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 unsigned Op = BO->getOpcode();
282 if (Op != Instruction::Add)
285 // If BO is already both nuw and nsw then there is nothing left to do
286 if (BO->hasNoUnsignedWrap() && BO->hasNoSignedWrap())
289 IntegerType *IT = cast<IntegerType>(IVOperand->getType());
290 Value *OtherOperand = nullptr;
291 if (BO->getOperand(0) == IVOperand) {
292 OtherOperand = BO->getOperand(1);
294 assert(BO->getOperand(1) == IVOperand && "only other use!");
295 OtherOperand = BO->getOperand(0);
298 bool Changed = false;
299 const SCEV *OtherOpSCEV = SE->getSCEV(OtherOperand);
300 if (OtherOpSCEV == SE->getCouldNotCompute())
303 const SCEV *IVOpSCEV = SE->getSCEV(IVOperand);
304 const SCEV *ZeroSCEV = SE->getConstant(IVOpSCEV->getType(), 0);
306 if (!BO->hasNoSignedWrap()) {
307 // Upgrade the add to an "add nsw" if we can prove that it will never
308 // sign-overflow or sign-underflow.
310 const SCEV *SignedMax =
311 SE->getConstant(APInt::getSignedMaxValue(IT->getBitWidth()));
312 const SCEV *SignedMin =
313 SE->getConstant(APInt::getSignedMinValue(IT->getBitWidth()));
315 // The addition "IVOperand + OtherOp" does not sign-overflow if the result
316 // is sign-representable in 2's complement in the given bit-width.
318 // If OtherOp is SLT 0, then for an IVOperand in [SignedMin - OtherOp,
319 // SignedMax], "IVOperand + OtherOp" is in [SignedMin, SignedMax + OtherOp].
320 // Everything in [SignedMin, SignedMax + OtherOp] is representable since
321 // SignedMax + OtherOp is at least -1.
323 // If OtherOp is SGE 0, then for an IVOperand in [SignedMin, SignedMax -
324 // OtherOp], "IVOperand + OtherOp" is in [SignedMin + OtherOp, SignedMax].
325 // Everything in [SignedMin + OtherOp, SignedMax] is representable since
326 // SignedMin + OtherOp is at most -1.
328 // It follows that for all values of IVOperand in [SignedMin - smin(0,
329 // OtherOp), SignedMax - smax(0, OtherOp)] the result of the add is
330 // representable (i.e. there is no sign-overflow).
332 const SCEV *UpperDelta = SE->getSMaxExpr(ZeroSCEV, OtherOpSCEV);
333 const SCEV *UpperLimit = SE->getMinusSCEV(SignedMax, UpperDelta);
335 bool NeverSignedOverflows =
336 SE->isKnownPredicate(ICmpInst::ICMP_SLE, IVOpSCEV, UpperLimit);
338 if (NeverSignedOverflows) {
339 const SCEV *LowerDelta = SE->getSMinExpr(ZeroSCEV, OtherOpSCEV);
340 const SCEV *LowerLimit = SE->getMinusSCEV(SignedMin, LowerDelta);
342 bool NeverSignedUnderflows =
343 SE->isKnownPredicate(ICmpInst::ICMP_SGE, IVOpSCEV, LowerLimit);
344 if (NeverSignedUnderflows) {
345 BO->setHasNoSignedWrap(true);
351 if (!BO->hasNoUnsignedWrap()) {
352 // Upgrade the add computing "IVOperand + OtherOp" to an "add nuw" if we can
353 // prove that it will never unsigned-overflow (i.e. the result will always
354 // be representable in the given bit-width).
356 // "IVOperand + OtherOp" is unsigned-representable in 2's complement iff it
357 // does not produce a carry. "IVOperand + OtherOp" produces no carry iff
358 // IVOperand ULE (UnsignedMax - OtherOp).
360 const SCEV *UnsignedMax =
361 SE->getConstant(APInt::getMaxValue(IT->getBitWidth()));
362 const SCEV *UpperLimit = SE->getMinusSCEV(UnsignedMax, OtherOpSCEV);
364 bool NeverUnsignedOverflows =
365 SE->isKnownPredicate(ICmpInst::ICMP_ULE, IVOpSCEV, UpperLimit);
367 if (NeverUnsignedOverflows) {
368 BO->setHasNoUnsignedWrap(true);
376 /// \brief Split sadd.with.overflow into add + sadd.with.overflow to allow
377 /// analysis and optimization.
379 /// \return A new value representing the non-overflowing add if possible,
380 /// otherwise return the original value.
381 Instruction *SimplifyIndvar::splitOverflowIntrinsic(Instruction *IVUser,
382 const DominatorTree *DT) {
383 IntrinsicInst *II = dyn_cast<IntrinsicInst>(IVUser);
384 if (!II || II->getIntrinsicID() != Intrinsic::sadd_with_overflow)
387 // Find a branch guarded by the overflow check.
388 BranchInst *Branch = nullptr;
389 Instruction *AddVal = nullptr;
390 for (User *U : II->users()) {
391 if (ExtractValueInst *ExtractInst = dyn_cast<ExtractValueInst>(U)) {
392 if (ExtractInst->getNumIndices() != 1)
394 if (ExtractInst->getIndices()[0] == 0)
395 AddVal = ExtractInst;
396 else if (ExtractInst->getIndices()[0] == 1 && ExtractInst->hasOneUse())
397 Branch = dyn_cast<BranchInst>(ExtractInst->user_back());
400 if (!AddVal || !Branch)
403 BasicBlock *ContinueBB = Branch->getSuccessor(1);
404 if (std::next(pred_begin(ContinueBB)) != pred_end(ContinueBB))
407 // Check if all users of the add are provably NSW.
409 for (Use &U : AddVal->uses()) {
410 if (Instruction *UseInst = dyn_cast<Instruction>(U.getUser())) {
411 BasicBlock *UseBB = UseInst->getParent();
412 if (PHINode *PHI = dyn_cast<PHINode>(UseInst))
413 UseBB = PHI->getIncomingBlock(U);
414 if (!DT->dominates(ContinueBB, UseBB)) {
424 IRBuilder<> Builder(IVUser);
425 Instruction *AddInst = dyn_cast<Instruction>(
426 Builder.CreateNSWAdd(II->getOperand(0), II->getOperand(1)));
428 // The caller expects the new add to have the same form as the intrinsic. The
429 // IV operand position must be the same.
430 assert((AddInst->getOpcode() == Instruction::Add &&
431 AddInst->getOperand(0) == II->getOperand(0)) &&
432 "Bad add instruction created from overflow intrinsic.");
434 AddVal->replaceAllUsesWith(AddInst);
435 DeadInsts.push_back(AddVal);
439 /// Add all uses of Def to the current IV's worklist.
440 static void pushIVUsers(
442 SmallPtrSet<Instruction*,16> &Simplified,
443 SmallVectorImpl< std::pair<Instruction*,Instruction*> > &SimpleIVUsers) {
445 for (User *U : Def->users()) {
446 Instruction *UI = cast<Instruction>(U);
448 // Avoid infinite or exponential worklist processing.
449 // Also ensure unique worklist users.
450 // If Def is a LoopPhi, it may not be in the Simplified set, so check for
452 if (UI != Def && Simplified.insert(UI).second)
453 SimpleIVUsers.push_back(std::make_pair(UI, Def));
457 /// Return true if this instruction generates a simple SCEV
458 /// expression in terms of that IV.
460 /// This is similar to IVUsers' isInteresting() but processes each instruction
461 /// non-recursively when the operand is already known to be a simpleIVUser.
463 static bool isSimpleIVUser(Instruction *I, const Loop *L, ScalarEvolution *SE) {
464 if (!SE->isSCEVable(I->getType()))
467 // Get the symbolic expression for this instruction.
468 const SCEV *S = SE->getSCEV(I);
470 // Only consider affine recurrences.
471 const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(S);
472 if (AR && AR->getLoop() == L)
478 /// Iteratively perform simplification on a worklist of users
479 /// of the specified induction variable. Each successive simplification may push
480 /// more users which may themselves be candidates for simplification.
482 /// This algorithm does not require IVUsers analysis. Instead, it simplifies
483 /// instructions in-place during analysis. Rather than rewriting induction
484 /// variables bottom-up from their users, it transforms a chain of IVUsers
485 /// top-down, updating the IR only when it encouters a clear optimization
488 /// Once DisableIVRewrite is default, LSR will be the only client of IVUsers.
490 void SimplifyIndvar::simplifyUsers(PHINode *CurrIV, IVVisitor *V) {
491 if (!SE->isSCEVable(CurrIV->getType()))
494 // Instructions processed by SimplifyIndvar for CurrIV.
495 SmallPtrSet<Instruction*,16> Simplified;
497 // Use-def pairs if IV users waiting to be processed for CurrIV.
498 SmallVector<std::pair<Instruction*, Instruction*>, 8> SimpleIVUsers;
500 // Push users of the current LoopPhi. In rare cases, pushIVUsers may be
501 // called multiple times for the same LoopPhi. This is the proper thing to
502 // do for loop header phis that use each other.
503 pushIVUsers(CurrIV, Simplified, SimpleIVUsers);
505 while (!SimpleIVUsers.empty()) {
506 std::pair<Instruction*, Instruction*> UseOper =
507 SimpleIVUsers.pop_back_val();
508 Instruction *UseInst = UseOper.first;
510 // Bypass back edges to avoid extra work.
511 if (UseInst == CurrIV) continue;
513 if (V && V->shouldSplitOverflowInstrinsics()) {
514 UseInst = splitOverflowIntrinsic(UseInst, V->getDomTree());
519 Instruction *IVOperand = UseOper.second;
520 for (unsigned N = 0; IVOperand; ++N) {
521 assert(N <= Simplified.size() && "runaway iteration");
523 Value *NewOper = foldIVUser(UseOper.first, IVOperand);
525 break; // done folding
526 IVOperand = dyn_cast<Instruction>(NewOper);
531 if (eliminateIVUser(UseOper.first, IVOperand)) {
532 pushIVUsers(IVOperand, Simplified, SimpleIVUsers);
536 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(UseOper.first)) {
537 if (isa<OverflowingBinaryOperator>(BO) &&
538 strengthenOverflowingOperation(BO, IVOperand)) {
539 // re-queue uses of the now modified binary operator and fall
540 // through to the checks that remain.
541 pushIVUsers(IVOperand, Simplified, SimpleIVUsers);
545 CastInst *Cast = dyn_cast<CastInst>(UseOper.first);
550 if (isSimpleIVUser(UseOper.first, L, SE)) {
551 pushIVUsers(UseOper.first, Simplified, SimpleIVUsers);
558 void IVVisitor::anchor() { }
560 /// Simplify instructions that use this induction variable
561 /// by using ScalarEvolution to analyze the IV's recurrence.
562 bool simplifyUsersOfIV(PHINode *CurrIV, ScalarEvolution *SE, LPPassManager *LPM,
563 SmallVectorImpl<WeakVH> &Dead, IVVisitor *V)
565 LoopInfo *LI = &LPM->getAnalysis<LoopInfo>();
566 SimplifyIndvar SIV(LI->getLoopFor(CurrIV->getParent()), SE, LPM, Dead);
567 SIV.simplifyUsers(CurrIV, V);
568 return SIV.hasChanged();
571 /// Simplify users of induction variables within this
572 /// loop. This does not actually change or add IVs.
573 bool simplifyLoopIVs(Loop *L, ScalarEvolution *SE, LPPassManager *LPM,
574 SmallVectorImpl<WeakVH> &Dead) {
575 bool Changed = false;
576 for (BasicBlock::iterator I = L->getHeader()->begin(); isa<PHINode>(I); ++I) {
577 Changed |= simplifyUsersOfIV(cast<PHINode>(I), SE, LPM, Dead);