1 //===- ScalarEvolution.cpp - Scalar Evolution Analysis --------------------===//
3 // The LLVM Compiler Infrastructure
5 // This file is distributed under the University of Illinois Open Source
6 // License. See LICENSE.TXT for details.
8 //===----------------------------------------------------------------------===//
10 // This file contains the implementation of the scalar evolution analysis
11 // engine, which is used primarily to analyze expressions involving induction
12 // variables in loops.
14 // There are several aspects to this library. First is the representation of
15 // scalar expressions, which are represented as subclasses of the SCEV class.
16 // These classes are used to represent certain types of subexpressions that we
17 // can handle. We only create one SCEV of a particular shape, so
18 // pointer-comparisons for equality are legal.
20 // One important aspect of the SCEV objects is that they are never cyclic, even
21 // if there is a cycle in the dataflow for an expression (ie, a PHI node). If
22 // the PHI node is one of the idioms that we can represent (e.g., a polynomial
23 // recurrence) then we represent it directly as a recurrence node, otherwise we
24 // represent it as a SCEVUnknown node.
26 // In addition to being able to represent expressions of various types, we also
27 // have folders that are used to build the *canonical* representation for a
28 // particular expression. These folders are capable of using a variety of
29 // rewrite rules to simplify the expressions.
31 // Once the folders are defined, we can implement the more interesting
32 // higher-level code, such as the code that recognizes PHI nodes of various
33 // types, computes the execution count of a loop, etc.
35 // TODO: We should use these routines and value representations to implement
36 // dependence analysis!
38 //===----------------------------------------------------------------------===//
40 // There are several good references for the techniques used in this analysis.
42 // Chains of recurrences -- a method to expedite the evaluation
43 // of closed-form functions
44 // Olaf Bachmann, Paul S. Wang, Eugene V. Zima
46 // On computational properties of chains of recurrences
49 // Symbolic Evaluation of Chains of Recurrences for Loop Optimization
50 // Robert A. van Engelen
52 // Efficient Symbolic Analysis for Optimizing Compilers
53 // Robert A. van Engelen
55 // Using the chains of recurrences algebra for data dependence testing and
56 // induction variable substitution
57 // MS Thesis, Johnie Birch
59 //===----------------------------------------------------------------------===//
61 #include "llvm/Analysis/ScalarEvolution.h"
62 #include "llvm/ADT/Optional.h"
63 #include "llvm/ADT/STLExtras.h"
64 #include "llvm/ADT/ScopeExit.h"
65 #include "llvm/ADT/Sequence.h"
66 #include "llvm/ADT/SmallPtrSet.h"
67 #include "llvm/ADT/Statistic.h"
68 #include "llvm/Analysis/AssumptionCache.h"
69 #include "llvm/Analysis/ConstantFolding.h"
70 #include "llvm/Analysis/InstructionSimplify.h"
71 #include "llvm/Analysis/LoopInfo.h"
72 #include "llvm/Analysis/ScalarEvolutionExpressions.h"
73 #include "llvm/Analysis/TargetLibraryInfo.h"
74 #include "llvm/Analysis/ValueTracking.h"
75 #include "llvm/IR/ConstantRange.h"
76 #include "llvm/IR/Constants.h"
77 #include "llvm/IR/DataLayout.h"
78 #include "llvm/IR/DerivedTypes.h"
79 #include "llvm/IR/Dominators.h"
80 #include "llvm/IR/GetElementPtrTypeIterator.h"
81 #include "llvm/IR/GlobalAlias.h"
82 #include "llvm/IR/GlobalVariable.h"
83 #include "llvm/IR/InstIterator.h"
84 #include "llvm/IR/Instructions.h"
85 #include "llvm/IR/LLVMContext.h"
86 #include "llvm/IR/Metadata.h"
87 #include "llvm/IR/Operator.h"
88 #include "llvm/IR/PatternMatch.h"
89 #include "llvm/Support/CommandLine.h"
90 #include "llvm/Support/Debug.h"
91 #include "llvm/Support/ErrorHandling.h"
92 #include "llvm/Support/MathExtras.h"
93 #include "llvm/Support/raw_ostream.h"
94 #include "llvm/Support/SaveAndRestore.h"
98 #define DEBUG_TYPE "scalar-evolution"
100 STATISTIC(NumArrayLenItCounts,
101 "Number of trip counts computed with array length");
102 STATISTIC(NumTripCountsComputed,
103 "Number of loops with predictable loop counts");
104 STATISTIC(NumTripCountsNotComputed,
105 "Number of loops without predictable loop counts");
106 STATISTIC(NumBruteForceTripCountsComputed,
107 "Number of loops with trip counts computed by force");
109 static cl::opt<unsigned>
110 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
111 cl::desc("Maximum number of iterations SCEV will "
112 "symbolically execute a constant "
116 // FIXME: Enable this with EXPENSIVE_CHECKS when the test suite is clean.
118 VerifySCEV("verify-scev",
119 cl::desc("Verify ScalarEvolution's backedge taken counts (slow)"));
121 VerifySCEVMap("verify-scev-maps",
122 cl::desc("Verify no dangling value in ScalarEvolution's "
123 "ExprValueMap (slow)"));
125 static cl::opt<unsigned> MulOpsInlineThreshold(
126 "scev-mulops-inline-threshold", cl::Hidden,
127 cl::desc("Threshold for inlining multiplication operands into a SCEV"),
130 static cl::opt<unsigned>
131 MaxCompareDepth("scalar-evolution-max-compare-depth", cl::Hidden,
132 cl::desc("Maximum depth of recursive compare complexity"),
135 //===----------------------------------------------------------------------===//
136 // SCEV class definitions
137 //===----------------------------------------------------------------------===//
139 //===----------------------------------------------------------------------===//
140 // Implementation of the SCEV class.
144 void SCEV::dump() const {
149 void SCEV::print(raw_ostream &OS) const {
150 switch (static_cast<SCEVTypes>(getSCEVType())) {
152 cast<SCEVConstant>(this)->getValue()->printAsOperand(OS, false);
155 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(this);
156 const SCEV *Op = Trunc->getOperand();
157 OS << "(trunc " << *Op->getType() << " " << *Op << " to "
158 << *Trunc->getType() << ")";
162 const SCEVZeroExtendExpr *ZExt = cast<SCEVZeroExtendExpr>(this);
163 const SCEV *Op = ZExt->getOperand();
164 OS << "(zext " << *Op->getType() << " " << *Op << " to "
165 << *ZExt->getType() << ")";
169 const SCEVSignExtendExpr *SExt = cast<SCEVSignExtendExpr>(this);
170 const SCEV *Op = SExt->getOperand();
171 OS << "(sext " << *Op->getType() << " " << *Op << " to "
172 << *SExt->getType() << ")";
176 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(this);
177 OS << "{" << *AR->getOperand(0);
178 for (unsigned i = 1, e = AR->getNumOperands(); i != e; ++i)
179 OS << ",+," << *AR->getOperand(i);
181 if (AR->hasNoUnsignedWrap())
183 if (AR->hasNoSignedWrap())
185 if (AR->hasNoSelfWrap() &&
186 !AR->getNoWrapFlags((NoWrapFlags)(FlagNUW | FlagNSW)))
188 AR->getLoop()->getHeader()->printAsOperand(OS, /*PrintType=*/false);
196 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(this);
197 const char *OpStr = nullptr;
198 switch (NAry->getSCEVType()) {
199 case scAddExpr: OpStr = " + "; break;
200 case scMulExpr: OpStr = " * "; break;
201 case scUMaxExpr: OpStr = " umax "; break;
202 case scSMaxExpr: OpStr = " smax "; break;
205 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
208 if (std::next(I) != E)
212 switch (NAry->getSCEVType()) {
215 if (NAry->hasNoUnsignedWrap())
217 if (NAry->hasNoSignedWrap())
223 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(this);
224 OS << "(" << *UDiv->getLHS() << " /u " << *UDiv->getRHS() << ")";
228 const SCEVUnknown *U = cast<SCEVUnknown>(this);
230 if (U->isSizeOf(AllocTy)) {
231 OS << "sizeof(" << *AllocTy << ")";
234 if (U->isAlignOf(AllocTy)) {
235 OS << "alignof(" << *AllocTy << ")";
241 if (U->isOffsetOf(CTy, FieldNo)) {
242 OS << "offsetof(" << *CTy << ", ";
243 FieldNo->printAsOperand(OS, false);
248 // Otherwise just print it normally.
249 U->getValue()->printAsOperand(OS, false);
252 case scCouldNotCompute:
253 OS << "***COULDNOTCOMPUTE***";
256 llvm_unreachable("Unknown SCEV kind!");
259 Type *SCEV::getType() const {
260 switch (static_cast<SCEVTypes>(getSCEVType())) {
262 return cast<SCEVConstant>(this)->getType();
266 return cast<SCEVCastExpr>(this)->getType();
271 return cast<SCEVNAryExpr>(this)->getType();
273 return cast<SCEVAddExpr>(this)->getType();
275 return cast<SCEVUDivExpr>(this)->getType();
277 return cast<SCEVUnknown>(this)->getType();
278 case scCouldNotCompute:
279 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
281 llvm_unreachable("Unknown SCEV kind!");
284 bool SCEV::isZero() const {
285 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
286 return SC->getValue()->isZero();
290 bool SCEV::isOne() const {
291 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
292 return SC->getValue()->isOne();
296 bool SCEV::isAllOnesValue() const {
297 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
298 return SC->getValue()->isAllOnesValue();
302 bool SCEV::isNonConstantNegative() const {
303 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(this);
304 if (!Mul) return false;
306 // If there is a constant factor, it will be first.
307 const SCEVConstant *SC = dyn_cast<SCEVConstant>(Mul->getOperand(0));
308 if (!SC) return false;
310 // Return true if the value is negative, this matches things like (-42 * V).
311 return SC->getAPInt().isNegative();
314 SCEVCouldNotCompute::SCEVCouldNotCompute() :
315 SCEV(FoldingSetNodeIDRef(), scCouldNotCompute) {}
317 bool SCEVCouldNotCompute::classof(const SCEV *S) {
318 return S->getSCEVType() == scCouldNotCompute;
321 const SCEV *ScalarEvolution::getConstant(ConstantInt *V) {
323 ID.AddInteger(scConstant);
326 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
327 SCEV *S = new (SCEVAllocator) SCEVConstant(ID.Intern(SCEVAllocator), V);
328 UniqueSCEVs.InsertNode(S, IP);
332 const SCEV *ScalarEvolution::getConstant(const APInt &Val) {
333 return getConstant(ConstantInt::get(getContext(), Val));
337 ScalarEvolution::getConstant(Type *Ty, uint64_t V, bool isSigned) {
338 IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty));
339 return getConstant(ConstantInt::get(ITy, V, isSigned));
342 SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID,
343 unsigned SCEVTy, const SCEV *op, Type *ty)
344 : SCEV(ID, SCEVTy), Op(op), Ty(ty) {}
346 SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID,
347 const SCEV *op, Type *ty)
348 : SCEVCastExpr(ID, scTruncate, op, ty) {
349 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
350 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
351 "Cannot truncate non-integer value!");
354 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID,
355 const SCEV *op, Type *ty)
356 : SCEVCastExpr(ID, scZeroExtend, op, ty) {
357 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
358 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
359 "Cannot zero extend non-integer value!");
362 SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID,
363 const SCEV *op, Type *ty)
364 : SCEVCastExpr(ID, scSignExtend, op, ty) {
365 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
366 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
367 "Cannot sign extend non-integer value!");
370 void SCEVUnknown::deleted() {
371 // Clear this SCEVUnknown from various maps.
372 SE->forgetMemoizedResults(this);
374 // Remove this SCEVUnknown from the uniquing map.
375 SE->UniqueSCEVs.RemoveNode(this);
377 // Release the value.
381 void SCEVUnknown::allUsesReplacedWith(Value *New) {
382 // Clear this SCEVUnknown from various maps.
383 SE->forgetMemoizedResults(this);
385 // Remove this SCEVUnknown from the uniquing map.
386 SE->UniqueSCEVs.RemoveNode(this);
388 // Update this SCEVUnknown to point to the new value. This is needed
389 // because there may still be outstanding SCEVs which still point to
394 bool SCEVUnknown::isSizeOf(Type *&AllocTy) const {
395 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
396 if (VCE->getOpcode() == Instruction::PtrToInt)
397 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
398 if (CE->getOpcode() == Instruction::GetElementPtr &&
399 CE->getOperand(0)->isNullValue() &&
400 CE->getNumOperands() == 2)
401 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1)))
403 AllocTy = cast<PointerType>(CE->getOperand(0)->getType())
411 bool SCEVUnknown::isAlignOf(Type *&AllocTy) const {
412 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
413 if (VCE->getOpcode() == Instruction::PtrToInt)
414 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
415 if (CE->getOpcode() == Instruction::GetElementPtr &&
416 CE->getOperand(0)->isNullValue()) {
418 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
419 if (StructType *STy = dyn_cast<StructType>(Ty))
420 if (!STy->isPacked() &&
421 CE->getNumOperands() == 3 &&
422 CE->getOperand(1)->isNullValue()) {
423 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2)))
425 STy->getNumElements() == 2 &&
426 STy->getElementType(0)->isIntegerTy(1)) {
427 AllocTy = STy->getElementType(1);
436 bool SCEVUnknown::isOffsetOf(Type *&CTy, Constant *&FieldNo) const {
437 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
438 if (VCE->getOpcode() == Instruction::PtrToInt)
439 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
440 if (CE->getOpcode() == Instruction::GetElementPtr &&
441 CE->getNumOperands() == 3 &&
442 CE->getOperand(0)->isNullValue() &&
443 CE->getOperand(1)->isNullValue()) {
445 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
446 // Ignore vector types here so that ScalarEvolutionExpander doesn't
447 // emit getelementptrs that index into vectors.
448 if (Ty->isStructTy() || Ty->isArrayTy()) {
450 FieldNo = CE->getOperand(2);
458 //===----------------------------------------------------------------------===//
460 //===----------------------------------------------------------------------===//
462 /// Compare the two values \p LV and \p RV in terms of their "complexity" where
463 /// "complexity" is a partial (and somewhat ad-hoc) relation used to order
464 /// operands in SCEV expressions. \p EqCache is a set of pairs of values that
465 /// have been previously deemed to be "equally complex" by this routine. It is
466 /// intended to avoid exponential time complexity in cases like:
476 /// CompareValueComplexity(%f, %c)
478 /// Since we do not continue running this routine on expression trees once we
479 /// have seen unequal values, there is no need to track them in the cache.
481 CompareValueComplexity(SmallSet<std::pair<Value *, Value *>, 8> &EqCache,
482 const LoopInfo *const LI, Value *LV, Value *RV,
484 if (Depth > MaxCompareDepth || EqCache.count({LV, RV}))
487 // Order pointer values after integer values. This helps SCEVExpander form
489 bool LIsPointer = LV->getType()->isPointerTy(),
490 RIsPointer = RV->getType()->isPointerTy();
491 if (LIsPointer != RIsPointer)
492 return (int)LIsPointer - (int)RIsPointer;
494 // Compare getValueID values.
495 unsigned LID = LV->getValueID(), RID = RV->getValueID();
497 return (int)LID - (int)RID;
499 // Sort arguments by their position.
500 if (const auto *LA = dyn_cast<Argument>(LV)) {
501 const auto *RA = cast<Argument>(RV);
502 unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo();
503 return (int)LArgNo - (int)RArgNo;
506 if (const auto *LGV = dyn_cast<GlobalValue>(LV)) {
507 const auto *RGV = cast<GlobalValue>(RV);
509 const auto IsGVNameSemantic = [&](const GlobalValue *GV) {
510 auto LT = GV->getLinkage();
511 return !(GlobalValue::isPrivateLinkage(LT) ||
512 GlobalValue::isInternalLinkage(LT));
515 // Use the names to distinguish the two values, but only if the
516 // names are semantically important.
517 if (IsGVNameSemantic(LGV) && IsGVNameSemantic(RGV))
518 return LGV->getName().compare(RGV->getName());
521 // For instructions, compare their loop depth, and their operand count. This
523 if (const auto *LInst = dyn_cast<Instruction>(LV)) {
524 const auto *RInst = cast<Instruction>(RV);
526 // Compare loop depths.
527 const BasicBlock *LParent = LInst->getParent(),
528 *RParent = RInst->getParent();
529 if (LParent != RParent) {
530 unsigned LDepth = LI->getLoopDepth(LParent),
531 RDepth = LI->getLoopDepth(RParent);
532 if (LDepth != RDepth)
533 return (int)LDepth - (int)RDepth;
536 // Compare the number of operands.
537 unsigned LNumOps = LInst->getNumOperands(),
538 RNumOps = RInst->getNumOperands();
539 if (LNumOps != RNumOps)
540 return (int)LNumOps - (int)RNumOps;
542 for (unsigned Idx : seq(0u, LNumOps)) {
544 CompareValueComplexity(EqCache, LI, LInst->getOperand(Idx),
545 RInst->getOperand(Idx), Depth + 1);
551 EqCache.insert({LV, RV});
555 // Return negative, zero, or positive, if LHS is less than, equal to, or greater
556 // than RHS, respectively. A three-way result allows recursive comparisons to be
558 static int CompareSCEVComplexity(
559 SmallSet<std::pair<const SCEV *, const SCEV *>, 8> &EqCacheSCEV,
560 const LoopInfo *const LI, const SCEV *LHS, const SCEV *RHS,
561 unsigned Depth = 0) {
562 // Fast-path: SCEVs are uniqued so we can do a quick equality check.
566 // Primarily, sort the SCEVs by their getSCEVType().
567 unsigned LType = LHS->getSCEVType(), RType = RHS->getSCEVType();
569 return (int)LType - (int)RType;
571 if (Depth > MaxCompareDepth || EqCacheSCEV.count({LHS, RHS}))
573 // Aside from the getSCEVType() ordering, the particular ordering
574 // isn't very important except that it's beneficial to be consistent,
575 // so that (a + b) and (b + a) don't end up as different expressions.
576 switch (static_cast<SCEVTypes>(LType)) {
578 const SCEVUnknown *LU = cast<SCEVUnknown>(LHS);
579 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
581 SmallSet<std::pair<Value *, Value *>, 8> EqCache;
582 int X = CompareValueComplexity(EqCache, LI, LU->getValue(), RU->getValue(),
585 EqCacheSCEV.insert({LHS, RHS});
590 const SCEVConstant *LC = cast<SCEVConstant>(LHS);
591 const SCEVConstant *RC = cast<SCEVConstant>(RHS);
593 // Compare constant values.
594 const APInt &LA = LC->getAPInt();
595 const APInt &RA = RC->getAPInt();
596 unsigned LBitWidth = LA.getBitWidth(), RBitWidth = RA.getBitWidth();
597 if (LBitWidth != RBitWidth)
598 return (int)LBitWidth - (int)RBitWidth;
599 return LA.ult(RA) ? -1 : 1;
603 const SCEVAddRecExpr *LA = cast<SCEVAddRecExpr>(LHS);
604 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS);
606 // Compare addrec loop depths.
607 const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop();
608 if (LLoop != RLoop) {
609 unsigned LDepth = LLoop->getLoopDepth(), RDepth = RLoop->getLoopDepth();
610 if (LDepth != RDepth)
611 return (int)LDepth - (int)RDepth;
614 // Addrec complexity grows with operand count.
615 unsigned LNumOps = LA->getNumOperands(), RNumOps = RA->getNumOperands();
616 if (LNumOps != RNumOps)
617 return (int)LNumOps - (int)RNumOps;
619 // Lexicographically compare.
620 for (unsigned i = 0; i != LNumOps; ++i) {
621 int X = CompareSCEVComplexity(EqCacheSCEV, LI, LA->getOperand(i),
622 RA->getOperand(i), Depth + 1);
626 EqCacheSCEV.insert({LHS, RHS});
634 const SCEVNAryExpr *LC = cast<SCEVNAryExpr>(LHS);
635 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
637 // Lexicographically compare n-ary expressions.
638 unsigned LNumOps = LC->getNumOperands(), RNumOps = RC->getNumOperands();
639 if (LNumOps != RNumOps)
640 return (int)LNumOps - (int)RNumOps;
642 for (unsigned i = 0; i != LNumOps; ++i) {
645 int X = CompareSCEVComplexity(EqCacheSCEV, LI, LC->getOperand(i),
646 RC->getOperand(i), Depth + 1);
650 EqCacheSCEV.insert({LHS, RHS});
655 const SCEVUDivExpr *LC = cast<SCEVUDivExpr>(LHS);
656 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
658 // Lexicographically compare udiv expressions.
659 int X = CompareSCEVComplexity(EqCacheSCEV, LI, LC->getLHS(), RC->getLHS(),
663 X = CompareSCEVComplexity(EqCacheSCEV, LI, LC->getRHS(), RC->getRHS(),
666 EqCacheSCEV.insert({LHS, RHS});
673 const SCEVCastExpr *LC = cast<SCEVCastExpr>(LHS);
674 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
676 // Compare cast expressions by operand.
677 int X = CompareSCEVComplexity(EqCacheSCEV, LI, LC->getOperand(),
678 RC->getOperand(), Depth + 1);
680 EqCacheSCEV.insert({LHS, RHS});
684 case scCouldNotCompute:
685 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
687 llvm_unreachable("Unknown SCEV kind!");
690 /// Given a list of SCEV objects, order them by their complexity, and group
691 /// objects of the same complexity together by value. When this routine is
692 /// finished, we know that any duplicates in the vector are consecutive and that
693 /// complexity is monotonically increasing.
695 /// Note that we go take special precautions to ensure that we get deterministic
696 /// results from this routine. In other words, we don't want the results of
697 /// this to depend on where the addresses of various SCEV objects happened to
700 static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops,
702 if (Ops.size() < 2) return; // Noop
704 SmallSet<std::pair<const SCEV *, const SCEV *>, 8> EqCache;
705 if (Ops.size() == 2) {
706 // This is the common case, which also happens to be trivially simple.
708 const SCEV *&LHS = Ops[0], *&RHS = Ops[1];
709 if (CompareSCEVComplexity(EqCache, LI, RHS, LHS) < 0)
714 // Do the rough sort by complexity.
715 std::stable_sort(Ops.begin(), Ops.end(),
716 [&EqCache, LI](const SCEV *LHS, const SCEV *RHS) {
717 return CompareSCEVComplexity(EqCache, LI, LHS, RHS) < 0;
720 // Now that we are sorted by complexity, group elements of the same
721 // complexity. Note that this is, at worst, N^2, but the vector is likely to
722 // be extremely short in practice. Note that we take this approach because we
723 // do not want to depend on the addresses of the objects we are grouping.
724 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
725 const SCEV *S = Ops[i];
726 unsigned Complexity = S->getSCEVType();
728 // If there are any objects of the same complexity and same value as this
730 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
731 if (Ops[j] == S) { // Found a duplicate.
732 // Move it to immediately after i'th element.
733 std::swap(Ops[i+1], Ops[j]);
734 ++i; // no need to rescan it.
735 if (i == e-2) return; // Done!
741 // Returns the size of the SCEV S.
742 static inline int sizeOfSCEV(const SCEV *S) {
743 struct FindSCEVSize {
745 FindSCEVSize() : Size(0) {}
747 bool follow(const SCEV *S) {
749 // Keep looking at all operands of S.
752 bool isDone() const {
758 SCEVTraversal<FindSCEVSize> ST(F);
765 struct SCEVDivision : public SCEVVisitor<SCEVDivision, void> {
767 // Computes the Quotient and Remainder of the division of Numerator by
769 static void divide(ScalarEvolution &SE, const SCEV *Numerator,
770 const SCEV *Denominator, const SCEV **Quotient,
771 const SCEV **Remainder) {
772 assert(Numerator && Denominator && "Uninitialized SCEV");
774 SCEVDivision D(SE, Numerator, Denominator);
776 // Check for the trivial case here to avoid having to check for it in the
778 if (Numerator == Denominator) {
784 if (Numerator->isZero()) {
790 // A simple case when N/1. The quotient is N.
791 if (Denominator->isOne()) {
792 *Quotient = Numerator;
797 // Split the Denominator when it is a product.
798 if (const SCEVMulExpr *T = dyn_cast<SCEVMulExpr>(Denominator)) {
800 *Quotient = Numerator;
801 for (const SCEV *Op : T->operands()) {
802 divide(SE, *Quotient, Op, &Q, &R);
805 // Bail out when the Numerator is not divisible by one of the terms of
809 *Remainder = Numerator;
818 *Quotient = D.Quotient;
819 *Remainder = D.Remainder;
822 // Except in the trivial case described above, we do not know how to divide
823 // Expr by Denominator for the following functions with empty implementation.
824 void visitTruncateExpr(const SCEVTruncateExpr *Numerator) {}
825 void visitZeroExtendExpr(const SCEVZeroExtendExpr *Numerator) {}
826 void visitSignExtendExpr(const SCEVSignExtendExpr *Numerator) {}
827 void visitUDivExpr(const SCEVUDivExpr *Numerator) {}
828 void visitSMaxExpr(const SCEVSMaxExpr *Numerator) {}
829 void visitUMaxExpr(const SCEVUMaxExpr *Numerator) {}
830 void visitUnknown(const SCEVUnknown *Numerator) {}
831 void visitCouldNotCompute(const SCEVCouldNotCompute *Numerator) {}
833 void visitConstant(const SCEVConstant *Numerator) {
834 if (const SCEVConstant *D = dyn_cast<SCEVConstant>(Denominator)) {
835 APInt NumeratorVal = Numerator->getAPInt();
836 APInt DenominatorVal = D->getAPInt();
837 uint32_t NumeratorBW = NumeratorVal.getBitWidth();
838 uint32_t DenominatorBW = DenominatorVal.getBitWidth();
840 if (NumeratorBW > DenominatorBW)
841 DenominatorVal = DenominatorVal.sext(NumeratorBW);
842 else if (NumeratorBW < DenominatorBW)
843 NumeratorVal = NumeratorVal.sext(DenominatorBW);
845 APInt QuotientVal(NumeratorVal.getBitWidth(), 0);
846 APInt RemainderVal(NumeratorVal.getBitWidth(), 0);
847 APInt::sdivrem(NumeratorVal, DenominatorVal, QuotientVal, RemainderVal);
848 Quotient = SE.getConstant(QuotientVal);
849 Remainder = SE.getConstant(RemainderVal);
854 void visitAddRecExpr(const SCEVAddRecExpr *Numerator) {
855 const SCEV *StartQ, *StartR, *StepQ, *StepR;
856 if (!Numerator->isAffine())
857 return cannotDivide(Numerator);
858 divide(SE, Numerator->getStart(), Denominator, &StartQ, &StartR);
859 divide(SE, Numerator->getStepRecurrence(SE), Denominator, &StepQ, &StepR);
860 // Bail out if the types do not match.
861 Type *Ty = Denominator->getType();
862 if (Ty != StartQ->getType() || Ty != StartR->getType() ||
863 Ty != StepQ->getType() || Ty != StepR->getType())
864 return cannotDivide(Numerator);
865 Quotient = SE.getAddRecExpr(StartQ, StepQ, Numerator->getLoop(),
866 Numerator->getNoWrapFlags());
867 Remainder = SE.getAddRecExpr(StartR, StepR, Numerator->getLoop(),
868 Numerator->getNoWrapFlags());
871 void visitAddExpr(const SCEVAddExpr *Numerator) {
872 SmallVector<const SCEV *, 2> Qs, Rs;
873 Type *Ty = Denominator->getType();
875 for (const SCEV *Op : Numerator->operands()) {
877 divide(SE, Op, Denominator, &Q, &R);
879 // Bail out if types do not match.
880 if (Ty != Q->getType() || Ty != R->getType())
881 return cannotDivide(Numerator);
887 if (Qs.size() == 1) {
893 Quotient = SE.getAddExpr(Qs);
894 Remainder = SE.getAddExpr(Rs);
897 void visitMulExpr(const SCEVMulExpr *Numerator) {
898 SmallVector<const SCEV *, 2> Qs;
899 Type *Ty = Denominator->getType();
901 bool FoundDenominatorTerm = false;
902 for (const SCEV *Op : Numerator->operands()) {
903 // Bail out if types do not match.
904 if (Ty != Op->getType())
905 return cannotDivide(Numerator);
907 if (FoundDenominatorTerm) {
912 // Check whether Denominator divides one of the product operands.
914 divide(SE, Op, Denominator, &Q, &R);
920 // Bail out if types do not match.
921 if (Ty != Q->getType())
922 return cannotDivide(Numerator);
924 FoundDenominatorTerm = true;
928 if (FoundDenominatorTerm) {
933 Quotient = SE.getMulExpr(Qs);
937 if (!isa<SCEVUnknown>(Denominator))
938 return cannotDivide(Numerator);
940 // The Remainder is obtained by replacing Denominator by 0 in Numerator.
941 ValueToValueMap RewriteMap;
942 RewriteMap[cast<SCEVUnknown>(Denominator)->getValue()] =
943 cast<SCEVConstant>(Zero)->getValue();
944 Remainder = SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true);
946 if (Remainder->isZero()) {
947 // The Quotient is obtained by replacing Denominator by 1 in Numerator.
948 RewriteMap[cast<SCEVUnknown>(Denominator)->getValue()] =
949 cast<SCEVConstant>(One)->getValue();
951 SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true);
955 // Quotient is (Numerator - Remainder) divided by Denominator.
957 const SCEV *Diff = SE.getMinusSCEV(Numerator, Remainder);
958 // This SCEV does not seem to simplify: fail the division here.
959 if (sizeOfSCEV(Diff) > sizeOfSCEV(Numerator))
960 return cannotDivide(Numerator);
961 divide(SE, Diff, Denominator, &Q, &R);
963 return cannotDivide(Numerator);
968 SCEVDivision(ScalarEvolution &S, const SCEV *Numerator,
969 const SCEV *Denominator)
970 : SE(S), Denominator(Denominator) {
971 Zero = SE.getZero(Denominator->getType());
972 One = SE.getOne(Denominator->getType());
974 // We generally do not know how to divide Expr by Denominator. We
975 // initialize the division to a "cannot divide" state to simplify the rest
977 cannotDivide(Numerator);
980 // Convenience function for giving up on the division. We set the quotient to
981 // be equal to zero and the remainder to be equal to the numerator.
982 void cannotDivide(const SCEV *Numerator) {
984 Remainder = Numerator;
988 const SCEV *Denominator, *Quotient, *Remainder, *Zero, *One;
993 //===----------------------------------------------------------------------===//
994 // Simple SCEV method implementations
995 //===----------------------------------------------------------------------===//
997 /// Compute BC(It, K). The result has width W. Assume, K > 0.
998 static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K,
1001 // Handle the simplest case efficiently.
1003 return SE.getTruncateOrZeroExtend(It, ResultTy);
1005 // We are using the following formula for BC(It, K):
1007 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
1009 // Suppose, W is the bitwidth of the return value. We must be prepared for
1010 // overflow. Hence, we must assure that the result of our computation is
1011 // equal to the accurate one modulo 2^W. Unfortunately, division isn't
1012 // safe in modular arithmetic.
1014 // However, this code doesn't use exactly that formula; the formula it uses
1015 // is something like the following, where T is the number of factors of 2 in
1016 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
1019 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
1021 // This formula is trivially equivalent to the previous formula. However,
1022 // this formula can be implemented much more efficiently. The trick is that
1023 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
1024 // arithmetic. To do exact division in modular arithmetic, all we have
1025 // to do is multiply by the inverse. Therefore, this step can be done at
1028 // The next issue is how to safely do the division by 2^T. The way this
1029 // is done is by doing the multiplication step at a width of at least W + T
1030 // bits. This way, the bottom W+T bits of the product are accurate. Then,
1031 // when we perform the division by 2^T (which is equivalent to a right shift
1032 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
1033 // truncated out after the division by 2^T.
1035 // In comparison to just directly using the first formula, this technique
1036 // is much more efficient; using the first formula requires W * K bits,
1037 // but this formula less than W + K bits. Also, the first formula requires
1038 // a division step, whereas this formula only requires multiplies and shifts.
1040 // It doesn't matter whether the subtraction step is done in the calculation
1041 // width or the input iteration count's width; if the subtraction overflows,
1042 // the result must be zero anyway. We prefer here to do it in the width of
1043 // the induction variable because it helps a lot for certain cases; CodeGen
1044 // isn't smart enough to ignore the overflow, which leads to much less
1045 // efficient code if the width of the subtraction is wider than the native
1048 // (It's possible to not widen at all by pulling out factors of 2 before
1049 // the multiplication; for example, K=2 can be calculated as
1050 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
1051 // extra arithmetic, so it's not an obvious win, and it gets
1052 // much more complicated for K > 3.)
1054 // Protection from insane SCEVs; this bound is conservative,
1055 // but it probably doesn't matter.
1057 return SE.getCouldNotCompute();
1059 unsigned W = SE.getTypeSizeInBits(ResultTy);
1061 // Calculate K! / 2^T and T; we divide out the factors of two before
1062 // multiplying for calculating K! / 2^T to avoid overflow.
1063 // Other overflow doesn't matter because we only care about the bottom
1064 // W bits of the result.
1065 APInt OddFactorial(W, 1);
1067 for (unsigned i = 3; i <= K; ++i) {
1069 unsigned TwoFactors = Mult.countTrailingZeros();
1071 Mult = Mult.lshr(TwoFactors);
1072 OddFactorial *= Mult;
1075 // We need at least W + T bits for the multiplication step
1076 unsigned CalculationBits = W + T;
1078 // Calculate 2^T, at width T+W.
1079 APInt DivFactor = APInt::getOneBitSet(CalculationBits, T);
1081 // Calculate the multiplicative inverse of K! / 2^T;
1082 // this multiplication factor will perform the exact division by
1084 APInt Mod = APInt::getSignedMinValue(W+1);
1085 APInt MultiplyFactor = OddFactorial.zext(W+1);
1086 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
1087 MultiplyFactor = MultiplyFactor.trunc(W);
1089 // Calculate the product, at width T+W
1090 IntegerType *CalculationTy = IntegerType::get(SE.getContext(),
1092 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
1093 for (unsigned i = 1; i != K; ++i) {
1094 const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i));
1095 Dividend = SE.getMulExpr(Dividend,
1096 SE.getTruncateOrZeroExtend(S, CalculationTy));
1100 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
1102 // Truncate the result, and divide by K! / 2^T.
1104 return SE.getMulExpr(SE.getConstant(MultiplyFactor),
1105 SE.getTruncateOrZeroExtend(DivResult, ResultTy));
1108 /// Return the value of this chain of recurrences at the specified iteration
1109 /// number. We can evaluate this recurrence by multiplying each element in the
1110 /// chain by the binomial coefficient corresponding to it. In other words, we
1111 /// can evaluate {A,+,B,+,C,+,D} as:
1113 /// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
1115 /// where BC(It, k) stands for binomial coefficient.
1117 const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It,
1118 ScalarEvolution &SE) const {
1119 const SCEV *Result = getStart();
1120 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
1121 // The computation is correct in the face of overflow provided that the
1122 // multiplication is performed _after_ the evaluation of the binomial
1124 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType());
1125 if (isa<SCEVCouldNotCompute>(Coeff))
1128 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
1133 //===----------------------------------------------------------------------===//
1134 // SCEV Expression folder implementations
1135 //===----------------------------------------------------------------------===//
1137 const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op,
1139 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
1140 "This is not a truncating conversion!");
1141 assert(isSCEVable(Ty) &&
1142 "This is not a conversion to a SCEVable type!");
1143 Ty = getEffectiveSCEVType(Ty);
1145 FoldingSetNodeID ID;
1146 ID.AddInteger(scTruncate);
1150 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1152 // Fold if the operand is constant.
1153 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1155 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty)));
1157 // trunc(trunc(x)) --> trunc(x)
1158 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
1159 return getTruncateExpr(ST->getOperand(), Ty);
1161 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
1162 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1163 return getTruncateOrSignExtend(SS->getOperand(), Ty);
1165 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
1166 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1167 return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
1169 // trunc(x1+x2+...+xN) --> trunc(x1)+trunc(x2)+...+trunc(xN) if we can
1170 // eliminate all the truncates, or we replace other casts with truncates.
1171 if (const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Op)) {
1172 SmallVector<const SCEV *, 4> Operands;
1173 bool hasTrunc = false;
1174 for (unsigned i = 0, e = SA->getNumOperands(); i != e && !hasTrunc; ++i) {
1175 const SCEV *S = getTruncateExpr(SA->getOperand(i), Ty);
1176 if (!isa<SCEVCastExpr>(SA->getOperand(i)))
1177 hasTrunc = isa<SCEVTruncateExpr>(S);
1178 Operands.push_back(S);
1181 return getAddExpr(Operands);
1182 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL.
1185 // trunc(x1*x2*...*xN) --> trunc(x1)*trunc(x2)*...*trunc(xN) if we can
1186 // eliminate all the truncates, or we replace other casts with truncates.
1187 if (const SCEVMulExpr *SM = dyn_cast<SCEVMulExpr>(Op)) {
1188 SmallVector<const SCEV *, 4> Operands;
1189 bool hasTrunc = false;
1190 for (unsigned i = 0, e = SM->getNumOperands(); i != e && !hasTrunc; ++i) {
1191 const SCEV *S = getTruncateExpr(SM->getOperand(i), Ty);
1192 if (!isa<SCEVCastExpr>(SM->getOperand(i)))
1193 hasTrunc = isa<SCEVTruncateExpr>(S);
1194 Operands.push_back(S);
1197 return getMulExpr(Operands);
1198 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL.
1201 // If the input value is a chrec scev, truncate the chrec's operands.
1202 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
1203 SmallVector<const SCEV *, 4> Operands;
1204 for (const SCEV *Op : AddRec->operands())
1205 Operands.push_back(getTruncateExpr(Op, Ty));
1206 return getAddRecExpr(Operands, AddRec->getLoop(), SCEV::FlagAnyWrap);
1209 // The cast wasn't folded; create an explicit cast node. We can reuse
1210 // the existing insert position since if we get here, we won't have
1211 // made any changes which would invalidate it.
1212 SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator),
1214 UniqueSCEVs.InsertNode(S, IP);
1218 // Get the limit of a recurrence such that incrementing by Step cannot cause
1219 // signed overflow as long as the value of the recurrence within the
1220 // loop does not exceed this limit before incrementing.
1221 static const SCEV *getSignedOverflowLimitForStep(const SCEV *Step,
1222 ICmpInst::Predicate *Pred,
1223 ScalarEvolution *SE) {
1224 unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
1225 if (SE->isKnownPositive(Step)) {
1226 *Pred = ICmpInst::ICMP_SLT;
1227 return SE->getConstant(APInt::getSignedMinValue(BitWidth) -
1228 SE->getSignedRange(Step).getSignedMax());
1230 if (SE->isKnownNegative(Step)) {
1231 *Pred = ICmpInst::ICMP_SGT;
1232 return SE->getConstant(APInt::getSignedMaxValue(BitWidth) -
1233 SE->getSignedRange(Step).getSignedMin());
1238 // Get the limit of a recurrence such that incrementing by Step cannot cause
1239 // unsigned overflow as long as the value of the recurrence within the loop does
1240 // not exceed this limit before incrementing.
1241 static const SCEV *getUnsignedOverflowLimitForStep(const SCEV *Step,
1242 ICmpInst::Predicate *Pred,
1243 ScalarEvolution *SE) {
1244 unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
1245 *Pred = ICmpInst::ICMP_ULT;
1247 return SE->getConstant(APInt::getMinValue(BitWidth) -
1248 SE->getUnsignedRange(Step).getUnsignedMax());
1253 struct ExtendOpTraitsBase {
1254 typedef const SCEV *(ScalarEvolution::*GetExtendExprTy)(const SCEV *, Type *);
1257 // Used to make code generic over signed and unsigned overflow.
1258 template <typename ExtendOp> struct ExtendOpTraits {
1261 // static const SCEV::NoWrapFlags WrapType;
1263 // static const ExtendOpTraitsBase::GetExtendExprTy GetExtendExpr;
1265 // static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1266 // ICmpInst::Predicate *Pred,
1267 // ScalarEvolution *SE);
1271 struct ExtendOpTraits<SCEVSignExtendExpr> : public ExtendOpTraitsBase {
1272 static const SCEV::NoWrapFlags WrapType = SCEV::FlagNSW;
1274 static const GetExtendExprTy GetExtendExpr;
1276 static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1277 ICmpInst::Predicate *Pred,
1278 ScalarEvolution *SE) {
1279 return getSignedOverflowLimitForStep(Step, Pred, SE);
1283 const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits<
1284 SCEVSignExtendExpr>::GetExtendExpr = &ScalarEvolution::getSignExtendExpr;
1287 struct ExtendOpTraits<SCEVZeroExtendExpr> : public ExtendOpTraitsBase {
1288 static const SCEV::NoWrapFlags WrapType = SCEV::FlagNUW;
1290 static const GetExtendExprTy GetExtendExpr;
1292 static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1293 ICmpInst::Predicate *Pred,
1294 ScalarEvolution *SE) {
1295 return getUnsignedOverflowLimitForStep(Step, Pred, SE);
1299 const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits<
1300 SCEVZeroExtendExpr>::GetExtendExpr = &ScalarEvolution::getZeroExtendExpr;
1303 // The recurrence AR has been shown to have no signed/unsigned wrap or something
1304 // close to it. Typically, if we can prove NSW/NUW for AR, then we can just as
1305 // easily prove NSW/NUW for its preincrement or postincrement sibling. This
1306 // allows normalizing a sign/zero extended AddRec as such: {sext/zext(Step +
1307 // Start),+,Step} => {(Step + sext/zext(Start),+,Step} As a result, the
1308 // expression "Step + sext/zext(PreIncAR)" is congruent with
1309 // "sext/zext(PostIncAR)"
1310 template <typename ExtendOpTy>
1311 static const SCEV *getPreStartForExtend(const SCEVAddRecExpr *AR, Type *Ty,
1312 ScalarEvolution *SE) {
1313 auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType;
1314 auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr;
1316 const Loop *L = AR->getLoop();
1317 const SCEV *Start = AR->getStart();
1318 const SCEV *Step = AR->getStepRecurrence(*SE);
1320 // Check for a simple looking step prior to loop entry.
1321 const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Start);
1325 // Create an AddExpr for "PreStart" after subtracting Step. Full SCEV
1326 // subtraction is expensive. For this purpose, perform a quick and dirty
1327 // difference, by checking for Step in the operand list.
1328 SmallVector<const SCEV *, 4> DiffOps;
1329 for (const SCEV *Op : SA->operands())
1331 DiffOps.push_back(Op);
1333 if (DiffOps.size() == SA->getNumOperands())
1336 // Try to prove `WrapType` (SCEV::FlagNSW or SCEV::FlagNUW) on `PreStart` +
1339 // 1. NSW/NUW flags on the step increment.
1340 auto PreStartFlags =
1341 ScalarEvolution::maskFlags(SA->getNoWrapFlags(), SCEV::FlagNUW);
1342 const SCEV *PreStart = SE->getAddExpr(DiffOps, PreStartFlags);
1343 const SCEVAddRecExpr *PreAR = dyn_cast<SCEVAddRecExpr>(
1344 SE->getAddRecExpr(PreStart, Step, L, SCEV::FlagAnyWrap));
1346 // "{S,+,X} is <nsw>/<nuw>" and "the backedge is taken at least once" implies
1347 // "S+X does not sign/unsign-overflow".
1350 const SCEV *BECount = SE->getBackedgeTakenCount(L);
1351 if (PreAR && PreAR->getNoWrapFlags(WrapType) &&
1352 !isa<SCEVCouldNotCompute>(BECount) && SE->isKnownPositive(BECount))
1355 // 2. Direct overflow check on the step operation's expression.
1356 unsigned BitWidth = SE->getTypeSizeInBits(AR->getType());
1357 Type *WideTy = IntegerType::get(SE->getContext(), BitWidth * 2);
1358 const SCEV *OperandExtendedStart =
1359 SE->getAddExpr((SE->*GetExtendExpr)(PreStart, WideTy),
1360 (SE->*GetExtendExpr)(Step, WideTy));
1361 if ((SE->*GetExtendExpr)(Start, WideTy) == OperandExtendedStart) {
1362 if (PreAR && AR->getNoWrapFlags(WrapType)) {
1363 // If we know `AR` == {`PreStart`+`Step`,+,`Step`} is `WrapType` (FlagNSW
1364 // or FlagNUW) and that `PreStart` + `Step` is `WrapType` too, then
1365 // `PreAR` == {`PreStart`,+,`Step`} is also `WrapType`. Cache this fact.
1366 const_cast<SCEVAddRecExpr *>(PreAR)->setNoWrapFlags(WrapType);
1371 // 3. Loop precondition.
1372 ICmpInst::Predicate Pred;
1373 const SCEV *OverflowLimit =
1374 ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep(Step, &Pred, SE);
1376 if (OverflowLimit &&
1377 SE->isLoopEntryGuardedByCond(L, Pred, PreStart, OverflowLimit))
1383 // Get the normalized zero or sign extended expression for this AddRec's Start.
1384 template <typename ExtendOpTy>
1385 static const SCEV *getExtendAddRecStart(const SCEVAddRecExpr *AR, Type *Ty,
1386 ScalarEvolution *SE) {
1387 auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr;
1389 const SCEV *PreStart = getPreStartForExtend<ExtendOpTy>(AR, Ty, SE);
1391 return (SE->*GetExtendExpr)(AR->getStart(), Ty);
1393 return SE->getAddExpr((SE->*GetExtendExpr)(AR->getStepRecurrence(*SE), Ty),
1394 (SE->*GetExtendExpr)(PreStart, Ty));
1397 // Try to prove away overflow by looking at "nearby" add recurrences. A
1398 // motivating example for this rule: if we know `{0,+,4}` is `ult` `-1` and it
1399 // does not itself wrap then we can conclude that `{1,+,4}` is `nuw`.
1403 // {S,+,X} == {S-T,+,X} + T
1404 // => Ext({S,+,X}) == Ext({S-T,+,X} + T)
1406 // If ({S-T,+,X} + T) does not overflow ... (1)
1408 // RHS == Ext({S-T,+,X} + T) == Ext({S-T,+,X}) + Ext(T)
1410 // If {S-T,+,X} does not overflow ... (2)
1412 // RHS == Ext({S-T,+,X}) + Ext(T) == {Ext(S-T),+,Ext(X)} + Ext(T)
1413 // == {Ext(S-T)+Ext(T),+,Ext(X)}
1415 // If (S-T)+T does not overflow ... (3)
1417 // RHS == {Ext(S-T)+Ext(T),+,Ext(X)} == {Ext(S-T+T),+,Ext(X)}
1418 // == {Ext(S),+,Ext(X)} == LHS
1420 // Thus, if (1), (2) and (3) are true for some T, then
1421 // Ext({S,+,X}) == {Ext(S),+,Ext(X)}
1423 // (3) is implied by (1) -- "(S-T)+T does not overflow" is simply "({S-T,+,X}+T)
1424 // does not overflow" restricted to the 0th iteration. Therefore we only need
1425 // to check for (1) and (2).
1427 // In the current context, S is `Start`, X is `Step`, Ext is `ExtendOpTy` and T
1428 // is `Delta` (defined below).
1430 template <typename ExtendOpTy>
1431 bool ScalarEvolution::proveNoWrapByVaryingStart(const SCEV *Start,
1434 auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType;
1436 // We restrict `Start` to a constant to prevent SCEV from spending too much
1437 // time here. It is correct (but more expensive) to continue with a
1438 // non-constant `Start` and do a general SCEV subtraction to compute
1439 // `PreStart` below.
1441 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start);
1445 APInt StartAI = StartC->getAPInt();
1447 for (unsigned Delta : {-2, -1, 1, 2}) {
1448 const SCEV *PreStart = getConstant(StartAI - Delta);
1450 FoldingSetNodeID ID;
1451 ID.AddInteger(scAddRecExpr);
1452 ID.AddPointer(PreStart);
1453 ID.AddPointer(Step);
1457 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1459 // Give up if we don't already have the add recurrence we need because
1460 // actually constructing an add recurrence is relatively expensive.
1461 if (PreAR && PreAR->getNoWrapFlags(WrapType)) { // proves (2)
1462 const SCEV *DeltaS = getConstant(StartC->getType(), Delta);
1463 ICmpInst::Predicate Pred = ICmpInst::BAD_ICMP_PREDICATE;
1464 const SCEV *Limit = ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep(
1465 DeltaS, &Pred, this);
1466 if (Limit && isKnownPredicate(Pred, PreAR, Limit)) // proves (1)
1474 const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op,
1476 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1477 "This is not an extending conversion!");
1478 assert(isSCEVable(Ty) &&
1479 "This is not a conversion to a SCEVable type!");
1480 Ty = getEffectiveSCEVType(Ty);
1482 // Fold if the operand is constant.
1483 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1485 cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(), Ty)));
1487 // zext(zext(x)) --> zext(x)
1488 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1489 return getZeroExtendExpr(SZ->getOperand(), Ty);
1491 // Before doing any expensive analysis, check to see if we've already
1492 // computed a SCEV for this Op and Ty.
1493 FoldingSetNodeID ID;
1494 ID.AddInteger(scZeroExtend);
1498 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1500 // zext(trunc(x)) --> zext(x) or x or trunc(x)
1501 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1502 // It's possible the bits taken off by the truncate were all zero bits. If
1503 // so, we should be able to simplify this further.
1504 const SCEV *X = ST->getOperand();
1505 ConstantRange CR = getUnsignedRange(X);
1506 unsigned TruncBits = getTypeSizeInBits(ST->getType());
1507 unsigned NewBits = getTypeSizeInBits(Ty);
1508 if (CR.truncate(TruncBits).zeroExtend(NewBits).contains(
1509 CR.zextOrTrunc(NewBits)))
1510 return getTruncateOrZeroExtend(X, Ty);
1513 // If the input value is a chrec scev, and we can prove that the value
1514 // did not overflow the old, smaller, value, we can zero extend all of the
1515 // operands (often constants). This allows analysis of something like
1516 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
1517 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1518 if (AR->isAffine()) {
1519 const SCEV *Start = AR->getStart();
1520 const SCEV *Step = AR->getStepRecurrence(*this);
1521 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1522 const Loop *L = AR->getLoop();
1524 if (!AR->hasNoUnsignedWrap()) {
1525 auto NewFlags = proveNoWrapViaConstantRanges(AR);
1526 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(NewFlags);
1529 // If we have special knowledge that this addrec won't overflow,
1530 // we don't need to do any further analysis.
1531 if (AR->hasNoUnsignedWrap())
1532 return getAddRecExpr(
1533 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1534 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1536 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1537 // Note that this serves two purposes: It filters out loops that are
1538 // simply not analyzable, and it covers the case where this code is
1539 // being called from within backedge-taken count analysis, such that
1540 // attempting to ask for the backedge-taken count would likely result
1541 // in infinite recursion. In the later case, the analysis code will
1542 // cope with a conservative value, and it will take care to purge
1543 // that value once it has finished.
1544 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1545 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1546 // Manually compute the final value for AR, checking for
1549 // Check whether the backedge-taken count can be losslessly casted to
1550 // the addrec's type. The count is always unsigned.
1551 const SCEV *CastedMaxBECount =
1552 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1553 const SCEV *RecastedMaxBECount =
1554 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1555 if (MaxBECount == RecastedMaxBECount) {
1556 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1557 // Check whether Start+Step*MaxBECount has no unsigned overflow.
1558 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step);
1559 const SCEV *ZAdd = getZeroExtendExpr(getAddExpr(Start, ZMul), WideTy);
1560 const SCEV *WideStart = getZeroExtendExpr(Start, WideTy);
1561 const SCEV *WideMaxBECount =
1562 getZeroExtendExpr(CastedMaxBECount, WideTy);
1563 const SCEV *OperandExtendedAdd =
1564 getAddExpr(WideStart,
1565 getMulExpr(WideMaxBECount,
1566 getZeroExtendExpr(Step, WideTy)));
1567 if (ZAdd == OperandExtendedAdd) {
1568 // Cache knowledge of AR NUW, which is propagated to this AddRec.
1569 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1570 // Return the expression with the addrec on the outside.
1571 return getAddRecExpr(
1572 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1573 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1575 // Similar to above, only this time treat the step value as signed.
1576 // This covers loops that count down.
1577 OperandExtendedAdd =
1578 getAddExpr(WideStart,
1579 getMulExpr(WideMaxBECount,
1580 getSignExtendExpr(Step, WideTy)));
1581 if (ZAdd == OperandExtendedAdd) {
1582 // Cache knowledge of AR NW, which is propagated to this AddRec.
1583 // Negative step causes unsigned wrap, but it still can't self-wrap.
1584 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1585 // Return the expression with the addrec on the outside.
1586 return getAddRecExpr(
1587 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1588 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1593 // Normally, in the cases we can prove no-overflow via a
1594 // backedge guarding condition, we can also compute a backedge
1595 // taken count for the loop. The exceptions are assumptions and
1596 // guards present in the loop -- SCEV is not great at exploiting
1597 // these to compute max backedge taken counts, but can still use
1598 // these to prove lack of overflow. Use this fact to avoid
1599 // doing extra work that may not pay off.
1600 if (!isa<SCEVCouldNotCompute>(MaxBECount) || HasGuards ||
1601 !AC.assumptions().empty()) {
1602 // If the backedge is guarded by a comparison with the pre-inc
1603 // value the addrec is safe. Also, if the entry is guarded by
1604 // a comparison with the start value and the backedge is
1605 // guarded by a comparison with the post-inc value, the addrec
1607 if (isKnownPositive(Step)) {
1608 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
1609 getUnsignedRange(Step).getUnsignedMax());
1610 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
1611 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) &&
1612 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT,
1613 AR->getPostIncExpr(*this), N))) {
1614 // Cache knowledge of AR NUW, which is propagated to this
1616 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1617 // Return the expression with the addrec on the outside.
1618 return getAddRecExpr(
1619 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1620 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1622 } else if (isKnownNegative(Step)) {
1623 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
1624 getSignedRange(Step).getSignedMin());
1625 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) ||
1626 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) &&
1627 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT,
1628 AR->getPostIncExpr(*this), N))) {
1629 // Cache knowledge of AR NW, which is propagated to this
1630 // AddRec. Negative step causes unsigned wrap, but it
1631 // still can't self-wrap.
1632 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1633 // Return the expression with the addrec on the outside.
1634 return getAddRecExpr(
1635 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1636 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1641 if (proveNoWrapByVaryingStart<SCEVZeroExtendExpr>(Start, Step, L)) {
1642 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1643 return getAddRecExpr(
1644 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1645 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1649 if (auto *SA = dyn_cast<SCEVAddExpr>(Op)) {
1650 // zext((A + B + ...)<nuw>) --> (zext(A) + zext(B) + ...)<nuw>
1651 if (SA->hasNoUnsignedWrap()) {
1652 // If the addition does not unsign overflow then we can, by definition,
1653 // commute the zero extension with the addition operation.
1654 SmallVector<const SCEV *, 4> Ops;
1655 for (const auto *Op : SA->operands())
1656 Ops.push_back(getZeroExtendExpr(Op, Ty));
1657 return getAddExpr(Ops, SCEV::FlagNUW);
1661 // The cast wasn't folded; create an explicit cast node.
1662 // Recompute the insert position, as it may have been invalidated.
1663 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1664 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
1666 UniqueSCEVs.InsertNode(S, IP);
1670 const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op,
1672 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1673 "This is not an extending conversion!");
1674 assert(isSCEVable(Ty) &&
1675 "This is not a conversion to a SCEVable type!");
1676 Ty = getEffectiveSCEVType(Ty);
1678 // Fold if the operand is constant.
1679 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1681 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), Ty)));
1683 // sext(sext(x)) --> sext(x)
1684 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1685 return getSignExtendExpr(SS->getOperand(), Ty);
1687 // sext(zext(x)) --> zext(x)
1688 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1689 return getZeroExtendExpr(SZ->getOperand(), Ty);
1691 // Before doing any expensive analysis, check to see if we've already
1692 // computed a SCEV for this Op and Ty.
1693 FoldingSetNodeID ID;
1694 ID.AddInteger(scSignExtend);
1698 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1700 // sext(trunc(x)) --> sext(x) or x or trunc(x)
1701 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1702 // It's possible the bits taken off by the truncate were all sign bits. If
1703 // so, we should be able to simplify this further.
1704 const SCEV *X = ST->getOperand();
1705 ConstantRange CR = getSignedRange(X);
1706 unsigned TruncBits = getTypeSizeInBits(ST->getType());
1707 unsigned NewBits = getTypeSizeInBits(Ty);
1708 if (CR.truncate(TruncBits).signExtend(NewBits).contains(
1709 CR.sextOrTrunc(NewBits)))
1710 return getTruncateOrSignExtend(X, Ty);
1713 // sext(C1 + (C2 * x)) --> C1 + sext(C2 * x) if C1 < C2
1714 if (auto *SA = dyn_cast<SCEVAddExpr>(Op)) {
1715 if (SA->getNumOperands() == 2) {
1716 auto *SC1 = dyn_cast<SCEVConstant>(SA->getOperand(0));
1717 auto *SMul = dyn_cast<SCEVMulExpr>(SA->getOperand(1));
1719 if (auto *SC2 = dyn_cast<SCEVConstant>(SMul->getOperand(0))) {
1720 const APInt &C1 = SC1->getAPInt();
1721 const APInt &C2 = SC2->getAPInt();
1722 if (C1.isStrictlyPositive() && C2.isStrictlyPositive() &&
1723 C2.ugt(C1) && C2.isPowerOf2())
1724 return getAddExpr(getSignExtendExpr(SC1, Ty),
1725 getSignExtendExpr(SMul, Ty));
1730 // sext((A + B + ...)<nsw>) --> (sext(A) + sext(B) + ...)<nsw>
1731 if (SA->hasNoSignedWrap()) {
1732 // If the addition does not sign overflow then we can, by definition,
1733 // commute the sign extension with the addition operation.
1734 SmallVector<const SCEV *, 4> Ops;
1735 for (const auto *Op : SA->operands())
1736 Ops.push_back(getSignExtendExpr(Op, Ty));
1737 return getAddExpr(Ops, SCEV::FlagNSW);
1740 // If the input value is a chrec scev, and we can prove that the value
1741 // did not overflow the old, smaller, value, we can sign extend all of the
1742 // operands (often constants). This allows analysis of something like
1743 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
1744 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1745 if (AR->isAffine()) {
1746 const SCEV *Start = AR->getStart();
1747 const SCEV *Step = AR->getStepRecurrence(*this);
1748 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1749 const Loop *L = AR->getLoop();
1751 if (!AR->hasNoSignedWrap()) {
1752 auto NewFlags = proveNoWrapViaConstantRanges(AR);
1753 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(NewFlags);
1756 // If we have special knowledge that this addrec won't overflow,
1757 // we don't need to do any further analysis.
1758 if (AR->hasNoSignedWrap())
1759 return getAddRecExpr(
1760 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1761 getSignExtendExpr(Step, Ty), L, SCEV::FlagNSW);
1763 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1764 // Note that this serves two purposes: It filters out loops that are
1765 // simply not analyzable, and it covers the case where this code is
1766 // being called from within backedge-taken count analysis, such that
1767 // attempting to ask for the backedge-taken count would likely result
1768 // in infinite recursion. In the later case, the analysis code will
1769 // cope with a conservative value, and it will take care to purge
1770 // that value once it has finished.
1771 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1772 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1773 // Manually compute the final value for AR, checking for
1776 // Check whether the backedge-taken count can be losslessly casted to
1777 // the addrec's type. The count is always unsigned.
1778 const SCEV *CastedMaxBECount =
1779 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1780 const SCEV *RecastedMaxBECount =
1781 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1782 if (MaxBECount == RecastedMaxBECount) {
1783 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1784 // Check whether Start+Step*MaxBECount has no signed overflow.
1785 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
1786 const SCEV *SAdd = getSignExtendExpr(getAddExpr(Start, SMul), WideTy);
1787 const SCEV *WideStart = getSignExtendExpr(Start, WideTy);
1788 const SCEV *WideMaxBECount =
1789 getZeroExtendExpr(CastedMaxBECount, WideTy);
1790 const SCEV *OperandExtendedAdd =
1791 getAddExpr(WideStart,
1792 getMulExpr(WideMaxBECount,
1793 getSignExtendExpr(Step, WideTy)));
1794 if (SAdd == OperandExtendedAdd) {
1795 // Cache knowledge of AR NSW, which is propagated to this AddRec.
1796 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1797 // Return the expression with the addrec on the outside.
1798 return getAddRecExpr(
1799 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1800 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1802 // Similar to above, only this time treat the step value as unsigned.
1803 // This covers loops that count up with an unsigned step.
1804 OperandExtendedAdd =
1805 getAddExpr(WideStart,
1806 getMulExpr(WideMaxBECount,
1807 getZeroExtendExpr(Step, WideTy)));
1808 if (SAdd == OperandExtendedAdd) {
1809 // If AR wraps around then
1811 // abs(Step) * MaxBECount > unsigned-max(AR->getType())
1812 // => SAdd != OperandExtendedAdd
1814 // Thus (AR is not NW => SAdd != OperandExtendedAdd) <=>
1815 // (SAdd == OperandExtendedAdd => AR is NW)
1817 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1819 // Return the expression with the addrec on the outside.
1820 return getAddRecExpr(
1821 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1822 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1827 // Normally, in the cases we can prove no-overflow via a
1828 // backedge guarding condition, we can also compute a backedge
1829 // taken count for the loop. The exceptions are assumptions and
1830 // guards present in the loop -- SCEV is not great at exploiting
1831 // these to compute max backedge taken counts, but can still use
1832 // these to prove lack of overflow. Use this fact to avoid
1833 // doing extra work that may not pay off.
1835 if (!isa<SCEVCouldNotCompute>(MaxBECount) || HasGuards ||
1836 !AC.assumptions().empty()) {
1837 // If the backedge is guarded by a comparison with the pre-inc
1838 // value the addrec is safe. Also, if the entry is guarded by
1839 // a comparison with the start value and the backedge is
1840 // guarded by a comparison with the post-inc value, the addrec
1842 ICmpInst::Predicate Pred;
1843 const SCEV *OverflowLimit =
1844 getSignedOverflowLimitForStep(Step, &Pred, this);
1845 if (OverflowLimit &&
1846 (isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) ||
1847 (isLoopEntryGuardedByCond(L, Pred, Start, OverflowLimit) &&
1848 isLoopBackedgeGuardedByCond(L, Pred, AR->getPostIncExpr(*this),
1850 // Cache knowledge of AR NSW, then propagate NSW to the wide AddRec.
1851 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1852 return getAddRecExpr(
1853 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1854 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1858 // If Start and Step are constants, check if we can apply this
1860 // sext{C1,+,C2} --> C1 + sext{0,+,C2} if C1 < C2
1861 auto *SC1 = dyn_cast<SCEVConstant>(Start);
1862 auto *SC2 = dyn_cast<SCEVConstant>(Step);
1864 const APInt &C1 = SC1->getAPInt();
1865 const APInt &C2 = SC2->getAPInt();
1866 if (C1.isStrictlyPositive() && C2.isStrictlyPositive() && C2.ugt(C1) &&
1868 Start = getSignExtendExpr(Start, Ty);
1869 const SCEV *NewAR = getAddRecExpr(getZero(AR->getType()), Step, L,
1870 AR->getNoWrapFlags());
1871 return getAddExpr(Start, getSignExtendExpr(NewAR, Ty));
1875 if (proveNoWrapByVaryingStart<SCEVSignExtendExpr>(Start, Step, L)) {
1876 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1877 return getAddRecExpr(
1878 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1879 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1883 // If the input value is provably positive and we could not simplify
1884 // away the sext build a zext instead.
1885 if (isKnownNonNegative(Op))
1886 return getZeroExtendExpr(Op, Ty);
1888 // The cast wasn't folded; create an explicit cast node.
1889 // Recompute the insert position, as it may have been invalidated.
1890 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1891 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
1893 UniqueSCEVs.InsertNode(S, IP);
1897 /// getAnyExtendExpr - Return a SCEV for the given operand extended with
1898 /// unspecified bits out to the given type.
1900 const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
1902 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1903 "This is not an extending conversion!");
1904 assert(isSCEVable(Ty) &&
1905 "This is not a conversion to a SCEVable type!");
1906 Ty = getEffectiveSCEVType(Ty);
1908 // Sign-extend negative constants.
1909 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1910 if (SC->getAPInt().isNegative())
1911 return getSignExtendExpr(Op, Ty);
1913 // Peel off a truncate cast.
1914 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
1915 const SCEV *NewOp = T->getOperand();
1916 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
1917 return getAnyExtendExpr(NewOp, Ty);
1918 return getTruncateOrNoop(NewOp, Ty);
1921 // Next try a zext cast. If the cast is folded, use it.
1922 const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
1923 if (!isa<SCEVZeroExtendExpr>(ZExt))
1926 // Next try a sext cast. If the cast is folded, use it.
1927 const SCEV *SExt = getSignExtendExpr(Op, Ty);
1928 if (!isa<SCEVSignExtendExpr>(SExt))
1931 // Force the cast to be folded into the operands of an addrec.
1932 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
1933 SmallVector<const SCEV *, 4> Ops;
1934 for (const SCEV *Op : AR->operands())
1935 Ops.push_back(getAnyExtendExpr(Op, Ty));
1936 return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW);
1939 // If the expression is obviously signed, use the sext cast value.
1940 if (isa<SCEVSMaxExpr>(Op))
1943 // Absent any other information, use the zext cast value.
1947 /// Process the given Ops list, which is a list of operands to be added under
1948 /// the given scale, update the given map. This is a helper function for
1949 /// getAddRecExpr. As an example of what it does, given a sequence of operands
1950 /// that would form an add expression like this:
1952 /// m + n + 13 + (A * (o + p + (B * (q + m + 29)))) + r + (-1 * r)
1954 /// where A and B are constants, update the map with these values:
1956 /// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
1958 /// and add 13 + A*B*29 to AccumulatedConstant.
1959 /// This will allow getAddRecExpr to produce this:
1961 /// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
1963 /// This form often exposes folding opportunities that are hidden in
1964 /// the original operand list.
1966 /// Return true iff it appears that any interesting folding opportunities
1967 /// may be exposed. This helps getAddRecExpr short-circuit extra work in
1968 /// the common case where no interesting opportunities are present, and
1969 /// is also used as a check to avoid infinite recursion.
1972 CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
1973 SmallVectorImpl<const SCEV *> &NewOps,
1974 APInt &AccumulatedConstant,
1975 const SCEV *const *Ops, size_t NumOperands,
1977 ScalarEvolution &SE) {
1978 bool Interesting = false;
1980 // Iterate over the add operands. They are sorted, with constants first.
1982 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1984 // Pull a buried constant out to the outside.
1985 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
1987 AccumulatedConstant += Scale * C->getAPInt();
1990 // Next comes everything else. We're especially interested in multiplies
1991 // here, but they're in the middle, so just visit the rest with one loop.
1992 for (; i != NumOperands; ++i) {
1993 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
1994 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
1996 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getAPInt();
1997 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
1998 // A multiplication of a constant with another add; recurse.
1999 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1));
2001 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
2002 Add->op_begin(), Add->getNumOperands(),
2005 // A multiplication of a constant with some other value. Update
2007 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
2008 const SCEV *Key = SE.getMulExpr(MulOps);
2009 auto Pair = M.insert({Key, NewScale});
2011 NewOps.push_back(Pair.first->first);
2013 Pair.first->second += NewScale;
2014 // The map already had an entry for this value, which may indicate
2015 // a folding opportunity.
2020 // An ordinary operand. Update the map.
2021 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
2022 M.insert({Ops[i], Scale});
2024 NewOps.push_back(Pair.first->first);
2026 Pair.first->second += Scale;
2027 // The map already had an entry for this value, which may indicate
2028 // a folding opportunity.
2037 // We're trying to construct a SCEV of type `Type' with `Ops' as operands and
2038 // `OldFlags' as can't-wrap behavior. Infer a more aggressive set of
2039 // can't-overflow flags for the operation if possible.
2040 static SCEV::NoWrapFlags
2041 StrengthenNoWrapFlags(ScalarEvolution *SE, SCEVTypes Type,
2042 const SmallVectorImpl<const SCEV *> &Ops,
2043 SCEV::NoWrapFlags Flags) {
2044 using namespace std::placeholders;
2045 typedef OverflowingBinaryOperator OBO;
2048 Type == scAddExpr || Type == scAddRecExpr || Type == scMulExpr;
2050 assert(CanAnalyze && "don't call from other places!");
2052 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
2053 SCEV::NoWrapFlags SignOrUnsignWrap =
2054 ScalarEvolution::maskFlags(Flags, SignOrUnsignMask);
2056 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
2057 auto IsKnownNonNegative = [&](const SCEV *S) {
2058 return SE->isKnownNonNegative(S);
2061 if (SignOrUnsignWrap == SCEV::FlagNSW && all_of(Ops, IsKnownNonNegative))
2063 ScalarEvolution::setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
2065 SignOrUnsignWrap = ScalarEvolution::maskFlags(Flags, SignOrUnsignMask);
2067 if (SignOrUnsignWrap != SignOrUnsignMask && Type == scAddExpr &&
2068 Ops.size() == 2 && isa<SCEVConstant>(Ops[0])) {
2070 // (A + C) --> (A + C)<nsw> if the addition does not sign overflow
2071 // (A + C) --> (A + C)<nuw> if the addition does not unsign overflow
2073 const APInt &C = cast<SCEVConstant>(Ops[0])->getAPInt();
2074 if (!(SignOrUnsignWrap & SCEV::FlagNSW)) {
2075 auto NSWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
2076 Instruction::Add, C, OBO::NoSignedWrap);
2077 if (NSWRegion.contains(SE->getSignedRange(Ops[1])))
2078 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW);
2080 if (!(SignOrUnsignWrap & SCEV::FlagNUW)) {
2081 auto NUWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
2082 Instruction::Add, C, OBO::NoUnsignedWrap);
2083 if (NUWRegion.contains(SE->getUnsignedRange(Ops[1])))
2084 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
2091 /// Get a canonical add expression, or something simpler if possible.
2092 const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
2093 SCEV::NoWrapFlags Flags) {
2094 assert(!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) &&
2095 "only nuw or nsw allowed");
2096 assert(!Ops.empty() && "Cannot get empty add!");
2097 if (Ops.size() == 1) return Ops[0];
2099 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2100 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2101 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2102 "SCEVAddExpr operand types don't match!");
2105 // Sort by complexity, this groups all similar expression types together.
2106 GroupByComplexity(Ops, &LI);
2108 Flags = StrengthenNoWrapFlags(this, scAddExpr, Ops, Flags);
2110 // If there are any constants, fold them together.
2112 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2114 assert(Idx < Ops.size());
2115 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2116 // We found two constants, fold them together!
2117 Ops[0] = getConstant(LHSC->getAPInt() + RHSC->getAPInt());
2118 if (Ops.size() == 2) return Ops[0];
2119 Ops.erase(Ops.begin()+1); // Erase the folded element
2120 LHSC = cast<SCEVConstant>(Ops[0]);
2123 // If we are left with a constant zero being added, strip it off.
2124 if (LHSC->getValue()->isZero()) {
2125 Ops.erase(Ops.begin());
2129 if (Ops.size() == 1) return Ops[0];
2132 // Okay, check to see if the same value occurs in the operand list more than
2133 // once. If so, merge them together into an multiply expression. Since we
2134 // sorted the list, these values are required to be adjacent.
2135 Type *Ty = Ops[0]->getType();
2136 bool FoundMatch = false;
2137 for (unsigned i = 0, e = Ops.size(); i != e-1; ++i)
2138 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
2139 // Scan ahead to count how many equal operands there are.
2141 while (i+Count != e && Ops[i+Count] == Ops[i])
2143 // Merge the values into a multiply.
2144 const SCEV *Scale = getConstant(Ty, Count);
2145 const SCEV *Mul = getMulExpr(Scale, Ops[i]);
2146 if (Ops.size() == Count)
2149 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count);
2150 --i; e -= Count - 1;
2154 return getAddExpr(Ops, Flags);
2156 // Check for truncates. If all the operands are truncated from the same
2157 // type, see if factoring out the truncate would permit the result to be
2158 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
2159 // if the contents of the resulting outer trunc fold to something simple.
2160 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
2161 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
2162 Type *DstType = Trunc->getType();
2163 Type *SrcType = Trunc->getOperand()->getType();
2164 SmallVector<const SCEV *, 8> LargeOps;
2166 // Check all the operands to see if they can be represented in the
2167 // source type of the truncate.
2168 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
2169 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
2170 if (T->getOperand()->getType() != SrcType) {
2174 LargeOps.push_back(T->getOperand());
2175 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
2176 LargeOps.push_back(getAnyExtendExpr(C, SrcType));
2177 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
2178 SmallVector<const SCEV *, 8> LargeMulOps;
2179 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
2180 if (const SCEVTruncateExpr *T =
2181 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
2182 if (T->getOperand()->getType() != SrcType) {
2186 LargeMulOps.push_back(T->getOperand());
2187 } else if (const auto *C = dyn_cast<SCEVConstant>(M->getOperand(j))) {
2188 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType));
2195 LargeOps.push_back(getMulExpr(LargeMulOps));
2202 // Evaluate the expression in the larger type.
2203 const SCEV *Fold = getAddExpr(LargeOps, Flags);
2204 // If it folds to something simple, use it. Otherwise, don't.
2205 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
2206 return getTruncateExpr(Fold, DstType);
2210 // Skip past any other cast SCEVs.
2211 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
2214 // If there are add operands they would be next.
2215 if (Idx < Ops.size()) {
2216 bool DeletedAdd = false;
2217 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
2218 // If we have an add, expand the add operands onto the end of the operands
2220 Ops.erase(Ops.begin()+Idx);
2221 Ops.append(Add->op_begin(), Add->op_end());
2225 // If we deleted at least one add, we added operands to the end of the list,
2226 // and they are not necessarily sorted. Recurse to resort and resimplify
2227 // any operands we just acquired.
2229 return getAddExpr(Ops);
2232 // Skip over the add expression until we get to a multiply.
2233 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
2236 // Check to see if there are any folding opportunities present with
2237 // operands multiplied by constant values.
2238 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
2239 uint64_t BitWidth = getTypeSizeInBits(Ty);
2240 DenseMap<const SCEV *, APInt> M;
2241 SmallVector<const SCEV *, 8> NewOps;
2242 APInt AccumulatedConstant(BitWidth, 0);
2243 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
2244 Ops.data(), Ops.size(),
2245 APInt(BitWidth, 1), *this)) {
2246 struct APIntCompare {
2247 bool operator()(const APInt &LHS, const APInt &RHS) const {
2248 return LHS.ult(RHS);
2252 // Some interesting folding opportunity is present, so its worthwhile to
2253 // re-generate the operands list. Group the operands by constant scale,
2254 // to avoid multiplying by the same constant scale multiple times.
2255 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
2256 for (const SCEV *NewOp : NewOps)
2257 MulOpLists[M.find(NewOp)->second].push_back(NewOp);
2258 // Re-generate the operands list.
2260 if (AccumulatedConstant != 0)
2261 Ops.push_back(getConstant(AccumulatedConstant));
2262 for (auto &MulOp : MulOpLists)
2263 if (MulOp.first != 0)
2264 Ops.push_back(getMulExpr(getConstant(MulOp.first),
2265 getAddExpr(MulOp.second)));
2268 if (Ops.size() == 1)
2270 return getAddExpr(Ops);
2274 // If we are adding something to a multiply expression, make sure the
2275 // something is not already an operand of the multiply. If so, merge it into
2277 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
2278 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
2279 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
2280 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
2281 if (isa<SCEVConstant>(MulOpSCEV))
2283 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
2284 if (MulOpSCEV == Ops[AddOp]) {
2285 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
2286 const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
2287 if (Mul->getNumOperands() != 2) {
2288 // If the multiply has more than two operands, we must get the
2290 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
2291 Mul->op_begin()+MulOp);
2292 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
2293 InnerMul = getMulExpr(MulOps);
2295 const SCEV *One = getOne(Ty);
2296 const SCEV *AddOne = getAddExpr(One, InnerMul);
2297 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV);
2298 if (Ops.size() == 2) return OuterMul;
2300 Ops.erase(Ops.begin()+AddOp);
2301 Ops.erase(Ops.begin()+Idx-1);
2303 Ops.erase(Ops.begin()+Idx);
2304 Ops.erase(Ops.begin()+AddOp-1);
2306 Ops.push_back(OuterMul);
2307 return getAddExpr(Ops);
2310 // Check this multiply against other multiplies being added together.
2311 for (unsigned OtherMulIdx = Idx+1;
2312 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
2314 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
2315 // If MulOp occurs in OtherMul, we can fold the two multiplies
2317 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
2318 OMulOp != e; ++OMulOp)
2319 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
2320 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
2321 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
2322 if (Mul->getNumOperands() != 2) {
2323 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
2324 Mul->op_begin()+MulOp);
2325 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
2326 InnerMul1 = getMulExpr(MulOps);
2328 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
2329 if (OtherMul->getNumOperands() != 2) {
2330 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
2331 OtherMul->op_begin()+OMulOp);
2332 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end());
2333 InnerMul2 = getMulExpr(MulOps);
2335 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
2336 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
2337 if (Ops.size() == 2) return OuterMul;
2338 Ops.erase(Ops.begin()+Idx);
2339 Ops.erase(Ops.begin()+OtherMulIdx-1);
2340 Ops.push_back(OuterMul);
2341 return getAddExpr(Ops);
2347 // If there are any add recurrences in the operands list, see if any other
2348 // added values are loop invariant. If so, we can fold them into the
2350 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2353 // Scan over all recurrences, trying to fold loop invariants into them.
2354 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
2355 // Scan all of the other operands to this add and add them to the vector if
2356 // they are loop invariant w.r.t. the recurrence.
2357 SmallVector<const SCEV *, 8> LIOps;
2358 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2359 const Loop *AddRecLoop = AddRec->getLoop();
2360 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2361 if (isLoopInvariant(Ops[i], AddRecLoop)) {
2362 LIOps.push_back(Ops[i]);
2363 Ops.erase(Ops.begin()+i);
2367 // If we found some loop invariants, fold them into the recurrence.
2368 if (!LIOps.empty()) {
2369 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
2370 LIOps.push_back(AddRec->getStart());
2372 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
2374 // This follows from the fact that the no-wrap flags on the outer add
2375 // expression are applicable on the 0th iteration, when the add recurrence
2376 // will be equal to its start value.
2377 AddRecOps[0] = getAddExpr(LIOps, Flags);
2379 // Build the new addrec. Propagate the NUW and NSW flags if both the
2380 // outer add and the inner addrec are guaranteed to have no overflow.
2381 // Always propagate NW.
2382 Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW));
2383 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags);
2385 // If all of the other operands were loop invariant, we are done.
2386 if (Ops.size() == 1) return NewRec;
2388 // Otherwise, add the folded AddRec by the non-invariant parts.
2389 for (unsigned i = 0;; ++i)
2390 if (Ops[i] == AddRec) {
2394 return getAddExpr(Ops);
2397 // Okay, if there weren't any loop invariants to be folded, check to see if
2398 // there are multiple AddRec's with the same loop induction variable being
2399 // added together. If so, we can fold them.
2400 for (unsigned OtherIdx = Idx+1;
2401 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2403 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
2404 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L>
2405 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
2407 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2409 if (const auto *OtherAddRec = dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]))
2410 if (OtherAddRec->getLoop() == AddRecLoop) {
2411 for (unsigned i = 0, e = OtherAddRec->getNumOperands();
2413 if (i >= AddRecOps.size()) {
2414 AddRecOps.append(OtherAddRec->op_begin()+i,
2415 OtherAddRec->op_end());
2418 AddRecOps[i] = getAddExpr(AddRecOps[i],
2419 OtherAddRec->getOperand(i));
2421 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2423 // Step size has changed, so we cannot guarantee no self-wraparound.
2424 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap);
2425 return getAddExpr(Ops);
2428 // Otherwise couldn't fold anything into this recurrence. Move onto the
2432 // Okay, it looks like we really DO need an add expr. Check to see if we
2433 // already have one, otherwise create a new one.
2434 FoldingSetNodeID ID;
2435 ID.AddInteger(scAddExpr);
2436 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2437 ID.AddPointer(Ops[i]);
2440 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2442 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2443 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2444 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator),
2446 UniqueSCEVs.InsertNode(S, IP);
2448 S->setNoWrapFlags(Flags);
2452 static uint64_t umul_ov(uint64_t i, uint64_t j, bool &Overflow) {
2454 if (j > 1 && k / j != i) Overflow = true;
2458 /// Compute the result of "n choose k", the binomial coefficient. If an
2459 /// intermediate computation overflows, Overflow will be set and the return will
2460 /// be garbage. Overflow is not cleared on absence of overflow.
2461 static uint64_t Choose(uint64_t n, uint64_t k, bool &Overflow) {
2462 // We use the multiplicative formula:
2463 // n(n-1)(n-2)...(n-(k-1)) / k(k-1)(k-2)...1 .
2464 // At each iteration, we take the n-th term of the numeral and divide by the
2465 // (k-n)th term of the denominator. This division will always produce an
2466 // integral result, and helps reduce the chance of overflow in the
2467 // intermediate computations. However, we can still overflow even when the
2468 // final result would fit.
2470 if (n == 0 || n == k) return 1;
2471 if (k > n) return 0;
2477 for (uint64_t i = 1; i <= k; ++i) {
2478 r = umul_ov(r, n-(i-1), Overflow);
2484 /// Determine if any of the operands in this SCEV are a constant or if
2485 /// any of the add or multiply expressions in this SCEV contain a constant.
2486 static bool containsConstantSomewhere(const SCEV *StartExpr) {
2487 SmallVector<const SCEV *, 4> Ops;
2488 Ops.push_back(StartExpr);
2489 while (!Ops.empty()) {
2490 const SCEV *CurrentExpr = Ops.pop_back_val();
2491 if (isa<SCEVConstant>(*CurrentExpr))
2494 if (isa<SCEVAddExpr>(*CurrentExpr) || isa<SCEVMulExpr>(*CurrentExpr)) {
2495 const auto *CurrentNAry = cast<SCEVNAryExpr>(CurrentExpr);
2496 Ops.append(CurrentNAry->op_begin(), CurrentNAry->op_end());
2502 /// Get a canonical multiply expression, or something simpler if possible.
2503 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
2504 SCEV::NoWrapFlags Flags) {
2505 assert(Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) &&
2506 "only nuw or nsw allowed");
2507 assert(!Ops.empty() && "Cannot get empty mul!");
2508 if (Ops.size() == 1) return Ops[0];
2510 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2511 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2512 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2513 "SCEVMulExpr operand types don't match!");
2516 // Sort by complexity, this groups all similar expression types together.
2517 GroupByComplexity(Ops, &LI);
2519 Flags = StrengthenNoWrapFlags(this, scMulExpr, Ops, Flags);
2521 // If there are any constants, fold them together.
2523 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2525 // C1*(C2+V) -> C1*C2 + C1*V
2526 if (Ops.size() == 2)
2527 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
2528 // If any of Add's ops are Adds or Muls with a constant,
2529 // apply this transformation as well.
2530 if (Add->getNumOperands() == 2)
2531 if (containsConstantSomewhere(Add))
2532 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
2533 getMulExpr(LHSC, Add->getOperand(1)));
2536 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2537 // We found two constants, fold them together!
2539 ConstantInt::get(getContext(), LHSC->getAPInt() * RHSC->getAPInt());
2540 Ops[0] = getConstant(Fold);
2541 Ops.erase(Ops.begin()+1); // Erase the folded element
2542 if (Ops.size() == 1) return Ops[0];
2543 LHSC = cast<SCEVConstant>(Ops[0]);
2546 // If we are left with a constant one being multiplied, strip it off.
2547 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
2548 Ops.erase(Ops.begin());
2550 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
2551 // If we have a multiply of zero, it will always be zero.
2553 } else if (Ops[0]->isAllOnesValue()) {
2554 // If we have a mul by -1 of an add, try distributing the -1 among the
2556 if (Ops.size() == 2) {
2557 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
2558 SmallVector<const SCEV *, 4> NewOps;
2559 bool AnyFolded = false;
2560 for (const SCEV *AddOp : Add->operands()) {
2561 const SCEV *Mul = getMulExpr(Ops[0], AddOp);
2562 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
2563 NewOps.push_back(Mul);
2566 return getAddExpr(NewOps);
2567 } else if (const auto *AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) {
2568 // Negation preserves a recurrence's no self-wrap property.
2569 SmallVector<const SCEV *, 4> Operands;
2570 for (const SCEV *AddRecOp : AddRec->operands())
2571 Operands.push_back(getMulExpr(Ops[0], AddRecOp));
2573 return getAddRecExpr(Operands, AddRec->getLoop(),
2574 AddRec->getNoWrapFlags(SCEV::FlagNW));
2579 if (Ops.size() == 1)
2583 // Skip over the add expression until we get to a multiply.
2584 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
2587 // If there are mul operands inline them all into this expression.
2588 if (Idx < Ops.size()) {
2589 bool DeletedMul = false;
2590 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
2591 if (Ops.size() > MulOpsInlineThreshold)
2593 // If we have an mul, expand the mul operands onto the end of the operands
2595 Ops.erase(Ops.begin()+Idx);
2596 Ops.append(Mul->op_begin(), Mul->op_end());
2600 // If we deleted at least one mul, we added operands to the end of the list,
2601 // and they are not necessarily sorted. Recurse to resort and resimplify
2602 // any operands we just acquired.
2604 return getMulExpr(Ops);
2607 // If there are any add recurrences in the operands list, see if any other
2608 // added values are loop invariant. If so, we can fold them into the
2610 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2613 // Scan over all recurrences, trying to fold loop invariants into them.
2614 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
2615 // Scan all of the other operands to this mul and add them to the vector if
2616 // they are loop invariant w.r.t. the recurrence.
2617 SmallVector<const SCEV *, 8> LIOps;
2618 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2619 const Loop *AddRecLoop = AddRec->getLoop();
2620 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2621 if (isLoopInvariant(Ops[i], AddRecLoop)) {
2622 LIOps.push_back(Ops[i]);
2623 Ops.erase(Ops.begin()+i);
2627 // If we found some loop invariants, fold them into the recurrence.
2628 if (!LIOps.empty()) {
2629 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
2630 SmallVector<const SCEV *, 4> NewOps;
2631 NewOps.reserve(AddRec->getNumOperands());
2632 const SCEV *Scale = getMulExpr(LIOps);
2633 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
2634 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
2636 // Build the new addrec. Propagate the NUW and NSW flags if both the
2637 // outer mul and the inner addrec are guaranteed to have no overflow.
2639 // No self-wrap cannot be guaranteed after changing the step size, but
2640 // will be inferred if either NUW or NSW is true.
2641 Flags = AddRec->getNoWrapFlags(clearFlags(Flags, SCEV::FlagNW));
2642 const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, Flags);
2644 // If all of the other operands were loop invariant, we are done.
2645 if (Ops.size() == 1) return NewRec;
2647 // Otherwise, multiply the folded AddRec by the non-invariant parts.
2648 for (unsigned i = 0;; ++i)
2649 if (Ops[i] == AddRec) {
2653 return getMulExpr(Ops);
2656 // Okay, if there weren't any loop invariants to be folded, check to see if
2657 // there are multiple AddRec's with the same loop induction variable being
2658 // multiplied together. If so, we can fold them.
2660 // {A1,+,A2,+,...,+,An}<L> * {B1,+,B2,+,...,+,Bn}<L>
2661 // = {x=1 in [ sum y=x..2x [ sum z=max(y-x, y-n)..min(x,n) [
2662 // choose(x, 2x)*choose(2x-y, x-z)*A_{y-z}*B_z
2663 // ]]],+,...up to x=2n}.
2664 // Note that the arguments to choose() are always integers with values
2665 // known at compile time, never SCEV objects.
2667 // The implementation avoids pointless extra computations when the two
2668 // addrec's are of different length (mathematically, it's equivalent to
2669 // an infinite stream of zeros on the right).
2670 bool OpsModified = false;
2671 for (unsigned OtherIdx = Idx+1;
2672 OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2674 const SCEVAddRecExpr *OtherAddRec =
2675 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]);
2676 if (!OtherAddRec || OtherAddRec->getLoop() != AddRecLoop)
2679 bool Overflow = false;
2680 Type *Ty = AddRec->getType();
2681 bool LargerThan64Bits = getTypeSizeInBits(Ty) > 64;
2682 SmallVector<const SCEV*, 7> AddRecOps;
2683 for (int x = 0, xe = AddRec->getNumOperands() +
2684 OtherAddRec->getNumOperands() - 1; x != xe && !Overflow; ++x) {
2685 const SCEV *Term = getZero(Ty);
2686 for (int y = x, ye = 2*x+1; y != ye && !Overflow; ++y) {
2687 uint64_t Coeff1 = Choose(x, 2*x - y, Overflow);
2688 for (int z = std::max(y-x, y-(int)AddRec->getNumOperands()+1),
2689 ze = std::min(x+1, (int)OtherAddRec->getNumOperands());
2690 z < ze && !Overflow; ++z) {
2691 uint64_t Coeff2 = Choose(2*x - y, x-z, Overflow);
2693 if (LargerThan64Bits)
2694 Coeff = umul_ov(Coeff1, Coeff2, Overflow);
2696 Coeff = Coeff1*Coeff2;
2697 const SCEV *CoeffTerm = getConstant(Ty, Coeff);
2698 const SCEV *Term1 = AddRec->getOperand(y-z);
2699 const SCEV *Term2 = OtherAddRec->getOperand(z);
2700 Term = getAddExpr(Term, getMulExpr(CoeffTerm, Term1,Term2));
2703 AddRecOps.push_back(Term);
2706 const SCEV *NewAddRec = getAddRecExpr(AddRecOps, AddRec->getLoop(),
2708 if (Ops.size() == 2) return NewAddRec;
2709 Ops[Idx] = NewAddRec;
2710 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2712 AddRec = dyn_cast<SCEVAddRecExpr>(NewAddRec);
2718 return getMulExpr(Ops);
2720 // Otherwise couldn't fold anything into this recurrence. Move onto the
2724 // Okay, it looks like we really DO need an mul expr. Check to see if we
2725 // already have one, otherwise create a new one.
2726 FoldingSetNodeID ID;
2727 ID.AddInteger(scMulExpr);
2728 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2729 ID.AddPointer(Ops[i]);
2732 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2734 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2735 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2736 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
2738 UniqueSCEVs.InsertNode(S, IP);
2740 S->setNoWrapFlags(Flags);
2744 /// Get a canonical unsigned division expression, or something simpler if
2746 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
2748 assert(getEffectiveSCEVType(LHS->getType()) ==
2749 getEffectiveSCEVType(RHS->getType()) &&
2750 "SCEVUDivExpr operand types don't match!");
2752 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
2753 if (RHSC->getValue()->equalsInt(1))
2754 return LHS; // X udiv 1 --> x
2755 // If the denominator is zero, the result of the udiv is undefined. Don't
2756 // try to analyze it, because the resolution chosen here may differ from
2757 // the resolution chosen in other parts of the compiler.
2758 if (!RHSC->getValue()->isZero()) {
2759 // Determine if the division can be folded into the operands of
2761 // TODO: Generalize this to non-constants by using known-bits information.
2762 Type *Ty = LHS->getType();
2763 unsigned LZ = RHSC->getAPInt().countLeadingZeros();
2764 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1;
2765 // For non-power-of-two values, effectively round the value up to the
2766 // nearest power of two.
2767 if (!RHSC->getAPInt().isPowerOf2())
2769 IntegerType *ExtTy =
2770 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
2771 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
2772 if (const SCEVConstant *Step =
2773 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) {
2774 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
2775 const APInt &StepInt = Step->getAPInt();
2776 const APInt &DivInt = RHSC->getAPInt();
2777 if (!StepInt.urem(DivInt) &&
2778 getZeroExtendExpr(AR, ExtTy) ==
2779 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2780 getZeroExtendExpr(Step, ExtTy),
2781 AR->getLoop(), SCEV::FlagAnyWrap)) {
2782 SmallVector<const SCEV *, 4> Operands;
2783 for (const SCEV *Op : AR->operands())
2784 Operands.push_back(getUDivExpr(Op, RHS));
2785 return getAddRecExpr(Operands, AR->getLoop(), SCEV::FlagNW);
2787 /// Get a canonical UDivExpr for a recurrence.
2788 /// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0.
2789 // We can currently only fold X%N if X is constant.
2790 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(AR->getStart());
2791 if (StartC && !DivInt.urem(StepInt) &&
2792 getZeroExtendExpr(AR, ExtTy) ==
2793 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2794 getZeroExtendExpr(Step, ExtTy),
2795 AR->getLoop(), SCEV::FlagAnyWrap)) {
2796 const APInt &StartInt = StartC->getAPInt();
2797 const APInt &StartRem = StartInt.urem(StepInt);
2799 LHS = getAddRecExpr(getConstant(StartInt - StartRem), Step,
2800 AR->getLoop(), SCEV::FlagNW);
2803 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
2804 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
2805 SmallVector<const SCEV *, 4> Operands;
2806 for (const SCEV *Op : M->operands())
2807 Operands.push_back(getZeroExtendExpr(Op, ExtTy));
2808 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
2809 // Find an operand that's safely divisible.
2810 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
2811 const SCEV *Op = M->getOperand(i);
2812 const SCEV *Div = getUDivExpr(Op, RHSC);
2813 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
2814 Operands = SmallVector<const SCEV *, 4>(M->op_begin(),
2817 return getMulExpr(Operands);
2821 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
2822 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) {
2823 SmallVector<const SCEV *, 4> Operands;
2824 for (const SCEV *Op : A->operands())
2825 Operands.push_back(getZeroExtendExpr(Op, ExtTy));
2826 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
2828 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
2829 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
2830 if (isa<SCEVUDivExpr>(Op) ||
2831 getMulExpr(Op, RHS) != A->getOperand(i))
2833 Operands.push_back(Op);
2835 if (Operands.size() == A->getNumOperands())
2836 return getAddExpr(Operands);
2840 // Fold if both operands are constant.
2841 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
2842 Constant *LHSCV = LHSC->getValue();
2843 Constant *RHSCV = RHSC->getValue();
2844 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
2850 FoldingSetNodeID ID;
2851 ID.AddInteger(scUDivExpr);
2855 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2856 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
2858 UniqueSCEVs.InsertNode(S, IP);
2862 static const APInt gcd(const SCEVConstant *C1, const SCEVConstant *C2) {
2863 APInt A = C1->getAPInt().abs();
2864 APInt B = C2->getAPInt().abs();
2865 uint32_t ABW = A.getBitWidth();
2866 uint32_t BBW = B.getBitWidth();
2873 return APIntOps::GreatestCommonDivisor(A, B);
2876 /// Get a canonical unsigned division expression, or something simpler if
2877 /// possible. There is no representation for an exact udiv in SCEV IR, but we
2878 /// can attempt to remove factors from the LHS and RHS. We can't do this when
2879 /// it's not exact because the udiv may be clearing bits.
2880 const SCEV *ScalarEvolution::getUDivExactExpr(const SCEV *LHS,
2882 // TODO: we could try to find factors in all sorts of things, but for now we
2883 // just deal with u/exact (multiply, constant). See SCEVDivision towards the
2884 // end of this file for inspiration.
2886 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(LHS);
2888 return getUDivExpr(LHS, RHS);
2890 if (const SCEVConstant *RHSCst = dyn_cast<SCEVConstant>(RHS)) {
2891 // If the mulexpr multiplies by a constant, then that constant must be the
2892 // first element of the mulexpr.
2893 if (const auto *LHSCst = dyn_cast<SCEVConstant>(Mul->getOperand(0))) {
2894 if (LHSCst == RHSCst) {
2895 SmallVector<const SCEV *, 2> Operands;
2896 Operands.append(Mul->op_begin() + 1, Mul->op_end());
2897 return getMulExpr(Operands);
2900 // We can't just assume that LHSCst divides RHSCst cleanly, it could be
2901 // that there's a factor provided by one of the other terms. We need to
2903 APInt Factor = gcd(LHSCst, RHSCst);
2904 if (!Factor.isIntN(1)) {
2906 cast<SCEVConstant>(getConstant(LHSCst->getAPInt().udiv(Factor)));
2908 cast<SCEVConstant>(getConstant(RHSCst->getAPInt().udiv(Factor)));
2909 SmallVector<const SCEV *, 2> Operands;
2910 Operands.push_back(LHSCst);
2911 Operands.append(Mul->op_begin() + 1, Mul->op_end());
2912 LHS = getMulExpr(Operands);
2914 Mul = dyn_cast<SCEVMulExpr>(LHS);
2916 return getUDivExactExpr(LHS, RHS);
2921 for (int i = 0, e = Mul->getNumOperands(); i != e; ++i) {
2922 if (Mul->getOperand(i) == RHS) {
2923 SmallVector<const SCEV *, 2> Operands;
2924 Operands.append(Mul->op_begin(), Mul->op_begin() + i);
2925 Operands.append(Mul->op_begin() + i + 1, Mul->op_end());
2926 return getMulExpr(Operands);
2930 return getUDivExpr(LHS, RHS);
2933 /// Get an add recurrence expression for the specified loop. Simplify the
2934 /// expression as much as possible.
2935 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step,
2937 SCEV::NoWrapFlags Flags) {
2938 SmallVector<const SCEV *, 4> Operands;
2939 Operands.push_back(Start);
2940 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
2941 if (StepChrec->getLoop() == L) {
2942 Operands.append(StepChrec->op_begin(), StepChrec->op_end());
2943 return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW));
2946 Operands.push_back(Step);
2947 return getAddRecExpr(Operands, L, Flags);
2950 /// Get an add recurrence expression for the specified loop. Simplify the
2951 /// expression as much as possible.
2953 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
2954 const Loop *L, SCEV::NoWrapFlags Flags) {
2955 if (Operands.size() == 1) return Operands[0];
2957 Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
2958 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
2959 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy &&
2960 "SCEVAddRecExpr operand types don't match!");
2961 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2962 assert(isLoopInvariant(Operands[i], L) &&
2963 "SCEVAddRecExpr operand is not loop-invariant!");
2966 if (Operands.back()->isZero()) {
2967 Operands.pop_back();
2968 return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0} --> X
2971 // It's tempting to want to call getMaxBackedgeTakenCount count here and
2972 // use that information to infer NUW and NSW flags. However, computing a
2973 // BE count requires calling getAddRecExpr, so we may not yet have a
2974 // meaningful BE count at this point (and if we don't, we'd be stuck
2975 // with a SCEVCouldNotCompute as the cached BE count).
2977 Flags = StrengthenNoWrapFlags(this, scAddRecExpr, Operands, Flags);
2979 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
2980 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
2981 const Loop *NestedLoop = NestedAR->getLoop();
2982 if (L->contains(NestedLoop)
2983 ? (L->getLoopDepth() < NestedLoop->getLoopDepth())
2984 : (!NestedLoop->contains(L) &&
2985 DT.dominates(L->getHeader(), NestedLoop->getHeader()))) {
2986 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
2987 NestedAR->op_end());
2988 Operands[0] = NestedAR->getStart();
2989 // AddRecs require their operands be loop-invariant with respect to their
2990 // loops. Don't perform this transformation if it would break this
2992 bool AllInvariant = all_of(
2993 Operands, [&](const SCEV *Op) { return isLoopInvariant(Op, L); });
2996 // Create a recurrence for the outer loop with the same step size.
2998 // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the
2999 // inner recurrence has the same property.
3000 SCEV::NoWrapFlags OuterFlags =
3001 maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags());
3003 NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags);
3004 AllInvariant = all_of(NestedOperands, [&](const SCEV *Op) {
3005 return isLoopInvariant(Op, NestedLoop);
3009 // Ok, both add recurrences are valid after the transformation.
3011 // The inner recurrence keeps its NW flag but only keeps NUW/NSW if
3012 // the outer recurrence has the same property.
3013 SCEV::NoWrapFlags InnerFlags =
3014 maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags);
3015 return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags);
3018 // Reset Operands to its original state.
3019 Operands[0] = NestedAR;
3023 // Okay, it looks like we really DO need an addrec expr. Check to see if we
3024 // already have one, otherwise create a new one.
3025 FoldingSetNodeID ID;
3026 ID.AddInteger(scAddRecExpr);
3027 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
3028 ID.AddPointer(Operands[i]);
3032 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
3034 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size());
3035 std::uninitialized_copy(Operands.begin(), Operands.end(), O);
3036 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator),
3037 O, Operands.size(), L);
3038 UniqueSCEVs.InsertNode(S, IP);
3040 S->setNoWrapFlags(Flags);
3045 ScalarEvolution::getGEPExpr(GEPOperator *GEP,
3046 const SmallVectorImpl<const SCEV *> &IndexExprs) {
3047 const SCEV *BaseExpr = getSCEV(GEP->getPointerOperand());
3048 // getSCEV(Base)->getType() has the same address space as Base->getType()
3049 // because SCEV::getType() preserves the address space.
3050 Type *IntPtrTy = getEffectiveSCEVType(BaseExpr->getType());
3051 // FIXME(PR23527): Don't blindly transfer the inbounds flag from the GEP
3052 // instruction to its SCEV, because the Instruction may be guarded by control
3053 // flow and the no-overflow bits may not be valid for the expression in any
3054 // context. This can be fixed similarly to how these flags are handled for
3056 SCEV::NoWrapFlags Wrap = GEP->isInBounds() ? SCEV::FlagNSW
3057 : SCEV::FlagAnyWrap;
3059 const SCEV *TotalOffset = getZero(IntPtrTy);
3060 // The array size is unimportant. The first thing we do on CurTy is getting
3061 // its element type.
3062 Type *CurTy = ArrayType::get(GEP->getSourceElementType(), 0);
3063 for (const SCEV *IndexExpr : IndexExprs) {
3064 // Compute the (potentially symbolic) offset in bytes for this index.
3065 if (StructType *STy = dyn_cast<StructType>(CurTy)) {
3066 // For a struct, add the member offset.
3067 ConstantInt *Index = cast<SCEVConstant>(IndexExpr)->getValue();
3068 unsigned FieldNo = Index->getZExtValue();
3069 const SCEV *FieldOffset = getOffsetOfExpr(IntPtrTy, STy, FieldNo);
3071 // Add the field offset to the running total offset.
3072 TotalOffset = getAddExpr(TotalOffset, FieldOffset);
3074 // Update CurTy to the type of the field at Index.
3075 CurTy = STy->getTypeAtIndex(Index);
3077 // Update CurTy to its element type.
3078 CurTy = cast<SequentialType>(CurTy)->getElementType();
3079 // For an array, add the element offset, explicitly scaled.
3080 const SCEV *ElementSize = getSizeOfExpr(IntPtrTy, CurTy);
3081 // Getelementptr indices are signed.
3082 IndexExpr = getTruncateOrSignExtend(IndexExpr, IntPtrTy);
3084 // Multiply the index by the element size to compute the element offset.
3085 const SCEV *LocalOffset = getMulExpr(IndexExpr, ElementSize, Wrap);
3087 // Add the element offset to the running total offset.
3088 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
3092 // Add the total offset from all the GEP indices to the base.
3093 return getAddExpr(BaseExpr, TotalOffset, Wrap);
3096 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
3098 SmallVector<const SCEV *, 2> Ops = {LHS, RHS};
3099 return getSMaxExpr(Ops);
3103 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
3104 assert(!Ops.empty() && "Cannot get empty smax!");
3105 if (Ops.size() == 1) return Ops[0];
3107 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
3108 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
3109 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
3110 "SCEVSMaxExpr operand types don't match!");
3113 // Sort by complexity, this groups all similar expression types together.
3114 GroupByComplexity(Ops, &LI);
3116 // If there are any constants, fold them together.
3118 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
3120 assert(Idx < Ops.size());
3121 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
3122 // We found two constants, fold them together!
3123 ConstantInt *Fold = ConstantInt::get(
3124 getContext(), APIntOps::smax(LHSC->getAPInt(), RHSC->getAPInt()));
3125 Ops[0] = getConstant(Fold);
3126 Ops.erase(Ops.begin()+1); // Erase the folded element
3127 if (Ops.size() == 1) return Ops[0];
3128 LHSC = cast<SCEVConstant>(Ops[0]);
3131 // If we are left with a constant minimum-int, strip it off.
3132 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
3133 Ops.erase(Ops.begin());
3135 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
3136 // If we have an smax with a constant maximum-int, it will always be
3141 if (Ops.size() == 1) return Ops[0];
3144 // Find the first SMax
3145 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
3148 // Check to see if one of the operands is an SMax. If so, expand its operands
3149 // onto our operand list, and recurse to simplify.
3150 if (Idx < Ops.size()) {
3151 bool DeletedSMax = false;
3152 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
3153 Ops.erase(Ops.begin()+Idx);
3154 Ops.append(SMax->op_begin(), SMax->op_end());
3159 return getSMaxExpr(Ops);
3162 // Okay, check to see if the same value occurs in the operand list twice. If
3163 // so, delete one. Since we sorted the list, these values are required to
3165 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
3166 // X smax Y smax Y --> X smax Y
3167 // X smax Y --> X, if X is always greater than Y
3168 if (Ops[i] == Ops[i+1] ||
3169 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) {
3170 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
3172 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) {
3173 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
3177 if (Ops.size() == 1) return Ops[0];
3179 assert(!Ops.empty() && "Reduced smax down to nothing!");
3181 // Okay, it looks like we really DO need an smax expr. Check to see if we
3182 // already have one, otherwise create a new one.
3183 FoldingSetNodeID ID;
3184 ID.AddInteger(scSMaxExpr);
3185 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
3186 ID.AddPointer(Ops[i]);
3188 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
3189 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
3190 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
3191 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator),
3193 UniqueSCEVs.InsertNode(S, IP);
3197 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
3199 SmallVector<const SCEV *, 2> Ops = {LHS, RHS};
3200 return getUMaxExpr(Ops);
3204 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
3205 assert(!Ops.empty() && "Cannot get empty umax!");
3206 if (Ops.size() == 1) return Ops[0];
3208 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
3209 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
3210 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
3211 "SCEVUMaxExpr operand types don't match!");
3214 // Sort by complexity, this groups all similar expression types together.
3215 GroupByComplexity(Ops, &LI);
3217 // If there are any constants, fold them together.
3219 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
3221 assert(Idx < Ops.size());
3222 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
3223 // We found two constants, fold them together!
3224 ConstantInt *Fold = ConstantInt::get(
3225 getContext(), APIntOps::umax(LHSC->getAPInt(), RHSC->getAPInt()));
3226 Ops[0] = getConstant(Fold);
3227 Ops.erase(Ops.begin()+1); // Erase the folded element
3228 if (Ops.size() == 1) return Ops[0];
3229 LHSC = cast<SCEVConstant>(Ops[0]);
3232 // If we are left with a constant minimum-int, strip it off.
3233 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
3234 Ops.erase(Ops.begin());
3236 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
3237 // If we have an umax with a constant maximum-int, it will always be
3242 if (Ops.size() == 1) return Ops[0];
3245 // Find the first UMax
3246 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
3249 // Check to see if one of the operands is a UMax. If so, expand its operands
3250 // onto our operand list, and recurse to simplify.
3251 if (Idx < Ops.size()) {
3252 bool DeletedUMax = false;
3253 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
3254 Ops.erase(Ops.begin()+Idx);
3255 Ops.append(UMax->op_begin(), UMax->op_end());
3260 return getUMaxExpr(Ops);
3263 // Okay, check to see if the same value occurs in the operand list twice. If
3264 // so, delete one. Since we sorted the list, these values are required to
3266 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
3267 // X umax Y umax Y --> X umax Y
3268 // X umax Y --> X, if X is always greater than Y
3269 if (Ops[i] == Ops[i+1] ||
3270 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) {
3271 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
3273 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) {
3274 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
3278 if (Ops.size() == 1) return Ops[0];
3280 assert(!Ops.empty() && "Reduced umax down to nothing!");
3282 // Okay, it looks like we really DO need a umax expr. Check to see if we
3283 // already have one, otherwise create a new one.
3284 FoldingSetNodeID ID;
3285 ID.AddInteger(scUMaxExpr);
3286 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
3287 ID.AddPointer(Ops[i]);
3289 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
3290 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
3291 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
3292 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator),
3294 UniqueSCEVs.InsertNode(S, IP);
3298 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
3300 // ~smax(~x, ~y) == smin(x, y).
3301 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
3304 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
3306 // ~umax(~x, ~y) == umin(x, y)
3307 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
3310 const SCEV *ScalarEvolution::getSizeOfExpr(Type *IntTy, Type *AllocTy) {
3311 // We can bypass creating a target-independent
3312 // constant expression and then folding it back into a ConstantInt.
3313 // This is just a compile-time optimization.
3314 return getConstant(IntTy, getDataLayout().getTypeAllocSize(AllocTy));
3317 const SCEV *ScalarEvolution::getOffsetOfExpr(Type *IntTy,
3320 // We can bypass creating a target-independent
3321 // constant expression and then folding it back into a ConstantInt.
3322 // This is just a compile-time optimization.
3324 IntTy, getDataLayout().getStructLayout(STy)->getElementOffset(FieldNo));
3327 const SCEV *ScalarEvolution::getUnknown(Value *V) {
3328 // Don't attempt to do anything other than create a SCEVUnknown object
3329 // here. createSCEV only calls getUnknown after checking for all other
3330 // interesting possibilities, and any other code that calls getUnknown
3331 // is doing so in order to hide a value from SCEV canonicalization.
3333 FoldingSetNodeID ID;
3334 ID.AddInteger(scUnknown);
3337 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
3338 assert(cast<SCEVUnknown>(S)->getValue() == V &&
3339 "Stale SCEVUnknown in uniquing map!");
3342 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
3344 FirstUnknown = cast<SCEVUnknown>(S);
3345 UniqueSCEVs.InsertNode(S, IP);
3349 //===----------------------------------------------------------------------===//
3350 // Basic SCEV Analysis and PHI Idiom Recognition Code
3353 /// Test if values of the given type are analyzable within the SCEV
3354 /// framework. This primarily includes integer types, and it can optionally
3355 /// include pointer types if the ScalarEvolution class has access to
3356 /// target-specific information.
3357 bool ScalarEvolution::isSCEVable(Type *Ty) const {
3358 // Integers and pointers are always SCEVable.
3359 return Ty->isIntegerTy() || Ty->isPointerTy();
3362 /// Return the size in bits of the specified type, for which isSCEVable must
3364 uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const {
3365 assert(isSCEVable(Ty) && "Type is not SCEVable!");
3366 return getDataLayout().getTypeSizeInBits(Ty);
3369 /// Return a type with the same bitwidth as the given type and which represents
3370 /// how SCEV will treat the given type, for which isSCEVable must return
3371 /// true. For pointer types, this is the pointer-sized integer type.
3372 Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const {
3373 assert(isSCEVable(Ty) && "Type is not SCEVable!");
3375 if (Ty->isIntegerTy())
3378 // The only other support type is pointer.
3379 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
3380 return getDataLayout().getIntPtrType(Ty);
3383 const SCEV *ScalarEvolution::getCouldNotCompute() {
3384 return CouldNotCompute.get();
3387 bool ScalarEvolution::checkValidity(const SCEV *S) const {
3388 bool ContainsNulls = SCEVExprContains(S, [](const SCEV *S) {
3389 auto *SU = dyn_cast<SCEVUnknown>(S);
3390 return SU && SU->getValue() == nullptr;
3393 return !ContainsNulls;
3396 bool ScalarEvolution::containsAddRecurrence(const SCEV *S) {
3397 HasRecMapType::iterator I = HasRecMap.find(S);
3398 if (I != HasRecMap.end())
3401 bool FoundAddRec = SCEVExprContains(S, isa<SCEVAddRecExpr, const SCEV *>);
3402 HasRecMap.insert({S, FoundAddRec});
3406 /// Try to split a SCEVAddExpr into a pair of {SCEV, ConstantInt}.
3407 /// If \p S is a SCEVAddExpr and is composed of a sub SCEV S' and an
3408 /// offset I, then return {S', I}, else return {\p S, nullptr}.
3409 static std::pair<const SCEV *, ConstantInt *> splitAddExpr(const SCEV *S) {
3410 const auto *Add = dyn_cast<SCEVAddExpr>(S);
3412 return {S, nullptr};
3414 if (Add->getNumOperands() != 2)
3415 return {S, nullptr};
3417 auto *ConstOp = dyn_cast<SCEVConstant>(Add->getOperand(0));
3419 return {S, nullptr};
3421 return {Add->getOperand(1), ConstOp->getValue()};
3424 /// Return the ValueOffsetPair set for \p S. \p S can be represented
3425 /// by the value and offset from any ValueOffsetPair in the set.
3426 SetVector<ScalarEvolution::ValueOffsetPair> *
3427 ScalarEvolution::getSCEVValues(const SCEV *S) {
3428 ExprValueMapType::iterator SI = ExprValueMap.find_as(S);
3429 if (SI == ExprValueMap.end())
3432 if (VerifySCEVMap) {
3433 // Check there is no dangling Value in the set returned.
3434 for (const auto &VE : SI->second)
3435 assert(ValueExprMap.count(VE.first));
3441 /// Erase Value from ValueExprMap and ExprValueMap. ValueExprMap.erase(V)
3442 /// cannot be used separately. eraseValueFromMap should be used to remove
3443 /// V from ValueExprMap and ExprValueMap at the same time.
3444 void ScalarEvolution::eraseValueFromMap(Value *V) {
3445 ValueExprMapType::iterator I = ValueExprMap.find_as(V);
3446 if (I != ValueExprMap.end()) {
3447 const SCEV *S = I->second;
3448 // Remove {V, 0} from the set of ExprValueMap[S]
3449 if (SetVector<ValueOffsetPair> *SV = getSCEVValues(S))
3450 SV->remove({V, nullptr});
3452 // Remove {V, Offset} from the set of ExprValueMap[Stripped]
3453 const SCEV *Stripped;
3454 ConstantInt *Offset;
3455 std::tie(Stripped, Offset) = splitAddExpr(S);
3456 if (Offset != nullptr) {
3457 if (SetVector<ValueOffsetPair> *SV = getSCEVValues(Stripped))
3458 SV->remove({V, Offset});
3460 ValueExprMap.erase(V);
3464 /// Return an existing SCEV if it exists, otherwise analyze the expression and
3465 /// create a new one.
3466 const SCEV *ScalarEvolution::getSCEV(Value *V) {
3467 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
3469 const SCEV *S = getExistingSCEV(V);
3472 // During PHI resolution, it is possible to create two SCEVs for the same
3473 // V, so it is needed to double check whether V->S is inserted into
3474 // ValueExprMap before insert S->{V, 0} into ExprValueMap.
3475 std::pair<ValueExprMapType::iterator, bool> Pair =
3476 ValueExprMap.insert({SCEVCallbackVH(V, this), S});
3478 ExprValueMap[S].insert({V, nullptr});
3480 // If S == Stripped + Offset, add Stripped -> {V, Offset} into
3482 const SCEV *Stripped = S;
3483 ConstantInt *Offset = nullptr;
3484 std::tie(Stripped, Offset) = splitAddExpr(S);
3485 // If stripped is SCEVUnknown, don't bother to save
3486 // Stripped -> {V, offset}. It doesn't simplify and sometimes even
3487 // increase the complexity of the expansion code.
3488 // If V is GetElementPtrInst, don't save Stripped -> {V, offset}
3489 // because it may generate add/sub instead of GEP in SCEV expansion.
3490 if (Offset != nullptr && !isa<SCEVUnknown>(Stripped) &&
3491 !isa<GetElementPtrInst>(V))
3492 ExprValueMap[Stripped].insert({V, Offset});
3498 const SCEV *ScalarEvolution::getExistingSCEV(Value *V) {
3499 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
3501 ValueExprMapType::iterator I = ValueExprMap.find_as(V);
3502 if (I != ValueExprMap.end()) {
3503 const SCEV *S = I->second;
3504 if (checkValidity(S))
3506 eraseValueFromMap(V);
3507 forgetMemoizedResults(S);
3512 /// Return a SCEV corresponding to -V = -1*V
3514 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V,
3515 SCEV::NoWrapFlags Flags) {
3516 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
3518 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
3520 Type *Ty = V->getType();
3521 Ty = getEffectiveSCEVType(Ty);
3523 V, getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))), Flags);
3526 /// Return a SCEV corresponding to ~V = -1-V
3527 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
3528 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
3530 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
3532 Type *Ty = V->getType();
3533 Ty = getEffectiveSCEVType(Ty);
3534 const SCEV *AllOnes =
3535 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
3536 return getMinusSCEV(AllOnes, V);
3539 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
3540 SCEV::NoWrapFlags Flags) {
3541 // Fast path: X - X --> 0.
3543 return getZero(LHS->getType());
3545 // We represent LHS - RHS as LHS + (-1)*RHS. This transformation
3546 // makes it so that we cannot make much use of NUW.
3547 auto AddFlags = SCEV::FlagAnyWrap;
3548 const bool RHSIsNotMinSigned =
3549 !getSignedRange(RHS).getSignedMin().isMinSignedValue();
3550 if (maskFlags(Flags, SCEV::FlagNSW) == SCEV::FlagNSW) {
3551 // Let M be the minimum representable signed value. Then (-1)*RHS
3552 // signed-wraps if and only if RHS is M. That can happen even for
3553 // a NSW subtraction because e.g. (-1)*M signed-wraps even though
3554 // -1 - M does not. So to transfer NSW from LHS - RHS to LHS +
3555 // (-1)*RHS, we need to prove that RHS != M.
3557 // If LHS is non-negative and we know that LHS - RHS does not
3558 // signed-wrap, then RHS cannot be M. So we can rule out signed-wrap
3559 // either by proving that RHS > M or that LHS >= 0.
3560 if (RHSIsNotMinSigned || isKnownNonNegative(LHS)) {
3561 AddFlags = SCEV::FlagNSW;
3565 // FIXME: Find a correct way to transfer NSW to (-1)*M when LHS -
3566 // RHS is NSW and LHS >= 0.
3568 // The difficulty here is that the NSW flag may have been proven
3569 // relative to a loop that is to be found in a recurrence in LHS and
3570 // not in RHS. Applying NSW to (-1)*M may then let the NSW have a
3571 // larger scope than intended.
3572 auto NegFlags = RHSIsNotMinSigned ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
3574 return getAddExpr(LHS, getNegativeSCEV(RHS, NegFlags), AddFlags);
3578 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty) {
3579 Type *SrcTy = V->getType();
3580 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3581 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3582 "Cannot truncate or zero extend with non-integer arguments!");
3583 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3584 return V; // No conversion
3585 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
3586 return getTruncateExpr(V, Ty);
3587 return getZeroExtendExpr(V, Ty);
3591 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
3593 Type *SrcTy = V->getType();
3594 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3595 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3596 "Cannot truncate or zero extend with non-integer arguments!");
3597 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3598 return V; // No conversion
3599 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
3600 return getTruncateExpr(V, Ty);
3601 return getSignExtendExpr(V, Ty);
3605 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) {
3606 Type *SrcTy = V->getType();
3607 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3608 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3609 "Cannot noop or zero extend with non-integer arguments!");
3610 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3611 "getNoopOrZeroExtend cannot truncate!");
3612 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3613 return V; // No conversion
3614 return getZeroExtendExpr(V, Ty);
3618 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) {
3619 Type *SrcTy = V->getType();
3620 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3621 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3622 "Cannot noop or sign extend with non-integer arguments!");
3623 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3624 "getNoopOrSignExtend cannot truncate!");
3625 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3626 return V; // No conversion
3627 return getSignExtendExpr(V, Ty);
3631 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) {
3632 Type *SrcTy = V->getType();
3633 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3634 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3635 "Cannot noop or any extend with non-integer arguments!");
3636 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3637 "getNoopOrAnyExtend cannot truncate!");
3638 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3639 return V; // No conversion
3640 return getAnyExtendExpr(V, Ty);
3644 ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) {
3645 Type *SrcTy = V->getType();
3646 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3647 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3648 "Cannot truncate or noop with non-integer arguments!");
3649 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
3650 "getTruncateOrNoop cannot extend!");
3651 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3652 return V; // No conversion
3653 return getTruncateExpr(V, Ty);
3656 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
3658 const SCEV *PromotedLHS = LHS;
3659 const SCEV *PromotedRHS = RHS;
3661 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
3662 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
3664 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
3666 return getUMaxExpr(PromotedLHS, PromotedRHS);
3669 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
3671 const SCEV *PromotedLHS = LHS;
3672 const SCEV *PromotedRHS = RHS;
3674 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
3675 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
3677 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
3679 return getUMinExpr(PromotedLHS, PromotedRHS);
3682 const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) {
3683 // A pointer operand may evaluate to a nonpointer expression, such as null.
3684 if (!V->getType()->isPointerTy())
3687 if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) {
3688 return getPointerBase(Cast->getOperand());
3689 } else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) {
3690 const SCEV *PtrOp = nullptr;
3691 for (const SCEV *NAryOp : NAry->operands()) {
3692 if (NAryOp->getType()->isPointerTy()) {
3693 // Cannot find the base of an expression with multiple pointer operands.
3701 return getPointerBase(PtrOp);
3706 /// Push users of the given Instruction onto the given Worklist.
3708 PushDefUseChildren(Instruction *I,
3709 SmallVectorImpl<Instruction *> &Worklist) {
3710 // Push the def-use children onto the Worklist stack.
3711 for (User *U : I->users())
3712 Worklist.push_back(cast<Instruction>(U));
3715 void ScalarEvolution::forgetSymbolicName(Instruction *PN, const SCEV *SymName) {
3716 SmallVector<Instruction *, 16> Worklist;
3717 PushDefUseChildren(PN, Worklist);
3719 SmallPtrSet<Instruction *, 8> Visited;
3721 while (!Worklist.empty()) {
3722 Instruction *I = Worklist.pop_back_val();
3723 if (!Visited.insert(I).second)
3726 auto It = ValueExprMap.find_as(static_cast<Value *>(I));
3727 if (It != ValueExprMap.end()) {
3728 const SCEV *Old = It->second;
3730 // Short-circuit the def-use traversal if the symbolic name
3731 // ceases to appear in expressions.
3732 if (Old != SymName && !hasOperand(Old, SymName))
3735 // SCEVUnknown for a PHI either means that it has an unrecognized
3736 // structure, it's a PHI that's in the progress of being computed
3737 // by createNodeForPHI, or it's a single-value PHI. In the first case,
3738 // additional loop trip count information isn't going to change anything.
3739 // In the second case, createNodeForPHI will perform the necessary
3740 // updates on its own when it gets to that point. In the third, we do
3741 // want to forget the SCEVUnknown.
3742 if (!isa<PHINode>(I) ||
3743 !isa<SCEVUnknown>(Old) ||
3744 (I != PN && Old == SymName)) {
3745 eraseValueFromMap(It->first);
3746 forgetMemoizedResults(Old);
3750 PushDefUseChildren(I, Worklist);
3755 class SCEVInitRewriter : public SCEVRewriteVisitor<SCEVInitRewriter> {
3757 static const SCEV *rewrite(const SCEV *S, const Loop *L,
3758 ScalarEvolution &SE) {
3759 SCEVInitRewriter Rewriter(L, SE);
3760 const SCEV *Result = Rewriter.visit(S);
3761 return Rewriter.isValid() ? Result : SE.getCouldNotCompute();
3764 SCEVInitRewriter(const Loop *L, ScalarEvolution &SE)
3765 : SCEVRewriteVisitor(SE), L(L), Valid(true) {}
3767 const SCEV *visitUnknown(const SCEVUnknown *Expr) {
3768 if (!(SE.getLoopDisposition(Expr, L) == ScalarEvolution::LoopInvariant))
3773 const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
3774 // Only allow AddRecExprs for this loop.
3775 if (Expr->getLoop() == L)
3776 return Expr->getStart();
3781 bool isValid() { return Valid; }
3788 class SCEVShiftRewriter : public SCEVRewriteVisitor<SCEVShiftRewriter> {
3790 static const SCEV *rewrite(const SCEV *S, const Loop *L,
3791 ScalarEvolution &SE) {
3792 SCEVShiftRewriter Rewriter(L, SE);
3793 const SCEV *Result = Rewriter.visit(S);
3794 return Rewriter.isValid() ? Result : SE.getCouldNotCompute();
3797 SCEVShiftRewriter(const Loop *L, ScalarEvolution &SE)
3798 : SCEVRewriteVisitor(SE), L(L), Valid(true) {}
3800 const SCEV *visitUnknown(const SCEVUnknown *Expr) {
3801 // Only allow AddRecExprs for this loop.
3802 if (!(SE.getLoopDisposition(Expr, L) == ScalarEvolution::LoopInvariant))
3807 const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
3808 if (Expr->getLoop() == L && Expr->isAffine())
3809 return SE.getMinusSCEV(Expr, Expr->getStepRecurrence(SE));
3813 bool isValid() { return Valid; }
3819 } // end anonymous namespace
3822 ScalarEvolution::proveNoWrapViaConstantRanges(const SCEVAddRecExpr *AR) {
3823 if (!AR->isAffine())
3824 return SCEV::FlagAnyWrap;
3826 typedef OverflowingBinaryOperator OBO;
3827 SCEV::NoWrapFlags Result = SCEV::FlagAnyWrap;
3829 if (!AR->hasNoSignedWrap()) {
3830 ConstantRange AddRecRange = getSignedRange(AR);
3831 ConstantRange IncRange = getSignedRange(AR->getStepRecurrence(*this));
3833 auto NSWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
3834 Instruction::Add, IncRange, OBO::NoSignedWrap);
3835 if (NSWRegion.contains(AddRecRange))
3836 Result = ScalarEvolution::setFlags(Result, SCEV::FlagNSW);
3839 if (!AR->hasNoUnsignedWrap()) {
3840 ConstantRange AddRecRange = getUnsignedRange(AR);
3841 ConstantRange IncRange = getUnsignedRange(AR->getStepRecurrence(*this));
3843 auto NUWRegion = ConstantRange::makeGuaranteedNoWrapRegion(
3844 Instruction::Add, IncRange, OBO::NoUnsignedWrap);
3845 if (NUWRegion.contains(AddRecRange))
3846 Result = ScalarEvolution::setFlags(Result, SCEV::FlagNUW);
3853 /// Represents an abstract binary operation. This may exist as a
3854 /// normal instruction or constant expression, or may have been
3855 /// derived from an expression tree.
3863 /// Op is set if this BinaryOp corresponds to a concrete LLVM instruction or
3864 /// constant expression.
3867 explicit BinaryOp(Operator *Op)
3868 : Opcode(Op->getOpcode()), LHS(Op->getOperand(0)), RHS(Op->getOperand(1)),
3869 IsNSW(false), IsNUW(false), Op(Op) {
3870 if (auto *OBO = dyn_cast<OverflowingBinaryOperator>(Op)) {
3871 IsNSW = OBO->hasNoSignedWrap();
3872 IsNUW = OBO->hasNoUnsignedWrap();
3876 explicit BinaryOp(unsigned Opcode, Value *LHS, Value *RHS, bool IsNSW = false,
3878 : Opcode(Opcode), LHS(LHS), RHS(RHS), IsNSW(IsNSW), IsNUW(IsNUW),
3884 /// Try to map \p V into a BinaryOp, and return \c None on failure.
3885 static Optional<BinaryOp> MatchBinaryOp(Value *V, DominatorTree &DT) {
3886 auto *Op = dyn_cast<Operator>(V);
3890 // Implementation detail: all the cleverness here should happen without
3891 // creating new SCEV expressions -- our caller knowns tricks to avoid creating
3892 // SCEV expressions when possible, and we should not break that.
3894 switch (Op->getOpcode()) {
3895 case Instruction::Add:
3896 case Instruction::Sub:
3897 case Instruction::Mul:
3898 case Instruction::UDiv:
3899 case Instruction::And:
3900 case Instruction::Or:
3901 case Instruction::AShr:
3902 case Instruction::Shl:
3903 return BinaryOp(Op);
3905 case Instruction::Xor:
3906 if (auto *RHSC = dyn_cast<ConstantInt>(Op->getOperand(1)))
3907 // If the RHS of the xor is a signbit, then this is just an add.
3908 // Instcombine turns add of signbit into xor as a strength reduction step.
3909 if (RHSC->getValue().isSignBit())
3910 return BinaryOp(Instruction::Add, Op->getOperand(0), Op->getOperand(1));
3911 return BinaryOp(Op);
3913 case Instruction::LShr:
3914 // Turn logical shift right of a constant into a unsigned divide.
3915 if (ConstantInt *SA = dyn_cast<ConstantInt>(Op->getOperand(1))) {
3916 uint32_t BitWidth = cast<IntegerType>(Op->getType())->getBitWidth();
3918 // If the shift count is not less than the bitwidth, the result of
3919 // the shift is undefined. Don't try to analyze it, because the
3920 // resolution chosen here may differ from the resolution chosen in
3921 // other parts of the compiler.
3922 if (SA->getValue().ult(BitWidth)) {
3924 ConstantInt::get(SA->getContext(),
3925 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
3926 return BinaryOp(Instruction::UDiv, Op->getOperand(0), X);
3929 return BinaryOp(Op);
3931 case Instruction::ExtractValue: {
3932 auto *EVI = cast<ExtractValueInst>(Op);
3933 if (EVI->getNumIndices() != 1 || EVI->getIndices()[0] != 0)
3936 auto *CI = dyn_cast<CallInst>(EVI->getAggregateOperand());
3940 if (auto *F = CI->getCalledFunction())
3941 switch (F->getIntrinsicID()) {
3942 case Intrinsic::sadd_with_overflow:
3943 case Intrinsic::uadd_with_overflow: {
3944 if (!isOverflowIntrinsicNoWrap(cast<IntrinsicInst>(CI), DT))
3945 return BinaryOp(Instruction::Add, CI->getArgOperand(0),
3946 CI->getArgOperand(1));
3948 // Now that we know that all uses of the arithmetic-result component of
3949 // CI are guarded by the overflow check, we can go ahead and pretend
3950 // that the arithmetic is non-overflowing.
3951 if (F->getIntrinsicID() == Intrinsic::sadd_with_overflow)
3952 return BinaryOp(Instruction::Add, CI->getArgOperand(0),
3953 CI->getArgOperand(1), /* IsNSW = */ true,
3954 /* IsNUW = */ false);
3956 return BinaryOp(Instruction::Add, CI->getArgOperand(0),
3957 CI->getArgOperand(1), /* IsNSW = */ false,
3961 case Intrinsic::ssub_with_overflow:
3962 case Intrinsic::usub_with_overflow:
3963 return BinaryOp(Instruction::Sub, CI->getArgOperand(0),
3964 CI->getArgOperand(1));
3966 case Intrinsic::smul_with_overflow:
3967 case Intrinsic::umul_with_overflow:
3968 return BinaryOp(Instruction::Mul, CI->getArgOperand(0),
3969 CI->getArgOperand(1));
3982 const SCEV *ScalarEvolution::createAddRecFromPHI(PHINode *PN) {
3983 const Loop *L = LI.getLoopFor(PN->getParent());
3984 if (!L || L->getHeader() != PN->getParent())
3987 // The loop may have multiple entrances or multiple exits; we can analyze
3988 // this phi as an addrec if it has a unique entry value and a unique
3990 Value *BEValueV = nullptr, *StartValueV = nullptr;
3991 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
3992 Value *V = PN->getIncomingValue(i);
3993 if (L->contains(PN->getIncomingBlock(i))) {
3996 } else if (BEValueV != V) {
4000 } else if (!StartValueV) {
4002 } else if (StartValueV != V) {
4003 StartValueV = nullptr;
4007 if (BEValueV && StartValueV) {
4008 // While we are analyzing this PHI node, handle its value symbolically.
4009 const SCEV *SymbolicName = getUnknown(PN);
4010 assert(ValueExprMap.find_as(PN) == ValueExprMap.end() &&
4011 "PHI node already processed?");
4012 ValueExprMap.insert({SCEVCallbackVH(PN, this), SymbolicName});
4014 // Using this symbolic name for the PHI, analyze the value coming around
4016 const SCEV *BEValue = getSCEV(BEValueV);
4018 // NOTE: If BEValue is loop invariant, we know that the PHI node just
4019 // has a special value for the first iteration of the loop.
4021 // If the value coming around the backedge is an add with the symbolic
4022 // value we just inserted, then we found a simple induction variable!
4023 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
4024 // If there is a single occurrence of the symbolic value, replace it
4025 // with a recurrence.
4026 unsigned FoundIndex = Add->getNumOperands();
4027 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
4028 if (Add->getOperand(i) == SymbolicName)
4029 if (FoundIndex == e) {
4034 if (FoundIndex != Add->getNumOperands()) {
4035 // Create an add with everything but the specified operand.
4036 SmallVector<const SCEV *, 8> Ops;
4037 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
4038 if (i != FoundIndex)
4039 Ops.push_back(Add->getOperand(i));
4040 const SCEV *Accum = getAddExpr(Ops);
4042 // This is not a valid addrec if the step amount is varying each
4043 // loop iteration, but is not itself an addrec in this loop.
4044 if (isLoopInvariant(Accum, L) ||
4045 (isa<SCEVAddRecExpr>(Accum) &&
4046 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
4047 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
4049 if (auto BO = MatchBinaryOp(BEValueV, DT)) {
4050 if (BO->Opcode == Instruction::Add && BO->LHS == PN) {
4052 Flags = setFlags(Flags, SCEV::FlagNUW);
4054 Flags = setFlags(Flags, SCEV::FlagNSW);
4056 } else if (GEPOperator *GEP = dyn_cast<GEPOperator>(BEValueV)) {
4057 // If the increment is an inbounds GEP, then we know the address
4058 // space cannot be wrapped around. We cannot make any guarantee
4059 // about signed or unsigned overflow because pointers are
4060 // unsigned but we may have a negative index from the base
4061 // pointer. We can guarantee that no unsigned wrap occurs if the
4062 // indices form a positive value.
4063 if (GEP->isInBounds() && GEP->getOperand(0) == PN) {
4064 Flags = setFlags(Flags, SCEV::FlagNW);
4066 const SCEV *Ptr = getSCEV(GEP->getPointerOperand());
4067 if (isKnownPositive(getMinusSCEV(getSCEV(GEP), Ptr)))
4068 Flags = setFlags(Flags, SCEV::FlagNUW);
4071 // We cannot transfer nuw and nsw flags from subtraction
4072 // operations -- sub nuw X, Y is not the same as add nuw X, -Y
4076 const SCEV *StartVal = getSCEV(StartValueV);
4077 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
4079 // Okay, for the entire analysis of this edge we assumed the PHI
4080 // to be symbolic. We now need to go back and purge all of the
4081 // entries for the scalars that use the symbolic expression.
4082 forgetSymbolicName(PN, SymbolicName);
4083 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
4085 // We can add Flags to the post-inc expression only if we
4086 // know that it us *undefined behavior* for BEValueV to
4088 if (auto *BEInst = dyn_cast<Instruction>(BEValueV))
4089 if (isLoopInvariant(Accum, L) && isAddRecNeverPoison(BEInst, L))
4090 (void)getAddRecExpr(getAddExpr(StartVal, Accum), Accum, L, Flags);
4096 // Otherwise, this could be a loop like this:
4097 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
4098 // In this case, j = {1,+,1} and BEValue is j.
4099 // Because the other in-value of i (0) fits the evolution of BEValue
4100 // i really is an addrec evolution.
4102 // We can generalize this saying that i is the shifted value of BEValue
4103 // by one iteration:
4104 // PHI(f(0), f({1,+,1})) --> f({0,+,1})
4105 const SCEV *Shifted = SCEVShiftRewriter::rewrite(BEValue, L, *this);
4106 const SCEV *Start = SCEVInitRewriter::rewrite(Shifted, L, *this);
4107 if (Shifted != getCouldNotCompute() &&
4108 Start != getCouldNotCompute()) {
4109 const SCEV *StartVal = getSCEV(StartValueV);
4110 if (Start == StartVal) {
4111 // Okay, for the entire analysis of this edge we assumed the PHI
4112 // to be symbolic. We now need to go back and purge all of the
4113 // entries for the scalars that use the symbolic expression.
4114 forgetSymbolicName(PN, SymbolicName);
4115 ValueExprMap[SCEVCallbackVH(PN, this)] = Shifted;
4121 // Remove the temporary PHI node SCEV that has been inserted while intending
4122 // to create an AddRecExpr for this PHI node. We can not keep this temporary
4123 // as it will prevent later (possibly simpler) SCEV expressions to be added
4124 // to the ValueExprMap.
4125 eraseValueFromMap(PN);
4131 // Checks if the SCEV S is available at BB. S is considered available at BB
4132 // if S can be materialized at BB without introducing a fault.
4133 static bool IsAvailableOnEntry(const Loop *L, DominatorTree &DT, const SCEV *S,
4135 struct CheckAvailable {
4136 bool TraversalDone = false;
4137 bool Available = true;
4139 const Loop *L = nullptr; // The loop BB is in (can be nullptr)
4140 BasicBlock *BB = nullptr;
4143 CheckAvailable(const Loop *L, BasicBlock *BB, DominatorTree &DT)
4144 : L(L), BB(BB), DT(DT) {}
4146 bool setUnavailable() {
4147 TraversalDone = true;
4152 bool follow(const SCEV *S) {
4153 switch (S->getSCEVType()) {
4154 case scConstant: case scTruncate: case scZeroExtend: case scSignExtend:
4155 case scAddExpr: case scMulExpr: case scUMaxExpr: case scSMaxExpr:
4156 // These expressions are available if their operand(s) is/are.
4159 case scAddRecExpr: {
4160 // We allow add recurrences that are on the loop BB is in, or some
4161 // outer loop. This guarantees availability because the value of the
4162 // add recurrence at BB is simply the "current" value of the induction
4163 // variable. We can relax this in the future; for instance an add
4164 // recurrence on a sibling dominating loop is also available at BB.
4165 const auto *ARLoop = cast<SCEVAddRecExpr>(S)->getLoop();
4166 if (L && (ARLoop == L || ARLoop->contains(L)))
4169 return setUnavailable();
4173 // For SCEVUnknown, we check for simple dominance.
4174 const auto *SU = cast<SCEVUnknown>(S);
4175 Value *V = SU->getValue();
4177 if (isa<Argument>(V))
4180 if (isa<Instruction>(V) && DT.dominates(cast<Instruction>(V), BB))
4183 return setUnavailable();
4187 case scCouldNotCompute:
4188 // We do not try to smart about these at all.
4189 return setUnavailable();
4191 llvm_unreachable("switch should be fully covered!");
4194 bool isDone() { return TraversalDone; }
4197 CheckAvailable CA(L, BB, DT);
4198 SCEVTraversal<CheckAvailable> ST(CA);
4201 return CA.Available;
4204 // Try to match a control flow sequence that branches out at BI and merges back
4205 // at Merge into a "C ? LHS : RHS" select pattern. Return true on a successful
4207 static bool BrPHIToSelect(DominatorTree &DT, BranchInst *BI, PHINode *Merge,
4208 Value *&C, Value *&LHS, Value *&RHS) {
4209 C = BI->getCondition();
4211 BasicBlockEdge LeftEdge(BI->getParent(), BI->getSuccessor(0));
4212 BasicBlockEdge RightEdge(BI->getParent(), BI->getSuccessor(1));
4214 if (!LeftEdge.isSingleEdge())
4217 assert(RightEdge.isSingleEdge() && "Follows from LeftEdge.isSingleEdge()");
4219 Use &LeftUse = Merge->getOperandUse(0);
4220 Use &RightUse = Merge->getOperandUse(1);
4222 if (DT.dominates(LeftEdge, LeftUse) && DT.dominates(RightEdge, RightUse)) {
4228 if (DT.dominates(LeftEdge, RightUse) && DT.dominates(RightEdge, LeftUse)) {
4237 const SCEV *ScalarEvolution::createNodeFromSelectLikePHI(PHINode *PN) {
4239 [&](BasicBlock *BB) { return DT.isReachableFromEntry(BB); };
4240 if (PN->getNumIncomingValues() == 2 && all_of(PN->blocks(), IsReachable)) {
4241 const Loop *L = LI.getLoopFor(PN->getParent());
4243 // We don't want to break LCSSA, even in a SCEV expression tree.
4244 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i)
4245 if (LI.getLoopFor(PN->getIncomingBlock(i)) != L)
4250 // br %cond, label %left, label %right
4256 // V = phi [ %x, %left ], [ %y, %right ]
4258 // as "select %cond, %x, %y"
4260 BasicBlock *IDom = DT[PN->getParent()]->getIDom()->getBlock();
4261 assert(IDom && "At least the entry block should dominate PN");
4263 auto *BI = dyn_cast<BranchInst>(IDom->getTerminator());
4264 Value *Cond = nullptr, *LHS = nullptr, *RHS = nullptr;
4266 if (BI && BI->isConditional() &&
4267 BrPHIToSelect(DT, BI, PN, Cond, LHS, RHS) &&
4268 IsAvailableOnEntry(L, DT, getSCEV(LHS), PN->getParent()) &&
4269 IsAvailableOnEntry(L, DT, getSCEV(RHS), PN->getParent()))
4270 return createNodeForSelectOrPHI(PN, Cond, LHS, RHS);
4276 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
4277 if (const SCEV *S = createAddRecFromPHI(PN))
4280 if (const SCEV *S = createNodeFromSelectLikePHI(PN))
4283 // If the PHI has a single incoming value, follow that value, unless the
4284 // PHI's incoming blocks are in a different loop, in which case doing so
4285 // risks breaking LCSSA form. Instcombine would normally zap these, but
4286 // it doesn't have DominatorTree information, so it may miss cases.
4287 if (Value *V = SimplifyInstruction(PN, getDataLayout(), &TLI, &DT, &AC))
4288 if (LI.replacementPreservesLCSSAForm(PN, V))
4291 // If it's not a loop phi, we can't handle it yet.
4292 return getUnknown(PN);
4295 const SCEV *ScalarEvolution::createNodeForSelectOrPHI(Instruction *I,
4299 // Handle "constant" branch or select. This can occur for instance when a
4300 // loop pass transforms an inner loop and moves on to process the outer loop.
4301 if (auto *CI = dyn_cast<ConstantInt>(Cond))
4302 return getSCEV(CI->isOne() ? TrueVal : FalseVal);
4304 // Try to match some simple smax or umax patterns.
4305 auto *ICI = dyn_cast<ICmpInst>(Cond);
4307 return getUnknown(I);
4309 Value *LHS = ICI->getOperand(0);
4310 Value *RHS = ICI->getOperand(1);
4312 switch (ICI->getPredicate()) {
4313 case ICmpInst::ICMP_SLT:
4314 case ICmpInst::ICMP_SLE:
4315 std::swap(LHS, RHS);
4317 case ICmpInst::ICMP_SGT:
4318 case ICmpInst::ICMP_SGE:
4319 // a >s b ? a+x : b+x -> smax(a, b)+x
4320 // a >s b ? b+x : a+x -> smin(a, b)+x
4321 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType())) {
4322 const SCEV *LS = getNoopOrSignExtend(getSCEV(LHS), I->getType());
4323 const SCEV *RS = getNoopOrSignExtend(getSCEV(RHS), I->getType());
4324 const SCEV *LA = getSCEV(TrueVal);
4325 const SCEV *RA = getSCEV(FalseVal);
4326 const SCEV *LDiff = getMinusSCEV(LA, LS);
4327 const SCEV *RDiff = getMinusSCEV(RA, RS);
4329 return getAddExpr(getSMaxExpr(LS, RS), LDiff);
4330 LDiff = getMinusSCEV(LA, RS);
4331 RDiff = getMinusSCEV(RA, LS);
4333 return getAddExpr(getSMinExpr(LS, RS), LDiff);
4336 case ICmpInst::ICMP_ULT:
4337 case ICmpInst::ICMP_ULE:
4338 std::swap(LHS, RHS);
4340 case ICmpInst::ICMP_UGT:
4341 case ICmpInst::ICMP_UGE:
4342 // a >u b ? a+x : b+x -> umax(a, b)+x
4343 // a >u b ? b+x : a+x -> umin(a, b)+x
4344 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType())) {
4345 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
4346 const SCEV *RS = getNoopOrZeroExtend(getSCEV(RHS), I->getType());
4347 const SCEV *LA = getSCEV(TrueVal);
4348 const SCEV *RA = getSCEV(FalseVal);
4349 const SCEV *LDiff = getMinusSCEV(LA, LS);
4350 const SCEV *RDiff = getMinusSCEV(RA, RS);
4352 return getAddExpr(getUMaxExpr(LS, RS), LDiff);
4353 LDiff = getMinusSCEV(LA, RS);
4354 RDiff = getMinusSCEV(RA, LS);
4356 return getAddExpr(getUMinExpr(LS, RS), LDiff);
4359 case ICmpInst::ICMP_NE:
4360 // n != 0 ? n+x : 1+x -> umax(n, 1)+x
4361 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType()) &&
4362 isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
4363 const SCEV *One = getOne(I->getType());
4364 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
4365 const SCEV *LA = getSCEV(TrueVal);
4366 const SCEV *RA = getSCEV(FalseVal);
4367 const SCEV *LDiff = getMinusSCEV(LA, LS);
4368 const SCEV *RDiff = getMinusSCEV(RA, One);
4370 return getAddExpr(getUMaxExpr(One, LS), LDiff);
4373 case ICmpInst::ICMP_EQ:
4374 // n == 0 ? 1+x : n+x -> umax(n, 1)+x
4375 if (getTypeSizeInBits(LHS->getType()) <= getTypeSizeInBits(I->getType()) &&
4376 isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
4377 const SCEV *One = getOne(I->getType());
4378 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), I->getType());
4379 const SCEV *LA = getSCEV(TrueVal);
4380 const SCEV *RA = getSCEV(FalseVal);
4381 const SCEV *LDiff = getMinusSCEV(LA, One);
4382 const SCEV *RDiff = getMinusSCEV(RA, LS);
4384 return getAddExpr(getUMaxExpr(One, LS), LDiff);
4391 return getUnknown(I);
4394 /// Expand GEP instructions into add and multiply operations. This allows them
4395 /// to be analyzed by regular SCEV code.
4396 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
4397 // Don't attempt to analyze GEPs over unsized objects.
4398 if (!GEP->getSourceElementType()->isSized())
4399 return getUnknown(GEP);
4401 SmallVector<const SCEV *, 4> IndexExprs;
4402 for (auto Index = GEP->idx_begin(); Index != GEP->idx_end(); ++Index)
4403 IndexExprs.push_back(getSCEV(*Index));
4404 return getGEPExpr(GEP, IndexExprs);
4408 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
4409 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
4410 return C->getAPInt().countTrailingZeros();
4412 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
4413 return std::min(GetMinTrailingZeros(T->getOperand()),
4414 (uint32_t)getTypeSizeInBits(T->getType()));
4416 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
4417 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
4418 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
4419 getTypeSizeInBits(E->getType()) : OpRes;
4422 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
4423 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
4424 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
4425 getTypeSizeInBits(E->getType()) : OpRes;
4428 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
4429 // The result is the min of all operands results.
4430 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
4431 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
4432 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
4436 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
4437 // The result is the sum of all operands results.
4438 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
4439 uint32_t BitWidth = getTypeSizeInBits(M->getType());
4440 for (unsigned i = 1, e = M->getNumOperands();
4441 SumOpRes != BitWidth && i != e; ++i)
4442 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
4447 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
4448 // The result is the min of all operands results.
4449 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
4450 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
4451 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
4455 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
4456 // The result is the min of all operands results.
4457 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
4458 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
4459 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
4463 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
4464 // The result is the min of all operands results.
4465 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
4466 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
4467 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
4471 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
4472 // For a SCEVUnknown, ask ValueTracking.
4473 unsigned BitWidth = getTypeSizeInBits(U->getType());
4474 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
4475 computeKnownBits(U->getValue(), Zeros, Ones, getDataLayout(), 0, &AC,
4477 return Zeros.countTrailingOnes();
4484 /// Helper method to assign a range to V from metadata present in the IR.
4485 static Optional<ConstantRange> GetRangeFromMetadata(Value *V) {
4486 if (Instruction *I = dyn_cast<Instruction>(V))
4487 if (MDNode *MD = I->getMetadata(LLVMContext::MD_range))
4488 return getConstantRangeFromMetadata(*MD);
4493 /// Determine the range for a particular SCEV. If SignHint is
4494 /// HINT_RANGE_UNSIGNED (resp. HINT_RANGE_SIGNED) then getRange prefers ranges
4495 /// with a "cleaner" unsigned (resp. signed) representation.
4497 ScalarEvolution::getRange(const SCEV *S,
4498 ScalarEvolution::RangeSignHint SignHint) {
4499 DenseMap<const SCEV *, ConstantRange> &Cache =
4500 SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED ? UnsignedRanges
4503 // See if we've computed this range already.
4504 DenseMap<const SCEV *, ConstantRange>::iterator I = Cache.find(S);
4505 if (I != Cache.end())
4508 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
4509 return setRange(C, SignHint, ConstantRange(C->getAPInt()));
4511 unsigned BitWidth = getTypeSizeInBits(S->getType());
4512 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
4514 // If the value has known zeros, the maximum value will have those known zeros
4516 uint32_t TZ = GetMinTrailingZeros(S);
4518 if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED)
4519 ConservativeResult =
4520 ConstantRange(APInt::getMinValue(BitWidth),
4521 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
4523 ConservativeResult = ConstantRange(
4524 APInt::getSignedMinValue(BitWidth),
4525 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
4528 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
4529 ConstantRange X = getRange(Add->getOperand(0), SignHint);
4530 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
4531 X = X.add(getRange(Add->getOperand(i), SignHint));
4532 return setRange(Add, SignHint, ConservativeResult.intersectWith(X));
4535 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
4536 ConstantRange X = getRange(Mul->getOperand(0), SignHint);
4537 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
4538 X = X.multiply(getRange(Mul->getOperand(i), SignHint));
4539 return setRange(Mul, SignHint, ConservativeResult.intersectWith(X));
4542 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
4543 ConstantRange X = getRange(SMax->getOperand(0), SignHint);
4544 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
4545 X = X.smax(getRange(SMax->getOperand(i), SignHint));
4546 return setRange(SMax, SignHint, ConservativeResult.intersectWith(X));
4549 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
4550 ConstantRange X = getRange(UMax->getOperand(0), SignHint);
4551 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
4552 X = X.umax(getRange(UMax->getOperand(i), SignHint));
4553 return setRange(UMax, SignHint, ConservativeResult.intersectWith(X));
4556 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
4557 ConstantRange X = getRange(UDiv->getLHS(), SignHint);
4558 ConstantRange Y = getRange(UDiv->getRHS(), SignHint);
4559 return setRange(UDiv, SignHint,
4560 ConservativeResult.intersectWith(X.udiv(Y)));
4563 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
4564 ConstantRange X = getRange(ZExt->getOperand(), SignHint);
4565 return setRange(ZExt, SignHint,
4566 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
4569 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
4570 ConstantRange X = getRange(SExt->getOperand(), SignHint);
4571 return setRange(SExt, SignHint,
4572 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
4575 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
4576 ConstantRange X = getRange(Trunc->getOperand(), SignHint);
4577 return setRange(Trunc, SignHint,
4578 ConservativeResult.intersectWith(X.truncate(BitWidth)));
4581 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
4582 // If there's no unsigned wrap, the value will never be less than its
4584 if (AddRec->hasNoUnsignedWrap())
4585 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
4586 if (!C->getValue()->isZero())
4587 ConservativeResult = ConservativeResult.intersectWith(
4588 ConstantRange(C->getAPInt(), APInt(BitWidth, 0)));
4590 // If there's no signed wrap, and all the operands have the same sign or
4591 // zero, the value won't ever change sign.
4592 if (AddRec->hasNoSignedWrap()) {
4593 bool AllNonNeg = true;
4594 bool AllNonPos = true;
4595 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
4596 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
4597 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
4600 ConservativeResult = ConservativeResult.intersectWith(
4601 ConstantRange(APInt(BitWidth, 0),
4602 APInt::getSignedMinValue(BitWidth)));
4604 ConservativeResult = ConservativeResult.intersectWith(
4605 ConstantRange(APInt::getSignedMinValue(BitWidth),
4606 APInt(BitWidth, 1)));
4609 // TODO: non-affine addrec
4610 if (AddRec->isAffine()) {
4611 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
4612 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
4613 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
4614 auto RangeFromAffine = getRangeForAffineAR(
4615 AddRec->getStart(), AddRec->getStepRecurrence(*this), MaxBECount,
4617 if (!RangeFromAffine.isFullSet())
4618 ConservativeResult =
4619 ConservativeResult.intersectWith(RangeFromAffine);
4621 auto RangeFromFactoring = getRangeViaFactoring(
4622 AddRec->getStart(), AddRec->getStepRecurrence(*this), MaxBECount,
4624 if (!RangeFromFactoring.isFullSet())
4625 ConservativeResult =
4626 ConservativeResult.intersectWith(RangeFromFactoring);
4630 return setRange(AddRec, SignHint, ConservativeResult);
4633 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
4634 // Check if the IR explicitly contains !range metadata.
4635 Optional<ConstantRange> MDRange = GetRangeFromMetadata(U->getValue());
4636 if (MDRange.hasValue())
4637 ConservativeResult = ConservativeResult.intersectWith(MDRange.getValue());
4639 // Split here to avoid paying the compile-time cost of calling both
4640 // computeKnownBits and ComputeNumSignBits. This restriction can be lifted
4642 const DataLayout &DL = getDataLayout();
4643 if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED) {
4644 // For a SCEVUnknown, ask ValueTracking.
4645 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
4646 computeKnownBits(U->getValue(), Zeros, Ones, DL, 0, &AC, nullptr, &DT);
4647 if (Ones != ~Zeros + 1)
4648 ConservativeResult =
4649 ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1));
4651 assert(SignHint == ScalarEvolution::HINT_RANGE_SIGNED &&
4652 "generalize as needed!");
4653 unsigned NS = ComputeNumSignBits(U->getValue(), DL, 0, &AC, nullptr, &DT);
4655 ConservativeResult = ConservativeResult.intersectWith(
4656 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
4657 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1) + 1));
4660 return setRange(U, SignHint, ConservativeResult);
4663 return setRange(S, SignHint, ConservativeResult);
4666 ConstantRange ScalarEvolution::getRangeForAffineAR(const SCEV *Start,
4668 const SCEV *MaxBECount,
4669 unsigned BitWidth) {
4670 assert(!isa<SCEVCouldNotCompute>(MaxBECount) &&
4671 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth &&
4674 ConstantRange Result(BitWidth, /* isFullSet = */ true);
4676 // Check for overflow. This must be done with ConstantRange arithmetic
4677 // because we could be called from within the ScalarEvolution overflow
4680 MaxBECount = getNoopOrZeroExtend(MaxBECount, Start->getType());
4681 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
4682 ConstantRange ZExtMaxBECountRange = MaxBECountRange.zextOrTrunc(BitWidth * 2);
4684 ConstantRange StepSRange = getSignedRange(Step);
4685 ConstantRange SExtStepSRange = StepSRange.sextOrTrunc(BitWidth * 2);
4687 ConstantRange StartURange = getUnsignedRange(Start);
4688 ConstantRange EndURange =
4689 StartURange.add(MaxBECountRange.multiply(StepSRange));
4691 // Check for unsigned overflow.
4692 ConstantRange ZExtStartURange = StartURange.zextOrTrunc(BitWidth * 2);
4693 ConstantRange ZExtEndURange = EndURange.zextOrTrunc(BitWidth * 2);
4694 if (ZExtStartURange.add(ZExtMaxBECountRange.multiply(SExtStepSRange)) ==
4696 APInt Min = APIntOps::umin(StartURange.getUnsignedMin(),
4697 EndURange.getUnsignedMin());
4698 APInt Max = APIntOps::umax(StartURange.getUnsignedMax(),
4699 EndURange.getUnsignedMax());
4700 bool IsFullRange = Min.isMinValue() && Max.isMaxValue();
4703 Result.intersectWith(ConstantRange(Min, Max + 1));
4706 ConstantRange StartSRange = getSignedRange(Start);
4707 ConstantRange EndSRange =
4708 StartSRange.add(MaxBECountRange.multiply(StepSRange));
4710 // Check for signed overflow. This must be done with ConstantRange
4711 // arithmetic because we could be called from within the ScalarEvolution
4712 // overflow checking code.
4713 ConstantRange SExtStartSRange = StartSRange.sextOrTrunc(BitWidth * 2);
4714 ConstantRange SExtEndSRange = EndSRange.sextOrTrunc(BitWidth * 2);
4715 if (SExtStartSRange.add(ZExtMaxBECountRange.multiply(SExtStepSRange)) ==
4718 APIntOps::smin(StartSRange.getSignedMin(), EndSRange.getSignedMin());
4720 APIntOps::smax(StartSRange.getSignedMax(), EndSRange.getSignedMax());
4721 bool IsFullRange = Min.isMinSignedValue() && Max.isMaxSignedValue();
4724 Result.intersectWith(ConstantRange(Min, Max + 1));
4730 ConstantRange ScalarEvolution::getRangeViaFactoring(const SCEV *Start,
4732 const SCEV *MaxBECount,
4733 unsigned BitWidth) {
4734 // RangeOf({C?A:B,+,C?P:Q}) == RangeOf(C?{A,+,P}:{B,+,Q})
4735 // == RangeOf({A,+,P}) union RangeOf({B,+,Q})
4737 struct SelectPattern {
4738 Value *Condition = nullptr;
4742 explicit SelectPattern(ScalarEvolution &SE, unsigned BitWidth,
4744 Optional<unsigned> CastOp;
4745 APInt Offset(BitWidth, 0);
4747 assert(SE.getTypeSizeInBits(S->getType()) == BitWidth &&
4750 // Peel off a constant offset:
4751 if (auto *SA = dyn_cast<SCEVAddExpr>(S)) {
4752 // In the future we could consider being smarter here and handle
4753 // {Start+Step,+,Step} too.
4754 if (SA->getNumOperands() != 2 || !isa<SCEVConstant>(SA->getOperand(0)))
4757 Offset = cast<SCEVConstant>(SA->getOperand(0))->getAPInt();
4758 S = SA->getOperand(1);
4761 // Peel off a cast operation
4762 if (auto *SCast = dyn_cast<SCEVCastExpr>(S)) {
4763 CastOp = SCast->getSCEVType();
4764 S = SCast->getOperand();
4767 using namespace llvm::PatternMatch;
4769 auto *SU = dyn_cast<SCEVUnknown>(S);
4770 const APInt *TrueVal, *FalseVal;
4772 !match(SU->getValue(), m_Select(m_Value(Condition), m_APInt(TrueVal),
4773 m_APInt(FalseVal)))) {
4774 Condition = nullptr;
4778 TrueValue = *TrueVal;
4779 FalseValue = *FalseVal;
4781 // Re-apply the cast we peeled off earlier
4782 if (CastOp.hasValue())
4785 llvm_unreachable("Unknown SCEV cast type!");
4788 TrueValue = TrueValue.trunc(BitWidth);
4789 FalseValue = FalseValue.trunc(BitWidth);
4792 TrueValue = TrueValue.zext(BitWidth);
4793 FalseValue = FalseValue.zext(BitWidth);
4796 TrueValue = TrueValue.sext(BitWidth);
4797 FalseValue = FalseValue.sext(BitWidth);
4801 // Re-apply the constant offset we peeled off earlier
4802 TrueValue += Offset;
4803 FalseValue += Offset;
4806 bool isRecognized() { return Condition != nullptr; }
4809 SelectPattern StartPattern(*this, BitWidth, Start);
4810 if (!StartPattern.isRecognized())
4811 return ConstantRange(BitWidth, /* isFullSet = */ true);
4813 SelectPattern StepPattern(*this, BitWidth, Step);
4814 if (!StepPattern.isRecognized())
4815 return ConstantRange(BitWidth, /* isFullSet = */ true);
4817 if (StartPattern.Condition != StepPattern.Condition) {
4818 // We don't handle this case today; but we could, by considering four
4819 // possibilities below instead of two. I'm not sure if there are cases where
4820 // that will help over what getRange already does, though.
4821 return ConstantRange(BitWidth, /* isFullSet = */ true);
4824 // NB! Calling ScalarEvolution::getConstant is fine, but we should not try to
4825 // construct arbitrary general SCEV expressions here. This function is called
4826 // from deep in the call stack, and calling getSCEV (on a sext instruction,
4827 // say) can end up caching a suboptimal value.
4829 // FIXME: without the explicit `this` receiver below, MSVC errors out with
4830 // C2352 and C2512 (otherwise it isn't needed).
4832 const SCEV *TrueStart = this->getConstant(StartPattern.TrueValue);
4833 const SCEV *TrueStep = this->getConstant(StepPattern.TrueValue);
4834 const SCEV *FalseStart = this->getConstant(StartPattern.FalseValue);
4835 const SCEV *FalseStep = this->getConstant(StepPattern.FalseValue);
4837 ConstantRange TrueRange =
4838 this->getRangeForAffineAR(TrueStart, TrueStep, MaxBECount, BitWidth);
4839 ConstantRange FalseRange =
4840 this->getRangeForAffineAR(FalseStart, FalseStep, MaxBECount, BitWidth);
4842 return TrueRange.unionWith(FalseRange);
4845 SCEV::NoWrapFlags ScalarEvolution::getNoWrapFlagsFromUB(const Value *V) {
4846 if (isa<ConstantExpr>(V)) return SCEV::FlagAnyWrap;
4847 const BinaryOperator *BinOp = cast<BinaryOperator>(V);
4849 // Return early if there are no flags to propagate to the SCEV.
4850 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
4851 if (BinOp->hasNoUnsignedWrap())
4852 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
4853 if (BinOp->hasNoSignedWrap())
4854 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW);
4855 if (Flags == SCEV::FlagAnyWrap)
4856 return SCEV::FlagAnyWrap;
4858 return isSCEVExprNeverPoison(BinOp) ? Flags : SCEV::FlagAnyWrap;
4861 bool ScalarEvolution::isSCEVExprNeverPoison(const Instruction *I) {
4862 // Here we check that I is in the header of the innermost loop containing I,
4863 // since we only deal with instructions in the loop header. The actual loop we
4864 // need to check later will come from an add recurrence, but getting that
4865 // requires computing the SCEV of the operands, which can be expensive. This
4866 // check we can do cheaply to rule out some cases early.
4867 Loop *InnermostContainingLoop = LI.getLoopFor(I->getParent());
4868 if (InnermostContainingLoop == nullptr ||
4869 InnermostContainingLoop->getHeader() != I->getParent())
4872 // Only proceed if we can prove that I does not yield poison.
4873 if (!isKnownNotFullPoison(I)) return false;
4875 // At this point we know that if I is executed, then it does not wrap
4876 // according to at least one of NSW or NUW. If I is not executed, then we do
4877 // not know if the calculation that I represents would wrap. Multiple
4878 // instructions can map to the same SCEV. If we apply NSW or NUW from I to
4879 // the SCEV, we must guarantee no wrapping for that SCEV also when it is
4880 // derived from other instructions that map to the same SCEV. We cannot make
4881 // that guarantee for cases where I is not executed. So we need to find the
4882 // loop that I is considered in relation to and prove that I is executed for
4883 // every iteration of that loop. That implies that the value that I
4884 // calculates does not wrap anywhere in the loop, so then we can apply the
4885 // flags to the SCEV.
4887 // We check isLoopInvariant to disambiguate in case we are adding recurrences
4888 // from different loops, so that we know which loop to prove that I is
4890 for (unsigned OpIndex = 0; OpIndex < I->getNumOperands(); ++OpIndex) {
4891 // I could be an extractvalue from a call to an overflow intrinsic.
4892 // TODO: We can do better here in some cases.
4893 if (!isSCEVable(I->getOperand(OpIndex)->getType()))
4895 const SCEV *Op = getSCEV(I->getOperand(OpIndex));
4896 if (auto *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
4897 bool AllOtherOpsLoopInvariant = true;
4898 for (unsigned OtherOpIndex = 0; OtherOpIndex < I->getNumOperands();
4900 if (OtherOpIndex != OpIndex) {
4901 const SCEV *OtherOp = getSCEV(I->getOperand(OtherOpIndex));
4902 if (!isLoopInvariant(OtherOp, AddRec->getLoop())) {
4903 AllOtherOpsLoopInvariant = false;
4908 if (AllOtherOpsLoopInvariant &&
4909 isGuaranteedToExecuteForEveryIteration(I, AddRec->getLoop()))
4916 bool ScalarEvolution::isAddRecNeverPoison(const Instruction *I, const Loop *L) {
4917 // If we know that \c I can never be poison period, then that's enough.
4918 if (isSCEVExprNeverPoison(I))
4921 // For an add recurrence specifically, we assume that infinite loops without
4922 // side effects are undefined behavior, and then reason as follows:
4924 // If the add recurrence is poison in any iteration, it is poison on all
4925 // future iterations (since incrementing poison yields poison). If the result
4926 // of the add recurrence is fed into the loop latch condition and the loop
4927 // does not contain any throws or exiting blocks other than the latch, we now
4928 // have the ability to "choose" whether the backedge is taken or not (by
4929 // choosing a sufficiently evil value for the poison feeding into the branch)
4930 // for every iteration including and after the one in which \p I first became
4931 // poison. There are two possibilities (let's call the iteration in which \p
4932 // I first became poison as K):
4934 // 1. In the set of iterations including and after K, the loop body executes
4935 // no side effects. In this case executing the backege an infinte number
4936 // of times will yield undefined behavior.
4938 // 2. In the set of iterations including and after K, the loop body executes
4939 // at least one side effect. In this case, that specific instance of side
4940 // effect is control dependent on poison, which also yields undefined
4943 auto *ExitingBB = L->getExitingBlock();
4944 auto *LatchBB = L->getLoopLatch();
4945 if (!ExitingBB || !LatchBB || ExitingBB != LatchBB)
4948 SmallPtrSet<const Instruction *, 16> Pushed;
4949 SmallVector<const Instruction *, 8> PoisonStack;
4951 // We start by assuming \c I, the post-inc add recurrence, is poison. Only
4952 // things that are known to be fully poison under that assumption go on the
4955 PoisonStack.push_back(I);
4957 bool LatchControlDependentOnPoison = false;
4958 while (!PoisonStack.empty() && !LatchControlDependentOnPoison) {
4959 const Instruction *Poison = PoisonStack.pop_back_val();
4961 for (auto *PoisonUser : Poison->users()) {
4962 if (propagatesFullPoison(cast<Instruction>(PoisonUser))) {
4963 if (Pushed.insert(cast<Instruction>(PoisonUser)).second)
4964 PoisonStack.push_back(cast<Instruction>(PoisonUser));
4965 } else if (auto *BI = dyn_cast<BranchInst>(PoisonUser)) {
4966 assert(BI->isConditional() && "Only possibility!");
4967 if (BI->getParent() == LatchBB) {
4968 LatchControlDependentOnPoison = true;
4975 return LatchControlDependentOnPoison && loopHasNoAbnormalExits(L);
4978 ScalarEvolution::LoopProperties
4979 ScalarEvolution::getLoopProperties(const Loop *L) {
4980 typedef ScalarEvolution::LoopProperties LoopProperties;
4982 auto Itr = LoopPropertiesCache.find(L);
4983 if (Itr == LoopPropertiesCache.end()) {
4984 auto HasSideEffects = [](Instruction *I) {
4985 if (auto *SI = dyn_cast<StoreInst>(I))
4986 return !SI->isSimple();
4988 return I->mayHaveSideEffects();
4991 LoopProperties LP = {/* HasNoAbnormalExits */ true,
4992 /*HasNoSideEffects*/ true};
4994 for (auto *BB : L->getBlocks())
4995 for (auto &I : *BB) {
4996 if (!isGuaranteedToTransferExecutionToSuccessor(&I))
4997 LP.HasNoAbnormalExits = false;
4998 if (HasSideEffects(&I))
4999 LP.HasNoSideEffects = false;
5000 if (!LP.HasNoAbnormalExits && !LP.HasNoSideEffects)
5001 break; // We're already as pessimistic as we can get.
5004 auto InsertPair = LoopPropertiesCache.insert({L, LP});
5005 assert(InsertPair.second && "We just checked!");
5006 Itr = InsertPair.first;
5012 const SCEV *ScalarEvolution::createSCEV(Value *V) {
5013 if (!isSCEVable(V->getType()))
5014 return getUnknown(V);
5016 if (Instruction *I = dyn_cast<Instruction>(V)) {
5017 // Don't attempt to analyze instructions in blocks that aren't
5018 // reachable. Such instructions don't matter, and they aren't required
5019 // to obey basic rules for definitions dominating uses which this
5020 // analysis depends on.
5021 if (!DT.isReachableFromEntry(I->getParent()))
5022 return getUnknown(V);
5023 } else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
5024 return getConstant(CI);
5025 else if (isa<ConstantPointerNull>(V))
5026 return getZero(V->getType());
5027 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
5028 return GA->isInterposable() ? getUnknown(V) : getSCEV(GA->getAliasee());
5029 else if (!isa<ConstantExpr>(V))
5030 return getUnknown(V);
5032 Operator *U = cast<Operator>(V);
5033 if (auto BO = MatchBinaryOp(U, DT)) {
5034 switch (BO->Opcode) {
5035 case Instruction::Add: {
5036 // The simple thing to do would be to just call getSCEV on both operands
5037 // and call getAddExpr with the result. However if we're looking at a
5038 // bunch of things all added together, this can be quite inefficient,
5039 // because it leads to N-1 getAddExpr calls for N ultimate operands.
5040 // Instead, gather up all the operands and make a single getAddExpr call.
5041 // LLVM IR canonical form means we need only traverse the left operands.
5042 SmallVector<const SCEV *, 4> AddOps;
5045 if (auto *OpSCEV = getExistingSCEV(BO->Op)) {
5046 AddOps.push_back(OpSCEV);
5050 // If a NUW or NSW flag can be applied to the SCEV for this
5051 // addition, then compute the SCEV for this addition by itself
5052 // with a separate call to getAddExpr. We need to do that
5053 // instead of pushing the operands of the addition onto AddOps,
5054 // since the flags are only known to apply to this particular
5055 // addition - they may not apply to other additions that can be
5056 // formed with operands from AddOps.
5057 const SCEV *RHS = getSCEV(BO->RHS);
5058 SCEV::NoWrapFlags Flags = getNoWrapFlagsFromUB(BO->Op);
5059 if (Flags != SCEV::FlagAnyWrap) {
5060 const SCEV *LHS = getSCEV(BO->LHS);
5061 if (BO->Opcode == Instruction::Sub)
5062 AddOps.push_back(getMinusSCEV(LHS, RHS, Flags));
5064 AddOps.push_back(getAddExpr(LHS, RHS, Flags));
5069 if (BO->Opcode == Instruction::Sub)
5070 AddOps.push_back(getNegativeSCEV(getSCEV(BO->RHS)));
5072 AddOps.push_back(getSCEV(BO->RHS));
5074 auto NewBO = MatchBinaryOp(BO->LHS, DT);
5075 if (!NewBO || (NewBO->Opcode != Instruction::Add &&
5076 NewBO->Opcode != Instruction::Sub)) {
5077 AddOps.push_back(getSCEV(BO->LHS));
5083 return getAddExpr(AddOps);
5086 case Instruction::Mul: {
5087 SmallVector<const SCEV *, 4> MulOps;
5090 if (auto *OpSCEV = getExistingSCEV(BO->Op)) {
5091 MulOps.push_back(OpSCEV);
5095 SCEV::NoWrapFlags Flags = getNoWrapFlagsFromUB(BO->Op);
5096 if (Flags != SCEV::FlagAnyWrap) {
5098 getMulExpr(getSCEV(BO->LHS), getSCEV(BO->RHS), Flags));
5103 MulOps.push_back(getSCEV(BO->RHS));
5104 auto NewBO = MatchBinaryOp(BO->LHS, DT);
5105 if (!NewBO || NewBO->Opcode != Instruction::Mul) {
5106 MulOps.push_back(getSCEV(BO->LHS));
5112 return getMulExpr(MulOps);
5114 case Instruction::UDiv:
5115 return getUDivExpr(getSCEV(BO->LHS), getSCEV(BO->RHS));
5116 case Instruction::Sub: {
5117 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
5119 Flags = getNoWrapFlagsFromUB(BO->Op);
5120 return getMinusSCEV(getSCEV(BO->LHS), getSCEV(BO->RHS), Flags);
5122 case Instruction::And:
5123 // For an expression like x&255 that merely masks off the high bits,
5124 // use zext(trunc(x)) as the SCEV expression.
5125 if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->RHS)) {
5126 if (CI->isNullValue())
5127 return getSCEV(BO->RHS);
5128 if (CI->isAllOnesValue())
5129 return getSCEV(BO->LHS);
5130 const APInt &A = CI->getValue();
5132 // Instcombine's ShrinkDemandedConstant may strip bits out of
5133 // constants, obscuring what would otherwise be a low-bits mask.
5134 // Use computeKnownBits to compute what ShrinkDemandedConstant
5135 // knew about to reconstruct a low-bits mask value.
5136 unsigned LZ = A.countLeadingZeros();
5137 unsigned TZ = A.countTrailingZeros();
5138 unsigned BitWidth = A.getBitWidth();
5139 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
5140 computeKnownBits(BO->LHS, KnownZero, KnownOne, getDataLayout(),
5141 0, &AC, nullptr, &DT);
5143 APInt EffectiveMask =
5144 APInt::getLowBitsSet(BitWidth, BitWidth - LZ - TZ).shl(TZ);
5145 if ((LZ != 0 || TZ != 0) && !((~A & ~KnownZero) & EffectiveMask)) {
5146 const SCEV *MulCount = getConstant(ConstantInt::get(
5147 getContext(), APInt::getOneBitSet(BitWidth, TZ)));
5151 getUDivExactExpr(getSCEV(BO->LHS), MulCount),
5152 IntegerType::get(getContext(), BitWidth - LZ - TZ)),
5153 BO->LHS->getType()),
5159 case Instruction::Or:
5160 // If the RHS of the Or is a constant, we may have something like:
5161 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
5162 // optimizations will transparently handle this case.
5164 // In order for this transformation to be safe, the LHS must be of the
5165 // form X*(2^n) and the Or constant must be less than 2^n.
5166 if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->RHS)) {
5167 const SCEV *LHS = getSCEV(BO->LHS);
5168 const APInt &CIVal = CI->getValue();
5169 if (GetMinTrailingZeros(LHS) >=
5170 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
5171 // Build a plain add SCEV.
5172 const SCEV *S = getAddExpr(LHS, getSCEV(CI));
5173 // If the LHS of the add was an addrec and it has no-wrap flags,
5174 // transfer the no-wrap flags, since an or won't introduce a wrap.
5175 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
5176 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
5177 const_cast<SCEVAddRecExpr *>(NewAR)->setNoWrapFlags(
5178 OldAR->getNoWrapFlags());
5185 case Instruction::Xor:
5186 if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->RHS)) {
5187 // If the RHS of xor is -1, then this is a not operation.
5188 if (CI->isAllOnesValue())
5189 return getNotSCEV(getSCEV(BO->LHS));
5191 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
5192 // This is a variant of the check for xor with -1, and it handles
5193 // the case where instcombine has trimmed non-demanded bits out
5194 // of an xor with -1.
5195 if (auto *LBO = dyn_cast<BinaryOperator>(BO->LHS))
5196 if (ConstantInt *LCI = dyn_cast<ConstantInt>(LBO->getOperand(1)))
5197 if (LBO->getOpcode() == Instruction::And &&
5198 LCI->getValue() == CI->getValue())
5199 if (const SCEVZeroExtendExpr *Z =
5200 dyn_cast<SCEVZeroExtendExpr>(getSCEV(BO->LHS))) {
5201 Type *UTy = BO->LHS->getType();
5202 const SCEV *Z0 = Z->getOperand();
5203 Type *Z0Ty = Z0->getType();
5204 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
5206 // If C is a low-bits mask, the zero extend is serving to
5207 // mask off the high bits. Complement the operand and
5208 // re-apply the zext.
5209 if (APIntOps::isMask(Z0TySize, CI->getValue()))
5210 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
5212 // If C is a single bit, it may be in the sign-bit position
5213 // before the zero-extend. In this case, represent the xor
5214 // using an add, which is equivalent, and re-apply the zext.
5215 APInt Trunc = CI->getValue().trunc(Z0TySize);
5216 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
5218 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
5224 case Instruction::Shl:
5225 // Turn shift left of a constant amount into a multiply.
5226 if (ConstantInt *SA = dyn_cast<ConstantInt>(BO->RHS)) {
5227 uint32_t BitWidth = cast<IntegerType>(SA->getType())->getBitWidth();
5229 // If the shift count is not less than the bitwidth, the result of
5230 // the shift is undefined. Don't try to analyze it, because the
5231 // resolution chosen here may differ from the resolution chosen in
5232 // other parts of the compiler.
5233 if (SA->getValue().uge(BitWidth))
5236 // It is currently not resolved how to interpret NSW for left
5237 // shift by BitWidth - 1, so we avoid applying flags in that
5238 // case. Remove this check (or this comment) once the situation
5240 // http://lists.llvm.org/pipermail/llvm-dev/2015-April/084195.html
5241 // and http://reviews.llvm.org/D8890 .
5242 auto Flags = SCEV::FlagAnyWrap;
5243 if (BO->Op && SA->getValue().ult(BitWidth - 1))
5244 Flags = getNoWrapFlagsFromUB(BO->Op);
5246 Constant *X = ConstantInt::get(getContext(),
5247 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
5248 return getMulExpr(getSCEV(BO->LHS), getSCEV(X), Flags);
5252 case Instruction::AShr:
5253 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
5254 if (ConstantInt *CI = dyn_cast<ConstantInt>(BO->RHS))
5255 if (Operator *L = dyn_cast<Operator>(BO->LHS))
5256 if (L->getOpcode() == Instruction::Shl &&
5257 L->getOperand(1) == BO->RHS) {
5258 uint64_t BitWidth = getTypeSizeInBits(BO->LHS->getType());
5260 // If the shift count is not less than the bitwidth, the result of
5261 // the shift is undefined. Don't try to analyze it, because the
5262 // resolution chosen here may differ from the resolution chosen in
5263 // other parts of the compiler.
5264 if (CI->getValue().uge(BitWidth))
5267 uint64_t Amt = BitWidth - CI->getZExtValue();
5268 if (Amt == BitWidth)
5269 return getSCEV(L->getOperand(0)); // shift by zero --> noop
5270 return getSignExtendExpr(
5271 getTruncateExpr(getSCEV(L->getOperand(0)),
5272 IntegerType::get(getContext(), Amt)),
5273 BO->LHS->getType());
5279 switch (U->getOpcode()) {
5280 case Instruction::Trunc:
5281 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
5283 case Instruction::ZExt:
5284 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
5286 case Instruction::SExt:
5287 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
5289 case Instruction::BitCast:
5290 // BitCasts are no-op casts so we just eliminate the cast.
5291 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
5292 return getSCEV(U->getOperand(0));
5295 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
5296 // lead to pointer expressions which cannot safely be expanded to GEPs,
5297 // because ScalarEvolution doesn't respect the GEP aliasing rules when
5298 // simplifying integer expressions.
5300 case Instruction::GetElementPtr:
5301 return createNodeForGEP(cast<GEPOperator>(U));
5303 case Instruction::PHI:
5304 return createNodeForPHI(cast<PHINode>(U));
5306 case Instruction::Select:
5307 // U can also be a select constant expr, which let fall through. Since
5308 // createNodeForSelect only works for a condition that is an `ICmpInst`, and
5309 // constant expressions cannot have instructions as operands, we'd have
5310 // returned getUnknown for a select constant expressions anyway.
5311 if (isa<Instruction>(U))
5312 return createNodeForSelectOrPHI(cast<Instruction>(U), U->getOperand(0),
5313 U->getOperand(1), U->getOperand(2));
5316 case Instruction::Call:
5317 case Instruction::Invoke:
5318 if (Value *RV = CallSite(U).getReturnedArgOperand())
5323 return getUnknown(V);
5328 //===----------------------------------------------------------------------===//
5329 // Iteration Count Computation Code
5332 static unsigned getConstantTripCount(const SCEVConstant *ExitCount) {
5336 ConstantInt *ExitConst = ExitCount->getValue();
5338 // Guard against huge trip counts.
5339 if (ExitConst->getValue().getActiveBits() > 32)
5342 // In case of integer overflow, this returns 0, which is correct.
5343 return ((unsigned)ExitConst->getZExtValue()) + 1;
5346 unsigned ScalarEvolution::getSmallConstantTripCount(Loop *L) {
5347 if (BasicBlock *ExitingBB = L->getExitingBlock())
5348 return getSmallConstantTripCount(L, ExitingBB);
5350 // No trip count information for multiple exits.
5354 unsigned ScalarEvolution::getSmallConstantTripCount(Loop *L,
5355 BasicBlock *ExitingBlock) {
5356 assert(ExitingBlock && "Must pass a non-null exiting block!");
5357 assert(L->isLoopExiting(ExitingBlock) &&
5358 "Exiting block must actually branch out of the loop!");
5359 const SCEVConstant *ExitCount =
5360 dyn_cast<SCEVConstant>(getExitCount(L, ExitingBlock));
5361 return getConstantTripCount(ExitCount);
5364 unsigned ScalarEvolution::getSmallConstantMaxTripCount(Loop *L) {
5365 const auto *MaxExitCount =
5366 dyn_cast<SCEVConstant>(getMaxBackedgeTakenCount(L));
5367 return getConstantTripCount(MaxExitCount);
5370 unsigned ScalarEvolution::getSmallConstantTripMultiple(Loop *L) {
5371 if (BasicBlock *ExitingBB = L->getExitingBlock())
5372 return getSmallConstantTripMultiple(L, ExitingBB);
5374 // No trip multiple information for multiple exits.
5378 /// Returns the largest constant divisor of the trip count of this loop as a
5379 /// normal unsigned value, if possible. This means that the actual trip count is
5380 /// always a multiple of the returned value (don't forget the trip count could
5381 /// very well be zero as well!).
5383 /// Returns 1 if the trip count is unknown or not guaranteed to be the
5384 /// multiple of a constant (which is also the case if the trip count is simply
5385 /// constant, use getSmallConstantTripCount for that case), Will also return 1
5386 /// if the trip count is very large (>= 2^32).
5388 /// As explained in the comments for getSmallConstantTripCount, this assumes
5389 /// that control exits the loop via ExitingBlock.
5391 ScalarEvolution::getSmallConstantTripMultiple(Loop *L,
5392 BasicBlock *ExitingBlock) {
5393 assert(ExitingBlock && "Must pass a non-null exiting block!");
5394 assert(L->isLoopExiting(ExitingBlock) &&
5395 "Exiting block must actually branch out of the loop!");
5396 const SCEV *ExitCount = getExitCount(L, ExitingBlock);
5397 if (ExitCount == getCouldNotCompute())
5400 // Get the trip count from the BE count by adding 1.
5401 const SCEV *TCMul = getAddExpr(ExitCount, getOne(ExitCount->getType()));
5402 // FIXME: SCEV distributes multiplication as V1*C1 + V2*C1. We could attempt
5403 // to factor simple cases.
5404 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(TCMul))
5405 TCMul = Mul->getOperand(0);
5407 const SCEVConstant *MulC = dyn_cast<SCEVConstant>(TCMul);
5411 ConstantInt *Result = MulC->getValue();
5413 // Guard against huge trip counts (this requires checking
5414 // for zero to handle the case where the trip count == -1 and the
5416 if (!Result || Result->getValue().getActiveBits() > 32 ||
5417 Result->getValue().getActiveBits() == 0)
5420 return (unsigned)Result->getZExtValue();
5423 /// Get the expression for the number of loop iterations for which this loop is
5424 /// guaranteed not to exit via ExitingBlock. Otherwise return
5425 /// SCEVCouldNotCompute.
5426 const SCEV *ScalarEvolution::getExitCount(Loop *L, BasicBlock *ExitingBlock) {
5427 return getBackedgeTakenInfo(L).getExact(ExitingBlock, this);
5431 ScalarEvolution::getPredicatedBackedgeTakenCount(const Loop *L,
5432 SCEVUnionPredicate &Preds) {
5433 return getPredicatedBackedgeTakenInfo(L).getExact(this, &Preds);
5436 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
5437 return getBackedgeTakenInfo(L).getExact(this);
5440 /// Similar to getBackedgeTakenCount, except return the least SCEV value that is
5441 /// known never to be less than the actual backedge taken count.
5442 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
5443 return getBackedgeTakenInfo(L).getMax(this);
5446 bool ScalarEvolution::isBackedgeTakenCountMaxOrZero(const Loop *L) {
5447 return getBackedgeTakenInfo(L).isMaxOrZero(this);
5450 /// Push PHI nodes in the header of the given loop onto the given Worklist.
5452 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
5453 BasicBlock *Header = L->getHeader();
5455 // Push all Loop-header PHIs onto the Worklist stack.
5456 for (BasicBlock::iterator I = Header->begin();
5457 PHINode *PN = dyn_cast<PHINode>(I); ++I)
5458 Worklist.push_back(PN);
5461 const ScalarEvolution::BackedgeTakenInfo &
5462 ScalarEvolution::getPredicatedBackedgeTakenInfo(const Loop *L) {
5463 auto &BTI = getBackedgeTakenInfo(L);
5464 if (BTI.hasFullInfo())
5467 auto Pair = PredicatedBackedgeTakenCounts.insert({L, BackedgeTakenInfo()});
5470 return Pair.first->second;
5472 BackedgeTakenInfo Result =
5473 computeBackedgeTakenCount(L, /*AllowPredicates=*/true);
5475 return PredicatedBackedgeTakenCounts.find(L)->second = std::move(Result);
5478 const ScalarEvolution::BackedgeTakenInfo &
5479 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
5480 // Initially insert an invalid entry for this loop. If the insertion
5481 // succeeds, proceed to actually compute a backedge-taken count and
5482 // update the value. The temporary CouldNotCompute value tells SCEV
5483 // code elsewhere that it shouldn't attempt to request a new
5484 // backedge-taken count, which could result in infinite recursion.
5485 std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
5486 BackedgeTakenCounts.insert({L, BackedgeTakenInfo()});
5488 return Pair.first->second;
5490 // computeBackedgeTakenCount may allocate memory for its result. Inserting it
5491 // into the BackedgeTakenCounts map transfers ownership. Otherwise, the result
5492 // must be cleared in this scope.
5493 BackedgeTakenInfo Result = computeBackedgeTakenCount(L);
5495 if (Result.getExact(this) != getCouldNotCompute()) {
5496 assert(isLoopInvariant(Result.getExact(this), L) &&
5497 isLoopInvariant(Result.getMax(this), L) &&
5498 "Computed backedge-taken count isn't loop invariant for loop!");
5499 ++NumTripCountsComputed;
5501 else if (Result.getMax(this) == getCouldNotCompute() &&
5502 isa<PHINode>(L->getHeader()->begin())) {
5503 // Only count loops that have phi nodes as not being computable.
5504 ++NumTripCountsNotComputed;
5507 // Now that we know more about the trip count for this loop, forget any
5508 // existing SCEV values for PHI nodes in this loop since they are only
5509 // conservative estimates made without the benefit of trip count
5510 // information. This is similar to the code in forgetLoop, except that
5511 // it handles SCEVUnknown PHI nodes specially.
5512 if (Result.hasAnyInfo()) {
5513 SmallVector<Instruction *, 16> Worklist;
5514 PushLoopPHIs(L, Worklist);
5516 SmallPtrSet<Instruction *, 8> Visited;
5517 while (!Worklist.empty()) {
5518 Instruction *I = Worklist.pop_back_val();
5519 if (!Visited.insert(I).second)
5522 ValueExprMapType::iterator It =
5523 ValueExprMap.find_as(static_cast<Value *>(I));
5524 if (It != ValueExprMap.end()) {
5525 const SCEV *Old = It->second;
5527 // SCEVUnknown for a PHI either means that it has an unrecognized
5528 // structure, or it's a PHI that's in the progress of being computed
5529 // by createNodeForPHI. In the former case, additional loop trip
5530 // count information isn't going to change anything. In the later
5531 // case, createNodeForPHI will perform the necessary updates on its
5532 // own when it gets to that point.
5533 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) {
5534 eraseValueFromMap(It->first);
5535 forgetMemoizedResults(Old);
5537 if (PHINode *PN = dyn_cast<PHINode>(I))
5538 ConstantEvolutionLoopExitValue.erase(PN);
5541 PushDefUseChildren(I, Worklist);
5545 // Re-lookup the insert position, since the call to
5546 // computeBackedgeTakenCount above could result in a
5547 // recusive call to getBackedgeTakenInfo (on a different
5548 // loop), which would invalidate the iterator computed
5550 return BackedgeTakenCounts.find(L)->second = std::move(Result);
5553 void ScalarEvolution::forgetLoop(const Loop *L) {
5554 // Drop any stored trip count value.
5555 auto RemoveLoopFromBackedgeMap =
5556 [L](DenseMap<const Loop *, BackedgeTakenInfo> &Map) {
5557 auto BTCPos = Map.find(L);
5558 if (BTCPos != Map.end()) {
5559 BTCPos->second.clear();
5564 RemoveLoopFromBackedgeMap(BackedgeTakenCounts);
5565 RemoveLoopFromBackedgeMap(PredicatedBackedgeTakenCounts);
5567 // Drop information about expressions based on loop-header PHIs.
5568 SmallVector<Instruction *, 16> Worklist;
5569 PushLoopPHIs(L, Worklist);
5571 SmallPtrSet<Instruction *, 8> Visited;
5572 while (!Worklist.empty()) {
5573 Instruction *I = Worklist.pop_back_val();
5574 if (!Visited.insert(I).second)
5577 ValueExprMapType::iterator It =
5578 ValueExprMap.find_as(static_cast<Value *>(I));
5579 if (It != ValueExprMap.end()) {
5580 eraseValueFromMap(It->first);
5581 forgetMemoizedResults(It->second);
5582 if (PHINode *PN = dyn_cast<PHINode>(I))
5583 ConstantEvolutionLoopExitValue.erase(PN);
5586 PushDefUseChildren(I, Worklist);
5589 // Forget all contained loops too, to avoid dangling entries in the
5590 // ValuesAtScopes map.
5594 LoopPropertiesCache.erase(L);
5597 void ScalarEvolution::forgetValue(Value *V) {
5598 Instruction *I = dyn_cast<Instruction>(V);
5601 // Drop information about expressions based on loop-header PHIs.
5602 SmallVector<Instruction *, 16> Worklist;
5603 Worklist.push_back(I);
5605 SmallPtrSet<Instruction *, 8> Visited;
5606 while (!Worklist.empty()) {
5607 I = Worklist.pop_back_val();
5608 if (!Visited.insert(I).second)
5611 ValueExprMapType::iterator It =
5612 ValueExprMap.find_as(static_cast<Value *>(I));
5613 if (It != ValueExprMap.end()) {
5614 eraseValueFromMap(It->first);
5615 forgetMemoizedResults(It->second);
5616 if (PHINode *PN = dyn_cast<PHINode>(I))
5617 ConstantEvolutionLoopExitValue.erase(PN);
5620 PushDefUseChildren(I, Worklist);
5624 /// Get the exact loop backedge taken count considering all loop exits. A
5625 /// computable result can only be returned for loops with a single exit.
5626 /// Returning the minimum taken count among all exits is incorrect because one
5627 /// of the loop's exit limit's may have been skipped. howFarToZero assumes that
5628 /// the limit of each loop test is never skipped. This is a valid assumption as
5629 /// long as the loop exits via that test. For precise results, it is the
5630 /// caller's responsibility to specify the relevant loop exit using
5631 /// getExact(ExitingBlock, SE).
5633 ScalarEvolution::BackedgeTakenInfo::getExact(ScalarEvolution *SE,
5634 SCEVUnionPredicate *Preds) const {
5635 // If any exits were not computable, the loop is not computable.
5636 if (!isComplete() || ExitNotTaken.empty())
5637 return SE->getCouldNotCompute();
5639 const SCEV *BECount = nullptr;
5640 for (auto &ENT : ExitNotTaken) {
5641 assert(ENT.ExactNotTaken != SE->getCouldNotCompute() && "bad exit SCEV");
5644 BECount = ENT.ExactNotTaken;
5645 else if (BECount != ENT.ExactNotTaken)
5646 return SE->getCouldNotCompute();
5647 if (Preds && !ENT.hasAlwaysTruePredicate())
5648 Preds->add(ENT.Predicate.get());
5650 assert((Preds || ENT.hasAlwaysTruePredicate()) &&
5651 "Predicate should be always true!");
5654 assert(BECount && "Invalid not taken count for loop exit");
5658 /// Get the exact not taken count for this loop exit.
5660 ScalarEvolution::BackedgeTakenInfo::getExact(BasicBlock *ExitingBlock,
5661 ScalarEvolution *SE) const {
5662 for (auto &ENT : ExitNotTaken)
5663 if (ENT.ExitingBlock == ExitingBlock && ENT.hasAlwaysTruePredicate())
5664 return ENT.ExactNotTaken;
5666 return SE->getCouldNotCompute();
5669 /// getMax - Get the max backedge taken count for the loop.
5671 ScalarEvolution::BackedgeTakenInfo::getMax(ScalarEvolution *SE) const {
5672 auto PredicateNotAlwaysTrue = [](const ExitNotTakenInfo &ENT) {
5673 return !ENT.hasAlwaysTruePredicate();
5676 if (any_of(ExitNotTaken, PredicateNotAlwaysTrue) || !getMax())
5677 return SE->getCouldNotCompute();
5682 bool ScalarEvolution::BackedgeTakenInfo::isMaxOrZero(ScalarEvolution *SE) const {
5683 auto PredicateNotAlwaysTrue = [](const ExitNotTakenInfo &ENT) {
5684 return !ENT.hasAlwaysTruePredicate();
5686 return MaxOrZero && !any_of(ExitNotTaken, PredicateNotAlwaysTrue);
5689 bool ScalarEvolution::BackedgeTakenInfo::hasOperand(const SCEV *S,
5690 ScalarEvolution *SE) const {
5691 if (getMax() && getMax() != SE->getCouldNotCompute() &&
5692 SE->hasOperand(getMax(), S))
5695 for (auto &ENT : ExitNotTaken)
5696 if (ENT.ExactNotTaken != SE->getCouldNotCompute() &&
5697 SE->hasOperand(ENT.ExactNotTaken, S))
5703 /// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each
5704 /// computable exit into a persistent ExitNotTakenInfo array.
5705 ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo(
5706 SmallVectorImpl<ScalarEvolution::BackedgeTakenInfo::EdgeExitInfo>
5708 bool Complete, const SCEV *MaxCount, bool MaxOrZero)
5709 : MaxAndComplete(MaxCount, Complete), MaxOrZero(MaxOrZero) {
5710 typedef ScalarEvolution::BackedgeTakenInfo::EdgeExitInfo EdgeExitInfo;
5711 ExitNotTaken.reserve(ExitCounts.size());
5713 ExitCounts.begin(), ExitCounts.end(), std::back_inserter(ExitNotTaken),
5714 [&](const EdgeExitInfo &EEI) {
5715 BasicBlock *ExitBB = EEI.first;
5716 const ExitLimit &EL = EEI.second;
5717 if (EL.Predicates.empty())
5718 return ExitNotTakenInfo(ExitBB, EL.ExactNotTaken, nullptr);
5720 std::unique_ptr<SCEVUnionPredicate> Predicate(new SCEVUnionPredicate);
5721 for (auto *Pred : EL.Predicates)
5722 Predicate->add(Pred);
5724 return ExitNotTakenInfo(ExitBB, EL.ExactNotTaken, std::move(Predicate));
5728 /// Invalidate this result and free the ExitNotTakenInfo array.
5729 void ScalarEvolution::BackedgeTakenInfo::clear() {
5730 ExitNotTaken.clear();
5733 /// Compute the number of times the backedge of the specified loop will execute.
5734 ScalarEvolution::BackedgeTakenInfo
5735 ScalarEvolution::computeBackedgeTakenCount(const Loop *L,
5736 bool AllowPredicates) {
5737 SmallVector<BasicBlock *, 8> ExitingBlocks;
5738 L->getExitingBlocks(ExitingBlocks);
5740 typedef ScalarEvolution::BackedgeTakenInfo::EdgeExitInfo EdgeExitInfo;
5742 SmallVector<EdgeExitInfo, 4> ExitCounts;
5743 bool CouldComputeBECount = true;
5744 BasicBlock *Latch = L->getLoopLatch(); // may be NULL.
5745 const SCEV *MustExitMaxBECount = nullptr;
5746 const SCEV *MayExitMaxBECount = nullptr;
5747 bool MustExitMaxOrZero = false;
5749 // Compute the ExitLimit for each loop exit. Use this to populate ExitCounts
5750 // and compute maxBECount.
5751 // Do a union of all the predicates here.
5752 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
5753 BasicBlock *ExitBB = ExitingBlocks[i];
5754 ExitLimit EL = computeExitLimit(L, ExitBB, AllowPredicates);
5756 assert((AllowPredicates || EL.Predicates.empty()) &&
5757 "Predicated exit limit when predicates are not allowed!");
5759 // 1. For each exit that can be computed, add an entry to ExitCounts.
5760 // CouldComputeBECount is true only if all exits can be computed.
5761 if (EL.ExactNotTaken == getCouldNotCompute())
5762 // We couldn't compute an exact value for this exit, so
5763 // we won't be able to compute an exact value for the loop.
5764 CouldComputeBECount = false;
5766 ExitCounts.emplace_back(ExitBB, EL);
5768 // 2. Derive the loop's MaxBECount from each exit's max number of
5769 // non-exiting iterations. Partition the loop exits into two kinds:
5770 // LoopMustExits and LoopMayExits.
5772 // If the exit dominates the loop latch, it is a LoopMustExit otherwise it
5773 // is a LoopMayExit. If any computable LoopMustExit is found, then
5774 // MaxBECount is the minimum EL.MaxNotTaken of computable
5775 // LoopMustExits. Otherwise, MaxBECount is conservatively the maximum
5776 // EL.MaxNotTaken, where CouldNotCompute is considered greater than any
5777 // computable EL.MaxNotTaken.
5778 if (EL.MaxNotTaken != getCouldNotCompute() && Latch &&
5779 DT.dominates(ExitBB, Latch)) {
5780 if (!MustExitMaxBECount) {
5781 MustExitMaxBECount = EL.MaxNotTaken;
5782 MustExitMaxOrZero = EL.MaxOrZero;
5784 MustExitMaxBECount =
5785 getUMinFromMismatchedTypes(MustExitMaxBECount, EL.MaxNotTaken);
5787 } else if (MayExitMaxBECount != getCouldNotCompute()) {
5788 if (!MayExitMaxBECount || EL.MaxNotTaken == getCouldNotCompute())
5789 MayExitMaxBECount = EL.MaxNotTaken;
5792 getUMaxFromMismatchedTypes(MayExitMaxBECount, EL.MaxNotTaken);
5796 const SCEV *MaxBECount = MustExitMaxBECount ? MustExitMaxBECount :
5797 (MayExitMaxBECount ? MayExitMaxBECount : getCouldNotCompute());
5798 // The loop backedge will be taken the maximum or zero times if there's
5799 // a single exit that must be taken the maximum or zero times.
5800 bool MaxOrZero = (MustExitMaxOrZero && ExitingBlocks.size() == 1);
5801 return BackedgeTakenInfo(std::move(ExitCounts), CouldComputeBECount,
5802 MaxBECount, MaxOrZero);
5805 ScalarEvolution::ExitLimit
5806 ScalarEvolution::computeExitLimit(const Loop *L, BasicBlock *ExitingBlock,
5807 bool AllowPredicates) {
5809 // Okay, we've chosen an exiting block. See what condition causes us to exit
5810 // at this block and remember the exit block and whether all other targets
5811 // lead to the loop header.
5812 bool MustExecuteLoopHeader = true;
5813 BasicBlock *Exit = nullptr;
5814 for (auto *SBB : successors(ExitingBlock))
5815 if (!L->contains(SBB)) {
5816 if (Exit) // Multiple exit successors.
5817 return getCouldNotCompute();
5819 } else if (SBB != L->getHeader()) {
5820 MustExecuteLoopHeader = false;
5823 // At this point, we know we have a conditional branch that determines whether
5824 // the loop is exited. However, we don't know if the branch is executed each
5825 // time through the loop. If not, then the execution count of the branch will
5826 // not be equal to the trip count of the loop.
5828 // Currently we check for this by checking to see if the Exit branch goes to
5829 // the loop header. If so, we know it will always execute the same number of
5830 // times as the loop. We also handle the case where the exit block *is* the
5831 // loop header. This is common for un-rotated loops.
5833 // If both of those tests fail, walk up the unique predecessor chain to the
5834 // header, stopping if there is an edge that doesn't exit the loop. If the
5835 // header is reached, the execution count of the branch will be equal to the
5836 // trip count of the loop.
5838 // More extensive analysis could be done to handle more cases here.
5840 if (!MustExecuteLoopHeader && ExitingBlock != L->getHeader()) {
5841 // The simple checks failed, try climbing the unique predecessor chain
5842 // up to the header.
5844 for (BasicBlock *BB = ExitingBlock; BB; ) {
5845 BasicBlock *Pred = BB->getUniquePredecessor();
5847 return getCouldNotCompute();
5848 TerminatorInst *PredTerm = Pred->getTerminator();
5849 for (const BasicBlock *PredSucc : PredTerm->successors()) {
5852 // If the predecessor has a successor that isn't BB and isn't
5853 // outside the loop, assume the worst.
5854 if (L->contains(PredSucc))
5855 return getCouldNotCompute();
5857 if (Pred == L->getHeader()) {
5864 return getCouldNotCompute();
5867 bool IsOnlyExit = (L->getExitingBlock() != nullptr);
5868 TerminatorInst *Term = ExitingBlock->getTerminator();
5869 if (BranchInst *BI = dyn_cast<BranchInst>(Term)) {
5870 assert(BI->isConditional() && "If unconditional, it can't be in loop!");
5871 // Proceed to the next level to examine the exit condition expression.
5872 return computeExitLimitFromCond(
5873 L, BI->getCondition(), BI->getSuccessor(0), BI->getSuccessor(1),
5874 /*ControlsExit=*/IsOnlyExit, AllowPredicates);
5877 if (SwitchInst *SI = dyn_cast<SwitchInst>(Term))
5878 return computeExitLimitFromSingleExitSwitch(L, SI, Exit,
5879 /*ControlsExit=*/IsOnlyExit);
5881 return getCouldNotCompute();
5884 ScalarEvolution::ExitLimit
5885 ScalarEvolution::computeExitLimitFromCond(const Loop *L,
5890 bool AllowPredicates) {
5891 // Check if the controlling expression for this loop is an And or Or.
5892 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
5893 if (BO->getOpcode() == Instruction::And) {
5894 // Recurse on the operands of the and.
5895 bool EitherMayExit = L->contains(TBB);
5896 ExitLimit EL0 = computeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
5897 ControlsExit && !EitherMayExit,
5899 ExitLimit EL1 = computeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
5900 ControlsExit && !EitherMayExit,
5902 const SCEV *BECount = getCouldNotCompute();
5903 const SCEV *MaxBECount = getCouldNotCompute();
5904 if (EitherMayExit) {
5905 // Both conditions must be true for the loop to continue executing.
5906 // Choose the less conservative count.
5907 if (EL0.ExactNotTaken == getCouldNotCompute() ||
5908 EL1.ExactNotTaken == getCouldNotCompute())
5909 BECount = getCouldNotCompute();
5912 getUMinFromMismatchedTypes(EL0.ExactNotTaken, EL1.ExactNotTaken);
5913 if (EL0.MaxNotTaken == getCouldNotCompute())
5914 MaxBECount = EL1.MaxNotTaken;
5915 else if (EL1.MaxNotTaken == getCouldNotCompute())
5916 MaxBECount = EL0.MaxNotTaken;
5919 getUMinFromMismatchedTypes(EL0.MaxNotTaken, EL1.MaxNotTaken);
5921 // Both conditions must be true at the same time for the loop to exit.
5922 // For now, be conservative.
5923 assert(L->contains(FBB) && "Loop block has no successor in loop!");
5924 if (EL0.MaxNotTaken == EL1.MaxNotTaken)
5925 MaxBECount = EL0.MaxNotTaken;
5926 if (EL0.ExactNotTaken == EL1.ExactNotTaken)
5927 BECount = EL0.ExactNotTaken;
5930 // There are cases (e.g. PR26207) where computeExitLimitFromCond is able
5931 // to be more aggressive when computing BECount than when computing
5932 // MaxBECount. In these cases it is possible for EL0.ExactNotTaken and
5933 // EL1.ExactNotTaken to match, but for EL0.MaxNotTaken and EL1.MaxNotTaken
5935 if (isa<SCEVCouldNotCompute>(MaxBECount) &&
5936 !isa<SCEVCouldNotCompute>(BECount))
5937 MaxBECount = BECount;
5939 return ExitLimit(BECount, MaxBECount, false,
5940 {&EL0.Predicates, &EL1.Predicates});
5942 if (BO->getOpcode() == Instruction::Or) {
5943 // Recurse on the operands of the or.
5944 bool EitherMayExit = L->contains(FBB);
5945 ExitLimit EL0 = computeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
5946 ControlsExit && !EitherMayExit,
5948 ExitLimit EL1 = computeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
5949 ControlsExit && !EitherMayExit,
5951 const SCEV *BECount = getCouldNotCompute();
5952 const SCEV *MaxBECount = getCouldNotCompute();
5953 if (EitherMayExit) {
5954 // Both conditions must be false for the loop to continue executing.
5955 // Choose the less conservative count.
5956 if (EL0.ExactNotTaken == getCouldNotCompute() ||
5957 EL1.ExactNotTaken == getCouldNotCompute())
5958 BECount = getCouldNotCompute();
5961 getUMinFromMismatchedTypes(EL0.ExactNotTaken, EL1.ExactNotTaken);
5962 if (EL0.MaxNotTaken == getCouldNotCompute())
5963 MaxBECount = EL1.MaxNotTaken;
5964 else if (EL1.MaxNotTaken == getCouldNotCompute())
5965 MaxBECount = EL0.MaxNotTaken;
5968 getUMinFromMismatchedTypes(EL0.MaxNotTaken, EL1.MaxNotTaken);
5970 // Both conditions must be false at the same time for the loop to exit.
5971 // For now, be conservative.
5972 assert(L->contains(TBB) && "Loop block has no successor in loop!");
5973 if (EL0.MaxNotTaken == EL1.MaxNotTaken)
5974 MaxBECount = EL0.MaxNotTaken;
5975 if (EL0.ExactNotTaken == EL1.ExactNotTaken)
5976 BECount = EL0.ExactNotTaken;
5979 return ExitLimit(BECount, MaxBECount, false,
5980 {&EL0.Predicates, &EL1.Predicates});
5984 // With an icmp, it may be feasible to compute an exact backedge-taken count.
5985 // Proceed to the next level to examine the icmp.
5986 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond)) {
5988 computeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB, ControlsExit);
5989 if (EL.hasFullInfo() || !AllowPredicates)
5992 // Try again, but use SCEV predicates this time.
5993 return computeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB, ControlsExit,
5994 /*AllowPredicates=*/true);
5997 // Check for a constant condition. These are normally stripped out by
5998 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
5999 // preserve the CFG and is temporarily leaving constant conditions
6001 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
6002 if (L->contains(FBB) == !CI->getZExtValue())
6003 // The backedge is always taken.
6004 return getCouldNotCompute();
6006 // The backedge is never taken.
6007 return getZero(CI->getType());
6010 // If it's not an integer or pointer comparison then compute it the hard way.
6011 return computeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
6014 ScalarEvolution::ExitLimit
6015 ScalarEvolution::computeExitLimitFromICmp(const Loop *L,
6020 bool AllowPredicates) {
6022 // If the condition was exit on true, convert the condition to exit on false
6023 ICmpInst::Predicate Cond;
6024 if (!L->contains(FBB))
6025 Cond = ExitCond->getPredicate();
6027 Cond = ExitCond->getInversePredicate();
6029 // Handle common loops like: for (X = "string"; *X; ++X)
6030 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
6031 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
6033 computeLoadConstantCompareExitLimit(LI, RHS, L, Cond);
6034 if (ItCnt.hasAnyInfo())
6038 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
6039 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
6041 // Try to evaluate any dependencies out of the loop.
6042 LHS = getSCEVAtScope(LHS, L);
6043 RHS = getSCEVAtScope(RHS, L);
6045 // At this point, we would like to compute how many iterations of the
6046 // loop the predicate will return true for these inputs.
6047 if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) {
6048 // If there is a loop-invariant, force it into the RHS.
6049 std::swap(LHS, RHS);
6050 Cond = ICmpInst::getSwappedPredicate(Cond);
6053 // Simplify the operands before analyzing them.
6054 (void)SimplifyICmpOperands(Cond, LHS, RHS);
6056 // If we have a comparison of a chrec against a constant, try to use value
6057 // ranges to answer this query.
6058 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
6059 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
6060 if (AddRec->getLoop() == L) {
6061 // Form the constant range.
6062 ConstantRange CompRange =
6063 ConstantRange::makeExactICmpRegion(Cond, RHSC->getAPInt());
6065 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
6066 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
6070 case ICmpInst::ICMP_NE: { // while (X != Y)
6071 // Convert to: while (X-Y != 0)
6072 ExitLimit EL = howFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit,
6074 if (EL.hasAnyInfo()) return EL;
6077 case ICmpInst::ICMP_EQ: { // while (X == Y)
6078 // Convert to: while (X-Y == 0)
6079 ExitLimit EL = howFarToNonZero(getMinusSCEV(LHS, RHS), L);
6080 if (EL.hasAnyInfo()) return EL;
6083 case ICmpInst::ICMP_SLT:
6084 case ICmpInst::ICMP_ULT: { // while (X < Y)
6085 bool IsSigned = Cond == ICmpInst::ICMP_SLT;
6086 ExitLimit EL = howManyLessThans(LHS, RHS, L, IsSigned, ControlsExit,
6088 if (EL.hasAnyInfo()) return EL;
6091 case ICmpInst::ICMP_SGT:
6092 case ICmpInst::ICMP_UGT: { // while (X > Y)
6093 bool IsSigned = Cond == ICmpInst::ICMP_SGT;
6095 howManyGreaterThans(LHS, RHS, L, IsSigned, ControlsExit,
6097 if (EL.hasAnyInfo()) return EL;
6104 auto *ExhaustiveCount =
6105 computeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
6107 if (!isa<SCEVCouldNotCompute>(ExhaustiveCount))
6108 return ExhaustiveCount;
6110 return computeShiftCompareExitLimit(ExitCond->getOperand(0),
6111 ExitCond->getOperand(1), L, Cond);
6114 ScalarEvolution::ExitLimit
6115 ScalarEvolution::computeExitLimitFromSingleExitSwitch(const Loop *L,
6117 BasicBlock *ExitingBlock,
6118 bool ControlsExit) {
6119 assert(!L->contains(ExitingBlock) && "Not an exiting block!");
6121 // Give up if the exit is the default dest of a switch.
6122 if (Switch->getDefaultDest() == ExitingBlock)
6123 return getCouldNotCompute();
6125 assert(L->contains(Switch->getDefaultDest()) &&
6126 "Default case must not exit the loop!");
6127 const SCEV *LHS = getSCEVAtScope(Switch->getCondition(), L);
6128 const SCEV *RHS = getConstant(Switch->findCaseDest(ExitingBlock));
6130 // while (X != Y) --> while (X-Y != 0)
6131 ExitLimit EL = howFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit);
6132 if (EL.hasAnyInfo())
6135 return getCouldNotCompute();
6138 static ConstantInt *
6139 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
6140 ScalarEvolution &SE) {
6141 const SCEV *InVal = SE.getConstant(C);
6142 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
6143 assert(isa<SCEVConstant>(Val) &&
6144 "Evaluation of SCEV at constant didn't fold correctly?");
6145 return cast<SCEVConstant>(Val)->getValue();
6148 /// Given an exit condition of 'icmp op load X, cst', try to see if we can
6149 /// compute the backedge execution count.
6150 ScalarEvolution::ExitLimit
6151 ScalarEvolution::computeLoadConstantCompareExitLimit(
6155 ICmpInst::Predicate predicate) {
6157 if (LI->isVolatile()) return getCouldNotCompute();
6159 // Check to see if the loaded pointer is a getelementptr of a global.
6160 // TODO: Use SCEV instead of manually grubbing with GEPs.
6161 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
6162 if (!GEP) return getCouldNotCompute();
6164 // Make sure that it is really a constant global we are gepping, with an
6165 // initializer, and make sure the first IDX is really 0.
6166 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
6167 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
6168 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
6169 !cast<Constant>(GEP->getOperand(1))->isNullValue())
6170 return getCouldNotCompute();
6172 // Okay, we allow one non-constant index into the GEP instruction.
6173 Value *VarIdx = nullptr;
6174 std::vector<Constant*> Indexes;
6175 unsigned VarIdxNum = 0;
6176 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
6177 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
6178 Indexes.push_back(CI);
6179 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
6180 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
6181 VarIdx = GEP->getOperand(i);
6183 Indexes.push_back(nullptr);
6186 // Loop-invariant loads may be a byproduct of loop optimization. Skip them.
6188 return getCouldNotCompute();
6190 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
6191 // Check to see if X is a loop variant variable value now.
6192 const SCEV *Idx = getSCEV(VarIdx);
6193 Idx = getSCEVAtScope(Idx, L);
6195 // We can only recognize very limited forms of loop index expressions, in
6196 // particular, only affine AddRec's like {C1,+,C2}.
6197 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
6198 if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) ||
6199 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
6200 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
6201 return getCouldNotCompute();
6203 unsigned MaxSteps = MaxBruteForceIterations;
6204 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
6205 ConstantInt *ItCst = ConstantInt::get(
6206 cast<IntegerType>(IdxExpr->getType()), IterationNum);
6207 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
6209 // Form the GEP offset.
6210 Indexes[VarIdxNum] = Val;
6212 Constant *Result = ConstantFoldLoadThroughGEPIndices(GV->getInitializer(),
6214 if (!Result) break; // Cannot compute!
6216 // Evaluate the condition for this iteration.
6217 Result = ConstantExpr::getICmp(predicate, Result, RHS);
6218 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
6219 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
6220 ++NumArrayLenItCounts;
6221 return getConstant(ItCst); // Found terminating iteration!
6224 return getCouldNotCompute();
6227 ScalarEvolution::ExitLimit ScalarEvolution::computeShiftCompareExitLimit(
6228 Value *LHS, Value *RHSV, const Loop *L, ICmpInst::Predicate Pred) {
6229 ConstantInt *RHS = dyn_cast<ConstantInt>(RHSV);
6231 return getCouldNotCompute();
6233 const BasicBlock *Latch = L->getLoopLatch();
6235 return getCouldNotCompute();
6237 const BasicBlock *Predecessor = L->getLoopPredecessor();
6239 return getCouldNotCompute();
6241 // Return true if V is of the form "LHS `shift_op` <positive constant>".
6242 // Return LHS in OutLHS and shift_opt in OutOpCode.
6243 auto MatchPositiveShift =
6244 [](Value *V, Value *&OutLHS, Instruction::BinaryOps &OutOpCode) {
6246 using namespace PatternMatch;
6248 ConstantInt *ShiftAmt;
6249 if (match(V, m_LShr(m_Value(OutLHS), m_ConstantInt(ShiftAmt))))
6250 OutOpCode = Instruction::LShr;
6251 else if (match(V, m_AShr(m_Value(OutLHS), m_ConstantInt(ShiftAmt))))
6252 OutOpCode = Instruction::AShr;
6253 else if (match(V, m_Shl(m_Value(OutLHS), m_ConstantInt(ShiftAmt))))
6254 OutOpCode = Instruction::Shl;
6258 return ShiftAmt->getValue().isStrictlyPositive();
6261 // Recognize a "shift recurrence" either of the form %iv or of %iv.shifted in
6264 // %iv = phi i32 [ %iv.shifted, %loop ], [ %val, %preheader ]
6265 // %iv.shifted = lshr i32 %iv, <positive constant>
6267 // Return true on a successful match. Return the corresponding PHI node (%iv
6268 // above) in PNOut and the opcode of the shift operation in OpCodeOut.
6269 auto MatchShiftRecurrence =
6270 [&](Value *V, PHINode *&PNOut, Instruction::BinaryOps &OpCodeOut) {
6271 Optional<Instruction::BinaryOps> PostShiftOpCode;
6274 Instruction::BinaryOps OpC;
6277 // If we encounter a shift instruction, "peel off" the shift operation,
6278 // and remember that we did so. Later when we inspect %iv's backedge
6279 // value, we will make sure that the backedge value uses the same
6282 // Note: the peeled shift operation does not have to be the same
6283 // instruction as the one feeding into the PHI's backedge value. We only
6284 // really care about it being the same *kind* of shift instruction --
6285 // that's all that is required for our later inferences to hold.
6286 if (MatchPositiveShift(LHS, V, OpC)) {
6287 PostShiftOpCode = OpC;
6292 PNOut = dyn_cast<PHINode>(LHS);
6293 if (!PNOut || PNOut->getParent() != L->getHeader())
6296 Value *BEValue = PNOut->getIncomingValueForBlock(Latch);
6300 // The backedge value for the PHI node must be a shift by a positive
6302 MatchPositiveShift(BEValue, OpLHS, OpCodeOut) &&
6304 // of the PHI node itself
6307 // and the kind of shift should be match the kind of shift we peeled
6309 (!PostShiftOpCode.hasValue() || *PostShiftOpCode == OpCodeOut);
6313 Instruction::BinaryOps OpCode;
6314 if (!MatchShiftRecurrence(LHS, PN, OpCode))
6315 return getCouldNotCompute();
6317 const DataLayout &DL = getDataLayout();
6319 // The key rationale for this optimization is that for some kinds of shift
6320 // recurrences, the value of the recurrence "stabilizes" to either 0 or -1
6321 // within a finite number of iterations. If the condition guarding the
6322 // backedge (in the sense that the backedge is taken if the condition is true)
6323 // is false for the value the shift recurrence stabilizes to, then we know
6324 // that the backedge is taken only a finite number of times.
6326 ConstantInt *StableValue = nullptr;
6329 llvm_unreachable("Impossible case!");
6331 case Instruction::AShr: {
6332 // {K,ashr,<positive-constant>} stabilizes to signum(K) in at most
6333 // bitwidth(K) iterations.
6334 Value *FirstValue = PN->getIncomingValueForBlock(Predecessor);
6335 bool KnownZero, KnownOne;
6336 ComputeSignBit(FirstValue, KnownZero, KnownOne, DL, 0, nullptr,
6337 Predecessor->getTerminator(), &DT);
6338 auto *Ty = cast<IntegerType>(RHS->getType());
6340 StableValue = ConstantInt::get(Ty, 0);
6342 StableValue = ConstantInt::get(Ty, -1, true);
6344 return getCouldNotCompute();
6348 case Instruction::LShr:
6349 case Instruction::Shl:
6350 // Both {K,lshr,<positive-constant>} and {K,shl,<positive-constant>}
6351 // stabilize to 0 in at most bitwidth(K) iterations.
6352 StableValue = ConstantInt::get(cast<IntegerType>(RHS->getType()), 0);
6357 ConstantFoldCompareInstOperands(Pred, StableValue, RHS, DL, &TLI);
6358 assert(Result->getType()->isIntegerTy(1) &&
6359 "Otherwise cannot be an operand to a branch instruction");
6361 if (Result->isZeroValue()) {
6362 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
6363 const SCEV *UpperBound =
6364 getConstant(getEffectiveSCEVType(RHS->getType()), BitWidth);
6365 return ExitLimit(getCouldNotCompute(), UpperBound, false);
6368 return getCouldNotCompute();
6371 /// Return true if we can constant fold an instruction of the specified type,
6372 /// assuming that all operands were constants.
6373 static bool CanConstantFold(const Instruction *I) {
6374 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
6375 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I) ||
6379 if (const CallInst *CI = dyn_cast<CallInst>(I))
6380 if (const Function *F = CI->getCalledFunction())
6381 return canConstantFoldCallTo(F);
6385 /// Determine whether this instruction can constant evolve within this loop
6386 /// assuming its operands can all constant evolve.
6387 static bool canConstantEvolve(Instruction *I, const Loop *L) {
6388 // An instruction outside of the loop can't be derived from a loop PHI.
6389 if (!L->contains(I)) return false;
6391 if (isa<PHINode>(I)) {
6392 // We don't currently keep track of the control flow needed to evaluate
6393 // PHIs, so we cannot handle PHIs inside of loops.
6394 return L->getHeader() == I->getParent();
6397 // If we won't be able to constant fold this expression even if the operands
6398 // are constants, bail early.
6399 return CanConstantFold(I);
6402 /// getConstantEvolvingPHIOperands - Implement getConstantEvolvingPHI by
6403 /// recursing through each instruction operand until reaching a loop header phi.
6405 getConstantEvolvingPHIOperands(Instruction *UseInst, const Loop *L,
6406 DenseMap<Instruction *, PHINode *> &PHIMap) {
6408 // Otherwise, we can evaluate this instruction if all of its operands are
6409 // constant or derived from a PHI node themselves.
6410 PHINode *PHI = nullptr;
6411 for (Value *Op : UseInst->operands()) {
6412 if (isa<Constant>(Op)) continue;
6414 Instruction *OpInst = dyn_cast<Instruction>(Op);
6415 if (!OpInst || !canConstantEvolve(OpInst, L)) return nullptr;
6417 PHINode *P = dyn_cast<PHINode>(OpInst);
6419 // If this operand is already visited, reuse the prior result.
6420 // We may have P != PHI if this is the deepest point at which the
6421 // inconsistent paths meet.
6422 P = PHIMap.lookup(OpInst);
6424 // Recurse and memoize the results, whether a phi is found or not.
6425 // This recursive call invalidates pointers into PHIMap.
6426 P = getConstantEvolvingPHIOperands(OpInst, L, PHIMap);
6430 return nullptr; // Not evolving from PHI
6431 if (PHI && PHI != P)
6432 return nullptr; // Evolving from multiple different PHIs.
6435 // This is a expression evolving from a constant PHI!
6439 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
6440 /// in the loop that V is derived from. We allow arbitrary operations along the
6441 /// way, but the operands of an operation must either be constants or a value
6442 /// derived from a constant PHI. If this expression does not fit with these
6443 /// constraints, return null.
6444 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
6445 Instruction *I = dyn_cast<Instruction>(V);
6446 if (!I || !canConstantEvolve(I, L)) return nullptr;
6448 if (PHINode *PN = dyn_cast<PHINode>(I))
6451 // Record non-constant instructions contained by the loop.
6452 DenseMap<Instruction *, PHINode *> PHIMap;
6453 return getConstantEvolvingPHIOperands(I, L, PHIMap);
6456 /// EvaluateExpression - Given an expression that passes the
6457 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
6458 /// in the loop has the value PHIVal. If we can't fold this expression for some
6459 /// reason, return null.
6460 static Constant *EvaluateExpression(Value *V, const Loop *L,
6461 DenseMap<Instruction *, Constant *> &Vals,
6462 const DataLayout &DL,
6463 const TargetLibraryInfo *TLI) {
6464 // Convenient constant check, but redundant for recursive calls.
6465 if (Constant *C = dyn_cast<Constant>(V)) return C;
6466 Instruction *I = dyn_cast<Instruction>(V);
6467 if (!I) return nullptr;
6469 if (Constant *C = Vals.lookup(I)) return C;
6471 // An instruction inside the loop depends on a value outside the loop that we
6472 // weren't given a mapping for, or a value such as a call inside the loop.
6473 if (!canConstantEvolve(I, L)) return nullptr;
6475 // An unmapped PHI can be due to a branch or another loop inside this loop,
6476 // or due to this not being the initial iteration through a loop where we
6477 // couldn't compute the evolution of this particular PHI last time.
6478 if (isa<PHINode>(I)) return nullptr;
6480 std::vector<Constant*> Operands(I->getNumOperands());
6482 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
6483 Instruction *Operand = dyn_cast<Instruction>(I->getOperand(i));
6485 Operands[i] = dyn_cast<Constant>(I->getOperand(i));
6486 if (!Operands[i]) return nullptr;
6489 Constant *C = EvaluateExpression(Operand, L, Vals, DL, TLI);
6491 if (!C) return nullptr;
6495 if (CmpInst *CI = dyn_cast<CmpInst>(I))
6496 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
6497 Operands[1], DL, TLI);
6498 if (LoadInst *LI = dyn_cast<LoadInst>(I)) {
6499 if (!LI->isVolatile())
6500 return ConstantFoldLoadFromConstPtr(Operands[0], LI->getType(), DL);
6502 return ConstantFoldInstOperands(I, Operands, DL, TLI);
6506 // If every incoming value to PN except the one for BB is a specific Constant,
6507 // return that, else return nullptr.
6508 static Constant *getOtherIncomingValue(PHINode *PN, BasicBlock *BB) {
6509 Constant *IncomingVal = nullptr;
6511 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
6512 if (PN->getIncomingBlock(i) == BB)
6515 auto *CurrentVal = dyn_cast<Constant>(PN->getIncomingValue(i));
6519 if (IncomingVal != CurrentVal) {
6522 IncomingVal = CurrentVal;
6529 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
6530 /// in the header of its containing loop, we know the loop executes a
6531 /// constant number of times, and the PHI node is just a recurrence
6532 /// involving constants, fold it.
6534 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
6537 auto I = ConstantEvolutionLoopExitValue.find(PN);
6538 if (I != ConstantEvolutionLoopExitValue.end())
6541 if (BEs.ugt(MaxBruteForceIterations))
6542 return ConstantEvolutionLoopExitValue[PN] = nullptr; // Not going to evaluate it.
6544 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
6546 DenseMap<Instruction *, Constant *> CurrentIterVals;
6547 BasicBlock *Header = L->getHeader();
6548 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
6550 BasicBlock *Latch = L->getLoopLatch();
6554 for (auto &I : *Header) {
6555 PHINode *PHI = dyn_cast<PHINode>(&I);
6557 auto *StartCST = getOtherIncomingValue(PHI, Latch);
6558 if (!StartCST) continue;
6559 CurrentIterVals[PHI] = StartCST;
6561 if (!CurrentIterVals.count(PN))
6562 return RetVal = nullptr;
6564 Value *BEValue = PN->getIncomingValueForBlock(Latch);
6566 // Execute the loop symbolically to determine the exit value.
6567 if (BEs.getActiveBits() >= 32)
6568 return RetVal = nullptr; // More than 2^32-1 iterations?? Not doing it!
6570 unsigned NumIterations = BEs.getZExtValue(); // must be in range
6571 unsigned IterationNum = 0;
6572 const DataLayout &DL = getDataLayout();
6573 for (; ; ++IterationNum) {
6574 if (IterationNum == NumIterations)
6575 return RetVal = CurrentIterVals[PN]; // Got exit value!
6577 // Compute the value of the PHIs for the next iteration.
6578 // EvaluateExpression adds non-phi values to the CurrentIterVals map.
6579 DenseMap<Instruction *, Constant *> NextIterVals;
6581 EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
6583 return nullptr; // Couldn't evaluate!
6584 NextIterVals[PN] = NextPHI;
6586 bool StoppedEvolving = NextPHI == CurrentIterVals[PN];
6588 // Also evaluate the other PHI nodes. However, we don't get to stop if we
6589 // cease to be able to evaluate one of them or if they stop evolving,
6590 // because that doesn't necessarily prevent us from computing PN.
6591 SmallVector<std::pair<PHINode *, Constant *>, 8> PHIsToCompute;
6592 for (const auto &I : CurrentIterVals) {
6593 PHINode *PHI = dyn_cast<PHINode>(I.first);
6594 if (!PHI || PHI == PN || PHI->getParent() != Header) continue;
6595 PHIsToCompute.emplace_back(PHI, I.second);
6597 // We use two distinct loops because EvaluateExpression may invalidate any
6598 // iterators into CurrentIterVals.
6599 for (const auto &I : PHIsToCompute) {
6600 PHINode *PHI = I.first;
6601 Constant *&NextPHI = NextIterVals[PHI];
6602 if (!NextPHI) { // Not already computed.
6603 Value *BEValue = PHI->getIncomingValueForBlock(Latch);
6604 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
6606 if (NextPHI != I.second)
6607 StoppedEvolving = false;
6610 // If all entries in CurrentIterVals == NextIterVals then we can stop
6611 // iterating, the loop can't continue to change.
6612 if (StoppedEvolving)
6613 return RetVal = CurrentIterVals[PN];
6615 CurrentIterVals.swap(NextIterVals);
6619 const SCEV *ScalarEvolution::computeExitCountExhaustively(const Loop *L,
6622 PHINode *PN = getConstantEvolvingPHI(Cond, L);
6623 if (!PN) return getCouldNotCompute();
6625 // If the loop is canonicalized, the PHI will have exactly two entries.
6626 // That's the only form we support here.
6627 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
6629 DenseMap<Instruction *, Constant *> CurrentIterVals;
6630 BasicBlock *Header = L->getHeader();
6631 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
6633 BasicBlock *Latch = L->getLoopLatch();
6634 assert(Latch && "Should follow from NumIncomingValues == 2!");
6636 for (auto &I : *Header) {
6637 PHINode *PHI = dyn_cast<PHINode>(&I);
6640 auto *StartCST = getOtherIncomingValue(PHI, Latch);
6641 if (!StartCST) continue;
6642 CurrentIterVals[PHI] = StartCST;
6644 if (!CurrentIterVals.count(PN))
6645 return getCouldNotCompute();
6647 // Okay, we find a PHI node that defines the trip count of this loop. Execute
6648 // the loop symbolically to determine when the condition gets a value of
6650 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
6651 const DataLayout &DL = getDataLayout();
6652 for (unsigned IterationNum = 0; IterationNum != MaxIterations;++IterationNum){
6653 auto *CondVal = dyn_cast_or_null<ConstantInt>(
6654 EvaluateExpression(Cond, L, CurrentIterVals, DL, &TLI));
6656 // Couldn't symbolically evaluate.
6657 if (!CondVal) return getCouldNotCompute();
6659 if (CondVal->getValue() == uint64_t(ExitWhen)) {
6660 ++NumBruteForceTripCountsComputed;
6661 return getConstant(Type::getInt32Ty(getContext()), IterationNum);
6664 // Update all the PHI nodes for the next iteration.
6665 DenseMap<Instruction *, Constant *> NextIterVals;
6667 // Create a list of which PHIs we need to compute. We want to do this before
6668 // calling EvaluateExpression on them because that may invalidate iterators
6669 // into CurrentIterVals.
6670 SmallVector<PHINode *, 8> PHIsToCompute;
6671 for (const auto &I : CurrentIterVals) {
6672 PHINode *PHI = dyn_cast<PHINode>(I.first);
6673 if (!PHI || PHI->getParent() != Header) continue;
6674 PHIsToCompute.push_back(PHI);
6676 for (PHINode *PHI : PHIsToCompute) {
6677 Constant *&NextPHI = NextIterVals[PHI];
6678 if (NextPHI) continue; // Already computed!
6680 Value *BEValue = PHI->getIncomingValueForBlock(Latch);
6681 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, &TLI);
6683 CurrentIterVals.swap(NextIterVals);
6686 // Too many iterations were needed to evaluate.
6687 return getCouldNotCompute();
6690 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
6691 SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values =
6693 // Check to see if we've folded this expression at this loop before.
6694 for (auto &LS : Values)
6696 return LS.second ? LS.second : V;
6698 Values.emplace_back(L, nullptr);
6700 // Otherwise compute it.
6701 const SCEV *C = computeSCEVAtScope(V, L);
6702 for (auto &LS : reverse(ValuesAtScopes[V]))
6703 if (LS.first == L) {
6710 /// This builds up a Constant using the ConstantExpr interface. That way, we
6711 /// will return Constants for objects which aren't represented by a
6712 /// SCEVConstant, because SCEVConstant is restricted to ConstantInt.
6713 /// Returns NULL if the SCEV isn't representable as a Constant.
6714 static Constant *BuildConstantFromSCEV(const SCEV *V) {
6715 switch (static_cast<SCEVTypes>(V->getSCEVType())) {
6716 case scCouldNotCompute:
6720 return cast<SCEVConstant>(V)->getValue();
6722 return dyn_cast<Constant>(cast<SCEVUnknown>(V)->getValue());
6723 case scSignExtend: {
6724 const SCEVSignExtendExpr *SS = cast<SCEVSignExtendExpr>(V);
6725 if (Constant *CastOp = BuildConstantFromSCEV(SS->getOperand()))
6726 return ConstantExpr::getSExt(CastOp, SS->getType());
6729 case scZeroExtend: {
6730 const SCEVZeroExtendExpr *SZ = cast<SCEVZeroExtendExpr>(V);
6731 if (Constant *CastOp = BuildConstantFromSCEV(SZ->getOperand()))
6732 return ConstantExpr::getZExt(CastOp, SZ->getType());
6736 const SCEVTruncateExpr *ST = cast<SCEVTruncateExpr>(V);
6737 if (Constant *CastOp = BuildConstantFromSCEV(ST->getOperand()))
6738 return ConstantExpr::getTrunc(CastOp, ST->getType());
6742 const SCEVAddExpr *SA = cast<SCEVAddExpr>(V);
6743 if (Constant *C = BuildConstantFromSCEV(SA->getOperand(0))) {
6744 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
6745 unsigned AS = PTy->getAddressSpace();
6746 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
6747 C = ConstantExpr::getBitCast(C, DestPtrTy);
6749 for (unsigned i = 1, e = SA->getNumOperands(); i != e; ++i) {
6750 Constant *C2 = BuildConstantFromSCEV(SA->getOperand(i));
6751 if (!C2) return nullptr;
6754 if (!C->getType()->isPointerTy() && C2->getType()->isPointerTy()) {
6755 unsigned AS = C2->getType()->getPointerAddressSpace();
6757 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
6758 // The offsets have been converted to bytes. We can add bytes to an
6759 // i8* by GEP with the byte count in the first index.
6760 C = ConstantExpr::getBitCast(C, DestPtrTy);
6763 // Don't bother trying to sum two pointers. We probably can't
6764 // statically compute a load that results from it anyway.
6765 if (C2->getType()->isPointerTy())
6768 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
6769 if (PTy->getElementType()->isStructTy())
6770 C2 = ConstantExpr::getIntegerCast(
6771 C2, Type::getInt32Ty(C->getContext()), true);
6772 C = ConstantExpr::getGetElementPtr(PTy->getElementType(), C, C2);
6774 C = ConstantExpr::getAdd(C, C2);
6781 const SCEVMulExpr *SM = cast<SCEVMulExpr>(V);
6782 if (Constant *C = BuildConstantFromSCEV(SM->getOperand(0))) {
6783 // Don't bother with pointers at all.
6784 if (C->getType()->isPointerTy()) return nullptr;
6785 for (unsigned i = 1, e = SM->getNumOperands(); i != e; ++i) {
6786 Constant *C2 = BuildConstantFromSCEV(SM->getOperand(i));
6787 if (!C2 || C2->getType()->isPointerTy()) return nullptr;
6788 C = ConstantExpr::getMul(C, C2);
6795 const SCEVUDivExpr *SU = cast<SCEVUDivExpr>(V);
6796 if (Constant *LHS = BuildConstantFromSCEV(SU->getLHS()))
6797 if (Constant *RHS = BuildConstantFromSCEV(SU->getRHS()))
6798 if (LHS->getType() == RHS->getType())
6799 return ConstantExpr::getUDiv(LHS, RHS);
6804 break; // TODO: smax, umax.
6809 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
6810 if (isa<SCEVConstant>(V)) return V;
6812 // If this instruction is evolved from a constant-evolving PHI, compute the
6813 // exit value from the loop without using SCEVs.
6814 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
6815 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
6816 const Loop *LI = this->LI[I->getParent()];
6817 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
6818 if (PHINode *PN = dyn_cast<PHINode>(I))
6819 if (PN->getParent() == LI->getHeader()) {
6820 // Okay, there is no closed form solution for the PHI node. Check
6821 // to see if the loop that contains it has a known backedge-taken
6822 // count. If so, we may be able to force computation of the exit
6824 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
6825 if (const SCEVConstant *BTCC =
6826 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
6827 // Okay, we know how many times the containing loop executes. If
6828 // this is a constant evolving PHI node, get the final value at
6829 // the specified iteration number.
6831 getConstantEvolutionLoopExitValue(PN, BTCC->getAPInt(), LI);
6832 if (RV) return getSCEV(RV);
6836 // Okay, this is an expression that we cannot symbolically evaluate
6837 // into a SCEV. Check to see if it's possible to symbolically evaluate
6838 // the arguments into constants, and if so, try to constant propagate the
6839 // result. This is particularly useful for computing loop exit values.
6840 if (CanConstantFold(I)) {
6841 SmallVector<Constant *, 4> Operands;
6842 bool MadeImprovement = false;
6843 for (Value *Op : I->operands()) {
6844 if (Constant *C = dyn_cast<Constant>(Op)) {
6845 Operands.push_back(C);
6849 // If any of the operands is non-constant and if they are
6850 // non-integer and non-pointer, don't even try to analyze them
6851 // with scev techniques.
6852 if (!isSCEVable(Op->getType()))
6855 const SCEV *OrigV = getSCEV(Op);
6856 const SCEV *OpV = getSCEVAtScope(OrigV, L);
6857 MadeImprovement |= OrigV != OpV;
6859 Constant *C = BuildConstantFromSCEV(OpV);
6861 if (C->getType() != Op->getType())
6862 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
6866 Operands.push_back(C);
6869 // Check to see if getSCEVAtScope actually made an improvement.
6870 if (MadeImprovement) {
6871 Constant *C = nullptr;
6872 const DataLayout &DL = getDataLayout();
6873 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
6874 C = ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
6875 Operands[1], DL, &TLI);
6876 else if (const LoadInst *LI = dyn_cast<LoadInst>(I)) {
6877 if (!LI->isVolatile())
6878 C = ConstantFoldLoadFromConstPtr(Operands[0], LI->getType(), DL);
6880 C = ConstantFoldInstOperands(I, Operands, DL, &TLI);
6887 // This is some other type of SCEVUnknown, just return it.
6891 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
6892 // Avoid performing the look-up in the common case where the specified
6893 // expression has no loop-variant portions.
6894 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
6895 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
6896 if (OpAtScope != Comm->getOperand(i)) {
6897 // Okay, at least one of these operands is loop variant but might be
6898 // foldable. Build a new instance of the folded commutative expression.
6899 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
6900 Comm->op_begin()+i);
6901 NewOps.push_back(OpAtScope);
6903 for (++i; i != e; ++i) {
6904 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
6905 NewOps.push_back(OpAtScope);
6907 if (isa<SCEVAddExpr>(Comm))
6908 return getAddExpr(NewOps);
6909 if (isa<SCEVMulExpr>(Comm))
6910 return getMulExpr(NewOps);
6911 if (isa<SCEVSMaxExpr>(Comm))
6912 return getSMaxExpr(NewOps);
6913 if (isa<SCEVUMaxExpr>(Comm))
6914 return getUMaxExpr(NewOps);
6915 llvm_unreachable("Unknown commutative SCEV type!");
6918 // If we got here, all operands are loop invariant.
6922 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
6923 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
6924 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
6925 if (LHS == Div->getLHS() && RHS == Div->getRHS())
6926 return Div; // must be loop invariant
6927 return getUDivExpr(LHS, RHS);
6930 // If this is a loop recurrence for a loop that does not contain L, then we
6931 // are dealing with the final value computed by the loop.
6932 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
6933 // First, attempt to evaluate each operand.
6934 // Avoid performing the look-up in the common case where the specified
6935 // expression has no loop-variant portions.
6936 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
6937 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
6938 if (OpAtScope == AddRec->getOperand(i))
6941 // Okay, at least one of these operands is loop variant but might be
6942 // foldable. Build a new instance of the folded commutative expression.
6943 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(),
6944 AddRec->op_begin()+i);
6945 NewOps.push_back(OpAtScope);
6946 for (++i; i != e; ++i)
6947 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
6949 const SCEV *FoldedRec =
6950 getAddRecExpr(NewOps, AddRec->getLoop(),
6951 AddRec->getNoWrapFlags(SCEV::FlagNW));
6952 AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec);
6953 // The addrec may be folded to a nonrecurrence, for example, if the
6954 // induction variable is multiplied by zero after constant folding. Go
6955 // ahead and return the folded value.
6961 // If the scope is outside the addrec's loop, evaluate it by using the
6962 // loop exit value of the addrec.
6963 if (!AddRec->getLoop()->contains(L)) {
6964 // To evaluate this recurrence, we need to know how many times the AddRec
6965 // loop iterates. Compute this now.
6966 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
6967 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
6969 // Then, evaluate the AddRec.
6970 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
6976 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
6977 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
6978 if (Op == Cast->getOperand())
6979 return Cast; // must be loop invariant
6980 return getZeroExtendExpr(Op, Cast->getType());
6983 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
6984 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
6985 if (Op == Cast->getOperand())
6986 return Cast; // must be loop invariant
6987 return getSignExtendExpr(Op, Cast->getType());
6990 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
6991 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
6992 if (Op == Cast->getOperand())
6993 return Cast; // must be loop invariant
6994 return getTruncateExpr(Op, Cast->getType());
6997 llvm_unreachable("Unknown SCEV type!");
7000 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
7001 return getSCEVAtScope(getSCEV(V), L);
7004 /// Finds the minimum unsigned root of the following equation:
7006 /// A * X = B (mod N)
7008 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
7009 /// A and B isn't important.
7011 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
7012 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
7013 ScalarEvolution &SE) {
7014 uint32_t BW = A.getBitWidth();
7015 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
7016 assert(A != 0 && "A must be non-zero.");
7020 // The gcd of A and N may have only one prime factor: 2. The number of
7021 // trailing zeros in A is its multiplicity
7022 uint32_t Mult2 = A.countTrailingZeros();
7025 // 2. Check if B is divisible by D.
7027 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
7028 // is not less than multiplicity of this prime factor for D.
7029 if (B.countTrailingZeros() < Mult2)
7030 return SE.getCouldNotCompute();
7032 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
7035 // If D == 1, (N / D) == N == 2^BW, so we need one extra bit to represent
7036 // (N / D) in general. The inverse itself always fits into BW bits, though,
7037 // so we immediately truncate it.
7038 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
7039 APInt Mod(BW + 1, 0);
7040 Mod.setBit(BW - Mult2); // Mod = N / D
7041 APInt I = AD.multiplicativeInverse(Mod).trunc(BW);
7043 // 4. Compute the minimum unsigned root of the equation:
7044 // I * (B / D) mod (N / D)
7045 // To simplify the computation, we factor out the divide by D:
7046 // (I * B mod N) / D
7047 APInt Result = (I * B).lshr(Mult2);
7049 return SE.getConstant(Result);
7052 /// Find the roots of the quadratic equation for the given quadratic chrec
7053 /// {L,+,M,+,N}. This returns either the two roots (which might be the same) or
7054 /// two SCEVCouldNotCompute objects.
7056 static Optional<std::pair<const SCEVConstant *,const SCEVConstant *>>
7057 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
7058 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
7059 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
7060 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
7061 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
7063 // We currently can only solve this if the coefficients are constants.
7064 if (!LC || !MC || !NC)
7067 uint32_t BitWidth = LC->getAPInt().getBitWidth();
7068 const APInt &L = LC->getAPInt();
7069 const APInt &M = MC->getAPInt();
7070 const APInt &N = NC->getAPInt();
7071 APInt Two(BitWidth, 2);
7072 APInt Four(BitWidth, 4);
7075 using namespace APIntOps;
7077 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
7078 // The B coefficient is M-N/2
7082 // The A coefficient is N/2
7083 APInt A(N.sdiv(Two));
7085 // Compute the B^2-4ac term.
7088 SqrtTerm -= Four * (A * C);
7090 if (SqrtTerm.isNegative()) {
7091 // The loop is provably infinite.
7095 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
7096 // integer value or else APInt::sqrt() will assert.
7097 APInt SqrtVal(SqrtTerm.sqrt());
7099 // Compute the two solutions for the quadratic formula.
7100 // The divisions must be performed as signed divisions.
7103 if (TwoA.isMinValue())
7106 LLVMContext &Context = SE.getContext();
7108 ConstantInt *Solution1 =
7109 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
7110 ConstantInt *Solution2 =
7111 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
7113 return std::make_pair(cast<SCEVConstant>(SE.getConstant(Solution1)),
7114 cast<SCEVConstant>(SE.getConstant(Solution2)));
7115 } // end APIntOps namespace
7118 ScalarEvolution::ExitLimit
7119 ScalarEvolution::howFarToZero(const SCEV *V, const Loop *L, bool ControlsExit,
7120 bool AllowPredicates) {
7122 // This is only used for loops with a "x != y" exit test. The exit condition
7123 // is now expressed as a single expression, V = x-y. So the exit test is
7124 // effectively V != 0. We know and take advantage of the fact that this
7125 // expression only being used in a comparison by zero context.
7127 SmallPtrSet<const SCEVPredicate *, 4> Predicates;
7128 // If the value is a constant
7129 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
7130 // If the value is already zero, the branch will execute zero times.
7131 if (C->getValue()->isZero()) return C;
7132 return getCouldNotCompute(); // Otherwise it will loop infinitely.
7135 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
7136 if (!AddRec && AllowPredicates)
7137 // Try to make this an AddRec using runtime tests, in the first X
7138 // iterations of this loop, where X is the SCEV expression found by the
7140 AddRec = convertSCEVToAddRecWithPredicates(V, L, Predicates);
7142 if (!AddRec || AddRec->getLoop() != L)
7143 return getCouldNotCompute();
7145 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
7146 // the quadratic equation to solve it.
7147 if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
7148 if (auto Roots = SolveQuadraticEquation(AddRec, *this)) {
7149 const SCEVConstant *R1 = Roots->first;
7150 const SCEVConstant *R2 = Roots->second;
7151 // Pick the smallest positive root value.
7152 if (ConstantInt *CB = dyn_cast<ConstantInt>(ConstantExpr::getICmp(
7153 CmpInst::ICMP_ULT, R1->getValue(), R2->getValue()))) {
7154 if (!CB->getZExtValue())
7155 std::swap(R1, R2); // R1 is the minimum root now.
7157 // We can only use this value if the chrec ends up with an exact zero
7158 // value at this index. When solving for "X*X != 5", for example, we
7159 // should not accept a root of 2.
7160 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
7162 // We found a quadratic root!
7163 return ExitLimit(R1, R1, false, Predicates);
7166 return getCouldNotCompute();
7169 // Otherwise we can only handle this if it is affine.
7170 if (!AddRec->isAffine())
7171 return getCouldNotCompute();
7173 // If this is an affine expression, the execution count of this branch is
7174 // the minimum unsigned root of the following equation:
7176 // Start + Step*N = 0 (mod 2^BW)
7180 // Step*N = -Start (mod 2^BW)
7182 // where BW is the common bit width of Start and Step.
7184 // Get the initial value for the loop.
7185 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
7186 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
7188 // For now we handle only constant steps.
7190 // TODO: Handle a nonconstant Step given AddRec<NUW>. If the
7191 // AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap
7192 // to 0, it must be counting down to equal 0. Consequently, N = Start / -Step.
7193 // We have not yet seen any such cases.
7194 const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step);
7195 if (!StepC || StepC->getValue()->equalsInt(0))
7196 return getCouldNotCompute();
7198 // For positive steps (counting up until unsigned overflow):
7199 // N = -Start/Step (as unsigned)
7200 // For negative steps (counting down to zero):
7202 // First compute the unsigned distance from zero in the direction of Step.
7203 bool CountDown = StepC->getAPInt().isNegative();
7204 const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start);
7206 // Handle unitary steps, which cannot wraparound.
7207 // 1*N = -Start; -1*N = Start (mod 2^BW), so:
7208 // N = Distance (as unsigned)
7209 if (StepC->getValue()->equalsInt(1) || StepC->getValue()->isAllOnesValue()) {
7210 APInt MaxBECount = getUnsignedRange(Distance).getUnsignedMax();
7212 // When a loop like "for (int i = 0; i != n; ++i) { /* body */ }" is rotated,
7213 // we end up with a loop whose backedge-taken count is n - 1. Detect this
7214 // case, and see if we can improve the bound.
7216 // Explicitly handling this here is necessary because getUnsignedRange
7217 // isn't context-sensitive; it doesn't know that we only care about the
7218 // range inside the loop.
7219 const SCEV *Zero = getZero(Distance->getType());
7220 const SCEV *One = getOne(Distance->getType());
7221 const SCEV *DistancePlusOne = getAddExpr(Distance, One);
7222 if (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_NE, DistancePlusOne, Zero)) {
7223 // If Distance + 1 doesn't overflow, we can compute the maximum distance
7224 // as "unsigned_max(Distance + 1) - 1".
7225 ConstantRange CR = getUnsignedRange(DistancePlusOne);
7226 MaxBECount = APIntOps::umin(MaxBECount, CR.getUnsignedMax() - 1);
7228 return ExitLimit(Distance, getConstant(MaxBECount), false, Predicates);
7231 // As a special case, handle the instance where Step is a positive power of
7232 // two. In this case, determining whether Step divides Distance evenly can be
7233 // done by counting and comparing the number of trailing zeros of Step and
7236 const APInt &StepV = StepC->getAPInt();
7237 // StepV.isPowerOf2() returns true if StepV is an positive power of two. It
7238 // also returns true if StepV is maximally negative (eg, INT_MIN), but that
7239 // case is not handled as this code is guarded by !CountDown.
7240 if (StepV.isPowerOf2() &&
7241 GetMinTrailingZeros(Distance) >= StepV.countTrailingZeros()) {
7242 // Here we've constrained the equation to be of the form
7244 // 2^(N + k) * Distance' = (StepV == 2^N) * X (mod 2^W) ... (0)
7246 // where we're operating on a W bit wide integer domain and k is
7247 // non-negative. The smallest unsigned solution for X is the trip count.
7249 // (0) is equivalent to:
7251 // 2^(N + k) * Distance' - 2^N * X = L * 2^W
7252 // <=> 2^N(2^k * Distance' - X) = L * 2^(W - N) * 2^N
7253 // <=> 2^k * Distance' - X = L * 2^(W - N)
7254 // <=> 2^k * Distance' = L * 2^(W - N) + X ... (1)
7256 // The smallest X satisfying (1) is unsigned remainder of dividing the LHS
7259 // <=> X = 2^k * Distance' URem 2^(W - N) ... (2)
7261 // E.g. say we're solving
7263 // 2 * Val = 2 * X (in i8) ... (3)
7265 // then from (2), we get X = Val URem i8 128 (k = 0 in this case).
7267 // Note: It is tempting to solve (3) by setting X = Val, but Val is not
7268 // necessarily the smallest unsigned value of X that satisfies (3).
7269 // E.g. if Val is i8 -127 then the smallest value of X that satisfies (3)
7270 // is i8 1, not i8 -127
7272 const auto *ModuloResult = getUDivExactExpr(Distance, Step);
7274 // Since SCEV does not have a URem node, we construct one using a truncate
7275 // and a zero extend.
7277 unsigned NarrowWidth = StepV.getBitWidth() - StepV.countTrailingZeros();
7278 auto *NarrowTy = IntegerType::get(getContext(), NarrowWidth);
7279 auto *WideTy = Distance->getType();
7282 getZeroExtendExpr(getTruncateExpr(ModuloResult, NarrowTy), WideTy);
7283 return ExitLimit(Limit, Limit, false, Predicates);
7287 // If the condition controls loop exit (the loop exits only if the expression
7288 // is true) and the addition is no-wrap we can use unsigned divide to
7289 // compute the backedge count. In this case, the step may not divide the
7290 // distance, but we don't care because if the condition is "missed" the loop
7291 // will have undefined behavior due to wrapping.
7292 if (ControlsExit && AddRec->hasNoSelfWrap() &&
7293 loopHasNoAbnormalExits(AddRec->getLoop())) {
7295 getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
7296 return ExitLimit(Exact, Exact, false, Predicates);
7299 // Then, try to solve the above equation provided that Start is constant.
7300 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) {
7301 const SCEV *E = SolveLinEquationWithOverflow(
7302 StepC->getValue()->getValue(), -StartC->getValue()->getValue(), *this);
7303 return ExitLimit(E, E, false, Predicates);
7305 return getCouldNotCompute();
7308 ScalarEvolution::ExitLimit
7309 ScalarEvolution::howFarToNonZero(const SCEV *V, const Loop *L) {
7310 // Loops that look like: while (X == 0) are very strange indeed. We don't
7311 // handle them yet except for the trivial case. This could be expanded in the
7312 // future as needed.
7314 // If the value is a constant, check to see if it is known to be non-zero
7315 // already. If so, the backedge will execute zero times.
7316 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
7317 if (!C->getValue()->isNullValue())
7318 return getZero(C->getType());
7319 return getCouldNotCompute(); // Otherwise it will loop infinitely.
7322 // We could implement others, but I really doubt anyone writes loops like
7323 // this, and if they did, they would already be constant folded.
7324 return getCouldNotCompute();
7327 std::pair<BasicBlock *, BasicBlock *>
7328 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
7329 // If the block has a unique predecessor, then there is no path from the
7330 // predecessor to the block that does not go through the direct edge
7331 // from the predecessor to the block.
7332 if (BasicBlock *Pred = BB->getSinglePredecessor())
7335 // A loop's header is defined to be a block that dominates the loop.
7336 // If the header has a unique predecessor outside the loop, it must be
7337 // a block that has exactly one successor that can reach the loop.
7338 if (Loop *L = LI.getLoopFor(BB))
7339 return {L->getLoopPredecessor(), L->getHeader()};
7341 return {nullptr, nullptr};
7344 /// SCEV structural equivalence is usually sufficient for testing whether two
7345 /// expressions are equal, however for the purposes of looking for a condition
7346 /// guarding a loop, it can be useful to be a little more general, since a
7347 /// front-end may have replicated the controlling expression.
7349 static bool HasSameValue(const SCEV *A, const SCEV *B) {
7350 // Quick check to see if they are the same SCEV.
7351 if (A == B) return true;
7353 auto ComputesEqualValues = [](const Instruction *A, const Instruction *B) {
7354 // Not all instructions that are "identical" compute the same value. For
7355 // instance, two distinct alloca instructions allocating the same type are
7356 // identical and do not read memory; but compute distinct values.
7357 return A->isIdenticalTo(B) && (isa<BinaryOperator>(A) || isa<GetElementPtrInst>(A));
7360 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
7361 // two different instructions with the same value. Check for this case.
7362 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
7363 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
7364 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
7365 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
7366 if (ComputesEqualValues(AI, BI))
7369 // Otherwise assume they may have a different value.
7373 bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
7374 const SCEV *&LHS, const SCEV *&RHS,
7376 bool Changed = false;
7378 // If we hit the max recursion limit bail out.
7382 // Canonicalize a constant to the right side.
7383 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
7384 // Check for both operands constant.
7385 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
7386 if (ConstantExpr::getICmp(Pred,
7388 RHSC->getValue())->isNullValue())
7389 goto trivially_false;
7391 goto trivially_true;
7393 // Otherwise swap the operands to put the constant on the right.
7394 std::swap(LHS, RHS);
7395 Pred = ICmpInst::getSwappedPredicate(Pred);
7399 // If we're comparing an addrec with a value which is loop-invariant in the
7400 // addrec's loop, put the addrec on the left. Also make a dominance check,
7401 // as both operands could be addrecs loop-invariant in each other's loop.
7402 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
7403 const Loop *L = AR->getLoop();
7404 if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) {
7405 std::swap(LHS, RHS);
7406 Pred = ICmpInst::getSwappedPredicate(Pred);
7411 // If there's a constant operand, canonicalize comparisons with boundary
7412 // cases, and canonicalize *-or-equal comparisons to regular comparisons.
7413 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
7414 const APInt &RA = RC->getAPInt();
7416 bool SimplifiedByConstantRange = false;
7418 if (!ICmpInst::isEquality(Pred)) {
7419 ConstantRange ExactCR = ConstantRange::makeExactICmpRegion(Pred, RA);
7420 if (ExactCR.isFullSet())
7421 goto trivially_true;
7422 else if (ExactCR.isEmptySet())
7423 goto trivially_false;
7426 CmpInst::Predicate NewPred;
7427 if (ExactCR.getEquivalentICmp(NewPred, NewRHS) &&
7428 ICmpInst::isEquality(NewPred)) {
7429 // We were able to convert an inequality to an equality.
7431 RHS = getConstant(NewRHS);
7432 Changed = SimplifiedByConstantRange = true;
7436 if (!SimplifiedByConstantRange) {
7440 case ICmpInst::ICMP_EQ:
7441 case ICmpInst::ICMP_NE:
7442 // Fold ((-1) * %a) + %b == 0 (equivalent to %b-%a == 0) into %a == %b.
7444 if (const SCEVAddExpr *AE = dyn_cast<SCEVAddExpr>(LHS))
7445 if (const SCEVMulExpr *ME =
7446 dyn_cast<SCEVMulExpr>(AE->getOperand(0)))
7447 if (AE->getNumOperands() == 2 && ME->getNumOperands() == 2 &&
7448 ME->getOperand(0)->isAllOnesValue()) {
7449 RHS = AE->getOperand(1);
7450 LHS = ME->getOperand(1);
7456 // The "Should have been caught earlier!" messages refer to the fact
7457 // that the ExactCR.isFullSet() or ExactCR.isEmptySet() check above
7458 // should have fired on the corresponding cases, and canonicalized the
7459 // check to trivially_true or trivially_false.
7461 case ICmpInst::ICMP_UGE:
7462 assert(!RA.isMinValue() && "Should have been caught earlier!");
7463 Pred = ICmpInst::ICMP_UGT;
7464 RHS = getConstant(RA - 1);
7467 case ICmpInst::ICMP_ULE:
7468 assert(!RA.isMaxValue() && "Should have been caught earlier!");
7469 Pred = ICmpInst::ICMP_ULT;
7470 RHS = getConstant(RA + 1);
7473 case ICmpInst::ICMP_SGE:
7474 assert(!RA.isMinSignedValue() && "Should have been caught earlier!");
7475 Pred = ICmpInst::ICMP_SGT;
7476 RHS = getConstant(RA - 1);
7479 case ICmpInst::ICMP_SLE:
7480 assert(!RA.isMaxSignedValue() && "Should have been caught earlier!");
7481 Pred = ICmpInst::ICMP_SLT;
7482 RHS = getConstant(RA + 1);
7489 // Check for obvious equality.
7490 if (HasSameValue(LHS, RHS)) {
7491 if (ICmpInst::isTrueWhenEqual(Pred))
7492 goto trivially_true;
7493 if (ICmpInst::isFalseWhenEqual(Pred))
7494 goto trivially_false;
7497 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
7498 // adding or subtracting 1 from one of the operands.
7500 case ICmpInst::ICMP_SLE:
7501 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) {
7502 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
7504 Pred = ICmpInst::ICMP_SLT;
7506 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) {
7507 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
7509 Pred = ICmpInst::ICMP_SLT;
7513 case ICmpInst::ICMP_SGE:
7514 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) {
7515 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
7517 Pred = ICmpInst::ICMP_SGT;
7519 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) {
7520 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
7522 Pred = ICmpInst::ICMP_SGT;
7526 case ICmpInst::ICMP_ULE:
7527 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) {
7528 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
7530 Pred = ICmpInst::ICMP_ULT;
7532 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) {
7533 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS);
7534 Pred = ICmpInst::ICMP_ULT;
7538 case ICmpInst::ICMP_UGE:
7539 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) {
7540 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS);
7541 Pred = ICmpInst::ICMP_UGT;
7543 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) {
7544 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
7546 Pred = ICmpInst::ICMP_UGT;
7554 // TODO: More simplifications are possible here.
7556 // Recursively simplify until we either hit a recursion limit or nothing
7559 return SimplifyICmpOperands(Pred, LHS, RHS, Depth+1);
7565 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
7566 Pred = ICmpInst::ICMP_EQ;
7571 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
7572 Pred = ICmpInst::ICMP_NE;
7576 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
7577 return getSignedRange(S).getSignedMax().isNegative();
7580 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
7581 return getSignedRange(S).getSignedMin().isStrictlyPositive();
7584 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
7585 return !getSignedRange(S).getSignedMin().isNegative();
7588 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
7589 return !getSignedRange(S).getSignedMax().isStrictlyPositive();
7592 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
7593 return isKnownNegative(S) || isKnownPositive(S);
7596 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
7597 const SCEV *LHS, const SCEV *RHS) {
7598 // Canonicalize the inputs first.
7599 (void)SimplifyICmpOperands(Pred, LHS, RHS);
7601 // If LHS or RHS is an addrec, check to see if the condition is true in
7602 // every iteration of the loop.
7603 // If LHS and RHS are both addrec, both conditions must be true in
7604 // every iteration of the loop.
7605 const SCEVAddRecExpr *LAR = dyn_cast<SCEVAddRecExpr>(LHS);
7606 const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS);
7607 bool LeftGuarded = false;
7608 bool RightGuarded = false;
7610 const Loop *L = LAR->getLoop();
7611 if (isLoopEntryGuardedByCond(L, Pred, LAR->getStart(), RHS) &&
7612 isLoopBackedgeGuardedByCond(L, Pred, LAR->getPostIncExpr(*this), RHS)) {
7613 if (!RAR) return true;
7618 const Loop *L = RAR->getLoop();
7619 if (isLoopEntryGuardedByCond(L, Pred, LHS, RAR->getStart()) &&
7620 isLoopBackedgeGuardedByCond(L, Pred, LHS, RAR->getPostIncExpr(*this))) {
7621 if (!LAR) return true;
7622 RightGuarded = true;
7625 if (LeftGuarded && RightGuarded)
7628 if (isKnownPredicateViaSplitting(Pred, LHS, RHS))
7631 // Otherwise see what can be done with known constant ranges.
7632 return isKnownPredicateViaConstantRanges(Pred, LHS, RHS);
7635 bool ScalarEvolution::isMonotonicPredicate(const SCEVAddRecExpr *LHS,
7636 ICmpInst::Predicate Pred,
7638 bool Result = isMonotonicPredicateImpl(LHS, Pred, Increasing);
7641 // Verify an invariant: inverting the predicate should turn a monotonically
7642 // increasing change to a monotonically decreasing one, and vice versa.
7643 bool IncreasingSwapped;
7644 bool ResultSwapped = isMonotonicPredicateImpl(
7645 LHS, ICmpInst::getSwappedPredicate(Pred), IncreasingSwapped);
7647 assert(Result == ResultSwapped && "should be able to analyze both!");
7649 assert(Increasing == !IncreasingSwapped &&
7650 "monotonicity should flip as we flip the predicate");
7656 bool ScalarEvolution::isMonotonicPredicateImpl(const SCEVAddRecExpr *LHS,
7657 ICmpInst::Predicate Pred,
7660 // A zero step value for LHS means the induction variable is essentially a
7661 // loop invariant value. We don't really depend on the predicate actually
7662 // flipping from false to true (for increasing predicates, and the other way
7663 // around for decreasing predicates), all we care about is that *if* the
7664 // predicate changes then it only changes from false to true.
7666 // A zero step value in itself is not very useful, but there may be places
7667 // where SCEV can prove X >= 0 but not prove X > 0, so it is helpful to be
7668 // as general as possible.
7672 return false; // Conservative answer
7674 case ICmpInst::ICMP_UGT:
7675 case ICmpInst::ICMP_UGE:
7676 case ICmpInst::ICMP_ULT:
7677 case ICmpInst::ICMP_ULE:
7678 if (!LHS->hasNoUnsignedWrap())
7681 Increasing = Pred == ICmpInst::ICMP_UGT || Pred == ICmpInst::ICMP_UGE;
7684 case ICmpInst::ICMP_SGT:
7685 case ICmpInst::ICMP_SGE:
7686 case ICmpInst::ICMP_SLT:
7687 case ICmpInst::ICMP_SLE: {
7688 if (!LHS->hasNoSignedWrap())
7691 const SCEV *Step = LHS->getStepRecurrence(*this);
7693 if (isKnownNonNegative(Step)) {
7694 Increasing = Pred == ICmpInst::ICMP_SGT || Pred == ICmpInst::ICMP_SGE;
7698 if (isKnownNonPositive(Step)) {
7699 Increasing = Pred == ICmpInst::ICMP_SLT || Pred == ICmpInst::ICMP_SLE;
7708 llvm_unreachable("switch has default clause!");
7711 bool ScalarEvolution::isLoopInvariantPredicate(
7712 ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS, const Loop *L,
7713 ICmpInst::Predicate &InvariantPred, const SCEV *&InvariantLHS,
7714 const SCEV *&InvariantRHS) {
7716 // If there is a loop-invariant, force it into the RHS, otherwise bail out.
7717 if (!isLoopInvariant(RHS, L)) {
7718 if (!isLoopInvariant(LHS, L))
7721 std::swap(LHS, RHS);
7722 Pred = ICmpInst::getSwappedPredicate(Pred);
7725 const SCEVAddRecExpr *ArLHS = dyn_cast<SCEVAddRecExpr>(LHS);
7726 if (!ArLHS || ArLHS->getLoop() != L)
7730 if (!isMonotonicPredicate(ArLHS, Pred, Increasing))
7733 // If the predicate "ArLHS `Pred` RHS" monotonically increases from false to
7734 // true as the loop iterates, and the backedge is control dependent on
7735 // "ArLHS `Pred` RHS" == true then we can reason as follows:
7737 // * if the predicate was false in the first iteration then the predicate
7738 // is never evaluated again, since the loop exits without taking the
7740 // * if the predicate was true in the first iteration then it will
7741 // continue to be true for all future iterations since it is
7742 // monotonically increasing.
7744 // For both the above possibilities, we can replace the loop varying
7745 // predicate with its value on the first iteration of the loop (which is
7748 // A similar reasoning applies for a monotonically decreasing predicate, by
7749 // replacing true with false and false with true in the above two bullets.
7751 auto P = Increasing ? Pred : ICmpInst::getInversePredicate(Pred);
7753 if (!isLoopBackedgeGuardedByCond(L, P, LHS, RHS))
7756 InvariantPred = Pred;
7757 InvariantLHS = ArLHS->getStart();
7762 bool ScalarEvolution::isKnownPredicateViaConstantRanges(
7763 ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS) {
7764 if (HasSameValue(LHS, RHS))
7765 return ICmpInst::isTrueWhenEqual(Pred);
7767 // This code is split out from isKnownPredicate because it is called from
7768 // within isLoopEntryGuardedByCond.
7771 [&](const ConstantRange &RangeLHS, const ConstantRange &RangeRHS) {
7772 return ConstantRange::makeSatisfyingICmpRegion(Pred, RangeRHS)
7773 .contains(RangeLHS);
7776 // The check at the top of the function catches the case where the values are
7777 // known to be equal.
7778 if (Pred == CmpInst::ICMP_EQ)
7781 if (Pred == CmpInst::ICMP_NE)
7782 return CheckRanges(getSignedRange(LHS), getSignedRange(RHS)) ||
7783 CheckRanges(getUnsignedRange(LHS), getUnsignedRange(RHS)) ||
7784 isKnownNonZero(getMinusSCEV(LHS, RHS));
7786 if (CmpInst::isSigned(Pred))
7787 return CheckRanges(getSignedRange(LHS), getSignedRange(RHS));
7789 return CheckRanges(getUnsignedRange(LHS), getUnsignedRange(RHS));
7792 bool ScalarEvolution::isKnownPredicateViaNoOverflow(ICmpInst::Predicate Pred,
7796 // Match Result to (X + Y)<ExpectedFlags> where Y is a constant integer.
7797 // Return Y via OutY.
7798 auto MatchBinaryAddToConst =
7799 [this](const SCEV *Result, const SCEV *X, APInt &OutY,
7800 SCEV::NoWrapFlags ExpectedFlags) {
7801 const SCEV *NonConstOp, *ConstOp;
7802 SCEV::NoWrapFlags FlagsPresent;
7804 if (!splitBinaryAdd(Result, ConstOp, NonConstOp, FlagsPresent) ||
7805 !isa<SCEVConstant>(ConstOp) || NonConstOp != X)
7808 OutY = cast<SCEVConstant>(ConstOp)->getAPInt();
7809 return (FlagsPresent & ExpectedFlags) == ExpectedFlags;
7818 case ICmpInst::ICMP_SGE:
7819 std::swap(LHS, RHS);
7820 case ICmpInst::ICMP_SLE:
7821 // X s<= (X + C)<nsw> if C >= 0
7822 if (MatchBinaryAddToConst(RHS, LHS, C, SCEV::FlagNSW) && C.isNonNegative())
7825 // (X + C)<nsw> s<= X if C <= 0
7826 if (MatchBinaryAddToConst(LHS, RHS, C, SCEV::FlagNSW) &&
7827 !C.isStrictlyPositive())
7831 case ICmpInst::ICMP_SGT:
7832 std::swap(LHS, RHS);
7833 case ICmpInst::ICMP_SLT:
7834 // X s< (X + C)<nsw> if C > 0
7835 if (MatchBinaryAddToConst(RHS, LHS, C, SCEV::FlagNSW) &&
7836 C.isStrictlyPositive())
7839 // (X + C)<nsw> s< X if C < 0
7840 if (MatchBinaryAddToConst(LHS, RHS, C, SCEV::FlagNSW) && C.isNegative())
7848 bool ScalarEvolution::isKnownPredicateViaSplitting(ICmpInst::Predicate Pred,
7851 if (Pred != ICmpInst::ICMP_ULT || ProvingSplitPredicate)
7854 // Allowing arbitrary number of activations of isKnownPredicateViaSplitting on
7855 // the stack can result in exponential time complexity.
7856 SaveAndRestore<bool> Restore(ProvingSplitPredicate, true);
7858 // If L >= 0 then I `ult` L <=> I >= 0 && I `slt` L
7860 // To prove L >= 0 we use isKnownNonNegative whereas to prove I >= 0 we use
7861 // isKnownPredicate. isKnownPredicate is more powerful, but also more
7862 // expensive; and using isKnownNonNegative(RHS) is sufficient for most of the
7863 // interesting cases seen in practice. We can consider "upgrading" L >= 0 to
7864 // use isKnownPredicate later if needed.
7865 return isKnownNonNegative(RHS) &&
7866 isKnownPredicate(CmpInst::ICMP_SGE, LHS, getZero(LHS->getType())) &&
7867 isKnownPredicate(CmpInst::ICMP_SLT, LHS, RHS);
7870 bool ScalarEvolution::isImpliedViaGuard(BasicBlock *BB,
7871 ICmpInst::Predicate Pred,
7872 const SCEV *LHS, const SCEV *RHS) {
7873 // No need to even try if we know the module has no guards.
7877 return any_of(*BB, [&](Instruction &I) {
7878 using namespace llvm::PatternMatch;
7881 return match(&I, m_Intrinsic<Intrinsic::experimental_guard>(
7882 m_Value(Condition))) &&
7883 isImpliedCond(Pred, LHS, RHS, Condition, false);
7887 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
7888 /// protected by a conditional between LHS and RHS. This is used to
7889 /// to eliminate casts.
7891 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
7892 ICmpInst::Predicate Pred,
7893 const SCEV *LHS, const SCEV *RHS) {
7894 // Interpret a null as meaning no loop, where there is obviously no guard
7895 // (interprocedural conditions notwithstanding).
7896 if (!L) return true;
7898 if (isKnownPredicateViaConstantRanges(Pred, LHS, RHS))
7901 BasicBlock *Latch = L->getLoopLatch();
7905 BranchInst *LoopContinuePredicate =
7906 dyn_cast<BranchInst>(Latch->getTerminator());
7907 if (LoopContinuePredicate && LoopContinuePredicate->isConditional() &&
7908 isImpliedCond(Pred, LHS, RHS,
7909 LoopContinuePredicate->getCondition(),
7910 LoopContinuePredicate->getSuccessor(0) != L->getHeader()))
7913 // We don't want more than one activation of the following loops on the stack
7914 // -- that can lead to O(n!) time complexity.
7915 if (WalkingBEDominatingConds)
7918 SaveAndRestore<bool> ClearOnExit(WalkingBEDominatingConds, true);
7920 // See if we can exploit a trip count to prove the predicate.
7921 const auto &BETakenInfo = getBackedgeTakenInfo(L);
7922 const SCEV *LatchBECount = BETakenInfo.getExact(Latch, this);
7923 if (LatchBECount != getCouldNotCompute()) {
7924 // We know that Latch branches back to the loop header exactly
7925 // LatchBECount times. This means the backdege condition at Latch is
7926 // equivalent to "{0,+,1} u< LatchBECount".
7927 Type *Ty = LatchBECount->getType();
7928 auto NoWrapFlags = SCEV::NoWrapFlags(SCEV::FlagNUW | SCEV::FlagNW);
7929 const SCEV *LoopCounter =
7930 getAddRecExpr(getZero(Ty), getOne(Ty), L, NoWrapFlags);
7931 if (isImpliedCond(Pred, LHS, RHS, ICmpInst::ICMP_ULT, LoopCounter,
7936 // Check conditions due to any @llvm.assume intrinsics.
7937 for (auto &AssumeVH : AC.assumptions()) {
7940 auto *CI = cast<CallInst>(AssumeVH);
7941 if (!DT.dominates(CI, Latch->getTerminator()))
7944 if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false))
7948 // If the loop is not reachable from the entry block, we risk running into an
7949 // infinite loop as we walk up into the dom tree. These loops do not matter
7950 // anyway, so we just return a conservative answer when we see them.
7951 if (!DT.isReachableFromEntry(L->getHeader()))
7954 if (isImpliedViaGuard(Latch, Pred, LHS, RHS))
7957 for (DomTreeNode *DTN = DT[Latch], *HeaderDTN = DT[L->getHeader()];
7958 DTN != HeaderDTN; DTN = DTN->getIDom()) {
7960 assert(DTN && "should reach the loop header before reaching the root!");
7962 BasicBlock *BB = DTN->getBlock();
7963 if (isImpliedViaGuard(BB, Pred, LHS, RHS))
7966 BasicBlock *PBB = BB->getSinglePredecessor();
7970 BranchInst *ContinuePredicate = dyn_cast<BranchInst>(PBB->getTerminator());
7971 if (!ContinuePredicate || !ContinuePredicate->isConditional())
7974 Value *Condition = ContinuePredicate->getCondition();
7976 // If we have an edge `E` within the loop body that dominates the only
7977 // latch, the condition guarding `E` also guards the backedge. This
7978 // reasoning works only for loops with a single latch.
7980 BasicBlockEdge DominatingEdge(PBB, BB);
7981 if (DominatingEdge.isSingleEdge()) {
7982 // We're constructively (and conservatively) enumerating edges within the
7983 // loop body that dominate the latch. The dominator tree better agree
7985 assert(DT.dominates(DominatingEdge, Latch) && "should be!");
7987 if (isImpliedCond(Pred, LHS, RHS, Condition,
7988 BB != ContinuePredicate->getSuccessor(0)))
7997 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
7998 ICmpInst::Predicate Pred,
7999 const SCEV *LHS, const SCEV *RHS) {
8000 // Interpret a null as meaning no loop, where there is obviously no guard
8001 // (interprocedural conditions notwithstanding).
8002 if (!L) return false;
8004 if (isKnownPredicateViaConstantRanges(Pred, LHS, RHS))
8007 // Starting at the loop predecessor, climb up the predecessor chain, as long
8008 // as there are predecessors that can be found that have unique successors
8009 // leading to the original header.
8010 for (std::pair<BasicBlock *, BasicBlock *>
8011 Pair(L->getLoopPredecessor(), L->getHeader());
8013 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
8015 if (isImpliedViaGuard(Pair.first, Pred, LHS, RHS))
8018 BranchInst *LoopEntryPredicate =
8019 dyn_cast<BranchInst>(Pair.first->getTerminator());
8020 if (!LoopEntryPredicate ||
8021 LoopEntryPredicate->isUnconditional())
8024 if (isImpliedCond(Pred, LHS, RHS,
8025 LoopEntryPredicate->getCondition(),
8026 LoopEntryPredicate->getSuccessor(0) != Pair.second))
8030 // Check conditions due to any @llvm.assume intrinsics.
8031 for (auto &AssumeVH : AC.assumptions()) {
8034 auto *CI = cast<CallInst>(AssumeVH);
8035 if (!DT.dominates(CI, L->getHeader()))
8038 if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false))
8045 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred,
8046 const SCEV *LHS, const SCEV *RHS,
8047 Value *FoundCondValue,
8049 if (!PendingLoopPredicates.insert(FoundCondValue).second)
8053 make_scope_exit([&]() { PendingLoopPredicates.erase(FoundCondValue); });
8055 // Recursively handle And and Or conditions.
8056 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) {
8057 if (BO->getOpcode() == Instruction::And) {
8059 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
8060 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
8061 } else if (BO->getOpcode() == Instruction::Or) {
8063 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
8064 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
8068 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue);
8069 if (!ICI) return false;
8071 // Now that we found a conditional branch that dominates the loop or controls
8072 // the loop latch. Check to see if it is the comparison we are looking for.
8073 ICmpInst::Predicate FoundPred;
8075 FoundPred = ICI->getInversePredicate();
8077 FoundPred = ICI->getPredicate();
8079 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
8080 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
8082 return isImpliedCond(Pred, LHS, RHS, FoundPred, FoundLHS, FoundRHS);
8085 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred, const SCEV *LHS,
8087 ICmpInst::Predicate FoundPred,
8088 const SCEV *FoundLHS,
8089 const SCEV *FoundRHS) {
8090 // Balance the types.
8091 if (getTypeSizeInBits(LHS->getType()) <
8092 getTypeSizeInBits(FoundLHS->getType())) {
8093 if (CmpInst::isSigned(Pred)) {
8094 LHS = getSignExtendExpr(LHS, FoundLHS->getType());
8095 RHS = getSignExtendExpr(RHS, FoundLHS->getType());
8097 LHS = getZeroExtendExpr(LHS, FoundLHS->getType());
8098 RHS = getZeroExtendExpr(RHS, FoundLHS->getType());
8100 } else if (getTypeSizeInBits(LHS->getType()) >
8101 getTypeSizeInBits(FoundLHS->getType())) {
8102 if (CmpInst::isSigned(FoundPred)) {
8103 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
8104 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
8106 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
8107 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
8111 // Canonicalize the query to match the way instcombine will have
8112 // canonicalized the comparison.
8113 if (SimplifyICmpOperands(Pred, LHS, RHS))
8115 return CmpInst::isTrueWhenEqual(Pred);
8116 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
8117 if (FoundLHS == FoundRHS)
8118 return CmpInst::isFalseWhenEqual(FoundPred);
8120 // Check to see if we can make the LHS or RHS match.
8121 if (LHS == FoundRHS || RHS == FoundLHS) {
8122 if (isa<SCEVConstant>(RHS)) {
8123 std::swap(FoundLHS, FoundRHS);
8124 FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
8126 std::swap(LHS, RHS);
8127 Pred = ICmpInst::getSwappedPredicate(Pred);
8131 // Check whether the found predicate is the same as the desired predicate.
8132 if (FoundPred == Pred)
8133 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
8135 // Check whether swapping the found predicate makes it the same as the
8136 // desired predicate.
8137 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
8138 if (isa<SCEVConstant>(RHS))
8139 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
8141 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
8142 RHS, LHS, FoundLHS, FoundRHS);
8145 // Unsigned comparison is the same as signed comparison when both the operands
8146 // are non-negative.
8147 if (CmpInst::isUnsigned(FoundPred) &&
8148 CmpInst::getSignedPredicate(FoundPred) == Pred &&
8149 isKnownNonNegative(FoundLHS) && isKnownNonNegative(FoundRHS))
8150 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
8152 // Check if we can make progress by sharpening ranges.
8153 if (FoundPred == ICmpInst::ICMP_NE &&
8154 (isa<SCEVConstant>(FoundLHS) || isa<SCEVConstant>(FoundRHS))) {
8156 const SCEVConstant *C = nullptr;
8157 const SCEV *V = nullptr;
8159 if (isa<SCEVConstant>(FoundLHS)) {
8160 C = cast<SCEVConstant>(FoundLHS);
8163 C = cast<SCEVConstant>(FoundRHS);
8167 // The guarding predicate tells us that C != V. If the known range
8168 // of V is [C, t), we can sharpen the range to [C + 1, t). The
8169 // range we consider has to correspond to same signedness as the
8170 // predicate we're interested in folding.
8172 APInt Min = ICmpInst::isSigned(Pred) ?
8173 getSignedRange(V).getSignedMin() : getUnsignedRange(V).getUnsignedMin();
8175 if (Min == C->getAPInt()) {
8176 // Given (V >= Min && V != Min) we conclude V >= (Min + 1).
8177 // This is true even if (Min + 1) wraps around -- in case of
8178 // wraparound, (Min + 1) < Min, so (V >= Min => V >= (Min + 1)).
8180 APInt SharperMin = Min + 1;
8183 case ICmpInst::ICMP_SGE:
8184 case ICmpInst::ICMP_UGE:
8185 // We know V `Pred` SharperMin. If this implies LHS `Pred`
8187 if (isImpliedCondOperands(Pred, LHS, RHS, V,
8188 getConstant(SharperMin)))
8191 case ICmpInst::ICMP_SGT:
8192 case ICmpInst::ICMP_UGT:
8193 // We know from the range information that (V `Pred` Min ||
8194 // V == Min). We know from the guarding condition that !(V
8195 // == Min). This gives us
8197 // V `Pred` Min || V == Min && !(V == Min)
8200 // If V `Pred` Min implies LHS `Pred` RHS, we're done.
8202 if (isImpliedCondOperands(Pred, LHS, RHS, V, getConstant(Min)))
8212 // Check whether the actual condition is beyond sufficient.
8213 if (FoundPred == ICmpInst::ICMP_EQ)
8214 if (ICmpInst::isTrueWhenEqual(Pred))
8215 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
8217 if (Pred == ICmpInst::ICMP_NE)
8218 if (!ICmpInst::isTrueWhenEqual(FoundPred))
8219 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
8222 // Otherwise assume the worst.
8226 bool ScalarEvolution::splitBinaryAdd(const SCEV *Expr,
8227 const SCEV *&L, const SCEV *&R,
8228 SCEV::NoWrapFlags &Flags) {
8229 const auto *AE = dyn_cast<SCEVAddExpr>(Expr);
8230 if (!AE || AE->getNumOperands() != 2)
8233 L = AE->getOperand(0);
8234 R = AE->getOperand(1);
8235 Flags = AE->getNoWrapFlags();
8239 Optional<APInt> ScalarEvolution::computeConstantDifference(const SCEV *More,
8241 // We avoid subtracting expressions here because this function is usually
8242 // fairly deep in the call stack (i.e. is called many times).
8244 if (isa<SCEVAddRecExpr>(Less) && isa<SCEVAddRecExpr>(More)) {
8245 const auto *LAR = cast<SCEVAddRecExpr>(Less);
8246 const auto *MAR = cast<SCEVAddRecExpr>(More);
8248 if (LAR->getLoop() != MAR->getLoop())
8251 // We look at affine expressions only; not for correctness but to keep
8252 // getStepRecurrence cheap.
8253 if (!LAR->isAffine() || !MAR->isAffine())
8256 if (LAR->getStepRecurrence(*this) != MAR->getStepRecurrence(*this))
8259 Less = LAR->getStart();
8260 More = MAR->getStart();
8265 if (isa<SCEVConstant>(Less) && isa<SCEVConstant>(More)) {
8266 const auto &M = cast<SCEVConstant>(More)->getAPInt();
8267 const auto &L = cast<SCEVConstant>(Less)->getAPInt();
8272 SCEV::NoWrapFlags Flags;
8273 if (splitBinaryAdd(Less, L, R, Flags))
8274 if (const auto *LC = dyn_cast<SCEVConstant>(L))
8276 return -(LC->getAPInt());
8278 if (splitBinaryAdd(More, L, R, Flags))
8279 if (const auto *LC = dyn_cast<SCEVConstant>(L))
8281 return LC->getAPInt();
8286 bool ScalarEvolution::isImpliedCondOperandsViaNoOverflow(
8287 ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS,
8288 const SCEV *FoundLHS, const SCEV *FoundRHS) {
8289 if (Pred != CmpInst::ICMP_SLT && Pred != CmpInst::ICMP_ULT)
8292 const auto *AddRecLHS = dyn_cast<SCEVAddRecExpr>(LHS);
8296 const auto *AddRecFoundLHS = dyn_cast<SCEVAddRecExpr>(FoundLHS);
8297 if (!AddRecFoundLHS)
8300 // We'd like to let SCEV reason about control dependencies, so we constrain
8301 // both the inequalities to be about add recurrences on the same loop. This
8302 // way we can use isLoopEntryGuardedByCond later.
8304 const Loop *L = AddRecFoundLHS->getLoop();
8305 if (L != AddRecLHS->getLoop())
8308 // FoundLHS u< FoundRHS u< -C => (FoundLHS + C) u< (FoundRHS + C) ... (1)
8310 // FoundLHS s< FoundRHS s< INT_MIN - C => (FoundLHS + C) s< (FoundRHS + C)
8313 // Informal proof for (2), assuming (1) [*]:
8315 // We'll also assume (A s< B) <=> ((A + INT_MIN) u< (B + INT_MIN)) ... (3)[**]
8319 // FoundLHS s< FoundRHS s< INT_MIN - C
8320 // <=> (FoundLHS + INT_MIN) u< (FoundRHS + INT_MIN) u< -C [ using (3) ]
8321 // <=> (FoundLHS + INT_MIN + C) u< (FoundRHS + INT_MIN + C) [ using (1) ]
8322 // <=> (FoundLHS + INT_MIN + C + INT_MIN) s<
8323 // (FoundRHS + INT_MIN + C + INT_MIN) [ using (3) ]
8324 // <=> FoundLHS + C s< FoundRHS + C
8326 // [*]: (1) can be proved by ruling out overflow.
8328 // [**]: This can be proved by analyzing all the four possibilities:
8329 // (A s< 0, B s< 0), (A s< 0, B s>= 0), (A s>= 0, B s< 0) and
8330 // (A s>= 0, B s>= 0).
8333 // Despite (2), "FoundRHS s< INT_MIN - C" does not mean that "FoundRHS + C"
8334 // will not sign underflow. For instance, say FoundLHS = (i8 -128), FoundRHS
8335 // = (i8 -127) and C = (i8 -100). Then INT_MIN - C = (i8 -28), and FoundRHS
8336 // s< (INT_MIN - C). Lack of sign overflow / underflow in "FoundRHS + C" is
8337 // neither necessary nor sufficient to prove "(FoundLHS + C) s< (FoundRHS +
8340 Optional<APInt> LDiff = computeConstantDifference(LHS, FoundLHS);
8341 Optional<APInt> RDiff = computeConstantDifference(RHS, FoundRHS);
8342 if (!LDiff || !RDiff || *LDiff != *RDiff)
8345 if (LDiff->isMinValue())
8348 APInt FoundRHSLimit;
8350 if (Pred == CmpInst::ICMP_ULT) {
8351 FoundRHSLimit = -(*RDiff);
8353 assert(Pred == CmpInst::ICMP_SLT && "Checked above!");
8354 FoundRHSLimit = APInt::getSignedMinValue(getTypeSizeInBits(RHS->getType())) - *RDiff;
8357 // Try to prove (1) or (2), as needed.
8358 return isLoopEntryGuardedByCond(L, Pred, FoundRHS,
8359 getConstant(FoundRHSLimit));
8362 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
8363 const SCEV *LHS, const SCEV *RHS,
8364 const SCEV *FoundLHS,
8365 const SCEV *FoundRHS) {
8366 if (isImpliedCondOperandsViaRanges(Pred, LHS, RHS, FoundLHS, FoundRHS))
8369 if (isImpliedCondOperandsViaNoOverflow(Pred, LHS, RHS, FoundLHS, FoundRHS))
8372 return isImpliedCondOperandsHelper(Pred, LHS, RHS,
8373 FoundLHS, FoundRHS) ||
8374 // ~x < ~y --> x > y
8375 isImpliedCondOperandsHelper(Pred, LHS, RHS,
8376 getNotSCEV(FoundRHS),
8377 getNotSCEV(FoundLHS));
8381 /// If Expr computes ~A, return A else return nullptr
8382 static const SCEV *MatchNotExpr(const SCEV *Expr) {
8383 const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Expr);
8384 if (!Add || Add->getNumOperands() != 2 ||
8385 !Add->getOperand(0)->isAllOnesValue())
8388 const SCEVMulExpr *AddRHS = dyn_cast<SCEVMulExpr>(Add->getOperand(1));
8389 if (!AddRHS || AddRHS->getNumOperands() != 2 ||
8390 !AddRHS->getOperand(0)->isAllOnesValue())
8393 return AddRHS->getOperand(1);
8397 /// Is MaybeMaxExpr an SMax or UMax of Candidate and some other values?
8398 template<typename MaxExprType>
8399 static bool IsMaxConsistingOf(const SCEV *MaybeMaxExpr,
8400 const SCEV *Candidate) {
8401 const MaxExprType *MaxExpr = dyn_cast<MaxExprType>(MaybeMaxExpr);
8402 if (!MaxExpr) return false;
8404 return find(MaxExpr->operands(), Candidate) != MaxExpr->op_end();
8408 /// Is MaybeMinExpr an SMin or UMin of Candidate and some other values?
8409 template<typename MaxExprType>
8410 static bool IsMinConsistingOf(ScalarEvolution &SE,
8411 const SCEV *MaybeMinExpr,
8412 const SCEV *Candidate) {
8413 const SCEV *MaybeMaxExpr = MatchNotExpr(MaybeMinExpr);
8417 return IsMaxConsistingOf<MaxExprType>(MaybeMaxExpr, SE.getNotSCEV(Candidate));
8420 static bool IsKnownPredicateViaAddRecStart(ScalarEvolution &SE,
8421 ICmpInst::Predicate Pred,
8422 const SCEV *LHS, const SCEV *RHS) {
8424 // If both sides are affine addrecs for the same loop, with equal
8425 // steps, and we know the recurrences don't wrap, then we only
8426 // need to check the predicate on the starting values.
8428 if (!ICmpInst::isRelational(Pred))
8431 const SCEVAddRecExpr *LAR = dyn_cast<SCEVAddRecExpr>(LHS);
8434 const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS);
8437 if (LAR->getLoop() != RAR->getLoop())
8439 if (!LAR->isAffine() || !RAR->isAffine())
8442 if (LAR->getStepRecurrence(SE) != RAR->getStepRecurrence(SE))
8445 SCEV::NoWrapFlags NW = ICmpInst::isSigned(Pred) ?
8446 SCEV::FlagNSW : SCEV::FlagNUW;
8447 if (!LAR->getNoWrapFlags(NW) || !RAR->getNoWrapFlags(NW))
8450 return SE.isKnownPredicate(Pred, LAR->getStart(), RAR->getStart());
8453 /// Is LHS `Pred` RHS true on the virtue of LHS or RHS being a Min or Max
8455 static bool IsKnownPredicateViaMinOrMax(ScalarEvolution &SE,
8456 ICmpInst::Predicate Pred,
8457 const SCEV *LHS, const SCEV *RHS) {
8462 case ICmpInst::ICMP_SGE:
8463 std::swap(LHS, RHS);
8465 case ICmpInst::ICMP_SLE:
8468 IsMinConsistingOf<SCEVSMaxExpr>(SE, LHS, RHS) ||
8470 IsMaxConsistingOf<SCEVSMaxExpr>(RHS, LHS);
8472 case ICmpInst::ICMP_UGE:
8473 std::swap(LHS, RHS);
8475 case ICmpInst::ICMP_ULE:
8478 IsMinConsistingOf<SCEVUMaxExpr>(SE, LHS, RHS) ||
8480 IsMaxConsistingOf<SCEVUMaxExpr>(RHS, LHS);
8483 llvm_unreachable("covered switch fell through?!");
8487 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
8488 const SCEV *LHS, const SCEV *RHS,
8489 const SCEV *FoundLHS,
8490 const SCEV *FoundRHS) {
8491 auto IsKnownPredicateFull =
8492 [this](ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS) {
8493 return isKnownPredicateViaConstantRanges(Pred, LHS, RHS) ||
8494 IsKnownPredicateViaMinOrMax(*this, Pred, LHS, RHS) ||
8495 IsKnownPredicateViaAddRecStart(*this, Pred, LHS, RHS) ||
8496 isKnownPredicateViaNoOverflow(Pred, LHS, RHS);
8500 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
8501 case ICmpInst::ICMP_EQ:
8502 case ICmpInst::ICMP_NE:
8503 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
8506 case ICmpInst::ICMP_SLT:
8507 case ICmpInst::ICMP_SLE:
8508 if (IsKnownPredicateFull(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
8509 IsKnownPredicateFull(ICmpInst::ICMP_SGE, RHS, FoundRHS))
8512 case ICmpInst::ICMP_SGT:
8513 case ICmpInst::ICMP_SGE:
8514 if (IsKnownPredicateFull(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
8515 IsKnownPredicateFull(ICmpInst::ICMP_SLE, RHS, FoundRHS))
8518 case ICmpInst::ICMP_ULT:
8519 case ICmpInst::ICMP_ULE:
8520 if (IsKnownPredicateFull(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
8521 IsKnownPredicateFull(ICmpInst::ICMP_UGE, RHS, FoundRHS))
8524 case ICmpInst::ICMP_UGT:
8525 case ICmpInst::ICMP_UGE:
8526 if (IsKnownPredicateFull(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
8527 IsKnownPredicateFull(ICmpInst::ICMP_ULE, RHS, FoundRHS))
8535 bool ScalarEvolution::isImpliedCondOperandsViaRanges(ICmpInst::Predicate Pred,
8538 const SCEV *FoundLHS,
8539 const SCEV *FoundRHS) {
8540 if (!isa<SCEVConstant>(RHS) || !isa<SCEVConstant>(FoundRHS))
8541 // The restriction on `FoundRHS` be lifted easily -- it exists only to
8542 // reduce the compile time impact of this optimization.
8545 Optional<APInt> Addend = computeConstantDifference(LHS, FoundLHS);
8549 APInt ConstFoundRHS = cast<SCEVConstant>(FoundRHS)->getAPInt();
8551 // `FoundLHSRange` is the range we know `FoundLHS` to be in by virtue of the
8552 // antecedent "`FoundLHS` `Pred` `FoundRHS`".
8553 ConstantRange FoundLHSRange =
8554 ConstantRange::makeAllowedICmpRegion(Pred, ConstFoundRHS);
8556 // Since `LHS` is `FoundLHS` + `Addend`, we can compute a range for `LHS`:
8557 ConstantRange LHSRange = FoundLHSRange.add(ConstantRange(*Addend));
8559 // We can also compute the range of values for `LHS` that satisfy the
8560 // consequent, "`LHS` `Pred` `RHS`":
8561 APInt ConstRHS = cast<SCEVConstant>(RHS)->getAPInt();
8562 ConstantRange SatisfyingLHSRange =
8563 ConstantRange::makeSatisfyingICmpRegion(Pred, ConstRHS);
8565 // The antecedent implies the consequent if every value of `LHS` that
8566 // satisfies the antecedent also satisfies the consequent.
8567 return SatisfyingLHSRange.contains(LHSRange);
8570 bool ScalarEvolution::doesIVOverflowOnLT(const SCEV *RHS, const SCEV *Stride,
8571 bool IsSigned, bool NoWrap) {
8572 assert(isKnownPositive(Stride) && "Positive stride expected!");
8574 if (NoWrap) return false;
8576 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
8577 const SCEV *One = getOne(Stride->getType());
8580 APInt MaxRHS = getSignedRange(RHS).getSignedMax();
8581 APInt MaxValue = APInt::getSignedMaxValue(BitWidth);
8582 APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
8585 // SMaxRHS + SMaxStrideMinusOne > SMaxValue => overflow!
8586 return (MaxValue - MaxStrideMinusOne).slt(MaxRHS);
8589 APInt MaxRHS = getUnsignedRange(RHS).getUnsignedMax();
8590 APInt MaxValue = APInt::getMaxValue(BitWidth);
8591 APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
8594 // UMaxRHS + UMaxStrideMinusOne > UMaxValue => overflow!
8595 return (MaxValue - MaxStrideMinusOne).ult(MaxRHS);
8598 bool ScalarEvolution::doesIVOverflowOnGT(const SCEV *RHS, const SCEV *Stride,
8599 bool IsSigned, bool NoWrap) {
8600 if (NoWrap) return false;
8602 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
8603 const SCEV *One = getOne(Stride->getType());
8606 APInt MinRHS = getSignedRange(RHS).getSignedMin();
8607 APInt MinValue = APInt::getSignedMinValue(BitWidth);
8608 APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
8611 // SMinRHS - SMaxStrideMinusOne < SMinValue => overflow!
8612 return (MinValue + MaxStrideMinusOne).sgt(MinRHS);
8615 APInt MinRHS = getUnsignedRange(RHS).getUnsignedMin();
8616 APInt MinValue = APInt::getMinValue(BitWidth);
8617 APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
8620 // UMinRHS - UMaxStrideMinusOne < UMinValue => overflow!
8621 return (MinValue + MaxStrideMinusOne).ugt(MinRHS);
8624 const SCEV *ScalarEvolution::computeBECount(const SCEV *Delta, const SCEV *Step,
8626 const SCEV *One = getOne(Step->getType());
8627 Delta = Equality ? getAddExpr(Delta, Step)
8628 : getAddExpr(Delta, getMinusSCEV(Step, One));
8629 return getUDivExpr(Delta, Step);
8632 ScalarEvolution::ExitLimit
8633 ScalarEvolution::howManyLessThans(const SCEV *LHS, const SCEV *RHS,
8634 const Loop *L, bool IsSigned,
8635 bool ControlsExit, bool AllowPredicates) {
8636 SmallPtrSet<const SCEVPredicate *, 4> Predicates;
8637 // We handle only IV < Invariant
8638 if (!isLoopInvariant(RHS, L))
8639 return getCouldNotCompute();
8641 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
8642 bool PredicatedIV = false;
8644 if (!IV && AllowPredicates) {
8645 // Try to make this an AddRec using runtime tests, in the first X
8646 // iterations of this loop, where X is the SCEV expression found by the
8648 IV = convertSCEVToAddRecWithPredicates(LHS, L, Predicates);
8649 PredicatedIV = true;
8652 // Avoid weird loops
8653 if (!IV || IV->getLoop() != L || !IV->isAffine())
8654 return getCouldNotCompute();
8656 bool NoWrap = ControlsExit &&
8657 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
8659 const SCEV *Stride = IV->getStepRecurrence(*this);
8661 bool PositiveStride = isKnownPositive(Stride);
8663 // Avoid negative or zero stride values.
8664 if (!PositiveStride) {
8665 // We can compute the correct backedge taken count for loops with unknown
8666 // strides if we can prove that the loop is not an infinite loop with side
8667 // effects. Here's the loop structure we are trying to handle -
8673 // } while (i < end);
8675 // The backedge taken count for such loops is evaluated as -
8676 // (max(end, start + stride) - start - 1) /u stride
8678 // The additional preconditions that we need to check to prove correctness
8679 // of the above formula is as follows -
8681 // a) IV is either nuw or nsw depending upon signedness (indicated by the
8683 // b) loop is single exit with no side effects.
8686 // Precondition a) implies that if the stride is negative, this is a single
8687 // trip loop. The backedge taken count formula reduces to zero in this case.
8689 // Precondition b) implies that the unknown stride cannot be zero otherwise
8692 // The positive stride case is the same as isKnownPositive(Stride) returning
8693 // true (original behavior of the function).
8695 // We want to make sure that the stride is truly unknown as there are edge
8696 // cases where ScalarEvolution propagates no wrap flags to the
8697 // post-increment/decrement IV even though the increment/decrement operation
8698 // itself is wrapping. The computed backedge taken count may be wrong in
8699 // such cases. This is prevented by checking that the stride is not known to
8700 // be either positive or non-positive. For example, no wrap flags are
8701 // propagated to the post-increment IV of this loop with a trip count of 2 -
8704 // for(i=127; i<128; i+=129)
8707 if (PredicatedIV || !NoWrap || isKnownNonPositive(Stride) ||
8708 !loopHasNoSideEffects(L))
8709 return getCouldNotCompute();
8711 } else if (!Stride->isOne() &&
8712 doesIVOverflowOnLT(RHS, Stride, IsSigned, NoWrap))
8713 // Avoid proven overflow cases: this will ensure that the backedge taken
8714 // count will not generate any unsigned overflow. Relaxed no-overflow
8715 // conditions exploit NoWrapFlags, allowing to optimize in presence of
8716 // undefined behaviors like the case of C language.
8717 return getCouldNotCompute();
8719 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SLT
8720 : ICmpInst::ICMP_ULT;
8721 const SCEV *Start = IV->getStart();
8722 const SCEV *End = RHS;
8723 // If the backedge is taken at least once, then it will be taken
8724 // (End-Start)/Stride times (rounded up to a multiple of Stride), where Start
8725 // is the LHS value of the less-than comparison the first time it is evaluated
8726 // and End is the RHS.
8727 const SCEV *BECountIfBackedgeTaken =
8728 computeBECount(getMinusSCEV(End, Start), Stride, false);
8729 // If the loop entry is guarded by the result of the backedge test of the
8730 // first loop iteration, then we know the backedge will be taken at least
8731 // once and so the backedge taken count is as above. If not then we use the
8732 // expression (max(End,Start)-Start)/Stride to describe the backedge count,
8733 // as if the backedge is taken at least once max(End,Start) is End and so the
8734 // result is as above, and if not max(End,Start) is Start so we get a backedge
8736 const SCEV *BECount;
8737 if (isLoopEntryGuardedByCond(L, Cond, getMinusSCEV(Start, Stride), RHS))
8738 BECount = BECountIfBackedgeTaken;
8740 End = IsSigned ? getSMaxExpr(RHS, Start) : getUMaxExpr(RHS, Start);
8741 BECount = computeBECount(getMinusSCEV(End, Start), Stride, false);
8744 const SCEV *MaxBECount;
8745 bool MaxOrZero = false;
8746 if (isa<SCEVConstant>(BECount))
8747 MaxBECount = BECount;
8748 else if (isa<SCEVConstant>(BECountIfBackedgeTaken)) {
8749 // If we know exactly how many times the backedge will be taken if it's
8750 // taken at least once, then the backedge count will either be that or
8752 MaxBECount = BECountIfBackedgeTaken;
8755 // Calculate the maximum backedge count based on the range of values
8756 // permitted by Start, End, and Stride.
8757 APInt MinStart = IsSigned ? getSignedRange(Start).getSignedMin()
8758 : getUnsignedRange(Start).getUnsignedMin();
8760 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
8762 APInt StrideForMaxBECount;
8765 StrideForMaxBECount =
8766 IsSigned ? getSignedRange(Stride).getSignedMin()
8767 : getUnsignedRange(Stride).getUnsignedMin();
8769 // Using a stride of 1 is safe when computing max backedge taken count for
8770 // a loop with unknown stride.
8771 StrideForMaxBECount = APInt(BitWidth, 1, IsSigned);
8774 IsSigned ? APInt::getSignedMaxValue(BitWidth) - (StrideForMaxBECount - 1)
8775 : APInt::getMaxValue(BitWidth) - (StrideForMaxBECount - 1);
8777 // Although End can be a MAX expression we estimate MaxEnd considering only
8778 // the case End = RHS. This is safe because in the other case (End - Start)
8779 // is zero, leading to a zero maximum backedge taken count.
8781 IsSigned ? APIntOps::smin(getSignedRange(RHS).getSignedMax(), Limit)
8782 : APIntOps::umin(getUnsignedRange(RHS).getUnsignedMax(), Limit);
8784 MaxBECount = computeBECount(getConstant(MaxEnd - MinStart),
8785 getConstant(StrideForMaxBECount), false);
8788 if (isa<SCEVCouldNotCompute>(MaxBECount))
8789 MaxBECount = BECount;
8791 return ExitLimit(BECount, MaxBECount, MaxOrZero, Predicates);
8794 ScalarEvolution::ExitLimit
8795 ScalarEvolution::howManyGreaterThans(const SCEV *LHS, const SCEV *RHS,
8796 const Loop *L, bool IsSigned,
8797 bool ControlsExit, bool AllowPredicates) {
8798 SmallPtrSet<const SCEVPredicate *, 4> Predicates;
8799 // We handle only IV > Invariant
8800 if (!isLoopInvariant(RHS, L))
8801 return getCouldNotCompute();
8803 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
8804 if (!IV && AllowPredicates)
8805 // Try to make this an AddRec using runtime tests, in the first X
8806 // iterations of this loop, where X is the SCEV expression found by the
8808 IV = convertSCEVToAddRecWithPredicates(LHS, L, Predicates);
8810 // Avoid weird loops
8811 if (!IV || IV->getLoop() != L || !IV->isAffine())
8812 return getCouldNotCompute();
8814 bool NoWrap = ControlsExit &&
8815 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
8817 const SCEV *Stride = getNegativeSCEV(IV->getStepRecurrence(*this));
8819 // Avoid negative or zero stride values
8820 if (!isKnownPositive(Stride))
8821 return getCouldNotCompute();
8823 // Avoid proven overflow cases: this will ensure that the backedge taken count
8824 // will not generate any unsigned overflow. Relaxed no-overflow conditions
8825 // exploit NoWrapFlags, allowing to optimize in presence of undefined
8826 // behaviors like the case of C language.
8827 if (!Stride->isOne() && doesIVOverflowOnGT(RHS, Stride, IsSigned, NoWrap))
8828 return getCouldNotCompute();
8830 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SGT
8831 : ICmpInst::ICMP_UGT;
8833 const SCEV *Start = IV->getStart();
8834 const SCEV *End = RHS;
8835 if (!isLoopEntryGuardedByCond(L, Cond, getAddExpr(Start, Stride), RHS))
8836 End = IsSigned ? getSMinExpr(RHS, Start) : getUMinExpr(RHS, Start);
8838 const SCEV *BECount = computeBECount(getMinusSCEV(Start, End), Stride, false);
8840 APInt MaxStart = IsSigned ? getSignedRange(Start).getSignedMax()
8841 : getUnsignedRange(Start).getUnsignedMax();
8843 APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
8844 : getUnsignedRange(Stride).getUnsignedMin();
8846 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
8847 APInt Limit = IsSigned ? APInt::getSignedMinValue(BitWidth) + (MinStride - 1)
8848 : APInt::getMinValue(BitWidth) + (MinStride - 1);
8850 // Although End can be a MIN expression we estimate MinEnd considering only
8851 // the case End = RHS. This is safe because in the other case (Start - End)
8852 // is zero, leading to a zero maximum backedge taken count.
8854 IsSigned ? APIntOps::smax(getSignedRange(RHS).getSignedMin(), Limit)
8855 : APIntOps::umax(getUnsignedRange(RHS).getUnsignedMin(), Limit);
8858 const SCEV *MaxBECount = getCouldNotCompute();
8859 if (isa<SCEVConstant>(BECount))
8860 MaxBECount = BECount;
8862 MaxBECount = computeBECount(getConstant(MaxStart - MinEnd),
8863 getConstant(MinStride), false);
8865 if (isa<SCEVCouldNotCompute>(MaxBECount))
8866 MaxBECount = BECount;
8868 return ExitLimit(BECount, MaxBECount, false, Predicates);
8871 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(const ConstantRange &Range,
8872 ScalarEvolution &SE) const {
8873 if (Range.isFullSet()) // Infinite loop.
8874 return SE.getCouldNotCompute();
8876 // If the start is a non-zero constant, shift the range to simplify things.
8877 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
8878 if (!SC->getValue()->isZero()) {
8879 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
8880 Operands[0] = SE.getZero(SC->getType());
8881 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(),
8882 getNoWrapFlags(FlagNW));
8883 if (const auto *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted))
8884 return ShiftedAddRec->getNumIterationsInRange(
8885 Range.subtract(SC->getAPInt()), SE);
8886 // This is strange and shouldn't happen.
8887 return SE.getCouldNotCompute();
8890 // The only time we can solve this is when we have all constant indices.
8891 // Otherwise, we cannot determine the overflow conditions.
8892 if (any_of(operands(), [](const SCEV *Op) { return !isa<SCEVConstant>(Op); }))
8893 return SE.getCouldNotCompute();
8895 // Okay at this point we know that all elements of the chrec are constants and
8896 // that the start element is zero.
8898 // First check to see if the range contains zero. If not, the first
8900 unsigned BitWidth = SE.getTypeSizeInBits(getType());
8901 if (!Range.contains(APInt(BitWidth, 0)))
8902 return SE.getZero(getType());
8905 // If this is an affine expression then we have this situation:
8906 // Solve {0,+,A} in Range === Ax in Range
8908 // We know that zero is in the range. If A is positive then we know that
8909 // the upper value of the range must be the first possible exit value.
8910 // If A is negative then the lower of the range is the last possible loop
8911 // value. Also note that we already checked for a full range.
8912 APInt One(BitWidth,1);
8913 APInt A = cast<SCEVConstant>(getOperand(1))->getAPInt();
8914 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
8916 // The exit value should be (End+A)/A.
8917 APInt ExitVal = (End + A).udiv(A);
8918 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
8920 // Evaluate at the exit value. If we really did fall out of the valid
8921 // range, then we computed our trip count, otherwise wrap around or other
8922 // things must have happened.
8923 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
8924 if (Range.contains(Val->getValue()))
8925 return SE.getCouldNotCompute(); // Something strange happened
8927 // Ensure that the previous value is in the range. This is a sanity check.
8928 assert(Range.contains(
8929 EvaluateConstantChrecAtConstant(this,
8930 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
8931 "Linear scev computation is off in a bad way!");
8932 return SE.getConstant(ExitValue);
8933 } else if (isQuadratic()) {
8934 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
8935 // quadratic equation to solve it. To do this, we must frame our problem in
8936 // terms of figuring out when zero is crossed, instead of when
8937 // Range.getUpper() is crossed.
8938 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
8939 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
8940 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop(), FlagAnyWrap);
8942 // Next, solve the constructed addrec
8944 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE)) {
8945 const SCEVConstant *R1 = Roots->first;
8946 const SCEVConstant *R2 = Roots->second;
8947 // Pick the smallest positive root value.
8948 if (ConstantInt *CB = dyn_cast<ConstantInt>(ConstantExpr::getICmp(
8949 ICmpInst::ICMP_ULT, R1->getValue(), R2->getValue()))) {
8950 if (!CB->getZExtValue())
8951 std::swap(R1, R2); // R1 is the minimum root now.
8953 // Make sure the root is not off by one. The returned iteration should
8954 // not be in the range, but the previous one should be. When solving
8955 // for "X*X < 5", for example, we should not return a root of 2.
8956 ConstantInt *R1Val =
8957 EvaluateConstantChrecAtConstant(this, R1->getValue(), SE);
8958 if (Range.contains(R1Val->getValue())) {
8959 // The next iteration must be out of the range...
8960 ConstantInt *NextVal =
8961 ConstantInt::get(SE.getContext(), R1->getAPInt() + 1);
8963 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
8964 if (!Range.contains(R1Val->getValue()))
8965 return SE.getConstant(NextVal);
8966 return SE.getCouldNotCompute(); // Something strange happened
8969 // If R1 was not in the range, then it is a good return value. Make
8970 // sure that R1-1 WAS in the range though, just in case.
8971 ConstantInt *NextVal =
8972 ConstantInt::get(SE.getContext(), R1->getAPInt() - 1);
8973 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
8974 if (Range.contains(R1Val->getValue()))
8976 return SE.getCouldNotCompute(); // Something strange happened
8981 return SE.getCouldNotCompute();
8984 // Return true when S contains at least an undef value.
8985 static inline bool containsUndefs(const SCEV *S) {
8986 return SCEVExprContains(S, [](const SCEV *S) {
8987 if (const auto *SU = dyn_cast<SCEVUnknown>(S))
8988 return isa<UndefValue>(SU->getValue());
8989 else if (const auto *SC = dyn_cast<SCEVConstant>(S))
8990 return isa<UndefValue>(SC->getValue());
8996 // Collect all steps of SCEV expressions.
8997 struct SCEVCollectStrides {
8998 ScalarEvolution &SE;
8999 SmallVectorImpl<const SCEV *> &Strides;
9001 SCEVCollectStrides(ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &S)
9002 : SE(SE), Strides(S) {}
9004 bool follow(const SCEV *S) {
9005 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(S))
9006 Strides.push_back(AR->getStepRecurrence(SE));
9009 bool isDone() const { return false; }
9012 // Collect all SCEVUnknown and SCEVMulExpr expressions.
9013 struct SCEVCollectTerms {
9014 SmallVectorImpl<const SCEV *> &Terms;
9016 SCEVCollectTerms(SmallVectorImpl<const SCEV *> &T)
9019 bool follow(const SCEV *S) {
9020 if (isa<SCEVUnknown>(S) || isa<SCEVMulExpr>(S) ||
9021 isa<SCEVSignExtendExpr>(S)) {
9022 if (!containsUndefs(S))
9025 // Stop recursion: once we collected a term, do not walk its operands.
9032 bool isDone() const { return false; }
9035 // Check if a SCEV contains an AddRecExpr.
9036 struct SCEVHasAddRec {
9037 bool &ContainsAddRec;
9039 SCEVHasAddRec(bool &ContainsAddRec) : ContainsAddRec(ContainsAddRec) {
9040 ContainsAddRec = false;
9043 bool follow(const SCEV *S) {
9044 if (isa<SCEVAddRecExpr>(S)) {
9045 ContainsAddRec = true;
9047 // Stop recursion: once we collected a term, do not walk its operands.
9054 bool isDone() const { return false; }
9057 // Find factors that are multiplied with an expression that (possibly as a
9058 // subexpression) contains an AddRecExpr. In the expression:
9060 // 8 * (100 + %p * %q * (%a + {0, +, 1}_loop))
9062 // "%p * %q" are factors multiplied by the expression "(%a + {0, +, 1}_loop)"
9063 // that contains the AddRec {0, +, 1}_loop. %p * %q are likely to be array size
9064 // parameters as they form a product with an induction variable.
9066 // This collector expects all array size parameters to be in the same MulExpr.
9067 // It might be necessary to later add support for collecting parameters that are
9068 // spread over different nested MulExpr.
9069 struct SCEVCollectAddRecMultiplies {
9070 SmallVectorImpl<const SCEV *> &Terms;
9071 ScalarEvolution &SE;
9073 SCEVCollectAddRecMultiplies(SmallVectorImpl<const SCEV *> &T, ScalarEvolution &SE)
9074 : Terms(T), SE(SE) {}
9076 bool follow(const SCEV *S) {
9077 if (auto *Mul = dyn_cast<SCEVMulExpr>(S)) {
9078 bool HasAddRec = false;
9079 SmallVector<const SCEV *, 0> Operands;
9080 for (auto Op : Mul->operands()) {
9081 if (isa<SCEVUnknown>(Op)) {
9082 Operands.push_back(Op);
9084 bool ContainsAddRec;
9085 SCEVHasAddRec ContiansAddRec(ContainsAddRec);
9086 visitAll(Op, ContiansAddRec);
9087 HasAddRec |= ContainsAddRec;
9090 if (Operands.size() == 0)
9096 Terms.push_back(SE.getMulExpr(Operands));
9097 // Stop recursion: once we collected a term, do not walk its operands.
9104 bool isDone() const { return false; }
9108 /// Find parametric terms in this SCEVAddRecExpr. We first for parameters in
9110 /// 1) The strides of AddRec expressions.
9111 /// 2) Unknowns that are multiplied with AddRec expressions.
9112 void ScalarEvolution::collectParametricTerms(const SCEV *Expr,
9113 SmallVectorImpl<const SCEV *> &Terms) {
9114 SmallVector<const SCEV *, 4> Strides;
9115 SCEVCollectStrides StrideCollector(*this, Strides);
9116 visitAll(Expr, StrideCollector);
9119 dbgs() << "Strides:\n";
9120 for (const SCEV *S : Strides)
9121 dbgs() << *S << "\n";
9124 for (const SCEV *S : Strides) {
9125 SCEVCollectTerms TermCollector(Terms);
9126 visitAll(S, TermCollector);
9130 dbgs() << "Terms:\n";
9131 for (const SCEV *T : Terms)
9132 dbgs() << *T << "\n";
9135 SCEVCollectAddRecMultiplies MulCollector(Terms, *this);
9136 visitAll(Expr, MulCollector);
9139 static bool findArrayDimensionsRec(ScalarEvolution &SE,
9140 SmallVectorImpl<const SCEV *> &Terms,
9141 SmallVectorImpl<const SCEV *> &Sizes) {
9142 int Last = Terms.size() - 1;
9143 const SCEV *Step = Terms[Last];
9145 // End of recursion.
9147 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Step)) {
9148 SmallVector<const SCEV *, 2> Qs;
9149 for (const SCEV *Op : M->operands())
9150 if (!isa<SCEVConstant>(Op))
9153 Step = SE.getMulExpr(Qs);
9156 Sizes.push_back(Step);
9160 for (const SCEV *&Term : Terms) {
9161 // Normalize the terms before the next call to findArrayDimensionsRec.
9163 SCEVDivision::divide(SE, Term, Step, &Q, &R);
9165 // Bail out when GCD does not evenly divide one of the terms.
9172 // Remove all SCEVConstants.
9174 remove_if(Terms, [](const SCEV *E) { return isa<SCEVConstant>(E); }),
9177 if (Terms.size() > 0)
9178 if (!findArrayDimensionsRec(SE, Terms, Sizes))
9181 Sizes.push_back(Step);
9186 // Returns true when one of the SCEVs of Terms contains a SCEVUnknown parameter.
9187 static inline bool containsParameters(SmallVectorImpl<const SCEV *> &Terms) {
9188 for (const SCEV *T : Terms)
9189 if (SCEVExprContains(T, isa<SCEVUnknown, const SCEV *>))
9194 // Return the number of product terms in S.
9195 static inline int numberOfTerms(const SCEV *S) {
9196 if (const SCEVMulExpr *Expr = dyn_cast<SCEVMulExpr>(S))
9197 return Expr->getNumOperands();
9201 static const SCEV *removeConstantFactors(ScalarEvolution &SE, const SCEV *T) {
9202 if (isa<SCEVConstant>(T))
9205 if (isa<SCEVUnknown>(T))
9208 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(T)) {
9209 SmallVector<const SCEV *, 2> Factors;
9210 for (const SCEV *Op : M->operands())
9211 if (!isa<SCEVConstant>(Op))
9212 Factors.push_back(Op);
9214 return SE.getMulExpr(Factors);
9220 /// Return the size of an element read or written by Inst.
9221 const SCEV *ScalarEvolution::getElementSize(Instruction *Inst) {
9223 if (StoreInst *Store = dyn_cast<StoreInst>(Inst))
9224 Ty = Store->getValueOperand()->getType();
9225 else if (LoadInst *Load = dyn_cast<LoadInst>(Inst))
9226 Ty = Load->getType();
9230 Type *ETy = getEffectiveSCEVType(PointerType::getUnqual(Ty));
9231 return getSizeOfExpr(ETy, Ty);
9234 void ScalarEvolution::findArrayDimensions(SmallVectorImpl<const SCEV *> &Terms,
9235 SmallVectorImpl<const SCEV *> &Sizes,
9236 const SCEV *ElementSize) const {
9237 if (Terms.size() < 1 || !ElementSize)
9240 // Early return when Terms do not contain parameters: we do not delinearize
9241 // non parametric SCEVs.
9242 if (!containsParameters(Terms))
9246 dbgs() << "Terms:\n";
9247 for (const SCEV *T : Terms)
9248 dbgs() << *T << "\n";
9251 // Remove duplicates.
9252 std::sort(Terms.begin(), Terms.end());
9253 Terms.erase(std::unique(Terms.begin(), Terms.end()), Terms.end());
9255 // Put larger terms first.
9256 std::sort(Terms.begin(), Terms.end(), [](const SCEV *LHS, const SCEV *RHS) {
9257 return numberOfTerms(LHS) > numberOfTerms(RHS);
9260 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
9262 // Try to divide all terms by the element size. If term is not divisible by
9263 // element size, proceed with the original term.
9264 for (const SCEV *&Term : Terms) {
9266 SCEVDivision::divide(SE, Term, ElementSize, &Q, &R);
9271 SmallVector<const SCEV *, 4> NewTerms;
9273 // Remove constant factors.
9274 for (const SCEV *T : Terms)
9275 if (const SCEV *NewT = removeConstantFactors(SE, T))
9276 NewTerms.push_back(NewT);
9279 dbgs() << "Terms after sorting:\n";
9280 for (const SCEV *T : NewTerms)
9281 dbgs() << *T << "\n";
9284 if (NewTerms.empty() ||
9285 !findArrayDimensionsRec(SE, NewTerms, Sizes)) {
9290 // The last element to be pushed into Sizes is the size of an element.
9291 Sizes.push_back(ElementSize);
9294 dbgs() << "Sizes:\n";
9295 for (const SCEV *S : Sizes)
9296 dbgs() << *S << "\n";
9300 void ScalarEvolution::computeAccessFunctions(
9301 const SCEV *Expr, SmallVectorImpl<const SCEV *> &Subscripts,
9302 SmallVectorImpl<const SCEV *> &Sizes) {
9304 // Early exit in case this SCEV is not an affine multivariate function.
9308 if (auto *AR = dyn_cast<SCEVAddRecExpr>(Expr))
9309 if (!AR->isAffine())
9312 const SCEV *Res = Expr;
9313 int Last = Sizes.size() - 1;
9314 for (int i = Last; i >= 0; i--) {
9316 SCEVDivision::divide(*this, Res, Sizes[i], &Q, &R);
9319 dbgs() << "Res: " << *Res << "\n";
9320 dbgs() << "Sizes[i]: " << *Sizes[i] << "\n";
9321 dbgs() << "Res divided by Sizes[i]:\n";
9322 dbgs() << "Quotient: " << *Q << "\n";
9323 dbgs() << "Remainder: " << *R << "\n";
9328 // Do not record the last subscript corresponding to the size of elements in
9332 // Bail out if the remainder is too complex.
9333 if (isa<SCEVAddRecExpr>(R)) {
9342 // Record the access function for the current subscript.
9343 Subscripts.push_back(R);
9346 // Also push in last position the remainder of the last division: it will be
9347 // the access function of the innermost dimension.
9348 Subscripts.push_back(Res);
9350 std::reverse(Subscripts.begin(), Subscripts.end());
9353 dbgs() << "Subscripts:\n";
9354 for (const SCEV *S : Subscripts)
9355 dbgs() << *S << "\n";
9359 /// Splits the SCEV into two vectors of SCEVs representing the subscripts and
9360 /// sizes of an array access. Returns the remainder of the delinearization that
9361 /// is the offset start of the array. The SCEV->delinearize algorithm computes
9362 /// the multiples of SCEV coefficients: that is a pattern matching of sub
9363 /// expressions in the stride and base of a SCEV corresponding to the
9364 /// computation of a GCD (greatest common divisor) of base and stride. When
9365 /// SCEV->delinearize fails, it returns the SCEV unchanged.
9367 /// For example: when analyzing the memory access A[i][j][k] in this loop nest
9369 /// void foo(long n, long m, long o, double A[n][m][o]) {
9371 /// for (long i = 0; i < n; i++)
9372 /// for (long j = 0; j < m; j++)
9373 /// for (long k = 0; k < o; k++)
9374 /// A[i][j][k] = 1.0;
9377 /// the delinearization input is the following AddRec SCEV:
9379 /// AddRec: {{{%A,+,(8 * %m * %o)}<%for.i>,+,(8 * %o)}<%for.j>,+,8}<%for.k>
9381 /// From this SCEV, we are able to say that the base offset of the access is %A
9382 /// because it appears as an offset that does not divide any of the strides in
9385 /// CHECK: Base offset: %A
9387 /// and then SCEV->delinearize determines the size of some of the dimensions of
9388 /// the array as these are the multiples by which the strides are happening:
9390 /// CHECK: ArrayDecl[UnknownSize][%m][%o] with elements of sizeof(double) bytes.
9392 /// Note that the outermost dimension remains of UnknownSize because there are
9393 /// no strides that would help identifying the size of the last dimension: when
9394 /// the array has been statically allocated, one could compute the size of that
9395 /// dimension by dividing the overall size of the array by the size of the known
9396 /// dimensions: %m * %o * 8.
9398 /// Finally delinearize provides the access functions for the array reference
9399 /// that does correspond to A[i][j][k] of the above C testcase:
9401 /// CHECK: ArrayRef[{0,+,1}<%for.i>][{0,+,1}<%for.j>][{0,+,1}<%for.k>]
9403 /// The testcases are checking the output of a function pass:
9404 /// DelinearizationPass that walks through all loads and stores of a function
9405 /// asking for the SCEV of the memory access with respect to all enclosing
9406 /// loops, calling SCEV->delinearize on that and printing the results.
9408 void ScalarEvolution::delinearize(const SCEV *Expr,
9409 SmallVectorImpl<const SCEV *> &Subscripts,
9410 SmallVectorImpl<const SCEV *> &Sizes,
9411 const SCEV *ElementSize) {
9412 // First step: collect parametric terms.
9413 SmallVector<const SCEV *, 4> Terms;
9414 collectParametricTerms(Expr, Terms);
9419 // Second step: find subscript sizes.
9420 findArrayDimensions(Terms, Sizes, ElementSize);
9425 // Third step: compute the access functions for each subscript.
9426 computeAccessFunctions(Expr, Subscripts, Sizes);
9428 if (Subscripts.empty())
9432 dbgs() << "succeeded to delinearize " << *Expr << "\n";
9433 dbgs() << "ArrayDecl[UnknownSize]";
9434 for (const SCEV *S : Sizes)
9435 dbgs() << "[" << *S << "]";
9437 dbgs() << "\nArrayRef";
9438 for (const SCEV *S : Subscripts)
9439 dbgs() << "[" << *S << "]";
9444 //===----------------------------------------------------------------------===//
9445 // SCEVCallbackVH Class Implementation
9446 //===----------------------------------------------------------------------===//
9448 void ScalarEvolution::SCEVCallbackVH::deleted() {
9449 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
9450 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
9451 SE->ConstantEvolutionLoopExitValue.erase(PN);
9452 SE->eraseValueFromMap(getValPtr());
9453 // this now dangles!
9456 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) {
9457 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
9459 // Forget all the expressions associated with users of the old value,
9460 // so that future queries will recompute the expressions using the new
9462 Value *Old = getValPtr();
9463 SmallVector<User *, 16> Worklist(Old->user_begin(), Old->user_end());
9464 SmallPtrSet<User *, 8> Visited;
9465 while (!Worklist.empty()) {
9466 User *U = Worklist.pop_back_val();
9467 // Deleting the Old value will cause this to dangle. Postpone
9468 // that until everything else is done.
9471 if (!Visited.insert(U).second)
9473 if (PHINode *PN = dyn_cast<PHINode>(U))
9474 SE->ConstantEvolutionLoopExitValue.erase(PN);
9475 SE->eraseValueFromMap(U);
9476 Worklist.insert(Worklist.end(), U->user_begin(), U->user_end());
9478 // Delete the Old value.
9479 if (PHINode *PN = dyn_cast<PHINode>(Old))
9480 SE->ConstantEvolutionLoopExitValue.erase(PN);
9481 SE->eraseValueFromMap(Old);
9482 // this now dangles!
9485 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
9486 : CallbackVH(V), SE(se) {}
9488 //===----------------------------------------------------------------------===//
9489 // ScalarEvolution Class Implementation
9490 //===----------------------------------------------------------------------===//
9492 ScalarEvolution::ScalarEvolution(Function &F, TargetLibraryInfo &TLI,
9493 AssumptionCache &AC, DominatorTree &DT,
9495 : F(F), TLI(TLI), AC(AC), DT(DT), LI(LI),
9496 CouldNotCompute(new SCEVCouldNotCompute()),
9497 WalkingBEDominatingConds(false), ProvingSplitPredicate(false),
9498 ValuesAtScopes(64), LoopDispositions(64), BlockDispositions(64),
9499 FirstUnknown(nullptr) {
9501 // To use guards for proving predicates, we need to scan every instruction in
9502 // relevant basic blocks, and not just terminators. Doing this is a waste of
9503 // time if the IR does not actually contain any calls to
9504 // @llvm.experimental.guard, so do a quick check and remember this beforehand.
9506 // This pessimizes the case where a pass that preserves ScalarEvolution wants
9507 // to _add_ guards to the module when there weren't any before, and wants
9508 // ScalarEvolution to optimize based on those guards. For now we prefer to be
9509 // efficient in lieu of being smart in that rather obscure case.
9511 auto *GuardDecl = F.getParent()->getFunction(
9512 Intrinsic::getName(Intrinsic::experimental_guard));
9513 HasGuards = GuardDecl && !GuardDecl->use_empty();
9516 ScalarEvolution::ScalarEvolution(ScalarEvolution &&Arg)
9517 : F(Arg.F), HasGuards(Arg.HasGuards), TLI(Arg.TLI), AC(Arg.AC), DT(Arg.DT),
9518 LI(Arg.LI), CouldNotCompute(std::move(Arg.CouldNotCompute)),
9519 ValueExprMap(std::move(Arg.ValueExprMap)),
9520 PendingLoopPredicates(std::move(Arg.PendingLoopPredicates)),
9521 WalkingBEDominatingConds(false), ProvingSplitPredicate(false),
9522 BackedgeTakenCounts(std::move(Arg.BackedgeTakenCounts)),
9523 PredicatedBackedgeTakenCounts(
9524 std::move(Arg.PredicatedBackedgeTakenCounts)),
9525 ConstantEvolutionLoopExitValue(
9526 std::move(Arg.ConstantEvolutionLoopExitValue)),
9527 ValuesAtScopes(std::move(Arg.ValuesAtScopes)),
9528 LoopDispositions(std::move(Arg.LoopDispositions)),
9529 LoopPropertiesCache(std::move(Arg.LoopPropertiesCache)),
9530 BlockDispositions(std::move(Arg.BlockDispositions)),
9531 UnsignedRanges(std::move(Arg.UnsignedRanges)),
9532 SignedRanges(std::move(Arg.SignedRanges)),
9533 UniqueSCEVs(std::move(Arg.UniqueSCEVs)),
9534 UniquePreds(std::move(Arg.UniquePreds)),
9535 SCEVAllocator(std::move(Arg.SCEVAllocator)),
9536 FirstUnknown(Arg.FirstUnknown) {
9537 Arg.FirstUnknown = nullptr;
9540 ScalarEvolution::~ScalarEvolution() {
9541 // Iterate through all the SCEVUnknown instances and call their
9542 // destructors, so that they release their references to their values.
9543 for (SCEVUnknown *U = FirstUnknown; U;) {
9544 SCEVUnknown *Tmp = U;
9546 Tmp->~SCEVUnknown();
9548 FirstUnknown = nullptr;
9550 ExprValueMap.clear();
9551 ValueExprMap.clear();
9554 // Free any extra memory created for ExitNotTakenInfo in the unlikely event
9555 // that a loop had multiple computable exits.
9556 for (auto &BTCI : BackedgeTakenCounts)
9557 BTCI.second.clear();
9558 for (auto &BTCI : PredicatedBackedgeTakenCounts)
9559 BTCI.second.clear();
9561 assert(PendingLoopPredicates.empty() && "isImpliedCond garbage");
9562 assert(!WalkingBEDominatingConds && "isLoopBackedgeGuardedByCond garbage!");
9563 assert(!ProvingSplitPredicate && "ProvingSplitPredicate garbage!");
9566 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
9567 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
9570 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
9572 // Print all inner loops first
9574 PrintLoopInfo(OS, SE, I);
9577 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
9580 SmallVector<BasicBlock *, 8> ExitBlocks;
9581 L->getExitBlocks(ExitBlocks);
9582 if (ExitBlocks.size() != 1)
9583 OS << "<multiple exits> ";
9585 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
9586 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
9588 OS << "Unpredictable backedge-taken count. ";
9593 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
9596 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
9597 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
9598 if (SE->isBackedgeTakenCountMaxOrZero(L))
9599 OS << ", actual taken count either this or zero.";
9601 OS << "Unpredictable max backedge-taken count. ";
9606 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
9609 SCEVUnionPredicate Pred;
9610 auto PBT = SE->getPredicatedBackedgeTakenCount(L, Pred);
9611 if (!isa<SCEVCouldNotCompute>(PBT)) {
9612 OS << "Predicated backedge-taken count is " << *PBT << "\n";
9613 OS << " Predicates:\n";
9616 OS << "Unpredictable predicated backedge-taken count. ";
9621 static StringRef loopDispositionToStr(ScalarEvolution::LoopDisposition LD) {
9623 case ScalarEvolution::LoopVariant:
9625 case ScalarEvolution::LoopInvariant:
9627 case ScalarEvolution::LoopComputable:
9628 return "Computable";
9630 llvm_unreachable("Unknown ScalarEvolution::LoopDisposition kind!");
9633 void ScalarEvolution::print(raw_ostream &OS) const {
9634 // ScalarEvolution's implementation of the print method is to print
9635 // out SCEV values of all instructions that are interesting. Doing
9636 // this potentially causes it to create new SCEV objects though,
9637 // which technically conflicts with the const qualifier. This isn't
9638 // observable from outside the class though, so casting away the
9639 // const isn't dangerous.
9640 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
9642 OS << "Classifying expressions for: ";
9643 F.printAsOperand(OS, /*PrintType=*/false);
9645 for (Instruction &I : instructions(F))
9646 if (isSCEVable(I.getType()) && !isa<CmpInst>(I)) {
9649 const SCEV *SV = SE.getSCEV(&I);
9651 if (!isa<SCEVCouldNotCompute>(SV)) {
9653 SE.getUnsignedRange(SV).print(OS);
9655 SE.getSignedRange(SV).print(OS);
9658 const Loop *L = LI.getLoopFor(I.getParent());
9660 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
9664 if (!isa<SCEVCouldNotCompute>(AtUse)) {
9666 SE.getUnsignedRange(AtUse).print(OS);
9668 SE.getSignedRange(AtUse).print(OS);
9673 OS << "\t\t" "Exits: ";
9674 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
9675 if (!SE.isLoopInvariant(ExitValue, L)) {
9676 OS << "<<Unknown>>";
9682 for (auto *Iter = L; Iter; Iter = Iter->getParentLoop()) {
9684 OS << "\t\t" "LoopDispositions: { ";
9690 Iter->getHeader()->printAsOperand(OS, /*PrintType=*/false);
9691 OS << ": " << loopDispositionToStr(SE.getLoopDisposition(SV, Iter));
9694 for (auto *InnerL : depth_first(L)) {
9698 OS << "\t\t" "LoopDispositions: { ";
9704 InnerL->getHeader()->printAsOperand(OS, /*PrintType=*/false);
9705 OS << ": " << loopDispositionToStr(SE.getLoopDisposition(SV, InnerL));
9714 OS << "Determining loop execution counts for: ";
9715 F.printAsOperand(OS, /*PrintType=*/false);
9718 PrintLoopInfo(OS, &SE, I);
9721 ScalarEvolution::LoopDisposition
9722 ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) {
9723 auto &Values = LoopDispositions[S];
9724 for (auto &V : Values) {
9725 if (V.getPointer() == L)
9728 Values.emplace_back(L, LoopVariant);
9729 LoopDisposition D = computeLoopDisposition(S, L);
9730 auto &Values2 = LoopDispositions[S];
9731 for (auto &V : make_range(Values2.rbegin(), Values2.rend())) {
9732 if (V.getPointer() == L) {
9740 ScalarEvolution::LoopDisposition
9741 ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) {
9742 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
9744 return LoopInvariant;
9748 return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L);
9749 case scAddRecExpr: {
9750 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
9752 // If L is the addrec's loop, it's computable.
9753 if (AR->getLoop() == L)
9754 return LoopComputable;
9756 // Add recurrences are never invariant in the function-body (null loop).
9760 // This recurrence is variant w.r.t. L if L contains AR's loop.
9761 if (L->contains(AR->getLoop()))
9764 // This recurrence is invariant w.r.t. L if AR's loop contains L.
9765 if (AR->getLoop()->contains(L))
9766 return LoopInvariant;
9768 // This recurrence is variant w.r.t. L if any of its operands
9770 for (auto *Op : AR->operands())
9771 if (!isLoopInvariant(Op, L))
9774 // Otherwise it's loop-invariant.
9775 return LoopInvariant;
9781 bool HasVarying = false;
9782 for (auto *Op : cast<SCEVNAryExpr>(S)->operands()) {
9783 LoopDisposition D = getLoopDisposition(Op, L);
9784 if (D == LoopVariant)
9786 if (D == LoopComputable)
9789 return HasVarying ? LoopComputable : LoopInvariant;
9792 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
9793 LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L);
9794 if (LD == LoopVariant)
9796 LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L);
9797 if (RD == LoopVariant)
9799 return (LD == LoopInvariant && RD == LoopInvariant) ?
9800 LoopInvariant : LoopComputable;
9803 // All non-instruction values are loop invariant. All instructions are loop
9804 // invariant if they are not contained in the specified loop.
9805 // Instructions are never considered invariant in the function body
9806 // (null loop) because they are defined within the "loop".
9807 if (auto *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue()))
9808 return (L && !L->contains(I)) ? LoopInvariant : LoopVariant;
9809 return LoopInvariant;
9810 case scCouldNotCompute:
9811 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
9813 llvm_unreachable("Unknown SCEV kind!");
9816 bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) {
9817 return getLoopDisposition(S, L) == LoopInvariant;
9820 bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) {
9821 return getLoopDisposition(S, L) == LoopComputable;
9824 ScalarEvolution::BlockDisposition
9825 ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) {
9826 auto &Values = BlockDispositions[S];
9827 for (auto &V : Values) {
9828 if (V.getPointer() == BB)
9831 Values.emplace_back(BB, DoesNotDominateBlock);
9832 BlockDisposition D = computeBlockDisposition(S, BB);
9833 auto &Values2 = BlockDispositions[S];
9834 for (auto &V : make_range(Values2.rbegin(), Values2.rend())) {
9835 if (V.getPointer() == BB) {
9843 ScalarEvolution::BlockDisposition
9844 ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) {
9845 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
9847 return ProperlyDominatesBlock;
9851 return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB);
9852 case scAddRecExpr: {
9853 // This uses a "dominates" query instead of "properly dominates" query
9854 // to test for proper dominance too, because the instruction which
9855 // produces the addrec's value is a PHI, and a PHI effectively properly
9856 // dominates its entire containing block.
9857 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
9858 if (!DT.dominates(AR->getLoop()->getHeader(), BB))
9859 return DoesNotDominateBlock;
9861 // Fall through into SCEVNAryExpr handling.
9868 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
9870 for (const SCEV *NAryOp : NAry->operands()) {
9871 BlockDisposition D = getBlockDisposition(NAryOp, BB);
9872 if (D == DoesNotDominateBlock)
9873 return DoesNotDominateBlock;
9874 if (D == DominatesBlock)
9877 return Proper ? ProperlyDominatesBlock : DominatesBlock;
9880 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
9881 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
9882 BlockDisposition LD = getBlockDisposition(LHS, BB);
9883 if (LD == DoesNotDominateBlock)
9884 return DoesNotDominateBlock;
9885 BlockDisposition RD = getBlockDisposition(RHS, BB);
9886 if (RD == DoesNotDominateBlock)
9887 return DoesNotDominateBlock;
9888 return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ?
9889 ProperlyDominatesBlock : DominatesBlock;
9892 if (Instruction *I =
9893 dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) {
9894 if (I->getParent() == BB)
9895 return DominatesBlock;
9896 if (DT.properlyDominates(I->getParent(), BB))
9897 return ProperlyDominatesBlock;
9898 return DoesNotDominateBlock;
9900 return ProperlyDominatesBlock;
9901 case scCouldNotCompute:
9902 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
9904 llvm_unreachable("Unknown SCEV kind!");
9907 bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) {
9908 return getBlockDisposition(S, BB) >= DominatesBlock;
9911 bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) {
9912 return getBlockDisposition(S, BB) == ProperlyDominatesBlock;
9915 bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const {
9916 return SCEVExprContains(S, [&](const SCEV *Expr) { return Expr == Op; });
9919 void ScalarEvolution::forgetMemoizedResults(const SCEV *S) {
9920 ValuesAtScopes.erase(S);
9921 LoopDispositions.erase(S);
9922 BlockDispositions.erase(S);
9923 UnsignedRanges.erase(S);
9924 SignedRanges.erase(S);
9925 ExprValueMap.erase(S);
9928 auto RemoveSCEVFromBackedgeMap =
9929 [S, this](DenseMap<const Loop *, BackedgeTakenInfo> &Map) {
9930 for (auto I = Map.begin(), E = Map.end(); I != E;) {
9931 BackedgeTakenInfo &BEInfo = I->second;
9932 if (BEInfo.hasOperand(S, this)) {
9940 RemoveSCEVFromBackedgeMap(BackedgeTakenCounts);
9941 RemoveSCEVFromBackedgeMap(PredicatedBackedgeTakenCounts);
9944 typedef DenseMap<const Loop *, std::string> VerifyMap;
9946 /// replaceSubString - Replaces all occurrences of From in Str with To.
9947 static void replaceSubString(std::string &Str, StringRef From, StringRef To) {
9949 while ((Pos = Str.find(From, Pos)) != std::string::npos) {
9950 Str.replace(Pos, From.size(), To.data(), To.size());
9955 /// getLoopBackedgeTakenCounts - Helper method for verifyAnalysis.
9957 getLoopBackedgeTakenCounts(Loop *L, VerifyMap &Map, ScalarEvolution &SE) {
9958 std::string &S = Map[L];
9960 raw_string_ostream OS(S);
9961 SE.getBackedgeTakenCount(L)->print(OS);
9963 // false and 0 are semantically equivalent. This can happen in dead loops.
9964 replaceSubString(OS.str(), "false", "0");
9965 // Remove wrap flags, their use in SCEV is highly fragile.
9966 // FIXME: Remove this when SCEV gets smarter about them.
9967 replaceSubString(OS.str(), "<nw>", "");
9968 replaceSubString(OS.str(), "<nsw>", "");
9969 replaceSubString(OS.str(), "<nuw>", "");
9972 for (auto *R : reverse(*L))
9973 getLoopBackedgeTakenCounts(R, Map, SE); // recurse.
9976 void ScalarEvolution::verify() const {
9977 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
9979 // Gather stringified backedge taken counts for all loops using SCEV's caches.
9980 // FIXME: It would be much better to store actual values instead of strings,
9981 // but SCEV pointers will change if we drop the caches.
9982 VerifyMap BackedgeDumpsOld, BackedgeDumpsNew;
9983 for (LoopInfo::reverse_iterator I = LI.rbegin(), E = LI.rend(); I != E; ++I)
9984 getLoopBackedgeTakenCounts(*I, BackedgeDumpsOld, SE);
9986 // Gather stringified backedge taken counts for all loops using a fresh
9987 // ScalarEvolution object.
9988 ScalarEvolution SE2(F, TLI, AC, DT, LI);
9989 for (LoopInfo::reverse_iterator I = LI.rbegin(), E = LI.rend(); I != E; ++I)
9990 getLoopBackedgeTakenCounts(*I, BackedgeDumpsNew, SE2);
9992 // Now compare whether they're the same with and without caches. This allows
9993 // verifying that no pass changed the cache.
9994 assert(BackedgeDumpsOld.size() == BackedgeDumpsNew.size() &&
9995 "New loops suddenly appeared!");
9997 for (VerifyMap::iterator OldI = BackedgeDumpsOld.begin(),
9998 OldE = BackedgeDumpsOld.end(),
9999 NewI = BackedgeDumpsNew.begin();
10000 OldI != OldE; ++OldI, ++NewI) {
10001 assert(OldI->first == NewI->first && "Loop order changed!");
10003 // Compare the stringified SCEVs. We don't care if undef backedgetaken count
10005 // FIXME: We currently ignore SCEV changes from/to CouldNotCompute. This
10006 // means that a pass is buggy or SCEV has to learn a new pattern but is
10007 // usually not harmful.
10008 if (OldI->second != NewI->second &&
10009 OldI->second.find("undef") == std::string::npos &&
10010 NewI->second.find("undef") == std::string::npos &&
10011 OldI->second != "***COULDNOTCOMPUTE***" &&
10012 NewI->second != "***COULDNOTCOMPUTE***") {
10013 dbgs() << "SCEVValidator: SCEV for loop '"
10014 << OldI->first->getHeader()->getName()
10015 << "' changed from '" << OldI->second
10016 << "' to '" << NewI->second << "'!\n";
10021 // TODO: Verify more things.
10024 bool ScalarEvolution::invalidate(
10025 Function &F, const PreservedAnalyses &PA,
10026 FunctionAnalysisManager::Invalidator &Inv) {
10027 // Invalidate the ScalarEvolution object whenever it isn't preserved or one
10028 // of its dependencies is invalidated.
10029 auto PAC = PA.getChecker<ScalarEvolutionAnalysis>();
10030 return !(PAC.preserved() || PAC.preservedSet<AllAnalysesOn<Function>>()) ||
10031 Inv.invalidate<AssumptionAnalysis>(F, PA) ||
10032 Inv.invalidate<DominatorTreeAnalysis>(F, PA) ||
10033 Inv.invalidate<LoopAnalysis>(F, PA);
10036 AnalysisKey ScalarEvolutionAnalysis::Key;
10038 ScalarEvolution ScalarEvolutionAnalysis::run(Function &F,
10039 FunctionAnalysisManager &AM) {
10040 return ScalarEvolution(F, AM.getResult<TargetLibraryAnalysis>(F),
10041 AM.getResult<AssumptionAnalysis>(F),
10042 AM.getResult<DominatorTreeAnalysis>(F),
10043 AM.getResult<LoopAnalysis>(F));
10047 ScalarEvolutionPrinterPass::run(Function &F, FunctionAnalysisManager &AM) {
10048 AM.getResult<ScalarEvolutionAnalysis>(F).print(OS);
10049 return PreservedAnalyses::all();
10052 INITIALIZE_PASS_BEGIN(ScalarEvolutionWrapperPass, "scalar-evolution",
10053 "Scalar Evolution Analysis", false, true)
10054 INITIALIZE_PASS_DEPENDENCY(AssumptionCacheTracker)
10055 INITIALIZE_PASS_DEPENDENCY(LoopInfoWrapperPass)
10056 INITIALIZE_PASS_DEPENDENCY(DominatorTreeWrapperPass)
10057 INITIALIZE_PASS_DEPENDENCY(TargetLibraryInfoWrapperPass)
10058 INITIALIZE_PASS_END(ScalarEvolutionWrapperPass, "scalar-evolution",
10059 "Scalar Evolution Analysis", false, true)
10060 char ScalarEvolutionWrapperPass::ID = 0;
10062 ScalarEvolutionWrapperPass::ScalarEvolutionWrapperPass() : FunctionPass(ID) {
10063 initializeScalarEvolutionWrapperPassPass(*PassRegistry::getPassRegistry());
10066 bool ScalarEvolutionWrapperPass::runOnFunction(Function &F) {
10067 SE.reset(new ScalarEvolution(
10068 F, getAnalysis<TargetLibraryInfoWrapperPass>().getTLI(),
10069 getAnalysis<AssumptionCacheTracker>().getAssumptionCache(F),
10070 getAnalysis<DominatorTreeWrapperPass>().getDomTree(),
10071 getAnalysis<LoopInfoWrapperPass>().getLoopInfo()));
10075 void ScalarEvolutionWrapperPass::releaseMemory() { SE.reset(); }
10077 void ScalarEvolutionWrapperPass::print(raw_ostream &OS, const Module *) const {
10081 void ScalarEvolutionWrapperPass::verifyAnalysis() const {
10088 void ScalarEvolutionWrapperPass::getAnalysisUsage(AnalysisUsage &AU) const {
10089 AU.setPreservesAll();
10090 AU.addRequiredTransitive<AssumptionCacheTracker>();
10091 AU.addRequiredTransitive<LoopInfoWrapperPass>();
10092 AU.addRequiredTransitive<DominatorTreeWrapperPass>();
10093 AU.addRequiredTransitive<TargetLibraryInfoWrapperPass>();
10096 const SCEVPredicate *
10097 ScalarEvolution::getEqualPredicate(const SCEVUnknown *LHS,
10098 const SCEVConstant *RHS) {
10099 FoldingSetNodeID ID;
10100 // Unique this node based on the arguments
10101 ID.AddInteger(SCEVPredicate::P_Equal);
10102 ID.AddPointer(LHS);
10103 ID.AddPointer(RHS);
10104 void *IP = nullptr;
10105 if (const auto *S = UniquePreds.FindNodeOrInsertPos(ID, IP))
10107 SCEVEqualPredicate *Eq = new (SCEVAllocator)
10108 SCEVEqualPredicate(ID.Intern(SCEVAllocator), LHS, RHS);
10109 UniquePreds.InsertNode(Eq, IP);
10113 const SCEVPredicate *ScalarEvolution::getWrapPredicate(
10114 const SCEVAddRecExpr *AR,
10115 SCEVWrapPredicate::IncrementWrapFlags AddedFlags) {
10116 FoldingSetNodeID ID;
10117 // Unique this node based on the arguments
10118 ID.AddInteger(SCEVPredicate::P_Wrap);
10120 ID.AddInteger(AddedFlags);
10121 void *IP = nullptr;
10122 if (const auto *S = UniquePreds.FindNodeOrInsertPos(ID, IP))
10124 auto *OF = new (SCEVAllocator)
10125 SCEVWrapPredicate(ID.Intern(SCEVAllocator), AR, AddedFlags);
10126 UniquePreds.InsertNode(OF, IP);
10132 class SCEVPredicateRewriter : public SCEVRewriteVisitor<SCEVPredicateRewriter> {
10134 /// Rewrites \p S in the context of a loop L and the SCEV predication
10135 /// infrastructure.
10137 /// If \p Pred is non-null, the SCEV expression is rewritten to respect the
10138 /// equivalences present in \p Pred.
10140 /// If \p NewPreds is non-null, rewrite is free to add further predicates to
10141 /// \p NewPreds such that the result will be an AddRecExpr.
10142 static const SCEV *rewrite(const SCEV *S, const Loop *L, ScalarEvolution &SE,
10143 SmallPtrSetImpl<const SCEVPredicate *> *NewPreds,
10144 SCEVUnionPredicate *Pred) {
10145 SCEVPredicateRewriter Rewriter(L, SE, NewPreds, Pred);
10146 return Rewriter.visit(S);
10149 SCEVPredicateRewriter(const Loop *L, ScalarEvolution &SE,
10150 SmallPtrSetImpl<const SCEVPredicate *> *NewPreds,
10151 SCEVUnionPredicate *Pred)
10152 : SCEVRewriteVisitor(SE), NewPreds(NewPreds), Pred(Pred), L(L) {}
10154 const SCEV *visitUnknown(const SCEVUnknown *Expr) {
10156 auto ExprPreds = Pred->getPredicatesForExpr(Expr);
10157 for (auto *Pred : ExprPreds)
10158 if (const auto *IPred = dyn_cast<SCEVEqualPredicate>(Pred))
10159 if (IPred->getLHS() == Expr)
10160 return IPred->getRHS();
10166 const SCEV *visitZeroExtendExpr(const SCEVZeroExtendExpr *Expr) {
10167 const SCEV *Operand = visit(Expr->getOperand());
10168 const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Operand);
10169 if (AR && AR->getLoop() == L && AR->isAffine()) {
10170 // This couldn't be folded because the operand didn't have the nuw
10171 // flag. Add the nusw flag as an assumption that we could make.
10172 const SCEV *Step = AR->getStepRecurrence(SE);
10173 Type *Ty = Expr->getType();
10174 if (addOverflowAssumption(AR, SCEVWrapPredicate::IncrementNUSW))
10175 return SE.getAddRecExpr(SE.getZeroExtendExpr(AR->getStart(), Ty),
10176 SE.getSignExtendExpr(Step, Ty), L,
10177 AR->getNoWrapFlags());
10179 return SE.getZeroExtendExpr(Operand, Expr->getType());
10182 const SCEV *visitSignExtendExpr(const SCEVSignExtendExpr *Expr) {
10183 const SCEV *Operand = visit(Expr->getOperand());
10184 const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Operand);
10185 if (AR && AR->getLoop() == L && AR->isAffine()) {
10186 // This couldn't be folded because the operand didn't have the nsw
10187 // flag. Add the nssw flag as an assumption that we could make.
10188 const SCEV *Step = AR->getStepRecurrence(SE);
10189 Type *Ty = Expr->getType();
10190 if (addOverflowAssumption(AR, SCEVWrapPredicate::IncrementNSSW))
10191 return SE.getAddRecExpr(SE.getSignExtendExpr(AR->getStart(), Ty),
10192 SE.getSignExtendExpr(Step, Ty), L,
10193 AR->getNoWrapFlags());
10195 return SE.getSignExtendExpr(Operand, Expr->getType());
10199 bool addOverflowAssumption(const SCEVAddRecExpr *AR,
10200 SCEVWrapPredicate::IncrementWrapFlags AddedFlags) {
10201 auto *A = SE.getWrapPredicate(AR, AddedFlags);
10203 // Check if we've already made this assumption.
10204 return Pred && Pred->implies(A);
10206 NewPreds->insert(A);
10210 SmallPtrSetImpl<const SCEVPredicate *> *NewPreds;
10211 SCEVUnionPredicate *Pred;
10214 } // end anonymous namespace
10216 const SCEV *ScalarEvolution::rewriteUsingPredicate(const SCEV *S, const Loop *L,
10217 SCEVUnionPredicate &Preds) {
10218 return SCEVPredicateRewriter::rewrite(S, L, *this, nullptr, &Preds);
10221 const SCEVAddRecExpr *ScalarEvolution::convertSCEVToAddRecWithPredicates(
10222 const SCEV *S, const Loop *L,
10223 SmallPtrSetImpl<const SCEVPredicate *> &Preds) {
10225 SmallPtrSet<const SCEVPredicate *, 4> TransformPreds;
10226 S = SCEVPredicateRewriter::rewrite(S, L, *this, &TransformPreds, nullptr);
10227 auto *AddRec = dyn_cast<SCEVAddRecExpr>(S);
10232 // Since the transformation was successful, we can now transfer the SCEV
10234 for (auto *P : TransformPreds)
10240 /// SCEV predicates
10241 SCEVPredicate::SCEVPredicate(const FoldingSetNodeIDRef ID,
10242 SCEVPredicateKind Kind)
10243 : FastID(ID), Kind(Kind) {}
10245 SCEVEqualPredicate::SCEVEqualPredicate(const FoldingSetNodeIDRef ID,
10246 const SCEVUnknown *LHS,
10247 const SCEVConstant *RHS)
10248 : SCEVPredicate(ID, P_Equal), LHS(LHS), RHS(RHS) {}
10250 bool SCEVEqualPredicate::implies(const SCEVPredicate *N) const {
10251 const auto *Op = dyn_cast<SCEVEqualPredicate>(N);
10256 return Op->LHS == LHS && Op->RHS == RHS;
10259 bool SCEVEqualPredicate::isAlwaysTrue() const { return false; }
10261 const SCEV *SCEVEqualPredicate::getExpr() const { return LHS; }
10263 void SCEVEqualPredicate::print(raw_ostream &OS, unsigned Depth) const {
10264 OS.indent(Depth) << "Equal predicate: " << *LHS << " == " << *RHS << "\n";
10267 SCEVWrapPredicate::SCEVWrapPredicate(const FoldingSetNodeIDRef ID,
10268 const SCEVAddRecExpr *AR,
10269 IncrementWrapFlags Flags)
10270 : SCEVPredicate(ID, P_Wrap), AR(AR), Flags(Flags) {}
10272 const SCEV *SCEVWrapPredicate::getExpr() const { return AR; }
10274 bool SCEVWrapPredicate::implies(const SCEVPredicate *N) const {
10275 const auto *Op = dyn_cast<SCEVWrapPredicate>(N);
10277 return Op && Op->AR == AR && setFlags(Flags, Op->Flags) == Flags;
10280 bool SCEVWrapPredicate::isAlwaysTrue() const {
10281 SCEV::NoWrapFlags ScevFlags = AR->getNoWrapFlags();
10282 IncrementWrapFlags IFlags = Flags;
10284 if (ScalarEvolution::setFlags(ScevFlags, SCEV::FlagNSW) == ScevFlags)
10285 IFlags = clearFlags(IFlags, IncrementNSSW);
10287 return IFlags == IncrementAnyWrap;
10290 void SCEVWrapPredicate::print(raw_ostream &OS, unsigned Depth) const {
10291 OS.indent(Depth) << *getExpr() << " Added Flags: ";
10292 if (SCEVWrapPredicate::IncrementNUSW & getFlags())
10294 if (SCEVWrapPredicate::IncrementNSSW & getFlags())
10299 SCEVWrapPredicate::IncrementWrapFlags
10300 SCEVWrapPredicate::getImpliedFlags(const SCEVAddRecExpr *AR,
10301 ScalarEvolution &SE) {
10302 IncrementWrapFlags ImpliedFlags = IncrementAnyWrap;
10303 SCEV::NoWrapFlags StaticFlags = AR->getNoWrapFlags();
10305 // We can safely transfer the NSW flag as NSSW.
10306 if (ScalarEvolution::setFlags(StaticFlags, SCEV::FlagNSW) == StaticFlags)
10307 ImpliedFlags = IncrementNSSW;
10309 if (ScalarEvolution::setFlags(StaticFlags, SCEV::FlagNUW) == StaticFlags) {
10310 // If the increment is positive, the SCEV NUW flag will also imply the
10311 // WrapPredicate NUSW flag.
10312 if (const auto *Step = dyn_cast<SCEVConstant>(AR->getStepRecurrence(SE)))
10313 if (Step->getValue()->getValue().isNonNegative())
10314 ImpliedFlags = setFlags(ImpliedFlags, IncrementNUSW);
10317 return ImpliedFlags;
10320 /// Union predicates don't get cached so create a dummy set ID for it.
10321 SCEVUnionPredicate::SCEVUnionPredicate()
10322 : SCEVPredicate(FoldingSetNodeIDRef(nullptr, 0), P_Union) {}
10324 bool SCEVUnionPredicate::isAlwaysTrue() const {
10325 return all_of(Preds,
10326 [](const SCEVPredicate *I) { return I->isAlwaysTrue(); });
10329 ArrayRef<const SCEVPredicate *>
10330 SCEVUnionPredicate::getPredicatesForExpr(const SCEV *Expr) {
10331 auto I = SCEVToPreds.find(Expr);
10332 if (I == SCEVToPreds.end())
10333 return ArrayRef<const SCEVPredicate *>();
10337 bool SCEVUnionPredicate::implies(const SCEVPredicate *N) const {
10338 if (const auto *Set = dyn_cast<SCEVUnionPredicate>(N))
10339 return all_of(Set->Preds,
10340 [this](const SCEVPredicate *I) { return this->implies(I); });
10342 auto ScevPredsIt = SCEVToPreds.find(N->getExpr());
10343 if (ScevPredsIt == SCEVToPreds.end())
10345 auto &SCEVPreds = ScevPredsIt->second;
10347 return any_of(SCEVPreds,
10348 [N](const SCEVPredicate *I) { return I->implies(N); });
10351 const SCEV *SCEVUnionPredicate::getExpr() const { return nullptr; }
10353 void SCEVUnionPredicate::print(raw_ostream &OS, unsigned Depth) const {
10354 for (auto Pred : Preds)
10355 Pred->print(OS, Depth);
10358 void SCEVUnionPredicate::add(const SCEVPredicate *N) {
10359 if (const auto *Set = dyn_cast<SCEVUnionPredicate>(N)) {
10360 for (auto Pred : Set->Preds)
10368 const SCEV *Key = N->getExpr();
10369 assert(Key && "Only SCEVUnionPredicate doesn't have an "
10370 " associated expression!");
10372 SCEVToPreds[Key].push_back(N);
10373 Preds.push_back(N);
10376 PredicatedScalarEvolution::PredicatedScalarEvolution(ScalarEvolution &SE,
10378 : SE(SE), L(L), Generation(0), BackedgeCount(nullptr) {}
10380 const SCEV *PredicatedScalarEvolution::getSCEV(Value *V) {
10381 const SCEV *Expr = SE.getSCEV(V);
10382 RewriteEntry &Entry = RewriteMap[Expr];
10384 // If we already have an entry and the version matches, return it.
10385 if (Entry.second && Generation == Entry.first)
10386 return Entry.second;
10388 // We found an entry but it's stale. Rewrite the stale entry
10389 // according to the current predicate.
10391 Expr = Entry.second;
10393 const SCEV *NewSCEV = SE.rewriteUsingPredicate(Expr, &L, Preds);
10394 Entry = {Generation, NewSCEV};
10399 const SCEV *PredicatedScalarEvolution::getBackedgeTakenCount() {
10400 if (!BackedgeCount) {
10401 SCEVUnionPredicate BackedgePred;
10402 BackedgeCount = SE.getPredicatedBackedgeTakenCount(&L, BackedgePred);
10403 addPredicate(BackedgePred);
10405 return BackedgeCount;
10408 void PredicatedScalarEvolution::addPredicate(const SCEVPredicate &Pred) {
10409 if (Preds.implies(&Pred))
10412 updateGeneration();
10415 const SCEVUnionPredicate &PredicatedScalarEvolution::getUnionPredicate() const {
10419 void PredicatedScalarEvolution::updateGeneration() {
10420 // If the generation number wrapped recompute everything.
10421 if (++Generation == 0) {
10422 for (auto &II : RewriteMap) {
10423 const SCEV *Rewritten = II.second.second;
10424 II.second = {Generation, SE.rewriteUsingPredicate(Rewritten, &L, Preds)};
10429 void PredicatedScalarEvolution::setNoOverflow(
10430 Value *V, SCEVWrapPredicate::IncrementWrapFlags Flags) {
10431 const SCEV *Expr = getSCEV(V);
10432 const auto *AR = cast<SCEVAddRecExpr>(Expr);
10434 auto ImpliedFlags = SCEVWrapPredicate::getImpliedFlags(AR, SE);
10436 // Clear the statically implied flags.
10437 Flags = SCEVWrapPredicate::clearFlags(Flags, ImpliedFlags);
10438 addPredicate(*SE.getWrapPredicate(AR, Flags));
10440 auto II = FlagsMap.insert({V, Flags});
10442 II.first->second = SCEVWrapPredicate::setFlags(Flags, II.first->second);
10445 bool PredicatedScalarEvolution::hasNoOverflow(
10446 Value *V, SCEVWrapPredicate::IncrementWrapFlags Flags) {
10447 const SCEV *Expr = getSCEV(V);
10448 const auto *AR = cast<SCEVAddRecExpr>(Expr);
10450 Flags = SCEVWrapPredicate::clearFlags(
10451 Flags, SCEVWrapPredicate::getImpliedFlags(AR, SE));
10453 auto II = FlagsMap.find(V);
10455 if (II != FlagsMap.end())
10456 Flags = SCEVWrapPredicate::clearFlags(Flags, II->second);
10458 return Flags == SCEVWrapPredicate::IncrementAnyWrap;
10461 const SCEVAddRecExpr *PredicatedScalarEvolution::getAsAddRec(Value *V) {
10462 const SCEV *Expr = this->getSCEV(V);
10463 SmallPtrSet<const SCEVPredicate *, 4> NewPreds;
10464 auto *New = SE.convertSCEVToAddRecWithPredicates(Expr, &L, NewPreds);
10469 for (auto *P : NewPreds)
10472 updateGeneration();
10473 RewriteMap[SE.getSCEV(V)] = {Generation, New};
10477 PredicatedScalarEvolution::PredicatedScalarEvolution(
10478 const PredicatedScalarEvolution &Init)
10479 : RewriteMap(Init.RewriteMap), SE(Init.SE), L(Init.L), Preds(Init.Preds),
10480 Generation(Init.Generation), BackedgeCount(Init.BackedgeCount) {
10481 for (const auto &I : Init.FlagsMap)
10482 FlagsMap.insert(I);
10485 void PredicatedScalarEvolution::print(raw_ostream &OS, unsigned Depth) const {
10487 for (auto *BB : L.getBlocks())
10488 for (auto &I : *BB) {
10489 if (!SE.isSCEVable(I.getType()))
10492 auto *Expr = SE.getSCEV(&I);
10493 auto II = RewriteMap.find(Expr);
10495 if (II == RewriteMap.end())
10498 // Don't print things that are not interesting.
10499 if (II->second.second == Expr)
10502 OS.indent(Depth) << "[PSE]" << I << ":\n";
10503 OS.indent(Depth + 2) << *Expr << "\n";
10504 OS.indent(Depth + 2) << "--> " << *II->second.second << "\n";