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/SmallPtrSet.h"
65 #include "llvm/ADT/Statistic.h"
66 #include "llvm/Analysis/AssumptionCache.h"
67 #include "llvm/Analysis/ConstantFolding.h"
68 #include "llvm/Analysis/InstructionSimplify.h"
69 #include "llvm/Analysis/LoopInfo.h"
70 #include "llvm/Analysis/ScalarEvolutionExpressions.h"
71 #include "llvm/Analysis/TargetLibraryInfo.h"
72 #include "llvm/Analysis/ValueTracking.h"
73 #include "llvm/IR/ConstantRange.h"
74 #include "llvm/IR/Constants.h"
75 #include "llvm/IR/DataLayout.h"
76 #include "llvm/IR/DerivedTypes.h"
77 #include "llvm/IR/Dominators.h"
78 #include "llvm/IR/GetElementPtrTypeIterator.h"
79 #include "llvm/IR/GlobalAlias.h"
80 #include "llvm/IR/GlobalVariable.h"
81 #include "llvm/IR/InstIterator.h"
82 #include "llvm/IR/Instructions.h"
83 #include "llvm/IR/LLVMContext.h"
84 #include "llvm/IR/Metadata.h"
85 #include "llvm/IR/Operator.h"
86 #include "llvm/Support/CommandLine.h"
87 #include "llvm/Support/Debug.h"
88 #include "llvm/Support/ErrorHandling.h"
89 #include "llvm/Support/MathExtras.h"
90 #include "llvm/Support/raw_ostream.h"
94 #define DEBUG_TYPE "scalar-evolution"
96 STATISTIC(NumArrayLenItCounts,
97 "Number of trip counts computed with array length");
98 STATISTIC(NumTripCountsComputed,
99 "Number of loops with predictable loop counts");
100 STATISTIC(NumTripCountsNotComputed,
101 "Number of loops without predictable loop counts");
102 STATISTIC(NumBruteForceTripCountsComputed,
103 "Number of loops with trip counts computed by force");
105 static cl::opt<unsigned>
106 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
107 cl::desc("Maximum number of iterations SCEV will "
108 "symbolically execute a constant "
112 // FIXME: Enable this with XDEBUG when the test suite is clean.
114 VerifySCEV("verify-scev",
115 cl::desc("Verify ScalarEvolution's backedge taken counts (slow)"));
117 INITIALIZE_PASS_BEGIN(ScalarEvolution, "scalar-evolution",
118 "Scalar Evolution Analysis", false, true)
119 INITIALIZE_PASS_DEPENDENCY(AssumptionCacheTracker)
120 INITIALIZE_PASS_DEPENDENCY(LoopInfoWrapperPass)
121 INITIALIZE_PASS_DEPENDENCY(DominatorTreeWrapperPass)
122 INITIALIZE_PASS_DEPENDENCY(TargetLibraryInfoWrapperPass)
123 INITIALIZE_PASS_END(ScalarEvolution, "scalar-evolution",
124 "Scalar Evolution Analysis", false, true)
125 char ScalarEvolution::ID = 0;
127 //===----------------------------------------------------------------------===//
128 // SCEV class definitions
129 //===----------------------------------------------------------------------===//
131 //===----------------------------------------------------------------------===//
132 // Implementation of the SCEV class.
135 #if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP)
136 void SCEV::dump() const {
142 void SCEV::print(raw_ostream &OS) const {
143 switch (static_cast<SCEVTypes>(getSCEVType())) {
145 cast<SCEVConstant>(this)->getValue()->printAsOperand(OS, false);
148 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(this);
149 const SCEV *Op = Trunc->getOperand();
150 OS << "(trunc " << *Op->getType() << " " << *Op << " to "
151 << *Trunc->getType() << ")";
155 const SCEVZeroExtendExpr *ZExt = cast<SCEVZeroExtendExpr>(this);
156 const SCEV *Op = ZExt->getOperand();
157 OS << "(zext " << *Op->getType() << " " << *Op << " to "
158 << *ZExt->getType() << ")";
162 const SCEVSignExtendExpr *SExt = cast<SCEVSignExtendExpr>(this);
163 const SCEV *Op = SExt->getOperand();
164 OS << "(sext " << *Op->getType() << " " << *Op << " to "
165 << *SExt->getType() << ")";
169 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(this);
170 OS << "{" << *AR->getOperand(0);
171 for (unsigned i = 1, e = AR->getNumOperands(); i != e; ++i)
172 OS << ",+," << *AR->getOperand(i);
174 if (AR->getNoWrapFlags(FlagNUW))
176 if (AR->getNoWrapFlags(FlagNSW))
178 if (AR->getNoWrapFlags(FlagNW) &&
179 !AR->getNoWrapFlags((NoWrapFlags)(FlagNUW | FlagNSW)))
181 AR->getLoop()->getHeader()->printAsOperand(OS, /*PrintType=*/false);
189 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(this);
190 const char *OpStr = nullptr;
191 switch (NAry->getSCEVType()) {
192 case scAddExpr: OpStr = " + "; break;
193 case scMulExpr: OpStr = " * "; break;
194 case scUMaxExpr: OpStr = " umax "; break;
195 case scSMaxExpr: OpStr = " smax "; break;
198 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
201 if (std::next(I) != E)
205 switch (NAry->getSCEVType()) {
208 if (NAry->getNoWrapFlags(FlagNUW))
210 if (NAry->getNoWrapFlags(FlagNSW))
216 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(this);
217 OS << "(" << *UDiv->getLHS() << " /u " << *UDiv->getRHS() << ")";
221 const SCEVUnknown *U = cast<SCEVUnknown>(this);
223 if (U->isSizeOf(AllocTy)) {
224 OS << "sizeof(" << *AllocTy << ")";
227 if (U->isAlignOf(AllocTy)) {
228 OS << "alignof(" << *AllocTy << ")";
234 if (U->isOffsetOf(CTy, FieldNo)) {
235 OS << "offsetof(" << *CTy << ", ";
236 FieldNo->printAsOperand(OS, false);
241 // Otherwise just print it normally.
242 U->getValue()->printAsOperand(OS, false);
245 case scCouldNotCompute:
246 OS << "***COULDNOTCOMPUTE***";
249 llvm_unreachable("Unknown SCEV kind!");
252 Type *SCEV::getType() const {
253 switch (static_cast<SCEVTypes>(getSCEVType())) {
255 return cast<SCEVConstant>(this)->getType();
259 return cast<SCEVCastExpr>(this)->getType();
264 return cast<SCEVNAryExpr>(this)->getType();
266 return cast<SCEVAddExpr>(this)->getType();
268 return cast<SCEVUDivExpr>(this)->getType();
270 return cast<SCEVUnknown>(this)->getType();
271 case scCouldNotCompute:
272 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
274 llvm_unreachable("Unknown SCEV kind!");
277 bool SCEV::isZero() const {
278 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
279 return SC->getValue()->isZero();
283 bool SCEV::isOne() const {
284 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
285 return SC->getValue()->isOne();
289 bool SCEV::isAllOnesValue() const {
290 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
291 return SC->getValue()->isAllOnesValue();
295 /// isNonConstantNegative - Return true if the specified scev is negated, but
297 bool SCEV::isNonConstantNegative() const {
298 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(this);
299 if (!Mul) return false;
301 // If there is a constant factor, it will be first.
302 const SCEVConstant *SC = dyn_cast<SCEVConstant>(Mul->getOperand(0));
303 if (!SC) return false;
305 // Return true if the value is negative, this matches things like (-42 * V).
306 return SC->getValue()->getValue().isNegative();
309 SCEVCouldNotCompute::SCEVCouldNotCompute() :
310 SCEV(FoldingSetNodeIDRef(), scCouldNotCompute) {}
312 bool SCEVCouldNotCompute::classof(const SCEV *S) {
313 return S->getSCEVType() == scCouldNotCompute;
316 const SCEV *ScalarEvolution::getConstant(ConstantInt *V) {
318 ID.AddInteger(scConstant);
321 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
322 SCEV *S = new (SCEVAllocator) SCEVConstant(ID.Intern(SCEVAllocator), V);
323 UniqueSCEVs.InsertNode(S, IP);
327 const SCEV *ScalarEvolution::getConstant(const APInt &Val) {
328 return getConstant(ConstantInt::get(getContext(), Val));
332 ScalarEvolution::getConstant(Type *Ty, uint64_t V, bool isSigned) {
333 IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty));
334 return getConstant(ConstantInt::get(ITy, V, isSigned));
337 SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID,
338 unsigned SCEVTy, const SCEV *op, Type *ty)
339 : SCEV(ID, SCEVTy), Op(op), Ty(ty) {}
341 SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID,
342 const SCEV *op, Type *ty)
343 : SCEVCastExpr(ID, scTruncate, op, ty) {
344 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
345 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
346 "Cannot truncate non-integer value!");
349 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID,
350 const SCEV *op, Type *ty)
351 : SCEVCastExpr(ID, scZeroExtend, op, ty) {
352 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
353 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
354 "Cannot zero extend non-integer value!");
357 SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID,
358 const SCEV *op, Type *ty)
359 : SCEVCastExpr(ID, scSignExtend, op, ty) {
360 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
361 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
362 "Cannot sign extend non-integer value!");
365 void SCEVUnknown::deleted() {
366 // Clear this SCEVUnknown from various maps.
367 SE->forgetMemoizedResults(this);
369 // Remove this SCEVUnknown from the uniquing map.
370 SE->UniqueSCEVs.RemoveNode(this);
372 // Release the value.
376 void SCEVUnknown::allUsesReplacedWith(Value *New) {
377 // Clear this SCEVUnknown from various maps.
378 SE->forgetMemoizedResults(this);
380 // Remove this SCEVUnknown from the uniquing map.
381 SE->UniqueSCEVs.RemoveNode(this);
383 // Update this SCEVUnknown to point to the new value. This is needed
384 // because there may still be outstanding SCEVs which still point to
389 bool SCEVUnknown::isSizeOf(Type *&AllocTy) const {
390 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
391 if (VCE->getOpcode() == Instruction::PtrToInt)
392 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
393 if (CE->getOpcode() == Instruction::GetElementPtr &&
394 CE->getOperand(0)->isNullValue() &&
395 CE->getNumOperands() == 2)
396 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1)))
398 AllocTy = cast<PointerType>(CE->getOperand(0)->getType())
406 bool SCEVUnknown::isAlignOf(Type *&AllocTy) const {
407 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
408 if (VCE->getOpcode() == Instruction::PtrToInt)
409 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
410 if (CE->getOpcode() == Instruction::GetElementPtr &&
411 CE->getOperand(0)->isNullValue()) {
413 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
414 if (StructType *STy = dyn_cast<StructType>(Ty))
415 if (!STy->isPacked() &&
416 CE->getNumOperands() == 3 &&
417 CE->getOperand(1)->isNullValue()) {
418 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2)))
420 STy->getNumElements() == 2 &&
421 STy->getElementType(0)->isIntegerTy(1)) {
422 AllocTy = STy->getElementType(1);
431 bool SCEVUnknown::isOffsetOf(Type *&CTy, Constant *&FieldNo) const {
432 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
433 if (VCE->getOpcode() == Instruction::PtrToInt)
434 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
435 if (CE->getOpcode() == Instruction::GetElementPtr &&
436 CE->getNumOperands() == 3 &&
437 CE->getOperand(0)->isNullValue() &&
438 CE->getOperand(1)->isNullValue()) {
440 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
441 // Ignore vector types here so that ScalarEvolutionExpander doesn't
442 // emit getelementptrs that index into vectors.
443 if (Ty->isStructTy() || Ty->isArrayTy()) {
445 FieldNo = CE->getOperand(2);
453 //===----------------------------------------------------------------------===//
455 //===----------------------------------------------------------------------===//
458 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
459 /// than the complexity of the RHS. This comparator is used to canonicalize
461 class SCEVComplexityCompare {
462 const LoopInfo *const LI;
464 explicit SCEVComplexityCompare(const LoopInfo *li) : LI(li) {}
466 // Return true or false if LHS is less than, or at least RHS, respectively.
467 bool operator()(const SCEV *LHS, const SCEV *RHS) const {
468 return compare(LHS, RHS) < 0;
471 // Return negative, zero, or positive, if LHS is less than, equal to, or
472 // greater than RHS, respectively. A three-way result allows recursive
473 // comparisons to be more efficient.
474 int compare(const SCEV *LHS, const SCEV *RHS) const {
475 // Fast-path: SCEVs are uniqued so we can do a quick equality check.
479 // Primarily, sort the SCEVs by their getSCEVType().
480 unsigned LType = LHS->getSCEVType(), RType = RHS->getSCEVType();
482 return (int)LType - (int)RType;
484 // Aside from the getSCEVType() ordering, the particular ordering
485 // isn't very important except that it's beneficial to be consistent,
486 // so that (a + b) and (b + a) don't end up as different expressions.
487 switch (static_cast<SCEVTypes>(LType)) {
489 const SCEVUnknown *LU = cast<SCEVUnknown>(LHS);
490 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
492 // Sort SCEVUnknown values with some loose heuristics. TODO: This is
493 // not as complete as it could be.
494 const Value *LV = LU->getValue(), *RV = RU->getValue();
496 // Order pointer values after integer values. This helps SCEVExpander
498 bool LIsPointer = LV->getType()->isPointerTy(),
499 RIsPointer = RV->getType()->isPointerTy();
500 if (LIsPointer != RIsPointer)
501 return (int)LIsPointer - (int)RIsPointer;
503 // Compare getValueID values.
504 unsigned LID = LV->getValueID(),
505 RID = RV->getValueID();
507 return (int)LID - (int)RID;
509 // Sort arguments by their position.
510 if (const Argument *LA = dyn_cast<Argument>(LV)) {
511 const Argument *RA = cast<Argument>(RV);
512 unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo();
513 return (int)LArgNo - (int)RArgNo;
516 // For instructions, compare their loop depth, and their operand
517 // count. This is pretty loose.
518 if (const Instruction *LInst = dyn_cast<Instruction>(LV)) {
519 const Instruction *RInst = cast<Instruction>(RV);
521 // Compare loop depths.
522 const BasicBlock *LParent = LInst->getParent(),
523 *RParent = RInst->getParent();
524 if (LParent != RParent) {
525 unsigned LDepth = LI->getLoopDepth(LParent),
526 RDepth = LI->getLoopDepth(RParent);
527 if (LDepth != RDepth)
528 return (int)LDepth - (int)RDepth;
531 // Compare the number of operands.
532 unsigned LNumOps = LInst->getNumOperands(),
533 RNumOps = RInst->getNumOperands();
534 return (int)LNumOps - (int)RNumOps;
541 const SCEVConstant *LC = cast<SCEVConstant>(LHS);
542 const SCEVConstant *RC = cast<SCEVConstant>(RHS);
544 // Compare constant values.
545 const APInt &LA = LC->getValue()->getValue();
546 const APInt &RA = RC->getValue()->getValue();
547 unsigned LBitWidth = LA.getBitWidth(), RBitWidth = RA.getBitWidth();
548 if (LBitWidth != RBitWidth)
549 return (int)LBitWidth - (int)RBitWidth;
550 return LA.ult(RA) ? -1 : 1;
554 const SCEVAddRecExpr *LA = cast<SCEVAddRecExpr>(LHS);
555 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS);
557 // Compare addrec loop depths.
558 const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop();
559 if (LLoop != RLoop) {
560 unsigned LDepth = LLoop->getLoopDepth(),
561 RDepth = RLoop->getLoopDepth();
562 if (LDepth != RDepth)
563 return (int)LDepth - (int)RDepth;
566 // Addrec complexity grows with operand count.
567 unsigned LNumOps = LA->getNumOperands(), RNumOps = RA->getNumOperands();
568 if (LNumOps != RNumOps)
569 return (int)LNumOps - (int)RNumOps;
571 // Lexicographically compare.
572 for (unsigned i = 0; i != LNumOps; ++i) {
573 long X = compare(LA->getOperand(i), RA->getOperand(i));
585 const SCEVNAryExpr *LC = cast<SCEVNAryExpr>(LHS);
586 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
588 // Lexicographically compare n-ary expressions.
589 unsigned LNumOps = LC->getNumOperands(), RNumOps = RC->getNumOperands();
590 if (LNumOps != RNumOps)
591 return (int)LNumOps - (int)RNumOps;
593 for (unsigned i = 0; i != LNumOps; ++i) {
596 long X = compare(LC->getOperand(i), RC->getOperand(i));
600 return (int)LNumOps - (int)RNumOps;
604 const SCEVUDivExpr *LC = cast<SCEVUDivExpr>(LHS);
605 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
607 // Lexicographically compare udiv expressions.
608 long X = compare(LC->getLHS(), RC->getLHS());
611 return compare(LC->getRHS(), RC->getRHS());
617 const SCEVCastExpr *LC = cast<SCEVCastExpr>(LHS);
618 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
620 // Compare cast expressions by operand.
621 return compare(LC->getOperand(), RC->getOperand());
624 case scCouldNotCompute:
625 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
627 llvm_unreachable("Unknown SCEV kind!");
632 /// GroupByComplexity - Given a list of SCEV objects, order them by their
633 /// complexity, and group objects of the same complexity together by value.
634 /// When this routine is finished, we know that any duplicates in the vector are
635 /// consecutive and that complexity is monotonically increasing.
637 /// Note that we go take special precautions to ensure that we get deterministic
638 /// results from this routine. In other words, we don't want the results of
639 /// this to depend on where the addresses of various SCEV objects happened to
642 static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops,
644 if (Ops.size() < 2) return; // Noop
645 if (Ops.size() == 2) {
646 // This is the common case, which also happens to be trivially simple.
648 const SCEV *&LHS = Ops[0], *&RHS = Ops[1];
649 if (SCEVComplexityCompare(LI)(RHS, LHS))
654 // Do the rough sort by complexity.
655 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI));
657 // Now that we are sorted by complexity, group elements of the same
658 // complexity. Note that this is, at worst, N^2, but the vector is likely to
659 // be extremely short in practice. Note that we take this approach because we
660 // do not want to depend on the addresses of the objects we are grouping.
661 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
662 const SCEV *S = Ops[i];
663 unsigned Complexity = S->getSCEVType();
665 // If there are any objects of the same complexity and same value as this
667 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
668 if (Ops[j] == S) { // Found a duplicate.
669 // Move it to immediately after i'th element.
670 std::swap(Ops[i+1], Ops[j]);
671 ++i; // no need to rescan it.
672 if (i == e-2) return; // Done!
679 struct FindSCEVSize {
681 FindSCEVSize() : Size(0) {}
683 bool follow(const SCEV *S) {
685 // Keep looking at all operands of S.
688 bool isDone() const {
694 // Returns the size of the SCEV S.
695 static inline int sizeOfSCEV(const SCEV *S) {
697 SCEVTraversal<FindSCEVSize> ST(F);
704 struct SCEVDivision : public SCEVVisitor<SCEVDivision, void> {
706 // Computes the Quotient and Remainder of the division of Numerator by
708 static void divide(ScalarEvolution &SE, const SCEV *Numerator,
709 const SCEV *Denominator, const SCEV **Quotient,
710 const SCEV **Remainder) {
711 assert(Numerator && Denominator && "Uninitialized SCEV");
713 SCEVDivision D(SE, Numerator, Denominator);
715 // Check for the trivial case here to avoid having to check for it in the
717 if (Numerator == Denominator) {
723 if (Numerator->isZero()) {
729 // A simple case when N/1. The quotient is N.
730 if (Denominator->isOne()) {
731 *Quotient = Numerator;
736 // Split the Denominator when it is a product.
737 if (const SCEVMulExpr *T = dyn_cast<const SCEVMulExpr>(Denominator)) {
739 *Quotient = Numerator;
740 for (const SCEV *Op : T->operands()) {
741 divide(SE, *Quotient, Op, &Q, &R);
744 // Bail out when the Numerator is not divisible by one of the terms of
748 *Remainder = Numerator;
757 *Quotient = D.Quotient;
758 *Remainder = D.Remainder;
761 // Except in the trivial case described above, we do not know how to divide
762 // Expr by Denominator for the following functions with empty implementation.
763 void visitTruncateExpr(const SCEVTruncateExpr *Numerator) {}
764 void visitZeroExtendExpr(const SCEVZeroExtendExpr *Numerator) {}
765 void visitSignExtendExpr(const SCEVSignExtendExpr *Numerator) {}
766 void visitUDivExpr(const SCEVUDivExpr *Numerator) {}
767 void visitSMaxExpr(const SCEVSMaxExpr *Numerator) {}
768 void visitUMaxExpr(const SCEVUMaxExpr *Numerator) {}
769 void visitUnknown(const SCEVUnknown *Numerator) {}
770 void visitCouldNotCompute(const SCEVCouldNotCompute *Numerator) {}
772 void visitConstant(const SCEVConstant *Numerator) {
773 if (const SCEVConstant *D = dyn_cast<SCEVConstant>(Denominator)) {
774 APInt NumeratorVal = Numerator->getValue()->getValue();
775 APInt DenominatorVal = D->getValue()->getValue();
776 uint32_t NumeratorBW = NumeratorVal.getBitWidth();
777 uint32_t DenominatorBW = DenominatorVal.getBitWidth();
779 if (NumeratorBW > DenominatorBW)
780 DenominatorVal = DenominatorVal.sext(NumeratorBW);
781 else if (NumeratorBW < DenominatorBW)
782 NumeratorVal = NumeratorVal.sext(DenominatorBW);
784 APInt QuotientVal(NumeratorVal.getBitWidth(), 0);
785 APInt RemainderVal(NumeratorVal.getBitWidth(), 0);
786 APInt::sdivrem(NumeratorVal, DenominatorVal, QuotientVal, RemainderVal);
787 Quotient = SE.getConstant(QuotientVal);
788 Remainder = SE.getConstant(RemainderVal);
793 void visitAddRecExpr(const SCEVAddRecExpr *Numerator) {
794 const SCEV *StartQ, *StartR, *StepQ, *StepR;
795 assert(Numerator->isAffine() && "Numerator should be affine");
796 divide(SE, Numerator->getStart(), Denominator, &StartQ, &StartR);
797 divide(SE, Numerator->getStepRecurrence(SE), Denominator, &StepQ, &StepR);
798 // Bail out if the types do not match.
799 Type *Ty = Denominator->getType();
800 if (Ty != StartQ->getType() || Ty != StartR->getType() ||
801 Ty != StepQ->getType() || Ty != StepR->getType()) {
803 Remainder = Numerator;
806 Quotient = SE.getAddRecExpr(StartQ, StepQ, Numerator->getLoop(),
807 Numerator->getNoWrapFlags());
808 Remainder = SE.getAddRecExpr(StartR, StepR, Numerator->getLoop(),
809 Numerator->getNoWrapFlags());
812 void visitAddExpr(const SCEVAddExpr *Numerator) {
813 SmallVector<const SCEV *, 2> Qs, Rs;
814 Type *Ty = Denominator->getType();
816 for (const SCEV *Op : Numerator->operands()) {
818 divide(SE, Op, Denominator, &Q, &R);
820 // Bail out if types do not match.
821 if (Ty != Q->getType() || Ty != R->getType()) {
823 Remainder = Numerator;
831 if (Qs.size() == 1) {
837 Quotient = SE.getAddExpr(Qs);
838 Remainder = SE.getAddExpr(Rs);
841 void visitMulExpr(const SCEVMulExpr *Numerator) {
842 SmallVector<const SCEV *, 2> Qs;
843 Type *Ty = Denominator->getType();
845 bool FoundDenominatorTerm = false;
846 for (const SCEV *Op : Numerator->operands()) {
847 // Bail out if types do not match.
848 if (Ty != Op->getType()) {
850 Remainder = Numerator;
854 if (FoundDenominatorTerm) {
859 // Check whether Denominator divides one of the product operands.
861 divide(SE, Op, Denominator, &Q, &R);
867 // Bail out if types do not match.
868 if (Ty != Q->getType()) {
870 Remainder = Numerator;
874 FoundDenominatorTerm = true;
878 if (FoundDenominatorTerm) {
883 Quotient = SE.getMulExpr(Qs);
887 if (!isa<SCEVUnknown>(Denominator)) {
889 Remainder = Numerator;
893 // The Remainder is obtained by replacing Denominator by 0 in Numerator.
894 ValueToValueMap RewriteMap;
895 RewriteMap[cast<SCEVUnknown>(Denominator)->getValue()] =
896 cast<SCEVConstant>(Zero)->getValue();
897 Remainder = SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true);
899 if (Remainder->isZero()) {
900 // The Quotient is obtained by replacing Denominator by 1 in Numerator.
901 RewriteMap[cast<SCEVUnknown>(Denominator)->getValue()] =
902 cast<SCEVConstant>(One)->getValue();
904 SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true);
908 // Quotient is (Numerator - Remainder) divided by Denominator.
910 const SCEV *Diff = SE.getMinusSCEV(Numerator, Remainder);
911 if (sizeOfSCEV(Diff) > sizeOfSCEV(Numerator)) {
912 // This SCEV does not seem to simplify: fail the division here.
914 Remainder = Numerator;
917 divide(SE, Diff, Denominator, &Q, &R);
919 "(Numerator - Remainder) should evenly divide Denominator");
924 SCEVDivision(ScalarEvolution &S, const SCEV *Numerator,
925 const SCEV *Denominator)
926 : SE(S), Denominator(Denominator) {
927 Zero = SE.getConstant(Denominator->getType(), 0);
928 One = SE.getConstant(Denominator->getType(), 1);
930 // By default, we don't know how to divide Expr by Denominator.
931 // Providing the default here simplifies the rest of the code.
933 Remainder = Numerator;
937 const SCEV *Denominator, *Quotient, *Remainder, *Zero, *One;
942 //===----------------------------------------------------------------------===//
943 // Simple SCEV method implementations
944 //===----------------------------------------------------------------------===//
946 /// BinomialCoefficient - Compute BC(It, K). The result has width W.
948 static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K,
951 // Handle the simplest case efficiently.
953 return SE.getTruncateOrZeroExtend(It, ResultTy);
955 // We are using the following formula for BC(It, K):
957 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
959 // Suppose, W is the bitwidth of the return value. We must be prepared for
960 // overflow. Hence, we must assure that the result of our computation is
961 // equal to the accurate one modulo 2^W. Unfortunately, division isn't
962 // safe in modular arithmetic.
964 // However, this code doesn't use exactly that formula; the formula it uses
965 // is something like the following, where T is the number of factors of 2 in
966 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
969 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
971 // This formula is trivially equivalent to the previous formula. However,
972 // this formula can be implemented much more efficiently. The trick is that
973 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
974 // arithmetic. To do exact division in modular arithmetic, all we have
975 // to do is multiply by the inverse. Therefore, this step can be done at
978 // The next issue is how to safely do the division by 2^T. The way this
979 // is done is by doing the multiplication step at a width of at least W + T
980 // bits. This way, the bottom W+T bits of the product are accurate. Then,
981 // when we perform the division by 2^T (which is equivalent to a right shift
982 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
983 // truncated out after the division by 2^T.
985 // In comparison to just directly using the first formula, this technique
986 // is much more efficient; using the first formula requires W * K bits,
987 // but this formula less than W + K bits. Also, the first formula requires
988 // a division step, whereas this formula only requires multiplies and shifts.
990 // It doesn't matter whether the subtraction step is done in the calculation
991 // width or the input iteration count's width; if the subtraction overflows,
992 // the result must be zero anyway. We prefer here to do it in the width of
993 // the induction variable because it helps a lot for certain cases; CodeGen
994 // isn't smart enough to ignore the overflow, which leads to much less
995 // efficient code if the width of the subtraction is wider than the native
998 // (It's possible to not widen at all by pulling out factors of 2 before
999 // the multiplication; for example, K=2 can be calculated as
1000 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
1001 // extra arithmetic, so it's not an obvious win, and it gets
1002 // much more complicated for K > 3.)
1004 // Protection from insane SCEVs; this bound is conservative,
1005 // but it probably doesn't matter.
1007 return SE.getCouldNotCompute();
1009 unsigned W = SE.getTypeSizeInBits(ResultTy);
1011 // Calculate K! / 2^T and T; we divide out the factors of two before
1012 // multiplying for calculating K! / 2^T to avoid overflow.
1013 // Other overflow doesn't matter because we only care about the bottom
1014 // W bits of the result.
1015 APInt OddFactorial(W, 1);
1017 for (unsigned i = 3; i <= K; ++i) {
1019 unsigned TwoFactors = Mult.countTrailingZeros();
1021 Mult = Mult.lshr(TwoFactors);
1022 OddFactorial *= Mult;
1025 // We need at least W + T bits for the multiplication step
1026 unsigned CalculationBits = W + T;
1028 // Calculate 2^T, at width T+W.
1029 APInt DivFactor = APInt::getOneBitSet(CalculationBits, T);
1031 // Calculate the multiplicative inverse of K! / 2^T;
1032 // this multiplication factor will perform the exact division by
1034 APInt Mod = APInt::getSignedMinValue(W+1);
1035 APInt MultiplyFactor = OddFactorial.zext(W+1);
1036 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
1037 MultiplyFactor = MultiplyFactor.trunc(W);
1039 // Calculate the product, at width T+W
1040 IntegerType *CalculationTy = IntegerType::get(SE.getContext(),
1042 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
1043 for (unsigned i = 1; i != K; ++i) {
1044 const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i));
1045 Dividend = SE.getMulExpr(Dividend,
1046 SE.getTruncateOrZeroExtend(S, CalculationTy));
1050 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
1052 // Truncate the result, and divide by K! / 2^T.
1054 return SE.getMulExpr(SE.getConstant(MultiplyFactor),
1055 SE.getTruncateOrZeroExtend(DivResult, ResultTy));
1058 /// evaluateAtIteration - Return the value of this chain of recurrences at
1059 /// the specified iteration number. We can evaluate this recurrence by
1060 /// multiplying each element in the chain by the binomial coefficient
1061 /// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
1063 /// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
1065 /// where BC(It, k) stands for binomial coefficient.
1067 const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It,
1068 ScalarEvolution &SE) const {
1069 const SCEV *Result = getStart();
1070 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
1071 // The computation is correct in the face of overflow provided that the
1072 // multiplication is performed _after_ the evaluation of the binomial
1074 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType());
1075 if (isa<SCEVCouldNotCompute>(Coeff))
1078 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
1083 //===----------------------------------------------------------------------===//
1084 // SCEV Expression folder implementations
1085 //===----------------------------------------------------------------------===//
1087 const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op,
1089 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
1090 "This is not a truncating conversion!");
1091 assert(isSCEVable(Ty) &&
1092 "This is not a conversion to a SCEVable type!");
1093 Ty = getEffectiveSCEVType(Ty);
1095 FoldingSetNodeID ID;
1096 ID.AddInteger(scTruncate);
1100 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1102 // Fold if the operand is constant.
1103 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1105 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty)));
1107 // trunc(trunc(x)) --> trunc(x)
1108 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
1109 return getTruncateExpr(ST->getOperand(), Ty);
1111 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
1112 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1113 return getTruncateOrSignExtend(SS->getOperand(), Ty);
1115 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
1116 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1117 return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
1119 // trunc(x1+x2+...+xN) --> trunc(x1)+trunc(x2)+...+trunc(xN) if we can
1120 // eliminate all the truncates, or we replace other casts with truncates.
1121 if (const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Op)) {
1122 SmallVector<const SCEV *, 4> Operands;
1123 bool hasTrunc = false;
1124 for (unsigned i = 0, e = SA->getNumOperands(); i != e && !hasTrunc; ++i) {
1125 const SCEV *S = getTruncateExpr(SA->getOperand(i), Ty);
1126 if (!isa<SCEVCastExpr>(SA->getOperand(i)))
1127 hasTrunc = isa<SCEVTruncateExpr>(S);
1128 Operands.push_back(S);
1131 return getAddExpr(Operands);
1132 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL.
1135 // trunc(x1*x2*...*xN) --> trunc(x1)*trunc(x2)*...*trunc(xN) if we can
1136 // eliminate all the truncates, or we replace other casts with truncates.
1137 if (const SCEVMulExpr *SM = dyn_cast<SCEVMulExpr>(Op)) {
1138 SmallVector<const SCEV *, 4> Operands;
1139 bool hasTrunc = false;
1140 for (unsigned i = 0, e = SM->getNumOperands(); i != e && !hasTrunc; ++i) {
1141 const SCEV *S = getTruncateExpr(SM->getOperand(i), Ty);
1142 if (!isa<SCEVCastExpr>(SM->getOperand(i)))
1143 hasTrunc = isa<SCEVTruncateExpr>(S);
1144 Operands.push_back(S);
1147 return getMulExpr(Operands);
1148 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL.
1151 // If the input value is a chrec scev, truncate the chrec's operands.
1152 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
1153 SmallVector<const SCEV *, 4> Operands;
1154 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
1155 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty));
1156 return getAddRecExpr(Operands, AddRec->getLoop(), SCEV::FlagAnyWrap);
1159 // The cast wasn't folded; create an explicit cast node. We can reuse
1160 // the existing insert position since if we get here, we won't have
1161 // made any changes which would invalidate it.
1162 SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator),
1164 UniqueSCEVs.InsertNode(S, IP);
1168 // Get the limit of a recurrence such that incrementing by Step cannot cause
1169 // signed overflow as long as the value of the recurrence within the
1170 // loop does not exceed this limit before incrementing.
1171 static const SCEV *getSignedOverflowLimitForStep(const SCEV *Step,
1172 ICmpInst::Predicate *Pred,
1173 ScalarEvolution *SE) {
1174 unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
1175 if (SE->isKnownPositive(Step)) {
1176 *Pred = ICmpInst::ICMP_SLT;
1177 return SE->getConstant(APInt::getSignedMinValue(BitWidth) -
1178 SE->getSignedRange(Step).getSignedMax());
1180 if (SE->isKnownNegative(Step)) {
1181 *Pred = ICmpInst::ICMP_SGT;
1182 return SE->getConstant(APInt::getSignedMaxValue(BitWidth) -
1183 SE->getSignedRange(Step).getSignedMin());
1188 // Get the limit of a recurrence such that incrementing by Step cannot cause
1189 // unsigned overflow as long as the value of the recurrence within the loop does
1190 // not exceed this limit before incrementing.
1191 static const SCEV *getUnsignedOverflowLimitForStep(const SCEV *Step,
1192 ICmpInst::Predicate *Pred,
1193 ScalarEvolution *SE) {
1194 unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
1195 *Pred = ICmpInst::ICMP_ULT;
1197 return SE->getConstant(APInt::getMinValue(BitWidth) -
1198 SE->getUnsignedRange(Step).getUnsignedMax());
1203 struct ExtendOpTraitsBase {
1204 typedef const SCEV *(ScalarEvolution::*GetExtendExprTy)(const SCEV *, Type *);
1207 // Used to make code generic over signed and unsigned overflow.
1208 template <typename ExtendOp> struct ExtendOpTraits {
1211 // static const SCEV::NoWrapFlags WrapType;
1213 // static const ExtendOpTraitsBase::GetExtendExprTy GetExtendExpr;
1215 // static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1216 // ICmpInst::Predicate *Pred,
1217 // ScalarEvolution *SE);
1221 struct ExtendOpTraits<SCEVSignExtendExpr> : public ExtendOpTraitsBase {
1222 static const SCEV::NoWrapFlags WrapType = SCEV::FlagNSW;
1224 static const GetExtendExprTy GetExtendExpr;
1226 static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1227 ICmpInst::Predicate *Pred,
1228 ScalarEvolution *SE) {
1229 return getSignedOverflowLimitForStep(Step, Pred, SE);
1233 const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits<
1234 SCEVSignExtendExpr>::GetExtendExpr = &ScalarEvolution::getSignExtendExpr;
1237 struct ExtendOpTraits<SCEVZeroExtendExpr> : public ExtendOpTraitsBase {
1238 static const SCEV::NoWrapFlags WrapType = SCEV::FlagNUW;
1240 static const GetExtendExprTy GetExtendExpr;
1242 static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1243 ICmpInst::Predicate *Pred,
1244 ScalarEvolution *SE) {
1245 return getUnsignedOverflowLimitForStep(Step, Pred, SE);
1249 const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits<
1250 SCEVZeroExtendExpr>::GetExtendExpr = &ScalarEvolution::getZeroExtendExpr;
1253 // The recurrence AR has been shown to have no signed/unsigned wrap or something
1254 // close to it. Typically, if we can prove NSW/NUW for AR, then we can just as
1255 // easily prove NSW/NUW for its preincrement or postincrement sibling. This
1256 // allows normalizing a sign/zero extended AddRec as such: {sext/zext(Step +
1257 // Start),+,Step} => {(Step + sext/zext(Start),+,Step} As a result, the
1258 // expression "Step + sext/zext(PreIncAR)" is congruent with
1259 // "sext/zext(PostIncAR)"
1260 template <typename ExtendOpTy>
1261 static const SCEV *getPreStartForExtend(const SCEVAddRecExpr *AR, Type *Ty,
1262 ScalarEvolution *SE) {
1263 auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType;
1264 auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr;
1266 const Loop *L = AR->getLoop();
1267 const SCEV *Start = AR->getStart();
1268 const SCEV *Step = AR->getStepRecurrence(*SE);
1270 // Check for a simple looking step prior to loop entry.
1271 const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Start);
1275 // Create an AddExpr for "PreStart" after subtracting Step. Full SCEV
1276 // subtraction is expensive. For this purpose, perform a quick and dirty
1277 // difference, by checking for Step in the operand list.
1278 SmallVector<const SCEV *, 4> DiffOps;
1279 for (const SCEV *Op : SA->operands())
1281 DiffOps.push_back(Op);
1283 if (DiffOps.size() == SA->getNumOperands())
1286 // Try to prove `WrapType` (SCEV::FlagNSW or SCEV::FlagNUW) on `PreStart` +
1289 // 1. NSW/NUW flags on the step increment.
1290 const SCEV *PreStart = SE->getAddExpr(DiffOps, SA->getNoWrapFlags());
1291 const SCEVAddRecExpr *PreAR = dyn_cast<SCEVAddRecExpr>(
1292 SE->getAddRecExpr(PreStart, Step, L, SCEV::FlagAnyWrap));
1294 // "{S,+,X} is <nsw>/<nuw>" and "the backedge is taken at least once" implies
1295 // "S+X does not sign/unsign-overflow".
1298 const SCEV *BECount = SE->getBackedgeTakenCount(L);
1299 if (PreAR && PreAR->getNoWrapFlags(WrapType) &&
1300 !isa<SCEVCouldNotCompute>(BECount) && SE->isKnownPositive(BECount))
1303 // 2. Direct overflow check on the step operation's expression.
1304 unsigned BitWidth = SE->getTypeSizeInBits(AR->getType());
1305 Type *WideTy = IntegerType::get(SE->getContext(), BitWidth * 2);
1306 const SCEV *OperandExtendedStart =
1307 SE->getAddExpr((SE->*GetExtendExpr)(PreStart, WideTy),
1308 (SE->*GetExtendExpr)(Step, WideTy));
1309 if ((SE->*GetExtendExpr)(Start, WideTy) == OperandExtendedStart) {
1310 if (PreAR && AR->getNoWrapFlags(WrapType)) {
1311 // If we know `AR` == {`PreStart`+`Step`,+,`Step`} is `WrapType` (FlagNSW
1312 // or FlagNUW) and that `PreStart` + `Step` is `WrapType` too, then
1313 // `PreAR` == {`PreStart`,+,`Step`} is also `WrapType`. Cache this fact.
1314 const_cast<SCEVAddRecExpr *>(PreAR)->setNoWrapFlags(WrapType);
1319 // 3. Loop precondition.
1320 ICmpInst::Predicate Pred;
1321 const SCEV *OverflowLimit =
1322 ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep(Step, &Pred, SE);
1324 if (OverflowLimit &&
1325 SE->isLoopEntryGuardedByCond(L, Pred, PreStart, OverflowLimit)) {
1331 // Get the normalized zero or sign extended expression for this AddRec's Start.
1332 template <typename ExtendOpTy>
1333 static const SCEV *getExtendAddRecStart(const SCEVAddRecExpr *AR, Type *Ty,
1334 ScalarEvolution *SE) {
1335 auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr;
1337 const SCEV *PreStart = getPreStartForExtend<ExtendOpTy>(AR, Ty, SE);
1339 return (SE->*GetExtendExpr)(AR->getStart(), Ty);
1341 return SE->getAddExpr((SE->*GetExtendExpr)(AR->getStepRecurrence(*SE), Ty),
1342 (SE->*GetExtendExpr)(PreStart, Ty));
1345 // Try to prove away overflow by looking at "nearby" add recurrences. A
1346 // motivating example for this rule: if we know `{0,+,4}` is `ult` `-1` and it
1347 // does not itself wrap then we can conclude that `{1,+,4}` is `nuw`.
1351 // {S,+,X} == {S-T,+,X} + T
1352 // => Ext({S,+,X}) == Ext({S-T,+,X} + T)
1354 // If ({S-T,+,X} + T) does not overflow ... (1)
1356 // RHS == Ext({S-T,+,X} + T) == Ext({S-T,+,X}) + Ext(T)
1358 // If {S-T,+,X} does not overflow ... (2)
1360 // RHS == Ext({S-T,+,X}) + Ext(T) == {Ext(S-T),+,Ext(X)} + Ext(T)
1361 // == {Ext(S-T)+Ext(T),+,Ext(X)}
1363 // If (S-T)+T does not overflow ... (3)
1365 // RHS == {Ext(S-T)+Ext(T),+,Ext(X)} == {Ext(S-T+T),+,Ext(X)}
1366 // == {Ext(S),+,Ext(X)} == LHS
1368 // Thus, if (1), (2) and (3) are true for some T, then
1369 // Ext({S,+,X}) == {Ext(S),+,Ext(X)}
1371 // (3) is implied by (1) -- "(S-T)+T does not overflow" is simply "({S-T,+,X}+T)
1372 // does not overflow" restricted to the 0th iteration. Therefore we only need
1373 // to check for (1) and (2).
1375 // In the current context, S is `Start`, X is `Step`, Ext is `ExtendOpTy` and T
1376 // is `Delta` (defined below).
1378 template <typename ExtendOpTy>
1379 bool ScalarEvolution::proveNoWrapByVaryingStart(const SCEV *Start,
1382 auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType;
1384 // We restrict `Start` to a constant to prevent SCEV from spending too much
1385 // time here. It is correct (but more expensive) to continue with a
1386 // non-constant `Start` and do a general SCEV subtraction to compute
1387 // `PreStart` below.
1389 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start);
1393 APInt StartAI = StartC->getValue()->getValue();
1395 for (unsigned Delta : {-2, -1, 1, 2}) {
1396 const SCEV *PreStart = getConstant(StartAI - Delta);
1398 // Give up if we don't already have the add recurrence we need because
1399 // actually constructing an add recurrence is relatively expensive.
1400 const SCEVAddRecExpr *PreAR = [&]() {
1401 FoldingSetNodeID ID;
1402 ID.AddInteger(scAddRecExpr);
1403 ID.AddPointer(PreStart);
1404 ID.AddPointer(Step);
1407 return static_cast<SCEVAddRecExpr *>(
1408 this->UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1411 if (PreAR && PreAR->getNoWrapFlags(WrapType)) { // proves (2)
1412 const SCEV *DeltaS = getConstant(StartC->getType(), Delta);
1413 ICmpInst::Predicate Pred = ICmpInst::BAD_ICMP_PREDICATE;
1414 const SCEV *Limit = ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep(
1415 DeltaS, &Pred, this);
1416 if (Limit && isKnownPredicate(Pred, PreAR, Limit)) // proves (1)
1424 const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op,
1426 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1427 "This is not an extending conversion!");
1428 assert(isSCEVable(Ty) &&
1429 "This is not a conversion to a SCEVable type!");
1430 Ty = getEffectiveSCEVType(Ty);
1432 // Fold if the operand is constant.
1433 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1435 cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(), Ty)));
1437 // zext(zext(x)) --> zext(x)
1438 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1439 return getZeroExtendExpr(SZ->getOperand(), Ty);
1441 // Before doing any expensive analysis, check to see if we've already
1442 // computed a SCEV for this Op and Ty.
1443 FoldingSetNodeID ID;
1444 ID.AddInteger(scZeroExtend);
1448 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1450 // zext(trunc(x)) --> zext(x) or x or trunc(x)
1451 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1452 // It's possible the bits taken off by the truncate were all zero bits. If
1453 // so, we should be able to simplify this further.
1454 const SCEV *X = ST->getOperand();
1455 ConstantRange CR = getUnsignedRange(X);
1456 unsigned TruncBits = getTypeSizeInBits(ST->getType());
1457 unsigned NewBits = getTypeSizeInBits(Ty);
1458 if (CR.truncate(TruncBits).zeroExtend(NewBits).contains(
1459 CR.zextOrTrunc(NewBits)))
1460 return getTruncateOrZeroExtend(X, Ty);
1463 // If the input value is a chrec scev, and we can prove that the value
1464 // did not overflow the old, smaller, value, we can zero extend all of the
1465 // operands (often constants). This allows analysis of something like
1466 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
1467 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1468 if (AR->isAffine()) {
1469 const SCEV *Start = AR->getStart();
1470 const SCEV *Step = AR->getStepRecurrence(*this);
1471 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1472 const Loop *L = AR->getLoop();
1474 // If we have special knowledge that this addrec won't overflow,
1475 // we don't need to do any further analysis.
1476 if (AR->getNoWrapFlags(SCEV::FlagNUW))
1477 return getAddRecExpr(
1478 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1479 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1481 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1482 // Note that this serves two purposes: It filters out loops that are
1483 // simply not analyzable, and it covers the case where this code is
1484 // being called from within backedge-taken count analysis, such that
1485 // attempting to ask for the backedge-taken count would likely result
1486 // in infinite recursion. In the later case, the analysis code will
1487 // cope with a conservative value, and it will take care to purge
1488 // that value once it has finished.
1489 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1490 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1491 // Manually compute the final value for AR, checking for
1494 // Check whether the backedge-taken count can be losslessly casted to
1495 // the addrec's type. The count is always unsigned.
1496 const SCEV *CastedMaxBECount =
1497 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1498 const SCEV *RecastedMaxBECount =
1499 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1500 if (MaxBECount == RecastedMaxBECount) {
1501 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1502 // Check whether Start+Step*MaxBECount has no unsigned overflow.
1503 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step);
1504 const SCEV *ZAdd = getZeroExtendExpr(getAddExpr(Start, ZMul), WideTy);
1505 const SCEV *WideStart = getZeroExtendExpr(Start, WideTy);
1506 const SCEV *WideMaxBECount =
1507 getZeroExtendExpr(CastedMaxBECount, WideTy);
1508 const SCEV *OperandExtendedAdd =
1509 getAddExpr(WideStart,
1510 getMulExpr(WideMaxBECount,
1511 getZeroExtendExpr(Step, WideTy)));
1512 if (ZAdd == OperandExtendedAdd) {
1513 // Cache knowledge of AR NUW, which is propagated to this AddRec.
1514 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1515 // Return the expression with the addrec on the outside.
1516 return getAddRecExpr(
1517 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1518 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1520 // Similar to above, only this time treat the step value as signed.
1521 // This covers loops that count down.
1522 OperandExtendedAdd =
1523 getAddExpr(WideStart,
1524 getMulExpr(WideMaxBECount,
1525 getSignExtendExpr(Step, WideTy)));
1526 if (ZAdd == OperandExtendedAdd) {
1527 // Cache knowledge of AR NW, which is propagated to this AddRec.
1528 // Negative step causes unsigned wrap, but it still can't self-wrap.
1529 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1530 // Return the expression with the addrec on the outside.
1531 return getAddRecExpr(
1532 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1533 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1537 // If the backedge is guarded by a comparison with the pre-inc value
1538 // the addrec is safe. Also, if the entry is guarded by a comparison
1539 // with the start value and the backedge is guarded by a comparison
1540 // with the post-inc value, the addrec is safe.
1541 if (isKnownPositive(Step)) {
1542 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
1543 getUnsignedRange(Step).getUnsignedMax());
1544 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
1545 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) &&
1546 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT,
1547 AR->getPostIncExpr(*this), N))) {
1548 // Cache knowledge of AR NUW, which is propagated to this AddRec.
1549 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1550 // Return the expression with the addrec on the outside.
1551 return getAddRecExpr(
1552 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1553 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1555 } else if (isKnownNegative(Step)) {
1556 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
1557 getSignedRange(Step).getSignedMin());
1558 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) ||
1559 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) &&
1560 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT,
1561 AR->getPostIncExpr(*this), N))) {
1562 // Cache knowledge of AR NW, which is propagated to this AddRec.
1563 // Negative step causes unsigned wrap, but it still can't self-wrap.
1564 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1565 // Return the expression with the addrec on the outside.
1566 return getAddRecExpr(
1567 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1568 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1573 if (proveNoWrapByVaryingStart<SCEVZeroExtendExpr>(Start, Step, L)) {
1574 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1575 return getAddRecExpr(
1576 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1577 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1581 // The cast wasn't folded; create an explicit cast node.
1582 // Recompute the insert position, as it may have been invalidated.
1583 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1584 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
1586 UniqueSCEVs.InsertNode(S, IP);
1590 const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op,
1592 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1593 "This is not an extending conversion!");
1594 assert(isSCEVable(Ty) &&
1595 "This is not a conversion to a SCEVable type!");
1596 Ty = getEffectiveSCEVType(Ty);
1598 // Fold if the operand is constant.
1599 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1601 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), Ty)));
1603 // sext(sext(x)) --> sext(x)
1604 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1605 return getSignExtendExpr(SS->getOperand(), Ty);
1607 // sext(zext(x)) --> zext(x)
1608 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1609 return getZeroExtendExpr(SZ->getOperand(), Ty);
1611 // Before doing any expensive analysis, check to see if we've already
1612 // computed a SCEV for this Op and Ty.
1613 FoldingSetNodeID ID;
1614 ID.AddInteger(scSignExtend);
1618 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1620 // If the input value is provably positive, build a zext instead.
1621 if (isKnownNonNegative(Op))
1622 return getZeroExtendExpr(Op, Ty);
1624 // sext(trunc(x)) --> sext(x) or x or trunc(x)
1625 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1626 // It's possible the bits taken off by the truncate were all sign bits. If
1627 // so, we should be able to simplify this further.
1628 const SCEV *X = ST->getOperand();
1629 ConstantRange CR = getSignedRange(X);
1630 unsigned TruncBits = getTypeSizeInBits(ST->getType());
1631 unsigned NewBits = getTypeSizeInBits(Ty);
1632 if (CR.truncate(TruncBits).signExtend(NewBits).contains(
1633 CR.sextOrTrunc(NewBits)))
1634 return getTruncateOrSignExtend(X, Ty);
1637 // sext(C1 + (C2 * x)) --> C1 + sext(C2 * x) if C1 < C2
1638 if (auto SA = dyn_cast<SCEVAddExpr>(Op)) {
1639 if (SA->getNumOperands() == 2) {
1640 auto SC1 = dyn_cast<SCEVConstant>(SA->getOperand(0));
1641 auto SMul = dyn_cast<SCEVMulExpr>(SA->getOperand(1));
1643 if (auto SC2 = dyn_cast<SCEVConstant>(SMul->getOperand(0))) {
1644 const APInt &C1 = SC1->getValue()->getValue();
1645 const APInt &C2 = SC2->getValue()->getValue();
1646 if (C1.isStrictlyPositive() && C2.isStrictlyPositive() &&
1647 C2.ugt(C1) && C2.isPowerOf2())
1648 return getAddExpr(getSignExtendExpr(SC1, Ty),
1649 getSignExtendExpr(SMul, Ty));
1654 // If the input value is a chrec scev, and we can prove that the value
1655 // did not overflow the old, smaller, value, we can sign extend all of the
1656 // operands (often constants). This allows analysis of something like
1657 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
1658 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1659 if (AR->isAffine()) {
1660 const SCEV *Start = AR->getStart();
1661 const SCEV *Step = AR->getStepRecurrence(*this);
1662 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1663 const Loop *L = AR->getLoop();
1665 // If we have special knowledge that this addrec won't overflow,
1666 // we don't need to do any further analysis.
1667 if (AR->getNoWrapFlags(SCEV::FlagNSW))
1668 return getAddRecExpr(
1669 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1670 getSignExtendExpr(Step, Ty), L, SCEV::FlagNSW);
1672 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1673 // Note that this serves two purposes: It filters out loops that are
1674 // simply not analyzable, and it covers the case where this code is
1675 // being called from within backedge-taken count analysis, such that
1676 // attempting to ask for the backedge-taken count would likely result
1677 // in infinite recursion. In the later case, the analysis code will
1678 // cope with a conservative value, and it will take care to purge
1679 // that value once it has finished.
1680 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1681 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1682 // Manually compute the final value for AR, checking for
1685 // Check whether the backedge-taken count can be losslessly casted to
1686 // the addrec's type. The count is always unsigned.
1687 const SCEV *CastedMaxBECount =
1688 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1689 const SCEV *RecastedMaxBECount =
1690 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1691 if (MaxBECount == RecastedMaxBECount) {
1692 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1693 // Check whether Start+Step*MaxBECount has no signed overflow.
1694 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
1695 const SCEV *SAdd = getSignExtendExpr(getAddExpr(Start, SMul), WideTy);
1696 const SCEV *WideStart = getSignExtendExpr(Start, WideTy);
1697 const SCEV *WideMaxBECount =
1698 getZeroExtendExpr(CastedMaxBECount, WideTy);
1699 const SCEV *OperandExtendedAdd =
1700 getAddExpr(WideStart,
1701 getMulExpr(WideMaxBECount,
1702 getSignExtendExpr(Step, WideTy)));
1703 if (SAdd == OperandExtendedAdd) {
1704 // Cache knowledge of AR NSW, which is propagated to this AddRec.
1705 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1706 // Return the expression with the addrec on the outside.
1707 return getAddRecExpr(
1708 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1709 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1711 // Similar to above, only this time treat the step value as unsigned.
1712 // This covers loops that count up with an unsigned step.
1713 OperandExtendedAdd =
1714 getAddExpr(WideStart,
1715 getMulExpr(WideMaxBECount,
1716 getZeroExtendExpr(Step, WideTy)));
1717 if (SAdd == OperandExtendedAdd) {
1718 // If AR wraps around then
1720 // abs(Step) * MaxBECount > unsigned-max(AR->getType())
1721 // => SAdd != OperandExtendedAdd
1723 // Thus (AR is not NW => SAdd != OperandExtendedAdd) <=>
1724 // (SAdd == OperandExtendedAdd => AR is NW)
1726 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1728 // Return the expression with the addrec on the outside.
1729 return getAddRecExpr(
1730 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1731 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1735 // If the backedge is guarded by a comparison with the pre-inc value
1736 // the addrec is safe. Also, if the entry is guarded by a comparison
1737 // with the start value and the backedge is guarded by a comparison
1738 // with the post-inc value, the addrec is safe.
1739 ICmpInst::Predicate Pred;
1740 const SCEV *OverflowLimit =
1741 getSignedOverflowLimitForStep(Step, &Pred, this);
1742 if (OverflowLimit &&
1743 (isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) ||
1744 (isLoopEntryGuardedByCond(L, Pred, Start, OverflowLimit) &&
1745 isLoopBackedgeGuardedByCond(L, Pred, AR->getPostIncExpr(*this),
1747 // Cache knowledge of AR NSW, then propagate NSW to the wide AddRec.
1748 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1749 return getAddRecExpr(
1750 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1751 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1754 // If Start and Step are constants, check if we can apply this
1756 // sext{C1,+,C2} --> C1 + sext{0,+,C2} if C1 < C2
1757 auto SC1 = dyn_cast<SCEVConstant>(Start);
1758 auto SC2 = dyn_cast<SCEVConstant>(Step);
1760 const APInt &C1 = SC1->getValue()->getValue();
1761 const APInt &C2 = SC2->getValue()->getValue();
1762 if (C1.isStrictlyPositive() && C2.isStrictlyPositive() && C2.ugt(C1) &&
1764 Start = getSignExtendExpr(Start, Ty);
1765 const SCEV *NewAR = getAddRecExpr(getConstant(AR->getType(), 0), Step,
1766 L, AR->getNoWrapFlags());
1767 return getAddExpr(Start, getSignExtendExpr(NewAR, Ty));
1771 if (proveNoWrapByVaryingStart<SCEVSignExtendExpr>(Start, Step, L)) {
1772 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1773 return getAddRecExpr(
1774 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1775 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1779 // The cast wasn't folded; create an explicit cast node.
1780 // Recompute the insert position, as it may have been invalidated.
1781 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1782 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
1784 UniqueSCEVs.InsertNode(S, IP);
1788 /// getAnyExtendExpr - Return a SCEV for the given operand extended with
1789 /// unspecified bits out to the given type.
1791 const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
1793 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1794 "This is not an extending conversion!");
1795 assert(isSCEVable(Ty) &&
1796 "This is not a conversion to a SCEVable type!");
1797 Ty = getEffectiveSCEVType(Ty);
1799 // Sign-extend negative constants.
1800 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1801 if (SC->getValue()->getValue().isNegative())
1802 return getSignExtendExpr(Op, Ty);
1804 // Peel off a truncate cast.
1805 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
1806 const SCEV *NewOp = T->getOperand();
1807 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
1808 return getAnyExtendExpr(NewOp, Ty);
1809 return getTruncateOrNoop(NewOp, Ty);
1812 // Next try a zext cast. If the cast is folded, use it.
1813 const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
1814 if (!isa<SCEVZeroExtendExpr>(ZExt))
1817 // Next try a sext cast. If the cast is folded, use it.
1818 const SCEV *SExt = getSignExtendExpr(Op, Ty);
1819 if (!isa<SCEVSignExtendExpr>(SExt))
1822 // Force the cast to be folded into the operands of an addrec.
1823 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
1824 SmallVector<const SCEV *, 4> Ops;
1825 for (const SCEV *Op : AR->operands())
1826 Ops.push_back(getAnyExtendExpr(Op, Ty));
1827 return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW);
1830 // If the expression is obviously signed, use the sext cast value.
1831 if (isa<SCEVSMaxExpr>(Op))
1834 // Absent any other information, use the zext cast value.
1838 /// CollectAddOperandsWithScales - Process the given Ops list, which is
1839 /// a list of operands to be added under the given scale, update the given
1840 /// map. This is a helper function for getAddRecExpr. As an example of
1841 /// what it does, given a sequence of operands that would form an add
1842 /// expression like this:
1844 /// m + n + 13 + (A * (o + p + (B * (q + m + 29)))) + r + (-1 * r)
1846 /// where A and B are constants, update the map with these values:
1848 /// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
1850 /// and add 13 + A*B*29 to AccumulatedConstant.
1851 /// This will allow getAddRecExpr to produce this:
1853 /// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
1855 /// This form often exposes folding opportunities that are hidden in
1856 /// the original operand list.
1858 /// Return true iff it appears that any interesting folding opportunities
1859 /// may be exposed. This helps getAddRecExpr short-circuit extra work in
1860 /// the common case where no interesting opportunities are present, and
1861 /// is also used as a check to avoid infinite recursion.
1864 CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
1865 SmallVectorImpl<const SCEV *> &NewOps,
1866 APInt &AccumulatedConstant,
1867 const SCEV *const *Ops, size_t NumOperands,
1869 ScalarEvolution &SE) {
1870 bool Interesting = false;
1872 // Iterate over the add operands. They are sorted, with constants first.
1874 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1876 // Pull a buried constant out to the outside.
1877 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
1879 AccumulatedConstant += Scale * C->getValue()->getValue();
1882 // Next comes everything else. We're especially interested in multiplies
1883 // here, but they're in the middle, so just visit the rest with one loop.
1884 for (; i != NumOperands; ++i) {
1885 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
1886 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
1888 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue();
1889 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
1890 // A multiplication of a constant with another add; recurse.
1891 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1));
1893 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1894 Add->op_begin(), Add->getNumOperands(),
1897 // A multiplication of a constant with some other value. Update
1899 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
1900 const SCEV *Key = SE.getMulExpr(MulOps);
1901 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1902 M.insert(std::make_pair(Key, NewScale));
1904 NewOps.push_back(Pair.first->first);
1906 Pair.first->second += NewScale;
1907 // The map already had an entry for this value, which may indicate
1908 // a folding opportunity.
1913 // An ordinary operand. Update the map.
1914 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1915 M.insert(std::make_pair(Ops[i], Scale));
1917 NewOps.push_back(Pair.first->first);
1919 Pair.first->second += Scale;
1920 // The map already had an entry for this value, which may indicate
1921 // a folding opportunity.
1931 struct APIntCompare {
1932 bool operator()(const APInt &LHS, const APInt &RHS) const {
1933 return LHS.ult(RHS);
1938 // We're trying to construct a SCEV of type `Type' with `Ops' as operands and
1939 // `OldFlags' as can't-wrap behavior. Infer a more aggressive set of
1940 // can't-overflow flags for the operation if possible.
1941 static SCEV::NoWrapFlags
1942 StrengthenNoWrapFlags(ScalarEvolution *SE, SCEVTypes Type,
1943 const SmallVectorImpl<const SCEV *> &Ops,
1944 SCEV::NoWrapFlags OldFlags) {
1945 using namespace std::placeholders;
1948 Type == scAddExpr || Type == scAddRecExpr || Type == scMulExpr;
1950 assert(CanAnalyze && "don't call from other places!");
1952 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
1953 SCEV::NoWrapFlags SignOrUnsignWrap =
1954 ScalarEvolution::maskFlags(OldFlags, SignOrUnsignMask);
1956 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
1957 auto IsKnownNonNegative =
1958 std::bind(std::mem_fn(&ScalarEvolution::isKnownNonNegative), SE, _1);
1960 if (SignOrUnsignWrap == SCEV::FlagNSW &&
1961 std::all_of(Ops.begin(), Ops.end(), IsKnownNonNegative))
1962 return ScalarEvolution::setFlags(OldFlags,
1963 (SCEV::NoWrapFlags)SignOrUnsignMask);
1968 /// getAddExpr - Get a canonical add expression, or something simpler if
1970 const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
1971 SCEV::NoWrapFlags Flags) {
1972 assert(!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) &&
1973 "only nuw or nsw allowed");
1974 assert(!Ops.empty() && "Cannot get empty add!");
1975 if (Ops.size() == 1) return Ops[0];
1977 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
1978 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1979 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
1980 "SCEVAddExpr operand types don't match!");
1983 Flags = StrengthenNoWrapFlags(this, scAddExpr, Ops, Flags);
1985 // Sort by complexity, this groups all similar expression types together.
1986 GroupByComplexity(Ops, LI);
1988 // If there are any constants, fold them together.
1990 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1992 assert(Idx < Ops.size());
1993 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1994 // We found two constants, fold them together!
1995 Ops[0] = getConstant(LHSC->getValue()->getValue() +
1996 RHSC->getValue()->getValue());
1997 if (Ops.size() == 2) return Ops[0];
1998 Ops.erase(Ops.begin()+1); // Erase the folded element
1999 LHSC = cast<SCEVConstant>(Ops[0]);
2002 // If we are left with a constant zero being added, strip it off.
2003 if (LHSC->getValue()->isZero()) {
2004 Ops.erase(Ops.begin());
2008 if (Ops.size() == 1) return Ops[0];
2011 // Okay, check to see if the same value occurs in the operand list more than
2012 // once. If so, merge them together into an multiply expression. Since we
2013 // sorted the list, these values are required to be adjacent.
2014 Type *Ty = Ops[0]->getType();
2015 bool FoundMatch = false;
2016 for (unsigned i = 0, e = Ops.size(); i != e-1; ++i)
2017 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
2018 // Scan ahead to count how many equal operands there are.
2020 while (i+Count != e && Ops[i+Count] == Ops[i])
2022 // Merge the values into a multiply.
2023 const SCEV *Scale = getConstant(Ty, Count);
2024 const SCEV *Mul = getMulExpr(Scale, Ops[i]);
2025 if (Ops.size() == Count)
2028 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count);
2029 --i; e -= Count - 1;
2033 return getAddExpr(Ops, Flags);
2035 // Check for truncates. If all the operands are truncated from the same
2036 // type, see if factoring out the truncate would permit the result to be
2037 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
2038 // if the contents of the resulting outer trunc fold to something simple.
2039 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
2040 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
2041 Type *DstType = Trunc->getType();
2042 Type *SrcType = Trunc->getOperand()->getType();
2043 SmallVector<const SCEV *, 8> LargeOps;
2045 // Check all the operands to see if they can be represented in the
2046 // source type of the truncate.
2047 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
2048 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
2049 if (T->getOperand()->getType() != SrcType) {
2053 LargeOps.push_back(T->getOperand());
2054 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
2055 LargeOps.push_back(getAnyExtendExpr(C, SrcType));
2056 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
2057 SmallVector<const SCEV *, 8> LargeMulOps;
2058 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
2059 if (const SCEVTruncateExpr *T =
2060 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
2061 if (T->getOperand()->getType() != SrcType) {
2065 LargeMulOps.push_back(T->getOperand());
2066 } else if (const SCEVConstant *C =
2067 dyn_cast<SCEVConstant>(M->getOperand(j))) {
2068 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType));
2075 LargeOps.push_back(getMulExpr(LargeMulOps));
2082 // Evaluate the expression in the larger type.
2083 const SCEV *Fold = getAddExpr(LargeOps, Flags);
2084 // If it folds to something simple, use it. Otherwise, don't.
2085 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
2086 return getTruncateExpr(Fold, DstType);
2090 // Skip past any other cast SCEVs.
2091 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
2094 // If there are add operands they would be next.
2095 if (Idx < Ops.size()) {
2096 bool DeletedAdd = false;
2097 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
2098 // If we have an add, expand the add operands onto the end of the operands
2100 Ops.erase(Ops.begin()+Idx);
2101 Ops.append(Add->op_begin(), Add->op_end());
2105 // If we deleted at least one add, we added operands to the end of the list,
2106 // and they are not necessarily sorted. Recurse to resort and resimplify
2107 // any operands we just acquired.
2109 return getAddExpr(Ops);
2112 // Skip over the add expression until we get to a multiply.
2113 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
2116 // Check to see if there are any folding opportunities present with
2117 // operands multiplied by constant values.
2118 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
2119 uint64_t BitWidth = getTypeSizeInBits(Ty);
2120 DenseMap<const SCEV *, APInt> M;
2121 SmallVector<const SCEV *, 8> NewOps;
2122 APInt AccumulatedConstant(BitWidth, 0);
2123 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
2124 Ops.data(), Ops.size(),
2125 APInt(BitWidth, 1), *this)) {
2126 // Some interesting folding opportunity is present, so its worthwhile to
2127 // re-generate the operands list. Group the operands by constant scale,
2128 // to avoid multiplying by the same constant scale multiple times.
2129 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
2130 for (SmallVectorImpl<const SCEV *>::const_iterator I = NewOps.begin(),
2131 E = NewOps.end(); I != E; ++I)
2132 MulOpLists[M.find(*I)->second].push_back(*I);
2133 // Re-generate the operands list.
2135 if (AccumulatedConstant != 0)
2136 Ops.push_back(getConstant(AccumulatedConstant));
2137 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator
2138 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I)
2140 Ops.push_back(getMulExpr(getConstant(I->first),
2141 getAddExpr(I->second)));
2143 return getConstant(Ty, 0);
2144 if (Ops.size() == 1)
2146 return getAddExpr(Ops);
2150 // If we are adding something to a multiply expression, make sure the
2151 // something is not already an operand of the multiply. If so, merge it into
2153 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
2154 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
2155 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
2156 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
2157 if (isa<SCEVConstant>(MulOpSCEV))
2159 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
2160 if (MulOpSCEV == Ops[AddOp]) {
2161 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
2162 const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
2163 if (Mul->getNumOperands() != 2) {
2164 // If the multiply has more than two operands, we must get the
2166 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
2167 Mul->op_begin()+MulOp);
2168 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
2169 InnerMul = getMulExpr(MulOps);
2171 const SCEV *One = getConstant(Ty, 1);
2172 const SCEV *AddOne = getAddExpr(One, InnerMul);
2173 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV);
2174 if (Ops.size() == 2) return OuterMul;
2176 Ops.erase(Ops.begin()+AddOp);
2177 Ops.erase(Ops.begin()+Idx-1);
2179 Ops.erase(Ops.begin()+Idx);
2180 Ops.erase(Ops.begin()+AddOp-1);
2182 Ops.push_back(OuterMul);
2183 return getAddExpr(Ops);
2186 // Check this multiply against other multiplies being added together.
2187 for (unsigned OtherMulIdx = Idx+1;
2188 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
2190 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
2191 // If MulOp occurs in OtherMul, we can fold the two multiplies
2193 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
2194 OMulOp != e; ++OMulOp)
2195 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
2196 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
2197 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
2198 if (Mul->getNumOperands() != 2) {
2199 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
2200 Mul->op_begin()+MulOp);
2201 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
2202 InnerMul1 = getMulExpr(MulOps);
2204 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
2205 if (OtherMul->getNumOperands() != 2) {
2206 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
2207 OtherMul->op_begin()+OMulOp);
2208 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end());
2209 InnerMul2 = getMulExpr(MulOps);
2211 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
2212 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
2213 if (Ops.size() == 2) return OuterMul;
2214 Ops.erase(Ops.begin()+Idx);
2215 Ops.erase(Ops.begin()+OtherMulIdx-1);
2216 Ops.push_back(OuterMul);
2217 return getAddExpr(Ops);
2223 // If there are any add recurrences in the operands list, see if any other
2224 // added values are loop invariant. If so, we can fold them into the
2226 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2229 // Scan over all recurrences, trying to fold loop invariants into them.
2230 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
2231 // Scan all of the other operands to this add and add them to the vector if
2232 // they are loop invariant w.r.t. the recurrence.
2233 SmallVector<const SCEV *, 8> LIOps;
2234 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2235 const Loop *AddRecLoop = AddRec->getLoop();
2236 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2237 if (isLoopInvariant(Ops[i], AddRecLoop)) {
2238 LIOps.push_back(Ops[i]);
2239 Ops.erase(Ops.begin()+i);
2243 // If we found some loop invariants, fold them into the recurrence.
2244 if (!LIOps.empty()) {
2245 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
2246 LIOps.push_back(AddRec->getStart());
2248 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
2250 AddRecOps[0] = getAddExpr(LIOps);
2252 // Build the new addrec. Propagate the NUW and NSW flags if both the
2253 // outer add and the inner addrec are guaranteed to have no overflow.
2254 // Always propagate NW.
2255 Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW));
2256 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags);
2258 // If all of the other operands were loop invariant, we are done.
2259 if (Ops.size() == 1) return NewRec;
2261 // Otherwise, add the folded AddRec by the non-invariant parts.
2262 for (unsigned i = 0;; ++i)
2263 if (Ops[i] == AddRec) {
2267 return getAddExpr(Ops);
2270 // Okay, if there weren't any loop invariants to be folded, check to see if
2271 // there are multiple AddRec's with the same loop induction variable being
2272 // added together. If so, we can fold them.
2273 for (unsigned OtherIdx = Idx+1;
2274 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2276 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
2277 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L>
2278 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
2280 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2282 if (const SCEVAddRecExpr *OtherAddRec =
2283 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]))
2284 if (OtherAddRec->getLoop() == AddRecLoop) {
2285 for (unsigned i = 0, e = OtherAddRec->getNumOperands();
2287 if (i >= AddRecOps.size()) {
2288 AddRecOps.append(OtherAddRec->op_begin()+i,
2289 OtherAddRec->op_end());
2292 AddRecOps[i] = getAddExpr(AddRecOps[i],
2293 OtherAddRec->getOperand(i));
2295 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2297 // Step size has changed, so we cannot guarantee no self-wraparound.
2298 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap);
2299 return getAddExpr(Ops);
2302 // Otherwise couldn't fold anything into this recurrence. Move onto the
2306 // Okay, it looks like we really DO need an add expr. Check to see if we
2307 // already have one, otherwise create a new one.
2308 FoldingSetNodeID ID;
2309 ID.AddInteger(scAddExpr);
2310 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2311 ID.AddPointer(Ops[i]);
2314 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2316 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2317 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2318 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator),
2320 UniqueSCEVs.InsertNode(S, IP);
2322 S->setNoWrapFlags(Flags);
2326 static uint64_t umul_ov(uint64_t i, uint64_t j, bool &Overflow) {
2328 if (j > 1 && k / j != i) Overflow = true;
2332 /// Compute the result of "n choose k", the binomial coefficient. If an
2333 /// intermediate computation overflows, Overflow will be set and the return will
2334 /// be garbage. Overflow is not cleared on absence of overflow.
2335 static uint64_t Choose(uint64_t n, uint64_t k, bool &Overflow) {
2336 // We use the multiplicative formula:
2337 // n(n-1)(n-2)...(n-(k-1)) / k(k-1)(k-2)...1 .
2338 // At each iteration, we take the n-th term of the numeral and divide by the
2339 // (k-n)th term of the denominator. This division will always produce an
2340 // integral result, and helps reduce the chance of overflow in the
2341 // intermediate computations. However, we can still overflow even when the
2342 // final result would fit.
2344 if (n == 0 || n == k) return 1;
2345 if (k > n) return 0;
2351 for (uint64_t i = 1; i <= k; ++i) {
2352 r = umul_ov(r, n-(i-1), Overflow);
2358 /// Determine if any of the operands in this SCEV are a constant or if
2359 /// any of the add or multiply expressions in this SCEV contain a constant.
2360 static bool containsConstantSomewhere(const SCEV *StartExpr) {
2361 SmallVector<const SCEV *, 4> Ops;
2362 Ops.push_back(StartExpr);
2363 while (!Ops.empty()) {
2364 const SCEV *CurrentExpr = Ops.pop_back_val();
2365 if (isa<SCEVConstant>(*CurrentExpr))
2368 if (isa<SCEVAddExpr>(*CurrentExpr) || isa<SCEVMulExpr>(*CurrentExpr)) {
2369 const auto *CurrentNAry = cast<SCEVNAryExpr>(CurrentExpr);
2370 Ops.append(CurrentNAry->op_begin(), CurrentNAry->op_end());
2376 /// getMulExpr - Get a canonical multiply expression, or something simpler if
2378 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
2379 SCEV::NoWrapFlags Flags) {
2380 assert(Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) &&
2381 "only nuw or nsw allowed");
2382 assert(!Ops.empty() && "Cannot get empty mul!");
2383 if (Ops.size() == 1) return Ops[0];
2385 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2386 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2387 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2388 "SCEVMulExpr operand types don't match!");
2391 Flags = StrengthenNoWrapFlags(this, scMulExpr, Ops, Flags);
2393 // Sort by complexity, this groups all similar expression types together.
2394 GroupByComplexity(Ops, LI);
2396 // If there are any constants, fold them together.
2398 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2400 // C1*(C2+V) -> C1*C2 + C1*V
2401 if (Ops.size() == 2)
2402 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
2403 // If any of Add's ops are Adds or Muls with a constant,
2404 // apply this transformation as well.
2405 if (Add->getNumOperands() == 2)
2406 if (containsConstantSomewhere(Add))
2407 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
2408 getMulExpr(LHSC, Add->getOperand(1)));
2411 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2412 // We found two constants, fold them together!
2413 ConstantInt *Fold = ConstantInt::get(getContext(),
2414 LHSC->getValue()->getValue() *
2415 RHSC->getValue()->getValue());
2416 Ops[0] = getConstant(Fold);
2417 Ops.erase(Ops.begin()+1); // Erase the folded element
2418 if (Ops.size() == 1) return Ops[0];
2419 LHSC = cast<SCEVConstant>(Ops[0]);
2422 // If we are left with a constant one being multiplied, strip it off.
2423 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
2424 Ops.erase(Ops.begin());
2426 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
2427 // If we have a multiply of zero, it will always be zero.
2429 } else if (Ops[0]->isAllOnesValue()) {
2430 // If we have a mul by -1 of an add, try distributing the -1 among the
2432 if (Ops.size() == 2) {
2433 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
2434 SmallVector<const SCEV *, 4> NewOps;
2435 bool AnyFolded = false;
2436 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(),
2437 E = Add->op_end(); I != E; ++I) {
2438 const SCEV *Mul = getMulExpr(Ops[0], *I);
2439 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
2440 NewOps.push_back(Mul);
2443 return getAddExpr(NewOps);
2445 else if (const SCEVAddRecExpr *
2446 AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) {
2447 // Negation preserves a recurrence's no self-wrap property.
2448 SmallVector<const SCEV *, 4> Operands;
2449 for (SCEVAddRecExpr::op_iterator I = AddRec->op_begin(),
2450 E = AddRec->op_end(); I != E; ++I) {
2451 Operands.push_back(getMulExpr(Ops[0], *I));
2453 return getAddRecExpr(Operands, AddRec->getLoop(),
2454 AddRec->getNoWrapFlags(SCEV::FlagNW));
2459 if (Ops.size() == 1)
2463 // Skip over the add expression until we get to a multiply.
2464 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
2467 // If there are mul operands inline them all into this expression.
2468 if (Idx < Ops.size()) {
2469 bool DeletedMul = false;
2470 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
2471 // If we have an mul, expand the mul operands onto the end of the operands
2473 Ops.erase(Ops.begin()+Idx);
2474 Ops.append(Mul->op_begin(), Mul->op_end());
2478 // If we deleted at least one mul, we added operands to the end of the list,
2479 // and they are not necessarily sorted. Recurse to resort and resimplify
2480 // any operands we just acquired.
2482 return getMulExpr(Ops);
2485 // If there are any add recurrences in the operands list, see if any other
2486 // added values are loop invariant. If so, we can fold them into the
2488 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2491 // Scan over all recurrences, trying to fold loop invariants into them.
2492 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
2493 // Scan all of the other operands to this mul and add them to the vector if
2494 // they are loop invariant w.r.t. the recurrence.
2495 SmallVector<const SCEV *, 8> LIOps;
2496 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2497 const Loop *AddRecLoop = AddRec->getLoop();
2498 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2499 if (isLoopInvariant(Ops[i], AddRecLoop)) {
2500 LIOps.push_back(Ops[i]);
2501 Ops.erase(Ops.begin()+i);
2505 // If we found some loop invariants, fold them into the recurrence.
2506 if (!LIOps.empty()) {
2507 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
2508 SmallVector<const SCEV *, 4> NewOps;
2509 NewOps.reserve(AddRec->getNumOperands());
2510 const SCEV *Scale = getMulExpr(LIOps);
2511 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
2512 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
2514 // Build the new addrec. Propagate the NUW and NSW flags if both the
2515 // outer mul and the inner addrec are guaranteed to have no overflow.
2517 // No self-wrap cannot be guaranteed after changing the step size, but
2518 // will be inferred if either NUW or NSW is true.
2519 Flags = AddRec->getNoWrapFlags(clearFlags(Flags, SCEV::FlagNW));
2520 const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, Flags);
2522 // If all of the other operands were loop invariant, we are done.
2523 if (Ops.size() == 1) return NewRec;
2525 // Otherwise, multiply the folded AddRec by the non-invariant parts.
2526 for (unsigned i = 0;; ++i)
2527 if (Ops[i] == AddRec) {
2531 return getMulExpr(Ops);
2534 // Okay, if there weren't any loop invariants to be folded, check to see if
2535 // there are multiple AddRec's with the same loop induction variable being
2536 // multiplied together. If so, we can fold them.
2538 // {A1,+,A2,+,...,+,An}<L> * {B1,+,B2,+,...,+,Bn}<L>
2539 // = {x=1 in [ sum y=x..2x [ sum z=max(y-x, y-n)..min(x,n) [
2540 // choose(x, 2x)*choose(2x-y, x-z)*A_{y-z}*B_z
2541 // ]]],+,...up to x=2n}.
2542 // Note that the arguments to choose() are always integers with values
2543 // known at compile time, never SCEV objects.
2545 // The implementation avoids pointless extra computations when the two
2546 // addrec's are of different length (mathematically, it's equivalent to
2547 // an infinite stream of zeros on the right).
2548 bool OpsModified = false;
2549 for (unsigned OtherIdx = Idx+1;
2550 OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2552 const SCEVAddRecExpr *OtherAddRec =
2553 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]);
2554 if (!OtherAddRec || OtherAddRec->getLoop() != AddRecLoop)
2557 bool Overflow = false;
2558 Type *Ty = AddRec->getType();
2559 bool LargerThan64Bits = getTypeSizeInBits(Ty) > 64;
2560 SmallVector<const SCEV*, 7> AddRecOps;
2561 for (int x = 0, xe = AddRec->getNumOperands() +
2562 OtherAddRec->getNumOperands() - 1; x != xe && !Overflow; ++x) {
2563 const SCEV *Term = getConstant(Ty, 0);
2564 for (int y = x, ye = 2*x+1; y != ye && !Overflow; ++y) {
2565 uint64_t Coeff1 = Choose(x, 2*x - y, Overflow);
2566 for (int z = std::max(y-x, y-(int)AddRec->getNumOperands()+1),
2567 ze = std::min(x+1, (int)OtherAddRec->getNumOperands());
2568 z < ze && !Overflow; ++z) {
2569 uint64_t Coeff2 = Choose(2*x - y, x-z, Overflow);
2571 if (LargerThan64Bits)
2572 Coeff = umul_ov(Coeff1, Coeff2, Overflow);
2574 Coeff = Coeff1*Coeff2;
2575 const SCEV *CoeffTerm = getConstant(Ty, Coeff);
2576 const SCEV *Term1 = AddRec->getOperand(y-z);
2577 const SCEV *Term2 = OtherAddRec->getOperand(z);
2578 Term = getAddExpr(Term, getMulExpr(CoeffTerm, Term1,Term2));
2581 AddRecOps.push_back(Term);
2584 const SCEV *NewAddRec = getAddRecExpr(AddRecOps, AddRec->getLoop(),
2586 if (Ops.size() == 2) return NewAddRec;
2587 Ops[Idx] = NewAddRec;
2588 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2590 AddRec = dyn_cast<SCEVAddRecExpr>(NewAddRec);
2596 return getMulExpr(Ops);
2598 // Otherwise couldn't fold anything into this recurrence. Move onto the
2602 // Okay, it looks like we really DO need an mul expr. Check to see if we
2603 // already have one, otherwise create a new one.
2604 FoldingSetNodeID ID;
2605 ID.AddInteger(scMulExpr);
2606 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2607 ID.AddPointer(Ops[i]);
2610 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2612 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2613 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2614 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
2616 UniqueSCEVs.InsertNode(S, IP);
2618 S->setNoWrapFlags(Flags);
2622 /// getUDivExpr - Get a canonical unsigned division expression, or something
2623 /// simpler if possible.
2624 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
2626 assert(getEffectiveSCEVType(LHS->getType()) ==
2627 getEffectiveSCEVType(RHS->getType()) &&
2628 "SCEVUDivExpr operand types don't match!");
2630 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
2631 if (RHSC->getValue()->equalsInt(1))
2632 return LHS; // X udiv 1 --> x
2633 // If the denominator is zero, the result of the udiv is undefined. Don't
2634 // try to analyze it, because the resolution chosen here may differ from
2635 // the resolution chosen in other parts of the compiler.
2636 if (!RHSC->getValue()->isZero()) {
2637 // Determine if the division can be folded into the operands of
2639 // TODO: Generalize this to non-constants by using known-bits information.
2640 Type *Ty = LHS->getType();
2641 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
2642 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1;
2643 // For non-power-of-two values, effectively round the value up to the
2644 // nearest power of two.
2645 if (!RHSC->getValue()->getValue().isPowerOf2())
2647 IntegerType *ExtTy =
2648 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
2649 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
2650 if (const SCEVConstant *Step =
2651 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) {
2652 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
2653 const APInt &StepInt = Step->getValue()->getValue();
2654 const APInt &DivInt = RHSC->getValue()->getValue();
2655 if (!StepInt.urem(DivInt) &&
2656 getZeroExtendExpr(AR, ExtTy) ==
2657 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2658 getZeroExtendExpr(Step, ExtTy),
2659 AR->getLoop(), SCEV::FlagAnyWrap)) {
2660 SmallVector<const SCEV *, 4> Operands;
2661 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i)
2662 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS));
2663 return getAddRecExpr(Operands, AR->getLoop(),
2666 /// Get a canonical UDivExpr for a recurrence.
2667 /// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0.
2668 // We can currently only fold X%N if X is constant.
2669 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(AR->getStart());
2670 if (StartC && !DivInt.urem(StepInt) &&
2671 getZeroExtendExpr(AR, ExtTy) ==
2672 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2673 getZeroExtendExpr(Step, ExtTy),
2674 AR->getLoop(), SCEV::FlagAnyWrap)) {
2675 const APInt &StartInt = StartC->getValue()->getValue();
2676 const APInt &StartRem = StartInt.urem(StepInt);
2678 LHS = getAddRecExpr(getConstant(StartInt - StartRem), Step,
2679 AR->getLoop(), SCEV::FlagNW);
2682 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
2683 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
2684 SmallVector<const SCEV *, 4> Operands;
2685 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i)
2686 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy));
2687 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
2688 // Find an operand that's safely divisible.
2689 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
2690 const SCEV *Op = M->getOperand(i);
2691 const SCEV *Div = getUDivExpr(Op, RHSC);
2692 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
2693 Operands = SmallVector<const SCEV *, 4>(M->op_begin(),
2696 return getMulExpr(Operands);
2700 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
2701 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) {
2702 SmallVector<const SCEV *, 4> Operands;
2703 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i)
2704 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy));
2705 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
2707 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
2708 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
2709 if (isa<SCEVUDivExpr>(Op) ||
2710 getMulExpr(Op, RHS) != A->getOperand(i))
2712 Operands.push_back(Op);
2714 if (Operands.size() == A->getNumOperands())
2715 return getAddExpr(Operands);
2719 // Fold if both operands are constant.
2720 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
2721 Constant *LHSCV = LHSC->getValue();
2722 Constant *RHSCV = RHSC->getValue();
2723 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
2729 FoldingSetNodeID ID;
2730 ID.AddInteger(scUDivExpr);
2734 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2735 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
2737 UniqueSCEVs.InsertNode(S, IP);
2741 static const APInt gcd(const SCEVConstant *C1, const SCEVConstant *C2) {
2742 APInt A = C1->getValue()->getValue().abs();
2743 APInt B = C2->getValue()->getValue().abs();
2744 uint32_t ABW = A.getBitWidth();
2745 uint32_t BBW = B.getBitWidth();
2752 return APIntOps::GreatestCommonDivisor(A, B);
2755 /// getUDivExactExpr - Get a canonical unsigned division expression, or
2756 /// something simpler if possible. There is no representation for an exact udiv
2757 /// in SCEV IR, but we can attempt to remove factors from the LHS and RHS.
2758 /// We can't do this when it's not exact because the udiv may be clearing bits.
2759 const SCEV *ScalarEvolution::getUDivExactExpr(const SCEV *LHS,
2761 // TODO: we could try to find factors in all sorts of things, but for now we
2762 // just deal with u/exact (multiply, constant). See SCEVDivision towards the
2763 // end of this file for inspiration.
2765 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(LHS);
2767 return getUDivExpr(LHS, RHS);
2769 if (const SCEVConstant *RHSCst = dyn_cast<SCEVConstant>(RHS)) {
2770 // If the mulexpr multiplies by a constant, then that constant must be the
2771 // first element of the mulexpr.
2772 if (const SCEVConstant *LHSCst =
2773 dyn_cast<SCEVConstant>(Mul->getOperand(0))) {
2774 if (LHSCst == RHSCst) {
2775 SmallVector<const SCEV *, 2> Operands;
2776 Operands.append(Mul->op_begin() + 1, Mul->op_end());
2777 return getMulExpr(Operands);
2780 // We can't just assume that LHSCst divides RHSCst cleanly, it could be
2781 // that there's a factor provided by one of the other terms. We need to
2783 APInt Factor = gcd(LHSCst, RHSCst);
2784 if (!Factor.isIntN(1)) {
2785 LHSCst = cast<SCEVConstant>(
2786 getConstant(LHSCst->getValue()->getValue().udiv(Factor)));
2787 RHSCst = cast<SCEVConstant>(
2788 getConstant(RHSCst->getValue()->getValue().udiv(Factor)));
2789 SmallVector<const SCEV *, 2> Operands;
2790 Operands.push_back(LHSCst);
2791 Operands.append(Mul->op_begin() + 1, Mul->op_end());
2792 LHS = getMulExpr(Operands);
2794 Mul = dyn_cast<SCEVMulExpr>(LHS);
2796 return getUDivExactExpr(LHS, RHS);
2801 for (int i = 0, e = Mul->getNumOperands(); i != e; ++i) {
2802 if (Mul->getOperand(i) == RHS) {
2803 SmallVector<const SCEV *, 2> Operands;
2804 Operands.append(Mul->op_begin(), Mul->op_begin() + i);
2805 Operands.append(Mul->op_begin() + i + 1, Mul->op_end());
2806 return getMulExpr(Operands);
2810 return getUDivExpr(LHS, RHS);
2813 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2814 /// Simplify the expression as much as possible.
2815 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step,
2817 SCEV::NoWrapFlags Flags) {
2818 SmallVector<const SCEV *, 4> Operands;
2819 Operands.push_back(Start);
2820 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
2821 if (StepChrec->getLoop() == L) {
2822 Operands.append(StepChrec->op_begin(), StepChrec->op_end());
2823 return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW));
2826 Operands.push_back(Step);
2827 return getAddRecExpr(Operands, L, Flags);
2830 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2831 /// Simplify the expression as much as possible.
2833 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
2834 const Loop *L, SCEV::NoWrapFlags Flags) {
2835 if (Operands.size() == 1) return Operands[0];
2837 Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
2838 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
2839 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy &&
2840 "SCEVAddRecExpr operand types don't match!");
2841 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2842 assert(isLoopInvariant(Operands[i], L) &&
2843 "SCEVAddRecExpr operand is not loop-invariant!");
2846 if (Operands.back()->isZero()) {
2847 Operands.pop_back();
2848 return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0} --> X
2851 // It's tempting to want to call getMaxBackedgeTakenCount count here and
2852 // use that information to infer NUW and NSW flags. However, computing a
2853 // BE count requires calling getAddRecExpr, so we may not yet have a
2854 // meaningful BE count at this point (and if we don't, we'd be stuck
2855 // with a SCEVCouldNotCompute as the cached BE count).
2857 Flags = StrengthenNoWrapFlags(this, scAddRecExpr, Operands, Flags);
2859 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
2860 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
2861 const Loop *NestedLoop = NestedAR->getLoop();
2862 if (L->contains(NestedLoop) ?
2863 (L->getLoopDepth() < NestedLoop->getLoopDepth()) :
2864 (!NestedLoop->contains(L) &&
2865 DT->dominates(L->getHeader(), NestedLoop->getHeader()))) {
2866 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
2867 NestedAR->op_end());
2868 Operands[0] = NestedAR->getStart();
2869 // AddRecs require their operands be loop-invariant with respect to their
2870 // loops. Don't perform this transformation if it would break this
2872 bool AllInvariant = true;
2873 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2874 if (!isLoopInvariant(Operands[i], L)) {
2875 AllInvariant = false;
2879 // Create a recurrence for the outer loop with the same step size.
2881 // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the
2882 // inner recurrence has the same property.
2883 SCEV::NoWrapFlags OuterFlags =
2884 maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags());
2886 NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags);
2887 AllInvariant = true;
2888 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i)
2889 if (!isLoopInvariant(NestedOperands[i], NestedLoop)) {
2890 AllInvariant = false;
2894 // Ok, both add recurrences are valid after the transformation.
2896 // The inner recurrence keeps its NW flag but only keeps NUW/NSW if
2897 // the outer recurrence has the same property.
2898 SCEV::NoWrapFlags InnerFlags =
2899 maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags);
2900 return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags);
2903 // Reset Operands to its original state.
2904 Operands[0] = NestedAR;
2908 // Okay, it looks like we really DO need an addrec expr. Check to see if we
2909 // already have one, otherwise create a new one.
2910 FoldingSetNodeID ID;
2911 ID.AddInteger(scAddRecExpr);
2912 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2913 ID.AddPointer(Operands[i]);
2917 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2919 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size());
2920 std::uninitialized_copy(Operands.begin(), Operands.end(), O);
2921 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator),
2922 O, Operands.size(), L);
2923 UniqueSCEVs.InsertNode(S, IP);
2925 S->setNoWrapFlags(Flags);
2930 ScalarEvolution::getGEPExpr(Type *PointeeType, const SCEV *BaseExpr,
2931 const SmallVectorImpl<const SCEV *> &IndexExprs,
2933 // getSCEV(Base)->getType() has the same address space as Base->getType()
2934 // because SCEV::getType() preserves the address space.
2935 Type *IntPtrTy = getEffectiveSCEVType(BaseExpr->getType());
2936 // FIXME(PR23527): Don't blindly transfer the inbounds flag from the GEP
2937 // instruction to its SCEV, because the Instruction may be guarded by control
2938 // flow and the no-overflow bits may not be valid for the expression in any
2940 SCEV::NoWrapFlags Wrap = InBounds ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
2942 const SCEV *TotalOffset = getConstant(IntPtrTy, 0);
2943 // The address space is unimportant. The first thing we do on CurTy is getting
2944 // its element type.
2945 Type *CurTy = PointerType::getUnqual(PointeeType);
2946 for (const SCEV *IndexExpr : IndexExprs) {
2947 // Compute the (potentially symbolic) offset in bytes for this index.
2948 if (StructType *STy = dyn_cast<StructType>(CurTy)) {
2949 // For a struct, add the member offset.
2950 ConstantInt *Index = cast<SCEVConstant>(IndexExpr)->getValue();
2951 unsigned FieldNo = Index->getZExtValue();
2952 const SCEV *FieldOffset = getOffsetOfExpr(IntPtrTy, STy, FieldNo);
2954 // Add the field offset to the running total offset.
2955 TotalOffset = getAddExpr(TotalOffset, FieldOffset);
2957 // Update CurTy to the type of the field at Index.
2958 CurTy = STy->getTypeAtIndex(Index);
2960 // Update CurTy to its element type.
2961 CurTy = cast<SequentialType>(CurTy)->getElementType();
2962 // For an array, add the element offset, explicitly scaled.
2963 const SCEV *ElementSize = getSizeOfExpr(IntPtrTy, CurTy);
2964 // Getelementptr indices are signed.
2965 IndexExpr = getTruncateOrSignExtend(IndexExpr, IntPtrTy);
2967 // Multiply the index by the element size to compute the element offset.
2968 const SCEV *LocalOffset = getMulExpr(IndexExpr, ElementSize, Wrap);
2970 // Add the element offset to the running total offset.
2971 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
2975 // Add the total offset from all the GEP indices to the base.
2976 return getAddExpr(BaseExpr, TotalOffset, Wrap);
2979 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
2981 SmallVector<const SCEV *, 2> Ops;
2984 return getSMaxExpr(Ops);
2988 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2989 assert(!Ops.empty() && "Cannot get empty smax!");
2990 if (Ops.size() == 1) return Ops[0];
2992 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2993 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2994 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2995 "SCEVSMaxExpr operand types don't match!");
2998 // Sort by complexity, this groups all similar expression types together.
2999 GroupByComplexity(Ops, LI);
3001 // If there are any constants, fold them together.
3003 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
3005 assert(Idx < Ops.size());
3006 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
3007 // We found two constants, fold them together!
3008 ConstantInt *Fold = ConstantInt::get(getContext(),
3009 APIntOps::smax(LHSC->getValue()->getValue(),
3010 RHSC->getValue()->getValue()));
3011 Ops[0] = getConstant(Fold);
3012 Ops.erase(Ops.begin()+1); // Erase the folded element
3013 if (Ops.size() == 1) return Ops[0];
3014 LHSC = cast<SCEVConstant>(Ops[0]);
3017 // If we are left with a constant minimum-int, strip it off.
3018 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
3019 Ops.erase(Ops.begin());
3021 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
3022 // If we have an smax with a constant maximum-int, it will always be
3027 if (Ops.size() == 1) return Ops[0];
3030 // Find the first SMax
3031 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
3034 // Check to see if one of the operands is an SMax. If so, expand its operands
3035 // onto our operand list, and recurse to simplify.
3036 if (Idx < Ops.size()) {
3037 bool DeletedSMax = false;
3038 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
3039 Ops.erase(Ops.begin()+Idx);
3040 Ops.append(SMax->op_begin(), SMax->op_end());
3045 return getSMaxExpr(Ops);
3048 // Okay, check to see if the same value occurs in the operand list twice. If
3049 // so, delete one. Since we sorted the list, these values are required to
3051 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
3052 // X smax Y smax Y --> X smax Y
3053 // X smax Y --> X, if X is always greater than Y
3054 if (Ops[i] == Ops[i+1] ||
3055 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) {
3056 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
3058 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) {
3059 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
3063 if (Ops.size() == 1) return Ops[0];
3065 assert(!Ops.empty() && "Reduced smax down to nothing!");
3067 // Okay, it looks like we really DO need an smax expr. Check to see if we
3068 // already have one, otherwise create a new one.
3069 FoldingSetNodeID ID;
3070 ID.AddInteger(scSMaxExpr);
3071 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
3072 ID.AddPointer(Ops[i]);
3074 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
3075 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
3076 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
3077 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator),
3079 UniqueSCEVs.InsertNode(S, IP);
3083 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
3085 SmallVector<const SCEV *, 2> Ops;
3088 return getUMaxExpr(Ops);
3092 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
3093 assert(!Ops.empty() && "Cannot get empty umax!");
3094 if (Ops.size() == 1) return Ops[0];
3096 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
3097 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
3098 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
3099 "SCEVUMaxExpr operand types don't match!");
3102 // Sort by complexity, this groups all similar expression types together.
3103 GroupByComplexity(Ops, LI);
3105 // If there are any constants, fold them together.
3107 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
3109 assert(Idx < Ops.size());
3110 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
3111 // We found two constants, fold them together!
3112 ConstantInt *Fold = ConstantInt::get(getContext(),
3113 APIntOps::umax(LHSC->getValue()->getValue(),
3114 RHSC->getValue()->getValue()));
3115 Ops[0] = getConstant(Fold);
3116 Ops.erase(Ops.begin()+1); // Erase the folded element
3117 if (Ops.size() == 1) return Ops[0];
3118 LHSC = cast<SCEVConstant>(Ops[0]);
3121 // If we are left with a constant minimum-int, strip it off.
3122 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
3123 Ops.erase(Ops.begin());
3125 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
3126 // If we have an umax with a constant maximum-int, it will always be
3131 if (Ops.size() == 1) return Ops[0];
3134 // Find the first UMax
3135 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
3138 // Check to see if one of the operands is a UMax. If so, expand its operands
3139 // onto our operand list, and recurse to simplify.
3140 if (Idx < Ops.size()) {
3141 bool DeletedUMax = false;
3142 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
3143 Ops.erase(Ops.begin()+Idx);
3144 Ops.append(UMax->op_begin(), UMax->op_end());
3149 return getUMaxExpr(Ops);
3152 // Okay, check to see if the same value occurs in the operand list twice. If
3153 // so, delete one. Since we sorted the list, these values are required to
3155 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
3156 // X umax Y umax Y --> X umax Y
3157 // X umax Y --> X, if X is always greater than Y
3158 if (Ops[i] == Ops[i+1] ||
3159 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) {
3160 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
3162 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) {
3163 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
3167 if (Ops.size() == 1) return Ops[0];
3169 assert(!Ops.empty() && "Reduced umax down to nothing!");
3171 // Okay, it looks like we really DO need a umax expr. Check to see if we
3172 // already have one, otherwise create a new one.
3173 FoldingSetNodeID ID;
3174 ID.AddInteger(scUMaxExpr);
3175 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
3176 ID.AddPointer(Ops[i]);
3178 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
3179 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
3180 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
3181 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator),
3183 UniqueSCEVs.InsertNode(S, IP);
3187 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
3189 // ~smax(~x, ~y) == smin(x, y).
3190 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
3193 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
3195 // ~umax(~x, ~y) == umin(x, y)
3196 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
3199 const SCEV *ScalarEvolution::getSizeOfExpr(Type *IntTy, Type *AllocTy) {
3200 // We can bypass creating a target-independent
3201 // constant expression and then folding it back into a ConstantInt.
3202 // This is just a compile-time optimization.
3203 return getConstant(IntTy,
3204 F->getParent()->getDataLayout().getTypeAllocSize(AllocTy));
3207 const SCEV *ScalarEvolution::getOffsetOfExpr(Type *IntTy,
3210 // We can bypass creating a target-independent
3211 // constant expression and then folding it back into a ConstantInt.
3212 // This is just a compile-time optimization.
3215 F->getParent()->getDataLayout().getStructLayout(STy)->getElementOffset(
3219 const SCEV *ScalarEvolution::getUnknown(Value *V) {
3220 // Don't attempt to do anything other than create a SCEVUnknown object
3221 // here. createSCEV only calls getUnknown after checking for all other
3222 // interesting possibilities, and any other code that calls getUnknown
3223 // is doing so in order to hide a value from SCEV canonicalization.
3225 FoldingSetNodeID ID;
3226 ID.AddInteger(scUnknown);
3229 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
3230 assert(cast<SCEVUnknown>(S)->getValue() == V &&
3231 "Stale SCEVUnknown in uniquing map!");
3234 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
3236 FirstUnknown = cast<SCEVUnknown>(S);
3237 UniqueSCEVs.InsertNode(S, IP);
3241 //===----------------------------------------------------------------------===//
3242 // Basic SCEV Analysis and PHI Idiom Recognition Code
3245 /// isSCEVable - Test if values of the given type are analyzable within
3246 /// the SCEV framework. This primarily includes integer types, and it
3247 /// can optionally include pointer types if the ScalarEvolution class
3248 /// has access to target-specific information.
3249 bool ScalarEvolution::isSCEVable(Type *Ty) const {
3250 // Integers and pointers are always SCEVable.
3251 return Ty->isIntegerTy() || Ty->isPointerTy();
3254 /// getTypeSizeInBits - Return the size in bits of the specified type,
3255 /// for which isSCEVable must return true.
3256 uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const {
3257 assert(isSCEVable(Ty) && "Type is not SCEVable!");
3258 return F->getParent()->getDataLayout().getTypeSizeInBits(Ty);
3261 /// getEffectiveSCEVType - Return a type with the same bitwidth as
3262 /// the given type and which represents how SCEV will treat the given
3263 /// type, for which isSCEVable must return true. For pointer types,
3264 /// this is the pointer-sized integer type.
3265 Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const {
3266 assert(isSCEVable(Ty) && "Type is not SCEVable!");
3268 if (Ty->isIntegerTy()) {
3272 // The only other support type is pointer.
3273 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
3274 return F->getParent()->getDataLayout().getIntPtrType(Ty);
3277 const SCEV *ScalarEvolution::getCouldNotCompute() {
3278 return &CouldNotCompute;
3282 // Helper class working with SCEVTraversal to figure out if a SCEV contains
3283 // a SCEVUnknown with null value-pointer. FindInvalidSCEVUnknown::FindOne
3284 // is set iff if find such SCEVUnknown.
3286 struct FindInvalidSCEVUnknown {
3288 FindInvalidSCEVUnknown() { FindOne = false; }
3289 bool follow(const SCEV *S) {
3290 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
3294 if (!cast<SCEVUnknown>(S)->getValue())
3301 bool isDone() const { return FindOne; }
3305 bool ScalarEvolution::checkValidity(const SCEV *S) const {
3306 FindInvalidSCEVUnknown F;
3307 SCEVTraversal<FindInvalidSCEVUnknown> ST(F);
3313 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
3314 /// expression and create a new one.
3315 const SCEV *ScalarEvolution::getSCEV(Value *V) {
3316 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
3318 ValueExprMapType::iterator I = ValueExprMap.find_as(V);
3319 if (I != ValueExprMap.end()) {
3320 const SCEV *S = I->second;
3321 if (checkValidity(S))
3324 ValueExprMap.erase(I);
3326 const SCEV *S = createSCEV(V);
3328 // The process of creating a SCEV for V may have caused other SCEVs
3329 // to have been created, so it's necessary to insert the new entry
3330 // from scratch, rather than trying to remember the insert position
3332 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(V, this), S));
3336 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
3338 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) {
3339 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
3341 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
3343 Type *Ty = V->getType();
3344 Ty = getEffectiveSCEVType(Ty);
3345 return getMulExpr(V,
3346 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))));
3349 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
3350 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
3351 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
3353 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
3355 Type *Ty = V->getType();
3356 Ty = getEffectiveSCEVType(Ty);
3357 const SCEV *AllOnes =
3358 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
3359 return getMinusSCEV(AllOnes, V);
3362 /// getMinusSCEV - Return LHS-RHS. Minus is represented in SCEV as A+B*-1.
3363 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
3364 SCEV::NoWrapFlags Flags) {
3365 assert(!maskFlags(Flags, SCEV::FlagNUW) && "subtraction does not have NUW");
3367 // Fast path: X - X --> 0.
3369 return getConstant(LHS->getType(), 0);
3371 // X - Y --> X + -Y.
3372 // X -(nsw || nuw) Y --> X + -Y.
3373 return getAddExpr(LHS, getNegativeSCEV(RHS));
3376 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
3377 /// input value to the specified type. If the type must be extended, it is zero
3380 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty) {
3381 Type *SrcTy = V->getType();
3382 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3383 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3384 "Cannot truncate or zero extend with non-integer arguments!");
3385 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3386 return V; // No conversion
3387 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
3388 return getTruncateExpr(V, Ty);
3389 return getZeroExtendExpr(V, Ty);
3392 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
3393 /// input value to the specified type. If the type must be extended, it is sign
3396 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
3398 Type *SrcTy = V->getType();
3399 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3400 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3401 "Cannot truncate or zero extend with non-integer arguments!");
3402 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3403 return V; // No conversion
3404 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
3405 return getTruncateExpr(V, Ty);
3406 return getSignExtendExpr(V, Ty);
3409 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
3410 /// input value to the specified type. If the type must be extended, it is zero
3411 /// extended. The conversion must not be narrowing.
3413 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) {
3414 Type *SrcTy = V->getType();
3415 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3416 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3417 "Cannot noop or zero extend with non-integer arguments!");
3418 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3419 "getNoopOrZeroExtend cannot truncate!");
3420 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3421 return V; // No conversion
3422 return getZeroExtendExpr(V, Ty);
3425 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
3426 /// input value to the specified type. If the type must be extended, it is sign
3427 /// extended. The conversion must not be narrowing.
3429 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) {
3430 Type *SrcTy = V->getType();
3431 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3432 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3433 "Cannot noop or sign extend with non-integer arguments!");
3434 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3435 "getNoopOrSignExtend cannot truncate!");
3436 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3437 return V; // No conversion
3438 return getSignExtendExpr(V, Ty);
3441 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
3442 /// the input value to the specified type. If the type must be extended,
3443 /// it is extended with unspecified bits. The conversion must not be
3446 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) {
3447 Type *SrcTy = V->getType();
3448 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3449 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3450 "Cannot noop or any extend with non-integer arguments!");
3451 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3452 "getNoopOrAnyExtend cannot truncate!");
3453 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3454 return V; // No conversion
3455 return getAnyExtendExpr(V, Ty);
3458 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
3459 /// input value to the specified type. The conversion must not be widening.
3461 ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) {
3462 Type *SrcTy = V->getType();
3463 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3464 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3465 "Cannot truncate or noop with non-integer arguments!");
3466 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
3467 "getTruncateOrNoop cannot extend!");
3468 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3469 return V; // No conversion
3470 return getTruncateExpr(V, Ty);
3473 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
3474 /// the types using zero-extension, and then perform a umax operation
3476 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
3478 const SCEV *PromotedLHS = LHS;
3479 const SCEV *PromotedRHS = RHS;
3481 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
3482 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
3484 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
3486 return getUMaxExpr(PromotedLHS, PromotedRHS);
3489 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
3490 /// the types using zero-extension, and then perform a umin operation
3492 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
3494 const SCEV *PromotedLHS = LHS;
3495 const SCEV *PromotedRHS = RHS;
3497 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
3498 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
3500 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
3502 return getUMinExpr(PromotedLHS, PromotedRHS);
3505 /// getPointerBase - Transitively follow the chain of pointer-type operands
3506 /// until reaching a SCEV that does not have a single pointer operand. This
3507 /// returns a SCEVUnknown pointer for well-formed pointer-type expressions,
3508 /// but corner cases do exist.
3509 const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) {
3510 // A pointer operand may evaluate to a nonpointer expression, such as null.
3511 if (!V->getType()->isPointerTy())
3514 if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) {
3515 return getPointerBase(Cast->getOperand());
3517 else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) {
3518 const SCEV *PtrOp = nullptr;
3519 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
3521 if ((*I)->getType()->isPointerTy()) {
3522 // Cannot find the base of an expression with multiple pointer operands.
3530 return getPointerBase(PtrOp);
3535 /// PushDefUseChildren - Push users of the given Instruction
3536 /// onto the given Worklist.
3538 PushDefUseChildren(Instruction *I,
3539 SmallVectorImpl<Instruction *> &Worklist) {
3540 // Push the def-use children onto the Worklist stack.
3541 for (User *U : I->users())
3542 Worklist.push_back(cast<Instruction>(U));
3545 /// ForgetSymbolicValue - This looks up computed SCEV values for all
3546 /// instructions that depend on the given instruction and removes them from
3547 /// the ValueExprMapType map if they reference SymName. This is used during PHI
3550 ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) {
3551 SmallVector<Instruction *, 16> Worklist;
3552 PushDefUseChildren(PN, Worklist);
3554 SmallPtrSet<Instruction *, 8> Visited;
3556 while (!Worklist.empty()) {
3557 Instruction *I = Worklist.pop_back_val();
3558 if (!Visited.insert(I).second)
3561 ValueExprMapType::iterator It =
3562 ValueExprMap.find_as(static_cast<Value *>(I));
3563 if (It != ValueExprMap.end()) {
3564 const SCEV *Old = It->second;
3566 // Short-circuit the def-use traversal if the symbolic name
3567 // ceases to appear in expressions.
3568 if (Old != SymName && !hasOperand(Old, SymName))
3571 // SCEVUnknown for a PHI either means that it has an unrecognized
3572 // structure, it's a PHI that's in the progress of being computed
3573 // by createNodeForPHI, or it's a single-value PHI. In the first case,
3574 // additional loop trip count information isn't going to change anything.
3575 // In the second case, createNodeForPHI will perform the necessary
3576 // updates on its own when it gets to that point. In the third, we do
3577 // want to forget the SCEVUnknown.
3578 if (!isa<PHINode>(I) ||
3579 !isa<SCEVUnknown>(Old) ||
3580 (I != PN && Old == SymName)) {
3581 forgetMemoizedResults(Old);
3582 ValueExprMap.erase(It);
3586 PushDefUseChildren(I, Worklist);
3590 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
3591 /// a loop header, making it a potential recurrence, or it doesn't.
3593 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
3594 if (const Loop *L = LI->getLoopFor(PN->getParent()))
3595 if (L->getHeader() == PN->getParent()) {
3596 // The loop may have multiple entrances or multiple exits; we can analyze
3597 // this phi as an addrec if it has a unique entry value and a unique
3599 Value *BEValueV = nullptr, *StartValueV = nullptr;
3600 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
3601 Value *V = PN->getIncomingValue(i);
3602 if (L->contains(PN->getIncomingBlock(i))) {
3605 } else if (BEValueV != V) {
3609 } else if (!StartValueV) {
3611 } else if (StartValueV != V) {
3612 StartValueV = nullptr;
3616 if (BEValueV && StartValueV) {
3617 // While we are analyzing this PHI node, handle its value symbolically.
3618 const SCEV *SymbolicName = getUnknown(PN);
3619 assert(ValueExprMap.find_as(PN) == ValueExprMap.end() &&
3620 "PHI node already processed?");
3621 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
3623 // Using this symbolic name for the PHI, analyze the value coming around
3625 const SCEV *BEValue = getSCEV(BEValueV);
3627 // NOTE: If BEValue is loop invariant, we know that the PHI node just
3628 // has a special value for the first iteration of the loop.
3630 // If the value coming around the backedge is an add with the symbolic
3631 // value we just inserted, then we found a simple induction variable!
3632 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
3633 // If there is a single occurrence of the symbolic value, replace it
3634 // with a recurrence.
3635 unsigned FoundIndex = Add->getNumOperands();
3636 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3637 if (Add->getOperand(i) == SymbolicName)
3638 if (FoundIndex == e) {
3643 if (FoundIndex != Add->getNumOperands()) {
3644 // Create an add with everything but the specified operand.
3645 SmallVector<const SCEV *, 8> Ops;
3646 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3647 if (i != FoundIndex)
3648 Ops.push_back(Add->getOperand(i));
3649 const SCEV *Accum = getAddExpr(Ops);
3651 // This is not a valid addrec if the step amount is varying each
3652 // loop iteration, but is not itself an addrec in this loop.
3653 if (isLoopInvariant(Accum, L) ||
3654 (isa<SCEVAddRecExpr>(Accum) &&
3655 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
3656 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
3658 // If the increment doesn't overflow, then neither the addrec nor
3659 // the post-increment will overflow.
3660 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) {
3661 if (OBO->getOperand(0) == PN) {
3662 if (OBO->hasNoUnsignedWrap())
3663 Flags = setFlags(Flags, SCEV::FlagNUW);
3664 if (OBO->hasNoSignedWrap())
3665 Flags = setFlags(Flags, SCEV::FlagNSW);
3667 } else if (GEPOperator *GEP = dyn_cast<GEPOperator>(BEValueV)) {
3668 // If the increment is an inbounds GEP, then we know the address
3669 // space cannot be wrapped around. We cannot make any guarantee
3670 // about signed or unsigned overflow because pointers are
3671 // unsigned but we may have a negative index from the base
3672 // pointer. We can guarantee that no unsigned wrap occurs if the
3673 // indices form a positive value.
3674 if (GEP->isInBounds() && GEP->getOperand(0) == PN) {
3675 Flags = setFlags(Flags, SCEV::FlagNW);
3677 const SCEV *Ptr = getSCEV(GEP->getPointerOperand());
3678 if (isKnownPositive(getMinusSCEV(getSCEV(GEP), Ptr)))
3679 Flags = setFlags(Flags, SCEV::FlagNUW);
3682 // We cannot transfer nuw and nsw flags from subtraction
3683 // operations -- sub nuw X, Y is not the same as add nuw X, -Y
3687 const SCEV *StartVal = getSCEV(StartValueV);
3688 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
3690 // Since the no-wrap flags are on the increment, they apply to the
3691 // post-incremented value as well.
3692 if (isLoopInvariant(Accum, L))
3693 (void)getAddRecExpr(getAddExpr(StartVal, Accum),
3696 // Okay, for the entire analysis of this edge we assumed the PHI
3697 // to be symbolic. We now need to go back and purge all of the
3698 // entries for the scalars that use the symbolic expression.
3699 ForgetSymbolicName(PN, SymbolicName);
3700 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3704 } else if (const SCEVAddRecExpr *AddRec =
3705 dyn_cast<SCEVAddRecExpr>(BEValue)) {
3706 // Otherwise, this could be a loop like this:
3707 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
3708 // In this case, j = {1,+,1} and BEValue is j.
3709 // Because the other in-value of i (0) fits the evolution of BEValue
3710 // i really is an addrec evolution.
3711 if (AddRec->getLoop() == L && AddRec->isAffine()) {
3712 const SCEV *StartVal = getSCEV(StartValueV);
3714 // If StartVal = j.start - j.stride, we can use StartVal as the
3715 // initial step of the addrec evolution.
3716 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
3717 AddRec->getOperand(1))) {
3718 // FIXME: For constant StartVal, we should be able to infer
3720 const SCEV *PHISCEV =
3721 getAddRecExpr(StartVal, AddRec->getOperand(1), L,
3724 // Okay, for the entire analysis of this edge we assumed the PHI
3725 // to be symbolic. We now need to go back and purge all of the
3726 // entries for the scalars that use the symbolic expression.
3727 ForgetSymbolicName(PN, SymbolicName);
3728 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3736 // If the PHI has a single incoming value, follow that value, unless the
3737 // PHI's incoming blocks are in a different loop, in which case doing so
3738 // risks breaking LCSSA form. Instcombine would normally zap these, but
3739 // it doesn't have DominatorTree information, so it may miss cases.
3741 SimplifyInstruction(PN, F->getParent()->getDataLayout(), TLI, DT, AC))
3742 if (LI->replacementPreservesLCSSAForm(PN, V))
3745 // If it's not a loop phi, we can't handle it yet.
3746 return getUnknown(PN);
3749 /// createNodeForGEP - Expand GEP instructions into add and multiply
3750 /// operations. This allows them to be analyzed by regular SCEV code.
3752 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
3753 Value *Base = GEP->getOperand(0);
3754 // Don't attempt to analyze GEPs over unsized objects.
3755 if (!Base->getType()->getPointerElementType()->isSized())
3756 return getUnknown(GEP);
3758 SmallVector<const SCEV *, 4> IndexExprs;
3759 for (auto Index = GEP->idx_begin(); Index != GEP->idx_end(); ++Index)
3760 IndexExprs.push_back(getSCEV(*Index));
3761 return getGEPExpr(GEP->getSourceElementType(), getSCEV(Base), IndexExprs,
3765 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
3766 /// guaranteed to end in (at every loop iteration). It is, at the same time,
3767 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
3768 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
3770 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
3771 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3772 return C->getValue()->getValue().countTrailingZeros();
3774 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
3775 return std::min(GetMinTrailingZeros(T->getOperand()),
3776 (uint32_t)getTypeSizeInBits(T->getType()));
3778 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
3779 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3780 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3781 getTypeSizeInBits(E->getType()) : OpRes;
3784 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
3785 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3786 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3787 getTypeSizeInBits(E->getType()) : OpRes;
3790 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
3791 // The result is the min of all operands results.
3792 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3793 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3794 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3798 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
3799 // The result is the sum of all operands results.
3800 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
3801 uint32_t BitWidth = getTypeSizeInBits(M->getType());
3802 for (unsigned i = 1, e = M->getNumOperands();
3803 SumOpRes != BitWidth && i != e; ++i)
3804 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
3809 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
3810 // The result is the min of all operands results.
3811 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3812 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3813 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3817 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
3818 // The result is the min of all operands results.
3819 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3820 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3821 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3825 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
3826 // The result is the min of all operands results.
3827 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3828 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3829 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3833 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3834 // For a SCEVUnknown, ask ValueTracking.
3835 unsigned BitWidth = getTypeSizeInBits(U->getType());
3836 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3837 computeKnownBits(U->getValue(), Zeros, Ones,
3838 F->getParent()->getDataLayout(), 0, AC, nullptr, DT);
3839 return Zeros.countTrailingOnes();
3846 /// GetRangeFromMetadata - Helper method to assign a range to V from
3847 /// metadata present in the IR.
3848 static Optional<ConstantRange> GetRangeFromMetadata(Value *V) {
3849 if (Instruction *I = dyn_cast<Instruction>(V)) {
3850 if (MDNode *MD = I->getMetadata(LLVMContext::MD_range)) {
3851 ConstantRange TotalRange(
3852 cast<IntegerType>(I->getType())->getBitWidth(), false);
3854 unsigned NumRanges = MD->getNumOperands() / 2;
3855 assert(NumRanges >= 1);
3857 for (unsigned i = 0; i < NumRanges; ++i) {
3858 ConstantInt *Lower =
3859 mdconst::extract<ConstantInt>(MD->getOperand(2 * i + 0));
3860 ConstantInt *Upper =
3861 mdconst::extract<ConstantInt>(MD->getOperand(2 * i + 1));
3862 ConstantRange Range(Lower->getValue(), Upper->getValue());
3863 TotalRange = TotalRange.unionWith(Range);
3873 /// getRange - Determine the range for a particular SCEV. If SignHint is
3874 /// HINT_RANGE_UNSIGNED (resp. HINT_RANGE_SIGNED) then getRange prefers ranges
3875 /// with a "cleaner" unsigned (resp. signed) representation.
3878 ScalarEvolution::getRange(const SCEV *S,
3879 ScalarEvolution::RangeSignHint SignHint) {
3880 DenseMap<const SCEV *, ConstantRange> &Cache =
3881 SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED ? UnsignedRanges
3884 // See if we've computed this range already.
3885 DenseMap<const SCEV *, ConstantRange>::iterator I = Cache.find(S);
3886 if (I != Cache.end())
3889 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3890 return setRange(C, SignHint, ConstantRange(C->getValue()->getValue()));
3892 unsigned BitWidth = getTypeSizeInBits(S->getType());
3893 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3895 // If the value has known zeros, the maximum value will have those known zeros
3897 uint32_t TZ = GetMinTrailingZeros(S);
3899 if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED)
3900 ConservativeResult =
3901 ConstantRange(APInt::getMinValue(BitWidth),
3902 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
3904 ConservativeResult = ConstantRange(
3905 APInt::getSignedMinValue(BitWidth),
3906 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
3909 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3910 ConstantRange X = getRange(Add->getOperand(0), SignHint);
3911 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3912 X = X.add(getRange(Add->getOperand(i), SignHint));
3913 return setRange(Add, SignHint, ConservativeResult.intersectWith(X));
3916 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3917 ConstantRange X = getRange(Mul->getOperand(0), SignHint);
3918 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3919 X = X.multiply(getRange(Mul->getOperand(i), SignHint));
3920 return setRange(Mul, SignHint, ConservativeResult.intersectWith(X));
3923 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3924 ConstantRange X = getRange(SMax->getOperand(0), SignHint);
3925 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3926 X = X.smax(getRange(SMax->getOperand(i), SignHint));
3927 return setRange(SMax, SignHint, ConservativeResult.intersectWith(X));
3930 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3931 ConstantRange X = getRange(UMax->getOperand(0), SignHint);
3932 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3933 X = X.umax(getRange(UMax->getOperand(i), SignHint));
3934 return setRange(UMax, SignHint, ConservativeResult.intersectWith(X));
3937 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3938 ConstantRange X = getRange(UDiv->getLHS(), SignHint);
3939 ConstantRange Y = getRange(UDiv->getRHS(), SignHint);
3940 return setRange(UDiv, SignHint,
3941 ConservativeResult.intersectWith(X.udiv(Y)));
3944 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3945 ConstantRange X = getRange(ZExt->getOperand(), SignHint);
3946 return setRange(ZExt, SignHint,
3947 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3950 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3951 ConstantRange X = getRange(SExt->getOperand(), SignHint);
3952 return setRange(SExt, SignHint,
3953 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3956 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3957 ConstantRange X = getRange(Trunc->getOperand(), SignHint);
3958 return setRange(Trunc, SignHint,
3959 ConservativeResult.intersectWith(X.truncate(BitWidth)));
3962 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3963 // If there's no unsigned wrap, the value will never be less than its
3965 if (AddRec->getNoWrapFlags(SCEV::FlagNUW))
3966 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
3967 if (!C->getValue()->isZero())
3968 ConservativeResult =
3969 ConservativeResult.intersectWith(
3970 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0)));
3972 // If there's no signed wrap, and all the operands have the same sign or
3973 // zero, the value won't ever change sign.
3974 if (AddRec->getNoWrapFlags(SCEV::FlagNSW)) {
3975 bool AllNonNeg = true;
3976 bool AllNonPos = true;
3977 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
3978 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
3979 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
3982 ConservativeResult = ConservativeResult.intersectWith(
3983 ConstantRange(APInt(BitWidth, 0),
3984 APInt::getSignedMinValue(BitWidth)));
3986 ConservativeResult = ConservativeResult.intersectWith(
3987 ConstantRange(APInt::getSignedMinValue(BitWidth),
3988 APInt(BitWidth, 1)));
3991 // TODO: non-affine addrec
3992 if (AddRec->isAffine()) {
3993 Type *Ty = AddRec->getType();
3994 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3995 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3996 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3998 // Check for overflow. This must be done with ConstantRange arithmetic
3999 // because we could be called from within the ScalarEvolution overflow
4002 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
4003 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
4004 ConstantRange ZExtMaxBECountRange =
4005 MaxBECountRange.zextOrTrunc(BitWidth * 2 + 1);
4007 const SCEV *Start = AddRec->getStart();
4008 const SCEV *Step = AddRec->getStepRecurrence(*this);
4009 ConstantRange StepSRange = getSignedRange(Step);
4010 ConstantRange SExtStepSRange = StepSRange.sextOrTrunc(BitWidth * 2 + 1);
4012 ConstantRange StartURange = getUnsignedRange(Start);
4013 ConstantRange EndURange =
4014 StartURange.add(MaxBECountRange.multiply(StepSRange));
4016 // Check for unsigned overflow.
4017 ConstantRange ZExtStartURange =
4018 StartURange.zextOrTrunc(BitWidth * 2 + 1);
4019 ConstantRange ZExtEndURange = EndURange.zextOrTrunc(BitWidth * 2 + 1);
4020 if (ZExtStartURange.add(ZExtMaxBECountRange.multiply(SExtStepSRange)) ==
4022 APInt Min = APIntOps::umin(StartURange.getUnsignedMin(),
4023 EndURange.getUnsignedMin());
4024 APInt Max = APIntOps::umax(StartURange.getUnsignedMax(),
4025 EndURange.getUnsignedMax());
4026 bool IsFullRange = Min.isMinValue() && Max.isMaxValue();
4028 ConservativeResult =
4029 ConservativeResult.intersectWith(ConstantRange(Min, Max + 1));
4032 ConstantRange StartSRange = getSignedRange(Start);
4033 ConstantRange EndSRange =
4034 StartSRange.add(MaxBECountRange.multiply(StepSRange));
4036 // Check for signed overflow. This must be done with ConstantRange
4037 // arithmetic because we could be called from within the ScalarEvolution
4038 // overflow checking code.
4039 ConstantRange SExtStartSRange =
4040 StartSRange.sextOrTrunc(BitWidth * 2 + 1);
4041 ConstantRange SExtEndSRange = EndSRange.sextOrTrunc(BitWidth * 2 + 1);
4042 if (SExtStartSRange.add(ZExtMaxBECountRange.multiply(SExtStepSRange)) ==
4044 APInt Min = APIntOps::smin(StartSRange.getSignedMin(),
4045 EndSRange.getSignedMin());
4046 APInt Max = APIntOps::smax(StartSRange.getSignedMax(),
4047 EndSRange.getSignedMax());
4048 bool IsFullRange = Min.isMinSignedValue() && Max.isMaxSignedValue();
4050 ConservativeResult =
4051 ConservativeResult.intersectWith(ConstantRange(Min, Max + 1));
4056 return setRange(AddRec, SignHint, ConservativeResult);
4059 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
4060 // Check if the IR explicitly contains !range metadata.
4061 Optional<ConstantRange> MDRange = GetRangeFromMetadata(U->getValue());
4062 if (MDRange.hasValue())
4063 ConservativeResult = ConservativeResult.intersectWith(MDRange.getValue());
4065 // Split here to avoid paying the compile-time cost of calling both
4066 // computeKnownBits and ComputeNumSignBits. This restriction can be lifted
4068 const DataLayout &DL = F->getParent()->getDataLayout();
4069 if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED) {
4070 // For a SCEVUnknown, ask ValueTracking.
4071 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
4072 computeKnownBits(U->getValue(), Zeros, Ones, DL, 0, AC, nullptr, DT);
4073 if (Ones != ~Zeros + 1)
4074 ConservativeResult =
4075 ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1));
4077 assert(SignHint == ScalarEvolution::HINT_RANGE_SIGNED &&
4078 "generalize as needed!");
4079 unsigned NS = ComputeNumSignBits(U->getValue(), DL, 0, AC, nullptr, DT);
4081 ConservativeResult = ConservativeResult.intersectWith(
4082 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
4083 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1) + 1));
4086 return setRange(U, SignHint, ConservativeResult);
4089 return setRange(S, SignHint, ConservativeResult);
4092 /// createSCEV - We know that there is no SCEV for the specified value.
4093 /// Analyze the expression.
4095 const SCEV *ScalarEvolution::createSCEV(Value *V) {
4096 if (!isSCEVable(V->getType()))
4097 return getUnknown(V);
4099 unsigned Opcode = Instruction::UserOp1;
4100 if (Instruction *I = dyn_cast<Instruction>(V)) {
4101 Opcode = I->getOpcode();
4103 // Don't attempt to analyze instructions in blocks that aren't
4104 // reachable. Such instructions don't matter, and they aren't required
4105 // to obey basic rules for definitions dominating uses which this
4106 // analysis depends on.
4107 if (!DT->isReachableFromEntry(I->getParent()))
4108 return getUnknown(V);
4109 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
4110 Opcode = CE->getOpcode();
4111 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
4112 return getConstant(CI);
4113 else if (isa<ConstantPointerNull>(V))
4114 return getConstant(V->getType(), 0);
4115 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
4116 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee());
4118 return getUnknown(V);
4120 Operator *U = cast<Operator>(V);
4122 case Instruction::Add: {
4123 // The simple thing to do would be to just call getSCEV on both operands
4124 // and call getAddExpr with the result. However if we're looking at a
4125 // bunch of things all added together, this can be quite inefficient,
4126 // because it leads to N-1 getAddExpr calls for N ultimate operands.
4127 // Instead, gather up all the operands and make a single getAddExpr call.
4128 // LLVM IR canonical form means we need only traverse the left operands.
4130 // Don't apply this instruction's NSW or NUW flags to the new
4131 // expression. The instruction may be guarded by control flow that the
4132 // no-wrap behavior depends on. Non-control-equivalent instructions can be
4133 // mapped to the same SCEV expression, and it would be incorrect to transfer
4134 // NSW/NUW semantics to those operations.
4135 SmallVector<const SCEV *, 4> AddOps;
4136 AddOps.push_back(getSCEV(U->getOperand(1)));
4137 for (Value *Op = U->getOperand(0); ; Op = U->getOperand(0)) {
4138 unsigned Opcode = Op->getValueID() - Value::InstructionVal;
4139 if (Opcode != Instruction::Add && Opcode != Instruction::Sub)
4141 U = cast<Operator>(Op);
4142 const SCEV *Op1 = getSCEV(U->getOperand(1));
4143 if (Opcode == Instruction::Sub)
4144 AddOps.push_back(getNegativeSCEV(Op1));
4146 AddOps.push_back(Op1);
4148 AddOps.push_back(getSCEV(U->getOperand(0)));
4149 return getAddExpr(AddOps);
4151 case Instruction::Mul: {
4152 // Don't transfer NSW/NUW for the same reason as AddExpr.
4153 SmallVector<const SCEV *, 4> MulOps;
4154 MulOps.push_back(getSCEV(U->getOperand(1)));
4155 for (Value *Op = U->getOperand(0);
4156 Op->getValueID() == Instruction::Mul + Value::InstructionVal;
4157 Op = U->getOperand(0)) {
4158 U = cast<Operator>(Op);
4159 MulOps.push_back(getSCEV(U->getOperand(1)));
4161 MulOps.push_back(getSCEV(U->getOperand(0)));
4162 return getMulExpr(MulOps);
4164 case Instruction::UDiv:
4165 return getUDivExpr(getSCEV(U->getOperand(0)),
4166 getSCEV(U->getOperand(1)));
4167 case Instruction::Sub:
4168 return getMinusSCEV(getSCEV(U->getOperand(0)),
4169 getSCEV(U->getOperand(1)));
4170 case Instruction::And:
4171 // For an expression like x&255 that merely masks off the high bits,
4172 // use zext(trunc(x)) as the SCEV expression.
4173 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
4174 if (CI->isNullValue())
4175 return getSCEV(U->getOperand(1));
4176 if (CI->isAllOnesValue())
4177 return getSCEV(U->getOperand(0));
4178 const APInt &A = CI->getValue();
4180 // Instcombine's ShrinkDemandedConstant may strip bits out of
4181 // constants, obscuring what would otherwise be a low-bits mask.
4182 // Use computeKnownBits to compute what ShrinkDemandedConstant
4183 // knew about to reconstruct a low-bits mask value.
4184 unsigned LZ = A.countLeadingZeros();
4185 unsigned TZ = A.countTrailingZeros();
4186 unsigned BitWidth = A.getBitWidth();
4187 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
4188 computeKnownBits(U->getOperand(0), KnownZero, KnownOne,
4189 F->getParent()->getDataLayout(), 0, AC, nullptr, DT);
4191 APInt EffectiveMask =
4192 APInt::getLowBitsSet(BitWidth, BitWidth - LZ - TZ).shl(TZ);
4193 if ((LZ != 0 || TZ != 0) && !((~A & ~KnownZero) & EffectiveMask)) {
4194 const SCEV *MulCount = getConstant(
4195 ConstantInt::get(getContext(), APInt::getOneBitSet(BitWidth, TZ)));
4199 getUDivExactExpr(getSCEV(U->getOperand(0)), MulCount),
4200 IntegerType::get(getContext(), BitWidth - LZ - TZ)),
4207 case Instruction::Or:
4208 // If the RHS of the Or is a constant, we may have something like:
4209 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
4210 // optimizations will transparently handle this case.
4212 // In order for this transformation to be safe, the LHS must be of the
4213 // form X*(2^n) and the Or constant must be less than 2^n.
4214 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
4215 const SCEV *LHS = getSCEV(U->getOperand(0));
4216 const APInt &CIVal = CI->getValue();
4217 if (GetMinTrailingZeros(LHS) >=
4218 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
4219 // Build a plain add SCEV.
4220 const SCEV *S = getAddExpr(LHS, getSCEV(CI));
4221 // If the LHS of the add was an addrec and it has no-wrap flags,
4222 // transfer the no-wrap flags, since an or won't introduce a wrap.
4223 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
4224 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
4225 const_cast<SCEVAddRecExpr *>(NewAR)->setNoWrapFlags(
4226 OldAR->getNoWrapFlags());
4232 case Instruction::Xor:
4233 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
4234 // If the RHS of the xor is a signbit, then this is just an add.
4235 // Instcombine turns add of signbit into xor as a strength reduction step.
4236 if (CI->getValue().isSignBit())
4237 return getAddExpr(getSCEV(U->getOperand(0)),
4238 getSCEV(U->getOperand(1)));
4240 // If the RHS of xor is -1, then this is a not operation.
4241 if (CI->isAllOnesValue())
4242 return getNotSCEV(getSCEV(U->getOperand(0)));
4244 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
4245 // This is a variant of the check for xor with -1, and it handles
4246 // the case where instcombine has trimmed non-demanded bits out
4247 // of an xor with -1.
4248 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
4249 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
4250 if (BO->getOpcode() == Instruction::And &&
4251 LCI->getValue() == CI->getValue())
4252 if (const SCEVZeroExtendExpr *Z =
4253 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
4254 Type *UTy = U->getType();
4255 const SCEV *Z0 = Z->getOperand();
4256 Type *Z0Ty = Z0->getType();
4257 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
4259 // If C is a low-bits mask, the zero extend is serving to
4260 // mask off the high bits. Complement the operand and
4261 // re-apply the zext.
4262 if (APIntOps::isMask(Z0TySize, CI->getValue()))
4263 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
4265 // If C is a single bit, it may be in the sign-bit position
4266 // before the zero-extend. In this case, represent the xor
4267 // using an add, which is equivalent, and re-apply the zext.
4268 APInt Trunc = CI->getValue().trunc(Z0TySize);
4269 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
4271 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
4277 case Instruction::Shl:
4278 // Turn shift left of a constant amount into a multiply.
4279 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
4280 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
4282 // If the shift count is not less than the bitwidth, the result of
4283 // the shift is undefined. Don't try to analyze it, because the
4284 // resolution chosen here may differ from the resolution chosen in
4285 // other parts of the compiler.
4286 if (SA->getValue().uge(BitWidth))
4289 Constant *X = ConstantInt::get(getContext(),
4290 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
4291 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
4295 case Instruction::LShr:
4296 // Turn logical shift right of a constant into a unsigned divide.
4297 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
4298 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
4300 // If the shift count is not less than the bitwidth, the result of
4301 // the shift is undefined. Don't try to analyze it, because the
4302 // resolution chosen here may differ from the resolution chosen in
4303 // other parts of the compiler.
4304 if (SA->getValue().uge(BitWidth))
4307 Constant *X = ConstantInt::get(getContext(),
4308 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
4309 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
4313 case Instruction::AShr:
4314 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
4315 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
4316 if (Operator *L = dyn_cast<Operator>(U->getOperand(0)))
4317 if (L->getOpcode() == Instruction::Shl &&
4318 L->getOperand(1) == U->getOperand(1)) {
4319 uint64_t BitWidth = getTypeSizeInBits(U->getType());
4321 // If the shift count is not less than the bitwidth, the result of
4322 // the shift is undefined. Don't try to analyze it, because the
4323 // resolution chosen here may differ from the resolution chosen in
4324 // other parts of the compiler.
4325 if (CI->getValue().uge(BitWidth))
4328 uint64_t Amt = BitWidth - CI->getZExtValue();
4329 if (Amt == BitWidth)
4330 return getSCEV(L->getOperand(0)); // shift by zero --> noop
4332 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
4333 IntegerType::get(getContext(),
4339 case Instruction::Trunc:
4340 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
4342 case Instruction::ZExt:
4343 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
4345 case Instruction::SExt:
4346 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
4348 case Instruction::BitCast:
4349 // BitCasts are no-op casts so we just eliminate the cast.
4350 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
4351 return getSCEV(U->getOperand(0));
4354 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
4355 // lead to pointer expressions which cannot safely be expanded to GEPs,
4356 // because ScalarEvolution doesn't respect the GEP aliasing rules when
4357 // simplifying integer expressions.
4359 case Instruction::GetElementPtr:
4360 return createNodeForGEP(cast<GEPOperator>(U));
4362 case Instruction::PHI:
4363 return createNodeForPHI(cast<PHINode>(U));
4365 case Instruction::Select:
4366 // This could be a smax or umax that was lowered earlier.
4367 // Try to recover it.
4368 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
4369 Value *LHS = ICI->getOperand(0);
4370 Value *RHS = ICI->getOperand(1);
4371 switch (ICI->getPredicate()) {
4372 case ICmpInst::ICMP_SLT:
4373 case ICmpInst::ICMP_SLE:
4374 std::swap(LHS, RHS);
4376 case ICmpInst::ICMP_SGT:
4377 case ICmpInst::ICMP_SGE:
4378 // a >s b ? a+x : b+x -> smax(a, b)+x
4379 // a >s b ? b+x : a+x -> smin(a, b)+x
4380 if (getTypeSizeInBits(LHS->getType()) <=
4381 getTypeSizeInBits(U->getType())) {
4382 const SCEV *LS = getNoopOrSignExtend(getSCEV(LHS), U->getType());
4383 const SCEV *RS = getNoopOrSignExtend(getSCEV(RHS), U->getType());
4384 const SCEV *LA = getSCEV(U->getOperand(1));
4385 const SCEV *RA = getSCEV(U->getOperand(2));
4386 const SCEV *LDiff = getMinusSCEV(LA, LS);
4387 const SCEV *RDiff = getMinusSCEV(RA, RS);
4389 return getAddExpr(getSMaxExpr(LS, RS), LDiff);
4390 LDiff = getMinusSCEV(LA, RS);
4391 RDiff = getMinusSCEV(RA, LS);
4393 return getAddExpr(getSMinExpr(LS, RS), LDiff);
4396 case ICmpInst::ICMP_ULT:
4397 case ICmpInst::ICMP_ULE:
4398 std::swap(LHS, RHS);
4400 case ICmpInst::ICMP_UGT:
4401 case ICmpInst::ICMP_UGE:
4402 // a >u b ? a+x : b+x -> umax(a, b)+x
4403 // a >u b ? b+x : a+x -> umin(a, b)+x
4404 if (getTypeSizeInBits(LHS->getType()) <=
4405 getTypeSizeInBits(U->getType())) {
4406 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), U->getType());
4407 const SCEV *RS = getNoopOrZeroExtend(getSCEV(RHS), U->getType());
4408 const SCEV *LA = getSCEV(U->getOperand(1));
4409 const SCEV *RA = getSCEV(U->getOperand(2));
4410 const SCEV *LDiff = getMinusSCEV(LA, LS);
4411 const SCEV *RDiff = getMinusSCEV(RA, RS);
4413 return getAddExpr(getUMaxExpr(LS, RS), LDiff);
4414 LDiff = getMinusSCEV(LA, RS);
4415 RDiff = getMinusSCEV(RA, LS);
4417 return getAddExpr(getUMinExpr(LS, RS), LDiff);
4420 case ICmpInst::ICMP_NE:
4421 // n != 0 ? n+x : 1+x -> umax(n, 1)+x
4422 if (getTypeSizeInBits(LHS->getType()) <=
4423 getTypeSizeInBits(U->getType()) &&
4424 isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
4425 const SCEV *One = getConstant(U->getType(), 1);
4426 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), U->getType());
4427 const SCEV *LA = getSCEV(U->getOperand(1));
4428 const SCEV *RA = getSCEV(U->getOperand(2));
4429 const SCEV *LDiff = getMinusSCEV(LA, LS);
4430 const SCEV *RDiff = getMinusSCEV(RA, One);
4432 return getAddExpr(getUMaxExpr(One, LS), LDiff);
4435 case ICmpInst::ICMP_EQ:
4436 // n == 0 ? 1+x : n+x -> umax(n, 1)+x
4437 if (getTypeSizeInBits(LHS->getType()) <=
4438 getTypeSizeInBits(U->getType()) &&
4439 isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
4440 const SCEV *One = getConstant(U->getType(), 1);
4441 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), U->getType());
4442 const SCEV *LA = getSCEV(U->getOperand(1));
4443 const SCEV *RA = getSCEV(U->getOperand(2));
4444 const SCEV *LDiff = getMinusSCEV(LA, One);
4445 const SCEV *RDiff = getMinusSCEV(RA, LS);
4447 return getAddExpr(getUMaxExpr(One, LS), LDiff);
4455 default: // We cannot analyze this expression.
4459 return getUnknown(V);
4464 //===----------------------------------------------------------------------===//
4465 // Iteration Count Computation Code
4468 unsigned ScalarEvolution::getSmallConstantTripCount(Loop *L) {
4469 if (BasicBlock *ExitingBB = L->getExitingBlock())
4470 return getSmallConstantTripCount(L, ExitingBB);
4472 // No trip count information for multiple exits.
4476 /// getSmallConstantTripCount - Returns the maximum trip count of this loop as a
4477 /// normal unsigned value. Returns 0 if the trip count is unknown or not
4478 /// constant. Will also return 0 if the maximum trip count is very large (>=
4481 /// This "trip count" assumes that control exits via ExitingBlock. More
4482 /// precisely, it is the number of times that control may reach ExitingBlock
4483 /// before taking the branch. For loops with multiple exits, it may not be the
4484 /// number times that the loop header executes because the loop may exit
4485 /// prematurely via another branch.
4486 unsigned ScalarEvolution::getSmallConstantTripCount(Loop *L,
4487 BasicBlock *ExitingBlock) {
4488 assert(ExitingBlock && "Must pass a non-null exiting block!");
4489 assert(L->isLoopExiting(ExitingBlock) &&
4490 "Exiting block must actually branch out of the loop!");
4491 const SCEVConstant *ExitCount =
4492 dyn_cast<SCEVConstant>(getExitCount(L, ExitingBlock));
4496 ConstantInt *ExitConst = ExitCount->getValue();
4498 // Guard against huge trip counts.
4499 if (ExitConst->getValue().getActiveBits() > 32)
4502 // In case of integer overflow, this returns 0, which is correct.
4503 return ((unsigned)ExitConst->getZExtValue()) + 1;
4506 unsigned ScalarEvolution::getSmallConstantTripMultiple(Loop *L) {
4507 if (BasicBlock *ExitingBB = L->getExitingBlock())
4508 return getSmallConstantTripMultiple(L, ExitingBB);
4510 // No trip multiple information for multiple exits.
4514 /// getSmallConstantTripMultiple - Returns the largest constant divisor of the
4515 /// trip count of this loop as a normal unsigned value, if possible. This
4516 /// means that the actual trip count is always a multiple of the returned
4517 /// value (don't forget the trip count could very well be zero as well!).
4519 /// Returns 1 if the trip count is unknown or not guaranteed to be the
4520 /// multiple of a constant (which is also the case if the trip count is simply
4521 /// constant, use getSmallConstantTripCount for that case), Will also return 1
4522 /// if the trip count is very large (>= 2^32).
4524 /// As explained in the comments for getSmallConstantTripCount, this assumes
4525 /// that control exits the loop via ExitingBlock.
4527 ScalarEvolution::getSmallConstantTripMultiple(Loop *L,
4528 BasicBlock *ExitingBlock) {
4529 assert(ExitingBlock && "Must pass a non-null exiting block!");
4530 assert(L->isLoopExiting(ExitingBlock) &&
4531 "Exiting block must actually branch out of the loop!");
4532 const SCEV *ExitCount = getExitCount(L, ExitingBlock);
4533 if (ExitCount == getCouldNotCompute())
4536 // Get the trip count from the BE count by adding 1.
4537 const SCEV *TCMul = getAddExpr(ExitCount,
4538 getConstant(ExitCount->getType(), 1));
4539 // FIXME: SCEV distributes multiplication as V1*C1 + V2*C1. We could attempt
4540 // to factor simple cases.
4541 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(TCMul))
4542 TCMul = Mul->getOperand(0);
4544 const SCEVConstant *MulC = dyn_cast<SCEVConstant>(TCMul);
4548 ConstantInt *Result = MulC->getValue();
4550 // Guard against huge trip counts (this requires checking
4551 // for zero to handle the case where the trip count == -1 and the
4553 if (!Result || Result->getValue().getActiveBits() > 32 ||
4554 Result->getValue().getActiveBits() == 0)
4557 return (unsigned)Result->getZExtValue();
4560 // getExitCount - Get the expression for the number of loop iterations for which
4561 // this loop is guaranteed not to exit via ExitingBlock. Otherwise return
4562 // SCEVCouldNotCompute.
4563 const SCEV *ScalarEvolution::getExitCount(Loop *L, BasicBlock *ExitingBlock) {
4564 return getBackedgeTakenInfo(L).getExact(ExitingBlock, this);
4567 /// getBackedgeTakenCount - If the specified loop has a predictable
4568 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
4569 /// object. The backedge-taken count is the number of times the loop header
4570 /// will be branched to from within the loop. This is one less than the
4571 /// trip count of the loop, since it doesn't count the first iteration,
4572 /// when the header is branched to from outside the loop.
4574 /// Note that it is not valid to call this method on a loop without a
4575 /// loop-invariant backedge-taken count (see
4576 /// hasLoopInvariantBackedgeTakenCount).
4578 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
4579 return getBackedgeTakenInfo(L).getExact(this);
4582 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
4583 /// return the least SCEV value that is known never to be less than the
4584 /// actual backedge taken count.
4585 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
4586 return getBackedgeTakenInfo(L).getMax(this);
4589 /// PushLoopPHIs - Push PHI nodes in the header of the given loop
4590 /// onto the given Worklist.
4592 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
4593 BasicBlock *Header = L->getHeader();
4595 // Push all Loop-header PHIs onto the Worklist stack.
4596 for (BasicBlock::iterator I = Header->begin();
4597 PHINode *PN = dyn_cast<PHINode>(I); ++I)
4598 Worklist.push_back(PN);
4601 const ScalarEvolution::BackedgeTakenInfo &
4602 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
4603 // Initially insert an invalid entry for this loop. If the insertion
4604 // succeeds, proceed to actually compute a backedge-taken count and
4605 // update the value. The temporary CouldNotCompute value tells SCEV
4606 // code elsewhere that it shouldn't attempt to request a new
4607 // backedge-taken count, which could result in infinite recursion.
4608 std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
4609 BackedgeTakenCounts.insert(std::make_pair(L, BackedgeTakenInfo()));
4611 return Pair.first->second;
4613 // ComputeBackedgeTakenCount may allocate memory for its result. Inserting it
4614 // into the BackedgeTakenCounts map transfers ownership. Otherwise, the result
4615 // must be cleared in this scope.
4616 BackedgeTakenInfo Result = ComputeBackedgeTakenCount(L);
4618 if (Result.getExact(this) != getCouldNotCompute()) {
4619 assert(isLoopInvariant(Result.getExact(this), L) &&
4620 isLoopInvariant(Result.getMax(this), L) &&
4621 "Computed backedge-taken count isn't loop invariant for loop!");
4622 ++NumTripCountsComputed;
4624 else if (Result.getMax(this) == getCouldNotCompute() &&
4625 isa<PHINode>(L->getHeader()->begin())) {
4626 // Only count loops that have phi nodes as not being computable.
4627 ++NumTripCountsNotComputed;
4630 // Now that we know more about the trip count for this loop, forget any
4631 // existing SCEV values for PHI nodes in this loop since they are only
4632 // conservative estimates made without the benefit of trip count
4633 // information. This is similar to the code in forgetLoop, except that
4634 // it handles SCEVUnknown PHI nodes specially.
4635 if (Result.hasAnyInfo()) {
4636 SmallVector<Instruction *, 16> Worklist;
4637 PushLoopPHIs(L, Worklist);
4639 SmallPtrSet<Instruction *, 8> Visited;
4640 while (!Worklist.empty()) {
4641 Instruction *I = Worklist.pop_back_val();
4642 if (!Visited.insert(I).second)
4645 ValueExprMapType::iterator It =
4646 ValueExprMap.find_as(static_cast<Value *>(I));
4647 if (It != ValueExprMap.end()) {
4648 const SCEV *Old = It->second;
4650 // SCEVUnknown for a PHI either means that it has an unrecognized
4651 // structure, or it's a PHI that's in the progress of being computed
4652 // by createNodeForPHI. In the former case, additional loop trip
4653 // count information isn't going to change anything. In the later
4654 // case, createNodeForPHI will perform the necessary updates on its
4655 // own when it gets to that point.
4656 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) {
4657 forgetMemoizedResults(Old);
4658 ValueExprMap.erase(It);
4660 if (PHINode *PN = dyn_cast<PHINode>(I))
4661 ConstantEvolutionLoopExitValue.erase(PN);
4664 PushDefUseChildren(I, Worklist);
4668 // Re-lookup the insert position, since the call to
4669 // ComputeBackedgeTakenCount above could result in a
4670 // recusive call to getBackedgeTakenInfo (on a different
4671 // loop), which would invalidate the iterator computed
4673 return BackedgeTakenCounts.find(L)->second = Result;
4676 /// forgetLoop - This method should be called by the client when it has
4677 /// changed a loop in a way that may effect ScalarEvolution's ability to
4678 /// compute a trip count, or if the loop is deleted.
4679 void ScalarEvolution::forgetLoop(const Loop *L) {
4680 // Drop any stored trip count value.
4681 DenseMap<const Loop*, BackedgeTakenInfo>::iterator BTCPos =
4682 BackedgeTakenCounts.find(L);
4683 if (BTCPos != BackedgeTakenCounts.end()) {
4684 BTCPos->second.clear();
4685 BackedgeTakenCounts.erase(BTCPos);
4688 // Drop information about expressions based on loop-header PHIs.
4689 SmallVector<Instruction *, 16> Worklist;
4690 PushLoopPHIs(L, Worklist);
4692 SmallPtrSet<Instruction *, 8> Visited;
4693 while (!Worklist.empty()) {
4694 Instruction *I = Worklist.pop_back_val();
4695 if (!Visited.insert(I).second)
4698 ValueExprMapType::iterator It =
4699 ValueExprMap.find_as(static_cast<Value *>(I));
4700 if (It != ValueExprMap.end()) {
4701 forgetMemoizedResults(It->second);
4702 ValueExprMap.erase(It);
4703 if (PHINode *PN = dyn_cast<PHINode>(I))
4704 ConstantEvolutionLoopExitValue.erase(PN);
4707 PushDefUseChildren(I, Worklist);
4710 // Forget all contained loops too, to avoid dangling entries in the
4711 // ValuesAtScopes map.
4712 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
4716 /// forgetValue - This method should be called by the client when it has
4717 /// changed a value in a way that may effect its value, or which may
4718 /// disconnect it from a def-use chain linking it to a loop.
4719 void ScalarEvolution::forgetValue(Value *V) {
4720 Instruction *I = dyn_cast<Instruction>(V);
4723 // Drop information about expressions based on loop-header PHIs.
4724 SmallVector<Instruction *, 16> Worklist;
4725 Worklist.push_back(I);
4727 SmallPtrSet<Instruction *, 8> Visited;
4728 while (!Worklist.empty()) {
4729 I = Worklist.pop_back_val();
4730 if (!Visited.insert(I).second)
4733 ValueExprMapType::iterator It =
4734 ValueExprMap.find_as(static_cast<Value *>(I));
4735 if (It != ValueExprMap.end()) {
4736 forgetMemoizedResults(It->second);
4737 ValueExprMap.erase(It);
4738 if (PHINode *PN = dyn_cast<PHINode>(I))
4739 ConstantEvolutionLoopExitValue.erase(PN);
4742 PushDefUseChildren(I, Worklist);
4746 /// getExact - Get the exact loop backedge taken count considering all loop
4747 /// exits. A computable result can only be returned for loops with a single
4748 /// exit. Returning the minimum taken count among all exits is incorrect
4749 /// because one of the loop's exit limit's may have been skipped. HowFarToZero
4750 /// assumes that the limit of each loop test is never skipped. This is a valid
4751 /// assumption as long as the loop exits via that test. For precise results, it
4752 /// is the caller's responsibility to specify the relevant loop exit using
4753 /// getExact(ExitingBlock, SE).
4755 ScalarEvolution::BackedgeTakenInfo::getExact(ScalarEvolution *SE) const {
4756 // If any exits were not computable, the loop is not computable.
4757 if (!ExitNotTaken.isCompleteList()) return SE->getCouldNotCompute();
4759 // We need exactly one computable exit.
4760 if (!ExitNotTaken.ExitingBlock) return SE->getCouldNotCompute();
4761 assert(ExitNotTaken.ExactNotTaken && "uninitialized not-taken info");
4763 const SCEV *BECount = nullptr;
4764 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4765 ENT != nullptr; ENT = ENT->getNextExit()) {
4767 assert(ENT->ExactNotTaken != SE->getCouldNotCompute() && "bad exit SCEV");
4770 BECount = ENT->ExactNotTaken;
4771 else if (BECount != ENT->ExactNotTaken)
4772 return SE->getCouldNotCompute();
4774 assert(BECount && "Invalid not taken count for loop exit");
4778 /// getExact - Get the exact not taken count for this loop exit.
4780 ScalarEvolution::BackedgeTakenInfo::getExact(BasicBlock *ExitingBlock,
4781 ScalarEvolution *SE) const {
4782 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4783 ENT != nullptr; ENT = ENT->getNextExit()) {
4785 if (ENT->ExitingBlock == ExitingBlock)
4786 return ENT->ExactNotTaken;
4788 return SE->getCouldNotCompute();
4791 /// getMax - Get the max backedge taken count for the loop.
4793 ScalarEvolution::BackedgeTakenInfo::getMax(ScalarEvolution *SE) const {
4794 return Max ? Max : SE->getCouldNotCompute();
4797 bool ScalarEvolution::BackedgeTakenInfo::hasOperand(const SCEV *S,
4798 ScalarEvolution *SE) const {
4799 if (Max && Max != SE->getCouldNotCompute() && SE->hasOperand(Max, S))
4802 if (!ExitNotTaken.ExitingBlock)
4805 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4806 ENT != nullptr; ENT = ENT->getNextExit()) {
4808 if (ENT->ExactNotTaken != SE->getCouldNotCompute()
4809 && SE->hasOperand(ENT->ExactNotTaken, S)) {
4816 /// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each
4817 /// computable exit into a persistent ExitNotTakenInfo array.
4818 ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo(
4819 SmallVectorImpl< std::pair<BasicBlock *, const SCEV *> > &ExitCounts,
4820 bool Complete, const SCEV *MaxCount) : Max(MaxCount) {
4823 ExitNotTaken.setIncomplete();
4825 unsigned NumExits = ExitCounts.size();
4826 if (NumExits == 0) return;
4828 ExitNotTaken.ExitingBlock = ExitCounts[0].first;
4829 ExitNotTaken.ExactNotTaken = ExitCounts[0].second;
4830 if (NumExits == 1) return;
4832 // Handle the rare case of multiple computable exits.
4833 ExitNotTakenInfo *ENT = new ExitNotTakenInfo[NumExits-1];
4835 ExitNotTakenInfo *PrevENT = &ExitNotTaken;
4836 for (unsigned i = 1; i < NumExits; ++i, PrevENT = ENT, ++ENT) {
4837 PrevENT->setNextExit(ENT);
4838 ENT->ExitingBlock = ExitCounts[i].first;
4839 ENT->ExactNotTaken = ExitCounts[i].second;
4843 /// clear - Invalidate this result and free the ExitNotTakenInfo array.
4844 void ScalarEvolution::BackedgeTakenInfo::clear() {
4845 ExitNotTaken.ExitingBlock = nullptr;
4846 ExitNotTaken.ExactNotTaken = nullptr;
4847 delete[] ExitNotTaken.getNextExit();
4850 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
4851 /// of the specified loop will execute.
4852 ScalarEvolution::BackedgeTakenInfo
4853 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
4854 SmallVector<BasicBlock *, 8> ExitingBlocks;
4855 L->getExitingBlocks(ExitingBlocks);
4857 SmallVector<std::pair<BasicBlock *, const SCEV *>, 4> ExitCounts;
4858 bool CouldComputeBECount = true;
4859 BasicBlock *Latch = L->getLoopLatch(); // may be NULL.
4860 const SCEV *MustExitMaxBECount = nullptr;
4861 const SCEV *MayExitMaxBECount = nullptr;
4863 // Compute the ExitLimit for each loop exit. Use this to populate ExitCounts
4864 // and compute maxBECount.
4865 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
4866 BasicBlock *ExitBB = ExitingBlocks[i];
4867 ExitLimit EL = ComputeExitLimit(L, ExitBB);
4869 // 1. For each exit that can be computed, add an entry to ExitCounts.
4870 // CouldComputeBECount is true only if all exits can be computed.
4871 if (EL.Exact == getCouldNotCompute())
4872 // We couldn't compute an exact value for this exit, so
4873 // we won't be able to compute an exact value for the loop.
4874 CouldComputeBECount = false;
4876 ExitCounts.push_back(std::make_pair(ExitBB, EL.Exact));
4878 // 2. Derive the loop's MaxBECount from each exit's max number of
4879 // non-exiting iterations. Partition the loop exits into two kinds:
4880 // LoopMustExits and LoopMayExits.
4882 // If the exit dominates the loop latch, it is a LoopMustExit otherwise it
4883 // is a LoopMayExit. If any computable LoopMustExit is found, then
4884 // MaxBECount is the minimum EL.Max of computable LoopMustExits. Otherwise,
4885 // MaxBECount is conservatively the maximum EL.Max, where CouldNotCompute is
4886 // considered greater than any computable EL.Max.
4887 if (EL.Max != getCouldNotCompute() && Latch &&
4888 DT->dominates(ExitBB, Latch)) {
4889 if (!MustExitMaxBECount)
4890 MustExitMaxBECount = EL.Max;
4892 MustExitMaxBECount =
4893 getUMinFromMismatchedTypes(MustExitMaxBECount, EL.Max);
4895 } else if (MayExitMaxBECount != getCouldNotCompute()) {
4896 if (!MayExitMaxBECount || EL.Max == getCouldNotCompute())
4897 MayExitMaxBECount = EL.Max;
4900 getUMaxFromMismatchedTypes(MayExitMaxBECount, EL.Max);
4904 const SCEV *MaxBECount = MustExitMaxBECount ? MustExitMaxBECount :
4905 (MayExitMaxBECount ? MayExitMaxBECount : getCouldNotCompute());
4906 return BackedgeTakenInfo(ExitCounts, CouldComputeBECount, MaxBECount);
4909 /// ComputeExitLimit - Compute the number of times the backedge of the specified
4910 /// loop will execute if it exits via the specified block.
4911 ScalarEvolution::ExitLimit
4912 ScalarEvolution::ComputeExitLimit(const Loop *L, BasicBlock *ExitingBlock) {
4914 // Okay, we've chosen an exiting block. See what condition causes us to
4915 // exit at this block and remember the exit block and whether all other targets
4916 // lead to the loop header.
4917 bool MustExecuteLoopHeader = true;
4918 BasicBlock *Exit = nullptr;
4919 for (succ_iterator SI = succ_begin(ExitingBlock), SE = succ_end(ExitingBlock);
4921 if (!L->contains(*SI)) {
4922 if (Exit) // Multiple exit successors.
4923 return getCouldNotCompute();
4925 } else if (*SI != L->getHeader()) {
4926 MustExecuteLoopHeader = false;
4929 // At this point, we know we have a conditional branch that determines whether
4930 // the loop is exited. However, we don't know if the branch is executed each
4931 // time through the loop. If not, then the execution count of the branch will
4932 // not be equal to the trip count of the loop.
4934 // Currently we check for this by checking to see if the Exit branch goes to
4935 // the loop header. If so, we know it will always execute the same number of
4936 // times as the loop. We also handle the case where the exit block *is* the
4937 // loop header. This is common for un-rotated loops.
4939 // If both of those tests fail, walk up the unique predecessor chain to the
4940 // header, stopping if there is an edge that doesn't exit the loop. If the
4941 // header is reached, the execution count of the branch will be equal to the
4942 // trip count of the loop.
4944 // More extensive analysis could be done to handle more cases here.
4946 if (!MustExecuteLoopHeader && ExitingBlock != L->getHeader()) {
4947 // The simple checks failed, try climbing the unique predecessor chain
4948 // up to the header.
4950 for (BasicBlock *BB = ExitingBlock; BB; ) {
4951 BasicBlock *Pred = BB->getUniquePredecessor();
4953 return getCouldNotCompute();
4954 TerminatorInst *PredTerm = Pred->getTerminator();
4955 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) {
4956 BasicBlock *PredSucc = PredTerm->getSuccessor(i);
4959 // If the predecessor has a successor that isn't BB and isn't
4960 // outside the loop, assume the worst.
4961 if (L->contains(PredSucc))
4962 return getCouldNotCompute();
4964 if (Pred == L->getHeader()) {
4971 return getCouldNotCompute();
4974 bool IsOnlyExit = (L->getExitingBlock() != nullptr);
4975 TerminatorInst *Term = ExitingBlock->getTerminator();
4976 if (BranchInst *BI = dyn_cast<BranchInst>(Term)) {
4977 assert(BI->isConditional() && "If unconditional, it can't be in loop!");
4978 // Proceed to the next level to examine the exit condition expression.
4979 return ComputeExitLimitFromCond(L, BI->getCondition(), BI->getSuccessor(0),
4980 BI->getSuccessor(1),
4981 /*ControlsExit=*/IsOnlyExit);
4984 if (SwitchInst *SI = dyn_cast<SwitchInst>(Term))
4985 return ComputeExitLimitFromSingleExitSwitch(L, SI, Exit,
4986 /*ControlsExit=*/IsOnlyExit);
4988 return getCouldNotCompute();
4991 /// ComputeExitLimitFromCond - Compute the number of times the
4992 /// backedge of the specified loop will execute if its exit condition
4993 /// were a conditional branch of ExitCond, TBB, and FBB.
4995 /// @param ControlsExit is true if ExitCond directly controls the exit
4996 /// branch. In this case, we can assume that the loop exits only if the
4997 /// condition is true and can infer that failing to meet the condition prior to
4998 /// integer wraparound results in undefined behavior.
4999 ScalarEvolution::ExitLimit
5000 ScalarEvolution::ComputeExitLimitFromCond(const Loop *L,
5004 bool ControlsExit) {
5005 // Check if the controlling expression for this loop is an And or Or.
5006 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
5007 if (BO->getOpcode() == Instruction::And) {
5008 // Recurse on the operands of the and.
5009 bool EitherMayExit = L->contains(TBB);
5010 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
5011 ControlsExit && !EitherMayExit);
5012 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
5013 ControlsExit && !EitherMayExit);
5014 const SCEV *BECount = getCouldNotCompute();
5015 const SCEV *MaxBECount = getCouldNotCompute();
5016 if (EitherMayExit) {
5017 // Both conditions must be true for the loop to continue executing.
5018 // Choose the less conservative count.
5019 if (EL0.Exact == getCouldNotCompute() ||
5020 EL1.Exact == getCouldNotCompute())
5021 BECount = getCouldNotCompute();
5023 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
5024 if (EL0.Max == getCouldNotCompute())
5025 MaxBECount = EL1.Max;
5026 else if (EL1.Max == getCouldNotCompute())
5027 MaxBECount = EL0.Max;
5029 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
5031 // Both conditions must be true at the same time for the loop to exit.
5032 // For now, be conservative.
5033 assert(L->contains(FBB) && "Loop block has no successor in loop!");
5034 if (EL0.Max == EL1.Max)
5035 MaxBECount = EL0.Max;
5036 if (EL0.Exact == EL1.Exact)
5037 BECount = EL0.Exact;
5040 return ExitLimit(BECount, MaxBECount);
5042 if (BO->getOpcode() == Instruction::Or) {
5043 // Recurse on the operands of the or.
5044 bool EitherMayExit = L->contains(FBB);
5045 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
5046 ControlsExit && !EitherMayExit);
5047 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
5048 ControlsExit && !EitherMayExit);
5049 const SCEV *BECount = getCouldNotCompute();
5050 const SCEV *MaxBECount = getCouldNotCompute();
5051 if (EitherMayExit) {
5052 // Both conditions must be false for the loop to continue executing.
5053 // Choose the less conservative count.
5054 if (EL0.Exact == getCouldNotCompute() ||
5055 EL1.Exact == getCouldNotCompute())
5056 BECount = getCouldNotCompute();
5058 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
5059 if (EL0.Max == getCouldNotCompute())
5060 MaxBECount = EL1.Max;
5061 else if (EL1.Max == getCouldNotCompute())
5062 MaxBECount = EL0.Max;
5064 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
5066 // Both conditions must be false at the same time for the loop to exit.
5067 // For now, be conservative.
5068 assert(L->contains(TBB) && "Loop block has no successor in loop!");
5069 if (EL0.Max == EL1.Max)
5070 MaxBECount = EL0.Max;
5071 if (EL0.Exact == EL1.Exact)
5072 BECount = EL0.Exact;
5075 return ExitLimit(BECount, MaxBECount);
5079 // With an icmp, it may be feasible to compute an exact backedge-taken count.
5080 // Proceed to the next level to examine the icmp.
5081 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
5082 return ComputeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB, ControlsExit);
5084 // Check for a constant condition. These are normally stripped out by
5085 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
5086 // preserve the CFG and is temporarily leaving constant conditions
5088 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
5089 if (L->contains(FBB) == !CI->getZExtValue())
5090 // The backedge is always taken.
5091 return getCouldNotCompute();
5093 // The backedge is never taken.
5094 return getConstant(CI->getType(), 0);
5097 // If it's not an integer or pointer comparison then compute it the hard way.
5098 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
5101 /// ComputeExitLimitFromICmp - Compute the number of times the
5102 /// backedge of the specified loop will execute if its exit condition
5103 /// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB.
5104 ScalarEvolution::ExitLimit
5105 ScalarEvolution::ComputeExitLimitFromICmp(const Loop *L,
5109 bool ControlsExit) {
5111 // If the condition was exit on true, convert the condition to exit on false
5112 ICmpInst::Predicate Cond;
5113 if (!L->contains(FBB))
5114 Cond = ExitCond->getPredicate();
5116 Cond = ExitCond->getInversePredicate();
5118 // Handle common loops like: for (X = "string"; *X; ++X)
5119 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
5120 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
5122 ComputeLoadConstantCompareExitLimit(LI, RHS, L, Cond);
5123 if (ItCnt.hasAnyInfo())
5127 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
5128 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
5130 // Try to evaluate any dependencies out of the loop.
5131 LHS = getSCEVAtScope(LHS, L);
5132 RHS = getSCEVAtScope(RHS, L);
5134 // At this point, we would like to compute how many iterations of the
5135 // loop the predicate will return true for these inputs.
5136 if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) {
5137 // If there is a loop-invariant, force it into the RHS.
5138 std::swap(LHS, RHS);
5139 Cond = ICmpInst::getSwappedPredicate(Cond);
5142 // Simplify the operands before analyzing them.
5143 (void)SimplifyICmpOperands(Cond, LHS, RHS);
5145 // If we have a comparison of a chrec against a constant, try to use value
5146 // ranges to answer this query.
5147 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
5148 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
5149 if (AddRec->getLoop() == L) {
5150 // Form the constant range.
5151 ConstantRange CompRange(
5152 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
5154 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
5155 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
5159 case ICmpInst::ICMP_NE: { // while (X != Y)
5160 // Convert to: while (X-Y != 0)
5161 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit);
5162 if (EL.hasAnyInfo()) return EL;
5165 case ICmpInst::ICMP_EQ: { // while (X == Y)
5166 // Convert to: while (X-Y == 0)
5167 ExitLimit EL = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
5168 if (EL.hasAnyInfo()) return EL;
5171 case ICmpInst::ICMP_SLT:
5172 case ICmpInst::ICMP_ULT: { // while (X < Y)
5173 bool IsSigned = Cond == ICmpInst::ICMP_SLT;
5174 ExitLimit EL = HowManyLessThans(LHS, RHS, L, IsSigned, ControlsExit);
5175 if (EL.hasAnyInfo()) return EL;
5178 case ICmpInst::ICMP_SGT:
5179 case ICmpInst::ICMP_UGT: { // while (X > Y)
5180 bool IsSigned = Cond == ICmpInst::ICMP_SGT;
5181 ExitLimit EL = HowManyGreaterThans(LHS, RHS, L, IsSigned, ControlsExit);
5182 if (EL.hasAnyInfo()) return EL;
5187 dbgs() << "ComputeBackedgeTakenCount ";
5188 if (ExitCond->getOperand(0)->getType()->isUnsigned())
5189 dbgs() << "[unsigned] ";
5190 dbgs() << *LHS << " "
5191 << Instruction::getOpcodeName(Instruction::ICmp)
5192 << " " << *RHS << "\n";
5196 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
5199 ScalarEvolution::ExitLimit
5200 ScalarEvolution::ComputeExitLimitFromSingleExitSwitch(const Loop *L,
5202 BasicBlock *ExitingBlock,
5203 bool ControlsExit) {
5204 assert(!L->contains(ExitingBlock) && "Not an exiting block!");
5206 // Give up if the exit is the default dest of a switch.
5207 if (Switch->getDefaultDest() == ExitingBlock)
5208 return getCouldNotCompute();
5210 assert(L->contains(Switch->getDefaultDest()) &&
5211 "Default case must not exit the loop!");
5212 const SCEV *LHS = getSCEVAtScope(Switch->getCondition(), L);
5213 const SCEV *RHS = getConstant(Switch->findCaseDest(ExitingBlock));
5215 // while (X != Y) --> while (X-Y != 0)
5216 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit);
5217 if (EL.hasAnyInfo())
5220 return getCouldNotCompute();
5223 static ConstantInt *
5224 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
5225 ScalarEvolution &SE) {
5226 const SCEV *InVal = SE.getConstant(C);
5227 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
5228 assert(isa<SCEVConstant>(Val) &&
5229 "Evaluation of SCEV at constant didn't fold correctly?");
5230 return cast<SCEVConstant>(Val)->getValue();
5233 /// ComputeLoadConstantCompareExitLimit - Given an exit condition of
5234 /// 'icmp op load X, cst', try to see if we can compute the backedge
5235 /// execution count.
5236 ScalarEvolution::ExitLimit
5237 ScalarEvolution::ComputeLoadConstantCompareExitLimit(
5241 ICmpInst::Predicate predicate) {
5243 if (LI->isVolatile()) return getCouldNotCompute();
5245 // Check to see if the loaded pointer is a getelementptr of a global.
5246 // TODO: Use SCEV instead of manually grubbing with GEPs.
5247 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
5248 if (!GEP) return getCouldNotCompute();
5250 // Make sure that it is really a constant global we are gepping, with an
5251 // initializer, and make sure the first IDX is really 0.
5252 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
5253 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
5254 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
5255 !cast<Constant>(GEP->getOperand(1))->isNullValue())
5256 return getCouldNotCompute();
5258 // Okay, we allow one non-constant index into the GEP instruction.
5259 Value *VarIdx = nullptr;
5260 std::vector<Constant*> Indexes;
5261 unsigned VarIdxNum = 0;
5262 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
5263 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
5264 Indexes.push_back(CI);
5265 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
5266 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
5267 VarIdx = GEP->getOperand(i);
5269 Indexes.push_back(nullptr);
5272 // Loop-invariant loads may be a byproduct of loop optimization. Skip them.
5274 return getCouldNotCompute();
5276 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
5277 // Check to see if X is a loop variant variable value now.
5278 const SCEV *Idx = getSCEV(VarIdx);
5279 Idx = getSCEVAtScope(Idx, L);
5281 // We can only recognize very limited forms of loop index expressions, in
5282 // particular, only affine AddRec's like {C1,+,C2}.
5283 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
5284 if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) ||
5285 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
5286 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
5287 return getCouldNotCompute();
5289 unsigned MaxSteps = MaxBruteForceIterations;
5290 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
5291 ConstantInt *ItCst = ConstantInt::get(
5292 cast<IntegerType>(IdxExpr->getType()), IterationNum);
5293 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
5295 // Form the GEP offset.
5296 Indexes[VarIdxNum] = Val;
5298 Constant *Result = ConstantFoldLoadThroughGEPIndices(GV->getInitializer(),
5300 if (!Result) break; // Cannot compute!
5302 // Evaluate the condition for this iteration.
5303 Result = ConstantExpr::getICmp(predicate, Result, RHS);
5304 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
5305 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
5307 dbgs() << "\n***\n*** Computed loop count " << *ItCst
5308 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
5311 ++NumArrayLenItCounts;
5312 return getConstant(ItCst); // Found terminating iteration!
5315 return getCouldNotCompute();
5319 /// CanConstantFold - Return true if we can constant fold an instruction of the
5320 /// specified type, assuming that all operands were constants.
5321 static bool CanConstantFold(const Instruction *I) {
5322 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
5323 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I) ||
5327 if (const CallInst *CI = dyn_cast<CallInst>(I))
5328 if (const Function *F = CI->getCalledFunction())
5329 return canConstantFoldCallTo(F);
5333 /// Determine whether this instruction can constant evolve within this loop
5334 /// assuming its operands can all constant evolve.
5335 static bool canConstantEvolve(Instruction *I, const Loop *L) {
5336 // An instruction outside of the loop can't be derived from a loop PHI.
5337 if (!L->contains(I)) return false;
5339 if (isa<PHINode>(I)) {
5340 // We don't currently keep track of the control flow needed to evaluate
5341 // PHIs, so we cannot handle PHIs inside of loops.
5342 return L->getHeader() == I->getParent();
5345 // If we won't be able to constant fold this expression even if the operands
5346 // are constants, bail early.
5347 return CanConstantFold(I);
5350 /// getConstantEvolvingPHIOperands - Implement getConstantEvolvingPHI by
5351 /// recursing through each instruction operand until reaching a loop header phi.
5353 getConstantEvolvingPHIOperands(Instruction *UseInst, const Loop *L,
5354 DenseMap<Instruction *, PHINode *> &PHIMap) {
5356 // Otherwise, we can evaluate this instruction if all of its operands are
5357 // constant or derived from a PHI node themselves.
5358 PHINode *PHI = nullptr;
5359 for (Instruction::op_iterator OpI = UseInst->op_begin(),
5360 OpE = UseInst->op_end(); OpI != OpE; ++OpI) {
5362 if (isa<Constant>(*OpI)) continue;
5364 Instruction *OpInst = dyn_cast<Instruction>(*OpI);
5365 if (!OpInst || !canConstantEvolve(OpInst, L)) return nullptr;
5367 PHINode *P = dyn_cast<PHINode>(OpInst);
5369 // If this operand is already visited, reuse the prior result.
5370 // We may have P != PHI if this is the deepest point at which the
5371 // inconsistent paths meet.
5372 P = PHIMap.lookup(OpInst);
5374 // Recurse and memoize the results, whether a phi is found or not.
5375 // This recursive call invalidates pointers into PHIMap.
5376 P = getConstantEvolvingPHIOperands(OpInst, L, PHIMap);
5380 return nullptr; // Not evolving from PHI
5381 if (PHI && PHI != P)
5382 return nullptr; // Evolving from multiple different PHIs.
5385 // This is a expression evolving from a constant PHI!
5389 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
5390 /// in the loop that V is derived from. We allow arbitrary operations along the
5391 /// way, but the operands of an operation must either be constants or a value
5392 /// derived from a constant PHI. If this expression does not fit with these
5393 /// constraints, return null.
5394 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
5395 Instruction *I = dyn_cast<Instruction>(V);
5396 if (!I || !canConstantEvolve(I, L)) return nullptr;
5398 if (PHINode *PN = dyn_cast<PHINode>(I)) {
5402 // Record non-constant instructions contained by the loop.
5403 DenseMap<Instruction *, PHINode *> PHIMap;
5404 return getConstantEvolvingPHIOperands(I, L, PHIMap);
5407 /// EvaluateExpression - Given an expression that passes the
5408 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
5409 /// in the loop has the value PHIVal. If we can't fold this expression for some
5410 /// reason, return null.
5411 static Constant *EvaluateExpression(Value *V, const Loop *L,
5412 DenseMap<Instruction *, Constant *> &Vals,
5413 const DataLayout &DL,
5414 const TargetLibraryInfo *TLI) {
5415 // Convenient constant check, but redundant for recursive calls.
5416 if (Constant *C = dyn_cast<Constant>(V)) return C;
5417 Instruction *I = dyn_cast<Instruction>(V);
5418 if (!I) return nullptr;
5420 if (Constant *C = Vals.lookup(I)) return C;
5422 // An instruction inside the loop depends on a value outside the loop that we
5423 // weren't given a mapping for, or a value such as a call inside the loop.
5424 if (!canConstantEvolve(I, L)) return nullptr;
5426 // An unmapped PHI can be due to a branch or another loop inside this loop,
5427 // or due to this not being the initial iteration through a loop where we
5428 // couldn't compute the evolution of this particular PHI last time.
5429 if (isa<PHINode>(I)) return nullptr;
5431 std::vector<Constant*> Operands(I->getNumOperands());
5433 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
5434 Instruction *Operand = dyn_cast<Instruction>(I->getOperand(i));
5436 Operands[i] = dyn_cast<Constant>(I->getOperand(i));
5437 if (!Operands[i]) return nullptr;
5440 Constant *C = EvaluateExpression(Operand, L, Vals, DL, TLI);
5442 if (!C) return nullptr;
5446 if (CmpInst *CI = dyn_cast<CmpInst>(I))
5447 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
5448 Operands[1], DL, TLI);
5449 if (LoadInst *LI = dyn_cast<LoadInst>(I)) {
5450 if (!LI->isVolatile())
5451 return ConstantFoldLoadFromConstPtr(Operands[0], DL);
5453 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), Operands, DL,
5457 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
5458 /// in the header of its containing loop, we know the loop executes a
5459 /// constant number of times, and the PHI node is just a recurrence
5460 /// involving constants, fold it.
5462 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
5465 DenseMap<PHINode*, Constant*>::const_iterator I =
5466 ConstantEvolutionLoopExitValue.find(PN);
5467 if (I != ConstantEvolutionLoopExitValue.end())
5470 if (BEs.ugt(MaxBruteForceIterations))
5471 return ConstantEvolutionLoopExitValue[PN] = nullptr; // Not going to evaluate it.
5473 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
5475 DenseMap<Instruction *, Constant *> CurrentIterVals;
5476 BasicBlock *Header = L->getHeader();
5477 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
5479 // Since the loop is canonicalized, the PHI node must have two entries. One
5480 // entry must be a constant (coming in from outside of the loop), and the
5481 // second must be derived from the same PHI.
5482 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
5483 PHINode *PHI = nullptr;
5484 for (BasicBlock::iterator I = Header->begin();
5485 (PHI = dyn_cast<PHINode>(I)); ++I) {
5486 Constant *StartCST =
5487 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
5488 if (!StartCST) continue;
5489 CurrentIterVals[PHI] = StartCST;
5491 if (!CurrentIterVals.count(PN))
5492 return RetVal = nullptr;
5494 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
5496 // Execute the loop symbolically to determine the exit value.
5497 if (BEs.getActiveBits() >= 32)
5498 return RetVal = nullptr; // More than 2^32-1 iterations?? Not doing it!
5500 unsigned NumIterations = BEs.getZExtValue(); // must be in range
5501 unsigned IterationNum = 0;
5502 const DataLayout &DL = F->getParent()->getDataLayout();
5503 for (; ; ++IterationNum) {
5504 if (IterationNum == NumIterations)
5505 return RetVal = CurrentIterVals[PN]; // Got exit value!
5507 // Compute the value of the PHIs for the next iteration.
5508 // EvaluateExpression adds non-phi values to the CurrentIterVals map.
5509 DenseMap<Instruction *, Constant *> NextIterVals;
5511 EvaluateExpression(BEValue, L, CurrentIterVals, DL, TLI);
5513 return nullptr; // Couldn't evaluate!
5514 NextIterVals[PN] = NextPHI;
5516 bool StoppedEvolving = NextPHI == CurrentIterVals[PN];
5518 // Also evaluate the other PHI nodes. However, we don't get to stop if we
5519 // cease to be able to evaluate one of them or if they stop evolving,
5520 // because that doesn't necessarily prevent us from computing PN.
5521 SmallVector<std::pair<PHINode *, Constant *>, 8> PHIsToCompute;
5522 for (DenseMap<Instruction *, Constant *>::const_iterator
5523 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
5524 PHINode *PHI = dyn_cast<PHINode>(I->first);
5525 if (!PHI || PHI == PN || PHI->getParent() != Header) continue;
5526 PHIsToCompute.push_back(std::make_pair(PHI, I->second));
5528 // We use two distinct loops because EvaluateExpression may invalidate any
5529 // iterators into CurrentIterVals.
5530 for (SmallVectorImpl<std::pair<PHINode *, Constant*> >::const_iterator
5531 I = PHIsToCompute.begin(), E = PHIsToCompute.end(); I != E; ++I) {
5532 PHINode *PHI = I->first;
5533 Constant *&NextPHI = NextIterVals[PHI];
5534 if (!NextPHI) { // Not already computed.
5535 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
5536 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, TLI);
5538 if (NextPHI != I->second)
5539 StoppedEvolving = false;
5542 // If all entries in CurrentIterVals == NextIterVals then we can stop
5543 // iterating, the loop can't continue to change.
5544 if (StoppedEvolving)
5545 return RetVal = CurrentIterVals[PN];
5547 CurrentIterVals.swap(NextIterVals);
5551 /// ComputeExitCountExhaustively - If the loop is known to execute a
5552 /// constant number of times (the condition evolves only from constants),
5553 /// try to evaluate a few iterations of the loop until we get the exit
5554 /// condition gets a value of ExitWhen (true or false). If we cannot
5555 /// evaluate the trip count of the loop, return getCouldNotCompute().
5556 const SCEV *ScalarEvolution::ComputeExitCountExhaustively(const Loop *L,
5559 PHINode *PN = getConstantEvolvingPHI(Cond, L);
5560 if (!PN) return getCouldNotCompute();
5562 // If the loop is canonicalized, the PHI will have exactly two entries.
5563 // That's the only form we support here.
5564 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
5566 DenseMap<Instruction *, Constant *> CurrentIterVals;
5567 BasicBlock *Header = L->getHeader();
5568 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
5570 // One entry must be a constant (coming in from outside of the loop), and the
5571 // second must be derived from the same PHI.
5572 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
5573 PHINode *PHI = nullptr;
5574 for (BasicBlock::iterator I = Header->begin();
5575 (PHI = dyn_cast<PHINode>(I)); ++I) {
5576 Constant *StartCST =
5577 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
5578 if (!StartCST) continue;
5579 CurrentIterVals[PHI] = StartCST;
5581 if (!CurrentIterVals.count(PN))
5582 return getCouldNotCompute();
5584 // Okay, we find a PHI node that defines the trip count of this loop. Execute
5585 // the loop symbolically to determine when the condition gets a value of
5587 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
5588 const DataLayout &DL = F->getParent()->getDataLayout();
5589 for (unsigned IterationNum = 0; IterationNum != MaxIterations;++IterationNum){
5590 ConstantInt *CondVal = dyn_cast_or_null<ConstantInt>(
5591 EvaluateExpression(Cond, L, CurrentIterVals, DL, TLI));
5593 // Couldn't symbolically evaluate.
5594 if (!CondVal) return getCouldNotCompute();
5596 if (CondVal->getValue() == uint64_t(ExitWhen)) {
5597 ++NumBruteForceTripCountsComputed;
5598 return getConstant(Type::getInt32Ty(getContext()), IterationNum);
5601 // Update all the PHI nodes for the next iteration.
5602 DenseMap<Instruction *, Constant *> NextIterVals;
5604 // Create a list of which PHIs we need to compute. We want to do this before
5605 // calling EvaluateExpression on them because that may invalidate iterators
5606 // into CurrentIterVals.
5607 SmallVector<PHINode *, 8> PHIsToCompute;
5608 for (DenseMap<Instruction *, Constant *>::const_iterator
5609 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
5610 PHINode *PHI = dyn_cast<PHINode>(I->first);
5611 if (!PHI || PHI->getParent() != Header) continue;
5612 PHIsToCompute.push_back(PHI);
5614 for (SmallVectorImpl<PHINode *>::const_iterator I = PHIsToCompute.begin(),
5615 E = PHIsToCompute.end(); I != E; ++I) {
5617 Constant *&NextPHI = NextIterVals[PHI];
5618 if (NextPHI) continue; // Already computed!
5620 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
5621 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, TLI);
5623 CurrentIterVals.swap(NextIterVals);
5626 // Too many iterations were needed to evaluate.
5627 return getCouldNotCompute();
5630 /// getSCEVAtScope - Return a SCEV expression for the specified value
5631 /// at the specified scope in the program. The L value specifies a loop
5632 /// nest to evaluate the expression at, where null is the top-level or a
5633 /// specified loop is immediately inside of the loop.
5635 /// This method can be used to compute the exit value for a variable defined
5636 /// in a loop by querying what the value will hold in the parent loop.
5638 /// In the case that a relevant loop exit value cannot be computed, the
5639 /// original value V is returned.
5640 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
5641 // Check to see if we've folded this expression at this loop before.
5642 SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values = ValuesAtScopes[V];
5643 for (unsigned u = 0; u < Values.size(); u++) {
5644 if (Values[u].first == L)
5645 return Values[u].second ? Values[u].second : V;
5647 Values.push_back(std::make_pair(L, static_cast<const SCEV *>(nullptr)));
5648 // Otherwise compute it.
5649 const SCEV *C = computeSCEVAtScope(V, L);
5650 SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values2 = ValuesAtScopes[V];
5651 for (unsigned u = Values2.size(); u > 0; u--) {
5652 if (Values2[u - 1].first == L) {
5653 Values2[u - 1].second = C;
5660 /// This builds up a Constant using the ConstantExpr interface. That way, we
5661 /// will return Constants for objects which aren't represented by a
5662 /// SCEVConstant, because SCEVConstant is restricted to ConstantInt.
5663 /// Returns NULL if the SCEV isn't representable as a Constant.
5664 static Constant *BuildConstantFromSCEV(const SCEV *V) {
5665 switch (static_cast<SCEVTypes>(V->getSCEVType())) {
5666 case scCouldNotCompute:
5670 return cast<SCEVConstant>(V)->getValue();
5672 return dyn_cast<Constant>(cast<SCEVUnknown>(V)->getValue());
5673 case scSignExtend: {
5674 const SCEVSignExtendExpr *SS = cast<SCEVSignExtendExpr>(V);
5675 if (Constant *CastOp = BuildConstantFromSCEV(SS->getOperand()))
5676 return ConstantExpr::getSExt(CastOp, SS->getType());
5679 case scZeroExtend: {
5680 const SCEVZeroExtendExpr *SZ = cast<SCEVZeroExtendExpr>(V);
5681 if (Constant *CastOp = BuildConstantFromSCEV(SZ->getOperand()))
5682 return ConstantExpr::getZExt(CastOp, SZ->getType());
5686 const SCEVTruncateExpr *ST = cast<SCEVTruncateExpr>(V);
5687 if (Constant *CastOp = BuildConstantFromSCEV(ST->getOperand()))
5688 return ConstantExpr::getTrunc(CastOp, ST->getType());
5692 const SCEVAddExpr *SA = cast<SCEVAddExpr>(V);
5693 if (Constant *C = BuildConstantFromSCEV(SA->getOperand(0))) {
5694 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
5695 unsigned AS = PTy->getAddressSpace();
5696 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
5697 C = ConstantExpr::getBitCast(C, DestPtrTy);
5699 for (unsigned i = 1, e = SA->getNumOperands(); i != e; ++i) {
5700 Constant *C2 = BuildConstantFromSCEV(SA->getOperand(i));
5701 if (!C2) return nullptr;
5704 if (!C->getType()->isPointerTy() && C2->getType()->isPointerTy()) {
5705 unsigned AS = C2->getType()->getPointerAddressSpace();
5707 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
5708 // The offsets have been converted to bytes. We can add bytes to an
5709 // i8* by GEP with the byte count in the first index.
5710 C = ConstantExpr::getBitCast(C, DestPtrTy);
5713 // Don't bother trying to sum two pointers. We probably can't
5714 // statically compute a load that results from it anyway.
5715 if (C2->getType()->isPointerTy())
5718 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
5719 if (PTy->getElementType()->isStructTy())
5720 C2 = ConstantExpr::getIntegerCast(
5721 C2, Type::getInt32Ty(C->getContext()), true);
5722 C = ConstantExpr::getGetElementPtr(PTy->getElementType(), C, C2);
5724 C = ConstantExpr::getAdd(C, C2);
5731 const SCEVMulExpr *SM = cast<SCEVMulExpr>(V);
5732 if (Constant *C = BuildConstantFromSCEV(SM->getOperand(0))) {
5733 // Don't bother with pointers at all.
5734 if (C->getType()->isPointerTy()) return nullptr;
5735 for (unsigned i = 1, e = SM->getNumOperands(); i != e; ++i) {
5736 Constant *C2 = BuildConstantFromSCEV(SM->getOperand(i));
5737 if (!C2 || C2->getType()->isPointerTy()) return nullptr;
5738 C = ConstantExpr::getMul(C, C2);
5745 const SCEVUDivExpr *SU = cast<SCEVUDivExpr>(V);
5746 if (Constant *LHS = BuildConstantFromSCEV(SU->getLHS()))
5747 if (Constant *RHS = BuildConstantFromSCEV(SU->getRHS()))
5748 if (LHS->getType() == RHS->getType())
5749 return ConstantExpr::getUDiv(LHS, RHS);
5754 break; // TODO: smax, umax.
5759 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
5760 if (isa<SCEVConstant>(V)) return V;
5762 // If this instruction is evolved from a constant-evolving PHI, compute the
5763 // exit value from the loop without using SCEVs.
5764 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
5765 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
5766 const Loop *LI = (*this->LI)[I->getParent()];
5767 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
5768 if (PHINode *PN = dyn_cast<PHINode>(I))
5769 if (PN->getParent() == LI->getHeader()) {
5770 // Okay, there is no closed form solution for the PHI node. Check
5771 // to see if the loop that contains it has a known backedge-taken
5772 // count. If so, we may be able to force computation of the exit
5774 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
5775 if (const SCEVConstant *BTCC =
5776 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
5777 // Okay, we know how many times the containing loop executes. If
5778 // this is a constant evolving PHI node, get the final value at
5779 // the specified iteration number.
5780 Constant *RV = getConstantEvolutionLoopExitValue(PN,
5781 BTCC->getValue()->getValue(),
5783 if (RV) return getSCEV(RV);
5787 // Okay, this is an expression that we cannot symbolically evaluate
5788 // into a SCEV. Check to see if it's possible to symbolically evaluate
5789 // the arguments into constants, and if so, try to constant propagate the
5790 // result. This is particularly useful for computing loop exit values.
5791 if (CanConstantFold(I)) {
5792 SmallVector<Constant *, 4> Operands;
5793 bool MadeImprovement = false;
5794 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
5795 Value *Op = I->getOperand(i);
5796 if (Constant *C = dyn_cast<Constant>(Op)) {
5797 Operands.push_back(C);
5801 // If any of the operands is non-constant and if they are
5802 // non-integer and non-pointer, don't even try to analyze them
5803 // with scev techniques.
5804 if (!isSCEVable(Op->getType()))
5807 const SCEV *OrigV = getSCEV(Op);
5808 const SCEV *OpV = getSCEVAtScope(OrigV, L);
5809 MadeImprovement |= OrigV != OpV;
5811 Constant *C = BuildConstantFromSCEV(OpV);
5813 if (C->getType() != Op->getType())
5814 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
5818 Operands.push_back(C);
5821 // Check to see if getSCEVAtScope actually made an improvement.
5822 if (MadeImprovement) {
5823 Constant *C = nullptr;
5824 const DataLayout &DL = F->getParent()->getDataLayout();
5825 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
5826 C = ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
5827 Operands[1], DL, TLI);
5828 else if (const LoadInst *LI = dyn_cast<LoadInst>(I)) {
5829 if (!LI->isVolatile())
5830 C = ConstantFoldLoadFromConstPtr(Operands[0], DL);
5832 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(), Operands,
5840 // This is some other type of SCEVUnknown, just return it.
5844 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
5845 // Avoid performing the look-up in the common case where the specified
5846 // expression has no loop-variant portions.
5847 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
5848 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
5849 if (OpAtScope != Comm->getOperand(i)) {
5850 // Okay, at least one of these operands is loop variant but might be
5851 // foldable. Build a new instance of the folded commutative expression.
5852 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
5853 Comm->op_begin()+i);
5854 NewOps.push_back(OpAtScope);
5856 for (++i; i != e; ++i) {
5857 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
5858 NewOps.push_back(OpAtScope);
5860 if (isa<SCEVAddExpr>(Comm))
5861 return getAddExpr(NewOps);
5862 if (isa<SCEVMulExpr>(Comm))
5863 return getMulExpr(NewOps);
5864 if (isa<SCEVSMaxExpr>(Comm))
5865 return getSMaxExpr(NewOps);
5866 if (isa<SCEVUMaxExpr>(Comm))
5867 return getUMaxExpr(NewOps);
5868 llvm_unreachable("Unknown commutative SCEV type!");
5871 // If we got here, all operands are loop invariant.
5875 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
5876 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
5877 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
5878 if (LHS == Div->getLHS() && RHS == Div->getRHS())
5879 return Div; // must be loop invariant
5880 return getUDivExpr(LHS, RHS);
5883 // If this is a loop recurrence for a loop that does not contain L, then we
5884 // are dealing with the final value computed by the loop.
5885 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
5886 // First, attempt to evaluate each operand.
5887 // Avoid performing the look-up in the common case where the specified
5888 // expression has no loop-variant portions.
5889 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
5890 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
5891 if (OpAtScope == AddRec->getOperand(i))
5894 // Okay, at least one of these operands is loop variant but might be
5895 // foldable. Build a new instance of the folded commutative expression.
5896 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(),
5897 AddRec->op_begin()+i);
5898 NewOps.push_back(OpAtScope);
5899 for (++i; i != e; ++i)
5900 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
5902 const SCEV *FoldedRec =
5903 getAddRecExpr(NewOps, AddRec->getLoop(),
5904 AddRec->getNoWrapFlags(SCEV::FlagNW));
5905 AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec);
5906 // The addrec may be folded to a nonrecurrence, for example, if the
5907 // induction variable is multiplied by zero after constant folding. Go
5908 // ahead and return the folded value.
5914 // If the scope is outside the addrec's loop, evaluate it by using the
5915 // loop exit value of the addrec.
5916 if (!AddRec->getLoop()->contains(L)) {
5917 // To evaluate this recurrence, we need to know how many times the AddRec
5918 // loop iterates. Compute this now.
5919 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
5920 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
5922 // Then, evaluate the AddRec.
5923 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
5929 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
5930 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5931 if (Op == Cast->getOperand())
5932 return Cast; // must be loop invariant
5933 return getZeroExtendExpr(Op, Cast->getType());
5936 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
5937 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5938 if (Op == Cast->getOperand())
5939 return Cast; // must be loop invariant
5940 return getSignExtendExpr(Op, Cast->getType());
5943 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
5944 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5945 if (Op == Cast->getOperand())
5946 return Cast; // must be loop invariant
5947 return getTruncateExpr(Op, Cast->getType());
5950 llvm_unreachable("Unknown SCEV type!");
5953 /// getSCEVAtScope - This is a convenience function which does
5954 /// getSCEVAtScope(getSCEV(V), L).
5955 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
5956 return getSCEVAtScope(getSCEV(V), L);
5959 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
5960 /// following equation:
5962 /// A * X = B (mod N)
5964 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
5965 /// A and B isn't important.
5967 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
5968 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
5969 ScalarEvolution &SE) {
5970 uint32_t BW = A.getBitWidth();
5971 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
5972 assert(A != 0 && "A must be non-zero.");
5976 // The gcd of A and N may have only one prime factor: 2. The number of
5977 // trailing zeros in A is its multiplicity
5978 uint32_t Mult2 = A.countTrailingZeros();
5981 // 2. Check if B is divisible by D.
5983 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
5984 // is not less than multiplicity of this prime factor for D.
5985 if (B.countTrailingZeros() < Mult2)
5986 return SE.getCouldNotCompute();
5988 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
5991 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
5992 // bit width during computations.
5993 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
5994 APInt Mod(BW + 1, 0);
5995 Mod.setBit(BW - Mult2); // Mod = N / D
5996 APInt I = AD.multiplicativeInverse(Mod);
5998 // 4. Compute the minimum unsigned root of the equation:
5999 // I * (B / D) mod (N / D)
6000 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
6002 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
6004 return SE.getConstant(Result.trunc(BW));
6007 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
6008 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
6009 /// might be the same) or two SCEVCouldNotCompute objects.
6011 static std::pair<const SCEV *,const SCEV *>
6012 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
6013 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
6014 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
6015 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
6016 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
6018 // We currently can only solve this if the coefficients are constants.
6019 if (!LC || !MC || !NC) {
6020 const SCEV *CNC = SE.getCouldNotCompute();
6021 return std::make_pair(CNC, CNC);
6024 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
6025 const APInt &L = LC->getValue()->getValue();
6026 const APInt &M = MC->getValue()->getValue();
6027 const APInt &N = NC->getValue()->getValue();
6028 APInt Two(BitWidth, 2);
6029 APInt Four(BitWidth, 4);
6032 using namespace APIntOps;
6034 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
6035 // The B coefficient is M-N/2
6039 // The A coefficient is N/2
6040 APInt A(N.sdiv(Two));
6042 // Compute the B^2-4ac term.
6045 SqrtTerm -= Four * (A * C);
6047 if (SqrtTerm.isNegative()) {
6048 // The loop is provably infinite.
6049 const SCEV *CNC = SE.getCouldNotCompute();
6050 return std::make_pair(CNC, CNC);
6053 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
6054 // integer value or else APInt::sqrt() will assert.
6055 APInt SqrtVal(SqrtTerm.sqrt());
6057 // Compute the two solutions for the quadratic formula.
6058 // The divisions must be performed as signed divisions.
6061 if (TwoA.isMinValue()) {
6062 const SCEV *CNC = SE.getCouldNotCompute();
6063 return std::make_pair(CNC, CNC);
6066 LLVMContext &Context = SE.getContext();
6068 ConstantInt *Solution1 =
6069 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
6070 ConstantInt *Solution2 =
6071 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
6073 return std::make_pair(SE.getConstant(Solution1),
6074 SE.getConstant(Solution2));
6075 } // end APIntOps namespace
6078 /// HowFarToZero - Return the number of times a backedge comparing the specified
6079 /// value to zero will execute. If not computable, return CouldNotCompute.
6081 /// This is only used for loops with a "x != y" exit test. The exit condition is
6082 /// now expressed as a single expression, V = x-y. So the exit test is
6083 /// effectively V != 0. We know and take advantage of the fact that this
6084 /// expression only being used in a comparison by zero context.
6085 ScalarEvolution::ExitLimit
6086 ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L, bool ControlsExit) {
6087 // If the value is a constant
6088 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
6089 // If the value is already zero, the branch will execute zero times.
6090 if (C->getValue()->isZero()) return C;
6091 return getCouldNotCompute(); // Otherwise it will loop infinitely.
6094 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
6095 if (!AddRec || AddRec->getLoop() != L)
6096 return getCouldNotCompute();
6098 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
6099 // the quadratic equation to solve it.
6100 if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
6101 std::pair<const SCEV *,const SCEV *> Roots =
6102 SolveQuadraticEquation(AddRec, *this);
6103 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
6104 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
6107 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1
6108 << " sol#2: " << *R2 << "\n";
6110 // Pick the smallest positive root value.
6111 if (ConstantInt *CB =
6112 dyn_cast<ConstantInt>(ConstantExpr::getICmp(CmpInst::ICMP_ULT,
6115 if (!CB->getZExtValue())
6116 std::swap(R1, R2); // R1 is the minimum root now.
6118 // We can only use this value if the chrec ends up with an exact zero
6119 // value at this index. When solving for "X*X != 5", for example, we
6120 // should not accept a root of 2.
6121 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
6123 return R1; // We found a quadratic root!
6126 return getCouldNotCompute();
6129 // Otherwise we can only handle this if it is affine.
6130 if (!AddRec->isAffine())
6131 return getCouldNotCompute();
6133 // If this is an affine expression, the execution count of this branch is
6134 // the minimum unsigned root of the following equation:
6136 // Start + Step*N = 0 (mod 2^BW)
6140 // Step*N = -Start (mod 2^BW)
6142 // where BW is the common bit width of Start and Step.
6144 // Get the initial value for the loop.
6145 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
6146 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
6148 // For now we handle only constant steps.
6150 // TODO: Handle a nonconstant Step given AddRec<NUW>. If the
6151 // AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap
6152 // to 0, it must be counting down to equal 0. Consequently, N = Start / -Step.
6153 // We have not yet seen any such cases.
6154 const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step);
6155 if (!StepC || StepC->getValue()->equalsInt(0))
6156 return getCouldNotCompute();
6158 // For positive steps (counting up until unsigned overflow):
6159 // N = -Start/Step (as unsigned)
6160 // For negative steps (counting down to zero):
6162 // First compute the unsigned distance from zero in the direction of Step.
6163 bool CountDown = StepC->getValue()->getValue().isNegative();
6164 const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start);
6166 // Handle unitary steps, which cannot wraparound.
6167 // 1*N = -Start; -1*N = Start (mod 2^BW), so:
6168 // N = Distance (as unsigned)
6169 if (StepC->getValue()->equalsInt(1) || StepC->getValue()->isAllOnesValue()) {
6170 ConstantRange CR = getUnsignedRange(Start);
6171 const SCEV *MaxBECount;
6172 if (!CountDown && CR.getUnsignedMin().isMinValue())
6173 // When counting up, the worst starting value is 1, not 0.
6174 MaxBECount = CR.getUnsignedMax().isMinValue()
6175 ? getConstant(APInt::getMinValue(CR.getBitWidth()))
6176 : getConstant(APInt::getMaxValue(CR.getBitWidth()));
6178 MaxBECount = getConstant(CountDown ? CR.getUnsignedMax()
6179 : -CR.getUnsignedMin());
6180 return ExitLimit(Distance, MaxBECount);
6183 // As a special case, handle the instance where Step is a positive power of
6184 // two. In this case, determining whether Step divides Distance evenly can be
6185 // done by counting and comparing the number of trailing zeros of Step and
6188 const APInt &StepV = StepC->getValue()->getValue();
6189 // StepV.isPowerOf2() returns true if StepV is an positive power of two. It
6190 // also returns true if StepV is maximally negative (eg, INT_MIN), but that
6191 // case is not handled as this code is guarded by !CountDown.
6192 if (StepV.isPowerOf2() &&
6193 GetMinTrailingZeros(Distance) >= StepV.countTrailingZeros())
6194 return getUDivExactExpr(Distance, Step);
6197 // If the condition controls loop exit (the loop exits only if the expression
6198 // is true) and the addition is no-wrap we can use unsigned divide to
6199 // compute the backedge count. In this case, the step may not divide the
6200 // distance, but we don't care because if the condition is "missed" the loop
6201 // will have undefined behavior due to wrapping.
6202 if (ControlsExit && AddRec->getNoWrapFlags(SCEV::FlagNW)) {
6204 getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
6205 return ExitLimit(Exact, Exact);
6208 // Then, try to solve the above equation provided that Start is constant.
6209 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
6210 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
6211 -StartC->getValue()->getValue(),
6213 return getCouldNotCompute();
6216 /// HowFarToNonZero - Return the number of times a backedge checking the
6217 /// specified value for nonzero will execute. If not computable, return
6219 ScalarEvolution::ExitLimit
6220 ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
6221 // Loops that look like: while (X == 0) are very strange indeed. We don't
6222 // handle them yet except for the trivial case. This could be expanded in the
6223 // future as needed.
6225 // If the value is a constant, check to see if it is known to be non-zero
6226 // already. If so, the backedge will execute zero times.
6227 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
6228 if (!C->getValue()->isNullValue())
6229 return getConstant(C->getType(), 0);
6230 return getCouldNotCompute(); // Otherwise it will loop infinitely.
6233 // We could implement others, but I really doubt anyone writes loops like
6234 // this, and if they did, they would already be constant folded.
6235 return getCouldNotCompute();
6238 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
6239 /// (which may not be an immediate predecessor) which has exactly one
6240 /// successor from which BB is reachable, or null if no such block is
6243 std::pair<BasicBlock *, BasicBlock *>
6244 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
6245 // If the block has a unique predecessor, then there is no path from the
6246 // predecessor to the block that does not go through the direct edge
6247 // from the predecessor to the block.
6248 if (BasicBlock *Pred = BB->getSinglePredecessor())
6249 return std::make_pair(Pred, BB);
6251 // A loop's header is defined to be a block that dominates the loop.
6252 // If the header has a unique predecessor outside the loop, it must be
6253 // a block that has exactly one successor that can reach the loop.
6254 if (Loop *L = LI->getLoopFor(BB))
6255 return std::make_pair(L->getLoopPredecessor(), L->getHeader());
6257 return std::pair<BasicBlock *, BasicBlock *>();
6260 /// HasSameValue - SCEV structural equivalence is usually sufficient for
6261 /// testing whether two expressions are equal, however for the purposes of
6262 /// looking for a condition guarding a loop, it can be useful to be a little
6263 /// more general, since a front-end may have replicated the controlling
6266 static bool HasSameValue(const SCEV *A, const SCEV *B) {
6267 // Quick check to see if they are the same SCEV.
6268 if (A == B) return true;
6270 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
6271 // two different instructions with the same value. Check for this case.
6272 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
6273 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
6274 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
6275 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
6276 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory())
6279 // Otherwise assume they may have a different value.
6283 /// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with
6284 /// predicate Pred. Return true iff any changes were made.
6286 bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
6287 const SCEV *&LHS, const SCEV *&RHS,
6289 bool Changed = false;
6291 // If we hit the max recursion limit bail out.
6295 // Canonicalize a constant to the right side.
6296 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
6297 // Check for both operands constant.
6298 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
6299 if (ConstantExpr::getICmp(Pred,
6301 RHSC->getValue())->isNullValue())
6302 goto trivially_false;
6304 goto trivially_true;
6306 // Otherwise swap the operands to put the constant on the right.
6307 std::swap(LHS, RHS);
6308 Pred = ICmpInst::getSwappedPredicate(Pred);
6312 // If we're comparing an addrec with a value which is loop-invariant in the
6313 // addrec's loop, put the addrec on the left. Also make a dominance check,
6314 // as both operands could be addrecs loop-invariant in each other's loop.
6315 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
6316 const Loop *L = AR->getLoop();
6317 if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) {
6318 std::swap(LHS, RHS);
6319 Pred = ICmpInst::getSwappedPredicate(Pred);
6324 // If there's a constant operand, canonicalize comparisons with boundary
6325 // cases, and canonicalize *-or-equal comparisons to regular comparisons.
6326 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
6327 const APInt &RA = RC->getValue()->getValue();
6329 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6330 case ICmpInst::ICMP_EQ:
6331 case ICmpInst::ICMP_NE:
6332 // Fold ((-1) * %a) + %b == 0 (equivalent to %b-%a == 0) into %a == %b.
6334 if (const SCEVAddExpr *AE = dyn_cast<SCEVAddExpr>(LHS))
6335 if (const SCEVMulExpr *ME = dyn_cast<SCEVMulExpr>(AE->getOperand(0)))
6336 if (AE->getNumOperands() == 2 && ME->getNumOperands() == 2 &&
6337 ME->getOperand(0)->isAllOnesValue()) {
6338 RHS = AE->getOperand(1);
6339 LHS = ME->getOperand(1);
6343 case ICmpInst::ICMP_UGE:
6344 if ((RA - 1).isMinValue()) {
6345 Pred = ICmpInst::ICMP_NE;
6346 RHS = getConstant(RA - 1);
6350 if (RA.isMaxValue()) {
6351 Pred = ICmpInst::ICMP_EQ;
6355 if (RA.isMinValue()) goto trivially_true;
6357 Pred = ICmpInst::ICMP_UGT;
6358 RHS = getConstant(RA - 1);
6361 case ICmpInst::ICMP_ULE:
6362 if ((RA + 1).isMaxValue()) {
6363 Pred = ICmpInst::ICMP_NE;
6364 RHS = getConstant(RA + 1);
6368 if (RA.isMinValue()) {
6369 Pred = ICmpInst::ICMP_EQ;
6373 if (RA.isMaxValue()) goto trivially_true;
6375 Pred = ICmpInst::ICMP_ULT;
6376 RHS = getConstant(RA + 1);
6379 case ICmpInst::ICMP_SGE:
6380 if ((RA - 1).isMinSignedValue()) {
6381 Pred = ICmpInst::ICMP_NE;
6382 RHS = getConstant(RA - 1);
6386 if (RA.isMaxSignedValue()) {
6387 Pred = ICmpInst::ICMP_EQ;
6391 if (RA.isMinSignedValue()) goto trivially_true;
6393 Pred = ICmpInst::ICMP_SGT;
6394 RHS = getConstant(RA - 1);
6397 case ICmpInst::ICMP_SLE:
6398 if ((RA + 1).isMaxSignedValue()) {
6399 Pred = ICmpInst::ICMP_NE;
6400 RHS = getConstant(RA + 1);
6404 if (RA.isMinSignedValue()) {
6405 Pred = ICmpInst::ICMP_EQ;
6409 if (RA.isMaxSignedValue()) goto trivially_true;
6411 Pred = ICmpInst::ICMP_SLT;
6412 RHS = getConstant(RA + 1);
6415 case ICmpInst::ICMP_UGT:
6416 if (RA.isMinValue()) {
6417 Pred = ICmpInst::ICMP_NE;
6421 if ((RA + 1).isMaxValue()) {
6422 Pred = ICmpInst::ICMP_EQ;
6423 RHS = getConstant(RA + 1);
6427 if (RA.isMaxValue()) goto trivially_false;
6429 case ICmpInst::ICMP_ULT:
6430 if (RA.isMaxValue()) {
6431 Pred = ICmpInst::ICMP_NE;
6435 if ((RA - 1).isMinValue()) {
6436 Pred = ICmpInst::ICMP_EQ;
6437 RHS = getConstant(RA - 1);
6441 if (RA.isMinValue()) goto trivially_false;
6443 case ICmpInst::ICMP_SGT:
6444 if (RA.isMinSignedValue()) {
6445 Pred = ICmpInst::ICMP_NE;
6449 if ((RA + 1).isMaxSignedValue()) {
6450 Pred = ICmpInst::ICMP_EQ;
6451 RHS = getConstant(RA + 1);
6455 if (RA.isMaxSignedValue()) goto trivially_false;
6457 case ICmpInst::ICMP_SLT:
6458 if (RA.isMaxSignedValue()) {
6459 Pred = ICmpInst::ICMP_NE;
6463 if ((RA - 1).isMinSignedValue()) {
6464 Pred = ICmpInst::ICMP_EQ;
6465 RHS = getConstant(RA - 1);
6469 if (RA.isMinSignedValue()) goto trivially_false;
6474 // Check for obvious equality.
6475 if (HasSameValue(LHS, RHS)) {
6476 if (ICmpInst::isTrueWhenEqual(Pred))
6477 goto trivially_true;
6478 if (ICmpInst::isFalseWhenEqual(Pred))
6479 goto trivially_false;
6482 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
6483 // adding or subtracting 1 from one of the operands.
6485 case ICmpInst::ICMP_SLE:
6486 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) {
6487 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
6489 Pred = ICmpInst::ICMP_SLT;
6491 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) {
6492 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
6494 Pred = ICmpInst::ICMP_SLT;
6498 case ICmpInst::ICMP_SGE:
6499 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) {
6500 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
6502 Pred = ICmpInst::ICMP_SGT;
6504 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) {
6505 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
6507 Pred = ICmpInst::ICMP_SGT;
6511 case ICmpInst::ICMP_ULE:
6512 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) {
6513 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
6515 Pred = ICmpInst::ICMP_ULT;
6517 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) {
6518 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
6520 Pred = ICmpInst::ICMP_ULT;
6524 case ICmpInst::ICMP_UGE:
6525 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) {
6526 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
6528 Pred = ICmpInst::ICMP_UGT;
6530 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) {
6531 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
6533 Pred = ICmpInst::ICMP_UGT;
6541 // TODO: More simplifications are possible here.
6543 // Recursively simplify until we either hit a recursion limit or nothing
6546 return SimplifyICmpOperands(Pred, LHS, RHS, Depth+1);
6552 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
6553 Pred = ICmpInst::ICMP_EQ;
6558 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
6559 Pred = ICmpInst::ICMP_NE;
6563 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
6564 return getSignedRange(S).getSignedMax().isNegative();
6567 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
6568 return getSignedRange(S).getSignedMin().isStrictlyPositive();
6571 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
6572 return !getSignedRange(S).getSignedMin().isNegative();
6575 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
6576 return !getSignedRange(S).getSignedMax().isStrictlyPositive();
6579 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
6580 return isKnownNegative(S) || isKnownPositive(S);
6583 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
6584 const SCEV *LHS, const SCEV *RHS) {
6585 // Canonicalize the inputs first.
6586 (void)SimplifyICmpOperands(Pred, LHS, RHS);
6588 // If LHS or RHS is an addrec, check to see if the condition is true in
6589 // every iteration of the loop.
6590 // If LHS and RHS are both addrec, both conditions must be true in
6591 // every iteration of the loop.
6592 const SCEVAddRecExpr *LAR = dyn_cast<SCEVAddRecExpr>(LHS);
6593 const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS);
6594 bool LeftGuarded = false;
6595 bool RightGuarded = false;
6597 const Loop *L = LAR->getLoop();
6598 if (isLoopEntryGuardedByCond(L, Pred, LAR->getStart(), RHS) &&
6599 isLoopBackedgeGuardedByCond(L, Pred, LAR->getPostIncExpr(*this), RHS)) {
6600 if (!RAR) return true;
6605 const Loop *L = RAR->getLoop();
6606 if (isLoopEntryGuardedByCond(L, Pred, LHS, RAR->getStart()) &&
6607 isLoopBackedgeGuardedByCond(L, Pred, LHS, RAR->getPostIncExpr(*this))) {
6608 if (!LAR) return true;
6609 RightGuarded = true;
6612 if (LeftGuarded && RightGuarded)
6615 // Otherwise see what can be done with known constant ranges.
6616 return isKnownPredicateWithRanges(Pred, LHS, RHS);
6620 ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred,
6621 const SCEV *LHS, const SCEV *RHS) {
6622 if (HasSameValue(LHS, RHS))
6623 return ICmpInst::isTrueWhenEqual(Pred);
6625 // This code is split out from isKnownPredicate because it is called from
6626 // within isLoopEntryGuardedByCond.
6629 llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6630 case ICmpInst::ICMP_SGT:
6631 std::swap(LHS, RHS);
6632 case ICmpInst::ICMP_SLT: {
6633 ConstantRange LHSRange = getSignedRange(LHS);
6634 ConstantRange RHSRange = getSignedRange(RHS);
6635 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
6637 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
6641 case ICmpInst::ICMP_SGE:
6642 std::swap(LHS, RHS);
6643 case ICmpInst::ICMP_SLE: {
6644 ConstantRange LHSRange = getSignedRange(LHS);
6645 ConstantRange RHSRange = getSignedRange(RHS);
6646 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
6648 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
6652 case ICmpInst::ICMP_UGT:
6653 std::swap(LHS, RHS);
6654 case ICmpInst::ICMP_ULT: {
6655 ConstantRange LHSRange = getUnsignedRange(LHS);
6656 ConstantRange RHSRange = getUnsignedRange(RHS);
6657 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
6659 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
6663 case ICmpInst::ICMP_UGE:
6664 std::swap(LHS, RHS);
6665 case ICmpInst::ICMP_ULE: {
6666 ConstantRange LHSRange = getUnsignedRange(LHS);
6667 ConstantRange RHSRange = getUnsignedRange(RHS);
6668 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
6670 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
6674 case ICmpInst::ICMP_NE: {
6675 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
6677 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
6680 const SCEV *Diff = getMinusSCEV(LHS, RHS);
6681 if (isKnownNonZero(Diff))
6685 case ICmpInst::ICMP_EQ:
6686 // The check at the top of the function catches the case where
6687 // the values are known to be equal.
6693 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
6694 /// protected by a conditional between LHS and RHS. This is used to
6695 /// to eliminate casts.
6697 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
6698 ICmpInst::Predicate Pred,
6699 const SCEV *LHS, const SCEV *RHS) {
6700 // Interpret a null as meaning no loop, where there is obviously no guard
6701 // (interprocedural conditions notwithstanding).
6702 if (!L) return true;
6704 if (isKnownPredicateWithRanges(Pred, LHS, RHS)) return true;
6706 BasicBlock *Latch = L->getLoopLatch();
6710 BranchInst *LoopContinuePredicate =
6711 dyn_cast<BranchInst>(Latch->getTerminator());
6712 if (LoopContinuePredicate && LoopContinuePredicate->isConditional() &&
6713 isImpliedCond(Pred, LHS, RHS,
6714 LoopContinuePredicate->getCondition(),
6715 LoopContinuePredicate->getSuccessor(0) != L->getHeader()))
6718 // Check conditions due to any @llvm.assume intrinsics.
6719 for (auto &AssumeVH : AC->assumptions()) {
6722 auto *CI = cast<CallInst>(AssumeVH);
6723 if (!DT->dominates(CI, Latch->getTerminator()))
6726 if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false))
6730 struct ClearWalkingBEDominatingCondsOnExit {
6731 ScalarEvolution &SE;
6733 explicit ClearWalkingBEDominatingCondsOnExit(ScalarEvolution &SE)
6736 ~ClearWalkingBEDominatingCondsOnExit() {
6737 SE.WalkingBEDominatingConds = false;
6741 // We don't want more than one activation of the following loop on the stack
6742 // -- that can lead to O(n!) time complexity.
6743 if (WalkingBEDominatingConds)
6746 WalkingBEDominatingConds = true;
6747 ClearWalkingBEDominatingCondsOnExit ClearOnExit(*this);
6749 // If the loop is not reachable from the entry block, we risk running into an
6750 // infinite loop as we walk up into the dom tree. These loops do not matter
6751 // anyway, so we just return a conservative answer when we see them.
6752 if (!DT->isReachableFromEntry(L->getHeader()))
6755 for (DomTreeNode *DTN = (*DT)[Latch], *HeaderDTN = (*DT)[L->getHeader()];
6757 DTN = DTN->getIDom()) {
6759 assert(DTN && "should reach the loop header before reaching the root!");
6761 BasicBlock *BB = DTN->getBlock();
6762 BasicBlock *PBB = BB->getSinglePredecessor();
6766 BranchInst *ContinuePredicate = dyn_cast<BranchInst>(PBB->getTerminator());
6767 if (!ContinuePredicate || !ContinuePredicate->isConditional())
6770 Value *Condition = ContinuePredicate->getCondition();
6772 // If we have an edge `E` within the loop body that dominates the only
6773 // latch, the condition guarding `E` also guards the backedge. This
6774 // reasoning works only for loops with a single latch.
6776 BasicBlockEdge DominatingEdge(PBB, BB);
6777 if (DominatingEdge.isSingleEdge()) {
6778 // We're constructively (and conservatively) enumerating edges within the
6779 // loop body that dominate the latch. The dominator tree better agree
6781 assert(DT->dominates(DominatingEdge, Latch) && "should be!");
6783 if (isImpliedCond(Pred, LHS, RHS, Condition,
6784 BB != ContinuePredicate->getSuccessor(0)))
6792 /// isLoopEntryGuardedByCond - Test whether entry to the loop is protected
6793 /// by a conditional between LHS and RHS. This is used to help avoid max
6794 /// expressions in loop trip counts, and to eliminate casts.
6796 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
6797 ICmpInst::Predicate Pred,
6798 const SCEV *LHS, const SCEV *RHS) {
6799 // Interpret a null as meaning no loop, where there is obviously no guard
6800 // (interprocedural conditions notwithstanding).
6801 if (!L) return false;
6803 if (isKnownPredicateWithRanges(Pred, LHS, RHS)) return true;
6805 // Starting at the loop predecessor, climb up the predecessor chain, as long
6806 // as there are predecessors that can be found that have unique successors
6807 // leading to the original header.
6808 for (std::pair<BasicBlock *, BasicBlock *>
6809 Pair(L->getLoopPredecessor(), L->getHeader());
6811 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
6813 BranchInst *LoopEntryPredicate =
6814 dyn_cast<BranchInst>(Pair.first->getTerminator());
6815 if (!LoopEntryPredicate ||
6816 LoopEntryPredicate->isUnconditional())
6819 if (isImpliedCond(Pred, LHS, RHS,
6820 LoopEntryPredicate->getCondition(),
6821 LoopEntryPredicate->getSuccessor(0) != Pair.second))
6825 // Check conditions due to any @llvm.assume intrinsics.
6826 for (auto &AssumeVH : AC->assumptions()) {
6829 auto *CI = cast<CallInst>(AssumeVH);
6830 if (!DT->dominates(CI, L->getHeader()))
6833 if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false))
6840 /// RAII wrapper to prevent recursive application of isImpliedCond.
6841 /// ScalarEvolution's PendingLoopPredicates set must be empty unless we are
6842 /// currently evaluating isImpliedCond.
6843 struct MarkPendingLoopPredicate {
6845 DenseSet<Value*> &LoopPreds;
6848 MarkPendingLoopPredicate(Value *C, DenseSet<Value*> &LP)
6849 : Cond(C), LoopPreds(LP) {
6850 Pending = !LoopPreds.insert(Cond).second;
6852 ~MarkPendingLoopPredicate() {
6854 LoopPreds.erase(Cond);
6858 /// isImpliedCond - Test whether the condition described by Pred, LHS,
6859 /// and RHS is true whenever the given Cond value evaluates to true.
6860 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred,
6861 const SCEV *LHS, const SCEV *RHS,
6862 Value *FoundCondValue,
6864 MarkPendingLoopPredicate Mark(FoundCondValue, PendingLoopPredicates);
6868 // Recursively handle And and Or conditions.
6869 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) {
6870 if (BO->getOpcode() == Instruction::And) {
6872 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
6873 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
6874 } else if (BO->getOpcode() == Instruction::Or) {
6876 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
6877 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
6881 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue);
6882 if (!ICI) return false;
6884 // Now that we found a conditional branch that dominates the loop or controls
6885 // the loop latch. Check to see if it is the comparison we are looking for.
6886 ICmpInst::Predicate FoundPred;
6888 FoundPred = ICI->getInversePredicate();
6890 FoundPred = ICI->getPredicate();
6892 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
6893 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
6895 // Balance the types.
6896 if (getTypeSizeInBits(LHS->getType()) <
6897 getTypeSizeInBits(FoundLHS->getType())) {
6898 if (CmpInst::isSigned(Pred)) {
6899 LHS = getSignExtendExpr(LHS, FoundLHS->getType());
6900 RHS = getSignExtendExpr(RHS, FoundLHS->getType());
6902 LHS = getZeroExtendExpr(LHS, FoundLHS->getType());
6903 RHS = getZeroExtendExpr(RHS, FoundLHS->getType());
6905 } else if (getTypeSizeInBits(LHS->getType()) >
6906 getTypeSizeInBits(FoundLHS->getType())) {
6907 if (CmpInst::isSigned(FoundPred)) {
6908 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
6909 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
6911 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
6912 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
6916 // Canonicalize the query to match the way instcombine will have
6917 // canonicalized the comparison.
6918 if (SimplifyICmpOperands(Pred, LHS, RHS))
6920 return CmpInst::isTrueWhenEqual(Pred);
6921 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
6922 if (FoundLHS == FoundRHS)
6923 return CmpInst::isFalseWhenEqual(FoundPred);
6925 // Check to see if we can make the LHS or RHS match.
6926 if (LHS == FoundRHS || RHS == FoundLHS) {
6927 if (isa<SCEVConstant>(RHS)) {
6928 std::swap(FoundLHS, FoundRHS);
6929 FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
6931 std::swap(LHS, RHS);
6932 Pred = ICmpInst::getSwappedPredicate(Pred);
6936 // Check whether the found predicate is the same as the desired predicate.
6937 if (FoundPred == Pred)
6938 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
6940 // Check whether swapping the found predicate makes it the same as the
6941 // desired predicate.
6942 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
6943 if (isa<SCEVConstant>(RHS))
6944 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
6946 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
6947 RHS, LHS, FoundLHS, FoundRHS);
6950 // Check if we can make progress by sharpening ranges.
6951 if (FoundPred == ICmpInst::ICMP_NE &&
6952 (isa<SCEVConstant>(FoundLHS) || isa<SCEVConstant>(FoundRHS))) {
6954 const SCEVConstant *C = nullptr;
6955 const SCEV *V = nullptr;
6957 if (isa<SCEVConstant>(FoundLHS)) {
6958 C = cast<SCEVConstant>(FoundLHS);
6961 C = cast<SCEVConstant>(FoundRHS);
6965 // The guarding predicate tells us that C != V. If the known range
6966 // of V is [C, t), we can sharpen the range to [C + 1, t). The
6967 // range we consider has to correspond to same signedness as the
6968 // predicate we're interested in folding.
6970 APInt Min = ICmpInst::isSigned(Pred) ?
6971 getSignedRange(V).getSignedMin() : getUnsignedRange(V).getUnsignedMin();
6973 if (Min == C->getValue()->getValue()) {
6974 // Given (V >= Min && V != Min) we conclude V >= (Min + 1).
6975 // This is true even if (Min + 1) wraps around -- in case of
6976 // wraparound, (Min + 1) < Min, so (V >= Min => V >= (Min + 1)).
6978 APInt SharperMin = Min + 1;
6981 case ICmpInst::ICMP_SGE:
6982 case ICmpInst::ICMP_UGE:
6983 // We know V `Pred` SharperMin. If this implies LHS `Pred`
6985 if (isImpliedCondOperands(Pred, LHS, RHS, V,
6986 getConstant(SharperMin)))
6989 case ICmpInst::ICMP_SGT:
6990 case ICmpInst::ICMP_UGT:
6991 // We know from the range information that (V `Pred` Min ||
6992 // V == Min). We know from the guarding condition that !(V
6993 // == Min). This gives us
6995 // V `Pred` Min || V == Min && !(V == Min)
6998 // If V `Pred` Min implies LHS `Pred` RHS, we're done.
7000 if (isImpliedCondOperands(Pred, LHS, RHS, V, getConstant(Min)))
7010 // Check whether the actual condition is beyond sufficient.
7011 if (FoundPred == ICmpInst::ICMP_EQ)
7012 if (ICmpInst::isTrueWhenEqual(Pred))
7013 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
7015 if (Pred == ICmpInst::ICMP_NE)
7016 if (!ICmpInst::isTrueWhenEqual(FoundPred))
7017 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
7020 // Otherwise assume the worst.
7024 /// isImpliedCondOperands - Test whether the condition described by Pred,
7025 /// LHS, and RHS is true whenever the condition described by Pred, FoundLHS,
7026 /// and FoundRHS is true.
7027 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
7028 const SCEV *LHS, const SCEV *RHS,
7029 const SCEV *FoundLHS,
7030 const SCEV *FoundRHS) {
7031 if (isImpliedCondOperandsViaRanges(Pred, LHS, RHS, FoundLHS, FoundRHS))
7034 return isImpliedCondOperandsHelper(Pred, LHS, RHS,
7035 FoundLHS, FoundRHS) ||
7036 // ~x < ~y --> x > y
7037 isImpliedCondOperandsHelper(Pred, LHS, RHS,
7038 getNotSCEV(FoundRHS),
7039 getNotSCEV(FoundLHS));
7043 /// If Expr computes ~A, return A else return nullptr
7044 static const SCEV *MatchNotExpr(const SCEV *Expr) {
7045 const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Expr);
7046 if (!Add || Add->getNumOperands() != 2) return nullptr;
7048 const SCEVConstant *AddLHS = dyn_cast<SCEVConstant>(Add->getOperand(0));
7049 if (!(AddLHS && AddLHS->getValue()->getValue().isAllOnesValue()))
7052 const SCEVMulExpr *AddRHS = dyn_cast<SCEVMulExpr>(Add->getOperand(1));
7053 if (!AddRHS || AddRHS->getNumOperands() != 2) return nullptr;
7055 const SCEVConstant *MulLHS = dyn_cast<SCEVConstant>(AddRHS->getOperand(0));
7056 if (!(MulLHS && MulLHS->getValue()->getValue().isAllOnesValue()))
7059 return AddRHS->getOperand(1);
7063 /// Is MaybeMaxExpr an SMax or UMax of Candidate and some other values?
7064 template<typename MaxExprType>
7065 static bool IsMaxConsistingOf(const SCEV *MaybeMaxExpr,
7066 const SCEV *Candidate) {
7067 const MaxExprType *MaxExpr = dyn_cast<MaxExprType>(MaybeMaxExpr);
7068 if (!MaxExpr) return false;
7070 auto It = std::find(MaxExpr->op_begin(), MaxExpr->op_end(), Candidate);
7071 return It != MaxExpr->op_end();
7075 /// Is MaybeMinExpr an SMin or UMin of Candidate and some other values?
7076 template<typename MaxExprType>
7077 static bool IsMinConsistingOf(ScalarEvolution &SE,
7078 const SCEV *MaybeMinExpr,
7079 const SCEV *Candidate) {
7080 const SCEV *MaybeMaxExpr = MatchNotExpr(MaybeMinExpr);
7084 return IsMaxConsistingOf<MaxExprType>(MaybeMaxExpr, SE.getNotSCEV(Candidate));
7088 /// Is LHS `Pred` RHS true on the virtue of LHS or RHS being a Min or Max
7090 static bool IsKnownPredicateViaMinOrMax(ScalarEvolution &SE,
7091 ICmpInst::Predicate Pred,
7092 const SCEV *LHS, const SCEV *RHS) {
7097 case ICmpInst::ICMP_SGE:
7098 std::swap(LHS, RHS);
7100 case ICmpInst::ICMP_SLE:
7103 IsMinConsistingOf<SCEVSMaxExpr>(SE, LHS, RHS) ||
7105 IsMaxConsistingOf<SCEVSMaxExpr>(RHS, LHS);
7107 case ICmpInst::ICMP_UGE:
7108 std::swap(LHS, RHS);
7110 case ICmpInst::ICMP_ULE:
7113 IsMinConsistingOf<SCEVUMaxExpr>(SE, LHS, RHS) ||
7115 IsMaxConsistingOf<SCEVUMaxExpr>(RHS, LHS);
7118 llvm_unreachable("covered switch fell through?!");
7121 /// isImpliedCondOperandsHelper - Test whether the condition described by
7122 /// Pred, LHS, and RHS is true whenever the condition described by Pred,
7123 /// FoundLHS, and FoundRHS is true.
7125 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
7126 const SCEV *LHS, const SCEV *RHS,
7127 const SCEV *FoundLHS,
7128 const SCEV *FoundRHS) {
7129 auto IsKnownPredicateFull =
7130 [this](ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS) {
7131 return isKnownPredicateWithRanges(Pred, LHS, RHS) ||
7132 IsKnownPredicateViaMinOrMax(*this, Pred, LHS, RHS);
7136 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
7137 case ICmpInst::ICMP_EQ:
7138 case ICmpInst::ICMP_NE:
7139 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
7142 case ICmpInst::ICMP_SLT:
7143 case ICmpInst::ICMP_SLE:
7144 if (IsKnownPredicateFull(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
7145 IsKnownPredicateFull(ICmpInst::ICMP_SGE, RHS, FoundRHS))
7148 case ICmpInst::ICMP_SGT:
7149 case ICmpInst::ICMP_SGE:
7150 if (IsKnownPredicateFull(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
7151 IsKnownPredicateFull(ICmpInst::ICMP_SLE, RHS, FoundRHS))
7154 case ICmpInst::ICMP_ULT:
7155 case ICmpInst::ICMP_ULE:
7156 if (IsKnownPredicateFull(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
7157 IsKnownPredicateFull(ICmpInst::ICMP_UGE, RHS, FoundRHS))
7160 case ICmpInst::ICMP_UGT:
7161 case ICmpInst::ICMP_UGE:
7162 if (IsKnownPredicateFull(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
7163 IsKnownPredicateFull(ICmpInst::ICMP_ULE, RHS, FoundRHS))
7171 /// isImpliedCondOperandsViaRanges - helper function for isImpliedCondOperands.
7172 /// Tries to get cases like "X `sgt` 0 => X - 1 `sgt` -1".
7173 bool ScalarEvolution::isImpliedCondOperandsViaRanges(ICmpInst::Predicate Pred,
7176 const SCEV *FoundLHS,
7177 const SCEV *FoundRHS) {
7178 if (!isa<SCEVConstant>(RHS) || !isa<SCEVConstant>(FoundRHS))
7179 // The restriction on `FoundRHS` be lifted easily -- it exists only to
7180 // reduce the compile time impact of this optimization.
7183 const SCEVAddExpr *AddLHS = dyn_cast<SCEVAddExpr>(LHS);
7184 if (!AddLHS || AddLHS->getOperand(1) != FoundLHS ||
7185 !isa<SCEVConstant>(AddLHS->getOperand(0)))
7188 APInt ConstFoundRHS = cast<SCEVConstant>(FoundRHS)->getValue()->getValue();
7190 // `FoundLHSRange` is the range we know `FoundLHS` to be in by virtue of the
7191 // antecedent "`FoundLHS` `Pred` `FoundRHS`".
7192 ConstantRange FoundLHSRange =
7193 ConstantRange::makeAllowedICmpRegion(Pred, ConstFoundRHS);
7195 // Since `LHS` is `FoundLHS` + `AddLHS->getOperand(0)`, we can compute a range
7198 cast<SCEVConstant>(AddLHS->getOperand(0))->getValue()->getValue();
7199 ConstantRange LHSRange = FoundLHSRange.add(ConstantRange(Addend));
7201 // We can also compute the range of values for `LHS` that satisfy the
7202 // consequent, "`LHS` `Pred` `RHS`":
7203 APInt ConstRHS = cast<SCEVConstant>(RHS)->getValue()->getValue();
7204 ConstantRange SatisfyingLHSRange =
7205 ConstantRange::makeSatisfyingICmpRegion(Pred, ConstRHS);
7207 // The antecedent implies the consequent if every value of `LHS` that
7208 // satisfies the antecedent also satisfies the consequent.
7209 return SatisfyingLHSRange.contains(LHSRange);
7212 // Verify if an linear IV with positive stride can overflow when in a
7213 // less-than comparison, knowing the invariant term of the comparison, the
7214 // stride and the knowledge of NSW/NUW flags on the recurrence.
7215 bool ScalarEvolution::doesIVOverflowOnLT(const SCEV *RHS, const SCEV *Stride,
7216 bool IsSigned, bool NoWrap) {
7217 if (NoWrap) return false;
7219 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
7220 const SCEV *One = getConstant(Stride->getType(), 1);
7223 APInt MaxRHS = getSignedRange(RHS).getSignedMax();
7224 APInt MaxValue = APInt::getSignedMaxValue(BitWidth);
7225 APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
7228 // SMaxRHS + SMaxStrideMinusOne > SMaxValue => overflow!
7229 return (MaxValue - MaxStrideMinusOne).slt(MaxRHS);
7232 APInt MaxRHS = getUnsignedRange(RHS).getUnsignedMax();
7233 APInt MaxValue = APInt::getMaxValue(BitWidth);
7234 APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
7237 // UMaxRHS + UMaxStrideMinusOne > UMaxValue => overflow!
7238 return (MaxValue - MaxStrideMinusOne).ult(MaxRHS);
7241 // Verify if an linear IV with negative stride can overflow when in a
7242 // greater-than comparison, knowing the invariant term of the comparison,
7243 // the stride and the knowledge of NSW/NUW flags on the recurrence.
7244 bool ScalarEvolution::doesIVOverflowOnGT(const SCEV *RHS, const SCEV *Stride,
7245 bool IsSigned, bool NoWrap) {
7246 if (NoWrap) return false;
7248 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
7249 const SCEV *One = getConstant(Stride->getType(), 1);
7252 APInt MinRHS = getSignedRange(RHS).getSignedMin();
7253 APInt MinValue = APInt::getSignedMinValue(BitWidth);
7254 APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
7257 // SMinRHS - SMaxStrideMinusOne < SMinValue => overflow!
7258 return (MinValue + MaxStrideMinusOne).sgt(MinRHS);
7261 APInt MinRHS = getUnsignedRange(RHS).getUnsignedMin();
7262 APInt MinValue = APInt::getMinValue(BitWidth);
7263 APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
7266 // UMinRHS - UMaxStrideMinusOne < UMinValue => overflow!
7267 return (MinValue + MaxStrideMinusOne).ugt(MinRHS);
7270 // Compute the backedge taken count knowing the interval difference, the
7271 // stride and presence of the equality in the comparison.
7272 const SCEV *ScalarEvolution::computeBECount(const SCEV *Delta, const SCEV *Step,
7274 const SCEV *One = getConstant(Step->getType(), 1);
7275 Delta = Equality ? getAddExpr(Delta, Step)
7276 : getAddExpr(Delta, getMinusSCEV(Step, One));
7277 return getUDivExpr(Delta, Step);
7280 /// HowManyLessThans - Return the number of times a backedge containing the
7281 /// specified less-than comparison will execute. If not computable, return
7282 /// CouldNotCompute.
7284 /// @param ControlsExit is true when the LHS < RHS condition directly controls
7285 /// the branch (loops exits only if condition is true). In this case, we can use
7286 /// NoWrapFlags to skip overflow checks.
7287 ScalarEvolution::ExitLimit
7288 ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
7289 const Loop *L, bool IsSigned,
7290 bool ControlsExit) {
7291 // We handle only IV < Invariant
7292 if (!isLoopInvariant(RHS, L))
7293 return getCouldNotCompute();
7295 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
7297 // Avoid weird loops
7298 if (!IV || IV->getLoop() != L || !IV->isAffine())
7299 return getCouldNotCompute();
7301 bool NoWrap = ControlsExit &&
7302 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
7304 const SCEV *Stride = IV->getStepRecurrence(*this);
7306 // Avoid negative or zero stride values
7307 if (!isKnownPositive(Stride))
7308 return getCouldNotCompute();
7310 // Avoid proven overflow cases: this will ensure that the backedge taken count
7311 // will not generate any unsigned overflow. Relaxed no-overflow conditions
7312 // exploit NoWrapFlags, allowing to optimize in presence of undefined
7313 // behaviors like the case of C language.
7314 if (!Stride->isOne() && doesIVOverflowOnLT(RHS, Stride, IsSigned, NoWrap))
7315 return getCouldNotCompute();
7317 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SLT
7318 : ICmpInst::ICMP_ULT;
7319 const SCEV *Start = IV->getStart();
7320 const SCEV *End = RHS;
7321 if (!isLoopEntryGuardedByCond(L, Cond, getMinusSCEV(Start, Stride), RHS)) {
7322 const SCEV *Diff = getMinusSCEV(RHS, Start);
7323 // If we have NoWrap set, then we can assume that the increment won't
7324 // overflow, in which case if RHS - Start is a constant, we don't need to
7325 // do a max operation since we can just figure it out statically
7326 if (NoWrap && isa<SCEVConstant>(Diff)) {
7327 APInt D = dyn_cast<const SCEVConstant>(Diff)->getValue()->getValue();
7331 End = IsSigned ? getSMaxExpr(RHS, Start)
7332 : getUMaxExpr(RHS, Start);
7335 const SCEV *BECount = computeBECount(getMinusSCEV(End, Start), Stride, false);
7337 APInt MinStart = IsSigned ? getSignedRange(Start).getSignedMin()
7338 : getUnsignedRange(Start).getUnsignedMin();
7340 APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
7341 : getUnsignedRange(Stride).getUnsignedMin();
7343 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
7344 APInt Limit = IsSigned ? APInt::getSignedMaxValue(BitWidth) - (MinStride - 1)
7345 : APInt::getMaxValue(BitWidth) - (MinStride - 1);
7347 // Although End can be a MAX expression we estimate MaxEnd considering only
7348 // the case End = RHS. This is safe because in the other case (End - Start)
7349 // is zero, leading to a zero maximum backedge taken count.
7351 IsSigned ? APIntOps::smin(getSignedRange(RHS).getSignedMax(), Limit)
7352 : APIntOps::umin(getUnsignedRange(RHS).getUnsignedMax(), Limit);
7354 const SCEV *MaxBECount;
7355 if (isa<SCEVConstant>(BECount))
7356 MaxBECount = BECount;
7358 MaxBECount = computeBECount(getConstant(MaxEnd - MinStart),
7359 getConstant(MinStride), false);
7361 if (isa<SCEVCouldNotCompute>(MaxBECount))
7362 MaxBECount = BECount;
7364 return ExitLimit(BECount, MaxBECount);
7367 ScalarEvolution::ExitLimit
7368 ScalarEvolution::HowManyGreaterThans(const SCEV *LHS, const SCEV *RHS,
7369 const Loop *L, bool IsSigned,
7370 bool ControlsExit) {
7371 // We handle only IV > Invariant
7372 if (!isLoopInvariant(RHS, L))
7373 return getCouldNotCompute();
7375 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
7377 // Avoid weird loops
7378 if (!IV || IV->getLoop() != L || !IV->isAffine())
7379 return getCouldNotCompute();
7381 bool NoWrap = ControlsExit &&
7382 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
7384 const SCEV *Stride = getNegativeSCEV(IV->getStepRecurrence(*this));
7386 // Avoid negative or zero stride values
7387 if (!isKnownPositive(Stride))
7388 return getCouldNotCompute();
7390 // Avoid proven overflow cases: this will ensure that the backedge taken count
7391 // will not generate any unsigned overflow. Relaxed no-overflow conditions
7392 // exploit NoWrapFlags, allowing to optimize in presence of undefined
7393 // behaviors like the case of C language.
7394 if (!Stride->isOne() && doesIVOverflowOnGT(RHS, Stride, IsSigned, NoWrap))
7395 return getCouldNotCompute();
7397 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SGT
7398 : ICmpInst::ICMP_UGT;
7400 const SCEV *Start = IV->getStart();
7401 const SCEV *End = RHS;
7402 if (!isLoopEntryGuardedByCond(L, Cond, getAddExpr(Start, Stride), RHS)) {
7403 const SCEV *Diff = getMinusSCEV(RHS, Start);
7404 // If we have NoWrap set, then we can assume that the increment won't
7405 // overflow, in which case if RHS - Start is a constant, we don't need to
7406 // do a max operation since we can just figure it out statically
7407 if (NoWrap && isa<SCEVConstant>(Diff)) {
7408 APInt D = dyn_cast<const SCEVConstant>(Diff)->getValue()->getValue();
7409 if (!D.isNegative())
7412 End = IsSigned ? getSMinExpr(RHS, Start)
7413 : getUMinExpr(RHS, Start);
7416 const SCEV *BECount = computeBECount(getMinusSCEV(Start, End), Stride, false);
7418 APInt MaxStart = IsSigned ? getSignedRange(Start).getSignedMax()
7419 : getUnsignedRange(Start).getUnsignedMax();
7421 APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
7422 : getUnsignedRange(Stride).getUnsignedMin();
7424 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
7425 APInt Limit = IsSigned ? APInt::getSignedMinValue(BitWidth) + (MinStride - 1)
7426 : APInt::getMinValue(BitWidth) + (MinStride - 1);
7428 // Although End can be a MIN expression we estimate MinEnd considering only
7429 // the case End = RHS. This is safe because in the other case (Start - End)
7430 // is zero, leading to a zero maximum backedge taken count.
7432 IsSigned ? APIntOps::smax(getSignedRange(RHS).getSignedMin(), Limit)
7433 : APIntOps::umax(getUnsignedRange(RHS).getUnsignedMin(), Limit);
7436 const SCEV *MaxBECount = getCouldNotCompute();
7437 if (isa<SCEVConstant>(BECount))
7438 MaxBECount = BECount;
7440 MaxBECount = computeBECount(getConstant(MaxStart - MinEnd),
7441 getConstant(MinStride), false);
7443 if (isa<SCEVCouldNotCompute>(MaxBECount))
7444 MaxBECount = BECount;
7446 return ExitLimit(BECount, MaxBECount);
7449 /// getNumIterationsInRange - Return the number of iterations of this loop that
7450 /// produce values in the specified constant range. Another way of looking at
7451 /// this is that it returns the first iteration number where the value is not in
7452 /// the condition, thus computing the exit count. If the iteration count can't
7453 /// be computed, an instance of SCEVCouldNotCompute is returned.
7454 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
7455 ScalarEvolution &SE) const {
7456 if (Range.isFullSet()) // Infinite loop.
7457 return SE.getCouldNotCompute();
7459 // If the start is a non-zero constant, shift the range to simplify things.
7460 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
7461 if (!SC->getValue()->isZero()) {
7462 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
7463 Operands[0] = SE.getConstant(SC->getType(), 0);
7464 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(),
7465 getNoWrapFlags(FlagNW));
7466 if (const SCEVAddRecExpr *ShiftedAddRec =
7467 dyn_cast<SCEVAddRecExpr>(Shifted))
7468 return ShiftedAddRec->getNumIterationsInRange(
7469 Range.subtract(SC->getValue()->getValue()), SE);
7470 // This is strange and shouldn't happen.
7471 return SE.getCouldNotCompute();
7474 // The only time we can solve this is when we have all constant indices.
7475 // Otherwise, we cannot determine the overflow conditions.
7476 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
7477 if (!isa<SCEVConstant>(getOperand(i)))
7478 return SE.getCouldNotCompute();
7481 // Okay at this point we know that all elements of the chrec are constants and
7482 // that the start element is zero.
7484 // First check to see if the range contains zero. If not, the first
7486 unsigned BitWidth = SE.getTypeSizeInBits(getType());
7487 if (!Range.contains(APInt(BitWidth, 0)))
7488 return SE.getConstant(getType(), 0);
7491 // If this is an affine expression then we have this situation:
7492 // Solve {0,+,A} in Range === Ax in Range
7494 // We know that zero is in the range. If A is positive then we know that
7495 // the upper value of the range must be the first possible exit value.
7496 // If A is negative then the lower of the range is the last possible loop
7497 // value. Also note that we already checked for a full range.
7498 APInt One(BitWidth,1);
7499 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
7500 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
7502 // The exit value should be (End+A)/A.
7503 APInt ExitVal = (End + A).udiv(A);
7504 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
7506 // Evaluate at the exit value. If we really did fall out of the valid
7507 // range, then we computed our trip count, otherwise wrap around or other
7508 // things must have happened.
7509 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
7510 if (Range.contains(Val->getValue()))
7511 return SE.getCouldNotCompute(); // Something strange happened
7513 // Ensure that the previous value is in the range. This is a sanity check.
7514 assert(Range.contains(
7515 EvaluateConstantChrecAtConstant(this,
7516 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
7517 "Linear scev computation is off in a bad way!");
7518 return SE.getConstant(ExitValue);
7519 } else if (isQuadratic()) {
7520 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
7521 // quadratic equation to solve it. To do this, we must frame our problem in
7522 // terms of figuring out when zero is crossed, instead of when
7523 // Range.getUpper() is crossed.
7524 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
7525 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
7526 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop(),
7527 // getNoWrapFlags(FlagNW)
7530 // Next, solve the constructed addrec
7531 std::pair<const SCEV *,const SCEV *> Roots =
7532 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
7533 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
7534 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
7536 // Pick the smallest positive root value.
7537 if (ConstantInt *CB =
7538 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
7539 R1->getValue(), R2->getValue()))) {
7540 if (!CB->getZExtValue())
7541 std::swap(R1, R2); // R1 is the minimum root now.
7543 // Make sure the root is not off by one. The returned iteration should
7544 // not be in the range, but the previous one should be. When solving
7545 // for "X*X < 5", for example, we should not return a root of 2.
7546 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
7549 if (Range.contains(R1Val->getValue())) {
7550 // The next iteration must be out of the range...
7551 ConstantInt *NextVal =
7552 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1);
7554 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
7555 if (!Range.contains(R1Val->getValue()))
7556 return SE.getConstant(NextVal);
7557 return SE.getCouldNotCompute(); // Something strange happened
7560 // If R1 was not in the range, then it is a good return value. Make
7561 // sure that R1-1 WAS in the range though, just in case.
7562 ConstantInt *NextVal =
7563 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1);
7564 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
7565 if (Range.contains(R1Val->getValue()))
7567 return SE.getCouldNotCompute(); // Something strange happened
7572 return SE.getCouldNotCompute();
7578 FindUndefs() : Found(false) {}
7580 bool follow(const SCEV *S) {
7581 if (const SCEVUnknown *C = dyn_cast<SCEVUnknown>(S)) {
7582 if (isa<UndefValue>(C->getValue()))
7584 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) {
7585 if (isa<UndefValue>(C->getValue()))
7589 // Keep looking if we haven't found it yet.
7592 bool isDone() const {
7593 // Stop recursion if we have found an undef.
7599 // Return true when S contains at least an undef value.
7601 containsUndefs(const SCEV *S) {
7603 SCEVTraversal<FindUndefs> ST(F);
7610 // Collect all steps of SCEV expressions.
7611 struct SCEVCollectStrides {
7612 ScalarEvolution &SE;
7613 SmallVectorImpl<const SCEV *> &Strides;
7615 SCEVCollectStrides(ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &S)
7616 : SE(SE), Strides(S) {}
7618 bool follow(const SCEV *S) {
7619 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(S))
7620 Strides.push_back(AR->getStepRecurrence(SE));
7623 bool isDone() const { return false; }
7626 // Collect all SCEVUnknown and SCEVMulExpr expressions.
7627 struct SCEVCollectTerms {
7628 SmallVectorImpl<const SCEV *> &Terms;
7630 SCEVCollectTerms(SmallVectorImpl<const SCEV *> &T)
7633 bool follow(const SCEV *S) {
7634 if (isa<SCEVUnknown>(S) || isa<SCEVMulExpr>(S)) {
7635 if (!containsUndefs(S))
7638 // Stop recursion: once we collected a term, do not walk its operands.
7645 bool isDone() const { return false; }
7649 /// Find parametric terms in this SCEVAddRecExpr.
7650 void ScalarEvolution::collectParametricTerms(const SCEV *Expr,
7651 SmallVectorImpl<const SCEV *> &Terms) {
7652 SmallVector<const SCEV *, 4> Strides;
7653 SCEVCollectStrides StrideCollector(*this, Strides);
7654 visitAll(Expr, StrideCollector);
7657 dbgs() << "Strides:\n";
7658 for (const SCEV *S : Strides)
7659 dbgs() << *S << "\n";
7662 for (const SCEV *S : Strides) {
7663 SCEVCollectTerms TermCollector(Terms);
7664 visitAll(S, TermCollector);
7668 dbgs() << "Terms:\n";
7669 for (const SCEV *T : Terms)
7670 dbgs() << *T << "\n";
7674 static bool findArrayDimensionsRec(ScalarEvolution &SE,
7675 SmallVectorImpl<const SCEV *> &Terms,
7676 SmallVectorImpl<const SCEV *> &Sizes) {
7677 int Last = Terms.size() - 1;
7678 const SCEV *Step = Terms[Last];
7680 // End of recursion.
7682 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Step)) {
7683 SmallVector<const SCEV *, 2> Qs;
7684 for (const SCEV *Op : M->operands())
7685 if (!isa<SCEVConstant>(Op))
7688 Step = SE.getMulExpr(Qs);
7691 Sizes.push_back(Step);
7695 for (const SCEV *&Term : Terms) {
7696 // Normalize the terms before the next call to findArrayDimensionsRec.
7698 SCEVDivision::divide(SE, Term, Step, &Q, &R);
7700 // Bail out when GCD does not evenly divide one of the terms.
7707 // Remove all SCEVConstants.
7708 Terms.erase(std::remove_if(Terms.begin(), Terms.end(), [](const SCEV *E) {
7709 return isa<SCEVConstant>(E);
7713 if (Terms.size() > 0)
7714 if (!findArrayDimensionsRec(SE, Terms, Sizes))
7717 Sizes.push_back(Step);
7722 struct FindParameter {
7723 bool FoundParameter;
7724 FindParameter() : FoundParameter(false) {}
7726 bool follow(const SCEV *S) {
7727 if (isa<SCEVUnknown>(S)) {
7728 FoundParameter = true;
7729 // Stop recursion: we found a parameter.
7735 bool isDone() const {
7736 // Stop recursion if we have found a parameter.
7737 return FoundParameter;
7742 // Returns true when S contains at least a SCEVUnknown parameter.
7744 containsParameters(const SCEV *S) {
7746 SCEVTraversal<FindParameter> ST(F);
7749 return F.FoundParameter;
7752 // Returns true when one of the SCEVs of Terms contains a SCEVUnknown parameter.
7754 containsParameters(SmallVectorImpl<const SCEV *> &Terms) {
7755 for (const SCEV *T : Terms)
7756 if (containsParameters(T))
7761 // Return the number of product terms in S.
7762 static inline int numberOfTerms(const SCEV *S) {
7763 if (const SCEVMulExpr *Expr = dyn_cast<SCEVMulExpr>(S))
7764 return Expr->getNumOperands();
7768 static const SCEV *removeConstantFactors(ScalarEvolution &SE, const SCEV *T) {
7769 if (isa<SCEVConstant>(T))
7772 if (isa<SCEVUnknown>(T))
7775 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(T)) {
7776 SmallVector<const SCEV *, 2> Factors;
7777 for (const SCEV *Op : M->operands())
7778 if (!isa<SCEVConstant>(Op))
7779 Factors.push_back(Op);
7781 return SE.getMulExpr(Factors);
7787 /// Return the size of an element read or written by Inst.
7788 const SCEV *ScalarEvolution::getElementSize(Instruction *Inst) {
7790 if (StoreInst *Store = dyn_cast<StoreInst>(Inst))
7791 Ty = Store->getValueOperand()->getType();
7792 else if (LoadInst *Load = dyn_cast<LoadInst>(Inst))
7793 Ty = Load->getType();
7797 Type *ETy = getEffectiveSCEVType(PointerType::getUnqual(Ty));
7798 return getSizeOfExpr(ETy, Ty);
7801 /// Second step of delinearization: compute the array dimensions Sizes from the
7802 /// set of Terms extracted from the memory access function of this SCEVAddRec.
7803 void ScalarEvolution::findArrayDimensions(SmallVectorImpl<const SCEV *> &Terms,
7804 SmallVectorImpl<const SCEV *> &Sizes,
7805 const SCEV *ElementSize) const {
7807 if (Terms.size() < 1 || !ElementSize)
7810 // Early return when Terms do not contain parameters: we do not delinearize
7811 // non parametric SCEVs.
7812 if (!containsParameters(Terms))
7816 dbgs() << "Terms:\n";
7817 for (const SCEV *T : Terms)
7818 dbgs() << *T << "\n";
7821 // Remove duplicates.
7822 std::sort(Terms.begin(), Terms.end());
7823 Terms.erase(std::unique(Terms.begin(), Terms.end()), Terms.end());
7825 // Put larger terms first.
7826 std::sort(Terms.begin(), Terms.end(), [](const SCEV *LHS, const SCEV *RHS) {
7827 return numberOfTerms(LHS) > numberOfTerms(RHS);
7830 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
7832 // Divide all terms by the element size.
7833 for (const SCEV *&Term : Terms) {
7835 SCEVDivision::divide(SE, Term, ElementSize, &Q, &R);
7839 SmallVector<const SCEV *, 4> NewTerms;
7841 // Remove constant factors.
7842 for (const SCEV *T : Terms)
7843 if (const SCEV *NewT = removeConstantFactors(SE, T))
7844 NewTerms.push_back(NewT);
7847 dbgs() << "Terms after sorting:\n";
7848 for (const SCEV *T : NewTerms)
7849 dbgs() << *T << "\n";
7852 if (NewTerms.empty() ||
7853 !findArrayDimensionsRec(SE, NewTerms, Sizes)) {
7858 // The last element to be pushed into Sizes is the size of an element.
7859 Sizes.push_back(ElementSize);
7862 dbgs() << "Sizes:\n";
7863 for (const SCEV *S : Sizes)
7864 dbgs() << *S << "\n";
7868 /// Third step of delinearization: compute the access functions for the
7869 /// Subscripts based on the dimensions in Sizes.
7870 void ScalarEvolution::computeAccessFunctions(
7871 const SCEV *Expr, SmallVectorImpl<const SCEV *> &Subscripts,
7872 SmallVectorImpl<const SCEV *> &Sizes) {
7874 // Early exit in case this SCEV is not an affine multivariate function.
7878 if (auto AR = dyn_cast<SCEVAddRecExpr>(Expr))
7879 if (!AR->isAffine())
7882 const SCEV *Res = Expr;
7883 int Last = Sizes.size() - 1;
7884 for (int i = Last; i >= 0; i--) {
7886 SCEVDivision::divide(*this, Res, Sizes[i], &Q, &R);
7889 dbgs() << "Res: " << *Res << "\n";
7890 dbgs() << "Sizes[i]: " << *Sizes[i] << "\n";
7891 dbgs() << "Res divided by Sizes[i]:\n";
7892 dbgs() << "Quotient: " << *Q << "\n";
7893 dbgs() << "Remainder: " << *R << "\n";
7898 // Do not record the last subscript corresponding to the size of elements in
7902 // Bail out if the remainder is too complex.
7903 if (isa<SCEVAddRecExpr>(R)) {
7912 // Record the access function for the current subscript.
7913 Subscripts.push_back(R);
7916 // Also push in last position the remainder of the last division: it will be
7917 // the access function of the innermost dimension.
7918 Subscripts.push_back(Res);
7920 std::reverse(Subscripts.begin(), Subscripts.end());
7923 dbgs() << "Subscripts:\n";
7924 for (const SCEV *S : Subscripts)
7925 dbgs() << *S << "\n";
7929 /// Splits the SCEV into two vectors of SCEVs representing the subscripts and
7930 /// sizes of an array access. Returns the remainder of the delinearization that
7931 /// is the offset start of the array. The SCEV->delinearize algorithm computes
7932 /// the multiples of SCEV coefficients: that is a pattern matching of sub
7933 /// expressions in the stride and base of a SCEV corresponding to the
7934 /// computation of a GCD (greatest common divisor) of base and stride. When
7935 /// SCEV->delinearize fails, it returns the SCEV unchanged.
7937 /// For example: when analyzing the memory access A[i][j][k] in this loop nest
7939 /// void foo(long n, long m, long o, double A[n][m][o]) {
7941 /// for (long i = 0; i < n; i++)
7942 /// for (long j = 0; j < m; j++)
7943 /// for (long k = 0; k < o; k++)
7944 /// A[i][j][k] = 1.0;
7947 /// the delinearization input is the following AddRec SCEV:
7949 /// AddRec: {{{%A,+,(8 * %m * %o)}<%for.i>,+,(8 * %o)}<%for.j>,+,8}<%for.k>
7951 /// From this SCEV, we are able to say that the base offset of the access is %A
7952 /// because it appears as an offset that does not divide any of the strides in
7955 /// CHECK: Base offset: %A
7957 /// and then SCEV->delinearize determines the size of some of the dimensions of
7958 /// the array as these are the multiples by which the strides are happening:
7960 /// CHECK: ArrayDecl[UnknownSize][%m][%o] with elements of sizeof(double) bytes.
7962 /// Note that the outermost dimension remains of UnknownSize because there are
7963 /// no strides that would help identifying the size of the last dimension: when
7964 /// the array has been statically allocated, one could compute the size of that
7965 /// dimension by dividing the overall size of the array by the size of the known
7966 /// dimensions: %m * %o * 8.
7968 /// Finally delinearize provides the access functions for the array reference
7969 /// that does correspond to A[i][j][k] of the above C testcase:
7971 /// CHECK: ArrayRef[{0,+,1}<%for.i>][{0,+,1}<%for.j>][{0,+,1}<%for.k>]
7973 /// The testcases are checking the output of a function pass:
7974 /// DelinearizationPass that walks through all loads and stores of a function
7975 /// asking for the SCEV of the memory access with respect to all enclosing
7976 /// loops, calling SCEV->delinearize on that and printing the results.
7978 void ScalarEvolution::delinearize(const SCEV *Expr,
7979 SmallVectorImpl<const SCEV *> &Subscripts,
7980 SmallVectorImpl<const SCEV *> &Sizes,
7981 const SCEV *ElementSize) {
7982 // First step: collect parametric terms.
7983 SmallVector<const SCEV *, 4> Terms;
7984 collectParametricTerms(Expr, Terms);
7989 // Second step: find subscript sizes.
7990 findArrayDimensions(Terms, Sizes, ElementSize);
7995 // Third step: compute the access functions for each subscript.
7996 computeAccessFunctions(Expr, Subscripts, Sizes);
7998 if (Subscripts.empty())
8002 dbgs() << "succeeded to delinearize " << *Expr << "\n";
8003 dbgs() << "ArrayDecl[UnknownSize]";
8004 for (const SCEV *S : Sizes)
8005 dbgs() << "[" << *S << "]";
8007 dbgs() << "\nArrayRef";
8008 for (const SCEV *S : Subscripts)
8009 dbgs() << "[" << *S << "]";
8014 //===----------------------------------------------------------------------===//
8015 // SCEVCallbackVH Class Implementation
8016 //===----------------------------------------------------------------------===//
8018 void ScalarEvolution::SCEVCallbackVH::deleted() {
8019 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
8020 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
8021 SE->ConstantEvolutionLoopExitValue.erase(PN);
8022 SE->ValueExprMap.erase(getValPtr());
8023 // this now dangles!
8026 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) {
8027 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
8029 // Forget all the expressions associated with users of the old value,
8030 // so that future queries will recompute the expressions using the new
8032 Value *Old = getValPtr();
8033 SmallVector<User *, 16> Worklist(Old->user_begin(), Old->user_end());
8034 SmallPtrSet<User *, 8> Visited;
8035 while (!Worklist.empty()) {
8036 User *U = Worklist.pop_back_val();
8037 // Deleting the Old value will cause this to dangle. Postpone
8038 // that until everything else is done.
8041 if (!Visited.insert(U).second)
8043 if (PHINode *PN = dyn_cast<PHINode>(U))
8044 SE->ConstantEvolutionLoopExitValue.erase(PN);
8045 SE->ValueExprMap.erase(U);
8046 Worklist.insert(Worklist.end(), U->user_begin(), U->user_end());
8048 // Delete the Old value.
8049 if (PHINode *PN = dyn_cast<PHINode>(Old))
8050 SE->ConstantEvolutionLoopExitValue.erase(PN);
8051 SE->ValueExprMap.erase(Old);
8052 // this now dangles!
8055 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
8056 : CallbackVH(V), SE(se) {}
8058 //===----------------------------------------------------------------------===//
8059 // ScalarEvolution Class Implementation
8060 //===----------------------------------------------------------------------===//
8062 ScalarEvolution::ScalarEvolution()
8063 : FunctionPass(ID), WalkingBEDominatingConds(false), ValuesAtScopes(64),
8064 LoopDispositions(64), BlockDispositions(64), FirstUnknown(nullptr) {
8065 initializeScalarEvolutionPass(*PassRegistry::getPassRegistry());
8068 bool ScalarEvolution::runOnFunction(Function &F) {
8070 AC = &getAnalysis<AssumptionCacheTracker>().getAssumptionCache(F);
8071 LI = &getAnalysis<LoopInfoWrapperPass>().getLoopInfo();
8072 TLI = &getAnalysis<TargetLibraryInfoWrapperPass>().getTLI();
8073 DT = &getAnalysis<DominatorTreeWrapperPass>().getDomTree();
8077 void ScalarEvolution::releaseMemory() {
8078 // Iterate through all the SCEVUnknown instances and call their
8079 // destructors, so that they release their references to their values.
8080 for (SCEVUnknown *U = FirstUnknown; U; U = U->Next)
8082 FirstUnknown = nullptr;
8084 ValueExprMap.clear();
8086 // Free any extra memory created for ExitNotTakenInfo in the unlikely event
8087 // that a loop had multiple computable exits.
8088 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
8089 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end();
8094 assert(PendingLoopPredicates.empty() && "isImpliedCond garbage");
8095 assert(!WalkingBEDominatingConds && "isLoopBackedgeGuardedByCond garbage!");
8097 BackedgeTakenCounts.clear();
8098 ConstantEvolutionLoopExitValue.clear();
8099 ValuesAtScopes.clear();
8100 LoopDispositions.clear();
8101 BlockDispositions.clear();
8102 UnsignedRanges.clear();
8103 SignedRanges.clear();
8104 UniqueSCEVs.clear();
8105 SCEVAllocator.Reset();
8108 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
8109 AU.setPreservesAll();
8110 AU.addRequired<AssumptionCacheTracker>();
8111 AU.addRequiredTransitive<LoopInfoWrapperPass>();
8112 AU.addRequiredTransitive<DominatorTreeWrapperPass>();
8113 AU.addRequired<TargetLibraryInfoWrapperPass>();
8116 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
8117 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
8120 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
8122 // Print all inner loops first
8123 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
8124 PrintLoopInfo(OS, SE, *I);
8127 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
8130 SmallVector<BasicBlock *, 8> ExitBlocks;
8131 L->getExitBlocks(ExitBlocks);
8132 if (ExitBlocks.size() != 1)
8133 OS << "<multiple exits> ";
8135 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
8136 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
8138 OS << "Unpredictable backedge-taken count. ";
8143 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
8146 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
8147 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
8149 OS << "Unpredictable max backedge-taken count. ";
8155 void ScalarEvolution::print(raw_ostream &OS, const Module *) const {
8156 // ScalarEvolution's implementation of the print method is to print
8157 // out SCEV values of all instructions that are interesting. Doing
8158 // this potentially causes it to create new SCEV objects though,
8159 // which technically conflicts with the const qualifier. This isn't
8160 // observable from outside the class though, so casting away the
8161 // const isn't dangerous.
8162 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
8164 OS << "Classifying expressions for: ";
8165 F->printAsOperand(OS, /*PrintType=*/false);
8167 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
8168 if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) {
8171 const SCEV *SV = SE.getSCEV(&*I);
8173 if (!isa<SCEVCouldNotCompute>(SV)) {
8175 SE.getUnsignedRange(SV).print(OS);
8177 SE.getSignedRange(SV).print(OS);
8180 const Loop *L = LI->getLoopFor((*I).getParent());
8182 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
8186 if (!isa<SCEVCouldNotCompute>(AtUse)) {
8188 SE.getUnsignedRange(AtUse).print(OS);
8190 SE.getSignedRange(AtUse).print(OS);
8195 OS << "\t\t" "Exits: ";
8196 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
8197 if (!SE.isLoopInvariant(ExitValue, L)) {
8198 OS << "<<Unknown>>";
8207 OS << "Determining loop execution counts for: ";
8208 F->printAsOperand(OS, /*PrintType=*/false);
8210 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
8211 PrintLoopInfo(OS, &SE, *I);
8214 ScalarEvolution::LoopDisposition
8215 ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) {
8216 auto &Values = LoopDispositions[S];
8217 for (auto &V : Values) {
8218 if (V.getPointer() == L)
8221 Values.emplace_back(L, LoopVariant);
8222 LoopDisposition D = computeLoopDisposition(S, L);
8223 auto &Values2 = LoopDispositions[S];
8224 for (auto &V : make_range(Values2.rbegin(), Values2.rend())) {
8225 if (V.getPointer() == L) {
8233 ScalarEvolution::LoopDisposition
8234 ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) {
8235 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
8237 return LoopInvariant;
8241 return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L);
8242 case scAddRecExpr: {
8243 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
8245 // If L is the addrec's loop, it's computable.
8246 if (AR->getLoop() == L)
8247 return LoopComputable;
8249 // Add recurrences are never invariant in the function-body (null loop).
8253 // This recurrence is variant w.r.t. L if L contains AR's loop.
8254 if (L->contains(AR->getLoop()))
8257 // This recurrence is invariant w.r.t. L if AR's loop contains L.
8258 if (AR->getLoop()->contains(L))
8259 return LoopInvariant;
8261 // This recurrence is variant w.r.t. L if any of its operands
8263 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
8265 if (!isLoopInvariant(*I, L))
8268 // Otherwise it's loop-invariant.
8269 return LoopInvariant;
8275 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
8276 bool HasVarying = false;
8277 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
8279 LoopDisposition D = getLoopDisposition(*I, L);
8280 if (D == LoopVariant)
8282 if (D == LoopComputable)
8285 return HasVarying ? LoopComputable : LoopInvariant;
8288 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
8289 LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L);
8290 if (LD == LoopVariant)
8292 LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L);
8293 if (RD == LoopVariant)
8295 return (LD == LoopInvariant && RD == LoopInvariant) ?
8296 LoopInvariant : LoopComputable;
8299 // All non-instruction values are loop invariant. All instructions are loop
8300 // invariant if they are not contained in the specified loop.
8301 // Instructions are never considered invariant in the function body
8302 // (null loop) because they are defined within the "loop".
8303 if (Instruction *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue()))
8304 return (L && !L->contains(I)) ? LoopInvariant : LoopVariant;
8305 return LoopInvariant;
8306 case scCouldNotCompute:
8307 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
8309 llvm_unreachable("Unknown SCEV kind!");
8312 bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) {
8313 return getLoopDisposition(S, L) == LoopInvariant;
8316 bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) {
8317 return getLoopDisposition(S, L) == LoopComputable;
8320 ScalarEvolution::BlockDisposition
8321 ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) {
8322 auto &Values = BlockDispositions[S];
8323 for (auto &V : Values) {
8324 if (V.getPointer() == BB)
8327 Values.emplace_back(BB, DoesNotDominateBlock);
8328 BlockDisposition D = computeBlockDisposition(S, BB);
8329 auto &Values2 = BlockDispositions[S];
8330 for (auto &V : make_range(Values2.rbegin(), Values2.rend())) {
8331 if (V.getPointer() == BB) {
8339 ScalarEvolution::BlockDisposition
8340 ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) {
8341 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
8343 return ProperlyDominatesBlock;
8347 return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB);
8348 case scAddRecExpr: {
8349 // This uses a "dominates" query instead of "properly dominates" query
8350 // to test for proper dominance too, because the instruction which
8351 // produces the addrec's value is a PHI, and a PHI effectively properly
8352 // dominates its entire containing block.
8353 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
8354 if (!DT->dominates(AR->getLoop()->getHeader(), BB))
8355 return DoesNotDominateBlock;
8357 // FALL THROUGH into SCEVNAryExpr handling.
8362 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
8364 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
8366 BlockDisposition D = getBlockDisposition(*I, BB);
8367 if (D == DoesNotDominateBlock)
8368 return DoesNotDominateBlock;
8369 if (D == DominatesBlock)
8372 return Proper ? ProperlyDominatesBlock : DominatesBlock;
8375 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
8376 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
8377 BlockDisposition LD = getBlockDisposition(LHS, BB);
8378 if (LD == DoesNotDominateBlock)
8379 return DoesNotDominateBlock;
8380 BlockDisposition RD = getBlockDisposition(RHS, BB);
8381 if (RD == DoesNotDominateBlock)
8382 return DoesNotDominateBlock;
8383 return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ?
8384 ProperlyDominatesBlock : DominatesBlock;
8387 if (Instruction *I =
8388 dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) {
8389 if (I->getParent() == BB)
8390 return DominatesBlock;
8391 if (DT->properlyDominates(I->getParent(), BB))
8392 return ProperlyDominatesBlock;
8393 return DoesNotDominateBlock;
8395 return ProperlyDominatesBlock;
8396 case scCouldNotCompute:
8397 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
8399 llvm_unreachable("Unknown SCEV kind!");
8402 bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) {
8403 return getBlockDisposition(S, BB) >= DominatesBlock;
8406 bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) {
8407 return getBlockDisposition(S, BB) == ProperlyDominatesBlock;
8411 // Search for a SCEV expression node within an expression tree.
8412 // Implements SCEVTraversal::Visitor.
8417 SCEVSearch(const SCEV *N): Node(N), IsFound(false) {}
8419 bool follow(const SCEV *S) {
8420 IsFound |= (S == Node);
8423 bool isDone() const { return IsFound; }
8427 bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const {
8428 SCEVSearch Search(Op);
8429 visitAll(S, Search);
8430 return Search.IsFound;
8433 void ScalarEvolution::forgetMemoizedResults(const SCEV *S) {
8434 ValuesAtScopes.erase(S);
8435 LoopDispositions.erase(S);
8436 BlockDispositions.erase(S);
8437 UnsignedRanges.erase(S);
8438 SignedRanges.erase(S);
8440 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
8441 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end(); I != E; ) {
8442 BackedgeTakenInfo &BEInfo = I->second;
8443 if (BEInfo.hasOperand(S, this)) {
8445 BackedgeTakenCounts.erase(I++);
8452 typedef DenseMap<const Loop *, std::string> VerifyMap;
8454 /// replaceSubString - Replaces all occurrences of From in Str with To.
8455 static void replaceSubString(std::string &Str, StringRef From, StringRef To) {
8457 while ((Pos = Str.find(From, Pos)) != std::string::npos) {
8458 Str.replace(Pos, From.size(), To.data(), To.size());
8463 /// getLoopBackedgeTakenCounts - Helper method for verifyAnalysis.
8465 getLoopBackedgeTakenCounts(Loop *L, VerifyMap &Map, ScalarEvolution &SE) {
8466 for (Loop::reverse_iterator I = L->rbegin(), E = L->rend(); I != E; ++I) {
8467 getLoopBackedgeTakenCounts(*I, Map, SE); // recurse.
8469 std::string &S = Map[L];
8471 raw_string_ostream OS(S);
8472 SE.getBackedgeTakenCount(L)->print(OS);
8474 // false and 0 are semantically equivalent. This can happen in dead loops.
8475 replaceSubString(OS.str(), "false", "0");
8476 // Remove wrap flags, their use in SCEV is highly fragile.
8477 // FIXME: Remove this when SCEV gets smarter about them.
8478 replaceSubString(OS.str(), "<nw>", "");
8479 replaceSubString(OS.str(), "<nsw>", "");
8480 replaceSubString(OS.str(), "<nuw>", "");
8485 void ScalarEvolution::verifyAnalysis() const {
8489 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
8491 // Gather stringified backedge taken counts for all loops using SCEV's caches.
8492 // FIXME: It would be much better to store actual values instead of strings,
8493 // but SCEV pointers will change if we drop the caches.
8494 VerifyMap BackedgeDumpsOld, BackedgeDumpsNew;
8495 for (LoopInfo::reverse_iterator I = LI->rbegin(), E = LI->rend(); I != E; ++I)
8496 getLoopBackedgeTakenCounts(*I, BackedgeDumpsOld, SE);
8498 // Gather stringified backedge taken counts for all loops without using
8501 for (LoopInfo::reverse_iterator I = LI->rbegin(), E = LI->rend(); I != E; ++I)
8502 getLoopBackedgeTakenCounts(*I, BackedgeDumpsNew, SE);
8504 // Now compare whether they're the same with and without caches. This allows
8505 // verifying that no pass changed the cache.
8506 assert(BackedgeDumpsOld.size() == BackedgeDumpsNew.size() &&
8507 "New loops suddenly appeared!");
8509 for (VerifyMap::iterator OldI = BackedgeDumpsOld.begin(),
8510 OldE = BackedgeDumpsOld.end(),
8511 NewI = BackedgeDumpsNew.begin();
8512 OldI != OldE; ++OldI, ++NewI) {
8513 assert(OldI->first == NewI->first && "Loop order changed!");
8515 // Compare the stringified SCEVs. We don't care if undef backedgetaken count
8517 // FIXME: We currently ignore SCEV changes from/to CouldNotCompute. This
8518 // means that a pass is buggy or SCEV has to learn a new pattern but is
8519 // usually not harmful.
8520 if (OldI->second != NewI->second &&
8521 OldI->second.find("undef") == std::string::npos &&
8522 NewI->second.find("undef") == std::string::npos &&
8523 OldI->second != "***COULDNOTCOMPUTE***" &&
8524 NewI->second != "***COULDNOTCOMPUTE***") {
8525 dbgs() << "SCEVValidator: SCEV for loop '"
8526 << OldI->first->getHeader()->getName()
8527 << "' changed from '" << OldI->second
8528 << "' to '" << NewI->second << "'!\n";
8533 // TODO: Verify more things.