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/Optional.h"
63 #include "llvm/ADT/STLExtras.h"
64 #include "llvm/ADT/ScopeExit.h"
65 #include "llvm/ADT/Sequence.h"
66 #include "llvm/ADT/SmallPtrSet.h"
67 #include "llvm/ADT/Statistic.h"
68 #include "llvm/Analysis/AssumptionCache.h"
69 #include "llvm/Analysis/ConstantFolding.h"
70 #include "llvm/Analysis/InstructionSimplify.h"
71 #include "llvm/Analysis/LoopInfo.h"
72 #include "llvm/Analysis/ScalarEvolutionExpressions.h"
73 #include "llvm/Analysis/TargetLibraryInfo.h"
74 #include "llvm/Analysis/ValueTracking.h"
75 #include "llvm/IR/ConstantRange.h"
76 #include "llvm/IR/Constants.h"
77 #include "llvm/IR/DataLayout.h"
78 #include "llvm/IR/DerivedTypes.h"
79 #include "llvm/IR/Dominators.h"
80 #include "llvm/IR/GetElementPtrTypeIterator.h"
81 #include "llvm/IR/GlobalAlias.h"
82 #include "llvm/IR/GlobalVariable.h"
83 #include "llvm/IR/InstIterator.h"
84 #include "llvm/IR/Instructions.h"
85 #include "llvm/IR/LLVMContext.h"
86 #include "llvm/IR/Metadata.h"
87 #include "llvm/IR/Operator.h"
88 #include "llvm/IR/PatternMatch.h"
89 #include "llvm/Support/CommandLine.h"
90 #include "llvm/Support/Debug.h"
91 #include "llvm/Support/ErrorHandling.h"
92 #include "llvm/Support/MathExtras.h"
93 #include "llvm/Support/raw_ostream.h"
94 #include "llvm/Support/SaveAndRestore.h"
98 #define DEBUG_TYPE "scalar-evolution"
100 STATISTIC(NumArrayLenItCounts,
101 "Number of trip counts computed with array length");
102 STATISTIC(NumTripCountsComputed,
103 "Number of loops with predictable loop counts");
104 STATISTIC(NumTripCountsNotComputed,
105 "Number of loops without predictable loop counts");
106 STATISTIC(NumBruteForceTripCountsComputed,
107 "Number of loops with trip counts computed by force");
109 static cl::opt<unsigned>
110 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
111 cl::desc("Maximum number of iterations SCEV will "
112 "symbolically execute a constant "
116 // FIXME: Enable this with EXPENSIVE_CHECKS when the test suite is clean.
118 VerifySCEV("verify-scev",
119 cl::desc("Verify ScalarEvolution's backedge taken counts (slow)"));
121 VerifySCEVMap("verify-scev-maps",
122 cl::desc("Verify no dangling value in ScalarEvolution's "
123 "ExprValueMap (slow)"));
125 static cl::opt<unsigned> MulOpsInlineThreshold(
126 "scev-mulops-inline-threshold", cl::Hidden,
127 cl::desc("Threshold for inlining multiplication operands into a SCEV"),
130 static cl::opt<unsigned> MaxSCEVCompareDepth(
131 "scalar-evolution-max-scev-compare-depth", cl::Hidden,
132 cl::desc("Maximum depth of recursive SCEV complexity comparisons"),
135 static cl::opt<unsigned> MaxValueCompareDepth(
136 "scalar-evolution-max-value-compare-depth", cl::Hidden,
137 cl::desc("Maximum depth of recursive value complexity comparisons"),
140 //===----------------------------------------------------------------------===//
141 // SCEV class definitions
142 //===----------------------------------------------------------------------===//
144 //===----------------------------------------------------------------------===//
145 // Implementation of the SCEV class.
149 void SCEV::dump() const {
154 void SCEV::print(raw_ostream &OS) const {
155 switch (static_cast<SCEVTypes>(getSCEVType())) {
157 cast<SCEVConstant>(this)->getValue()->printAsOperand(OS, false);
160 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(this);
161 const SCEV *Op = Trunc->getOperand();
162 OS << "(trunc " << *Op->getType() << " " << *Op << " to "
163 << *Trunc->getType() << ")";
167 const SCEVZeroExtendExpr *ZExt = cast<SCEVZeroExtendExpr>(this);
168 const SCEV *Op = ZExt->getOperand();
169 OS << "(zext " << *Op->getType() << " " << *Op << " to "
170 << *ZExt->getType() << ")";
174 const SCEVSignExtendExpr *SExt = cast<SCEVSignExtendExpr>(this);
175 const SCEV *Op = SExt->getOperand();
176 OS << "(sext " << *Op->getType() << " " << *Op << " to "
177 << *SExt->getType() << ")";
181 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(this);
182 OS << "{" << *AR->getOperand(0);
183 for (unsigned i = 1, e = AR->getNumOperands(); i != e; ++i)
184 OS << ",+," << *AR->getOperand(i);
186 if (AR->hasNoUnsignedWrap())
188 if (AR->hasNoSignedWrap())
190 if (AR->hasNoSelfWrap() &&
191 !AR->getNoWrapFlags((NoWrapFlags)(FlagNUW | FlagNSW)))
193 AR->getLoop()->getHeader()->printAsOperand(OS, /*PrintType=*/false);
201 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(this);
202 const char *OpStr = nullptr;
203 switch (NAry->getSCEVType()) {
204 case scAddExpr: OpStr = " + "; break;
205 case scMulExpr: OpStr = " * "; break;
206 case scUMaxExpr: OpStr = " umax "; break;
207 case scSMaxExpr: OpStr = " smax "; break;
210 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
213 if (std::next(I) != E)
217 switch (NAry->getSCEVType()) {
220 if (NAry->hasNoUnsignedWrap())
222 if (NAry->hasNoSignedWrap())
228 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(this);
229 OS << "(" << *UDiv->getLHS() << " /u " << *UDiv->getRHS() << ")";
233 const SCEVUnknown *U = cast<SCEVUnknown>(this);
235 if (U->isSizeOf(AllocTy)) {
236 OS << "sizeof(" << *AllocTy << ")";
239 if (U->isAlignOf(AllocTy)) {
240 OS << "alignof(" << *AllocTy << ")";
246 if (U->isOffsetOf(CTy, FieldNo)) {
247 OS << "offsetof(" << *CTy << ", ";
248 FieldNo->printAsOperand(OS, false);
253 // Otherwise just print it normally.
254 U->getValue()->printAsOperand(OS, false);
257 case scCouldNotCompute:
258 OS << "***COULDNOTCOMPUTE***";
261 llvm_unreachable("Unknown SCEV kind!");
264 Type *SCEV::getType() const {
265 switch (static_cast<SCEVTypes>(getSCEVType())) {
267 return cast<SCEVConstant>(this)->getType();
271 return cast<SCEVCastExpr>(this)->getType();
276 return cast<SCEVNAryExpr>(this)->getType();
278 return cast<SCEVAddExpr>(this)->getType();
280 return cast<SCEVUDivExpr>(this)->getType();
282 return cast<SCEVUnknown>(this)->getType();
283 case scCouldNotCompute:
284 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
286 llvm_unreachable("Unknown SCEV kind!");
289 bool SCEV::isZero() const {
290 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
291 return SC->getValue()->isZero();
295 bool SCEV::isOne() const {
296 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
297 return SC->getValue()->isOne();
301 bool SCEV::isAllOnesValue() const {
302 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
303 return SC->getValue()->isAllOnesValue();
307 bool SCEV::isNonConstantNegative() const {
308 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(this);
309 if (!Mul) return false;
311 // If there is a constant factor, it will be first.
312 const SCEVConstant *SC = dyn_cast<SCEVConstant>(Mul->getOperand(0));
313 if (!SC) return false;
315 // Return true if the value is negative, this matches things like (-42 * V).
316 return SC->getAPInt().isNegative();
319 SCEVCouldNotCompute::SCEVCouldNotCompute() :
320 SCEV(FoldingSetNodeIDRef(), scCouldNotCompute) {}
322 bool SCEVCouldNotCompute::classof(const SCEV *S) {
323 return S->getSCEVType() == scCouldNotCompute;
326 const SCEV *ScalarEvolution::getConstant(ConstantInt *V) {
328 ID.AddInteger(scConstant);
331 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
332 SCEV *S = new (SCEVAllocator) SCEVConstant(ID.Intern(SCEVAllocator), V);
333 UniqueSCEVs.InsertNode(S, IP);
337 const SCEV *ScalarEvolution::getConstant(const APInt &Val) {
338 return getConstant(ConstantInt::get(getContext(), Val));
342 ScalarEvolution::getConstant(Type *Ty, uint64_t V, bool isSigned) {
343 IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty));
344 return getConstant(ConstantInt::get(ITy, V, isSigned));
347 SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID,
348 unsigned SCEVTy, const SCEV *op, Type *ty)
349 : SCEV(ID, SCEVTy), Op(op), Ty(ty) {}
351 SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID,
352 const SCEV *op, Type *ty)
353 : SCEVCastExpr(ID, scTruncate, op, ty) {
354 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
355 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
356 "Cannot truncate non-integer value!");
359 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID,
360 const SCEV *op, Type *ty)
361 : SCEVCastExpr(ID, scZeroExtend, op, ty) {
362 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
363 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
364 "Cannot zero extend non-integer value!");
367 SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID,
368 const SCEV *op, Type *ty)
369 : SCEVCastExpr(ID, scSignExtend, op, ty) {
370 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
371 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
372 "Cannot sign extend non-integer value!");
375 void SCEVUnknown::deleted() {
376 // Clear this SCEVUnknown from various maps.
377 SE->forgetMemoizedResults(this);
379 // Remove this SCEVUnknown from the uniquing map.
380 SE->UniqueSCEVs.RemoveNode(this);
382 // Release the value.
386 void SCEVUnknown::allUsesReplacedWith(Value *New) {
387 // Clear this SCEVUnknown from various maps.
388 SE->forgetMemoizedResults(this);
390 // Remove this SCEVUnknown from the uniquing map.
391 SE->UniqueSCEVs.RemoveNode(this);
393 // Update this SCEVUnknown to point to the new value. This is needed
394 // because there may still be outstanding SCEVs which still point to
399 bool SCEVUnknown::isSizeOf(Type *&AllocTy) const {
400 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
401 if (VCE->getOpcode() == Instruction::PtrToInt)
402 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
403 if (CE->getOpcode() == Instruction::GetElementPtr &&
404 CE->getOperand(0)->isNullValue() &&
405 CE->getNumOperands() == 2)
406 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1)))
408 AllocTy = cast<PointerType>(CE->getOperand(0)->getType())
416 bool SCEVUnknown::isAlignOf(Type *&AllocTy) const {
417 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
418 if (VCE->getOpcode() == Instruction::PtrToInt)
419 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
420 if (CE->getOpcode() == Instruction::GetElementPtr &&
421 CE->getOperand(0)->isNullValue()) {
423 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
424 if (StructType *STy = dyn_cast<StructType>(Ty))
425 if (!STy->isPacked() &&
426 CE->getNumOperands() == 3 &&
427 CE->getOperand(1)->isNullValue()) {
428 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2)))
430 STy->getNumElements() == 2 &&
431 STy->getElementType(0)->isIntegerTy(1)) {
432 AllocTy = STy->getElementType(1);
441 bool SCEVUnknown::isOffsetOf(Type *&CTy, Constant *&FieldNo) const {
442 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
443 if (VCE->getOpcode() == Instruction::PtrToInt)
444 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
445 if (CE->getOpcode() == Instruction::GetElementPtr &&
446 CE->getNumOperands() == 3 &&
447 CE->getOperand(0)->isNullValue() &&
448 CE->getOperand(1)->isNullValue()) {
450 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
451 // Ignore vector types here so that ScalarEvolutionExpander doesn't
452 // emit getelementptrs that index into vectors.
453 if (Ty->isStructTy() || Ty->isArrayTy()) {
455 FieldNo = CE->getOperand(2);
463 //===----------------------------------------------------------------------===//
465 //===----------------------------------------------------------------------===//
467 /// Compare the two values \p LV and \p RV in terms of their "complexity" where
468 /// "complexity" is a partial (and somewhat ad-hoc) relation used to order
469 /// operands in SCEV expressions. \p EqCache is a set of pairs of values that
470 /// have been previously deemed to be "equally complex" by this routine. It is
471 /// intended to avoid exponential time complexity in cases like:
481 /// CompareValueComplexity(%f, %c)
483 /// Since we do not continue running this routine on expression trees once we
484 /// have seen unequal values, there is no need to track them in the cache.
486 CompareValueComplexity(SmallSet<std::pair<Value *, Value *>, 8> &EqCache,
487 const LoopInfo *const LI, Value *LV, Value *RV,
489 if (Depth > MaxValueCompareDepth || EqCache.count({LV, RV}))
492 // Order pointer values after integer values. This helps SCEVExpander form
494 bool LIsPointer = LV->getType()->isPointerTy(),
495 RIsPointer = RV->getType()->isPointerTy();
496 if (LIsPointer != RIsPointer)
497 return (int)LIsPointer - (int)RIsPointer;
499 // Compare getValueID values.
500 unsigned LID = LV->getValueID(), RID = RV->getValueID();
502 return (int)LID - (int)RID;
504 // Sort arguments by their position.
505 if (const auto *LA = dyn_cast<Argument>(LV)) {
506 const auto *RA = cast<Argument>(RV);
507 unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo();
508 return (int)LArgNo - (int)RArgNo;
511 if (const auto *LGV = dyn_cast<GlobalValue>(LV)) {
512 const auto *RGV = cast<GlobalValue>(RV);
514 const auto IsGVNameSemantic = [&](const GlobalValue *GV) {
515 auto LT = GV->getLinkage();
516 return !(GlobalValue::isPrivateLinkage(LT) ||
517 GlobalValue::isInternalLinkage(LT));
520 // Use the names to distinguish the two values, but only if the
521 // names are semantically important.
522 if (IsGVNameSemantic(LGV) && IsGVNameSemantic(RGV))
523 return LGV->getName().compare(RGV->getName());
526 // For instructions, compare their loop depth, and their operand count. This
528 if (const auto *LInst = dyn_cast<Instruction>(LV)) {
529 const auto *RInst = cast<Instruction>(RV);
531 // Compare loop depths.
532 const BasicBlock *LParent = LInst->getParent(),
533 *RParent = RInst->getParent();
534 if (LParent != RParent) {
535 unsigned LDepth = LI->getLoopDepth(LParent),
536 RDepth = LI->getLoopDepth(RParent);
537 if (LDepth != RDepth)
538 return (int)LDepth - (int)RDepth;
541 // Compare the number of operands.
542 unsigned LNumOps = LInst->getNumOperands(),
543 RNumOps = RInst->getNumOperands();
544 if (LNumOps != RNumOps)
545 return (int)LNumOps - (int)RNumOps;
547 for (unsigned Idx : seq(0u, LNumOps)) {
549 CompareValueComplexity(EqCache, LI, LInst->getOperand(Idx),
550 RInst->getOperand(Idx), Depth + 1);
556 EqCache.insert({LV, RV});
560 // Return negative, zero, or positive, if LHS is less than, equal to, or greater
561 // than RHS, respectively. A three-way result allows recursive comparisons to be
563 static int CompareSCEVComplexity(
564 SmallSet<std::pair<const SCEV *, const SCEV *>, 8> &EqCacheSCEV,
565 const LoopInfo *const LI, const SCEV *LHS, const SCEV *RHS,
566 unsigned Depth = 0) {
567 // Fast-path: SCEVs are uniqued so we can do a quick equality check.
571 // Primarily, sort the SCEVs by their getSCEVType().
572 unsigned LType = LHS->getSCEVType(), RType = RHS->getSCEVType();
574 return (int)LType - (int)RType;
576 if (Depth > MaxSCEVCompareDepth || EqCacheSCEV.count({LHS, RHS}))
578 // Aside from the getSCEVType() ordering, the particular ordering
579 // isn't very important except that it's beneficial to be consistent,
580 // so that (a + b) and (b + a) don't end up as different expressions.
581 switch (static_cast<SCEVTypes>(LType)) {
583 const SCEVUnknown *LU = cast<SCEVUnknown>(LHS);
584 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
586 SmallSet<std::pair<Value *, Value *>, 8> EqCache;
587 int X = CompareValueComplexity(EqCache, LI, LU->getValue(), RU->getValue(),
590 EqCacheSCEV.insert({LHS, RHS});
595 const SCEVConstant *LC = cast<SCEVConstant>(LHS);
596 const SCEVConstant *RC = cast<SCEVConstant>(RHS);
598 // Compare constant values.
599 const APInt &LA = LC->getAPInt();
600 const APInt &RA = RC->getAPInt();
601 unsigned LBitWidth = LA.getBitWidth(), RBitWidth = RA.getBitWidth();
602 if (LBitWidth != RBitWidth)
603 return (int)LBitWidth - (int)RBitWidth;
604 return LA.ult(RA) ? -1 : 1;
608 const SCEVAddRecExpr *LA = cast<SCEVAddRecExpr>(LHS);
609 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS);
611 // Compare addrec loop depths.
612 const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop();
613 if (LLoop != RLoop) {
614 unsigned LDepth = LLoop->getLoopDepth(), RDepth = RLoop->getLoopDepth();
615 if (LDepth != RDepth)
616 return (int)LDepth - (int)RDepth;
619 // Addrec complexity grows with operand count.
620 unsigned LNumOps = LA->getNumOperands(), RNumOps = RA->getNumOperands();
621 if (LNumOps != RNumOps)
622 return (int)LNumOps - (int)RNumOps;
624 // Lexicographically compare.
625 for (unsigned i = 0; i != LNumOps; ++i) {
626 int X = CompareSCEVComplexity(EqCacheSCEV, LI, LA->getOperand(i),
627 RA->getOperand(i), Depth + 1);
631 EqCacheSCEV.insert({LHS, RHS});
639 const SCEVNAryExpr *LC = cast<SCEVNAryExpr>(LHS);
640 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
642 // Lexicographically compare n-ary expressions.
643 unsigned LNumOps = LC->getNumOperands(), RNumOps = RC->getNumOperands();
644 if (LNumOps != RNumOps)
645 return (int)LNumOps - (int)RNumOps;
647 for (unsigned i = 0; i != LNumOps; ++i) {
650 int X = CompareSCEVComplexity(EqCacheSCEV, LI, LC->getOperand(i),
651 RC->getOperand(i), Depth + 1);
655 EqCacheSCEV.insert({LHS, RHS});
660 const SCEVUDivExpr *LC = cast<SCEVUDivExpr>(LHS);
661 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
663 // Lexicographically compare udiv expressions.
664 int X = CompareSCEVComplexity(EqCacheSCEV, LI, LC->getLHS(), RC->getLHS(),
668 X = CompareSCEVComplexity(EqCacheSCEV, LI, LC->getRHS(), RC->getRHS(),
671 EqCacheSCEV.insert({LHS, RHS});
678 const SCEVCastExpr *LC = cast<SCEVCastExpr>(LHS);
679 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
681 // Compare cast expressions by operand.
682 int X = CompareSCEVComplexity(EqCacheSCEV, LI, LC->getOperand(),
683 RC->getOperand(), Depth + 1);
685 EqCacheSCEV.insert({LHS, RHS});
689 case scCouldNotCompute:
690 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
692 llvm_unreachable("Unknown SCEV kind!");
695 /// Given a list of SCEV objects, order them by their complexity, and group
696 /// objects of the same complexity together by value. When this routine is
697 /// finished, we know that any duplicates in the vector are consecutive and that
698 /// complexity is monotonically increasing.
700 /// Note that we go take special precautions to ensure that we get deterministic
701 /// results from this routine. In other words, we don't want the results of
702 /// this to depend on where the addresses of various SCEV objects happened to
705 static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops,
707 if (Ops.size() < 2) return; // Noop
709 SmallSet<std::pair<const SCEV *, const SCEV *>, 8> EqCache;
710 if (Ops.size() == 2) {
711 // This is the common case, which also happens to be trivially simple.
713 const SCEV *&LHS = Ops[0], *&RHS = Ops[1];
714 if (CompareSCEVComplexity(EqCache, LI, RHS, LHS) < 0)
719 // Do the rough sort by complexity.
720 std::stable_sort(Ops.begin(), Ops.end(),
721 [&EqCache, LI](const SCEV *LHS, const SCEV *RHS) {
722 return CompareSCEVComplexity(EqCache, LI, LHS, RHS) < 0;
725 // Now that we are sorted by complexity, group elements of the same
726 // complexity. Note that this is, at worst, N^2, but the vector is likely to
727 // be extremely short in practice. Note that we take this approach because we
728 // do not want to depend on the addresses of the objects we are grouping.
729 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
730 const SCEV *S = Ops[i];
731 unsigned Complexity = S->getSCEVType();
733 // If there are any objects of the same complexity and same value as this
735 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
736 if (Ops[j] == S) { // Found a duplicate.
737 // Move it to immediately after i'th element.
738 std::swap(Ops[i+1], Ops[j]);
739 ++i; // no need to rescan it.
740 if (i == e-2) return; // Done!
746 // Returns the size of the SCEV S.
747 static inline int sizeOfSCEV(const SCEV *S) {
748 struct FindSCEVSize {
750 FindSCEVSize() : Size(0) {}
752 bool follow(const SCEV *S) {
754 // Keep looking at all operands of S.
757 bool isDone() const {
763 SCEVTraversal<FindSCEVSize> ST(F);
770 struct SCEVDivision : public SCEVVisitor<SCEVDivision, void> {
772 // Computes the Quotient and Remainder of the division of Numerator by
774 static void divide(ScalarEvolution &SE, const SCEV *Numerator,
775 const SCEV *Denominator, const SCEV **Quotient,
776 const SCEV **Remainder) {
777 assert(Numerator && Denominator && "Uninitialized SCEV");
779 SCEVDivision D(SE, Numerator, Denominator);
781 // Check for the trivial case here to avoid having to check for it in the
783 if (Numerator == Denominator) {
789 if (Numerator->isZero()) {
795 // A simple case when N/1. The quotient is N.
796 if (Denominator->isOne()) {
797 *Quotient = Numerator;
802 // Split the Denominator when it is a product.
803 if (const SCEVMulExpr *T = dyn_cast<SCEVMulExpr>(Denominator)) {
805 *Quotient = Numerator;
806 for (const SCEV *Op : T->operands()) {
807 divide(SE, *Quotient, Op, &Q, &R);
810 // Bail out when the Numerator is not divisible by one of the terms of
814 *Remainder = Numerator;
823 *Quotient = D.Quotient;
824 *Remainder = D.Remainder;
827 // Except in the trivial case described above, we do not know how to divide
828 // Expr by Denominator for the following functions with empty implementation.
829 void visitTruncateExpr(const SCEVTruncateExpr *Numerator) {}
830 void visitZeroExtendExpr(const SCEVZeroExtendExpr *Numerator) {}
831 void visitSignExtendExpr(const SCEVSignExtendExpr *Numerator) {}
832 void visitUDivExpr(const SCEVUDivExpr *Numerator) {}
833 void visitSMaxExpr(const SCEVSMaxExpr *Numerator) {}
834 void visitUMaxExpr(const SCEVUMaxExpr *Numerator) {}
835 void visitUnknown(const SCEVUnknown *Numerator) {}
836 void visitCouldNotCompute(const SCEVCouldNotCompute *Numerator) {}
838 void visitConstant(const SCEVConstant *Numerator) {
839 if (const SCEVConstant *D = dyn_cast<SCEVConstant>(Denominator)) {
840 APInt NumeratorVal = Numerator->getAPInt();
841 APInt DenominatorVal = D->getAPInt();
842 uint32_t NumeratorBW = NumeratorVal.getBitWidth();
843 uint32_t DenominatorBW = DenominatorVal.getBitWidth();
845 if (NumeratorBW > DenominatorBW)
846 DenominatorVal = DenominatorVal.sext(NumeratorBW);
847 else if (NumeratorBW < DenominatorBW)
848 NumeratorVal = NumeratorVal.sext(DenominatorBW);
850 APInt QuotientVal(NumeratorVal.getBitWidth(), 0);
851 APInt RemainderVal(NumeratorVal.getBitWidth(), 0);
852 APInt::sdivrem(NumeratorVal, DenominatorVal, QuotientVal, RemainderVal);
853 Quotient = SE.getConstant(QuotientVal);
854 Remainder = SE.getConstant(RemainderVal);
859 void visitAddRecExpr(const SCEVAddRecExpr *Numerator) {
860 const SCEV *StartQ, *StartR, *StepQ, *StepR;
861 if (!Numerator->isAffine())
862 return cannotDivide(Numerator);
863 divide(SE, Numerator->getStart(), Denominator, &StartQ, &StartR);
864 divide(SE, Numerator->getStepRecurrence(SE), Denominator, &StepQ, &StepR);
865 // Bail out if the types do not match.
866 Type *Ty = Denominator->getType();
867 if (Ty != StartQ->getType() || Ty != StartR->getType() ||
868 Ty != StepQ->getType() || Ty != StepR->getType())
869 return cannotDivide(Numerator);
870 Quotient = SE.getAddRecExpr(StartQ, StepQ, Numerator->getLoop(),
871 Numerator->getNoWrapFlags());
872 Remainder = SE.getAddRecExpr(StartR, StepR, Numerator->getLoop(),
873 Numerator->getNoWrapFlags());
876 void visitAddExpr(const SCEVAddExpr *Numerator) {
877 SmallVector<const SCEV *, 2> Qs, Rs;
878 Type *Ty = Denominator->getType();
880 for (const SCEV *Op : Numerator->operands()) {
882 divide(SE, Op, Denominator, &Q, &R);
884 // Bail out if types do not match.
885 if (Ty != Q->getType() || Ty != R->getType())
886 return cannotDivide(Numerator);
892 if (Qs.size() == 1) {
898 Quotient = SE.getAddExpr(Qs);
899 Remainder = SE.getAddExpr(Rs);
902 void visitMulExpr(const SCEVMulExpr *Numerator) {
903 SmallVector<const SCEV *, 2> Qs;
904 Type *Ty = Denominator->getType();
906 bool FoundDenominatorTerm = false;
907 for (const SCEV *Op : Numerator->operands()) {
908 // Bail out if types do not match.
909 if (Ty != Op->getType())
910 return cannotDivide(Numerator);
912 if (FoundDenominatorTerm) {
917 // Check whether Denominator divides one of the product operands.
919 divide(SE, Op, Denominator, &Q, &R);
925 // Bail out if types do not match.
926 if (Ty != Q->getType())
927 return cannotDivide(Numerator);
929 FoundDenominatorTerm = true;
933 if (FoundDenominatorTerm) {
938 Quotient = SE.getMulExpr(Qs);
942 if (!isa<SCEVUnknown>(Denominator))
943 return cannotDivide(Numerator);
945 // The Remainder is obtained by replacing Denominator by 0 in Numerator.
946 ValueToValueMap RewriteMap;
947 RewriteMap[cast<SCEVUnknown>(Denominator)->getValue()] =
948 cast<SCEVConstant>(Zero)->getValue();
949 Remainder = SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true);
951 if (Remainder->isZero()) {
952 // The Quotient is obtained by replacing Denominator by 1 in Numerator.
953 RewriteMap[cast<SCEVUnknown>(Denominator)->getValue()] =
954 cast<SCEVConstant>(One)->getValue();
956 SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true);
960 // Quotient is (Numerator - Remainder) divided by Denominator.
962 const SCEV *Diff = SE.getMinusSCEV(Numerator, Remainder);
963 // This SCEV does not seem to simplify: fail the division here.
964 if (sizeOfSCEV(Diff) > sizeOfSCEV(Numerator))
965 return cannotDivide(Numerator);
966 divide(SE, Diff, Denominator, &Q, &R);
968 return cannotDivide(Numerator);
973 SCEVDivision(ScalarEvolution &S, const SCEV *Numerator,
974 const SCEV *Denominator)
975 : SE(S), Denominator(Denominator) {
976 Zero = SE.getZero(Denominator->getType());
977 One = SE.getOne(Denominator->getType());
979 // We generally do not know how to divide Expr by Denominator. We
980 // initialize the division to a "cannot divide" state to simplify the rest
982 cannotDivide(Numerator);
985 // Convenience function for giving up on the division. We set the quotient to
986 // be equal to zero and the remainder to be equal to the numerator.
987 void cannotDivide(const SCEV *Numerator) {
989 Remainder = Numerator;
993 const SCEV *Denominator, *Quotient, *Remainder, *Zero, *One;
998 //===----------------------------------------------------------------------===//
999 // Simple SCEV method implementations
1000 //===----------------------------------------------------------------------===//
1002 /// Compute BC(It, K). The result has width W. Assume, K > 0.
1003 static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K,
1004 ScalarEvolution &SE,
1006 // Handle the simplest case efficiently.
1008 return SE.getTruncateOrZeroExtend(It, ResultTy);
1010 // We are using the following formula for BC(It, K):
1012 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
1014 // Suppose, W is the bitwidth of the return value. We must be prepared for
1015 // overflow. Hence, we must assure that the result of our computation is
1016 // equal to the accurate one modulo 2^W. Unfortunately, division isn't
1017 // safe in modular arithmetic.
1019 // However, this code doesn't use exactly that formula; the formula it uses
1020 // is something like the following, where T is the number of factors of 2 in
1021 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
1024 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
1026 // This formula is trivially equivalent to the previous formula. However,
1027 // this formula can be implemented much more efficiently. The trick is that
1028 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
1029 // arithmetic. To do exact division in modular arithmetic, all we have
1030 // to do is multiply by the inverse. Therefore, this step can be done at
1033 // The next issue is how to safely do the division by 2^T. The way this
1034 // is done is by doing the multiplication step at a width of at least W + T
1035 // bits. This way, the bottom W+T bits of the product are accurate. Then,
1036 // when we perform the division by 2^T (which is equivalent to a right shift
1037 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
1038 // truncated out after the division by 2^T.
1040 // In comparison to just directly using the first formula, this technique
1041 // is much more efficient; using the first formula requires W * K bits,
1042 // but this formula less than W + K bits. Also, the first formula requires
1043 // a division step, whereas this formula only requires multiplies and shifts.
1045 // It doesn't matter whether the subtraction step is done in the calculation
1046 // width or the input iteration count's width; if the subtraction overflows,
1047 // the result must be zero anyway. We prefer here to do it in the width of
1048 // the induction variable because it helps a lot for certain cases; CodeGen
1049 // isn't smart enough to ignore the overflow, which leads to much less
1050 // efficient code if the width of the subtraction is wider than the native
1053 // (It's possible to not widen at all by pulling out factors of 2 before
1054 // the multiplication; for example, K=2 can be calculated as
1055 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
1056 // extra arithmetic, so it's not an obvious win, and it gets
1057 // much more complicated for K > 3.)
1059 // Protection from insane SCEVs; this bound is conservative,
1060 // but it probably doesn't matter.
1062 return SE.getCouldNotCompute();
1064 unsigned W = SE.getTypeSizeInBits(ResultTy);
1066 // Calculate K! / 2^T and T; we divide out the factors of two before
1067 // multiplying for calculating K! / 2^T to avoid overflow.
1068 // Other overflow doesn't matter because we only care about the bottom
1069 // W bits of the result.
1070 APInt OddFactorial(W, 1);
1072 for (unsigned i = 3; i <= K; ++i) {
1074 unsigned TwoFactors = Mult.countTrailingZeros();
1076 Mult = Mult.lshr(TwoFactors);
1077 OddFactorial *= Mult;
1080 // We need at least W + T bits for the multiplication step
1081 unsigned CalculationBits = W + T;
1083 // Calculate 2^T, at width T+W.
1084 APInt DivFactor = APInt::getOneBitSet(CalculationBits, T);
1086 // Calculate the multiplicative inverse of K! / 2^T;
1087 // this multiplication factor will perform the exact division by
1089 APInt Mod = APInt::getSignedMinValue(W+1);
1090 APInt MultiplyFactor = OddFactorial.zext(W+1);
1091 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
1092 MultiplyFactor = MultiplyFactor.trunc(W);
1094 // Calculate the product, at width T+W
1095 IntegerType *CalculationTy = IntegerType::get(SE.getContext(),
1097 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
1098 for (unsigned i = 1; i != K; ++i) {
1099 const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i));
1100 Dividend = SE.getMulExpr(Dividend,
1101 SE.getTruncateOrZeroExtend(S, CalculationTy));
1105 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
1107 // Truncate the result, and divide by K! / 2^T.
1109 return SE.getMulExpr(SE.getConstant(MultiplyFactor),
1110 SE.getTruncateOrZeroExtend(DivResult, ResultTy));
1113 /// Return the value of this chain of recurrences at the specified iteration
1114 /// number. We can evaluate this recurrence by multiplying each element in the
1115 /// chain by the binomial coefficient corresponding to it. In other words, we
1116 /// can evaluate {A,+,B,+,C,+,D} as:
1118 /// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
1120 /// where BC(It, k) stands for binomial coefficient.
1122 const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It,
1123 ScalarEvolution &SE) const {
1124 const SCEV *Result = getStart();
1125 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
1126 // The computation is correct in the face of overflow provided that the
1127 // multiplication is performed _after_ the evaluation of the binomial
1129 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType());
1130 if (isa<SCEVCouldNotCompute>(Coeff))
1133 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
1138 //===----------------------------------------------------------------------===//
1139 // SCEV Expression folder implementations
1140 //===----------------------------------------------------------------------===//
1142 const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op,
1144 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
1145 "This is not a truncating conversion!");
1146 assert(isSCEVable(Ty) &&
1147 "This is not a conversion to a SCEVable type!");
1148 Ty = getEffectiveSCEVType(Ty);
1150 FoldingSetNodeID ID;
1151 ID.AddInteger(scTruncate);
1155 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1157 // Fold if the operand is constant.
1158 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1160 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty)));
1162 // trunc(trunc(x)) --> trunc(x)
1163 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
1164 return getTruncateExpr(ST->getOperand(), Ty);
1166 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
1167 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1168 return getTruncateOrSignExtend(SS->getOperand(), Ty);
1170 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
1171 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1172 return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
1174 // trunc(x1+x2+...+xN) --> trunc(x1)+trunc(x2)+...+trunc(xN) if we can
1175 // eliminate all the truncates, or we replace other casts with truncates.
1176 if (const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Op)) {
1177 SmallVector<const SCEV *, 4> Operands;
1178 bool hasTrunc = false;
1179 for (unsigned i = 0, e = SA->getNumOperands(); i != e && !hasTrunc; ++i) {
1180 const SCEV *S = getTruncateExpr(SA->getOperand(i), Ty);
1181 if (!isa<SCEVCastExpr>(SA->getOperand(i)))
1182 hasTrunc = isa<SCEVTruncateExpr>(S);
1183 Operands.push_back(S);
1186 return getAddExpr(Operands);
1187 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL.
1190 // trunc(x1*x2*...*xN) --> trunc(x1)*trunc(x2)*...*trunc(xN) if we can
1191 // eliminate all the truncates, or we replace other casts with truncates.
1192 if (const SCEVMulExpr *SM = dyn_cast<SCEVMulExpr>(Op)) {
1193 SmallVector<const SCEV *, 4> Operands;
1194 bool hasTrunc = false;
1195 for (unsigned i = 0, e = SM->getNumOperands(); i != e && !hasTrunc; ++i) {
1196 const SCEV *S = getTruncateExpr(SM->getOperand(i), Ty);
1197 if (!isa<SCEVCastExpr>(SM->getOperand(i)))
1198 hasTrunc = isa<SCEVTruncateExpr>(S);
1199 Operands.push_back(S);
1202 return getMulExpr(Operands);
1203 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL.
1206 // If the input value is a chrec scev, truncate the chrec's operands.
1207 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
1208 SmallVector<const SCEV *, 4> Operands;
1209 for (const SCEV *Op : AddRec->operands())
1210 Operands.push_back(getTruncateExpr(Op, Ty));
1211 return getAddRecExpr(Operands, AddRec->getLoop(), SCEV::FlagAnyWrap);
1214 // The cast wasn't folded; create an explicit cast node. We can reuse
1215 // the existing insert position since if we get here, we won't have
1216 // made any changes which would invalidate it.
1217 SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator),
1219 UniqueSCEVs.InsertNode(S, IP);
1223 // Get the limit of a recurrence such that incrementing by Step cannot cause
1224 // signed overflow as long as the value of the recurrence within the
1225 // loop does not exceed this limit before incrementing.
1226 static const SCEV *getSignedOverflowLimitForStep(const SCEV *Step,
1227 ICmpInst::Predicate *Pred,
1228 ScalarEvolution *SE) {
1229 unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
1230 if (SE->isKnownPositive(Step)) {
1231 *Pred = ICmpInst::ICMP_SLT;
1232 return SE->getConstant(APInt::getSignedMinValue(BitWidth) -
1233 SE->getSignedRange(Step).getSignedMax());
1235 if (SE->isKnownNegative(Step)) {
1236 *Pred = ICmpInst::ICMP_SGT;
1237 return SE->getConstant(APInt::getSignedMaxValue(BitWidth) -
1238 SE->getSignedRange(Step).getSignedMin());
1243 // Get the limit of a recurrence such that incrementing by Step cannot cause
1244 // unsigned overflow as long as the value of the recurrence within the loop does
1245 // not exceed this limit before incrementing.
1246 static const SCEV *getUnsignedOverflowLimitForStep(const SCEV *Step,
1247 ICmpInst::Predicate *Pred,
1248 ScalarEvolution *SE) {
1249 unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
1250 *Pred = ICmpInst::ICMP_ULT;
1252 return SE->getConstant(APInt::getMinValue(BitWidth) -
1253 SE->getUnsignedRange(Step).getUnsignedMax());
1258 struct ExtendOpTraitsBase {
1259 typedef const SCEV *(ScalarEvolution::*GetExtendExprTy)(const SCEV *, Type *);
1262 // Used to make code generic over signed and unsigned overflow.
1263 template <typename ExtendOp> struct ExtendOpTraits {
1266 // static const SCEV::NoWrapFlags WrapType;
1268 // static const ExtendOpTraitsBase::GetExtendExprTy GetExtendExpr;
1270 // static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1271 // ICmpInst::Predicate *Pred,
1272 // ScalarEvolution *SE);
1276 struct ExtendOpTraits<SCEVSignExtendExpr> : public ExtendOpTraitsBase {
1277 static const SCEV::NoWrapFlags WrapType = SCEV::FlagNSW;
1279 static const GetExtendExprTy GetExtendExpr;
1281 static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1282 ICmpInst::Predicate *Pred,
1283 ScalarEvolution *SE) {
1284 return getSignedOverflowLimitForStep(Step, Pred, SE);
1288 const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits<
1289 SCEVSignExtendExpr>::GetExtendExpr = &ScalarEvolution::getSignExtendExpr;
1292 struct ExtendOpTraits<SCEVZeroExtendExpr> : public ExtendOpTraitsBase {
1293 static const SCEV::NoWrapFlags WrapType = SCEV::FlagNUW;
1295 static const GetExtendExprTy GetExtendExpr;
1297 static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1298 ICmpInst::Predicate *Pred,
1299 ScalarEvolution *SE) {
1300 return getUnsignedOverflowLimitForStep(Step, Pred, SE);
1304 const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits<
1305 SCEVZeroExtendExpr>::GetExtendExpr = &ScalarEvolution::getZeroExtendExpr;
1308 // The recurrence AR has been shown to have no signed/unsigned wrap or something
1309 // close to it. Typically, if we can prove NSW/NUW for AR, then we can just as
1310 // easily prove NSW/NUW for its preincrement or postincrement sibling. This
1311 // allows normalizing a sign/zero extended AddRec as such: {sext/zext(Step +
1312 // Start),+,Step} => {(Step + sext/zext(Start),+,Step} As a result, the
1313 // expression "Step + sext/zext(PreIncAR)" is congruent with
1314 // "sext/zext(PostIncAR)"
1315 template <typename ExtendOpTy>
1316 static const SCEV *getPreStartForExtend(const SCEVAddRecExpr *AR, Type *Ty,
1317 ScalarEvolution *SE) {
1318 auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType;
1319 auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr;
1321 const Loop *L = AR->getLoop();
1322 const SCEV *Start = AR->getStart();
1323 const SCEV *Step = AR->getStepRecurrence(*SE);
1325 // Check for a simple looking step prior to loop entry.
1326 const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Start);
1330 // Create an AddExpr for "PreStart" after subtracting Step. Full SCEV
1331 // subtraction is expensive. For this purpose, perform a quick and dirty
1332 // difference, by checking for Step in the operand list.
1333 SmallVector<const SCEV *, 4> DiffOps;
1334 for (const SCEV *Op : SA->operands())
1336 DiffOps.push_back(Op);
1338 if (DiffOps.size() == SA->getNumOperands())
1341 // Try to prove `WrapType` (SCEV::FlagNSW or SCEV::FlagNUW) on `PreStart` +
1344 // 1. NSW/NUW flags on the step increment.
1345 auto PreStartFlags =
1346 ScalarEvolution::maskFlags(SA->getNoWrapFlags(), SCEV::FlagNUW);
1347 const SCEV *PreStart = SE->getAddExpr(DiffOps, PreStartFlags);
1348 const SCEVAddRecExpr *PreAR = dyn_cast<SCEVAddRecExpr>(
1349 SE->getAddRecExpr(PreStart, Step, L, SCEV::FlagAnyWrap));
1351 // "{S,+,X} is <nsw>/<nuw>" and "the backedge is taken at least once" implies
1352 // "S+X does not sign/unsign-overflow".
1355 const SCEV *BECount = SE->getBackedgeTakenCount(L);
1356 if (PreAR && PreAR->getNoWrapFlags(WrapType) &&
1357 !isa<SCEVCouldNotCompute>(BECount) && SE->isKnownPositive(BECount))
1360 // 2. Direct overflow check on the step operation's expression.
1361 unsigned BitWidth = SE->getTypeSizeInBits(AR->getType());
1362 Type *WideTy = IntegerType::get(SE->getContext(), BitWidth * 2);
1363 const SCEV *OperandExtendedStart =
1364 SE->getAddExpr((SE->*GetExtendExpr)(PreStart, WideTy),
1365 (SE->*GetExtendExpr)(Step, WideTy));
1366 if ((SE->*GetExtendExpr)(Start, WideTy) == OperandExtendedStart) {
1367 if (PreAR && AR->getNoWrapFlags(WrapType)) {
1368 // If we know `AR` == {`PreStart`+`Step`,+,`Step`} is `WrapType` (FlagNSW
1369 // or FlagNUW) and that `PreStart` + `Step` is `WrapType` too, then
1370 // `PreAR` == {`PreStart`,+,`Step`} is also `WrapType`. Cache this fact.
1371 const_cast<SCEVAddRecExpr *>(PreAR)->setNoWrapFlags(WrapType);
1376 // 3. Loop precondition.
1377 ICmpInst::Predicate Pred;
1378 const SCEV *OverflowLimit =
1379 ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep(Step, &Pred, SE);
1381 if (OverflowLimit &&
1382 SE->isLoopEntryGuardedByCond(L, Pred, PreStart, OverflowLimit))
1388 // Get the normalized zero or sign extended expression for this AddRec's Start.
1389 template <typename ExtendOpTy>
1390 static const SCEV *getExtendAddRecStart(const SCEVAddRecExpr *AR, Type *Ty,
1391 ScalarEvolution *SE) {
1392 auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr;
1394 const SCEV *PreStart = getPreStartForExtend<ExtendOpTy>(AR, Ty, SE);
1396 return (SE->*GetExtendExpr)(AR->getStart(), Ty);
1398 return SE->getAddExpr((SE->*GetExtendExpr)(AR->getStepRecurrence(*SE), Ty),
1399 (SE->*GetExtendExpr)(PreStart, Ty));
1402 // Try to prove away overflow by looking at "nearby" add recurrences. A
1403 // motivating example for this rule: if we know `{0,+,4}` is `ult` `-1` and it
1404 // does not itself wrap then we can conclude that `{1,+,4}` is `nuw`.
1408 // {S,+,X} == {S-T,+,X} + T
1409 // => Ext({S,+,X}) == Ext({S-T,+,X} + T)
1411 // If ({S-T,+,X} + T) does not overflow ... (1)
1413 // RHS == Ext({S-T,+,X} + T) == Ext({S-T,+,X}) + Ext(T)
1415 // If {S-T,+,X} does not overflow ... (2)
1417 // RHS == Ext({S-T,+,X}) + Ext(T) == {Ext(S-T),+,Ext(X)} + Ext(T)
1418 // == {Ext(S-T)+Ext(T),+,Ext(X)}
1420 // If (S-T)+T does not overflow ... (3)
1422 // RHS == {Ext(S-T)+Ext(T),+,Ext(X)} == {Ext(S-T+T),+,Ext(X)}
1423 // == {Ext(S),+,Ext(X)} == LHS
1425 // Thus, if (1), (2) and (3) are true for some T, then
1426 // Ext({S,+,X}) == {Ext(S),+,Ext(X)}
1428 // (3) is implied by (1) -- "(S-T)+T does not overflow" is simply "({S-T,+,X}+T)
1429 // does not overflow" restricted to the 0th iteration. Therefore we only need
1430 // to check for (1) and (2).
1432 // In the current context, S is `Start`, X is `Step`, Ext is `ExtendOpTy` and T
1433 // is `Delta` (defined below).
1435 template <typename ExtendOpTy>
1436 bool ScalarEvolution::proveNoWrapByVaryingStart(const SCEV *Start,
1439 auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType;
1441 // We restrict `Start` to a constant to prevent SCEV from spending too much
1442 // time here. It is correct (but more expensive) to continue with a
1443 // non-constant `Start` and do a general SCEV subtraction to compute
1444 // `PreStart` below.
1446 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start);
1450 APInt StartAI = StartC->getAPInt();
1452 for (unsigned Delta : {-2, -1, 1, 2}) {
1453 const SCEV *PreStart = getConstant(StartAI - Delta);
1455 FoldingSetNodeID ID;
1456 ID.AddInteger(scAddRecExpr);
1457 ID.AddPointer(PreStart);
1458 ID.AddPointer(Step);
1462 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1464 // Give up if we don't already have the add recurrence we need because
1465 // actually constructing an add recurrence is relatively expensive.
1466 if (PreAR && PreAR->getNoWrapFlags(WrapType)) { // proves (2)
1467 const SCEV *DeltaS = getConstant(StartC->getType(), Delta);
1468 ICmpInst::Predicate Pred = ICmpInst::BAD_ICMP_PREDICATE;
1469 const SCEV *Limit = ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep(
1470 DeltaS, &Pred, this);
1471 if (Limit && isKnownPredicate(Pred, PreAR, Limit)) // proves (1)
1479 const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op,
1481 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1482 "This is not an extending conversion!");
1483 assert(isSCEVable(Ty) &&
1484 "This is not a conversion to a SCEVable type!");
1485 Ty = getEffectiveSCEVType(Ty);
1487 // Fold if the operand is constant.
1488 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1490 cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(), Ty)));
1492 // zext(zext(x)) --> zext(x)
1493 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1494 return getZeroExtendExpr(SZ->getOperand(), Ty);
1496 // Before doing any expensive analysis, check to see if we've already
1497 // computed a SCEV for this Op and Ty.
1498 FoldingSetNodeID ID;
1499 ID.AddInteger(scZeroExtend);
1503 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1505 // zext(trunc(x)) --> zext(x) or x or trunc(x)
1506 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1507 // It's possible the bits taken off by the truncate were all zero bits. If
1508 // so, we should be able to simplify this further.
1509 const SCEV *X = ST->getOperand();
1510 ConstantRange CR = getUnsignedRange(X);
1511 unsigned TruncBits = getTypeSizeInBits(ST->getType());
1512 unsigned NewBits = getTypeSizeInBits(Ty);
1513 if (CR.truncate(TruncBits).zeroExtend(NewBits).contains(
1514 CR.zextOrTrunc(NewBits)))
1515 return getTruncateOrZeroExtend(X, Ty);
1518 // If the input value is a chrec scev, and we can prove that the value
1519 // did not overflow the old, smaller, value, we can zero extend all of the
1520 // operands (often constants). This allows analysis of something like
1521 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
1522 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1523 if (AR->isAffine()) {
1524 const SCEV *Start = AR->getStart();
1525 const SCEV *Step = AR->getStepRecurrence(*this);
1526 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1527 const Loop *L = AR->getLoop();
1529 if (!AR->hasNoUnsignedWrap()) {
1530 auto NewFlags = proveNoWrapViaConstantRanges(AR);
1531 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(NewFlags);
1534 // If we have special knowledge that this addrec won't overflow,
1535 // we don't need to do any further analysis.
1536 if (AR->hasNoUnsignedWrap())
1537 return getAddRecExpr(
1538 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1539 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1541 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1542 // Note that this serves two purposes: It filters out loops that are
1543 // simply not analyzable, and it covers the case where this code is
1544 // being called from within backedge-taken count analysis, such that
1545 // attempting to ask for the backedge-taken count would likely result
1546 // in infinite recursion. In the later case, the analysis code will
1547 // cope with a conservative value, and it will take care to purge
1548 // that value once it has finished.
1549 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1550 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1551 // Manually compute the final value for AR, checking for
1554 // Check whether the backedge-taken count can be losslessly casted to
1555 // the addrec's type. The count is always unsigned.
1556 const SCEV *CastedMaxBECount =
1557 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1558 const SCEV *RecastedMaxBECount =
1559 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1560 if (MaxBECount == RecastedMaxBECount) {
1561 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1562 // Check whether Start+Step*MaxBECount has no unsigned overflow.
1563 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step);
1564 const SCEV *ZAdd = getZeroExtendExpr(getAddExpr(Start, ZMul), WideTy);
1565 const SCEV *WideStart = getZeroExtendExpr(Start, WideTy);
1566 const SCEV *WideMaxBECount =
1567 getZeroExtendExpr(CastedMaxBECount, WideTy);
1568 const SCEV *OperandExtendedAdd =
1569 getAddExpr(WideStart,
1570 getMulExpr(WideMaxBECount,
1571 getZeroExtendExpr(Step, WideTy)));
1572 if (ZAdd == OperandExtendedAdd) {
1573 // Cache knowledge of AR NUW, which is propagated to this AddRec.
1574 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1575 // Return the expression with the addrec on the outside.
1576 return getAddRecExpr(
1577 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1578 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1580 // Similar to above, only this time treat the step value as signed.
1581 // This covers loops that count down.
1582 OperandExtendedAdd =
1583 getAddExpr(WideStart,
1584 getMulExpr(WideMaxBECount,
1585 getSignExtendExpr(Step, WideTy)));
1586 if (ZAdd == OperandExtendedAdd) {
1587 // Cache knowledge of AR NW, which is propagated to this AddRec.
1588 // Negative step causes unsigned wrap, but it still can't self-wrap.
1589 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1590 // Return the expression with the addrec on the outside.
1591 return getAddRecExpr(
1592 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1593 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1598 // Normally, in the cases we can prove no-overflow via a
1599 // backedge guarding condition, we can also compute a backedge
1600 // taken count for the loop. The exceptions are assumptions and
1601 // guards present in the loop -- SCEV is not great at exploiting
1602 // these to compute max backedge taken counts, but can still use
1603 // these to prove lack of overflow. Use this fact to avoid
1604 // doing extra work that may not pay off.
1605 if (!isa<SCEVCouldNotCompute>(MaxBECount) || HasGuards ||
1606 !AC.assumptions().empty()) {
1607 // If the backedge is guarded by a comparison with the pre-inc
1608 // value the addrec is safe. Also, if the entry is guarded by
1609 // a comparison with the start value and the backedge is
1610 // guarded by a comparison with the post-inc value, the addrec
1612 if (isKnownPositive(Step)) {
1613 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
1614 getUnsignedRange(Step).getUnsignedMax());
1615 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
1616 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) &&
1617 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT,
1618 AR->getPostIncExpr(*this), N))) {
1619 // Cache knowledge of AR NUW, which is propagated to this
1621 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1622 // Return the expression with the addrec on the outside.
1623 return getAddRecExpr(
1624 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1625 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1627 } else if (isKnownNegative(Step)) {
1628 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
1629 getSignedRange(Step).getSignedMin());
1630 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) ||
1631 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) &&
1632 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT,
1633 AR->getPostIncExpr(*this), N))) {
1634 // Cache knowledge of AR NW, which is propagated to this
1635 // AddRec. Negative step causes unsigned wrap, but it
1636 // still can't self-wrap.
1637 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1638 // Return the expression with the addrec on the outside.
1639 return getAddRecExpr(
1640 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1641 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1646 if (proveNoWrapByVaryingStart<SCEVZeroExtendExpr>(Start, Step, L)) {
1647 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1648 return getAddRecExpr(
1649 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1650 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1654 if (auto *SA = dyn_cast<SCEVAddExpr>(Op)) {
1655 // zext((A + B + ...)<nuw>) --> (zext(A) + zext(B) + ...)<nuw>
1656 if (SA->hasNoUnsignedWrap()) {
1657 // If the addition does not unsign overflow then we can, by definition,
1658 // commute the zero extension with the addition operation.
1659 SmallVector<const SCEV *, 4> Ops;
1660 for (const auto *Op : SA->operands())
1661 Ops.push_back(getZeroExtendExpr(Op, Ty));
1662 return getAddExpr(Ops, SCEV::FlagNUW);
1666 // The cast wasn't folded; create an explicit cast node.
1667 // Recompute the insert position, as it may have been invalidated.
1668 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1669 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
1671 UniqueSCEVs.InsertNode(S, IP);
1675 const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op,
1677 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1678 "This is not an extending conversion!");
1679 assert(isSCEVable(Ty) &&
1680 "This is not a conversion to a SCEVable type!");
1681 Ty = getEffectiveSCEVType(Ty);
1683 // Fold if the operand is constant.
1684 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1686 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), Ty)));
1688 // sext(sext(x)) --> sext(x)
1689 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1690 return getSignExtendExpr(SS->getOperand(), Ty);
1692 // sext(zext(x)) --> zext(x)
1693 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1694 return getZeroExtendExpr(SZ->getOperand(), Ty);
1696 // Before doing any expensive analysis, check to see if we've already
1697 // computed a SCEV for this Op and Ty.
1698 FoldingSetNodeID ID;
1699 ID.AddInteger(scSignExtend);
1703 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1705 // sext(trunc(x)) --> sext(x) or x or trunc(x)
1706 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1707 // It's possible the bits taken off by the truncate were all sign bits. If
1708 // so, we should be able to simplify this further.
1709 const SCEV *X = ST->getOperand();
1710 ConstantRange CR = getSignedRange(X);
1711 unsigned TruncBits = getTypeSizeInBits(ST->getType());
1712 unsigned NewBits = getTypeSizeInBits(Ty);
1713 if (CR.truncate(TruncBits).signExtend(NewBits).contains(
1714 CR.sextOrTrunc(NewBits)))
1715 return getTruncateOrSignExtend(X, Ty);
1718 // sext(C1 + (C2 * x)) --> C1 + sext(C2 * x) if C1 < C2
1719 if (auto *SA = dyn_cast<SCEVAddExpr>(Op)) {
1720 if (SA->getNumOperands() == 2) {
1721 auto *SC1 = dyn_cast<SCEVConstant>(SA->getOperand(0));
1722 auto *SMul = dyn_cast<SCEVMulExpr>(SA->getOperand(1));
1724 if (auto *SC2 = dyn_cast<SCEVConstant>(SMul->getOperand(0))) {
1725 const APInt &C1 = SC1->getAPInt();
1726 const APInt &C2 = SC2->getAPInt();
1727 if (C1.isStrictlyPositive() && C2.isStrictlyPositive() &&
1728 C2.ugt(C1) && C2.isPowerOf2())
1729 return getAddExpr(getSignExtendExpr(SC1, Ty),
1730 getSignExtendExpr(SMul, Ty));
1735 // sext((A + B + ...)<nsw>) --> (sext(A) + sext(B) + ...)<nsw>
1736 if (SA->hasNoSignedWrap()) {
1737 // If the addition does not sign overflow then we can, by definition,
1738 // commute the sign extension with the addition operation.
1739 SmallVector<const SCEV *, 4> Ops;
1740 for (const auto *Op : SA->operands())
1741 Ops.push_back(getSignExtendExpr(Op, Ty));
1742 return getAddExpr(Ops, SCEV::FlagNSW);
1745 // If the input value is a chrec scev, and we can prove that the value
1746 // did not overflow the old, smaller, value, we can sign extend all of the
1747 // operands (often constants). This allows analysis of something like
1748 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
1749 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1750 if (AR->isAffine()) {
1751 const SCEV *Start = AR->getStart();
1752 const SCEV *Step = AR->getStepRecurrence(*this);
1753 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1754 const Loop *L = AR->getLoop();
1756 if (!AR->hasNoSignedWrap()) {
1757 auto NewFlags = proveNoWrapViaConstantRanges(AR);
1758 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(NewFlags);
1761 // If we have special knowledge that this addrec won't overflow,
1762 // we don't need to do any further analysis.
1763 if (AR->hasNoSignedWrap())
1764 return getAddRecExpr(
1765 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1766 getSignExtendExpr(Step, Ty), L, SCEV::FlagNSW);
1768 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1769 // Note that this serves two purposes: It filters out loops that are
1770 // simply not analyzable, and it covers the case where this code is
1771 // being called from within backedge-taken count analysis, such that
1772 // attempting to ask for the backedge-taken count would likely result
1773 // in infinite recursion. In the later case, the analysis code will
1774 // cope with a conservative value, and it will take care to purge
1775 // that value once it has finished.
1776 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1777 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1778 // Manually compute the final value for AR, checking for
1781 // Check whether the backedge-taken count can be losslessly casted to
1782 // the addrec's type. The count is always unsigned.
1783 const SCEV *CastedMaxBECount =
1784 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1785 const SCEV *RecastedMaxBECount =
1786 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1787 if (MaxBECount == RecastedMaxBECount) {
1788 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1789 // Check whether Start+Step*MaxBECount has no signed overflow.
1790 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
1791 const SCEV *SAdd = getSignExtendExpr(getAddExpr(Start, SMul), WideTy);
1792 const SCEV *WideStart = getSignExtendExpr(Start, WideTy);
1793 const SCEV *WideMaxBECount =
1794 getZeroExtendExpr(CastedMaxBECount, WideTy);
1795 const SCEV *OperandExtendedAdd =
1796 getAddExpr(WideStart,
1797 getMulExpr(WideMaxBECount,
1798 getSignExtendExpr(Step, WideTy)));
1799 if (SAdd == OperandExtendedAdd) {
1800 // Cache knowledge of AR NSW, which is propagated to this AddRec.
1801 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1802 // Return the expression with the addrec on the outside.
1803 return getAddRecExpr(
1804 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1805 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1807 // Similar to above, only this time treat the step value as unsigned.
1808 // This covers loops that count up with an unsigned step.
1809 OperandExtendedAdd =
1810 getAddExpr(WideStart,
1811 getMulExpr(WideMaxBECount,
1812 getZeroExtendExpr(Step, WideTy)));
1813 if (SAdd == OperandExtendedAdd) {
1814 // If AR wraps around then
1816 // abs(Step) * MaxBECount > unsigned-max(AR->getType())
1817 // => SAdd != OperandExtendedAdd
1819 // Thus (AR is not NW => SAdd != OperandExtendedAdd) <=>
1820 // (SAdd == OperandExtendedAdd => AR is NW)
1822 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1824 // Return the expression with the addrec on the outside.
1825 return getAddRecExpr(
1826 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1827 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1832 // Normally, in the cases we can prove no-overflow via a
1833 // backedge guarding condition, we can also compute a backedge
1834 // taken count for the loop. The exceptions are assumptions and
1835 // guards present in the loop -- SCEV is not great at exploiting
1836 // these to compute max backedge taken counts, but can still use
1837 // these to prove lack of overflow. Use this fact to avoid
1838 // doing extra work that may not pay off.
1840 if (!isa<SCEVCouldNotCompute>(MaxBECount) || HasGuards ||
1841 !AC.assumptions().empty()) {
1842 // If the backedge is guarded by a comparison with the pre-inc
1843 // value the addrec is safe. Also, if the entry is guarded by
1844 // a comparison with the start value and the backedge is
1845 // guarded by a comparison with the post-inc value, the addrec
1847 ICmpInst::Predicate Pred;
1848 const SCEV *OverflowLimit =
1849 getSignedOverflowLimitForStep(Step, &Pred, this);
1850 if (OverflowLimit &&
1851 (isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) ||
1852 (isLoopEntryGuardedByCond(L, Pred, Start, OverflowLimit) &&
1853 isLoopBackedgeGuardedByCond(L, Pred, AR->getPostIncExpr(*this),
1855 // Cache knowledge of AR NSW, then propagate NSW to the wide AddRec.
1856 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1857 return getAddRecExpr(
1858 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1859 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1863 // If Start and Step are constants, check if we can apply this
1865 // sext{C1,+,C2} --> C1 + sext{0,+,C2} if C1 < C2
1866 auto *SC1 = dyn_cast<SCEVConstant>(Start);
1867 auto *SC2 = dyn_cast<SCEVConstant>(Step);
1869 const APInt &C1 = SC1->getAPInt();
1870 const APInt &C2 = SC2->getAPInt();
1871 if (C1.isStrictlyPositive() && C2.isStrictlyPositive() && C2.ugt(C1) &&
1873 Start = getSignExtendExpr(Start, Ty);
1874 const SCEV *NewAR = getAddRecExpr(getZero(AR->getType()), Step, L,
1875 AR->getNoWrapFlags());
1876 return getAddExpr(Start, getSignExtendExpr(NewAR, Ty));
1880 if (proveNoWrapByVaryingStart<SCEVSignExtendExpr>(Start, Step, L)) {
1881 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1882 return getAddRecExpr(
1883 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1884 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1888 // If the input value is provably positive and we could not simplify
1889 // away the sext build a zext instead.
1890 if (isKnownNonNegative(Op))
1891 return getZeroExtendExpr(Op, Ty);
1893 // The cast wasn't folded; create an explicit cast node.
1894 // Recompute the insert position, as it may have been invalidated.
1895 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1896 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
1898 UniqueSCEVs.InsertNode(S, IP);
1902 /// getAnyExtendExpr - Return a SCEV for the given operand extended with
1903 /// unspecified bits out to the given type.
1905 const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
1907 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1908 "This is not an extending conversion!");
1909 assert(isSCEVable(Ty) &&
1910 "This is not a conversion to a SCEVable type!");
1911 Ty = getEffectiveSCEVType(Ty);
1913 // Sign-extend negative constants.
1914 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1915 if (SC->getAPInt().isNegative())
1916 return getSignExtendExpr(Op, Ty);
1918 // Peel off a truncate cast.
1919 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
1920 const SCEV *NewOp = T->getOperand();
1921 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
1922 return getAnyExtendExpr(NewOp, Ty);
1923 return getTruncateOrNoop(NewOp, Ty);
1926 // Next try a zext cast. If the cast is folded, use it.
1927 const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
1928 if (!isa<SCEVZeroExtendExpr>(ZExt))
1931 // Next try a sext cast. If the cast is folded, use it.
1932 const SCEV *SExt = getSignExtendExpr(Op, Ty);
1933 if (!isa<SCEVSignExtendExpr>(SExt))
1936 // Force the cast to be folded into the operands of an addrec.
1937 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
1938 SmallVector<const SCEV *, 4> Ops;
1939 for (const SCEV *Op : AR->operands())
1940 Ops.push_back(getAnyExtendExpr(Op, Ty));
1941 return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW);
1944 // If the expression is obviously signed, use the sext cast value.
1945 if (isa<SCEVSMaxExpr>(Op))
1948 // Absent any other information, use the zext cast value.
1952 /// Process the given Ops list, which is a list of operands to be added under
1953 /// the given scale, update the given map. This is a helper function for
1954 /// getAddRecExpr. As an example of what it does, given a sequence of operands
1955 /// that would form an add expression like this:
1957 /// m + n + 13 + (A * (o + p + (B * (q + m + 29)))) + r + (-1 * r)
1959 /// where A and B are constants, update the map with these values:
1961 /// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
1963 /// and add 13 + A*B*29 to AccumulatedConstant.
1964 /// This will allow getAddRecExpr to produce this:
1966 /// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
1968 /// This form often exposes folding opportunities that are hidden in
1969 /// the original operand list.
1971 /// Return true iff it appears that any interesting folding opportunities
1972 /// may be exposed. This helps getAddRecExpr short-circuit extra work in
1973 /// the common case where no interesting opportunities are present, and
1974 /// is also used as a check to avoid infinite recursion.
1977 CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
1978 SmallVectorImpl<const SCEV *> &NewOps,
1979 APInt &AccumulatedConstant,
1980 const SCEV *const *Ops, size_t NumOperands,
1982 ScalarEvolution &SE) {
1983 bool Interesting = false;
1985 // Iterate over the add operands. They are sorted, with constants first.
1987 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1989 // Pull a buried constant out to the outside.
1990 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
1992 AccumulatedConstant += Scale * C->getAPInt();
1995 // Next comes everything else. We're especially interested in multiplies
1996 // here, but they're in the middle, so just visit the rest with one loop.
1997 for (; i != NumOperands; ++i) {
1998 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
1999 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
2001 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getAPInt();
2002 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
2003 // A multiplication of a constant with another add; recurse.
2004 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1));
2006 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
2007 Add->op_begin(), Add->getNumOperands(),
2010 // A multiplication of a constant with some other value. Update
2012 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
2013 const SCEV *Key = SE.getMulExpr(MulOps);
2014 auto Pair = M.insert({Key, NewScale});
2016 NewOps.push_back(Pair.first->first);
2018 Pair.first->second += NewScale;
2019 // The map already had an entry for this value, which may indicate
2020 // a folding opportunity.
2025 // An ordinary operand. Update the map.
2026 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
2027 M.insert({Ops[i], Scale});
2029 NewOps.push_back(Pair.first->first);
2031 Pair.first->second += Scale;
2032 // The map already had an entry for this value, which may indicate
2033 // a folding opportunity.
2042 // We're trying to construct a SCEV of type `Type' with `Ops' as operands and
2043 // `OldFlags' as can't-wrap behavior. Infer a more aggressive set of
2044 // can't-overflow flags for the operation if possible.
2045 static SCEV::NoWrapFlags
2046 StrengthenNoWrapFlags(ScalarEvolution *SE, SCEVTypes Type,
2047 const SmallVectorImpl<const SCEV *> &Ops,
2048 SCEV::NoWrapFlags Flags) {
2049 using namespace std::placeholders;
2050 typedef OverflowingBinaryOperator OBO;
2053 Type == scAddExpr || Type == scAddRecExpr || Type == scMulExpr;
2055 assert(CanAnalyze && "don't call from other places!");
2057 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
2058 SCEV::NoWrapFlags SignOrUnsignWrap =
2059 ScalarEvolution::maskFlags(Flags, SignOrUnsignMask);
2061 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
2062 auto IsKnownNonNegative = [&](const SCEV *S) {
2063 return SE->isKnownNonNegative(S);
2066 if (SignOrUnsignWrap == SCEV::FlagNSW && all_of(Ops, IsKnownNonNegative))
2068 ScalarEvolution::setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
2070 SignOrUnsignWrap = ScalarEvolution::maskFlags(Flags, SignOrUnsignMask);
2072 if (SignOrUnsignWrap != SignOrUnsignMask && Type == scAddExpr &&
2073 Ops.size() == 2 && isa<SCEVConstant>(Ops[0])) {
2075 // (A + C) --> (A + C)<nsw> if the addition does not sign overflow
2076 // (A + C) --> (A + C)<nuw> if the addition does not unsign overflow
2078 const APInt &C = cast<SCEVConstant>(Ops[0])->getAPInt();
2079 if (!(SignOrUnsignWrap & SCEV::FlagNSW)) {
2080 auto NSWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
2081 Instruction::Add, C, OBO::NoSignedWrap);
2082 if (NSWRegion.contains(SE->getSignedRange(Ops[1])))
2083 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW);
2085 if (!(SignOrUnsignWrap & SCEV::FlagNUW)) {
2086 auto NUWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
2087 Instruction::Add, C, OBO::NoUnsignedWrap);
2088 if (NUWRegion.contains(SE->getUnsignedRange(Ops[1])))
2089 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
2096 /// Get a canonical add expression, or something simpler if possible.
2097 const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
2098 SCEV::NoWrapFlags Flags) {
2099 assert(!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) &&
2100 "only nuw or nsw allowed");
2101 assert(!Ops.empty() && "Cannot get empty add!");
2102 if (Ops.size() == 1) return Ops[0];
2104 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2105 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2106 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2107 "SCEVAddExpr operand types don't match!");
2110 // Sort by complexity, this groups all similar expression types together.
2111 GroupByComplexity(Ops, &LI);
2113 Flags = StrengthenNoWrapFlags(this, scAddExpr, Ops, Flags);
2115 // If there are any constants, fold them together.
2117 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2119 assert(Idx < Ops.size());
2120 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2121 // We found two constants, fold them together!
2122 Ops[0] = getConstant(LHSC->getAPInt() + RHSC->getAPInt());
2123 if (Ops.size() == 2) return Ops[0];
2124 Ops.erase(Ops.begin()+1); // Erase the folded element
2125 LHSC = cast<SCEVConstant>(Ops[0]);
2128 // If we are left with a constant zero being added, strip it off.
2129 if (LHSC->getValue()->isZero()) {
2130 Ops.erase(Ops.begin());
2134 if (Ops.size() == 1) return Ops[0];
2137 // Okay, check to see if the same value occurs in the operand list more than
2138 // once. If so, merge them together into an multiply expression. Since we
2139 // sorted the list, these values are required to be adjacent.
2140 Type *Ty = Ops[0]->getType();
2141 bool FoundMatch = false;
2142 for (unsigned i = 0, e = Ops.size(); i != e-1; ++i)
2143 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
2144 // Scan ahead to count how many equal operands there are.
2146 while (i+Count != e && Ops[i+Count] == Ops[i])
2148 // Merge the values into a multiply.
2149 const SCEV *Scale = getConstant(Ty, Count);
2150 const SCEV *Mul = getMulExpr(Scale, Ops[i]);
2151 if (Ops.size() == Count)
2154 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count);
2155 --i; e -= Count - 1;
2159 return getAddExpr(Ops, Flags);
2161 // Check for truncates. If all the operands are truncated from the same
2162 // type, see if factoring out the truncate would permit the result to be
2163 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
2164 // if the contents of the resulting outer trunc fold to something simple.
2165 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
2166 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
2167 Type *DstType = Trunc->getType();
2168 Type *SrcType = Trunc->getOperand()->getType();
2169 SmallVector<const SCEV *, 8> LargeOps;
2171 // Check all the operands to see if they can be represented in the
2172 // source type of the truncate.
2173 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
2174 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
2175 if (T->getOperand()->getType() != SrcType) {
2179 LargeOps.push_back(T->getOperand());
2180 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
2181 LargeOps.push_back(getAnyExtendExpr(C, SrcType));
2182 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
2183 SmallVector<const SCEV *, 8> LargeMulOps;
2184 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
2185 if (const SCEVTruncateExpr *T =
2186 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
2187 if (T->getOperand()->getType() != SrcType) {
2191 LargeMulOps.push_back(T->getOperand());
2192 } else if (const auto *C = dyn_cast<SCEVConstant>(M->getOperand(j))) {
2193 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType));
2200 LargeOps.push_back(getMulExpr(LargeMulOps));
2207 // Evaluate the expression in the larger type.
2208 const SCEV *Fold = getAddExpr(LargeOps, Flags);
2209 // If it folds to something simple, use it. Otherwise, don't.
2210 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
2211 return getTruncateExpr(Fold, DstType);
2215 // Skip past any other cast SCEVs.
2216 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
2219 // If there are add operands they would be next.
2220 if (Idx < Ops.size()) {
2221 bool DeletedAdd = false;
2222 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
2223 // If we have an add, expand the add operands onto the end of the operands
2225 Ops.erase(Ops.begin()+Idx);
2226 Ops.append(Add->op_begin(), Add->op_end());
2230 // If we deleted at least one add, we added operands to the end of the list,
2231 // and they are not necessarily sorted. Recurse to resort and resimplify
2232 // any operands we just acquired.
2234 return getAddExpr(Ops);
2237 // Skip over the add expression until we get to a multiply.
2238 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
2241 // Check to see if there are any folding opportunities present with
2242 // operands multiplied by constant values.
2243 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
2244 uint64_t BitWidth = getTypeSizeInBits(Ty);
2245 DenseMap<const SCEV *, APInt> M;
2246 SmallVector<const SCEV *, 8> NewOps;
2247 APInt AccumulatedConstant(BitWidth, 0);
2248 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
2249 Ops.data(), Ops.size(),
2250 APInt(BitWidth, 1), *this)) {
2251 struct APIntCompare {
2252 bool operator()(const APInt &LHS, const APInt &RHS) const {
2253 return LHS.ult(RHS);
2257 // Some interesting folding opportunity is present, so its worthwhile to
2258 // re-generate the operands list. Group the operands by constant scale,
2259 // to avoid multiplying by the same constant scale multiple times.
2260 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
2261 for (const SCEV *NewOp : NewOps)
2262 MulOpLists[M.find(NewOp)->second].push_back(NewOp);
2263 // Re-generate the operands list.
2265 if (AccumulatedConstant != 0)
2266 Ops.push_back(getConstant(AccumulatedConstant));
2267 for (auto &MulOp : MulOpLists)
2268 if (MulOp.first != 0)
2269 Ops.push_back(getMulExpr(getConstant(MulOp.first),
2270 getAddExpr(MulOp.second)));
2273 if (Ops.size() == 1)
2275 return getAddExpr(Ops);
2279 // If we are adding something to a multiply expression, make sure the
2280 // something is not already an operand of the multiply. If so, merge it into
2282 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
2283 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
2284 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
2285 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
2286 if (isa<SCEVConstant>(MulOpSCEV))
2288 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
2289 if (MulOpSCEV == Ops[AddOp]) {
2290 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
2291 const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
2292 if (Mul->getNumOperands() != 2) {
2293 // If the multiply has more than two operands, we must get the
2295 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
2296 Mul->op_begin()+MulOp);
2297 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
2298 InnerMul = getMulExpr(MulOps);
2300 const SCEV *One = getOne(Ty);
2301 const SCEV *AddOne = getAddExpr(One, InnerMul);
2302 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV);
2303 if (Ops.size() == 2) return OuterMul;
2305 Ops.erase(Ops.begin()+AddOp);
2306 Ops.erase(Ops.begin()+Idx-1);
2308 Ops.erase(Ops.begin()+Idx);
2309 Ops.erase(Ops.begin()+AddOp-1);
2311 Ops.push_back(OuterMul);
2312 return getAddExpr(Ops);
2315 // Check this multiply against other multiplies being added together.
2316 for (unsigned OtherMulIdx = Idx+1;
2317 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
2319 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
2320 // If MulOp occurs in OtherMul, we can fold the two multiplies
2322 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
2323 OMulOp != e; ++OMulOp)
2324 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
2325 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
2326 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
2327 if (Mul->getNumOperands() != 2) {
2328 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
2329 Mul->op_begin()+MulOp);
2330 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
2331 InnerMul1 = getMulExpr(MulOps);
2333 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
2334 if (OtherMul->getNumOperands() != 2) {
2335 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
2336 OtherMul->op_begin()+OMulOp);
2337 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end());
2338 InnerMul2 = getMulExpr(MulOps);
2340 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
2341 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
2342 if (Ops.size() == 2) return OuterMul;
2343 Ops.erase(Ops.begin()+Idx);
2344 Ops.erase(Ops.begin()+OtherMulIdx-1);
2345 Ops.push_back(OuterMul);
2346 return getAddExpr(Ops);
2352 // If there are any add recurrences in the operands list, see if any other
2353 // added values are loop invariant. If so, we can fold them into the
2355 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2358 // Scan over all recurrences, trying to fold loop invariants into them.
2359 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
2360 // Scan all of the other operands to this add and add them to the vector if
2361 // they are loop invariant w.r.t. the recurrence.
2362 SmallVector<const SCEV *, 8> LIOps;
2363 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2364 const Loop *AddRecLoop = AddRec->getLoop();
2365 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2366 if (isLoopInvariant(Ops[i], AddRecLoop)) {
2367 LIOps.push_back(Ops[i]);
2368 Ops.erase(Ops.begin()+i);
2372 // If we found some loop invariants, fold them into the recurrence.
2373 if (!LIOps.empty()) {
2374 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
2375 LIOps.push_back(AddRec->getStart());
2377 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
2379 // This follows from the fact that the no-wrap flags on the outer add
2380 // expression are applicable on the 0th iteration, when the add recurrence
2381 // will be equal to its start value.
2382 AddRecOps[0] = getAddExpr(LIOps, Flags);
2384 // Build the new addrec. Propagate the NUW and NSW flags if both the
2385 // outer add and the inner addrec are guaranteed to have no overflow.
2386 // Always propagate NW.
2387 Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW));
2388 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags);
2390 // If all of the other operands were loop invariant, we are done.
2391 if (Ops.size() == 1) return NewRec;
2393 // Otherwise, add the folded AddRec by the non-invariant parts.
2394 for (unsigned i = 0;; ++i)
2395 if (Ops[i] == AddRec) {
2399 return getAddExpr(Ops);
2402 // Okay, if there weren't any loop invariants to be folded, check to see if
2403 // there are multiple AddRec's with the same loop induction variable being
2404 // added together. If so, we can fold them.
2405 for (unsigned OtherIdx = Idx+1;
2406 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2408 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
2409 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L>
2410 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
2412 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2414 if (const auto *OtherAddRec = dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]))
2415 if (OtherAddRec->getLoop() == AddRecLoop) {
2416 for (unsigned i = 0, e = OtherAddRec->getNumOperands();
2418 if (i >= AddRecOps.size()) {
2419 AddRecOps.append(OtherAddRec->op_begin()+i,
2420 OtherAddRec->op_end());
2423 AddRecOps[i] = getAddExpr(AddRecOps[i],
2424 OtherAddRec->getOperand(i));
2426 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2428 // Step size has changed, so we cannot guarantee no self-wraparound.
2429 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap);
2430 return getAddExpr(Ops);
2433 // Otherwise couldn't fold anything into this recurrence. Move onto the
2437 // Okay, it looks like we really DO need an add expr. Check to see if we
2438 // already have one, otherwise create a new one.
2439 FoldingSetNodeID ID;
2440 ID.AddInteger(scAddExpr);
2441 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2442 ID.AddPointer(Ops[i]);
2445 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2447 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2448 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2449 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator),
2451 UniqueSCEVs.InsertNode(S, IP);
2453 S->setNoWrapFlags(Flags);
2457 static uint64_t umul_ov(uint64_t i, uint64_t j, bool &Overflow) {
2459 if (j > 1 && k / j != i) Overflow = true;
2463 /// Compute the result of "n choose k", the binomial coefficient. If an
2464 /// intermediate computation overflows, Overflow will be set and the return will
2465 /// be garbage. Overflow is not cleared on absence of overflow.
2466 static uint64_t Choose(uint64_t n, uint64_t k, bool &Overflow) {
2467 // We use the multiplicative formula:
2468 // n(n-1)(n-2)...(n-(k-1)) / k(k-1)(k-2)...1 .
2469 // At each iteration, we take the n-th term of the numeral and divide by the
2470 // (k-n)th term of the denominator. This division will always produce an
2471 // integral result, and helps reduce the chance of overflow in the
2472 // intermediate computations. However, we can still overflow even when the
2473 // final result would fit.
2475 if (n == 0 || n == k) return 1;
2476 if (k > n) return 0;
2482 for (uint64_t i = 1; i <= k; ++i) {
2483 r = umul_ov(r, n-(i-1), Overflow);
2489 /// Determine if any of the operands in this SCEV are a constant or if
2490 /// any of the add or multiply expressions in this SCEV contain a constant.
2491 static bool containsConstantSomewhere(const SCEV *StartExpr) {
2492 SmallVector<const SCEV *, 4> Ops;
2493 Ops.push_back(StartExpr);
2494 while (!Ops.empty()) {
2495 const SCEV *CurrentExpr = Ops.pop_back_val();
2496 if (isa<SCEVConstant>(*CurrentExpr))
2499 if (isa<SCEVAddExpr>(*CurrentExpr) || isa<SCEVMulExpr>(*CurrentExpr)) {
2500 const auto *CurrentNAry = cast<SCEVNAryExpr>(CurrentExpr);
2501 Ops.append(CurrentNAry->op_begin(), CurrentNAry->op_end());
2507 /// Get a canonical multiply expression, or something simpler if possible.
2508 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
2509 SCEV::NoWrapFlags Flags) {
2510 assert(Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) &&
2511 "only nuw or nsw allowed");
2512 assert(!Ops.empty() && "Cannot get empty mul!");
2513 if (Ops.size() == 1) return Ops[0];
2515 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2516 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2517 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2518 "SCEVMulExpr operand types don't match!");
2521 // Sort by complexity, this groups all similar expression types together.
2522 GroupByComplexity(Ops, &LI);
2524 Flags = StrengthenNoWrapFlags(this, scMulExpr, Ops, Flags);
2526 // If there are any constants, fold them together.
2528 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2530 // C1*(C2+V) -> C1*C2 + C1*V
2531 if (Ops.size() == 2)
2532 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
2533 // If any of Add's ops are Adds or Muls with a constant,
2534 // apply this transformation as well.
2535 if (Add->getNumOperands() == 2)
2536 if (containsConstantSomewhere(Add))
2537 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
2538 getMulExpr(LHSC, Add->getOperand(1)));
2541 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2542 // We found two constants, fold them together!
2544 ConstantInt::get(getContext(), LHSC->getAPInt() * RHSC->getAPInt());
2545 Ops[0] = getConstant(Fold);
2546 Ops.erase(Ops.begin()+1); // Erase the folded element
2547 if (Ops.size() == 1) return Ops[0];
2548 LHSC = cast<SCEVConstant>(Ops[0]);
2551 // If we are left with a constant one being multiplied, strip it off.
2552 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
2553 Ops.erase(Ops.begin());
2555 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
2556 // If we have a multiply of zero, it will always be zero.
2558 } else if (Ops[0]->isAllOnesValue()) {
2559 // If we have a mul by -1 of an add, try distributing the -1 among the
2561 if (Ops.size() == 2) {
2562 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
2563 SmallVector<const SCEV *, 4> NewOps;
2564 bool AnyFolded = false;
2565 for (const SCEV *AddOp : Add->operands()) {
2566 const SCEV *Mul = getMulExpr(Ops[0], AddOp);
2567 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
2568 NewOps.push_back(Mul);
2571 return getAddExpr(NewOps);
2572 } else if (const auto *AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) {
2573 // Negation preserves a recurrence's no self-wrap property.
2574 SmallVector<const SCEV *, 4> Operands;
2575 for (const SCEV *AddRecOp : AddRec->operands())
2576 Operands.push_back(getMulExpr(Ops[0], AddRecOp));
2578 return getAddRecExpr(Operands, AddRec->getLoop(),
2579 AddRec->getNoWrapFlags(SCEV::FlagNW));
2584 if (Ops.size() == 1)
2588 // Skip over the add expression until we get to a multiply.
2589 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
2592 // If there are mul operands inline them all into this expression.
2593 if (Idx < Ops.size()) {
2594 bool DeletedMul = false;
2595 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
2596 if (Ops.size() > MulOpsInlineThreshold)
2598 // If we have an mul, expand the mul operands onto the end of the operands
2600 Ops.erase(Ops.begin()+Idx);
2601 Ops.append(Mul->op_begin(), Mul->op_end());
2605 // If we deleted at least one mul, we added operands to the end of the list,
2606 // and they are not necessarily sorted. Recurse to resort and resimplify
2607 // any operands we just acquired.
2609 return getMulExpr(Ops);
2612 // If there are any add recurrences in the operands list, see if any other
2613 // added values are loop invariant. If so, we can fold them into the
2615 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2618 // Scan over all recurrences, trying to fold loop invariants into them.
2619 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
2620 // Scan all of the other operands to this mul and add them to the vector if
2621 // they are loop invariant w.r.t. the recurrence.
2622 SmallVector<const SCEV *, 8> LIOps;
2623 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2624 const Loop *AddRecLoop = AddRec->getLoop();
2625 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2626 if (isLoopInvariant(Ops[i], AddRecLoop)) {
2627 LIOps.push_back(Ops[i]);
2628 Ops.erase(Ops.begin()+i);
2632 // If we found some loop invariants, fold them into the recurrence.
2633 if (!LIOps.empty()) {
2634 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
2635 SmallVector<const SCEV *, 4> NewOps;
2636 NewOps.reserve(AddRec->getNumOperands());
2637 const SCEV *Scale = getMulExpr(LIOps);
2638 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
2639 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
2641 // Build the new addrec. Propagate the NUW and NSW flags if both the
2642 // outer mul and the inner addrec are guaranteed to have no overflow.
2644 // No self-wrap cannot be guaranteed after changing the step size, but
2645 // will be inferred if either NUW or NSW is true.
2646 Flags = AddRec->getNoWrapFlags(clearFlags(Flags, SCEV::FlagNW));
2647 const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, Flags);
2649 // If all of the other operands were loop invariant, we are done.
2650 if (Ops.size() == 1) return NewRec;
2652 // Otherwise, multiply the folded AddRec by the non-invariant parts.
2653 for (unsigned i = 0;; ++i)
2654 if (Ops[i] == AddRec) {
2658 return getMulExpr(Ops);
2661 // Okay, if there weren't any loop invariants to be folded, check to see if
2662 // there are multiple AddRec's with the same loop induction variable being
2663 // multiplied together. If so, we can fold them.
2665 // {A1,+,A2,+,...,+,An}<L> * {B1,+,B2,+,...,+,Bn}<L>
2666 // = {x=1 in [ sum y=x..2x [ sum z=max(y-x, y-n)..min(x,n) [
2667 // choose(x, 2x)*choose(2x-y, x-z)*A_{y-z}*B_z
2668 // ]]],+,...up to x=2n}.
2669 // Note that the arguments to choose() are always integers with values
2670 // known at compile time, never SCEV objects.
2672 // The implementation avoids pointless extra computations when the two
2673 // addrec's are of different length (mathematically, it's equivalent to
2674 // an infinite stream of zeros on the right).
2675 bool OpsModified = false;
2676 for (unsigned OtherIdx = Idx+1;
2677 OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2679 const SCEVAddRecExpr *OtherAddRec =
2680 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]);
2681 if (!OtherAddRec || OtherAddRec->getLoop() != AddRecLoop)
2684 bool Overflow = false;
2685 Type *Ty = AddRec->getType();
2686 bool LargerThan64Bits = getTypeSizeInBits(Ty) > 64;
2687 SmallVector<const SCEV*, 7> AddRecOps;
2688 for (int x = 0, xe = AddRec->getNumOperands() +
2689 OtherAddRec->getNumOperands() - 1; x != xe && !Overflow; ++x) {
2690 const SCEV *Term = getZero(Ty);
2691 for (int y = x, ye = 2*x+1; y != ye && !Overflow; ++y) {
2692 uint64_t Coeff1 = Choose(x, 2*x - y, Overflow);
2693 for (int z = std::max(y-x, y-(int)AddRec->getNumOperands()+1),
2694 ze = std::min(x+1, (int)OtherAddRec->getNumOperands());
2695 z < ze && !Overflow; ++z) {
2696 uint64_t Coeff2 = Choose(2*x - y, x-z, Overflow);
2698 if (LargerThan64Bits)
2699 Coeff = umul_ov(Coeff1, Coeff2, Overflow);
2701 Coeff = Coeff1*Coeff2;
2702 const SCEV *CoeffTerm = getConstant(Ty, Coeff);
2703 const SCEV *Term1 = AddRec->getOperand(y-z);
2704 const SCEV *Term2 = OtherAddRec->getOperand(z);
2705 Term = getAddExpr(Term, getMulExpr(CoeffTerm, Term1,Term2));
2708 AddRecOps.push_back(Term);
2711 const SCEV *NewAddRec = getAddRecExpr(AddRecOps, AddRec->getLoop(),
2713 if (Ops.size() == 2) return NewAddRec;
2714 Ops[Idx] = NewAddRec;
2715 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2717 AddRec = dyn_cast<SCEVAddRecExpr>(NewAddRec);
2723 return getMulExpr(Ops);
2725 // Otherwise couldn't fold anything into this recurrence. Move onto the
2729 // Okay, it looks like we really DO need an mul expr. Check to see if we
2730 // already have one, otherwise create a new one.
2731 FoldingSetNodeID ID;
2732 ID.AddInteger(scMulExpr);
2733 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2734 ID.AddPointer(Ops[i]);
2737 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2739 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2740 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2741 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
2743 UniqueSCEVs.InsertNode(S, IP);
2745 S->setNoWrapFlags(Flags);
2749 /// Get a canonical unsigned division expression, or something simpler if
2751 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
2753 assert(getEffectiveSCEVType(LHS->getType()) ==
2754 getEffectiveSCEVType(RHS->getType()) &&
2755 "SCEVUDivExpr operand types don't match!");
2757 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
2758 if (RHSC->getValue()->equalsInt(1))
2759 return LHS; // X udiv 1 --> x
2760 // If the denominator is zero, the result of the udiv is undefined. Don't
2761 // try to analyze it, because the resolution chosen here may differ from
2762 // the resolution chosen in other parts of the compiler.
2763 if (!RHSC->getValue()->isZero()) {
2764 // Determine if the division can be folded into the operands of
2766 // TODO: Generalize this to non-constants by using known-bits information.
2767 Type *Ty = LHS->getType();
2768 unsigned LZ = RHSC->getAPInt().countLeadingZeros();
2769 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1;
2770 // For non-power-of-two values, effectively round the value up to the
2771 // nearest power of two.
2772 if (!RHSC->getAPInt().isPowerOf2())
2774 IntegerType *ExtTy =
2775 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
2776 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
2777 if (const SCEVConstant *Step =
2778 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) {
2779 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
2780 const APInt &StepInt = Step->getAPInt();
2781 const APInt &DivInt = RHSC->getAPInt();
2782 if (!StepInt.urem(DivInt) &&
2783 getZeroExtendExpr(AR, ExtTy) ==
2784 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2785 getZeroExtendExpr(Step, ExtTy),
2786 AR->getLoop(), SCEV::FlagAnyWrap)) {
2787 SmallVector<const SCEV *, 4> Operands;
2788 for (const SCEV *Op : AR->operands())
2789 Operands.push_back(getUDivExpr(Op, RHS));
2790 return getAddRecExpr(Operands, AR->getLoop(), SCEV::FlagNW);
2792 /// Get a canonical UDivExpr for a recurrence.
2793 /// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0.
2794 // We can currently only fold X%N if X is constant.
2795 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(AR->getStart());
2796 if (StartC && !DivInt.urem(StepInt) &&
2797 getZeroExtendExpr(AR, ExtTy) ==
2798 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2799 getZeroExtendExpr(Step, ExtTy),
2800 AR->getLoop(), SCEV::FlagAnyWrap)) {
2801 const APInt &StartInt = StartC->getAPInt();
2802 const APInt &StartRem = StartInt.urem(StepInt);
2804 LHS = getAddRecExpr(getConstant(StartInt - StartRem), Step,
2805 AR->getLoop(), SCEV::FlagNW);
2808 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
2809 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
2810 SmallVector<const SCEV *, 4> Operands;
2811 for (const SCEV *Op : M->operands())
2812 Operands.push_back(getZeroExtendExpr(Op, ExtTy));
2813 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
2814 // Find an operand that's safely divisible.
2815 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
2816 const SCEV *Op = M->getOperand(i);
2817 const SCEV *Div = getUDivExpr(Op, RHSC);
2818 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
2819 Operands = SmallVector<const SCEV *, 4>(M->op_begin(),
2822 return getMulExpr(Operands);
2826 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
2827 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) {
2828 SmallVector<const SCEV *, 4> Operands;
2829 for (const SCEV *Op : A->operands())
2830 Operands.push_back(getZeroExtendExpr(Op, ExtTy));
2831 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
2833 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
2834 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
2835 if (isa<SCEVUDivExpr>(Op) ||
2836 getMulExpr(Op, RHS) != A->getOperand(i))
2838 Operands.push_back(Op);
2840 if (Operands.size() == A->getNumOperands())
2841 return getAddExpr(Operands);
2845 // Fold if both operands are constant.
2846 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
2847 Constant *LHSCV = LHSC->getValue();
2848 Constant *RHSCV = RHSC->getValue();
2849 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
2855 FoldingSetNodeID ID;
2856 ID.AddInteger(scUDivExpr);
2860 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2861 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
2863 UniqueSCEVs.InsertNode(S, IP);
2867 static const APInt gcd(const SCEVConstant *C1, const SCEVConstant *C2) {
2868 APInt A = C1->getAPInt().abs();
2869 APInt B = C2->getAPInt().abs();
2870 uint32_t ABW = A.getBitWidth();
2871 uint32_t BBW = B.getBitWidth();
2878 return APIntOps::GreatestCommonDivisor(A, B);
2881 /// Get a canonical unsigned division expression, or something simpler if
2882 /// possible. There is no representation for an exact udiv in SCEV IR, but we
2883 /// can attempt to remove factors from the LHS and RHS. We can't do this when
2884 /// it's not exact because the udiv may be clearing bits.
2885 const SCEV *ScalarEvolution::getUDivExactExpr(const SCEV *LHS,
2887 // TODO: we could try to find factors in all sorts of things, but for now we
2888 // just deal with u/exact (multiply, constant). See SCEVDivision towards the
2889 // end of this file for inspiration.
2891 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(LHS);
2893 return getUDivExpr(LHS, RHS);
2895 if (const SCEVConstant *RHSCst = dyn_cast<SCEVConstant>(RHS)) {
2896 // If the mulexpr multiplies by a constant, then that constant must be the
2897 // first element of the mulexpr.
2898 if (const auto *LHSCst = dyn_cast<SCEVConstant>(Mul->getOperand(0))) {
2899 if (LHSCst == RHSCst) {
2900 SmallVector<const SCEV *, 2> Operands;
2901 Operands.append(Mul->op_begin() + 1, Mul->op_end());
2902 return getMulExpr(Operands);
2905 // We can't just assume that LHSCst divides RHSCst cleanly, it could be
2906 // that there's a factor provided by one of the other terms. We need to
2908 APInt Factor = gcd(LHSCst, RHSCst);
2909 if (!Factor.isIntN(1)) {
2911 cast<SCEVConstant>(getConstant(LHSCst->getAPInt().udiv(Factor)));
2913 cast<SCEVConstant>(getConstant(RHSCst->getAPInt().udiv(Factor)));
2914 SmallVector<const SCEV *, 2> Operands;
2915 Operands.push_back(LHSCst);
2916 Operands.append(Mul->op_begin() + 1, Mul->op_end());
2917 LHS = getMulExpr(Operands);
2919 Mul = dyn_cast<SCEVMulExpr>(LHS);
2921 return getUDivExactExpr(LHS, RHS);
2926 for (int i = 0, e = Mul->getNumOperands(); i != e; ++i) {
2927 if (Mul->getOperand(i) == RHS) {
2928 SmallVector<const SCEV *, 2> Operands;
2929 Operands.append(Mul->op_begin(), Mul->op_begin() + i);
2930 Operands.append(Mul->op_begin() + i + 1, Mul->op_end());
2931 return getMulExpr(Operands);
2935 return getUDivExpr(LHS, RHS);
2938 /// Get an add recurrence expression for the specified loop. Simplify the
2939 /// expression as much as possible.
2940 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step,
2942 SCEV::NoWrapFlags Flags) {
2943 SmallVector<const SCEV *, 4> Operands;
2944 Operands.push_back(Start);
2945 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
2946 if (StepChrec->getLoop() == L) {
2947 Operands.append(StepChrec->op_begin(), StepChrec->op_end());
2948 return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW));
2951 Operands.push_back(Step);
2952 return getAddRecExpr(Operands, L, Flags);
2955 /// Get an add recurrence expression for the specified loop. Simplify the
2956 /// expression as much as possible.
2958 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
2959 const Loop *L, SCEV::NoWrapFlags Flags) {
2960 if (Operands.size() == 1) return Operands[0];
2962 Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
2963 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
2964 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy &&
2965 "SCEVAddRecExpr operand types don't match!");
2966 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2967 assert(isLoopInvariant(Operands[i], L) &&
2968 "SCEVAddRecExpr operand is not loop-invariant!");
2971 if (Operands.back()->isZero()) {
2972 Operands.pop_back();
2973 return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0} --> X
2976 // It's tempting to want to call getMaxBackedgeTakenCount count here and
2977 // use that information to infer NUW and NSW flags. However, computing a
2978 // BE count requires calling getAddRecExpr, so we may not yet have a
2979 // meaningful BE count at this point (and if we don't, we'd be stuck
2980 // with a SCEVCouldNotCompute as the cached BE count).
2982 Flags = StrengthenNoWrapFlags(this, scAddRecExpr, Operands, Flags);
2984 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
2985 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
2986 const Loop *NestedLoop = NestedAR->getLoop();
2987 if (L->contains(NestedLoop)
2988 ? (L->getLoopDepth() < NestedLoop->getLoopDepth())
2989 : (!NestedLoop->contains(L) &&
2990 DT.dominates(L->getHeader(), NestedLoop->getHeader()))) {
2991 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
2992 NestedAR->op_end());
2993 Operands[0] = NestedAR->getStart();
2994 // AddRecs require their operands be loop-invariant with respect to their
2995 // loops. Don't perform this transformation if it would break this
2997 bool AllInvariant = all_of(
2998 Operands, [&](const SCEV *Op) { return isLoopInvariant(Op, L); });
3001 // Create a recurrence for the outer loop with the same step size.
3003 // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the
3004 // inner recurrence has the same property.
3005 SCEV::NoWrapFlags OuterFlags =
3006 maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags());
3008 NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags);
3009 AllInvariant = all_of(NestedOperands, [&](const SCEV *Op) {
3010 return isLoopInvariant(Op, NestedLoop);
3014 // Ok, both add recurrences are valid after the transformation.
3016 // The inner recurrence keeps its NW flag but only keeps NUW/NSW if
3017 // the outer recurrence has the same property.
3018 SCEV::NoWrapFlags InnerFlags =
3019 maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags);
3020 return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags);
3023 // Reset Operands to its original state.
3024 Operands[0] = NestedAR;
3028 // Okay, it looks like we really DO need an addrec expr. Check to see if we
3029 // already have one, otherwise create a new one.
3030 FoldingSetNodeID ID;
3031 ID.AddInteger(scAddRecExpr);
3032 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
3033 ID.AddPointer(Operands[i]);
3037 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
3039 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size());
3040 std::uninitialized_copy(Operands.begin(), Operands.end(), O);
3041 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator),
3042 O, Operands.size(), L);
3043 UniqueSCEVs.InsertNode(S, IP);
3045 S->setNoWrapFlags(Flags);
3050 ScalarEvolution::getGEPExpr(GEPOperator *GEP,
3051 const SmallVectorImpl<const SCEV *> &IndexExprs) {
3052 const SCEV *BaseExpr = getSCEV(GEP->getPointerOperand());
3053 // getSCEV(Base)->getType() has the same address space as Base->getType()
3054 // because SCEV::getType() preserves the address space.
3055 Type *IntPtrTy = getEffectiveSCEVType(BaseExpr->getType());
3056 // FIXME(PR23527): Don't blindly transfer the inbounds flag from the GEP
3057 // instruction to its SCEV, because the Instruction may be guarded by control
3058 // flow and the no-overflow bits may not be valid for the expression in any
3059 // context. This can be fixed similarly to how these flags are handled for
3061 SCEV::NoWrapFlags Wrap = GEP->isInBounds() ? SCEV::FlagNSW
3062 : SCEV::FlagAnyWrap;
3064 const SCEV *TotalOffset = getZero(IntPtrTy);
3065 // The array size is unimportant. The first thing we do on CurTy is getting
3066 // its element type.
3067 Type *CurTy = ArrayType::get(GEP->getSourceElementType(), 0);
3068 for (const SCEV *IndexExpr : IndexExprs) {
3069 // Compute the (potentially symbolic) offset in bytes for this index.
3070 if (StructType *STy = dyn_cast<StructType>(CurTy)) {
3071 // For a struct, add the member offset.
3072 ConstantInt *Index = cast<SCEVConstant>(IndexExpr)->getValue();
3073 unsigned FieldNo = Index->getZExtValue();
3074 const SCEV *FieldOffset = getOffsetOfExpr(IntPtrTy, STy, FieldNo);
3076 // Add the field offset to the running total offset.
3077 TotalOffset = getAddExpr(TotalOffset, FieldOffset);
3079 // Update CurTy to the type of the field at Index.
3080 CurTy = STy->getTypeAtIndex(Index);
3082 // Update CurTy to its element type.
3083 CurTy = cast<SequentialType>(CurTy)->getElementType();
3084 // For an array, add the element offset, explicitly scaled.
3085 const SCEV *ElementSize = getSizeOfExpr(IntPtrTy, CurTy);
3086 // Getelementptr indices are signed.
3087 IndexExpr = getTruncateOrSignExtend(IndexExpr, IntPtrTy);
3089 // Multiply the index by the element size to compute the element offset.
3090 const SCEV *LocalOffset = getMulExpr(IndexExpr, ElementSize, Wrap);
3092 // Add the element offset to the running total offset.
3093 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
3097 // Add the total offset from all the GEP indices to the base.
3098 return getAddExpr(BaseExpr, TotalOffset, Wrap);
3101 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
3103 SmallVector<const SCEV *, 2> Ops = {LHS, RHS};
3104 return getSMaxExpr(Ops);
3108 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
3109 assert(!Ops.empty() && "Cannot get empty smax!");
3110 if (Ops.size() == 1) return Ops[0];
3112 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
3113 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
3114 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
3115 "SCEVSMaxExpr operand types don't match!");
3118 // Sort by complexity, this groups all similar expression types together.
3119 GroupByComplexity(Ops, &LI);
3121 // If there are any constants, fold them together.
3123 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
3125 assert(Idx < Ops.size());
3126 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
3127 // We found two constants, fold them together!
3128 ConstantInt *Fold = ConstantInt::get(
3129 getContext(), APIntOps::smax(LHSC->getAPInt(), RHSC->getAPInt()));
3130 Ops[0] = getConstant(Fold);
3131 Ops.erase(Ops.begin()+1); // Erase the folded element
3132 if (Ops.size() == 1) return Ops[0];
3133 LHSC = cast<SCEVConstant>(Ops[0]);
3136 // If we are left with a constant minimum-int, strip it off.
3137 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
3138 Ops.erase(Ops.begin());
3140 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
3141 // If we have an smax with a constant maximum-int, it will always be
3146 if (Ops.size() == 1) return Ops[0];
3149 // Find the first SMax
3150 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
3153 // Check to see if one of the operands is an SMax. If so, expand its operands
3154 // onto our operand list, and recurse to simplify.
3155 if (Idx < Ops.size()) {
3156 bool DeletedSMax = false;
3157 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
3158 Ops.erase(Ops.begin()+Idx);
3159 Ops.append(SMax->op_begin(), SMax->op_end());
3164 return getSMaxExpr(Ops);
3167 // Okay, check to see if the same value occurs in the operand list twice. If
3168 // so, delete one. Since we sorted the list, these values are required to
3170 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
3171 // X smax Y smax Y --> X smax Y
3172 // X smax Y --> X, if X is always greater than Y
3173 if (Ops[i] == Ops[i+1] ||
3174 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) {
3175 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
3177 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) {
3178 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
3182 if (Ops.size() == 1) return Ops[0];
3184 assert(!Ops.empty() && "Reduced smax down to nothing!");
3186 // Okay, it looks like we really DO need an smax expr. Check to see if we
3187 // already have one, otherwise create a new one.
3188 FoldingSetNodeID ID;
3189 ID.AddInteger(scSMaxExpr);
3190 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
3191 ID.AddPointer(Ops[i]);
3193 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
3194 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
3195 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
3196 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator),
3198 UniqueSCEVs.InsertNode(S, IP);
3202 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
3204 SmallVector<const SCEV *, 2> Ops = {LHS, RHS};
3205 return getUMaxExpr(Ops);
3209 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
3210 assert(!Ops.empty() && "Cannot get empty umax!");
3211 if (Ops.size() == 1) return Ops[0];
3213 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
3214 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
3215 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
3216 "SCEVUMaxExpr operand types don't match!");
3219 // Sort by complexity, this groups all similar expression types together.
3220 GroupByComplexity(Ops, &LI);
3222 // If there are any constants, fold them together.
3224 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
3226 assert(Idx < Ops.size());
3227 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
3228 // We found two constants, fold them together!
3229 ConstantInt *Fold = ConstantInt::get(
3230 getContext(), APIntOps::umax(LHSC->getAPInt(), RHSC->getAPInt()));
3231 Ops[0] = getConstant(Fold);
3232 Ops.erase(Ops.begin()+1); // Erase the folded element
3233 if (Ops.size() == 1) return Ops[0];
3234 LHSC = cast<SCEVConstant>(Ops[0]);
3237 // If we are left with a constant minimum-int, strip it off.
3238 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
3239 Ops.erase(Ops.begin());
3241 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
3242 // If we have an umax with a constant maximum-int, it will always be
3247 if (Ops.size() == 1) return Ops[0];
3250 // Find the first UMax
3251 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
3254 // Check to see if one of the operands is a UMax. If so, expand its operands
3255 // onto our operand list, and recurse to simplify.
3256 if (Idx < Ops.size()) {
3257 bool DeletedUMax = false;
3258 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
3259 Ops.erase(Ops.begin()+Idx);
3260 Ops.append(UMax->op_begin(), UMax->op_end());
3265 return getUMaxExpr(Ops);
3268 // Okay, check to see if the same value occurs in the operand list twice. If
3269 // so, delete one. Since we sorted the list, these values are required to
3271 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
3272 // X umax Y umax Y --> X umax Y
3273 // X umax Y --> X, if X is always greater than Y
3274 if (Ops[i] == Ops[i+1] ||
3275 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) {
3276 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
3278 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) {
3279 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
3283 if (Ops.size() == 1) return Ops[0];
3285 assert(!Ops.empty() && "Reduced umax down to nothing!");
3287 // Okay, it looks like we really DO need a umax expr. Check to see if we
3288 // already have one, otherwise create a new one.
3289 FoldingSetNodeID ID;
3290 ID.AddInteger(scUMaxExpr);
3291 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
3292 ID.AddPointer(Ops[i]);
3294 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
3295 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
3296 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
3297 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator),
3299 UniqueSCEVs.InsertNode(S, IP);
3303 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
3305 // ~smax(~x, ~y) == smin(x, y).
3306 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
3309 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
3311 // ~umax(~x, ~y) == umin(x, y)
3312 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
3315 const SCEV *ScalarEvolution::getSizeOfExpr(Type *IntTy, Type *AllocTy) {
3316 // We can bypass creating a target-independent
3317 // constant expression and then folding it back into a ConstantInt.
3318 // This is just a compile-time optimization.
3319 return getConstant(IntTy, getDataLayout().getTypeAllocSize(AllocTy));
3322 const SCEV *ScalarEvolution::getOffsetOfExpr(Type *IntTy,
3325 // We can bypass creating a target-independent
3326 // constant expression and then folding it back into a ConstantInt.
3327 // This is just a compile-time optimization.
3329 IntTy, getDataLayout().getStructLayout(STy)->getElementOffset(FieldNo));
3332 const SCEV *ScalarEvolution::getUnknown(Value *V) {
3333 // Don't attempt to do anything other than create a SCEVUnknown object
3334 // here. createSCEV only calls getUnknown after checking for all other
3335 // interesting possibilities, and any other code that calls getUnknown
3336 // is doing so in order to hide a value from SCEV canonicalization.
3338 FoldingSetNodeID ID;
3339 ID.AddInteger(scUnknown);
3342 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
3343 assert(cast<SCEVUnknown>(S)->getValue() == V &&
3344 "Stale SCEVUnknown in uniquing map!");
3347 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
3349 FirstUnknown = cast<SCEVUnknown>(S);
3350 UniqueSCEVs.InsertNode(S, IP);
3354 //===----------------------------------------------------------------------===//
3355 // Basic SCEV Analysis and PHI Idiom Recognition Code
3358 /// Test if values of the given type are analyzable within the SCEV
3359 /// framework. This primarily includes integer types, and it can optionally
3360 /// include pointer types if the ScalarEvolution class has access to
3361 /// target-specific information.
3362 bool ScalarEvolution::isSCEVable(Type *Ty) const {
3363 // Integers and pointers are always SCEVable.
3364 return Ty->isIntegerTy() || Ty->isPointerTy();
3367 /// Return the size in bits of the specified type, for which isSCEVable must
3369 uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const {
3370 assert(isSCEVable(Ty) && "Type is not SCEVable!");
3371 return getDataLayout().getTypeSizeInBits(Ty);
3374 /// Return a type with the same bitwidth as the given type and which represents
3375 /// how SCEV will treat the given type, for which isSCEVable must return
3376 /// true. For pointer types, this is the pointer-sized integer type.
3377 Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const {
3378 assert(isSCEVable(Ty) && "Type is not SCEVable!");
3380 if (Ty->isIntegerTy())
3383 // The only other support type is pointer.
3384 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
3385 return getDataLayout().getIntPtrType(Ty);
3388 const SCEV *ScalarEvolution::getCouldNotCompute() {
3389 return CouldNotCompute.get();
3392 bool ScalarEvolution::checkValidity(const SCEV *S) const {
3393 bool ContainsNulls = SCEVExprContains(S, [](const SCEV *S) {
3394 auto *SU = dyn_cast<SCEVUnknown>(S);
3395 return SU && SU->getValue() == nullptr;
3398 return !ContainsNulls;
3401 bool ScalarEvolution::containsAddRecurrence(const SCEV *S) {
3402 HasRecMapType::iterator I = HasRecMap.find(S);
3403 if (I != HasRecMap.end())
3406 bool FoundAddRec = SCEVExprContains(S, isa<SCEVAddRecExpr, const SCEV *>);
3407 HasRecMap.insert({S, FoundAddRec});
3411 /// Try to split a SCEVAddExpr into a pair of {SCEV, ConstantInt}.
3412 /// If \p S is a SCEVAddExpr and is composed of a sub SCEV S' and an
3413 /// offset I, then return {S', I}, else return {\p S, nullptr}.
3414 static std::pair<const SCEV *, ConstantInt *> splitAddExpr(const SCEV *S) {
3415 const auto *Add = dyn_cast<SCEVAddExpr>(S);
3417 return {S, nullptr};
3419 if (Add->getNumOperands() != 2)
3420 return {S, nullptr};
3422 auto *ConstOp = dyn_cast<SCEVConstant>(Add->getOperand(0));
3424 return {S, nullptr};
3426 return {Add->getOperand(1), ConstOp->getValue()};
3429 /// Return the ValueOffsetPair set for \p S. \p S can be represented
3430 /// by the value and offset from any ValueOffsetPair in the set.
3431 SetVector<ScalarEvolution::ValueOffsetPair> *
3432 ScalarEvolution::getSCEVValues(const SCEV *S) {
3433 ExprValueMapType::iterator SI = ExprValueMap.find_as(S);
3434 if (SI == ExprValueMap.end())
3437 if (VerifySCEVMap) {
3438 // Check there is no dangling Value in the set returned.
3439 for (const auto &VE : SI->second)
3440 assert(ValueExprMap.count(VE.first));
3446 /// Erase Value from ValueExprMap and ExprValueMap. ValueExprMap.erase(V)
3447 /// cannot be used separately. eraseValueFromMap should be used to remove
3448 /// V from ValueExprMap and ExprValueMap at the same time.
3449 void ScalarEvolution::eraseValueFromMap(Value *V) {
3450 ValueExprMapType::iterator I = ValueExprMap.find_as(V);
3451 if (I != ValueExprMap.end()) {
3452 const SCEV *S = I->second;
3453 // Remove {V, 0} from the set of ExprValueMap[S]
3454 if (SetVector<ValueOffsetPair> *SV = getSCEVValues(S))
3455 SV->remove({V, nullptr});
3457 // Remove {V, Offset} from the set of ExprValueMap[Stripped]
3458 const SCEV *Stripped;
3459 ConstantInt *Offset;
3460 std::tie(Stripped, Offset) = splitAddExpr(S);
3461 if (Offset != nullptr) {
3462 if (SetVector<ValueOffsetPair> *SV = getSCEVValues(Stripped))
3463 SV->remove({V, Offset});
3465 ValueExprMap.erase(V);
3469 /// Return an existing SCEV if it exists, otherwise analyze the expression and
3470 /// create a new one.
3471 const SCEV *ScalarEvolution::getSCEV(Value *V) {
3472 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
3474 const SCEV *S = getExistingSCEV(V);
3477 // During PHI resolution, it is possible to create two SCEVs for the same
3478 // V, so it is needed to double check whether V->S is inserted into
3479 // ValueExprMap before insert S->{V, 0} into ExprValueMap.
3480 std::pair<ValueExprMapType::iterator, bool> Pair =
3481 ValueExprMap.insert({SCEVCallbackVH(V, this), S});
3483 ExprValueMap[S].insert({V, nullptr});
3485 // If S == Stripped + Offset, add Stripped -> {V, Offset} into
3487 const SCEV *Stripped = S;
3488 ConstantInt *Offset = nullptr;
3489 std::tie(Stripped, Offset) = splitAddExpr(S);
3490 // If stripped is SCEVUnknown, don't bother to save
3491 // Stripped -> {V, offset}. It doesn't simplify and sometimes even
3492 // increase the complexity of the expansion code.
3493 // If V is GetElementPtrInst, don't save Stripped -> {V, offset}
3494 // because it may generate add/sub instead of GEP in SCEV expansion.
3495 if (Offset != nullptr && !isa<SCEVUnknown>(Stripped) &&
3496 !isa<GetElementPtrInst>(V))
3497 ExprValueMap[Stripped].insert({V, Offset});
3503 const SCEV *ScalarEvolution::getExistingSCEV(Value *V) {
3504 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
3506 ValueExprMapType::iterator I = ValueExprMap.find_as(V);
3507 if (I != ValueExprMap.end()) {
3508 const SCEV *S = I->second;
3509 if (checkValidity(S))
3511 eraseValueFromMap(V);
3512 forgetMemoizedResults(S);
3517 /// Return a SCEV corresponding to -V = -1*V
3519 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V,
3520 SCEV::NoWrapFlags Flags) {
3521 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
3523 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
3525 Type *Ty = V->getType();
3526 Ty = getEffectiveSCEVType(Ty);
3528 V, getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))), Flags);
3531 /// Return a SCEV corresponding to ~V = -1-V
3532 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
3533 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
3535 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
3537 Type *Ty = V->getType();
3538 Ty = getEffectiveSCEVType(Ty);
3539 const SCEV *AllOnes =
3540 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
3541 return getMinusSCEV(AllOnes, V);
3544 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
3545 SCEV::NoWrapFlags Flags) {
3546 // Fast path: X - X --> 0.
3548 return getZero(LHS->getType());
3550 // We represent LHS - RHS as LHS + (-1)*RHS. This transformation
3551 // makes it so that we cannot make much use of NUW.
3552 auto AddFlags = SCEV::FlagAnyWrap;
3553 const bool RHSIsNotMinSigned =
3554 !getSignedRange(RHS).getSignedMin().isMinSignedValue();
3555 if (maskFlags(Flags, SCEV::FlagNSW) == SCEV::FlagNSW) {
3556 // Let M be the minimum representable signed value. Then (-1)*RHS
3557 // signed-wraps if and only if RHS is M. That can happen even for
3558 // a NSW subtraction because e.g. (-1)*M signed-wraps even though
3559 // -1 - M does not. So to transfer NSW from LHS - RHS to LHS +
3560 // (-1)*RHS, we need to prove that RHS != M.
3562 // If LHS is non-negative and we know that LHS - RHS does not
3563 // signed-wrap, then RHS cannot be M. So we can rule out signed-wrap
3564 // either by proving that RHS > M or that LHS >= 0.
3565 if (RHSIsNotMinSigned || isKnownNonNegative(LHS)) {
3566 AddFlags = SCEV::FlagNSW;
3570 // FIXME: Find a correct way to transfer NSW to (-1)*M when LHS -
3571 // RHS is NSW and LHS >= 0.
3573 // The difficulty here is that the NSW flag may have been proven
3574 // relative to a loop that is to be found in a recurrence in LHS and
3575 // not in RHS. Applying NSW to (-1)*M may then let the NSW have a
3576 // larger scope than intended.
3577 auto NegFlags = RHSIsNotMinSigned ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
3579 return getAddExpr(LHS, getNegativeSCEV(RHS, NegFlags), AddFlags);
3583 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty) {
3584 Type *SrcTy = V->getType();
3585 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3586 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3587 "Cannot truncate or zero extend with non-integer arguments!");
3588 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3589 return V; // No conversion
3590 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
3591 return getTruncateExpr(V, Ty);
3592 return getZeroExtendExpr(V, Ty);
3596 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
3598 Type *SrcTy = V->getType();
3599 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3600 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3601 "Cannot truncate or zero extend with non-integer arguments!");
3602 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3603 return V; // No conversion
3604 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
3605 return getTruncateExpr(V, Ty);
3606 return getSignExtendExpr(V, Ty);
3610 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) {
3611 Type *SrcTy = V->getType();
3612 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3613 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3614 "Cannot noop or zero extend with non-integer arguments!");
3615 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3616 "getNoopOrZeroExtend cannot truncate!");
3617 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3618 return V; // No conversion
3619 return getZeroExtendExpr(V, Ty);
3623 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) {
3624 Type *SrcTy = V->getType();
3625 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3626 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3627 "Cannot noop or sign extend with non-integer arguments!");
3628 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3629 "getNoopOrSignExtend cannot truncate!");
3630 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3631 return V; // No conversion
3632 return getSignExtendExpr(V, Ty);
3636 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) {
3637 Type *SrcTy = V->getType();
3638 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3639 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3640 "Cannot noop or any extend with non-integer arguments!");
3641 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3642 "getNoopOrAnyExtend cannot truncate!");
3643 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3644 return V; // No conversion
3645 return getAnyExtendExpr(V, Ty);
3649 ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) {
3650 Type *SrcTy = V->getType();
3651 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3652 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3653 "Cannot truncate or noop with non-integer arguments!");
3654 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
3655 "getTruncateOrNoop cannot extend!");
3656 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3657 return V; // No conversion
3658 return getTruncateExpr(V, Ty);
3661 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
3663 const SCEV *PromotedLHS = LHS;
3664 const SCEV *PromotedRHS = RHS;
3666 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
3667 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
3669 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
3671 return getUMaxExpr(PromotedLHS, PromotedRHS);
3674 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
3676 const SCEV *PromotedLHS = LHS;
3677 const SCEV *PromotedRHS = RHS;
3679 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
3680 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
3682 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
3684 return getUMinExpr(PromotedLHS, PromotedRHS);
3687 const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) {
3688 // A pointer operand may evaluate to a nonpointer expression, such as null.
3689 if (!V->getType()->isPointerTy())
3692 if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) {
3693 return getPointerBase(Cast->getOperand());
3694 } else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) {
3695 const SCEV *PtrOp = nullptr;
3696 for (const SCEV *NAryOp : NAry->operands()) {
3697 if (NAryOp->getType()->isPointerTy()) {
3698 // Cannot find the base of an expression with multiple pointer operands.
3706 return getPointerBase(PtrOp);
3711 /// Push users of the given Instruction onto the given Worklist.
3713 PushDefUseChildren(Instruction *I,
3714 SmallVectorImpl<Instruction *> &Worklist) {
3715 // Push the def-use children onto the Worklist stack.
3716 for (User *U : I->users())
3717 Worklist.push_back(cast<Instruction>(U));
3720 void ScalarEvolution::forgetSymbolicName(Instruction *PN, const SCEV *SymName) {
3721 SmallVector<Instruction *, 16> Worklist;
3722 PushDefUseChildren(PN, Worklist);
3724 SmallPtrSet<Instruction *, 8> Visited;
3726 while (!Worklist.empty()) {
3727 Instruction *I = Worklist.pop_back_val();
3728 if (!Visited.insert(I).second)
3731 auto It = ValueExprMap.find_as(static_cast<Value *>(I));
3732 if (It != ValueExprMap.end()) {
3733 const SCEV *Old = It->second;
3735 // Short-circuit the def-use traversal if the symbolic name
3736 // ceases to appear in expressions.
3737 if (Old != SymName && !hasOperand(Old, SymName))
3740 // SCEVUnknown for a PHI either means that it has an unrecognized
3741 // structure, it's a PHI that's in the progress of being computed
3742 // by createNodeForPHI, or it's a single-value PHI. In the first case,
3743 // additional loop trip count information isn't going to change anything.
3744 // In the second case, createNodeForPHI will perform the necessary
3745 // updates on its own when it gets to that point. In the third, we do
3746 // want to forget the SCEVUnknown.
3747 if (!isa<PHINode>(I) ||
3748 !isa<SCEVUnknown>(Old) ||
3749 (I != PN && Old == SymName)) {
3750 eraseValueFromMap(It->first);
3751 forgetMemoizedResults(Old);
3755 PushDefUseChildren(I, Worklist);
3760 class SCEVInitRewriter : public SCEVRewriteVisitor<SCEVInitRewriter> {
3762 static const SCEV *rewrite(const SCEV *S, const Loop *L,
3763 ScalarEvolution &SE) {
3764 SCEVInitRewriter Rewriter(L, SE);
3765 const SCEV *Result = Rewriter.visit(S);
3766 return Rewriter.isValid() ? Result : SE.getCouldNotCompute();
3769 SCEVInitRewriter(const Loop *L, ScalarEvolution &SE)
3770 : SCEVRewriteVisitor(SE), L(L), Valid(true) {}
3772 const SCEV *visitUnknown(const SCEVUnknown *Expr) {
3773 if (!(SE.getLoopDisposition(Expr, L) == ScalarEvolution::LoopInvariant))
3778 const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
3779 // Only allow AddRecExprs for this loop.
3780 if (Expr->getLoop() == L)
3781 return Expr->getStart();
3786 bool isValid() { return Valid; }
3793 class SCEVShiftRewriter : public SCEVRewriteVisitor<SCEVShiftRewriter> {
3795 static const SCEV *rewrite(const SCEV *S, const Loop *L,
3796 ScalarEvolution &SE) {
3797 SCEVShiftRewriter Rewriter(L, SE);
3798 const SCEV *Result = Rewriter.visit(S);
3799 return Rewriter.isValid() ? Result : SE.getCouldNotCompute();
3802 SCEVShiftRewriter(const Loop *L, ScalarEvolution &SE)
3803 : SCEVRewriteVisitor(SE), L(L), Valid(true) {}
3805 const SCEV *visitUnknown(const SCEVUnknown *Expr) {
3806 // Only allow AddRecExprs for this loop.
3807 if (!(SE.getLoopDisposition(Expr, L) == ScalarEvolution::LoopInvariant))
3812 const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
3813 if (Expr->getLoop() == L && Expr->isAffine())
3814 return SE.getMinusSCEV(Expr, Expr->getStepRecurrence(SE));
3818 bool isValid() { return Valid; }
3824 } // end anonymous namespace
3827 ScalarEvolution::proveNoWrapViaConstantRanges(const SCEVAddRecExpr *AR) {
3828 if (!AR->isAffine())
3829 return SCEV::FlagAnyWrap;
3831 typedef OverflowingBinaryOperator OBO;
3832 SCEV::NoWrapFlags Result = SCEV::FlagAnyWrap;
3834 if (!AR->hasNoSignedWrap()) {
3835 ConstantRange AddRecRange = getSignedRange(AR);
3836 ConstantRange IncRange = getSignedRange(AR->getStepRecurrence(*this));
3838 auto NSWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
3839 Instruction::Add, IncRange, OBO::NoSignedWrap);
3840 if (NSWRegion.contains(AddRecRange))
3841 Result = ScalarEvolution::setFlags(Result, SCEV::FlagNSW);
3844 if (!AR->hasNoUnsignedWrap()) {
3845 ConstantRange AddRecRange = getUnsignedRange(AR);
3846 ConstantRange IncRange = getUnsignedRange(AR->getStepRecurrence(*this));
3848 auto NUWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
3849 Instruction::Add, IncRange, OBO::NoUnsignedWrap);
3850 if (NUWRegion.contains(AddRecRange))
3851 Result = ScalarEvolution::setFlags(Result, SCEV::FlagNUW);
3858 /// Represents an abstract binary operation. This may exist as a
3859 /// normal instruction or constant expression, or may have been
3860 /// derived from an expression tree.
3868 /// Op is set if this BinaryOp corresponds to a concrete LLVM instruction or
3869 /// constant expression.
3872 explicit BinaryOp(Operator *Op)
3873 : Opcode(Op->getOpcode()), LHS(Op->getOperand(0)), RHS(Op->getOperand(1)),
3874 IsNSW(false), IsNUW(false), Op(Op) {
3875 if (auto *OBO = dyn_cast<OverflowingBinaryOperator>(Op)) {
3876 IsNSW = OBO->hasNoSignedWrap();
3877 IsNUW = OBO->hasNoUnsignedWrap();
3881 explicit BinaryOp(unsigned Opcode, Value *LHS, Value *RHS, bool IsNSW = false,
3883 : Opcode(Opcode), LHS(LHS), RHS(RHS), IsNSW(IsNSW), IsNUW(IsNUW),
3889 /// Try to map \p V into a BinaryOp, and return \c None on failure.
3890 static Optional<BinaryOp> MatchBinaryOp(Value *V, DominatorTree &DT) {
3891 auto *Op = dyn_cast<Operator>(V);
3895 // Implementation detail: all the cleverness here should happen without
3896 // creating new SCEV expressions -- our caller knowns tricks to avoid creating
3897 // SCEV expressions when possible, and we should not break that.
3899 switch (Op->getOpcode()) {
3900 case Instruction::Add:
3901 case Instruction::Sub:
3902 case Instruction::Mul:
3903 case Instruction::UDiv:
3904 case Instruction::And:
3905 case Instruction::Or:
3906 case Instruction::AShr:
3907 case Instruction::Shl:
3908 return BinaryOp(Op);
3910 case Instruction::Xor:
3911 if (auto *RHSC = dyn_cast<ConstantInt>(Op->getOperand(1)))
3912 // If the RHS of the xor is a signbit, then this is just an add.
3913 // Instcombine turns add of signbit into xor as a strength reduction step.
3914 if (RHSC->getValue().isSignBit())
3915 return BinaryOp(Instruction::Add, Op->getOperand(0), Op->getOperand(1));
3916 return BinaryOp(Op);
3918 case Instruction::LShr:
3919 // Turn logical shift right of a constant into a unsigned divide.
3920 if (ConstantInt *SA = dyn_cast<ConstantInt>(Op->getOperand(1))) {
3921 uint32_t BitWidth = cast<IntegerType>(Op->getType())->getBitWidth();
3923 // If the shift count is not less than the bitwidth, the result of
3924 // the shift is undefined. Don't try to analyze it, because the
3925 // resolution chosen here may differ from the resolution chosen in
3926 // other parts of the compiler.
3927 if (SA->getValue().ult(BitWidth)) {
3929 ConstantInt::get(SA->getContext(),
3930 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
3931 return BinaryOp(Instruction::UDiv, Op->getOperand(0), X);
3934 return BinaryOp(Op);
3936 case Instruction::ExtractValue: {
3937 auto *EVI = cast<ExtractValueInst>(Op);
3938 if (EVI->getNumIndices() != 1 || EVI->getIndices()[0] != 0)
3941 auto *CI = dyn_cast<CallInst>(EVI->getAggregateOperand());
3945 if (auto *F = CI->getCalledFunction())
3946 switch (F->getIntrinsicID()) {
3947 case Intrinsic::sadd_with_overflow:
3948 case Intrinsic::uadd_with_overflow: {
3949 if (!isOverflowIntrinsicNoWrap(cast<IntrinsicInst>(CI), DT))
3950 return BinaryOp(Instruction::Add, CI->getArgOperand(0),
3951 CI->getArgOperand(1));
3953 // Now that we know that all uses of the arithmetic-result component of
3954 // CI are guarded by the overflow check, we can go ahead and pretend
3955 // that the arithmetic is non-overflowing.
3956 if (F->getIntrinsicID() == Intrinsic::sadd_with_overflow)
3957 return BinaryOp(Instruction::Add, CI->getArgOperand(0),
3958 CI->getArgOperand(1), /* IsNSW = */ true,
3959 /* IsNUW = */ false);
3961 return BinaryOp(Instruction::Add, CI->getArgOperand(0),
3962 CI->getArgOperand(1), /* IsNSW = */ false,
3966 case Intrinsic::ssub_with_overflow:
3967 case Intrinsic::usub_with_overflow:
3968 return BinaryOp(Instruction::Sub, CI->getArgOperand(0),
3969 CI->getArgOperand(1));
3971 case Intrinsic::smul_with_overflow:
3972 case Intrinsic::umul_with_overflow:
3973 return BinaryOp(Instruction::Mul, CI->getArgOperand(0),
3974 CI->getArgOperand(1));
3987 const SCEV *ScalarEvolution::createAddRecFromPHI(PHINode *PN) {
3988 const Loop *L = LI.getLoopFor(PN->getParent());
3989 if (!L || L->getHeader() != PN->getParent())
3992 // The loop may have multiple entrances or multiple exits; we can analyze
3993 // this phi as an addrec if it has a unique entry value and a unique
3995 Value *BEValueV = nullptr, *StartValueV = nullptr;
3996 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
3997 Value *V = PN->getIncomingValue(i);
3998 if (L->contains(PN->getIncomingBlock(i))) {
4001 } else if (BEValueV != V) {
4005 } else if (!StartValueV) {
4007 } else if (StartValueV != V) {
4008 StartValueV = nullptr;
4012 if (BEValueV && StartValueV) {
4013 // While we are analyzing this PHI node, handle its value symbolically.
4014 const SCEV *SymbolicName = getUnknown(PN);
4015 assert(ValueExprMap.find_as(PN) == ValueExprMap.end() &&
4016 "PHI node already processed?");
4017 ValueExprMap.insert({SCEVCallbackVH(PN, this), SymbolicName});
4019 // Using this symbolic name for the PHI, analyze the value coming around
4021 const SCEV *BEValue = getSCEV(BEValueV);
4023 // NOTE: If BEValue is loop invariant, we know that the PHI node just
4024 // has a special value for the first iteration of the loop.
4026 // If the value coming around the backedge is an add with the symbolic
4027 // value we just inserted, then we found a simple induction variable!
4028 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
4029 // If there is a single occurrence of the symbolic value, replace it
4030 // with a recurrence.
4031 unsigned FoundIndex = Add->getNumOperands();
4032 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
4033 if (Add->getOperand(i) == SymbolicName)
4034 if (FoundIndex == e) {
4039 if (FoundIndex != Add->getNumOperands()) {
4040 // Create an add with everything but the specified operand.
4041 SmallVector<const SCEV *, 8> Ops;
4042 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
4043 if (i != FoundIndex)
4044 Ops.push_back(Add->getOperand(i));
4045 const SCEV *Accum = getAddExpr(Ops);
4047 // This is not a valid addrec if the step amount is varying each
4048 // loop iteration, but is not itself an addrec in this loop.
4049 if (isLoopInvariant(Accum, L) ||
4050 (isa<SCEVAddRecExpr>(Accum) &&
4051 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
4052 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
4054 if (auto BO = MatchBinaryOp(BEValueV, DT)) {
4055 if (BO->Opcode == Instruction::Add && BO->LHS == PN) {
4057 Flags = setFlags(Flags, SCEV::FlagNUW);
4059 Flags = setFlags(Flags, SCEV::FlagNSW);
4061 } else if (GEPOperator *GEP = dyn_cast<GEPOperator>(BEValueV)) {
4062 // If the increment is an inbounds GEP, then we know the address
4063 // space cannot be wrapped around. We cannot make any guarantee
4064 // about signed or unsigned overflow because pointers are
4065 // unsigned but we may have a negative index from the base
4066 // pointer. We can guarantee that no unsigned wrap occurs if the
4067 // indices form a positive value.
4068 if (GEP->isInBounds() && GEP->getOperand(0) == PN) {
4069 Flags = setFlags(Flags, SCEV::FlagNW);
4071 const SCEV *Ptr = getSCEV(GEP->getPointerOperand());
4072 if (isKnownPositive(getMinusSCEV(getSCEV(GEP), Ptr)))
4073 Flags = setFlags(Flags, SCEV::FlagNUW);
4076 // We cannot transfer nuw and nsw flags from subtraction
4077 // operations -- sub nuw X, Y is not the same as add nuw X, -Y
4081 const SCEV *StartVal = getSCEV(StartValueV);
4082 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
4084 // Okay, for the entire analysis of this edge we assumed the PHI
4085 // to be symbolic. We now need to go back and purge all of the
4086 // entries for the scalars that use the symbolic expression.
4087 forgetSymbolicName(PN, SymbolicName);
4088 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
4090 // We can add Flags to the post-inc expression only if we
4091 // know that it us *undefined behavior* for BEValueV to
4093 if (auto *BEInst = dyn_cast<Instruction>(BEValueV))
4094 if (isLoopInvariant(Accum, L) && isAddRecNeverPoison(BEInst, L))
4095 (void)getAddRecExpr(getAddExpr(StartVal, Accum), Accum, L, Flags);
4101 // Otherwise, this could be a loop like this:
4102 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
4103 // In this case, j = {1,+,1} and BEValue is j.
4104 // Because the other in-value of i (0) fits the evolution of BEValue
4105 // i really is an addrec evolution.
4107 // We can generalize this saying that i is the shifted value of BEValue
4108 // by one iteration:
4109 // PHI(f(0), f({1,+,1})) --> f({0,+,1})
4110 const SCEV *Shifted = SCEVShiftRewriter::rewrite(BEValue, L, *this);
4111 const SCEV *Start = SCEVInitRewriter::rewrite(Shifted, L, *this);
4112 if (Shifted != getCouldNotCompute() &&
4113 Start != getCouldNotCompute()) {
4114 const SCEV *StartVal = getSCEV(StartValueV);
4115 if (Start == StartVal) {
4116 // Okay, for the entire analysis of this edge we assumed the PHI
4117 // to be symbolic. We now need to go back and purge all of the
4118 // entries for the scalars that use the symbolic expression.
4119 forgetSymbolicName(PN, SymbolicName);
4120 ValueExprMap[SCEVCallbackVH(PN, this)] = Shifted;
4126 // Remove the temporary PHI node SCEV that has been inserted while intending
4127 // to create an AddRecExpr for this PHI node. We can not keep this temporary
4128 // as it will prevent later (possibly simpler) SCEV expressions to be added
4129 // to the ValueExprMap.
4130 eraseValueFromMap(PN);
4136 // Checks if the SCEV S is available at BB. S is considered available at BB
4137 // if S can be materialized at BB without introducing a fault.
4138 static bool IsAvailableOnEntry(const Loop *L, DominatorTree &DT, const SCEV *S,
4140 struct CheckAvailable {
4141 bool TraversalDone = false;
4142 bool Available = true;
4144 const Loop *L = nullptr; // The loop BB is in (can be nullptr)
4145 BasicBlock *BB = nullptr;
4148 CheckAvailable(const Loop *L, BasicBlock *BB, DominatorTree &DT)
4149 : L(L), BB(BB), DT(DT) {}
4151 bool setUnavailable() {
4152 TraversalDone = true;
4157 bool follow(const SCEV *S) {
4158 switch (S->getSCEVType()) {
4159 case scConstant: case scTruncate: case scZeroExtend: case scSignExtend:
4160 case scAddExpr: case scMulExpr: case scUMaxExpr: case scSMaxExpr:
4161 // These expressions are available if their operand(s) is/are.
4164 case scAddRecExpr: {
4165 // We allow add recurrences that are on the loop BB is in, or some
4166 // outer loop. This guarantees availability because the value of the
4167 // add recurrence at BB is simply the "current" value of the induction
4168 // variable. We can relax this in the future; for instance an add
4169 // recurrence on a sibling dominating loop is also available at BB.
4170 const auto *ARLoop = cast<SCEVAddRecExpr>(S)->getLoop();
4171 if (L && (ARLoop == L || ARLoop->contains(L)))
4174 return setUnavailable();
4178 // For SCEVUnknown, we check for simple dominance.
4179 const auto *SU = cast<SCEVUnknown>(S);
4180 Value *V = SU->getValue();
4182 if (isa<Argument>(V))
4185 if (isa<Instruction>(V) && DT.dominates(cast<Instruction>(V), BB))
4188 return setUnavailable();
4192 case scCouldNotCompute:
4193 // We do not try to smart about these at all.
4194 return setUnavailable();
4196 llvm_unreachable("switch should be fully covered!");
4199 bool isDone() { return TraversalDone; }
4202 CheckAvailable CA(L, BB, DT);
4203 SCEVTraversal<CheckAvailable> ST(CA);
4206 return CA.Available;
4209 // Try to match a control flow sequence that branches out at BI and merges back
4210 // at Merge into a "C ? LHS : RHS" select pattern. Return true on a successful
4212 static bool BrPHIToSelect(DominatorTree &DT, BranchInst *BI, PHINode *Merge,
4213 Value *&C, Value *&LHS, Value *&RHS) {
4214 C = BI->getCondition();
4216 BasicBlockEdge LeftEdge(BI->getParent(), BI->getSuccessor(0));
4217 BasicBlockEdge RightEdge(BI->getParent(), BI->getSuccessor(1));
4219 if (!LeftEdge.isSingleEdge())
4222 assert(RightEdge.isSingleEdge() && "Follows from LeftEdge.isSingleEdge()");
4224 Use &LeftUse = Merge->getOperandUse(0);
4225 Use &RightUse = Merge->getOperandUse(1);
4227 if (DT.dominates(LeftEdge, LeftUse) && DT.dominates(RightEdge, RightUse)) {
4233 if (DT.dominates(LeftEdge, RightUse) && DT.dominates(RightEdge, LeftUse)) {
4242 const SCEV *ScalarEvolution::createNodeFromSelectLikePHI(PHINode *PN) {
4244 [&](BasicBlock *BB) { return DT.isReachableFromEntry(BB); };
4245 if (PN->getNumIncomingValues() == 2 && all_of(PN->blocks(), IsReachable)) {
4246 const Loop *L = LI.getLoopFor(PN->getParent());
4248 // We don't want to break LCSSA, even in a SCEV expression tree.
4249 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i)
4250 if (LI.getLoopFor(PN->getIncomingBlock(i)) != L)
4255 // br %cond, label %left, label %right
4261 // V = phi [ %x, %left ], [ %y, %right ]
4263 // as "select %cond, %x, %y"
4265 BasicBlock *IDom = DT[PN->getParent()]->getIDom()->getBlock();
4266 assert(IDom && "At least the entry block should dominate PN");
4268 auto *BI = dyn_cast<BranchInst>(IDom->getTerminator());
4269 Value *Cond = nullptr, *LHS = nullptr, *RHS = nullptr;
4271 if (BI && BI->isConditional() &&
4272 BrPHIToSelect(DT, BI, PN, Cond, LHS, RHS) &&
4273 IsAvailableOnEntry(L, DT, getSCEV(LHS), PN->getParent()) &&
4274 IsAvailableOnEntry(L, DT, getSCEV(RHS), PN->getParent()))
4275 return createNodeForSelectOrPHI(PN, Cond, LHS, RHS);
4281 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
4282 if (const SCEV *S = createAddRecFromPHI(PN))
4285 if (const SCEV *S = createNodeFromSelectLikePHI(PN))
4288 // If the PHI has a single incoming value, follow that value, unless the
4289 // PHI's incoming blocks are in a different loop, in which case doing so
4290 // risks breaking LCSSA form. Instcombine would normally zap these, but
4291 // it doesn't have DominatorTree information, so it may miss cases.
4292 if (Value *V = SimplifyInstruction(PN, getDataLayout(), &TLI, &DT, &AC))
4293 if (LI.replacementPreservesLCSSAForm(PN, V))
4296 // If it's not a loop phi, we can't handle it yet.
4297 return getUnknown(PN);
4300 const SCEV *ScalarEvolution::createNodeForSelectOrPHI(Instruction *I,
4304 // Handle "constant" branch or select. This can occur for instance when a
4305 // loop pass transforms an inner loop and moves on to process the outer loop.
4306 if (auto *CI = dyn_cast<ConstantInt>(Cond))
4307 return getSCEV(CI->isOne() ? TrueVal : FalseVal);
4309 // Try to match some simple smax or umax patterns.
4310 auto *ICI = dyn_cast<ICmpInst>(Cond);
4312 return getUnknown(I);
4314 Value *LHS = ICI->getOperand(0);
4315 Value *RHS = ICI->getOperand(1);
4317 switch (ICI->getPredicate()) {
4318 case ICmpInst::ICMP_SLT:
4319 case ICmpInst::ICMP_SLE:
4320 std::swap(LHS, RHS);
4322 case ICmpInst::ICMP_SGT:
4323 case ICmpInst::ICMP_SGE:
4324 // a >s b ? a+x : b+x -> smax(a, b)+x
4325 // a >s b ? b+x : a+x -> smin(a, b)+x
4326 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType())) {
4327 const SCEV *LS = getNoopOrSignExtend(getSCEV(LHS), I->getType());
4328 const SCEV *RS = getNoopOrSignExtend(getSCEV(RHS), I->getType());
4329 const SCEV *LA = getSCEV(TrueVal);
4330 const SCEV *RA = getSCEV(FalseVal);
4331 const SCEV *LDiff = getMinusSCEV(LA, LS);
4332 const SCEV *RDiff = getMinusSCEV(RA, RS);
4334 return getAddExpr(getSMaxExpr(LS, RS), LDiff);
4335 LDiff = getMinusSCEV(LA, RS);
4336 RDiff = getMinusSCEV(RA, LS);
4338 return getAddExpr(getSMinExpr(LS, RS), LDiff);
4341 case ICmpInst::ICMP_ULT:
4342 case ICmpInst::ICMP_ULE:
4343 std::swap(LHS, RHS);
4345 case ICmpInst::ICMP_UGT:
4346 case ICmpInst::ICMP_UGE:
4347 // a >u b ? a+x : b+x -> umax(a, b)+x
4348 // a >u b ? b+x : a+x -> umin(a, b)+x
4349 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType())) {
4350 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
4351 const SCEV *RS = getNoopOrZeroExtend(getSCEV(RHS), I->getType());
4352 const SCEV *LA = getSCEV(TrueVal);
4353 const SCEV *RA = getSCEV(FalseVal);
4354 const SCEV *LDiff = getMinusSCEV(LA, LS);
4355 const SCEV *RDiff = getMinusSCEV(RA, RS);
4357 return getAddExpr(getUMaxExpr(LS, RS), LDiff);
4358 LDiff = getMinusSCEV(LA, RS);
4359 RDiff = getMinusSCEV(RA, LS);
4361 return getAddExpr(getUMinExpr(LS, RS), LDiff);
4364 case ICmpInst::ICMP_NE:
4365 // n != 0 ? n+x : 1+x -> umax(n, 1)+x
4366 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType()) &&
4367 isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
4368 const SCEV *One = getOne(I->getType());
4369 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
4370 const SCEV *LA = getSCEV(TrueVal);
4371 const SCEV *RA = getSCEV(FalseVal);
4372 const SCEV *LDiff = getMinusSCEV(LA, LS);
4373 const SCEV *RDiff = getMinusSCEV(RA, One);
4375 return getAddExpr(getUMaxExpr(One, LS), LDiff);
4378 case ICmpInst::ICMP_EQ:
4379 // n == 0 ? 1+x : n+x -> umax(n, 1)+x
4380 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType()) &&
4381 isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
4382 const SCEV *One = getOne(I->getType());
4383 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
4384 const SCEV *LA = getSCEV(TrueVal);
4385 const SCEV *RA = getSCEV(FalseVal);
4386 const SCEV *LDiff = getMinusSCEV(LA, One);
4387 const SCEV *RDiff = getMinusSCEV(RA, LS);
4389 return getAddExpr(getUMaxExpr(One, LS), LDiff);
4396 return getUnknown(I);
4399 /// Expand GEP instructions into add and multiply operations. This allows them
4400 /// to be analyzed by regular SCEV code.
4401 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
4402 // Don't attempt to analyze GEPs over unsized objects.
4403 if (!GEP->getSourceElementType()->isSized())
4404 return getUnknown(GEP);
4406 SmallVector<const SCEV *, 4> IndexExprs;
4407 for (auto Index = GEP->idx_begin(); Index != GEP->idx_end(); ++Index)
4408 IndexExprs.push_back(getSCEV(*Index));
4409 return getGEPExpr(GEP, IndexExprs);
4413 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
4414 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
4415 return C->getAPInt().countTrailingZeros();
4417 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
4418 return std::min(GetMinTrailingZeros(T->getOperand()),
4419 (uint32_t)getTypeSizeInBits(T->getType()));
4421 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
4422 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
4423 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
4424 getTypeSizeInBits(E->getType()) : OpRes;
4427 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
4428 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
4429 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
4430 getTypeSizeInBits(E->getType()) : OpRes;
4433 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
4434 // The result is the min of all operands results.
4435 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
4436 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
4437 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
4441 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
4442 // The result is the sum of all operands results.
4443 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
4444 uint32_t BitWidth = getTypeSizeInBits(M->getType());
4445 for (unsigned i = 1, e = M->getNumOperands();
4446 SumOpRes != BitWidth && i != e; ++i)
4447 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
4452 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
4453 // The result is the min of all operands results.
4454 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
4455 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
4456 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
4460 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
4461 // The result is the min of all operands results.
4462 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
4463 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
4464 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
4468 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
4469 // The result is the min of all operands results.
4470 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
4471 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
4472 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
4476 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
4477 // For a SCEVUnknown, ask ValueTracking.
4478 unsigned BitWidth = getTypeSizeInBits(U->getType());
4479 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
4480 computeKnownBits(U->getValue(), Zeros, Ones, getDataLayout(), 0, &AC,
4482 return Zeros.countTrailingOnes();
4489 /// Helper method to assign a range to V from metadata present in the IR.
4490 static Optional<ConstantRange> GetRangeFromMetadata(Value *V) {
4491 if (Instruction *I = dyn_cast<Instruction>(V))
4492 if (MDNode *MD = I->getMetadata(LLVMContext::MD_range))
4493 return getConstantRangeFromMetadata(*MD);
4498 /// Determine the range for a particular SCEV. If SignHint is
4499 /// HINT_RANGE_UNSIGNED (resp. HINT_RANGE_SIGNED) then getRange prefers ranges
4500 /// with a "cleaner" unsigned (resp. signed) representation.
4502 ScalarEvolution::getRange(const SCEV *S,
4503 ScalarEvolution::RangeSignHint SignHint) {
4504 DenseMap<const SCEV *, ConstantRange> &Cache =
4505 SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED ? UnsignedRanges
4508 // See if we've computed this range already.
4509 DenseMap<const SCEV *, ConstantRange>::iterator I = Cache.find(S);
4510 if (I != Cache.end())
4513 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
4514 return setRange(C, SignHint, ConstantRange(C->getAPInt()));
4516 unsigned BitWidth = getTypeSizeInBits(S->getType());
4517 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
4519 // If the value has known zeros, the maximum value will have those known zeros
4521 uint32_t TZ = GetMinTrailingZeros(S);
4523 if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED)
4524 ConservativeResult =
4525 ConstantRange(APInt::getMinValue(BitWidth),
4526 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
4528 ConservativeResult = ConstantRange(
4529 APInt::getSignedMinValue(BitWidth),
4530 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
4533 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
4534 ConstantRange X = getRange(Add->getOperand(0), SignHint);
4535 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
4536 X = X.add(getRange(Add->getOperand(i), SignHint));
4537 return setRange(Add, SignHint, ConservativeResult.intersectWith(X));
4540 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
4541 ConstantRange X = getRange(Mul->getOperand(0), SignHint);
4542 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
4543 X = X.multiply(getRange(Mul->getOperand(i), SignHint));
4544 return setRange(Mul, SignHint, ConservativeResult.intersectWith(X));
4547 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
4548 ConstantRange X = getRange(SMax->getOperand(0), SignHint);
4549 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
4550 X = X.smax(getRange(SMax->getOperand(i), SignHint));
4551 return setRange(SMax, SignHint, ConservativeResult.intersectWith(X));
4554 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
4555 ConstantRange X = getRange(UMax->getOperand(0), SignHint);
4556 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
4557 X = X.umax(getRange(UMax->getOperand(i), SignHint));
4558 return setRange(UMax, SignHint, ConservativeResult.intersectWith(X));
4561 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
4562 ConstantRange X = getRange(UDiv->getLHS(), SignHint);
4563 ConstantRange Y = getRange(UDiv->getRHS(), SignHint);
4564 return setRange(UDiv, SignHint,
4565 ConservativeResult.intersectWith(X.udiv(Y)));
4568 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
4569 ConstantRange X = getRange(ZExt->getOperand(), SignHint);
4570 return setRange(ZExt, SignHint,
4571 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
4574 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
4575 ConstantRange X = getRange(SExt->getOperand(), SignHint);
4576 return setRange(SExt, SignHint,
4577 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
4580 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
4581 ConstantRange X = getRange(Trunc->getOperand(), SignHint);
4582 return setRange(Trunc, SignHint,
4583 ConservativeResult.intersectWith(X.truncate(BitWidth)));
4586 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
4587 // If there's no unsigned wrap, the value will never be less than its
4589 if (AddRec->hasNoUnsignedWrap())
4590 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
4591 if (!C->getValue()->isZero())
4592 ConservativeResult = ConservativeResult.intersectWith(
4593 ConstantRange(C->getAPInt(), APInt(BitWidth, 0)));
4595 // If there's no signed wrap, and all the operands have the same sign or
4596 // zero, the value won't ever change sign.
4597 if (AddRec->hasNoSignedWrap()) {
4598 bool AllNonNeg = true;
4599 bool AllNonPos = true;
4600 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
4601 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
4602 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
4605 ConservativeResult = ConservativeResult.intersectWith(
4606 ConstantRange(APInt(BitWidth, 0),
4607 APInt::getSignedMinValue(BitWidth)));
4609 ConservativeResult = ConservativeResult.intersectWith(
4610 ConstantRange(APInt::getSignedMinValue(BitWidth),
4611 APInt(BitWidth, 1)));
4614 // TODO: non-affine addrec
4615 if (AddRec->isAffine()) {
4616 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
4617 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
4618 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
4619 auto RangeFromAffine = getRangeForAffineAR(
4620 AddRec->getStart(), AddRec->getStepRecurrence(*this), MaxBECount,
4622 if (!RangeFromAffine.isFullSet())
4623 ConservativeResult =
4624 ConservativeResult.intersectWith(RangeFromAffine);
4626 auto RangeFromFactoring = getRangeViaFactoring(
4627 AddRec->getStart(), AddRec->getStepRecurrence(*this), MaxBECount,
4629 if (!RangeFromFactoring.isFullSet())
4630 ConservativeResult =
4631 ConservativeResult.intersectWith(RangeFromFactoring);
4635 return setRange(AddRec, SignHint, ConservativeResult);
4638 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
4639 // Check if the IR explicitly contains !range metadata.
4640 Optional<ConstantRange> MDRange = GetRangeFromMetadata(U->getValue());
4641 if (MDRange.hasValue())
4642 ConservativeResult = ConservativeResult.intersectWith(MDRange.getValue());
4644 // Split here to avoid paying the compile-time cost of calling both
4645 // computeKnownBits and ComputeNumSignBits. This restriction can be lifted
4647 const DataLayout &DL = getDataLayout();
4648 if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED) {
4649 // For a SCEVUnknown, ask ValueTracking.
4650 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
4651 computeKnownBits(U->getValue(), Zeros, Ones, DL, 0, &AC, nullptr, &DT);
4652 if (Ones != ~Zeros + 1)
4653 ConservativeResult =
4654 ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1));
4656 assert(SignHint == ScalarEvolution::HINT_RANGE_SIGNED &&
4657 "generalize as needed!");
4658 unsigned NS = ComputeNumSignBits(U->getValue(), DL, 0, &AC, nullptr, &DT);
4660 ConservativeResult = ConservativeResult.intersectWith(
4661 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
4662 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1) + 1));
4665 return setRange(U, SignHint, ConservativeResult);
4668 return setRange(S, SignHint, ConservativeResult);
4671 ConstantRange ScalarEvolution::getRangeForAffineAR(const SCEV *Start,
4673 const SCEV *MaxBECount,
4674 unsigned BitWidth) {
4675 assert(!isa<SCEVCouldNotCompute>(MaxBECount) &&
4676 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth &&
4679 ConstantRange Result(BitWidth, /* isFullSet = */ true);
4681 // Check for overflow. This must be done with ConstantRange arithmetic
4682 // because we could be called from within the ScalarEvolution overflow
4685 MaxBECount = getNoopOrZeroExtend(MaxBECount, Start->getType());
4686 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
4687 ConstantRange ZExtMaxBECountRange = MaxBECountRange.zextOrTrunc(BitWidth * 2);
4689 ConstantRange StepSRange = getSignedRange(Step);
4690 ConstantRange SExtStepSRange = StepSRange.sextOrTrunc(BitWidth * 2);
4692 ConstantRange StartURange = getUnsignedRange(Start);
4693 ConstantRange EndURange =
4694 StartURange.add(MaxBECountRange.multiply(StepSRange));
4696 // Check for unsigned overflow.
4697 ConstantRange ZExtStartURange = StartURange.zextOrTrunc(BitWidth * 2);
4698 ConstantRange ZExtEndURange = EndURange.zextOrTrunc(BitWidth * 2);
4699 if (ZExtStartURange.add(ZExtMaxBECountRange.multiply(SExtStepSRange)) ==
4701 APInt Min = APIntOps::umin(StartURange.getUnsignedMin(),
4702 EndURange.getUnsignedMin());
4703 APInt Max = APIntOps::umax(StartURange.getUnsignedMax(),
4704 EndURange.getUnsignedMax());
4705 bool IsFullRange = Min.isMinValue() && Max.isMaxValue();
4708 Result.intersectWith(ConstantRange(Min, Max + 1));
4711 ConstantRange StartSRange = getSignedRange(Start);
4712 ConstantRange EndSRange =
4713 StartSRange.add(MaxBECountRange.multiply(StepSRange));
4715 // Check for signed overflow. This must be done with ConstantRange
4716 // arithmetic because we could be called from within the ScalarEvolution
4717 // overflow checking code.
4718 ConstantRange SExtStartSRange = StartSRange.sextOrTrunc(BitWidth * 2);
4719 ConstantRange SExtEndSRange = EndSRange.sextOrTrunc(BitWidth * 2);
4720 if (SExtStartSRange.add(ZExtMaxBECountRange.multiply(SExtStepSRange)) ==
4723 APIntOps::smin(StartSRange.getSignedMin(), EndSRange.getSignedMin());
4725 APIntOps::smax(StartSRange.getSignedMax(), EndSRange.getSignedMax());
4726 bool IsFullRange = Min.isMinSignedValue() && Max.isMaxSignedValue();
4729 Result.intersectWith(ConstantRange(Min, Max + 1));
4735 ConstantRange ScalarEvolution::getRangeViaFactoring(const SCEV *Start,
4737 const SCEV *MaxBECount,
4738 unsigned BitWidth) {
4739 // RangeOf({C?A:B,+,C?P:Q}) == RangeOf(C?{A,+,P}:{B,+,Q})
4740 // == RangeOf({A,+,P}) union RangeOf({B,+,Q})
4742 struct SelectPattern {
4743 Value *Condition = nullptr;
4747 explicit SelectPattern(ScalarEvolution &SE, unsigned BitWidth,
4749 Optional<unsigned> CastOp;
4750 APInt Offset(BitWidth, 0);
4752 assert(SE.getTypeSizeInBits(S->getType()) == BitWidth &&
4755 // Peel off a constant offset:
4756 if (auto *SA = dyn_cast<SCEVAddExpr>(S)) {
4757 // In the future we could consider being smarter here and handle
4758 // {Start+Step,+,Step} too.
4759 if (SA->getNumOperands() != 2 || !isa<SCEVConstant>(SA->getOperand(0)))
4762 Offset = cast<SCEVConstant>(SA->getOperand(0))->getAPInt();
4763 S = SA->getOperand(1);
4766 // Peel off a cast operation
4767 if (auto *SCast = dyn_cast<SCEVCastExpr>(S)) {
4768 CastOp = SCast->getSCEVType();
4769 S = SCast->getOperand();
4772 using namespace llvm::PatternMatch;
4774 auto *SU = dyn_cast<SCEVUnknown>(S);
4775 const APInt *TrueVal, *FalseVal;
4777 !match(SU->getValue(), m_Select(m_Value(Condition), m_APInt(TrueVal),
4778 m_APInt(FalseVal)))) {
4779 Condition = nullptr;
4783 TrueValue = *TrueVal;
4784 FalseValue = *FalseVal;
4786 // Re-apply the cast we peeled off earlier
4787 if (CastOp.hasValue())
4790 llvm_unreachable("Unknown SCEV cast type!");
4793 TrueValue = TrueValue.trunc(BitWidth);
4794 FalseValue = FalseValue.trunc(BitWidth);
4797 TrueValue = TrueValue.zext(BitWidth);
4798 FalseValue = FalseValue.zext(BitWidth);
4801 TrueValue = TrueValue.sext(BitWidth);
4802 FalseValue = FalseValue.sext(BitWidth);
4806 // Re-apply the constant offset we peeled off earlier
4807 TrueValue += Offset;
4808 FalseValue += Offset;
4811 bool isRecognized() { return Condition != nullptr; }
4814 SelectPattern StartPattern(*this, BitWidth, Start);
4815 if (!StartPattern.isRecognized())
4816 return ConstantRange(BitWidth, /* isFullSet = */ true);
4818 SelectPattern StepPattern(*this, BitWidth, Step);
4819 if (!StepPattern.isRecognized())
4820 return ConstantRange(BitWidth, /* isFullSet = */ true);
4822 if (StartPattern.Condition != StepPattern.Condition) {
4823 // We don't handle this case today; but we could, by considering four
4824 // possibilities below instead of two. I'm not sure if there are cases where
4825 // that will help over what getRange already does, though.
4826 return ConstantRange(BitWidth, /* isFullSet = */ true);
4829 // NB! Calling ScalarEvolution::getConstant is fine, but we should not try to
4830 // construct arbitrary general SCEV expressions here. This function is called
4831 // from deep in the call stack, and calling getSCEV (on a sext instruction,
4832 // say) can end up caching a suboptimal value.
4834 // FIXME: without the explicit `this` receiver below, MSVC errors out with
4835 // C2352 and C2512 (otherwise it isn't needed).
4837 const SCEV *TrueStart = this->getConstant(StartPattern.TrueValue);
4838 const SCEV *TrueStep = this->getConstant(StepPattern.TrueValue);
4839 const SCEV *FalseStart = this->getConstant(StartPattern.FalseValue);
4840 const SCEV *FalseStep = this->getConstant(StepPattern.FalseValue);
4842 ConstantRange TrueRange =
4843 this->getRangeForAffineAR(TrueStart, TrueStep, MaxBECount, BitWidth);
4844 ConstantRange FalseRange =
4845 this->getRangeForAffineAR(FalseStart, FalseStep, MaxBECount, BitWidth);
4847 return TrueRange.unionWith(FalseRange);
4850 SCEV::NoWrapFlags ScalarEvolution::getNoWrapFlagsFromUB(const Value *V) {
4851 if (isa<ConstantExpr>(V)) return SCEV::FlagAnyWrap;
4852 const BinaryOperator *BinOp = cast<BinaryOperator>(V);
4854 // Return early if there are no flags to propagate to the SCEV.
4855 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
4856 if (BinOp->hasNoUnsignedWrap())
4857 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
4858 if (BinOp->hasNoSignedWrap())
4859 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW);
4860 if (Flags == SCEV::FlagAnyWrap)
4861 return SCEV::FlagAnyWrap;
4863 return isSCEVExprNeverPoison(BinOp) ? Flags : SCEV::FlagAnyWrap;
4866 bool ScalarEvolution::isSCEVExprNeverPoison(const Instruction *I) {
4867 // Here we check that I is in the header of the innermost loop containing I,
4868 // since we only deal with instructions in the loop header. The actual loop we
4869 // need to check later will come from an add recurrence, but getting that
4870 // requires computing the SCEV of the operands, which can be expensive. This
4871 // check we can do cheaply to rule out some cases early.
4872 Loop *InnermostContainingLoop = LI.getLoopFor(I->getParent());
4873 if (InnermostContainingLoop == nullptr ||
4874 InnermostContainingLoop->getHeader() != I->getParent())
4877 // Only proceed if we can prove that I does not yield poison.
4878 if (!isKnownNotFullPoison(I)) return false;
4880 // At this point we know that if I is executed, then it does not wrap
4881 // according to at least one of NSW or NUW. If I is not executed, then we do
4882 // not know if the calculation that I represents would wrap. Multiple
4883 // instructions can map to the same SCEV. If we apply NSW or NUW from I to
4884 // the SCEV, we must guarantee no wrapping for that SCEV also when it is
4885 // derived from other instructions that map to the same SCEV. We cannot make
4886 // that guarantee for cases where I is not executed. So we need to find the
4887 // loop that I is considered in relation to and prove that I is executed for
4888 // every iteration of that loop. That implies that the value that I
4889 // calculates does not wrap anywhere in the loop, so then we can apply the
4890 // flags to the SCEV.
4892 // We check isLoopInvariant to disambiguate in case we are adding recurrences
4893 // from different loops, so that we know which loop to prove that I is
4895 for (unsigned OpIndex = 0; OpIndex < I->getNumOperands(); ++OpIndex) {
4896 // I could be an extractvalue from a call to an overflow intrinsic.
4897 // TODO: We can do better here in some cases.
4898 if (!isSCEVable(I->getOperand(OpIndex)->getType()))
4900 const SCEV *Op = getSCEV(I->getOperand(OpIndex));
4901 if (auto *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
4902 bool AllOtherOpsLoopInvariant = true;
4903 for (unsigned OtherOpIndex = 0; OtherOpIndex < I->getNumOperands();
4905 if (OtherOpIndex != OpIndex) {
4906 const SCEV *OtherOp = getSCEV(I->getOperand(OtherOpIndex));
4907 if (!isLoopInvariant(OtherOp, AddRec->getLoop())) {
4908 AllOtherOpsLoopInvariant = false;
4913 if (AllOtherOpsLoopInvariant &&
4914 isGuaranteedToExecuteForEveryIteration(I, AddRec->getLoop()))
4921 bool ScalarEvolution::isAddRecNeverPoison(const Instruction *I, const Loop *L) {
4922 // If we know that \c I can never be poison period, then that's enough.
4923 if (isSCEVExprNeverPoison(I))
4926 // For an add recurrence specifically, we assume that infinite loops without
4927 // side effects are undefined behavior, and then reason as follows:
4929 // If the add recurrence is poison in any iteration, it is poison on all
4930 // future iterations (since incrementing poison yields poison). If the result
4931 // of the add recurrence is fed into the loop latch condition and the loop
4932 // does not contain any throws or exiting blocks other than the latch, we now
4933 // have the ability to "choose" whether the backedge is taken or not (by
4934 // choosing a sufficiently evil value for the poison feeding into the branch)
4935 // for every iteration including and after the one in which \p I first became
4936 // poison. There are two possibilities (let's call the iteration in which \p
4937 // I first became poison as K):
4939 // 1. In the set of iterations including and after K, the loop body executes
4940 // no side effects. In this case executing the backege an infinte number
4941 // of times will yield undefined behavior.
4943 // 2. In the set of iterations including and after K, the loop body executes
4944 // at least one side effect. In this case, that specific instance of side
4945 // effect is control dependent on poison, which also yields undefined
4948 auto *ExitingBB = L->getExitingBlock();
4949 auto *LatchBB = L->getLoopLatch();
4950 if (!ExitingBB || !LatchBB || ExitingBB != LatchBB)
4953 SmallPtrSet<const Instruction *, 16> Pushed;
4954 SmallVector<const Instruction *, 8> PoisonStack;
4956 // We start by assuming \c I, the post-inc add recurrence, is poison. Only
4957 // things that are known to be fully poison under that assumption go on the
4960 PoisonStack.push_back(I);
4962 bool LatchControlDependentOnPoison = false;
4963 while (!PoisonStack.empty() && !LatchControlDependentOnPoison) {
4964 const Instruction *Poison = PoisonStack.pop_back_val();
4966 for (auto *PoisonUser : Poison->users()) {
4967 if (propagatesFullPoison(cast<Instruction>(PoisonUser))) {
4968 if (Pushed.insert(cast<Instruction>(PoisonUser)).second)
4969 PoisonStack.push_back(cast<Instruction>(PoisonUser));
4970 } else if (auto *BI = dyn_cast<BranchInst>(PoisonUser)) {
4971 assert(BI->isConditional() && "Only possibility!");
4972 if (BI->getParent() == LatchBB) {
4973 LatchControlDependentOnPoison = true;
4980 return LatchControlDependentOnPoison && loopHasNoAbnormalExits(L);
4983 ScalarEvolution::LoopProperties
4984 ScalarEvolution::getLoopProperties(const Loop *L) {
4985 typedef ScalarEvolution::LoopProperties LoopProperties;
4987 auto Itr = LoopPropertiesCache.find(L);
4988 if (Itr == LoopPropertiesCache.end()) {
4989 auto HasSideEffects = [](Instruction *I) {
4990 if (auto *SI = dyn_cast<StoreInst>(I))
4991 return !SI->isSimple();
4993 return I->mayHaveSideEffects();
4996 LoopProperties LP = {/* HasNoAbnormalExits */ true,
4997 /*HasNoSideEffects*/ true};
4999 for (auto *BB : L->getBlocks())
5000 for (auto &I : *BB) {
5001 if (!isGuaranteedToTransferExecutionToSuccessor(&I))
5002 LP.HasNoAbnormalExits = false;
5003 if (HasSideEffects(&I))
5004 LP.HasNoSideEffects = false;
5005 if (!LP.HasNoAbnormalExits && !LP.HasNoSideEffects)
5006 break; // We're already as pessimistic as we can get.
5009 auto InsertPair = LoopPropertiesCache.insert({L, LP});
5010 assert(InsertPair.second && "We just checked!");
5011 Itr = InsertPair.first;
5017 const SCEV *ScalarEvolution::createSCEV(Value *V) {
5018 if (!isSCEVable(V->getType()))
5019 return getUnknown(V);
5021 if (Instruction *I = dyn_cast<Instruction>(V)) {
5022 // Don't attempt to analyze instructions in blocks that aren't
5023 // reachable. Such instructions don't matter, and they aren't required
5024 // to obey basic rules for definitions dominating uses which this
5025 // analysis depends on.
5026 if (!DT.isReachableFromEntry(I->getParent()))
5027 return getUnknown(V);
5028 } else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
5029 return getConstant(CI);
5030 else if (isa<ConstantPointerNull>(V))
5031 return getZero(V->getType());
5032 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
5033 return GA->isInterposable() ? getUnknown(V) : getSCEV(GA->getAliasee());
5034 else if (!isa<ConstantExpr>(V))
5035 return getUnknown(V);
5037 Operator *U = cast<Operator>(V);
5038 if (auto BO = MatchBinaryOp(U, DT)) {
5039 switch (BO->Opcode) {
5040 case Instruction::Add: {
5041 // The simple thing to do would be to just call getSCEV on both operands
5042 // and call getAddExpr with the result. However if we're looking at a
5043 // bunch of things all added together, this can be quite inefficient,
5044 // because it leads to N-1 getAddExpr calls for N ultimate operands.
5045 // Instead, gather up all the operands and make a single getAddExpr call.
5046 // LLVM IR canonical form means we need only traverse the left operands.
5047 SmallVector<const SCEV *, 4> AddOps;
5050 if (auto *OpSCEV = getExistingSCEV(BO->Op)) {
5051 AddOps.push_back(OpSCEV);
5055 // If a NUW or NSW flag can be applied to the SCEV for this
5056 // addition, then compute the SCEV for this addition by itself
5057 // with a separate call to getAddExpr. We need to do that
5058 // instead of pushing the operands of the addition onto AddOps,
5059 // since the flags are only known to apply to this particular
5060 // addition - they may not apply to other additions that can be
5061 // formed with operands from AddOps.
5062 const SCEV *RHS = getSCEV(BO->RHS);
5063 SCEV::NoWrapFlags Flags = getNoWrapFlagsFromUB(BO->Op);
5064 if (Flags != SCEV::FlagAnyWrap) {
5065 const SCEV *LHS = getSCEV(BO->LHS);
5066 if (BO->Opcode == Instruction::Sub)
5067 AddOps.push_back(getMinusSCEV(LHS, RHS, Flags));
5069 AddOps.push_back(getAddExpr(LHS, RHS, Flags));
5074 if (BO->Opcode == Instruction::Sub)
5075 AddOps.push_back(getNegativeSCEV(getSCEV(BO->RHS)));
5077 AddOps.push_back(getSCEV(BO->RHS));
5079 auto NewBO = MatchBinaryOp(BO->LHS, DT);
5080 if (!NewBO || (NewBO->Opcode != Instruction::Add &&
5081 NewBO->Opcode != Instruction::Sub)) {
5082 AddOps.push_back(getSCEV(BO->LHS));
5088 return getAddExpr(AddOps);
5091 case Instruction::Mul: {
5092 SmallVector<const SCEV *, 4> MulOps;
5095 if (auto *OpSCEV = getExistingSCEV(BO->Op)) {
5096 MulOps.push_back(OpSCEV);
5100 SCEV::NoWrapFlags Flags = getNoWrapFlagsFromUB(BO->Op);
5101 if (Flags != SCEV::FlagAnyWrap) {
5103 getMulExpr(getSCEV(BO->LHS), getSCEV(BO->RHS), Flags));
5108 MulOps.push_back(getSCEV(BO->RHS));
5109 auto NewBO = MatchBinaryOp(BO->LHS, DT);
5110 if (!NewBO || NewBO->Opcode != Instruction::Mul) {
5111 MulOps.push_back(getSCEV(BO->LHS));
5117 return getMulExpr(MulOps);
5119 case Instruction::UDiv:
5120 return getUDivExpr(getSCEV(BO->LHS), getSCEV(BO->RHS));
5121 case Instruction::Sub: {
5122 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
5124 Flags = getNoWrapFlagsFromUB(BO->Op);
5125 return getMinusSCEV(getSCEV(BO->LHS), getSCEV(BO->RHS), Flags);
5127 case Instruction::And:
5128 // For an expression like x&255 that merely masks off the high bits,
5129 // use zext(trunc(x)) as the SCEV expression.
5130 if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->RHS)) {
5131 if (CI->isNullValue())
5132 return getSCEV(BO->RHS);
5133 if (CI->isAllOnesValue())
5134 return getSCEV(BO->LHS);
5135 const APInt &A = CI->getValue();
5137 // Instcombine's ShrinkDemandedConstant may strip bits out of
5138 // constants, obscuring what would otherwise be a low-bits mask.
5139 // Use computeKnownBits to compute what ShrinkDemandedConstant
5140 // knew about to reconstruct a low-bits mask value.
5141 unsigned LZ = A.countLeadingZeros();
5142 unsigned TZ = A.countTrailingZeros();
5143 unsigned BitWidth = A.getBitWidth();
5144 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
5145 computeKnownBits(BO->LHS, KnownZero, KnownOne, getDataLayout(),
5146 0, &AC, nullptr, &DT);
5148 APInt EffectiveMask =
5149 APInt::getLowBitsSet(BitWidth, BitWidth - LZ - TZ).shl(TZ);
5150 if ((LZ != 0 || TZ != 0) && !((~A & ~KnownZero) & EffectiveMask)) {
5151 const SCEV *MulCount = getConstant(ConstantInt::get(
5152 getContext(), APInt::getOneBitSet(BitWidth, TZ)));
5156 getUDivExactExpr(getSCEV(BO->LHS), MulCount),
5157 IntegerType::get(getContext(), BitWidth - LZ - TZ)),
5158 BO->LHS->getType()),
5164 case Instruction::Or:
5165 // If the RHS of the Or is a constant, we may have something like:
5166 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
5167 // optimizations will transparently handle this case.
5169 // In order for this transformation to be safe, the LHS must be of the
5170 // form X*(2^n) and the Or constant must be less than 2^n.
5171 if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->RHS)) {
5172 const SCEV *LHS = getSCEV(BO->LHS);
5173 const APInt &CIVal = CI->getValue();
5174 if (GetMinTrailingZeros(LHS) >=
5175 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
5176 // Build a plain add SCEV.
5177 const SCEV *S = getAddExpr(LHS, getSCEV(CI));
5178 // If the LHS of the add was an addrec and it has no-wrap flags,
5179 // transfer the no-wrap flags, since an or won't introduce a wrap.
5180 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
5181 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
5182 const_cast<SCEVAddRecExpr *>(NewAR)->setNoWrapFlags(
5183 OldAR->getNoWrapFlags());
5190 case Instruction::Xor:
5191 if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->RHS)) {
5192 // If the RHS of xor is -1, then this is a not operation.
5193 if (CI->isAllOnesValue())
5194 return getNotSCEV(getSCEV(BO->LHS));
5196 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
5197 // This is a variant of the check for xor with -1, and it handles
5198 // the case where instcombine has trimmed non-demanded bits out
5199 // of an xor with -1.
5200 if (auto *LBO = dyn_cast<BinaryOperator>(BO->LHS))
5201 if (ConstantInt *LCI = dyn_cast<ConstantInt>(LBO->getOperand(1)))
5202 if (LBO->getOpcode() == Instruction::And &&
5203 LCI->getValue() == CI->getValue())
5204 if (const SCEVZeroExtendExpr *Z =
5205 dyn_cast<SCEVZeroExtendExpr>(getSCEV(BO->LHS))) {
5206 Type *UTy = BO->LHS->getType();
5207 const SCEV *Z0 = Z->getOperand();
5208 Type *Z0Ty = Z0->getType();
5209 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
5211 // If C is a low-bits mask, the zero extend is serving to
5212 // mask off the high bits. Complement the operand and
5213 // re-apply the zext.
5214 if (APIntOps::isMask(Z0TySize, CI->getValue()))
5215 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
5217 // If C is a single bit, it may be in the sign-bit position
5218 // before the zero-extend. In this case, represent the xor
5219 // using an add, which is equivalent, and re-apply the zext.
5220 APInt Trunc = CI->getValue().trunc(Z0TySize);
5221 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
5223 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
5229 case Instruction::Shl:
5230 // Turn shift left of a constant amount into a multiply.
5231 if (ConstantInt *SA = dyn_cast<ConstantInt>(BO->RHS)) {
5232 uint32_t BitWidth = cast<IntegerType>(SA->getType())->getBitWidth();
5234 // If the shift count is not less than the bitwidth, the result of
5235 // the shift is undefined. Don't try to analyze it, because the
5236 // resolution chosen here may differ from the resolution chosen in
5237 // other parts of the compiler.
5238 if (SA->getValue().uge(BitWidth))
5241 // It is currently not resolved how to interpret NSW for left
5242 // shift by BitWidth - 1, so we avoid applying flags in that
5243 // case. Remove this check (or this comment) once the situation
5245 // http://lists.llvm.org/pipermail/llvm-dev/2015-April/084195.html
5246 // and http://reviews.llvm.org/D8890 .
5247 auto Flags = SCEV::FlagAnyWrap;
5248 if (BO->Op && SA->getValue().ult(BitWidth - 1))
5249 Flags = getNoWrapFlagsFromUB(BO->Op);
5251 Constant *X = ConstantInt::get(getContext(),
5252 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
5253 return getMulExpr(getSCEV(BO->LHS), getSCEV(X), Flags);
5257 case Instruction::AShr:
5258 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
5259 if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->RHS))
5260 if (Operator *L = dyn_cast<Operator>(BO->LHS))
5261 if (L->getOpcode() == Instruction::Shl &&
5262 L->getOperand(1) == BO->RHS) {
5263 uint64_t BitWidth = getTypeSizeInBits(BO->LHS->getType());
5265 // If the shift count is not less than the bitwidth, the result of
5266 // the shift is undefined. Don't try to analyze it, because the
5267 // resolution chosen here may differ from the resolution chosen in
5268 // other parts of the compiler.
5269 if (CI->getValue().uge(BitWidth))
5272 uint64_t Amt = BitWidth - CI->getZExtValue();
5273 if (Amt == BitWidth)
5274 return getSCEV(L->getOperand(0)); // shift by zero --> noop
5275 return getSignExtendExpr(
5276 getTruncateExpr(getSCEV(L->getOperand(0)),
5277 IntegerType::get(getContext(), Amt)),
5278 BO->LHS->getType());
5284 switch (U->getOpcode()) {
5285 case Instruction::Trunc:
5286 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
5288 case Instruction::ZExt:
5289 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
5291 case Instruction::SExt:
5292 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
5294 case Instruction::BitCast:
5295 // BitCasts are no-op casts so we just eliminate the cast.
5296 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
5297 return getSCEV(U->getOperand(0));
5300 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
5301 // lead to pointer expressions which cannot safely be expanded to GEPs,
5302 // because ScalarEvolution doesn't respect the GEP aliasing rules when
5303 // simplifying integer expressions.
5305 case Instruction::GetElementPtr:
5306 return createNodeForGEP(cast<GEPOperator>(U));
5308 case Instruction::PHI:
5309 return createNodeForPHI(cast<PHINode>(U));
5311 case Instruction::Select:
5312 // U can also be a select constant expr, which let fall through. Since
5313 // createNodeForSelect only works for a condition that is an `ICmpInst`, and
5314 // constant expressions cannot have instructions as operands, we'd have
5315 // returned getUnknown for a select constant expressions anyway.
5316 if (isa<Instruction>(U))
5317 return createNodeForSelectOrPHI(cast<Instruction>(U), U->getOperand(0),
5318 U->getOperand(1), U->getOperand(2));
5321 case Instruction::Call:
5322 case Instruction::Invoke:
5323 if (Value *RV = CallSite(U).getReturnedArgOperand())
5328 return getUnknown(V);
5333 //===----------------------------------------------------------------------===//
5334 // Iteration Count Computation Code
5337 static unsigned getConstantTripCount(const SCEVConstant *ExitCount) {
5341 ConstantInt *ExitConst = ExitCount->getValue();
5343 // Guard against huge trip counts.
5344 if (ExitConst->getValue().getActiveBits() > 32)
5347 // In case of integer overflow, this returns 0, which is correct.
5348 return ((unsigned)ExitConst->getZExtValue()) + 1;
5351 unsigned ScalarEvolution::getSmallConstantTripCount(Loop *L) {
5352 if (BasicBlock *ExitingBB = L->getExitingBlock())
5353 return getSmallConstantTripCount(L, ExitingBB);
5355 // No trip count information for multiple exits.
5359 unsigned ScalarEvolution::getSmallConstantTripCount(Loop *L,
5360 BasicBlock *ExitingBlock) {
5361 assert(ExitingBlock && "Must pass a non-null exiting block!");
5362 assert(L->isLoopExiting(ExitingBlock) &&
5363 "Exiting block must actually branch out of the loop!");
5364 const SCEVConstant *ExitCount =
5365 dyn_cast<SCEVConstant>(getExitCount(L, ExitingBlock));
5366 return getConstantTripCount(ExitCount);
5369 unsigned ScalarEvolution::getSmallConstantMaxTripCount(Loop *L) {
5370 const auto *MaxExitCount =
5371 dyn_cast<SCEVConstant>(getMaxBackedgeTakenCount(L));
5372 return getConstantTripCount(MaxExitCount);
5375 unsigned ScalarEvolution::getSmallConstantTripMultiple(Loop *L) {
5376 if (BasicBlock *ExitingBB = L->getExitingBlock())
5377 return getSmallConstantTripMultiple(L, ExitingBB);
5379 // No trip multiple information for multiple exits.
5383 /// Returns the largest constant divisor of the trip count of this loop as a
5384 /// normal unsigned value, if possible. This means that the actual trip count is
5385 /// always a multiple of the returned value (don't forget the trip count could
5386 /// very well be zero as well!).
5388 /// Returns 1 if the trip count is unknown or not guaranteed to be the
5389 /// multiple of a constant (which is also the case if the trip count is simply
5390 /// constant, use getSmallConstantTripCount for that case), Will also return 1
5391 /// if the trip count is very large (>= 2^32).
5393 /// As explained in the comments for getSmallConstantTripCount, this assumes
5394 /// that control exits the loop via ExitingBlock.
5396 ScalarEvolution::getSmallConstantTripMultiple(Loop *L,
5397 BasicBlock *ExitingBlock) {
5398 assert(ExitingBlock && "Must pass a non-null exiting block!");
5399 assert(L->isLoopExiting(ExitingBlock) &&
5400 "Exiting block must actually branch out of the loop!");
5401 const SCEV *ExitCount = getExitCount(L, ExitingBlock);
5402 if (ExitCount == getCouldNotCompute())
5405 // Get the trip count from the BE count by adding 1.
5406 const SCEV *TCMul = getAddExpr(ExitCount, getOne(ExitCount->getType()));
5407 // FIXME: SCEV distributes multiplication as V1*C1 + V2*C1. We could attempt
5408 // to factor simple cases.
5409 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(TCMul))
5410 TCMul = Mul->getOperand(0);
5412 const SCEVConstant *MulC = dyn_cast<SCEVConstant>(TCMul);
5416 ConstantInt *Result = MulC->getValue();
5418 // Guard against huge trip counts (this requires checking
5419 // for zero to handle the case where the trip count == -1 and the
5421 if (!Result || Result->getValue().getActiveBits() > 32 ||
5422 Result->getValue().getActiveBits() == 0)
5425 return (unsigned)Result->getZExtValue();
5428 /// Get the expression for the number of loop iterations for which this loop is
5429 /// guaranteed not to exit via ExitingBlock. Otherwise return
5430 /// SCEVCouldNotCompute.
5431 const SCEV *ScalarEvolution::getExitCount(Loop *L, BasicBlock *ExitingBlock) {
5432 return getBackedgeTakenInfo(L).getExact(ExitingBlock, this);
5436 ScalarEvolution::getPredicatedBackedgeTakenCount(const Loop *L,
5437 SCEVUnionPredicate &Preds) {
5438 return getPredicatedBackedgeTakenInfo(L).getExact(this, &Preds);
5441 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
5442 return getBackedgeTakenInfo(L).getExact(this);
5445 /// Similar to getBackedgeTakenCount, except return the least SCEV value that is
5446 /// known never to be less than the actual backedge taken count.
5447 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
5448 return getBackedgeTakenInfo(L).getMax(this);
5451 bool ScalarEvolution::isBackedgeTakenCountMaxOrZero(const Loop *L) {
5452 return getBackedgeTakenInfo(L).isMaxOrZero(this);
5455 /// Push PHI nodes in the header of the given loop onto the given Worklist.
5457 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
5458 BasicBlock *Header = L->getHeader();
5460 // Push all Loop-header PHIs onto the Worklist stack.
5461 for (BasicBlock::iterator I = Header->begin();
5462 PHINode *PN = dyn_cast<PHINode>(I); ++I)
5463 Worklist.push_back(PN);
5466 const ScalarEvolution::BackedgeTakenInfo &
5467 ScalarEvolution::getPredicatedBackedgeTakenInfo(const Loop *L) {
5468 auto &BTI = getBackedgeTakenInfo(L);
5469 if (BTI.hasFullInfo())
5472 auto Pair = PredicatedBackedgeTakenCounts.insert({L, BackedgeTakenInfo()});
5475 return Pair.first->second;
5477 BackedgeTakenInfo Result =
5478 computeBackedgeTakenCount(L, /*AllowPredicates=*/true);
5480 return PredicatedBackedgeTakenCounts.find(L)->second = std::move(Result);
5483 const ScalarEvolution::BackedgeTakenInfo &
5484 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
5485 // Initially insert an invalid entry for this loop. If the insertion
5486 // succeeds, proceed to actually compute a backedge-taken count and
5487 // update the value. The temporary CouldNotCompute value tells SCEV
5488 // code elsewhere that it shouldn't attempt to request a new
5489 // backedge-taken count, which could result in infinite recursion.
5490 std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
5491 BackedgeTakenCounts.insert({L, BackedgeTakenInfo()});
5493 return Pair.first->second;
5495 // computeBackedgeTakenCount may allocate memory for its result. Inserting it
5496 // into the BackedgeTakenCounts map transfers ownership. Otherwise, the result
5497 // must be cleared in this scope.
5498 BackedgeTakenInfo Result = computeBackedgeTakenCount(L);
5500 if (Result.getExact(this) != getCouldNotCompute()) {
5501 assert(isLoopInvariant(Result.getExact(this), L) &&
5502 isLoopInvariant(Result.getMax(this), L) &&
5503 "Computed backedge-taken count isn't loop invariant for loop!");
5504 ++NumTripCountsComputed;
5506 else if (Result.getMax(this) == getCouldNotCompute() &&
5507 isa<PHINode>(L->getHeader()->begin())) {
5508 // Only count loops that have phi nodes as not being computable.
5509 ++NumTripCountsNotComputed;
5512 // Now that we know more about the trip count for this loop, forget any
5513 // existing SCEV values for PHI nodes in this loop since they are only
5514 // conservative estimates made without the benefit of trip count
5515 // information. This is similar to the code in forgetLoop, except that
5516 // it handles SCEVUnknown PHI nodes specially.
5517 if (Result.hasAnyInfo()) {
5518 SmallVector<Instruction *, 16> Worklist;
5519 PushLoopPHIs(L, Worklist);
5521 SmallPtrSet<Instruction *, 8> Visited;
5522 while (!Worklist.empty()) {
5523 Instruction *I = Worklist.pop_back_val();
5524 if (!Visited.insert(I).second)
5527 ValueExprMapType::iterator It =
5528 ValueExprMap.find_as(static_cast<Value *>(I));
5529 if (It != ValueExprMap.end()) {
5530 const SCEV *Old = It->second;
5532 // SCEVUnknown for a PHI either means that it has an unrecognized
5533 // structure, or it's a PHI that's in the progress of being computed
5534 // by createNodeForPHI. In the former case, additional loop trip
5535 // count information isn't going to change anything. In the later
5536 // case, createNodeForPHI will perform the necessary updates on its
5537 // own when it gets to that point.
5538 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) {
5539 eraseValueFromMap(It->first);
5540 forgetMemoizedResults(Old);
5542 if (PHINode *PN = dyn_cast<PHINode>(I))
5543 ConstantEvolutionLoopExitValue.erase(PN);
5546 PushDefUseChildren(I, Worklist);
5550 // Re-lookup the insert position, since the call to
5551 // computeBackedgeTakenCount above could result in a
5552 // recusive call to getBackedgeTakenInfo (on a different
5553 // loop), which would invalidate the iterator computed
5555 return BackedgeTakenCounts.find(L)->second = std::move(Result);
5558 void ScalarEvolution::forgetLoop(const Loop *L) {
5559 // Drop any stored trip count value.
5560 auto RemoveLoopFromBackedgeMap =
5561 [L](DenseMap<const Loop *, BackedgeTakenInfo> &Map) {
5562 auto BTCPos = Map.find(L);
5563 if (BTCPos != Map.end()) {
5564 BTCPos->second.clear();
5569 RemoveLoopFromBackedgeMap(BackedgeTakenCounts);
5570 RemoveLoopFromBackedgeMap(PredicatedBackedgeTakenCounts);
5572 // Drop information about expressions based on loop-header PHIs.
5573 SmallVector<Instruction *, 16> Worklist;
5574 PushLoopPHIs(L, Worklist);
5576 SmallPtrSet<Instruction *, 8> Visited;
5577 while (!Worklist.empty()) {
5578 Instruction *I = Worklist.pop_back_val();
5579 if (!Visited.insert(I).second)
5582 ValueExprMapType::iterator It =
5583 ValueExprMap.find_as(static_cast<Value *>(I));
5584 if (It != ValueExprMap.end()) {
5585 eraseValueFromMap(It->first);
5586 forgetMemoizedResults(It->second);
5587 if (PHINode *PN = dyn_cast<PHINode>(I))
5588 ConstantEvolutionLoopExitValue.erase(PN);
5591 PushDefUseChildren(I, Worklist);
5594 // Forget all contained loops too, to avoid dangling entries in the
5595 // ValuesAtScopes map.
5599 LoopPropertiesCache.erase(L);
5602 void ScalarEvolution::forgetValue(Value *V) {
5603 Instruction *I = dyn_cast<Instruction>(V);
5606 // Drop information about expressions based on loop-header PHIs.
5607 SmallVector<Instruction *, 16> Worklist;
5608 Worklist.push_back(I);
5610 SmallPtrSet<Instruction *, 8> Visited;
5611 while (!Worklist.empty()) {
5612 I = Worklist.pop_back_val();
5613 if (!Visited.insert(I).second)
5616 ValueExprMapType::iterator It =
5617 ValueExprMap.find_as(static_cast<Value *>(I));
5618 if (It != ValueExprMap.end()) {
5619 eraseValueFromMap(It->first);
5620 forgetMemoizedResults(It->second);
5621 if (PHINode *PN = dyn_cast<PHINode>(I))
5622 ConstantEvolutionLoopExitValue.erase(PN);
5625 PushDefUseChildren(I, Worklist);
5629 /// Get the exact loop backedge taken count considering all loop exits. A
5630 /// computable result can only be returned for loops with a single exit.
5631 /// Returning the minimum taken count among all exits is incorrect because one
5632 /// of the loop's exit limit's may have been skipped. howFarToZero assumes that
5633 /// the limit of each loop test is never skipped. This is a valid assumption as
5634 /// long as the loop exits via that test. For precise results, it is the
5635 /// caller's responsibility to specify the relevant loop exit using
5636 /// getExact(ExitingBlock, SE).
5638 ScalarEvolution::BackedgeTakenInfo::getExact(ScalarEvolution *SE,
5639 SCEVUnionPredicate *Preds) const {
5640 // If any exits were not computable, the loop is not computable.
5641 if (!isComplete() || ExitNotTaken.empty())
5642 return SE->getCouldNotCompute();
5644 const SCEV *BECount = nullptr;
5645 for (auto &ENT : ExitNotTaken) {
5646 assert(ENT.ExactNotTaken != SE->getCouldNotCompute() && "bad exit SCEV");
5649 BECount = ENT.ExactNotTaken;
5650 else if (BECount != ENT.ExactNotTaken)
5651 return SE->getCouldNotCompute();
5652 if (Preds && !ENT.hasAlwaysTruePredicate())
5653 Preds->add(ENT.Predicate.get());
5655 assert((Preds || ENT.hasAlwaysTruePredicate()) &&
5656 "Predicate should be always true!");
5659 assert(BECount && "Invalid not taken count for loop exit");
5663 /// Get the exact not taken count for this loop exit.
5665 ScalarEvolution::BackedgeTakenInfo::getExact(BasicBlock *ExitingBlock,
5666 ScalarEvolution *SE) const {
5667 for (auto &ENT : ExitNotTaken)
5668 if (ENT.ExitingBlock == ExitingBlock && ENT.hasAlwaysTruePredicate())
5669 return ENT.ExactNotTaken;
5671 return SE->getCouldNotCompute();
5674 /// getMax - Get the max backedge taken count for the loop.
5676 ScalarEvolution::BackedgeTakenInfo::getMax(ScalarEvolution *SE) const {
5677 auto PredicateNotAlwaysTrue = [](const ExitNotTakenInfo &ENT) {
5678 return !ENT.hasAlwaysTruePredicate();
5681 if (any_of(ExitNotTaken, PredicateNotAlwaysTrue) || !getMax())
5682 return SE->getCouldNotCompute();
5687 bool ScalarEvolution::BackedgeTakenInfo::isMaxOrZero(ScalarEvolution *SE) const {
5688 auto PredicateNotAlwaysTrue = [](const ExitNotTakenInfo &ENT) {
5689 return !ENT.hasAlwaysTruePredicate();
5691 return MaxOrZero && !any_of(ExitNotTaken, PredicateNotAlwaysTrue);
5694 bool ScalarEvolution::BackedgeTakenInfo::hasOperand(const SCEV *S,
5695 ScalarEvolution *SE) const {
5696 if (getMax() && getMax() != SE->getCouldNotCompute() &&
5697 SE->hasOperand(getMax(), S))
5700 for (auto &ENT : ExitNotTaken)
5701 if (ENT.ExactNotTaken != SE->getCouldNotCompute() &&
5702 SE->hasOperand(ENT.ExactNotTaken, S))
5708 /// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each
5709 /// computable exit into a persistent ExitNotTakenInfo array.
5710 ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo(
5711 SmallVectorImpl<ScalarEvolution::BackedgeTakenInfo::EdgeExitInfo>
5713 bool Complete, const SCEV *MaxCount, bool MaxOrZero)
5714 : MaxAndComplete(MaxCount, Complete), MaxOrZero(MaxOrZero) {
5715 typedef ScalarEvolution::BackedgeTakenInfo::EdgeExitInfo EdgeExitInfo;
5716 ExitNotTaken.reserve(ExitCounts.size());
5718 ExitCounts.begin(), ExitCounts.end(), std::back_inserter(ExitNotTaken),
5719 [&](const EdgeExitInfo &EEI) {
5720 BasicBlock *ExitBB = EEI.first;
5721 const ExitLimit &EL = EEI.second;
5722 if (EL.Predicates.empty())
5723 return ExitNotTakenInfo(ExitBB, EL.ExactNotTaken, nullptr);
5725 std::unique_ptr<SCEVUnionPredicate> Predicate(new SCEVUnionPredicate);
5726 for (auto *Pred : EL.Predicates)
5727 Predicate->add(Pred);
5729 return ExitNotTakenInfo(ExitBB, EL.ExactNotTaken, std::move(Predicate));
5733 /// Invalidate this result and free the ExitNotTakenInfo array.
5734 void ScalarEvolution::BackedgeTakenInfo::clear() {
5735 ExitNotTaken.clear();
5738 /// Compute the number of times the backedge of the specified loop will execute.
5739 ScalarEvolution::BackedgeTakenInfo
5740 ScalarEvolution::computeBackedgeTakenCount(const Loop *L,
5741 bool AllowPredicates) {
5742 SmallVector<BasicBlock *, 8> ExitingBlocks;
5743 L->getExitingBlocks(ExitingBlocks);
5745 typedef ScalarEvolution::BackedgeTakenInfo::EdgeExitInfo EdgeExitInfo;
5747 SmallVector<EdgeExitInfo, 4> ExitCounts;
5748 bool CouldComputeBECount = true;
5749 BasicBlock *Latch = L->getLoopLatch(); // may be NULL.
5750 const SCEV *MustExitMaxBECount = nullptr;
5751 const SCEV *MayExitMaxBECount = nullptr;
5752 bool MustExitMaxOrZero = false;
5754 // Compute the ExitLimit for each loop exit. Use this to populate ExitCounts
5755 // and compute maxBECount.
5756 // Do a union of all the predicates here.
5757 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
5758 BasicBlock *ExitBB = ExitingBlocks[i];
5759 ExitLimit EL = computeExitLimit(L, ExitBB, AllowPredicates);
5761 assert((AllowPredicates || EL.Predicates.empty()) &&
5762 "Predicated exit limit when predicates are not allowed!");
5764 // 1. For each exit that can be computed, add an entry to ExitCounts.
5765 // CouldComputeBECount is true only if all exits can be computed.
5766 if (EL.ExactNotTaken == getCouldNotCompute())
5767 // We couldn't compute an exact value for this exit, so
5768 // we won't be able to compute an exact value for the loop.
5769 CouldComputeBECount = false;
5771 ExitCounts.emplace_back(ExitBB, EL);
5773 // 2. Derive the loop's MaxBECount from each exit's max number of
5774 // non-exiting iterations. Partition the loop exits into two kinds:
5775 // LoopMustExits and LoopMayExits.
5777 // If the exit dominates the loop latch, it is a LoopMustExit otherwise it
5778 // is a LoopMayExit. If any computable LoopMustExit is found, then
5779 // MaxBECount is the minimum EL.MaxNotTaken of computable
5780 // LoopMustExits. Otherwise, MaxBECount is conservatively the maximum
5781 // EL.MaxNotTaken, where CouldNotCompute is considered greater than any
5782 // computable EL.MaxNotTaken.
5783 if (EL.MaxNotTaken != getCouldNotCompute() && Latch &&
5784 DT.dominates(ExitBB, Latch)) {
5785 if (!MustExitMaxBECount) {
5786 MustExitMaxBECount = EL.MaxNotTaken;
5787 MustExitMaxOrZero = EL.MaxOrZero;
5789 MustExitMaxBECount =
5790 getUMinFromMismatchedTypes(MustExitMaxBECount, EL.MaxNotTaken);
5792 } else if (MayExitMaxBECount != getCouldNotCompute()) {
5793 if (!MayExitMaxBECount || EL.MaxNotTaken == getCouldNotCompute())
5794 MayExitMaxBECount = EL.MaxNotTaken;
5797 getUMaxFromMismatchedTypes(MayExitMaxBECount, EL.MaxNotTaken);
5801 const SCEV *MaxBECount = MustExitMaxBECount ? MustExitMaxBECount :
5802 (MayExitMaxBECount ? MayExitMaxBECount : getCouldNotCompute());
5803 // The loop backedge will be taken the maximum or zero times if there's
5804 // a single exit that must be taken the maximum or zero times.
5805 bool MaxOrZero = (MustExitMaxOrZero && ExitingBlocks.size() == 1);
5806 return BackedgeTakenInfo(std::move(ExitCounts), CouldComputeBECount,
5807 MaxBECount, MaxOrZero);
5810 ScalarEvolution::ExitLimit
5811 ScalarEvolution::computeExitLimit(const Loop *L, BasicBlock *ExitingBlock,
5812 bool AllowPredicates) {
5814 // Okay, we've chosen an exiting block. See what condition causes us to exit
5815 // at this block and remember the exit block and whether all other targets
5816 // lead to the loop header.
5817 bool MustExecuteLoopHeader = true;
5818 BasicBlock *Exit = nullptr;
5819 for (auto *SBB : successors(ExitingBlock))
5820 if (!L->contains(SBB)) {
5821 if (Exit) // Multiple exit successors.
5822 return getCouldNotCompute();
5824 } else if (SBB != L->getHeader()) {
5825 MustExecuteLoopHeader = false;
5828 // At this point, we know we have a conditional branch that determines whether
5829 // the loop is exited. However, we don't know if the branch is executed each
5830 // time through the loop. If not, then the execution count of the branch will
5831 // not be equal to the trip count of the loop.
5833 // Currently we check for this by checking to see if the Exit branch goes to
5834 // the loop header. If so, we know it will always execute the same number of
5835 // times as the loop. We also handle the case where the exit block *is* the
5836 // loop header. This is common for un-rotated loops.
5838 // If both of those tests fail, walk up the unique predecessor chain to the
5839 // header, stopping if there is an edge that doesn't exit the loop. If the
5840 // header is reached, the execution count of the branch will be equal to the
5841 // trip count of the loop.
5843 // More extensive analysis could be done to handle more cases here.
5845 if (!MustExecuteLoopHeader && ExitingBlock != L->getHeader()) {
5846 // The simple checks failed, try climbing the unique predecessor chain
5847 // up to the header.
5849 for (BasicBlock *BB = ExitingBlock; BB; ) {
5850 BasicBlock *Pred = BB->getUniquePredecessor();
5852 return getCouldNotCompute();
5853 TerminatorInst *PredTerm = Pred->getTerminator();
5854 for (const BasicBlock *PredSucc : PredTerm->successors()) {
5857 // If the predecessor has a successor that isn't BB and isn't
5858 // outside the loop, assume the worst.
5859 if (L->contains(PredSucc))
5860 return getCouldNotCompute();
5862 if (Pred == L->getHeader()) {
5869 return getCouldNotCompute();
5872 bool IsOnlyExit = (L->getExitingBlock() != nullptr);
5873 TerminatorInst *Term = ExitingBlock->getTerminator();
5874 if (BranchInst *BI = dyn_cast<BranchInst>(Term)) {
5875 assert(BI->isConditional() && "If unconditional, it can't be in loop!");
5876 // Proceed to the next level to examine the exit condition expression.
5877 return computeExitLimitFromCond(
5878 L, BI->getCondition(), BI->getSuccessor(0), BI->getSuccessor(1),
5879 /*ControlsExit=*/IsOnlyExit, AllowPredicates);
5882 if (SwitchInst *SI = dyn_cast<SwitchInst>(Term))
5883 return computeExitLimitFromSingleExitSwitch(L, SI, Exit,
5884 /*ControlsExit=*/IsOnlyExit);
5886 return getCouldNotCompute();
5889 ScalarEvolution::ExitLimit
5890 ScalarEvolution::computeExitLimitFromCond(const Loop *L,
5895 bool AllowPredicates) {
5896 // Check if the controlling expression for this loop is an And or Or.
5897 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
5898 if (BO->getOpcode() == Instruction::And) {
5899 // Recurse on the operands of the and.
5900 bool EitherMayExit = L->contains(TBB);
5901 ExitLimit EL0 = computeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
5902 ControlsExit && !EitherMayExit,
5904 ExitLimit EL1 = computeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
5905 ControlsExit && !EitherMayExit,
5907 const SCEV *BECount = getCouldNotCompute();
5908 const SCEV *MaxBECount = getCouldNotCompute();
5909 if (EitherMayExit) {
5910 // Both conditions must be true for the loop to continue executing.
5911 // Choose the less conservative count.
5912 if (EL0.ExactNotTaken == getCouldNotCompute() ||
5913 EL1.ExactNotTaken == getCouldNotCompute())
5914 BECount = getCouldNotCompute();
5917 getUMinFromMismatchedTypes(EL0.ExactNotTaken, EL1.ExactNotTaken);
5918 if (EL0.MaxNotTaken == getCouldNotCompute())
5919 MaxBECount = EL1.MaxNotTaken;
5920 else if (EL1.MaxNotTaken == getCouldNotCompute())
5921 MaxBECount = EL0.MaxNotTaken;
5924 getUMinFromMismatchedTypes(EL0.MaxNotTaken, EL1.MaxNotTaken);
5926 // Both conditions must be true at the same time for the loop to exit.
5927 // For now, be conservative.
5928 assert(L->contains(FBB) && "Loop block has no successor in loop!");
5929 if (EL0.MaxNotTaken == EL1.MaxNotTaken)
5930 MaxBECount = EL0.MaxNotTaken;
5931 if (EL0.ExactNotTaken == EL1.ExactNotTaken)
5932 BECount = EL0.ExactNotTaken;
5935 // There are cases (e.g. PR26207) where computeExitLimitFromCond is able
5936 // to be more aggressive when computing BECount than when computing
5937 // MaxBECount. In these cases it is possible for EL0.ExactNotTaken and
5938 // EL1.ExactNotTaken to match, but for EL0.MaxNotTaken and EL1.MaxNotTaken
5940 if (isa<SCEVCouldNotCompute>(MaxBECount) &&
5941 !isa<SCEVCouldNotCompute>(BECount))
5942 MaxBECount = BECount;
5944 return ExitLimit(BECount, MaxBECount, false,
5945 {&EL0.Predicates, &EL1.Predicates});
5947 if (BO->getOpcode() == Instruction::Or) {
5948 // Recurse on the operands of the or.
5949 bool EitherMayExit = L->contains(FBB);
5950 ExitLimit EL0 = computeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
5951 ControlsExit && !EitherMayExit,
5953 ExitLimit EL1 = computeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
5954 ControlsExit && !EitherMayExit,
5956 const SCEV *BECount = getCouldNotCompute();
5957 const SCEV *MaxBECount = getCouldNotCompute();
5958 if (EitherMayExit) {
5959 // Both conditions must be false for the loop to continue executing.
5960 // Choose the less conservative count.
5961 if (EL0.ExactNotTaken == getCouldNotCompute() ||
5962 EL1.ExactNotTaken == getCouldNotCompute())
5963 BECount = getCouldNotCompute();
5966 getUMinFromMismatchedTypes(EL0.ExactNotTaken, EL1.ExactNotTaken);
5967 if (EL0.MaxNotTaken == getCouldNotCompute())
5968 MaxBECount = EL1.MaxNotTaken;
5969 else if (EL1.MaxNotTaken == getCouldNotCompute())
5970 MaxBECount = EL0.MaxNotTaken;
5973 getUMinFromMismatchedTypes(EL0.MaxNotTaken, EL1.MaxNotTaken);
5975 // Both conditions must be false at the same time for the loop to exit.
5976 // For now, be conservative.
5977 assert(L->contains(TBB) && "Loop block has no successor in loop!");
5978 if (EL0.MaxNotTaken == EL1.MaxNotTaken)
5979 MaxBECount = EL0.MaxNotTaken;
5980 if (EL0.ExactNotTaken == EL1.ExactNotTaken)
5981 BECount = EL0.ExactNotTaken;
5984 return ExitLimit(BECount, MaxBECount, false,
5985 {&EL0.Predicates, &EL1.Predicates});
5989 // With an icmp, it may be feasible to compute an exact backedge-taken count.
5990 // Proceed to the next level to examine the icmp.
5991 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond)) {
5993 computeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB, ControlsExit);
5994 if (EL.hasFullInfo() || !AllowPredicates)
5997 // Try again, but use SCEV predicates this time.
5998 return computeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB, ControlsExit,
5999 /*AllowPredicates=*/true);
6002 // Check for a constant condition. These are normally stripped out by
6003 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
6004 // preserve the CFG and is temporarily leaving constant conditions
6006 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
6007 if (L->contains(FBB) == !CI->getZExtValue())
6008 // The backedge is always taken.
6009 return getCouldNotCompute();
6011 // The backedge is never taken.
6012 return getZero(CI->getType());
6015 // If it's not an integer or pointer comparison then compute it the hard way.
6016 return computeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
6019 ScalarEvolution::ExitLimit
6020 ScalarEvolution::computeExitLimitFromICmp(const Loop *L,
6025 bool AllowPredicates) {
6027 // If the condition was exit on true, convert the condition to exit on false
6028 ICmpInst::Predicate Cond;
6029 if (!L->contains(FBB))
6030 Cond = ExitCond->getPredicate();
6032 Cond = ExitCond->getInversePredicate();
6034 // Handle common loops like: for (X = "string"; *X; ++X)
6035 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
6036 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
6038 computeLoadConstantCompareExitLimit(LI, RHS, L, Cond);
6039 if (ItCnt.hasAnyInfo())
6043 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
6044 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
6046 // Try to evaluate any dependencies out of the loop.
6047 LHS = getSCEVAtScope(LHS, L);
6048 RHS = getSCEVAtScope(RHS, L);
6050 // At this point, we would like to compute how many iterations of the
6051 // loop the predicate will return true for these inputs.
6052 if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) {
6053 // If there is a loop-invariant, force it into the RHS.
6054 std::swap(LHS, RHS);
6055 Cond = ICmpInst::getSwappedPredicate(Cond);
6058 // Simplify the operands before analyzing them.
6059 (void)SimplifyICmpOperands(Cond, LHS, RHS);
6061 // If we have a comparison of a chrec against a constant, try to use value
6062 // ranges to answer this query.
6063 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
6064 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
6065 if (AddRec->getLoop() == L) {
6066 // Form the constant range.
6067 ConstantRange CompRange =
6068 ConstantRange::makeExactICmpRegion(Cond, RHSC->getAPInt());
6070 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
6071 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
6075 case ICmpInst::ICMP_NE: { // while (X != Y)
6076 // Convert to: while (X-Y != 0)
6077 ExitLimit EL = howFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit,
6079 if (EL.hasAnyInfo()) return EL;
6082 case ICmpInst::ICMP_EQ: { // while (X == Y)
6083 // Convert to: while (X-Y == 0)
6084 ExitLimit EL = howFarToNonZero(getMinusSCEV(LHS, RHS), L);
6085 if (EL.hasAnyInfo()) return EL;
6088 case ICmpInst::ICMP_SLT:
6089 case ICmpInst::ICMP_ULT: { // while (X < Y)
6090 bool IsSigned = Cond == ICmpInst::ICMP_SLT;
6091 ExitLimit EL = howManyLessThans(LHS, RHS, L, IsSigned, ControlsExit,
6093 if (EL.hasAnyInfo()) return EL;
6096 case ICmpInst::ICMP_SGT:
6097 case ICmpInst::ICMP_UGT: { // while (X > Y)
6098 bool IsSigned = Cond == ICmpInst::ICMP_SGT;
6100 howManyGreaterThans(LHS, RHS, L, IsSigned, ControlsExit,
6102 if (EL.hasAnyInfo()) return EL;
6109 auto *ExhaustiveCount =
6110 computeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
6112 if (!isa<SCEVCouldNotCompute>(ExhaustiveCount))
6113 return ExhaustiveCount;
6115 return computeShiftCompareExitLimit(ExitCond->getOperand(0),
6116 ExitCond->getOperand(1), L, Cond);
6119 ScalarEvolution::ExitLimit
6120 ScalarEvolution::computeExitLimitFromSingleExitSwitch(const Loop *L,
6122 BasicBlock *ExitingBlock,
6123 bool ControlsExit) {
6124 assert(!L->contains(ExitingBlock) && "Not an exiting block!");
6126 // Give up if the exit is the default dest of a switch.
6127 if (Switch->getDefaultDest() == ExitingBlock)
6128 return getCouldNotCompute();
6130 assert(L->contains(Switch->getDefaultDest()) &&
6131 "Default case must not exit the loop!");
6132 const SCEV *LHS = getSCEVAtScope(Switch->getCondition(), L);
6133 const SCEV *RHS = getConstant(Switch->findCaseDest(ExitingBlock));
6135 // while (X != Y) --> while (X-Y != 0)
6136 ExitLimit EL = howFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit);
6137 if (EL.hasAnyInfo())
6140 return getCouldNotCompute();
6143 static ConstantInt *
6144 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
6145 ScalarEvolution &SE) {
6146 const SCEV *InVal = SE.getConstant(C);
6147 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
6148 assert(isa<SCEVConstant>(Val) &&
6149 "Evaluation of SCEV at constant didn't fold correctly?");
6150 return cast<SCEVConstant>(Val)->getValue();
6153 /// Given an exit condition of 'icmp op load X, cst', try to see if we can
6154 /// compute the backedge execution count.
6155 ScalarEvolution::ExitLimit
6156 ScalarEvolution::computeLoadConstantCompareExitLimit(
6160 ICmpInst::Predicate predicate) {
6162 if (LI->isVolatile()) return getCouldNotCompute();
6164 // Check to see if the loaded pointer is a getelementptr of a global.
6165 // TODO: Use SCEV instead of manually grubbing with GEPs.
6166 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
6167 if (!GEP) return getCouldNotCompute();
6169 // Make sure that it is really a constant global we are gepping, with an
6170 // initializer, and make sure the first IDX is really 0.
6171 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
6172 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
6173 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
6174 !cast<Constant>(GEP->getOperand(1))->isNullValue())
6175 return getCouldNotCompute();
6177 // Okay, we allow one non-constant index into the GEP instruction.
6178 Value *VarIdx = nullptr;
6179 std::vector<Constant*> Indexes;
6180 unsigned VarIdxNum = 0;
6181 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
6182 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
6183 Indexes.push_back(CI);
6184 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
6185 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
6186 VarIdx = GEP->getOperand(i);
6188 Indexes.push_back(nullptr);
6191 // Loop-invariant loads may be a byproduct of loop optimization. Skip them.
6193 return getCouldNotCompute();
6195 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
6196 // Check to see if X is a loop variant variable value now.
6197 const SCEV *Idx = getSCEV(VarIdx);
6198 Idx = getSCEVAtScope(Idx, L);
6200 // We can only recognize very limited forms of loop index expressions, in
6201 // particular, only affine AddRec's like {C1,+,C2}.
6202 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
6203 if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) ||
6204 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
6205 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
6206 return getCouldNotCompute();
6208 unsigned MaxSteps = MaxBruteForceIterations;
6209 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
6210 ConstantInt *ItCst = ConstantInt::get(
6211 cast<IntegerType>(IdxExpr->getType()), IterationNum);
6212 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
6214 // Form the GEP offset.
6215 Indexes[VarIdxNum] = Val;
6217 Constant *Result = ConstantFoldLoadThroughGEPIndices(GV->getInitializer(),
6219 if (!Result) break; // Cannot compute!
6221 // Evaluate the condition for this iteration.
6222 Result = ConstantExpr::getICmp(predicate, Result, RHS);
6223 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
6224 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
6225 ++NumArrayLenItCounts;
6226 return getConstant(ItCst); // Found terminating iteration!
6229 return getCouldNotCompute();
6232 ScalarEvolution::ExitLimit ScalarEvolution::computeShiftCompareExitLimit(
6233 Value *LHS, Value *RHSV, const Loop *L, ICmpInst::Predicate Pred) {
6234 ConstantInt *RHS = dyn_cast<ConstantInt>(RHSV);
6236 return getCouldNotCompute();
6238 const BasicBlock *Latch = L->getLoopLatch();
6240 return getCouldNotCompute();
6242 const BasicBlock *Predecessor = L->getLoopPredecessor();
6244 return getCouldNotCompute();
6246 // Return true if V is of the form "LHS `shift_op` <positive constant>".
6247 // Return LHS in OutLHS and shift_opt in OutOpCode.
6248 auto MatchPositiveShift =
6249 [](Value *V, Value *&OutLHS, Instruction::BinaryOps &OutOpCode) {
6251 using namespace PatternMatch;
6253 ConstantInt *ShiftAmt;
6254 if (match(V, m_LShr(m_Value(OutLHS), m_ConstantInt(ShiftAmt))))
6255 OutOpCode = Instruction::LShr;
6256 else if (match(V, m_AShr(m_Value(OutLHS), m_ConstantInt(ShiftAmt))))
6257 OutOpCode = Instruction::AShr;
6258 else if (match(V, m_Shl(m_Value(OutLHS), m_ConstantInt(ShiftAmt))))
6259 OutOpCode = Instruction::Shl;
6263 return ShiftAmt->getValue().isStrictlyPositive();
6266 // Recognize a "shift recurrence" either of the form %iv or of %iv.shifted in
6269 // %iv = phi i32 [ %iv.shifted, %loop ], [ %val, %preheader ]
6270 // %iv.shifted = lshr i32 %iv, <positive constant>
6272 // Return true on a successful match. Return the corresponding PHI node (%iv
6273 // above) in PNOut and the opcode of the shift operation in OpCodeOut.
6274 auto MatchShiftRecurrence =
6275 [&](Value *V, PHINode *&PNOut, Instruction::BinaryOps &OpCodeOut) {
6276 Optional<Instruction::BinaryOps> PostShiftOpCode;
6279 Instruction::BinaryOps OpC;
6282 // If we encounter a shift instruction, "peel off" the shift operation,
6283 // and remember that we did so. Later when we inspect %iv's backedge
6284 // value, we will make sure that the backedge value uses the same
6287 // Note: the peeled shift operation does not have to be the same
6288 // instruction as the one feeding into the PHI's backedge value. We only
6289 // really care about it being the same *kind* of shift instruction --
6290 // that's all that is required for our later inferences to hold.
6291 if (MatchPositiveShift(LHS, V, OpC)) {
6292 PostShiftOpCode = OpC;
6297 PNOut = dyn_cast<PHINode>(LHS);
6298 if (!PNOut || PNOut->getParent() != L->getHeader())
6301 Value *BEValue = PNOut->getIncomingValueForBlock(Latch);
6305 // The backedge value for the PHI node must be a shift by a positive
6307 MatchPositiveShift(BEValue, OpLHS, OpCodeOut) &&
6309 // of the PHI node itself
6312 // and the kind of shift should be match the kind of shift we peeled
6314 (!PostShiftOpCode.hasValue() || *PostShiftOpCode == OpCodeOut);
6318 Instruction::BinaryOps OpCode;
6319 if (!MatchShiftRecurrence(LHS, PN, OpCode))
6320 return getCouldNotCompute();
6322 const DataLayout &DL = getDataLayout();
6324 // The key rationale for this optimization is that for some kinds of shift
6325 // recurrences, the value of the recurrence "stabilizes" to either 0 or -1
6326 // within a finite number of iterations. If the condition guarding the
6327 // backedge (in the sense that the backedge is taken if the condition is true)
6328 // is false for the value the shift recurrence stabilizes to, then we know
6329 // that the backedge is taken only a finite number of times.
6331 ConstantInt *StableValue = nullptr;
6334 llvm_unreachable("Impossible case!");
6336 case Instruction::AShr: {
6337 // {K,ashr,<positive-constant>} stabilizes to signum(K) in at most
6338 // bitwidth(K) iterations.
6339 Value *FirstValue = PN->getIncomingValueForBlock(Predecessor);
6340 bool KnownZero, KnownOne;
6341 ComputeSignBit(FirstValue, KnownZero, KnownOne, DL, 0, nullptr,
6342 Predecessor->getTerminator(), &DT);
6343 auto *Ty = cast<IntegerType>(RHS->getType());
6345 StableValue = ConstantInt::get(Ty, 0);
6347 StableValue = ConstantInt::get(Ty, -1, true);
6349 return getCouldNotCompute();
6353 case Instruction::LShr:
6354 case Instruction::Shl:
6355 // Both {K,lshr,<positive-constant>} and {K,shl,<positive-constant>}
6356 // stabilize to 0 in at most bitwidth(K) iterations.
6357 StableValue = ConstantInt::get(cast<IntegerType>(RHS->getType()), 0);
6362 ConstantFoldCompareInstOperands(Pred, StableValue, RHS, DL, &TLI);
6363 assert(Result->getType()->isIntegerTy(1) &&
6364 "Otherwise cannot be an operand to a branch instruction");
6366 if (Result->isZeroValue()) {
6367 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
6368 const SCEV *UpperBound =
6369 getConstant(getEffectiveSCEVType(RHS->getType()), BitWidth);
6370 return ExitLimit(getCouldNotCompute(), UpperBound, false);
6373 return getCouldNotCompute();
6376 /// Return true if we can constant fold an instruction of the specified type,
6377 /// assuming that all operands were constants.
6378 static bool CanConstantFold(const Instruction *I) {
6379 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
6380 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I) ||
6384 if (const CallInst *CI = dyn_cast<CallInst>(I))
6385 if (const Function *F = CI->getCalledFunction())
6386 return canConstantFoldCallTo(F);
6390 /// Determine whether this instruction can constant evolve within this loop
6391 /// assuming its operands can all constant evolve.
6392 static bool canConstantEvolve(Instruction *I, const Loop *L) {
6393 // An instruction outside of the loop can't be derived from a loop PHI.
6394 if (!L->contains(I)) return false;
6396 if (isa<PHINode>(I)) {
6397 // We don't currently keep track of the control flow needed to evaluate
6398 // PHIs, so we cannot handle PHIs inside of loops.
6399 return L->getHeader() == I->getParent();
6402 // If we won't be able to constant fold this expression even if the operands
6403 // are constants, bail early.
6404 return CanConstantFold(I);
6407 /// getConstantEvolvingPHIOperands - Implement getConstantEvolvingPHI by
6408 /// recursing through each instruction operand until reaching a loop header phi.
6410 getConstantEvolvingPHIOperands(Instruction *UseInst, const Loop *L,
6411 DenseMap<Instruction *, PHINode *> &PHIMap) {
6413 // Otherwise, we can evaluate this instruction if all of its operands are
6414 // constant or derived from a PHI node themselves.
6415 PHINode *PHI = nullptr;
6416 for (Value *Op : UseInst->operands()) {
6417 if (isa<Constant>(Op)) continue;
6419 Instruction *OpInst = dyn_cast<Instruction>(Op);
6420 if (!OpInst || !canConstantEvolve(OpInst, L)) return nullptr;
6422 PHINode *P = dyn_cast<PHINode>(OpInst);
6424 // If this operand is already visited, reuse the prior result.
6425 // We may have P != PHI if this is the deepest point at which the
6426 // inconsistent paths meet.
6427 P = PHIMap.lookup(OpInst);
6429 // Recurse and memoize the results, whether a phi is found or not.
6430 // This recursive call invalidates pointers into PHIMap.
6431 P = getConstantEvolvingPHIOperands(OpInst, L, PHIMap);
6435 return nullptr; // Not evolving from PHI
6436 if (PHI && PHI != P)
6437 return nullptr; // Evolving from multiple different PHIs.
6440 // This is a expression evolving from a constant PHI!
6444 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
6445 /// in the loop that V is derived from. We allow arbitrary operations along the
6446 /// way, but the operands of an operation must either be constants or a value
6447 /// derived from a constant PHI. If this expression does not fit with these
6448 /// constraints, return null.
6449 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
6450 Instruction *I = dyn_cast<Instruction>(V);
6451 if (!I || !canConstantEvolve(I, L)) return nullptr;
6453 if (PHINode *PN = dyn_cast<PHINode>(I))
6456 // Record non-constant instructions contained by the loop.
6457 DenseMap<Instruction *, PHINode *> PHIMap;
6458 return getConstantEvolvingPHIOperands(I, L, PHIMap);
6461 /// EvaluateExpression - Given an expression that passes the
6462 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
6463 /// in the loop has the value PHIVal. If we can't fold this expression for some
6464 /// reason, return null.
6465 static Constant *EvaluateExpression(Value *V, const Loop *L,
6466 DenseMap<Instruction *, Constant *> &Vals,
6467 const DataLayout &DL,
6468 const TargetLibraryInfo *TLI) {
6469 // Convenient constant check, but redundant for recursive calls.
6470 if (Constant *C = dyn_cast<Constant>(V)) return C;
6471 Instruction *I = dyn_cast<Instruction>(V);
6472 if (!I) return nullptr;
6474 if (Constant *C = Vals.lookup(I)) return C;
6476 // An instruction inside the loop depends on a value outside the loop that we
6477 // weren't given a mapping for, or a value such as a call inside the loop.
6478 if (!canConstantEvolve(I, L)) return nullptr;
6480 // An unmapped PHI can be due to a branch or another loop inside this loop,
6481 // or due to this not being the initial iteration through a loop where we
6482 // couldn't compute the evolution of this particular PHI last time.
6483 if (isa<PHINode>(I)) return nullptr;
6485 std::vector<Constant*> Operands(I->getNumOperands());
6487 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
6488 Instruction *Operand = dyn_cast<Instruction>(I->getOperand(i));
6490 Operands[i] = dyn_cast<Constant>(I->getOperand(i));
6491 if (!Operands[i]) return nullptr;
6494 Constant *C = EvaluateExpression(Operand, L, Vals, DL, TLI);
6496 if (!C) return nullptr;
6500 if (CmpInst *CI = dyn_cast<CmpInst>(I))
6501 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
6502 Operands[1], DL, TLI);
6503 if (LoadInst *LI = dyn_cast<LoadInst>(I)) {
6504 if (!LI->isVolatile())
6505 return ConstantFoldLoadFromConstPtr(Operands[0], LI->getType(), DL);
6507 return ConstantFoldInstOperands(I, Operands, DL, TLI);
6511 // If every incoming value to PN except the one for BB is a specific Constant,
6512 // return that, else return nullptr.
6513 static Constant *getOtherIncomingValue(PHINode *PN, BasicBlock *BB) {
6514 Constant *IncomingVal = nullptr;
6516 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
6517 if (PN->getIncomingBlock(i) == BB)
6520 auto *CurrentVal = dyn_cast<Constant>(PN->getIncomingValue(i));
6524 if (IncomingVal != CurrentVal) {
6527 IncomingVal = CurrentVal;
6534 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
6535 /// in the header of its containing loop, we know the loop executes a
6536 /// constant number of times, and the PHI node is just a recurrence
6537 /// involving constants, fold it.
6539 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
6542 auto I = ConstantEvolutionLoopExitValue.find(PN);
6543 if (I != ConstantEvolutionLoopExitValue.end())
6546 if (BEs.ugt(MaxBruteForceIterations))
6547 return ConstantEvolutionLoopExitValue[PN] = nullptr; // Not going to evaluate it.
6549 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
6551 DenseMap<Instruction *, Constant *> CurrentIterVals;
6552 BasicBlock *Header = L->getHeader();
6553 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
6555 BasicBlock *Latch = L->getLoopLatch();
6559 for (auto &I : *Header) {
6560 PHINode *PHI = dyn_cast<PHINode>(&I);
6562 auto *StartCST = getOtherIncomingValue(PHI, Latch);
6563 if (!StartCST) continue;
6564 CurrentIterVals[PHI] = StartCST;
6566 if (!CurrentIterVals.count(PN))
6567 return RetVal = nullptr;
6569 Value *BEValue = PN->getIncomingValueForBlock(Latch);
6571 // Execute the loop symbolically to determine the exit value.
6572 if (BEs.getActiveBits() >= 32)
6573 return RetVal = nullptr; // More than 2^32-1 iterations?? Not doing it!
6575 unsigned NumIterations = BEs.getZExtValue(); // must be in range
6576 unsigned IterationNum = 0;
6577 const DataLayout &DL = getDataLayout();
6578 for (; ; ++IterationNum) {
6579 if (IterationNum == NumIterations)
6580 return RetVal = CurrentIterVals[PN]; // Got exit value!
6582 // Compute the value of the PHIs for the next iteration.
6583 // EvaluateExpression adds non-phi values to the CurrentIterVals map.
6584 DenseMap<Instruction *, Constant *> NextIterVals;
6586 EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
6588 return nullptr; // Couldn't evaluate!
6589 NextIterVals[PN] = NextPHI;
6591 bool StoppedEvolving = NextPHI == CurrentIterVals[PN];
6593 // Also evaluate the other PHI nodes. However, we don't get to stop if we
6594 // cease to be able to evaluate one of them or if they stop evolving,
6595 // because that doesn't necessarily prevent us from computing PN.
6596 SmallVector<std::pair<PHINode *, Constant *>, 8> PHIsToCompute;
6597 for (const auto &I : CurrentIterVals) {
6598 PHINode *PHI = dyn_cast<PHINode>(I.first);
6599 if (!PHI || PHI == PN || PHI->getParent() != Header) continue;
6600 PHIsToCompute.emplace_back(PHI, I.second);
6602 // We use two distinct loops because EvaluateExpression may invalidate any
6603 // iterators into CurrentIterVals.
6604 for (const auto &I : PHIsToCompute) {
6605 PHINode *PHI = I.first;
6606 Constant *&NextPHI = NextIterVals[PHI];
6607 if (!NextPHI) { // Not already computed.
6608 Value *BEValue = PHI->getIncomingValueForBlock(Latch);
6609 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
6611 if (NextPHI != I.second)
6612 StoppedEvolving = false;
6615 // If all entries in CurrentIterVals == NextIterVals then we can stop
6616 // iterating, the loop can't continue to change.
6617 if (StoppedEvolving)
6618 return RetVal = CurrentIterVals[PN];
6620 CurrentIterVals.swap(NextIterVals);
6624 const SCEV *ScalarEvolution::computeExitCountExhaustively(const Loop *L,
6627 PHINode *PN = getConstantEvolvingPHI(Cond, L);
6628 if (!PN) return getCouldNotCompute();
6630 // If the loop is canonicalized, the PHI will have exactly two entries.
6631 // That's the only form we support here.
6632 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
6634 DenseMap<Instruction *, Constant *> CurrentIterVals;
6635 BasicBlock *Header = L->getHeader();
6636 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
6638 BasicBlock *Latch = L->getLoopLatch();
6639 assert(Latch && "Should follow from NumIncomingValues == 2!");
6641 for (auto &I : *Header) {
6642 PHINode *PHI = dyn_cast<PHINode>(&I);
6645 auto *StartCST = getOtherIncomingValue(PHI, Latch);
6646 if (!StartCST) continue;
6647 CurrentIterVals[PHI] = StartCST;
6649 if (!CurrentIterVals.count(PN))
6650 return getCouldNotCompute();
6652 // Okay, we find a PHI node that defines the trip count of this loop. Execute
6653 // the loop symbolically to determine when the condition gets a value of
6655 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
6656 const DataLayout &DL = getDataLayout();
6657 for (unsigned IterationNum = 0; IterationNum != MaxIterations;++IterationNum){
6658 auto *CondVal = dyn_cast_or_null<ConstantInt>(
6659 EvaluateExpression(Cond, L, CurrentIterVals, DL, &TLI));
6661 // Couldn't symbolically evaluate.
6662 if (!CondVal) return getCouldNotCompute();
6664 if (CondVal->getValue() == uint64_t(ExitWhen)) {
6665 ++NumBruteForceTripCountsComputed;
6666 return getConstant(Type::getInt32Ty(getContext()), IterationNum);
6669 // Update all the PHI nodes for the next iteration.
6670 DenseMap<Instruction *, Constant *> NextIterVals;
6672 // Create a list of which PHIs we need to compute. We want to do this before
6673 // calling EvaluateExpression on them because that may invalidate iterators
6674 // into CurrentIterVals.
6675 SmallVector<PHINode *, 8> PHIsToCompute;
6676 for (const auto &I : CurrentIterVals) {
6677 PHINode *PHI = dyn_cast<PHINode>(I.first);
6678 if (!PHI || PHI->getParent() != Header) continue;
6679 PHIsToCompute.push_back(PHI);
6681 for (PHINode *PHI : PHIsToCompute) {
6682 Constant *&NextPHI = NextIterVals[PHI];
6683 if (NextPHI) continue; // Already computed!
6685 Value *BEValue = PHI->getIncomingValueForBlock(Latch);
6686 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
6688 CurrentIterVals.swap(NextIterVals);
6691 // Too many iterations were needed to evaluate.
6692 return getCouldNotCompute();
6695 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
6696 SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values =
6698 // Check to see if we've folded this expression at this loop before.
6699 for (auto &LS : Values)
6701 return LS.second ? LS.second : V;
6703 Values.emplace_back(L, nullptr);
6705 // Otherwise compute it.
6706 const SCEV *C = computeSCEVAtScope(V, L);
6707 for (auto &LS : reverse(ValuesAtScopes[V]))
6708 if (LS.first == L) {
6715 /// This builds up a Constant using the ConstantExpr interface. That way, we
6716 /// will return Constants for objects which aren't represented by a
6717 /// SCEVConstant, because SCEVConstant is restricted to ConstantInt.
6718 /// Returns NULL if the SCEV isn't representable as a Constant.
6719 static Constant *BuildConstantFromSCEV(const SCEV *V) {
6720 switch (static_cast<SCEVTypes>(V->getSCEVType())) {
6721 case scCouldNotCompute:
6725 return cast<SCEVConstant>(V)->getValue();
6727 return dyn_cast<Constant>(cast<SCEVUnknown>(V)->getValue());
6728 case scSignExtend: {
6729 const SCEVSignExtendExpr *SS = cast<SCEVSignExtendExpr>(V);
6730 if (Constant *CastOp = BuildConstantFromSCEV(SS->getOperand()))
6731 return ConstantExpr::getSExt(CastOp, SS->getType());
6734 case scZeroExtend: {
6735 const SCEVZeroExtendExpr *SZ = cast<SCEVZeroExtendExpr>(V);
6736 if (Constant *CastOp = BuildConstantFromSCEV(SZ->getOperand()))
6737 return ConstantExpr::getZExt(CastOp, SZ->getType());
6741 const SCEVTruncateExpr *ST = cast<SCEVTruncateExpr>(V);
6742 if (Constant *CastOp = BuildConstantFromSCEV(ST->getOperand()))
6743 return ConstantExpr::getTrunc(CastOp, ST->getType());
6747 const SCEVAddExpr *SA = cast<SCEVAddExpr>(V);
6748 if (Constant *C = BuildConstantFromSCEV(SA->getOperand(0))) {
6749 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
6750 unsigned AS = PTy->getAddressSpace();
6751 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
6752 C = ConstantExpr::getBitCast(C, DestPtrTy);
6754 for (unsigned i = 1, e = SA->getNumOperands(); i != e; ++i) {
6755 Constant *C2 = BuildConstantFromSCEV(SA->getOperand(i));
6756 if (!C2) return nullptr;
6759 if (!C->getType()->isPointerTy() && C2->getType()->isPointerTy()) {
6760 unsigned AS = C2->getType()->getPointerAddressSpace();
6762 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
6763 // The offsets have been converted to bytes. We can add bytes to an
6764 // i8* by GEP with the byte count in the first index.
6765 C = ConstantExpr::getBitCast(C, DestPtrTy);
6768 // Don't bother trying to sum two pointers. We probably can't
6769 // statically compute a load that results from it anyway.
6770 if (C2->getType()->isPointerTy())
6773 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
6774 if (PTy->getElementType()->isStructTy())
6775 C2 = ConstantExpr::getIntegerCast(
6776 C2, Type::getInt32Ty(C->getContext()), true);
6777 C = ConstantExpr::getGetElementPtr(PTy->getElementType(), C, C2);
6779 C = ConstantExpr::getAdd(C, C2);
6786 const SCEVMulExpr *SM = cast<SCEVMulExpr>(V);
6787 if (Constant *C = BuildConstantFromSCEV(SM->getOperand(0))) {
6788 // Don't bother with pointers at all.
6789 if (C->getType()->isPointerTy()) return nullptr;
6790 for (unsigned i = 1, e = SM->getNumOperands(); i != e; ++i) {
6791 Constant *C2 = BuildConstantFromSCEV(SM->getOperand(i));
6792 if (!C2 || C2->getType()->isPointerTy()) return nullptr;
6793 C = ConstantExpr::getMul(C, C2);
6800 const SCEVUDivExpr *SU = cast<SCEVUDivExpr>(V);
6801 if (Constant *LHS = BuildConstantFromSCEV(SU->getLHS()))
6802 if (Constant *RHS = BuildConstantFromSCEV(SU->getRHS()))
6803 if (LHS->getType() == RHS->getType())
6804 return ConstantExpr::getUDiv(LHS, RHS);
6809 break; // TODO: smax, umax.
6814 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
6815 if (isa<SCEVConstant>(V)) return V;
6817 // If this instruction is evolved from a constant-evolving PHI, compute the
6818 // exit value from the loop without using SCEVs.
6819 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
6820 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
6821 const Loop *LI = this->LI[I->getParent()];
6822 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
6823 if (PHINode *PN = dyn_cast<PHINode>(I))
6824 if (PN->getParent() == LI->getHeader()) {
6825 // Okay, there is no closed form solution for the PHI node. Check
6826 // to see if the loop that contains it has a known backedge-taken
6827 // count. If so, we may be able to force computation of the exit
6829 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
6830 if (const SCEVConstant *BTCC =
6831 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
6832 // Okay, we know how many times the containing loop executes. If
6833 // this is a constant evolving PHI node, get the final value at
6834 // the specified iteration number.
6836 getConstantEvolutionLoopExitValue(PN, BTCC->getAPInt(), LI);
6837 if (RV) return getSCEV(RV);
6841 // Okay, this is an expression that we cannot symbolically evaluate
6842 // into a SCEV. Check to see if it's possible to symbolically evaluate
6843 // the arguments into constants, and if so, try to constant propagate the
6844 // result. This is particularly useful for computing loop exit values.
6845 if (CanConstantFold(I)) {
6846 SmallVector<Constant *, 4> Operands;
6847 bool MadeImprovement = false;
6848 for (Value *Op : I->operands()) {
6849 if (Constant *C = dyn_cast<Constant>(Op)) {
6850 Operands.push_back(C);
6854 // If any of the operands is non-constant and if they are
6855 // non-integer and non-pointer, don't even try to analyze them
6856 // with scev techniques.
6857 if (!isSCEVable(Op->getType()))
6860 const SCEV *OrigV = getSCEV(Op);
6861 const SCEV *OpV = getSCEVAtScope(OrigV, L);
6862 MadeImprovement |= OrigV != OpV;
6864 Constant *C = BuildConstantFromSCEV(OpV);
6866 if (C->getType() != Op->getType())
6867 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
6871 Operands.push_back(C);
6874 // Check to see if getSCEVAtScope actually made an improvement.
6875 if (MadeImprovement) {
6876 Constant *C = nullptr;
6877 const DataLayout &DL = getDataLayout();
6878 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
6879 C = ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
6880 Operands[1], DL, &TLI);
6881 else if (const LoadInst *LI = dyn_cast<LoadInst>(I)) {
6882 if (!LI->isVolatile())
6883 C = ConstantFoldLoadFromConstPtr(Operands[0], LI->getType(), DL);
6885 C = ConstantFoldInstOperands(I, Operands, DL, &TLI);
6892 // This is some other type of SCEVUnknown, just return it.
6896 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
6897 // Avoid performing the look-up in the common case where the specified
6898 // expression has no loop-variant portions.
6899 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
6900 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
6901 if (OpAtScope != Comm->getOperand(i)) {
6902 // Okay, at least one of these operands is loop variant but might be
6903 // foldable. Build a new instance of the folded commutative expression.
6904 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
6905 Comm->op_begin()+i);
6906 NewOps.push_back(OpAtScope);
6908 for (++i; i != e; ++i) {
6909 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
6910 NewOps.push_back(OpAtScope);
6912 if (isa<SCEVAddExpr>(Comm))
6913 return getAddExpr(NewOps);
6914 if (isa<SCEVMulExpr>(Comm))
6915 return getMulExpr(NewOps);
6916 if (isa<SCEVSMaxExpr>(Comm))
6917 return getSMaxExpr(NewOps);
6918 if (isa<SCEVUMaxExpr>(Comm))
6919 return getUMaxExpr(NewOps);
6920 llvm_unreachable("Unknown commutative SCEV type!");
6923 // If we got here, all operands are loop invariant.
6927 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
6928 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
6929 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
6930 if (LHS == Div->getLHS() && RHS == Div->getRHS())
6931 return Div; // must be loop invariant
6932 return getUDivExpr(LHS, RHS);
6935 // If this is a loop recurrence for a loop that does not contain L, then we
6936 // are dealing with the final value computed by the loop.
6937 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
6938 // First, attempt to evaluate each operand.
6939 // Avoid performing the look-up in the common case where the specified
6940 // expression has no loop-variant portions.
6941 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
6942 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
6943 if (OpAtScope == AddRec->getOperand(i))
6946 // Okay, at least one of these operands is loop variant but might be
6947 // foldable. Build a new instance of the folded commutative expression.
6948 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(),
6949 AddRec->op_begin()+i);
6950 NewOps.push_back(OpAtScope);
6951 for (++i; i != e; ++i)
6952 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
6954 const SCEV *FoldedRec =
6955 getAddRecExpr(NewOps, AddRec->getLoop(),
6956 AddRec->getNoWrapFlags(SCEV::FlagNW));
6957 AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec);
6958 // The addrec may be folded to a nonrecurrence, for example, if the
6959 // induction variable is multiplied by zero after constant folding. Go
6960 // ahead and return the folded value.
6966 // If the scope is outside the addrec's loop, evaluate it by using the
6967 // loop exit value of the addrec.
6968 if (!AddRec->getLoop()->contains(L)) {
6969 // To evaluate this recurrence, we need to know how many times the AddRec
6970 // loop iterates. Compute this now.
6971 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
6972 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
6974 // Then, evaluate the AddRec.
6975 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
6981 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
6982 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
6983 if (Op == Cast->getOperand())
6984 return Cast; // must be loop invariant
6985 return getZeroExtendExpr(Op, Cast->getType());
6988 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
6989 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
6990 if (Op == Cast->getOperand())
6991 return Cast; // must be loop invariant
6992 return getSignExtendExpr(Op, Cast->getType());
6995 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
6996 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
6997 if (Op == Cast->getOperand())
6998 return Cast; // must be loop invariant
6999 return getTruncateExpr(Op, Cast->getType());
7002 llvm_unreachable("Unknown SCEV type!");
7005 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
7006 return getSCEVAtScope(getSCEV(V), L);
7009 /// Finds the minimum unsigned root of the following equation:
7011 /// A * X = B (mod N)
7013 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
7014 /// A and B isn't important.
7016 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
7017 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
7018 ScalarEvolution &SE) {
7019 uint32_t BW = A.getBitWidth();
7020 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
7021 assert(A != 0 && "A must be non-zero.");
7025 // The gcd of A and N may have only one prime factor: 2. The number of
7026 // trailing zeros in A is its multiplicity
7027 uint32_t Mult2 = A.countTrailingZeros();
7030 // 2. Check if B is divisible by D.
7032 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
7033 // is not less than multiplicity of this prime factor for D.
7034 if (B.countTrailingZeros() < Mult2)
7035 return SE.getCouldNotCompute();
7037 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
7040 // If D == 1, (N / D) == N == 2^BW, so we need one extra bit to represent
7041 // (N / D) in general. The inverse itself always fits into BW bits, though,
7042 // so we immediately truncate it.
7043 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
7044 APInt Mod(BW + 1, 0);
7045 Mod.setBit(BW - Mult2); // Mod = N / D
7046 APInt I = AD.multiplicativeInverse(Mod).trunc(BW);
7048 // 4. Compute the minimum unsigned root of the equation:
7049 // I * (B / D) mod (N / D)
7050 // To simplify the computation, we factor out the divide by D:
7051 // (I * B mod N) / D
7052 APInt Result = (I * B).lshr(Mult2);
7054 return SE.getConstant(Result);
7057 /// Find the roots of the quadratic equation for the given quadratic chrec
7058 /// {L,+,M,+,N}. This returns either the two roots (which might be the same) or
7059 /// two SCEVCouldNotCompute objects.
7061 static Optional<std::pair<const SCEVConstant *,const SCEVConstant *>>
7062 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
7063 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
7064 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
7065 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
7066 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
7068 // We currently can only solve this if the coefficients are constants.
7069 if (!LC || !MC || !NC)
7072 uint32_t BitWidth = LC->getAPInt().getBitWidth();
7073 const APInt &L = LC->getAPInt();
7074 const APInt &M = MC->getAPInt();
7075 const APInt &N = NC->getAPInt();
7076 APInt Two(BitWidth, 2);
7077 APInt Four(BitWidth, 4);
7080 using namespace APIntOps;
7082 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
7083 // The B coefficient is M-N/2
7087 // The A coefficient is N/2
7088 APInt A(N.sdiv(Two));
7090 // Compute the B^2-4ac term.
7093 SqrtTerm -= Four * (A * C);
7095 if (SqrtTerm.isNegative()) {
7096 // The loop is provably infinite.
7100 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
7101 // integer value or else APInt::sqrt() will assert.
7102 APInt SqrtVal(SqrtTerm.sqrt());
7104 // Compute the two solutions for the quadratic formula.
7105 // The divisions must be performed as signed divisions.
7108 if (TwoA.isMinValue())
7111 LLVMContext &Context = SE.getContext();
7113 ConstantInt *Solution1 =
7114 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
7115 ConstantInt *Solution2 =
7116 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
7118 return std::make_pair(cast<SCEVConstant>(SE.getConstant(Solution1)),
7119 cast<SCEVConstant>(SE.getConstant(Solution2)));
7120 } // end APIntOps namespace
7123 ScalarEvolution::ExitLimit
7124 ScalarEvolution::howFarToZero(const SCEV *V, const Loop *L, bool ControlsExit,
7125 bool AllowPredicates) {
7127 // This is only used for loops with a "x != y" exit test. The exit condition
7128 // is now expressed as a single expression, V = x-y. So the exit test is
7129 // effectively V != 0. We know and take advantage of the fact that this
7130 // expression only being used in a comparison by zero context.
7132 SmallPtrSet<const SCEVPredicate *, 4> Predicates;
7133 // If the value is a constant
7134 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
7135 // If the value is already zero, the branch will execute zero times.
7136 if (C->getValue()->isZero()) return C;
7137 return getCouldNotCompute(); // Otherwise it will loop infinitely.
7140 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
7141 if (!AddRec && AllowPredicates)
7142 // Try to make this an AddRec using runtime tests, in the first X
7143 // iterations of this loop, where X is the SCEV expression found by the
7145 AddRec = convertSCEVToAddRecWithPredicates(V, L, Predicates);
7147 if (!AddRec || AddRec->getLoop() != L)
7148 return getCouldNotCompute();
7150 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
7151 // the quadratic equation to solve it.
7152 if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
7153 if (auto Roots = SolveQuadraticEquation(AddRec, *this)) {
7154 const SCEVConstant *R1 = Roots->first;
7155 const SCEVConstant *R2 = Roots->second;
7156 // Pick the smallest positive root value.
7157 if (ConstantInt *CB = dyn_cast<ConstantInt>(ConstantExpr::getICmp(
7158 CmpInst::ICMP_ULT, R1->getValue(), R2->getValue()))) {
7159 if (!CB->getZExtValue())
7160 std::swap(R1, R2); // R1 is the minimum root now.
7162 // We can only use this value if the chrec ends up with an exact zero
7163 // value at this index. When solving for "X*X != 5", for example, we
7164 // should not accept a root of 2.
7165 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
7167 // We found a quadratic root!
7168 return ExitLimit(R1, R1, false, Predicates);
7171 return getCouldNotCompute();
7174 // Otherwise we can only handle this if it is affine.
7175 if (!AddRec->isAffine())
7176 return getCouldNotCompute();
7178 // If this is an affine expression, the execution count of this branch is
7179 // the minimum unsigned root of the following equation:
7181 // Start + Step*N = 0 (mod 2^BW)
7185 // Step*N = -Start (mod 2^BW)
7187 // where BW is the common bit width of Start and Step.
7189 // Get the initial value for the loop.
7190 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
7191 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
7193 // For now we handle only constant steps.
7195 // TODO: Handle a nonconstant Step given AddRec<NUW>. If the
7196 // AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap
7197 // to 0, it must be counting down to equal 0. Consequently, N = Start / -Step.
7198 // We have not yet seen any such cases.
7199 const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step);
7200 if (!StepC || StepC->getValue()->equalsInt(0))
7201 return getCouldNotCompute();
7203 // For positive steps (counting up until unsigned overflow):
7204 // N = -Start/Step (as unsigned)
7205 // For negative steps (counting down to zero):
7207 // First compute the unsigned distance from zero in the direction of Step.
7208 bool CountDown = StepC->getAPInt().isNegative();
7209 const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start);
7211 // Handle unitary steps, which cannot wraparound.
7212 // 1*N = -Start; -1*N = Start (mod 2^BW), so:
7213 // N = Distance (as unsigned)
7214 if (StepC->getValue()->equalsInt(1) || StepC->getValue()->isAllOnesValue()) {
7215 APInt MaxBECount = getUnsignedRange(Distance).getUnsignedMax();
7217 // When a loop like "for (int i = 0; i != n; ++i) { /* body */ }" is rotated,
7218 // we end up with a loop whose backedge-taken count is n - 1. Detect this
7219 // case, and see if we can improve the bound.
7221 // Explicitly handling this here is necessary because getUnsignedRange
7222 // isn't context-sensitive; it doesn't know that we only care about the
7223 // range inside the loop.
7224 const SCEV *Zero = getZero(Distance->getType());
7225 const SCEV *One = getOne(Distance->getType());
7226 const SCEV *DistancePlusOne = getAddExpr(Distance, One);
7227 if (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_NE, DistancePlusOne, Zero)) {
7228 // If Distance + 1 doesn't overflow, we can compute the maximum distance
7229 // as "unsigned_max(Distance + 1) - 1".
7230 ConstantRange CR = getUnsignedRange(DistancePlusOne);
7231 MaxBECount = APIntOps::umin(MaxBECount, CR.getUnsignedMax() - 1);
7233 return ExitLimit(Distance, getConstant(MaxBECount), false, Predicates);
7236 // As a special case, handle the instance where Step is a positive power of
7237 // two. In this case, determining whether Step divides Distance evenly can be
7238 // done by counting and comparing the number of trailing zeros of Step and
7241 const APInt &StepV = StepC->getAPInt();
7242 // StepV.isPowerOf2() returns true if StepV is an positive power of two. It
7243 // also returns true if StepV is maximally negative (eg, INT_MIN), but that
7244 // case is not handled as this code is guarded by !CountDown.
7245 if (StepV.isPowerOf2() &&
7246 GetMinTrailingZeros(Distance) >= StepV.countTrailingZeros()) {
7247 // Here we've constrained the equation to be of the form
7249 // 2^(N + k) * Distance' = (StepV == 2^N) * X (mod 2^W) ... (0)
7251 // where we're operating on a W bit wide integer domain and k is
7252 // non-negative. The smallest unsigned solution for X is the trip count.
7254 // (0) is equivalent to:
7256 // 2^(N + k) * Distance' - 2^N * X = L * 2^W
7257 // <=> 2^N(2^k * Distance' - X) = L * 2^(W - N) * 2^N
7258 // <=> 2^k * Distance' - X = L * 2^(W - N)
7259 // <=> 2^k * Distance' = L * 2^(W - N) + X ... (1)
7261 // The smallest X satisfying (1) is unsigned remainder of dividing the LHS
7264 // <=> X = 2^k * Distance' URem 2^(W - N) ... (2)
7266 // E.g. say we're solving
7268 // 2 * Val = 2 * X (in i8) ... (3)
7270 // then from (2), we get X = Val URem i8 128 (k = 0 in this case).
7272 // Note: It is tempting to solve (3) by setting X = Val, but Val is not
7273 // necessarily the smallest unsigned value of X that satisfies (3).
7274 // E.g. if Val is i8 -127 then the smallest value of X that satisfies (3)
7275 // is i8 1, not i8 -127
7277 const auto *ModuloResult = getUDivExactExpr(Distance, Step);
7279 // Since SCEV does not have a URem node, we construct one using a truncate
7280 // and a zero extend.
7282 unsigned NarrowWidth = StepV.getBitWidth() - StepV.countTrailingZeros();
7283 auto *NarrowTy = IntegerType::get(getContext(), NarrowWidth);
7284 auto *WideTy = Distance->getType();
7287 getZeroExtendExpr(getTruncateExpr(ModuloResult, NarrowTy), WideTy);
7288 return ExitLimit(Limit, Limit, false, Predicates);
7292 // If the condition controls loop exit (the loop exits only if the expression
7293 // is true) and the addition is no-wrap we can use unsigned divide to
7294 // compute the backedge count. In this case, the step may not divide the
7295 // distance, but we don't care because if the condition is "missed" the loop
7296 // will have undefined behavior due to wrapping.
7297 if (ControlsExit && AddRec->hasNoSelfWrap() &&
7298 loopHasNoAbnormalExits(AddRec->getLoop())) {
7300 getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
7301 return ExitLimit(Exact, Exact, false, Predicates);
7304 // Then, try to solve the above equation provided that Start is constant.
7305 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) {
7306 const SCEV *E = SolveLinEquationWithOverflow(
7307 StepC->getValue()->getValue(), -StartC->getValue()->getValue(), *this);
7308 return ExitLimit(E, E, false, Predicates);
7310 return getCouldNotCompute();
7313 ScalarEvolution::ExitLimit
7314 ScalarEvolution::howFarToNonZero(const SCEV *V, const Loop *L) {
7315 // Loops that look like: while (X == 0) are very strange indeed. We don't
7316 // handle them yet except for the trivial case. This could be expanded in the
7317 // future as needed.
7319 // If the value is a constant, check to see if it is known to be non-zero
7320 // already. If so, the backedge will execute zero times.
7321 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
7322 if (!C->getValue()->isNullValue())
7323 return getZero(C->getType());
7324 return getCouldNotCompute(); // Otherwise it will loop infinitely.
7327 // We could implement others, but I really doubt anyone writes loops like
7328 // this, and if they did, they would already be constant folded.
7329 return getCouldNotCompute();
7332 std::pair<BasicBlock *, BasicBlock *>
7333 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
7334 // If the block has a unique predecessor, then there is no path from the
7335 // predecessor to the block that does not go through the direct edge
7336 // from the predecessor to the block.
7337 if (BasicBlock *Pred = BB->getSinglePredecessor())
7340 // A loop's header is defined to be a block that dominates the loop.
7341 // If the header has a unique predecessor outside the loop, it must be
7342 // a block that has exactly one successor that can reach the loop.
7343 if (Loop *L = LI.getLoopFor(BB))
7344 return {L->getLoopPredecessor(), L->getHeader()};
7346 return {nullptr, nullptr};
7349 /// SCEV structural equivalence is usually sufficient for testing whether two
7350 /// expressions are equal, however for the purposes of looking for a condition
7351 /// guarding a loop, it can be useful to be a little more general, since a
7352 /// front-end may have replicated the controlling expression.
7354 static bool HasSameValue(const SCEV *A, const SCEV *B) {
7355 // Quick check to see if they are the same SCEV.
7356 if (A == B) return true;
7358 auto ComputesEqualValues = [](const Instruction *A, const Instruction *B) {
7359 // Not all instructions that are "identical" compute the same value. For
7360 // instance, two distinct alloca instructions allocating the same type are
7361 // identical and do not read memory; but compute distinct values.
7362 return A->isIdenticalTo(B) && (isa<BinaryOperator>(A) || isa<GetElementPtrInst>(A));
7365 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
7366 // two different instructions with the same value. Check for this case.
7367 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
7368 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
7369 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
7370 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
7371 if (ComputesEqualValues(AI, BI))
7374 // Otherwise assume they may have a different value.
7378 bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
7379 const SCEV *&LHS, const SCEV *&RHS,
7381 bool Changed = false;
7383 // If we hit the max recursion limit bail out.
7387 // Canonicalize a constant to the right side.
7388 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
7389 // Check for both operands constant.
7390 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
7391 if (ConstantExpr::getICmp(Pred,
7393 RHSC->getValue())->isNullValue())
7394 goto trivially_false;
7396 goto trivially_true;
7398 // Otherwise swap the operands to put the constant on the right.
7399 std::swap(LHS, RHS);
7400 Pred = ICmpInst::getSwappedPredicate(Pred);
7404 // If we're comparing an addrec with a value which is loop-invariant in the
7405 // addrec's loop, put the addrec on the left. Also make a dominance check,
7406 // as both operands could be addrecs loop-invariant in each other's loop.
7407 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
7408 const Loop *L = AR->getLoop();
7409 if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) {
7410 std::swap(LHS, RHS);
7411 Pred = ICmpInst::getSwappedPredicate(Pred);
7416 // If there's a constant operand, canonicalize comparisons with boundary
7417 // cases, and canonicalize *-or-equal comparisons to regular comparisons.
7418 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
7419 const APInt &RA = RC->getAPInt();
7421 bool SimplifiedByConstantRange = false;
7423 if (!ICmpInst::isEquality(Pred)) {
7424 ConstantRange ExactCR = ConstantRange::makeExactICmpRegion(Pred, RA);
7425 if (ExactCR.isFullSet())
7426 goto trivially_true;
7427 else if (ExactCR.isEmptySet())
7428 goto trivially_false;
7431 CmpInst::Predicate NewPred;
7432 if (ExactCR.getEquivalentICmp(NewPred, NewRHS) &&
7433 ICmpInst::isEquality(NewPred)) {
7434 // We were able to convert an inequality to an equality.
7436 RHS = getConstant(NewRHS);
7437 Changed = SimplifiedByConstantRange = true;
7441 if (!SimplifiedByConstantRange) {
7445 case ICmpInst::ICMP_EQ:
7446 case ICmpInst::ICMP_NE:
7447 // Fold ((-1) * %a) + %b == 0 (equivalent to %b-%a == 0) into %a == %b.
7449 if (const SCEVAddExpr *AE = dyn_cast<SCEVAddExpr>(LHS))
7450 if (const SCEVMulExpr *ME =
7451 dyn_cast<SCEVMulExpr>(AE->getOperand(0)))
7452 if (AE->getNumOperands() == 2 && ME->getNumOperands() == 2 &&
7453 ME->getOperand(0)->isAllOnesValue()) {
7454 RHS = AE->getOperand(1);
7455 LHS = ME->getOperand(1);
7461 // The "Should have been caught earlier!" messages refer to the fact
7462 // that the ExactCR.isFullSet() or ExactCR.isEmptySet() check above
7463 // should have fired on the corresponding cases, and canonicalized the
7464 // check to trivially_true or trivially_false.
7466 case ICmpInst::ICMP_UGE:
7467 assert(!RA.isMinValue() && "Should have been caught earlier!");
7468 Pred = ICmpInst::ICMP_UGT;
7469 RHS = getConstant(RA - 1);
7472 case ICmpInst::ICMP_ULE:
7473 assert(!RA.isMaxValue() && "Should have been caught earlier!");
7474 Pred = ICmpInst::ICMP_ULT;
7475 RHS = getConstant(RA + 1);
7478 case ICmpInst::ICMP_SGE:
7479 assert(!RA.isMinSignedValue() && "Should have been caught earlier!");
7480 Pred = ICmpInst::ICMP_SGT;
7481 RHS = getConstant(RA - 1);
7484 case ICmpInst::ICMP_SLE:
7485 assert(!RA.isMaxSignedValue() && "Should have been caught earlier!");
7486 Pred = ICmpInst::ICMP_SLT;
7487 RHS = getConstant(RA + 1);
7494 // Check for obvious equality.
7495 if (HasSameValue(LHS, RHS)) {
7496 if (ICmpInst::isTrueWhenEqual(Pred))
7497 goto trivially_true;
7498 if (ICmpInst::isFalseWhenEqual(Pred))
7499 goto trivially_false;
7502 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
7503 // adding or subtracting 1 from one of the operands.
7505 case ICmpInst::ICMP_SLE:
7506 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) {
7507 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
7509 Pred = ICmpInst::ICMP_SLT;
7511 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) {
7512 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
7514 Pred = ICmpInst::ICMP_SLT;
7518 case ICmpInst::ICMP_SGE:
7519 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) {
7520 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
7522 Pred = ICmpInst::ICMP_SGT;
7524 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) {
7525 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
7527 Pred = ICmpInst::ICMP_SGT;
7531 case ICmpInst::ICMP_ULE:
7532 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) {
7533 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
7535 Pred = ICmpInst::ICMP_ULT;
7537 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) {
7538 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS);
7539 Pred = ICmpInst::ICMP_ULT;
7543 case ICmpInst::ICMP_UGE:
7544 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) {
7545 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS);
7546 Pred = ICmpInst::ICMP_UGT;
7548 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) {
7549 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
7551 Pred = ICmpInst::ICMP_UGT;
7559 // TODO: More simplifications are possible here.
7561 // Recursively simplify until we either hit a recursion limit or nothing
7564 return SimplifyICmpOperands(Pred, LHS, RHS, Depth+1);
7570 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
7571 Pred = ICmpInst::ICMP_EQ;
7576 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
7577 Pred = ICmpInst::ICMP_NE;
7581 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
7582 return getSignedRange(S).getSignedMax().isNegative();
7585 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
7586 return getSignedRange(S).getSignedMin().isStrictlyPositive();
7589 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
7590 return !getSignedRange(S).getSignedMin().isNegative();
7593 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
7594 return !getSignedRange(S).getSignedMax().isStrictlyPositive();
7597 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
7598 return isKnownNegative(S) || isKnownPositive(S);
7601 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
7602 const SCEV *LHS, const SCEV *RHS) {
7603 // Canonicalize the inputs first.
7604 (void)SimplifyICmpOperands(Pred, LHS, RHS);
7606 // If LHS or RHS is an addrec, check to see if the condition is true in
7607 // every iteration of the loop.
7608 // If LHS and RHS are both addrec, both conditions must be true in
7609 // every iteration of the loop.
7610 const SCEVAddRecExpr *LAR = dyn_cast<SCEVAddRecExpr>(LHS);
7611 const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS);
7612 bool LeftGuarded = false;
7613 bool RightGuarded = false;
7615 const Loop *L = LAR->getLoop();
7616 if (isLoopEntryGuardedByCond(L, Pred, LAR->getStart(), RHS) &&
7617 isLoopBackedgeGuardedByCond(L, Pred, LAR->getPostIncExpr(*this), RHS)) {
7618 if (!RAR) return true;
7623 const Loop *L = RAR->getLoop();
7624 if (isLoopEntryGuardedByCond(L, Pred, LHS, RAR->getStart()) &&
7625 isLoopBackedgeGuardedByCond(L, Pred, LHS, RAR->getPostIncExpr(*this))) {
7626 if (!LAR) return true;
7627 RightGuarded = true;
7630 if (LeftGuarded && RightGuarded)
7633 if (isKnownPredicateViaSplitting(Pred, LHS, RHS))
7636 // Otherwise see what can be done with known constant ranges.
7637 return isKnownPredicateViaConstantRanges(Pred, LHS, RHS);
7640 bool ScalarEvolution::isMonotonicPredicate(const SCEVAddRecExpr *LHS,
7641 ICmpInst::Predicate Pred,
7643 bool Result = isMonotonicPredicateImpl(LHS, Pred, Increasing);
7646 // Verify an invariant: inverting the predicate should turn a monotonically
7647 // increasing change to a monotonically decreasing one, and vice versa.
7648 bool IncreasingSwapped;
7649 bool ResultSwapped = isMonotonicPredicateImpl(
7650 LHS, ICmpInst::getSwappedPredicate(Pred), IncreasingSwapped);
7652 assert(Result == ResultSwapped && "should be able to analyze both!");
7654 assert(Increasing == !IncreasingSwapped &&
7655 "monotonicity should flip as we flip the predicate");
7661 bool ScalarEvolution::isMonotonicPredicateImpl(const SCEVAddRecExpr *LHS,
7662 ICmpInst::Predicate Pred,
7665 // A zero step value for LHS means the induction variable is essentially a
7666 // loop invariant value. We don't really depend on the predicate actually
7667 // flipping from false to true (for increasing predicates, and the other way
7668 // around for decreasing predicates), all we care about is that *if* the
7669 // predicate changes then it only changes from false to true.
7671 // A zero step value in itself is not very useful, but there may be places
7672 // where SCEV can prove X >= 0 but not prove X > 0, so it is helpful to be
7673 // as general as possible.
7677 return false; // Conservative answer
7679 case ICmpInst::ICMP_UGT:
7680 case ICmpInst::ICMP_UGE:
7681 case ICmpInst::ICMP_ULT:
7682 case ICmpInst::ICMP_ULE:
7683 if (!LHS->hasNoUnsignedWrap())
7686 Increasing = Pred == ICmpInst::ICMP_UGT || Pred == ICmpInst::ICMP_UGE;
7689 case ICmpInst::ICMP_SGT:
7690 case ICmpInst::ICMP_SGE:
7691 case ICmpInst::ICMP_SLT:
7692 case ICmpInst::ICMP_SLE: {
7693 if (!LHS->hasNoSignedWrap())
7696 const SCEV *Step = LHS->getStepRecurrence(*this);
7698 if (isKnownNonNegative(Step)) {
7699 Increasing = Pred == ICmpInst::ICMP_SGT || Pred == ICmpInst::ICMP_SGE;
7703 if (isKnownNonPositive(Step)) {
7704 Increasing = Pred == ICmpInst::ICMP_SLT || Pred == ICmpInst::ICMP_SLE;
7713 llvm_unreachable("switch has default clause!");
7716 bool ScalarEvolution::isLoopInvariantPredicate(
7717 ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS, const Loop *L,
7718 ICmpInst::Predicate &InvariantPred, const SCEV *&InvariantLHS,
7719 const SCEV *&InvariantRHS) {
7721 // If there is a loop-invariant, force it into the RHS, otherwise bail out.
7722 if (!isLoopInvariant(RHS, L)) {
7723 if (!isLoopInvariant(LHS, L))
7726 std::swap(LHS, RHS);
7727 Pred = ICmpInst::getSwappedPredicate(Pred);
7730 const SCEVAddRecExpr *ArLHS = dyn_cast<SCEVAddRecExpr>(LHS);
7731 if (!ArLHS || ArLHS->getLoop() != L)
7735 if (!isMonotonicPredicate(ArLHS, Pred, Increasing))
7738 // If the predicate "ArLHS `Pred` RHS" monotonically increases from false to
7739 // true as the loop iterates, and the backedge is control dependent on
7740 // "ArLHS `Pred` RHS" == true then we can reason as follows:
7742 // * if the predicate was false in the first iteration then the predicate
7743 // is never evaluated again, since the loop exits without taking the
7745 // * if the predicate was true in the first iteration then it will
7746 // continue to be true for all future iterations since it is
7747 // monotonically increasing.
7749 // For both the above possibilities, we can replace the loop varying
7750 // predicate with its value on the first iteration of the loop (which is
7753 // A similar reasoning applies for a monotonically decreasing predicate, by
7754 // replacing true with false and false with true in the above two bullets.
7756 auto P = Increasing ? Pred : ICmpInst::getInversePredicate(Pred);
7758 if (!isLoopBackedgeGuardedByCond(L, P, LHS, RHS))
7761 InvariantPred = Pred;
7762 InvariantLHS = ArLHS->getStart();
7767 bool ScalarEvolution::isKnownPredicateViaConstantRanges(
7768 ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS) {
7769 if (HasSameValue(LHS, RHS))
7770 return ICmpInst::isTrueWhenEqual(Pred);
7772 // This code is split out from isKnownPredicate because it is called from
7773 // within isLoopEntryGuardedByCond.
7776 [&](const ConstantRange &RangeLHS, const ConstantRange &RangeRHS) {
7777 return ConstantRange::makeSatisfyingICmpRegion(Pred, RangeRHS)
7778 .contains(RangeLHS);
7781 // The check at the top of the function catches the case where the values are
7782 // known to be equal.
7783 if (Pred == CmpInst::ICMP_EQ)
7786 if (Pred == CmpInst::ICMP_NE)
7787 return CheckRanges(getSignedRange(LHS), getSignedRange(RHS)) ||
7788 CheckRanges(getUnsignedRange(LHS), getUnsignedRange(RHS)) ||
7789 isKnownNonZero(getMinusSCEV(LHS, RHS));
7791 if (CmpInst::isSigned(Pred))
7792 return CheckRanges(getSignedRange(LHS), getSignedRange(RHS));
7794 return CheckRanges(getUnsignedRange(LHS), getUnsignedRange(RHS));
7797 bool ScalarEvolution::isKnownPredicateViaNoOverflow(ICmpInst::Predicate Pred,
7801 // Match Result to (X + Y)<ExpectedFlags> where Y is a constant integer.
7802 // Return Y via OutY.
7803 auto MatchBinaryAddToConst =
7804 [this](const SCEV *Result, const SCEV *X, APInt &OutY,
7805 SCEV::NoWrapFlags ExpectedFlags) {
7806 const SCEV *NonConstOp, *ConstOp;
7807 SCEV::NoWrapFlags FlagsPresent;
7809 if (!splitBinaryAdd(Result, ConstOp, NonConstOp, FlagsPresent) ||
7810 !isa<SCEVConstant>(ConstOp) || NonConstOp != X)
7813 OutY = cast<SCEVConstant>(ConstOp)->getAPInt();
7814 return (FlagsPresent & ExpectedFlags) == ExpectedFlags;
7823 case ICmpInst::ICMP_SGE:
7824 std::swap(LHS, RHS);
7825 case ICmpInst::ICMP_SLE:
7826 // X s<= (X + C)<nsw> if C >= 0
7827 if (MatchBinaryAddToConst(RHS, LHS, C, SCEV::FlagNSW) && C.isNonNegative())
7830 // (X + C)<nsw> s<= X if C <= 0
7831 if (MatchBinaryAddToConst(LHS, RHS, C, SCEV::FlagNSW) &&
7832 !C.isStrictlyPositive())
7836 case ICmpInst::ICMP_SGT:
7837 std::swap(LHS, RHS);
7838 case ICmpInst::ICMP_SLT:
7839 // X s< (X + C)<nsw> if C > 0
7840 if (MatchBinaryAddToConst(RHS, LHS, C, SCEV::FlagNSW) &&
7841 C.isStrictlyPositive())
7844 // (X + C)<nsw> s< X if C < 0
7845 if (MatchBinaryAddToConst(LHS, RHS, C, SCEV::FlagNSW) && C.isNegative())
7853 bool ScalarEvolution::isKnownPredicateViaSplitting(ICmpInst::Predicate Pred,
7856 if (Pred != ICmpInst::ICMP_ULT || ProvingSplitPredicate)
7859 // Allowing arbitrary number of activations of isKnownPredicateViaSplitting on
7860 // the stack can result in exponential time complexity.
7861 SaveAndRestore<bool> Restore(ProvingSplitPredicate, true);
7863 // If L >= 0 then I `ult` L <=> I >= 0 && I `slt` L
7865 // To prove L >= 0 we use isKnownNonNegative whereas to prove I >= 0 we use
7866 // isKnownPredicate. isKnownPredicate is more powerful, but also more
7867 // expensive; and using isKnownNonNegative(RHS) is sufficient for most of the
7868 // interesting cases seen in practice. We can consider "upgrading" L >= 0 to
7869 // use isKnownPredicate later if needed.
7870 return isKnownNonNegative(RHS) &&
7871 isKnownPredicate(CmpInst::ICMP_SGE, LHS, getZero(LHS->getType())) &&
7872 isKnownPredicate(CmpInst::ICMP_SLT, LHS, RHS);
7875 bool ScalarEvolution::isImpliedViaGuard(BasicBlock *BB,
7876 ICmpInst::Predicate Pred,
7877 const SCEV *LHS, const SCEV *RHS) {
7878 // No need to even try if we know the module has no guards.
7882 return any_of(*BB, [&](Instruction &I) {
7883 using namespace llvm::PatternMatch;
7886 return match(&I, m_Intrinsic<Intrinsic::experimental_guard>(
7887 m_Value(Condition))) &&
7888 isImpliedCond(Pred, LHS, RHS, Condition, false);
7892 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
7893 /// protected by a conditional between LHS and RHS. This is used to
7894 /// to eliminate casts.
7896 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
7897 ICmpInst::Predicate Pred,
7898 const SCEV *LHS, const SCEV *RHS) {
7899 // Interpret a null as meaning no loop, where there is obviously no guard
7900 // (interprocedural conditions notwithstanding).
7901 if (!L) return true;
7903 if (isKnownPredicateViaConstantRanges(Pred, LHS, RHS))
7906 BasicBlock *Latch = L->getLoopLatch();
7910 BranchInst *LoopContinuePredicate =
7911 dyn_cast<BranchInst>(Latch->getTerminator());
7912 if (LoopContinuePredicate && LoopContinuePredicate->isConditional() &&
7913 isImpliedCond(Pred, LHS, RHS,
7914 LoopContinuePredicate->getCondition(),
7915 LoopContinuePredicate->getSuccessor(0) != L->getHeader()))
7918 // We don't want more than one activation of the following loops on the stack
7919 // -- that can lead to O(n!) time complexity.
7920 if (WalkingBEDominatingConds)
7923 SaveAndRestore<bool> ClearOnExit(WalkingBEDominatingConds, true);
7925 // See if we can exploit a trip count to prove the predicate.
7926 const auto &BETakenInfo = getBackedgeTakenInfo(L);
7927 const SCEV *LatchBECount = BETakenInfo.getExact(Latch, this);
7928 if (LatchBECount != getCouldNotCompute()) {
7929 // We know that Latch branches back to the loop header exactly
7930 // LatchBECount times. This means the backdege condition at Latch is
7931 // equivalent to "{0,+,1} u< LatchBECount".
7932 Type *Ty = LatchBECount->getType();
7933 auto NoWrapFlags = SCEV::NoWrapFlags(SCEV::FlagNUW | SCEV::FlagNW);
7934 const SCEV *LoopCounter =
7935 getAddRecExpr(getZero(Ty), getOne(Ty), L, NoWrapFlags);
7936 if (isImpliedCond(Pred, LHS, RHS, ICmpInst::ICMP_ULT, LoopCounter,
7941 // Check conditions due to any @llvm.assume intrinsics.
7942 for (auto &AssumeVH : AC.assumptions()) {
7945 auto *CI = cast<CallInst>(AssumeVH);
7946 if (!DT.dominates(CI, Latch->getTerminator()))
7949 if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false))
7953 // If the loop is not reachable from the entry block, we risk running into an
7954 // infinite loop as we walk up into the dom tree. These loops do not matter
7955 // anyway, so we just return a conservative answer when we see them.
7956 if (!DT.isReachableFromEntry(L->getHeader()))
7959 if (isImpliedViaGuard(Latch, Pred, LHS, RHS))
7962 for (DomTreeNode *DTN = DT[Latch], *HeaderDTN = DT[L->getHeader()];
7963 DTN != HeaderDTN; DTN = DTN->getIDom()) {
7965 assert(DTN && "should reach the loop header before reaching the root!");
7967 BasicBlock *BB = DTN->getBlock();
7968 if (isImpliedViaGuard(BB, Pred, LHS, RHS))
7971 BasicBlock *PBB = BB->getSinglePredecessor();
7975 BranchInst *ContinuePredicate = dyn_cast<BranchInst>(PBB->getTerminator());
7976 if (!ContinuePredicate || !ContinuePredicate->isConditional())
7979 Value *Condition = ContinuePredicate->getCondition();
7981 // If we have an edge `E` within the loop body that dominates the only
7982 // latch, the condition guarding `E` also guards the backedge. This
7983 // reasoning works only for loops with a single latch.
7985 BasicBlockEdge DominatingEdge(PBB, BB);
7986 if (DominatingEdge.isSingleEdge()) {
7987 // We're constructively (and conservatively) enumerating edges within the
7988 // loop body that dominate the latch. The dominator tree better agree
7990 assert(DT.dominates(DominatingEdge, Latch) && "should be!");
7992 if (isImpliedCond(Pred, LHS, RHS, Condition,
7993 BB != ContinuePredicate->getSuccessor(0)))
8002 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
8003 ICmpInst::Predicate Pred,
8004 const SCEV *LHS, const SCEV *RHS) {
8005 // Interpret a null as meaning no loop, where there is obviously no guard
8006 // (interprocedural conditions notwithstanding).
8007 if (!L) return false;
8009 if (isKnownPredicateViaConstantRanges(Pred, LHS, RHS))
8012 // Starting at the loop predecessor, climb up the predecessor chain, as long
8013 // as there are predecessors that can be found that have unique successors
8014 // leading to the original header.
8015 for (std::pair<BasicBlock *, BasicBlock *>
8016 Pair(L->getLoopPredecessor(), L->getHeader());
8018 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
8020 if (isImpliedViaGuard(Pair.first, Pred, LHS, RHS))
8023 BranchInst *LoopEntryPredicate =
8024 dyn_cast<BranchInst>(Pair.first->getTerminator());
8025 if (!LoopEntryPredicate ||
8026 LoopEntryPredicate->isUnconditional())
8029 if (isImpliedCond(Pred, LHS, RHS,
8030 LoopEntryPredicate->getCondition(),
8031 LoopEntryPredicate->getSuccessor(0) != Pair.second))
8035 // Check conditions due to any @llvm.assume intrinsics.
8036 for (auto &AssumeVH : AC.assumptions()) {
8039 auto *CI = cast<CallInst>(AssumeVH);
8040 if (!DT.dominates(CI, L->getHeader()))
8043 if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false))
8050 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred,
8051 const SCEV *LHS, const SCEV *RHS,
8052 Value *FoundCondValue,
8054 if (!PendingLoopPredicates.insert(FoundCondValue).second)
8058 make_scope_exit([&]() { PendingLoopPredicates.erase(FoundCondValue); });
8060 // Recursively handle And and Or conditions.
8061 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) {
8062 if (BO->getOpcode() == Instruction::And) {
8064 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
8065 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
8066 } else if (BO->getOpcode() == Instruction::Or) {
8068 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
8069 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
8073 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue);
8074 if (!ICI) return false;
8076 // Now that we found a conditional branch that dominates the loop or controls
8077 // the loop latch. Check to see if it is the comparison we are looking for.
8078 ICmpInst::Predicate FoundPred;
8080 FoundPred = ICI->getInversePredicate();
8082 FoundPred = ICI->getPredicate();
8084 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
8085 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
8087 return isImpliedCond(Pred, LHS, RHS, FoundPred, FoundLHS, FoundRHS);
8090 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred, const SCEV *LHS,
8092 ICmpInst::Predicate FoundPred,
8093 const SCEV *FoundLHS,
8094 const SCEV *FoundRHS) {
8095 // Balance the types.
8096 if (getTypeSizeInBits(LHS->getType()) <
8097 getTypeSizeInBits(FoundLHS->getType())) {
8098 if (CmpInst::isSigned(Pred)) {
8099 LHS = getSignExtendExpr(LHS, FoundLHS->getType());
8100 RHS = getSignExtendExpr(RHS, FoundLHS->getType());
8102 LHS = getZeroExtendExpr(LHS, FoundLHS->getType());
8103 RHS = getZeroExtendExpr(RHS, FoundLHS->getType());
8105 } else if (getTypeSizeInBits(LHS->getType()) >
8106 getTypeSizeInBits(FoundLHS->getType())) {
8107 if (CmpInst::isSigned(FoundPred)) {
8108 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
8109 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
8111 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
8112 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
8116 // Canonicalize the query to match the way instcombine will have
8117 // canonicalized the comparison.
8118 if (SimplifyICmpOperands(Pred, LHS, RHS))
8120 return CmpInst::isTrueWhenEqual(Pred);
8121 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
8122 if (FoundLHS == FoundRHS)
8123 return CmpInst::isFalseWhenEqual(FoundPred);
8125 // Check to see if we can make the LHS or RHS match.
8126 if (LHS == FoundRHS || RHS == FoundLHS) {
8127 if (isa<SCEVConstant>(RHS)) {
8128 std::swap(FoundLHS, FoundRHS);
8129 FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
8131 std::swap(LHS, RHS);
8132 Pred = ICmpInst::getSwappedPredicate(Pred);
8136 // Check whether the found predicate is the same as the desired predicate.
8137 if (FoundPred == Pred)
8138 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
8140 // Check whether swapping the found predicate makes it the same as the
8141 // desired predicate.
8142 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
8143 if (isa<SCEVConstant>(RHS))
8144 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
8146 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
8147 RHS, LHS, FoundLHS, FoundRHS);
8150 // Unsigned comparison is the same as signed comparison when both the operands
8151 // are non-negative.
8152 if (CmpInst::isUnsigned(FoundPred) &&
8153 CmpInst::getSignedPredicate(FoundPred) == Pred &&
8154 isKnownNonNegative(FoundLHS) && isKnownNonNegative(FoundRHS))
8155 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
8157 // Check if we can make progress by sharpening ranges.
8158 if (FoundPred == ICmpInst::ICMP_NE &&
8159 (isa<SCEVConstant>(FoundLHS) || isa<SCEVConstant>(FoundRHS))) {
8161 const SCEVConstant *C = nullptr;
8162 const SCEV *V = nullptr;
8164 if (isa<SCEVConstant>(FoundLHS)) {
8165 C = cast<SCEVConstant>(FoundLHS);
8168 C = cast<SCEVConstant>(FoundRHS);
8172 // The guarding predicate tells us that C != V. If the known range
8173 // of V is [C, t), we can sharpen the range to [C + 1, t). The
8174 // range we consider has to correspond to same signedness as the
8175 // predicate we're interested in folding.
8177 APInt Min = ICmpInst::isSigned(Pred) ?
8178 getSignedRange(V).getSignedMin() : getUnsignedRange(V).getUnsignedMin();
8180 if (Min == C->getAPInt()) {
8181 // Given (V >= Min && V != Min) we conclude V >= (Min + 1).
8182 // This is true even if (Min + 1) wraps around -- in case of
8183 // wraparound, (Min + 1) < Min, so (V >= Min => V >= (Min + 1)).
8185 APInt SharperMin = Min + 1;
8188 case ICmpInst::ICMP_SGE:
8189 case ICmpInst::ICMP_UGE:
8190 // We know V `Pred` SharperMin. If this implies LHS `Pred`
8192 if (isImpliedCondOperands(Pred, LHS, RHS, V,
8193 getConstant(SharperMin)))
8196 case ICmpInst::ICMP_SGT:
8197 case ICmpInst::ICMP_UGT:
8198 // We know from the range information that (V `Pred` Min ||
8199 // V == Min). We know from the guarding condition that !(V
8200 // == Min). This gives us
8202 // V `Pred` Min || V == Min && !(V == Min)
8205 // If V `Pred` Min implies LHS `Pred` RHS, we're done.
8207 if (isImpliedCondOperands(Pred, LHS, RHS, V, getConstant(Min)))
8217 // Check whether the actual condition is beyond sufficient.
8218 if (FoundPred == ICmpInst::ICMP_EQ)
8219 if (ICmpInst::isTrueWhenEqual(Pred))
8220 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
8222 if (Pred == ICmpInst::ICMP_NE)
8223 if (!ICmpInst::isTrueWhenEqual(FoundPred))
8224 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
8227 // Otherwise assume the worst.
8231 bool ScalarEvolution::splitBinaryAdd(const SCEV *Expr,
8232 const SCEV *&L, const SCEV *&R,
8233 SCEV::NoWrapFlags &Flags) {
8234 const auto *AE = dyn_cast<SCEVAddExpr>(Expr);
8235 if (!AE || AE->getNumOperands() != 2)
8238 L = AE->getOperand(0);
8239 R = AE->getOperand(1);
8240 Flags = AE->getNoWrapFlags();
8244 Optional<APInt> ScalarEvolution::computeConstantDifference(const SCEV *More,
8246 // We avoid subtracting expressions here because this function is usually
8247 // fairly deep in the call stack (i.e. is called many times).
8249 if (isa<SCEVAddRecExpr>(Less) && isa<SCEVAddRecExpr>(More)) {
8250 const auto *LAR = cast<SCEVAddRecExpr>(Less);
8251 const auto *MAR = cast<SCEVAddRecExpr>(More);
8253 if (LAR->getLoop() != MAR->getLoop())
8256 // We look at affine expressions only; not for correctness but to keep
8257 // getStepRecurrence cheap.
8258 if (!LAR->isAffine() || !MAR->isAffine())
8261 if (LAR->getStepRecurrence(*this) != MAR->getStepRecurrence(*this))
8264 Less = LAR->getStart();
8265 More = MAR->getStart();
8270 if (isa<SCEVConstant>(Less) && isa<SCEVConstant>(More)) {
8271 const auto &M = cast<SCEVConstant>(More)->getAPInt();
8272 const auto &L = cast<SCEVConstant>(Less)->getAPInt();
8277 SCEV::NoWrapFlags Flags;
8278 if (splitBinaryAdd(Less, L, R, Flags))
8279 if (const auto *LC = dyn_cast<SCEVConstant>(L))
8281 return -(LC->getAPInt());
8283 if (splitBinaryAdd(More, L, R, Flags))
8284 if (const auto *LC = dyn_cast<SCEVConstant>(L))
8286 return LC->getAPInt();
8291 bool ScalarEvolution::isImpliedCondOperandsViaNoOverflow(
8292 ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS,
8293 const SCEV *FoundLHS, const SCEV *FoundRHS) {
8294 if (Pred != CmpInst::ICMP_SLT && Pred != CmpInst::ICMP_ULT)
8297 const auto *AddRecLHS = dyn_cast<SCEVAddRecExpr>(LHS);
8301 const auto *AddRecFoundLHS = dyn_cast<SCEVAddRecExpr>(FoundLHS);
8302 if (!AddRecFoundLHS)
8305 // We'd like to let SCEV reason about control dependencies, so we constrain
8306 // both the inequalities to be about add recurrences on the same loop. This
8307 // way we can use isLoopEntryGuardedByCond later.
8309 const Loop *L = AddRecFoundLHS->getLoop();
8310 if (L != AddRecLHS->getLoop())
8313 // FoundLHS u< FoundRHS u< -C => (FoundLHS + C) u< (FoundRHS + C) ... (1)
8315 // FoundLHS s< FoundRHS s< INT_MIN - C => (FoundLHS + C) s< (FoundRHS + C)
8318 // Informal proof for (2), assuming (1) [*]:
8320 // We'll also assume (A s< B) <=> ((A + INT_MIN) u< (B + INT_MIN)) ... (3)[**]
8324 // FoundLHS s< FoundRHS s< INT_MIN - C
8325 // <=> (FoundLHS + INT_MIN) u< (FoundRHS + INT_MIN) u< -C [ using (3) ]
8326 // <=> (FoundLHS + INT_MIN + C) u< (FoundRHS + INT_MIN + C) [ using (1) ]
8327 // <=> (FoundLHS + INT_MIN + C + INT_MIN) s<
8328 // (FoundRHS + INT_MIN + C + INT_MIN) [ using (3) ]
8329 // <=> FoundLHS + C s< FoundRHS + C
8331 // [*]: (1) can be proved by ruling out overflow.
8333 // [**]: This can be proved by analyzing all the four possibilities:
8334 // (A s< 0, B s< 0), (A s< 0, B s>= 0), (A s>= 0, B s< 0) and
8335 // (A s>= 0, B s>= 0).
8338 // Despite (2), "FoundRHS s< INT_MIN - C" does not mean that "FoundRHS + C"
8339 // will not sign underflow. For instance, say FoundLHS = (i8 -128), FoundRHS
8340 // = (i8 -127) and C = (i8 -100). Then INT_MIN - C = (i8 -28), and FoundRHS
8341 // s< (INT_MIN - C). Lack of sign overflow / underflow in "FoundRHS + C" is
8342 // neither necessary nor sufficient to prove "(FoundLHS + C) s< (FoundRHS +
8345 Optional<APInt> LDiff = computeConstantDifference(LHS, FoundLHS);
8346 Optional<APInt> RDiff = computeConstantDifference(RHS, FoundRHS);
8347 if (!LDiff || !RDiff || *LDiff != *RDiff)
8350 if (LDiff->isMinValue())
8353 APInt FoundRHSLimit;
8355 if (Pred == CmpInst::ICMP_ULT) {
8356 FoundRHSLimit = -(*RDiff);
8358 assert(Pred == CmpInst::ICMP_SLT && "Checked above!");
8359 FoundRHSLimit = APInt::getSignedMinValue(getTypeSizeInBits(RHS->getType())) - *RDiff;
8362 // Try to prove (1) or (2), as needed.
8363 return isLoopEntryGuardedByCond(L, Pred, FoundRHS,
8364 getConstant(FoundRHSLimit));
8367 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
8368 const SCEV *LHS, const SCEV *RHS,
8369 const SCEV *FoundLHS,
8370 const SCEV *FoundRHS) {
8371 if (isImpliedCondOperandsViaRanges(Pred, LHS, RHS, FoundLHS, FoundRHS))
8374 if (isImpliedCondOperandsViaNoOverflow(Pred, LHS, RHS, FoundLHS, FoundRHS))
8377 return isImpliedCondOperandsHelper(Pred, LHS, RHS,
8378 FoundLHS, FoundRHS) ||
8379 // ~x < ~y --> x > y
8380 isImpliedCondOperandsHelper(Pred, LHS, RHS,
8381 getNotSCEV(FoundRHS),
8382 getNotSCEV(FoundLHS));
8386 /// If Expr computes ~A, return A else return nullptr
8387 static const SCEV *MatchNotExpr(const SCEV *Expr) {
8388 const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Expr);
8389 if (!Add || Add->getNumOperands() != 2 ||
8390 !Add->getOperand(0)->isAllOnesValue())
8393 const SCEVMulExpr *AddRHS = dyn_cast<SCEVMulExpr>(Add->getOperand(1));
8394 if (!AddRHS || AddRHS->getNumOperands() != 2 ||
8395 !AddRHS->getOperand(0)->isAllOnesValue())
8398 return AddRHS->getOperand(1);
8402 /// Is MaybeMaxExpr an SMax or UMax of Candidate and some other values?
8403 template<typename MaxExprType>
8404 static bool IsMaxConsistingOf(const SCEV *MaybeMaxExpr,
8405 const SCEV *Candidate) {
8406 const MaxExprType *MaxExpr = dyn_cast<MaxExprType>(MaybeMaxExpr);
8407 if (!MaxExpr) return false;
8409 return find(MaxExpr->operands(), Candidate) != MaxExpr->op_end();
8413 /// Is MaybeMinExpr an SMin or UMin of Candidate and some other values?
8414 template<typename MaxExprType>
8415 static bool IsMinConsistingOf(ScalarEvolution &SE,
8416 const SCEV *MaybeMinExpr,
8417 const SCEV *Candidate) {
8418 const SCEV *MaybeMaxExpr = MatchNotExpr(MaybeMinExpr);
8422 return IsMaxConsistingOf<MaxExprType>(MaybeMaxExpr, SE.getNotSCEV(Candidate));
8425 static bool IsKnownPredicateViaAddRecStart(ScalarEvolution &SE,
8426 ICmpInst::Predicate Pred,
8427 const SCEV *LHS, const SCEV *RHS) {
8429 // If both sides are affine addrecs for the same loop, with equal
8430 // steps, and we know the recurrences don't wrap, then we only
8431 // need to check the predicate on the starting values.
8433 if (!ICmpInst::isRelational(Pred))
8436 const SCEVAddRecExpr *LAR = dyn_cast<SCEVAddRecExpr>(LHS);
8439 const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS);
8442 if (LAR->getLoop() != RAR->getLoop())
8444 if (!LAR->isAffine() || !RAR->isAffine())
8447 if (LAR->getStepRecurrence(SE) != RAR->getStepRecurrence(SE))
8450 SCEV::NoWrapFlags NW = ICmpInst::isSigned(Pred) ?
8451 SCEV::FlagNSW : SCEV::FlagNUW;
8452 if (!LAR->getNoWrapFlags(NW) || !RAR->getNoWrapFlags(NW))
8455 return SE.isKnownPredicate(Pred, LAR->getStart(), RAR->getStart());
8458 /// Is LHS `Pred` RHS true on the virtue of LHS or RHS being a Min or Max
8460 static bool IsKnownPredicateViaMinOrMax(ScalarEvolution &SE,
8461 ICmpInst::Predicate Pred,
8462 const SCEV *LHS, const SCEV *RHS) {
8467 case ICmpInst::ICMP_SGE:
8468 std::swap(LHS, RHS);
8470 case ICmpInst::ICMP_SLE:
8473 IsMinConsistingOf<SCEVSMaxExpr>(SE, LHS, RHS) ||
8475 IsMaxConsistingOf<SCEVSMaxExpr>(RHS, LHS);
8477 case ICmpInst::ICMP_UGE:
8478 std::swap(LHS, RHS);
8480 case ICmpInst::ICMP_ULE:
8483 IsMinConsistingOf<SCEVUMaxExpr>(SE, LHS, RHS) ||
8485 IsMaxConsistingOf<SCEVUMaxExpr>(RHS, LHS);
8488 llvm_unreachable("covered switch fell through?!");
8492 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
8493 const SCEV *LHS, const SCEV *RHS,
8494 const SCEV *FoundLHS,
8495 const SCEV *FoundRHS) {
8496 auto IsKnownPredicateFull =
8497 [this](ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS) {
8498 return isKnownPredicateViaConstantRanges(Pred, LHS, RHS) ||
8499 IsKnownPredicateViaMinOrMax(*this, Pred, LHS, RHS) ||
8500 IsKnownPredicateViaAddRecStart(*this, Pred, LHS, RHS) ||
8501 isKnownPredicateViaNoOverflow(Pred, LHS, RHS);
8505 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
8506 case ICmpInst::ICMP_EQ:
8507 case ICmpInst::ICMP_NE:
8508 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
8511 case ICmpInst::ICMP_SLT:
8512 case ICmpInst::ICMP_SLE:
8513 if (IsKnownPredicateFull(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
8514 IsKnownPredicateFull(ICmpInst::ICMP_SGE, RHS, FoundRHS))
8517 case ICmpInst::ICMP_SGT:
8518 case ICmpInst::ICMP_SGE:
8519 if (IsKnownPredicateFull(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
8520 IsKnownPredicateFull(ICmpInst::ICMP_SLE, RHS, FoundRHS))
8523 case ICmpInst::ICMP_ULT:
8524 case ICmpInst::ICMP_ULE:
8525 if (IsKnownPredicateFull(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
8526 IsKnownPredicateFull(ICmpInst::ICMP_UGE, RHS, FoundRHS))
8529 case ICmpInst::ICMP_UGT:
8530 case ICmpInst::ICMP_UGE:
8531 if (IsKnownPredicateFull(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
8532 IsKnownPredicateFull(ICmpInst::ICMP_ULE, RHS, FoundRHS))
8540 bool ScalarEvolution::isImpliedCondOperandsViaRanges(ICmpInst::Predicate Pred,
8543 const SCEV *FoundLHS,
8544 const SCEV *FoundRHS) {
8545 if (!isa<SCEVConstant>(RHS) || !isa<SCEVConstant>(FoundRHS))
8546 // The restriction on `FoundRHS` be lifted easily -- it exists only to
8547 // reduce the compile time impact of this optimization.
8550 Optional<APInt> Addend = computeConstantDifference(LHS, FoundLHS);
8554 APInt ConstFoundRHS = cast<SCEVConstant>(FoundRHS)->getAPInt();
8556 // `FoundLHSRange` is the range we know `FoundLHS` to be in by virtue of the
8557 // antecedent "`FoundLHS` `Pred` `FoundRHS`".
8558 ConstantRange FoundLHSRange =
8559 ConstantRange::makeAllowedICmpRegion(Pred, ConstFoundRHS);
8561 // Since `LHS` is `FoundLHS` + `Addend`, we can compute a range for `LHS`:
8562 ConstantRange LHSRange = FoundLHSRange.add(ConstantRange(*Addend));
8564 // We can also compute the range of values for `LHS` that satisfy the
8565 // consequent, "`LHS` `Pred` `RHS`":
8566 APInt ConstRHS = cast<SCEVConstant>(RHS)->getAPInt();
8567 ConstantRange SatisfyingLHSRange =
8568 ConstantRange::makeSatisfyingICmpRegion(Pred, ConstRHS);
8570 // The antecedent implies the consequent if every value of `LHS` that
8571 // satisfies the antecedent also satisfies the consequent.
8572 return SatisfyingLHSRange.contains(LHSRange);
8575 bool ScalarEvolution::doesIVOverflowOnLT(const SCEV *RHS, const SCEV *Stride,
8576 bool IsSigned, bool NoWrap) {
8577 assert(isKnownPositive(Stride) && "Positive stride expected!");
8579 if (NoWrap) return false;
8581 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
8582 const SCEV *One = getOne(Stride->getType());
8585 APInt MaxRHS = getSignedRange(RHS).getSignedMax();
8586 APInt MaxValue = APInt::getSignedMaxValue(BitWidth);
8587 APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
8590 // SMaxRHS + SMaxStrideMinusOne > SMaxValue => overflow!
8591 return (MaxValue - MaxStrideMinusOne).slt(MaxRHS);
8594 APInt MaxRHS = getUnsignedRange(RHS).getUnsignedMax();
8595 APInt MaxValue = APInt::getMaxValue(BitWidth);
8596 APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
8599 // UMaxRHS + UMaxStrideMinusOne > UMaxValue => overflow!
8600 return (MaxValue - MaxStrideMinusOne).ult(MaxRHS);
8603 bool ScalarEvolution::doesIVOverflowOnGT(const SCEV *RHS, const SCEV *Stride,
8604 bool IsSigned, bool NoWrap) {
8605 if (NoWrap) return false;
8607 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
8608 const SCEV *One = getOne(Stride->getType());
8611 APInt MinRHS = getSignedRange(RHS).getSignedMin();
8612 APInt MinValue = APInt::getSignedMinValue(BitWidth);
8613 APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
8616 // SMinRHS - SMaxStrideMinusOne < SMinValue => overflow!
8617 return (MinValue + MaxStrideMinusOne).sgt(MinRHS);
8620 APInt MinRHS = getUnsignedRange(RHS).getUnsignedMin();
8621 APInt MinValue = APInt::getMinValue(BitWidth);
8622 APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
8625 // UMinRHS - UMaxStrideMinusOne < UMinValue => overflow!
8626 return (MinValue + MaxStrideMinusOne).ugt(MinRHS);
8629 const SCEV *ScalarEvolution::computeBECount(const SCEV *Delta, const SCEV *Step,
8631 const SCEV *One = getOne(Step->getType());
8632 Delta = Equality ? getAddExpr(Delta, Step)
8633 : getAddExpr(Delta, getMinusSCEV(Step, One));
8634 return getUDivExpr(Delta, Step);
8637 ScalarEvolution::ExitLimit
8638 ScalarEvolution::howManyLessThans(const SCEV *LHS, const SCEV *RHS,
8639 const Loop *L, bool IsSigned,
8640 bool ControlsExit, bool AllowPredicates) {
8641 SmallPtrSet<const SCEVPredicate *, 4> Predicates;
8642 // We handle only IV < Invariant
8643 if (!isLoopInvariant(RHS, L))
8644 return getCouldNotCompute();
8646 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
8647 bool PredicatedIV = false;
8649 if (!IV && AllowPredicates) {
8650 // Try to make this an AddRec using runtime tests, in the first X
8651 // iterations of this loop, where X is the SCEV expression found by the
8653 IV = convertSCEVToAddRecWithPredicates(LHS, L, Predicates);
8654 PredicatedIV = true;
8657 // Avoid weird loops
8658 if (!IV || IV->getLoop() != L || !IV->isAffine())
8659 return getCouldNotCompute();
8661 bool NoWrap = ControlsExit &&
8662 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
8664 const SCEV *Stride = IV->getStepRecurrence(*this);
8666 bool PositiveStride = isKnownPositive(Stride);
8668 // Avoid negative or zero stride values.
8669 if (!PositiveStride) {
8670 // We can compute the correct backedge taken count for loops with unknown
8671 // strides if we can prove that the loop is not an infinite loop with side
8672 // effects. Here's the loop structure we are trying to handle -
8678 // } while (i < end);
8680 // The backedge taken count for such loops is evaluated as -
8681 // (max(end, start + stride) - start - 1) /u stride
8683 // The additional preconditions that we need to check to prove correctness
8684 // of the above formula is as follows -
8686 // a) IV is either nuw or nsw depending upon signedness (indicated by the
8688 // b) loop is single exit with no side effects.
8691 // Precondition a) implies that if the stride is negative, this is a single
8692 // trip loop. The backedge taken count formula reduces to zero in this case.
8694 // Precondition b) implies that the unknown stride cannot be zero otherwise
8697 // The positive stride case is the same as isKnownPositive(Stride) returning
8698 // true (original behavior of the function).
8700 // We want to make sure that the stride is truly unknown as there are edge
8701 // cases where ScalarEvolution propagates no wrap flags to the
8702 // post-increment/decrement IV even though the increment/decrement operation
8703 // itself is wrapping. The computed backedge taken count may be wrong in
8704 // such cases. This is prevented by checking that the stride is not known to
8705 // be either positive or non-positive. For example, no wrap flags are
8706 // propagated to the post-increment IV of this loop with a trip count of 2 -
8709 // for(i=127; i<128; i+=129)
8712 if (PredicatedIV || !NoWrap || isKnownNonPositive(Stride) ||
8713 !loopHasNoSideEffects(L))
8714 return getCouldNotCompute();
8716 } else if (!Stride->isOne() &&
8717 doesIVOverflowOnLT(RHS, Stride, IsSigned, NoWrap))
8718 // Avoid proven overflow cases: this will ensure that the backedge taken
8719 // count will not generate any unsigned overflow. Relaxed no-overflow
8720 // conditions exploit NoWrapFlags, allowing to optimize in presence of
8721 // undefined behaviors like the case of C language.
8722 return getCouldNotCompute();
8724 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SLT
8725 : ICmpInst::ICMP_ULT;
8726 const SCEV *Start = IV->getStart();
8727 const SCEV *End = RHS;
8728 // If the backedge is taken at least once, then it will be taken
8729 // (End-Start)/Stride times (rounded up to a multiple of Stride), where Start
8730 // is the LHS value of the less-than comparison the first time it is evaluated
8731 // and End is the RHS.
8732 const SCEV *BECountIfBackedgeTaken =
8733 computeBECount(getMinusSCEV(End, Start), Stride, false);
8734 // If the loop entry is guarded by the result of the backedge test of the
8735 // first loop iteration, then we know the backedge will be taken at least
8736 // once and so the backedge taken count is as above. If not then we use the
8737 // expression (max(End,Start)-Start)/Stride to describe the backedge count,
8738 // as if the backedge is taken at least once max(End,Start) is End and so the
8739 // result is as above, and if not max(End,Start) is Start so we get a backedge
8741 const SCEV *BECount;
8742 if (isLoopEntryGuardedByCond(L, Cond, getMinusSCEV(Start, Stride), RHS))
8743 BECount = BECountIfBackedgeTaken;
8745 End = IsSigned ? getSMaxExpr(RHS, Start) : getUMaxExpr(RHS, Start);
8746 BECount = computeBECount(getMinusSCEV(End, Start), Stride, false);
8749 const SCEV *MaxBECount;
8750 bool MaxOrZero = false;
8751 if (isa<SCEVConstant>(BECount))
8752 MaxBECount = BECount;
8753 else if (isa<SCEVConstant>(BECountIfBackedgeTaken)) {
8754 // If we know exactly how many times the backedge will be taken if it's
8755 // taken at least once, then the backedge count will either be that or
8757 MaxBECount = BECountIfBackedgeTaken;
8760 // Calculate the maximum backedge count based on the range of values
8761 // permitted by Start, End, and Stride.
8762 APInt MinStart = IsSigned ? getSignedRange(Start).getSignedMin()
8763 : getUnsignedRange(Start).getUnsignedMin();
8765 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
8767 APInt StrideForMaxBECount;
8770 StrideForMaxBECount =
8771 IsSigned ? getSignedRange(Stride).getSignedMin()
8772 : getUnsignedRange(Stride).getUnsignedMin();
8774 // Using a stride of 1 is safe when computing max backedge taken count for
8775 // a loop with unknown stride.
8776 StrideForMaxBECount = APInt(BitWidth, 1, IsSigned);
8779 IsSigned ? APInt::getSignedMaxValue(BitWidth) - (StrideForMaxBECount - 1)
8780 : APInt::getMaxValue(BitWidth) - (StrideForMaxBECount - 1);
8782 // Although End can be a MAX expression we estimate MaxEnd considering only
8783 // the case End = RHS. This is safe because in the other case (End - Start)
8784 // is zero, leading to a zero maximum backedge taken count.
8786 IsSigned ? APIntOps::smin(getSignedRange(RHS).getSignedMax(), Limit)
8787 : APIntOps::umin(getUnsignedRange(RHS).getUnsignedMax(), Limit);
8789 MaxBECount = computeBECount(getConstant(MaxEnd - MinStart),
8790 getConstant(StrideForMaxBECount), false);
8793 if (isa<SCEVCouldNotCompute>(MaxBECount))
8794 MaxBECount = BECount;
8796 return ExitLimit(BECount, MaxBECount, MaxOrZero, Predicates);
8799 ScalarEvolution::ExitLimit
8800 ScalarEvolution::howManyGreaterThans(const SCEV *LHS, const SCEV *RHS,
8801 const Loop *L, bool IsSigned,
8802 bool ControlsExit, bool AllowPredicates) {
8803 SmallPtrSet<const SCEVPredicate *, 4> Predicates;
8804 // We handle only IV > Invariant
8805 if (!isLoopInvariant(RHS, L))
8806 return getCouldNotCompute();
8808 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
8809 if (!IV && AllowPredicates)
8810 // Try to make this an AddRec using runtime tests, in the first X
8811 // iterations of this loop, where X is the SCEV expression found by the
8813 IV = convertSCEVToAddRecWithPredicates(LHS, L, Predicates);
8815 // Avoid weird loops
8816 if (!IV || IV->getLoop() != L || !IV->isAffine())
8817 return getCouldNotCompute();
8819 bool NoWrap = ControlsExit &&
8820 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
8822 const SCEV *Stride = getNegativeSCEV(IV->getStepRecurrence(*this));
8824 // Avoid negative or zero stride values
8825 if (!isKnownPositive(Stride))
8826 return getCouldNotCompute();
8828 // Avoid proven overflow cases: this will ensure that the backedge taken count
8829 // will not generate any unsigned overflow. Relaxed no-overflow conditions
8830 // exploit NoWrapFlags, allowing to optimize in presence of undefined
8831 // behaviors like the case of C language.
8832 if (!Stride->isOne() && doesIVOverflowOnGT(RHS, Stride, IsSigned, NoWrap))
8833 return getCouldNotCompute();
8835 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SGT
8836 : ICmpInst::ICMP_UGT;
8838 const SCEV *Start = IV->getStart();
8839 const SCEV *End = RHS;
8840 if (!isLoopEntryGuardedByCond(L, Cond, getAddExpr(Start, Stride), RHS))
8841 End = IsSigned ? getSMinExpr(RHS, Start) : getUMinExpr(RHS, Start);
8843 const SCEV *BECount = computeBECount(getMinusSCEV(Start, End), Stride, false);
8845 APInt MaxStart = IsSigned ? getSignedRange(Start).getSignedMax()
8846 : getUnsignedRange(Start).getUnsignedMax();
8848 APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
8849 : getUnsignedRange(Stride).getUnsignedMin();
8851 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
8852 APInt Limit = IsSigned ? APInt::getSignedMinValue(BitWidth) + (MinStride - 1)
8853 : APInt::getMinValue(BitWidth) + (MinStride - 1);
8855 // Although End can be a MIN expression we estimate MinEnd considering only
8856 // the case End = RHS. This is safe because in the other case (Start - End)
8857 // is zero, leading to a zero maximum backedge taken count.
8859 IsSigned ? APIntOps::smax(getSignedRange(RHS).getSignedMin(), Limit)
8860 : APIntOps::umax(getUnsignedRange(RHS).getUnsignedMin(), Limit);
8863 const SCEV *MaxBECount = getCouldNotCompute();
8864 if (isa<SCEVConstant>(BECount))
8865 MaxBECount = BECount;
8867 MaxBECount = computeBECount(getConstant(MaxStart - MinEnd),
8868 getConstant(MinStride), false);
8870 if (isa<SCEVCouldNotCompute>(MaxBECount))
8871 MaxBECount = BECount;
8873 return ExitLimit(BECount, MaxBECount, false, Predicates);
8876 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(const ConstantRange &Range,
8877 ScalarEvolution &SE) const {
8878 if (Range.isFullSet()) // Infinite loop.
8879 return SE.getCouldNotCompute();
8881 // If the start is a non-zero constant, shift the range to simplify things.
8882 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
8883 if (!SC->getValue()->isZero()) {
8884 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
8885 Operands[0] = SE.getZero(SC->getType());
8886 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(),
8887 getNoWrapFlags(FlagNW));
8888 if (const auto *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted))
8889 return ShiftedAddRec->getNumIterationsInRange(
8890 Range.subtract(SC->getAPInt()), SE);
8891 // This is strange and shouldn't happen.
8892 return SE.getCouldNotCompute();
8895 // The only time we can solve this is when we have all constant indices.
8896 // Otherwise, we cannot determine the overflow conditions.
8897 if (any_of(operands(), [](const SCEV *Op) { return !isa<SCEVConstant>(Op); }))
8898 return SE.getCouldNotCompute();
8900 // Okay at this point we know that all elements of the chrec are constants and
8901 // that the start element is zero.
8903 // First check to see if the range contains zero. If not, the first
8905 unsigned BitWidth = SE.getTypeSizeInBits(getType());
8906 if (!Range.contains(APInt(BitWidth, 0)))
8907 return SE.getZero(getType());
8910 // If this is an affine expression then we have this situation:
8911 // Solve {0,+,A} in Range === Ax in Range
8913 // We know that zero is in the range. If A is positive then we know that
8914 // the upper value of the range must be the first possible exit value.
8915 // If A is negative then the lower of the range is the last possible loop
8916 // value. Also note that we already checked for a full range.
8917 APInt One(BitWidth,1);
8918 APInt A = cast<SCEVConstant>(getOperand(1))->getAPInt();
8919 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
8921 // The exit value should be (End+A)/A.
8922 APInt ExitVal = (End + A).udiv(A);
8923 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
8925 // Evaluate at the exit value. If we really did fall out of the valid
8926 // range, then we computed our trip count, otherwise wrap around or other
8927 // things must have happened.
8928 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
8929 if (Range.contains(Val->getValue()))
8930 return SE.getCouldNotCompute(); // Something strange happened
8932 // Ensure that the previous value is in the range. This is a sanity check.
8933 assert(Range.contains(
8934 EvaluateConstantChrecAtConstant(this,
8935 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
8936 "Linear scev computation is off in a bad way!");
8937 return SE.getConstant(ExitValue);
8938 } else if (isQuadratic()) {
8939 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
8940 // quadratic equation to solve it. To do this, we must frame our problem in
8941 // terms of figuring out when zero is crossed, instead of when
8942 // Range.getUpper() is crossed.
8943 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
8944 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
8945 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop(), FlagAnyWrap);
8947 // Next, solve the constructed addrec
8949 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE)) {
8950 const SCEVConstant *R1 = Roots->first;
8951 const SCEVConstant *R2 = Roots->second;
8952 // Pick the smallest positive root value.
8953 if (ConstantInt *CB = dyn_cast<ConstantInt>(ConstantExpr::getICmp(
8954 ICmpInst::ICMP_ULT, R1->getValue(), R2->getValue()))) {
8955 if (!CB->getZExtValue())
8956 std::swap(R1, R2); // R1 is the minimum root now.
8958 // Make sure the root is not off by one. The returned iteration should
8959 // not be in the range, but the previous one should be. When solving
8960 // for "X*X < 5", for example, we should not return a root of 2.
8961 ConstantInt *R1Val =
8962 EvaluateConstantChrecAtConstant(this, R1->getValue(), SE);
8963 if (Range.contains(R1Val->getValue())) {
8964 // The next iteration must be out of the range...
8965 ConstantInt *NextVal =
8966 ConstantInt::get(SE.getContext(), R1->getAPInt() + 1);
8968 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
8969 if (!Range.contains(R1Val->getValue()))
8970 return SE.getConstant(NextVal);
8971 return SE.getCouldNotCompute(); // Something strange happened
8974 // If R1 was not in the range, then it is a good return value. Make
8975 // sure that R1-1 WAS in the range though, just in case.
8976 ConstantInt *NextVal =
8977 ConstantInt::get(SE.getContext(), R1->getAPInt() - 1);
8978 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
8979 if (Range.contains(R1Val->getValue()))
8981 return SE.getCouldNotCompute(); // Something strange happened
8986 return SE.getCouldNotCompute();
8989 // Return true when S contains at least an undef value.
8990 static inline bool containsUndefs(const SCEV *S) {
8991 return SCEVExprContains(S, [](const SCEV *S) {
8992 if (const auto *SU = dyn_cast<SCEVUnknown>(S))
8993 return isa<UndefValue>(SU->getValue());
8994 else if (const auto *SC = dyn_cast<SCEVConstant>(S))
8995 return isa<UndefValue>(SC->getValue());
9001 // Collect all steps of SCEV expressions.
9002 struct SCEVCollectStrides {
9003 ScalarEvolution &SE;
9004 SmallVectorImpl<const SCEV *> &Strides;
9006 SCEVCollectStrides(ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &S)
9007 : SE(SE), Strides(S) {}
9009 bool follow(const SCEV *S) {
9010 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(S))
9011 Strides.push_back(AR->getStepRecurrence(SE));
9014 bool isDone() const { return false; }
9017 // Collect all SCEVUnknown and SCEVMulExpr expressions.
9018 struct SCEVCollectTerms {
9019 SmallVectorImpl<const SCEV *> &Terms;
9021 SCEVCollectTerms(SmallVectorImpl<const SCEV *> &T)
9024 bool follow(const SCEV *S) {
9025 if (isa<SCEVUnknown>(S) || isa<SCEVMulExpr>(S) ||
9026 isa<SCEVSignExtendExpr>(S)) {
9027 if (!containsUndefs(S))
9030 // Stop recursion: once we collected a term, do not walk its operands.
9037 bool isDone() const { return false; }
9040 // Check if a SCEV contains an AddRecExpr.
9041 struct SCEVHasAddRec {
9042 bool &ContainsAddRec;
9044 SCEVHasAddRec(bool &ContainsAddRec) : ContainsAddRec(ContainsAddRec) {
9045 ContainsAddRec = false;
9048 bool follow(const SCEV *S) {
9049 if (isa<SCEVAddRecExpr>(S)) {
9050 ContainsAddRec = true;
9052 // Stop recursion: once we collected a term, do not walk its operands.
9059 bool isDone() const { return false; }
9062 // Find factors that are multiplied with an expression that (possibly as a
9063 // subexpression) contains an AddRecExpr. In the expression:
9065 // 8 * (100 + %p * %q * (%a + {0, +, 1}_loop))
9067 // "%p * %q" are factors multiplied by the expression "(%a + {0, +, 1}_loop)"
9068 // that contains the AddRec {0, +, 1}_loop. %p * %q are likely to be array size
9069 // parameters as they form a product with an induction variable.
9071 // This collector expects all array size parameters to be in the same MulExpr.
9072 // It might be necessary to later add support for collecting parameters that are
9073 // spread over different nested MulExpr.
9074 struct SCEVCollectAddRecMultiplies {
9075 SmallVectorImpl<const SCEV *> &Terms;
9076 ScalarEvolution &SE;
9078 SCEVCollectAddRecMultiplies(SmallVectorImpl<const SCEV *> &T, ScalarEvolution &SE)
9079 : Terms(T), SE(SE) {}
9081 bool follow(const SCEV *S) {
9082 if (auto *Mul = dyn_cast<SCEVMulExpr>(S)) {
9083 bool HasAddRec = false;
9084 SmallVector<const SCEV *, 0> Operands;
9085 for (auto Op : Mul->operands()) {
9086 if (isa<SCEVUnknown>(Op)) {
9087 Operands.push_back(Op);
9089 bool ContainsAddRec;
9090 SCEVHasAddRec ContiansAddRec(ContainsAddRec);
9091 visitAll(Op, ContiansAddRec);
9092 HasAddRec |= ContainsAddRec;
9095 if (Operands.size() == 0)
9101 Terms.push_back(SE.getMulExpr(Operands));
9102 // Stop recursion: once we collected a term, do not walk its operands.
9109 bool isDone() const { return false; }
9113 /// Find parametric terms in this SCEVAddRecExpr. We first for parameters in
9115 /// 1) The strides of AddRec expressions.
9116 /// 2) Unknowns that are multiplied with AddRec expressions.
9117 void ScalarEvolution::collectParametricTerms(const SCEV *Expr,
9118 SmallVectorImpl<const SCEV *> &Terms) {
9119 SmallVector<const SCEV *, 4> Strides;
9120 SCEVCollectStrides StrideCollector(*this, Strides);
9121 visitAll(Expr, StrideCollector);
9124 dbgs() << "Strides:\n";
9125 for (const SCEV *S : Strides)
9126 dbgs() << *S << "\n";
9129 for (const SCEV *S : Strides) {
9130 SCEVCollectTerms TermCollector(Terms);
9131 visitAll(S, TermCollector);
9135 dbgs() << "Terms:\n";
9136 for (const SCEV *T : Terms)
9137 dbgs() << *T << "\n";
9140 SCEVCollectAddRecMultiplies MulCollector(Terms, *this);
9141 visitAll(Expr, MulCollector);
9144 static bool findArrayDimensionsRec(ScalarEvolution &SE,
9145 SmallVectorImpl<const SCEV *> &Terms,
9146 SmallVectorImpl<const SCEV *> &Sizes) {
9147 int Last = Terms.size() - 1;
9148 const SCEV *Step = Terms[Last];
9150 // End of recursion.
9152 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Step)) {
9153 SmallVector<const SCEV *, 2> Qs;
9154 for (const SCEV *Op : M->operands())
9155 if (!isa<SCEVConstant>(Op))
9158 Step = SE.getMulExpr(Qs);
9161 Sizes.push_back(Step);
9165 for (const SCEV *&Term : Terms) {
9166 // Normalize the terms before the next call to findArrayDimensionsRec.
9168 SCEVDivision::divide(SE, Term, Step, &Q, &R);
9170 // Bail out when GCD does not evenly divide one of the terms.
9177 // Remove all SCEVConstants.
9179 remove_if(Terms, [](const SCEV *E) { return isa<SCEVConstant>(E); }),
9182 if (Terms.size() > 0)
9183 if (!findArrayDimensionsRec(SE, Terms, Sizes))
9186 Sizes.push_back(Step);
9191 // Returns true when one of the SCEVs of Terms contains a SCEVUnknown parameter.
9192 static inline bool containsParameters(SmallVectorImpl<const SCEV *> &Terms) {
9193 for (const SCEV *T : Terms)
9194 if (SCEVExprContains(T, isa<SCEVUnknown, const SCEV *>))
9199 // Return the number of product terms in S.
9200 static inline int numberOfTerms(const SCEV *S) {
9201 if (const SCEVMulExpr *Expr = dyn_cast<SCEVMulExpr>(S))
9202 return Expr->getNumOperands();
9206 static const SCEV *removeConstantFactors(ScalarEvolution &SE, const SCEV *T) {
9207 if (isa<SCEVConstant>(T))
9210 if (isa<SCEVUnknown>(T))
9213 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(T)) {
9214 SmallVector<const SCEV *, 2> Factors;
9215 for (const SCEV *Op : M->operands())
9216 if (!isa<SCEVConstant>(Op))
9217 Factors.push_back(Op);
9219 return SE.getMulExpr(Factors);
9225 /// Return the size of an element read or written by Inst.
9226 const SCEV *ScalarEvolution::getElementSize(Instruction *Inst) {
9228 if (StoreInst *Store = dyn_cast<StoreInst>(Inst))
9229 Ty = Store->getValueOperand()->getType();
9230 else if (LoadInst *Load = dyn_cast<LoadInst>(Inst))
9231 Ty = Load->getType();
9235 Type *ETy = getEffectiveSCEVType(PointerType::getUnqual(Ty));
9236 return getSizeOfExpr(ETy, Ty);
9239 void ScalarEvolution::findArrayDimensions(SmallVectorImpl<const SCEV *> &Terms,
9240 SmallVectorImpl<const SCEV *> &Sizes,
9241 const SCEV *ElementSize) const {
9242 if (Terms.size() < 1 || !ElementSize)
9245 // Early return when Terms do not contain parameters: we do not delinearize
9246 // non parametric SCEVs.
9247 if (!containsParameters(Terms))
9251 dbgs() << "Terms:\n";
9252 for (const SCEV *T : Terms)
9253 dbgs() << *T << "\n";
9256 // Remove duplicates.
9257 std::sort(Terms.begin(), Terms.end());
9258 Terms.erase(std::unique(Terms.begin(), Terms.end()), Terms.end());
9260 // Put larger terms first.
9261 std::sort(Terms.begin(), Terms.end(), [](const SCEV *LHS, const SCEV *RHS) {
9262 return numberOfTerms(LHS) > numberOfTerms(RHS);
9265 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
9267 // Try to divide all terms by the element size. If term is not divisible by
9268 // element size, proceed with the original term.
9269 for (const SCEV *&Term : Terms) {
9271 SCEVDivision::divide(SE, Term, ElementSize, &Q, &R);
9276 SmallVector<const SCEV *, 4> NewTerms;
9278 // Remove constant factors.
9279 for (const SCEV *T : Terms)
9280 if (const SCEV *NewT = removeConstantFactors(SE, T))
9281 NewTerms.push_back(NewT);
9284 dbgs() << "Terms after sorting:\n";
9285 for (const SCEV *T : NewTerms)
9286 dbgs() << *T << "\n";
9289 if (NewTerms.empty() ||
9290 !findArrayDimensionsRec(SE, NewTerms, Sizes)) {
9295 // The last element to be pushed into Sizes is the size of an element.
9296 Sizes.push_back(ElementSize);
9299 dbgs() << "Sizes:\n";
9300 for (const SCEV *S : Sizes)
9301 dbgs() << *S << "\n";
9305 void ScalarEvolution::computeAccessFunctions(
9306 const SCEV *Expr, SmallVectorImpl<const SCEV *> &Subscripts,
9307 SmallVectorImpl<const SCEV *> &Sizes) {
9309 // Early exit in case this SCEV is not an affine multivariate function.
9313 if (auto *AR = dyn_cast<SCEVAddRecExpr>(Expr))
9314 if (!AR->isAffine())
9317 const SCEV *Res = Expr;
9318 int Last = Sizes.size() - 1;
9319 for (int i = Last; i >= 0; i--) {
9321 SCEVDivision::divide(*this, Res, Sizes[i], &Q, &R);
9324 dbgs() << "Res: " << *Res << "\n";
9325 dbgs() << "Sizes[i]: " << *Sizes[i] << "\n";
9326 dbgs() << "Res divided by Sizes[i]:\n";
9327 dbgs() << "Quotient: " << *Q << "\n";
9328 dbgs() << "Remainder: " << *R << "\n";
9333 // Do not record the last subscript corresponding to the size of elements in
9337 // Bail out if the remainder is too complex.
9338 if (isa<SCEVAddRecExpr>(R)) {
9347 // Record the access function for the current subscript.
9348 Subscripts.push_back(R);
9351 // Also push in last position the remainder of the last division: it will be
9352 // the access function of the innermost dimension.
9353 Subscripts.push_back(Res);
9355 std::reverse(Subscripts.begin(), Subscripts.end());
9358 dbgs() << "Subscripts:\n";
9359 for (const SCEV *S : Subscripts)
9360 dbgs() << *S << "\n";
9364 /// Splits the SCEV into two vectors of SCEVs representing the subscripts and
9365 /// sizes of an array access. Returns the remainder of the delinearization that
9366 /// is the offset start of the array. The SCEV->delinearize algorithm computes
9367 /// the multiples of SCEV coefficients: that is a pattern matching of sub
9368 /// expressions in the stride and base of a SCEV corresponding to the
9369 /// computation of a GCD (greatest common divisor) of base and stride. When
9370 /// SCEV->delinearize fails, it returns the SCEV unchanged.
9372 /// For example: when analyzing the memory access A[i][j][k] in this loop nest
9374 /// void foo(long n, long m, long o, double A[n][m][o]) {
9376 /// for (long i = 0; i < n; i++)
9377 /// for (long j = 0; j < m; j++)
9378 /// for (long k = 0; k < o; k++)
9379 /// A[i][j][k] = 1.0;
9382 /// the delinearization input is the following AddRec SCEV:
9384 /// AddRec: {{{%A,+,(8 * %m * %o)}<%for.i>,+,(8 * %o)}<%for.j>,+,8}<%for.k>
9386 /// From this SCEV, we are able to say that the base offset of the access is %A
9387 /// because it appears as an offset that does not divide any of the strides in
9390 /// CHECK: Base offset: %A
9392 /// and then SCEV->delinearize determines the size of some of the dimensions of
9393 /// the array as these are the multiples by which the strides are happening:
9395 /// CHECK: ArrayDecl[UnknownSize][%m][%o] with elements of sizeof(double) bytes.
9397 /// Note that the outermost dimension remains of UnknownSize because there are
9398 /// no strides that would help identifying the size of the last dimension: when
9399 /// the array has been statically allocated, one could compute the size of that
9400 /// dimension by dividing the overall size of the array by the size of the known
9401 /// dimensions: %m * %o * 8.
9403 /// Finally delinearize provides the access functions for the array reference
9404 /// that does correspond to A[i][j][k] of the above C testcase:
9406 /// CHECK: ArrayRef[{0,+,1}<%for.i>][{0,+,1}<%for.j>][{0,+,1}<%for.k>]
9408 /// The testcases are checking the output of a function pass:
9409 /// DelinearizationPass that walks through all loads and stores of a function
9410 /// asking for the SCEV of the memory access with respect to all enclosing
9411 /// loops, calling SCEV->delinearize on that and printing the results.
9413 void ScalarEvolution::delinearize(const SCEV *Expr,
9414 SmallVectorImpl<const SCEV *> &Subscripts,
9415 SmallVectorImpl<const SCEV *> &Sizes,
9416 const SCEV *ElementSize) {
9417 // First step: collect parametric terms.
9418 SmallVector<const SCEV *, 4> Terms;
9419 collectParametricTerms(Expr, Terms);
9424 // Second step: find subscript sizes.
9425 findArrayDimensions(Terms, Sizes, ElementSize);
9430 // Third step: compute the access functions for each subscript.
9431 computeAccessFunctions(Expr, Subscripts, Sizes);
9433 if (Subscripts.empty())
9437 dbgs() << "succeeded to delinearize " << *Expr << "\n";
9438 dbgs() << "ArrayDecl[UnknownSize]";
9439 for (const SCEV *S : Sizes)
9440 dbgs() << "[" << *S << "]";
9442 dbgs() << "\nArrayRef";
9443 for (const SCEV *S : Subscripts)
9444 dbgs() << "[" << *S << "]";
9449 //===----------------------------------------------------------------------===//
9450 // SCEVCallbackVH Class Implementation
9451 //===----------------------------------------------------------------------===//
9453 void ScalarEvolution::SCEVCallbackVH::deleted() {
9454 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
9455 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
9456 SE->ConstantEvolutionLoopExitValue.erase(PN);
9457 SE->eraseValueFromMap(getValPtr());
9458 // this now dangles!
9461 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) {
9462 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
9464 // Forget all the expressions associated with users of the old value,
9465 // so that future queries will recompute the expressions using the new
9467 Value *Old = getValPtr();
9468 SmallVector<User *, 16> Worklist(Old->user_begin(), Old->user_end());
9469 SmallPtrSet<User *, 8> Visited;
9470 while (!Worklist.empty()) {
9471 User *U = Worklist.pop_back_val();
9472 // Deleting the Old value will cause this to dangle. Postpone
9473 // that until everything else is done.
9476 if (!Visited.insert(U).second)
9478 if (PHINode *PN = dyn_cast<PHINode>(U))
9479 SE->ConstantEvolutionLoopExitValue.erase(PN);
9480 SE->eraseValueFromMap(U);
9481 Worklist.insert(Worklist.end(), U->user_begin(), U->user_end());
9483 // Delete the Old value.
9484 if (PHINode *PN = dyn_cast<PHINode>(Old))
9485 SE->ConstantEvolutionLoopExitValue.erase(PN);
9486 SE->eraseValueFromMap(Old);
9487 // this now dangles!
9490 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
9491 : CallbackVH(V), SE(se) {}
9493 //===----------------------------------------------------------------------===//
9494 // ScalarEvolution Class Implementation
9495 //===----------------------------------------------------------------------===//
9497 ScalarEvolution::ScalarEvolution(Function &F, TargetLibraryInfo &TLI,
9498 AssumptionCache &AC, DominatorTree &DT,
9500 : F(F), TLI(TLI), AC(AC), DT(DT), LI(LI),
9501 CouldNotCompute(new SCEVCouldNotCompute()),
9502 WalkingBEDominatingConds(false), ProvingSplitPredicate(false),
9503 ValuesAtScopes(64), LoopDispositions(64), BlockDispositions(64),
9504 FirstUnknown(nullptr) {
9506 // To use guards for proving predicates, we need to scan every instruction in
9507 // relevant basic blocks, and not just terminators. Doing this is a waste of
9508 // time if the IR does not actually contain any calls to
9509 // @llvm.experimental.guard, so do a quick check and remember this beforehand.
9511 // This pessimizes the case where a pass that preserves ScalarEvolution wants
9512 // to _add_ guards to the module when there weren't any before, and wants
9513 // ScalarEvolution to optimize based on those guards. For now we prefer to be
9514 // efficient in lieu of being smart in that rather obscure case.
9516 auto *GuardDecl = F.getParent()->getFunction(
9517 Intrinsic::getName(Intrinsic::experimental_guard));
9518 HasGuards = GuardDecl && !GuardDecl->use_empty();
9521 ScalarEvolution::ScalarEvolution(ScalarEvolution &&Arg)
9522 : F(Arg.F), HasGuards(Arg.HasGuards), TLI(Arg.TLI), AC(Arg.AC), DT(Arg.DT),
9523 LI(Arg.LI), CouldNotCompute(std::move(Arg.CouldNotCompute)),
9524 ValueExprMap(std::move(Arg.ValueExprMap)),
9525 PendingLoopPredicates(std::move(Arg.PendingLoopPredicates)),
9526 WalkingBEDominatingConds(false), ProvingSplitPredicate(false),
9527 BackedgeTakenCounts(std::move(Arg.BackedgeTakenCounts)),
9528 PredicatedBackedgeTakenCounts(
9529 std::move(Arg.PredicatedBackedgeTakenCounts)),
9530 ConstantEvolutionLoopExitValue(
9531 std::move(Arg.ConstantEvolutionLoopExitValue)),
9532 ValuesAtScopes(std::move(Arg.ValuesAtScopes)),
9533 LoopDispositions(std::move(Arg.LoopDispositions)),
9534 LoopPropertiesCache(std::move(Arg.LoopPropertiesCache)),
9535 BlockDispositions(std::move(Arg.BlockDispositions)),
9536 UnsignedRanges(std::move(Arg.UnsignedRanges)),
9537 SignedRanges(std::move(Arg.SignedRanges)),
9538 UniqueSCEVs(std::move(Arg.UniqueSCEVs)),
9539 UniquePreds(std::move(Arg.UniquePreds)),
9540 SCEVAllocator(std::move(Arg.SCEVAllocator)),
9541 FirstUnknown(Arg.FirstUnknown) {
9542 Arg.FirstUnknown = nullptr;
9545 ScalarEvolution::~ScalarEvolution() {
9546 // Iterate through all the SCEVUnknown instances and call their
9547 // destructors, so that they release their references to their values.
9548 for (SCEVUnknown *U = FirstUnknown; U;) {
9549 SCEVUnknown *Tmp = U;
9551 Tmp->~SCEVUnknown();
9553 FirstUnknown = nullptr;
9555 ExprValueMap.clear();
9556 ValueExprMap.clear();
9559 // Free any extra memory created for ExitNotTakenInfo in the unlikely event
9560 // that a loop had multiple computable exits.
9561 for (auto &BTCI : BackedgeTakenCounts)
9562 BTCI.second.clear();
9563 for (auto &BTCI : PredicatedBackedgeTakenCounts)
9564 BTCI.second.clear();
9566 assert(PendingLoopPredicates.empty() && "isImpliedCond garbage");
9567 assert(!WalkingBEDominatingConds && "isLoopBackedgeGuardedByCond garbage!");
9568 assert(!ProvingSplitPredicate && "ProvingSplitPredicate garbage!");
9571 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
9572 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
9575 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
9577 // Print all inner loops first
9579 PrintLoopInfo(OS, SE, I);
9582 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
9585 SmallVector<BasicBlock *, 8> ExitBlocks;
9586 L->getExitBlocks(ExitBlocks);
9587 if (ExitBlocks.size() != 1)
9588 OS << "<multiple exits> ";
9590 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
9591 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
9593 OS << "Unpredictable backedge-taken count. ";
9598 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
9601 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
9602 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
9603 if (SE->isBackedgeTakenCountMaxOrZero(L))
9604 OS << ", actual taken count either this or zero.";
9606 OS << "Unpredictable max backedge-taken count. ";
9611 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
9614 SCEVUnionPredicate Pred;
9615 auto PBT = SE->getPredicatedBackedgeTakenCount(L, Pred);
9616 if (!isa<SCEVCouldNotCompute>(PBT)) {
9617 OS << "Predicated backedge-taken count is " << *PBT << "\n";
9618 OS << " Predicates:\n";
9621 OS << "Unpredictable predicated backedge-taken count. ";
9626 static StringRef loopDispositionToStr(ScalarEvolution::LoopDisposition LD) {
9628 case ScalarEvolution::LoopVariant:
9630 case ScalarEvolution::LoopInvariant:
9632 case ScalarEvolution::LoopComputable:
9633 return "Computable";
9635 llvm_unreachable("Unknown ScalarEvolution::LoopDisposition kind!");
9638 void ScalarEvolution::print(raw_ostream &OS) const {
9639 // ScalarEvolution's implementation of the print method is to print
9640 // out SCEV values of all instructions that are interesting. Doing
9641 // this potentially causes it to create new SCEV objects though,
9642 // which technically conflicts with the const qualifier. This isn't
9643 // observable from outside the class though, so casting away the
9644 // const isn't dangerous.
9645 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
9647 OS << "Classifying expressions for: ";
9648 F.printAsOperand(OS, /*PrintType=*/false);
9650 for (Instruction &I : instructions(F))
9651 if (isSCEVable(I.getType()) && !isa<CmpInst>(I)) {
9654 const SCEV *SV = SE.getSCEV(&I);
9656 if (!isa<SCEVCouldNotCompute>(SV)) {
9658 SE.getUnsignedRange(SV).print(OS);
9660 SE.getSignedRange(SV).print(OS);
9663 const Loop *L = LI.getLoopFor(I.getParent());
9665 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
9669 if (!isa<SCEVCouldNotCompute>(AtUse)) {
9671 SE.getUnsignedRange(AtUse).print(OS);
9673 SE.getSignedRange(AtUse).print(OS);
9678 OS << "\t\t" "Exits: ";
9679 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
9680 if (!SE.isLoopInvariant(ExitValue, L)) {
9681 OS << "<<Unknown>>";
9687 for (auto *Iter = L; Iter; Iter = Iter->getParentLoop()) {
9689 OS << "\t\t" "LoopDispositions: { ";
9695 Iter->getHeader()->printAsOperand(OS, /*PrintType=*/false);
9696 OS << ": " << loopDispositionToStr(SE.getLoopDisposition(SV, Iter));
9699 for (auto *InnerL : depth_first(L)) {
9703 OS << "\t\t" "LoopDispositions: { ";
9709 InnerL->getHeader()->printAsOperand(OS, /*PrintType=*/false);
9710 OS << ": " << loopDispositionToStr(SE.getLoopDisposition(SV, InnerL));
9719 OS << "Determining loop execution counts for: ";
9720 F.printAsOperand(OS, /*PrintType=*/false);
9723 PrintLoopInfo(OS, &SE, I);
9726 ScalarEvolution::LoopDisposition
9727 ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) {
9728 auto &Values = LoopDispositions[S];
9729 for (auto &V : Values) {
9730 if (V.getPointer() == L)
9733 Values.emplace_back(L, LoopVariant);
9734 LoopDisposition D = computeLoopDisposition(S, L);
9735 auto &Values2 = LoopDispositions[S];
9736 for (auto &V : make_range(Values2.rbegin(), Values2.rend())) {
9737 if (V.getPointer() == L) {
9745 ScalarEvolution::LoopDisposition
9746 ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) {
9747 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
9749 return LoopInvariant;
9753 return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L);
9754 case scAddRecExpr: {
9755 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
9757 // If L is the addrec's loop, it's computable.
9758 if (AR->getLoop() == L)
9759 return LoopComputable;
9761 // Add recurrences are never invariant in the function-body (null loop).
9765 // This recurrence is variant w.r.t. L if L contains AR's loop.
9766 if (L->contains(AR->getLoop()))
9769 // This recurrence is invariant w.r.t. L if AR's loop contains L.
9770 if (AR->getLoop()->contains(L))
9771 return LoopInvariant;
9773 // This recurrence is variant w.r.t. L if any of its operands
9775 for (auto *Op : AR->operands())
9776 if (!isLoopInvariant(Op, L))
9779 // Otherwise it's loop-invariant.
9780 return LoopInvariant;
9786 bool HasVarying = false;
9787 for (auto *Op : cast<SCEVNAryExpr>(S)->operands()) {
9788 LoopDisposition D = getLoopDisposition(Op, L);
9789 if (D == LoopVariant)
9791 if (D == LoopComputable)
9794 return HasVarying ? LoopComputable : LoopInvariant;
9797 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
9798 LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L);
9799 if (LD == LoopVariant)
9801 LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L);
9802 if (RD == LoopVariant)
9804 return (LD == LoopInvariant && RD == LoopInvariant) ?
9805 LoopInvariant : LoopComputable;
9808 // All non-instruction values are loop invariant. All instructions are loop
9809 // invariant if they are not contained in the specified loop.
9810 // Instructions are never considered invariant in the function body
9811 // (null loop) because they are defined within the "loop".
9812 if (auto *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue()))
9813 return (L && !L->contains(I)) ? LoopInvariant : LoopVariant;
9814 return LoopInvariant;
9815 case scCouldNotCompute:
9816 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
9818 llvm_unreachable("Unknown SCEV kind!");
9821 bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) {
9822 return getLoopDisposition(S, L) == LoopInvariant;
9825 bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) {
9826 return getLoopDisposition(S, L) == LoopComputable;
9829 ScalarEvolution::BlockDisposition
9830 ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) {
9831 auto &Values = BlockDispositions[S];
9832 for (auto &V : Values) {
9833 if (V.getPointer() == BB)
9836 Values.emplace_back(BB, DoesNotDominateBlock);
9837 BlockDisposition D = computeBlockDisposition(S, BB);
9838 auto &Values2 = BlockDispositions[S];
9839 for (auto &V : make_range(Values2.rbegin(), Values2.rend())) {
9840 if (V.getPointer() == BB) {
9848 ScalarEvolution::BlockDisposition
9849 ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) {
9850 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
9852 return ProperlyDominatesBlock;
9856 return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB);
9857 case scAddRecExpr: {
9858 // This uses a "dominates" query instead of "properly dominates" query
9859 // to test for proper dominance too, because the instruction which
9860 // produces the addrec's value is a PHI, and a PHI effectively properly
9861 // dominates its entire containing block.
9862 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
9863 if (!DT.dominates(AR->getLoop()->getHeader(), BB))
9864 return DoesNotDominateBlock;
9866 // Fall through into SCEVNAryExpr handling.
9873 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
9875 for (const SCEV *NAryOp : NAry->operands()) {
9876 BlockDisposition D = getBlockDisposition(NAryOp, BB);
9877 if (D == DoesNotDominateBlock)
9878 return DoesNotDominateBlock;
9879 if (D == DominatesBlock)
9882 return Proper ? ProperlyDominatesBlock : DominatesBlock;
9885 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
9886 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
9887 BlockDisposition LD = getBlockDisposition(LHS, BB);
9888 if (LD == DoesNotDominateBlock)
9889 return DoesNotDominateBlock;
9890 BlockDisposition RD = getBlockDisposition(RHS, BB);
9891 if (RD == DoesNotDominateBlock)
9892 return DoesNotDominateBlock;
9893 return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ?
9894 ProperlyDominatesBlock : DominatesBlock;
9897 if (Instruction *I =
9898 dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) {
9899 if (I->getParent() == BB)
9900 return DominatesBlock;
9901 if (DT.properlyDominates(I->getParent(), BB))
9902 return ProperlyDominatesBlock;
9903 return DoesNotDominateBlock;
9905 return ProperlyDominatesBlock;
9906 case scCouldNotCompute:
9907 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
9909 llvm_unreachable("Unknown SCEV kind!");
9912 bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) {
9913 return getBlockDisposition(S, BB) >= DominatesBlock;
9916 bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) {
9917 return getBlockDisposition(S, BB) == ProperlyDominatesBlock;
9920 bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const {
9921 return SCEVExprContains(S, [&](const SCEV *Expr) { return Expr == Op; });
9924 void ScalarEvolution::forgetMemoizedResults(const SCEV *S) {
9925 ValuesAtScopes.erase(S);
9926 LoopDispositions.erase(S);
9927 BlockDispositions.erase(S);
9928 UnsignedRanges.erase(S);
9929 SignedRanges.erase(S);
9930 ExprValueMap.erase(S);
9933 auto RemoveSCEVFromBackedgeMap =
9934 [S, this](DenseMap<const Loop *, BackedgeTakenInfo> &Map) {
9935 for (auto I = Map.begin(), E = Map.end(); I != E;) {
9936 BackedgeTakenInfo &BEInfo = I->second;
9937 if (BEInfo.hasOperand(S, this)) {
9945 RemoveSCEVFromBackedgeMap(BackedgeTakenCounts);
9946 RemoveSCEVFromBackedgeMap(PredicatedBackedgeTakenCounts);
9949 typedef DenseMap<const Loop *, std::string> VerifyMap;
9951 /// replaceSubString - Replaces all occurrences of From in Str with To.
9952 static void replaceSubString(std::string &Str, StringRef From, StringRef To) {
9954 while ((Pos = Str.find(From, Pos)) != std::string::npos) {
9955 Str.replace(Pos, From.size(), To.data(), To.size());
9960 /// getLoopBackedgeTakenCounts - Helper method for verifyAnalysis.
9962 getLoopBackedgeTakenCounts(Loop *L, VerifyMap &Map, ScalarEvolution &SE) {
9963 std::string &S = Map[L];
9965 raw_string_ostream OS(S);
9966 SE.getBackedgeTakenCount(L)->print(OS);
9968 // false and 0 are semantically equivalent. This can happen in dead loops.
9969 replaceSubString(OS.str(), "false", "0");
9970 // Remove wrap flags, their use in SCEV is highly fragile.
9971 // FIXME: Remove this when SCEV gets smarter about them.
9972 replaceSubString(OS.str(), "<nw>", "");
9973 replaceSubString(OS.str(), "<nsw>", "");
9974 replaceSubString(OS.str(), "<nuw>", "");
9977 for (auto *R : reverse(*L))
9978 getLoopBackedgeTakenCounts(R, Map, SE); // recurse.
9981 void ScalarEvolution::verify() const {
9982 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
9984 // Gather stringified backedge taken counts for all loops using SCEV's caches.
9985 // FIXME: It would be much better to store actual values instead of strings,
9986 // but SCEV pointers will change if we drop the caches.
9987 VerifyMap BackedgeDumpsOld, BackedgeDumpsNew;
9988 for (LoopInfo::reverse_iterator I = LI.rbegin(), E = LI.rend(); I != E; ++I)
9989 getLoopBackedgeTakenCounts(*I, BackedgeDumpsOld, SE);
9991 // Gather stringified backedge taken counts for all loops using a fresh
9992 // ScalarEvolution object.
9993 ScalarEvolution SE2(F, TLI, AC, DT, LI);
9994 for (LoopInfo::reverse_iterator I = LI.rbegin(), E = LI.rend(); I != E; ++I)
9995 getLoopBackedgeTakenCounts(*I, BackedgeDumpsNew, SE2);
9997 // Now compare whether they're the same with and without caches. This allows
9998 // verifying that no pass changed the cache.
9999 assert(BackedgeDumpsOld.size() == BackedgeDumpsNew.size() &&
10000 "New loops suddenly appeared!");
10002 for (VerifyMap::iterator OldI = BackedgeDumpsOld.begin(),
10003 OldE = BackedgeDumpsOld.end(),
10004 NewI = BackedgeDumpsNew.begin();
10005 OldI != OldE; ++OldI, ++NewI) {
10006 assert(OldI->first == NewI->first && "Loop order changed!");
10008 // Compare the stringified SCEVs. We don't care if undef backedgetaken count
10010 // FIXME: We currently ignore SCEV changes from/to CouldNotCompute. This
10011 // means that a pass is buggy or SCEV has to learn a new pattern but is
10012 // usually not harmful.
10013 if (OldI->second != NewI->second &&
10014 OldI->second.find("undef") == std::string::npos &&
10015 NewI->second.find("undef") == std::string::npos &&
10016 OldI->second != "***COULDNOTCOMPUTE***" &&
10017 NewI->second != "***COULDNOTCOMPUTE***") {
10018 dbgs() << "SCEVValidator: SCEV for loop '"
10019 << OldI->first->getHeader()->getName()
10020 << "' changed from '" << OldI->second
10021 << "' to '" << NewI->second << "'!\n";
10026 // TODO: Verify more things.
10029 bool ScalarEvolution::invalidate(
10030 Function &F, const PreservedAnalyses &PA,
10031 FunctionAnalysisManager::Invalidator &Inv) {
10032 // Invalidate the ScalarEvolution object whenever it isn't preserved or one
10033 // of its dependencies is invalidated.
10034 auto PAC = PA.getChecker<ScalarEvolutionAnalysis>();
10035 return !(PAC.preserved() || PAC.preservedSet<AllAnalysesOn<Function>>()) ||
10036 Inv.invalidate<AssumptionAnalysis>(F, PA) ||
10037 Inv.invalidate<DominatorTreeAnalysis>(F, PA) ||
10038 Inv.invalidate<LoopAnalysis>(F, PA);
10041 AnalysisKey ScalarEvolutionAnalysis::Key;
10043 ScalarEvolution ScalarEvolutionAnalysis::run(Function &F,
10044 FunctionAnalysisManager &AM) {
10045 return ScalarEvolution(F, AM.getResult<TargetLibraryAnalysis>(F),
10046 AM.getResult<AssumptionAnalysis>(F),
10047 AM.getResult<DominatorTreeAnalysis>(F),
10048 AM.getResult<LoopAnalysis>(F));
10052 ScalarEvolutionPrinterPass::run(Function &F, FunctionAnalysisManager &AM) {
10053 AM.getResult<ScalarEvolutionAnalysis>(F).print(OS);
10054 return PreservedAnalyses::all();
10057 INITIALIZE_PASS_BEGIN(ScalarEvolutionWrapperPass, "scalar-evolution",
10058 "Scalar Evolution Analysis", false, true)
10059 INITIALIZE_PASS_DEPENDENCY(AssumptionCacheTracker)
10060 INITIALIZE_PASS_DEPENDENCY(LoopInfoWrapperPass)
10061 INITIALIZE_PASS_DEPENDENCY(DominatorTreeWrapperPass)
10062 INITIALIZE_PASS_DEPENDENCY(TargetLibraryInfoWrapperPass)
10063 INITIALIZE_PASS_END(ScalarEvolutionWrapperPass, "scalar-evolution",
10064 "Scalar Evolution Analysis", false, true)
10065 char ScalarEvolutionWrapperPass::ID = 0;
10067 ScalarEvolutionWrapperPass::ScalarEvolutionWrapperPass() : FunctionPass(ID) {
10068 initializeScalarEvolutionWrapperPassPass(*PassRegistry::getPassRegistry());
10071 bool ScalarEvolutionWrapperPass::runOnFunction(Function &F) {
10072 SE.reset(new ScalarEvolution(
10073 F, getAnalysis<TargetLibraryInfoWrapperPass>().getTLI(),
10074 getAnalysis<AssumptionCacheTracker>().getAssumptionCache(F),
10075 getAnalysis<DominatorTreeWrapperPass>().getDomTree(),
10076 getAnalysis<LoopInfoWrapperPass>().getLoopInfo()));
10080 void ScalarEvolutionWrapperPass::releaseMemory() { SE.reset(); }
10082 void ScalarEvolutionWrapperPass::print(raw_ostream &OS, const Module *) const {
10086 void ScalarEvolutionWrapperPass::verifyAnalysis() const {
10093 void ScalarEvolutionWrapperPass::getAnalysisUsage(AnalysisUsage &AU) const {
10094 AU.setPreservesAll();
10095 AU.addRequiredTransitive<AssumptionCacheTracker>();
10096 AU.addRequiredTransitive<LoopInfoWrapperPass>();
10097 AU.addRequiredTransitive<DominatorTreeWrapperPass>();
10098 AU.addRequiredTransitive<TargetLibraryInfoWrapperPass>();
10101 const SCEVPredicate *
10102 ScalarEvolution::getEqualPredicate(const SCEVUnknown *LHS,
10103 const SCEVConstant *RHS) {
10104 FoldingSetNodeID ID;
10105 // Unique this node based on the arguments
10106 ID.AddInteger(SCEVPredicate::P_Equal);
10107 ID.AddPointer(LHS);
10108 ID.AddPointer(RHS);
10109 void *IP = nullptr;
10110 if (const auto *S = UniquePreds.FindNodeOrInsertPos(ID, IP))
10112 SCEVEqualPredicate *Eq = new (SCEVAllocator)
10113 SCEVEqualPredicate(ID.Intern(SCEVAllocator), LHS, RHS);
10114 UniquePreds.InsertNode(Eq, IP);
10118 const SCEVPredicate *ScalarEvolution::getWrapPredicate(
10119 const SCEVAddRecExpr *AR,
10120 SCEVWrapPredicate::IncrementWrapFlags AddedFlags) {
10121 FoldingSetNodeID ID;
10122 // Unique this node based on the arguments
10123 ID.AddInteger(SCEVPredicate::P_Wrap);
10125 ID.AddInteger(AddedFlags);
10126 void *IP = nullptr;
10127 if (const auto *S = UniquePreds.FindNodeOrInsertPos(ID, IP))
10129 auto *OF = new (SCEVAllocator)
10130 SCEVWrapPredicate(ID.Intern(SCEVAllocator), AR, AddedFlags);
10131 UniquePreds.InsertNode(OF, IP);
10137 class SCEVPredicateRewriter : public SCEVRewriteVisitor<SCEVPredicateRewriter> {
10139 /// Rewrites \p S in the context of a loop L and the SCEV predication
10140 /// infrastructure.
10142 /// If \p Pred is non-null, the SCEV expression is rewritten to respect the
10143 /// equivalences present in \p Pred.
10145 /// If \p NewPreds is non-null, rewrite is free to add further predicates to
10146 /// \p NewPreds such that the result will be an AddRecExpr.
10147 static const SCEV *rewrite(const SCEV *S, const Loop *L, ScalarEvolution &SE,
10148 SmallPtrSetImpl<const SCEVPredicate *> *NewPreds,
10149 SCEVUnionPredicate *Pred) {
10150 SCEVPredicateRewriter Rewriter(L, SE, NewPreds, Pred);
10151 return Rewriter.visit(S);
10154 SCEVPredicateRewriter(const Loop *L, ScalarEvolution &SE,
10155 SmallPtrSetImpl<const SCEVPredicate *> *NewPreds,
10156 SCEVUnionPredicate *Pred)
10157 : SCEVRewriteVisitor(SE), NewPreds(NewPreds), Pred(Pred), L(L) {}
10159 const SCEV *visitUnknown(const SCEVUnknown *Expr) {
10161 auto ExprPreds = Pred->getPredicatesForExpr(Expr);
10162 for (auto *Pred : ExprPreds)
10163 if (const auto *IPred = dyn_cast<SCEVEqualPredicate>(Pred))
10164 if (IPred->getLHS() == Expr)
10165 return IPred->getRHS();
10171 const SCEV *visitZeroExtendExpr(const SCEVZeroExtendExpr *Expr) {
10172 const SCEV *Operand = visit(Expr->getOperand());
10173 const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Operand);
10174 if (AR && AR->getLoop() == L && AR->isAffine()) {
10175 // This couldn't be folded because the operand didn't have the nuw
10176 // flag. Add the nusw flag as an assumption that we could make.
10177 const SCEV *Step = AR->getStepRecurrence(SE);
10178 Type *Ty = Expr->getType();
10179 if (addOverflowAssumption(AR, SCEVWrapPredicate::IncrementNUSW))
10180 return SE.getAddRecExpr(SE.getZeroExtendExpr(AR->getStart(), Ty),
10181 SE.getSignExtendExpr(Step, Ty), L,
10182 AR->getNoWrapFlags());
10184 return SE.getZeroExtendExpr(Operand, Expr->getType());
10187 const SCEV *visitSignExtendExpr(const SCEVSignExtendExpr *Expr) {
10188 const SCEV *Operand = visit(Expr->getOperand());
10189 const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Operand);
10190 if (AR && AR->getLoop() == L && AR->isAffine()) {
10191 // This couldn't be folded because the operand didn't have the nsw
10192 // flag. Add the nssw flag as an assumption that we could make.
10193 const SCEV *Step = AR->getStepRecurrence(SE);
10194 Type *Ty = Expr->getType();
10195 if (addOverflowAssumption(AR, SCEVWrapPredicate::IncrementNSSW))
10196 return SE.getAddRecExpr(SE.getSignExtendExpr(AR->getStart(), Ty),
10197 SE.getSignExtendExpr(Step, Ty), L,
10198 AR->getNoWrapFlags());
10200 return SE.getSignExtendExpr(Operand, Expr->getType());
10204 bool addOverflowAssumption(const SCEVAddRecExpr *AR,
10205 SCEVWrapPredicate::IncrementWrapFlags AddedFlags) {
10206 auto *A = SE.getWrapPredicate(AR, AddedFlags);
10208 // Check if we've already made this assumption.
10209 return Pred && Pred->implies(A);
10211 NewPreds->insert(A);
10215 SmallPtrSetImpl<const SCEVPredicate *> *NewPreds;
10216 SCEVUnionPredicate *Pred;
10219 } // end anonymous namespace
10221 const SCEV *ScalarEvolution::rewriteUsingPredicate(const SCEV *S, const Loop *L,
10222 SCEVUnionPredicate &Preds) {
10223 return SCEVPredicateRewriter::rewrite(S, L, *this, nullptr, &Preds);
10226 const SCEVAddRecExpr *ScalarEvolution::convertSCEVToAddRecWithPredicates(
10227 const SCEV *S, const Loop *L,
10228 SmallPtrSetImpl<const SCEVPredicate *> &Preds) {
10230 SmallPtrSet<const SCEVPredicate *, 4> TransformPreds;
10231 S = SCEVPredicateRewriter::rewrite(S, L, *this, &TransformPreds, nullptr);
10232 auto *AddRec = dyn_cast<SCEVAddRecExpr>(S);
10237 // Since the transformation was successful, we can now transfer the SCEV
10239 for (auto *P : TransformPreds)
10245 /// SCEV predicates
10246 SCEVPredicate::SCEVPredicate(const FoldingSetNodeIDRef ID,
10247 SCEVPredicateKind Kind)
10248 : FastID(ID), Kind(Kind) {}
10250 SCEVEqualPredicate::SCEVEqualPredicate(const FoldingSetNodeIDRef ID,
10251 const SCEVUnknown *LHS,
10252 const SCEVConstant *RHS)
10253 : SCEVPredicate(ID, P_Equal), LHS(LHS), RHS(RHS) {}
10255 bool SCEVEqualPredicate::implies(const SCEVPredicate *N) const {
10256 const auto *Op = dyn_cast<SCEVEqualPredicate>(N);
10261 return Op->LHS == LHS && Op->RHS == RHS;
10264 bool SCEVEqualPredicate::isAlwaysTrue() const { return false; }
10266 const SCEV *SCEVEqualPredicate::getExpr() const { return LHS; }
10268 void SCEVEqualPredicate::print(raw_ostream &OS, unsigned Depth) const {
10269 OS.indent(Depth) << "Equal predicate: " << *LHS << " == " << *RHS << "\n";
10272 SCEVWrapPredicate::SCEVWrapPredicate(const FoldingSetNodeIDRef ID,
10273 const SCEVAddRecExpr *AR,
10274 IncrementWrapFlags Flags)
10275 : SCEVPredicate(ID, P_Wrap), AR(AR), Flags(Flags) {}
10277 const SCEV *SCEVWrapPredicate::getExpr() const { return AR; }
10279 bool SCEVWrapPredicate::implies(const SCEVPredicate *N) const {
10280 const auto *Op = dyn_cast<SCEVWrapPredicate>(N);
10282 return Op && Op->AR == AR && setFlags(Flags, Op->Flags) == Flags;
10285 bool SCEVWrapPredicate::isAlwaysTrue() const {
10286 SCEV::NoWrapFlags ScevFlags = AR->getNoWrapFlags();
10287 IncrementWrapFlags IFlags = Flags;
10289 if (ScalarEvolution::setFlags(ScevFlags, SCEV::FlagNSW) == ScevFlags)
10290 IFlags = clearFlags(IFlags, IncrementNSSW);
10292 return IFlags == IncrementAnyWrap;
10295 void SCEVWrapPredicate::print(raw_ostream &OS, unsigned Depth) const {
10296 OS.indent(Depth) << *getExpr() << " Added Flags: ";
10297 if (SCEVWrapPredicate::IncrementNUSW & getFlags())
10299 if (SCEVWrapPredicate::IncrementNSSW & getFlags())
10304 SCEVWrapPredicate::IncrementWrapFlags
10305 SCEVWrapPredicate::getImpliedFlags(const SCEVAddRecExpr *AR,
10306 ScalarEvolution &SE) {
10307 IncrementWrapFlags ImpliedFlags = IncrementAnyWrap;
10308 SCEV::NoWrapFlags StaticFlags = AR->getNoWrapFlags();
10310 // We can safely transfer the NSW flag as NSSW.
10311 if (ScalarEvolution::setFlags(StaticFlags, SCEV::FlagNSW) == StaticFlags)
10312 ImpliedFlags = IncrementNSSW;
10314 if (ScalarEvolution::setFlags(StaticFlags, SCEV::FlagNUW) == StaticFlags) {
10315 // If the increment is positive, the SCEV NUW flag will also imply the
10316 // WrapPredicate NUSW flag.
10317 if (const auto *Step = dyn_cast<SCEVConstant>(AR->getStepRecurrence(SE)))
10318 if (Step->getValue()->getValue().isNonNegative())
10319 ImpliedFlags = setFlags(ImpliedFlags, IncrementNUSW);
10322 return ImpliedFlags;
10325 /// Union predicates don't get cached so create a dummy set ID for it.
10326 SCEVUnionPredicate::SCEVUnionPredicate()
10327 : SCEVPredicate(FoldingSetNodeIDRef(nullptr, 0), P_Union) {}
10329 bool SCEVUnionPredicate::isAlwaysTrue() const {
10330 return all_of(Preds,
10331 [](const SCEVPredicate *I) { return I->isAlwaysTrue(); });
10334 ArrayRef<const SCEVPredicate *>
10335 SCEVUnionPredicate::getPredicatesForExpr(const SCEV *Expr) {
10336 auto I = SCEVToPreds.find(Expr);
10337 if (I == SCEVToPreds.end())
10338 return ArrayRef<const SCEVPredicate *>();
10342 bool SCEVUnionPredicate::implies(const SCEVPredicate *N) const {
10343 if (const auto *Set = dyn_cast<SCEVUnionPredicate>(N))
10344 return all_of(Set->Preds,
10345 [this](const SCEVPredicate *I) { return this->implies(I); });
10347 auto ScevPredsIt = SCEVToPreds.find(N->getExpr());
10348 if (ScevPredsIt == SCEVToPreds.end())
10350 auto &SCEVPreds = ScevPredsIt->second;
10352 return any_of(SCEVPreds,
10353 [N](const SCEVPredicate *I) { return I->implies(N); });
10356 const SCEV *SCEVUnionPredicate::getExpr() const { return nullptr; }
10358 void SCEVUnionPredicate::print(raw_ostream &OS, unsigned Depth) const {
10359 for (auto Pred : Preds)
10360 Pred->print(OS, Depth);
10363 void SCEVUnionPredicate::add(const SCEVPredicate *N) {
10364 if (const auto *Set = dyn_cast<SCEVUnionPredicate>(N)) {
10365 for (auto Pred : Set->Preds)
10373 const SCEV *Key = N->getExpr();
10374 assert(Key && "Only SCEVUnionPredicate doesn't have an "
10375 " associated expression!");
10377 SCEVToPreds[Key].push_back(N);
10378 Preds.push_back(N);
10381 PredicatedScalarEvolution::PredicatedScalarEvolution(ScalarEvolution &SE,
10383 : SE(SE), L(L), Generation(0), BackedgeCount(nullptr) {}
10385 const SCEV *PredicatedScalarEvolution::getSCEV(Value *V) {
10386 const SCEV *Expr = SE.getSCEV(V);
10387 RewriteEntry &Entry = RewriteMap[Expr];
10389 // If we already have an entry and the version matches, return it.
10390 if (Entry.second && Generation == Entry.first)
10391 return Entry.second;
10393 // We found an entry but it's stale. Rewrite the stale entry
10394 // according to the current predicate.
10396 Expr = Entry.second;
10398 const SCEV *NewSCEV = SE.rewriteUsingPredicate(Expr, &L, Preds);
10399 Entry = {Generation, NewSCEV};
10404 const SCEV *PredicatedScalarEvolution::getBackedgeTakenCount() {
10405 if (!BackedgeCount) {
10406 SCEVUnionPredicate BackedgePred;
10407 BackedgeCount = SE.getPredicatedBackedgeTakenCount(&L, BackedgePred);
10408 addPredicate(BackedgePred);
10410 return BackedgeCount;
10413 void PredicatedScalarEvolution::addPredicate(const SCEVPredicate &Pred) {
10414 if (Preds.implies(&Pred))
10417 updateGeneration();
10420 const SCEVUnionPredicate &PredicatedScalarEvolution::getUnionPredicate() const {
10424 void PredicatedScalarEvolution::updateGeneration() {
10425 // If the generation number wrapped recompute everything.
10426 if (++Generation == 0) {
10427 for (auto &II : RewriteMap) {
10428 const SCEV *Rewritten = II.second.second;
10429 II.second = {Generation, SE.rewriteUsingPredicate(Rewritten, &L, Preds)};
10434 void PredicatedScalarEvolution::setNoOverflow(
10435 Value *V, SCEVWrapPredicate::IncrementWrapFlags Flags) {
10436 const SCEV *Expr = getSCEV(V);
10437 const auto *AR = cast<SCEVAddRecExpr>(Expr);
10439 auto ImpliedFlags = SCEVWrapPredicate::getImpliedFlags(AR, SE);
10441 // Clear the statically implied flags.
10442 Flags = SCEVWrapPredicate::clearFlags(Flags, ImpliedFlags);
10443 addPredicate(*SE.getWrapPredicate(AR, Flags));
10445 auto II = FlagsMap.insert({V, Flags});
10447 II.first->second = SCEVWrapPredicate::setFlags(Flags, II.first->second);
10450 bool PredicatedScalarEvolution::hasNoOverflow(
10451 Value *V, SCEVWrapPredicate::IncrementWrapFlags Flags) {
10452 const SCEV *Expr = getSCEV(V);
10453 const auto *AR = cast<SCEVAddRecExpr>(Expr);
10455 Flags = SCEVWrapPredicate::clearFlags(
10456 Flags, SCEVWrapPredicate::getImpliedFlags(AR, SE));
10458 auto II = FlagsMap.find(V);
10460 if (II != FlagsMap.end())
10461 Flags = SCEVWrapPredicate::clearFlags(Flags, II->second);
10463 return Flags == SCEVWrapPredicate::IncrementAnyWrap;
10466 const SCEVAddRecExpr *PredicatedScalarEvolution::getAsAddRec(Value *V) {
10467 const SCEV *Expr = this->getSCEV(V);
10468 SmallPtrSet<const SCEVPredicate *, 4> NewPreds;
10469 auto *New = SE.convertSCEVToAddRecWithPredicates(Expr, &L, NewPreds);
10474 for (auto *P : NewPreds)
10477 updateGeneration();
10478 RewriteMap[SE.getSCEV(V)] = {Generation, New};
10482 PredicatedScalarEvolution::PredicatedScalarEvolution(
10483 const PredicatedScalarEvolution &Init)
10484 : RewriteMap(Init.RewriteMap), SE(Init.SE), L(Init.L), Preds(Init.Preds),
10485 Generation(Init.Generation), BackedgeCount(Init.BackedgeCount) {
10486 for (const auto &I : Init.FlagsMap)
10487 FlagsMap.insert(I);
10490 void PredicatedScalarEvolution::print(raw_ostream &OS, unsigned Depth) const {
10492 for (auto *BB : L.getBlocks())
10493 for (auto &I : *BB) {
10494 if (!SE.isSCEVable(I.getType()))
10497 auto *Expr = SE.getSCEV(&I);
10498 auto II = RewriteMap.find(Expr);
10500 if (II == RewriteMap.end())
10503 // Don't print things that are not interesting.
10504 if (II->second.second == Expr)
10507 OS.indent(Depth) << "[PSE]" << I << ":\n";
10508 OS.indent(Depth + 2) << *Expr << "\n";
10509 OS.indent(Depth + 2) << "--> " << *II->second.second << "\n";