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//===- ScalarEvolutionExpander.cpp - Scalar Evolution Analysis ------------===//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
// This file contains the implementation of the scalar evolution expander,
// which is used to generate the code corresponding to a given scalar evolution
// expression.
#include "llvm/Transforms/Utils/ScalarEvolutionExpander.h"
#include "llvm/ADT/STLExtras.h"
#include "llvm/ADT/ScopeExit.h"
#include "llvm/ADT/SmallSet.h"
#include "llvm/Analysis/InstructionSimplify.h"
#include "llvm/Analysis/LoopInfo.h"
#include "llvm/Analysis/TargetTransformInfo.h"
#include "llvm/Analysis/ValueTracking.h"
#include "llvm/IR/DataLayout.h"
#include "llvm/IR/Dominators.h"
#include "llvm/IR/IntrinsicInst.h"
#include "llvm/IR/PatternMatch.h"
#include "llvm/Support/CommandLine.h"
#include "llvm/Support/raw_ostream.h"
#include "llvm/Transforms/Utils/LoopUtils.h"
using namespace llvm;
cl::opt<unsigned> llvm::SCEVCheapExpansionBudget(
"scev-cheap-expansion-budget", cl::Hidden, cl::init(4),
cl::desc("When performing SCEV expansion only if it is cheap to do, this "
"controls the budget that is considered cheap (default = 4)"));
using namespace PatternMatch;
PoisonFlags::PoisonFlags(const Instruction *I) {
NUW = false;
NSW = false;
Exact = false;
Disjoint = false;
NNeg = false;
if (auto *OBO = dyn_cast<OverflowingBinaryOperator>(I)) {
NUW = OBO->hasNoUnsignedWrap();
NSW = OBO->hasNoSignedWrap();
if (auto *PEO = dyn_cast<PossiblyExactOperator>(I))
Exact = PEO->isExact();
if (auto *PDI = dyn_cast<PossiblyDisjointInst>(I))
Disjoint = PDI->isDisjoint();
if (auto *PNI = dyn_cast<PossiblyNonNegInst>(I))
NNeg = PNI->hasNonNeg();
if (auto *TI = dyn_cast<TruncInst>(I)) {
NUW = TI->hasNoUnsignedWrap();
NSW = TI->hasNoSignedWrap();
void PoisonFlags::apply(Instruction *I) {
if (isa<OverflowingBinaryOperator>(I)) {
if (isa<PossiblyExactOperator>(I))
if (auto *PDI = dyn_cast<PossiblyDisjointInst>(I))
if (auto *PNI = dyn_cast<PossiblyNonNegInst>(I))
if (isa<TruncInst>(I)) {
/// ReuseOrCreateCast - Arrange for there to be a cast of V to Ty at IP,
/// reusing an existing cast if a suitable one (= dominating IP) exists, or
/// creating a new one.
Value *SCEVExpander::ReuseOrCreateCast(Value *V, Type *Ty,
Instruction::CastOps Op,
BasicBlock::iterator IP) {
// This function must be called with the builder having a valid insertion
// point. It doesn't need to be the actual IP where the uses of the returned
// cast will be added, but it must dominate such IP.
// We use this precondition to produce a cast that will dominate all its
// uses. In particular, this is crucial for the case where the builder's
// insertion point *is* the point where we were asked to put the cast.
// Since we don't know the builder's insertion point is actually
// where the uses will be added (only that it dominates it), we are
// not allowed to move it.
BasicBlock::iterator BIP = Builder.GetInsertPoint();
Value *Ret = nullptr;
// Check to see if there is already a cast!
for (User *U : V->users()) {
if (U->getType() != Ty)
CastInst *CI = dyn_cast<CastInst>(U);
if (!CI || CI->getOpcode() != Op)
// Found a suitable cast that is at IP or comes before IP. Use it. Note that
// the cast must also properly dominate the Builder's insertion point.
if (IP->getParent() == CI->getParent() && &*BIP != CI &&
(&*IP == CI || CI->comesBefore(&*IP))) {
Ret = CI;
// Create a new cast.
if (!Ret) {
SCEVInsertPointGuard Guard(Builder, this);
Ret = Builder.CreateCast(Op, V, Ty, V->getName());
// We assert at the end of the function since IP might point to an
// instruction with different dominance properties than a cast
// (an invoke for example) and not dominate BIP (but the cast does).
assert(!isa<Instruction>(Ret) ||
SE.DT.dominates(cast<Instruction>(Ret), &*BIP));
return Ret;
SCEVExpander::findInsertPointAfter(Instruction *I,
Instruction *MustDominate) const {
BasicBlock::iterator IP = ++I->getIterator();
if (auto *II = dyn_cast<InvokeInst>(I))
IP = II->getNormalDest()->begin();
while (isa<PHINode>(IP))
if (isa<FuncletPadInst>(IP) || isa<LandingPadInst>(IP)) {
} else if (isa<CatchSwitchInst>(IP)) {
IP = MustDominate->getParent()->getFirstInsertionPt();
} else {
assert(!IP->isEHPad() && "unexpected eh pad!");
// Adjust insert point to be after instructions inserted by the expander, so
// we can re-use already inserted instructions. Avoid skipping past the
// original \p MustDominate, in case it is an inserted instruction.
while (isInsertedInstruction(&*IP) && &*IP != MustDominate)
return IP;
SCEVExpander::GetOptimalInsertionPointForCastOf(Value *V) const {
// Cast the argument at the beginning of the entry block, after
// any bitcasts of other arguments.
if (Argument *A = dyn_cast<Argument>(V)) {
BasicBlock::iterator IP = A->getParent()->getEntryBlock().begin();
while ((isa<BitCastInst>(IP) &&
isa<Argument>(cast<BitCastInst>(IP)->getOperand(0)) &&
cast<BitCastInst>(IP)->getOperand(0) != A) ||
return IP;
// Cast the instruction immediately after the instruction.
if (Instruction *I = dyn_cast<Instruction>(V))
return findInsertPointAfter(I, &*Builder.GetInsertPoint());
// Otherwise, this must be some kind of a constant,
// so let's plop this cast into the function's entry block.
assert(isa<Constant>(V) &&
"Expected the cast argument to be a global/constant");
return Builder.GetInsertBlock()
/// InsertNoopCastOfTo - Insert a cast of V to the specified type,
/// which must be possible with a noop cast, doing what we can to share
/// the casts.
Value *SCEVExpander::InsertNoopCastOfTo(Value *V, Type *Ty) {
Instruction::CastOps Op = CastInst::getCastOpcode(V, false, Ty, false);
assert((Op == Instruction::BitCast ||
Op == Instruction::PtrToInt ||
Op == Instruction::IntToPtr) &&
"InsertNoopCastOfTo cannot perform non-noop casts!");
assert(SE.getTypeSizeInBits(V->getType()) == SE.getTypeSizeInBits(Ty) &&
"InsertNoopCastOfTo cannot change sizes!");
// inttoptr only works for integral pointers. For non-integral pointers, we
// can create a GEP on null with the integral value as index. Note that
// it is safe to use GEP of null instead of inttoptr here, because only
// expressions already based on a GEP of null should be converted to pointers
// during expansion.
if (Op == Instruction::IntToPtr) {
auto *PtrTy = cast<PointerType>(Ty);
if (DL.isNonIntegralPointerType(PtrTy))
return Builder.CreatePtrAdd(Constant::getNullValue(PtrTy), V, "scevgep");
// Short-circuit unnecessary bitcasts.
if (Op == Instruction::BitCast) {
if (V->getType() == Ty)
return V;
if (CastInst *CI = dyn_cast<CastInst>(V)) {
if (CI->getOperand(0)->getType() == Ty)
return CI->getOperand(0);
// Short-circuit unnecessary inttoptr<->ptrtoint casts.
if ((Op == Instruction::PtrToInt || Op == Instruction::IntToPtr) &&
SE.getTypeSizeInBits(Ty) == SE.getTypeSizeInBits(V->getType())) {
if (CastInst *CI = dyn_cast<CastInst>(V))
if ((CI->getOpcode() == Instruction::PtrToInt ||
CI->getOpcode() == Instruction::IntToPtr) &&
SE.getTypeSizeInBits(CI->getType()) ==
return CI->getOperand(0);
if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
if ((CE->getOpcode() == Instruction::PtrToInt ||
CE->getOpcode() == Instruction::IntToPtr) &&
SE.getTypeSizeInBits(CE->getType()) ==
return CE->getOperand(0);
// Fold a cast of a constant.
if (Constant *C = dyn_cast<Constant>(V))
return ConstantExpr::getCast(Op, C, Ty);
// Try to reuse existing cast, or insert one.
return ReuseOrCreateCast(V, Ty, Op, GetOptimalInsertionPointForCastOf(V));
/// InsertBinop - Insert the specified binary operator, doing a small amount
/// of work to avoid inserting an obviously redundant operation, and hoisting
/// to an outer loop when the opportunity is there and it is safe.
Value *SCEVExpander::InsertBinop(Instruction::BinaryOps Opcode,
Value *LHS, Value *RHS,
SCEV::NoWrapFlags Flags, bool IsSafeToHoist) {
// Fold a binop with constant operands.
if (Constant *CLHS = dyn_cast<Constant>(LHS))
if (Constant *CRHS = dyn_cast<Constant>(RHS))
if (Constant *Res = ConstantFoldBinaryOpOperands(Opcode, CLHS, CRHS, DL))
return Res;
// Do a quick scan to see if we have this binop nearby. If so, reuse it.
unsigned ScanLimit = 6;
BasicBlock::iterator BlockBegin = Builder.GetInsertBlock()->begin();
// Scanning starts from the last instruction before the insertion point.
BasicBlock::iterator IP = Builder.GetInsertPoint();
if (IP != BlockBegin) {
for (; ScanLimit; --IP, --ScanLimit) {
// Don't count dbg.value against the ScanLimit, to avoid perturbing the
// generated code.
if (isa<DbgInfoIntrinsic>(IP))
auto canGenerateIncompatiblePoison = [&Flags](Instruction *I) {
// Ensure that no-wrap flags match.
if (isa<OverflowingBinaryOperator>(I)) {
if (I->hasNoSignedWrap() != (Flags & SCEV::FlagNSW))
return true;
if (I->hasNoUnsignedWrap() != (Flags & SCEV::FlagNUW))
return true;
// Conservatively, do not use any instruction which has any of exact
// flags installed.
if (isa<PossiblyExactOperator>(I) && I->isExact())
return true;
return false;
if (IP->getOpcode() == (unsigned)Opcode && IP->getOperand(0) == LHS &&
IP->getOperand(1) == RHS && !canGenerateIncompatiblePoison(&*IP))
return &*IP;
if (IP == BlockBegin) break;
// Save the original insertion point so we can restore it when we're done.
DebugLoc Loc = Builder.GetInsertPoint()->getDebugLoc();
SCEVInsertPointGuard Guard(Builder, this);
if (IsSafeToHoist) {
// Move the insertion point out of as many loops as we can.
while (const Loop *L = SE.LI.getLoopFor(Builder.GetInsertBlock())) {
if (!L->isLoopInvariant(LHS) || !L->isLoopInvariant(RHS)) break;
BasicBlock *Preheader = L->getLoopPreheader();
if (!Preheader) break;
// Ok, move up a level.
// If we haven't found this binop, insert it.
// TODO: Use the Builder, which will make CreateBinOp below fold with
// InstSimplifyFolder.
Instruction *BO = Builder.Insert(BinaryOperator::Create(Opcode, LHS, RHS));
if (Flags & SCEV::FlagNUW)
if (Flags & SCEV::FlagNSW)
return BO;
/// expandAddToGEP - Expand an addition expression with a pointer type into
/// a GEP instead of using ptrtoint+arithmetic+inttoptr. This helps
/// BasicAliasAnalysis and other passes analyze the result. See the rules
/// for getelementptr vs. inttoptr in
/// for details.
/// Design note: The correctness of using getelementptr here depends on
/// ScalarEvolution not recognizing inttoptr and ptrtoint operators, as
/// they may introduce pointer arithmetic which may not be safely converted
/// into getelementptr.
/// Design note: It might seem desirable for this function to be more
/// loop-aware. If some of the indices are loop-invariant while others
/// aren't, it might seem desirable to emit multiple GEPs, keeping the
/// loop-invariant portions of the overall computation outside the loop.
/// However, there are a few reasons this is not done here. Hoisting simple
/// arithmetic is a low-level optimization that often isn't very
/// important until late in the optimization process. In fact, passes
/// like InstructionCombining will combine GEPs, even if it means
/// pushing loop-invariant computation down into loops, so even if the
/// GEPs were split here, the work would quickly be undone. The
/// LoopStrengthReduction pass, which is usually run quite late (and
/// after the last InstructionCombining pass), takes care of hoisting
/// loop-invariant portions of expressions, after considering what
/// can be folded using target addressing modes.
Value *SCEVExpander::expandAddToGEP(const SCEV *Offset, Value *V) {
assert(!isa<Instruction>(V) ||
SE.DT.dominates(cast<Instruction>(V), &*Builder.GetInsertPoint()));
Value *Idx = expand(Offset);
// Fold a GEP with constant operands.
if (Constant *CLHS = dyn_cast<Constant>(V))
if (Constant *CRHS = dyn_cast<Constant>(Idx))
return Builder.CreatePtrAdd(CLHS, CRHS);
// Do a quick scan to see if we have this GEP nearby. If so, reuse it.
unsigned ScanLimit = 6;
BasicBlock::iterator BlockBegin = Builder.GetInsertBlock()->begin();
// Scanning starts from the last instruction before the insertion point.
BasicBlock::iterator IP = Builder.GetInsertPoint();
if (IP != BlockBegin) {
for (; ScanLimit; --IP, --ScanLimit) {
// Don't count dbg.value against the ScanLimit, to avoid perturbing the
// generated code.
if (isa<DbgInfoIntrinsic>(IP))
if (IP->getOpcode() == Instruction::GetElementPtr &&
IP->getOperand(0) == V && IP->getOperand(1) == Idx &&
cast<GEPOperator>(&*IP)->getSourceElementType() ==
return &*IP;
if (IP == BlockBegin) break;
// Save the original insertion point so we can restore it when we're done.
SCEVInsertPointGuard Guard(Builder, this);
// Move the insertion point out of as many loops as we can.
while (const Loop *L = SE.LI.getLoopFor(Builder.GetInsertBlock())) {
if (!L->isLoopInvariant(V) || !L->isLoopInvariant(Idx)) break;
BasicBlock *Preheader = L->getLoopPreheader();
if (!Preheader) break;
// Ok, move up a level.
// Emit a GEP.
return Builder.CreatePtrAdd(V, Idx, "scevgep");
/// PickMostRelevantLoop - Given two loops pick the one that's most relevant for
/// SCEV expansion. If they are nested, this is the most nested. If they are
/// neighboring, pick the later.
static const Loop *PickMostRelevantLoop(const Loop *A, const Loop *B,
DominatorTree &DT) {
if (!A) return B;
if (!B) return A;
if (A->contains(B)) return B;
if (B->contains(A)) return A;
if (DT.dominates(A->getHeader(), B->getHeader())) return B;
if (DT.dominates(B->getHeader(), A->getHeader())) return A;
return A; // Arbitrarily break the tie.
/// getRelevantLoop - Get the most relevant loop associated with the given
/// expression, according to PickMostRelevantLoop.
const Loop *SCEVExpander::getRelevantLoop(const SCEV *S) {
// Test whether we've already computed the most relevant loop for this SCEV.
auto Pair = RelevantLoops.insert(std::make_pair(S, nullptr));
if (!Pair.second)
return Pair.first->second;
switch (S->getSCEVType()) {
case scConstant:
case scVScale:
return nullptr; // A constant has no relevant loops.
case scTruncate:
case scZeroExtend:
case scSignExtend:
case scPtrToInt:
case scAddExpr:
case scMulExpr:
case scUDivExpr:
case scAddRecExpr:
case scUMaxExpr:
case scSMaxExpr:
case scUMinExpr:
case scSMinExpr:
case scSequentialUMinExpr: {
const Loop *L = nullptr;
if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(S))
L = AR->getLoop();
for (const SCEV *Op : S->operands())
L = PickMostRelevantLoop(L, getRelevantLoop(Op), SE.DT);
return RelevantLoops[S] = L;
case scUnknown: {
const SCEVUnknown *U = cast<SCEVUnknown>(S);
if (const Instruction *I = dyn_cast<Instruction>(U->getValue()))
return Pair.first->second = SE.LI.getLoopFor(I->getParent());
// A non-instruction has no relevant loops.
return nullptr;
case scCouldNotCompute:
llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
llvm_unreachable("Unexpected SCEV type!");
namespace {
/// LoopCompare - Compare loops by PickMostRelevantLoop.
class LoopCompare {
DominatorTree &DT;
explicit LoopCompare(DominatorTree &dt) : DT(dt) {}
bool operator()(std::pair<const Loop *, const SCEV *> LHS,
std::pair<const Loop *, const SCEV *> RHS) const {
// Keep pointer operands sorted at the end.
if (LHS.second->getType()->isPointerTy() !=
return LHS.second->getType()->isPointerTy();
// Compare loops with PickMostRelevantLoop.
if (LHS.first != RHS.first)
return PickMostRelevantLoop(LHS.first, RHS.first, DT) != LHS.first;
// If one operand is a non-constant negative and the other is not,
// put the non-constant negative on the right so that a sub can
// be used instead of a negate and add.
if (LHS.second->isNonConstantNegative()) {
if (!RHS.second->isNonConstantNegative())
return false;
} else if (RHS.second->isNonConstantNegative())
return true;
// Otherwise they are equivalent according to this comparison.
return false;
Value *SCEVExpander::visitAddExpr(const SCEVAddExpr *S) {
// Collect all the add operands in a loop, along with their associated loops.
// Iterate in reverse so that constants are emitted last, all else equal, and
// so that pointer operands are inserted first, which the code below relies on
// to form more involved GEPs.
SmallVector<std::pair<const Loop *, const SCEV *>, 8> OpsAndLoops;
for (const SCEV *Op : reverse(S->operands()))
OpsAndLoops.push_back(std::make_pair(getRelevantLoop(Op), Op));
// Sort by loop. Use a stable sort so that constants follow non-constants and
// pointer operands precede non-pointer operands.
llvm::stable_sort(OpsAndLoops, LoopCompare(SE.DT));
// Emit instructions to add all the operands. Hoist as much as possible
// out of loops, and form meaningful getelementptrs where possible.
Value *Sum = nullptr;
for (auto I = OpsAndLoops.begin(), E = OpsAndLoops.end(); I != E;) {
const Loop *CurLoop = I->first;
const SCEV *Op = I->second;
if (!Sum) {
// This is the first operand. Just expand it.
Sum = expand(Op);
assert(!Op->getType()->isPointerTy() && "Only first op can be pointer");
if (isa<PointerType>(Sum->getType())) {
// The running sum expression is a pointer. Try to form a getelementptr
// at this level with that as the base.
SmallVector<const SCEV *, 4> NewOps;
for (; I != E && I->first == CurLoop; ++I) {
// If the operand is SCEVUnknown and not instructions, peek through
// it, to enable more of it to be folded into the GEP.
const SCEV *X = I->second;
if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(X))
if (!isa<Instruction>(U->getValue()))
X = SE.getSCEV(U->getValue());
Sum = expandAddToGEP(SE.getAddExpr(NewOps), Sum);
} else if (Op->isNonConstantNegative()) {
// Instead of doing a negate and add, just do a subtract.
Value *W = expand(SE.getNegativeSCEV(Op));
Sum = InsertBinop(Instruction::Sub, Sum, W, SCEV::FlagAnyWrap,
/*IsSafeToHoist*/ true);
} else {
// A simple add.
Value *W = expand(Op);
// Canonicalize a constant to the RHS.
if (isa<Constant>(Sum))
std::swap(Sum, W);
Sum = InsertBinop(Instruction::Add, Sum, W, S->getNoWrapFlags(),
/*IsSafeToHoist*/ true);
return Sum;
Value *SCEVExpander::visitMulExpr(const SCEVMulExpr *S) {
Type *Ty = S->getType();
// Collect all the mul operands in a loop, along with their associated loops.
// Iterate in reverse so that constants are emitted last, all else equal.
SmallVector<std::pair<const Loop *, const SCEV *>, 8> OpsAndLoops;
for (const SCEV *Op : reverse(S->operands()))
OpsAndLoops.push_back(std::make_pair(getRelevantLoop(Op), Op));
// Sort by loop. Use a stable sort so that constants follow non-constants.
llvm::stable_sort(OpsAndLoops, LoopCompare(SE.DT));
// Emit instructions to mul all the operands. Hoist as much as possible
// out of loops.
Value *Prod = nullptr;
auto I = OpsAndLoops.begin();
// Expand the calculation of X pow N in the following manner:
// Let N = P1 + P2 + ... + PK, where all P are powers of 2. Then:
// X pow N = (X pow P1) * (X pow P2) * ... * (X pow PK).
const auto ExpandOpBinPowN = [this, &I, &OpsAndLoops]() {
auto E = I;
// Calculate how many times the same operand from the same loop is included
// into this power.
uint64_t Exponent = 0;
const uint64_t MaxExponent = UINT64_MAX >> 1;
// No one sane will ever try to calculate such huge exponents, but if we
// need this, we stop on UINT64_MAX / 2 because we need to exit the loop
// below when the power of 2 exceeds our Exponent, and we want it to be
// 1u << 31 at most to not deal with unsigned overflow.
while (E != OpsAndLoops.end() && *I == *E && Exponent != MaxExponent) {
assert(Exponent > 0 && "Trying to calculate a zeroth exponent of operand?");
// Calculate powers with exponents 1, 2, 4, 8 etc. and include those of them
// that are needed into the result.
Value *P = expand(I->second);
Value *Result = nullptr;
if (Exponent & 1)
Result = P;
for (uint64_t BinExp = 2; BinExp <= Exponent; BinExp <<= 1) {
P = InsertBinop(Instruction::Mul, P, P, SCEV::FlagAnyWrap,
/*IsSafeToHoist*/ true);
if (Exponent & BinExp)
Result = Result ? InsertBinop(Instruction::Mul, Result, P,
/*IsSafeToHoist*/ true)
: P;
I = E;
assert(Result && "Nothing was expanded?");
return Result;
while (I != OpsAndLoops.end()) {
if (!Prod) {
// This is the first operand. Just expand it.
Prod = ExpandOpBinPowN();
} else if (I->second->isAllOnesValue()) {
// Instead of doing a multiply by negative one, just do a negate.
Prod = InsertBinop(Instruction::Sub, Constant::getNullValue(Ty), Prod,
SCEV::FlagAnyWrap, /*IsSafeToHoist*/ true);
} else {
// A simple mul.
Value *W = ExpandOpBinPowN();
// Canonicalize a constant to the RHS.
if (isa<Constant>(Prod)) std::swap(Prod, W);
const APInt *RHS;
if (match(W, m_Power2(RHS))) {
// Canonicalize Prod*(1<<C) to Prod<<C.
assert(!Ty->isVectorTy() && "vector types are not SCEVable");
auto NWFlags = S->getNoWrapFlags();
// clear nsw flag if shl will produce poison value.
if (RHS->logBase2() == RHS->getBitWidth() - 1)
NWFlags = ScalarEvolution::clearFlags(NWFlags, SCEV::FlagNSW);
Prod = InsertBinop(Instruction::Shl, Prod,
ConstantInt::get(Ty, RHS->logBase2()), NWFlags,
/*IsSafeToHoist*/ true);
} else {
Prod = InsertBinop(Instruction::Mul, Prod, W, S->getNoWrapFlags(),
/*IsSafeToHoist*/ true);
return Prod;
Value *SCEVExpander::visitUDivExpr(const SCEVUDivExpr *S) {
Value *LHS = expand(S->getLHS());
if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(S->getRHS())) {
const APInt &RHS = SC->getAPInt();
if (RHS.isPowerOf2())
return InsertBinop(Instruction::LShr, LHS,
ConstantInt::get(SC->getType(), RHS.logBase2()),
SCEV::FlagAnyWrap, /*IsSafeToHoist*/ true);
Value *RHS = expand(S->getRHS());
return InsertBinop(Instruction::UDiv, LHS, RHS, SCEV::FlagAnyWrap,
/*IsSafeToHoist*/ SE.isKnownNonZero(S->getRHS()));
/// Determine if this is a well-behaved chain of instructions leading back to
/// the PHI. If so, it may be reused by expanded expressions.
bool SCEVExpander::isNormalAddRecExprPHI(PHINode *PN, Instruction *IncV,
const Loop *L) {
if (IncV->getNumOperands() == 0 || isa<PHINode>(IncV) ||
(isa<CastInst>(IncV) && !isa<BitCastInst>(IncV)))
return false;
// If any of the operands don't dominate the insert position, bail.
// Addrec operands are always loop-invariant, so this can only happen
// if there are instructions which haven't been hoisted.
if (L == IVIncInsertLoop) {
for (Use &Op : llvm::drop_begin(IncV->operands()))
if (Instruction *OInst = dyn_cast<Instruction>(Op))
if (!SE.DT.dominates(OInst, IVIncInsertPos))
return false;
// Advance to the next instruction.
IncV = dyn_cast<Instruction>(IncV->getOperand(0));
if (!IncV)
return false;
if (IncV->mayHaveSideEffects())
return false;
if (IncV == PN)
return true;
return isNormalAddRecExprPHI(PN, IncV, L);
/// getIVIncOperand returns an induction variable increment's induction
/// variable operand.
/// If allowScale is set, any type of GEP is allowed as long as the nonIV
/// operands dominate InsertPos.
/// If allowScale is not set, ensure that a GEP increment conforms to one of the
/// simple patterns generated by getAddRecExprPHILiterally and
/// expandAddtoGEP. If the pattern isn't recognized, return NULL.
Instruction *SCEVExpander::getIVIncOperand(Instruction *IncV,
Instruction *InsertPos,
bool allowScale) {
if (IncV == InsertPos)
return nullptr;
switch (IncV->getOpcode()) {
return nullptr;
// Check for a simple Add/Sub or GEP of a loop invariant step.
case Instruction::Add:
case Instruction::Sub: {
Instruction *OInst = dyn_cast<Instruction>(IncV->getOperand(1));
if (!OInst || SE.DT.dominates(OInst, InsertPos))
return dyn_cast<Instruction>(IncV->getOperand(0));
return nullptr;
case Instruction::BitCast:
return dyn_cast<Instruction>(IncV->getOperand(0));
case Instruction::GetElementPtr:
for (Use &U : llvm::drop_begin(IncV->operands())) {
if (isa<Constant>(U))
if (Instruction *OInst = dyn_cast<Instruction>(U)) {
if (!SE.DT.dominates(OInst, InsertPos))
return nullptr;
if (allowScale) {
// allow any kind of GEP as long as it can be hoisted.
// GEPs produced by SCEVExpander use i8 element type.
if (!cast<GEPOperator>(IncV)->getSourceElementType()->isIntegerTy(8))
return nullptr;
return dyn_cast<Instruction>(IncV->getOperand(0));
/// If the insert point of the current builder or any of the builders on the
/// stack of saved builders has 'I' as its insert point, update it to point to
/// the instruction after 'I'. This is intended to be used when the instruction
/// 'I' is being moved. If this fixup is not done and 'I' is moved to a
/// different block, the inconsistent insert point (with a mismatched
/// Instruction and Block) can lead to an instruction being inserted in a block
/// other than its parent.
void SCEVExpander::fixupInsertPoints(Instruction *I) {
BasicBlock::iterator It(*I);
BasicBlock::iterator NewInsertPt = std::next(It);
if (Builder.GetInsertPoint() == It)
for (auto *InsertPtGuard : InsertPointGuards)
if (InsertPtGuard->GetInsertPoint() == It)
/// hoistStep - Attempt to hoist a simple IV increment above InsertPos to make
/// it available to other uses in this loop. Recursively hoist any operands,
/// until we reach a value that dominates InsertPos.
bool SCEVExpander::hoistIVInc(Instruction *IncV, Instruction *InsertPos,
bool RecomputePoisonFlags) {
auto FixupPoisonFlags = [this](Instruction *I) {
// Drop flags that are potentially inferred from old context and infer flags
// in new context.
if (auto *OBO = dyn_cast<OverflowingBinaryOperator>(I))
if (auto Flags = SE.getStrengthenedNoWrapFlagsFromBinOp(OBO)) {
auto *BO = cast<BinaryOperator>(I);
ScalarEvolution::maskFlags(*Flags, SCEV::FlagNUW) == SCEV::FlagNUW);
ScalarEvolution::maskFlags(*Flags, SCEV::FlagNSW) == SCEV::FlagNSW);
if (SE.DT.dominates(IncV, InsertPos)) {
if (RecomputePoisonFlags)
return true;
// InsertPos must itself dominate IncV so that IncV's new position satisfies
// its existing users.
if (isa<PHINode>(InsertPos) ||
!SE.DT.dominates(InsertPos->getParent(), IncV->getParent()))
return false;
if (!SE.LI.movementPreservesLCSSAForm(IncV, InsertPos))
return false;
// Check that the chain of IV operands leading back to Phi can be hoisted.
SmallVector<Instruction*, 4> IVIncs;
for(;;) {
Instruction *Oper = getIVIncOperand(IncV, InsertPos, /*allowScale*/true);
if (!Oper)
return false;
// IncV is safe to hoist.
IncV = Oper;
if (SE.DT.dominates(IncV, InsertPos))
for (Instruction *I : llvm::reverse(IVIncs)) {
if (RecomputePoisonFlags)
return true;
bool SCEVExpander::canReuseFlagsFromOriginalIVInc(PHINode *OrigPhi,
PHINode *WidePhi,
Instruction *OrigInc,
Instruction *WideInc) {
return match(OrigInc, m_c_BinOp(m_Specific(OrigPhi), m_Value())) &&
match(WideInc, m_c_BinOp(m_Specific(WidePhi), m_Value())) &&
OrigInc->getOpcode() == WideInc->getOpcode();
/// Determine if this cyclic phi is in a form that would have been generated by
/// LSR. We don't care if the phi was actually expanded in this pass, as long
/// as it is in a low-cost form, for example, no implied multiplication. This
/// should match any patterns generated by getAddRecExprPHILiterally and
/// expandAddtoGEP.
bool SCEVExpander::isExpandedAddRecExprPHI(PHINode *PN, Instruction *IncV,
const Loop *L) {
for(Instruction *IVOper = IncV;
(IVOper = getIVIncOperand(IVOper, L->getLoopPreheader()->getTerminator(),
/*allowScale=*/false));) {
if (IVOper == PN)
return true;
return false;
/// expandIVInc - Expand an IV increment at Builder's current InsertPos.
/// Typically this is the LatchBlock terminator or IVIncInsertPos, but we may
/// need to materialize IV increments elsewhere to handle difficult situations.
Value *SCEVExpander::expandIVInc(PHINode *PN, Value *StepV, const Loop *L,
bool useSubtract) {
Value *IncV;
// If the PHI is a pointer, use a GEP, otherwise use an add or sub.
if (PN->getType()->isPointerTy()) {
// TODO: Change name to
IncV = Builder.CreatePtrAdd(PN, StepV, "scevgep");
} else {
IncV = useSubtract ?
Builder.CreateSub(PN, StepV, Twine(IVName) + "") :
Builder.CreateAdd(PN, StepV, Twine(IVName) + "");
return IncV;
/// Check whether we can cheaply express the requested SCEV in terms of
/// the available PHI SCEV by truncation and/or inversion of the step.
static bool canBeCheaplyTransformed(ScalarEvolution &SE,
const SCEVAddRecExpr *Phi,
const SCEVAddRecExpr *Requested,
bool &InvertStep) {
// We can't transform to match a pointer PHI.
Type *PhiTy = Phi->getType();
Type *RequestedTy = Requested->getType();
if (PhiTy->isPointerTy() || RequestedTy->isPointerTy())
return false;
if (RequestedTy->getIntegerBitWidth() > PhiTy->getIntegerBitWidth())
return false;
// Try truncate it if necessary.
Phi = dyn_cast<SCEVAddRecExpr>(SE.getTruncateOrNoop(Phi, RequestedTy));
if (!Phi)
return false;
// Check whether truncation will help.
if (Phi == Requested) {
InvertStep = false;
return true;
// Check whether inverting will help: {R,+,-1} == R - {0,+,1}.
if (SE.getMinusSCEV(Requested->getStart(), Requested) == Phi) {
InvertStep = true;
return true;
return false;
static bool IsIncrementNSW(ScalarEvolution &SE, const SCEVAddRecExpr *AR) {
if (!isa<IntegerType>(AR->getType()))
return false;
unsigned BitWidth = cast<IntegerType>(AR->getType())->getBitWidth();
Type *WideTy = IntegerType::get(AR->getType()->getContext(), BitWidth * 2);
const SCEV *Step = AR->getStepRecurrence(SE);
const SCEV *OpAfterExtend = SE.getAddExpr(SE.getSignExtendExpr(Step, WideTy),
SE.getSignExtendExpr(AR, WideTy));
const SCEV *ExtendAfterOp =
SE.getSignExtendExpr(SE.getAddExpr(AR, Step), WideTy);
return ExtendAfterOp == OpAfterExtend;
static bool IsIncrementNUW(ScalarEvolution &SE, const SCEVAddRecExpr *AR) {
if (!isa<IntegerType>(AR->getType()))
return false;
unsigned BitWidth = cast<IntegerType>(AR->getType())->getBitWidth();
Type *WideTy = IntegerType::get(AR->getType()->getContext(), BitWidth * 2);
const SCEV *Step = AR->getStepRecurrence(SE);
const SCEV *OpAfterExtend = SE.getAddExpr(SE.getZeroExtendExpr(Step, WideTy),
SE.getZeroExtendExpr(AR, WideTy));
const SCEV *ExtendAfterOp =
SE.getZeroExtendExpr(SE.getAddExpr(AR, Step), WideTy);
return ExtendAfterOp == OpAfterExtend;
/// getAddRecExprPHILiterally - Helper for expandAddRecExprLiterally. Expand
/// the base addrec, which is the addrec without any non-loop-dominating
/// values, and return the PHI.
PHINode *
SCEVExpander::getAddRecExprPHILiterally(const SCEVAddRecExpr *Normalized,
const Loop *L, Type *&TruncTy,
bool &InvertStep) {
assert((!IVIncInsertLoop || IVIncInsertPos) &&
"Uninitialized insert position");
// Reuse a previously-inserted PHI, if present.
BasicBlock *LatchBlock = L->getLoopLatch();
if (LatchBlock) {
PHINode *AddRecPhiMatch = nullptr;
Instruction *IncV = nullptr;
TruncTy = nullptr;
InvertStep = false;
// Only try partially matching scevs that need truncation and/or
// step-inversion if we know this loop is outside the current loop.
bool TryNonMatchingSCEV =
IVIncInsertLoop &&
SE.DT.properlyDominates(LatchBlock, IVIncInsertLoop->getHeader());
for (PHINode &PN : L->getHeader()->phis()) {
if (!SE.isSCEVable(PN.getType()))
// We should not look for a incomplete PHI. Getting SCEV for a incomplete
// PHI has no meaning at all.
if (!PN.isComplete()) {
DebugType, dbgs() << "One incomplete PHI is found: " << PN << "\n");
const SCEVAddRecExpr *PhiSCEV = dyn_cast<SCEVAddRecExpr>(SE.getSCEV(&PN));
if (!PhiSCEV)
bool IsMatchingSCEV = PhiSCEV == Normalized;
// We only handle truncation and inversion of phi recurrences for the
// expanded expression if the expanded expression's loop dominates the
// loop we insert to. Check now, so we can bail out early.
if (!IsMatchingSCEV && !TryNonMatchingSCEV)
// TODO: this possibly can be reworked to avoid this cast at all.
Instruction *TempIncV =
if (!TempIncV)
// Check whether we can reuse this PHI node.
if (LSRMode) {
if (!isExpandedAddRecExprPHI(&PN, TempIncV, L))
} else {
if (!isNormalAddRecExprPHI(&PN, TempIncV, L))
// Stop if we have found an exact match SCEV.
if (IsMatchingSCEV) {
IncV = TempIncV;
TruncTy = nullptr;
InvertStep = false;
AddRecPhiMatch = &PN;
// Try whether the phi can be translated into the requested form
// (truncated and/or offset by a constant).
if ((!TruncTy || InvertStep) &&
canBeCheaplyTransformed(SE, PhiSCEV, Normalized, InvertStep)) {
// Record the phi node. But don't stop we might find an exact match
// later.
AddRecPhiMatch = &PN;
IncV = TempIncV;
TruncTy = Normalized->getType();
if (AddRecPhiMatch) {
// Ok, the add recurrence looks usable.
// Remember this PHI, even in post-inc mode.
// Remember the increment.
// Those values were not actually inserted but re-used.
return AddRecPhiMatch;
// Save the original insertion point so we can restore it when we're done.
SCEVInsertPointGuard Guard(Builder, this);
// Another AddRec may need to be recursively expanded below. For example, if
// this AddRec is quadratic, the StepV may itself be an AddRec in this
// loop. Remove this loop from the PostIncLoops set before expanding such
// AddRecs. Otherwise, we cannot find a valid position for the step
// (i.e. StepV can never dominate its loop header). Ideally, we could do
// SavedIncLoops.swap(PostIncLoops), but we generally have a single element,
// so it's not worth implementing SmallPtrSet::swap.
PostIncLoopSet SavedPostIncLoops = PostIncLoops;
// Expand code for the start value into the loop preheader.
assert(L->getLoopPreheader() &&
"Can't expand add recurrences without a loop preheader!");
Value *StartV =
expand(Normalized->getStart(), L->getLoopPreheader()->getTerminator());
// StartV must have been be inserted into L's preheader to dominate the new
// phi.
assert(!isa<Instruction>(StartV) ||
// Expand code for the step value. Do this before creating the PHI so that PHI
// reuse code doesn't see an incomplete PHI.
const SCEV *Step = Normalized->getStepRecurrence(SE);
Type *ExpandTy = Normalized->getType();
// If the stride is negative, insert a sub instead of an add for the increment
// (unless it's a constant, because subtracts of constants are canonicalized
// to adds).
bool useSubtract = !ExpandTy->isPointerTy() && Step->isNonConstantNegative();
if (useSubtract)
Step = SE.getNegativeSCEV(Step);
// Expand the step somewhere that dominates the loop header.
Value *StepV = expand(Step, L->getHeader()->getFirstInsertionPt());
// The no-wrap behavior proved by IsIncrement(NUW|NSW) is only applicable if
// we actually do emit an addition. It does not apply if we emit a
// subtraction.
bool IncrementIsNUW = !useSubtract && IsIncrementNUW(SE, Normalized);
bool IncrementIsNSW = !useSubtract && IsIncrementNSW(SE, Normalized);
// Create the PHI.
BasicBlock *Header = L->getHeader();
Builder.SetInsertPoint(Header, Header->begin());
PHINode *PN =
Builder.CreatePHI(ExpandTy, pred_size(Header), Twine(IVName) + ".iv");
// Create the step instructions and populate the PHI.
for (BasicBlock *Pred : predecessors(Header)) {
// Add a start value.
if (!L->contains(Pred)) {
PN->addIncoming(StartV, Pred);
// Create a step value and add it to the PHI.
// If IVIncInsertLoop is non-null and equal to the addrec's loop, insert the
// instructions at IVIncInsertPos.
Instruction *InsertPos = L == IVIncInsertLoop ?
IVIncInsertPos : Pred->getTerminator();
Value *IncV = expandIVInc(PN, StepV, L, useSubtract);
if (isa<OverflowingBinaryOperator>(IncV)) {
if (IncrementIsNUW)
if (IncrementIsNSW)
PN->addIncoming(IncV, Pred);
// After expanding subexpressions, restore the PostIncLoops set so the caller
// can ensure that IVIncrement dominates the current uses.
PostIncLoops = SavedPostIncLoops;
// Remember this PHI, even in post-inc mode. LSR SCEV-based salvaging is most
// effective when we are able to use an IV inserted here, so record it.
return PN;
Value *SCEVExpander::expandAddRecExprLiterally(const SCEVAddRecExpr *S) {
const Loop *L = S->getLoop();
// Determine a normalized form of this expression, which is the expression
// before any post-inc adjustment is made.
const SCEVAddRecExpr *Normalized = S;
if (PostIncLoops.count(L)) {
PostIncLoopSet Loops;
Normalized = cast<SCEVAddRecExpr>(
normalizeForPostIncUse(S, Loops, SE, /*CheckInvertible=*/false));
[[maybe_unused]] const SCEV *Start = Normalized->getStart();
const SCEV *Step = Normalized->getStepRecurrence(SE);
assert(SE.properlyDominates(Start, L->getHeader()) &&
"Start does not properly dominate loop header");
assert(SE.dominates(Step, L->getHeader()) && "Step not dominate loop header");
// In some cases, we decide to reuse an existing phi node but need to truncate
// it and/or invert the step.
Type *TruncTy = nullptr;
bool InvertStep = false;
PHINode *PN = getAddRecExprPHILiterally(Normalized, L, TruncTy, InvertStep);
// Accommodate post-inc mode, if necessary.
Value *Result;
if (!PostIncLoops.count(L))
Result = PN;
else {
// In PostInc mode, use the post-incremented value.
BasicBlock *LatchBlock = L->getLoopLatch();
assert(LatchBlock && "PostInc mode requires a unique loop latch!");
Result = PN->getIncomingValueForBlock(LatchBlock);
// We might be introducing a new use of the post-inc IV that is not poison
// safe, in which case we should drop poison generating flags. Only keep
// those flags for which SCEV has proven that they always hold.
if (isa<OverflowingBinaryOperator>(Result)) {
auto *I = cast<Instruction>(Result);
if (!S->hasNoUnsignedWrap())
if (!S->hasNoSignedWrap())
// For an expansion to use the postinc form, the client must call
// expandCodeFor with an InsertPoint that is either outside the PostIncLoop
// or dominated by IVIncInsertPos.
if (isa<Instruction>(Result) &&
&*Builder.GetInsertPoint())) {
// The induction variable's postinc expansion does not dominate this use.
// IVUsers tries to prevent this case, so it is rare. However, it can
// happen when an IVUser outside the loop is not dominated by the latch
// block. Adjusting IVIncInsertPos before expansion begins cannot handle
// all cases. Consider a phi outside whose operand is replaced during
// expansion with the value of the postinc user. Without fundamentally
// changing the way postinc users are tracked, the only remedy is
// inserting an extra IV increment. StepV might fold into PostLoopOffset,
// but hopefully expandCodeFor handles that.
bool useSubtract =
!S->getType()->isPointerTy() && Step->isNonConstantNegative();
if (useSubtract)
Step = SE.getNegativeSCEV(Step);
Value *StepV;
// Expand the step somewhere that dominates the loop header.
SCEVInsertPointGuard Guard(Builder, this);
StepV = expand(Step, L->getHeader()->getFirstInsertionPt());
Result = expandIVInc(PN, StepV, L, useSubtract);
// We have decided to reuse an induction variable of a dominating loop. Apply
// truncation and/or inversion of the step.
if (TruncTy) {
// Truncate the result.
if (TruncTy != Result->getType())
Result = Builder.CreateTrunc(Result, TruncTy);
// Invert the result.
if (InvertStep)
Result = Builder.CreateSub(expand(Normalized->getStart()), Result);
return Result;
Value *SCEVExpander::visitAddRecExpr(const SCEVAddRecExpr *S) {
// In canonical mode we compute the addrec as an expression of a canonical IV
// using evaluateAtIteration and expand the resulting SCEV expression. This
// way we avoid introducing new IVs to carry on the computation of the addrec
// throughout the loop.
// For nested addrecs evaluateAtIteration might need a canonical IV of a
// type wider than the addrec itself. Emitting a canonical IV of the
// proper type might produce non-legal types, for example expanding an i64
// {0,+,2,+,1} addrec would need an i65 canonical IV. To avoid this just fall
// back to non-canonical mode for nested addrecs.
if (!CanonicalMode || (S->getNumOperands() > 2))
return expandAddRecExprLiterally(S);
Type *Ty = SE.getEffectiveSCEVType(S->getType());
const Loop *L = S->getLoop();
// First check for an existing canonical IV in a suitable type.
PHINode *CanonicalIV = nullptr;
if (PHINode *PN = L->getCanonicalInductionVariable())
if (SE.getTypeSizeInBits(PN->getType()) >= SE.getTypeSizeInBits(Ty))
CanonicalIV = PN;
// Rewrite an AddRec in terms of the canonical induction variable, if
// its type is more narrow.
if (CanonicalIV &&
SE.getTypeSizeInBits(CanonicalIV->getType()) > SE.getTypeSizeInBits(Ty) &&
!S->getType()->isPointerTy()) {
SmallVector<const SCEV *, 4> NewOps(S->getNumOperands());
for (unsigned i = 0, e = S->getNumOperands(); i != e; ++i)
NewOps[i] = SE.getAnyExtendExpr(S->getOperand(i), CanonicalIV->getType());
Value *V = expand(SE.getAddRecExpr(NewOps, S->getLoop(),
BasicBlock::iterator NewInsertPt =
findInsertPointAfter(cast<Instruction>(V), &*Builder.GetInsertPoint());
V = expand(SE.getTruncateExpr(SE.getUnknown(V), Ty), NewInsertPt);
return V;
// {X,+,F} --> X + {0,+,F}
if (!S->getStart()->isZero()) {
if (isa<PointerType>(S->getType())) {
Value *StartV = expand(SE.getPointerBase(S));
return expandAddToGEP(SE.removePointerBase(S), StartV);
SmallVector<const SCEV *, 4> NewOps(S->operands());
NewOps[0] = SE.getConstant(Ty, 0);
const SCEV *Rest = SE.getAddRecExpr(NewOps, L,
// Just do a normal add. Pre-expand the operands to suppress folding.
// The LHS and RHS values are factored out of the expand call to make the
// output independent of the argument evaluation order.
const SCEV *AddExprLHS = SE.getUnknown(expand(S->getStart()));
const SCEV *AddExprRHS = SE.getUnknown(expand(Rest));
return expand(SE.getAddExpr(AddExprLHS, AddExprRHS));
// If we don't yet have a canonical IV, create one.
if (!CanonicalIV) {
// Create and insert the PHI node for the induction variable in the
// specified loop.
BasicBlock *Header = L->getHeader();
pred_iterator HPB = pred_begin(Header), HPE = pred_end(Header);
CanonicalIV = PHINode::Create(Ty, std::distance(HPB, HPE), "indvar");
SmallSet<BasicBlock *, 4> PredSeen;
Constant *One = ConstantInt::get(Ty, 1);
for (pred_iterator HPI = HPB; HPI != HPE; ++HPI) {
BasicBlock *HP = *HPI;
if (!PredSeen.insert(HP).second) {
// There must be an incoming value for each predecessor, even the
// duplicates!
CanonicalIV->addIncoming(CanonicalIV->getIncomingValueForBlock(HP), HP);
if (L->contains(HP)) {
// Insert a unit add instruction right before the terminator
// corresponding to the back-edge.
Instruction *Add = BinaryOperator::CreateAdd(CanonicalIV, One,
CanonicalIV->addIncoming(Add, HP);
} else {
CanonicalIV->addIncoming(Constant::getNullValue(Ty), HP);
// {0,+,1} --> Insert a canonical induction variable into the loop!
if (S->isAffine() && S->getOperand(1)->isOne()) {
assert(Ty == SE.getEffectiveSCEVType(CanonicalIV->getType()) &&
"IVs with types different from the canonical IV should "
"already have been handled!");
return CanonicalIV;
// {0,+,F} --> {0,+,1} * F
// If this is a simple linear addrec, emit it now as a special case.
if (S->isAffine()) // {0,+,F} --> i*F
// If this is a chain of recurrences, turn it into a closed form, using the
// folders, then expandCodeFor the closed form. This allows the folders to
// simplify the expression without having to build a bunch of special code
// into this folder.
const SCEV *IH = SE.getUnknown(CanonicalIV); // Get I as a "symbolic" SCEV.
// Promote S up to the canonical IV type, if the cast is foldable.
const SCEV *NewS = S;
const SCEV *Ext = SE.getNoopOrAnyExtend(S, CanonicalIV->getType());
if (isa<SCEVAddRecExpr>(Ext))
NewS = Ext;
const SCEV *V = cast<SCEVAddRecExpr>(NewS)->evaluateAtIteration(IH, SE);
// Truncate the result down to the original type, if needed.
const SCEV *T = SE.getTruncateOrNoop(V, Ty);
return expand(T);
Value *SCEVExpander::visitPtrToIntExpr(const SCEVPtrToIntExpr *S) {
Value *V = expand(S->getOperand());
return ReuseOrCreateCast(V, S->getType(), CastInst::PtrToInt,
Value *SCEVExpander::visitTruncateExpr(const SCEVTruncateExpr *S) {
Value *V = expand(S->getOperand());
return Builder.CreateTrunc(V, S->getType());
Value *SCEVExpander::visitZeroExtendExpr(const SCEVZeroExtendExpr *S) {
Value *V = expand(S->getOperand());
return Builder.CreateZExt(V, S->getType(), "",
Value *SCEVExpander::visitSignExtendExpr(const SCEVSignExtendExpr *S) {
Value *V = expand(S->getOperand());
return Builder.CreateSExt(V, S->getType());
Value *SCEVExpander::expandMinMaxExpr(const SCEVNAryExpr *S,
Intrinsic::ID IntrinID, Twine Name,
bool IsSequential) {
Value *LHS = expand(S->getOperand(S->getNumOperands() - 1));
Type *Ty = LHS->getType();
if (IsSequential)
LHS = Builder.CreateFreeze(LHS);
for (int i = S->getNumOperands() - 2; i >= 0; --i) {
Value *RHS = expand(S->getOperand(i));
if (IsSequential && i != 0)
RHS = Builder.CreateFreeze(RHS);
Value *Sel;
if (Ty->isIntegerTy())
Sel = Builder.CreateIntrinsic(IntrinID, {Ty}, {LHS, RHS},
/*FMFSource=*/nullptr, Name);
else {
Value *ICmp =
Builder.CreateICmp(MinMaxIntrinsic::getPredicate(IntrinID), LHS, RHS);
Sel = Builder.CreateSelect(ICmp, LHS, RHS, Name);
LHS = Sel;
return LHS;
Value *SCEVExpander::visitSMaxExpr(const SCEVSMaxExpr *S) {
return expandMinMaxExpr(S, Intrinsic::smax, "smax");
Value *SCEVExpander::visitUMaxExpr(const SCEVUMaxExpr *S) {
return expandMinMaxExpr(S, Intrinsic::umax, "umax");
Value *SCEVExpander::visitSMinExpr(const SCEVSMinExpr *S) {
return expandMinMaxExpr(S, Intrinsic::smin, "smin");
Value *SCEVExpander::visitUMinExpr(const SCEVUMinExpr *S) {
return expandMinMaxExpr(S, Intrinsic::umin, "umin");
Value *SCEVExpander::visitSequentialUMinExpr(const SCEVSequentialUMinExpr *S) {
return expandMinMaxExpr(S, Intrinsic::umin, "umin", /*IsSequential*/true);
Value *SCEVExpander::visitVScale(const SCEVVScale *S) {
return Builder.CreateVScale(ConstantInt::get(S->getType(), 1));
Value *SCEVExpander::expandCodeFor(const SCEV *SH, Type *Ty,
BasicBlock::iterator IP) {
Value *V = expandCodeFor(SH, Ty);
return V;
Value *SCEVExpander::expandCodeFor(const SCEV *SH, Type *Ty) {
// Expand the code for this SCEV.
Value *V = expand(SH);
if (Ty) {
assert(SE.getTypeSizeInBits(Ty) == SE.getTypeSizeInBits(SH->getType()) &&
"non-trivial casts should be done with the SCEVs directly!");
V = InsertNoopCastOfTo(V, Ty);
return V;
Value *SCEVExpander::FindValueInExprValueMap(
const SCEV *S, const Instruction *InsertPt,
SmallVectorImpl<Instruction *> &DropPoisonGeneratingInsts) {
// If the expansion is not in CanonicalMode, and the SCEV contains any
// sub scAddRecExpr type SCEV, it is required to expand the SCEV literally.
if (!CanonicalMode && SE.containsAddRecurrence(S))
return nullptr;
// If S is a constant, it may be worse to reuse an existing Value.
if (isa<SCEVConstant>(S))
return nullptr;
for (Value *V : SE.getSCEVValues(S)) {
Instruction *EntInst = dyn_cast<Instruction>(V);
if (!EntInst)
// Choose a Value from the set which dominates the InsertPt.
// InsertPt should be inside the Value's parent loop so as not to break
// the LCSSA form.
assert(EntInst->getFunction() == InsertPt->getFunction());
if (S->getType() != V->getType() || !SE.DT.dominates(EntInst, InsertPt) ||
!(SE.LI.getLoopFor(EntInst->getParent()) == nullptr ||
// Make sure reusing the instruction is poison-safe.
if (SE.canReuseInstruction(S, EntInst, DropPoisonGeneratingInsts))
return V;
return nullptr;
// The expansion of SCEV will either reuse a previous Value in ExprValueMap,
// or expand the SCEV literally. Specifically, if the expansion is in LSRMode,
// and the SCEV contains any sub scAddRecExpr type SCEV, it will be expanded
// literally, to prevent LSR's transformed SCEV from being reverted. Otherwise,
// the expansion will try to reuse Value from ExprValueMap, and only when it
// fails, expand the SCEV literally.
Value *SCEVExpander::expand(const SCEV *S) {
// Compute an insertion point for this SCEV object. Hoist the instructions
// as far out in the loop nest as possible.
BasicBlock::iterator InsertPt = Builder.GetInsertPoint();
// We can move insertion point only if there is no div or rem operations
// otherwise we are risky to move it over the check for zero denominator.
auto SafeToHoist = [](const SCEV *S) {
return !SCEVExprContains(S, [](const SCEV *S) {
if (const auto *D = dyn_cast<SCEVUDivExpr>(S)) {
if (const auto *SC = dyn_cast<SCEVConstant>(D->getRHS()))
// Division by non-zero constants can be hoisted.
return SC->getValue()->isZero();
// All other divisions should not be moved as they may be
// divisions by zero and should be kept within the
// conditions of the surrounding loops that guard their
// execution (see PR35406).
return true;
return false;
if (SafeToHoist(S)) {
for (Loop *L = SE.LI.getLoopFor(Builder.GetInsertBlock());;
L = L->getParentLoop()) {
if (SE.isLoopInvariant(S, L)) {
if (!L) break;
if (BasicBlock *Preheader = L->getLoopPreheader()) {
InsertPt = Preheader->getTerminator()->getIterator();
} else {
// LSR sets the insertion point for AddRec start/step values to the
// block start to simplify value reuse, even though it's an invalid
// position. SCEVExpander must correct for this in all cases.
InsertPt = L->getHeader()->getFirstInsertionPt();
} else {
// If the SCEV is computable at this level, insert it into the header
// after the PHIs (and after any other instructions that we've inserted
// there) so that it is guaranteed to dominate any user inside the loop.
if (L && SE.hasComputableLoopEvolution(S, L) && !PostIncLoops.count(L))
InsertPt = L->getHeader()->getFirstInsertionPt();
while (InsertPt != Builder.GetInsertPoint() &&
(isInsertedInstruction(&*InsertPt) ||
isa<DbgInfoIntrinsic>(&*InsertPt))) {
InsertPt = std::next(InsertPt);
// Check to see if we already expanded this here.
auto I = InsertedExpressions.find(std::make_pair(S, &*InsertPt));
if (I != InsertedExpressions.end())
return I->second;
SCEVInsertPointGuard Guard(Builder, this);
Builder.SetInsertPoint(InsertPt->getParent(), InsertPt);
// Expand the expression into instructions.
SmallVector<Instruction *> DropPoisonGeneratingInsts;
Value *V = FindValueInExprValueMap(S, &*InsertPt, DropPoisonGeneratingInsts);
if (!V) {
V = visit(S);
V = fixupLCSSAFormFor(V);
} else {
for (Instruction *I : DropPoisonGeneratingInsts) {
// See if we can re-infer from first principles any of the flags we just
// dropped.
if (auto *OBO = dyn_cast<OverflowingBinaryOperator>(I))
if (auto Flags = SE.getStrengthenedNoWrapFlagsFromBinOp(OBO)) {
auto *BO = cast<BinaryOperator>(I);
ScalarEvolution::maskFlags(*Flags, SCEV::FlagNUW) == SCEV::FlagNUW);
ScalarEvolution::maskFlags(*Flags, SCEV::FlagNSW) == SCEV::FlagNSW);
if (auto *NNI = dyn_cast<PossiblyNonNegInst>(I)) {
auto *Src = NNI->getOperand(0);
if (isImpliedByDomCondition(ICmpInst::ICMP_SGE, Src,
Constant::getNullValue(Src->getType()), I,
// Remember the expanded value for this SCEV at this location.
// This is independent of PostIncLoops. The mapped value simply materializes
// the expression at this insertion point. If the mapped value happened to be
// a postinc expansion, it could be reused by a non-postinc user, but only if
// its insertion point was already at the head of the loop.
InsertedExpressions[std::make_pair(S, &*InsertPt)] = V;
return V;
void SCEVExpander::rememberInstruction(Value *I) {
auto DoInsert = [this](Value *V) {
if (!PostIncLoops.empty())
void SCEVExpander::rememberFlags(Instruction *I) {
// If we already have flags for the instruction, keep the existing ones.
OrigFlags.try_emplace(I, PoisonFlags(I));
void SCEVExpander::replaceCongruentIVInc(
PHINode *&Phi, PHINode *&OrigPhi, Loop *L, const DominatorTree *DT,
SmallVectorImpl<WeakTrackingVH> &DeadInsts) {
BasicBlock *LatchBlock = L->getLoopLatch();
if (!LatchBlock)
Instruction *OrigInc =
Instruction *IsomorphicInc =
if (!OrigInc || !IsomorphicInc)
// If this phi has the same width but is more canonical, replace the
// original with it. As part of the "more canonical" determination,
// respect a prior decision to use an IV chain.
if (OrigPhi->getType() == Phi->getType() &&
!(ChainedPhis.count(Phi) ||
isExpandedAddRecExprPHI(OrigPhi, OrigInc, L)) &&
(ChainedPhis.count(Phi) ||
isExpandedAddRecExprPHI(Phi, IsomorphicInc, L))) {
std::swap(OrigPhi, Phi);
std::swap(OrigInc, IsomorphicInc);
// Replacing the congruent phi is sufficient because acyclic
// redundancy elimination, CSE/GVN, should handle the
// rest. However, once SCEV proves that a phi is congruent,
// it's often the head of an IV user cycle that is isomorphic
// with the original phi. It's worth eagerly cleaning up the
// common case of a single IV increment so that DeleteDeadPHIs
// can remove cycles that had postinc uses.
// Because we may potentially introduce a new use of OrigIV that didn't
// exist before at this point, its poison flags need readjustment.
const SCEV *TruncExpr =
SE.getTruncateOrNoop(SE.getSCEV(OrigInc), IsomorphicInc->getType());
if (OrigInc == IsomorphicInc || TruncExpr != SE.getSCEV(IsomorphicInc) ||
!SE.LI.replacementPreservesLCSSAForm(IsomorphicInc, OrigInc))
bool BothHaveNUW = false;
bool BothHaveNSW = false;
auto *OBOIncV = dyn_cast<OverflowingBinaryOperator>(OrigInc);
auto *OBOIsomorphic = dyn_cast<OverflowingBinaryOperator>(IsomorphicInc);
if (OBOIncV && OBOIsomorphic) {
BothHaveNUW =
OBOIncV->hasNoUnsignedWrap() && OBOIsomorphic->hasNoUnsignedWrap();
BothHaveNSW =
OBOIncV->hasNoSignedWrap() && OBOIsomorphic->hasNoSignedWrap();
if (!hoistIVInc(OrigInc, IsomorphicInc,
/*RecomputePoisonFlags*/ true))
// We are replacing with a wider increment. If both OrigInc and IsomorphicInc
// are NUW/NSW, then we can preserve them on the wider increment; the narrower
// IsomorphicInc would wrap before the wider OrigInc, so the replacement won't
// make IsomorphicInc's uses more poisonous.
assert(OrigInc->getType()->getScalarSizeInBits() >=
IsomorphicInc->getType()->getScalarSizeInBits() &&
"Should only replace an increment with a wider one.");
if (BothHaveNUW || BothHaveNSW) {
OrigInc->setHasNoUnsignedWrap(OBOIncV->hasNoUnsignedWrap() || BothHaveNUW);
OrigInc->setHasNoSignedWrap(OBOIncV->hasNoSignedWrap() || BothHaveNSW);
dbgs() << "INDVARS: Eliminated congruent "
<< *IsomorphicInc << '\n');
Value *NewInc = OrigInc;
if (OrigInc->getType() != IsomorphicInc->getType()) {
BasicBlock::iterator IP;
if (PHINode *PN = dyn_cast<PHINode>(OrigInc))
IP = PN->getParent()->getFirstInsertionPt();
IP = OrigInc->getNextNonDebugInstruction()->getIterator();
IRBuilder<> Builder(IP->getParent(), IP);
NewInc =
Builder.CreateTruncOrBitCast(OrigInc, IsomorphicInc->getType(), IVName);
/// replaceCongruentIVs - Check for congruent phis in this loop header and
/// replace them with their most canonical representative. Return the number of
/// phis eliminated.
/// This does not depend on any SCEVExpander state but should be used in
/// the same context that SCEVExpander is used.
SCEVExpander::replaceCongruentIVs(Loop *L, const DominatorTree *DT,
SmallVectorImpl<WeakTrackingVH> &DeadInsts,
const TargetTransformInfo *TTI) {
// Find integer phis in order of increasing width.
SmallVector<PHINode*, 8> Phis;
for (PHINode &PN : L->getHeader()->phis())
if (TTI)
// Use stable_sort to preserve order of equivalent PHIs, so the order
// of the sorted Phis is the same from run to run on the same loop.
llvm::stable_sort(Phis, [](Value *LHS, Value *RHS) {
// Put pointers at the back and make sure pointer < pointer = false.
if (!LHS->getType()->isIntegerTy() || !RHS->getType()->isIntegerTy())
return RHS->getType()->isIntegerTy() && !LHS->getType()->isIntegerTy();
return RHS->getType()->getPrimitiveSizeInBits().getFixedValue() <
unsigned NumElim = 0;
DenseMap<const SCEV *, PHINode *> ExprToIVMap;
// Process phis from wide to narrow. Map wide phis to their truncation
// so narrow phis can reuse them.
for (PHINode *Phi : Phis) {
auto SimplifyPHINode = [&](PHINode *PN) -> Value * {
if (Value *V = simplifyInstruction(PN, {DL, &SE.TLI, &SE.DT, &SE.AC}))
return V;
if (!SE.isSCEVable(PN->getType()))
return nullptr;
auto *Const = dyn_cast<SCEVConstant>(SE.getSCEV(PN));
if (!Const)
return nullptr;
return Const->getValue();
// Fold constant phis. They may be congruent to other constant phis and
// would confuse the logic below that expects proper IVs.
if (Value *V = SimplifyPHINode(Phi)) {
if (V->getType() != Phi->getType())
dbgs() << "INDVARS: Eliminated constant iv: " << *Phi
<< '\n');
if (!SE.isSCEVable(Phi->getType()))
PHINode *&OrigPhiRef = ExprToIVMap[SE.getSCEV(Phi)];
if (!OrigPhiRef) {
OrigPhiRef = Phi;
if (Phi->getType()->isIntegerTy() && TTI &&
TTI->isTruncateFree(Phi->getType(), Phis.back()->getType())) {
// Make sure we only rewrite using simple induction variables;
// otherwise, we can make the trip count of a loop unanalyzable
// to SCEV.
const SCEV *PhiExpr = SE.getSCEV(Phi);
if (isa<SCEVAddRecExpr>(PhiExpr)) {
// This phi can be freely truncated to the narrowest phi type. Map the
// truncated expression to it so it will be reused for narrow types.
const SCEV *TruncExpr =
SE.getTruncateExpr(PhiExpr, Phis.back()->getType());
ExprToIVMap[TruncExpr] = Phi;
// Replacing a pointer phi with an integer phi or vice-versa doesn't make
// sense.
if (OrigPhiRef->getType()->isPointerTy() != Phi->getType()->isPointerTy())
replaceCongruentIVInc(Phi, OrigPhiRef, L, DT, DeadInsts);
dbgs() << "INDVARS: Eliminated congruent iv: " << *Phi
<< '\n');
DebugType, dbgs() << "INDVARS: Original iv: " << *OrigPhiRef << '\n');
Value *NewIV = OrigPhiRef;
if (OrigPhiRef->getType() != Phi->getType()) {
IRBuilder<> Builder(L->getHeader(),
NewIV = Builder.CreateTruncOrBitCast(OrigPhiRef, Phi->getType(), IVName);
return NumElim;
bool SCEVExpander::hasRelatedExistingExpansion(const SCEV *S,
const Instruction *At,
Loop *L) {
using namespace llvm::PatternMatch;
SmallVector<BasicBlock *, 4> ExitingBlocks;
// Look for suitable value in simple conditions at the loop exits.
for (BasicBlock *BB : ExitingBlocks) {
ICmpInst::Predicate Pred;
Instruction *LHS, *RHS;
if (!match(BB->getTerminator(),
m_Br(m_ICmp(Pred, m_Instruction(LHS), m_Instruction(RHS)),
m_BasicBlock(), m_BasicBlock())))
if (SE.getSCEV(LHS) == S && SE.DT.dominates(LHS, At))
return true;
if (SE.getSCEV(RHS) == S && SE.DT.dominates(RHS, At))
return true;
// Use expand's logic which is used for reusing a previous Value in
// ExprValueMap. Note that we don't currently model the cost of
// needing to drop poison generating flags on the instruction if we
// want to reuse it. We effectively assume that has zero cost.
SmallVector<Instruction *> DropPoisonGeneratingInsts;
return FindValueInExprValueMap(S, At, DropPoisonGeneratingInsts) != nullptr;
template<typename T> static InstructionCost costAndCollectOperands(
const SCEVOperand &WorkItem, const TargetTransformInfo &TTI,
TargetTransformInfo::TargetCostKind CostKind,
SmallVectorImpl<SCEVOperand> &Worklist) {
const T *S = cast<T>(WorkItem.S);
InstructionCost Cost = 0;
// Object to help map SCEV operands to expanded IR instructions.
struct OperationIndices {
OperationIndices(unsigned Opc, size_t min, size_t max) :
Opcode(Opc), MinIdx(min), MaxIdx(max) { }
unsigned Opcode;
size_t MinIdx;
size_t MaxIdx;
// Collect the operations of all the instructions that will be needed to
// expand the SCEVExpr. This is so that when we come to cost the operands,
// we know what the generated user(s) will be.
SmallVector<OperationIndices, 2> Operations;
auto CastCost = [&](unsigned Opcode) -> InstructionCost {
Operations.emplace_back(Opcode, 0, 0);
return TTI.getCastInstrCost(Opcode, S->getType(),
TTI::CastContextHint::None, CostKind);
auto ArithCost = [&](unsigned Opcode, unsigned NumRequired,
unsigned MinIdx = 0,
unsigned MaxIdx = 1) -> InstructionCost {
Operations.emplace_back(Opcode, MinIdx, MaxIdx);
return NumRequired *
TTI.getArithmeticInstrCost(Opcode, S->getType(), CostKind);
auto CmpSelCost = [&](unsigned Opcode, unsigned NumRequired, unsigned MinIdx,
unsigned MaxIdx) -> InstructionCost {
Operations.emplace_back(Opcode, MinIdx, MaxIdx);
Type *OpType = S->getType();
return NumRequired * TTI.getCmpSelInstrCost(
Opcode, OpType, CmpInst::makeCmpResultType(OpType),
switch (S->getSCEVType()) {
case scCouldNotCompute:
llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
case scUnknown:
case scConstant:
case scVScale:
return 0;
case scPtrToInt:
Cost = CastCost(Instruction::PtrToInt);
case scTruncate:
Cost = CastCost(Instruction::Trunc);
case scZeroExtend:
Cost = CastCost(Instruction::ZExt);
case scSignExtend:
Cost = CastCost(Instruction::SExt);
case scUDivExpr: {
unsigned Opcode = Instruction::UDiv;
if (auto *SC = dyn_cast<SCEVConstant>(S->getOperand(1)))
if (SC->getAPInt().isPowerOf2())
Opcode = Instruction::LShr;
Cost = ArithCost(Opcode, 1);
case scAddExpr:
Cost = ArithCost(Instruction::Add, S->getNumOperands() - 1);
case scMulExpr:
// TODO: this is a very pessimistic cost modelling for Mul,
// because of Bin Pow algorithm actually used by the expander,
// see SCEVExpander::visitMulExpr(), ExpandOpBinPowN().
Cost = ArithCost(Instruction::Mul, S->getNumOperands() - 1);
case scSMaxExpr:
case scUMaxExpr:
case scSMinExpr:
case scUMinExpr:
case scSequentialUMinExpr: {
// FIXME: should this ask the cost for Intrinsic's?
// The reduction tree.
Cost += CmpSelCost(Instruction::ICmp, S->getNumOperands() - 1, 0, 1);
Cost += CmpSelCost(Instruction::Select, S->getNumOperands() - 1, 0, 2);
switch (S->getSCEVType()) {
case scSequentialUMinExpr: {
// The safety net against poison.
// FIXME: this is broken.
Cost += CmpSelCost(Instruction::ICmp, S->getNumOperands() - 1, 0, 0);
Cost += ArithCost(Instruction::Or,
S->getNumOperands() > 2 ? S->getNumOperands() - 2 : 0);
Cost += CmpSelCost(Instruction::Select, 1, 0, 1);
assert(!isa<SCEVSequentialMinMaxExpr>(S) &&
"Unhandled SCEV expression type?");
case scAddRecExpr: {
// In this polynominal, we may have some zero operands, and we shouldn't
// really charge for those. So how many non-zero coefficients are there?
int NumTerms = llvm::count_if(S->operands(), [](const SCEV *Op) {
return !Op->isZero();
assert(NumTerms >= 1 && "Polynominal should have at least one term.");
assert(!(*std::prev(S->operands().end()))->isZero() &&
"Last operand should not be zero");
// Ignoring constant term (operand 0), how many of the coefficients are u> 1?
int NumNonZeroDegreeNonOneTerms =
llvm::count_if(S->operands(), [](const SCEV *Op) {
auto *SConst = dyn_cast<SCEVConstant>(Op);
return !SConst || SConst->getAPInt().ugt(1);
// Much like with normal add expr, the polynominal will require
// one less addition than the number of it's terms.
InstructionCost AddCost = ArithCost(Instruction::Add, NumTerms - 1,
/*MinIdx*/ 1, /*MaxIdx*/ 1);
// Here, *each* one of those will require a multiplication.
InstructionCost MulCost =
ArithCost(Instruction::Mul, NumNonZeroDegreeNonOneTerms);
Cost = AddCost + MulCost;
// What is the degree of this polynominal?
int PolyDegree = S->getNumOperands() - 1;
assert(PolyDegree >= 1 && "Should be at least affine.");
// The final term will be:
// Op_{PolyDegree} * x ^ {PolyDegree}
// Where x ^ {PolyDegree} will again require PolyDegree-1 mul operations.
// Note that x ^ {PolyDegree} = x * x ^ {PolyDegree-1} so charging for
// x ^ {PolyDegree} will give us x ^ {2} .. x ^ {PolyDegree-1} for free.
// FIXME: this is conservatively correct, but might be overly pessimistic.
Cost += MulCost * (PolyDegree - 1);
for (auto &CostOp : Operations) {
for (auto SCEVOp : enumerate(S->operands())) {
// Clamp the index to account for multiple IR operations being chained.
size_t MinIdx = std::max(SCEVOp.index(), CostOp.MinIdx);
size_t OpIdx = std::min(MinIdx, CostOp.MaxIdx);
Worklist.emplace_back(CostOp.Opcode, OpIdx, SCEVOp.value());
return Cost;
bool SCEVExpander::isHighCostExpansionHelper(
const SCEVOperand &WorkItem, Loop *L, const Instruction &At,
InstructionCost &Cost, unsigned Budget, const TargetTransformInfo &TTI,
SmallPtrSetImpl<const SCEV *> &Processed,
SmallVectorImpl<SCEVOperand> &Worklist) {
if (Cost > Budget)
return true; // Already run out of budget, give up.
const SCEV *S = WorkItem.S;
// Was the cost of expansion of this expression already accounted for?
if (!isa<SCEVConstant>(S) && !Processed.insert(S).second)
return false; // We have already accounted for this expression.
// If we can find an existing value for this scev available at the point "At"
// then consider the expression cheap.
if (hasRelatedExistingExpansion(S, &At, L))
return false; // Consider the expression to be free.
TargetTransformInfo::TargetCostKind CostKind =
? TargetTransformInfo::TCK_CodeSize
: TargetTransformInfo::TCK_RecipThroughput;
switch (S->getSCEVType()) {
case scCouldNotCompute:
llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
case scUnknown:
case scVScale:
// Assume to be zero-cost.
return false;
case scConstant: {
// Only evalulate the costs of constants when optimizing for size.
if (CostKind != TargetTransformInfo::TCK_CodeSize)
return false;
const APInt &Imm = cast<SCEVConstant>(S)->getAPInt();
Type *Ty = S->getType();
Cost += TTI.getIntImmCostInst(
WorkItem.ParentOpcode, WorkItem.OperandIdx, Imm, Ty, CostKind);
return Cost > Budget;
case scTruncate:
case scPtrToInt:
case scZeroExtend:
case scSignExtend: {
Cost +=
costAndCollectOperands<SCEVCastExpr>(WorkItem, TTI, CostKind, Worklist);
return false; // Will answer upon next entry into this function.
case scUDivExpr: {
// UDivExpr is very likely a UDiv that ScalarEvolution's HowFarToZero or
// HowManyLessThans produced to compute a precise expression, rather than a
// UDiv from the user's code. If we can't find a UDiv in the code with some
// simple searching, we need to account for it's cost.
// At the beginning of this function we already tried to find existing
// value for plain 'S'. Now try to lookup 'S + 1' since it is common
// pattern involving division. This is just a simple search heuristic.
if (hasRelatedExistingExpansion(
SE.getAddExpr(S, SE.getConstant(S->getType(), 1)), &At, L))
return false; // Consider it to be free.
Cost +=
costAndCollectOperands<SCEVUDivExpr>(WorkItem, TTI, CostKind, Worklist);
return false; // Will answer upon next entry into this function.
case scAddExpr:
case scMulExpr:
case scUMaxExpr:
case scSMaxExpr:
case scUMinExpr:
case scSMinExpr:
case scSequentialUMinExpr: {
assert(cast<SCEVNAryExpr>(S)->getNumOperands() > 1 &&
"Nary expr should have more than 1 operand.");
// The simple nary expr will require one less op (or pair of ops)
// than the number of it's terms.
Cost +=
costAndCollectOperands<SCEVNAryExpr>(WorkItem, TTI, CostKind, Worklist);
return Cost > Budget;
case scAddRecExpr: {
assert(cast<SCEVAddRecExpr>(S)->getNumOperands() >= 2 &&
"Polynomial should be at least linear");
Cost += costAndCollectOperands<SCEVAddRecExpr>(
WorkItem, TTI, CostKind, Worklist);
return Cost > Budget;
llvm_unreachable("Unknown SCEV kind!");
Value *SCEVExpander::expandCodeForPredicate(const SCEVPredicate *Pred,
Instruction *IP) {
switch (Pred->getKind()) {
case SCEVPredicate::P_Union:
return expandUnionPredicate(cast<SCEVUnionPredicate>(Pred), IP);
case SCEVPredicate::P_Compare:
return expandComparePredicate(cast<SCEVComparePredicate>(Pred), IP);
case SCEVPredicate::P_Wrap: {
auto *AddRecPred = cast<SCEVWrapPredicate>(Pred);
return expandWrapPredicate(AddRecPred, IP);
llvm_unreachable("Unknown SCEV predicate type");
Value *SCEVExpander::expandComparePredicate(const SCEVComparePredicate *Pred,
Instruction *IP) {
Value *Expr0 = expand(Pred->getLHS(), IP);
Value *Expr1 = expand(Pred->getRHS(), IP);
auto InvPred = ICmpInst::getInversePredicate(Pred->getPredicate());
auto *I = Builder.CreateICmp(InvPred, Expr0, Expr1, "ident.check");
return I;
Value *SCEVExpander::generateOverflowCheck(const SCEVAddRecExpr *AR,
Instruction *Loc, bool Signed) {
assert(AR->isAffine() && "Cannot generate RT check for "
"non-affine expression");
// FIXME: It is highly suspicious that we're ignoring the predicates here.
SmallVector<const SCEVPredicate *, 4> Pred;
const SCEV *ExitCount =
SE.getPredicatedBackedgeTakenCount(AR->getLoop(), Pred);
assert(!isa<SCEVCouldNotCompute>(ExitCount) && "Invalid loop count");
const SCEV *Step = AR->getStepRecurrence(SE);
const SCEV *Start = AR->getStart();
Type *ARTy = AR->getType();
unsigned SrcBits = SE.getTypeSizeInBits(ExitCount->getType());
unsigned DstBits = SE.getTypeSizeInBits(ARTy);
// The expression {Start,+,Step} has nusw/nssw if
// Step < 0, Start - |Step| * Backedge <= Start
// Step >= 0, Start + |Step| * Backedge > Start
// and |Step| * Backedge doesn't unsigned overflow.
Value *TripCountVal = expand(ExitCount, Loc);
IntegerType *Ty =
IntegerType::get(Loc->getContext(), SE.getTypeSizeInBits(ARTy));
Value *StepValue = expand(Step, Loc);
Value *NegStepValue = expand(SE.getNegativeSCEV(Step), Loc);
Value *StartValue = expand(Start, Loc);
ConstantInt *Zero =
ConstantInt::get(Loc->getContext(), APInt::getZero(DstBits));
// Compute |Step|
Value *StepCompare = Builder.CreateICmp(ICmpInst::ICMP_SLT, StepValue, Zero);
Value *AbsStep = Builder.CreateSelect(StepCompare, NegStepValue, StepValue);
// Compute |Step| * Backedge
// Compute:
// 1. Start + |Step| * Backedge < Start
// 2. Start - |Step| * Backedge > Start
// And select either 1. or 2. depending on whether step is positive or
// negative. If Step is known to be positive or negative, only create
// either 1. or 2.
auto ComputeEndCheck = [&]() -> Value * {
// Checking <u 0 is always false.
if (!Signed && Start->isZero() && SE.isKnownPositive(Step))
return ConstantInt::getFalse(Loc->getContext());
// Get the backedge taken count and truncate or extended to the AR type.
Value *TruncTripCount = Builder.CreateZExtOrTrunc(TripCountVal, Ty);
Value *MulV, *OfMul;
if (Step->isOne()) {
// Special-case Step of one. Potentially-costly `umul_with_overflow` isn't
// needed, there is never an overflow, so to avoid artificially inflating
// the cost of the check, directly emit the optimized IR.
MulV = TruncTripCount;
OfMul = ConstantInt::getFalse(MulV->getContext());
} else {
auto *MulF = Intrinsic::getDeclaration(Loc->getModule(),
Intrinsic::umul_with_overflow, Ty);
CallInst *Mul =
Builder.CreateCall(MulF, {AbsStep, TruncTripCount}, "mul");
MulV = Builder.CreateExtractValue(Mul, 0, "mul.result");
OfMul = Builder.CreateExtractValue(Mul, 1, "mul.overflow");
Value *Add = nullptr, *Sub = nullptr;
bool NeedPosCheck = !SE.isKnownNegative(Step);
bool NeedNegCheck = !SE.isKnownPositive(Step);
if (isa<PointerType>(ARTy)) {
Value *NegMulV = Builder.CreateNeg(MulV);
if (NeedPosCheck)
Add = Builder.CreatePtrAdd(StartValue, MulV);
if (NeedNegCheck)
Sub = Builder.CreatePtrAdd(StartValue, NegMulV);
} else {
if (NeedPosCheck)
Add = Builder.CreateAdd(StartValue, MulV);
if (NeedNegCheck)
Sub = Builder.CreateSub(StartValue, MulV);
Value *EndCompareLT = nullptr;
Value *EndCompareGT = nullptr;
Value *EndCheck = nullptr;
if (NeedPosCheck)
EndCheck = EndCompareLT = Builder.CreateICmp(
Signed ? ICmpInst::ICMP_SLT : ICmpInst::ICMP_ULT, Add, StartValue);
if (NeedNegCheck)
EndCheck = EndCompareGT = Builder.CreateICmp(
Signed ? ICmpInst::ICMP_SGT : ICmpInst::ICMP_UGT, Sub, StartValue);
if (NeedPosCheck && NeedNegCheck) {
// Select the answer based on the sign of Step.
EndCheck = Builder.CreateSelect(StepCompare, EndCompareGT, EndCompareLT);
return Builder.CreateOr(EndCheck, OfMul);
Value *EndCheck = ComputeEndCheck();
// If the backedge taken count type is larger than the AR type,
// check that we don't drop any bits by truncating it. If we are
// dropping bits, then we have overflow (unless the step is zero).
if (SrcBits > DstBits) {
auto MaxVal = APInt::getMaxValue(DstBits).zext(SrcBits);
auto *BackedgeCheck =
Builder.CreateICmp(ICmpInst::ICMP_UGT, TripCountVal,
ConstantInt::get(Loc->getContext(), MaxVal));
BackedgeCheck = Builder.CreateAnd(
BackedgeCheck, Builder.CreateICmp(ICmpInst::ICMP_NE, StepValue, Zero));
EndCheck = Builder.CreateOr(EndCheck, BackedgeCheck);
return EndCheck;
Value *SCEVExpander::expandWrapPredicate(const SCEVWrapPredicate *Pred,
Instruction *IP) {
const auto *A = cast<SCEVAddRecExpr>(Pred->getExpr());
Value *NSSWCheck = nullptr, *NUSWCheck = nullptr;
// Add a check for NUSW
if (Pred->getFlags() & SCEVWrapPredicate::IncrementNUSW)
NUSWCheck = generateOverflowCheck(A, IP, false);
// Add a check for NSSW
if (Pred->getFlags() & SCEVWrapPredicate::IncrementNSSW)
NSSWCheck = generateOverflowCheck(A, IP, true);
if (NUSWCheck && NSSWCheck)
return Builder.CreateOr(NUSWCheck, NSSWCheck);
if (NUSWCheck)
return NUSWCheck;
if (NSSWCheck)
return NSSWCheck;
return ConstantInt::getFalse(IP->getContext());
Value *SCEVExpander::expandUnionPredicate(const SCEVUnionPredicate *Union,
Instruction *IP) {
// Loop over all checks in this set.
SmallVector<Value *> Checks;
for (const auto *Pred : Union->getPredicates()) {
Checks.push_back(expandCodeForPredicate(Pred, IP));
if (Checks.empty())
return ConstantInt::getFalse(IP->getContext());
return Builder.CreateOr(Checks);
Value *SCEVExpander::fixupLCSSAFormFor(Value *V) {
auto *DefI = dyn_cast<Instruction>(V);
if (!PreserveLCSSA || !DefI)
return V;
BasicBlock::iterator InsertPt = Builder.GetInsertPoint();
Loop *DefLoop = SE.LI.getLoopFor(DefI->getParent());
Loop *UseLoop = SE.LI.getLoopFor(InsertPt->getParent());
if (!DefLoop || UseLoop == DefLoop || DefLoop->contains(UseLoop))
return V;
// Create a temporary instruction to at the current insertion point, so we
// can hand it off to the helper to create LCSSA PHIs if required for the
// new use.
// FIXME: Ideally formLCSSAForInstructions (used in fixupLCSSAFormFor)
// would accept a insertion point and return an LCSSA phi for that
// insertion point, so there is no need to insert & remove the temporary
// instruction.
Type *ToTy;
if (DefI->getType()->isIntegerTy())
ToTy = PointerType::get(DefI->getContext(), 0);
ToTy = Type::getInt32Ty(DefI->getContext());
Instruction *User =
CastInst::CreateBitOrPointerCast(DefI, ToTy, "tmp.lcssa.user", InsertPt);
auto RemoveUserOnExit =
make_scope_exit([User]() { User->eraseFromParent(); });
SmallVector<Instruction *, 1> ToUpdate;
SmallVector<PHINode *, 16> PHIsToRemove;
SmallVector<PHINode *, 16> InsertedPHIs;
formLCSSAForInstructions(ToUpdate, SE.DT, SE.LI, &SE, &PHIsToRemove,
for (PHINode *PN : InsertedPHIs)
for (PHINode *PN : PHIsToRemove) {
if (!PN->use_empty())
return User->getOperand(0);
namespace {
// Search for a SCEV subexpression that is not safe to expand. Any expression
// that may expand to a !isSafeToSpeculativelyExecute value is unsafe, namely
// UDiv expressions. We don't know if the UDiv is derived from an IR divide
// instruction, but the important thing is that we prove the denominator is
// nonzero before expansion.
// IVUsers already checks that IV-derived expressions are safe. So this check is
// only needed when the expression includes some subexpression that is not IV
// derived.
// Currently, we only allow division by a value provably non-zero here.
// We cannot generally expand recurrences unless the step dominates the loop
// header. The expander handles the special case of affine recurrences by
// scaling the recurrence outside the loop, but this technique isn't generally
// applicable. Expanding a nested recurrence outside a loop requires computing
// binomial coefficients. This could be done, but the recurrence has to be in a
// perfectly reduced form, which can't be guaranteed.
struct SCEVFindUnsafe {
ScalarEvolution &SE;
bool CanonicalMode;
bool IsUnsafe = false;
SCEVFindUnsafe(ScalarEvolution &SE, bool CanonicalMode)
: SE(SE), CanonicalMode(CanonicalMode) {}
bool follow(const SCEV *S) {
if (const SCEVUDivExpr *D = dyn_cast<SCEVUDivExpr>(S)) {
if (!SE.isKnownNonZero(D->getRHS())) {
IsUnsafe = true;
return false;
if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(S)) {
// For non-affine addrecs or in non-canonical mode we need a preheader
// to insert into.
if (!AR->getLoop()->getLoopPreheader() &&
(!CanonicalMode || !AR->isAffine())) {
IsUnsafe = true;
return false;
return true;
bool isDone() const { return IsUnsafe; }
} // namespace
bool SCEVExpander::isSafeToExpand(const SCEV *S) const {
SCEVFindUnsafe Search(SE, CanonicalMode);
visitAll(S, Search);
return !Search.IsUnsafe;
bool SCEVExpander::isSafeToExpandAt(const SCEV *S,
const Instruction *InsertionPoint) const {
if (!isSafeToExpand(S))
return false;
// We have to prove that the expanded site of S dominates InsertionPoint.
// This is easy when not in the same block, but hard when S is an instruction
// to be expanded somewhere inside the same block as our insertion point.
// What we really need here is something analogous to an OrderedBasicBlock,
// but for the moment, we paper over the problem by handling two common and
// cheap to check cases.
if (SE.properlyDominates(S, InsertionPoint->getParent()))
return true;
if (SE.dominates(S, InsertionPoint->getParent())) {
if (InsertionPoint->getParent()->getTerminator() == InsertionPoint)
return true;
if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S))
if (llvm::is_contained(InsertionPoint->operand_values(), U->getValue()))
return true;
return false;
void SCEVExpanderCleaner::cleanup() {
// Result is used, nothing to remove.
if (ResultUsed)
// Restore original poison flags.
for (auto [I, Flags] : Expander.OrigFlags)
auto InsertedInstructions = Expander.getAllInsertedInstructions();
#ifndef NDEBUG
SmallPtrSet<Instruction *, 8> InsertedSet(InsertedInstructions.begin(),
// Remove sets with value handles.
// Remove all inserted instructions.
for (Instruction *I : reverse(InsertedInstructions)) {
#ifndef NDEBUG
[&InsertedSet](Value *U) {
return InsertedSet.contains(cast<Instruction>(U));
}) &&
"removed instruction should only be used by instructions inserted "
"during expansion");
assert(!I->getType()->isVoidTy() &&
"inserted instruction should have non-void types");