1 //===-- SimplifyIndVar.cpp - Induction variable simplification ------------===//
3 // The LLVM Compiler Infrastructure
5 // This file is distributed under the University of Illinois Open Source
6 // License. See LICENSE.TXT for details.
8 //===----------------------------------------------------------------------===//
10 // This file implements induction variable simplification. It does
11 // not define any actual pass or policy, but provides a single function to
12 // simplify a loop's induction variables based on ScalarEvolution.
14 //===----------------------------------------------------------------------===//
16 #include "llvm/Transforms/Utils/SimplifyIndVar.h"
17 #include "llvm/ADT/STLExtras.h"
18 #include "llvm/ADT/SmallVector.h"
19 #include "llvm/ADT/Statistic.h"
20 #include "llvm/Analysis/IVUsers.h"
21 #include "llvm/Analysis/LoopInfo.h"
22 #include "llvm/Analysis/LoopPass.h"
23 #include "llvm/Analysis/ScalarEvolutionExpressions.h"
24 #include "llvm/IR/DataLayout.h"
25 #include "llvm/IR/Dominators.h"
26 #include "llvm/IR/IRBuilder.h"
27 #include "llvm/IR/Instructions.h"
28 #include "llvm/IR/IntrinsicInst.h"
29 #include "llvm/Support/CommandLine.h"
30 #include "llvm/Support/Debug.h"
31 #include "llvm/Support/raw_ostream.h"
35 #define DEBUG_TYPE "indvars"
37 STATISTIC(NumElimIdentity, "Number of IV identities eliminated");
38 STATISTIC(NumElimOperand, "Number of IV operands folded into a use");
39 STATISTIC(NumElimRem , "Number of IV remainder operations eliminated");
40 STATISTIC(NumElimCmp , "Number of IV comparisons eliminated");
43 /// This is a utility for simplifying induction variables
44 /// based on ScalarEvolution. It is the primary instrument of the
45 /// IndvarSimplify pass, but it may also be directly invoked to cleanup after
46 /// other loop passes that preserve SCEV.
47 class SimplifyIndvar {
52 SmallVectorImpl<WeakVH> &DeadInsts;
57 SimplifyIndvar(Loop *Loop, ScalarEvolution *SE, LoopInfo *LI,
58 SmallVectorImpl<WeakVH> &Dead, IVUsers *IVU = nullptr)
59 : L(Loop), LI(LI), SE(SE), DeadInsts(Dead), Changed(false) {
60 assert(LI && "IV simplification requires LoopInfo");
63 bool hasChanged() const { return Changed; }
65 /// Iteratively perform simplification on a worklist of users of the
66 /// specified induction variable. This is the top-level driver that applies
67 /// all simplicitions to users of an IV.
68 void simplifyUsers(PHINode *CurrIV, IVVisitor *V = nullptr);
70 Value *foldIVUser(Instruction *UseInst, Instruction *IVOperand);
72 bool eliminateIVUser(Instruction *UseInst, Instruction *IVOperand);
73 void eliminateIVComparison(ICmpInst *ICmp, Value *IVOperand);
74 void eliminateIVRemainder(BinaryOperator *Rem, Value *IVOperand,
76 bool strengthenOverflowingOperation(BinaryOperator *OBO, Value *IVOperand);
78 Instruction *splitOverflowIntrinsic(Instruction *IVUser,
79 const DominatorTree *DT);
83 /// Fold an IV operand into its use. This removes increments of an
84 /// aligned IV when used by a instruction that ignores the low bits.
86 /// IVOperand is guaranteed SCEVable, but UseInst may not be.
88 /// Return the operand of IVOperand for this induction variable if IVOperand can
89 /// be folded (in case more folding opportunities have been exposed).
90 /// Otherwise return null.
91 Value *SimplifyIndvar::foldIVUser(Instruction *UseInst, Instruction *IVOperand) {
92 Value *IVSrc = nullptr;
94 const SCEV *FoldedExpr = nullptr;
95 switch (UseInst->getOpcode()) {
98 case Instruction::UDiv:
99 case Instruction::LShr:
100 // We're only interested in the case where we know something about
101 // the numerator and have a constant denominator.
102 if (IVOperand != UseInst->getOperand(OperIdx) ||
103 !isa<ConstantInt>(UseInst->getOperand(1)))
106 // Attempt to fold a binary operator with constant operand.
107 // e.g. ((I + 1) >> 2) => I >> 2
108 if (!isa<BinaryOperator>(IVOperand)
109 || !isa<ConstantInt>(IVOperand->getOperand(1)))
112 IVSrc = IVOperand->getOperand(0);
113 // IVSrc must be the (SCEVable) IV, since the other operand is const.
114 assert(SE->isSCEVable(IVSrc->getType()) && "Expect SCEVable IV operand");
116 ConstantInt *D = cast<ConstantInt>(UseInst->getOperand(1));
117 if (UseInst->getOpcode() == Instruction::LShr) {
118 // Get a constant for the divisor. See createSCEV.
119 uint32_t BitWidth = cast<IntegerType>(UseInst->getType())->getBitWidth();
120 if (D->getValue().uge(BitWidth))
123 D = ConstantInt::get(UseInst->getContext(),
124 APInt::getOneBitSet(BitWidth, D->getZExtValue()));
126 FoldedExpr = SE->getUDivExpr(SE->getSCEV(IVSrc), SE->getSCEV(D));
128 // We have something that might fold it's operand. Compare SCEVs.
129 if (!SE->isSCEVable(UseInst->getType()))
132 // Bypass the operand if SCEV can prove it has no effect.
133 if (SE->getSCEV(UseInst) != FoldedExpr)
136 DEBUG(dbgs() << "INDVARS: Eliminated IV operand: " << *IVOperand
137 << " -> " << *UseInst << '\n');
139 UseInst->setOperand(OperIdx, IVSrc);
140 assert(SE->getSCEV(UseInst) == FoldedExpr && "bad SCEV with folded oper");
144 if (IVOperand->use_empty())
145 DeadInsts.push_back(IVOperand);
149 /// SimplifyIVUsers helper for eliminating useless
150 /// comparisons against an induction variable.
151 void SimplifyIndvar::eliminateIVComparison(ICmpInst *ICmp, Value *IVOperand) {
152 unsigned IVOperIdx = 0;
153 ICmpInst::Predicate Pred = ICmp->getPredicate();
154 if (IVOperand != ICmp->getOperand(0)) {
156 assert(IVOperand == ICmp->getOperand(1) && "Can't find IVOperand");
158 Pred = ICmpInst::getSwappedPredicate(Pred);
161 // Get the SCEVs for the ICmp operands.
162 const SCEV *S = SE->getSCEV(ICmp->getOperand(IVOperIdx));
163 const SCEV *X = SE->getSCEV(ICmp->getOperand(1 - IVOperIdx));
165 // Simplify unnecessary loops away.
166 const Loop *ICmpLoop = LI->getLoopFor(ICmp->getParent());
167 S = SE->getSCEVAtScope(S, ICmpLoop);
168 X = SE->getSCEVAtScope(X, ICmpLoop);
170 // If the condition is always true or always false, replace it with
172 if (SE->isKnownPredicate(Pred, S, X))
173 ICmp->replaceAllUsesWith(ConstantInt::getTrue(ICmp->getContext()));
174 else if (SE->isKnownPredicate(ICmpInst::getInversePredicate(Pred), S, X))
175 ICmp->replaceAllUsesWith(ConstantInt::getFalse(ICmp->getContext()));
179 DEBUG(dbgs() << "INDVARS: Eliminated comparison: " << *ICmp << '\n');
182 DeadInsts.push_back(ICmp);
185 /// SimplifyIVUsers helper for eliminating useless
186 /// remainder operations operating on an induction variable.
187 void SimplifyIndvar::eliminateIVRemainder(BinaryOperator *Rem,
190 // We're only interested in the case where we know something about
192 if (IVOperand != Rem->getOperand(0))
195 // Get the SCEVs for the ICmp operands.
196 const SCEV *S = SE->getSCEV(Rem->getOperand(0));
197 const SCEV *X = SE->getSCEV(Rem->getOperand(1));
199 // Simplify unnecessary loops away.
200 const Loop *ICmpLoop = LI->getLoopFor(Rem->getParent());
201 S = SE->getSCEVAtScope(S, ICmpLoop);
202 X = SE->getSCEVAtScope(X, ICmpLoop);
204 // i % n --> i if i is in [0,n).
205 if ((!IsSigned || SE->isKnownNonNegative(S)) &&
206 SE->isKnownPredicate(IsSigned ? ICmpInst::ICMP_SLT : ICmpInst::ICMP_ULT,
208 Rem->replaceAllUsesWith(Rem->getOperand(0));
210 // (i+1) % n --> (i+1)==n?0:(i+1) if i is in [0,n).
211 const SCEV *LessOne =
212 SE->getMinusSCEV(S, SE->getConstant(S->getType(), 1));
213 if (IsSigned && !SE->isKnownNonNegative(LessOne))
216 if (!SE->isKnownPredicate(IsSigned ?
217 ICmpInst::ICMP_SLT : ICmpInst::ICMP_ULT,
221 ICmpInst *ICmp = new ICmpInst(Rem, ICmpInst::ICMP_EQ,
222 Rem->getOperand(0), Rem->getOperand(1));
224 SelectInst::Create(ICmp,
225 ConstantInt::get(Rem->getType(), 0),
226 Rem->getOperand(0), "tmp", Rem);
227 Rem->replaceAllUsesWith(Sel);
230 DEBUG(dbgs() << "INDVARS: Simplified rem: " << *Rem << '\n');
233 DeadInsts.push_back(Rem);
236 /// Eliminate an operation that consumes a simple IV and has
237 /// no observable side-effect given the range of IV values.
238 /// IVOperand is guaranteed SCEVable, but UseInst may not be.
239 bool SimplifyIndvar::eliminateIVUser(Instruction *UseInst,
240 Instruction *IVOperand) {
241 if (ICmpInst *ICmp = dyn_cast<ICmpInst>(UseInst)) {
242 eliminateIVComparison(ICmp, IVOperand);
245 if (BinaryOperator *Rem = dyn_cast<BinaryOperator>(UseInst)) {
246 bool IsSigned = Rem->getOpcode() == Instruction::SRem;
247 if (IsSigned || Rem->getOpcode() == Instruction::URem) {
248 eliminateIVRemainder(Rem, IVOperand, IsSigned);
253 // Eliminate any operation that SCEV can prove is an identity function.
254 if (!SE->isSCEVable(UseInst->getType()) ||
255 (UseInst->getType() != IVOperand->getType()) ||
256 (SE->getSCEV(UseInst) != SE->getSCEV(IVOperand)))
259 DEBUG(dbgs() << "INDVARS: Eliminated identity: " << *UseInst << '\n');
261 UseInst->replaceAllUsesWith(IVOperand);
264 DeadInsts.push_back(UseInst);
268 /// Annotate BO with nsw / nuw if it provably does not signed-overflow /
269 /// unsigned-overflow. Returns true if anything changed, false otherwise.
270 bool SimplifyIndvar::strengthenOverflowingOperation(BinaryOperator *BO,
273 // Currently we only handle instructions of the form "add <indvar> <value>"
274 unsigned Op = BO->getOpcode();
275 if (Op != Instruction::Add)
278 // If BO is already both nuw and nsw then there is nothing left to do
279 if (BO->hasNoUnsignedWrap() && BO->hasNoSignedWrap())
282 IntegerType *IT = cast<IntegerType>(IVOperand->getType());
283 Value *OtherOperand = nullptr;
284 if (BO->getOperand(0) == IVOperand) {
285 OtherOperand = BO->getOperand(1);
287 assert(BO->getOperand(1) == IVOperand && "only other use!");
288 OtherOperand = BO->getOperand(0);
291 bool Changed = false;
292 const SCEV *OtherOpSCEV = SE->getSCEV(OtherOperand);
293 if (OtherOpSCEV == SE->getCouldNotCompute())
296 const SCEV *IVOpSCEV = SE->getSCEV(IVOperand);
297 const SCEV *ZeroSCEV = SE->getConstant(IVOpSCEV->getType(), 0);
299 if (!BO->hasNoSignedWrap()) {
300 // Upgrade the add to an "add nsw" if we can prove that it will never
301 // sign-overflow or sign-underflow.
303 const SCEV *SignedMax =
304 SE->getConstant(APInt::getSignedMaxValue(IT->getBitWidth()));
305 const SCEV *SignedMin =
306 SE->getConstant(APInt::getSignedMinValue(IT->getBitWidth()));
308 // The addition "IVOperand + OtherOp" does not sign-overflow if the result
309 // is sign-representable in 2's complement in the given bit-width.
311 // If OtherOp is SLT 0, then for an IVOperand in [SignedMin - OtherOp,
312 // SignedMax], "IVOperand + OtherOp" is in [SignedMin, SignedMax + OtherOp].
313 // Everything in [SignedMin, SignedMax + OtherOp] is representable since
314 // SignedMax + OtherOp is at least -1.
316 // If OtherOp is SGE 0, then for an IVOperand in [SignedMin, SignedMax -
317 // OtherOp], "IVOperand + OtherOp" is in [SignedMin + OtherOp, SignedMax].
318 // Everything in [SignedMin + OtherOp, SignedMax] is representable since
319 // SignedMin + OtherOp is at most -1.
321 // It follows that for all values of IVOperand in [SignedMin - smin(0,
322 // OtherOp), SignedMax - smax(0, OtherOp)] the result of the add is
323 // representable (i.e. there is no sign-overflow).
325 const SCEV *UpperDelta = SE->getSMaxExpr(ZeroSCEV, OtherOpSCEV);
326 const SCEV *UpperLimit = SE->getMinusSCEV(SignedMax, UpperDelta);
328 bool NeverSignedOverflows =
329 SE->isKnownPredicate(ICmpInst::ICMP_SLE, IVOpSCEV, UpperLimit);
331 if (NeverSignedOverflows) {
332 const SCEV *LowerDelta = SE->getSMinExpr(ZeroSCEV, OtherOpSCEV);
333 const SCEV *LowerLimit = SE->getMinusSCEV(SignedMin, LowerDelta);
335 bool NeverSignedUnderflows =
336 SE->isKnownPredicate(ICmpInst::ICMP_SGE, IVOpSCEV, LowerLimit);
337 if (NeverSignedUnderflows) {
338 BO->setHasNoSignedWrap(true);
344 if (!BO->hasNoUnsignedWrap()) {
345 // Upgrade the add computing "IVOperand + OtherOp" to an "add nuw" if we can
346 // prove that it will never unsigned-overflow (i.e. the result will always
347 // be representable in the given bit-width).
349 // "IVOperand + OtherOp" is unsigned-representable in 2's complement iff it
350 // does not produce a carry. "IVOperand + OtherOp" produces no carry iff
351 // IVOperand ULE (UnsignedMax - OtherOp).
353 const SCEV *UnsignedMax =
354 SE->getConstant(APInt::getMaxValue(IT->getBitWidth()));
355 const SCEV *UpperLimit = SE->getMinusSCEV(UnsignedMax, OtherOpSCEV);
357 bool NeverUnsignedOverflows =
358 SE->isKnownPredicate(ICmpInst::ICMP_ULE, IVOpSCEV, UpperLimit);
360 if (NeverUnsignedOverflows) {
361 BO->setHasNoUnsignedWrap(true);
369 /// \brief Split sadd.with.overflow into add + sadd.with.overflow to allow
370 /// analysis and optimization.
372 /// \return A new value representing the non-overflowing add if possible,
373 /// otherwise return the original value.
374 Instruction *SimplifyIndvar::splitOverflowIntrinsic(Instruction *IVUser,
375 const DominatorTree *DT) {
376 IntrinsicInst *II = dyn_cast<IntrinsicInst>(IVUser);
377 if (!II || II->getIntrinsicID() != Intrinsic::sadd_with_overflow)
380 // Find a branch guarded by the overflow check.
381 BranchInst *Branch = nullptr;
382 Instruction *AddVal = nullptr;
383 for (User *U : II->users()) {
384 if (ExtractValueInst *ExtractInst = dyn_cast<ExtractValueInst>(U)) {
385 if (ExtractInst->getNumIndices() != 1)
387 if (ExtractInst->getIndices()[0] == 0)
388 AddVal = ExtractInst;
389 else if (ExtractInst->getIndices()[0] == 1 && ExtractInst->hasOneUse())
390 Branch = dyn_cast<BranchInst>(ExtractInst->user_back());
393 if (!AddVal || !Branch)
396 BasicBlock *ContinueBB = Branch->getSuccessor(1);
397 if (std::next(pred_begin(ContinueBB)) != pred_end(ContinueBB))
400 // Check if all users of the add are provably NSW.
402 for (Use &U : AddVal->uses()) {
403 if (Instruction *UseInst = dyn_cast<Instruction>(U.getUser())) {
404 BasicBlock *UseBB = UseInst->getParent();
405 if (PHINode *PHI = dyn_cast<PHINode>(UseInst))
406 UseBB = PHI->getIncomingBlock(U);
407 if (!DT->dominates(ContinueBB, UseBB)) {
417 IRBuilder<> Builder(IVUser);
418 Instruction *AddInst = dyn_cast<Instruction>(
419 Builder.CreateNSWAdd(II->getOperand(0), II->getOperand(1)));
421 // The caller expects the new add to have the same form as the intrinsic. The
422 // IV operand position must be the same.
423 assert((AddInst->getOpcode() == Instruction::Add &&
424 AddInst->getOperand(0) == II->getOperand(0)) &&
425 "Bad add instruction created from overflow intrinsic.");
427 AddVal->replaceAllUsesWith(AddInst);
428 DeadInsts.push_back(AddVal);
432 /// Add all uses of Def to the current IV's worklist.
433 static void pushIVUsers(
435 SmallPtrSet<Instruction*,16> &Simplified,
436 SmallVectorImpl< std::pair<Instruction*,Instruction*> > &SimpleIVUsers) {
438 for (User *U : Def->users()) {
439 Instruction *UI = cast<Instruction>(U);
441 // Avoid infinite or exponential worklist processing.
442 // Also ensure unique worklist users.
443 // If Def is a LoopPhi, it may not be in the Simplified set, so check for
445 if (UI != Def && Simplified.insert(UI).second)
446 SimpleIVUsers.push_back(std::make_pair(UI, Def));
450 /// Return true if this instruction generates a simple SCEV
451 /// expression in terms of that IV.
453 /// This is similar to IVUsers' isInteresting() but processes each instruction
454 /// non-recursively when the operand is already known to be a simpleIVUser.
456 static bool isSimpleIVUser(Instruction *I, const Loop *L, ScalarEvolution *SE) {
457 if (!SE->isSCEVable(I->getType()))
460 // Get the symbolic expression for this instruction.
461 const SCEV *S = SE->getSCEV(I);
463 // Only consider affine recurrences.
464 const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(S);
465 if (AR && AR->getLoop() == L)
471 /// Iteratively perform simplification on a worklist of users
472 /// of the specified induction variable. Each successive simplification may push
473 /// more users which may themselves be candidates for simplification.
475 /// This algorithm does not require IVUsers analysis. Instead, it simplifies
476 /// instructions in-place during analysis. Rather than rewriting induction
477 /// variables bottom-up from their users, it transforms a chain of IVUsers
478 /// top-down, updating the IR only when it encouters a clear optimization
481 /// Once DisableIVRewrite is default, LSR will be the only client of IVUsers.
483 void SimplifyIndvar::simplifyUsers(PHINode *CurrIV, IVVisitor *V) {
484 if (!SE->isSCEVable(CurrIV->getType()))
487 // Instructions processed by SimplifyIndvar for CurrIV.
488 SmallPtrSet<Instruction*,16> Simplified;
490 // Use-def pairs if IV users waiting to be processed for CurrIV.
491 SmallVector<std::pair<Instruction*, Instruction*>, 8> SimpleIVUsers;
493 // Push users of the current LoopPhi. In rare cases, pushIVUsers may be
494 // called multiple times for the same LoopPhi. This is the proper thing to
495 // do for loop header phis that use each other.
496 pushIVUsers(CurrIV, Simplified, SimpleIVUsers);
498 while (!SimpleIVUsers.empty()) {
499 std::pair<Instruction*, Instruction*> UseOper =
500 SimpleIVUsers.pop_back_val();
501 Instruction *UseInst = UseOper.first;
503 // Bypass back edges to avoid extra work.
504 if (UseInst == CurrIV) continue;
506 if (V && V->shouldSplitOverflowInstrinsics()) {
507 UseInst = splitOverflowIntrinsic(UseInst, V->getDomTree());
512 Instruction *IVOperand = UseOper.second;
513 for (unsigned N = 0; IVOperand; ++N) {
514 assert(N <= Simplified.size() && "runaway iteration");
516 Value *NewOper = foldIVUser(UseOper.first, IVOperand);
518 break; // done folding
519 IVOperand = dyn_cast<Instruction>(NewOper);
524 if (eliminateIVUser(UseOper.first, IVOperand)) {
525 pushIVUsers(IVOperand, Simplified, SimpleIVUsers);
529 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(UseOper.first)) {
530 if (isa<OverflowingBinaryOperator>(BO) &&
531 strengthenOverflowingOperation(BO, IVOperand)) {
532 // re-queue uses of the now modified binary operator and fall
533 // through to the checks that remain.
534 pushIVUsers(IVOperand, Simplified, SimpleIVUsers);
538 CastInst *Cast = dyn_cast<CastInst>(UseOper.first);
543 if (isSimpleIVUser(UseOper.first, L, SE)) {
544 pushIVUsers(UseOper.first, Simplified, SimpleIVUsers);
551 void IVVisitor::anchor() { }
553 /// Simplify instructions that use this induction variable
554 /// by using ScalarEvolution to analyze the IV's recurrence.
555 bool simplifyUsersOfIV(PHINode *CurrIV, ScalarEvolution *SE, LPPassManager *LPM,
556 SmallVectorImpl<WeakVH> &Dead, IVVisitor *V)
558 LoopInfo *LI = &LPM->getAnalysis<LoopInfoWrapperPass>().getLoopInfo();
559 SimplifyIndvar SIV(LI->getLoopFor(CurrIV->getParent()), SE, LI, Dead);
560 SIV.simplifyUsers(CurrIV, V);
561 return SIV.hasChanged();
564 /// Simplify users of induction variables within this
565 /// loop. This does not actually change or add IVs.
566 bool simplifyLoopIVs(Loop *L, ScalarEvolution *SE, LPPassManager *LPM,
567 SmallVectorImpl<WeakVH> &Dead) {
568 bool Changed = false;
569 for (BasicBlock::iterator I = L->getHeader()->begin(); isa<PHINode>(I); ++I) {
570 Changed |= simplifyUsersOfIV(cast<PHINode>(I), SE, LPM, Dead);