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 {
51 const DataLayout *DL; // May be NULL
53 SmallVectorImpl<WeakVH> &DeadInsts;
58 SimplifyIndvar(Loop *Loop, ScalarEvolution *SE, LPPassManager *LPM,
59 SmallVectorImpl<WeakVH> &Dead, IVUsers *IVU = nullptr) :
61 LI(LPM->getAnalysisIfAvailable<LoopInfo>()),
65 DataLayoutPass *DLP = LPM->getAnalysisIfAvailable<DataLayoutPass>();
66 DL = DLP ? &DLP->getDataLayout() : nullptr;
67 assert(LI && "IV simplification requires LoopInfo");
70 bool hasChanged() const { return Changed; }
72 /// Iteratively perform simplification on a worklist of users of the
73 /// specified induction variable. This is the top-level driver that applies
74 /// all simplicitions to users of an IV.
75 void simplifyUsers(PHINode *CurrIV, IVVisitor *V = nullptr);
77 Value *foldIVUser(Instruction *UseInst, Instruction *IVOperand);
79 bool eliminateIVUser(Instruction *UseInst, Instruction *IVOperand);
80 void eliminateIVComparison(ICmpInst *ICmp, Value *IVOperand);
81 void eliminateIVRemainder(BinaryOperator *Rem, Value *IVOperand,
83 bool strengthenOverflowingOperation(BinaryOperator *OBO, Value *IVOperand);
85 Instruction *splitOverflowIntrinsic(Instruction *IVUser,
86 const DominatorTree *DT);
90 /// Fold an IV operand into its use. This removes increments of an
91 /// aligned IV when used by a instruction that ignores the low bits.
93 /// IVOperand is guaranteed SCEVable, but UseInst may not be.
95 /// Return the operand of IVOperand for this induction variable if IVOperand can
96 /// be folded (in case more folding opportunities have been exposed).
97 /// Otherwise return null.
98 Value *SimplifyIndvar::foldIVUser(Instruction *UseInst, Instruction *IVOperand) {
99 Value *IVSrc = nullptr;
100 unsigned OperIdx = 0;
101 const SCEV *FoldedExpr = nullptr;
102 switch (UseInst->getOpcode()) {
105 case Instruction::UDiv:
106 case Instruction::LShr:
107 // We're only interested in the case where we know something about
108 // the numerator and have a constant denominator.
109 if (IVOperand != UseInst->getOperand(OperIdx) ||
110 !isa<ConstantInt>(UseInst->getOperand(1)))
113 // Attempt to fold a binary operator with constant operand.
114 // e.g. ((I + 1) >> 2) => I >> 2
115 if (!isa<BinaryOperator>(IVOperand)
116 || !isa<ConstantInt>(IVOperand->getOperand(1)))
119 IVSrc = IVOperand->getOperand(0);
120 // IVSrc must be the (SCEVable) IV, since the other operand is const.
121 assert(SE->isSCEVable(IVSrc->getType()) && "Expect SCEVable IV operand");
123 ConstantInt *D = cast<ConstantInt>(UseInst->getOperand(1));
124 if (UseInst->getOpcode() == Instruction::LShr) {
125 // Get a constant for the divisor. See createSCEV.
126 uint32_t BitWidth = cast<IntegerType>(UseInst->getType())->getBitWidth();
127 if (D->getValue().uge(BitWidth))
130 D = ConstantInt::get(UseInst->getContext(),
131 APInt::getOneBitSet(BitWidth, D->getZExtValue()));
133 FoldedExpr = SE->getUDivExpr(SE->getSCEV(IVSrc), SE->getSCEV(D));
135 // We have something that might fold it's operand. Compare SCEVs.
136 if (!SE->isSCEVable(UseInst->getType()))
139 // Bypass the operand if SCEV can prove it has no effect.
140 if (SE->getSCEV(UseInst) != FoldedExpr)
143 DEBUG(dbgs() << "INDVARS: Eliminated IV operand: " << *IVOperand
144 << " -> " << *UseInst << '\n');
146 UseInst->setOperand(OperIdx, IVSrc);
147 assert(SE->getSCEV(UseInst) == FoldedExpr && "bad SCEV with folded oper");
151 if (IVOperand->use_empty())
152 DeadInsts.push_back(IVOperand);
156 /// SimplifyIVUsers helper for eliminating useless
157 /// comparisons against an induction variable.
158 void SimplifyIndvar::eliminateIVComparison(ICmpInst *ICmp, Value *IVOperand) {
159 unsigned IVOperIdx = 0;
160 ICmpInst::Predicate Pred = ICmp->getPredicate();
161 if (IVOperand != ICmp->getOperand(0)) {
163 assert(IVOperand == ICmp->getOperand(1) && "Can't find IVOperand");
165 Pred = ICmpInst::getSwappedPredicate(Pred);
168 // Get the SCEVs for the ICmp operands.
169 const SCEV *S = SE->getSCEV(ICmp->getOperand(IVOperIdx));
170 const SCEV *X = SE->getSCEV(ICmp->getOperand(1 - IVOperIdx));
172 // Simplify unnecessary loops away.
173 const Loop *ICmpLoop = LI->getLoopFor(ICmp->getParent());
174 S = SE->getSCEVAtScope(S, ICmpLoop);
175 X = SE->getSCEVAtScope(X, ICmpLoop);
177 // If the condition is always true or always false, replace it with
179 if (SE->isKnownPredicate(Pred, S, X))
180 ICmp->replaceAllUsesWith(ConstantInt::getTrue(ICmp->getContext()));
181 else if (SE->isKnownPredicate(ICmpInst::getInversePredicate(Pred), S, X))
182 ICmp->replaceAllUsesWith(ConstantInt::getFalse(ICmp->getContext()));
186 DEBUG(dbgs() << "INDVARS: Eliminated comparison: " << *ICmp << '\n');
189 DeadInsts.push_back(ICmp);
192 /// SimplifyIVUsers helper for eliminating useless
193 /// remainder operations operating on an induction variable.
194 void SimplifyIndvar::eliminateIVRemainder(BinaryOperator *Rem,
197 // We're only interested in the case where we know something about
199 if (IVOperand != Rem->getOperand(0))
202 // Get the SCEVs for the ICmp operands.
203 const SCEV *S = SE->getSCEV(Rem->getOperand(0));
204 const SCEV *X = SE->getSCEV(Rem->getOperand(1));
206 // Simplify unnecessary loops away.
207 const Loop *ICmpLoop = LI->getLoopFor(Rem->getParent());
208 S = SE->getSCEVAtScope(S, ICmpLoop);
209 X = SE->getSCEVAtScope(X, ICmpLoop);
211 // i % n --> i if i is in [0,n).
212 if ((!IsSigned || SE->isKnownNonNegative(S)) &&
213 SE->isKnownPredicate(IsSigned ? ICmpInst::ICMP_SLT : ICmpInst::ICMP_ULT,
215 Rem->replaceAllUsesWith(Rem->getOperand(0));
217 // (i+1) % n --> (i+1)==n?0:(i+1) if i is in [0,n).
218 const SCEV *LessOne =
219 SE->getMinusSCEV(S, SE->getConstant(S->getType(), 1));
220 if (IsSigned && !SE->isKnownNonNegative(LessOne))
223 if (!SE->isKnownPredicate(IsSigned ?
224 ICmpInst::ICMP_SLT : ICmpInst::ICMP_ULT,
228 ICmpInst *ICmp = new ICmpInst(Rem, ICmpInst::ICMP_EQ,
229 Rem->getOperand(0), Rem->getOperand(1));
231 SelectInst::Create(ICmp,
232 ConstantInt::get(Rem->getType(), 0),
233 Rem->getOperand(0), "tmp", Rem);
234 Rem->replaceAllUsesWith(Sel);
237 DEBUG(dbgs() << "INDVARS: Simplified rem: " << *Rem << '\n');
240 DeadInsts.push_back(Rem);
243 /// Eliminate an operation that consumes a simple IV and has
244 /// no observable side-effect given the range of IV values.
245 /// IVOperand is guaranteed SCEVable, but UseInst may not be.
246 bool SimplifyIndvar::eliminateIVUser(Instruction *UseInst,
247 Instruction *IVOperand) {
248 if (ICmpInst *ICmp = dyn_cast<ICmpInst>(UseInst)) {
249 eliminateIVComparison(ICmp, IVOperand);
252 if (BinaryOperator *Rem = dyn_cast<BinaryOperator>(UseInst)) {
253 bool IsSigned = Rem->getOpcode() == Instruction::SRem;
254 if (IsSigned || Rem->getOpcode() == Instruction::URem) {
255 eliminateIVRemainder(Rem, IVOperand, IsSigned);
260 // Eliminate any operation that SCEV can prove is an identity function.
261 if (!SE->isSCEVable(UseInst->getType()) ||
262 (UseInst->getType() != IVOperand->getType()) ||
263 (SE->getSCEV(UseInst) != SE->getSCEV(IVOperand)))
266 DEBUG(dbgs() << "INDVARS: Eliminated identity: " << *UseInst << '\n');
268 UseInst->replaceAllUsesWith(IVOperand);
271 DeadInsts.push_back(UseInst);
275 /// Annotate BO with nsw / nuw if it provably does not signed-overflow /
276 /// unsigned-overflow. Returns true if anything changed, false otherwise.
277 bool SimplifyIndvar::strengthenOverflowingOperation(BinaryOperator *BO,
280 // Currently we only handle instructions of the form "add <indvar> <value>"
281 // and "sub <indvar> <value>".
282 unsigned Op = BO->getOpcode();
283 if (!(Op == Instruction::Add || Op == Instruction::Sub))
286 // If BO is already both nuw and nsw then there is nothing left to do
287 if (BO->hasNoUnsignedWrap() && BO->hasNoSignedWrap())
290 IntegerType *IT = cast<IntegerType>(IVOperand->getType());
291 Value *OtherOperand = nullptr;
292 int OtherOperandIdx = -1;
293 if (BO->getOperand(0) == IVOperand) {
294 OtherOperand = BO->getOperand(1);
297 assert(BO->getOperand(1) == IVOperand && "only other use!");
298 OtherOperand = BO->getOperand(0);
302 bool Changed = false;
303 const SCEV *OtherOpSCEV = SE->getSCEV(OtherOperand);
304 if (OtherOpSCEV == SE->getCouldNotCompute())
307 if (Op == Instruction::Sub) {
308 // If the subtraction is of the form "sub <indvar>, <op>", then pretend it
309 // is "add <indvar>, -<op>" and continue, else bail out.
310 if (OtherOperandIdx != 1)
313 OtherOpSCEV = SE->getNegativeSCEV(OtherOpSCEV);
316 const SCEV *IVOpSCEV = SE->getSCEV(IVOperand);
317 const SCEV *ZeroSCEV = SE->getConstant(IVOpSCEV->getType(), 0);
319 if (!BO->hasNoSignedWrap()) {
320 // Upgrade the add to an "add nsw" if we can prove that it will never
321 // sign-overflow or sign-underflow.
323 const SCEV *SignedMax =
324 SE->getConstant(APInt::getSignedMaxValue(IT->getBitWidth()));
325 const SCEV *SignedMin =
326 SE->getConstant(APInt::getSignedMinValue(IT->getBitWidth()));
328 // The addition "IVOperand + OtherOp" does not sign-overflow if the result
329 // is sign-representable in 2's complement in the given bit-width.
331 // If OtherOp is SLT 0, then for an IVOperand in [SignedMin - OtherOp,
332 // SignedMax], "IVOperand + OtherOp" is in [SignedMin, SignedMax + OtherOp].
333 // Everything in [SignedMin, SignedMax + OtherOp] is representable since
334 // SignedMax + OtherOp is at least -1.
336 // If OtherOp is SGE 0, then for an IVOperand in [SignedMin, SignedMax -
337 // OtherOp], "IVOperand + OtherOp" is in [SignedMin + OtherOp, SignedMax].
338 // Everything in [SignedMin + OtherOp, SignedMax] is representable since
339 // SignedMin + OtherOp is at most -1.
341 // It follows that for all values of IVOperand in [SignedMin - smin(0,
342 // OtherOp), SignedMax - smax(0, OtherOp)] the result of the add is
343 // representable (i.e. there is no sign-overflow).
345 const SCEV *UpperDelta = SE->getSMaxExpr(ZeroSCEV, OtherOpSCEV);
346 const SCEV *UpperLimit = SE->getMinusSCEV(SignedMax, UpperDelta);
348 bool NeverSignedOverflows =
349 SE->isKnownPredicate(ICmpInst::ICMP_SLE, IVOpSCEV, UpperLimit);
351 if (NeverSignedOverflows) {
352 const SCEV *LowerDelta = SE->getSMinExpr(ZeroSCEV, OtherOpSCEV);
353 const SCEV *LowerLimit = SE->getMinusSCEV(SignedMin, LowerDelta);
355 bool NeverSignedUnderflows =
356 SE->isKnownPredicate(ICmpInst::ICMP_SGE, IVOpSCEV, LowerLimit);
357 if (NeverSignedUnderflows) {
358 BO->setHasNoSignedWrap(true);
364 if (!BO->hasNoUnsignedWrap()) {
365 // Upgrade the add computing "IVOperand + OtherOp" to an "add nuw" if we can
366 // prove that it will never unsigned-overflow (i.e. the result will always
367 // be representable in the given bit-width).
369 // "IVOperand + OtherOp" is unsigned-representable in 2's complement iff it
370 // does not produce a carry. "IVOperand + OtherOp" produces no carry iff
371 // IVOperand ULE (UnsignedMax - OtherOp).
373 const SCEV *UnsignedMax =
374 SE->getConstant(APInt::getMaxValue(IT->getBitWidth()));
375 const SCEV *UpperLimit = SE->getMinusSCEV(UnsignedMax, OtherOpSCEV);
377 bool NeverUnsignedOverflows =
378 SE->isKnownPredicate(ICmpInst::ICMP_ULE, IVOpSCEV, UpperLimit);
380 if (NeverUnsignedOverflows) {
381 BO->setHasNoUnsignedWrap(true);
389 /// \brief Split sadd.with.overflow into add + sadd.with.overflow to allow
390 /// analysis and optimization.
392 /// \return A new value representing the non-overflowing add if possible,
393 /// otherwise return the original value.
394 Instruction *SimplifyIndvar::splitOverflowIntrinsic(Instruction *IVUser,
395 const DominatorTree *DT) {
396 IntrinsicInst *II = dyn_cast<IntrinsicInst>(IVUser);
397 if (!II || II->getIntrinsicID() != Intrinsic::sadd_with_overflow)
400 // Find a branch guarded by the overflow check.
401 BranchInst *Branch = nullptr;
402 Instruction *AddVal = nullptr;
403 for (User *U : II->users()) {
404 if (ExtractValueInst *ExtractInst = dyn_cast<ExtractValueInst>(U)) {
405 if (ExtractInst->getNumIndices() != 1)
407 if (ExtractInst->getIndices()[0] == 0)
408 AddVal = ExtractInst;
409 else if (ExtractInst->getIndices()[0] == 1 && ExtractInst->hasOneUse())
410 Branch = dyn_cast<BranchInst>(ExtractInst->user_back());
413 if (!AddVal || !Branch)
416 BasicBlock *ContinueBB = Branch->getSuccessor(1);
417 if (std::next(pred_begin(ContinueBB)) != pred_end(ContinueBB))
420 // Check if all users of the add are provably NSW.
422 for (Use &U : AddVal->uses()) {
423 if (Instruction *UseInst = dyn_cast<Instruction>(U.getUser())) {
424 BasicBlock *UseBB = UseInst->getParent();
425 if (PHINode *PHI = dyn_cast<PHINode>(UseInst))
426 UseBB = PHI->getIncomingBlock(U);
427 if (!DT->dominates(ContinueBB, UseBB)) {
437 IRBuilder<> Builder(IVUser);
438 Instruction *AddInst = dyn_cast<Instruction>(
439 Builder.CreateNSWAdd(II->getOperand(0), II->getOperand(1)));
441 // The caller expects the new add to have the same form as the intrinsic. The
442 // IV operand position must be the same.
443 assert((AddInst->getOpcode() == Instruction::Add &&
444 AddInst->getOperand(0) == II->getOperand(0)) &&
445 "Bad add instruction created from overflow intrinsic.");
447 AddVal->replaceAllUsesWith(AddInst);
448 DeadInsts.push_back(AddVal);
452 /// Add all uses of Def to the current IV's worklist.
453 static void pushIVUsers(
455 SmallPtrSet<Instruction*,16> &Simplified,
456 SmallVectorImpl< std::pair<Instruction*,Instruction*> > &SimpleIVUsers) {
458 for (User *U : Def->users()) {
459 Instruction *UI = cast<Instruction>(U);
461 // Avoid infinite or exponential worklist processing.
462 // Also ensure unique worklist users.
463 // If Def is a LoopPhi, it may not be in the Simplified set, so check for
465 if (UI != Def && Simplified.insert(UI).second)
466 SimpleIVUsers.push_back(std::make_pair(UI, Def));
470 /// Return true if this instruction generates a simple SCEV
471 /// expression in terms of that IV.
473 /// This is similar to IVUsers' isInteresting() but processes each instruction
474 /// non-recursively when the operand is already known to be a simpleIVUser.
476 static bool isSimpleIVUser(Instruction *I, const Loop *L, ScalarEvolution *SE) {
477 if (!SE->isSCEVable(I->getType()))
480 // Get the symbolic expression for this instruction.
481 const SCEV *S = SE->getSCEV(I);
483 // Only consider affine recurrences.
484 const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(S);
485 if (AR && AR->getLoop() == L)
491 /// Iteratively perform simplification on a worklist of users
492 /// of the specified induction variable. Each successive simplification may push
493 /// more users which may themselves be candidates for simplification.
495 /// This algorithm does not require IVUsers analysis. Instead, it simplifies
496 /// instructions in-place during analysis. Rather than rewriting induction
497 /// variables bottom-up from their users, it transforms a chain of IVUsers
498 /// top-down, updating the IR only when it encouters a clear optimization
501 /// Once DisableIVRewrite is default, LSR will be the only client of IVUsers.
503 void SimplifyIndvar::simplifyUsers(PHINode *CurrIV, IVVisitor *V) {
504 if (!SE->isSCEVable(CurrIV->getType()))
507 // Instructions processed by SimplifyIndvar for CurrIV.
508 SmallPtrSet<Instruction*,16> Simplified;
510 // Use-def pairs if IV users waiting to be processed for CurrIV.
511 SmallVector<std::pair<Instruction*, Instruction*>, 8> SimpleIVUsers;
513 // Push users of the current LoopPhi. In rare cases, pushIVUsers may be
514 // called multiple times for the same LoopPhi. This is the proper thing to
515 // do for loop header phis that use each other.
516 pushIVUsers(CurrIV, Simplified, SimpleIVUsers);
518 while (!SimpleIVUsers.empty()) {
519 std::pair<Instruction*, Instruction*> UseOper =
520 SimpleIVUsers.pop_back_val();
521 Instruction *UseInst = UseOper.first;
523 // Bypass back edges to avoid extra work.
524 if (UseInst == CurrIV) continue;
526 if (V && V->shouldSplitOverflowInstrinsics()) {
527 UseInst = splitOverflowIntrinsic(UseInst, V->getDomTree());
532 Instruction *IVOperand = UseOper.second;
533 for (unsigned N = 0; IVOperand; ++N) {
534 assert(N <= Simplified.size() && "runaway iteration");
536 Value *NewOper = foldIVUser(UseOper.first, IVOperand);
538 break; // done folding
539 IVOperand = dyn_cast<Instruction>(NewOper);
544 if (eliminateIVUser(UseOper.first, IVOperand)) {
545 pushIVUsers(IVOperand, Simplified, SimpleIVUsers);
549 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(UseOper.first)) {
550 if (isa<OverflowingBinaryOperator>(BO) &&
551 strengthenOverflowingOperation(BO, IVOperand)) {
552 // re-queue uses of the now modified binary operator and fall
553 // through to the checks that remain.
554 pushIVUsers(IVOperand, Simplified, SimpleIVUsers);
558 CastInst *Cast = dyn_cast<CastInst>(UseOper.first);
563 if (isSimpleIVUser(UseOper.first, L, SE)) {
564 pushIVUsers(UseOper.first, Simplified, SimpleIVUsers);
571 void IVVisitor::anchor() { }
573 /// Simplify instructions that use this induction variable
574 /// by using ScalarEvolution to analyze the IV's recurrence.
575 bool simplifyUsersOfIV(PHINode *CurrIV, ScalarEvolution *SE, LPPassManager *LPM,
576 SmallVectorImpl<WeakVH> &Dead, IVVisitor *V)
578 LoopInfo *LI = &LPM->getAnalysis<LoopInfo>();
579 SimplifyIndvar SIV(LI->getLoopFor(CurrIV->getParent()), SE, LPM, Dead);
580 SIV.simplifyUsers(CurrIV, V);
581 return SIV.hasChanged();
584 /// Simplify users of induction variables within this
585 /// loop. This does not actually change or add IVs.
586 bool simplifyLoopIVs(Loop *L, ScalarEvolution *SE, LPPassManager *LPM,
587 SmallVectorImpl<WeakVH> &Dead) {
588 bool Changed = false;
589 for (BasicBlock::iterator I = L->getHeader()->begin(); isa<PHINode>(I); ++I) {
590 Changed |= simplifyUsersOfIV(cast<PHINode>(I), SE, LPM, Dead);