1 //===- ScalarEvolution.cpp - Scalar Evolution Analysis --------------------===//
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 contains the implementation of the scalar evolution analysis
11 // engine, which is used primarily to analyze expressions involving induction
12 // variables in loops.
14 // There are several aspects to this library. First is the representation of
15 // scalar expressions, which are represented as subclasses of the SCEV class.
16 // These classes are used to represent certain types of subexpressions that we
17 // can handle. We only create one SCEV of a particular shape, so
18 // pointer-comparisons for equality are legal.
20 // One important aspect of the SCEV objects is that they are never cyclic, even
21 // if there is a cycle in the dataflow for an expression (ie, a PHI node). If
22 // the PHI node is one of the idioms that we can represent (e.g., a polynomial
23 // recurrence) then we represent it directly as a recurrence node, otherwise we
24 // represent it as a SCEVUnknown node.
26 // In addition to being able to represent expressions of various types, we also
27 // have folders that are used to build the *canonical* representation for a
28 // particular expression. These folders are capable of using a variety of
29 // rewrite rules to simplify the expressions.
31 // Once the folders are defined, we can implement the more interesting
32 // higher-level code, such as the code that recognizes PHI nodes of various
33 // types, computes the execution count of a loop, etc.
35 // TODO: We should use these routines and value representations to implement
36 // dependence analysis!
38 //===----------------------------------------------------------------------===//
40 // There are several good references for the techniques used in this analysis.
42 // Chains of recurrences -- a method to expedite the evaluation
43 // of closed-form functions
44 // Olaf Bachmann, Paul S. Wang, Eugene V. Zima
46 // On computational properties of chains of recurrences
49 // Symbolic Evaluation of Chains of Recurrences for Loop Optimization
50 // Robert A. van Engelen
52 // Efficient Symbolic Analysis for Optimizing Compilers
53 // Robert A. van Engelen
55 // Using the chains of recurrences algebra for data dependence testing and
56 // induction variable substitution
57 // MS Thesis, Johnie Birch
59 //===----------------------------------------------------------------------===//
61 #include "llvm/Analysis/ScalarEvolution.h"
62 #include "llvm/ADT/APInt.h"
63 #include "llvm/ADT/ArrayRef.h"
64 #include "llvm/ADT/DenseMap.h"
65 #include "llvm/ADT/DepthFirstIterator.h"
66 #include "llvm/ADT/EquivalenceClasses.h"
67 #include "llvm/ADT/FoldingSet.h"
68 #include "llvm/ADT/None.h"
69 #include "llvm/ADT/Optional.h"
70 #include "llvm/ADT/STLExtras.h"
71 #include "llvm/ADT/ScopeExit.h"
72 #include "llvm/ADT/Sequence.h"
73 #include "llvm/ADT/SetVector.h"
74 #include "llvm/ADT/SmallPtrSet.h"
75 #include "llvm/ADT/SmallSet.h"
76 #include "llvm/ADT/SmallVector.h"
77 #include "llvm/ADT/Statistic.h"
78 #include "llvm/ADT/StringRef.h"
79 #include "llvm/Analysis/AssumptionCache.h"
80 #include "llvm/Analysis/ConstantFolding.h"
81 #include "llvm/Analysis/InstructionSimplify.h"
82 #include "llvm/Analysis/LoopInfo.h"
83 #include "llvm/Analysis/ScalarEvolutionExpressions.h"
84 #include "llvm/Analysis/TargetLibraryInfo.h"
85 #include "llvm/Analysis/ValueTracking.h"
86 #include "llvm/IR/Argument.h"
87 #include "llvm/IR/BasicBlock.h"
88 #include "llvm/IR/CFG.h"
89 #include "llvm/IR/CallSite.h"
90 #include "llvm/IR/Constant.h"
91 #include "llvm/IR/ConstantRange.h"
92 #include "llvm/IR/Constants.h"
93 #include "llvm/IR/DataLayout.h"
94 #include "llvm/IR/DerivedTypes.h"
95 #include "llvm/IR/Dominators.h"
96 #include "llvm/IR/Function.h"
97 #include "llvm/IR/GlobalAlias.h"
98 #include "llvm/IR/GlobalValue.h"
99 #include "llvm/IR/GlobalVariable.h"
100 #include "llvm/IR/InstIterator.h"
101 #include "llvm/IR/InstrTypes.h"
102 #include "llvm/IR/Instruction.h"
103 #include "llvm/IR/Instructions.h"
104 #include "llvm/IR/IntrinsicInst.h"
105 #include "llvm/IR/Intrinsics.h"
106 #include "llvm/IR/LLVMContext.h"
107 #include "llvm/IR/Metadata.h"
108 #include "llvm/IR/Operator.h"
109 #include "llvm/IR/PatternMatch.h"
110 #include "llvm/IR/Type.h"
111 #include "llvm/IR/Use.h"
112 #include "llvm/IR/User.h"
113 #include "llvm/IR/Value.h"
114 #include "llvm/Pass.h"
115 #include "llvm/Support/Casting.h"
116 #include "llvm/Support/CommandLine.h"
117 #include "llvm/Support/Compiler.h"
118 #include "llvm/Support/Debug.h"
119 #include "llvm/Support/ErrorHandling.h"
120 #include "llvm/Support/KnownBits.h"
121 #include "llvm/Support/SaveAndRestore.h"
122 #include "llvm/Support/raw_ostream.h"
135 using namespace llvm;
137 #define DEBUG_TYPE "scalar-evolution"
139 STATISTIC(NumArrayLenItCounts,
140 "Number of trip counts computed with array length");
141 STATISTIC(NumTripCountsComputed,
142 "Number of loops with predictable loop counts");
143 STATISTIC(NumTripCountsNotComputed,
144 "Number of loops without predictable loop counts");
145 STATISTIC(NumBruteForceTripCountsComputed,
146 "Number of loops with trip counts computed by force");
148 static cl::opt<unsigned>
149 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
150 cl::desc("Maximum number of iterations SCEV will "
151 "symbolically execute a constant "
155 // FIXME: Enable this with EXPENSIVE_CHECKS when the test suite is clean.
156 static cl::opt<bool> VerifySCEV(
157 "verify-scev", cl::Hidden,
158 cl::desc("Verify ScalarEvolution's backedge taken counts (slow)"));
160 VerifySCEVMap("verify-scev-maps", cl::Hidden,
161 cl::desc("Verify no dangling value in ScalarEvolution's "
162 "ExprValueMap (slow)"));
164 static cl::opt<unsigned> MulOpsInlineThreshold(
165 "scev-mulops-inline-threshold", cl::Hidden,
166 cl::desc("Threshold for inlining multiplication operands into a SCEV"),
169 static cl::opt<unsigned> AddOpsInlineThreshold(
170 "scev-addops-inline-threshold", cl::Hidden,
171 cl::desc("Threshold for inlining addition operands into a SCEV"),
174 static cl::opt<unsigned> MaxSCEVCompareDepth(
175 "scalar-evolution-max-scev-compare-depth", cl::Hidden,
176 cl::desc("Maximum depth of recursive SCEV complexity comparisons"),
179 static cl::opt<unsigned> MaxSCEVOperationsImplicationDepth(
180 "scalar-evolution-max-scev-operations-implication-depth", cl::Hidden,
181 cl::desc("Maximum depth of recursive SCEV operations implication analysis"),
184 static cl::opt<unsigned> MaxValueCompareDepth(
185 "scalar-evolution-max-value-compare-depth", cl::Hidden,
186 cl::desc("Maximum depth of recursive value complexity comparisons"),
189 static cl::opt<unsigned>
190 MaxArithDepth("scalar-evolution-max-arith-depth", cl::Hidden,
191 cl::desc("Maximum depth of recursive arithmetics"),
194 static cl::opt<unsigned> MaxConstantEvolvingDepth(
195 "scalar-evolution-max-constant-evolving-depth", cl::Hidden,
196 cl::desc("Maximum depth of recursive constant evolving"), cl::init(32));
198 static cl::opt<unsigned>
199 MaxExtDepth("scalar-evolution-max-ext-depth", cl::Hidden,
200 cl::desc("Maximum depth of recursive SExt/ZExt"),
203 static cl::opt<unsigned>
204 MaxAddRecSize("scalar-evolution-max-add-rec-size", cl::Hidden,
205 cl::desc("Max coefficients in AddRec during evolving"),
208 //===----------------------------------------------------------------------===//
209 // SCEV class definitions
210 //===----------------------------------------------------------------------===//
212 //===----------------------------------------------------------------------===//
213 // Implementation of the SCEV class.
216 #if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP)
217 LLVM_DUMP_METHOD void SCEV::dump() const {
223 void SCEV::print(raw_ostream &OS) const {
224 switch (static_cast<SCEVTypes>(getSCEVType())) {
226 cast<SCEVConstant>(this)->getValue()->printAsOperand(OS, false);
229 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(this);
230 const SCEV *Op = Trunc->getOperand();
231 OS << "(trunc " << *Op->getType() << " " << *Op << " to "
232 << *Trunc->getType() << ")";
236 const SCEVZeroExtendExpr *ZExt = cast<SCEVZeroExtendExpr>(this);
237 const SCEV *Op = ZExt->getOperand();
238 OS << "(zext " << *Op->getType() << " " << *Op << " to "
239 << *ZExt->getType() << ")";
243 const SCEVSignExtendExpr *SExt = cast<SCEVSignExtendExpr>(this);
244 const SCEV *Op = SExt->getOperand();
245 OS << "(sext " << *Op->getType() << " " << *Op << " to "
246 << *SExt->getType() << ")";
250 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(this);
251 OS << "{" << *AR->getOperand(0);
252 for (unsigned i = 1, e = AR->getNumOperands(); i != e; ++i)
253 OS << ",+," << *AR->getOperand(i);
255 if (AR->hasNoUnsignedWrap())
257 if (AR->hasNoSignedWrap())
259 if (AR->hasNoSelfWrap() &&
260 !AR->getNoWrapFlags((NoWrapFlags)(FlagNUW | FlagNSW)))
262 AR->getLoop()->getHeader()->printAsOperand(OS, /*PrintType=*/false);
270 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(this);
271 const char *OpStr = nullptr;
272 switch (NAry->getSCEVType()) {
273 case scAddExpr: OpStr = " + "; break;
274 case scMulExpr: OpStr = " * "; break;
275 case scUMaxExpr: OpStr = " umax "; break;
276 case scSMaxExpr: OpStr = " smax "; break;
279 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
282 if (std::next(I) != E)
286 switch (NAry->getSCEVType()) {
289 if (NAry->hasNoUnsignedWrap())
291 if (NAry->hasNoSignedWrap())
297 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(this);
298 OS << "(" << *UDiv->getLHS() << " /u " << *UDiv->getRHS() << ")";
302 const SCEVUnknown *U = cast<SCEVUnknown>(this);
304 if (U->isSizeOf(AllocTy)) {
305 OS << "sizeof(" << *AllocTy << ")";
308 if (U->isAlignOf(AllocTy)) {
309 OS << "alignof(" << *AllocTy << ")";
315 if (U->isOffsetOf(CTy, FieldNo)) {
316 OS << "offsetof(" << *CTy << ", ";
317 FieldNo->printAsOperand(OS, false);
322 // Otherwise just print it normally.
323 U->getValue()->printAsOperand(OS, false);
326 case scCouldNotCompute:
327 OS << "***COULDNOTCOMPUTE***";
330 llvm_unreachable("Unknown SCEV kind!");
333 Type *SCEV::getType() const {
334 switch (static_cast<SCEVTypes>(getSCEVType())) {
336 return cast<SCEVConstant>(this)->getType();
340 return cast<SCEVCastExpr>(this)->getType();
345 return cast<SCEVNAryExpr>(this)->getType();
347 return cast<SCEVAddExpr>(this)->getType();
349 return cast<SCEVUDivExpr>(this)->getType();
351 return cast<SCEVUnknown>(this)->getType();
352 case scCouldNotCompute:
353 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
355 llvm_unreachable("Unknown SCEV kind!");
358 bool SCEV::isZero() const {
359 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
360 return SC->getValue()->isZero();
364 bool SCEV::isOne() const {
365 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
366 return SC->getValue()->isOne();
370 bool SCEV::isAllOnesValue() const {
371 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
372 return SC->getValue()->isMinusOne();
376 bool SCEV::isNonConstantNegative() const {
377 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(this);
378 if (!Mul) return false;
380 // If there is a constant factor, it will be first.
381 const SCEVConstant *SC = dyn_cast<SCEVConstant>(Mul->getOperand(0));
382 if (!SC) return false;
384 // Return true if the value is negative, this matches things like (-42 * V).
385 return SC->getAPInt().isNegative();
388 SCEVCouldNotCompute::SCEVCouldNotCompute() :
389 SCEV(FoldingSetNodeIDRef(), scCouldNotCompute) {}
391 bool SCEVCouldNotCompute::classof(const SCEV *S) {
392 return S->getSCEVType() == scCouldNotCompute;
395 const SCEV *ScalarEvolution::getConstant(ConstantInt *V) {
397 ID.AddInteger(scConstant);
400 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
401 SCEV *S = new (SCEVAllocator) SCEVConstant(ID.Intern(SCEVAllocator), V);
402 UniqueSCEVs.InsertNode(S, IP);
406 const SCEV *ScalarEvolution::getConstant(const APInt &Val) {
407 return getConstant(ConstantInt::get(getContext(), Val));
411 ScalarEvolution::getConstant(Type *Ty, uint64_t V, bool isSigned) {
412 IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty));
413 return getConstant(ConstantInt::get(ITy, V, isSigned));
416 SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID,
417 unsigned SCEVTy, const SCEV *op, Type *ty)
418 : SCEV(ID, SCEVTy), Op(op), Ty(ty) {}
420 SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID,
421 const SCEV *op, Type *ty)
422 : SCEVCastExpr(ID, scTruncate, op, ty) {
423 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
424 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
425 "Cannot truncate non-integer value!");
428 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID,
429 const SCEV *op, Type *ty)
430 : SCEVCastExpr(ID, scZeroExtend, op, ty) {
431 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
432 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
433 "Cannot zero extend non-integer value!");
436 SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID,
437 const SCEV *op, Type *ty)
438 : SCEVCastExpr(ID, scSignExtend, op, ty) {
439 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
440 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
441 "Cannot sign extend non-integer value!");
444 void SCEVUnknown::deleted() {
445 // Clear this SCEVUnknown from various maps.
446 SE->forgetMemoizedResults(this);
448 // Remove this SCEVUnknown from the uniquing map.
449 SE->UniqueSCEVs.RemoveNode(this);
451 // Release the value.
455 void SCEVUnknown::allUsesReplacedWith(Value *New) {
456 // Remove this SCEVUnknown from the uniquing map.
457 SE->UniqueSCEVs.RemoveNode(this);
459 // Update this SCEVUnknown to point to the new value. This is needed
460 // because there may still be outstanding SCEVs which still point to
465 bool SCEVUnknown::isSizeOf(Type *&AllocTy) const {
466 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
467 if (VCE->getOpcode() == Instruction::PtrToInt)
468 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
469 if (CE->getOpcode() == Instruction::GetElementPtr &&
470 CE->getOperand(0)->isNullValue() &&
471 CE->getNumOperands() == 2)
472 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1)))
474 AllocTy = cast<PointerType>(CE->getOperand(0)->getType())
482 bool SCEVUnknown::isAlignOf(Type *&AllocTy) const {
483 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
484 if (VCE->getOpcode() == Instruction::PtrToInt)
485 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
486 if (CE->getOpcode() == Instruction::GetElementPtr &&
487 CE->getOperand(0)->isNullValue()) {
489 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
490 if (StructType *STy = dyn_cast<StructType>(Ty))
491 if (!STy->isPacked() &&
492 CE->getNumOperands() == 3 &&
493 CE->getOperand(1)->isNullValue()) {
494 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2)))
496 STy->getNumElements() == 2 &&
497 STy->getElementType(0)->isIntegerTy(1)) {
498 AllocTy = STy->getElementType(1);
507 bool SCEVUnknown::isOffsetOf(Type *&CTy, Constant *&FieldNo) const {
508 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
509 if (VCE->getOpcode() == Instruction::PtrToInt)
510 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
511 if (CE->getOpcode() == Instruction::GetElementPtr &&
512 CE->getNumOperands() == 3 &&
513 CE->getOperand(0)->isNullValue() &&
514 CE->getOperand(1)->isNullValue()) {
516 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
517 // Ignore vector types here so that ScalarEvolutionExpander doesn't
518 // emit getelementptrs that index into vectors.
519 if (Ty->isStructTy() || Ty->isArrayTy()) {
521 FieldNo = CE->getOperand(2);
529 //===----------------------------------------------------------------------===//
531 //===----------------------------------------------------------------------===//
533 /// Compare the two values \p LV and \p RV in terms of their "complexity" where
534 /// "complexity" is a partial (and somewhat ad-hoc) relation used to order
535 /// operands in SCEV expressions. \p EqCache is a set of pairs of values that
536 /// have been previously deemed to be "equally complex" by this routine. It is
537 /// intended to avoid exponential time complexity in cases like:
547 /// CompareValueComplexity(%f, %c)
549 /// Since we do not continue running this routine on expression trees once we
550 /// have seen unequal values, there is no need to track them in the cache.
552 CompareValueComplexity(EquivalenceClasses<const Value *> &EqCacheValue,
553 const LoopInfo *const LI, Value *LV, Value *RV,
555 if (Depth > MaxValueCompareDepth || EqCacheValue.isEquivalent(LV, RV))
558 // Order pointer values after integer values. This helps SCEVExpander form
560 bool LIsPointer = LV->getType()->isPointerTy(),
561 RIsPointer = RV->getType()->isPointerTy();
562 if (LIsPointer != RIsPointer)
563 return (int)LIsPointer - (int)RIsPointer;
565 // Compare getValueID values.
566 unsigned LID = LV->getValueID(), RID = RV->getValueID();
568 return (int)LID - (int)RID;
570 // Sort arguments by their position.
571 if (const auto *LA = dyn_cast<Argument>(LV)) {
572 const auto *RA = cast<Argument>(RV);
573 unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo();
574 return (int)LArgNo - (int)RArgNo;
577 if (const auto *LGV = dyn_cast<GlobalValue>(LV)) {
578 const auto *RGV = cast<GlobalValue>(RV);
580 const auto IsGVNameSemantic = [&](const GlobalValue *GV) {
581 auto LT = GV->getLinkage();
582 return !(GlobalValue::isPrivateLinkage(LT) ||
583 GlobalValue::isInternalLinkage(LT));
586 // Use the names to distinguish the two values, but only if the
587 // names are semantically important.
588 if (IsGVNameSemantic(LGV) && IsGVNameSemantic(RGV))
589 return LGV->getName().compare(RGV->getName());
592 // For instructions, compare their loop depth, and their operand count. This
594 if (const auto *LInst = dyn_cast<Instruction>(LV)) {
595 const auto *RInst = cast<Instruction>(RV);
597 // Compare loop depths.
598 const BasicBlock *LParent = LInst->getParent(),
599 *RParent = RInst->getParent();
600 if (LParent != RParent) {
601 unsigned LDepth = LI->getLoopDepth(LParent),
602 RDepth = LI->getLoopDepth(RParent);
603 if (LDepth != RDepth)
604 return (int)LDepth - (int)RDepth;
607 // Compare the number of operands.
608 unsigned LNumOps = LInst->getNumOperands(),
609 RNumOps = RInst->getNumOperands();
610 if (LNumOps != RNumOps)
611 return (int)LNumOps - (int)RNumOps;
613 for (unsigned Idx : seq(0u, LNumOps)) {
615 CompareValueComplexity(EqCacheValue, LI, LInst->getOperand(Idx),
616 RInst->getOperand(Idx), Depth + 1);
622 EqCacheValue.unionSets(LV, RV);
626 // Return negative, zero, or positive, if LHS is less than, equal to, or greater
627 // than RHS, respectively. A three-way result allows recursive comparisons to be
629 static int CompareSCEVComplexity(
630 EquivalenceClasses<const SCEV *> &EqCacheSCEV,
631 EquivalenceClasses<const Value *> &EqCacheValue,
632 const LoopInfo *const LI, const SCEV *LHS, const SCEV *RHS,
633 DominatorTree &DT, unsigned Depth = 0) {
634 // Fast-path: SCEVs are uniqued so we can do a quick equality check.
638 // Primarily, sort the SCEVs by their getSCEVType().
639 unsigned LType = LHS->getSCEVType(), RType = RHS->getSCEVType();
641 return (int)LType - (int)RType;
643 if (Depth > MaxSCEVCompareDepth || EqCacheSCEV.isEquivalent(LHS, RHS))
645 // Aside from the getSCEVType() ordering, the particular ordering
646 // isn't very important except that it's beneficial to be consistent,
647 // so that (a + b) and (b + a) don't end up as different expressions.
648 switch (static_cast<SCEVTypes>(LType)) {
650 const SCEVUnknown *LU = cast<SCEVUnknown>(LHS);
651 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
653 int X = CompareValueComplexity(EqCacheValue, LI, LU->getValue(),
654 RU->getValue(), Depth + 1);
656 EqCacheSCEV.unionSets(LHS, RHS);
661 const SCEVConstant *LC = cast<SCEVConstant>(LHS);
662 const SCEVConstant *RC = cast<SCEVConstant>(RHS);
664 // Compare constant values.
665 const APInt &LA = LC->getAPInt();
666 const APInt &RA = RC->getAPInt();
667 unsigned LBitWidth = LA.getBitWidth(), RBitWidth = RA.getBitWidth();
668 if (LBitWidth != RBitWidth)
669 return (int)LBitWidth - (int)RBitWidth;
670 return LA.ult(RA) ? -1 : 1;
674 const SCEVAddRecExpr *LA = cast<SCEVAddRecExpr>(LHS);
675 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS);
677 // There is always a dominance between two recs that are used by one SCEV,
678 // so we can safely sort recs by loop header dominance. We require such
679 // order in getAddExpr.
680 const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop();
681 if (LLoop != RLoop) {
682 const BasicBlock *LHead = LLoop->getHeader(), *RHead = RLoop->getHeader();
683 assert(LHead != RHead && "Two loops share the same header?");
684 if (DT.dominates(LHead, RHead))
687 assert(DT.dominates(RHead, LHead) &&
688 "No dominance between recurrences used by one SCEV?");
692 // Addrec complexity grows with operand count.
693 unsigned LNumOps = LA->getNumOperands(), RNumOps = RA->getNumOperands();
694 if (LNumOps != RNumOps)
695 return (int)LNumOps - (int)RNumOps;
697 // Compare NoWrap flags.
698 if (LA->getNoWrapFlags() != RA->getNoWrapFlags())
699 return (int)LA->getNoWrapFlags() - (int)RA->getNoWrapFlags();
701 // Lexicographically compare.
702 for (unsigned i = 0; i != LNumOps; ++i) {
703 int X = CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI,
704 LA->getOperand(i), RA->getOperand(i), DT,
709 EqCacheSCEV.unionSets(LHS, RHS);
717 const SCEVNAryExpr *LC = cast<SCEVNAryExpr>(LHS);
718 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
720 // Lexicographically compare n-ary expressions.
721 unsigned LNumOps = LC->getNumOperands(), RNumOps = RC->getNumOperands();
722 if (LNumOps != RNumOps)
723 return (int)LNumOps - (int)RNumOps;
725 // Compare NoWrap flags.
726 if (LC->getNoWrapFlags() != RC->getNoWrapFlags())
727 return (int)LC->getNoWrapFlags() - (int)RC->getNoWrapFlags();
729 for (unsigned i = 0; i != LNumOps; ++i) {
730 int X = CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI,
731 LC->getOperand(i), RC->getOperand(i), DT,
736 EqCacheSCEV.unionSets(LHS, RHS);
741 const SCEVUDivExpr *LC = cast<SCEVUDivExpr>(LHS);
742 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
744 // Lexicographically compare udiv expressions.
745 int X = CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI, LC->getLHS(),
746 RC->getLHS(), DT, Depth + 1);
749 X = CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI, LC->getRHS(),
750 RC->getRHS(), DT, Depth + 1);
752 EqCacheSCEV.unionSets(LHS, RHS);
759 const SCEVCastExpr *LC = cast<SCEVCastExpr>(LHS);
760 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
762 // Compare cast expressions by operand.
763 int X = CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI,
764 LC->getOperand(), RC->getOperand(), DT,
767 EqCacheSCEV.unionSets(LHS, RHS);
771 case scCouldNotCompute:
772 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
774 llvm_unreachable("Unknown SCEV kind!");
777 /// Given a list of SCEV objects, order them by their complexity, and group
778 /// objects of the same complexity together by value. When this routine is
779 /// finished, we know that any duplicates in the vector are consecutive and that
780 /// complexity is monotonically increasing.
782 /// Note that we go take special precautions to ensure that we get deterministic
783 /// results from this routine. In other words, we don't want the results of
784 /// this to depend on where the addresses of various SCEV objects happened to
786 static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops,
787 LoopInfo *LI, DominatorTree &DT) {
788 if (Ops.size() < 2) return; // Noop
790 EquivalenceClasses<const SCEV *> EqCacheSCEV;
791 EquivalenceClasses<const Value *> EqCacheValue;
792 if (Ops.size() == 2) {
793 // This is the common case, which also happens to be trivially simple.
795 const SCEV *&LHS = Ops[0], *&RHS = Ops[1];
796 if (CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI, RHS, LHS, DT) < 0)
801 // Do the rough sort by complexity.
802 std::stable_sort(Ops.begin(), Ops.end(),
803 [&](const SCEV *LHS, const SCEV *RHS) {
804 return CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI,
808 // Now that we are sorted by complexity, group elements of the same
809 // complexity. Note that this is, at worst, N^2, but the vector is likely to
810 // be extremely short in practice. Note that we take this approach because we
811 // do not want to depend on the addresses of the objects we are grouping.
812 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
813 const SCEV *S = Ops[i];
814 unsigned Complexity = S->getSCEVType();
816 // If there are any objects of the same complexity and same value as this
818 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
819 if (Ops[j] == S) { // Found a duplicate.
820 // Move it to immediately after i'th element.
821 std::swap(Ops[i+1], Ops[j]);
822 ++i; // no need to rescan it.
823 if (i == e-2) return; // Done!
829 // Returns the size of the SCEV S.
830 static inline int sizeOfSCEV(const SCEV *S) {
831 struct FindSCEVSize {
834 FindSCEVSize() = default;
836 bool follow(const SCEV *S) {
838 // Keep looking at all operands of S.
842 bool isDone() const {
848 SCEVTraversal<FindSCEVSize> ST(F);
855 struct SCEVDivision : public SCEVVisitor<SCEVDivision, void> {
857 // Computes the Quotient and Remainder of the division of Numerator by
859 static void divide(ScalarEvolution &SE, const SCEV *Numerator,
860 const SCEV *Denominator, const SCEV **Quotient,
861 const SCEV **Remainder) {
862 assert(Numerator && Denominator && "Uninitialized SCEV");
864 SCEVDivision D(SE, Numerator, Denominator);
866 // Check for the trivial case here to avoid having to check for it in the
868 if (Numerator == Denominator) {
874 if (Numerator->isZero()) {
880 // A simple case when N/1. The quotient is N.
881 if (Denominator->isOne()) {
882 *Quotient = Numerator;
887 // Split the Denominator when it is a product.
888 if (const SCEVMulExpr *T = dyn_cast<SCEVMulExpr>(Denominator)) {
890 *Quotient = Numerator;
891 for (const SCEV *Op : T->operands()) {
892 divide(SE, *Quotient, Op, &Q, &R);
895 // Bail out when the Numerator is not divisible by one of the terms of
899 *Remainder = Numerator;
908 *Quotient = D.Quotient;
909 *Remainder = D.Remainder;
912 // Except in the trivial case described above, we do not know how to divide
913 // Expr by Denominator for the following functions with empty implementation.
914 void visitTruncateExpr(const SCEVTruncateExpr *Numerator) {}
915 void visitZeroExtendExpr(const SCEVZeroExtendExpr *Numerator) {}
916 void visitSignExtendExpr(const SCEVSignExtendExpr *Numerator) {}
917 void visitUDivExpr(const SCEVUDivExpr *Numerator) {}
918 void visitSMaxExpr(const SCEVSMaxExpr *Numerator) {}
919 void visitUMaxExpr(const SCEVUMaxExpr *Numerator) {}
920 void visitUnknown(const SCEVUnknown *Numerator) {}
921 void visitCouldNotCompute(const SCEVCouldNotCompute *Numerator) {}
923 void visitConstant(const SCEVConstant *Numerator) {
924 if (const SCEVConstant *D = dyn_cast<SCEVConstant>(Denominator)) {
925 APInt NumeratorVal = Numerator->getAPInt();
926 APInt DenominatorVal = D->getAPInt();
927 uint32_t NumeratorBW = NumeratorVal.getBitWidth();
928 uint32_t DenominatorBW = DenominatorVal.getBitWidth();
930 if (NumeratorBW > DenominatorBW)
931 DenominatorVal = DenominatorVal.sext(NumeratorBW);
932 else if (NumeratorBW < DenominatorBW)
933 NumeratorVal = NumeratorVal.sext(DenominatorBW);
935 APInt QuotientVal(NumeratorVal.getBitWidth(), 0);
936 APInt RemainderVal(NumeratorVal.getBitWidth(), 0);
937 APInt::sdivrem(NumeratorVal, DenominatorVal, QuotientVal, RemainderVal);
938 Quotient = SE.getConstant(QuotientVal);
939 Remainder = SE.getConstant(RemainderVal);
944 void visitAddRecExpr(const SCEVAddRecExpr *Numerator) {
945 const SCEV *StartQ, *StartR, *StepQ, *StepR;
946 if (!Numerator->isAffine())
947 return cannotDivide(Numerator);
948 divide(SE, Numerator->getStart(), Denominator, &StartQ, &StartR);
949 divide(SE, Numerator->getStepRecurrence(SE), Denominator, &StepQ, &StepR);
950 // Bail out if the types do not match.
951 Type *Ty = Denominator->getType();
952 if (Ty != StartQ->getType() || Ty != StartR->getType() ||
953 Ty != StepQ->getType() || Ty != StepR->getType())
954 return cannotDivide(Numerator);
955 Quotient = SE.getAddRecExpr(StartQ, StepQ, Numerator->getLoop(),
956 Numerator->getNoWrapFlags());
957 Remainder = SE.getAddRecExpr(StartR, StepR, Numerator->getLoop(),
958 Numerator->getNoWrapFlags());
961 void visitAddExpr(const SCEVAddExpr *Numerator) {
962 SmallVector<const SCEV *, 2> Qs, Rs;
963 Type *Ty = Denominator->getType();
965 for (const SCEV *Op : Numerator->operands()) {
967 divide(SE, Op, Denominator, &Q, &R);
969 // Bail out if types do not match.
970 if (Ty != Q->getType() || Ty != R->getType())
971 return cannotDivide(Numerator);
977 if (Qs.size() == 1) {
983 Quotient = SE.getAddExpr(Qs);
984 Remainder = SE.getAddExpr(Rs);
987 void visitMulExpr(const SCEVMulExpr *Numerator) {
988 SmallVector<const SCEV *, 2> Qs;
989 Type *Ty = Denominator->getType();
991 bool FoundDenominatorTerm = false;
992 for (const SCEV *Op : Numerator->operands()) {
993 // Bail out if types do not match.
994 if (Ty != Op->getType())
995 return cannotDivide(Numerator);
997 if (FoundDenominatorTerm) {
1002 // Check whether Denominator divides one of the product operands.
1004 divide(SE, Op, Denominator, &Q, &R);
1010 // Bail out if types do not match.
1011 if (Ty != Q->getType())
1012 return cannotDivide(Numerator);
1014 FoundDenominatorTerm = true;
1018 if (FoundDenominatorTerm) {
1023 Quotient = SE.getMulExpr(Qs);
1027 if (!isa<SCEVUnknown>(Denominator))
1028 return cannotDivide(Numerator);
1030 // The Remainder is obtained by replacing Denominator by 0 in Numerator.
1031 ValueToValueMap RewriteMap;
1032 RewriteMap[cast<SCEVUnknown>(Denominator)->getValue()] =
1033 cast<SCEVConstant>(Zero)->getValue();
1034 Remainder = SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true);
1036 if (Remainder->isZero()) {
1037 // The Quotient is obtained by replacing Denominator by 1 in Numerator.
1038 RewriteMap[cast<SCEVUnknown>(Denominator)->getValue()] =
1039 cast<SCEVConstant>(One)->getValue();
1041 SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true);
1045 // Quotient is (Numerator - Remainder) divided by Denominator.
1047 const SCEV *Diff = SE.getMinusSCEV(Numerator, Remainder);
1048 // This SCEV does not seem to simplify: fail the division here.
1049 if (sizeOfSCEV(Diff) > sizeOfSCEV(Numerator))
1050 return cannotDivide(Numerator);
1051 divide(SE, Diff, Denominator, &Q, &R);
1053 return cannotDivide(Numerator);
1058 SCEVDivision(ScalarEvolution &S, const SCEV *Numerator,
1059 const SCEV *Denominator)
1060 : SE(S), Denominator(Denominator) {
1061 Zero = SE.getZero(Denominator->getType());
1062 One = SE.getOne(Denominator->getType());
1064 // We generally do not know how to divide Expr by Denominator. We
1065 // initialize the division to a "cannot divide" state to simplify the rest
1067 cannotDivide(Numerator);
1070 // Convenience function for giving up on the division. We set the quotient to
1071 // be equal to zero and the remainder to be equal to the numerator.
1072 void cannotDivide(const SCEV *Numerator) {
1074 Remainder = Numerator;
1077 ScalarEvolution &SE;
1078 const SCEV *Denominator, *Quotient, *Remainder, *Zero, *One;
1081 } // end anonymous namespace
1083 //===----------------------------------------------------------------------===//
1084 // Simple SCEV method implementations
1085 //===----------------------------------------------------------------------===//
1087 /// Compute BC(It, K). The result has width W. Assume, K > 0.
1088 static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K,
1089 ScalarEvolution &SE,
1091 // Handle the simplest case efficiently.
1093 return SE.getTruncateOrZeroExtend(It, ResultTy);
1095 // We are using the following formula for BC(It, K):
1097 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
1099 // Suppose, W is the bitwidth of the return value. We must be prepared for
1100 // overflow. Hence, we must assure that the result of our computation is
1101 // equal to the accurate one modulo 2^W. Unfortunately, division isn't
1102 // safe in modular arithmetic.
1104 // However, this code doesn't use exactly that formula; the formula it uses
1105 // is something like the following, where T is the number of factors of 2 in
1106 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
1109 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
1111 // This formula is trivially equivalent to the previous formula. However,
1112 // this formula can be implemented much more efficiently. The trick is that
1113 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
1114 // arithmetic. To do exact division in modular arithmetic, all we have
1115 // to do is multiply by the inverse. Therefore, this step can be done at
1118 // The next issue is how to safely do the division by 2^T. The way this
1119 // is done is by doing the multiplication step at a width of at least W + T
1120 // bits. This way, the bottom W+T bits of the product are accurate. Then,
1121 // when we perform the division by 2^T (which is equivalent to a right shift
1122 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
1123 // truncated out after the division by 2^T.
1125 // In comparison to just directly using the first formula, this technique
1126 // is much more efficient; using the first formula requires W * K bits,
1127 // but this formula less than W + K bits. Also, the first formula requires
1128 // a division step, whereas this formula only requires multiplies and shifts.
1130 // It doesn't matter whether the subtraction step is done in the calculation
1131 // width or the input iteration count's width; if the subtraction overflows,
1132 // the result must be zero anyway. We prefer here to do it in the width of
1133 // the induction variable because it helps a lot for certain cases; CodeGen
1134 // isn't smart enough to ignore the overflow, which leads to much less
1135 // efficient code if the width of the subtraction is wider than the native
1138 // (It's possible to not widen at all by pulling out factors of 2 before
1139 // the multiplication; for example, K=2 can be calculated as
1140 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
1141 // extra arithmetic, so it's not an obvious win, and it gets
1142 // much more complicated for K > 3.)
1144 // Protection from insane SCEVs; this bound is conservative,
1145 // but it probably doesn't matter.
1147 return SE.getCouldNotCompute();
1149 unsigned W = SE.getTypeSizeInBits(ResultTy);
1151 // Calculate K! / 2^T and T; we divide out the factors of two before
1152 // multiplying for calculating K! / 2^T to avoid overflow.
1153 // Other overflow doesn't matter because we only care about the bottom
1154 // W bits of the result.
1155 APInt OddFactorial(W, 1);
1157 for (unsigned i = 3; i <= K; ++i) {
1159 unsigned TwoFactors = Mult.countTrailingZeros();
1161 Mult.lshrInPlace(TwoFactors);
1162 OddFactorial *= Mult;
1165 // We need at least W + T bits for the multiplication step
1166 unsigned CalculationBits = W + T;
1168 // Calculate 2^T, at width T+W.
1169 APInt DivFactor = APInt::getOneBitSet(CalculationBits, T);
1171 // Calculate the multiplicative inverse of K! / 2^T;
1172 // this multiplication factor will perform the exact division by
1174 APInt Mod = APInt::getSignedMinValue(W+1);
1175 APInt MultiplyFactor = OddFactorial.zext(W+1);
1176 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
1177 MultiplyFactor = MultiplyFactor.trunc(W);
1179 // Calculate the product, at width T+W
1180 IntegerType *CalculationTy = IntegerType::get(SE.getContext(),
1182 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
1183 for (unsigned i = 1; i != K; ++i) {
1184 const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i));
1185 Dividend = SE.getMulExpr(Dividend,
1186 SE.getTruncateOrZeroExtend(S, CalculationTy));
1190 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
1192 // Truncate the result, and divide by K! / 2^T.
1194 return SE.getMulExpr(SE.getConstant(MultiplyFactor),
1195 SE.getTruncateOrZeroExtend(DivResult, ResultTy));
1198 /// Return the value of this chain of recurrences at the specified iteration
1199 /// number. We can evaluate this recurrence by multiplying each element in the
1200 /// chain by the binomial coefficient corresponding to it. In other words, we
1201 /// can evaluate {A,+,B,+,C,+,D} as:
1203 /// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
1205 /// where BC(It, k) stands for binomial coefficient.
1206 const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It,
1207 ScalarEvolution &SE) const {
1208 const SCEV *Result = getStart();
1209 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
1210 // The computation is correct in the face of overflow provided that the
1211 // multiplication is performed _after_ the evaluation of the binomial
1213 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType());
1214 if (isa<SCEVCouldNotCompute>(Coeff))
1217 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
1222 //===----------------------------------------------------------------------===//
1223 // SCEV Expression folder implementations
1224 //===----------------------------------------------------------------------===//
1226 const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op,
1228 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
1229 "This is not a truncating conversion!");
1230 assert(isSCEVable(Ty) &&
1231 "This is not a conversion to a SCEVable type!");
1232 Ty = getEffectiveSCEVType(Ty);
1234 FoldingSetNodeID ID;
1235 ID.AddInteger(scTruncate);
1239 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1241 // Fold if the operand is constant.
1242 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1244 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty)));
1246 // trunc(trunc(x)) --> trunc(x)
1247 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
1248 return getTruncateExpr(ST->getOperand(), Ty);
1250 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
1251 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1252 return getTruncateOrSignExtend(SS->getOperand(), Ty);
1254 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
1255 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1256 return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
1258 // trunc(x1+x2+...+xN) --> trunc(x1)+trunc(x2)+...+trunc(xN) if we can
1259 // eliminate all the truncates, or we replace other casts with truncates.
1260 if (const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Op)) {
1261 SmallVector<const SCEV *, 4> Operands;
1262 bool hasTrunc = false;
1263 for (unsigned i = 0, e = SA->getNumOperands(); i != e && !hasTrunc; ++i) {
1264 const SCEV *S = getTruncateExpr(SA->getOperand(i), Ty);
1265 if (!isa<SCEVCastExpr>(SA->getOperand(i)))
1266 hasTrunc = isa<SCEVTruncateExpr>(S);
1267 Operands.push_back(S);
1270 return getAddExpr(Operands);
1271 // In spite we checked in the beginning that ID is not in the cache,
1272 // it is possible that during recursion and different modification
1273 // ID came to cache, so if we found it, just return it.
1274 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP))
1278 // trunc(x1*x2*...*xN) --> trunc(x1)*trunc(x2)*...*trunc(xN) if we can
1279 // eliminate all the truncates, or we replace other casts with truncates.
1280 if (const SCEVMulExpr *SM = dyn_cast<SCEVMulExpr>(Op)) {
1281 SmallVector<const SCEV *, 4> Operands;
1282 bool hasTrunc = false;
1283 for (unsigned i = 0, e = SM->getNumOperands(); i != e && !hasTrunc; ++i) {
1284 const SCEV *S = getTruncateExpr(SM->getOperand(i), Ty);
1285 if (!isa<SCEVCastExpr>(SM->getOperand(i)))
1286 hasTrunc = isa<SCEVTruncateExpr>(S);
1287 Operands.push_back(S);
1290 return getMulExpr(Operands);
1291 // In spite we checked in the beginning that ID is not in the cache,
1292 // it is possible that during recursion and different modification
1293 // ID came to cache, so if we found it, just return it.
1294 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP))
1298 // If the input value is a chrec scev, truncate the chrec's operands.
1299 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
1300 SmallVector<const SCEV *, 4> Operands;
1301 for (const SCEV *Op : AddRec->operands())
1302 Operands.push_back(getTruncateExpr(Op, Ty));
1303 return getAddRecExpr(Operands, AddRec->getLoop(), SCEV::FlagAnyWrap);
1306 // The cast wasn't folded; create an explicit cast node. We can reuse
1307 // the existing insert position since if we get here, we won't have
1308 // made any changes which would invalidate it.
1309 SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator),
1311 UniqueSCEVs.InsertNode(S, IP);
1312 addToLoopUseLists(S);
1316 // Get the limit of a recurrence such that incrementing by Step cannot cause
1317 // signed overflow as long as the value of the recurrence within the
1318 // loop does not exceed this limit before incrementing.
1319 static const SCEV *getSignedOverflowLimitForStep(const SCEV *Step,
1320 ICmpInst::Predicate *Pred,
1321 ScalarEvolution *SE) {
1322 unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
1323 if (SE->isKnownPositive(Step)) {
1324 *Pred = ICmpInst::ICMP_SLT;
1325 return SE->getConstant(APInt::getSignedMinValue(BitWidth) -
1326 SE->getSignedRangeMax(Step));
1328 if (SE->isKnownNegative(Step)) {
1329 *Pred = ICmpInst::ICMP_SGT;
1330 return SE->getConstant(APInt::getSignedMaxValue(BitWidth) -
1331 SE->getSignedRangeMin(Step));
1336 // Get the limit of a recurrence such that incrementing by Step cannot cause
1337 // unsigned overflow as long as the value of the recurrence within the loop does
1338 // not exceed this limit before incrementing.
1339 static const SCEV *getUnsignedOverflowLimitForStep(const SCEV *Step,
1340 ICmpInst::Predicate *Pred,
1341 ScalarEvolution *SE) {
1342 unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
1343 *Pred = ICmpInst::ICMP_ULT;
1345 return SE->getConstant(APInt::getMinValue(BitWidth) -
1346 SE->getUnsignedRangeMax(Step));
1351 struct ExtendOpTraitsBase {
1352 typedef const SCEV *(ScalarEvolution::*GetExtendExprTy)(const SCEV *, Type *,
1356 // Used to make code generic over signed and unsigned overflow.
1357 template <typename ExtendOp> struct ExtendOpTraits {
1360 // static const SCEV::NoWrapFlags WrapType;
1362 // static const ExtendOpTraitsBase::GetExtendExprTy GetExtendExpr;
1364 // static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1365 // ICmpInst::Predicate *Pred,
1366 // ScalarEvolution *SE);
1370 struct ExtendOpTraits<SCEVSignExtendExpr> : public ExtendOpTraitsBase {
1371 static const SCEV::NoWrapFlags WrapType = SCEV::FlagNSW;
1373 static const GetExtendExprTy GetExtendExpr;
1375 static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1376 ICmpInst::Predicate *Pred,
1377 ScalarEvolution *SE) {
1378 return getSignedOverflowLimitForStep(Step, Pred, SE);
1382 const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits<
1383 SCEVSignExtendExpr>::GetExtendExpr = &ScalarEvolution::getSignExtendExpr;
1386 struct ExtendOpTraits<SCEVZeroExtendExpr> : public ExtendOpTraitsBase {
1387 static const SCEV::NoWrapFlags WrapType = SCEV::FlagNUW;
1389 static const GetExtendExprTy GetExtendExpr;
1391 static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1392 ICmpInst::Predicate *Pred,
1393 ScalarEvolution *SE) {
1394 return getUnsignedOverflowLimitForStep(Step, Pred, SE);
1398 const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits<
1399 SCEVZeroExtendExpr>::GetExtendExpr = &ScalarEvolution::getZeroExtendExpr;
1401 } // end anonymous namespace
1403 // The recurrence AR has been shown to have no signed/unsigned wrap or something
1404 // close to it. Typically, if we can prove NSW/NUW for AR, then we can just as
1405 // easily prove NSW/NUW for its preincrement or postincrement sibling. This
1406 // allows normalizing a sign/zero extended AddRec as such: {sext/zext(Step +
1407 // Start),+,Step} => {(Step + sext/zext(Start),+,Step} As a result, the
1408 // expression "Step + sext/zext(PreIncAR)" is congruent with
1409 // "sext/zext(PostIncAR)"
1410 template <typename ExtendOpTy>
1411 static const SCEV *getPreStartForExtend(const SCEVAddRecExpr *AR, Type *Ty,
1412 ScalarEvolution *SE, unsigned Depth) {
1413 auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType;
1414 auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr;
1416 const Loop *L = AR->getLoop();
1417 const SCEV *Start = AR->getStart();
1418 const SCEV *Step = AR->getStepRecurrence(*SE);
1420 // Check for a simple looking step prior to loop entry.
1421 const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Start);
1425 // Create an AddExpr for "PreStart" after subtracting Step. Full SCEV
1426 // subtraction is expensive. For this purpose, perform a quick and dirty
1427 // difference, by checking for Step in the operand list.
1428 SmallVector<const SCEV *, 4> DiffOps;
1429 for (const SCEV *Op : SA->operands())
1431 DiffOps.push_back(Op);
1433 if (DiffOps.size() == SA->getNumOperands())
1436 // Try to prove `WrapType` (SCEV::FlagNSW or SCEV::FlagNUW) on `PreStart` +
1439 // 1. NSW/NUW flags on the step increment.
1440 auto PreStartFlags =
1441 ScalarEvolution::maskFlags(SA->getNoWrapFlags(), SCEV::FlagNUW);
1442 const SCEV *PreStart = SE->getAddExpr(DiffOps, PreStartFlags);
1443 const SCEVAddRecExpr *PreAR = dyn_cast<SCEVAddRecExpr>(
1444 SE->getAddRecExpr(PreStart, Step, L, SCEV::FlagAnyWrap));
1446 // "{S,+,X} is <nsw>/<nuw>" and "the backedge is taken at least once" implies
1447 // "S+X does not sign/unsign-overflow".
1450 const SCEV *BECount = SE->getBackedgeTakenCount(L);
1451 if (PreAR && PreAR->getNoWrapFlags(WrapType) &&
1452 !isa<SCEVCouldNotCompute>(BECount) && SE->isKnownPositive(BECount))
1455 // 2. Direct overflow check on the step operation's expression.
1456 unsigned BitWidth = SE->getTypeSizeInBits(AR->getType());
1457 Type *WideTy = IntegerType::get(SE->getContext(), BitWidth * 2);
1458 const SCEV *OperandExtendedStart =
1459 SE->getAddExpr((SE->*GetExtendExpr)(PreStart, WideTy, Depth),
1460 (SE->*GetExtendExpr)(Step, WideTy, Depth));
1461 if ((SE->*GetExtendExpr)(Start, WideTy, Depth) == OperandExtendedStart) {
1462 if (PreAR && AR->getNoWrapFlags(WrapType)) {
1463 // If we know `AR` == {`PreStart`+`Step`,+,`Step`} is `WrapType` (FlagNSW
1464 // or FlagNUW) and that `PreStart` + `Step` is `WrapType` too, then
1465 // `PreAR` == {`PreStart`,+,`Step`} is also `WrapType`. Cache this fact.
1466 const_cast<SCEVAddRecExpr *>(PreAR)->setNoWrapFlags(WrapType);
1471 // 3. Loop precondition.
1472 ICmpInst::Predicate Pred;
1473 const SCEV *OverflowLimit =
1474 ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep(Step, &Pred, SE);
1476 if (OverflowLimit &&
1477 SE->isLoopEntryGuardedByCond(L, Pred, PreStart, OverflowLimit))
1483 // Get the normalized zero or sign extended expression for this AddRec's Start.
1484 template <typename ExtendOpTy>
1485 static const SCEV *getExtendAddRecStart(const SCEVAddRecExpr *AR, Type *Ty,
1486 ScalarEvolution *SE,
1488 auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr;
1490 const SCEV *PreStart = getPreStartForExtend<ExtendOpTy>(AR, Ty, SE, Depth);
1492 return (SE->*GetExtendExpr)(AR->getStart(), Ty, Depth);
1494 return SE->getAddExpr((SE->*GetExtendExpr)(AR->getStepRecurrence(*SE), Ty,
1496 (SE->*GetExtendExpr)(PreStart, Ty, Depth));
1499 // Try to prove away overflow by looking at "nearby" add recurrences. A
1500 // motivating example for this rule: if we know `{0,+,4}` is `ult` `-1` and it
1501 // does not itself wrap then we can conclude that `{1,+,4}` is `nuw`.
1505 // {S,+,X} == {S-T,+,X} + T
1506 // => Ext({S,+,X}) == Ext({S-T,+,X} + T)
1508 // If ({S-T,+,X} + T) does not overflow ... (1)
1510 // RHS == Ext({S-T,+,X} + T) == Ext({S-T,+,X}) + Ext(T)
1512 // If {S-T,+,X} does not overflow ... (2)
1514 // RHS == Ext({S-T,+,X}) + Ext(T) == {Ext(S-T),+,Ext(X)} + Ext(T)
1515 // == {Ext(S-T)+Ext(T),+,Ext(X)}
1517 // If (S-T)+T does not overflow ... (3)
1519 // RHS == {Ext(S-T)+Ext(T),+,Ext(X)} == {Ext(S-T+T),+,Ext(X)}
1520 // == {Ext(S),+,Ext(X)} == LHS
1522 // Thus, if (1), (2) and (3) are true for some T, then
1523 // Ext({S,+,X}) == {Ext(S),+,Ext(X)}
1525 // (3) is implied by (1) -- "(S-T)+T does not overflow" is simply "({S-T,+,X}+T)
1526 // does not overflow" restricted to the 0th iteration. Therefore we only need
1527 // to check for (1) and (2).
1529 // In the current context, S is `Start`, X is `Step`, Ext is `ExtendOpTy` and T
1530 // is `Delta` (defined below).
1531 template <typename ExtendOpTy>
1532 bool ScalarEvolution::proveNoWrapByVaryingStart(const SCEV *Start,
1535 auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType;
1537 // We restrict `Start` to a constant to prevent SCEV from spending too much
1538 // time here. It is correct (but more expensive) to continue with a
1539 // non-constant `Start` and do a general SCEV subtraction to compute
1540 // `PreStart` below.
1541 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start);
1545 APInt StartAI = StartC->getAPInt();
1547 for (unsigned Delta : {-2, -1, 1, 2}) {
1548 const SCEV *PreStart = getConstant(StartAI - Delta);
1550 FoldingSetNodeID ID;
1551 ID.AddInteger(scAddRecExpr);
1552 ID.AddPointer(PreStart);
1553 ID.AddPointer(Step);
1557 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1559 // Give up if we don't already have the add recurrence we need because
1560 // actually constructing an add recurrence is relatively expensive.
1561 if (PreAR && PreAR->getNoWrapFlags(WrapType)) { // proves (2)
1562 const SCEV *DeltaS = getConstant(StartC->getType(), Delta);
1563 ICmpInst::Predicate Pred = ICmpInst::BAD_ICMP_PREDICATE;
1564 const SCEV *Limit = ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep(
1565 DeltaS, &Pred, this);
1566 if (Limit && isKnownPredicate(Pred, PreAR, Limit)) // proves (1)
1575 ScalarEvolution::getZeroExtendExpr(const SCEV *Op, Type *Ty, unsigned Depth) {
1576 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1577 "This is not an extending conversion!");
1578 assert(isSCEVable(Ty) &&
1579 "This is not a conversion to a SCEVable type!");
1580 Ty = getEffectiveSCEVType(Ty);
1582 // Fold if the operand is constant.
1583 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1585 cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(), Ty)));
1587 // zext(zext(x)) --> zext(x)
1588 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1589 return getZeroExtendExpr(SZ->getOperand(), Ty, Depth + 1);
1591 // Before doing any expensive analysis, check to see if we've already
1592 // computed a SCEV for this Op and Ty.
1593 FoldingSetNodeID ID;
1594 ID.AddInteger(scZeroExtend);
1598 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1599 if (Depth > MaxExtDepth) {
1600 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
1602 UniqueSCEVs.InsertNode(S, IP);
1603 addToLoopUseLists(S);
1607 // zext(trunc(x)) --> zext(x) or x or trunc(x)
1608 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1609 // It's possible the bits taken off by the truncate were all zero bits. If
1610 // so, we should be able to simplify this further.
1611 const SCEV *X = ST->getOperand();
1612 ConstantRange CR = getUnsignedRange(X);
1613 unsigned TruncBits = getTypeSizeInBits(ST->getType());
1614 unsigned NewBits = getTypeSizeInBits(Ty);
1615 if (CR.truncate(TruncBits).zeroExtend(NewBits).contains(
1616 CR.zextOrTrunc(NewBits)))
1617 return getTruncateOrZeroExtend(X, Ty);
1620 // If the input value is a chrec scev, and we can prove that the value
1621 // did not overflow the old, smaller, value, we can zero extend all of the
1622 // operands (often constants). This allows analysis of something like
1623 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
1624 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1625 if (AR->isAffine()) {
1626 const SCEV *Start = AR->getStart();
1627 const SCEV *Step = AR->getStepRecurrence(*this);
1628 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1629 const Loop *L = AR->getLoop();
1631 if (!AR->hasNoUnsignedWrap()) {
1632 auto NewFlags = proveNoWrapViaConstantRanges(AR);
1633 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(NewFlags);
1636 // If we have special knowledge that this addrec won't overflow,
1637 // we don't need to do any further analysis.
1638 if (AR->hasNoUnsignedWrap())
1639 return getAddRecExpr(
1640 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this, Depth + 1),
1641 getZeroExtendExpr(Step, Ty, Depth + 1), L, AR->getNoWrapFlags());
1643 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1644 // Note that this serves two purposes: It filters out loops that are
1645 // simply not analyzable, and it covers the case where this code is
1646 // being called from within backedge-taken count analysis, such that
1647 // attempting to ask for the backedge-taken count would likely result
1648 // in infinite recursion. In the later case, the analysis code will
1649 // cope with a conservative value, and it will take care to purge
1650 // that value once it has finished.
1651 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1652 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1653 // Manually compute the final value for AR, checking for
1656 // Check whether the backedge-taken count can be losslessly casted to
1657 // the addrec's type. The count is always unsigned.
1658 const SCEV *CastedMaxBECount =
1659 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1660 const SCEV *RecastedMaxBECount =
1661 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1662 if (MaxBECount == RecastedMaxBECount) {
1663 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1664 // Check whether Start+Step*MaxBECount has no unsigned overflow.
1665 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step,
1666 SCEV::FlagAnyWrap, Depth + 1);
1667 const SCEV *ZAdd = getZeroExtendExpr(getAddExpr(Start, ZMul,
1671 const SCEV *WideStart = getZeroExtendExpr(Start, WideTy, Depth + 1);
1672 const SCEV *WideMaxBECount =
1673 getZeroExtendExpr(CastedMaxBECount, WideTy, Depth + 1);
1674 const SCEV *OperandExtendedAdd =
1675 getAddExpr(WideStart,
1676 getMulExpr(WideMaxBECount,
1677 getZeroExtendExpr(Step, WideTy, Depth + 1),
1678 SCEV::FlagAnyWrap, Depth + 1),
1679 SCEV::FlagAnyWrap, Depth + 1);
1680 if (ZAdd == OperandExtendedAdd) {
1681 // Cache knowledge of AR NUW, which is propagated to this AddRec.
1682 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1683 // Return the expression with the addrec on the outside.
1684 return getAddRecExpr(
1685 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this,
1687 getZeroExtendExpr(Step, Ty, Depth + 1), L,
1688 AR->getNoWrapFlags());
1690 // Similar to above, only this time treat the step value as signed.
1691 // This covers loops that count down.
1692 OperandExtendedAdd =
1693 getAddExpr(WideStart,
1694 getMulExpr(WideMaxBECount,
1695 getSignExtendExpr(Step, WideTy, Depth + 1),
1696 SCEV::FlagAnyWrap, Depth + 1),
1697 SCEV::FlagAnyWrap, Depth + 1);
1698 if (ZAdd == OperandExtendedAdd) {
1699 // Cache knowledge of AR NW, which is propagated to this AddRec.
1700 // Negative step causes unsigned wrap, but it still can't self-wrap.
1701 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1702 // Return the expression with the addrec on the outside.
1703 return getAddRecExpr(
1704 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this,
1706 getSignExtendExpr(Step, Ty, Depth + 1), L,
1707 AR->getNoWrapFlags());
1712 // Normally, in the cases we can prove no-overflow via a
1713 // backedge guarding condition, we can also compute a backedge
1714 // taken count for the loop. The exceptions are assumptions and
1715 // guards present in the loop -- SCEV is not great at exploiting
1716 // these to compute max backedge taken counts, but can still use
1717 // these to prove lack of overflow. Use this fact to avoid
1718 // doing extra work that may not pay off.
1719 if (!isa<SCEVCouldNotCompute>(MaxBECount) || HasGuards ||
1720 !AC.assumptions().empty()) {
1721 // If the backedge is guarded by a comparison with the pre-inc
1722 // value the addrec is safe. Also, if the entry is guarded by
1723 // a comparison with the start value and the backedge is
1724 // guarded by a comparison with the post-inc value, the addrec
1726 if (isKnownPositive(Step)) {
1727 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
1728 getUnsignedRangeMax(Step));
1729 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
1730 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) &&
1731 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT,
1732 AR->getPostIncExpr(*this), N))) {
1733 // Cache knowledge of AR NUW, which is propagated to this
1735 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1736 // Return the expression with the addrec on the outside.
1737 return getAddRecExpr(
1738 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this,
1740 getZeroExtendExpr(Step, Ty, Depth + 1), L,
1741 AR->getNoWrapFlags());
1743 } else if (isKnownNegative(Step)) {
1744 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
1745 getSignedRangeMin(Step));
1746 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) ||
1747 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) &&
1748 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT,
1749 AR->getPostIncExpr(*this), N))) {
1750 // Cache knowledge of AR NW, which is propagated to this
1751 // AddRec. Negative step causes unsigned wrap, but it
1752 // still can't self-wrap.
1753 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1754 // Return the expression with the addrec on the outside.
1755 return getAddRecExpr(
1756 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this,
1758 getSignExtendExpr(Step, Ty, Depth + 1), L,
1759 AR->getNoWrapFlags());
1764 if (proveNoWrapByVaryingStart<SCEVZeroExtendExpr>(Start, Step, L)) {
1765 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1766 return getAddRecExpr(
1767 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this, Depth + 1),
1768 getZeroExtendExpr(Step, Ty, Depth + 1), L, AR->getNoWrapFlags());
1772 if (auto *SA = dyn_cast<SCEVAddExpr>(Op)) {
1773 // zext((A + B + ...)<nuw>) --> (zext(A) + zext(B) + ...)<nuw>
1774 if (SA->hasNoUnsignedWrap()) {
1775 // If the addition does not unsign overflow then we can, by definition,
1776 // commute the zero extension with the addition operation.
1777 SmallVector<const SCEV *, 4> Ops;
1778 for (const auto *Op : SA->operands())
1779 Ops.push_back(getZeroExtendExpr(Op, Ty, Depth + 1));
1780 return getAddExpr(Ops, SCEV::FlagNUW, Depth + 1);
1784 // The cast wasn't folded; create an explicit cast node.
1785 // Recompute the insert position, as it may have been invalidated.
1786 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1787 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
1789 UniqueSCEVs.InsertNode(S, IP);
1790 addToLoopUseLists(S);
1795 ScalarEvolution::getSignExtendExpr(const SCEV *Op, Type *Ty, unsigned Depth) {
1796 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1797 "This is not an extending conversion!");
1798 assert(isSCEVable(Ty) &&
1799 "This is not a conversion to a SCEVable type!");
1800 Ty = getEffectiveSCEVType(Ty);
1802 // Fold if the operand is constant.
1803 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1805 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), Ty)));
1807 // sext(sext(x)) --> sext(x)
1808 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1809 return getSignExtendExpr(SS->getOperand(), Ty, Depth + 1);
1811 // sext(zext(x)) --> zext(x)
1812 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1813 return getZeroExtendExpr(SZ->getOperand(), Ty, Depth + 1);
1815 // Before doing any expensive analysis, check to see if we've already
1816 // computed a SCEV for this Op and Ty.
1817 FoldingSetNodeID ID;
1818 ID.AddInteger(scSignExtend);
1822 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1823 // Limit recursion depth.
1824 if (Depth > MaxExtDepth) {
1825 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
1827 UniqueSCEVs.InsertNode(S, IP);
1828 addToLoopUseLists(S);
1832 // sext(trunc(x)) --> sext(x) or x or trunc(x)
1833 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1834 // It's possible the bits taken off by the truncate were all sign bits. If
1835 // so, we should be able to simplify this further.
1836 const SCEV *X = ST->getOperand();
1837 ConstantRange CR = getSignedRange(X);
1838 unsigned TruncBits = getTypeSizeInBits(ST->getType());
1839 unsigned NewBits = getTypeSizeInBits(Ty);
1840 if (CR.truncate(TruncBits).signExtend(NewBits).contains(
1841 CR.sextOrTrunc(NewBits)))
1842 return getTruncateOrSignExtend(X, Ty);
1845 // sext(C1 + (C2 * x)) --> C1 + sext(C2 * x) if C1 < C2
1846 if (auto *SA = dyn_cast<SCEVAddExpr>(Op)) {
1847 if (SA->getNumOperands() == 2) {
1848 auto *SC1 = dyn_cast<SCEVConstant>(SA->getOperand(0));
1849 auto *SMul = dyn_cast<SCEVMulExpr>(SA->getOperand(1));
1851 if (auto *SC2 = dyn_cast<SCEVConstant>(SMul->getOperand(0))) {
1852 const APInt &C1 = SC1->getAPInt();
1853 const APInt &C2 = SC2->getAPInt();
1854 if (C1.isStrictlyPositive() && C2.isStrictlyPositive() &&
1855 C2.ugt(C1) && C2.isPowerOf2())
1856 return getAddExpr(getSignExtendExpr(SC1, Ty, Depth + 1),
1857 getSignExtendExpr(SMul, Ty, Depth + 1),
1858 SCEV::FlagAnyWrap, Depth + 1);
1863 // sext((A + B + ...)<nsw>) --> (sext(A) + sext(B) + ...)<nsw>
1864 if (SA->hasNoSignedWrap()) {
1865 // If the addition does not sign overflow then we can, by definition,
1866 // commute the sign extension with the addition operation.
1867 SmallVector<const SCEV *, 4> Ops;
1868 for (const auto *Op : SA->operands())
1869 Ops.push_back(getSignExtendExpr(Op, Ty, Depth + 1));
1870 return getAddExpr(Ops, SCEV::FlagNSW, Depth + 1);
1873 // If the input value is a chrec scev, and we can prove that the value
1874 // did not overflow the old, smaller, value, we can sign extend all of the
1875 // operands (often constants). This allows analysis of something like
1876 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
1877 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1878 if (AR->isAffine()) {
1879 const SCEV *Start = AR->getStart();
1880 const SCEV *Step = AR->getStepRecurrence(*this);
1881 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1882 const Loop *L = AR->getLoop();
1884 if (!AR->hasNoSignedWrap()) {
1885 auto NewFlags = proveNoWrapViaConstantRanges(AR);
1886 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(NewFlags);
1889 // If we have special knowledge that this addrec won't overflow,
1890 // we don't need to do any further analysis.
1891 if (AR->hasNoSignedWrap())
1892 return getAddRecExpr(
1893 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this, Depth + 1),
1894 getSignExtendExpr(Step, Ty, Depth + 1), L, SCEV::FlagNSW);
1896 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1897 // Note that this serves two purposes: It filters out loops that are
1898 // simply not analyzable, and it covers the case where this code is
1899 // being called from within backedge-taken count analysis, such that
1900 // attempting to ask for the backedge-taken count would likely result
1901 // in infinite recursion. In the later case, the analysis code will
1902 // cope with a conservative value, and it will take care to purge
1903 // that value once it has finished.
1904 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1905 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1906 // Manually compute the final value for AR, checking for
1909 // Check whether the backedge-taken count can be losslessly casted to
1910 // the addrec's type. The count is always unsigned.
1911 const SCEV *CastedMaxBECount =
1912 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1913 const SCEV *RecastedMaxBECount =
1914 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1915 if (MaxBECount == RecastedMaxBECount) {
1916 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1917 // Check whether Start+Step*MaxBECount has no signed overflow.
1918 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step,
1919 SCEV::FlagAnyWrap, Depth + 1);
1920 const SCEV *SAdd = getSignExtendExpr(getAddExpr(Start, SMul,
1924 const SCEV *WideStart = getSignExtendExpr(Start, WideTy, Depth + 1);
1925 const SCEV *WideMaxBECount =
1926 getZeroExtendExpr(CastedMaxBECount, WideTy, Depth + 1);
1927 const SCEV *OperandExtendedAdd =
1928 getAddExpr(WideStart,
1929 getMulExpr(WideMaxBECount,
1930 getSignExtendExpr(Step, WideTy, Depth + 1),
1931 SCEV::FlagAnyWrap, Depth + 1),
1932 SCEV::FlagAnyWrap, Depth + 1);
1933 if (SAdd == OperandExtendedAdd) {
1934 // Cache knowledge of AR NSW, which is propagated to this AddRec.
1935 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1936 // Return the expression with the addrec on the outside.
1937 return getAddRecExpr(
1938 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this,
1940 getSignExtendExpr(Step, Ty, Depth + 1), L,
1941 AR->getNoWrapFlags());
1943 // Similar to above, only this time treat the step value as unsigned.
1944 // This covers loops that count up with an unsigned step.
1945 OperandExtendedAdd =
1946 getAddExpr(WideStart,
1947 getMulExpr(WideMaxBECount,
1948 getZeroExtendExpr(Step, WideTy, Depth + 1),
1949 SCEV::FlagAnyWrap, Depth + 1),
1950 SCEV::FlagAnyWrap, Depth + 1);
1951 if (SAdd == OperandExtendedAdd) {
1952 // If AR wraps around then
1954 // abs(Step) * MaxBECount > unsigned-max(AR->getType())
1955 // => SAdd != OperandExtendedAdd
1957 // Thus (AR is not NW => SAdd != OperandExtendedAdd) <=>
1958 // (SAdd == OperandExtendedAdd => AR is NW)
1960 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1962 // Return the expression with the addrec on the outside.
1963 return getAddRecExpr(
1964 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this,
1966 getZeroExtendExpr(Step, Ty, Depth + 1), L,
1967 AR->getNoWrapFlags());
1972 // Normally, in the cases we can prove no-overflow via a
1973 // backedge guarding condition, we can also compute a backedge
1974 // taken count for the loop. The exceptions are assumptions and
1975 // guards present in the loop -- SCEV is not great at exploiting
1976 // these to compute max backedge taken counts, but can still use
1977 // these to prove lack of overflow. Use this fact to avoid
1978 // doing extra work that may not pay off.
1980 if (!isa<SCEVCouldNotCompute>(MaxBECount) || HasGuards ||
1981 !AC.assumptions().empty()) {
1982 // If the backedge is guarded by a comparison with the pre-inc
1983 // value the addrec is safe. Also, if the entry is guarded by
1984 // a comparison with the start value and the backedge is
1985 // guarded by a comparison with the post-inc value, the addrec
1987 ICmpInst::Predicate Pred;
1988 const SCEV *OverflowLimit =
1989 getSignedOverflowLimitForStep(Step, &Pred, this);
1990 if (OverflowLimit &&
1991 (isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) ||
1992 (isLoopEntryGuardedByCond(L, Pred, Start, OverflowLimit) &&
1993 isLoopBackedgeGuardedByCond(L, Pred, AR->getPostIncExpr(*this),
1995 // Cache knowledge of AR NSW, then propagate NSW to the wide AddRec.
1996 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1997 return getAddRecExpr(
1998 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this, Depth + 1),
1999 getSignExtendExpr(Step, Ty, Depth + 1), L, AR->getNoWrapFlags());
2003 // If Start and Step are constants, check if we can apply this
2005 // sext{C1,+,C2} --> C1 + sext{0,+,C2} if C1 < C2
2006 auto *SC1 = dyn_cast<SCEVConstant>(Start);
2007 auto *SC2 = dyn_cast<SCEVConstant>(Step);
2009 const APInt &C1 = SC1->getAPInt();
2010 const APInt &C2 = SC2->getAPInt();
2011 if (C1.isStrictlyPositive() && C2.isStrictlyPositive() && C2.ugt(C1) &&
2013 Start = getSignExtendExpr(Start, Ty, Depth + 1);
2014 const SCEV *NewAR = getAddRecExpr(getZero(AR->getType()), Step, L,
2015 AR->getNoWrapFlags());
2016 return getAddExpr(Start, getSignExtendExpr(NewAR, Ty, Depth + 1),
2017 SCEV::FlagAnyWrap, Depth + 1);
2021 if (proveNoWrapByVaryingStart<SCEVSignExtendExpr>(Start, Step, L)) {
2022 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
2023 return getAddRecExpr(
2024 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this, Depth + 1),
2025 getSignExtendExpr(Step, Ty, Depth + 1), L, AR->getNoWrapFlags());
2029 // If the input value is provably positive and we could not simplify
2030 // away the sext build a zext instead.
2031 if (isKnownNonNegative(Op))
2032 return getZeroExtendExpr(Op, Ty, Depth + 1);
2034 // The cast wasn't folded; create an explicit cast node.
2035 // Recompute the insert position, as it may have been invalidated.
2036 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2037 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
2039 UniqueSCEVs.InsertNode(S, IP);
2040 addToLoopUseLists(S);
2044 /// getAnyExtendExpr - Return a SCEV for the given operand extended with
2045 /// unspecified bits out to the given type.
2046 const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
2048 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
2049 "This is not an extending conversion!");
2050 assert(isSCEVable(Ty) &&
2051 "This is not a conversion to a SCEVable type!");
2052 Ty = getEffectiveSCEVType(Ty);
2054 // Sign-extend negative constants.
2055 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
2056 if (SC->getAPInt().isNegative())
2057 return getSignExtendExpr(Op, Ty);
2059 // Peel off a truncate cast.
2060 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
2061 const SCEV *NewOp = T->getOperand();
2062 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
2063 return getAnyExtendExpr(NewOp, Ty);
2064 return getTruncateOrNoop(NewOp, Ty);
2067 // Next try a zext cast. If the cast is folded, use it.
2068 const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
2069 if (!isa<SCEVZeroExtendExpr>(ZExt))
2072 // Next try a sext cast. If the cast is folded, use it.
2073 const SCEV *SExt = getSignExtendExpr(Op, Ty);
2074 if (!isa<SCEVSignExtendExpr>(SExt))
2077 // Force the cast to be folded into the operands of an addrec.
2078 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
2079 SmallVector<const SCEV *, 4> Ops;
2080 for (const SCEV *Op : AR->operands())
2081 Ops.push_back(getAnyExtendExpr(Op, Ty));
2082 return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW);
2085 // If the expression is obviously signed, use the sext cast value.
2086 if (isa<SCEVSMaxExpr>(Op))
2089 // Absent any other information, use the zext cast value.
2093 /// Process the given Ops list, which is a list of operands to be added under
2094 /// the given scale, update the given map. This is a helper function for
2095 /// getAddRecExpr. As an example of what it does, given a sequence of operands
2096 /// that would form an add expression like this:
2098 /// m + n + 13 + (A * (o + p + (B * (q + m + 29)))) + r + (-1 * r)
2100 /// where A and B are constants, update the map with these values:
2102 /// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
2104 /// and add 13 + A*B*29 to AccumulatedConstant.
2105 /// This will allow getAddRecExpr to produce this:
2107 /// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
2109 /// This form often exposes folding opportunities that are hidden in
2110 /// the original operand list.
2112 /// Return true iff it appears that any interesting folding opportunities
2113 /// may be exposed. This helps getAddRecExpr short-circuit extra work in
2114 /// the common case where no interesting opportunities are present, and
2115 /// is also used as a check to avoid infinite recursion.
2117 CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
2118 SmallVectorImpl<const SCEV *> &NewOps,
2119 APInt &AccumulatedConstant,
2120 const SCEV *const *Ops, size_t NumOperands,
2122 ScalarEvolution &SE) {
2123 bool Interesting = false;
2125 // Iterate over the add operands. They are sorted, with constants first.
2127 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
2129 // Pull a buried constant out to the outside.
2130 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
2132 AccumulatedConstant += Scale * C->getAPInt();
2135 // Next comes everything else. We're especially interested in multiplies
2136 // here, but they're in the middle, so just visit the rest with one loop.
2137 for (; i != NumOperands; ++i) {
2138 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
2139 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
2141 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getAPInt();
2142 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
2143 // A multiplication of a constant with another add; recurse.
2144 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1));
2146 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
2147 Add->op_begin(), Add->getNumOperands(),
2150 // A multiplication of a constant with some other value. Update
2152 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
2153 const SCEV *Key = SE.getMulExpr(MulOps);
2154 auto Pair = M.insert({Key, NewScale});
2156 NewOps.push_back(Pair.first->first);
2158 Pair.first->second += NewScale;
2159 // The map already had an entry for this value, which may indicate
2160 // a folding opportunity.
2165 // An ordinary operand. Update the map.
2166 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
2167 M.insert({Ops[i], Scale});
2169 NewOps.push_back(Pair.first->first);
2171 Pair.first->second += Scale;
2172 // The map already had an entry for this value, which may indicate
2173 // a folding opportunity.
2182 // We're trying to construct a SCEV of type `Type' with `Ops' as operands and
2183 // `OldFlags' as can't-wrap behavior. Infer a more aggressive set of
2184 // can't-overflow flags for the operation if possible.
2185 static SCEV::NoWrapFlags
2186 StrengthenNoWrapFlags(ScalarEvolution *SE, SCEVTypes Type,
2187 const SmallVectorImpl<const SCEV *> &Ops,
2188 SCEV::NoWrapFlags Flags) {
2189 using namespace std::placeholders;
2191 using OBO = OverflowingBinaryOperator;
2194 Type == scAddExpr || Type == scAddRecExpr || Type == scMulExpr;
2196 assert(CanAnalyze && "don't call from other places!");
2198 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
2199 SCEV::NoWrapFlags SignOrUnsignWrap =
2200 ScalarEvolution::maskFlags(Flags, SignOrUnsignMask);
2202 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
2203 auto IsKnownNonNegative = [&](const SCEV *S) {
2204 return SE->isKnownNonNegative(S);
2207 if (SignOrUnsignWrap == SCEV::FlagNSW && all_of(Ops, IsKnownNonNegative))
2209 ScalarEvolution::setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
2211 SignOrUnsignWrap = ScalarEvolution::maskFlags(Flags, SignOrUnsignMask);
2213 if (SignOrUnsignWrap != SignOrUnsignMask && Type == scAddExpr &&
2214 Ops.size() == 2 && isa<SCEVConstant>(Ops[0])) {
2216 // (A + C) --> (A + C)<nsw> if the addition does not sign overflow
2217 // (A + C) --> (A + C)<nuw> if the addition does not unsign overflow
2219 const APInt &C = cast<SCEVConstant>(Ops[0])->getAPInt();
2220 if (!(SignOrUnsignWrap & SCEV::FlagNSW)) {
2221 auto NSWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
2222 Instruction::Add, C, OBO::NoSignedWrap);
2223 if (NSWRegion.contains(SE->getSignedRange(Ops[1])))
2224 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW);
2226 if (!(SignOrUnsignWrap & SCEV::FlagNUW)) {
2227 auto NUWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
2228 Instruction::Add, C, OBO::NoUnsignedWrap);
2229 if (NUWRegion.contains(SE->getUnsignedRange(Ops[1])))
2230 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
2237 bool ScalarEvolution::isAvailableAtLoopEntry(const SCEV *S, const Loop *L) {
2238 if (!isLoopInvariant(S, L))
2240 // If a value depends on a SCEVUnknown which is defined after the loop, we
2241 // conservatively assume that we cannot calculate it at the loop's entry.
2242 struct FindDominatedSCEVUnknown {
2248 FindDominatedSCEVUnknown(const Loop *L, DominatorTree &DT, LoopInfo &LI)
2249 : L(L), DT(DT), LI(LI) {}
2251 bool checkSCEVUnknown(const SCEVUnknown *SU) {
2252 if (auto *I = dyn_cast<Instruction>(SU->getValue())) {
2253 if (DT.dominates(L->getHeader(), I->getParent()))
2256 assert(DT.dominates(I->getParent(), L->getHeader()) &&
2257 "No dominance relationship between SCEV and loop?");
2262 bool follow(const SCEV *S) {
2263 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
2277 return checkSCEVUnknown(cast<SCEVUnknown>(S));
2278 case scCouldNotCompute:
2279 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
2284 bool isDone() { return Found; }
2287 FindDominatedSCEVUnknown FSU(L, DT, LI);
2288 SCEVTraversal<FindDominatedSCEVUnknown> ST(FSU);
2293 /// Get a canonical add expression, or something simpler if possible.
2294 const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
2295 SCEV::NoWrapFlags Flags,
2297 assert(!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) &&
2298 "only nuw or nsw allowed");
2299 assert(!Ops.empty() && "Cannot get empty add!");
2300 if (Ops.size() == 1) return Ops[0];
2302 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2303 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2304 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2305 "SCEVAddExpr operand types don't match!");
2308 // Sort by complexity, this groups all similar expression types together.
2309 GroupByComplexity(Ops, &LI, DT);
2311 Flags = StrengthenNoWrapFlags(this, scAddExpr, Ops, Flags);
2313 // If there are any constants, fold them together.
2315 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2317 assert(Idx < Ops.size());
2318 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2319 // We found two constants, fold them together!
2320 Ops[0] = getConstant(LHSC->getAPInt() + RHSC->getAPInt());
2321 if (Ops.size() == 2) return Ops[0];
2322 Ops.erase(Ops.begin()+1); // Erase the folded element
2323 LHSC = cast<SCEVConstant>(Ops[0]);
2326 // If we are left with a constant zero being added, strip it off.
2327 if (LHSC->getValue()->isZero()) {
2328 Ops.erase(Ops.begin());
2332 if (Ops.size() == 1) return Ops[0];
2335 // Limit recursion calls depth.
2336 if (Depth > MaxArithDepth)
2337 return getOrCreateAddExpr(Ops, Flags);
2339 // Okay, check to see if the same value occurs in the operand list more than
2340 // once. If so, merge them together into an multiply expression. Since we
2341 // sorted the list, these values are required to be adjacent.
2342 Type *Ty = Ops[0]->getType();
2343 bool FoundMatch = false;
2344 for (unsigned i = 0, e = Ops.size(); i != e-1; ++i)
2345 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
2346 // Scan ahead to count how many equal operands there are.
2348 while (i+Count != e && Ops[i+Count] == Ops[i])
2350 // Merge the values into a multiply.
2351 const SCEV *Scale = getConstant(Ty, Count);
2352 const SCEV *Mul = getMulExpr(Scale, Ops[i], SCEV::FlagAnyWrap, Depth + 1);
2353 if (Ops.size() == Count)
2356 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count);
2357 --i; e -= Count - 1;
2361 return getAddExpr(Ops, Flags, Depth + 1);
2363 // Check for truncates. If all the operands are truncated from the same
2364 // type, see if factoring out the truncate would permit the result to be
2365 // folded. eg., n*trunc(x) + m*trunc(y) --> trunc(trunc(m)*x + trunc(n)*y)
2366 // if the contents of the resulting outer trunc fold to something simple.
2367 auto FindTruncSrcType = [&]() -> Type * {
2368 // We're ultimately looking to fold an addrec of truncs and muls of only
2369 // constants and truncs, so if we find any other types of SCEV
2370 // as operands of the addrec then we bail and return nullptr here.
2371 // Otherwise, we return the type of the operand of a trunc that we find.
2372 if (auto *T = dyn_cast<SCEVTruncateExpr>(Ops[Idx]))
2373 return T->getOperand()->getType();
2374 if (const auto *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
2375 const auto *LastOp = Mul->getOperand(Mul->getNumOperands() - 1);
2376 if (const auto *T = dyn_cast<SCEVTruncateExpr>(LastOp))
2377 return T->getOperand()->getType();
2381 if (auto *SrcType = FindTruncSrcType()) {
2382 SmallVector<const SCEV *, 8> LargeOps;
2384 // Check all the operands to see if they can be represented in the
2385 // source type of the truncate.
2386 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
2387 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
2388 if (T->getOperand()->getType() != SrcType) {
2392 LargeOps.push_back(T->getOperand());
2393 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
2394 LargeOps.push_back(getAnyExtendExpr(C, SrcType));
2395 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
2396 SmallVector<const SCEV *, 8> LargeMulOps;
2397 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
2398 if (const SCEVTruncateExpr *T =
2399 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
2400 if (T->getOperand()->getType() != SrcType) {
2404 LargeMulOps.push_back(T->getOperand());
2405 } else if (const auto *C = dyn_cast<SCEVConstant>(M->getOperand(j))) {
2406 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType));
2413 LargeOps.push_back(getMulExpr(LargeMulOps, SCEV::FlagAnyWrap, Depth + 1));
2420 // Evaluate the expression in the larger type.
2421 const SCEV *Fold = getAddExpr(LargeOps, Flags, Depth + 1);
2422 // If it folds to something simple, use it. Otherwise, don't.
2423 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
2424 return getTruncateExpr(Fold, Ty);
2428 // Skip past any other cast SCEVs.
2429 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
2432 // If there are add operands they would be next.
2433 if (Idx < Ops.size()) {
2434 bool DeletedAdd = false;
2435 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
2436 if (Ops.size() > AddOpsInlineThreshold ||
2437 Add->getNumOperands() > AddOpsInlineThreshold)
2439 // If we have an add, expand the add operands onto the end of the operands
2441 Ops.erase(Ops.begin()+Idx);
2442 Ops.append(Add->op_begin(), Add->op_end());
2446 // If we deleted at least one add, we added operands to the end of the list,
2447 // and they are not necessarily sorted. Recurse to resort and resimplify
2448 // any operands we just acquired.
2450 return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
2453 // Skip over the add expression until we get to a multiply.
2454 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
2457 // Check to see if there are any folding opportunities present with
2458 // operands multiplied by constant values.
2459 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
2460 uint64_t BitWidth = getTypeSizeInBits(Ty);
2461 DenseMap<const SCEV *, APInt> M;
2462 SmallVector<const SCEV *, 8> NewOps;
2463 APInt AccumulatedConstant(BitWidth, 0);
2464 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
2465 Ops.data(), Ops.size(),
2466 APInt(BitWidth, 1), *this)) {
2467 struct APIntCompare {
2468 bool operator()(const APInt &LHS, const APInt &RHS) const {
2469 return LHS.ult(RHS);
2473 // Some interesting folding opportunity is present, so its worthwhile to
2474 // re-generate the operands list. Group the operands by constant scale,
2475 // to avoid multiplying by the same constant scale multiple times.
2476 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
2477 for (const SCEV *NewOp : NewOps)
2478 MulOpLists[M.find(NewOp)->second].push_back(NewOp);
2479 // Re-generate the operands list.
2481 if (AccumulatedConstant != 0)
2482 Ops.push_back(getConstant(AccumulatedConstant));
2483 for (auto &MulOp : MulOpLists)
2484 if (MulOp.first != 0)
2485 Ops.push_back(getMulExpr(
2486 getConstant(MulOp.first),
2487 getAddExpr(MulOp.second, SCEV::FlagAnyWrap, Depth + 1),
2488 SCEV::FlagAnyWrap, Depth + 1));
2491 if (Ops.size() == 1)
2493 return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
2497 // If we are adding something to a multiply expression, make sure the
2498 // something is not already an operand of the multiply. If so, merge it into
2500 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
2501 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
2502 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
2503 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
2504 if (isa<SCEVConstant>(MulOpSCEV))
2506 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
2507 if (MulOpSCEV == Ops[AddOp]) {
2508 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
2509 const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
2510 if (Mul->getNumOperands() != 2) {
2511 // If the multiply has more than two operands, we must get the
2513 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
2514 Mul->op_begin()+MulOp);
2515 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
2516 InnerMul = getMulExpr(MulOps, SCEV::FlagAnyWrap, Depth + 1);
2518 SmallVector<const SCEV *, 2> TwoOps = {getOne(Ty), InnerMul};
2519 const SCEV *AddOne = getAddExpr(TwoOps, SCEV::FlagAnyWrap, Depth + 1);
2520 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV,
2521 SCEV::FlagAnyWrap, Depth + 1);
2522 if (Ops.size() == 2) return OuterMul;
2524 Ops.erase(Ops.begin()+AddOp);
2525 Ops.erase(Ops.begin()+Idx-1);
2527 Ops.erase(Ops.begin()+Idx);
2528 Ops.erase(Ops.begin()+AddOp-1);
2530 Ops.push_back(OuterMul);
2531 return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
2534 // Check this multiply against other multiplies being added together.
2535 for (unsigned OtherMulIdx = Idx+1;
2536 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
2538 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
2539 // If MulOp occurs in OtherMul, we can fold the two multiplies
2541 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
2542 OMulOp != e; ++OMulOp)
2543 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
2544 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
2545 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
2546 if (Mul->getNumOperands() != 2) {
2547 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
2548 Mul->op_begin()+MulOp);
2549 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
2550 InnerMul1 = getMulExpr(MulOps, SCEV::FlagAnyWrap, Depth + 1);
2552 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
2553 if (OtherMul->getNumOperands() != 2) {
2554 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
2555 OtherMul->op_begin()+OMulOp);
2556 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end());
2557 InnerMul2 = getMulExpr(MulOps, SCEV::FlagAnyWrap, Depth + 1);
2559 SmallVector<const SCEV *, 2> TwoOps = {InnerMul1, InnerMul2};
2560 const SCEV *InnerMulSum =
2561 getAddExpr(TwoOps, SCEV::FlagAnyWrap, Depth + 1);
2562 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum,
2563 SCEV::FlagAnyWrap, Depth + 1);
2564 if (Ops.size() == 2) return OuterMul;
2565 Ops.erase(Ops.begin()+Idx);
2566 Ops.erase(Ops.begin()+OtherMulIdx-1);
2567 Ops.push_back(OuterMul);
2568 return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
2574 // If there are any add recurrences in the operands list, see if any other
2575 // added values are loop invariant. If so, we can fold them into the
2577 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2580 // Scan over all recurrences, trying to fold loop invariants into them.
2581 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
2582 // Scan all of the other operands to this add and add them to the vector if
2583 // they are loop invariant w.r.t. the recurrence.
2584 SmallVector<const SCEV *, 8> LIOps;
2585 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2586 const Loop *AddRecLoop = AddRec->getLoop();
2587 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2588 if (isAvailableAtLoopEntry(Ops[i], AddRecLoop)) {
2589 LIOps.push_back(Ops[i]);
2590 Ops.erase(Ops.begin()+i);
2594 // If we found some loop invariants, fold them into the recurrence.
2595 if (!LIOps.empty()) {
2596 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
2597 LIOps.push_back(AddRec->getStart());
2599 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
2601 // This follows from the fact that the no-wrap flags on the outer add
2602 // expression are applicable on the 0th iteration, when the add recurrence
2603 // will be equal to its start value.
2604 AddRecOps[0] = getAddExpr(LIOps, Flags, Depth + 1);
2606 // Build the new addrec. Propagate the NUW and NSW flags if both the
2607 // outer add and the inner addrec are guaranteed to have no overflow.
2608 // Always propagate NW.
2609 Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW));
2610 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags);
2612 // If all of the other operands were loop invariant, we are done.
2613 if (Ops.size() == 1) return NewRec;
2615 // Otherwise, add the folded AddRec by the non-invariant parts.
2616 for (unsigned i = 0;; ++i)
2617 if (Ops[i] == AddRec) {
2621 return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
2624 // Okay, if there weren't any loop invariants to be folded, check to see if
2625 // there are multiple AddRec's with the same loop induction variable being
2626 // added together. If so, we can fold them.
2627 for (unsigned OtherIdx = Idx+1;
2628 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2630 // We expect the AddRecExpr's to be sorted in reverse dominance order,
2631 // so that the 1st found AddRecExpr is dominated by all others.
2632 assert(DT.dominates(
2633 cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()->getHeader(),
2634 AddRec->getLoop()->getHeader()) &&
2635 "AddRecExprs are not sorted in reverse dominance order?");
2636 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
2637 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L>
2638 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
2640 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2642 const auto *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
2643 if (OtherAddRec->getLoop() == AddRecLoop) {
2644 for (unsigned i = 0, e = OtherAddRec->getNumOperands();
2646 if (i >= AddRecOps.size()) {
2647 AddRecOps.append(OtherAddRec->op_begin()+i,
2648 OtherAddRec->op_end());
2651 SmallVector<const SCEV *, 2> TwoOps = {
2652 AddRecOps[i], OtherAddRec->getOperand(i)};
2653 AddRecOps[i] = getAddExpr(TwoOps, SCEV::FlagAnyWrap, Depth + 1);
2655 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2658 // Step size has changed, so we cannot guarantee no self-wraparound.
2659 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap);
2660 return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
2664 // Otherwise couldn't fold anything into this recurrence. Move onto the
2668 // Okay, it looks like we really DO need an add expr. Check to see if we
2669 // already have one, otherwise create a new one.
2670 return getOrCreateAddExpr(Ops, Flags);
2674 ScalarEvolution::getOrCreateAddExpr(SmallVectorImpl<const SCEV *> &Ops,
2675 SCEV::NoWrapFlags Flags) {
2676 FoldingSetNodeID ID;
2677 ID.AddInteger(scAddExpr);
2678 for (const SCEV *Op : Ops)
2682 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2684 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2685 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2686 S = new (SCEVAllocator)
2687 SCEVAddExpr(ID.Intern(SCEVAllocator), O, Ops.size());
2688 UniqueSCEVs.InsertNode(S, IP);
2689 addToLoopUseLists(S);
2691 S->setNoWrapFlags(Flags);
2696 ScalarEvolution::getOrCreateMulExpr(SmallVectorImpl<const SCEV *> &Ops,
2697 SCEV::NoWrapFlags Flags) {
2698 FoldingSetNodeID ID;
2699 ID.AddInteger(scMulExpr);
2700 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2701 ID.AddPointer(Ops[i]);
2704 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2706 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2707 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2708 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
2710 UniqueSCEVs.InsertNode(S, IP);
2711 addToLoopUseLists(S);
2713 S->setNoWrapFlags(Flags);
2717 static uint64_t umul_ov(uint64_t i, uint64_t j, bool &Overflow) {
2719 if (j > 1 && k / j != i) Overflow = true;
2723 /// Compute the result of "n choose k", the binomial coefficient. If an
2724 /// intermediate computation overflows, Overflow will be set and the return will
2725 /// be garbage. Overflow is not cleared on absence of overflow.
2726 static uint64_t Choose(uint64_t n, uint64_t k, bool &Overflow) {
2727 // We use the multiplicative formula:
2728 // n(n-1)(n-2)...(n-(k-1)) / k(k-1)(k-2)...1 .
2729 // At each iteration, we take the n-th term of the numeral and divide by the
2730 // (k-n)th term of the denominator. This division will always produce an
2731 // integral result, and helps reduce the chance of overflow in the
2732 // intermediate computations. However, we can still overflow even when the
2733 // final result would fit.
2735 if (n == 0 || n == k) return 1;
2736 if (k > n) return 0;
2742 for (uint64_t i = 1; i <= k; ++i) {
2743 r = umul_ov(r, n-(i-1), Overflow);
2749 /// Determine if any of the operands in this SCEV are a constant or if
2750 /// any of the add or multiply expressions in this SCEV contain a constant.
2751 static bool containsConstantInAddMulChain(const SCEV *StartExpr) {
2752 struct FindConstantInAddMulChain {
2753 bool FoundConstant = false;
2755 bool follow(const SCEV *S) {
2756 FoundConstant |= isa<SCEVConstant>(S);
2757 return isa<SCEVAddExpr>(S) || isa<SCEVMulExpr>(S);
2760 bool isDone() const {
2761 return FoundConstant;
2765 FindConstantInAddMulChain F;
2766 SCEVTraversal<FindConstantInAddMulChain> ST(F);
2767 ST.visitAll(StartExpr);
2768 return F.FoundConstant;
2771 /// Get a canonical multiply expression, or something simpler if possible.
2772 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
2773 SCEV::NoWrapFlags Flags,
2775 assert(Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) &&
2776 "only nuw or nsw allowed");
2777 assert(!Ops.empty() && "Cannot get empty mul!");
2778 if (Ops.size() == 1) return Ops[0];
2780 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2781 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2782 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2783 "SCEVMulExpr operand types don't match!");
2786 // Sort by complexity, this groups all similar expression types together.
2787 GroupByComplexity(Ops, &LI, DT);
2789 Flags = StrengthenNoWrapFlags(this, scMulExpr, Ops, Flags);
2791 // Limit recursion calls depth.
2792 if (Depth > MaxArithDepth)
2793 return getOrCreateMulExpr(Ops, Flags);
2795 // If there are any constants, fold them together.
2797 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2799 // C1*(C2+V) -> C1*C2 + C1*V
2800 if (Ops.size() == 2)
2801 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
2802 // If any of Add's ops are Adds or Muls with a constant,
2803 // apply this transformation as well.
2804 if (Add->getNumOperands() == 2)
2805 // TODO: There are some cases where this transformation is not
2806 // profitable, for example:
2807 // Add = (C0 + X) * Y + Z.
2808 // Maybe the scope of this transformation should be narrowed down.
2809 if (containsConstantInAddMulChain(Add))
2810 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0),
2811 SCEV::FlagAnyWrap, Depth + 1),
2812 getMulExpr(LHSC, Add->getOperand(1),
2813 SCEV::FlagAnyWrap, Depth + 1),
2814 SCEV::FlagAnyWrap, Depth + 1);
2817 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2818 // We found two constants, fold them together!
2820 ConstantInt::get(getContext(), LHSC->getAPInt() * RHSC->getAPInt());
2821 Ops[0] = getConstant(Fold);
2822 Ops.erase(Ops.begin()+1); // Erase the folded element
2823 if (Ops.size() == 1) return Ops[0];
2824 LHSC = cast<SCEVConstant>(Ops[0]);
2827 // If we are left with a constant one being multiplied, strip it off.
2828 if (cast<SCEVConstant>(Ops[0])->getValue()->isOne()) {
2829 Ops.erase(Ops.begin());
2831 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
2832 // If we have a multiply of zero, it will always be zero.
2834 } else if (Ops[0]->isAllOnesValue()) {
2835 // If we have a mul by -1 of an add, try distributing the -1 among the
2837 if (Ops.size() == 2) {
2838 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
2839 SmallVector<const SCEV *, 4> NewOps;
2840 bool AnyFolded = false;
2841 for (const SCEV *AddOp : Add->operands()) {
2842 const SCEV *Mul = getMulExpr(Ops[0], AddOp, SCEV::FlagAnyWrap,
2844 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
2845 NewOps.push_back(Mul);
2848 return getAddExpr(NewOps, SCEV::FlagAnyWrap, Depth + 1);
2849 } else if (const auto *AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) {
2850 // Negation preserves a recurrence's no self-wrap property.
2851 SmallVector<const SCEV *, 4> Operands;
2852 for (const SCEV *AddRecOp : AddRec->operands())
2853 Operands.push_back(getMulExpr(Ops[0], AddRecOp, SCEV::FlagAnyWrap,
2856 return getAddRecExpr(Operands, AddRec->getLoop(),
2857 AddRec->getNoWrapFlags(SCEV::FlagNW));
2862 if (Ops.size() == 1)
2866 // Skip over the add expression until we get to a multiply.
2867 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
2870 // If there are mul operands inline them all into this expression.
2871 if (Idx < Ops.size()) {
2872 bool DeletedMul = false;
2873 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
2874 if (Ops.size() > MulOpsInlineThreshold)
2876 // If we have an mul, expand the mul operands onto the end of the
2878 Ops.erase(Ops.begin()+Idx);
2879 Ops.append(Mul->op_begin(), Mul->op_end());
2883 // If we deleted at least one mul, we added operands to the end of the
2884 // list, and they are not necessarily sorted. Recurse to resort and
2885 // resimplify any operands we just acquired.
2887 return getMulExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
2890 // If there are any add recurrences in the operands list, see if any other
2891 // added values are loop invariant. If so, we can fold them into the
2893 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2896 // Scan over all recurrences, trying to fold loop invariants into them.
2897 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
2898 // Scan all of the other operands to this mul and add them to the vector
2899 // if they are loop invariant w.r.t. the recurrence.
2900 SmallVector<const SCEV *, 8> LIOps;
2901 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2902 const Loop *AddRecLoop = AddRec->getLoop();
2903 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2904 if (isAvailableAtLoopEntry(Ops[i], AddRecLoop)) {
2905 LIOps.push_back(Ops[i]);
2906 Ops.erase(Ops.begin()+i);
2910 // If we found some loop invariants, fold them into the recurrence.
2911 if (!LIOps.empty()) {
2912 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
2913 SmallVector<const SCEV *, 4> NewOps;
2914 NewOps.reserve(AddRec->getNumOperands());
2915 const SCEV *Scale = getMulExpr(LIOps, SCEV::FlagAnyWrap, Depth + 1);
2916 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
2917 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i),
2918 SCEV::FlagAnyWrap, Depth + 1));
2920 // Build the new addrec. Propagate the NUW and NSW flags if both the
2921 // outer mul and the inner addrec are guaranteed to have no overflow.
2923 // No self-wrap cannot be guaranteed after changing the step size, but
2924 // will be inferred if either NUW or NSW is true.
2925 Flags = AddRec->getNoWrapFlags(clearFlags(Flags, SCEV::FlagNW));
2926 const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, Flags);
2928 // If all of the other operands were loop invariant, we are done.
2929 if (Ops.size() == 1) return NewRec;
2931 // Otherwise, multiply the folded AddRec by the non-invariant parts.
2932 for (unsigned i = 0;; ++i)
2933 if (Ops[i] == AddRec) {
2937 return getMulExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
2940 // Okay, if there weren't any loop invariants to be folded, check to see
2941 // if there are multiple AddRec's with the same loop induction variable
2942 // being multiplied together. If so, we can fold them.
2944 // {A1,+,A2,+,...,+,An}<L> * {B1,+,B2,+,...,+,Bn}<L>
2945 // = {x=1 in [ sum y=x..2x [ sum z=max(y-x, y-n)..min(x,n) [
2946 // choose(x, 2x)*choose(2x-y, x-z)*A_{y-z}*B_z
2947 // ]]],+,...up to x=2n}.
2948 // Note that the arguments to choose() are always integers with values
2949 // known at compile time, never SCEV objects.
2951 // The implementation avoids pointless extra computations when the two
2952 // addrec's are of different length (mathematically, it's equivalent to
2953 // an infinite stream of zeros on the right).
2954 bool OpsModified = false;
2955 for (unsigned OtherIdx = Idx+1;
2956 OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2958 const SCEVAddRecExpr *OtherAddRec =
2959 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]);
2960 if (!OtherAddRec || OtherAddRec->getLoop() != AddRecLoop)
2963 // Limit max number of arguments to avoid creation of unreasonably big
2964 // SCEVAddRecs with very complex operands.
2965 if (AddRec->getNumOperands() + OtherAddRec->getNumOperands() - 1 >
2969 bool Overflow = false;
2970 Type *Ty = AddRec->getType();
2971 bool LargerThan64Bits = getTypeSizeInBits(Ty) > 64;
2972 SmallVector<const SCEV*, 7> AddRecOps;
2973 for (int x = 0, xe = AddRec->getNumOperands() +
2974 OtherAddRec->getNumOperands() - 1; x != xe && !Overflow; ++x) {
2975 const SCEV *Term = getZero(Ty);
2976 for (int y = x, ye = 2*x+1; y != ye && !Overflow; ++y) {
2977 uint64_t Coeff1 = Choose(x, 2*x - y, Overflow);
2978 for (int z = std::max(y-x, y-(int)AddRec->getNumOperands()+1),
2979 ze = std::min(x+1, (int)OtherAddRec->getNumOperands());
2980 z < ze && !Overflow; ++z) {
2981 uint64_t Coeff2 = Choose(2*x - y, x-z, Overflow);
2983 if (LargerThan64Bits)
2984 Coeff = umul_ov(Coeff1, Coeff2, Overflow);
2986 Coeff = Coeff1*Coeff2;
2987 const SCEV *CoeffTerm = getConstant(Ty, Coeff);
2988 const SCEV *Term1 = AddRec->getOperand(y-z);
2989 const SCEV *Term2 = OtherAddRec->getOperand(z);
2990 Term = getAddExpr(Term, getMulExpr(CoeffTerm, Term1, Term2,
2991 SCEV::FlagAnyWrap, Depth + 1),
2992 SCEV::FlagAnyWrap, Depth + 1);
2995 AddRecOps.push_back(Term);
2998 const SCEV *NewAddRec = getAddRecExpr(AddRecOps, AddRec->getLoop(),
3000 if (Ops.size() == 2) return NewAddRec;
3001 Ops[Idx] = NewAddRec;
3002 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
3004 AddRec = dyn_cast<SCEVAddRecExpr>(NewAddRec);
3010 return getMulExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
3012 // Otherwise couldn't fold anything into this recurrence. Move onto the
3016 // Okay, it looks like we really DO need an mul expr. Check to see if we
3017 // already have one, otherwise create a new one.
3018 return getOrCreateMulExpr(Ops, Flags);
3021 /// Represents an unsigned remainder expression based on unsigned division.
3022 const SCEV *ScalarEvolution::getURemExpr(const SCEV *LHS,
3024 assert(getEffectiveSCEVType(LHS->getType()) ==
3025 getEffectiveSCEVType(RHS->getType()) &&
3026 "SCEVURemExpr operand types don't match!");
3028 // Short-circuit easy cases
3029 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
3030 // If constant is one, the result is trivial
3031 if (RHSC->getValue()->isOne())
3032 return getZero(LHS->getType()); // X urem 1 --> 0
3034 // If constant is a power of two, fold into a zext(trunc(LHS)).
3035 if (RHSC->getAPInt().isPowerOf2()) {
3036 Type *FullTy = LHS->getType();
3038 IntegerType::get(getContext(), RHSC->getAPInt().logBase2());
3039 return getZeroExtendExpr(getTruncateExpr(LHS, TruncTy), FullTy);
3043 // Fallback to %a == %x urem %y == %x -<nuw> ((%x udiv %y) *<nuw> %y)
3044 const SCEV *UDiv = getUDivExpr(LHS, RHS);
3045 const SCEV *Mult = getMulExpr(UDiv, RHS, SCEV::FlagNUW);
3046 return getMinusSCEV(LHS, Mult, SCEV::FlagNUW);
3049 /// Get a canonical unsigned division expression, or something simpler if
3051 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
3053 assert(getEffectiveSCEVType(LHS->getType()) ==
3054 getEffectiveSCEVType(RHS->getType()) &&
3055 "SCEVUDivExpr operand types don't match!");
3057 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
3058 if (RHSC->getValue()->isOne())
3059 return LHS; // X udiv 1 --> x
3060 // If the denominator is zero, the result of the udiv is undefined. Don't
3061 // try to analyze it, because the resolution chosen here may differ from
3062 // the resolution chosen in other parts of the compiler.
3063 if (!RHSC->getValue()->isZero()) {
3064 // Determine if the division can be folded into the operands of
3066 // TODO: Generalize this to non-constants by using known-bits information.
3067 Type *Ty = LHS->getType();
3068 unsigned LZ = RHSC->getAPInt().countLeadingZeros();
3069 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1;
3070 // For non-power-of-two values, effectively round the value up to the
3071 // nearest power of two.
3072 if (!RHSC->getAPInt().isPowerOf2())
3074 IntegerType *ExtTy =
3075 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
3076 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
3077 if (const SCEVConstant *Step =
3078 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) {
3079 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
3080 const APInt &StepInt = Step->getAPInt();
3081 const APInt &DivInt = RHSC->getAPInt();
3082 if (!StepInt.urem(DivInt) &&
3083 getZeroExtendExpr(AR, ExtTy) ==
3084 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
3085 getZeroExtendExpr(Step, ExtTy),
3086 AR->getLoop(), SCEV::FlagAnyWrap)) {
3087 SmallVector<const SCEV *, 4> Operands;
3088 for (const SCEV *Op : AR->operands())
3089 Operands.push_back(getUDivExpr(Op, RHS));
3090 return getAddRecExpr(Operands, AR->getLoop(), SCEV::FlagNW);
3092 /// Get a canonical UDivExpr for a recurrence.
3093 /// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0.
3094 // We can currently only fold X%N if X is constant.
3095 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(AR->getStart());
3096 if (StartC && !DivInt.urem(StepInt) &&
3097 getZeroExtendExpr(AR, ExtTy) ==
3098 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
3099 getZeroExtendExpr(Step, ExtTy),
3100 AR->getLoop(), SCEV::FlagAnyWrap)) {
3101 const APInt &StartInt = StartC->getAPInt();
3102 const APInt &StartRem = StartInt.urem(StepInt);
3104 LHS = getAddRecExpr(getConstant(StartInt - StartRem), Step,
3105 AR->getLoop(), SCEV::FlagNW);
3108 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
3109 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
3110 SmallVector<const SCEV *, 4> Operands;
3111 for (const SCEV *Op : M->operands())
3112 Operands.push_back(getZeroExtendExpr(Op, ExtTy));
3113 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
3114 // Find an operand that's safely divisible.
3115 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
3116 const SCEV *Op = M->getOperand(i);
3117 const SCEV *Div = getUDivExpr(Op, RHSC);
3118 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
3119 Operands = SmallVector<const SCEV *, 4>(M->op_begin(),
3122 return getMulExpr(Operands);
3126 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
3127 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) {
3128 SmallVector<const SCEV *, 4> Operands;
3129 for (const SCEV *Op : A->operands())
3130 Operands.push_back(getZeroExtendExpr(Op, ExtTy));
3131 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
3133 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
3134 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
3135 if (isa<SCEVUDivExpr>(Op) ||
3136 getMulExpr(Op, RHS) != A->getOperand(i))
3138 Operands.push_back(Op);
3140 if (Operands.size() == A->getNumOperands())
3141 return getAddExpr(Operands);
3145 // Fold if both operands are constant.
3146 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
3147 Constant *LHSCV = LHSC->getValue();
3148 Constant *RHSCV = RHSC->getValue();
3149 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
3155 FoldingSetNodeID ID;
3156 ID.AddInteger(scUDivExpr);
3160 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
3161 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
3163 UniqueSCEVs.InsertNode(S, IP);
3164 addToLoopUseLists(S);
3168 static const APInt gcd(const SCEVConstant *C1, const SCEVConstant *C2) {
3169 APInt A = C1->getAPInt().abs();
3170 APInt B = C2->getAPInt().abs();
3171 uint32_t ABW = A.getBitWidth();
3172 uint32_t BBW = B.getBitWidth();
3179 return APIntOps::GreatestCommonDivisor(std::move(A), std::move(B));
3182 /// Get a canonical unsigned division expression, or something simpler if
3183 /// possible. There is no representation for an exact udiv in SCEV IR, but we
3184 /// can attempt to remove factors from the LHS and RHS. We can't do this when
3185 /// it's not exact because the udiv may be clearing bits.
3186 const SCEV *ScalarEvolution::getUDivExactExpr(const SCEV *LHS,
3188 // TODO: we could try to find factors in all sorts of things, but for now we
3189 // just deal with u/exact (multiply, constant). See SCEVDivision towards the
3190 // end of this file for inspiration.
3192 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(LHS);
3193 if (!Mul || !Mul->hasNoUnsignedWrap())
3194 return getUDivExpr(LHS, RHS);
3196 if (const SCEVConstant *RHSCst = dyn_cast<SCEVConstant>(RHS)) {
3197 // If the mulexpr multiplies by a constant, then that constant must be the
3198 // first element of the mulexpr.
3199 if (const auto *LHSCst = dyn_cast<SCEVConstant>(Mul->getOperand(0))) {
3200 if (LHSCst == RHSCst) {
3201 SmallVector<const SCEV *, 2> Operands;
3202 Operands.append(Mul->op_begin() + 1, Mul->op_end());
3203 return getMulExpr(Operands);
3206 // We can't just assume that LHSCst divides RHSCst cleanly, it could be
3207 // that there's a factor provided by one of the other terms. We need to
3209 APInt Factor = gcd(LHSCst, RHSCst);
3210 if (!Factor.isIntN(1)) {
3212 cast<SCEVConstant>(getConstant(LHSCst->getAPInt().udiv(Factor)));
3214 cast<SCEVConstant>(getConstant(RHSCst->getAPInt().udiv(Factor)));
3215 SmallVector<const SCEV *, 2> Operands;
3216 Operands.push_back(LHSCst);
3217 Operands.append(Mul->op_begin() + 1, Mul->op_end());
3218 LHS = getMulExpr(Operands);
3220 Mul = dyn_cast<SCEVMulExpr>(LHS);
3222 return getUDivExactExpr(LHS, RHS);
3227 for (int i = 0, e = Mul->getNumOperands(); i != e; ++i) {
3228 if (Mul->getOperand(i) == RHS) {
3229 SmallVector<const SCEV *, 2> Operands;
3230 Operands.append(Mul->op_begin(), Mul->op_begin() + i);
3231 Operands.append(Mul->op_begin() + i + 1, Mul->op_end());
3232 return getMulExpr(Operands);
3236 return getUDivExpr(LHS, RHS);
3239 /// Get an add recurrence expression for the specified loop. Simplify the
3240 /// expression as much as possible.
3241 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step,
3243 SCEV::NoWrapFlags Flags) {
3244 SmallVector<const SCEV *, 4> Operands;
3245 Operands.push_back(Start);
3246 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
3247 if (StepChrec->getLoop() == L) {
3248 Operands.append(StepChrec->op_begin(), StepChrec->op_end());
3249 return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW));
3252 Operands.push_back(Step);
3253 return getAddRecExpr(Operands, L, Flags);
3256 /// Get an add recurrence expression for the specified loop. Simplify the
3257 /// expression as much as possible.
3259 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
3260 const Loop *L, SCEV::NoWrapFlags Flags) {
3261 if (Operands.size() == 1) return Operands[0];
3263 Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
3264 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
3265 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy &&
3266 "SCEVAddRecExpr operand types don't match!");
3267 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
3268 assert(isLoopInvariant(Operands[i], L) &&
3269 "SCEVAddRecExpr operand is not loop-invariant!");
3272 if (Operands.back()->isZero()) {
3273 Operands.pop_back();
3274 return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0} --> X
3277 // It's tempting to want to call getMaxBackedgeTakenCount count here and
3278 // use that information to infer NUW and NSW flags. However, computing a
3279 // BE count requires calling getAddRecExpr, so we may not yet have a
3280 // meaningful BE count at this point (and if we don't, we'd be stuck
3281 // with a SCEVCouldNotCompute as the cached BE count).
3283 Flags = StrengthenNoWrapFlags(this, scAddRecExpr, Operands, Flags);
3285 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
3286 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
3287 const Loop *NestedLoop = NestedAR->getLoop();
3288 if (L->contains(NestedLoop)
3289 ? (L->getLoopDepth() < NestedLoop->getLoopDepth())
3290 : (!NestedLoop->contains(L) &&
3291 DT.dominates(L->getHeader(), NestedLoop->getHeader()))) {
3292 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
3293 NestedAR->op_end());
3294 Operands[0] = NestedAR->getStart();
3295 // AddRecs require their operands be loop-invariant with respect to their
3296 // loops. Don't perform this transformation if it would break this
3298 bool AllInvariant = all_of(
3299 Operands, [&](const SCEV *Op) { return isLoopInvariant(Op, L); });
3302 // Create a recurrence for the outer loop with the same step size.
3304 // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the
3305 // inner recurrence has the same property.
3306 SCEV::NoWrapFlags OuterFlags =
3307 maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags());
3309 NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags);
3310 AllInvariant = all_of(NestedOperands, [&](const SCEV *Op) {
3311 return isLoopInvariant(Op, NestedLoop);
3315 // Ok, both add recurrences are valid after the transformation.
3317 // The inner recurrence keeps its NW flag but only keeps NUW/NSW if
3318 // the outer recurrence has the same property.
3319 SCEV::NoWrapFlags InnerFlags =
3320 maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags);
3321 return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags);
3324 // Reset Operands to its original state.
3325 Operands[0] = NestedAR;
3329 // Okay, it looks like we really DO need an addrec expr. Check to see if we
3330 // already have one, otherwise create a new one.
3331 FoldingSetNodeID ID;
3332 ID.AddInteger(scAddRecExpr);
3333 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
3334 ID.AddPointer(Operands[i]);
3338 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
3340 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size());
3341 std::uninitialized_copy(Operands.begin(), Operands.end(), O);
3342 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator),
3343 O, Operands.size(), L);
3344 UniqueSCEVs.InsertNode(S, IP);
3345 addToLoopUseLists(S);
3347 S->setNoWrapFlags(Flags);
3352 ScalarEvolution::getGEPExpr(GEPOperator *GEP,
3353 const SmallVectorImpl<const SCEV *> &IndexExprs) {
3354 const SCEV *BaseExpr = getSCEV(GEP->getPointerOperand());
3355 // getSCEV(Base)->getType() has the same address space as Base->getType()
3356 // because SCEV::getType() preserves the address space.
3357 Type *IntPtrTy = getEffectiveSCEVType(BaseExpr->getType());
3358 // FIXME(PR23527): Don't blindly transfer the inbounds flag from the GEP
3359 // instruction to its SCEV, because the Instruction may be guarded by control
3360 // flow and the no-overflow bits may not be valid for the expression in any
3361 // context. This can be fixed similarly to how these flags are handled for
3363 SCEV::NoWrapFlags Wrap = GEP->isInBounds() ? SCEV::FlagNSW
3364 : SCEV::FlagAnyWrap;
3366 const SCEV *TotalOffset = getZero(IntPtrTy);
3367 // The array size is unimportant. The first thing we do on CurTy is getting
3368 // its element type.
3369 Type *CurTy = ArrayType::get(GEP->getSourceElementType(), 0);
3370 for (const SCEV *IndexExpr : IndexExprs) {
3371 // Compute the (potentially symbolic) offset in bytes for this index.
3372 if (StructType *STy = dyn_cast<StructType>(CurTy)) {
3373 // For a struct, add the member offset.
3374 ConstantInt *Index = cast<SCEVConstant>(IndexExpr)->getValue();
3375 unsigned FieldNo = Index->getZExtValue();
3376 const SCEV *FieldOffset = getOffsetOfExpr(IntPtrTy, STy, FieldNo);
3378 // Add the field offset to the running total offset.
3379 TotalOffset = getAddExpr(TotalOffset, FieldOffset);
3381 // Update CurTy to the type of the field at Index.
3382 CurTy = STy->getTypeAtIndex(Index);
3384 // Update CurTy to its element type.
3385 CurTy = cast<SequentialType>(CurTy)->getElementType();
3386 // For an array, add the element offset, explicitly scaled.
3387 const SCEV *ElementSize = getSizeOfExpr(IntPtrTy, CurTy);
3388 // Getelementptr indices are signed.
3389 IndexExpr = getTruncateOrSignExtend(IndexExpr, IntPtrTy);
3391 // Multiply the index by the element size to compute the element offset.
3392 const SCEV *LocalOffset = getMulExpr(IndexExpr, ElementSize, Wrap);
3394 // Add the element offset to the running total offset.
3395 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
3399 // Add the total offset from all the GEP indices to the base.
3400 return getAddExpr(BaseExpr, TotalOffset, Wrap);
3403 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
3405 SmallVector<const SCEV *, 2> Ops = {LHS, RHS};
3406 return getSMaxExpr(Ops);
3410 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
3411 assert(!Ops.empty() && "Cannot get empty smax!");
3412 if (Ops.size() == 1) return Ops[0];
3414 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
3415 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
3416 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
3417 "SCEVSMaxExpr operand types don't match!");
3420 // Sort by complexity, this groups all similar expression types together.
3421 GroupByComplexity(Ops, &LI, DT);
3423 // If there are any constants, fold them together.
3425 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
3427 assert(Idx < Ops.size());
3428 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
3429 // We found two constants, fold them together!
3430 ConstantInt *Fold = ConstantInt::get(
3431 getContext(), APIntOps::smax(LHSC->getAPInt(), RHSC->getAPInt()));
3432 Ops[0] = getConstant(Fold);
3433 Ops.erase(Ops.begin()+1); // Erase the folded element
3434 if (Ops.size() == 1) return Ops[0];
3435 LHSC = cast<SCEVConstant>(Ops[0]);
3438 // If we are left with a constant minimum-int, strip it off.
3439 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
3440 Ops.erase(Ops.begin());
3442 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
3443 // If we have an smax with a constant maximum-int, it will always be
3448 if (Ops.size() == 1) return Ops[0];
3451 // Find the first SMax
3452 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
3455 // Check to see if one of the operands is an SMax. If so, expand its operands
3456 // onto our operand list, and recurse to simplify.
3457 if (Idx < Ops.size()) {
3458 bool DeletedSMax = false;
3459 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
3460 Ops.erase(Ops.begin()+Idx);
3461 Ops.append(SMax->op_begin(), SMax->op_end());
3466 return getSMaxExpr(Ops);
3469 // Okay, check to see if the same value occurs in the operand list twice. If
3470 // so, delete one. Since we sorted the list, these values are required to
3472 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
3473 // X smax Y smax Y --> X smax Y
3474 // X smax Y --> X, if X is always greater than Y
3475 if (Ops[i] == Ops[i+1] ||
3476 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) {
3477 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
3479 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) {
3480 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
3484 if (Ops.size() == 1) return Ops[0];
3486 assert(!Ops.empty() && "Reduced smax down to nothing!");
3488 // Okay, it looks like we really DO need an smax expr. Check to see if we
3489 // already have one, otherwise create a new one.
3490 FoldingSetNodeID ID;
3491 ID.AddInteger(scSMaxExpr);
3492 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
3493 ID.AddPointer(Ops[i]);
3495 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
3496 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
3497 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
3498 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator),
3500 UniqueSCEVs.InsertNode(S, IP);
3501 addToLoopUseLists(S);
3505 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
3507 SmallVector<const SCEV *, 2> Ops = {LHS, RHS};
3508 return getUMaxExpr(Ops);
3512 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
3513 assert(!Ops.empty() && "Cannot get empty umax!");
3514 if (Ops.size() == 1) return Ops[0];
3516 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
3517 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
3518 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
3519 "SCEVUMaxExpr operand types don't match!");
3522 // Sort by complexity, this groups all similar expression types together.
3523 GroupByComplexity(Ops, &LI, DT);
3525 // If there are any constants, fold them together.
3527 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
3529 assert(Idx < Ops.size());
3530 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
3531 // We found two constants, fold them together!
3532 ConstantInt *Fold = ConstantInt::get(
3533 getContext(), APIntOps::umax(LHSC->getAPInt(), RHSC->getAPInt()));
3534 Ops[0] = getConstant(Fold);
3535 Ops.erase(Ops.begin()+1); // Erase the folded element
3536 if (Ops.size() == 1) return Ops[0];
3537 LHSC = cast<SCEVConstant>(Ops[0]);
3540 // If we are left with a constant minimum-int, strip it off.
3541 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
3542 Ops.erase(Ops.begin());
3544 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
3545 // If we have an umax with a constant maximum-int, it will always be
3550 if (Ops.size() == 1) return Ops[0];
3553 // Find the first UMax
3554 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
3557 // Check to see if one of the operands is a UMax. If so, expand its operands
3558 // onto our operand list, and recurse to simplify.
3559 if (Idx < Ops.size()) {
3560 bool DeletedUMax = false;
3561 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
3562 Ops.erase(Ops.begin()+Idx);
3563 Ops.append(UMax->op_begin(), UMax->op_end());
3568 return getUMaxExpr(Ops);
3571 // Okay, check to see if the same value occurs in the operand list twice. If
3572 // so, delete one. Since we sorted the list, these values are required to
3574 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
3575 // X umax Y umax Y --> X umax Y
3576 // X umax Y --> X, if X is always greater than Y
3577 if (Ops[i] == Ops[i+1] ||
3578 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) {
3579 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
3581 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) {
3582 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
3586 if (Ops.size() == 1) return Ops[0];
3588 assert(!Ops.empty() && "Reduced umax down to nothing!");
3590 // Okay, it looks like we really DO need a umax expr. Check to see if we
3591 // already have one, otherwise create a new one.
3592 FoldingSetNodeID ID;
3593 ID.AddInteger(scUMaxExpr);
3594 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
3595 ID.AddPointer(Ops[i]);
3597 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
3598 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
3599 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
3600 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator),
3602 UniqueSCEVs.InsertNode(S, IP);
3603 addToLoopUseLists(S);
3607 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
3609 // ~smax(~x, ~y) == smin(x, y).
3610 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
3613 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
3615 // ~umax(~x, ~y) == umin(x, y)
3616 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
3619 const SCEV *ScalarEvolution::getSizeOfExpr(Type *IntTy, Type *AllocTy) {
3620 // We can bypass creating a target-independent
3621 // constant expression and then folding it back into a ConstantInt.
3622 // This is just a compile-time optimization.
3623 return getConstant(IntTy, getDataLayout().getTypeAllocSize(AllocTy));
3626 const SCEV *ScalarEvolution::getOffsetOfExpr(Type *IntTy,
3629 // We can bypass creating a target-independent
3630 // constant expression and then folding it back into a ConstantInt.
3631 // This is just a compile-time optimization.
3633 IntTy, getDataLayout().getStructLayout(STy)->getElementOffset(FieldNo));
3636 const SCEV *ScalarEvolution::getUnknown(Value *V) {
3637 // Don't attempt to do anything other than create a SCEVUnknown object
3638 // here. createSCEV only calls getUnknown after checking for all other
3639 // interesting possibilities, and any other code that calls getUnknown
3640 // is doing so in order to hide a value from SCEV canonicalization.
3642 FoldingSetNodeID ID;
3643 ID.AddInteger(scUnknown);
3646 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
3647 assert(cast<SCEVUnknown>(S)->getValue() == V &&
3648 "Stale SCEVUnknown in uniquing map!");
3651 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
3653 FirstUnknown = cast<SCEVUnknown>(S);
3654 UniqueSCEVs.InsertNode(S, IP);
3658 //===----------------------------------------------------------------------===//
3659 // Basic SCEV Analysis and PHI Idiom Recognition Code
3662 /// Test if values of the given type are analyzable within the SCEV
3663 /// framework. This primarily includes integer types, and it can optionally
3664 /// include pointer types if the ScalarEvolution class has access to
3665 /// target-specific information.
3666 bool ScalarEvolution::isSCEVable(Type *Ty) const {
3667 // Integers and pointers are always SCEVable.
3668 return Ty->isIntegerTy() || Ty->isPointerTy();
3671 /// Return the size in bits of the specified type, for which isSCEVable must
3673 uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const {
3674 assert(isSCEVable(Ty) && "Type is not SCEVable!");
3675 return getDataLayout().getTypeSizeInBits(Ty);
3678 /// Return a type with the same bitwidth as the given type and which represents
3679 /// how SCEV will treat the given type, for which isSCEVable must return
3680 /// true. For pointer types, this is the pointer-sized integer type.
3681 Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const {
3682 assert(isSCEVable(Ty) && "Type is not SCEVable!");
3684 if (Ty->isIntegerTy())
3687 // The only other support type is pointer.
3688 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
3689 return getDataLayout().getIntPtrType(Ty);
3692 Type *ScalarEvolution::getWiderType(Type *T1, Type *T2) const {
3693 return getTypeSizeInBits(T1) >= getTypeSizeInBits(T2) ? T1 : T2;
3696 const SCEV *ScalarEvolution::getCouldNotCompute() {
3697 return CouldNotCompute.get();
3700 bool ScalarEvolution::checkValidity(const SCEV *S) const {
3701 bool ContainsNulls = SCEVExprContains(S, [](const SCEV *S) {
3702 auto *SU = dyn_cast<SCEVUnknown>(S);
3703 return SU && SU->getValue() == nullptr;
3706 return !ContainsNulls;
3709 bool ScalarEvolution::containsAddRecurrence(const SCEV *S) {
3710 HasRecMapType::iterator I = HasRecMap.find(S);
3711 if (I != HasRecMap.end())
3714 bool FoundAddRec = SCEVExprContains(S, isa<SCEVAddRecExpr, const SCEV *>);
3715 HasRecMap.insert({S, FoundAddRec});
3719 /// Try to split a SCEVAddExpr into a pair of {SCEV, ConstantInt}.
3720 /// If \p S is a SCEVAddExpr and is composed of a sub SCEV S' and an
3721 /// offset I, then return {S', I}, else return {\p S, nullptr}.
3722 static std::pair<const SCEV *, ConstantInt *> splitAddExpr(const SCEV *S) {
3723 const auto *Add = dyn_cast<SCEVAddExpr>(S);
3725 return {S, nullptr};
3727 if (Add->getNumOperands() != 2)
3728 return {S, nullptr};
3730 auto *ConstOp = dyn_cast<SCEVConstant>(Add->getOperand(0));
3732 return {S, nullptr};
3734 return {Add->getOperand(1), ConstOp->getValue()};
3737 /// Return the ValueOffsetPair set for \p S. \p S can be represented
3738 /// by the value and offset from any ValueOffsetPair in the set.
3739 SetVector<ScalarEvolution::ValueOffsetPair> *
3740 ScalarEvolution::getSCEVValues(const SCEV *S) {
3741 ExprValueMapType::iterator SI = ExprValueMap.find_as(S);
3742 if (SI == ExprValueMap.end())
3745 if (VerifySCEVMap) {
3746 // Check there is no dangling Value in the set returned.
3747 for (const auto &VE : SI->second)
3748 assert(ValueExprMap.count(VE.first));
3754 /// Erase Value from ValueExprMap and ExprValueMap. ValueExprMap.erase(V)
3755 /// cannot be used separately. eraseValueFromMap should be used to remove
3756 /// V from ValueExprMap and ExprValueMap at the same time.
3757 void ScalarEvolution::eraseValueFromMap(Value *V) {
3758 ValueExprMapType::iterator I = ValueExprMap.find_as(V);
3759 if (I != ValueExprMap.end()) {
3760 const SCEV *S = I->second;
3761 // Remove {V, 0} from the set of ExprValueMap[S]
3762 if (SetVector<ValueOffsetPair> *SV = getSCEVValues(S))
3763 SV->remove({V, nullptr});
3765 // Remove {V, Offset} from the set of ExprValueMap[Stripped]
3766 const SCEV *Stripped;
3767 ConstantInt *Offset;
3768 std::tie(Stripped, Offset) = splitAddExpr(S);
3769 if (Offset != nullptr) {
3770 if (SetVector<ValueOffsetPair> *SV = getSCEVValues(Stripped))
3771 SV->remove({V, Offset});
3773 ValueExprMap.erase(V);
3777 /// Return an existing SCEV if it exists, otherwise analyze the expression and
3778 /// create a new one.
3779 const SCEV *ScalarEvolution::getSCEV(Value *V) {
3780 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
3782 const SCEV *S = getExistingSCEV(V);
3785 // During PHI resolution, it is possible to create two SCEVs for the same
3786 // V, so it is needed to double check whether V->S is inserted into
3787 // ValueExprMap before insert S->{V, 0} into ExprValueMap.
3788 std::pair<ValueExprMapType::iterator, bool> Pair =
3789 ValueExprMap.insert({SCEVCallbackVH(V, this), S});
3791 ExprValueMap[S].insert({V, nullptr});
3793 // If S == Stripped + Offset, add Stripped -> {V, Offset} into
3795 const SCEV *Stripped = S;
3796 ConstantInt *Offset = nullptr;
3797 std::tie(Stripped, Offset) = splitAddExpr(S);
3798 // If stripped is SCEVUnknown, don't bother to save
3799 // Stripped -> {V, offset}. It doesn't simplify and sometimes even
3800 // increase the complexity of the expansion code.
3801 // If V is GetElementPtrInst, don't save Stripped -> {V, offset}
3802 // because it may generate add/sub instead of GEP in SCEV expansion.
3803 if (Offset != nullptr && !isa<SCEVUnknown>(Stripped) &&
3804 !isa<GetElementPtrInst>(V))
3805 ExprValueMap[Stripped].insert({V, Offset});
3811 const SCEV *ScalarEvolution::getExistingSCEV(Value *V) {
3812 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
3814 ValueExprMapType::iterator I = ValueExprMap.find_as(V);
3815 if (I != ValueExprMap.end()) {
3816 const SCEV *S = I->second;
3817 if (checkValidity(S))
3819 eraseValueFromMap(V);
3820 forgetMemoizedResults(S);
3825 /// Return a SCEV corresponding to -V = -1*V
3826 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V,
3827 SCEV::NoWrapFlags Flags) {
3828 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
3830 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
3832 Type *Ty = V->getType();
3833 Ty = getEffectiveSCEVType(Ty);
3835 V, getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))), Flags);
3838 /// Return a SCEV corresponding to ~V = -1-V
3839 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
3840 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
3842 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
3844 Type *Ty = V->getType();
3845 Ty = getEffectiveSCEVType(Ty);
3846 const SCEV *AllOnes =
3847 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
3848 return getMinusSCEV(AllOnes, V);
3851 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
3852 SCEV::NoWrapFlags Flags,
3854 // Fast path: X - X --> 0.
3856 return getZero(LHS->getType());
3858 // We represent LHS - RHS as LHS + (-1)*RHS. This transformation
3859 // makes it so that we cannot make much use of NUW.
3860 auto AddFlags = SCEV::FlagAnyWrap;
3861 const bool RHSIsNotMinSigned =
3862 !getSignedRangeMin(RHS).isMinSignedValue();
3863 if (maskFlags(Flags, SCEV::FlagNSW) == SCEV::FlagNSW) {
3864 // Let M be the minimum representable signed value. Then (-1)*RHS
3865 // signed-wraps if and only if RHS is M. That can happen even for
3866 // a NSW subtraction because e.g. (-1)*M signed-wraps even though
3867 // -1 - M does not. So to transfer NSW from LHS - RHS to LHS +
3868 // (-1)*RHS, we need to prove that RHS != M.
3870 // If LHS is non-negative and we know that LHS - RHS does not
3871 // signed-wrap, then RHS cannot be M. So we can rule out signed-wrap
3872 // either by proving that RHS > M or that LHS >= 0.
3873 if (RHSIsNotMinSigned || isKnownNonNegative(LHS)) {
3874 AddFlags = SCEV::FlagNSW;
3878 // FIXME: Find a correct way to transfer NSW to (-1)*M when LHS -
3879 // RHS is NSW and LHS >= 0.
3881 // The difficulty here is that the NSW flag may have been proven
3882 // relative to a loop that is to be found in a recurrence in LHS and
3883 // not in RHS. Applying NSW to (-1)*M may then let the NSW have a
3884 // larger scope than intended.
3885 auto NegFlags = RHSIsNotMinSigned ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
3887 return getAddExpr(LHS, getNegativeSCEV(RHS, NegFlags), AddFlags, Depth);
3891 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty) {
3892 Type *SrcTy = V->getType();
3893 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3894 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3895 "Cannot truncate or zero extend with non-integer arguments!");
3896 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3897 return V; // No conversion
3898 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
3899 return getTruncateExpr(V, Ty);
3900 return getZeroExtendExpr(V, Ty);
3904 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
3906 Type *SrcTy = V->getType();
3907 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3908 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3909 "Cannot truncate or zero extend with non-integer arguments!");
3910 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3911 return V; // No conversion
3912 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
3913 return getTruncateExpr(V, Ty);
3914 return getSignExtendExpr(V, Ty);
3918 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) {
3919 Type *SrcTy = V->getType();
3920 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3921 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3922 "Cannot noop or zero extend with non-integer arguments!");
3923 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3924 "getNoopOrZeroExtend cannot truncate!");
3925 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3926 return V; // No conversion
3927 return getZeroExtendExpr(V, Ty);
3931 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) {
3932 Type *SrcTy = V->getType();
3933 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3934 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3935 "Cannot noop or sign extend with non-integer arguments!");
3936 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3937 "getNoopOrSignExtend cannot truncate!");
3938 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3939 return V; // No conversion
3940 return getSignExtendExpr(V, Ty);
3944 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) {
3945 Type *SrcTy = V->getType();
3946 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3947 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3948 "Cannot noop or any extend with non-integer arguments!");
3949 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3950 "getNoopOrAnyExtend cannot truncate!");
3951 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3952 return V; // No conversion
3953 return getAnyExtendExpr(V, Ty);
3957 ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) {
3958 Type *SrcTy = V->getType();
3959 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3960 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3961 "Cannot truncate or noop with non-integer arguments!");
3962 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
3963 "getTruncateOrNoop cannot extend!");
3964 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3965 return V; // No conversion
3966 return getTruncateExpr(V, Ty);
3969 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
3971 const SCEV *PromotedLHS = LHS;
3972 const SCEV *PromotedRHS = RHS;
3974 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
3975 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
3977 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
3979 return getUMaxExpr(PromotedLHS, PromotedRHS);
3982 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
3984 const SCEV *PromotedLHS = LHS;
3985 const SCEV *PromotedRHS = RHS;
3987 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
3988 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
3990 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
3992 return getUMinExpr(PromotedLHS, PromotedRHS);
3995 const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) {
3996 // A pointer operand may evaluate to a nonpointer expression, such as null.
3997 if (!V->getType()->isPointerTy())
4000 if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) {
4001 return getPointerBase(Cast->getOperand());
4002 } else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) {
4003 const SCEV *PtrOp = nullptr;
4004 for (const SCEV *NAryOp : NAry->operands()) {
4005 if (NAryOp->getType()->isPointerTy()) {
4006 // Cannot find the base of an expression with multiple pointer operands.
4014 return getPointerBase(PtrOp);
4019 /// Push users of the given Instruction onto the given Worklist.
4021 PushDefUseChildren(Instruction *I,
4022 SmallVectorImpl<Instruction *> &Worklist) {
4023 // Push the def-use children onto the Worklist stack.
4024 for (User *U : I->users())
4025 Worklist.push_back(cast<Instruction>(U));
4028 void ScalarEvolution::forgetSymbolicName(Instruction *PN, const SCEV *SymName) {
4029 SmallVector<Instruction *, 16> Worklist;
4030 PushDefUseChildren(PN, Worklist);
4032 SmallPtrSet<Instruction *, 8> Visited;
4034 while (!Worklist.empty()) {
4035 Instruction *I = Worklist.pop_back_val();
4036 if (!Visited.insert(I).second)
4039 auto It = ValueExprMap.find_as(static_cast<Value *>(I));
4040 if (It != ValueExprMap.end()) {
4041 const SCEV *Old = It->second;
4043 // Short-circuit the def-use traversal if the symbolic name
4044 // ceases to appear in expressions.
4045 if (Old != SymName && !hasOperand(Old, SymName))
4048 // SCEVUnknown for a PHI either means that it has an unrecognized
4049 // structure, it's a PHI that's in the progress of being computed
4050 // by createNodeForPHI, or it's a single-value PHI. In the first case,
4051 // additional loop trip count information isn't going to change anything.
4052 // In the second case, createNodeForPHI will perform the necessary
4053 // updates on its own when it gets to that point. In the third, we do
4054 // want to forget the SCEVUnknown.
4055 if (!isa<PHINode>(I) ||
4056 !isa<SCEVUnknown>(Old) ||
4057 (I != PN && Old == SymName)) {
4058 eraseValueFromMap(It->first);
4059 forgetMemoizedResults(Old);
4063 PushDefUseChildren(I, Worklist);
4069 class SCEVInitRewriter : public SCEVRewriteVisitor<SCEVInitRewriter> {
4071 static const SCEV *rewrite(const SCEV *S, const Loop *L,
4072 ScalarEvolution &SE) {
4073 SCEVInitRewriter Rewriter(L, SE);
4074 const SCEV *Result = Rewriter.visit(S);
4075 return Rewriter.isValid() ? Result : SE.getCouldNotCompute();
4078 const SCEV *visitUnknown(const SCEVUnknown *Expr) {
4079 if (!SE.isLoopInvariant(Expr, L))
4084 const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
4085 // Only allow AddRecExprs for this loop.
4086 if (Expr->getLoop() == L)
4087 return Expr->getStart();
4092 bool isValid() { return Valid; }
4095 explicit SCEVInitRewriter(const Loop *L, ScalarEvolution &SE)
4096 : SCEVRewriteVisitor(SE), L(L) {}
4102 /// This class evaluates the compare condition by matching it against the
4103 /// condition of loop latch. If there is a match we assume a true value
4104 /// for the condition while building SCEV nodes.
4105 class SCEVBackedgeConditionFolder
4106 : public SCEVRewriteVisitor<SCEVBackedgeConditionFolder> {
4108 static const SCEV *rewrite(const SCEV *S, const Loop *L,
4109 ScalarEvolution &SE) {
4110 bool IsPosBECond = false;
4111 Value *BECond = nullptr;
4112 if (BasicBlock *Latch = L->getLoopLatch()) {
4113 BranchInst *BI = dyn_cast<BranchInst>(Latch->getTerminator());
4114 if (BI && BI->isConditional()) {
4115 assert(BI->getSuccessor(0) != BI->getSuccessor(1) &&
4116 "Both outgoing branches should not target same header!");
4117 BECond = BI->getCondition();
4118 IsPosBECond = BI->getSuccessor(0) == L->getHeader();
4123 SCEVBackedgeConditionFolder Rewriter(L, BECond, IsPosBECond, SE);
4124 return Rewriter.visit(S);
4127 const SCEV *visitUnknown(const SCEVUnknown *Expr) {
4128 const SCEV *Result = Expr;
4129 bool InvariantF = SE.isLoopInvariant(Expr, L);
4132 Instruction *I = cast<Instruction>(Expr->getValue());
4133 switch (I->getOpcode()) {
4134 case Instruction::Select: {
4135 SelectInst *SI = cast<SelectInst>(I);
4136 Optional<const SCEV *> Res =
4137 compareWithBackedgeCondition(SI->getCondition());
4138 if (Res.hasValue()) {
4139 bool IsOne = cast<SCEVConstant>(Res.getValue())->getValue()->isOne();
4140 Result = SE.getSCEV(IsOne ? SI->getTrueValue() : SI->getFalseValue());
4145 Optional<const SCEV *> Res = compareWithBackedgeCondition(I);
4147 Result = Res.getValue();
4156 explicit SCEVBackedgeConditionFolder(const Loop *L, Value *BECond,
4157 bool IsPosBECond, ScalarEvolution &SE)
4158 : SCEVRewriteVisitor(SE), L(L), BackedgeCond(BECond),
4159 IsPositiveBECond(IsPosBECond) {}
4161 Optional<const SCEV *> compareWithBackedgeCondition(Value *IC);
4164 /// Loop back condition.
4165 Value *BackedgeCond = nullptr;
4166 /// Set to true if loop back is on positive branch condition.
4167 bool IsPositiveBECond;
4170 Optional<const SCEV *>
4171 SCEVBackedgeConditionFolder::compareWithBackedgeCondition(Value *IC) {
4173 // If value matches the backedge condition for loop latch,
4174 // then return a constant evolution node based on loopback
4176 if (BackedgeCond == IC)
4177 return IsPositiveBECond ? SE.getOne(Type::getInt1Ty(SE.getContext()))
4178 : SE.getZero(Type::getInt1Ty(SE.getContext()));
4182 class SCEVShiftRewriter : public SCEVRewriteVisitor<SCEVShiftRewriter> {
4184 static const SCEV *rewrite(const SCEV *S, const Loop *L,
4185 ScalarEvolution &SE) {
4186 SCEVShiftRewriter Rewriter(L, SE);
4187 const SCEV *Result = Rewriter.visit(S);
4188 return Rewriter.isValid() ? Result : SE.getCouldNotCompute();
4191 const SCEV *visitUnknown(const SCEVUnknown *Expr) {
4192 // Only allow AddRecExprs for this loop.
4193 if (!SE.isLoopInvariant(Expr, L))
4198 const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
4199 if (Expr->getLoop() == L && Expr->isAffine())
4200 return SE.getMinusSCEV(Expr, Expr->getStepRecurrence(SE));
4205 bool isValid() { return Valid; }
4208 explicit SCEVShiftRewriter(const Loop *L, ScalarEvolution &SE)
4209 : SCEVRewriteVisitor(SE), L(L) {}
4215 } // end anonymous namespace
4218 ScalarEvolution::proveNoWrapViaConstantRanges(const SCEVAddRecExpr *AR) {
4219 if (!AR->isAffine())
4220 return SCEV::FlagAnyWrap;
4222 using OBO = OverflowingBinaryOperator;
4224 SCEV::NoWrapFlags Result = SCEV::FlagAnyWrap;
4226 if (!AR->hasNoSignedWrap()) {
4227 ConstantRange AddRecRange = getSignedRange(AR);
4228 ConstantRange IncRange = getSignedRange(AR->getStepRecurrence(*this));
4230 auto NSWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
4231 Instruction::Add, IncRange, OBO::NoSignedWrap);
4232 if (NSWRegion.contains(AddRecRange))
4233 Result = ScalarEvolution::setFlags(Result, SCEV::FlagNSW);
4236 if (!AR->hasNoUnsignedWrap()) {
4237 ConstantRange AddRecRange = getUnsignedRange(AR);
4238 ConstantRange IncRange = getUnsignedRange(AR->getStepRecurrence(*this));
4240 auto NUWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
4241 Instruction::Add, IncRange, OBO::NoUnsignedWrap);
4242 if (NUWRegion.contains(AddRecRange))
4243 Result = ScalarEvolution::setFlags(Result, SCEV::FlagNUW);
4251 /// Represents an abstract binary operation. This may exist as a
4252 /// normal instruction or constant expression, or may have been
4253 /// derived from an expression tree.
4261 /// Op is set if this BinaryOp corresponds to a concrete LLVM instruction or
4262 /// constant expression.
4263 Operator *Op = nullptr;
4265 explicit BinaryOp(Operator *Op)
4266 : Opcode(Op->getOpcode()), LHS(Op->getOperand(0)), RHS(Op->getOperand(1)),
4268 if (auto *OBO = dyn_cast<OverflowingBinaryOperator>(Op)) {
4269 IsNSW = OBO->hasNoSignedWrap();
4270 IsNUW = OBO->hasNoUnsignedWrap();
4274 explicit BinaryOp(unsigned Opcode, Value *LHS, Value *RHS, bool IsNSW = false,
4276 : Opcode(Opcode), LHS(LHS), RHS(RHS), IsNSW(IsNSW), IsNUW(IsNUW) {}
4279 } // end anonymous namespace
4281 /// Try to map \p V into a BinaryOp, and return \c None on failure.
4282 static Optional<BinaryOp> MatchBinaryOp(Value *V, DominatorTree &DT) {
4283 auto *Op = dyn_cast<Operator>(V);
4287 // Implementation detail: all the cleverness here should happen without
4288 // creating new SCEV expressions -- our caller knowns tricks to avoid creating
4289 // SCEV expressions when possible, and we should not break that.
4291 switch (Op->getOpcode()) {
4292 case Instruction::Add:
4293 case Instruction::Sub:
4294 case Instruction::Mul:
4295 case Instruction::UDiv:
4296 case Instruction::URem:
4297 case Instruction::And:
4298 case Instruction::Or:
4299 case Instruction::AShr:
4300 case Instruction::Shl:
4301 return BinaryOp(Op);
4303 case Instruction::Xor:
4304 if (auto *RHSC = dyn_cast<ConstantInt>(Op->getOperand(1)))
4305 // If the RHS of the xor is a signmask, then this is just an add.
4306 // Instcombine turns add of signmask into xor as a strength reduction step.
4307 if (RHSC->getValue().isSignMask())
4308 return BinaryOp(Instruction::Add, Op->getOperand(0), Op->getOperand(1));
4309 return BinaryOp(Op);
4311 case Instruction::LShr:
4312 // Turn logical shift right of a constant into a unsigned divide.
4313 if (ConstantInt *SA = dyn_cast<ConstantInt>(Op->getOperand(1))) {
4314 uint32_t BitWidth = cast<IntegerType>(Op->getType())->getBitWidth();
4316 // If the shift count is not less than the bitwidth, the result of
4317 // the shift is undefined. Don't try to analyze it, because the
4318 // resolution chosen here may differ from the resolution chosen in
4319 // other parts of the compiler.
4320 if (SA->getValue().ult(BitWidth)) {
4322 ConstantInt::get(SA->getContext(),
4323 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
4324 return BinaryOp(Instruction::UDiv, Op->getOperand(0), X);
4327 return BinaryOp(Op);
4329 case Instruction::ExtractValue: {
4330 auto *EVI = cast<ExtractValueInst>(Op);
4331 if (EVI->getNumIndices() != 1 || EVI->getIndices()[0] != 0)
4334 auto *CI = dyn_cast<CallInst>(EVI->getAggregateOperand());
4338 if (auto *F = CI->getCalledFunction())
4339 switch (F->getIntrinsicID()) {
4340 case Intrinsic::sadd_with_overflow:
4341 case Intrinsic::uadd_with_overflow:
4342 if (!isOverflowIntrinsicNoWrap(cast<IntrinsicInst>(CI), DT))
4343 return BinaryOp(Instruction::Add, CI->getArgOperand(0),
4344 CI->getArgOperand(1));
4346 // Now that we know that all uses of the arithmetic-result component of
4347 // CI are guarded by the overflow check, we can go ahead and pretend
4348 // that the arithmetic is non-overflowing.
4349 if (F->getIntrinsicID() == Intrinsic::sadd_with_overflow)
4350 return BinaryOp(Instruction::Add, CI->getArgOperand(0),
4351 CI->getArgOperand(1), /* IsNSW = */ true,
4352 /* IsNUW = */ false);
4354 return BinaryOp(Instruction::Add, CI->getArgOperand(0),
4355 CI->getArgOperand(1), /* IsNSW = */ false,
4357 case Intrinsic::ssub_with_overflow:
4358 case Intrinsic::usub_with_overflow:
4359 if (!isOverflowIntrinsicNoWrap(cast<IntrinsicInst>(CI), DT))
4360 return BinaryOp(Instruction::Sub, CI->getArgOperand(0),
4361 CI->getArgOperand(1));
4363 // The same reasoning as sadd/uadd above.
4364 if (F->getIntrinsicID() == Intrinsic::ssub_with_overflow)
4365 return BinaryOp(Instruction::Sub, CI->getArgOperand(0),
4366 CI->getArgOperand(1), /* IsNSW = */ true,
4367 /* IsNUW = */ false);
4369 return BinaryOp(Instruction::Sub, CI->getArgOperand(0),
4370 CI->getArgOperand(1), /* IsNSW = */ false,
4371 /* IsNUW = */ true);
4372 case Intrinsic::smul_with_overflow:
4373 case Intrinsic::umul_with_overflow:
4374 return BinaryOp(Instruction::Mul, CI->getArgOperand(0),
4375 CI->getArgOperand(1));
4389 /// Helper function to createAddRecFromPHIWithCasts. We have a phi
4390 /// node whose symbolic (unknown) SCEV is \p SymbolicPHI, which is updated via
4391 /// the loop backedge by a SCEVAddExpr, possibly also with a few casts on the
4392 /// way. This function checks if \p Op, an operand of this SCEVAddExpr,
4393 /// follows one of the following patterns:
4394 /// Op == (SExt ix (Trunc iy (%SymbolicPHI) to ix) to iy)
4395 /// Op == (ZExt ix (Trunc iy (%SymbolicPHI) to ix) to iy)
4396 /// If the SCEV expression of \p Op conforms with one of the expected patterns
4397 /// we return the type of the truncation operation, and indicate whether the
4398 /// truncated type should be treated as signed/unsigned by setting
4399 /// \p Signed to true/false, respectively.
4400 static Type *isSimpleCastedPHI(const SCEV *Op, const SCEVUnknown *SymbolicPHI,
4401 bool &Signed, ScalarEvolution &SE) {
4402 // The case where Op == SymbolicPHI (that is, with no type conversions on
4403 // the way) is handled by the regular add recurrence creating logic and
4404 // would have already been triggered in createAddRecForPHI. Reaching it here
4405 // means that createAddRecFromPHI had failed for this PHI before (e.g.,
4406 // because one of the other operands of the SCEVAddExpr updating this PHI is
4409 // Here we look for the case where Op = (ext(trunc(SymbolicPHI))), and in
4410 // this case predicates that allow us to prove that Op == SymbolicPHI will
4412 if (Op == SymbolicPHI)
4415 unsigned SourceBits = SE.getTypeSizeInBits(SymbolicPHI->getType());
4416 unsigned NewBits = SE.getTypeSizeInBits(Op->getType());
4417 if (SourceBits != NewBits)
4420 const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(Op);
4421 const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(Op);
4424 const SCEVTruncateExpr *Trunc =
4425 SExt ? dyn_cast<SCEVTruncateExpr>(SExt->getOperand())
4426 : dyn_cast<SCEVTruncateExpr>(ZExt->getOperand());
4429 const SCEV *X = Trunc->getOperand();
4430 if (X != SymbolicPHI)
4432 Signed = SExt != nullptr;
4433 return Trunc->getType();
4436 static const Loop *isIntegerLoopHeaderPHI(const PHINode *PN, LoopInfo &LI) {
4437 if (!PN->getType()->isIntegerTy())
4439 const Loop *L = LI.getLoopFor(PN->getParent());
4440 if (!L || L->getHeader() != PN->getParent())
4445 // Analyze \p SymbolicPHI, a SCEV expression of a phi node, and check if the
4446 // computation that updates the phi follows the following pattern:
4447 // (SExt/ZExt ix (Trunc iy (%SymbolicPHI) to ix) to iy) + InvariantAccum
4448 // which correspond to a phi->trunc->sext/zext->add->phi update chain.
4449 // If so, try to see if it can be rewritten as an AddRecExpr under some
4450 // Predicates. If successful, return them as a pair. Also cache the results
4453 // Example usage scenario:
4454 // Say the Rewriter is called for the following SCEV:
4455 // 8 * ((sext i32 (trunc i64 %X to i32) to i64) + %Step)
4457 // %X = phi i64 (%Start, %BEValue)
4458 // It will visitMul->visitAdd->visitSExt->visitTrunc->visitUnknown(%X),
4459 // and call this function with %SymbolicPHI = %X.
4461 // The analysis will find that the value coming around the backedge has
4462 // the following SCEV:
4463 // BEValue = ((sext i32 (trunc i64 %X to i32) to i64) + %Step)
4464 // Upon concluding that this matches the desired pattern, the function
4465 // will return the pair {NewAddRec, SmallPredsVec} where:
4466 // NewAddRec = {%Start,+,%Step}
4467 // SmallPredsVec = {P1, P2, P3} as follows:
4468 // P1(WrapPred): AR: {trunc(%Start),+,(trunc %Step)}<nsw> Flags: <nssw>
4469 // P2(EqualPred): %Start == (sext i32 (trunc i64 %Start to i32) to i64)
4470 // P3(EqualPred): %Step == (sext i32 (trunc i64 %Step to i32) to i64)
4471 // The returned pair means that SymbolicPHI can be rewritten into NewAddRec
4472 // under the predicates {P1,P2,P3}.
4473 // This predicated rewrite will be cached in PredicatedSCEVRewrites:
4474 // PredicatedSCEVRewrites[{%X,L}] = {NewAddRec, {P1,P2,P3)}
4478 // 1) Extend the Induction descriptor to also support inductions that involve
4479 // casts: When needed (namely, when we are called in the context of the
4480 // vectorizer induction analysis), a Set of cast instructions will be
4481 // populated by this method, and provided back to isInductionPHI. This is
4482 // needed to allow the vectorizer to properly record them to be ignored by
4483 // the cost model and to avoid vectorizing them (otherwise these casts,
4484 // which are redundant under the runtime overflow checks, will be
4485 // vectorized, which can be costly).
4487 // 2) Support additional induction/PHISCEV patterns: We also want to support
4488 // inductions where the sext-trunc / zext-trunc operations (partly) occur
4489 // after the induction update operation (the induction increment):
4491 // (Trunc iy (SExt/ZExt ix (%SymbolicPHI + InvariantAccum) to iy) to ix)
4492 // which correspond to a phi->add->trunc->sext/zext->phi update chain.
4494 // (Trunc iy ((SExt/ZExt ix (%SymbolicPhi) to iy) + InvariantAccum) to ix)
4495 // which correspond to a phi->trunc->add->sext/zext->phi update chain.
4497 // 3) Outline common code with createAddRecFromPHI to avoid duplication.
4498 Optional<std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>>
4499 ScalarEvolution::createAddRecFromPHIWithCastsImpl(const SCEVUnknown *SymbolicPHI) {
4500 SmallVector<const SCEVPredicate *, 3> Predicates;
4502 // *** Part1: Analyze if we have a phi-with-cast pattern for which we can
4503 // return an AddRec expression under some predicate.
4505 auto *PN = cast<PHINode>(SymbolicPHI->getValue());
4506 const Loop *L = isIntegerLoopHeaderPHI(PN, LI);
4507 assert(L && "Expecting an integer loop header phi");
4509 // The loop may have multiple entrances or multiple exits; we can analyze
4510 // this phi as an addrec if it has a unique entry value and a unique
4512 Value *BEValueV = nullptr, *StartValueV = nullptr;
4513 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
4514 Value *V = PN->getIncomingValue(i);
4515 if (L->contains(PN->getIncomingBlock(i))) {
4518 } else if (BEValueV != V) {
4522 } else if (!StartValueV) {
4524 } else if (StartValueV != V) {
4525 StartValueV = nullptr;
4529 if (!BEValueV || !StartValueV)
4532 const SCEV *BEValue = getSCEV(BEValueV);
4534 // If the value coming around the backedge is an add with the symbolic
4535 // value we just inserted, possibly with casts that we can ignore under
4536 // an appropriate runtime guard, then we found a simple induction variable!
4537 const auto *Add = dyn_cast<SCEVAddExpr>(BEValue);
4541 // If there is a single occurrence of the symbolic value, possibly
4542 // casted, replace it with a recurrence.
4543 unsigned FoundIndex = Add->getNumOperands();
4544 Type *TruncTy = nullptr;
4546 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
4548 isSimpleCastedPHI(Add->getOperand(i), SymbolicPHI, Signed, *this)))
4549 if (FoundIndex == e) {
4554 if (FoundIndex == Add->getNumOperands())
4557 // Create an add with everything but the specified operand.
4558 SmallVector<const SCEV *, 8> Ops;
4559 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
4560 if (i != FoundIndex)
4561 Ops.push_back(Add->getOperand(i));
4562 const SCEV *Accum = getAddExpr(Ops);
4564 // The runtime checks will not be valid if the step amount is
4565 // varying inside the loop.
4566 if (!isLoopInvariant(Accum, L))
4569 // *** Part2: Create the predicates
4571 // Analysis was successful: we have a phi-with-cast pattern for which we
4572 // can return an AddRec expression under the following predicates:
4574 // P1: A Wrap predicate that guarantees that Trunc(Start) + i*Trunc(Accum)
4575 // fits within the truncated type (does not overflow) for i = 0 to n-1.
4576 // P2: An Equal predicate that guarantees that
4577 // Start = (Ext ix (Trunc iy (Start) to ix) to iy)
4578 // P3: An Equal predicate that guarantees that
4579 // Accum = (Ext ix (Trunc iy (Accum) to ix) to iy)
4581 // As we next prove, the above predicates guarantee that:
4582 // Start + i*Accum = (Ext ix (Trunc iy ( Start + i*Accum ) to ix) to iy)
4585 // More formally, we want to prove that:
4586 // Expr(i+1) = Start + (i+1) * Accum
4587 // = (Ext ix (Trunc iy (Expr(i)) to ix) to iy) + Accum
4590 // 1) Expr(0) = Start
4591 // 2) Expr(1) = Start + Accum
4592 // = (Ext ix (Trunc iy (Start) to ix) to iy) + Accum :: from P2
4593 // 3) Induction hypothesis (step i):
4594 // Expr(i) = (Ext ix (Trunc iy (Expr(i-1)) to ix) to iy) + Accum
4598 // = Start + (i+1)*Accum
4599 // = (Start + i*Accum) + Accum
4600 // = Expr(i) + Accum
4601 // = (Ext ix (Trunc iy (Expr(i-1)) to ix) to iy) + Accum + Accum
4604 // = (Ext ix (Trunc iy (Start + (i-1)*Accum) to ix) to iy) + Accum + Accum
4606 // = (Ext ix (Trunc iy (Start + (i-1)*Accum) to ix) to iy)
4607 // + (Ext ix (Trunc iy (Accum) to ix) to iy)
4608 // + Accum :: from P3
4610 // = (Ext ix (Trunc iy ((Start + (i-1)*Accum) + Accum) to ix) to iy)
4611 // + Accum :: from P1: Ext(x)+Ext(y)=>Ext(x+y)
4613 // = (Ext ix (Trunc iy (Start + i*Accum) to ix) to iy) + Accum
4614 // = (Ext ix (Trunc iy (Expr(i)) to ix) to iy) + Accum
4616 // By induction, the same applies to all iterations 1<=i<n:
4619 // Create a truncated addrec for which we will add a no overflow check (P1).
4620 const SCEV *StartVal = getSCEV(StartValueV);
4621 const SCEV *PHISCEV =
4622 getAddRecExpr(getTruncateExpr(StartVal, TruncTy),
4623 getTruncateExpr(Accum, TruncTy), L, SCEV::FlagAnyWrap);
4625 // PHISCEV can be either a SCEVConstant or a SCEVAddRecExpr.
4626 // ex: If truncated Accum is 0 and StartVal is a constant, then PHISCEV
4627 // will be constant.
4629 // If PHISCEV is a constant, then P1 degenerates into P2 or P3, so we don't
4631 if (const auto *AR = dyn_cast<SCEVAddRecExpr>(PHISCEV)) {
4632 SCEVWrapPredicate::IncrementWrapFlags AddedFlags =
4633 Signed ? SCEVWrapPredicate::IncrementNSSW
4634 : SCEVWrapPredicate::IncrementNUSW;
4635 const SCEVPredicate *AddRecPred = getWrapPredicate(AR, AddedFlags);
4636 Predicates.push_back(AddRecPred);
4639 // Create the Equal Predicates P2,P3:
4641 // It is possible that the predicates P2 and/or P3 are computable at
4642 // compile time due to StartVal and/or Accum being constants.
4643 // If either one is, then we can check that now and escape if either P2
4646 // Construct the extended SCEV: (Ext ix (Trunc iy (Expr) to ix) to iy)
4647 // for each of StartVal and Accum
4648 auto getExtendedExpr = [&](const SCEV *Expr,
4649 bool CreateSignExtend) -> const SCEV * {
4650 assert(isLoopInvariant(Expr, L) && "Expr is expected to be invariant");
4651 const SCEV *TruncatedExpr = getTruncateExpr(Expr, TruncTy);
4652 const SCEV *ExtendedExpr =
4653 CreateSignExtend ? getSignExtendExpr(TruncatedExpr, Expr->getType())
4654 : getZeroExtendExpr(TruncatedExpr, Expr->getType());
4655 return ExtendedExpr;
4659 // ExtendedExpr = (Ext ix (Trunc iy (Expr) to ix) to iy
4660 // = getExtendedExpr(Expr)
4661 // Determine whether the predicate P: Expr == ExtendedExpr
4662 // is known to be false at compile time
4663 auto PredIsKnownFalse = [&](const SCEV *Expr,
4664 const SCEV *ExtendedExpr) -> bool {
4665 return Expr != ExtendedExpr &&
4666 isKnownPredicate(ICmpInst::ICMP_NE, Expr, ExtendedExpr);
4669 const SCEV *StartExtended = getExtendedExpr(StartVal, Signed);
4670 if (PredIsKnownFalse(StartVal, StartExtended)) {
4671 DEBUG(dbgs() << "P2 is compile-time false\n";);
4675 // The Step is always Signed (because the overflow checks are either
4677 const SCEV *AccumExtended = getExtendedExpr(Accum, /*CreateSignExtend=*/true);
4678 if (PredIsKnownFalse(Accum, AccumExtended)) {
4679 DEBUG(dbgs() << "P3 is compile-time false\n";);
4683 auto AppendPredicate = [&](const SCEV *Expr,
4684 const SCEV *ExtendedExpr) -> void {
4685 if (Expr != ExtendedExpr &&
4686 !isKnownPredicate(ICmpInst::ICMP_EQ, Expr, ExtendedExpr)) {
4687 const SCEVPredicate *Pred = getEqualPredicate(Expr, ExtendedExpr);
4688 DEBUG (dbgs() << "Added Predicate: " << *Pred);
4689 Predicates.push_back(Pred);
4693 AppendPredicate(StartVal, StartExtended);
4694 AppendPredicate(Accum, AccumExtended);
4696 // *** Part3: Predicates are ready. Now go ahead and create the new addrec in
4697 // which the casts had been folded away. The caller can rewrite SymbolicPHI
4698 // into NewAR if it will also add the runtime overflow checks specified in
4700 auto *NewAR = getAddRecExpr(StartVal, Accum, L, SCEV::FlagAnyWrap);
4702 std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>> PredRewrite =
4703 std::make_pair(NewAR, Predicates);
4704 // Remember the result of the analysis for this SCEV at this locayyytion.
4705 PredicatedSCEVRewrites[{SymbolicPHI, L}] = PredRewrite;
4709 Optional<std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>>
4710 ScalarEvolution::createAddRecFromPHIWithCasts(const SCEVUnknown *SymbolicPHI) {
4711 auto *PN = cast<PHINode>(SymbolicPHI->getValue());
4712 const Loop *L = isIntegerLoopHeaderPHI(PN, LI);
4716 // Check to see if we already analyzed this PHI.
4717 auto I = PredicatedSCEVRewrites.find({SymbolicPHI, L});
4718 if (I != PredicatedSCEVRewrites.end()) {
4719 std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>> Rewrite =
4721 // Analysis was done before and failed to create an AddRec:
4722 if (Rewrite.first == SymbolicPHI)
4724 // Analysis was done before and succeeded to create an AddRec under
4726 assert(isa<SCEVAddRecExpr>(Rewrite.first) && "Expected an AddRec");
4727 assert(!(Rewrite.second).empty() && "Expected to find Predicates");
4731 Optional<std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>>
4732 Rewrite = createAddRecFromPHIWithCastsImpl(SymbolicPHI);
4734 // Record in the cache that the analysis failed
4736 SmallVector<const SCEVPredicate *, 3> Predicates;
4737 PredicatedSCEVRewrites[{SymbolicPHI, L}] = {SymbolicPHI, Predicates};
4744 // FIXME: This utility is currently required because the Rewriter currently
4745 // does not rewrite this expression:
4746 // {0, +, (sext ix (trunc iy to ix) to iy)}
4747 // into {0, +, %step},
4748 // even when the following Equal predicate exists:
4749 // "%step == (sext ix (trunc iy to ix) to iy)".
4750 bool PredicatedScalarEvolution::areAddRecsEqualWithPreds(
4751 const SCEVAddRecExpr *AR1, const SCEVAddRecExpr *AR2) const {
4755 auto areExprsEqual = [&](const SCEV *Expr1, const SCEV *Expr2) -> bool {
4756 if (Expr1 != Expr2 && !Preds.implies(SE.getEqualPredicate(Expr1, Expr2)) &&
4757 !Preds.implies(SE.getEqualPredicate(Expr2, Expr1)))
4762 if (!areExprsEqual(AR1->getStart(), AR2->getStart()) ||
4763 !areExprsEqual(AR1->getStepRecurrence(SE), AR2->getStepRecurrence(SE)))
4768 /// A helper function for createAddRecFromPHI to handle simple cases.
4770 /// This function tries to find an AddRec expression for the simplest (yet most
4771 /// common) cases: PN = PHI(Start, OP(Self, LoopInvariant)).
4772 /// If it fails, createAddRecFromPHI will use a more general, but slow,
4773 /// technique for finding the AddRec expression.
4774 const SCEV *ScalarEvolution::createSimpleAffineAddRec(PHINode *PN,
4776 Value *StartValueV) {
4777 const Loop *L = LI.getLoopFor(PN->getParent());
4778 assert(L && L->getHeader() == PN->getParent());
4779 assert(BEValueV && StartValueV);
4781 auto BO = MatchBinaryOp(BEValueV, DT);
4785 if (BO->Opcode != Instruction::Add)
4788 const SCEV *Accum = nullptr;
4789 if (BO->LHS == PN && L->isLoopInvariant(BO->RHS))
4790 Accum = getSCEV(BO->RHS);
4791 else if (BO->RHS == PN && L->isLoopInvariant(BO->LHS))
4792 Accum = getSCEV(BO->LHS);
4797 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
4799 Flags = setFlags(Flags, SCEV::FlagNUW);
4801 Flags = setFlags(Flags, SCEV::FlagNSW);
4803 const SCEV *StartVal = getSCEV(StartValueV);
4804 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
4806 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
4808 // We can add Flags to the post-inc expression only if we
4809 // know that it is *undefined behavior* for BEValueV to
4811 if (auto *BEInst = dyn_cast<Instruction>(BEValueV))
4812 if (isLoopInvariant(Accum, L) && isAddRecNeverPoison(BEInst, L))
4813 (void)getAddRecExpr(getAddExpr(StartVal, Accum), Accum, L, Flags);
4818 const SCEV *ScalarEvolution::createAddRecFromPHI(PHINode *PN) {
4819 const Loop *L = LI.getLoopFor(PN->getParent());
4820 if (!L || L->getHeader() != PN->getParent())
4823 // The loop may have multiple entrances or multiple exits; we can analyze
4824 // this phi as an addrec if it has a unique entry value and a unique
4826 Value *BEValueV = nullptr, *StartValueV = nullptr;
4827 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
4828 Value *V = PN->getIncomingValue(i);
4829 if (L->contains(PN->getIncomingBlock(i))) {
4832 } else if (BEValueV != V) {
4836 } else if (!StartValueV) {
4838 } else if (StartValueV != V) {
4839 StartValueV = nullptr;
4843 if (!BEValueV || !StartValueV)
4846 assert(ValueExprMap.find_as(PN) == ValueExprMap.end() &&
4847 "PHI node already processed?");
4849 // First, try to find AddRec expression without creating a fictituos symbolic
4851 if (auto *S = createSimpleAffineAddRec(PN, BEValueV, StartValueV))
4854 // Handle PHI node value symbolically.
4855 const SCEV *SymbolicName = getUnknown(PN);
4856 ValueExprMap.insert({SCEVCallbackVH(PN, this), SymbolicName});
4858 // Using this symbolic name for the PHI, analyze the value coming around
4860 const SCEV *BEValue = getSCEV(BEValueV);
4862 // NOTE: If BEValue is loop invariant, we know that the PHI node just
4863 // has a special value for the first iteration of the loop.
4865 // If the value coming around the backedge is an add with the symbolic
4866 // value we just inserted, then we found a simple induction variable!
4867 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
4868 // If there is a single occurrence of the symbolic value, replace it
4869 // with a recurrence.
4870 unsigned FoundIndex = Add->getNumOperands();
4871 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
4872 if (Add->getOperand(i) == SymbolicName)
4873 if (FoundIndex == e) {
4878 if (FoundIndex != Add->getNumOperands()) {
4879 // Create an add with everything but the specified operand.
4880 SmallVector<const SCEV *, 8> Ops;
4881 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
4882 if (i != FoundIndex)
4883 Ops.push_back(SCEVBackedgeConditionFolder::rewrite(Add->getOperand(i),
4885 const SCEV *Accum = getAddExpr(Ops);
4887 // This is not a valid addrec if the step amount is varying each
4888 // loop iteration, but is not itself an addrec in this loop.
4889 if (isLoopInvariant(Accum, L) ||
4890 (isa<SCEVAddRecExpr>(Accum) &&
4891 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
4892 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
4894 if (auto BO = MatchBinaryOp(BEValueV, DT)) {
4895 if (BO->Opcode == Instruction::Add && BO->LHS == PN) {
4897 Flags = setFlags(Flags, SCEV::FlagNUW);
4899 Flags = setFlags(Flags, SCEV::FlagNSW);
4901 } else if (GEPOperator *GEP = dyn_cast<GEPOperator>(BEValueV)) {
4902 // If the increment is an inbounds GEP, then we know the address
4903 // space cannot be wrapped around. We cannot make any guarantee
4904 // about signed or unsigned overflow because pointers are
4905 // unsigned but we may have a negative index from the base
4906 // pointer. We can guarantee that no unsigned wrap occurs if the
4907 // indices form a positive value.
4908 if (GEP->isInBounds() && GEP->getOperand(0) == PN) {
4909 Flags = setFlags(Flags, SCEV::FlagNW);
4911 const SCEV *Ptr = getSCEV(GEP->getPointerOperand());
4912 if (isKnownPositive(getMinusSCEV(getSCEV(GEP), Ptr)))
4913 Flags = setFlags(Flags, SCEV::FlagNUW);
4916 // We cannot transfer nuw and nsw flags from subtraction
4917 // operations -- sub nuw X, Y is not the same as add nuw X, -Y
4921 const SCEV *StartVal = getSCEV(StartValueV);
4922 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
4924 // Okay, for the entire analysis of this edge we assumed the PHI
4925 // to be symbolic. We now need to go back and purge all of the
4926 // entries for the scalars that use the symbolic expression.
4927 forgetSymbolicName(PN, SymbolicName);
4928 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
4930 // We can add Flags to the post-inc expression only if we
4931 // know that it is *undefined behavior* for BEValueV to
4933 if (auto *BEInst = dyn_cast<Instruction>(BEValueV))
4934 if (isLoopInvariant(Accum, L) && isAddRecNeverPoison(BEInst, L))
4935 (void)getAddRecExpr(getAddExpr(StartVal, Accum), Accum, L, Flags);
4941 // Otherwise, this could be a loop like this:
4942 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
4943 // In this case, j = {1,+,1} and BEValue is j.
4944 // Because the other in-value of i (0) fits the evolution of BEValue
4945 // i really is an addrec evolution.
4947 // We can generalize this saying that i is the shifted value of BEValue
4948 // by one iteration:
4949 // PHI(f(0), f({1,+,1})) --> f({0,+,1})
4950 const SCEV *Shifted = SCEVShiftRewriter::rewrite(BEValue, L, *this);
4951 const SCEV *Start = SCEVInitRewriter::rewrite(Shifted, L, *this);
4952 if (Shifted != getCouldNotCompute() &&
4953 Start != getCouldNotCompute()) {
4954 const SCEV *StartVal = getSCEV(StartValueV);
4955 if (Start == StartVal) {
4956 // Okay, for the entire analysis of this edge we assumed the PHI
4957 // to be symbolic. We now need to go back and purge all of the
4958 // entries for the scalars that use the symbolic expression.
4959 forgetSymbolicName(PN, SymbolicName);
4960 ValueExprMap[SCEVCallbackVH(PN, this)] = Shifted;
4966 // Remove the temporary PHI node SCEV that has been inserted while intending
4967 // to create an AddRecExpr for this PHI node. We can not keep this temporary
4968 // as it will prevent later (possibly simpler) SCEV expressions to be added
4969 // to the ValueExprMap.
4970 eraseValueFromMap(PN);
4975 // Checks if the SCEV S is available at BB. S is considered available at BB
4976 // if S can be materialized at BB without introducing a fault.
4977 static bool IsAvailableOnEntry(const Loop *L, DominatorTree &DT, const SCEV *S,
4979 struct CheckAvailable {
4980 bool TraversalDone = false;
4981 bool Available = true;
4983 const Loop *L = nullptr; // The loop BB is in (can be nullptr)
4984 BasicBlock *BB = nullptr;
4987 CheckAvailable(const Loop *L, BasicBlock *BB, DominatorTree &DT)
4988 : L(L), BB(BB), DT(DT) {}
4990 bool setUnavailable() {
4991 TraversalDone = true;
4996 bool follow(const SCEV *S) {
4997 switch (S->getSCEVType()) {
4998 case scConstant: case scTruncate: case scZeroExtend: case scSignExtend:
4999 case scAddExpr: case scMulExpr: case scUMaxExpr: case scSMaxExpr:
5000 // These expressions are available if their operand(s) is/are.
5003 case scAddRecExpr: {
5004 // We allow add recurrences that are on the loop BB is in, or some
5005 // outer loop. This guarantees availability because the value of the
5006 // add recurrence at BB is simply the "current" value of the induction
5007 // variable. We can relax this in the future; for instance an add
5008 // recurrence on a sibling dominating loop is also available at BB.
5009 const auto *ARLoop = cast<SCEVAddRecExpr>(S)->getLoop();
5010 if (L && (ARLoop == L || ARLoop->contains(L)))
5013 return setUnavailable();
5017 // For SCEVUnknown, we check for simple dominance.
5018 const auto *SU = cast<SCEVUnknown>(S);
5019 Value *V = SU->getValue();
5021 if (isa<Argument>(V))
5024 if (isa<Instruction>(V) && DT.dominates(cast<Instruction>(V), BB))
5027 return setUnavailable();
5031 case scCouldNotCompute:
5032 // We do not try to smart about these at all.
5033 return setUnavailable();
5035 llvm_unreachable("switch should be fully covered!");
5038 bool isDone() { return TraversalDone; }
5041 CheckAvailable CA(L, BB, DT);
5042 SCEVTraversal<CheckAvailable> ST(CA);
5045 return CA.Available;
5048 // Try to match a control flow sequence that branches out at BI and merges back
5049 // at Merge into a "C ? LHS : RHS" select pattern. Return true on a successful
5051 static bool BrPHIToSelect(DominatorTree &DT, BranchInst *BI, PHINode *Merge,
5052 Value *&C, Value *&LHS, Value *&RHS) {
5053 C = BI->getCondition();
5055 BasicBlockEdge LeftEdge(BI->getParent(), BI->getSuccessor(0));
5056 BasicBlockEdge RightEdge(BI->getParent(), BI->getSuccessor(1));
5058 if (!LeftEdge.isSingleEdge())
5061 assert(RightEdge.isSingleEdge() && "Follows from LeftEdge.isSingleEdge()");
5063 Use &LeftUse = Merge->getOperandUse(0);
5064 Use &RightUse = Merge->getOperandUse(1);
5066 if (DT.dominates(LeftEdge, LeftUse) && DT.dominates(RightEdge, RightUse)) {
5072 if (DT.dominates(LeftEdge, RightUse) && DT.dominates(RightEdge, LeftUse)) {
5081 const SCEV *ScalarEvolution::createNodeFromSelectLikePHI(PHINode *PN) {
5083 [&](BasicBlock *BB) { return DT.isReachableFromEntry(BB); };
5084 if (PN->getNumIncomingValues() == 2 && all_of(PN->blocks(), IsReachable)) {
5085 const Loop *L = LI.getLoopFor(PN->getParent());
5087 // We don't want to break LCSSA, even in a SCEV expression tree.
5088 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i)
5089 if (LI.getLoopFor(PN->getIncomingBlock(i)) != L)
5094 // br %cond, label %left, label %right
5100 // V = phi [ %x, %left ], [ %y, %right ]
5102 // as "select %cond, %x, %y"
5104 BasicBlock *IDom = DT[PN->getParent()]->getIDom()->getBlock();
5105 assert(IDom && "At least the entry block should dominate PN");
5107 auto *BI = dyn_cast<BranchInst>(IDom->getTerminator());
5108 Value *Cond = nullptr, *LHS = nullptr, *RHS = nullptr;
5110 if (BI && BI->isConditional() &&
5111 BrPHIToSelect(DT, BI, PN, Cond, LHS, RHS) &&
5112 IsAvailableOnEntry(L, DT, getSCEV(LHS), PN->getParent()) &&
5113 IsAvailableOnEntry(L, DT, getSCEV(RHS), PN->getParent()))
5114 return createNodeForSelectOrPHI(PN, Cond, LHS, RHS);
5120 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
5121 if (const SCEV *S = createAddRecFromPHI(PN))
5124 if (const SCEV *S = createNodeFromSelectLikePHI(PN))
5127 // If the PHI has a single incoming value, follow that value, unless the
5128 // PHI's incoming blocks are in a different loop, in which case doing so
5129 // risks breaking LCSSA form. Instcombine would normally zap these, but
5130 // it doesn't have DominatorTree information, so it may miss cases.
5131 if (Value *V = SimplifyInstruction(PN, {getDataLayout(), &TLI, &DT, &AC}))
5132 if (LI.replacementPreservesLCSSAForm(PN, V))
5135 // If it's not a loop phi, we can't handle it yet.
5136 return getUnknown(PN);
5139 const SCEV *ScalarEvolution::createNodeForSelectOrPHI(Instruction *I,
5143 // Handle "constant" branch or select. This can occur for instance when a
5144 // loop pass transforms an inner loop and moves on to process the outer loop.
5145 if (auto *CI = dyn_cast<ConstantInt>(Cond))
5146 return getSCEV(CI->isOne() ? TrueVal : FalseVal);
5148 // Try to match some simple smax or umax patterns.
5149 auto *ICI = dyn_cast<ICmpInst>(Cond);
5151 return getUnknown(I);
5153 Value *LHS = ICI->getOperand(0);
5154 Value *RHS = ICI->getOperand(1);
5156 switch (ICI->getPredicate()) {
5157 case ICmpInst::ICMP_SLT:
5158 case ICmpInst::ICMP_SLE:
5159 std::swap(LHS, RHS);
5161 case ICmpInst::ICMP_SGT:
5162 case ICmpInst::ICMP_SGE:
5163 // a >s b ? a+x : b+x -> smax(a, b)+x
5164 // a >s b ? b+x : a+x -> smin(a, b)+x
5165 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType())) {
5166 const SCEV *LS = getNoopOrSignExtend(getSCEV(LHS), I->getType());
5167 const SCEV *RS = getNoopOrSignExtend(getSCEV(RHS), I->getType());
5168 const SCEV *LA = getSCEV(TrueVal);
5169 const SCEV *RA = getSCEV(FalseVal);
5170 const SCEV *LDiff = getMinusSCEV(LA, LS);
5171 const SCEV *RDiff = getMinusSCEV(RA, RS);
5173 return getAddExpr(getSMaxExpr(LS, RS), LDiff);
5174 LDiff = getMinusSCEV(LA, RS);
5175 RDiff = getMinusSCEV(RA, LS);
5177 return getAddExpr(getSMinExpr(LS, RS), LDiff);
5180 case ICmpInst::ICMP_ULT:
5181 case ICmpInst::ICMP_ULE:
5182 std::swap(LHS, RHS);
5184 case ICmpInst::ICMP_UGT:
5185 case ICmpInst::ICMP_UGE:
5186 // a >u b ? a+x : b+x -> umax(a, b)+x
5187 // a >u b ? b+x : a+x -> umin(a, b)+x
5188 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType())) {
5189 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
5190 const SCEV *RS = getNoopOrZeroExtend(getSCEV(RHS), I->getType());
5191 const SCEV *LA = getSCEV(TrueVal);
5192 const SCEV *RA = getSCEV(FalseVal);
5193 const SCEV *LDiff = getMinusSCEV(LA, LS);
5194 const SCEV *RDiff = getMinusSCEV(RA, RS);
5196 return getAddExpr(getUMaxExpr(LS, RS), LDiff);
5197 LDiff = getMinusSCEV(LA, RS);
5198 RDiff = getMinusSCEV(RA, LS);
5200 return getAddExpr(getUMinExpr(LS, RS), LDiff);
5203 case ICmpInst::ICMP_NE:
5204 // n != 0 ? n+x : 1+x -> umax(n, 1)+x
5205 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType()) &&
5206 isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
5207 const SCEV *One = getOne(I->getType());
5208 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
5209 const SCEV *LA = getSCEV(TrueVal);
5210 const SCEV *RA = getSCEV(FalseVal);
5211 const SCEV *LDiff = getMinusSCEV(LA, LS);
5212 const SCEV *RDiff = getMinusSCEV(RA, One);
5214 return getAddExpr(getUMaxExpr(One, LS), LDiff);
5217 case ICmpInst::ICMP_EQ:
5218 // n == 0 ? 1+x : n+x -> umax(n, 1)+x
5219 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType()) &&
5220 isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
5221 const SCEV *One = getOne(I->getType());
5222 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
5223 const SCEV *LA = getSCEV(TrueVal);
5224 const SCEV *RA = getSCEV(FalseVal);
5225 const SCEV *LDiff = getMinusSCEV(LA, One);
5226 const SCEV *RDiff = getMinusSCEV(RA, LS);
5228 return getAddExpr(getUMaxExpr(One, LS), LDiff);
5235 return getUnknown(I);
5238 /// Expand GEP instructions into add and multiply operations. This allows them
5239 /// to be analyzed by regular SCEV code.
5240 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
5241 // Don't attempt to analyze GEPs over unsized objects.
5242 if (!GEP->getSourceElementType()->isSized())
5243 return getUnknown(GEP);
5245 SmallVector<const SCEV *, 4> IndexExprs;
5246 for (auto Index = GEP->idx_begin(); Index != GEP->idx_end(); ++Index)
5247 IndexExprs.push_back(getSCEV(*Index));
5248 return getGEPExpr(GEP, IndexExprs);
5251 uint32_t ScalarEvolution::GetMinTrailingZerosImpl(const SCEV *S) {
5252 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
5253 return C->getAPInt().countTrailingZeros();
5255 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
5256 return std::min(GetMinTrailingZeros(T->getOperand()),
5257 (uint32_t)getTypeSizeInBits(T->getType()));
5259 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
5260 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
5261 return OpRes == getTypeSizeInBits(E->getOperand()->getType())
5262 ? getTypeSizeInBits(E->getType())
5266 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
5267 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
5268 return OpRes == getTypeSizeInBits(E->getOperand()->getType())
5269 ? getTypeSizeInBits(E->getType())
5273 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
5274 // The result is the min of all operands results.
5275 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
5276 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
5277 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
5281 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
5282 // The result is the sum of all operands results.
5283 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
5284 uint32_t BitWidth = getTypeSizeInBits(M->getType());
5285 for (unsigned i = 1, e = M->getNumOperands();
5286 SumOpRes != BitWidth && i != e; ++i)
5288 std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)), BitWidth);
5292 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
5293 // The result is the min of all operands results.
5294 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
5295 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
5296 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
5300 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
5301 // The result is the min of all operands results.
5302 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
5303 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
5304 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
5308 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
5309 // The result is the min of all operands results.
5310 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
5311 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
5312 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
5316 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
5317 // For a SCEVUnknown, ask ValueTracking.
5318 KnownBits Known = computeKnownBits(U->getValue(), getDataLayout(), 0, &AC, nullptr, &DT);
5319 return Known.countMinTrailingZeros();
5326 uint32_t ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
5327 auto I = MinTrailingZerosCache.find(S);
5328 if (I != MinTrailingZerosCache.end())
5331 uint32_t Result = GetMinTrailingZerosImpl(S);
5332 auto InsertPair = MinTrailingZerosCache.insert({S, Result});
5333 assert(InsertPair.second && "Should insert a new key");
5334 return InsertPair.first->second;
5337 /// Helper method to assign a range to V from metadata present in the IR.
5338 static Optional<ConstantRange> GetRangeFromMetadata(Value *V) {
5339 if (Instruction *I = dyn_cast<Instruction>(V))
5340 if (MDNode *MD = I->getMetadata(LLVMContext::MD_range))
5341 return getConstantRangeFromMetadata(*MD);
5346 /// Determine the range for a particular SCEV. If SignHint is
5347 /// HINT_RANGE_UNSIGNED (resp. HINT_RANGE_SIGNED) then getRange prefers ranges
5348 /// with a "cleaner" unsigned (resp. signed) representation.
5349 const ConstantRange &
5350 ScalarEvolution::getRangeRef(const SCEV *S,
5351 ScalarEvolution::RangeSignHint SignHint) {
5352 DenseMap<const SCEV *, ConstantRange> &Cache =
5353 SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED ? UnsignedRanges
5356 // See if we've computed this range already.
5357 DenseMap<const SCEV *, ConstantRange>::iterator I = Cache.find(S);
5358 if (I != Cache.end())
5361 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
5362 return setRange(C, SignHint, ConstantRange(C->getAPInt()));
5364 unsigned BitWidth = getTypeSizeInBits(S->getType());
5365 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
5367 // If the value has known zeros, the maximum value will have those known zeros
5369 uint32_t TZ = GetMinTrailingZeros(S);
5371 if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED)
5372 ConservativeResult =
5373 ConstantRange(APInt::getMinValue(BitWidth),
5374 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
5376 ConservativeResult = ConstantRange(
5377 APInt::getSignedMinValue(BitWidth),
5378 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
5381 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
5382 ConstantRange X = getRangeRef(Add->getOperand(0), SignHint);
5383 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
5384 X = X.add(getRangeRef(Add->getOperand(i), SignHint));
5385 return setRange(Add, SignHint, ConservativeResult.intersectWith(X));
5388 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
5389 ConstantRange X = getRangeRef(Mul->getOperand(0), SignHint);
5390 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
5391 X = X.multiply(getRangeRef(Mul->getOperand(i), SignHint));
5392 return setRange(Mul, SignHint, ConservativeResult.intersectWith(X));
5395 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
5396 ConstantRange X = getRangeRef(SMax->getOperand(0), SignHint);
5397 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
5398 X = X.smax(getRangeRef(SMax->getOperand(i), SignHint));
5399 return setRange(SMax, SignHint, ConservativeResult.intersectWith(X));
5402 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
5403 ConstantRange X = getRangeRef(UMax->getOperand(0), SignHint);
5404 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
5405 X = X.umax(getRangeRef(UMax->getOperand(i), SignHint));
5406 return setRange(UMax, SignHint, ConservativeResult.intersectWith(X));
5409 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
5410 ConstantRange X = getRangeRef(UDiv->getLHS(), SignHint);
5411 ConstantRange Y = getRangeRef(UDiv->getRHS(), SignHint);
5412 return setRange(UDiv, SignHint,
5413 ConservativeResult.intersectWith(X.udiv(Y)));
5416 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
5417 ConstantRange X = getRangeRef(ZExt->getOperand(), SignHint);
5418 return setRange(ZExt, SignHint,
5419 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
5422 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
5423 ConstantRange X = getRangeRef(SExt->getOperand(), SignHint);
5424 return setRange(SExt, SignHint,
5425 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
5428 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
5429 ConstantRange X = getRangeRef(Trunc->getOperand(), SignHint);
5430 return setRange(Trunc, SignHint,
5431 ConservativeResult.intersectWith(X.truncate(BitWidth)));
5434 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
5435 // If there's no unsigned wrap, the value will never be less than its
5437 if (AddRec->hasNoUnsignedWrap())
5438 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
5439 if (!C->getValue()->isZero())
5440 ConservativeResult = ConservativeResult.intersectWith(
5441 ConstantRange(C->getAPInt(), APInt(BitWidth, 0)));
5443 // If there's no signed wrap, and all the operands have the same sign or
5444 // zero, the value won't ever change sign.
5445 if (AddRec->hasNoSignedWrap()) {
5446 bool AllNonNeg = true;
5447 bool AllNonPos = true;
5448 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
5449 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
5450 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
5453 ConservativeResult = ConservativeResult.intersectWith(
5454 ConstantRange(APInt(BitWidth, 0),
5455 APInt::getSignedMinValue(BitWidth)));
5457 ConservativeResult = ConservativeResult.intersectWith(
5458 ConstantRange(APInt::getSignedMinValue(BitWidth),
5459 APInt(BitWidth, 1)));
5462 // TODO: non-affine addrec
5463 if (AddRec->isAffine()) {
5464 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
5465 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
5466 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
5467 auto RangeFromAffine = getRangeForAffineAR(
5468 AddRec->getStart(), AddRec->getStepRecurrence(*this), MaxBECount,
5470 if (!RangeFromAffine.isFullSet())
5471 ConservativeResult =
5472 ConservativeResult.intersectWith(RangeFromAffine);
5474 auto RangeFromFactoring = getRangeViaFactoring(
5475 AddRec->getStart(), AddRec->getStepRecurrence(*this), MaxBECount,
5477 if (!RangeFromFactoring.isFullSet())
5478 ConservativeResult =
5479 ConservativeResult.intersectWith(RangeFromFactoring);
5483 return setRange(AddRec, SignHint, std::move(ConservativeResult));
5486 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
5487 // Check if the IR explicitly contains !range metadata.
5488 Optional<ConstantRange> MDRange = GetRangeFromMetadata(U->getValue());
5489 if (MDRange.hasValue())
5490 ConservativeResult = ConservativeResult.intersectWith(MDRange.getValue());
5492 // Split here to avoid paying the compile-time cost of calling both
5493 // computeKnownBits and ComputeNumSignBits. This restriction can be lifted
5495 const DataLayout &DL = getDataLayout();
5496 if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED) {
5497 // For a SCEVUnknown, ask ValueTracking.
5498 KnownBits Known = computeKnownBits(U->getValue(), DL, 0, &AC, nullptr, &DT);
5499 if (Known.One != ~Known.Zero + 1)
5500 ConservativeResult =
5501 ConservativeResult.intersectWith(ConstantRange(Known.One,
5504 assert(SignHint == ScalarEvolution::HINT_RANGE_SIGNED &&
5505 "generalize as needed!");
5506 unsigned NS = ComputeNumSignBits(U->getValue(), DL, 0, &AC, nullptr, &DT);
5508 ConservativeResult = ConservativeResult.intersectWith(
5509 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
5510 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1) + 1));
5513 return setRange(U, SignHint, std::move(ConservativeResult));
5516 return setRange(S, SignHint, std::move(ConservativeResult));
5519 // Given a StartRange, Step and MaxBECount for an expression compute a range of
5520 // values that the expression can take. Initially, the expression has a value
5521 // from StartRange and then is changed by Step up to MaxBECount times. Signed
5522 // argument defines if we treat Step as signed or unsigned.
5523 static ConstantRange getRangeForAffineARHelper(APInt Step,
5524 const ConstantRange &StartRange,
5525 const APInt &MaxBECount,
5526 unsigned BitWidth, bool Signed) {
5527 // If either Step or MaxBECount is 0, then the expression won't change, and we
5528 // just need to return the initial range.
5529 if (Step == 0 || MaxBECount == 0)
5532 // If we don't know anything about the initial value (i.e. StartRange is
5533 // FullRange), then we don't know anything about the final range either.
5534 // Return FullRange.
5535 if (StartRange.isFullSet())
5536 return ConstantRange(BitWidth, /* isFullSet = */ true);
5538 // If Step is signed and negative, then we use its absolute value, but we also
5539 // note that we're moving in the opposite direction.
5540 bool Descending = Signed && Step.isNegative();
5543 // This is correct even for INT_SMIN. Let's look at i8 to illustrate this:
5544 // abs(INT_SMIN) = abs(-128) = abs(0x80) = -0x80 = 0x80 = 128.
5545 // This equations hold true due to the well-defined wrap-around behavior of
5549 // Check if Offset is more than full span of BitWidth. If it is, the
5550 // expression is guaranteed to overflow.
5551 if (APInt::getMaxValue(StartRange.getBitWidth()).udiv(Step).ult(MaxBECount))
5552 return ConstantRange(BitWidth, /* isFullSet = */ true);
5554 // Offset is by how much the expression can change. Checks above guarantee no
5556 APInt Offset = Step * MaxBECount;
5558 // Minimum value of the final range will match the minimal value of StartRange
5559 // if the expression is increasing and will be decreased by Offset otherwise.
5560 // Maximum value of the final range will match the maximal value of StartRange
5561 // if the expression is decreasing and will be increased by Offset otherwise.
5562 APInt StartLower = StartRange.getLower();
5563 APInt StartUpper = StartRange.getUpper() - 1;
5564 APInt MovedBoundary = Descending ? (StartLower - std::move(Offset))
5565 : (StartUpper + std::move(Offset));
5567 // It's possible that the new minimum/maximum value will fall into the initial
5568 // range (due to wrap around). This means that the expression can take any
5569 // value in this bitwidth, and we have to return full range.
5570 if (StartRange.contains(MovedBoundary))
5571 return ConstantRange(BitWidth, /* isFullSet = */ true);
5574 Descending ? std::move(MovedBoundary) : std::move(StartLower);
5576 Descending ? std::move(StartUpper) : std::move(MovedBoundary);
5579 // If we end up with full range, return a proper full range.
5580 if (NewLower == NewUpper)
5581 return ConstantRange(BitWidth, /* isFullSet = */ true);
5583 // No overflow detected, return [StartLower, StartUpper + Offset + 1) range.
5584 return ConstantRange(std::move(NewLower), std::move(NewUpper));
5587 ConstantRange ScalarEvolution::getRangeForAffineAR(const SCEV *Start,
5589 const SCEV *MaxBECount,
5590 unsigned BitWidth) {
5591 assert(!isa<SCEVCouldNotCompute>(MaxBECount) &&
5592 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth &&
5595 MaxBECount = getNoopOrZeroExtend(MaxBECount, Start->getType());
5596 APInt MaxBECountValue = getUnsignedRangeMax(MaxBECount);
5598 // First, consider step signed.
5599 ConstantRange StartSRange = getSignedRange(Start);
5600 ConstantRange StepSRange = getSignedRange(Step);
5602 // If Step can be both positive and negative, we need to find ranges for the
5603 // maximum absolute step values in both directions and union them.
5605 getRangeForAffineARHelper(StepSRange.getSignedMin(), StartSRange,
5606 MaxBECountValue, BitWidth, /* Signed = */ true);
5607 SR = SR.unionWith(getRangeForAffineARHelper(StepSRange.getSignedMax(),
5608 StartSRange, MaxBECountValue,
5609 BitWidth, /* Signed = */ true));
5611 // Next, consider step unsigned.
5612 ConstantRange UR = getRangeForAffineARHelper(
5613 getUnsignedRangeMax(Step), getUnsignedRange(Start),
5614 MaxBECountValue, BitWidth, /* Signed = */ false);
5616 // Finally, intersect signed and unsigned ranges.
5617 return SR.intersectWith(UR);
5620 ConstantRange ScalarEvolution::getRangeViaFactoring(const SCEV *Start,
5622 const SCEV *MaxBECount,
5623 unsigned BitWidth) {
5624 // RangeOf({C?A:B,+,C?P:Q}) == RangeOf(C?{A,+,P}:{B,+,Q})
5625 // == RangeOf({A,+,P}) union RangeOf({B,+,Q})
5627 struct SelectPattern {
5628 Value *Condition = nullptr;
5632 explicit SelectPattern(ScalarEvolution &SE, unsigned BitWidth,
5634 Optional<unsigned> CastOp;
5635 APInt Offset(BitWidth, 0);
5637 assert(SE.getTypeSizeInBits(S->getType()) == BitWidth &&
5640 // Peel off a constant offset:
5641 if (auto *SA = dyn_cast<SCEVAddExpr>(S)) {
5642 // In the future we could consider being smarter here and handle
5643 // {Start+Step,+,Step} too.
5644 if (SA->getNumOperands() != 2 || !isa<SCEVConstant>(SA->getOperand(0)))
5647 Offset = cast<SCEVConstant>(SA->getOperand(0))->getAPInt();
5648 S = SA->getOperand(1);
5651 // Peel off a cast operation
5652 if (auto *SCast = dyn_cast<SCEVCastExpr>(S)) {
5653 CastOp = SCast->getSCEVType();
5654 S = SCast->getOperand();
5657 using namespace llvm::PatternMatch;
5659 auto *SU = dyn_cast<SCEVUnknown>(S);
5660 const APInt *TrueVal, *FalseVal;
5662 !match(SU->getValue(), m_Select(m_Value(Condition), m_APInt(TrueVal),
5663 m_APInt(FalseVal)))) {
5664 Condition = nullptr;
5668 TrueValue = *TrueVal;
5669 FalseValue = *FalseVal;
5671 // Re-apply the cast we peeled off earlier
5672 if (CastOp.hasValue())
5675 llvm_unreachable("Unknown SCEV cast type!");
5678 TrueValue = TrueValue.trunc(BitWidth);
5679 FalseValue = FalseValue.trunc(BitWidth);
5682 TrueValue = TrueValue.zext(BitWidth);
5683 FalseValue = FalseValue.zext(BitWidth);
5686 TrueValue = TrueValue.sext(BitWidth);
5687 FalseValue = FalseValue.sext(BitWidth);
5691 // Re-apply the constant offset we peeled off earlier
5692 TrueValue += Offset;
5693 FalseValue += Offset;
5696 bool isRecognized() { return Condition != nullptr; }
5699 SelectPattern StartPattern(*this, BitWidth, Start);
5700 if (!StartPattern.isRecognized())
5701 return ConstantRange(BitWidth, /* isFullSet = */ true);
5703 SelectPattern StepPattern(*this, BitWidth, Step);
5704 if (!StepPattern.isRecognized())
5705 return ConstantRange(BitWidth, /* isFullSet = */ true);
5707 if (StartPattern.Condition != StepPattern.Condition) {
5708 // We don't handle this case today; but we could, by considering four
5709 // possibilities below instead of two. I'm not sure if there are cases where
5710 // that will help over what getRange already does, though.
5711 return ConstantRange(BitWidth, /* isFullSet = */ true);
5714 // NB! Calling ScalarEvolution::getConstant is fine, but we should not try to
5715 // construct arbitrary general SCEV expressions here. This function is called
5716 // from deep in the call stack, and calling getSCEV (on a sext instruction,
5717 // say) can end up caching a suboptimal value.
5719 // FIXME: without the explicit `this` receiver below, MSVC errors out with
5720 // C2352 and C2512 (otherwise it isn't needed).
5722 const SCEV *TrueStart = this->getConstant(StartPattern.TrueValue);
5723 const SCEV *TrueStep = this->getConstant(StepPattern.TrueValue);
5724 const SCEV *FalseStart = this->getConstant(StartPattern.FalseValue);
5725 const SCEV *FalseStep = this->getConstant(StepPattern.FalseValue);
5727 ConstantRange TrueRange =
5728 this->getRangeForAffineAR(TrueStart, TrueStep, MaxBECount, BitWidth);
5729 ConstantRange FalseRange =
5730 this->getRangeForAffineAR(FalseStart, FalseStep, MaxBECount, BitWidth);
5732 return TrueRange.unionWith(FalseRange);
5735 SCEV::NoWrapFlags ScalarEvolution::getNoWrapFlagsFromUB(const Value *V) {
5736 if (isa<ConstantExpr>(V)) return SCEV::FlagAnyWrap;
5737 const BinaryOperator *BinOp = cast<BinaryOperator>(V);
5739 // Return early if there are no flags to propagate to the SCEV.
5740 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
5741 if (BinOp->hasNoUnsignedWrap())
5742 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
5743 if (BinOp->hasNoSignedWrap())
5744 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW);
5745 if (Flags == SCEV::FlagAnyWrap)
5746 return SCEV::FlagAnyWrap;
5748 return isSCEVExprNeverPoison(BinOp) ? Flags : SCEV::FlagAnyWrap;
5751 bool ScalarEvolution::isSCEVExprNeverPoison(const Instruction *I) {
5752 // Here we check that I is in the header of the innermost loop containing I,
5753 // since we only deal with instructions in the loop header. The actual loop we
5754 // need to check later will come from an add recurrence, but getting that
5755 // requires computing the SCEV of the operands, which can be expensive. This
5756 // check we can do cheaply to rule out some cases early.
5757 Loop *InnermostContainingLoop = LI.getLoopFor(I->getParent());
5758 if (InnermostContainingLoop == nullptr ||
5759 InnermostContainingLoop->getHeader() != I->getParent())
5762 // Only proceed if we can prove that I does not yield poison.
5763 if (!programUndefinedIfFullPoison(I))
5766 // At this point we know that if I is executed, then it does not wrap
5767 // according to at least one of NSW or NUW. If I is not executed, then we do
5768 // not know if the calculation that I represents would wrap. Multiple
5769 // instructions can map to the same SCEV. If we apply NSW or NUW from I to
5770 // the SCEV, we must guarantee no wrapping for that SCEV also when it is
5771 // derived from other instructions that map to the same SCEV. We cannot make
5772 // that guarantee for cases where I is not executed. So we need to find the
5773 // loop that I is considered in relation to and prove that I is executed for
5774 // every iteration of that loop. That implies that the value that I
5775 // calculates does not wrap anywhere in the loop, so then we can apply the
5776 // flags to the SCEV.
5778 // We check isLoopInvariant to disambiguate in case we are adding recurrences
5779 // from different loops, so that we know which loop to prove that I is
5781 for (unsigned OpIndex = 0; OpIndex < I->getNumOperands(); ++OpIndex) {
5782 // I could be an extractvalue from a call to an overflow intrinsic.
5783 // TODO: We can do better here in some cases.
5784 if (!isSCEVable(I->getOperand(OpIndex)->getType()))
5786 const SCEV *Op = getSCEV(I->getOperand(OpIndex));
5787 if (auto *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
5788 bool AllOtherOpsLoopInvariant = true;
5789 for (unsigned OtherOpIndex = 0; OtherOpIndex < I->getNumOperands();
5791 if (OtherOpIndex != OpIndex) {
5792 const SCEV *OtherOp = getSCEV(I->getOperand(OtherOpIndex));
5793 if (!isLoopInvariant(OtherOp, AddRec->getLoop())) {
5794 AllOtherOpsLoopInvariant = false;
5799 if (AllOtherOpsLoopInvariant &&
5800 isGuaranteedToExecuteForEveryIteration(I, AddRec->getLoop()))
5807 bool ScalarEvolution::isAddRecNeverPoison(const Instruction *I, const Loop *L) {
5808 // If we know that \c I can never be poison period, then that's enough.
5809 if (isSCEVExprNeverPoison(I))
5812 // For an add recurrence specifically, we assume that infinite loops without
5813 // side effects are undefined behavior, and then reason as follows:
5815 // If the add recurrence is poison in any iteration, it is poison on all
5816 // future iterations (since incrementing poison yields poison). If the result
5817 // of the add recurrence is fed into the loop latch condition and the loop
5818 // does not contain any throws or exiting blocks other than the latch, we now
5819 // have the ability to "choose" whether the backedge is taken or not (by
5820 // choosing a sufficiently evil value for the poison feeding into the branch)
5821 // for every iteration including and after the one in which \p I first became
5822 // poison. There are two possibilities (let's call the iteration in which \p
5823 // I first became poison as K):
5825 // 1. In the set of iterations including and after K, the loop body executes
5826 // no side effects. In this case executing the backege an infinte number
5827 // of times will yield undefined behavior.
5829 // 2. In the set of iterations including and after K, the loop body executes
5830 // at least one side effect. In this case, that specific instance of side
5831 // effect is control dependent on poison, which also yields undefined
5834 auto *ExitingBB = L->getExitingBlock();
5835 auto *LatchBB = L->getLoopLatch();
5836 if (!ExitingBB || !LatchBB || ExitingBB != LatchBB)
5839 SmallPtrSet<const Instruction *, 16> Pushed;
5840 SmallVector<const Instruction *, 8> PoisonStack;
5842 // We start by assuming \c I, the post-inc add recurrence, is poison. Only
5843 // things that are known to be fully poison under that assumption go on the
5846 PoisonStack.push_back(I);
5848 bool LatchControlDependentOnPoison = false;
5849 while (!PoisonStack.empty() && !LatchControlDependentOnPoison) {
5850 const Instruction *Poison = PoisonStack.pop_back_val();
5852 for (auto *PoisonUser : Poison->users()) {
5853 if (propagatesFullPoison(cast<Instruction>(PoisonUser))) {
5854 if (Pushed.insert(cast<Instruction>(PoisonUser)).second)
5855 PoisonStack.push_back(cast<Instruction>(PoisonUser));
5856 } else if (auto *BI = dyn_cast<BranchInst>(PoisonUser)) {
5857 assert(BI->isConditional() && "Only possibility!");
5858 if (BI->getParent() == LatchBB) {
5859 LatchControlDependentOnPoison = true;
5866 return LatchControlDependentOnPoison && loopHasNoAbnormalExits(L);
5869 ScalarEvolution::LoopProperties
5870 ScalarEvolution::getLoopProperties(const Loop *L) {
5871 using LoopProperties = ScalarEvolution::LoopProperties;
5873 auto Itr = LoopPropertiesCache.find(L);
5874 if (Itr == LoopPropertiesCache.end()) {
5875 auto HasSideEffects = [](Instruction *I) {
5876 if (auto *SI = dyn_cast<StoreInst>(I))
5877 return !SI->isSimple();
5879 return I->mayHaveSideEffects();
5882 LoopProperties LP = {/* HasNoAbnormalExits */ true,
5883 /*HasNoSideEffects*/ true};
5885 for (auto *BB : L->getBlocks())
5886 for (auto &I : *BB) {
5887 if (!isGuaranteedToTransferExecutionToSuccessor(&I))
5888 LP.HasNoAbnormalExits = false;
5889 if (HasSideEffects(&I))
5890 LP.HasNoSideEffects = false;
5891 if (!LP.HasNoAbnormalExits && !LP.HasNoSideEffects)
5892 break; // We're already as pessimistic as we can get.
5895 auto InsertPair = LoopPropertiesCache.insert({L, LP});
5896 assert(InsertPair.second && "We just checked!");
5897 Itr = InsertPair.first;
5903 const SCEV *ScalarEvolution::createSCEV(Value *V) {
5904 if (!isSCEVable(V->getType()))
5905 return getUnknown(V);
5907 if (Instruction *I = dyn_cast<Instruction>(V)) {
5908 // Don't attempt to analyze instructions in blocks that aren't
5909 // reachable. Such instructions don't matter, and they aren't required
5910 // to obey basic rules for definitions dominating uses which this
5911 // analysis depends on.
5912 if (!DT.isReachableFromEntry(I->getParent()))
5913 return getUnknown(V);
5914 } else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
5915 return getConstant(CI);
5916 else if (isa<ConstantPointerNull>(V))
5917 return getZero(V->getType());
5918 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
5919 return GA->isInterposable() ? getUnknown(V) : getSCEV(GA->getAliasee());
5920 else if (!isa<ConstantExpr>(V))
5921 return getUnknown(V);
5923 Operator *U = cast<Operator>(V);
5924 if (auto BO = MatchBinaryOp(U, DT)) {
5925 switch (BO->Opcode) {
5926 case Instruction::Add: {
5927 // The simple thing to do would be to just call getSCEV on both operands
5928 // and call getAddExpr with the result. However if we're looking at a
5929 // bunch of things all added together, this can be quite inefficient,
5930 // because it leads to N-1 getAddExpr calls for N ultimate operands.
5931 // Instead, gather up all the operands and make a single getAddExpr call.
5932 // LLVM IR canonical form means we need only traverse the left operands.
5933 SmallVector<const SCEV *, 4> AddOps;
5936 if (auto *OpSCEV = getExistingSCEV(BO->Op)) {
5937 AddOps.push_back(OpSCEV);
5941 // If a NUW or NSW flag can be applied to the SCEV for this
5942 // addition, then compute the SCEV for this addition by itself
5943 // with a separate call to getAddExpr. We need to do that
5944 // instead of pushing the operands of the addition onto AddOps,
5945 // since the flags are only known to apply to this particular
5946 // addition - they may not apply to other additions that can be
5947 // formed with operands from AddOps.
5948 const SCEV *RHS = getSCEV(BO->RHS);
5949 SCEV::NoWrapFlags Flags = getNoWrapFlagsFromUB(BO->Op);
5950 if (Flags != SCEV::FlagAnyWrap) {
5951 const SCEV *LHS = getSCEV(BO->LHS);
5952 if (BO->Opcode == Instruction::Sub)
5953 AddOps.push_back(getMinusSCEV(LHS, RHS, Flags));
5955 AddOps.push_back(getAddExpr(LHS, RHS, Flags));
5960 if (BO->Opcode == Instruction::Sub)
5961 AddOps.push_back(getNegativeSCEV(getSCEV(BO->RHS)));
5963 AddOps.push_back(getSCEV(BO->RHS));
5965 auto NewBO = MatchBinaryOp(BO->LHS, DT);
5966 if (!NewBO || (NewBO->Opcode != Instruction::Add &&
5967 NewBO->Opcode != Instruction::Sub)) {
5968 AddOps.push_back(getSCEV(BO->LHS));
5974 return getAddExpr(AddOps);
5977 case Instruction::Mul: {
5978 SmallVector<const SCEV *, 4> MulOps;
5981 if (auto *OpSCEV = getExistingSCEV(BO->Op)) {
5982 MulOps.push_back(OpSCEV);
5986 SCEV::NoWrapFlags Flags = getNoWrapFlagsFromUB(BO->Op);
5987 if (Flags != SCEV::FlagAnyWrap) {
5989 getMulExpr(getSCEV(BO->LHS), getSCEV(BO->RHS), Flags));
5994 MulOps.push_back(getSCEV(BO->RHS));
5995 auto NewBO = MatchBinaryOp(BO->LHS, DT);
5996 if (!NewBO || NewBO->Opcode != Instruction::Mul) {
5997 MulOps.push_back(getSCEV(BO->LHS));
6003 return getMulExpr(MulOps);
6005 case Instruction::UDiv:
6006 return getUDivExpr(getSCEV(BO->LHS), getSCEV(BO->RHS));
6007 case Instruction::URem:
6008 return getURemExpr(getSCEV(BO->LHS), getSCEV(BO->RHS));
6009 case Instruction::Sub: {
6010 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
6012 Flags = getNoWrapFlagsFromUB(BO->Op);
6013 return getMinusSCEV(getSCEV(BO->LHS), getSCEV(BO->RHS), Flags);
6015 case Instruction::And:
6016 // For an expression like x&255 that merely masks off the high bits,
6017 // use zext(trunc(x)) as the SCEV expression.
6018 if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->RHS)) {
6020 return getSCEV(BO->RHS);
6021 if (CI->isMinusOne())
6022 return getSCEV(BO->LHS);
6023 const APInt &A = CI->getValue();
6025 // Instcombine's ShrinkDemandedConstant may strip bits out of
6026 // constants, obscuring what would otherwise be a low-bits mask.
6027 // Use computeKnownBits to compute what ShrinkDemandedConstant
6028 // knew about to reconstruct a low-bits mask value.
6029 unsigned LZ = A.countLeadingZeros();
6030 unsigned TZ = A.countTrailingZeros();
6031 unsigned BitWidth = A.getBitWidth();
6032 KnownBits Known(BitWidth);
6033 computeKnownBits(BO->LHS, Known, getDataLayout(),
6034 0, &AC, nullptr, &DT);
6036 APInt EffectiveMask =
6037 APInt::getLowBitsSet(BitWidth, BitWidth - LZ - TZ).shl(TZ);
6038 if ((LZ != 0 || TZ != 0) && !((~A & ~Known.Zero) & EffectiveMask)) {
6039 const SCEV *MulCount = getConstant(APInt::getOneBitSet(BitWidth, TZ));
6040 const SCEV *LHS = getSCEV(BO->LHS);
6041 const SCEV *ShiftedLHS = nullptr;
6042 if (auto *LHSMul = dyn_cast<SCEVMulExpr>(LHS)) {
6043 if (auto *OpC = dyn_cast<SCEVConstant>(LHSMul->getOperand(0))) {
6044 // For an expression like (x * 8) & 8, simplify the multiply.
6045 unsigned MulZeros = OpC->getAPInt().countTrailingZeros();
6046 unsigned GCD = std::min(MulZeros, TZ);
6047 APInt DivAmt = APInt::getOneBitSet(BitWidth, TZ - GCD);
6048 SmallVector<const SCEV*, 4> MulOps;
6049 MulOps.push_back(getConstant(OpC->getAPInt().lshr(GCD)));
6050 MulOps.append(LHSMul->op_begin() + 1, LHSMul->op_end());
6051 auto *NewMul = getMulExpr(MulOps, LHSMul->getNoWrapFlags());
6052 ShiftedLHS = getUDivExpr(NewMul, getConstant(DivAmt));
6056 ShiftedLHS = getUDivExpr(LHS, MulCount);
6059 getTruncateExpr(ShiftedLHS,
6060 IntegerType::get(getContext(), BitWidth - LZ - TZ)),
6061 BO->LHS->getType()),
6067 case Instruction::Or:
6068 // If the RHS of the Or is a constant, we may have something like:
6069 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
6070 // optimizations will transparently handle this case.
6072 // In order for this transformation to be safe, the LHS must be of the
6073 // form X*(2^n) and the Or constant must be less than 2^n.
6074 if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->RHS)) {
6075 const SCEV *LHS = getSCEV(BO->LHS);
6076 const APInt &CIVal = CI->getValue();
6077 if (GetMinTrailingZeros(LHS) >=
6078 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
6079 // Build a plain add SCEV.
6080 const SCEV *S = getAddExpr(LHS, getSCEV(CI));
6081 // If the LHS of the add was an addrec and it has no-wrap flags,
6082 // transfer the no-wrap flags, since an or won't introduce a wrap.
6083 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
6084 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
6085 const_cast<SCEVAddRecExpr *>(NewAR)->setNoWrapFlags(
6086 OldAR->getNoWrapFlags());
6093 case Instruction::Xor:
6094 if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->RHS)) {
6095 // If the RHS of xor is -1, then this is a not operation.
6096 if (CI->isMinusOne())
6097 return getNotSCEV(getSCEV(BO->LHS));
6099 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
6100 // This is a variant of the check for xor with -1, and it handles
6101 // the case where instcombine has trimmed non-demanded bits out
6102 // of an xor with -1.
6103 if (auto *LBO = dyn_cast<BinaryOperator>(BO->LHS))
6104 if (ConstantInt *LCI = dyn_cast<ConstantInt>(LBO->getOperand(1)))
6105 if (LBO->getOpcode() == Instruction::And &&
6106 LCI->getValue() == CI->getValue())
6107 if (const SCEVZeroExtendExpr *Z =
6108 dyn_cast<SCEVZeroExtendExpr>(getSCEV(BO->LHS))) {
6109 Type *UTy = BO->LHS->getType();
6110 const SCEV *Z0 = Z->getOperand();
6111 Type *Z0Ty = Z0->getType();
6112 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
6114 // If C is a low-bits mask, the zero extend is serving to
6115 // mask off the high bits. Complement the operand and
6116 // re-apply the zext.
6117 if (CI->getValue().isMask(Z0TySize))
6118 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
6120 // If C is a single bit, it may be in the sign-bit position
6121 // before the zero-extend. In this case, represent the xor
6122 // using an add, which is equivalent, and re-apply the zext.
6123 APInt Trunc = CI->getValue().trunc(Z0TySize);
6124 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
6126 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
6132 case Instruction::Shl:
6133 // Turn shift left of a constant amount into a multiply.
6134 if (ConstantInt *SA = dyn_cast<ConstantInt>(BO->RHS)) {
6135 uint32_t BitWidth = cast<IntegerType>(SA->getType())->getBitWidth();
6137 // If the shift count is not less than the bitwidth, the result of
6138 // the shift is undefined. Don't try to analyze it, because the
6139 // resolution chosen here may differ from the resolution chosen in
6140 // other parts of the compiler.
6141 if (SA->getValue().uge(BitWidth))
6144 // It is currently not resolved how to interpret NSW for left
6145 // shift by BitWidth - 1, so we avoid applying flags in that
6146 // case. Remove this check (or this comment) once the situation
6148 // http://lists.llvm.org/pipermail/llvm-dev/2015-April/084195.html
6149 // and http://reviews.llvm.org/D8890 .
6150 auto Flags = SCEV::FlagAnyWrap;
6151 if (BO->Op && SA->getValue().ult(BitWidth - 1))
6152 Flags = getNoWrapFlagsFromUB(BO->Op);
6154 Constant *X = ConstantInt::get(getContext(),
6155 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
6156 return getMulExpr(getSCEV(BO->LHS), getSCEV(X), Flags);
6160 case Instruction::AShr: {
6161 // AShr X, C, where C is a constant.
6162 ConstantInt *CI = dyn_cast<ConstantInt>(BO->RHS);
6166 Type *OuterTy = BO->LHS->getType();
6167 uint64_t BitWidth = getTypeSizeInBits(OuterTy);
6168 // If the shift count is not less than the bitwidth, the result of
6169 // the shift is undefined. Don't try to analyze it, because the
6170 // resolution chosen here may differ from the resolution chosen in
6171 // other parts of the compiler.
6172 if (CI->getValue().uge(BitWidth))
6176 return getSCEV(BO->LHS); // shift by zero --> noop
6178 uint64_t AShrAmt = CI->getZExtValue();
6179 Type *TruncTy = IntegerType::get(getContext(), BitWidth - AShrAmt);
6181 Operator *L = dyn_cast<Operator>(BO->LHS);
6182 if (L && L->getOpcode() == Instruction::Shl) {
6185 // Both n and m are constant.
6187 const SCEV *ShlOp0SCEV = getSCEV(L->getOperand(0));
6188 if (L->getOperand(1) == BO->RHS)
6189 // For a two-shift sext-inreg, i.e. n = m,
6190 // use sext(trunc(x)) as the SCEV expression.
6191 return getSignExtendExpr(
6192 getTruncateExpr(ShlOp0SCEV, TruncTy), OuterTy);
6194 ConstantInt *ShlAmtCI = dyn_cast<ConstantInt>(L->getOperand(1));
6195 if (ShlAmtCI && ShlAmtCI->getValue().ult(BitWidth)) {
6196 uint64_t ShlAmt = ShlAmtCI->getZExtValue();
6197 if (ShlAmt > AShrAmt) {
6198 // When n > m, use sext(mul(trunc(x), 2^(n-m)))) as the SCEV
6199 // expression. We already checked that ShlAmt < BitWidth, so
6200 // the multiplier, 1 << (ShlAmt - AShrAmt), fits into TruncTy as
6201 // ShlAmt - AShrAmt < Amt.
6202 APInt Mul = APInt::getOneBitSet(BitWidth - AShrAmt,
6204 return getSignExtendExpr(
6205 getMulExpr(getTruncateExpr(ShlOp0SCEV, TruncTy),
6206 getConstant(Mul)), OuterTy);
6215 switch (U->getOpcode()) {
6216 case Instruction::Trunc:
6217 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
6219 case Instruction::ZExt:
6220 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
6222 case Instruction::SExt:
6223 if (auto BO = MatchBinaryOp(U->getOperand(0), DT)) {
6224 // The NSW flag of a subtract does not always survive the conversion to
6225 // A + (-1)*B. By pushing sign extension onto its operands we are much
6226 // more likely to preserve NSW and allow later AddRec optimisations.
6228 // NOTE: This is effectively duplicating this logic from getSignExtend:
6229 // sext((A + B + ...)<nsw>) --> (sext(A) + sext(B) + ...)<nsw>
6230 // but by that point the NSW information has potentially been lost.
6231 if (BO->Opcode == Instruction::Sub && BO->IsNSW) {
6232 Type *Ty = U->getType();
6233 auto *V1 = getSignExtendExpr(getSCEV(BO->LHS), Ty);
6234 auto *V2 = getSignExtendExpr(getSCEV(BO->RHS), Ty);
6235 return getMinusSCEV(V1, V2, SCEV::FlagNSW);
6238 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
6240 case Instruction::BitCast:
6241 // BitCasts are no-op casts so we just eliminate the cast.
6242 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
6243 return getSCEV(U->getOperand(0));
6246 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
6247 // lead to pointer expressions which cannot safely be expanded to GEPs,
6248 // because ScalarEvolution doesn't respect the GEP aliasing rules when
6249 // simplifying integer expressions.
6251 case Instruction::GetElementPtr:
6252 return createNodeForGEP(cast<GEPOperator>(U));
6254 case Instruction::PHI:
6255 return createNodeForPHI(cast<PHINode>(U));
6257 case Instruction::Select:
6258 // U can also be a select constant expr, which let fall through. Since
6259 // createNodeForSelect only works for a condition that is an `ICmpInst`, and
6260 // constant expressions cannot have instructions as operands, we'd have
6261 // returned getUnknown for a select constant expressions anyway.
6262 if (isa<Instruction>(U))
6263 return createNodeForSelectOrPHI(cast<Instruction>(U), U->getOperand(0),
6264 U->getOperand(1), U->getOperand(2));
6267 case Instruction::Call:
6268 case Instruction::Invoke:
6269 if (Value *RV = CallSite(U).getReturnedArgOperand())
6274 return getUnknown(V);
6277 //===----------------------------------------------------------------------===//
6278 // Iteration Count Computation Code
6281 static unsigned getConstantTripCount(const SCEVConstant *ExitCount) {
6285 ConstantInt *ExitConst = ExitCount->getValue();
6287 // Guard against huge trip counts.
6288 if (ExitConst->getValue().getActiveBits() > 32)
6291 // In case of integer overflow, this returns 0, which is correct.
6292 return ((unsigned)ExitConst->getZExtValue()) + 1;
6295 unsigned ScalarEvolution::getSmallConstantTripCount(const Loop *L) {
6296 if (BasicBlock *ExitingBB = L->getExitingBlock())
6297 return getSmallConstantTripCount(L, ExitingBB);
6299 // No trip count information for multiple exits.
6303 unsigned ScalarEvolution::getSmallConstantTripCount(const Loop *L,
6304 BasicBlock *ExitingBlock) {
6305 assert(ExitingBlock && "Must pass a non-null exiting block!");
6306 assert(L->isLoopExiting(ExitingBlock) &&
6307 "Exiting block must actually branch out of the loop!");
6308 const SCEVConstant *ExitCount =
6309 dyn_cast<SCEVConstant>(getExitCount(L, ExitingBlock));
6310 return getConstantTripCount(ExitCount);
6313 unsigned ScalarEvolution::getSmallConstantMaxTripCount(const Loop *L) {
6314 const auto *MaxExitCount =
6315 dyn_cast<SCEVConstant>(getMaxBackedgeTakenCount(L));
6316 return getConstantTripCount(MaxExitCount);
6319 unsigned ScalarEvolution::getSmallConstantTripMultiple(const Loop *L) {
6320 if (BasicBlock *ExitingBB = L->getExitingBlock())
6321 return getSmallConstantTripMultiple(L, ExitingBB);
6323 // No trip multiple information for multiple exits.
6327 /// Returns the largest constant divisor of the trip count of this loop as a
6328 /// normal unsigned value, if possible. This means that the actual trip count is
6329 /// always a multiple of the returned value (don't forget the trip count could
6330 /// very well be zero as well!).
6332 /// Returns 1 if the trip count is unknown or not guaranteed to be the
6333 /// multiple of a constant (which is also the case if the trip count is simply
6334 /// constant, use getSmallConstantTripCount for that case), Will also return 1
6335 /// if the trip count is very large (>= 2^32).
6337 /// As explained in the comments for getSmallConstantTripCount, this assumes
6338 /// that control exits the loop via ExitingBlock.
6340 ScalarEvolution::getSmallConstantTripMultiple(const Loop *L,
6341 BasicBlock *ExitingBlock) {
6342 assert(ExitingBlock && "Must pass a non-null exiting block!");
6343 assert(L->isLoopExiting(ExitingBlock) &&
6344 "Exiting block must actually branch out of the loop!");
6345 const SCEV *ExitCount = getExitCount(L, ExitingBlock);
6346 if (ExitCount == getCouldNotCompute())
6349 // Get the trip count from the BE count by adding 1.
6350 const SCEV *TCExpr = getAddExpr(ExitCount, getOne(ExitCount->getType()));
6352 const SCEVConstant *TC = dyn_cast<SCEVConstant>(TCExpr);
6354 // Attempt to factor more general cases. Returns the greatest power of
6355 // two divisor. If overflow happens, the trip count expression is still
6356 // divisible by the greatest power of 2 divisor returned.
6357 return 1U << std::min((uint32_t)31, GetMinTrailingZeros(TCExpr));
6359 ConstantInt *Result = TC->getValue();
6361 // Guard against huge trip counts (this requires checking
6362 // for zero to handle the case where the trip count == -1 and the
6364 if (!Result || Result->getValue().getActiveBits() > 32 ||
6365 Result->getValue().getActiveBits() == 0)
6368 return (unsigned)Result->getZExtValue();
6371 /// Get the expression for the number of loop iterations for which this loop is
6372 /// guaranteed not to exit via ExitingBlock. Otherwise return
6373 /// SCEVCouldNotCompute.
6374 const SCEV *ScalarEvolution::getExitCount(const Loop *L,
6375 BasicBlock *ExitingBlock) {
6376 return getBackedgeTakenInfo(L).getExact(ExitingBlock, this);
6380 ScalarEvolution::getPredicatedBackedgeTakenCount(const Loop *L,
6381 SCEVUnionPredicate &Preds) {
6382 return getPredicatedBackedgeTakenInfo(L).getExact(this, &Preds);
6385 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
6386 return getBackedgeTakenInfo(L).getExact(this);
6389 /// Similar to getBackedgeTakenCount, except return the least SCEV value that is
6390 /// known never to be less than the actual backedge taken count.
6391 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
6392 return getBackedgeTakenInfo(L).getMax(this);
6395 bool ScalarEvolution::isBackedgeTakenCountMaxOrZero(const Loop *L) {
6396 return getBackedgeTakenInfo(L).isMaxOrZero(this);
6399 /// Push PHI nodes in the header of the given loop onto the given Worklist.
6401 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
6402 BasicBlock *Header = L->getHeader();
6404 // Push all Loop-header PHIs onto the Worklist stack.
6405 for (PHINode &PN : Header->phis())
6406 Worklist.push_back(&PN);
6409 const ScalarEvolution::BackedgeTakenInfo &
6410 ScalarEvolution::getPredicatedBackedgeTakenInfo(const Loop *L) {
6411 auto &BTI = getBackedgeTakenInfo(L);
6412 if (BTI.hasFullInfo())
6415 auto Pair = PredicatedBackedgeTakenCounts.insert({L, BackedgeTakenInfo()});
6418 return Pair.first->second;
6420 BackedgeTakenInfo Result =
6421 computeBackedgeTakenCount(L, /*AllowPredicates=*/true);
6423 return PredicatedBackedgeTakenCounts.find(L)->second = std::move(Result);
6426 const ScalarEvolution::BackedgeTakenInfo &
6427 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
6428 // Initially insert an invalid entry for this loop. If the insertion
6429 // succeeds, proceed to actually compute a backedge-taken count and
6430 // update the value. The temporary CouldNotCompute value tells SCEV
6431 // code elsewhere that it shouldn't attempt to request a new
6432 // backedge-taken count, which could result in infinite recursion.
6433 std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
6434 BackedgeTakenCounts.insert({L, BackedgeTakenInfo()});
6436 return Pair.first->second;
6438 // computeBackedgeTakenCount may allocate memory for its result. Inserting it
6439 // into the BackedgeTakenCounts map transfers ownership. Otherwise, the result
6440 // must be cleared in this scope.
6441 BackedgeTakenInfo Result = computeBackedgeTakenCount(L);
6443 if (Result.getExact(this) != getCouldNotCompute()) {
6444 assert(isLoopInvariant(Result.getExact(this), L) &&
6445 isLoopInvariant(Result.getMax(this), L) &&
6446 "Computed backedge-taken count isn't loop invariant for loop!");
6447 ++NumTripCountsComputed;
6449 else if (Result.getMax(this) == getCouldNotCompute() &&
6450 isa<PHINode>(L->getHeader()->begin())) {
6451 // Only count loops that have phi nodes as not being computable.
6452 ++NumTripCountsNotComputed;
6455 // Now that we know more about the trip count for this loop, forget any
6456 // existing SCEV values for PHI nodes in this loop since they are only
6457 // conservative estimates made without the benefit of trip count
6458 // information. This is similar to the code in forgetLoop, except that
6459 // it handles SCEVUnknown PHI nodes specially.
6460 if (Result.hasAnyInfo()) {
6461 SmallVector<Instruction *, 16> Worklist;
6462 PushLoopPHIs(L, Worklist);
6464 SmallPtrSet<Instruction *, 8> Discovered;
6465 while (!Worklist.empty()) {
6466 Instruction *I = Worklist.pop_back_val();
6468 ValueExprMapType::iterator It =
6469 ValueExprMap.find_as(static_cast<Value *>(I));
6470 if (It != ValueExprMap.end()) {
6471 const SCEV *Old = It->second;
6473 // SCEVUnknown for a PHI either means that it has an unrecognized
6474 // structure, or it's a PHI that's in the progress of being computed
6475 // by createNodeForPHI. In the former case, additional loop trip
6476 // count information isn't going to change anything. In the later
6477 // case, createNodeForPHI will perform the necessary updates on its
6478 // own when it gets to that point.
6479 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) {
6480 eraseValueFromMap(It->first);
6481 forgetMemoizedResults(Old);
6483 if (PHINode *PN = dyn_cast<PHINode>(I))
6484 ConstantEvolutionLoopExitValue.erase(PN);
6487 // Since we don't need to invalidate anything for correctness and we're
6488 // only invalidating to make SCEV's results more precise, we get to stop
6489 // early to avoid invalidating too much. This is especially important in
6492 // %v = f(pn0, pn1) // pn0 and pn1 used through some other phi node
6500 // where both loop0 and loop1's backedge taken count uses the SCEV
6501 // expression for %v. If we don't have the early stop below then in cases
6502 // like the above, getBackedgeTakenInfo(loop1) will clear out the trip
6503 // count for loop0 and getBackedgeTakenInfo(loop0) will clear out the trip
6504 // count for loop1, effectively nullifying SCEV's trip count cache.
6505 for (auto *U : I->users())
6506 if (auto *I = dyn_cast<Instruction>(U)) {
6507 auto *LoopForUser = LI.getLoopFor(I->getParent());
6508 if (LoopForUser && L->contains(LoopForUser) &&
6509 Discovered.insert(I).second)
6510 Worklist.push_back(I);
6515 // Re-lookup the insert position, since the call to
6516 // computeBackedgeTakenCount above could result in a
6517 // recusive call to getBackedgeTakenInfo (on a different
6518 // loop), which would invalidate the iterator computed
6520 return BackedgeTakenCounts.find(L)->second = std::move(Result);
6523 void ScalarEvolution::forgetLoop(const Loop *L) {
6524 // Drop any stored trip count value.
6525 auto RemoveLoopFromBackedgeMap =
6526 [](DenseMap<const Loop *, BackedgeTakenInfo> &Map, const Loop *L) {
6527 auto BTCPos = Map.find(L);
6528 if (BTCPos != Map.end()) {
6529 BTCPos->second.clear();
6534 SmallVector<const Loop *, 16> LoopWorklist(1, L);
6535 SmallVector<Instruction *, 32> Worklist;
6536 SmallPtrSet<Instruction *, 16> Visited;
6538 // Iterate over all the loops and sub-loops to drop SCEV information.
6539 while (!LoopWorklist.empty()) {
6540 auto *CurrL = LoopWorklist.pop_back_val();
6542 RemoveLoopFromBackedgeMap(BackedgeTakenCounts, CurrL);
6543 RemoveLoopFromBackedgeMap(PredicatedBackedgeTakenCounts, CurrL);
6545 // Drop information about predicated SCEV rewrites for this loop.
6546 for (auto I = PredicatedSCEVRewrites.begin();
6547 I != PredicatedSCEVRewrites.end();) {
6548 std::pair<const SCEV *, const Loop *> Entry = I->first;
6549 if (Entry.second == CurrL)
6550 PredicatedSCEVRewrites.erase(I++);
6555 auto LoopUsersItr = LoopUsers.find(CurrL);
6556 if (LoopUsersItr != LoopUsers.end()) {
6557 for (auto *S : LoopUsersItr->second)
6558 forgetMemoizedResults(S);
6559 LoopUsers.erase(LoopUsersItr);
6562 // Drop information about expressions based on loop-header PHIs.
6563 PushLoopPHIs(CurrL, Worklist);
6565 while (!Worklist.empty()) {
6566 Instruction *I = Worklist.pop_back_val();
6567 if (!Visited.insert(I).second)
6570 ValueExprMapType::iterator It =
6571 ValueExprMap.find_as(static_cast<Value *>(I));
6572 if (It != ValueExprMap.end()) {
6573 eraseValueFromMap(It->first);
6574 forgetMemoizedResults(It->second);
6575 if (PHINode *PN = dyn_cast<PHINode>(I))
6576 ConstantEvolutionLoopExitValue.erase(PN);
6579 PushDefUseChildren(I, Worklist);
6582 LoopPropertiesCache.erase(CurrL);
6583 // Forget all contained loops too, to avoid dangling entries in the
6584 // ValuesAtScopes map.
6585 LoopWorklist.append(CurrL->begin(), CurrL->end());
6589 void ScalarEvolution::forgetValue(Value *V) {
6590 Instruction *I = dyn_cast<Instruction>(V);
6593 // Drop information about expressions based on loop-header PHIs.
6594 SmallVector<Instruction *, 16> Worklist;
6595 Worklist.push_back(I);
6597 SmallPtrSet<Instruction *, 8> Visited;
6598 while (!Worklist.empty()) {
6599 I = Worklist.pop_back_val();
6600 if (!Visited.insert(I).second)
6603 ValueExprMapType::iterator It =
6604 ValueExprMap.find_as(static_cast<Value *>(I));
6605 if (It != ValueExprMap.end()) {
6606 eraseValueFromMap(It->first);
6607 forgetMemoizedResults(It->second);
6608 if (PHINode *PN = dyn_cast<PHINode>(I))
6609 ConstantEvolutionLoopExitValue.erase(PN);
6612 PushDefUseChildren(I, Worklist);
6616 /// Get the exact loop backedge taken count considering all loop exits. A
6617 /// computable result can only be returned for loops with a single exit.
6618 /// Returning the minimum taken count among all exits is incorrect because one
6619 /// of the loop's exit limit's may have been skipped. howFarToZero assumes that
6620 /// the limit of each loop test is never skipped. This is a valid assumption as
6621 /// long as the loop exits via that test. For precise results, it is the
6622 /// caller's responsibility to specify the relevant loop exit using
6623 /// getExact(ExitingBlock, SE).
6625 ScalarEvolution::BackedgeTakenInfo::getExact(ScalarEvolution *SE,
6626 SCEVUnionPredicate *Preds) const {
6627 // If any exits were not computable, the loop is not computable.
6628 if (!isComplete() || ExitNotTaken.empty())
6629 return SE->getCouldNotCompute();
6631 const SCEV *BECount = nullptr;
6632 for (auto &ENT : ExitNotTaken) {
6633 assert(ENT.ExactNotTaken != SE->getCouldNotCompute() && "bad exit SCEV");
6636 BECount = ENT.ExactNotTaken;
6637 else if (BECount != ENT.ExactNotTaken)
6638 return SE->getCouldNotCompute();
6639 if (Preds && !ENT.hasAlwaysTruePredicate())
6640 Preds->add(ENT.Predicate.get());
6642 assert((Preds || ENT.hasAlwaysTruePredicate()) &&
6643 "Predicate should be always true!");
6646 assert(BECount && "Invalid not taken count for loop exit");
6650 /// Get the exact not taken count for this loop exit.
6652 ScalarEvolution::BackedgeTakenInfo::getExact(BasicBlock *ExitingBlock,
6653 ScalarEvolution *SE) const {
6654 for (auto &ENT : ExitNotTaken)
6655 if (ENT.ExitingBlock == ExitingBlock && ENT.hasAlwaysTruePredicate())
6656 return ENT.ExactNotTaken;
6658 return SE->getCouldNotCompute();
6661 /// getMax - Get the max backedge taken count for the loop.
6663 ScalarEvolution::BackedgeTakenInfo::getMax(ScalarEvolution *SE) const {
6664 auto PredicateNotAlwaysTrue = [](const ExitNotTakenInfo &ENT) {
6665 return !ENT.hasAlwaysTruePredicate();
6668 if (any_of(ExitNotTaken, PredicateNotAlwaysTrue) || !getMax())
6669 return SE->getCouldNotCompute();
6671 assert((isa<SCEVCouldNotCompute>(getMax()) || isa<SCEVConstant>(getMax())) &&
6672 "No point in having a non-constant max backedge taken count!");
6676 bool ScalarEvolution::BackedgeTakenInfo::isMaxOrZero(ScalarEvolution *SE) const {
6677 auto PredicateNotAlwaysTrue = [](const ExitNotTakenInfo &ENT) {
6678 return !ENT.hasAlwaysTruePredicate();
6680 return MaxOrZero && !any_of(ExitNotTaken, PredicateNotAlwaysTrue);
6683 bool ScalarEvolution::BackedgeTakenInfo::hasOperand(const SCEV *S,
6684 ScalarEvolution *SE) const {
6685 if (getMax() && getMax() != SE->getCouldNotCompute() &&
6686 SE->hasOperand(getMax(), S))
6689 for (auto &ENT : ExitNotTaken)
6690 if (ENT.ExactNotTaken != SE->getCouldNotCompute() &&
6691 SE->hasOperand(ENT.ExactNotTaken, S))
6697 ScalarEvolution::ExitLimit::ExitLimit(const SCEV *E)
6698 : ExactNotTaken(E), MaxNotTaken(E) {
6699 assert((isa<SCEVCouldNotCompute>(MaxNotTaken) ||
6700 isa<SCEVConstant>(MaxNotTaken)) &&
6701 "No point in having a non-constant max backedge taken count!");
6704 ScalarEvolution::ExitLimit::ExitLimit(
6705 const SCEV *E, const SCEV *M, bool MaxOrZero,
6706 ArrayRef<const SmallPtrSetImpl<const SCEVPredicate *> *> PredSetList)
6707 : ExactNotTaken(E), MaxNotTaken(M), MaxOrZero(MaxOrZero) {
6708 assert((isa<SCEVCouldNotCompute>(ExactNotTaken) ||
6709 !isa<SCEVCouldNotCompute>(MaxNotTaken)) &&
6710 "Exact is not allowed to be less precise than Max");
6711 assert((isa<SCEVCouldNotCompute>(MaxNotTaken) ||
6712 isa<SCEVConstant>(MaxNotTaken)) &&
6713 "No point in having a non-constant max backedge taken count!");
6714 for (auto *PredSet : PredSetList)
6715 for (auto *P : *PredSet)
6719 ScalarEvolution::ExitLimit::ExitLimit(
6720 const SCEV *E, const SCEV *M, bool MaxOrZero,
6721 const SmallPtrSetImpl<const SCEVPredicate *> &PredSet)
6722 : ExitLimit(E, M, MaxOrZero, {&PredSet}) {
6723 assert((isa<SCEVCouldNotCompute>(MaxNotTaken) ||
6724 isa<SCEVConstant>(MaxNotTaken)) &&
6725 "No point in having a non-constant max backedge taken count!");
6728 ScalarEvolution::ExitLimit::ExitLimit(const SCEV *E, const SCEV *M,
6730 : ExitLimit(E, M, MaxOrZero, None) {
6731 assert((isa<SCEVCouldNotCompute>(MaxNotTaken) ||
6732 isa<SCEVConstant>(MaxNotTaken)) &&
6733 "No point in having a non-constant max backedge taken count!");
6736 /// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each
6737 /// computable exit into a persistent ExitNotTakenInfo array.
6738 ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo(
6739 SmallVectorImpl<ScalarEvolution::BackedgeTakenInfo::EdgeExitInfo>
6741 bool Complete, const SCEV *MaxCount, bool MaxOrZero)
6742 : MaxAndComplete(MaxCount, Complete), MaxOrZero(MaxOrZero) {
6743 using EdgeExitInfo = ScalarEvolution::BackedgeTakenInfo::EdgeExitInfo;
6745 ExitNotTaken.reserve(ExitCounts.size());
6747 ExitCounts.begin(), ExitCounts.end(), std::back_inserter(ExitNotTaken),
6748 [&](const EdgeExitInfo &EEI) {
6749 BasicBlock *ExitBB = EEI.first;
6750 const ExitLimit &EL = EEI.second;
6751 if (EL.Predicates.empty())
6752 return ExitNotTakenInfo(ExitBB, EL.ExactNotTaken, nullptr);
6754 std::unique_ptr<SCEVUnionPredicate> Predicate(new SCEVUnionPredicate);
6755 for (auto *Pred : EL.Predicates)
6756 Predicate->add(Pred);
6758 return ExitNotTakenInfo(ExitBB, EL.ExactNotTaken, std::move(Predicate));
6760 assert((isa<SCEVCouldNotCompute>(MaxCount) || isa<SCEVConstant>(MaxCount)) &&
6761 "No point in having a non-constant max backedge taken count!");
6764 /// Invalidate this result and free the ExitNotTakenInfo array.
6765 void ScalarEvolution::BackedgeTakenInfo::clear() {
6766 ExitNotTaken.clear();
6769 /// Compute the number of times the backedge of the specified loop will execute.
6770 ScalarEvolution::BackedgeTakenInfo
6771 ScalarEvolution::computeBackedgeTakenCount(const Loop *L,
6772 bool AllowPredicates) {
6773 SmallVector<BasicBlock *, 8> ExitingBlocks;
6774 L->getExitingBlocks(ExitingBlocks);
6776 using EdgeExitInfo = ScalarEvolution::BackedgeTakenInfo::EdgeExitInfo;
6778 SmallVector<EdgeExitInfo, 4> ExitCounts;
6779 bool CouldComputeBECount = true;
6780 BasicBlock *Latch = L->getLoopLatch(); // may be NULL.
6781 const SCEV *MustExitMaxBECount = nullptr;
6782 const SCEV *MayExitMaxBECount = nullptr;
6783 bool MustExitMaxOrZero = false;
6785 // Compute the ExitLimit for each loop exit. Use this to populate ExitCounts
6786 // and compute maxBECount.
6787 // Do a union of all the predicates here.
6788 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
6789 BasicBlock *ExitBB = ExitingBlocks[i];
6790 ExitLimit EL = computeExitLimit(L, ExitBB, AllowPredicates);
6792 assert((AllowPredicates || EL.Predicates.empty()) &&
6793 "Predicated exit limit when predicates are not allowed!");
6795 // 1. For each exit that can be computed, add an entry to ExitCounts.
6796 // CouldComputeBECount is true only if all exits can be computed.
6797 if (EL.ExactNotTaken == getCouldNotCompute())
6798 // We couldn't compute an exact value for this exit, so
6799 // we won't be able to compute an exact value for the loop.
6800 CouldComputeBECount = false;
6802 ExitCounts.emplace_back(ExitBB, EL);
6804 // 2. Derive the loop's MaxBECount from each exit's max number of
6805 // non-exiting iterations. Partition the loop exits into two kinds:
6806 // LoopMustExits and LoopMayExits.
6808 // If the exit dominates the loop latch, it is a LoopMustExit otherwise it
6809 // is a LoopMayExit. If any computable LoopMustExit is found, then
6810 // MaxBECount is the minimum EL.MaxNotTaken of computable
6811 // LoopMustExits. Otherwise, MaxBECount is conservatively the maximum
6812 // EL.MaxNotTaken, where CouldNotCompute is considered greater than any
6813 // computable EL.MaxNotTaken.
6814 if (EL.MaxNotTaken != getCouldNotCompute() && Latch &&
6815 DT.dominates(ExitBB, Latch)) {
6816 if (!MustExitMaxBECount) {
6817 MustExitMaxBECount = EL.MaxNotTaken;
6818 MustExitMaxOrZero = EL.MaxOrZero;
6820 MustExitMaxBECount =
6821 getUMinFromMismatchedTypes(MustExitMaxBECount, EL.MaxNotTaken);
6823 } else if (MayExitMaxBECount != getCouldNotCompute()) {
6824 if (!MayExitMaxBECount || EL.MaxNotTaken == getCouldNotCompute())
6825 MayExitMaxBECount = EL.MaxNotTaken;
6828 getUMaxFromMismatchedTypes(MayExitMaxBECount, EL.MaxNotTaken);
6832 const SCEV *MaxBECount = MustExitMaxBECount ? MustExitMaxBECount :
6833 (MayExitMaxBECount ? MayExitMaxBECount : getCouldNotCompute());
6834 // The loop backedge will be taken the maximum or zero times if there's
6835 // a single exit that must be taken the maximum or zero times.
6836 bool MaxOrZero = (MustExitMaxOrZero && ExitingBlocks.size() == 1);
6837 return BackedgeTakenInfo(std::move(ExitCounts), CouldComputeBECount,
6838 MaxBECount, MaxOrZero);
6841 ScalarEvolution::ExitLimit
6842 ScalarEvolution::computeExitLimit(const Loop *L, BasicBlock *ExitingBlock,
6843 bool AllowPredicates) {
6844 // Okay, we've chosen an exiting block. See what condition causes us to exit
6845 // at this block and remember the exit block and whether all other targets
6846 // lead to the loop header.
6847 bool MustExecuteLoopHeader = true;
6848 BasicBlock *Exit = nullptr;
6849 for (auto *SBB : successors(ExitingBlock))
6850 if (!L->contains(SBB)) {
6851 if (Exit) // Multiple exit successors.
6852 return getCouldNotCompute();
6854 } else if (SBB != L->getHeader()) {
6855 MustExecuteLoopHeader = false;
6858 // At this point, we know we have a conditional branch that determines whether
6859 // the loop is exited. However, we don't know if the branch is executed each
6860 // time through the loop. If not, then the execution count of the branch will
6861 // not be equal to the trip count of the loop.
6863 // Currently we check for this by checking to see if the Exit branch goes to
6864 // the loop header. If so, we know it will always execute the same number of
6865 // times as the loop. We also handle the case where the exit block *is* the
6866 // loop header. This is common for un-rotated loops.
6868 // If both of those tests fail, walk up the unique predecessor chain to the
6869 // header, stopping if there is an edge that doesn't exit the loop. If the
6870 // header is reached, the execution count of the branch will be equal to the
6871 // trip count of the loop.
6873 // More extensive analysis could be done to handle more cases here.
6875 if (!MustExecuteLoopHeader && ExitingBlock != L->getHeader()) {
6876 // The simple checks failed, try climbing the unique predecessor chain
6877 // up to the header.
6879 for (BasicBlock *BB = ExitingBlock; BB; ) {
6880 BasicBlock *Pred = BB->getUniquePredecessor();
6882 return getCouldNotCompute();
6883 TerminatorInst *PredTerm = Pred->getTerminator();
6884 for (const BasicBlock *PredSucc : PredTerm->successors()) {
6887 // If the predecessor has a successor that isn't BB and isn't
6888 // outside the loop, assume the worst.
6889 if (L->contains(PredSucc))
6890 return getCouldNotCompute();
6892 if (Pred == L->getHeader()) {
6899 return getCouldNotCompute();
6902 bool IsOnlyExit = (L->getExitingBlock() != nullptr);
6903 TerminatorInst *Term = ExitingBlock->getTerminator();
6904 if (BranchInst *BI = dyn_cast<BranchInst>(Term)) {
6905 assert(BI->isConditional() && "If unconditional, it can't be in loop!");
6906 // Proceed to the next level to examine the exit condition expression.
6907 return computeExitLimitFromCond(
6908 L, BI->getCondition(), BI->getSuccessor(0), BI->getSuccessor(1),
6909 /*ControlsExit=*/IsOnlyExit, AllowPredicates);
6912 if (SwitchInst *SI = dyn_cast<SwitchInst>(Term))
6913 return computeExitLimitFromSingleExitSwitch(L, SI, Exit,
6914 /*ControlsExit=*/IsOnlyExit);
6916 return getCouldNotCompute();
6919 ScalarEvolution::ExitLimit ScalarEvolution::computeExitLimitFromCond(
6920 const Loop *L, Value *ExitCond, BasicBlock *TBB, BasicBlock *FBB,
6921 bool ControlsExit, bool AllowPredicates) {
6922 ScalarEvolution::ExitLimitCacheTy Cache(L, TBB, FBB, AllowPredicates);
6923 return computeExitLimitFromCondCached(Cache, L, ExitCond, TBB, FBB,
6924 ControlsExit, AllowPredicates);
6927 Optional<ScalarEvolution::ExitLimit>
6928 ScalarEvolution::ExitLimitCache::find(const Loop *L, Value *ExitCond,
6929 BasicBlock *TBB, BasicBlock *FBB,
6930 bool ControlsExit, bool AllowPredicates) {
6934 (void)this->AllowPredicates;
6936 assert(this->L == L && this->TBB == TBB && this->FBB == FBB &&
6937 this->AllowPredicates == AllowPredicates &&
6938 "Variance in assumed invariant key components!");
6939 auto Itr = TripCountMap.find({ExitCond, ControlsExit});
6940 if (Itr == TripCountMap.end())
6945 void ScalarEvolution::ExitLimitCache::insert(const Loop *L, Value *ExitCond,
6946 BasicBlock *TBB, BasicBlock *FBB,
6948 bool AllowPredicates,
6949 const ExitLimit &EL) {
6950 assert(this->L == L && this->TBB == TBB && this->FBB == FBB &&
6951 this->AllowPredicates == AllowPredicates &&
6952 "Variance in assumed invariant key components!");
6954 auto InsertResult = TripCountMap.insert({{ExitCond, ControlsExit}, EL});
6955 assert(InsertResult.second && "Expected successful insertion!");
6959 ScalarEvolution::ExitLimit ScalarEvolution::computeExitLimitFromCondCached(
6960 ExitLimitCacheTy &Cache, const Loop *L, Value *ExitCond, BasicBlock *TBB,
6961 BasicBlock *FBB, bool ControlsExit, bool AllowPredicates) {
6964 Cache.find(L, ExitCond, TBB, FBB, ControlsExit, AllowPredicates))
6967 ExitLimit EL = computeExitLimitFromCondImpl(Cache, L, ExitCond, TBB, FBB,
6968 ControlsExit, AllowPredicates);
6969 Cache.insert(L, ExitCond, TBB, FBB, ControlsExit, AllowPredicates, EL);
6973 ScalarEvolution::ExitLimit ScalarEvolution::computeExitLimitFromCondImpl(
6974 ExitLimitCacheTy &Cache, const Loop *L, Value *ExitCond, BasicBlock *TBB,
6975 BasicBlock *FBB, bool ControlsExit, bool AllowPredicates) {
6976 // Check if the controlling expression for this loop is an And or Or.
6977 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
6978 if (BO->getOpcode() == Instruction::And) {
6979 // Recurse on the operands of the and.
6980 bool EitherMayExit = L->contains(TBB);
6981 ExitLimit EL0 = computeExitLimitFromCondCached(
6982 Cache, L, BO->getOperand(0), TBB, FBB, ControlsExit && !EitherMayExit,
6984 ExitLimit EL1 = computeExitLimitFromCondCached(
6985 Cache, L, BO->getOperand(1), TBB, FBB, ControlsExit && !EitherMayExit,
6987 const SCEV *BECount = getCouldNotCompute();
6988 const SCEV *MaxBECount = getCouldNotCompute();
6989 if (EitherMayExit) {
6990 // Both conditions must be true for the loop to continue executing.
6991 // Choose the less conservative count.
6992 if (EL0.ExactNotTaken == getCouldNotCompute() ||
6993 EL1.ExactNotTaken == getCouldNotCompute())
6994 BECount = getCouldNotCompute();
6997 getUMinFromMismatchedTypes(EL0.ExactNotTaken, EL1.ExactNotTaken);
6998 if (EL0.MaxNotTaken == getCouldNotCompute())
6999 MaxBECount = EL1.MaxNotTaken;
7000 else if (EL1.MaxNotTaken == getCouldNotCompute())
7001 MaxBECount = EL0.MaxNotTaken;
7004 getUMinFromMismatchedTypes(EL0.MaxNotTaken, EL1.MaxNotTaken);
7006 // Both conditions must be true at the same time for the loop to exit.
7007 // For now, be conservative.
7008 assert(L->contains(FBB) && "Loop block has no successor in loop!");
7009 if (EL0.MaxNotTaken == EL1.MaxNotTaken)
7010 MaxBECount = EL0.MaxNotTaken;
7011 if (EL0.ExactNotTaken == EL1.ExactNotTaken)
7012 BECount = EL0.ExactNotTaken;
7015 // There are cases (e.g. PR26207) where computeExitLimitFromCond is able
7016 // to be more aggressive when computing BECount than when computing
7017 // MaxBECount. In these cases it is possible for EL0.ExactNotTaken and
7018 // EL1.ExactNotTaken to match, but for EL0.MaxNotTaken and EL1.MaxNotTaken
7020 if (isa<SCEVCouldNotCompute>(MaxBECount) &&
7021 !isa<SCEVCouldNotCompute>(BECount))
7022 MaxBECount = getConstant(getUnsignedRangeMax(BECount));
7024 return ExitLimit(BECount, MaxBECount, false,
7025 {&EL0.Predicates, &EL1.Predicates});
7027 if (BO->getOpcode() == Instruction::Or) {
7028 // Recurse on the operands of the or.
7029 bool EitherMayExit = L->contains(FBB);
7030 ExitLimit EL0 = computeExitLimitFromCondCached(
7031 Cache, L, BO->getOperand(0), TBB, FBB, ControlsExit && !EitherMayExit,
7033 ExitLimit EL1 = computeExitLimitFromCondCached(
7034 Cache, L, BO->getOperand(1), TBB, FBB, ControlsExit && !EitherMayExit,
7036 const SCEV *BECount = getCouldNotCompute();
7037 const SCEV *MaxBECount = getCouldNotCompute();
7038 if (EitherMayExit) {
7039 // Both conditions must be false for the loop to continue executing.
7040 // Choose the less conservative count.
7041 if (EL0.ExactNotTaken == getCouldNotCompute() ||
7042 EL1.ExactNotTaken == getCouldNotCompute())
7043 BECount = getCouldNotCompute();
7046 getUMinFromMismatchedTypes(EL0.ExactNotTaken, EL1.ExactNotTaken);
7047 if (EL0.MaxNotTaken == getCouldNotCompute())
7048 MaxBECount = EL1.MaxNotTaken;
7049 else if (EL1.MaxNotTaken == getCouldNotCompute())
7050 MaxBECount = EL0.MaxNotTaken;
7053 getUMinFromMismatchedTypes(EL0.MaxNotTaken, EL1.MaxNotTaken);
7055 // Both conditions must be false at the same time for the loop to exit.
7056 // For now, be conservative.
7057 assert(L->contains(TBB) && "Loop block has no successor in loop!");
7058 if (EL0.MaxNotTaken == EL1.MaxNotTaken)
7059 MaxBECount = EL0.MaxNotTaken;
7060 if (EL0.ExactNotTaken == EL1.ExactNotTaken)
7061 BECount = EL0.ExactNotTaken;
7064 return ExitLimit(BECount, MaxBECount, false,
7065 {&EL0.Predicates, &EL1.Predicates});
7069 // With an icmp, it may be feasible to compute an exact backedge-taken count.
7070 // Proceed to the next level to examine the icmp.
7071 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond)) {
7073 computeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB, ControlsExit);
7074 if (EL.hasFullInfo() || !AllowPredicates)
7077 // Try again, but use SCEV predicates this time.
7078 return computeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB, ControlsExit,
7079 /*AllowPredicates=*/true);
7082 // Check for a constant condition. These are normally stripped out by
7083 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
7084 // preserve the CFG and is temporarily leaving constant conditions
7086 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
7087 if (L->contains(FBB) == !CI->getZExtValue())
7088 // The backedge is always taken.
7089 return getCouldNotCompute();
7091 // The backedge is never taken.
7092 return getZero(CI->getType());
7095 // If it's not an integer or pointer comparison then compute it the hard way.
7096 return computeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
7099 ScalarEvolution::ExitLimit
7100 ScalarEvolution::computeExitLimitFromICmp(const Loop *L,
7105 bool AllowPredicates) {
7106 // If the condition was exit on true, convert the condition to exit on false
7107 ICmpInst::Predicate Pred;
7108 if (!L->contains(FBB))
7109 Pred = ExitCond->getPredicate();
7111 Pred = ExitCond->getInversePredicate();
7112 const ICmpInst::Predicate OriginalPred = Pred;
7114 // Handle common loops like: for (X = "string"; *X; ++X)
7115 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
7116 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
7118 computeLoadConstantCompareExitLimit(LI, RHS, L, Pred);
7119 if (ItCnt.hasAnyInfo())
7123 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
7124 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
7126 // Try to evaluate any dependencies out of the loop.
7127 LHS = getSCEVAtScope(LHS, L);
7128 RHS = getSCEVAtScope(RHS, L);
7130 // At this point, we would like to compute how many iterations of the
7131 // loop the predicate will return true for these inputs.
7132 if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) {
7133 // If there is a loop-invariant, force it into the RHS.
7134 std::swap(LHS, RHS);
7135 Pred = ICmpInst::getSwappedPredicate(Pred);
7138 // Simplify the operands before analyzing them.
7139 (void)SimplifyICmpOperands(Pred, LHS, RHS);
7141 // If we have a comparison of a chrec against a constant, try to use value
7142 // ranges to answer this query.
7143 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
7144 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
7145 if (AddRec->getLoop() == L) {
7146 // Form the constant range.
7147 ConstantRange CompRange =
7148 ConstantRange::makeExactICmpRegion(Pred, RHSC->getAPInt());
7150 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
7151 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
7155 case ICmpInst::ICMP_NE: { // while (X != Y)
7156 // Convert to: while (X-Y != 0)
7157 ExitLimit EL = howFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit,
7159 if (EL.hasAnyInfo()) return EL;
7162 case ICmpInst::ICMP_EQ: { // while (X == Y)
7163 // Convert to: while (X-Y == 0)
7164 ExitLimit EL = howFarToNonZero(getMinusSCEV(LHS, RHS), L);
7165 if (EL.hasAnyInfo()) return EL;
7168 case ICmpInst::ICMP_SLT:
7169 case ICmpInst::ICMP_ULT: { // while (X < Y)
7170 bool IsSigned = Pred == ICmpInst::ICMP_SLT;
7171 ExitLimit EL = howManyLessThans(LHS, RHS, L, IsSigned, ControlsExit,
7173 if (EL.hasAnyInfo()) return EL;
7176 case ICmpInst::ICMP_SGT:
7177 case ICmpInst::ICMP_UGT: { // while (X > Y)
7178 bool IsSigned = Pred == ICmpInst::ICMP_SGT;
7180 howManyGreaterThans(LHS, RHS, L, IsSigned, ControlsExit,
7182 if (EL.hasAnyInfo()) return EL;
7189 auto *ExhaustiveCount =
7190 computeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
7192 if (!isa<SCEVCouldNotCompute>(ExhaustiveCount))
7193 return ExhaustiveCount;
7195 return computeShiftCompareExitLimit(ExitCond->getOperand(0),
7196 ExitCond->getOperand(1), L, OriginalPred);
7199 ScalarEvolution::ExitLimit
7200 ScalarEvolution::computeExitLimitFromSingleExitSwitch(const Loop *L,
7202 BasicBlock *ExitingBlock,
7203 bool ControlsExit) {
7204 assert(!L->contains(ExitingBlock) && "Not an exiting block!");
7206 // Give up if the exit is the default dest of a switch.
7207 if (Switch->getDefaultDest() == ExitingBlock)
7208 return getCouldNotCompute();
7210 assert(L->contains(Switch->getDefaultDest()) &&
7211 "Default case must not exit the loop!");
7212 const SCEV *LHS = getSCEVAtScope(Switch->getCondition(), L);
7213 const SCEV *RHS = getConstant(Switch->findCaseDest(ExitingBlock));
7215 // while (X != Y) --> while (X-Y != 0)
7216 ExitLimit EL = howFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit);
7217 if (EL.hasAnyInfo())
7220 return getCouldNotCompute();
7223 static ConstantInt *
7224 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
7225 ScalarEvolution &SE) {
7226 const SCEV *InVal = SE.getConstant(C);
7227 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
7228 assert(isa<SCEVConstant>(Val) &&
7229 "Evaluation of SCEV at constant didn't fold correctly?");
7230 return cast<SCEVConstant>(Val)->getValue();
7233 /// Given an exit condition of 'icmp op load X, cst', try to see if we can
7234 /// compute the backedge execution count.
7235 ScalarEvolution::ExitLimit
7236 ScalarEvolution::computeLoadConstantCompareExitLimit(
7240 ICmpInst::Predicate predicate) {
7241 if (LI->isVolatile()) return getCouldNotCompute();
7243 // Check to see if the loaded pointer is a getelementptr of a global.
7244 // TODO: Use SCEV instead of manually grubbing with GEPs.
7245 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
7246 if (!GEP) return getCouldNotCompute();
7248 // Make sure that it is really a constant global we are gepping, with an
7249 // initializer, and make sure the first IDX is really 0.
7250 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
7251 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
7252 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
7253 !cast<Constant>(GEP->getOperand(1))->isNullValue())
7254 return getCouldNotCompute();
7256 // Okay, we allow one non-constant index into the GEP instruction.
7257 Value *VarIdx = nullptr;
7258 std::vector<Constant*> Indexes;
7259 unsigned VarIdxNum = 0;
7260 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
7261 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
7262 Indexes.push_back(CI);
7263 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
7264 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
7265 VarIdx = GEP->getOperand(i);
7267 Indexes.push_back(nullptr);
7270 // Loop-invariant loads may be a byproduct of loop optimization. Skip them.
7272 return getCouldNotCompute();
7274 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
7275 // Check to see if X is a loop variant variable value now.
7276 const SCEV *Idx = getSCEV(VarIdx);
7277 Idx = getSCEVAtScope(Idx, L);
7279 // We can only recognize very limited forms of loop index expressions, in
7280 // particular, only affine AddRec's like {C1,+,C2}.
7281 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
7282 if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) ||
7283 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
7284 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
7285 return getCouldNotCompute();
7287 unsigned MaxSteps = MaxBruteForceIterations;
7288 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
7289 ConstantInt *ItCst = ConstantInt::get(
7290 cast<IntegerType>(IdxExpr->getType()), IterationNum);
7291 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
7293 // Form the GEP offset.
7294 Indexes[VarIdxNum] = Val;
7296 Constant *Result = ConstantFoldLoadThroughGEPIndices(GV->getInitializer(),
7298 if (!Result) break; // Cannot compute!
7300 // Evaluate the condition for this iteration.
7301 Result = ConstantExpr::getICmp(predicate, Result, RHS);
7302 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
7303 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
7304 ++NumArrayLenItCounts;
7305 return getConstant(ItCst); // Found terminating iteration!
7308 return getCouldNotCompute();
7311 ScalarEvolution::ExitLimit ScalarEvolution::computeShiftCompareExitLimit(
7312 Value *LHS, Value *RHSV, const Loop *L, ICmpInst::Predicate Pred) {
7313 ConstantInt *RHS = dyn_cast<ConstantInt>(RHSV);
7315 return getCouldNotCompute();
7317 const BasicBlock *Latch = L->getLoopLatch();
7319 return getCouldNotCompute();
7321 const BasicBlock *Predecessor = L->getLoopPredecessor();
7323 return getCouldNotCompute();
7325 // Return true if V is of the form "LHS `shift_op` <positive constant>".
7326 // Return LHS in OutLHS and shift_opt in OutOpCode.
7327 auto MatchPositiveShift =
7328 [](Value *V, Value *&OutLHS, Instruction::BinaryOps &OutOpCode) {
7330 using namespace PatternMatch;
7332 ConstantInt *ShiftAmt;
7333 if (match(V, m_LShr(m_Value(OutLHS), m_ConstantInt(ShiftAmt))))
7334 OutOpCode = Instruction::LShr;
7335 else if (match(V, m_AShr(m_Value(OutLHS), m_ConstantInt(ShiftAmt))))
7336 OutOpCode = Instruction::AShr;
7337 else if (match(V, m_Shl(m_Value(OutLHS), m_ConstantInt(ShiftAmt))))
7338 OutOpCode = Instruction::Shl;
7342 return ShiftAmt->getValue().isStrictlyPositive();
7345 // Recognize a "shift recurrence" either of the form %iv or of %iv.shifted in
7348 // %iv = phi i32 [ %iv.shifted, %loop ], [ %val, %preheader ]
7349 // %iv.shifted = lshr i32 %iv, <positive constant>
7351 // Return true on a successful match. Return the corresponding PHI node (%iv
7352 // above) in PNOut and the opcode of the shift operation in OpCodeOut.
7353 auto MatchShiftRecurrence =
7354 [&](Value *V, PHINode *&PNOut, Instruction::BinaryOps &OpCodeOut) {
7355 Optional<Instruction::BinaryOps> PostShiftOpCode;
7358 Instruction::BinaryOps OpC;
7361 // If we encounter a shift instruction, "peel off" the shift operation,
7362 // and remember that we did so. Later when we inspect %iv's backedge
7363 // value, we will make sure that the backedge value uses the same
7366 // Note: the peeled shift operation does not have to be the same
7367 // instruction as the one feeding into the PHI's backedge value. We only
7368 // really care about it being the same *kind* of shift instruction --
7369 // that's all that is required for our later inferences to hold.
7370 if (MatchPositiveShift(LHS, V, OpC)) {
7371 PostShiftOpCode = OpC;
7376 PNOut = dyn_cast<PHINode>(LHS);
7377 if (!PNOut || PNOut->getParent() != L->getHeader())
7380 Value *BEValue = PNOut->getIncomingValueForBlock(Latch);
7384 // The backedge value for the PHI node must be a shift by a positive
7386 MatchPositiveShift(BEValue, OpLHS, OpCodeOut) &&
7388 // of the PHI node itself
7391 // and the kind of shift should be match the kind of shift we peeled
7393 (!PostShiftOpCode.hasValue() || *PostShiftOpCode == OpCodeOut);
7397 Instruction::BinaryOps OpCode;
7398 if (!MatchShiftRecurrence(LHS, PN, OpCode))
7399 return getCouldNotCompute();
7401 const DataLayout &DL = getDataLayout();
7403 // The key rationale for this optimization is that for some kinds of shift
7404 // recurrences, the value of the recurrence "stabilizes" to either 0 or -1
7405 // within a finite number of iterations. If the condition guarding the
7406 // backedge (in the sense that the backedge is taken if the condition is true)
7407 // is false for the value the shift recurrence stabilizes to, then we know
7408 // that the backedge is taken only a finite number of times.
7410 ConstantInt *StableValue = nullptr;
7413 llvm_unreachable("Impossible case!");
7415 case Instruction::AShr: {
7416 // {K,ashr,<positive-constant>} stabilizes to signum(K) in at most
7417 // bitwidth(K) iterations.
7418 Value *FirstValue = PN->getIncomingValueForBlock(Predecessor);
7419 KnownBits Known = computeKnownBits(FirstValue, DL, 0, nullptr,
7420 Predecessor->getTerminator(), &DT);
7421 auto *Ty = cast<IntegerType>(RHS->getType());
7422 if (Known.isNonNegative())
7423 StableValue = ConstantInt::get(Ty, 0);
7424 else if (Known.isNegative())
7425 StableValue = ConstantInt::get(Ty, -1, true);
7427 return getCouldNotCompute();
7431 case Instruction::LShr:
7432 case Instruction::Shl:
7433 // Both {K,lshr,<positive-constant>} and {K,shl,<positive-constant>}
7434 // stabilize to 0 in at most bitwidth(K) iterations.
7435 StableValue = ConstantInt::get(cast<IntegerType>(RHS->getType()), 0);
7440 ConstantFoldCompareInstOperands(Pred, StableValue, RHS, DL, &TLI);
7441 assert(Result->getType()->isIntegerTy(1) &&
7442 "Otherwise cannot be an operand to a branch instruction");
7444 if (Result->isZeroValue()) {
7445 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
7446 const SCEV *UpperBound =
7447 getConstant(getEffectiveSCEVType(RHS->getType()), BitWidth);
7448 return ExitLimit(getCouldNotCompute(), UpperBound, false);
7451 return getCouldNotCompute();
7454 /// Return true if we can constant fold an instruction of the specified type,
7455 /// assuming that all operands were constants.
7456 static bool CanConstantFold(const Instruction *I) {
7457 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
7458 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I) ||
7462 if (const CallInst *CI = dyn_cast<CallInst>(I))
7463 if (const Function *F = CI->getCalledFunction())
7464 return canConstantFoldCallTo(CI, F);
7468 /// Determine whether this instruction can constant evolve within this loop
7469 /// assuming its operands can all constant evolve.
7470 static bool canConstantEvolve(Instruction *I, const Loop *L) {
7471 // An instruction outside of the loop can't be derived from a loop PHI.
7472 if (!L->contains(I)) return false;
7474 if (isa<PHINode>(I)) {
7475 // We don't currently keep track of the control flow needed to evaluate
7476 // PHIs, so we cannot handle PHIs inside of loops.
7477 return L->getHeader() == I->getParent();
7480 // If we won't be able to constant fold this expression even if the operands
7481 // are constants, bail early.
7482 return CanConstantFold(I);
7485 /// getConstantEvolvingPHIOperands - Implement getConstantEvolvingPHI by
7486 /// recursing through each instruction operand until reaching a loop header phi.
7488 getConstantEvolvingPHIOperands(Instruction *UseInst, const Loop *L,
7489 DenseMap<Instruction *, PHINode *> &PHIMap,
7491 if (Depth > MaxConstantEvolvingDepth)
7494 // Otherwise, we can evaluate this instruction if all of its operands are
7495 // constant or derived from a PHI node themselves.
7496 PHINode *PHI = nullptr;
7497 for (Value *Op : UseInst->operands()) {
7498 if (isa<Constant>(Op)) continue;
7500 Instruction *OpInst = dyn_cast<Instruction>(Op);
7501 if (!OpInst || !canConstantEvolve(OpInst, L)) return nullptr;
7503 PHINode *P = dyn_cast<PHINode>(OpInst);
7505 // If this operand is already visited, reuse the prior result.
7506 // We may have P != PHI if this is the deepest point at which the
7507 // inconsistent paths meet.
7508 P = PHIMap.lookup(OpInst);
7510 // Recurse and memoize the results, whether a phi is found or not.
7511 // This recursive call invalidates pointers into PHIMap.
7512 P = getConstantEvolvingPHIOperands(OpInst, L, PHIMap, Depth + 1);
7516 return nullptr; // Not evolving from PHI
7517 if (PHI && PHI != P)
7518 return nullptr; // Evolving from multiple different PHIs.
7521 // This is a expression evolving from a constant PHI!
7525 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
7526 /// in the loop that V is derived from. We allow arbitrary operations along the
7527 /// way, but the operands of an operation must either be constants or a value
7528 /// derived from a constant PHI. If this expression does not fit with these
7529 /// constraints, return null.
7530 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
7531 Instruction *I = dyn_cast<Instruction>(V);
7532 if (!I || !canConstantEvolve(I, L)) return nullptr;
7534 if (PHINode *PN = dyn_cast<PHINode>(I))
7537 // Record non-constant instructions contained by the loop.
7538 DenseMap<Instruction *, PHINode *> PHIMap;
7539 return getConstantEvolvingPHIOperands(I, L, PHIMap, 0);
7542 /// EvaluateExpression - Given an expression that passes the
7543 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
7544 /// in the loop has the value PHIVal. If we can't fold this expression for some
7545 /// reason, return null.
7546 static Constant *EvaluateExpression(Value *V, const Loop *L,
7547 DenseMap<Instruction *, Constant *> &Vals,
7548 const DataLayout &DL,
7549 const TargetLibraryInfo *TLI) {
7550 // Convenient constant check, but redundant for recursive calls.
7551 if (Constant *C = dyn_cast<Constant>(V)) return C;
7552 Instruction *I = dyn_cast<Instruction>(V);
7553 if (!I) return nullptr;
7555 if (Constant *C = Vals.lookup(I)) return C;
7557 // An instruction inside the loop depends on a value outside the loop that we
7558 // weren't given a mapping for, or a value such as a call inside the loop.
7559 if (!canConstantEvolve(I, L)) return nullptr;
7561 // An unmapped PHI can be due to a branch or another loop inside this loop,
7562 // or due to this not being the initial iteration through a loop where we
7563 // couldn't compute the evolution of this particular PHI last time.
7564 if (isa<PHINode>(I)) return nullptr;
7566 std::vector<Constant*> Operands(I->getNumOperands());
7568 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
7569 Instruction *Operand = dyn_cast<Instruction>(I->getOperand(i));
7571 Operands[i] = dyn_cast<Constant>(I->getOperand(i));
7572 if (!Operands[i]) return nullptr;
7575 Constant *C = EvaluateExpression(Operand, L, Vals, DL, TLI);
7577 if (!C) return nullptr;
7581 if (CmpInst *CI = dyn_cast<CmpInst>(I))
7582 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
7583 Operands[1], DL, TLI);
7584 if (LoadInst *LI = dyn_cast<LoadInst>(I)) {
7585 if (!LI->isVolatile())
7586 return ConstantFoldLoadFromConstPtr(Operands[0], LI->getType(), DL);
7588 return ConstantFoldInstOperands(I, Operands, DL, TLI);
7592 // If every incoming value to PN except the one for BB is a specific Constant,
7593 // return that, else return nullptr.
7594 static Constant *getOtherIncomingValue(PHINode *PN, BasicBlock *BB) {
7595 Constant *IncomingVal = nullptr;
7597 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
7598 if (PN->getIncomingBlock(i) == BB)
7601 auto *CurrentVal = dyn_cast<Constant>(PN->getIncomingValue(i));
7605 if (IncomingVal != CurrentVal) {
7608 IncomingVal = CurrentVal;
7615 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
7616 /// in the header of its containing loop, we know the loop executes a
7617 /// constant number of times, and the PHI node is just a recurrence
7618 /// involving constants, fold it.
7620 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
7623 auto I = ConstantEvolutionLoopExitValue.find(PN);
7624 if (I != ConstantEvolutionLoopExitValue.end())
7627 if (BEs.ugt(MaxBruteForceIterations))
7628 return ConstantEvolutionLoopExitValue[PN] = nullptr; // Not going to evaluate it.
7630 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
7632 DenseMap<Instruction *, Constant *> CurrentIterVals;
7633 BasicBlock *Header = L->getHeader();
7634 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
7636 BasicBlock *Latch = L->getLoopLatch();
7640 for (PHINode &PHI : Header->phis()) {
7641 if (auto *StartCST = getOtherIncomingValue(&PHI, Latch))
7642 CurrentIterVals[&PHI] = StartCST;
7644 if (!CurrentIterVals.count(PN))
7645 return RetVal = nullptr;
7647 Value *BEValue = PN->getIncomingValueForBlock(Latch);
7649 // Execute the loop symbolically to determine the exit value.
7650 assert(BEs.getActiveBits() < CHAR_BIT * sizeof(unsigned) &&
7651 "BEs is <= MaxBruteForceIterations which is an 'unsigned'!");
7653 unsigned NumIterations = BEs.getZExtValue(); // must be in range
7654 unsigned IterationNum = 0;
7655 const DataLayout &DL = getDataLayout();
7656 for (; ; ++IterationNum) {
7657 if (IterationNum == NumIterations)
7658 return RetVal = CurrentIterVals[PN]; // Got exit value!
7660 // Compute the value of the PHIs for the next iteration.
7661 // EvaluateExpression adds non-phi values to the CurrentIterVals map.
7662 DenseMap<Instruction *, Constant *> NextIterVals;
7664 EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
7666 return nullptr; // Couldn't evaluate!
7667 NextIterVals[PN] = NextPHI;
7669 bool StoppedEvolving = NextPHI == CurrentIterVals[PN];
7671 // Also evaluate the other PHI nodes. However, we don't get to stop if we
7672 // cease to be able to evaluate one of them or if they stop evolving,
7673 // because that doesn't necessarily prevent us from computing PN.
7674 SmallVector<std::pair<PHINode *, Constant *>, 8> PHIsToCompute;
7675 for (const auto &I : CurrentIterVals) {
7676 PHINode *PHI = dyn_cast<PHINode>(I.first);
7677 if (!PHI || PHI == PN || PHI->getParent() != Header) continue;
7678 PHIsToCompute.emplace_back(PHI, I.second);
7680 // We use two distinct loops because EvaluateExpression may invalidate any
7681 // iterators into CurrentIterVals.
7682 for (const auto &I : PHIsToCompute) {
7683 PHINode *PHI = I.first;
7684 Constant *&NextPHI = NextIterVals[PHI];
7685 if (!NextPHI) { // Not already computed.
7686 Value *BEValue = PHI->getIncomingValueForBlock(Latch);
7687 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
7689 if (NextPHI != I.second)
7690 StoppedEvolving = false;
7693 // If all entries in CurrentIterVals == NextIterVals then we can stop
7694 // iterating, the loop can't continue to change.
7695 if (StoppedEvolving)
7696 return RetVal = CurrentIterVals[PN];
7698 CurrentIterVals.swap(NextIterVals);
7702 const SCEV *ScalarEvolution::computeExitCountExhaustively(const Loop *L,
7705 PHINode *PN = getConstantEvolvingPHI(Cond, L);
7706 if (!PN) return getCouldNotCompute();
7708 // If the loop is canonicalized, the PHI will have exactly two entries.
7709 // That's the only form we support here.
7710 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
7712 DenseMap<Instruction *, Constant *> CurrentIterVals;
7713 BasicBlock *Header = L->getHeader();
7714 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
7716 BasicBlock *Latch = L->getLoopLatch();
7717 assert(Latch && "Should follow from NumIncomingValues == 2!");
7719 for (PHINode &PHI : Header->phis()) {
7720 if (auto *StartCST = getOtherIncomingValue(&PHI, Latch))
7721 CurrentIterVals[&PHI] = StartCST;
7723 if (!CurrentIterVals.count(PN))
7724 return getCouldNotCompute();
7726 // Okay, we find a PHI node that defines the trip count of this loop. Execute
7727 // the loop symbolically to determine when the condition gets a value of
7729 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
7730 const DataLayout &DL = getDataLayout();
7731 for (unsigned IterationNum = 0; IterationNum != MaxIterations;++IterationNum){
7732 auto *CondVal = dyn_cast_or_null<ConstantInt>(
7733 EvaluateExpression(Cond, L, CurrentIterVals, DL, &TLI));
7735 // Couldn't symbolically evaluate.
7736 if (!CondVal) return getCouldNotCompute();
7738 if (CondVal->getValue() == uint64_t(ExitWhen)) {
7739 ++NumBruteForceTripCountsComputed;
7740 return getConstant(Type::getInt32Ty(getContext()), IterationNum);
7743 // Update all the PHI nodes for the next iteration.
7744 DenseMap<Instruction *, Constant *> NextIterVals;
7746 // Create a list of which PHIs we need to compute. We want to do this before
7747 // calling EvaluateExpression on them because that may invalidate iterators
7748 // into CurrentIterVals.
7749 SmallVector<PHINode *, 8> PHIsToCompute;
7750 for (const auto &I : CurrentIterVals) {
7751 PHINode *PHI = dyn_cast<PHINode>(I.first);
7752 if (!PHI || PHI->getParent() != Header) continue;
7753 PHIsToCompute.push_back(PHI);
7755 for (PHINode *PHI : PHIsToCompute) {
7756 Constant *&NextPHI = NextIterVals[PHI];
7757 if (NextPHI) continue; // Already computed!
7759 Value *BEValue = PHI->getIncomingValueForBlock(Latch);
7760 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
7762 CurrentIterVals.swap(NextIterVals);
7765 // Too many iterations were needed to evaluate.
7766 return getCouldNotCompute();
7769 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
7770 SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values =
7772 // Check to see if we've folded this expression at this loop before.
7773 for (auto &LS : Values)
7775 return LS.second ? LS.second : V;
7777 Values.emplace_back(L, nullptr);
7779 // Otherwise compute it.
7780 const SCEV *C = computeSCEVAtScope(V, L);
7781 for (auto &LS : reverse(ValuesAtScopes[V]))
7782 if (LS.first == L) {
7789 /// This builds up a Constant using the ConstantExpr interface. That way, we
7790 /// will return Constants for objects which aren't represented by a
7791 /// SCEVConstant, because SCEVConstant is restricted to ConstantInt.
7792 /// Returns NULL if the SCEV isn't representable as a Constant.
7793 static Constant *BuildConstantFromSCEV(const SCEV *V) {
7794 switch (static_cast<SCEVTypes>(V->getSCEVType())) {
7795 case scCouldNotCompute:
7799 return cast<SCEVConstant>(V)->getValue();
7801 return dyn_cast<Constant>(cast<SCEVUnknown>(V)->getValue());
7802 case scSignExtend: {
7803 const SCEVSignExtendExpr *SS = cast<SCEVSignExtendExpr>(V);
7804 if (Constant *CastOp = BuildConstantFromSCEV(SS->getOperand()))
7805 return ConstantExpr::getSExt(CastOp, SS->getType());
7808 case scZeroExtend: {
7809 const SCEVZeroExtendExpr *SZ = cast<SCEVZeroExtendExpr>(V);
7810 if (Constant *CastOp = BuildConstantFromSCEV(SZ->getOperand()))
7811 return ConstantExpr::getZExt(CastOp, SZ->getType());
7815 const SCEVTruncateExpr *ST = cast<SCEVTruncateExpr>(V);
7816 if (Constant *CastOp = BuildConstantFromSCEV(ST->getOperand()))
7817 return ConstantExpr::getTrunc(CastOp, ST->getType());
7821 const SCEVAddExpr *SA = cast<SCEVAddExpr>(V);
7822 if (Constant *C = BuildConstantFromSCEV(SA->getOperand(0))) {
7823 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
7824 unsigned AS = PTy->getAddressSpace();
7825 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
7826 C = ConstantExpr::getBitCast(C, DestPtrTy);
7828 for (unsigned i = 1, e = SA->getNumOperands(); i != e; ++i) {
7829 Constant *C2 = BuildConstantFromSCEV(SA->getOperand(i));
7830 if (!C2) return nullptr;
7833 if (!C->getType()->isPointerTy() && C2->getType()->isPointerTy()) {
7834 unsigned AS = C2->getType()->getPointerAddressSpace();
7836 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
7837 // The offsets have been converted to bytes. We can add bytes to an
7838 // i8* by GEP with the byte count in the first index.
7839 C = ConstantExpr::getBitCast(C, DestPtrTy);
7842 // Don't bother trying to sum two pointers. We probably can't
7843 // statically compute a load that results from it anyway.
7844 if (C2->getType()->isPointerTy())
7847 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
7848 if (PTy->getElementType()->isStructTy())
7849 C2 = ConstantExpr::getIntegerCast(
7850 C2, Type::getInt32Ty(C->getContext()), true);
7851 C = ConstantExpr::getGetElementPtr(PTy->getElementType(), C, C2);
7853 C = ConstantExpr::getAdd(C, C2);
7860 const SCEVMulExpr *SM = cast<SCEVMulExpr>(V);
7861 if (Constant *C = BuildConstantFromSCEV(SM->getOperand(0))) {
7862 // Don't bother with pointers at all.
7863 if (C->getType()->isPointerTy()) return nullptr;
7864 for (unsigned i = 1, e = SM->getNumOperands(); i != e; ++i) {
7865 Constant *C2 = BuildConstantFromSCEV(SM->getOperand(i));
7866 if (!C2 || C2->getType()->isPointerTy()) return nullptr;
7867 C = ConstantExpr::getMul(C, C2);
7874 const SCEVUDivExpr *SU = cast<SCEVUDivExpr>(V);
7875 if (Constant *LHS = BuildConstantFromSCEV(SU->getLHS()))
7876 if (Constant *RHS = BuildConstantFromSCEV(SU->getRHS()))
7877 if (LHS->getType() == RHS->getType())
7878 return ConstantExpr::getUDiv(LHS, RHS);
7883 break; // TODO: smax, umax.
7888 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
7889 if (isa<SCEVConstant>(V)) return V;
7891 // If this instruction is evolved from a constant-evolving PHI, compute the
7892 // exit value from the loop without using SCEVs.
7893 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
7894 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
7895 const Loop *LI = this->LI[I->getParent()];
7896 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
7897 if (PHINode *PN = dyn_cast<PHINode>(I))
7898 if (PN->getParent() == LI->getHeader()) {
7899 // Okay, there is no closed form solution for the PHI node. Check
7900 // to see if the loop that contains it has a known backedge-taken
7901 // count. If so, we may be able to force computation of the exit
7903 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
7904 if (const SCEVConstant *BTCC =
7905 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
7907 // This trivial case can show up in some degenerate cases where
7908 // the incoming IR has not yet been fully simplified.
7909 if (BTCC->getValue()->isZero()) {
7910 Value *InitValue = nullptr;
7911 bool MultipleInitValues = false;
7912 for (unsigned i = 0; i < PN->getNumIncomingValues(); i++) {
7913 if (!LI->contains(PN->getIncomingBlock(i))) {
7915 InitValue = PN->getIncomingValue(i);
7916 else if (InitValue != PN->getIncomingValue(i)) {
7917 MultipleInitValues = true;
7921 if (!MultipleInitValues && InitValue)
7922 return getSCEV(InitValue);
7925 // Okay, we know how many times the containing loop executes. If
7926 // this is a constant evolving PHI node, get the final value at
7927 // the specified iteration number.
7929 getConstantEvolutionLoopExitValue(PN, BTCC->getAPInt(), LI);
7930 if (RV) return getSCEV(RV);
7934 // Okay, this is an expression that we cannot symbolically evaluate
7935 // into a SCEV. Check to see if it's possible to symbolically evaluate
7936 // the arguments into constants, and if so, try to constant propagate the
7937 // result. This is particularly useful for computing loop exit values.
7938 if (CanConstantFold(I)) {
7939 SmallVector<Constant *, 4> Operands;
7940 bool MadeImprovement = false;
7941 for (Value *Op : I->operands()) {
7942 if (Constant *C = dyn_cast<Constant>(Op)) {
7943 Operands.push_back(C);
7947 // If any of the operands is non-constant and if they are
7948 // non-integer and non-pointer, don't even try to analyze them
7949 // with scev techniques.
7950 if (!isSCEVable(Op->getType()))
7953 const SCEV *OrigV = getSCEV(Op);
7954 const SCEV *OpV = getSCEVAtScope(OrigV, L);
7955 MadeImprovement |= OrigV != OpV;
7957 Constant *C = BuildConstantFromSCEV(OpV);
7959 if (C->getType() != Op->getType())
7960 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
7964 Operands.push_back(C);
7967 // Check to see if getSCEVAtScope actually made an improvement.
7968 if (MadeImprovement) {
7969 Constant *C = nullptr;
7970 const DataLayout &DL = getDataLayout();
7971 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
7972 C = ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
7973 Operands[1], DL, &TLI);
7974 else if (const LoadInst *LI = dyn_cast<LoadInst>(I)) {
7975 if (!LI->isVolatile())
7976 C = ConstantFoldLoadFromConstPtr(Operands[0], LI->getType(), DL);
7978 C = ConstantFoldInstOperands(I, Operands, DL, &TLI);
7985 // This is some other type of SCEVUnknown, just return it.
7989 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
7990 // Avoid performing the look-up in the common case where the specified
7991 // expression has no loop-variant portions.
7992 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
7993 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
7994 if (OpAtScope != Comm->getOperand(i)) {
7995 // Okay, at least one of these operands is loop variant but might be
7996 // foldable. Build a new instance of the folded commutative expression.
7997 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
7998 Comm->op_begin()+i);
7999 NewOps.push_back(OpAtScope);
8001 for (++i; i != e; ++i) {
8002 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
8003 NewOps.push_back(OpAtScope);
8005 if (isa<SCEVAddExpr>(Comm))
8006 return getAddExpr(NewOps);
8007 if (isa<SCEVMulExpr>(Comm))
8008 return getMulExpr(NewOps);
8009 if (isa<SCEVSMaxExpr>(Comm))
8010 return getSMaxExpr(NewOps);
8011 if (isa<SCEVUMaxExpr>(Comm))
8012 return getUMaxExpr(NewOps);
8013 llvm_unreachable("Unknown commutative SCEV type!");
8016 // If we got here, all operands are loop invariant.
8020 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
8021 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
8022 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
8023 if (LHS == Div->getLHS() && RHS == Div->getRHS())
8024 return Div; // must be loop invariant
8025 return getUDivExpr(LHS, RHS);
8028 // If this is a loop recurrence for a loop that does not contain L, then we
8029 // are dealing with the final value computed by the loop.
8030 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
8031 // First, attempt to evaluate each operand.
8032 // Avoid performing the look-up in the common case where the specified
8033 // expression has no loop-variant portions.
8034 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
8035 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
8036 if (OpAtScope == AddRec->getOperand(i))
8039 // Okay, at least one of these operands is loop variant but might be
8040 // foldable. Build a new instance of the folded commutative expression.
8041 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(),
8042 AddRec->op_begin()+i);
8043 NewOps.push_back(OpAtScope);
8044 for (++i; i != e; ++i)
8045 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
8047 const SCEV *FoldedRec =
8048 getAddRecExpr(NewOps, AddRec->getLoop(),
8049 AddRec->getNoWrapFlags(SCEV::FlagNW));
8050 AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec);
8051 // The addrec may be folded to a nonrecurrence, for example, if the
8052 // induction variable is multiplied by zero after constant folding. Go
8053 // ahead and return the folded value.
8059 // If the scope is outside the addrec's loop, evaluate it by using the
8060 // loop exit value of the addrec.
8061 if (!AddRec->getLoop()->contains(L)) {
8062 // To evaluate this recurrence, we need to know how many times the AddRec
8063 // loop iterates. Compute this now.
8064 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
8065 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
8067 // Then, evaluate the AddRec.
8068 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
8074 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
8075 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
8076 if (Op == Cast->getOperand())
8077 return Cast; // must be loop invariant
8078 return getZeroExtendExpr(Op, Cast->getType());
8081 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
8082 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
8083 if (Op == Cast->getOperand())
8084 return Cast; // must be loop invariant
8085 return getSignExtendExpr(Op, Cast->getType());
8088 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
8089 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
8090 if (Op == Cast->getOperand())
8091 return Cast; // must be loop invariant
8092 return getTruncateExpr(Op, Cast->getType());
8095 llvm_unreachable("Unknown SCEV type!");
8098 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
8099 return getSCEVAtScope(getSCEV(V), L);
8102 /// Finds the minimum unsigned root of the following equation:
8104 /// A * X = B (mod N)
8106 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
8107 /// A and B isn't important.
8109 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
8110 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const SCEV *B,
8111 ScalarEvolution &SE) {
8112 uint32_t BW = A.getBitWidth();
8113 assert(BW == SE.getTypeSizeInBits(B->getType()));
8114 assert(A != 0 && "A must be non-zero.");
8118 // The gcd of A and N may have only one prime factor: 2. The number of
8119 // trailing zeros in A is its multiplicity
8120 uint32_t Mult2 = A.countTrailingZeros();
8123 // 2. Check if B is divisible by D.
8125 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
8126 // is not less than multiplicity of this prime factor for D.
8127 if (SE.GetMinTrailingZeros(B) < Mult2)
8128 return SE.getCouldNotCompute();
8130 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
8133 // If D == 1, (N / D) == N == 2^BW, so we need one extra bit to represent
8134 // (N / D) in general. The inverse itself always fits into BW bits, though,
8135 // so we immediately truncate it.
8136 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
8137 APInt Mod(BW + 1, 0);
8138 Mod.setBit(BW - Mult2); // Mod = N / D
8139 APInt I = AD.multiplicativeInverse(Mod).trunc(BW);
8141 // 4. Compute the minimum unsigned root of the equation:
8142 // I * (B / D) mod (N / D)
8143 // To simplify the computation, we factor out the divide by D:
8144 // (I * B mod N) / D
8145 const SCEV *D = SE.getConstant(APInt::getOneBitSet(BW, Mult2));
8146 return SE.getUDivExactExpr(SE.getMulExpr(B, SE.getConstant(I)), D);
8149 /// Find the roots of the quadratic equation for the given quadratic chrec
8150 /// {L,+,M,+,N}. This returns either the two roots (which might be the same) or
8151 /// two SCEVCouldNotCompute objects.
8152 static Optional<std::pair<const SCEVConstant *,const SCEVConstant *>>
8153 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
8154 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
8155 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
8156 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
8157 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
8159 // We currently can only solve this if the coefficients are constants.
8160 if (!LC || !MC || !NC)
8163 uint32_t BitWidth = LC->getAPInt().getBitWidth();
8164 const APInt &L = LC->getAPInt();
8165 const APInt &M = MC->getAPInt();
8166 const APInt &N = NC->getAPInt();
8167 APInt Two(BitWidth, 2);
8169 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
8171 // The A coefficient is N/2
8172 APInt A = N.sdiv(Two);
8174 // The B coefficient is M-N/2
8176 B -= A; // A is the same as N/2.
8178 // The C coefficient is L.
8181 // Compute the B^2-4ac term.
8184 SqrtTerm -= 4 * (A * C);
8186 if (SqrtTerm.isNegative()) {
8187 // The loop is provably infinite.
8191 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
8192 // integer value or else APInt::sqrt() will assert.
8193 APInt SqrtVal = SqrtTerm.sqrt();
8195 // Compute the two solutions for the quadratic formula.
8196 // The divisions must be performed as signed divisions.
8197 APInt NegB = -std::move(B);
8198 APInt TwoA = std::move(A);
8200 if (TwoA.isNullValue())
8203 LLVMContext &Context = SE.getContext();
8205 ConstantInt *Solution1 =
8206 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
8207 ConstantInt *Solution2 =
8208 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
8210 return std::make_pair(cast<SCEVConstant>(SE.getConstant(Solution1)),
8211 cast<SCEVConstant>(SE.getConstant(Solution2)));
8214 ScalarEvolution::ExitLimit
8215 ScalarEvolution::howFarToZero(const SCEV *V, const Loop *L, bool ControlsExit,
8216 bool AllowPredicates) {
8218 // This is only used for loops with a "x != y" exit test. The exit condition
8219 // is now expressed as a single expression, V = x-y. So the exit test is
8220 // effectively V != 0. We know and take advantage of the fact that this
8221 // expression only being used in a comparison by zero context.
8223 SmallPtrSet<const SCEVPredicate *, 4> Predicates;
8224 // If the value is a constant
8225 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
8226 // If the value is already zero, the branch will execute zero times.
8227 if (C->getValue()->isZero()) return C;
8228 return getCouldNotCompute(); // Otherwise it will loop infinitely.
8231 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
8232 if (!AddRec && AllowPredicates)
8233 // Try to make this an AddRec using runtime tests, in the first X
8234 // iterations of this loop, where X is the SCEV expression found by the
8236 AddRec = convertSCEVToAddRecWithPredicates(V, L, Predicates);
8238 if (!AddRec || AddRec->getLoop() != L)
8239 return getCouldNotCompute();
8241 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
8242 // the quadratic equation to solve it.
8243 if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
8244 if (auto Roots = SolveQuadraticEquation(AddRec, *this)) {
8245 const SCEVConstant *R1 = Roots->first;
8246 const SCEVConstant *R2 = Roots->second;
8247 // Pick the smallest positive root value.
8248 if (ConstantInt *CB = dyn_cast<ConstantInt>(ConstantExpr::getICmp(
8249 CmpInst::ICMP_ULT, R1->getValue(), R2->getValue()))) {
8250 if (!CB->getZExtValue())
8251 std::swap(R1, R2); // R1 is the minimum root now.
8253 // We can only use this value if the chrec ends up with an exact zero
8254 // value at this index. When solving for "X*X != 5", for example, we
8255 // should not accept a root of 2.
8256 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
8258 // We found a quadratic root!
8259 return ExitLimit(R1, R1, false, Predicates);
8262 return getCouldNotCompute();
8265 // Otherwise we can only handle this if it is affine.
8266 if (!AddRec->isAffine())
8267 return getCouldNotCompute();
8269 // If this is an affine expression, the execution count of this branch is
8270 // the minimum unsigned root of the following equation:
8272 // Start + Step*N = 0 (mod 2^BW)
8276 // Step*N = -Start (mod 2^BW)
8278 // where BW is the common bit width of Start and Step.
8280 // Get the initial value for the loop.
8281 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
8282 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
8284 // For now we handle only constant steps.
8286 // TODO: Handle a nonconstant Step given AddRec<NUW>. If the
8287 // AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap
8288 // to 0, it must be counting down to equal 0. Consequently, N = Start / -Step.
8289 // We have not yet seen any such cases.
8290 const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step);
8291 if (!StepC || StepC->getValue()->isZero())
8292 return getCouldNotCompute();
8294 // For positive steps (counting up until unsigned overflow):
8295 // N = -Start/Step (as unsigned)
8296 // For negative steps (counting down to zero):
8298 // First compute the unsigned distance from zero in the direction of Step.
8299 bool CountDown = StepC->getAPInt().isNegative();
8300 const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start);
8302 // Handle unitary steps, which cannot wraparound.
8303 // 1*N = -Start; -1*N = Start (mod 2^BW), so:
8304 // N = Distance (as unsigned)
8305 if (StepC->getValue()->isOne() || StepC->getValue()->isMinusOne()) {
8306 APInt MaxBECount = getUnsignedRangeMax(Distance);
8308 // When a loop like "for (int i = 0; i != n; ++i) { /* body */ }" is rotated,
8309 // we end up with a loop whose backedge-taken count is n - 1. Detect this
8310 // case, and see if we can improve the bound.
8312 // Explicitly handling this here is necessary because getUnsignedRange
8313 // isn't context-sensitive; it doesn't know that we only care about the
8314 // range inside the loop.
8315 const SCEV *Zero = getZero(Distance->getType());
8316 const SCEV *One = getOne(Distance->getType());
8317 const SCEV *DistancePlusOne = getAddExpr(Distance, One);
8318 if (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_NE, DistancePlusOne, Zero)) {
8319 // If Distance + 1 doesn't overflow, we can compute the maximum distance
8320 // as "unsigned_max(Distance + 1) - 1".
8321 ConstantRange CR = getUnsignedRange(DistancePlusOne);
8322 MaxBECount = APIntOps::umin(MaxBECount, CR.getUnsignedMax() - 1);
8324 return ExitLimit(Distance, getConstant(MaxBECount), false, Predicates);
8327 // If the condition controls loop exit (the loop exits only if the expression
8328 // is true) and the addition is no-wrap we can use unsigned divide to
8329 // compute the backedge count. In this case, the step may not divide the
8330 // distance, but we don't care because if the condition is "missed" the loop
8331 // will have undefined behavior due to wrapping.
8332 if (ControlsExit && AddRec->hasNoSelfWrap() &&
8333 loopHasNoAbnormalExits(AddRec->getLoop())) {
8335 getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
8337 Exact == getCouldNotCompute()
8339 : getConstant(getUnsignedRangeMax(Exact));
8340 return ExitLimit(Exact, Max, false, Predicates);
8343 // Solve the general equation.
8344 const SCEV *E = SolveLinEquationWithOverflow(StepC->getAPInt(),
8345 getNegativeSCEV(Start), *this);
8346 const SCEV *M = E == getCouldNotCompute()
8348 : getConstant(getUnsignedRangeMax(E));
8349 return ExitLimit(E, M, false, Predicates);
8352 ScalarEvolution::ExitLimit
8353 ScalarEvolution::howFarToNonZero(const SCEV *V, const Loop *L) {
8354 // Loops that look like: while (X == 0) are very strange indeed. We don't
8355 // handle them yet except for the trivial case. This could be expanded in the
8356 // future as needed.
8358 // If the value is a constant, check to see if it is known to be non-zero
8359 // already. If so, the backedge will execute zero times.
8360 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
8361 if (!C->getValue()->isZero())
8362 return getZero(C->getType());
8363 return getCouldNotCompute(); // Otherwise it will loop infinitely.
8366 // We could implement others, but I really doubt anyone writes loops like
8367 // this, and if they did, they would already be constant folded.
8368 return getCouldNotCompute();
8371 std::pair<BasicBlock *, BasicBlock *>
8372 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
8373 // If the block has a unique predecessor, then there is no path from the
8374 // predecessor to the block that does not go through the direct edge
8375 // from the predecessor to the block.
8376 if (BasicBlock *Pred = BB->getSinglePredecessor())
8379 // A loop's header is defined to be a block that dominates the loop.
8380 // If the header has a unique predecessor outside the loop, it must be
8381 // a block that has exactly one successor that can reach the loop.
8382 if (Loop *L = LI.getLoopFor(BB))
8383 return {L->getLoopPredecessor(), L->getHeader()};
8385 return {nullptr, nullptr};
8388 /// SCEV structural equivalence is usually sufficient for testing whether two
8389 /// expressions are equal, however for the purposes of looking for a condition
8390 /// guarding a loop, it can be useful to be a little more general, since a
8391 /// front-end may have replicated the controlling expression.
8392 static bool HasSameValue(const SCEV *A, const SCEV *B) {
8393 // Quick check to see if they are the same SCEV.
8394 if (A == B) return true;
8396 auto ComputesEqualValues = [](const Instruction *A, const Instruction *B) {
8397 // Not all instructions that are "identical" compute the same value. For
8398 // instance, two distinct alloca instructions allocating the same type are
8399 // identical and do not read memory; but compute distinct values.
8400 return A->isIdenticalTo(B) && (isa<BinaryOperator>(A) || isa<GetElementPtrInst>(A));
8403 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
8404 // two different instructions with the same value. Check for this case.
8405 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
8406 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
8407 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
8408 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
8409 if (ComputesEqualValues(AI, BI))
8412 // Otherwise assume they may have a different value.
8416 bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
8417 const SCEV *&LHS, const SCEV *&RHS,
8419 bool Changed = false;
8421 // If we hit the max recursion limit bail out.
8425 // Canonicalize a constant to the right side.
8426 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
8427 // Check for both operands constant.
8428 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
8429 if (ConstantExpr::getICmp(Pred,
8431 RHSC->getValue())->isNullValue())
8432 goto trivially_false;
8434 goto trivially_true;
8436 // Otherwise swap the operands to put the constant on the right.
8437 std::swap(LHS, RHS);
8438 Pred = ICmpInst::getSwappedPredicate(Pred);
8442 // If we're comparing an addrec with a value which is loop-invariant in the
8443 // addrec's loop, put the addrec on the left. Also make a dominance check,
8444 // as both operands could be addrecs loop-invariant in each other's loop.
8445 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
8446 const Loop *L = AR->getLoop();
8447 if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) {
8448 std::swap(LHS, RHS);
8449 Pred = ICmpInst::getSwappedPredicate(Pred);
8454 // If there's a constant operand, canonicalize comparisons with boundary
8455 // cases, and canonicalize *-or-equal comparisons to regular comparisons.
8456 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
8457 const APInt &RA = RC->getAPInt();
8459 bool SimplifiedByConstantRange = false;
8461 if (!ICmpInst::isEquality(Pred)) {
8462 ConstantRange ExactCR = ConstantRange::makeExactICmpRegion(Pred, RA);
8463 if (ExactCR.isFullSet())
8464 goto trivially_true;
8465 else if (ExactCR.isEmptySet())
8466 goto trivially_false;
8469 CmpInst::Predicate NewPred;
8470 if (ExactCR.getEquivalentICmp(NewPred, NewRHS) &&
8471 ICmpInst::isEquality(NewPred)) {
8472 // We were able to convert an inequality to an equality.
8474 RHS = getConstant(NewRHS);
8475 Changed = SimplifiedByConstantRange = true;
8479 if (!SimplifiedByConstantRange) {
8483 case ICmpInst::ICMP_EQ:
8484 case ICmpInst::ICMP_NE:
8485 // Fold ((-1) * %a) + %b == 0 (equivalent to %b-%a == 0) into %a == %b.
8487 if (const SCEVAddExpr *AE = dyn_cast<SCEVAddExpr>(LHS))
8488 if (const SCEVMulExpr *ME =
8489 dyn_cast<SCEVMulExpr>(AE->getOperand(0)))
8490 if (AE->getNumOperands() == 2 && ME->getNumOperands() == 2 &&
8491 ME->getOperand(0)->isAllOnesValue()) {
8492 RHS = AE->getOperand(1);
8493 LHS = ME->getOperand(1);
8499 // The "Should have been caught earlier!" messages refer to the fact
8500 // that the ExactCR.isFullSet() or ExactCR.isEmptySet() check above
8501 // should have fired on the corresponding cases, and canonicalized the
8502 // check to trivially_true or trivially_false.
8504 case ICmpInst::ICMP_UGE:
8505 assert(!RA.isMinValue() && "Should have been caught earlier!");
8506 Pred = ICmpInst::ICMP_UGT;
8507 RHS = getConstant(RA - 1);
8510 case ICmpInst::ICMP_ULE:
8511 assert(!RA.isMaxValue() && "Should have been caught earlier!");
8512 Pred = ICmpInst::ICMP_ULT;
8513 RHS = getConstant(RA + 1);
8516 case ICmpInst::ICMP_SGE:
8517 assert(!RA.isMinSignedValue() && "Should have been caught earlier!");
8518 Pred = ICmpInst::ICMP_SGT;
8519 RHS = getConstant(RA - 1);
8522 case ICmpInst::ICMP_SLE:
8523 assert(!RA.isMaxSignedValue() && "Should have been caught earlier!");
8524 Pred = ICmpInst::ICMP_SLT;
8525 RHS = getConstant(RA + 1);
8532 // Check for obvious equality.
8533 if (HasSameValue(LHS, RHS)) {
8534 if (ICmpInst::isTrueWhenEqual(Pred))
8535 goto trivially_true;
8536 if (ICmpInst::isFalseWhenEqual(Pred))
8537 goto trivially_false;
8540 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
8541 // adding or subtracting 1 from one of the operands.
8543 case ICmpInst::ICMP_SLE:
8544 if (!getSignedRangeMax(RHS).isMaxSignedValue()) {
8545 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
8547 Pred = ICmpInst::ICMP_SLT;
8549 } else if (!getSignedRangeMin(LHS).isMinSignedValue()) {
8550 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
8552 Pred = ICmpInst::ICMP_SLT;
8556 case ICmpInst::ICMP_SGE:
8557 if (!getSignedRangeMin(RHS).isMinSignedValue()) {
8558 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
8560 Pred = ICmpInst::ICMP_SGT;
8562 } else if (!getSignedRangeMax(LHS).isMaxSignedValue()) {
8563 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
8565 Pred = ICmpInst::ICMP_SGT;
8569 case ICmpInst::ICMP_ULE:
8570 if (!getUnsignedRangeMax(RHS).isMaxValue()) {
8571 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
8573 Pred = ICmpInst::ICMP_ULT;
8575 } else if (!getUnsignedRangeMin(LHS).isMinValue()) {
8576 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS);
8577 Pred = ICmpInst::ICMP_ULT;
8581 case ICmpInst::ICMP_UGE:
8582 if (!getUnsignedRangeMin(RHS).isMinValue()) {
8583 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS);
8584 Pred = ICmpInst::ICMP_UGT;
8586 } else if (!getUnsignedRangeMax(LHS).isMaxValue()) {
8587 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
8589 Pred = ICmpInst::ICMP_UGT;
8597 // TODO: More simplifications are possible here.
8599 // Recursively simplify until we either hit a recursion limit or nothing
8602 return SimplifyICmpOperands(Pred, LHS, RHS, Depth+1);
8608 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
8609 Pred = ICmpInst::ICMP_EQ;
8614 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
8615 Pred = ICmpInst::ICMP_NE;
8619 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
8620 return getSignedRangeMax(S).isNegative();
8623 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
8624 return getSignedRangeMin(S).isStrictlyPositive();
8627 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
8628 return !getSignedRangeMin(S).isNegative();
8631 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
8632 return !getSignedRangeMax(S).isStrictlyPositive();
8635 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
8636 return isKnownNegative(S) || isKnownPositive(S);
8639 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
8640 const SCEV *LHS, const SCEV *RHS) {
8641 // Canonicalize the inputs first.
8642 (void)SimplifyICmpOperands(Pred, LHS, RHS);
8644 // If LHS or RHS is an addrec, check to see if the condition is true in
8645 // every iteration of the loop.
8646 // If LHS and RHS are both addrec, both conditions must be true in
8647 // every iteration of the loop.
8648 const SCEVAddRecExpr *LAR = dyn_cast<SCEVAddRecExpr>(LHS);
8649 const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS);
8650 bool LeftGuarded = false;
8651 bool RightGuarded = false;
8653 const Loop *L = LAR->getLoop();
8654 if (isLoopEntryGuardedByCond(L, Pred, LAR->getStart(), RHS) &&
8655 isLoopBackedgeGuardedByCond(L, Pred, LAR->getPostIncExpr(*this), RHS)) {
8656 if (!RAR) return true;
8661 const Loop *L = RAR->getLoop();
8662 if (isLoopEntryGuardedByCond(L, Pred, LHS, RAR->getStart()) &&
8663 isLoopBackedgeGuardedByCond(L, Pred, LHS, RAR->getPostIncExpr(*this))) {
8664 if (!LAR) return true;
8665 RightGuarded = true;
8668 if (LeftGuarded && RightGuarded)
8671 if (isKnownPredicateViaSplitting(Pred, LHS, RHS))
8674 // Otherwise see what can be done with known constant ranges.
8675 return isKnownPredicateViaConstantRanges(Pred, LHS, RHS);
8678 bool ScalarEvolution::isMonotonicPredicate(const SCEVAddRecExpr *LHS,
8679 ICmpInst::Predicate Pred,
8681 bool Result = isMonotonicPredicateImpl(LHS, Pred, Increasing);
8684 // Verify an invariant: inverting the predicate should turn a monotonically
8685 // increasing change to a monotonically decreasing one, and vice versa.
8686 bool IncreasingSwapped;
8687 bool ResultSwapped = isMonotonicPredicateImpl(
8688 LHS, ICmpInst::getSwappedPredicate(Pred), IncreasingSwapped);
8690 assert(Result == ResultSwapped && "should be able to analyze both!");
8692 assert(Increasing == !IncreasingSwapped &&
8693 "monotonicity should flip as we flip the predicate");
8699 bool ScalarEvolution::isMonotonicPredicateImpl(const SCEVAddRecExpr *LHS,
8700 ICmpInst::Predicate Pred,
8703 // A zero step value for LHS means the induction variable is essentially a
8704 // loop invariant value. We don't really depend on the predicate actually
8705 // flipping from false to true (for increasing predicates, and the other way
8706 // around for decreasing predicates), all we care about is that *if* the
8707 // predicate changes then it only changes from false to true.
8709 // A zero step value in itself is not very useful, but there may be places
8710 // where SCEV can prove X >= 0 but not prove X > 0, so it is helpful to be
8711 // as general as possible.
8715 return false; // Conservative answer
8717 case ICmpInst::ICMP_UGT:
8718 case ICmpInst::ICMP_UGE:
8719 case ICmpInst::ICMP_ULT:
8720 case ICmpInst::ICMP_ULE:
8721 if (!LHS->hasNoUnsignedWrap())
8724 Increasing = Pred == ICmpInst::ICMP_UGT || Pred == ICmpInst::ICMP_UGE;
8727 case ICmpInst::ICMP_SGT:
8728 case ICmpInst::ICMP_SGE:
8729 case ICmpInst::ICMP_SLT:
8730 case ICmpInst::ICMP_SLE: {
8731 if (!LHS->hasNoSignedWrap())
8734 const SCEV *Step = LHS->getStepRecurrence(*this);
8736 if (isKnownNonNegative(Step)) {
8737 Increasing = Pred == ICmpInst::ICMP_SGT || Pred == ICmpInst::ICMP_SGE;
8741 if (isKnownNonPositive(Step)) {
8742 Increasing = Pred == ICmpInst::ICMP_SLT || Pred == ICmpInst::ICMP_SLE;
8751 llvm_unreachable("switch has default clause!");
8754 bool ScalarEvolution::isLoopInvariantPredicate(
8755 ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS, const Loop *L,
8756 ICmpInst::Predicate &InvariantPred, const SCEV *&InvariantLHS,
8757 const SCEV *&InvariantRHS) {
8759 // If there is a loop-invariant, force it into the RHS, otherwise bail out.
8760 if (!isLoopInvariant(RHS, L)) {
8761 if (!isLoopInvariant(LHS, L))
8764 std::swap(LHS, RHS);
8765 Pred = ICmpInst::getSwappedPredicate(Pred);
8768 const SCEVAddRecExpr *ArLHS = dyn_cast<SCEVAddRecExpr>(LHS);
8769 if (!ArLHS || ArLHS->getLoop() != L)
8773 if (!isMonotonicPredicate(ArLHS, Pred, Increasing))
8776 // If the predicate "ArLHS `Pred` RHS" monotonically increases from false to
8777 // true as the loop iterates, and the backedge is control dependent on
8778 // "ArLHS `Pred` RHS" == true then we can reason as follows:
8780 // * if the predicate was false in the first iteration then the predicate
8781 // is never evaluated again, since the loop exits without taking the
8783 // * if the predicate was true in the first iteration then it will
8784 // continue to be true for all future iterations since it is
8785 // monotonically increasing.
8787 // For both the above possibilities, we can replace the loop varying
8788 // predicate with its value on the first iteration of the loop (which is
8791 // A similar reasoning applies for a monotonically decreasing predicate, by
8792 // replacing true with false and false with true in the above two bullets.
8794 auto P = Increasing ? Pred : ICmpInst::getInversePredicate(Pred);
8796 if (!isLoopBackedgeGuardedByCond(L, P, LHS, RHS))
8799 InvariantPred = Pred;
8800 InvariantLHS = ArLHS->getStart();
8805 bool ScalarEvolution::isKnownPredicateViaConstantRanges(
8806 ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS) {
8807 if (HasSameValue(LHS, RHS))
8808 return ICmpInst::isTrueWhenEqual(Pred);
8810 // This code is split out from isKnownPredicate because it is called from
8811 // within isLoopEntryGuardedByCond.
8814 [&](const ConstantRange &RangeLHS, const ConstantRange &RangeRHS) {
8815 return ConstantRange::makeSatisfyingICmpRegion(Pred, RangeRHS)
8816 .contains(RangeLHS);
8819 // The check at the top of the function catches the case where the values are
8820 // known to be equal.
8821 if (Pred == CmpInst::ICMP_EQ)
8824 if (Pred == CmpInst::ICMP_NE)
8825 return CheckRanges(getSignedRange(LHS), getSignedRange(RHS)) ||
8826 CheckRanges(getUnsignedRange(LHS), getUnsignedRange(RHS)) ||
8827 isKnownNonZero(getMinusSCEV(LHS, RHS));
8829 if (CmpInst::isSigned(Pred))
8830 return CheckRanges(getSignedRange(LHS), getSignedRange(RHS));
8832 return CheckRanges(getUnsignedRange(LHS), getUnsignedRange(RHS));
8835 bool ScalarEvolution::isKnownPredicateViaNoOverflow(ICmpInst::Predicate Pred,
8838 // Match Result to (X + Y)<ExpectedFlags> where Y is a constant integer.
8839 // Return Y via OutY.
8840 auto MatchBinaryAddToConst =
8841 [this](const SCEV *Result, const SCEV *X, APInt &OutY,
8842 SCEV::NoWrapFlags ExpectedFlags) {
8843 const SCEV *NonConstOp, *ConstOp;
8844 SCEV::NoWrapFlags FlagsPresent;
8846 if (!splitBinaryAdd(Result, ConstOp, NonConstOp, FlagsPresent) ||
8847 !isa<SCEVConstant>(ConstOp) || NonConstOp != X)
8850 OutY = cast<SCEVConstant>(ConstOp)->getAPInt();
8851 return (FlagsPresent & ExpectedFlags) == ExpectedFlags;
8860 case ICmpInst::ICMP_SGE:
8861 std::swap(LHS, RHS);
8863 case ICmpInst::ICMP_SLE:
8864 // X s<= (X + C)<nsw> if C >= 0
8865 if (MatchBinaryAddToConst(RHS, LHS, C, SCEV::FlagNSW) && C.isNonNegative())
8868 // (X + C)<nsw> s<= X if C <= 0
8869 if (MatchBinaryAddToConst(LHS, RHS, C, SCEV::FlagNSW) &&
8870 !C.isStrictlyPositive())
8874 case ICmpInst::ICMP_SGT:
8875 std::swap(LHS, RHS);
8877 case ICmpInst::ICMP_SLT:
8878 // X s< (X + C)<nsw> if C > 0
8879 if (MatchBinaryAddToConst(RHS, LHS, C, SCEV::FlagNSW) &&
8880 C.isStrictlyPositive())
8883 // (X + C)<nsw> s< X if C < 0
8884 if (MatchBinaryAddToConst(LHS, RHS, C, SCEV::FlagNSW) && C.isNegative())
8892 bool ScalarEvolution::isKnownPredicateViaSplitting(ICmpInst::Predicate Pred,
8895 if (Pred != ICmpInst::ICMP_ULT || ProvingSplitPredicate)
8898 // Allowing arbitrary number of activations of isKnownPredicateViaSplitting on
8899 // the stack can result in exponential time complexity.
8900 SaveAndRestore<bool> Restore(ProvingSplitPredicate, true);
8902 // If L >= 0 then I `ult` L <=> I >= 0 && I `slt` L
8904 // To prove L >= 0 we use isKnownNonNegative whereas to prove I >= 0 we use
8905 // isKnownPredicate. isKnownPredicate is more powerful, but also more
8906 // expensive; and using isKnownNonNegative(RHS) is sufficient for most of the
8907 // interesting cases seen in practice. We can consider "upgrading" L >= 0 to
8908 // use isKnownPredicate later if needed.
8909 return isKnownNonNegative(RHS) &&
8910 isKnownPredicate(CmpInst::ICMP_SGE, LHS, getZero(LHS->getType())) &&
8911 isKnownPredicate(CmpInst::ICMP_SLT, LHS, RHS);
8914 bool ScalarEvolution::isImpliedViaGuard(BasicBlock *BB,
8915 ICmpInst::Predicate Pred,
8916 const SCEV *LHS, const SCEV *RHS) {
8917 // No need to even try if we know the module has no guards.
8921 return any_of(*BB, [&](Instruction &I) {
8922 using namespace llvm::PatternMatch;
8925 return match(&I, m_Intrinsic<Intrinsic::experimental_guard>(
8926 m_Value(Condition))) &&
8927 isImpliedCond(Pred, LHS, RHS, Condition, false);
8931 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
8932 /// protected by a conditional between LHS and RHS. This is used to
8933 /// to eliminate casts.
8935 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
8936 ICmpInst::Predicate Pred,
8937 const SCEV *LHS, const SCEV *RHS) {
8938 // Interpret a null as meaning no loop, where there is obviously no guard
8939 // (interprocedural conditions notwithstanding).
8940 if (!L) return true;
8942 if (isKnownPredicateViaConstantRanges(Pred, LHS, RHS))
8945 BasicBlock *Latch = L->getLoopLatch();
8949 BranchInst *LoopContinuePredicate =
8950 dyn_cast<BranchInst>(Latch->getTerminator());
8951 if (LoopContinuePredicate && LoopContinuePredicate->isConditional() &&
8952 isImpliedCond(Pred, LHS, RHS,
8953 LoopContinuePredicate->getCondition(),
8954 LoopContinuePredicate->getSuccessor(0) != L->getHeader()))
8957 // We don't want more than one activation of the following loops on the stack
8958 // -- that can lead to O(n!) time complexity.
8959 if (WalkingBEDominatingConds)
8962 SaveAndRestore<bool> ClearOnExit(WalkingBEDominatingConds, true);
8964 // See if we can exploit a trip count to prove the predicate.
8965 const auto &BETakenInfo = getBackedgeTakenInfo(L);
8966 const SCEV *LatchBECount = BETakenInfo.getExact(Latch, this);
8967 if (LatchBECount != getCouldNotCompute()) {
8968 // We know that Latch branches back to the loop header exactly
8969 // LatchBECount times. This means the backdege condition at Latch is
8970 // equivalent to "{0,+,1} u< LatchBECount".
8971 Type *Ty = LatchBECount->getType();
8972 auto NoWrapFlags = SCEV::NoWrapFlags(SCEV::FlagNUW | SCEV::FlagNW);
8973 const SCEV *LoopCounter =
8974 getAddRecExpr(getZero(Ty), getOne(Ty), L, NoWrapFlags);
8975 if (isImpliedCond(Pred, LHS, RHS, ICmpInst::ICMP_ULT, LoopCounter,
8980 // Check conditions due to any @llvm.assume intrinsics.
8981 for (auto &AssumeVH : AC.assumptions()) {
8984 auto *CI = cast<CallInst>(AssumeVH);
8985 if (!DT.dominates(CI, Latch->getTerminator()))
8988 if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false))
8992 // If the loop is not reachable from the entry block, we risk running into an
8993 // infinite loop as we walk up into the dom tree. These loops do not matter
8994 // anyway, so we just return a conservative answer when we see them.
8995 if (!DT.isReachableFromEntry(L->getHeader()))
8998 if (isImpliedViaGuard(Latch, Pred, LHS, RHS))
9001 for (DomTreeNode *DTN = DT[Latch], *HeaderDTN = DT[L->getHeader()];
9002 DTN != HeaderDTN; DTN = DTN->getIDom()) {
9003 assert(DTN && "should reach the loop header before reaching the root!");
9005 BasicBlock *BB = DTN->getBlock();
9006 if (isImpliedViaGuard(BB, Pred, LHS, RHS))
9009 BasicBlock *PBB = BB->getSinglePredecessor();
9013 BranchInst *ContinuePredicate = dyn_cast<BranchInst>(PBB->getTerminator());
9014 if (!ContinuePredicate || !ContinuePredicate->isConditional())
9017 Value *Condition = ContinuePredicate->getCondition();
9019 // If we have an edge `E` within the loop body that dominates the only
9020 // latch, the condition guarding `E` also guards the backedge. This
9021 // reasoning works only for loops with a single latch.
9023 BasicBlockEdge DominatingEdge(PBB, BB);
9024 if (DominatingEdge.isSingleEdge()) {
9025 // We're constructively (and conservatively) enumerating edges within the
9026 // loop body that dominate the latch. The dominator tree better agree
9028 assert(DT.dominates(DominatingEdge, Latch) && "should be!");
9030 if (isImpliedCond(Pred, LHS, RHS, Condition,
9031 BB != ContinuePredicate->getSuccessor(0)))
9040 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
9041 ICmpInst::Predicate Pred,
9042 const SCEV *LHS, const SCEV *RHS) {
9043 // Interpret a null as meaning no loop, where there is obviously no guard
9044 // (interprocedural conditions notwithstanding).
9045 if (!L) return false;
9047 if (isKnownPredicateViaConstantRanges(Pred, LHS, RHS))
9050 // Starting at the loop predecessor, climb up the predecessor chain, as long
9051 // as there are predecessors that can be found that have unique successors
9052 // leading to the original header.
9053 for (std::pair<BasicBlock *, BasicBlock *>
9054 Pair(L->getLoopPredecessor(), L->getHeader());
9056 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
9058 if (isImpliedViaGuard(Pair.first, Pred, LHS, RHS))
9061 BranchInst *LoopEntryPredicate =
9062 dyn_cast<BranchInst>(Pair.first->getTerminator());
9063 if (!LoopEntryPredicate ||
9064 LoopEntryPredicate->isUnconditional())
9067 if (isImpliedCond(Pred, LHS, RHS,
9068 LoopEntryPredicate->getCondition(),
9069 LoopEntryPredicate->getSuccessor(0) != Pair.second))
9073 // Check conditions due to any @llvm.assume intrinsics.
9074 for (auto &AssumeVH : AC.assumptions()) {
9077 auto *CI = cast<CallInst>(AssumeVH);
9078 if (!DT.dominates(CI, L->getHeader()))
9081 if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false))
9088 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred,
9089 const SCEV *LHS, const SCEV *RHS,
9090 Value *FoundCondValue,
9092 if (!PendingLoopPredicates.insert(FoundCondValue).second)
9096 make_scope_exit([&]() { PendingLoopPredicates.erase(FoundCondValue); });
9098 // Recursively handle And and Or conditions.
9099 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) {
9100 if (BO->getOpcode() == Instruction::And) {
9102 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
9103 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
9104 } else if (BO->getOpcode() == Instruction::Or) {
9106 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
9107 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
9111 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue);
9112 if (!ICI) return false;
9114 // Now that we found a conditional branch that dominates the loop or controls
9115 // the loop latch. Check to see if it is the comparison we are looking for.
9116 ICmpInst::Predicate FoundPred;
9118 FoundPred = ICI->getInversePredicate();
9120 FoundPred = ICI->getPredicate();
9122 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
9123 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
9125 return isImpliedCond(Pred, LHS, RHS, FoundPred, FoundLHS, FoundRHS);
9128 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred, const SCEV *LHS,
9130 ICmpInst::Predicate FoundPred,
9131 const SCEV *FoundLHS,
9132 const SCEV *FoundRHS) {
9133 // Balance the types.
9134 if (getTypeSizeInBits(LHS->getType()) <
9135 getTypeSizeInBits(FoundLHS->getType())) {
9136 if (CmpInst::isSigned(Pred)) {
9137 LHS = getSignExtendExpr(LHS, FoundLHS->getType());
9138 RHS = getSignExtendExpr(RHS, FoundLHS->getType());
9140 LHS = getZeroExtendExpr(LHS, FoundLHS->getType());
9141 RHS = getZeroExtendExpr(RHS, FoundLHS->getType());
9143 } else if (getTypeSizeInBits(LHS->getType()) >
9144 getTypeSizeInBits(FoundLHS->getType())) {
9145 if (CmpInst::isSigned(FoundPred)) {
9146 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
9147 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
9149 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
9150 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
9154 // Canonicalize the query to match the way instcombine will have
9155 // canonicalized the comparison.
9156 if (SimplifyICmpOperands(Pred, LHS, RHS))
9158 return CmpInst::isTrueWhenEqual(Pred);
9159 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
9160 if (FoundLHS == FoundRHS)
9161 return CmpInst::isFalseWhenEqual(FoundPred);
9163 // Check to see if we can make the LHS or RHS match.
9164 if (LHS == FoundRHS || RHS == FoundLHS) {
9165 if (isa<SCEVConstant>(RHS)) {
9166 std::swap(FoundLHS, FoundRHS);
9167 FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
9169 std::swap(LHS, RHS);
9170 Pred = ICmpInst::getSwappedPredicate(Pred);
9174 // Check whether the found predicate is the same as the desired predicate.
9175 if (FoundPred == Pred)
9176 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
9178 // Check whether swapping the found predicate makes it the same as the
9179 // desired predicate.
9180 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
9181 if (isa<SCEVConstant>(RHS))
9182 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
9184 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
9185 RHS, LHS, FoundLHS, FoundRHS);
9188 // Unsigned comparison is the same as signed comparison when both the operands
9189 // are non-negative.
9190 if (CmpInst::isUnsigned(FoundPred) &&
9191 CmpInst::getSignedPredicate(FoundPred) == Pred &&
9192 isKnownNonNegative(FoundLHS) && isKnownNonNegative(FoundRHS))
9193 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
9195 // Check if we can make progress by sharpening ranges.
9196 if (FoundPred == ICmpInst::ICMP_NE &&
9197 (isa<SCEVConstant>(FoundLHS) || isa<SCEVConstant>(FoundRHS))) {
9199 const SCEVConstant *C = nullptr;
9200 const SCEV *V = nullptr;
9202 if (isa<SCEVConstant>(FoundLHS)) {
9203 C = cast<SCEVConstant>(FoundLHS);
9206 C = cast<SCEVConstant>(FoundRHS);
9210 // The guarding predicate tells us that C != V. If the known range
9211 // of V is [C, t), we can sharpen the range to [C + 1, t). The
9212 // range we consider has to correspond to same signedness as the
9213 // predicate we're interested in folding.
9215 APInt Min = ICmpInst::isSigned(Pred) ?
9216 getSignedRangeMin(V) : getUnsignedRangeMin(V);
9218 if (Min == C->getAPInt()) {
9219 // Given (V >= Min && V != Min) we conclude V >= (Min + 1).
9220 // This is true even if (Min + 1) wraps around -- in case of
9221 // wraparound, (Min + 1) < Min, so (V >= Min => V >= (Min + 1)).
9223 APInt SharperMin = Min + 1;
9226 case ICmpInst::ICMP_SGE:
9227 case ICmpInst::ICMP_UGE:
9228 // We know V `Pred` SharperMin. If this implies LHS `Pred`
9230 if (isImpliedCondOperands(Pred, LHS, RHS, V,
9231 getConstant(SharperMin)))
9235 case ICmpInst::ICMP_SGT:
9236 case ICmpInst::ICMP_UGT:
9237 // We know from the range information that (V `Pred` Min ||
9238 // V == Min). We know from the guarding condition that !(V
9239 // == Min). This gives us
9241 // V `Pred` Min || V == Min && !(V == Min)
9244 // If V `Pred` Min implies LHS `Pred` RHS, we're done.
9246 if (isImpliedCondOperands(Pred, LHS, RHS, V, getConstant(Min)))
9257 // Check whether the actual condition is beyond sufficient.
9258 if (FoundPred == ICmpInst::ICMP_EQ)
9259 if (ICmpInst::isTrueWhenEqual(Pred))
9260 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
9262 if (Pred == ICmpInst::ICMP_NE)
9263 if (!ICmpInst::isTrueWhenEqual(FoundPred))
9264 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
9267 // Otherwise assume the worst.
9271 bool ScalarEvolution::splitBinaryAdd(const SCEV *Expr,
9272 const SCEV *&L, const SCEV *&R,
9273 SCEV::NoWrapFlags &Flags) {
9274 const auto *AE = dyn_cast<SCEVAddExpr>(Expr);
9275 if (!AE || AE->getNumOperands() != 2)
9278 L = AE->getOperand(0);
9279 R = AE->getOperand(1);
9280 Flags = AE->getNoWrapFlags();
9284 Optional<APInt> ScalarEvolution::computeConstantDifference(const SCEV *More,
9286 // We avoid subtracting expressions here because this function is usually
9287 // fairly deep in the call stack (i.e. is called many times).
9289 if (isa<SCEVAddRecExpr>(Less) && isa<SCEVAddRecExpr>(More)) {
9290 const auto *LAR = cast<SCEVAddRecExpr>(Less);
9291 const auto *MAR = cast<SCEVAddRecExpr>(More);
9293 if (LAR->getLoop() != MAR->getLoop())
9296 // We look at affine expressions only; not for correctness but to keep
9297 // getStepRecurrence cheap.
9298 if (!LAR->isAffine() || !MAR->isAffine())
9301 if (LAR->getStepRecurrence(*this) != MAR->getStepRecurrence(*this))
9304 Less = LAR->getStart();
9305 More = MAR->getStart();
9310 if (isa<SCEVConstant>(Less) && isa<SCEVConstant>(More)) {
9311 const auto &M = cast<SCEVConstant>(More)->getAPInt();
9312 const auto &L = cast<SCEVConstant>(Less)->getAPInt();
9317 SCEV::NoWrapFlags Flags;
9318 if (splitBinaryAdd(Less, L, R, Flags))
9319 if (const auto *LC = dyn_cast<SCEVConstant>(L))
9321 return -(LC->getAPInt());
9323 if (splitBinaryAdd(More, L, R, Flags))
9324 if (const auto *LC = dyn_cast<SCEVConstant>(L))
9326 return LC->getAPInt();
9331 bool ScalarEvolution::isImpliedCondOperandsViaNoOverflow(
9332 ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS,
9333 const SCEV *FoundLHS, const SCEV *FoundRHS) {
9334 if (Pred != CmpInst::ICMP_SLT && Pred != CmpInst::ICMP_ULT)
9337 const auto *AddRecLHS = dyn_cast<SCEVAddRecExpr>(LHS);
9341 const auto *AddRecFoundLHS = dyn_cast<SCEVAddRecExpr>(FoundLHS);
9342 if (!AddRecFoundLHS)
9345 // We'd like to let SCEV reason about control dependencies, so we constrain
9346 // both the inequalities to be about add recurrences on the same loop. This
9347 // way we can use isLoopEntryGuardedByCond later.
9349 const Loop *L = AddRecFoundLHS->getLoop();
9350 if (L != AddRecLHS->getLoop())
9353 // FoundLHS u< FoundRHS u< -C => (FoundLHS + C) u< (FoundRHS + C) ... (1)
9355 // FoundLHS s< FoundRHS s< INT_MIN - C => (FoundLHS + C) s< (FoundRHS + C)
9358 // Informal proof for (2), assuming (1) [*]:
9360 // We'll also assume (A s< B) <=> ((A + INT_MIN) u< (B + INT_MIN)) ... (3)[**]
9364 // FoundLHS s< FoundRHS s< INT_MIN - C
9365 // <=> (FoundLHS + INT_MIN) u< (FoundRHS + INT_MIN) u< -C [ using (3) ]
9366 // <=> (FoundLHS + INT_MIN + C) u< (FoundRHS + INT_MIN + C) [ using (1) ]
9367 // <=> (FoundLHS + INT_MIN + C + INT_MIN) s<
9368 // (FoundRHS + INT_MIN + C + INT_MIN) [ using (3) ]
9369 // <=> FoundLHS + C s< FoundRHS + C
9371 // [*]: (1) can be proved by ruling out overflow.
9373 // [**]: This can be proved by analyzing all the four possibilities:
9374 // (A s< 0, B s< 0), (A s< 0, B s>= 0), (A s>= 0, B s< 0) and
9375 // (A s>= 0, B s>= 0).
9378 // Despite (2), "FoundRHS s< INT_MIN - C" does not mean that "FoundRHS + C"
9379 // will not sign underflow. For instance, say FoundLHS = (i8 -128), FoundRHS
9380 // = (i8 -127) and C = (i8 -100). Then INT_MIN - C = (i8 -28), and FoundRHS
9381 // s< (INT_MIN - C). Lack of sign overflow / underflow in "FoundRHS + C" is
9382 // neither necessary nor sufficient to prove "(FoundLHS + C) s< (FoundRHS +
9385 Optional<APInt> LDiff = computeConstantDifference(LHS, FoundLHS);
9386 Optional<APInt> RDiff = computeConstantDifference(RHS, FoundRHS);
9387 if (!LDiff || !RDiff || *LDiff != *RDiff)
9390 if (LDiff->isMinValue())
9393 APInt FoundRHSLimit;
9395 if (Pred == CmpInst::ICMP_ULT) {
9396 FoundRHSLimit = -(*RDiff);
9398 assert(Pred == CmpInst::ICMP_SLT && "Checked above!");
9399 FoundRHSLimit = APInt::getSignedMinValue(getTypeSizeInBits(RHS->getType())) - *RDiff;
9402 // Try to prove (1) or (2), as needed.
9403 return isLoopEntryGuardedByCond(L, Pred, FoundRHS,
9404 getConstant(FoundRHSLimit));
9407 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
9408 const SCEV *LHS, const SCEV *RHS,
9409 const SCEV *FoundLHS,
9410 const SCEV *FoundRHS) {
9411 if (isImpliedCondOperandsViaRanges(Pred, LHS, RHS, FoundLHS, FoundRHS))
9414 if (isImpliedCondOperandsViaNoOverflow(Pred, LHS, RHS, FoundLHS, FoundRHS))
9417 return isImpliedCondOperandsHelper(Pred, LHS, RHS,
9418 FoundLHS, FoundRHS) ||
9419 // ~x < ~y --> x > y
9420 isImpliedCondOperandsHelper(Pred, LHS, RHS,
9421 getNotSCEV(FoundRHS),
9422 getNotSCEV(FoundLHS));
9425 /// If Expr computes ~A, return A else return nullptr
9426 static const SCEV *MatchNotExpr(const SCEV *Expr) {
9427 const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Expr);
9428 if (!Add || Add->getNumOperands() != 2 ||
9429 !Add->getOperand(0)->isAllOnesValue())
9432 const SCEVMulExpr *AddRHS = dyn_cast<SCEVMulExpr>(Add->getOperand(1));
9433 if (!AddRHS || AddRHS->getNumOperands() != 2 ||
9434 !AddRHS->getOperand(0)->isAllOnesValue())
9437 return AddRHS->getOperand(1);
9440 /// Is MaybeMaxExpr an SMax or UMax of Candidate and some other values?
9441 template<typename MaxExprType>
9442 static bool IsMaxConsistingOf(const SCEV *MaybeMaxExpr,
9443 const SCEV *Candidate) {
9444 const MaxExprType *MaxExpr = dyn_cast<MaxExprType>(MaybeMaxExpr);
9445 if (!MaxExpr) return false;
9447 return find(MaxExpr->operands(), Candidate) != MaxExpr->op_end();
9450 /// Is MaybeMinExpr an SMin or UMin of Candidate and some other values?
9451 template<typename MaxExprType>
9452 static bool IsMinConsistingOf(ScalarEvolution &SE,
9453 const SCEV *MaybeMinExpr,
9454 const SCEV *Candidate) {
9455 const SCEV *MaybeMaxExpr = MatchNotExpr(MaybeMinExpr);
9459 return IsMaxConsistingOf<MaxExprType>(MaybeMaxExpr, SE.getNotSCEV(Candidate));
9462 static bool IsKnownPredicateViaAddRecStart(ScalarEvolution &SE,
9463 ICmpInst::Predicate Pred,
9464 const SCEV *LHS, const SCEV *RHS) {
9465 // If both sides are affine addrecs for the same loop, with equal
9466 // steps, and we know the recurrences don't wrap, then we only
9467 // need to check the predicate on the starting values.
9469 if (!ICmpInst::isRelational(Pred))
9472 const SCEVAddRecExpr *LAR = dyn_cast<SCEVAddRecExpr>(LHS);
9475 const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS);
9478 if (LAR->getLoop() != RAR->getLoop())
9480 if (!LAR->isAffine() || !RAR->isAffine())
9483 if (LAR->getStepRecurrence(SE) != RAR->getStepRecurrence(SE))
9486 SCEV::NoWrapFlags NW = ICmpInst::isSigned(Pred) ?
9487 SCEV::FlagNSW : SCEV::FlagNUW;
9488 if (!LAR->getNoWrapFlags(NW) || !RAR->getNoWrapFlags(NW))
9491 return SE.isKnownPredicate(Pred, LAR->getStart(), RAR->getStart());
9494 /// Is LHS `Pred` RHS true on the virtue of LHS or RHS being a Min or Max
9496 static bool IsKnownPredicateViaMinOrMax(ScalarEvolution &SE,
9497 ICmpInst::Predicate Pred,
9498 const SCEV *LHS, const SCEV *RHS) {
9503 case ICmpInst::ICMP_SGE:
9504 std::swap(LHS, RHS);
9506 case ICmpInst::ICMP_SLE:
9509 IsMinConsistingOf<SCEVSMaxExpr>(SE, LHS, RHS) ||
9511 IsMaxConsistingOf<SCEVSMaxExpr>(RHS, LHS);
9513 case ICmpInst::ICMP_UGE:
9514 std::swap(LHS, RHS);
9516 case ICmpInst::ICMP_ULE:
9519 IsMinConsistingOf<SCEVUMaxExpr>(SE, LHS, RHS) ||
9521 IsMaxConsistingOf<SCEVUMaxExpr>(RHS, LHS);
9524 llvm_unreachable("covered switch fell through?!");
9527 bool ScalarEvolution::isImpliedViaOperations(ICmpInst::Predicate Pred,
9528 const SCEV *LHS, const SCEV *RHS,
9529 const SCEV *FoundLHS,
9530 const SCEV *FoundRHS,
9532 assert(getTypeSizeInBits(LHS->getType()) ==
9533 getTypeSizeInBits(RHS->getType()) &&
9534 "LHS and RHS have different sizes?");
9535 assert(getTypeSizeInBits(FoundLHS->getType()) ==
9536 getTypeSizeInBits(FoundRHS->getType()) &&
9537 "FoundLHS and FoundRHS have different sizes?");
9538 // We want to avoid hurting the compile time with analysis of too big trees.
9539 if (Depth > MaxSCEVOperationsImplicationDepth)
9541 // We only want to work with ICMP_SGT comparison so far.
9542 // TODO: Extend to ICMP_UGT?
9543 if (Pred == ICmpInst::ICMP_SLT) {
9544 Pred = ICmpInst::ICMP_SGT;
9545 std::swap(LHS, RHS);
9546 std::swap(FoundLHS, FoundRHS);
9548 if (Pred != ICmpInst::ICMP_SGT)
9551 auto GetOpFromSExt = [&](const SCEV *S) {
9552 if (auto *Ext = dyn_cast<SCEVSignExtendExpr>(S))
9553 return Ext->getOperand();
9554 // TODO: If S is a SCEVConstant then you can cheaply "strip" the sext off
9555 // the constant in some cases.
9559 // Acquire values from extensions.
9560 auto *OrigFoundLHS = FoundLHS;
9561 LHS = GetOpFromSExt(LHS);
9562 FoundLHS = GetOpFromSExt(FoundLHS);
9564 // Is the SGT predicate can be proved trivially or using the found context.
9565 auto IsSGTViaContext = [&](const SCEV *S1, const SCEV *S2) {
9566 return isKnownViaSimpleReasoning(ICmpInst::ICMP_SGT, S1, S2) ||
9567 isImpliedViaOperations(ICmpInst::ICMP_SGT, S1, S2, OrigFoundLHS,
9568 FoundRHS, Depth + 1);
9571 if (auto *LHSAddExpr = dyn_cast<SCEVAddExpr>(LHS)) {
9572 // We want to avoid creation of any new non-constant SCEV. Since we are
9573 // going to compare the operands to RHS, we should be certain that we don't
9574 // need any size extensions for this. So let's decline all cases when the
9575 // sizes of types of LHS and RHS do not match.
9576 // TODO: Maybe try to get RHS from sext to catch more cases?
9577 if (getTypeSizeInBits(LHS->getType()) != getTypeSizeInBits(RHS->getType()))
9580 // Should not overflow.
9581 if (!LHSAddExpr->hasNoSignedWrap())
9584 auto *LL = LHSAddExpr->getOperand(0);
9585 auto *LR = LHSAddExpr->getOperand(1);
9586 auto *MinusOne = getNegativeSCEV(getOne(RHS->getType()));
9588 // Checks that S1 >= 0 && S2 > RHS, trivially or using the found context.
9589 auto IsSumGreaterThanRHS = [&](const SCEV *S1, const SCEV *S2) {
9590 return IsSGTViaContext(S1, MinusOne) && IsSGTViaContext(S2, RHS);
9592 // Try to prove the following rule:
9593 // (LHS = LL + LR) && (LL >= 0) && (LR > RHS) => (LHS > RHS).
9594 // (LHS = LL + LR) && (LR >= 0) && (LL > RHS) => (LHS > RHS).
9595 if (IsSumGreaterThanRHS(LL, LR) || IsSumGreaterThanRHS(LR, LL))
9597 } else if (auto *LHSUnknownExpr = dyn_cast<SCEVUnknown>(LHS)) {
9599 // FIXME: Once we have SDiv implemented, we can get rid of this matching.
9601 using namespace llvm::PatternMatch;
9603 if (match(LHSUnknownExpr->getValue(), m_SDiv(m_Value(LL), m_Value(LR)))) {
9604 // Rules for division.
9605 // We are going to perform some comparisons with Denominator and its
9606 // derivative expressions. In general case, creating a SCEV for it may
9607 // lead to a complex analysis of the entire graph, and in particular it
9608 // can request trip count recalculation for the same loop. This would
9609 // cache as SCEVCouldNotCompute to avoid the infinite recursion. To avoid
9610 // this, we only want to create SCEVs that are constants in this section.
9611 // So we bail if Denominator is not a constant.
9612 if (!isa<ConstantInt>(LR))
9615 auto *Denominator = cast<SCEVConstant>(getSCEV(LR));
9617 // We want to make sure that LHS = FoundLHS / Denominator. If it is so,
9618 // then a SCEV for the numerator already exists and matches with FoundLHS.
9619 auto *Numerator = getExistingSCEV(LL);
9620 if (!Numerator || Numerator->getType() != FoundLHS->getType())
9623 // Make sure that the numerator matches with FoundLHS and the denominator
9625 if (!HasSameValue(Numerator, FoundLHS) || !isKnownPositive(Denominator))
9628 auto *DTy = Denominator->getType();
9629 auto *FRHSTy = FoundRHS->getType();
9630 if (DTy->isPointerTy() != FRHSTy->isPointerTy())
9631 // One of types is a pointer and another one is not. We cannot extend
9632 // them properly to a wider type, so let us just reject this case.
9633 // TODO: Usage of getEffectiveSCEVType for DTy, FRHSTy etc should help
9634 // to avoid this check.
9638 // FoundLHS > FoundRHS, LHS = FoundLHS / Denominator, Denominator > 0.
9639 auto *WTy = getWiderType(DTy, FRHSTy);
9640 auto *DenominatorExt = getNoopOrSignExtend(Denominator, WTy);
9641 auto *FoundRHSExt = getNoopOrSignExtend(FoundRHS, WTy);
9643 // Try to prove the following rule:
9644 // (FoundRHS > Denominator - 2) && (RHS <= 0) => (LHS > RHS).
9645 // For example, given that FoundLHS > 2. It means that FoundLHS is at
9646 // least 3. If we divide it by Denominator < 4, we will have at least 1.
9647 auto *DenomMinusTwo = getMinusSCEV(DenominatorExt, getConstant(WTy, 2));
9648 if (isKnownNonPositive(RHS) &&
9649 IsSGTViaContext(FoundRHSExt, DenomMinusTwo))
9652 // Try to prove the following rule:
9653 // (FoundRHS > -1 - Denominator) && (RHS < 0) => (LHS > RHS).
9654 // For example, given that FoundLHS > -3. Then FoundLHS is at least -2.
9655 // If we divide it by Denominator > 2, then:
9656 // 1. If FoundLHS is negative, then the result is 0.
9657 // 2. If FoundLHS is non-negative, then the result is non-negative.
9658 // Anyways, the result is non-negative.
9659 auto *MinusOne = getNegativeSCEV(getOne(WTy));
9660 auto *NegDenomMinusOne = getMinusSCEV(MinusOne, DenominatorExt);
9661 if (isKnownNegative(RHS) &&
9662 IsSGTViaContext(FoundRHSExt, NegDenomMinusOne))
9671 ScalarEvolution::isKnownViaSimpleReasoning(ICmpInst::Predicate Pred,
9672 const SCEV *LHS, const SCEV *RHS) {
9673 return isKnownPredicateViaConstantRanges(Pred, LHS, RHS) ||
9674 IsKnownPredicateViaMinOrMax(*this, Pred, LHS, RHS) ||
9675 IsKnownPredicateViaAddRecStart(*this, Pred, LHS, RHS) ||
9676 isKnownPredicateViaNoOverflow(Pred, LHS, RHS);
9680 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
9681 const SCEV *LHS, const SCEV *RHS,
9682 const SCEV *FoundLHS,
9683 const SCEV *FoundRHS) {
9685 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
9686 case ICmpInst::ICMP_EQ:
9687 case ICmpInst::ICMP_NE:
9688 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
9691 case ICmpInst::ICMP_SLT:
9692 case ICmpInst::ICMP_SLE:
9693 if (isKnownViaSimpleReasoning(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
9694 isKnownViaSimpleReasoning(ICmpInst::ICMP_SGE, RHS, FoundRHS))
9697 case ICmpInst::ICMP_SGT:
9698 case ICmpInst::ICMP_SGE:
9699 if (isKnownViaSimpleReasoning(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
9700 isKnownViaSimpleReasoning(ICmpInst::ICMP_SLE, RHS, FoundRHS))
9703 case ICmpInst::ICMP_ULT:
9704 case ICmpInst::ICMP_ULE:
9705 if (isKnownViaSimpleReasoning(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
9706 isKnownViaSimpleReasoning(ICmpInst::ICMP_UGE, RHS, FoundRHS))
9709 case ICmpInst::ICMP_UGT:
9710 case ICmpInst::ICMP_UGE:
9711 if (isKnownViaSimpleReasoning(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
9712 isKnownViaSimpleReasoning(ICmpInst::ICMP_ULE, RHS, FoundRHS))
9717 // Maybe it can be proved via operations?
9718 if (isImpliedViaOperations(Pred, LHS, RHS, FoundLHS, FoundRHS))
9724 bool ScalarEvolution::isImpliedCondOperandsViaRanges(ICmpInst::Predicate Pred,
9727 const SCEV *FoundLHS,
9728 const SCEV *FoundRHS) {
9729 if (!isa<SCEVConstant>(RHS) || !isa<SCEVConstant>(FoundRHS))
9730 // The restriction on `FoundRHS` be lifted easily -- it exists only to
9731 // reduce the compile time impact of this optimization.
9734 Optional<APInt> Addend = computeConstantDifference(LHS, FoundLHS);
9738 const APInt &ConstFoundRHS = cast<SCEVConstant>(FoundRHS)->getAPInt();
9740 // `FoundLHSRange` is the range we know `FoundLHS` to be in by virtue of the
9741 // antecedent "`FoundLHS` `Pred` `FoundRHS`".
9742 ConstantRange FoundLHSRange =
9743 ConstantRange::makeAllowedICmpRegion(Pred, ConstFoundRHS);
9745 // Since `LHS` is `FoundLHS` + `Addend`, we can compute a range for `LHS`:
9746 ConstantRange LHSRange = FoundLHSRange.add(ConstantRange(*Addend));
9748 // We can also compute the range of values for `LHS` that satisfy the
9749 // consequent, "`LHS` `Pred` `RHS`":
9750 const APInt &ConstRHS = cast<SCEVConstant>(RHS)->getAPInt();
9751 ConstantRange SatisfyingLHSRange =
9752 ConstantRange::makeSatisfyingICmpRegion(Pred, ConstRHS);
9754 // The antecedent implies the consequent if every value of `LHS` that
9755 // satisfies the antecedent also satisfies the consequent.
9756 return SatisfyingLHSRange.contains(LHSRange);
9759 bool ScalarEvolution::doesIVOverflowOnLT(const SCEV *RHS, const SCEV *Stride,
9760 bool IsSigned, bool NoWrap) {
9761 assert(isKnownPositive(Stride) && "Positive stride expected!");
9763 if (NoWrap) return false;
9765 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
9766 const SCEV *One = getOne(Stride->getType());
9769 APInt MaxRHS = getSignedRangeMax(RHS);
9770 APInt MaxValue = APInt::getSignedMaxValue(BitWidth);
9771 APInt MaxStrideMinusOne = getSignedRangeMax(getMinusSCEV(Stride, One));
9773 // SMaxRHS + SMaxStrideMinusOne > SMaxValue => overflow!
9774 return (std::move(MaxValue) - MaxStrideMinusOne).slt(MaxRHS);
9777 APInt MaxRHS = getUnsignedRangeMax(RHS);
9778 APInt MaxValue = APInt::getMaxValue(BitWidth);
9779 APInt MaxStrideMinusOne = getUnsignedRangeMax(getMinusSCEV(Stride, One));
9781 // UMaxRHS + UMaxStrideMinusOne > UMaxValue => overflow!
9782 return (std::move(MaxValue) - MaxStrideMinusOne).ult(MaxRHS);
9785 bool ScalarEvolution::doesIVOverflowOnGT(const SCEV *RHS, const SCEV *Stride,
9786 bool IsSigned, bool NoWrap) {
9787 if (NoWrap) return false;
9789 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
9790 const SCEV *One = getOne(Stride->getType());
9793 APInt MinRHS = getSignedRangeMin(RHS);
9794 APInt MinValue = APInt::getSignedMinValue(BitWidth);
9795 APInt MaxStrideMinusOne = getSignedRangeMax(getMinusSCEV(Stride, One));
9797 // SMinRHS - SMaxStrideMinusOne < SMinValue => overflow!
9798 return (std::move(MinValue) + MaxStrideMinusOne).sgt(MinRHS);
9801 APInt MinRHS = getUnsignedRangeMin(RHS);
9802 APInt MinValue = APInt::getMinValue(BitWidth);
9803 APInt MaxStrideMinusOne = getUnsignedRangeMax(getMinusSCEV(Stride, One));
9805 // UMinRHS - UMaxStrideMinusOne < UMinValue => overflow!
9806 return (std::move(MinValue) + MaxStrideMinusOne).ugt(MinRHS);
9809 const SCEV *ScalarEvolution::computeBECount(const SCEV *Delta, const SCEV *Step,
9811 const SCEV *One = getOne(Step->getType());
9812 Delta = Equality ? getAddExpr(Delta, Step)
9813 : getAddExpr(Delta, getMinusSCEV(Step, One));
9814 return getUDivExpr(Delta, Step);
9817 const SCEV *ScalarEvolution::computeMaxBECountForLT(const SCEV *Start,
9823 assert(!isKnownNonPositive(Stride) &&
9824 "Stride is expected strictly positive!");
9825 // Calculate the maximum backedge count based on the range of values
9826 // permitted by Start, End, and Stride.
9827 const SCEV *MaxBECount;
9829 IsSigned ? getSignedRangeMin(Start) : getUnsignedRangeMin(Start);
9831 APInt StrideForMaxBECount =
9832 IsSigned ? getSignedRangeMin(Stride) : getUnsignedRangeMin(Stride);
9834 // We already know that the stride is positive, so we paper over conservatism
9835 // in our range computation by forcing StrideForMaxBECount to be at least one.
9836 // In theory this is unnecessary, but we expect MaxBECount to be a
9837 // SCEVConstant, and (udiv <constant> 0) is not constant folded by SCEV (there
9838 // is nothing to constant fold it to).
9839 APInt One(BitWidth, 1, IsSigned);
9840 StrideForMaxBECount = APIntOps::smax(One, StrideForMaxBECount);
9842 APInt MaxValue = IsSigned ? APInt::getSignedMaxValue(BitWidth)
9843 : APInt::getMaxValue(BitWidth);
9844 APInt Limit = MaxValue - (StrideForMaxBECount - 1);
9846 // Although End can be a MAX expression we estimate MaxEnd considering only
9847 // the case End = RHS of the loop termination condition. This is safe because
9848 // in the other case (End - Start) is zero, leading to a zero maximum backedge
9850 APInt MaxEnd = IsSigned ? APIntOps::smin(getSignedRangeMax(End), Limit)
9851 : APIntOps::umin(getUnsignedRangeMax(End), Limit);
9853 MaxBECount = computeBECount(getConstant(MaxEnd - MinStart) /* Delta */,
9854 getConstant(StrideForMaxBECount) /* Step */,
9855 false /* Equality */);
9860 ScalarEvolution::ExitLimit
9861 ScalarEvolution::howManyLessThans(const SCEV *LHS, const SCEV *RHS,
9862 const Loop *L, bool IsSigned,
9863 bool ControlsExit, bool AllowPredicates) {
9864 SmallPtrSet<const SCEVPredicate *, 4> Predicates;
9866 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
9867 bool PredicatedIV = false;
9869 if (!IV && AllowPredicates) {
9870 // Try to make this an AddRec using runtime tests, in the first X
9871 // iterations of this loop, where X is the SCEV expression found by the
9873 IV = convertSCEVToAddRecWithPredicates(LHS, L, Predicates);
9874 PredicatedIV = true;
9877 // Avoid weird loops
9878 if (!IV || IV->getLoop() != L || !IV->isAffine())
9879 return getCouldNotCompute();
9881 bool NoWrap = ControlsExit &&
9882 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
9884 const SCEV *Stride = IV->getStepRecurrence(*this);
9886 bool PositiveStride = isKnownPositive(Stride);
9888 // Avoid negative or zero stride values.
9889 if (!PositiveStride) {
9890 // We can compute the correct backedge taken count for loops with unknown
9891 // strides if we can prove that the loop is not an infinite loop with side
9892 // effects. Here's the loop structure we are trying to handle -
9898 // } while (i < end);
9900 // The backedge taken count for such loops is evaluated as -
9901 // (max(end, start + stride) - start - 1) /u stride
9903 // The additional preconditions that we need to check to prove correctness
9904 // of the above formula is as follows -
9906 // a) IV is either nuw or nsw depending upon signedness (indicated by the
9908 // b) loop is single exit with no side effects.
9911 // Precondition a) implies that if the stride is negative, this is a single
9912 // trip loop. The backedge taken count formula reduces to zero in this case.
9914 // Precondition b) implies that the unknown stride cannot be zero otherwise
9917 // The positive stride case is the same as isKnownPositive(Stride) returning
9918 // true (original behavior of the function).
9920 // We want to make sure that the stride is truly unknown as there are edge
9921 // cases where ScalarEvolution propagates no wrap flags to the
9922 // post-increment/decrement IV even though the increment/decrement operation
9923 // itself is wrapping. The computed backedge taken count may be wrong in
9924 // such cases. This is prevented by checking that the stride is not known to
9925 // be either positive or non-positive. For example, no wrap flags are
9926 // propagated to the post-increment IV of this loop with a trip count of 2 -
9929 // for(i=127; i<128; i+=129)
9932 if (PredicatedIV || !NoWrap || isKnownNonPositive(Stride) ||
9933 !loopHasNoSideEffects(L))
9934 return getCouldNotCompute();
9935 } else if (!Stride->isOne() &&
9936 doesIVOverflowOnLT(RHS, Stride, IsSigned, NoWrap))
9937 // Avoid proven overflow cases: this will ensure that the backedge taken
9938 // count will not generate any unsigned overflow. Relaxed no-overflow
9939 // conditions exploit NoWrapFlags, allowing to optimize in presence of
9940 // undefined behaviors like the case of C language.
9941 return getCouldNotCompute();
9943 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SLT
9944 : ICmpInst::ICMP_ULT;
9945 const SCEV *Start = IV->getStart();
9946 const SCEV *End = RHS;
9947 // When the RHS is not invariant, we do not know the end bound of the loop and
9948 // cannot calculate the ExactBECount needed by ExitLimit. However, we can
9949 // calculate the MaxBECount, given the start, stride and max value for the end
9950 // bound of the loop (RHS), and the fact that IV does not overflow (which is
9952 if (!isLoopInvariant(RHS, L)) {
9953 const SCEV *MaxBECount = computeMaxBECountForLT(
9954 Start, Stride, RHS, getTypeSizeInBits(LHS->getType()), IsSigned);
9955 return ExitLimit(getCouldNotCompute() /* ExactNotTaken */, MaxBECount,
9956 false /*MaxOrZero*/, Predicates);
9958 // If the backedge is taken at least once, then it will be taken
9959 // (End-Start)/Stride times (rounded up to a multiple of Stride), where Start
9960 // is the LHS value of the less-than comparison the first time it is evaluated
9961 // and End is the RHS.
9962 const SCEV *BECountIfBackedgeTaken =
9963 computeBECount(getMinusSCEV(End, Start), Stride, false);
9964 // If the loop entry is guarded by the result of the backedge test of the
9965 // first loop iteration, then we know the backedge will be taken at least
9966 // once and so the backedge taken count is as above. If not then we use the
9967 // expression (max(End,Start)-Start)/Stride to describe the backedge count,
9968 // as if the backedge is taken at least once max(End,Start) is End and so the
9969 // result is as above, and if not max(End,Start) is Start so we get a backedge
9971 const SCEV *BECount;
9972 if (isLoopEntryGuardedByCond(L, Cond, getMinusSCEV(Start, Stride), RHS))
9973 BECount = BECountIfBackedgeTaken;
9975 End = IsSigned ? getSMaxExpr(RHS, Start) : getUMaxExpr(RHS, Start);
9976 BECount = computeBECount(getMinusSCEV(End, Start), Stride, false);
9979 const SCEV *MaxBECount;
9980 bool MaxOrZero = false;
9981 if (isa<SCEVConstant>(BECount))
9982 MaxBECount = BECount;
9983 else if (isa<SCEVConstant>(BECountIfBackedgeTaken)) {
9984 // If we know exactly how many times the backedge will be taken if it's
9985 // taken at least once, then the backedge count will either be that or
9987 MaxBECount = BECountIfBackedgeTaken;
9990 MaxBECount = computeMaxBECountForLT(
9991 Start, Stride, RHS, getTypeSizeInBits(LHS->getType()), IsSigned);
9994 if (isa<SCEVCouldNotCompute>(MaxBECount) &&
9995 !isa<SCEVCouldNotCompute>(BECount))
9996 MaxBECount = getConstant(getUnsignedRangeMax(BECount));
9998 return ExitLimit(BECount, MaxBECount, MaxOrZero, Predicates);
10001 ScalarEvolution::ExitLimit
10002 ScalarEvolution::howManyGreaterThans(const SCEV *LHS, const SCEV *RHS,
10003 const Loop *L, bool IsSigned,
10004 bool ControlsExit, bool AllowPredicates) {
10005 SmallPtrSet<const SCEVPredicate *, 4> Predicates;
10006 // We handle only IV > Invariant
10007 if (!isLoopInvariant(RHS, L))
10008 return getCouldNotCompute();
10010 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
10011 if (!IV && AllowPredicates)
10012 // Try to make this an AddRec using runtime tests, in the first X
10013 // iterations of this loop, where X is the SCEV expression found by the
10014 // algorithm below.
10015 IV = convertSCEVToAddRecWithPredicates(LHS, L, Predicates);
10017 // Avoid weird loops
10018 if (!IV || IV->getLoop() != L || !IV->isAffine())
10019 return getCouldNotCompute();
10021 bool NoWrap = ControlsExit &&
10022 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
10024 const SCEV *Stride = getNegativeSCEV(IV->getStepRecurrence(*this));
10026 // Avoid negative or zero stride values
10027 if (!isKnownPositive(Stride))
10028 return getCouldNotCompute();
10030 // Avoid proven overflow cases: this will ensure that the backedge taken count
10031 // will not generate any unsigned overflow. Relaxed no-overflow conditions
10032 // exploit NoWrapFlags, allowing to optimize in presence of undefined
10033 // behaviors like the case of C language.
10034 if (!Stride->isOne() && doesIVOverflowOnGT(RHS, Stride, IsSigned, NoWrap))
10035 return getCouldNotCompute();
10037 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SGT
10038 : ICmpInst::ICMP_UGT;
10040 const SCEV *Start = IV->getStart();
10041 const SCEV *End = RHS;
10042 if (!isLoopEntryGuardedByCond(L, Cond, getAddExpr(Start, Stride), RHS))
10043 End = IsSigned ? getSMinExpr(RHS, Start) : getUMinExpr(RHS, Start);
10045 const SCEV *BECount = computeBECount(getMinusSCEV(Start, End), Stride, false);
10047 APInt MaxStart = IsSigned ? getSignedRangeMax(Start)
10048 : getUnsignedRangeMax(Start);
10050 APInt MinStride = IsSigned ? getSignedRangeMin(Stride)
10051 : getUnsignedRangeMin(Stride);
10053 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
10054 APInt Limit = IsSigned ? APInt::getSignedMinValue(BitWidth) + (MinStride - 1)
10055 : APInt::getMinValue(BitWidth) + (MinStride - 1);
10057 // Although End can be a MIN expression we estimate MinEnd considering only
10058 // the case End = RHS. This is safe because in the other case (Start - End)
10059 // is zero, leading to a zero maximum backedge taken count.
10061 IsSigned ? APIntOps::smax(getSignedRangeMin(RHS), Limit)
10062 : APIntOps::umax(getUnsignedRangeMin(RHS), Limit);
10065 const SCEV *MaxBECount = getCouldNotCompute();
10066 if (isa<SCEVConstant>(BECount))
10067 MaxBECount = BECount;
10069 MaxBECount = computeBECount(getConstant(MaxStart - MinEnd),
10070 getConstant(MinStride), false);
10072 if (isa<SCEVCouldNotCompute>(MaxBECount))
10073 MaxBECount = BECount;
10075 return ExitLimit(BECount, MaxBECount, false, Predicates);
10078 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(const ConstantRange &Range,
10079 ScalarEvolution &SE) const {
10080 if (Range.isFullSet()) // Infinite loop.
10081 return SE.getCouldNotCompute();
10083 // If the start is a non-zero constant, shift the range to simplify things.
10084 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
10085 if (!SC->getValue()->isZero()) {
10086 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
10087 Operands[0] = SE.getZero(SC->getType());
10088 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(),
10089 getNoWrapFlags(FlagNW));
10090 if (const auto *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted))
10091 return ShiftedAddRec->getNumIterationsInRange(
10092 Range.subtract(SC->getAPInt()), SE);
10093 // This is strange and shouldn't happen.
10094 return SE.getCouldNotCompute();
10097 // The only time we can solve this is when we have all constant indices.
10098 // Otherwise, we cannot determine the overflow conditions.
10099 if (any_of(operands(), [](const SCEV *Op) { return !isa<SCEVConstant>(Op); }))
10100 return SE.getCouldNotCompute();
10102 // Okay at this point we know that all elements of the chrec are constants and
10103 // that the start element is zero.
10105 // First check to see if the range contains zero. If not, the first
10106 // iteration exits.
10107 unsigned BitWidth = SE.getTypeSizeInBits(getType());
10108 if (!Range.contains(APInt(BitWidth, 0)))
10109 return SE.getZero(getType());
10112 // If this is an affine expression then we have this situation:
10113 // Solve {0,+,A} in Range === Ax in Range
10115 // We know that zero is in the range. If A is positive then we know that
10116 // the upper value of the range must be the first possible exit value.
10117 // If A is negative then the lower of the range is the last possible loop
10118 // value. Also note that we already checked for a full range.
10119 APInt A = cast<SCEVConstant>(getOperand(1))->getAPInt();
10120 APInt End = A.sge(1) ? (Range.getUpper() - 1) : Range.getLower();
10122 // The exit value should be (End+A)/A.
10123 APInt ExitVal = (End + A).udiv(A);
10124 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
10126 // Evaluate at the exit value. If we really did fall out of the valid
10127 // range, then we computed our trip count, otherwise wrap around or other
10128 // things must have happened.
10129 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
10130 if (Range.contains(Val->getValue()))
10131 return SE.getCouldNotCompute(); // Something strange happened
10133 // Ensure that the previous value is in the range. This is a sanity check.
10134 assert(Range.contains(
10135 EvaluateConstantChrecAtConstant(this,
10136 ConstantInt::get(SE.getContext(), ExitVal - 1), SE)->getValue()) &&
10137 "Linear scev computation is off in a bad way!");
10138 return SE.getConstant(ExitValue);
10139 } else if (isQuadratic()) {
10140 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
10141 // quadratic equation to solve it. To do this, we must frame our problem in
10142 // terms of figuring out when zero is crossed, instead of when
10143 // Range.getUpper() is crossed.
10144 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
10145 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
10146 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop(), FlagAnyWrap);
10148 // Next, solve the constructed addrec
10150 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE)) {
10151 const SCEVConstant *R1 = Roots->first;
10152 const SCEVConstant *R2 = Roots->second;
10153 // Pick the smallest positive root value.
10154 if (ConstantInt *CB = dyn_cast<ConstantInt>(ConstantExpr::getICmp(
10155 ICmpInst::ICMP_ULT, R1->getValue(), R2->getValue()))) {
10156 if (!CB->getZExtValue())
10157 std::swap(R1, R2); // R1 is the minimum root now.
10159 // Make sure the root is not off by one. The returned iteration should
10160 // not be in the range, but the previous one should be. When solving
10161 // for "X*X < 5", for example, we should not return a root of 2.
10162 ConstantInt *R1Val =
10163 EvaluateConstantChrecAtConstant(this, R1->getValue(), SE);
10164 if (Range.contains(R1Val->getValue())) {
10165 // The next iteration must be out of the range...
10166 ConstantInt *NextVal =
10167 ConstantInt::get(SE.getContext(), R1->getAPInt() + 1);
10169 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
10170 if (!Range.contains(R1Val->getValue()))
10171 return SE.getConstant(NextVal);
10172 return SE.getCouldNotCompute(); // Something strange happened
10175 // If R1 was not in the range, then it is a good return value. Make
10176 // sure that R1-1 WAS in the range though, just in case.
10177 ConstantInt *NextVal =
10178 ConstantInt::get(SE.getContext(), R1->getAPInt() - 1);
10179 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
10180 if (Range.contains(R1Val->getValue()))
10182 return SE.getCouldNotCompute(); // Something strange happened
10187 return SE.getCouldNotCompute();
10190 // Return true when S contains at least an undef value.
10191 static inline bool containsUndefs(const SCEV *S) {
10192 return SCEVExprContains(S, [](const SCEV *S) {
10193 if (const auto *SU = dyn_cast<SCEVUnknown>(S))
10194 return isa<UndefValue>(SU->getValue());
10195 else if (const auto *SC = dyn_cast<SCEVConstant>(S))
10196 return isa<UndefValue>(SC->getValue());
10203 // Collect all steps of SCEV expressions.
10204 struct SCEVCollectStrides {
10205 ScalarEvolution &SE;
10206 SmallVectorImpl<const SCEV *> &Strides;
10208 SCEVCollectStrides(ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &S)
10209 : SE(SE), Strides(S) {}
10211 bool follow(const SCEV *S) {
10212 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(S))
10213 Strides.push_back(AR->getStepRecurrence(SE));
10217 bool isDone() const { return false; }
10220 // Collect all SCEVUnknown and SCEVMulExpr expressions.
10221 struct SCEVCollectTerms {
10222 SmallVectorImpl<const SCEV *> &Terms;
10224 SCEVCollectTerms(SmallVectorImpl<const SCEV *> &T) : Terms(T) {}
10226 bool follow(const SCEV *S) {
10227 if (isa<SCEVUnknown>(S) || isa<SCEVMulExpr>(S) ||
10228 isa<SCEVSignExtendExpr>(S)) {
10229 if (!containsUndefs(S))
10230 Terms.push_back(S);
10232 // Stop recursion: once we collected a term, do not walk its operands.
10240 bool isDone() const { return false; }
10243 // Check if a SCEV contains an AddRecExpr.
10244 struct SCEVHasAddRec {
10245 bool &ContainsAddRec;
10247 SCEVHasAddRec(bool &ContainsAddRec) : ContainsAddRec(ContainsAddRec) {
10248 ContainsAddRec = false;
10251 bool follow(const SCEV *S) {
10252 if (isa<SCEVAddRecExpr>(S)) {
10253 ContainsAddRec = true;
10255 // Stop recursion: once we collected a term, do not walk its operands.
10263 bool isDone() const { return false; }
10266 // Find factors that are multiplied with an expression that (possibly as a
10267 // subexpression) contains an AddRecExpr. In the expression:
10269 // 8 * (100 + %p * %q * (%a + {0, +, 1}_loop))
10271 // "%p * %q" are factors multiplied by the expression "(%a + {0, +, 1}_loop)"
10272 // that contains the AddRec {0, +, 1}_loop. %p * %q are likely to be array size
10273 // parameters as they form a product with an induction variable.
10275 // This collector expects all array size parameters to be in the same MulExpr.
10276 // It might be necessary to later add support for collecting parameters that are
10277 // spread over different nested MulExpr.
10278 struct SCEVCollectAddRecMultiplies {
10279 SmallVectorImpl<const SCEV *> &Terms;
10280 ScalarEvolution &SE;
10282 SCEVCollectAddRecMultiplies(SmallVectorImpl<const SCEV *> &T, ScalarEvolution &SE)
10283 : Terms(T), SE(SE) {}
10285 bool follow(const SCEV *S) {
10286 if (auto *Mul = dyn_cast<SCEVMulExpr>(S)) {
10287 bool HasAddRec = false;
10288 SmallVector<const SCEV *, 0> Operands;
10289 for (auto Op : Mul->operands()) {
10290 const SCEVUnknown *Unknown = dyn_cast<SCEVUnknown>(Op);
10291 if (Unknown && !isa<CallInst>(Unknown->getValue())) {
10292 Operands.push_back(Op);
10293 } else if (Unknown) {
10296 bool ContainsAddRec;
10297 SCEVHasAddRec ContiansAddRec(ContainsAddRec);
10298 visitAll(Op, ContiansAddRec);
10299 HasAddRec |= ContainsAddRec;
10302 if (Operands.size() == 0)
10308 Terms.push_back(SE.getMulExpr(Operands));
10309 // Stop recursion: once we collected a term, do not walk its operands.
10317 bool isDone() const { return false; }
10320 } // end anonymous namespace
10322 /// Find parametric terms in this SCEVAddRecExpr. We first for parameters in
10324 /// 1) The strides of AddRec expressions.
10325 /// 2) Unknowns that are multiplied with AddRec expressions.
10326 void ScalarEvolution::collectParametricTerms(const SCEV *Expr,
10327 SmallVectorImpl<const SCEV *> &Terms) {
10328 SmallVector<const SCEV *, 4> Strides;
10329 SCEVCollectStrides StrideCollector(*this, Strides);
10330 visitAll(Expr, StrideCollector);
10333 dbgs() << "Strides:\n";
10334 for (const SCEV *S : Strides)
10335 dbgs() << *S << "\n";
10338 for (const SCEV *S : Strides) {
10339 SCEVCollectTerms TermCollector(Terms);
10340 visitAll(S, TermCollector);
10344 dbgs() << "Terms:\n";
10345 for (const SCEV *T : Terms)
10346 dbgs() << *T << "\n";
10349 SCEVCollectAddRecMultiplies MulCollector(Terms, *this);
10350 visitAll(Expr, MulCollector);
10353 static bool findArrayDimensionsRec(ScalarEvolution &SE,
10354 SmallVectorImpl<const SCEV *> &Terms,
10355 SmallVectorImpl<const SCEV *> &Sizes) {
10356 int Last = Terms.size() - 1;
10357 const SCEV *Step = Terms[Last];
10359 // End of recursion.
10361 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Step)) {
10362 SmallVector<const SCEV *, 2> Qs;
10363 for (const SCEV *Op : M->operands())
10364 if (!isa<SCEVConstant>(Op))
10367 Step = SE.getMulExpr(Qs);
10370 Sizes.push_back(Step);
10374 for (const SCEV *&Term : Terms) {
10375 // Normalize the terms before the next call to findArrayDimensionsRec.
10377 SCEVDivision::divide(SE, Term, Step, &Q, &R);
10379 // Bail out when GCD does not evenly divide one of the terms.
10386 // Remove all SCEVConstants.
10388 remove_if(Terms, [](const SCEV *E) { return isa<SCEVConstant>(E); }),
10391 if (Terms.size() > 0)
10392 if (!findArrayDimensionsRec(SE, Terms, Sizes))
10395 Sizes.push_back(Step);
10399 // Returns true when one of the SCEVs of Terms contains a SCEVUnknown parameter.
10400 static inline bool containsParameters(SmallVectorImpl<const SCEV *> &Terms) {
10401 for (const SCEV *T : Terms)
10402 if (SCEVExprContains(T, isa<SCEVUnknown, const SCEV *>))
10407 // Return the number of product terms in S.
10408 static inline int numberOfTerms(const SCEV *S) {
10409 if (const SCEVMulExpr *Expr = dyn_cast<SCEVMulExpr>(S))
10410 return Expr->getNumOperands();
10414 static const SCEV *removeConstantFactors(ScalarEvolution &SE, const SCEV *T) {
10415 if (isa<SCEVConstant>(T))
10418 if (isa<SCEVUnknown>(T))
10421 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(T)) {
10422 SmallVector<const SCEV *, 2> Factors;
10423 for (const SCEV *Op : M->operands())
10424 if (!isa<SCEVConstant>(Op))
10425 Factors.push_back(Op);
10427 return SE.getMulExpr(Factors);
10433 /// Return the size of an element read or written by Inst.
10434 const SCEV *ScalarEvolution::getElementSize(Instruction *Inst) {
10436 if (StoreInst *Store = dyn_cast<StoreInst>(Inst))
10437 Ty = Store->getValueOperand()->getType();
10438 else if (LoadInst *Load = dyn_cast<LoadInst>(Inst))
10439 Ty = Load->getType();
10443 Type *ETy = getEffectiveSCEVType(PointerType::getUnqual(Ty));
10444 return getSizeOfExpr(ETy, Ty);
10447 void ScalarEvolution::findArrayDimensions(SmallVectorImpl<const SCEV *> &Terms,
10448 SmallVectorImpl<const SCEV *> &Sizes,
10449 const SCEV *ElementSize) {
10450 if (Terms.size() < 1 || !ElementSize)
10453 // Early return when Terms do not contain parameters: we do not delinearize
10454 // non parametric SCEVs.
10455 if (!containsParameters(Terms))
10459 dbgs() << "Terms:\n";
10460 for (const SCEV *T : Terms)
10461 dbgs() << *T << "\n";
10464 // Remove duplicates.
10465 array_pod_sort(Terms.begin(), Terms.end());
10466 Terms.erase(std::unique(Terms.begin(), Terms.end()), Terms.end());
10468 // Put larger terms first.
10469 std::sort(Terms.begin(), Terms.end(), [](const SCEV *LHS, const SCEV *RHS) {
10470 return numberOfTerms(LHS) > numberOfTerms(RHS);
10473 // Try to divide all terms by the element size. If term is not divisible by
10474 // element size, proceed with the original term.
10475 for (const SCEV *&Term : Terms) {
10477 SCEVDivision::divide(*this, Term, ElementSize, &Q, &R);
10482 SmallVector<const SCEV *, 4> NewTerms;
10484 // Remove constant factors.
10485 for (const SCEV *T : Terms)
10486 if (const SCEV *NewT = removeConstantFactors(*this, T))
10487 NewTerms.push_back(NewT);
10490 dbgs() << "Terms after sorting:\n";
10491 for (const SCEV *T : NewTerms)
10492 dbgs() << *T << "\n";
10495 if (NewTerms.empty() || !findArrayDimensionsRec(*this, NewTerms, Sizes)) {
10500 // The last element to be pushed into Sizes is the size of an element.
10501 Sizes.push_back(ElementSize);
10504 dbgs() << "Sizes:\n";
10505 for (const SCEV *S : Sizes)
10506 dbgs() << *S << "\n";
10510 void ScalarEvolution::computeAccessFunctions(
10511 const SCEV *Expr, SmallVectorImpl<const SCEV *> &Subscripts,
10512 SmallVectorImpl<const SCEV *> &Sizes) {
10513 // Early exit in case this SCEV is not an affine multivariate function.
10517 if (auto *AR = dyn_cast<SCEVAddRecExpr>(Expr))
10518 if (!AR->isAffine())
10521 const SCEV *Res = Expr;
10522 int Last = Sizes.size() - 1;
10523 for (int i = Last; i >= 0; i--) {
10525 SCEVDivision::divide(*this, Res, Sizes[i], &Q, &R);
10528 dbgs() << "Res: " << *Res << "\n";
10529 dbgs() << "Sizes[i]: " << *Sizes[i] << "\n";
10530 dbgs() << "Res divided by Sizes[i]:\n";
10531 dbgs() << "Quotient: " << *Q << "\n";
10532 dbgs() << "Remainder: " << *R << "\n";
10537 // Do not record the last subscript corresponding to the size of elements in
10541 // Bail out if the remainder is too complex.
10542 if (isa<SCEVAddRecExpr>(R)) {
10543 Subscripts.clear();
10551 // Record the access function for the current subscript.
10552 Subscripts.push_back(R);
10555 // Also push in last position the remainder of the last division: it will be
10556 // the access function of the innermost dimension.
10557 Subscripts.push_back(Res);
10559 std::reverse(Subscripts.begin(), Subscripts.end());
10562 dbgs() << "Subscripts:\n";
10563 for (const SCEV *S : Subscripts)
10564 dbgs() << *S << "\n";
10568 /// Splits the SCEV into two vectors of SCEVs representing the subscripts and
10569 /// sizes of an array access. Returns the remainder of the delinearization that
10570 /// is the offset start of the array. The SCEV->delinearize algorithm computes
10571 /// the multiples of SCEV coefficients: that is a pattern matching of sub
10572 /// expressions in the stride and base of a SCEV corresponding to the
10573 /// computation of a GCD (greatest common divisor) of base and stride. When
10574 /// SCEV->delinearize fails, it returns the SCEV unchanged.
10576 /// For example: when analyzing the memory access A[i][j][k] in this loop nest
10578 /// void foo(long n, long m, long o, double A[n][m][o]) {
10580 /// for (long i = 0; i < n; i++)
10581 /// for (long j = 0; j < m; j++)
10582 /// for (long k = 0; k < o; k++)
10583 /// A[i][j][k] = 1.0;
10586 /// the delinearization input is the following AddRec SCEV:
10588 /// AddRec: {{{%A,+,(8 * %m * %o)}<%for.i>,+,(8 * %o)}<%for.j>,+,8}<%for.k>
10590 /// From this SCEV, we are able to say that the base offset of the access is %A
10591 /// because it appears as an offset that does not divide any of the strides in
10594 /// CHECK: Base offset: %A
10596 /// and then SCEV->delinearize determines the size of some of the dimensions of
10597 /// the array as these are the multiples by which the strides are happening:
10599 /// CHECK: ArrayDecl[UnknownSize][%m][%o] with elements of sizeof(double) bytes.
10601 /// Note that the outermost dimension remains of UnknownSize because there are
10602 /// no strides that would help identifying the size of the last dimension: when
10603 /// the array has been statically allocated, one could compute the size of that
10604 /// dimension by dividing the overall size of the array by the size of the known
10605 /// dimensions: %m * %o * 8.
10607 /// Finally delinearize provides the access functions for the array reference
10608 /// that does correspond to A[i][j][k] of the above C testcase:
10610 /// CHECK: ArrayRef[{0,+,1}<%for.i>][{0,+,1}<%for.j>][{0,+,1}<%for.k>]
10612 /// The testcases are checking the output of a function pass:
10613 /// DelinearizationPass that walks through all loads and stores of a function
10614 /// asking for the SCEV of the memory access with respect to all enclosing
10615 /// loops, calling SCEV->delinearize on that and printing the results.
10616 void ScalarEvolution::delinearize(const SCEV *Expr,
10617 SmallVectorImpl<const SCEV *> &Subscripts,
10618 SmallVectorImpl<const SCEV *> &Sizes,
10619 const SCEV *ElementSize) {
10620 // First step: collect parametric terms.
10621 SmallVector<const SCEV *, 4> Terms;
10622 collectParametricTerms(Expr, Terms);
10627 // Second step: find subscript sizes.
10628 findArrayDimensions(Terms, Sizes, ElementSize);
10633 // Third step: compute the access functions for each subscript.
10634 computeAccessFunctions(Expr, Subscripts, Sizes);
10636 if (Subscripts.empty())
10640 dbgs() << "succeeded to delinearize " << *Expr << "\n";
10641 dbgs() << "ArrayDecl[UnknownSize]";
10642 for (const SCEV *S : Sizes)
10643 dbgs() << "[" << *S << "]";
10645 dbgs() << "\nArrayRef";
10646 for (const SCEV *S : Subscripts)
10647 dbgs() << "[" << *S << "]";
10652 //===----------------------------------------------------------------------===//
10653 // SCEVCallbackVH Class Implementation
10654 //===----------------------------------------------------------------------===//
10656 void ScalarEvolution::SCEVCallbackVH::deleted() {
10657 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
10658 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
10659 SE->ConstantEvolutionLoopExitValue.erase(PN);
10660 SE->eraseValueFromMap(getValPtr());
10661 // this now dangles!
10664 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) {
10665 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
10667 // Forget all the expressions associated with users of the old value,
10668 // so that future queries will recompute the expressions using the new
10670 Value *Old = getValPtr();
10671 SmallVector<User *, 16> Worklist(Old->user_begin(), Old->user_end());
10672 SmallPtrSet<User *, 8> Visited;
10673 while (!Worklist.empty()) {
10674 User *U = Worklist.pop_back_val();
10675 // Deleting the Old value will cause this to dangle. Postpone
10676 // that until everything else is done.
10679 if (!Visited.insert(U).second)
10681 if (PHINode *PN = dyn_cast<PHINode>(U))
10682 SE->ConstantEvolutionLoopExitValue.erase(PN);
10683 SE->eraseValueFromMap(U);
10684 Worklist.insert(Worklist.end(), U->user_begin(), U->user_end());
10686 // Delete the Old value.
10687 if (PHINode *PN = dyn_cast<PHINode>(Old))
10688 SE->ConstantEvolutionLoopExitValue.erase(PN);
10689 SE->eraseValueFromMap(Old);
10690 // this now dangles!
10693 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
10694 : CallbackVH(V), SE(se) {}
10696 //===----------------------------------------------------------------------===//
10697 // ScalarEvolution Class Implementation
10698 //===----------------------------------------------------------------------===//
10700 ScalarEvolution::ScalarEvolution(Function &F, TargetLibraryInfo &TLI,
10701 AssumptionCache &AC, DominatorTree &DT,
10703 : F(F), TLI(TLI), AC(AC), DT(DT), LI(LI),
10704 CouldNotCompute(new SCEVCouldNotCompute()), ValuesAtScopes(64),
10705 LoopDispositions(64), BlockDispositions(64) {
10706 // To use guards for proving predicates, we need to scan every instruction in
10707 // relevant basic blocks, and not just terminators. Doing this is a waste of
10708 // time if the IR does not actually contain any calls to
10709 // @llvm.experimental.guard, so do a quick check and remember this beforehand.
10711 // This pessimizes the case where a pass that preserves ScalarEvolution wants
10712 // to _add_ guards to the module when there weren't any before, and wants
10713 // ScalarEvolution to optimize based on those guards. For now we prefer to be
10714 // efficient in lieu of being smart in that rather obscure case.
10716 auto *GuardDecl = F.getParent()->getFunction(
10717 Intrinsic::getName(Intrinsic::experimental_guard));
10718 HasGuards = GuardDecl && !GuardDecl->use_empty();
10721 ScalarEvolution::ScalarEvolution(ScalarEvolution &&Arg)
10722 : F(Arg.F), HasGuards(Arg.HasGuards), TLI(Arg.TLI), AC(Arg.AC), DT(Arg.DT),
10723 LI(Arg.LI), CouldNotCompute(std::move(Arg.CouldNotCompute)),
10724 ValueExprMap(std::move(Arg.ValueExprMap)),
10725 PendingLoopPredicates(std::move(Arg.PendingLoopPredicates)),
10726 MinTrailingZerosCache(std::move(Arg.MinTrailingZerosCache)),
10727 BackedgeTakenCounts(std::move(Arg.BackedgeTakenCounts)),
10728 PredicatedBackedgeTakenCounts(
10729 std::move(Arg.PredicatedBackedgeTakenCounts)),
10730 ConstantEvolutionLoopExitValue(
10731 std::move(Arg.ConstantEvolutionLoopExitValue)),
10732 ValuesAtScopes(std::move(Arg.ValuesAtScopes)),
10733 LoopDispositions(std::move(Arg.LoopDispositions)),
10734 LoopPropertiesCache(std::move(Arg.LoopPropertiesCache)),
10735 BlockDispositions(std::move(Arg.BlockDispositions)),
10736 UnsignedRanges(std::move(Arg.UnsignedRanges)),
10737 SignedRanges(std::move(Arg.SignedRanges)),
10738 UniqueSCEVs(std::move(Arg.UniqueSCEVs)),
10739 UniquePreds(std::move(Arg.UniquePreds)),
10740 SCEVAllocator(std::move(Arg.SCEVAllocator)),
10741 LoopUsers(std::move(Arg.LoopUsers)),
10742 PredicatedSCEVRewrites(std::move(Arg.PredicatedSCEVRewrites)),
10743 FirstUnknown(Arg.FirstUnknown) {
10744 Arg.FirstUnknown = nullptr;
10747 ScalarEvolution::~ScalarEvolution() {
10748 // Iterate through all the SCEVUnknown instances and call their
10749 // destructors, so that they release their references to their values.
10750 for (SCEVUnknown *U = FirstUnknown; U;) {
10751 SCEVUnknown *Tmp = U;
10753 Tmp->~SCEVUnknown();
10755 FirstUnknown = nullptr;
10757 ExprValueMap.clear();
10758 ValueExprMap.clear();
10761 // Free any extra memory created for ExitNotTakenInfo in the unlikely event
10762 // that a loop had multiple computable exits.
10763 for (auto &BTCI : BackedgeTakenCounts)
10764 BTCI.second.clear();
10765 for (auto &BTCI : PredicatedBackedgeTakenCounts)
10766 BTCI.second.clear();
10768 assert(PendingLoopPredicates.empty() && "isImpliedCond garbage");
10769 assert(!WalkingBEDominatingConds && "isLoopBackedgeGuardedByCond garbage!");
10770 assert(!ProvingSplitPredicate && "ProvingSplitPredicate garbage!");
10773 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
10774 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
10777 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
10779 // Print all inner loops first
10781 PrintLoopInfo(OS, SE, I);
10784 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
10787 SmallVector<BasicBlock *, 8> ExitBlocks;
10788 L->getExitBlocks(ExitBlocks);
10789 if (ExitBlocks.size() != 1)
10790 OS << "<multiple exits> ";
10792 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
10793 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
10795 OS << "Unpredictable backedge-taken count. ";
10800 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
10803 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
10804 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
10805 if (SE->isBackedgeTakenCountMaxOrZero(L))
10806 OS << ", actual taken count either this or zero.";
10808 OS << "Unpredictable max backedge-taken count. ";
10813 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
10816 SCEVUnionPredicate Pred;
10817 auto PBT = SE->getPredicatedBackedgeTakenCount(L, Pred);
10818 if (!isa<SCEVCouldNotCompute>(PBT)) {
10819 OS << "Predicated backedge-taken count is " << *PBT << "\n";
10820 OS << " Predicates:\n";
10823 OS << "Unpredictable predicated backedge-taken count. ";
10827 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
10829 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
10831 OS << "Trip multiple is " << SE->getSmallConstantTripMultiple(L) << "\n";
10835 static StringRef loopDispositionToStr(ScalarEvolution::LoopDisposition LD) {
10837 case ScalarEvolution::LoopVariant:
10839 case ScalarEvolution::LoopInvariant:
10840 return "Invariant";
10841 case ScalarEvolution::LoopComputable:
10842 return "Computable";
10844 llvm_unreachable("Unknown ScalarEvolution::LoopDisposition kind!");
10847 void ScalarEvolution::print(raw_ostream &OS) const {
10848 // ScalarEvolution's implementation of the print method is to print
10849 // out SCEV values of all instructions that are interesting. Doing
10850 // this potentially causes it to create new SCEV objects though,
10851 // which technically conflicts with the const qualifier. This isn't
10852 // observable from outside the class though, so casting away the
10853 // const isn't dangerous.
10854 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
10856 OS << "Classifying expressions for: ";
10857 F.printAsOperand(OS, /*PrintType=*/false);
10859 for (Instruction &I : instructions(F))
10860 if (isSCEVable(I.getType()) && !isa<CmpInst>(I)) {
10863 const SCEV *SV = SE.getSCEV(&I);
10865 if (!isa<SCEVCouldNotCompute>(SV)) {
10867 SE.getUnsignedRange(SV).print(OS);
10869 SE.getSignedRange(SV).print(OS);
10872 const Loop *L = LI.getLoopFor(I.getParent());
10874 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
10878 if (!isa<SCEVCouldNotCompute>(AtUse)) {
10880 SE.getUnsignedRange(AtUse).print(OS);
10882 SE.getSignedRange(AtUse).print(OS);
10887 OS << "\t\t" "Exits: ";
10888 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
10889 if (!SE.isLoopInvariant(ExitValue, L)) {
10890 OS << "<<Unknown>>";
10896 for (auto *Iter = L; Iter; Iter = Iter->getParentLoop()) {
10898 OS << "\t\t" "LoopDispositions: { ";
10904 Iter->getHeader()->printAsOperand(OS, /*PrintType=*/false);
10905 OS << ": " << loopDispositionToStr(SE.getLoopDisposition(SV, Iter));
10908 for (auto *InnerL : depth_first(L)) {
10912 OS << "\t\t" "LoopDispositions: { ";
10918 InnerL->getHeader()->printAsOperand(OS, /*PrintType=*/false);
10919 OS << ": " << loopDispositionToStr(SE.getLoopDisposition(SV, InnerL));
10928 OS << "Determining loop execution counts for: ";
10929 F.printAsOperand(OS, /*PrintType=*/false);
10932 PrintLoopInfo(OS, &SE, I);
10935 ScalarEvolution::LoopDisposition
10936 ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) {
10937 auto &Values = LoopDispositions[S];
10938 for (auto &V : Values) {
10939 if (V.getPointer() == L)
10942 Values.emplace_back(L, LoopVariant);
10943 LoopDisposition D = computeLoopDisposition(S, L);
10944 auto &Values2 = LoopDispositions[S];
10945 for (auto &V : make_range(Values2.rbegin(), Values2.rend())) {
10946 if (V.getPointer() == L) {
10954 ScalarEvolution::LoopDisposition
10955 ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) {
10956 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
10958 return LoopInvariant;
10962 return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L);
10963 case scAddRecExpr: {
10964 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
10966 // If L is the addrec's loop, it's computable.
10967 if (AR->getLoop() == L)
10968 return LoopComputable;
10970 // Add recurrences are never invariant in the function-body (null loop).
10972 return LoopVariant;
10974 // Everything that is not defined at loop entry is variant.
10975 if (DT.dominates(L->getHeader(), AR->getLoop()->getHeader()))
10976 return LoopVariant;
10977 assert(!L->contains(AR->getLoop()) && "Containing loop's header does not"
10978 " dominate the contained loop's header?");
10980 // This recurrence is invariant w.r.t. L if AR's loop contains L.
10981 if (AR->getLoop()->contains(L))
10982 return LoopInvariant;
10984 // This recurrence is variant w.r.t. L if any of its operands
10986 for (auto *Op : AR->operands())
10987 if (!isLoopInvariant(Op, L))
10988 return LoopVariant;
10990 // Otherwise it's loop-invariant.
10991 return LoopInvariant;
10997 bool HasVarying = false;
10998 for (auto *Op : cast<SCEVNAryExpr>(S)->operands()) {
10999 LoopDisposition D = getLoopDisposition(Op, L);
11000 if (D == LoopVariant)
11001 return LoopVariant;
11002 if (D == LoopComputable)
11005 return HasVarying ? LoopComputable : LoopInvariant;
11008 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
11009 LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L);
11010 if (LD == LoopVariant)
11011 return LoopVariant;
11012 LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L);
11013 if (RD == LoopVariant)
11014 return LoopVariant;
11015 return (LD == LoopInvariant && RD == LoopInvariant) ?
11016 LoopInvariant : LoopComputable;
11019 // All non-instruction values are loop invariant. All instructions are loop
11020 // invariant if they are not contained in the specified loop.
11021 // Instructions are never considered invariant in the function body
11022 // (null loop) because they are defined within the "loop".
11023 if (auto *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue()))
11024 return (L && !L->contains(I)) ? LoopInvariant : LoopVariant;
11025 return LoopInvariant;
11026 case scCouldNotCompute:
11027 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
11029 llvm_unreachable("Unknown SCEV kind!");
11032 bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) {
11033 return getLoopDisposition(S, L) == LoopInvariant;
11036 bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) {
11037 return getLoopDisposition(S, L) == LoopComputable;
11040 ScalarEvolution::BlockDisposition
11041 ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) {
11042 auto &Values = BlockDispositions[S];
11043 for (auto &V : Values) {
11044 if (V.getPointer() == BB)
11047 Values.emplace_back(BB, DoesNotDominateBlock);
11048 BlockDisposition D = computeBlockDisposition(S, BB);
11049 auto &Values2 = BlockDispositions[S];
11050 for (auto &V : make_range(Values2.rbegin(), Values2.rend())) {
11051 if (V.getPointer() == BB) {
11059 ScalarEvolution::BlockDisposition
11060 ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) {
11061 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
11063 return ProperlyDominatesBlock;
11067 return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB);
11068 case scAddRecExpr: {
11069 // This uses a "dominates" query instead of "properly dominates" query
11070 // to test for proper dominance too, because the instruction which
11071 // produces the addrec's value is a PHI, and a PHI effectively properly
11072 // dominates its entire containing block.
11073 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
11074 if (!DT.dominates(AR->getLoop()->getHeader(), BB))
11075 return DoesNotDominateBlock;
11077 // Fall through into SCEVNAryExpr handling.
11084 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
11085 bool Proper = true;
11086 for (const SCEV *NAryOp : NAry->operands()) {
11087 BlockDisposition D = getBlockDisposition(NAryOp, BB);
11088 if (D == DoesNotDominateBlock)
11089 return DoesNotDominateBlock;
11090 if (D == DominatesBlock)
11093 return Proper ? ProperlyDominatesBlock : DominatesBlock;
11096 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
11097 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
11098 BlockDisposition LD = getBlockDisposition(LHS, BB);
11099 if (LD == DoesNotDominateBlock)
11100 return DoesNotDominateBlock;
11101 BlockDisposition RD = getBlockDisposition(RHS, BB);
11102 if (RD == DoesNotDominateBlock)
11103 return DoesNotDominateBlock;
11104 return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ?
11105 ProperlyDominatesBlock : DominatesBlock;
11108 if (Instruction *I =
11109 dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) {
11110 if (I->getParent() == BB)
11111 return DominatesBlock;
11112 if (DT.properlyDominates(I->getParent(), BB))
11113 return ProperlyDominatesBlock;
11114 return DoesNotDominateBlock;
11116 return ProperlyDominatesBlock;
11117 case scCouldNotCompute:
11118 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
11120 llvm_unreachable("Unknown SCEV kind!");
11123 bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) {
11124 return getBlockDisposition(S, BB) >= DominatesBlock;
11127 bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) {
11128 return getBlockDisposition(S, BB) == ProperlyDominatesBlock;
11131 bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const {
11132 return SCEVExprContains(S, [&](const SCEV *Expr) { return Expr == Op; });
11135 bool ScalarEvolution::ExitLimit::hasOperand(const SCEV *S) const {
11136 auto IsS = [&](const SCEV *X) { return S == X; };
11137 auto ContainsS = [&](const SCEV *X) {
11138 return !isa<SCEVCouldNotCompute>(X) && SCEVExprContains(X, IsS);
11140 return ContainsS(ExactNotTaken) || ContainsS(MaxNotTaken);
11144 ScalarEvolution::forgetMemoizedResults(const SCEV *S) {
11145 ValuesAtScopes.erase(S);
11146 LoopDispositions.erase(S);
11147 BlockDispositions.erase(S);
11148 UnsignedRanges.erase(S);
11149 SignedRanges.erase(S);
11150 ExprValueMap.erase(S);
11151 HasRecMap.erase(S);
11152 MinTrailingZerosCache.erase(S);
11154 for (auto I = PredicatedSCEVRewrites.begin();
11155 I != PredicatedSCEVRewrites.end();) {
11156 std::pair<const SCEV *, const Loop *> Entry = I->first;
11157 if (Entry.first == S)
11158 PredicatedSCEVRewrites.erase(I++);
11163 auto RemoveSCEVFromBackedgeMap =
11164 [S, this](DenseMap<const Loop *, BackedgeTakenInfo> &Map) {
11165 for (auto I = Map.begin(), E = Map.end(); I != E;) {
11166 BackedgeTakenInfo &BEInfo = I->second;
11167 if (BEInfo.hasOperand(S, this)) {
11175 RemoveSCEVFromBackedgeMap(BackedgeTakenCounts);
11176 RemoveSCEVFromBackedgeMap(PredicatedBackedgeTakenCounts);
11179 void ScalarEvolution::addToLoopUseLists(const SCEV *S) {
11180 struct FindUsedLoops {
11181 SmallPtrSet<const Loop *, 8> LoopsUsed;
11182 bool follow(const SCEV *S) {
11183 if (auto *AR = dyn_cast<SCEVAddRecExpr>(S))
11184 LoopsUsed.insert(AR->getLoop());
11188 bool isDone() const { return false; }
11192 SCEVTraversal<FindUsedLoops>(F).visitAll(S);
11194 for (auto *L : F.LoopsUsed)
11195 LoopUsers[L].push_back(S);
11198 void ScalarEvolution::verify() const {
11199 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
11200 ScalarEvolution SE2(F, TLI, AC, DT, LI);
11202 SmallVector<Loop *, 8> LoopStack(LI.begin(), LI.end());
11204 // Map's SCEV expressions from one ScalarEvolution "universe" to another.
11205 struct SCEVMapper : public SCEVRewriteVisitor<SCEVMapper> {
11206 SCEVMapper(ScalarEvolution &SE) : SCEVRewriteVisitor<SCEVMapper>(SE) {}
11208 const SCEV *visitConstant(const SCEVConstant *Constant) {
11209 return SE.getConstant(Constant->getAPInt());
11212 const SCEV *visitUnknown(const SCEVUnknown *Expr) {
11213 return SE.getUnknown(Expr->getValue());
11216 const SCEV *visitCouldNotCompute(const SCEVCouldNotCompute *Expr) {
11217 return SE.getCouldNotCompute();
11221 SCEVMapper SCM(SE2);
11223 while (!LoopStack.empty()) {
11224 auto *L = LoopStack.pop_back_val();
11225 LoopStack.insert(LoopStack.end(), L->begin(), L->end());
11227 auto *CurBECount = SCM.visit(
11228 const_cast<ScalarEvolution *>(this)->getBackedgeTakenCount(L));
11229 auto *NewBECount = SE2.getBackedgeTakenCount(L);
11231 if (CurBECount == SE2.getCouldNotCompute() ||
11232 NewBECount == SE2.getCouldNotCompute()) {
11233 // NB! This situation is legal, but is very suspicious -- whatever pass
11234 // change the loop to make a trip count go from could not compute to
11235 // computable or vice-versa *should have* invalidated SCEV. However, we
11236 // choose not to assert here (for now) since we don't want false
11241 if (containsUndefs(CurBECount) || containsUndefs(NewBECount)) {
11242 // SCEV treats "undef" as an unknown but consistent value (i.e. it does
11243 // not propagate undef aggressively). This means we can (and do) fail
11244 // verification in cases where a transform makes the trip count of a loop
11245 // go from "undef" to "undef+1" (say). The transform is fine, since in
11246 // both cases the loop iterates "undef" times, but SCEV thinks we
11247 // increased the trip count of the loop by 1 incorrectly.
11251 if (SE.getTypeSizeInBits(CurBECount->getType()) >
11252 SE.getTypeSizeInBits(NewBECount->getType()))
11253 NewBECount = SE2.getZeroExtendExpr(NewBECount, CurBECount->getType());
11254 else if (SE.getTypeSizeInBits(CurBECount->getType()) <
11255 SE.getTypeSizeInBits(NewBECount->getType()))
11256 CurBECount = SE2.getZeroExtendExpr(CurBECount, NewBECount->getType());
11258 auto *ConstantDelta =
11259 dyn_cast<SCEVConstant>(SE2.getMinusSCEV(CurBECount, NewBECount));
11261 if (ConstantDelta && ConstantDelta->getAPInt() != 0) {
11262 dbgs() << "Trip Count Changed!\n";
11263 dbgs() << "Old: " << *CurBECount << "\n";
11264 dbgs() << "New: " << *NewBECount << "\n";
11265 dbgs() << "Delta: " << *ConstantDelta << "\n";
11271 bool ScalarEvolution::invalidate(
11272 Function &F, const PreservedAnalyses &PA,
11273 FunctionAnalysisManager::Invalidator &Inv) {
11274 // Invalidate the ScalarEvolution object whenever it isn't preserved or one
11275 // of its dependencies is invalidated.
11276 auto PAC = PA.getChecker<ScalarEvolutionAnalysis>();
11277 return !(PAC.preserved() || PAC.preservedSet<AllAnalysesOn<Function>>()) ||
11278 Inv.invalidate<AssumptionAnalysis>(F, PA) ||
11279 Inv.invalidate<DominatorTreeAnalysis>(F, PA) ||
11280 Inv.invalidate<LoopAnalysis>(F, PA);
11283 AnalysisKey ScalarEvolutionAnalysis::Key;
11285 ScalarEvolution ScalarEvolutionAnalysis::run(Function &F,
11286 FunctionAnalysisManager &AM) {
11287 return ScalarEvolution(F, AM.getResult<TargetLibraryAnalysis>(F),
11288 AM.getResult<AssumptionAnalysis>(F),
11289 AM.getResult<DominatorTreeAnalysis>(F),
11290 AM.getResult<LoopAnalysis>(F));
11294 ScalarEvolutionPrinterPass::run(Function &F, FunctionAnalysisManager &AM) {
11295 AM.getResult<ScalarEvolutionAnalysis>(F).print(OS);
11296 return PreservedAnalyses::all();
11299 INITIALIZE_PASS_BEGIN(ScalarEvolutionWrapperPass, "scalar-evolution",
11300 "Scalar Evolution Analysis", false, true)
11301 INITIALIZE_PASS_DEPENDENCY(AssumptionCacheTracker)
11302 INITIALIZE_PASS_DEPENDENCY(LoopInfoWrapperPass)
11303 INITIALIZE_PASS_DEPENDENCY(DominatorTreeWrapperPass)
11304 INITIALIZE_PASS_DEPENDENCY(TargetLibraryInfoWrapperPass)
11305 INITIALIZE_PASS_END(ScalarEvolutionWrapperPass, "scalar-evolution",
11306 "Scalar Evolution Analysis", false, true)
11308 char ScalarEvolutionWrapperPass::ID = 0;
11310 ScalarEvolutionWrapperPass::ScalarEvolutionWrapperPass() : FunctionPass(ID) {
11311 initializeScalarEvolutionWrapperPassPass(*PassRegistry::getPassRegistry());
11314 bool ScalarEvolutionWrapperPass::runOnFunction(Function &F) {
11315 SE.reset(new ScalarEvolution(
11316 F, getAnalysis<TargetLibraryInfoWrapperPass>().getTLI(),
11317 getAnalysis<AssumptionCacheTracker>().getAssumptionCache(F),
11318 getAnalysis<DominatorTreeWrapperPass>().getDomTree(),
11319 getAnalysis<LoopInfoWrapperPass>().getLoopInfo()));
11323 void ScalarEvolutionWrapperPass::releaseMemory() { SE.reset(); }
11325 void ScalarEvolutionWrapperPass::print(raw_ostream &OS, const Module *) const {
11329 void ScalarEvolutionWrapperPass::verifyAnalysis() const {
11336 void ScalarEvolutionWrapperPass::getAnalysisUsage(AnalysisUsage &AU) const {
11337 AU.setPreservesAll();
11338 AU.addRequiredTransitive<AssumptionCacheTracker>();
11339 AU.addRequiredTransitive<LoopInfoWrapperPass>();
11340 AU.addRequiredTransitive<DominatorTreeWrapperPass>();
11341 AU.addRequiredTransitive<TargetLibraryInfoWrapperPass>();
11344 const SCEVPredicate *ScalarEvolution::getEqualPredicate(const SCEV *LHS,
11346 FoldingSetNodeID ID;
11347 assert(LHS->getType() == RHS->getType() &&
11348 "Type mismatch between LHS and RHS");
11349 // Unique this node based on the arguments
11350 ID.AddInteger(SCEVPredicate::P_Equal);
11351 ID.AddPointer(LHS);
11352 ID.AddPointer(RHS);
11353 void *IP = nullptr;
11354 if (const auto *S = UniquePreds.FindNodeOrInsertPos(ID, IP))
11356 SCEVEqualPredicate *Eq = new (SCEVAllocator)
11357 SCEVEqualPredicate(ID.Intern(SCEVAllocator), LHS, RHS);
11358 UniquePreds.InsertNode(Eq, IP);
11362 const SCEVPredicate *ScalarEvolution::getWrapPredicate(
11363 const SCEVAddRecExpr *AR,
11364 SCEVWrapPredicate::IncrementWrapFlags AddedFlags) {
11365 FoldingSetNodeID ID;
11366 // Unique this node based on the arguments
11367 ID.AddInteger(SCEVPredicate::P_Wrap);
11369 ID.AddInteger(AddedFlags);
11370 void *IP = nullptr;
11371 if (const auto *S = UniquePreds.FindNodeOrInsertPos(ID, IP))
11373 auto *OF = new (SCEVAllocator)
11374 SCEVWrapPredicate(ID.Intern(SCEVAllocator), AR, AddedFlags);
11375 UniquePreds.InsertNode(OF, IP);
11381 class SCEVPredicateRewriter : public SCEVRewriteVisitor<SCEVPredicateRewriter> {
11384 /// Rewrites \p S in the context of a loop L and the SCEV predication
11385 /// infrastructure.
11387 /// If \p Pred is non-null, the SCEV expression is rewritten to respect the
11388 /// equivalences present in \p Pred.
11390 /// If \p NewPreds is non-null, rewrite is free to add further predicates to
11391 /// \p NewPreds such that the result will be an AddRecExpr.
11392 static const SCEV *rewrite(const SCEV *S, const Loop *L, ScalarEvolution &SE,
11393 SmallPtrSetImpl<const SCEVPredicate *> *NewPreds,
11394 SCEVUnionPredicate *Pred) {
11395 SCEVPredicateRewriter Rewriter(L, SE, NewPreds, Pred);
11396 return Rewriter.visit(S);
11399 const SCEV *visitUnknown(const SCEVUnknown *Expr) {
11401 auto ExprPreds = Pred->getPredicatesForExpr(Expr);
11402 for (auto *Pred : ExprPreds)
11403 if (const auto *IPred = dyn_cast<SCEVEqualPredicate>(Pred))
11404 if (IPred->getLHS() == Expr)
11405 return IPred->getRHS();
11407 return convertToAddRecWithPreds(Expr);
11410 const SCEV *visitZeroExtendExpr(const SCEVZeroExtendExpr *Expr) {
11411 const SCEV *Operand = visit(Expr->getOperand());
11412 const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Operand);
11413 if (AR && AR->getLoop() == L && AR->isAffine()) {
11414 // This couldn't be folded because the operand didn't have the nuw
11415 // flag. Add the nusw flag as an assumption that we could make.
11416 const SCEV *Step = AR->getStepRecurrence(SE);
11417 Type *Ty = Expr->getType();
11418 if (addOverflowAssumption(AR, SCEVWrapPredicate::IncrementNUSW))
11419 return SE.getAddRecExpr(SE.getZeroExtendExpr(AR->getStart(), Ty),
11420 SE.getSignExtendExpr(Step, Ty), L,
11421 AR->getNoWrapFlags());
11423 return SE.getZeroExtendExpr(Operand, Expr->getType());
11426 const SCEV *visitSignExtendExpr(const SCEVSignExtendExpr *Expr) {
11427 const SCEV *Operand = visit(Expr->getOperand());
11428 const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Operand);
11429 if (AR && AR->getLoop() == L && AR->isAffine()) {
11430 // This couldn't be folded because the operand didn't have the nsw
11431 // flag. Add the nssw flag as an assumption that we could make.
11432 const SCEV *Step = AR->getStepRecurrence(SE);
11433 Type *Ty = Expr->getType();
11434 if (addOverflowAssumption(AR, SCEVWrapPredicate::IncrementNSSW))
11435 return SE.getAddRecExpr(SE.getSignExtendExpr(AR->getStart(), Ty),
11436 SE.getSignExtendExpr(Step, Ty), L,
11437 AR->getNoWrapFlags());
11439 return SE.getSignExtendExpr(Operand, Expr->getType());
11443 explicit SCEVPredicateRewriter(const Loop *L, ScalarEvolution &SE,
11444 SmallPtrSetImpl<const SCEVPredicate *> *NewPreds,
11445 SCEVUnionPredicate *Pred)
11446 : SCEVRewriteVisitor(SE), NewPreds(NewPreds), Pred(Pred), L(L) {}
11448 bool addOverflowAssumption(const SCEVPredicate *P) {
11450 // Check if we've already made this assumption.
11451 return Pred && Pred->implies(P);
11453 NewPreds->insert(P);
11457 bool addOverflowAssumption(const SCEVAddRecExpr *AR,
11458 SCEVWrapPredicate::IncrementWrapFlags AddedFlags) {
11459 auto *A = SE.getWrapPredicate(AR, AddedFlags);
11460 return addOverflowAssumption(A);
11463 // If \p Expr represents a PHINode, we try to see if it can be represented
11464 // as an AddRec, possibly under a predicate (PHISCEVPred). If it is possible
11465 // to add this predicate as a runtime overflow check, we return the AddRec.
11466 // If \p Expr does not meet these conditions (is not a PHI node, or we
11467 // couldn't create an AddRec for it, or couldn't add the predicate), we just
11469 const SCEV *convertToAddRecWithPreds(const SCEVUnknown *Expr) {
11470 if (!isa<PHINode>(Expr->getValue()))
11472 Optional<std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>>
11473 PredicatedRewrite = SE.createAddRecFromPHIWithCasts(Expr);
11474 if (!PredicatedRewrite)
11476 for (auto *P : PredicatedRewrite->second){
11477 if (!addOverflowAssumption(P))
11480 return PredicatedRewrite->first;
11483 SmallPtrSetImpl<const SCEVPredicate *> *NewPreds;
11484 SCEVUnionPredicate *Pred;
11488 } // end anonymous namespace
11490 const SCEV *ScalarEvolution::rewriteUsingPredicate(const SCEV *S, const Loop *L,
11491 SCEVUnionPredicate &Preds) {
11492 return SCEVPredicateRewriter::rewrite(S, L, *this, nullptr, &Preds);
11495 const SCEVAddRecExpr *ScalarEvolution::convertSCEVToAddRecWithPredicates(
11496 const SCEV *S, const Loop *L,
11497 SmallPtrSetImpl<const SCEVPredicate *> &Preds) {
11498 SmallPtrSet<const SCEVPredicate *, 4> TransformPreds;
11499 S = SCEVPredicateRewriter::rewrite(S, L, *this, &TransformPreds, nullptr);
11500 auto *AddRec = dyn_cast<SCEVAddRecExpr>(S);
11505 // Since the transformation was successful, we can now transfer the SCEV
11507 for (auto *P : TransformPreds)
11513 /// SCEV predicates
11514 SCEVPredicate::SCEVPredicate(const FoldingSetNodeIDRef ID,
11515 SCEVPredicateKind Kind)
11516 : FastID(ID), Kind(Kind) {}
11518 SCEVEqualPredicate::SCEVEqualPredicate(const FoldingSetNodeIDRef ID,
11519 const SCEV *LHS, const SCEV *RHS)
11520 : SCEVPredicate(ID, P_Equal), LHS(LHS), RHS(RHS) {
11521 assert(LHS->getType() == RHS->getType() && "LHS and RHS types don't match");
11522 assert(LHS != RHS && "LHS and RHS are the same SCEV");
11525 bool SCEVEqualPredicate::implies(const SCEVPredicate *N) const {
11526 const auto *Op = dyn_cast<SCEVEqualPredicate>(N);
11531 return Op->LHS == LHS && Op->RHS == RHS;
11534 bool SCEVEqualPredicate::isAlwaysTrue() const { return false; }
11536 const SCEV *SCEVEqualPredicate::getExpr() const { return LHS; }
11538 void SCEVEqualPredicate::print(raw_ostream &OS, unsigned Depth) const {
11539 OS.indent(Depth) << "Equal predicate: " << *LHS << " == " << *RHS << "\n";
11542 SCEVWrapPredicate::SCEVWrapPredicate(const FoldingSetNodeIDRef ID,
11543 const SCEVAddRecExpr *AR,
11544 IncrementWrapFlags Flags)
11545 : SCEVPredicate(ID, P_Wrap), AR(AR), Flags(Flags) {}
11547 const SCEV *SCEVWrapPredicate::getExpr() const { return AR; }
11549 bool SCEVWrapPredicate::implies(const SCEVPredicate *N) const {
11550 const auto *Op = dyn_cast<SCEVWrapPredicate>(N);
11552 return Op && Op->AR == AR && setFlags(Flags, Op->Flags) == Flags;
11555 bool SCEVWrapPredicate::isAlwaysTrue() const {
11556 SCEV::NoWrapFlags ScevFlags = AR->getNoWrapFlags();
11557 IncrementWrapFlags IFlags = Flags;
11559 if (ScalarEvolution::setFlags(ScevFlags, SCEV::FlagNSW) == ScevFlags)
11560 IFlags = clearFlags(IFlags, IncrementNSSW);
11562 return IFlags == IncrementAnyWrap;
11565 void SCEVWrapPredicate::print(raw_ostream &OS, unsigned Depth) const {
11566 OS.indent(Depth) << *getExpr() << " Added Flags: ";
11567 if (SCEVWrapPredicate::IncrementNUSW & getFlags())
11569 if (SCEVWrapPredicate::IncrementNSSW & getFlags())
11574 SCEVWrapPredicate::IncrementWrapFlags
11575 SCEVWrapPredicate::getImpliedFlags(const SCEVAddRecExpr *AR,
11576 ScalarEvolution &SE) {
11577 IncrementWrapFlags ImpliedFlags = IncrementAnyWrap;
11578 SCEV::NoWrapFlags StaticFlags = AR->getNoWrapFlags();
11580 // We can safely transfer the NSW flag as NSSW.
11581 if (ScalarEvolution::setFlags(StaticFlags, SCEV::FlagNSW) == StaticFlags)
11582 ImpliedFlags = IncrementNSSW;
11584 if (ScalarEvolution::setFlags(StaticFlags, SCEV::FlagNUW) == StaticFlags) {
11585 // If the increment is positive, the SCEV NUW flag will also imply the
11586 // WrapPredicate NUSW flag.
11587 if (const auto *Step = dyn_cast<SCEVConstant>(AR->getStepRecurrence(SE)))
11588 if (Step->getValue()->getValue().isNonNegative())
11589 ImpliedFlags = setFlags(ImpliedFlags, IncrementNUSW);
11592 return ImpliedFlags;
11595 /// Union predicates don't get cached so create a dummy set ID for it.
11596 SCEVUnionPredicate::SCEVUnionPredicate()
11597 : SCEVPredicate(FoldingSetNodeIDRef(nullptr, 0), P_Union) {}
11599 bool SCEVUnionPredicate::isAlwaysTrue() const {
11600 return all_of(Preds,
11601 [](const SCEVPredicate *I) { return I->isAlwaysTrue(); });
11604 ArrayRef<const SCEVPredicate *>
11605 SCEVUnionPredicate::getPredicatesForExpr(const SCEV *Expr) {
11606 auto I = SCEVToPreds.find(Expr);
11607 if (I == SCEVToPreds.end())
11608 return ArrayRef<const SCEVPredicate *>();
11612 bool SCEVUnionPredicate::implies(const SCEVPredicate *N) const {
11613 if (const auto *Set = dyn_cast<SCEVUnionPredicate>(N))
11614 return all_of(Set->Preds,
11615 [this](const SCEVPredicate *I) { return this->implies(I); });
11617 auto ScevPredsIt = SCEVToPreds.find(N->getExpr());
11618 if (ScevPredsIt == SCEVToPreds.end())
11620 auto &SCEVPreds = ScevPredsIt->second;
11622 return any_of(SCEVPreds,
11623 [N](const SCEVPredicate *I) { return I->implies(N); });
11626 const SCEV *SCEVUnionPredicate::getExpr() const { return nullptr; }
11628 void SCEVUnionPredicate::print(raw_ostream &OS, unsigned Depth) const {
11629 for (auto Pred : Preds)
11630 Pred->print(OS, Depth);
11633 void SCEVUnionPredicate::add(const SCEVPredicate *N) {
11634 if (const auto *Set = dyn_cast<SCEVUnionPredicate>(N)) {
11635 for (auto Pred : Set->Preds)
11643 const SCEV *Key = N->getExpr();
11644 assert(Key && "Only SCEVUnionPredicate doesn't have an "
11645 " associated expression!");
11647 SCEVToPreds[Key].push_back(N);
11648 Preds.push_back(N);
11651 PredicatedScalarEvolution::PredicatedScalarEvolution(ScalarEvolution &SE,
11655 const SCEV *PredicatedScalarEvolution::getSCEV(Value *V) {
11656 const SCEV *Expr = SE.getSCEV(V);
11657 RewriteEntry &Entry = RewriteMap[Expr];
11659 // If we already have an entry and the version matches, return it.
11660 if (Entry.second && Generation == Entry.first)
11661 return Entry.second;
11663 // We found an entry but it's stale. Rewrite the stale entry
11664 // according to the current predicate.
11666 Expr = Entry.second;
11668 const SCEV *NewSCEV = SE.rewriteUsingPredicate(Expr, &L, Preds);
11669 Entry = {Generation, NewSCEV};
11674 const SCEV *PredicatedScalarEvolution::getBackedgeTakenCount() {
11675 if (!BackedgeCount) {
11676 SCEVUnionPredicate BackedgePred;
11677 BackedgeCount = SE.getPredicatedBackedgeTakenCount(&L, BackedgePred);
11678 addPredicate(BackedgePred);
11680 return BackedgeCount;
11683 void PredicatedScalarEvolution::addPredicate(const SCEVPredicate &Pred) {
11684 if (Preds.implies(&Pred))
11687 updateGeneration();
11690 const SCEVUnionPredicate &PredicatedScalarEvolution::getUnionPredicate() const {
11694 void PredicatedScalarEvolution::updateGeneration() {
11695 // If the generation number wrapped recompute everything.
11696 if (++Generation == 0) {
11697 for (auto &II : RewriteMap) {
11698 const SCEV *Rewritten = II.second.second;
11699 II.second = {Generation, SE.rewriteUsingPredicate(Rewritten, &L, Preds)};
11704 void PredicatedScalarEvolution::setNoOverflow(
11705 Value *V, SCEVWrapPredicate::IncrementWrapFlags Flags) {
11706 const SCEV *Expr = getSCEV(V);
11707 const auto *AR = cast<SCEVAddRecExpr>(Expr);
11709 auto ImpliedFlags = SCEVWrapPredicate::getImpliedFlags(AR, SE);
11711 // Clear the statically implied flags.
11712 Flags = SCEVWrapPredicate::clearFlags(Flags, ImpliedFlags);
11713 addPredicate(*SE.getWrapPredicate(AR, Flags));
11715 auto II = FlagsMap.insert({V, Flags});
11717 II.first->second = SCEVWrapPredicate::setFlags(Flags, II.first->second);
11720 bool PredicatedScalarEvolution::hasNoOverflow(
11721 Value *V, SCEVWrapPredicate::IncrementWrapFlags Flags) {
11722 const SCEV *Expr = getSCEV(V);
11723 const auto *AR = cast<SCEVAddRecExpr>(Expr);
11725 Flags = SCEVWrapPredicate::clearFlags(
11726 Flags, SCEVWrapPredicate::getImpliedFlags(AR, SE));
11728 auto II = FlagsMap.find(V);
11730 if (II != FlagsMap.end())
11731 Flags = SCEVWrapPredicate::clearFlags(Flags, II->second);
11733 return Flags == SCEVWrapPredicate::IncrementAnyWrap;
11736 const SCEVAddRecExpr *PredicatedScalarEvolution::getAsAddRec(Value *V) {
11737 const SCEV *Expr = this->getSCEV(V);
11738 SmallPtrSet<const SCEVPredicate *, 4> NewPreds;
11739 auto *New = SE.convertSCEVToAddRecWithPredicates(Expr, &L, NewPreds);
11744 for (auto *P : NewPreds)
11747 updateGeneration();
11748 RewriteMap[SE.getSCEV(V)] = {Generation, New};
11752 PredicatedScalarEvolution::PredicatedScalarEvolution(
11753 const PredicatedScalarEvolution &Init)
11754 : RewriteMap(Init.RewriteMap), SE(Init.SE), L(Init.L), Preds(Init.Preds),
11755 Generation(Init.Generation), BackedgeCount(Init.BackedgeCount) {
11756 for (const auto &I : Init.FlagsMap)
11757 FlagsMap.insert(I);
11760 void PredicatedScalarEvolution::print(raw_ostream &OS, unsigned Depth) const {
11762 for (auto *BB : L.getBlocks())
11763 for (auto &I : *BB) {
11764 if (!SE.isSCEVable(I.getType()))
11767 auto *Expr = SE.getSCEV(&I);
11768 auto II = RewriteMap.find(Expr);
11770 if (II == RewriteMap.end())
11773 // Don't print things that are not interesting.
11774 if (II->second.second == Expr)
11777 OS.indent(Depth) << "[PSE]" << I << ":\n";
11778 OS.indent(Depth + 2) << *Expr << "\n";
11779 OS.indent(Depth + 2) << "--> " << *II->second.second << "\n";