diff options
Diffstat (limited to 'llvm/lib/Analysis/ScalarEvolution.cpp')
| -rw-r--r-- | llvm/lib/Analysis/ScalarEvolution.cpp | 12530 |
1 files changed, 12530 insertions, 0 deletions
diff --git a/llvm/lib/Analysis/ScalarEvolution.cpp b/llvm/lib/Analysis/ScalarEvolution.cpp new file mode 100644 index 000000000000..5ce0a1adeaa0 --- /dev/null +++ b/llvm/lib/Analysis/ScalarEvolution.cpp @@ -0,0 +1,12530 @@ +//===- 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/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/CallSite.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/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 <algorithm> +#include <cassert> +#include <climits> +#include <cstddef> +#include <cstdint> +#include <cstdlib> +#include <map> +#include <memory> +#include <tuple> +#include <utility> +#include <vector> + +using namespace llvm; + +#define DEBUG_TYPE "scalar-evolution" + +STATISTIC(NumArrayLenItCounts, + "Number of trip counts computed with array length"); +STATISTIC(NumTripCountsComputed, + "Number of loops with predictable loop counts"); +STATISTIC(NumTripCountsNotComputed, + "Number of loops without predictable loop counts"); +STATISTIC(NumBruteForceTripCountsComputed, + "Number of loops with trip counts computed by force"); + +static cl::opt<unsigned> +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<bool> VerifySCEV( + "verify-scev", cl::Hidden, + cl::desc("Verify ScalarEvolution's backedge taken counts (slow)")); +static cl::opt<bool> VerifySCEVStrict( + "verify-scev-strict", cl::Hidden, + cl::desc("Enable stricter verification with -verify-scev is passed")); +static cl::opt<bool> + VerifySCEVMap("verify-scev-maps", cl::Hidden, + cl::desc("Verify no dangling value in ScalarEvolution's " + "ExprValueMap (slow)")); + +static cl::opt<bool> VerifyIR( + "scev-verify-ir", cl::Hidden, + cl::desc("Verify IR correctness when making sensitive SCEV queries (slow)"), + cl::init(false)); + +static cl::opt<unsigned> MulOpsInlineThreshold( + "scev-mulops-inline-threshold", cl::Hidden, + cl::desc("Threshold for inlining multiplication operands into a SCEV"), + cl::init(32)); + +static cl::opt<unsigned> AddOpsInlineThreshold( + "scev-addops-inline-threshold", cl::Hidden, + cl::desc("Threshold for inlining addition operands into a SCEV"), + cl::init(500)); + +static cl::opt<unsigned> MaxSCEVCompareDepth( + "scalar-evolution-max-scev-compare-depth", cl::Hidden, + cl::desc("Maximum depth of recursive SCEV complexity comparisons"), + cl::init(32)); + +static cl::opt<unsigned> 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<unsigned> MaxValueCompareDepth( + "scalar-evolution-max-value-compare-depth", cl::Hidden, + cl::desc("Maximum depth of recursive value complexity comparisons"), + cl::init(2)); + +static cl::opt<unsigned> + MaxArithDepth("scalar-evolution-max-arith-depth", cl::Hidden, + cl::desc("Maximum depth of recursive arithmetics"), + cl::init(32)); + +static cl::opt<unsigned> MaxConstantEvolvingDepth( + "scalar-evolution-max-constant-evolving-depth", cl::Hidden, + cl::desc("Maximum depth of recursive constant evolving"), cl::init(32)); + +static cl::opt<unsigned> + MaxCastDepth("scalar-evolution-max-cast-depth", cl::Hidden, + cl::desc("Maximum depth of recursive SExt/ZExt/Trunc"), + cl::init(8)); + +static cl::opt<unsigned> + MaxAddRecSize("scalar-evolution-max-add-rec-size", cl::Hidden, + cl::desc("Max coefficients in AddRec during evolving"), + cl::init(8)); + +static cl::opt<unsigned> + HugeExprThreshold("scalar-evolution-huge-expr-threshold", cl::Hidden, + cl::desc("Size of the expression which is considered huge"), + cl::init(4096)); + +//===----------------------------------------------------------------------===// +// 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 (static_cast<SCEVTypes>(getSCEVType())) { + case scConstant: + cast<SCEVConstant>(this)->getValue()->printAsOperand(OS, false); + return; + case scTruncate: { + const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(this); + const SCEV *Op = Trunc->getOperand(); + OS << "(trunc " << *Op->getType() << " " << *Op << " to " + << *Trunc->getType() << ")"; + return; + } + case scZeroExtend: { + const SCEVZeroExtendExpr *ZExt = cast<SCEVZeroExtendExpr>(this); + const SCEV *Op = ZExt->getOperand(); + OS << "(zext " << *Op->getType() << " " << *Op << " to " + << *ZExt->getType() << ")"; + return; + } + case scSignExtend: { + const SCEVSignExtendExpr *SExt = cast<SCEVSignExtendExpr>(this); + const SCEV *Op = SExt->getOperand(); + OS << "(sext " << *Op->getType() << " " << *Op << " to " + << *SExt->getType() << ")"; + return; + } + case scAddRecExpr: { + const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(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<SCEVNAryExpr>(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; + } + OS << "("; + for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end(); + I != E; ++I) { + OS << **I; + if (std::next(I) != E) + OS << OpStr; + } + OS << ")"; + switch (NAry->getSCEVType()) { + case scAddExpr: + case scMulExpr: + if (NAry->hasNoUnsignedWrap()) + OS << "<nuw>"; + if (NAry->hasNoSignedWrap()) + OS << "<nsw>"; + } + return; + } + case scUDivExpr: { + const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(this); + OS << "(" << *UDiv->getLHS() << " /u " << *UDiv->getRHS() << ")"; + return; + } + case scUnknown: { + const SCEVUnknown *U = cast<SCEVUnknown>(this); + Type *AllocTy; + if (U->isSizeOf(AllocTy)) { + OS << "sizeof(" << *AllocTy << ")"; + return; + } + if (U->isAlignOf(AllocTy)) { + OS << "alignof(" << *AllocTy << ")"; + return; + } + + Type *CTy; + Constant *FieldNo; + if (U->isOffsetOf(CTy, FieldNo)) { + OS << "offsetof(" << *CTy << ", "; + FieldNo->printAsOperand(OS, false); + OS << ")"; + return; + } + + // Otherwise just print it normally. + U->getValue()->printAsOperand(OS, false); + return; + } + case scCouldNotCompute: + OS << "***COULDNOTCOMPUTE***"; + return; + } + llvm_unreachable("Unknown SCEV kind!"); +} + +Type *SCEV::getType() const { + switch (static_cast<SCEVTypes>(getSCEVType())) { + case scConstant: + return cast<SCEVConstant>(this)->getType(); + case scTruncate: + case scZeroExtend: + case scSignExtend: + return cast<SCEVCastExpr>(this)->getType(); + case scAddRecExpr: + case scMulExpr: + case scUMaxExpr: + case scSMaxExpr: + case scUMinExpr: + case scSMinExpr: + return cast<SCEVNAryExpr>(this)->getType(); + case scAddExpr: + return cast<SCEVAddExpr>(this)->getType(); + case scUDivExpr: + return cast<SCEVUDivExpr>(this)->getType(); + case scUnknown: + return cast<SCEVUnknown>(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<SCEVConstant>(this)) + return SC->getValue()->isZero(); + return false; +} + +bool SCEV::isOne() const { + if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) + return SC->getValue()->isOne(); + return false; +} + +bool SCEV::isAllOnesValue() const { + if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this)) + return SC->getValue()->isMinusOne(); + return false; +} + +bool SCEV::isNonConstantNegative() const { + const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(this); + if (!Mul) return false; + + // If there is a constant factor, it will be first. + const SCEVConstant *SC = dyn_cast<SCEVConstant>(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<IntegerType>(getEffectiveSCEVType(Ty)); + return getConstant(ConstantInt::get(ITy, V, isSigned)); +} + +SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID, + unsigned SCEVTy, const SCEV *op, Type *ty) + : SCEV(ID, SCEVTy, computeExpressionSize(op)), Op(op), Ty(ty) {} + +SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID, + const SCEV *op, Type *ty) + : SCEVCastExpr(ID, scTruncate, op, ty) { + assert(Op->getType()->isIntOrPtrTy() && Ty->isIntOrPtrTy() && + "Cannot truncate non-integer value!"); +} + +SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID, + const SCEV *op, Type *ty) + : SCEVCastExpr(ID, scZeroExtend, op, ty) { + assert(Op->getType()->isIntOrPtrTy() && Ty->isIntOrPtrTy() && + "Cannot zero extend non-integer value!"); +} + +SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID, + const SCEV *op, Type *ty) + : SCEVCastExpr(ID, scSignExtend, op, ty) { + assert(Op->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<ConstantExpr>(getValue())) + if (VCE->getOpcode() == Instruction::PtrToInt) + if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) + if (CE->getOpcode() == Instruction::GetElementPtr && + CE->getOperand(0)->isNullValue() && + CE->getNumOperands() == 2) + if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1))) + if (CI->isOne()) { + AllocTy = cast<PointerType>(CE->getOperand(0)->getType()) + ->getElementType(); + return true; + } + + return false; +} + +bool SCEVUnknown::isAlignOf(Type *&AllocTy) const { + if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue())) + if (VCE->getOpcode() == Instruction::PtrToInt) + if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) + if (CE->getOpcode() == Instruction::GetElementPtr && + CE->getOperand(0)->isNullValue()) { + Type *Ty = + cast<PointerType>(CE->getOperand(0)->getType())->getElementType(); + if (StructType *STy = dyn_cast<StructType>(Ty)) + if (!STy->isPacked() && + CE->getNumOperands() == 3 && + CE->getOperand(1)->isNullValue()) { + if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2))) + if (CI->isOne() && + STy->getNumElements() == 2 && + STy->getElementType(0)->isIntegerTy(1)) { + AllocTy = STy->getElementType(1); + return true; + } + } + } + + return false; +} + +bool SCEVUnknown::isOffsetOf(Type *&CTy, Constant *&FieldNo) const { + if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue())) + if (VCE->getOpcode() == Instruction::PtrToInt) + if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0))) + if (CE->getOpcode() == Instruction::GetElementPtr && + CE->getNumOperands() == 3 && + CE->getOperand(0)->isNullValue() && + CE->getOperand(1)->isNullValue()) { + Type *Ty = + cast<PointerType>(CE->getOperand(0)->getType())->getElementType(); + // Ignore vector types here so that ScalarEvolutionExpander doesn't + // emit getelementptrs that index into vectors. + if (Ty->isStructTy() || Ty->isArrayTy()) { + CTy = Ty; + FieldNo = CE->getOperand(2); + return true; + } + } + + return false; +} + +//===----------------------------------------------------------------------===// +// 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<const Value *> &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<Argument>(LV)) { + const auto *RA = cast<Argument>(RV); + unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo(); + return (int)LArgNo - (int)RArgNo; + } + + if (const auto *LGV = dyn_cast<GlobalValue>(LV)) { + const auto *RGV = cast<GlobalValue>(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<Instruction>(LV)) { + const auto *RInst = cast<Instruction>(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. +static int CompareSCEVComplexity( + EquivalenceClasses<const SCEV *> &EqCacheSCEV, + EquivalenceClasses<const Value *> &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(). + unsigned LType = LHS->getSCEVType(), RType = RHS->getSCEVType(); + if (LType != RType) + return (int)LType - (int)RType; + + if (Depth > MaxSCEVCompareDepth || EqCacheSCEV.isEquivalent(LHS, RHS)) + return 0; + // Aside from the getSCEVType() ordering, the particular ordering + // isn't very important except that it's beneficial to be consistent, + // so that (a + b) and (b + a) don't end up as different expressions. + switch (static_cast<SCEVTypes>(LType)) { + case scUnknown: { + const SCEVUnknown *LU = cast<SCEVUnknown>(LHS); + const SCEVUnknown *RU = cast<SCEVUnknown>(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<SCEVConstant>(LHS); + const SCEVConstant *RC = cast<SCEVConstant>(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<SCEVAddRecExpr>(LHS); + const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(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) { + int 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<SCEVNAryExpr>(LHS); + const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(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) { + int 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<SCEVUDivExpr>(LHS); + const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS); + + // Lexicographically compare udiv expressions. + int 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 scTruncate: + case scZeroExtend: + case scSignExtend: { + const SCEVCastExpr *LC = cast<SCEVCastExpr>(LHS); + const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS); + + // Compare cast expressions by operand. + int 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<const SCEV *> &Ops, + LoopInfo *LI, DominatorTree &DT) { + if (Ops.size() < 2) return; // Noop + + EquivalenceClasses<const SCEV *> EqCacheSCEV; + EquivalenceClasses<const Value *> EqCacheValue; + 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 (CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI, RHS, LHS, DT) < 0) + std::swap(LHS, RHS); + return; + } + + // Do the rough sort by complexity. + llvm::stable_sort(Ops, [&](const SCEV *LHS, const SCEV *RHS) { + return CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI, LHS, RHS, DT) < + 0; + }); + + // 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 the size of the SCEV S. +static inline int sizeOfSCEV(const SCEV *S) { + struct FindSCEVSize { + int Size = 0; + + FindSCEVSize() = default; + + bool follow(const SCEV *S) { + ++Size; + // Keep looking at all operands of S. + return true; + } + + bool isDone() const { + return false; + } + }; + + FindSCEVSize F; + SCEVTraversal<FindSCEVSize> ST(F); + ST.visitAll(S); + return F.Size; +} + +/// Returns true if the subtree of \p S contains at least HugeExprThreshold +/// nodes. +static bool isHugeExpression(const SCEV *S) { + return S->getExpressionSize() >= HugeExprThreshold; +} + +/// Returns true of \p Ops contains a huge SCEV (see definition above). +static bool hasHugeExpression(ArrayRef<const SCEV *> Ops) { + return any_of(Ops, isHugeExpression); +} + +namespace { + +struct SCEVDivision : public SCEVVisitor<SCEVDivision, void> { +public: + // Computes the Quotient and Remainder of the division of Numerator by + // Denominator. + static void divide(ScalarEvolution &SE, const SCEV *Numerator, + const SCEV *Denominator, const SCEV **Quotient, + const SCEV **Remainder) { + assert(Numerator && Denominator && "Uninitialized SCEV"); + + SCEVDivision D(SE, Numerator, Denominator); + + // Check for the trivial case here to avoid having to check for it in the + // rest of the code. + if (Numerator == Denominator) { + *Quotient = D.One; + *Remainder = D.Zero; + return; + } + + if (Numerator->isZero()) { + *Quotient = D.Zero; + *Remainder = D.Zero; + return; + } + + // A simple case when N/1. The quotient is N. + if (Denominator->isOne()) { + *Quotient = Numerator; + *Remainder = D.Zero; + return; + } + + // Split the Denominator when it is a product. + if (const SCEVMulExpr *T = dyn_cast<SCEVMulExpr>(Denominator)) { + const SCEV *Q, *R; + *Quotient = Numerator; + for (const SCEV *Op : T->operands()) { + divide(SE, *Quotient, Op, &Q, &R); + *Quotient = Q; + + // Bail out when the Numerator is not divisible by one of the terms of + // the Denominator. + if (!R->isZero()) { + *Quotient = D.Zero; + *Remainder = Numerator; + return; + } + } + *Remainder = D.Zero; + return; + } + + D.visit(Numerator); + *Quotient = D.Quotient; + *Remainder = D.Remainder; + } + + // Except in the trivial case described above, we do not know how to divide + // Expr by Denominator for the following functions with empty implementation. + void visitTruncateExpr(const SCEVTruncateExpr *Numerator) {} + void visitZeroExtendExpr(const SCEVZeroExtendExpr *Numerator) {} + void visitSignExtendExpr(const SCEVSignExtendExpr *Numerator) {} + void visitUDivExpr(const SCEVUDivExpr *Numerator) {} + void visitSMaxExpr(const SCEVSMaxExpr *Numerator) {} + void visitUMaxExpr(const SCEVUMaxExpr *Numerator) {} + void visitSMinExpr(const SCEVSMinExpr *Numerator) {} + void visitUMinExpr(const SCEVUMinExpr *Numerator) {} + void visitUnknown(const SCEVUnknown *Numerator) {} + void visitCouldNotCompute(const SCEVCouldNotCompute *Numerator) {} + + void visitConstant(const SCEVConstant *Numerator) { + if (const SCEVConstant *D = dyn_cast<SCEVConstant>(Denominator)) { + APInt NumeratorVal = Numerator->getAPInt(); + APInt DenominatorVal = D->getAPInt(); + uint32_t NumeratorBW = NumeratorVal.getBitWidth(); + uint32_t DenominatorBW = DenominatorVal.getBitWidth(); + + if (NumeratorBW > DenominatorBW) + DenominatorVal = DenominatorVal.sext(NumeratorBW); + else if (NumeratorBW < DenominatorBW) + NumeratorVal = NumeratorVal.sext(DenominatorBW); + + APInt QuotientVal(NumeratorVal.getBitWidth(), 0); + APInt RemainderVal(NumeratorVal.getBitWidth(), 0); + APInt::sdivrem(NumeratorVal, DenominatorVal, QuotientVal, RemainderVal); + Quotient = SE.getConstant(QuotientVal); + Remainder = SE.getConstant(RemainderVal); + return; + } + } + + void visitAddRecExpr(const SCEVAddRecExpr *Numerator) { + const SCEV *StartQ, *StartR, *StepQ, *StepR; + if (!Numerator->isAffine()) + return cannotDivide(Numerator); + divide(SE, Numerator->getStart(), Denominator, &StartQ, &StartR); + divide(SE, Numerator->getStepRecurrence(SE), Denominator, &StepQ, &StepR); + // Bail out if the types do not match. + Type *Ty = Denominator->getType(); + if (Ty != StartQ->getType() || Ty != StartR->getType() || + Ty != StepQ->getType() || Ty != StepR->getType()) + return cannotDivide(Numerator); + Quotient = SE.getAddRecExpr(StartQ, StepQ, Numerator->getLoop(), + Numerator->getNoWrapFlags()); + Remainder = SE.getAddRecExpr(StartR, StepR, Numerator->getLoop(), + Numerator->getNoWrapFlags()); + } + + void visitAddExpr(const SCEVAddExpr *Numerator) { + SmallVector<const SCEV *, 2> Qs, Rs; + Type *Ty = Denominator->getType(); + + for (const SCEV *Op : Numerator->operands()) { + const SCEV *Q, *R; + divide(SE, Op, Denominator, &Q, &R); + + // Bail out if types do not match. + if (Ty != Q->getType() || Ty != R->getType()) + return cannotDivide(Numerator); + + Qs.push_back(Q); + Rs.push_back(R); + } + + if (Qs.size() == 1) { + Quotient = Qs[0]; + Remainder = Rs[0]; + return; + } + + Quotient = SE.getAddExpr(Qs); + Remainder = SE.getAddExpr(Rs); + } + + void visitMulExpr(const SCEVMulExpr *Numerator) { + SmallVector<const SCEV *, 2> Qs; + Type *Ty = Denominator->getType(); + + bool FoundDenominatorTerm = false; + for (const SCEV *Op : Numerator->operands()) { + // Bail out if types do not match. + if (Ty != Op->getType()) + return cannotDivide(Numerator); + + if (FoundDenominatorTerm) { + Qs.push_back(Op); + continue; + } + + // Check whether Denominator divides one of the product operands. + const SCEV *Q, *R; + divide(SE, Op, Denominator, &Q, &R); + if (!R->isZero()) { + Qs.push_back(Op); + continue; + } + + // Bail out if types do not match. + if (Ty != Q->getType()) + return cannotDivide(Numerator); + + FoundDenominatorTerm = true; + Qs.push_back(Q); + } + + if (FoundDenominatorTerm) { + Remainder = Zero; + if (Qs.size() == 1) + Quotient = Qs[0]; + else + Quotient = SE.getMulExpr(Qs); + return; + } + + if (!isa<SCEVUnknown>(Denominator)) + return cannotDivide(Numerator); + + // The Remainder is obtained by replacing Denominator by 0 in Numerator. + ValueToValueMap RewriteMap; + RewriteMap[cast<SCEVUnknown>(Denominator)->getValue()] = + cast<SCEVConstant>(Zero)->getValue(); + Remainder = SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true); + + if (Remainder->isZero()) { + // The Quotient is obtained by replacing Denominator by 1 in Numerator. + RewriteMap[cast<SCEVUnknown>(Denominator)->getValue()] = + cast<SCEVConstant>(One)->getValue(); + Quotient = + SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true); + return; + } + + // Quotient is (Numerator - Remainder) divided by Denominator. + const SCEV *Q, *R; + const SCEV *Diff = SE.getMinusSCEV(Numerator, Remainder); + // This SCEV does not seem to simplify: fail the division here. + if (sizeOfSCEV(Diff) > sizeOfSCEV(Numerator)) + return cannotDivide(Numerator); + divide(SE, Diff, Denominator, &Q, &R); + if (R != Zero) + return cannotDivide(Numerator); + Quotient = Q; + } + +private: + SCEVDivision(ScalarEvolution &S, const SCEV *Numerator, + const SCEV *Denominator) + : SE(S), Denominator(Denominator) { + Zero = SE.getZero(Denominator->getType()); + One = SE.getOne(Denominator->getType()); + + // We generally do not know how to divide Expr by Denominator. We + // initialize the division to a "cannot divide" state to simplify the rest + // of the code. + cannotDivide(Numerator); + } + + // Convenience function for giving up on the division. We set the quotient to + // be equal to zero and the remainder to be equal to the numerator. + void cannotDivide(const SCEV *Numerator) { + Quotient = Zero; + Remainder = Numerator; + } + + ScalarEvolution &SE; + const SCEV *Denominator, *Quotient, *Remainder, *Zero, *One; +}; + +} // end anonymous namespace + +//===----------------------------------------------------------------------===// +// 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 { + const SCEV *Result = getStart(); + for (unsigned i = 1, e = getNumOperands(); i != e; ++i) { + // The computation is correct in the face of overflow provided that the + // multiplication is performed _after_ the evaluation of the binomial + // coefficient. + const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType()); + if (isa<SCEVCouldNotCompute>(Coeff)) + return Coeff; + + Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff)); + } + return Result; +} + +//===----------------------------------------------------------------------===// +// SCEV Expression folder implementations +//===----------------------------------------------------------------------===// + +const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op, 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!"); + 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<SCEVConstant>(Op)) + return getConstant( + cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty))); + + // trunc(trunc(x)) --> trunc(x) + if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) + return getTruncateExpr(ST->getOperand(), Ty, Depth + 1); + + // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing + if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) + return getTruncateOrSignExtend(SS->getOperand(), Ty, Depth + 1); + + // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing + if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op)) + return getTruncateOrZeroExtend(SZ->getOperand(), Ty, 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<SCEVAddExpr>(Op) || isa<SCEVMulExpr>(Op)) { + auto *CommOp = cast<SCEVCommutativeExpr>(Op); + SmallVector<const SCEV *, 4> 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<SCEVCastExpr>(CommOp->getOperand(i)) && isa<SCEVTruncateExpr>(S)) + numTruncs++; + Operands.push_back(S); + } + if (numTruncs < 2) { + if (isa<SCEVAddExpr>(Op)) + return getAddExpr(Operands); + else if (isa<SCEVMulExpr>(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<SCEVAddRecExpr>(Op)) { + SmallVector<const SCEV *, 4> Operands; + for (const SCEV *Op : AddRec->operands()) + Operands.push_back(getTruncateExpr(Op, Ty, Depth + 1)); + return getAddRecExpr(Operands, AddRec->getLoop(), SCEV::FlagAnyWrap); + } + + // The cast wasn't folded; create an explicit cast node. We can reuse + // the existing insert position since if we get here, we won't have + // made any changes which would invalidate it. + SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator), + Op, Ty); + UniqueSCEVs.InsertNode(S, IP); + 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 <typename ExtendOp> 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<SCEVSignExtendExpr> : 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<SCEVZeroExtendExpr> : 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 <typename ExtendOpTy> +static const SCEV *getPreStartForExtend(const SCEVAddRecExpr *AR, Type *Ty, + ScalarEvolution *SE, unsigned Depth) { + auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType; + auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::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<SCEVAddExpr>(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<const SCEV *, 4> 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<SCEVAddRecExpr>( + SE->getAddRecExpr(PreStart, Step, L, SCEV::FlagAnyWrap)); + + // "{S,+,X} is <nsw>/<nuw>" 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<SCEVCouldNotCompute>(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. + const_cast<SCEVAddRecExpr *>(PreAR)->setNoWrapFlags(WrapType); + } + return PreStart; + } + + // 3. Loop precondition. + ICmpInst::Predicate Pred; + const SCEV *OverflowLimit = + ExtendOpTraits<ExtendOpTy>::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 <typename ExtendOpTy> +static const SCEV *getExtendAddRecStart(const SCEVAddRecExpr *AR, Type *Ty, + ScalarEvolution *SE, + unsigned Depth) { + auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr; + + const SCEV *PreStart = getPreStartForExtend<ExtendOpTy>(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 <typename ExtendOpTy> +bool ScalarEvolution::proveNoWrapByVaryingStart(const SCEV *Start, + const SCEV *Step, + const Loop *L) { + auto WrapType = ExtendOpTraits<ExtendOpTy>::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<SCEVConstant>(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<SCEVAddRecExpr *>(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<ExtendOpTy>::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!"); + Ty = getEffectiveSCEVType(Ty); + + // Fold if the operand is constant. + if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) + return getConstant( + cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(), Ty))); + + // zext(zext(x)) --> zext(x) + if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(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<SCEVTruncateExpr>(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<SCEVAddRecExpr>(Op)) + if (AR->isAffine()) { + const SCEV *Start = AR->getStart(); + const SCEV *Step = AR->getStepRecurrence(*this); + unsigned BitWidth = getTypeSizeInBits(AR->getType()); + const Loop *L = AR->getLoop(); + + if (!AR->hasNoUnsignedWrap()) { + auto NewFlags = proveNoWrapViaConstantRanges(AR); + const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(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<SCEVZeroExtendExpr>(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<SCEVCouldNotCompute>(MaxBECount)) { + // Manually compute the final value for AR, checking for + // overflow. + + // Check whether the backedge-taken count can be losslessly casted to + // the addrec's type. The count is always unsigned. + const SCEV *CastedMaxBECount = + getTruncateOrZeroExtend(MaxBECount, Start->getType(), 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. + const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW); + // Return the expression with the addrec on the outside. + return getAddRecExpr( + getExtendAddRecStart<SCEVZeroExtendExpr>(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. + const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW); + // Return the expression with the addrec on the outside. + return getAddRecExpr( + getExtendAddRecStart<SCEVZeroExtendExpr>(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<SCEVCouldNotCompute>(MaxBECount) || HasGuards || + !AC.assumptions().empty()) { + // 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)) { + // Cache knowledge of AR NUW, which is propagated to this + // AddRec. + const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW); + // Return the expression with the addrec on the outside. + return getAddRecExpr( + getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this, + Depth + 1), + getZeroExtendExpr(Step, Ty, Depth + 1), L, + AR->getNoWrapFlags()); + } + } else 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. + const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW); + // Return the expression with the addrec on the outside. + return getAddRecExpr( + getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this, + Depth + 1), + getSignExtendExpr(Step, Ty, Depth + 1), L, + AR->getNoWrapFlags()); + } + } + } + + // zext({C,+,Step}) --> (zext(D) + zext({C-D,+,Step}))<nuw><nsw> + // 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<SCEVConstant>(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<SCEVZeroExtendExpr>(Start, Step, L)) { + const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW); + return getAddRecExpr( + getExtendAddRecStart<SCEVZeroExtendExpr>(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<SCEVUDivExpr>(Op)) + return getUDivExpr(getZeroExtendExpr(Div->getLHS(), Ty, Depth + 1), + getZeroExtendExpr(Div->getRHS(), Ty, Depth + 1)); + + if (auto *SA = dyn_cast<SCEVAddExpr>(Op)) { + // zext((A + B + ...)<nuw>) --> (zext(A) + zext(B) + ...)<nuw> + if (SA->hasNoUnsignedWrap()) { + // If the addition does not unsign overflow then we can, by definition, + // commute the zero extension with the addition operation. + SmallVector<const SCEV *, 4> 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<SCEVConstant>(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<SCEVMulExpr>(Op)) { + // zext((A * B * ...)<nuw>) --> (zext(A) * zext(B) * ...)<nuw> + if (SM->hasNoUnsignedWrap()) { + // If the multiply does not unsign overflow then we can, by definition, + // commute the zero extension with the multiply operation. + SmallVector<const SCEV *, 4> 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)<nuw> + // + // 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)<nuw> to iM + // (because shl removes the top K bits) + // = zext((2^K * (trunc X to i{N-K}))<nuw>) to iM + // = (2^K * (zext(trunc X to i{N-K}) to iM))<nuw>. + // + if (SM->getNumOperands() == 2) + if (auto *MulLHS = dyn_cast<SCEVConstant>(SM->getOperand(0))) + if (MulLHS->getAPInt().isPowerOf2()) + if (auto *TruncRHS = dyn_cast<SCEVTruncateExpr>(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!"); + Ty = getEffectiveSCEVType(Ty); + + // Fold if the operand is constant. + if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) + return getConstant( + cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), Ty))); + + // sext(sext(x)) --> sext(x) + if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op)) + return getSignExtendExpr(SS->getOperand(), Ty, Depth + 1); + + // sext(zext(x)) --> zext(x) + if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(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<SCEVTruncateExpr>(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<SCEVAddExpr>(Op)) { + // sext((A + B + ...)<nsw>) --> (sext(A) + sext(B) + ...)<nsw> + if (SA->hasNoSignedWrap()) { + // If the addition does not sign overflow then we can, by definition, + // commute the sign extension with the addition operation. + SmallVector<const SCEV *, 4> 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<SCEVConstant>(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<SCEVAddRecExpr>(Op)) + if (AR->isAffine()) { + const SCEV *Start = AR->getStart(); + const SCEV *Step = AR->getStepRecurrence(*this); + unsigned BitWidth = getTypeSizeInBits(AR->getType()); + const Loop *L = AR->getLoop(); + + if (!AR->hasNoSignedWrap()) { + auto NewFlags = proveNoWrapViaConstantRanges(AR); + const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(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<SCEVSignExtendExpr>(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<SCEVCouldNotCompute>(MaxBECount)) { + // Manually compute the final value for AR, checking for + // overflow. + + // Check whether the backedge-taken count can be losslessly casted to + // the addrec's type. The count is always unsigned. + const SCEV *CastedMaxBECount = + getTruncateOrZeroExtend(MaxBECount, Start->getType(), 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. + const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW); + // Return the expression with the addrec on the outside. + return getAddRecExpr( + getExtendAddRecStart<SCEVSignExtendExpr>(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) + + const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW); + + // Return the expression with the addrec on the outside. + return getAddRecExpr( + getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this, + Depth + 1), + getZeroExtendExpr(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<SCEVCouldNotCompute>(MaxBECount) || HasGuards || + !AC.assumptions().empty()) { + // 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))) { + // Cache knowledge of AR NSW, then propagate NSW to the wide AddRec. + const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW); + return getAddRecExpr( + getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this, Depth + 1), + getSignExtendExpr(Step, Ty, Depth + 1), L, AR->getNoWrapFlags()); + } + } + + // sext({C,+,Step}) --> (sext(D) + sext({C-D,+,Step}))<nuw><nsw> + // 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<SCEVConstant>(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<SCEVSignExtendExpr>(Start, Step, L)) { + const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW); + return getAddRecExpr( + getExtendAddRecStart<SCEVSignExtendExpr>(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<SCEVConstant>(Op)) + if (SC->getAPInt().isNegative()) + return getSignExtendExpr(Op, Ty); + + // Peel off a truncate cast. + if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) { + const SCEV *NewOp = T->getOperand(); + if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty)) + return getAnyExtendExpr(NewOp, Ty); + return getTruncateOrNoop(NewOp, Ty); + } + + // Next try a zext cast. If the cast is folded, use it. + const SCEV *ZExt = getZeroExtendExpr(Op, Ty); + if (!isa<SCEVZeroExtendExpr>(ZExt)) + return ZExt; + + // Next try a sext cast. If the cast is folded, use it. + const SCEV *SExt = getSignExtendExpr(Op, Ty); + if (!isa<SCEVSignExtendExpr>(SExt)) + return SExt; + + // Force the cast to be folded into the operands of an addrec. + if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) { + SmallVector<const SCEV *, 4> Ops; + for (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<SCEVSMaxExpr>(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<const SCEV *, APInt> &M, + SmallVectorImpl<const SCEV *> &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<SCEVConstant>(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<SCEVMulExpr>(Ops[i]); + if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) { + APInt NewScale = + Scale * cast<SCEVConstant>(Mul->getOperand(0))->getAPInt(); + if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) { + // A multiplication of a constant with another add; recurse. + const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1)); + Interesting |= + CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, + Add->op_begin(), Add->getNumOperands(), + NewScale, SE); + } else { + // A multiplication of a constant with some other value. Update + // the map. + SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end()); + const SCEV *Key = SE.getMulExpr(MulOps); + 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<DenseMap<const SCEV *, APInt>::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; +} + +// 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<const SCEV *> 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<SCEVConstant>(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<SCEVConstant>(Ops[0])->getAPInt(); + + // (A <opcode> C) --> (A <opcode> C)<nsw> 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 <opcode> C) --> (A <opcode> C)<nuw> 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<const SCEV *> &Ops, + SCEV::NoWrapFlags Flags, + unsigned Depth) { + assert(!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) && + "only nuw or nsw allowed"); + assert(!Ops.empty() && "Cannot get empty add!"); + if (Ops.size() == 1) return Ops[0]; +#ifndef NDEBUG + Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); + for (unsigned i = 1, e = Ops.size(); i != e; ++i) + assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && + "SCEVAddExpr operand types don't match!"); +#endif + + // Sort by complexity, this groups all similar expression types together. + GroupByComplexity(Ops, &LI, DT); + + Flags = StrengthenNoWrapFlags(this, scAddExpr, Ops, Flags); + + // If there are any constants, fold them together. + unsigned Idx = 0; + if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { + ++Idx; + assert(Idx < Ops.size()); + while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { + // We found two constants, fold them together! + Ops[0] = getConstant(LHSC->getAPInt() + RHSC->getAPInt()); + if (Ops.size() == 2) return Ops[0]; + Ops.erase(Ops.begin()+1); // Erase the folded element + LHSC = cast<SCEVConstant>(Ops[0]); + } + + // If we are left with a constant zero being added, strip it off. + if (LHSC->getValue()->isZero()) { + Ops.erase(Ops.begin()); + --Idx; + } + + if (Ops.size() == 1) return Ops[0]; + } + + // Limit recursion calls depth. + if (Depth > MaxArithDepth || hasHugeExpression(Ops)) + return getOrCreateAddExpr(Ops, Flags); + + // 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, Flags, 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<SCEVTruncateExpr>(Ops[Idx])) + return T->getOperand()->getType(); + if (const auto *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) { + const auto *LastOp = Mul->getOperand(Mul->getNumOperands() - 1); + if (const auto *T = dyn_cast<SCEVTruncateExpr>(LastOp)) + return T->getOperand()->getType(); + } + return nullptr; + }; + if (auto *SrcType = FindTruncSrcType()) { + SmallVector<const SCEV *, 8> LargeOps; + bool Ok = true; + // Check all the operands to see if they can be represented in the + // source type of the truncate. + for (unsigned i = 0, e = Ops.size(); i != e; ++i) { + if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) { + if (T->getOperand()->getType() != SrcType) { + Ok = false; + break; + } + LargeOps.push_back(T->getOperand()); + } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) { + LargeOps.push_back(getAnyExtendExpr(C, SrcType)); + } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) { + SmallVector<const SCEV *, 8> LargeMulOps; + for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) { + if (const SCEVTruncateExpr *T = + dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) { + if (T->getOperand()->getType() != SrcType) { + Ok = false; + break; + } + LargeMulOps.push_back(T->getOperand()); + } else if (const auto *C = dyn_cast<SCEVConstant>(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<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold)) + return getTruncateExpr(Fold, Ty); + } + } + + // Skip past any other cast SCEVs. + while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr) + ++Idx; + + // If there are add operands they would be next. + if (Idx < Ops.size()) { + bool DeletedAdd = false; + while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) { + if (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; + } + + // 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, SCEV::FlagAnyWrap, 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<SCEVMulExpr>(Ops[Idx])) { + uint64_t BitWidth = getTypeSizeInBits(Ty); + DenseMap<const SCEV *, APInt> M; + SmallVector<const SCEV *, 8> NewOps; + APInt AccumulatedConstant(BitWidth, 0); + if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant, + Ops.data(), Ops.size(), + APInt(BitWidth, 1), *this)) { + 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<APInt, SmallVector<const SCEV *, 4>, 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 != 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<SCEVMulExpr>(Ops[Idx]); ++Idx) { + const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]); + for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) { + const SCEV *MulOpSCEV = Mul->getOperand(MulOp); + if (isa<SCEVConstant>(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<const SCEV *, 4> 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<const SCEV *, 2> 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<SCEVMulExpr>(Ops[OtherMulIdx]); + ++OtherMulIdx) { + const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]); + // If MulOp occurs in OtherMul, we can fold the two multiplies + // together. + for (unsigned OMulOp = 0, e = OtherMul->getNumOperands(); + OMulOp != e; ++OMulOp) + if (OtherMul->getOperand(OMulOp) == MulOpSCEV) { + // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E)) + const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0); + if (Mul->getNumOperands() != 2) { + SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), + Mul->op_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<const SCEV *, 4> 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<const SCEV *, 2> 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<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { + // Scan all of the other operands to this add and add them to the vector if + // they are loop invariant w.r.t. the recurrence. + SmallVector<const SCEV *, 8> LIOps; + const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); + const Loop *AddRecLoop = AddRec->getLoop(); + for (unsigned i = 0, e = Ops.size(); i != e; ++i) + if (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,+,Step} + LIOps.push_back(AddRec->getStart()); + + SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(), + AddRec->op_end()); + // 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<SCEVAddRecExpr>(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<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()->getHeader(), + AddRec->getLoop()->getHeader()) && + "AddRecExprs are not sorted in reverse dominance order?"); + if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) { + // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L> + SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(), + AddRec->op_end()); + for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]); + ++OtherIdx) { + const auto *OtherAddRec = cast<SCEVAddRecExpr>(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<const SCEV *, 2> 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, Flags); +} + +const SCEV * +ScalarEvolution::getOrCreateAddExpr(ArrayRef<const SCEV *> Ops, + SCEV::NoWrapFlags Flags) { + FoldingSetNodeID ID; + ID.AddInteger(scAddExpr); + for (const SCEV *Op : Ops) + ID.AddPointer(Op); + void *IP = nullptr; + SCEVAddExpr *S = + static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); + if (!S) { + const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); + std::uninitialized_copy(Ops.begin(), Ops.end(), O); + S = new (SCEVAllocator) + SCEVAddExpr(ID.Intern(SCEVAllocator), O, Ops.size()); + UniqueSCEVs.InsertNode(S, IP); + addToLoopUseLists(S); + } + S->setNoWrapFlags(Flags); + return S; +} + +const SCEV * +ScalarEvolution::getOrCreateAddRecExpr(ArrayRef<const SCEV *> 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<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); + if (!S) { + const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); + std::uninitialized_copy(Ops.begin(), Ops.end(), O); + S = new (SCEVAllocator) + SCEVAddRecExpr(ID.Intern(SCEVAllocator), O, Ops.size(), L); + UniqueSCEVs.InsertNode(S, IP); + addToLoopUseLists(S); + } + S->setNoWrapFlags(Flags); + return S; +} + +const SCEV * +ScalarEvolution::getOrCreateMulExpr(ArrayRef<const SCEV *> 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<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP)); + if (!S) { + const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size()); + std::uninitialized_copy(Ops.begin(), Ops.end(), O); + S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator), + O, Ops.size()); + UniqueSCEVs.InsertNode(S, IP); + 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<SCEVConstant>(S); + return isa<SCEVAddExpr>(S) || isa<SCEVMulExpr>(S); + } + + bool isDone() const { + return FoundConstant; + } + }; + + FindConstantInAddMulChain F; + SCEVTraversal<FindConstantInAddMulChain> ST(F); + ST.visitAll(StartExpr); + return F.FoundConstant; +} + +/// Get a canonical multiply expression, or something simpler if possible. +const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops, + SCEV::NoWrapFlags Flags, + unsigned Depth) { + assert(Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) && + "only nuw or nsw allowed"); + assert(!Ops.empty() && "Cannot get empty mul!"); + if (Ops.size() == 1) return Ops[0]; +#ifndef NDEBUG + Type *ETy = getEffectiveSCEVType(Ops[0]->getType()); + for (unsigned i = 1, e = Ops.size(); i != e; ++i) + assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy && + "SCEVMulExpr operand types don't match!"); +#endif + + // Sort by complexity, this groups all similar expression types together. + GroupByComplexity(Ops, &LI, DT); + + Flags = StrengthenNoWrapFlags(this, scMulExpr, Ops, Flags); + + // Limit recursion calls depth. + if (Depth > MaxArithDepth || hasHugeExpression(Ops)) + return getOrCreateMulExpr(Ops, Flags); + + // If there are any constants, fold them together. + unsigned Idx = 0; + if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) { + + if (Ops.size() == 2) + // C1*(C2+V) -> C1*C2 + C1*V + if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(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); + + ++Idx; + while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) { + // We found two constants, fold them together! + ConstantInt *Fold = + ConstantInt::get(getContext(), 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<SCEVConstant>(Ops[0]); + } + + // If we are left with a constant one being multiplied, strip it off. + if (cast<SCEVConstant>(Ops[0])->getValue()->isOne()) { + Ops.erase(Ops.begin()); + --Idx; + } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) { + // If we have a multiply of zero, it will always be zero. + return Ops[0]; + } else if (Ops[0]->isAllOnesValue()) { + // If we have a mul by -1 of an add, try distributing the -1 among the + // add operands. + if (Ops.size() == 2) { + if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) { + SmallVector<const SCEV *, 4> NewOps; + bool AnyFolded = false; + for (const SCEV *AddOp : Add->operands()) { + const SCEV *Mul = getMulExpr(Ops[0], AddOp, SCEV::FlagAnyWrap, + Depth + 1); + if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true; + NewOps.push_back(Mul); + } + if (AnyFolded) + return getAddExpr(NewOps, SCEV::FlagAnyWrap, Depth + 1); + } else if (const auto *AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) { + // Negation preserves a recurrence's no self-wrap property. + SmallVector<const SCEV *, 4> 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)); + } + } + } + + if (Ops.size() == 1) + return Ops[0]; + } + + // Skip over the add expression until we get to a multiply. + while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr) + ++Idx; + + // If there are mul operands inline them all into this expression. + if (Idx < Ops.size()) { + bool DeletedMul = false; + while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) { + if (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<SCEVAddRecExpr>(Ops[Idx]); ++Idx) { + // Scan all of the other operands to this mul and add them to the vector + // if they are loop invariant w.r.t. the recurrence. + SmallVector<const SCEV *, 8> LIOps; + const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]); + 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<const SCEV *, 4> 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. + Flags = AddRec->getNoWrapFlags(clearFlags(Flags, SCEV::FlagNW)); + const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, Flags); + + // If all of the other operands were loop invariant, we are done. + if (Ops.size() == 1) return NewRec; + + // Otherwise, multiply the folded AddRec by the non-invariant parts. + for (unsigned i = 0;; ++i) + if (Ops[i] == AddRec) { + Ops[i] = NewRec; + break; + } + return getMulExpr(Ops, 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}<L> * {B1,+,B2,+,...,+,Bn}<L> + // = {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<SCEVAddRecExpr>(Ops[OtherIdx]); + ++OtherIdx) { + const SCEVAddRecExpr *OtherAddRec = + dyn_cast<SCEVAddRecExpr>(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 || isHugeExpression(AddRec) || + isHugeExpression(OtherAddRec)) + continue; + + bool Overflow = false; + Type *Ty = AddRec->getType(); + bool LargerThan64Bits = getTypeSizeInBits(Ty) > 64; + SmallVector<const SCEV*, 7> AddRecOps; + for (int x = 0, xe = AddRec->getNumOperands() + + OtherAddRec->getNumOperands() - 1; x != xe && !Overflow; ++x) { + SmallVector <const SCEV *, 7> 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<SCEVAddRecExpr>(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, Flags); +} + +/// 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<SCEVConstant>(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 -<nuw> ((%x udiv %y) *<nuw> %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(getEffectiveSCEVType(LHS->getType()) == + getEffectiveSCEVType(RHS->getType()) && + "SCEVUDivExpr operand types don't match!"); + + if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(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<SCEVAddRecExpr>(LHS)) + if (const SCEVConstant *Step = + dyn_cast<SCEVConstant>(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<const SCEV *, 4> 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<SCEVConstant>(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) + LHS = getAddRecExpr(getConstant(StartInt - StartRem), Step, + AR->getLoop(), SCEV::FlagNW); + } + } + // (A*B)/C --> A*(B/C) if safe and B/C can be folded. + if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) { + SmallVector<const SCEV *, 4> 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<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) { + Operands = SmallVector<const SCEV *, 4>(M->op_begin(), + M->op_end()); + Operands[i] = Div; + return getMulExpr(Operands); + } + } + } + + // (A/B)/C --> A/(B*C) if safe and B*C can be folded. + if (const SCEVUDivExpr *OtherDiv = dyn_cast<SCEVUDivExpr>(LHS)) { + if (auto *DivisorConstant = + dyn_cast<SCEVConstant>(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<SCEVAddExpr>(LHS)) { + SmallVector<const SCEV *, 4> 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<SCEVUDivExpr>(Op) || + getMulExpr(Op, RHS) != A->getOperand(i)) + break; + Operands.push_back(Op); + } + if (Operands.size() == A->getNumOperands()) + return getAddExpr(Operands); + } + } + + // Fold if both operands are constant. + if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) { + Constant *LHSCV = LHSC->getValue(); + Constant *RHSCV = RHSC->getValue(); + return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV, + RHSCV))); + } + } + } + + FoldingSetNodeID ID; + ID.AddInteger(scUDivExpr); + ID.AddPointer(LHS); + ID.AddPointer(RHS); + void *IP = 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<SCEVMulExpr>(LHS); + if (!Mul || !Mul->hasNoUnsignedWrap()) + return getUDivExpr(LHS, RHS); + + if (const SCEVConstant *RHSCst = dyn_cast<SCEVConstant>(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<SCEVConstant>(Mul->getOperand(0))) { + if (LHSCst == RHSCst) { + SmallVector<const SCEV *, 2> Operands; + Operands.append(Mul->op_begin() + 1, Mul->op_end()); + return getMulExpr(Operands); + } + + // We can't just assume that LHSCst divides RHSCst cleanly, it could be + // that there's a factor provided by one of the other terms. We need to + // check. + APInt Factor = gcd(LHSCst, RHSCst); + if (!Factor.isIntN(1)) { + LHSCst = + cast<SCEVConstant>(getConstant(LHSCst->getAPInt().udiv(Factor))); + RHSCst = + cast<SCEVConstant>(getConstant(RHSCst->getAPInt().udiv(Factor))); + SmallVector<const SCEV *, 2> Operands; + Operands.push_back(LHSCst); + Operands.append(Mul->op_begin() + 1, Mul->op_end()); + LHS = getMulExpr(Operands); + RHS = RHSCst; + Mul = dyn_cast<SCEVMulExpr>(LHS); + if (!Mul) + return getUDivExactExpr(LHS, RHS); + } + } + } + + for (int i = 0, e = Mul->getNumOperands(); i != e; ++i) { + if (Mul->getOperand(i) == RHS) { + SmallVector<const SCEV *, 2> 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<const SCEV *, 4> Operands; + Operands.push_back(Start); + if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(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<const SCEV *> &Operands, + const Loop *L, SCEV::NoWrapFlags Flags) { + if (Operands.size() == 1) return Operands[0]; +#ifndef NDEBUG + Type *ETy = getEffectiveSCEVType(Operands[0]->getType()); + for (unsigned i = 1, e = Operands.size(); i != e; ++i) + assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy && + "SCEVAddRecExpr operand types don't match!"); + for (unsigned i = 0, e = Operands.size(); i != e; ++i) + assert(isLoopInvariant(Operands[i], L) && + "SCEVAddRecExpr operand is not loop-invariant!"); +#endif + + if (Operands.back()->isZero()) { + Operands.pop_back(); + return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0} --> X + } + + // It's tempting to want to call 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<SCEVAddRecExpr>(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<const SCEV *, 4> NestedOperands(NestedAR->op_begin(), + NestedAR->op_end()); + Operands[0] = NestedAR->getStart(); + // AddRecs require their operands be loop-invariant with respect to their + // loops. Don't perform this transformation if it would break this + // requirement. + bool AllInvariant = 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<const SCEV *> &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 *IntPtrTy = 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 Wrap = GEP->isInBounds() ? SCEV::FlagNSW + : SCEV::FlagAnyWrap; + + const SCEV *TotalOffset = getZero(IntPtrTy); + // The array size is unimportant. The first thing we do on CurTy is getting + // its element type. + Type *CurTy = ArrayType::get(GEP->getSourceElementType(), 0); + for (const SCEV *IndexExpr : IndexExprs) { + // Compute the (potentially symbolic) offset in bytes for this index. + if (StructType *STy = dyn_cast<StructType>(CurTy)) { + // For a struct, add the member offset. + ConstantInt *Index = cast<SCEVConstant>(IndexExpr)->getValue(); + unsigned FieldNo = Index->getZExtValue(); + const SCEV *FieldOffset = getOffsetOfExpr(IntPtrTy, STy, FieldNo); + + // Add the field offset to the running total offset. + TotalOffset = getAddExpr(TotalOffset, FieldOffset); + + // Update CurTy to the type of the field at Index. + CurTy = STy->getTypeAtIndex(Index); + } else { + // Update CurTy to its element type. + CurTy = cast<SequentialType>(CurTy)->getElementType(); + // For an array, add the element offset, explicitly scaled. + const SCEV *ElementSize = getSizeOfExpr(IntPtrTy, CurTy); + // Getelementptr indices are signed. + IndexExpr = getTruncateOrSignExtend(IndexExpr, IntPtrTy); + + // Multiply the index by the element size to compute the element offset. + const SCEV *LocalOffset = getMulExpr(IndexExpr, ElementSize, Wrap); + + // Add the element offset to the running total offset. + TotalOffset = getAddExpr(TotalOffset, LocalOffset); + } + } + + // Add the total offset from all the GEP indices to the base. + return getAddExpr(BaseExpr, TotalOffset, Wrap); +} + +std::tuple<const SCEV *, FoldingSetNodeID, void *> +ScalarEvolution::findExistingSCEVInCache(int SCEVType, + ArrayRef<const SCEV *> 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<const SCEV *, FoldingSetNodeID, void *>( + UniqueSCEVs.FindNodeOrInsertPos(ID, IP), std::move(ID), IP); +} + +const SCEV *ScalarEvolution::getMinMaxExpr(unsigned Kind, + SmallVectorImpl<const SCEV *> &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!"); +#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<SCEVConstant>(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<SCEVConstant>(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<SCEVConstant>(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<SCEVMinMaxExpr>(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<const SCEV *>(Ops.size()); + std::uninitialized_copy(Ops.begin(), Ops.end(), O); + SCEV *S = new (SCEVAllocator) SCEVMinMaxExpr( + ID.Intern(SCEVAllocator), static_cast<SCEVTypes>(Kind), O, Ops.size()); + + UniqueSCEVs.InsertNode(S, IP); + addToLoopUseLists(S); + return S; +} + +const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS, const SCEV *RHS) { + SmallVector<const SCEV *, 2> Ops = {LHS, RHS}; + return getSMaxExpr(Ops); +} + +const SCEV *ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { + return getMinMaxExpr(scSMaxExpr, Ops); +} + +const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS, const SCEV *RHS) { + SmallVector<const SCEV *, 2> Ops = {LHS, RHS}; + return getUMaxExpr(Ops); +} + +const SCEV *ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) { + return getMinMaxExpr(scUMaxExpr, Ops); +} + +const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS, + const SCEV *RHS) { + SmallVector<const SCEV *, 2> Ops = { LHS, RHS }; + return getSMinExpr(Ops); +} + +const SCEV *ScalarEvolution::getSMinExpr(SmallVectorImpl<const SCEV *> &Ops) { + return getMinMaxExpr(scSMinExpr, Ops); +} + +const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS, + const SCEV *RHS) { + SmallVector<const SCEV *, 2> Ops = { LHS, RHS }; + return getUMinExpr(Ops); +} + +const SCEV *ScalarEvolution::getUMinExpr(SmallVectorImpl<const SCEV *> &Ops) { + return getMinMaxExpr(scUMinExpr, Ops); +} + +const SCEV *ScalarEvolution::getSizeOfExpr(Type *IntTy, Type *AllocTy) { + // 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::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<SCEVUnknown>(S)->getValue() == V && + "Stale SCEVUnknown in uniquing map!"); + return S; + } + SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this, + FirstUnknown); + FirstUnknown = cast<SCEVUnknown>(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-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().getIntPtrType(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<SCEVUnknown>(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, isa<SCEVAddRecExpr, const SCEV *>); + 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<const SCEV *, ConstantInt *> splitAddExpr(const SCEV *S) { + const auto *Add = dyn_cast<SCEVAddExpr>(S); + if (!Add) + return {S, nullptr}; + + if (Add->getNumOperands() != 2) + return {S, nullptr}; + + auto *ConstOp = dyn_cast<SCEVConstant>(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. +SetVector<ScalarEvolution::ValueOffsetPair> * +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 (SetVector<ValueOffsetPair> *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 (SetVector<ValueOffsetPair> *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<Instruction>(V)) { + if (isa<OverflowingBinaryOperator>(I)) { + if (auto *NS = dyn_cast<SCEVNAryExpr>(S)) { + if (I->hasNoSignedWrap() && !NS->hasNoSignedWrap()) + return true; + if (I->hasNoUnsignedWrap() && !NS->hasNoUnsignedWrap()) + return true; + } + } else if (isa<PossiblyExactOperator>(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<ValueExprMapType::iterator, bool> 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<SCEVUnknown>(Stripped) && + !isa<GetElementPtrInst>(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<SCEVConstant>(V)) + return getConstant( + cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue()))); + + Type *Ty = V->getType(); + Ty = getEffectiveSCEVType(Ty); + return getMulExpr( + V, getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))), Flags); +} + +/// If Expr computes ~A, return A else return nullptr +static const SCEV *MatchNotExpr(const SCEV *Expr) { + const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Expr); + if (!Add || Add->getNumOperands() != 2 || + !Add->getOperand(0)->isAllOnesValue()) + return nullptr; + + const SCEVMulExpr *AddRHS = dyn_cast<SCEVMulExpr>(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<SCEVConstant>(V)) + return getConstant( + cast<ConstantInt>(ConstantExpr::getNot(VC->getValue()))); + + // Fold ~(u|s)(min|max)(~x, ~y) to (u|s)(max|min)(x, y) + if (const SCEVMinMaxExpr *MME = dyn_cast<SCEVMinMaxExpr>(V)) { + auto MatchMinMaxNegation = [&](const SCEVMinMaxExpr *MME) { + SmallVector<const SCEV *, 2> 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(static_cast<SCEVTypes>(MME->getSCEVType())), + MatchedOperands); + }; + if (const SCEV *Replaced = MatchMinMaxNegation(MME)) + return Replaced; + } + + Type *Ty = V->getType(); + Ty = getEffectiveSCEVType(Ty); + const SCEV *AllOnes = + getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))); + return getMinusSCEV(AllOnes, V); +} + +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()); + + // 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<const SCEV *, 2> Ops = { LHS, RHS }; + return getUMinFromMismatchedTypes(Ops); +} + +const SCEV *ScalarEvolution::getUMinFromMismatchedTypes( + SmallVectorImpl<const SCEV *> &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(); + + // Extend all ops to max type. + SmallVector<const SCEV *, 2> 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; + + if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) { + return getPointerBase(Cast->getOperand()); + } else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) { + const SCEV *PtrOp = nullptr; + for (const SCEV *NAryOp : NAry->operands()) { + if (NAryOp->getType()->isPointerTy()) { + // Cannot find the base of an expression with multiple pointer operands. + if (PtrOp) + return V; + PtrOp = NAryOp; + } + } + if (!PtrOp) + return V; + return getPointerBase(PtrOp); + } + return V; +} + +/// Push users of the given Instruction onto the given Worklist. +static void +PushDefUseChildren(Instruction *I, + SmallVectorImpl<Instruction *> &Worklist) { + // Push the def-use children onto the Worklist stack. + for (User *U : I->users()) + Worklist.push_back(cast<Instruction>(U)); +} + +void ScalarEvolution::forgetSymbolicName(Instruction *PN, const SCEV *SymName) { + SmallVector<Instruction *, 16> Worklist; + PushDefUseChildren(PN, Worklist); + + SmallPtrSet<Instruction *, 8> Visited; + Visited.insert(PN); + while (!Worklist.empty()) { + Instruction *I = Worklist.pop_back_val(); + if (!Visited.insert(I).second) + continue; + + auto It = ValueExprMap.find_as(static_cast<Value *>(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<PHINode>(I) || + !isa<SCEVUnknown>(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<SCEVInitRewriter> { +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<SCEVPostIncRewriter> { +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<SCEVBackedgeConditionFolder> { +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<BranchInst>(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<Instruction>(Expr->getValue()); + switch (I->getOpcode()) { + case Instruction::Select: { + SelectInst *SI = cast<SelectInst>(I); + Optional<const SCEV *> Res = + compareWithBackedgeCondition(SI->getCondition()); + if (Res.hasValue()) { + bool IsOne = cast<SCEVConstant>(Res.getValue())->getValue()->isOne(); + Result = SE.getSCEV(IsOne ? SI->getTrueValue() : SI->getFalseValue()); + } + break; + } + default: { + Optional<const SCEV *> 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<const SCEV *> 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<const SCEV *> +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<SCEVShiftRewriter> { +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; +} + +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<OverflowingBinaryOperator>(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<BinaryOp> MatchBinaryOp(Value *V, DominatorTree &DT) { + auto *Op = dyn_cast<Operator>(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<ConstantInt>(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<ConstantInt>(Op->getOperand(1))) { + uint32_t BitWidth = cast<IntegerType>(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<ExtractValueInst>(Op); + if (EVI->getNumIndices() != 1 || EVI->getIndices()[0] != 0) + break; + + auto *WO = dyn_cast<WithOverflowInst>(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; + } + + 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<SCEVSignExtendExpr>(Op); + const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(Op); + if (!SExt && !ZExt) + return nullptr; + const SCEVTruncateExpr *Trunc = + SExt ? dyn_cast<SCEVTruncateExpr>(SExt->getOperand()) + : dyn_cast<SCEVTruncateExpr>(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)}<nsw> Flags: <nssw> +// 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<std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>> +ScalarEvolution::createAddRecFromPHIWithCastsImpl(const SCEVUnknown *SymbolicPHI) { + SmallVector<const SCEVPredicate *, 3> 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<PHINode>(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<SCEVAddExpr>(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<const SCEV *, 8> Ops; + for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) + if (i != FoundIndex) + Ops.push_back(Add->getOperand(i)); + const SCEV *Accum = getAddExpr(Ops); + + // 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<n: + // + + // Create a truncated addrec for which we will add a no overflow check (P1). + const SCEV *StartVal = getSCEV(StartValueV); + const SCEV *PHISCEV = + getAddRecExpr(getTruncateExpr(StartVal, TruncTy), + getTruncateExpr(Accum, TruncTy), L, SCEV::FlagAnyWrap); + + // PHISCEV can be either a SCEVConstant or a SCEVAddRecExpr. + // ex: If truncated Accum is 0 and StartVal is a constant, then PHISCEV + // will be constant. + // + // If PHISCEV is a constant, then P1 degenerates into P2 or P3, so we don't + // add P1. + if (const auto *AR = dyn_cast<SCEVAddRecExpr>(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<const SCEV *, SmallVector<const SCEVPredicate *, 3>> 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<std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>> +ScalarEvolution::createAddRecFromPHIWithCasts(const SCEVUnknown *SymbolicPHI) { + auto *PN = cast<PHINode>(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<const SCEV *, SmallVector<const SCEVPredicate *, 3>> 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<SCEVAddRecExpr>(Rewrite.first) && "Expected an AddRec"); + assert(!(Rewrite.second).empty() && "Expected to find Predicates"); + return Rewrite; + } + + Optional<std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>> + Rewrite = createAddRecFromPHIWithCastsImpl(SymbolicPHI); + + // Record in the cache that the analysis failed + if (!Rewrite) { + SmallVector<const SCEVPredicate *, 3> 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<Instruction>(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<SCEVAddExpr>(BEValue)) { + // If there is a single occurrence of the symbolic value, replace it + // with a recurrence. + unsigned FoundIndex = Add->getNumOperands(); + for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) + if (Add->getOperand(i) == SymbolicName) + if (FoundIndex == e) { + FoundIndex = i; + break; + } + + if (FoundIndex != Add->getNumOperands()) { + // Create an add with everything but the specified operand. + SmallVector<const SCEV *, 8> Ops; + for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i) + if (i != FoundIndex) + Ops.push_back(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<SCEVAddRecExpr>(Accum) && + cast<SCEVAddRecExpr>(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<GEPOperator>(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<Instruction>(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 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<SCEVAddRecExpr>(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<SCEVUnknown>(S); + Value *V = SU->getValue(); + + if (isa<Argument>(V)) + return false; + + if (isa<Instruction>(V) && DT.dominates(cast<Instruction>(V), BB)) + return false; + + return setUnavailable(); + } + + case scUDivExpr: + case scCouldNotCompute: + // We do not try to smart about these at all. + return setUnavailable(); + } + llvm_unreachable("switch should be fully covered!"); + } + + bool isDone() { return TraversalDone; } + }; + + CheckAvailable CA(L, BB, DT); + SCEVTraversal<CheckAvailable> 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<BranchInst>(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<ConstantInt>(Cond)) + return getSCEV(CI->isOne() ? TrueVal : FalseVal); + + // Try to match some simple smax or umax patterns. + auto *ICI = dyn_cast<ICmpInst>(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: + std::swap(LHS, RHS); + LLVM_FALLTHROUGH; + case ICmpInst::ICMP_SGT: + case ICmpInst::ICMP_SGE: + // a >s b ? a+x : b+x -> smax(a, b)+x + // a >s b ? b+x : a+x -> smin(a, b)+x + if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType())) { + const SCEV *LS = getNoopOrSignExtend(getSCEV(LHS), I->getType()); + const SCEV *RS = getNoopOrSignExtend(getSCEV(RHS), I->getType()); + const SCEV *LA = getSCEV(TrueVal); + const SCEV *RA = getSCEV(FalseVal); + const SCEV *LDiff = getMinusSCEV(LA, LS); + const SCEV *RDiff = getMinusSCEV(RA, RS); + if (LDiff == RDiff) + return getAddExpr(getSMaxExpr(LS, RS), LDiff); + LDiff = getMinusSCEV(LA, RS); + RDiff = getMinusSCEV(RA, LS); + if (LDiff == RDiff) + return getAddExpr(getSMinExpr(LS, RS), LDiff); + } + break; + case ICmpInst::ICMP_ULT: + case ICmpInst::ICMP_ULE: + std::swap(LHS, RHS); + LLVM_FALLTHROUGH; + case ICmpInst::ICMP_UGT: + case ICmpInst::ICMP_UGE: + // a >u b ? a+x : b+x -> umax(a, b)+x + // a >u b ? b+x : a+x -> umin(a, b)+x + if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType())) { + const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType()); + const SCEV *RS = getNoopOrZeroExtend(getSCEV(RHS), I->getType()); + const SCEV *LA = getSCEV(TrueVal); + const SCEV *RA = getSCEV(FalseVal); + const SCEV *LDiff = getMinusSCEV(LA, LS); + const SCEV *RDiff = getMinusSCEV(RA, RS); + if (LDiff == RDiff) + return getAddExpr(getUMaxExpr(LS, RS), LDiff); + LDiff = getMinusSCEV(LA, RS); + RDiff = getMinusSCEV(RA, LS); + if (LDiff == RDiff) + return getAddExpr(getUMinExpr(LS, RS), LDiff); + } + break; + case ICmpInst::ICMP_NE: + // n != 0 ? n+x : 1+x -> umax(n, 1)+x + if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType()) && + isa<ConstantInt>(RHS) && cast<ConstantInt>(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<ConstantInt>(RHS) && cast<ConstantInt>(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<const SCEV *, 4> IndexExprs; + for (auto Index = GEP->idx_begin(); Index != GEP->idx_end(); ++Index) + IndexExprs.push_back(getSCEV(*Index)); + return getGEPExpr(GEP, IndexExprs); +} + +uint32_t ScalarEvolution::GetMinTrailingZerosImpl(const SCEV *S) { + if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) + return C->getAPInt().countTrailingZeros(); + + if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S)) + return std::min(GetMinTrailingZeros(T->getOperand()), + (uint32_t)getTypeSizeInBits(T->getType())); + + if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) { + uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); + return OpRes == getTypeSizeInBits(E->getOperand()->getType()) + ? getTypeSizeInBits(E->getType()) + : OpRes; + } + + if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) { + uint32_t OpRes = GetMinTrailingZeros(E->getOperand()); + return OpRes == getTypeSizeInBits(E->getOperand()->getType()) + ? getTypeSizeInBits(E->getType()) + : OpRes; + } + + if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) { + // The result is the min of all operands results. + uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); + for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) + MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); + return MinOpRes; + } + + if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) { + // The result is the sum of all operands results. + uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0)); + uint32_t BitWidth = getTypeSizeInBits(M->getType()); + for (unsigned i = 1, e = M->getNumOperands(); + SumOpRes != BitWidth && i != e; ++i) + SumOpRes = + std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)), BitWidth); + return SumOpRes; + } + + if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) { + // The result is the min of all operands results. + uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0)); + for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i) + MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i))); + return MinOpRes; + } + + if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) { + // The result is the min of all operands results. + uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); + for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) + MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); + return MinOpRes; + } + + if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) { + // The result is the min of all operands results. + uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0)); + for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i) + MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i))); + return MinOpRes; + } + + if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { + // For a SCEVUnknown, ask ValueTracking. + 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<ConstantRange> GetRangeFromMetadata(Value *V) { + if (Instruction *I = dyn_cast<Instruction>(V)) + if (MDNode *MD = I->getMetadata(LLVMContext::MD_range)) + return getConstantRangeFromMetadata(*MD); + + return None; +} + +/// 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<const SCEV *, ConstantRange> &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<const SCEV *, ConstantRange>::iterator I = Cache.find(S); + if (I != Cache.end()) + return I->second; + + if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) + return setRange(C, SignHint, ConstantRange(C->getAPInt())); + + unsigned BitWidth = getTypeSizeInBits(S->getType()); + ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true); + + // 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<SCEVAddExpr>(S)) { + ConstantRange X = getRangeRef(Add->getOperand(0), SignHint); + for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i) + X = X.add(getRangeRef(Add->getOperand(i), SignHint)); + return setRange(Add, SignHint, + ConservativeResult.intersectWith(X, RangeType)); + } + + if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(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<SCEVSMaxExpr>(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<SCEVUMaxExpr>(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<SCEVSMinExpr>(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<SCEVUMinExpr>(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<SCEVUDivExpr>(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<SCEVZeroExtendExpr>(S)) { + ConstantRange X = getRangeRef(ZExt->getOperand(), SignHint); + return setRange(ZExt, SignHint, + ConservativeResult.intersectWith(X.zeroExtend(BitWidth), + RangeType)); + } + + if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) { + ConstantRange X = getRangeRef(SExt->getOperand(), SignHint); + return setRange(SExt, SignHint, + ConservativeResult.intersectWith(X.signExtend(BitWidth), + RangeType)); + } + + if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) { + ConstantRange X = getRangeRef(Trunc->getOperand(), SignHint); + return setRange(Trunc, SignHint, + ConservativeResult.intersectWith(X.truncate(BitWidth), + RangeType)); + } + + if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) { + // If there's no unsigned wrap, the value will never be less than its + // initial value. + if (AddRec->hasNoUnsignedWrap()) + if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart())) + if (!C->getValue()->isZero()) + ConservativeResult = ConservativeResult.intersectWith( + ConstantRange(C->getAPInt(), APInt(BitWidth, 0)), RangeType); + + // If there's no signed wrap, and all the operands have the same sign or + // zero, the value won't ever change sign. + if (AddRec->hasNoSignedWrap()) { + bool AllNonNeg = true; + bool AllNonPos = true; + for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) { + if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false; + if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false; + } + if (AllNonNeg) + ConservativeResult = ConservativeResult.intersectWith( + ConstantRange(APInt(BitWidth, 0), + APInt::getSignedMinValue(BitWidth)), RangeType); + else if (AllNonPos) + ConservativeResult = ConservativeResult.intersectWith( + ConstantRange(APInt::getSignedMinValue(BitWidth), + APInt(BitWidth, 1)), RangeType); + } + + // TODO: non-affine addrec + if (AddRec->isAffine()) { + const SCEV *MaxBECount = getConstantMaxBackedgeTakenCount(AddRec->getLoop()); + if (!isa<SCEVCouldNotCompute>(MaxBECount) && + getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) { + auto RangeFromAffine = getRangeForAffineAR( + AddRec->getStart(), AddRec->getStepRecurrence(*this), MaxBECount, + BitWidth); + if (!RangeFromAffine.isFullSet()) + ConservativeResult = + ConservativeResult.intersectWith(RangeFromAffine, RangeType); + + auto RangeFromFactoring = getRangeViaFactoring( + AddRec->getStart(), AddRec->getStepRecurrence(*this), MaxBECount, + BitWidth); + if (!RangeFromFactoring.isFullSet()) + ConservativeResult = + ConservativeResult.intersectWith(RangeFromFactoring, RangeType); + } + } + + return setRange(AddRec, SignHint, std::move(ConservativeResult)); + } + + if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) { + // Check if the IR explicitly contains !range metadata. + Optional<ConstantRange> MDRange = GetRangeFromMetadata(U->getValue()); + if (MDRange.hasValue()) + ConservativeResult = ConservativeResult.intersectWith(MDRange.getValue(), + RangeType); + + // Split here to avoid paying the compile-time cost of calling both + // computeKnownBits and ComputeNumSignBits. This restriction can be lifted + // if needed. + const DataLayout &DL = getDataLayout(); + if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED) { + // For a SCEVUnknown, ask ValueTracking. + KnownBits Known = computeKnownBits(U->getValue(), DL, 0, &AC, nullptr, &DT); + if (Known.One != ~Known.Zero + 1) + ConservativeResult = + ConservativeResult.intersectWith( + ConstantRange(Known.One, ~Known.Zero + 1), RangeType); + } else { + assert(SignHint == ScalarEvolution::HINT_RANGE_SIGNED && + "generalize as needed!"); + unsigned NS = ComputeNumSignBits(U->getValue(), DL, 0, &AC, nullptr, &DT); + 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<PHINode>(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<SCEVCouldNotCompute>(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::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<unsigned> CastOp; + APInt Offset(BitWidth, 0); + + assert(SE.getTypeSizeInBits(S->getType()) == BitWidth && + "Should be!"); + + // Peel off a constant offset: + if (auto *SA = dyn_cast<SCEVAddExpr>(S)) { + // In the future we could consider being smarter here and handle + // {Start+Step,+,Step} too. + if (SA->getNumOperands() != 2 || !isa<SCEVConstant>(SA->getOperand(0))) + return; + + Offset = cast<SCEVConstant>(SA->getOperand(0))->getAPInt(); + S = SA->getOperand(1); + } + + // Peel off a cast operation + if (auto *SCast = dyn_cast<SCEVCastExpr>(S)) { + CastOp = SCast->getSCEVType(); + S = SCast->getOperand(); + } + + using namespace llvm::PatternMatch; + + auto *SU = dyn_cast<SCEVUnknown>(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<ConstantExpr>(V)) return SCEV::FlagAnyWrap; + const BinaryOperator *BinOp = cast<BinaryOperator>(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 (!programUndefinedIfFullPoison(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<SCEVAddRecExpr>(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<const Instruction *, 16> Pushed; + SmallVector<const Instruction *, 8> PoisonStack; + + // We start by assuming \c I, the post-inc add recurrence, is poison. Only + // things that are known to be fully 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 (propagatesFullPoison(cast<Instruction>(PoisonUser))) { + if (Pushed.insert(cast<Instruction>(PoisonUser)).second) + PoisonStack.push_back(cast<Instruction>(PoisonUser)); + } else if (auto *BI = dyn_cast<BranchInst>(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<StoreInst>(I)) + return !SI->isSimple(); + + return I->mayHaveSideEffects(); + }; + + 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; +} + +const SCEV *ScalarEvolution::createSCEV(Value *V) { + if (!isSCEVable(V->getType())) + return getUnknown(V); + + if (Instruction *I = dyn_cast<Instruction>(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<ConstantInt>(V)) + return getConstant(CI); + else if (isa<ConstantPointerNull>(V)) + return getZero(V->getType()); + else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V)) + return GA->isInterposable() ? getUnknown(V) : getSCEV(GA->getAliasee()); + else if (!isa<ConstantExpr>(V)) + return getUnknown(V); + + Operator *U = cast<Operator>(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<const SCEV *, 4> 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<const SCEV *, 4> 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<ConstantInt>(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<SCEVMulExpr>(LHS)) { + if (auto *OpC = dyn_cast<SCEVConstant>(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<const SCEV*, 4> 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<ConstantInt>(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. + const SCEV *S = getAddExpr(LHS, getSCEV(CI)); + // If the LHS of the add was an addrec and it has no-wrap flags, + // transfer the no-wrap flags, since an or won't introduce a wrap. + if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) { + const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS); + const_cast<SCEVAddRecExpr *>(NewAR)->setNoWrapFlags( + OldAR->getNoWrapFlags()); + } + return S; + } + } + break; + + case Instruction::Xor: + if (ConstantInt *CI = dyn_cast<ConstantInt>(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<BinaryOperator>(BO->LHS)) + if (ConstantInt *LCI = dyn_cast<ConstantInt>(LBO->getOperand(1))) + if (LBO->getOpcode() == Instruction::And && + LCI->getValue() == CI->getValue()) + if (const SCEVZeroExtendExpr *Z = + dyn_cast<SCEVZeroExtendExpr>(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<ConstantInt>(BO->RHS)) { + uint32_t BitWidth = cast<IntegerType>(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; + + // It is currently not resolved how to interpret NSW for left + // shift by BitWidth - 1, so we avoid applying flags in that + // case. Remove this check (or this comment) once the situation + // is resolved. See + // http://lists.llvm.org/pipermail/llvm-dev/2015-April/084195.html + // and http://reviews.llvm.org/D8890 . + auto Flags = SCEV::FlagAnyWrap; + if (BO->Op && SA->getValue().ult(BitWidth - 1)) + Flags = getNoWrapFlagsFromUB(BO->Op); + + 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<ConstantInt>(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<Operator>(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<ConstantInt>(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 + ...)<nsw>) --> (sext(A) + sext(B) + ...)<nsw> + // 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; + + // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can + // lead to pointer expressions which cannot safely be expanded to GEPs, + // because ScalarEvolution doesn't respect the GEP aliasing rules when + // simplifying integer expressions. + + case Instruction::GetElementPtr: + return createNodeForGEP(cast<GEPOperator>(U)); + + case Instruction::PHI: + return createNodeForPHI(cast<PHINode>(U)); + + case Instruction::Select: + // 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<Instruction>(U)) + return createNodeForSelectOrPHI(cast<Instruction>(U), U->getOperand(0), + U->getOperand(1), U->getOperand(2)); + break; + + case Instruction::Call: + case Instruction::Invoke: + if (Value *RV = CallSite(U).getReturnedArgOperand()) + return getSCEV(RV); + break; + } + + return getUnknown(V); +} + +//===----------------------------------------------------------------------===// +// Iteration Count Computation Code +// + +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) { + if (BasicBlock *ExitingBB = L->getExitingBlock()) + return getSmallConstantTripCount(L, ExitingBB); + + // No trip count information for multiple exits. + return 0; +} + +unsigned ScalarEvolution::getSmallConstantTripCount(const Loop *L, + BasicBlock *ExitingBlock) { + assert(ExitingBlock && "Must pass a non-null exiting block!"); + assert(L->isLoopExiting(ExitingBlock) && + "Exiting block must actually branch out of the loop!"); + const SCEVConstant *ExitCount = + dyn_cast<SCEVConstant>(getExitCount(L, ExitingBlock)); + return getConstantTripCount(ExitCount); +} + +unsigned ScalarEvolution::getSmallConstantMaxTripCount(const Loop *L) { + const auto *MaxExitCount = + dyn_cast<SCEVConstant>(getConstantMaxBackedgeTakenCount(L)); + return getConstantTripCount(MaxExitCount); +} + +unsigned ScalarEvolution::getSmallConstantTripMultiple(const Loop *L) { + if (BasicBlock *ExitingBB = L->getExitingBlock()) + return getSmallConstantTripMultiple(L, ExitingBB); + + // No trip multiple information for multiple exits. + return 0; +} + +/// 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, + BasicBlock *ExitingBlock) { + assert(ExitingBlock && "Must pass a non-null exiting block!"); + assert(L->isLoopExiting(ExitingBlock) && + "Exiting block must actually branch out of the loop!"); + const SCEV *ExitCount = getExitCount(L, ExitingBlock); + if (ExitCount == getCouldNotCompute()) + return 1; + + // Get the trip count from the BE count by adding 1. + const SCEV *TCExpr = getAddExpr(ExitCount, getOne(ExitCount->getType())); + + const SCEVConstant *TC = dyn_cast<SCEVConstant>(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(TCExpr)); + + 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(); +} + +/// Get the expression for the number of loop iterations for which this loop is +/// guaranteed not to exit via ExitingBlock. Otherwise return +/// SCEVCouldNotCompute. +const SCEV *ScalarEvolution::getExitCount(const Loop *L, + BasicBlock *ExitingBlock) { + return getBackedgeTakenInfo(L).getExact(ExitingBlock, this); +} + +const SCEV * +ScalarEvolution::getPredicatedBackedgeTakenCount(const Loop *L, + SCEVUnionPredicate &Preds) { + return getPredicatedBackedgeTakenInfo(L).getExact(L, this, &Preds); +} + +const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) { + return getBackedgeTakenInfo(L).getExact(L, this); +} + +/// Similar to getBackedgeTakenCount, except return the least SCEV value that is +/// known never to be less than the actual backedge taken count. +const SCEV *ScalarEvolution::getConstantMaxBackedgeTakenCount(const Loop *L) { + return getBackedgeTakenInfo(L).getMax(this); +} + +bool ScalarEvolution::isBackedgeTakenCountMaxOrZero(const Loop *L) { + return getBackedgeTakenInfo(L).isMaxOrZero(this); +} + +/// Push PHI nodes in the header of the given loop onto the given Worklist. +static void +PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) { + BasicBlock *Header = L->getHeader(); + + // Push all Loop-header PHIs onto the Worklist stack. + for (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); +} + +const ScalarEvolution::BackedgeTakenInfo & +ScalarEvolution::getBackedgeTakenInfo(const Loop *L) { + // Initially insert an invalid entry for this loop. If the insertion + // succeeds, proceed to actually compute a backedge-taken count and + // update the value. The temporary CouldNotCompute value tells SCEV + // code elsewhere that it shouldn't attempt to request a new + // backedge-taken count, which could result in infinite recursion. + std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::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.getMax(this), L) && + "Computed backedge-taken count isn't loop invariant for loop!"); + ++NumTripCountsComputed; + } + else if (Result.getMax(this) == getCouldNotCompute() && + isa<PHINode>(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<Instruction *, 16> Worklist; + PushLoopPHIs(L, Worklist); + + SmallPtrSet<Instruction *, 8> Discovered; + while (!Worklist.empty()) { + Instruction *I = Worklist.pop_back_val(); + + ValueExprMapType::iterator It = + ValueExprMap.find_as(static_cast<Value *>(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<PHINode>(I) || !isa<SCEVUnknown>(Old)) { + eraseValueFromMap(It->first); + forgetMemoizedResults(Old); + } + if (PHINode *PN = dyn_cast<PHINode>(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<Instruction>(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) { + // Drop any stored trip count value. + auto RemoveLoopFromBackedgeMap = + [](DenseMap<const Loop *, BackedgeTakenInfo> &Map, const Loop *L) { + auto BTCPos = Map.find(L); + if (BTCPos != Map.end()) { + BTCPos->second.clear(); + Map.erase(BTCPos); + } + }; + + SmallVector<const Loop *, 16> LoopWorklist(1, L); + SmallVector<Instruction *, 32> Worklist; + SmallPtrSet<Instruction *, 16> Visited; + + // Iterate over all the loops and sub-loops to drop SCEV information. + while (!LoopWorklist.empty()) { + auto *CurrL = LoopWorklist.pop_back_val(); + + RemoveLoopFromBackedgeMap(BackedgeTakenCounts, CurrL); + RemoveLoopFromBackedgeMap(PredicatedBackedgeTakenCounts, CurrL); + + // Drop information about predicated SCEV rewrites for this loop. + for (auto I = PredicatedSCEVRewrites.begin(); + I != PredicatedSCEVRewrites.end();) { + std::pair<const SCEV *, const Loop *> 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<Value *>(I)); + if (It != ValueExprMap.end()) { + eraseValueFromMap(It->first); + forgetMemoizedResults(It->second); + if (PHINode *PN = dyn_cast<PHINode>(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<Instruction>(V); + if (!I) return; + + // Drop information about expressions based on loop-header PHIs. + SmallVector<Instruction *, 16> Worklist; + Worklist.push_back(I); + + SmallPtrSet<Instruction *, 8> Visited; + while (!Worklist.empty()) { + I = Worklist.pop_back_val(); + if (!Visited.insert(I).second) + continue; + + ValueExprMapType::iterator It = + ValueExprMap.find_as(static_cast<Value *>(I)); + if (It != ValueExprMap.end()) { + eraseValueFromMap(It->first); + forgetMemoizedResults(It->second); + if (PHINode *PN = dyn_cast<PHINode>(I)) + ConstantEvolutionLoopExitValue.erase(PN); + } + + PushDefUseChildren(I, Worklist); + } +} + +/// 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<const SCEV *, 2> 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(BasicBlock *ExitingBlock, + ScalarEvolution *SE) const { + for (auto &ENT : ExitNotTaken) + if (ENT.ExitingBlock == ExitingBlock && ENT.hasAlwaysTruePredicate()) + return ENT.ExactNotTaken; + + return SE->getCouldNotCompute(); +} + +/// getMax - Get the max backedge taken count for the loop. +const SCEV * +ScalarEvolution::BackedgeTakenInfo::getMax(ScalarEvolution *SE) const { + auto PredicateNotAlwaysTrue = [](const ExitNotTakenInfo &ENT) { + return !ENT.hasAlwaysTruePredicate(); + }; + + if (any_of(ExitNotTaken, PredicateNotAlwaysTrue) || !getMax()) + return SE->getCouldNotCompute(); + + assert((isa<SCEVCouldNotCompute>(getMax()) || isa<SCEVConstant>(getMax())) && + "No point in having a non-constant max backedge taken count!"); + return getMax(); +} + +bool ScalarEvolution::BackedgeTakenInfo::isMaxOrZero(ScalarEvolution *SE) const { + auto PredicateNotAlwaysTrue = [](const ExitNotTakenInfo &ENT) { + return !ENT.hasAlwaysTruePredicate(); + }; + return MaxOrZero && !any_of(ExitNotTaken, PredicateNotAlwaysTrue); +} + +bool ScalarEvolution::BackedgeTakenInfo::hasOperand(const SCEV *S, + ScalarEvolution *SE) const { + if (getMax() && getMax() != SE->getCouldNotCompute() && + SE->hasOperand(getMax(), S)) + return true; + + for (auto &ENT : ExitNotTaken) + if (ENT.ExactNotTaken != SE->getCouldNotCompute() && + SE->hasOperand(ENT.ExactNotTaken, S)) + return true; + + return false; +} + +ScalarEvolution::ExitLimit::ExitLimit(const SCEV *E) + : ExactNotTaken(E), MaxNotTaken(E) { + assert((isa<SCEVCouldNotCompute>(MaxNotTaken) || + isa<SCEVConstant>(MaxNotTaken)) && + "No point in having a non-constant max backedge taken count!"); +} + +ScalarEvolution::ExitLimit::ExitLimit( + const SCEV *E, const SCEV *M, bool MaxOrZero, + ArrayRef<const SmallPtrSetImpl<const SCEVPredicate *> *> PredSetList) + : ExactNotTaken(E), MaxNotTaken(M), MaxOrZero(MaxOrZero) { + assert((isa<SCEVCouldNotCompute>(ExactNotTaken) || + !isa<SCEVCouldNotCompute>(MaxNotTaken)) && + "Exact is not allowed to be less precise than Max"); + assert((isa<SCEVCouldNotCompute>(MaxNotTaken) || + isa<SCEVConstant>(MaxNotTaken)) && + "No point in having a non-constant max backedge taken count!"); + for (auto *PredSet : PredSetList) + for (auto *P : *PredSet) + addPredicate(P); +} + +ScalarEvolution::ExitLimit::ExitLimit( + const SCEV *E, const SCEV *M, bool MaxOrZero, + const SmallPtrSetImpl<const SCEVPredicate *> &PredSet) + : ExitLimit(E, M, MaxOrZero, {&PredSet}) { + assert((isa<SCEVCouldNotCompute>(MaxNotTaken) || + isa<SCEVConstant>(MaxNotTaken)) && + "No point in having a non-constant max backedge taken count!"); +} + +ScalarEvolution::ExitLimit::ExitLimit(const SCEV *E, const SCEV *M, + bool MaxOrZero) + : ExitLimit(E, M, MaxOrZero, None) { + assert((isa<SCEVCouldNotCompute>(MaxNotTaken) || + isa<SCEVConstant>(MaxNotTaken)) && + "No point in having a non-constant max backedge taken count!"); +} + +/// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each +/// computable exit into a persistent ExitNotTakenInfo array. +ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo( + ArrayRef<ScalarEvolution::BackedgeTakenInfo::EdgeExitInfo> + ExitCounts, + bool Complete, const SCEV *MaxCount, bool MaxOrZero) + : MaxAndComplete(MaxCount, Complete), 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, nullptr); + + std::unique_ptr<SCEVUnionPredicate> Predicate(new SCEVUnionPredicate); + for (auto *Pred : EL.Predicates) + Predicate->add(Pred); + + return ExitNotTakenInfo(ExitBB, EL.ExactNotTaken, std::move(Predicate)); + }); + assert((isa<SCEVCouldNotCompute>(MaxCount) || isa<SCEVConstant>(MaxCount)) && + "No point in having a non-constant max backedge taken count!"); +} + +/// Invalidate this result and free the ExitNotTakenInfo array. +void ScalarEvolution::BackedgeTakenInfo::clear() { + ExitNotTaken.clear(); +} + +/// Compute the number of times the backedge of the specified loop will execute. +ScalarEvolution::BackedgeTakenInfo +ScalarEvolution::computeBackedgeTakenCount(const Loop *L, + bool AllowPredicates) { + SmallVector<BasicBlock *, 8> ExitingBlocks; + L->getExitingBlocks(ExitingBlocks); + + using EdgeExitInfo = ScalarEvolution::BackedgeTakenInfo::EdgeExitInfo; + + SmallVector<EdgeExitInfo, 4> 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]; + 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<BranchInst>(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<SwitchInst>(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::ExitLimit> +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) { + // Check if the controlling expression for this loop is an And or Or. + if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) { + if (BO->getOpcode() == Instruction::And) { + // Recurse on the operands of the and. + bool EitherMayExit = !ExitIfTrue; + ExitLimit EL0 = computeExitLimitFromCondCached( + Cache, L, BO->getOperand(0), ExitIfTrue, + ControlsExit && !EitherMayExit, AllowPredicates); + ExitLimit EL1 = computeExitLimitFromCondCached( + Cache, L, BO->getOperand(1), ExitIfTrue, + ControlsExit && !EitherMayExit, AllowPredicates); + const SCEV *BECount = getCouldNotCompute(); + const SCEV *MaxBECount = getCouldNotCompute(); + if (EitherMayExit) { + // Both conditions must be true for the loop to continue executing. + // Choose the less conservative count. + if (EL0.ExactNotTaken == getCouldNotCompute() || + EL1.ExactNotTaken == getCouldNotCompute()) + BECount = getCouldNotCompute(); + else + BECount = + getUMinFromMismatchedTypes(EL0.ExactNotTaken, EL1.ExactNotTaken); + 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 true at the same time for the loop to exit. + // For now, be conservative. + if (EL0.MaxNotTaken == EL1.MaxNotTaken) + MaxBECount = EL0.MaxNotTaken; + 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<SCEVCouldNotCompute>(MaxBECount) && + !isa<SCEVCouldNotCompute>(BECount)) + MaxBECount = getConstant(getUnsignedRangeMax(BECount)); + + return ExitLimit(BECount, MaxBECount, false, + {&EL0.Predicates, &EL1.Predicates}); + } + if (BO->getOpcode() == Instruction::Or) { + // Recurse on the operands of the or. + bool EitherMayExit = ExitIfTrue; + ExitLimit EL0 = computeExitLimitFromCondCached( + Cache, L, BO->getOperand(0), ExitIfTrue, + ControlsExit && !EitherMayExit, AllowPredicates); + ExitLimit EL1 = computeExitLimitFromCondCached( + Cache, L, BO->getOperand(1), ExitIfTrue, + ControlsExit && !EitherMayExit, AllowPredicates); + const SCEV *BECount = getCouldNotCompute(); + const SCEV *MaxBECount = getCouldNotCompute(); + if (EitherMayExit) { + // Both conditions must be false for the loop to continue executing. + // Choose the less conservative count. + if (EL0.ExactNotTaken == getCouldNotCompute() || + EL1.ExactNotTaken == getCouldNotCompute()) + BECount = getCouldNotCompute(); + else + BECount = + getUMinFromMismatchedTypes(EL0.ExactNotTaken, EL1.ExactNotTaken); + 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 false at the same time for the loop to exit. + // For now, be conservative. + if (EL0.MaxNotTaken == EL1.MaxNotTaken) + MaxBECount = EL0.MaxNotTaken; + 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<SCEVCouldNotCompute>(MaxBECount) && + !isa<SCEVCouldNotCompute>(BECount)) + MaxBECount = getConstant(getUnsignedRangeMax(BECount)); + + return ExitLimit(BECount, MaxBECount, false, + {&EL0.Predicates, &EL1.Predicates}); + } + } + + // With an icmp, it may be feasible to compute an exact backedge-taken count. + // Proceed to the next level to examine the icmp. + if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond)) { + 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<ConstantInt>(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); +} + +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<LoadInst>(ExitCond->getOperand(0))) + if (Constant *RHS = dyn_cast<Constant>(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<SCEVConstant>(RHS)) + if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(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<SCEVCouldNotCompute>(Ret)) return Ret; + } + + switch (Pred) { + case ICmpInst::ICMP_NE: { // while (X != Y) + // Convert to: while (X-Y != 0) + 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) + 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<SCEVCouldNotCompute>(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<SCEVConstant>(Val) && + "Evaluation of SCEV at constant didn't fold correctly?"); + return cast<SCEVConstant>(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<GetElementPtrInst>(LI->getOperand(0)); + if (!GEP) return getCouldNotCompute(); + + // Make sure that it is really a constant global we are gepping, with an + // initializer, and make sure the first IDX is really 0. + GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0)); + if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() || + GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) || + !cast<Constant>(GEP->getOperand(1))->isNullValue()) + return getCouldNotCompute(); + + // Okay, we allow one non-constant index into the GEP instruction. + Value *VarIdx = nullptr; + std::vector<Constant*> Indexes; + unsigned VarIdxNum = 0; + for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i) + if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) { + Indexes.push_back(CI); + } else if (!isa<ConstantInt>(GEP->getOperand(i))) { + if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's. + VarIdx = GEP->getOperand(i); + VarIdxNum = i-2; + Indexes.push_back(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<SCEVAddRecExpr>(Idx); + if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) || + !isa<SCEVConstant>(IdxExpr->getOperand(0)) || + !isa<SCEVConstant>(IdxExpr->getOperand(1))) + return getCouldNotCompute(); + + unsigned MaxSteps = MaxBruteForceIterations; + for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) { + ConstantInt *ItCst = ConstantInt::get( + cast<IntegerType>(IdxExpr->getType()), IterationNum); + ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this); + + // Form the GEP offset. + Indexes[VarIdxNum] = Val; + + Constant *Result = ConstantFoldLoadThroughGEPIndices(GV->getInitializer(), + Indexes); + if (!Result) break; // Cannot compute! + + // Evaluate the condition for this iteration. + Result = ConstantExpr::getICmp(predicate, Result, RHS); + if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure + if (cast<ConstantInt>(Result)->getValue().isMinValue()) { + ++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<ConstantInt>(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` <positive constant>". + // 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, <positive constant> + // + // 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<Instruction::BinaryOps> 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<PHINode>(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,<positive-constant>} stabilizes to signum(K) in at most + // bitwidth(K) iterations. + Value *FirstValue = PN->getIncomingValueForBlock(Predecessor); + KnownBits Known = computeKnownBits(FirstValue, DL, 0, nullptr, + Predecessor->getTerminator(), &DT); + auto *Ty = cast<IntegerType>(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,<positive-constant>} and {K,shl,<positive-constant>} + // stabilize to 0 in at most bitwidth(K) iterations. + StableValue = ConstantInt::get(cast<IntegerType>(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<BinaryOperator>(I) || isa<CmpInst>(I) || + isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I) || + isa<LoadInst>(I) || isa<ExtractValueInst>(I)) + return true; + + if (const CallInst *CI = dyn_cast<CallInst>(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<PHINode>(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<Instruction *, PHINode *> &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<Constant>(Op)) continue; + + Instruction *OpInst = dyn_cast<Instruction>(Op); + if (!OpInst || !canConstantEvolve(OpInst, L)) return nullptr; + + PHINode *P = dyn_cast<PHINode>(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<Instruction>(V); + if (!I || !canConstantEvolve(I, L)) return nullptr; + + if (PHINode *PN = dyn_cast<PHINode>(I)) + return PN; + + // Record non-constant instructions contained by the loop. + DenseMap<Instruction *, PHINode *> 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<Instruction *, Constant *> &Vals, + const DataLayout &DL, + const TargetLibraryInfo *TLI) { + // Convenient constant check, but redundant for recursive calls. + if (Constant *C = dyn_cast<Constant>(V)) return C; + Instruction *I = dyn_cast<Instruction>(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<PHINode>(I)) return nullptr; + + std::vector<Constant*> Operands(I->getNumOperands()); + + for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) { + Instruction *Operand = dyn_cast<Instruction>(I->getOperand(i)); + if (!Operand) { + Operands[i] = dyn_cast<Constant>(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<CmpInst>(I)) + return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0], + Operands[1], DL, TLI); + if (LoadInst *LI = dyn_cast<LoadInst>(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<Constant>(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<Instruction *, Constant *> 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<Instruction *, Constant *> 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<std::pair<PHINode *, Constant *>, 8> PHIsToCompute; + for (const auto &I : CurrentIterVals) { + PHINode *PHI = dyn_cast<PHINode>(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<Instruction *, Constant *> 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<ConstantInt>( + 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<Instruction *, Constant *> 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<PHINode *, 8> PHIsToCompute; + for (const auto &I : CurrentIterVals) { + PHINode *PHI = dyn_cast<PHINode>(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<std::pair<const Loop *, const SCEV *>, 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 (static_cast<SCEVTypes>(V->getSCEVType())) { + case scCouldNotCompute: + case scAddRecExpr: + break; + case scConstant: + return cast<SCEVConstant>(V)->getValue(); + case scUnknown: + return dyn_cast<Constant>(cast<SCEVUnknown>(V)->getValue()); + case scSignExtend: { + const SCEVSignExtendExpr *SS = cast<SCEVSignExtendExpr>(V); + if (Constant *CastOp = BuildConstantFromSCEV(SS->getOperand())) + return ConstantExpr::getSExt(CastOp, SS->getType()); + break; + } + case scZeroExtend: { + const SCEVZeroExtendExpr *SZ = cast<SCEVZeroExtendExpr>(V); + if (Constant *CastOp = BuildConstantFromSCEV(SZ->getOperand())) + return ConstantExpr::getZExt(CastOp, SZ->getType()); + break; + } + case scTruncate: { + const SCEVTruncateExpr *ST = cast<SCEVTruncateExpr>(V); + if (Constant *CastOp = BuildConstantFromSCEV(ST->getOperand())) + return ConstantExpr::getTrunc(CastOp, ST->getType()); + break; + } + case scAddExpr: { + const SCEVAddExpr *SA = cast<SCEVAddExpr>(V); + if (Constant *C = BuildConstantFromSCEV(SA->getOperand(0))) { + if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) { + unsigned AS = PTy->getAddressSpace(); + Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS); + C = ConstantExpr::getBitCast(C, DestPtrTy); + } + for (unsigned i = 1, e = SA->getNumOperands(); i != e; ++i) { + Constant *C2 = BuildConstantFromSCEV(SA->getOperand(i)); + if (!C2) return nullptr; + + // First pointer! + if (!C->getType()->isPointerTy() && C2->getType()->isPointerTy()) { + unsigned AS = C2->getType()->getPointerAddressSpace(); + std::swap(C, C2); + Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS); + // The offsets have been converted to bytes. We can add bytes to an + // i8* by GEP with the byte count in the first index. + C = ConstantExpr::getBitCast(C, DestPtrTy); + } + + // Don't bother trying to sum two pointers. We probably can't + // statically compute a load that results from it anyway. + if (C2->getType()->isPointerTy()) + return nullptr; + + if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) { + if (PTy->getElementType()->isStructTy()) + C2 = ConstantExpr::getIntegerCast( + C2, Type::getInt32Ty(C->getContext()), true); + C = ConstantExpr::getGetElementPtr(PTy->getElementType(), C, C2); + } else + C = ConstantExpr::getAdd(C, C2); + } + return C; + } + break; + } + case scMulExpr: { + const SCEVMulExpr *SM = cast<SCEVMulExpr>(V); + if (Constant *C = BuildConstantFromSCEV(SM->getOperand(0))) { + // Don't bother with pointers at all. + if (C->getType()->isPointerTy()) return nullptr; + for (unsigned i = 1, e = SM->getNumOperands(); i != e; ++i) { + Constant *C2 = BuildConstantFromSCEV(SM->getOperand(i)); + if (!C2 || C2->getType()->isPointerTy()) return nullptr; + C = ConstantExpr::getMul(C, C2); + } + return C; + } + break; + } + case scUDivExpr: { + const SCEVUDivExpr *SU = cast<SCEVUDivExpr>(V); + if (Constant *LHS = BuildConstantFromSCEV(SU->getLHS())) + if (Constant *RHS = BuildConstantFromSCEV(SU->getRHS())) + if (LHS->getType() == RHS->getType()) + return ConstantExpr::getUDiv(LHS, RHS); + break; + } + case scSMaxExpr: + case scUMaxExpr: + case scSMinExpr: + case scUMinExpr: + break; // TODO: smax, umax, smin, umax. + } + return nullptr; +} + +const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) { + if (isa<SCEVConstant>(V)) return V; + + // If this instruction is evolved from a constant-evolving PHI, compute the + // exit value from the loop without using SCEVs. + if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) { + if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) { + if (PHINode *PN = dyn_cast<PHINode>(I)) { + const Loop *LI = this->LI[I->getParent()]; + // Looking for loop exit value. + if (LI && LI->getParentLoop() == L && + PN->getParent() == LI->getHeader()) { + // Okay, there is no closed form solution for the PHI node. Check + // to see if the loop that contains it has a known backedge-taken + // count. If so, we may be able to force computation of the exit + // value. + const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI); + // 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 (!LI->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<SCEVCouldNotCompute>(BackedgeTakenCount) && + isKnownPositive(BackedgeTakenCount) && + PN->getNumIncomingValues() == 2) { + unsigned InLoopPred = LI->contains(PN->getIncomingBlock(0)) ? 0 : 1; + const SCEV *OnBackedge = getSCEV(PN->getIncomingValue(InLoopPred)); + if (IsAvailableOnEntry(LI, DT, OnBackedge, PN->getParent())) + return OnBackedge; + } + if (auto *BTCC = dyn_cast<SCEVConstant>(BackedgeTakenCount)) { + // Okay, we know how many times the containing loop executes. If + // this is a constant evolving PHI node, get the final value at + // the specified iteration number. + Constant *RV = + getConstantEvolutionLoopExitValue(PN, BTCC->getAPInt(), LI); + 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<SCEVConstant>(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<Constant *, 4> Operands; + bool MadeImprovement = false; + for (Value *Op : I->operands()) { + if (Constant *C = dyn_cast<Constant>(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<CmpInst>(I)) + C = ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0], + Operands[1], DL, &TLI); + else if (const LoadInst *LI = dyn_cast<LoadInst>(I)) { + if (!LI->isVolatile()) + C = ConstantFoldLoadFromConstPtr(Operands[0], LI->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<SCEVCommutativeExpr>(V)) { + // Avoid performing the look-up in the common case where the specified + // expression has no loop-variant portions. + for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) { + const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); + if (OpAtScope != Comm->getOperand(i)) { + // Okay, at least one of these operands is loop variant but might be + // foldable. Build a new instance of the folded commutative expression. + SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(), + Comm->op_begin()+i); + NewOps.push_back(OpAtScope); + + for (++i; i != e; ++i) { + OpAtScope = getSCEVAtScope(Comm->getOperand(i), L); + NewOps.push_back(OpAtScope); + } + if (isa<SCEVAddExpr>(Comm)) + return getAddExpr(NewOps, Comm->getNoWrapFlags()); + if (isa<SCEVMulExpr>(Comm)) + return getMulExpr(NewOps, Comm->getNoWrapFlags()); + if (isa<SCEVMinMaxExpr>(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<SCEVUDivExpr>(V)) { + const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L); + const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L); + if (LHS == Div->getLHS() && RHS == Div->getRHS()) + return Div; // must be loop invariant + return getUDivExpr(LHS, RHS); + } + + // If this is a loop recurrence for a loop that does not contain L, then we + // are dealing with the final value computed by the loop. + if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) { + // 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<const SCEV *, 8> 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<SCEVAddRecExpr>(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<SCEVZeroExtendExpr>(V)) { + const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); + if (Op == Cast->getOperand()) + return Cast; // must be loop invariant + return getZeroExtendExpr(Op, Cast->getType()); + } + + if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) { + const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); + if (Op == Cast->getOperand()) + return Cast; // must be loop invariant + return getSignExtendExpr(Op, Cast->getType()); + } + + if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) { + const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L); + if (Op == Cast->getOperand()) + return Cast; // must be loop invariant + return getTruncateExpr(Op, Cast->getType()); + } + + llvm_unreachable("Unknown SCEV type!"); +} + +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<SCEVZeroExtendExpr>(S)) + return stripInjectiveFunctions(ZExt->getOperand()); + if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(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<std::tuple<APInt, APInt, APInt, APInt, unsigned>> +GetQuadraticEquation(const SCEVAddRecExpr *AddRec) { + assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!"); + const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0)); + const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1)); + const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2)); + 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<APInt> MinOptional(Optional<APInt> X, Optional<APInt> 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<APInt> TruncIfPossible(Optional<APInt> 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<APInt> +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<APInt> 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<APInt> +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<Optional<APInt>,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<APInt> 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<APInt> 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<APInt> Min = MinOptional(SO, UO); + if (LeavesRange(*Min)) + return { Min, true }; + Optional<APInt> 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<const SCEVPredicate *, 4> Predicates; + // If the value is a constant + if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) { + // If the value is already zero, the branch will execute zero times. + if (C->getValue()->isZero()) return C; + return getCouldNotCompute(); // Otherwise it will loop infinitely. + } + + const SCEVAddRecExpr *AddRec = + dyn_cast<SCEVAddRecExpr>(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<SCEVConstant>(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<NUW>. 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<SCEVConstant>(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(Distance); + + // 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 = + Exact == getCouldNotCompute() + ? Exact + : getConstant(getUnsignedRangeMax(Exact)); + 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<SCEVConstant>(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<BasicBlock *, BasicBlock *> +ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) { + // If the block has a unique predecessor, then there is no path from the + // predecessor to the block that does not go through the direct edge + // from the predecessor to the block. + if (BasicBlock *Pred = BB->getSinglePredecessor()) + return {Pred, BB}; + + // A loop's header is defined to be a block that dominates the loop. + // If the header has a unique predecessor outside the loop, it must be + // a block that has exactly one successor that can reach the loop. + if (Loop *L = LI.getLoopFor(BB)) + return {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<BinaryOperator>(A) || isa<GetElementPtrInst>(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<SCEVUnknown>(A)) + if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B)) + if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue())) + if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue())) + if (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<SCEVConstant>(LHS)) { + // Check for both operands constant. + if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(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<SCEVAddRecExpr>(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<SCEVConstant>(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<SCEVAddExpr>(LHS)) + if (const SCEVMulExpr *ME = + dyn_cast<SCEVMulExpr>(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 isKnownNegative(S) || isKnownPositive(S); +} + +std::pair<const SCEV *, const SCEV *> +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<const Loop *, 8> 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; + + return isLoopEntryGuardedByCond(MDL, Pred, SplitLHS.first, SplitRHS.first) && + isLoopBackedgeGuardedByCond(MDL, Pred, SplitLHS.second, + SplitRHS.second); +} + +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); +} + +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); +} + +bool ScalarEvolution::isMonotonicPredicate(const SCEVAddRecExpr *LHS, + ICmpInst::Predicate Pred, + bool &Increasing) { + bool Result = isMonotonicPredicateImpl(LHS, Pred, Increasing); + +#ifndef NDEBUG + // Verify an invariant: inverting the predicate should turn a monotonically + // increasing change to a monotonically decreasing one, and vice versa. + bool IncreasingSwapped; + bool ResultSwapped = isMonotonicPredicateImpl( + LHS, ICmpInst::getSwappedPredicate(Pred), IncreasingSwapped); + + assert(Result == ResultSwapped && "should be able to analyze both!"); + if (ResultSwapped) + assert(Increasing == !IncreasingSwapped && + "monotonicity should flip as we flip the predicate"); +#endif + + return Result; +} + +bool ScalarEvolution::isMonotonicPredicateImpl(const SCEVAddRecExpr *LHS, + ICmpInst::Predicate Pred, + bool &Increasing) { + + // 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. + + switch (Pred) { + default: + return false; // Conservative answer + + case ICmpInst::ICMP_UGT: + case ICmpInst::ICMP_UGE: + case ICmpInst::ICMP_ULT: + case ICmpInst::ICMP_ULE: + if (!LHS->hasNoUnsignedWrap()) + return false; + + Increasing = Pred == ICmpInst::ICMP_UGT || Pred == ICmpInst::ICMP_UGE; + return true; + + case ICmpInst::ICMP_SGT: + case ICmpInst::ICMP_SGE: + case ICmpInst::ICMP_SLT: + case ICmpInst::ICMP_SLE: { + if (!LHS->hasNoSignedWrap()) + return false; + + const SCEV *Step = LHS->getStepRecurrence(*this); + + if (isKnownNonNegative(Step)) { + Increasing = Pred == ICmpInst::ICMP_SGT || Pred == ICmpInst::ICMP_SGE; + return true; + } + + if (isKnownNonPositive(Step)) { + Increasing = Pred == ICmpInst::ICMP_SLT || Pred == ICmpInst::ICMP_SLE; + return true; + } + + return false; + } + + } + + llvm_unreachable("switch has default clause!"); +} + +bool ScalarEvolution::isLoopInvariantPredicate( + ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS, const Loop *L, + ICmpInst::Predicate &InvariantPred, const SCEV *&InvariantLHS, + const SCEV *&InvariantRHS) { + + // If there is a loop-invariant, force it into the RHS, otherwise bail out. + if (!isLoopInvariant(RHS, L)) { + if (!isLoopInvariant(LHS, L)) + return false; + + std::swap(LHS, RHS); + Pred = ICmpInst::getSwappedPredicate(Pred); + } + + const SCEVAddRecExpr *ArLHS = dyn_cast<SCEVAddRecExpr>(LHS); + if (!ArLHS || ArLHS->getLoop() != L) + return false; + + bool Increasing; + if (!isMonotonicPredicate(ArLHS, Pred, Increasing)) + return false; + + // 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. + + auto P = Increasing ? Pred : ICmpInst::getInversePredicate(Pred); + + if (!isLoopBackedgeGuardedByCond(L, P, LHS, RHS)) + return false; + + InvariantPred = Pred; + InvariantLHS = ArLHS->getStart(); + InvariantRHS = RHS; + return true; +} + +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 ConstantRange::makeSatisfyingICmpRegion(Pred, RangeRHS) + .contains(RangeLHS); + }; + + // 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) + return CheckRanges(getSignedRange(LHS), getSignedRange(RHS)) || + CheckRanges(getUnsignedRange(LHS), getUnsignedRange(RHS)) || + isKnownNonZero(getMinusSCEV(LHS, RHS)); + + 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 Result to (X + Y)<ExpectedFlags> where Y is a constant integer. + // Return Y via OutY. + auto MatchBinaryAddToConst = + [this](const SCEV *Result, const SCEV *X, APInt &OutY, + SCEV::NoWrapFlags ExpectedFlags) { + const SCEV *NonConstOp, *ConstOp; + SCEV::NoWrapFlags FlagsPresent; + + if (!splitBinaryAdd(Result, ConstOp, NonConstOp, FlagsPresent) || + !isa<SCEVConstant>(ConstOp) || NonConstOp != X) + return false; + + OutY = cast<SCEVConstant>(ConstOp)->getAPInt(); + return (FlagsPresent & ExpectedFlags) == ExpectedFlags; + }; + + APInt C; + + switch (Pred) { + default: + break; + + case ICmpInst::ICMP_SGE: + std::swap(LHS, RHS); + LLVM_FALLTHROUGH; + case ICmpInst::ICMP_SLE: + // X s<= (X + C)<nsw> if C >= 0 + if (MatchBinaryAddToConst(RHS, LHS, C, SCEV::FlagNSW) && C.isNonNegative()) + return true; + + // (X + C)<nsw> s<= X if C <= 0 + if (MatchBinaryAddToConst(LHS, RHS, C, SCEV::FlagNSW) && + !C.isStrictlyPositive()) + return true; + break; + + case ICmpInst::ICMP_SGT: + std::swap(LHS, RHS); + LLVM_FALLTHROUGH; + case ICmpInst::ICMP_SLT: + // X s< (X + C)<nsw> if C > 0 + if (MatchBinaryAddToConst(RHS, LHS, C, SCEV::FlagNSW) && + C.isStrictlyPositive()) + return true; + + // (X + C)<nsw> s< X if C < 0 + if (MatchBinaryAddToConst(LHS, RHS, C, SCEV::FlagNSW) && C.isNegative()) + 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<bool> 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(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, [&](Instruction &I) { + using namespace llvm::PatternMatch; + + Value *Condition; + return match(&I, m_Intrinsic<Intrinsic::experimental_guard>( + 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<BranchInst>(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<bool> 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<CallInst>(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<BranchInst>(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::isLoopEntryGuardedByCond(const Loop *L, + ICmpInst::Predicate Pred, + const SCEV *LHS, const SCEV *RHS) { + // Interpret a null as meaning no loop, where there is obviously no guard + // (interprocedural conditions notwithstanding). + if (!L) return false; + + if (VerifyIR) + assert(!verifyFunction(*L->getHeader()->getParent(), &dbgs()) && + "This cannot be done on broken IR!"); + + // 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; + + // 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; + + if (ProvingStrictComparison) { + ProvedNonStrictComparison = + isKnownViaNonRecursiveReasoning(NonStrictPredicate, LHS, RHS); + ProvedNonEquality = + isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_NE, LHS, RHS); + if (ProvedNonStrictComparison && ProvedNonEquality) + return true; + } + + // Try to prove (Pred, LHS, RHS) using isImpliedViaGuard. + auto ProveViaGuard = [&](BasicBlock *Block) { + if (isImpliedViaGuard(Block, Pred, LHS, RHS)) + return true; + if (ProvingStrictComparison) { + if (!ProvedNonStrictComparison) + ProvedNonStrictComparison = + isImpliedViaGuard(Block, NonStrictPredicate, LHS, RHS); + if (!ProvedNonEquality) + ProvedNonEquality = + isImpliedViaGuard(Block, ICmpInst::ICMP_NE, LHS, RHS); + if (ProvedNonStrictComparison && ProvedNonEquality) + return true; + } + return false; + }; + + // Try to prove (Pred, LHS, RHS) using isImpliedCond. + auto ProveViaCond = [&](Value *Condition, bool Inverse) { + if (isImpliedCond(Pred, LHS, RHS, Condition, Inverse)) + return true; + if (ProvingStrictComparison) { + if (!ProvedNonStrictComparison) + ProvedNonStrictComparison = + isImpliedCond(NonStrictPredicate, LHS, RHS, Condition, Inverse); + if (!ProvedNonEquality) + ProvedNonEquality = + isImpliedCond(ICmpInst::ICMP_NE, LHS, RHS, Condition, Inverse); + if (ProvedNonStrictComparison && ProvedNonEquality) + return true; + } + return false; + }; + + // Starting at the loop predecessor, climb up the predecessor chain, as long + // as there are predecessors that can be found that have unique successors + // leading to the original header. + for (std::pair<BasicBlock *, BasicBlock *> + Pair(L->getLoopPredecessor(), L->getHeader()); + Pair.first; + Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) { + + if (ProveViaGuard(Pair.first)) + return true; + + BranchInst *LoopEntryPredicate = + dyn_cast<BranchInst>(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<CallInst>(AssumeVH); + if (!DT.dominates(CI, L->getHeader())) + continue; + + if (ProveViaCond(CI->getArgOperand(0), false)) + return true; + } + + return false; +} + +bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred, + const SCEV *LHS, const SCEV *RHS, + Value *FoundCondValue, + bool Inverse) { + if (!PendingLoopPredicates.insert(FoundCondValue).second) + return false; + + auto ClearOnExit = + make_scope_exit([&]() { PendingLoopPredicates.erase(FoundCondValue); }); + + // Recursively handle And and Or conditions. + if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) { + if (BO->getOpcode() == Instruction::And) { + if (!Inverse) + return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) || + isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse); + } else if (BO->getOpcode() == Instruction::Or) { + if (Inverse) + return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) || + isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse); + } + } + + ICmpInst *ICI = dyn_cast<ICmpInst>(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); +} + +bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred, const SCEV *LHS, + const SCEV *RHS, + ICmpInst::Predicate FoundPred, + const SCEV *FoundLHS, + const SCEV *FoundRHS) { + // Balance the types. + if (getTypeSizeInBits(LHS->getType()) < + getTypeSizeInBits(FoundLHS->getType())) { + 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 (CmpInst::isSigned(FoundPred)) { + FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType()); + FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType()); + } else { + FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType()); + FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType()); + } + } + + // Canonicalize the query to match the way instcombine will have + // canonicalized the comparison. + if (SimplifyICmpOperands(Pred, LHS, RHS)) + if (LHS == RHS) + return CmpInst::isTrueWhenEqual(Pred); + if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS)) + if (FoundLHS == FoundRHS) + return CmpInst::isFalseWhenEqual(FoundPred); + + // Check to see if we can make the LHS or RHS match. + if (LHS == FoundRHS || RHS == FoundLHS) { + if (isa<SCEVConstant>(RHS)) { + std::swap(FoundLHS, FoundRHS); + FoundPred = ICmpInst::getSwappedPredicate(FoundPred); + } else { + std::swap(LHS, RHS); + Pred = ICmpInst::getSwappedPredicate(Pred); + } + } + + // Check whether the found predicate is the same as the desired predicate. + if (FoundPred == Pred) + return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS); + + // Check whether swapping the found predicate makes it the same as the + // desired predicate. + if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) { + if (isa<SCEVConstant>(RHS)) + return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS); + else + return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred), + RHS, LHS, FoundLHS, FoundRHS); + } + + // 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); + + // Check if we can make progress by sharpening ranges. + if (FoundPred == ICmpInst::ICMP_NE && + (isa<SCEVConstant>(FoundLHS) || isa<SCEVConstant>(FoundRHS))) { + + const SCEVConstant *C = nullptr; + const SCEV *V = nullptr; + + if (isa<SCEVConstant>(FoundLHS)) { + C = cast<SCEVConstant>(FoundLHS); + V = FoundRHS; + } else { + C = cast<SCEVConstant>(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))) + 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))) + return true; + LLVM_FALLTHROUGH; + + default: + // No change + break; + } + } + } + + // Check whether the actual condition is beyond sufficient. + if (FoundPred == ICmpInst::ICMP_EQ) + if (ICmpInst::isTrueWhenEqual(Pred)) + if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS)) + return true; + if (Pred == ICmpInst::ICMP_NE) + if (!ICmpInst::isTrueWhenEqual(FoundPred)) + if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS)) + return true; + + // Otherwise assume the worst. + return false; +} + +bool ScalarEvolution::splitBinaryAdd(const SCEV *Expr, + const SCEV *&L, const SCEV *&R, + SCEV::NoWrapFlags &Flags) { + const auto *AE = dyn_cast<SCEVAddExpr>(Expr); + if (!AE || AE->getNumOperands() != 2) + return false; + + L = AE->getOperand(0); + R = AE->getOperand(1); + Flags = AE->getNoWrapFlags(); + return true; +} + +Optional<APInt> 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<SCEVAddRecExpr>(Less) && isa<SCEVAddRecExpr>(More)) { + const auto *LAR = cast<SCEVAddRecExpr>(Less); + const auto *MAR = cast<SCEVAddRecExpr>(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<SCEVConstant>(Less) && isa<SCEVConstant>(More)) { + const auto &M = cast<SCEVConstant>(More)->getAPInt(); + const auto &L = cast<SCEVConstant>(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<SCEVConstant>(LLess))) + if (RLess == More) + return -(C1->getAPInt()); + + // Compare X vs (X + C2). + if (splitBinaryAdd(More, LMore, RMore, Flags)) + if ((C2 = dyn_cast<SCEVConstant>(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::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<SCEVAddRecExpr>(LHS); + if (!AddRecLHS) + return false; + + const auto *AddRecFoundLHS = dyn_cast<SCEVAddRecExpr>(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<APInt> LDiff = computeConstantDifference(LHS, FoundLHS); + Optional<APInt> 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<SCEVUnknown>(LHS)) + if (auto *Phi = dyn_cast<PHINode>(LU->getValue())) { + if (!PendingMerges.insert(Phi).second) + return false; + LPhi = Phi; + } + if (const SCEVUnknown *RU = dyn_cast<SCEVUnknown>(RHS)) + if (auto *Phi = dyn_cast<PHINode>(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<SCEVAddRecExpr>(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)); + 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) { + if (isImpliedCondOperandsViaRanges(Pred, LHS, RHS, FoundLHS, FoundRHS)) + return true; + + if (isImpliedCondOperandsViaNoOverflow(Pred, LHS, RHS, FoundLHS, FoundRHS)) + return true; + + return isImpliedCondOperandsHelper(Pred, LHS, RHS, + FoundLHS, FoundRHS) || + // ~x < ~y --> x > y + isImpliedCondOperandsHelper(Pred, LHS, RHS, + getNotSCEV(FoundRHS), + getNotSCEV(FoundLHS)); +} + +/// Is MaybeMinMaxExpr an (U|S)(Min|Max) of Candidate and some other values? +template <typename MinMaxExprType> +static bool IsMinMaxConsistingOf(const SCEV *MaybeMinMaxExpr, + const SCEV *Candidate) { + const MinMaxExprType *MinMaxExpr = dyn_cast<MinMaxExprType>(MaybeMinMaxExpr); + if (!MinMaxExpr) + return false; + + return find(MinMaxExpr->operands(), Candidate) != MinMaxExpr->op_end(); +} + +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<SCEVAddRecExpr>(LHS); + if (!LAR) + return false; + const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(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<SCEVSMinExpr>(LHS, RHS) || + // A <= max(A, ...) + IsMinMaxConsistingOf<SCEVSMaxExpr>(RHS, LHS); + + case ICmpInst::ICMP_UGE: + std::swap(LHS, RHS); + LLVM_FALLTHROUGH; + case ICmpInst::ICMP_ULE: + return + // min(A, ...) <= A + IsMinMaxConsistingOf<SCEVUMinExpr>(LHS, RHS) || + // A <= max(A, ...) + IsMinMaxConsistingOf<SCEVUMaxExpr>(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 ICMP_SGT comparison so far. + // TODO: Extend to ICMP_UGT? + if (Pred == ICmpInst::ICMP_SLT) { + Pred = ICmpInst::ICMP_SGT; + std::swap(LHS, RHS); + std::swap(FoundLHS, FoundRHS); + } + if (Pred != ICmpInst::ICMP_SGT) + return false; + + auto GetOpFromSExt = [&](const SCEV *S) { + if (auto *Ext = dyn_cast<SCEVSignExtendExpr>(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<SCEVAddExpr>(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 = getNegativeSCEV(getOne(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<SCEVUnknown>(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<ConstantInt>(LR)) + return false; + + auto *Denominator = cast<SCEVConstant>(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 = getNegativeSCEV(getOne(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 <s 0 then SExt <s ZExt. + const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(LHS); + const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(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 <s 0 then ZExt <u SExt. + const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(LHS); + const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(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<SCEVConstant>(RHS) || !isa<SCEVConstant>(FoundRHS)) + // The restriction on `FoundRHS` be lifted easily -- it exists only to + // reduce the compile time impact of this optimization. + return false; + + Optional<APInt> Addend = computeConstantDifference(LHS, FoundLHS); + if (!Addend) + return false; + + const APInt &ConstFoundRHS = cast<SCEVConstant>(FoundRHS)->getAPInt(); + + // `FoundLHSRange` is the range we know `FoundLHS` to be in by virtue of the + // antecedent "`FoundLHS` `Pred` `FoundRHS`". + ConstantRange FoundLHSRange = + ConstantRange::makeAllowedICmpRegion(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<SCEVConstant>(RHS)->getAPInt(); + ConstantRange SatisfyingLHSRange = + ConstantRange::makeSatisfyingICmpRegion(Pred, ConstRHS); + + // The antecedent implies the consequent if every value of `LHS` that + // satisfies the antecedent also satisfies the consequent. + return SatisfyingLHSRange.contains(LHSRange); +} + +bool ScalarEvolution::doesIVOverflowOnLT(const SCEV *RHS, const SCEV *Stride, + bool IsSigned, bool NoWrap) { + assert(isKnownPositive(Stride) && "Positive stride expected!"); + + if (NoWrap) return false; + + 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::doesIVOverflowOnGT(const SCEV *RHS, const SCEV *Stride, + bool IsSigned, bool NoWrap) { + if (NoWrap) return false; + + 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::computeBECount(const SCEV *Delta, const SCEV *Step, + bool Equality) { + const SCEV *One = getOne(Step->getType()); + Delta = Equality ? getAddExpr(Delta, Step) + : getAddExpr(Delta, getMinusSCEV(Step, One)); + return getUDivExpr(Delta, Step); +} + +const SCEV *ScalarEvolution::computeMaxBECountForLT(const SCEV *Start, + const SCEV *Stride, + const SCEV *End, + unsigned BitWidth, + bool IsSigned) { + + assert(!isKnownNonPositive(Stride) && + "Stride is expected strictly positive!"); + // Calculate the maximum backedge count based on the range of values + // permitted by Start, End, and Stride. + const SCEV *MaxBECount; + APInt MinStart = + IsSigned ? getSignedRangeMin(Start) : getUnsignedRangeMin(Start); + + APInt StrideForMaxBECount = + IsSigned ? getSignedRangeMin(Stride) : getUnsignedRangeMin(Stride); + + // We already know that the stride is positive, so we paper over conservatism + // in our range computation by forcing StrideForMaxBECount to be at least one. + // In theory this is unnecessary, but we expect MaxBECount to be a + // SCEVConstant, and (udiv <constant> 0) is not constant folded by SCEV (there + // is nothing to constant fold it to). + APInt One(BitWidth, 1, IsSigned); + StrideForMaxBECount = APIntOps::smax(One, StrideForMaxBECount); + + 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 = computeBECount(getConstant(MaxEnd - MinStart) /* Delta */, + getConstant(StrideForMaxBECount) /* Step */, + false /* Equality */); + + return MaxBECount; +} + +ScalarEvolution::ExitLimit +ScalarEvolution::howManyLessThans(const SCEV *LHS, const SCEV *RHS, + const Loop *L, bool IsSigned, + bool ControlsExit, bool AllowPredicates) { + SmallPtrSet<const SCEVPredicate *, 4> Predicates; + + const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(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(); + + bool NoWrap = ControlsExit && + IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW); + + 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 the unknown stride cannot be zero otherwise + // we have 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) || + !loopHasNoSideEffects(L)) + return getCouldNotCompute(); + } else if (!Stride->isOne() && + doesIVOverflowOnLT(RHS, Stride, IsSigned, NoWrap)) + // 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. + return getCouldNotCompute(); + + ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SLT + : ICmpInst::ICMP_ULT; + const SCEV *Start = IV->getStart(); + const SCEV *End = 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); + } + // If the backedge is taken at least once, then it will be taken + // (End-Start)/Stride times (rounded up to a multiple of Stride), where Start + // is the LHS value of the less-than comparison the first time it is evaluated + // and End is the RHS. + const SCEV *BECountIfBackedgeTaken = + computeBECount(getMinusSCEV(End, Start), Stride, false); + // If the loop entry is guarded by the result of the backedge test of the + // first loop iteration, then we know the backedge will be taken at least + // once and so the backedge taken count is as above. If not then 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; + if (isLoopEntryGuardedByCond(L, Cond, getMinusSCEV(Start, Stride), RHS)) + BECount = BECountIfBackedgeTaken; + else { + End = IsSigned ? getSMaxExpr(RHS, Start) : getUMaxExpr(RHS, Start); + BECount = computeBECount(getMinusSCEV(End, Start), Stride, false); + } + + const SCEV *MaxBECount; + bool MaxOrZero = false; + if (isa<SCEVConstant>(BECount)) + MaxBECount = BECount; + else if (isa<SCEVConstant>(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<SCEVCouldNotCompute>(MaxBECount) && + !isa<SCEVCouldNotCompute>(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<const SCEVPredicate *, 4> Predicates; + // We handle only IV > Invariant + if (!isLoopInvariant(RHS, L)) + return getCouldNotCompute(); + + const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(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(); + + bool NoWrap = ControlsExit && + IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW); + + const SCEV *Stride = getNegativeSCEV(IV->getStepRecurrence(*this)); + + // Avoid negative or zero stride values + if (!isKnownPositive(Stride)) + return getCouldNotCompute(); + + // Avoid proven overflow cases: this will ensure that the backedge taken count + // will not generate any unsigned overflow. Relaxed no-overflow conditions + // exploit NoWrapFlags, allowing to optimize in presence of undefined + // behaviors like the case of C language. + if (!Stride->isOne() && doesIVOverflowOnGT(RHS, Stride, IsSigned, NoWrap)) + return getCouldNotCompute(); + + ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SGT + : ICmpInst::ICMP_UGT; + + const SCEV *Start = IV->getStart(); + const SCEV *End = RHS; + if (!isLoopEntryGuardedByCond(L, Cond, getAddExpr(Start, Stride), RHS)) + End = IsSigned ? getSMinExpr(RHS, Start) : getUMinExpr(RHS, Start); + + const SCEV *BECount = computeBECount(getMinusSCEV(Start, End), Stride, false); + + 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<SCEVConstant>(BECount) + ? BECount + : computeBECount(getConstant(MaxStart - MinEnd), + getConstant(MinStride), false); + + if (isa<SCEVCouldNotCompute>(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<SCEVConstant>(getStart())) + if (!SC->getValue()->isZero()) { + SmallVector<const SCEV *, 4> Operands(op_begin(), op_end()); + Operands[0] = SE.getZero(SC->getType()); + const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(), + getNoWrapFlags(FlagNW)); + if (const auto *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(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<SCEVConstant>(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<SCEVConstant>(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<const SCEV *, 3> 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<SCEVAddRecExpr>(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<SCEVUnknown>(S)) + return isa<UndefValue>(SU->getValue()); + return false; + }); +} + +namespace { + +// Collect all steps of SCEV expressions. +struct SCEVCollectStrides { + ScalarEvolution &SE; + SmallVectorImpl<const SCEV *> &Strides; + + SCEVCollectStrides(ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &S) + : SE(SE), Strides(S) {} + + bool follow(const SCEV *S) { + if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(S)) + Strides.push_back(AR->getStepRecurrence(SE)); + return true; + } + + bool isDone() const { return false; } +}; + +// Collect all SCEVUnknown and SCEVMulExpr expressions. +struct SCEVCollectTerms { + SmallVectorImpl<const SCEV *> &Terms; + + SCEVCollectTerms(SmallVectorImpl<const SCEV *> &T) : Terms(T) {} + + bool follow(const SCEV *S) { + if (isa<SCEVUnknown>(S) || isa<SCEVMulExpr>(S) || + isa<SCEVSignExtendExpr>(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<SCEVAddRecExpr>(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<const SCEV *> &Terms; + ScalarEvolution &SE; + + SCEVCollectAddRecMultiplies(SmallVectorImpl<const SCEV *> &T, ScalarEvolution &SE) + : Terms(T), SE(SE) {} + + bool follow(const SCEV *S) { + if (auto *Mul = dyn_cast<SCEVMulExpr>(S)) { + bool HasAddRec = false; + SmallVector<const SCEV *, 0> Operands; + for (auto Op : Mul->operands()) { + const SCEVUnknown *Unknown = dyn_cast<SCEVUnknown>(Op); + if (Unknown && !isa<CallInst>(Unknown->getValue())) { + Operands.push_back(Op); + } else if (Unknown) { + HasAddRec = true; + } else { + bool ContainsAddRec; + 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<const SCEV *> &Terms) { + SmallVector<const SCEV *, 4> 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<const SCEV *> &Terms, + SmallVectorImpl<const SCEV *> &Sizes) { + int Last = Terms.size() - 1; + const SCEV *Step = Terms[Last]; + + // End of recursion. + if (Last == 0) { + if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Step)) { + SmallVector<const SCEV *, 2> Qs; + for (const SCEV *Op : M->operands()) + if (!isa<SCEVConstant>(Op)) + Qs.push_back(Op); + + Step = SE.getMulExpr(Qs); + } + + Sizes.push_back(Step); + return true; + } + + for (const SCEV *&Term : Terms) { + // Normalize the terms before the next call to findArrayDimensionsRec. + const SCEV *Q, *R; + SCEVDivision::divide(SE, Term, Step, &Q, &R); + + // Bail out when GCD does not evenly divide one of the terms. + if (!R->isZero()) + return false; + + Term = Q; + } + + // Remove all SCEVConstants. + Terms.erase( + remove_if(Terms, [](const SCEV *E) { return isa<SCEVConstant>(E); }), + Terms.end()); + + 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<const SCEV *> &Terms) { + for (const SCEV *T : Terms) + if (SCEVExprContains(T, isa<SCEVUnknown, const SCEV *>)) + 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<SCEVMulExpr>(S)) + return Expr->getNumOperands(); + return 1; +} + +static const SCEV *removeConstantFactors(ScalarEvolution &SE, const SCEV *T) { + if (isa<SCEVConstant>(T)) + return nullptr; + + if (isa<SCEVUnknown>(T)) + return T; + + if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(T)) { + SmallVector<const SCEV *, 2> Factors; + for (const SCEV *Op : M->operands()) + if (!isa<SCEVConstant>(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<StoreInst>(Inst)) + Ty = Store->getValueOperand()->getType(); + else if (LoadInst *Load = dyn_cast<LoadInst>(Inst)) + Ty = Load->getType(); + else + return nullptr; + + Type *ETy = getEffectiveSCEVType(PointerType::getUnqual(Ty)); + return getSizeOfExpr(ETy, Ty); +} + +void ScalarEvolution::findArrayDimensions(SmallVectorImpl<const SCEV *> &Terms, + SmallVectorImpl<const SCEV *> &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<const SCEV *, 4> 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<const SCEV *> &Subscripts, + SmallVectorImpl<const SCEV *> &Sizes) { + // Early exit in case this SCEV is not an affine multivariate function. + if (Sizes.empty()) + return; + + if (auto *AR = dyn_cast<SCEVAddRecExpr>(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<SCEVAddRecExpr>(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<const SCEV *> &Subscripts, + SmallVectorImpl<const SCEV *> &Sizes, + const SCEV *ElementSize) { + // First step: collect parametric terms. + SmallVector<const SCEV *, 4> 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"; + }); +} + +//===----------------------------------------------------------------------===// +// SCEVCallbackVH Class Implementation +//===----------------------------------------------------------------------===// + +void ScalarEvolution::SCEVCallbackVH::deleted() { + assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!"); + if (PHINode *PN = dyn_cast<PHINode>(getValPtr())) + SE->ConstantEvolutionLoopExitValue.erase(PN); + SE->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<User *, 16> Worklist(Old->user_begin(), Old->user_end()); + SmallPtrSet<User *, 8> 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<PHINode>(U)) + SE->ConstantEvolutionLoopExitValue.erase(PN); + SE->eraseValueFromMap(U); + Worklist.insert(Worklist.end(), U->user_begin(), U->user_end()); + } + // Delete the Old value. + if (PHINode *PN = dyn_cast<PHINode>(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(); + + // Free any extra memory created for ExitNotTakenInfo in the unlikely event + // that a loop had multiple computable exits. + for (auto &BTCI : BackedgeTakenCounts) + BTCI.second.clear(); + for (auto &BTCI : PredicatedBackedgeTakenCounts) + BTCI.second.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<SCEVCouldNotCompute>(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<BasicBlock *, 8> ExitingBlocks; + L->getExitingBlocks(ExitingBlocks); + if (ExitingBlocks.size() != 1) + OS << "<multiple exits> "; + + 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<SCEVCouldNotCompute>(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<SCEVCouldNotCompute>(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<ScalarEvolution *>(this); + + OS << "Classifying expressions for: "; + F.printAsOperand(OS, /*PrintType=*/false); + OS << "\n"; + for (Instruction &I : instructions(F)) + if (isSCEVable(I.getType()) && !isa<CmpInst>(I)) { + OS << I << '\n'; + OS << " --> "; + const SCEV *SV = SE.getSCEV(&I); + SV->print(OS); + if (!isa<SCEVCouldNotCompute>(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<SCEVCouldNotCompute>(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 << "<<Unknown>>"; + } 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 (static_cast<SCEVTypes>(S->getSCEVType())) { + case scConstant: + return LoopInvariant; + case scTruncate: + case scZeroExtend: + case scSignExtend: + return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L); + case scAddRecExpr: { + const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(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<SCEVNAryExpr>(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<SCEVUDivExpr>(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<Instruction>(cast<SCEVUnknown>(S)->getValue())) + return (L && !L->contains(I)) ? LoopInvariant : LoopVariant; + return LoopInvariant; + case scCouldNotCompute: + llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!"); + } + llvm_unreachable("Unknown SCEV kind!"); +} + +bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) { + return getLoopDisposition(S, L) == LoopInvariant; +} + +bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) { + return getLoopDisposition(S, L) == LoopComputable; +} + +ScalarEvolution::BlockDisposition +ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) { + auto &Values = BlockDispositions[S]; + for (auto &V : Values) { + if (V.getPointer() == BB) + return V.getInt(); + } + Values.emplace_back(BB, DoesNotDominateBlock); + BlockDisposition D = computeBlockDisposition(S, BB); + auto &Values2 = BlockDispositions[S]; + for (auto &V : make_range(Values2.rbegin(), Values2.rend())) { + if (V.getPointer() == BB) { + V.setInt(D); + break; + } + } + return D; +} + +ScalarEvolution::BlockDisposition +ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) { + switch (static_cast<SCEVTypes>(S->getSCEVType())) { + case scConstant: + return ProperlyDominatesBlock; + case scTruncate: + case scZeroExtend: + case scSignExtend: + return getBlockDisposition(cast<SCEVCastExpr>(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<SCEVAddRecExpr>(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<SCEVNAryExpr>(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<SCEVUDivExpr>(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<Instruction>(cast<SCEVUnknown>(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; }); +} + +bool ScalarEvolution::ExitLimit::hasOperand(const SCEV *S) const { + auto IsS = [&](const SCEV *X) { return S == X; }; + auto ContainsS = [&](const SCEV *X) { + return !isa<SCEVCouldNotCompute>(X) && SCEVExprContains(X, IsS); + }; + return ContainsS(ExactNotTaken) || ContainsS(MaxNotTaken); +} + +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<const SCEV *, const Loop *> Entry = I->first; + if (Entry.first == S) + PredicatedSCEVRewrites.erase(I++); + else + ++I; + } + + auto RemoveSCEVFromBackedgeMap = + [S, this](DenseMap<const Loop *, BackedgeTakenInfo> &Map) { + for (auto I = Map.begin(), E = Map.end(); I != E;) { + BackedgeTakenInfo &BEInfo = I->second; + if (BEInfo.hasOperand(S, this)) { + BEInfo.clear(); + Map.erase(I++); + } else + ++I; + } + }; + + RemoveSCEVFromBackedgeMap(BackedgeTakenCounts); + RemoveSCEVFromBackedgeMap(PredicatedBackedgeTakenCounts); +} + +void +ScalarEvolution::getUsedLoops(const SCEV *S, + SmallPtrSetImpl<const Loop *> &LoopsUsed) { + struct FindUsedLoops { + FindUsedLoops(SmallPtrSetImpl<const Loop *> &LoopsUsed) + : LoopsUsed(LoopsUsed) {} + SmallPtrSetImpl<const Loop *> &LoopsUsed; + bool follow(const SCEV *S) { + if (auto *AR = dyn_cast<SCEVAddRecExpr>(S)) + LoopsUsed.insert(AR->getLoop()); + return true; + } + + bool isDone() const { return false; } + }; + + FindUsedLoops F(LoopsUsed); + SCEVTraversal<FindUsedLoops>(F).visitAll(S); +} + +void ScalarEvolution::addToLoopUseLists(const SCEV *S) { + SmallPtrSet<const Loop *, 8> LoopsUsed; + getUsedLoops(S, LoopsUsed); + for (auto *L : LoopsUsed) + LoopUsers[L].push_back(S); +} + +void ScalarEvolution::verify() const { + ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this); + ScalarEvolution SE2(F, TLI, AC, DT, LI); + + SmallVector<Loop *, 8> LoopStack(LI.begin(), LI.end()); + + // Map's SCEV expressions from one ScalarEvolution "universe" to another. + struct SCEVMapper : public SCEVRewriteVisitor<SCEVMapper> { + SCEVMapper(ScalarEvolution &SE) : SCEVRewriteVisitor<SCEVMapper>(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(); + LoopStack.insert(LoopStack.end(), L->begin(), L->end()); + + auto *CurBECount = SCM.visit( + const_cast<ScalarEvolution *>(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<SCEVConstant>(Delta)) && !Delta->isZero()) { + dbgs() << "Trip Count for " << *L << " Changed!\n"; + dbgs() << "Old: " << *CurBECount << "\n"; + dbgs() << "New: " << *NewBECount << "\n"; + dbgs() << "Delta: " << *Delta << "\n"; + std::abort(); + } + } +} + +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<ScalarEvolutionAnalysis>(); + return !(PAC.preserved() || PAC.preservedSet<AllAnalysesOn<Function>>()) || + Inv.invalidate<AssumptionAnalysis>(F, PA) || + Inv.invalidate<DominatorTreeAnalysis>(F, PA) || + Inv.invalidate<LoopAnalysis>(F, PA); +} + +AnalysisKey ScalarEvolutionAnalysis::Key; + +ScalarEvolution ScalarEvolutionAnalysis::run(Function &F, + FunctionAnalysisManager &AM) { + return ScalarEvolution(F, AM.getResult<TargetLibraryAnalysis>(F), + AM.getResult<AssumptionAnalysis>(F), + AM.getResult<DominatorTreeAnalysis>(F), + AM.getResult<LoopAnalysis>(F)); +} + +PreservedAnalyses +ScalarEvolutionPrinterPass::run(Function &F, FunctionAnalysisManager &AM) { + AM.getResult<ScalarEvolutionAnalysis>(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<TargetLibraryInfoWrapperPass>().getTLI(F), + getAnalysis<AssumptionCacheTracker>().getAssumptionCache(F), + getAnalysis<DominatorTreeWrapperPass>().getDomTree(), + getAnalysis<LoopInfoWrapperPass>().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<AssumptionCacheTracker>(); + AU.addRequiredTransitive<LoopInfoWrapperPass>(); + AU.addRequiredTransitive<DominatorTreeWrapperPass>(); + AU.addRequiredTransitive<TargetLibraryInfoWrapperPass>(); +} + +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<SCEVPredicateRewriter> { +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<const SCEVPredicate *> *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<SCEVEqualPredicate>(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<SCEVAddRecExpr>(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<SCEVAddRecExpr>(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<const SCEVPredicate *> *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<PHINode>(Expr->getValue())) + return Expr; + Optional<std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>> + 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<const SCEVWrapPredicate>(P)) { + auto *AR = cast<const SCEVAddRecExpr>(WP->getExpr()); + if (L != AR->getLoop()) + return Expr; + } + if (!addOverflowAssumption(P)) + return Expr; + } + return PredicatedRewrite->first; + } + + SmallPtrSetImpl<const SCEVPredicate *> *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<const SCEVPredicate *> &Preds) { + SmallPtrSet<const SCEVPredicate *, 4> TransformPreds; + S = SCEVPredicateRewriter::rewrite(S, L, *this, &TransformPreds, nullptr); + auto *AddRec = dyn_cast<SCEVAddRecExpr>(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<SCEVEqualPredicate>(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<SCEVWrapPredicate>(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 << "<nusw>"; + if (SCEVWrapPredicate::IncrementNSSW & getFlags()) + OS << "<nssw>"; + 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<SCEVConstant>(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<const SCEVPredicate *> +SCEVUnionPredicate::getPredicatesForExpr(const SCEV *Expr) { + auto I = SCEVToPreds.find(Expr); + if (I == SCEVToPreds.end()) + return ArrayRef<const SCEVPredicate *>(); + return I->second; +} + +bool SCEVUnionPredicate::implies(const SCEVPredicate *N) const { + if (const auto *Set = dyn_cast<SCEVUnionPredicate>(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<SCEVUnionPredicate>(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<SCEVAddRecExpr>(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<SCEVAddRecExpr>(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<const SCEVPredicate *, 4> 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 (const 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. +// 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) { + const auto *Add = dyn_cast<SCEVAddExpr>(Expr); + if (Add == nullptr || Add->getNumOperands() != 2) + return false; + + const SCEV *A = Add->getOperand(1); + const auto *Mul = dyn_cast<SCEVMulExpr>(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<SCEVConstant>(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; +} |