, LHS->getStart(), RHS) && isLoopBackedgeGuardedByCond(L, Pred, LHS->getPostIncExpr(*this), RHS); } Optional ScalarEvolution::getMonotonicPredicateType(const SCEVAddRecExpr *LHS, ICmpInst::Predicate Pred) { auto Result = getMonotonicPredicateTypeImpl(LHS, Pred); #ifndef NDEBUG // Verify an invariant: inverting the predicate should turn a monotonically // increasing change to a monotonically decreasing one, and vice versa. if (Result) { auto ResultSwapped = getMonotonicPredicateTypeImpl(LHS, ICmpInst::getSwappedPredicate(Pred)); assert(ResultSwapped.hasValue() && "should be able to analyze both!"); assert(ResultSwapped.getValue() != Result.getValue() && "monotonicity should flip as we flip the predicate"); } #endif return Result; } Optional ScalarEvolution::getMonotonicPredicateTypeImpl(const SCEVAddRecExpr *LHS, ICmpInst::Predicate Pred) { // A zero step value for LHS means the induction variable is essentially a // loop invariant value. We don't really depend on the predicate actually // flipping from false to true (for increasing predicates, and the other way // around for decreasing predicates), all we care about is that *if* the // predicate changes then it only changes from false to true. // // A zero step value in itself is not very useful, but there may be places // where SCEV can prove X >= 0 but not prove X > 0, so it is helpful to be // as general as possible. // Only handle LE/LT/GE/GT predicates. if (!ICmpInst::isRelational(Pred)) return None; bool IsGreater = ICmpInst::isGE(Pred) || ICmpInst::isGT(Pred); assert((IsGreater || ICmpInst::isLE(Pred) || ICmpInst::isLT(Pred)) && "Should be greater or less!"); // Check that AR does not wrap. if (ICmpInst::isUnsigned(Pred)) { if (!LHS->hasNoUnsignedWrap()) return None; return IsGreater ? MonotonicallyIncreasing : MonotonicallyDecreasing; } else { assert(ICmpInst::isSigned(Pred) && "Relational predicate is either signed or unsigned!"); if (!LHS->hasNoSignedWrap()) return None; const SCEV *Step = LHS->getStepRecurrence(*this); if (isKnownNonNegative(Step)) return IsGreater ? MonotonicallyIncreasing : MonotonicallyDecreasing; if (isKnownNonPositive(Step)) return !IsGreater ? MonotonicallyIncreasing : MonotonicallyDecreasing; return None; } } Optional ScalarEvolution::getLoopInvariantPredicate(ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS, const Loop *L) { // If there is a loop-invariant, force it into the RHS, otherwise bail out. if (!isLoopInvariant(RHS, L)) { if (!isLoopInvariant(LHS, L)) return None; std::swap(LHS, RHS); Pred = ICmpInst::getSwappedPredicate(Pred); } const SCEVAddRecExpr *ArLHS = dyn_cast(LHS); if (!ArLHS || ArLHS->getLoop() != L) return None; auto MonotonicType = getMonotonicPredicateType(ArLHS, Pred); if (!MonotonicType) return None; // If the predicate "ArLHS `Pred` RHS" monotonically increases from false to // true as the loop iterates, and the backedge is control dependent on // "ArLHS `Pred` RHS" == true then we can reason as follows: // // * if the predicate was false in the first iteration then the predicate // is never evaluated again, since the loop exits without taking the // backedge. // * if the predicate was true in the first iteration then it will // continue to be true for all future iterations since it is // monotonically increasing. // // For both the above possibilities, we can replace the loop varying // predicate with its value on the first iteration of the loop (which is // loop invariant). // // A similar reasoning applies for a monotonically decreasing predicate, by // replacing true with false and false with true in the above two bullets. bool Increasing = *MonotonicType == ScalarEvolution::MonotonicallyIncreasing; auto P = Increasing ? Pred : ICmpInst::getInversePredicate(Pred); if (!isLoopBackedgeGuardedByCond(L, P, LHS, RHS)) return None; return ScalarEvolution::LoopInvariantPredicate(Pred, ArLHS->getStart(), RHS); } Optional ScalarEvolution::getLoopInvariantExitCondDuringFirstIterations( ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS, const Loop *L, const Instruction *Context, const SCEV *MaxIter) { // Try to prove the following set of facts: // - The predicate is monotonic in the iteration space. // - If the check does not fail on the 1st iteration: // - No overflow will happen during first MaxIter iterations; // - It will not fail on the MaxIter'th iteration. // If the check does fail on the 1st iteration, we leave the loop and no // other checks matter. // If there is a loop-invariant, force it into the RHS, otherwise bail out. if (!isLoopInvariant(RHS, L)) { if (!isLoopInvariant(LHS, L)) return None; std::swap(LHS, RHS); Pred = ICmpInst::getSwappedPredicate(Pred); } auto *AR = dyn_cast(LHS); if (!AR || AR->getLoop() != L) return None; // The predicate must be relational (i.e. <, <=, >=, >). if (!ICmpInst::isRelational(Pred)) return None; // TODO: Support steps other than +/- 1. const SCEV *Step = AR->getStepRecurrence(*this); auto *One = getOne(Step->getType()); auto *MinusOne = getNegativeSCEV(One); if (Step != One && Step != MinusOne) return None; // Type mismatch here means that MaxIter is potentially larger than max // unsigned value in start type, which mean we cannot prove no wrap for the // indvar. if (AR->getType() != MaxIter->getType()) return None; // Value of IV on suggested last iteration. const SCEV *Last = AR->evaluateAtIteration(MaxIter, *this); // Does it still meet the requirement? if (!isLoopBackedgeGuardedByCond(L, Pred, Last, RHS)) return None; // Because step is +/- 1 and MaxIter has same type as Start (i.e. it does // not exceed max unsigned value of this type), this effectively proves // that there is no wrap during the iteration. To prove that there is no // signed/unsigned wrap, we need to check that // Start <= Last for step = 1 or Start >= Last for step = -1. ICmpInst::Predicate NoOverflowPred = CmpInst::isSigned(Pred) ? ICmpInst::ICMP_SLE : ICmpInst::ICMP_ULE; if (Step == MinusOne) NoOverflowPred = CmpInst::getSwappedPredicate(NoOverflowPred); const SCEV *Start = AR->getStart(); if (!isKnownPredicateAt(NoOverflowPred, Start, Last, Context)) return None; // Everything is fine. return ScalarEvolution::LoopInvariantPredicate(Pred, Start, RHS); } bool ScalarEvolution::isKnownPredicateViaConstantRanges( 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. auto CheckRanges = [&](const ConstantRange &RangeLHS, const ConstantRange &RangeRHS) { return RangeLHS.icmp(Pred, RangeRHS); }; // The check at the top of the function catches the case where the values are // known to be equal. if (Pred == CmpInst::ICMP_EQ) return false; if (Pred == CmpInst::ICMP_NE) { if (CheckRanges(getSignedRange(LHS), getSignedRange(RHS)) || CheckRanges(getUnsignedRange(LHS), getUnsignedRange(RHS))) return true; auto *Diff = getMinusSCEV(LHS, RHS); return !isa(Diff) && isKnownNonZero(Diff); } if (CmpInst::isSigned(Pred)) return CheckRanges(getSignedRange(LHS), getSignedRange(RHS)); return CheckRanges(getUnsignedRange(LHS), getUnsignedRange(RHS)); } bool ScalarEvolution::isKnownPredicateViaNoOverflow(ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS) { // Match X to (A + C1) and Y to (A + C2), where // C1 and C2 are constant integers. If either X or Y are not add expressions, // consider them as X + 0 and Y + 0 respectively. C1 and C2 are returned via // OutC1 and OutC2. auto MatchBinaryAddToConst = [this](const SCEV *X, const SCEV *Y, APInt &OutC1, APInt &OutC2, SCEV::NoWrapFlags ExpectedFlags) { const SCEV *XNonConstOp, *XConstOp; const SCEV *YNonConstOp, *YConstOp; SCEV::NoWrapFlags XFlagsPresent; SCEV::NoWrapFlags YFlagsPresent; if (!splitBinaryAdd(X, XConstOp, XNonConstOp, XFlagsPresent)) { XConstOp = getZero(X->getType()); XNonConstOp = X; XFlagsPresent = ExpectedFlags; } if (!isa(XConstOp) || (XFlagsPresent & ExpectedFlags) != ExpectedFlags) return false; if (!splitBinaryAdd(Y, YConstOp, YNonConstOp, YFlagsPresent)) { YConstOp = getZero(Y->getType()); YNonConstOp = Y; YFlagsPresent = ExpectedFlags; } if (!isa(YConstOp) || (YFlagsPresent & ExpectedFlags) != ExpectedFlags) return false; if (YNonConstOp != XNonConstOp) return false; OutC1 = cast(XConstOp)->getAPInt(); OutC2 = cast(YConstOp)->getAPInt(); return true; }; APInt C1; APInt C2; switch (Pred) { default: break; case ICmpInst::ICMP_SGE: std::swap(LHS, RHS); LLVM_FALLTHROUGH; case ICmpInst::ICMP_SLE: // (X + C1) s<= (X + C2) if C1 s<= C2. if (MatchBinaryAddToConst(LHS, RHS, C1, C2, SCEV::FlagNSW) && C1.sle(C2)) return true; break; case ICmpInst::ICMP_SGT: std::swap(LHS, RHS); LLVM_FALLTHROUGH; case ICmpInst::ICMP_SLT: // (X + C1) s< (X + C2) if C1 s< C2. if (MatchBinaryAddToConst(LHS, RHS, C1, C2, SCEV::FlagNSW) && C1.slt(C2)) return true; break; case ICmpInst::ICMP_UGE: std::swap(LHS, RHS); LLVM_FALLTHROUGH; case ICmpInst::ICMP_ULE: // (X + C1) u<= (X + C2) for C1 u<= C2. if (MatchBinaryAddToConst(RHS, LHS, C2, C1, SCEV::FlagNUW) && C1.ule(C2)) return true; break; case ICmpInst::ICMP_UGT: std::swap(LHS, RHS); LLVM_FALLTHROUGH; case ICmpInst::ICMP_ULT: // (X + C1) u< (X + C2) if C1 u< C2. if (MatchBinaryAddToConst(RHS, LHS, C2, C1, SCEV::FlagNUW) && C1.ult(C2)) return true; break; } return false; } bool ScalarEvolution::isKnownPredicateViaSplitting(ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS) { if (Pred != ICmpInst::ICMP_ULT || ProvingSplitPredicate) return false; // Allowing arbitrary number of activations of isKnownPredicateViaSplitting on // the stack can result in exponential time complexity. SaveAndRestore Restore(ProvingSplitPredicate, true); // If L >= 0 then I `ult` L <=> I >= 0 && I `slt` L // // To prove L >= 0 we use isKnownNonNegative whereas to prove I >= 0 we use // isKnownPredicate. isKnownPredicate is more powerful, but also more // expensive; and using isKnownNonNegative(RHS) is sufficient for most of the // interesting cases seen in practice. We can consider "upgrading" L >= 0 to // use isKnownPredicate later if needed. return isKnownNonNegative(RHS) && isKnownPredicate(CmpInst::ICMP_SGE, LHS, getZero(LHS->getType())) && isKnownPredicate(CmpInst::ICMP_SLT, LHS, RHS); } bool ScalarEvolution::isImpliedViaGuard(const BasicBlock *BB, ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS) { // No need to even try if we know the module has no guards. if (!HasGuards) return false; return any_of(*BB, [&](const Instruction &I) { using namespace llvm::PatternMatch; Value *Condition; return match(&I, m_Intrinsic( m_Value(Condition))) && isImpliedCond(Pred, LHS, RHS, Condition, 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 (VerifyIR) assert(!verifyFunction(*L->getHeader()->getParent(), &dbgs()) && "This cannot be done on broken IR!"); if (isKnownViaNonRecursiveReasoning(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; // We don't want more than one activation of the following loops on the stack // -- that can lead to O(n!) time complexity. if (WalkingBEDominatingConds) return false; SaveAndRestore ClearOnExit(WalkingBEDominatingConds, true); // See if we can exploit a trip count to prove the predicate. const auto &BETakenInfo = getBackedgeTakenInfo(L); const SCEV *LatchBECount = BETakenInfo.getExact(Latch, this); if (LatchBECount != getCouldNotCompute()) { // We know that Latch branches back to the loop header exactly // LatchBECount times. This means the backdege condition at Latch is // equivalent to "{0,+,1} u< LatchBECount". Type *Ty = LatchBECount->getType(); auto NoWrapFlags = SCEV::NoWrapFlags(SCEV::FlagNUW | SCEV::FlagNW); const SCEV *LoopCounter = getAddRecExpr(getZero(Ty), getOne(Ty), L, NoWrapFlags); if (isImpliedCond(Pred, LHS, RHS, ICmpInst::ICMP_ULT, LoopCounter, LatchBECount)) 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; } // If the loop is not reachable from the entry block, we risk running into an // infinite loop as we walk up into the dom tree. These loops do not matter // anyway, so we just return a conservative answer when we see them. if (!DT.isReachableFromEntry(L->getHeader())) return false; if (isImpliedViaGuard(Latch, Pred, LHS, RHS)) return true; for (DomTreeNode *DTN = DT[Latch], *HeaderDTN = DT[L->getHeader()]; DTN != HeaderDTN; DTN = DTN->getIDom()) { assert(DTN && "should reach the loop header before reaching the root!"); BasicBlock *BB = DTN->getBlock(); if (isImpliedViaGuard(BB, Pred, LHS, RHS)) return true; BasicBlock *PBB = BB->getSinglePredecessor(); if (!PBB) continue; BranchInst *ContinuePredicate = dyn_cast(PBB->getTerminator()); if (!ContinuePredicate || !ContinuePredicate->isConditional()) continue; Value *Condition = ContinuePredicate->getCondition(); // If we have an edge `E` within the loop body that dominates the only // latch, the condition guarding `E` also guards the backedge. This // reasoning works only for loops with a single latch. BasicBlockEdge DominatingEdge(PBB, BB); if (DominatingEdge.isSingleEdge()) { // We're constructively (and conservatively) enumerating edges within the // loop body that dominate the latch. The dominator tree better agree // with us on this: assert(DT.dominates(DominatingEdge, Latch) && "should be!"); if (isImpliedCond(Pred, LHS, RHS, Condition, BB != ContinuePredicate->getSuccessor(0))) return true; } } return false; } bool ScalarEvolution::isBasicBlockEntryGuardedByCond(const BasicBlock *BB, ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS) { if (VerifyIR) assert(!verifyFunction(*BB->getParent(), &dbgs()) && "This cannot be done on broken IR!"); // If we cannot prove strict comparison (e.g. a > b), maybe we can prove // the facts (a >= b && a != b) separately. A typical situation is when the // non-strict comparison is known from ranges and non-equality is known from // dominating predicates. If we are proving strict comparison, we always try // to prove non-equality and non-strict comparison separately. auto NonStrictPredicate = ICmpInst::getNonStrictPredicate(Pred); const bool ProvingStrictComparison = (Pred != NonStrictPredicate); bool ProvedNonStrictComparison = false; bool ProvedNonEquality = false; auto SplitAndProve = [&](std::function Fn) -> bool { if (!ProvedNonStrictComparison) ProvedNonStrictComparison = Fn(NonStrictPredicate); if (!ProvedNonEquality) ProvedNonEquality = Fn(ICmpInst::ICMP_NE); if (ProvedNonStrictComparison && ProvedNonEquality) return true; return false; }; if (ProvingStrictComparison) { auto ProofFn = [&](ICmpInst::Predicate P) { return isKnownViaNonRecursiveReasoning(P, LHS, RHS); }; if (SplitAndProve(ProofFn)) return true; } // Try to prove (Pred, LHS, RHS) using isImpliedViaGuard. auto ProveViaGuard = [&](const BasicBlock *Block) { if (isImpliedViaGuard(Block, Pred, LHS, RHS)) return true; if (ProvingStrictComparison) { auto ProofFn = [&](ICmpInst::Predicate P) { return isImpliedViaGuard(Block, P, LHS, RHS); }; if (SplitAndProve(ProofFn)) return true; } return false; }; // Try to prove (Pred, LHS, RHS) using isImpliedCond. auto ProveViaCond = [&](const Value *Condition, bool Inverse) { const Instruction *Context = &BB->front(); if (isImpliedCond(Pred, LHS, RHS, Condition, Inverse, Context)) return true; if (ProvingStrictComparison) { auto ProofFn = [&](ICmpInst::Predicate P) { return isImpliedCond(P, LHS, RHS, Condition, Inverse, Context); }; if (SplitAndProve(ProofFn)) return true; } return false; }; // Starting at the block's predecessor, climb up the predecessor chain, as long // as there are predecessors that can be found that have unique successors // leading to the original block. const Loop *ContainingLoop = LI.getLoopFor(BB); const BasicBlock *PredBB; if (ContainingLoop && ContainingLoop->getHeader() == BB) PredBB = ContainingLoop->getLoopPredecessor(); else PredBB = BB->getSinglePredecessor(); for (std::pair Pair(PredBB, BB); Pair.first; Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) { if (ProveViaGuard(Pair.first)) return true; const BranchInst *LoopEntryPredicate = dyn_cast(Pair.first->getTerminator()); if (!LoopEntryPredicate || LoopEntryPredicate->isUnconditional()) continue; if (ProveViaCond(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, BB)) continue; if (ProveViaCond(CI->getArgOperand(0), false)) return true; } return false; } 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; // Both LHS and RHS must be available at loop entry. assert(isAvailableAtLoopEntry(LHS, L) && "LHS is not available at Loop Entry"); assert(isAvailableAtLoopEntry(RHS, L) && "RHS is not available at Loop Entry"); if (isKnownViaNonRecursiveReasoning(Pred, LHS, RHS)) return true; return isBasicBlockEntryGuardedByCond(L->getHeader(), Pred, LHS, RHS); } bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS, const Value *FoundCondValue, bool Inverse, const Instruction *Context) { // False conditions implies anything. Do not bother analyzing it further. if (FoundCondValue == ConstantInt::getBool(FoundCondValue->getContext(), Inverse)) return true; if (!PendingLoopPredicates.insert(FoundCondValue).second) return false; auto ClearOnExit = make_scope_exit([&]() { PendingLoopPredicates.erase(FoundCondValue); }); // Recursively handle And and Or conditions. const Value *Op0, *Op1; if (match(FoundCondValue, m_LogicalAnd(m_Value(Op0), m_Value(Op1)))) { if (!Inverse) return isImpliedCond(Pred, LHS, RHS, Op0, Inverse, Context) || isImpliedCond(Pred, LHS, RHS, Op1, Inverse, Context); } else if (match(FoundCondValue, m_LogicalOr(m_Value(Op0), m_Value(Op1)))) { if (Inverse) return isImpliedCond(Pred, LHS, RHS, Op0, Inverse, Context) || isImpliedCond(Pred, LHS, RHS, Op1, Inverse, Context); } const ICmpInst *ICI = dyn_cast(FoundCondValue); if (!ICI) 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)); return isImpliedCond(Pred, LHS, RHS, FoundPred, FoundLHS, FoundRHS, Context); } bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS, ICmpInst::Predicate FoundPred, const SCEV *FoundLHS, const SCEV *FoundRHS, const Instruction *Context) { // Balance the types. if (getTypeSizeInBits(LHS->getType()) < getTypeSizeInBits(FoundLHS->getType())) { // For unsigned and equality predicates, try to prove that both found // operands fit into narrow unsigned range. If so, try to prove facts in // narrow types. if (!CmpInst::isSigned(FoundPred) && !FoundLHS->getType()->isPointerTy()) { auto *NarrowType = LHS->getType(); auto *WideType = FoundLHS->getType(); auto BitWidth = getTypeSizeInBits(NarrowType); const SCEV *MaxValue = getZeroExtendExpr( getConstant(APInt::getMaxValue(BitWidth)), WideType); if (isKnownPredicate(ICmpInst::ICMP_ULE, FoundLHS, MaxValue) && isKnownPredicate(ICmpInst::ICMP_ULE, FoundRHS, MaxValue)) { const SCEV *TruncFoundLHS = getTruncateExpr(FoundLHS, NarrowType); const SCEV *TruncFoundRHS = getTruncateExpr(FoundRHS, NarrowType); if (isImpliedCondBalancedTypes(Pred, LHS, RHS, FoundPred, TruncFoundLHS, TruncFoundRHS, Context)) return true; } } if (LHS->getType()->isPointerTy()) return false; if (CmpInst::isSigned(Pred)) { LHS = getSignExtendExpr(LHS, FoundLHS->getType()); RHS = getSignExtendExpr(RHS, FoundLHS->getType()); } else { LHS = getZeroExtendExpr(LHS, FoundLHS->getType()); RHS = getZeroExtendExpr(RHS, FoundLHS->getType()); } } else if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(FoundLHS->getType())) { if (FoundLHS->getType()->isPointerTy()) return false; 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()); } } return isImpliedCondBalancedTypes(Pred, LHS, RHS, FoundPred, FoundLHS, FoundRHS, Context); } bool ScalarEvolution::isImpliedCondBalancedTypes( ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS, ICmpInst::Predicate FoundPred, const SCEV *FoundLHS, const SCEV *FoundRHS, const Instruction *Context) { assert(getTypeSizeInBits(LHS->getType()) == getTypeSizeInBits(FoundLHS->getType()) && "Types should be balanced!"); // 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, Context); // Check whether swapping the found predicate makes it the same as the // desired predicate. if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) { // We can write the implication // 0. LHS Pred RHS <- FoundLHS SwapPred FoundRHS // using one of the following ways: // 1. LHS Pred RHS <- FoundRHS Pred FoundLHS // 2. RHS SwapPred LHS <- FoundLHS SwapPred FoundRHS // 3. LHS Pred RHS <- ~FoundLHS Pred ~FoundRHS // 4. ~LHS SwapPred ~RHS <- FoundLHS SwapPred FoundRHS // Forms 1. and 2. require swapping the operands of one condition. Don't // do this if it would break canonical constant/addrec ordering. if (!isa(RHS) && !isa(LHS)) return isImpliedCondOperands(FoundPred, RHS, LHS, FoundLHS, FoundRHS, Context); if (!isa(FoundRHS) && !isa(FoundLHS)) return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS, Context); // Don't try to getNotSCEV pointers. if (LHS->getType()->isPointerTy() || FoundLHS->getType()->isPointerTy()) return false; // There's no clear preference between forms 3. and 4., try both. return isImpliedCondOperands(FoundPred, getNotSCEV(LHS), getNotSCEV(RHS), FoundLHS, FoundRHS, Context) || isImpliedCondOperands(Pred, LHS, RHS, getNotSCEV(FoundLHS), getNotSCEV(FoundRHS), Context); } // Unsigned comparison is the same as signed comparison when both the operands // are non-negative. if (CmpInst::isUnsigned(FoundPred) && CmpInst::getSignedPredicate(FoundPred) == Pred && isKnownNonNegative(FoundLHS) && isKnownNonNegative(FoundRHS)) return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS, Context); // 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) ? getSignedRangeMin(V) : getUnsignedRangeMin(V); if (Min == C->getAPInt()) { // 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), Context)) return true; LLVM_FALLTHROUGH; 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), Context)) return true; break; // `LHS < RHS` and `LHS <= RHS` are handled in the same way as `RHS > LHS` and `RHS >= LHS` respectively. case ICmpInst::ICMP_SLE: case ICmpInst::ICMP_ULE: if (isImpliedCondOperands(CmpInst::getSwappedPredicate(Pred), RHS, LHS, V, getConstant(SharperMin), Context)) return true; LLVM_FALLTHROUGH; case ICmpInst::ICMP_SLT: case ICmpInst::ICMP_ULT: if (isImpliedCondOperands(CmpInst::getSwappedPredicate(Pred), RHS, LHS, V, getConstant(Min), Context)) return true; break; 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, Context)) return true; if (Pred == ICmpInst::ICMP_NE) if (!ICmpInst::isTrueWhenEqual(FoundPred)) if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS, Context)) return true; // Otherwise assume the worst. return false; } bool ScalarEvolution::splitBinaryAdd(const SCEV *Expr, const SCEV *&L, const SCEV *&R, SCEV::NoWrapFlags &Flags) { const auto *AE = dyn_cast(Expr); if (!AE || AE->getNumOperands() != 2) return false; L = AE->getOperand(0); R = AE->getOperand(1); Flags = AE->getNoWrapFlags(); return true; } Optional ScalarEvolution::computeConstantDifference(const SCEV *More, const SCEV *Less) { // We avoid subtracting expressions here because this function is usually // fairly deep in the call stack (i.e. is called many times). // X - X = 0. if (More == Less) return APInt(getTypeSizeInBits(More->getType()), 0); if (isa(Less) && isa(More)) { const auto *LAR = cast(Less); const auto *MAR = cast(More); if (LAR->getLoop() != MAR->getLoop()) return None; // We look at affine expressions only; not for correctness but to keep // getStepRecurrence cheap. if (!LAR->isAffine() || !MAR->isAffine()) return None; if (LAR->getStepRecurrence(*this) != MAR->getStepRecurrence(*this)) return None; Less = LAR->getStart(); More = MAR->getStart(); // fall through } if (isa(Less) && isa(More)) { const auto &M = cast(More)->getAPInt(); const auto &L = cast(Less)->getAPInt(); return M - L; } SCEV::NoWrapFlags Flags; const SCEV *LLess = nullptr, *RLess = nullptr; const SCEV *LMore = nullptr, *RMore = nullptr; const SCEVConstant *C1 = nullptr, *C2 = nullptr; // Compare (X + C1) vs X. if (splitBinaryAdd(Less, LLess, RLess, Flags)) if ((C1 = dyn_cast(LLess))) if (RLess == More) return -(C1->getAPInt()); // Compare X vs (X + C2). if (splitBinaryAdd(More, LMore, RMore, Flags)) if ((C2 = dyn_cast(LMore))) if (RMore == Less) return C2->getAPInt(); // Compare (X + C1) vs (X + C2). if (C1 && C2 && RLess == RMore) return C2->getAPInt() - C1->getAPInt(); return None; } bool ScalarEvolution::isImpliedCondOperandsViaAddRecStart( ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS, const SCEV *FoundLHS, const SCEV *FoundRHS, const Instruction *Context) { // Try to recognize the following pattern: // // FoundRHS = ... // ... // loop: // FoundLHS = {Start,+,W} // context_bb: // Basic block from the same loop // known(Pred, FoundLHS, FoundRHS) // // If some predicate is known in the context of a loop, it is also known on // each iteration of this loop, including the first iteration. Therefore, in // this case, `FoundLHS Pred FoundRHS` implies `Start Pred FoundRHS`. Try to // prove the original pred using this fact. if (!Context) return false; const BasicBlock *ContextBB = Context->getParent(); // Make sure AR varies in the context block. if (auto *AR = dyn_cast(FoundLHS)) { const Loop *L = AR->getLoop(); // Make sure that context belongs to the loop and executes on 1st iteration // (if it ever executes at all). if (!L->contains(ContextBB) || !DT.dominates(ContextBB, L->getLoopLatch())) return false; if (!isAvailableAtLoopEntry(FoundRHS, AR->getLoop())) return false; return isImpliedCondOperands(Pred, LHS, RHS, AR->getStart(), FoundRHS); } if (auto *AR = dyn_cast(FoundRHS)) { const Loop *L = AR->getLoop(); // Make sure that context belongs to the loop and executes on 1st iteration // (if it ever executes at all). if (!L->contains(ContextBB) || !DT.dominates(ContextBB, L->getLoopLatch())) return false; if (!isAvailableAtLoopEntry(FoundLHS, AR->getLoop())) return false; return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, AR->getStart()); } return false; } bool ScalarEvolution::isImpliedCondOperandsViaNoOverflow( ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS, const SCEV *FoundLHS, const SCEV *FoundRHS) { if (Pred != CmpInst::ICMP_SLT && Pred != CmpInst::ICMP_ULT) return false; const auto *AddRecLHS = dyn_cast(LHS); if (!AddRecLHS) return false; const auto *AddRecFoundLHS = dyn_cast(FoundLHS); if (!AddRecFoundLHS) return false; // We'd like to let SCEV reason about control dependencies, so we constrain // both the inequalities to be about add recurrences on the same loop. This // way we can use isLoopEntryGuardedByCond later. const Loop *L = AddRecFoundLHS->getLoop(); if (L != AddRecLHS->getLoop()) return false; // FoundLHS u< FoundRHS u< -C => (FoundLHS + C) u< (FoundRHS + C) ... (1) // // FoundLHS s< FoundRHS s< INT_MIN - C => (FoundLHS + C) s< (FoundRHS + C) // ... (2) // // Informal proof for (2), assuming (1) [*]: // // We'll also assume (A s< B) <=> ((A + INT_MIN) u< (B + INT_MIN)) ... (3)[**] // // Then // // FoundLHS s< FoundRHS s< INT_MIN - C // <=> (FoundLHS + INT_MIN) u< (FoundRHS + INT_MIN) u< -C [ using (3) ] // <=> (FoundLHS + INT_MIN + C) u< (FoundRHS + INT_MIN + C) [ using (1) ] // <=> (FoundLHS + INT_MIN + C + INT_MIN) s< // (FoundRHS + INT_MIN + C + INT_MIN) [ using (3) ] // <=> FoundLHS + C s< FoundRHS + C // // [*]: (1) can be proved by ruling out overflow. // // [**]: This can be proved by analyzing all the four possibilities: // (A s< 0, B s< 0), (A s< 0, B s>= 0), (A s>= 0, B s< 0) and // (A s>= 0, B s>= 0). // // Note: // Despite (2), "FoundRHS s< INT_MIN - C" does not mean that "FoundRHS + C" // will not sign underflow. For instance, say FoundLHS = (i8 -128), FoundRHS // = (i8 -127) and C = (i8 -100). Then INT_MIN - C = (i8 -28), and FoundRHS // s< (INT_MIN - C). Lack of sign overflow / underflow in "FoundRHS + C" is // neither necessary nor sufficient to prove "(FoundLHS + C) s< (FoundRHS + // C)". Optional LDiff = computeConstantDifference(LHS, FoundLHS); Optional RDiff = computeConstantDifference(RHS, FoundRHS); if (!LDiff || !RDiff || *LDiff != *RDiff) return false; if (LDiff->isMinValue()) return true; APInt FoundRHSLimit; if (Pred == CmpInst::ICMP_ULT) { FoundRHSLimit = -(*RDiff); } else { assert(Pred == CmpInst::ICMP_SLT && "Checked above!"); FoundRHSLimit = APInt::getSignedMinValue(getTypeSizeInBits(RHS->getType())) - *RDiff; } // Try to prove (1) or (2), as needed. return isAvailableAtLoopEntry(FoundRHS, L) && isLoopEntryGuardedByCond(L, Pred, FoundRHS, getConstant(FoundRHSLimit)); } bool ScalarEvolution::isImpliedViaMerge(ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS, const SCEV *FoundLHS, const SCEV *FoundRHS, unsigned Depth) { const PHINode *LPhi = nullptr, *RPhi = nullptr; auto ClearOnExit = make_scope_exit([&]() { if (LPhi) { bool Erased = PendingMerges.erase(LPhi); assert(Erased && "Failed to erase LPhi!"); (void)Erased; } if (RPhi) { bool Erased = PendingMerges.erase(RPhi); assert(Erased && "Failed to erase RPhi!"); (void)Erased; } }); // Find respective Phis and check that they are not being pending. if (const SCEVUnknown *LU = dyn_cast(LHS)) if (auto *Phi = dyn_cast(LU->getValue())) { if (!PendingMerges.insert(Phi).second) return false; LPhi = Phi; } if (const SCEVUnknown *RU = dyn_cast(RHS)) if (auto *Phi = dyn_cast(RU->getValue())) { // If we detect a loop of Phi nodes being processed by this method, for // example: // // %a = phi i32 [ %some1, %preheader ], [ %b, %latch ] // %b = phi i32 [ %some2, %preheader ], [ %a, %latch ] // // we don't want to deal with a case that complex, so return conservative // answer false. if (!PendingMerges.insert(Phi).second) return false; RPhi = Phi; } // If none of LHS, RHS is a Phi, nothing to do here. if (!LPhi && !RPhi) return false; // If there is a SCEVUnknown Phi we are interested in, make it left. if (!LPhi) { std::swap(LHS, RHS); std::swap(FoundLHS, FoundRHS); std::swap(LPhi, RPhi); Pred = ICmpInst::getSwappedPredicate(Pred); } assert(LPhi && "LPhi should definitely be a SCEVUnknown Phi!"); const BasicBlock *LBB = LPhi->getParent(); const SCEVAddRecExpr *RAR = dyn_cast(RHS); auto ProvedEasily = [&](const SCEV *S1, const SCEV *S2) { return isKnownViaNonRecursiveReasoning(Pred, S1, S2) || isImpliedCondOperandsViaRanges(Pred, S1, S2, FoundLHS, FoundRHS) || isImpliedViaOperations(Pred, S1, S2, FoundLHS, FoundRHS, Depth); }; if (RPhi && RPhi->getParent() == LBB) { // Case one: RHS is also a SCEVUnknown Phi from the same basic block. // If we compare two Phis from the same block, and for each entry block // the predicate is true for incoming values from this block, then the // predicate is also true for the Phis. for (const BasicBlock *IncBB : predecessors(LBB)) { const SCEV *L = getSCEV(LPhi->getIncomingValueForBlock(IncBB)); const SCEV *R = getSCEV(RPhi->getIncomingValueForBlock(IncBB)); if (!ProvedEasily(L, R)) return false; } } else if (RAR && RAR->getLoop()->getHeader() == LBB) { // Case two: RHS is also a Phi from the same basic block, and it is an // AddRec. It means that there is a loop which has both AddRec and Unknown // PHIs, for it we can compare incoming values of AddRec from above the loop // and latch with their respective incoming values of LPhi. // TODO: Generalize to handle loops with many inputs in a header. if (LPhi->getNumIncomingValues() != 2) return false; auto *RLoop = RAR->getLoop(); auto *Predecessor = RLoop->getLoopPredecessor(); assert(Predecessor && "Loop with AddRec with no predecessor?"); const SCEV *L1 = getSCEV(LPhi->getIncomingValueForBlock(Predecessor)); if (!ProvedEasily(L1, RAR->getStart())) return false; auto *Latch = RLoop->getLoopLatch(); assert(Latch && "Loop with AddRec with no latch?"); const SCEV *L2 = getSCEV(LPhi->getIncomingValueForBlock(Latch)); if (!ProvedEasily(L2, RAR->getPostIncExpr(*this))) return false; } else { // In all other cases go over inputs of LHS and compare each of them to RHS, // the predicate is true for (LHS, RHS) if it is true for all such pairs. // At this point RHS is either a non-Phi, or it is a Phi from some block // different from LBB. for (const BasicBlock *IncBB : predecessors(LBB)) { // Check that RHS is available in this block. if (!dominates(RHS, IncBB)) return false; const SCEV *L = getSCEV(LPhi->getIncomingValueForBlock(IncBB)); // Make sure L does not refer to a value from a potentially previous // iteration of a loop. if (!properlyDominates(L, IncBB)) return false; if (!ProvedEasily(L, RHS)) return false; } } return true; } bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS, const SCEV *FoundLHS, const SCEV *FoundRHS, const Instruction *Context) { if (isImpliedCondOperandsViaRanges(Pred, LHS, RHS, FoundLHS, FoundRHS)) return true; if (isImpliedCondOperandsViaNoOverflow(Pred, LHS, RHS, FoundLHS, FoundRHS)) return true; if (isImpliedCondOperandsViaAddRecStart(Pred, LHS, RHS, FoundLHS, FoundRHS, Context)) return true; return isImpliedCondOperandsHelper(Pred, LHS, RHS, FoundLHS, FoundRHS); } /// Is MaybeMinMaxExpr an (U|S)(Min|Max) of Candidate and some other values? template static bool IsMinMaxConsistingOf(const SCEV *MaybeMinMaxExpr, const SCEV *Candidate) { const MinMaxExprType *MinMaxExpr = dyn_cast(MaybeMinMaxExpr); if (!MinMaxExpr) return false; return is_contained(MinMaxExpr->operands(), Candidate); } static bool IsKnownPredicateViaAddRecStart(ScalarEvolution &SE, ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS) { // If both sides are affine addrecs for the same loop, with equal // steps, and we know the recurrences don't wrap, then we only // need to check the predicate on the starting values. if (!ICmpInst::isRelational(Pred)) return false; const SCEVAddRecExpr *LAR = dyn_cast(LHS); if (!LAR) return false; const SCEVAddRecExpr *RAR = dyn_cast(RHS); if (!RAR) return false; if (LAR->getLoop() != RAR->getLoop()) return false; if (!LAR->isAffine() || !RAR->isAffine()) return false; if (LAR->getStepRecurrence(SE) != RAR->getStepRecurrence(SE)) return false; SCEV::NoWrapFlags NW = ICmpInst::isSigned(Pred) ? SCEV::FlagNSW : SCEV::FlagNUW; if (!LAR->getNoWrapFlags(NW) || !RAR->getNoWrapFlags(NW)) return false; return SE.isKnownPredicate(Pred, LAR->getStart(), RAR->getStart()); } /// 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); LLVM_FALLTHROUGH; case ICmpInst::ICMP_SLE: return // min(A, ...) <= A IsMinMaxConsistingOf(LHS, RHS) || // A <= max(A, ...) IsMinMaxConsistingOf(RHS, LHS); case ICmpInst::ICMP_UGE: std::swap(LHS, RHS); LLVM_FALLTHROUGH; case ICmpInst::ICMP_ULE: return // min(A, ...) <= A IsMinMaxConsistingOf(LHS, RHS) || // A <= max(A, ...) IsMinMaxConsistingOf(RHS, LHS); } llvm_unreachable("covered switch fell through?!"); } bool ScalarEvolution::isImpliedViaOperations(ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS, const SCEV *FoundLHS, const SCEV *FoundRHS, unsigned Depth) { assert(getTypeSizeInBits(LHS->getType()) == getTypeSizeInBits(RHS->getType()) && "LHS and RHS have different sizes?"); assert(getTypeSizeInBits(FoundLHS->getType()) == getTypeSizeInBits(FoundRHS->getType()) && "FoundLHS and FoundRHS have different sizes?"); // We want to avoid hurting the compile time with analysis of too big trees. if (Depth > MaxSCEVOperationsImplicationDepth) return false; // We only want to work with GT comparison so far. if (Pred == ICmpInst::ICMP_ULT || Pred == ICmpInst::ICMP_SLT) { Pred = CmpInst::getSwappedPredicate(Pred); std::swap(LHS, RHS); std::swap(FoundLHS, FoundRHS); } // For unsigned, try to reduce it to corresponding signed comparison. if (Pred == ICmpInst::ICMP_UGT) // We can replace unsigned predicate with its signed counterpart if all // involved values are non-negative. // TODO: We could have better support for unsigned. if (isKnownNonNegative(FoundLHS) && isKnownNonNegative(FoundRHS)) { // Knowing that both FoundLHS and FoundRHS are non-negative, and knowing // FoundLHS >u FoundRHS, we also know that FoundLHS >s FoundRHS. Let us // use this fact to prove that LHS and RHS are non-negative. const SCEV *MinusOne = getMinusOne(LHS->getType()); if (isImpliedCondOperands(ICmpInst::ICMP_SGT, LHS, MinusOne, FoundLHS, FoundRHS) && isImpliedCondOperands(ICmpInst::ICMP_SGT, RHS, MinusOne, FoundLHS, FoundRHS)) Pred = ICmpInst::ICMP_SGT; } if (Pred != ICmpInst::ICMP_SGT) return false; auto GetOpFromSExt = [&](const SCEV *S) { if (auto *Ext = dyn_cast(S)) return Ext->getOperand(); // TODO: If S is a SCEVConstant then you can cheaply "strip" the sext off // the constant in some cases. return S; }; // Acquire values from extensions. auto *OrigLHS = LHS; auto *OrigFoundLHS = FoundLHS; LHS = GetOpFromSExt(LHS); FoundLHS = GetOpFromSExt(FoundLHS); // Is the SGT predicate can be proved trivially or using the found context. auto IsSGTViaContext = [&](const SCEV *S1, const SCEV *S2) { return isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_SGT, S1, S2) || isImpliedViaOperations(ICmpInst::ICMP_SGT, S1, S2, OrigFoundLHS, FoundRHS, Depth + 1); }; if (auto *LHSAddExpr = dyn_cast(LHS)) { // We want to avoid creation of any new non-constant SCEV. Since we are // going to compare the operands to RHS, we should be certain that we don't // need any size extensions for this. So let's decline all cases when the // sizes of types of LHS and RHS do not match. // TODO: Maybe try to get RHS from sext to catch more cases? if (getTypeSizeInBits(LHS->getType()) != getTypeSizeInBits(RHS->getType())) return false; // Should not overflow. if (!LHSAddExpr->hasNoSignedWrap()) return false; auto *LL = LHSAddExpr->getOperand(0); auto *LR = LHSAddExpr->getOperand(1); auto *MinusOne = getMinusOne(RHS->getType()); // Checks that S1 >= 0 && S2 > RHS, trivially or using the found context. auto IsSumGreaterThanRHS = [&](const SCEV *S1, const SCEV *S2) { return IsSGTViaContext(S1, MinusOne) && IsSGTViaContext(S2, RHS); }; // Try to prove the following rule: // (LHS = LL + LR) && (LL >= 0) && (LR > RHS) => (LHS > RHS). // (LHS = LL + LR) && (LR >= 0) && (LL > RHS) => (LHS > RHS). if (IsSumGreaterThanRHS(LL, LR) || IsSumGreaterThanRHS(LR, LL)) return true; } else if (auto *LHSUnknownExpr = dyn_cast(LHS)) { Value *LL, *LR; // FIXME: Once we have SDiv implemented, we can get rid of this matching. using namespace llvm::PatternMatch; if (match(LHSUnknownExpr->getValue(), m_SDiv(m_Value(LL), m_Value(LR)))) { // Rules for division. // We are going to perform some comparisons with Denominator and its // derivative expressions. In general case, creating a SCEV for it may // lead to a complex analysis of the entire graph, and in particular it // can request trip count recalculation for the same loop. This would // cache as SCEVCouldNotCompute to avoid the infinite recursion. To avoid // this, we only want to create SCEVs that are constants in this section. // So we bail if Denominator is not a constant. if (!isa(LR)) return false; auto *Denominator = cast(getSCEV(LR)); // We want to make sure that LHS = FoundLHS / Denominator. If it is so, // then a SCEV for the numerator already exists and matches with FoundLHS. auto *Numerator = getExistingSCEV(LL); if (!Numerator || Numerator->getType() != FoundLHS->getType()) return false; // Make sure that the numerator matches with FoundLHS and the denominator // is positive. if (!HasSameValue(Numerator, FoundLHS) || !isKnownPositive(Denominator)) return false; auto *DTy = Denominator->getType(); auto *FRHSTy = FoundRHS->getType(); if (DTy->isPointerTy() != FRHSTy->isPointerTy()) // One of types is a pointer and another one is not. We cannot extend // them properly to a wider type, so let us just reject this case. // TODO: Usage of getEffectiveSCEVType for DTy, FRHSTy etc should help // to avoid this check. return false; // Given that: // FoundLHS > FoundRHS, LHS = FoundLHS / Denominator, Denominator > 0. auto *WTy = getWiderType(DTy, FRHSTy); auto *DenominatorExt = getNoopOrSignExtend(Denominator, WTy); auto *FoundRHSExt = getNoopOrSignExtend(FoundRHS, WTy); // Try to prove the following rule: // (FoundRHS > Denominator - 2) && (RHS <= 0) => (LHS > RHS). // For example, given that FoundLHS > 2. It means that FoundLHS is at // least 3. If we divide it by Denominator < 4, we will have at least 1. auto *DenomMinusTwo = getMinusSCEV(DenominatorExt, getConstant(WTy, 2)); if (isKnownNonPositive(RHS) && IsSGTViaContext(FoundRHSExt, DenomMinusTwo)) return true; // Try to prove the following rule: // (FoundRHS > -1 - Denominator) && (RHS < 0) => (LHS > RHS). // For example, given that FoundLHS > -3. Then FoundLHS is at least -2. // If we divide it by Denominator > 2, then: // 1. If FoundLHS is negative, then the result is 0. // 2. If FoundLHS is non-negative, then the result is non-negative. // Anyways, the result is non-negative. auto *MinusOne = getMinusOne(WTy); auto *NegDenomMinusOne = getMinusSCEV(MinusOne, DenominatorExt); if (isKnownNegative(RHS) && IsSGTViaContext(FoundRHSExt, NegDenomMinusOne)) return true; } } // If our expression contained SCEVUnknown Phis, and we split it down and now // need to prove something for them, try to prove the predicate for every // possible incoming values of those Phis. if (isImpliedViaMerge(Pred, OrigLHS, RHS, OrigFoundLHS, FoundRHS, Depth + 1)) return true; return false; } static bool isKnownPredicateExtendIdiom(ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS) { // zext x u<= sext x, sext x s<= zext x switch (Pred) { case ICmpInst::ICMP_SGE: std::swap(LHS, RHS); LLVM_FALLTHROUGH; case ICmpInst::ICMP_SLE: { // If operand >=s 0 then ZExt == SExt. If operand (LHS); const SCEVZeroExtendExpr *ZExt = dyn_cast(RHS); if (SExt && ZExt && SExt->getOperand() == ZExt->getOperand()) return true; break; } case ICmpInst::ICMP_UGE: std::swap(LHS, RHS); LLVM_FALLTHROUGH; case ICmpInst::ICMP_ULE: { // If operand >=s 0 then ZExt == SExt. If operand (LHS); const SCEVSignExtendExpr *SExt = dyn_cast(RHS); if (SExt && ZExt && SExt->getOperand() == ZExt->getOperand()) return true; break; } default: break; }; return false; } bool ScalarEvolution::isKnownViaNonRecursiveReasoning(ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS) { return isKnownPredicateExtendIdiom(Pred, LHS, RHS) || isKnownPredicateViaConstantRanges(Pred, LHS, RHS) || IsKnownPredicateViaMinOrMax(*this, Pred, LHS, RHS) || IsKnownPredicateViaAddRecStart(*this, Pred, LHS, RHS) || isKnownPredicateViaNoOverflow(Pred, LHS, RHS); } bool ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS, const SCEV *FoundLHS, const SCEV *FoundRHS) { switch (Pred) { default: llvm_unreachable("Unexpected ICmpInst::Predicate value!"); case ICmpInst::ICMP_EQ: case ICmpInst::ICMP_NE: if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS)) return true; break; case ICmpInst::ICMP_SLT: case ICmpInst::ICMP_SLE: if (isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_SLE, LHS, FoundLHS) && isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_SGE, RHS, FoundRHS)) return true; break; case ICmpInst::ICMP_SGT: case ICmpInst::ICMP_SGE: if (isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_SGE, LHS, FoundLHS) && isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_SLE, RHS, FoundRHS)) return true; break; case ICmpInst::ICMP_ULT: case ICmpInst::ICMP_ULE: if (isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_ULE, LHS, FoundLHS) && isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_UGE, RHS, FoundRHS)) return true; break; case ICmpInst::ICMP_UGT: case ICmpInst::ICMP_UGE: if (isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_UGE, LHS, FoundLHS) && isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_ULE, RHS, FoundRHS)) return true; break; } // Maybe it can be proved via operations? if (isImpliedViaOperations(Pred, LHS, RHS, FoundLHS, FoundRHS)) return true; return false; } bool ScalarEvolution::isImpliedCondOperandsViaRanges(ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS, const SCEV *FoundLHS, const SCEV *FoundRHS) { if (!isa(RHS) || !isa(FoundRHS)) // The restriction on `FoundRHS` be lifted easily -- it exists only to // reduce the compile time impact of this optimization. return false; Optional Addend = computeConstantDifference(LHS, FoundLHS); if (!Addend) return false; const APInt &ConstFoundRHS = cast(FoundRHS)->getAPInt(); // `FoundLHSRange` is the range we know `FoundLHS` to be in by virtue of the // antecedent "`FoundLHS` `Pred` `FoundRHS`". ConstantRange FoundLHSRange = ConstantRange::makeExactICmpRegion(Pred, ConstFoundRHS); // Since `LHS` is `FoundLHS` + `Addend`, we can compute a range for `LHS`: ConstantRange LHSRange = FoundLHSRange.add(ConstantRange(*Addend)); // We can also compute the range of values for `LHS` that satisfy the // consequent, "`LHS` `Pred` `RHS`": const APInt &ConstRHS = cast(RHS)->getAPInt(); // The antecedent implies the consequent if every value of `LHS` that // satisfies the antecedent also satisfies the consequent. return LHSRange.icmp(Pred, ConstRHS); } bool ScalarEvolution::canIVOverflowOnLT(const SCEV *RHS, const SCEV *Stride, bool IsSigned) { assert(isKnownPositive(Stride) && "Positive stride expected!"); unsigned BitWidth = getTypeSizeInBits(RHS->getType()); const SCEV *One = getOne(Stride->getType()); if (IsSigned) { APInt MaxRHS = getSignedRangeMax(RHS); APInt MaxValue = APInt::getSignedMaxValue(BitWidth); APInt MaxStrideMinusOne = getSignedRangeMax(getMinusSCEV(Stride, One)); // SMaxRHS + SMaxStrideMinusOne > SMaxValue => overflow! return (std::move(MaxValue) - MaxStrideMinusOne).slt(MaxRHS); } APInt MaxRHS = getUnsignedRangeMax(RHS); APInt MaxValue = APInt::getMaxValue(BitWidth); APInt MaxStrideMinusOne = getUnsignedRangeMax(getMinusSCEV(Stride, One)); // UMaxRHS + UMaxStrideMinusOne > UMaxValue => overflow! return (std::move(MaxValue) - MaxStrideMinusOne).ult(MaxRHS); } bool ScalarEvolution::canIVOverflowOnGT(const SCEV *RHS, const SCEV *Stride, bool IsSigned) { unsigned BitWidth = getTypeSizeInBits(RHS->getType()); const SCEV *One = getOne(Stride->getType()); if (IsSigned) { APInt MinRHS = getSignedRangeMin(RHS); APInt MinValue = APInt::getSignedMinValue(BitWidth); APInt MaxStrideMinusOne = getSignedRangeMax(getMinusSCEV(Stride, One)); // SMinRHS - SMaxStrideMinusOne < SMinValue => overflow! return (std::move(MinValue) + MaxStrideMinusOne).sgt(MinRHS); } APInt MinRHS = getUnsignedRangeMin(RHS); APInt MinValue = APInt::getMinValue(BitWidth); APInt MaxStrideMinusOne = getUnsignedRangeMax(getMinusSCEV(Stride, One)); // UMinRHS - UMaxStrideMinusOne < UMinValue => overflow! return (std::move(MinValue) + MaxStrideMinusOne).ugt(MinRHS); } const SCEV *ScalarEvolution::getUDivCeilSCEV(const SCEV *N, const SCEV *D) { // umin(N, 1) + floor((N - umin(N, 1)) / D) // This is equivalent to "1 + floor((N - 1) / D)" for N != 0. The umin // expression fixes the case of N=0. const SCEV *MinNOne = getUMinExpr(N, getOne(N->getType())); const SCEV *NMinusOne = getMinusSCEV(N, MinNOne); return getAddExpr(MinNOne, getUDivExpr(NMinusOne, D)); } const SCEV *ScalarEvolution::computeMaxBECountForLT(const SCEV *Start, const SCEV *Stride, const SCEV *End, unsigned BitWidth, bool IsSigned) { // The logic in this function assumes we can represent a positive stride. // If we can't, the backedge-taken count must be zero. if (IsSigned && BitWidth == 1) return getZero(Stride->getType()); // Calculate the maximum backedge count based on the range of values // permitted by Start, End, and Stride. APInt MinStart = IsSigned ? getSignedRangeMin(Start) : getUnsignedRangeMin(Start); APInt MinStride = IsSigned ? getSignedRangeMin(Stride) : getUnsignedRangeMin(Stride); // We assume either the stride is positive, or the backedge-taken count // is zero. So force StrideForMaxBECount to be at least one. APInt One(BitWidth, 1); APInt StrideForMaxBECount = IsSigned ? APIntOps::smax(One, MinStride) : APIntOps::umax(One, MinStride); APInt MaxValue = IsSigned ? APInt::getSignedMaxValue(BitWidth) : APInt::getMaxValue(BitWidth); APInt Limit = MaxValue - (StrideForMaxBECount - 1); // Although End can be a MAX expression we estimate MaxEnd considering only // the case End = RHS of the loop termination condition. 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(getSignedRangeMax(End), Limit) : APIntOps::umin(getUnsignedRangeMax(End), Limit); // MaxBECount = ceil((max(MaxEnd, MinStart) - MinStart) / Stride) MaxEnd = IsSigned ? APIntOps::smax(MaxEnd, MinStart) : APIntOps::umax(MaxEnd, MinStart); return getUDivCeilSCEV(getConstant(MaxEnd - MinStart) /* Delta */, getConstant(StrideForMaxBECount) /* Step */); } ScalarEvolution::ExitLimit ScalarEvolution::howManyLessThans(const SCEV *LHS, const SCEV *RHS, const Loop *L, bool IsSigned, bool ControlsExit, bool AllowPredicates) { SmallPtrSet Predicates; const SCEVAddRecExpr *IV = dyn_cast(LHS); bool PredicatedIV = false; if (!IV && AllowPredicates) { // Try to make this an AddRec using runtime tests, in the first X // iterations of this loop, where X is the SCEV expression found by the // algorithm below. IV = convertSCEVToAddRecWithPredicates(LHS, L, Predicates); PredicatedIV = true; } // Avoid weird loops if (!IV || IV->getLoop() != L || !IV->isAffine()) return getCouldNotCompute(); // A precondition of this method is that the condition being analyzed // reaches an exiting branch which dominates the latch. Given that, we can // assume that an increment which violates the nowrap specification and // produces poison must cause undefined behavior when the resulting poison // value is branched upon and thus we can conclude that the backedge is // taken no more often than would be required to produce that poison value. // Note that a well defined loop can exit on the iteration which violates // the nowrap specification if there is another exit (either explicit or // implicit/exceptional) which causes the loop to execute before the // exiting instruction we're analyzing would trigger UB. auto WrapType = IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW; bool NoWrap = ControlsExit && IV->getNoWrapFlags(WrapType); ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SLT : ICmpInst::ICMP_ULT; const SCEV *Stride = IV->getStepRecurrence(*this); bool PositiveStride = isKnownPositive(Stride); // Avoid negative or zero stride values. if (!PositiveStride) { // We can compute the correct backedge taken count for loops with unknown // strides if we can prove that the loop is not an infinite loop with side // effects. Here's the loop structure we are trying to handle - // // i = start // do { // A[i] = i; // i += s; // } while (i < end); // // The backedge taken count for such loops is evaluated as - // (max(end, start + stride) - start - 1) /u stride // // The additional preconditions that we need to check to prove correctness // of the above formula is as follows - // // a) IV is either nuw or nsw depending upon signedness (indicated by the // NoWrap flag). // b) loop is single exit with no side effects. // // // Precondition a) implies that if the stride is negative, this is a single // trip loop. The backedge taken count formula reduces to zero in this case. // // Precondition b) implies that if rhs is invariant in L, then unknown // stride being zero means the backedge can't be taken without UB. // // The positive stride case is the same as isKnownPositive(Stride) returning // true (original behavior of the function). // // We want to make sure that the stride is truly unknown as there are edge // cases where ScalarEvolution propagates no wrap flags to the // post-increment/decrement IV even though the increment/decrement operation // itself is wrapping. The computed backedge taken count may be wrong in // such cases. This is prevented by checking that the stride is not known to // be either positive or non-positive. For example, no wrap flags are // propagated to the post-increment IV of this loop with a trip count of 2 - // // unsigned char i; // for(i=127; i<128; i+=129) // A[i] = i; // if (PredicatedIV || !NoWrap || isKnownNonPositive(Stride) || !loopIsFiniteByAssumption(L)) return getCouldNotCompute(); if (!isKnownNonZero(Stride)) { // If we have a step of zero, and RHS isn't invariant in L, we don't know // if it might eventually be greater than start and if so, on which // iteration. We can't even produce a useful upper bound. if (!isLoopInvariant(RHS, L)) return getCouldNotCompute(); // We allow a potentially zero stride, but we need to divide by stride // below. Since the loop can't be infinite and this check must control // the sole exit, we can infer the exit must be taken on the first // iteration (e.g. backedge count = 0) if the stride is zero. Given that, // we know the numerator in the divides below must be zero, so we can // pick an arbitrary non-zero value for the denominator (e.g. stride) // and produce the right result. // FIXME: Handle the case where Stride is poison? auto wouldZeroStrideBeUB = [&]() { // Proof by contradiction. Suppose the stride were zero. If we can // prove that the backedge *is* taken on the first iteration, then since // we know this condition controls the sole exit, we must have an // infinite loop. We can't have a (well defined) infinite loop per // check just above. // Note: The (Start - Stride) term is used to get the start' term from // (start' + stride,+,stride). Remember that we only care about the // result of this expression when stride == 0 at runtime. auto *StartIfZero = getMinusSCEV(IV->getStart(), Stride); return isLoopEntryGuardedByCond(L, Cond, StartIfZero, RHS); }; if (!wouldZeroStrideBeUB()) { Stride = getUMaxExpr(Stride, getOne(Stride->getType())); } } } else if (!Stride->isOne() && !NoWrap) { auto isUBOnWrap = [&]() { // Can we prove this loop *must* be UB if overflow of IV occurs? // Reasoning goes as follows: // * Suppose the IV did self wrap. // * If Stride evenly divides the iteration space, then once wrap // occurs, the loop must revisit the same values. // * We know that RHS is invariant, and that none of those values // caused this exit to be taken previously. Thus, this exit is // dynamically dead. // * If this is the sole exit, then a dead exit implies the loop // must be infinite if there are no abnormal exits. // * If the loop were infinite, then it must either not be mustprogress // or have side effects. Otherwise, it must be UB. // * It can't (by assumption), be UB so we have contradicted our // premise and can conclude the IV did not in fact self-wrap. // From no-self-wrap, we need to then prove no-(un)signed-wrap. This // follows trivially from the fact that every (un)signed-wrapped, but // not self-wrapped value must be LT than the last value before // (un)signed wrap. Since we know that last value didn't exit, nor // will any smaller one. if (!isLoopInvariant(RHS, L)) return false; auto *StrideC = dyn_cast(Stride); if (!StrideC || !StrideC->getAPInt().isPowerOf2()) return false; if (!ControlsExit || !loopHasNoAbnormalExits(L)) return false; return loopIsFiniteByAssumption(L); }; // 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 (canIVOverflowOnLT(RHS, Stride, IsSigned) && !isUBOnWrap()) return getCouldNotCompute(); } // On all paths just preceeding, we established the following invariant: // IV can be assumed not to overflow up to and including the exiting // iteration. We proved this in one of two ways: // 1) We can show overflow doesn't occur before the exiting iteration // 1a) canIVOverflowOnLT, and b) step of one // 2) We can show that if overflow occurs, the loop must execute UB // before any possible exit. // Note that we have not yet proved RHS invariant (in general). const SCEV *Start = IV->getStart(); // Preserve pointer-typed Start/RHS to pass to isLoopEntryGuardedByCond. // Use integer-typed versions for actual computation. const SCEV *OrigStart = Start; const SCEV *OrigRHS = RHS; if (Start->getType()->isPointerTy()) { Start = getLosslessPtrToIntExpr(Start); if (isa(Start)) return Start; } if (RHS->getType()->isPointerTy()) { RHS = getLosslessPtrToIntExpr(RHS); if (isa(RHS)) return RHS; } // When the RHS is not invariant, we do not know the end bound of the loop and // cannot calculate the ExactBECount needed by ExitLimit. However, we can // calculate the MaxBECount, given the start, stride and max value for the end // bound of the loop (RHS), and the fact that IV does not overflow (which is // checked above). if (!isLoopInvariant(RHS, L)) { const SCEV *MaxBECount = computeMaxBECountForLT( Start, Stride, RHS, getTypeSizeInBits(LHS->getType()), IsSigned); return ExitLimit(getCouldNotCompute() /* ExactNotTaken */, MaxBECount, false /*MaxOrZero*/, Predicates); } // We use the expression (max(End,Start)-Start)/Stride to describe the // backedge count, as if the backedge is taken at least once max(End,Start) // is End and so the result is as above, and if not max(End,Start) is Start // so we get a backedge count of zero. const SCEV *BECount = nullptr; auto *StartMinusStride = getMinusSCEV(OrigStart, Stride); // Can we prove (max(RHS,Start) > Start - Stride? if (isLoopEntryGuardedByCond(L, Cond, StartMinusStride, Start) && isLoopEntryGuardedByCond(L, Cond, StartMinusStride, RHS)) { // In this case, we can use a refined formula for computing backedge taken // count. The general formula remains: // "End-Start /uceiling Stride" where "End = max(RHS,Start)" // We want to use the alternate formula: // "((End - 1) - (Start - Stride)) /u Stride" // Let's do a quick case analysis to show these are equivalent under // our precondition that max(RHS,Start) > Start - Stride. // * For RHS <= Start, the backedge-taken count must be zero. // "((End - 1) - (Start - Stride)) /u Stride" reduces to // "((Start - 1) - (Start - Stride)) /u Stride" which simplies to // "Stride - 1 /u Stride" which is indeed zero for all non-zero values // of Stride. For 0 stride, we've use umin(1,Stride) above, reducing // this to the stride of 1 case. // * For RHS >= Start, the backedge count must be "RHS-Start /uceil Stride". // "((End - 1) - (Start - Stride)) /u Stride" reduces to // "((RHS - 1) - (Start - Stride)) /u Stride" reassociates to // "((RHS - (Start - Stride) - 1) /u Stride". // Our preconditions trivially imply no overflow in that form. const SCEV *MinusOne = getMinusOne(Stride->getType()); const SCEV *Numerator = getMinusSCEV(getAddExpr(RHS, MinusOne), StartMinusStride); if (!isa(Numerator)) { BECount = getUDivExpr(Numerator, Stride); } } const SCEV *BECountIfBackedgeTaken = nullptr; if (!BECount) { auto canProveRHSGreaterThanEqualStart = [&]() { auto CondGE = IsSigned ? ICmpInst::ICMP_SGE : ICmpInst::ICMP_UGE; if (isLoopEntryGuardedByCond(L, CondGE, OrigRHS, OrigStart)) return true; // (RHS > Start - 1) implies RHS >= Start. // * "RHS >= Start" is trivially equivalent to "RHS > Start - 1" if // "Start - 1" doesn't overflow. // * For signed comparison, if Start - 1 does overflow, it's equal // to INT_MAX, and "RHS >s INT_MAX" is trivially false. // * For unsigned comparison, if Start - 1 does overflow, it's equal // to UINT_MAX, and "RHS >u UINT_MAX" is trivially false. // // FIXME: Should isLoopEntryGuardedByCond do this for us? auto CondGT = IsSigned ? ICmpInst::ICMP_SGT : ICmpInst::ICMP_UGT; auto *StartMinusOne = getAddExpr(OrigStart, getMinusOne(OrigStart->getType())); return isLoopEntryGuardedByCond(L, CondGT, OrigRHS, StartMinusOne); }; // If we know that RHS >= Start in the context of loop, then we know that // max(RHS, Start) = RHS at this point. const SCEV *End; if (canProveRHSGreaterThanEqualStart()) { End = RHS; } else { // If RHS < Start, the backedge will be taken zero times. So in // general, we can write the backedge-taken count as: // // RHS >= Start ? ceil(RHS - Start) / Stride : 0 // // We convert it to the following to make it more convenient for SCEV: // // ceil(max(RHS, Start) - Start) / Stride End = IsSigned ? getSMaxExpr(RHS, Start) : getUMaxExpr(RHS, Start); // See what would happen if we assume the backedge is taken. This is // used to compute MaxBECount. BECountIfBackedgeTaken = getUDivCeilSCEV(getMinusSCEV(RHS, Start), Stride); } // At this point, we know: // // 1. If IsSigned, Start <=s End; otherwise, Start <=u End // 2. The index variable doesn't overflow. // // Therefore, we know N exists such that // (Start + Stride * N) >= End, and computing "(Start + Stride * N)" // doesn't overflow. // // Using this information, try to prove whether the addition in // "(Start - End) + (Stride - 1)" has unsigned overflow. const SCEV *One = getOne(Stride->getType()); bool MayAddOverflow = [&] { if (auto *StrideC = dyn_cast(Stride)) { if (StrideC->getAPInt().isPowerOf2()) { // Suppose Stride is a power of two, and Start/End are unsigned // integers. Let UMAX be the largest representable unsigned // integer. // // By the preconditions of this function, we know // "(Start + Stride * N) >= End", and this doesn't overflow. // As a formula: // // End <= (Start + Stride * N) <= UMAX // // Subtracting Start from all the terms: // // End - Start <= Stride * N <= UMAX - Start // // Since Start is unsigned, UMAX - Start <= UMAX. Therefore: // // End - Start <= Stride * N <= UMAX // // Stride * N is a multiple of Stride. Therefore, // // End - Start <= Stride * N <= UMAX - (UMAX mod Stride) // // Since Stride is a power of two, UMAX + 1 is divisible by Stride. // Therefore, UMAX mod Stride == Stride - 1. So we can write: // // End - Start <= Stride * N <= UMAX - Stride - 1 // // Dropping the middle term: // // End - Start <= UMAX - Stride - 1 // // Adding Stride - 1 to both sides: // // (End - Start) + (Stride - 1) <= UMAX // // In other words, the addition doesn't have unsigned overflow. // // A similar proof works if we treat Start/End as signed values. // Just rewrite steps before "End - Start <= Stride * N <= UMAX" to // use signed max instead of unsigned max. Note that we're trying // to prove a lack of unsigned overflow in either case. return false; } } if (Start == Stride || Start == getMinusSCEV(Stride, One)) { // If Start is equal to Stride, (End - Start) + (Stride - 1) == End - 1. // If !IsSigned, 0 (BECount)) { MaxBECount = BECount; } else if (BECountIfBackedgeTaken && isa(BECountIfBackedgeTaken)) { // If we know exactly how many times the backedge will be taken if it's // taken at least once, then the backedge count will either be that or // zero. MaxBECount = BECountIfBackedgeTaken; MaxOrZero = true; } else { MaxBECount = computeMaxBECountForLT( Start, Stride, RHS, getTypeSizeInBits(LHS->getType()), IsSigned); } if (isa(MaxBECount) && !isa(BECount)) MaxBECount = getConstant(getUnsignedRangeMax(BECount)); return ExitLimit(BECount, MaxBECount, MaxOrZero, Predicates); } ScalarEvolution::ExitLimit ScalarEvolution::howManyGreaterThans(const SCEV *LHS, const SCEV *RHS, const Loop *L, bool IsSigned, bool ControlsExit, bool AllowPredicates) { SmallPtrSet Predicates; // We handle only IV > Invariant if (!isLoopInvariant(RHS, L)) return getCouldNotCompute(); const SCEVAddRecExpr *IV = dyn_cast(LHS); if (!IV && AllowPredicates) // Try to make this an AddRec using runtime tests, in the first X // iterations of this loop, where X is the SCEV expression found by the // algorithm below. IV = convertSCEVToAddRecWithPredicates(LHS, L, Predicates); // Avoid weird loops if (!IV || IV->getLoop() != L || !IV->isAffine()) return getCouldNotCompute(); auto WrapType = IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW; bool NoWrap = ControlsExit && IV->getNoWrapFlags(WrapType); ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SGT : ICmpInst::ICMP_UGT; 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() && !NoWrap) if (canIVOverflowOnGT(RHS, Stride, IsSigned)) return getCouldNotCompute(); const SCEV *Start = IV->getStart(); const SCEV *End = RHS; if (!isLoopEntryGuardedByCond(L, Cond, getAddExpr(Start, Stride), RHS)) { // If we know that Start >= RHS in the context of loop, then we know that // min(RHS, Start) = RHS at this point. if (isLoopEntryGuardedByCond( L, IsSigned ? ICmpInst::ICMP_SGE : ICmpInst::ICMP_UGE, Start, RHS)) End = RHS; else End = IsSigned ? getSMinExpr(RHS, Start) : getUMinExpr(RHS, Start); } if (Start->getType()->isPointerTy()) { Start = getLosslessPtrToIntExpr(Start); if (isa(Start)) return Start; } if (End->getType()->isPointerTy()) { End = getLosslessPtrToIntExpr(End); if (isa(End)) return End; } // Compute ((Start - End) + (Stride - 1)) / Stride. // FIXME: This can overflow. Holding off on fixing this for now; // howManyGreaterThans will hopefully be gone soon. const SCEV *One = getOne(Stride->getType()); const SCEV *BECount = getUDivExpr( getAddExpr(getMinusSCEV(Start, End), getMinusSCEV(Stride, One)), Stride); APInt MaxStart = IsSigned ? getSignedRangeMax(Start) : getUnsignedRangeMax(Start); APInt MinStride = IsSigned ? getSignedRangeMin(Stride) : getUnsignedRangeMin(Stride); 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(getSignedRangeMin(RHS), Limit) : APIntOps::umax(getUnsignedRangeMin(RHS), Limit); const SCEV *MaxBECount = isa(BECount) ? BECount : getUDivCeilSCEV(getConstant(MaxStart - MinEnd), getConstant(MinStride)); if (isa(MaxBECount)) MaxBECount = BECount; return ExitLimit(BECount, MaxBECount, false, Predicates); } const SCEV *SCEVAddRecExpr::getNumIterationsInRange(const 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(operands()); Operands[0] = SE.getZero(SC->getType()); const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(), getNoWrapFlags(FlagNW)); if (const auto *ShiftedAddRec = dyn_cast(Shifted)) return ShiftedAddRec->getNumIterationsInRange( Range.subtract(SC->getAPInt()), 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. if (any_of(operands(), [](const SCEV *Op) { return !isa(Op); })) 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.getZero(getType()); 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 A = cast(getOperand(1))->getAPInt(); APInt End = A.sge(1) ? (Range.getUpper() - 1) : 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 - 1), SE)->getValue()) && "Linear scev computation is off in a bad way!"); return SE.getConstant(ExitValue); } if (isQuadratic()) { if (auto S = SolveQuadraticAddRecRange(this, Range, SE)) return SE.getConstant(S.getValue()); } return SE.getCouldNotCompute(); } const SCEVAddRecExpr * SCEVAddRecExpr::getPostIncExpr(ScalarEvolution &SE) const { assert(getNumOperands() > 1 && "AddRec with zero step?"); // There is a temptation to just call getAddExpr(this, getStepRecurrence(SE)), // but in this case we cannot guarantee that the value returned will be an // AddRec because SCEV does not have a fixed point where it stops // simplification: it is legal to return ({rec1} + {rec2}). For example, it // may happen if we reach arithmetic depth limit while simplifying. So we // construct the returned value explicitly. SmallVector Ops; // If this is {A,+,B,+,C,...,+,N}, then its step is {B,+,C,+,...,+,N}, and // (this + Step) is {A+B,+,B+C,+...,+,N}. for (unsigned i = 0, e = getNumOperands() - 1; i < e; ++i) Ops.push_back(SE.getAddExpr(getOperand(i), getOperand(i + 1))); // We know that the last operand is not a constant zero (otherwise it would // have been popped out earlier). This guarantees us that if the result has // the same last operand, then it will also not be popped out, meaning that // the returned value will be an AddRec. const SCEV *Last = getOperand(getNumOperands() - 1); assert(!Last->isZero() && "Recurrency with zero step?"); Ops.push_back(Last); return cast(SE.getAddRecExpr(Ops, getLoop(), SCEV::FlagAnyWrap)); } // Return true when S contains at least an undef value. static inline bool containsUndefs(const SCEV *S) { return SCEVExprContains(S, [](const SCEV *S) { if (const auto *SU = dyn_cast(S)) return isa(SU->getValue()); return false; }); } 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) || 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; } }; // Check if a SCEV contains an AddRecExpr. struct SCEVHasAddRec { bool &ContainsAddRec; SCEVHasAddRec(bool &ContainsAddRec) : ContainsAddRec(ContainsAddRec) { ContainsAddRec = false; } bool follow(const SCEV *S) { if (isa(S)) { ContainsAddRec = true; // Stop recursion: once we collected a term, do not walk its operands. return false; } // Keep looking. return true; } bool isDone() const { return false; } }; // Find factors that are multiplied with an expression that (possibly as a // subexpression) contains an AddRecExpr. In the expression: // // 8 * (100 + %p * %q * (%a + {0, +, 1}_loop)) // // "%p * %q" are factors multiplied by the expression "(%a + {0, +, 1}_loop)" // that contains the AddRec {0, +, 1}_loop. %p * %q are likely to be array size // parameters as they form a product with an induction variable. // // This collector expects all array size parameters to be in the same MulExpr. // It might be necessary to later add support for collecting parameters that are // spread over different nested MulExpr. struct SCEVCollectAddRecMultiplies { SmallVectorImpl &Terms; ScalarEvolution &SE; SCEVCollectAddRecMultiplies(SmallVectorImpl &T, ScalarEvolution &SE) : Terms(T), SE(SE) {} bool follow(const SCEV *S) { if (auto *Mul = dyn_cast(S)) { bool HasAddRec = false; SmallVector Operands; for (auto Op : Mul->operands()) { const SCEVUnknown *Unknown = dyn_cast(Op); if (Unknown && !isa(Unknown->getValue())) { Operands.push_back(Op); } else if (Unknown) { HasAddRec = true; } else { bool ContainsAddRec = false; SCEVHasAddRec ContiansAddRec(ContainsAddRec); visitAll(Op, ContiansAddRec); HasAddRec |= ContainsAddRec; } } if (Operands.size() == 0) return true; if (!HasAddRec) return false; Terms.push_back(SE.getMulExpr(Operands)); // Stop recursion: once we collected a term, do not walk its operands. return false; } // Keep looking. return true; } bool isDone() const { return false; } }; } // end anonymous namespace /// Find parametric terms in this SCEVAddRecExpr. We first for parameters in /// two places: /// 1) The strides of AddRec expressions. /// 2) Unknowns that are multiplied with AddRec expressions. void ScalarEvolution::collectParametricTerms(const SCEV *Expr, SmallVectorImpl &Terms) { SmallVector Strides; SCEVCollectStrides StrideCollector(*this, Strides); visitAll(Expr, StrideCollector); LLVM_DEBUG({ dbgs() << "Strides:\n"; for (const SCEV *S : Strides) dbgs() << *S << "\n"; }); for (const SCEV *S : Strides) { SCEVCollectTerms TermCollector(Terms); visitAll(S, TermCollector); } LLVM_DEBUG({ dbgs() << "Terms:\n"; for (const SCEV *T : Terms) dbgs() << *T << "\n"; }); SCEVCollectAddRecMultiplies MulCollector(Terms, *this); visitAll(Expr, MulCollector); } 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. erase_if(Terms, [](const SCEV *E) { return isa(E); }); if (Terms.size() > 0) if (!findArrayDimensionsRec(SE, Terms, Sizes)) return false; Sizes.push_back(Step); return true; } // 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 (SCEVExprContains(T, [](const SCEV *S) { return isa(S); })) 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); } void ScalarEvolution::findArrayDimensions(SmallVectorImpl &Terms, SmallVectorImpl &Sizes, const SCEV *ElementSize) { 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; LLVM_DEBUG({ dbgs() << "Terms:\n"; for (const SCEV *T : Terms) dbgs() << *T << "\n"; }); // Remove duplicates. array_pod_sort(Terms.begin(), Terms.end()); Terms.erase(std::unique(Terms.begin(), Terms.end()), Terms.end()); // Put larger terms first. llvm::sort(Terms, [](const SCEV *LHS, const SCEV *RHS) { return numberOfTerms(LHS) > numberOfTerms(RHS); }); // Try to divide all terms by the element size. If term is not divisible by // element size, proceed with the original term. for (const SCEV *&Term : Terms) { const SCEV *Q, *R; SCEVDivision::divide(*this, Term, ElementSize, &Q, &R); if (!Q->isZero()) Term = Q; } SmallVector NewTerms; // Remove constant factors. for (const SCEV *T : Terms) if (const SCEV *NewT = removeConstantFactors(*this, T)) NewTerms.push_back(NewT); LLVM_DEBUG({ dbgs() << "Terms after sorting:\n"; for (const SCEV *T : NewTerms) dbgs() << *T << "\n"; }); if (NewTerms.empty() || !findArrayDimensionsRec(*this, NewTerms, Sizes)) { Sizes.clear(); return; } // The last element to be pushed into Sizes is the size of an element. Sizes.push_back(ElementSize); LLVM_DEBUG({ dbgs() << "Sizes:\n"; for (const SCEV *S : Sizes) dbgs() << *S << "\n"; }); } void ScalarEvolution::computeAccessFunctions( const SCEV *Expr, SmallVectorImpl &Subscripts, SmallVectorImpl &Sizes) { // Early exit in case this SCEV is not an affine multivariate function. if (Sizes.empty()) return; if (auto *AR = dyn_cast(Expr)) if (!AR->isAffine()) return; const SCEV *Res = Expr; int Last = Sizes.size() - 1; for (int i = Last; i >= 0; i--) { const SCEV *Q, *R; SCEVDivision::divide(*this, Res, Sizes[i], &Q, &R); LLVM_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()); LLVM_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 ScalarEvolution::delinearize(const SCEV *Expr, SmallVectorImpl &Subscripts, SmallVectorImpl &Sizes, const SCEV *ElementSize) { // First step: collect parametric terms. SmallVector Terms; collectParametricTerms(Expr, Terms); if (Terms.empty()) return; // Second step: find subscript sizes. findArrayDimensions(Terms, Sizes, ElementSize); if (Sizes.empty()) return; // Third step: compute the access functions for each subscript. computeAccessFunctions(Expr, Subscripts, Sizes); if (Subscripts.empty()) return; LLVM_DEBUG({ dbgs() << "succeeded to delinearize " << *Expr << "\n"; dbgs() << "ArrayDecl[UnknownSize]"; for (const SCEV *S : Sizes) dbgs() << "[" << *S << "]"; dbgs() << "\nArrayRef"; for (const SCEV *S : Subscripts) dbgs() << "[" << *S << "]"; dbgs() << "\n"; }); } bool ScalarEvolution::getIndexExpressionsFromGEP( const GetElementPtrInst *GEP, SmallVectorImpl &Subscripts, SmallVectorImpl &Sizes) { assert(Subscripts.empty() && Sizes.empty() && "Expected output lists to be empty on entry to this function."); assert(GEP && "getIndexExpressionsFromGEP called with a null GEP"); Type *Ty = nullptr; bool DroppedFirstDim = false; for (unsigned i = 1; i < GEP->getNumOperands(); i++) { const SCEV *Expr = getSCEV(GEP->getOperand(i)); if (i == 1) { Ty = GEP->getSourceElementType(); if (auto *Const = dyn_cast(Expr)) if (Const->getValue()->isZero()) { DroppedFirstDim = true; continue; } Subscripts.push_back(Expr); continue; } auto *ArrayTy = dyn_cast(Ty); if (!ArrayTy) { Subscripts.clear(); Sizes.clear(); return false; } Subscripts.push_back(Expr); if (!(DroppedFirstDim && i == 2)) Sizes.push_back(ArrayTy->getNumElements()); Ty = ArrayTy->getElementType(); } return !Subscripts.empty(); } //===----------------------------------------------------------------------===// // 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->eraseValueFromMap(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->users()); 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->eraseValueFromMap(U); llvm::append_range(Worklist, U->users()); } // Delete the Old value. if (PHINode *PN = dyn_cast(Old)) SE->ConstantEvolutionLoopExitValue.erase(PN); SE->eraseValueFromMap(Old); // this now dangles! } ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se) : CallbackVH(V), SE(se) {} //===----------------------------------------------------------------------===// // ScalarEvolution Class Implementation //===----------------------------------------------------------------------===// ScalarEvolution::ScalarEvolution(Function &F, TargetLibraryInfo &TLI, AssumptionCache &AC, DominatorTree &DT, LoopInfo &LI) : F(F), TLI(TLI), AC(AC), DT(DT), LI(LI), CouldNotCompute(new SCEVCouldNotCompute()), ValuesAtScopes(64), LoopDispositions(64), BlockDispositions(64) { // To use guards for proving predicates, we need to scan every instruction in // relevant basic blocks, and not just terminators. Doing this is a waste of // time if the IR does not actually contain any calls to // @llvm.experimental.guard, so do a quick check and remember this beforehand. // // This pessimizes the case where a pass that preserves ScalarEvolution wants // to _add_ guards to the module when there weren't any before, and wants // ScalarEvolution to optimize based on those guards. For now we prefer to be // efficient in lieu of being smart in that rather obscure case. auto *GuardDecl = F.getParent()->getFunction( Intrinsic::getName(Intrinsic::experimental_guard)); HasGuards = GuardDecl && !GuardDecl->use_empty(); } ScalarEvolution::ScalarEvolution(ScalarEvolution &&Arg) : F(Arg.F), HasGuards(Arg.HasGuards), TLI(Arg.TLI), AC(Arg.AC), DT(Arg.DT), LI(Arg.LI), CouldNotCompute(std::move(Arg.CouldNotCompute)), ValueExprMap(std::move(Arg.ValueExprMap)), PendingLoopPredicates(std::move(Arg.PendingLoopPredicates)), PendingPhiRanges(std::move(Arg.PendingPhiRanges)), PendingMerges(std::move(Arg.PendingMerges)), MinTrailingZerosCache(std::move(Arg.MinTrailingZerosCache)), BackedgeTakenCounts(std::move(Arg.BackedgeTakenCounts)), PredicatedBackedgeTakenCounts( std::move(Arg.PredicatedBackedgeTakenCounts)), ConstantEvolutionLoopExitValue( std::move(Arg.ConstantEvolutionLoopExitValue)), ValuesAtScopes(std::move(Arg.ValuesAtScopes)), LoopDispositions(std::move(Arg.LoopDispositions)), LoopPropertiesCache(std::move(Arg.LoopPropertiesCache)), BlockDispositions(std::move(Arg.BlockDispositions)), UnsignedRanges(std::move(Arg.UnsignedRanges)), SignedRanges(std::move(Arg.SignedRanges)), UniqueSCEVs(std::move(Arg.UniqueSCEVs)), UniquePreds(std::move(Arg.UniquePreds)), SCEVAllocator(std::move(Arg.SCEVAllocator)), LoopUsers(std::move(Arg.LoopUsers)), PredicatedSCEVRewrites(std::move(Arg.PredicatedSCEVRewrites)), FirstUnknown(Arg.FirstUnknown) { Arg.FirstUnknown = nullptr; } ScalarEvolution::~ScalarEvolution() { // Iterate through all the SCEVUnknown instances and call their // destructors, so that they release their references to their values. for (SCEVUnknown *U = FirstUnknown; U;) { SCEVUnknown *Tmp = U; U = U->Next; Tmp->~SCEVUnknown(); } FirstUnknown = nullptr; ExprValueMap.clear(); ValueExprMap.clear(); HasRecMap.clear(); BackedgeTakenCounts.clear(); PredicatedBackedgeTakenCounts.clear(); assert(PendingLoopPredicates.empty() && "isImpliedCond garbage"); assert(PendingPhiRanges.empty() && "getRangeRef garbage"); assert(PendingMerges.empty() && "isImpliedViaMerge garbage"); assert(!WalkingBEDominatingConds && "isLoopBackedgeGuardedByCond garbage!"); assert(!ProvingSplitPredicate && "ProvingSplitPredicate garbage!"); } 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 *I : *L) PrintLoopInfo(OS, SE, I); OS << "Loop "; L->getHeader()->printAsOperand(OS, /*PrintType=*/false); OS << ": "; SmallVector ExitingBlocks; L->getExitingBlocks(ExitingBlocks); if (ExitingBlocks.size() != 1) OS << " "; if (SE->hasLoopInvariantBackedgeTakenCount(L)) OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L) << "\n"; else OS << "Unpredictable backedge-taken count.\n"; if (ExitingBlocks.size() > 1) for (BasicBlock *ExitingBlock : ExitingBlocks) { OS << " exit count for " << ExitingBlock->getName() << ": " << *SE->getExitCount(L, ExitingBlock) << "\n"; } OS << "Loop "; L->getHeader()->printAsOperand(OS, /*PrintType=*/false); OS << ": "; if (!isa(SE->getConstantMaxBackedgeTakenCount(L))) { OS << "max backedge-taken count is " << *SE->getConstantMaxBackedgeTakenCount(L); if (SE->isBackedgeTakenCountMaxOrZero(L)) OS << ", actual taken count either this or zero."; } else { OS << "Unpredictable max backedge-taken count. "; } OS << "\n" "Loop "; L->getHeader()->printAsOperand(OS, /*PrintType=*/false); OS << ": "; SCEVUnionPredicate Pred; auto PBT = SE->getPredicatedBackedgeTakenCount(L, Pred); if (!isa(PBT)) { OS << "Predicated backedge-taken count is " << *PBT << "\n"; OS << " Predicates:\n"; Pred.print(OS, 4); } else { OS << "Unpredictable predicated backedge-taken count. "; } OS << "\n"; if (SE->hasLoopInvariantBackedgeTakenCount(L)) { OS << "Loop "; L->getHeader()->printAsOperand(OS, /*PrintType=*/false); OS << ": "; OS << "Trip multiple is " << SE->getSmallConstantTripMultiple(L) << "\n"; } } static StringRef loopDispositionToStr(ScalarEvolution::LoopDisposition LD) { switch (LD) { case ScalarEvolution::LoopVariant: return "Variant"; case ScalarEvolution::LoopInvariant: return "Invariant"; case ScalarEvolution::LoopComputable: return "Computable"; } llvm_unreachable("Unknown ScalarEvolution::LoopDisposition kind!"); } void ScalarEvolution::print(raw_ostream &OS) 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); if (ClassifyExpressions) { OS << "Classifying expressions for: "; F.printAsOperand(OS, /*PrintType=*/false); OS << "\n"; for (Instruction &I : instructions(F)) if (isSCEVable(I.getType()) && !isa(I)) { OS << I << '\n'; OS << " --> "; const SCEV *SV = SE.getSCEV(&I); SV->print(OS); if (!isa(SV)) { OS << " U: "; SE.getUnsignedRange(SV).print(OS); OS << " S: "; SE.getSignedRange(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 (!isa(AtUse)) { OS << " U: "; SE.getUnsignedRange(AtUse).print(OS); OS << " S: "; SE.getSignedRange(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; } bool First = true; for (auto *Iter = L; Iter; Iter = Iter->getParentLoop()) { if (First) { OS << "\t\t" "LoopDispositions: { "; First = false; } else { OS << ", "; } Iter->getHeader()->printAsOperand(OS, /*PrintType=*/false); OS << ": " << loopDispositionToStr(SE.getLoopDisposition(SV, Iter)); } for (auto *InnerL : depth_first(L)) { if (InnerL == L) continue; if (First) { OS << "\t\t" "LoopDispositions: { "; First = false; } else { OS << ", "; } InnerL->getHeader()->printAsOperand(OS, /*PrintType=*/false); OS << ": " << loopDispositionToStr(SE.getLoopDisposition(SV, InnerL)); } OS << " }"; } OS << "\n"; } } OS << "Determining loop execution counts for: "; F.printAsOperand(OS, /*PrintType=*/false); OS << "\n"; for (Loop *I : LI) 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 (S->getSCEVType()) { case scConstant: return LoopInvariant; case scPtrToInt: 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; // Everything that is not defined at loop entry is variant. if (DT.dominates(L->getHeader(), AR->getLoop()->getHeader())) return LoopVariant; assert(!L->contains(AR->getLoop()) && "Containing loop's header does not" " dominate the contained loop's header?"); // 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 (auto *Op : AR->operands()) if (!isLoopInvariant(Op, L)) return LoopVariant; // Otherwise it's loop-invariant. return LoopInvariant; } case scAddExpr: case scMulExpr: case scUMaxExpr: case scSMaxExpr: case scUMinExpr: case scSMinExpr: { bool HasVarying = false; for (auto *Op : cast(S)->operands()) { LoopDisposition D = getLoopDisposition(Op, 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 (auto *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 (S->getSCEVType()) { case scConstant: return ProperlyDominatesBlock; case scPtrToInt: 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. LLVM_FALLTHROUGH; } case scAddExpr: case scMulExpr: case scUMaxExpr: case scSMaxExpr: case scUMinExpr: case scSMinExpr: { const SCEVNAryExpr *NAry = cast(S); bool Proper = true; for (const SCEV *NAryOp : NAry->operands()) { BlockDisposition D = getBlockDisposition(NAryOp, 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; } bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const { return SCEVExprContains(S, [&](const SCEV *Expr) { return Expr == Op; }); } void ScalarEvolution::forgetMemoizedResults(const SCEV *S) { ValuesAtScopes.erase(S); LoopDispositions.erase(S); BlockDispositions.erase(S); UnsignedRanges.erase(S); SignedRanges.erase(S); ExprValueMap.erase(S); HasRecMap.erase(S); MinTrailingZerosCache.erase(S); for (auto I = PredicatedSCEVRewrites.begin(); I != PredicatedSCEVRewrites.end();) { std::pair Entry = I->first; if (Entry.first == S) PredicatedSCEVRewrites.erase(I++); else ++I; } auto RemoveSCEVFromBackedgeMap = [S](DenseMap &Map) { for (auto I = Map.begin(), E = Map.end(); I != E;) { BackedgeTakenInfo &BEInfo = I->second; if (BEInfo.hasOperand(S)) Map.erase(I++); else ++I; } }; RemoveSCEVFromBackedgeMap(BackedgeTakenCounts); RemoveSCEVFromBackedgeMap(PredicatedBackedgeTakenCounts); } void ScalarEvolution::getUsedLoops(const SCEV *S, SmallPtrSetImpl &LoopsUsed) { struct FindUsedLoops { FindUsedLoops(SmallPtrSetImpl &LoopsUsed) : LoopsUsed(LoopsUsed) {} SmallPtrSetImpl &LoopsUsed; bool follow(const SCEV *S) { if (auto *AR = dyn_cast(S)) LoopsUsed.insert(AR->getLoop()); return true; } bool isDone() const { return false; } }; FindUsedLoops F(LoopsUsed); SCEVTraversal(F).visitAll(S); } void ScalarEvolution::addToLoopUseLists(const SCEV *S) { SmallPtrSet LoopsUsed; getUsedLoops(S, LoopsUsed); for (auto *L : LoopsUsed) LoopUsers[L].push_back(S); } void ScalarEvolution::verify() const { ScalarEvolution &SE = *const_cast(this); ScalarEvolution SE2(F, TLI, AC, DT, LI); SmallVector LoopStack(LI.begin(), LI.end()); // Map's SCEV expressions from one ScalarEvolution "universe" to another. struct SCEVMapper : public SCEVRewriteVisitor { SCEVMapper(ScalarEvolution &SE) : SCEVRewriteVisitor(SE) {} const SCEV *visitConstant(const SCEVConstant *Constant) { return SE.getConstant(Constant->getAPInt()); } const SCEV *visitUnknown(const SCEVUnknown *Expr) { return SE.getUnknown(Expr->getValue()); } const SCEV *visitCouldNotCompute(const SCEVCouldNotCompute *Expr) { return SE.getCouldNotCompute(); } }; SCEVMapper SCM(SE2); while (!LoopStack.empty()) { auto *L = LoopStack.pop_back_val(); llvm::append_range(LoopStack, *L); auto *CurBECount = SCM.visit( const_cast(this)->getBackedgeTakenCount(L)); auto *NewBECount = SE2.getBackedgeTakenCount(L); if (CurBECount == SE2.getCouldNotCompute() || NewBECount == SE2.getCouldNotCompute()) { // NB! This situation is legal, but is very suspicious -- whatever pass // change the loop to make a trip count go from could not compute to // computable or vice-versa *should have* invalidated SCEV. However, we // choose not to assert here (for now) since we don't want false // positives. continue; } if (containsUndefs(CurBECount) || containsUndefs(NewBECount)) { // SCEV treats "undef" as an unknown but consistent value (i.e. it does // not propagate undef aggressively). This means we can (and do) fail // verification in cases where a transform makes the trip count of a loop // go from "undef" to "undef+1" (say). The transform is fine, since in // both cases the loop iterates "undef" times, but SCEV thinks we // increased the trip count of the loop by 1 incorrectly. continue; } if (SE.getTypeSizeInBits(CurBECount->getType()) > SE.getTypeSizeInBits(NewBECount->getType())) NewBECount = SE2.getZeroExtendExpr(NewBECount, CurBECount->getType()); else if (SE.getTypeSizeInBits(CurBECount->getType()) < SE.getTypeSizeInBits(NewBECount->getType())) CurBECount = SE2.getZeroExtendExpr(CurBECount, NewBECount->getType()); const SCEV *Delta = SE2.getMinusSCEV(CurBECount, NewBECount); // Unless VerifySCEVStrict is set, we only compare constant deltas. if ((VerifySCEVStrict || isa(Delta)) && !Delta->isZero()) { dbgs() << "Trip Count for " << *L << " Changed!\n"; dbgs() << "Old: " << *CurBECount << "\n"; dbgs() << "New: " << *NewBECount << "\n"; dbgs() << "Delta: " << *Delta << "\n"; std::abort(); } } // Collect all valid loops currently in LoopInfo. SmallPtrSet ValidLoops; SmallVector Worklist(LI.begin(), LI.end()); while (!Worklist.empty()) { Loop *L = Worklist.pop_back_val(); if (ValidLoops.contains(L)) continue; ValidLoops.insert(L); Worklist.append(L->begin(), L->end()); } // Check for SCEV expressions referencing invalid/deleted loops. for (auto &KV : ValueExprMap) { auto *AR = dyn_cast(KV.second); if (!AR) continue; assert(ValidLoops.contains(AR->getLoop()) && "AddRec references invalid loop"); } } bool ScalarEvolution::invalidate( Function &F, const PreservedAnalyses &PA, FunctionAnalysisManager::Invalidator &Inv) { // Invalidate the ScalarEvolution object whenever it isn't preserved or one // of its dependencies is invalidated. auto PAC = PA.getChecker(); return !(PAC.preserved() || PAC.preservedSet>()) || Inv.invalidate(F, PA) || Inv.invalidate(F, PA) || Inv.invalidate(F, PA); } AnalysisKey ScalarEvolutionAnalysis::Key; ScalarEvolution ScalarEvolutionAnalysis::run(Function &F, FunctionAnalysisManager &AM) { return ScalarEvolution(F, AM.getResult(F), AM.getResult(F), AM.getResult(F), AM.getResult(F)); } PreservedAnalyses ScalarEvolutionVerifierPass::run(Function &F, FunctionAnalysisManager &AM) { AM.getResult(F).verify(); return PreservedAnalyses::all(); } PreservedAnalyses ScalarEvolutionPrinterPass::run(Function &F, FunctionAnalysisManager &AM) { // For compatibility with opt's -analyze feature under legacy pass manager // which was not ported to NPM. This keeps tests using // update_analyze_test_checks.py working. OS << "Printing analysis 'Scalar Evolution Analysis' for function '" << F.getName() << "':\n"; AM.getResult(F).print(OS); return PreservedAnalyses::all(); } INITIALIZE_PASS_BEGIN(ScalarEvolutionWrapperPass, "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(ScalarEvolutionWrapperPass, "scalar-evolution", "Scalar Evolution Analysis", false, true) char ScalarEvolutionWrapperPass::ID = 0; ScalarEvolutionWrapperPass::ScalarEvolutionWrapperPass() : FunctionPass(ID) { initializeScalarEvolutionWrapperPassPass(*PassRegistry::getPassRegistry()); } bool ScalarEvolutionWrapperPass::runOnFunction(Function &F) { SE.reset(new ScalarEvolution( F, getAnalysis().getTLI(F), getAnalysis().getAssumptionCache(F), getAnalysis().getDomTree(), getAnalysis().getLoopInfo())); return false; } void ScalarEvolutionWrapperPass::releaseMemory() { SE.reset(); } void ScalarEvolutionWrapperPass::print(raw_ostream &OS, const Module *) const { SE->print(OS); } void ScalarEvolutionWrapperPass::verifyAnalysis() const { if (!VerifySCEV) return; SE->verify(); } void ScalarEvolutionWrapperPass::getAnalysisUsage(AnalysisUsage &AU) const { AU.setPreservesAll(); AU.addRequiredTransitive(); AU.addRequiredTransitive(); AU.addRequiredTransitive(); AU.addRequiredTransitive(); } const SCEVPredicate *ScalarEvolution::getEqualPredicate(const SCEV *LHS, const SCEV *RHS) { FoldingSetNodeID ID; assert(LHS->getType() == RHS->getType() && "Type mismatch between LHS and RHS"); // Unique this node based on the arguments ID.AddInteger(SCEVPredicate::P_Equal); ID.AddPointer(LHS); ID.AddPointer(RHS); void *IP = nullptr; if (const auto *S = UniquePreds.FindNodeOrInsertPos(ID, IP)) return S; SCEVEqualPredicate *Eq = new (SCEVAllocator) SCEVEqualPredicate(ID.Intern(SCEVAllocator), LHS, RHS); UniquePreds.InsertNode(Eq, IP); return Eq; } const SCEVPredicate *ScalarEvolution::getWrapPredicate( const SCEVAddRecExpr *AR, SCEVWrapPredicate::IncrementWrapFlags AddedFlags) { FoldingSetNodeID ID; // Unique this node based on the arguments ID.AddInteger(SCEVPredicate::P_Wrap); ID.AddPointer(AR); ID.AddInteger(AddedFlags); void *IP = nullptr; if (const auto *S = UniquePreds.FindNodeOrInsertPos(ID, IP)) return S; auto *OF = new (SCEVAllocator) SCEVWrapPredicate(ID.Intern(SCEVAllocator), AR, AddedFlags); UniquePreds.InsertNode(OF, IP); return OF; } namespace { class SCEVPredicateRewriter : public SCEVRewriteVisitor { public: /// Rewrites \p S in the context of a loop L and the SCEV predication /// infrastructure. /// /// If \p Pred is non-null, the SCEV expression is rewritten to respect the /// equivalences present in \p Pred. /// /// If \p NewPreds is non-null, rewrite is free to add further predicates to /// \p NewPreds such that the result will be an AddRecExpr. static const SCEV *rewrite(const SCEV *S, const Loop *L, ScalarEvolution &SE, SmallPtrSetImpl *NewPreds, SCEVUnionPredicate *Pred) { SCEVPredicateRewriter Rewriter(L, SE, NewPreds, Pred); return Rewriter.visit(S); } const SCEV *visitUnknown(const SCEVUnknown *Expr) { if (Pred) { auto ExprPreds = Pred->getPredicatesForExpr(Expr); for (auto *Pred : ExprPreds) if (const auto *IPred = dyn_cast(Pred)) if (IPred->getLHS() == Expr) return IPred->getRHS(); } return convertToAddRecWithPreds(Expr); } const SCEV *visitZeroExtendExpr(const SCEVZeroExtendExpr *Expr) { const SCEV *Operand = visit(Expr->getOperand()); const SCEVAddRecExpr *AR = dyn_cast(Operand); if (AR && AR->getLoop() == L && AR->isAffine()) { // This couldn't be folded because the operand didn't have the nuw // flag. Add the nusw flag as an assumption that we could make. const SCEV *Step = AR->getStepRecurrence(SE); Type *Ty = Expr->getType(); if (addOverflowAssumption(AR, SCEVWrapPredicate::IncrementNUSW)) return SE.getAddRecExpr(SE.getZeroExtendExpr(AR->getStart(), Ty), SE.getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags()); } return SE.getZeroExtendExpr(Operand, Expr->getType()); } const SCEV *visitSignExtendExpr(const SCEVSignExtendExpr *Expr) { const SCEV *Operand = visit(Expr->getOperand()); const SCEVAddRecExpr *AR = dyn_cast(Operand); if (AR && AR->getLoop() == L && AR->isAffine()) { // This couldn't be folded because the operand didn't have the nsw // flag. Add the nssw flag as an assumption that we could make. const SCEV *Step = AR->getStepRecurrence(SE); Type *Ty = Expr->getType(); if (addOverflowAssumption(AR, SCEVWrapPredicate::IncrementNSSW)) return SE.getAddRecExpr(SE.getSignExtendExpr(AR->getStart(), Ty), SE.getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags()); } return SE.getSignExtendExpr(Operand, Expr->getType()); } private: explicit SCEVPredicateRewriter(const Loop *L, ScalarEvolution &SE, SmallPtrSetImpl *NewPreds, SCEVUnionPredicate *Pred) : SCEVRewriteVisitor(SE), NewPreds(NewPreds), Pred(Pred), L(L) {} bool addOverflowAssumption(const SCEVPredicate *P) { if (!NewPreds) { // Check if we've already made this assumption. return Pred && Pred->implies(P); } NewPreds->insert(P); return true; } bool addOverflowAssumption(const SCEVAddRecExpr *AR, SCEVWrapPredicate::IncrementWrapFlags AddedFlags) { auto *A = SE.getWrapPredicate(AR, AddedFlags); return addOverflowAssumption(A); } // If \p Expr represents a PHINode, we try to see if it can be represented // as an AddRec, possibly under a predicate (PHISCEVPred). If it is possible // to add this predicate as a runtime overflow check, we return the AddRec. // If \p Expr does not meet these conditions (is not a PHI node, or we // couldn't create an AddRec for it, or couldn't add the predicate), we just // return \p Expr. const SCEV *convertToAddRecWithPreds(const SCEVUnknown *Expr) { if (!isa(Expr->getValue())) return Expr; Optional>> PredicatedRewrite = SE.createAddRecFromPHIWithCasts(Expr); if (!PredicatedRewrite) return Expr; for (auto *P : PredicatedRewrite->second){ // Wrap predicates from outer loops are not supported. if (auto *WP = dyn_cast(P)) { auto *AR = cast(WP->getExpr()); if (L != AR->getLoop()) return Expr; } if (!addOverflowAssumption(P)) return Expr; } return PredicatedRewrite->first; } SmallPtrSetImpl *NewPreds; SCEVUnionPredicate *Pred; const Loop *L; }; } // end anonymous namespace const SCEV *ScalarEvolution::rewriteUsingPredicate(const SCEV *S, const Loop *L, SCEVUnionPredicate &Preds) { return SCEVPredicateRewriter::rewrite(S, L, *this, nullptr, &Preds); } const SCEVAddRecExpr *ScalarEvolution::convertSCEVToAddRecWithPredicates( const SCEV *S, const Loop *L, SmallPtrSetImpl &Preds) { SmallPtrSet TransformPreds; S = SCEVPredicateRewriter::rewrite(S, L, *this, &TransformPreds, nullptr); auto *AddRec = dyn_cast(S); if (!AddRec) return nullptr; // Since the transformation was successful, we can now transfer the SCEV // predicates. for (auto *P : TransformPreds) Preds.insert(P); return AddRec; } /// SCEV predicates SCEVPredicate::SCEVPredicate(const FoldingSetNodeIDRef ID, SCEVPredicateKind Kind) : FastID(ID), Kind(Kind) {} SCEVEqualPredicate::SCEVEqualPredicate(const FoldingSetNodeIDRef ID, const SCEV *LHS, const SCEV *RHS) : SCEVPredicate(ID, P_Equal), LHS(LHS), RHS(RHS) { assert(LHS->getType() == RHS->getType() && "LHS and RHS types don't match"); assert(LHS != RHS && "LHS and RHS are the same SCEV"); } bool SCEVEqualPredicate::implies(const SCEVPredicate *N) const { const auto *Op = dyn_cast(N); if (!Op) return false; return Op->LHS == LHS && Op->RHS == RHS; } bool SCEVEqualPredicate::isAlwaysTrue() const { return false; } const SCEV *SCEVEqualPredicate::getExpr() const { return LHS; } void SCEVEqualPredicate::print(raw_ostream &OS, unsigned Depth) const { OS.indent(Depth) << "Equal predicate: " << *LHS << " == " << *RHS << "\n"; } SCEVWrapPredicate::SCEVWrapPredicate(const FoldingSetNodeIDRef ID, const SCEVAddRecExpr *AR, IncrementWrapFlags Flags) : SCEVPredicate(ID, P_Wrap), AR(AR), Flags(Flags) {} const SCEV *SCEVWrapPredicate::getExpr() const { return AR; } bool SCEVWrapPredicate::implies(const SCEVPredicate *N) const { const auto *Op = dyn_cast(N); return Op && Op->AR == AR && setFlags(Flags, Op->Flags) == Flags; } bool SCEVWrapPredicate::isAlwaysTrue() const { SCEV::NoWrapFlags ScevFlags = AR->getNoWrapFlags(); IncrementWrapFlags IFlags = Flags; if (ScalarEvolution::setFlags(ScevFlags, SCEV::FlagNSW) == ScevFlags) IFlags = clearFlags(IFlags, IncrementNSSW); return IFlags == IncrementAnyWrap; } void SCEVWrapPredicate::print(raw_ostream &OS, unsigned Depth) const { OS.indent(Depth) << *getExpr() << " Added Flags: "; if (SCEVWrapPredicate::IncrementNUSW & getFlags()) OS << ""; if (SCEVWrapPredicate::IncrementNSSW & getFlags()) OS << ""; OS << "\n"; } SCEVWrapPredicate::IncrementWrapFlags SCEVWrapPredicate::getImpliedFlags(const SCEVAddRecExpr *AR, ScalarEvolution &SE) { IncrementWrapFlags ImpliedFlags = IncrementAnyWrap; SCEV::NoWrapFlags StaticFlags = AR->getNoWrapFlags(); // We can safely transfer the NSW flag as NSSW. if (ScalarEvolution::setFlags(StaticFlags, SCEV::FlagNSW) == StaticFlags) ImpliedFlags = IncrementNSSW; if (ScalarEvolution::setFlags(StaticFlags, SCEV::FlagNUW) == StaticFlags) { // If the increment is positive, the SCEV NUW flag will also imply the // WrapPredicate NUSW flag. if (const auto *Step = dyn_cast(AR->getStepRecurrence(SE))) if (Step->getValue()->getValue().isNonNegative()) ImpliedFlags = setFlags(ImpliedFlags, IncrementNUSW); } return ImpliedFlags; } /// Union predicates don't get cached so create a dummy set ID for it. SCEVUnionPredicate::SCEVUnionPredicate() : SCEVPredicate(FoldingSetNodeIDRef(nullptr, 0), P_Union) {} bool SCEVUnionPredicate::isAlwaysTrue() const { return all_of(Preds, [](const SCEVPredicate *I) { return I->isAlwaysTrue(); }); } ArrayRef SCEVUnionPredicate::getPredicatesForExpr(const SCEV *Expr) { auto I = SCEVToPreds.find(Expr); if (I == SCEVToPreds.end()) return ArrayRef(); return I->second; } bool SCEVUnionPredicate::implies(const SCEVPredicate *N) const { if (const auto *Set = dyn_cast(N)) return all_of(Set->Preds, [this](const SCEVPredicate *I) { return this->implies(I); }); auto ScevPredsIt = SCEVToPreds.find(N->getExpr()); if (ScevPredsIt == SCEVToPreds.end()) return false; auto &SCEVPreds = ScevPredsIt->second; return any_of(SCEVPreds, [N](const SCEVPredicate *I) { return I->implies(N); }); } const SCEV *SCEVUnionPredicate::getExpr() const { return nullptr; } void SCEVUnionPredicate::print(raw_ostream &OS, unsigned Depth) const { for (auto Pred : Preds) Pred->print(OS, Depth); } void SCEVUnionPredicate::add(const SCEVPredicate *N) { if (const auto *Set = dyn_cast(N)) { for (auto Pred : Set->Preds) add(Pred); return; } if (implies(N)) return; const SCEV *Key = N->getExpr(); assert(Key && "Only SCEVUnionPredicate doesn't have an " " associated expression!"); SCEVToPreds[Key].push_back(N); Preds.push_back(N); } PredicatedScalarEvolution::PredicatedScalarEvolution(ScalarEvolution &SE, Loop &L) : SE(SE), L(L) {} const SCEV *PredicatedScalarEvolution::getSCEV(Value *V) { const SCEV *Expr = SE.getSCEV(V); RewriteEntry &Entry = RewriteMap[Expr]; // If we already have an entry and the version matches, return it. if (Entry.second && Generation == Entry.first) return Entry.second; // We found an entry but it's stale. Rewrite the stale entry // according to the current predicate. if (Entry.second) Expr = Entry.second; const SCEV *NewSCEV = SE.rewriteUsingPredicate(Expr, &L, Preds); Entry = {Generation, NewSCEV}; return NewSCEV; } const SCEV *PredicatedScalarEvolution::getBackedgeTakenCount() { if (!BackedgeCount) { SCEVUnionPredicate BackedgePred; BackedgeCount = SE.getPredicatedBackedgeTakenCount(&L, BackedgePred); addPredicate(BackedgePred); } return BackedgeCount; } void PredicatedScalarEvolution::addPredicate(const SCEVPredicate &Pred) { if (Preds.implies(&Pred)) return; Preds.add(&Pred); updateGeneration(); } const SCEVUnionPredicate &PredicatedScalarEvolution::getUnionPredicate() const { return Preds; } void PredicatedScalarEvolution::updateGeneration() { // If the generation number wrapped recompute everything. if (++Generation == 0) { for (auto &II : RewriteMap) { const SCEV *Rewritten = II.second.second; II.second = {Generation, SE.rewriteUsingPredicate(Rewritten, &L, Preds)}; } } } void PredicatedScalarEvolution::setNoOverflow( Value *V, SCEVWrapPredicate::IncrementWrapFlags Flags) { const SCEV *Expr = getSCEV(V); const auto *AR = cast(Expr); auto ImpliedFlags = SCEVWrapPredicate::getImpliedFlags(AR, SE); // Clear the statically implied flags. Flags = SCEVWrapPredicate::clearFlags(Flags, ImpliedFlags); addPredicate(*SE.getWrapPredicate(AR, Flags)); auto II = FlagsMap.insert({V, Flags}); if (!II.second) II.first->second = SCEVWrapPredicate::setFlags(Flags, II.first->second); } bool PredicatedScalarEvolution::hasNoOverflow( Value *V, SCEVWrapPredicate::IncrementWrapFlags Flags) { const SCEV *Expr = getSCEV(V); const auto *AR = cast(Expr); Flags = SCEVWrapPredicate::clearFlags( Flags, SCEVWrapPredicate::getImpliedFlags(AR, SE)); auto II = FlagsMap.find(V); if (II != FlagsMap.end()) Flags = SCEVWrapPredicate::clearFlags(Flags, II->second); return Flags == SCEVWrapPredicate::IncrementAnyWrap; } const SCEVAddRecExpr *PredicatedScalarEvolution::getAsAddRec(Value *V) { const SCEV *Expr = this->getSCEV(V); SmallPtrSet NewPreds; auto *New = SE.convertSCEVToAddRecWithPredicates(Expr, &L, NewPreds); if (!New) return nullptr; for (auto *P : NewPreds) Preds.add(P); updateGeneration(); RewriteMap[SE.getSCEV(V)] = {Generation, New}; return New; } PredicatedScalarEvolution::PredicatedScalarEvolution( const PredicatedScalarEvolution &Init) : RewriteMap(Init.RewriteMap), SE(Init.SE), L(Init.L), Preds(Init.Preds), Generation(Init.Generation), BackedgeCount(Init.BackedgeCount) { for (auto I : Init.FlagsMap) FlagsMap.insert(I); } void PredicatedScalarEvolution::print(raw_ostream &OS, unsigned Depth) const { // For each block. for (auto *BB : L.getBlocks()) for (auto &I : *BB) { if (!SE.isSCEVable(I.getType())) continue; auto *Expr = SE.getSCEV(&I); auto II = RewriteMap.find(Expr); if (II == RewriteMap.end()) continue; // Don't print things that are not interesting. if (II->second.second == Expr) continue; OS.indent(Depth) << "[PSE]" << I << ":\n"; OS.indent(Depth + 2) << *Expr << "\n"; OS.indent(Depth + 2) << "--> " << *II->second.second << "\n"; } } // Match the mathematical pattern A - (A / B) * B, where A and B can be // arbitrary expressions. Also match zext (trunc A to iB) to iY, which is used // for URem with constant power-of-2 second operands. // It's not always easy, as A and B can be folded (imagine A is X / 2, and B is // 4, A / B becomes X / 8). bool ScalarEvolution::matchURem(const SCEV *Expr, const SCEV *&LHS, const SCEV *&RHS) { // Try to match 'zext (trunc A to iB) to iY', which is used // for URem with constant power-of-2 second operands. Make sure the size of // the operand A matches the size of the whole expressions. if (const auto *ZExt = dyn_cast(Expr)) if (const auto *Trunc = dyn_cast(ZExt->getOperand(0))) { LHS = Trunc->getOperand(); // Bail out if the type of the LHS is larger than the type of the // expression for now. if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(Expr->getType())) return false; if (LHS->getType() != Expr->getType()) LHS = getZeroExtendExpr(LHS, Expr->getType()); RHS = getConstant(APInt(getTypeSizeInBits(Expr->getType()), 1) << getTypeSizeInBits(Trunc->getType())); return true; } const auto *Add = dyn_cast(Expr); if (Add == nullptr || Add->getNumOperands() != 2) return false; const SCEV *A = Add->getOperand(1); const auto *Mul = dyn_cast(Add->getOperand(0)); if (Mul == nullptr) return false; const auto MatchURemWithDivisor = [&](const SCEV *B) { // (SomeExpr + (-(SomeExpr / B) * B)). if (Expr == getURemExpr(A, B)) { LHS = A; RHS = B; return true; } return false; }; // (SomeExpr + (-1 * (SomeExpr / B) * B)). if (Mul->getNumOperands() == 3 && isa(Mul->getOperand(0))) return MatchURemWithDivisor(Mul->getOperand(1)) || MatchURemWithDivisor(Mul->getOperand(2)); // (SomeExpr + ((-SomeExpr / B) * B)) or (SomeExpr + ((SomeExpr / B) * -B)). if (Mul->getNumOperands() == 2) return MatchURemWithDivisor(Mul->getOperand(1)) || MatchURemWithDivisor(Mul->getOperand(0)) || MatchURemWithDivisor(getNegativeSCEV(Mul->getOperand(1))) || MatchURemWithDivisor(getNegativeSCEV(Mul->getOperand(0))); return false; } const SCEV * ScalarEvolution::computeSymbolicMaxBackedgeTakenCount(const Loop *L) { SmallVector ExitingBlocks; L->getExitingBlocks(ExitingBlocks); // Form an expression for the maximum exit count possible for this loop. We // merge the max and exact information to approximate a version of // getConstantMaxBackedgeTakenCount which isn't restricted to just constants. SmallVector ExitCounts; for (BasicBlock *ExitingBB : ExitingBlocks) { const SCEV *ExitCount = getExitCount(L, ExitingBB); if (isa(ExitCount)) ExitCount = getExitCount(L, ExitingBB, ScalarEvolution::ConstantMaximum); if (!isa(ExitCount)) { assert(DT.dominates(ExitingBB, L->getLoopLatch()) && "We should only have known counts for exiting blocks that " "dominate latch!"); ExitCounts.push_back(ExitCount); } } if (ExitCounts.empty()) return getCouldNotCompute(); return getUMinFromMismatchedTypes(ExitCounts); } /// This rewriter is similar to SCEVParameterRewriter (it replaces SCEVUnknown /// components following the Map (Value -> SCEV)), but skips AddRecExpr because /// we cannot guarantee that the replacement is loop invariant in the loop of /// the AddRec. class SCEVLoopGuardRewriter : public SCEVRewriteVisitor { ValueToSCEVMapTy ⤅ public: SCEVLoopGuardRewriter(ScalarEvolution &SE, ValueToSCEVMapTy &M) : SCEVRewriteVisitor(SE), Map(M) {} const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) { return Expr; } const SCEV *visitUnknown(const SCEVUnknown *Expr) { auto I = Map.find(Expr->getValue()); if (I == Map.end()) return Expr; return I->second; } }; const SCEV *ScalarEvolution::applyLoopGuards(const SCEV *Expr, const Loop *L) { auto CollectCondition = [&](ICmpInst::Predicate Predicate, const SCEV *LHS, const SCEV *RHS, ValueToSCEVMapTy &RewriteMap) { // If we have LHS == 0, check if LHS is computing a property of some unknown // SCEV %v which we can rewrite %v to express explicitly. const SCEVConstant *RHSC = dyn_cast(RHS); if (Predicate == CmpInst::ICMP_EQ && RHSC && RHSC->getValue()->isNullValue()) { // If LHS is A % B, i.e. A % B == 0, rewrite A to (A /u B) * B to // explicitly express that. const SCEV *URemLHS = nullptr; const SCEV *URemRHS = nullptr; if (matchURem(LHS, URemLHS, URemRHS)) { if (const SCEVUnknown *LHSUnknown = dyn_cast(URemLHS)) { Value *V = LHSUnknown->getValue(); auto Multiple = getMulExpr(getUDivExpr(URemLHS, URemRHS), URemRHS, (SCEV::NoWrapFlags)(SCEV::FlagNUW | SCEV::FlagNSW)); RewriteMap[V] = Multiple; return; } } } if (!isa(LHS) && isa(RHS)) { std::swap(LHS, RHS); Predicate = CmpInst::getSwappedPredicate(Predicate); } // Check for a condition of the form (-C1 + X < C2). InstCombine will // create this form when combining two checks of the form (X u< C2 + C1) and // (X >=u C1). auto MatchRangeCheckIdiom = [this, Predicate, LHS, RHS, &RewriteMap]() { auto *AddExpr = dyn_cast(LHS); if (!AddExpr || AddExpr->getNumOperands() != 2) return false; auto *C1 = dyn_cast(AddExpr->getOperand(0)); auto *LHSUnknown = dyn_cast(AddExpr->getOperand(1)); auto *C2 = dyn_cast(RHS); if (!C1 || !C2 || !LHSUnknown) return false; auto ExactRegion = ConstantRange::makeExactICmpRegion(Predicate, C2->getAPInt()) .sub(C1->getAPInt()); // Bail out, unless we have a non-wrapping, monotonic range. if (ExactRegion.isWrappedSet() || ExactRegion.isFullSet()) return false; auto I = RewriteMap.find(LHSUnknown->getValue()); const SCEV *RewrittenLHS = I != RewriteMap.end() ? I->second : LHSUnknown; RewriteMap[LHSUnknown->getValue()] = getUMaxExpr( getConstant(ExactRegion.getUnsignedMin()), getUMinExpr(RewrittenLHS, getConstant(ExactRegion.getUnsignedMax()))); return true; }; if (MatchRangeCheckIdiom()) return; // For now, limit to conditions that provide information about unknown // expressions. RHS also cannot contain add recurrences. auto *LHSUnknown = dyn_cast(LHS); if (!LHSUnknown || containsAddRecurrence(RHS)) return; // Check whether LHS has already been rewritten. In that case we want to // chain further rewrites onto the already rewritten value. auto I = RewriteMap.find(LHSUnknown->getValue()); const SCEV *RewrittenLHS = I != RewriteMap.end() ? I->second : LHS; const SCEV *RewrittenRHS = nullptr; switch (Predicate) { case CmpInst::ICMP_ULT: RewrittenRHS = getUMinExpr(RewrittenLHS, getMinusSCEV(RHS, getOne(RHS->getType()))); break; case CmpInst::ICMP_SLT: RewrittenRHS = getSMinExpr(RewrittenLHS, getMinusSCEV(RHS, getOne(RHS->getType()))); break; case CmpInst::ICMP_ULE: RewrittenRHS = getUMinExpr(RewrittenLHS, RHS); break; case CmpInst::ICMP_SLE: RewrittenRHS = getSMinExpr(RewrittenLHS, RHS); break; case CmpInst::ICMP_UGT: RewrittenRHS = getUMaxExpr(RewrittenLHS, getAddExpr(RHS, getOne(RHS->getType()))); break; case CmpInst::ICMP_SGT: RewrittenRHS = getSMaxExpr(RewrittenLHS, getAddExpr(RHS, getOne(RHS->getType()))); break; case CmpInst::ICMP_UGE: RewrittenRHS = getUMaxExpr(RewrittenLHS, RHS); break; case CmpInst::ICMP_SGE: RewrittenRHS = getSMaxExpr(RewrittenLHS, RHS); break; case CmpInst::ICMP_EQ: if (isa(RHS)) RewrittenRHS = RHS; break; case CmpInst::ICMP_NE: if (isa(RHS) && cast(RHS)->getValue()->isNullValue()) RewrittenRHS = getUMaxExpr(RewrittenLHS, getOne(RHS->getType())); break; default: break; } if (RewrittenRHS) RewriteMap[LHSUnknown->getValue()] = RewrittenRHS; }; // 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. // TODO: share this logic with isLoopEntryGuardedByCond. ValueToSCEVMapTy RewriteMap; for (std::pair Pair( L->getLoopPredecessor(), L->getHeader()); Pair.first; Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) { const BranchInst *LoopEntryPredicate = dyn_cast(Pair.first->getTerminator()); if (!LoopEntryPredicate || LoopEntryPredicate->isUnconditional()) continue; bool EnterIfTrue = LoopEntryPredicate->getSuccessor(0) == Pair.second; SmallVector Worklist; SmallPtrSet Visited; Worklist.push_back(LoopEntryPredicate->getCondition()); while (!Worklist.empty()) { Value *Cond = Worklist.pop_back_val(); if (!Visited.insert(Cond).second) continue; if (auto *Cmp = dyn_cast(Cond)) { auto Predicate = EnterIfTrue ? Cmp->getPredicate() : Cmp->getInversePredicate(); CollectCondition(Predicate, getSCEV(Cmp->getOperand(0)), getSCEV(Cmp->getOperand(1)), RewriteMap); continue; } Value *L, *R; if (EnterIfTrue ? match(Cond, m_LogicalAnd(m_Value(L), m_Value(R))) : match(Cond, m_LogicalOr(m_Value(L), m_Value(R)))) { Worklist.push_back(L); Worklist.push_back(R); } } } // Also collect information from assumptions dominating the loop. for (auto &AssumeVH : AC.assumptions()) { if (!AssumeVH) continue; auto *AssumeI = cast(AssumeVH); auto *Cmp = dyn_cast(AssumeI->getOperand(0)); if (!Cmp || !DT.dominates(AssumeI, L->getHeader())) continue; CollectCondition(Cmp->getPredicate(), getSCEV(Cmp->getOperand(0)), getSCEV(Cmp->getOperand(1)), RewriteMap); } if (RewriteMap.empty()) return Expr; SCEVLoopGuardRewriter Rewriter(*this, RewriteMap); return Rewriter.visit(Expr); }