1 //===- ScalarEvolution.cpp - Scalar Evolution Analysis --------------------===//
3 // The LLVM Compiler Infrastructure
5 // This file is distributed under the University of Illinois Open Source
6 // License. See LICENSE.TXT for details.
8 //===----------------------------------------------------------------------===//
10 // This file contains the implementation of the scalar evolution analysis
11 // engine, which is used primarily to analyze expressions involving induction
12 // variables in loops.
14 // There are several aspects to this library. First is the representation of
15 // scalar expressions, which are represented as subclasses of the SCEV class.
16 // These classes are used to represent certain types of subexpressions that we
17 // can handle. We only create one SCEV of a particular shape, so
18 // pointer-comparisons for equality are legal.
20 // One important aspect of the SCEV objects is that they are never cyclic, even
21 // if there is a cycle in the dataflow for an expression (ie, a PHI node). If
22 // the PHI node is one of the idioms that we can represent (e.g., a polynomial
23 // recurrence) then we represent it directly as a recurrence node, otherwise we
24 // represent it as a SCEVUnknown node.
26 // In addition to being able to represent expressions of various types, we also
27 // have folders that are used to build the *canonical* representation for a
28 // particular expression. These folders are capable of using a variety of
29 // rewrite rules to simplify the expressions.
31 // Once the folders are defined, we can implement the more interesting
32 // higher-level code, such as the code that recognizes PHI nodes of various
33 // types, computes the execution count of a loop, etc.
35 // TODO: We should use these routines and value representations to implement
36 // dependence analysis!
38 //===----------------------------------------------------------------------===//
40 // There are several good references for the techniques used in this analysis.
42 // Chains of recurrences -- a method to expedite the evaluation
43 // of closed-form functions
44 // Olaf Bachmann, Paul S. Wang, Eugene V. Zima
46 // On computational properties of chains of recurrences
49 // Symbolic Evaluation of Chains of Recurrences for Loop Optimization
50 // Robert A. van Engelen
52 // Efficient Symbolic Analysis for Optimizing Compilers
53 // Robert A. van Engelen
55 // Using the chains of recurrences algebra for data dependence testing and
56 // induction variable substitution
57 // MS Thesis, Johnie Birch
59 //===----------------------------------------------------------------------===//
61 #include "llvm/Analysis/ScalarEvolution.h"
62 #include "llvm/ADT/Optional.h"
63 #include "llvm/ADT/STLExtras.h"
64 #include "llvm/ADT/SmallPtrSet.h"
65 #include "llvm/ADT/Statistic.h"
66 #include "llvm/Analysis/AssumptionCache.h"
67 #include "llvm/Analysis/ConstantFolding.h"
68 #include "llvm/Analysis/InstructionSimplify.h"
69 #include "llvm/Analysis/LoopInfo.h"
70 #include "llvm/Analysis/ScalarEvolutionExpressions.h"
71 #include "llvm/Analysis/TargetLibraryInfo.h"
72 #include "llvm/Analysis/ValueTracking.h"
73 #include "llvm/IR/ConstantRange.h"
74 #include "llvm/IR/Constants.h"
75 #include "llvm/IR/DataLayout.h"
76 #include "llvm/IR/DerivedTypes.h"
77 #include "llvm/IR/Dominators.h"
78 #include "llvm/IR/GetElementPtrTypeIterator.h"
79 #include "llvm/IR/GlobalAlias.h"
80 #include "llvm/IR/GlobalVariable.h"
81 #include "llvm/IR/InstIterator.h"
82 #include "llvm/IR/Instructions.h"
83 #include "llvm/IR/LLVMContext.h"
84 #include "llvm/IR/Metadata.h"
85 #include "llvm/IR/Operator.h"
86 #include "llvm/Support/CommandLine.h"
87 #include "llvm/Support/Debug.h"
88 #include "llvm/Support/ErrorHandling.h"
89 #include "llvm/Support/MathExtras.h"
90 #include "llvm/Support/raw_ostream.h"
94 #define DEBUG_TYPE "scalar-evolution"
96 STATISTIC(NumArrayLenItCounts,
97 "Number of trip counts computed with array length");
98 STATISTIC(NumTripCountsComputed,
99 "Number of loops with predictable loop counts");
100 STATISTIC(NumTripCountsNotComputed,
101 "Number of loops without predictable loop counts");
102 STATISTIC(NumBruteForceTripCountsComputed,
103 "Number of loops with trip counts computed by force");
105 static cl::opt<unsigned>
106 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
107 cl::desc("Maximum number of iterations SCEV will "
108 "symbolically execute a constant "
112 // FIXME: Enable this with XDEBUG when the test suite is clean.
114 VerifySCEV("verify-scev",
115 cl::desc("Verify ScalarEvolution's backedge taken counts (slow)"));
117 INITIALIZE_PASS_BEGIN(ScalarEvolution, "scalar-evolution",
118 "Scalar Evolution Analysis", false, true)
119 INITIALIZE_PASS_DEPENDENCY(AssumptionCacheTracker)
120 INITIALIZE_PASS_DEPENDENCY(LoopInfoWrapperPass)
121 INITIALIZE_PASS_DEPENDENCY(DominatorTreeWrapperPass)
122 INITIALIZE_PASS_DEPENDENCY(TargetLibraryInfoWrapperPass)
123 INITIALIZE_PASS_END(ScalarEvolution, "scalar-evolution",
124 "Scalar Evolution Analysis", false, true)
125 char ScalarEvolution::ID = 0;
127 //===----------------------------------------------------------------------===//
128 // SCEV class definitions
129 //===----------------------------------------------------------------------===//
131 //===----------------------------------------------------------------------===//
132 // Implementation of the SCEV class.
135 #if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP)
136 void SCEV::dump() const {
142 void SCEV::print(raw_ostream &OS) const {
143 switch (static_cast<SCEVTypes>(getSCEVType())) {
145 cast<SCEVConstant>(this)->getValue()->printAsOperand(OS, false);
148 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(this);
149 const SCEV *Op = Trunc->getOperand();
150 OS << "(trunc " << *Op->getType() << " " << *Op << " to "
151 << *Trunc->getType() << ")";
155 const SCEVZeroExtendExpr *ZExt = cast<SCEVZeroExtendExpr>(this);
156 const SCEV *Op = ZExt->getOperand();
157 OS << "(zext " << *Op->getType() << " " << *Op << " to "
158 << *ZExt->getType() << ")";
162 const SCEVSignExtendExpr *SExt = cast<SCEVSignExtendExpr>(this);
163 const SCEV *Op = SExt->getOperand();
164 OS << "(sext " << *Op->getType() << " " << *Op << " to "
165 << *SExt->getType() << ")";
169 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(this);
170 OS << "{" << *AR->getOperand(0);
171 for (unsigned i = 1, e = AR->getNumOperands(); i != e; ++i)
172 OS << ",+," << *AR->getOperand(i);
174 if (AR->getNoWrapFlags(FlagNUW))
176 if (AR->getNoWrapFlags(FlagNSW))
178 if (AR->getNoWrapFlags(FlagNW) &&
179 !AR->getNoWrapFlags((NoWrapFlags)(FlagNUW | FlagNSW)))
181 AR->getLoop()->getHeader()->printAsOperand(OS, /*PrintType=*/false);
189 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(this);
190 const char *OpStr = nullptr;
191 switch (NAry->getSCEVType()) {
192 case scAddExpr: OpStr = " + "; break;
193 case scMulExpr: OpStr = " * "; break;
194 case scUMaxExpr: OpStr = " umax "; break;
195 case scSMaxExpr: OpStr = " smax "; break;
198 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
201 if (std::next(I) != E)
205 switch (NAry->getSCEVType()) {
208 if (NAry->getNoWrapFlags(FlagNUW))
210 if (NAry->getNoWrapFlags(FlagNSW))
216 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(this);
217 OS << "(" << *UDiv->getLHS() << " /u " << *UDiv->getRHS() << ")";
221 const SCEVUnknown *U = cast<SCEVUnknown>(this);
223 if (U->isSizeOf(AllocTy)) {
224 OS << "sizeof(" << *AllocTy << ")";
227 if (U->isAlignOf(AllocTy)) {
228 OS << "alignof(" << *AllocTy << ")";
234 if (U->isOffsetOf(CTy, FieldNo)) {
235 OS << "offsetof(" << *CTy << ", ";
236 FieldNo->printAsOperand(OS, false);
241 // Otherwise just print it normally.
242 U->getValue()->printAsOperand(OS, false);
245 case scCouldNotCompute:
246 OS << "***COULDNOTCOMPUTE***";
249 llvm_unreachable("Unknown SCEV kind!");
252 Type *SCEV::getType() const {
253 switch (static_cast<SCEVTypes>(getSCEVType())) {
255 return cast<SCEVConstant>(this)->getType();
259 return cast<SCEVCastExpr>(this)->getType();
264 return cast<SCEVNAryExpr>(this)->getType();
266 return cast<SCEVAddExpr>(this)->getType();
268 return cast<SCEVUDivExpr>(this)->getType();
270 return cast<SCEVUnknown>(this)->getType();
271 case scCouldNotCompute:
272 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
274 llvm_unreachable("Unknown SCEV kind!");
277 bool SCEV::isZero() const {
278 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
279 return SC->getValue()->isZero();
283 bool SCEV::isOne() const {
284 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
285 return SC->getValue()->isOne();
289 bool SCEV::isAllOnesValue() const {
290 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
291 return SC->getValue()->isAllOnesValue();
295 /// isNonConstantNegative - Return true if the specified scev is negated, but
297 bool SCEV::isNonConstantNegative() const {
298 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(this);
299 if (!Mul) return false;
301 // If there is a constant factor, it will be first.
302 const SCEVConstant *SC = dyn_cast<SCEVConstant>(Mul->getOperand(0));
303 if (!SC) return false;
305 // Return true if the value is negative, this matches things like (-42 * V).
306 return SC->getValue()->getValue().isNegative();
309 SCEVCouldNotCompute::SCEVCouldNotCompute() :
310 SCEV(FoldingSetNodeIDRef(), scCouldNotCompute) {}
312 bool SCEVCouldNotCompute::classof(const SCEV *S) {
313 return S->getSCEVType() == scCouldNotCompute;
316 const SCEV *ScalarEvolution::getConstant(ConstantInt *V) {
318 ID.AddInteger(scConstant);
321 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
322 SCEV *S = new (SCEVAllocator) SCEVConstant(ID.Intern(SCEVAllocator), V);
323 UniqueSCEVs.InsertNode(S, IP);
327 const SCEV *ScalarEvolution::getConstant(const APInt &Val) {
328 return getConstant(ConstantInt::get(getContext(), Val));
332 ScalarEvolution::getConstant(Type *Ty, uint64_t V, bool isSigned) {
333 IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty));
334 return getConstant(ConstantInt::get(ITy, V, isSigned));
337 SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID,
338 unsigned SCEVTy, const SCEV *op, Type *ty)
339 : SCEV(ID, SCEVTy), Op(op), Ty(ty) {}
341 SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID,
342 const SCEV *op, Type *ty)
343 : SCEVCastExpr(ID, scTruncate, op, ty) {
344 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
345 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
346 "Cannot truncate non-integer value!");
349 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID,
350 const SCEV *op, Type *ty)
351 : SCEVCastExpr(ID, scZeroExtend, op, ty) {
352 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
353 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
354 "Cannot zero extend non-integer value!");
357 SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID,
358 const SCEV *op, Type *ty)
359 : SCEVCastExpr(ID, scSignExtend, op, ty) {
360 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
361 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
362 "Cannot sign extend non-integer value!");
365 void SCEVUnknown::deleted() {
366 // Clear this SCEVUnknown from various maps.
367 SE->forgetMemoizedResults(this);
369 // Remove this SCEVUnknown from the uniquing map.
370 SE->UniqueSCEVs.RemoveNode(this);
372 // Release the value.
376 void SCEVUnknown::allUsesReplacedWith(Value *New) {
377 // Clear this SCEVUnknown from various maps.
378 SE->forgetMemoizedResults(this);
380 // Remove this SCEVUnknown from the uniquing map.
381 SE->UniqueSCEVs.RemoveNode(this);
383 // Update this SCEVUnknown to point to the new value. This is needed
384 // because there may still be outstanding SCEVs which still point to
389 bool SCEVUnknown::isSizeOf(Type *&AllocTy) const {
390 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
391 if (VCE->getOpcode() == Instruction::PtrToInt)
392 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
393 if (CE->getOpcode() == Instruction::GetElementPtr &&
394 CE->getOperand(0)->isNullValue() &&
395 CE->getNumOperands() == 2)
396 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1)))
398 AllocTy = cast<PointerType>(CE->getOperand(0)->getType())
406 bool SCEVUnknown::isAlignOf(Type *&AllocTy) const {
407 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
408 if (VCE->getOpcode() == Instruction::PtrToInt)
409 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
410 if (CE->getOpcode() == Instruction::GetElementPtr &&
411 CE->getOperand(0)->isNullValue()) {
413 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
414 if (StructType *STy = dyn_cast<StructType>(Ty))
415 if (!STy->isPacked() &&
416 CE->getNumOperands() == 3 &&
417 CE->getOperand(1)->isNullValue()) {
418 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2)))
420 STy->getNumElements() == 2 &&
421 STy->getElementType(0)->isIntegerTy(1)) {
422 AllocTy = STy->getElementType(1);
431 bool SCEVUnknown::isOffsetOf(Type *&CTy, Constant *&FieldNo) const {
432 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
433 if (VCE->getOpcode() == Instruction::PtrToInt)
434 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
435 if (CE->getOpcode() == Instruction::GetElementPtr &&
436 CE->getNumOperands() == 3 &&
437 CE->getOperand(0)->isNullValue() &&
438 CE->getOperand(1)->isNullValue()) {
440 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
441 // Ignore vector types here so that ScalarEvolutionExpander doesn't
442 // emit getelementptrs that index into vectors.
443 if (Ty->isStructTy() || Ty->isArrayTy()) {
445 FieldNo = CE->getOperand(2);
453 //===----------------------------------------------------------------------===//
455 //===----------------------------------------------------------------------===//
458 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
459 /// than the complexity of the RHS. This comparator is used to canonicalize
461 class SCEVComplexityCompare {
462 const LoopInfo *const LI;
464 explicit SCEVComplexityCompare(const LoopInfo *li) : LI(li) {}
466 // Return true or false if LHS is less than, or at least RHS, respectively.
467 bool operator()(const SCEV *LHS, const SCEV *RHS) const {
468 return compare(LHS, RHS) < 0;
471 // Return negative, zero, or positive, if LHS is less than, equal to, or
472 // greater than RHS, respectively. A three-way result allows recursive
473 // comparisons to be more efficient.
474 int compare(const SCEV *LHS, const SCEV *RHS) const {
475 // Fast-path: SCEVs are uniqued so we can do a quick equality check.
479 // Primarily, sort the SCEVs by their getSCEVType().
480 unsigned LType = LHS->getSCEVType(), RType = RHS->getSCEVType();
482 return (int)LType - (int)RType;
484 // Aside from the getSCEVType() ordering, the particular ordering
485 // isn't very important except that it's beneficial to be consistent,
486 // so that (a + b) and (b + a) don't end up as different expressions.
487 switch (static_cast<SCEVTypes>(LType)) {
489 const SCEVUnknown *LU = cast<SCEVUnknown>(LHS);
490 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
492 // Sort SCEVUnknown values with some loose heuristics. TODO: This is
493 // not as complete as it could be.
494 const Value *LV = LU->getValue(), *RV = RU->getValue();
496 // Order pointer values after integer values. This helps SCEVExpander
498 bool LIsPointer = LV->getType()->isPointerTy(),
499 RIsPointer = RV->getType()->isPointerTy();
500 if (LIsPointer != RIsPointer)
501 return (int)LIsPointer - (int)RIsPointer;
503 // Compare getValueID values.
504 unsigned LID = LV->getValueID(),
505 RID = RV->getValueID();
507 return (int)LID - (int)RID;
509 // Sort arguments by their position.
510 if (const Argument *LA = dyn_cast<Argument>(LV)) {
511 const Argument *RA = cast<Argument>(RV);
512 unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo();
513 return (int)LArgNo - (int)RArgNo;
516 // For instructions, compare their loop depth, and their operand
517 // count. This is pretty loose.
518 if (const Instruction *LInst = dyn_cast<Instruction>(LV)) {
519 const Instruction *RInst = cast<Instruction>(RV);
521 // Compare loop depths.
522 const BasicBlock *LParent = LInst->getParent(),
523 *RParent = RInst->getParent();
524 if (LParent != RParent) {
525 unsigned LDepth = LI->getLoopDepth(LParent),
526 RDepth = LI->getLoopDepth(RParent);
527 if (LDepth != RDepth)
528 return (int)LDepth - (int)RDepth;
531 // Compare the number of operands.
532 unsigned LNumOps = LInst->getNumOperands(),
533 RNumOps = RInst->getNumOperands();
534 return (int)LNumOps - (int)RNumOps;
541 const SCEVConstant *LC = cast<SCEVConstant>(LHS);
542 const SCEVConstant *RC = cast<SCEVConstant>(RHS);
544 // Compare constant values.
545 const APInt &LA = LC->getValue()->getValue();
546 const APInt &RA = RC->getValue()->getValue();
547 unsigned LBitWidth = LA.getBitWidth(), RBitWidth = RA.getBitWidth();
548 if (LBitWidth != RBitWidth)
549 return (int)LBitWidth - (int)RBitWidth;
550 return LA.ult(RA) ? -1 : 1;
554 const SCEVAddRecExpr *LA = cast<SCEVAddRecExpr>(LHS);
555 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS);
557 // Compare addrec loop depths.
558 const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop();
559 if (LLoop != RLoop) {
560 unsigned LDepth = LLoop->getLoopDepth(),
561 RDepth = RLoop->getLoopDepth();
562 if (LDepth != RDepth)
563 return (int)LDepth - (int)RDepth;
566 // Addrec complexity grows with operand count.
567 unsigned LNumOps = LA->getNumOperands(), RNumOps = RA->getNumOperands();
568 if (LNumOps != RNumOps)
569 return (int)LNumOps - (int)RNumOps;
571 // Lexicographically compare.
572 for (unsigned i = 0; i != LNumOps; ++i) {
573 long X = compare(LA->getOperand(i), RA->getOperand(i));
585 const SCEVNAryExpr *LC = cast<SCEVNAryExpr>(LHS);
586 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
588 // Lexicographically compare n-ary expressions.
589 unsigned LNumOps = LC->getNumOperands(), RNumOps = RC->getNumOperands();
590 if (LNumOps != RNumOps)
591 return (int)LNumOps - (int)RNumOps;
593 for (unsigned i = 0; i != LNumOps; ++i) {
596 long X = compare(LC->getOperand(i), RC->getOperand(i));
600 return (int)LNumOps - (int)RNumOps;
604 const SCEVUDivExpr *LC = cast<SCEVUDivExpr>(LHS);
605 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
607 // Lexicographically compare udiv expressions.
608 long X = compare(LC->getLHS(), RC->getLHS());
611 return compare(LC->getRHS(), RC->getRHS());
617 const SCEVCastExpr *LC = cast<SCEVCastExpr>(LHS);
618 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
620 // Compare cast expressions by operand.
621 return compare(LC->getOperand(), RC->getOperand());
624 case scCouldNotCompute:
625 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
627 llvm_unreachable("Unknown SCEV kind!");
632 /// GroupByComplexity - Given a list of SCEV objects, order them by their
633 /// complexity, and group objects of the same complexity together by value.
634 /// When this routine is finished, we know that any duplicates in the vector are
635 /// consecutive and that complexity is monotonically increasing.
637 /// Note that we go take special precautions to ensure that we get deterministic
638 /// results from this routine. In other words, we don't want the results of
639 /// this to depend on where the addresses of various SCEV objects happened to
642 static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops,
644 if (Ops.size() < 2) return; // Noop
645 if (Ops.size() == 2) {
646 // This is the common case, which also happens to be trivially simple.
648 const SCEV *&LHS = Ops[0], *&RHS = Ops[1];
649 if (SCEVComplexityCompare(LI)(RHS, LHS))
654 // Do the rough sort by complexity.
655 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI));
657 // Now that we are sorted by complexity, group elements of the same
658 // complexity. Note that this is, at worst, N^2, but the vector is likely to
659 // be extremely short in practice. Note that we take this approach because we
660 // do not want to depend on the addresses of the objects we are grouping.
661 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
662 const SCEV *S = Ops[i];
663 unsigned Complexity = S->getSCEVType();
665 // If there are any objects of the same complexity and same value as this
667 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
668 if (Ops[j] == S) { // Found a duplicate.
669 // Move it to immediately after i'th element.
670 std::swap(Ops[i+1], Ops[j]);
671 ++i; // no need to rescan it.
672 if (i == e-2) return; // Done!
679 struct FindSCEVSize {
681 FindSCEVSize() : Size(0) {}
683 bool follow(const SCEV *S) {
685 // Keep looking at all operands of S.
688 bool isDone() const {
694 // Returns the size of the SCEV S.
695 static inline int sizeOfSCEV(const SCEV *S) {
697 SCEVTraversal<FindSCEVSize> ST(F);
704 struct SCEVDivision : public SCEVVisitor<SCEVDivision, void> {
706 // Computes the Quotient and Remainder of the division of Numerator by
708 static void divide(ScalarEvolution &SE, const SCEV *Numerator,
709 const SCEV *Denominator, const SCEV **Quotient,
710 const SCEV **Remainder) {
711 assert(Numerator && Denominator && "Uninitialized SCEV");
713 SCEVDivision D(SE, Numerator, Denominator);
715 // Check for the trivial case here to avoid having to check for it in the
717 if (Numerator == Denominator) {
723 if (Numerator->isZero()) {
729 // Split the Denominator when it is a product.
730 if (const SCEVMulExpr *T = dyn_cast<const SCEVMulExpr>(Denominator)) {
732 *Quotient = Numerator;
733 for (const SCEV *Op : T->operands()) {
734 divide(SE, *Quotient, Op, &Q, &R);
737 // Bail out when the Numerator is not divisible by one of the terms of
741 *Remainder = Numerator;
750 *Quotient = D.Quotient;
751 *Remainder = D.Remainder;
754 // Except in the trivial case described above, we do not know how to divide
755 // Expr by Denominator for the following functions with empty implementation.
756 void visitTruncateExpr(const SCEVTruncateExpr *Numerator) {}
757 void visitZeroExtendExpr(const SCEVZeroExtendExpr *Numerator) {}
758 void visitSignExtendExpr(const SCEVSignExtendExpr *Numerator) {}
759 void visitUDivExpr(const SCEVUDivExpr *Numerator) {}
760 void visitSMaxExpr(const SCEVSMaxExpr *Numerator) {}
761 void visitUMaxExpr(const SCEVUMaxExpr *Numerator) {}
762 void visitUnknown(const SCEVUnknown *Numerator) {}
763 void visitCouldNotCompute(const SCEVCouldNotCompute *Numerator) {}
765 void visitConstant(const SCEVConstant *Numerator) {
766 if (const SCEVConstant *D = dyn_cast<SCEVConstant>(Denominator)) {
767 APInt NumeratorVal = Numerator->getValue()->getValue();
768 APInt DenominatorVal = D->getValue()->getValue();
769 uint32_t NumeratorBW = NumeratorVal.getBitWidth();
770 uint32_t DenominatorBW = DenominatorVal.getBitWidth();
772 if (NumeratorBW > DenominatorBW)
773 DenominatorVal = DenominatorVal.sext(NumeratorBW);
774 else if (NumeratorBW < DenominatorBW)
775 NumeratorVal = NumeratorVal.sext(DenominatorBW);
777 APInt QuotientVal(NumeratorVal.getBitWidth(), 0);
778 APInt RemainderVal(NumeratorVal.getBitWidth(), 0);
779 APInt::sdivrem(NumeratorVal, DenominatorVal, QuotientVal, RemainderVal);
780 Quotient = SE.getConstant(QuotientVal);
781 Remainder = SE.getConstant(RemainderVal);
786 void visitAddRecExpr(const SCEVAddRecExpr *Numerator) {
787 const SCEV *StartQ, *StartR, *StepQ, *StepR;
788 assert(Numerator->isAffine() && "Numerator should be affine");
789 divide(SE, Numerator->getStart(), Denominator, &StartQ, &StartR);
790 divide(SE, Numerator->getStepRecurrence(SE), Denominator, &StepQ, &StepR);
791 Quotient = SE.getAddRecExpr(StartQ, StepQ, Numerator->getLoop(),
792 Numerator->getNoWrapFlags());
793 Remainder = SE.getAddRecExpr(StartR, StepR, Numerator->getLoop(),
794 Numerator->getNoWrapFlags());
797 void visitAddExpr(const SCEVAddExpr *Numerator) {
798 SmallVector<const SCEV *, 2> Qs, Rs;
799 Type *Ty = Denominator->getType();
801 for (const SCEV *Op : Numerator->operands()) {
803 divide(SE, Op, Denominator, &Q, &R);
805 // Bail out if types do not match.
806 if (Ty != Q->getType() || Ty != R->getType()) {
808 Remainder = Numerator;
816 if (Qs.size() == 1) {
822 Quotient = SE.getAddExpr(Qs);
823 Remainder = SE.getAddExpr(Rs);
826 void visitMulExpr(const SCEVMulExpr *Numerator) {
827 SmallVector<const SCEV *, 2> Qs;
828 Type *Ty = Denominator->getType();
830 bool FoundDenominatorTerm = false;
831 for (const SCEV *Op : Numerator->operands()) {
832 // Bail out if types do not match.
833 if (Ty != Op->getType()) {
835 Remainder = Numerator;
839 if (FoundDenominatorTerm) {
844 // Check whether Denominator divides one of the product operands.
846 divide(SE, Op, Denominator, &Q, &R);
852 // Bail out if types do not match.
853 if (Ty != Q->getType()) {
855 Remainder = Numerator;
859 FoundDenominatorTerm = true;
863 if (FoundDenominatorTerm) {
868 Quotient = SE.getMulExpr(Qs);
872 if (!isa<SCEVUnknown>(Denominator)) {
874 Remainder = Numerator;
878 // The Remainder is obtained by replacing Denominator by 0 in Numerator.
879 ValueToValueMap RewriteMap;
880 RewriteMap[cast<SCEVUnknown>(Denominator)->getValue()] =
881 cast<SCEVConstant>(Zero)->getValue();
882 Remainder = SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true);
884 if (Remainder->isZero()) {
885 // The Quotient is obtained by replacing Denominator by 1 in Numerator.
886 RewriteMap[cast<SCEVUnknown>(Denominator)->getValue()] =
887 cast<SCEVConstant>(One)->getValue();
889 SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true);
893 // Quotient is (Numerator - Remainder) divided by Denominator.
895 const SCEV *Diff = SE.getMinusSCEV(Numerator, Remainder);
896 if (sizeOfSCEV(Diff) > sizeOfSCEV(Numerator)) {
897 // This SCEV does not seem to simplify: fail the division here.
899 Remainder = Numerator;
902 divide(SE, Diff, Denominator, &Q, &R);
904 "(Numerator - Remainder) should evenly divide Denominator");
909 SCEVDivision(ScalarEvolution &S, const SCEV *Numerator,
910 const SCEV *Denominator)
911 : SE(S), Denominator(Denominator) {
912 Zero = SE.getConstant(Denominator->getType(), 0);
913 One = SE.getConstant(Denominator->getType(), 1);
915 // By default, we don't know how to divide Expr by Denominator.
916 // Providing the default here simplifies the rest of the code.
918 Remainder = Numerator;
922 const SCEV *Denominator, *Quotient, *Remainder, *Zero, *One;
927 //===----------------------------------------------------------------------===//
928 // Simple SCEV method implementations
929 //===----------------------------------------------------------------------===//
931 /// BinomialCoefficient - Compute BC(It, K). The result has width W.
933 static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K,
936 // Handle the simplest case efficiently.
938 return SE.getTruncateOrZeroExtend(It, ResultTy);
940 // We are using the following formula for BC(It, K):
942 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
944 // Suppose, W is the bitwidth of the return value. We must be prepared for
945 // overflow. Hence, we must assure that the result of our computation is
946 // equal to the accurate one modulo 2^W. Unfortunately, division isn't
947 // safe in modular arithmetic.
949 // However, this code doesn't use exactly that formula; the formula it uses
950 // is something like the following, where T is the number of factors of 2 in
951 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
954 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
956 // This formula is trivially equivalent to the previous formula. However,
957 // this formula can be implemented much more efficiently. The trick is that
958 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
959 // arithmetic. To do exact division in modular arithmetic, all we have
960 // to do is multiply by the inverse. Therefore, this step can be done at
963 // The next issue is how to safely do the division by 2^T. The way this
964 // is done is by doing the multiplication step at a width of at least W + T
965 // bits. This way, the bottom W+T bits of the product are accurate. Then,
966 // when we perform the division by 2^T (which is equivalent to a right shift
967 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
968 // truncated out after the division by 2^T.
970 // In comparison to just directly using the first formula, this technique
971 // is much more efficient; using the first formula requires W * K bits,
972 // but this formula less than W + K bits. Also, the first formula requires
973 // a division step, whereas this formula only requires multiplies and shifts.
975 // It doesn't matter whether the subtraction step is done in the calculation
976 // width or the input iteration count's width; if the subtraction overflows,
977 // the result must be zero anyway. We prefer here to do it in the width of
978 // the induction variable because it helps a lot for certain cases; CodeGen
979 // isn't smart enough to ignore the overflow, which leads to much less
980 // efficient code if the width of the subtraction is wider than the native
983 // (It's possible to not widen at all by pulling out factors of 2 before
984 // the multiplication; for example, K=2 can be calculated as
985 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
986 // extra arithmetic, so it's not an obvious win, and it gets
987 // much more complicated for K > 3.)
989 // Protection from insane SCEVs; this bound is conservative,
990 // but it probably doesn't matter.
992 return SE.getCouldNotCompute();
994 unsigned W = SE.getTypeSizeInBits(ResultTy);
996 // Calculate K! / 2^T and T; we divide out the factors of two before
997 // multiplying for calculating K! / 2^T to avoid overflow.
998 // Other overflow doesn't matter because we only care about the bottom
999 // W bits of the result.
1000 APInt OddFactorial(W, 1);
1002 for (unsigned i = 3; i <= K; ++i) {
1004 unsigned TwoFactors = Mult.countTrailingZeros();
1006 Mult = Mult.lshr(TwoFactors);
1007 OddFactorial *= Mult;
1010 // We need at least W + T bits for the multiplication step
1011 unsigned CalculationBits = W + T;
1013 // Calculate 2^T, at width T+W.
1014 APInt DivFactor = APInt::getOneBitSet(CalculationBits, T);
1016 // Calculate the multiplicative inverse of K! / 2^T;
1017 // this multiplication factor will perform the exact division by
1019 APInt Mod = APInt::getSignedMinValue(W+1);
1020 APInt MultiplyFactor = OddFactorial.zext(W+1);
1021 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
1022 MultiplyFactor = MultiplyFactor.trunc(W);
1024 // Calculate the product, at width T+W
1025 IntegerType *CalculationTy = IntegerType::get(SE.getContext(),
1027 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
1028 for (unsigned i = 1; i != K; ++i) {
1029 const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i));
1030 Dividend = SE.getMulExpr(Dividend,
1031 SE.getTruncateOrZeroExtend(S, CalculationTy));
1035 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
1037 // Truncate the result, and divide by K! / 2^T.
1039 return SE.getMulExpr(SE.getConstant(MultiplyFactor),
1040 SE.getTruncateOrZeroExtend(DivResult, ResultTy));
1043 /// evaluateAtIteration - Return the value of this chain of recurrences at
1044 /// the specified iteration number. We can evaluate this recurrence by
1045 /// multiplying each element in the chain by the binomial coefficient
1046 /// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
1048 /// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
1050 /// where BC(It, k) stands for binomial coefficient.
1052 const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It,
1053 ScalarEvolution &SE) const {
1054 const SCEV *Result = getStart();
1055 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
1056 // The computation is correct in the face of overflow provided that the
1057 // multiplication is performed _after_ the evaluation of the binomial
1059 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType());
1060 if (isa<SCEVCouldNotCompute>(Coeff))
1063 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
1068 //===----------------------------------------------------------------------===//
1069 // SCEV Expression folder implementations
1070 //===----------------------------------------------------------------------===//
1072 const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op,
1074 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
1075 "This is not a truncating conversion!");
1076 assert(isSCEVable(Ty) &&
1077 "This is not a conversion to a SCEVable type!");
1078 Ty = getEffectiveSCEVType(Ty);
1080 FoldingSetNodeID ID;
1081 ID.AddInteger(scTruncate);
1085 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1087 // Fold if the operand is constant.
1088 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1090 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty)));
1092 // trunc(trunc(x)) --> trunc(x)
1093 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
1094 return getTruncateExpr(ST->getOperand(), Ty);
1096 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
1097 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1098 return getTruncateOrSignExtend(SS->getOperand(), Ty);
1100 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
1101 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1102 return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
1104 // trunc(x1+x2+...+xN) --> trunc(x1)+trunc(x2)+...+trunc(xN) if we can
1105 // eliminate all the truncates.
1106 if (const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Op)) {
1107 SmallVector<const SCEV *, 4> Operands;
1108 bool hasTrunc = false;
1109 for (unsigned i = 0, e = SA->getNumOperands(); i != e && !hasTrunc; ++i) {
1110 const SCEV *S = getTruncateExpr(SA->getOperand(i), Ty);
1111 hasTrunc = isa<SCEVTruncateExpr>(S);
1112 Operands.push_back(S);
1115 return getAddExpr(Operands);
1116 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL.
1119 // trunc(x1*x2*...*xN) --> trunc(x1)*trunc(x2)*...*trunc(xN) if we can
1120 // eliminate all the truncates.
1121 if (const SCEVMulExpr *SM = dyn_cast<SCEVMulExpr>(Op)) {
1122 SmallVector<const SCEV *, 4> Operands;
1123 bool hasTrunc = false;
1124 for (unsigned i = 0, e = SM->getNumOperands(); i != e && !hasTrunc; ++i) {
1125 const SCEV *S = getTruncateExpr(SM->getOperand(i), Ty);
1126 hasTrunc = isa<SCEVTruncateExpr>(S);
1127 Operands.push_back(S);
1130 return getMulExpr(Operands);
1131 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL.
1134 // If the input value is a chrec scev, truncate the chrec's operands.
1135 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
1136 SmallVector<const SCEV *, 4> Operands;
1137 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
1138 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty));
1139 return getAddRecExpr(Operands, AddRec->getLoop(), SCEV::FlagAnyWrap);
1142 // The cast wasn't folded; create an explicit cast node. We can reuse
1143 // the existing insert position since if we get here, we won't have
1144 // made any changes which would invalidate it.
1145 SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator),
1147 UniqueSCEVs.InsertNode(S, IP);
1151 const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op,
1153 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1154 "This is not an extending conversion!");
1155 assert(isSCEVable(Ty) &&
1156 "This is not a conversion to a SCEVable type!");
1157 Ty = getEffectiveSCEVType(Ty);
1159 // Fold if the operand is constant.
1160 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1162 cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(), Ty)));
1164 // zext(zext(x)) --> zext(x)
1165 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1166 return getZeroExtendExpr(SZ->getOperand(), Ty);
1168 // Before doing any expensive analysis, check to see if we've already
1169 // computed a SCEV for this Op and Ty.
1170 FoldingSetNodeID ID;
1171 ID.AddInteger(scZeroExtend);
1175 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1177 // zext(trunc(x)) --> zext(x) or x or trunc(x)
1178 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1179 // It's possible the bits taken off by the truncate were all zero bits. If
1180 // so, we should be able to simplify this further.
1181 const SCEV *X = ST->getOperand();
1182 ConstantRange CR = getUnsignedRange(X);
1183 unsigned TruncBits = getTypeSizeInBits(ST->getType());
1184 unsigned NewBits = getTypeSizeInBits(Ty);
1185 if (CR.truncate(TruncBits).zeroExtend(NewBits).contains(
1186 CR.zextOrTrunc(NewBits)))
1187 return getTruncateOrZeroExtend(X, Ty);
1190 // If the input value is a chrec scev, and we can prove that the value
1191 // did not overflow the old, smaller, value, we can zero extend all of the
1192 // operands (often constants). This allows analysis of something like
1193 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
1194 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1195 if (AR->isAffine()) {
1196 const SCEV *Start = AR->getStart();
1197 const SCEV *Step = AR->getStepRecurrence(*this);
1198 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1199 const Loop *L = AR->getLoop();
1201 // If we have special knowledge that this addrec won't overflow,
1202 // we don't need to do any further analysis.
1203 if (AR->getNoWrapFlags(SCEV::FlagNUW))
1204 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1205 getZeroExtendExpr(Step, Ty),
1206 L, AR->getNoWrapFlags());
1208 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1209 // Note that this serves two purposes: It filters out loops that are
1210 // simply not analyzable, and it covers the case where this code is
1211 // being called from within backedge-taken count analysis, such that
1212 // attempting to ask for the backedge-taken count would likely result
1213 // in infinite recursion. In the later case, the analysis code will
1214 // cope with a conservative value, and it will take care to purge
1215 // that value once it has finished.
1216 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1217 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1218 // Manually compute the final value for AR, checking for
1221 // Check whether the backedge-taken count can be losslessly casted to
1222 // the addrec's type. The count is always unsigned.
1223 const SCEV *CastedMaxBECount =
1224 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1225 const SCEV *RecastedMaxBECount =
1226 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1227 if (MaxBECount == RecastedMaxBECount) {
1228 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1229 // Check whether Start+Step*MaxBECount has no unsigned overflow.
1230 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step);
1231 const SCEV *ZAdd = getZeroExtendExpr(getAddExpr(Start, ZMul), WideTy);
1232 const SCEV *WideStart = getZeroExtendExpr(Start, WideTy);
1233 const SCEV *WideMaxBECount =
1234 getZeroExtendExpr(CastedMaxBECount, WideTy);
1235 const SCEV *OperandExtendedAdd =
1236 getAddExpr(WideStart,
1237 getMulExpr(WideMaxBECount,
1238 getZeroExtendExpr(Step, WideTy)));
1239 if (ZAdd == OperandExtendedAdd) {
1240 // Cache knowledge of AR NUW, which is propagated to this AddRec.
1241 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1242 // Return the expression with the addrec on the outside.
1243 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1244 getZeroExtendExpr(Step, Ty),
1245 L, AR->getNoWrapFlags());
1247 // Similar to above, only this time treat the step value as signed.
1248 // This covers loops that count down.
1249 OperandExtendedAdd =
1250 getAddExpr(WideStart,
1251 getMulExpr(WideMaxBECount,
1252 getSignExtendExpr(Step, WideTy)));
1253 if (ZAdd == OperandExtendedAdd) {
1254 // Cache knowledge of AR NW, which is propagated to this AddRec.
1255 // Negative step causes unsigned wrap, but it still can't self-wrap.
1256 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1257 // Return the expression with the addrec on the outside.
1258 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1259 getSignExtendExpr(Step, Ty),
1260 L, AR->getNoWrapFlags());
1264 // If the backedge is guarded by a comparison with the pre-inc value
1265 // the addrec is safe. Also, if the entry is guarded by a comparison
1266 // with the start value and the backedge is guarded by a comparison
1267 // with the post-inc value, the addrec is safe.
1268 if (isKnownPositive(Step)) {
1269 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
1270 getUnsignedRange(Step).getUnsignedMax());
1271 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
1272 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) &&
1273 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT,
1274 AR->getPostIncExpr(*this), N))) {
1275 // Cache knowledge of AR NUW, which is propagated to this AddRec.
1276 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1277 // Return the expression with the addrec on the outside.
1278 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1279 getZeroExtendExpr(Step, Ty),
1280 L, AR->getNoWrapFlags());
1282 } else if (isKnownNegative(Step)) {
1283 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
1284 getSignedRange(Step).getSignedMin());
1285 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) ||
1286 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) &&
1287 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT,
1288 AR->getPostIncExpr(*this), N))) {
1289 // Cache knowledge of AR NW, which is propagated to this AddRec.
1290 // Negative step causes unsigned wrap, but it still can't self-wrap.
1291 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1292 // Return the expression with the addrec on the outside.
1293 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1294 getSignExtendExpr(Step, Ty),
1295 L, AR->getNoWrapFlags());
1301 // The cast wasn't folded; create an explicit cast node.
1302 // Recompute the insert position, as it may have been invalidated.
1303 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1304 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
1306 UniqueSCEVs.InsertNode(S, IP);
1310 // Get the limit of a recurrence such that incrementing by Step cannot cause
1311 // signed overflow as long as the value of the recurrence within the loop does
1312 // not exceed this limit before incrementing.
1313 static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1314 ICmpInst::Predicate *Pred,
1315 ScalarEvolution *SE) {
1316 unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
1317 if (SE->isKnownPositive(Step)) {
1318 *Pred = ICmpInst::ICMP_SLT;
1319 return SE->getConstant(APInt::getSignedMinValue(BitWidth) -
1320 SE->getSignedRange(Step).getSignedMax());
1322 if (SE->isKnownNegative(Step)) {
1323 *Pred = ICmpInst::ICMP_SGT;
1324 return SE->getConstant(APInt::getSignedMaxValue(BitWidth) -
1325 SE->getSignedRange(Step).getSignedMin());
1330 // The recurrence AR has been shown to have no signed wrap. Typically, if we can
1331 // prove NSW for AR, then we can just as easily prove NSW for its preincrement
1332 // or postincrement sibling. This allows normalizing a sign extended AddRec as
1333 // such: {sext(Step + Start),+,Step} => {(Step + sext(Start),+,Step} As a
1334 // result, the expression "Step + sext(PreIncAR)" is congruent with
1335 // "sext(PostIncAR)"
1336 static const SCEV *getPreStartForSignExtend(const SCEVAddRecExpr *AR,
1338 ScalarEvolution *SE) {
1339 const Loop *L = AR->getLoop();
1340 const SCEV *Start = AR->getStart();
1341 const SCEV *Step = AR->getStepRecurrence(*SE);
1343 // Check for a simple looking step prior to loop entry.
1344 const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Start);
1348 // Create an AddExpr for "PreStart" after subtracting Step. Full SCEV
1349 // subtraction is expensive. For this purpose, perform a quick and dirty
1350 // difference, by checking for Step in the operand list.
1351 SmallVector<const SCEV *, 4> DiffOps;
1352 for (const SCEV *Op : SA->operands())
1354 DiffOps.push_back(Op);
1356 if (DiffOps.size() == SA->getNumOperands())
1359 // This is a postinc AR. Check for overflow on the preinc recurrence using the
1360 // same three conditions that getSignExtendedExpr checks.
1362 // 1. NSW flags on the step increment.
1363 const SCEV *PreStart = SE->getAddExpr(DiffOps, SA->getNoWrapFlags());
1364 const SCEVAddRecExpr *PreAR = dyn_cast<SCEVAddRecExpr>(
1365 SE->getAddRecExpr(PreStart, Step, L, SCEV::FlagAnyWrap));
1367 if (PreAR && PreAR->getNoWrapFlags(SCEV::FlagNSW))
1370 // 2. Direct overflow check on the step operation's expression.
1371 unsigned BitWidth = SE->getTypeSizeInBits(AR->getType());
1372 Type *WideTy = IntegerType::get(SE->getContext(), BitWidth * 2);
1373 const SCEV *OperandExtendedStart =
1374 SE->getAddExpr(SE->getSignExtendExpr(PreStart, WideTy),
1375 SE->getSignExtendExpr(Step, WideTy));
1376 if (SE->getSignExtendExpr(Start, WideTy) == OperandExtendedStart) {
1377 // Cache knowledge of PreAR NSW.
1379 const_cast<SCEVAddRecExpr *>(PreAR)->setNoWrapFlags(SCEV::FlagNSW);
1380 // FIXME: this optimization needs a unit test
1381 DEBUG(dbgs() << "SCEV: untested prestart overflow check\n");
1385 // 3. Loop precondition.
1386 ICmpInst::Predicate Pred;
1387 const SCEV *OverflowLimit = getOverflowLimitForStep(Step, &Pred, SE);
1389 if (OverflowLimit &&
1390 SE->isLoopEntryGuardedByCond(L, Pred, PreStart, OverflowLimit)) {
1396 // Get the normalized sign-extended expression for this AddRec's Start.
1397 static const SCEV *getSignExtendAddRecStart(const SCEVAddRecExpr *AR,
1399 ScalarEvolution *SE) {
1400 const SCEV *PreStart = getPreStartForSignExtend(AR, Ty, SE);
1402 return SE->getSignExtendExpr(AR->getStart(), Ty);
1404 return SE->getAddExpr(SE->getSignExtendExpr(AR->getStepRecurrence(*SE), Ty),
1405 SE->getSignExtendExpr(PreStart, Ty));
1408 const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op,
1410 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1411 "This is not an extending conversion!");
1412 assert(isSCEVable(Ty) &&
1413 "This is not a conversion to a SCEVable type!");
1414 Ty = getEffectiveSCEVType(Ty);
1416 // Fold if the operand is constant.
1417 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1419 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), Ty)));
1421 // sext(sext(x)) --> sext(x)
1422 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1423 return getSignExtendExpr(SS->getOperand(), Ty);
1425 // sext(zext(x)) --> zext(x)
1426 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1427 return getZeroExtendExpr(SZ->getOperand(), Ty);
1429 // Before doing any expensive analysis, check to see if we've already
1430 // computed a SCEV for this Op and Ty.
1431 FoldingSetNodeID ID;
1432 ID.AddInteger(scSignExtend);
1436 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1438 // If the input value is provably positive, build a zext instead.
1439 if (isKnownNonNegative(Op))
1440 return getZeroExtendExpr(Op, Ty);
1442 // sext(trunc(x)) --> sext(x) or x or trunc(x)
1443 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1444 // It's possible the bits taken off by the truncate were all sign bits. If
1445 // so, we should be able to simplify this further.
1446 const SCEV *X = ST->getOperand();
1447 ConstantRange CR = getSignedRange(X);
1448 unsigned TruncBits = getTypeSizeInBits(ST->getType());
1449 unsigned NewBits = getTypeSizeInBits(Ty);
1450 if (CR.truncate(TruncBits).signExtend(NewBits).contains(
1451 CR.sextOrTrunc(NewBits)))
1452 return getTruncateOrSignExtend(X, Ty);
1455 // sext(C1 + (C2 * x)) --> C1 + sext(C2 * x) if C1 < C2
1456 if (auto SA = dyn_cast<SCEVAddExpr>(Op)) {
1457 if (SA->getNumOperands() == 2) {
1458 auto SC1 = dyn_cast<SCEVConstant>(SA->getOperand(0));
1459 auto SMul = dyn_cast<SCEVMulExpr>(SA->getOperand(1));
1461 if (auto SC2 = dyn_cast<SCEVConstant>(SMul->getOperand(0))) {
1462 const APInt &C1 = SC1->getValue()->getValue();
1463 const APInt &C2 = SC2->getValue()->getValue();
1464 if (C1.isStrictlyPositive() && C2.isStrictlyPositive() &&
1465 C2.ugt(C1) && C2.isPowerOf2())
1466 return getAddExpr(getSignExtendExpr(SC1, Ty),
1467 getSignExtendExpr(SMul, Ty));
1472 // If the input value is a chrec scev, and we can prove that the value
1473 // did not overflow the old, smaller, value, we can sign extend all of the
1474 // operands (often constants). This allows analysis of something like
1475 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
1476 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1477 if (AR->isAffine()) {
1478 const SCEV *Start = AR->getStart();
1479 const SCEV *Step = AR->getStepRecurrence(*this);
1480 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1481 const Loop *L = AR->getLoop();
1483 // If we have special knowledge that this addrec won't overflow,
1484 // we don't need to do any further analysis.
1485 if (AR->getNoWrapFlags(SCEV::FlagNSW))
1486 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1487 getSignExtendExpr(Step, Ty),
1490 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1491 // Note that this serves two purposes: It filters out loops that are
1492 // simply not analyzable, and it covers the case where this code is
1493 // being called from within backedge-taken count analysis, such that
1494 // attempting to ask for the backedge-taken count would likely result
1495 // in infinite recursion. In the later case, the analysis code will
1496 // cope with a conservative value, and it will take care to purge
1497 // that value once it has finished.
1498 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1499 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1500 // Manually compute the final value for AR, checking for
1503 // Check whether the backedge-taken count can be losslessly casted to
1504 // the addrec's type. The count is always unsigned.
1505 const SCEV *CastedMaxBECount =
1506 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1507 const SCEV *RecastedMaxBECount =
1508 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1509 if (MaxBECount == RecastedMaxBECount) {
1510 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1511 // Check whether Start+Step*MaxBECount has no signed overflow.
1512 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
1513 const SCEV *SAdd = getSignExtendExpr(getAddExpr(Start, SMul), WideTy);
1514 const SCEV *WideStart = getSignExtendExpr(Start, WideTy);
1515 const SCEV *WideMaxBECount =
1516 getZeroExtendExpr(CastedMaxBECount, WideTy);
1517 const SCEV *OperandExtendedAdd =
1518 getAddExpr(WideStart,
1519 getMulExpr(WideMaxBECount,
1520 getSignExtendExpr(Step, WideTy)));
1521 if (SAdd == OperandExtendedAdd) {
1522 // Cache knowledge of AR NSW, which is propagated to this AddRec.
1523 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1524 // Return the expression with the addrec on the outside.
1525 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1526 getSignExtendExpr(Step, Ty),
1527 L, AR->getNoWrapFlags());
1529 // Similar to above, only this time treat the step value as unsigned.
1530 // This covers loops that count up with an unsigned step.
1531 OperandExtendedAdd =
1532 getAddExpr(WideStart,
1533 getMulExpr(WideMaxBECount,
1534 getZeroExtendExpr(Step, WideTy)));
1535 if (SAdd == OperandExtendedAdd) {
1536 // Cache knowledge of AR NSW, which is propagated to this AddRec.
1537 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1538 // Return the expression with the addrec on the outside.
1539 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1540 getZeroExtendExpr(Step, Ty),
1541 L, AR->getNoWrapFlags());
1545 // If the backedge is guarded by a comparison with the pre-inc value
1546 // the addrec is safe. Also, if the entry is guarded by a comparison
1547 // with the start value and the backedge is guarded by a comparison
1548 // with the post-inc value, the addrec is safe.
1549 ICmpInst::Predicate Pred;
1550 const SCEV *OverflowLimit = getOverflowLimitForStep(Step, &Pred, this);
1551 if (OverflowLimit &&
1552 (isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) ||
1553 (isLoopEntryGuardedByCond(L, Pred, Start, OverflowLimit) &&
1554 isLoopBackedgeGuardedByCond(L, Pred, AR->getPostIncExpr(*this),
1556 // Cache knowledge of AR NSW, then propagate NSW to the wide AddRec.
1557 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1558 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1559 getSignExtendExpr(Step, Ty),
1560 L, AR->getNoWrapFlags());
1563 // If Start and Step are constants, check if we can apply this
1565 // sext{C1,+,C2} --> C1 + sext{0,+,C2} if C1 < C2
1566 auto SC1 = dyn_cast<SCEVConstant>(Start);
1567 auto SC2 = dyn_cast<SCEVConstant>(Step);
1569 const APInt &C1 = SC1->getValue()->getValue();
1570 const APInt &C2 = SC2->getValue()->getValue();
1571 if (C1.isStrictlyPositive() && C2.isStrictlyPositive() && C2.ugt(C1) &&
1573 Start = getSignExtendExpr(Start, Ty);
1574 const SCEV *NewAR = getAddRecExpr(getConstant(AR->getType(), 0), Step,
1575 L, AR->getNoWrapFlags());
1576 return getAddExpr(Start, getSignExtendExpr(NewAR, Ty));
1581 // The cast wasn't folded; create an explicit cast node.
1582 // Recompute the insert position, as it may have been invalidated.
1583 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1584 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
1586 UniqueSCEVs.InsertNode(S, IP);
1590 /// getAnyExtendExpr - Return a SCEV for the given operand extended with
1591 /// unspecified bits out to the given type.
1593 const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
1595 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1596 "This is not an extending conversion!");
1597 assert(isSCEVable(Ty) &&
1598 "This is not a conversion to a SCEVable type!");
1599 Ty = getEffectiveSCEVType(Ty);
1601 // Sign-extend negative constants.
1602 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1603 if (SC->getValue()->getValue().isNegative())
1604 return getSignExtendExpr(Op, Ty);
1606 // Peel off a truncate cast.
1607 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
1608 const SCEV *NewOp = T->getOperand();
1609 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
1610 return getAnyExtendExpr(NewOp, Ty);
1611 return getTruncateOrNoop(NewOp, Ty);
1614 // Next try a zext cast. If the cast is folded, use it.
1615 const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
1616 if (!isa<SCEVZeroExtendExpr>(ZExt))
1619 // Next try a sext cast. If the cast is folded, use it.
1620 const SCEV *SExt = getSignExtendExpr(Op, Ty);
1621 if (!isa<SCEVSignExtendExpr>(SExt))
1624 // Force the cast to be folded into the operands of an addrec.
1625 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
1626 SmallVector<const SCEV *, 4> Ops;
1627 for (const SCEV *Op : AR->operands())
1628 Ops.push_back(getAnyExtendExpr(Op, Ty));
1629 return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW);
1632 // If the expression is obviously signed, use the sext cast value.
1633 if (isa<SCEVSMaxExpr>(Op))
1636 // Absent any other information, use the zext cast value.
1640 /// CollectAddOperandsWithScales - Process the given Ops list, which is
1641 /// a list of operands to be added under the given scale, update the given
1642 /// map. This is a helper function for getAddRecExpr. As an example of
1643 /// what it does, given a sequence of operands that would form an add
1644 /// expression like this:
1646 /// m + n + 13 + (A * (o + p + (B * (q + m + 29)))) + r + (-1 * r)
1648 /// where A and B are constants, update the map with these values:
1650 /// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
1652 /// and add 13 + A*B*29 to AccumulatedConstant.
1653 /// This will allow getAddRecExpr to produce this:
1655 /// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
1657 /// This form often exposes folding opportunities that are hidden in
1658 /// the original operand list.
1660 /// Return true iff it appears that any interesting folding opportunities
1661 /// may be exposed. This helps getAddRecExpr short-circuit extra work in
1662 /// the common case where no interesting opportunities are present, and
1663 /// is also used as a check to avoid infinite recursion.
1666 CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
1667 SmallVectorImpl<const SCEV *> &NewOps,
1668 APInt &AccumulatedConstant,
1669 const SCEV *const *Ops, size_t NumOperands,
1671 ScalarEvolution &SE) {
1672 bool Interesting = false;
1674 // Iterate over the add operands. They are sorted, with constants first.
1676 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1678 // Pull a buried constant out to the outside.
1679 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
1681 AccumulatedConstant += Scale * C->getValue()->getValue();
1684 // Next comes everything else. We're especially interested in multiplies
1685 // here, but they're in the middle, so just visit the rest with one loop.
1686 for (; i != NumOperands; ++i) {
1687 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
1688 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
1690 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue();
1691 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
1692 // A multiplication of a constant with another add; recurse.
1693 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1));
1695 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1696 Add->op_begin(), Add->getNumOperands(),
1699 // A multiplication of a constant with some other value. Update
1701 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
1702 const SCEV *Key = SE.getMulExpr(MulOps);
1703 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1704 M.insert(std::make_pair(Key, NewScale));
1706 NewOps.push_back(Pair.first->first);
1708 Pair.first->second += NewScale;
1709 // The map already had an entry for this value, which may indicate
1710 // a folding opportunity.
1715 // An ordinary operand. Update the map.
1716 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1717 M.insert(std::make_pair(Ops[i], Scale));
1719 NewOps.push_back(Pair.first->first);
1721 Pair.first->second += Scale;
1722 // The map already had an entry for this value, which may indicate
1723 // a folding opportunity.
1733 struct APIntCompare {
1734 bool operator()(const APInt &LHS, const APInt &RHS) const {
1735 return LHS.ult(RHS);
1740 // We're trying to construct a SCEV of type `Type' with `Ops' as operands and
1741 // `OldFlags' as can't-wrap behavior. Infer a more aggressive set of
1742 // can't-overflow flags for the operation if possible.
1743 static SCEV::NoWrapFlags
1744 StrengthenNoWrapFlags(ScalarEvolution *SE, SCEVTypes Type,
1745 const SmallVectorImpl<const SCEV *> &Ops,
1746 SCEV::NoWrapFlags OldFlags) {
1747 using namespace std::placeholders;
1750 Type == scAddExpr || Type == scAddRecExpr || Type == scMulExpr;
1752 assert(CanAnalyze && "don't call from other places!");
1754 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
1755 SCEV::NoWrapFlags SignOrUnsignWrap =
1756 ScalarEvolution::maskFlags(OldFlags, SignOrUnsignMask);
1758 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
1759 auto IsKnownNonNegative =
1760 std::bind(std::mem_fn(&ScalarEvolution::isKnownNonNegative), SE, _1);
1762 if (SignOrUnsignWrap == SCEV::FlagNSW &&
1763 std::all_of(Ops.begin(), Ops.end(), IsKnownNonNegative))
1764 return ScalarEvolution::setFlags(OldFlags,
1765 (SCEV::NoWrapFlags)SignOrUnsignMask);
1770 /// getAddExpr - Get a canonical add expression, or something simpler if
1772 const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
1773 SCEV::NoWrapFlags Flags) {
1774 assert(!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) &&
1775 "only nuw or nsw allowed");
1776 assert(!Ops.empty() && "Cannot get empty add!");
1777 if (Ops.size() == 1) return Ops[0];
1779 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
1780 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1781 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
1782 "SCEVAddExpr operand types don't match!");
1785 Flags = StrengthenNoWrapFlags(this, scAddExpr, Ops, Flags);
1787 // Sort by complexity, this groups all similar expression types together.
1788 GroupByComplexity(Ops, LI);
1790 // If there are any constants, fold them together.
1792 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1794 assert(Idx < Ops.size());
1795 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1796 // We found two constants, fold them together!
1797 Ops[0] = getConstant(LHSC->getValue()->getValue() +
1798 RHSC->getValue()->getValue());
1799 if (Ops.size() == 2) return Ops[0];
1800 Ops.erase(Ops.begin()+1); // Erase the folded element
1801 LHSC = cast<SCEVConstant>(Ops[0]);
1804 // If we are left with a constant zero being added, strip it off.
1805 if (LHSC->getValue()->isZero()) {
1806 Ops.erase(Ops.begin());
1810 if (Ops.size() == 1) return Ops[0];
1813 // Okay, check to see if the same value occurs in the operand list more than
1814 // once. If so, merge them together into an multiply expression. Since we
1815 // sorted the list, these values are required to be adjacent.
1816 Type *Ty = Ops[0]->getType();
1817 bool FoundMatch = false;
1818 for (unsigned i = 0, e = Ops.size(); i != e-1; ++i)
1819 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
1820 // Scan ahead to count how many equal operands there are.
1822 while (i+Count != e && Ops[i+Count] == Ops[i])
1824 // Merge the values into a multiply.
1825 const SCEV *Scale = getConstant(Ty, Count);
1826 const SCEV *Mul = getMulExpr(Scale, Ops[i]);
1827 if (Ops.size() == Count)
1830 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count);
1831 --i; e -= Count - 1;
1835 return getAddExpr(Ops, Flags);
1837 // Check for truncates. If all the operands are truncated from the same
1838 // type, see if factoring out the truncate would permit the result to be
1839 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
1840 // if the contents of the resulting outer trunc fold to something simple.
1841 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
1842 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
1843 Type *DstType = Trunc->getType();
1844 Type *SrcType = Trunc->getOperand()->getType();
1845 SmallVector<const SCEV *, 8> LargeOps;
1847 // Check all the operands to see if they can be represented in the
1848 // source type of the truncate.
1849 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1850 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
1851 if (T->getOperand()->getType() != SrcType) {
1855 LargeOps.push_back(T->getOperand());
1856 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1857 LargeOps.push_back(getAnyExtendExpr(C, SrcType));
1858 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
1859 SmallVector<const SCEV *, 8> LargeMulOps;
1860 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
1861 if (const SCEVTruncateExpr *T =
1862 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
1863 if (T->getOperand()->getType() != SrcType) {
1867 LargeMulOps.push_back(T->getOperand());
1868 } else if (const SCEVConstant *C =
1869 dyn_cast<SCEVConstant>(M->getOperand(j))) {
1870 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType));
1877 LargeOps.push_back(getMulExpr(LargeMulOps));
1884 // Evaluate the expression in the larger type.
1885 const SCEV *Fold = getAddExpr(LargeOps, Flags);
1886 // If it folds to something simple, use it. Otherwise, don't.
1887 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
1888 return getTruncateExpr(Fold, DstType);
1892 // Skip past any other cast SCEVs.
1893 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
1896 // If there are add operands they would be next.
1897 if (Idx < Ops.size()) {
1898 bool DeletedAdd = false;
1899 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
1900 // If we have an add, expand the add operands onto the end of the operands
1902 Ops.erase(Ops.begin()+Idx);
1903 Ops.append(Add->op_begin(), Add->op_end());
1907 // If we deleted at least one add, we added operands to the end of the list,
1908 // and they are not necessarily sorted. Recurse to resort and resimplify
1909 // any operands we just acquired.
1911 return getAddExpr(Ops);
1914 // Skip over the add expression until we get to a multiply.
1915 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1918 // Check to see if there are any folding opportunities present with
1919 // operands multiplied by constant values.
1920 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
1921 uint64_t BitWidth = getTypeSizeInBits(Ty);
1922 DenseMap<const SCEV *, APInt> M;
1923 SmallVector<const SCEV *, 8> NewOps;
1924 APInt AccumulatedConstant(BitWidth, 0);
1925 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1926 Ops.data(), Ops.size(),
1927 APInt(BitWidth, 1), *this)) {
1928 // Some interesting folding opportunity is present, so its worthwhile to
1929 // re-generate the operands list. Group the operands by constant scale,
1930 // to avoid multiplying by the same constant scale multiple times.
1931 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
1932 for (SmallVectorImpl<const SCEV *>::const_iterator I = NewOps.begin(),
1933 E = NewOps.end(); I != E; ++I)
1934 MulOpLists[M.find(*I)->second].push_back(*I);
1935 // Re-generate the operands list.
1937 if (AccumulatedConstant != 0)
1938 Ops.push_back(getConstant(AccumulatedConstant));
1939 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator
1940 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I)
1942 Ops.push_back(getMulExpr(getConstant(I->first),
1943 getAddExpr(I->second)));
1945 return getConstant(Ty, 0);
1946 if (Ops.size() == 1)
1948 return getAddExpr(Ops);
1952 // If we are adding something to a multiply expression, make sure the
1953 // something is not already an operand of the multiply. If so, merge it into
1955 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
1956 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
1957 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
1958 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
1959 if (isa<SCEVConstant>(MulOpSCEV))
1961 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
1962 if (MulOpSCEV == Ops[AddOp]) {
1963 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
1964 const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
1965 if (Mul->getNumOperands() != 2) {
1966 // If the multiply has more than two operands, we must get the
1968 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
1969 Mul->op_begin()+MulOp);
1970 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
1971 InnerMul = getMulExpr(MulOps);
1973 const SCEV *One = getConstant(Ty, 1);
1974 const SCEV *AddOne = getAddExpr(One, InnerMul);
1975 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV);
1976 if (Ops.size() == 2) return OuterMul;
1978 Ops.erase(Ops.begin()+AddOp);
1979 Ops.erase(Ops.begin()+Idx-1);
1981 Ops.erase(Ops.begin()+Idx);
1982 Ops.erase(Ops.begin()+AddOp-1);
1984 Ops.push_back(OuterMul);
1985 return getAddExpr(Ops);
1988 // Check this multiply against other multiplies being added together.
1989 for (unsigned OtherMulIdx = Idx+1;
1990 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
1992 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
1993 // If MulOp occurs in OtherMul, we can fold the two multiplies
1995 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
1996 OMulOp != e; ++OMulOp)
1997 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
1998 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
1999 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
2000 if (Mul->getNumOperands() != 2) {
2001 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
2002 Mul->op_begin()+MulOp);
2003 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
2004 InnerMul1 = getMulExpr(MulOps);
2006 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
2007 if (OtherMul->getNumOperands() != 2) {
2008 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
2009 OtherMul->op_begin()+OMulOp);
2010 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end());
2011 InnerMul2 = getMulExpr(MulOps);
2013 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
2014 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
2015 if (Ops.size() == 2) return OuterMul;
2016 Ops.erase(Ops.begin()+Idx);
2017 Ops.erase(Ops.begin()+OtherMulIdx-1);
2018 Ops.push_back(OuterMul);
2019 return getAddExpr(Ops);
2025 // If there are any add recurrences in the operands list, see if any other
2026 // added values are loop invariant. If so, we can fold them into the
2028 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2031 // Scan over all recurrences, trying to fold loop invariants into them.
2032 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
2033 // Scan all of the other operands to this add and add them to the vector if
2034 // they are loop invariant w.r.t. the recurrence.
2035 SmallVector<const SCEV *, 8> LIOps;
2036 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2037 const Loop *AddRecLoop = AddRec->getLoop();
2038 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2039 if (isLoopInvariant(Ops[i], AddRecLoop)) {
2040 LIOps.push_back(Ops[i]);
2041 Ops.erase(Ops.begin()+i);
2045 // If we found some loop invariants, fold them into the recurrence.
2046 if (!LIOps.empty()) {
2047 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
2048 LIOps.push_back(AddRec->getStart());
2050 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
2052 AddRecOps[0] = getAddExpr(LIOps);
2054 // Build the new addrec. Propagate the NUW and NSW flags if both the
2055 // outer add and the inner addrec are guaranteed to have no overflow.
2056 // Always propagate NW.
2057 Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW));
2058 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags);
2060 // If all of the other operands were loop invariant, we are done.
2061 if (Ops.size() == 1) return NewRec;
2063 // Otherwise, add the folded AddRec by the non-invariant parts.
2064 for (unsigned i = 0;; ++i)
2065 if (Ops[i] == AddRec) {
2069 return getAddExpr(Ops);
2072 // Okay, if there weren't any loop invariants to be folded, check to see if
2073 // there are multiple AddRec's with the same loop induction variable being
2074 // added together. If so, we can fold them.
2075 for (unsigned OtherIdx = Idx+1;
2076 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2078 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
2079 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L>
2080 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
2082 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2084 if (const SCEVAddRecExpr *OtherAddRec =
2085 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]))
2086 if (OtherAddRec->getLoop() == AddRecLoop) {
2087 for (unsigned i = 0, e = OtherAddRec->getNumOperands();
2089 if (i >= AddRecOps.size()) {
2090 AddRecOps.append(OtherAddRec->op_begin()+i,
2091 OtherAddRec->op_end());
2094 AddRecOps[i] = getAddExpr(AddRecOps[i],
2095 OtherAddRec->getOperand(i));
2097 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2099 // Step size has changed, so we cannot guarantee no self-wraparound.
2100 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap);
2101 return getAddExpr(Ops);
2104 // Otherwise couldn't fold anything into this recurrence. Move onto the
2108 // Okay, it looks like we really DO need an add expr. Check to see if we
2109 // already have one, otherwise create a new one.
2110 FoldingSetNodeID ID;
2111 ID.AddInteger(scAddExpr);
2112 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2113 ID.AddPointer(Ops[i]);
2116 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2118 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2119 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2120 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator),
2122 UniqueSCEVs.InsertNode(S, IP);
2124 S->setNoWrapFlags(Flags);
2128 static uint64_t umul_ov(uint64_t i, uint64_t j, bool &Overflow) {
2130 if (j > 1 && k / j != i) Overflow = true;
2134 /// Compute the result of "n choose k", the binomial coefficient. If an
2135 /// intermediate computation overflows, Overflow will be set and the return will
2136 /// be garbage. Overflow is not cleared on absence of overflow.
2137 static uint64_t Choose(uint64_t n, uint64_t k, bool &Overflow) {
2138 // We use the multiplicative formula:
2139 // n(n-1)(n-2)...(n-(k-1)) / k(k-1)(k-2)...1 .
2140 // At each iteration, we take the n-th term of the numeral and divide by the
2141 // (k-n)th term of the denominator. This division will always produce an
2142 // integral result, and helps reduce the chance of overflow in the
2143 // intermediate computations. However, we can still overflow even when the
2144 // final result would fit.
2146 if (n == 0 || n == k) return 1;
2147 if (k > n) return 0;
2153 for (uint64_t i = 1; i <= k; ++i) {
2154 r = umul_ov(r, n-(i-1), Overflow);
2160 /// Determine if any of the operands in this SCEV are a constant or if
2161 /// any of the add or multiply expressions in this SCEV contain a constant.
2162 static bool containsConstantSomewhere(const SCEV *StartExpr) {
2163 SmallVector<const SCEV *, 4> Ops;
2164 Ops.push_back(StartExpr);
2165 while (!Ops.empty()) {
2166 const SCEV *CurrentExpr = Ops.pop_back_val();
2167 if (isa<SCEVConstant>(*CurrentExpr))
2170 if (isa<SCEVAddExpr>(*CurrentExpr) || isa<SCEVMulExpr>(*CurrentExpr)) {
2171 const auto *CurrentNAry = cast<SCEVNAryExpr>(CurrentExpr);
2172 for (const SCEV *Operand : CurrentNAry->operands())
2173 Ops.push_back(Operand);
2179 /// getMulExpr - Get a canonical multiply expression, or something simpler if
2181 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
2182 SCEV::NoWrapFlags Flags) {
2183 assert(Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) &&
2184 "only nuw or nsw allowed");
2185 assert(!Ops.empty() && "Cannot get empty mul!");
2186 if (Ops.size() == 1) return Ops[0];
2188 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2189 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2190 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2191 "SCEVMulExpr operand types don't match!");
2194 Flags = StrengthenNoWrapFlags(this, scMulExpr, Ops, Flags);
2196 // Sort by complexity, this groups all similar expression types together.
2197 GroupByComplexity(Ops, LI);
2199 // If there are any constants, fold them together.
2201 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2203 // C1*(C2+V) -> C1*C2 + C1*V
2204 if (Ops.size() == 2)
2205 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
2206 // If any of Add's ops are Adds or Muls with a constant,
2207 // apply this transformation as well.
2208 if (Add->getNumOperands() == 2)
2209 if (containsConstantSomewhere(Add))
2210 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
2211 getMulExpr(LHSC, Add->getOperand(1)));
2214 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2215 // We found two constants, fold them together!
2216 ConstantInt *Fold = ConstantInt::get(getContext(),
2217 LHSC->getValue()->getValue() *
2218 RHSC->getValue()->getValue());
2219 Ops[0] = getConstant(Fold);
2220 Ops.erase(Ops.begin()+1); // Erase the folded element
2221 if (Ops.size() == 1) return Ops[0];
2222 LHSC = cast<SCEVConstant>(Ops[0]);
2225 // If we are left with a constant one being multiplied, strip it off.
2226 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
2227 Ops.erase(Ops.begin());
2229 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
2230 // If we have a multiply of zero, it will always be zero.
2232 } else if (Ops[0]->isAllOnesValue()) {
2233 // If we have a mul by -1 of an add, try distributing the -1 among the
2235 if (Ops.size() == 2) {
2236 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
2237 SmallVector<const SCEV *, 4> NewOps;
2238 bool AnyFolded = false;
2239 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(),
2240 E = Add->op_end(); I != E; ++I) {
2241 const SCEV *Mul = getMulExpr(Ops[0], *I);
2242 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
2243 NewOps.push_back(Mul);
2246 return getAddExpr(NewOps);
2248 else if (const SCEVAddRecExpr *
2249 AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) {
2250 // Negation preserves a recurrence's no self-wrap property.
2251 SmallVector<const SCEV *, 4> Operands;
2252 for (SCEVAddRecExpr::op_iterator I = AddRec->op_begin(),
2253 E = AddRec->op_end(); I != E; ++I) {
2254 Operands.push_back(getMulExpr(Ops[0], *I));
2256 return getAddRecExpr(Operands, AddRec->getLoop(),
2257 AddRec->getNoWrapFlags(SCEV::FlagNW));
2262 if (Ops.size() == 1)
2266 // Skip over the add expression until we get to a multiply.
2267 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
2270 // If there are mul operands inline them all into this expression.
2271 if (Idx < Ops.size()) {
2272 bool DeletedMul = false;
2273 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
2274 // If we have an mul, expand the mul operands onto the end of the operands
2276 Ops.erase(Ops.begin()+Idx);
2277 Ops.append(Mul->op_begin(), Mul->op_end());
2281 // If we deleted at least one mul, we added operands to the end of the list,
2282 // and they are not necessarily sorted. Recurse to resort and resimplify
2283 // any operands we just acquired.
2285 return getMulExpr(Ops);
2288 // If there are any add recurrences in the operands list, see if any other
2289 // added values are loop invariant. If so, we can fold them into the
2291 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2294 // Scan over all recurrences, trying to fold loop invariants into them.
2295 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
2296 // Scan all of the other operands to this mul and add them to the vector if
2297 // they are loop invariant w.r.t. the recurrence.
2298 SmallVector<const SCEV *, 8> LIOps;
2299 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2300 const Loop *AddRecLoop = AddRec->getLoop();
2301 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2302 if (isLoopInvariant(Ops[i], AddRecLoop)) {
2303 LIOps.push_back(Ops[i]);
2304 Ops.erase(Ops.begin()+i);
2308 // If we found some loop invariants, fold them into the recurrence.
2309 if (!LIOps.empty()) {
2310 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
2311 SmallVector<const SCEV *, 4> NewOps;
2312 NewOps.reserve(AddRec->getNumOperands());
2313 const SCEV *Scale = getMulExpr(LIOps);
2314 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
2315 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
2317 // Build the new addrec. Propagate the NUW and NSW flags if both the
2318 // outer mul and the inner addrec are guaranteed to have no overflow.
2320 // No self-wrap cannot be guaranteed after changing the step size, but
2321 // will be inferred if either NUW or NSW is true.
2322 Flags = AddRec->getNoWrapFlags(clearFlags(Flags, SCEV::FlagNW));
2323 const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, Flags);
2325 // If all of the other operands were loop invariant, we are done.
2326 if (Ops.size() == 1) return NewRec;
2328 // Otherwise, multiply the folded AddRec by the non-invariant parts.
2329 for (unsigned i = 0;; ++i)
2330 if (Ops[i] == AddRec) {
2334 return getMulExpr(Ops);
2337 // Okay, if there weren't any loop invariants to be folded, check to see if
2338 // there are multiple AddRec's with the same loop induction variable being
2339 // multiplied together. If so, we can fold them.
2341 // {A1,+,A2,+,...,+,An}<L> * {B1,+,B2,+,...,+,Bn}<L>
2342 // = {x=1 in [ sum y=x..2x [ sum z=max(y-x, y-n)..min(x,n) [
2343 // choose(x, 2x)*choose(2x-y, x-z)*A_{y-z}*B_z
2344 // ]]],+,...up to x=2n}.
2345 // Note that the arguments to choose() are always integers with values
2346 // known at compile time, never SCEV objects.
2348 // The implementation avoids pointless extra computations when the two
2349 // addrec's are of different length (mathematically, it's equivalent to
2350 // an infinite stream of zeros on the right).
2351 bool OpsModified = false;
2352 for (unsigned OtherIdx = Idx+1;
2353 OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2355 const SCEVAddRecExpr *OtherAddRec =
2356 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]);
2357 if (!OtherAddRec || OtherAddRec->getLoop() != AddRecLoop)
2360 bool Overflow = false;
2361 Type *Ty = AddRec->getType();
2362 bool LargerThan64Bits = getTypeSizeInBits(Ty) > 64;
2363 SmallVector<const SCEV*, 7> AddRecOps;
2364 for (int x = 0, xe = AddRec->getNumOperands() +
2365 OtherAddRec->getNumOperands() - 1; x != xe && !Overflow; ++x) {
2366 const SCEV *Term = getConstant(Ty, 0);
2367 for (int y = x, ye = 2*x+1; y != ye && !Overflow; ++y) {
2368 uint64_t Coeff1 = Choose(x, 2*x - y, Overflow);
2369 for (int z = std::max(y-x, y-(int)AddRec->getNumOperands()+1),
2370 ze = std::min(x+1, (int)OtherAddRec->getNumOperands());
2371 z < ze && !Overflow; ++z) {
2372 uint64_t Coeff2 = Choose(2*x - y, x-z, Overflow);
2374 if (LargerThan64Bits)
2375 Coeff = umul_ov(Coeff1, Coeff2, Overflow);
2377 Coeff = Coeff1*Coeff2;
2378 const SCEV *CoeffTerm = getConstant(Ty, Coeff);
2379 const SCEV *Term1 = AddRec->getOperand(y-z);
2380 const SCEV *Term2 = OtherAddRec->getOperand(z);
2381 Term = getAddExpr(Term, getMulExpr(CoeffTerm, Term1,Term2));
2384 AddRecOps.push_back(Term);
2387 const SCEV *NewAddRec = getAddRecExpr(AddRecOps, AddRec->getLoop(),
2389 if (Ops.size() == 2) return NewAddRec;
2390 Ops[Idx] = NewAddRec;
2391 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2393 AddRec = dyn_cast<SCEVAddRecExpr>(NewAddRec);
2399 return getMulExpr(Ops);
2401 // Otherwise couldn't fold anything into this recurrence. Move onto the
2405 // Okay, it looks like we really DO need an mul expr. Check to see if we
2406 // already have one, otherwise create a new one.
2407 FoldingSetNodeID ID;
2408 ID.AddInteger(scMulExpr);
2409 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2410 ID.AddPointer(Ops[i]);
2413 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2415 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2416 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2417 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
2419 UniqueSCEVs.InsertNode(S, IP);
2421 S->setNoWrapFlags(Flags);
2425 /// getUDivExpr - Get a canonical unsigned division expression, or something
2426 /// simpler if possible.
2427 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
2429 assert(getEffectiveSCEVType(LHS->getType()) ==
2430 getEffectiveSCEVType(RHS->getType()) &&
2431 "SCEVUDivExpr operand types don't match!");
2433 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
2434 if (RHSC->getValue()->equalsInt(1))
2435 return LHS; // X udiv 1 --> x
2436 // If the denominator is zero, the result of the udiv is undefined. Don't
2437 // try to analyze it, because the resolution chosen here may differ from
2438 // the resolution chosen in other parts of the compiler.
2439 if (!RHSC->getValue()->isZero()) {
2440 // Determine if the division can be folded into the operands of
2442 // TODO: Generalize this to non-constants by using known-bits information.
2443 Type *Ty = LHS->getType();
2444 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
2445 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1;
2446 // For non-power-of-two values, effectively round the value up to the
2447 // nearest power of two.
2448 if (!RHSC->getValue()->getValue().isPowerOf2())
2450 IntegerType *ExtTy =
2451 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
2452 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
2453 if (const SCEVConstant *Step =
2454 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) {
2455 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
2456 const APInt &StepInt = Step->getValue()->getValue();
2457 const APInt &DivInt = RHSC->getValue()->getValue();
2458 if (!StepInt.urem(DivInt) &&
2459 getZeroExtendExpr(AR, ExtTy) ==
2460 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2461 getZeroExtendExpr(Step, ExtTy),
2462 AR->getLoop(), SCEV::FlagAnyWrap)) {
2463 SmallVector<const SCEV *, 4> Operands;
2464 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i)
2465 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS));
2466 return getAddRecExpr(Operands, AR->getLoop(),
2469 /// Get a canonical UDivExpr for a recurrence.
2470 /// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0.
2471 // We can currently only fold X%N if X is constant.
2472 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(AR->getStart());
2473 if (StartC && !DivInt.urem(StepInt) &&
2474 getZeroExtendExpr(AR, ExtTy) ==
2475 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2476 getZeroExtendExpr(Step, ExtTy),
2477 AR->getLoop(), SCEV::FlagAnyWrap)) {
2478 const APInt &StartInt = StartC->getValue()->getValue();
2479 const APInt &StartRem = StartInt.urem(StepInt);
2481 LHS = getAddRecExpr(getConstant(StartInt - StartRem), Step,
2482 AR->getLoop(), SCEV::FlagNW);
2485 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
2486 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
2487 SmallVector<const SCEV *, 4> Operands;
2488 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i)
2489 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy));
2490 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
2491 // Find an operand that's safely divisible.
2492 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
2493 const SCEV *Op = M->getOperand(i);
2494 const SCEV *Div = getUDivExpr(Op, RHSC);
2495 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
2496 Operands = SmallVector<const SCEV *, 4>(M->op_begin(),
2499 return getMulExpr(Operands);
2503 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
2504 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) {
2505 SmallVector<const SCEV *, 4> Operands;
2506 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i)
2507 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy));
2508 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
2510 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
2511 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
2512 if (isa<SCEVUDivExpr>(Op) ||
2513 getMulExpr(Op, RHS) != A->getOperand(i))
2515 Operands.push_back(Op);
2517 if (Operands.size() == A->getNumOperands())
2518 return getAddExpr(Operands);
2522 // Fold if both operands are constant.
2523 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
2524 Constant *LHSCV = LHSC->getValue();
2525 Constant *RHSCV = RHSC->getValue();
2526 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
2532 FoldingSetNodeID ID;
2533 ID.AddInteger(scUDivExpr);
2537 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2538 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
2540 UniqueSCEVs.InsertNode(S, IP);
2544 static const APInt gcd(const SCEVConstant *C1, const SCEVConstant *C2) {
2545 APInt A = C1->getValue()->getValue().abs();
2546 APInt B = C2->getValue()->getValue().abs();
2547 uint32_t ABW = A.getBitWidth();
2548 uint32_t BBW = B.getBitWidth();
2555 return APIntOps::GreatestCommonDivisor(A, B);
2558 /// getUDivExactExpr - Get a canonical unsigned division expression, or
2559 /// something simpler if possible. There is no representation for an exact udiv
2560 /// in SCEV IR, but we can attempt to remove factors from the LHS and RHS.
2561 /// We can't do this when it's not exact because the udiv may be clearing bits.
2562 const SCEV *ScalarEvolution::getUDivExactExpr(const SCEV *LHS,
2564 // TODO: we could try to find factors in all sorts of things, but for now we
2565 // just deal with u/exact (multiply, constant). See SCEVDivision towards the
2566 // end of this file for inspiration.
2568 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(LHS);
2570 return getUDivExpr(LHS, RHS);
2572 if (const SCEVConstant *RHSCst = dyn_cast<SCEVConstant>(RHS)) {
2573 // If the mulexpr multiplies by a constant, then that constant must be the
2574 // first element of the mulexpr.
2575 if (const SCEVConstant *LHSCst =
2576 dyn_cast<SCEVConstant>(Mul->getOperand(0))) {
2577 if (LHSCst == RHSCst) {
2578 SmallVector<const SCEV *, 2> Operands;
2579 Operands.append(Mul->op_begin() + 1, Mul->op_end());
2580 return getMulExpr(Operands);
2583 // We can't just assume that LHSCst divides RHSCst cleanly, it could be
2584 // that there's a factor provided by one of the other terms. We need to
2586 APInt Factor = gcd(LHSCst, RHSCst);
2587 if (!Factor.isIntN(1)) {
2588 LHSCst = cast<SCEVConstant>(
2589 getConstant(LHSCst->getValue()->getValue().udiv(Factor)));
2590 RHSCst = cast<SCEVConstant>(
2591 getConstant(RHSCst->getValue()->getValue().udiv(Factor)));
2592 SmallVector<const SCEV *, 2> Operands;
2593 Operands.push_back(LHSCst);
2594 Operands.append(Mul->op_begin() + 1, Mul->op_end());
2595 LHS = getMulExpr(Operands);
2597 Mul = dyn_cast<SCEVMulExpr>(LHS);
2599 return getUDivExactExpr(LHS, RHS);
2604 for (int i = 0, e = Mul->getNumOperands(); i != e; ++i) {
2605 if (Mul->getOperand(i) == RHS) {
2606 SmallVector<const SCEV *, 2> Operands;
2607 Operands.append(Mul->op_begin(), Mul->op_begin() + i);
2608 Operands.append(Mul->op_begin() + i + 1, Mul->op_end());
2609 return getMulExpr(Operands);
2613 return getUDivExpr(LHS, RHS);
2616 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2617 /// Simplify the expression as much as possible.
2618 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step,
2620 SCEV::NoWrapFlags Flags) {
2621 SmallVector<const SCEV *, 4> Operands;
2622 Operands.push_back(Start);
2623 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
2624 if (StepChrec->getLoop() == L) {
2625 Operands.append(StepChrec->op_begin(), StepChrec->op_end());
2626 return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW));
2629 Operands.push_back(Step);
2630 return getAddRecExpr(Operands, L, Flags);
2633 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2634 /// Simplify the expression as much as possible.
2636 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
2637 const Loop *L, SCEV::NoWrapFlags Flags) {
2638 if (Operands.size() == 1) return Operands[0];
2640 Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
2641 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
2642 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy &&
2643 "SCEVAddRecExpr operand types don't match!");
2644 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2645 assert(isLoopInvariant(Operands[i], L) &&
2646 "SCEVAddRecExpr operand is not loop-invariant!");
2649 if (Operands.back()->isZero()) {
2650 Operands.pop_back();
2651 return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0} --> X
2654 // It's tempting to want to call getMaxBackedgeTakenCount count here and
2655 // use that information to infer NUW and NSW flags. However, computing a
2656 // BE count requires calling getAddRecExpr, so we may not yet have a
2657 // meaningful BE count at this point (and if we don't, we'd be stuck
2658 // with a SCEVCouldNotCompute as the cached BE count).
2660 Flags = StrengthenNoWrapFlags(this, scAddRecExpr, Operands, Flags);
2662 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
2663 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
2664 const Loop *NestedLoop = NestedAR->getLoop();
2665 if (L->contains(NestedLoop) ?
2666 (L->getLoopDepth() < NestedLoop->getLoopDepth()) :
2667 (!NestedLoop->contains(L) &&
2668 DT->dominates(L->getHeader(), NestedLoop->getHeader()))) {
2669 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
2670 NestedAR->op_end());
2671 Operands[0] = NestedAR->getStart();
2672 // AddRecs require their operands be loop-invariant with respect to their
2673 // loops. Don't perform this transformation if it would break this
2675 bool AllInvariant = true;
2676 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2677 if (!isLoopInvariant(Operands[i], L)) {
2678 AllInvariant = false;
2682 // Create a recurrence for the outer loop with the same step size.
2684 // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the
2685 // inner recurrence has the same property.
2686 SCEV::NoWrapFlags OuterFlags =
2687 maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags());
2689 NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags);
2690 AllInvariant = true;
2691 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i)
2692 if (!isLoopInvariant(NestedOperands[i], NestedLoop)) {
2693 AllInvariant = false;
2697 // Ok, both add recurrences are valid after the transformation.
2699 // The inner recurrence keeps its NW flag but only keeps NUW/NSW if
2700 // the outer recurrence has the same property.
2701 SCEV::NoWrapFlags InnerFlags =
2702 maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags);
2703 return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags);
2706 // Reset Operands to its original state.
2707 Operands[0] = NestedAR;
2711 // Okay, it looks like we really DO need an addrec expr. Check to see if we
2712 // already have one, otherwise create a new one.
2713 FoldingSetNodeID ID;
2714 ID.AddInteger(scAddRecExpr);
2715 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2716 ID.AddPointer(Operands[i]);
2720 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2722 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size());
2723 std::uninitialized_copy(Operands.begin(), Operands.end(), O);
2724 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator),
2725 O, Operands.size(), L);
2726 UniqueSCEVs.InsertNode(S, IP);
2728 S->setNoWrapFlags(Flags);
2732 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
2734 SmallVector<const SCEV *, 2> Ops;
2737 return getSMaxExpr(Ops);
2741 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2742 assert(!Ops.empty() && "Cannot get empty smax!");
2743 if (Ops.size() == 1) return Ops[0];
2745 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2746 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2747 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2748 "SCEVSMaxExpr operand types don't match!");
2751 // Sort by complexity, this groups all similar expression types together.
2752 GroupByComplexity(Ops, LI);
2754 // If there are any constants, fold them together.
2756 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2758 assert(Idx < Ops.size());
2759 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2760 // We found two constants, fold them together!
2761 ConstantInt *Fold = ConstantInt::get(getContext(),
2762 APIntOps::smax(LHSC->getValue()->getValue(),
2763 RHSC->getValue()->getValue()));
2764 Ops[0] = getConstant(Fold);
2765 Ops.erase(Ops.begin()+1); // Erase the folded element
2766 if (Ops.size() == 1) return Ops[0];
2767 LHSC = cast<SCEVConstant>(Ops[0]);
2770 // If we are left with a constant minimum-int, strip it off.
2771 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
2772 Ops.erase(Ops.begin());
2774 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
2775 // If we have an smax with a constant maximum-int, it will always be
2780 if (Ops.size() == 1) return Ops[0];
2783 // Find the first SMax
2784 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
2787 // Check to see if one of the operands is an SMax. If so, expand its operands
2788 // onto our operand list, and recurse to simplify.
2789 if (Idx < Ops.size()) {
2790 bool DeletedSMax = false;
2791 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
2792 Ops.erase(Ops.begin()+Idx);
2793 Ops.append(SMax->op_begin(), SMax->op_end());
2798 return getSMaxExpr(Ops);
2801 // Okay, check to see if the same value occurs in the operand list twice. If
2802 // so, delete one. Since we sorted the list, these values are required to
2804 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2805 // X smax Y smax Y --> X smax Y
2806 // X smax Y --> X, if X is always greater than Y
2807 if (Ops[i] == Ops[i+1] ||
2808 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) {
2809 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2811 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) {
2812 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2816 if (Ops.size() == 1) return Ops[0];
2818 assert(!Ops.empty() && "Reduced smax down to nothing!");
2820 // Okay, it looks like we really DO need an smax expr. Check to see if we
2821 // already have one, otherwise create a new one.
2822 FoldingSetNodeID ID;
2823 ID.AddInteger(scSMaxExpr);
2824 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2825 ID.AddPointer(Ops[i]);
2827 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2828 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2829 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2830 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator),
2832 UniqueSCEVs.InsertNode(S, IP);
2836 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
2838 SmallVector<const SCEV *, 2> Ops;
2841 return getUMaxExpr(Ops);
2845 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2846 assert(!Ops.empty() && "Cannot get empty umax!");
2847 if (Ops.size() == 1) return Ops[0];
2849 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2850 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2851 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2852 "SCEVUMaxExpr operand types don't match!");
2855 // Sort by complexity, this groups all similar expression types together.
2856 GroupByComplexity(Ops, LI);
2858 // If there are any constants, fold them together.
2860 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2862 assert(Idx < Ops.size());
2863 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2864 // We found two constants, fold them together!
2865 ConstantInt *Fold = ConstantInt::get(getContext(),
2866 APIntOps::umax(LHSC->getValue()->getValue(),
2867 RHSC->getValue()->getValue()));
2868 Ops[0] = getConstant(Fold);
2869 Ops.erase(Ops.begin()+1); // Erase the folded element
2870 if (Ops.size() == 1) return Ops[0];
2871 LHSC = cast<SCEVConstant>(Ops[0]);
2874 // If we are left with a constant minimum-int, strip it off.
2875 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
2876 Ops.erase(Ops.begin());
2878 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
2879 // If we have an umax with a constant maximum-int, it will always be
2884 if (Ops.size() == 1) return Ops[0];
2887 // Find the first UMax
2888 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
2891 // Check to see if one of the operands is a UMax. If so, expand its operands
2892 // onto our operand list, and recurse to simplify.
2893 if (Idx < Ops.size()) {
2894 bool DeletedUMax = false;
2895 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
2896 Ops.erase(Ops.begin()+Idx);
2897 Ops.append(UMax->op_begin(), UMax->op_end());
2902 return getUMaxExpr(Ops);
2905 // Okay, check to see if the same value occurs in the operand list twice. If
2906 // so, delete one. Since we sorted the list, these values are required to
2908 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2909 // X umax Y umax Y --> X umax Y
2910 // X umax Y --> X, if X is always greater than Y
2911 if (Ops[i] == Ops[i+1] ||
2912 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) {
2913 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2915 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) {
2916 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2920 if (Ops.size() == 1) return Ops[0];
2922 assert(!Ops.empty() && "Reduced umax down to nothing!");
2924 // Okay, it looks like we really DO need a umax expr. Check to see if we
2925 // already have one, otherwise create a new one.
2926 FoldingSetNodeID ID;
2927 ID.AddInteger(scUMaxExpr);
2928 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2929 ID.AddPointer(Ops[i]);
2931 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2932 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2933 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2934 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator),
2936 UniqueSCEVs.InsertNode(S, IP);
2940 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
2942 // ~smax(~x, ~y) == smin(x, y).
2943 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2946 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
2948 // ~umax(~x, ~y) == umin(x, y)
2949 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2952 const SCEV *ScalarEvolution::getSizeOfExpr(Type *IntTy, Type *AllocTy) {
2953 // If we have DataLayout, we can bypass creating a target-independent
2954 // constant expression and then folding it back into a ConstantInt.
2955 // This is just a compile-time optimization.
2957 return getConstant(IntTy, DL->getTypeAllocSize(AllocTy));
2959 Constant *C = ConstantExpr::getSizeOf(AllocTy);
2960 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2961 if (Constant *Folded = ConstantFoldConstantExpression(CE, DL, TLI))
2963 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2964 assert(Ty == IntTy && "Effective SCEV type doesn't match");
2965 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2968 const SCEV *ScalarEvolution::getOffsetOfExpr(Type *IntTy,
2971 // If we have DataLayout, we can bypass creating a target-independent
2972 // constant expression and then folding it back into a ConstantInt.
2973 // This is just a compile-time optimization.
2975 return getConstant(IntTy,
2976 DL->getStructLayout(STy)->getElementOffset(FieldNo));
2979 Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo);
2980 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2981 if (Constant *Folded = ConstantFoldConstantExpression(CE, DL, TLI))
2984 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy));
2985 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2988 const SCEV *ScalarEvolution::getUnknown(Value *V) {
2989 // Don't attempt to do anything other than create a SCEVUnknown object
2990 // here. createSCEV only calls getUnknown after checking for all other
2991 // interesting possibilities, and any other code that calls getUnknown
2992 // is doing so in order to hide a value from SCEV canonicalization.
2994 FoldingSetNodeID ID;
2995 ID.AddInteger(scUnknown);
2998 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
2999 assert(cast<SCEVUnknown>(S)->getValue() == V &&
3000 "Stale SCEVUnknown in uniquing map!");
3003 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
3005 FirstUnknown = cast<SCEVUnknown>(S);
3006 UniqueSCEVs.InsertNode(S, IP);
3010 //===----------------------------------------------------------------------===//
3011 // Basic SCEV Analysis and PHI Idiom Recognition Code
3014 /// isSCEVable - Test if values of the given type are analyzable within
3015 /// the SCEV framework. This primarily includes integer types, and it
3016 /// can optionally include pointer types if the ScalarEvolution class
3017 /// has access to target-specific information.
3018 bool ScalarEvolution::isSCEVable(Type *Ty) const {
3019 // Integers and pointers are always SCEVable.
3020 return Ty->isIntegerTy() || Ty->isPointerTy();
3023 /// getTypeSizeInBits - Return the size in bits of the specified type,
3024 /// for which isSCEVable must return true.
3025 uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const {
3026 assert(isSCEVable(Ty) && "Type is not SCEVable!");
3028 // If we have a DataLayout, use it!
3030 return DL->getTypeSizeInBits(Ty);
3032 // Integer types have fixed sizes.
3033 if (Ty->isIntegerTy())
3034 return Ty->getPrimitiveSizeInBits();
3036 // The only other support type is pointer. Without DataLayout, conservatively
3037 // assume pointers are 64-bit.
3038 assert(Ty->isPointerTy() && "isSCEVable permitted a non-SCEVable type!");
3042 /// getEffectiveSCEVType - Return a type with the same bitwidth as
3043 /// the given type and which represents how SCEV will treat the given
3044 /// type, for which isSCEVable must return true. For pointer types,
3045 /// this is the pointer-sized integer type.
3046 Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const {
3047 assert(isSCEVable(Ty) && "Type is not SCEVable!");
3049 if (Ty->isIntegerTy()) {
3053 // The only other support type is pointer.
3054 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
3057 return DL->getIntPtrType(Ty);
3059 // Without DataLayout, conservatively assume pointers are 64-bit.
3060 return Type::getInt64Ty(getContext());
3063 const SCEV *ScalarEvolution::getCouldNotCompute() {
3064 return &CouldNotCompute;
3068 // Helper class working with SCEVTraversal to figure out if a SCEV contains
3069 // a SCEVUnknown with null value-pointer. FindInvalidSCEVUnknown::FindOne
3070 // is set iff if find such SCEVUnknown.
3072 struct FindInvalidSCEVUnknown {
3074 FindInvalidSCEVUnknown() { FindOne = false; }
3075 bool follow(const SCEV *S) {
3076 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
3080 if (!cast<SCEVUnknown>(S)->getValue())
3087 bool isDone() const { return FindOne; }
3091 bool ScalarEvolution::checkValidity(const SCEV *S) const {
3092 FindInvalidSCEVUnknown F;
3093 SCEVTraversal<FindInvalidSCEVUnknown> ST(F);
3099 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
3100 /// expression and create a new one.
3101 const SCEV *ScalarEvolution::getSCEV(Value *V) {
3102 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
3104 ValueExprMapType::iterator I = ValueExprMap.find_as(V);
3105 if (I != ValueExprMap.end()) {
3106 const SCEV *S = I->second;
3107 if (checkValidity(S))
3110 ValueExprMap.erase(I);
3112 const SCEV *S = createSCEV(V);
3114 // The process of creating a SCEV for V may have caused other SCEVs
3115 // to have been created, so it's necessary to insert the new entry
3116 // from scratch, rather than trying to remember the insert position
3118 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(V, this), S));
3122 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
3124 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) {
3125 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
3127 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
3129 Type *Ty = V->getType();
3130 Ty = getEffectiveSCEVType(Ty);
3131 return getMulExpr(V,
3132 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))));
3135 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
3136 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
3137 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
3139 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
3141 Type *Ty = V->getType();
3142 Ty = getEffectiveSCEVType(Ty);
3143 const SCEV *AllOnes =
3144 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
3145 return getMinusSCEV(AllOnes, V);
3148 /// getMinusSCEV - Return LHS-RHS. Minus is represented in SCEV as A+B*-1.
3149 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
3150 SCEV::NoWrapFlags Flags) {
3151 assert(!maskFlags(Flags, SCEV::FlagNUW) && "subtraction does not have NUW");
3153 // Fast path: X - X --> 0.
3155 return getConstant(LHS->getType(), 0);
3158 return getAddExpr(LHS, getNegativeSCEV(RHS), Flags);
3161 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
3162 /// input value to the specified type. If the type must be extended, it is zero
3165 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty) {
3166 Type *SrcTy = V->getType();
3167 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3168 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3169 "Cannot truncate or zero extend with non-integer arguments!");
3170 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3171 return V; // No conversion
3172 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
3173 return getTruncateExpr(V, Ty);
3174 return getZeroExtendExpr(V, Ty);
3177 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
3178 /// input value to the specified type. If the type must be extended, it is sign
3181 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
3183 Type *SrcTy = V->getType();
3184 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3185 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3186 "Cannot truncate or zero extend with non-integer arguments!");
3187 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3188 return V; // No conversion
3189 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
3190 return getTruncateExpr(V, Ty);
3191 return getSignExtendExpr(V, Ty);
3194 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
3195 /// input value to the specified type. If the type must be extended, it is zero
3196 /// extended. The conversion must not be narrowing.
3198 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) {
3199 Type *SrcTy = V->getType();
3200 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3201 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3202 "Cannot noop or zero extend with non-integer arguments!");
3203 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3204 "getNoopOrZeroExtend cannot truncate!");
3205 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3206 return V; // No conversion
3207 return getZeroExtendExpr(V, Ty);
3210 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
3211 /// input value to the specified type. If the type must be extended, it is sign
3212 /// extended. The conversion must not be narrowing.
3214 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) {
3215 Type *SrcTy = V->getType();
3216 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3217 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3218 "Cannot noop or sign extend with non-integer arguments!");
3219 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3220 "getNoopOrSignExtend cannot truncate!");
3221 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3222 return V; // No conversion
3223 return getSignExtendExpr(V, Ty);
3226 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
3227 /// the input value to the specified type. If the type must be extended,
3228 /// it is extended with unspecified bits. The conversion must not be
3231 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) {
3232 Type *SrcTy = V->getType();
3233 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3234 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3235 "Cannot noop or any extend with non-integer arguments!");
3236 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3237 "getNoopOrAnyExtend cannot truncate!");
3238 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3239 return V; // No conversion
3240 return getAnyExtendExpr(V, Ty);
3243 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
3244 /// input value to the specified type. The conversion must not be widening.
3246 ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) {
3247 Type *SrcTy = V->getType();
3248 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3249 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3250 "Cannot truncate or noop with non-integer arguments!");
3251 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
3252 "getTruncateOrNoop cannot extend!");
3253 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3254 return V; // No conversion
3255 return getTruncateExpr(V, Ty);
3258 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
3259 /// the types using zero-extension, and then perform a umax operation
3261 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
3263 const SCEV *PromotedLHS = LHS;
3264 const SCEV *PromotedRHS = RHS;
3266 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
3267 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
3269 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
3271 return getUMaxExpr(PromotedLHS, PromotedRHS);
3274 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
3275 /// the types using zero-extension, and then perform a umin operation
3277 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
3279 const SCEV *PromotedLHS = LHS;
3280 const SCEV *PromotedRHS = RHS;
3282 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
3283 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
3285 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
3287 return getUMinExpr(PromotedLHS, PromotedRHS);
3290 /// getPointerBase - Transitively follow the chain of pointer-type operands
3291 /// until reaching a SCEV that does not have a single pointer operand. This
3292 /// returns a SCEVUnknown pointer for well-formed pointer-type expressions,
3293 /// but corner cases do exist.
3294 const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) {
3295 // A pointer operand may evaluate to a nonpointer expression, such as null.
3296 if (!V->getType()->isPointerTy())
3299 if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) {
3300 return getPointerBase(Cast->getOperand());
3302 else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) {
3303 const SCEV *PtrOp = nullptr;
3304 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
3306 if ((*I)->getType()->isPointerTy()) {
3307 // Cannot find the base of an expression with multiple pointer operands.
3315 return getPointerBase(PtrOp);
3320 /// PushDefUseChildren - Push users of the given Instruction
3321 /// onto the given Worklist.
3323 PushDefUseChildren(Instruction *I,
3324 SmallVectorImpl<Instruction *> &Worklist) {
3325 // Push the def-use children onto the Worklist stack.
3326 for (User *U : I->users())
3327 Worklist.push_back(cast<Instruction>(U));
3330 /// ForgetSymbolicValue - This looks up computed SCEV values for all
3331 /// instructions that depend on the given instruction and removes them from
3332 /// the ValueExprMapType map if they reference SymName. This is used during PHI
3335 ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) {
3336 SmallVector<Instruction *, 16> Worklist;
3337 PushDefUseChildren(PN, Worklist);
3339 SmallPtrSet<Instruction *, 8> Visited;
3341 while (!Worklist.empty()) {
3342 Instruction *I = Worklist.pop_back_val();
3343 if (!Visited.insert(I).second)
3346 ValueExprMapType::iterator It =
3347 ValueExprMap.find_as(static_cast<Value *>(I));
3348 if (It != ValueExprMap.end()) {
3349 const SCEV *Old = It->second;
3351 // Short-circuit the def-use traversal if the symbolic name
3352 // ceases to appear in expressions.
3353 if (Old != SymName && !hasOperand(Old, SymName))
3356 // SCEVUnknown for a PHI either means that it has an unrecognized
3357 // structure, it's a PHI that's in the progress of being computed
3358 // by createNodeForPHI, or it's a single-value PHI. In the first case,
3359 // additional loop trip count information isn't going to change anything.
3360 // In the second case, createNodeForPHI will perform the necessary
3361 // updates on its own when it gets to that point. In the third, we do
3362 // want to forget the SCEVUnknown.
3363 if (!isa<PHINode>(I) ||
3364 !isa<SCEVUnknown>(Old) ||
3365 (I != PN && Old == SymName)) {
3366 forgetMemoizedResults(Old);
3367 ValueExprMap.erase(It);
3371 PushDefUseChildren(I, Worklist);
3375 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
3376 /// a loop header, making it a potential recurrence, or it doesn't.
3378 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
3379 if (const Loop *L = LI->getLoopFor(PN->getParent()))
3380 if (L->getHeader() == PN->getParent()) {
3381 // The loop may have multiple entrances or multiple exits; we can analyze
3382 // this phi as an addrec if it has a unique entry value and a unique
3384 Value *BEValueV = nullptr, *StartValueV = nullptr;
3385 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
3386 Value *V = PN->getIncomingValue(i);
3387 if (L->contains(PN->getIncomingBlock(i))) {
3390 } else if (BEValueV != V) {
3394 } else if (!StartValueV) {
3396 } else if (StartValueV != V) {
3397 StartValueV = nullptr;
3401 if (BEValueV && StartValueV) {
3402 // While we are analyzing this PHI node, handle its value symbolically.
3403 const SCEV *SymbolicName = getUnknown(PN);
3404 assert(ValueExprMap.find_as(PN) == ValueExprMap.end() &&
3405 "PHI node already processed?");
3406 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
3408 // Using this symbolic name for the PHI, analyze the value coming around
3410 const SCEV *BEValue = getSCEV(BEValueV);
3412 // NOTE: If BEValue is loop invariant, we know that the PHI node just
3413 // has a special value for the first iteration of the loop.
3415 // If the value coming around the backedge is an add with the symbolic
3416 // value we just inserted, then we found a simple induction variable!
3417 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
3418 // If there is a single occurrence of the symbolic value, replace it
3419 // with a recurrence.
3420 unsigned FoundIndex = Add->getNumOperands();
3421 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3422 if (Add->getOperand(i) == SymbolicName)
3423 if (FoundIndex == e) {
3428 if (FoundIndex != Add->getNumOperands()) {
3429 // Create an add with everything but the specified operand.
3430 SmallVector<const SCEV *, 8> Ops;
3431 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3432 if (i != FoundIndex)
3433 Ops.push_back(Add->getOperand(i));
3434 const SCEV *Accum = getAddExpr(Ops);
3436 // This is not a valid addrec if the step amount is varying each
3437 // loop iteration, but is not itself an addrec in this loop.
3438 if (isLoopInvariant(Accum, L) ||
3439 (isa<SCEVAddRecExpr>(Accum) &&
3440 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
3441 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
3443 // If the increment doesn't overflow, then neither the addrec nor
3444 // the post-increment will overflow.
3445 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) {
3446 if (OBO->hasNoUnsignedWrap())
3447 Flags = setFlags(Flags, SCEV::FlagNUW);
3448 if (OBO->hasNoSignedWrap())
3449 Flags = setFlags(Flags, SCEV::FlagNSW);
3450 } else if (GEPOperator *GEP = dyn_cast<GEPOperator>(BEValueV)) {
3451 // If the increment is an inbounds GEP, then we know the address
3452 // space cannot be wrapped around. We cannot make any guarantee
3453 // about signed or unsigned overflow because pointers are
3454 // unsigned but we may have a negative index from the base
3455 // pointer. We can guarantee that no unsigned wrap occurs if the
3456 // indices form a positive value.
3457 if (GEP->isInBounds()) {
3458 Flags = setFlags(Flags, SCEV::FlagNW);
3460 const SCEV *Ptr = getSCEV(GEP->getPointerOperand());
3461 if (isKnownPositive(getMinusSCEV(getSCEV(GEP), Ptr)))
3462 Flags = setFlags(Flags, SCEV::FlagNUW);
3464 } else if (const SubOperator *OBO =
3465 dyn_cast<SubOperator>(BEValueV)) {
3466 if (OBO->hasNoUnsignedWrap())
3467 Flags = setFlags(Flags, SCEV::FlagNUW);
3468 if (OBO->hasNoSignedWrap())
3469 Flags = setFlags(Flags, SCEV::FlagNSW);
3472 const SCEV *StartVal = getSCEV(StartValueV);
3473 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
3475 // Since the no-wrap flags are on the increment, they apply to the
3476 // post-incremented value as well.
3477 if (isLoopInvariant(Accum, L))
3478 (void)getAddRecExpr(getAddExpr(StartVal, Accum),
3481 // Okay, for the entire analysis of this edge we assumed the PHI
3482 // to be symbolic. We now need to go back and purge all of the
3483 // entries for the scalars that use the symbolic expression.
3484 ForgetSymbolicName(PN, SymbolicName);
3485 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3489 } else if (const SCEVAddRecExpr *AddRec =
3490 dyn_cast<SCEVAddRecExpr>(BEValue)) {
3491 // Otherwise, this could be a loop like this:
3492 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
3493 // In this case, j = {1,+,1} and BEValue is j.
3494 // Because the other in-value of i (0) fits the evolution of BEValue
3495 // i really is an addrec evolution.
3496 if (AddRec->getLoop() == L && AddRec->isAffine()) {
3497 const SCEV *StartVal = getSCEV(StartValueV);
3499 // If StartVal = j.start - j.stride, we can use StartVal as the
3500 // initial step of the addrec evolution.
3501 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
3502 AddRec->getOperand(1))) {
3503 // FIXME: For constant StartVal, we should be able to infer
3505 const SCEV *PHISCEV =
3506 getAddRecExpr(StartVal, AddRec->getOperand(1), L,
3509 // Okay, for the entire analysis of this edge we assumed the PHI
3510 // to be symbolic. We now need to go back and purge all of the
3511 // entries for the scalars that use the symbolic expression.
3512 ForgetSymbolicName(PN, SymbolicName);
3513 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3521 // If the PHI has a single incoming value, follow that value, unless the
3522 // PHI's incoming blocks are in a different loop, in which case doing so
3523 // risks breaking LCSSA form. Instcombine would normally zap these, but
3524 // it doesn't have DominatorTree information, so it may miss cases.
3525 if (Value *V = SimplifyInstruction(PN, DL, TLI, DT, AC))
3526 if (LI->replacementPreservesLCSSAForm(PN, V))
3529 // If it's not a loop phi, we can't handle it yet.
3530 return getUnknown(PN);
3533 /// createNodeForGEP - Expand GEP instructions into add and multiply
3534 /// operations. This allows them to be analyzed by regular SCEV code.
3536 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
3537 Type *IntPtrTy = getEffectiveSCEVType(GEP->getType());
3538 Value *Base = GEP->getOperand(0);
3539 // Don't attempt to analyze GEPs over unsized objects.
3540 if (!Base->getType()->getPointerElementType()->isSized())
3541 return getUnknown(GEP);
3543 // Don't blindly transfer the inbounds flag from the GEP instruction to the
3544 // Add expression, because the Instruction may be guarded by control flow
3545 // and the no-overflow bits may not be valid for the expression in any
3547 SCEV::NoWrapFlags Wrap = GEP->isInBounds() ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
3549 const SCEV *TotalOffset = getConstant(IntPtrTy, 0);
3550 gep_type_iterator GTI = gep_type_begin(GEP);
3551 for (GetElementPtrInst::op_iterator I = std::next(GEP->op_begin()),
3555 // Compute the (potentially symbolic) offset in bytes for this index.
3556 if (StructType *STy = dyn_cast<StructType>(*GTI++)) {
3557 // For a struct, add the member offset.
3558 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
3559 const SCEV *FieldOffset = getOffsetOfExpr(IntPtrTy, STy, FieldNo);
3561 // Add the field offset to the running total offset.
3562 TotalOffset = getAddExpr(TotalOffset, FieldOffset);
3564 // For an array, add the element offset, explicitly scaled.
3565 const SCEV *ElementSize = getSizeOfExpr(IntPtrTy, *GTI);
3566 const SCEV *IndexS = getSCEV(Index);
3567 // Getelementptr indices are signed.
3568 IndexS = getTruncateOrSignExtend(IndexS, IntPtrTy);
3570 // Multiply the index by the element size to compute the element offset.
3571 const SCEV *LocalOffset = getMulExpr(IndexS, ElementSize, Wrap);
3573 // Add the element offset to the running total offset.
3574 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
3578 // Get the SCEV for the GEP base.
3579 const SCEV *BaseS = getSCEV(Base);
3581 // Add the total offset from all the GEP indices to the base.
3582 return getAddExpr(BaseS, TotalOffset, Wrap);
3585 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
3586 /// guaranteed to end in (at every loop iteration). It is, at the same time,
3587 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
3588 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
3590 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
3591 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3592 return C->getValue()->getValue().countTrailingZeros();
3594 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
3595 return std::min(GetMinTrailingZeros(T->getOperand()),
3596 (uint32_t)getTypeSizeInBits(T->getType()));
3598 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
3599 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3600 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3601 getTypeSizeInBits(E->getType()) : OpRes;
3604 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
3605 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3606 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3607 getTypeSizeInBits(E->getType()) : OpRes;
3610 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
3611 // The result is the min of all operands results.
3612 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3613 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3614 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3618 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
3619 // The result is the sum of all operands results.
3620 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
3621 uint32_t BitWidth = getTypeSizeInBits(M->getType());
3622 for (unsigned i = 1, e = M->getNumOperands();
3623 SumOpRes != BitWidth && i != e; ++i)
3624 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
3629 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
3630 // The result is the min of all operands results.
3631 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3632 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3633 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3637 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
3638 // The result is the min of all operands results.
3639 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3640 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3641 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3645 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
3646 // The result is the min of all operands results.
3647 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3648 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3649 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3653 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3654 // For a SCEVUnknown, ask ValueTracking.
3655 unsigned BitWidth = getTypeSizeInBits(U->getType());
3656 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3657 computeKnownBits(U->getValue(), Zeros, Ones, DL, 0, AC, nullptr, DT);
3658 return Zeros.countTrailingOnes();
3665 /// GetRangeFromMetadata - Helper method to assign a range to V from
3666 /// metadata present in the IR.
3667 static Optional<ConstantRange> GetRangeFromMetadata(Value *V) {
3668 if (Instruction *I = dyn_cast<Instruction>(V)) {
3669 if (MDNode *MD = I->getMetadata(LLVMContext::MD_range)) {
3670 ConstantRange TotalRange(
3671 cast<IntegerType>(I->getType())->getBitWidth(), false);
3673 unsigned NumRanges = MD->getNumOperands() / 2;
3674 assert(NumRanges >= 1);
3676 for (unsigned i = 0; i < NumRanges; ++i) {
3677 ConstantInt *Lower =
3678 mdconst::extract<ConstantInt>(MD->getOperand(2 * i + 0));
3679 ConstantInt *Upper =
3680 mdconst::extract<ConstantInt>(MD->getOperand(2 * i + 1));
3681 ConstantRange Range(Lower->getValue(), Upper->getValue());
3682 TotalRange = TotalRange.unionWith(Range);
3692 /// getUnsignedRange - Determine the unsigned range for a particular SCEV.
3695 ScalarEvolution::getUnsignedRange(const SCEV *S) {
3696 // See if we've computed this range already.
3697 DenseMap<const SCEV *, ConstantRange>::iterator I = UnsignedRanges.find(S);
3698 if (I != UnsignedRanges.end())
3701 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3702 return setUnsignedRange(C, ConstantRange(C->getValue()->getValue()));
3704 unsigned BitWidth = getTypeSizeInBits(S->getType());
3705 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3707 // If the value has known zeros, the maximum unsigned value will have those
3708 // known zeros as well.
3709 uint32_t TZ = GetMinTrailingZeros(S);
3711 ConservativeResult =
3712 ConstantRange(APInt::getMinValue(BitWidth),
3713 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
3715 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3716 ConstantRange X = getUnsignedRange(Add->getOperand(0));
3717 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3718 X = X.add(getUnsignedRange(Add->getOperand(i)));
3719 return setUnsignedRange(Add, ConservativeResult.intersectWith(X));
3722 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3723 ConstantRange X = getUnsignedRange(Mul->getOperand(0));
3724 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3725 X = X.multiply(getUnsignedRange(Mul->getOperand(i)));
3726 return setUnsignedRange(Mul, ConservativeResult.intersectWith(X));
3729 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3730 ConstantRange X = getUnsignedRange(SMax->getOperand(0));
3731 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3732 X = X.smax(getUnsignedRange(SMax->getOperand(i)));
3733 return setUnsignedRange(SMax, ConservativeResult.intersectWith(X));
3736 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3737 ConstantRange X = getUnsignedRange(UMax->getOperand(0));
3738 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3739 X = X.umax(getUnsignedRange(UMax->getOperand(i)));
3740 return setUnsignedRange(UMax, ConservativeResult.intersectWith(X));
3743 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3744 ConstantRange X = getUnsignedRange(UDiv->getLHS());
3745 ConstantRange Y = getUnsignedRange(UDiv->getRHS());
3746 return setUnsignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y)));
3749 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3750 ConstantRange X = getUnsignedRange(ZExt->getOperand());
3751 return setUnsignedRange(ZExt,
3752 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3755 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3756 ConstantRange X = getUnsignedRange(SExt->getOperand());
3757 return setUnsignedRange(SExt,
3758 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3761 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3762 ConstantRange X = getUnsignedRange(Trunc->getOperand());
3763 return setUnsignedRange(Trunc,
3764 ConservativeResult.intersectWith(X.truncate(BitWidth)));
3767 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3768 // If there's no unsigned wrap, the value will never be less than its
3770 if (AddRec->getNoWrapFlags(SCEV::FlagNUW))
3771 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
3772 if (!C->getValue()->isZero())
3773 ConservativeResult =
3774 ConservativeResult.intersectWith(
3775 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0)));
3777 // TODO: non-affine addrec
3778 if (AddRec->isAffine()) {
3779 Type *Ty = AddRec->getType();
3780 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3781 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3782 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3783 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3785 const SCEV *Start = AddRec->getStart();
3786 const SCEV *Step = AddRec->getStepRecurrence(*this);
3788 ConstantRange StartRange = getUnsignedRange(Start);
3789 ConstantRange StepRange = getSignedRange(Step);
3790 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3791 ConstantRange EndRange =
3792 StartRange.add(MaxBECountRange.multiply(StepRange));
3794 // Check for overflow. This must be done with ConstantRange arithmetic
3795 // because we could be called from within the ScalarEvolution overflow
3797 ConstantRange ExtStartRange = StartRange.zextOrTrunc(BitWidth*2+1);
3798 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3799 ConstantRange ExtMaxBECountRange =
3800 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3801 ConstantRange ExtEndRange = EndRange.zextOrTrunc(BitWidth*2+1);
3802 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3804 return setUnsignedRange(AddRec, ConservativeResult);
3806 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(),
3807 EndRange.getUnsignedMin());
3808 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(),
3809 EndRange.getUnsignedMax());
3810 if (Min.isMinValue() && Max.isMaxValue())
3811 return setUnsignedRange(AddRec, ConservativeResult);
3812 return setUnsignedRange(AddRec,
3813 ConservativeResult.intersectWith(ConstantRange(Min, Max+1)));
3817 return setUnsignedRange(AddRec, ConservativeResult);
3820 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3821 // Check if the IR explicitly contains !range metadata.
3822 Optional<ConstantRange> MDRange = GetRangeFromMetadata(U->getValue());
3823 if (MDRange.hasValue())
3824 ConservativeResult = ConservativeResult.intersectWith(MDRange.getValue());
3826 // For a SCEVUnknown, ask ValueTracking.
3827 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3828 computeKnownBits(U->getValue(), Zeros, Ones, DL, 0, AC, nullptr, DT);
3829 if (Ones == ~Zeros + 1)
3830 return setUnsignedRange(U, ConservativeResult);
3831 return setUnsignedRange(U,
3832 ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1)));
3835 return setUnsignedRange(S, ConservativeResult);
3838 /// getSignedRange - Determine the signed range for a particular SCEV.
3841 ScalarEvolution::getSignedRange(const SCEV *S) {
3842 // See if we've computed this range already.
3843 DenseMap<const SCEV *, ConstantRange>::iterator I = SignedRanges.find(S);
3844 if (I != SignedRanges.end())
3847 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3848 return setSignedRange(C, ConstantRange(C->getValue()->getValue()));
3850 unsigned BitWidth = getTypeSizeInBits(S->getType());
3851 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3853 // If the value has known zeros, the maximum signed value will have those
3854 // known zeros as well.
3855 uint32_t TZ = GetMinTrailingZeros(S);
3857 ConservativeResult =
3858 ConstantRange(APInt::getSignedMinValue(BitWidth),
3859 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
3861 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3862 ConstantRange X = getSignedRange(Add->getOperand(0));
3863 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3864 X = X.add(getSignedRange(Add->getOperand(i)));
3865 return setSignedRange(Add, ConservativeResult.intersectWith(X));
3868 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3869 ConstantRange X = getSignedRange(Mul->getOperand(0));
3870 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3871 X = X.multiply(getSignedRange(Mul->getOperand(i)));
3872 return setSignedRange(Mul, ConservativeResult.intersectWith(X));
3875 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3876 ConstantRange X = getSignedRange(SMax->getOperand(0));
3877 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3878 X = X.smax(getSignedRange(SMax->getOperand(i)));
3879 return setSignedRange(SMax, ConservativeResult.intersectWith(X));
3882 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3883 ConstantRange X = getSignedRange(UMax->getOperand(0));
3884 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3885 X = X.umax(getSignedRange(UMax->getOperand(i)));
3886 return setSignedRange(UMax, ConservativeResult.intersectWith(X));
3889 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3890 ConstantRange X = getSignedRange(UDiv->getLHS());
3891 ConstantRange Y = getSignedRange(UDiv->getRHS());
3892 return setSignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y)));
3895 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3896 ConstantRange X = getSignedRange(ZExt->getOperand());
3897 return setSignedRange(ZExt,
3898 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3901 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3902 ConstantRange X = getSignedRange(SExt->getOperand());
3903 return setSignedRange(SExt,
3904 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3907 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3908 ConstantRange X = getSignedRange(Trunc->getOperand());
3909 return setSignedRange(Trunc,
3910 ConservativeResult.intersectWith(X.truncate(BitWidth)));
3913 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3914 // If there's no signed wrap, and all the operands have the same sign or
3915 // zero, the value won't ever change sign.
3916 if (AddRec->getNoWrapFlags(SCEV::FlagNSW)) {
3917 bool AllNonNeg = true;
3918 bool AllNonPos = true;
3919 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
3920 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
3921 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
3924 ConservativeResult = ConservativeResult.intersectWith(
3925 ConstantRange(APInt(BitWidth, 0),
3926 APInt::getSignedMinValue(BitWidth)));
3928 ConservativeResult = ConservativeResult.intersectWith(
3929 ConstantRange(APInt::getSignedMinValue(BitWidth),
3930 APInt(BitWidth, 1)));
3933 // TODO: non-affine addrec
3934 if (AddRec->isAffine()) {
3935 Type *Ty = AddRec->getType();
3936 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3937 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3938 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3939 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3941 const SCEV *Start = AddRec->getStart();
3942 const SCEV *Step = AddRec->getStepRecurrence(*this);
3944 ConstantRange StartRange = getSignedRange(Start);
3945 ConstantRange StepRange = getSignedRange(Step);
3946 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3947 ConstantRange EndRange =
3948 StartRange.add(MaxBECountRange.multiply(StepRange));
3950 // Check for overflow. This must be done with ConstantRange arithmetic
3951 // because we could be called from within the ScalarEvolution overflow
3953 ConstantRange ExtStartRange = StartRange.sextOrTrunc(BitWidth*2+1);
3954 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3955 ConstantRange ExtMaxBECountRange =
3956 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3957 ConstantRange ExtEndRange = EndRange.sextOrTrunc(BitWidth*2+1);
3958 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3960 return setSignedRange(AddRec, ConservativeResult);
3962 APInt Min = APIntOps::smin(StartRange.getSignedMin(),
3963 EndRange.getSignedMin());
3964 APInt Max = APIntOps::smax(StartRange.getSignedMax(),
3965 EndRange.getSignedMax());
3966 if (Min.isMinSignedValue() && Max.isMaxSignedValue())
3967 return setSignedRange(AddRec, ConservativeResult);
3968 return setSignedRange(AddRec,
3969 ConservativeResult.intersectWith(ConstantRange(Min, Max+1)));
3973 return setSignedRange(AddRec, ConservativeResult);
3976 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3977 // Check if the IR explicitly contains !range metadata.
3978 Optional<ConstantRange> MDRange = GetRangeFromMetadata(U->getValue());
3979 if (MDRange.hasValue())
3980 ConservativeResult = ConservativeResult.intersectWith(MDRange.getValue());
3982 // For a SCEVUnknown, ask ValueTracking.
3983 if (!U->getValue()->getType()->isIntegerTy() && !DL)
3984 return setSignedRange(U, ConservativeResult);
3985 unsigned NS = ComputeNumSignBits(U->getValue(), DL, 0, AC, nullptr, DT);
3987 return setSignedRange(U, ConservativeResult);
3988 return setSignedRange(U, ConservativeResult.intersectWith(
3989 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
3990 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1)));
3993 return setSignedRange(S, ConservativeResult);
3996 /// createSCEV - We know that there is no SCEV for the specified value.
3997 /// Analyze the expression.
3999 const SCEV *ScalarEvolution::createSCEV(Value *V) {
4000 if (!isSCEVable(V->getType()))
4001 return getUnknown(V);
4003 unsigned Opcode = Instruction::UserOp1;
4004 if (Instruction *I = dyn_cast<Instruction>(V)) {
4005 Opcode = I->getOpcode();
4007 // Don't attempt to analyze instructions in blocks that aren't
4008 // reachable. Such instructions don't matter, and they aren't required
4009 // to obey basic rules for definitions dominating uses which this
4010 // analysis depends on.
4011 if (!DT->isReachableFromEntry(I->getParent()))
4012 return getUnknown(V);
4013 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
4014 Opcode = CE->getOpcode();
4015 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
4016 return getConstant(CI);
4017 else if (isa<ConstantPointerNull>(V))
4018 return getConstant(V->getType(), 0);
4019 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
4020 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee());
4022 return getUnknown(V);
4024 Operator *U = cast<Operator>(V);
4026 case Instruction::Add: {
4027 // The simple thing to do would be to just call getSCEV on both operands
4028 // and call getAddExpr with the result. However if we're looking at a
4029 // bunch of things all added together, this can be quite inefficient,
4030 // because it leads to N-1 getAddExpr calls for N ultimate operands.
4031 // Instead, gather up all the operands and make a single getAddExpr call.
4032 // LLVM IR canonical form means we need only traverse the left operands.
4034 // Don't apply this instruction's NSW or NUW flags to the new
4035 // expression. The instruction may be guarded by control flow that the
4036 // no-wrap behavior depends on. Non-control-equivalent instructions can be
4037 // mapped to the same SCEV expression, and it would be incorrect to transfer
4038 // NSW/NUW semantics to those operations.
4039 SmallVector<const SCEV *, 4> AddOps;
4040 AddOps.push_back(getSCEV(U->getOperand(1)));
4041 for (Value *Op = U->getOperand(0); ; Op = U->getOperand(0)) {
4042 unsigned Opcode = Op->getValueID() - Value::InstructionVal;
4043 if (Opcode != Instruction::Add && Opcode != Instruction::Sub)
4045 U = cast<Operator>(Op);
4046 const SCEV *Op1 = getSCEV(U->getOperand(1));
4047 if (Opcode == Instruction::Sub)
4048 AddOps.push_back(getNegativeSCEV(Op1));
4050 AddOps.push_back(Op1);
4052 AddOps.push_back(getSCEV(U->getOperand(0)));
4053 return getAddExpr(AddOps);
4055 case Instruction::Mul: {
4056 // Don't transfer NSW/NUW for the same reason as AddExpr.
4057 SmallVector<const SCEV *, 4> MulOps;
4058 MulOps.push_back(getSCEV(U->getOperand(1)));
4059 for (Value *Op = U->getOperand(0);
4060 Op->getValueID() == Instruction::Mul + Value::InstructionVal;
4061 Op = U->getOperand(0)) {
4062 U = cast<Operator>(Op);
4063 MulOps.push_back(getSCEV(U->getOperand(1)));
4065 MulOps.push_back(getSCEV(U->getOperand(0)));
4066 return getMulExpr(MulOps);
4068 case Instruction::UDiv:
4069 return getUDivExpr(getSCEV(U->getOperand(0)),
4070 getSCEV(U->getOperand(1)));
4071 case Instruction::Sub:
4072 return getMinusSCEV(getSCEV(U->getOperand(0)),
4073 getSCEV(U->getOperand(1)));
4074 case Instruction::And:
4075 // For an expression like x&255 that merely masks off the high bits,
4076 // use zext(trunc(x)) as the SCEV expression.
4077 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
4078 if (CI->isNullValue())
4079 return getSCEV(U->getOperand(1));
4080 if (CI->isAllOnesValue())
4081 return getSCEV(U->getOperand(0));
4082 const APInt &A = CI->getValue();
4084 // Instcombine's ShrinkDemandedConstant may strip bits out of
4085 // constants, obscuring what would otherwise be a low-bits mask.
4086 // Use computeKnownBits to compute what ShrinkDemandedConstant
4087 // knew about to reconstruct a low-bits mask value.
4088 unsigned LZ = A.countLeadingZeros();
4089 unsigned TZ = A.countTrailingZeros();
4090 unsigned BitWidth = A.getBitWidth();
4091 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
4092 computeKnownBits(U->getOperand(0), KnownZero, KnownOne, DL, 0, AC,
4095 APInt EffectiveMask =
4096 APInt::getLowBitsSet(BitWidth, BitWidth - LZ - TZ).shl(TZ);
4097 if ((LZ != 0 || TZ != 0) && !((~A & ~KnownZero) & EffectiveMask)) {
4098 const SCEV *MulCount = getConstant(
4099 ConstantInt::get(getContext(), APInt::getOneBitSet(BitWidth, TZ)));
4103 getUDivExactExpr(getSCEV(U->getOperand(0)), MulCount),
4104 IntegerType::get(getContext(), BitWidth - LZ - TZ)),
4111 case Instruction::Or:
4112 // If the RHS of the Or is a constant, we may have something like:
4113 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
4114 // optimizations will transparently handle this case.
4116 // In order for this transformation to be safe, the LHS must be of the
4117 // form X*(2^n) and the Or constant must be less than 2^n.
4118 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
4119 const SCEV *LHS = getSCEV(U->getOperand(0));
4120 const APInt &CIVal = CI->getValue();
4121 if (GetMinTrailingZeros(LHS) >=
4122 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
4123 // Build a plain add SCEV.
4124 const SCEV *S = getAddExpr(LHS, getSCEV(CI));
4125 // If the LHS of the add was an addrec and it has no-wrap flags,
4126 // transfer the no-wrap flags, since an or won't introduce a wrap.
4127 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
4128 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
4129 const_cast<SCEVAddRecExpr *>(NewAR)->setNoWrapFlags(
4130 OldAR->getNoWrapFlags());
4136 case Instruction::Xor:
4137 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
4138 // If the RHS of the xor is a signbit, then this is just an add.
4139 // Instcombine turns add of signbit into xor as a strength reduction step.
4140 if (CI->getValue().isSignBit())
4141 return getAddExpr(getSCEV(U->getOperand(0)),
4142 getSCEV(U->getOperand(1)));
4144 // If the RHS of xor is -1, then this is a not operation.
4145 if (CI->isAllOnesValue())
4146 return getNotSCEV(getSCEV(U->getOperand(0)));
4148 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
4149 // This is a variant of the check for xor with -1, and it handles
4150 // the case where instcombine has trimmed non-demanded bits out
4151 // of an xor with -1.
4152 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
4153 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
4154 if (BO->getOpcode() == Instruction::And &&
4155 LCI->getValue() == CI->getValue())
4156 if (const SCEVZeroExtendExpr *Z =
4157 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
4158 Type *UTy = U->getType();
4159 const SCEV *Z0 = Z->getOperand();
4160 Type *Z0Ty = Z0->getType();
4161 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
4163 // If C is a low-bits mask, the zero extend is serving to
4164 // mask off the high bits. Complement the operand and
4165 // re-apply the zext.
4166 if (APIntOps::isMask(Z0TySize, CI->getValue()))
4167 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
4169 // If C is a single bit, it may be in the sign-bit position
4170 // before the zero-extend. In this case, represent the xor
4171 // using an add, which is equivalent, and re-apply the zext.
4172 APInt Trunc = CI->getValue().trunc(Z0TySize);
4173 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
4175 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
4181 case Instruction::Shl:
4182 // Turn shift left of a constant amount into a multiply.
4183 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
4184 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
4186 // If the shift count is not less than the bitwidth, the result of
4187 // the shift is undefined. Don't try to analyze it, because the
4188 // resolution chosen here may differ from the resolution chosen in
4189 // other parts of the compiler.
4190 if (SA->getValue().uge(BitWidth))
4193 Constant *X = ConstantInt::get(getContext(),
4194 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
4195 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
4199 case Instruction::LShr:
4200 // Turn logical shift right of a constant into a unsigned divide.
4201 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
4202 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
4204 // If the shift count is not less than the bitwidth, the result of
4205 // the shift is undefined. Don't try to analyze it, because the
4206 // resolution chosen here may differ from the resolution chosen in
4207 // other parts of the compiler.
4208 if (SA->getValue().uge(BitWidth))
4211 Constant *X = ConstantInt::get(getContext(),
4212 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
4213 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
4217 case Instruction::AShr:
4218 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
4219 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
4220 if (Operator *L = dyn_cast<Operator>(U->getOperand(0)))
4221 if (L->getOpcode() == Instruction::Shl &&
4222 L->getOperand(1) == U->getOperand(1)) {
4223 uint64_t BitWidth = getTypeSizeInBits(U->getType());
4225 // If the shift count is not less than the bitwidth, the result of
4226 // the shift is undefined. Don't try to analyze it, because the
4227 // resolution chosen here may differ from the resolution chosen in
4228 // other parts of the compiler.
4229 if (CI->getValue().uge(BitWidth))
4232 uint64_t Amt = BitWidth - CI->getZExtValue();
4233 if (Amt == BitWidth)
4234 return getSCEV(L->getOperand(0)); // shift by zero --> noop
4236 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
4237 IntegerType::get(getContext(),
4243 case Instruction::Trunc:
4244 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
4246 case Instruction::ZExt:
4247 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
4249 case Instruction::SExt:
4250 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
4252 case Instruction::BitCast:
4253 // BitCasts are no-op casts so we just eliminate the cast.
4254 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
4255 return getSCEV(U->getOperand(0));
4258 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
4259 // lead to pointer expressions which cannot safely be expanded to GEPs,
4260 // because ScalarEvolution doesn't respect the GEP aliasing rules when
4261 // simplifying integer expressions.
4263 case Instruction::GetElementPtr:
4264 return createNodeForGEP(cast<GEPOperator>(U));
4266 case Instruction::PHI:
4267 return createNodeForPHI(cast<PHINode>(U));
4269 case Instruction::Select:
4270 // This could be a smax or umax that was lowered earlier.
4271 // Try to recover it.
4272 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
4273 Value *LHS = ICI->getOperand(0);
4274 Value *RHS = ICI->getOperand(1);
4275 switch (ICI->getPredicate()) {
4276 case ICmpInst::ICMP_SLT:
4277 case ICmpInst::ICMP_SLE:
4278 std::swap(LHS, RHS);
4280 case ICmpInst::ICMP_SGT:
4281 case ICmpInst::ICMP_SGE:
4282 // a >s b ? a+x : b+x -> smax(a, b)+x
4283 // a >s b ? b+x : a+x -> smin(a, b)+x
4284 if (LHS->getType() == U->getType()) {
4285 const SCEV *LS = getSCEV(LHS);
4286 const SCEV *RS = getSCEV(RHS);
4287 const SCEV *LA = getSCEV(U->getOperand(1));
4288 const SCEV *RA = getSCEV(U->getOperand(2));
4289 const SCEV *LDiff = getMinusSCEV(LA, LS);
4290 const SCEV *RDiff = getMinusSCEV(RA, RS);
4292 return getAddExpr(getSMaxExpr(LS, RS), LDiff);
4293 LDiff = getMinusSCEV(LA, RS);
4294 RDiff = getMinusSCEV(RA, LS);
4296 return getAddExpr(getSMinExpr(LS, RS), LDiff);
4299 case ICmpInst::ICMP_ULT:
4300 case ICmpInst::ICMP_ULE:
4301 std::swap(LHS, RHS);
4303 case ICmpInst::ICMP_UGT:
4304 case ICmpInst::ICMP_UGE:
4305 // a >u b ? a+x : b+x -> umax(a, b)+x
4306 // a >u b ? b+x : a+x -> umin(a, b)+x
4307 if (LHS->getType() == U->getType()) {
4308 const SCEV *LS = getSCEV(LHS);
4309 const SCEV *RS = getSCEV(RHS);
4310 const SCEV *LA = getSCEV(U->getOperand(1));
4311 const SCEV *RA = getSCEV(U->getOperand(2));
4312 const SCEV *LDiff = getMinusSCEV(LA, LS);
4313 const SCEV *RDiff = getMinusSCEV(RA, RS);
4315 return getAddExpr(getUMaxExpr(LS, RS), LDiff);
4316 LDiff = getMinusSCEV(LA, RS);
4317 RDiff = getMinusSCEV(RA, LS);
4319 return getAddExpr(getUMinExpr(LS, RS), LDiff);
4322 case ICmpInst::ICMP_NE:
4323 // n != 0 ? n+x : 1+x -> umax(n, 1)+x
4324 if (LHS->getType() == U->getType() &&
4325 isa<ConstantInt>(RHS) &&
4326 cast<ConstantInt>(RHS)->isZero()) {
4327 const SCEV *One = getConstant(LHS->getType(), 1);
4328 const SCEV *LS = getSCEV(LHS);
4329 const SCEV *LA = getSCEV(U->getOperand(1));
4330 const SCEV *RA = getSCEV(U->getOperand(2));
4331 const SCEV *LDiff = getMinusSCEV(LA, LS);
4332 const SCEV *RDiff = getMinusSCEV(RA, One);
4334 return getAddExpr(getUMaxExpr(One, LS), LDiff);
4337 case ICmpInst::ICMP_EQ:
4338 // n == 0 ? 1+x : n+x -> umax(n, 1)+x
4339 if (LHS->getType() == U->getType() &&
4340 isa<ConstantInt>(RHS) &&
4341 cast<ConstantInt>(RHS)->isZero()) {
4342 const SCEV *One = getConstant(LHS->getType(), 1);
4343 const SCEV *LS = getSCEV(LHS);
4344 const SCEV *LA = getSCEV(U->getOperand(1));
4345 const SCEV *RA = getSCEV(U->getOperand(2));
4346 const SCEV *LDiff = getMinusSCEV(LA, One);
4347 const SCEV *RDiff = getMinusSCEV(RA, LS);
4349 return getAddExpr(getUMaxExpr(One, LS), LDiff);
4357 default: // We cannot analyze this expression.
4361 return getUnknown(V);
4366 //===----------------------------------------------------------------------===//
4367 // Iteration Count Computation Code
4370 unsigned ScalarEvolution::getSmallConstantTripCount(Loop *L) {
4371 if (BasicBlock *ExitingBB = L->getExitingBlock())
4372 return getSmallConstantTripCount(L, ExitingBB);
4374 // No trip count information for multiple exits.
4378 /// getSmallConstantTripCount - Returns the maximum trip count of this loop as a
4379 /// normal unsigned value. Returns 0 if the trip count is unknown or not
4380 /// constant. Will also return 0 if the maximum trip count is very large (>=
4383 /// This "trip count" assumes that control exits via ExitingBlock. More
4384 /// precisely, it is the number of times that control may reach ExitingBlock
4385 /// before taking the branch. For loops with multiple exits, it may not be the
4386 /// number times that the loop header executes because the loop may exit
4387 /// prematurely via another branch.
4388 unsigned ScalarEvolution::getSmallConstantTripCount(Loop *L,
4389 BasicBlock *ExitingBlock) {
4390 assert(ExitingBlock && "Must pass a non-null exiting block!");
4391 assert(L->isLoopExiting(ExitingBlock) &&
4392 "Exiting block must actually branch out of the loop!");
4393 const SCEVConstant *ExitCount =
4394 dyn_cast<SCEVConstant>(getExitCount(L, ExitingBlock));
4398 ConstantInt *ExitConst = ExitCount->getValue();
4400 // Guard against huge trip counts.
4401 if (ExitConst->getValue().getActiveBits() > 32)
4404 // In case of integer overflow, this returns 0, which is correct.
4405 return ((unsigned)ExitConst->getZExtValue()) + 1;
4408 unsigned ScalarEvolution::getSmallConstantTripMultiple(Loop *L) {
4409 if (BasicBlock *ExitingBB = L->getExitingBlock())
4410 return getSmallConstantTripMultiple(L, ExitingBB);
4412 // No trip multiple information for multiple exits.
4416 /// getSmallConstantTripMultiple - Returns the largest constant divisor of the
4417 /// trip count of this loop as a normal unsigned value, if possible. This
4418 /// means that the actual trip count is always a multiple of the returned
4419 /// value (don't forget the trip count could very well be zero as well!).
4421 /// Returns 1 if the trip count is unknown or not guaranteed to be the
4422 /// multiple of a constant (which is also the case if the trip count is simply
4423 /// constant, use getSmallConstantTripCount for that case), Will also return 1
4424 /// if the trip count is very large (>= 2^32).
4426 /// As explained in the comments for getSmallConstantTripCount, this assumes
4427 /// that control exits the loop via ExitingBlock.
4429 ScalarEvolution::getSmallConstantTripMultiple(Loop *L,
4430 BasicBlock *ExitingBlock) {
4431 assert(ExitingBlock && "Must pass a non-null exiting block!");
4432 assert(L->isLoopExiting(ExitingBlock) &&
4433 "Exiting block must actually branch out of the loop!");
4434 const SCEV *ExitCount = getExitCount(L, ExitingBlock);
4435 if (ExitCount == getCouldNotCompute())
4438 // Get the trip count from the BE count by adding 1.
4439 const SCEV *TCMul = getAddExpr(ExitCount,
4440 getConstant(ExitCount->getType(), 1));
4441 // FIXME: SCEV distributes multiplication as V1*C1 + V2*C1. We could attempt
4442 // to factor simple cases.
4443 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(TCMul))
4444 TCMul = Mul->getOperand(0);
4446 const SCEVConstant *MulC = dyn_cast<SCEVConstant>(TCMul);
4450 ConstantInt *Result = MulC->getValue();
4452 // Guard against huge trip counts (this requires checking
4453 // for zero to handle the case where the trip count == -1 and the
4455 if (!Result || Result->getValue().getActiveBits() > 32 ||
4456 Result->getValue().getActiveBits() == 0)
4459 return (unsigned)Result->getZExtValue();
4462 // getExitCount - Get the expression for the number of loop iterations for which
4463 // this loop is guaranteed not to exit via ExitingBlock. Otherwise return
4464 // SCEVCouldNotCompute.
4465 const SCEV *ScalarEvolution::getExitCount(Loop *L, BasicBlock *ExitingBlock) {
4466 return getBackedgeTakenInfo(L).getExact(ExitingBlock, this);
4469 /// getBackedgeTakenCount - If the specified loop has a predictable
4470 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
4471 /// object. The backedge-taken count is the number of times the loop header
4472 /// will be branched to from within the loop. This is one less than the
4473 /// trip count of the loop, since it doesn't count the first iteration,
4474 /// when the header is branched to from outside the loop.
4476 /// Note that it is not valid to call this method on a loop without a
4477 /// loop-invariant backedge-taken count (see
4478 /// hasLoopInvariantBackedgeTakenCount).
4480 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
4481 return getBackedgeTakenInfo(L).getExact(this);
4484 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
4485 /// return the least SCEV value that is known never to be less than the
4486 /// actual backedge taken count.
4487 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
4488 return getBackedgeTakenInfo(L).getMax(this);
4491 /// PushLoopPHIs - Push PHI nodes in the header of the given loop
4492 /// onto the given Worklist.
4494 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
4495 BasicBlock *Header = L->getHeader();
4497 // Push all Loop-header PHIs onto the Worklist stack.
4498 for (BasicBlock::iterator I = Header->begin();
4499 PHINode *PN = dyn_cast<PHINode>(I); ++I)
4500 Worklist.push_back(PN);
4503 const ScalarEvolution::BackedgeTakenInfo &
4504 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
4505 // Initially insert an invalid entry for this loop. If the insertion
4506 // succeeds, proceed to actually compute a backedge-taken count and
4507 // update the value. The temporary CouldNotCompute value tells SCEV
4508 // code elsewhere that it shouldn't attempt to request a new
4509 // backedge-taken count, which could result in infinite recursion.
4510 std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
4511 BackedgeTakenCounts.insert(std::make_pair(L, BackedgeTakenInfo()));
4513 return Pair.first->second;
4515 // ComputeBackedgeTakenCount may allocate memory for its result. Inserting it
4516 // into the BackedgeTakenCounts map transfers ownership. Otherwise, the result
4517 // must be cleared in this scope.
4518 BackedgeTakenInfo Result = ComputeBackedgeTakenCount(L);
4520 if (Result.getExact(this) != getCouldNotCompute()) {
4521 assert(isLoopInvariant(Result.getExact(this), L) &&
4522 isLoopInvariant(Result.getMax(this), L) &&
4523 "Computed backedge-taken count isn't loop invariant for loop!");
4524 ++NumTripCountsComputed;
4526 else if (Result.getMax(this) == getCouldNotCompute() &&
4527 isa<PHINode>(L->getHeader()->begin())) {
4528 // Only count loops that have phi nodes as not being computable.
4529 ++NumTripCountsNotComputed;
4532 // Now that we know more about the trip count for this loop, forget any
4533 // existing SCEV values for PHI nodes in this loop since they are only
4534 // conservative estimates made without the benefit of trip count
4535 // information. This is similar to the code in forgetLoop, except that
4536 // it handles SCEVUnknown PHI nodes specially.
4537 if (Result.hasAnyInfo()) {
4538 SmallVector<Instruction *, 16> Worklist;
4539 PushLoopPHIs(L, Worklist);
4541 SmallPtrSet<Instruction *, 8> Visited;
4542 while (!Worklist.empty()) {
4543 Instruction *I = Worklist.pop_back_val();
4544 if (!Visited.insert(I).second)
4547 ValueExprMapType::iterator It =
4548 ValueExprMap.find_as(static_cast<Value *>(I));
4549 if (It != ValueExprMap.end()) {
4550 const SCEV *Old = It->second;
4552 // SCEVUnknown for a PHI either means that it has an unrecognized
4553 // structure, or it's a PHI that's in the progress of being computed
4554 // by createNodeForPHI. In the former case, additional loop trip
4555 // count information isn't going to change anything. In the later
4556 // case, createNodeForPHI will perform the necessary updates on its
4557 // own when it gets to that point.
4558 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) {
4559 forgetMemoizedResults(Old);
4560 ValueExprMap.erase(It);
4562 if (PHINode *PN = dyn_cast<PHINode>(I))
4563 ConstantEvolutionLoopExitValue.erase(PN);
4566 PushDefUseChildren(I, Worklist);
4570 // Re-lookup the insert position, since the call to
4571 // ComputeBackedgeTakenCount above could result in a
4572 // recusive call to getBackedgeTakenInfo (on a different
4573 // loop), which would invalidate the iterator computed
4575 return BackedgeTakenCounts.find(L)->second = Result;
4578 /// forgetLoop - This method should be called by the client when it has
4579 /// changed a loop in a way that may effect ScalarEvolution's ability to
4580 /// compute a trip count, or if the loop is deleted.
4581 void ScalarEvolution::forgetLoop(const Loop *L) {
4582 // Drop any stored trip count value.
4583 DenseMap<const Loop*, BackedgeTakenInfo>::iterator BTCPos =
4584 BackedgeTakenCounts.find(L);
4585 if (BTCPos != BackedgeTakenCounts.end()) {
4586 BTCPos->second.clear();
4587 BackedgeTakenCounts.erase(BTCPos);
4590 // Drop information about expressions based on loop-header PHIs.
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 forgetMemoizedResults(It->second);
4604 ValueExprMap.erase(It);
4605 if (PHINode *PN = dyn_cast<PHINode>(I))
4606 ConstantEvolutionLoopExitValue.erase(PN);
4609 PushDefUseChildren(I, Worklist);
4612 // Forget all contained loops too, to avoid dangling entries in the
4613 // ValuesAtScopes map.
4614 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
4618 /// forgetValue - This method should be called by the client when it has
4619 /// changed a value in a way that may effect its value, or which may
4620 /// disconnect it from a def-use chain linking it to a loop.
4621 void ScalarEvolution::forgetValue(Value *V) {
4622 Instruction *I = dyn_cast<Instruction>(V);
4625 // Drop information about expressions based on loop-header PHIs.
4626 SmallVector<Instruction *, 16> Worklist;
4627 Worklist.push_back(I);
4629 SmallPtrSet<Instruction *, 8> Visited;
4630 while (!Worklist.empty()) {
4631 I = Worklist.pop_back_val();
4632 if (!Visited.insert(I).second)
4635 ValueExprMapType::iterator It =
4636 ValueExprMap.find_as(static_cast<Value *>(I));
4637 if (It != ValueExprMap.end()) {
4638 forgetMemoizedResults(It->second);
4639 ValueExprMap.erase(It);
4640 if (PHINode *PN = dyn_cast<PHINode>(I))
4641 ConstantEvolutionLoopExitValue.erase(PN);
4644 PushDefUseChildren(I, Worklist);
4648 /// getExact - Get the exact loop backedge taken count considering all loop
4649 /// exits. A computable result can only be return for loops with a single exit.
4650 /// Returning the minimum taken count among all exits is incorrect because one
4651 /// of the loop's exit limit's may have been skipped. HowFarToZero assumes that
4652 /// the limit of each loop test is never skipped. This is a valid assumption as
4653 /// long as the loop exits via that test. For precise results, it is the
4654 /// caller's responsibility to specify the relevant loop exit using
4655 /// getExact(ExitingBlock, SE).
4657 ScalarEvolution::BackedgeTakenInfo::getExact(ScalarEvolution *SE) const {
4658 // If any exits were not computable, the loop is not computable.
4659 if (!ExitNotTaken.isCompleteList()) return SE->getCouldNotCompute();
4661 // We need exactly one computable exit.
4662 if (!ExitNotTaken.ExitingBlock) return SE->getCouldNotCompute();
4663 assert(ExitNotTaken.ExactNotTaken && "uninitialized not-taken info");
4665 const SCEV *BECount = nullptr;
4666 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4667 ENT != nullptr; ENT = ENT->getNextExit()) {
4669 assert(ENT->ExactNotTaken != SE->getCouldNotCompute() && "bad exit SCEV");
4672 BECount = ENT->ExactNotTaken;
4673 else if (BECount != ENT->ExactNotTaken)
4674 return SE->getCouldNotCompute();
4676 assert(BECount && "Invalid not taken count for loop exit");
4680 /// getExact - Get the exact not taken count for this loop exit.
4682 ScalarEvolution::BackedgeTakenInfo::getExact(BasicBlock *ExitingBlock,
4683 ScalarEvolution *SE) const {
4684 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4685 ENT != nullptr; ENT = ENT->getNextExit()) {
4687 if (ENT->ExitingBlock == ExitingBlock)
4688 return ENT->ExactNotTaken;
4690 return SE->getCouldNotCompute();
4693 /// getMax - Get the max backedge taken count for the loop.
4695 ScalarEvolution::BackedgeTakenInfo::getMax(ScalarEvolution *SE) const {
4696 return Max ? Max : SE->getCouldNotCompute();
4699 bool ScalarEvolution::BackedgeTakenInfo::hasOperand(const SCEV *S,
4700 ScalarEvolution *SE) const {
4701 if (Max && Max != SE->getCouldNotCompute() && SE->hasOperand(Max, S))
4704 if (!ExitNotTaken.ExitingBlock)
4707 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4708 ENT != nullptr; ENT = ENT->getNextExit()) {
4710 if (ENT->ExactNotTaken != SE->getCouldNotCompute()
4711 && SE->hasOperand(ENT->ExactNotTaken, S)) {
4718 /// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each
4719 /// computable exit into a persistent ExitNotTakenInfo array.
4720 ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo(
4721 SmallVectorImpl< std::pair<BasicBlock *, const SCEV *> > &ExitCounts,
4722 bool Complete, const SCEV *MaxCount) : Max(MaxCount) {
4725 ExitNotTaken.setIncomplete();
4727 unsigned NumExits = ExitCounts.size();
4728 if (NumExits == 0) return;
4730 ExitNotTaken.ExitingBlock = ExitCounts[0].first;
4731 ExitNotTaken.ExactNotTaken = ExitCounts[0].second;
4732 if (NumExits == 1) return;
4734 // Handle the rare case of multiple computable exits.
4735 ExitNotTakenInfo *ENT = new ExitNotTakenInfo[NumExits-1];
4737 ExitNotTakenInfo *PrevENT = &ExitNotTaken;
4738 for (unsigned i = 1; i < NumExits; ++i, PrevENT = ENT, ++ENT) {
4739 PrevENT->setNextExit(ENT);
4740 ENT->ExitingBlock = ExitCounts[i].first;
4741 ENT->ExactNotTaken = ExitCounts[i].second;
4745 /// clear - Invalidate this result and free the ExitNotTakenInfo array.
4746 void ScalarEvolution::BackedgeTakenInfo::clear() {
4747 ExitNotTaken.ExitingBlock = nullptr;
4748 ExitNotTaken.ExactNotTaken = nullptr;
4749 delete[] ExitNotTaken.getNextExit();
4752 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
4753 /// of the specified loop will execute.
4754 ScalarEvolution::BackedgeTakenInfo
4755 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
4756 SmallVector<BasicBlock *, 8> ExitingBlocks;
4757 L->getExitingBlocks(ExitingBlocks);
4759 SmallVector<std::pair<BasicBlock *, const SCEV *>, 4> ExitCounts;
4760 bool CouldComputeBECount = true;
4761 BasicBlock *Latch = L->getLoopLatch(); // may be NULL.
4762 const SCEV *MustExitMaxBECount = nullptr;
4763 const SCEV *MayExitMaxBECount = nullptr;
4765 // Compute the ExitLimit for each loop exit. Use this to populate ExitCounts
4766 // and compute maxBECount.
4767 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
4768 BasicBlock *ExitBB = ExitingBlocks[i];
4769 ExitLimit EL = ComputeExitLimit(L, ExitBB);
4771 // 1. For each exit that can be computed, add an entry to ExitCounts.
4772 // CouldComputeBECount is true only if all exits can be computed.
4773 if (EL.Exact == getCouldNotCompute())
4774 // We couldn't compute an exact value for this exit, so
4775 // we won't be able to compute an exact value for the loop.
4776 CouldComputeBECount = false;
4778 ExitCounts.push_back(std::make_pair(ExitBB, EL.Exact));
4780 // 2. Derive the loop's MaxBECount from each exit's max number of
4781 // non-exiting iterations. Partition the loop exits into two kinds:
4782 // LoopMustExits and LoopMayExits.
4784 // If the exit dominates the loop latch, it is a LoopMustExit otherwise it
4785 // is a LoopMayExit. If any computable LoopMustExit is found, then
4786 // MaxBECount is the minimum EL.Max of computable LoopMustExits. Otherwise,
4787 // MaxBECount is conservatively the maximum EL.Max, where CouldNotCompute is
4788 // considered greater than any computable EL.Max.
4789 if (EL.Max != getCouldNotCompute() && Latch &&
4790 DT->dominates(ExitBB, Latch)) {
4791 if (!MustExitMaxBECount)
4792 MustExitMaxBECount = EL.Max;
4794 MustExitMaxBECount =
4795 getUMinFromMismatchedTypes(MustExitMaxBECount, EL.Max);
4797 } else if (MayExitMaxBECount != getCouldNotCompute()) {
4798 if (!MayExitMaxBECount || EL.Max == getCouldNotCompute())
4799 MayExitMaxBECount = EL.Max;
4802 getUMaxFromMismatchedTypes(MayExitMaxBECount, EL.Max);
4806 const SCEV *MaxBECount = MustExitMaxBECount ? MustExitMaxBECount :
4807 (MayExitMaxBECount ? MayExitMaxBECount : getCouldNotCompute());
4808 return BackedgeTakenInfo(ExitCounts, CouldComputeBECount, MaxBECount);
4811 /// ComputeExitLimit - Compute the number of times the backedge of the specified
4812 /// loop will execute if it exits via the specified block.
4813 ScalarEvolution::ExitLimit
4814 ScalarEvolution::ComputeExitLimit(const Loop *L, BasicBlock *ExitingBlock) {
4816 // Okay, we've chosen an exiting block. See what condition causes us to
4817 // exit at this block and remember the exit block and whether all other targets
4818 // lead to the loop header.
4819 bool MustExecuteLoopHeader = true;
4820 BasicBlock *Exit = nullptr;
4821 for (succ_iterator SI = succ_begin(ExitingBlock), SE = succ_end(ExitingBlock);
4823 if (!L->contains(*SI)) {
4824 if (Exit) // Multiple exit successors.
4825 return getCouldNotCompute();
4827 } else if (*SI != L->getHeader()) {
4828 MustExecuteLoopHeader = false;
4831 // At this point, we know we have a conditional branch that determines whether
4832 // the loop is exited. However, we don't know if the branch is executed each
4833 // time through the loop. If not, then the execution count of the branch will
4834 // not be equal to the trip count of the loop.
4836 // Currently we check for this by checking to see if the Exit branch goes to
4837 // the loop header. If so, we know it will always execute the same number of
4838 // times as the loop. We also handle the case where the exit block *is* the
4839 // loop header. This is common for un-rotated loops.
4841 // If both of those tests fail, walk up the unique predecessor chain to the
4842 // header, stopping if there is an edge that doesn't exit the loop. If the
4843 // header is reached, the execution count of the branch will be equal to the
4844 // trip count of the loop.
4846 // More extensive analysis could be done to handle more cases here.
4848 if (!MustExecuteLoopHeader && ExitingBlock != L->getHeader()) {
4849 // The simple checks failed, try climbing the unique predecessor chain
4850 // up to the header.
4852 for (BasicBlock *BB = ExitingBlock; BB; ) {
4853 BasicBlock *Pred = BB->getUniquePredecessor();
4855 return getCouldNotCompute();
4856 TerminatorInst *PredTerm = Pred->getTerminator();
4857 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) {
4858 BasicBlock *PredSucc = PredTerm->getSuccessor(i);
4861 // If the predecessor has a successor that isn't BB and isn't
4862 // outside the loop, assume the worst.
4863 if (L->contains(PredSucc))
4864 return getCouldNotCompute();
4866 if (Pred == L->getHeader()) {
4873 return getCouldNotCompute();
4876 bool IsOnlyExit = (L->getExitingBlock() != nullptr);
4877 TerminatorInst *Term = ExitingBlock->getTerminator();
4878 if (BranchInst *BI = dyn_cast<BranchInst>(Term)) {
4879 assert(BI->isConditional() && "If unconditional, it can't be in loop!");
4880 // Proceed to the next level to examine the exit condition expression.
4881 return ComputeExitLimitFromCond(L, BI->getCondition(), BI->getSuccessor(0),
4882 BI->getSuccessor(1),
4883 /*ControlsExit=*/IsOnlyExit);
4886 if (SwitchInst *SI = dyn_cast<SwitchInst>(Term))
4887 return ComputeExitLimitFromSingleExitSwitch(L, SI, Exit,
4888 /*ControlsExit=*/IsOnlyExit);
4890 return getCouldNotCompute();
4893 /// ComputeExitLimitFromCond - Compute the number of times the
4894 /// backedge of the specified loop will execute if its exit condition
4895 /// were a conditional branch of ExitCond, TBB, and FBB.
4897 /// @param ControlsExit is true if ExitCond directly controls the exit
4898 /// branch. In this case, we can assume that the loop exits only if the
4899 /// condition is true and can infer that failing to meet the condition prior to
4900 /// integer wraparound results in undefined behavior.
4901 ScalarEvolution::ExitLimit
4902 ScalarEvolution::ComputeExitLimitFromCond(const Loop *L,
4906 bool ControlsExit) {
4907 // Check if the controlling expression for this loop is an And or Or.
4908 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
4909 if (BO->getOpcode() == Instruction::And) {
4910 // Recurse on the operands of the and.
4911 bool EitherMayExit = L->contains(TBB);
4912 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
4913 ControlsExit && !EitherMayExit);
4914 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
4915 ControlsExit && !EitherMayExit);
4916 const SCEV *BECount = getCouldNotCompute();
4917 const SCEV *MaxBECount = getCouldNotCompute();
4918 if (EitherMayExit) {
4919 // Both conditions must be true for the loop to continue executing.
4920 // Choose the less conservative count.
4921 if (EL0.Exact == getCouldNotCompute() ||
4922 EL1.Exact == getCouldNotCompute())
4923 BECount = getCouldNotCompute();
4925 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
4926 if (EL0.Max == getCouldNotCompute())
4927 MaxBECount = EL1.Max;
4928 else if (EL1.Max == getCouldNotCompute())
4929 MaxBECount = EL0.Max;
4931 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
4933 // Both conditions must be true at the same time for the loop to exit.
4934 // For now, be conservative.
4935 assert(L->contains(FBB) && "Loop block has no successor in loop!");
4936 if (EL0.Max == EL1.Max)
4937 MaxBECount = EL0.Max;
4938 if (EL0.Exact == EL1.Exact)
4939 BECount = EL0.Exact;
4942 return ExitLimit(BECount, MaxBECount);
4944 if (BO->getOpcode() == Instruction::Or) {
4945 // Recurse on the operands of the or.
4946 bool EitherMayExit = L->contains(FBB);
4947 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
4948 ControlsExit && !EitherMayExit);
4949 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
4950 ControlsExit && !EitherMayExit);
4951 const SCEV *BECount = getCouldNotCompute();
4952 const SCEV *MaxBECount = getCouldNotCompute();
4953 if (EitherMayExit) {
4954 // Both conditions must be false for the loop to continue executing.
4955 // Choose the less conservative count.
4956 if (EL0.Exact == getCouldNotCompute() ||
4957 EL1.Exact == getCouldNotCompute())
4958 BECount = getCouldNotCompute();
4960 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
4961 if (EL0.Max == getCouldNotCompute())
4962 MaxBECount = EL1.Max;
4963 else if (EL1.Max == getCouldNotCompute())
4964 MaxBECount = EL0.Max;
4966 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
4968 // Both conditions must be false at the same time for the loop to exit.
4969 // For now, be conservative.
4970 assert(L->contains(TBB) && "Loop block has no successor in loop!");
4971 if (EL0.Max == EL1.Max)
4972 MaxBECount = EL0.Max;
4973 if (EL0.Exact == EL1.Exact)
4974 BECount = EL0.Exact;
4977 return ExitLimit(BECount, MaxBECount);
4981 // With an icmp, it may be feasible to compute an exact backedge-taken count.
4982 // Proceed to the next level to examine the icmp.
4983 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
4984 return ComputeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB, ControlsExit);
4986 // Check for a constant condition. These are normally stripped out by
4987 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
4988 // preserve the CFG and is temporarily leaving constant conditions
4990 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
4991 if (L->contains(FBB) == !CI->getZExtValue())
4992 // The backedge is always taken.
4993 return getCouldNotCompute();
4995 // The backedge is never taken.
4996 return getConstant(CI->getType(), 0);
4999 // If it's not an integer or pointer comparison then compute it the hard way.
5000 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
5003 /// ComputeExitLimitFromICmp - Compute the number of times the
5004 /// backedge of the specified loop will execute if its exit condition
5005 /// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB.
5006 ScalarEvolution::ExitLimit
5007 ScalarEvolution::ComputeExitLimitFromICmp(const Loop *L,
5011 bool ControlsExit) {
5013 // If the condition was exit on true, convert the condition to exit on false
5014 ICmpInst::Predicate Cond;
5015 if (!L->contains(FBB))
5016 Cond = ExitCond->getPredicate();
5018 Cond = ExitCond->getInversePredicate();
5020 // Handle common loops like: for (X = "string"; *X; ++X)
5021 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
5022 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
5024 ComputeLoadConstantCompareExitLimit(LI, RHS, L, Cond);
5025 if (ItCnt.hasAnyInfo())
5029 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
5030 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
5032 // Try to evaluate any dependencies out of the loop.
5033 LHS = getSCEVAtScope(LHS, L);
5034 RHS = getSCEVAtScope(RHS, L);
5036 // At this point, we would like to compute how many iterations of the
5037 // loop the predicate will return true for these inputs.
5038 if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) {
5039 // If there is a loop-invariant, force it into the RHS.
5040 std::swap(LHS, RHS);
5041 Cond = ICmpInst::getSwappedPredicate(Cond);
5044 // Simplify the operands before analyzing them.
5045 (void)SimplifyICmpOperands(Cond, LHS, RHS);
5047 // If we have a comparison of a chrec against a constant, try to use value
5048 // ranges to answer this query.
5049 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
5050 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
5051 if (AddRec->getLoop() == L) {
5052 // Form the constant range.
5053 ConstantRange CompRange(
5054 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
5056 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
5057 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
5061 case ICmpInst::ICMP_NE: { // while (X != Y)
5062 // Convert to: while (X-Y != 0)
5063 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit);
5064 if (EL.hasAnyInfo()) return EL;
5067 case ICmpInst::ICMP_EQ: { // while (X == Y)
5068 // Convert to: while (X-Y == 0)
5069 ExitLimit EL = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
5070 if (EL.hasAnyInfo()) return EL;
5073 case ICmpInst::ICMP_SLT:
5074 case ICmpInst::ICMP_ULT: { // while (X < Y)
5075 bool IsSigned = Cond == ICmpInst::ICMP_SLT;
5076 ExitLimit EL = HowManyLessThans(LHS, RHS, L, IsSigned, ControlsExit);
5077 if (EL.hasAnyInfo()) return EL;
5080 case ICmpInst::ICMP_SGT:
5081 case ICmpInst::ICMP_UGT: { // while (X > Y)
5082 bool IsSigned = Cond == ICmpInst::ICMP_SGT;
5083 ExitLimit EL = HowManyGreaterThans(LHS, RHS, L, IsSigned, ControlsExit);
5084 if (EL.hasAnyInfo()) return EL;
5089 dbgs() << "ComputeBackedgeTakenCount ";
5090 if (ExitCond->getOperand(0)->getType()->isUnsigned())
5091 dbgs() << "[unsigned] ";
5092 dbgs() << *LHS << " "
5093 << Instruction::getOpcodeName(Instruction::ICmp)
5094 << " " << *RHS << "\n";
5098 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
5101 ScalarEvolution::ExitLimit
5102 ScalarEvolution::ComputeExitLimitFromSingleExitSwitch(const Loop *L,
5104 BasicBlock *ExitingBlock,
5105 bool ControlsExit) {
5106 assert(!L->contains(ExitingBlock) && "Not an exiting block!");
5108 // Give up if the exit is the default dest of a switch.
5109 if (Switch->getDefaultDest() == ExitingBlock)
5110 return getCouldNotCompute();
5112 assert(L->contains(Switch->getDefaultDest()) &&
5113 "Default case must not exit the loop!");
5114 const SCEV *LHS = getSCEVAtScope(Switch->getCondition(), L);
5115 const SCEV *RHS = getConstant(Switch->findCaseDest(ExitingBlock));
5117 // while (X != Y) --> while (X-Y != 0)
5118 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit);
5119 if (EL.hasAnyInfo())
5122 return getCouldNotCompute();
5125 static ConstantInt *
5126 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
5127 ScalarEvolution &SE) {
5128 const SCEV *InVal = SE.getConstant(C);
5129 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
5130 assert(isa<SCEVConstant>(Val) &&
5131 "Evaluation of SCEV at constant didn't fold correctly?");
5132 return cast<SCEVConstant>(Val)->getValue();
5135 /// ComputeLoadConstantCompareExitLimit - Given an exit condition of
5136 /// 'icmp op load X, cst', try to see if we can compute the backedge
5137 /// execution count.
5138 ScalarEvolution::ExitLimit
5139 ScalarEvolution::ComputeLoadConstantCompareExitLimit(
5143 ICmpInst::Predicate predicate) {
5145 if (LI->isVolatile()) return getCouldNotCompute();
5147 // Check to see if the loaded pointer is a getelementptr of a global.
5148 // TODO: Use SCEV instead of manually grubbing with GEPs.
5149 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
5150 if (!GEP) return getCouldNotCompute();
5152 // Make sure that it is really a constant global we are gepping, with an
5153 // initializer, and make sure the first IDX is really 0.
5154 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
5155 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
5156 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
5157 !cast<Constant>(GEP->getOperand(1))->isNullValue())
5158 return getCouldNotCompute();
5160 // Okay, we allow one non-constant index into the GEP instruction.
5161 Value *VarIdx = nullptr;
5162 std::vector<Constant*> Indexes;
5163 unsigned VarIdxNum = 0;
5164 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
5165 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
5166 Indexes.push_back(CI);
5167 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
5168 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
5169 VarIdx = GEP->getOperand(i);
5171 Indexes.push_back(nullptr);
5174 // Loop-invariant loads may be a byproduct of loop optimization. Skip them.
5176 return getCouldNotCompute();
5178 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
5179 // Check to see if X is a loop variant variable value now.
5180 const SCEV *Idx = getSCEV(VarIdx);
5181 Idx = getSCEVAtScope(Idx, L);
5183 // We can only recognize very limited forms of loop index expressions, in
5184 // particular, only affine AddRec's like {C1,+,C2}.
5185 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
5186 if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) ||
5187 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
5188 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
5189 return getCouldNotCompute();
5191 unsigned MaxSteps = MaxBruteForceIterations;
5192 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
5193 ConstantInt *ItCst = ConstantInt::get(
5194 cast<IntegerType>(IdxExpr->getType()), IterationNum);
5195 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
5197 // Form the GEP offset.
5198 Indexes[VarIdxNum] = Val;
5200 Constant *Result = ConstantFoldLoadThroughGEPIndices(GV->getInitializer(),
5202 if (!Result) break; // Cannot compute!
5204 // Evaluate the condition for this iteration.
5205 Result = ConstantExpr::getICmp(predicate, Result, RHS);
5206 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
5207 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
5209 dbgs() << "\n***\n*** Computed loop count " << *ItCst
5210 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
5213 ++NumArrayLenItCounts;
5214 return getConstant(ItCst); // Found terminating iteration!
5217 return getCouldNotCompute();
5221 /// CanConstantFold - Return true if we can constant fold an instruction of the
5222 /// specified type, assuming that all operands were constants.
5223 static bool CanConstantFold(const Instruction *I) {
5224 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
5225 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I) ||
5229 if (const CallInst *CI = dyn_cast<CallInst>(I))
5230 if (const Function *F = CI->getCalledFunction())
5231 return canConstantFoldCallTo(F);
5235 /// Determine whether this instruction can constant evolve within this loop
5236 /// assuming its operands can all constant evolve.
5237 static bool canConstantEvolve(Instruction *I, const Loop *L) {
5238 // An instruction outside of the loop can't be derived from a loop PHI.
5239 if (!L->contains(I)) return false;
5241 if (isa<PHINode>(I)) {
5242 if (L->getHeader() == I->getParent())
5245 // We don't currently keep track of the control flow needed to evaluate
5246 // PHIs, so we cannot handle PHIs inside of loops.
5250 // If we won't be able to constant fold this expression even if the operands
5251 // are constants, bail early.
5252 return CanConstantFold(I);
5255 /// getConstantEvolvingPHIOperands - Implement getConstantEvolvingPHI by
5256 /// recursing through each instruction operand until reaching a loop header phi.
5258 getConstantEvolvingPHIOperands(Instruction *UseInst, const Loop *L,
5259 DenseMap<Instruction *, PHINode *> &PHIMap) {
5261 // Otherwise, we can evaluate this instruction if all of its operands are
5262 // constant or derived from a PHI node themselves.
5263 PHINode *PHI = nullptr;
5264 for (Instruction::op_iterator OpI = UseInst->op_begin(),
5265 OpE = UseInst->op_end(); OpI != OpE; ++OpI) {
5267 if (isa<Constant>(*OpI)) continue;
5269 Instruction *OpInst = dyn_cast<Instruction>(*OpI);
5270 if (!OpInst || !canConstantEvolve(OpInst, L)) return nullptr;
5272 PHINode *P = dyn_cast<PHINode>(OpInst);
5274 // If this operand is already visited, reuse the prior result.
5275 // We may have P != PHI if this is the deepest point at which the
5276 // inconsistent paths meet.
5277 P = PHIMap.lookup(OpInst);
5279 // Recurse and memoize the results, whether a phi is found or not.
5280 // This recursive call invalidates pointers into PHIMap.
5281 P = getConstantEvolvingPHIOperands(OpInst, L, PHIMap);
5285 return nullptr; // Not evolving from PHI
5286 if (PHI && PHI != P)
5287 return nullptr; // Evolving from multiple different PHIs.
5290 // This is a expression evolving from a constant PHI!
5294 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
5295 /// in the loop that V is derived from. We allow arbitrary operations along the
5296 /// way, but the operands of an operation must either be constants or a value
5297 /// derived from a constant PHI. If this expression does not fit with these
5298 /// constraints, return null.
5299 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
5300 Instruction *I = dyn_cast<Instruction>(V);
5301 if (!I || !canConstantEvolve(I, L)) return nullptr;
5303 if (PHINode *PN = dyn_cast<PHINode>(I)) {
5307 // Record non-constant instructions contained by the loop.
5308 DenseMap<Instruction *, PHINode *> PHIMap;
5309 return getConstantEvolvingPHIOperands(I, L, PHIMap);
5312 /// EvaluateExpression - Given an expression that passes the
5313 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
5314 /// in the loop has the value PHIVal. If we can't fold this expression for some
5315 /// reason, return null.
5316 static Constant *EvaluateExpression(Value *V, const Loop *L,
5317 DenseMap<Instruction *, Constant *> &Vals,
5318 const DataLayout *DL,
5319 const TargetLibraryInfo *TLI) {
5320 // Convenient constant check, but redundant for recursive calls.
5321 if (Constant *C = dyn_cast<Constant>(V)) return C;
5322 Instruction *I = dyn_cast<Instruction>(V);
5323 if (!I) return nullptr;
5325 if (Constant *C = Vals.lookup(I)) return C;
5327 // An instruction inside the loop depends on a value outside the loop that we
5328 // weren't given a mapping for, or a value such as a call inside the loop.
5329 if (!canConstantEvolve(I, L)) return nullptr;
5331 // An unmapped PHI can be due to a branch or another loop inside this loop,
5332 // or due to this not being the initial iteration through a loop where we
5333 // couldn't compute the evolution of this particular PHI last time.
5334 if (isa<PHINode>(I)) return nullptr;
5336 std::vector<Constant*> Operands(I->getNumOperands());
5338 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
5339 Instruction *Operand = dyn_cast<Instruction>(I->getOperand(i));
5341 Operands[i] = dyn_cast<Constant>(I->getOperand(i));
5342 if (!Operands[i]) return nullptr;
5345 Constant *C = EvaluateExpression(Operand, L, Vals, DL, TLI);
5347 if (!C) return nullptr;
5351 if (CmpInst *CI = dyn_cast<CmpInst>(I))
5352 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
5353 Operands[1], DL, TLI);
5354 if (LoadInst *LI = dyn_cast<LoadInst>(I)) {
5355 if (!LI->isVolatile())
5356 return ConstantFoldLoadFromConstPtr(Operands[0], DL);
5358 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), Operands, DL,
5362 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
5363 /// in the header of its containing loop, we know the loop executes a
5364 /// constant number of times, and the PHI node is just a recurrence
5365 /// involving constants, fold it.
5367 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
5370 DenseMap<PHINode*, Constant*>::const_iterator I =
5371 ConstantEvolutionLoopExitValue.find(PN);
5372 if (I != ConstantEvolutionLoopExitValue.end())
5375 if (BEs.ugt(MaxBruteForceIterations))
5376 return ConstantEvolutionLoopExitValue[PN] = nullptr; // Not going to evaluate it.
5378 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
5380 DenseMap<Instruction *, Constant *> CurrentIterVals;
5381 BasicBlock *Header = L->getHeader();
5382 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
5384 // Since the loop is canonicalized, the PHI node must have two entries. One
5385 // entry must be a constant (coming in from outside of the loop), and the
5386 // second must be derived from the same PHI.
5387 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
5388 PHINode *PHI = nullptr;
5389 for (BasicBlock::iterator I = Header->begin();
5390 (PHI = dyn_cast<PHINode>(I)); ++I) {
5391 Constant *StartCST =
5392 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
5393 if (!StartCST) continue;
5394 CurrentIterVals[PHI] = StartCST;
5396 if (!CurrentIterVals.count(PN))
5397 return RetVal = nullptr;
5399 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
5401 // Execute the loop symbolically to determine the exit value.
5402 if (BEs.getActiveBits() >= 32)
5403 return RetVal = nullptr; // More than 2^32-1 iterations?? Not doing it!
5405 unsigned NumIterations = BEs.getZExtValue(); // must be in range
5406 unsigned IterationNum = 0;
5407 for (; ; ++IterationNum) {
5408 if (IterationNum == NumIterations)
5409 return RetVal = CurrentIterVals[PN]; // Got exit value!
5411 // Compute the value of the PHIs for the next iteration.
5412 // EvaluateExpression adds non-phi values to the CurrentIterVals map.
5413 DenseMap<Instruction *, Constant *> NextIterVals;
5414 Constant *NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL,
5417 return nullptr; // Couldn't evaluate!
5418 NextIterVals[PN] = NextPHI;
5420 bool StoppedEvolving = NextPHI == CurrentIterVals[PN];
5422 // Also evaluate the other PHI nodes. However, we don't get to stop if we
5423 // cease to be able to evaluate one of them or if they stop evolving,
5424 // because that doesn't necessarily prevent us from computing PN.
5425 SmallVector<std::pair<PHINode *, Constant *>, 8> PHIsToCompute;
5426 for (DenseMap<Instruction *, Constant *>::const_iterator
5427 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
5428 PHINode *PHI = dyn_cast<PHINode>(I->first);
5429 if (!PHI || PHI == PN || PHI->getParent() != Header) continue;
5430 PHIsToCompute.push_back(std::make_pair(PHI, I->second));
5432 // We use two distinct loops because EvaluateExpression may invalidate any
5433 // iterators into CurrentIterVals.
5434 for (SmallVectorImpl<std::pair<PHINode *, Constant*> >::const_iterator
5435 I = PHIsToCompute.begin(), E = PHIsToCompute.end(); I != E; ++I) {
5436 PHINode *PHI = I->first;
5437 Constant *&NextPHI = NextIterVals[PHI];
5438 if (!NextPHI) { // Not already computed.
5439 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
5440 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, TLI);
5442 if (NextPHI != I->second)
5443 StoppedEvolving = false;
5446 // If all entries in CurrentIterVals == NextIterVals then we can stop
5447 // iterating, the loop can't continue to change.
5448 if (StoppedEvolving)
5449 return RetVal = CurrentIterVals[PN];
5451 CurrentIterVals.swap(NextIterVals);
5455 /// ComputeExitCountExhaustively - If the loop is known to execute a
5456 /// constant number of times (the condition evolves only from constants),
5457 /// try to evaluate a few iterations of the loop until we get the exit
5458 /// condition gets a value of ExitWhen (true or false). If we cannot
5459 /// evaluate the trip count of the loop, return getCouldNotCompute().
5460 const SCEV *ScalarEvolution::ComputeExitCountExhaustively(const Loop *L,
5463 PHINode *PN = getConstantEvolvingPHI(Cond, L);
5464 if (!PN) return getCouldNotCompute();
5466 // If the loop is canonicalized, the PHI will have exactly two entries.
5467 // That's the only form we support here.
5468 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
5470 DenseMap<Instruction *, Constant *> CurrentIterVals;
5471 BasicBlock *Header = L->getHeader();
5472 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
5474 // One entry must be a constant (coming in from outside of the loop), and the
5475 // second must be derived from the same PHI.
5476 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
5477 PHINode *PHI = nullptr;
5478 for (BasicBlock::iterator I = Header->begin();
5479 (PHI = dyn_cast<PHINode>(I)); ++I) {
5480 Constant *StartCST =
5481 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
5482 if (!StartCST) continue;
5483 CurrentIterVals[PHI] = StartCST;
5485 if (!CurrentIterVals.count(PN))
5486 return getCouldNotCompute();
5488 // Okay, we find a PHI node that defines the trip count of this loop. Execute
5489 // the loop symbolically to determine when the condition gets a value of
5492 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
5493 for (unsigned IterationNum = 0; IterationNum != MaxIterations;++IterationNum){
5494 ConstantInt *CondVal =
5495 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, L, CurrentIterVals,
5498 // Couldn't symbolically evaluate.
5499 if (!CondVal) return getCouldNotCompute();
5501 if (CondVal->getValue() == uint64_t(ExitWhen)) {
5502 ++NumBruteForceTripCountsComputed;
5503 return getConstant(Type::getInt32Ty(getContext()), IterationNum);
5506 // Update all the PHI nodes for the next iteration.
5507 DenseMap<Instruction *, Constant *> NextIterVals;
5509 // Create a list of which PHIs we need to compute. We want to do this before
5510 // calling EvaluateExpression on them because that may invalidate iterators
5511 // into CurrentIterVals.
5512 SmallVector<PHINode *, 8> PHIsToCompute;
5513 for (DenseMap<Instruction *, Constant *>::const_iterator
5514 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
5515 PHINode *PHI = dyn_cast<PHINode>(I->first);
5516 if (!PHI || PHI->getParent() != Header) continue;
5517 PHIsToCompute.push_back(PHI);
5519 for (SmallVectorImpl<PHINode *>::const_iterator I = PHIsToCompute.begin(),
5520 E = PHIsToCompute.end(); I != E; ++I) {
5522 Constant *&NextPHI = NextIterVals[PHI];
5523 if (NextPHI) continue; // Already computed!
5525 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
5526 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, TLI);
5528 CurrentIterVals.swap(NextIterVals);
5531 // Too many iterations were needed to evaluate.
5532 return getCouldNotCompute();
5535 /// getSCEVAtScope - Return a SCEV expression for the specified value
5536 /// at the specified scope in the program. The L value specifies a loop
5537 /// nest to evaluate the expression at, where null is the top-level or a
5538 /// specified loop is immediately inside of the loop.
5540 /// This method can be used to compute the exit value for a variable defined
5541 /// in a loop by querying what the value will hold in the parent loop.
5543 /// In the case that a relevant loop exit value cannot be computed, the
5544 /// original value V is returned.
5545 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
5546 // Check to see if we've folded this expression at this loop before.
5547 SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values = ValuesAtScopes[V];
5548 for (unsigned u = 0; u < Values.size(); u++) {
5549 if (Values[u].first == L)
5550 return Values[u].second ? Values[u].second : V;
5552 Values.push_back(std::make_pair(L, static_cast<const SCEV *>(nullptr)));
5553 // Otherwise compute it.
5554 const SCEV *C = computeSCEVAtScope(V, L);
5555 SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values2 = ValuesAtScopes[V];
5556 for (unsigned u = Values2.size(); u > 0; u--) {
5557 if (Values2[u - 1].first == L) {
5558 Values2[u - 1].second = C;
5565 /// This builds up a Constant using the ConstantExpr interface. That way, we
5566 /// will return Constants for objects which aren't represented by a
5567 /// SCEVConstant, because SCEVConstant is restricted to ConstantInt.
5568 /// Returns NULL if the SCEV isn't representable as a Constant.
5569 static Constant *BuildConstantFromSCEV(const SCEV *V) {
5570 switch (static_cast<SCEVTypes>(V->getSCEVType())) {
5571 case scCouldNotCompute:
5575 return cast<SCEVConstant>(V)->getValue();
5577 return dyn_cast<Constant>(cast<SCEVUnknown>(V)->getValue());
5578 case scSignExtend: {
5579 const SCEVSignExtendExpr *SS = cast<SCEVSignExtendExpr>(V);
5580 if (Constant *CastOp = BuildConstantFromSCEV(SS->getOperand()))
5581 return ConstantExpr::getSExt(CastOp, SS->getType());
5584 case scZeroExtend: {
5585 const SCEVZeroExtendExpr *SZ = cast<SCEVZeroExtendExpr>(V);
5586 if (Constant *CastOp = BuildConstantFromSCEV(SZ->getOperand()))
5587 return ConstantExpr::getZExt(CastOp, SZ->getType());
5591 const SCEVTruncateExpr *ST = cast<SCEVTruncateExpr>(V);
5592 if (Constant *CastOp = BuildConstantFromSCEV(ST->getOperand()))
5593 return ConstantExpr::getTrunc(CastOp, ST->getType());
5597 const SCEVAddExpr *SA = cast<SCEVAddExpr>(V);
5598 if (Constant *C = BuildConstantFromSCEV(SA->getOperand(0))) {
5599 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
5600 unsigned AS = PTy->getAddressSpace();
5601 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
5602 C = ConstantExpr::getBitCast(C, DestPtrTy);
5604 for (unsigned i = 1, e = SA->getNumOperands(); i != e; ++i) {
5605 Constant *C2 = BuildConstantFromSCEV(SA->getOperand(i));
5606 if (!C2) return nullptr;
5609 if (!C->getType()->isPointerTy() && C2->getType()->isPointerTy()) {
5610 unsigned AS = C2->getType()->getPointerAddressSpace();
5612 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
5613 // The offsets have been converted to bytes. We can add bytes to an
5614 // i8* by GEP with the byte count in the first index.
5615 C = ConstantExpr::getBitCast(C, DestPtrTy);
5618 // Don't bother trying to sum two pointers. We probably can't
5619 // statically compute a load that results from it anyway.
5620 if (C2->getType()->isPointerTy())
5623 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
5624 if (PTy->getElementType()->isStructTy())
5625 C2 = ConstantExpr::getIntegerCast(
5626 C2, Type::getInt32Ty(C->getContext()), true);
5627 C = ConstantExpr::getGetElementPtr(C, C2);
5629 C = ConstantExpr::getAdd(C, C2);
5636 const SCEVMulExpr *SM = cast<SCEVMulExpr>(V);
5637 if (Constant *C = BuildConstantFromSCEV(SM->getOperand(0))) {
5638 // Don't bother with pointers at all.
5639 if (C->getType()->isPointerTy()) return nullptr;
5640 for (unsigned i = 1, e = SM->getNumOperands(); i != e; ++i) {
5641 Constant *C2 = BuildConstantFromSCEV(SM->getOperand(i));
5642 if (!C2 || C2->getType()->isPointerTy()) return nullptr;
5643 C = ConstantExpr::getMul(C, C2);
5650 const SCEVUDivExpr *SU = cast<SCEVUDivExpr>(V);
5651 if (Constant *LHS = BuildConstantFromSCEV(SU->getLHS()))
5652 if (Constant *RHS = BuildConstantFromSCEV(SU->getRHS()))
5653 if (LHS->getType() == RHS->getType())
5654 return ConstantExpr::getUDiv(LHS, RHS);
5659 break; // TODO: smax, umax.
5664 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
5665 if (isa<SCEVConstant>(V)) return V;
5667 // If this instruction is evolved from a constant-evolving PHI, compute the
5668 // exit value from the loop without using SCEVs.
5669 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
5670 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
5671 const Loop *LI = (*this->LI)[I->getParent()];
5672 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
5673 if (PHINode *PN = dyn_cast<PHINode>(I))
5674 if (PN->getParent() == LI->getHeader()) {
5675 // Okay, there is no closed form solution for the PHI node. Check
5676 // to see if the loop that contains it has a known backedge-taken
5677 // count. If so, we may be able to force computation of the exit
5679 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
5680 if (const SCEVConstant *BTCC =
5681 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
5682 // Okay, we know how many times the containing loop executes. If
5683 // this is a constant evolving PHI node, get the final value at
5684 // the specified iteration number.
5685 Constant *RV = getConstantEvolutionLoopExitValue(PN,
5686 BTCC->getValue()->getValue(),
5688 if (RV) return getSCEV(RV);
5692 // Okay, this is an expression that we cannot symbolically evaluate
5693 // into a SCEV. Check to see if it's possible to symbolically evaluate
5694 // the arguments into constants, and if so, try to constant propagate the
5695 // result. This is particularly useful for computing loop exit values.
5696 if (CanConstantFold(I)) {
5697 SmallVector<Constant *, 4> Operands;
5698 bool MadeImprovement = false;
5699 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
5700 Value *Op = I->getOperand(i);
5701 if (Constant *C = dyn_cast<Constant>(Op)) {
5702 Operands.push_back(C);
5706 // If any of the operands is non-constant and if they are
5707 // non-integer and non-pointer, don't even try to analyze them
5708 // with scev techniques.
5709 if (!isSCEVable(Op->getType()))
5712 const SCEV *OrigV = getSCEV(Op);
5713 const SCEV *OpV = getSCEVAtScope(OrigV, L);
5714 MadeImprovement |= OrigV != OpV;
5716 Constant *C = BuildConstantFromSCEV(OpV);
5718 if (C->getType() != Op->getType())
5719 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
5723 Operands.push_back(C);
5726 // Check to see if getSCEVAtScope actually made an improvement.
5727 if (MadeImprovement) {
5728 Constant *C = nullptr;
5729 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
5730 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
5731 Operands[0], Operands[1], DL,
5733 else if (const LoadInst *LI = dyn_cast<LoadInst>(I)) {
5734 if (!LI->isVolatile())
5735 C = ConstantFoldLoadFromConstPtr(Operands[0], DL);
5737 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
5745 // This is some other type of SCEVUnknown, just return it.
5749 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
5750 // Avoid performing the look-up in the common case where the specified
5751 // expression has no loop-variant portions.
5752 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
5753 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
5754 if (OpAtScope != Comm->getOperand(i)) {
5755 // Okay, at least one of these operands is loop variant but might be
5756 // foldable. Build a new instance of the folded commutative expression.
5757 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
5758 Comm->op_begin()+i);
5759 NewOps.push_back(OpAtScope);
5761 for (++i; i != e; ++i) {
5762 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
5763 NewOps.push_back(OpAtScope);
5765 if (isa<SCEVAddExpr>(Comm))
5766 return getAddExpr(NewOps);
5767 if (isa<SCEVMulExpr>(Comm))
5768 return getMulExpr(NewOps);
5769 if (isa<SCEVSMaxExpr>(Comm))
5770 return getSMaxExpr(NewOps);
5771 if (isa<SCEVUMaxExpr>(Comm))
5772 return getUMaxExpr(NewOps);
5773 llvm_unreachable("Unknown commutative SCEV type!");
5776 // If we got here, all operands are loop invariant.
5780 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
5781 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
5782 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
5783 if (LHS == Div->getLHS() && RHS == Div->getRHS())
5784 return Div; // must be loop invariant
5785 return getUDivExpr(LHS, RHS);
5788 // If this is a loop recurrence for a loop that does not contain L, then we
5789 // are dealing with the final value computed by the loop.
5790 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
5791 // First, attempt to evaluate each operand.
5792 // Avoid performing the look-up in the common case where the specified
5793 // expression has no loop-variant portions.
5794 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
5795 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
5796 if (OpAtScope == AddRec->getOperand(i))
5799 // Okay, at least one of these operands is loop variant but might be
5800 // foldable. Build a new instance of the folded commutative expression.
5801 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(),
5802 AddRec->op_begin()+i);
5803 NewOps.push_back(OpAtScope);
5804 for (++i; i != e; ++i)
5805 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
5807 const SCEV *FoldedRec =
5808 getAddRecExpr(NewOps, AddRec->getLoop(),
5809 AddRec->getNoWrapFlags(SCEV::FlagNW));
5810 AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec);
5811 // The addrec may be folded to a nonrecurrence, for example, if the
5812 // induction variable is multiplied by zero after constant folding. Go
5813 // ahead and return the folded value.
5819 // If the scope is outside the addrec's loop, evaluate it by using the
5820 // loop exit value of the addrec.
5821 if (!AddRec->getLoop()->contains(L)) {
5822 // To evaluate this recurrence, we need to know how many times the AddRec
5823 // loop iterates. Compute this now.
5824 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
5825 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
5827 // Then, evaluate the AddRec.
5828 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
5834 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
5835 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5836 if (Op == Cast->getOperand())
5837 return Cast; // must be loop invariant
5838 return getZeroExtendExpr(Op, Cast->getType());
5841 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
5842 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5843 if (Op == Cast->getOperand())
5844 return Cast; // must be loop invariant
5845 return getSignExtendExpr(Op, Cast->getType());
5848 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
5849 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5850 if (Op == Cast->getOperand())
5851 return Cast; // must be loop invariant
5852 return getTruncateExpr(Op, Cast->getType());
5855 llvm_unreachable("Unknown SCEV type!");
5858 /// getSCEVAtScope - This is a convenience function which does
5859 /// getSCEVAtScope(getSCEV(V), L).
5860 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
5861 return getSCEVAtScope(getSCEV(V), L);
5864 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
5865 /// following equation:
5867 /// A * X = B (mod N)
5869 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
5870 /// A and B isn't important.
5872 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
5873 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
5874 ScalarEvolution &SE) {
5875 uint32_t BW = A.getBitWidth();
5876 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
5877 assert(A != 0 && "A must be non-zero.");
5881 // The gcd of A and N may have only one prime factor: 2. The number of
5882 // trailing zeros in A is its multiplicity
5883 uint32_t Mult2 = A.countTrailingZeros();
5886 // 2. Check if B is divisible by D.
5888 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
5889 // is not less than multiplicity of this prime factor for D.
5890 if (B.countTrailingZeros() < Mult2)
5891 return SE.getCouldNotCompute();
5893 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
5896 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
5897 // bit width during computations.
5898 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
5899 APInt Mod(BW + 1, 0);
5900 Mod.setBit(BW - Mult2); // Mod = N / D
5901 APInt I = AD.multiplicativeInverse(Mod);
5903 // 4. Compute the minimum unsigned root of the equation:
5904 // I * (B / D) mod (N / D)
5905 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
5907 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
5909 return SE.getConstant(Result.trunc(BW));
5912 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
5913 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
5914 /// might be the same) or two SCEVCouldNotCompute objects.
5916 static std::pair<const SCEV *,const SCEV *>
5917 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
5918 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
5919 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
5920 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
5921 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
5923 // We currently can only solve this if the coefficients are constants.
5924 if (!LC || !MC || !NC) {
5925 const SCEV *CNC = SE.getCouldNotCompute();
5926 return std::make_pair(CNC, CNC);
5929 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
5930 const APInt &L = LC->getValue()->getValue();
5931 const APInt &M = MC->getValue()->getValue();
5932 const APInt &N = NC->getValue()->getValue();
5933 APInt Two(BitWidth, 2);
5934 APInt Four(BitWidth, 4);
5937 using namespace APIntOps;
5939 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
5940 // The B coefficient is M-N/2
5944 // The A coefficient is N/2
5945 APInt A(N.sdiv(Two));
5947 // Compute the B^2-4ac term.
5950 SqrtTerm -= Four * (A * C);
5952 if (SqrtTerm.isNegative()) {
5953 // The loop is provably infinite.
5954 const SCEV *CNC = SE.getCouldNotCompute();
5955 return std::make_pair(CNC, CNC);
5958 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
5959 // integer value or else APInt::sqrt() will assert.
5960 APInt SqrtVal(SqrtTerm.sqrt());
5962 // Compute the two solutions for the quadratic formula.
5963 // The divisions must be performed as signed divisions.
5966 if (TwoA.isMinValue()) {
5967 const SCEV *CNC = SE.getCouldNotCompute();
5968 return std::make_pair(CNC, CNC);
5971 LLVMContext &Context = SE.getContext();
5973 ConstantInt *Solution1 =
5974 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
5975 ConstantInt *Solution2 =
5976 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
5978 return std::make_pair(SE.getConstant(Solution1),
5979 SE.getConstant(Solution2));
5980 } // end APIntOps namespace
5983 /// HowFarToZero - Return the number of times a backedge comparing the specified
5984 /// value to zero will execute. If not computable, return CouldNotCompute.
5986 /// This is only used for loops with a "x != y" exit test. The exit condition is
5987 /// now expressed as a single expression, V = x-y. So the exit test is
5988 /// effectively V != 0. We know and take advantage of the fact that this
5989 /// expression only being used in a comparison by zero context.
5990 ScalarEvolution::ExitLimit
5991 ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L, bool ControlsExit) {
5992 // If the value is a constant
5993 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
5994 // If the value is already zero, the branch will execute zero times.
5995 if (C->getValue()->isZero()) return C;
5996 return getCouldNotCompute(); // Otherwise it will loop infinitely.
5999 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
6000 if (!AddRec || AddRec->getLoop() != L)
6001 return getCouldNotCompute();
6003 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
6004 // the quadratic equation to solve it.
6005 if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
6006 std::pair<const SCEV *,const SCEV *> Roots =
6007 SolveQuadraticEquation(AddRec, *this);
6008 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
6009 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
6012 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1
6013 << " sol#2: " << *R2 << "\n";
6015 // Pick the smallest positive root value.
6016 if (ConstantInt *CB =
6017 dyn_cast<ConstantInt>(ConstantExpr::getICmp(CmpInst::ICMP_ULT,
6020 if (CB->getZExtValue() == false)
6021 std::swap(R1, R2); // R1 is the minimum root now.
6023 // We can only use this value if the chrec ends up with an exact zero
6024 // value at this index. When solving for "X*X != 5", for example, we
6025 // should not accept a root of 2.
6026 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
6028 return R1; // We found a quadratic root!
6031 return getCouldNotCompute();
6034 // Otherwise we can only handle this if it is affine.
6035 if (!AddRec->isAffine())
6036 return getCouldNotCompute();
6038 // If this is an affine expression, the execution count of this branch is
6039 // the minimum unsigned root of the following equation:
6041 // Start + Step*N = 0 (mod 2^BW)
6045 // Step*N = -Start (mod 2^BW)
6047 // where BW is the common bit width of Start and Step.
6049 // Get the initial value for the loop.
6050 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
6051 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
6053 // For now we handle only constant steps.
6055 // TODO: Handle a nonconstant Step given AddRec<NUW>. If the
6056 // AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap
6057 // to 0, it must be counting down to equal 0. Consequently, N = Start / -Step.
6058 // We have not yet seen any such cases.
6059 const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step);
6060 if (!StepC || StepC->getValue()->equalsInt(0))
6061 return getCouldNotCompute();
6063 // For positive steps (counting up until unsigned overflow):
6064 // N = -Start/Step (as unsigned)
6065 // For negative steps (counting down to zero):
6067 // First compute the unsigned distance from zero in the direction of Step.
6068 bool CountDown = StepC->getValue()->getValue().isNegative();
6069 const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start);
6071 // Handle unitary steps, which cannot wraparound.
6072 // 1*N = -Start; -1*N = Start (mod 2^BW), so:
6073 // N = Distance (as unsigned)
6074 if (StepC->getValue()->equalsInt(1) || StepC->getValue()->isAllOnesValue()) {
6075 ConstantRange CR = getUnsignedRange(Start);
6076 const SCEV *MaxBECount;
6077 if (!CountDown && CR.getUnsignedMin().isMinValue())
6078 // When counting up, the worst starting value is 1, not 0.
6079 MaxBECount = CR.getUnsignedMax().isMinValue()
6080 ? getConstant(APInt::getMinValue(CR.getBitWidth()))
6081 : getConstant(APInt::getMaxValue(CR.getBitWidth()));
6083 MaxBECount = getConstant(CountDown ? CR.getUnsignedMax()
6084 : -CR.getUnsignedMin());
6085 return ExitLimit(Distance, MaxBECount);
6088 // As a special case, handle the instance where Step is a positive power of
6089 // two. In this case, determining whether Step divides Distance evenly can be
6090 // done by counting and comparing the number of trailing zeros of Step and
6093 const APInt &StepV = StepC->getValue()->getValue();
6094 // StepV.isPowerOf2() returns true if StepV is an positive power of two. It
6095 // also returns true if StepV is maximally negative (eg, INT_MIN), but that
6096 // case is not handled as this code is guarded by !CountDown.
6097 if (StepV.isPowerOf2() &&
6098 GetMinTrailingZeros(Distance) >= StepV.countTrailingZeros())
6099 return getUDivExactExpr(Distance, Step);
6102 // If the condition controls loop exit (the loop exits only if the expression
6103 // is true) and the addition is no-wrap we can use unsigned divide to
6104 // compute the backedge count. In this case, the step may not divide the
6105 // distance, but we don't care because if the condition is "missed" the loop
6106 // will have undefined behavior due to wrapping.
6107 if (ControlsExit && AddRec->getNoWrapFlags(SCEV::FlagNW)) {
6109 getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
6110 return ExitLimit(Exact, Exact);
6113 // Then, try to solve the above equation provided that Start is constant.
6114 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
6115 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
6116 -StartC->getValue()->getValue(),
6118 return getCouldNotCompute();
6121 /// HowFarToNonZero - Return the number of times a backedge checking the
6122 /// specified value for nonzero will execute. If not computable, return
6124 ScalarEvolution::ExitLimit
6125 ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
6126 // Loops that look like: while (X == 0) are very strange indeed. We don't
6127 // handle them yet except for the trivial case. This could be expanded in the
6128 // future as needed.
6130 // If the value is a constant, check to see if it is known to be non-zero
6131 // already. If so, the backedge will execute zero times.
6132 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
6133 if (!C->getValue()->isNullValue())
6134 return getConstant(C->getType(), 0);
6135 return getCouldNotCompute(); // Otherwise it will loop infinitely.
6138 // We could implement others, but I really doubt anyone writes loops like
6139 // this, and if they did, they would already be constant folded.
6140 return getCouldNotCompute();
6143 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
6144 /// (which may not be an immediate predecessor) which has exactly one
6145 /// successor from which BB is reachable, or null if no such block is
6148 std::pair<BasicBlock *, BasicBlock *>
6149 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
6150 // If the block has a unique predecessor, then there is no path from the
6151 // predecessor to the block that does not go through the direct edge
6152 // from the predecessor to the block.
6153 if (BasicBlock *Pred = BB->getSinglePredecessor())
6154 return std::make_pair(Pred, BB);
6156 // A loop's header is defined to be a block that dominates the loop.
6157 // If the header has a unique predecessor outside the loop, it must be
6158 // a block that has exactly one successor that can reach the loop.
6159 if (Loop *L = LI->getLoopFor(BB))
6160 return std::make_pair(L->getLoopPredecessor(), L->getHeader());
6162 return std::pair<BasicBlock *, BasicBlock *>();
6165 /// HasSameValue - SCEV structural equivalence is usually sufficient for
6166 /// testing whether two expressions are equal, however for the purposes of
6167 /// looking for a condition guarding a loop, it can be useful to be a little
6168 /// more general, since a front-end may have replicated the controlling
6171 static bool HasSameValue(const SCEV *A, const SCEV *B) {
6172 // Quick check to see if they are the same SCEV.
6173 if (A == B) return true;
6175 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
6176 // two different instructions with the same value. Check for this case.
6177 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
6178 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
6179 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
6180 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
6181 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory())
6184 // Otherwise assume they may have a different value.
6188 /// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with
6189 /// predicate Pred. Return true iff any changes were made.
6191 bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
6192 const SCEV *&LHS, const SCEV *&RHS,
6194 bool Changed = false;
6196 // If we hit the max recursion limit bail out.
6200 // Canonicalize a constant to the right side.
6201 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
6202 // Check for both operands constant.
6203 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
6204 if (ConstantExpr::getICmp(Pred,
6206 RHSC->getValue())->isNullValue())
6207 goto trivially_false;
6209 goto trivially_true;
6211 // Otherwise swap the operands to put the constant on the right.
6212 std::swap(LHS, RHS);
6213 Pred = ICmpInst::getSwappedPredicate(Pred);
6217 // If we're comparing an addrec with a value which is loop-invariant in the
6218 // addrec's loop, put the addrec on the left. Also make a dominance check,
6219 // as both operands could be addrecs loop-invariant in each other's loop.
6220 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
6221 const Loop *L = AR->getLoop();
6222 if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) {
6223 std::swap(LHS, RHS);
6224 Pred = ICmpInst::getSwappedPredicate(Pred);
6229 // If there's a constant operand, canonicalize comparisons with boundary
6230 // cases, and canonicalize *-or-equal comparisons to regular comparisons.
6231 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
6232 const APInt &RA = RC->getValue()->getValue();
6234 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6235 case ICmpInst::ICMP_EQ:
6236 case ICmpInst::ICMP_NE:
6237 // Fold ((-1) * %a) + %b == 0 (equivalent to %b-%a == 0) into %a == %b.
6239 if (const SCEVAddExpr *AE = dyn_cast<SCEVAddExpr>(LHS))
6240 if (const SCEVMulExpr *ME = dyn_cast<SCEVMulExpr>(AE->getOperand(0)))
6241 if (AE->getNumOperands() == 2 && ME->getNumOperands() == 2 &&
6242 ME->getOperand(0)->isAllOnesValue()) {
6243 RHS = AE->getOperand(1);
6244 LHS = ME->getOperand(1);
6248 case ICmpInst::ICMP_UGE:
6249 if ((RA - 1).isMinValue()) {
6250 Pred = ICmpInst::ICMP_NE;
6251 RHS = getConstant(RA - 1);
6255 if (RA.isMaxValue()) {
6256 Pred = ICmpInst::ICMP_EQ;
6260 if (RA.isMinValue()) goto trivially_true;
6262 Pred = ICmpInst::ICMP_UGT;
6263 RHS = getConstant(RA - 1);
6266 case ICmpInst::ICMP_ULE:
6267 if ((RA + 1).isMaxValue()) {
6268 Pred = ICmpInst::ICMP_NE;
6269 RHS = getConstant(RA + 1);
6273 if (RA.isMinValue()) {
6274 Pred = ICmpInst::ICMP_EQ;
6278 if (RA.isMaxValue()) goto trivially_true;
6280 Pred = ICmpInst::ICMP_ULT;
6281 RHS = getConstant(RA + 1);
6284 case ICmpInst::ICMP_SGE:
6285 if ((RA - 1).isMinSignedValue()) {
6286 Pred = ICmpInst::ICMP_NE;
6287 RHS = getConstant(RA - 1);
6291 if (RA.isMaxSignedValue()) {
6292 Pred = ICmpInst::ICMP_EQ;
6296 if (RA.isMinSignedValue()) goto trivially_true;
6298 Pred = ICmpInst::ICMP_SGT;
6299 RHS = getConstant(RA - 1);
6302 case ICmpInst::ICMP_SLE:
6303 if ((RA + 1).isMaxSignedValue()) {
6304 Pred = ICmpInst::ICMP_NE;
6305 RHS = getConstant(RA + 1);
6309 if (RA.isMinSignedValue()) {
6310 Pred = ICmpInst::ICMP_EQ;
6314 if (RA.isMaxSignedValue()) goto trivially_true;
6316 Pred = ICmpInst::ICMP_SLT;
6317 RHS = getConstant(RA + 1);
6320 case ICmpInst::ICMP_UGT:
6321 if (RA.isMinValue()) {
6322 Pred = ICmpInst::ICMP_NE;
6326 if ((RA + 1).isMaxValue()) {
6327 Pred = ICmpInst::ICMP_EQ;
6328 RHS = getConstant(RA + 1);
6332 if (RA.isMaxValue()) goto trivially_false;
6334 case ICmpInst::ICMP_ULT:
6335 if (RA.isMaxValue()) {
6336 Pred = ICmpInst::ICMP_NE;
6340 if ((RA - 1).isMinValue()) {
6341 Pred = ICmpInst::ICMP_EQ;
6342 RHS = getConstant(RA - 1);
6346 if (RA.isMinValue()) goto trivially_false;
6348 case ICmpInst::ICMP_SGT:
6349 if (RA.isMinSignedValue()) {
6350 Pred = ICmpInst::ICMP_NE;
6354 if ((RA + 1).isMaxSignedValue()) {
6355 Pred = ICmpInst::ICMP_EQ;
6356 RHS = getConstant(RA + 1);
6360 if (RA.isMaxSignedValue()) goto trivially_false;
6362 case ICmpInst::ICMP_SLT:
6363 if (RA.isMaxSignedValue()) {
6364 Pred = ICmpInst::ICMP_NE;
6368 if ((RA - 1).isMinSignedValue()) {
6369 Pred = ICmpInst::ICMP_EQ;
6370 RHS = getConstant(RA - 1);
6374 if (RA.isMinSignedValue()) goto trivially_false;
6379 // Check for obvious equality.
6380 if (HasSameValue(LHS, RHS)) {
6381 if (ICmpInst::isTrueWhenEqual(Pred))
6382 goto trivially_true;
6383 if (ICmpInst::isFalseWhenEqual(Pred))
6384 goto trivially_false;
6387 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
6388 // adding or subtracting 1 from one of the operands.
6390 case ICmpInst::ICMP_SLE:
6391 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) {
6392 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
6394 Pred = ICmpInst::ICMP_SLT;
6396 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) {
6397 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
6399 Pred = ICmpInst::ICMP_SLT;
6403 case ICmpInst::ICMP_SGE:
6404 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) {
6405 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
6407 Pred = ICmpInst::ICMP_SGT;
6409 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) {
6410 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
6412 Pred = ICmpInst::ICMP_SGT;
6416 case ICmpInst::ICMP_ULE:
6417 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) {
6418 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
6420 Pred = ICmpInst::ICMP_ULT;
6422 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) {
6423 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
6425 Pred = ICmpInst::ICMP_ULT;
6429 case ICmpInst::ICMP_UGE:
6430 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) {
6431 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
6433 Pred = ICmpInst::ICMP_UGT;
6435 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) {
6436 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
6438 Pred = ICmpInst::ICMP_UGT;
6446 // TODO: More simplifications are possible here.
6448 // Recursively simplify until we either hit a recursion limit or nothing
6451 return SimplifyICmpOperands(Pred, LHS, RHS, Depth+1);
6457 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
6458 Pred = ICmpInst::ICMP_EQ;
6463 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
6464 Pred = ICmpInst::ICMP_NE;
6468 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
6469 return getSignedRange(S).getSignedMax().isNegative();
6472 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
6473 return getSignedRange(S).getSignedMin().isStrictlyPositive();
6476 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
6477 return !getSignedRange(S).getSignedMin().isNegative();
6480 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
6481 return !getSignedRange(S).getSignedMax().isStrictlyPositive();
6484 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
6485 return isKnownNegative(S) || isKnownPositive(S);
6488 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
6489 const SCEV *LHS, const SCEV *RHS) {
6490 // Canonicalize the inputs first.
6491 (void)SimplifyICmpOperands(Pred, LHS, RHS);
6493 // If LHS or RHS is an addrec, check to see if the condition is true in
6494 // every iteration of the loop.
6495 // If LHS and RHS are both addrec, both conditions must be true in
6496 // every iteration of the loop.
6497 const SCEVAddRecExpr *LAR = dyn_cast<SCEVAddRecExpr>(LHS);
6498 const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS);
6499 bool LeftGuarded = false;
6500 bool RightGuarded = false;
6502 const Loop *L = LAR->getLoop();
6503 if (isLoopEntryGuardedByCond(L, Pred, LAR->getStart(), RHS) &&
6504 isLoopBackedgeGuardedByCond(L, Pred, LAR->getPostIncExpr(*this), RHS)) {
6505 if (!RAR) return true;
6510 const Loop *L = RAR->getLoop();
6511 if (isLoopEntryGuardedByCond(L, Pred, LHS, RAR->getStart()) &&
6512 isLoopBackedgeGuardedByCond(L, Pred, LHS, RAR->getPostIncExpr(*this))) {
6513 if (!LAR) return true;
6514 RightGuarded = true;
6517 if (LeftGuarded && RightGuarded)
6520 // Otherwise see what can be done with known constant ranges.
6521 return isKnownPredicateWithRanges(Pred, LHS, RHS);
6525 ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred,
6526 const SCEV *LHS, const SCEV *RHS) {
6527 if (HasSameValue(LHS, RHS))
6528 return ICmpInst::isTrueWhenEqual(Pred);
6530 // This code is split out from isKnownPredicate because it is called from
6531 // within isLoopEntryGuardedByCond.
6534 llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6535 case ICmpInst::ICMP_SGT:
6536 std::swap(LHS, RHS);
6537 case ICmpInst::ICMP_SLT: {
6538 ConstantRange LHSRange = getSignedRange(LHS);
6539 ConstantRange RHSRange = getSignedRange(RHS);
6540 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
6542 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
6546 case ICmpInst::ICMP_SGE:
6547 std::swap(LHS, RHS);
6548 case ICmpInst::ICMP_SLE: {
6549 ConstantRange LHSRange = getSignedRange(LHS);
6550 ConstantRange RHSRange = getSignedRange(RHS);
6551 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
6553 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
6557 case ICmpInst::ICMP_UGT:
6558 std::swap(LHS, RHS);
6559 case ICmpInst::ICMP_ULT: {
6560 ConstantRange LHSRange = getUnsignedRange(LHS);
6561 ConstantRange RHSRange = getUnsignedRange(RHS);
6562 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
6564 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
6568 case ICmpInst::ICMP_UGE:
6569 std::swap(LHS, RHS);
6570 case ICmpInst::ICMP_ULE: {
6571 ConstantRange LHSRange = getUnsignedRange(LHS);
6572 ConstantRange RHSRange = getUnsignedRange(RHS);
6573 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
6575 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
6579 case ICmpInst::ICMP_NE: {
6580 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
6582 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
6585 const SCEV *Diff = getMinusSCEV(LHS, RHS);
6586 if (isKnownNonZero(Diff))
6590 case ICmpInst::ICMP_EQ:
6591 // The check at the top of the function catches the case where
6592 // the values are known to be equal.
6598 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
6599 /// protected by a conditional between LHS and RHS. This is used to
6600 /// to eliminate casts.
6602 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
6603 ICmpInst::Predicate Pred,
6604 const SCEV *LHS, const SCEV *RHS) {
6605 // Interpret a null as meaning no loop, where there is obviously no guard
6606 // (interprocedural conditions notwithstanding).
6607 if (!L) return true;
6609 if (isKnownPredicateWithRanges(Pred, LHS, RHS)) return true;
6611 BasicBlock *Latch = L->getLoopLatch();
6615 BranchInst *LoopContinuePredicate =
6616 dyn_cast<BranchInst>(Latch->getTerminator());
6617 if (LoopContinuePredicate && LoopContinuePredicate->isConditional() &&
6618 isImpliedCond(Pred, LHS, RHS,
6619 LoopContinuePredicate->getCondition(),
6620 LoopContinuePredicate->getSuccessor(0) != L->getHeader()))
6623 // Check conditions due to any @llvm.assume intrinsics.
6624 for (auto &AssumeVH : AC->assumptions()) {
6627 auto *CI = cast<CallInst>(AssumeVH);
6628 if (!DT->dominates(CI, Latch->getTerminator()))
6631 if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false))
6638 /// isLoopEntryGuardedByCond - Test whether entry to the loop is protected
6639 /// by a conditional between LHS and RHS. This is used to help avoid max
6640 /// expressions in loop trip counts, and to eliminate casts.
6642 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
6643 ICmpInst::Predicate Pred,
6644 const SCEV *LHS, const SCEV *RHS) {
6645 // Interpret a null as meaning no loop, where there is obviously no guard
6646 // (interprocedural conditions notwithstanding).
6647 if (!L) return false;
6649 if (isKnownPredicateWithRanges(Pred, LHS, RHS)) return true;
6651 // Starting at the loop predecessor, climb up the predecessor chain, as long
6652 // as there are predecessors that can be found that have unique successors
6653 // leading to the original header.
6654 for (std::pair<BasicBlock *, BasicBlock *>
6655 Pair(L->getLoopPredecessor(), L->getHeader());
6657 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
6659 BranchInst *LoopEntryPredicate =
6660 dyn_cast<BranchInst>(Pair.first->getTerminator());
6661 if (!LoopEntryPredicate ||
6662 LoopEntryPredicate->isUnconditional())
6665 if (isImpliedCond(Pred, LHS, RHS,
6666 LoopEntryPredicate->getCondition(),
6667 LoopEntryPredicate->getSuccessor(0) != Pair.second))
6671 // Check conditions due to any @llvm.assume intrinsics.
6672 for (auto &AssumeVH : AC->assumptions()) {
6675 auto *CI = cast<CallInst>(AssumeVH);
6676 if (!DT->dominates(CI, L->getHeader()))
6679 if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false))
6686 /// RAII wrapper to prevent recursive application of isImpliedCond.
6687 /// ScalarEvolution's PendingLoopPredicates set must be empty unless we are
6688 /// currently evaluating isImpliedCond.
6689 struct MarkPendingLoopPredicate {
6691 DenseSet<Value*> &LoopPreds;
6694 MarkPendingLoopPredicate(Value *C, DenseSet<Value*> &LP)
6695 : Cond(C), LoopPreds(LP) {
6696 Pending = !LoopPreds.insert(Cond).second;
6698 ~MarkPendingLoopPredicate() {
6700 LoopPreds.erase(Cond);
6704 /// isImpliedCond - Test whether the condition described by Pred, LHS,
6705 /// and RHS is true whenever the given Cond value evaluates to true.
6706 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred,
6707 const SCEV *LHS, const SCEV *RHS,
6708 Value *FoundCondValue,
6710 MarkPendingLoopPredicate Mark(FoundCondValue, PendingLoopPredicates);
6714 // Recursively handle And and Or conditions.
6715 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) {
6716 if (BO->getOpcode() == Instruction::And) {
6718 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
6719 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
6720 } else if (BO->getOpcode() == Instruction::Or) {
6722 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
6723 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
6727 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue);
6728 if (!ICI) return false;
6730 // Bail if the ICmp's operands' types are wider than the needed type
6731 // before attempting to call getSCEV on them. This avoids infinite
6732 // recursion, since the analysis of widening casts can require loop
6733 // exit condition information for overflow checking, which would
6735 if (getTypeSizeInBits(LHS->getType()) <
6736 getTypeSizeInBits(ICI->getOperand(0)->getType()))
6739 // Now that we found a conditional branch that dominates the loop or controls
6740 // the loop latch. Check to see if it is the comparison we are looking for.
6741 ICmpInst::Predicate FoundPred;
6743 FoundPred = ICI->getInversePredicate();
6745 FoundPred = ICI->getPredicate();
6747 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
6748 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
6750 // Balance the types. The case where FoundLHS' type is wider than
6751 // LHS' type is checked for above.
6752 if (getTypeSizeInBits(LHS->getType()) >
6753 getTypeSizeInBits(FoundLHS->getType())) {
6754 if (CmpInst::isSigned(FoundPred)) {
6755 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
6756 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
6758 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
6759 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
6763 // Canonicalize the query to match the way instcombine will have
6764 // canonicalized the comparison.
6765 if (SimplifyICmpOperands(Pred, LHS, RHS))
6767 return CmpInst::isTrueWhenEqual(Pred);
6768 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
6769 if (FoundLHS == FoundRHS)
6770 return CmpInst::isFalseWhenEqual(FoundPred);
6772 // Check to see if we can make the LHS or RHS match.
6773 if (LHS == FoundRHS || RHS == FoundLHS) {
6774 if (isa<SCEVConstant>(RHS)) {
6775 std::swap(FoundLHS, FoundRHS);
6776 FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
6778 std::swap(LHS, RHS);
6779 Pred = ICmpInst::getSwappedPredicate(Pred);
6783 // Check whether the found predicate is the same as the desired predicate.
6784 if (FoundPred == Pred)
6785 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
6787 // Check whether swapping the found predicate makes it the same as the
6788 // desired predicate.
6789 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
6790 if (isa<SCEVConstant>(RHS))
6791 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
6793 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
6794 RHS, LHS, FoundLHS, FoundRHS);
6797 // Check if we can make progress by sharpening ranges.
6798 if (FoundPred == ICmpInst::ICMP_NE &&
6799 (isa<SCEVConstant>(FoundLHS) || isa<SCEVConstant>(FoundRHS))) {
6801 const SCEVConstant *C = nullptr;
6802 const SCEV *V = nullptr;
6804 if (isa<SCEVConstant>(FoundLHS)) {
6805 C = cast<SCEVConstant>(FoundLHS);
6808 C = cast<SCEVConstant>(FoundRHS);
6812 // The guarding predicate tells us that C != V. If the known range
6813 // of V is [C, t), we can sharpen the range to [C + 1, t). The
6814 // range we consider has to correspond to same signedness as the
6815 // predicate we're interested in folding.
6817 APInt Min = ICmpInst::isSigned(Pred) ?
6818 getSignedRange(V).getSignedMin() : getUnsignedRange(V).getUnsignedMin();
6820 if (Min == C->getValue()->getValue()) {
6821 // Given (V >= Min && V != Min) we conclude V >= (Min + 1).
6822 // This is true even if (Min + 1) wraps around -- in case of
6823 // wraparound, (Min + 1) < Min, so (V >= Min => V >= (Min + 1)).
6825 APInt SharperMin = Min + 1;
6828 case ICmpInst::ICMP_SGE:
6829 case ICmpInst::ICMP_UGE:
6830 // We know V `Pred` SharperMin. If this implies LHS `Pred`
6832 if (isImpliedCondOperands(Pred, LHS, RHS, V,
6833 getConstant(SharperMin)))
6836 case ICmpInst::ICMP_SGT:
6837 case ICmpInst::ICMP_UGT:
6838 // We know from the range information that (V `Pred` Min ||
6839 // V == Min). We know from the guarding condition that !(V
6840 // == Min). This gives us
6842 // V `Pred` Min || V == Min && !(V == Min)
6845 // If V `Pred` Min implies LHS `Pred` RHS, we're done.
6847 if (isImpliedCondOperands(Pred, LHS, RHS, V, getConstant(Min)))
6857 // Check whether the actual condition is beyond sufficient.
6858 if (FoundPred == ICmpInst::ICMP_EQ)
6859 if (ICmpInst::isTrueWhenEqual(Pred))
6860 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
6862 if (Pred == ICmpInst::ICMP_NE)
6863 if (!ICmpInst::isTrueWhenEqual(FoundPred))
6864 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
6867 // Otherwise assume the worst.
6871 /// isImpliedCondOperands - Test whether the condition described by Pred,
6872 /// LHS, and RHS is true whenever the condition described by Pred, FoundLHS,
6873 /// and FoundRHS is true.
6874 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
6875 const SCEV *LHS, const SCEV *RHS,
6876 const SCEV *FoundLHS,
6877 const SCEV *FoundRHS) {
6878 return isImpliedCondOperandsHelper(Pred, LHS, RHS,
6879 FoundLHS, FoundRHS) ||
6880 // ~x < ~y --> x > y
6881 isImpliedCondOperandsHelper(Pred, LHS, RHS,
6882 getNotSCEV(FoundRHS),
6883 getNotSCEV(FoundLHS));
6887 /// If Expr computes ~A, return A else return nullptr
6888 static const SCEV *MatchNotExpr(const SCEV *Expr) {
6889 const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Expr);
6890 if (!Add || Add->getNumOperands() != 2) return nullptr;
6892 const SCEVConstant *AddLHS = dyn_cast<SCEVConstant>(Add->getOperand(0));
6893 if (!(AddLHS && AddLHS->getValue()->getValue().isAllOnesValue()))
6896 const SCEVMulExpr *AddRHS = dyn_cast<SCEVMulExpr>(Add->getOperand(1));
6897 if (!AddRHS || AddRHS->getNumOperands() != 2) return nullptr;
6899 const SCEVConstant *MulLHS = dyn_cast<SCEVConstant>(AddRHS->getOperand(0));
6900 if (!(MulLHS && MulLHS->getValue()->getValue().isAllOnesValue()))
6903 return AddRHS->getOperand(1);
6907 /// Is MaybeMaxExpr an SMax or UMax of Candidate and some other values?
6908 template<typename MaxExprType>
6909 static bool IsMaxConsistingOf(const SCEV *MaybeMaxExpr,
6910 const SCEV *Candidate) {
6911 const MaxExprType *MaxExpr = dyn_cast<MaxExprType>(MaybeMaxExpr);
6912 if (!MaxExpr) return false;
6914 auto It = std::find(MaxExpr->op_begin(), MaxExpr->op_end(), Candidate);
6915 return It != MaxExpr->op_end();
6919 /// Is MaybeMinExpr an SMin or UMin of Candidate and some other values?
6920 template<typename MaxExprType>
6921 static bool IsMinConsistingOf(ScalarEvolution &SE,
6922 const SCEV *MaybeMinExpr,
6923 const SCEV *Candidate) {
6924 const SCEV *MaybeMaxExpr = MatchNotExpr(MaybeMinExpr);
6928 return IsMaxConsistingOf<MaxExprType>(MaybeMaxExpr, SE.getNotSCEV(Candidate));
6932 /// Is LHS `Pred` RHS true on the virtue of LHS or RHS being a Min or Max
6934 static bool IsKnownPredicateViaMinOrMax(ScalarEvolution &SE,
6935 ICmpInst::Predicate Pred,
6936 const SCEV *LHS, const SCEV *RHS) {
6941 case ICmpInst::ICMP_SGE:
6942 std::swap(LHS, RHS);
6944 case ICmpInst::ICMP_SLE:
6947 IsMinConsistingOf<SCEVSMaxExpr>(SE, LHS, RHS) ||
6949 IsMaxConsistingOf<SCEVSMaxExpr>(RHS, LHS);
6951 case ICmpInst::ICMP_UGE:
6952 std::swap(LHS, RHS);
6954 case ICmpInst::ICMP_ULE:
6957 IsMinConsistingOf<SCEVUMaxExpr>(SE, LHS, RHS) ||
6959 IsMaxConsistingOf<SCEVUMaxExpr>(RHS, LHS);
6962 llvm_unreachable("covered switch fell through?!");
6965 /// isImpliedCondOperandsHelper - Test whether the condition described by
6966 /// Pred, LHS, and RHS is true whenever the condition described by Pred,
6967 /// FoundLHS, and FoundRHS is true.
6969 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
6970 const SCEV *LHS, const SCEV *RHS,
6971 const SCEV *FoundLHS,
6972 const SCEV *FoundRHS) {
6973 auto IsKnownPredicateFull =
6974 [this](ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS) {
6975 return isKnownPredicateWithRanges(Pred, LHS, RHS) ||
6976 IsKnownPredicateViaMinOrMax(*this, Pred, LHS, RHS);
6980 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6981 case ICmpInst::ICMP_EQ:
6982 case ICmpInst::ICMP_NE:
6983 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
6986 case ICmpInst::ICMP_SLT:
6987 case ICmpInst::ICMP_SLE:
6988 if (IsKnownPredicateFull(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
6989 IsKnownPredicateFull(ICmpInst::ICMP_SGE, RHS, FoundRHS))
6992 case ICmpInst::ICMP_SGT:
6993 case ICmpInst::ICMP_SGE:
6994 if (IsKnownPredicateFull(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
6995 IsKnownPredicateFull(ICmpInst::ICMP_SLE, RHS, FoundRHS))
6998 case ICmpInst::ICMP_ULT:
6999 case ICmpInst::ICMP_ULE:
7000 if (IsKnownPredicateFull(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
7001 IsKnownPredicateFull(ICmpInst::ICMP_UGE, RHS, FoundRHS))
7004 case ICmpInst::ICMP_UGT:
7005 case ICmpInst::ICMP_UGE:
7006 if (IsKnownPredicateFull(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
7007 IsKnownPredicateFull(ICmpInst::ICMP_ULE, RHS, FoundRHS))
7015 // Verify if an linear IV with positive stride can overflow when in a
7016 // less-than comparison, knowing the invariant term of the comparison, the
7017 // stride and the knowledge of NSW/NUW flags on the recurrence.
7018 bool ScalarEvolution::doesIVOverflowOnLT(const SCEV *RHS, const SCEV *Stride,
7019 bool IsSigned, bool NoWrap) {
7020 if (NoWrap) return false;
7022 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
7023 const SCEV *One = getConstant(Stride->getType(), 1);
7026 APInt MaxRHS = getSignedRange(RHS).getSignedMax();
7027 APInt MaxValue = APInt::getSignedMaxValue(BitWidth);
7028 APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
7031 // SMaxRHS + SMaxStrideMinusOne > SMaxValue => overflow!
7032 return (MaxValue - MaxStrideMinusOne).slt(MaxRHS);
7035 APInt MaxRHS = getUnsignedRange(RHS).getUnsignedMax();
7036 APInt MaxValue = APInt::getMaxValue(BitWidth);
7037 APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
7040 // UMaxRHS + UMaxStrideMinusOne > UMaxValue => overflow!
7041 return (MaxValue - MaxStrideMinusOne).ult(MaxRHS);
7044 // Verify if an linear IV with negative stride can overflow when in a
7045 // greater-than comparison, knowing the invariant term of the comparison,
7046 // the stride and the knowledge of NSW/NUW flags on the recurrence.
7047 bool ScalarEvolution::doesIVOverflowOnGT(const SCEV *RHS, const SCEV *Stride,
7048 bool IsSigned, bool NoWrap) {
7049 if (NoWrap) return false;
7051 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
7052 const SCEV *One = getConstant(Stride->getType(), 1);
7055 APInt MinRHS = getSignedRange(RHS).getSignedMin();
7056 APInt MinValue = APInt::getSignedMinValue(BitWidth);
7057 APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
7060 // SMinRHS - SMaxStrideMinusOne < SMinValue => overflow!
7061 return (MinValue + MaxStrideMinusOne).sgt(MinRHS);
7064 APInt MinRHS = getUnsignedRange(RHS).getUnsignedMin();
7065 APInt MinValue = APInt::getMinValue(BitWidth);
7066 APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
7069 // UMinRHS - UMaxStrideMinusOne < UMinValue => overflow!
7070 return (MinValue + MaxStrideMinusOne).ugt(MinRHS);
7073 // Compute the backedge taken count knowing the interval difference, the
7074 // stride and presence of the equality in the comparison.
7075 const SCEV *ScalarEvolution::computeBECount(const SCEV *Delta, const SCEV *Step,
7077 const SCEV *One = getConstant(Step->getType(), 1);
7078 Delta = Equality ? getAddExpr(Delta, Step)
7079 : getAddExpr(Delta, getMinusSCEV(Step, One));
7080 return getUDivExpr(Delta, Step);
7083 /// HowManyLessThans - Return the number of times a backedge containing the
7084 /// specified less-than comparison will execute. If not computable, return
7085 /// CouldNotCompute.
7087 /// @param ControlsExit is true when the LHS < RHS condition directly controls
7088 /// the branch (loops exits only if condition is true). In this case, we can use
7089 /// NoWrapFlags to skip overflow checks.
7090 ScalarEvolution::ExitLimit
7091 ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
7092 const Loop *L, bool IsSigned,
7093 bool ControlsExit) {
7094 // We handle only IV < Invariant
7095 if (!isLoopInvariant(RHS, L))
7096 return getCouldNotCompute();
7098 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
7100 // Avoid weird loops
7101 if (!IV || IV->getLoop() != L || !IV->isAffine())
7102 return getCouldNotCompute();
7104 bool NoWrap = ControlsExit &&
7105 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
7107 const SCEV *Stride = IV->getStepRecurrence(*this);
7109 // Avoid negative or zero stride values
7110 if (!isKnownPositive(Stride))
7111 return getCouldNotCompute();
7113 // Avoid proven overflow cases: this will ensure that the backedge taken count
7114 // will not generate any unsigned overflow. Relaxed no-overflow conditions
7115 // exploit NoWrapFlags, allowing to optimize in presence of undefined
7116 // behaviors like the case of C language.
7117 if (!Stride->isOne() && doesIVOverflowOnLT(RHS, Stride, IsSigned, NoWrap))
7118 return getCouldNotCompute();
7120 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SLT
7121 : ICmpInst::ICMP_ULT;
7122 const SCEV *Start = IV->getStart();
7123 const SCEV *End = RHS;
7124 if (!isLoopEntryGuardedByCond(L, Cond, getMinusSCEV(Start, Stride), RHS)) {
7125 const SCEV *Diff = getMinusSCEV(RHS, Start);
7126 // If we have NoWrap set, then we can assume that the increment won't
7127 // overflow, in which case if RHS - Start is a constant, we don't need to
7128 // do a max operation since we can just figure it out statically
7129 if (NoWrap && isa<SCEVConstant>(Diff)) {
7130 APInt D = dyn_cast<const SCEVConstant>(Diff)->getValue()->getValue();
7134 End = IsSigned ? getSMaxExpr(RHS, Start)
7135 : getUMaxExpr(RHS, Start);
7138 const SCEV *BECount = computeBECount(getMinusSCEV(End, Start), Stride, false);
7140 APInt MinStart = IsSigned ? getSignedRange(Start).getSignedMin()
7141 : getUnsignedRange(Start).getUnsignedMin();
7143 APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
7144 : getUnsignedRange(Stride).getUnsignedMin();
7146 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
7147 APInt Limit = IsSigned ? APInt::getSignedMaxValue(BitWidth) - (MinStride - 1)
7148 : APInt::getMaxValue(BitWidth) - (MinStride - 1);
7150 // Although End can be a MAX expression we estimate MaxEnd considering only
7151 // the case End = RHS. This is safe because in the other case (End - Start)
7152 // is zero, leading to a zero maximum backedge taken count.
7154 IsSigned ? APIntOps::smin(getSignedRange(RHS).getSignedMax(), Limit)
7155 : APIntOps::umin(getUnsignedRange(RHS).getUnsignedMax(), Limit);
7157 const SCEV *MaxBECount;
7158 if (isa<SCEVConstant>(BECount))
7159 MaxBECount = BECount;
7161 MaxBECount = computeBECount(getConstant(MaxEnd - MinStart),
7162 getConstant(MinStride), false);
7164 if (isa<SCEVCouldNotCompute>(MaxBECount))
7165 MaxBECount = BECount;
7167 return ExitLimit(BECount, MaxBECount);
7170 ScalarEvolution::ExitLimit
7171 ScalarEvolution::HowManyGreaterThans(const SCEV *LHS, const SCEV *RHS,
7172 const Loop *L, bool IsSigned,
7173 bool ControlsExit) {
7174 // We handle only IV > Invariant
7175 if (!isLoopInvariant(RHS, L))
7176 return getCouldNotCompute();
7178 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
7180 // Avoid weird loops
7181 if (!IV || IV->getLoop() != L || !IV->isAffine())
7182 return getCouldNotCompute();
7184 bool NoWrap = ControlsExit &&
7185 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
7187 const SCEV *Stride = getNegativeSCEV(IV->getStepRecurrence(*this));
7189 // Avoid negative or zero stride values
7190 if (!isKnownPositive(Stride))
7191 return getCouldNotCompute();
7193 // Avoid proven overflow cases: this will ensure that the backedge taken count
7194 // will not generate any unsigned overflow. Relaxed no-overflow conditions
7195 // exploit NoWrapFlags, allowing to optimize in presence of undefined
7196 // behaviors like the case of C language.
7197 if (!Stride->isOne() && doesIVOverflowOnGT(RHS, Stride, IsSigned, NoWrap))
7198 return getCouldNotCompute();
7200 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SGT
7201 : ICmpInst::ICMP_UGT;
7203 const SCEV *Start = IV->getStart();
7204 const SCEV *End = RHS;
7205 if (!isLoopEntryGuardedByCond(L, Cond, getAddExpr(Start, Stride), RHS)) {
7206 const SCEV *Diff = getMinusSCEV(RHS, Start);
7207 // If we have NoWrap set, then we can assume that the increment won't
7208 // overflow, in which case if RHS - Start is a constant, we don't need to
7209 // do a max operation since we can just figure it out statically
7210 if (NoWrap && isa<SCEVConstant>(Diff)) {
7211 APInt D = dyn_cast<const SCEVConstant>(Diff)->getValue()->getValue();
7212 if (!D.isNegative())
7215 End = IsSigned ? getSMinExpr(RHS, Start)
7216 : getUMinExpr(RHS, Start);
7219 const SCEV *BECount = computeBECount(getMinusSCEV(Start, End), Stride, false);
7221 APInt MaxStart = IsSigned ? getSignedRange(Start).getSignedMax()
7222 : getUnsignedRange(Start).getUnsignedMax();
7224 APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
7225 : getUnsignedRange(Stride).getUnsignedMin();
7227 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
7228 APInt Limit = IsSigned ? APInt::getSignedMinValue(BitWidth) + (MinStride - 1)
7229 : APInt::getMinValue(BitWidth) + (MinStride - 1);
7231 // Although End can be a MIN expression we estimate MinEnd considering only
7232 // the case End = RHS. This is safe because in the other case (Start - End)
7233 // is zero, leading to a zero maximum backedge taken count.
7235 IsSigned ? APIntOps::smax(getSignedRange(RHS).getSignedMin(), Limit)
7236 : APIntOps::umax(getUnsignedRange(RHS).getUnsignedMin(), Limit);
7239 const SCEV *MaxBECount = getCouldNotCompute();
7240 if (isa<SCEVConstant>(BECount))
7241 MaxBECount = BECount;
7243 MaxBECount = computeBECount(getConstant(MaxStart - MinEnd),
7244 getConstant(MinStride), false);
7246 if (isa<SCEVCouldNotCompute>(MaxBECount))
7247 MaxBECount = BECount;
7249 return ExitLimit(BECount, MaxBECount);
7252 /// getNumIterationsInRange - Return the number of iterations of this loop that
7253 /// produce values in the specified constant range. Another way of looking at
7254 /// this is that it returns the first iteration number where the value is not in
7255 /// the condition, thus computing the exit count. If the iteration count can't
7256 /// be computed, an instance of SCEVCouldNotCompute is returned.
7257 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
7258 ScalarEvolution &SE) const {
7259 if (Range.isFullSet()) // Infinite loop.
7260 return SE.getCouldNotCompute();
7262 // If the start is a non-zero constant, shift the range to simplify things.
7263 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
7264 if (!SC->getValue()->isZero()) {
7265 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
7266 Operands[0] = SE.getConstant(SC->getType(), 0);
7267 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(),
7268 getNoWrapFlags(FlagNW));
7269 if (const SCEVAddRecExpr *ShiftedAddRec =
7270 dyn_cast<SCEVAddRecExpr>(Shifted))
7271 return ShiftedAddRec->getNumIterationsInRange(
7272 Range.subtract(SC->getValue()->getValue()), SE);
7273 // This is strange and shouldn't happen.
7274 return SE.getCouldNotCompute();
7277 // The only time we can solve this is when we have all constant indices.
7278 // Otherwise, we cannot determine the overflow conditions.
7279 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
7280 if (!isa<SCEVConstant>(getOperand(i)))
7281 return SE.getCouldNotCompute();
7284 // Okay at this point we know that all elements of the chrec are constants and
7285 // that the start element is zero.
7287 // First check to see if the range contains zero. If not, the first
7289 unsigned BitWidth = SE.getTypeSizeInBits(getType());
7290 if (!Range.contains(APInt(BitWidth, 0)))
7291 return SE.getConstant(getType(), 0);
7294 // If this is an affine expression then we have this situation:
7295 // Solve {0,+,A} in Range === Ax in Range
7297 // We know that zero is in the range. If A is positive then we know that
7298 // the upper value of the range must be the first possible exit value.
7299 // If A is negative then the lower of the range is the last possible loop
7300 // value. Also note that we already checked for a full range.
7301 APInt One(BitWidth,1);
7302 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
7303 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
7305 // The exit value should be (End+A)/A.
7306 APInt ExitVal = (End + A).udiv(A);
7307 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
7309 // Evaluate at the exit value. If we really did fall out of the valid
7310 // range, then we computed our trip count, otherwise wrap around or other
7311 // things must have happened.
7312 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
7313 if (Range.contains(Val->getValue()))
7314 return SE.getCouldNotCompute(); // Something strange happened
7316 // Ensure that the previous value is in the range. This is a sanity check.
7317 assert(Range.contains(
7318 EvaluateConstantChrecAtConstant(this,
7319 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
7320 "Linear scev computation is off in a bad way!");
7321 return SE.getConstant(ExitValue);
7322 } else if (isQuadratic()) {
7323 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
7324 // quadratic equation to solve it. To do this, we must frame our problem in
7325 // terms of figuring out when zero is crossed, instead of when
7326 // Range.getUpper() is crossed.
7327 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
7328 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
7329 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop(),
7330 // getNoWrapFlags(FlagNW)
7333 // Next, solve the constructed addrec
7334 std::pair<const SCEV *,const SCEV *> Roots =
7335 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
7336 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
7337 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
7339 // Pick the smallest positive root value.
7340 if (ConstantInt *CB =
7341 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
7342 R1->getValue(), R2->getValue()))) {
7343 if (CB->getZExtValue() == false)
7344 std::swap(R1, R2); // R1 is the minimum root now.
7346 // Make sure the root is not off by one. The returned iteration should
7347 // not be in the range, but the previous one should be. When solving
7348 // for "X*X < 5", for example, we should not return a root of 2.
7349 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
7352 if (Range.contains(R1Val->getValue())) {
7353 // The next iteration must be out of the range...
7354 ConstantInt *NextVal =
7355 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1);
7357 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
7358 if (!Range.contains(R1Val->getValue()))
7359 return SE.getConstant(NextVal);
7360 return SE.getCouldNotCompute(); // Something strange happened
7363 // If R1 was not in the range, then it is a good return value. Make
7364 // sure that R1-1 WAS in the range though, just in case.
7365 ConstantInt *NextVal =
7366 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1);
7367 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
7368 if (Range.contains(R1Val->getValue()))
7370 return SE.getCouldNotCompute(); // Something strange happened
7375 return SE.getCouldNotCompute();
7381 FindUndefs() : Found(false) {}
7383 bool follow(const SCEV *S) {
7384 if (const SCEVUnknown *C = dyn_cast<SCEVUnknown>(S)) {
7385 if (isa<UndefValue>(C->getValue()))
7387 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) {
7388 if (isa<UndefValue>(C->getValue()))
7392 // Keep looking if we haven't found it yet.
7395 bool isDone() const {
7396 // Stop recursion if we have found an undef.
7402 // Return true when S contains at least an undef value.
7404 containsUndefs(const SCEV *S) {
7406 SCEVTraversal<FindUndefs> ST(F);
7413 // Collect all steps of SCEV expressions.
7414 struct SCEVCollectStrides {
7415 ScalarEvolution &SE;
7416 SmallVectorImpl<const SCEV *> &Strides;
7418 SCEVCollectStrides(ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &S)
7419 : SE(SE), Strides(S) {}
7421 bool follow(const SCEV *S) {
7422 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(S))
7423 Strides.push_back(AR->getStepRecurrence(SE));
7426 bool isDone() const { return false; }
7429 // Collect all SCEVUnknown and SCEVMulExpr expressions.
7430 struct SCEVCollectTerms {
7431 SmallVectorImpl<const SCEV *> &Terms;
7433 SCEVCollectTerms(SmallVectorImpl<const SCEV *> &T)
7436 bool follow(const SCEV *S) {
7437 if (isa<SCEVUnknown>(S) || isa<SCEVMulExpr>(S)) {
7438 if (!containsUndefs(S))
7441 // Stop recursion: once we collected a term, do not walk its operands.
7448 bool isDone() const { return false; }
7452 /// Find parametric terms in this SCEVAddRecExpr.
7453 void SCEVAddRecExpr::collectParametricTerms(
7454 ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &Terms) const {
7455 SmallVector<const SCEV *, 4> Strides;
7456 SCEVCollectStrides StrideCollector(SE, Strides);
7457 visitAll(this, StrideCollector);
7460 dbgs() << "Strides:\n";
7461 for (const SCEV *S : Strides)
7462 dbgs() << *S << "\n";
7465 for (const SCEV *S : Strides) {
7466 SCEVCollectTerms TermCollector(Terms);
7467 visitAll(S, TermCollector);
7471 dbgs() << "Terms:\n";
7472 for (const SCEV *T : Terms)
7473 dbgs() << *T << "\n";
7477 static bool findArrayDimensionsRec(ScalarEvolution &SE,
7478 SmallVectorImpl<const SCEV *> &Terms,
7479 SmallVectorImpl<const SCEV *> &Sizes) {
7480 int Last = Terms.size() - 1;
7481 const SCEV *Step = Terms[Last];
7483 // End of recursion.
7485 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Step)) {
7486 SmallVector<const SCEV *, 2> Qs;
7487 for (const SCEV *Op : M->operands())
7488 if (!isa<SCEVConstant>(Op))
7491 Step = SE.getMulExpr(Qs);
7494 Sizes.push_back(Step);
7498 for (const SCEV *&Term : Terms) {
7499 // Normalize the terms before the next call to findArrayDimensionsRec.
7501 SCEVDivision::divide(SE, Term, Step, &Q, &R);
7503 // Bail out when GCD does not evenly divide one of the terms.
7510 // Remove all SCEVConstants.
7511 Terms.erase(std::remove_if(Terms.begin(), Terms.end(), [](const SCEV *E) {
7512 return isa<SCEVConstant>(E);
7516 if (Terms.size() > 0)
7517 if (!findArrayDimensionsRec(SE, Terms, Sizes))
7520 Sizes.push_back(Step);
7525 struct FindParameter {
7526 bool FoundParameter;
7527 FindParameter() : FoundParameter(false) {}
7529 bool follow(const SCEV *S) {
7530 if (isa<SCEVUnknown>(S)) {
7531 FoundParameter = true;
7532 // Stop recursion: we found a parameter.
7538 bool isDone() const {
7539 // Stop recursion if we have found a parameter.
7540 return FoundParameter;
7545 // Returns true when S contains at least a SCEVUnknown parameter.
7547 containsParameters(const SCEV *S) {
7549 SCEVTraversal<FindParameter> ST(F);
7552 return F.FoundParameter;
7555 // Returns true when one of the SCEVs of Terms contains a SCEVUnknown parameter.
7557 containsParameters(SmallVectorImpl<const SCEV *> &Terms) {
7558 for (const SCEV *T : Terms)
7559 if (containsParameters(T))
7564 // Return the number of product terms in S.
7565 static inline int numberOfTerms(const SCEV *S) {
7566 if (const SCEVMulExpr *Expr = dyn_cast<SCEVMulExpr>(S))
7567 return Expr->getNumOperands();
7571 static const SCEV *removeConstantFactors(ScalarEvolution &SE, const SCEV *T) {
7572 if (isa<SCEVConstant>(T))
7575 if (isa<SCEVUnknown>(T))
7578 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(T)) {
7579 SmallVector<const SCEV *, 2> Factors;
7580 for (const SCEV *Op : M->operands())
7581 if (!isa<SCEVConstant>(Op))
7582 Factors.push_back(Op);
7584 return SE.getMulExpr(Factors);
7590 /// Return the size of an element read or written by Inst.
7591 const SCEV *ScalarEvolution::getElementSize(Instruction *Inst) {
7593 if (StoreInst *Store = dyn_cast<StoreInst>(Inst))
7594 Ty = Store->getValueOperand()->getType();
7595 else if (LoadInst *Load = dyn_cast<LoadInst>(Inst))
7596 Ty = Load->getType();
7600 Type *ETy = getEffectiveSCEVType(PointerType::getUnqual(Ty));
7601 return getSizeOfExpr(ETy, Ty);
7604 /// Second step of delinearization: compute the array dimensions Sizes from the
7605 /// set of Terms extracted from the memory access function of this SCEVAddRec.
7606 void ScalarEvolution::findArrayDimensions(SmallVectorImpl<const SCEV *> &Terms,
7607 SmallVectorImpl<const SCEV *> &Sizes,
7608 const SCEV *ElementSize) const {
7610 if (Terms.size() < 1 || !ElementSize)
7613 // Early return when Terms do not contain parameters: we do not delinearize
7614 // non parametric SCEVs.
7615 if (!containsParameters(Terms))
7619 dbgs() << "Terms:\n";
7620 for (const SCEV *T : Terms)
7621 dbgs() << *T << "\n";
7624 // Remove duplicates.
7625 std::sort(Terms.begin(), Terms.end());
7626 Terms.erase(std::unique(Terms.begin(), Terms.end()), Terms.end());
7628 // Put larger terms first.
7629 std::sort(Terms.begin(), Terms.end(), [](const SCEV *LHS, const SCEV *RHS) {
7630 return numberOfTerms(LHS) > numberOfTerms(RHS);
7633 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
7635 // Divide all terms by the element size.
7636 for (const SCEV *&Term : Terms) {
7638 SCEVDivision::divide(SE, Term, ElementSize, &Q, &R);
7642 SmallVector<const SCEV *, 4> NewTerms;
7644 // Remove constant factors.
7645 for (const SCEV *T : Terms)
7646 if (const SCEV *NewT = removeConstantFactors(SE, T))
7647 NewTerms.push_back(NewT);
7650 dbgs() << "Terms after sorting:\n";
7651 for (const SCEV *T : NewTerms)
7652 dbgs() << *T << "\n";
7655 if (NewTerms.empty() ||
7656 !findArrayDimensionsRec(SE, NewTerms, Sizes)) {
7661 // The last element to be pushed into Sizes is the size of an element.
7662 Sizes.push_back(ElementSize);
7665 dbgs() << "Sizes:\n";
7666 for (const SCEV *S : Sizes)
7667 dbgs() << *S << "\n";
7671 /// Third step of delinearization: compute the access functions for the
7672 /// Subscripts based on the dimensions in Sizes.
7673 void SCEVAddRecExpr::computeAccessFunctions(
7674 ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &Subscripts,
7675 SmallVectorImpl<const SCEV *> &Sizes) const {
7677 // Early exit in case this SCEV is not an affine multivariate function.
7678 if (Sizes.empty() || !this->isAffine())
7681 const SCEV *Res = this;
7682 int Last = Sizes.size() - 1;
7683 for (int i = Last; i >= 0; i--) {
7685 SCEVDivision::divide(SE, Res, Sizes[i], &Q, &R);
7688 dbgs() << "Res: " << *Res << "\n";
7689 dbgs() << "Sizes[i]: " << *Sizes[i] << "\n";
7690 dbgs() << "Res divided by Sizes[i]:\n";
7691 dbgs() << "Quotient: " << *Q << "\n";
7692 dbgs() << "Remainder: " << *R << "\n";
7697 // Do not record the last subscript corresponding to the size of elements in
7701 // Bail out if the remainder is too complex.
7702 if (isa<SCEVAddRecExpr>(R)) {
7711 // Record the access function for the current subscript.
7712 Subscripts.push_back(R);
7715 // Also push in last position the remainder of the last division: it will be
7716 // the access function of the innermost dimension.
7717 Subscripts.push_back(Res);
7719 std::reverse(Subscripts.begin(), Subscripts.end());
7722 dbgs() << "Subscripts:\n";
7723 for (const SCEV *S : Subscripts)
7724 dbgs() << *S << "\n";
7728 /// Splits the SCEV into two vectors of SCEVs representing the subscripts and
7729 /// sizes of an array access. Returns the remainder of the delinearization that
7730 /// is the offset start of the array. The SCEV->delinearize algorithm computes
7731 /// the multiples of SCEV coefficients: that is a pattern matching of sub
7732 /// expressions in the stride and base of a SCEV corresponding to the
7733 /// computation of a GCD (greatest common divisor) of base and stride. When
7734 /// SCEV->delinearize fails, it returns the SCEV unchanged.
7736 /// For example: when analyzing the memory access A[i][j][k] in this loop nest
7738 /// void foo(long n, long m, long o, double A[n][m][o]) {
7740 /// for (long i = 0; i < n; i++)
7741 /// for (long j = 0; j < m; j++)
7742 /// for (long k = 0; k < o; k++)
7743 /// A[i][j][k] = 1.0;
7746 /// the delinearization input is the following AddRec SCEV:
7748 /// AddRec: {{{%A,+,(8 * %m * %o)}<%for.i>,+,(8 * %o)}<%for.j>,+,8}<%for.k>
7750 /// From this SCEV, we are able to say that the base offset of the access is %A
7751 /// because it appears as an offset that does not divide any of the strides in
7754 /// CHECK: Base offset: %A
7756 /// and then SCEV->delinearize determines the size of some of the dimensions of
7757 /// the array as these are the multiples by which the strides are happening:
7759 /// CHECK: ArrayDecl[UnknownSize][%m][%o] with elements of sizeof(double) bytes.
7761 /// Note that the outermost dimension remains of UnknownSize because there are
7762 /// no strides that would help identifying the size of the last dimension: when
7763 /// the array has been statically allocated, one could compute the size of that
7764 /// dimension by dividing the overall size of the array by the size of the known
7765 /// dimensions: %m * %o * 8.
7767 /// Finally delinearize provides the access functions for the array reference
7768 /// that does correspond to A[i][j][k] of the above C testcase:
7770 /// CHECK: ArrayRef[{0,+,1}<%for.i>][{0,+,1}<%for.j>][{0,+,1}<%for.k>]
7772 /// The testcases are checking the output of a function pass:
7773 /// DelinearizationPass that walks through all loads and stores of a function
7774 /// asking for the SCEV of the memory access with respect to all enclosing
7775 /// loops, calling SCEV->delinearize on that and printing the results.
7777 void SCEVAddRecExpr::delinearize(ScalarEvolution &SE,
7778 SmallVectorImpl<const SCEV *> &Subscripts,
7779 SmallVectorImpl<const SCEV *> &Sizes,
7780 const SCEV *ElementSize) const {
7781 // First step: collect parametric terms.
7782 SmallVector<const SCEV *, 4> Terms;
7783 collectParametricTerms(SE, Terms);
7788 // Second step: find subscript sizes.
7789 SE.findArrayDimensions(Terms, Sizes, ElementSize);
7794 // Third step: compute the access functions for each subscript.
7795 computeAccessFunctions(SE, Subscripts, Sizes);
7797 if (Subscripts.empty())
7801 dbgs() << "succeeded to delinearize " << *this << "\n";
7802 dbgs() << "ArrayDecl[UnknownSize]";
7803 for (const SCEV *S : Sizes)
7804 dbgs() << "[" << *S << "]";
7806 dbgs() << "\nArrayRef";
7807 for (const SCEV *S : Subscripts)
7808 dbgs() << "[" << *S << "]";
7813 //===----------------------------------------------------------------------===//
7814 // SCEVCallbackVH Class Implementation
7815 //===----------------------------------------------------------------------===//
7817 void ScalarEvolution::SCEVCallbackVH::deleted() {
7818 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
7819 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
7820 SE->ConstantEvolutionLoopExitValue.erase(PN);
7821 SE->ValueExprMap.erase(getValPtr());
7822 // this now dangles!
7825 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) {
7826 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
7828 // Forget all the expressions associated with users of the old value,
7829 // so that future queries will recompute the expressions using the new
7831 Value *Old = getValPtr();
7832 SmallVector<User *, 16> Worklist(Old->user_begin(), Old->user_end());
7833 SmallPtrSet<User *, 8> Visited;
7834 while (!Worklist.empty()) {
7835 User *U = Worklist.pop_back_val();
7836 // Deleting the Old value will cause this to dangle. Postpone
7837 // that until everything else is done.
7840 if (!Visited.insert(U).second)
7842 if (PHINode *PN = dyn_cast<PHINode>(U))
7843 SE->ConstantEvolutionLoopExitValue.erase(PN);
7844 SE->ValueExprMap.erase(U);
7845 Worklist.insert(Worklist.end(), U->user_begin(), U->user_end());
7847 // Delete the Old value.
7848 if (PHINode *PN = dyn_cast<PHINode>(Old))
7849 SE->ConstantEvolutionLoopExitValue.erase(PN);
7850 SE->ValueExprMap.erase(Old);
7851 // this now dangles!
7854 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
7855 : CallbackVH(V), SE(se) {}
7857 //===----------------------------------------------------------------------===//
7858 // ScalarEvolution Class Implementation
7859 //===----------------------------------------------------------------------===//
7861 ScalarEvolution::ScalarEvolution()
7862 : FunctionPass(ID), ValuesAtScopes(64), LoopDispositions(64),
7863 BlockDispositions(64), FirstUnknown(nullptr) {
7864 initializeScalarEvolutionPass(*PassRegistry::getPassRegistry());
7867 bool ScalarEvolution::runOnFunction(Function &F) {
7869 AC = &getAnalysis<AssumptionCacheTracker>().getAssumptionCache(F);
7870 LI = &getAnalysis<LoopInfoWrapperPass>().getLoopInfo();
7871 DataLayoutPass *DLP = getAnalysisIfAvailable<DataLayoutPass>();
7872 DL = DLP ? &DLP->getDataLayout() : nullptr;
7873 TLI = &getAnalysis<TargetLibraryInfoWrapperPass>().getTLI();
7874 DT = &getAnalysis<DominatorTreeWrapperPass>().getDomTree();
7878 void ScalarEvolution::releaseMemory() {
7879 // Iterate through all the SCEVUnknown instances and call their
7880 // destructors, so that they release their references to their values.
7881 for (SCEVUnknown *U = FirstUnknown; U; U = U->Next)
7883 FirstUnknown = nullptr;
7885 ValueExprMap.clear();
7887 // Free any extra memory created for ExitNotTakenInfo in the unlikely event
7888 // that a loop had multiple computable exits.
7889 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
7890 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end();
7895 assert(PendingLoopPredicates.empty() && "isImpliedCond garbage");
7897 BackedgeTakenCounts.clear();
7898 ConstantEvolutionLoopExitValue.clear();
7899 ValuesAtScopes.clear();
7900 LoopDispositions.clear();
7901 BlockDispositions.clear();
7902 UnsignedRanges.clear();
7903 SignedRanges.clear();
7904 UniqueSCEVs.clear();
7905 SCEVAllocator.Reset();
7908 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
7909 AU.setPreservesAll();
7910 AU.addRequired<AssumptionCacheTracker>();
7911 AU.addRequiredTransitive<LoopInfoWrapperPass>();
7912 AU.addRequiredTransitive<DominatorTreeWrapperPass>();
7913 AU.addRequired<TargetLibraryInfoWrapperPass>();
7916 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
7917 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
7920 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
7922 // Print all inner loops first
7923 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
7924 PrintLoopInfo(OS, SE, *I);
7927 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
7930 SmallVector<BasicBlock *, 8> ExitBlocks;
7931 L->getExitBlocks(ExitBlocks);
7932 if (ExitBlocks.size() != 1)
7933 OS << "<multiple exits> ";
7935 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
7936 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
7938 OS << "Unpredictable backedge-taken count. ";
7943 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
7946 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
7947 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
7949 OS << "Unpredictable max backedge-taken count. ";
7955 void ScalarEvolution::print(raw_ostream &OS, const Module *) const {
7956 // ScalarEvolution's implementation of the print method is to print
7957 // out SCEV values of all instructions that are interesting. Doing
7958 // this potentially causes it to create new SCEV objects though,
7959 // which technically conflicts with the const qualifier. This isn't
7960 // observable from outside the class though, so casting away the
7961 // const isn't dangerous.
7962 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
7964 OS << "Classifying expressions for: ";
7965 F->printAsOperand(OS, /*PrintType=*/false);
7967 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
7968 if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) {
7971 const SCEV *SV = SE.getSCEV(&*I);
7974 const Loop *L = LI->getLoopFor((*I).getParent());
7976 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
7983 OS << "\t\t" "Exits: ";
7984 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
7985 if (!SE.isLoopInvariant(ExitValue, L)) {
7986 OS << "<<Unknown>>";
7995 OS << "Determining loop execution counts for: ";
7996 F->printAsOperand(OS, /*PrintType=*/false);
7998 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
7999 PrintLoopInfo(OS, &SE, *I);
8002 ScalarEvolution::LoopDisposition
8003 ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) {
8004 SmallVector<std::pair<const Loop *, LoopDisposition>, 2> &Values = LoopDispositions[S];
8005 for (unsigned u = 0; u < Values.size(); u++) {
8006 if (Values[u].first == L)
8007 return Values[u].second;
8009 Values.push_back(std::make_pair(L, LoopVariant));
8010 LoopDisposition D = computeLoopDisposition(S, L);
8011 SmallVector<std::pair<const Loop *, LoopDisposition>, 2> &Values2 = LoopDispositions[S];
8012 for (unsigned u = Values2.size(); u > 0; u--) {
8013 if (Values2[u - 1].first == L) {
8014 Values2[u - 1].second = D;
8021 ScalarEvolution::LoopDisposition
8022 ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) {
8023 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
8025 return LoopInvariant;
8029 return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L);
8030 case scAddRecExpr: {
8031 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
8033 // If L is the addrec's loop, it's computable.
8034 if (AR->getLoop() == L)
8035 return LoopComputable;
8037 // Add recurrences are never invariant in the function-body (null loop).
8041 // This recurrence is variant w.r.t. L if L contains AR's loop.
8042 if (L->contains(AR->getLoop()))
8045 // This recurrence is invariant w.r.t. L if AR's loop contains L.
8046 if (AR->getLoop()->contains(L))
8047 return LoopInvariant;
8049 // This recurrence is variant w.r.t. L if any of its operands
8051 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
8053 if (!isLoopInvariant(*I, L))
8056 // Otherwise it's loop-invariant.
8057 return LoopInvariant;
8063 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
8064 bool HasVarying = false;
8065 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
8067 LoopDisposition D = getLoopDisposition(*I, L);
8068 if (D == LoopVariant)
8070 if (D == LoopComputable)
8073 return HasVarying ? LoopComputable : LoopInvariant;
8076 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
8077 LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L);
8078 if (LD == LoopVariant)
8080 LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L);
8081 if (RD == LoopVariant)
8083 return (LD == LoopInvariant && RD == LoopInvariant) ?
8084 LoopInvariant : LoopComputable;
8087 // All non-instruction values are loop invariant. All instructions are loop
8088 // invariant if they are not contained in the specified loop.
8089 // Instructions are never considered invariant in the function body
8090 // (null loop) because they are defined within the "loop".
8091 if (Instruction *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue()))
8092 return (L && !L->contains(I)) ? LoopInvariant : LoopVariant;
8093 return LoopInvariant;
8094 case scCouldNotCompute:
8095 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
8097 llvm_unreachable("Unknown SCEV kind!");
8100 bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) {
8101 return getLoopDisposition(S, L) == LoopInvariant;
8104 bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) {
8105 return getLoopDisposition(S, L) == LoopComputable;
8108 ScalarEvolution::BlockDisposition
8109 ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) {
8110 SmallVector<std::pair<const BasicBlock *, BlockDisposition>, 2> &Values = BlockDispositions[S];
8111 for (unsigned u = 0; u < Values.size(); u++) {
8112 if (Values[u].first == BB)
8113 return Values[u].second;
8115 Values.push_back(std::make_pair(BB, DoesNotDominateBlock));
8116 BlockDisposition D = computeBlockDisposition(S, BB);
8117 SmallVector<std::pair<const BasicBlock *, BlockDisposition>, 2> &Values2 = BlockDispositions[S];
8118 for (unsigned u = Values2.size(); u > 0; u--) {
8119 if (Values2[u - 1].first == BB) {
8120 Values2[u - 1].second = D;
8127 ScalarEvolution::BlockDisposition
8128 ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) {
8129 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
8131 return ProperlyDominatesBlock;
8135 return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB);
8136 case scAddRecExpr: {
8137 // This uses a "dominates" query instead of "properly dominates" query
8138 // to test for proper dominance too, because the instruction which
8139 // produces the addrec's value is a PHI, and a PHI effectively properly
8140 // dominates its entire containing block.
8141 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
8142 if (!DT->dominates(AR->getLoop()->getHeader(), BB))
8143 return DoesNotDominateBlock;
8145 // FALL THROUGH into SCEVNAryExpr handling.
8150 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
8152 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
8154 BlockDisposition D = getBlockDisposition(*I, BB);
8155 if (D == DoesNotDominateBlock)
8156 return DoesNotDominateBlock;
8157 if (D == DominatesBlock)
8160 return Proper ? ProperlyDominatesBlock : DominatesBlock;
8163 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
8164 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
8165 BlockDisposition LD = getBlockDisposition(LHS, BB);
8166 if (LD == DoesNotDominateBlock)
8167 return DoesNotDominateBlock;
8168 BlockDisposition RD = getBlockDisposition(RHS, BB);
8169 if (RD == DoesNotDominateBlock)
8170 return DoesNotDominateBlock;
8171 return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ?
8172 ProperlyDominatesBlock : DominatesBlock;
8175 if (Instruction *I =
8176 dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) {
8177 if (I->getParent() == BB)
8178 return DominatesBlock;
8179 if (DT->properlyDominates(I->getParent(), BB))
8180 return ProperlyDominatesBlock;
8181 return DoesNotDominateBlock;
8183 return ProperlyDominatesBlock;
8184 case scCouldNotCompute:
8185 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
8187 llvm_unreachable("Unknown SCEV kind!");
8190 bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) {
8191 return getBlockDisposition(S, BB) >= DominatesBlock;
8194 bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) {
8195 return getBlockDisposition(S, BB) == ProperlyDominatesBlock;
8199 // Search for a SCEV expression node within an expression tree.
8200 // Implements SCEVTraversal::Visitor.
8205 SCEVSearch(const SCEV *N): Node(N), IsFound(false) {}
8207 bool follow(const SCEV *S) {
8208 IsFound |= (S == Node);
8211 bool isDone() const { return IsFound; }
8215 bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const {
8216 SCEVSearch Search(Op);
8217 visitAll(S, Search);
8218 return Search.IsFound;
8221 void ScalarEvolution::forgetMemoizedResults(const SCEV *S) {
8222 ValuesAtScopes.erase(S);
8223 LoopDispositions.erase(S);
8224 BlockDispositions.erase(S);
8225 UnsignedRanges.erase(S);
8226 SignedRanges.erase(S);
8228 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
8229 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end(); I != E; ) {
8230 BackedgeTakenInfo &BEInfo = I->second;
8231 if (BEInfo.hasOperand(S, this)) {
8233 BackedgeTakenCounts.erase(I++);
8240 typedef DenseMap<const Loop *, std::string> VerifyMap;
8242 /// replaceSubString - Replaces all occurrences of From in Str with To.
8243 static void replaceSubString(std::string &Str, StringRef From, StringRef To) {
8245 while ((Pos = Str.find(From, Pos)) != std::string::npos) {
8246 Str.replace(Pos, From.size(), To.data(), To.size());
8251 /// getLoopBackedgeTakenCounts - Helper method for verifyAnalysis.
8253 getLoopBackedgeTakenCounts(Loop *L, VerifyMap &Map, ScalarEvolution &SE) {
8254 for (Loop::reverse_iterator I = L->rbegin(), E = L->rend(); I != E; ++I) {
8255 getLoopBackedgeTakenCounts(*I, Map, SE); // recurse.
8257 std::string &S = Map[L];
8259 raw_string_ostream OS(S);
8260 SE.getBackedgeTakenCount(L)->print(OS);
8262 // false and 0 are semantically equivalent. This can happen in dead loops.
8263 replaceSubString(OS.str(), "false", "0");
8264 // Remove wrap flags, their use in SCEV is highly fragile.
8265 // FIXME: Remove this when SCEV gets smarter about them.
8266 replaceSubString(OS.str(), "<nw>", "");
8267 replaceSubString(OS.str(), "<nsw>", "");
8268 replaceSubString(OS.str(), "<nuw>", "");
8273 void ScalarEvolution::verifyAnalysis() const {
8277 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
8279 // Gather stringified backedge taken counts for all loops using SCEV's caches.
8280 // FIXME: It would be much better to store actual values instead of strings,
8281 // but SCEV pointers will change if we drop the caches.
8282 VerifyMap BackedgeDumpsOld, BackedgeDumpsNew;
8283 for (LoopInfo::reverse_iterator I = LI->rbegin(), E = LI->rend(); I != E; ++I)
8284 getLoopBackedgeTakenCounts(*I, BackedgeDumpsOld, SE);
8286 // Gather stringified backedge taken counts for all loops without using
8289 for (LoopInfo::reverse_iterator I = LI->rbegin(), E = LI->rend(); I != E; ++I)
8290 getLoopBackedgeTakenCounts(*I, BackedgeDumpsNew, SE);
8292 // Now compare whether they're the same with and without caches. This allows
8293 // verifying that no pass changed the cache.
8294 assert(BackedgeDumpsOld.size() == BackedgeDumpsNew.size() &&
8295 "New loops suddenly appeared!");
8297 for (VerifyMap::iterator OldI = BackedgeDumpsOld.begin(),
8298 OldE = BackedgeDumpsOld.end(),
8299 NewI = BackedgeDumpsNew.begin();
8300 OldI != OldE; ++OldI, ++NewI) {
8301 assert(OldI->first == NewI->first && "Loop order changed!");
8303 // Compare the stringified SCEVs. We don't care if undef backedgetaken count
8305 // FIXME: We currently ignore SCEV changes from/to CouldNotCompute. This
8306 // means that a pass is buggy or SCEV has to learn a new pattern but is
8307 // usually not harmful.
8308 if (OldI->second != NewI->second &&
8309 OldI->second.find("undef") == std::string::npos &&
8310 NewI->second.find("undef") == std::string::npos &&
8311 OldI->second != "***COULDNOTCOMPUTE***" &&
8312 NewI->second != "***COULDNOTCOMPUTE***") {
8313 dbgs() << "SCEVValidator: SCEV for loop '"
8314 << OldI->first->getHeader()->getName()
8315 << "' changed from '" << OldI->second
8316 << "' to '" << NewI->second << "'!\n";
8321 // TODO: Verify more things.