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/AssumptionTracker.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/ValueTracking.h"
72 #include "llvm/IR/ConstantRange.h"
73 #include "llvm/IR/Constants.h"
74 #include "llvm/IR/DataLayout.h"
75 #include "llvm/IR/DerivedTypes.h"
76 #include "llvm/IR/Dominators.h"
77 #include "llvm/IR/GetElementPtrTypeIterator.h"
78 #include "llvm/IR/GlobalAlias.h"
79 #include "llvm/IR/GlobalVariable.h"
80 #include "llvm/IR/InstIterator.h"
81 #include "llvm/IR/Instructions.h"
82 #include "llvm/IR/LLVMContext.h"
83 #include "llvm/IR/Metadata.h"
84 #include "llvm/IR/Operator.h"
85 #include "llvm/Support/CommandLine.h"
86 #include "llvm/Support/Debug.h"
87 #include "llvm/Support/ErrorHandling.h"
88 #include "llvm/Support/MathExtras.h"
89 #include "llvm/Support/raw_ostream.h"
90 #include "llvm/Target/TargetLibraryInfo.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(AssumptionTracker)
120 INITIALIZE_PASS_DEPENDENCY(LoopInfo)
121 INITIALIZE_PASS_DEPENDENCY(DominatorTreeWrapperPass)
122 INITIALIZE_PASS_DEPENDENCY(TargetLibraryInfo)
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!
678 static const APInt srem(const SCEVConstant *C1, const SCEVConstant *C2) {
679 APInt A = C1->getValue()->getValue();
680 APInt B = C2->getValue()->getValue();
681 uint32_t ABW = A.getBitWidth();
682 uint32_t BBW = B.getBitWidth();
689 return APIntOps::srem(A, B);
692 static const APInt sdiv(const SCEVConstant *C1, const SCEVConstant *C2) {
693 APInt A = C1->getValue()->getValue();
694 APInt B = C2->getValue()->getValue();
695 uint32_t ABW = A.getBitWidth();
696 uint32_t BBW = B.getBitWidth();
703 return APIntOps::sdiv(A, B);
706 static const APInt urem(const SCEVConstant *C1, const SCEVConstant *C2) {
707 APInt A = C1->getValue()->getValue();
708 APInt B = C2->getValue()->getValue();
709 uint32_t ABW = A.getBitWidth();
710 uint32_t BBW = B.getBitWidth();
717 return APIntOps::urem(A, B);
720 static const APInt udiv(const SCEVConstant *C1, const SCEVConstant *C2) {
721 APInt A = C1->getValue()->getValue();
722 APInt B = C2->getValue()->getValue();
723 uint32_t ABW = A.getBitWidth();
724 uint32_t BBW = B.getBitWidth();
731 return APIntOps::udiv(A, B);
735 struct FindSCEVSize {
737 FindSCEVSize() : Size(0) {}
739 bool follow(const SCEV *S) {
741 // Keep looking at all operands of S.
744 bool isDone() const {
750 // Returns the size of the SCEV S.
751 static inline int sizeOfSCEV(const SCEV *S) {
753 SCEVTraversal<FindSCEVSize> ST(F);
760 template <typename Derived>
761 struct SCEVDivision : public SCEVVisitor<Derived, void> {
763 // Computes the Quotient and Remainder of the division of Numerator by
765 static void divide(ScalarEvolution &SE, const SCEV *Numerator,
766 const SCEV *Denominator, const SCEV **Quotient,
767 const SCEV **Remainder) {
768 assert(Numerator && Denominator && "Uninitialized SCEV");
770 Derived D(SE, Numerator, Denominator);
772 // Check for the trivial case here to avoid having to check for it in the
774 if (Numerator == Denominator) {
780 if (Numerator->isZero()) {
786 // Split the Denominator when it is a product.
787 if (const SCEVMulExpr *T = dyn_cast<const SCEVMulExpr>(Denominator)) {
789 *Quotient = Numerator;
790 for (const SCEV *Op : T->operands()) {
791 divide(SE, *Quotient, Op, &Q, &R);
794 // Bail out when the Numerator is not divisible by one of the terms of
798 *Remainder = Numerator;
807 *Quotient = D.Quotient;
808 *Remainder = D.Remainder;
811 // Except in the trivial case described above, we do not know how to divide
812 // Expr by Denominator for the following functions with empty implementation.
813 void visitTruncateExpr(const SCEVTruncateExpr *Numerator) {}
814 void visitZeroExtendExpr(const SCEVZeroExtendExpr *Numerator) {}
815 void visitSignExtendExpr(const SCEVSignExtendExpr *Numerator) {}
816 void visitUDivExpr(const SCEVUDivExpr *Numerator) {}
817 void visitSMaxExpr(const SCEVSMaxExpr *Numerator) {}
818 void visitUMaxExpr(const SCEVUMaxExpr *Numerator) {}
819 void visitUnknown(const SCEVUnknown *Numerator) {}
820 void visitCouldNotCompute(const SCEVCouldNotCompute *Numerator) {}
822 void visitAddRecExpr(const SCEVAddRecExpr *Numerator) {
823 const SCEV *StartQ, *StartR, *StepQ, *StepR;
824 assert(Numerator->isAffine() && "Numerator should be affine");
825 divide(SE, Numerator->getStart(), Denominator, &StartQ, &StartR);
826 divide(SE, Numerator->getStepRecurrence(SE), Denominator, &StepQ, &StepR);
827 Quotient = SE.getAddRecExpr(StartQ, StepQ, Numerator->getLoop(),
828 Numerator->getNoWrapFlags());
829 Remainder = SE.getAddRecExpr(StartR, StepR, Numerator->getLoop(),
830 Numerator->getNoWrapFlags());
833 void visitAddExpr(const SCEVAddExpr *Numerator) {
834 SmallVector<const SCEV *, 2> Qs, Rs;
835 Type *Ty = Denominator->getType();
837 for (const SCEV *Op : Numerator->operands()) {
839 divide(SE, Op, Denominator, &Q, &R);
841 // Bail out if types do not match.
842 if (Ty != Q->getType() || Ty != R->getType()) {
844 Remainder = Numerator;
852 if (Qs.size() == 1) {
858 Quotient = SE.getAddExpr(Qs);
859 Remainder = SE.getAddExpr(Rs);
862 void visitMulExpr(const SCEVMulExpr *Numerator) {
863 SmallVector<const SCEV *, 2> Qs;
864 Type *Ty = Denominator->getType();
866 bool FoundDenominatorTerm = false;
867 for (const SCEV *Op : Numerator->operands()) {
868 // Bail out if types do not match.
869 if (Ty != Op->getType()) {
871 Remainder = Numerator;
875 if (FoundDenominatorTerm) {
880 // Check whether Denominator divides one of the product operands.
882 divide(SE, Op, Denominator, &Q, &R);
888 // Bail out if types do not match.
889 if (Ty != Q->getType()) {
891 Remainder = Numerator;
895 FoundDenominatorTerm = true;
899 if (FoundDenominatorTerm) {
904 Quotient = SE.getMulExpr(Qs);
908 if (!isa<SCEVUnknown>(Denominator)) {
910 Remainder = Numerator;
914 // The Remainder is obtained by replacing Denominator by 0 in Numerator.
915 ValueToValueMap RewriteMap;
916 RewriteMap[cast<SCEVUnknown>(Denominator)->getValue()] =
917 cast<SCEVConstant>(Zero)->getValue();
918 Remainder = SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true);
920 if (Remainder->isZero()) {
921 // The Quotient is obtained by replacing Denominator by 1 in Numerator.
922 RewriteMap[cast<SCEVUnknown>(Denominator)->getValue()] =
923 cast<SCEVConstant>(One)->getValue();
925 SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true);
929 // Quotient is (Numerator - Remainder) divided by Denominator.
931 const SCEV *Diff = SE.getMinusSCEV(Numerator, Remainder);
932 if (sizeOfSCEV(Diff) > sizeOfSCEV(Numerator)) {
933 // This SCEV does not seem to simplify: fail the division here.
935 Remainder = Numerator;
938 divide(SE, Diff, Denominator, &Q, &R);
940 "(Numerator - Remainder) should evenly divide Denominator");
945 SCEVDivision(ScalarEvolution &S, const SCEV *Numerator,
946 const SCEV *Denominator)
947 : SE(S), Denominator(Denominator) {
948 Zero = SE.getConstant(Denominator->getType(), 0);
949 One = SE.getConstant(Denominator->getType(), 1);
951 // By default, we don't know how to divide Expr by Denominator.
952 // Providing the default here simplifies the rest of the code.
954 Remainder = Numerator;
958 const SCEV *Denominator, *Quotient, *Remainder, *Zero, *One;
960 friend struct SCEVSDivision;
961 friend struct SCEVUDivision;
964 struct SCEVSDivision : public SCEVDivision<SCEVSDivision> {
965 SCEVSDivision(ScalarEvolution &S, const SCEV *Numerator,
966 const SCEV *Denominator)
967 : SCEVDivision(S, Numerator, Denominator) {}
969 void visitConstant(const SCEVConstant *Numerator) {
970 if (const SCEVConstant *D = dyn_cast<SCEVConstant>(Denominator)) {
971 Quotient = SE.getConstant(sdiv(Numerator, D));
972 Remainder = SE.getConstant(srem(Numerator, D));
978 struct SCEVUDivision : public SCEVDivision<SCEVUDivision> {
979 SCEVUDivision(ScalarEvolution &S, const SCEV *Numerator,
980 const SCEV *Denominator)
981 : SCEVDivision(S, Numerator, Denominator) {}
983 void visitConstant(const SCEVConstant *Numerator) {
984 if (const SCEVConstant *D = dyn_cast<SCEVConstant>(Denominator)) {
985 Quotient = SE.getConstant(udiv(Numerator, D));
986 Remainder = SE.getConstant(urem(Numerator, D));
994 //===----------------------------------------------------------------------===//
995 // Simple SCEV method implementations
996 //===----------------------------------------------------------------------===//
998 /// BinomialCoefficient - Compute BC(It, K). The result has width W.
1000 static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K,
1001 ScalarEvolution &SE,
1003 // Handle the simplest case efficiently.
1005 return SE.getTruncateOrZeroExtend(It, ResultTy);
1007 // We are using the following formula for BC(It, K):
1009 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
1011 // Suppose, W is the bitwidth of the return value. We must be prepared for
1012 // overflow. Hence, we must assure that the result of our computation is
1013 // equal to the accurate one modulo 2^W. Unfortunately, division isn't
1014 // safe in modular arithmetic.
1016 // However, this code doesn't use exactly that formula; the formula it uses
1017 // is something like the following, where T is the number of factors of 2 in
1018 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
1021 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
1023 // This formula is trivially equivalent to the previous formula. However,
1024 // this formula can be implemented much more efficiently. The trick is that
1025 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
1026 // arithmetic. To do exact division in modular arithmetic, all we have
1027 // to do is multiply by the inverse. Therefore, this step can be done at
1030 // The next issue is how to safely do the division by 2^T. The way this
1031 // is done is by doing the multiplication step at a width of at least W + T
1032 // bits. This way, the bottom W+T bits of the product are accurate. Then,
1033 // when we perform the division by 2^T (which is equivalent to a right shift
1034 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
1035 // truncated out after the division by 2^T.
1037 // In comparison to just directly using the first formula, this technique
1038 // is much more efficient; using the first formula requires W * K bits,
1039 // but this formula less than W + K bits. Also, the first formula requires
1040 // a division step, whereas this formula only requires multiplies and shifts.
1042 // It doesn't matter whether the subtraction step is done in the calculation
1043 // width or the input iteration count's width; if the subtraction overflows,
1044 // the result must be zero anyway. We prefer here to do it in the width of
1045 // the induction variable because it helps a lot for certain cases; CodeGen
1046 // isn't smart enough to ignore the overflow, which leads to much less
1047 // efficient code if the width of the subtraction is wider than the native
1050 // (It's possible to not widen at all by pulling out factors of 2 before
1051 // the multiplication; for example, K=2 can be calculated as
1052 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
1053 // extra arithmetic, so it's not an obvious win, and it gets
1054 // much more complicated for K > 3.)
1056 // Protection from insane SCEVs; this bound is conservative,
1057 // but it probably doesn't matter.
1059 return SE.getCouldNotCompute();
1061 unsigned W = SE.getTypeSizeInBits(ResultTy);
1063 // Calculate K! / 2^T and T; we divide out the factors of two before
1064 // multiplying for calculating K! / 2^T to avoid overflow.
1065 // Other overflow doesn't matter because we only care about the bottom
1066 // W bits of the result.
1067 APInt OddFactorial(W, 1);
1069 for (unsigned i = 3; i <= K; ++i) {
1071 unsigned TwoFactors = Mult.countTrailingZeros();
1073 Mult = Mult.lshr(TwoFactors);
1074 OddFactorial *= Mult;
1077 // We need at least W + T bits for the multiplication step
1078 unsigned CalculationBits = W + T;
1080 // Calculate 2^T, at width T+W.
1081 APInt DivFactor = APInt::getOneBitSet(CalculationBits, T);
1083 // Calculate the multiplicative inverse of K! / 2^T;
1084 // this multiplication factor will perform the exact division by
1086 APInt Mod = APInt::getSignedMinValue(W+1);
1087 APInt MultiplyFactor = OddFactorial.zext(W+1);
1088 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
1089 MultiplyFactor = MultiplyFactor.trunc(W);
1091 // Calculate the product, at width T+W
1092 IntegerType *CalculationTy = IntegerType::get(SE.getContext(),
1094 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
1095 for (unsigned i = 1; i != K; ++i) {
1096 const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i));
1097 Dividend = SE.getMulExpr(Dividend,
1098 SE.getTruncateOrZeroExtend(S, CalculationTy));
1102 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
1104 // Truncate the result, and divide by K! / 2^T.
1106 return SE.getMulExpr(SE.getConstant(MultiplyFactor),
1107 SE.getTruncateOrZeroExtend(DivResult, ResultTy));
1110 /// evaluateAtIteration - Return the value of this chain of recurrences at
1111 /// the specified iteration number. We can evaluate this recurrence by
1112 /// multiplying each element in the chain by the binomial coefficient
1113 /// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
1115 /// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
1117 /// where BC(It, k) stands for binomial coefficient.
1119 const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It,
1120 ScalarEvolution &SE) const {
1121 const SCEV *Result = getStart();
1122 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
1123 // The computation is correct in the face of overflow provided that the
1124 // multiplication is performed _after_ the evaluation of the binomial
1126 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType());
1127 if (isa<SCEVCouldNotCompute>(Coeff))
1130 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
1135 //===----------------------------------------------------------------------===//
1136 // SCEV Expression folder implementations
1137 //===----------------------------------------------------------------------===//
1139 const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op,
1141 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
1142 "This is not a truncating conversion!");
1143 assert(isSCEVable(Ty) &&
1144 "This is not a conversion to a SCEVable type!");
1145 Ty = getEffectiveSCEVType(Ty);
1147 FoldingSetNodeID ID;
1148 ID.AddInteger(scTruncate);
1152 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1154 // Fold if the operand is constant.
1155 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1157 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty)));
1159 // trunc(trunc(x)) --> trunc(x)
1160 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
1161 return getTruncateExpr(ST->getOperand(), Ty);
1163 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
1164 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1165 return getTruncateOrSignExtend(SS->getOperand(), Ty);
1167 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
1168 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1169 return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
1171 // trunc(x1+x2+...+xN) --> trunc(x1)+trunc(x2)+...+trunc(xN) if we can
1172 // eliminate all the truncates.
1173 if (const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Op)) {
1174 SmallVector<const SCEV *, 4> Operands;
1175 bool hasTrunc = false;
1176 for (unsigned i = 0, e = SA->getNumOperands(); i != e && !hasTrunc; ++i) {
1177 const SCEV *S = getTruncateExpr(SA->getOperand(i), Ty);
1178 hasTrunc = isa<SCEVTruncateExpr>(S);
1179 Operands.push_back(S);
1182 return getAddExpr(Operands);
1183 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL.
1186 // trunc(x1*x2*...*xN) --> trunc(x1)*trunc(x2)*...*trunc(xN) if we can
1187 // eliminate all the truncates.
1188 if (const SCEVMulExpr *SM = dyn_cast<SCEVMulExpr>(Op)) {
1189 SmallVector<const SCEV *, 4> Operands;
1190 bool hasTrunc = false;
1191 for (unsigned i = 0, e = SM->getNumOperands(); i != e && !hasTrunc; ++i) {
1192 const SCEV *S = getTruncateExpr(SM->getOperand(i), Ty);
1193 hasTrunc = isa<SCEVTruncateExpr>(S);
1194 Operands.push_back(S);
1197 return getMulExpr(Operands);
1198 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL.
1201 // If the input value is a chrec scev, truncate the chrec's operands.
1202 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
1203 SmallVector<const SCEV *, 4> Operands;
1204 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
1205 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty));
1206 return getAddRecExpr(Operands, AddRec->getLoop(), SCEV::FlagAnyWrap);
1209 // The cast wasn't folded; create an explicit cast node. We can reuse
1210 // the existing insert position since if we get here, we won't have
1211 // made any changes which would invalidate it.
1212 SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator),
1214 UniqueSCEVs.InsertNode(S, IP);
1218 const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op,
1220 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1221 "This is not an extending conversion!");
1222 assert(isSCEVable(Ty) &&
1223 "This is not a conversion to a SCEVable type!");
1224 Ty = getEffectiveSCEVType(Ty);
1226 // Fold if the operand is constant.
1227 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1229 cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(), Ty)));
1231 // zext(zext(x)) --> zext(x)
1232 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1233 return getZeroExtendExpr(SZ->getOperand(), Ty);
1235 // Before doing any expensive analysis, check to see if we've already
1236 // computed a SCEV for this Op and Ty.
1237 FoldingSetNodeID ID;
1238 ID.AddInteger(scZeroExtend);
1242 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1244 // zext(trunc(x)) --> zext(x) or x or trunc(x)
1245 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1246 // It's possible the bits taken off by the truncate were all zero bits. If
1247 // so, we should be able to simplify this further.
1248 const SCEV *X = ST->getOperand();
1249 ConstantRange CR = getUnsignedRange(X);
1250 unsigned TruncBits = getTypeSizeInBits(ST->getType());
1251 unsigned NewBits = getTypeSizeInBits(Ty);
1252 if (CR.truncate(TruncBits).zeroExtend(NewBits).contains(
1253 CR.zextOrTrunc(NewBits)))
1254 return getTruncateOrZeroExtend(X, Ty);
1257 // If the input value is a chrec scev, and we can prove that the value
1258 // did not overflow the old, smaller, value, we can zero extend all of the
1259 // operands (often constants). This allows analysis of something like
1260 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
1261 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1262 if (AR->isAffine()) {
1263 const SCEV *Start = AR->getStart();
1264 const SCEV *Step = AR->getStepRecurrence(*this);
1265 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1266 const Loop *L = AR->getLoop();
1268 // If we have special knowledge that this addrec won't overflow,
1269 // we don't need to do any further analysis.
1270 if (AR->getNoWrapFlags(SCEV::FlagNUW))
1271 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1272 getZeroExtendExpr(Step, Ty),
1273 L, AR->getNoWrapFlags());
1275 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1276 // Note that this serves two purposes: It filters out loops that are
1277 // simply not analyzable, and it covers the case where this code is
1278 // being called from within backedge-taken count analysis, such that
1279 // attempting to ask for the backedge-taken count would likely result
1280 // in infinite recursion. In the later case, the analysis code will
1281 // cope with a conservative value, and it will take care to purge
1282 // that value once it has finished.
1283 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1284 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1285 // Manually compute the final value for AR, checking for
1288 // Check whether the backedge-taken count can be losslessly casted to
1289 // the addrec's type. The count is always unsigned.
1290 const SCEV *CastedMaxBECount =
1291 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1292 const SCEV *RecastedMaxBECount =
1293 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1294 if (MaxBECount == RecastedMaxBECount) {
1295 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1296 // Check whether Start+Step*MaxBECount has no unsigned overflow.
1297 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step);
1298 const SCEV *ZAdd = getZeroExtendExpr(getAddExpr(Start, ZMul), WideTy);
1299 const SCEV *WideStart = getZeroExtendExpr(Start, WideTy);
1300 const SCEV *WideMaxBECount =
1301 getZeroExtendExpr(CastedMaxBECount, WideTy);
1302 const SCEV *OperandExtendedAdd =
1303 getAddExpr(WideStart,
1304 getMulExpr(WideMaxBECount,
1305 getZeroExtendExpr(Step, WideTy)));
1306 if (ZAdd == OperandExtendedAdd) {
1307 // Cache knowledge of AR NUW, which is propagated to this AddRec.
1308 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1309 // Return the expression with the addrec on the outside.
1310 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1311 getZeroExtendExpr(Step, Ty),
1312 L, AR->getNoWrapFlags());
1314 // Similar to above, only this time treat the step value as signed.
1315 // This covers loops that count down.
1316 OperandExtendedAdd =
1317 getAddExpr(WideStart,
1318 getMulExpr(WideMaxBECount,
1319 getSignExtendExpr(Step, WideTy)));
1320 if (ZAdd == OperandExtendedAdd) {
1321 // Cache knowledge of AR NW, which is propagated to this AddRec.
1322 // Negative step causes unsigned wrap, but it still can't self-wrap.
1323 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1324 // Return the expression with the addrec on the outside.
1325 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1326 getSignExtendExpr(Step, Ty),
1327 L, AR->getNoWrapFlags());
1331 // If the backedge is guarded by a comparison with the pre-inc value
1332 // the addrec is safe. Also, if the entry is guarded by a comparison
1333 // with the start value and the backedge is guarded by a comparison
1334 // with the post-inc value, the addrec is safe.
1335 if (isKnownPositive(Step)) {
1336 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
1337 getUnsignedRange(Step).getUnsignedMax());
1338 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
1339 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) &&
1340 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT,
1341 AR->getPostIncExpr(*this), N))) {
1342 // Cache knowledge of AR NUW, which is propagated to this AddRec.
1343 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1344 // Return the expression with the addrec on the outside.
1345 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1346 getZeroExtendExpr(Step, Ty),
1347 L, AR->getNoWrapFlags());
1349 } else if (isKnownNegative(Step)) {
1350 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
1351 getSignedRange(Step).getSignedMin());
1352 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) ||
1353 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) &&
1354 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT,
1355 AR->getPostIncExpr(*this), N))) {
1356 // Cache knowledge of AR NW, which is propagated to this AddRec.
1357 // Negative step causes unsigned wrap, but it still can't self-wrap.
1358 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1359 // Return the expression with the addrec on the outside.
1360 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1361 getSignExtendExpr(Step, Ty),
1362 L, AR->getNoWrapFlags());
1368 // The cast wasn't folded; create an explicit cast node.
1369 // Recompute the insert position, as it may have been invalidated.
1370 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1371 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
1373 UniqueSCEVs.InsertNode(S, IP);
1377 // Get the limit of a recurrence such that incrementing by Step cannot cause
1378 // signed overflow as long as the value of the recurrence within the loop does
1379 // not exceed this limit before incrementing.
1380 static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1381 ICmpInst::Predicate *Pred,
1382 ScalarEvolution *SE) {
1383 unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
1384 if (SE->isKnownPositive(Step)) {
1385 *Pred = ICmpInst::ICMP_SLT;
1386 return SE->getConstant(APInt::getSignedMinValue(BitWidth) -
1387 SE->getSignedRange(Step).getSignedMax());
1389 if (SE->isKnownNegative(Step)) {
1390 *Pred = ICmpInst::ICMP_SGT;
1391 return SE->getConstant(APInt::getSignedMaxValue(BitWidth) -
1392 SE->getSignedRange(Step).getSignedMin());
1397 // The recurrence AR has been shown to have no signed wrap. Typically, if we can
1398 // prove NSW for AR, then we can just as easily prove NSW for its preincrement
1399 // or postincrement sibling. This allows normalizing a sign extended AddRec as
1400 // such: {sext(Step + Start),+,Step} => {(Step + sext(Start),+,Step} As a
1401 // result, the expression "Step + sext(PreIncAR)" is congruent with
1402 // "sext(PostIncAR)"
1403 static const SCEV *getPreStartForSignExtend(const SCEVAddRecExpr *AR,
1405 ScalarEvolution *SE) {
1406 const Loop *L = AR->getLoop();
1407 const SCEV *Start = AR->getStart();
1408 const SCEV *Step = AR->getStepRecurrence(*SE);
1410 // Check for a simple looking step prior to loop entry.
1411 const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Start);
1415 // Create an AddExpr for "PreStart" after subtracting Step. Full SCEV
1416 // subtraction is expensive. For this purpose, perform a quick and dirty
1417 // difference, by checking for Step in the operand list.
1418 SmallVector<const SCEV *, 4> DiffOps;
1419 for (const SCEV *Op : SA->operands())
1421 DiffOps.push_back(Op);
1423 if (DiffOps.size() == SA->getNumOperands())
1426 // This is a postinc AR. Check for overflow on the preinc recurrence using the
1427 // same three conditions that getSignExtendedExpr checks.
1429 // 1. NSW flags on the step increment.
1430 const SCEV *PreStart = SE->getAddExpr(DiffOps, SA->getNoWrapFlags());
1431 const SCEVAddRecExpr *PreAR = dyn_cast<SCEVAddRecExpr>(
1432 SE->getAddRecExpr(PreStart, Step, L, SCEV::FlagAnyWrap));
1434 if (PreAR && PreAR->getNoWrapFlags(SCEV::FlagNSW))
1437 // 2. Direct overflow check on the step operation's expression.
1438 unsigned BitWidth = SE->getTypeSizeInBits(AR->getType());
1439 Type *WideTy = IntegerType::get(SE->getContext(), BitWidth * 2);
1440 const SCEV *OperandExtendedStart =
1441 SE->getAddExpr(SE->getSignExtendExpr(PreStart, WideTy),
1442 SE->getSignExtendExpr(Step, WideTy));
1443 if (SE->getSignExtendExpr(Start, WideTy) == OperandExtendedStart) {
1444 // Cache knowledge of PreAR NSW.
1446 const_cast<SCEVAddRecExpr *>(PreAR)->setNoWrapFlags(SCEV::FlagNSW);
1447 // FIXME: this optimization needs a unit test
1448 DEBUG(dbgs() << "SCEV: untested prestart overflow check\n");
1452 // 3. Loop precondition.
1453 ICmpInst::Predicate Pred;
1454 const SCEV *OverflowLimit = getOverflowLimitForStep(Step, &Pred, SE);
1456 if (OverflowLimit &&
1457 SE->isLoopEntryGuardedByCond(L, Pred, PreStart, OverflowLimit)) {
1463 // Get the normalized sign-extended expression for this AddRec's Start.
1464 static const SCEV *getSignExtendAddRecStart(const SCEVAddRecExpr *AR,
1466 ScalarEvolution *SE) {
1467 const SCEV *PreStart = getPreStartForSignExtend(AR, Ty, SE);
1469 return SE->getSignExtendExpr(AR->getStart(), Ty);
1471 return SE->getAddExpr(SE->getSignExtendExpr(AR->getStepRecurrence(*SE), Ty),
1472 SE->getSignExtendExpr(PreStart, Ty));
1475 const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op,
1477 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1478 "This is not an extending conversion!");
1479 assert(isSCEVable(Ty) &&
1480 "This is not a conversion to a SCEVable type!");
1481 Ty = getEffectiveSCEVType(Ty);
1483 // Fold if the operand is constant.
1484 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1486 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), Ty)));
1488 // sext(sext(x)) --> sext(x)
1489 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1490 return getSignExtendExpr(SS->getOperand(), Ty);
1492 // sext(zext(x)) --> zext(x)
1493 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1494 return getZeroExtendExpr(SZ->getOperand(), Ty);
1496 // Before doing any expensive analysis, check to see if we've already
1497 // computed a SCEV for this Op and Ty.
1498 FoldingSetNodeID ID;
1499 ID.AddInteger(scSignExtend);
1503 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1505 // If the input value is provably positive, build a zext instead.
1506 if (isKnownNonNegative(Op))
1507 return getZeroExtendExpr(Op, Ty);
1509 // sext(trunc(x)) --> sext(x) or x or trunc(x)
1510 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1511 // It's possible the bits taken off by the truncate were all sign bits. If
1512 // so, we should be able to simplify this further.
1513 const SCEV *X = ST->getOperand();
1514 ConstantRange CR = getSignedRange(X);
1515 unsigned TruncBits = getTypeSizeInBits(ST->getType());
1516 unsigned NewBits = getTypeSizeInBits(Ty);
1517 if (CR.truncate(TruncBits).signExtend(NewBits).contains(
1518 CR.sextOrTrunc(NewBits)))
1519 return getTruncateOrSignExtend(X, Ty);
1522 // sext(C1 + (C2 * x)) --> C1 + sext(C2 * x) if C1 < C2
1523 if (auto SA = dyn_cast<SCEVAddExpr>(Op)) {
1524 if (SA->getNumOperands() == 2) {
1525 auto SC1 = dyn_cast<SCEVConstant>(SA->getOperand(0));
1526 auto SMul = dyn_cast<SCEVMulExpr>(SA->getOperand(1));
1528 if (auto SC2 = dyn_cast<SCEVConstant>(SMul->getOperand(0))) {
1529 const APInt &C1 = SC1->getValue()->getValue();
1530 const APInt &C2 = SC2->getValue()->getValue();
1531 if (C1.isStrictlyPositive() && C2.isStrictlyPositive() &&
1532 C2.ugt(C1) && C2.isPowerOf2())
1533 return getAddExpr(getSignExtendExpr(SC1, Ty),
1534 getSignExtendExpr(SMul, Ty));
1539 // If the input value is a chrec scev, and we can prove that the value
1540 // did not overflow the old, smaller, value, we can sign extend all of the
1541 // operands (often constants). This allows analysis of something like
1542 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
1543 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1544 if (AR->isAffine()) {
1545 const SCEV *Start = AR->getStart();
1546 const SCEV *Step = AR->getStepRecurrence(*this);
1547 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1548 const Loop *L = AR->getLoop();
1550 // If we have special knowledge that this addrec won't overflow,
1551 // we don't need to do any further analysis.
1552 if (AR->getNoWrapFlags(SCEV::FlagNSW))
1553 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1554 getSignExtendExpr(Step, Ty),
1557 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1558 // Note that this serves two purposes: It filters out loops that are
1559 // simply not analyzable, and it covers the case where this code is
1560 // being called from within backedge-taken count analysis, such that
1561 // attempting to ask for the backedge-taken count would likely result
1562 // in infinite recursion. In the later case, the analysis code will
1563 // cope with a conservative value, and it will take care to purge
1564 // that value once it has finished.
1565 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1566 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1567 // Manually compute the final value for AR, checking for
1570 // Check whether the backedge-taken count can be losslessly casted to
1571 // the addrec's type. The count is always unsigned.
1572 const SCEV *CastedMaxBECount =
1573 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1574 const SCEV *RecastedMaxBECount =
1575 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1576 if (MaxBECount == RecastedMaxBECount) {
1577 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1578 // Check whether Start+Step*MaxBECount has no signed overflow.
1579 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
1580 const SCEV *SAdd = getSignExtendExpr(getAddExpr(Start, SMul), WideTy);
1581 const SCEV *WideStart = getSignExtendExpr(Start, WideTy);
1582 const SCEV *WideMaxBECount =
1583 getZeroExtendExpr(CastedMaxBECount, WideTy);
1584 const SCEV *OperandExtendedAdd =
1585 getAddExpr(WideStart,
1586 getMulExpr(WideMaxBECount,
1587 getSignExtendExpr(Step, WideTy)));
1588 if (SAdd == OperandExtendedAdd) {
1589 // Cache knowledge of AR NSW, which is propagated to this AddRec.
1590 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1591 // Return the expression with the addrec on the outside.
1592 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1593 getSignExtendExpr(Step, Ty),
1594 L, AR->getNoWrapFlags());
1596 // Similar to above, only this time treat the step value as unsigned.
1597 // This covers loops that count up with an unsigned step.
1598 OperandExtendedAdd =
1599 getAddExpr(WideStart,
1600 getMulExpr(WideMaxBECount,
1601 getZeroExtendExpr(Step, WideTy)));
1602 if (SAdd == OperandExtendedAdd) {
1603 // Cache knowledge of AR NSW, which is propagated to this AddRec.
1604 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1605 // Return the expression with the addrec on the outside.
1606 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1607 getZeroExtendExpr(Step, Ty),
1608 L, AR->getNoWrapFlags());
1612 // If the backedge is guarded by a comparison with the pre-inc value
1613 // the addrec is safe. Also, if the entry is guarded by a comparison
1614 // with the start value and the backedge is guarded by a comparison
1615 // with the post-inc value, the addrec is safe.
1616 ICmpInst::Predicate Pred;
1617 const SCEV *OverflowLimit = getOverflowLimitForStep(Step, &Pred, this);
1618 if (OverflowLimit &&
1619 (isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) ||
1620 (isLoopEntryGuardedByCond(L, Pred, Start, OverflowLimit) &&
1621 isLoopBackedgeGuardedByCond(L, Pred, AR->getPostIncExpr(*this),
1623 // Cache knowledge of AR NSW, then propagate NSW to the wide AddRec.
1624 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1625 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1626 getSignExtendExpr(Step, Ty),
1627 L, AR->getNoWrapFlags());
1630 // If Start and Step are constants, check if we can apply this
1632 // sext{C1,+,C2} --> C1 + sext{0,+,C2} if C1 < C2
1633 auto SC1 = dyn_cast<SCEVConstant>(Start);
1634 auto SC2 = dyn_cast<SCEVConstant>(Step);
1636 const APInt &C1 = SC1->getValue()->getValue();
1637 const APInt &C2 = SC2->getValue()->getValue();
1638 if (C1.isStrictlyPositive() && C2.isStrictlyPositive() && C2.ugt(C1) &&
1640 Start = getSignExtendExpr(Start, Ty);
1641 const SCEV *NewAR = getAddRecExpr(getConstant(AR->getType(), 0), Step,
1642 L, AR->getNoWrapFlags());
1643 return getAddExpr(Start, getSignExtendExpr(NewAR, Ty));
1648 // The cast wasn't folded; create an explicit cast node.
1649 // Recompute the insert position, as it may have been invalidated.
1650 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1651 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
1653 UniqueSCEVs.InsertNode(S, IP);
1657 /// getAnyExtendExpr - Return a SCEV for the given operand extended with
1658 /// unspecified bits out to the given type.
1660 const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
1662 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1663 "This is not an extending conversion!");
1664 assert(isSCEVable(Ty) &&
1665 "This is not a conversion to a SCEVable type!");
1666 Ty = getEffectiveSCEVType(Ty);
1668 // Sign-extend negative constants.
1669 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1670 if (SC->getValue()->getValue().isNegative())
1671 return getSignExtendExpr(Op, Ty);
1673 // Peel off a truncate cast.
1674 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
1675 const SCEV *NewOp = T->getOperand();
1676 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
1677 return getAnyExtendExpr(NewOp, Ty);
1678 return getTruncateOrNoop(NewOp, Ty);
1681 // Next try a zext cast. If the cast is folded, use it.
1682 const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
1683 if (!isa<SCEVZeroExtendExpr>(ZExt))
1686 // Next try a sext cast. If the cast is folded, use it.
1687 const SCEV *SExt = getSignExtendExpr(Op, Ty);
1688 if (!isa<SCEVSignExtendExpr>(SExt))
1691 // Force the cast to be folded into the operands of an addrec.
1692 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
1693 SmallVector<const SCEV *, 4> Ops;
1694 for (const SCEV *Op : AR->operands())
1695 Ops.push_back(getAnyExtendExpr(Op, Ty));
1696 return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW);
1699 // If the expression is obviously signed, use the sext cast value.
1700 if (isa<SCEVSMaxExpr>(Op))
1703 // Absent any other information, use the zext cast value.
1707 /// CollectAddOperandsWithScales - Process the given Ops list, which is
1708 /// a list of operands to be added under the given scale, update the given
1709 /// map. This is a helper function for getAddRecExpr. As an example of
1710 /// what it does, given a sequence of operands that would form an add
1711 /// expression like this:
1713 /// m + n + 13 + (A * (o + p + (B * (q + m + 29)))) + r + (-1 * r)
1715 /// where A and B are constants, update the map with these values:
1717 /// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
1719 /// and add 13 + A*B*29 to AccumulatedConstant.
1720 /// This will allow getAddRecExpr to produce this:
1722 /// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
1724 /// This form often exposes folding opportunities that are hidden in
1725 /// the original operand list.
1727 /// Return true iff it appears that any interesting folding opportunities
1728 /// may be exposed. This helps getAddRecExpr short-circuit extra work in
1729 /// the common case where no interesting opportunities are present, and
1730 /// is also used as a check to avoid infinite recursion.
1733 CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
1734 SmallVectorImpl<const SCEV *> &NewOps,
1735 APInt &AccumulatedConstant,
1736 const SCEV *const *Ops, size_t NumOperands,
1738 ScalarEvolution &SE) {
1739 bool Interesting = false;
1741 // Iterate over the add operands. They are sorted, with constants first.
1743 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1745 // Pull a buried constant out to the outside.
1746 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
1748 AccumulatedConstant += Scale * C->getValue()->getValue();
1751 // Next comes everything else. We're especially interested in multiplies
1752 // here, but they're in the middle, so just visit the rest with one loop.
1753 for (; i != NumOperands; ++i) {
1754 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
1755 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
1757 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue();
1758 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
1759 // A multiplication of a constant with another add; recurse.
1760 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1));
1762 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1763 Add->op_begin(), Add->getNumOperands(),
1766 // A multiplication of a constant with some other value. Update
1768 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
1769 const SCEV *Key = SE.getMulExpr(MulOps);
1770 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1771 M.insert(std::make_pair(Key, NewScale));
1773 NewOps.push_back(Pair.first->first);
1775 Pair.first->second += NewScale;
1776 // The map already had an entry for this value, which may indicate
1777 // a folding opportunity.
1782 // An ordinary operand. Update the map.
1783 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1784 M.insert(std::make_pair(Ops[i], Scale));
1786 NewOps.push_back(Pair.first->first);
1788 Pair.first->second += Scale;
1789 // The map already had an entry for this value, which may indicate
1790 // a folding opportunity.
1800 struct APIntCompare {
1801 bool operator()(const APInt &LHS, const APInt &RHS) const {
1802 return LHS.ult(RHS);
1807 /// getAddExpr - Get a canonical add expression, or something simpler if
1809 const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
1810 SCEV::NoWrapFlags Flags) {
1811 assert(!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) &&
1812 "only nuw or nsw allowed");
1813 assert(!Ops.empty() && "Cannot get empty add!");
1814 if (Ops.size() == 1) return Ops[0];
1816 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
1817 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1818 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
1819 "SCEVAddExpr operand types don't match!");
1822 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
1824 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
1825 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask);
1826 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) {
1828 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(),
1829 E = Ops.end(); I != E; ++I)
1830 if (!isKnownNonNegative(*I)) {
1834 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
1837 // Sort by complexity, this groups all similar expression types together.
1838 GroupByComplexity(Ops, LI);
1840 // If there are any constants, fold them together.
1842 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1844 assert(Idx < Ops.size());
1845 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1846 // We found two constants, fold them together!
1847 Ops[0] = getConstant(LHSC->getValue()->getValue() +
1848 RHSC->getValue()->getValue());
1849 if (Ops.size() == 2) return Ops[0];
1850 Ops.erase(Ops.begin()+1); // Erase the folded element
1851 LHSC = cast<SCEVConstant>(Ops[0]);
1854 // If we are left with a constant zero being added, strip it off.
1855 if (LHSC->getValue()->isZero()) {
1856 Ops.erase(Ops.begin());
1860 if (Ops.size() == 1) return Ops[0];
1863 // Okay, check to see if the same value occurs in the operand list more than
1864 // once. If so, merge them together into an multiply expression. Since we
1865 // sorted the list, these values are required to be adjacent.
1866 Type *Ty = Ops[0]->getType();
1867 bool FoundMatch = false;
1868 for (unsigned i = 0, e = Ops.size(); i != e-1; ++i)
1869 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
1870 // Scan ahead to count how many equal operands there are.
1872 while (i+Count != e && Ops[i+Count] == Ops[i])
1874 // Merge the values into a multiply.
1875 const SCEV *Scale = getConstant(Ty, Count);
1876 const SCEV *Mul = getMulExpr(Scale, Ops[i]);
1877 if (Ops.size() == Count)
1880 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count);
1881 --i; e -= Count - 1;
1885 return getAddExpr(Ops, Flags);
1887 // Check for truncates. If all the operands are truncated from the same
1888 // type, see if factoring out the truncate would permit the result to be
1889 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
1890 // if the contents of the resulting outer trunc fold to something simple.
1891 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
1892 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
1893 Type *DstType = Trunc->getType();
1894 Type *SrcType = Trunc->getOperand()->getType();
1895 SmallVector<const SCEV *, 8> LargeOps;
1897 // Check all the operands to see if they can be represented in the
1898 // source type of the truncate.
1899 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1900 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
1901 if (T->getOperand()->getType() != SrcType) {
1905 LargeOps.push_back(T->getOperand());
1906 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1907 LargeOps.push_back(getAnyExtendExpr(C, SrcType));
1908 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
1909 SmallVector<const SCEV *, 8> LargeMulOps;
1910 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
1911 if (const SCEVTruncateExpr *T =
1912 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
1913 if (T->getOperand()->getType() != SrcType) {
1917 LargeMulOps.push_back(T->getOperand());
1918 } else if (const SCEVConstant *C =
1919 dyn_cast<SCEVConstant>(M->getOperand(j))) {
1920 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType));
1927 LargeOps.push_back(getMulExpr(LargeMulOps));
1934 // Evaluate the expression in the larger type.
1935 const SCEV *Fold = getAddExpr(LargeOps, Flags);
1936 // If it folds to something simple, use it. Otherwise, don't.
1937 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
1938 return getTruncateExpr(Fold, DstType);
1942 // Skip past any other cast SCEVs.
1943 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
1946 // If there are add operands they would be next.
1947 if (Idx < Ops.size()) {
1948 bool DeletedAdd = false;
1949 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
1950 // If we have an add, expand the add operands onto the end of the operands
1952 Ops.erase(Ops.begin()+Idx);
1953 Ops.append(Add->op_begin(), Add->op_end());
1957 // If we deleted at least one add, we added operands to the end of the list,
1958 // and they are not necessarily sorted. Recurse to resort and resimplify
1959 // any operands we just acquired.
1961 return getAddExpr(Ops);
1964 // Skip over the add expression until we get to a multiply.
1965 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1968 // Check to see if there are any folding opportunities present with
1969 // operands multiplied by constant values.
1970 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
1971 uint64_t BitWidth = getTypeSizeInBits(Ty);
1972 DenseMap<const SCEV *, APInt> M;
1973 SmallVector<const SCEV *, 8> NewOps;
1974 APInt AccumulatedConstant(BitWidth, 0);
1975 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1976 Ops.data(), Ops.size(),
1977 APInt(BitWidth, 1), *this)) {
1978 // Some interesting folding opportunity is present, so its worthwhile to
1979 // re-generate the operands list. Group the operands by constant scale,
1980 // to avoid multiplying by the same constant scale multiple times.
1981 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
1982 for (SmallVectorImpl<const SCEV *>::const_iterator I = NewOps.begin(),
1983 E = NewOps.end(); I != E; ++I)
1984 MulOpLists[M.find(*I)->second].push_back(*I);
1985 // Re-generate the operands list.
1987 if (AccumulatedConstant != 0)
1988 Ops.push_back(getConstant(AccumulatedConstant));
1989 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator
1990 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I)
1992 Ops.push_back(getMulExpr(getConstant(I->first),
1993 getAddExpr(I->second)));
1995 return getConstant(Ty, 0);
1996 if (Ops.size() == 1)
1998 return getAddExpr(Ops);
2002 // If we are adding something to a multiply expression, make sure the
2003 // something is not already an operand of the multiply. If so, merge it into
2005 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
2006 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
2007 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
2008 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
2009 if (isa<SCEVConstant>(MulOpSCEV))
2011 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
2012 if (MulOpSCEV == Ops[AddOp]) {
2013 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
2014 const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
2015 if (Mul->getNumOperands() != 2) {
2016 // If the multiply has more than two operands, we must get the
2018 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
2019 Mul->op_begin()+MulOp);
2020 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
2021 InnerMul = getMulExpr(MulOps);
2023 const SCEV *One = getConstant(Ty, 1);
2024 const SCEV *AddOne = getAddExpr(One, InnerMul);
2025 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV);
2026 if (Ops.size() == 2) return OuterMul;
2028 Ops.erase(Ops.begin()+AddOp);
2029 Ops.erase(Ops.begin()+Idx-1);
2031 Ops.erase(Ops.begin()+Idx);
2032 Ops.erase(Ops.begin()+AddOp-1);
2034 Ops.push_back(OuterMul);
2035 return getAddExpr(Ops);
2038 // Check this multiply against other multiplies being added together.
2039 for (unsigned OtherMulIdx = Idx+1;
2040 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
2042 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
2043 // If MulOp occurs in OtherMul, we can fold the two multiplies
2045 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
2046 OMulOp != e; ++OMulOp)
2047 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
2048 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
2049 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
2050 if (Mul->getNumOperands() != 2) {
2051 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
2052 Mul->op_begin()+MulOp);
2053 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
2054 InnerMul1 = getMulExpr(MulOps);
2056 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
2057 if (OtherMul->getNumOperands() != 2) {
2058 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
2059 OtherMul->op_begin()+OMulOp);
2060 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end());
2061 InnerMul2 = getMulExpr(MulOps);
2063 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
2064 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
2065 if (Ops.size() == 2) return OuterMul;
2066 Ops.erase(Ops.begin()+Idx);
2067 Ops.erase(Ops.begin()+OtherMulIdx-1);
2068 Ops.push_back(OuterMul);
2069 return getAddExpr(Ops);
2075 // If there are any add recurrences in the operands list, see if any other
2076 // added values are loop invariant. If so, we can fold them into the
2078 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2081 // Scan over all recurrences, trying to fold loop invariants into them.
2082 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
2083 // Scan all of the other operands to this add and add them to the vector if
2084 // they are loop invariant w.r.t. the recurrence.
2085 SmallVector<const SCEV *, 8> LIOps;
2086 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2087 const Loop *AddRecLoop = AddRec->getLoop();
2088 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2089 if (isLoopInvariant(Ops[i], AddRecLoop)) {
2090 LIOps.push_back(Ops[i]);
2091 Ops.erase(Ops.begin()+i);
2095 // If we found some loop invariants, fold them into the recurrence.
2096 if (!LIOps.empty()) {
2097 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
2098 LIOps.push_back(AddRec->getStart());
2100 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
2102 AddRecOps[0] = getAddExpr(LIOps);
2104 // Build the new addrec. Propagate the NUW and NSW flags if both the
2105 // outer add and the inner addrec are guaranteed to have no overflow.
2106 // Always propagate NW.
2107 Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW));
2108 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags);
2110 // If all of the other operands were loop invariant, we are done.
2111 if (Ops.size() == 1) return NewRec;
2113 // Otherwise, add the folded AddRec by the non-invariant parts.
2114 for (unsigned i = 0;; ++i)
2115 if (Ops[i] == AddRec) {
2119 return getAddExpr(Ops);
2122 // Okay, if there weren't any loop invariants to be folded, check to see if
2123 // there are multiple AddRec's with the same loop induction variable being
2124 // added together. If so, we can fold them.
2125 for (unsigned OtherIdx = Idx+1;
2126 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2128 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
2129 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L>
2130 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
2132 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2134 if (const SCEVAddRecExpr *OtherAddRec =
2135 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]))
2136 if (OtherAddRec->getLoop() == AddRecLoop) {
2137 for (unsigned i = 0, e = OtherAddRec->getNumOperands();
2139 if (i >= AddRecOps.size()) {
2140 AddRecOps.append(OtherAddRec->op_begin()+i,
2141 OtherAddRec->op_end());
2144 AddRecOps[i] = getAddExpr(AddRecOps[i],
2145 OtherAddRec->getOperand(i));
2147 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2149 // Step size has changed, so we cannot guarantee no self-wraparound.
2150 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap);
2151 return getAddExpr(Ops);
2154 // Otherwise couldn't fold anything into this recurrence. Move onto the
2158 // Okay, it looks like we really DO need an add expr. Check to see if we
2159 // already have one, otherwise create a new one.
2160 FoldingSetNodeID ID;
2161 ID.AddInteger(scAddExpr);
2162 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2163 ID.AddPointer(Ops[i]);
2166 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2168 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2169 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2170 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator),
2172 UniqueSCEVs.InsertNode(S, IP);
2174 S->setNoWrapFlags(Flags);
2178 static uint64_t umul_ov(uint64_t i, uint64_t j, bool &Overflow) {
2180 if (j > 1 && k / j != i) Overflow = true;
2184 /// Compute the result of "n choose k", the binomial coefficient. If an
2185 /// intermediate computation overflows, Overflow will be set and the return will
2186 /// be garbage. Overflow is not cleared on absence of overflow.
2187 static uint64_t Choose(uint64_t n, uint64_t k, bool &Overflow) {
2188 // We use the multiplicative formula:
2189 // n(n-1)(n-2)...(n-(k-1)) / k(k-1)(k-2)...1 .
2190 // At each iteration, we take the n-th term of the numeral and divide by the
2191 // (k-n)th term of the denominator. This division will always produce an
2192 // integral result, and helps reduce the chance of overflow in the
2193 // intermediate computations. However, we can still overflow even when the
2194 // final result would fit.
2196 if (n == 0 || n == k) return 1;
2197 if (k > n) return 0;
2203 for (uint64_t i = 1; i <= k; ++i) {
2204 r = umul_ov(r, n-(i-1), Overflow);
2210 /// getMulExpr - Get a canonical multiply expression, or something simpler if
2212 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
2213 SCEV::NoWrapFlags Flags) {
2214 assert(Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) &&
2215 "only nuw or nsw allowed");
2216 assert(!Ops.empty() && "Cannot get empty mul!");
2217 if (Ops.size() == 1) return Ops[0];
2219 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2220 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2221 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2222 "SCEVMulExpr operand types don't match!");
2225 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
2227 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
2228 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask);
2229 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) {
2231 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(),
2232 E = Ops.end(); I != E; ++I)
2233 if (!isKnownNonNegative(*I)) {
2237 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
2240 // Sort by complexity, this groups all similar expression types together.
2241 GroupByComplexity(Ops, LI);
2243 // If there are any constants, fold them together.
2245 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2247 // C1*(C2+V) -> C1*C2 + C1*V
2248 if (Ops.size() == 2)
2249 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
2250 if (Add->getNumOperands() == 2 &&
2251 isa<SCEVConstant>(Add->getOperand(0)))
2252 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
2253 getMulExpr(LHSC, Add->getOperand(1)));
2256 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2257 // We found two constants, fold them together!
2258 ConstantInt *Fold = ConstantInt::get(getContext(),
2259 LHSC->getValue()->getValue() *
2260 RHSC->getValue()->getValue());
2261 Ops[0] = getConstant(Fold);
2262 Ops.erase(Ops.begin()+1); // Erase the folded element
2263 if (Ops.size() == 1) return Ops[0];
2264 LHSC = cast<SCEVConstant>(Ops[0]);
2267 // If we are left with a constant one being multiplied, strip it off.
2268 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
2269 Ops.erase(Ops.begin());
2271 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
2272 // If we have a multiply of zero, it will always be zero.
2274 } else if (Ops[0]->isAllOnesValue()) {
2275 // If we have a mul by -1 of an add, try distributing the -1 among the
2277 if (Ops.size() == 2) {
2278 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
2279 SmallVector<const SCEV *, 4> NewOps;
2280 bool AnyFolded = false;
2281 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(),
2282 E = Add->op_end(); I != E; ++I) {
2283 const SCEV *Mul = getMulExpr(Ops[0], *I);
2284 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
2285 NewOps.push_back(Mul);
2288 return getAddExpr(NewOps);
2290 else if (const SCEVAddRecExpr *
2291 AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) {
2292 // Negation preserves a recurrence's no self-wrap property.
2293 SmallVector<const SCEV *, 4> Operands;
2294 for (SCEVAddRecExpr::op_iterator I = AddRec->op_begin(),
2295 E = AddRec->op_end(); I != E; ++I) {
2296 Operands.push_back(getMulExpr(Ops[0], *I));
2298 return getAddRecExpr(Operands, AddRec->getLoop(),
2299 AddRec->getNoWrapFlags(SCEV::FlagNW));
2304 if (Ops.size() == 1)
2308 // Skip over the add expression until we get to a multiply.
2309 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
2312 // If there are mul operands inline them all into this expression.
2313 if (Idx < Ops.size()) {
2314 bool DeletedMul = false;
2315 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
2316 // If we have an mul, expand the mul operands onto the end of the operands
2318 Ops.erase(Ops.begin()+Idx);
2319 Ops.append(Mul->op_begin(), Mul->op_end());
2323 // If we deleted at least one mul, we added operands to the end of the list,
2324 // and they are not necessarily sorted. Recurse to resort and resimplify
2325 // any operands we just acquired.
2327 return getMulExpr(Ops);
2330 // If there are any add recurrences in the operands list, see if any other
2331 // added values are loop invariant. If so, we can fold them into the
2333 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2336 // Scan over all recurrences, trying to fold loop invariants into them.
2337 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
2338 // Scan all of the other operands to this mul and add them to the vector if
2339 // they are loop invariant w.r.t. the recurrence.
2340 SmallVector<const SCEV *, 8> LIOps;
2341 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2342 const Loop *AddRecLoop = AddRec->getLoop();
2343 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2344 if (isLoopInvariant(Ops[i], AddRecLoop)) {
2345 LIOps.push_back(Ops[i]);
2346 Ops.erase(Ops.begin()+i);
2350 // If we found some loop invariants, fold them into the recurrence.
2351 if (!LIOps.empty()) {
2352 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
2353 SmallVector<const SCEV *, 4> NewOps;
2354 NewOps.reserve(AddRec->getNumOperands());
2355 const SCEV *Scale = getMulExpr(LIOps);
2356 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
2357 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
2359 // Build the new addrec. Propagate the NUW and NSW flags if both the
2360 // outer mul and the inner addrec are guaranteed to have no overflow.
2362 // No self-wrap cannot be guaranteed after changing the step size, but
2363 // will be inferred if either NUW or NSW is true.
2364 Flags = AddRec->getNoWrapFlags(clearFlags(Flags, SCEV::FlagNW));
2365 const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, Flags);
2367 // If all of the other operands were loop invariant, we are done.
2368 if (Ops.size() == 1) return NewRec;
2370 // Otherwise, multiply the folded AddRec by the non-invariant parts.
2371 for (unsigned i = 0;; ++i)
2372 if (Ops[i] == AddRec) {
2376 return getMulExpr(Ops);
2379 // Okay, if there weren't any loop invariants to be folded, check to see if
2380 // there are multiple AddRec's with the same loop induction variable being
2381 // multiplied together. If so, we can fold them.
2383 // {A1,+,A2,+,...,+,An}<L> * {B1,+,B2,+,...,+,Bn}<L>
2384 // = {x=1 in [ sum y=x..2x [ sum z=max(y-x, y-n)..min(x,n) [
2385 // choose(x, 2x)*choose(2x-y, x-z)*A_{y-z}*B_z
2386 // ]]],+,...up to x=2n}.
2387 // Note that the arguments to choose() are always integers with values
2388 // known at compile time, never SCEV objects.
2390 // The implementation avoids pointless extra computations when the two
2391 // addrec's are of different length (mathematically, it's equivalent to
2392 // an infinite stream of zeros on the right).
2393 bool OpsModified = false;
2394 for (unsigned OtherIdx = Idx+1;
2395 OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2397 const SCEVAddRecExpr *OtherAddRec =
2398 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]);
2399 if (!OtherAddRec || OtherAddRec->getLoop() != AddRecLoop)
2402 bool Overflow = false;
2403 Type *Ty = AddRec->getType();
2404 bool LargerThan64Bits = getTypeSizeInBits(Ty) > 64;
2405 SmallVector<const SCEV*, 7> AddRecOps;
2406 for (int x = 0, xe = AddRec->getNumOperands() +
2407 OtherAddRec->getNumOperands() - 1; x != xe && !Overflow; ++x) {
2408 const SCEV *Term = getConstant(Ty, 0);
2409 for (int y = x, ye = 2*x+1; y != ye && !Overflow; ++y) {
2410 uint64_t Coeff1 = Choose(x, 2*x - y, Overflow);
2411 for (int z = std::max(y-x, y-(int)AddRec->getNumOperands()+1),
2412 ze = std::min(x+1, (int)OtherAddRec->getNumOperands());
2413 z < ze && !Overflow; ++z) {
2414 uint64_t Coeff2 = Choose(2*x - y, x-z, Overflow);
2416 if (LargerThan64Bits)
2417 Coeff = umul_ov(Coeff1, Coeff2, Overflow);
2419 Coeff = Coeff1*Coeff2;
2420 const SCEV *CoeffTerm = getConstant(Ty, Coeff);
2421 const SCEV *Term1 = AddRec->getOperand(y-z);
2422 const SCEV *Term2 = OtherAddRec->getOperand(z);
2423 Term = getAddExpr(Term, getMulExpr(CoeffTerm, Term1,Term2));
2426 AddRecOps.push_back(Term);
2429 const SCEV *NewAddRec = getAddRecExpr(AddRecOps, AddRec->getLoop(),
2431 if (Ops.size() == 2) return NewAddRec;
2432 Ops[Idx] = NewAddRec;
2433 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2435 AddRec = dyn_cast<SCEVAddRecExpr>(NewAddRec);
2441 return getMulExpr(Ops);
2443 // Otherwise couldn't fold anything into this recurrence. Move onto the
2447 // Okay, it looks like we really DO need an mul expr. Check to see if we
2448 // already have one, otherwise create a new one.
2449 FoldingSetNodeID ID;
2450 ID.AddInteger(scMulExpr);
2451 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2452 ID.AddPointer(Ops[i]);
2455 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2457 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2458 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2459 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
2461 UniqueSCEVs.InsertNode(S, IP);
2463 S->setNoWrapFlags(Flags);
2467 /// getUDivExpr - Get a canonical unsigned division expression, or something
2468 /// simpler if possible.
2469 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
2471 assert(getEffectiveSCEVType(LHS->getType()) ==
2472 getEffectiveSCEVType(RHS->getType()) &&
2473 "SCEVUDivExpr operand types don't match!");
2475 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
2476 if (RHSC->getValue()->equalsInt(1))
2477 return LHS; // X udiv 1 --> x
2478 // If the denominator is zero, the result of the udiv is undefined. Don't
2479 // try to analyze it, because the resolution chosen here may differ from
2480 // the resolution chosen in other parts of the compiler.
2481 if (!RHSC->getValue()->isZero()) {
2482 // Determine if the division can be folded into the operands of
2484 // TODO: Generalize this to non-constants by using known-bits information.
2485 Type *Ty = LHS->getType();
2486 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
2487 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1;
2488 // For non-power-of-two values, effectively round the value up to the
2489 // nearest power of two.
2490 if (!RHSC->getValue()->getValue().isPowerOf2())
2492 IntegerType *ExtTy =
2493 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
2494 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
2495 if (const SCEVConstant *Step =
2496 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) {
2497 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
2498 const APInt &StepInt = Step->getValue()->getValue();
2499 const APInt &DivInt = RHSC->getValue()->getValue();
2500 if (!StepInt.urem(DivInt) &&
2501 getZeroExtendExpr(AR, ExtTy) ==
2502 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2503 getZeroExtendExpr(Step, ExtTy),
2504 AR->getLoop(), SCEV::FlagAnyWrap)) {
2505 SmallVector<const SCEV *, 4> Operands;
2506 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i)
2507 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS));
2508 return getAddRecExpr(Operands, AR->getLoop(),
2511 /// Get a canonical UDivExpr for a recurrence.
2512 /// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0.
2513 // We can currently only fold X%N if X is constant.
2514 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(AR->getStart());
2515 if (StartC && !DivInt.urem(StepInt) &&
2516 getZeroExtendExpr(AR, ExtTy) ==
2517 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2518 getZeroExtendExpr(Step, ExtTy),
2519 AR->getLoop(), SCEV::FlagAnyWrap)) {
2520 const APInt &StartInt = StartC->getValue()->getValue();
2521 const APInt &StartRem = StartInt.urem(StepInt);
2523 LHS = getAddRecExpr(getConstant(StartInt - StartRem), Step,
2524 AR->getLoop(), SCEV::FlagNW);
2527 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
2528 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
2529 SmallVector<const SCEV *, 4> Operands;
2530 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i)
2531 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy));
2532 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
2533 // Find an operand that's safely divisible.
2534 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
2535 const SCEV *Op = M->getOperand(i);
2536 const SCEV *Div = getUDivExpr(Op, RHSC);
2537 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
2538 Operands = SmallVector<const SCEV *, 4>(M->op_begin(),
2541 return getMulExpr(Operands);
2545 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
2546 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) {
2547 SmallVector<const SCEV *, 4> Operands;
2548 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i)
2549 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy));
2550 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
2552 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
2553 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
2554 if (isa<SCEVUDivExpr>(Op) ||
2555 getMulExpr(Op, RHS) != A->getOperand(i))
2557 Operands.push_back(Op);
2559 if (Operands.size() == A->getNumOperands())
2560 return getAddExpr(Operands);
2564 // Fold if both operands are constant.
2565 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
2566 Constant *LHSCV = LHSC->getValue();
2567 Constant *RHSCV = RHSC->getValue();
2568 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
2574 FoldingSetNodeID ID;
2575 ID.AddInteger(scUDivExpr);
2579 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2580 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
2582 UniqueSCEVs.InsertNode(S, IP);
2586 static const APInt gcd(const SCEVConstant *C1, const SCEVConstant *C2) {
2587 APInt A = C1->getValue()->getValue().abs();
2588 APInt B = C2->getValue()->getValue().abs();
2589 uint32_t ABW = A.getBitWidth();
2590 uint32_t BBW = B.getBitWidth();
2597 return APIntOps::GreatestCommonDivisor(A, B);
2600 /// getUDivExactExpr - Get a canonical unsigned division expression, or
2601 /// something simpler if possible. There is no representation for an exact udiv
2602 /// in SCEV IR, but we can attempt to remove factors from the LHS and RHS.
2603 /// We can't do this when it's not exact because the udiv may be clearing bits.
2604 const SCEV *ScalarEvolution::getUDivExactExpr(const SCEV *LHS,
2606 // TODO: we could try to find factors in all sorts of things, but for now we
2607 // just deal with u/exact (multiply, constant). See SCEVDivision towards the
2608 // end of this file for inspiration.
2610 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(LHS);
2612 return getUDivExpr(LHS, RHS);
2614 if (const SCEVConstant *RHSCst = dyn_cast<SCEVConstant>(RHS)) {
2615 // If the mulexpr multiplies by a constant, then that constant must be the
2616 // first element of the mulexpr.
2617 if (const SCEVConstant *LHSCst =
2618 dyn_cast<SCEVConstant>(Mul->getOperand(0))) {
2619 if (LHSCst == RHSCst) {
2620 SmallVector<const SCEV *, 2> Operands;
2621 Operands.append(Mul->op_begin() + 1, Mul->op_end());
2622 return getMulExpr(Operands);
2625 // We can't just assume that LHSCst divides RHSCst cleanly, it could be
2626 // that there's a factor provided by one of the other terms. We need to
2628 APInt Factor = gcd(LHSCst, RHSCst);
2629 if (!Factor.isIntN(1)) {
2630 LHSCst = cast<SCEVConstant>(
2631 getConstant(LHSCst->getValue()->getValue().udiv(Factor)));
2632 RHSCst = cast<SCEVConstant>(
2633 getConstant(RHSCst->getValue()->getValue().udiv(Factor)));
2634 SmallVector<const SCEV *, 2> Operands;
2635 Operands.push_back(LHSCst);
2636 Operands.append(Mul->op_begin() + 1, Mul->op_end());
2637 LHS = getMulExpr(Operands);
2639 Mul = dyn_cast<SCEVMulExpr>(LHS);
2641 return getUDivExactExpr(LHS, RHS);
2646 for (int i = 0, e = Mul->getNumOperands(); i != e; ++i) {
2647 if (Mul->getOperand(i) == RHS) {
2648 SmallVector<const SCEV *, 2> Operands;
2649 Operands.append(Mul->op_begin(), Mul->op_begin() + i);
2650 Operands.append(Mul->op_begin() + i + 1, Mul->op_end());
2651 return getMulExpr(Operands);
2655 return getUDivExpr(LHS, RHS);
2658 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2659 /// Simplify the expression as much as possible.
2660 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step,
2662 SCEV::NoWrapFlags Flags) {
2663 SmallVector<const SCEV *, 4> Operands;
2664 Operands.push_back(Start);
2665 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
2666 if (StepChrec->getLoop() == L) {
2667 Operands.append(StepChrec->op_begin(), StepChrec->op_end());
2668 return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW));
2671 Operands.push_back(Step);
2672 return getAddRecExpr(Operands, L, Flags);
2675 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2676 /// Simplify the expression as much as possible.
2678 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
2679 const Loop *L, SCEV::NoWrapFlags Flags) {
2680 if (Operands.size() == 1) return Operands[0];
2682 Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
2683 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
2684 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy &&
2685 "SCEVAddRecExpr operand types don't match!");
2686 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2687 assert(isLoopInvariant(Operands[i], L) &&
2688 "SCEVAddRecExpr operand is not loop-invariant!");
2691 if (Operands.back()->isZero()) {
2692 Operands.pop_back();
2693 return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0} --> X
2696 // It's tempting to want to call getMaxBackedgeTakenCount count here and
2697 // use that information to infer NUW and NSW flags. However, computing a
2698 // BE count requires calling getAddRecExpr, so we may not yet have a
2699 // meaningful BE count at this point (and if we don't, we'd be stuck
2700 // with a SCEVCouldNotCompute as the cached BE count).
2702 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
2704 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
2705 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask);
2706 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) {
2708 for (SmallVectorImpl<const SCEV *>::const_iterator I = Operands.begin(),
2709 E = Operands.end(); I != E; ++I)
2710 if (!isKnownNonNegative(*I)) {
2714 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
2717 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
2718 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
2719 const Loop *NestedLoop = NestedAR->getLoop();
2720 if (L->contains(NestedLoop) ?
2721 (L->getLoopDepth() < NestedLoop->getLoopDepth()) :
2722 (!NestedLoop->contains(L) &&
2723 DT->dominates(L->getHeader(), NestedLoop->getHeader()))) {
2724 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
2725 NestedAR->op_end());
2726 Operands[0] = NestedAR->getStart();
2727 // AddRecs require their operands be loop-invariant with respect to their
2728 // loops. Don't perform this transformation if it would break this
2730 bool AllInvariant = true;
2731 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2732 if (!isLoopInvariant(Operands[i], L)) {
2733 AllInvariant = false;
2737 // Create a recurrence for the outer loop with the same step size.
2739 // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the
2740 // inner recurrence has the same property.
2741 SCEV::NoWrapFlags OuterFlags =
2742 maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags());
2744 NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags);
2745 AllInvariant = true;
2746 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i)
2747 if (!isLoopInvariant(NestedOperands[i], NestedLoop)) {
2748 AllInvariant = false;
2752 // Ok, both add recurrences are valid after the transformation.
2754 // The inner recurrence keeps its NW flag but only keeps NUW/NSW if
2755 // the outer recurrence has the same property.
2756 SCEV::NoWrapFlags InnerFlags =
2757 maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags);
2758 return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags);
2761 // Reset Operands to its original state.
2762 Operands[0] = NestedAR;
2766 // Okay, it looks like we really DO need an addrec expr. Check to see if we
2767 // already have one, otherwise create a new one.
2768 FoldingSetNodeID ID;
2769 ID.AddInteger(scAddRecExpr);
2770 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2771 ID.AddPointer(Operands[i]);
2775 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2777 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size());
2778 std::uninitialized_copy(Operands.begin(), Operands.end(), O);
2779 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator),
2780 O, Operands.size(), L);
2781 UniqueSCEVs.InsertNode(S, IP);
2783 S->setNoWrapFlags(Flags);
2787 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
2789 SmallVector<const SCEV *, 2> Ops;
2792 return getSMaxExpr(Ops);
2796 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2797 assert(!Ops.empty() && "Cannot get empty smax!");
2798 if (Ops.size() == 1) return Ops[0];
2800 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2801 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2802 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2803 "SCEVSMaxExpr operand types don't match!");
2806 // Sort by complexity, this groups all similar expression types together.
2807 GroupByComplexity(Ops, LI);
2809 // If there are any constants, fold them together.
2811 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2813 assert(Idx < Ops.size());
2814 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2815 // We found two constants, fold them together!
2816 ConstantInt *Fold = ConstantInt::get(getContext(),
2817 APIntOps::smax(LHSC->getValue()->getValue(),
2818 RHSC->getValue()->getValue()));
2819 Ops[0] = getConstant(Fold);
2820 Ops.erase(Ops.begin()+1); // Erase the folded element
2821 if (Ops.size() == 1) return Ops[0];
2822 LHSC = cast<SCEVConstant>(Ops[0]);
2825 // If we are left with a constant minimum-int, strip it off.
2826 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
2827 Ops.erase(Ops.begin());
2829 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
2830 // If we have an smax with a constant maximum-int, it will always be
2835 if (Ops.size() == 1) return Ops[0];
2838 // Find the first SMax
2839 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
2842 // Check to see if one of the operands is an SMax. If so, expand its operands
2843 // onto our operand list, and recurse to simplify.
2844 if (Idx < Ops.size()) {
2845 bool DeletedSMax = false;
2846 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
2847 Ops.erase(Ops.begin()+Idx);
2848 Ops.append(SMax->op_begin(), SMax->op_end());
2853 return getSMaxExpr(Ops);
2856 // Okay, check to see if the same value occurs in the operand list twice. If
2857 // so, delete one. Since we sorted the list, these values are required to
2859 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2860 // X smax Y smax Y --> X smax Y
2861 // X smax Y --> X, if X is always greater than Y
2862 if (Ops[i] == Ops[i+1] ||
2863 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) {
2864 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2866 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) {
2867 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2871 if (Ops.size() == 1) return Ops[0];
2873 assert(!Ops.empty() && "Reduced smax down to nothing!");
2875 // Okay, it looks like we really DO need an smax expr. Check to see if we
2876 // already have one, otherwise create a new one.
2877 FoldingSetNodeID ID;
2878 ID.AddInteger(scSMaxExpr);
2879 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2880 ID.AddPointer(Ops[i]);
2882 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2883 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2884 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2885 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator),
2887 UniqueSCEVs.InsertNode(S, IP);
2891 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
2893 SmallVector<const SCEV *, 2> Ops;
2896 return getUMaxExpr(Ops);
2900 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2901 assert(!Ops.empty() && "Cannot get empty umax!");
2902 if (Ops.size() == 1) return Ops[0];
2904 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2905 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2906 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2907 "SCEVUMaxExpr operand types don't match!");
2910 // Sort by complexity, this groups all similar expression types together.
2911 GroupByComplexity(Ops, LI);
2913 // If there are any constants, fold them together.
2915 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2917 assert(Idx < Ops.size());
2918 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2919 // We found two constants, fold them together!
2920 ConstantInt *Fold = ConstantInt::get(getContext(),
2921 APIntOps::umax(LHSC->getValue()->getValue(),
2922 RHSC->getValue()->getValue()));
2923 Ops[0] = getConstant(Fold);
2924 Ops.erase(Ops.begin()+1); // Erase the folded element
2925 if (Ops.size() == 1) return Ops[0];
2926 LHSC = cast<SCEVConstant>(Ops[0]);
2929 // If we are left with a constant minimum-int, strip it off.
2930 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
2931 Ops.erase(Ops.begin());
2933 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
2934 // If we have an umax with a constant maximum-int, it will always be
2939 if (Ops.size() == 1) return Ops[0];
2942 // Find the first UMax
2943 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
2946 // Check to see if one of the operands is a UMax. If so, expand its operands
2947 // onto our operand list, and recurse to simplify.
2948 if (Idx < Ops.size()) {
2949 bool DeletedUMax = false;
2950 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
2951 Ops.erase(Ops.begin()+Idx);
2952 Ops.append(UMax->op_begin(), UMax->op_end());
2957 return getUMaxExpr(Ops);
2960 // Okay, check to see if the same value occurs in the operand list twice. If
2961 // so, delete one. Since we sorted the list, these values are required to
2963 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2964 // X umax Y umax Y --> X umax Y
2965 // X umax Y --> X, if X is always greater than Y
2966 if (Ops[i] == Ops[i+1] ||
2967 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) {
2968 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2970 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) {
2971 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2975 if (Ops.size() == 1) return Ops[0];
2977 assert(!Ops.empty() && "Reduced umax down to nothing!");
2979 // Okay, it looks like we really DO need a umax expr. Check to see if we
2980 // already have one, otherwise create a new one.
2981 FoldingSetNodeID ID;
2982 ID.AddInteger(scUMaxExpr);
2983 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2984 ID.AddPointer(Ops[i]);
2986 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2987 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2988 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2989 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator),
2991 UniqueSCEVs.InsertNode(S, IP);
2995 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
2997 // ~smax(~x, ~y) == smin(x, y).
2998 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
3001 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
3003 // ~umax(~x, ~y) == umin(x, y)
3004 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
3007 const SCEV *ScalarEvolution::getSizeOfExpr(Type *IntTy, Type *AllocTy) {
3008 // If we have DataLayout, we can bypass creating a target-independent
3009 // constant expression and then folding it back into a ConstantInt.
3010 // This is just a compile-time optimization.
3012 return getConstant(IntTy, DL->getTypeAllocSize(AllocTy));
3014 Constant *C = ConstantExpr::getSizeOf(AllocTy);
3015 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
3016 if (Constant *Folded = ConstantFoldConstantExpression(CE, DL, TLI))
3018 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
3019 assert(Ty == IntTy && "Effective SCEV type doesn't match");
3020 return getTruncateOrZeroExtend(getSCEV(C), Ty);
3023 const SCEV *ScalarEvolution::getOffsetOfExpr(Type *IntTy,
3026 // If we have DataLayout, we can bypass creating a target-independent
3027 // constant expression and then folding it back into a ConstantInt.
3028 // This is just a compile-time optimization.
3030 return getConstant(IntTy,
3031 DL->getStructLayout(STy)->getElementOffset(FieldNo));
3034 Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo);
3035 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
3036 if (Constant *Folded = ConstantFoldConstantExpression(CE, DL, TLI))
3039 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy));
3040 return getTruncateOrZeroExtend(getSCEV(C), Ty);
3043 const SCEV *ScalarEvolution::getUnknown(Value *V) {
3044 // Don't attempt to do anything other than create a SCEVUnknown object
3045 // here. createSCEV only calls getUnknown after checking for all other
3046 // interesting possibilities, and any other code that calls getUnknown
3047 // is doing so in order to hide a value from SCEV canonicalization.
3049 FoldingSetNodeID ID;
3050 ID.AddInteger(scUnknown);
3053 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
3054 assert(cast<SCEVUnknown>(S)->getValue() == V &&
3055 "Stale SCEVUnknown in uniquing map!");
3058 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
3060 FirstUnknown = cast<SCEVUnknown>(S);
3061 UniqueSCEVs.InsertNode(S, IP);
3065 //===----------------------------------------------------------------------===//
3066 // Basic SCEV Analysis and PHI Idiom Recognition Code
3069 /// isSCEVable - Test if values of the given type are analyzable within
3070 /// the SCEV framework. This primarily includes integer types, and it
3071 /// can optionally include pointer types if the ScalarEvolution class
3072 /// has access to target-specific information.
3073 bool ScalarEvolution::isSCEVable(Type *Ty) const {
3074 // Integers and pointers are always SCEVable.
3075 return Ty->isIntegerTy() || Ty->isPointerTy();
3078 /// getTypeSizeInBits - Return the size in bits of the specified type,
3079 /// for which isSCEVable must return true.
3080 uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const {
3081 assert(isSCEVable(Ty) && "Type is not SCEVable!");
3083 // If we have a DataLayout, use it!
3085 return DL->getTypeSizeInBits(Ty);
3087 // Integer types have fixed sizes.
3088 if (Ty->isIntegerTy())
3089 return Ty->getPrimitiveSizeInBits();
3091 // The only other support type is pointer. Without DataLayout, conservatively
3092 // assume pointers are 64-bit.
3093 assert(Ty->isPointerTy() && "isSCEVable permitted a non-SCEVable type!");
3097 /// getEffectiveSCEVType - Return a type with the same bitwidth as
3098 /// the given type and which represents how SCEV will treat the given
3099 /// type, for which isSCEVable must return true. For pointer types,
3100 /// this is the pointer-sized integer type.
3101 Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const {
3102 assert(isSCEVable(Ty) && "Type is not SCEVable!");
3104 if (Ty->isIntegerTy()) {
3108 // The only other support type is pointer.
3109 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
3112 return DL->getIntPtrType(Ty);
3114 // Without DataLayout, conservatively assume pointers are 64-bit.
3115 return Type::getInt64Ty(getContext());
3118 const SCEV *ScalarEvolution::getCouldNotCompute() {
3119 return &CouldNotCompute;
3123 // Helper class working with SCEVTraversal to figure out if a SCEV contains
3124 // a SCEVUnknown with null value-pointer. FindInvalidSCEVUnknown::FindOne
3125 // is set iff if find such SCEVUnknown.
3127 struct FindInvalidSCEVUnknown {
3129 FindInvalidSCEVUnknown() { FindOne = false; }
3130 bool follow(const SCEV *S) {
3131 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
3135 if (!cast<SCEVUnknown>(S)->getValue())
3142 bool isDone() const { return FindOne; }
3146 bool ScalarEvolution::checkValidity(const SCEV *S) const {
3147 FindInvalidSCEVUnknown F;
3148 SCEVTraversal<FindInvalidSCEVUnknown> ST(F);
3154 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
3155 /// expression and create a new one.
3156 const SCEV *ScalarEvolution::getSCEV(Value *V) {
3157 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
3159 ValueExprMapType::iterator I = ValueExprMap.find_as(V);
3160 if (I != ValueExprMap.end()) {
3161 const SCEV *S = I->second;
3162 if (checkValidity(S))
3165 ValueExprMap.erase(I);
3167 const SCEV *S = createSCEV(V);
3169 // The process of creating a SCEV for V may have caused other SCEVs
3170 // to have been created, so it's necessary to insert the new entry
3171 // from scratch, rather than trying to remember the insert position
3173 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(V, this), S));
3177 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
3179 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) {
3180 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
3182 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
3184 Type *Ty = V->getType();
3185 Ty = getEffectiveSCEVType(Ty);
3186 return getMulExpr(V,
3187 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))));
3190 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
3191 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
3192 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
3194 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
3196 Type *Ty = V->getType();
3197 Ty = getEffectiveSCEVType(Ty);
3198 const SCEV *AllOnes =
3199 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
3200 return getMinusSCEV(AllOnes, V);
3203 /// getMinusSCEV - Return LHS-RHS. Minus is represented in SCEV as A+B*-1.
3204 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
3205 SCEV::NoWrapFlags Flags) {
3206 assert(!maskFlags(Flags, SCEV::FlagNUW) && "subtraction does not have NUW");
3208 // Fast path: X - X --> 0.
3210 return getConstant(LHS->getType(), 0);
3213 return getAddExpr(LHS, getNegativeSCEV(RHS), Flags);
3216 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
3217 /// input value to the specified type. If the type must be extended, it is zero
3220 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty) {
3221 Type *SrcTy = V->getType();
3222 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3223 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3224 "Cannot truncate or zero extend with non-integer arguments!");
3225 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3226 return V; // No conversion
3227 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
3228 return getTruncateExpr(V, Ty);
3229 return getZeroExtendExpr(V, Ty);
3232 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
3233 /// input value to the specified type. If the type must be extended, it is sign
3236 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
3238 Type *SrcTy = V->getType();
3239 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3240 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3241 "Cannot truncate or zero extend with non-integer arguments!");
3242 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3243 return V; // No conversion
3244 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
3245 return getTruncateExpr(V, Ty);
3246 return getSignExtendExpr(V, Ty);
3249 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
3250 /// input value to the specified type. If the type must be extended, it is zero
3251 /// extended. The conversion must not be narrowing.
3253 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) {
3254 Type *SrcTy = V->getType();
3255 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3256 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3257 "Cannot noop or zero extend with non-integer arguments!");
3258 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3259 "getNoopOrZeroExtend cannot truncate!");
3260 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3261 return V; // No conversion
3262 return getZeroExtendExpr(V, Ty);
3265 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
3266 /// input value to the specified type. If the type must be extended, it is sign
3267 /// extended. The conversion must not be narrowing.
3269 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) {
3270 Type *SrcTy = V->getType();
3271 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3272 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3273 "Cannot noop or sign extend with non-integer arguments!");
3274 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3275 "getNoopOrSignExtend cannot truncate!");
3276 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3277 return V; // No conversion
3278 return getSignExtendExpr(V, Ty);
3281 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
3282 /// the input value to the specified type. If the type must be extended,
3283 /// it is extended with unspecified bits. The conversion must not be
3286 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) {
3287 Type *SrcTy = V->getType();
3288 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3289 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3290 "Cannot noop or any extend with non-integer arguments!");
3291 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3292 "getNoopOrAnyExtend cannot truncate!");
3293 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3294 return V; // No conversion
3295 return getAnyExtendExpr(V, Ty);
3298 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
3299 /// input value to the specified type. The conversion must not be widening.
3301 ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) {
3302 Type *SrcTy = V->getType();
3303 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3304 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3305 "Cannot truncate or noop with non-integer arguments!");
3306 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
3307 "getTruncateOrNoop cannot extend!");
3308 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3309 return V; // No conversion
3310 return getTruncateExpr(V, Ty);
3313 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
3314 /// the types using zero-extension, and then perform a umax operation
3316 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
3318 const SCEV *PromotedLHS = LHS;
3319 const SCEV *PromotedRHS = RHS;
3321 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
3322 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
3324 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
3326 return getUMaxExpr(PromotedLHS, PromotedRHS);
3329 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
3330 /// the types using zero-extension, and then perform a umin operation
3332 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
3334 const SCEV *PromotedLHS = LHS;
3335 const SCEV *PromotedRHS = RHS;
3337 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
3338 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
3340 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
3342 return getUMinExpr(PromotedLHS, PromotedRHS);
3345 /// getPointerBase - Transitively follow the chain of pointer-type operands
3346 /// until reaching a SCEV that does not have a single pointer operand. This
3347 /// returns a SCEVUnknown pointer for well-formed pointer-type expressions,
3348 /// but corner cases do exist.
3349 const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) {
3350 // A pointer operand may evaluate to a nonpointer expression, such as null.
3351 if (!V->getType()->isPointerTy())
3354 if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) {
3355 return getPointerBase(Cast->getOperand());
3357 else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) {
3358 const SCEV *PtrOp = nullptr;
3359 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
3361 if ((*I)->getType()->isPointerTy()) {
3362 // Cannot find the base of an expression with multiple pointer operands.
3370 return getPointerBase(PtrOp);
3375 /// PushDefUseChildren - Push users of the given Instruction
3376 /// onto the given Worklist.
3378 PushDefUseChildren(Instruction *I,
3379 SmallVectorImpl<Instruction *> &Worklist) {
3380 // Push the def-use children onto the Worklist stack.
3381 for (User *U : I->users())
3382 Worklist.push_back(cast<Instruction>(U));
3385 /// ForgetSymbolicValue - This looks up computed SCEV values for all
3386 /// instructions that depend on the given instruction and removes them from
3387 /// the ValueExprMapType map if they reference SymName. This is used during PHI
3390 ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) {
3391 SmallVector<Instruction *, 16> Worklist;
3392 PushDefUseChildren(PN, Worklist);
3394 SmallPtrSet<Instruction *, 8> Visited;
3396 while (!Worklist.empty()) {
3397 Instruction *I = Worklist.pop_back_val();
3398 if (!Visited.insert(I).second)
3401 ValueExprMapType::iterator It =
3402 ValueExprMap.find_as(static_cast<Value *>(I));
3403 if (It != ValueExprMap.end()) {
3404 const SCEV *Old = It->second;
3406 // Short-circuit the def-use traversal if the symbolic name
3407 // ceases to appear in expressions.
3408 if (Old != SymName && !hasOperand(Old, SymName))
3411 // SCEVUnknown for a PHI either means that it has an unrecognized
3412 // structure, it's a PHI that's in the progress of being computed
3413 // by createNodeForPHI, or it's a single-value PHI. In the first case,
3414 // additional loop trip count information isn't going to change anything.
3415 // In the second case, createNodeForPHI will perform the necessary
3416 // updates on its own when it gets to that point. In the third, we do
3417 // want to forget the SCEVUnknown.
3418 if (!isa<PHINode>(I) ||
3419 !isa<SCEVUnknown>(Old) ||
3420 (I != PN && Old == SymName)) {
3421 forgetMemoizedResults(Old);
3422 ValueExprMap.erase(It);
3426 PushDefUseChildren(I, Worklist);
3430 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
3431 /// a loop header, making it a potential recurrence, or it doesn't.
3433 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
3434 if (const Loop *L = LI->getLoopFor(PN->getParent()))
3435 if (L->getHeader() == PN->getParent()) {
3436 // The loop may have multiple entrances or multiple exits; we can analyze
3437 // this phi as an addrec if it has a unique entry value and a unique
3439 Value *BEValueV = nullptr, *StartValueV = nullptr;
3440 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
3441 Value *V = PN->getIncomingValue(i);
3442 if (L->contains(PN->getIncomingBlock(i))) {
3445 } else if (BEValueV != V) {
3449 } else if (!StartValueV) {
3451 } else if (StartValueV != V) {
3452 StartValueV = nullptr;
3456 if (BEValueV && StartValueV) {
3457 // While we are analyzing this PHI node, handle its value symbolically.
3458 const SCEV *SymbolicName = getUnknown(PN);
3459 assert(ValueExprMap.find_as(PN) == ValueExprMap.end() &&
3460 "PHI node already processed?");
3461 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
3463 // Using this symbolic name for the PHI, analyze the value coming around
3465 const SCEV *BEValue = getSCEV(BEValueV);
3467 // NOTE: If BEValue is loop invariant, we know that the PHI node just
3468 // has a special value for the first iteration of the loop.
3470 // If the value coming around the backedge is an add with the symbolic
3471 // value we just inserted, then we found a simple induction variable!
3472 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
3473 // If there is a single occurrence of the symbolic value, replace it
3474 // with a recurrence.
3475 unsigned FoundIndex = Add->getNumOperands();
3476 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3477 if (Add->getOperand(i) == SymbolicName)
3478 if (FoundIndex == e) {
3483 if (FoundIndex != Add->getNumOperands()) {
3484 // Create an add with everything but the specified operand.
3485 SmallVector<const SCEV *, 8> Ops;
3486 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3487 if (i != FoundIndex)
3488 Ops.push_back(Add->getOperand(i));
3489 const SCEV *Accum = getAddExpr(Ops);
3491 // This is not a valid addrec if the step amount is varying each
3492 // loop iteration, but is not itself an addrec in this loop.
3493 if (isLoopInvariant(Accum, L) ||
3494 (isa<SCEVAddRecExpr>(Accum) &&
3495 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
3496 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
3498 // If the increment doesn't overflow, then neither the addrec nor
3499 // the post-increment will overflow.
3500 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) {
3501 if (OBO->hasNoUnsignedWrap())
3502 Flags = setFlags(Flags, SCEV::FlagNUW);
3503 if (OBO->hasNoSignedWrap())
3504 Flags = setFlags(Flags, SCEV::FlagNSW);
3505 } else if (GEPOperator *GEP = dyn_cast<GEPOperator>(BEValueV)) {
3506 // If the increment is an inbounds GEP, then we know the address
3507 // space cannot be wrapped around. We cannot make any guarantee
3508 // about signed or unsigned overflow because pointers are
3509 // unsigned but we may have a negative index from the base
3510 // pointer. We can guarantee that no unsigned wrap occurs if the
3511 // indices form a positive value.
3512 if (GEP->isInBounds()) {
3513 Flags = setFlags(Flags, SCEV::FlagNW);
3515 const SCEV *Ptr = getSCEV(GEP->getPointerOperand());
3516 if (isKnownPositive(getMinusSCEV(getSCEV(GEP), Ptr)))
3517 Flags = setFlags(Flags, SCEV::FlagNUW);
3519 } else if (const SubOperator *OBO =
3520 dyn_cast<SubOperator>(BEValueV)) {
3521 if (OBO->hasNoUnsignedWrap())
3522 Flags = setFlags(Flags, SCEV::FlagNUW);
3523 if (OBO->hasNoSignedWrap())
3524 Flags = setFlags(Flags, SCEV::FlagNSW);
3527 const SCEV *StartVal = getSCEV(StartValueV);
3528 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
3530 // Since the no-wrap flags are on the increment, they apply to the
3531 // post-incremented value as well.
3532 if (isLoopInvariant(Accum, L))
3533 (void)getAddRecExpr(getAddExpr(StartVal, Accum),
3536 // Okay, for the entire analysis of this edge we assumed the PHI
3537 // to be symbolic. We now need to go back and purge all of the
3538 // entries for the scalars that use the symbolic expression.
3539 ForgetSymbolicName(PN, SymbolicName);
3540 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3544 } else if (const SCEVAddRecExpr *AddRec =
3545 dyn_cast<SCEVAddRecExpr>(BEValue)) {
3546 // Otherwise, this could be a loop like this:
3547 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
3548 // In this case, j = {1,+,1} and BEValue is j.
3549 // Because the other in-value of i (0) fits the evolution of BEValue
3550 // i really is an addrec evolution.
3551 if (AddRec->getLoop() == L && AddRec->isAffine()) {
3552 const SCEV *StartVal = getSCEV(StartValueV);
3554 // If StartVal = j.start - j.stride, we can use StartVal as the
3555 // initial step of the addrec evolution.
3556 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
3557 AddRec->getOperand(1))) {
3558 // FIXME: For constant StartVal, we should be able to infer
3560 const SCEV *PHISCEV =
3561 getAddRecExpr(StartVal, AddRec->getOperand(1), L,
3564 // Okay, for the entire analysis of this edge we assumed the PHI
3565 // to be symbolic. We now need to go back and purge all of the
3566 // entries for the scalars that use the symbolic expression.
3567 ForgetSymbolicName(PN, SymbolicName);
3568 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3576 // If the PHI has a single incoming value, follow that value, unless the
3577 // PHI's incoming blocks are in a different loop, in which case doing so
3578 // risks breaking LCSSA form. Instcombine would normally zap these, but
3579 // it doesn't have DominatorTree information, so it may miss cases.
3580 if (Value *V = SimplifyInstruction(PN, DL, TLI, DT, AT))
3581 if (LI->replacementPreservesLCSSAForm(PN, V))
3584 // If it's not a loop phi, we can't handle it yet.
3585 return getUnknown(PN);
3588 /// createNodeForGEP - Expand GEP instructions into add and multiply
3589 /// operations. This allows them to be analyzed by regular SCEV code.
3591 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
3592 Type *IntPtrTy = getEffectiveSCEVType(GEP->getType());
3593 Value *Base = GEP->getOperand(0);
3594 // Don't attempt to analyze GEPs over unsized objects.
3595 if (!Base->getType()->getPointerElementType()->isSized())
3596 return getUnknown(GEP);
3598 // Don't blindly transfer the inbounds flag from the GEP instruction to the
3599 // Add expression, because the Instruction may be guarded by control flow
3600 // and the no-overflow bits may not be valid for the expression in any
3602 SCEV::NoWrapFlags Wrap = GEP->isInBounds() ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
3604 const SCEV *TotalOffset = getConstant(IntPtrTy, 0);
3605 gep_type_iterator GTI = gep_type_begin(GEP);
3606 for (GetElementPtrInst::op_iterator I = std::next(GEP->op_begin()),
3610 // Compute the (potentially symbolic) offset in bytes for this index.
3611 if (StructType *STy = dyn_cast<StructType>(*GTI++)) {
3612 // For a struct, add the member offset.
3613 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
3614 const SCEV *FieldOffset = getOffsetOfExpr(IntPtrTy, STy, FieldNo);
3616 // Add the field offset to the running total offset.
3617 TotalOffset = getAddExpr(TotalOffset, FieldOffset);
3619 // For an array, add the element offset, explicitly scaled.
3620 const SCEV *ElementSize = getSizeOfExpr(IntPtrTy, *GTI);
3621 const SCEV *IndexS = getSCEV(Index);
3622 // Getelementptr indices are signed.
3623 IndexS = getTruncateOrSignExtend(IndexS, IntPtrTy);
3625 // Multiply the index by the element size to compute the element offset.
3626 const SCEV *LocalOffset = getMulExpr(IndexS, ElementSize, Wrap);
3628 // Add the element offset to the running total offset.
3629 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
3633 // Get the SCEV for the GEP base.
3634 const SCEV *BaseS = getSCEV(Base);
3636 // Add the total offset from all the GEP indices to the base.
3637 return getAddExpr(BaseS, TotalOffset, Wrap);
3640 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
3641 /// guaranteed to end in (at every loop iteration). It is, at the same time,
3642 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
3643 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
3645 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
3646 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3647 return C->getValue()->getValue().countTrailingZeros();
3649 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
3650 return std::min(GetMinTrailingZeros(T->getOperand()),
3651 (uint32_t)getTypeSizeInBits(T->getType()));
3653 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
3654 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3655 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3656 getTypeSizeInBits(E->getType()) : OpRes;
3659 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
3660 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3661 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3662 getTypeSizeInBits(E->getType()) : OpRes;
3665 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
3666 // The result is the min of all operands results.
3667 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3668 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3669 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3673 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
3674 // The result is the sum of all operands results.
3675 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
3676 uint32_t BitWidth = getTypeSizeInBits(M->getType());
3677 for (unsigned i = 1, e = M->getNumOperands();
3678 SumOpRes != BitWidth && i != e; ++i)
3679 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
3684 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
3685 // The result is the min of all operands results.
3686 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3687 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3688 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3692 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
3693 // The result is the min of all operands results.
3694 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3695 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3696 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3700 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
3701 // The result is the min of all operands results.
3702 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3703 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3704 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3708 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3709 // For a SCEVUnknown, ask ValueTracking.
3710 unsigned BitWidth = getTypeSizeInBits(U->getType());
3711 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3712 computeKnownBits(U->getValue(), Zeros, Ones, DL, 0, AT, nullptr, DT);
3713 return Zeros.countTrailingOnes();
3720 /// GetRangeFromMetadata - Helper method to assign a range to V from
3721 /// metadata present in the IR.
3722 static Optional<ConstantRange> GetRangeFromMetadata(Value *V) {
3723 if (Instruction *I = dyn_cast<Instruction>(V)) {
3724 if (MDNode *MD = I->getMetadata(LLVMContext::MD_range)) {
3725 ConstantRange TotalRange(
3726 cast<IntegerType>(I->getType())->getBitWidth(), false);
3728 unsigned NumRanges = MD->getNumOperands() / 2;
3729 assert(NumRanges >= 1);
3731 for (unsigned i = 0; i < NumRanges; ++i) {
3732 ConstantInt *Lower = cast<ConstantInt>(MD->getOperand(2*i + 0));
3733 ConstantInt *Upper = cast<ConstantInt>(MD->getOperand(2*i + 1));
3734 ConstantRange Range(Lower->getValue(), Upper->getValue());
3735 TotalRange = TotalRange.unionWith(Range);
3745 /// getUnsignedRange - Determine the unsigned range for a particular SCEV.
3748 ScalarEvolution::getUnsignedRange(const SCEV *S) {
3749 // See if we've computed this range already.
3750 DenseMap<const SCEV *, ConstantRange>::iterator I = UnsignedRanges.find(S);
3751 if (I != UnsignedRanges.end())
3754 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3755 return setUnsignedRange(C, ConstantRange(C->getValue()->getValue()));
3757 unsigned BitWidth = getTypeSizeInBits(S->getType());
3758 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3760 // If the value has known zeros, the maximum unsigned value will have those
3761 // known zeros as well.
3762 uint32_t TZ = GetMinTrailingZeros(S);
3764 ConservativeResult =
3765 ConstantRange(APInt::getMinValue(BitWidth),
3766 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
3768 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3769 ConstantRange X = getUnsignedRange(Add->getOperand(0));
3770 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3771 X = X.add(getUnsignedRange(Add->getOperand(i)));
3772 return setUnsignedRange(Add, ConservativeResult.intersectWith(X));
3775 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3776 ConstantRange X = getUnsignedRange(Mul->getOperand(0));
3777 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3778 X = X.multiply(getUnsignedRange(Mul->getOperand(i)));
3779 return setUnsignedRange(Mul, ConservativeResult.intersectWith(X));
3782 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3783 ConstantRange X = getUnsignedRange(SMax->getOperand(0));
3784 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3785 X = X.smax(getUnsignedRange(SMax->getOperand(i)));
3786 return setUnsignedRange(SMax, ConservativeResult.intersectWith(X));
3789 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3790 ConstantRange X = getUnsignedRange(UMax->getOperand(0));
3791 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3792 X = X.umax(getUnsignedRange(UMax->getOperand(i)));
3793 return setUnsignedRange(UMax, ConservativeResult.intersectWith(X));
3796 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3797 ConstantRange X = getUnsignedRange(UDiv->getLHS());
3798 ConstantRange Y = getUnsignedRange(UDiv->getRHS());
3799 return setUnsignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y)));
3802 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3803 ConstantRange X = getUnsignedRange(ZExt->getOperand());
3804 return setUnsignedRange(ZExt,
3805 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3808 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3809 ConstantRange X = getUnsignedRange(SExt->getOperand());
3810 return setUnsignedRange(SExt,
3811 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3814 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3815 ConstantRange X = getUnsignedRange(Trunc->getOperand());
3816 return setUnsignedRange(Trunc,
3817 ConservativeResult.intersectWith(X.truncate(BitWidth)));
3820 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3821 // If there's no unsigned wrap, the value will never be less than its
3823 if (AddRec->getNoWrapFlags(SCEV::FlagNUW))
3824 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
3825 if (!C->getValue()->isZero())
3826 ConservativeResult =
3827 ConservativeResult.intersectWith(
3828 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0)));
3830 // TODO: non-affine addrec
3831 if (AddRec->isAffine()) {
3832 Type *Ty = AddRec->getType();
3833 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3834 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3835 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3836 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3838 const SCEV *Start = AddRec->getStart();
3839 const SCEV *Step = AddRec->getStepRecurrence(*this);
3841 ConstantRange StartRange = getUnsignedRange(Start);
3842 ConstantRange StepRange = getSignedRange(Step);
3843 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3844 ConstantRange EndRange =
3845 StartRange.add(MaxBECountRange.multiply(StepRange));
3847 // Check for overflow. This must be done with ConstantRange arithmetic
3848 // because we could be called from within the ScalarEvolution overflow
3850 ConstantRange ExtStartRange = StartRange.zextOrTrunc(BitWidth*2+1);
3851 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3852 ConstantRange ExtMaxBECountRange =
3853 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3854 ConstantRange ExtEndRange = EndRange.zextOrTrunc(BitWidth*2+1);
3855 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3857 return setUnsignedRange(AddRec, ConservativeResult);
3859 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(),
3860 EndRange.getUnsignedMin());
3861 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(),
3862 EndRange.getUnsignedMax());
3863 if (Min.isMinValue() && Max.isMaxValue())
3864 return setUnsignedRange(AddRec, ConservativeResult);
3865 return setUnsignedRange(AddRec,
3866 ConservativeResult.intersectWith(ConstantRange(Min, Max+1)));
3870 return setUnsignedRange(AddRec, ConservativeResult);
3873 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3874 // Check if the IR explicitly contains !range metadata.
3875 Optional<ConstantRange> MDRange = GetRangeFromMetadata(U->getValue());
3876 if (MDRange.hasValue())
3877 ConservativeResult = ConservativeResult.intersectWith(MDRange.getValue());
3879 // For a SCEVUnknown, ask ValueTracking.
3880 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3881 computeKnownBits(U->getValue(), Zeros, Ones, DL, 0, AT, nullptr, DT);
3882 if (Ones == ~Zeros + 1)
3883 return setUnsignedRange(U, ConservativeResult);
3884 return setUnsignedRange(U,
3885 ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1)));
3888 return setUnsignedRange(S, ConservativeResult);
3891 /// getSignedRange - Determine the signed range for a particular SCEV.
3894 ScalarEvolution::getSignedRange(const SCEV *S) {
3895 // See if we've computed this range already.
3896 DenseMap<const SCEV *, ConstantRange>::iterator I = SignedRanges.find(S);
3897 if (I != SignedRanges.end())
3900 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3901 return setSignedRange(C, ConstantRange(C->getValue()->getValue()));
3903 unsigned BitWidth = getTypeSizeInBits(S->getType());
3904 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3906 // If the value has known zeros, the maximum signed value will have those
3907 // known zeros as well.
3908 uint32_t TZ = GetMinTrailingZeros(S);
3910 ConservativeResult =
3911 ConstantRange(APInt::getSignedMinValue(BitWidth),
3912 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
3914 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3915 ConstantRange X = getSignedRange(Add->getOperand(0));
3916 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3917 X = X.add(getSignedRange(Add->getOperand(i)));
3918 return setSignedRange(Add, ConservativeResult.intersectWith(X));
3921 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3922 ConstantRange X = getSignedRange(Mul->getOperand(0));
3923 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3924 X = X.multiply(getSignedRange(Mul->getOperand(i)));
3925 return setSignedRange(Mul, ConservativeResult.intersectWith(X));
3928 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3929 ConstantRange X = getSignedRange(SMax->getOperand(0));
3930 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3931 X = X.smax(getSignedRange(SMax->getOperand(i)));
3932 return setSignedRange(SMax, ConservativeResult.intersectWith(X));
3935 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3936 ConstantRange X = getSignedRange(UMax->getOperand(0));
3937 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3938 X = X.umax(getSignedRange(UMax->getOperand(i)));
3939 return setSignedRange(UMax, ConservativeResult.intersectWith(X));
3942 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3943 ConstantRange X = getSignedRange(UDiv->getLHS());
3944 ConstantRange Y = getSignedRange(UDiv->getRHS());
3945 return setSignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y)));
3948 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3949 ConstantRange X = getSignedRange(ZExt->getOperand());
3950 return setSignedRange(ZExt,
3951 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3954 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3955 ConstantRange X = getSignedRange(SExt->getOperand());
3956 return setSignedRange(SExt,
3957 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3960 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3961 ConstantRange X = getSignedRange(Trunc->getOperand());
3962 return setSignedRange(Trunc,
3963 ConservativeResult.intersectWith(X.truncate(BitWidth)));
3966 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3967 // If there's no signed wrap, and all the operands have the same sign or
3968 // zero, the value won't ever change sign.
3969 if (AddRec->getNoWrapFlags(SCEV::FlagNSW)) {
3970 bool AllNonNeg = true;
3971 bool AllNonPos = true;
3972 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
3973 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
3974 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
3977 ConservativeResult = ConservativeResult.intersectWith(
3978 ConstantRange(APInt(BitWidth, 0),
3979 APInt::getSignedMinValue(BitWidth)));
3981 ConservativeResult = ConservativeResult.intersectWith(
3982 ConstantRange(APInt::getSignedMinValue(BitWidth),
3983 APInt(BitWidth, 1)));
3986 // TODO: non-affine addrec
3987 if (AddRec->isAffine()) {
3988 Type *Ty = AddRec->getType();
3989 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3990 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3991 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3992 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3994 const SCEV *Start = AddRec->getStart();
3995 const SCEV *Step = AddRec->getStepRecurrence(*this);
3997 ConstantRange StartRange = getSignedRange(Start);
3998 ConstantRange StepRange = getSignedRange(Step);
3999 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
4000 ConstantRange EndRange =
4001 StartRange.add(MaxBECountRange.multiply(StepRange));
4003 // Check for overflow. This must be done with ConstantRange arithmetic
4004 // because we could be called from within the ScalarEvolution overflow
4006 ConstantRange ExtStartRange = StartRange.sextOrTrunc(BitWidth*2+1);
4007 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
4008 ConstantRange ExtMaxBECountRange =
4009 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
4010 ConstantRange ExtEndRange = EndRange.sextOrTrunc(BitWidth*2+1);
4011 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
4013 return setSignedRange(AddRec, ConservativeResult);
4015 APInt Min = APIntOps::smin(StartRange.getSignedMin(),
4016 EndRange.getSignedMin());
4017 APInt Max = APIntOps::smax(StartRange.getSignedMax(),
4018 EndRange.getSignedMax());
4019 if (Min.isMinSignedValue() && Max.isMaxSignedValue())
4020 return setSignedRange(AddRec, ConservativeResult);
4021 return setSignedRange(AddRec,
4022 ConservativeResult.intersectWith(ConstantRange(Min, Max+1)));
4026 return setSignedRange(AddRec, ConservativeResult);
4029 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
4030 // Check if the IR explicitly contains !range metadata.
4031 Optional<ConstantRange> MDRange = GetRangeFromMetadata(U->getValue());
4032 if (MDRange.hasValue())
4033 ConservativeResult = ConservativeResult.intersectWith(MDRange.getValue());
4035 // For a SCEVUnknown, ask ValueTracking.
4036 if (!U->getValue()->getType()->isIntegerTy() && !DL)
4037 return setSignedRange(U, ConservativeResult);
4038 unsigned NS = ComputeNumSignBits(U->getValue(), DL, 0, AT, nullptr, DT);
4040 return setSignedRange(U, ConservativeResult);
4041 return setSignedRange(U, ConservativeResult.intersectWith(
4042 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
4043 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1)));
4046 return setSignedRange(S, ConservativeResult);
4049 /// createSCEV - We know that there is no SCEV for the specified value.
4050 /// Analyze the expression.
4052 const SCEV *ScalarEvolution::createSCEV(Value *V) {
4053 if (!isSCEVable(V->getType()))
4054 return getUnknown(V);
4056 unsigned Opcode = Instruction::UserOp1;
4057 if (Instruction *I = dyn_cast<Instruction>(V)) {
4058 Opcode = I->getOpcode();
4060 // Don't attempt to analyze instructions in blocks that aren't
4061 // reachable. Such instructions don't matter, and they aren't required
4062 // to obey basic rules for definitions dominating uses which this
4063 // analysis depends on.
4064 if (!DT->isReachableFromEntry(I->getParent()))
4065 return getUnknown(V);
4066 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
4067 Opcode = CE->getOpcode();
4068 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
4069 return getConstant(CI);
4070 else if (isa<ConstantPointerNull>(V))
4071 return getConstant(V->getType(), 0);
4072 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
4073 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee());
4075 return getUnknown(V);
4077 Operator *U = cast<Operator>(V);
4079 case Instruction::Add: {
4080 // The simple thing to do would be to just call getSCEV on both operands
4081 // and call getAddExpr with the result. However if we're looking at a
4082 // bunch of things all added together, this can be quite inefficient,
4083 // because it leads to N-1 getAddExpr calls for N ultimate operands.
4084 // Instead, gather up all the operands and make a single getAddExpr call.
4085 // LLVM IR canonical form means we need only traverse the left operands.
4087 // Don't apply this instruction's NSW or NUW flags to the new
4088 // expression. The instruction may be guarded by control flow that the
4089 // no-wrap behavior depends on. Non-control-equivalent instructions can be
4090 // mapped to the same SCEV expression, and it would be incorrect to transfer
4091 // NSW/NUW semantics to those operations.
4092 SmallVector<const SCEV *, 4> AddOps;
4093 AddOps.push_back(getSCEV(U->getOperand(1)));
4094 for (Value *Op = U->getOperand(0); ; Op = U->getOperand(0)) {
4095 unsigned Opcode = Op->getValueID() - Value::InstructionVal;
4096 if (Opcode != Instruction::Add && Opcode != Instruction::Sub)
4098 U = cast<Operator>(Op);
4099 const SCEV *Op1 = getSCEV(U->getOperand(1));
4100 if (Opcode == Instruction::Sub)
4101 AddOps.push_back(getNegativeSCEV(Op1));
4103 AddOps.push_back(Op1);
4105 AddOps.push_back(getSCEV(U->getOperand(0)));
4106 return getAddExpr(AddOps);
4108 case Instruction::Mul: {
4109 // Don't transfer NSW/NUW for the same reason as AddExpr.
4110 SmallVector<const SCEV *, 4> MulOps;
4111 MulOps.push_back(getSCEV(U->getOperand(1)));
4112 for (Value *Op = U->getOperand(0);
4113 Op->getValueID() == Instruction::Mul + Value::InstructionVal;
4114 Op = U->getOperand(0)) {
4115 U = cast<Operator>(Op);
4116 MulOps.push_back(getSCEV(U->getOperand(1)));
4118 MulOps.push_back(getSCEV(U->getOperand(0)));
4119 return getMulExpr(MulOps);
4121 case Instruction::UDiv:
4122 return getUDivExpr(getSCEV(U->getOperand(0)),
4123 getSCEV(U->getOperand(1)));
4124 case Instruction::Sub:
4125 return getMinusSCEV(getSCEV(U->getOperand(0)),
4126 getSCEV(U->getOperand(1)));
4127 case Instruction::And:
4128 // For an expression like x&255 that merely masks off the high bits,
4129 // use zext(trunc(x)) as the SCEV expression.
4130 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
4131 if (CI->isNullValue())
4132 return getSCEV(U->getOperand(1));
4133 if (CI->isAllOnesValue())
4134 return getSCEV(U->getOperand(0));
4135 const APInt &A = CI->getValue();
4137 // Instcombine's ShrinkDemandedConstant may strip bits out of
4138 // constants, obscuring what would otherwise be a low-bits mask.
4139 // Use computeKnownBits to compute what ShrinkDemandedConstant
4140 // knew about to reconstruct a low-bits mask value.
4141 unsigned LZ = A.countLeadingZeros();
4142 unsigned TZ = A.countTrailingZeros();
4143 unsigned BitWidth = A.getBitWidth();
4144 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
4145 computeKnownBits(U->getOperand(0), KnownZero, KnownOne, DL,
4146 0, AT, nullptr, DT);
4148 APInt EffectiveMask =
4149 APInt::getLowBitsSet(BitWidth, BitWidth - LZ - TZ).shl(TZ);
4150 if ((LZ != 0 || TZ != 0) && !((~A & ~KnownZero) & EffectiveMask)) {
4151 const SCEV *MulCount = getConstant(
4152 ConstantInt::get(getContext(), APInt::getOneBitSet(BitWidth, TZ)));
4156 getUDivExactExpr(getSCEV(U->getOperand(0)), MulCount),
4157 IntegerType::get(getContext(), BitWidth - LZ - TZ)),
4164 case Instruction::Or:
4165 // If the RHS of the Or is a constant, we may have something like:
4166 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
4167 // optimizations will transparently handle this case.
4169 // In order for this transformation to be safe, the LHS must be of the
4170 // form X*(2^n) and the Or constant must be less than 2^n.
4171 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
4172 const SCEV *LHS = getSCEV(U->getOperand(0));
4173 const APInt &CIVal = CI->getValue();
4174 if (GetMinTrailingZeros(LHS) >=
4175 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
4176 // Build a plain add SCEV.
4177 const SCEV *S = getAddExpr(LHS, getSCEV(CI));
4178 // If the LHS of the add was an addrec and it has no-wrap flags,
4179 // transfer the no-wrap flags, since an or won't introduce a wrap.
4180 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
4181 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
4182 const_cast<SCEVAddRecExpr *>(NewAR)->setNoWrapFlags(
4183 OldAR->getNoWrapFlags());
4189 case Instruction::Xor:
4190 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
4191 // If the RHS of the xor is a signbit, then this is just an add.
4192 // Instcombine turns add of signbit into xor as a strength reduction step.
4193 if (CI->getValue().isSignBit())
4194 return getAddExpr(getSCEV(U->getOperand(0)),
4195 getSCEV(U->getOperand(1)));
4197 // If the RHS of xor is -1, then this is a not operation.
4198 if (CI->isAllOnesValue())
4199 return getNotSCEV(getSCEV(U->getOperand(0)));
4201 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
4202 // This is a variant of the check for xor with -1, and it handles
4203 // the case where instcombine has trimmed non-demanded bits out
4204 // of an xor with -1.
4205 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
4206 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
4207 if (BO->getOpcode() == Instruction::And &&
4208 LCI->getValue() == CI->getValue())
4209 if (const SCEVZeroExtendExpr *Z =
4210 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
4211 Type *UTy = U->getType();
4212 const SCEV *Z0 = Z->getOperand();
4213 Type *Z0Ty = Z0->getType();
4214 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
4216 // If C is a low-bits mask, the zero extend is serving to
4217 // mask off the high bits. Complement the operand and
4218 // re-apply the zext.
4219 if (APIntOps::isMask(Z0TySize, CI->getValue()))
4220 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
4222 // If C is a single bit, it may be in the sign-bit position
4223 // before the zero-extend. In this case, represent the xor
4224 // using an add, which is equivalent, and re-apply the zext.
4225 APInt Trunc = CI->getValue().trunc(Z0TySize);
4226 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
4228 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
4234 case Instruction::Shl:
4235 // Turn shift left of a constant amount into a multiply.
4236 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
4237 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
4239 // If the shift count is not less than the bitwidth, the result of
4240 // the shift is undefined. Don't try to analyze it, because the
4241 // resolution chosen here may differ from the resolution chosen in
4242 // other parts of the compiler.
4243 if (SA->getValue().uge(BitWidth))
4246 Constant *X = ConstantInt::get(getContext(),
4247 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
4248 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
4252 case Instruction::LShr:
4253 // Turn logical shift right of a constant into a unsigned divide.
4254 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
4255 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
4257 // If the shift count is not less than the bitwidth, the result of
4258 // the shift is undefined. Don't try to analyze it, because the
4259 // resolution chosen here may differ from the resolution chosen in
4260 // other parts of the compiler.
4261 if (SA->getValue().uge(BitWidth))
4264 Constant *X = ConstantInt::get(getContext(),
4265 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
4266 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
4270 case Instruction::AShr:
4271 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
4272 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
4273 if (Operator *L = dyn_cast<Operator>(U->getOperand(0)))
4274 if (L->getOpcode() == Instruction::Shl &&
4275 L->getOperand(1) == U->getOperand(1)) {
4276 uint64_t BitWidth = getTypeSizeInBits(U->getType());
4278 // If the shift count is not less than the bitwidth, the result of
4279 // the shift is undefined. Don't try to analyze it, because the
4280 // resolution chosen here may differ from the resolution chosen in
4281 // other parts of the compiler.
4282 if (CI->getValue().uge(BitWidth))
4285 uint64_t Amt = BitWidth - CI->getZExtValue();
4286 if (Amt == BitWidth)
4287 return getSCEV(L->getOperand(0)); // shift by zero --> noop
4289 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
4290 IntegerType::get(getContext(),
4296 case Instruction::Trunc:
4297 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
4299 case Instruction::ZExt:
4300 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
4302 case Instruction::SExt:
4303 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
4305 case Instruction::BitCast:
4306 // BitCasts are no-op casts so we just eliminate the cast.
4307 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
4308 return getSCEV(U->getOperand(0));
4311 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
4312 // lead to pointer expressions which cannot safely be expanded to GEPs,
4313 // because ScalarEvolution doesn't respect the GEP aliasing rules when
4314 // simplifying integer expressions.
4316 case Instruction::GetElementPtr:
4317 return createNodeForGEP(cast<GEPOperator>(U));
4319 case Instruction::PHI:
4320 return createNodeForPHI(cast<PHINode>(U));
4322 case Instruction::Select:
4323 // This could be a smax or umax that was lowered earlier.
4324 // Try to recover it.
4325 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
4326 Value *LHS = ICI->getOperand(0);
4327 Value *RHS = ICI->getOperand(1);
4328 switch (ICI->getPredicate()) {
4329 case ICmpInst::ICMP_SLT:
4330 case ICmpInst::ICMP_SLE:
4331 std::swap(LHS, RHS);
4333 case ICmpInst::ICMP_SGT:
4334 case ICmpInst::ICMP_SGE:
4335 // a >s b ? a+x : b+x -> smax(a, b)+x
4336 // a >s b ? b+x : a+x -> smin(a, b)+x
4337 if (LHS->getType() == U->getType()) {
4338 const SCEV *LS = getSCEV(LHS);
4339 const SCEV *RS = getSCEV(RHS);
4340 const SCEV *LA = getSCEV(U->getOperand(1));
4341 const SCEV *RA = getSCEV(U->getOperand(2));
4342 const SCEV *LDiff = getMinusSCEV(LA, LS);
4343 const SCEV *RDiff = getMinusSCEV(RA, RS);
4345 return getAddExpr(getSMaxExpr(LS, RS), LDiff);
4346 LDiff = getMinusSCEV(LA, RS);
4347 RDiff = getMinusSCEV(RA, LS);
4349 return getAddExpr(getSMinExpr(LS, RS), LDiff);
4352 case ICmpInst::ICMP_ULT:
4353 case ICmpInst::ICMP_ULE:
4354 std::swap(LHS, RHS);
4356 case ICmpInst::ICMP_UGT:
4357 case ICmpInst::ICMP_UGE:
4358 // a >u b ? a+x : b+x -> umax(a, b)+x
4359 // a >u b ? b+x : a+x -> umin(a, b)+x
4360 if (LHS->getType() == U->getType()) {
4361 const SCEV *LS = getSCEV(LHS);
4362 const SCEV *RS = getSCEV(RHS);
4363 const SCEV *LA = getSCEV(U->getOperand(1));
4364 const SCEV *RA = getSCEV(U->getOperand(2));
4365 const SCEV *LDiff = getMinusSCEV(LA, LS);
4366 const SCEV *RDiff = getMinusSCEV(RA, RS);
4368 return getAddExpr(getUMaxExpr(LS, RS), LDiff);
4369 LDiff = getMinusSCEV(LA, RS);
4370 RDiff = getMinusSCEV(RA, LS);
4372 return getAddExpr(getUMinExpr(LS, RS), LDiff);
4375 case ICmpInst::ICMP_NE:
4376 // n != 0 ? n+x : 1+x -> umax(n, 1)+x
4377 if (LHS->getType() == U->getType() &&
4378 isa<ConstantInt>(RHS) &&
4379 cast<ConstantInt>(RHS)->isZero()) {
4380 const SCEV *One = getConstant(LHS->getType(), 1);
4381 const SCEV *LS = getSCEV(LHS);
4382 const SCEV *LA = getSCEV(U->getOperand(1));
4383 const SCEV *RA = getSCEV(U->getOperand(2));
4384 const SCEV *LDiff = getMinusSCEV(LA, LS);
4385 const SCEV *RDiff = getMinusSCEV(RA, One);
4387 return getAddExpr(getUMaxExpr(One, LS), LDiff);
4390 case ICmpInst::ICMP_EQ:
4391 // n == 0 ? 1+x : n+x -> umax(n, 1)+x
4392 if (LHS->getType() == U->getType() &&
4393 isa<ConstantInt>(RHS) &&
4394 cast<ConstantInt>(RHS)->isZero()) {
4395 const SCEV *One = getConstant(LHS->getType(), 1);
4396 const SCEV *LS = getSCEV(LHS);
4397 const SCEV *LA = getSCEV(U->getOperand(1));
4398 const SCEV *RA = getSCEV(U->getOperand(2));
4399 const SCEV *LDiff = getMinusSCEV(LA, One);
4400 const SCEV *RDiff = getMinusSCEV(RA, LS);
4402 return getAddExpr(getUMaxExpr(One, LS), LDiff);
4410 default: // We cannot analyze this expression.
4414 return getUnknown(V);
4419 //===----------------------------------------------------------------------===//
4420 // Iteration Count Computation Code
4423 unsigned ScalarEvolution::getSmallConstantTripCount(Loop *L) {
4424 if (BasicBlock *ExitingBB = L->getExitingBlock())
4425 return getSmallConstantTripCount(L, ExitingBB);
4427 // No trip count information for multiple exits.
4431 /// getSmallConstantTripCount - Returns the maximum trip count of this loop as a
4432 /// normal unsigned value. Returns 0 if the trip count is unknown or not
4433 /// constant. Will also return 0 if the maximum trip count is very large (>=
4436 /// This "trip count" assumes that control exits via ExitingBlock. More
4437 /// precisely, it is the number of times that control may reach ExitingBlock
4438 /// before taking the branch. For loops with multiple exits, it may not be the
4439 /// number times that the loop header executes because the loop may exit
4440 /// prematurely via another branch.
4441 unsigned ScalarEvolution::getSmallConstantTripCount(Loop *L,
4442 BasicBlock *ExitingBlock) {
4443 assert(ExitingBlock && "Must pass a non-null exiting block!");
4444 assert(L->isLoopExiting(ExitingBlock) &&
4445 "Exiting block must actually branch out of the loop!");
4446 const SCEVConstant *ExitCount =
4447 dyn_cast<SCEVConstant>(getExitCount(L, ExitingBlock));
4451 ConstantInt *ExitConst = ExitCount->getValue();
4453 // Guard against huge trip counts.
4454 if (ExitConst->getValue().getActiveBits() > 32)
4457 // In case of integer overflow, this returns 0, which is correct.
4458 return ((unsigned)ExitConst->getZExtValue()) + 1;
4461 unsigned ScalarEvolution::getSmallConstantTripMultiple(Loop *L) {
4462 if (BasicBlock *ExitingBB = L->getExitingBlock())
4463 return getSmallConstantTripMultiple(L, ExitingBB);
4465 // No trip multiple information for multiple exits.
4469 /// getSmallConstantTripMultiple - Returns the largest constant divisor of the
4470 /// trip count of this loop as a normal unsigned value, if possible. This
4471 /// means that the actual trip count is always a multiple of the returned
4472 /// value (don't forget the trip count could very well be zero as well!).
4474 /// Returns 1 if the trip count is unknown or not guaranteed to be the
4475 /// multiple of a constant (which is also the case if the trip count is simply
4476 /// constant, use getSmallConstantTripCount for that case), Will also return 1
4477 /// if the trip count is very large (>= 2^32).
4479 /// As explained in the comments for getSmallConstantTripCount, this assumes
4480 /// that control exits the loop via ExitingBlock.
4482 ScalarEvolution::getSmallConstantTripMultiple(Loop *L,
4483 BasicBlock *ExitingBlock) {
4484 assert(ExitingBlock && "Must pass a non-null exiting block!");
4485 assert(L->isLoopExiting(ExitingBlock) &&
4486 "Exiting block must actually branch out of the loop!");
4487 const SCEV *ExitCount = getExitCount(L, ExitingBlock);
4488 if (ExitCount == getCouldNotCompute())
4491 // Get the trip count from the BE count by adding 1.
4492 const SCEV *TCMul = getAddExpr(ExitCount,
4493 getConstant(ExitCount->getType(), 1));
4494 // FIXME: SCEV distributes multiplication as V1*C1 + V2*C1. We could attempt
4495 // to factor simple cases.
4496 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(TCMul))
4497 TCMul = Mul->getOperand(0);
4499 const SCEVConstant *MulC = dyn_cast<SCEVConstant>(TCMul);
4503 ConstantInt *Result = MulC->getValue();
4505 // Guard against huge trip counts (this requires checking
4506 // for zero to handle the case where the trip count == -1 and the
4508 if (!Result || Result->getValue().getActiveBits() > 32 ||
4509 Result->getValue().getActiveBits() == 0)
4512 return (unsigned)Result->getZExtValue();
4515 // getExitCount - Get the expression for the number of loop iterations for which
4516 // this loop is guaranteed not to exit via ExitingBlock. Otherwise return
4517 // SCEVCouldNotCompute.
4518 const SCEV *ScalarEvolution::getExitCount(Loop *L, BasicBlock *ExitingBlock) {
4519 return getBackedgeTakenInfo(L).getExact(ExitingBlock, this);
4522 /// getBackedgeTakenCount - If the specified loop has a predictable
4523 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
4524 /// object. The backedge-taken count is the number of times the loop header
4525 /// will be branched to from within the loop. This is one less than the
4526 /// trip count of the loop, since it doesn't count the first iteration,
4527 /// when the header is branched to from outside the loop.
4529 /// Note that it is not valid to call this method on a loop without a
4530 /// loop-invariant backedge-taken count (see
4531 /// hasLoopInvariantBackedgeTakenCount).
4533 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
4534 return getBackedgeTakenInfo(L).getExact(this);
4537 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
4538 /// return the least SCEV value that is known never to be less than the
4539 /// actual backedge taken count.
4540 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
4541 return getBackedgeTakenInfo(L).getMax(this);
4544 /// PushLoopPHIs - Push PHI nodes in the header of the given loop
4545 /// onto the given Worklist.
4547 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
4548 BasicBlock *Header = L->getHeader();
4550 // Push all Loop-header PHIs onto the Worklist stack.
4551 for (BasicBlock::iterator I = Header->begin();
4552 PHINode *PN = dyn_cast<PHINode>(I); ++I)
4553 Worklist.push_back(PN);
4556 const ScalarEvolution::BackedgeTakenInfo &
4557 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
4558 // Initially insert an invalid entry for this loop. If the insertion
4559 // succeeds, proceed to actually compute a backedge-taken count and
4560 // update the value. The temporary CouldNotCompute value tells SCEV
4561 // code elsewhere that it shouldn't attempt to request a new
4562 // backedge-taken count, which could result in infinite recursion.
4563 std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
4564 BackedgeTakenCounts.insert(std::make_pair(L, BackedgeTakenInfo()));
4566 return Pair.first->second;
4568 // ComputeBackedgeTakenCount may allocate memory for its result. Inserting it
4569 // into the BackedgeTakenCounts map transfers ownership. Otherwise, the result
4570 // must be cleared in this scope.
4571 BackedgeTakenInfo Result = ComputeBackedgeTakenCount(L);
4573 if (Result.getExact(this) != getCouldNotCompute()) {
4574 assert(isLoopInvariant(Result.getExact(this), L) &&
4575 isLoopInvariant(Result.getMax(this), L) &&
4576 "Computed backedge-taken count isn't loop invariant for loop!");
4577 ++NumTripCountsComputed;
4579 else if (Result.getMax(this) == getCouldNotCompute() &&
4580 isa<PHINode>(L->getHeader()->begin())) {
4581 // Only count loops that have phi nodes as not being computable.
4582 ++NumTripCountsNotComputed;
4585 // Now that we know more about the trip count for this loop, forget any
4586 // existing SCEV values for PHI nodes in this loop since they are only
4587 // conservative estimates made without the benefit of trip count
4588 // information. This is similar to the code in forgetLoop, except that
4589 // it handles SCEVUnknown PHI nodes specially.
4590 if (Result.hasAnyInfo()) {
4591 SmallVector<Instruction *, 16> Worklist;
4592 PushLoopPHIs(L, Worklist);
4594 SmallPtrSet<Instruction *, 8> Visited;
4595 while (!Worklist.empty()) {
4596 Instruction *I = Worklist.pop_back_val();
4597 if (!Visited.insert(I).second)
4600 ValueExprMapType::iterator It =
4601 ValueExprMap.find_as(static_cast<Value *>(I));
4602 if (It != ValueExprMap.end()) {
4603 const SCEV *Old = It->second;
4605 // SCEVUnknown for a PHI either means that it has an unrecognized
4606 // structure, or it's a PHI that's in the progress of being computed
4607 // by createNodeForPHI. In the former case, additional loop trip
4608 // count information isn't going to change anything. In the later
4609 // case, createNodeForPHI will perform the necessary updates on its
4610 // own when it gets to that point.
4611 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) {
4612 forgetMemoizedResults(Old);
4613 ValueExprMap.erase(It);
4615 if (PHINode *PN = dyn_cast<PHINode>(I))
4616 ConstantEvolutionLoopExitValue.erase(PN);
4619 PushDefUseChildren(I, Worklist);
4623 // Re-lookup the insert position, since the call to
4624 // ComputeBackedgeTakenCount above could result in a
4625 // recusive call to getBackedgeTakenInfo (on a different
4626 // loop), which would invalidate the iterator computed
4628 return BackedgeTakenCounts.find(L)->second = Result;
4631 /// forgetLoop - This method should be called by the client when it has
4632 /// changed a loop in a way that may effect ScalarEvolution's ability to
4633 /// compute a trip count, or if the loop is deleted.
4634 void ScalarEvolution::forgetLoop(const Loop *L) {
4635 // Drop any stored trip count value.
4636 DenseMap<const Loop*, BackedgeTakenInfo>::iterator BTCPos =
4637 BackedgeTakenCounts.find(L);
4638 if (BTCPos != BackedgeTakenCounts.end()) {
4639 BTCPos->second.clear();
4640 BackedgeTakenCounts.erase(BTCPos);
4643 // Drop information about expressions based on loop-header PHIs.
4644 SmallVector<Instruction *, 16> Worklist;
4645 PushLoopPHIs(L, Worklist);
4647 SmallPtrSet<Instruction *, 8> Visited;
4648 while (!Worklist.empty()) {
4649 Instruction *I = Worklist.pop_back_val();
4650 if (!Visited.insert(I).second)
4653 ValueExprMapType::iterator It =
4654 ValueExprMap.find_as(static_cast<Value *>(I));
4655 if (It != ValueExprMap.end()) {
4656 forgetMemoizedResults(It->second);
4657 ValueExprMap.erase(It);
4658 if (PHINode *PN = dyn_cast<PHINode>(I))
4659 ConstantEvolutionLoopExitValue.erase(PN);
4662 PushDefUseChildren(I, Worklist);
4665 // Forget all contained loops too, to avoid dangling entries in the
4666 // ValuesAtScopes map.
4667 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
4671 /// forgetValue - This method should be called by the client when it has
4672 /// changed a value in a way that may effect its value, or which may
4673 /// disconnect it from a def-use chain linking it to a loop.
4674 void ScalarEvolution::forgetValue(Value *V) {
4675 Instruction *I = dyn_cast<Instruction>(V);
4678 // Drop information about expressions based on loop-header PHIs.
4679 SmallVector<Instruction *, 16> Worklist;
4680 Worklist.push_back(I);
4682 SmallPtrSet<Instruction *, 8> Visited;
4683 while (!Worklist.empty()) {
4684 I = Worklist.pop_back_val();
4685 if (!Visited.insert(I).second)
4688 ValueExprMapType::iterator It =
4689 ValueExprMap.find_as(static_cast<Value *>(I));
4690 if (It != ValueExprMap.end()) {
4691 forgetMemoizedResults(It->second);
4692 ValueExprMap.erase(It);
4693 if (PHINode *PN = dyn_cast<PHINode>(I))
4694 ConstantEvolutionLoopExitValue.erase(PN);
4697 PushDefUseChildren(I, Worklist);
4701 /// getExact - Get the exact loop backedge taken count considering all loop
4702 /// exits. A computable result can only be return for loops with a single exit.
4703 /// Returning the minimum taken count among all exits is incorrect because one
4704 /// of the loop's exit limit's may have been skipped. HowFarToZero assumes that
4705 /// the limit of each loop test is never skipped. This is a valid assumption as
4706 /// long as the loop exits via that test. For precise results, it is the
4707 /// caller's responsibility to specify the relevant loop exit using
4708 /// getExact(ExitingBlock, SE).
4710 ScalarEvolution::BackedgeTakenInfo::getExact(ScalarEvolution *SE) const {
4711 // If any exits were not computable, the loop is not computable.
4712 if (!ExitNotTaken.isCompleteList()) return SE->getCouldNotCompute();
4714 // We need exactly one computable exit.
4715 if (!ExitNotTaken.ExitingBlock) return SE->getCouldNotCompute();
4716 assert(ExitNotTaken.ExactNotTaken && "uninitialized not-taken info");
4718 const SCEV *BECount = nullptr;
4719 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4720 ENT != nullptr; ENT = ENT->getNextExit()) {
4722 assert(ENT->ExactNotTaken != SE->getCouldNotCompute() && "bad exit SCEV");
4725 BECount = ENT->ExactNotTaken;
4726 else if (BECount != ENT->ExactNotTaken)
4727 return SE->getCouldNotCompute();
4729 assert(BECount && "Invalid not taken count for loop exit");
4733 /// getExact - Get the exact not taken count for this loop exit.
4735 ScalarEvolution::BackedgeTakenInfo::getExact(BasicBlock *ExitingBlock,
4736 ScalarEvolution *SE) const {
4737 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4738 ENT != nullptr; ENT = ENT->getNextExit()) {
4740 if (ENT->ExitingBlock == ExitingBlock)
4741 return ENT->ExactNotTaken;
4743 return SE->getCouldNotCompute();
4746 /// getMax - Get the max backedge taken count for the loop.
4748 ScalarEvolution::BackedgeTakenInfo::getMax(ScalarEvolution *SE) const {
4749 return Max ? Max : SE->getCouldNotCompute();
4752 bool ScalarEvolution::BackedgeTakenInfo::hasOperand(const SCEV *S,
4753 ScalarEvolution *SE) const {
4754 if (Max && Max != SE->getCouldNotCompute() && SE->hasOperand(Max, S))
4757 if (!ExitNotTaken.ExitingBlock)
4760 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4761 ENT != nullptr; ENT = ENT->getNextExit()) {
4763 if (ENT->ExactNotTaken != SE->getCouldNotCompute()
4764 && SE->hasOperand(ENT->ExactNotTaken, S)) {
4771 /// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each
4772 /// computable exit into a persistent ExitNotTakenInfo array.
4773 ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo(
4774 SmallVectorImpl< std::pair<BasicBlock *, const SCEV *> > &ExitCounts,
4775 bool Complete, const SCEV *MaxCount) : Max(MaxCount) {
4778 ExitNotTaken.setIncomplete();
4780 unsigned NumExits = ExitCounts.size();
4781 if (NumExits == 0) return;
4783 ExitNotTaken.ExitingBlock = ExitCounts[0].first;
4784 ExitNotTaken.ExactNotTaken = ExitCounts[0].second;
4785 if (NumExits == 1) return;
4787 // Handle the rare case of multiple computable exits.
4788 ExitNotTakenInfo *ENT = new ExitNotTakenInfo[NumExits-1];
4790 ExitNotTakenInfo *PrevENT = &ExitNotTaken;
4791 for (unsigned i = 1; i < NumExits; ++i, PrevENT = ENT, ++ENT) {
4792 PrevENT->setNextExit(ENT);
4793 ENT->ExitingBlock = ExitCounts[i].first;
4794 ENT->ExactNotTaken = ExitCounts[i].second;
4798 /// clear - Invalidate this result and free the ExitNotTakenInfo array.
4799 void ScalarEvolution::BackedgeTakenInfo::clear() {
4800 ExitNotTaken.ExitingBlock = nullptr;
4801 ExitNotTaken.ExactNotTaken = nullptr;
4802 delete[] ExitNotTaken.getNextExit();
4805 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
4806 /// of the specified loop will execute.
4807 ScalarEvolution::BackedgeTakenInfo
4808 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
4809 SmallVector<BasicBlock *, 8> ExitingBlocks;
4810 L->getExitingBlocks(ExitingBlocks);
4812 SmallVector<std::pair<BasicBlock *, const SCEV *>, 4> ExitCounts;
4813 bool CouldComputeBECount = true;
4814 BasicBlock *Latch = L->getLoopLatch(); // may be NULL.
4815 const SCEV *MustExitMaxBECount = nullptr;
4816 const SCEV *MayExitMaxBECount = nullptr;
4818 // Compute the ExitLimit for each loop exit. Use this to populate ExitCounts
4819 // and compute maxBECount.
4820 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
4821 BasicBlock *ExitBB = ExitingBlocks[i];
4822 ExitLimit EL = ComputeExitLimit(L, ExitBB);
4824 // 1. For each exit that can be computed, add an entry to ExitCounts.
4825 // CouldComputeBECount is true only if all exits can be computed.
4826 if (EL.Exact == getCouldNotCompute())
4827 // We couldn't compute an exact value for this exit, so
4828 // we won't be able to compute an exact value for the loop.
4829 CouldComputeBECount = false;
4831 ExitCounts.push_back(std::make_pair(ExitBB, EL.Exact));
4833 // 2. Derive the loop's MaxBECount from each exit's max number of
4834 // non-exiting iterations. Partition the loop exits into two kinds:
4835 // LoopMustExits and LoopMayExits.
4837 // If the exit dominates the loop latch, it is a LoopMustExit otherwise it
4838 // is a LoopMayExit. If any computable LoopMustExit is found, then
4839 // MaxBECount is the minimum EL.Max of computable LoopMustExits. Otherwise,
4840 // MaxBECount is conservatively the maximum EL.Max, where CouldNotCompute is
4841 // considered greater than any computable EL.Max.
4842 if (EL.Max != getCouldNotCompute() && Latch &&
4843 DT->dominates(ExitBB, Latch)) {
4844 if (!MustExitMaxBECount)
4845 MustExitMaxBECount = EL.Max;
4847 MustExitMaxBECount =
4848 getUMinFromMismatchedTypes(MustExitMaxBECount, EL.Max);
4850 } else if (MayExitMaxBECount != getCouldNotCompute()) {
4851 if (!MayExitMaxBECount || EL.Max == getCouldNotCompute())
4852 MayExitMaxBECount = EL.Max;
4855 getUMaxFromMismatchedTypes(MayExitMaxBECount, EL.Max);
4859 const SCEV *MaxBECount = MustExitMaxBECount ? MustExitMaxBECount :
4860 (MayExitMaxBECount ? MayExitMaxBECount : getCouldNotCompute());
4861 return BackedgeTakenInfo(ExitCounts, CouldComputeBECount, MaxBECount);
4864 /// ComputeExitLimit - Compute the number of times the backedge of the specified
4865 /// loop will execute if it exits via the specified block.
4866 ScalarEvolution::ExitLimit
4867 ScalarEvolution::ComputeExitLimit(const Loop *L, BasicBlock *ExitingBlock) {
4869 // Okay, we've chosen an exiting block. See what condition causes us to
4870 // exit at this block and remember the exit block and whether all other targets
4871 // lead to the loop header.
4872 bool MustExecuteLoopHeader = true;
4873 BasicBlock *Exit = nullptr;
4874 for (succ_iterator SI = succ_begin(ExitingBlock), SE = succ_end(ExitingBlock);
4876 if (!L->contains(*SI)) {
4877 if (Exit) // Multiple exit successors.
4878 return getCouldNotCompute();
4880 } else if (*SI != L->getHeader()) {
4881 MustExecuteLoopHeader = false;
4884 // At this point, we know we have a conditional branch that determines whether
4885 // the loop is exited. However, we don't know if the branch is executed each
4886 // time through the loop. If not, then the execution count of the branch will
4887 // not be equal to the trip count of the loop.
4889 // Currently we check for this by checking to see if the Exit branch goes to
4890 // the loop header. If so, we know it will always execute the same number of
4891 // times as the loop. We also handle the case where the exit block *is* the
4892 // loop header. This is common for un-rotated loops.
4894 // If both of those tests fail, walk up the unique predecessor chain to the
4895 // header, stopping if there is an edge that doesn't exit the loop. If the
4896 // header is reached, the execution count of the branch will be equal to the
4897 // trip count of the loop.
4899 // More extensive analysis could be done to handle more cases here.
4901 if (!MustExecuteLoopHeader && ExitingBlock != L->getHeader()) {
4902 // The simple checks failed, try climbing the unique predecessor chain
4903 // up to the header.
4905 for (BasicBlock *BB = ExitingBlock; BB; ) {
4906 BasicBlock *Pred = BB->getUniquePredecessor();
4908 return getCouldNotCompute();
4909 TerminatorInst *PredTerm = Pred->getTerminator();
4910 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) {
4911 BasicBlock *PredSucc = PredTerm->getSuccessor(i);
4914 // If the predecessor has a successor that isn't BB and isn't
4915 // outside the loop, assume the worst.
4916 if (L->contains(PredSucc))
4917 return getCouldNotCompute();
4919 if (Pred == L->getHeader()) {
4926 return getCouldNotCompute();
4929 bool IsOnlyExit = (L->getExitingBlock() != nullptr);
4930 TerminatorInst *Term = ExitingBlock->getTerminator();
4931 if (BranchInst *BI = dyn_cast<BranchInst>(Term)) {
4932 assert(BI->isConditional() && "If unconditional, it can't be in loop!");
4933 // Proceed to the next level to examine the exit condition expression.
4934 return ComputeExitLimitFromCond(L, BI->getCondition(), BI->getSuccessor(0),
4935 BI->getSuccessor(1),
4936 /*ControlsExit=*/IsOnlyExit);
4939 if (SwitchInst *SI = dyn_cast<SwitchInst>(Term))
4940 return ComputeExitLimitFromSingleExitSwitch(L, SI, Exit,
4941 /*ControlsExit=*/IsOnlyExit);
4943 return getCouldNotCompute();
4946 /// ComputeExitLimitFromCond - Compute the number of times the
4947 /// backedge of the specified loop will execute if its exit condition
4948 /// were a conditional branch of ExitCond, TBB, and FBB.
4950 /// @param ControlsExit is true if ExitCond directly controls the exit
4951 /// branch. In this case, we can assume that the loop exits only if the
4952 /// condition is true and can infer that failing to meet the condition prior to
4953 /// integer wraparound results in undefined behavior.
4954 ScalarEvolution::ExitLimit
4955 ScalarEvolution::ComputeExitLimitFromCond(const Loop *L,
4959 bool ControlsExit) {
4960 // Check if the controlling expression for this loop is an And or Or.
4961 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
4962 if (BO->getOpcode() == Instruction::And) {
4963 // Recurse on the operands of the and.
4964 bool EitherMayExit = L->contains(TBB);
4965 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
4966 ControlsExit && !EitherMayExit);
4967 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
4968 ControlsExit && !EitherMayExit);
4969 const SCEV *BECount = getCouldNotCompute();
4970 const SCEV *MaxBECount = getCouldNotCompute();
4971 if (EitherMayExit) {
4972 // Both conditions must be true for the loop to continue executing.
4973 // Choose the less conservative count.
4974 if (EL0.Exact == getCouldNotCompute() ||
4975 EL1.Exact == getCouldNotCompute())
4976 BECount = getCouldNotCompute();
4978 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
4979 if (EL0.Max == getCouldNotCompute())
4980 MaxBECount = EL1.Max;
4981 else if (EL1.Max == getCouldNotCompute())
4982 MaxBECount = EL0.Max;
4984 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
4986 // Both conditions must be true at the same time for the loop to exit.
4987 // For now, be conservative.
4988 assert(L->contains(FBB) && "Loop block has no successor in loop!");
4989 if (EL0.Max == EL1.Max)
4990 MaxBECount = EL0.Max;
4991 if (EL0.Exact == EL1.Exact)
4992 BECount = EL0.Exact;
4995 return ExitLimit(BECount, MaxBECount);
4997 if (BO->getOpcode() == Instruction::Or) {
4998 // Recurse on the operands of the or.
4999 bool EitherMayExit = L->contains(FBB);
5000 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
5001 ControlsExit && !EitherMayExit);
5002 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
5003 ControlsExit && !EitherMayExit);
5004 const SCEV *BECount = getCouldNotCompute();
5005 const SCEV *MaxBECount = getCouldNotCompute();
5006 if (EitherMayExit) {
5007 // Both conditions must be false for the loop to continue executing.
5008 // Choose the less conservative count.
5009 if (EL0.Exact == getCouldNotCompute() ||
5010 EL1.Exact == getCouldNotCompute())
5011 BECount = getCouldNotCompute();
5013 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
5014 if (EL0.Max == getCouldNotCompute())
5015 MaxBECount = EL1.Max;
5016 else if (EL1.Max == getCouldNotCompute())
5017 MaxBECount = EL0.Max;
5019 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
5021 // Both conditions must be false at the same time for the loop to exit.
5022 // For now, be conservative.
5023 assert(L->contains(TBB) && "Loop block has no successor in loop!");
5024 if (EL0.Max == EL1.Max)
5025 MaxBECount = EL0.Max;
5026 if (EL0.Exact == EL1.Exact)
5027 BECount = EL0.Exact;
5030 return ExitLimit(BECount, MaxBECount);
5034 // With an icmp, it may be feasible to compute an exact backedge-taken count.
5035 // Proceed to the next level to examine the icmp.
5036 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
5037 return ComputeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB, ControlsExit);
5039 // Check for a constant condition. These are normally stripped out by
5040 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
5041 // preserve the CFG and is temporarily leaving constant conditions
5043 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
5044 if (L->contains(FBB) == !CI->getZExtValue())
5045 // The backedge is always taken.
5046 return getCouldNotCompute();
5048 // The backedge is never taken.
5049 return getConstant(CI->getType(), 0);
5052 // If it's not an integer or pointer comparison then compute it the hard way.
5053 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
5056 /// ComputeExitLimitFromICmp - Compute the number of times the
5057 /// backedge of the specified loop will execute if its exit condition
5058 /// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB.
5059 ScalarEvolution::ExitLimit
5060 ScalarEvolution::ComputeExitLimitFromICmp(const Loop *L,
5064 bool ControlsExit) {
5066 // If the condition was exit on true, convert the condition to exit on false
5067 ICmpInst::Predicate Cond;
5068 if (!L->contains(FBB))
5069 Cond = ExitCond->getPredicate();
5071 Cond = ExitCond->getInversePredicate();
5073 // Handle common loops like: for (X = "string"; *X; ++X)
5074 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
5075 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
5077 ComputeLoadConstantCompareExitLimit(LI, RHS, L, Cond);
5078 if (ItCnt.hasAnyInfo())
5082 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
5083 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
5085 // Try to evaluate any dependencies out of the loop.
5086 LHS = getSCEVAtScope(LHS, L);
5087 RHS = getSCEVAtScope(RHS, L);
5089 // At this point, we would like to compute how many iterations of the
5090 // loop the predicate will return true for these inputs.
5091 if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) {
5092 // If there is a loop-invariant, force it into the RHS.
5093 std::swap(LHS, RHS);
5094 Cond = ICmpInst::getSwappedPredicate(Cond);
5097 // Simplify the operands before analyzing them.
5098 (void)SimplifyICmpOperands(Cond, LHS, RHS);
5100 // If we have a comparison of a chrec against a constant, try to use value
5101 // ranges to answer this query.
5102 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
5103 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
5104 if (AddRec->getLoop() == L) {
5105 // Form the constant range.
5106 ConstantRange CompRange(
5107 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
5109 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
5110 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
5114 case ICmpInst::ICMP_NE: { // while (X != Y)
5115 // Convert to: while (X-Y != 0)
5116 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit);
5117 if (EL.hasAnyInfo()) return EL;
5120 case ICmpInst::ICMP_EQ: { // while (X == Y)
5121 // Convert to: while (X-Y == 0)
5122 ExitLimit EL = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
5123 if (EL.hasAnyInfo()) return EL;
5126 case ICmpInst::ICMP_SLT:
5127 case ICmpInst::ICMP_ULT: { // while (X < Y)
5128 bool IsSigned = Cond == ICmpInst::ICMP_SLT;
5129 ExitLimit EL = HowManyLessThans(LHS, RHS, L, IsSigned, ControlsExit);
5130 if (EL.hasAnyInfo()) return EL;
5133 case ICmpInst::ICMP_SGT:
5134 case ICmpInst::ICMP_UGT: { // while (X > Y)
5135 bool IsSigned = Cond == ICmpInst::ICMP_SGT;
5136 ExitLimit EL = HowManyGreaterThans(LHS, RHS, L, IsSigned, ControlsExit);
5137 if (EL.hasAnyInfo()) return EL;
5142 dbgs() << "ComputeBackedgeTakenCount ";
5143 if (ExitCond->getOperand(0)->getType()->isUnsigned())
5144 dbgs() << "[unsigned] ";
5145 dbgs() << *LHS << " "
5146 << Instruction::getOpcodeName(Instruction::ICmp)
5147 << " " << *RHS << "\n";
5151 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
5154 ScalarEvolution::ExitLimit
5155 ScalarEvolution::ComputeExitLimitFromSingleExitSwitch(const Loop *L,
5157 BasicBlock *ExitingBlock,
5158 bool ControlsExit) {
5159 assert(!L->contains(ExitingBlock) && "Not an exiting block!");
5161 // Give up if the exit is the default dest of a switch.
5162 if (Switch->getDefaultDest() == ExitingBlock)
5163 return getCouldNotCompute();
5165 assert(L->contains(Switch->getDefaultDest()) &&
5166 "Default case must not exit the loop!");
5167 const SCEV *LHS = getSCEVAtScope(Switch->getCondition(), L);
5168 const SCEV *RHS = getConstant(Switch->findCaseDest(ExitingBlock));
5170 // while (X != Y) --> while (X-Y != 0)
5171 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit);
5172 if (EL.hasAnyInfo())
5175 return getCouldNotCompute();
5178 static ConstantInt *
5179 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
5180 ScalarEvolution &SE) {
5181 const SCEV *InVal = SE.getConstant(C);
5182 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
5183 assert(isa<SCEVConstant>(Val) &&
5184 "Evaluation of SCEV at constant didn't fold correctly?");
5185 return cast<SCEVConstant>(Val)->getValue();
5188 /// ComputeLoadConstantCompareExitLimit - Given an exit condition of
5189 /// 'icmp op load X, cst', try to see if we can compute the backedge
5190 /// execution count.
5191 ScalarEvolution::ExitLimit
5192 ScalarEvolution::ComputeLoadConstantCompareExitLimit(
5196 ICmpInst::Predicate predicate) {
5198 if (LI->isVolatile()) return getCouldNotCompute();
5200 // Check to see if the loaded pointer is a getelementptr of a global.
5201 // TODO: Use SCEV instead of manually grubbing with GEPs.
5202 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
5203 if (!GEP) return getCouldNotCompute();
5205 // Make sure that it is really a constant global we are gepping, with an
5206 // initializer, and make sure the first IDX is really 0.
5207 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
5208 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
5209 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
5210 !cast<Constant>(GEP->getOperand(1))->isNullValue())
5211 return getCouldNotCompute();
5213 // Okay, we allow one non-constant index into the GEP instruction.
5214 Value *VarIdx = nullptr;
5215 std::vector<Constant*> Indexes;
5216 unsigned VarIdxNum = 0;
5217 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
5218 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
5219 Indexes.push_back(CI);
5220 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
5221 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
5222 VarIdx = GEP->getOperand(i);
5224 Indexes.push_back(nullptr);
5227 // Loop-invariant loads may be a byproduct of loop optimization. Skip them.
5229 return getCouldNotCompute();
5231 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
5232 // Check to see if X is a loop variant variable value now.
5233 const SCEV *Idx = getSCEV(VarIdx);
5234 Idx = getSCEVAtScope(Idx, L);
5236 // We can only recognize very limited forms of loop index expressions, in
5237 // particular, only affine AddRec's like {C1,+,C2}.
5238 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
5239 if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) ||
5240 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
5241 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
5242 return getCouldNotCompute();
5244 unsigned MaxSteps = MaxBruteForceIterations;
5245 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
5246 ConstantInt *ItCst = ConstantInt::get(
5247 cast<IntegerType>(IdxExpr->getType()), IterationNum);
5248 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
5250 // Form the GEP offset.
5251 Indexes[VarIdxNum] = Val;
5253 Constant *Result = ConstantFoldLoadThroughGEPIndices(GV->getInitializer(),
5255 if (!Result) break; // Cannot compute!
5257 // Evaluate the condition for this iteration.
5258 Result = ConstantExpr::getICmp(predicate, Result, RHS);
5259 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
5260 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
5262 dbgs() << "\n***\n*** Computed loop count " << *ItCst
5263 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
5266 ++NumArrayLenItCounts;
5267 return getConstant(ItCst); // Found terminating iteration!
5270 return getCouldNotCompute();
5274 /// CanConstantFold - Return true if we can constant fold an instruction of the
5275 /// specified type, assuming that all operands were constants.
5276 static bool CanConstantFold(const Instruction *I) {
5277 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
5278 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I) ||
5282 if (const CallInst *CI = dyn_cast<CallInst>(I))
5283 if (const Function *F = CI->getCalledFunction())
5284 return canConstantFoldCallTo(F);
5288 /// Determine whether this instruction can constant evolve within this loop
5289 /// assuming its operands can all constant evolve.
5290 static bool canConstantEvolve(Instruction *I, const Loop *L) {
5291 // An instruction outside of the loop can't be derived from a loop PHI.
5292 if (!L->contains(I)) return false;
5294 if (isa<PHINode>(I)) {
5295 if (L->getHeader() == I->getParent())
5298 // We don't currently keep track of the control flow needed to evaluate
5299 // PHIs, so we cannot handle PHIs inside of loops.
5303 // If we won't be able to constant fold this expression even if the operands
5304 // are constants, bail early.
5305 return CanConstantFold(I);
5308 /// getConstantEvolvingPHIOperands - Implement getConstantEvolvingPHI by
5309 /// recursing through each instruction operand until reaching a loop header phi.
5311 getConstantEvolvingPHIOperands(Instruction *UseInst, const Loop *L,
5312 DenseMap<Instruction *, PHINode *> &PHIMap) {
5314 // Otherwise, we can evaluate this instruction if all of its operands are
5315 // constant or derived from a PHI node themselves.
5316 PHINode *PHI = nullptr;
5317 for (Instruction::op_iterator OpI = UseInst->op_begin(),
5318 OpE = UseInst->op_end(); OpI != OpE; ++OpI) {
5320 if (isa<Constant>(*OpI)) continue;
5322 Instruction *OpInst = dyn_cast<Instruction>(*OpI);
5323 if (!OpInst || !canConstantEvolve(OpInst, L)) return nullptr;
5325 PHINode *P = dyn_cast<PHINode>(OpInst);
5327 // If this operand is already visited, reuse the prior result.
5328 // We may have P != PHI if this is the deepest point at which the
5329 // inconsistent paths meet.
5330 P = PHIMap.lookup(OpInst);
5332 // Recurse and memoize the results, whether a phi is found or not.
5333 // This recursive call invalidates pointers into PHIMap.
5334 P = getConstantEvolvingPHIOperands(OpInst, L, PHIMap);
5338 return nullptr; // Not evolving from PHI
5339 if (PHI && PHI != P)
5340 return nullptr; // Evolving from multiple different PHIs.
5343 // This is a expression evolving from a constant PHI!
5347 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
5348 /// in the loop that V is derived from. We allow arbitrary operations along the
5349 /// way, but the operands of an operation must either be constants or a value
5350 /// derived from a constant PHI. If this expression does not fit with these
5351 /// constraints, return null.
5352 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
5353 Instruction *I = dyn_cast<Instruction>(V);
5354 if (!I || !canConstantEvolve(I, L)) return nullptr;
5356 if (PHINode *PN = dyn_cast<PHINode>(I)) {
5360 // Record non-constant instructions contained by the loop.
5361 DenseMap<Instruction *, PHINode *> PHIMap;
5362 return getConstantEvolvingPHIOperands(I, L, PHIMap);
5365 /// EvaluateExpression - Given an expression that passes the
5366 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
5367 /// in the loop has the value PHIVal. If we can't fold this expression for some
5368 /// reason, return null.
5369 static Constant *EvaluateExpression(Value *V, const Loop *L,
5370 DenseMap<Instruction *, Constant *> &Vals,
5371 const DataLayout *DL,
5372 const TargetLibraryInfo *TLI) {
5373 // Convenient constant check, but redundant for recursive calls.
5374 if (Constant *C = dyn_cast<Constant>(V)) return C;
5375 Instruction *I = dyn_cast<Instruction>(V);
5376 if (!I) return nullptr;
5378 if (Constant *C = Vals.lookup(I)) return C;
5380 // An instruction inside the loop depends on a value outside the loop that we
5381 // weren't given a mapping for, or a value such as a call inside the loop.
5382 if (!canConstantEvolve(I, L)) return nullptr;
5384 // An unmapped PHI can be due to a branch or another loop inside this loop,
5385 // or due to this not being the initial iteration through a loop where we
5386 // couldn't compute the evolution of this particular PHI last time.
5387 if (isa<PHINode>(I)) return nullptr;
5389 std::vector<Constant*> Operands(I->getNumOperands());
5391 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
5392 Instruction *Operand = dyn_cast<Instruction>(I->getOperand(i));
5394 Operands[i] = dyn_cast<Constant>(I->getOperand(i));
5395 if (!Operands[i]) return nullptr;
5398 Constant *C = EvaluateExpression(Operand, L, Vals, DL, TLI);
5400 if (!C) return nullptr;
5404 if (CmpInst *CI = dyn_cast<CmpInst>(I))
5405 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
5406 Operands[1], DL, TLI);
5407 if (LoadInst *LI = dyn_cast<LoadInst>(I)) {
5408 if (!LI->isVolatile())
5409 return ConstantFoldLoadFromConstPtr(Operands[0], DL);
5411 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), Operands, DL,
5415 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
5416 /// in the header of its containing loop, we know the loop executes a
5417 /// constant number of times, and the PHI node is just a recurrence
5418 /// involving constants, fold it.
5420 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
5423 DenseMap<PHINode*, Constant*>::const_iterator I =
5424 ConstantEvolutionLoopExitValue.find(PN);
5425 if (I != ConstantEvolutionLoopExitValue.end())
5428 if (BEs.ugt(MaxBruteForceIterations))
5429 return ConstantEvolutionLoopExitValue[PN] = nullptr; // Not going to evaluate it.
5431 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
5433 DenseMap<Instruction *, Constant *> CurrentIterVals;
5434 BasicBlock *Header = L->getHeader();
5435 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
5437 // Since the loop is canonicalized, the PHI node must have two entries. One
5438 // entry must be a constant (coming in from outside of the loop), and the
5439 // second must be derived from the same PHI.
5440 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
5441 PHINode *PHI = nullptr;
5442 for (BasicBlock::iterator I = Header->begin();
5443 (PHI = dyn_cast<PHINode>(I)); ++I) {
5444 Constant *StartCST =
5445 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
5446 if (!StartCST) continue;
5447 CurrentIterVals[PHI] = StartCST;
5449 if (!CurrentIterVals.count(PN))
5450 return RetVal = nullptr;
5452 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
5454 // Execute the loop symbolically to determine the exit value.
5455 if (BEs.getActiveBits() >= 32)
5456 return RetVal = nullptr; // More than 2^32-1 iterations?? Not doing it!
5458 unsigned NumIterations = BEs.getZExtValue(); // must be in range
5459 unsigned IterationNum = 0;
5460 for (; ; ++IterationNum) {
5461 if (IterationNum == NumIterations)
5462 return RetVal = CurrentIterVals[PN]; // Got exit value!
5464 // Compute the value of the PHIs for the next iteration.
5465 // EvaluateExpression adds non-phi values to the CurrentIterVals map.
5466 DenseMap<Instruction *, Constant *> NextIterVals;
5467 Constant *NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL,
5470 return nullptr; // Couldn't evaluate!
5471 NextIterVals[PN] = NextPHI;
5473 bool StoppedEvolving = NextPHI == CurrentIterVals[PN];
5475 // Also evaluate the other PHI nodes. However, we don't get to stop if we
5476 // cease to be able to evaluate one of them or if they stop evolving,
5477 // because that doesn't necessarily prevent us from computing PN.
5478 SmallVector<std::pair<PHINode *, Constant *>, 8> PHIsToCompute;
5479 for (DenseMap<Instruction *, Constant *>::const_iterator
5480 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
5481 PHINode *PHI = dyn_cast<PHINode>(I->first);
5482 if (!PHI || PHI == PN || PHI->getParent() != Header) continue;
5483 PHIsToCompute.push_back(std::make_pair(PHI, I->second));
5485 // We use two distinct loops because EvaluateExpression may invalidate any
5486 // iterators into CurrentIterVals.
5487 for (SmallVectorImpl<std::pair<PHINode *, Constant*> >::const_iterator
5488 I = PHIsToCompute.begin(), E = PHIsToCompute.end(); I != E; ++I) {
5489 PHINode *PHI = I->first;
5490 Constant *&NextPHI = NextIterVals[PHI];
5491 if (!NextPHI) { // Not already computed.
5492 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
5493 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, TLI);
5495 if (NextPHI != I->second)
5496 StoppedEvolving = false;
5499 // If all entries in CurrentIterVals == NextIterVals then we can stop
5500 // iterating, the loop can't continue to change.
5501 if (StoppedEvolving)
5502 return RetVal = CurrentIterVals[PN];
5504 CurrentIterVals.swap(NextIterVals);
5508 /// ComputeExitCountExhaustively - If the loop is known to execute a
5509 /// constant number of times (the condition evolves only from constants),
5510 /// try to evaluate a few iterations of the loop until we get the exit
5511 /// condition gets a value of ExitWhen (true or false). If we cannot
5512 /// evaluate the trip count of the loop, return getCouldNotCompute().
5513 const SCEV *ScalarEvolution::ComputeExitCountExhaustively(const Loop *L,
5516 PHINode *PN = getConstantEvolvingPHI(Cond, L);
5517 if (!PN) return getCouldNotCompute();
5519 // If the loop is canonicalized, the PHI will have exactly two entries.
5520 // That's the only form we support here.
5521 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
5523 DenseMap<Instruction *, Constant *> CurrentIterVals;
5524 BasicBlock *Header = L->getHeader();
5525 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
5527 // One entry must be a constant (coming in from outside of the loop), and the
5528 // second must be derived from the same PHI.
5529 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
5530 PHINode *PHI = nullptr;
5531 for (BasicBlock::iterator I = Header->begin();
5532 (PHI = dyn_cast<PHINode>(I)); ++I) {
5533 Constant *StartCST =
5534 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
5535 if (!StartCST) continue;
5536 CurrentIterVals[PHI] = StartCST;
5538 if (!CurrentIterVals.count(PN))
5539 return getCouldNotCompute();
5541 // Okay, we find a PHI node that defines the trip count of this loop. Execute
5542 // the loop symbolically to determine when the condition gets a value of
5545 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
5546 for (unsigned IterationNum = 0; IterationNum != MaxIterations;++IterationNum){
5547 ConstantInt *CondVal =
5548 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, L, CurrentIterVals,
5551 // Couldn't symbolically evaluate.
5552 if (!CondVal) return getCouldNotCompute();
5554 if (CondVal->getValue() == uint64_t(ExitWhen)) {
5555 ++NumBruteForceTripCountsComputed;
5556 return getConstant(Type::getInt32Ty(getContext()), IterationNum);
5559 // Update all the PHI nodes for the next iteration.
5560 DenseMap<Instruction *, Constant *> NextIterVals;
5562 // Create a list of which PHIs we need to compute. We want to do this before
5563 // calling EvaluateExpression on them because that may invalidate iterators
5564 // into CurrentIterVals.
5565 SmallVector<PHINode *, 8> PHIsToCompute;
5566 for (DenseMap<Instruction *, Constant *>::const_iterator
5567 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
5568 PHINode *PHI = dyn_cast<PHINode>(I->first);
5569 if (!PHI || PHI->getParent() != Header) continue;
5570 PHIsToCompute.push_back(PHI);
5572 for (SmallVectorImpl<PHINode *>::const_iterator I = PHIsToCompute.begin(),
5573 E = PHIsToCompute.end(); I != E; ++I) {
5575 Constant *&NextPHI = NextIterVals[PHI];
5576 if (NextPHI) continue; // Already computed!
5578 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
5579 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, TLI);
5581 CurrentIterVals.swap(NextIterVals);
5584 // Too many iterations were needed to evaluate.
5585 return getCouldNotCompute();
5588 /// getSCEVAtScope - Return a SCEV expression for the specified value
5589 /// at the specified scope in the program. The L value specifies a loop
5590 /// nest to evaluate the expression at, where null is the top-level or a
5591 /// specified loop is immediately inside of the loop.
5593 /// This method can be used to compute the exit value for a variable defined
5594 /// in a loop by querying what the value will hold in the parent loop.
5596 /// In the case that a relevant loop exit value cannot be computed, the
5597 /// original value V is returned.
5598 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
5599 // Check to see if we've folded this expression at this loop before.
5600 SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values = ValuesAtScopes[V];
5601 for (unsigned u = 0; u < Values.size(); u++) {
5602 if (Values[u].first == L)
5603 return Values[u].second ? Values[u].second : V;
5605 Values.push_back(std::make_pair(L, static_cast<const SCEV *>(nullptr)));
5606 // Otherwise compute it.
5607 const SCEV *C = computeSCEVAtScope(V, L);
5608 SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values2 = ValuesAtScopes[V];
5609 for (unsigned u = Values2.size(); u > 0; u--) {
5610 if (Values2[u - 1].first == L) {
5611 Values2[u - 1].second = C;
5618 /// This builds up a Constant using the ConstantExpr interface. That way, we
5619 /// will return Constants for objects which aren't represented by a
5620 /// SCEVConstant, because SCEVConstant is restricted to ConstantInt.
5621 /// Returns NULL if the SCEV isn't representable as a Constant.
5622 static Constant *BuildConstantFromSCEV(const SCEV *V) {
5623 switch (static_cast<SCEVTypes>(V->getSCEVType())) {
5624 case scCouldNotCompute:
5628 return cast<SCEVConstant>(V)->getValue();
5630 return dyn_cast<Constant>(cast<SCEVUnknown>(V)->getValue());
5631 case scSignExtend: {
5632 const SCEVSignExtendExpr *SS = cast<SCEVSignExtendExpr>(V);
5633 if (Constant *CastOp = BuildConstantFromSCEV(SS->getOperand()))
5634 return ConstantExpr::getSExt(CastOp, SS->getType());
5637 case scZeroExtend: {
5638 const SCEVZeroExtendExpr *SZ = cast<SCEVZeroExtendExpr>(V);
5639 if (Constant *CastOp = BuildConstantFromSCEV(SZ->getOperand()))
5640 return ConstantExpr::getZExt(CastOp, SZ->getType());
5644 const SCEVTruncateExpr *ST = cast<SCEVTruncateExpr>(V);
5645 if (Constant *CastOp = BuildConstantFromSCEV(ST->getOperand()))
5646 return ConstantExpr::getTrunc(CastOp, ST->getType());
5650 const SCEVAddExpr *SA = cast<SCEVAddExpr>(V);
5651 if (Constant *C = BuildConstantFromSCEV(SA->getOperand(0))) {
5652 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
5653 unsigned AS = PTy->getAddressSpace();
5654 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
5655 C = ConstantExpr::getBitCast(C, DestPtrTy);
5657 for (unsigned i = 1, e = SA->getNumOperands(); i != e; ++i) {
5658 Constant *C2 = BuildConstantFromSCEV(SA->getOperand(i));
5659 if (!C2) return nullptr;
5662 if (!C->getType()->isPointerTy() && C2->getType()->isPointerTy()) {
5663 unsigned AS = C2->getType()->getPointerAddressSpace();
5665 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
5666 // The offsets have been converted to bytes. We can add bytes to an
5667 // i8* by GEP with the byte count in the first index.
5668 C = ConstantExpr::getBitCast(C, DestPtrTy);
5671 // Don't bother trying to sum two pointers. We probably can't
5672 // statically compute a load that results from it anyway.
5673 if (C2->getType()->isPointerTy())
5676 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
5677 if (PTy->getElementType()->isStructTy())
5678 C2 = ConstantExpr::getIntegerCast(
5679 C2, Type::getInt32Ty(C->getContext()), true);
5680 C = ConstantExpr::getGetElementPtr(C, C2);
5682 C = ConstantExpr::getAdd(C, C2);
5689 const SCEVMulExpr *SM = cast<SCEVMulExpr>(V);
5690 if (Constant *C = BuildConstantFromSCEV(SM->getOperand(0))) {
5691 // Don't bother with pointers at all.
5692 if (C->getType()->isPointerTy()) return nullptr;
5693 for (unsigned i = 1, e = SM->getNumOperands(); i != e; ++i) {
5694 Constant *C2 = BuildConstantFromSCEV(SM->getOperand(i));
5695 if (!C2 || C2->getType()->isPointerTy()) return nullptr;
5696 C = ConstantExpr::getMul(C, C2);
5703 const SCEVUDivExpr *SU = cast<SCEVUDivExpr>(V);
5704 if (Constant *LHS = BuildConstantFromSCEV(SU->getLHS()))
5705 if (Constant *RHS = BuildConstantFromSCEV(SU->getRHS()))
5706 if (LHS->getType() == RHS->getType())
5707 return ConstantExpr::getUDiv(LHS, RHS);
5712 break; // TODO: smax, umax.
5717 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
5718 if (isa<SCEVConstant>(V)) return V;
5720 // If this instruction is evolved from a constant-evolving PHI, compute the
5721 // exit value from the loop without using SCEVs.
5722 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
5723 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
5724 const Loop *LI = (*this->LI)[I->getParent()];
5725 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
5726 if (PHINode *PN = dyn_cast<PHINode>(I))
5727 if (PN->getParent() == LI->getHeader()) {
5728 // Okay, there is no closed form solution for the PHI node. Check
5729 // to see if the loop that contains it has a known backedge-taken
5730 // count. If so, we may be able to force computation of the exit
5732 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
5733 if (const SCEVConstant *BTCC =
5734 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
5735 // Okay, we know how many times the containing loop executes. If
5736 // this is a constant evolving PHI node, get the final value at
5737 // the specified iteration number.
5738 Constant *RV = getConstantEvolutionLoopExitValue(PN,
5739 BTCC->getValue()->getValue(),
5741 if (RV) return getSCEV(RV);
5745 // Okay, this is an expression that we cannot symbolically evaluate
5746 // into a SCEV. Check to see if it's possible to symbolically evaluate
5747 // the arguments into constants, and if so, try to constant propagate the
5748 // result. This is particularly useful for computing loop exit values.
5749 if (CanConstantFold(I)) {
5750 SmallVector<Constant *, 4> Operands;
5751 bool MadeImprovement = false;
5752 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
5753 Value *Op = I->getOperand(i);
5754 if (Constant *C = dyn_cast<Constant>(Op)) {
5755 Operands.push_back(C);
5759 // If any of the operands is non-constant and if they are
5760 // non-integer and non-pointer, don't even try to analyze them
5761 // with scev techniques.
5762 if (!isSCEVable(Op->getType()))
5765 const SCEV *OrigV = getSCEV(Op);
5766 const SCEV *OpV = getSCEVAtScope(OrigV, L);
5767 MadeImprovement |= OrigV != OpV;
5769 Constant *C = BuildConstantFromSCEV(OpV);
5771 if (C->getType() != Op->getType())
5772 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
5776 Operands.push_back(C);
5779 // Check to see if getSCEVAtScope actually made an improvement.
5780 if (MadeImprovement) {
5781 Constant *C = nullptr;
5782 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
5783 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
5784 Operands[0], Operands[1], DL,
5786 else if (const LoadInst *LI = dyn_cast<LoadInst>(I)) {
5787 if (!LI->isVolatile())
5788 C = ConstantFoldLoadFromConstPtr(Operands[0], DL);
5790 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
5798 // This is some other type of SCEVUnknown, just return it.
5802 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
5803 // Avoid performing the look-up in the common case where the specified
5804 // expression has no loop-variant portions.
5805 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
5806 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
5807 if (OpAtScope != Comm->getOperand(i)) {
5808 // Okay, at least one of these operands is loop variant but might be
5809 // foldable. Build a new instance of the folded commutative expression.
5810 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
5811 Comm->op_begin()+i);
5812 NewOps.push_back(OpAtScope);
5814 for (++i; i != e; ++i) {
5815 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
5816 NewOps.push_back(OpAtScope);
5818 if (isa<SCEVAddExpr>(Comm))
5819 return getAddExpr(NewOps);
5820 if (isa<SCEVMulExpr>(Comm))
5821 return getMulExpr(NewOps);
5822 if (isa<SCEVSMaxExpr>(Comm))
5823 return getSMaxExpr(NewOps);
5824 if (isa<SCEVUMaxExpr>(Comm))
5825 return getUMaxExpr(NewOps);
5826 llvm_unreachable("Unknown commutative SCEV type!");
5829 // If we got here, all operands are loop invariant.
5833 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
5834 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
5835 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
5836 if (LHS == Div->getLHS() && RHS == Div->getRHS())
5837 return Div; // must be loop invariant
5838 return getUDivExpr(LHS, RHS);
5841 // If this is a loop recurrence for a loop that does not contain L, then we
5842 // are dealing with the final value computed by the loop.
5843 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
5844 // First, attempt to evaluate each operand.
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 = AddRec->getNumOperands(); i != e; ++i) {
5848 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
5849 if (OpAtScope == AddRec->getOperand(i))
5852 // Okay, at least one of these operands is loop variant but might be
5853 // foldable. Build a new instance of the folded commutative expression.
5854 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(),
5855 AddRec->op_begin()+i);
5856 NewOps.push_back(OpAtScope);
5857 for (++i; i != e; ++i)
5858 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
5860 const SCEV *FoldedRec =
5861 getAddRecExpr(NewOps, AddRec->getLoop(),
5862 AddRec->getNoWrapFlags(SCEV::FlagNW));
5863 AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec);
5864 // The addrec may be folded to a nonrecurrence, for example, if the
5865 // induction variable is multiplied by zero after constant folding. Go
5866 // ahead and return the folded value.
5872 // If the scope is outside the addrec's loop, evaluate it by using the
5873 // loop exit value of the addrec.
5874 if (!AddRec->getLoop()->contains(L)) {
5875 // To evaluate this recurrence, we need to know how many times the AddRec
5876 // loop iterates. Compute this now.
5877 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
5878 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
5880 // Then, evaluate the AddRec.
5881 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
5887 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
5888 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5889 if (Op == Cast->getOperand())
5890 return Cast; // must be loop invariant
5891 return getZeroExtendExpr(Op, Cast->getType());
5894 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
5895 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5896 if (Op == Cast->getOperand())
5897 return Cast; // must be loop invariant
5898 return getSignExtendExpr(Op, Cast->getType());
5901 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
5902 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5903 if (Op == Cast->getOperand())
5904 return Cast; // must be loop invariant
5905 return getTruncateExpr(Op, Cast->getType());
5908 llvm_unreachable("Unknown SCEV type!");
5911 /// getSCEVAtScope - This is a convenience function which does
5912 /// getSCEVAtScope(getSCEV(V), L).
5913 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
5914 return getSCEVAtScope(getSCEV(V), L);
5917 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
5918 /// following equation:
5920 /// A * X = B (mod N)
5922 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
5923 /// A and B isn't important.
5925 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
5926 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
5927 ScalarEvolution &SE) {
5928 uint32_t BW = A.getBitWidth();
5929 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
5930 assert(A != 0 && "A must be non-zero.");
5934 // The gcd of A and N may have only one prime factor: 2. The number of
5935 // trailing zeros in A is its multiplicity
5936 uint32_t Mult2 = A.countTrailingZeros();
5939 // 2. Check if B is divisible by D.
5941 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
5942 // is not less than multiplicity of this prime factor for D.
5943 if (B.countTrailingZeros() < Mult2)
5944 return SE.getCouldNotCompute();
5946 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
5949 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
5950 // bit width during computations.
5951 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
5952 APInt Mod(BW + 1, 0);
5953 Mod.setBit(BW - Mult2); // Mod = N / D
5954 APInt I = AD.multiplicativeInverse(Mod);
5956 // 4. Compute the minimum unsigned root of the equation:
5957 // I * (B / D) mod (N / D)
5958 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
5960 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
5962 return SE.getConstant(Result.trunc(BW));
5965 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
5966 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
5967 /// might be the same) or two SCEVCouldNotCompute objects.
5969 static std::pair<const SCEV *,const SCEV *>
5970 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
5971 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
5972 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
5973 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
5974 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
5976 // We currently can only solve this if the coefficients are constants.
5977 if (!LC || !MC || !NC) {
5978 const SCEV *CNC = SE.getCouldNotCompute();
5979 return std::make_pair(CNC, CNC);
5982 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
5983 const APInt &L = LC->getValue()->getValue();
5984 const APInt &M = MC->getValue()->getValue();
5985 const APInt &N = NC->getValue()->getValue();
5986 APInt Two(BitWidth, 2);
5987 APInt Four(BitWidth, 4);
5990 using namespace APIntOps;
5992 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
5993 // The B coefficient is M-N/2
5997 // The A coefficient is N/2
5998 APInt A(N.sdiv(Two));
6000 // Compute the B^2-4ac term.
6003 SqrtTerm -= Four * (A * C);
6005 if (SqrtTerm.isNegative()) {
6006 // The loop is provably infinite.
6007 const SCEV *CNC = SE.getCouldNotCompute();
6008 return std::make_pair(CNC, CNC);
6011 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
6012 // integer value or else APInt::sqrt() will assert.
6013 APInt SqrtVal(SqrtTerm.sqrt());
6015 // Compute the two solutions for the quadratic formula.
6016 // The divisions must be performed as signed divisions.
6019 if (TwoA.isMinValue()) {
6020 const SCEV *CNC = SE.getCouldNotCompute();
6021 return std::make_pair(CNC, CNC);
6024 LLVMContext &Context = SE.getContext();
6026 ConstantInt *Solution1 =
6027 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
6028 ConstantInt *Solution2 =
6029 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
6031 return std::make_pair(SE.getConstant(Solution1),
6032 SE.getConstant(Solution2));
6033 } // end APIntOps namespace
6036 /// HowFarToZero - Return the number of times a backedge comparing the specified
6037 /// value to zero will execute. If not computable, return CouldNotCompute.
6039 /// This is only used for loops with a "x != y" exit test. The exit condition is
6040 /// now expressed as a single expression, V = x-y. So the exit test is
6041 /// effectively V != 0. We know and take advantage of the fact that this
6042 /// expression only being used in a comparison by zero context.
6043 ScalarEvolution::ExitLimit
6044 ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L, bool ControlsExit) {
6045 // If the value is a constant
6046 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
6047 // If the value is already zero, the branch will execute zero times.
6048 if (C->getValue()->isZero()) return C;
6049 return getCouldNotCompute(); // Otherwise it will loop infinitely.
6052 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
6053 if (!AddRec || AddRec->getLoop() != L)
6054 return getCouldNotCompute();
6056 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
6057 // the quadratic equation to solve it.
6058 if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
6059 std::pair<const SCEV *,const SCEV *> Roots =
6060 SolveQuadraticEquation(AddRec, *this);
6061 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
6062 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
6065 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1
6066 << " sol#2: " << *R2 << "\n";
6068 // Pick the smallest positive root value.
6069 if (ConstantInt *CB =
6070 dyn_cast<ConstantInt>(ConstantExpr::getICmp(CmpInst::ICMP_ULT,
6073 if (CB->getZExtValue() == false)
6074 std::swap(R1, R2); // R1 is the minimum root now.
6076 // We can only use this value if the chrec ends up with an exact zero
6077 // value at this index. When solving for "X*X != 5", for example, we
6078 // should not accept a root of 2.
6079 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
6081 return R1; // We found a quadratic root!
6084 return getCouldNotCompute();
6087 // Otherwise we can only handle this if it is affine.
6088 if (!AddRec->isAffine())
6089 return getCouldNotCompute();
6091 // If this is an affine expression, the execution count of this branch is
6092 // the minimum unsigned root of the following equation:
6094 // Start + Step*N = 0 (mod 2^BW)
6098 // Step*N = -Start (mod 2^BW)
6100 // where BW is the common bit width of Start and Step.
6102 // Get the initial value for the loop.
6103 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
6104 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
6106 // For now we handle only constant steps.
6108 // TODO: Handle a nonconstant Step given AddRec<NUW>. If the
6109 // AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap
6110 // to 0, it must be counting down to equal 0. Consequently, N = Start / -Step.
6111 // We have not yet seen any such cases.
6112 const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step);
6113 if (!StepC || StepC->getValue()->equalsInt(0))
6114 return getCouldNotCompute();
6116 // For positive steps (counting up until unsigned overflow):
6117 // N = -Start/Step (as unsigned)
6118 // For negative steps (counting down to zero):
6120 // First compute the unsigned distance from zero in the direction of Step.
6121 bool CountDown = StepC->getValue()->getValue().isNegative();
6122 const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start);
6124 // Handle unitary steps, which cannot wraparound.
6125 // 1*N = -Start; -1*N = Start (mod 2^BW), so:
6126 // N = Distance (as unsigned)
6127 if (StepC->getValue()->equalsInt(1) || StepC->getValue()->isAllOnesValue()) {
6128 ConstantRange CR = getUnsignedRange(Start);
6129 const SCEV *MaxBECount;
6130 if (!CountDown && CR.getUnsignedMin().isMinValue())
6131 // When counting up, the worst starting value is 1, not 0.
6132 MaxBECount = CR.getUnsignedMax().isMinValue()
6133 ? getConstant(APInt::getMinValue(CR.getBitWidth()))
6134 : getConstant(APInt::getMaxValue(CR.getBitWidth()));
6136 MaxBECount = getConstant(CountDown ? CR.getUnsignedMax()
6137 : -CR.getUnsignedMin());
6138 return ExitLimit(Distance, MaxBECount);
6141 // If the step exactly divides the distance then unsigned divide computes the
6144 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
6145 SCEVUDivision::divide(SE, Distance, Step, &Q, &R);
6148 getUDivExactExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
6149 return ExitLimit(Exact, Exact);
6152 // If the condition controls loop exit (the loop exits only if the expression
6153 // is true) and the addition is no-wrap we can use unsigned divide to
6154 // compute the backedge count. In this case, the step may not divide the
6155 // distance, but we don't care because if the condition is "missed" the loop
6156 // will have undefined behavior due to wrapping.
6157 if (ControlsExit && AddRec->getNoWrapFlags(SCEV::FlagNW)) {
6159 getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
6160 return ExitLimit(Exact, Exact);
6163 // Then, try to solve the above equation provided that Start is constant.
6164 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
6165 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
6166 -StartC->getValue()->getValue(),
6168 return getCouldNotCompute();
6171 /// HowFarToNonZero - Return the number of times a backedge checking the
6172 /// specified value for nonzero will execute. If not computable, return
6174 ScalarEvolution::ExitLimit
6175 ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
6176 // Loops that look like: while (X == 0) are very strange indeed. We don't
6177 // handle them yet except for the trivial case. This could be expanded in the
6178 // future as needed.
6180 // If the value is a constant, check to see if it is known to be non-zero
6181 // already. If so, the backedge will execute zero times.
6182 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
6183 if (!C->getValue()->isNullValue())
6184 return getConstant(C->getType(), 0);
6185 return getCouldNotCompute(); // Otherwise it will loop infinitely.
6188 // We could implement others, but I really doubt anyone writes loops like
6189 // this, and if they did, they would already be constant folded.
6190 return getCouldNotCompute();
6193 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
6194 /// (which may not be an immediate predecessor) which has exactly one
6195 /// successor from which BB is reachable, or null if no such block is
6198 std::pair<BasicBlock *, BasicBlock *>
6199 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
6200 // If the block has a unique predecessor, then there is no path from the
6201 // predecessor to the block that does not go through the direct edge
6202 // from the predecessor to the block.
6203 if (BasicBlock *Pred = BB->getSinglePredecessor())
6204 return std::make_pair(Pred, BB);
6206 // A loop's header is defined to be a block that dominates the loop.
6207 // If the header has a unique predecessor outside the loop, it must be
6208 // a block that has exactly one successor that can reach the loop.
6209 if (Loop *L = LI->getLoopFor(BB))
6210 return std::make_pair(L->getLoopPredecessor(), L->getHeader());
6212 return std::pair<BasicBlock *, BasicBlock *>();
6215 /// HasSameValue - SCEV structural equivalence is usually sufficient for
6216 /// testing whether two expressions are equal, however for the purposes of
6217 /// looking for a condition guarding a loop, it can be useful to be a little
6218 /// more general, since a front-end may have replicated the controlling
6221 static bool HasSameValue(const SCEV *A, const SCEV *B) {
6222 // Quick check to see if they are the same SCEV.
6223 if (A == B) return true;
6225 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
6226 // two different instructions with the same value. Check for this case.
6227 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
6228 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
6229 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
6230 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
6231 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory())
6234 // Otherwise assume they may have a different value.
6238 /// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with
6239 /// predicate Pred. Return true iff any changes were made.
6241 bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
6242 const SCEV *&LHS, const SCEV *&RHS,
6244 bool Changed = false;
6246 // If we hit the max recursion limit bail out.
6250 // Canonicalize a constant to the right side.
6251 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
6252 // Check for both operands constant.
6253 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
6254 if (ConstantExpr::getICmp(Pred,
6256 RHSC->getValue())->isNullValue())
6257 goto trivially_false;
6259 goto trivially_true;
6261 // Otherwise swap the operands to put the constant on the right.
6262 std::swap(LHS, RHS);
6263 Pred = ICmpInst::getSwappedPredicate(Pred);
6267 // If we're comparing an addrec with a value which is loop-invariant in the
6268 // addrec's loop, put the addrec on the left. Also make a dominance check,
6269 // as both operands could be addrecs loop-invariant in each other's loop.
6270 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
6271 const Loop *L = AR->getLoop();
6272 if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) {
6273 std::swap(LHS, RHS);
6274 Pred = ICmpInst::getSwappedPredicate(Pred);
6279 // If there's a constant operand, canonicalize comparisons with boundary
6280 // cases, and canonicalize *-or-equal comparisons to regular comparisons.
6281 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
6282 const APInt &RA = RC->getValue()->getValue();
6284 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6285 case ICmpInst::ICMP_EQ:
6286 case ICmpInst::ICMP_NE:
6287 // Fold ((-1) * %a) + %b == 0 (equivalent to %b-%a == 0) into %a == %b.
6289 if (const SCEVAddExpr *AE = dyn_cast<SCEVAddExpr>(LHS))
6290 if (const SCEVMulExpr *ME = dyn_cast<SCEVMulExpr>(AE->getOperand(0)))
6291 if (AE->getNumOperands() == 2 && ME->getNumOperands() == 2 &&
6292 ME->getOperand(0)->isAllOnesValue()) {
6293 RHS = AE->getOperand(1);
6294 LHS = ME->getOperand(1);
6298 case ICmpInst::ICMP_UGE:
6299 if ((RA - 1).isMinValue()) {
6300 Pred = ICmpInst::ICMP_NE;
6301 RHS = getConstant(RA - 1);
6305 if (RA.isMaxValue()) {
6306 Pred = ICmpInst::ICMP_EQ;
6310 if (RA.isMinValue()) goto trivially_true;
6312 Pred = ICmpInst::ICMP_UGT;
6313 RHS = getConstant(RA - 1);
6316 case ICmpInst::ICMP_ULE:
6317 if ((RA + 1).isMaxValue()) {
6318 Pred = ICmpInst::ICMP_NE;
6319 RHS = getConstant(RA + 1);
6323 if (RA.isMinValue()) {
6324 Pred = ICmpInst::ICMP_EQ;
6328 if (RA.isMaxValue()) goto trivially_true;
6330 Pred = ICmpInst::ICMP_ULT;
6331 RHS = getConstant(RA + 1);
6334 case ICmpInst::ICMP_SGE:
6335 if ((RA - 1).isMinSignedValue()) {
6336 Pred = ICmpInst::ICMP_NE;
6337 RHS = getConstant(RA - 1);
6341 if (RA.isMaxSignedValue()) {
6342 Pred = ICmpInst::ICMP_EQ;
6346 if (RA.isMinSignedValue()) goto trivially_true;
6348 Pred = ICmpInst::ICMP_SGT;
6349 RHS = getConstant(RA - 1);
6352 case ICmpInst::ICMP_SLE:
6353 if ((RA + 1).isMaxSignedValue()) {
6354 Pred = ICmpInst::ICMP_NE;
6355 RHS = getConstant(RA + 1);
6359 if (RA.isMinSignedValue()) {
6360 Pred = ICmpInst::ICMP_EQ;
6364 if (RA.isMaxSignedValue()) goto trivially_true;
6366 Pred = ICmpInst::ICMP_SLT;
6367 RHS = getConstant(RA + 1);
6370 case ICmpInst::ICMP_UGT:
6371 if (RA.isMinValue()) {
6372 Pred = ICmpInst::ICMP_NE;
6376 if ((RA + 1).isMaxValue()) {
6377 Pred = ICmpInst::ICMP_EQ;
6378 RHS = getConstant(RA + 1);
6382 if (RA.isMaxValue()) goto trivially_false;
6384 case ICmpInst::ICMP_ULT:
6385 if (RA.isMaxValue()) {
6386 Pred = ICmpInst::ICMP_NE;
6390 if ((RA - 1).isMinValue()) {
6391 Pred = ICmpInst::ICMP_EQ;
6392 RHS = getConstant(RA - 1);
6396 if (RA.isMinValue()) goto trivially_false;
6398 case ICmpInst::ICMP_SGT:
6399 if (RA.isMinSignedValue()) {
6400 Pred = ICmpInst::ICMP_NE;
6404 if ((RA + 1).isMaxSignedValue()) {
6405 Pred = ICmpInst::ICMP_EQ;
6406 RHS = getConstant(RA + 1);
6410 if (RA.isMaxSignedValue()) goto trivially_false;
6412 case ICmpInst::ICMP_SLT:
6413 if (RA.isMaxSignedValue()) {
6414 Pred = ICmpInst::ICMP_NE;
6418 if ((RA - 1).isMinSignedValue()) {
6419 Pred = ICmpInst::ICMP_EQ;
6420 RHS = getConstant(RA - 1);
6424 if (RA.isMinSignedValue()) goto trivially_false;
6429 // Check for obvious equality.
6430 if (HasSameValue(LHS, RHS)) {
6431 if (ICmpInst::isTrueWhenEqual(Pred))
6432 goto trivially_true;
6433 if (ICmpInst::isFalseWhenEqual(Pred))
6434 goto trivially_false;
6437 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
6438 // adding or subtracting 1 from one of the operands.
6440 case ICmpInst::ICMP_SLE:
6441 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) {
6442 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
6444 Pred = ICmpInst::ICMP_SLT;
6446 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) {
6447 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
6449 Pred = ICmpInst::ICMP_SLT;
6453 case ICmpInst::ICMP_SGE:
6454 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) {
6455 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
6457 Pred = ICmpInst::ICMP_SGT;
6459 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) {
6460 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
6462 Pred = ICmpInst::ICMP_SGT;
6466 case ICmpInst::ICMP_ULE:
6467 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) {
6468 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
6470 Pred = ICmpInst::ICMP_ULT;
6472 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) {
6473 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
6475 Pred = ICmpInst::ICMP_ULT;
6479 case ICmpInst::ICMP_UGE:
6480 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) {
6481 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
6483 Pred = ICmpInst::ICMP_UGT;
6485 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) {
6486 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
6488 Pred = ICmpInst::ICMP_UGT;
6496 // TODO: More simplifications are possible here.
6498 // Recursively simplify until we either hit a recursion limit or nothing
6501 return SimplifyICmpOperands(Pred, LHS, RHS, Depth+1);
6507 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
6508 Pred = ICmpInst::ICMP_EQ;
6513 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
6514 Pred = ICmpInst::ICMP_NE;
6518 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
6519 return getSignedRange(S).getSignedMax().isNegative();
6522 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
6523 return getSignedRange(S).getSignedMin().isStrictlyPositive();
6526 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
6527 return !getSignedRange(S).getSignedMin().isNegative();
6530 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
6531 return !getSignedRange(S).getSignedMax().isStrictlyPositive();
6534 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
6535 return isKnownNegative(S) || isKnownPositive(S);
6538 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
6539 const SCEV *LHS, const SCEV *RHS) {
6540 // Canonicalize the inputs first.
6541 (void)SimplifyICmpOperands(Pred, LHS, RHS);
6543 // If LHS or RHS is an addrec, check to see if the condition is true in
6544 // every iteration of the loop.
6545 // If LHS and RHS are both addrec, both conditions must be true in
6546 // every iteration of the loop.
6547 const SCEVAddRecExpr *LAR = dyn_cast<SCEVAddRecExpr>(LHS);
6548 const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS);
6549 bool LeftGuarded = false;
6550 bool RightGuarded = false;
6552 const Loop *L = LAR->getLoop();
6553 if (isLoopEntryGuardedByCond(L, Pred, LAR->getStart(), RHS) &&
6554 isLoopBackedgeGuardedByCond(L, Pred, LAR->getPostIncExpr(*this), RHS)) {
6555 if (!RAR) return true;
6560 const Loop *L = RAR->getLoop();
6561 if (isLoopEntryGuardedByCond(L, Pred, LHS, RAR->getStart()) &&
6562 isLoopBackedgeGuardedByCond(L, Pred, LHS, RAR->getPostIncExpr(*this))) {
6563 if (!LAR) return true;
6564 RightGuarded = true;
6567 if (LeftGuarded && RightGuarded)
6570 // Otherwise see what can be done with known constant ranges.
6571 return isKnownPredicateWithRanges(Pred, LHS, RHS);
6575 ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred,
6576 const SCEV *LHS, const SCEV *RHS) {
6577 if (HasSameValue(LHS, RHS))
6578 return ICmpInst::isTrueWhenEqual(Pred);
6580 // This code is split out from isKnownPredicate because it is called from
6581 // within isLoopEntryGuardedByCond.
6584 llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6585 case ICmpInst::ICMP_SGT:
6586 std::swap(LHS, RHS);
6587 case ICmpInst::ICMP_SLT: {
6588 ConstantRange LHSRange = getSignedRange(LHS);
6589 ConstantRange RHSRange = getSignedRange(RHS);
6590 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
6592 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
6596 case ICmpInst::ICMP_SGE:
6597 std::swap(LHS, RHS);
6598 case ICmpInst::ICMP_SLE: {
6599 ConstantRange LHSRange = getSignedRange(LHS);
6600 ConstantRange RHSRange = getSignedRange(RHS);
6601 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
6603 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
6607 case ICmpInst::ICMP_UGT:
6608 std::swap(LHS, RHS);
6609 case ICmpInst::ICMP_ULT: {
6610 ConstantRange LHSRange = getUnsignedRange(LHS);
6611 ConstantRange RHSRange = getUnsignedRange(RHS);
6612 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
6614 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
6618 case ICmpInst::ICMP_UGE:
6619 std::swap(LHS, RHS);
6620 case ICmpInst::ICMP_ULE: {
6621 ConstantRange LHSRange = getUnsignedRange(LHS);
6622 ConstantRange RHSRange = getUnsignedRange(RHS);
6623 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
6625 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
6629 case ICmpInst::ICMP_NE: {
6630 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
6632 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
6635 const SCEV *Diff = getMinusSCEV(LHS, RHS);
6636 if (isKnownNonZero(Diff))
6640 case ICmpInst::ICMP_EQ:
6641 // The check at the top of the function catches the case where
6642 // the values are known to be equal.
6648 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
6649 /// protected by a conditional between LHS and RHS. This is used to
6650 /// to eliminate casts.
6652 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
6653 ICmpInst::Predicate Pred,
6654 const SCEV *LHS, const SCEV *RHS) {
6655 // Interpret a null as meaning no loop, where there is obviously no guard
6656 // (interprocedural conditions notwithstanding).
6657 if (!L) return true;
6659 if (isKnownPredicateWithRanges(Pred, LHS, RHS)) return true;
6661 BasicBlock *Latch = L->getLoopLatch();
6665 BranchInst *LoopContinuePredicate =
6666 dyn_cast<BranchInst>(Latch->getTerminator());
6667 if (LoopContinuePredicate && LoopContinuePredicate->isConditional() &&
6668 isImpliedCond(Pred, LHS, RHS,
6669 LoopContinuePredicate->getCondition(),
6670 LoopContinuePredicate->getSuccessor(0) != L->getHeader()))
6673 // Check conditions due to any @llvm.assume intrinsics.
6674 for (auto &CI : AT->assumptions(F)) {
6675 if (!DT->dominates(CI, Latch->getTerminator()))
6678 if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false))
6685 /// isLoopEntryGuardedByCond - Test whether entry to the loop is protected
6686 /// by a conditional between LHS and RHS. This is used to help avoid max
6687 /// expressions in loop trip counts, and to eliminate casts.
6689 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
6690 ICmpInst::Predicate Pred,
6691 const SCEV *LHS, const SCEV *RHS) {
6692 // Interpret a null as meaning no loop, where there is obviously no guard
6693 // (interprocedural conditions notwithstanding).
6694 if (!L) return false;
6696 if (isKnownPredicateWithRanges(Pred, LHS, RHS)) return true;
6698 // Starting at the loop predecessor, climb up the predecessor chain, as long
6699 // as there are predecessors that can be found that have unique successors
6700 // leading to the original header.
6701 for (std::pair<BasicBlock *, BasicBlock *>
6702 Pair(L->getLoopPredecessor(), L->getHeader());
6704 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
6706 BranchInst *LoopEntryPredicate =
6707 dyn_cast<BranchInst>(Pair.first->getTerminator());
6708 if (!LoopEntryPredicate ||
6709 LoopEntryPredicate->isUnconditional())
6712 if (isImpliedCond(Pred, LHS, RHS,
6713 LoopEntryPredicate->getCondition(),
6714 LoopEntryPredicate->getSuccessor(0) != Pair.second))
6718 // Check conditions due to any @llvm.assume intrinsics.
6719 for (auto &CI : AT->assumptions(F)) {
6720 if (!DT->dominates(CI, L->getHeader()))
6723 if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false))
6730 /// RAII wrapper to prevent recursive application of isImpliedCond.
6731 /// ScalarEvolution's PendingLoopPredicates set must be empty unless we are
6732 /// currently evaluating isImpliedCond.
6733 struct MarkPendingLoopPredicate {
6735 DenseSet<Value*> &LoopPreds;
6738 MarkPendingLoopPredicate(Value *C, DenseSet<Value*> &LP)
6739 : Cond(C), LoopPreds(LP) {
6740 Pending = !LoopPreds.insert(Cond).second;
6742 ~MarkPendingLoopPredicate() {
6744 LoopPreds.erase(Cond);
6748 /// isImpliedCond - Test whether the condition described by Pred, LHS,
6749 /// and RHS is true whenever the given Cond value evaluates to true.
6750 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred,
6751 const SCEV *LHS, const SCEV *RHS,
6752 Value *FoundCondValue,
6754 MarkPendingLoopPredicate Mark(FoundCondValue, PendingLoopPredicates);
6758 // Recursively handle And and Or conditions.
6759 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) {
6760 if (BO->getOpcode() == Instruction::And) {
6762 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
6763 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
6764 } else if (BO->getOpcode() == Instruction::Or) {
6766 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
6767 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
6771 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue);
6772 if (!ICI) return false;
6774 // Bail if the ICmp's operands' types are wider than the needed type
6775 // before attempting to call getSCEV on them. This avoids infinite
6776 // recursion, since the analysis of widening casts can require loop
6777 // exit condition information for overflow checking, which would
6779 if (getTypeSizeInBits(LHS->getType()) <
6780 getTypeSizeInBits(ICI->getOperand(0)->getType()))
6783 // Now that we found a conditional branch that dominates the loop or controls
6784 // the loop latch. Check to see if it is the comparison we are looking for.
6785 ICmpInst::Predicate FoundPred;
6787 FoundPred = ICI->getInversePredicate();
6789 FoundPred = ICI->getPredicate();
6791 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
6792 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
6794 // Balance the types. The case where FoundLHS' type is wider than
6795 // LHS' type is checked for above.
6796 if (getTypeSizeInBits(LHS->getType()) >
6797 getTypeSizeInBits(FoundLHS->getType())) {
6798 if (CmpInst::isSigned(FoundPred)) {
6799 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
6800 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
6802 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
6803 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
6807 // Canonicalize the query to match the way instcombine will have
6808 // canonicalized the comparison.
6809 if (SimplifyICmpOperands(Pred, LHS, RHS))
6811 return CmpInst::isTrueWhenEqual(Pred);
6812 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
6813 if (FoundLHS == FoundRHS)
6814 return CmpInst::isFalseWhenEqual(FoundPred);
6816 // Check to see if we can make the LHS or RHS match.
6817 if (LHS == FoundRHS || RHS == FoundLHS) {
6818 if (isa<SCEVConstant>(RHS)) {
6819 std::swap(FoundLHS, FoundRHS);
6820 FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
6822 std::swap(LHS, RHS);
6823 Pred = ICmpInst::getSwappedPredicate(Pred);
6827 // Check whether the found predicate is the same as the desired predicate.
6828 if (FoundPred == Pred)
6829 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
6831 // Check whether swapping the found predicate makes it the same as the
6832 // desired predicate.
6833 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
6834 if (isa<SCEVConstant>(RHS))
6835 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
6837 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
6838 RHS, LHS, FoundLHS, FoundRHS);
6841 // Check if we can make progress by sharpening ranges.
6842 if (FoundPred == ICmpInst::ICMP_NE &&
6843 (isa<SCEVConstant>(FoundLHS) || isa<SCEVConstant>(FoundRHS))) {
6845 const SCEVConstant *C = nullptr;
6846 const SCEV *V = nullptr;
6848 if (isa<SCEVConstant>(FoundLHS)) {
6849 C = cast<SCEVConstant>(FoundLHS);
6852 C = cast<SCEVConstant>(FoundRHS);
6856 // The guarding predicate tells us that C != V. If the known range
6857 // of V is [C, t), we can sharpen the range to [C + 1, t). The
6858 // range we consider has to correspond to same signedness as the
6859 // predicate we're interested in folding.
6861 APInt Min = ICmpInst::isSigned(Pred) ?
6862 getSignedRange(V).getSignedMin() : getUnsignedRange(V).getUnsignedMin();
6864 if (Min == C->getValue()->getValue()) {
6865 // Given (V >= Min && V != Min) we conclude V >= (Min + 1).
6866 // This is true even if (Min + 1) wraps around -- in case of
6867 // wraparound, (Min + 1) < Min, so (V >= Min => V >= (Min + 1)).
6869 APInt SharperMin = Min + 1;
6872 case ICmpInst::ICMP_SGE:
6873 case ICmpInst::ICMP_UGE:
6874 // We know V `Pred` SharperMin. If this implies LHS `Pred`
6876 if (isImpliedCondOperands(Pred, LHS, RHS, V,
6877 getConstant(SharperMin)))
6880 case ICmpInst::ICMP_SGT:
6881 case ICmpInst::ICMP_UGT:
6882 // We know from the range information that (V `Pred` Min ||
6883 // V == Min). We know from the guarding condition that !(V
6884 // == Min). This gives us
6886 // V `Pred` Min || V == Min && !(V == Min)
6889 // If V `Pred` Min implies LHS `Pred` RHS, we're done.
6891 if (isImpliedCondOperands(Pred, LHS, RHS, V, getConstant(Min)))
6901 // Check whether the actual condition is beyond sufficient.
6902 if (FoundPred == ICmpInst::ICMP_EQ)
6903 if (ICmpInst::isTrueWhenEqual(Pred))
6904 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
6906 if (Pred == ICmpInst::ICMP_NE)
6907 if (!ICmpInst::isTrueWhenEqual(FoundPred))
6908 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
6911 // Otherwise assume the worst.
6915 /// isImpliedCondOperands - Test whether the condition described by Pred,
6916 /// LHS, and RHS is true whenever the condition described by Pred, FoundLHS,
6917 /// and FoundRHS is true.
6918 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
6919 const SCEV *LHS, const SCEV *RHS,
6920 const SCEV *FoundLHS,
6921 const SCEV *FoundRHS) {
6922 return isImpliedCondOperandsHelper(Pred, LHS, RHS,
6923 FoundLHS, FoundRHS) ||
6924 // ~x < ~y --> x > y
6925 isImpliedCondOperandsHelper(Pred, LHS, RHS,
6926 getNotSCEV(FoundRHS),
6927 getNotSCEV(FoundLHS));
6930 /// isImpliedCondOperandsHelper - Test whether the condition described by
6931 /// Pred, LHS, and RHS is true whenever the condition described by Pred,
6932 /// FoundLHS, and FoundRHS is true.
6934 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
6935 const SCEV *LHS, const SCEV *RHS,
6936 const SCEV *FoundLHS,
6937 const SCEV *FoundRHS) {
6939 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6940 case ICmpInst::ICMP_EQ:
6941 case ICmpInst::ICMP_NE:
6942 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
6945 case ICmpInst::ICMP_SLT:
6946 case ICmpInst::ICMP_SLE:
6947 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
6948 isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, RHS, FoundRHS))
6951 case ICmpInst::ICMP_SGT:
6952 case ICmpInst::ICMP_SGE:
6953 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
6954 isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, RHS, FoundRHS))
6957 case ICmpInst::ICMP_ULT:
6958 case ICmpInst::ICMP_ULE:
6959 if (isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
6960 isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, RHS, FoundRHS))
6963 case ICmpInst::ICMP_UGT:
6964 case ICmpInst::ICMP_UGE:
6965 if (isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
6966 isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, RHS, FoundRHS))
6974 // Verify if an linear IV with positive stride can overflow when in a
6975 // less-than comparison, knowing the invariant term of the comparison, the
6976 // stride and the knowledge of NSW/NUW flags on the recurrence.
6977 bool ScalarEvolution::doesIVOverflowOnLT(const SCEV *RHS, const SCEV *Stride,
6978 bool IsSigned, bool NoWrap) {
6979 if (NoWrap) return false;
6981 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
6982 const SCEV *One = getConstant(Stride->getType(), 1);
6985 APInt MaxRHS = getSignedRange(RHS).getSignedMax();
6986 APInt MaxValue = APInt::getSignedMaxValue(BitWidth);
6987 APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
6990 // SMaxRHS + SMaxStrideMinusOne > SMaxValue => overflow!
6991 return (MaxValue - MaxStrideMinusOne).slt(MaxRHS);
6994 APInt MaxRHS = getUnsignedRange(RHS).getUnsignedMax();
6995 APInt MaxValue = APInt::getMaxValue(BitWidth);
6996 APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
6999 // UMaxRHS + UMaxStrideMinusOne > UMaxValue => overflow!
7000 return (MaxValue - MaxStrideMinusOne).ult(MaxRHS);
7003 // Verify if an linear IV with negative stride can overflow when in a
7004 // greater-than comparison, knowing the invariant term of the comparison,
7005 // the stride and the knowledge of NSW/NUW flags on the recurrence.
7006 bool ScalarEvolution::doesIVOverflowOnGT(const SCEV *RHS, const SCEV *Stride,
7007 bool IsSigned, bool NoWrap) {
7008 if (NoWrap) return false;
7010 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
7011 const SCEV *One = getConstant(Stride->getType(), 1);
7014 APInt MinRHS = getSignedRange(RHS).getSignedMin();
7015 APInt MinValue = APInt::getSignedMinValue(BitWidth);
7016 APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
7019 // SMinRHS - SMaxStrideMinusOne < SMinValue => overflow!
7020 return (MinValue + MaxStrideMinusOne).sgt(MinRHS);
7023 APInt MinRHS = getUnsignedRange(RHS).getUnsignedMin();
7024 APInt MinValue = APInt::getMinValue(BitWidth);
7025 APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
7028 // UMinRHS - UMaxStrideMinusOne < UMinValue => overflow!
7029 return (MinValue + MaxStrideMinusOne).ugt(MinRHS);
7032 // Compute the backedge taken count knowing the interval difference, the
7033 // stride and presence of the equality in the comparison.
7034 const SCEV *ScalarEvolution::computeBECount(const SCEV *Delta, const SCEV *Step,
7036 const SCEV *One = getConstant(Step->getType(), 1);
7037 Delta = Equality ? getAddExpr(Delta, Step)
7038 : getAddExpr(Delta, getMinusSCEV(Step, One));
7039 return getUDivExpr(Delta, Step);
7042 /// HowManyLessThans - Return the number of times a backedge containing the
7043 /// specified less-than comparison will execute. If not computable, return
7044 /// CouldNotCompute.
7046 /// @param ControlsExit is true when the LHS < RHS condition directly controls
7047 /// the branch (loops exits only if condition is true). In this case, we can use
7048 /// NoWrapFlags to skip overflow checks.
7049 ScalarEvolution::ExitLimit
7050 ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
7051 const Loop *L, bool IsSigned,
7052 bool ControlsExit) {
7053 // We handle only IV < Invariant
7054 if (!isLoopInvariant(RHS, L))
7055 return getCouldNotCompute();
7057 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
7059 // Avoid weird loops
7060 if (!IV || IV->getLoop() != L || !IV->isAffine())
7061 return getCouldNotCompute();
7063 bool NoWrap = ControlsExit &&
7064 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
7066 const SCEV *Stride = IV->getStepRecurrence(*this);
7068 // Avoid negative or zero stride values
7069 if (!isKnownPositive(Stride))
7070 return getCouldNotCompute();
7072 // Avoid proven overflow cases: this will ensure that the backedge taken count
7073 // will not generate any unsigned overflow. Relaxed no-overflow conditions
7074 // exploit NoWrapFlags, allowing to optimize in presence of undefined
7075 // behaviors like the case of C language.
7076 if (!Stride->isOne() && doesIVOverflowOnLT(RHS, Stride, IsSigned, NoWrap))
7077 return getCouldNotCompute();
7079 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SLT
7080 : ICmpInst::ICMP_ULT;
7081 const SCEV *Start = IV->getStart();
7082 const SCEV *End = RHS;
7083 if (!isLoopEntryGuardedByCond(L, Cond, getMinusSCEV(Start, Stride), RHS)) {
7084 const SCEV *Diff = getMinusSCEV(RHS, Start);
7085 // If we have NoWrap set, then we can assume that the increment won't
7086 // overflow, in which case if RHS - Start is a constant, we don't need to
7087 // do a max operation since we can just figure it out statically
7088 if (NoWrap && isa<SCEVConstant>(Diff)) {
7089 APInt D = dyn_cast<const SCEVConstant>(Diff)->getValue()->getValue();
7093 End = IsSigned ? getSMaxExpr(RHS, Start)
7094 : getUMaxExpr(RHS, Start);
7097 const SCEV *BECount = computeBECount(getMinusSCEV(End, Start), Stride, false);
7099 APInt MinStart = IsSigned ? getSignedRange(Start).getSignedMin()
7100 : getUnsignedRange(Start).getUnsignedMin();
7102 APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
7103 : getUnsignedRange(Stride).getUnsignedMin();
7105 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
7106 APInt Limit = IsSigned ? APInt::getSignedMaxValue(BitWidth) - (MinStride - 1)
7107 : APInt::getMaxValue(BitWidth) - (MinStride - 1);
7109 // Although End can be a MAX expression we estimate MaxEnd considering only
7110 // the case End = RHS. This is safe because in the other case (End - Start)
7111 // is zero, leading to a zero maximum backedge taken count.
7113 IsSigned ? APIntOps::smin(getSignedRange(RHS).getSignedMax(), Limit)
7114 : APIntOps::umin(getUnsignedRange(RHS).getUnsignedMax(), Limit);
7116 const SCEV *MaxBECount;
7117 if (isa<SCEVConstant>(BECount))
7118 MaxBECount = BECount;
7120 MaxBECount = computeBECount(getConstant(MaxEnd - MinStart),
7121 getConstant(MinStride), false);
7123 if (isa<SCEVCouldNotCompute>(MaxBECount))
7124 MaxBECount = BECount;
7126 return ExitLimit(BECount, MaxBECount);
7129 ScalarEvolution::ExitLimit
7130 ScalarEvolution::HowManyGreaterThans(const SCEV *LHS, const SCEV *RHS,
7131 const Loop *L, bool IsSigned,
7132 bool ControlsExit) {
7133 // We handle only IV > Invariant
7134 if (!isLoopInvariant(RHS, L))
7135 return getCouldNotCompute();
7137 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
7139 // Avoid weird loops
7140 if (!IV || IV->getLoop() != L || !IV->isAffine())
7141 return getCouldNotCompute();
7143 bool NoWrap = ControlsExit &&
7144 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
7146 const SCEV *Stride = getNegativeSCEV(IV->getStepRecurrence(*this));
7148 // Avoid negative or zero stride values
7149 if (!isKnownPositive(Stride))
7150 return getCouldNotCompute();
7152 // Avoid proven overflow cases: this will ensure that the backedge taken count
7153 // will not generate any unsigned overflow. Relaxed no-overflow conditions
7154 // exploit NoWrapFlags, allowing to optimize in presence of undefined
7155 // behaviors like the case of C language.
7156 if (!Stride->isOne() && doesIVOverflowOnGT(RHS, Stride, IsSigned, NoWrap))
7157 return getCouldNotCompute();
7159 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SGT
7160 : ICmpInst::ICMP_UGT;
7162 const SCEV *Start = IV->getStart();
7163 const SCEV *End = RHS;
7164 if (!isLoopEntryGuardedByCond(L, Cond, getAddExpr(Start, Stride), RHS)) {
7165 const SCEV *Diff = getMinusSCEV(RHS, Start);
7166 // If we have NoWrap set, then we can assume that the increment won't
7167 // overflow, in which case if RHS - Start is a constant, we don't need to
7168 // do a max operation since we can just figure it out statically
7169 if (NoWrap && isa<SCEVConstant>(Diff)) {
7170 APInt D = dyn_cast<const SCEVConstant>(Diff)->getValue()->getValue();
7171 if (!D.isNegative())
7174 End = IsSigned ? getSMinExpr(RHS, Start)
7175 : getUMinExpr(RHS, Start);
7178 const SCEV *BECount = computeBECount(getMinusSCEV(Start, End), Stride, false);
7180 APInt MaxStart = IsSigned ? getSignedRange(Start).getSignedMax()
7181 : getUnsignedRange(Start).getUnsignedMax();
7183 APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
7184 : getUnsignedRange(Stride).getUnsignedMin();
7186 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
7187 APInt Limit = IsSigned ? APInt::getSignedMinValue(BitWidth) + (MinStride - 1)
7188 : APInt::getMinValue(BitWidth) + (MinStride - 1);
7190 // Although End can be a MIN expression we estimate MinEnd considering only
7191 // the case End = RHS. This is safe because in the other case (Start - End)
7192 // is zero, leading to a zero maximum backedge taken count.
7194 IsSigned ? APIntOps::smax(getSignedRange(RHS).getSignedMin(), Limit)
7195 : APIntOps::umax(getUnsignedRange(RHS).getUnsignedMin(), Limit);
7198 const SCEV *MaxBECount = getCouldNotCompute();
7199 if (isa<SCEVConstant>(BECount))
7200 MaxBECount = BECount;
7202 MaxBECount = computeBECount(getConstant(MaxStart - MinEnd),
7203 getConstant(MinStride), false);
7205 if (isa<SCEVCouldNotCompute>(MaxBECount))
7206 MaxBECount = BECount;
7208 return ExitLimit(BECount, MaxBECount);
7211 /// getNumIterationsInRange - Return the number of iterations of this loop that
7212 /// produce values in the specified constant range. Another way of looking at
7213 /// this is that it returns the first iteration number where the value is not in
7214 /// the condition, thus computing the exit count. If the iteration count can't
7215 /// be computed, an instance of SCEVCouldNotCompute is returned.
7216 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
7217 ScalarEvolution &SE) const {
7218 if (Range.isFullSet()) // Infinite loop.
7219 return SE.getCouldNotCompute();
7221 // If the start is a non-zero constant, shift the range to simplify things.
7222 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
7223 if (!SC->getValue()->isZero()) {
7224 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
7225 Operands[0] = SE.getConstant(SC->getType(), 0);
7226 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(),
7227 getNoWrapFlags(FlagNW));
7228 if (const SCEVAddRecExpr *ShiftedAddRec =
7229 dyn_cast<SCEVAddRecExpr>(Shifted))
7230 return ShiftedAddRec->getNumIterationsInRange(
7231 Range.subtract(SC->getValue()->getValue()), SE);
7232 // This is strange and shouldn't happen.
7233 return SE.getCouldNotCompute();
7236 // The only time we can solve this is when we have all constant indices.
7237 // Otherwise, we cannot determine the overflow conditions.
7238 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
7239 if (!isa<SCEVConstant>(getOperand(i)))
7240 return SE.getCouldNotCompute();
7243 // Okay at this point we know that all elements of the chrec are constants and
7244 // that the start element is zero.
7246 // First check to see if the range contains zero. If not, the first
7248 unsigned BitWidth = SE.getTypeSizeInBits(getType());
7249 if (!Range.contains(APInt(BitWidth, 0)))
7250 return SE.getConstant(getType(), 0);
7253 // If this is an affine expression then we have this situation:
7254 // Solve {0,+,A} in Range === Ax in Range
7256 // We know that zero is in the range. If A is positive then we know that
7257 // the upper value of the range must be the first possible exit value.
7258 // If A is negative then the lower of the range is the last possible loop
7259 // value. Also note that we already checked for a full range.
7260 APInt One(BitWidth,1);
7261 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
7262 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
7264 // The exit value should be (End+A)/A.
7265 APInt ExitVal = (End + A).udiv(A);
7266 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
7268 // Evaluate at the exit value. If we really did fall out of the valid
7269 // range, then we computed our trip count, otherwise wrap around or other
7270 // things must have happened.
7271 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
7272 if (Range.contains(Val->getValue()))
7273 return SE.getCouldNotCompute(); // Something strange happened
7275 // Ensure that the previous value is in the range. This is a sanity check.
7276 assert(Range.contains(
7277 EvaluateConstantChrecAtConstant(this,
7278 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
7279 "Linear scev computation is off in a bad way!");
7280 return SE.getConstant(ExitValue);
7281 } else if (isQuadratic()) {
7282 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
7283 // quadratic equation to solve it. To do this, we must frame our problem in
7284 // terms of figuring out when zero is crossed, instead of when
7285 // Range.getUpper() is crossed.
7286 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
7287 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
7288 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop(),
7289 // getNoWrapFlags(FlagNW)
7292 // Next, solve the constructed addrec
7293 std::pair<const SCEV *,const SCEV *> Roots =
7294 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
7295 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
7296 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
7298 // Pick the smallest positive root value.
7299 if (ConstantInt *CB =
7300 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
7301 R1->getValue(), R2->getValue()))) {
7302 if (CB->getZExtValue() == false)
7303 std::swap(R1, R2); // R1 is the minimum root now.
7305 // Make sure the root is not off by one. The returned iteration should
7306 // not be in the range, but the previous one should be. When solving
7307 // for "X*X < 5", for example, we should not return a root of 2.
7308 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
7311 if (Range.contains(R1Val->getValue())) {
7312 // The next iteration must be out of the range...
7313 ConstantInt *NextVal =
7314 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1);
7316 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
7317 if (!Range.contains(R1Val->getValue()))
7318 return SE.getConstant(NextVal);
7319 return SE.getCouldNotCompute(); // Something strange happened
7322 // If R1 was not in the range, then it is a good return value. Make
7323 // sure that R1-1 WAS in the range though, just in case.
7324 ConstantInt *NextVal =
7325 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1);
7326 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
7327 if (Range.contains(R1Val->getValue()))
7329 return SE.getCouldNotCompute(); // Something strange happened
7334 return SE.getCouldNotCompute();
7340 FindUndefs() : Found(false) {}
7342 bool follow(const SCEV *S) {
7343 if (const SCEVUnknown *C = dyn_cast<SCEVUnknown>(S)) {
7344 if (isa<UndefValue>(C->getValue()))
7346 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) {
7347 if (isa<UndefValue>(C->getValue()))
7351 // Keep looking if we haven't found it yet.
7354 bool isDone() const {
7355 // Stop recursion if we have found an undef.
7361 // Return true when S contains at least an undef value.
7363 containsUndefs(const SCEV *S) {
7365 SCEVTraversal<FindUndefs> ST(F);
7372 // Collect all steps of SCEV expressions.
7373 struct SCEVCollectStrides {
7374 ScalarEvolution &SE;
7375 SmallVectorImpl<const SCEV *> &Strides;
7377 SCEVCollectStrides(ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &S)
7378 : SE(SE), Strides(S) {}
7380 bool follow(const SCEV *S) {
7381 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(S))
7382 Strides.push_back(AR->getStepRecurrence(SE));
7385 bool isDone() const { return false; }
7388 // Collect all SCEVUnknown and SCEVMulExpr expressions.
7389 struct SCEVCollectTerms {
7390 SmallVectorImpl<const SCEV *> &Terms;
7392 SCEVCollectTerms(SmallVectorImpl<const SCEV *> &T)
7395 bool follow(const SCEV *S) {
7396 if (isa<SCEVUnknown>(S) || isa<SCEVMulExpr>(S)) {
7397 if (!containsUndefs(S))
7400 // Stop recursion: once we collected a term, do not walk its operands.
7407 bool isDone() const { return false; }
7411 /// Find parametric terms in this SCEVAddRecExpr.
7412 void SCEVAddRecExpr::collectParametricTerms(
7413 ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &Terms) const {
7414 SmallVector<const SCEV *, 4> Strides;
7415 SCEVCollectStrides StrideCollector(SE, Strides);
7416 visitAll(this, StrideCollector);
7419 dbgs() << "Strides:\n";
7420 for (const SCEV *S : Strides)
7421 dbgs() << *S << "\n";
7424 for (const SCEV *S : Strides) {
7425 SCEVCollectTerms TermCollector(Terms);
7426 visitAll(S, TermCollector);
7430 dbgs() << "Terms:\n";
7431 for (const SCEV *T : Terms)
7432 dbgs() << *T << "\n";
7436 static bool findArrayDimensionsRec(ScalarEvolution &SE,
7437 SmallVectorImpl<const SCEV *> &Terms,
7438 SmallVectorImpl<const SCEV *> &Sizes) {
7439 int Last = Terms.size() - 1;
7440 const SCEV *Step = Terms[Last];
7442 // End of recursion.
7444 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Step)) {
7445 SmallVector<const SCEV *, 2> Qs;
7446 for (const SCEV *Op : M->operands())
7447 if (!isa<SCEVConstant>(Op))
7450 Step = SE.getMulExpr(Qs);
7453 Sizes.push_back(Step);
7457 for (const SCEV *&Term : Terms) {
7458 // Normalize the terms before the next call to findArrayDimensionsRec.
7460 SCEVSDivision::divide(SE, Term, Step, &Q, &R);
7462 // Bail out when GCD does not evenly divide one of the terms.
7469 // Remove all SCEVConstants.
7470 Terms.erase(std::remove_if(Terms.begin(), Terms.end(), [](const SCEV *E) {
7471 return isa<SCEVConstant>(E);
7475 if (Terms.size() > 0)
7476 if (!findArrayDimensionsRec(SE, Terms, Sizes))
7479 Sizes.push_back(Step);
7484 struct FindParameter {
7485 bool FoundParameter;
7486 FindParameter() : FoundParameter(false) {}
7488 bool follow(const SCEV *S) {
7489 if (isa<SCEVUnknown>(S)) {
7490 FoundParameter = true;
7491 // Stop recursion: we found a parameter.
7497 bool isDone() const {
7498 // Stop recursion if we have found a parameter.
7499 return FoundParameter;
7504 // Returns true when S contains at least a SCEVUnknown parameter.
7506 containsParameters(const SCEV *S) {
7508 SCEVTraversal<FindParameter> ST(F);
7511 return F.FoundParameter;
7514 // Returns true when one of the SCEVs of Terms contains a SCEVUnknown parameter.
7516 containsParameters(SmallVectorImpl<const SCEV *> &Terms) {
7517 for (const SCEV *T : Terms)
7518 if (containsParameters(T))
7523 // Return the number of product terms in S.
7524 static inline int numberOfTerms(const SCEV *S) {
7525 if (const SCEVMulExpr *Expr = dyn_cast<SCEVMulExpr>(S))
7526 return Expr->getNumOperands();
7530 static const SCEV *removeConstantFactors(ScalarEvolution &SE, const SCEV *T) {
7531 if (isa<SCEVConstant>(T))
7534 if (isa<SCEVUnknown>(T))
7537 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(T)) {
7538 SmallVector<const SCEV *, 2> Factors;
7539 for (const SCEV *Op : M->operands())
7540 if (!isa<SCEVConstant>(Op))
7541 Factors.push_back(Op);
7543 return SE.getMulExpr(Factors);
7549 /// Return the size of an element read or written by Inst.
7550 const SCEV *ScalarEvolution::getElementSize(Instruction *Inst) {
7552 if (StoreInst *Store = dyn_cast<StoreInst>(Inst))
7553 Ty = Store->getValueOperand()->getType();
7554 else if (LoadInst *Load = dyn_cast<LoadInst>(Inst))
7555 Ty = Load->getType();
7559 Type *ETy = getEffectiveSCEVType(PointerType::getUnqual(Ty));
7560 return getSizeOfExpr(ETy, Ty);
7563 /// Second step of delinearization: compute the array dimensions Sizes from the
7564 /// set of Terms extracted from the memory access function of this SCEVAddRec.
7565 void ScalarEvolution::findArrayDimensions(SmallVectorImpl<const SCEV *> &Terms,
7566 SmallVectorImpl<const SCEV *> &Sizes,
7567 const SCEV *ElementSize) const {
7569 if (Terms.size() < 1 || !ElementSize)
7572 // Early return when Terms do not contain parameters: we do not delinearize
7573 // non parametric SCEVs.
7574 if (!containsParameters(Terms))
7578 dbgs() << "Terms:\n";
7579 for (const SCEV *T : Terms)
7580 dbgs() << *T << "\n";
7583 // Remove duplicates.
7584 std::sort(Terms.begin(), Terms.end());
7585 Terms.erase(std::unique(Terms.begin(), Terms.end()), Terms.end());
7587 // Put larger terms first.
7588 std::sort(Terms.begin(), Terms.end(), [](const SCEV *LHS, const SCEV *RHS) {
7589 return numberOfTerms(LHS) > numberOfTerms(RHS);
7592 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
7594 // Divide all terms by the element size.
7595 for (const SCEV *&Term : Terms) {
7597 SCEVSDivision::divide(SE, Term, ElementSize, &Q, &R);
7601 SmallVector<const SCEV *, 4> NewTerms;
7603 // Remove constant factors.
7604 for (const SCEV *T : Terms)
7605 if (const SCEV *NewT = removeConstantFactors(SE, T))
7606 NewTerms.push_back(NewT);
7609 dbgs() << "Terms after sorting:\n";
7610 for (const SCEV *T : NewTerms)
7611 dbgs() << *T << "\n";
7614 if (NewTerms.empty() ||
7615 !findArrayDimensionsRec(SE, NewTerms, Sizes)) {
7620 // The last element to be pushed into Sizes is the size of an element.
7621 Sizes.push_back(ElementSize);
7624 dbgs() << "Sizes:\n";
7625 for (const SCEV *S : Sizes)
7626 dbgs() << *S << "\n";
7630 /// Third step of delinearization: compute the access functions for the
7631 /// Subscripts based on the dimensions in Sizes.
7632 void SCEVAddRecExpr::computeAccessFunctions(
7633 ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &Subscripts,
7634 SmallVectorImpl<const SCEV *> &Sizes) const {
7636 // Early exit in case this SCEV is not an affine multivariate function.
7637 if (Sizes.empty() || !this->isAffine())
7640 const SCEV *Res = this;
7641 int Last = Sizes.size() - 1;
7642 for (int i = Last; i >= 0; i--) {
7644 SCEVSDivision::divide(SE, Res, Sizes[i], &Q, &R);
7647 dbgs() << "Res: " << *Res << "\n";
7648 dbgs() << "Sizes[i]: " << *Sizes[i] << "\n";
7649 dbgs() << "Res divided by Sizes[i]:\n";
7650 dbgs() << "Quotient: " << *Q << "\n";
7651 dbgs() << "Remainder: " << *R << "\n";
7656 // Do not record the last subscript corresponding to the size of elements in
7660 // Bail out if the remainder is too complex.
7661 if (isa<SCEVAddRecExpr>(R)) {
7670 // Record the access function for the current subscript.
7671 Subscripts.push_back(R);
7674 // Also push in last position the remainder of the last division: it will be
7675 // the access function of the innermost dimension.
7676 Subscripts.push_back(Res);
7678 std::reverse(Subscripts.begin(), Subscripts.end());
7681 dbgs() << "Subscripts:\n";
7682 for (const SCEV *S : Subscripts)
7683 dbgs() << *S << "\n";
7687 /// Splits the SCEV into two vectors of SCEVs representing the subscripts and
7688 /// sizes of an array access. Returns the remainder of the delinearization that
7689 /// is the offset start of the array. The SCEV->delinearize algorithm computes
7690 /// the multiples of SCEV coefficients: that is a pattern matching of sub
7691 /// expressions in the stride and base of a SCEV corresponding to the
7692 /// computation of a GCD (greatest common divisor) of base and stride. When
7693 /// SCEV->delinearize fails, it returns the SCEV unchanged.
7695 /// For example: when analyzing the memory access A[i][j][k] in this loop nest
7697 /// void foo(long n, long m, long o, double A[n][m][o]) {
7699 /// for (long i = 0; i < n; i++)
7700 /// for (long j = 0; j < m; j++)
7701 /// for (long k = 0; k < o; k++)
7702 /// A[i][j][k] = 1.0;
7705 /// the delinearization input is the following AddRec SCEV:
7707 /// AddRec: {{{%A,+,(8 * %m * %o)}<%for.i>,+,(8 * %o)}<%for.j>,+,8}<%for.k>
7709 /// From this SCEV, we are able to say that the base offset of the access is %A
7710 /// because it appears as an offset that does not divide any of the strides in
7713 /// CHECK: Base offset: %A
7715 /// and then SCEV->delinearize determines the size of some of the dimensions of
7716 /// the array as these are the multiples by which the strides are happening:
7718 /// CHECK: ArrayDecl[UnknownSize][%m][%o] with elements of sizeof(double) bytes.
7720 /// Note that the outermost dimension remains of UnknownSize because there are
7721 /// no strides that would help identifying the size of the last dimension: when
7722 /// the array has been statically allocated, one could compute the size of that
7723 /// dimension by dividing the overall size of the array by the size of the known
7724 /// dimensions: %m * %o * 8.
7726 /// Finally delinearize provides the access functions for the array reference
7727 /// that does correspond to A[i][j][k] of the above C testcase:
7729 /// CHECK: ArrayRef[{0,+,1}<%for.i>][{0,+,1}<%for.j>][{0,+,1}<%for.k>]
7731 /// The testcases are checking the output of a function pass:
7732 /// DelinearizationPass that walks through all loads and stores of a function
7733 /// asking for the SCEV of the memory access with respect to all enclosing
7734 /// loops, calling SCEV->delinearize on that and printing the results.
7736 void SCEVAddRecExpr::delinearize(ScalarEvolution &SE,
7737 SmallVectorImpl<const SCEV *> &Subscripts,
7738 SmallVectorImpl<const SCEV *> &Sizes,
7739 const SCEV *ElementSize) const {
7740 // First step: collect parametric terms.
7741 SmallVector<const SCEV *, 4> Terms;
7742 collectParametricTerms(SE, Terms);
7747 // Second step: find subscript sizes.
7748 SE.findArrayDimensions(Terms, Sizes, ElementSize);
7753 // Third step: compute the access functions for each subscript.
7754 computeAccessFunctions(SE, Subscripts, Sizes);
7756 if (Subscripts.empty())
7760 dbgs() << "succeeded to delinearize " << *this << "\n";
7761 dbgs() << "ArrayDecl[UnknownSize]";
7762 for (const SCEV *S : Sizes)
7763 dbgs() << "[" << *S << "]";
7765 dbgs() << "\nArrayRef";
7766 for (const SCEV *S : Subscripts)
7767 dbgs() << "[" << *S << "]";
7772 //===----------------------------------------------------------------------===//
7773 // SCEVCallbackVH Class Implementation
7774 //===----------------------------------------------------------------------===//
7776 void ScalarEvolution::SCEVCallbackVH::deleted() {
7777 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
7778 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
7779 SE->ConstantEvolutionLoopExitValue.erase(PN);
7780 SE->ValueExprMap.erase(getValPtr());
7781 // this now dangles!
7784 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) {
7785 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
7787 // Forget all the expressions associated with users of the old value,
7788 // so that future queries will recompute the expressions using the new
7790 Value *Old = getValPtr();
7791 SmallVector<User *, 16> Worklist(Old->user_begin(), Old->user_end());
7792 SmallPtrSet<User *, 8> Visited;
7793 while (!Worklist.empty()) {
7794 User *U = Worklist.pop_back_val();
7795 // Deleting the Old value will cause this to dangle. Postpone
7796 // that until everything else is done.
7799 if (!Visited.insert(U).second)
7801 if (PHINode *PN = dyn_cast<PHINode>(U))
7802 SE->ConstantEvolutionLoopExitValue.erase(PN);
7803 SE->ValueExprMap.erase(U);
7804 Worklist.insert(Worklist.end(), U->user_begin(), U->user_end());
7806 // Delete the Old value.
7807 if (PHINode *PN = dyn_cast<PHINode>(Old))
7808 SE->ConstantEvolutionLoopExitValue.erase(PN);
7809 SE->ValueExprMap.erase(Old);
7810 // this now dangles!
7813 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
7814 : CallbackVH(V), SE(se) {}
7816 //===----------------------------------------------------------------------===//
7817 // ScalarEvolution Class Implementation
7818 //===----------------------------------------------------------------------===//
7820 ScalarEvolution::ScalarEvolution()
7821 : FunctionPass(ID), ValuesAtScopes(64), LoopDispositions(64),
7822 BlockDispositions(64), FirstUnknown(nullptr) {
7823 initializeScalarEvolutionPass(*PassRegistry::getPassRegistry());
7826 bool ScalarEvolution::runOnFunction(Function &F) {
7828 AT = &getAnalysis<AssumptionTracker>();
7829 LI = &getAnalysis<LoopInfo>();
7830 DataLayoutPass *DLP = getAnalysisIfAvailable<DataLayoutPass>();
7831 DL = DLP ? &DLP->getDataLayout() : nullptr;
7832 TLI = &getAnalysis<TargetLibraryInfo>();
7833 DT = &getAnalysis<DominatorTreeWrapperPass>().getDomTree();
7837 void ScalarEvolution::releaseMemory() {
7838 // Iterate through all the SCEVUnknown instances and call their
7839 // destructors, so that they release their references to their values.
7840 for (SCEVUnknown *U = FirstUnknown; U; U = U->Next)
7842 FirstUnknown = nullptr;
7844 ValueExprMap.clear();
7846 // Free any extra memory created for ExitNotTakenInfo in the unlikely event
7847 // that a loop had multiple computable exits.
7848 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
7849 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end();
7854 assert(PendingLoopPredicates.empty() && "isImpliedCond garbage");
7856 BackedgeTakenCounts.clear();
7857 ConstantEvolutionLoopExitValue.clear();
7858 ValuesAtScopes.clear();
7859 LoopDispositions.clear();
7860 BlockDispositions.clear();
7861 UnsignedRanges.clear();
7862 SignedRanges.clear();
7863 UniqueSCEVs.clear();
7864 SCEVAllocator.Reset();
7867 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
7868 AU.setPreservesAll();
7869 AU.addRequired<AssumptionTracker>();
7870 AU.addRequiredTransitive<LoopInfo>();
7871 AU.addRequiredTransitive<DominatorTreeWrapperPass>();
7872 AU.addRequired<TargetLibraryInfo>();
7875 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
7876 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
7879 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
7881 // Print all inner loops first
7882 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
7883 PrintLoopInfo(OS, SE, *I);
7886 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
7889 SmallVector<BasicBlock *, 8> ExitBlocks;
7890 L->getExitBlocks(ExitBlocks);
7891 if (ExitBlocks.size() != 1)
7892 OS << "<multiple exits> ";
7894 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
7895 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
7897 OS << "Unpredictable backedge-taken count. ";
7902 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
7905 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
7906 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
7908 OS << "Unpredictable max backedge-taken count. ";
7914 void ScalarEvolution::print(raw_ostream &OS, const Module *) const {
7915 // ScalarEvolution's implementation of the print method is to print
7916 // out SCEV values of all instructions that are interesting. Doing
7917 // this potentially causes it to create new SCEV objects though,
7918 // which technically conflicts with the const qualifier. This isn't
7919 // observable from outside the class though, so casting away the
7920 // const isn't dangerous.
7921 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
7923 OS << "Classifying expressions for: ";
7924 F->printAsOperand(OS, /*PrintType=*/false);
7926 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
7927 if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) {
7930 const SCEV *SV = SE.getSCEV(&*I);
7933 const Loop *L = LI->getLoopFor((*I).getParent());
7935 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
7942 OS << "\t\t" "Exits: ";
7943 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
7944 if (!SE.isLoopInvariant(ExitValue, L)) {
7945 OS << "<<Unknown>>";
7954 OS << "Determining loop execution counts for: ";
7955 F->printAsOperand(OS, /*PrintType=*/false);
7957 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
7958 PrintLoopInfo(OS, &SE, *I);
7961 ScalarEvolution::LoopDisposition
7962 ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) {
7963 SmallVector<std::pair<const Loop *, LoopDisposition>, 2> &Values = LoopDispositions[S];
7964 for (unsigned u = 0; u < Values.size(); u++) {
7965 if (Values[u].first == L)
7966 return Values[u].second;
7968 Values.push_back(std::make_pair(L, LoopVariant));
7969 LoopDisposition D = computeLoopDisposition(S, L);
7970 SmallVector<std::pair<const Loop *, LoopDisposition>, 2> &Values2 = LoopDispositions[S];
7971 for (unsigned u = Values2.size(); u > 0; u--) {
7972 if (Values2[u - 1].first == L) {
7973 Values2[u - 1].second = D;
7980 ScalarEvolution::LoopDisposition
7981 ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) {
7982 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
7984 return LoopInvariant;
7988 return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L);
7989 case scAddRecExpr: {
7990 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
7992 // If L is the addrec's loop, it's computable.
7993 if (AR->getLoop() == L)
7994 return LoopComputable;
7996 // Add recurrences are never invariant in the function-body (null loop).
8000 // This recurrence is variant w.r.t. L if L contains AR's loop.
8001 if (L->contains(AR->getLoop()))
8004 // This recurrence is invariant w.r.t. L if AR's loop contains L.
8005 if (AR->getLoop()->contains(L))
8006 return LoopInvariant;
8008 // This recurrence is variant w.r.t. L if any of its operands
8010 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
8012 if (!isLoopInvariant(*I, L))
8015 // Otherwise it's loop-invariant.
8016 return LoopInvariant;
8022 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
8023 bool HasVarying = false;
8024 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
8026 LoopDisposition D = getLoopDisposition(*I, L);
8027 if (D == LoopVariant)
8029 if (D == LoopComputable)
8032 return HasVarying ? LoopComputable : LoopInvariant;
8035 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
8036 LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L);
8037 if (LD == LoopVariant)
8039 LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L);
8040 if (RD == LoopVariant)
8042 return (LD == LoopInvariant && RD == LoopInvariant) ?
8043 LoopInvariant : LoopComputable;
8046 // All non-instruction values are loop invariant. All instructions are loop
8047 // invariant if they are not contained in the specified loop.
8048 // Instructions are never considered invariant in the function body
8049 // (null loop) because they are defined within the "loop".
8050 if (Instruction *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue()))
8051 return (L && !L->contains(I)) ? LoopInvariant : LoopVariant;
8052 return LoopInvariant;
8053 case scCouldNotCompute:
8054 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
8056 llvm_unreachable("Unknown SCEV kind!");
8059 bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) {
8060 return getLoopDisposition(S, L) == LoopInvariant;
8063 bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) {
8064 return getLoopDisposition(S, L) == LoopComputable;
8067 ScalarEvolution::BlockDisposition
8068 ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) {
8069 SmallVector<std::pair<const BasicBlock *, BlockDisposition>, 2> &Values = BlockDispositions[S];
8070 for (unsigned u = 0; u < Values.size(); u++) {
8071 if (Values[u].first == BB)
8072 return Values[u].second;
8074 Values.push_back(std::make_pair(BB, DoesNotDominateBlock));
8075 BlockDisposition D = computeBlockDisposition(S, BB);
8076 SmallVector<std::pair<const BasicBlock *, BlockDisposition>, 2> &Values2 = BlockDispositions[S];
8077 for (unsigned u = Values2.size(); u > 0; u--) {
8078 if (Values2[u - 1].first == BB) {
8079 Values2[u - 1].second = D;
8086 ScalarEvolution::BlockDisposition
8087 ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) {
8088 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
8090 return ProperlyDominatesBlock;
8094 return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB);
8095 case scAddRecExpr: {
8096 // This uses a "dominates" query instead of "properly dominates" query
8097 // to test for proper dominance too, because the instruction which
8098 // produces the addrec's value is a PHI, and a PHI effectively properly
8099 // dominates its entire containing block.
8100 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
8101 if (!DT->dominates(AR->getLoop()->getHeader(), BB))
8102 return DoesNotDominateBlock;
8104 // FALL THROUGH into SCEVNAryExpr handling.
8109 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
8111 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
8113 BlockDisposition D = getBlockDisposition(*I, BB);
8114 if (D == DoesNotDominateBlock)
8115 return DoesNotDominateBlock;
8116 if (D == DominatesBlock)
8119 return Proper ? ProperlyDominatesBlock : DominatesBlock;
8122 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
8123 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
8124 BlockDisposition LD = getBlockDisposition(LHS, BB);
8125 if (LD == DoesNotDominateBlock)
8126 return DoesNotDominateBlock;
8127 BlockDisposition RD = getBlockDisposition(RHS, BB);
8128 if (RD == DoesNotDominateBlock)
8129 return DoesNotDominateBlock;
8130 return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ?
8131 ProperlyDominatesBlock : DominatesBlock;
8134 if (Instruction *I =
8135 dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) {
8136 if (I->getParent() == BB)
8137 return DominatesBlock;
8138 if (DT->properlyDominates(I->getParent(), BB))
8139 return ProperlyDominatesBlock;
8140 return DoesNotDominateBlock;
8142 return ProperlyDominatesBlock;
8143 case scCouldNotCompute:
8144 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
8146 llvm_unreachable("Unknown SCEV kind!");
8149 bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) {
8150 return getBlockDisposition(S, BB) >= DominatesBlock;
8153 bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) {
8154 return getBlockDisposition(S, BB) == ProperlyDominatesBlock;
8158 // Search for a SCEV expression node within an expression tree.
8159 // Implements SCEVTraversal::Visitor.
8164 SCEVSearch(const SCEV *N): Node(N), IsFound(false) {}
8166 bool follow(const SCEV *S) {
8167 IsFound |= (S == Node);
8170 bool isDone() const { return IsFound; }
8174 bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const {
8175 SCEVSearch Search(Op);
8176 visitAll(S, Search);
8177 return Search.IsFound;
8180 void ScalarEvolution::forgetMemoizedResults(const SCEV *S) {
8181 ValuesAtScopes.erase(S);
8182 LoopDispositions.erase(S);
8183 BlockDispositions.erase(S);
8184 UnsignedRanges.erase(S);
8185 SignedRanges.erase(S);
8187 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
8188 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end(); I != E; ) {
8189 BackedgeTakenInfo &BEInfo = I->second;
8190 if (BEInfo.hasOperand(S, this)) {
8192 BackedgeTakenCounts.erase(I++);
8199 typedef DenseMap<const Loop *, std::string> VerifyMap;
8201 /// replaceSubString - Replaces all occurrences of From in Str with To.
8202 static void replaceSubString(std::string &Str, StringRef From, StringRef To) {
8204 while ((Pos = Str.find(From, Pos)) != std::string::npos) {
8205 Str.replace(Pos, From.size(), To.data(), To.size());
8210 /// getLoopBackedgeTakenCounts - Helper method for verifyAnalysis.
8212 getLoopBackedgeTakenCounts(Loop *L, VerifyMap &Map, ScalarEvolution &SE) {
8213 for (Loop::reverse_iterator I = L->rbegin(), E = L->rend(); I != E; ++I) {
8214 getLoopBackedgeTakenCounts(*I, Map, SE); // recurse.
8216 std::string &S = Map[L];
8218 raw_string_ostream OS(S);
8219 SE.getBackedgeTakenCount(L)->print(OS);
8221 // false and 0 are semantically equivalent. This can happen in dead loops.
8222 replaceSubString(OS.str(), "false", "0");
8223 // Remove wrap flags, their use in SCEV is highly fragile.
8224 // FIXME: Remove this when SCEV gets smarter about them.
8225 replaceSubString(OS.str(), "<nw>", "");
8226 replaceSubString(OS.str(), "<nsw>", "");
8227 replaceSubString(OS.str(), "<nuw>", "");
8232 void ScalarEvolution::verifyAnalysis() const {
8236 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
8238 // Gather stringified backedge taken counts for all loops using SCEV's caches.
8239 // FIXME: It would be much better to store actual values instead of strings,
8240 // but SCEV pointers will change if we drop the caches.
8241 VerifyMap BackedgeDumpsOld, BackedgeDumpsNew;
8242 for (LoopInfo::reverse_iterator I = LI->rbegin(), E = LI->rend(); I != E; ++I)
8243 getLoopBackedgeTakenCounts(*I, BackedgeDumpsOld, SE);
8245 // Gather stringified backedge taken counts for all loops without using
8248 for (LoopInfo::reverse_iterator I = LI->rbegin(), E = LI->rend(); I != E; ++I)
8249 getLoopBackedgeTakenCounts(*I, BackedgeDumpsNew, SE);
8251 // Now compare whether they're the same with and without caches. This allows
8252 // verifying that no pass changed the cache.
8253 assert(BackedgeDumpsOld.size() == BackedgeDumpsNew.size() &&
8254 "New loops suddenly appeared!");
8256 for (VerifyMap::iterator OldI = BackedgeDumpsOld.begin(),
8257 OldE = BackedgeDumpsOld.end(),
8258 NewI = BackedgeDumpsNew.begin();
8259 OldI != OldE; ++OldI, ++NewI) {
8260 assert(OldI->first == NewI->first && "Loop order changed!");
8262 // Compare the stringified SCEVs. We don't care if undef backedgetaken count
8264 // FIXME: We currently ignore SCEV changes from/to CouldNotCompute. This
8265 // means that a pass is buggy or SCEV has to learn a new pattern but is
8266 // usually not harmful.
8267 if (OldI->second != NewI->second &&
8268 OldI->second.find("undef") == std::string::npos &&
8269 NewI->second.find("undef") == std::string::npos &&
8270 OldI->second != "***COULDNOTCOMPUTE***" &&
8271 NewI->second != "***COULDNOTCOMPUTE***") {
8272 dbgs() << "SCEVValidator: SCEV for loop '"
8273 << OldI->first->getHeader()->getName()
8274 << "' changed from '" << OldI->second
8275 << "' to '" << NewI->second << "'!\n";
8280 // TODO: Verify more things.