1 //===- ScalarEvolution.cpp - Scalar Evolution Analysis --------------------===//
3 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
4 // See https://llvm.org/LICENSE.txt for license information.
5 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
7 //===----------------------------------------------------------------------===//
9 // This file contains the implementation of the scalar evolution analysis
10 // engine, which is used primarily to analyze expressions involving induction
11 // variables in loops.
13 // There are several aspects to this library. First is the representation of
14 // scalar expressions, which are represented as subclasses of the SCEV class.
15 // These classes are used to represent certain types of subexpressions that we
16 // can handle. We only create one SCEV of a particular shape, so
17 // pointer-comparisons for equality are legal.
19 // One important aspect of the SCEV objects is that they are never cyclic, even
20 // if there is a cycle in the dataflow for an expression (ie, a PHI node). If
21 // the PHI node is one of the idioms that we can represent (e.g., a polynomial
22 // recurrence) then we represent it directly as a recurrence node, otherwise we
23 // represent it as a SCEVUnknown node.
25 // In addition to being able to represent expressions of various types, we also
26 // have folders that are used to build the *canonical* representation for a
27 // particular expression. These folders are capable of using a variety of
28 // rewrite rules to simplify the expressions.
30 // Once the folders are defined, we can implement the more interesting
31 // higher-level code, such as the code that recognizes PHI nodes of various
32 // types, computes the execution count of a loop, etc.
34 // TODO: We should use these routines and value representations to implement
35 // dependence analysis!
37 //===----------------------------------------------------------------------===//
39 // There are several good references for the techniques used in this analysis.
41 // Chains of recurrences -- a method to expedite the evaluation
42 // of closed-form functions
43 // Olaf Bachmann, Paul S. Wang, Eugene V. Zima
45 // On computational properties of chains of recurrences
48 // Symbolic Evaluation of Chains of Recurrences for Loop Optimization
49 // Robert A. van Engelen
51 // Efficient Symbolic Analysis for Optimizing Compilers
52 // Robert A. van Engelen
54 // Using the chains of recurrences algebra for data dependence testing and
55 // induction variable substitution
56 // MS Thesis, Johnie Birch
58 //===----------------------------------------------------------------------===//
60 #include "llvm/Analysis/ScalarEvolution.h"
61 #include "llvm/ADT/APInt.h"
62 #include "llvm/ADT/ArrayRef.h"
63 #include "llvm/ADT/DenseMap.h"
64 #include "llvm/ADT/DepthFirstIterator.h"
65 #include "llvm/ADT/EquivalenceClasses.h"
66 #include "llvm/ADT/FoldingSet.h"
67 #include "llvm/ADT/None.h"
68 #include "llvm/ADT/Optional.h"
69 #include "llvm/ADT/STLExtras.h"
70 #include "llvm/ADT/ScopeExit.h"
71 #include "llvm/ADT/Sequence.h"
72 #include "llvm/ADT/SetVector.h"
73 #include "llvm/ADT/SmallPtrSet.h"
74 #include "llvm/ADT/SmallSet.h"
75 #include "llvm/ADT/SmallVector.h"
76 #include "llvm/ADT/Statistic.h"
77 #include "llvm/ADT/StringRef.h"
78 #include "llvm/Analysis/AssumptionCache.h"
79 #include "llvm/Analysis/ConstantFolding.h"
80 #include "llvm/Analysis/InstructionSimplify.h"
81 #include "llvm/Analysis/LoopInfo.h"
82 #include "llvm/Analysis/ScalarEvolutionDivision.h"
83 #include "llvm/Analysis/ScalarEvolutionExpressions.h"
84 #include "llvm/Analysis/TargetLibraryInfo.h"
85 #include "llvm/Analysis/ValueTracking.h"
86 #include "llvm/Config/llvm-config.h"
87 #include "llvm/IR/Argument.h"
88 #include "llvm/IR/BasicBlock.h"
89 #include "llvm/IR/CFG.h"
90 #include "llvm/IR/Constant.h"
91 #include "llvm/IR/ConstantRange.h"
92 #include "llvm/IR/Constants.h"
93 #include "llvm/IR/DataLayout.h"
94 #include "llvm/IR/DerivedTypes.h"
95 #include "llvm/IR/Dominators.h"
96 #include "llvm/IR/Function.h"
97 #include "llvm/IR/GlobalAlias.h"
98 #include "llvm/IR/GlobalValue.h"
99 #include "llvm/IR/GlobalVariable.h"
100 #include "llvm/IR/InstIterator.h"
101 #include "llvm/IR/InstrTypes.h"
102 #include "llvm/IR/Instruction.h"
103 #include "llvm/IR/Instructions.h"
104 #include "llvm/IR/IntrinsicInst.h"
105 #include "llvm/IR/Intrinsics.h"
106 #include "llvm/IR/LLVMContext.h"
107 #include "llvm/IR/Metadata.h"
108 #include "llvm/IR/Operator.h"
109 #include "llvm/IR/PatternMatch.h"
110 #include "llvm/IR/Type.h"
111 #include "llvm/IR/Use.h"
112 #include "llvm/IR/User.h"
113 #include "llvm/IR/Value.h"
114 #include "llvm/IR/Verifier.h"
115 #include "llvm/InitializePasses.h"
116 #include "llvm/Pass.h"
117 #include "llvm/Support/Casting.h"
118 #include "llvm/Support/CommandLine.h"
119 #include "llvm/Support/Compiler.h"
120 #include "llvm/Support/Debug.h"
121 #include "llvm/Support/ErrorHandling.h"
122 #include "llvm/Support/KnownBits.h"
123 #include "llvm/Support/SaveAndRestore.h"
124 #include "llvm/Support/raw_ostream.h"
137 using namespace llvm;
139 #define DEBUG_TYPE "scalar-evolution"
141 STATISTIC(NumArrayLenItCounts,
142 "Number of trip counts computed with array length");
143 STATISTIC(NumTripCountsComputed,
144 "Number of loops with predictable loop counts");
145 STATISTIC(NumTripCountsNotComputed,
146 "Number of loops without predictable loop counts");
147 STATISTIC(NumBruteForceTripCountsComputed,
148 "Number of loops with trip counts computed by force");
150 static cl::opt<unsigned>
151 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
153 cl::desc("Maximum number of iterations SCEV will "
154 "symbolically execute a constant "
158 // FIXME: Enable this with EXPENSIVE_CHECKS when the test suite is clean.
159 static cl::opt<bool> VerifySCEV(
160 "verify-scev", cl::Hidden,
161 cl::desc("Verify ScalarEvolution's backedge taken counts (slow)"));
162 static cl::opt<bool> VerifySCEVStrict(
163 "verify-scev-strict", cl::Hidden,
164 cl::desc("Enable stricter verification with -verify-scev is passed"));
166 VerifySCEVMap("verify-scev-maps", cl::Hidden,
167 cl::desc("Verify no dangling value in ScalarEvolution's "
168 "ExprValueMap (slow)"));
170 static cl::opt<bool> VerifyIR(
171 "scev-verify-ir", cl::Hidden,
172 cl::desc("Verify IR correctness when making sensitive SCEV queries (slow)"),
175 static cl::opt<unsigned> MulOpsInlineThreshold(
176 "scev-mulops-inline-threshold", cl::Hidden,
177 cl::desc("Threshold for inlining multiplication operands into a SCEV"),
180 static cl::opt<unsigned> AddOpsInlineThreshold(
181 "scev-addops-inline-threshold", cl::Hidden,
182 cl::desc("Threshold for inlining addition operands into a SCEV"),
185 static cl::opt<unsigned> MaxSCEVCompareDepth(
186 "scalar-evolution-max-scev-compare-depth", cl::Hidden,
187 cl::desc("Maximum depth of recursive SCEV complexity comparisons"),
190 static cl::opt<unsigned> MaxSCEVOperationsImplicationDepth(
191 "scalar-evolution-max-scev-operations-implication-depth", cl::Hidden,
192 cl::desc("Maximum depth of recursive SCEV operations implication analysis"),
195 static cl::opt<unsigned> MaxValueCompareDepth(
196 "scalar-evolution-max-value-compare-depth", cl::Hidden,
197 cl::desc("Maximum depth of recursive value complexity comparisons"),
200 static cl::opt<unsigned>
201 MaxArithDepth("scalar-evolution-max-arith-depth", cl::Hidden,
202 cl::desc("Maximum depth of recursive arithmetics"),
205 static cl::opt<unsigned> MaxConstantEvolvingDepth(
206 "scalar-evolution-max-constant-evolving-depth", cl::Hidden,
207 cl::desc("Maximum depth of recursive constant evolving"), cl::init(32));
209 static cl::opt<unsigned>
210 MaxCastDepth("scalar-evolution-max-cast-depth", cl::Hidden,
211 cl::desc("Maximum depth of recursive SExt/ZExt/Trunc"),
214 static cl::opt<unsigned>
215 MaxAddRecSize("scalar-evolution-max-add-rec-size", cl::Hidden,
216 cl::desc("Max coefficients in AddRec during evolving"),
219 static cl::opt<unsigned>
220 HugeExprThreshold("scalar-evolution-huge-expr-threshold", cl::Hidden,
221 cl::desc("Size of the expression which is considered huge"),
225 ClassifyExpressions("scalar-evolution-classify-expressions",
226 cl::Hidden, cl::init(true),
227 cl::desc("When printing analysis, include information on every instruction"));
230 //===----------------------------------------------------------------------===//
231 // SCEV class definitions
232 //===----------------------------------------------------------------------===//
234 //===----------------------------------------------------------------------===//
235 // Implementation of the SCEV class.
238 #if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP)
239 LLVM_DUMP_METHOD void SCEV::dump() const {
245 void SCEV::print(raw_ostream &OS) const {
246 switch (static_cast<SCEVTypes>(getSCEVType())) {
248 cast<SCEVConstant>(this)->getValue()->printAsOperand(OS, false);
251 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(this);
252 const SCEV *Op = Trunc->getOperand();
253 OS << "(trunc " << *Op->getType() << " " << *Op << " to "
254 << *Trunc->getType() << ")";
258 const SCEVZeroExtendExpr *ZExt = cast<SCEVZeroExtendExpr>(this);
259 const SCEV *Op = ZExt->getOperand();
260 OS << "(zext " << *Op->getType() << " " << *Op << " to "
261 << *ZExt->getType() << ")";
265 const SCEVSignExtendExpr *SExt = cast<SCEVSignExtendExpr>(this);
266 const SCEV *Op = SExt->getOperand();
267 OS << "(sext " << *Op->getType() << " " << *Op << " to "
268 << *SExt->getType() << ")";
272 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(this);
273 OS << "{" << *AR->getOperand(0);
274 for (unsigned i = 1, e = AR->getNumOperands(); i != e; ++i)
275 OS << ",+," << *AR->getOperand(i);
277 if (AR->hasNoUnsignedWrap())
279 if (AR->hasNoSignedWrap())
281 if (AR->hasNoSelfWrap() &&
282 !AR->getNoWrapFlags((NoWrapFlags)(FlagNUW | FlagNSW)))
284 AR->getLoop()->getHeader()->printAsOperand(OS, /*PrintType=*/false);
294 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(this);
295 const char *OpStr = nullptr;
296 switch (NAry->getSCEVType()) {
297 case scAddExpr: OpStr = " + "; break;
298 case scMulExpr: OpStr = " * "; break;
299 case scUMaxExpr: OpStr = " umax "; break;
300 case scSMaxExpr: OpStr = " smax "; break;
309 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
312 if (std::next(I) != E)
316 switch (NAry->getSCEVType()) {
319 if (NAry->hasNoUnsignedWrap())
321 if (NAry->hasNoSignedWrap())
327 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(this);
328 OS << "(" << *UDiv->getLHS() << " /u " << *UDiv->getRHS() << ")";
332 const SCEVUnknown *U = cast<SCEVUnknown>(this);
334 if (U->isSizeOf(AllocTy)) {
335 OS << "sizeof(" << *AllocTy << ")";
338 if (U->isAlignOf(AllocTy)) {
339 OS << "alignof(" << *AllocTy << ")";
345 if (U->isOffsetOf(CTy, FieldNo)) {
346 OS << "offsetof(" << *CTy << ", ";
347 FieldNo->printAsOperand(OS, false);
352 // Otherwise just print it normally.
353 U->getValue()->printAsOperand(OS, false);
356 case scCouldNotCompute:
357 OS << "***COULDNOTCOMPUTE***";
360 llvm_unreachable("Unknown SCEV kind!");
363 Type *SCEV::getType() const {
364 switch (static_cast<SCEVTypes>(getSCEVType())) {
366 return cast<SCEVConstant>(this)->getType();
370 return cast<SCEVCastExpr>(this)->getType();
377 return cast<SCEVNAryExpr>(this)->getType();
379 return cast<SCEVAddExpr>(this)->getType();
381 return cast<SCEVUDivExpr>(this)->getType();
383 return cast<SCEVUnknown>(this)->getType();
384 case scCouldNotCompute:
385 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
387 llvm_unreachable("Unknown SCEV kind!");
390 bool SCEV::isZero() const {
391 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
392 return SC->getValue()->isZero();
396 bool SCEV::isOne() const {
397 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
398 return SC->getValue()->isOne();
402 bool SCEV::isAllOnesValue() const {
403 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
404 return SC->getValue()->isMinusOne();
408 bool SCEV::isNonConstantNegative() const {
409 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(this);
410 if (!Mul) return false;
412 // If there is a constant factor, it will be first.
413 const SCEVConstant *SC = dyn_cast<SCEVConstant>(Mul->getOperand(0));
414 if (!SC) return false;
416 // Return true if the value is negative, this matches things like (-42 * V).
417 return SC->getAPInt().isNegative();
420 SCEVCouldNotCompute::SCEVCouldNotCompute() :
421 SCEV(FoldingSetNodeIDRef(), scCouldNotCompute, 0) {}
423 bool SCEVCouldNotCompute::classof(const SCEV *S) {
424 return S->getSCEVType() == scCouldNotCompute;
427 const SCEV *ScalarEvolution::getConstant(ConstantInt *V) {
429 ID.AddInteger(scConstant);
432 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
433 SCEV *S = new (SCEVAllocator) SCEVConstant(ID.Intern(SCEVAllocator), V);
434 UniqueSCEVs.InsertNode(S, IP);
438 const SCEV *ScalarEvolution::getConstant(const APInt &Val) {
439 return getConstant(ConstantInt::get(getContext(), Val));
443 ScalarEvolution::getConstant(Type *Ty, uint64_t V, bool isSigned) {
444 IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty));
445 return getConstant(ConstantInt::get(ITy, V, isSigned));
448 SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID,
449 unsigned SCEVTy, const SCEV *op, Type *ty)
450 : SCEV(ID, SCEVTy, computeExpressionSize(op)), Op(op), Ty(ty) {}
452 SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID,
453 const SCEV *op, Type *ty)
454 : SCEVCastExpr(ID, scTruncate, op, ty) {
455 assert(Op->getType()->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
456 "Cannot truncate non-integer value!");
459 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID,
460 const SCEV *op, Type *ty)
461 : SCEVCastExpr(ID, scZeroExtend, op, ty) {
462 assert(Op->getType()->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
463 "Cannot zero extend non-integer value!");
466 SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID,
467 const SCEV *op, Type *ty)
468 : SCEVCastExpr(ID, scSignExtend, op, ty) {
469 assert(Op->getType()->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
470 "Cannot sign extend non-integer value!");
473 void SCEVUnknown::deleted() {
474 // Clear this SCEVUnknown from various maps.
475 SE->forgetMemoizedResults(this);
477 // Remove this SCEVUnknown from the uniquing map.
478 SE->UniqueSCEVs.RemoveNode(this);
480 // Release the value.
484 void SCEVUnknown::allUsesReplacedWith(Value *New) {
485 // Remove this SCEVUnknown from the uniquing map.
486 SE->UniqueSCEVs.RemoveNode(this);
488 // Update this SCEVUnknown to point to the new value. This is needed
489 // because there may still be outstanding SCEVs which still point to
494 bool SCEVUnknown::isSizeOf(Type *&AllocTy) const {
495 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
496 if (VCE->getOpcode() == Instruction::PtrToInt)
497 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
498 if (CE->getOpcode() == Instruction::GetElementPtr &&
499 CE->getOperand(0)->isNullValue() &&
500 CE->getNumOperands() == 2)
501 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1)))
503 AllocTy = cast<PointerType>(CE->getOperand(0)->getType())
511 bool SCEVUnknown::isAlignOf(Type *&AllocTy) const {
512 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
513 if (VCE->getOpcode() == Instruction::PtrToInt)
514 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
515 if (CE->getOpcode() == Instruction::GetElementPtr &&
516 CE->getOperand(0)->isNullValue()) {
518 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
519 if (StructType *STy = dyn_cast<StructType>(Ty))
520 if (!STy->isPacked() &&
521 CE->getNumOperands() == 3 &&
522 CE->getOperand(1)->isNullValue()) {
523 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2)))
525 STy->getNumElements() == 2 &&
526 STy->getElementType(0)->isIntegerTy(1)) {
527 AllocTy = STy->getElementType(1);
536 bool SCEVUnknown::isOffsetOf(Type *&CTy, Constant *&FieldNo) const {
537 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
538 if (VCE->getOpcode() == Instruction::PtrToInt)
539 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
540 if (CE->getOpcode() == Instruction::GetElementPtr &&
541 CE->getNumOperands() == 3 &&
542 CE->getOperand(0)->isNullValue() &&
543 CE->getOperand(1)->isNullValue()) {
545 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
546 // Ignore vector types here so that ScalarEvolutionExpander doesn't
547 // emit getelementptrs that index into vectors.
548 if (Ty->isStructTy() || Ty->isArrayTy()) {
550 FieldNo = CE->getOperand(2);
558 //===----------------------------------------------------------------------===//
560 //===----------------------------------------------------------------------===//
562 /// Compare the two values \p LV and \p RV in terms of their "complexity" where
563 /// "complexity" is a partial (and somewhat ad-hoc) relation used to order
564 /// operands in SCEV expressions. \p EqCache is a set of pairs of values that
565 /// have been previously deemed to be "equally complex" by this routine. It is
566 /// intended to avoid exponential time complexity in cases like:
576 /// CompareValueComplexity(%f, %c)
578 /// Since we do not continue running this routine on expression trees once we
579 /// have seen unequal values, there is no need to track them in the cache.
581 CompareValueComplexity(EquivalenceClasses<const Value *> &EqCacheValue,
582 const LoopInfo *const LI, Value *LV, Value *RV,
584 if (Depth > MaxValueCompareDepth || EqCacheValue.isEquivalent(LV, RV))
587 // Order pointer values after integer values. This helps SCEVExpander form
589 bool LIsPointer = LV->getType()->isPointerTy(),
590 RIsPointer = RV->getType()->isPointerTy();
591 if (LIsPointer != RIsPointer)
592 return (int)LIsPointer - (int)RIsPointer;
594 // Compare getValueID values.
595 unsigned LID = LV->getValueID(), RID = RV->getValueID();
597 return (int)LID - (int)RID;
599 // Sort arguments by their position.
600 if (const auto *LA = dyn_cast<Argument>(LV)) {
601 const auto *RA = cast<Argument>(RV);
602 unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo();
603 return (int)LArgNo - (int)RArgNo;
606 if (const auto *LGV = dyn_cast<GlobalValue>(LV)) {
607 const auto *RGV = cast<GlobalValue>(RV);
609 const auto IsGVNameSemantic = [&](const GlobalValue *GV) {
610 auto LT = GV->getLinkage();
611 return !(GlobalValue::isPrivateLinkage(LT) ||
612 GlobalValue::isInternalLinkage(LT));
615 // Use the names to distinguish the two values, but only if the
616 // names are semantically important.
617 if (IsGVNameSemantic(LGV) && IsGVNameSemantic(RGV))
618 return LGV->getName().compare(RGV->getName());
621 // For instructions, compare their loop depth, and their operand count. This
623 if (const auto *LInst = dyn_cast<Instruction>(LV)) {
624 const auto *RInst = cast<Instruction>(RV);
626 // Compare loop depths.
627 const BasicBlock *LParent = LInst->getParent(),
628 *RParent = RInst->getParent();
629 if (LParent != RParent) {
630 unsigned LDepth = LI->getLoopDepth(LParent),
631 RDepth = LI->getLoopDepth(RParent);
632 if (LDepth != RDepth)
633 return (int)LDepth - (int)RDepth;
636 // Compare the number of operands.
637 unsigned LNumOps = LInst->getNumOperands(),
638 RNumOps = RInst->getNumOperands();
639 if (LNumOps != RNumOps)
640 return (int)LNumOps - (int)RNumOps;
642 for (unsigned Idx : seq(0u, LNumOps)) {
644 CompareValueComplexity(EqCacheValue, LI, LInst->getOperand(Idx),
645 RInst->getOperand(Idx), Depth + 1);
651 EqCacheValue.unionSets(LV, RV);
655 // Return negative, zero, or positive, if LHS is less than, equal to, or greater
656 // than RHS, respectively. A three-way result allows recursive comparisons to be
658 static int CompareSCEVComplexity(
659 EquivalenceClasses<const SCEV *> &EqCacheSCEV,
660 EquivalenceClasses<const Value *> &EqCacheValue,
661 const LoopInfo *const LI, const SCEV *LHS, const SCEV *RHS,
662 DominatorTree &DT, unsigned Depth = 0) {
663 // Fast-path: SCEVs are uniqued so we can do a quick equality check.
667 // Primarily, sort the SCEVs by their getSCEVType().
668 unsigned LType = LHS->getSCEVType(), RType = RHS->getSCEVType();
670 return (int)LType - (int)RType;
672 if (Depth > MaxSCEVCompareDepth || EqCacheSCEV.isEquivalent(LHS, RHS))
674 // Aside from the getSCEVType() ordering, the particular ordering
675 // isn't very important except that it's beneficial to be consistent,
676 // so that (a + b) and (b + a) don't end up as different expressions.
677 switch (static_cast<SCEVTypes>(LType)) {
679 const SCEVUnknown *LU = cast<SCEVUnknown>(LHS);
680 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
682 int X = CompareValueComplexity(EqCacheValue, LI, LU->getValue(),
683 RU->getValue(), Depth + 1);
685 EqCacheSCEV.unionSets(LHS, RHS);
690 const SCEVConstant *LC = cast<SCEVConstant>(LHS);
691 const SCEVConstant *RC = cast<SCEVConstant>(RHS);
693 // Compare constant values.
694 const APInt &LA = LC->getAPInt();
695 const APInt &RA = RC->getAPInt();
696 unsigned LBitWidth = LA.getBitWidth(), RBitWidth = RA.getBitWidth();
697 if (LBitWidth != RBitWidth)
698 return (int)LBitWidth - (int)RBitWidth;
699 return LA.ult(RA) ? -1 : 1;
703 const SCEVAddRecExpr *LA = cast<SCEVAddRecExpr>(LHS);
704 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS);
706 // There is always a dominance between two recs that are used by one SCEV,
707 // so we can safely sort recs by loop header dominance. We require such
708 // order in getAddExpr.
709 const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop();
710 if (LLoop != RLoop) {
711 const BasicBlock *LHead = LLoop->getHeader(), *RHead = RLoop->getHeader();
712 assert(LHead != RHead && "Two loops share the same header?");
713 if (DT.dominates(LHead, RHead))
716 assert(DT.dominates(RHead, LHead) &&
717 "No dominance between recurrences used by one SCEV?");
721 // Addrec complexity grows with operand count.
722 unsigned LNumOps = LA->getNumOperands(), RNumOps = RA->getNumOperands();
723 if (LNumOps != RNumOps)
724 return (int)LNumOps - (int)RNumOps;
726 // Lexicographically compare.
727 for (unsigned i = 0; i != LNumOps; ++i) {
728 int X = CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI,
729 LA->getOperand(i), RA->getOperand(i), DT,
734 EqCacheSCEV.unionSets(LHS, RHS);
744 const SCEVNAryExpr *LC = cast<SCEVNAryExpr>(LHS);
745 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
747 // Lexicographically compare n-ary expressions.
748 unsigned LNumOps = LC->getNumOperands(), RNumOps = RC->getNumOperands();
749 if (LNumOps != RNumOps)
750 return (int)LNumOps - (int)RNumOps;
752 for (unsigned i = 0; i != LNumOps; ++i) {
753 int X = CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI,
754 LC->getOperand(i), RC->getOperand(i), DT,
759 EqCacheSCEV.unionSets(LHS, RHS);
764 const SCEVUDivExpr *LC = cast<SCEVUDivExpr>(LHS);
765 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
767 // Lexicographically compare udiv expressions.
768 int X = CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI, LC->getLHS(),
769 RC->getLHS(), DT, Depth + 1);
772 X = CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI, LC->getRHS(),
773 RC->getRHS(), DT, Depth + 1);
775 EqCacheSCEV.unionSets(LHS, RHS);
782 const SCEVCastExpr *LC = cast<SCEVCastExpr>(LHS);
783 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
785 // Compare cast expressions by operand.
786 int X = CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI,
787 LC->getOperand(), RC->getOperand(), DT,
790 EqCacheSCEV.unionSets(LHS, RHS);
794 case scCouldNotCompute:
795 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
797 llvm_unreachable("Unknown SCEV kind!");
800 /// Given a list of SCEV objects, order them by their complexity, and group
801 /// objects of the same complexity together by value. When this routine is
802 /// finished, we know that any duplicates in the vector are consecutive and that
803 /// complexity is monotonically increasing.
805 /// Note that we go take special precautions to ensure that we get deterministic
806 /// results from this routine. In other words, we don't want the results of
807 /// this to depend on where the addresses of various SCEV objects happened to
809 static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops,
810 LoopInfo *LI, DominatorTree &DT) {
811 if (Ops.size() < 2) return; // Noop
813 EquivalenceClasses<const SCEV *> EqCacheSCEV;
814 EquivalenceClasses<const Value *> EqCacheValue;
815 if (Ops.size() == 2) {
816 // This is the common case, which also happens to be trivially simple.
818 const SCEV *&LHS = Ops[0], *&RHS = Ops[1];
819 if (CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI, RHS, LHS, DT) < 0)
824 // Do the rough sort by complexity.
825 llvm::stable_sort(Ops, [&](const SCEV *LHS, const SCEV *RHS) {
826 return CompareSCEVComplexity(EqCacheSCEV, EqCacheValue, LI, LHS, RHS, DT) <
830 // Now that we are sorted by complexity, group elements of the same
831 // complexity. Note that this is, at worst, N^2, but the vector is likely to
832 // be extremely short in practice. Note that we take this approach because we
833 // do not want to depend on the addresses of the objects we are grouping.
834 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
835 const SCEV *S = Ops[i];
836 unsigned Complexity = S->getSCEVType();
838 // If there are any objects of the same complexity and same value as this
840 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
841 if (Ops[j] == S) { // Found a duplicate.
842 // Move it to immediately after i'th element.
843 std::swap(Ops[i+1], Ops[j]);
844 ++i; // no need to rescan it.
845 if (i == e-2) return; // Done!
851 /// Returns true if \p Ops contains a huge SCEV (the subtree of S contains at
852 /// least HugeExprThreshold nodes).
853 static bool hasHugeExpression(ArrayRef<const SCEV *> Ops) {
854 return any_of(Ops, [](const SCEV *S) {
855 return S->getExpressionSize() >= HugeExprThreshold;
859 //===----------------------------------------------------------------------===//
860 // Simple SCEV method implementations
861 //===----------------------------------------------------------------------===//
863 /// Compute BC(It, K). The result has width W. Assume, K > 0.
864 static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K,
867 // Handle the simplest case efficiently.
869 return SE.getTruncateOrZeroExtend(It, ResultTy);
871 // We are using the following formula for BC(It, K):
873 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
875 // Suppose, W is the bitwidth of the return value. We must be prepared for
876 // overflow. Hence, we must assure that the result of our computation is
877 // equal to the accurate one modulo 2^W. Unfortunately, division isn't
878 // safe in modular arithmetic.
880 // However, this code doesn't use exactly that formula; the formula it uses
881 // is something like the following, where T is the number of factors of 2 in
882 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
885 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
887 // This formula is trivially equivalent to the previous formula. However,
888 // this formula can be implemented much more efficiently. The trick is that
889 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
890 // arithmetic. To do exact division in modular arithmetic, all we have
891 // to do is multiply by the inverse. Therefore, this step can be done at
894 // The next issue is how to safely do the division by 2^T. The way this
895 // is done is by doing the multiplication step at a width of at least W + T
896 // bits. This way, the bottom W+T bits of the product are accurate. Then,
897 // when we perform the division by 2^T (which is equivalent to a right shift
898 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
899 // truncated out after the division by 2^T.
901 // In comparison to just directly using the first formula, this technique
902 // is much more efficient; using the first formula requires W * K bits,
903 // but this formula less than W + K bits. Also, the first formula requires
904 // a division step, whereas this formula only requires multiplies and shifts.
906 // It doesn't matter whether the subtraction step is done in the calculation
907 // width or the input iteration count's width; if the subtraction overflows,
908 // the result must be zero anyway. We prefer here to do it in the width of
909 // the induction variable because it helps a lot for certain cases; CodeGen
910 // isn't smart enough to ignore the overflow, which leads to much less
911 // efficient code if the width of the subtraction is wider than the native
914 // (It's possible to not widen at all by pulling out factors of 2 before
915 // the multiplication; for example, K=2 can be calculated as
916 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
917 // extra arithmetic, so it's not an obvious win, and it gets
918 // much more complicated for K > 3.)
920 // Protection from insane SCEVs; this bound is conservative,
921 // but it probably doesn't matter.
923 return SE.getCouldNotCompute();
925 unsigned W = SE.getTypeSizeInBits(ResultTy);
927 // Calculate K! / 2^T and T; we divide out the factors of two before
928 // multiplying for calculating K! / 2^T to avoid overflow.
929 // Other overflow doesn't matter because we only care about the bottom
930 // W bits of the result.
931 APInt OddFactorial(W, 1);
933 for (unsigned i = 3; i <= K; ++i) {
935 unsigned TwoFactors = Mult.countTrailingZeros();
937 Mult.lshrInPlace(TwoFactors);
938 OddFactorial *= Mult;
941 // We need at least W + T bits for the multiplication step
942 unsigned CalculationBits = W + T;
944 // Calculate 2^T, at width T+W.
945 APInt DivFactor = APInt::getOneBitSet(CalculationBits, T);
947 // Calculate the multiplicative inverse of K! / 2^T;
948 // this multiplication factor will perform the exact division by
950 APInt Mod = APInt::getSignedMinValue(W+1);
951 APInt MultiplyFactor = OddFactorial.zext(W+1);
952 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
953 MultiplyFactor = MultiplyFactor.trunc(W);
955 // Calculate the product, at width T+W
956 IntegerType *CalculationTy = IntegerType::get(SE.getContext(),
958 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
959 for (unsigned i = 1; i != K; ++i) {
960 const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i));
961 Dividend = SE.getMulExpr(Dividend,
962 SE.getTruncateOrZeroExtend(S, CalculationTy));
966 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
968 // Truncate the result, and divide by K! / 2^T.
970 return SE.getMulExpr(SE.getConstant(MultiplyFactor),
971 SE.getTruncateOrZeroExtend(DivResult, ResultTy));
974 /// Return the value of this chain of recurrences at the specified iteration
975 /// number. We can evaluate this recurrence by multiplying each element in the
976 /// chain by the binomial coefficient corresponding to it. In other words, we
977 /// can evaluate {A,+,B,+,C,+,D} as:
979 /// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
981 /// where BC(It, k) stands for binomial coefficient.
982 const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It,
983 ScalarEvolution &SE) const {
984 const SCEV *Result = getStart();
985 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
986 // The computation is correct in the face of overflow provided that the
987 // multiplication is performed _after_ the evaluation of the binomial
989 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType());
990 if (isa<SCEVCouldNotCompute>(Coeff))
993 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
998 //===----------------------------------------------------------------------===//
999 // SCEV Expression folder implementations
1000 //===----------------------------------------------------------------------===//
1002 const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op, Type *Ty,
1004 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
1005 "This is not a truncating conversion!");
1006 assert(isSCEVable(Ty) &&
1007 "This is not a conversion to a SCEVable type!");
1008 Ty = getEffectiveSCEVType(Ty);
1010 FoldingSetNodeID ID;
1011 ID.AddInteger(scTruncate);
1015 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1017 // Fold if the operand is constant.
1018 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1020 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty)));
1022 // trunc(trunc(x)) --> trunc(x)
1023 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
1024 return getTruncateExpr(ST->getOperand(), Ty, Depth + 1);
1026 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
1027 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1028 return getTruncateOrSignExtend(SS->getOperand(), Ty, Depth + 1);
1030 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
1031 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1032 return getTruncateOrZeroExtend(SZ->getOperand(), Ty, Depth + 1);
1034 if (Depth > MaxCastDepth) {
1036 new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator), Op, Ty);
1037 UniqueSCEVs.InsertNode(S, IP);
1038 addToLoopUseLists(S);
1042 // trunc(x1 + ... + xN) --> trunc(x1) + ... + trunc(xN) and
1043 // trunc(x1 * ... * xN) --> trunc(x1) * ... * trunc(xN),
1044 // if after transforming we have at most one truncate, not counting truncates
1045 // that replace other casts.
1046 if (isa<SCEVAddExpr>(Op) || isa<SCEVMulExpr>(Op)) {
1047 auto *CommOp = cast<SCEVCommutativeExpr>(Op);
1048 SmallVector<const SCEV *, 4> Operands;
1049 unsigned numTruncs = 0;
1050 for (unsigned i = 0, e = CommOp->getNumOperands(); i != e && numTruncs < 2;
1052 const SCEV *S = getTruncateExpr(CommOp->getOperand(i), Ty, Depth + 1);
1053 if (!isa<SCEVCastExpr>(CommOp->getOperand(i)) && isa<SCEVTruncateExpr>(S))
1055 Operands.push_back(S);
1057 if (numTruncs < 2) {
1058 if (isa<SCEVAddExpr>(Op))
1059 return getAddExpr(Operands);
1060 else if (isa<SCEVMulExpr>(Op))
1061 return getMulExpr(Operands);
1063 llvm_unreachable("Unexpected SCEV type for Op.");
1065 // Although we checked in the beginning that ID is not in the cache, it is
1066 // possible that during recursion and different modification ID was inserted
1067 // into the cache. So if we find it, just return it.
1068 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP))
1072 // If the input value is a chrec scev, truncate the chrec's operands.
1073 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
1074 SmallVector<const SCEV *, 4> Operands;
1075 for (const SCEV *Op : AddRec->operands())
1076 Operands.push_back(getTruncateExpr(Op, Ty, Depth + 1));
1077 return getAddRecExpr(Operands, AddRec->getLoop(), SCEV::FlagAnyWrap);
1080 // The cast wasn't folded; create an explicit cast node. We can reuse
1081 // the existing insert position since if we get here, we won't have
1082 // made any changes which would invalidate it.
1083 SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator),
1085 UniqueSCEVs.InsertNode(S, IP);
1086 addToLoopUseLists(S);
1090 // Get the limit of a recurrence such that incrementing by Step cannot cause
1091 // signed overflow as long as the value of the recurrence within the
1092 // loop does not exceed this limit before incrementing.
1093 static const SCEV *getSignedOverflowLimitForStep(const SCEV *Step,
1094 ICmpInst::Predicate *Pred,
1095 ScalarEvolution *SE) {
1096 unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
1097 if (SE->isKnownPositive(Step)) {
1098 *Pred = ICmpInst::ICMP_SLT;
1099 return SE->getConstant(APInt::getSignedMinValue(BitWidth) -
1100 SE->getSignedRangeMax(Step));
1102 if (SE->isKnownNegative(Step)) {
1103 *Pred = ICmpInst::ICMP_SGT;
1104 return SE->getConstant(APInt::getSignedMaxValue(BitWidth) -
1105 SE->getSignedRangeMin(Step));
1110 // Get the limit of a recurrence such that incrementing by Step cannot cause
1111 // unsigned overflow as long as the value of the recurrence within the loop does
1112 // not exceed this limit before incrementing.
1113 static const SCEV *getUnsignedOverflowLimitForStep(const SCEV *Step,
1114 ICmpInst::Predicate *Pred,
1115 ScalarEvolution *SE) {
1116 unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
1117 *Pred = ICmpInst::ICMP_ULT;
1119 return SE->getConstant(APInt::getMinValue(BitWidth) -
1120 SE->getUnsignedRangeMax(Step));
1125 struct ExtendOpTraitsBase {
1126 typedef const SCEV *(ScalarEvolution::*GetExtendExprTy)(const SCEV *, Type *,
1130 // Used to make code generic over signed and unsigned overflow.
1131 template <typename ExtendOp> struct ExtendOpTraits {
1134 // static const SCEV::NoWrapFlags WrapType;
1136 // static const ExtendOpTraitsBase::GetExtendExprTy GetExtendExpr;
1138 // static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1139 // ICmpInst::Predicate *Pred,
1140 // ScalarEvolution *SE);
1144 struct ExtendOpTraits<SCEVSignExtendExpr> : public ExtendOpTraitsBase {
1145 static const SCEV::NoWrapFlags WrapType = SCEV::FlagNSW;
1147 static const GetExtendExprTy GetExtendExpr;
1149 static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1150 ICmpInst::Predicate *Pred,
1151 ScalarEvolution *SE) {
1152 return getSignedOverflowLimitForStep(Step, Pred, SE);
1156 const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits<
1157 SCEVSignExtendExpr>::GetExtendExpr = &ScalarEvolution::getSignExtendExpr;
1160 struct ExtendOpTraits<SCEVZeroExtendExpr> : public ExtendOpTraitsBase {
1161 static const SCEV::NoWrapFlags WrapType = SCEV::FlagNUW;
1163 static const GetExtendExprTy GetExtendExpr;
1165 static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1166 ICmpInst::Predicate *Pred,
1167 ScalarEvolution *SE) {
1168 return getUnsignedOverflowLimitForStep(Step, Pred, SE);
1172 const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits<
1173 SCEVZeroExtendExpr>::GetExtendExpr = &ScalarEvolution::getZeroExtendExpr;
1175 } // end anonymous namespace
1177 // The recurrence AR has been shown to have no signed/unsigned wrap or something
1178 // close to it. Typically, if we can prove NSW/NUW for AR, then we can just as
1179 // easily prove NSW/NUW for its preincrement or postincrement sibling. This
1180 // allows normalizing a sign/zero extended AddRec as such: {sext/zext(Step +
1181 // Start),+,Step} => {(Step + sext/zext(Start),+,Step} As a result, the
1182 // expression "Step + sext/zext(PreIncAR)" is congruent with
1183 // "sext/zext(PostIncAR)"
1184 template <typename ExtendOpTy>
1185 static const SCEV *getPreStartForExtend(const SCEVAddRecExpr *AR, Type *Ty,
1186 ScalarEvolution *SE, unsigned Depth) {
1187 auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType;
1188 auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr;
1190 const Loop *L = AR->getLoop();
1191 const SCEV *Start = AR->getStart();
1192 const SCEV *Step = AR->getStepRecurrence(*SE);
1194 // Check for a simple looking step prior to loop entry.
1195 const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Start);
1199 // Create an AddExpr for "PreStart" after subtracting Step. Full SCEV
1200 // subtraction is expensive. For this purpose, perform a quick and dirty
1201 // difference, by checking for Step in the operand list.
1202 SmallVector<const SCEV *, 4> DiffOps;
1203 for (const SCEV *Op : SA->operands())
1205 DiffOps.push_back(Op);
1207 if (DiffOps.size() == SA->getNumOperands())
1210 // Try to prove `WrapType` (SCEV::FlagNSW or SCEV::FlagNUW) on `PreStart` +
1213 // 1. NSW/NUW flags on the step increment.
1214 auto PreStartFlags =
1215 ScalarEvolution::maskFlags(SA->getNoWrapFlags(), SCEV::FlagNUW);
1216 const SCEV *PreStart = SE->getAddExpr(DiffOps, PreStartFlags);
1217 const SCEVAddRecExpr *PreAR = dyn_cast<SCEVAddRecExpr>(
1218 SE->getAddRecExpr(PreStart, Step, L, SCEV::FlagAnyWrap));
1220 // "{S,+,X} is <nsw>/<nuw>" and "the backedge is taken at least once" implies
1221 // "S+X does not sign/unsign-overflow".
1224 const SCEV *BECount = SE->getBackedgeTakenCount(L);
1225 if (PreAR && PreAR->getNoWrapFlags(WrapType) &&
1226 !isa<SCEVCouldNotCompute>(BECount) && SE->isKnownPositive(BECount))
1229 // 2. Direct overflow check on the step operation's expression.
1230 unsigned BitWidth = SE->getTypeSizeInBits(AR->getType());
1231 Type *WideTy = IntegerType::get(SE->getContext(), BitWidth * 2);
1232 const SCEV *OperandExtendedStart =
1233 SE->getAddExpr((SE->*GetExtendExpr)(PreStart, WideTy, Depth),
1234 (SE->*GetExtendExpr)(Step, WideTy, Depth));
1235 if ((SE->*GetExtendExpr)(Start, WideTy, Depth) == OperandExtendedStart) {
1236 if (PreAR && AR->getNoWrapFlags(WrapType)) {
1237 // If we know `AR` == {`PreStart`+`Step`,+,`Step`} is `WrapType` (FlagNSW
1238 // or FlagNUW) and that `PreStart` + `Step` is `WrapType` too, then
1239 // `PreAR` == {`PreStart`,+,`Step`} is also `WrapType`. Cache this fact.
1240 const_cast<SCEVAddRecExpr *>(PreAR)->setNoWrapFlags(WrapType);
1245 // 3. Loop precondition.
1246 ICmpInst::Predicate Pred;
1247 const SCEV *OverflowLimit =
1248 ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep(Step, &Pred, SE);
1250 if (OverflowLimit &&
1251 SE->isLoopEntryGuardedByCond(L, Pred, PreStart, OverflowLimit))
1257 // Get the normalized zero or sign extended expression for this AddRec's Start.
1258 template <typename ExtendOpTy>
1259 static const SCEV *getExtendAddRecStart(const SCEVAddRecExpr *AR, Type *Ty,
1260 ScalarEvolution *SE,
1262 auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr;
1264 const SCEV *PreStart = getPreStartForExtend<ExtendOpTy>(AR, Ty, SE, Depth);
1266 return (SE->*GetExtendExpr)(AR->getStart(), Ty, Depth);
1268 return SE->getAddExpr((SE->*GetExtendExpr)(AR->getStepRecurrence(*SE), Ty,
1270 (SE->*GetExtendExpr)(PreStart, Ty, Depth));
1273 // Try to prove away overflow by looking at "nearby" add recurrences. A
1274 // motivating example for this rule: if we know `{0,+,4}` is `ult` `-1` and it
1275 // does not itself wrap then we can conclude that `{1,+,4}` is `nuw`.
1279 // {S,+,X} == {S-T,+,X} + T
1280 // => Ext({S,+,X}) == Ext({S-T,+,X} + T)
1282 // If ({S-T,+,X} + T) does not overflow ... (1)
1284 // RHS == Ext({S-T,+,X} + T) == Ext({S-T,+,X}) + Ext(T)
1286 // If {S-T,+,X} does not overflow ... (2)
1288 // RHS == Ext({S-T,+,X}) + Ext(T) == {Ext(S-T),+,Ext(X)} + Ext(T)
1289 // == {Ext(S-T)+Ext(T),+,Ext(X)}
1291 // If (S-T)+T does not overflow ... (3)
1293 // RHS == {Ext(S-T)+Ext(T),+,Ext(X)} == {Ext(S-T+T),+,Ext(X)}
1294 // == {Ext(S),+,Ext(X)} == LHS
1296 // Thus, if (1), (2) and (3) are true for some T, then
1297 // Ext({S,+,X}) == {Ext(S),+,Ext(X)}
1299 // (3) is implied by (1) -- "(S-T)+T does not overflow" is simply "({S-T,+,X}+T)
1300 // does not overflow" restricted to the 0th iteration. Therefore we only need
1301 // to check for (1) and (2).
1303 // In the current context, S is `Start`, X is `Step`, Ext is `ExtendOpTy` and T
1304 // is `Delta` (defined below).
1305 template <typename ExtendOpTy>
1306 bool ScalarEvolution::proveNoWrapByVaryingStart(const SCEV *Start,
1309 auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType;
1311 // We restrict `Start` to a constant to prevent SCEV from spending too much
1312 // time here. It is correct (but more expensive) to continue with a
1313 // non-constant `Start` and do a general SCEV subtraction to compute
1314 // `PreStart` below.
1315 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start);
1319 APInt StartAI = StartC->getAPInt();
1321 for (unsigned Delta : {-2, -1, 1, 2}) {
1322 const SCEV *PreStart = getConstant(StartAI - Delta);
1324 FoldingSetNodeID ID;
1325 ID.AddInteger(scAddRecExpr);
1326 ID.AddPointer(PreStart);
1327 ID.AddPointer(Step);
1331 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1333 // Give up if we don't already have the add recurrence we need because
1334 // actually constructing an add recurrence is relatively expensive.
1335 if (PreAR && PreAR->getNoWrapFlags(WrapType)) { // proves (2)
1336 const SCEV *DeltaS = getConstant(StartC->getType(), Delta);
1337 ICmpInst::Predicate Pred = ICmpInst::BAD_ICMP_PREDICATE;
1338 const SCEV *Limit = ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep(
1339 DeltaS, &Pred, this);
1340 if (Limit && isKnownPredicate(Pred, PreAR, Limit)) // proves (1)
1348 // Finds an integer D for an expression (C + x + y + ...) such that the top
1349 // level addition in (D + (C - D + x + y + ...)) would not wrap (signed or
1350 // unsigned) and the number of trailing zeros of (C - D + x + y + ...) is
1351 // maximized, where C is the \p ConstantTerm, x, y, ... are arbitrary SCEVs, and
1352 // the (C + x + y + ...) expression is \p WholeAddExpr.
1353 static APInt extractConstantWithoutWrapping(ScalarEvolution &SE,
1354 const SCEVConstant *ConstantTerm,
1355 const SCEVAddExpr *WholeAddExpr) {
1356 const APInt &C = ConstantTerm->getAPInt();
1357 const unsigned BitWidth = C.getBitWidth();
1358 // Find number of trailing zeros of (x + y + ...) w/o the C first:
1359 uint32_t TZ = BitWidth;
1360 for (unsigned I = 1, E = WholeAddExpr->getNumOperands(); I < E && TZ; ++I)
1361 TZ = std::min(TZ, SE.GetMinTrailingZeros(WholeAddExpr->getOperand(I)));
1363 // Set D to be as many least significant bits of C as possible while still
1364 // guaranteeing that adding D to (C - D + x + y + ...) won't cause a wrap:
1365 return TZ < BitWidth ? C.trunc(TZ).zext(BitWidth) : C;
1367 return APInt(BitWidth, 0);
1370 // Finds an integer D for an affine AddRec expression {C,+,x} such that the top
1371 // level addition in (D + {C-D,+,x}) would not wrap (signed or unsigned) and the
1372 // number of trailing zeros of (C - D + x * n) is maximized, where C is the \p
1373 // ConstantStart, x is an arbitrary \p Step, and n is the loop trip count.
1374 static APInt extractConstantWithoutWrapping(ScalarEvolution &SE,
1375 const APInt &ConstantStart,
1377 const unsigned BitWidth = ConstantStart.getBitWidth();
1378 const uint32_t TZ = SE.GetMinTrailingZeros(Step);
1380 return TZ < BitWidth ? ConstantStart.trunc(TZ).zext(BitWidth)
1382 return APInt(BitWidth, 0);
1386 ScalarEvolution::getZeroExtendExpr(const SCEV *Op, Type *Ty, unsigned Depth) {
1387 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1388 "This is not an extending conversion!");
1389 assert(isSCEVable(Ty) &&
1390 "This is not a conversion to a SCEVable type!");
1391 Ty = getEffectiveSCEVType(Ty);
1393 // Fold if the operand is constant.
1394 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1396 cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(), Ty)));
1398 // zext(zext(x)) --> zext(x)
1399 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1400 return getZeroExtendExpr(SZ->getOperand(), Ty, Depth + 1);
1402 // Before doing any expensive analysis, check to see if we've already
1403 // computed a SCEV for this Op and Ty.
1404 FoldingSetNodeID ID;
1405 ID.AddInteger(scZeroExtend);
1409 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1410 if (Depth > MaxCastDepth) {
1411 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
1413 UniqueSCEVs.InsertNode(S, IP);
1414 addToLoopUseLists(S);
1418 // zext(trunc(x)) --> zext(x) or x or trunc(x)
1419 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1420 // It's possible the bits taken off by the truncate were all zero bits. If
1421 // so, we should be able to simplify this further.
1422 const SCEV *X = ST->getOperand();
1423 ConstantRange CR = getUnsignedRange(X);
1424 unsigned TruncBits = getTypeSizeInBits(ST->getType());
1425 unsigned NewBits = getTypeSizeInBits(Ty);
1426 if (CR.truncate(TruncBits).zeroExtend(NewBits).contains(
1427 CR.zextOrTrunc(NewBits)))
1428 return getTruncateOrZeroExtend(X, Ty, Depth);
1431 // If the input value is a chrec scev, and we can prove that the value
1432 // did not overflow the old, smaller, value, we can zero extend all of the
1433 // operands (often constants). This allows analysis of something like
1434 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
1435 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1436 if (AR->isAffine()) {
1437 const SCEV *Start = AR->getStart();
1438 const SCEV *Step = AR->getStepRecurrence(*this);
1439 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1440 const Loop *L = AR->getLoop();
1442 if (!AR->hasNoUnsignedWrap()) {
1443 auto NewFlags = proveNoWrapViaConstantRanges(AR);
1444 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(NewFlags);
1447 // If we have special knowledge that this addrec won't overflow,
1448 // we don't need to do any further analysis.
1449 if (AR->hasNoUnsignedWrap())
1450 return getAddRecExpr(
1451 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this, Depth + 1),
1452 getZeroExtendExpr(Step, Ty, Depth + 1), L, AR->getNoWrapFlags());
1454 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1455 // Note that this serves two purposes: It filters out loops that are
1456 // simply not analyzable, and it covers the case where this code is
1457 // being called from within backedge-taken count analysis, such that
1458 // attempting to ask for the backedge-taken count would likely result
1459 // in infinite recursion. In the later case, the analysis code will
1460 // cope with a conservative value, and it will take care to purge
1461 // that value once it has finished.
1462 const SCEV *MaxBECount = getConstantMaxBackedgeTakenCount(L);
1463 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1464 // Manually compute the final value for AR, checking for
1467 // Check whether the backedge-taken count can be losslessly casted to
1468 // the addrec's type. The count is always unsigned.
1469 const SCEV *CastedMaxBECount =
1470 getTruncateOrZeroExtend(MaxBECount, Start->getType(), Depth);
1471 const SCEV *RecastedMaxBECount = getTruncateOrZeroExtend(
1472 CastedMaxBECount, MaxBECount->getType(), Depth);
1473 if (MaxBECount == RecastedMaxBECount) {
1474 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1475 // Check whether Start+Step*MaxBECount has no unsigned overflow.
1476 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step,
1477 SCEV::FlagAnyWrap, Depth + 1);
1478 const SCEV *ZAdd = getZeroExtendExpr(getAddExpr(Start, ZMul,
1482 const SCEV *WideStart = getZeroExtendExpr(Start, WideTy, Depth + 1);
1483 const SCEV *WideMaxBECount =
1484 getZeroExtendExpr(CastedMaxBECount, WideTy, Depth + 1);
1485 const SCEV *OperandExtendedAdd =
1486 getAddExpr(WideStart,
1487 getMulExpr(WideMaxBECount,
1488 getZeroExtendExpr(Step, WideTy, Depth + 1),
1489 SCEV::FlagAnyWrap, Depth + 1),
1490 SCEV::FlagAnyWrap, Depth + 1);
1491 if (ZAdd == OperandExtendedAdd) {
1492 // Cache knowledge of AR NUW, which is propagated to this AddRec.
1493 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1494 // Return the expression with the addrec on the outside.
1495 return getAddRecExpr(
1496 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this,
1498 getZeroExtendExpr(Step, Ty, Depth + 1), L,
1499 AR->getNoWrapFlags());
1501 // Similar to above, only this time treat the step value as signed.
1502 // This covers loops that count down.
1503 OperandExtendedAdd =
1504 getAddExpr(WideStart,
1505 getMulExpr(WideMaxBECount,
1506 getSignExtendExpr(Step, WideTy, Depth + 1),
1507 SCEV::FlagAnyWrap, Depth + 1),
1508 SCEV::FlagAnyWrap, Depth + 1);
1509 if (ZAdd == OperandExtendedAdd) {
1510 // Cache knowledge of AR NW, which is propagated to this AddRec.
1511 // Negative step causes unsigned wrap, but it still can't self-wrap.
1512 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1513 // Return the expression with the addrec on the outside.
1514 return getAddRecExpr(
1515 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this,
1517 getSignExtendExpr(Step, Ty, Depth + 1), L,
1518 AR->getNoWrapFlags());
1523 // Normally, in the cases we can prove no-overflow via a
1524 // backedge guarding condition, we can also compute a backedge
1525 // taken count for the loop. The exceptions are assumptions and
1526 // guards present in the loop -- SCEV is not great at exploiting
1527 // these to compute max backedge taken counts, but can still use
1528 // these to prove lack of overflow. Use this fact to avoid
1529 // doing extra work that may not pay off.
1530 if (!isa<SCEVCouldNotCompute>(MaxBECount) || HasGuards ||
1531 !AC.assumptions().empty()) {
1532 // If the backedge is guarded by a comparison with the pre-inc
1533 // value the addrec is safe. Also, if the entry is guarded by
1534 // a comparison with the start value and the backedge is
1535 // guarded by a comparison with the post-inc value, the addrec
1537 if (isKnownPositive(Step)) {
1538 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
1539 getUnsignedRangeMax(Step));
1540 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
1541 isKnownOnEveryIteration(ICmpInst::ICMP_ULT, AR, N)) {
1542 // Cache knowledge of AR NUW, which is propagated to this
1544 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1545 // Return the expression with the addrec on the outside.
1546 return getAddRecExpr(
1547 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this,
1549 getZeroExtendExpr(Step, Ty, Depth + 1), L,
1550 AR->getNoWrapFlags());
1552 } else if (isKnownNegative(Step)) {
1553 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
1554 getSignedRangeMin(Step));
1555 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) ||
1556 isKnownOnEveryIteration(ICmpInst::ICMP_UGT, AR, N)) {
1557 // Cache knowledge of AR NW, which is propagated to this
1558 // AddRec. Negative step causes unsigned wrap, but it
1559 // still can't self-wrap.
1560 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1561 // Return the expression with the addrec on the outside.
1562 return getAddRecExpr(
1563 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this,
1565 getSignExtendExpr(Step, Ty, Depth + 1), L,
1566 AR->getNoWrapFlags());
1571 // zext({C,+,Step}) --> (zext(D) + zext({C-D,+,Step}))<nuw><nsw>
1572 // if D + (C - D + Step * n) could be proven to not unsigned wrap
1573 // where D maximizes the number of trailing zeros of (C - D + Step * n)
1574 if (const auto *SC = dyn_cast<SCEVConstant>(Start)) {
1575 const APInt &C = SC->getAPInt();
1576 const APInt &D = extractConstantWithoutWrapping(*this, C, Step);
1578 const SCEV *SZExtD = getZeroExtendExpr(getConstant(D), Ty, Depth);
1579 const SCEV *SResidual =
1580 getAddRecExpr(getConstant(C - D), Step, L, AR->getNoWrapFlags());
1581 const SCEV *SZExtR = getZeroExtendExpr(SResidual, Ty, Depth + 1);
1582 return getAddExpr(SZExtD, SZExtR,
1583 (SCEV::NoWrapFlags)(SCEV::FlagNSW | SCEV::FlagNUW),
1588 if (proveNoWrapByVaryingStart<SCEVZeroExtendExpr>(Start, Step, L)) {
1589 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1590 return getAddRecExpr(
1591 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this, Depth + 1),
1592 getZeroExtendExpr(Step, Ty, Depth + 1), L, AR->getNoWrapFlags());
1596 // zext(A % B) --> zext(A) % zext(B)
1600 if (matchURem(Op, LHS, RHS))
1601 return getURemExpr(getZeroExtendExpr(LHS, Ty, Depth + 1),
1602 getZeroExtendExpr(RHS, Ty, Depth + 1));
1605 // zext(A / B) --> zext(A) / zext(B).
1606 if (auto *Div = dyn_cast<SCEVUDivExpr>(Op))
1607 return getUDivExpr(getZeroExtendExpr(Div->getLHS(), Ty, Depth + 1),
1608 getZeroExtendExpr(Div->getRHS(), Ty, Depth + 1));
1610 if (auto *SA = dyn_cast<SCEVAddExpr>(Op)) {
1611 // zext((A + B + ...)<nuw>) --> (zext(A) + zext(B) + ...)<nuw>
1612 if (SA->hasNoUnsignedWrap()) {
1613 // If the addition does not unsign overflow then we can, by definition,
1614 // commute the zero extension with the addition operation.
1615 SmallVector<const SCEV *, 4> Ops;
1616 for (const auto *Op : SA->operands())
1617 Ops.push_back(getZeroExtendExpr(Op, Ty, Depth + 1));
1618 return getAddExpr(Ops, SCEV::FlagNUW, Depth + 1);
1621 // zext(C + x + y + ...) --> (zext(D) + zext((C - D) + x + y + ...))
1622 // if D + (C - D + x + y + ...) could be proven to not unsigned wrap
1623 // where D maximizes the number of trailing zeros of (C - D + x + y + ...)
1625 // Often address arithmetics contain expressions like
1626 // (zext (add (shl X, C1), C2)), for instance, (zext (5 + (4 * X))).
1627 // This transformation is useful while proving that such expressions are
1628 // equal or differ by a small constant amount, see LoadStoreVectorizer pass.
1629 if (const auto *SC = dyn_cast<SCEVConstant>(SA->getOperand(0))) {
1630 const APInt &D = extractConstantWithoutWrapping(*this, SC, SA);
1632 const SCEV *SZExtD = getZeroExtendExpr(getConstant(D), Ty, Depth);
1633 const SCEV *SResidual =
1634 getAddExpr(getConstant(-D), SA, SCEV::FlagAnyWrap, Depth);
1635 const SCEV *SZExtR = getZeroExtendExpr(SResidual, Ty, Depth + 1);
1636 return getAddExpr(SZExtD, SZExtR,
1637 (SCEV::NoWrapFlags)(SCEV::FlagNSW | SCEV::FlagNUW),
1643 if (auto *SM = dyn_cast<SCEVMulExpr>(Op)) {
1644 // zext((A * B * ...)<nuw>) --> (zext(A) * zext(B) * ...)<nuw>
1645 if (SM->hasNoUnsignedWrap()) {
1646 // If the multiply does not unsign overflow then we can, by definition,
1647 // commute the zero extension with the multiply operation.
1648 SmallVector<const SCEV *, 4> Ops;
1649 for (const auto *Op : SM->operands())
1650 Ops.push_back(getZeroExtendExpr(Op, Ty, Depth + 1));
1651 return getMulExpr(Ops, SCEV::FlagNUW, Depth + 1);
1654 // zext(2^K * (trunc X to iN)) to iM ->
1655 // 2^K * (zext(trunc X to i{N-K}) to iM)<nuw>
1659 // zext(2^K * (trunc X to iN)) to iM
1660 // = zext((trunc X to iN) << K) to iM
1661 // = zext((trunc X to i{N-K}) << K)<nuw> to iM
1662 // (because shl removes the top K bits)
1663 // = zext((2^K * (trunc X to i{N-K}))<nuw>) to iM
1664 // = (2^K * (zext(trunc X to i{N-K}) to iM))<nuw>.
1666 if (SM->getNumOperands() == 2)
1667 if (auto *MulLHS = dyn_cast<SCEVConstant>(SM->getOperand(0)))
1668 if (MulLHS->getAPInt().isPowerOf2())
1669 if (auto *TruncRHS = dyn_cast<SCEVTruncateExpr>(SM->getOperand(1))) {
1670 int NewTruncBits = getTypeSizeInBits(TruncRHS->getType()) -
1671 MulLHS->getAPInt().logBase2();
1672 Type *NewTruncTy = IntegerType::get(getContext(), NewTruncBits);
1674 getZeroExtendExpr(MulLHS, Ty),
1676 getTruncateExpr(TruncRHS->getOperand(), NewTruncTy), Ty),
1677 SCEV::FlagNUW, Depth + 1);
1681 // The cast wasn't folded; create an explicit cast node.
1682 // Recompute the insert position, as it may have been invalidated.
1683 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1684 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
1686 UniqueSCEVs.InsertNode(S, IP);
1687 addToLoopUseLists(S);
1692 ScalarEvolution::getSignExtendExpr(const SCEV *Op, Type *Ty, unsigned Depth) {
1693 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1694 "This is not an extending conversion!");
1695 assert(isSCEVable(Ty) &&
1696 "This is not a conversion to a SCEVable type!");
1697 Ty = getEffectiveSCEVType(Ty);
1699 // Fold if the operand is constant.
1700 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1702 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), Ty)));
1704 // sext(sext(x)) --> sext(x)
1705 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1706 return getSignExtendExpr(SS->getOperand(), Ty, Depth + 1);
1708 // sext(zext(x)) --> zext(x)
1709 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1710 return getZeroExtendExpr(SZ->getOperand(), Ty, Depth + 1);
1712 // Before doing any expensive analysis, check to see if we've already
1713 // computed a SCEV for this Op and Ty.
1714 FoldingSetNodeID ID;
1715 ID.AddInteger(scSignExtend);
1719 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1720 // Limit recursion depth.
1721 if (Depth > MaxCastDepth) {
1722 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
1724 UniqueSCEVs.InsertNode(S, IP);
1725 addToLoopUseLists(S);
1729 // sext(trunc(x)) --> sext(x) or x or trunc(x)
1730 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1731 // It's possible the bits taken off by the truncate were all sign bits. If
1732 // so, we should be able to simplify this further.
1733 const SCEV *X = ST->getOperand();
1734 ConstantRange CR = getSignedRange(X);
1735 unsigned TruncBits = getTypeSizeInBits(ST->getType());
1736 unsigned NewBits = getTypeSizeInBits(Ty);
1737 if (CR.truncate(TruncBits).signExtend(NewBits).contains(
1738 CR.sextOrTrunc(NewBits)))
1739 return getTruncateOrSignExtend(X, Ty, Depth);
1742 if (auto *SA = dyn_cast<SCEVAddExpr>(Op)) {
1743 // sext((A + B + ...)<nsw>) --> (sext(A) + sext(B) + ...)<nsw>
1744 if (SA->hasNoSignedWrap()) {
1745 // If the addition does not sign overflow then we can, by definition,
1746 // commute the sign extension with the addition operation.
1747 SmallVector<const SCEV *, 4> Ops;
1748 for (const auto *Op : SA->operands())
1749 Ops.push_back(getSignExtendExpr(Op, Ty, Depth + 1));
1750 return getAddExpr(Ops, SCEV::FlagNSW, Depth + 1);
1753 // sext(C + x + y + ...) --> (sext(D) + sext((C - D) + x + y + ...))
1754 // if D + (C - D + x + y + ...) could be proven to not signed wrap
1755 // where D maximizes the number of trailing zeros of (C - D + x + y + ...)
1757 // For instance, this will bring two seemingly different expressions:
1758 // 1 + sext(5 + 20 * %x + 24 * %y) and
1759 // sext(6 + 20 * %x + 24 * %y)
1760 // to the same form:
1761 // 2 + sext(4 + 20 * %x + 24 * %y)
1762 if (const auto *SC = dyn_cast<SCEVConstant>(SA->getOperand(0))) {
1763 const APInt &D = extractConstantWithoutWrapping(*this, SC, SA);
1765 const SCEV *SSExtD = getSignExtendExpr(getConstant(D), Ty, Depth);
1766 const SCEV *SResidual =
1767 getAddExpr(getConstant(-D), SA, SCEV::FlagAnyWrap, Depth);
1768 const SCEV *SSExtR = getSignExtendExpr(SResidual, Ty, Depth + 1);
1769 return getAddExpr(SSExtD, SSExtR,
1770 (SCEV::NoWrapFlags)(SCEV::FlagNSW | SCEV::FlagNUW),
1775 // If the input value is a chrec scev, and we can prove that the value
1776 // did not overflow the old, smaller, value, we can sign extend all of the
1777 // operands (often constants). This allows analysis of something like
1778 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
1779 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1780 if (AR->isAffine()) {
1781 const SCEV *Start = AR->getStart();
1782 const SCEV *Step = AR->getStepRecurrence(*this);
1783 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1784 const Loop *L = AR->getLoop();
1786 if (!AR->hasNoSignedWrap()) {
1787 auto NewFlags = proveNoWrapViaConstantRanges(AR);
1788 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(NewFlags);
1791 // If we have special knowledge that this addrec won't overflow,
1792 // we don't need to do any further analysis.
1793 if (AR->hasNoSignedWrap())
1794 return getAddRecExpr(
1795 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this, Depth + 1),
1796 getSignExtendExpr(Step, Ty, Depth + 1), L, SCEV::FlagNSW);
1798 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1799 // Note that this serves two purposes: It filters out loops that are
1800 // simply not analyzable, and it covers the case where this code is
1801 // being called from within backedge-taken count analysis, such that
1802 // attempting to ask for the backedge-taken count would likely result
1803 // in infinite recursion. In the later case, the analysis code will
1804 // cope with a conservative value, and it will take care to purge
1805 // that value once it has finished.
1806 const SCEV *MaxBECount = getConstantMaxBackedgeTakenCount(L);
1807 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1808 // Manually compute the final value for AR, checking for
1811 // Check whether the backedge-taken count can be losslessly casted to
1812 // the addrec's type. The count is always unsigned.
1813 const SCEV *CastedMaxBECount =
1814 getTruncateOrZeroExtend(MaxBECount, Start->getType(), Depth);
1815 const SCEV *RecastedMaxBECount = getTruncateOrZeroExtend(
1816 CastedMaxBECount, MaxBECount->getType(), Depth);
1817 if (MaxBECount == RecastedMaxBECount) {
1818 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1819 // Check whether Start+Step*MaxBECount has no signed overflow.
1820 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step,
1821 SCEV::FlagAnyWrap, Depth + 1);
1822 const SCEV *SAdd = getSignExtendExpr(getAddExpr(Start, SMul,
1826 const SCEV *WideStart = getSignExtendExpr(Start, WideTy, Depth + 1);
1827 const SCEV *WideMaxBECount =
1828 getZeroExtendExpr(CastedMaxBECount, WideTy, Depth + 1);
1829 const SCEV *OperandExtendedAdd =
1830 getAddExpr(WideStart,
1831 getMulExpr(WideMaxBECount,
1832 getSignExtendExpr(Step, WideTy, Depth + 1),
1833 SCEV::FlagAnyWrap, Depth + 1),
1834 SCEV::FlagAnyWrap, Depth + 1);
1835 if (SAdd == OperandExtendedAdd) {
1836 // Cache knowledge of AR NSW, which is propagated to this AddRec.
1837 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1838 // Return the expression with the addrec on the outside.
1839 return getAddRecExpr(
1840 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this,
1842 getSignExtendExpr(Step, Ty, Depth + 1), L,
1843 AR->getNoWrapFlags());
1845 // Similar to above, only this time treat the step value as unsigned.
1846 // This covers loops that count up with an unsigned step.
1847 OperandExtendedAdd =
1848 getAddExpr(WideStart,
1849 getMulExpr(WideMaxBECount,
1850 getZeroExtendExpr(Step, WideTy, Depth + 1),
1851 SCEV::FlagAnyWrap, Depth + 1),
1852 SCEV::FlagAnyWrap, Depth + 1);
1853 if (SAdd == OperandExtendedAdd) {
1854 // If AR wraps around then
1856 // abs(Step) * MaxBECount > unsigned-max(AR->getType())
1857 // => SAdd != OperandExtendedAdd
1859 // Thus (AR is not NW => SAdd != OperandExtendedAdd) <=>
1860 // (SAdd == OperandExtendedAdd => AR is NW)
1862 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1864 // Return the expression with the addrec on the outside.
1865 return getAddRecExpr(
1866 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this,
1868 getZeroExtendExpr(Step, Ty, Depth + 1), L,
1869 AR->getNoWrapFlags());
1874 // Normally, in the cases we can prove no-overflow via a
1875 // backedge guarding condition, we can also compute a backedge
1876 // taken count for the loop. The exceptions are assumptions and
1877 // guards present in the loop -- SCEV is not great at exploiting
1878 // these to compute max backedge taken counts, but can still use
1879 // these to prove lack of overflow. Use this fact to avoid
1880 // doing extra work that may not pay off.
1882 if (!isa<SCEVCouldNotCompute>(MaxBECount) || HasGuards ||
1883 !AC.assumptions().empty()) {
1884 // If the backedge is guarded by a comparison with the pre-inc
1885 // value the addrec is safe. Also, if the entry is guarded by
1886 // a comparison with the start value and the backedge is
1887 // guarded by a comparison with the post-inc value, the addrec
1889 ICmpInst::Predicate Pred;
1890 const SCEV *OverflowLimit =
1891 getSignedOverflowLimitForStep(Step, &Pred, this);
1892 if (OverflowLimit &&
1893 (isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) ||
1894 isKnownOnEveryIteration(Pred, AR, OverflowLimit))) {
1895 // Cache knowledge of AR NSW, then propagate NSW to the wide AddRec.
1896 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1897 return getAddRecExpr(
1898 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this, Depth + 1),
1899 getSignExtendExpr(Step, Ty, Depth + 1), L, AR->getNoWrapFlags());
1903 // sext({C,+,Step}) --> (sext(D) + sext({C-D,+,Step}))<nuw><nsw>
1904 // if D + (C - D + Step * n) could be proven to not signed wrap
1905 // where D maximizes the number of trailing zeros of (C - D + Step * n)
1906 if (const auto *SC = dyn_cast<SCEVConstant>(Start)) {
1907 const APInt &C = SC->getAPInt();
1908 const APInt &D = extractConstantWithoutWrapping(*this, C, Step);
1910 const SCEV *SSExtD = getSignExtendExpr(getConstant(D), Ty, Depth);
1911 const SCEV *SResidual =
1912 getAddRecExpr(getConstant(C - D), Step, L, AR->getNoWrapFlags());
1913 const SCEV *SSExtR = getSignExtendExpr(SResidual, Ty, Depth + 1);
1914 return getAddExpr(SSExtD, SSExtR,
1915 (SCEV::NoWrapFlags)(SCEV::FlagNSW | SCEV::FlagNUW),
1920 if (proveNoWrapByVaryingStart<SCEVSignExtendExpr>(Start, Step, L)) {
1921 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1922 return getAddRecExpr(
1923 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this, Depth + 1),
1924 getSignExtendExpr(Step, Ty, Depth + 1), L, AR->getNoWrapFlags());
1928 // If the input value is provably positive and we could not simplify
1929 // away the sext build a zext instead.
1930 if (isKnownNonNegative(Op))
1931 return getZeroExtendExpr(Op, Ty, Depth + 1);
1933 // The cast wasn't folded; create an explicit cast node.
1934 // Recompute the insert position, as it may have been invalidated.
1935 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1936 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
1938 UniqueSCEVs.InsertNode(S, IP);
1939 addToLoopUseLists(S);
1943 /// getAnyExtendExpr - Return a SCEV for the given operand extended with
1944 /// unspecified bits out to the given type.
1945 const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
1947 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1948 "This is not an extending conversion!");
1949 assert(isSCEVable(Ty) &&
1950 "This is not a conversion to a SCEVable type!");
1951 Ty = getEffectiveSCEVType(Ty);
1953 // Sign-extend negative constants.
1954 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1955 if (SC->getAPInt().isNegative())
1956 return getSignExtendExpr(Op, Ty);
1958 // Peel off a truncate cast.
1959 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
1960 const SCEV *NewOp = T->getOperand();
1961 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
1962 return getAnyExtendExpr(NewOp, Ty);
1963 return getTruncateOrNoop(NewOp, Ty);
1966 // Next try a zext cast. If the cast is folded, use it.
1967 const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
1968 if (!isa<SCEVZeroExtendExpr>(ZExt))
1971 // Next try a sext cast. If the cast is folded, use it.
1972 const SCEV *SExt = getSignExtendExpr(Op, Ty);
1973 if (!isa<SCEVSignExtendExpr>(SExt))
1976 // Force the cast to be folded into the operands of an addrec.
1977 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
1978 SmallVector<const SCEV *, 4> Ops;
1979 for (const SCEV *Op : AR->operands())
1980 Ops.push_back(getAnyExtendExpr(Op, Ty));
1981 return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW);
1984 // If the expression is obviously signed, use the sext cast value.
1985 if (isa<SCEVSMaxExpr>(Op))
1988 // Absent any other information, use the zext cast value.
1992 /// Process the given Ops list, which is a list of operands to be added under
1993 /// the given scale, update the given map. This is a helper function for
1994 /// getAddRecExpr. As an example of what it does, given a sequence of operands
1995 /// that would form an add expression like this:
1997 /// m + n + 13 + (A * (o + p + (B * (q + m + 29)))) + r + (-1 * r)
1999 /// where A and B are constants, update the map with these values:
2001 /// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
2003 /// and add 13 + A*B*29 to AccumulatedConstant.
2004 /// This will allow getAddRecExpr to produce this:
2006 /// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
2008 /// This form often exposes folding opportunities that are hidden in
2009 /// the original operand list.
2011 /// Return true iff it appears that any interesting folding opportunities
2012 /// may be exposed. This helps getAddRecExpr short-circuit extra work in
2013 /// the common case where no interesting opportunities are present, and
2014 /// is also used as a check to avoid infinite recursion.
2016 CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
2017 SmallVectorImpl<const SCEV *> &NewOps,
2018 APInt &AccumulatedConstant,
2019 const SCEV *const *Ops, size_t NumOperands,
2021 ScalarEvolution &SE) {
2022 bool Interesting = false;
2024 // Iterate over the add operands. They are sorted, with constants first.
2026 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
2028 // Pull a buried constant out to the outside.
2029 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
2031 AccumulatedConstant += Scale * C->getAPInt();
2034 // Next comes everything else. We're especially interested in multiplies
2035 // here, but they're in the middle, so just visit the rest with one loop.
2036 for (; i != NumOperands; ++i) {
2037 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
2038 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
2040 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getAPInt();
2041 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
2042 // A multiplication of a constant with another add; recurse.
2043 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1));
2045 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
2046 Add->op_begin(), Add->getNumOperands(),
2049 // A multiplication of a constant with some other value. Update
2051 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
2052 const SCEV *Key = SE.getMulExpr(MulOps);
2053 auto Pair = M.insert({Key, NewScale});
2055 NewOps.push_back(Pair.first->first);
2057 Pair.first->second += NewScale;
2058 // The map already had an entry for this value, which may indicate
2059 // a folding opportunity.
2064 // An ordinary operand. Update the map.
2065 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
2066 M.insert({Ops[i], Scale});
2068 NewOps.push_back(Pair.first->first);
2070 Pair.first->second += Scale;
2071 // The map already had an entry for this value, which may indicate
2072 // a folding opportunity.
2081 // We're trying to construct a SCEV of type `Type' with `Ops' as operands and
2082 // `OldFlags' as can't-wrap behavior. Infer a more aggressive set of
2083 // can't-overflow flags for the operation if possible.
2084 static SCEV::NoWrapFlags
2085 StrengthenNoWrapFlags(ScalarEvolution *SE, SCEVTypes Type,
2086 const ArrayRef<const SCEV *> Ops,
2087 SCEV::NoWrapFlags Flags) {
2088 using namespace std::placeholders;
2090 using OBO = OverflowingBinaryOperator;
2093 Type == scAddExpr || Type == scAddRecExpr || Type == scMulExpr;
2095 assert(CanAnalyze && "don't call from other places!");
2097 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
2098 SCEV::NoWrapFlags SignOrUnsignWrap =
2099 ScalarEvolution::maskFlags(Flags, SignOrUnsignMask);
2101 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
2102 auto IsKnownNonNegative = [&](const SCEV *S) {
2103 return SE->isKnownNonNegative(S);
2106 if (SignOrUnsignWrap == SCEV::FlagNSW && all_of(Ops, IsKnownNonNegative))
2108 ScalarEvolution::setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
2110 SignOrUnsignWrap = ScalarEvolution::maskFlags(Flags, SignOrUnsignMask);
2112 if (SignOrUnsignWrap != SignOrUnsignMask &&
2113 (Type == scAddExpr || Type == scMulExpr) && Ops.size() == 2 &&
2114 isa<SCEVConstant>(Ops[0])) {
2119 return Instruction::Add;
2121 return Instruction::Mul;
2123 llvm_unreachable("Unexpected SCEV op.");
2127 const APInt &C = cast<SCEVConstant>(Ops[0])->getAPInt();
2129 // (A <opcode> C) --> (A <opcode> C)<nsw> if the op doesn't sign overflow.
2130 if (!(SignOrUnsignWrap & SCEV::FlagNSW)) {
2131 auto NSWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
2132 Opcode, C, OBO::NoSignedWrap);
2133 if (NSWRegion.contains(SE->getSignedRange(Ops[1])))
2134 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW);
2137 // (A <opcode> C) --> (A <opcode> C)<nuw> if the op doesn't unsign overflow.
2138 if (!(SignOrUnsignWrap & SCEV::FlagNUW)) {
2139 auto NUWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
2140 Opcode, C, OBO::NoUnsignedWrap);
2141 if (NUWRegion.contains(SE->getUnsignedRange(Ops[1])))
2142 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
2149 bool ScalarEvolution::isAvailableAtLoopEntry(const SCEV *S, const Loop *L) {
2150 return isLoopInvariant(S, L) && properlyDominates(S, L->getHeader());
2153 /// Get a canonical add expression, or something simpler if possible.
2154 const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
2155 SCEV::NoWrapFlags Flags,
2157 assert(!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) &&
2158 "only nuw or nsw allowed");
2159 assert(!Ops.empty() && "Cannot get empty add!");
2160 if (Ops.size() == 1) return Ops[0];
2162 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2163 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2164 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2165 "SCEVAddExpr operand types don't match!");
2168 // Sort by complexity, this groups all similar expression types together.
2169 GroupByComplexity(Ops, &LI, DT);
2171 Flags = StrengthenNoWrapFlags(this, scAddExpr, Ops, Flags);
2173 // If there are any constants, fold them together.
2175 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2177 assert(Idx < Ops.size());
2178 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2179 // We found two constants, fold them together!
2180 Ops[0] = getConstant(LHSC->getAPInt() + RHSC->getAPInt());
2181 if (Ops.size() == 2) return Ops[0];
2182 Ops.erase(Ops.begin()+1); // Erase the folded element
2183 LHSC = cast<SCEVConstant>(Ops[0]);
2186 // If we are left with a constant zero being added, strip it off.
2187 if (LHSC->getValue()->isZero()) {
2188 Ops.erase(Ops.begin());
2192 if (Ops.size() == 1) return Ops[0];
2195 // Limit recursion calls depth.
2196 if (Depth > MaxArithDepth || hasHugeExpression(Ops))
2197 return getOrCreateAddExpr(Ops, Flags);
2199 if (SCEV *S = std::get<0>(findExistingSCEVInCache(scAddExpr, Ops))) {
2200 static_cast<SCEVAddExpr *>(S)->setNoWrapFlags(Flags);
2204 // Okay, check to see if the same value occurs in the operand list more than
2205 // once. If so, merge them together into an multiply expression. Since we
2206 // sorted the list, these values are required to be adjacent.
2207 Type *Ty = Ops[0]->getType();
2208 bool FoundMatch = false;
2209 for (unsigned i = 0, e = Ops.size(); i != e-1; ++i)
2210 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
2211 // Scan ahead to count how many equal operands there are.
2213 while (i+Count != e && Ops[i+Count] == Ops[i])
2215 // Merge the values into a multiply.
2216 const SCEV *Scale = getConstant(Ty, Count);
2217 const SCEV *Mul = getMulExpr(Scale, Ops[i], SCEV::FlagAnyWrap, Depth + 1);
2218 if (Ops.size() == Count)
2221 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count);
2222 --i; e -= Count - 1;
2226 return getAddExpr(Ops, Flags, Depth + 1);
2228 // Check for truncates. If all the operands are truncated from the same
2229 // type, see if factoring out the truncate would permit the result to be
2230 // folded. eg., n*trunc(x) + m*trunc(y) --> trunc(trunc(m)*x + trunc(n)*y)
2231 // if the contents of the resulting outer trunc fold to something simple.
2232 auto FindTruncSrcType = [&]() -> Type * {
2233 // We're ultimately looking to fold an addrec of truncs and muls of only
2234 // constants and truncs, so if we find any other types of SCEV
2235 // as operands of the addrec then we bail and return nullptr here.
2236 // Otherwise, we return the type of the operand of a trunc that we find.
2237 if (auto *T = dyn_cast<SCEVTruncateExpr>(Ops[Idx]))
2238 return T->getOperand()->getType();
2239 if (const auto *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
2240 const auto *LastOp = Mul->getOperand(Mul->getNumOperands() - 1);
2241 if (const auto *T = dyn_cast<SCEVTruncateExpr>(LastOp))
2242 return T->getOperand()->getType();
2246 if (auto *SrcType = FindTruncSrcType()) {
2247 SmallVector<const SCEV *, 8> LargeOps;
2249 // Check all the operands to see if they can be represented in the
2250 // source type of the truncate.
2251 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
2252 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
2253 if (T->getOperand()->getType() != SrcType) {
2257 LargeOps.push_back(T->getOperand());
2258 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
2259 LargeOps.push_back(getAnyExtendExpr(C, SrcType));
2260 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
2261 SmallVector<const SCEV *, 8> LargeMulOps;
2262 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
2263 if (const SCEVTruncateExpr *T =
2264 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
2265 if (T->getOperand()->getType() != SrcType) {
2269 LargeMulOps.push_back(T->getOperand());
2270 } else if (const auto *C = dyn_cast<SCEVConstant>(M->getOperand(j))) {
2271 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType));
2278 LargeOps.push_back(getMulExpr(LargeMulOps, SCEV::FlagAnyWrap, Depth + 1));
2285 // Evaluate the expression in the larger type.
2286 const SCEV *Fold = getAddExpr(LargeOps, SCEV::FlagAnyWrap, Depth + 1);
2287 // If it folds to something simple, use it. Otherwise, don't.
2288 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
2289 return getTruncateExpr(Fold, Ty);
2293 // Skip past any other cast SCEVs.
2294 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
2297 // If there are add operands they would be next.
2298 if (Idx < Ops.size()) {
2299 bool DeletedAdd = false;
2300 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
2301 if (Ops.size() > AddOpsInlineThreshold ||
2302 Add->getNumOperands() > AddOpsInlineThreshold)
2304 // If we have an add, expand the add operands onto the end of the operands
2306 Ops.erase(Ops.begin()+Idx);
2307 Ops.append(Add->op_begin(), Add->op_end());
2311 // If we deleted at least one add, we added operands to the end of the list,
2312 // and they are not necessarily sorted. Recurse to resort and resimplify
2313 // any operands we just acquired.
2315 return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
2318 // Skip over the add expression until we get to a multiply.
2319 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
2322 // Check to see if there are any folding opportunities present with
2323 // operands multiplied by constant values.
2324 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
2325 uint64_t BitWidth = getTypeSizeInBits(Ty);
2326 DenseMap<const SCEV *, APInt> M;
2327 SmallVector<const SCEV *, 8> NewOps;
2328 APInt AccumulatedConstant(BitWidth, 0);
2329 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
2330 Ops.data(), Ops.size(),
2331 APInt(BitWidth, 1), *this)) {
2332 struct APIntCompare {
2333 bool operator()(const APInt &LHS, const APInt &RHS) const {
2334 return LHS.ult(RHS);
2338 // Some interesting folding opportunity is present, so its worthwhile to
2339 // re-generate the operands list. Group the operands by constant scale,
2340 // to avoid multiplying by the same constant scale multiple times.
2341 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
2342 for (const SCEV *NewOp : NewOps)
2343 MulOpLists[M.find(NewOp)->second].push_back(NewOp);
2344 // Re-generate the operands list.
2346 if (AccumulatedConstant != 0)
2347 Ops.push_back(getConstant(AccumulatedConstant));
2348 for (auto &MulOp : MulOpLists)
2349 if (MulOp.first != 0)
2350 Ops.push_back(getMulExpr(
2351 getConstant(MulOp.first),
2352 getAddExpr(MulOp.second, SCEV::FlagAnyWrap, Depth + 1),
2353 SCEV::FlagAnyWrap, Depth + 1));
2356 if (Ops.size() == 1)
2358 return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
2362 // If we are adding something to a multiply expression, make sure the
2363 // something is not already an operand of the multiply. If so, merge it into
2365 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
2366 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
2367 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
2368 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
2369 if (isa<SCEVConstant>(MulOpSCEV))
2371 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
2372 if (MulOpSCEV == Ops[AddOp]) {
2373 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
2374 const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
2375 if (Mul->getNumOperands() != 2) {
2376 // If the multiply has more than two operands, we must get the
2378 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
2379 Mul->op_begin()+MulOp);
2380 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
2381 InnerMul = getMulExpr(MulOps, SCEV::FlagAnyWrap, Depth + 1);
2383 SmallVector<const SCEV *, 2> TwoOps = {getOne(Ty), InnerMul};
2384 const SCEV *AddOne = getAddExpr(TwoOps, SCEV::FlagAnyWrap, Depth + 1);
2385 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV,
2386 SCEV::FlagAnyWrap, Depth + 1);
2387 if (Ops.size() == 2) return OuterMul;
2389 Ops.erase(Ops.begin()+AddOp);
2390 Ops.erase(Ops.begin()+Idx-1);
2392 Ops.erase(Ops.begin()+Idx);
2393 Ops.erase(Ops.begin()+AddOp-1);
2395 Ops.push_back(OuterMul);
2396 return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
2399 // Check this multiply against other multiplies being added together.
2400 for (unsigned OtherMulIdx = Idx+1;
2401 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
2403 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
2404 // If MulOp occurs in OtherMul, we can fold the two multiplies
2406 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
2407 OMulOp != e; ++OMulOp)
2408 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
2409 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
2410 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
2411 if (Mul->getNumOperands() != 2) {
2412 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
2413 Mul->op_begin()+MulOp);
2414 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
2415 InnerMul1 = getMulExpr(MulOps, SCEV::FlagAnyWrap, Depth + 1);
2417 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
2418 if (OtherMul->getNumOperands() != 2) {
2419 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
2420 OtherMul->op_begin()+OMulOp);
2421 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end());
2422 InnerMul2 = getMulExpr(MulOps, SCEV::FlagAnyWrap, Depth + 1);
2424 SmallVector<const SCEV *, 2> TwoOps = {InnerMul1, InnerMul2};
2425 const SCEV *InnerMulSum =
2426 getAddExpr(TwoOps, SCEV::FlagAnyWrap, Depth + 1);
2427 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum,
2428 SCEV::FlagAnyWrap, Depth + 1);
2429 if (Ops.size() == 2) return OuterMul;
2430 Ops.erase(Ops.begin()+Idx);
2431 Ops.erase(Ops.begin()+OtherMulIdx-1);
2432 Ops.push_back(OuterMul);
2433 return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
2439 // If there are any add recurrences in the operands list, see if any other
2440 // added values are loop invariant. If so, we can fold them into the
2442 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2445 // Scan over all recurrences, trying to fold loop invariants into them.
2446 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
2447 // Scan all of the other operands to this add and add them to the vector if
2448 // they are loop invariant w.r.t. the recurrence.
2449 SmallVector<const SCEV *, 8> LIOps;
2450 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2451 const Loop *AddRecLoop = AddRec->getLoop();
2452 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2453 if (isAvailableAtLoopEntry(Ops[i], AddRecLoop)) {
2454 LIOps.push_back(Ops[i]);
2455 Ops.erase(Ops.begin()+i);
2459 // If we found some loop invariants, fold them into the recurrence.
2460 if (!LIOps.empty()) {
2461 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
2462 LIOps.push_back(AddRec->getStart());
2464 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
2466 // This follows from the fact that the no-wrap flags on the outer add
2467 // expression are applicable on the 0th iteration, when the add recurrence
2468 // will be equal to its start value.
2469 AddRecOps[0] = getAddExpr(LIOps, Flags, Depth + 1);
2471 // Build the new addrec. Propagate the NUW and NSW flags if both the
2472 // outer add and the inner addrec are guaranteed to have no overflow.
2473 // Always propagate NW.
2474 Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW));
2475 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags);
2477 // If all of the other operands were loop invariant, we are done.
2478 if (Ops.size() == 1) return NewRec;
2480 // Otherwise, add the folded AddRec by the non-invariant parts.
2481 for (unsigned i = 0;; ++i)
2482 if (Ops[i] == AddRec) {
2486 return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
2489 // Okay, if there weren't any loop invariants to be folded, check to see if
2490 // there are multiple AddRec's with the same loop induction variable being
2491 // added together. If so, we can fold them.
2492 for (unsigned OtherIdx = Idx+1;
2493 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2495 // We expect the AddRecExpr's to be sorted in reverse dominance order,
2496 // so that the 1st found AddRecExpr is dominated by all others.
2497 assert(DT.dominates(
2498 cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()->getHeader(),
2499 AddRec->getLoop()->getHeader()) &&
2500 "AddRecExprs are not sorted in reverse dominance order?");
2501 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
2502 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L>
2503 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
2505 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2507 const auto *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
2508 if (OtherAddRec->getLoop() == AddRecLoop) {
2509 for (unsigned i = 0, e = OtherAddRec->getNumOperands();
2511 if (i >= AddRecOps.size()) {
2512 AddRecOps.append(OtherAddRec->op_begin()+i,
2513 OtherAddRec->op_end());
2516 SmallVector<const SCEV *, 2> TwoOps = {
2517 AddRecOps[i], OtherAddRec->getOperand(i)};
2518 AddRecOps[i] = getAddExpr(TwoOps, SCEV::FlagAnyWrap, Depth + 1);
2520 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2523 // Step size has changed, so we cannot guarantee no self-wraparound.
2524 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap);
2525 return getAddExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
2529 // Otherwise couldn't fold anything into this recurrence. Move onto the
2533 // Okay, it looks like we really DO need an add expr. Check to see if we
2534 // already have one, otherwise create a new one.
2535 return getOrCreateAddExpr(Ops, Flags);
2539 ScalarEvolution::getOrCreateAddExpr(ArrayRef<const SCEV *> Ops,
2540 SCEV::NoWrapFlags Flags) {
2541 FoldingSetNodeID ID;
2542 ID.AddInteger(scAddExpr);
2543 for (const SCEV *Op : Ops)
2547 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2549 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2550 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2551 S = new (SCEVAllocator)
2552 SCEVAddExpr(ID.Intern(SCEVAllocator), O, Ops.size());
2553 UniqueSCEVs.InsertNode(S, IP);
2554 addToLoopUseLists(S);
2556 S->setNoWrapFlags(Flags);
2561 ScalarEvolution::getOrCreateAddRecExpr(ArrayRef<const SCEV *> Ops,
2562 const Loop *L, SCEV::NoWrapFlags Flags) {
2563 FoldingSetNodeID ID;
2564 ID.AddInteger(scAddRecExpr);
2565 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2566 ID.AddPointer(Ops[i]);
2570 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2572 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2573 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2574 S = new (SCEVAllocator)
2575 SCEVAddRecExpr(ID.Intern(SCEVAllocator), O, Ops.size(), L);
2576 UniqueSCEVs.InsertNode(S, IP);
2577 addToLoopUseLists(S);
2579 S->setNoWrapFlags(Flags);
2584 ScalarEvolution::getOrCreateMulExpr(ArrayRef<const SCEV *> Ops,
2585 SCEV::NoWrapFlags Flags) {
2586 FoldingSetNodeID ID;
2587 ID.AddInteger(scMulExpr);
2588 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2589 ID.AddPointer(Ops[i]);
2592 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2594 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2595 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2596 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
2598 UniqueSCEVs.InsertNode(S, IP);
2599 addToLoopUseLists(S);
2601 S->setNoWrapFlags(Flags);
2605 static uint64_t umul_ov(uint64_t i, uint64_t j, bool &Overflow) {
2607 if (j > 1 && k / j != i) Overflow = true;
2611 /// Compute the result of "n choose k", the binomial coefficient. If an
2612 /// intermediate computation overflows, Overflow will be set and the return will
2613 /// be garbage. Overflow is not cleared on absence of overflow.
2614 static uint64_t Choose(uint64_t n, uint64_t k, bool &Overflow) {
2615 // We use the multiplicative formula:
2616 // n(n-1)(n-2)...(n-(k-1)) / k(k-1)(k-2)...1 .
2617 // At each iteration, we take the n-th term of the numeral and divide by the
2618 // (k-n)th term of the denominator. This division will always produce an
2619 // integral result, and helps reduce the chance of overflow in the
2620 // intermediate computations. However, we can still overflow even when the
2621 // final result would fit.
2623 if (n == 0 || n == k) return 1;
2624 if (k > n) return 0;
2630 for (uint64_t i = 1; i <= k; ++i) {
2631 r = umul_ov(r, n-(i-1), Overflow);
2637 /// Determine if any of the operands in this SCEV are a constant or if
2638 /// any of the add or multiply expressions in this SCEV contain a constant.
2639 static bool containsConstantInAddMulChain(const SCEV *StartExpr) {
2640 struct FindConstantInAddMulChain {
2641 bool FoundConstant = false;
2643 bool follow(const SCEV *S) {
2644 FoundConstant |= isa<SCEVConstant>(S);
2645 return isa<SCEVAddExpr>(S) || isa<SCEVMulExpr>(S);
2648 bool isDone() const {
2649 return FoundConstant;
2653 FindConstantInAddMulChain F;
2654 SCEVTraversal<FindConstantInAddMulChain> ST(F);
2655 ST.visitAll(StartExpr);
2656 return F.FoundConstant;
2659 /// Get a canonical multiply expression, or something simpler if possible.
2660 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
2661 SCEV::NoWrapFlags Flags,
2663 assert(Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) &&
2664 "only nuw or nsw allowed");
2665 assert(!Ops.empty() && "Cannot get empty mul!");
2666 if (Ops.size() == 1) return Ops[0];
2668 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2669 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2670 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2671 "SCEVMulExpr operand types don't match!");
2674 // Sort by complexity, this groups all similar expression types together.
2675 GroupByComplexity(Ops, &LI, DT);
2677 Flags = StrengthenNoWrapFlags(this, scMulExpr, Ops, Flags);
2679 // Limit recursion calls depth, but fold all-constant expressions.
2680 // `Ops` is sorted, so it's enough to check just last one.
2681 if ((Depth > MaxArithDepth || hasHugeExpression(Ops)) &&
2682 !isa<SCEVConstant>(Ops.back()))
2683 return getOrCreateMulExpr(Ops, Flags);
2685 if (SCEV *S = std::get<0>(findExistingSCEVInCache(scMulExpr, Ops))) {
2686 static_cast<SCEVMulExpr *>(S)->setNoWrapFlags(Flags);
2690 // If there are any constants, fold them together.
2692 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2694 if (Ops.size() == 2)
2695 // C1*(C2+V) -> C1*C2 + C1*V
2696 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
2697 // If any of Add's ops are Adds or Muls with a constant, apply this
2698 // transformation as well.
2700 // TODO: There are some cases where this transformation is not
2701 // profitable; for example, Add = (C0 + X) * Y + Z. Maybe the scope of
2702 // this transformation should be narrowed down.
2703 if (Add->getNumOperands() == 2 && containsConstantInAddMulChain(Add))
2704 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0),
2705 SCEV::FlagAnyWrap, Depth + 1),
2706 getMulExpr(LHSC, Add->getOperand(1),
2707 SCEV::FlagAnyWrap, Depth + 1),
2708 SCEV::FlagAnyWrap, Depth + 1);
2711 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2712 // We found two constants, fold them together!
2714 ConstantInt::get(getContext(), LHSC->getAPInt() * RHSC->getAPInt());
2715 Ops[0] = getConstant(Fold);
2716 Ops.erase(Ops.begin()+1); // Erase the folded element
2717 if (Ops.size() == 1) return Ops[0];
2718 LHSC = cast<SCEVConstant>(Ops[0]);
2721 // If we are left with a constant one being multiplied, strip it off.
2722 if (cast<SCEVConstant>(Ops[0])->getValue()->isOne()) {
2723 Ops.erase(Ops.begin());
2725 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
2726 // If we have a multiply of zero, it will always be zero.
2728 } else if (Ops[0]->isAllOnesValue()) {
2729 // If we have a mul by -1 of an add, try distributing the -1 among the
2731 if (Ops.size() == 2) {
2732 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
2733 SmallVector<const SCEV *, 4> NewOps;
2734 bool AnyFolded = false;
2735 for (const SCEV *AddOp : Add->operands()) {
2736 const SCEV *Mul = getMulExpr(Ops[0], AddOp, SCEV::FlagAnyWrap,
2738 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
2739 NewOps.push_back(Mul);
2742 return getAddExpr(NewOps, SCEV::FlagAnyWrap, Depth + 1);
2743 } else if (const auto *AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) {
2744 // Negation preserves a recurrence's no self-wrap property.
2745 SmallVector<const SCEV *, 4> Operands;
2746 for (const SCEV *AddRecOp : AddRec->operands())
2747 Operands.push_back(getMulExpr(Ops[0], AddRecOp, SCEV::FlagAnyWrap,
2750 return getAddRecExpr(Operands, AddRec->getLoop(),
2751 AddRec->getNoWrapFlags(SCEV::FlagNW));
2756 if (Ops.size() == 1)
2760 // Skip over the add expression until we get to a multiply.
2761 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
2764 // If there are mul operands inline them all into this expression.
2765 if (Idx < Ops.size()) {
2766 bool DeletedMul = false;
2767 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
2768 if (Ops.size() > MulOpsInlineThreshold)
2770 // If we have an mul, expand the mul operands onto the end of the
2772 Ops.erase(Ops.begin()+Idx);
2773 Ops.append(Mul->op_begin(), Mul->op_end());
2777 // If we deleted at least one mul, we added operands to the end of the
2778 // list, and they are not necessarily sorted. Recurse to resort and
2779 // resimplify any operands we just acquired.
2781 return getMulExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
2784 // If there are any add recurrences in the operands list, see if any other
2785 // added values are loop invariant. If so, we can fold them into the
2787 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2790 // Scan over all recurrences, trying to fold loop invariants into them.
2791 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
2792 // Scan all of the other operands to this mul and add them to the vector
2793 // if they are loop invariant w.r.t. the recurrence.
2794 SmallVector<const SCEV *, 8> LIOps;
2795 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2796 const Loop *AddRecLoop = AddRec->getLoop();
2797 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2798 if (isAvailableAtLoopEntry(Ops[i], AddRecLoop)) {
2799 LIOps.push_back(Ops[i]);
2800 Ops.erase(Ops.begin()+i);
2804 // If we found some loop invariants, fold them into the recurrence.
2805 if (!LIOps.empty()) {
2806 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
2807 SmallVector<const SCEV *, 4> NewOps;
2808 NewOps.reserve(AddRec->getNumOperands());
2809 const SCEV *Scale = getMulExpr(LIOps, SCEV::FlagAnyWrap, Depth + 1);
2810 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
2811 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i),
2812 SCEV::FlagAnyWrap, Depth + 1));
2814 // Build the new addrec. Propagate the NUW and NSW flags if both the
2815 // outer mul and the inner addrec are guaranteed to have no overflow.
2817 // No self-wrap cannot be guaranteed after changing the step size, but
2818 // will be inferred if either NUW or NSW is true.
2819 Flags = AddRec->getNoWrapFlags(clearFlags(Flags, SCEV::FlagNW));
2820 const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, Flags);
2822 // If all of the other operands were loop invariant, we are done.
2823 if (Ops.size() == 1) return NewRec;
2825 // Otherwise, multiply the folded AddRec by the non-invariant parts.
2826 for (unsigned i = 0;; ++i)
2827 if (Ops[i] == AddRec) {
2831 return getMulExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
2834 // Okay, if there weren't any loop invariants to be folded, check to see
2835 // if there are multiple AddRec's with the same loop induction variable
2836 // being multiplied together. If so, we can fold them.
2838 // {A1,+,A2,+,...,+,An}<L> * {B1,+,B2,+,...,+,Bn}<L>
2839 // = {x=1 in [ sum y=x..2x [ sum z=max(y-x, y-n)..min(x,n) [
2840 // choose(x, 2x)*choose(2x-y, x-z)*A_{y-z}*B_z
2841 // ]]],+,...up to x=2n}.
2842 // Note that the arguments to choose() are always integers with values
2843 // known at compile time, never SCEV objects.
2845 // The implementation avoids pointless extra computations when the two
2846 // addrec's are of different length (mathematically, it's equivalent to
2847 // an infinite stream of zeros on the right).
2848 bool OpsModified = false;
2849 for (unsigned OtherIdx = Idx+1;
2850 OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2852 const SCEVAddRecExpr *OtherAddRec =
2853 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]);
2854 if (!OtherAddRec || OtherAddRec->getLoop() != AddRecLoop)
2857 // Limit max number of arguments to avoid creation of unreasonably big
2858 // SCEVAddRecs with very complex operands.
2859 if (AddRec->getNumOperands() + OtherAddRec->getNumOperands() - 1 >
2860 MaxAddRecSize || hasHugeExpression({AddRec, OtherAddRec}))
2863 bool Overflow = false;
2864 Type *Ty = AddRec->getType();
2865 bool LargerThan64Bits = getTypeSizeInBits(Ty) > 64;
2866 SmallVector<const SCEV*, 7> AddRecOps;
2867 for (int x = 0, xe = AddRec->getNumOperands() +
2868 OtherAddRec->getNumOperands() - 1; x != xe && !Overflow; ++x) {
2869 SmallVector <const SCEV *, 7> SumOps;
2870 for (int y = x, ye = 2*x+1; y != ye && !Overflow; ++y) {
2871 uint64_t Coeff1 = Choose(x, 2*x - y, Overflow);
2872 for (int z = std::max(y-x, y-(int)AddRec->getNumOperands()+1),
2873 ze = std::min(x+1, (int)OtherAddRec->getNumOperands());
2874 z < ze && !Overflow; ++z) {
2875 uint64_t Coeff2 = Choose(2*x - y, x-z, Overflow);
2877 if (LargerThan64Bits)
2878 Coeff = umul_ov(Coeff1, Coeff2, Overflow);
2880 Coeff = Coeff1*Coeff2;
2881 const SCEV *CoeffTerm = getConstant(Ty, Coeff);
2882 const SCEV *Term1 = AddRec->getOperand(y-z);
2883 const SCEV *Term2 = OtherAddRec->getOperand(z);
2884 SumOps.push_back(getMulExpr(CoeffTerm, Term1, Term2,
2885 SCEV::FlagAnyWrap, Depth + 1));
2889 SumOps.push_back(getZero(Ty));
2890 AddRecOps.push_back(getAddExpr(SumOps, SCEV::FlagAnyWrap, Depth + 1));
2893 const SCEV *NewAddRec = getAddRecExpr(AddRecOps, AddRecLoop,
2895 if (Ops.size() == 2) return NewAddRec;
2896 Ops[Idx] = NewAddRec;
2897 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2899 AddRec = dyn_cast<SCEVAddRecExpr>(NewAddRec);
2905 return getMulExpr(Ops, SCEV::FlagAnyWrap, Depth + 1);
2907 // Otherwise couldn't fold anything into this recurrence. Move onto the
2911 // Okay, it looks like we really DO need an mul expr. Check to see if we
2912 // already have one, otherwise create a new one.
2913 return getOrCreateMulExpr(Ops, Flags);
2916 /// Represents an unsigned remainder expression based on unsigned division.
2917 const SCEV *ScalarEvolution::getURemExpr(const SCEV *LHS,
2919 assert(getEffectiveSCEVType(LHS->getType()) ==
2920 getEffectiveSCEVType(RHS->getType()) &&
2921 "SCEVURemExpr operand types don't match!");
2923 // Short-circuit easy cases
2924 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
2925 // If constant is one, the result is trivial
2926 if (RHSC->getValue()->isOne())
2927 return getZero(LHS->getType()); // X urem 1 --> 0
2929 // If constant is a power of two, fold into a zext(trunc(LHS)).
2930 if (RHSC->getAPInt().isPowerOf2()) {
2931 Type *FullTy = LHS->getType();
2933 IntegerType::get(getContext(), RHSC->getAPInt().logBase2());
2934 return getZeroExtendExpr(getTruncateExpr(LHS, TruncTy), FullTy);
2938 // Fallback to %a == %x urem %y == %x -<nuw> ((%x udiv %y) *<nuw> %y)
2939 const SCEV *UDiv = getUDivExpr(LHS, RHS);
2940 const SCEV *Mult = getMulExpr(UDiv, RHS, SCEV::FlagNUW);
2941 return getMinusSCEV(LHS, Mult, SCEV::FlagNUW);
2944 /// Get a canonical unsigned division expression, or something simpler if
2946 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
2948 assert(getEffectiveSCEVType(LHS->getType()) ==
2949 getEffectiveSCEVType(RHS->getType()) &&
2950 "SCEVUDivExpr operand types don't match!");
2952 FoldingSetNodeID ID;
2953 ID.AddInteger(scUDivExpr);
2957 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP))
2960 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
2961 if (RHSC->getValue()->isOne())
2962 return LHS; // X udiv 1 --> x
2963 // If the denominator is zero, the result of the udiv is undefined. Don't
2964 // try to analyze it, because the resolution chosen here may differ from
2965 // the resolution chosen in other parts of the compiler.
2966 if (!RHSC->getValue()->isZero()) {
2967 // Determine if the division can be folded into the operands of
2969 // TODO: Generalize this to non-constants by using known-bits information.
2970 Type *Ty = LHS->getType();
2971 unsigned LZ = RHSC->getAPInt().countLeadingZeros();
2972 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1;
2973 // For non-power-of-two values, effectively round the value up to the
2974 // nearest power of two.
2975 if (!RHSC->getAPInt().isPowerOf2())
2977 IntegerType *ExtTy =
2978 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
2979 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
2980 if (const SCEVConstant *Step =
2981 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) {
2982 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
2983 const APInt &StepInt = Step->getAPInt();
2984 const APInt &DivInt = RHSC->getAPInt();
2985 if (!StepInt.urem(DivInt) &&
2986 getZeroExtendExpr(AR, ExtTy) ==
2987 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2988 getZeroExtendExpr(Step, ExtTy),
2989 AR->getLoop(), SCEV::FlagAnyWrap)) {
2990 SmallVector<const SCEV *, 4> Operands;
2991 for (const SCEV *Op : AR->operands())
2992 Operands.push_back(getUDivExpr(Op, RHS));
2993 return getAddRecExpr(Operands, AR->getLoop(), SCEV::FlagNW);
2995 /// Get a canonical UDivExpr for a recurrence.
2996 /// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0.
2997 // We can currently only fold X%N if X is constant.
2998 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(AR->getStart());
2999 if (StartC && !DivInt.urem(StepInt) &&
3000 getZeroExtendExpr(AR, ExtTy) ==
3001 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
3002 getZeroExtendExpr(Step, ExtTy),
3003 AR->getLoop(), SCEV::FlagAnyWrap)) {
3004 const APInt &StartInt = StartC->getAPInt();
3005 const APInt &StartRem = StartInt.urem(StepInt);
3006 if (StartRem != 0) {
3007 const SCEV *NewLHS =
3008 getAddRecExpr(getConstant(StartInt - StartRem), Step,
3009 AR->getLoop(), SCEV::FlagNW);
3010 if (LHS != NewLHS) {
3013 // Reset the ID to include the new LHS, and check if it is
3016 ID.AddInteger(scUDivExpr);
3020 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP))
3026 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
3027 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
3028 SmallVector<const SCEV *, 4> Operands;
3029 for (const SCEV *Op : M->operands())
3030 Operands.push_back(getZeroExtendExpr(Op, ExtTy));
3031 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
3032 // Find an operand that's safely divisible.
3033 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
3034 const SCEV *Op = M->getOperand(i);
3035 const SCEV *Div = getUDivExpr(Op, RHSC);
3036 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
3037 Operands = SmallVector<const SCEV *, 4>(M->op_begin(),
3040 return getMulExpr(Operands);
3045 // (A/B)/C --> A/(B*C) if safe and B*C can be folded.
3046 if (const SCEVUDivExpr *OtherDiv = dyn_cast<SCEVUDivExpr>(LHS)) {
3047 if (auto *DivisorConstant =
3048 dyn_cast<SCEVConstant>(OtherDiv->getRHS())) {
3049 bool Overflow = false;
3051 DivisorConstant->getAPInt().umul_ov(RHSC->getAPInt(), Overflow);
3053 return getConstant(RHSC->getType(), 0, false);
3055 return getUDivExpr(OtherDiv->getLHS(), getConstant(NewRHS));
3059 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
3060 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) {
3061 SmallVector<const SCEV *, 4> Operands;
3062 for (const SCEV *Op : A->operands())
3063 Operands.push_back(getZeroExtendExpr(Op, ExtTy));
3064 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
3066 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
3067 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
3068 if (isa<SCEVUDivExpr>(Op) ||
3069 getMulExpr(Op, RHS) != A->getOperand(i))
3071 Operands.push_back(Op);
3073 if (Operands.size() == A->getNumOperands())
3074 return getAddExpr(Operands);
3078 // Fold if both operands are constant.
3079 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
3080 Constant *LHSCV = LHSC->getValue();
3081 Constant *RHSCV = RHSC->getValue();
3082 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
3088 // The Insertion Point (IP) might be invalid by now (due to UniqueSCEVs
3089 // changes). Make sure we get a new one.
3091 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
3092 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
3094 UniqueSCEVs.InsertNode(S, IP);
3095 addToLoopUseLists(S);
3099 static const APInt gcd(const SCEVConstant *C1, const SCEVConstant *C2) {
3100 APInt A = C1->getAPInt().abs();
3101 APInt B = C2->getAPInt().abs();
3102 uint32_t ABW = A.getBitWidth();
3103 uint32_t BBW = B.getBitWidth();
3110 return APIntOps::GreatestCommonDivisor(std::move(A), std::move(B));
3113 /// Get a canonical unsigned division expression, or something simpler if
3114 /// possible. There is no representation for an exact udiv in SCEV IR, but we
3115 /// can attempt to remove factors from the LHS and RHS. We can't do this when
3116 /// it's not exact because the udiv may be clearing bits.
3117 const SCEV *ScalarEvolution::getUDivExactExpr(const SCEV *LHS,
3119 // TODO: we could try to find factors in all sorts of things, but for now we
3120 // just deal with u/exact (multiply, constant). See SCEVDivision towards the
3121 // end of this file for inspiration.
3123 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(LHS);
3124 if (!Mul || !Mul->hasNoUnsignedWrap())
3125 return getUDivExpr(LHS, RHS);
3127 if (const SCEVConstant *RHSCst = dyn_cast<SCEVConstant>(RHS)) {
3128 // If the mulexpr multiplies by a constant, then that constant must be the
3129 // first element of the mulexpr.
3130 if (const auto *LHSCst = dyn_cast<SCEVConstant>(Mul->getOperand(0))) {
3131 if (LHSCst == RHSCst) {
3132 SmallVector<const SCEV *, 2> Operands;
3133 Operands.append(Mul->op_begin() + 1, Mul->op_end());
3134 return getMulExpr(Operands);
3137 // We can't just assume that LHSCst divides RHSCst cleanly, it could be
3138 // that there's a factor provided by one of the other terms. We need to
3140 APInt Factor = gcd(LHSCst, RHSCst);
3141 if (!Factor.isIntN(1)) {
3143 cast<SCEVConstant>(getConstant(LHSCst->getAPInt().udiv(Factor)));
3145 cast<SCEVConstant>(getConstant(RHSCst->getAPInt().udiv(Factor)));
3146 SmallVector<const SCEV *, 2> Operands;
3147 Operands.push_back(LHSCst);
3148 Operands.append(Mul->op_begin() + 1, Mul->op_end());
3149 LHS = getMulExpr(Operands);
3151 Mul = dyn_cast<SCEVMulExpr>(LHS);
3153 return getUDivExactExpr(LHS, RHS);
3158 for (int i = 0, e = Mul->getNumOperands(); i != e; ++i) {
3159 if (Mul->getOperand(i) == RHS) {
3160 SmallVector<const SCEV *, 2> Operands;
3161 Operands.append(Mul->op_begin(), Mul->op_begin() + i);
3162 Operands.append(Mul->op_begin() + i + 1, Mul->op_end());
3163 return getMulExpr(Operands);
3167 return getUDivExpr(LHS, RHS);
3170 /// Get an add recurrence expression for the specified loop. Simplify the
3171 /// expression as much as possible.
3172 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step,
3174 SCEV::NoWrapFlags Flags) {
3175 SmallVector<const SCEV *, 4> Operands;
3176 Operands.push_back(Start);
3177 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
3178 if (StepChrec->getLoop() == L) {
3179 Operands.append(StepChrec->op_begin(), StepChrec->op_end());
3180 return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW));
3183 Operands.push_back(Step);
3184 return getAddRecExpr(Operands, L, Flags);
3187 /// Get an add recurrence expression for the specified loop. Simplify the
3188 /// expression as much as possible.
3190 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
3191 const Loop *L, SCEV::NoWrapFlags Flags) {
3192 if (Operands.size() == 1) return Operands[0];
3194 Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
3195 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
3196 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy &&
3197 "SCEVAddRecExpr operand types don't match!");
3198 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
3199 assert(isLoopInvariant(Operands[i], L) &&
3200 "SCEVAddRecExpr operand is not loop-invariant!");
3203 if (Operands.back()->isZero()) {
3204 Operands.pop_back();
3205 return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0} --> X
3208 // It's tempting to want to call getConstantMaxBackedgeTakenCount count here and
3209 // use that information to infer NUW and NSW flags. However, computing a
3210 // BE count requires calling getAddRecExpr, so we may not yet have a
3211 // meaningful BE count at this point (and if we don't, we'd be stuck
3212 // with a SCEVCouldNotCompute as the cached BE count).
3214 Flags = StrengthenNoWrapFlags(this, scAddRecExpr, Operands, Flags);
3216 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
3217 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
3218 const Loop *NestedLoop = NestedAR->getLoop();
3219 if (L->contains(NestedLoop)
3220 ? (L->getLoopDepth() < NestedLoop->getLoopDepth())
3221 : (!NestedLoop->contains(L) &&
3222 DT.dominates(L->getHeader(), NestedLoop->getHeader()))) {
3223 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
3224 NestedAR->op_end());
3225 Operands[0] = NestedAR->getStart();
3226 // AddRecs require their operands be loop-invariant with respect to their
3227 // loops. Don't perform this transformation if it would break this
3229 bool AllInvariant = all_of(
3230 Operands, [&](const SCEV *Op) { return isLoopInvariant(Op, L); });
3233 // Create a recurrence for the outer loop with the same step size.
3235 // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the
3236 // inner recurrence has the same property.
3237 SCEV::NoWrapFlags OuterFlags =
3238 maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags());
3240 NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags);
3241 AllInvariant = all_of(NestedOperands, [&](const SCEV *Op) {
3242 return isLoopInvariant(Op, NestedLoop);
3246 // Ok, both add recurrences are valid after the transformation.
3248 // The inner recurrence keeps its NW flag but only keeps NUW/NSW if
3249 // the outer recurrence has the same property.
3250 SCEV::NoWrapFlags InnerFlags =
3251 maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags);
3252 return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags);
3255 // Reset Operands to its original state.
3256 Operands[0] = NestedAR;
3260 // Okay, it looks like we really DO need an addrec expr. Check to see if we
3261 // already have one, otherwise create a new one.
3262 return getOrCreateAddRecExpr(Operands, L, Flags);
3266 ScalarEvolution::getGEPExpr(GEPOperator *GEP,
3267 const SmallVectorImpl<const SCEV *> &IndexExprs) {
3268 const SCEV *BaseExpr = getSCEV(GEP->getPointerOperand());
3269 // getSCEV(Base)->getType() has the same address space as Base->getType()
3270 // because SCEV::getType() preserves the address space.
3271 Type *IntIdxTy = getEffectiveSCEVType(BaseExpr->getType());
3272 // FIXME(PR23527): Don't blindly transfer the inbounds flag from the GEP
3273 // instruction to its SCEV, because the Instruction may be guarded by control
3274 // flow and the no-overflow bits may not be valid for the expression in any
3275 // context. This can be fixed similarly to how these flags are handled for
3277 SCEV::NoWrapFlags Wrap = GEP->isInBounds() ? SCEV::FlagNSW
3278 : SCEV::FlagAnyWrap;
3280 const SCEV *TotalOffset = getZero(IntIdxTy);
3281 Type *CurTy = GEP->getType();
3282 bool FirstIter = true;
3283 for (const SCEV *IndexExpr : IndexExprs) {
3284 // Compute the (potentially symbolic) offset in bytes for this index.
3285 if (StructType *STy = dyn_cast<StructType>(CurTy)) {
3286 // For a struct, add the member offset.
3287 ConstantInt *Index = cast<SCEVConstant>(IndexExpr)->getValue();
3288 unsigned FieldNo = Index->getZExtValue();
3289 const SCEV *FieldOffset = getOffsetOfExpr(IntIdxTy, STy, FieldNo);
3291 // Add the field offset to the running total offset.
3292 TotalOffset = getAddExpr(TotalOffset, FieldOffset);
3294 // Update CurTy to the type of the field at Index.
3295 CurTy = STy->getTypeAtIndex(Index);
3297 // Update CurTy to its element type.
3299 assert(isa<PointerType>(CurTy) &&
3300 "The first index of a GEP indexes a pointer");
3301 CurTy = GEP->getSourceElementType();
3304 CurTy = GetElementPtrInst::getTypeAtIndex(CurTy, (uint64_t)0);
3306 // For an array, add the element offset, explicitly scaled.
3307 const SCEV *ElementSize = getSizeOfExpr(IntIdxTy, CurTy);
3308 // Getelementptr indices are signed.
3309 IndexExpr = getTruncateOrSignExtend(IndexExpr, IntIdxTy);
3311 // Multiply the index by the element size to compute the element offset.
3312 const SCEV *LocalOffset = getMulExpr(IndexExpr, ElementSize, Wrap);
3314 // Add the element offset to the running total offset.
3315 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
3319 // Add the total offset from all the GEP indices to the base.
3320 return getAddExpr(BaseExpr, TotalOffset, Wrap);
3323 std::tuple<SCEV *, FoldingSetNodeID, void *>
3324 ScalarEvolution::findExistingSCEVInCache(int SCEVType,
3325 ArrayRef<const SCEV *> Ops) {
3326 FoldingSetNodeID ID;
3328 ID.AddInteger(SCEVType);
3329 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
3330 ID.AddPointer(Ops[i]);
3331 return std::tuple<SCEV *, FoldingSetNodeID, void *>(
3332 UniqueSCEVs.FindNodeOrInsertPos(ID, IP), std::move(ID), IP);
3335 const SCEV *ScalarEvolution::getMinMaxExpr(unsigned Kind,
3336 SmallVectorImpl<const SCEV *> &Ops) {
3337 assert(!Ops.empty() && "Cannot get empty (u|s)(min|max)!");
3338 if (Ops.size() == 1) return Ops[0];
3340 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
3341 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
3342 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
3343 "Operand types don't match!");
3346 bool IsSigned = Kind == scSMaxExpr || Kind == scSMinExpr;
3347 bool IsMax = Kind == scSMaxExpr || Kind == scUMaxExpr;
3349 // Sort by complexity, this groups all similar expression types together.
3350 GroupByComplexity(Ops, &LI, DT);
3352 // Check if we have created the same expression before.
3353 if (const SCEV *S = std::get<0>(findExistingSCEVInCache(Kind, Ops))) {
3357 // If there are any constants, fold them together.
3359 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
3361 assert(Idx < Ops.size());
3362 auto FoldOp = [&](const APInt &LHS, const APInt &RHS) {
3363 if (Kind == scSMaxExpr)
3364 return APIntOps::smax(LHS, RHS);
3365 else if (Kind == scSMinExpr)
3366 return APIntOps::smin(LHS, RHS);
3367 else if (Kind == scUMaxExpr)
3368 return APIntOps::umax(LHS, RHS);
3369 else if (Kind == scUMinExpr)
3370 return APIntOps::umin(LHS, RHS);
3371 llvm_unreachable("Unknown SCEV min/max opcode");
3374 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
3375 // We found two constants, fold them together!
3376 ConstantInt *Fold = ConstantInt::get(
3377 getContext(), FoldOp(LHSC->getAPInt(), RHSC->getAPInt()));
3378 Ops[0] = getConstant(Fold);
3379 Ops.erase(Ops.begin()+1); // Erase the folded element
3380 if (Ops.size() == 1) return Ops[0];
3381 LHSC = cast<SCEVConstant>(Ops[0]);
3384 bool IsMinV = LHSC->getValue()->isMinValue(IsSigned);
3385 bool IsMaxV = LHSC->getValue()->isMaxValue(IsSigned);
3387 if (IsMax ? IsMinV : IsMaxV) {
3388 // If we are left with a constant minimum(/maximum)-int, strip it off.
3389 Ops.erase(Ops.begin());
3391 } else if (IsMax ? IsMaxV : IsMinV) {
3392 // If we have a max(/min) with a constant maximum(/minimum)-int,
3393 // it will always be the extremum.
3397 if (Ops.size() == 1) return Ops[0];
3400 // Find the first operation of the same kind
3401 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < Kind)
3404 // Check to see if one of the operands is of the same kind. If so, expand its
3405 // operands onto our operand list, and recurse to simplify.
3406 if (Idx < Ops.size()) {
3407 bool DeletedAny = false;
3408 while (Ops[Idx]->getSCEVType() == Kind) {
3409 const SCEVMinMaxExpr *SMME = cast<SCEVMinMaxExpr>(Ops[Idx]);
3410 Ops.erase(Ops.begin()+Idx);
3411 Ops.append(SMME->op_begin(), SMME->op_end());
3416 return getMinMaxExpr(Kind, Ops);
3419 // Okay, check to see if the same value occurs in the operand list twice. If
3420 // so, delete one. Since we sorted the list, these values are required to
3422 llvm::CmpInst::Predicate GEPred =
3423 IsSigned ? ICmpInst::ICMP_SGE : ICmpInst::ICMP_UGE;
3424 llvm::CmpInst::Predicate LEPred =
3425 IsSigned ? ICmpInst::ICMP_SLE : ICmpInst::ICMP_ULE;
3426 llvm::CmpInst::Predicate FirstPred = IsMax ? GEPred : LEPred;
3427 llvm::CmpInst::Predicate SecondPred = IsMax ? LEPred : GEPred;
3428 for (unsigned i = 0, e = Ops.size() - 1; i != e; ++i) {
3429 if (Ops[i] == Ops[i + 1] ||
3430 isKnownViaNonRecursiveReasoning(FirstPred, Ops[i], Ops[i + 1])) {
3431 // X op Y op Y --> X op Y
3432 // X op Y --> X, if we know X, Y are ordered appropriately
3433 Ops.erase(Ops.begin() + i + 1, Ops.begin() + i + 2);
3436 } else if (isKnownViaNonRecursiveReasoning(SecondPred, Ops[i],
3438 // X op Y --> Y, if we know X, Y are ordered appropriately
3439 Ops.erase(Ops.begin() + i, Ops.begin() + i + 1);
3445 if (Ops.size() == 1) return Ops[0];
3447 assert(!Ops.empty() && "Reduced smax down to nothing!");
3449 // Okay, it looks like we really DO need an expr. Check to see if we
3450 // already have one, otherwise create a new one.
3451 const SCEV *ExistingSCEV;
3452 FoldingSetNodeID ID;
3454 std::tie(ExistingSCEV, ID, IP) = findExistingSCEVInCache(Kind, Ops);
3456 return ExistingSCEV;
3457 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
3458 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
3459 SCEV *S = new (SCEVAllocator) SCEVMinMaxExpr(
3460 ID.Intern(SCEVAllocator), static_cast<SCEVTypes>(Kind), O, Ops.size());
3462 UniqueSCEVs.InsertNode(S, IP);
3463 addToLoopUseLists(S);
3467 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS, const SCEV *RHS) {
3468 SmallVector<const SCEV *, 2> Ops = {LHS, RHS};
3469 return getSMaxExpr(Ops);
3472 const SCEV *ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
3473 return getMinMaxExpr(scSMaxExpr, Ops);
3476 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS, const SCEV *RHS) {
3477 SmallVector<const SCEV *, 2> Ops = {LHS, RHS};
3478 return getUMaxExpr(Ops);
3481 const SCEV *ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
3482 return getMinMaxExpr(scUMaxExpr, Ops);
3485 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
3487 SmallVector<const SCEV *, 2> Ops = { LHS, RHS };
3488 return getSMinExpr(Ops);
3491 const SCEV *ScalarEvolution::getSMinExpr(SmallVectorImpl<const SCEV *> &Ops) {
3492 return getMinMaxExpr(scSMinExpr, Ops);
3495 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
3497 SmallVector<const SCEV *, 2> Ops = { LHS, RHS };
3498 return getUMinExpr(Ops);
3501 const SCEV *ScalarEvolution::getUMinExpr(SmallVectorImpl<const SCEV *> &Ops) {
3502 return getMinMaxExpr(scUMinExpr, Ops);
3505 const SCEV *ScalarEvolution::getSizeOfExpr(Type *IntTy, Type *AllocTy) {
3506 // We can bypass creating a target-independent
3507 // constant expression and then folding it back into a ConstantInt.
3508 // This is just a compile-time optimization.
3509 if (isa<ScalableVectorType>(AllocTy)) {
3510 Constant *NullPtr = Constant::getNullValue(AllocTy->getPointerTo());
3511 Constant *One = ConstantInt::get(IntTy, 1);
3512 Constant *GEP = ConstantExpr::getGetElementPtr(AllocTy, NullPtr, One);
3513 return getSCEV(ConstantExpr::getPtrToInt(GEP, IntTy));
3515 return getConstant(IntTy, getDataLayout().getTypeAllocSize(AllocTy));
3518 const SCEV *ScalarEvolution::getOffsetOfExpr(Type *IntTy,
3521 // We can bypass creating a target-independent
3522 // constant expression and then folding it back into a ConstantInt.
3523 // This is just a compile-time optimization.
3525 IntTy, getDataLayout().getStructLayout(STy)->getElementOffset(FieldNo));
3528 const SCEV *ScalarEvolution::getUnknown(Value *V) {
3529 // Don't attempt to do anything other than create a SCEVUnknown object
3530 // here. createSCEV only calls getUnknown after checking for all other
3531 // interesting possibilities, and any other code that calls getUnknown
3532 // is doing so in order to hide a value from SCEV canonicalization.
3534 FoldingSetNodeID ID;
3535 ID.AddInteger(scUnknown);
3538 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
3539 assert(cast<SCEVUnknown>(S)->getValue() == V &&
3540 "Stale SCEVUnknown in uniquing map!");
3543 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
3545 FirstUnknown = cast<SCEVUnknown>(S);
3546 UniqueSCEVs.InsertNode(S, IP);
3550 //===----------------------------------------------------------------------===//
3551 // Basic SCEV Analysis and PHI Idiom Recognition Code
3554 /// Test if values of the given type are analyzable within the SCEV
3555 /// framework. This primarily includes integer types, and it can optionally
3556 /// include pointer types if the ScalarEvolution class has access to
3557 /// target-specific information.
3558 bool ScalarEvolution::isSCEVable(Type *Ty) const {
3559 // Integers and pointers are always SCEVable.
3560 return Ty->isIntOrPtrTy();
3563 /// Return the size in bits of the specified type, for which isSCEVable must
3565 uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const {
3566 assert(isSCEVable(Ty) && "Type is not SCEVable!");
3567 if (Ty->isPointerTy())
3568 return getDataLayout().getIndexTypeSizeInBits(Ty);
3569 return getDataLayout().getTypeSizeInBits(Ty);
3572 /// Return a type with the same bitwidth as the given type and which represents
3573 /// how SCEV will treat the given type, for which isSCEVable must return
3574 /// true. For pointer types, this is the pointer index sized integer type.
3575 Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const {
3576 assert(isSCEVable(Ty) && "Type is not SCEVable!");
3578 if (Ty->isIntegerTy())
3581 // The only other support type is pointer.
3582 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
3583 return getDataLayout().getIndexType(Ty);
3586 Type *ScalarEvolution::getWiderType(Type *T1, Type *T2) const {
3587 return getTypeSizeInBits(T1) >= getTypeSizeInBits(T2) ? T1 : T2;
3590 const SCEV *ScalarEvolution::getCouldNotCompute() {
3591 return CouldNotCompute.get();
3594 bool ScalarEvolution::checkValidity(const SCEV *S) const {
3595 bool ContainsNulls = SCEVExprContains(S, [](const SCEV *S) {
3596 auto *SU = dyn_cast<SCEVUnknown>(S);
3597 return SU && SU->getValue() == nullptr;
3600 return !ContainsNulls;
3603 bool ScalarEvolution::containsAddRecurrence(const SCEV *S) {
3604 HasRecMapType::iterator I = HasRecMap.find(S);
3605 if (I != HasRecMap.end())
3609 SCEVExprContains(S, [](const SCEV *S) { return isa<SCEVAddRecExpr>(S); });
3610 HasRecMap.insert({S, FoundAddRec});
3614 /// Try to split a SCEVAddExpr into a pair of {SCEV, ConstantInt}.
3615 /// If \p S is a SCEVAddExpr and is composed of a sub SCEV S' and an
3616 /// offset I, then return {S', I}, else return {\p S, nullptr}.
3617 static std::pair<const SCEV *, ConstantInt *> splitAddExpr(const SCEV *S) {
3618 const auto *Add = dyn_cast<SCEVAddExpr>(S);
3620 return {S, nullptr};
3622 if (Add->getNumOperands() != 2)
3623 return {S, nullptr};
3625 auto *ConstOp = dyn_cast<SCEVConstant>(Add->getOperand(0));
3627 return {S, nullptr};
3629 return {Add->getOperand(1), ConstOp->getValue()};
3632 /// Return the ValueOffsetPair set for \p S. \p S can be represented
3633 /// by the value and offset from any ValueOffsetPair in the set.
3634 SetVector<ScalarEvolution::ValueOffsetPair> *
3635 ScalarEvolution::getSCEVValues(const SCEV *S) {
3636 ExprValueMapType::iterator SI = ExprValueMap.find_as(S);
3637 if (SI == ExprValueMap.end())
3640 if (VerifySCEVMap) {
3641 // Check there is no dangling Value in the set returned.
3642 for (const auto &VE : SI->second)
3643 assert(ValueExprMap.count(VE.first));
3649 /// Erase Value from ValueExprMap and ExprValueMap. ValueExprMap.erase(V)
3650 /// cannot be used separately. eraseValueFromMap should be used to remove
3651 /// V from ValueExprMap and ExprValueMap at the same time.
3652 void ScalarEvolution::eraseValueFromMap(Value *V) {
3653 ValueExprMapType::iterator I = ValueExprMap.find_as(V);
3654 if (I != ValueExprMap.end()) {
3655 const SCEV *S = I->second;
3656 // Remove {V, 0} from the set of ExprValueMap[S]
3657 if (SetVector<ValueOffsetPair> *SV = getSCEVValues(S))
3658 SV->remove({V, nullptr});
3660 // Remove {V, Offset} from the set of ExprValueMap[Stripped]
3661 const SCEV *Stripped;
3662 ConstantInt *Offset;
3663 std::tie(Stripped, Offset) = splitAddExpr(S);
3664 if (Offset != nullptr) {
3665 if (SetVector<ValueOffsetPair> *SV = getSCEVValues(Stripped))
3666 SV->remove({V, Offset});
3668 ValueExprMap.erase(V);
3672 /// Check whether value has nuw/nsw/exact set but SCEV does not.
3673 /// TODO: In reality it is better to check the poison recursively
3674 /// but this is better than nothing.
3675 static bool SCEVLostPoisonFlags(const SCEV *S, const Value *V) {
3676 if (auto *I = dyn_cast<Instruction>(V)) {
3677 if (isa<OverflowingBinaryOperator>(I)) {
3678 if (auto *NS = dyn_cast<SCEVNAryExpr>(S)) {
3679 if (I->hasNoSignedWrap() && !NS->hasNoSignedWrap())
3681 if (I->hasNoUnsignedWrap() && !NS->hasNoUnsignedWrap())
3684 } else if (isa<PossiblyExactOperator>(I) && I->isExact())
3690 /// Return an existing SCEV if it exists, otherwise analyze the expression and
3691 /// create a new one.
3692 const SCEV *ScalarEvolution::getSCEV(Value *V) {
3693 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
3695 const SCEV *S = getExistingSCEV(V);
3698 // During PHI resolution, it is possible to create two SCEVs for the same
3699 // V, so it is needed to double check whether V->S is inserted into
3700 // ValueExprMap before insert S->{V, 0} into ExprValueMap.
3701 std::pair<ValueExprMapType::iterator, bool> Pair =
3702 ValueExprMap.insert({SCEVCallbackVH(V, this), S});
3703 if (Pair.second && !SCEVLostPoisonFlags(S, V)) {
3704 ExprValueMap[S].insert({V, nullptr});
3706 // If S == Stripped + Offset, add Stripped -> {V, Offset} into
3708 const SCEV *Stripped = S;
3709 ConstantInt *Offset = nullptr;
3710 std::tie(Stripped, Offset) = splitAddExpr(S);
3711 // If stripped is SCEVUnknown, don't bother to save
3712 // Stripped -> {V, offset}. It doesn't simplify and sometimes even
3713 // increase the complexity of the expansion code.
3714 // If V is GetElementPtrInst, don't save Stripped -> {V, offset}
3715 // because it may generate add/sub instead of GEP in SCEV expansion.
3716 if (Offset != nullptr && !isa<SCEVUnknown>(Stripped) &&
3717 !isa<GetElementPtrInst>(V))
3718 ExprValueMap[Stripped].insert({V, Offset});
3724 const SCEV *ScalarEvolution::getExistingSCEV(Value *V) {
3725 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
3727 ValueExprMapType::iterator I = ValueExprMap.find_as(V);
3728 if (I != ValueExprMap.end()) {
3729 const SCEV *S = I->second;
3730 if (checkValidity(S))
3732 eraseValueFromMap(V);
3733 forgetMemoizedResults(S);
3738 /// Return a SCEV corresponding to -V = -1*V
3739 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V,
3740 SCEV::NoWrapFlags Flags) {
3741 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
3743 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
3745 Type *Ty = V->getType();
3746 Ty = getEffectiveSCEVType(Ty);
3748 V, getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))), Flags);
3751 /// If Expr computes ~A, return A else return nullptr
3752 static const SCEV *MatchNotExpr(const SCEV *Expr) {
3753 const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Expr);
3754 if (!Add || Add->getNumOperands() != 2 ||
3755 !Add->getOperand(0)->isAllOnesValue())
3758 const SCEVMulExpr *AddRHS = dyn_cast<SCEVMulExpr>(Add->getOperand(1));
3759 if (!AddRHS || AddRHS->getNumOperands() != 2 ||
3760 !AddRHS->getOperand(0)->isAllOnesValue())
3763 return AddRHS->getOperand(1);
3766 /// Return a SCEV corresponding to ~V = -1-V
3767 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
3768 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
3770 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
3772 // Fold ~(u|s)(min|max)(~x, ~y) to (u|s)(max|min)(x, y)
3773 if (const SCEVMinMaxExpr *MME = dyn_cast<SCEVMinMaxExpr>(V)) {
3774 auto MatchMinMaxNegation = [&](const SCEVMinMaxExpr *MME) {
3775 SmallVector<const SCEV *, 2> MatchedOperands;
3776 for (const SCEV *Operand : MME->operands()) {
3777 const SCEV *Matched = MatchNotExpr(Operand);
3779 return (const SCEV *)nullptr;
3780 MatchedOperands.push_back(Matched);
3782 return getMinMaxExpr(
3783 SCEVMinMaxExpr::negate(static_cast<SCEVTypes>(MME->getSCEVType())),
3786 if (const SCEV *Replaced = MatchMinMaxNegation(MME))
3790 Type *Ty = V->getType();
3791 Ty = getEffectiveSCEVType(Ty);
3792 const SCEV *AllOnes =
3793 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
3794 return getMinusSCEV(AllOnes, V);
3797 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
3798 SCEV::NoWrapFlags Flags,
3800 // Fast path: X - X --> 0.
3802 return getZero(LHS->getType());
3804 // We represent LHS - RHS as LHS + (-1)*RHS. This transformation
3805 // makes it so that we cannot make much use of NUW.
3806 auto AddFlags = SCEV::FlagAnyWrap;
3807 const bool RHSIsNotMinSigned =
3808 !getSignedRangeMin(RHS).isMinSignedValue();
3809 if (maskFlags(Flags, SCEV::FlagNSW) == SCEV::FlagNSW) {
3810 // Let M be the minimum representable signed value. Then (-1)*RHS
3811 // signed-wraps if and only if RHS is M. That can happen even for
3812 // a NSW subtraction because e.g. (-1)*M signed-wraps even though
3813 // -1 - M does not. So to transfer NSW from LHS - RHS to LHS +
3814 // (-1)*RHS, we need to prove that RHS != M.
3816 // If LHS is non-negative and we know that LHS - RHS does not
3817 // signed-wrap, then RHS cannot be M. So we can rule out signed-wrap
3818 // either by proving that RHS > M or that LHS >= 0.
3819 if (RHSIsNotMinSigned || isKnownNonNegative(LHS)) {
3820 AddFlags = SCEV::FlagNSW;
3824 // FIXME: Find a correct way to transfer NSW to (-1)*M when LHS -
3825 // RHS is NSW and LHS >= 0.
3827 // The difficulty here is that the NSW flag may have been proven
3828 // relative to a loop that is to be found in a recurrence in LHS and
3829 // not in RHS. Applying NSW to (-1)*M may then let the NSW have a
3830 // larger scope than intended.
3831 auto NegFlags = RHSIsNotMinSigned ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
3833 return getAddExpr(LHS, getNegativeSCEV(RHS, NegFlags), AddFlags, Depth);
3836 const SCEV *ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty,
3838 Type *SrcTy = V->getType();
3839 assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
3840 "Cannot truncate or zero extend with non-integer arguments!");
3841 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3842 return V; // No conversion
3843 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
3844 return getTruncateExpr(V, Ty, Depth);
3845 return getZeroExtendExpr(V, Ty, Depth);
3848 const SCEV *ScalarEvolution::getTruncateOrSignExtend(const SCEV *V, Type *Ty,
3850 Type *SrcTy = V->getType();
3851 assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
3852 "Cannot truncate or zero extend with non-integer arguments!");
3853 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3854 return V; // No conversion
3855 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
3856 return getTruncateExpr(V, Ty, Depth);
3857 return getSignExtendExpr(V, Ty, Depth);
3861 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) {
3862 Type *SrcTy = V->getType();
3863 assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
3864 "Cannot noop or zero extend with non-integer arguments!");
3865 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3866 "getNoopOrZeroExtend cannot truncate!");
3867 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3868 return V; // No conversion
3869 return getZeroExtendExpr(V, Ty);
3873 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) {
3874 Type *SrcTy = V->getType();
3875 assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
3876 "Cannot noop or sign extend with non-integer arguments!");
3877 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3878 "getNoopOrSignExtend cannot truncate!");
3879 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3880 return V; // No conversion
3881 return getSignExtendExpr(V, Ty);
3885 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) {
3886 Type *SrcTy = V->getType();
3887 assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
3888 "Cannot noop or any extend with non-integer arguments!");
3889 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3890 "getNoopOrAnyExtend cannot truncate!");
3891 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3892 return V; // No conversion
3893 return getAnyExtendExpr(V, Ty);
3897 ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) {
3898 Type *SrcTy = V->getType();
3899 assert(SrcTy->isIntOrPtrTy() && Ty->isIntOrPtrTy() &&
3900 "Cannot truncate or noop with non-integer arguments!");
3901 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
3902 "getTruncateOrNoop cannot extend!");
3903 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3904 return V; // No conversion
3905 return getTruncateExpr(V, Ty);
3908 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
3910 const SCEV *PromotedLHS = LHS;
3911 const SCEV *PromotedRHS = RHS;
3913 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
3914 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
3916 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
3918 return getUMaxExpr(PromotedLHS, PromotedRHS);
3921 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
3923 SmallVector<const SCEV *, 2> Ops = { LHS, RHS };
3924 return getUMinFromMismatchedTypes(Ops);
3927 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(
3928 SmallVectorImpl<const SCEV *> &Ops) {
3929 assert(!Ops.empty() && "At least one operand must be!");
3931 if (Ops.size() == 1)
3934 // Find the max type first.
3935 Type *MaxType = nullptr;
3938 MaxType = getWiderType(MaxType, S->getType());
3940 MaxType = S->getType();
3942 // Extend all ops to max type.
3943 SmallVector<const SCEV *, 2> PromotedOps;
3945 PromotedOps.push_back(getNoopOrZeroExtend(S, MaxType));
3948 return getUMinExpr(PromotedOps);
3951 const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) {
3952 // A pointer operand may evaluate to a nonpointer expression, such as null.
3953 if (!V->getType()->isPointerTy())
3957 if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) {
3958 V = Cast->getOperand();
3959 } else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) {
3960 const SCEV *PtrOp = nullptr;
3961 for (const SCEV *NAryOp : NAry->operands()) {
3962 if (NAryOp->getType()->isPointerTy()) {
3963 // Cannot find the base of an expression with multiple pointer ops.
3969 if (!PtrOp) // All operands were non-pointer.
3972 } else // Not something we can look further into.
3977 /// Push users of the given Instruction onto the given Worklist.
3979 PushDefUseChildren(Instruction *I,
3980 SmallVectorImpl<Instruction *> &Worklist) {
3981 // Push the def-use children onto the Worklist stack.
3982 for (User *U : I->users())
3983 Worklist.push_back(cast<Instruction>(U));
3986 void ScalarEvolution::forgetSymbolicName(Instruction *PN, const SCEV *SymName) {
3987 SmallVector<Instruction *, 16> Worklist;
3988 PushDefUseChildren(PN, Worklist);
3990 SmallPtrSet<Instruction *, 8> Visited;
3992 while (!Worklist.empty()) {
3993 Instruction *I = Worklist.pop_back_val();
3994 if (!Visited.insert(I).second)
3997 auto It = ValueExprMap.find_as(static_cast<Value *>(I));
3998 if (It != ValueExprMap.end()) {
3999 const SCEV *Old = It->second;
4001 // Short-circuit the def-use traversal if the symbolic name
4002 // ceases to appear in expressions.
4003 if (Old != SymName && !hasOperand(Old, SymName))
4006 // SCEVUnknown for a PHI either means that it has an unrecognized
4007 // structure, it's a PHI that's in the progress of being computed
4008 // by createNodeForPHI, or it's a single-value PHI. In the first case,
4009 // additional loop trip count information isn't going to change anything.
4010 // In the second case, createNodeForPHI will perform the necessary
4011 // updates on its own when it gets to that point. In the third, we do
4012 // want to forget the SCEVUnknown.
4013 if (!isa<PHINode>(I) ||
4014 !isa<SCEVUnknown>(Old) ||
4015 (I != PN && Old == SymName)) {
4016 eraseValueFromMap(It->first);
4017 forgetMemoizedResults(Old);
4021 PushDefUseChildren(I, Worklist);
4027 /// Takes SCEV S and Loop L. For each AddRec sub-expression, use its start
4028 /// expression in case its Loop is L. If it is not L then
4029 /// if IgnoreOtherLoops is true then use AddRec itself
4030 /// otherwise rewrite cannot be done.
4031 /// If SCEV contains non-invariant unknown SCEV rewrite cannot be done.
4032 class SCEVInitRewriter : public SCEVRewriteVisitor<SCEVInitRewriter> {
4034 static const SCEV *rewrite(const SCEV *S, const Loop *L, ScalarEvolution &SE,
4035 bool IgnoreOtherLoops = true) {
4036 SCEVInitRewriter Rewriter(L, SE);
4037 const SCEV *Result = Rewriter.visit(S);
4038 if (Rewriter.hasSeenLoopVariantSCEVUnknown())
4039 return SE.getCouldNotCompute();
4040 return Rewriter.hasSeenOtherLoops() && !IgnoreOtherLoops
4041 ? SE.getCouldNotCompute()
4045 const SCEV *visitUnknown(const SCEVUnknown *Expr) {
4046 if (!SE.isLoopInvariant(Expr, L))
4047 SeenLoopVariantSCEVUnknown = true;
4051 const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
4052 // Only re-write AddRecExprs for this loop.
4053 if (Expr->getLoop() == L)
4054 return Expr->getStart();
4055 SeenOtherLoops = true;
4059 bool hasSeenLoopVariantSCEVUnknown() { return SeenLoopVariantSCEVUnknown; }
4061 bool hasSeenOtherLoops() { return SeenOtherLoops; }
4064 explicit SCEVInitRewriter(const Loop *L, ScalarEvolution &SE)
4065 : SCEVRewriteVisitor(SE), L(L) {}
4068 bool SeenLoopVariantSCEVUnknown = false;
4069 bool SeenOtherLoops = false;
4072 /// Takes SCEV S and Loop L. For each AddRec sub-expression, use its post
4073 /// increment expression in case its Loop is L. If it is not L then
4074 /// use AddRec itself.
4075 /// If SCEV contains non-invariant unknown SCEV rewrite cannot be done.
4076 class SCEVPostIncRewriter : public SCEVRewriteVisitor<SCEVPostIncRewriter> {
4078 static const SCEV *rewrite(const SCEV *S, const Loop *L, ScalarEvolution &SE) {
4079 SCEVPostIncRewriter Rewriter(L, SE);
4080 const SCEV *Result = Rewriter.visit(S);
4081 return Rewriter.hasSeenLoopVariantSCEVUnknown()
4082 ? SE.getCouldNotCompute()
4086 const SCEV *visitUnknown(const SCEVUnknown *Expr) {
4087 if (!SE.isLoopInvariant(Expr, L))
4088 SeenLoopVariantSCEVUnknown = true;
4092 const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
4093 // Only re-write AddRecExprs for this loop.
4094 if (Expr->getLoop() == L)
4095 return Expr->getPostIncExpr(SE);
4096 SeenOtherLoops = true;
4100 bool hasSeenLoopVariantSCEVUnknown() { return SeenLoopVariantSCEVUnknown; }
4102 bool hasSeenOtherLoops() { return SeenOtherLoops; }
4105 explicit SCEVPostIncRewriter(const Loop *L, ScalarEvolution &SE)
4106 : SCEVRewriteVisitor(SE), L(L) {}
4109 bool SeenLoopVariantSCEVUnknown = false;
4110 bool SeenOtherLoops = false;
4113 /// This class evaluates the compare condition by matching it against the
4114 /// condition of loop latch. If there is a match we assume a true value
4115 /// for the condition while building SCEV nodes.
4116 class SCEVBackedgeConditionFolder
4117 : public SCEVRewriteVisitor<SCEVBackedgeConditionFolder> {
4119 static const SCEV *rewrite(const SCEV *S, const Loop *L,
4120 ScalarEvolution &SE) {
4121 bool IsPosBECond = false;
4122 Value *BECond = nullptr;
4123 if (BasicBlock *Latch = L->getLoopLatch()) {
4124 BranchInst *BI = dyn_cast<BranchInst>(Latch->getTerminator());
4125 if (BI && BI->isConditional()) {
4126 assert(BI->getSuccessor(0) != BI->getSuccessor(1) &&
4127 "Both outgoing branches should not target same header!");
4128 BECond = BI->getCondition();
4129 IsPosBECond = BI->getSuccessor(0) == L->getHeader();
4134 SCEVBackedgeConditionFolder Rewriter(L, BECond, IsPosBECond, SE);
4135 return Rewriter.visit(S);
4138 const SCEV *visitUnknown(const SCEVUnknown *Expr) {
4139 const SCEV *Result = Expr;
4140 bool InvariantF = SE.isLoopInvariant(Expr, L);
4143 Instruction *I = cast<Instruction>(Expr->getValue());
4144 switch (I->getOpcode()) {
4145 case Instruction::Select: {
4146 SelectInst *SI = cast<SelectInst>(I);
4147 Optional<const SCEV *> Res =
4148 compareWithBackedgeCondition(SI->getCondition());
4149 if (Res.hasValue()) {
4150 bool IsOne = cast<SCEVConstant>(Res.getValue())->getValue()->isOne();
4151 Result = SE.getSCEV(IsOne ? SI->getTrueValue() : SI->getFalseValue());
4156 Optional<const SCEV *> Res = compareWithBackedgeCondition(I);
4158 Result = Res.getValue();
4167 explicit SCEVBackedgeConditionFolder(const Loop *L, Value *BECond,
4168 bool IsPosBECond, ScalarEvolution &SE)
4169 : SCEVRewriteVisitor(SE), L(L), BackedgeCond(BECond),
4170 IsPositiveBECond(IsPosBECond) {}
4172 Optional<const SCEV *> compareWithBackedgeCondition(Value *IC);
4175 /// Loop back condition.
4176 Value *BackedgeCond = nullptr;
4177 /// Set to true if loop back is on positive branch condition.
4178 bool IsPositiveBECond;
4181 Optional<const SCEV *>
4182 SCEVBackedgeConditionFolder::compareWithBackedgeCondition(Value *IC) {
4184 // If value matches the backedge condition for loop latch,
4185 // then return a constant evolution node based on loopback
4187 if (BackedgeCond == IC)
4188 return IsPositiveBECond ? SE.getOne(Type::getInt1Ty(SE.getContext()))
4189 : SE.getZero(Type::getInt1Ty(SE.getContext()));
4193 class SCEVShiftRewriter : public SCEVRewriteVisitor<SCEVShiftRewriter> {
4195 static const SCEV *rewrite(const SCEV *S, const Loop *L,
4196 ScalarEvolution &SE) {
4197 SCEVShiftRewriter Rewriter(L, SE);
4198 const SCEV *Result = Rewriter.visit(S);
4199 return Rewriter.isValid() ? Result : SE.getCouldNotCompute();
4202 const SCEV *visitUnknown(const SCEVUnknown *Expr) {
4203 // Only allow AddRecExprs for this loop.
4204 if (!SE.isLoopInvariant(Expr, L))
4209 const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
4210 if (Expr->getLoop() == L && Expr->isAffine())
4211 return SE.getMinusSCEV(Expr, Expr->getStepRecurrence(SE));
4216 bool isValid() { return Valid; }
4219 explicit SCEVShiftRewriter(const Loop *L, ScalarEvolution &SE)
4220 : SCEVRewriteVisitor(SE), L(L) {}
4226 } // end anonymous namespace
4229 ScalarEvolution::proveNoWrapViaConstantRanges(const SCEVAddRecExpr *AR) {
4230 if (!AR->isAffine())
4231 return SCEV::FlagAnyWrap;
4233 using OBO = OverflowingBinaryOperator;
4235 SCEV::NoWrapFlags Result = SCEV::FlagAnyWrap;
4237 if (!AR->hasNoSignedWrap()) {
4238 ConstantRange AddRecRange = getSignedRange(AR);
4239 ConstantRange IncRange = getSignedRange(AR->getStepRecurrence(*this));
4241 auto NSWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
4242 Instruction::Add, IncRange, OBO::NoSignedWrap);
4243 if (NSWRegion.contains(AddRecRange))
4244 Result = ScalarEvolution::setFlags(Result, SCEV::FlagNSW);
4247 if (!AR->hasNoUnsignedWrap()) {
4248 ConstantRange AddRecRange = getUnsignedRange(AR);
4249 ConstantRange IncRange = getUnsignedRange(AR->getStepRecurrence(*this));
4251 auto NUWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
4252 Instruction::Add, IncRange, OBO::NoUnsignedWrap);
4253 if (NUWRegion.contains(AddRecRange))
4254 Result = ScalarEvolution::setFlags(Result, SCEV::FlagNUW);
4262 /// Represents an abstract binary operation. This may exist as a
4263 /// normal instruction or constant expression, or may have been
4264 /// derived from an expression tree.
4272 /// Op is set if this BinaryOp corresponds to a concrete LLVM instruction or
4273 /// constant expression.
4274 Operator *Op = nullptr;
4276 explicit BinaryOp(Operator *Op)
4277 : Opcode(Op->getOpcode()), LHS(Op->getOperand(0)), RHS(Op->getOperand(1)),
4279 if (auto *OBO = dyn_cast<OverflowingBinaryOperator>(Op)) {
4280 IsNSW = OBO->hasNoSignedWrap();
4281 IsNUW = OBO->hasNoUnsignedWrap();
4285 explicit BinaryOp(unsigned Opcode, Value *LHS, Value *RHS, bool IsNSW = false,
4287 : Opcode(Opcode), LHS(LHS), RHS(RHS), IsNSW(IsNSW), IsNUW(IsNUW) {}
4290 } // end anonymous namespace
4292 /// Try to map \p V into a BinaryOp, and return \c None on failure.
4293 static Optional<BinaryOp> MatchBinaryOp(Value *V, DominatorTree &DT) {
4294 auto *Op = dyn_cast<Operator>(V);
4298 // Implementation detail: all the cleverness here should happen without
4299 // creating new SCEV expressions -- our caller knowns tricks to avoid creating
4300 // SCEV expressions when possible, and we should not break that.
4302 switch (Op->getOpcode()) {
4303 case Instruction::Add:
4304 case Instruction::Sub:
4305 case Instruction::Mul:
4306 case Instruction::UDiv:
4307 case Instruction::URem:
4308 case Instruction::And:
4309 case Instruction::Or:
4310 case Instruction::AShr:
4311 case Instruction::Shl:
4312 return BinaryOp(Op);
4314 case Instruction::Xor:
4315 if (auto *RHSC = dyn_cast<ConstantInt>(Op->getOperand(1)))
4316 // If the RHS of the xor is a signmask, then this is just an add.
4317 // Instcombine turns add of signmask into xor as a strength reduction step.
4318 if (RHSC->getValue().isSignMask())
4319 return BinaryOp(Instruction::Add, Op->getOperand(0), Op->getOperand(1));
4320 return BinaryOp(Op);
4322 case Instruction::LShr:
4323 // Turn logical shift right of a constant into a unsigned divide.
4324 if (ConstantInt *SA = dyn_cast<ConstantInt>(Op->getOperand(1))) {
4325 uint32_t BitWidth = cast<IntegerType>(Op->getType())->getBitWidth();
4327 // If the shift count is not less than the bitwidth, the result of
4328 // the shift is undefined. Don't try to analyze it, because the
4329 // resolution chosen here may differ from the resolution chosen in
4330 // other parts of the compiler.
4331 if (SA->getValue().ult(BitWidth)) {
4333 ConstantInt::get(SA->getContext(),
4334 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
4335 return BinaryOp(Instruction::UDiv, Op->getOperand(0), X);
4338 return BinaryOp(Op);
4340 case Instruction::ExtractValue: {
4341 auto *EVI = cast<ExtractValueInst>(Op);
4342 if (EVI->getNumIndices() != 1 || EVI->getIndices()[0] != 0)
4345 auto *WO = dyn_cast<WithOverflowInst>(EVI->getAggregateOperand());
4349 Instruction::BinaryOps BinOp = WO->getBinaryOp();
4350 bool Signed = WO->isSigned();
4351 // TODO: Should add nuw/nsw flags for mul as well.
4352 if (BinOp == Instruction::Mul || !isOverflowIntrinsicNoWrap(WO, DT))
4353 return BinaryOp(BinOp, WO->getLHS(), WO->getRHS());
4355 // Now that we know that all uses of the arithmetic-result component of
4356 // CI are guarded by the overflow check, we can go ahead and pretend
4357 // that the arithmetic is non-overflowing.
4358 return BinaryOp(BinOp, WO->getLHS(), WO->getRHS(),
4359 /* IsNSW = */ Signed, /* IsNUW = */ !Signed);
4366 // Recognise intrinsic loop.decrement.reg, and as this has exactly the same
4367 // semantics as a Sub, return a binary sub expression.
4368 if (auto *II = dyn_cast<IntrinsicInst>(V))
4369 if (II->getIntrinsicID() == Intrinsic::loop_decrement_reg)
4370 return BinaryOp(Instruction::Sub, II->getOperand(0), II->getOperand(1));
4375 /// Helper function to createAddRecFromPHIWithCasts. We have a phi
4376 /// node whose symbolic (unknown) SCEV is \p SymbolicPHI, which is updated via
4377 /// the loop backedge by a SCEVAddExpr, possibly also with a few casts on the
4378 /// way. This function checks if \p Op, an operand of this SCEVAddExpr,
4379 /// follows one of the following patterns:
4380 /// Op == (SExt ix (Trunc iy (%SymbolicPHI) to ix) to iy)
4381 /// Op == (ZExt ix (Trunc iy (%SymbolicPHI) to ix) to iy)
4382 /// If the SCEV expression of \p Op conforms with one of the expected patterns
4383 /// we return the type of the truncation operation, and indicate whether the
4384 /// truncated type should be treated as signed/unsigned by setting
4385 /// \p Signed to true/false, respectively.
4386 static Type *isSimpleCastedPHI(const SCEV *Op, const SCEVUnknown *SymbolicPHI,
4387 bool &Signed, ScalarEvolution &SE) {
4388 // The case where Op == SymbolicPHI (that is, with no type conversions on
4389 // the way) is handled by the regular add recurrence creating logic and
4390 // would have already been triggered in createAddRecForPHI. Reaching it here
4391 // means that createAddRecFromPHI had failed for this PHI before (e.g.,
4392 // because one of the other operands of the SCEVAddExpr updating this PHI is
4395 // Here we look for the case where Op = (ext(trunc(SymbolicPHI))), and in
4396 // this case predicates that allow us to prove that Op == SymbolicPHI will
4398 if (Op == SymbolicPHI)
4401 unsigned SourceBits = SE.getTypeSizeInBits(SymbolicPHI->getType());
4402 unsigned NewBits = SE.getTypeSizeInBits(Op->getType());
4403 if (SourceBits != NewBits)
4406 const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(Op);
4407 const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(Op);
4410 const SCEVTruncateExpr *Trunc =
4411 SExt ? dyn_cast<SCEVTruncateExpr>(SExt->getOperand())
4412 : dyn_cast<SCEVTruncateExpr>(ZExt->getOperand());
4415 const SCEV *X = Trunc->getOperand();
4416 if (X != SymbolicPHI)
4418 Signed = SExt != nullptr;
4419 return Trunc->getType();
4422 static const Loop *isIntegerLoopHeaderPHI(const PHINode *PN, LoopInfo &LI) {
4423 if (!PN->getType()->isIntegerTy())
4425 const Loop *L = LI.getLoopFor(PN->getParent());
4426 if (!L || L->getHeader() != PN->getParent())
4431 // Analyze \p SymbolicPHI, a SCEV expression of a phi node, and check if the
4432 // computation that updates the phi follows the following pattern:
4433 // (SExt/ZExt ix (Trunc iy (%SymbolicPHI) to ix) to iy) + InvariantAccum
4434 // which correspond to a phi->trunc->sext/zext->add->phi update chain.
4435 // If so, try to see if it can be rewritten as an AddRecExpr under some
4436 // Predicates. If successful, return them as a pair. Also cache the results
4439 // Example usage scenario:
4440 // Say the Rewriter is called for the following SCEV:
4441 // 8 * ((sext i32 (trunc i64 %X to i32) to i64) + %Step)
4443 // %X = phi i64 (%Start, %BEValue)
4444 // It will visitMul->visitAdd->visitSExt->visitTrunc->visitUnknown(%X),
4445 // and call this function with %SymbolicPHI = %X.
4447 // The analysis will find that the value coming around the backedge has
4448 // the following SCEV:
4449 // BEValue = ((sext i32 (trunc i64 %X to i32) to i64) + %Step)
4450 // Upon concluding that this matches the desired pattern, the function
4451 // will return the pair {NewAddRec, SmallPredsVec} where:
4452 // NewAddRec = {%Start,+,%Step}
4453 // SmallPredsVec = {P1, P2, P3} as follows:
4454 // P1(WrapPred): AR: {trunc(%Start),+,(trunc %Step)}<nsw> Flags: <nssw>
4455 // P2(EqualPred): %Start == (sext i32 (trunc i64 %Start to i32) to i64)
4456 // P3(EqualPred): %Step == (sext i32 (trunc i64 %Step to i32) to i64)
4457 // The returned pair means that SymbolicPHI can be rewritten into NewAddRec
4458 // under the predicates {P1,P2,P3}.
4459 // This predicated rewrite will be cached in PredicatedSCEVRewrites:
4460 // PredicatedSCEVRewrites[{%X,L}] = {NewAddRec, {P1,P2,P3)}
4464 // 1) Extend the Induction descriptor to also support inductions that involve
4465 // casts: When needed (namely, when we are called in the context of the
4466 // vectorizer induction analysis), a Set of cast instructions will be
4467 // populated by this method, and provided back to isInductionPHI. This is
4468 // needed to allow the vectorizer to properly record them to be ignored by
4469 // the cost model and to avoid vectorizing them (otherwise these casts,
4470 // which are redundant under the runtime overflow checks, will be
4471 // vectorized, which can be costly).
4473 // 2) Support additional induction/PHISCEV patterns: We also want to support
4474 // inductions where the sext-trunc / zext-trunc operations (partly) occur
4475 // after the induction update operation (the induction increment):
4477 // (Trunc iy (SExt/ZExt ix (%SymbolicPHI + InvariantAccum) to iy) to ix)
4478 // which correspond to a phi->add->trunc->sext/zext->phi update chain.
4480 // (Trunc iy ((SExt/ZExt ix (%SymbolicPhi) to iy) + InvariantAccum) to ix)
4481 // which correspond to a phi->trunc->add->sext/zext->phi update chain.
4483 // 3) Outline common code with createAddRecFromPHI to avoid duplication.
4484 Optional<std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>>
4485 ScalarEvolution::createAddRecFromPHIWithCastsImpl(const SCEVUnknown *SymbolicPHI) {
4486 SmallVector<const SCEVPredicate *, 3> Predicates;
4488 // *** Part1: Analyze if we have a phi-with-cast pattern for which we can
4489 // return an AddRec expression under some predicate.
4491 auto *PN = cast<PHINode>(SymbolicPHI->getValue());
4492 const Loop *L = isIntegerLoopHeaderPHI(PN, LI);
4493 assert(L && "Expecting an integer loop header phi");
4495 // The loop may have multiple entrances or multiple exits; we can analyze
4496 // this phi as an addrec if it has a unique entry value and a unique
4498 Value *BEValueV = nullptr, *StartValueV = nullptr;
4499 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
4500 Value *V = PN->getIncomingValue(i);
4501 if (L->contains(PN->getIncomingBlock(i))) {
4504 } else if (BEValueV != V) {
4508 } else if (!StartValueV) {
4510 } else if (StartValueV != V) {
4511 StartValueV = nullptr;
4515 if (!BEValueV || !StartValueV)
4518 const SCEV *BEValue = getSCEV(BEValueV);
4520 // If the value coming around the backedge is an add with the symbolic
4521 // value we just inserted, possibly with casts that we can ignore under
4522 // an appropriate runtime guard, then we found a simple induction variable!
4523 const auto *Add = dyn_cast<SCEVAddExpr>(BEValue);
4527 // If there is a single occurrence of the symbolic value, possibly
4528 // casted, replace it with a recurrence.
4529 unsigned FoundIndex = Add->getNumOperands();
4530 Type *TruncTy = nullptr;
4532 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
4534 isSimpleCastedPHI(Add->getOperand(i), SymbolicPHI, Signed, *this)))
4535 if (FoundIndex == e) {
4540 if (FoundIndex == Add->getNumOperands())
4543 // Create an add with everything but the specified operand.
4544 SmallVector<const SCEV *, 8> Ops;
4545 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
4546 if (i != FoundIndex)
4547 Ops.push_back(Add->getOperand(i));
4548 const SCEV *Accum = getAddExpr(Ops);
4550 // The runtime checks will not be valid if the step amount is
4551 // varying inside the loop.
4552 if (!isLoopInvariant(Accum, L))
4555 // *** Part2: Create the predicates
4557 // Analysis was successful: we have a phi-with-cast pattern for which we
4558 // can return an AddRec expression under the following predicates:
4560 // P1: A Wrap predicate that guarantees that Trunc(Start) + i*Trunc(Accum)
4561 // fits within the truncated type (does not overflow) for i = 0 to n-1.
4562 // P2: An Equal predicate that guarantees that
4563 // Start = (Ext ix (Trunc iy (Start) to ix) to iy)
4564 // P3: An Equal predicate that guarantees that
4565 // Accum = (Ext ix (Trunc iy (Accum) to ix) to iy)
4567 // As we next prove, the above predicates guarantee that:
4568 // Start + i*Accum = (Ext ix (Trunc iy ( Start + i*Accum ) to ix) to iy)
4571 // More formally, we want to prove that:
4572 // Expr(i+1) = Start + (i+1) * Accum
4573 // = (Ext ix (Trunc iy (Expr(i)) to ix) to iy) + Accum
4576 // 1) Expr(0) = Start
4577 // 2) Expr(1) = Start + Accum
4578 // = (Ext ix (Trunc iy (Start) to ix) to iy) + Accum :: from P2
4579 // 3) Induction hypothesis (step i):
4580 // Expr(i) = (Ext ix (Trunc iy (Expr(i-1)) to ix) to iy) + Accum
4584 // = Start + (i+1)*Accum
4585 // = (Start + i*Accum) + Accum
4586 // = Expr(i) + Accum
4587 // = (Ext ix (Trunc iy (Expr(i-1)) to ix) to iy) + Accum + Accum
4590 // = (Ext ix (Trunc iy (Start + (i-1)*Accum) to ix) to iy) + Accum + Accum
4592 // = (Ext ix (Trunc iy (Start + (i-1)*Accum) to ix) to iy)
4593 // + (Ext ix (Trunc iy (Accum) to ix) to iy)
4594 // + Accum :: from P3
4596 // = (Ext ix (Trunc iy ((Start + (i-1)*Accum) + Accum) to ix) to iy)
4597 // + Accum :: from P1: Ext(x)+Ext(y)=>Ext(x+y)
4599 // = (Ext ix (Trunc iy (Start + i*Accum) to ix) to iy) + Accum
4600 // = (Ext ix (Trunc iy (Expr(i)) to ix) to iy) + Accum
4602 // By induction, the same applies to all iterations 1<=i<n:
4605 // Create a truncated addrec for which we will add a no overflow check (P1).
4606 const SCEV *StartVal = getSCEV(StartValueV);
4607 const SCEV *PHISCEV =
4608 getAddRecExpr(getTruncateExpr(StartVal, TruncTy),
4609 getTruncateExpr(Accum, TruncTy), L, SCEV::FlagAnyWrap);
4611 // PHISCEV can be either a SCEVConstant or a SCEVAddRecExpr.
4612 // ex: If truncated Accum is 0 and StartVal is a constant, then PHISCEV
4613 // will be constant.
4615 // If PHISCEV is a constant, then P1 degenerates into P2 or P3, so we don't
4617 if (const auto *AR = dyn_cast<SCEVAddRecExpr>(PHISCEV)) {
4618 SCEVWrapPredicate::IncrementWrapFlags AddedFlags =
4619 Signed ? SCEVWrapPredicate::IncrementNSSW
4620 : SCEVWrapPredicate::IncrementNUSW;
4621 const SCEVPredicate *AddRecPred = getWrapPredicate(AR, AddedFlags);
4622 Predicates.push_back(AddRecPred);
4625 // Create the Equal Predicates P2,P3:
4627 // It is possible that the predicates P2 and/or P3 are computable at
4628 // compile time due to StartVal and/or Accum being constants.
4629 // If either one is, then we can check that now and escape if either P2
4632 // Construct the extended SCEV: (Ext ix (Trunc iy (Expr) to ix) to iy)
4633 // for each of StartVal and Accum
4634 auto getExtendedExpr = [&](const SCEV *Expr,
4635 bool CreateSignExtend) -> const SCEV * {
4636 assert(isLoopInvariant(Expr, L) && "Expr is expected to be invariant");
4637 const SCEV *TruncatedExpr = getTruncateExpr(Expr, TruncTy);
4638 const SCEV *ExtendedExpr =
4639 CreateSignExtend ? getSignExtendExpr(TruncatedExpr, Expr->getType())
4640 : getZeroExtendExpr(TruncatedExpr, Expr->getType());
4641 return ExtendedExpr;
4645 // ExtendedExpr = (Ext ix (Trunc iy (Expr) to ix) to iy
4646 // = getExtendedExpr(Expr)
4647 // Determine whether the predicate P: Expr == ExtendedExpr
4648 // is known to be false at compile time
4649 auto PredIsKnownFalse = [&](const SCEV *Expr,
4650 const SCEV *ExtendedExpr) -> bool {
4651 return Expr != ExtendedExpr &&
4652 isKnownPredicate(ICmpInst::ICMP_NE, Expr, ExtendedExpr);
4655 const SCEV *StartExtended = getExtendedExpr(StartVal, Signed);
4656 if (PredIsKnownFalse(StartVal, StartExtended)) {
4657 LLVM_DEBUG(dbgs() << "P2 is compile-time false\n";);
4661 // The Step is always Signed (because the overflow checks are either
4663 const SCEV *AccumExtended = getExtendedExpr(Accum, /*CreateSignExtend=*/true);
4664 if (PredIsKnownFalse(Accum, AccumExtended)) {
4665 LLVM_DEBUG(dbgs() << "P3 is compile-time false\n";);
4669 auto AppendPredicate = [&](const SCEV *Expr,
4670 const SCEV *ExtendedExpr) -> void {
4671 if (Expr != ExtendedExpr &&
4672 !isKnownPredicate(ICmpInst::ICMP_EQ, Expr, ExtendedExpr)) {
4673 const SCEVPredicate *Pred = getEqualPredicate(Expr, ExtendedExpr);
4674 LLVM_DEBUG(dbgs() << "Added Predicate: " << *Pred);
4675 Predicates.push_back(Pred);
4679 AppendPredicate(StartVal, StartExtended);
4680 AppendPredicate(Accum, AccumExtended);
4682 // *** Part3: Predicates are ready. Now go ahead and create the new addrec in
4683 // which the casts had been folded away. The caller can rewrite SymbolicPHI
4684 // into NewAR if it will also add the runtime overflow checks specified in
4686 auto *NewAR = getAddRecExpr(StartVal, Accum, L, SCEV::FlagAnyWrap);
4688 std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>> PredRewrite =
4689 std::make_pair(NewAR, Predicates);
4690 // Remember the result of the analysis for this SCEV at this locayyytion.
4691 PredicatedSCEVRewrites[{SymbolicPHI, L}] = PredRewrite;
4695 Optional<std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>>
4696 ScalarEvolution::createAddRecFromPHIWithCasts(const SCEVUnknown *SymbolicPHI) {
4697 auto *PN = cast<PHINode>(SymbolicPHI->getValue());
4698 const Loop *L = isIntegerLoopHeaderPHI(PN, LI);
4702 // Check to see if we already analyzed this PHI.
4703 auto I = PredicatedSCEVRewrites.find({SymbolicPHI, L});
4704 if (I != PredicatedSCEVRewrites.end()) {
4705 std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>> Rewrite =
4707 // Analysis was done before and failed to create an AddRec:
4708 if (Rewrite.first == SymbolicPHI)
4710 // Analysis was done before and succeeded to create an AddRec under
4712 assert(isa<SCEVAddRecExpr>(Rewrite.first) && "Expected an AddRec");
4713 assert(!(Rewrite.second).empty() && "Expected to find Predicates");
4717 Optional<std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>>
4718 Rewrite = createAddRecFromPHIWithCastsImpl(SymbolicPHI);
4720 // Record in the cache that the analysis failed
4722 SmallVector<const SCEVPredicate *, 3> Predicates;
4723 PredicatedSCEVRewrites[{SymbolicPHI, L}] = {SymbolicPHI, Predicates};
4730 // FIXME: This utility is currently required because the Rewriter currently
4731 // does not rewrite this expression:
4732 // {0, +, (sext ix (trunc iy to ix) to iy)}
4733 // into {0, +, %step},
4734 // even when the following Equal predicate exists:
4735 // "%step == (sext ix (trunc iy to ix) to iy)".
4736 bool PredicatedScalarEvolution::areAddRecsEqualWithPreds(
4737 const SCEVAddRecExpr *AR1, const SCEVAddRecExpr *AR2) const {
4741 auto areExprsEqual = [&](const SCEV *Expr1, const SCEV *Expr2) -> bool {
4742 if (Expr1 != Expr2 && !Preds.implies(SE.getEqualPredicate(Expr1, Expr2)) &&
4743 !Preds.implies(SE.getEqualPredicate(Expr2, Expr1)))
4748 if (!areExprsEqual(AR1->getStart(), AR2->getStart()) ||
4749 !areExprsEqual(AR1->getStepRecurrence(SE), AR2->getStepRecurrence(SE)))
4754 /// A helper function for createAddRecFromPHI to handle simple cases.
4756 /// This function tries to find an AddRec expression for the simplest (yet most
4757 /// common) cases: PN = PHI(Start, OP(Self, LoopInvariant)).
4758 /// If it fails, createAddRecFromPHI will use a more general, but slow,
4759 /// technique for finding the AddRec expression.
4760 const SCEV *ScalarEvolution::createSimpleAffineAddRec(PHINode *PN,
4762 Value *StartValueV) {
4763 const Loop *L = LI.getLoopFor(PN->getParent());
4764 assert(L && L->getHeader() == PN->getParent());
4765 assert(BEValueV && StartValueV);
4767 auto BO = MatchBinaryOp(BEValueV, DT);
4771 if (BO->Opcode != Instruction::Add)
4774 const SCEV *Accum = nullptr;
4775 if (BO->LHS == PN && L->isLoopInvariant(BO->RHS))
4776 Accum = getSCEV(BO->RHS);
4777 else if (BO->RHS == PN && L->isLoopInvariant(BO->LHS))
4778 Accum = getSCEV(BO->LHS);
4783 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
4785 Flags = setFlags(Flags, SCEV::FlagNUW);
4787 Flags = setFlags(Flags, SCEV::FlagNSW);
4789 const SCEV *StartVal = getSCEV(StartValueV);
4790 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
4792 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
4794 // We can add Flags to the post-inc expression only if we
4795 // know that it is *undefined behavior* for BEValueV to
4797 if (auto *BEInst = dyn_cast<Instruction>(BEValueV))
4798 if (isLoopInvariant(Accum, L) && isAddRecNeverPoison(BEInst, L))
4799 (void)getAddRecExpr(getAddExpr(StartVal, Accum), Accum, L, Flags);
4804 const SCEV *ScalarEvolution::createAddRecFromPHI(PHINode *PN) {
4805 const Loop *L = LI.getLoopFor(PN->getParent());
4806 if (!L || L->getHeader() != PN->getParent())
4809 // The loop may have multiple entrances or multiple exits; we can analyze
4810 // this phi as an addrec if it has a unique entry value and a unique
4812 Value *BEValueV = nullptr, *StartValueV = nullptr;
4813 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
4814 Value *V = PN->getIncomingValue(i);
4815 if (L->contains(PN->getIncomingBlock(i))) {
4818 } else if (BEValueV != V) {
4822 } else if (!StartValueV) {
4824 } else if (StartValueV != V) {
4825 StartValueV = nullptr;
4829 if (!BEValueV || !StartValueV)
4832 assert(ValueExprMap.find_as(PN) == ValueExprMap.end() &&
4833 "PHI node already processed?");
4835 // First, try to find AddRec expression without creating a fictituos symbolic
4837 if (auto *S = createSimpleAffineAddRec(PN, BEValueV, StartValueV))
4840 // Handle PHI node value symbolically.
4841 const SCEV *SymbolicName = getUnknown(PN);
4842 ValueExprMap.insert({SCEVCallbackVH(PN, this), SymbolicName});
4844 // Using this symbolic name for the PHI, analyze the value coming around
4846 const SCEV *BEValue = getSCEV(BEValueV);
4848 // NOTE: If BEValue is loop invariant, we know that the PHI node just
4849 // has a special value for the first iteration of the loop.
4851 // If the value coming around the backedge is an add with the symbolic
4852 // value we just inserted, then we found a simple induction variable!
4853 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
4854 // If there is a single occurrence of the symbolic value, replace it
4855 // with a recurrence.
4856 unsigned FoundIndex = Add->getNumOperands();
4857 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
4858 if (Add->getOperand(i) == SymbolicName)
4859 if (FoundIndex == e) {
4864 if (FoundIndex != Add->getNumOperands()) {
4865 // Create an add with everything but the specified operand.
4866 SmallVector<const SCEV *, 8> Ops;
4867 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
4868 if (i != FoundIndex)
4869 Ops.push_back(SCEVBackedgeConditionFolder::rewrite(Add->getOperand(i),
4871 const SCEV *Accum = getAddExpr(Ops);
4873 // This is not a valid addrec if the step amount is varying each
4874 // loop iteration, but is not itself an addrec in this loop.
4875 if (isLoopInvariant(Accum, L) ||
4876 (isa<SCEVAddRecExpr>(Accum) &&
4877 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
4878 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
4880 if (auto BO = MatchBinaryOp(BEValueV, DT)) {
4881 if (BO->Opcode == Instruction::Add && BO->LHS == PN) {
4883 Flags = setFlags(Flags, SCEV::FlagNUW);
4885 Flags = setFlags(Flags, SCEV::FlagNSW);
4887 } else if (GEPOperator *GEP = dyn_cast<GEPOperator>(BEValueV)) {
4888 // If the increment is an inbounds GEP, then we know the address
4889 // space cannot be wrapped around. We cannot make any guarantee
4890 // about signed or unsigned overflow because pointers are
4891 // unsigned but we may have a negative index from the base
4892 // pointer. We can guarantee that no unsigned wrap occurs if the
4893 // indices form a positive value.
4894 if (GEP->isInBounds() && GEP->getOperand(0) == PN) {
4895 Flags = setFlags(Flags, SCEV::FlagNW);
4897 const SCEV *Ptr = getSCEV(GEP->getPointerOperand());
4898 if (isKnownPositive(getMinusSCEV(getSCEV(GEP), Ptr)))
4899 Flags = setFlags(Flags, SCEV::FlagNUW);
4902 // We cannot transfer nuw and nsw flags from subtraction
4903 // operations -- sub nuw X, Y is not the same as add nuw X, -Y
4907 const SCEV *StartVal = getSCEV(StartValueV);
4908 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
4910 // Okay, for the entire analysis of this edge we assumed the PHI
4911 // to be symbolic. We now need to go back and purge all of the
4912 // entries for the scalars that use the symbolic expression.
4913 forgetSymbolicName(PN, SymbolicName);
4914 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
4916 // We can add Flags to the post-inc expression only if we
4917 // know that it is *undefined behavior* for BEValueV to
4919 if (auto *BEInst = dyn_cast<Instruction>(BEValueV))
4920 if (isLoopInvariant(Accum, L) && isAddRecNeverPoison(BEInst, L))
4921 (void)getAddRecExpr(getAddExpr(StartVal, Accum), Accum, L, Flags);
4927 // Otherwise, this could be a loop like this:
4928 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
4929 // In this case, j = {1,+,1} and BEValue is j.
4930 // Because the other in-value of i (0) fits the evolution of BEValue
4931 // i really is an addrec evolution.
4933 // We can generalize this saying that i is the shifted value of BEValue
4934 // by one iteration:
4935 // PHI(f(0), f({1,+,1})) --> f({0,+,1})
4936 const SCEV *Shifted = SCEVShiftRewriter::rewrite(BEValue, L, *this);
4937 const SCEV *Start = SCEVInitRewriter::rewrite(Shifted, L, *this, false);
4938 if (Shifted != getCouldNotCompute() &&
4939 Start != getCouldNotCompute()) {
4940 const SCEV *StartVal = getSCEV(StartValueV);
4941 if (Start == StartVal) {
4942 // Okay, for the entire analysis of this edge we assumed the PHI
4943 // to be symbolic. We now need to go back and purge all of the
4944 // entries for the scalars that use the symbolic expression.
4945 forgetSymbolicName(PN, SymbolicName);
4946 ValueExprMap[SCEVCallbackVH(PN, this)] = Shifted;
4952 // Remove the temporary PHI node SCEV that has been inserted while intending
4953 // to create an AddRecExpr for this PHI node. We can not keep this temporary
4954 // as it will prevent later (possibly simpler) SCEV expressions to be added
4955 // to the ValueExprMap.
4956 eraseValueFromMap(PN);
4961 // Checks if the SCEV S is available at BB. S is considered available at BB
4962 // if S can be materialized at BB without introducing a fault.
4963 static bool IsAvailableOnEntry(const Loop *L, DominatorTree &DT, const SCEV *S,
4965 struct CheckAvailable {
4966 bool TraversalDone = false;
4967 bool Available = true;
4969 const Loop *L = nullptr; // The loop BB is in (can be nullptr)
4970 BasicBlock *BB = nullptr;
4973 CheckAvailable(const Loop *L, BasicBlock *BB, DominatorTree &DT)
4974 : L(L), BB(BB), DT(DT) {}
4976 bool setUnavailable() {
4977 TraversalDone = true;
4982 bool follow(const SCEV *S) {
4983 switch (S->getSCEVType()) {
4984 case scConstant: case scTruncate: case scZeroExtend: case scSignExtend:
4985 case scAddExpr: case scMulExpr: case scUMaxExpr: case scSMaxExpr:
4988 // These expressions are available if their operand(s) is/are.
4991 case scAddRecExpr: {
4992 // We allow add recurrences that are on the loop BB is in, or some
4993 // outer loop. This guarantees availability because the value of the
4994 // add recurrence at BB is simply the "current" value of the induction
4995 // variable. We can relax this in the future; for instance an add
4996 // recurrence on a sibling dominating loop is also available at BB.
4997 const auto *ARLoop = cast<SCEVAddRecExpr>(S)->getLoop();
4998 if (L && (ARLoop == L || ARLoop->contains(L)))
5001 return setUnavailable();
5005 // For SCEVUnknown, we check for simple dominance.
5006 const auto *SU = cast<SCEVUnknown>(S);
5007 Value *V = SU->getValue();
5009 if (isa<Argument>(V))
5012 if (isa<Instruction>(V) && DT.dominates(cast<Instruction>(V), BB))
5015 return setUnavailable();
5019 case scCouldNotCompute:
5020 // We do not try to smart about these at all.
5021 return setUnavailable();
5023 llvm_unreachable("switch should be fully covered!");
5026 bool isDone() { return TraversalDone; }
5029 CheckAvailable CA(L, BB, DT);
5030 SCEVTraversal<CheckAvailable> ST(CA);
5033 return CA.Available;
5036 // Try to match a control flow sequence that branches out at BI and merges back
5037 // at Merge into a "C ? LHS : RHS" select pattern. Return true on a successful
5039 static bool BrPHIToSelect(DominatorTree &DT, BranchInst *BI, PHINode *Merge,
5040 Value *&C, Value *&LHS, Value *&RHS) {
5041 C = BI->getCondition();
5043 BasicBlockEdge LeftEdge(BI->getParent(), BI->getSuccessor(0));
5044 BasicBlockEdge RightEdge(BI->getParent(), BI->getSuccessor(1));
5046 if (!LeftEdge.isSingleEdge())
5049 assert(RightEdge.isSingleEdge() && "Follows from LeftEdge.isSingleEdge()");
5051 Use &LeftUse = Merge->getOperandUse(0);
5052 Use &RightUse = Merge->getOperandUse(1);
5054 if (DT.dominates(LeftEdge, LeftUse) && DT.dominates(RightEdge, RightUse)) {
5060 if (DT.dominates(LeftEdge, RightUse) && DT.dominates(RightEdge, LeftUse)) {
5069 const SCEV *ScalarEvolution::createNodeFromSelectLikePHI(PHINode *PN) {
5071 [&](BasicBlock *BB) { return DT.isReachableFromEntry(BB); };
5072 if (PN->getNumIncomingValues() == 2 && all_of(PN->blocks(), IsReachable)) {
5073 const Loop *L = LI.getLoopFor(PN->getParent());
5075 // We don't want to break LCSSA, even in a SCEV expression tree.
5076 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i)
5077 if (LI.getLoopFor(PN->getIncomingBlock(i)) != L)
5082 // br %cond, label %left, label %right
5088 // V = phi [ %x, %left ], [ %y, %right ]
5090 // as "select %cond, %x, %y"
5092 BasicBlock *IDom = DT[PN->getParent()]->getIDom()->getBlock();
5093 assert(IDom && "At least the entry block should dominate PN");
5095 auto *BI = dyn_cast<BranchInst>(IDom->getTerminator());
5096 Value *Cond = nullptr, *LHS = nullptr, *RHS = nullptr;
5098 if (BI && BI->isConditional() &&
5099 BrPHIToSelect(DT, BI, PN, Cond, LHS, RHS) &&
5100 IsAvailableOnEntry(L, DT, getSCEV(LHS), PN->getParent()) &&
5101 IsAvailableOnEntry(L, DT, getSCEV(RHS), PN->getParent()))
5102 return createNodeForSelectOrPHI(PN, Cond, LHS, RHS);
5108 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
5109 if (const SCEV *S = createAddRecFromPHI(PN))
5112 if (const SCEV *S = createNodeFromSelectLikePHI(PN))
5115 // If the PHI has a single incoming value, follow that value, unless the
5116 // PHI's incoming blocks are in a different loop, in which case doing so
5117 // risks breaking LCSSA form. Instcombine would normally zap these, but
5118 // it doesn't have DominatorTree information, so it may miss cases.
5119 if (Value *V = SimplifyInstruction(PN, {getDataLayout(), &TLI, &DT, &AC}))
5120 if (LI.replacementPreservesLCSSAForm(PN, V))
5123 // If it's not a loop phi, we can't handle it yet.
5124 return getUnknown(PN);
5127 const SCEV *ScalarEvolution::createNodeForSelectOrPHI(Instruction *I,
5131 // Handle "constant" branch or select. This can occur for instance when a
5132 // loop pass transforms an inner loop and moves on to process the outer loop.
5133 if (auto *CI = dyn_cast<ConstantInt>(Cond))
5134 return getSCEV(CI->isOne() ? TrueVal : FalseVal);
5136 // Try to match some simple smax or umax patterns.
5137 auto *ICI = dyn_cast<ICmpInst>(Cond);
5139 return getUnknown(I);
5141 Value *LHS = ICI->getOperand(0);
5142 Value *RHS = ICI->getOperand(1);
5144 switch (ICI->getPredicate()) {
5145 case ICmpInst::ICMP_SLT:
5146 case ICmpInst::ICMP_SLE:
5147 std::swap(LHS, RHS);
5149 case ICmpInst::ICMP_SGT:
5150 case ICmpInst::ICMP_SGE:
5151 // a >s b ? a+x : b+x -> smax(a, b)+x
5152 // a >s b ? b+x : a+x -> smin(a, b)+x
5153 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType())) {
5154 const SCEV *LS = getNoopOrSignExtend(getSCEV(LHS), I->getType());
5155 const SCEV *RS = getNoopOrSignExtend(getSCEV(RHS), I->getType());
5156 const SCEV *LA = getSCEV(TrueVal);
5157 const SCEV *RA = getSCEV(FalseVal);
5158 const SCEV *LDiff = getMinusSCEV(LA, LS);
5159 const SCEV *RDiff = getMinusSCEV(RA, RS);
5161 return getAddExpr(getSMaxExpr(LS, RS), LDiff);
5162 LDiff = getMinusSCEV(LA, RS);
5163 RDiff = getMinusSCEV(RA, LS);
5165 return getAddExpr(getSMinExpr(LS, RS), LDiff);
5168 case ICmpInst::ICMP_ULT:
5169 case ICmpInst::ICMP_ULE:
5170 std::swap(LHS, RHS);
5172 case ICmpInst::ICMP_UGT:
5173 case ICmpInst::ICMP_UGE:
5174 // a >u b ? a+x : b+x -> umax(a, b)+x
5175 // a >u b ? b+x : a+x -> umin(a, b)+x
5176 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType())) {
5177 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
5178 const SCEV *RS = getNoopOrZeroExtend(getSCEV(RHS), I->getType());
5179 const SCEV *LA = getSCEV(TrueVal);
5180 const SCEV *RA = getSCEV(FalseVal);
5181 const SCEV *LDiff = getMinusSCEV(LA, LS);
5182 const SCEV *RDiff = getMinusSCEV(RA, RS);
5184 return getAddExpr(getUMaxExpr(LS, RS), LDiff);
5185 LDiff = getMinusSCEV(LA, RS);
5186 RDiff = getMinusSCEV(RA, LS);
5188 return getAddExpr(getUMinExpr(LS, RS), LDiff);
5191 case ICmpInst::ICMP_NE:
5192 // n != 0 ? n+x : 1+x -> umax(n, 1)+x
5193 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType()) &&
5194 isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
5195 const SCEV *One = getOne(I->getType());
5196 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
5197 const SCEV *LA = getSCEV(TrueVal);
5198 const SCEV *RA = getSCEV(FalseVal);
5199 const SCEV *LDiff = getMinusSCEV(LA, LS);
5200 const SCEV *RDiff = getMinusSCEV(RA, One);
5202 return getAddExpr(getUMaxExpr(One, LS), LDiff);
5205 case ICmpInst::ICMP_EQ:
5206 // n == 0 ? 1+x : n+x -> umax(n, 1)+x
5207 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType()) &&
5208 isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
5209 const SCEV *One = getOne(I->getType());
5210 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
5211 const SCEV *LA = getSCEV(TrueVal);
5212 const SCEV *RA = getSCEV(FalseVal);
5213 const SCEV *LDiff = getMinusSCEV(LA, One);
5214 const SCEV *RDiff = getMinusSCEV(RA, LS);
5216 return getAddExpr(getUMaxExpr(One, LS), LDiff);
5223 return getUnknown(I);
5226 /// Expand GEP instructions into add and multiply operations. This allows them
5227 /// to be analyzed by regular SCEV code.
5228 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
5229 // Don't attempt to analyze GEPs over unsized objects.
5230 if (!GEP->getSourceElementType()->isSized())
5231 return getUnknown(GEP);
5233 SmallVector<const SCEV *, 4> IndexExprs;
5234 for (auto Index = GEP->idx_begin(); Index != GEP->idx_end(); ++Index)
5235 IndexExprs.push_back(getSCEV(*Index));
5236 return getGEPExpr(GEP, IndexExprs);
5239 uint32_t ScalarEvolution::GetMinTrailingZerosImpl(const SCEV *S) {
5240 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
5241 return C->getAPInt().countTrailingZeros();
5243 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
5244 return std::min(GetMinTrailingZeros(T->getOperand()),
5245 (uint32_t)getTypeSizeInBits(T->getType()));
5247 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
5248 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
5249 return OpRes == getTypeSizeInBits(E->getOperand()->getType())
5250 ? getTypeSizeInBits(E->getType())
5254 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
5255 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
5256 return OpRes == getTypeSizeInBits(E->getOperand()->getType())
5257 ? getTypeSizeInBits(E->getType())
5261 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
5262 // The result is the min of all operands results.
5263 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
5264 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
5265 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
5269 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
5270 // The result is the sum of all operands results.
5271 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
5272 uint32_t BitWidth = getTypeSizeInBits(M->getType());
5273 for (unsigned i = 1, e = M->getNumOperands();
5274 SumOpRes != BitWidth && i != e; ++i)
5276 std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)), BitWidth);
5280 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
5281 // The result is the min of all operands results.
5282 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
5283 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
5284 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
5288 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
5289 // The result is the min of all operands results.
5290 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
5291 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
5292 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
5296 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
5297 // The result is the min of all operands results.
5298 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
5299 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
5300 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
5304 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
5305 // For a SCEVUnknown, ask ValueTracking.
5306 KnownBits Known = computeKnownBits(U->getValue(), getDataLayout(), 0, &AC, nullptr, &DT);
5307 return Known.countMinTrailingZeros();
5314 uint32_t ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
5315 auto I = MinTrailingZerosCache.find(S);
5316 if (I != MinTrailingZerosCache.end())
5319 uint32_t Result = GetMinTrailingZerosImpl(S);
5320 auto InsertPair = MinTrailingZerosCache.insert({S, Result});
5321 assert(InsertPair.second && "Should insert a new key");
5322 return InsertPair.first->second;
5325 /// Helper method to assign a range to V from metadata present in the IR.
5326 static Optional<ConstantRange> GetRangeFromMetadata(Value *V) {
5327 if (Instruction *I = dyn_cast<Instruction>(V))
5328 if (MDNode *MD = I->getMetadata(LLVMContext::MD_range))
5329 return getConstantRangeFromMetadata(*MD);
5334 /// Determine the range for a particular SCEV. If SignHint is
5335 /// HINT_RANGE_UNSIGNED (resp. HINT_RANGE_SIGNED) then getRange prefers ranges
5336 /// with a "cleaner" unsigned (resp. signed) representation.
5337 const ConstantRange &
5338 ScalarEvolution::getRangeRef(const SCEV *S,
5339 ScalarEvolution::RangeSignHint SignHint) {
5340 DenseMap<const SCEV *, ConstantRange> &Cache =
5341 SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED ? UnsignedRanges
5343 ConstantRange::PreferredRangeType RangeType =
5344 SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED
5345 ? ConstantRange::Unsigned : ConstantRange::Signed;
5347 // See if we've computed this range already.
5348 DenseMap<const SCEV *, ConstantRange>::iterator I = Cache.find(S);
5349 if (I != Cache.end())
5352 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
5353 return setRange(C, SignHint, ConstantRange(C->getAPInt()));
5355 unsigned BitWidth = getTypeSizeInBits(S->getType());
5356 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
5357 using OBO = OverflowingBinaryOperator;
5359 // If the value has known zeros, the maximum value will have those known zeros
5361 uint32_t TZ = GetMinTrailingZeros(S);
5363 if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED)
5364 ConservativeResult =
5365 ConstantRange(APInt::getMinValue(BitWidth),
5366 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
5368 ConservativeResult = ConstantRange(
5369 APInt::getSignedMinValue(BitWidth),
5370 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
5373 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
5374 ConstantRange X = getRangeRef(Add->getOperand(0), SignHint);
5375 unsigned WrapType = OBO::AnyWrap;
5376 if (Add->hasNoSignedWrap())
5377 WrapType |= OBO::NoSignedWrap;
5378 if (Add->hasNoUnsignedWrap())
5379 WrapType |= OBO::NoUnsignedWrap;
5380 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
5381 X = X.addWithNoWrap(getRangeRef(Add->getOperand(i), SignHint),
5382 WrapType, RangeType);
5383 return setRange(Add, SignHint,
5384 ConservativeResult.intersectWith(X, RangeType));
5387 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
5388 ConstantRange X = getRangeRef(Mul->getOperand(0), SignHint);
5389 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
5390 X = X.multiply(getRangeRef(Mul->getOperand(i), SignHint));
5391 return setRange(Mul, SignHint,
5392 ConservativeResult.intersectWith(X, RangeType));
5395 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
5396 ConstantRange X = getRangeRef(SMax->getOperand(0), SignHint);
5397 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
5398 X = X.smax(getRangeRef(SMax->getOperand(i), SignHint));
5399 return setRange(SMax, SignHint,
5400 ConservativeResult.intersectWith(X, RangeType));
5403 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
5404 ConstantRange X = getRangeRef(UMax->getOperand(0), SignHint);
5405 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
5406 X = X.umax(getRangeRef(UMax->getOperand(i), SignHint));
5407 return setRange(UMax, SignHint,
5408 ConservativeResult.intersectWith(X, RangeType));
5411 if (const SCEVSMinExpr *SMin = dyn_cast<SCEVSMinExpr>(S)) {
5412 ConstantRange X = getRangeRef(SMin->getOperand(0), SignHint);
5413 for (unsigned i = 1, e = SMin->getNumOperands(); i != e; ++i)
5414 X = X.smin(getRangeRef(SMin->getOperand(i), SignHint));
5415 return setRange(SMin, SignHint,
5416 ConservativeResult.intersectWith(X, RangeType));
5419 if (const SCEVUMinExpr *UMin = dyn_cast<SCEVUMinExpr>(S)) {
5420 ConstantRange X = getRangeRef(UMin->getOperand(0), SignHint);
5421 for (unsigned i = 1, e = UMin->getNumOperands(); i != e; ++i)
5422 X = X.umin(getRangeRef(UMin->getOperand(i), SignHint));
5423 return setRange(UMin, SignHint,
5424 ConservativeResult.intersectWith(X, RangeType));
5427 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
5428 ConstantRange X = getRangeRef(UDiv->getLHS(), SignHint);
5429 ConstantRange Y = getRangeRef(UDiv->getRHS(), SignHint);
5430 return setRange(UDiv, SignHint,
5431 ConservativeResult.intersectWith(X.udiv(Y), RangeType));
5434 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
5435 ConstantRange X = getRangeRef(ZExt->getOperand(), SignHint);
5436 return setRange(ZExt, SignHint,
5437 ConservativeResult.intersectWith(X.zeroExtend(BitWidth),
5441 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
5442 ConstantRange X = getRangeRef(SExt->getOperand(), SignHint);
5443 return setRange(SExt, SignHint,
5444 ConservativeResult.intersectWith(X.signExtend(BitWidth),
5448 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
5449 ConstantRange X = getRangeRef(Trunc->getOperand(), SignHint);
5450 return setRange(Trunc, SignHint,
5451 ConservativeResult.intersectWith(X.truncate(BitWidth),
5455 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
5456 // If there's no unsigned wrap, the value will never be less than its
5458 if (AddRec->hasNoUnsignedWrap()) {
5459 APInt UnsignedMinValue = getUnsignedRangeMin(AddRec->getStart());
5460 if (!UnsignedMinValue.isNullValue())
5461 ConservativeResult = ConservativeResult.intersectWith(
5462 ConstantRange(UnsignedMinValue, APInt(BitWidth, 0)), RangeType);
5465 // If there's no signed wrap, and all the operands except initial value have
5466 // the same sign or zero, the value won't ever be:
5467 // 1: smaller than initial value if operands are non negative,
5468 // 2: bigger than initial value if operands are non positive.
5469 // For both cases, value can not cross signed min/max boundary.
5470 if (AddRec->hasNoSignedWrap()) {
5471 bool AllNonNeg = true;
5472 bool AllNonPos = true;
5473 for (unsigned i = 1, e = AddRec->getNumOperands(); i != e; ++i) {
5474 if (!isKnownNonNegative(AddRec->getOperand(i)))
5476 if (!isKnownNonPositive(AddRec->getOperand(i)))
5480 ConservativeResult = ConservativeResult.intersectWith(
5481 ConstantRange::getNonEmpty(getSignedRangeMin(AddRec->getStart()),
5482 APInt::getSignedMinValue(BitWidth)),
5485 ConservativeResult = ConservativeResult.intersectWith(
5486 ConstantRange::getNonEmpty(
5487 APInt::getSignedMinValue(BitWidth),
5488 getSignedRangeMax(AddRec->getStart()) + 1),
5492 // TODO: non-affine addrec
5493 if (AddRec->isAffine()) {
5494 const SCEV *MaxBECount = getConstantMaxBackedgeTakenCount(AddRec->getLoop());
5495 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
5496 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
5497 auto RangeFromAffine = getRangeForAffineAR(
5498 AddRec->getStart(), AddRec->getStepRecurrence(*this), MaxBECount,
5500 if (!RangeFromAffine.isFullSet())
5501 ConservativeResult =
5502 ConservativeResult.intersectWith(RangeFromAffine, RangeType);
5504 auto RangeFromFactoring = getRangeViaFactoring(
5505 AddRec->getStart(), AddRec->getStepRecurrence(*this), MaxBECount,
5507 if (!RangeFromFactoring.isFullSet())
5508 ConservativeResult =
5509 ConservativeResult.intersectWith(RangeFromFactoring, RangeType);
5513 return setRange(AddRec, SignHint, std::move(ConservativeResult));
5516 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
5517 // Check if the IR explicitly contains !range metadata.
5518 Optional<ConstantRange> MDRange = GetRangeFromMetadata(U->getValue());
5519 if (MDRange.hasValue())
5520 ConservativeResult = ConservativeResult.intersectWith(MDRange.getValue(),
5523 // Split here to avoid paying the compile-time cost of calling both
5524 // computeKnownBits and ComputeNumSignBits. This restriction can be lifted
5526 const DataLayout &DL = getDataLayout();
5527 if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED) {
5528 // For a SCEVUnknown, ask ValueTracking.
5529 KnownBits Known = computeKnownBits(U->getValue(), DL, 0, &AC, nullptr, &DT);
5530 if (Known.getBitWidth() != BitWidth)
5531 Known = Known.zextOrTrunc(BitWidth);
5532 // If Known does not result in full-set, intersect with it.
5533 if (Known.getMinValue() != Known.getMaxValue() + 1)
5534 ConservativeResult = ConservativeResult.intersectWith(
5535 ConstantRange(Known.getMinValue(), Known.getMaxValue() + 1),
5538 assert(SignHint == ScalarEvolution::HINT_RANGE_SIGNED &&
5539 "generalize as needed!");
5540 unsigned NS = ComputeNumSignBits(U->getValue(), DL, 0, &AC, nullptr, &DT);
5541 // If the pointer size is larger than the index size type, this can cause
5542 // NS to be larger than BitWidth. So compensate for this.
5543 if (U->getType()->isPointerTy()) {
5544 unsigned ptrSize = DL.getPointerTypeSizeInBits(U->getType());
5545 int ptrIdxDiff = ptrSize - BitWidth;
5546 if (ptrIdxDiff > 0 && ptrSize > BitWidth && NS > (unsigned)ptrIdxDiff)
5551 ConservativeResult = ConservativeResult.intersectWith(
5552 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
5553 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1) + 1),
5557 // A range of Phi is a subset of union of all ranges of its input.
5558 if (const PHINode *Phi = dyn_cast<PHINode>(U->getValue())) {
5559 // Make sure that we do not run over cycled Phis.
5560 if (PendingPhiRanges.insert(Phi).second) {
5561 ConstantRange RangeFromOps(BitWidth, /*isFullSet=*/false);
5562 for (auto &Op : Phi->operands()) {
5563 auto OpRange = getRangeRef(getSCEV(Op), SignHint);
5564 RangeFromOps = RangeFromOps.unionWith(OpRange);
5565 // No point to continue if we already have a full set.
5566 if (RangeFromOps.isFullSet())
5569 ConservativeResult =
5570 ConservativeResult.intersectWith(RangeFromOps, RangeType);
5571 bool Erased = PendingPhiRanges.erase(Phi);
5572 assert(Erased && "Failed to erase Phi properly?");
5577 return setRange(U, SignHint, std::move(ConservativeResult));
5580 return setRange(S, SignHint, std::move(ConservativeResult));
5583 // Given a StartRange, Step and MaxBECount for an expression compute a range of
5584 // values that the expression can take. Initially, the expression has a value
5585 // from StartRange and then is changed by Step up to MaxBECount times. Signed
5586 // argument defines if we treat Step as signed or unsigned.
5587 static ConstantRange getRangeForAffineARHelper(APInt Step,
5588 const ConstantRange &StartRange,
5589 const APInt &MaxBECount,
5590 unsigned BitWidth, bool Signed) {
5591 // If either Step or MaxBECount is 0, then the expression won't change, and we
5592 // just need to return the initial range.
5593 if (Step == 0 || MaxBECount == 0)
5596 // If we don't know anything about the initial value (i.e. StartRange is
5597 // FullRange), then we don't know anything about the final range either.
5598 // Return FullRange.
5599 if (StartRange.isFullSet())
5600 return ConstantRange::getFull(BitWidth);
5602 // If Step is signed and negative, then we use its absolute value, but we also
5603 // note that we're moving in the opposite direction.
5604 bool Descending = Signed && Step.isNegative();
5607 // This is correct even for INT_SMIN. Let's look at i8 to illustrate this:
5608 // abs(INT_SMIN) = abs(-128) = abs(0x80) = -0x80 = 0x80 = 128.
5609 // This equations hold true due to the well-defined wrap-around behavior of
5613 // Check if Offset is more than full span of BitWidth. If it is, the
5614 // expression is guaranteed to overflow.
5615 if (APInt::getMaxValue(StartRange.getBitWidth()).udiv(Step).ult(MaxBECount))
5616 return ConstantRange::getFull(BitWidth);
5618 // Offset is by how much the expression can change. Checks above guarantee no
5620 APInt Offset = Step * MaxBECount;
5622 // Minimum value of the final range will match the minimal value of StartRange
5623 // if the expression is increasing and will be decreased by Offset otherwise.
5624 // Maximum value of the final range will match the maximal value of StartRange
5625 // if the expression is decreasing and will be increased by Offset otherwise.
5626 APInt StartLower = StartRange.getLower();
5627 APInt StartUpper = StartRange.getUpper() - 1;
5628 APInt MovedBoundary = Descending ? (StartLower - std::move(Offset))
5629 : (StartUpper + std::move(Offset));
5631 // It's possible that the new minimum/maximum value will fall into the initial
5632 // range (due to wrap around). This means that the expression can take any
5633 // value in this bitwidth, and we have to return full range.
5634 if (StartRange.contains(MovedBoundary))
5635 return ConstantRange::getFull(BitWidth);
5638 Descending ? std::move(MovedBoundary) : std::move(StartLower);
5640 Descending ? std::move(StartUpper) : std::move(MovedBoundary);
5643 // No overflow detected, return [StartLower, StartUpper + Offset + 1) range.
5644 return ConstantRange::getNonEmpty(std::move(NewLower), std::move(NewUpper));
5647 ConstantRange ScalarEvolution::getRangeForAffineAR(const SCEV *Start,
5649 const SCEV *MaxBECount,
5650 unsigned BitWidth) {
5651 assert(!isa<SCEVCouldNotCompute>(MaxBECount) &&
5652 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth &&
5655 MaxBECount = getNoopOrZeroExtend(MaxBECount, Start->getType());
5656 APInt MaxBECountValue = getUnsignedRangeMax(MaxBECount);
5658 // First, consider step signed.
5659 ConstantRange StartSRange = getSignedRange(Start);
5660 ConstantRange StepSRange = getSignedRange(Step);
5662 // If Step can be both positive and negative, we need to find ranges for the
5663 // maximum absolute step values in both directions and union them.
5665 getRangeForAffineARHelper(StepSRange.getSignedMin(), StartSRange,
5666 MaxBECountValue, BitWidth, /* Signed = */ true);
5667 SR = SR.unionWith(getRangeForAffineARHelper(StepSRange.getSignedMax(),
5668 StartSRange, MaxBECountValue,
5669 BitWidth, /* Signed = */ true));
5671 // Next, consider step unsigned.
5672 ConstantRange UR = getRangeForAffineARHelper(
5673 getUnsignedRangeMax(Step), getUnsignedRange(Start),
5674 MaxBECountValue, BitWidth, /* Signed = */ false);
5676 // Finally, intersect signed and unsigned ranges.
5677 return SR.intersectWith(UR, ConstantRange::Smallest);
5680 ConstantRange ScalarEvolution::getRangeViaFactoring(const SCEV *Start,
5682 const SCEV *MaxBECount,
5683 unsigned BitWidth) {
5684 // RangeOf({C?A:B,+,C?P:Q}) == RangeOf(C?{A,+,P}:{B,+,Q})
5685 // == RangeOf({A,+,P}) union RangeOf({B,+,Q})
5687 struct SelectPattern {
5688 Value *Condition = nullptr;
5692 explicit SelectPattern(ScalarEvolution &SE, unsigned BitWidth,
5694 Optional<unsigned> CastOp;
5695 APInt Offset(BitWidth, 0);
5697 assert(SE.getTypeSizeInBits(S->getType()) == BitWidth &&
5700 // Peel off a constant offset:
5701 if (auto *SA = dyn_cast<SCEVAddExpr>(S)) {
5702 // In the future we could consider being smarter here and handle
5703 // {Start+Step,+,Step} too.
5704 if (SA->getNumOperands() != 2 || !isa<SCEVConstant>(SA->getOperand(0)))
5707 Offset = cast<SCEVConstant>(SA->getOperand(0))->getAPInt();
5708 S = SA->getOperand(1);
5711 // Peel off a cast operation
5712 if (auto *SCast = dyn_cast<SCEVCastExpr>(S)) {
5713 CastOp = SCast->getSCEVType();
5714 S = SCast->getOperand();
5717 using namespace llvm::PatternMatch;
5719 auto *SU = dyn_cast<SCEVUnknown>(S);
5720 const APInt *TrueVal, *FalseVal;
5722 !match(SU->getValue(), m_Select(m_Value(Condition), m_APInt(TrueVal),
5723 m_APInt(FalseVal)))) {
5724 Condition = nullptr;
5728 TrueValue = *TrueVal;
5729 FalseValue = *FalseVal;
5731 // Re-apply the cast we peeled off earlier
5732 if (CastOp.hasValue())
5735 llvm_unreachable("Unknown SCEV cast type!");
5738 TrueValue = TrueValue.trunc(BitWidth);
5739 FalseValue = FalseValue.trunc(BitWidth);
5742 TrueValue = TrueValue.zext(BitWidth);
5743 FalseValue = FalseValue.zext(BitWidth);
5746 TrueValue = TrueValue.sext(BitWidth);
5747 FalseValue = FalseValue.sext(BitWidth);
5751 // Re-apply the constant offset we peeled off earlier
5752 TrueValue += Offset;
5753 FalseValue += Offset;
5756 bool isRecognized() { return Condition != nullptr; }
5759 SelectPattern StartPattern(*this, BitWidth, Start);
5760 if (!StartPattern.isRecognized())
5761 return ConstantRange::getFull(BitWidth);
5763 SelectPattern StepPattern(*this, BitWidth, Step);
5764 if (!StepPattern.isRecognized())
5765 return ConstantRange::getFull(BitWidth);
5767 if (StartPattern.Condition != StepPattern.Condition) {
5768 // We don't handle this case today; but we could, by considering four
5769 // possibilities below instead of two. I'm not sure if there are cases where
5770 // that will help over what getRange already does, though.
5771 return ConstantRange::getFull(BitWidth);
5774 // NB! Calling ScalarEvolution::getConstant is fine, but we should not try to
5775 // construct arbitrary general SCEV expressions here. This function is called
5776 // from deep in the call stack, and calling getSCEV (on a sext instruction,
5777 // say) can end up caching a suboptimal value.
5779 // FIXME: without the explicit `this` receiver below, MSVC errors out with
5780 // C2352 and C2512 (otherwise it isn't needed).
5782 const SCEV *TrueStart = this->getConstant(StartPattern.TrueValue);
5783 const SCEV *TrueStep = this->getConstant(StepPattern.TrueValue);
5784 const SCEV *FalseStart = this->getConstant(StartPattern.FalseValue);
5785 const SCEV *FalseStep = this->getConstant(StepPattern.FalseValue);
5787 ConstantRange TrueRange =
5788 this->getRangeForAffineAR(TrueStart, TrueStep, MaxBECount, BitWidth);
5789 ConstantRange FalseRange =
5790 this->getRangeForAffineAR(FalseStart, FalseStep, MaxBECount, BitWidth);
5792 return TrueRange.unionWith(FalseRange);
5795 SCEV::NoWrapFlags ScalarEvolution::getNoWrapFlagsFromUB(const Value *V) {
5796 if (isa<ConstantExpr>(V)) return SCEV::FlagAnyWrap;
5797 const BinaryOperator *BinOp = cast<BinaryOperator>(V);
5799 // Return early if there are no flags to propagate to the SCEV.
5800 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
5801 if (BinOp->hasNoUnsignedWrap())
5802 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
5803 if (BinOp->hasNoSignedWrap())
5804 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW);
5805 if (Flags == SCEV::FlagAnyWrap)
5806 return SCEV::FlagAnyWrap;
5808 return isSCEVExprNeverPoison(BinOp) ? Flags : SCEV::FlagAnyWrap;
5811 bool ScalarEvolution::isSCEVExprNeverPoison(const Instruction *I) {
5812 // Here we check that I is in the header of the innermost loop containing I,
5813 // since we only deal with instructions in the loop header. The actual loop we
5814 // need to check later will come from an add recurrence, but getting that
5815 // requires computing the SCEV of the operands, which can be expensive. This
5816 // check we can do cheaply to rule out some cases early.
5817 Loop *InnermostContainingLoop = LI.getLoopFor(I->getParent());
5818 if (InnermostContainingLoop == nullptr ||
5819 InnermostContainingLoop->getHeader() != I->getParent())
5822 // Only proceed if we can prove that I does not yield poison.
5823 if (!programUndefinedIfPoison(I))
5826 // At this point we know that if I is executed, then it does not wrap
5827 // according to at least one of NSW or NUW. If I is not executed, then we do
5828 // not know if the calculation that I represents would wrap. Multiple
5829 // instructions can map to the same SCEV. If we apply NSW or NUW from I to
5830 // the SCEV, we must guarantee no wrapping for that SCEV also when it is
5831 // derived from other instructions that map to the same SCEV. We cannot make
5832 // that guarantee for cases where I is not executed. So we need to find the
5833 // loop that I is considered in relation to and prove that I is executed for
5834 // every iteration of that loop. That implies that the value that I
5835 // calculates does not wrap anywhere in the loop, so then we can apply the
5836 // flags to the SCEV.
5838 // We check isLoopInvariant to disambiguate in case we are adding recurrences
5839 // from different loops, so that we know which loop to prove that I is
5841 for (unsigned OpIndex = 0; OpIndex < I->getNumOperands(); ++OpIndex) {
5842 // I could be an extractvalue from a call to an overflow intrinsic.
5843 // TODO: We can do better here in some cases.
5844 if (!isSCEVable(I->getOperand(OpIndex)->getType()))
5846 const SCEV *Op = getSCEV(I->getOperand(OpIndex));
5847 if (auto *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
5848 bool AllOtherOpsLoopInvariant = true;
5849 for (unsigned OtherOpIndex = 0; OtherOpIndex < I->getNumOperands();
5851 if (OtherOpIndex != OpIndex) {
5852 const SCEV *OtherOp = getSCEV(I->getOperand(OtherOpIndex));
5853 if (!isLoopInvariant(OtherOp, AddRec->getLoop())) {
5854 AllOtherOpsLoopInvariant = false;
5859 if (AllOtherOpsLoopInvariant &&
5860 isGuaranteedToExecuteForEveryIteration(I, AddRec->getLoop()))
5867 bool ScalarEvolution::isAddRecNeverPoison(const Instruction *I, const Loop *L) {
5868 // If we know that \c I can never be poison period, then that's enough.
5869 if (isSCEVExprNeverPoison(I))
5872 // For an add recurrence specifically, we assume that infinite loops without
5873 // side effects are undefined behavior, and then reason as follows:
5875 // If the add recurrence is poison in any iteration, it is poison on all
5876 // future iterations (since incrementing poison yields poison). If the result
5877 // of the add recurrence is fed into the loop latch condition and the loop
5878 // does not contain any throws or exiting blocks other than the latch, we now
5879 // have the ability to "choose" whether the backedge is taken or not (by
5880 // choosing a sufficiently evil value for the poison feeding into the branch)
5881 // for every iteration including and after the one in which \p I first became
5882 // poison. There are two possibilities (let's call the iteration in which \p
5883 // I first became poison as K):
5885 // 1. In the set of iterations including and after K, the loop body executes
5886 // no side effects. In this case executing the backege an infinte number
5887 // of times will yield undefined behavior.
5889 // 2. In the set of iterations including and after K, the loop body executes
5890 // at least one side effect. In this case, that specific instance of side
5891 // effect is control dependent on poison, which also yields undefined
5894 auto *ExitingBB = L->getExitingBlock();
5895 auto *LatchBB = L->getLoopLatch();
5896 if (!ExitingBB || !LatchBB || ExitingBB != LatchBB)
5899 SmallPtrSet<const Instruction *, 16> Pushed;
5900 SmallVector<const Instruction *, 8> PoisonStack;
5902 // We start by assuming \c I, the post-inc add recurrence, is poison. Only
5903 // things that are known to be poison under that assumption go on the
5906 PoisonStack.push_back(I);
5908 bool LatchControlDependentOnPoison = false;
5909 while (!PoisonStack.empty() && !LatchControlDependentOnPoison) {
5910 const Instruction *Poison = PoisonStack.pop_back_val();
5912 for (auto *PoisonUser : Poison->users()) {
5913 if (propagatesPoison(cast<Instruction>(PoisonUser))) {
5914 if (Pushed.insert(cast<Instruction>(PoisonUser)).second)
5915 PoisonStack.push_back(cast<Instruction>(PoisonUser));
5916 } else if (auto *BI = dyn_cast<BranchInst>(PoisonUser)) {
5917 assert(BI->isConditional() && "Only possibility!");
5918 if (BI->getParent() == LatchBB) {
5919 LatchControlDependentOnPoison = true;
5926 return LatchControlDependentOnPoison && loopHasNoAbnormalExits(L);
5929 ScalarEvolution::LoopProperties
5930 ScalarEvolution::getLoopProperties(const Loop *L) {
5931 using LoopProperties = ScalarEvolution::LoopProperties;
5933 auto Itr = LoopPropertiesCache.find(L);
5934 if (Itr == LoopPropertiesCache.end()) {
5935 auto HasSideEffects = [](Instruction *I) {
5936 if (auto *SI = dyn_cast<StoreInst>(I))
5937 return !SI->isSimple();
5939 return I->mayHaveSideEffects();
5942 LoopProperties LP = {/* HasNoAbnormalExits */ true,
5943 /*HasNoSideEffects*/ true};
5945 for (auto *BB : L->getBlocks())
5946 for (auto &I : *BB) {
5947 if (!isGuaranteedToTransferExecutionToSuccessor(&I))
5948 LP.HasNoAbnormalExits = false;
5949 if (HasSideEffects(&I))
5950 LP.HasNoSideEffects = false;
5951 if (!LP.HasNoAbnormalExits && !LP.HasNoSideEffects)
5952 break; // We're already as pessimistic as we can get.
5955 auto InsertPair = LoopPropertiesCache.insert({L, LP});
5956 assert(InsertPair.second && "We just checked!");
5957 Itr = InsertPair.first;
5963 const SCEV *ScalarEvolution::createSCEV(Value *V) {
5964 if (!isSCEVable(V->getType()))
5965 return getUnknown(V);
5967 if (Instruction *I = dyn_cast<Instruction>(V)) {
5968 // Don't attempt to analyze instructions in blocks that aren't
5969 // reachable. Such instructions don't matter, and they aren't required
5970 // to obey basic rules for definitions dominating uses which this
5971 // analysis depends on.
5972 if (!DT.isReachableFromEntry(I->getParent()))
5973 return getUnknown(UndefValue::get(V->getType()));
5974 } else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
5975 return getConstant(CI);
5976 else if (isa<ConstantPointerNull>(V))
5977 return getZero(V->getType());
5978 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
5979 return GA->isInterposable() ? getUnknown(V) : getSCEV(GA->getAliasee());
5980 else if (!isa<ConstantExpr>(V))
5981 return getUnknown(V);
5983 Operator *U = cast<Operator>(V);
5984 if (auto BO = MatchBinaryOp(U, DT)) {
5985 switch (BO->Opcode) {
5986 case Instruction::Add: {
5987 // The simple thing to do would be to just call getSCEV on both operands
5988 // and call getAddExpr with the result. However if we're looking at a
5989 // bunch of things all added together, this can be quite inefficient,
5990 // because it leads to N-1 getAddExpr calls for N ultimate operands.
5991 // Instead, gather up all the operands and make a single getAddExpr call.
5992 // LLVM IR canonical form means we need only traverse the left operands.
5993 SmallVector<const SCEV *, 4> AddOps;
5996 if (auto *OpSCEV = getExistingSCEV(BO->Op)) {
5997 AddOps.push_back(OpSCEV);
6001 // If a NUW or NSW flag can be applied to the SCEV for this
6002 // addition, then compute the SCEV for this addition by itself
6003 // with a separate call to getAddExpr. We need to do that
6004 // instead of pushing the operands of the addition onto AddOps,
6005 // since the flags are only known to apply to this particular
6006 // addition - they may not apply to other additions that can be
6007 // formed with operands from AddOps.
6008 const SCEV *RHS = getSCEV(BO->RHS);
6009 SCEV::NoWrapFlags Flags = getNoWrapFlagsFromUB(BO->Op);
6010 if (Flags != SCEV::FlagAnyWrap) {
6011 const SCEV *LHS = getSCEV(BO->LHS);
6012 if (BO->Opcode == Instruction::Sub)
6013 AddOps.push_back(getMinusSCEV(LHS, RHS, Flags));
6015 AddOps.push_back(getAddExpr(LHS, RHS, Flags));
6020 if (BO->Opcode == Instruction::Sub)
6021 AddOps.push_back(getNegativeSCEV(getSCEV(BO->RHS)));
6023 AddOps.push_back(getSCEV(BO->RHS));
6025 auto NewBO = MatchBinaryOp(BO->LHS, DT);
6026 if (!NewBO || (NewBO->Opcode != Instruction::Add &&
6027 NewBO->Opcode != Instruction::Sub)) {
6028 AddOps.push_back(getSCEV(BO->LHS));
6034 return getAddExpr(AddOps);
6037 case Instruction::Mul: {
6038 SmallVector<const SCEV *, 4> MulOps;
6041 if (auto *OpSCEV = getExistingSCEV(BO->Op)) {
6042 MulOps.push_back(OpSCEV);
6046 SCEV::NoWrapFlags Flags = getNoWrapFlagsFromUB(BO->Op);
6047 if (Flags != SCEV::FlagAnyWrap) {
6049 getMulExpr(getSCEV(BO->LHS), getSCEV(BO->RHS), Flags));
6054 MulOps.push_back(getSCEV(BO->RHS));
6055 auto NewBO = MatchBinaryOp(BO->LHS, DT);
6056 if (!NewBO || NewBO->Opcode != Instruction::Mul) {
6057 MulOps.push_back(getSCEV(BO->LHS));
6063 return getMulExpr(MulOps);
6065 case Instruction::UDiv:
6066 return getUDivExpr(getSCEV(BO->LHS), getSCEV(BO->RHS));
6067 case Instruction::URem:
6068 return getURemExpr(getSCEV(BO->LHS), getSCEV(BO->RHS));
6069 case Instruction::Sub: {
6070 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
6072 Flags = getNoWrapFlagsFromUB(BO->Op);
6073 return getMinusSCEV(getSCEV(BO->LHS), getSCEV(BO->RHS), Flags);
6075 case Instruction::And:
6076 // For an expression like x&255 that merely masks off the high bits,
6077 // use zext(trunc(x)) as the SCEV expression.
6078 if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->RHS)) {
6080 return getSCEV(BO->RHS);
6081 if (CI->isMinusOne())
6082 return getSCEV(BO->LHS);
6083 const APInt &A = CI->getValue();
6085 // Instcombine's ShrinkDemandedConstant may strip bits out of
6086 // constants, obscuring what would otherwise be a low-bits mask.
6087 // Use computeKnownBits to compute what ShrinkDemandedConstant
6088 // knew about to reconstruct a low-bits mask value.
6089 unsigned LZ = A.countLeadingZeros();
6090 unsigned TZ = A.countTrailingZeros();
6091 unsigned BitWidth = A.getBitWidth();
6092 KnownBits Known(BitWidth);
6093 computeKnownBits(BO->LHS, Known, getDataLayout(),
6094 0, &AC, nullptr, &DT);
6096 APInt EffectiveMask =
6097 APInt::getLowBitsSet(BitWidth, BitWidth - LZ - TZ).shl(TZ);
6098 if ((LZ != 0 || TZ != 0) && !((~A & ~Known.Zero) & EffectiveMask)) {
6099 const SCEV *MulCount = getConstant(APInt::getOneBitSet(BitWidth, TZ));
6100 const SCEV *LHS = getSCEV(BO->LHS);
6101 const SCEV *ShiftedLHS = nullptr;
6102 if (auto *LHSMul = dyn_cast<SCEVMulExpr>(LHS)) {
6103 if (auto *OpC = dyn_cast<SCEVConstant>(LHSMul->getOperand(0))) {
6104 // For an expression like (x * 8) & 8, simplify the multiply.
6105 unsigned MulZeros = OpC->getAPInt().countTrailingZeros();
6106 unsigned GCD = std::min(MulZeros, TZ);
6107 APInt DivAmt = APInt::getOneBitSet(BitWidth, TZ - GCD);
6108 SmallVector<const SCEV*, 4> MulOps;
6109 MulOps.push_back(getConstant(OpC->getAPInt().lshr(GCD)));
6110 MulOps.append(LHSMul->op_begin() + 1, LHSMul->op_end());
6111 auto *NewMul = getMulExpr(MulOps, LHSMul->getNoWrapFlags());
6112 ShiftedLHS = getUDivExpr(NewMul, getConstant(DivAmt));
6116 ShiftedLHS = getUDivExpr(LHS, MulCount);
6119 getTruncateExpr(ShiftedLHS,
6120 IntegerType::get(getContext(), BitWidth - LZ - TZ)),
6121 BO->LHS->getType()),
6127 case Instruction::Or:
6128 // If the RHS of the Or is a constant, we may have something like:
6129 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
6130 // optimizations will transparently handle this case.
6132 // In order for this transformation to be safe, the LHS must be of the
6133 // form X*(2^n) and the Or constant must be less than 2^n.
6134 if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->RHS)) {
6135 const SCEV *LHS = getSCEV(BO->LHS);
6136 const APInt &CIVal = CI->getValue();
6137 if (GetMinTrailingZeros(LHS) >=
6138 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
6139 // Build a plain add SCEV.
6140 return getAddExpr(LHS, getSCEV(CI),
6141 (SCEV::NoWrapFlags)(SCEV::FlagNUW | SCEV::FlagNSW));
6146 case Instruction::Xor:
6147 if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->RHS)) {
6148 // If the RHS of xor is -1, then this is a not operation.
6149 if (CI->isMinusOne())
6150 return getNotSCEV(getSCEV(BO->LHS));
6152 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
6153 // This is a variant of the check for xor with -1, and it handles
6154 // the case where instcombine has trimmed non-demanded bits out
6155 // of an xor with -1.
6156 if (auto *LBO = dyn_cast<BinaryOperator>(BO->LHS))
6157 if (ConstantInt *LCI = dyn_cast<ConstantInt>(LBO->getOperand(1)))
6158 if (LBO->getOpcode() == Instruction::And &&
6159 LCI->getValue() == CI->getValue())
6160 if (const SCEVZeroExtendExpr *Z =
6161 dyn_cast<SCEVZeroExtendExpr>(getSCEV(BO->LHS))) {
6162 Type *UTy = BO->LHS->getType();
6163 const SCEV *Z0 = Z->getOperand();
6164 Type *Z0Ty = Z0->getType();
6165 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
6167 // If C is a low-bits mask, the zero extend is serving to
6168 // mask off the high bits. Complement the operand and
6169 // re-apply the zext.
6170 if (CI->getValue().isMask(Z0TySize))
6171 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
6173 // If C is a single bit, it may be in the sign-bit position
6174 // before the zero-extend. In this case, represent the xor
6175 // using an add, which is equivalent, and re-apply the zext.
6176 APInt Trunc = CI->getValue().trunc(Z0TySize);
6177 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
6179 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
6185 case Instruction::Shl:
6186 // Turn shift left of a constant amount into a multiply.
6187 if (ConstantInt *SA = dyn_cast<ConstantInt>(BO->RHS)) {
6188 uint32_t BitWidth = cast<IntegerType>(SA->getType())->getBitWidth();
6190 // If the shift count is not less than the bitwidth, the result of
6191 // the shift is undefined. Don't try to analyze it, because the
6192 // resolution chosen here may differ from the resolution chosen in
6193 // other parts of the compiler.
6194 if (SA->getValue().uge(BitWidth))
6197 // We can safely preserve the nuw flag in all cases. It's also safe to
6198 // turn a nuw nsw shl into a nuw nsw mul. However, nsw in isolation
6199 // requires special handling. It can be preserved as long as we're not
6200 // left shifting by bitwidth - 1.
6201 auto Flags = SCEV::FlagAnyWrap;
6203 auto MulFlags = getNoWrapFlagsFromUB(BO->Op);
6204 if ((MulFlags & SCEV::FlagNSW) &&
6205 ((MulFlags & SCEV::FlagNUW) || SA->getValue().ult(BitWidth - 1)))
6206 Flags = (SCEV::NoWrapFlags)(Flags | SCEV::FlagNSW);
6207 if (MulFlags & SCEV::FlagNUW)
6208 Flags = (SCEV::NoWrapFlags)(Flags | SCEV::FlagNUW);
6211 Constant *X = ConstantInt::get(
6212 getContext(), APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
6213 return getMulExpr(getSCEV(BO->LHS), getSCEV(X), Flags);
6217 case Instruction::AShr: {
6218 // AShr X, C, where C is a constant.
6219 ConstantInt *CI = dyn_cast<ConstantInt>(BO->RHS);
6223 Type *OuterTy = BO->LHS->getType();
6224 uint64_t BitWidth = getTypeSizeInBits(OuterTy);
6225 // If the shift count is not less than the bitwidth, the result of
6226 // the shift is undefined. Don't try to analyze it, because the
6227 // resolution chosen here may differ from the resolution chosen in
6228 // other parts of the compiler.
6229 if (CI->getValue().uge(BitWidth))
6233 return getSCEV(BO->LHS); // shift by zero --> noop
6235 uint64_t AShrAmt = CI->getZExtValue();
6236 Type *TruncTy = IntegerType::get(getContext(), BitWidth - AShrAmt);
6238 Operator *L = dyn_cast<Operator>(BO->LHS);
6239 if (L && L->getOpcode() == Instruction::Shl) {
6242 // Both n and m are constant.
6244 const SCEV *ShlOp0SCEV = getSCEV(L->getOperand(0));
6245 if (L->getOperand(1) == BO->RHS)
6246 // For a two-shift sext-inreg, i.e. n = m,
6247 // use sext(trunc(x)) as the SCEV expression.
6248 return getSignExtendExpr(
6249 getTruncateExpr(ShlOp0SCEV, TruncTy), OuterTy);
6251 ConstantInt *ShlAmtCI = dyn_cast<ConstantInt>(L->getOperand(1));
6252 if (ShlAmtCI && ShlAmtCI->getValue().ult(BitWidth)) {
6253 uint64_t ShlAmt = ShlAmtCI->getZExtValue();
6254 if (ShlAmt > AShrAmt) {
6255 // When n > m, use sext(mul(trunc(x), 2^(n-m)))) as the SCEV
6256 // expression. We already checked that ShlAmt < BitWidth, so
6257 // the multiplier, 1 << (ShlAmt - AShrAmt), fits into TruncTy as
6258 // ShlAmt - AShrAmt < Amt.
6259 APInt Mul = APInt::getOneBitSet(BitWidth - AShrAmt,
6261 return getSignExtendExpr(
6262 getMulExpr(getTruncateExpr(ShlOp0SCEV, TruncTy),
6263 getConstant(Mul)), OuterTy);
6272 switch (U->getOpcode()) {
6273 case Instruction::Trunc:
6274 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
6276 case Instruction::ZExt:
6277 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
6279 case Instruction::SExt:
6280 if (auto BO = MatchBinaryOp(U->getOperand(0), DT)) {
6281 // The NSW flag of a subtract does not always survive the conversion to
6282 // A + (-1)*B. By pushing sign extension onto its operands we are much
6283 // more likely to preserve NSW and allow later AddRec optimisations.
6285 // NOTE: This is effectively duplicating this logic from getSignExtend:
6286 // sext((A + B + ...)<nsw>) --> (sext(A) + sext(B) + ...)<nsw>
6287 // but by that point the NSW information has potentially been lost.
6288 if (BO->Opcode == Instruction::Sub && BO->IsNSW) {
6289 Type *Ty = U->getType();
6290 auto *V1 = getSignExtendExpr(getSCEV(BO->LHS), Ty);
6291 auto *V2 = getSignExtendExpr(getSCEV(BO->RHS), Ty);
6292 return getMinusSCEV(V1, V2, SCEV::FlagNSW);
6295 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
6297 case Instruction::BitCast:
6298 // BitCasts are no-op casts so we just eliminate the cast.
6299 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
6300 return getSCEV(U->getOperand(0));
6303 case Instruction::SDiv:
6304 // If both operands are non-negative, this is just an udiv.
6305 if (isKnownNonNegative(getSCEV(U->getOperand(0))) &&
6306 isKnownNonNegative(getSCEV(U->getOperand(1))))
6307 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(U->getOperand(1)));
6310 case Instruction::SRem:
6311 // If both operands are non-negative, this is just an urem.
6312 if (isKnownNonNegative(getSCEV(U->getOperand(0))) &&
6313 isKnownNonNegative(getSCEV(U->getOperand(1))))
6314 return getURemExpr(getSCEV(U->getOperand(0)), getSCEV(U->getOperand(1)));
6317 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
6318 // lead to pointer expressions which cannot safely be expanded to GEPs,
6319 // because ScalarEvolution doesn't respect the GEP aliasing rules when
6320 // simplifying integer expressions.
6322 case Instruction::GetElementPtr:
6323 return createNodeForGEP(cast<GEPOperator>(U));
6325 case Instruction::PHI:
6326 return createNodeForPHI(cast<PHINode>(U));
6328 case Instruction::Select:
6329 // U can also be a select constant expr, which let fall through. Since
6330 // createNodeForSelect only works for a condition that is an `ICmpInst`, and
6331 // constant expressions cannot have instructions as operands, we'd have
6332 // returned getUnknown for a select constant expressions anyway.
6333 if (isa<Instruction>(U))
6334 return createNodeForSelectOrPHI(cast<Instruction>(U), U->getOperand(0),
6335 U->getOperand(1), U->getOperand(2));
6338 case Instruction::Call:
6339 case Instruction::Invoke:
6340 if (Value *RV = cast<CallBase>(U)->getReturnedArgOperand())
6345 return getUnknown(V);
6348 //===----------------------------------------------------------------------===//
6349 // Iteration Count Computation Code
6352 static unsigned getConstantTripCount(const SCEVConstant *ExitCount) {
6356 ConstantInt *ExitConst = ExitCount->getValue();
6358 // Guard against huge trip counts.
6359 if (ExitConst->getValue().getActiveBits() > 32)
6362 // In case of integer overflow, this returns 0, which is correct.
6363 return ((unsigned)ExitConst->getZExtValue()) + 1;
6366 unsigned ScalarEvolution::getSmallConstantTripCount(const Loop *L) {
6367 if (BasicBlock *ExitingBB = L->getExitingBlock())
6368 return getSmallConstantTripCount(L, ExitingBB);
6370 // No trip count information for multiple exits.
6374 unsigned ScalarEvolution::getSmallConstantTripCount(const Loop *L,
6375 BasicBlock *ExitingBlock) {
6376 assert(ExitingBlock && "Must pass a non-null exiting block!");
6377 assert(L->isLoopExiting(ExitingBlock) &&
6378 "Exiting block must actually branch out of the loop!");
6379 const SCEVConstant *ExitCount =
6380 dyn_cast<SCEVConstant>(getExitCount(L, ExitingBlock));
6381 return getConstantTripCount(ExitCount);
6384 unsigned ScalarEvolution::getSmallConstantMaxTripCount(const Loop *L) {
6385 const auto *MaxExitCount =
6386 dyn_cast<SCEVConstant>(getConstantMaxBackedgeTakenCount(L));
6387 return getConstantTripCount(MaxExitCount);
6390 unsigned ScalarEvolution::getSmallConstantTripMultiple(const Loop *L) {
6391 if (BasicBlock *ExitingBB = L->getExitingBlock())
6392 return getSmallConstantTripMultiple(L, ExitingBB);
6394 // No trip multiple information for multiple exits.
6398 /// Returns the largest constant divisor of the trip count of this loop as a
6399 /// normal unsigned value, if possible. This means that the actual trip count is
6400 /// always a multiple of the returned value (don't forget the trip count could
6401 /// very well be zero as well!).
6403 /// Returns 1 if the trip count is unknown or not guaranteed to be the
6404 /// multiple of a constant (which is also the case if the trip count is simply
6405 /// constant, use getSmallConstantTripCount for that case), Will also return 1
6406 /// if the trip count is very large (>= 2^32).
6408 /// As explained in the comments for getSmallConstantTripCount, this assumes
6409 /// that control exits the loop via ExitingBlock.
6411 ScalarEvolution::getSmallConstantTripMultiple(const Loop *L,
6412 BasicBlock *ExitingBlock) {
6413 assert(ExitingBlock && "Must pass a non-null exiting block!");
6414 assert(L->isLoopExiting(ExitingBlock) &&
6415 "Exiting block must actually branch out of the loop!");
6416 const SCEV *ExitCount = getExitCount(L, ExitingBlock);
6417 if (ExitCount == getCouldNotCompute())
6420 // Get the trip count from the BE count by adding 1.
6421 const SCEV *TCExpr = getAddExpr(ExitCount, getOne(ExitCount->getType()));
6423 const SCEVConstant *TC = dyn_cast<SCEVConstant>(TCExpr);
6425 // Attempt to factor more general cases. Returns the greatest power of
6426 // two divisor. If overflow happens, the trip count expression is still
6427 // divisible by the greatest power of 2 divisor returned.
6428 return 1U << std::min((uint32_t)31, GetMinTrailingZeros(TCExpr));
6430 ConstantInt *Result = TC->getValue();
6432 // Guard against huge trip counts (this requires checking
6433 // for zero to handle the case where the trip count == -1 and the
6435 if (!Result || Result->getValue().getActiveBits() > 32 ||
6436 Result->getValue().getActiveBits() == 0)
6439 return (unsigned)Result->getZExtValue();
6442 const SCEV *ScalarEvolution::getExitCount(const Loop *L,
6443 BasicBlock *ExitingBlock,
6444 ExitCountKind Kind) {
6447 return getBackedgeTakenInfo(L).getExact(ExitingBlock, this);
6448 case ConstantMaximum:
6449 return getBackedgeTakenInfo(L).getMax(ExitingBlock, this);
6451 llvm_unreachable("Invalid ExitCountKind!");
6455 ScalarEvolution::getPredicatedBackedgeTakenCount(const Loop *L,
6456 SCEVUnionPredicate &Preds) {
6457 return getPredicatedBackedgeTakenInfo(L).getExact(L, this, &Preds);
6460 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L,
6461 ExitCountKind Kind) {
6464 return getBackedgeTakenInfo(L).getExact(L, this);
6465 case ConstantMaximum:
6466 return getBackedgeTakenInfo(L).getMax(this);
6468 llvm_unreachable("Invalid ExitCountKind!");
6471 bool ScalarEvolution::isBackedgeTakenCountMaxOrZero(const Loop *L) {
6472 return getBackedgeTakenInfo(L).isMaxOrZero(this);
6475 /// Push PHI nodes in the header of the given loop onto the given Worklist.
6477 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
6478 BasicBlock *Header = L->getHeader();
6480 // Push all Loop-header PHIs onto the Worklist stack.
6481 for (PHINode &PN : Header->phis())
6482 Worklist.push_back(&PN);
6485 const ScalarEvolution::BackedgeTakenInfo &
6486 ScalarEvolution::getPredicatedBackedgeTakenInfo(const Loop *L) {
6487 auto &BTI = getBackedgeTakenInfo(L);
6488 if (BTI.hasFullInfo())
6491 auto Pair = PredicatedBackedgeTakenCounts.insert({L, BackedgeTakenInfo()});
6494 return Pair.first->second;
6496 BackedgeTakenInfo Result =
6497 computeBackedgeTakenCount(L, /*AllowPredicates=*/true);
6499 return PredicatedBackedgeTakenCounts.find(L)->second = std::move(Result);
6502 const ScalarEvolution::BackedgeTakenInfo &
6503 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
6504 // Initially insert an invalid entry for this loop. If the insertion
6505 // succeeds, proceed to actually compute a backedge-taken count and
6506 // update the value. The temporary CouldNotCompute value tells SCEV
6507 // code elsewhere that it shouldn't attempt to request a new
6508 // backedge-taken count, which could result in infinite recursion.
6509 std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
6510 BackedgeTakenCounts.insert({L, BackedgeTakenInfo()});
6512 return Pair.first->second;
6514 // computeBackedgeTakenCount may allocate memory for its result. Inserting it
6515 // into the BackedgeTakenCounts map transfers ownership. Otherwise, the result
6516 // must be cleared in this scope.
6517 BackedgeTakenInfo Result = computeBackedgeTakenCount(L);
6519 // In product build, there are no usage of statistic.
6520 (void)NumTripCountsComputed;
6521 (void)NumTripCountsNotComputed;
6522 #if LLVM_ENABLE_STATS || !defined(NDEBUG)
6523 const SCEV *BEExact = Result.getExact(L, this);
6524 if (BEExact != getCouldNotCompute()) {
6525 assert(isLoopInvariant(BEExact, L) &&
6526 isLoopInvariant(Result.getMax(this), L) &&
6527 "Computed backedge-taken count isn't loop invariant for loop!");
6528 ++NumTripCountsComputed;
6530 else if (Result.getMax(this) == getCouldNotCompute() &&
6531 isa<PHINode>(L->getHeader()->begin())) {
6532 // Only count loops that have phi nodes as not being computable.
6533 ++NumTripCountsNotComputed;
6535 #endif // LLVM_ENABLE_STATS || !defined(NDEBUG)
6537 // Now that we know more about the trip count for this loop, forget any
6538 // existing SCEV values for PHI nodes in this loop since they are only
6539 // conservative estimates made without the benefit of trip count
6540 // information. This is similar to the code in forgetLoop, except that
6541 // it handles SCEVUnknown PHI nodes specially.
6542 if (Result.hasAnyInfo()) {
6543 SmallVector<Instruction *, 16> Worklist;
6544 PushLoopPHIs(L, Worklist);
6546 SmallPtrSet<Instruction *, 8> Discovered;
6547 while (!Worklist.empty()) {
6548 Instruction *I = Worklist.pop_back_val();
6550 ValueExprMapType::iterator It =
6551 ValueExprMap.find_as(static_cast<Value *>(I));
6552 if (It != ValueExprMap.end()) {
6553 const SCEV *Old = It->second;
6555 // SCEVUnknown for a PHI either means that it has an unrecognized
6556 // structure, or it's a PHI that's in the progress of being computed
6557 // by createNodeForPHI. In the former case, additional loop trip
6558 // count information isn't going to change anything. In the later
6559 // case, createNodeForPHI will perform the necessary updates on its
6560 // own when it gets to that point.
6561 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) {
6562 eraseValueFromMap(It->first);
6563 forgetMemoizedResults(Old);
6565 if (PHINode *PN = dyn_cast<PHINode>(I))
6566 ConstantEvolutionLoopExitValue.erase(PN);
6569 // Since we don't need to invalidate anything for correctness and we're
6570 // only invalidating to make SCEV's results more precise, we get to stop
6571 // early to avoid invalidating too much. This is especially important in
6574 // %v = f(pn0, pn1) // pn0 and pn1 used through some other phi node
6582 // where both loop0 and loop1's backedge taken count uses the SCEV
6583 // expression for %v. If we don't have the early stop below then in cases
6584 // like the above, getBackedgeTakenInfo(loop1) will clear out the trip
6585 // count for loop0 and getBackedgeTakenInfo(loop0) will clear out the trip
6586 // count for loop1, effectively nullifying SCEV's trip count cache.
6587 for (auto *U : I->users())
6588 if (auto *I = dyn_cast<Instruction>(U)) {
6589 auto *LoopForUser = LI.getLoopFor(I->getParent());
6590 if (LoopForUser && L->contains(LoopForUser) &&
6591 Discovered.insert(I).second)
6592 Worklist.push_back(I);
6597 // Re-lookup the insert position, since the call to
6598 // computeBackedgeTakenCount above could result in a
6599 // recusive call to getBackedgeTakenInfo (on a different
6600 // loop), which would invalidate the iterator computed
6602 return BackedgeTakenCounts.find(L)->second = std::move(Result);
6605 void ScalarEvolution::forgetAllLoops() {
6606 // This method is intended to forget all info about loops. It should
6607 // invalidate caches as if the following happened:
6608 // - The trip counts of all loops have changed arbitrarily
6609 // - Every llvm::Value has been updated in place to produce a different
6611 BackedgeTakenCounts.clear();
6612 PredicatedBackedgeTakenCounts.clear();
6613 LoopPropertiesCache.clear();
6614 ConstantEvolutionLoopExitValue.clear();
6615 ValueExprMap.clear();
6616 ValuesAtScopes.clear();
6617 LoopDispositions.clear();
6618 BlockDispositions.clear();
6619 UnsignedRanges.clear();
6620 SignedRanges.clear();
6621 ExprValueMap.clear();
6623 MinTrailingZerosCache.clear();
6624 PredicatedSCEVRewrites.clear();
6627 void ScalarEvolution::forgetLoop(const Loop *L) {
6628 // Drop any stored trip count value.
6629 auto RemoveLoopFromBackedgeMap =
6630 [](DenseMap<const Loop *, BackedgeTakenInfo> &Map, const Loop *L) {
6631 auto BTCPos = Map.find(L);
6632 if (BTCPos != Map.end()) {
6633 BTCPos->second.clear();
6638 SmallVector<const Loop *, 16> LoopWorklist(1, L);
6639 SmallVector<Instruction *, 32> Worklist;
6640 SmallPtrSet<Instruction *, 16> Visited;
6642 // Iterate over all the loops and sub-loops to drop SCEV information.
6643 while (!LoopWorklist.empty()) {
6644 auto *CurrL = LoopWorklist.pop_back_val();
6646 RemoveLoopFromBackedgeMap(BackedgeTakenCounts, CurrL);
6647 RemoveLoopFromBackedgeMap(PredicatedBackedgeTakenCounts, CurrL);
6649 // Drop information about predicated SCEV rewrites for this loop.
6650 for (auto I = PredicatedSCEVRewrites.begin();
6651 I != PredicatedSCEVRewrites.end();) {
6652 std::pair<const SCEV *, const Loop *> Entry = I->first;
6653 if (Entry.second == CurrL)
6654 PredicatedSCEVRewrites.erase(I++);
6659 auto LoopUsersItr = LoopUsers.find(CurrL);
6660 if (LoopUsersItr != LoopUsers.end()) {
6661 for (auto *S : LoopUsersItr->second)
6662 forgetMemoizedResults(S);
6663 LoopUsers.erase(LoopUsersItr);
6666 // Drop information about expressions based on loop-header PHIs.
6667 PushLoopPHIs(CurrL, Worklist);
6669 while (!Worklist.empty()) {
6670 Instruction *I = Worklist.pop_back_val();
6671 if (!Visited.insert(I).second)
6674 ValueExprMapType::iterator It =
6675 ValueExprMap.find_as(static_cast<Value *>(I));
6676 if (It != ValueExprMap.end()) {
6677 eraseValueFromMap(It->first);
6678 forgetMemoizedResults(It->second);
6679 if (PHINode *PN = dyn_cast<PHINode>(I))
6680 ConstantEvolutionLoopExitValue.erase(PN);
6683 PushDefUseChildren(I, Worklist);
6686 LoopPropertiesCache.erase(CurrL);
6687 // Forget all contained loops too, to avoid dangling entries in the
6688 // ValuesAtScopes map.
6689 LoopWorklist.append(CurrL->begin(), CurrL->end());
6693 void ScalarEvolution::forgetTopmostLoop(const Loop *L) {
6694 while (Loop *Parent = L->getParentLoop())
6699 void ScalarEvolution::forgetValue(Value *V) {
6700 Instruction *I = dyn_cast<Instruction>(V);
6703 // Drop information about expressions based on loop-header PHIs.
6704 SmallVector<Instruction *, 16> Worklist;
6705 Worklist.push_back(I);
6707 SmallPtrSet<Instruction *, 8> Visited;
6708 while (!Worklist.empty()) {
6709 I = Worklist.pop_back_val();
6710 if (!Visited.insert(I).second)
6713 ValueExprMapType::iterator It =
6714 ValueExprMap.find_as(static_cast<Value *>(I));
6715 if (It != ValueExprMap.end()) {
6716 eraseValueFromMap(It->first);
6717 forgetMemoizedResults(It->second);
6718 if (PHINode *PN = dyn_cast<PHINode>(I))
6719 ConstantEvolutionLoopExitValue.erase(PN);
6722 PushDefUseChildren(I, Worklist);
6726 void ScalarEvolution::forgetLoopDispositions(const Loop *L) {
6727 LoopDispositions.clear();
6730 /// Get the exact loop backedge taken count considering all loop exits. A
6731 /// computable result can only be returned for loops with all exiting blocks
6732 /// dominating the latch. howFarToZero assumes that the limit of each loop test
6733 /// is never skipped. This is a valid assumption as long as the loop exits via
6734 /// that test. For precise results, it is the caller's responsibility to specify
6735 /// the relevant loop exiting block using getExact(ExitingBlock, SE).
6737 ScalarEvolution::BackedgeTakenInfo::getExact(const Loop *L, ScalarEvolution *SE,
6738 SCEVUnionPredicate *Preds) const {
6739 // If any exits were not computable, the loop is not computable.
6740 if (!isComplete() || ExitNotTaken.empty())
6741 return SE->getCouldNotCompute();
6743 const BasicBlock *Latch = L->getLoopLatch();
6744 // All exiting blocks we have collected must dominate the only backedge.
6746 return SE->getCouldNotCompute();
6748 // All exiting blocks we have gathered dominate loop's latch, so exact trip
6749 // count is simply a minimum out of all these calculated exit counts.
6750 SmallVector<const SCEV *, 2> Ops;
6751 for (auto &ENT : ExitNotTaken) {
6752 const SCEV *BECount = ENT.ExactNotTaken;
6753 assert(BECount != SE->getCouldNotCompute() && "Bad exit SCEV!");
6754 assert(SE->DT.dominates(ENT.ExitingBlock, Latch) &&
6755 "We should only have known counts for exiting blocks that dominate "
6758 Ops.push_back(BECount);
6760 if (Preds && !ENT.hasAlwaysTruePredicate())
6761 Preds->add(ENT.Predicate.get());
6763 assert((Preds || ENT.hasAlwaysTruePredicate()) &&
6764 "Predicate should be always true!");
6767 return SE->getUMinFromMismatchedTypes(Ops);
6770 /// Get the exact not taken count for this loop exit.
6772 ScalarEvolution::BackedgeTakenInfo::getExact(BasicBlock *ExitingBlock,
6773 ScalarEvolution *SE) const {
6774 for (auto &ENT : ExitNotTaken)
6775 if (ENT.ExitingBlock == ExitingBlock && ENT.hasAlwaysTruePredicate())
6776 return ENT.ExactNotTaken;
6778 return SE->getCouldNotCompute();
6782 ScalarEvolution::BackedgeTakenInfo::getMax(BasicBlock *ExitingBlock,
6783 ScalarEvolution *SE) const {
6784 for (auto &ENT : ExitNotTaken)
6785 if (ENT.ExitingBlock == ExitingBlock && ENT.hasAlwaysTruePredicate())
6786 return ENT.MaxNotTaken;
6788 return SE->getCouldNotCompute();
6791 /// getMax - Get the max backedge taken count for the loop.
6793 ScalarEvolution::BackedgeTakenInfo::getMax(ScalarEvolution *SE) const {
6794 auto PredicateNotAlwaysTrue = [](const ExitNotTakenInfo &ENT) {
6795 return !ENT.hasAlwaysTruePredicate();
6798 if (any_of(ExitNotTaken, PredicateNotAlwaysTrue) || !getMax())
6799 return SE->getCouldNotCompute();
6801 assert((isa<SCEVCouldNotCompute>(getMax()) || isa<SCEVConstant>(getMax())) &&
6802 "No point in having a non-constant max backedge taken count!");
6806 bool ScalarEvolution::BackedgeTakenInfo::isMaxOrZero(ScalarEvolution *SE) const {
6807 auto PredicateNotAlwaysTrue = [](const ExitNotTakenInfo &ENT) {
6808 return !ENT.hasAlwaysTruePredicate();
6810 return MaxOrZero && !any_of(ExitNotTaken, PredicateNotAlwaysTrue);
6813 bool ScalarEvolution::BackedgeTakenInfo::hasOperand(const SCEV *S,
6814 ScalarEvolution *SE) const {
6815 if (getMax() && getMax() != SE->getCouldNotCompute() &&
6816 SE->hasOperand(getMax(), S))
6819 for (auto &ENT : ExitNotTaken)
6820 if (ENT.ExactNotTaken != SE->getCouldNotCompute() &&
6821 SE->hasOperand(ENT.ExactNotTaken, S))
6827 ScalarEvolution::ExitLimit::ExitLimit(const SCEV *E)
6828 : ExactNotTaken(E), MaxNotTaken(E) {
6829 assert((isa<SCEVCouldNotCompute>(MaxNotTaken) ||
6830 isa<SCEVConstant>(MaxNotTaken)) &&
6831 "No point in having a non-constant max backedge taken count!");
6834 ScalarEvolution::ExitLimit::ExitLimit(
6835 const SCEV *E, const SCEV *M, bool MaxOrZero,
6836 ArrayRef<const SmallPtrSetImpl<const SCEVPredicate *> *> PredSetList)
6837 : ExactNotTaken(E), MaxNotTaken(M), MaxOrZero(MaxOrZero) {
6838 assert((isa<SCEVCouldNotCompute>(ExactNotTaken) ||
6839 !isa<SCEVCouldNotCompute>(MaxNotTaken)) &&
6840 "Exact is not allowed to be less precise than Max");
6841 assert((isa<SCEVCouldNotCompute>(MaxNotTaken) ||
6842 isa<SCEVConstant>(MaxNotTaken)) &&
6843 "No point in having a non-constant max backedge taken count!");
6844 for (auto *PredSet : PredSetList)
6845 for (auto *P : *PredSet)
6849 ScalarEvolution::ExitLimit::ExitLimit(
6850 const SCEV *E, const SCEV *M, bool MaxOrZero,
6851 const SmallPtrSetImpl<const SCEVPredicate *> &PredSet)
6852 : ExitLimit(E, M, MaxOrZero, {&PredSet}) {
6853 assert((isa<SCEVCouldNotCompute>(MaxNotTaken) ||
6854 isa<SCEVConstant>(MaxNotTaken)) &&
6855 "No point in having a non-constant max backedge taken count!");
6858 ScalarEvolution::ExitLimit::ExitLimit(const SCEV *E, const SCEV *M,
6860 : ExitLimit(E, M, MaxOrZero, None) {
6861 assert((isa<SCEVCouldNotCompute>(MaxNotTaken) ||
6862 isa<SCEVConstant>(MaxNotTaken)) &&
6863 "No point in having a non-constant max backedge taken count!");
6866 /// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each
6867 /// computable exit into a persistent ExitNotTakenInfo array.
6868 ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo(
6869 ArrayRef<ScalarEvolution::BackedgeTakenInfo::EdgeExitInfo>
6871 bool Complete, const SCEV *MaxCount, bool MaxOrZero)
6872 : MaxAndComplete(MaxCount, Complete), MaxOrZero(MaxOrZero) {
6873 using EdgeExitInfo = ScalarEvolution::BackedgeTakenInfo::EdgeExitInfo;
6875 ExitNotTaken.reserve(ExitCounts.size());
6877 ExitCounts.begin(), ExitCounts.end(), std::back_inserter(ExitNotTaken),
6878 [&](const EdgeExitInfo &EEI) {
6879 BasicBlock *ExitBB = EEI.first;
6880 const ExitLimit &EL = EEI.second;
6881 if (EL.Predicates.empty())
6882 return ExitNotTakenInfo(ExitBB, EL.ExactNotTaken, EL.MaxNotTaken,
6885 std::unique_ptr<SCEVUnionPredicate> Predicate(new SCEVUnionPredicate);
6886 for (auto *Pred : EL.Predicates)
6887 Predicate->add(Pred);
6889 return ExitNotTakenInfo(ExitBB, EL.ExactNotTaken, EL.MaxNotTaken,
6890 std::move(Predicate));
6892 assert((isa<SCEVCouldNotCompute>(MaxCount) || isa<SCEVConstant>(MaxCount)) &&
6893 "No point in having a non-constant max backedge taken count!");
6896 /// Invalidate this result and free the ExitNotTakenInfo array.
6897 void ScalarEvolution::BackedgeTakenInfo::clear() {
6898 ExitNotTaken.clear();
6901 /// Compute the number of times the backedge of the specified loop will execute.
6902 ScalarEvolution::BackedgeTakenInfo
6903 ScalarEvolution::computeBackedgeTakenCount(const Loop *L,
6904 bool AllowPredicates) {
6905 SmallVector<BasicBlock *, 8> ExitingBlocks;
6906 L->getExitingBlocks(ExitingBlocks);
6908 using EdgeExitInfo = ScalarEvolution::BackedgeTakenInfo::EdgeExitInfo;
6910 SmallVector<EdgeExitInfo, 4> ExitCounts;
6911 bool CouldComputeBECount = true;
6912 BasicBlock *Latch = L->getLoopLatch(); // may be NULL.
6913 const SCEV *MustExitMaxBECount = nullptr;
6914 const SCEV *MayExitMaxBECount = nullptr;
6915 bool MustExitMaxOrZero = false;
6917 // Compute the ExitLimit for each loop exit. Use this to populate ExitCounts
6918 // and compute maxBECount.
6919 // Do a union of all the predicates here.
6920 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
6921 BasicBlock *ExitBB = ExitingBlocks[i];
6923 // We canonicalize untaken exits to br (constant), ignore them so that
6924 // proving an exit untaken doesn't negatively impact our ability to reason
6925 // about the loop as whole.
6926 if (auto *BI = dyn_cast<BranchInst>(ExitBB->getTerminator()))
6927 if (auto *CI = dyn_cast<ConstantInt>(BI->getCondition())) {
6928 bool ExitIfTrue = !L->contains(BI->getSuccessor(0));
6929 if ((ExitIfTrue && CI->isZero()) || (!ExitIfTrue && CI->isOne()))
6933 ExitLimit EL = computeExitLimit(L, ExitBB, AllowPredicates);
6935 assert((AllowPredicates || EL.Predicates.empty()) &&
6936 "Predicated exit limit when predicates are not allowed!");
6938 // 1. For each exit that can be computed, add an entry to ExitCounts.
6939 // CouldComputeBECount is true only if all exits can be computed.
6940 if (EL.ExactNotTaken == getCouldNotCompute())
6941 // We couldn't compute an exact value for this exit, so
6942 // we won't be able to compute an exact value for the loop.
6943 CouldComputeBECount = false;
6945 ExitCounts.emplace_back(ExitBB, EL);
6947 // 2. Derive the loop's MaxBECount from each exit's max number of
6948 // non-exiting iterations. Partition the loop exits into two kinds:
6949 // LoopMustExits and LoopMayExits.
6951 // If the exit dominates the loop latch, it is a LoopMustExit otherwise it
6952 // is a LoopMayExit. If any computable LoopMustExit is found, then
6953 // MaxBECount is the minimum EL.MaxNotTaken of computable
6954 // LoopMustExits. Otherwise, MaxBECount is conservatively the maximum
6955 // EL.MaxNotTaken, where CouldNotCompute is considered greater than any
6956 // computable EL.MaxNotTaken.
6957 if (EL.MaxNotTaken != getCouldNotCompute() && Latch &&
6958 DT.dominates(ExitBB, Latch)) {
6959 if (!MustExitMaxBECount) {
6960 MustExitMaxBECount = EL.MaxNotTaken;
6961 MustExitMaxOrZero = EL.MaxOrZero;
6963 MustExitMaxBECount =
6964 getUMinFromMismatchedTypes(MustExitMaxBECount, EL.MaxNotTaken);
6966 } else if (MayExitMaxBECount != getCouldNotCompute()) {
6967 if (!MayExitMaxBECount || EL.MaxNotTaken == getCouldNotCompute())
6968 MayExitMaxBECount = EL.MaxNotTaken;
6971 getUMaxFromMismatchedTypes(MayExitMaxBECount, EL.MaxNotTaken);
6975 const SCEV *MaxBECount = MustExitMaxBECount ? MustExitMaxBECount :
6976 (MayExitMaxBECount ? MayExitMaxBECount : getCouldNotCompute());
6977 // The loop backedge will be taken the maximum or zero times if there's
6978 // a single exit that must be taken the maximum or zero times.
6979 bool MaxOrZero = (MustExitMaxOrZero && ExitingBlocks.size() == 1);
6980 return BackedgeTakenInfo(std::move(ExitCounts), CouldComputeBECount,
6981 MaxBECount, MaxOrZero);
6984 ScalarEvolution::ExitLimit
6985 ScalarEvolution::computeExitLimit(const Loop *L, BasicBlock *ExitingBlock,
6986 bool AllowPredicates) {
6987 assert(L->contains(ExitingBlock) && "Exit count for non-loop block?");
6988 // If our exiting block does not dominate the latch, then its connection with
6989 // loop's exit limit may be far from trivial.
6990 const BasicBlock *Latch = L->getLoopLatch();
6991 if (!Latch || !DT.dominates(ExitingBlock, Latch))
6992 return getCouldNotCompute();
6994 bool IsOnlyExit = (L->getExitingBlock() != nullptr);
6995 Instruction *Term = ExitingBlock->getTerminator();
6996 if (BranchInst *BI = dyn_cast<BranchInst>(Term)) {
6997 assert(BI->isConditional() && "If unconditional, it can't be in loop!");
6998 bool ExitIfTrue = !L->contains(BI->getSuccessor(0));
6999 assert(ExitIfTrue == L->contains(BI->getSuccessor(1)) &&
7000 "It should have one successor in loop and one exit block!");
7001 // Proceed to the next level to examine the exit condition expression.
7002 return computeExitLimitFromCond(
7003 L, BI->getCondition(), ExitIfTrue,
7004 /*ControlsExit=*/IsOnlyExit, AllowPredicates);
7007 if (SwitchInst *SI = dyn_cast<SwitchInst>(Term)) {
7008 // For switch, make sure that there is a single exit from the loop.
7009 BasicBlock *Exit = nullptr;
7010 for (auto *SBB : successors(ExitingBlock))
7011 if (!L->contains(SBB)) {
7012 if (Exit) // Multiple exit successors.
7013 return getCouldNotCompute();
7016 assert(Exit && "Exiting block must have at least one exit");
7017 return computeExitLimitFromSingleExitSwitch(L, SI, Exit,
7018 /*ControlsExit=*/IsOnlyExit);
7021 return getCouldNotCompute();
7024 ScalarEvolution::ExitLimit ScalarEvolution::computeExitLimitFromCond(
7025 const Loop *L, Value *ExitCond, bool ExitIfTrue,
7026 bool ControlsExit, bool AllowPredicates) {
7027 ScalarEvolution::ExitLimitCacheTy Cache(L, ExitIfTrue, AllowPredicates);
7028 return computeExitLimitFromCondCached(Cache, L, ExitCond, ExitIfTrue,
7029 ControlsExit, AllowPredicates);
7032 Optional<ScalarEvolution::ExitLimit>
7033 ScalarEvolution::ExitLimitCache::find(const Loop *L, Value *ExitCond,
7034 bool ExitIfTrue, bool ControlsExit,
7035 bool AllowPredicates) {
7037 (void)this->ExitIfTrue;
7038 (void)this->AllowPredicates;
7040 assert(this->L == L && this->ExitIfTrue == ExitIfTrue &&
7041 this->AllowPredicates == AllowPredicates &&
7042 "Variance in assumed invariant key components!");
7043 auto Itr = TripCountMap.find({ExitCond, ControlsExit});
7044 if (Itr == TripCountMap.end())
7049 void ScalarEvolution::ExitLimitCache::insert(const Loop *L, Value *ExitCond,
7052 bool AllowPredicates,
7053 const ExitLimit &EL) {
7054 assert(this->L == L && this->ExitIfTrue == ExitIfTrue &&
7055 this->AllowPredicates == AllowPredicates &&
7056 "Variance in assumed invariant key components!");
7058 auto InsertResult = TripCountMap.insert({{ExitCond, ControlsExit}, EL});
7059 assert(InsertResult.second && "Expected successful insertion!");
7064 ScalarEvolution::ExitLimit ScalarEvolution::computeExitLimitFromCondCached(
7065 ExitLimitCacheTy &Cache, const Loop *L, Value *ExitCond, bool ExitIfTrue,
7066 bool ControlsExit, bool AllowPredicates) {
7069 Cache.find(L, ExitCond, ExitIfTrue, ControlsExit, AllowPredicates))
7072 ExitLimit EL = computeExitLimitFromCondImpl(Cache, L, ExitCond, ExitIfTrue,
7073 ControlsExit, AllowPredicates);
7074 Cache.insert(L, ExitCond, ExitIfTrue, ControlsExit, AllowPredicates, EL);
7078 ScalarEvolution::ExitLimit ScalarEvolution::computeExitLimitFromCondImpl(
7079 ExitLimitCacheTy &Cache, const Loop *L, Value *ExitCond, bool ExitIfTrue,
7080 bool ControlsExit, bool AllowPredicates) {
7081 // Check if the controlling expression for this loop is an And or Or.
7082 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
7083 if (BO->getOpcode() == Instruction::And) {
7084 // Recurse on the operands of the and.
7085 bool EitherMayExit = !ExitIfTrue;
7086 ExitLimit EL0 = computeExitLimitFromCondCached(
7087 Cache, L, BO->getOperand(0), ExitIfTrue,
7088 ControlsExit && !EitherMayExit, AllowPredicates);
7089 ExitLimit EL1 = computeExitLimitFromCondCached(
7090 Cache, L, BO->getOperand(1), ExitIfTrue,
7091 ControlsExit && !EitherMayExit, AllowPredicates);
7092 // Be robust against unsimplified IR for the form "and i1 X, true"
7093 if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->getOperand(1)))
7094 return CI->isOne() ? EL0 : EL1;
7095 if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->getOperand(0)))
7096 return CI->isOne() ? EL1 : EL0;
7097 const SCEV *BECount = getCouldNotCompute();
7098 const SCEV *MaxBECount = getCouldNotCompute();
7099 if (EitherMayExit) {
7100 // Both conditions must be true for the loop to continue executing.
7101 // Choose the less conservative count.
7102 if (EL0.ExactNotTaken == getCouldNotCompute() ||
7103 EL1.ExactNotTaken == getCouldNotCompute())
7104 BECount = getCouldNotCompute();
7107 getUMinFromMismatchedTypes(EL0.ExactNotTaken, EL1.ExactNotTaken);
7108 if (EL0.MaxNotTaken == getCouldNotCompute())
7109 MaxBECount = EL1.MaxNotTaken;
7110 else if (EL1.MaxNotTaken == getCouldNotCompute())
7111 MaxBECount = EL0.MaxNotTaken;
7114 getUMinFromMismatchedTypes(EL0.MaxNotTaken, EL1.MaxNotTaken);
7116 // Both conditions must be true at the same time for the loop to exit.
7117 // For now, be conservative.
7118 if (EL0.MaxNotTaken == EL1.MaxNotTaken)
7119 MaxBECount = EL0.MaxNotTaken;
7120 if (EL0.ExactNotTaken == EL1.ExactNotTaken)
7121 BECount = EL0.ExactNotTaken;
7124 // There are cases (e.g. PR26207) where computeExitLimitFromCond is able
7125 // to be more aggressive when computing BECount than when computing
7126 // MaxBECount. In these cases it is possible for EL0.ExactNotTaken and
7127 // EL1.ExactNotTaken to match, but for EL0.MaxNotTaken and EL1.MaxNotTaken
7129 if (isa<SCEVCouldNotCompute>(MaxBECount) &&
7130 !isa<SCEVCouldNotCompute>(BECount))
7131 MaxBECount = getConstant(getUnsignedRangeMax(BECount));
7133 return ExitLimit(BECount, MaxBECount, false,
7134 {&EL0.Predicates, &EL1.Predicates});
7136 if (BO->getOpcode() == Instruction::Or) {
7137 // Recurse on the operands of the or.
7138 bool EitherMayExit = ExitIfTrue;
7139 ExitLimit EL0 = computeExitLimitFromCondCached(
7140 Cache, L, BO->getOperand(0), ExitIfTrue,
7141 ControlsExit && !EitherMayExit, AllowPredicates);
7142 ExitLimit EL1 = computeExitLimitFromCondCached(
7143 Cache, L, BO->getOperand(1), ExitIfTrue,
7144 ControlsExit && !EitherMayExit, AllowPredicates);
7145 // Be robust against unsimplified IR for the form "or i1 X, true"
7146 if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->getOperand(1)))
7147 return CI->isZero() ? EL0 : EL1;
7148 if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->getOperand(0)))
7149 return CI->isZero() ? EL1 : EL0;
7150 const SCEV *BECount = getCouldNotCompute();
7151 const SCEV *MaxBECount = getCouldNotCompute();
7152 if (EitherMayExit) {
7153 // Both conditions must be false for the loop to continue executing.
7154 // Choose the less conservative count.
7155 if (EL0.ExactNotTaken == getCouldNotCompute() ||
7156 EL1.ExactNotTaken == getCouldNotCompute())
7157 BECount = getCouldNotCompute();
7160 getUMinFromMismatchedTypes(EL0.ExactNotTaken, EL1.ExactNotTaken);
7161 if (EL0.MaxNotTaken == getCouldNotCompute())
7162 MaxBECount = EL1.MaxNotTaken;
7163 else if (EL1.MaxNotTaken == getCouldNotCompute())
7164 MaxBECount = EL0.MaxNotTaken;
7167 getUMinFromMismatchedTypes(EL0.MaxNotTaken, EL1.MaxNotTaken);
7169 // Both conditions must be false at the same time for the loop to exit.
7170 // For now, be conservative.
7171 if (EL0.MaxNotTaken == EL1.MaxNotTaken)
7172 MaxBECount = EL0.MaxNotTaken;
7173 if (EL0.ExactNotTaken == EL1.ExactNotTaken)
7174 BECount = EL0.ExactNotTaken;
7176 // There are cases (e.g. PR26207) where computeExitLimitFromCond is able
7177 // to be more aggressive when computing BECount than when computing
7178 // MaxBECount. In these cases it is possible for EL0.ExactNotTaken and
7179 // EL1.ExactNotTaken to match, but for EL0.MaxNotTaken and EL1.MaxNotTaken
7181 if (isa<SCEVCouldNotCompute>(MaxBECount) &&
7182 !isa<SCEVCouldNotCompute>(BECount))
7183 MaxBECount = getConstant(getUnsignedRangeMax(BECount));
7185 return ExitLimit(BECount, MaxBECount, false,
7186 {&EL0.Predicates, &EL1.Predicates});
7190 // With an icmp, it may be feasible to compute an exact backedge-taken count.
7191 // Proceed to the next level to examine the icmp.
7192 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond)) {
7194 computeExitLimitFromICmp(L, ExitCondICmp, ExitIfTrue, ControlsExit);
7195 if (EL.hasFullInfo() || !AllowPredicates)
7198 // Try again, but use SCEV predicates this time.
7199 return computeExitLimitFromICmp(L, ExitCondICmp, ExitIfTrue, ControlsExit,
7200 /*AllowPredicates=*/true);
7203 // Check for a constant condition. These are normally stripped out by
7204 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
7205 // preserve the CFG and is temporarily leaving constant conditions
7207 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
7208 if (ExitIfTrue == !CI->getZExtValue())
7209 // The backedge is always taken.
7210 return getCouldNotCompute();
7212 // The backedge is never taken.
7213 return getZero(CI->getType());
7216 // If it's not an integer or pointer comparison then compute it the hard way.
7217 return computeExitCountExhaustively(L, ExitCond, ExitIfTrue);
7220 ScalarEvolution::ExitLimit
7221 ScalarEvolution::computeExitLimitFromICmp(const Loop *L,
7225 bool AllowPredicates) {
7226 // If the condition was exit on true, convert the condition to exit on false
7227 ICmpInst::Predicate Pred;
7229 Pred = ExitCond->getPredicate();
7231 Pred = ExitCond->getInversePredicate();
7232 const ICmpInst::Predicate OriginalPred = Pred;
7234 // Handle common loops like: for (X = "string"; *X; ++X)
7235 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
7236 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
7238 computeLoadConstantCompareExitLimit(LI, RHS, L, Pred);
7239 if (ItCnt.hasAnyInfo())
7243 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
7244 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
7246 // Try to evaluate any dependencies out of the loop.
7247 LHS = getSCEVAtScope(LHS, L);
7248 RHS = getSCEVAtScope(RHS, L);
7250 // At this point, we would like to compute how many iterations of the
7251 // loop the predicate will return true for these inputs.
7252 if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) {
7253 // If there is a loop-invariant, force it into the RHS.
7254 std::swap(LHS, RHS);
7255 Pred = ICmpInst::getSwappedPredicate(Pred);
7258 // Simplify the operands before analyzing them.
7259 (void)SimplifyICmpOperands(Pred, LHS, RHS);
7261 // If we have a comparison of a chrec against a constant, try to use value
7262 // ranges to answer this query.
7263 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
7264 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
7265 if (AddRec->getLoop() == L) {
7266 // Form the constant range.
7267 ConstantRange CompRange =
7268 ConstantRange::makeExactICmpRegion(Pred, RHSC->getAPInt());
7270 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
7271 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
7275 case ICmpInst::ICMP_NE: { // while (X != Y)
7276 // Convert to: while (X-Y != 0)
7277 ExitLimit EL = howFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit,
7279 if (EL.hasAnyInfo()) return EL;
7282 case ICmpInst::ICMP_EQ: { // while (X == Y)
7283 // Convert to: while (X-Y == 0)
7284 ExitLimit EL = howFarToNonZero(getMinusSCEV(LHS, RHS), L);
7285 if (EL.hasAnyInfo()) return EL;
7288 case ICmpInst::ICMP_SLT:
7289 case ICmpInst::ICMP_ULT: { // while (X < Y)
7290 bool IsSigned = Pred == ICmpInst::ICMP_SLT;
7291 ExitLimit EL = howManyLessThans(LHS, RHS, L, IsSigned, ControlsExit,
7293 if (EL.hasAnyInfo()) return EL;
7296 case ICmpInst::ICMP_SGT:
7297 case ICmpInst::ICMP_UGT: { // while (X > Y)
7298 bool IsSigned = Pred == ICmpInst::ICMP_SGT;
7300 howManyGreaterThans(LHS, RHS, L, IsSigned, ControlsExit,
7302 if (EL.hasAnyInfo()) return EL;
7309 auto *ExhaustiveCount =
7310 computeExitCountExhaustively(L, ExitCond, ExitIfTrue);
7312 if (!isa<SCEVCouldNotCompute>(ExhaustiveCount))
7313 return ExhaustiveCount;
7315 return computeShiftCompareExitLimit(ExitCond->getOperand(0),
7316 ExitCond->getOperand(1), L, OriginalPred);
7319 ScalarEvolution::ExitLimit
7320 ScalarEvolution::computeExitLimitFromSingleExitSwitch(const Loop *L,
7322 BasicBlock *ExitingBlock,
7323 bool ControlsExit) {
7324 assert(!L->contains(ExitingBlock) && "Not an exiting block!");
7326 // Give up if the exit is the default dest of a switch.
7327 if (Switch->getDefaultDest() == ExitingBlock)
7328 return getCouldNotCompute();
7330 assert(L->contains(Switch->getDefaultDest()) &&
7331 "Default case must not exit the loop!");
7332 const SCEV *LHS = getSCEVAtScope(Switch->getCondition(), L);
7333 const SCEV *RHS = getConstant(Switch->findCaseDest(ExitingBlock));
7335 // while (X != Y) --> while (X-Y != 0)
7336 ExitLimit EL = howFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit);
7337 if (EL.hasAnyInfo())
7340 return getCouldNotCompute();
7343 static ConstantInt *
7344 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
7345 ScalarEvolution &SE) {
7346 const SCEV *InVal = SE.getConstant(C);
7347 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
7348 assert(isa<SCEVConstant>(Val) &&
7349 "Evaluation of SCEV at constant didn't fold correctly?");
7350 return cast<SCEVConstant>(Val)->getValue();
7353 /// Given an exit condition of 'icmp op load X, cst', try to see if we can
7354 /// compute the backedge execution count.
7355 ScalarEvolution::ExitLimit
7356 ScalarEvolution::computeLoadConstantCompareExitLimit(
7360 ICmpInst::Predicate predicate) {
7361 if (LI->isVolatile()) return getCouldNotCompute();
7363 // Check to see if the loaded pointer is a getelementptr of a global.
7364 // TODO: Use SCEV instead of manually grubbing with GEPs.
7365 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
7366 if (!GEP) return getCouldNotCompute();
7368 // Make sure that it is really a constant global we are gepping, with an
7369 // initializer, and make sure the first IDX is really 0.
7370 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
7371 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
7372 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
7373 !cast<Constant>(GEP->getOperand(1))->isNullValue())
7374 return getCouldNotCompute();
7376 // Okay, we allow one non-constant index into the GEP instruction.
7377 Value *VarIdx = nullptr;
7378 std::vector<Constant*> Indexes;
7379 unsigned VarIdxNum = 0;
7380 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
7381 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
7382 Indexes.push_back(CI);
7383 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
7384 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
7385 VarIdx = GEP->getOperand(i);
7387 Indexes.push_back(nullptr);
7390 // Loop-invariant loads may be a byproduct of loop optimization. Skip them.
7392 return getCouldNotCompute();
7394 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
7395 // Check to see if X is a loop variant variable value now.
7396 const SCEV *Idx = getSCEV(VarIdx);
7397 Idx = getSCEVAtScope(Idx, L);
7399 // We can only recognize very limited forms of loop index expressions, in
7400 // particular, only affine AddRec's like {C1,+,C2}.
7401 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
7402 if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) ||
7403 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
7404 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
7405 return getCouldNotCompute();
7407 unsigned MaxSteps = MaxBruteForceIterations;
7408 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
7409 ConstantInt *ItCst = ConstantInt::get(
7410 cast<IntegerType>(IdxExpr->getType()), IterationNum);
7411 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
7413 // Form the GEP offset.
7414 Indexes[VarIdxNum] = Val;
7416 Constant *Result = ConstantFoldLoadThroughGEPIndices(GV->getInitializer(),
7418 if (!Result) break; // Cannot compute!
7420 // Evaluate the condition for this iteration.
7421 Result = ConstantExpr::getICmp(predicate, Result, RHS);
7422 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
7423 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
7424 ++NumArrayLenItCounts;
7425 return getConstant(ItCst); // Found terminating iteration!
7428 return getCouldNotCompute();
7431 ScalarEvolution::ExitLimit ScalarEvolution::computeShiftCompareExitLimit(
7432 Value *LHS, Value *RHSV, const Loop *L, ICmpInst::Predicate Pred) {
7433 ConstantInt *RHS = dyn_cast<ConstantInt>(RHSV);
7435 return getCouldNotCompute();
7437 const BasicBlock *Latch = L->getLoopLatch();
7439 return getCouldNotCompute();
7441 const BasicBlock *Predecessor = L->getLoopPredecessor();
7443 return getCouldNotCompute();
7445 // Return true if V is of the form "LHS `shift_op` <positive constant>".
7446 // Return LHS in OutLHS and shift_opt in OutOpCode.
7447 auto MatchPositiveShift =
7448 [](Value *V, Value *&OutLHS, Instruction::BinaryOps &OutOpCode) {
7450 using namespace PatternMatch;
7452 ConstantInt *ShiftAmt;
7453 if (match(V, m_LShr(m_Value(OutLHS), m_ConstantInt(ShiftAmt))))
7454 OutOpCode = Instruction::LShr;
7455 else if (match(V, m_AShr(m_Value(OutLHS), m_ConstantInt(ShiftAmt))))
7456 OutOpCode = Instruction::AShr;
7457 else if (match(V, m_Shl(m_Value(OutLHS), m_ConstantInt(ShiftAmt))))
7458 OutOpCode = Instruction::Shl;
7462 return ShiftAmt->getValue().isStrictlyPositive();
7465 // Recognize a "shift recurrence" either of the form %iv or of %iv.shifted in
7468 // %iv = phi i32 [ %iv.shifted, %loop ], [ %val, %preheader ]
7469 // %iv.shifted = lshr i32 %iv, <positive constant>
7471 // Return true on a successful match. Return the corresponding PHI node (%iv
7472 // above) in PNOut and the opcode of the shift operation in OpCodeOut.
7473 auto MatchShiftRecurrence =
7474 [&](Value *V, PHINode *&PNOut, Instruction::BinaryOps &OpCodeOut) {
7475 Optional<Instruction::BinaryOps> PostShiftOpCode;
7478 Instruction::BinaryOps OpC;
7481 // If we encounter a shift instruction, "peel off" the shift operation,
7482 // and remember that we did so. Later when we inspect %iv's backedge
7483 // value, we will make sure that the backedge value uses the same
7486 // Note: the peeled shift operation does not have to be the same
7487 // instruction as the one feeding into the PHI's backedge value. We only
7488 // really care about it being the same *kind* of shift instruction --
7489 // that's all that is required for our later inferences to hold.
7490 if (MatchPositiveShift(LHS, V, OpC)) {
7491 PostShiftOpCode = OpC;
7496 PNOut = dyn_cast<PHINode>(LHS);
7497 if (!PNOut || PNOut->getParent() != L->getHeader())
7500 Value *BEValue = PNOut->getIncomingValueForBlock(Latch);
7504 // The backedge value for the PHI node must be a shift by a positive
7506 MatchPositiveShift(BEValue, OpLHS, OpCodeOut) &&
7508 // of the PHI node itself
7511 // and the kind of shift should be match the kind of shift we peeled
7513 (!PostShiftOpCode.hasValue() || *PostShiftOpCode == OpCodeOut);
7517 Instruction::BinaryOps OpCode;
7518 if (!MatchShiftRecurrence(LHS, PN, OpCode))
7519 return getCouldNotCompute();
7521 const DataLayout &DL = getDataLayout();
7523 // The key rationale for this optimization is that for some kinds of shift
7524 // recurrences, the value of the recurrence "stabilizes" to either 0 or -1
7525 // within a finite number of iterations. If the condition guarding the
7526 // backedge (in the sense that the backedge is taken if the condition is true)
7527 // is false for the value the shift recurrence stabilizes to, then we know
7528 // that the backedge is taken only a finite number of times.
7530 ConstantInt *StableValue = nullptr;
7533 llvm_unreachable("Impossible case!");
7535 case Instruction::AShr: {
7536 // {K,ashr,<positive-constant>} stabilizes to signum(K) in at most
7537 // bitwidth(K) iterations.
7538 Value *FirstValue = PN->getIncomingValueForBlock(Predecessor);
7539 KnownBits Known = computeKnownBits(FirstValue, DL, 0, nullptr,
7540 Predecessor->getTerminator(), &DT);
7541 auto *Ty = cast<IntegerType>(RHS->getType());
7542 if (Known.isNonNegative())
7543 StableValue = ConstantInt::get(Ty, 0);
7544 else if (Known.isNegative())
7545 StableValue = ConstantInt::get(Ty, -1, true);
7547 return getCouldNotCompute();
7551 case Instruction::LShr:
7552 case Instruction::Shl:
7553 // Both {K,lshr,<positive-constant>} and {K,shl,<positive-constant>}
7554 // stabilize to 0 in at most bitwidth(K) iterations.
7555 StableValue = ConstantInt::get(cast<IntegerType>(RHS->getType()), 0);
7560 ConstantFoldCompareInstOperands(Pred, StableValue, RHS, DL, &TLI);
7561 assert(Result->getType()->isIntegerTy(1) &&
7562 "Otherwise cannot be an operand to a branch instruction");
7564 if (Result->isZeroValue()) {
7565 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
7566 const SCEV *UpperBound =
7567 getConstant(getEffectiveSCEVType(RHS->getType()), BitWidth);
7568 return ExitLimit(getCouldNotCompute(), UpperBound, false);
7571 return getCouldNotCompute();
7574 /// Return true if we can constant fold an instruction of the specified type,
7575 /// assuming that all operands were constants.
7576 static bool CanConstantFold(const Instruction *I) {
7577 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
7578 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I) ||
7579 isa<LoadInst>(I) || isa<ExtractValueInst>(I))
7582 if (const CallInst *CI = dyn_cast<CallInst>(I))
7583 if (const Function *F = CI->getCalledFunction())
7584 return canConstantFoldCallTo(CI, F);
7588 /// Determine whether this instruction can constant evolve within this loop
7589 /// assuming its operands can all constant evolve.
7590 static bool canConstantEvolve(Instruction *I, const Loop *L) {
7591 // An instruction outside of the loop can't be derived from a loop PHI.
7592 if (!L->contains(I)) return false;
7594 if (isa<PHINode>(I)) {
7595 // We don't currently keep track of the control flow needed to evaluate
7596 // PHIs, so we cannot handle PHIs inside of loops.
7597 return L->getHeader() == I->getParent();
7600 // If we won't be able to constant fold this expression even if the operands
7601 // are constants, bail early.
7602 return CanConstantFold(I);
7605 /// getConstantEvolvingPHIOperands - Implement getConstantEvolvingPHI by
7606 /// recursing through each instruction operand until reaching a loop header phi.
7608 getConstantEvolvingPHIOperands(Instruction *UseInst, const Loop *L,
7609 DenseMap<Instruction *, PHINode *> &PHIMap,
7611 if (Depth > MaxConstantEvolvingDepth)
7614 // Otherwise, we can evaluate this instruction if all of its operands are
7615 // constant or derived from a PHI node themselves.
7616 PHINode *PHI = nullptr;
7617 for (Value *Op : UseInst->operands()) {
7618 if (isa<Constant>(Op)) continue;
7620 Instruction *OpInst = dyn_cast<Instruction>(Op);
7621 if (!OpInst || !canConstantEvolve(OpInst, L)) return nullptr;
7623 PHINode *P = dyn_cast<PHINode>(OpInst);
7625 // If this operand is already visited, reuse the prior result.
7626 // We may have P != PHI if this is the deepest point at which the
7627 // inconsistent paths meet.
7628 P = PHIMap.lookup(OpInst);
7630 // Recurse and memoize the results, whether a phi is found or not.
7631 // This recursive call invalidates pointers into PHIMap.
7632 P = getConstantEvolvingPHIOperands(OpInst, L, PHIMap, Depth + 1);
7636 return nullptr; // Not evolving from PHI
7637 if (PHI && PHI != P)
7638 return nullptr; // Evolving from multiple different PHIs.
7641 // This is a expression evolving from a constant PHI!
7645 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
7646 /// in the loop that V is derived from. We allow arbitrary operations along the
7647 /// way, but the operands of an operation must either be constants or a value
7648 /// derived from a constant PHI. If this expression does not fit with these
7649 /// constraints, return null.
7650 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
7651 Instruction *I = dyn_cast<Instruction>(V);
7652 if (!I || !canConstantEvolve(I, L)) return nullptr;
7654 if (PHINode *PN = dyn_cast<PHINode>(I))
7657 // Record non-constant instructions contained by the loop.
7658 DenseMap<Instruction *, PHINode *> PHIMap;
7659 return getConstantEvolvingPHIOperands(I, L, PHIMap, 0);
7662 /// EvaluateExpression - Given an expression that passes the
7663 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
7664 /// in the loop has the value PHIVal. If we can't fold this expression for some
7665 /// reason, return null.
7666 static Constant *EvaluateExpression(Value *V, const Loop *L,
7667 DenseMap<Instruction *, Constant *> &Vals,
7668 const DataLayout &DL,
7669 const TargetLibraryInfo *TLI) {
7670 // Convenient constant check, but redundant for recursive calls.
7671 if (Constant *C = dyn_cast<Constant>(V)) return C;
7672 Instruction *I = dyn_cast<Instruction>(V);
7673 if (!I) return nullptr;
7675 if (Constant *C = Vals.lookup(I)) return C;
7677 // An instruction inside the loop depends on a value outside the loop that we
7678 // weren't given a mapping for, or a value such as a call inside the loop.
7679 if (!canConstantEvolve(I, L)) return nullptr;
7681 // An unmapped PHI can be due to a branch or another loop inside this loop,
7682 // or due to this not being the initial iteration through a loop where we
7683 // couldn't compute the evolution of this particular PHI last time.
7684 if (isa<PHINode>(I)) return nullptr;
7686 std::vector<Constant*> Operands(I->getNumOperands());
7688 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
7689 Instruction *Operand = dyn_cast<Instruction>(I->getOperand(i));
7691 Operands[i] = dyn_cast<Constant>(I->getOperand(i));
7692 if (!Operands[i]) return nullptr;
7695 Constant *C = EvaluateExpression(Operand, L, Vals, DL, TLI);
7697 if (!C) return nullptr;
7701 if (CmpInst *CI = dyn_cast<CmpInst>(I))
7702 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
7703 Operands[1], DL, TLI);
7704 if (LoadInst *LI = dyn_cast<LoadInst>(I)) {
7705 if (!LI->isVolatile())
7706 return ConstantFoldLoadFromConstPtr(Operands[0], LI->getType(), DL);
7708 return ConstantFoldInstOperands(I, Operands, DL, TLI);
7712 // If every incoming value to PN except the one for BB is a specific Constant,
7713 // return that, else return nullptr.
7714 static Constant *getOtherIncomingValue(PHINode *PN, BasicBlock *BB) {
7715 Constant *IncomingVal = nullptr;
7717 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
7718 if (PN->getIncomingBlock(i) == BB)
7721 auto *CurrentVal = dyn_cast<Constant>(PN->getIncomingValue(i));
7725 if (IncomingVal != CurrentVal) {
7728 IncomingVal = CurrentVal;
7735 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
7736 /// in the header of its containing loop, we know the loop executes a
7737 /// constant number of times, and the PHI node is just a recurrence
7738 /// involving constants, fold it.
7740 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
7743 auto I = ConstantEvolutionLoopExitValue.find(PN);
7744 if (I != ConstantEvolutionLoopExitValue.end())
7747 if (BEs.ugt(MaxBruteForceIterations))
7748 return ConstantEvolutionLoopExitValue[PN] = nullptr; // Not going to evaluate it.
7750 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
7752 DenseMap<Instruction *, Constant *> CurrentIterVals;
7753 BasicBlock *Header = L->getHeader();
7754 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
7756 BasicBlock *Latch = L->getLoopLatch();
7760 for (PHINode &PHI : Header->phis()) {
7761 if (auto *StartCST = getOtherIncomingValue(&PHI, Latch))
7762 CurrentIterVals[&PHI] = StartCST;
7764 if (!CurrentIterVals.count(PN))
7765 return RetVal = nullptr;
7767 Value *BEValue = PN->getIncomingValueForBlock(Latch);
7769 // Execute the loop symbolically to determine the exit value.
7770 assert(BEs.getActiveBits() < CHAR_BIT * sizeof(unsigned) &&
7771 "BEs is <= MaxBruteForceIterations which is an 'unsigned'!");
7773 unsigned NumIterations = BEs.getZExtValue(); // must be in range
7774 unsigned IterationNum = 0;
7775 const DataLayout &DL = getDataLayout();
7776 for (; ; ++IterationNum) {
7777 if (IterationNum == NumIterations)
7778 return RetVal = CurrentIterVals[PN]; // Got exit value!
7780 // Compute the value of the PHIs for the next iteration.
7781 // EvaluateExpression adds non-phi values to the CurrentIterVals map.
7782 DenseMap<Instruction *, Constant *> NextIterVals;
7784 EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
7786 return nullptr; // Couldn't evaluate!
7787 NextIterVals[PN] = NextPHI;
7789 bool StoppedEvolving = NextPHI == CurrentIterVals[PN];
7791 // Also evaluate the other PHI nodes. However, we don't get to stop if we
7792 // cease to be able to evaluate one of them or if they stop evolving,
7793 // because that doesn't necessarily prevent us from computing PN.
7794 SmallVector<std::pair<PHINode *, Constant *>, 8> PHIsToCompute;
7795 for (const auto &I : CurrentIterVals) {
7796 PHINode *PHI = dyn_cast<PHINode>(I.first);
7797 if (!PHI || PHI == PN || PHI->getParent() != Header) continue;
7798 PHIsToCompute.emplace_back(PHI, I.second);
7800 // We use two distinct loops because EvaluateExpression may invalidate any
7801 // iterators into CurrentIterVals.
7802 for (const auto &I : PHIsToCompute) {
7803 PHINode *PHI = I.first;
7804 Constant *&NextPHI = NextIterVals[PHI];
7805 if (!NextPHI) { // Not already computed.
7806 Value *BEValue = PHI->getIncomingValueForBlock(Latch);
7807 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
7809 if (NextPHI != I.second)
7810 StoppedEvolving = false;
7813 // If all entries in CurrentIterVals == NextIterVals then we can stop
7814 // iterating, the loop can't continue to change.
7815 if (StoppedEvolving)
7816 return RetVal = CurrentIterVals[PN];
7818 CurrentIterVals.swap(NextIterVals);
7822 const SCEV *ScalarEvolution::computeExitCountExhaustively(const Loop *L,
7825 PHINode *PN = getConstantEvolvingPHI(Cond, L);
7826 if (!PN) return getCouldNotCompute();
7828 // If the loop is canonicalized, the PHI will have exactly two entries.
7829 // That's the only form we support here.
7830 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
7832 DenseMap<Instruction *, Constant *> CurrentIterVals;
7833 BasicBlock *Header = L->getHeader();
7834 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
7836 BasicBlock *Latch = L->getLoopLatch();
7837 assert(Latch && "Should follow from NumIncomingValues == 2!");
7839 for (PHINode &PHI : Header->phis()) {
7840 if (auto *StartCST = getOtherIncomingValue(&PHI, Latch))
7841 CurrentIterVals[&PHI] = StartCST;
7843 if (!CurrentIterVals.count(PN))
7844 return getCouldNotCompute();
7846 // Okay, we find a PHI node that defines the trip count of this loop. Execute
7847 // the loop symbolically to determine when the condition gets a value of
7849 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
7850 const DataLayout &DL = getDataLayout();
7851 for (unsigned IterationNum = 0; IterationNum != MaxIterations;++IterationNum){
7852 auto *CondVal = dyn_cast_or_null<ConstantInt>(
7853 EvaluateExpression(Cond, L, CurrentIterVals, DL, &TLI));
7855 // Couldn't symbolically evaluate.
7856 if (!CondVal) return getCouldNotCompute();
7858 if (CondVal->getValue() == uint64_t(ExitWhen)) {
7859 ++NumBruteForceTripCountsComputed;
7860 return getConstant(Type::getInt32Ty(getContext()), IterationNum);
7863 // Update all the PHI nodes for the next iteration.
7864 DenseMap<Instruction *, Constant *> NextIterVals;
7866 // Create a list of which PHIs we need to compute. We want to do this before
7867 // calling EvaluateExpression on them because that may invalidate iterators
7868 // into CurrentIterVals.
7869 SmallVector<PHINode *, 8> PHIsToCompute;
7870 for (const auto &I : CurrentIterVals) {
7871 PHINode *PHI = dyn_cast<PHINode>(I.first);
7872 if (!PHI || PHI->getParent() != Header) continue;
7873 PHIsToCompute.push_back(PHI);
7875 for (PHINode *PHI : PHIsToCompute) {
7876 Constant *&NextPHI = NextIterVals[PHI];
7877 if (NextPHI) continue; // Already computed!
7879 Value *BEValue = PHI->getIncomingValueForBlock(Latch);
7880 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
7882 CurrentIterVals.swap(NextIterVals);
7885 // Too many iterations were needed to evaluate.
7886 return getCouldNotCompute();
7889 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
7890 SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values =
7892 // Check to see if we've folded this expression at this loop before.
7893 for (auto &LS : Values)
7895 return LS.second ? LS.second : V;
7897 Values.emplace_back(L, nullptr);
7899 // Otherwise compute it.
7900 const SCEV *C = computeSCEVAtScope(V, L);
7901 for (auto &LS : reverse(ValuesAtScopes[V]))
7902 if (LS.first == L) {
7909 /// This builds up a Constant using the ConstantExpr interface. That way, we
7910 /// will return Constants for objects which aren't represented by a
7911 /// SCEVConstant, because SCEVConstant is restricted to ConstantInt.
7912 /// Returns NULL if the SCEV isn't representable as a Constant.
7913 static Constant *BuildConstantFromSCEV(const SCEV *V) {
7914 switch (static_cast<SCEVTypes>(V->getSCEVType())) {
7915 case scCouldNotCompute:
7919 return cast<SCEVConstant>(V)->getValue();
7921 return dyn_cast<Constant>(cast<SCEVUnknown>(V)->getValue());
7922 case scSignExtend: {
7923 const SCEVSignExtendExpr *SS = cast<SCEVSignExtendExpr>(V);
7924 if (Constant *CastOp = BuildConstantFromSCEV(SS->getOperand()))
7925 return ConstantExpr::getSExt(CastOp, SS->getType());
7928 case scZeroExtend: {
7929 const SCEVZeroExtendExpr *SZ = cast<SCEVZeroExtendExpr>(V);
7930 if (Constant *CastOp = BuildConstantFromSCEV(SZ->getOperand()))
7931 return ConstantExpr::getZExt(CastOp, SZ->getType());
7935 const SCEVTruncateExpr *ST = cast<SCEVTruncateExpr>(V);
7936 if (Constant *CastOp = BuildConstantFromSCEV(ST->getOperand()))
7937 return ConstantExpr::getTrunc(CastOp, ST->getType());
7941 const SCEVAddExpr *SA = cast<SCEVAddExpr>(V);
7942 if (Constant *C = BuildConstantFromSCEV(SA->getOperand(0))) {
7943 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
7944 unsigned AS = PTy->getAddressSpace();
7945 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
7946 C = ConstantExpr::getBitCast(C, DestPtrTy);
7948 for (unsigned i = 1, e = SA->getNumOperands(); i != e; ++i) {
7949 Constant *C2 = BuildConstantFromSCEV(SA->getOperand(i));
7950 if (!C2) return nullptr;
7953 if (!C->getType()->isPointerTy() && C2->getType()->isPointerTy()) {
7954 unsigned AS = C2->getType()->getPointerAddressSpace();
7956 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
7957 // The offsets have been converted to bytes. We can add bytes to an
7958 // i8* by GEP with the byte count in the first index.
7959 C = ConstantExpr::getBitCast(C, DestPtrTy);
7962 // Don't bother trying to sum two pointers. We probably can't
7963 // statically compute a load that results from it anyway.
7964 if (C2->getType()->isPointerTy())
7967 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
7968 if (PTy->getElementType()->isStructTy())
7969 C2 = ConstantExpr::getIntegerCast(
7970 C2, Type::getInt32Ty(C->getContext()), true);
7971 C = ConstantExpr::getGetElementPtr(PTy->getElementType(), C, C2);
7973 C = ConstantExpr::getAdd(C, C2);
7980 const SCEVMulExpr *SM = cast<SCEVMulExpr>(V);
7981 if (Constant *C = BuildConstantFromSCEV(SM->getOperand(0))) {
7982 // Don't bother with pointers at all.
7983 if (C->getType()->isPointerTy()) return nullptr;
7984 for (unsigned i = 1, e = SM->getNumOperands(); i != e; ++i) {
7985 Constant *C2 = BuildConstantFromSCEV(SM->getOperand(i));
7986 if (!C2 || C2->getType()->isPointerTy()) return nullptr;
7987 C = ConstantExpr::getMul(C, C2);
7994 const SCEVUDivExpr *SU = cast<SCEVUDivExpr>(V);
7995 if (Constant *LHS = BuildConstantFromSCEV(SU->getLHS()))
7996 if (Constant *RHS = BuildConstantFromSCEV(SU->getRHS()))
7997 if (LHS->getType() == RHS->getType())
7998 return ConstantExpr::getUDiv(LHS, RHS);
8005 break; // TODO: smax, umax, smin, umax.
8010 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
8011 if (isa<SCEVConstant>(V)) return V;
8013 // If this instruction is evolved from a constant-evolving PHI, compute the
8014 // exit value from the loop without using SCEVs.
8015 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
8016 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
8017 if (PHINode *PN = dyn_cast<PHINode>(I)) {
8018 const Loop *LI = this->LI[I->getParent()];
8019 // Looking for loop exit value.
8020 if (LI && LI->getParentLoop() == L &&
8021 PN->getParent() == LI->getHeader()) {
8022 // Okay, there is no closed form solution for the PHI node. Check
8023 // to see if the loop that contains it has a known backedge-taken
8024 // count. If so, we may be able to force computation of the exit
8026 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
8027 // This trivial case can show up in some degenerate cases where
8028 // the incoming IR has not yet been fully simplified.
8029 if (BackedgeTakenCount->isZero()) {
8030 Value *InitValue = nullptr;
8031 bool MultipleInitValues = false;
8032 for (unsigned i = 0; i < PN->getNumIncomingValues(); i++) {
8033 if (!LI->contains(PN->getIncomingBlock(i))) {
8035 InitValue = PN->getIncomingValue(i);
8036 else if (InitValue != PN->getIncomingValue(i)) {
8037 MultipleInitValues = true;
8042 if (!MultipleInitValues && InitValue)
8043 return getSCEV(InitValue);
8045 // Do we have a loop invariant value flowing around the backedge
8046 // for a loop which must execute the backedge?
8047 if (!isa<SCEVCouldNotCompute>(BackedgeTakenCount) &&
8048 isKnownPositive(BackedgeTakenCount) &&
8049 PN->getNumIncomingValues() == 2) {
8051 unsigned InLoopPred = LI->contains(PN->getIncomingBlock(0)) ? 0 : 1;
8052 Value *BackedgeVal = PN->getIncomingValue(InLoopPred);
8053 if (LI->isLoopInvariant(BackedgeVal))
8054 return getSCEV(BackedgeVal);
8056 if (auto *BTCC = dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
8057 // Okay, we know how many times the containing loop executes. If
8058 // this is a constant evolving PHI node, get the final value at
8059 // the specified iteration number.
8061 getConstantEvolutionLoopExitValue(PN, BTCC->getAPInt(), LI);
8062 if (RV) return getSCEV(RV);
8066 // If there is a single-input Phi, evaluate it at our scope. If we can
8067 // prove that this replacement does not break LCSSA form, use new value.
8068 if (PN->getNumOperands() == 1) {
8069 const SCEV *Input = getSCEV(PN->getOperand(0));
8070 const SCEV *InputAtScope = getSCEVAtScope(Input, L);
8071 // TODO: We can generalize it using LI.replacementPreservesLCSSAForm,
8072 // for the simplest case just support constants.
8073 if (isa<SCEVConstant>(InputAtScope)) return InputAtScope;
8077 // Okay, this is an expression that we cannot symbolically evaluate
8078 // into a SCEV. Check to see if it's possible to symbolically evaluate
8079 // the arguments into constants, and if so, try to constant propagate the
8080 // result. This is particularly useful for computing loop exit values.
8081 if (CanConstantFold(I)) {
8082 SmallVector<Constant *, 4> Operands;
8083 bool MadeImprovement = false;
8084 for (Value *Op : I->operands()) {
8085 if (Constant *C = dyn_cast<Constant>(Op)) {
8086 Operands.push_back(C);
8090 // If any of the operands is non-constant and if they are
8091 // non-integer and non-pointer, don't even try to analyze them
8092 // with scev techniques.
8093 if (!isSCEVable(Op->getType()))
8096 const SCEV *OrigV = getSCEV(Op);
8097 const SCEV *OpV = getSCEVAtScope(OrigV, L);
8098 MadeImprovement |= OrigV != OpV;
8100 Constant *C = BuildConstantFromSCEV(OpV);
8102 if (C->getType() != Op->getType())
8103 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
8107 Operands.push_back(C);
8110 // Check to see if getSCEVAtScope actually made an improvement.
8111 if (MadeImprovement) {
8112 Constant *C = nullptr;
8113 const DataLayout &DL = getDataLayout();
8114 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
8115 C = ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
8116 Operands[1], DL, &TLI);
8117 else if (const LoadInst *LI = dyn_cast<LoadInst>(I)) {
8118 if (!LI->isVolatile())
8119 C = ConstantFoldLoadFromConstPtr(Operands[0], LI->getType(), DL);
8121 C = ConstantFoldInstOperands(I, Operands, DL, &TLI);
8128 // This is some other type of SCEVUnknown, just return it.
8132 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
8133 // Avoid performing the look-up in the common case where the specified
8134 // expression has no loop-variant portions.
8135 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
8136 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
8137 if (OpAtScope != Comm->getOperand(i)) {
8138 // Okay, at least one of these operands is loop variant but might be
8139 // foldable. Build a new instance of the folded commutative expression.
8140 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
8141 Comm->op_begin()+i);
8142 NewOps.push_back(OpAtScope);
8144 for (++i; i != e; ++i) {
8145 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
8146 NewOps.push_back(OpAtScope);
8148 if (isa<SCEVAddExpr>(Comm))
8149 return getAddExpr(NewOps, Comm->getNoWrapFlags());
8150 if (isa<SCEVMulExpr>(Comm))
8151 return getMulExpr(NewOps, Comm->getNoWrapFlags());
8152 if (isa<SCEVMinMaxExpr>(Comm))
8153 return getMinMaxExpr(Comm->getSCEVType(), NewOps);
8154 llvm_unreachable("Unknown commutative SCEV type!");
8157 // If we got here, all operands are loop invariant.
8161 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
8162 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
8163 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
8164 if (LHS == Div->getLHS() && RHS == Div->getRHS())
8165 return Div; // must be loop invariant
8166 return getUDivExpr(LHS, RHS);
8169 // If this is a loop recurrence for a loop that does not contain L, then we
8170 // are dealing with the final value computed by the loop.
8171 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
8172 // First, attempt to evaluate each operand.
8173 // Avoid performing the look-up in the common case where the specified
8174 // expression has no loop-variant portions.
8175 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
8176 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
8177 if (OpAtScope == AddRec->getOperand(i))
8180 // Okay, at least one of these operands is loop variant but might be
8181 // foldable. Build a new instance of the folded commutative expression.
8182 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(),
8183 AddRec->op_begin()+i);
8184 NewOps.push_back(OpAtScope);
8185 for (++i; i != e; ++i)
8186 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
8188 const SCEV *FoldedRec =
8189 getAddRecExpr(NewOps, AddRec->getLoop(),
8190 AddRec->getNoWrapFlags(SCEV::FlagNW));
8191 AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec);
8192 // The addrec may be folded to a nonrecurrence, for example, if the
8193 // induction variable is multiplied by zero after constant folding. Go
8194 // ahead and return the folded value.
8200 // If the scope is outside the addrec's loop, evaluate it by using the
8201 // loop exit value of the addrec.
8202 if (!AddRec->getLoop()->contains(L)) {
8203 // To evaluate this recurrence, we need to know how many times the AddRec
8204 // loop iterates. Compute this now.
8205 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
8206 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
8208 // Then, evaluate the AddRec.
8209 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
8215 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
8216 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
8217 if (Op == Cast->getOperand())
8218 return Cast; // must be loop invariant
8219 return getZeroExtendExpr(Op, Cast->getType());
8222 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
8223 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
8224 if (Op == Cast->getOperand())
8225 return Cast; // must be loop invariant
8226 return getSignExtendExpr(Op, Cast->getType());
8229 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
8230 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
8231 if (Op == Cast->getOperand())
8232 return Cast; // must be loop invariant
8233 return getTruncateExpr(Op, Cast->getType());
8236 llvm_unreachable("Unknown SCEV type!");
8239 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
8240 return getSCEVAtScope(getSCEV(V), L);
8243 const SCEV *ScalarEvolution::stripInjectiveFunctions(const SCEV *S) const {
8244 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S))
8245 return stripInjectiveFunctions(ZExt->getOperand());
8246 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S))
8247 return stripInjectiveFunctions(SExt->getOperand());
8251 /// Finds the minimum unsigned root of the following equation:
8253 /// A * X = B (mod N)
8255 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
8256 /// A and B isn't important.
8258 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
8259 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const SCEV *B,
8260 ScalarEvolution &SE) {
8261 uint32_t BW = A.getBitWidth();
8262 assert(BW == SE.getTypeSizeInBits(B->getType()));
8263 assert(A != 0 && "A must be non-zero.");
8267 // The gcd of A and N may have only one prime factor: 2. The number of
8268 // trailing zeros in A is its multiplicity
8269 uint32_t Mult2 = A.countTrailingZeros();
8272 // 2. Check if B is divisible by D.
8274 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
8275 // is not less than multiplicity of this prime factor for D.
8276 if (SE.GetMinTrailingZeros(B) < Mult2)
8277 return SE.getCouldNotCompute();
8279 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
8282 // If D == 1, (N / D) == N == 2^BW, so we need one extra bit to represent
8283 // (N / D) in general. The inverse itself always fits into BW bits, though,
8284 // so we immediately truncate it.
8285 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
8286 APInt Mod(BW + 1, 0);
8287 Mod.setBit(BW - Mult2); // Mod = N / D
8288 APInt I = AD.multiplicativeInverse(Mod).trunc(BW);
8290 // 4. Compute the minimum unsigned root of the equation:
8291 // I * (B / D) mod (N / D)
8292 // To simplify the computation, we factor out the divide by D:
8293 // (I * B mod N) / D
8294 const SCEV *D = SE.getConstant(APInt::getOneBitSet(BW, Mult2));
8295 return SE.getUDivExactExpr(SE.getMulExpr(B, SE.getConstant(I)), D);
8298 /// For a given quadratic addrec, generate coefficients of the corresponding
8299 /// quadratic equation, multiplied by a common value to ensure that they are
8301 /// The returned value is a tuple { A, B, C, M, BitWidth }, where
8302 /// Ax^2 + Bx + C is the quadratic function, M is the value that A, B and C
8303 /// were multiplied by, and BitWidth is the bit width of the original addrec
8305 /// This function returns None if the addrec coefficients are not compile-
8307 static Optional<std::tuple<APInt, APInt, APInt, APInt, unsigned>>
8308 GetQuadraticEquation(const SCEVAddRecExpr *AddRec) {
8309 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
8310 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
8311 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
8312 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
8313 LLVM_DEBUG(dbgs() << __func__ << ": analyzing quadratic addrec: "
8314 << *AddRec << '\n');
8316 // We currently can only solve this if the coefficients are constants.
8317 if (!LC || !MC || !NC) {
8318 LLVM_DEBUG(dbgs() << __func__ << ": coefficients are not constant\n");
8322 APInt L = LC->getAPInt();
8323 APInt M = MC->getAPInt();
8324 APInt N = NC->getAPInt();
8325 assert(!N.isNullValue() && "This is not a quadratic addrec");
8327 unsigned BitWidth = LC->getAPInt().getBitWidth();
8328 unsigned NewWidth = BitWidth + 1;
8329 LLVM_DEBUG(dbgs() << __func__ << ": addrec coeff bw: "
8330 << BitWidth << '\n');
8331 // The sign-extension (as opposed to a zero-extension) here matches the
8332 // extension used in SolveQuadraticEquationWrap (with the same motivation).
8333 N = N.sext(NewWidth);
8334 M = M.sext(NewWidth);
8335 L = L.sext(NewWidth);
8337 // The increments are M, M+N, M+2N, ..., so the accumulated values are
8338 // L+M, (L+M)+(M+N), (L+M)+(M+N)+(M+2N), ..., that is,
8339 // L+M, L+2M+N, L+3M+3N, ...
8340 // After n iterations the accumulated value Acc is L + nM + n(n-1)/2 N.
8342 // The equation Acc = 0 is then
8343 // L + nM + n(n-1)/2 N = 0, or 2L + 2M n + n(n-1) N = 0.
8344 // In a quadratic form it becomes:
8345 // N n^2 + (2M-N) n + 2L = 0.
8348 APInt B = 2 * M - A;
8350 APInt T = APInt(NewWidth, 2);
8351 LLVM_DEBUG(dbgs() << __func__ << ": equation " << A << "x^2 + " << B
8352 << "x + " << C << ", coeff bw: " << NewWidth
8353 << ", multiplied by " << T << '\n');
8354 return std::make_tuple(A, B, C, T, BitWidth);
8357 /// Helper function to compare optional APInts:
8358 /// (a) if X and Y both exist, return min(X, Y),
8359 /// (b) if neither X nor Y exist, return None,
8360 /// (c) if exactly one of X and Y exists, return that value.
8361 static Optional<APInt> MinOptional(Optional<APInt> X, Optional<APInt> Y) {
8362 if (X.hasValue() && Y.hasValue()) {
8363 unsigned W = std::max(X->getBitWidth(), Y->getBitWidth());
8364 APInt XW = X->sextOrSelf(W);
8365 APInt YW = Y->sextOrSelf(W);
8366 return XW.slt(YW) ? *X : *Y;
8368 if (!X.hasValue() && !Y.hasValue())
8370 return X.hasValue() ? *X : *Y;
8373 /// Helper function to truncate an optional APInt to a given BitWidth.
8374 /// When solving addrec-related equations, it is preferable to return a value
8375 /// that has the same bit width as the original addrec's coefficients. If the
8376 /// solution fits in the original bit width, truncate it (except for i1).
8377 /// Returning a value of a different bit width may inhibit some optimizations.
8379 /// In general, a solution to a quadratic equation generated from an addrec
8380 /// may require BW+1 bits, where BW is the bit width of the addrec's
8381 /// coefficients. The reason is that the coefficients of the quadratic
8382 /// equation are BW+1 bits wide (to avoid truncation when converting from
8383 /// the addrec to the equation).
8384 static Optional<APInt> TruncIfPossible(Optional<APInt> X, unsigned BitWidth) {
8387 unsigned W = X->getBitWidth();
8388 if (BitWidth > 1 && BitWidth < W && X->isIntN(BitWidth))
8389 return X->trunc(BitWidth);
8393 /// Let c(n) be the value of the quadratic chrec {L,+,M,+,N} after n
8394 /// iterations. The values L, M, N are assumed to be signed, and they
8395 /// should all have the same bit widths.
8396 /// Find the least n >= 0 such that c(n) = 0 in the arithmetic modulo 2^BW,
8397 /// where BW is the bit width of the addrec's coefficients.
8398 /// If the calculated value is a BW-bit integer (for BW > 1), it will be
8399 /// returned as such, otherwise the bit width of the returned value may
8400 /// be greater than BW.
8402 /// This function returns None if
8403 /// (a) the addrec coefficients are not constant, or
8404 /// (b) SolveQuadraticEquationWrap was unable to find a solution. For cases
8405 /// like x^2 = 5, no integer solutions exist, in other cases an integer
8406 /// solution may exist, but SolveQuadraticEquationWrap may fail to find it.
8407 static Optional<APInt>
8408 SolveQuadraticAddRecExact(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
8411 auto T = GetQuadraticEquation(AddRec);
8415 std::tie(A, B, C, M, BitWidth) = *T;
8416 LLVM_DEBUG(dbgs() << __func__ << ": solving for unsigned overflow\n");
8417 Optional<APInt> X = APIntOps::SolveQuadraticEquationWrap(A, B, C, BitWidth+1);
8421 ConstantInt *CX = ConstantInt::get(SE.getContext(), *X);
8422 ConstantInt *V = EvaluateConstantChrecAtConstant(AddRec, CX, SE);
8426 return TruncIfPossible(X, BitWidth);
8429 /// Let c(n) be the value of the quadratic chrec {0,+,M,+,N} after n
8430 /// iterations. The values M, N are assumed to be signed, and they
8431 /// should all have the same bit widths.
8432 /// Find the least n such that c(n) does not belong to the given range,
8433 /// while c(n-1) does.
8435 /// This function returns None if
8436 /// (a) the addrec coefficients are not constant, or
8437 /// (b) SolveQuadraticEquationWrap was unable to find a solution for the
8438 /// bounds of the range.
8439 static Optional<APInt>
8440 SolveQuadraticAddRecRange(const SCEVAddRecExpr *AddRec,
8441 const ConstantRange &Range, ScalarEvolution &SE) {
8442 assert(AddRec->getOperand(0)->isZero() &&
8443 "Starting value of addrec should be 0");
8444 LLVM_DEBUG(dbgs() << __func__ << ": solving boundary crossing for range "
8445 << Range << ", addrec " << *AddRec << '\n');
8446 // This case is handled in getNumIterationsInRange. Here we can assume that
8447 // we start in the range.
8448 assert(Range.contains(APInt(SE.getTypeSizeInBits(AddRec->getType()), 0)) &&
8449 "Addrec's initial value should be in range");
8453 auto T = GetQuadraticEquation(AddRec);
8457 // Be careful about the return value: there can be two reasons for not
8458 // returning an actual number. First, if no solutions to the equations
8459 // were found, and second, if the solutions don't leave the given range.
8460 // The first case means that the actual solution is "unknown", the second
8461 // means that it's known, but not valid. If the solution is unknown, we
8462 // cannot make any conclusions.
8463 // Return a pair: the optional solution and a flag indicating if the
8464 // solution was found.
8465 auto SolveForBoundary = [&](APInt Bound) -> std::pair<Optional<APInt>,bool> {
8466 // Solve for signed overflow and unsigned overflow, pick the lower
8468 LLVM_DEBUG(dbgs() << "SolveQuadraticAddRecRange: checking boundary "
8469 << Bound << " (before multiplying by " << M << ")\n");
8470 Bound *= M; // The quadratic equation multiplier.
8472 Optional<APInt> SO = None;
8474 LLVM_DEBUG(dbgs() << "SolveQuadraticAddRecRange: solving for "
8475 "signed overflow\n");
8476 SO = APIntOps::SolveQuadraticEquationWrap(A, B, -Bound, BitWidth);
8478 LLVM_DEBUG(dbgs() << "SolveQuadraticAddRecRange: solving for "
8479 "unsigned overflow\n");
8480 Optional<APInt> UO = APIntOps::SolveQuadraticEquationWrap(A, B, -Bound,
8483 auto LeavesRange = [&] (const APInt &X) {
8484 ConstantInt *C0 = ConstantInt::get(SE.getContext(), X);
8485 ConstantInt *V0 = EvaluateConstantChrecAtConstant(AddRec, C0, SE);
8486 if (Range.contains(V0->getValue()))
8488 // X should be at least 1, so X-1 is non-negative.
8489 ConstantInt *C1 = ConstantInt::get(SE.getContext(), X-1);
8490 ConstantInt *V1 = EvaluateConstantChrecAtConstant(AddRec, C1, SE);
8491 if (Range.contains(V1->getValue()))
8496 // If SolveQuadraticEquationWrap returns None, it means that there can
8497 // be a solution, but the function failed to find it. We cannot treat it
8498 // as "no solution".
8499 if (!SO.hasValue() || !UO.hasValue())
8500 return { None, false };
8502 // Check the smaller value first to see if it leaves the range.
8503 // At this point, both SO and UO must have values.
8504 Optional<APInt> Min = MinOptional(SO, UO);
8505 if (LeavesRange(*Min))
8506 return { Min, true };
8507 Optional<APInt> Max = Min == SO ? UO : SO;
8508 if (LeavesRange(*Max))
8509 return { Max, true };
8511 // Solutions were found, but were eliminated, hence the "true".
8512 return { None, true };
8515 std::tie(A, B, C, M, BitWidth) = *T;
8516 // Lower bound is inclusive, subtract 1 to represent the exiting value.
8517 APInt Lower = Range.getLower().sextOrSelf(A.getBitWidth()) - 1;
8518 APInt Upper = Range.getUpper().sextOrSelf(A.getBitWidth());
8519 auto SL = SolveForBoundary(Lower);
8520 auto SU = SolveForBoundary(Upper);
8521 // If any of the solutions was unknown, no meaninigful conclusions can
8523 if (!SL.second || !SU.second)
8526 // Claim: The correct solution is not some value between Min and Max.
8528 // Justification: Assuming that Min and Max are different values, one of
8529 // them is when the first signed overflow happens, the other is when the
8530 // first unsigned overflow happens. Crossing the range boundary is only
8531 // possible via an overflow (treating 0 as a special case of it, modeling
8532 // an overflow as crossing k*2^W for some k).
8534 // The interesting case here is when Min was eliminated as an invalid
8535 // solution, but Max was not. The argument is that if there was another
8536 // overflow between Min and Max, it would also have been eliminated if
8537 // it was considered.
8539 // For a given boundary, it is possible to have two overflows of the same
8540 // type (signed/unsigned) without having the other type in between: this
8541 // can happen when the vertex of the parabola is between the iterations
8542 // corresponding to the overflows. This is only possible when the two
8543 // overflows cross k*2^W for the same k. In such case, if the second one
8544 // left the range (and was the first one to do so), the first overflow
8545 // would have to enter the range, which would mean that either we had left
8546 // the range before or that we started outside of it. Both of these cases
8547 // are contradictions.
8549 // Claim: In the case where SolveForBoundary returns None, the correct
8550 // solution is not some value between the Max for this boundary and the
8551 // Min of the other boundary.
8553 // Justification: Assume that we had such Max_A and Min_B corresponding
8554 // to range boundaries A and B and such that Max_A < Min_B. If there was
8555 // a solution between Max_A and Min_B, it would have to be caused by an
8556 // overflow corresponding to either A or B. It cannot correspond to B,
8557 // since Min_B is the first occurrence of such an overflow. If it
8558 // corresponded to A, it would have to be either a signed or an unsigned
8559 // overflow that is larger than both eliminated overflows for A. But
8560 // between the eliminated overflows and this overflow, the values would
8561 // cover the entire value space, thus crossing the other boundary, which
8562 // is a contradiction.
8564 return TruncIfPossible(MinOptional(SL.first, SU.first), BitWidth);
8567 ScalarEvolution::ExitLimit
8568 ScalarEvolution::howFarToZero(const SCEV *V, const Loop *L, bool ControlsExit,
8569 bool AllowPredicates) {
8571 // This is only used for loops with a "x != y" exit test. The exit condition
8572 // is now expressed as a single expression, V = x-y. So the exit test is
8573 // effectively V != 0. We know and take advantage of the fact that this
8574 // expression only being used in a comparison by zero context.
8576 SmallPtrSet<const SCEVPredicate *, 4> Predicates;
8577 // If the value is a constant
8578 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
8579 // If the value is already zero, the branch will execute zero times.
8580 if (C->getValue()->isZero()) return C;
8581 return getCouldNotCompute(); // Otherwise it will loop infinitely.
8584 const SCEVAddRecExpr *AddRec =
8585 dyn_cast<SCEVAddRecExpr>(stripInjectiveFunctions(V));
8587 if (!AddRec && AllowPredicates)
8588 // Try to make this an AddRec using runtime tests, in the first X
8589 // iterations of this loop, where X is the SCEV expression found by the
8591 AddRec = convertSCEVToAddRecWithPredicates(V, L, Predicates);
8593 if (!AddRec || AddRec->getLoop() != L)
8594 return getCouldNotCompute();
8596 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
8597 // the quadratic equation to solve it.
8598 if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
8599 // We can only use this value if the chrec ends up with an exact zero
8600 // value at this index. When solving for "X*X != 5", for example, we
8601 // should not accept a root of 2.
8602 if (auto S = SolveQuadraticAddRecExact(AddRec, *this)) {
8603 const auto *R = cast<SCEVConstant>(getConstant(S.getValue()));
8604 return ExitLimit(R, R, false, Predicates);
8606 return getCouldNotCompute();
8609 // Otherwise we can only handle this if it is affine.
8610 if (!AddRec->isAffine())
8611 return getCouldNotCompute();
8613 // If this is an affine expression, the execution count of this branch is
8614 // the minimum unsigned root of the following equation:
8616 // Start + Step*N = 0 (mod 2^BW)
8620 // Step*N = -Start (mod 2^BW)
8622 // where BW is the common bit width of Start and Step.
8624 // Get the initial value for the loop.
8625 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
8626 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
8628 // For now we handle only constant steps.
8630 // TODO: Handle a nonconstant Step given AddRec<NUW>. If the
8631 // AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap
8632 // to 0, it must be counting down to equal 0. Consequently, N = Start / -Step.
8633 // We have not yet seen any such cases.
8634 const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step);
8635 if (!StepC || StepC->getValue()->isZero())
8636 return getCouldNotCompute();
8638 // For positive steps (counting up until unsigned overflow):
8639 // N = -Start/Step (as unsigned)
8640 // For negative steps (counting down to zero):
8642 // First compute the unsigned distance from zero in the direction of Step.
8643 bool CountDown = StepC->getAPInt().isNegative();
8644 const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start);
8646 // Handle unitary steps, which cannot wraparound.
8647 // 1*N = -Start; -1*N = Start (mod 2^BW), so:
8648 // N = Distance (as unsigned)
8649 if (StepC->getValue()->isOne() || StepC->getValue()->isMinusOne()) {
8650 APInt MaxBECount = getUnsignedRangeMax(Distance);
8652 // When a loop like "for (int i = 0; i != n; ++i) { /* body */ }" is rotated,
8653 // we end up with a loop whose backedge-taken count is n - 1. Detect this
8654 // case, and see if we can improve the bound.
8656 // Explicitly handling this here is necessary because getUnsignedRange
8657 // isn't context-sensitive; it doesn't know that we only care about the
8658 // range inside the loop.
8659 const SCEV *Zero = getZero(Distance->getType());
8660 const SCEV *One = getOne(Distance->getType());
8661 const SCEV *DistancePlusOne = getAddExpr(Distance, One);
8662 if (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_NE, DistancePlusOne, Zero)) {
8663 // If Distance + 1 doesn't overflow, we can compute the maximum distance
8664 // as "unsigned_max(Distance + 1) - 1".
8665 ConstantRange CR = getUnsignedRange(DistancePlusOne);
8666 MaxBECount = APIntOps::umin(MaxBECount, CR.getUnsignedMax() - 1);
8668 return ExitLimit(Distance, getConstant(MaxBECount), false, Predicates);
8671 // If the condition controls loop exit (the loop exits only if the expression
8672 // is true) and the addition is no-wrap we can use unsigned divide to
8673 // compute the backedge count. In this case, the step may not divide the
8674 // distance, but we don't care because if the condition is "missed" the loop
8675 // will have undefined behavior due to wrapping.
8676 if (ControlsExit && AddRec->hasNoSelfWrap() &&
8677 loopHasNoAbnormalExits(AddRec->getLoop())) {
8679 getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
8681 Exact == getCouldNotCompute()
8683 : getConstant(getUnsignedRangeMax(Exact));
8684 return ExitLimit(Exact, Max, false, Predicates);
8687 // Solve the general equation.
8688 const SCEV *E = SolveLinEquationWithOverflow(StepC->getAPInt(),
8689 getNegativeSCEV(Start), *this);
8690 const SCEV *M = E == getCouldNotCompute()
8692 : getConstant(getUnsignedRangeMax(E));
8693 return ExitLimit(E, M, false, Predicates);
8696 ScalarEvolution::ExitLimit
8697 ScalarEvolution::howFarToNonZero(const SCEV *V, const Loop *L) {
8698 // Loops that look like: while (X == 0) are very strange indeed. We don't
8699 // handle them yet except for the trivial case. This could be expanded in the
8700 // future as needed.
8702 // If the value is a constant, check to see if it is known to be non-zero
8703 // already. If so, the backedge will execute zero times.
8704 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
8705 if (!C->getValue()->isZero())
8706 return getZero(C->getType());
8707 return getCouldNotCompute(); // Otherwise it will loop infinitely.
8710 // We could implement others, but I really doubt anyone writes loops like
8711 // this, and if they did, they would already be constant folded.
8712 return getCouldNotCompute();
8715 std::pair<BasicBlock *, BasicBlock *>
8716 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
8717 // If the block has a unique predecessor, then there is no path from the
8718 // predecessor to the block that does not go through the direct edge
8719 // from the predecessor to the block.
8720 if (BasicBlock *Pred = BB->getSinglePredecessor())
8723 // A loop's header is defined to be a block that dominates the loop.
8724 // If the header has a unique predecessor outside the loop, it must be
8725 // a block that has exactly one successor that can reach the loop.
8726 if (Loop *L = LI.getLoopFor(BB))
8727 return {L->getLoopPredecessor(), L->getHeader()};
8729 return {nullptr, nullptr};
8732 /// SCEV structural equivalence is usually sufficient for testing whether two
8733 /// expressions are equal, however for the purposes of looking for a condition
8734 /// guarding a loop, it can be useful to be a little more general, since a
8735 /// front-end may have replicated the controlling expression.
8736 static bool HasSameValue(const SCEV *A, const SCEV *B) {
8737 // Quick check to see if they are the same SCEV.
8738 if (A == B) return true;
8740 auto ComputesEqualValues = [](const Instruction *A, const Instruction *B) {
8741 // Not all instructions that are "identical" compute the same value. For
8742 // instance, two distinct alloca instructions allocating the same type are
8743 // identical and do not read memory; but compute distinct values.
8744 return A->isIdenticalTo(B) && (isa<BinaryOperator>(A) || isa<GetElementPtrInst>(A));
8747 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
8748 // two different instructions with the same value. Check for this case.
8749 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
8750 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
8751 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
8752 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
8753 if (ComputesEqualValues(AI, BI))
8756 // Otherwise assume they may have a different value.
8760 bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
8761 const SCEV *&LHS, const SCEV *&RHS,
8763 bool Changed = false;
8764 // Simplifies ICMP to trivial true or false by turning it into '0 == 0' or
8766 auto TrivialCase = [&](bool TriviallyTrue) {
8767 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
8768 Pred = TriviallyTrue ? ICmpInst::ICMP_EQ : ICmpInst::ICMP_NE;
8771 // If we hit the max recursion limit bail out.
8775 // Canonicalize a constant to the right side.
8776 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
8777 // Check for both operands constant.
8778 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
8779 if (ConstantExpr::getICmp(Pred,
8781 RHSC->getValue())->isNullValue())
8782 return TrivialCase(false);
8784 return TrivialCase(true);
8786 // Otherwise swap the operands to put the constant on the right.
8787 std::swap(LHS, RHS);
8788 Pred = ICmpInst::getSwappedPredicate(Pred);
8792 // If we're comparing an addrec with a value which is loop-invariant in the
8793 // addrec's loop, put the addrec on the left. Also make a dominance check,
8794 // as both operands could be addrecs loop-invariant in each other's loop.
8795 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
8796 const Loop *L = AR->getLoop();
8797 if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) {
8798 std::swap(LHS, RHS);
8799 Pred = ICmpInst::getSwappedPredicate(Pred);
8804 // If there's a constant operand, canonicalize comparisons with boundary
8805 // cases, and canonicalize *-or-equal comparisons to regular comparisons.
8806 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
8807 const APInt &RA = RC->getAPInt();
8809 bool SimplifiedByConstantRange = false;
8811 if (!ICmpInst::isEquality(Pred)) {
8812 ConstantRange ExactCR = ConstantRange::makeExactICmpRegion(Pred, RA);
8813 if (ExactCR.isFullSet())
8814 return TrivialCase(true);
8815 else if (ExactCR.isEmptySet())
8816 return TrivialCase(false);
8819 CmpInst::Predicate NewPred;
8820 if (ExactCR.getEquivalentICmp(NewPred, NewRHS) &&
8821 ICmpInst::isEquality(NewPred)) {
8822 // We were able to convert an inequality to an equality.
8824 RHS = getConstant(NewRHS);
8825 Changed = SimplifiedByConstantRange = true;
8829 if (!SimplifiedByConstantRange) {
8833 case ICmpInst::ICMP_EQ:
8834 case ICmpInst::ICMP_NE:
8835 // Fold ((-1) * %a) + %b == 0 (equivalent to %b-%a == 0) into %a == %b.
8837 if (const SCEVAddExpr *AE = dyn_cast<SCEVAddExpr>(LHS))
8838 if (const SCEVMulExpr *ME =
8839 dyn_cast<SCEVMulExpr>(AE->getOperand(0)))
8840 if (AE->getNumOperands() == 2 && ME->getNumOperands() == 2 &&
8841 ME->getOperand(0)->isAllOnesValue()) {
8842 RHS = AE->getOperand(1);
8843 LHS = ME->getOperand(1);
8849 // The "Should have been caught earlier!" messages refer to the fact
8850 // that the ExactCR.isFullSet() or ExactCR.isEmptySet() check above
8851 // should have fired on the corresponding cases, and canonicalized the
8852 // check to trivial case.
8854 case ICmpInst::ICMP_UGE:
8855 assert(!RA.isMinValue() && "Should have been caught earlier!");
8856 Pred = ICmpInst::ICMP_UGT;
8857 RHS = getConstant(RA - 1);
8860 case ICmpInst::ICMP_ULE:
8861 assert(!RA.isMaxValue() && "Should have been caught earlier!");
8862 Pred = ICmpInst::ICMP_ULT;
8863 RHS = getConstant(RA + 1);
8866 case ICmpInst::ICMP_SGE:
8867 assert(!RA.isMinSignedValue() && "Should have been caught earlier!");
8868 Pred = ICmpInst::ICMP_SGT;
8869 RHS = getConstant(RA - 1);
8872 case ICmpInst::ICMP_SLE:
8873 assert(!RA.isMaxSignedValue() && "Should have been caught earlier!");
8874 Pred = ICmpInst::ICMP_SLT;
8875 RHS = getConstant(RA + 1);
8882 // Check for obvious equality.
8883 if (HasSameValue(LHS, RHS)) {
8884 if (ICmpInst::isTrueWhenEqual(Pred))
8885 return TrivialCase(true);
8886 if (ICmpInst::isFalseWhenEqual(Pred))
8887 return TrivialCase(false);
8890 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
8891 // adding or subtracting 1 from one of the operands.
8893 case ICmpInst::ICMP_SLE:
8894 if (!getSignedRangeMax(RHS).isMaxSignedValue()) {
8895 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
8897 Pred = ICmpInst::ICMP_SLT;
8899 } else if (!getSignedRangeMin(LHS).isMinSignedValue()) {
8900 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
8902 Pred = ICmpInst::ICMP_SLT;
8906 case ICmpInst::ICMP_SGE:
8907 if (!getSignedRangeMin(RHS).isMinSignedValue()) {
8908 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
8910 Pred = ICmpInst::ICMP_SGT;
8912 } else if (!getSignedRangeMax(LHS).isMaxSignedValue()) {
8913 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
8915 Pred = ICmpInst::ICMP_SGT;
8919 case ICmpInst::ICMP_ULE:
8920 if (!getUnsignedRangeMax(RHS).isMaxValue()) {
8921 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
8923 Pred = ICmpInst::ICMP_ULT;
8925 } else if (!getUnsignedRangeMin(LHS).isMinValue()) {
8926 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS);
8927 Pred = ICmpInst::ICMP_ULT;
8931 case ICmpInst::ICMP_UGE:
8932 if (!getUnsignedRangeMin(RHS).isMinValue()) {
8933 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS);
8934 Pred = ICmpInst::ICMP_UGT;
8936 } else if (!getUnsignedRangeMax(LHS).isMaxValue()) {
8937 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
8939 Pred = ICmpInst::ICMP_UGT;
8947 // TODO: More simplifications are possible here.
8949 // Recursively simplify until we either hit a recursion limit or nothing
8952 return SimplifyICmpOperands(Pred, LHS, RHS, Depth+1);
8957 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
8958 return getSignedRangeMax(S).isNegative();
8961 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
8962 return getSignedRangeMin(S).isStrictlyPositive();
8965 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
8966 return !getSignedRangeMin(S).isNegative();
8969 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
8970 return !getSignedRangeMax(S).isStrictlyPositive();
8973 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
8974 return isKnownNegative(S) || isKnownPositive(S);
8977 std::pair<const SCEV *, const SCEV *>
8978 ScalarEvolution::SplitIntoInitAndPostInc(const Loop *L, const SCEV *S) {
8979 // Compute SCEV on entry of loop L.
8980 const SCEV *Start = SCEVInitRewriter::rewrite(S, L, *this);
8981 if (Start == getCouldNotCompute())
8982 return { Start, Start };
8983 // Compute post increment SCEV for loop L.
8984 const SCEV *PostInc = SCEVPostIncRewriter::rewrite(S, L, *this);
8985 assert(PostInc != getCouldNotCompute() && "Unexpected could not compute");
8986 return { Start, PostInc };
8989 bool ScalarEvolution::isKnownViaInduction(ICmpInst::Predicate Pred,
8990 const SCEV *LHS, const SCEV *RHS) {
8991 // First collect all loops.
8992 SmallPtrSet<const Loop *, 8> LoopsUsed;
8993 getUsedLoops(LHS, LoopsUsed);
8994 getUsedLoops(RHS, LoopsUsed);
8996 if (LoopsUsed.empty())
8999 // Domination relationship must be a linear order on collected loops.
9001 for (auto *L1 : LoopsUsed)
9002 for (auto *L2 : LoopsUsed)
9003 assert((DT.dominates(L1->getHeader(), L2->getHeader()) ||
9004 DT.dominates(L2->getHeader(), L1->getHeader())) &&
9005 "Domination relationship is not a linear order");
9009 *std::max_element(LoopsUsed.begin(), LoopsUsed.end(),
9010 [&](const Loop *L1, const Loop *L2) {
9011 return DT.properlyDominates(L1->getHeader(), L2->getHeader());
9014 // Get init and post increment value for LHS.
9015 auto SplitLHS = SplitIntoInitAndPostInc(MDL, LHS);
9016 // if LHS contains unknown non-invariant SCEV then bail out.
9017 if (SplitLHS.first == getCouldNotCompute())
9019 assert (SplitLHS.second != getCouldNotCompute() && "Unexpected CNC");
9020 // Get init and post increment value for RHS.
9021 auto SplitRHS = SplitIntoInitAndPostInc(MDL, RHS);
9022 // if RHS contains unknown non-invariant SCEV then bail out.
9023 if (SplitRHS.first == getCouldNotCompute())
9025 assert (SplitRHS.second != getCouldNotCompute() && "Unexpected CNC");
9026 // It is possible that init SCEV contains an invariant load but it does
9027 // not dominate MDL and is not available at MDL loop entry, so we should
9029 if (!isAvailableAtLoopEntry(SplitLHS.first, MDL) ||
9030 !isAvailableAtLoopEntry(SplitRHS.first, MDL))
9033 // It seems backedge guard check is faster than entry one so in some cases
9034 // it can speed up whole estimation by short circuit
9035 return isLoopBackedgeGuardedByCond(MDL, Pred, SplitLHS.second,
9037 isLoopEntryGuardedByCond(MDL, Pred, SplitLHS.first, SplitRHS.first);
9040 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
9041 const SCEV *LHS, const SCEV *RHS) {
9042 // Canonicalize the inputs first.
9043 (void)SimplifyICmpOperands(Pred, LHS, RHS);
9045 if (isKnownViaInduction(Pred, LHS, RHS))
9048 if (isKnownPredicateViaSplitting(Pred, LHS, RHS))
9051 // Otherwise see what can be done with some simple reasoning.
9052 return isKnownViaNonRecursiveReasoning(Pred, LHS, RHS);
9055 bool ScalarEvolution::isKnownOnEveryIteration(ICmpInst::Predicate Pred,
9056 const SCEVAddRecExpr *LHS,
9058 const Loop *L = LHS->getLoop();
9059 return isLoopEntryGuardedByCond(L, Pred, LHS->getStart(), RHS) &&
9060 isLoopBackedgeGuardedByCond(L, Pred, LHS->getPostIncExpr(*this), RHS);
9063 bool ScalarEvolution::isMonotonicPredicate(const SCEVAddRecExpr *LHS,
9064 ICmpInst::Predicate Pred,
9066 bool Result = isMonotonicPredicateImpl(LHS, Pred, Increasing);
9069 // Verify an invariant: inverting the predicate should turn a monotonically
9070 // increasing change to a monotonically decreasing one, and vice versa.
9071 bool IncreasingSwapped;
9072 bool ResultSwapped = isMonotonicPredicateImpl(
9073 LHS, ICmpInst::getSwappedPredicate(Pred), IncreasingSwapped);
9075 assert(Result == ResultSwapped && "should be able to analyze both!");
9077 assert(Increasing == !IncreasingSwapped &&
9078 "monotonicity should flip as we flip the predicate");
9084 bool ScalarEvolution::isMonotonicPredicateImpl(const SCEVAddRecExpr *LHS,
9085 ICmpInst::Predicate Pred,
9088 // A zero step value for LHS means the induction variable is essentially a
9089 // loop invariant value. We don't really depend on the predicate actually
9090 // flipping from false to true (for increasing predicates, and the other way
9091 // around for decreasing predicates), all we care about is that *if* the
9092 // predicate changes then it only changes from false to true.
9094 // A zero step value in itself is not very useful, but there may be places
9095 // where SCEV can prove X >= 0 but not prove X > 0, so it is helpful to be
9096 // as general as possible.
9100 return false; // Conservative answer
9102 case ICmpInst::ICMP_UGT:
9103 case ICmpInst::ICMP_UGE:
9104 case ICmpInst::ICMP_ULT:
9105 case ICmpInst::ICMP_ULE:
9106 if (!LHS->hasNoUnsignedWrap())
9109 Increasing = Pred == ICmpInst::ICMP_UGT || Pred == ICmpInst::ICMP_UGE;
9112 case ICmpInst::ICMP_SGT:
9113 case ICmpInst::ICMP_SGE:
9114 case ICmpInst::ICMP_SLT:
9115 case ICmpInst::ICMP_SLE: {
9116 if (!LHS->hasNoSignedWrap())
9119 const SCEV *Step = LHS->getStepRecurrence(*this);
9121 if (isKnownNonNegative(Step)) {
9122 Increasing = Pred == ICmpInst::ICMP_SGT || Pred == ICmpInst::ICMP_SGE;
9126 if (isKnownNonPositive(Step)) {
9127 Increasing = Pred == ICmpInst::ICMP_SLT || Pred == ICmpInst::ICMP_SLE;
9136 llvm_unreachable("switch has default clause!");
9139 bool ScalarEvolution::isLoopInvariantPredicate(
9140 ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS, const Loop *L,
9141 ICmpInst::Predicate &InvariantPred, const SCEV *&InvariantLHS,
9142 const SCEV *&InvariantRHS) {
9144 // If there is a loop-invariant, force it into the RHS, otherwise bail out.
9145 if (!isLoopInvariant(RHS, L)) {
9146 if (!isLoopInvariant(LHS, L))
9149 std::swap(LHS, RHS);
9150 Pred = ICmpInst::getSwappedPredicate(Pred);
9153 const SCEVAddRecExpr *ArLHS = dyn_cast<SCEVAddRecExpr>(LHS);
9154 if (!ArLHS || ArLHS->getLoop() != L)
9158 if (!isMonotonicPredicate(ArLHS, Pred, Increasing))
9161 // If the predicate "ArLHS `Pred` RHS" monotonically increases from false to
9162 // true as the loop iterates, and the backedge is control dependent on
9163 // "ArLHS `Pred` RHS" == true then we can reason as follows:
9165 // * if the predicate was false in the first iteration then the predicate
9166 // is never evaluated again, since the loop exits without taking the
9168 // * if the predicate was true in the first iteration then it will
9169 // continue to be true for all future iterations since it is
9170 // monotonically increasing.
9172 // For both the above possibilities, we can replace the loop varying
9173 // predicate with its value on the first iteration of the loop (which is
9176 // A similar reasoning applies for a monotonically decreasing predicate, by
9177 // replacing true with false and false with true in the above two bullets.
9179 auto P = Increasing ? Pred : ICmpInst::getInversePredicate(Pred);
9181 if (!isLoopBackedgeGuardedByCond(L, P, LHS, RHS))
9184 InvariantPred = Pred;
9185 InvariantLHS = ArLHS->getStart();
9190 bool ScalarEvolution::isKnownPredicateViaConstantRanges(
9191 ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS) {
9192 if (HasSameValue(LHS, RHS))
9193 return ICmpInst::isTrueWhenEqual(Pred);
9195 // This code is split out from isKnownPredicate because it is called from
9196 // within isLoopEntryGuardedByCond.
9199 [&](const ConstantRange &RangeLHS, const ConstantRange &RangeRHS) {
9200 return ConstantRange::makeSatisfyingICmpRegion(Pred, RangeRHS)
9201 .contains(RangeLHS);
9204 // The check at the top of the function catches the case where the values are
9205 // known to be equal.
9206 if (Pred == CmpInst::ICMP_EQ)
9209 if (Pred == CmpInst::ICMP_NE)
9210 return CheckRanges(getSignedRange(LHS), getSignedRange(RHS)) ||
9211 CheckRanges(getUnsignedRange(LHS), getUnsignedRange(RHS)) ||
9212 isKnownNonZero(getMinusSCEV(LHS, RHS));
9214 if (CmpInst::isSigned(Pred))
9215 return CheckRanges(getSignedRange(LHS), getSignedRange(RHS));
9217 return CheckRanges(getUnsignedRange(LHS), getUnsignedRange(RHS));
9220 bool ScalarEvolution::isKnownPredicateViaNoOverflow(ICmpInst::Predicate Pred,
9223 // Match Result to (X + Y)<ExpectedFlags> where Y is a constant integer.
9224 // Return Y via OutY.
9225 auto MatchBinaryAddToConst =
9226 [this](const SCEV *Result, const SCEV *X, APInt &OutY,
9227 SCEV::NoWrapFlags ExpectedFlags) {
9228 const SCEV *NonConstOp, *ConstOp;
9229 SCEV::NoWrapFlags FlagsPresent;
9231 if (!splitBinaryAdd(Result, ConstOp, NonConstOp, FlagsPresent) ||
9232 !isa<SCEVConstant>(ConstOp) || NonConstOp != X)
9235 OutY = cast<SCEVConstant>(ConstOp)->getAPInt();
9236 return (FlagsPresent & ExpectedFlags) == ExpectedFlags;
9245 case ICmpInst::ICMP_SGE:
9246 std::swap(LHS, RHS);
9248 case ICmpInst::ICMP_SLE:
9249 // X s<= (X + C)<nsw> if C >= 0
9250 if (MatchBinaryAddToConst(RHS, LHS, C, SCEV::FlagNSW) && C.isNonNegative())
9253 // (X + C)<nsw> s<= X if C <= 0
9254 if (MatchBinaryAddToConst(LHS, RHS, C, SCEV::FlagNSW) &&
9255 !C.isStrictlyPositive())
9259 case ICmpInst::ICMP_SGT:
9260 std::swap(LHS, RHS);
9262 case ICmpInst::ICMP_SLT:
9263 // X s< (X + C)<nsw> if C > 0
9264 if (MatchBinaryAddToConst(RHS, LHS, C, SCEV::FlagNSW) &&
9265 C.isStrictlyPositive())
9268 // (X + C)<nsw> s< X if C < 0
9269 if (MatchBinaryAddToConst(LHS, RHS, C, SCEV::FlagNSW) && C.isNegative())
9277 bool ScalarEvolution::isKnownPredicateViaSplitting(ICmpInst::Predicate Pred,
9280 if (Pred != ICmpInst::ICMP_ULT || ProvingSplitPredicate)
9283 // Allowing arbitrary number of activations of isKnownPredicateViaSplitting on
9284 // the stack can result in exponential time complexity.
9285 SaveAndRestore<bool> Restore(ProvingSplitPredicate, true);
9287 // If L >= 0 then I `ult` L <=> I >= 0 && I `slt` L
9289 // To prove L >= 0 we use isKnownNonNegative whereas to prove I >= 0 we use
9290 // isKnownPredicate. isKnownPredicate is more powerful, but also more
9291 // expensive; and using isKnownNonNegative(RHS) is sufficient for most of the
9292 // interesting cases seen in practice. We can consider "upgrading" L >= 0 to
9293 // use isKnownPredicate later if needed.
9294 return isKnownNonNegative(RHS) &&
9295 isKnownPredicate(CmpInst::ICMP_SGE, LHS, getZero(LHS->getType())) &&
9296 isKnownPredicate(CmpInst::ICMP_SLT, LHS, RHS);
9299 bool ScalarEvolution::isImpliedViaGuard(BasicBlock *BB,
9300 ICmpInst::Predicate Pred,
9301 const SCEV *LHS, const SCEV *RHS) {
9302 // No need to even try if we know the module has no guards.
9306 return any_of(*BB, [&](Instruction &I) {
9307 using namespace llvm::PatternMatch;
9310 return match(&I, m_Intrinsic<Intrinsic::experimental_guard>(
9311 m_Value(Condition))) &&
9312 isImpliedCond(Pred, LHS, RHS, Condition, false);
9316 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
9317 /// protected by a conditional between LHS and RHS. This is used to
9318 /// to eliminate casts.
9320 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
9321 ICmpInst::Predicate Pred,
9322 const SCEV *LHS, const SCEV *RHS) {
9323 // Interpret a null as meaning no loop, where there is obviously no guard
9324 // (interprocedural conditions notwithstanding).
9325 if (!L) return true;
9328 assert(!verifyFunction(*L->getHeader()->getParent(), &dbgs()) &&
9329 "This cannot be done on broken IR!");
9332 if (isKnownViaNonRecursiveReasoning(Pred, LHS, RHS))
9335 BasicBlock *Latch = L->getLoopLatch();
9339 BranchInst *LoopContinuePredicate =
9340 dyn_cast<BranchInst>(Latch->getTerminator());
9341 if (LoopContinuePredicate && LoopContinuePredicate->isConditional() &&
9342 isImpliedCond(Pred, LHS, RHS,
9343 LoopContinuePredicate->getCondition(),
9344 LoopContinuePredicate->getSuccessor(0) != L->getHeader()))
9347 // We don't want more than one activation of the following loops on the stack
9348 // -- that can lead to O(n!) time complexity.
9349 if (WalkingBEDominatingConds)
9352 SaveAndRestore<bool> ClearOnExit(WalkingBEDominatingConds, true);
9354 // See if we can exploit a trip count to prove the predicate.
9355 const auto &BETakenInfo = getBackedgeTakenInfo(L);
9356 const SCEV *LatchBECount = BETakenInfo.getExact(Latch, this);
9357 if (LatchBECount != getCouldNotCompute()) {
9358 // We know that Latch branches back to the loop header exactly
9359 // LatchBECount times. This means the backdege condition at Latch is
9360 // equivalent to "{0,+,1} u< LatchBECount".
9361 Type *Ty = LatchBECount->getType();
9362 auto NoWrapFlags = SCEV::NoWrapFlags(SCEV::FlagNUW | SCEV::FlagNW);
9363 const SCEV *LoopCounter =
9364 getAddRecExpr(getZero(Ty), getOne(Ty), L, NoWrapFlags);
9365 if (isImpliedCond(Pred, LHS, RHS, ICmpInst::ICMP_ULT, LoopCounter,
9370 // Check conditions due to any @llvm.assume intrinsics.
9371 for (auto &AssumeVH : AC.assumptions()) {
9374 auto *CI = cast<CallInst>(AssumeVH);
9375 if (!DT.dominates(CI, Latch->getTerminator()))
9378 if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false))
9382 // If the loop is not reachable from the entry block, we risk running into an
9383 // infinite loop as we walk up into the dom tree. These loops do not matter
9384 // anyway, so we just return a conservative answer when we see them.
9385 if (!DT.isReachableFromEntry(L->getHeader()))
9388 if (isImpliedViaGuard(Latch, Pred, LHS, RHS))
9391 for (DomTreeNode *DTN = DT[Latch], *HeaderDTN = DT[L->getHeader()];
9392 DTN != HeaderDTN; DTN = DTN->getIDom()) {
9393 assert(DTN && "should reach the loop header before reaching the root!");
9395 BasicBlock *BB = DTN->getBlock();
9396 if (isImpliedViaGuard(BB, Pred, LHS, RHS))
9399 BasicBlock *PBB = BB->getSinglePredecessor();
9403 BranchInst *ContinuePredicate = dyn_cast<BranchInst>(PBB->getTerminator());
9404 if (!ContinuePredicate || !ContinuePredicate->isConditional())
9407 Value *Condition = ContinuePredicate->getCondition();
9409 // If we have an edge `E` within the loop body that dominates the only
9410 // latch, the condition guarding `E` also guards the backedge. This
9411 // reasoning works only for loops with a single latch.
9413 BasicBlockEdge DominatingEdge(PBB, BB);
9414 if (DominatingEdge.isSingleEdge()) {
9415 // We're constructively (and conservatively) enumerating edges within the
9416 // loop body that dominate the latch. The dominator tree better agree
9418 assert(DT.dominates(DominatingEdge, Latch) && "should be!");
9420 if (isImpliedCond(Pred, LHS, RHS, Condition,
9421 BB != ContinuePredicate->getSuccessor(0)))
9430 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
9431 ICmpInst::Predicate Pred,
9432 const SCEV *LHS, const SCEV *RHS) {
9433 // Interpret a null as meaning no loop, where there is obviously no guard
9434 // (interprocedural conditions notwithstanding).
9435 if (!L) return false;
9438 assert(!verifyFunction(*L->getHeader()->getParent(), &dbgs()) &&
9439 "This cannot be done on broken IR!");
9441 // Both LHS and RHS must be available at loop entry.
9442 assert(isAvailableAtLoopEntry(LHS, L) &&
9443 "LHS is not available at Loop Entry");
9444 assert(isAvailableAtLoopEntry(RHS, L) &&
9445 "RHS is not available at Loop Entry");
9447 if (isKnownViaNonRecursiveReasoning(Pred, LHS, RHS))
9450 // If we cannot prove strict comparison (e.g. a > b), maybe we can prove
9451 // the facts (a >= b && a != b) separately. A typical situation is when the
9452 // non-strict comparison is known from ranges and non-equality is known from
9453 // dominating predicates. If we are proving strict comparison, we always try
9454 // to prove non-equality and non-strict comparison separately.
9455 auto NonStrictPredicate = ICmpInst::getNonStrictPredicate(Pred);
9456 const bool ProvingStrictComparison = (Pred != NonStrictPredicate);
9457 bool ProvedNonStrictComparison = false;
9458 bool ProvedNonEquality = false;
9460 if (ProvingStrictComparison) {
9461 ProvedNonStrictComparison =
9462 isKnownViaNonRecursiveReasoning(NonStrictPredicate, LHS, RHS);
9464 isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_NE, LHS, RHS);
9465 if (ProvedNonStrictComparison && ProvedNonEquality)
9469 // Try to prove (Pred, LHS, RHS) using isImpliedViaGuard.
9470 auto ProveViaGuard = [&](BasicBlock *Block) {
9471 if (isImpliedViaGuard(Block, Pred, LHS, RHS))
9473 if (ProvingStrictComparison) {
9474 if (!ProvedNonStrictComparison)
9475 ProvedNonStrictComparison =
9476 isImpliedViaGuard(Block, NonStrictPredicate, LHS, RHS);
9477 if (!ProvedNonEquality)
9479 isImpliedViaGuard(Block, ICmpInst::ICMP_NE, LHS, RHS);
9480 if (ProvedNonStrictComparison && ProvedNonEquality)
9486 // Try to prove (Pred, LHS, RHS) using isImpliedCond.
9487 auto ProveViaCond = [&](Value *Condition, bool Inverse) {
9488 if (isImpliedCond(Pred, LHS, RHS, Condition, Inverse))
9490 if (ProvingStrictComparison) {
9491 if (!ProvedNonStrictComparison)
9492 ProvedNonStrictComparison =
9493 isImpliedCond(NonStrictPredicate, LHS, RHS, Condition, Inverse);
9494 if (!ProvedNonEquality)
9496 isImpliedCond(ICmpInst::ICMP_NE, LHS, RHS, Condition, Inverse);
9497 if (ProvedNonStrictComparison && ProvedNonEquality)
9503 // Starting at the loop predecessor, climb up the predecessor chain, as long
9504 // as there are predecessors that can be found that have unique successors
9505 // leading to the original header.
9506 for (std::pair<BasicBlock *, BasicBlock *>
9507 Pair(L->getLoopPredecessor(), L->getHeader());
9509 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
9511 if (ProveViaGuard(Pair.first))
9514 BranchInst *LoopEntryPredicate =
9515 dyn_cast<BranchInst>(Pair.first->getTerminator());
9516 if (!LoopEntryPredicate ||
9517 LoopEntryPredicate->isUnconditional())
9520 if (ProveViaCond(LoopEntryPredicate->getCondition(),
9521 LoopEntryPredicate->getSuccessor(0) != Pair.second))
9525 // Check conditions due to any @llvm.assume intrinsics.
9526 for (auto &AssumeVH : AC.assumptions()) {
9529 auto *CI = cast<CallInst>(AssumeVH);
9530 if (!DT.dominates(CI, L->getHeader()))
9533 if (ProveViaCond(CI->getArgOperand(0), false))
9540 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred,
9541 const SCEV *LHS, const SCEV *RHS,
9542 Value *FoundCondValue,
9544 if (!PendingLoopPredicates.insert(FoundCondValue).second)
9548 make_scope_exit([&]() { PendingLoopPredicates.erase(FoundCondValue); });
9550 // Recursively handle And and Or conditions.
9551 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) {
9552 if (BO->getOpcode() == Instruction::And) {
9554 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
9555 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
9556 } else if (BO->getOpcode() == Instruction::Or) {
9558 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
9559 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
9563 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue);
9564 if (!ICI) return false;
9566 // Now that we found a conditional branch that dominates the loop or controls
9567 // the loop latch. Check to see if it is the comparison we are looking for.
9568 ICmpInst::Predicate FoundPred;
9570 FoundPred = ICI->getInversePredicate();
9572 FoundPred = ICI->getPredicate();
9574 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
9575 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
9577 return isImpliedCond(Pred, LHS, RHS, FoundPred, FoundLHS, FoundRHS);
9580 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred, const SCEV *LHS,
9582 ICmpInst::Predicate FoundPred,
9583 const SCEV *FoundLHS,
9584 const SCEV *FoundRHS) {
9585 // Balance the types.
9586 if (getTypeSizeInBits(LHS->getType()) <
9587 getTypeSizeInBits(FoundLHS->getType())) {
9588 if (CmpInst::isSigned(Pred)) {
9589 LHS = getSignExtendExpr(LHS, FoundLHS->getType());
9590 RHS = getSignExtendExpr(RHS, FoundLHS->getType());
9592 LHS = getZeroExtendExpr(LHS, FoundLHS->getType());
9593 RHS = getZeroExtendExpr(RHS, FoundLHS->getType());
9595 } else if (getTypeSizeInBits(LHS->getType()) >
9596 getTypeSizeInBits(FoundLHS->getType())) {
9597 if (CmpInst::isSigned(FoundPred)) {
9598 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
9599 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
9601 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
9602 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
9606 // Canonicalize the query to match the way instcombine will have
9607 // canonicalized the comparison.
9608 if (SimplifyICmpOperands(Pred, LHS, RHS))
9610 return CmpInst::isTrueWhenEqual(Pred);
9611 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
9612 if (FoundLHS == FoundRHS)
9613 return CmpInst::isFalseWhenEqual(FoundPred);
9615 // Check to see if we can make the LHS or RHS match.
9616 if (LHS == FoundRHS || RHS == FoundLHS) {
9617 if (isa<SCEVConstant>(RHS)) {
9618 std::swap(FoundLHS, FoundRHS);
9619 FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
9621 std::swap(LHS, RHS);
9622 Pred = ICmpInst::getSwappedPredicate(Pred);
9626 // Check whether the found predicate is the same as the desired predicate.
9627 if (FoundPred == Pred)
9628 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
9630 // Check whether swapping the found predicate makes it the same as the
9631 // desired predicate.
9632 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
9633 if (isa<SCEVConstant>(RHS))
9634 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
9636 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
9637 RHS, LHS, FoundLHS, FoundRHS);
9640 // Unsigned comparison is the same as signed comparison when both the operands
9641 // are non-negative.
9642 if (CmpInst::isUnsigned(FoundPred) &&
9643 CmpInst::getSignedPredicate(FoundPred) == Pred &&
9644 isKnownNonNegative(FoundLHS) && isKnownNonNegative(FoundRHS))
9645 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
9647 // Check if we can make progress by sharpening ranges.
9648 if (FoundPred == ICmpInst::ICMP_NE &&
9649 (isa<SCEVConstant>(FoundLHS) || isa<SCEVConstant>(FoundRHS))) {
9651 const SCEVConstant *C = nullptr;
9652 const SCEV *V = nullptr;
9654 if (isa<SCEVConstant>(FoundLHS)) {
9655 C = cast<SCEVConstant>(FoundLHS);
9658 C = cast<SCEVConstant>(FoundRHS);
9662 // The guarding predicate tells us that C != V. If the known range
9663 // of V is [C, t), we can sharpen the range to [C + 1, t). The
9664 // range we consider has to correspond to same signedness as the
9665 // predicate we're interested in folding.
9667 APInt Min = ICmpInst::isSigned(Pred) ?
9668 getSignedRangeMin(V) : getUnsignedRangeMin(V);
9670 if (Min == C->getAPInt()) {
9671 // Given (V >= Min && V != Min) we conclude V >= (Min + 1).
9672 // This is true even if (Min + 1) wraps around -- in case of
9673 // wraparound, (Min + 1) < Min, so (V >= Min => V >= (Min + 1)).
9675 APInt SharperMin = Min + 1;
9678 case ICmpInst::ICMP_SGE:
9679 case ICmpInst::ICMP_UGE:
9680 // We know V `Pred` SharperMin. If this implies LHS `Pred`
9682 if (isImpliedCondOperands(Pred, LHS, RHS, V,
9683 getConstant(SharperMin)))
9687 case ICmpInst::ICMP_SGT:
9688 case ICmpInst::ICMP_UGT:
9689 // We know from the range information that (V `Pred` Min ||
9690 // V == Min). We know from the guarding condition that !(V
9691 // == Min). This gives us
9693 // V `Pred` Min || V == Min && !(V == Min)
9696 // If V `Pred` Min implies LHS `Pred` RHS, we're done.
9698 if (isImpliedCondOperands(Pred, LHS, RHS, V, getConstant(Min)))
9709 // Check whether the actual condition is beyond sufficient.
9710 if (FoundPred == ICmpInst::ICMP_EQ)
9711 if (ICmpInst::isTrueWhenEqual(Pred))
9712 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
9714 if (Pred == ICmpInst::ICMP_NE)
9715 if (!ICmpInst::isTrueWhenEqual(FoundPred))
9716 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
9719 // Otherwise assume the worst.
9723 bool ScalarEvolution::splitBinaryAdd(const SCEV *Expr,
9724 const SCEV *&L, const SCEV *&R,
9725 SCEV::NoWrapFlags &Flags) {
9726 const auto *AE = dyn_cast<SCEVAddExpr>(Expr);
9727 if (!AE || AE->getNumOperands() != 2)
9730 L = AE->getOperand(0);
9731 R = AE->getOperand(1);
9732 Flags = AE->getNoWrapFlags();
9736 Optional<APInt> ScalarEvolution::computeConstantDifference(const SCEV *More,
9738 // We avoid subtracting expressions here because this function is usually
9739 // fairly deep in the call stack (i.e. is called many times).
9743 return APInt(getTypeSizeInBits(More->getType()), 0);
9745 if (isa<SCEVAddRecExpr>(Less) && isa<SCEVAddRecExpr>(More)) {
9746 const auto *LAR = cast<SCEVAddRecExpr>(Less);
9747 const auto *MAR = cast<SCEVAddRecExpr>(More);
9749 if (LAR->getLoop() != MAR->getLoop())
9752 // We look at affine expressions only; not for correctness but to keep
9753 // getStepRecurrence cheap.
9754 if (!LAR->isAffine() || !MAR->isAffine())
9757 if (LAR->getStepRecurrence(*this) != MAR->getStepRecurrence(*this))
9760 Less = LAR->getStart();
9761 More = MAR->getStart();
9766 if (isa<SCEVConstant>(Less) && isa<SCEVConstant>(More)) {
9767 const auto &M = cast<SCEVConstant>(More)->getAPInt();
9768 const auto &L = cast<SCEVConstant>(Less)->getAPInt();
9772 SCEV::NoWrapFlags Flags;
9773 const SCEV *LLess = nullptr, *RLess = nullptr;
9774 const SCEV *LMore = nullptr, *RMore = nullptr;
9775 const SCEVConstant *C1 = nullptr, *C2 = nullptr;
9776 // Compare (X + C1) vs X.
9777 if (splitBinaryAdd(Less, LLess, RLess, Flags))
9778 if ((C1 = dyn_cast<SCEVConstant>(LLess)))
9780 return -(C1->getAPInt());
9782 // Compare X vs (X + C2).
9783 if (splitBinaryAdd(More, LMore, RMore, Flags))
9784 if ((C2 = dyn_cast<SCEVConstant>(LMore)))
9786 return C2->getAPInt();
9788 // Compare (X + C1) vs (X + C2).
9789 if (C1 && C2 && RLess == RMore)
9790 return C2->getAPInt() - C1->getAPInt();
9795 bool ScalarEvolution::isImpliedCondOperandsViaNoOverflow(
9796 ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS,
9797 const SCEV *FoundLHS, const SCEV *FoundRHS) {
9798 if (Pred != CmpInst::ICMP_SLT && Pred != CmpInst::ICMP_ULT)
9801 const auto *AddRecLHS = dyn_cast<SCEVAddRecExpr>(LHS);
9805 const auto *AddRecFoundLHS = dyn_cast<SCEVAddRecExpr>(FoundLHS);
9806 if (!AddRecFoundLHS)
9809 // We'd like to let SCEV reason about control dependencies, so we constrain
9810 // both the inequalities to be about add recurrences on the same loop. This
9811 // way we can use isLoopEntryGuardedByCond later.
9813 const Loop *L = AddRecFoundLHS->getLoop();
9814 if (L != AddRecLHS->getLoop())
9817 // FoundLHS u< FoundRHS u< -C => (FoundLHS + C) u< (FoundRHS + C) ... (1)
9819 // FoundLHS s< FoundRHS s< INT_MIN - C => (FoundLHS + C) s< (FoundRHS + C)
9822 // Informal proof for (2), assuming (1) [*]:
9824 // We'll also assume (A s< B) <=> ((A + INT_MIN) u< (B + INT_MIN)) ... (3)[**]
9828 // FoundLHS s< FoundRHS s< INT_MIN - C
9829 // <=> (FoundLHS + INT_MIN) u< (FoundRHS + INT_MIN) u< -C [ using (3) ]
9830 // <=> (FoundLHS + INT_MIN + C) u< (FoundRHS + INT_MIN + C) [ using (1) ]
9831 // <=> (FoundLHS + INT_MIN + C + INT_MIN) s<
9832 // (FoundRHS + INT_MIN + C + INT_MIN) [ using (3) ]
9833 // <=> FoundLHS + C s< FoundRHS + C
9835 // [*]: (1) can be proved by ruling out overflow.
9837 // [**]: This can be proved by analyzing all the four possibilities:
9838 // (A s< 0, B s< 0), (A s< 0, B s>= 0), (A s>= 0, B s< 0) and
9839 // (A s>= 0, B s>= 0).
9842 // Despite (2), "FoundRHS s< INT_MIN - C" does not mean that "FoundRHS + C"
9843 // will not sign underflow. For instance, say FoundLHS = (i8 -128), FoundRHS
9844 // = (i8 -127) and C = (i8 -100). Then INT_MIN - C = (i8 -28), and FoundRHS
9845 // s< (INT_MIN - C). Lack of sign overflow / underflow in "FoundRHS + C" is
9846 // neither necessary nor sufficient to prove "(FoundLHS + C) s< (FoundRHS +
9849 Optional<APInt> LDiff = computeConstantDifference(LHS, FoundLHS);
9850 Optional<APInt> RDiff = computeConstantDifference(RHS, FoundRHS);
9851 if (!LDiff || !RDiff || *LDiff != *RDiff)
9854 if (LDiff->isMinValue())
9857 APInt FoundRHSLimit;
9859 if (Pred == CmpInst::ICMP_ULT) {
9860 FoundRHSLimit = -(*RDiff);
9862 assert(Pred == CmpInst::ICMP_SLT && "Checked above!");
9863 FoundRHSLimit = APInt::getSignedMinValue(getTypeSizeInBits(RHS->getType())) - *RDiff;
9866 // Try to prove (1) or (2), as needed.
9867 return isAvailableAtLoopEntry(FoundRHS, L) &&
9868 isLoopEntryGuardedByCond(L, Pred, FoundRHS,
9869 getConstant(FoundRHSLimit));
9872 bool ScalarEvolution::isImpliedViaMerge(ICmpInst::Predicate Pred,
9873 const SCEV *LHS, const SCEV *RHS,
9874 const SCEV *FoundLHS,
9875 const SCEV *FoundRHS, unsigned Depth) {
9876 const PHINode *LPhi = nullptr, *RPhi = nullptr;
9878 auto ClearOnExit = make_scope_exit([&]() {
9880 bool Erased = PendingMerges.erase(LPhi);
9881 assert(Erased && "Failed to erase LPhi!");
9885 bool Erased = PendingMerges.erase(RPhi);
9886 assert(Erased && "Failed to erase RPhi!");
9891 // Find respective Phis and check that they are not being pending.
9892 if (const SCEVUnknown *LU = dyn_cast<SCEVUnknown>(LHS))
9893 if (auto *Phi = dyn_cast<PHINode>(LU->getValue())) {
9894 if (!PendingMerges.insert(Phi).second)
9898 if (const SCEVUnknown *RU = dyn_cast<SCEVUnknown>(RHS))
9899 if (auto *Phi = dyn_cast<PHINode>(RU->getValue())) {
9900 // If we detect a loop of Phi nodes being processed by this method, for
9903 // %a = phi i32 [ %some1, %preheader ], [ %b, %latch ]
9904 // %b = phi i32 [ %some2, %preheader ], [ %a, %latch ]
9906 // we don't want to deal with a case that complex, so return conservative
9908 if (!PendingMerges.insert(Phi).second)
9913 // If none of LHS, RHS is a Phi, nothing to do here.
9917 // If there is a SCEVUnknown Phi we are interested in, make it left.
9919 std::swap(LHS, RHS);
9920 std::swap(FoundLHS, FoundRHS);
9921 std::swap(LPhi, RPhi);
9922 Pred = ICmpInst::getSwappedPredicate(Pred);
9925 assert(LPhi && "LPhi should definitely be a SCEVUnknown Phi!");
9926 const BasicBlock *LBB = LPhi->getParent();
9927 const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS);
9929 auto ProvedEasily = [&](const SCEV *S1, const SCEV *S2) {
9930 return isKnownViaNonRecursiveReasoning(Pred, S1, S2) ||
9931 isImpliedCondOperandsViaRanges(Pred, S1, S2, FoundLHS, FoundRHS) ||
9932 isImpliedViaOperations(Pred, S1, S2, FoundLHS, FoundRHS, Depth);
9935 if (RPhi && RPhi->getParent() == LBB) {
9936 // Case one: RHS is also a SCEVUnknown Phi from the same basic block.
9937 // If we compare two Phis from the same block, and for each entry block
9938 // the predicate is true for incoming values from this block, then the
9939 // predicate is also true for the Phis.
9940 for (const BasicBlock *IncBB : predecessors(LBB)) {
9941 const SCEV *L = getSCEV(LPhi->getIncomingValueForBlock(IncBB));
9942 const SCEV *R = getSCEV(RPhi->getIncomingValueForBlock(IncBB));
9943 if (!ProvedEasily(L, R))
9946 } else if (RAR && RAR->getLoop()->getHeader() == LBB) {
9947 // Case two: RHS is also a Phi from the same basic block, and it is an
9948 // AddRec. It means that there is a loop which has both AddRec and Unknown
9949 // PHIs, for it we can compare incoming values of AddRec from above the loop
9950 // and latch with their respective incoming values of LPhi.
9951 // TODO: Generalize to handle loops with many inputs in a header.
9952 if (LPhi->getNumIncomingValues() != 2) return false;
9954 auto *RLoop = RAR->getLoop();
9955 auto *Predecessor = RLoop->getLoopPredecessor();
9956 assert(Predecessor && "Loop with AddRec with no predecessor?");
9957 const SCEV *L1 = getSCEV(LPhi->getIncomingValueForBlock(Predecessor));
9958 if (!ProvedEasily(L1, RAR->getStart()))
9960 auto *Latch = RLoop->getLoopLatch();
9961 assert(Latch && "Loop with AddRec with no latch?");
9962 const SCEV *L2 = getSCEV(LPhi->getIncomingValueForBlock(Latch));
9963 if (!ProvedEasily(L2, RAR->getPostIncExpr(*this)))
9966 // In all other cases go over inputs of LHS and compare each of them to RHS,
9967 // the predicate is true for (LHS, RHS) if it is true for all such pairs.
9968 // At this point RHS is either a non-Phi, or it is a Phi from some block
9969 // different from LBB.
9970 for (const BasicBlock *IncBB : predecessors(LBB)) {
9971 // Check that RHS is available in this block.
9972 if (!dominates(RHS, IncBB))
9974 const SCEV *L = getSCEV(LPhi->getIncomingValueForBlock(IncBB));
9975 if (!ProvedEasily(L, RHS))
9982 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
9983 const SCEV *LHS, const SCEV *RHS,
9984 const SCEV *FoundLHS,
9985 const SCEV *FoundRHS) {
9986 if (isImpliedCondOperandsViaRanges(Pred, LHS, RHS, FoundLHS, FoundRHS))
9989 if (isImpliedCondOperandsViaNoOverflow(Pred, LHS, RHS, FoundLHS, FoundRHS))
9992 return isImpliedCondOperandsHelper(Pred, LHS, RHS,
9993 FoundLHS, FoundRHS) ||
9994 // ~x < ~y --> x > y
9995 isImpliedCondOperandsHelper(Pred, LHS, RHS,
9996 getNotSCEV(FoundRHS),
9997 getNotSCEV(FoundLHS));
10000 /// Is MaybeMinMaxExpr an (U|S)(Min|Max) of Candidate and some other values?
10001 template <typename MinMaxExprType>
10002 static bool IsMinMaxConsistingOf(const SCEV *MaybeMinMaxExpr,
10003 const SCEV *Candidate) {
10004 const MinMaxExprType *MinMaxExpr = dyn_cast<MinMaxExprType>(MaybeMinMaxExpr);
10008 return find(MinMaxExpr->operands(), Candidate) != MinMaxExpr->op_end();
10011 static bool IsKnownPredicateViaAddRecStart(ScalarEvolution &SE,
10012 ICmpInst::Predicate Pred,
10013 const SCEV *LHS, const SCEV *RHS) {
10014 // If both sides are affine addrecs for the same loop, with equal
10015 // steps, and we know the recurrences don't wrap, then we only
10016 // need to check the predicate on the starting values.
10018 if (!ICmpInst::isRelational(Pred))
10021 const SCEVAddRecExpr *LAR = dyn_cast<SCEVAddRecExpr>(LHS);
10024 const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS);
10027 if (LAR->getLoop() != RAR->getLoop())
10029 if (!LAR->isAffine() || !RAR->isAffine())
10032 if (LAR->getStepRecurrence(SE) != RAR->getStepRecurrence(SE))
10035 SCEV::NoWrapFlags NW = ICmpInst::isSigned(Pred) ?
10036 SCEV::FlagNSW : SCEV::FlagNUW;
10037 if (!LAR->getNoWrapFlags(NW) || !RAR->getNoWrapFlags(NW))
10040 return SE.isKnownPredicate(Pred, LAR->getStart(), RAR->getStart());
10043 /// Is LHS `Pred` RHS true on the virtue of LHS or RHS being a Min or Max
10045 static bool IsKnownPredicateViaMinOrMax(ScalarEvolution &SE,
10046 ICmpInst::Predicate Pred,
10047 const SCEV *LHS, const SCEV *RHS) {
10052 case ICmpInst::ICMP_SGE:
10053 std::swap(LHS, RHS);
10055 case ICmpInst::ICMP_SLE:
10057 // min(A, ...) <= A
10058 IsMinMaxConsistingOf<SCEVSMinExpr>(LHS, RHS) ||
10059 // A <= max(A, ...)
10060 IsMinMaxConsistingOf<SCEVSMaxExpr>(RHS, LHS);
10062 case ICmpInst::ICMP_UGE:
10063 std::swap(LHS, RHS);
10065 case ICmpInst::ICMP_ULE:
10067 // min(A, ...) <= A
10068 IsMinMaxConsistingOf<SCEVUMinExpr>(LHS, RHS) ||
10069 // A <= max(A, ...)
10070 IsMinMaxConsistingOf<SCEVUMaxExpr>(RHS, LHS);
10073 llvm_unreachable("covered switch fell through?!");
10076 bool ScalarEvolution::isImpliedViaOperations(ICmpInst::Predicate Pred,
10077 const SCEV *LHS, const SCEV *RHS,
10078 const SCEV *FoundLHS,
10079 const SCEV *FoundRHS,
10081 assert(getTypeSizeInBits(LHS->getType()) ==
10082 getTypeSizeInBits(RHS->getType()) &&
10083 "LHS and RHS have different sizes?");
10084 assert(getTypeSizeInBits(FoundLHS->getType()) ==
10085 getTypeSizeInBits(FoundRHS->getType()) &&
10086 "FoundLHS and FoundRHS have different sizes?");
10087 // We want to avoid hurting the compile time with analysis of too big trees.
10088 if (Depth > MaxSCEVOperationsImplicationDepth)
10090 // We only want to work with ICMP_SGT comparison so far.
10091 // TODO: Extend to ICMP_UGT?
10092 if (Pred == ICmpInst::ICMP_SLT) {
10093 Pred = ICmpInst::ICMP_SGT;
10094 std::swap(LHS, RHS);
10095 std::swap(FoundLHS, FoundRHS);
10097 if (Pred != ICmpInst::ICMP_SGT)
10100 auto GetOpFromSExt = [&](const SCEV *S) {
10101 if (auto *Ext = dyn_cast<SCEVSignExtendExpr>(S))
10102 return Ext->getOperand();
10103 // TODO: If S is a SCEVConstant then you can cheaply "strip" the sext off
10104 // the constant in some cases.
10108 // Acquire values from extensions.
10109 auto *OrigLHS = LHS;
10110 auto *OrigFoundLHS = FoundLHS;
10111 LHS = GetOpFromSExt(LHS);
10112 FoundLHS = GetOpFromSExt(FoundLHS);
10114 // Is the SGT predicate can be proved trivially or using the found context.
10115 auto IsSGTViaContext = [&](const SCEV *S1, const SCEV *S2) {
10116 return isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_SGT, S1, S2) ||
10117 isImpliedViaOperations(ICmpInst::ICMP_SGT, S1, S2, OrigFoundLHS,
10118 FoundRHS, Depth + 1);
10121 if (auto *LHSAddExpr = dyn_cast<SCEVAddExpr>(LHS)) {
10122 // We want to avoid creation of any new non-constant SCEV. Since we are
10123 // going to compare the operands to RHS, we should be certain that we don't
10124 // need any size extensions for this. So let's decline all cases when the
10125 // sizes of types of LHS and RHS do not match.
10126 // TODO: Maybe try to get RHS from sext to catch more cases?
10127 if (getTypeSizeInBits(LHS->getType()) != getTypeSizeInBits(RHS->getType()))
10130 // Should not overflow.
10131 if (!LHSAddExpr->hasNoSignedWrap())
10134 auto *LL = LHSAddExpr->getOperand(0);
10135 auto *LR = LHSAddExpr->getOperand(1);
10136 auto *MinusOne = getNegativeSCEV(getOne(RHS->getType()));
10138 // Checks that S1 >= 0 && S2 > RHS, trivially or using the found context.
10139 auto IsSumGreaterThanRHS = [&](const SCEV *S1, const SCEV *S2) {
10140 return IsSGTViaContext(S1, MinusOne) && IsSGTViaContext(S2, RHS);
10142 // Try to prove the following rule:
10143 // (LHS = LL + LR) && (LL >= 0) && (LR > RHS) => (LHS > RHS).
10144 // (LHS = LL + LR) && (LR >= 0) && (LL > RHS) => (LHS > RHS).
10145 if (IsSumGreaterThanRHS(LL, LR) || IsSumGreaterThanRHS(LR, LL))
10147 } else if (auto *LHSUnknownExpr = dyn_cast<SCEVUnknown>(LHS)) {
10149 // FIXME: Once we have SDiv implemented, we can get rid of this matching.
10151 using namespace llvm::PatternMatch;
10153 if (match(LHSUnknownExpr->getValue(), m_SDiv(m_Value(LL), m_Value(LR)))) {
10154 // Rules for division.
10155 // We are going to perform some comparisons with Denominator and its
10156 // derivative expressions. In general case, creating a SCEV for it may
10157 // lead to a complex analysis of the entire graph, and in particular it
10158 // can request trip count recalculation for the same loop. This would
10159 // cache as SCEVCouldNotCompute to avoid the infinite recursion. To avoid
10160 // this, we only want to create SCEVs that are constants in this section.
10161 // So we bail if Denominator is not a constant.
10162 if (!isa<ConstantInt>(LR))
10165 auto *Denominator = cast<SCEVConstant>(getSCEV(LR));
10167 // We want to make sure that LHS = FoundLHS / Denominator. If it is so,
10168 // then a SCEV for the numerator already exists and matches with FoundLHS.
10169 auto *Numerator = getExistingSCEV(LL);
10170 if (!Numerator || Numerator->getType() != FoundLHS->getType())
10173 // Make sure that the numerator matches with FoundLHS and the denominator
10175 if (!HasSameValue(Numerator, FoundLHS) || !isKnownPositive(Denominator))
10178 auto *DTy = Denominator->getType();
10179 auto *FRHSTy = FoundRHS->getType();
10180 if (DTy->isPointerTy() != FRHSTy->isPointerTy())
10181 // One of types is a pointer and another one is not. We cannot extend
10182 // them properly to a wider type, so let us just reject this case.
10183 // TODO: Usage of getEffectiveSCEVType for DTy, FRHSTy etc should help
10184 // to avoid this check.
10188 // FoundLHS > FoundRHS, LHS = FoundLHS / Denominator, Denominator > 0.
10189 auto *WTy = getWiderType(DTy, FRHSTy);
10190 auto *DenominatorExt = getNoopOrSignExtend(Denominator, WTy);
10191 auto *FoundRHSExt = getNoopOrSignExtend(FoundRHS, WTy);
10193 // Try to prove the following rule:
10194 // (FoundRHS > Denominator - 2) && (RHS <= 0) => (LHS > RHS).
10195 // For example, given that FoundLHS > 2. It means that FoundLHS is at
10196 // least 3. If we divide it by Denominator < 4, we will have at least 1.
10197 auto *DenomMinusTwo = getMinusSCEV(DenominatorExt, getConstant(WTy, 2));
10198 if (isKnownNonPositive(RHS) &&
10199 IsSGTViaContext(FoundRHSExt, DenomMinusTwo))
10202 // Try to prove the following rule:
10203 // (FoundRHS > -1 - Denominator) && (RHS < 0) => (LHS > RHS).
10204 // For example, given that FoundLHS > -3. Then FoundLHS is at least -2.
10205 // If we divide it by Denominator > 2, then:
10206 // 1. If FoundLHS is negative, then the result is 0.
10207 // 2. If FoundLHS is non-negative, then the result is non-negative.
10208 // Anyways, the result is non-negative.
10209 auto *MinusOne = getNegativeSCEV(getOne(WTy));
10210 auto *NegDenomMinusOne = getMinusSCEV(MinusOne, DenominatorExt);
10211 if (isKnownNegative(RHS) &&
10212 IsSGTViaContext(FoundRHSExt, NegDenomMinusOne))
10217 // If our expression contained SCEVUnknown Phis, and we split it down and now
10218 // need to prove something for them, try to prove the predicate for every
10219 // possible incoming values of those Phis.
10220 if (isImpliedViaMerge(Pred, OrigLHS, RHS, OrigFoundLHS, FoundRHS, Depth + 1))
10226 static bool isKnownPredicateExtendIdiom(ICmpInst::Predicate Pred,
10227 const SCEV *LHS, const SCEV *RHS) {
10228 // zext x u<= sext x, sext x s<= zext x
10230 case ICmpInst::ICMP_SGE:
10231 std::swap(LHS, RHS);
10233 case ICmpInst::ICMP_SLE: {
10234 // If operand >=s 0 then ZExt == SExt. If operand <s 0 then SExt <s ZExt.
10235 const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(LHS);
10236 const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(RHS);
10237 if (SExt && ZExt && SExt->getOperand() == ZExt->getOperand())
10241 case ICmpInst::ICMP_UGE:
10242 std::swap(LHS, RHS);
10244 case ICmpInst::ICMP_ULE: {
10245 // If operand >=s 0 then ZExt == SExt. If operand <s 0 then ZExt <u SExt.
10246 const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(LHS);
10247 const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(RHS);
10248 if (SExt && ZExt && SExt->getOperand() == ZExt->getOperand())
10259 ScalarEvolution::isKnownViaNonRecursiveReasoning(ICmpInst::Predicate Pred,
10260 const SCEV *LHS, const SCEV *RHS) {
10261 return isKnownPredicateExtendIdiom(Pred, LHS, RHS) ||
10262 isKnownPredicateViaConstantRanges(Pred, LHS, RHS) ||
10263 IsKnownPredicateViaMinOrMax(*this, Pred, LHS, RHS) ||
10264 IsKnownPredicateViaAddRecStart(*this, Pred, LHS, RHS) ||
10265 isKnownPredicateViaNoOverflow(Pred, LHS, RHS);
10269 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
10270 const SCEV *LHS, const SCEV *RHS,
10271 const SCEV *FoundLHS,
10272 const SCEV *FoundRHS) {
10274 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
10275 case ICmpInst::ICMP_EQ:
10276 case ICmpInst::ICMP_NE:
10277 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
10280 case ICmpInst::ICMP_SLT:
10281 case ICmpInst::ICMP_SLE:
10282 if (isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
10283 isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_SGE, RHS, FoundRHS))
10286 case ICmpInst::ICMP_SGT:
10287 case ICmpInst::ICMP_SGE:
10288 if (isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
10289 isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_SLE, RHS, FoundRHS))
10292 case ICmpInst::ICMP_ULT:
10293 case ICmpInst::ICMP_ULE:
10294 if (isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
10295 isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_UGE, RHS, FoundRHS))
10298 case ICmpInst::ICMP_UGT:
10299 case ICmpInst::ICMP_UGE:
10300 if (isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
10301 isKnownViaNonRecursiveReasoning(ICmpInst::ICMP_ULE, RHS, FoundRHS))
10306 // Maybe it can be proved via operations?
10307 if (isImpliedViaOperations(Pred, LHS, RHS, FoundLHS, FoundRHS))
10313 bool ScalarEvolution::isImpliedCondOperandsViaRanges(ICmpInst::Predicate Pred,
10316 const SCEV *FoundLHS,
10317 const SCEV *FoundRHS) {
10318 if (!isa<SCEVConstant>(RHS) || !isa<SCEVConstant>(FoundRHS))
10319 // The restriction on `FoundRHS` be lifted easily -- it exists only to
10320 // reduce the compile time impact of this optimization.
10323 Optional<APInt> Addend = computeConstantDifference(LHS, FoundLHS);
10327 const APInt &ConstFoundRHS = cast<SCEVConstant>(FoundRHS)->getAPInt();
10329 // `FoundLHSRange` is the range we know `FoundLHS` to be in by virtue of the
10330 // antecedent "`FoundLHS` `Pred` `FoundRHS`".
10331 ConstantRange FoundLHSRange =
10332 ConstantRange::makeAllowedICmpRegion(Pred, ConstFoundRHS);
10334 // Since `LHS` is `FoundLHS` + `Addend`, we can compute a range for `LHS`:
10335 ConstantRange LHSRange = FoundLHSRange.add(ConstantRange(*Addend));
10337 // We can also compute the range of values for `LHS` that satisfy the
10338 // consequent, "`LHS` `Pred` `RHS`":
10339 const APInt &ConstRHS = cast<SCEVConstant>(RHS)->getAPInt();
10340 ConstantRange SatisfyingLHSRange =
10341 ConstantRange::makeSatisfyingICmpRegion(Pred, ConstRHS);
10343 // The antecedent implies the consequent if every value of `LHS` that
10344 // satisfies the antecedent also satisfies the consequent.
10345 return SatisfyingLHSRange.contains(LHSRange);
10348 bool ScalarEvolution::doesIVOverflowOnLT(const SCEV *RHS, const SCEV *Stride,
10349 bool IsSigned, bool NoWrap) {
10350 assert(isKnownPositive(Stride) && "Positive stride expected!");
10352 if (NoWrap) return false;
10354 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
10355 const SCEV *One = getOne(Stride->getType());
10358 APInt MaxRHS = getSignedRangeMax(RHS);
10359 APInt MaxValue = APInt::getSignedMaxValue(BitWidth);
10360 APInt MaxStrideMinusOne = getSignedRangeMax(getMinusSCEV(Stride, One));
10362 // SMaxRHS + SMaxStrideMinusOne > SMaxValue => overflow!
10363 return (std::move(MaxValue) - MaxStrideMinusOne).slt(MaxRHS);
10366 APInt MaxRHS = getUnsignedRangeMax(RHS);
10367 APInt MaxValue = APInt::getMaxValue(BitWidth);
10368 APInt MaxStrideMinusOne = getUnsignedRangeMax(getMinusSCEV(Stride, One));
10370 // UMaxRHS + UMaxStrideMinusOne > UMaxValue => overflow!
10371 return (std::move(MaxValue) - MaxStrideMinusOne).ult(MaxRHS);
10374 bool ScalarEvolution::doesIVOverflowOnGT(const SCEV *RHS, const SCEV *Stride,
10375 bool IsSigned, bool NoWrap) {
10376 if (NoWrap) return false;
10378 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
10379 const SCEV *One = getOne(Stride->getType());
10382 APInt MinRHS = getSignedRangeMin(RHS);
10383 APInt MinValue = APInt::getSignedMinValue(BitWidth);
10384 APInt MaxStrideMinusOne = getSignedRangeMax(getMinusSCEV(Stride, One));
10386 // SMinRHS - SMaxStrideMinusOne < SMinValue => overflow!
10387 return (std::move(MinValue) + MaxStrideMinusOne).sgt(MinRHS);
10390 APInt MinRHS = getUnsignedRangeMin(RHS);
10391 APInt MinValue = APInt::getMinValue(BitWidth);
10392 APInt MaxStrideMinusOne = getUnsignedRangeMax(getMinusSCEV(Stride, One));
10394 // UMinRHS - UMaxStrideMinusOne < UMinValue => overflow!
10395 return (std::move(MinValue) + MaxStrideMinusOne).ugt(MinRHS);
10398 const SCEV *ScalarEvolution::computeBECount(const SCEV *Delta, const SCEV *Step,
10400 const SCEV *One = getOne(Step->getType());
10401 Delta = Equality ? getAddExpr(Delta, Step)
10402 : getAddExpr(Delta, getMinusSCEV(Step, One));
10403 return getUDivExpr(Delta, Step);
10406 const SCEV *ScalarEvolution::computeMaxBECountForLT(const SCEV *Start,
10407 const SCEV *Stride,
10412 assert(!isKnownNonPositive(Stride) &&
10413 "Stride is expected strictly positive!");
10414 // Calculate the maximum backedge count based on the range of values
10415 // permitted by Start, End, and Stride.
10416 const SCEV *MaxBECount;
10418 IsSigned ? getSignedRangeMin(Start) : getUnsignedRangeMin(Start);
10420 APInt StrideForMaxBECount =
10421 IsSigned ? getSignedRangeMin(Stride) : getUnsignedRangeMin(Stride);
10423 // We already know that the stride is positive, so we paper over conservatism
10424 // in our range computation by forcing StrideForMaxBECount to be at least one.
10425 // In theory this is unnecessary, but we expect MaxBECount to be a
10426 // SCEVConstant, and (udiv <constant> 0) is not constant folded by SCEV (there
10427 // is nothing to constant fold it to).
10428 APInt One(BitWidth, 1, IsSigned);
10429 StrideForMaxBECount = APIntOps::smax(One, StrideForMaxBECount);
10431 APInt MaxValue = IsSigned ? APInt::getSignedMaxValue(BitWidth)
10432 : APInt::getMaxValue(BitWidth);
10433 APInt Limit = MaxValue - (StrideForMaxBECount - 1);
10435 // Although End can be a MAX expression we estimate MaxEnd considering only
10436 // the case End = RHS of the loop termination condition. This is safe because
10437 // in the other case (End - Start) is zero, leading to a zero maximum backedge
10439 APInt MaxEnd = IsSigned ? APIntOps::smin(getSignedRangeMax(End), Limit)
10440 : APIntOps::umin(getUnsignedRangeMax(End), Limit);
10442 MaxBECount = computeBECount(getConstant(MaxEnd - MinStart) /* Delta */,
10443 getConstant(StrideForMaxBECount) /* Step */,
10444 false /* Equality */);
10449 ScalarEvolution::ExitLimit
10450 ScalarEvolution::howManyLessThans(const SCEV *LHS, const SCEV *RHS,
10451 const Loop *L, bool IsSigned,
10452 bool ControlsExit, bool AllowPredicates) {
10453 SmallPtrSet<const SCEVPredicate *, 4> Predicates;
10455 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
10456 bool PredicatedIV = false;
10458 if (!IV && AllowPredicates) {
10459 // Try to make this an AddRec using runtime tests, in the first X
10460 // iterations of this loop, where X is the SCEV expression found by the
10461 // algorithm below.
10462 IV = convertSCEVToAddRecWithPredicates(LHS, L, Predicates);
10463 PredicatedIV = true;
10466 // Avoid weird loops
10467 if (!IV || IV->getLoop() != L || !IV->isAffine())
10468 return getCouldNotCompute();
10470 bool NoWrap = ControlsExit &&
10471 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
10473 const SCEV *Stride = IV->getStepRecurrence(*this);
10475 bool PositiveStride = isKnownPositive(Stride);
10477 // Avoid negative or zero stride values.
10478 if (!PositiveStride) {
10479 // We can compute the correct backedge taken count for loops with unknown
10480 // strides if we can prove that the loop is not an infinite loop with side
10481 // effects. Here's the loop structure we are trying to handle -
10487 // } while (i < end);
10489 // The backedge taken count for such loops is evaluated as -
10490 // (max(end, start + stride) - start - 1) /u stride
10492 // The additional preconditions that we need to check to prove correctness
10493 // of the above formula is as follows -
10495 // a) IV is either nuw or nsw depending upon signedness (indicated by the
10497 // b) loop is single exit with no side effects.
10500 // Precondition a) implies that if the stride is negative, this is a single
10501 // trip loop. The backedge taken count formula reduces to zero in this case.
10503 // Precondition b) implies that the unknown stride cannot be zero otherwise
10506 // The positive stride case is the same as isKnownPositive(Stride) returning
10507 // true (original behavior of the function).
10509 // We want to make sure that the stride is truly unknown as there are edge
10510 // cases where ScalarEvolution propagates no wrap flags to the
10511 // post-increment/decrement IV even though the increment/decrement operation
10512 // itself is wrapping. The computed backedge taken count may be wrong in
10513 // such cases. This is prevented by checking that the stride is not known to
10514 // be either positive or non-positive. For example, no wrap flags are
10515 // propagated to the post-increment IV of this loop with a trip count of 2 -
10517 // unsigned char i;
10518 // for(i=127; i<128; i+=129)
10521 if (PredicatedIV || !NoWrap || isKnownNonPositive(Stride) ||
10522 !loopHasNoSideEffects(L))
10523 return getCouldNotCompute();
10524 } else if (!Stride->isOne() &&
10525 doesIVOverflowOnLT(RHS, Stride, IsSigned, NoWrap))
10526 // Avoid proven overflow cases: this will ensure that the backedge taken
10527 // count will not generate any unsigned overflow. Relaxed no-overflow
10528 // conditions exploit NoWrapFlags, allowing to optimize in presence of
10529 // undefined behaviors like the case of C language.
10530 return getCouldNotCompute();
10532 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SLT
10533 : ICmpInst::ICMP_ULT;
10534 const SCEV *Start = IV->getStart();
10535 const SCEV *End = RHS;
10536 // When the RHS is not invariant, we do not know the end bound of the loop and
10537 // cannot calculate the ExactBECount needed by ExitLimit. However, we can
10538 // calculate the MaxBECount, given the start, stride and max value for the end
10539 // bound of the loop (RHS), and the fact that IV does not overflow (which is
10541 if (!isLoopInvariant(RHS, L)) {
10542 const SCEV *MaxBECount = computeMaxBECountForLT(
10543 Start, Stride, RHS, getTypeSizeInBits(LHS->getType()), IsSigned);
10544 return ExitLimit(getCouldNotCompute() /* ExactNotTaken */, MaxBECount,
10545 false /*MaxOrZero*/, Predicates);
10547 // If the backedge is taken at least once, then it will be taken
10548 // (End-Start)/Stride times (rounded up to a multiple of Stride), where Start
10549 // is the LHS value of the less-than comparison the first time it is evaluated
10550 // and End is the RHS.
10551 const SCEV *BECountIfBackedgeTaken =
10552 computeBECount(getMinusSCEV(End, Start), Stride, false);
10553 // If the loop entry is guarded by the result of the backedge test of the
10554 // first loop iteration, then we know the backedge will be taken at least
10555 // once and so the backedge taken count is as above. If not then we use the
10556 // expression (max(End,Start)-Start)/Stride to describe the backedge count,
10557 // as if the backedge is taken at least once max(End,Start) is End and so the
10558 // result is as above, and if not max(End,Start) is Start so we get a backedge
10560 const SCEV *BECount;
10561 if (isLoopEntryGuardedByCond(L, Cond, getMinusSCEV(Start, Stride), RHS))
10562 BECount = BECountIfBackedgeTaken;
10564 End = IsSigned ? getSMaxExpr(RHS, Start) : getUMaxExpr(RHS, Start);
10565 BECount = computeBECount(getMinusSCEV(End, Start), Stride, false);
10568 const SCEV *MaxBECount;
10569 bool MaxOrZero = false;
10570 if (isa<SCEVConstant>(BECount))
10571 MaxBECount = BECount;
10572 else if (isa<SCEVConstant>(BECountIfBackedgeTaken)) {
10573 // If we know exactly how many times the backedge will be taken if it's
10574 // taken at least once, then the backedge count will either be that or
10576 MaxBECount = BECountIfBackedgeTaken;
10579 MaxBECount = computeMaxBECountForLT(
10580 Start, Stride, RHS, getTypeSizeInBits(LHS->getType()), IsSigned);
10583 if (isa<SCEVCouldNotCompute>(MaxBECount) &&
10584 !isa<SCEVCouldNotCompute>(BECount))
10585 MaxBECount = getConstant(getUnsignedRangeMax(BECount));
10587 return ExitLimit(BECount, MaxBECount, MaxOrZero, Predicates);
10590 ScalarEvolution::ExitLimit
10591 ScalarEvolution::howManyGreaterThans(const SCEV *LHS, const SCEV *RHS,
10592 const Loop *L, bool IsSigned,
10593 bool ControlsExit, bool AllowPredicates) {
10594 SmallPtrSet<const SCEVPredicate *, 4> Predicates;
10595 // We handle only IV > Invariant
10596 if (!isLoopInvariant(RHS, L))
10597 return getCouldNotCompute();
10599 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
10600 if (!IV && AllowPredicates)
10601 // Try to make this an AddRec using runtime tests, in the first X
10602 // iterations of this loop, where X is the SCEV expression found by the
10603 // algorithm below.
10604 IV = convertSCEVToAddRecWithPredicates(LHS, L, Predicates);
10606 // Avoid weird loops
10607 if (!IV || IV->getLoop() != L || !IV->isAffine())
10608 return getCouldNotCompute();
10610 bool NoWrap = ControlsExit &&
10611 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
10613 const SCEV *Stride = getNegativeSCEV(IV->getStepRecurrence(*this));
10615 // Avoid negative or zero stride values
10616 if (!isKnownPositive(Stride))
10617 return getCouldNotCompute();
10619 // Avoid proven overflow cases: this will ensure that the backedge taken count
10620 // will not generate any unsigned overflow. Relaxed no-overflow conditions
10621 // exploit NoWrapFlags, allowing to optimize in presence of undefined
10622 // behaviors like the case of C language.
10623 if (!Stride->isOne() && doesIVOverflowOnGT(RHS, Stride, IsSigned, NoWrap))
10624 return getCouldNotCompute();
10626 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SGT
10627 : ICmpInst::ICMP_UGT;
10629 const SCEV *Start = IV->getStart();
10630 const SCEV *End = RHS;
10631 if (!isLoopEntryGuardedByCond(L, Cond, getAddExpr(Start, Stride), RHS))
10632 End = IsSigned ? getSMinExpr(RHS, Start) : getUMinExpr(RHS, Start);
10634 const SCEV *BECount = computeBECount(getMinusSCEV(Start, End), Stride, false);
10636 APInt MaxStart = IsSigned ? getSignedRangeMax(Start)
10637 : getUnsignedRangeMax(Start);
10639 APInt MinStride = IsSigned ? getSignedRangeMin(Stride)
10640 : getUnsignedRangeMin(Stride);
10642 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
10643 APInt Limit = IsSigned ? APInt::getSignedMinValue(BitWidth) + (MinStride - 1)
10644 : APInt::getMinValue(BitWidth) + (MinStride - 1);
10646 // Although End can be a MIN expression we estimate MinEnd considering only
10647 // the case End = RHS. This is safe because in the other case (Start - End)
10648 // is zero, leading to a zero maximum backedge taken count.
10650 IsSigned ? APIntOps::smax(getSignedRangeMin(RHS), Limit)
10651 : APIntOps::umax(getUnsignedRangeMin(RHS), Limit);
10653 const SCEV *MaxBECount = isa<SCEVConstant>(BECount)
10655 : computeBECount(getConstant(MaxStart - MinEnd),
10656 getConstant(MinStride), false);
10658 if (isa<SCEVCouldNotCompute>(MaxBECount))
10659 MaxBECount = BECount;
10661 return ExitLimit(BECount, MaxBECount, false, Predicates);
10664 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(const ConstantRange &Range,
10665 ScalarEvolution &SE) const {
10666 if (Range.isFullSet()) // Infinite loop.
10667 return SE.getCouldNotCompute();
10669 // If the start is a non-zero constant, shift the range to simplify things.
10670 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
10671 if (!SC->getValue()->isZero()) {
10672 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
10673 Operands[0] = SE.getZero(SC->getType());
10674 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(),
10675 getNoWrapFlags(FlagNW));
10676 if (const auto *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted))
10677 return ShiftedAddRec->getNumIterationsInRange(
10678 Range.subtract(SC->getAPInt()), SE);
10679 // This is strange and shouldn't happen.
10680 return SE.getCouldNotCompute();
10683 // The only time we can solve this is when we have all constant indices.
10684 // Otherwise, we cannot determine the overflow conditions.
10685 if (any_of(operands(), [](const SCEV *Op) { return !isa<SCEVConstant>(Op); }))
10686 return SE.getCouldNotCompute();
10688 // Okay at this point we know that all elements of the chrec are constants and
10689 // that the start element is zero.
10691 // First check to see if the range contains zero. If not, the first
10692 // iteration exits.
10693 unsigned BitWidth = SE.getTypeSizeInBits(getType());
10694 if (!Range.contains(APInt(BitWidth, 0)))
10695 return SE.getZero(getType());
10698 // If this is an affine expression then we have this situation:
10699 // Solve {0,+,A} in Range === Ax in Range
10701 // We know that zero is in the range. If A is positive then we know that
10702 // the upper value of the range must be the first possible exit value.
10703 // If A is negative then the lower of the range is the last possible loop
10704 // value. Also note that we already checked for a full range.
10705 APInt A = cast<SCEVConstant>(getOperand(1))->getAPInt();
10706 APInt End = A.sge(1) ? (Range.getUpper() - 1) : Range.getLower();
10708 // The exit value should be (End+A)/A.
10709 APInt ExitVal = (End + A).udiv(A);
10710 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
10712 // Evaluate at the exit value. If we really did fall out of the valid
10713 // range, then we computed our trip count, otherwise wrap around or other
10714 // things must have happened.
10715 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
10716 if (Range.contains(Val->getValue()))
10717 return SE.getCouldNotCompute(); // Something strange happened
10719 // Ensure that the previous value is in the range. This is a sanity check.
10720 assert(Range.contains(
10721 EvaluateConstantChrecAtConstant(this,
10722 ConstantInt::get(SE.getContext(), ExitVal - 1), SE)->getValue()) &&
10723 "Linear scev computation is off in a bad way!");
10724 return SE.getConstant(ExitValue);
10727 if (isQuadratic()) {
10728 if (auto S = SolveQuadraticAddRecRange(this, Range, SE))
10729 return SE.getConstant(S.getValue());
10732 return SE.getCouldNotCompute();
10735 const SCEVAddRecExpr *
10736 SCEVAddRecExpr::getPostIncExpr(ScalarEvolution &SE) const {
10737 assert(getNumOperands() > 1 && "AddRec with zero step?");
10738 // There is a temptation to just call getAddExpr(this, getStepRecurrence(SE)),
10739 // but in this case we cannot guarantee that the value returned will be an
10740 // AddRec because SCEV does not have a fixed point where it stops
10741 // simplification: it is legal to return ({rec1} + {rec2}). For example, it
10742 // may happen if we reach arithmetic depth limit while simplifying. So we
10743 // construct the returned value explicitly.
10744 SmallVector<const SCEV *, 3> Ops;
10745 // If this is {A,+,B,+,C,...,+,N}, then its step is {B,+,C,+,...,+,N}, and
10746 // (this + Step) is {A+B,+,B+C,+...,+,N}.
10747 for (unsigned i = 0, e = getNumOperands() - 1; i < e; ++i)
10748 Ops.push_back(SE.getAddExpr(getOperand(i), getOperand(i + 1)));
10749 // We know that the last operand is not a constant zero (otherwise it would
10750 // have been popped out earlier). This guarantees us that if the result has
10751 // the same last operand, then it will also not be popped out, meaning that
10752 // the returned value will be an AddRec.
10753 const SCEV *Last = getOperand(getNumOperands() - 1);
10754 assert(!Last->isZero() && "Recurrency with zero step?");
10755 Ops.push_back(Last);
10756 return cast<SCEVAddRecExpr>(SE.getAddRecExpr(Ops, getLoop(),
10757 SCEV::FlagAnyWrap));
10760 // Return true when S contains at least an undef value.
10761 static inline bool containsUndefs(const SCEV *S) {
10762 return SCEVExprContains(S, [](const SCEV *S) {
10763 if (const auto *SU = dyn_cast<SCEVUnknown>(S))
10764 return isa<UndefValue>(SU->getValue());
10771 // Collect all steps of SCEV expressions.
10772 struct SCEVCollectStrides {
10773 ScalarEvolution &SE;
10774 SmallVectorImpl<const SCEV *> &Strides;
10776 SCEVCollectStrides(ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &S)
10777 : SE(SE), Strides(S) {}
10779 bool follow(const SCEV *S) {
10780 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(S))
10781 Strides.push_back(AR->getStepRecurrence(SE));
10785 bool isDone() const { return false; }
10788 // Collect all SCEVUnknown and SCEVMulExpr expressions.
10789 struct SCEVCollectTerms {
10790 SmallVectorImpl<const SCEV *> &Terms;
10792 SCEVCollectTerms(SmallVectorImpl<const SCEV *> &T) : Terms(T) {}
10794 bool follow(const SCEV *S) {
10795 if (isa<SCEVUnknown>(S) || isa<SCEVMulExpr>(S) ||
10796 isa<SCEVSignExtendExpr>(S)) {
10797 if (!containsUndefs(S))
10798 Terms.push_back(S);
10800 // Stop recursion: once we collected a term, do not walk its operands.
10808 bool isDone() const { return false; }
10811 // Check if a SCEV contains an AddRecExpr.
10812 struct SCEVHasAddRec {
10813 bool &ContainsAddRec;
10815 SCEVHasAddRec(bool &ContainsAddRec) : ContainsAddRec(ContainsAddRec) {
10816 ContainsAddRec = false;
10819 bool follow(const SCEV *S) {
10820 if (isa<SCEVAddRecExpr>(S)) {
10821 ContainsAddRec = true;
10823 // Stop recursion: once we collected a term, do not walk its operands.
10831 bool isDone() const { return false; }
10834 // Find factors that are multiplied with an expression that (possibly as a
10835 // subexpression) contains an AddRecExpr. In the expression:
10837 // 8 * (100 + %p * %q * (%a + {0, +, 1}_loop))
10839 // "%p * %q" are factors multiplied by the expression "(%a + {0, +, 1}_loop)"
10840 // that contains the AddRec {0, +, 1}_loop. %p * %q are likely to be array size
10841 // parameters as they form a product with an induction variable.
10843 // This collector expects all array size parameters to be in the same MulExpr.
10844 // It might be necessary to later add support for collecting parameters that are
10845 // spread over different nested MulExpr.
10846 struct SCEVCollectAddRecMultiplies {
10847 SmallVectorImpl<const SCEV *> &Terms;
10848 ScalarEvolution &SE;
10850 SCEVCollectAddRecMultiplies(SmallVectorImpl<const SCEV *> &T, ScalarEvolution &SE)
10851 : Terms(T), SE(SE) {}
10853 bool follow(const SCEV *S) {
10854 if (auto *Mul = dyn_cast<SCEVMulExpr>(S)) {
10855 bool HasAddRec = false;
10856 SmallVector<const SCEV *, 0> Operands;
10857 for (auto Op : Mul->operands()) {
10858 const SCEVUnknown *Unknown = dyn_cast<SCEVUnknown>(Op);
10859 if (Unknown && !isa<CallInst>(Unknown->getValue())) {
10860 Operands.push_back(Op);
10861 } else if (Unknown) {
10864 bool ContainsAddRec = false;
10865 SCEVHasAddRec ContiansAddRec(ContainsAddRec);
10866 visitAll(Op, ContiansAddRec);
10867 HasAddRec |= ContainsAddRec;
10870 if (Operands.size() == 0)
10876 Terms.push_back(SE.getMulExpr(Operands));
10877 // Stop recursion: once we collected a term, do not walk its operands.
10885 bool isDone() const { return false; }
10888 } // end anonymous namespace
10890 /// Find parametric terms in this SCEVAddRecExpr. We first for parameters in
10892 /// 1) The strides of AddRec expressions.
10893 /// 2) Unknowns that are multiplied with AddRec expressions.
10894 void ScalarEvolution::collectParametricTerms(const SCEV *Expr,
10895 SmallVectorImpl<const SCEV *> &Terms) {
10896 SmallVector<const SCEV *, 4> Strides;
10897 SCEVCollectStrides StrideCollector(*this, Strides);
10898 visitAll(Expr, StrideCollector);
10901 dbgs() << "Strides:\n";
10902 for (const SCEV *S : Strides)
10903 dbgs() << *S << "\n";
10906 for (const SCEV *S : Strides) {
10907 SCEVCollectTerms TermCollector(Terms);
10908 visitAll(S, TermCollector);
10912 dbgs() << "Terms:\n";
10913 for (const SCEV *T : Terms)
10914 dbgs() << *T << "\n";
10917 SCEVCollectAddRecMultiplies MulCollector(Terms, *this);
10918 visitAll(Expr, MulCollector);
10921 static bool findArrayDimensionsRec(ScalarEvolution &SE,
10922 SmallVectorImpl<const SCEV *> &Terms,
10923 SmallVectorImpl<const SCEV *> &Sizes) {
10924 int Last = Terms.size() - 1;
10925 const SCEV *Step = Terms[Last];
10927 // End of recursion.
10929 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Step)) {
10930 SmallVector<const SCEV *, 2> Qs;
10931 for (const SCEV *Op : M->operands())
10932 if (!isa<SCEVConstant>(Op))
10935 Step = SE.getMulExpr(Qs);
10938 Sizes.push_back(Step);
10942 for (const SCEV *&Term : Terms) {
10943 // Normalize the terms before the next call to findArrayDimensionsRec.
10945 SCEVDivision::divide(SE, Term, Step, &Q, &R);
10947 // Bail out when GCD does not evenly divide one of the terms.
10954 // Remove all SCEVConstants.
10956 remove_if(Terms, [](const SCEV *E) { return isa<SCEVConstant>(E); }),
10959 if (Terms.size() > 0)
10960 if (!findArrayDimensionsRec(SE, Terms, Sizes))
10963 Sizes.push_back(Step);
10967 // Returns true when one of the SCEVs of Terms contains a SCEVUnknown parameter.
10968 static inline bool containsParameters(SmallVectorImpl<const SCEV *> &Terms) {
10969 for (const SCEV *T : Terms)
10970 if (SCEVExprContains(T, [](const SCEV *S) { return isa<SCEVUnknown>(S); }))
10976 // Return the number of product terms in S.
10977 static inline int numberOfTerms(const SCEV *S) {
10978 if (const SCEVMulExpr *Expr = dyn_cast<SCEVMulExpr>(S))
10979 return Expr->getNumOperands();
10983 static const SCEV *removeConstantFactors(ScalarEvolution &SE, const SCEV *T) {
10984 if (isa<SCEVConstant>(T))
10987 if (isa<SCEVUnknown>(T))
10990 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(T)) {
10991 SmallVector<const SCEV *, 2> Factors;
10992 for (const SCEV *Op : M->operands())
10993 if (!isa<SCEVConstant>(Op))
10994 Factors.push_back(Op);
10996 return SE.getMulExpr(Factors);
11002 /// Return the size of an element read or written by Inst.
11003 const SCEV *ScalarEvolution::getElementSize(Instruction *Inst) {
11005 if (StoreInst *Store = dyn_cast<StoreInst>(Inst))
11006 Ty = Store->getValueOperand()->getType();
11007 else if (LoadInst *Load = dyn_cast<LoadInst>(Inst))
11008 Ty = Load->getType();
11012 Type *ETy = getEffectiveSCEVType(PointerType::getUnqual(Ty));
11013 return getSizeOfExpr(ETy, Ty);
11016 void ScalarEvolution::findArrayDimensions(SmallVectorImpl<const SCEV *> &Terms,
11017 SmallVectorImpl<const SCEV *> &Sizes,
11018 const SCEV *ElementSize) {
11019 if (Terms.size() < 1 || !ElementSize)
11022 // Early return when Terms do not contain parameters: we do not delinearize
11023 // non parametric SCEVs.
11024 if (!containsParameters(Terms))
11028 dbgs() << "Terms:\n";
11029 for (const SCEV *T : Terms)
11030 dbgs() << *T << "\n";
11033 // Remove duplicates.
11034 array_pod_sort(Terms.begin(), Terms.end());
11035 Terms.erase(std::unique(Terms.begin(), Terms.end()), Terms.end());
11037 // Put larger terms first.
11038 llvm::sort(Terms, [](const SCEV *LHS, const SCEV *RHS) {
11039 return numberOfTerms(LHS) > numberOfTerms(RHS);
11042 // Try to divide all terms by the element size. If term is not divisible by
11043 // element size, proceed with the original term.
11044 for (const SCEV *&Term : Terms) {
11046 SCEVDivision::divide(*this, Term, ElementSize, &Q, &R);
11051 SmallVector<const SCEV *, 4> NewTerms;
11053 // Remove constant factors.
11054 for (const SCEV *T : Terms)
11055 if (const SCEV *NewT = removeConstantFactors(*this, T))
11056 NewTerms.push_back(NewT);
11059 dbgs() << "Terms after sorting:\n";
11060 for (const SCEV *T : NewTerms)
11061 dbgs() << *T << "\n";
11064 if (NewTerms.empty() || !findArrayDimensionsRec(*this, NewTerms, Sizes)) {
11069 // The last element to be pushed into Sizes is the size of an element.
11070 Sizes.push_back(ElementSize);
11073 dbgs() << "Sizes:\n";
11074 for (const SCEV *S : Sizes)
11075 dbgs() << *S << "\n";
11079 void ScalarEvolution::computeAccessFunctions(
11080 const SCEV *Expr, SmallVectorImpl<const SCEV *> &Subscripts,
11081 SmallVectorImpl<const SCEV *> &Sizes) {
11082 // Early exit in case this SCEV is not an affine multivariate function.
11086 if (auto *AR = dyn_cast<SCEVAddRecExpr>(Expr))
11087 if (!AR->isAffine())
11090 const SCEV *Res = Expr;
11091 int Last = Sizes.size() - 1;
11092 for (int i = Last; i >= 0; i--) {
11094 SCEVDivision::divide(*this, Res, Sizes[i], &Q, &R);
11097 dbgs() << "Res: " << *Res << "\n";
11098 dbgs() << "Sizes[i]: " << *Sizes[i] << "\n";
11099 dbgs() << "Res divided by Sizes[i]:\n";
11100 dbgs() << "Quotient: " << *Q << "\n";
11101 dbgs() << "Remainder: " << *R << "\n";
11106 // Do not record the last subscript corresponding to the size of elements in
11110 // Bail out if the remainder is too complex.
11111 if (isa<SCEVAddRecExpr>(R)) {
11112 Subscripts.clear();
11120 // Record the access function for the current subscript.
11121 Subscripts.push_back(R);
11124 // Also push in last position the remainder of the last division: it will be
11125 // the access function of the innermost dimension.
11126 Subscripts.push_back(Res);
11128 std::reverse(Subscripts.begin(), Subscripts.end());
11131 dbgs() << "Subscripts:\n";
11132 for (const SCEV *S : Subscripts)
11133 dbgs() << *S << "\n";
11137 /// Splits the SCEV into two vectors of SCEVs representing the subscripts and
11138 /// sizes of an array access. Returns the remainder of the delinearization that
11139 /// is the offset start of the array. The SCEV->delinearize algorithm computes
11140 /// the multiples of SCEV coefficients: that is a pattern matching of sub
11141 /// expressions in the stride and base of a SCEV corresponding to the
11142 /// computation of a GCD (greatest common divisor) of base and stride. When
11143 /// SCEV->delinearize fails, it returns the SCEV unchanged.
11145 /// For example: when analyzing the memory access A[i][j][k] in this loop nest
11147 /// void foo(long n, long m, long o, double A[n][m][o]) {
11149 /// for (long i = 0; i < n; i++)
11150 /// for (long j = 0; j < m; j++)
11151 /// for (long k = 0; k < o; k++)
11152 /// A[i][j][k] = 1.0;
11155 /// the delinearization input is the following AddRec SCEV:
11157 /// AddRec: {{{%A,+,(8 * %m * %o)}<%for.i>,+,(8 * %o)}<%for.j>,+,8}<%for.k>
11159 /// From this SCEV, we are able to say that the base offset of the access is %A
11160 /// because it appears as an offset that does not divide any of the strides in
11163 /// CHECK: Base offset: %A
11165 /// and then SCEV->delinearize determines the size of some of the dimensions of
11166 /// the array as these are the multiples by which the strides are happening:
11168 /// CHECK: ArrayDecl[UnknownSize][%m][%o] with elements of sizeof(double) bytes.
11170 /// Note that the outermost dimension remains of UnknownSize because there are
11171 /// no strides that would help identifying the size of the last dimension: when
11172 /// the array has been statically allocated, one could compute the size of that
11173 /// dimension by dividing the overall size of the array by the size of the known
11174 /// dimensions: %m * %o * 8.
11176 /// Finally delinearize provides the access functions for the array reference
11177 /// that does correspond to A[i][j][k] of the above C testcase:
11179 /// CHECK: ArrayRef[{0,+,1}<%for.i>][{0,+,1}<%for.j>][{0,+,1}<%for.k>]
11181 /// The testcases are checking the output of a function pass:
11182 /// DelinearizationPass that walks through all loads and stores of a function
11183 /// asking for the SCEV of the memory access with respect to all enclosing
11184 /// loops, calling SCEV->delinearize on that and printing the results.
11185 void ScalarEvolution::delinearize(const SCEV *Expr,
11186 SmallVectorImpl<const SCEV *> &Subscripts,
11187 SmallVectorImpl<const SCEV *> &Sizes,
11188 const SCEV *ElementSize) {
11189 // First step: collect parametric terms.
11190 SmallVector<const SCEV *, 4> Terms;
11191 collectParametricTerms(Expr, Terms);
11196 // Second step: find subscript sizes.
11197 findArrayDimensions(Terms, Sizes, ElementSize);
11202 // Third step: compute the access functions for each subscript.
11203 computeAccessFunctions(Expr, Subscripts, Sizes);
11205 if (Subscripts.empty())
11209 dbgs() << "succeeded to delinearize " << *Expr << "\n";
11210 dbgs() << "ArrayDecl[UnknownSize]";
11211 for (const SCEV *S : Sizes)
11212 dbgs() << "[" << *S << "]";
11214 dbgs() << "\nArrayRef";
11215 for (const SCEV *S : Subscripts)
11216 dbgs() << "[" << *S << "]";
11221 bool ScalarEvolution::getIndexExpressionsFromGEP(
11222 const GetElementPtrInst *GEP, SmallVectorImpl<const SCEV *> &Subscripts,
11223 SmallVectorImpl<int> &Sizes) {
11224 assert(Subscripts.empty() && Sizes.empty() &&
11225 "Expected output lists to be empty on entry to this function.");
11226 assert(GEP && "getIndexExpressionsFromGEP called with a null GEP");
11227 Type *Ty = GEP->getPointerOperandType();
11228 bool DroppedFirstDim = false;
11229 for (unsigned i = 1; i < GEP->getNumOperands(); i++) {
11230 const SCEV *Expr = getSCEV(GEP->getOperand(i));
11232 if (auto *PtrTy = dyn_cast<PointerType>(Ty)) {
11233 Ty = PtrTy->getElementType();
11234 } else if (auto *ArrayTy = dyn_cast<ArrayType>(Ty)) {
11235 Ty = ArrayTy->getElementType();
11237 Subscripts.clear();
11241 if (auto *Const = dyn_cast<SCEVConstant>(Expr))
11242 if (Const->getValue()->isZero()) {
11243 DroppedFirstDim = true;
11246 Subscripts.push_back(Expr);
11250 auto *ArrayTy = dyn_cast<ArrayType>(Ty);
11252 Subscripts.clear();
11257 Subscripts.push_back(Expr);
11258 if (!(DroppedFirstDim && i == 2))
11259 Sizes.push_back(ArrayTy->getNumElements());
11261 Ty = ArrayTy->getElementType();
11263 return !Subscripts.empty();
11266 //===----------------------------------------------------------------------===//
11267 // SCEVCallbackVH Class Implementation
11268 //===----------------------------------------------------------------------===//
11270 void ScalarEvolution::SCEVCallbackVH::deleted() {
11271 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
11272 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
11273 SE->ConstantEvolutionLoopExitValue.erase(PN);
11274 SE->eraseValueFromMap(getValPtr());
11275 // this now dangles!
11278 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) {
11279 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
11281 // Forget all the expressions associated with users of the old value,
11282 // so that future queries will recompute the expressions using the new
11284 Value *Old = getValPtr();
11285 SmallVector<User *, 16> Worklist(Old->user_begin(), Old->user_end());
11286 SmallPtrSet<User *, 8> Visited;
11287 while (!Worklist.empty()) {
11288 User *U = Worklist.pop_back_val();
11289 // Deleting the Old value will cause this to dangle. Postpone
11290 // that until everything else is done.
11293 if (!Visited.insert(U).second)
11295 if (PHINode *PN = dyn_cast<PHINode>(U))
11296 SE->ConstantEvolutionLoopExitValue.erase(PN);
11297 SE->eraseValueFromMap(U);
11298 Worklist.insert(Worklist.end(), U->user_begin(), U->user_end());
11300 // Delete the Old value.
11301 if (PHINode *PN = dyn_cast<PHINode>(Old))
11302 SE->ConstantEvolutionLoopExitValue.erase(PN);
11303 SE->eraseValueFromMap(Old);
11304 // this now dangles!
11307 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
11308 : CallbackVH(V), SE(se) {}
11310 //===----------------------------------------------------------------------===//
11311 // ScalarEvolution Class Implementation
11312 //===----------------------------------------------------------------------===//
11314 ScalarEvolution::ScalarEvolution(Function &F, TargetLibraryInfo &TLI,
11315 AssumptionCache &AC, DominatorTree &DT,
11317 : F(F), TLI(TLI), AC(AC), DT(DT), LI(LI),
11318 CouldNotCompute(new SCEVCouldNotCompute()), ValuesAtScopes(64),
11319 LoopDispositions(64), BlockDispositions(64) {
11320 // To use guards for proving predicates, we need to scan every instruction in
11321 // relevant basic blocks, and not just terminators. Doing this is a waste of
11322 // time if the IR does not actually contain any calls to
11323 // @llvm.experimental.guard, so do a quick check and remember this beforehand.
11325 // This pessimizes the case where a pass that preserves ScalarEvolution wants
11326 // to _add_ guards to the module when there weren't any before, and wants
11327 // ScalarEvolution to optimize based on those guards. For now we prefer to be
11328 // efficient in lieu of being smart in that rather obscure case.
11330 auto *GuardDecl = F.getParent()->getFunction(
11331 Intrinsic::getName(Intrinsic::experimental_guard));
11332 HasGuards = GuardDecl && !GuardDecl->use_empty();
11335 ScalarEvolution::ScalarEvolution(ScalarEvolution &&Arg)
11336 : F(Arg.F), HasGuards(Arg.HasGuards), TLI(Arg.TLI), AC(Arg.AC), DT(Arg.DT),
11337 LI(Arg.LI), CouldNotCompute(std::move(Arg.CouldNotCompute)),
11338 ValueExprMap(std::move(Arg.ValueExprMap)),
11339 PendingLoopPredicates(std::move(Arg.PendingLoopPredicates)),
11340 PendingPhiRanges(std::move(Arg.PendingPhiRanges)),
11341 PendingMerges(std::move(Arg.PendingMerges)),
11342 MinTrailingZerosCache(std::move(Arg.MinTrailingZerosCache)),
11343 BackedgeTakenCounts(std::move(Arg.BackedgeTakenCounts)),
11344 PredicatedBackedgeTakenCounts(
11345 std::move(Arg.PredicatedBackedgeTakenCounts)),
11346 ConstantEvolutionLoopExitValue(
11347 std::move(Arg.ConstantEvolutionLoopExitValue)),
11348 ValuesAtScopes(std::move(Arg.ValuesAtScopes)),
11349 LoopDispositions(std::move(Arg.LoopDispositions)),
11350 LoopPropertiesCache(std::move(Arg.LoopPropertiesCache)),
11351 BlockDispositions(std::move(Arg.BlockDispositions)),
11352 UnsignedRanges(std::move(Arg.UnsignedRanges)),
11353 SignedRanges(std::move(Arg.SignedRanges)),
11354 UniqueSCEVs(std::move(Arg.UniqueSCEVs)),
11355 UniquePreds(std::move(Arg.UniquePreds)),
11356 SCEVAllocator(std::move(Arg.SCEVAllocator)),
11357 LoopUsers(std::move(Arg.LoopUsers)),
11358 PredicatedSCEVRewrites(std::move(Arg.PredicatedSCEVRewrites)),
11359 FirstUnknown(Arg.FirstUnknown) {
11360 Arg.FirstUnknown = nullptr;
11363 ScalarEvolution::~ScalarEvolution() {
11364 // Iterate through all the SCEVUnknown instances and call their
11365 // destructors, so that they release their references to their values.
11366 for (SCEVUnknown *U = FirstUnknown; U;) {
11367 SCEVUnknown *Tmp = U;
11369 Tmp->~SCEVUnknown();
11371 FirstUnknown = nullptr;
11373 ExprValueMap.clear();
11374 ValueExprMap.clear();
11377 // Free any extra memory created for ExitNotTakenInfo in the unlikely event
11378 // that a loop had multiple computable exits.
11379 for (auto &BTCI : BackedgeTakenCounts)
11380 BTCI.second.clear();
11381 for (auto &BTCI : PredicatedBackedgeTakenCounts)
11382 BTCI.second.clear();
11384 assert(PendingLoopPredicates.empty() && "isImpliedCond garbage");
11385 assert(PendingPhiRanges.empty() && "getRangeRef garbage");
11386 assert(PendingMerges.empty() && "isImpliedViaMerge garbage");
11387 assert(!WalkingBEDominatingConds && "isLoopBackedgeGuardedByCond garbage!");
11388 assert(!ProvingSplitPredicate && "ProvingSplitPredicate garbage!");
11391 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
11392 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
11395 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
11397 // Print all inner loops first
11399 PrintLoopInfo(OS, SE, I);
11402 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
11405 SmallVector<BasicBlock *, 8> ExitingBlocks;
11406 L->getExitingBlocks(ExitingBlocks);
11407 if (ExitingBlocks.size() != 1)
11408 OS << "<multiple exits> ";
11410 if (SE->hasLoopInvariantBackedgeTakenCount(L))
11411 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L) << "\n";
11413 OS << "Unpredictable backedge-taken count.\n";
11415 if (ExitingBlocks.size() > 1)
11416 for (BasicBlock *ExitingBlock : ExitingBlocks) {
11417 OS << " exit count for " << ExitingBlock->getName() << ": "
11418 << *SE->getExitCount(L, ExitingBlock) << "\n";
11422 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
11425 if (!isa<SCEVCouldNotCompute>(SE->getConstantMaxBackedgeTakenCount(L))) {
11426 OS << "max backedge-taken count is " << *SE->getConstantMaxBackedgeTakenCount(L);
11427 if (SE->isBackedgeTakenCountMaxOrZero(L))
11428 OS << ", actual taken count either this or zero.";
11430 OS << "Unpredictable max backedge-taken count. ";
11435 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
11438 SCEVUnionPredicate Pred;
11439 auto PBT = SE->getPredicatedBackedgeTakenCount(L, Pred);
11440 if (!isa<SCEVCouldNotCompute>(PBT)) {
11441 OS << "Predicated backedge-taken count is " << *PBT << "\n";
11442 OS << " Predicates:\n";
11445 OS << "Unpredictable predicated backedge-taken count. ";
11449 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
11451 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
11453 OS << "Trip multiple is " << SE->getSmallConstantTripMultiple(L) << "\n";
11457 static StringRef loopDispositionToStr(ScalarEvolution::LoopDisposition LD) {
11459 case ScalarEvolution::LoopVariant:
11461 case ScalarEvolution::LoopInvariant:
11462 return "Invariant";
11463 case ScalarEvolution::LoopComputable:
11464 return "Computable";
11466 llvm_unreachable("Unknown ScalarEvolution::LoopDisposition kind!");
11469 void ScalarEvolution::print(raw_ostream &OS) const {
11470 // ScalarEvolution's implementation of the print method is to print
11471 // out SCEV values of all instructions that are interesting. Doing
11472 // this potentially causes it to create new SCEV objects though,
11473 // which technically conflicts with the const qualifier. This isn't
11474 // observable from outside the class though, so casting away the
11475 // const isn't dangerous.
11476 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
11478 if (ClassifyExpressions) {
11479 OS << "Classifying expressions for: ";
11480 F.printAsOperand(OS, /*PrintType=*/false);
11482 for (Instruction &I : instructions(F))
11483 if (isSCEVable(I.getType()) && !isa<CmpInst>(I)) {
11486 const SCEV *SV = SE.getSCEV(&I);
11488 if (!isa<SCEVCouldNotCompute>(SV)) {
11490 SE.getUnsignedRange(SV).print(OS);
11492 SE.getSignedRange(SV).print(OS);
11495 const Loop *L = LI.getLoopFor(I.getParent());
11497 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
11501 if (!isa<SCEVCouldNotCompute>(AtUse)) {
11503 SE.getUnsignedRange(AtUse).print(OS);
11505 SE.getSignedRange(AtUse).print(OS);
11510 OS << "\t\t" "Exits: ";
11511 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
11512 if (!SE.isLoopInvariant(ExitValue, L)) {
11513 OS << "<<Unknown>>";
11519 for (auto *Iter = L; Iter; Iter = Iter->getParentLoop()) {
11521 OS << "\t\t" "LoopDispositions: { ";
11527 Iter->getHeader()->printAsOperand(OS, /*PrintType=*/false);
11528 OS << ": " << loopDispositionToStr(SE.getLoopDisposition(SV, Iter));
11531 for (auto *InnerL : depth_first(L)) {
11535 OS << "\t\t" "LoopDispositions: { ";
11541 InnerL->getHeader()->printAsOperand(OS, /*PrintType=*/false);
11542 OS << ": " << loopDispositionToStr(SE.getLoopDisposition(SV, InnerL));
11552 OS << "Determining loop execution counts for: ";
11553 F.printAsOperand(OS, /*PrintType=*/false);
11556 PrintLoopInfo(OS, &SE, I);
11559 ScalarEvolution::LoopDisposition
11560 ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) {
11561 auto &Values = LoopDispositions[S];
11562 for (auto &V : Values) {
11563 if (V.getPointer() == L)
11566 Values.emplace_back(L, LoopVariant);
11567 LoopDisposition D = computeLoopDisposition(S, L);
11568 auto &Values2 = LoopDispositions[S];
11569 for (auto &V : make_range(Values2.rbegin(), Values2.rend())) {
11570 if (V.getPointer() == L) {
11578 ScalarEvolution::LoopDisposition
11579 ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) {
11580 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
11582 return LoopInvariant;
11586 return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L);
11587 case scAddRecExpr: {
11588 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
11590 // If L is the addrec's loop, it's computable.
11591 if (AR->getLoop() == L)
11592 return LoopComputable;
11594 // Add recurrences are never invariant in the function-body (null loop).
11596 return LoopVariant;
11598 // Everything that is not defined at loop entry is variant.
11599 if (DT.dominates(L->getHeader(), AR->getLoop()->getHeader()))
11600 return LoopVariant;
11601 assert(!L->contains(AR->getLoop()) && "Containing loop's header does not"
11602 " dominate the contained loop's header?");
11604 // This recurrence is invariant w.r.t. L if AR's loop contains L.
11605 if (AR->getLoop()->contains(L))
11606 return LoopInvariant;
11608 // This recurrence is variant w.r.t. L if any of its operands
11610 for (auto *Op : AR->operands())
11611 if (!isLoopInvariant(Op, L))
11612 return LoopVariant;
11614 // Otherwise it's loop-invariant.
11615 return LoopInvariant;
11623 bool HasVarying = false;
11624 for (auto *Op : cast<SCEVNAryExpr>(S)->operands()) {
11625 LoopDisposition D = getLoopDisposition(Op, L);
11626 if (D == LoopVariant)
11627 return LoopVariant;
11628 if (D == LoopComputable)
11631 return HasVarying ? LoopComputable : LoopInvariant;
11634 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
11635 LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L);
11636 if (LD == LoopVariant)
11637 return LoopVariant;
11638 LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L);
11639 if (RD == LoopVariant)
11640 return LoopVariant;
11641 return (LD == LoopInvariant && RD == LoopInvariant) ?
11642 LoopInvariant : LoopComputable;
11645 // All non-instruction values are loop invariant. All instructions are loop
11646 // invariant if they are not contained in the specified loop.
11647 // Instructions are never considered invariant in the function body
11648 // (null loop) because they are defined within the "loop".
11649 if (auto *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue()))
11650 return (L && !L->contains(I)) ? LoopInvariant : LoopVariant;
11651 return LoopInvariant;
11652 case scCouldNotCompute:
11653 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
11655 llvm_unreachable("Unknown SCEV kind!");
11658 bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) {
11659 return getLoopDisposition(S, L) == LoopInvariant;
11662 bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) {
11663 return getLoopDisposition(S, L) == LoopComputable;
11666 ScalarEvolution::BlockDisposition
11667 ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) {
11668 auto &Values = BlockDispositions[S];
11669 for (auto &V : Values) {
11670 if (V.getPointer() == BB)
11673 Values.emplace_back(BB, DoesNotDominateBlock);
11674 BlockDisposition D = computeBlockDisposition(S, BB);
11675 auto &Values2 = BlockDispositions[S];
11676 for (auto &V : make_range(Values2.rbegin(), Values2.rend())) {
11677 if (V.getPointer() == BB) {
11685 ScalarEvolution::BlockDisposition
11686 ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) {
11687 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
11689 return ProperlyDominatesBlock;
11693 return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB);
11694 case scAddRecExpr: {
11695 // This uses a "dominates" query instead of "properly dominates" query
11696 // to test for proper dominance too, because the instruction which
11697 // produces the addrec's value is a PHI, and a PHI effectively properly
11698 // dominates its entire containing block.
11699 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
11700 if (!DT.dominates(AR->getLoop()->getHeader(), BB))
11701 return DoesNotDominateBlock;
11703 // Fall through into SCEVNAryExpr handling.
11712 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
11713 bool Proper = true;
11714 for (const SCEV *NAryOp : NAry->operands()) {
11715 BlockDisposition D = getBlockDisposition(NAryOp, BB);
11716 if (D == DoesNotDominateBlock)
11717 return DoesNotDominateBlock;
11718 if (D == DominatesBlock)
11721 return Proper ? ProperlyDominatesBlock : DominatesBlock;
11724 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
11725 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
11726 BlockDisposition LD = getBlockDisposition(LHS, BB);
11727 if (LD == DoesNotDominateBlock)
11728 return DoesNotDominateBlock;
11729 BlockDisposition RD = getBlockDisposition(RHS, BB);
11730 if (RD == DoesNotDominateBlock)
11731 return DoesNotDominateBlock;
11732 return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ?
11733 ProperlyDominatesBlock : DominatesBlock;
11736 if (Instruction *I =
11737 dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) {
11738 if (I->getParent() == BB)
11739 return DominatesBlock;
11740 if (DT.properlyDominates(I->getParent(), BB))
11741 return ProperlyDominatesBlock;
11742 return DoesNotDominateBlock;
11744 return ProperlyDominatesBlock;
11745 case scCouldNotCompute:
11746 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
11748 llvm_unreachable("Unknown SCEV kind!");
11751 bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) {
11752 return getBlockDisposition(S, BB) >= DominatesBlock;
11755 bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) {
11756 return getBlockDisposition(S, BB) == ProperlyDominatesBlock;
11759 bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const {
11760 return SCEVExprContains(S, [&](const SCEV *Expr) { return Expr == Op; });
11763 bool ScalarEvolution::ExitLimit::hasOperand(const SCEV *S) const {
11764 auto IsS = [&](const SCEV *X) { return S == X; };
11765 auto ContainsS = [&](const SCEV *X) {
11766 return !isa<SCEVCouldNotCompute>(X) && SCEVExprContains(X, IsS);
11768 return ContainsS(ExactNotTaken) || ContainsS(MaxNotTaken);
11772 ScalarEvolution::forgetMemoizedResults(const SCEV *S) {
11773 ValuesAtScopes.erase(S);
11774 LoopDispositions.erase(S);
11775 BlockDispositions.erase(S);
11776 UnsignedRanges.erase(S);
11777 SignedRanges.erase(S);
11778 ExprValueMap.erase(S);
11779 HasRecMap.erase(S);
11780 MinTrailingZerosCache.erase(S);
11782 for (auto I = PredicatedSCEVRewrites.begin();
11783 I != PredicatedSCEVRewrites.end();) {
11784 std::pair<const SCEV *, const Loop *> Entry = I->first;
11785 if (Entry.first == S)
11786 PredicatedSCEVRewrites.erase(I++);
11791 auto RemoveSCEVFromBackedgeMap =
11792 [S, this](DenseMap<const Loop *, BackedgeTakenInfo> &Map) {
11793 for (auto I = Map.begin(), E = Map.end(); I != E;) {
11794 BackedgeTakenInfo &BEInfo = I->second;
11795 if (BEInfo.hasOperand(S, this)) {
11803 RemoveSCEVFromBackedgeMap(BackedgeTakenCounts);
11804 RemoveSCEVFromBackedgeMap(PredicatedBackedgeTakenCounts);
11808 ScalarEvolution::getUsedLoops(const SCEV *S,
11809 SmallPtrSetImpl<const Loop *> &LoopsUsed) {
11810 struct FindUsedLoops {
11811 FindUsedLoops(SmallPtrSetImpl<const Loop *> &LoopsUsed)
11812 : LoopsUsed(LoopsUsed) {}
11813 SmallPtrSetImpl<const Loop *> &LoopsUsed;
11814 bool follow(const SCEV *S) {
11815 if (auto *AR = dyn_cast<SCEVAddRecExpr>(S))
11816 LoopsUsed.insert(AR->getLoop());
11820 bool isDone() const { return false; }
11823 FindUsedLoops F(LoopsUsed);
11824 SCEVTraversal<FindUsedLoops>(F).visitAll(S);
11827 void ScalarEvolution::addToLoopUseLists(const SCEV *S) {
11828 SmallPtrSet<const Loop *, 8> LoopsUsed;
11829 getUsedLoops(S, LoopsUsed);
11830 for (auto *L : LoopsUsed)
11831 LoopUsers[L].push_back(S);
11834 void ScalarEvolution::verify() const {
11835 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
11836 ScalarEvolution SE2(F, TLI, AC, DT, LI);
11838 SmallVector<Loop *, 8> LoopStack(LI.begin(), LI.end());
11840 // Map's SCEV expressions from one ScalarEvolution "universe" to another.
11841 struct SCEVMapper : public SCEVRewriteVisitor<SCEVMapper> {
11842 SCEVMapper(ScalarEvolution &SE) : SCEVRewriteVisitor<SCEVMapper>(SE) {}
11844 const SCEV *visitConstant(const SCEVConstant *Constant) {
11845 return SE.getConstant(Constant->getAPInt());
11848 const SCEV *visitUnknown(const SCEVUnknown *Expr) {
11849 return SE.getUnknown(Expr->getValue());
11852 const SCEV *visitCouldNotCompute(const SCEVCouldNotCompute *Expr) {
11853 return SE.getCouldNotCompute();
11857 SCEVMapper SCM(SE2);
11859 while (!LoopStack.empty()) {
11860 auto *L = LoopStack.pop_back_val();
11861 LoopStack.insert(LoopStack.end(), L->begin(), L->end());
11863 auto *CurBECount = SCM.visit(
11864 const_cast<ScalarEvolution *>(this)->getBackedgeTakenCount(L));
11865 auto *NewBECount = SE2.getBackedgeTakenCount(L);
11867 if (CurBECount == SE2.getCouldNotCompute() ||
11868 NewBECount == SE2.getCouldNotCompute()) {
11869 // NB! This situation is legal, but is very suspicious -- whatever pass
11870 // change the loop to make a trip count go from could not compute to
11871 // computable or vice-versa *should have* invalidated SCEV. However, we
11872 // choose not to assert here (for now) since we don't want false
11877 if (containsUndefs(CurBECount) || containsUndefs(NewBECount)) {
11878 // SCEV treats "undef" as an unknown but consistent value (i.e. it does
11879 // not propagate undef aggressively). This means we can (and do) fail
11880 // verification in cases where a transform makes the trip count of a loop
11881 // go from "undef" to "undef+1" (say). The transform is fine, since in
11882 // both cases the loop iterates "undef" times, but SCEV thinks we
11883 // increased the trip count of the loop by 1 incorrectly.
11887 if (SE.getTypeSizeInBits(CurBECount->getType()) >
11888 SE.getTypeSizeInBits(NewBECount->getType()))
11889 NewBECount = SE2.getZeroExtendExpr(NewBECount, CurBECount->getType());
11890 else if (SE.getTypeSizeInBits(CurBECount->getType()) <
11891 SE.getTypeSizeInBits(NewBECount->getType()))
11892 CurBECount = SE2.getZeroExtendExpr(CurBECount, NewBECount->getType());
11894 const SCEV *Delta = SE2.getMinusSCEV(CurBECount, NewBECount);
11896 // Unless VerifySCEVStrict is set, we only compare constant deltas.
11897 if ((VerifySCEVStrict || isa<SCEVConstant>(Delta)) && !Delta->isZero()) {
11898 dbgs() << "Trip Count for " << *L << " Changed!\n";
11899 dbgs() << "Old: " << *CurBECount << "\n";
11900 dbgs() << "New: " << *NewBECount << "\n";
11901 dbgs() << "Delta: " << *Delta << "\n";
11907 bool ScalarEvolution::invalidate(
11908 Function &F, const PreservedAnalyses &PA,
11909 FunctionAnalysisManager::Invalidator &Inv) {
11910 // Invalidate the ScalarEvolution object whenever it isn't preserved or one
11911 // of its dependencies is invalidated.
11912 auto PAC = PA.getChecker<ScalarEvolutionAnalysis>();
11913 return !(PAC.preserved() || PAC.preservedSet<AllAnalysesOn<Function>>()) ||
11914 Inv.invalidate<AssumptionAnalysis>(F, PA) ||
11915 Inv.invalidate<DominatorTreeAnalysis>(F, PA) ||
11916 Inv.invalidate<LoopAnalysis>(F, PA);
11919 AnalysisKey ScalarEvolutionAnalysis::Key;
11921 ScalarEvolution ScalarEvolutionAnalysis::run(Function &F,
11922 FunctionAnalysisManager &AM) {
11923 return ScalarEvolution(F, AM.getResult<TargetLibraryAnalysis>(F),
11924 AM.getResult<AssumptionAnalysis>(F),
11925 AM.getResult<DominatorTreeAnalysis>(F),
11926 AM.getResult<LoopAnalysis>(F));
11930 ScalarEvolutionVerifierPass::run(Function &F, FunctionAnalysisManager &AM) {
11931 AM.getResult<ScalarEvolutionAnalysis>(F).verify();
11932 return PreservedAnalyses::all();
11936 ScalarEvolutionPrinterPass::run(Function &F, FunctionAnalysisManager &AM) {
11937 AM.getResult<ScalarEvolutionAnalysis>(F).print(OS);
11938 return PreservedAnalyses::all();
11941 INITIALIZE_PASS_BEGIN(ScalarEvolutionWrapperPass, "scalar-evolution",
11942 "Scalar Evolution Analysis", false, true)
11943 INITIALIZE_PASS_DEPENDENCY(AssumptionCacheTracker)
11944 INITIALIZE_PASS_DEPENDENCY(LoopInfoWrapperPass)
11945 INITIALIZE_PASS_DEPENDENCY(DominatorTreeWrapperPass)
11946 INITIALIZE_PASS_DEPENDENCY(TargetLibraryInfoWrapperPass)
11947 INITIALIZE_PASS_END(ScalarEvolutionWrapperPass, "scalar-evolution",
11948 "Scalar Evolution Analysis", false, true)
11950 char ScalarEvolutionWrapperPass::ID = 0;
11952 ScalarEvolutionWrapperPass::ScalarEvolutionWrapperPass() : FunctionPass(ID) {
11953 initializeScalarEvolutionWrapperPassPass(*PassRegistry::getPassRegistry());
11956 bool ScalarEvolutionWrapperPass::runOnFunction(Function &F) {
11957 SE.reset(new ScalarEvolution(
11958 F, getAnalysis<TargetLibraryInfoWrapperPass>().getTLI(F),
11959 getAnalysis<AssumptionCacheTracker>().getAssumptionCache(F),
11960 getAnalysis<DominatorTreeWrapperPass>().getDomTree(),
11961 getAnalysis<LoopInfoWrapperPass>().getLoopInfo()));
11965 void ScalarEvolutionWrapperPass::releaseMemory() { SE.reset(); }
11967 void ScalarEvolutionWrapperPass::print(raw_ostream &OS, const Module *) const {
11971 void ScalarEvolutionWrapperPass::verifyAnalysis() const {
11978 void ScalarEvolutionWrapperPass::getAnalysisUsage(AnalysisUsage &AU) const {
11979 AU.setPreservesAll();
11980 AU.addRequiredTransitive<AssumptionCacheTracker>();
11981 AU.addRequiredTransitive<LoopInfoWrapperPass>();
11982 AU.addRequiredTransitive<DominatorTreeWrapperPass>();
11983 AU.addRequiredTransitive<TargetLibraryInfoWrapperPass>();
11986 const SCEVPredicate *ScalarEvolution::getEqualPredicate(const SCEV *LHS,
11988 FoldingSetNodeID ID;
11989 assert(LHS->getType() == RHS->getType() &&
11990 "Type mismatch between LHS and RHS");
11991 // Unique this node based on the arguments
11992 ID.AddInteger(SCEVPredicate::P_Equal);
11993 ID.AddPointer(LHS);
11994 ID.AddPointer(RHS);
11995 void *IP = nullptr;
11996 if (const auto *S = UniquePreds.FindNodeOrInsertPos(ID, IP))
11998 SCEVEqualPredicate *Eq = new (SCEVAllocator)
11999 SCEVEqualPredicate(ID.Intern(SCEVAllocator), LHS, RHS);
12000 UniquePreds.InsertNode(Eq, IP);
12004 const SCEVPredicate *ScalarEvolution::getWrapPredicate(
12005 const SCEVAddRecExpr *AR,
12006 SCEVWrapPredicate::IncrementWrapFlags AddedFlags) {
12007 FoldingSetNodeID ID;
12008 // Unique this node based on the arguments
12009 ID.AddInteger(SCEVPredicate::P_Wrap);
12011 ID.AddInteger(AddedFlags);
12012 void *IP = nullptr;
12013 if (const auto *S = UniquePreds.FindNodeOrInsertPos(ID, IP))
12015 auto *OF = new (SCEVAllocator)
12016 SCEVWrapPredicate(ID.Intern(SCEVAllocator), AR, AddedFlags);
12017 UniquePreds.InsertNode(OF, IP);
12023 class SCEVPredicateRewriter : public SCEVRewriteVisitor<SCEVPredicateRewriter> {
12026 /// Rewrites \p S in the context of a loop L and the SCEV predication
12027 /// infrastructure.
12029 /// If \p Pred is non-null, the SCEV expression is rewritten to respect the
12030 /// equivalences present in \p Pred.
12032 /// If \p NewPreds is non-null, rewrite is free to add further predicates to
12033 /// \p NewPreds such that the result will be an AddRecExpr.
12034 static const SCEV *rewrite(const SCEV *S, const Loop *L, ScalarEvolution &SE,
12035 SmallPtrSetImpl<const SCEVPredicate *> *NewPreds,
12036 SCEVUnionPredicate *Pred) {
12037 SCEVPredicateRewriter Rewriter(L, SE, NewPreds, Pred);
12038 return Rewriter.visit(S);
12041 const SCEV *visitUnknown(const SCEVUnknown *Expr) {
12043 auto ExprPreds = Pred->getPredicatesForExpr(Expr);
12044 for (auto *Pred : ExprPreds)
12045 if (const auto *IPred = dyn_cast<SCEVEqualPredicate>(Pred))
12046 if (IPred->getLHS() == Expr)
12047 return IPred->getRHS();
12049 return convertToAddRecWithPreds(Expr);
12052 const SCEV *visitZeroExtendExpr(const SCEVZeroExtendExpr *Expr) {
12053 const SCEV *Operand = visit(Expr->getOperand());
12054 const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Operand);
12055 if (AR && AR->getLoop() == L && AR->isAffine()) {
12056 // This couldn't be folded because the operand didn't have the nuw
12057 // flag. Add the nusw flag as an assumption that we could make.
12058 const SCEV *Step = AR->getStepRecurrence(SE);
12059 Type *Ty = Expr->getType();
12060 if (addOverflowAssumption(AR, SCEVWrapPredicate::IncrementNUSW))
12061 return SE.getAddRecExpr(SE.getZeroExtendExpr(AR->getStart(), Ty),
12062 SE.getSignExtendExpr(Step, Ty), L,
12063 AR->getNoWrapFlags());
12065 return SE.getZeroExtendExpr(Operand, Expr->getType());
12068 const SCEV *visitSignExtendExpr(const SCEVSignExtendExpr *Expr) {
12069 const SCEV *Operand = visit(Expr->getOperand());
12070 const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Operand);
12071 if (AR && AR->getLoop() == L && AR->isAffine()) {
12072 // This couldn't be folded because the operand didn't have the nsw
12073 // flag. Add the nssw flag as an assumption that we could make.
12074 const SCEV *Step = AR->getStepRecurrence(SE);
12075 Type *Ty = Expr->getType();
12076 if (addOverflowAssumption(AR, SCEVWrapPredicate::IncrementNSSW))
12077 return SE.getAddRecExpr(SE.getSignExtendExpr(AR->getStart(), Ty),
12078 SE.getSignExtendExpr(Step, Ty), L,
12079 AR->getNoWrapFlags());
12081 return SE.getSignExtendExpr(Operand, Expr->getType());
12085 explicit SCEVPredicateRewriter(const Loop *L, ScalarEvolution &SE,
12086 SmallPtrSetImpl<const SCEVPredicate *> *NewPreds,
12087 SCEVUnionPredicate *Pred)
12088 : SCEVRewriteVisitor(SE), NewPreds(NewPreds), Pred(Pred), L(L) {}
12090 bool addOverflowAssumption(const SCEVPredicate *P) {
12092 // Check if we've already made this assumption.
12093 return Pred && Pred->implies(P);
12095 NewPreds->insert(P);
12099 bool addOverflowAssumption(const SCEVAddRecExpr *AR,
12100 SCEVWrapPredicate::IncrementWrapFlags AddedFlags) {
12101 auto *A = SE.getWrapPredicate(AR, AddedFlags);
12102 return addOverflowAssumption(A);
12105 // If \p Expr represents a PHINode, we try to see if it can be represented
12106 // as an AddRec, possibly under a predicate (PHISCEVPred). If it is possible
12107 // to add this predicate as a runtime overflow check, we return the AddRec.
12108 // If \p Expr does not meet these conditions (is not a PHI node, or we
12109 // couldn't create an AddRec for it, or couldn't add the predicate), we just
12111 const SCEV *convertToAddRecWithPreds(const SCEVUnknown *Expr) {
12112 if (!isa<PHINode>(Expr->getValue()))
12114 Optional<std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>>
12115 PredicatedRewrite = SE.createAddRecFromPHIWithCasts(Expr);
12116 if (!PredicatedRewrite)
12118 for (auto *P : PredicatedRewrite->second){
12119 // Wrap predicates from outer loops are not supported.
12120 if (auto *WP = dyn_cast<const SCEVWrapPredicate>(P)) {
12121 auto *AR = cast<const SCEVAddRecExpr>(WP->getExpr());
12122 if (L != AR->getLoop())
12125 if (!addOverflowAssumption(P))
12128 return PredicatedRewrite->first;
12131 SmallPtrSetImpl<const SCEVPredicate *> *NewPreds;
12132 SCEVUnionPredicate *Pred;
12136 } // end anonymous namespace
12138 const SCEV *ScalarEvolution::rewriteUsingPredicate(const SCEV *S, const Loop *L,
12139 SCEVUnionPredicate &Preds) {
12140 return SCEVPredicateRewriter::rewrite(S, L, *this, nullptr, &Preds);
12143 const SCEVAddRecExpr *ScalarEvolution::convertSCEVToAddRecWithPredicates(
12144 const SCEV *S, const Loop *L,
12145 SmallPtrSetImpl<const SCEVPredicate *> &Preds) {
12146 SmallPtrSet<const SCEVPredicate *, 4> TransformPreds;
12147 S = SCEVPredicateRewriter::rewrite(S, L, *this, &TransformPreds, nullptr);
12148 auto *AddRec = dyn_cast<SCEVAddRecExpr>(S);
12153 // Since the transformation was successful, we can now transfer the SCEV
12155 for (auto *P : TransformPreds)
12161 /// SCEV predicates
12162 SCEVPredicate::SCEVPredicate(const FoldingSetNodeIDRef ID,
12163 SCEVPredicateKind Kind)
12164 : FastID(ID), Kind(Kind) {}
12166 SCEVEqualPredicate::SCEVEqualPredicate(const FoldingSetNodeIDRef ID,
12167 const SCEV *LHS, const SCEV *RHS)
12168 : SCEVPredicate(ID, P_Equal), LHS(LHS), RHS(RHS) {
12169 assert(LHS->getType() == RHS->getType() && "LHS and RHS types don't match");
12170 assert(LHS != RHS && "LHS and RHS are the same SCEV");
12173 bool SCEVEqualPredicate::implies(const SCEVPredicate *N) const {
12174 const auto *Op = dyn_cast<SCEVEqualPredicate>(N);
12179 return Op->LHS == LHS && Op->RHS == RHS;
12182 bool SCEVEqualPredicate::isAlwaysTrue() const { return false; }
12184 const SCEV *SCEVEqualPredicate::getExpr() const { return LHS; }
12186 void SCEVEqualPredicate::print(raw_ostream &OS, unsigned Depth) const {
12187 OS.indent(Depth) << "Equal predicate: " << *LHS << " == " << *RHS << "\n";
12190 SCEVWrapPredicate::SCEVWrapPredicate(const FoldingSetNodeIDRef ID,
12191 const SCEVAddRecExpr *AR,
12192 IncrementWrapFlags Flags)
12193 : SCEVPredicate(ID, P_Wrap), AR(AR), Flags(Flags) {}
12195 const SCEV *SCEVWrapPredicate::getExpr() const { return AR; }
12197 bool SCEVWrapPredicate::implies(const SCEVPredicate *N) const {
12198 const auto *Op = dyn_cast<SCEVWrapPredicate>(N);
12200 return Op && Op->AR == AR && setFlags(Flags, Op->Flags) == Flags;
12203 bool SCEVWrapPredicate::isAlwaysTrue() const {
12204 SCEV::NoWrapFlags ScevFlags = AR->getNoWrapFlags();
12205 IncrementWrapFlags IFlags = Flags;
12207 if (ScalarEvolution::setFlags(ScevFlags, SCEV::FlagNSW) == ScevFlags)
12208 IFlags = clearFlags(IFlags, IncrementNSSW);
12210 return IFlags == IncrementAnyWrap;
12213 void SCEVWrapPredicate::print(raw_ostream &OS, unsigned Depth) const {
12214 OS.indent(Depth) << *getExpr() << " Added Flags: ";
12215 if (SCEVWrapPredicate::IncrementNUSW & getFlags())
12217 if (SCEVWrapPredicate::IncrementNSSW & getFlags())
12222 SCEVWrapPredicate::IncrementWrapFlags
12223 SCEVWrapPredicate::getImpliedFlags(const SCEVAddRecExpr *AR,
12224 ScalarEvolution &SE) {
12225 IncrementWrapFlags ImpliedFlags = IncrementAnyWrap;
12226 SCEV::NoWrapFlags StaticFlags = AR->getNoWrapFlags();
12228 // We can safely transfer the NSW flag as NSSW.
12229 if (ScalarEvolution::setFlags(StaticFlags, SCEV::FlagNSW) == StaticFlags)
12230 ImpliedFlags = IncrementNSSW;
12232 if (ScalarEvolution::setFlags(StaticFlags, SCEV::FlagNUW) == StaticFlags) {
12233 // If the increment is positive, the SCEV NUW flag will also imply the
12234 // WrapPredicate NUSW flag.
12235 if (const auto *Step = dyn_cast<SCEVConstant>(AR->getStepRecurrence(SE)))
12236 if (Step->getValue()->getValue().isNonNegative())
12237 ImpliedFlags = setFlags(ImpliedFlags, IncrementNUSW);
12240 return ImpliedFlags;
12243 /// Union predicates don't get cached so create a dummy set ID for it.
12244 SCEVUnionPredicate::SCEVUnionPredicate()
12245 : SCEVPredicate(FoldingSetNodeIDRef(nullptr, 0), P_Union) {}
12247 bool SCEVUnionPredicate::isAlwaysTrue() const {
12248 return all_of(Preds,
12249 [](const SCEVPredicate *I) { return I->isAlwaysTrue(); });
12252 ArrayRef<const SCEVPredicate *>
12253 SCEVUnionPredicate::getPredicatesForExpr(const SCEV *Expr) {
12254 auto I = SCEVToPreds.find(Expr);
12255 if (I == SCEVToPreds.end())
12256 return ArrayRef<const SCEVPredicate *>();
12260 bool SCEVUnionPredicate::implies(const SCEVPredicate *N) const {
12261 if (const auto *Set = dyn_cast<SCEVUnionPredicate>(N))
12262 return all_of(Set->Preds,
12263 [this](const SCEVPredicate *I) { return this->implies(I); });
12265 auto ScevPredsIt = SCEVToPreds.find(N->getExpr());
12266 if (ScevPredsIt == SCEVToPreds.end())
12268 auto &SCEVPreds = ScevPredsIt->second;
12270 return any_of(SCEVPreds,
12271 [N](const SCEVPredicate *I) { return I->implies(N); });
12274 const SCEV *SCEVUnionPredicate::getExpr() const { return nullptr; }
12276 void SCEVUnionPredicate::print(raw_ostream &OS, unsigned Depth) const {
12277 for (auto Pred : Preds)
12278 Pred->print(OS, Depth);
12281 void SCEVUnionPredicate::add(const SCEVPredicate *N) {
12282 if (const auto *Set = dyn_cast<SCEVUnionPredicate>(N)) {
12283 for (auto Pred : Set->Preds)
12291 const SCEV *Key = N->getExpr();
12292 assert(Key && "Only SCEVUnionPredicate doesn't have an "
12293 " associated expression!");
12295 SCEVToPreds[Key].push_back(N);
12296 Preds.push_back(N);
12299 PredicatedScalarEvolution::PredicatedScalarEvolution(ScalarEvolution &SE,
12303 const SCEV *PredicatedScalarEvolution::getSCEV(Value *V) {
12304 const SCEV *Expr = SE.getSCEV(V);
12305 RewriteEntry &Entry = RewriteMap[Expr];
12307 // If we already have an entry and the version matches, return it.
12308 if (Entry.second && Generation == Entry.first)
12309 return Entry.second;
12311 // We found an entry but it's stale. Rewrite the stale entry
12312 // according to the current predicate.
12314 Expr = Entry.second;
12316 const SCEV *NewSCEV = SE.rewriteUsingPredicate(Expr, &L, Preds);
12317 Entry = {Generation, NewSCEV};
12322 const SCEV *PredicatedScalarEvolution::getBackedgeTakenCount() {
12323 if (!BackedgeCount) {
12324 SCEVUnionPredicate BackedgePred;
12325 BackedgeCount = SE.getPredicatedBackedgeTakenCount(&L, BackedgePred);
12326 addPredicate(BackedgePred);
12328 return BackedgeCount;
12331 void PredicatedScalarEvolution::addPredicate(const SCEVPredicate &Pred) {
12332 if (Preds.implies(&Pred))
12335 updateGeneration();
12338 const SCEVUnionPredicate &PredicatedScalarEvolution::getUnionPredicate() const {
12342 void PredicatedScalarEvolution::updateGeneration() {
12343 // If the generation number wrapped recompute everything.
12344 if (++Generation == 0) {
12345 for (auto &II : RewriteMap) {
12346 const SCEV *Rewritten = II.second.second;
12347 II.second = {Generation, SE.rewriteUsingPredicate(Rewritten, &L, Preds)};
12352 void PredicatedScalarEvolution::setNoOverflow(
12353 Value *V, SCEVWrapPredicate::IncrementWrapFlags Flags) {
12354 const SCEV *Expr = getSCEV(V);
12355 const auto *AR = cast<SCEVAddRecExpr>(Expr);
12357 auto ImpliedFlags = SCEVWrapPredicate::getImpliedFlags(AR, SE);
12359 // Clear the statically implied flags.
12360 Flags = SCEVWrapPredicate::clearFlags(Flags, ImpliedFlags);
12361 addPredicate(*SE.getWrapPredicate(AR, Flags));
12363 auto II = FlagsMap.insert({V, Flags});
12365 II.first->second = SCEVWrapPredicate::setFlags(Flags, II.first->second);
12368 bool PredicatedScalarEvolution::hasNoOverflow(
12369 Value *V, SCEVWrapPredicate::IncrementWrapFlags Flags) {
12370 const SCEV *Expr = getSCEV(V);
12371 const auto *AR = cast<SCEVAddRecExpr>(Expr);
12373 Flags = SCEVWrapPredicate::clearFlags(
12374 Flags, SCEVWrapPredicate::getImpliedFlags(AR, SE));
12376 auto II = FlagsMap.find(V);
12378 if (II != FlagsMap.end())
12379 Flags = SCEVWrapPredicate::clearFlags(Flags, II->second);
12381 return Flags == SCEVWrapPredicate::IncrementAnyWrap;
12384 const SCEVAddRecExpr *PredicatedScalarEvolution::getAsAddRec(Value *V) {
12385 const SCEV *Expr = this->getSCEV(V);
12386 SmallPtrSet<const SCEVPredicate *, 4> NewPreds;
12387 auto *New = SE.convertSCEVToAddRecWithPredicates(Expr, &L, NewPreds);
12392 for (auto *P : NewPreds)
12395 updateGeneration();
12396 RewriteMap[SE.getSCEV(V)] = {Generation, New};
12400 PredicatedScalarEvolution::PredicatedScalarEvolution(
12401 const PredicatedScalarEvolution &Init)
12402 : RewriteMap(Init.RewriteMap), SE(Init.SE), L(Init.L), Preds(Init.Preds),
12403 Generation(Init.Generation), BackedgeCount(Init.BackedgeCount) {
12404 for (auto I : Init.FlagsMap)
12405 FlagsMap.insert(I);
12408 void PredicatedScalarEvolution::print(raw_ostream &OS, unsigned Depth) const {
12410 for (auto *BB : L.getBlocks())
12411 for (auto &I : *BB) {
12412 if (!SE.isSCEVable(I.getType()))
12415 auto *Expr = SE.getSCEV(&I);
12416 auto II = RewriteMap.find(Expr);
12418 if (II == RewriteMap.end())
12421 // Don't print things that are not interesting.
12422 if (II->second.second == Expr)
12425 OS.indent(Depth) << "[PSE]" << I << ":\n";
12426 OS.indent(Depth + 2) << *Expr << "\n";
12427 OS.indent(Depth + 2) << "--> " << *II->second.second << "\n";
12431 // Match the mathematical pattern A - (A / B) * B, where A and B can be
12432 // arbitrary expressions.
12433 // It's not always easy, as A and B can be folded (imagine A is X / 2, and B is
12434 // 4, A / B becomes X / 8).
12435 bool ScalarEvolution::matchURem(const SCEV *Expr, const SCEV *&LHS,
12436 const SCEV *&RHS) {
12437 const auto *Add = dyn_cast<SCEVAddExpr>(Expr);
12438 if (Add == nullptr || Add->getNumOperands() != 2)
12441 const SCEV *A = Add->getOperand(1);
12442 const auto *Mul = dyn_cast<SCEVMulExpr>(Add->getOperand(0));
12444 if (Mul == nullptr)
12447 const auto MatchURemWithDivisor = [&](const SCEV *B) {
12448 // (SomeExpr + (-(SomeExpr / B) * B)).
12449 if (Expr == getURemExpr(A, B)) {
12457 // (SomeExpr + (-1 * (SomeExpr / B) * B)).
12458 if (Mul->getNumOperands() == 3 && isa<SCEVConstant>(Mul->getOperand(0)))
12459 return MatchURemWithDivisor(Mul->getOperand(1)) ||
12460 MatchURemWithDivisor(Mul->getOperand(2));
12462 // (SomeExpr + ((-SomeExpr / B) * B)) or (SomeExpr + ((SomeExpr / B) * -B)).
12463 if (Mul->getNumOperands() == 2)
12464 return MatchURemWithDivisor(Mul->getOperand(1)) ||
12465 MatchURemWithDivisor(Mul->getOperand(0)) ||
12466 MatchURemWithDivisor(getNegativeSCEV(Mul->getOperand(1))) ||
12467 MatchURemWithDivisor(getNegativeSCEV(Mul->getOperand(0)));