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 // WARNING: FIXME: the optimization below assumes that a sign-overflowing nsw
1368 // operation is undefined behavior. This is strictly more aggressive than the
1369 // interpretation of nsw in other parts of LLVM (for instance, they may
1370 // unconditionally hoist nsw arithmetic through control flow). This logic
1371 // needs to be revisited once we have a consistent semantics for poison
1374 // "{S,+,X} is <nsw>" and "{S,+,X} is evaluated at least once" implies "S+X
1375 // does not sign-overflow" (we'd have undefined behavior if it did). If
1376 // `L->getExitingBlock() == L->getLoopLatch()` then `PreAR` (= {S,+,X}<nsw>)
1377 // is evaluated every-time `AR` (= {S+X,+,X}) is evaluated, and hence within
1378 // `AR` we are safe to assume that "S+X" will not sign-overflow.
1381 BasicBlock *ExitingBlock = L->getExitingBlock();
1382 BasicBlock *LatchBlock = L->getLoopLatch();
1383 if (PreAR && PreAR->getNoWrapFlags(SCEV::FlagNSW) &&
1384 ExitingBlock != nullptr && ExitingBlock == LatchBlock)
1387 // 2. Direct overflow check on the step operation's expression.
1388 unsigned BitWidth = SE->getTypeSizeInBits(AR->getType());
1389 Type *WideTy = IntegerType::get(SE->getContext(), BitWidth * 2);
1390 const SCEV *OperandExtendedStart =
1391 SE->getAddExpr(SE->getSignExtendExpr(PreStart, WideTy),
1392 SE->getSignExtendExpr(Step, WideTy));
1393 if (SE->getSignExtendExpr(Start, WideTy) == OperandExtendedStart) {
1394 // Cache knowledge of PreAR NSW.
1396 const_cast<SCEVAddRecExpr *>(PreAR)->setNoWrapFlags(SCEV::FlagNSW);
1397 // FIXME: this optimization needs a unit test
1398 DEBUG(dbgs() << "SCEV: untested prestart overflow check\n");
1402 // 3. Loop precondition.
1403 ICmpInst::Predicate Pred;
1404 const SCEV *OverflowLimit = getOverflowLimitForStep(Step, &Pred, SE);
1406 if (OverflowLimit &&
1407 SE->isLoopEntryGuardedByCond(L, Pred, PreStart, OverflowLimit)) {
1413 // Get the normalized sign-extended expression for this AddRec's Start.
1414 static const SCEV *getSignExtendAddRecStart(const SCEVAddRecExpr *AR,
1416 ScalarEvolution *SE) {
1417 const SCEV *PreStart = getPreStartForSignExtend(AR, Ty, SE);
1419 return SE->getSignExtendExpr(AR->getStart(), Ty);
1421 return SE->getAddExpr(SE->getSignExtendExpr(AR->getStepRecurrence(*SE), Ty),
1422 SE->getSignExtendExpr(PreStart, Ty));
1425 const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op,
1427 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1428 "This is not an extending conversion!");
1429 assert(isSCEVable(Ty) &&
1430 "This is not a conversion to a SCEVable type!");
1431 Ty = getEffectiveSCEVType(Ty);
1433 // Fold if the operand is constant.
1434 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1436 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), Ty)));
1438 // sext(sext(x)) --> sext(x)
1439 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1440 return getSignExtendExpr(SS->getOperand(), Ty);
1442 // sext(zext(x)) --> zext(x)
1443 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1444 return getZeroExtendExpr(SZ->getOperand(), Ty);
1446 // Before doing any expensive analysis, check to see if we've already
1447 // computed a SCEV for this Op and Ty.
1448 FoldingSetNodeID ID;
1449 ID.AddInteger(scSignExtend);
1453 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1455 // If the input value is provably positive, build a zext instead.
1456 if (isKnownNonNegative(Op))
1457 return getZeroExtendExpr(Op, Ty);
1459 // sext(trunc(x)) --> sext(x) or x or trunc(x)
1460 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1461 // It's possible the bits taken off by the truncate were all sign bits. If
1462 // so, we should be able to simplify this further.
1463 const SCEV *X = ST->getOperand();
1464 ConstantRange CR = getSignedRange(X);
1465 unsigned TruncBits = getTypeSizeInBits(ST->getType());
1466 unsigned NewBits = getTypeSizeInBits(Ty);
1467 if (CR.truncate(TruncBits).signExtend(NewBits).contains(
1468 CR.sextOrTrunc(NewBits)))
1469 return getTruncateOrSignExtend(X, Ty);
1472 // sext(C1 + (C2 * x)) --> C1 + sext(C2 * x) if C1 < C2
1473 if (auto SA = dyn_cast<SCEVAddExpr>(Op)) {
1474 if (SA->getNumOperands() == 2) {
1475 auto SC1 = dyn_cast<SCEVConstant>(SA->getOperand(0));
1476 auto SMul = dyn_cast<SCEVMulExpr>(SA->getOperand(1));
1478 if (auto SC2 = dyn_cast<SCEVConstant>(SMul->getOperand(0))) {
1479 const APInt &C1 = SC1->getValue()->getValue();
1480 const APInt &C2 = SC2->getValue()->getValue();
1481 if (C1.isStrictlyPositive() && C2.isStrictlyPositive() &&
1482 C2.ugt(C1) && C2.isPowerOf2())
1483 return getAddExpr(getSignExtendExpr(SC1, Ty),
1484 getSignExtendExpr(SMul, Ty));
1489 // If the input value is a chrec scev, and we can prove that the value
1490 // did not overflow the old, smaller, value, we can sign extend all of the
1491 // operands (often constants). This allows analysis of something like
1492 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
1493 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1494 if (AR->isAffine()) {
1495 const SCEV *Start = AR->getStart();
1496 const SCEV *Step = AR->getStepRecurrence(*this);
1497 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1498 const Loop *L = AR->getLoop();
1500 // If we have special knowledge that this addrec won't overflow,
1501 // we don't need to do any further analysis.
1502 if (AR->getNoWrapFlags(SCEV::FlagNSW))
1503 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1504 getSignExtendExpr(Step, Ty),
1507 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1508 // Note that this serves two purposes: It filters out loops that are
1509 // simply not analyzable, and it covers the case where this code is
1510 // being called from within backedge-taken count analysis, such that
1511 // attempting to ask for the backedge-taken count would likely result
1512 // in infinite recursion. In the later case, the analysis code will
1513 // cope with a conservative value, and it will take care to purge
1514 // that value once it has finished.
1515 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1516 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1517 // Manually compute the final value for AR, checking for
1520 // Check whether the backedge-taken count can be losslessly casted to
1521 // the addrec's type. The count is always unsigned.
1522 const SCEV *CastedMaxBECount =
1523 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1524 const SCEV *RecastedMaxBECount =
1525 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1526 if (MaxBECount == RecastedMaxBECount) {
1527 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1528 // Check whether Start+Step*MaxBECount has no signed overflow.
1529 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
1530 const SCEV *SAdd = getSignExtendExpr(getAddExpr(Start, SMul), WideTy);
1531 const SCEV *WideStart = getSignExtendExpr(Start, WideTy);
1532 const SCEV *WideMaxBECount =
1533 getZeroExtendExpr(CastedMaxBECount, WideTy);
1534 const SCEV *OperandExtendedAdd =
1535 getAddExpr(WideStart,
1536 getMulExpr(WideMaxBECount,
1537 getSignExtendExpr(Step, WideTy)));
1538 if (SAdd == OperandExtendedAdd) {
1539 // Cache knowledge of AR NSW, which is propagated to this AddRec.
1540 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1541 // Return the expression with the addrec on the outside.
1542 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1543 getSignExtendExpr(Step, Ty),
1544 L, AR->getNoWrapFlags());
1546 // Similar to above, only this time treat the step value as unsigned.
1547 // This covers loops that count up with an unsigned step.
1548 OperandExtendedAdd =
1549 getAddExpr(WideStart,
1550 getMulExpr(WideMaxBECount,
1551 getZeroExtendExpr(Step, WideTy)));
1552 if (SAdd == OperandExtendedAdd) {
1553 // If AR wraps around then
1555 // abs(Step) * MaxBECount > unsigned-max(AR->getType())
1556 // => SAdd != OperandExtendedAdd
1558 // Thus (AR is not NW => SAdd != OperandExtendedAdd) <=>
1559 // (SAdd == OperandExtendedAdd => AR is NW)
1561 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1563 // Return the expression with the addrec on the outside.
1564 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1565 getZeroExtendExpr(Step, Ty),
1566 L, AR->getNoWrapFlags());
1570 // If the backedge is guarded by a comparison with the pre-inc value
1571 // the addrec is safe. Also, if the entry is guarded by a comparison
1572 // with the start value and the backedge is guarded by a comparison
1573 // with the post-inc value, the addrec is safe.
1574 ICmpInst::Predicate Pred;
1575 const SCEV *OverflowLimit = getOverflowLimitForStep(Step, &Pred, this);
1576 if (OverflowLimit &&
1577 (isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) ||
1578 (isLoopEntryGuardedByCond(L, Pred, Start, OverflowLimit) &&
1579 isLoopBackedgeGuardedByCond(L, Pred, AR->getPostIncExpr(*this),
1581 // Cache knowledge of AR NSW, then propagate NSW to the wide AddRec.
1582 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1583 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1584 getSignExtendExpr(Step, Ty),
1585 L, AR->getNoWrapFlags());
1588 // If Start and Step are constants, check if we can apply this
1590 // sext{C1,+,C2} --> C1 + sext{0,+,C2} if C1 < C2
1591 auto SC1 = dyn_cast<SCEVConstant>(Start);
1592 auto SC2 = dyn_cast<SCEVConstant>(Step);
1594 const APInt &C1 = SC1->getValue()->getValue();
1595 const APInt &C2 = SC2->getValue()->getValue();
1596 if (C1.isStrictlyPositive() && C2.isStrictlyPositive() && C2.ugt(C1) &&
1598 Start = getSignExtendExpr(Start, Ty);
1599 const SCEV *NewAR = getAddRecExpr(getConstant(AR->getType(), 0), Step,
1600 L, AR->getNoWrapFlags());
1601 return getAddExpr(Start, getSignExtendExpr(NewAR, Ty));
1606 // The cast wasn't folded; create an explicit cast node.
1607 // Recompute the insert position, as it may have been invalidated.
1608 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1609 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
1611 UniqueSCEVs.InsertNode(S, IP);
1615 /// getAnyExtendExpr - Return a SCEV for the given operand extended with
1616 /// unspecified bits out to the given type.
1618 const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
1620 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1621 "This is not an extending conversion!");
1622 assert(isSCEVable(Ty) &&
1623 "This is not a conversion to a SCEVable type!");
1624 Ty = getEffectiveSCEVType(Ty);
1626 // Sign-extend negative constants.
1627 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1628 if (SC->getValue()->getValue().isNegative())
1629 return getSignExtendExpr(Op, Ty);
1631 // Peel off a truncate cast.
1632 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
1633 const SCEV *NewOp = T->getOperand();
1634 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
1635 return getAnyExtendExpr(NewOp, Ty);
1636 return getTruncateOrNoop(NewOp, Ty);
1639 // Next try a zext cast. If the cast is folded, use it.
1640 const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
1641 if (!isa<SCEVZeroExtendExpr>(ZExt))
1644 // Next try a sext cast. If the cast is folded, use it.
1645 const SCEV *SExt = getSignExtendExpr(Op, Ty);
1646 if (!isa<SCEVSignExtendExpr>(SExt))
1649 // Force the cast to be folded into the operands of an addrec.
1650 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
1651 SmallVector<const SCEV *, 4> Ops;
1652 for (const SCEV *Op : AR->operands())
1653 Ops.push_back(getAnyExtendExpr(Op, Ty));
1654 return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW);
1657 // If the expression is obviously signed, use the sext cast value.
1658 if (isa<SCEVSMaxExpr>(Op))
1661 // Absent any other information, use the zext cast value.
1665 /// CollectAddOperandsWithScales - Process the given Ops list, which is
1666 /// a list of operands to be added under the given scale, update the given
1667 /// map. This is a helper function for getAddRecExpr. As an example of
1668 /// what it does, given a sequence of operands that would form an add
1669 /// expression like this:
1671 /// m + n + 13 + (A * (o + p + (B * (q + m + 29)))) + r + (-1 * r)
1673 /// where A and B are constants, update the map with these values:
1675 /// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
1677 /// and add 13 + A*B*29 to AccumulatedConstant.
1678 /// This will allow getAddRecExpr to produce this:
1680 /// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
1682 /// This form often exposes folding opportunities that are hidden in
1683 /// the original operand list.
1685 /// Return true iff it appears that any interesting folding opportunities
1686 /// may be exposed. This helps getAddRecExpr short-circuit extra work in
1687 /// the common case where no interesting opportunities are present, and
1688 /// is also used as a check to avoid infinite recursion.
1691 CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
1692 SmallVectorImpl<const SCEV *> &NewOps,
1693 APInt &AccumulatedConstant,
1694 const SCEV *const *Ops, size_t NumOperands,
1696 ScalarEvolution &SE) {
1697 bool Interesting = false;
1699 // Iterate over the add operands. They are sorted, with constants first.
1701 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1703 // Pull a buried constant out to the outside.
1704 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
1706 AccumulatedConstant += Scale * C->getValue()->getValue();
1709 // Next comes everything else. We're especially interested in multiplies
1710 // here, but they're in the middle, so just visit the rest with one loop.
1711 for (; i != NumOperands; ++i) {
1712 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
1713 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
1715 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue();
1716 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
1717 // A multiplication of a constant with another add; recurse.
1718 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1));
1720 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1721 Add->op_begin(), Add->getNumOperands(),
1724 // A multiplication of a constant with some other value. Update
1726 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
1727 const SCEV *Key = SE.getMulExpr(MulOps);
1728 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1729 M.insert(std::make_pair(Key, NewScale));
1731 NewOps.push_back(Pair.first->first);
1733 Pair.first->second += NewScale;
1734 // The map already had an entry for this value, which may indicate
1735 // a folding opportunity.
1740 // An ordinary operand. Update the map.
1741 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1742 M.insert(std::make_pair(Ops[i], Scale));
1744 NewOps.push_back(Pair.first->first);
1746 Pair.first->second += Scale;
1747 // The map already had an entry for this value, which may indicate
1748 // a folding opportunity.
1758 struct APIntCompare {
1759 bool operator()(const APInt &LHS, const APInt &RHS) const {
1760 return LHS.ult(RHS);
1765 // We're trying to construct a SCEV of type `Type' with `Ops' as operands and
1766 // `OldFlags' as can't-wrap behavior. Infer a more aggressive set of
1767 // can't-overflow flags for the operation if possible.
1768 static SCEV::NoWrapFlags
1769 StrengthenNoWrapFlags(ScalarEvolution *SE, SCEVTypes Type,
1770 const SmallVectorImpl<const SCEV *> &Ops,
1771 SCEV::NoWrapFlags OldFlags) {
1772 using namespace std::placeholders;
1775 Type == scAddExpr || Type == scAddRecExpr || Type == scMulExpr;
1777 assert(CanAnalyze && "don't call from other places!");
1779 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
1780 SCEV::NoWrapFlags SignOrUnsignWrap =
1781 ScalarEvolution::maskFlags(OldFlags, SignOrUnsignMask);
1783 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
1784 auto IsKnownNonNegative =
1785 std::bind(std::mem_fn(&ScalarEvolution::isKnownNonNegative), SE, _1);
1787 if (SignOrUnsignWrap == SCEV::FlagNSW &&
1788 std::all_of(Ops.begin(), Ops.end(), IsKnownNonNegative))
1789 return ScalarEvolution::setFlags(OldFlags,
1790 (SCEV::NoWrapFlags)SignOrUnsignMask);
1795 /// getAddExpr - Get a canonical add expression, or something simpler if
1797 const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
1798 SCEV::NoWrapFlags Flags) {
1799 assert(!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) &&
1800 "only nuw or nsw allowed");
1801 assert(!Ops.empty() && "Cannot get empty add!");
1802 if (Ops.size() == 1) return Ops[0];
1804 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
1805 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1806 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
1807 "SCEVAddExpr operand types don't match!");
1810 Flags = StrengthenNoWrapFlags(this, scAddExpr, Ops, Flags);
1812 // Sort by complexity, this groups all similar expression types together.
1813 GroupByComplexity(Ops, LI);
1815 // If there are any constants, fold them together.
1817 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1819 assert(Idx < Ops.size());
1820 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1821 // We found two constants, fold them together!
1822 Ops[0] = getConstant(LHSC->getValue()->getValue() +
1823 RHSC->getValue()->getValue());
1824 if (Ops.size() == 2) return Ops[0];
1825 Ops.erase(Ops.begin()+1); // Erase the folded element
1826 LHSC = cast<SCEVConstant>(Ops[0]);
1829 // If we are left with a constant zero being added, strip it off.
1830 if (LHSC->getValue()->isZero()) {
1831 Ops.erase(Ops.begin());
1835 if (Ops.size() == 1) return Ops[0];
1838 // Okay, check to see if the same value occurs in the operand list more than
1839 // once. If so, merge them together into an multiply expression. Since we
1840 // sorted the list, these values are required to be adjacent.
1841 Type *Ty = Ops[0]->getType();
1842 bool FoundMatch = false;
1843 for (unsigned i = 0, e = Ops.size(); i != e-1; ++i)
1844 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
1845 // Scan ahead to count how many equal operands there are.
1847 while (i+Count != e && Ops[i+Count] == Ops[i])
1849 // Merge the values into a multiply.
1850 const SCEV *Scale = getConstant(Ty, Count);
1851 const SCEV *Mul = getMulExpr(Scale, Ops[i]);
1852 if (Ops.size() == Count)
1855 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count);
1856 --i; e -= Count - 1;
1860 return getAddExpr(Ops, Flags);
1862 // Check for truncates. If all the operands are truncated from the same
1863 // type, see if factoring out the truncate would permit the result to be
1864 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
1865 // if the contents of the resulting outer trunc fold to something simple.
1866 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
1867 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
1868 Type *DstType = Trunc->getType();
1869 Type *SrcType = Trunc->getOperand()->getType();
1870 SmallVector<const SCEV *, 8> LargeOps;
1872 // Check all the operands to see if they can be represented in the
1873 // source type of the truncate.
1874 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1875 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
1876 if (T->getOperand()->getType() != SrcType) {
1880 LargeOps.push_back(T->getOperand());
1881 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1882 LargeOps.push_back(getAnyExtendExpr(C, SrcType));
1883 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
1884 SmallVector<const SCEV *, 8> LargeMulOps;
1885 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
1886 if (const SCEVTruncateExpr *T =
1887 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
1888 if (T->getOperand()->getType() != SrcType) {
1892 LargeMulOps.push_back(T->getOperand());
1893 } else if (const SCEVConstant *C =
1894 dyn_cast<SCEVConstant>(M->getOperand(j))) {
1895 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType));
1902 LargeOps.push_back(getMulExpr(LargeMulOps));
1909 // Evaluate the expression in the larger type.
1910 const SCEV *Fold = getAddExpr(LargeOps, Flags);
1911 // If it folds to something simple, use it. Otherwise, don't.
1912 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
1913 return getTruncateExpr(Fold, DstType);
1917 // Skip past any other cast SCEVs.
1918 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
1921 // If there are add operands they would be next.
1922 if (Idx < Ops.size()) {
1923 bool DeletedAdd = false;
1924 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
1925 // If we have an add, expand the add operands onto the end of the operands
1927 Ops.erase(Ops.begin()+Idx);
1928 Ops.append(Add->op_begin(), Add->op_end());
1932 // If we deleted at least one add, we added operands to the end of the list,
1933 // and they are not necessarily sorted. Recurse to resort and resimplify
1934 // any operands we just acquired.
1936 return getAddExpr(Ops);
1939 // Skip over the add expression until we get to a multiply.
1940 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1943 // Check to see if there are any folding opportunities present with
1944 // operands multiplied by constant values.
1945 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
1946 uint64_t BitWidth = getTypeSizeInBits(Ty);
1947 DenseMap<const SCEV *, APInt> M;
1948 SmallVector<const SCEV *, 8> NewOps;
1949 APInt AccumulatedConstant(BitWidth, 0);
1950 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1951 Ops.data(), Ops.size(),
1952 APInt(BitWidth, 1), *this)) {
1953 // Some interesting folding opportunity is present, so its worthwhile to
1954 // re-generate the operands list. Group the operands by constant scale,
1955 // to avoid multiplying by the same constant scale multiple times.
1956 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
1957 for (SmallVectorImpl<const SCEV *>::const_iterator I = NewOps.begin(),
1958 E = NewOps.end(); I != E; ++I)
1959 MulOpLists[M.find(*I)->second].push_back(*I);
1960 // Re-generate the operands list.
1962 if (AccumulatedConstant != 0)
1963 Ops.push_back(getConstant(AccumulatedConstant));
1964 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator
1965 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I)
1967 Ops.push_back(getMulExpr(getConstant(I->first),
1968 getAddExpr(I->second)));
1970 return getConstant(Ty, 0);
1971 if (Ops.size() == 1)
1973 return getAddExpr(Ops);
1977 // If we are adding something to a multiply expression, make sure the
1978 // something is not already an operand of the multiply. If so, merge it into
1980 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
1981 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
1982 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
1983 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
1984 if (isa<SCEVConstant>(MulOpSCEV))
1986 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
1987 if (MulOpSCEV == Ops[AddOp]) {
1988 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
1989 const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
1990 if (Mul->getNumOperands() != 2) {
1991 // If the multiply has more than two operands, we must get the
1993 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
1994 Mul->op_begin()+MulOp);
1995 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
1996 InnerMul = getMulExpr(MulOps);
1998 const SCEV *One = getConstant(Ty, 1);
1999 const SCEV *AddOne = getAddExpr(One, InnerMul);
2000 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV);
2001 if (Ops.size() == 2) return OuterMul;
2003 Ops.erase(Ops.begin()+AddOp);
2004 Ops.erase(Ops.begin()+Idx-1);
2006 Ops.erase(Ops.begin()+Idx);
2007 Ops.erase(Ops.begin()+AddOp-1);
2009 Ops.push_back(OuterMul);
2010 return getAddExpr(Ops);
2013 // Check this multiply against other multiplies being added together.
2014 for (unsigned OtherMulIdx = Idx+1;
2015 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
2017 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
2018 // If MulOp occurs in OtherMul, we can fold the two multiplies
2020 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
2021 OMulOp != e; ++OMulOp)
2022 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
2023 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
2024 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
2025 if (Mul->getNumOperands() != 2) {
2026 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
2027 Mul->op_begin()+MulOp);
2028 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
2029 InnerMul1 = getMulExpr(MulOps);
2031 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
2032 if (OtherMul->getNumOperands() != 2) {
2033 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
2034 OtherMul->op_begin()+OMulOp);
2035 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end());
2036 InnerMul2 = getMulExpr(MulOps);
2038 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
2039 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
2040 if (Ops.size() == 2) return OuterMul;
2041 Ops.erase(Ops.begin()+Idx);
2042 Ops.erase(Ops.begin()+OtherMulIdx-1);
2043 Ops.push_back(OuterMul);
2044 return getAddExpr(Ops);
2050 // If there are any add recurrences in the operands list, see if any other
2051 // added values are loop invariant. If so, we can fold them into the
2053 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2056 // Scan over all recurrences, trying to fold loop invariants into them.
2057 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
2058 // Scan all of the other operands to this add and add them to the vector if
2059 // they are loop invariant w.r.t. the recurrence.
2060 SmallVector<const SCEV *, 8> LIOps;
2061 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2062 const Loop *AddRecLoop = AddRec->getLoop();
2063 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2064 if (isLoopInvariant(Ops[i], AddRecLoop)) {
2065 LIOps.push_back(Ops[i]);
2066 Ops.erase(Ops.begin()+i);
2070 // If we found some loop invariants, fold them into the recurrence.
2071 if (!LIOps.empty()) {
2072 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
2073 LIOps.push_back(AddRec->getStart());
2075 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
2077 AddRecOps[0] = getAddExpr(LIOps);
2079 // Build the new addrec. Propagate the NUW and NSW flags if both the
2080 // outer add and the inner addrec are guaranteed to have no overflow.
2081 // Always propagate NW.
2082 Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW));
2083 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags);
2085 // If all of the other operands were loop invariant, we are done.
2086 if (Ops.size() == 1) return NewRec;
2088 // Otherwise, add the folded AddRec by the non-invariant parts.
2089 for (unsigned i = 0;; ++i)
2090 if (Ops[i] == AddRec) {
2094 return getAddExpr(Ops);
2097 // Okay, if there weren't any loop invariants to be folded, check to see if
2098 // there are multiple AddRec's with the same loop induction variable being
2099 // added together. If so, we can fold them.
2100 for (unsigned OtherIdx = Idx+1;
2101 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2103 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
2104 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L>
2105 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
2107 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2109 if (const SCEVAddRecExpr *OtherAddRec =
2110 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]))
2111 if (OtherAddRec->getLoop() == AddRecLoop) {
2112 for (unsigned i = 0, e = OtherAddRec->getNumOperands();
2114 if (i >= AddRecOps.size()) {
2115 AddRecOps.append(OtherAddRec->op_begin()+i,
2116 OtherAddRec->op_end());
2119 AddRecOps[i] = getAddExpr(AddRecOps[i],
2120 OtherAddRec->getOperand(i));
2122 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2124 // Step size has changed, so we cannot guarantee no self-wraparound.
2125 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap);
2126 return getAddExpr(Ops);
2129 // Otherwise couldn't fold anything into this recurrence. Move onto the
2133 // Okay, it looks like we really DO need an add expr. Check to see if we
2134 // already have one, otherwise create a new one.
2135 FoldingSetNodeID ID;
2136 ID.AddInteger(scAddExpr);
2137 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2138 ID.AddPointer(Ops[i]);
2141 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2143 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2144 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2145 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator),
2147 UniqueSCEVs.InsertNode(S, IP);
2149 S->setNoWrapFlags(Flags);
2153 static uint64_t umul_ov(uint64_t i, uint64_t j, bool &Overflow) {
2155 if (j > 1 && k / j != i) Overflow = true;
2159 /// Compute the result of "n choose k", the binomial coefficient. If an
2160 /// intermediate computation overflows, Overflow will be set and the return will
2161 /// be garbage. Overflow is not cleared on absence of overflow.
2162 static uint64_t Choose(uint64_t n, uint64_t k, bool &Overflow) {
2163 // We use the multiplicative formula:
2164 // n(n-1)(n-2)...(n-(k-1)) / k(k-1)(k-2)...1 .
2165 // At each iteration, we take the n-th term of the numeral and divide by the
2166 // (k-n)th term of the denominator. This division will always produce an
2167 // integral result, and helps reduce the chance of overflow in the
2168 // intermediate computations. However, we can still overflow even when the
2169 // final result would fit.
2171 if (n == 0 || n == k) return 1;
2172 if (k > n) return 0;
2178 for (uint64_t i = 1; i <= k; ++i) {
2179 r = umul_ov(r, n-(i-1), Overflow);
2185 /// Determine if any of the operands in this SCEV are a constant or if
2186 /// any of the add or multiply expressions in this SCEV contain a constant.
2187 static bool containsConstantSomewhere(const SCEV *StartExpr) {
2188 SmallVector<const SCEV *, 4> Ops;
2189 Ops.push_back(StartExpr);
2190 while (!Ops.empty()) {
2191 const SCEV *CurrentExpr = Ops.pop_back_val();
2192 if (isa<SCEVConstant>(*CurrentExpr))
2195 if (isa<SCEVAddExpr>(*CurrentExpr) || isa<SCEVMulExpr>(*CurrentExpr)) {
2196 const auto *CurrentNAry = cast<SCEVNAryExpr>(CurrentExpr);
2197 for (const SCEV *Operand : CurrentNAry->operands())
2198 Ops.push_back(Operand);
2204 /// getMulExpr - Get a canonical multiply expression, or something simpler if
2206 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
2207 SCEV::NoWrapFlags Flags) {
2208 assert(Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) &&
2209 "only nuw or nsw allowed");
2210 assert(!Ops.empty() && "Cannot get empty mul!");
2211 if (Ops.size() == 1) return Ops[0];
2213 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2214 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2215 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2216 "SCEVMulExpr operand types don't match!");
2219 Flags = StrengthenNoWrapFlags(this, scMulExpr, Ops, Flags);
2221 // Sort by complexity, this groups all similar expression types together.
2222 GroupByComplexity(Ops, LI);
2224 // If there are any constants, fold them together.
2226 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2228 // C1*(C2+V) -> C1*C2 + C1*V
2229 if (Ops.size() == 2)
2230 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
2231 // If any of Add's ops are Adds or Muls with a constant,
2232 // apply this transformation as well.
2233 if (Add->getNumOperands() == 2)
2234 if (containsConstantSomewhere(Add))
2235 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
2236 getMulExpr(LHSC, Add->getOperand(1)));
2239 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2240 // We found two constants, fold them together!
2241 ConstantInt *Fold = ConstantInt::get(getContext(),
2242 LHSC->getValue()->getValue() *
2243 RHSC->getValue()->getValue());
2244 Ops[0] = getConstant(Fold);
2245 Ops.erase(Ops.begin()+1); // Erase the folded element
2246 if (Ops.size() == 1) return Ops[0];
2247 LHSC = cast<SCEVConstant>(Ops[0]);
2250 // If we are left with a constant one being multiplied, strip it off.
2251 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
2252 Ops.erase(Ops.begin());
2254 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
2255 // If we have a multiply of zero, it will always be zero.
2257 } else if (Ops[0]->isAllOnesValue()) {
2258 // If we have a mul by -1 of an add, try distributing the -1 among the
2260 if (Ops.size() == 2) {
2261 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
2262 SmallVector<const SCEV *, 4> NewOps;
2263 bool AnyFolded = false;
2264 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(),
2265 E = Add->op_end(); I != E; ++I) {
2266 const SCEV *Mul = getMulExpr(Ops[0], *I);
2267 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
2268 NewOps.push_back(Mul);
2271 return getAddExpr(NewOps);
2273 else if (const SCEVAddRecExpr *
2274 AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) {
2275 // Negation preserves a recurrence's no self-wrap property.
2276 SmallVector<const SCEV *, 4> Operands;
2277 for (SCEVAddRecExpr::op_iterator I = AddRec->op_begin(),
2278 E = AddRec->op_end(); I != E; ++I) {
2279 Operands.push_back(getMulExpr(Ops[0], *I));
2281 return getAddRecExpr(Operands, AddRec->getLoop(),
2282 AddRec->getNoWrapFlags(SCEV::FlagNW));
2287 if (Ops.size() == 1)
2291 // Skip over the add expression until we get to a multiply.
2292 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
2295 // If there are mul operands inline them all into this expression.
2296 if (Idx < Ops.size()) {
2297 bool DeletedMul = false;
2298 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
2299 // If we have an mul, expand the mul operands onto the end of the operands
2301 Ops.erase(Ops.begin()+Idx);
2302 Ops.append(Mul->op_begin(), Mul->op_end());
2306 // If we deleted at least one mul, we added operands to the end of the list,
2307 // and they are not necessarily sorted. Recurse to resort and resimplify
2308 // any operands we just acquired.
2310 return getMulExpr(Ops);
2313 // If there are any add recurrences in the operands list, see if any other
2314 // added values are loop invariant. If so, we can fold them into the
2316 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2319 // Scan over all recurrences, trying to fold loop invariants into them.
2320 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
2321 // Scan all of the other operands to this mul and add them to the vector if
2322 // they are loop invariant w.r.t. the recurrence.
2323 SmallVector<const SCEV *, 8> LIOps;
2324 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2325 const Loop *AddRecLoop = AddRec->getLoop();
2326 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2327 if (isLoopInvariant(Ops[i], AddRecLoop)) {
2328 LIOps.push_back(Ops[i]);
2329 Ops.erase(Ops.begin()+i);
2333 // If we found some loop invariants, fold them into the recurrence.
2334 if (!LIOps.empty()) {
2335 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
2336 SmallVector<const SCEV *, 4> NewOps;
2337 NewOps.reserve(AddRec->getNumOperands());
2338 const SCEV *Scale = getMulExpr(LIOps);
2339 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
2340 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
2342 // Build the new addrec. Propagate the NUW and NSW flags if both the
2343 // outer mul and the inner addrec are guaranteed to have no overflow.
2345 // No self-wrap cannot be guaranteed after changing the step size, but
2346 // will be inferred if either NUW or NSW is true.
2347 Flags = AddRec->getNoWrapFlags(clearFlags(Flags, SCEV::FlagNW));
2348 const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, Flags);
2350 // If all of the other operands were loop invariant, we are done.
2351 if (Ops.size() == 1) return NewRec;
2353 // Otherwise, multiply the folded AddRec by the non-invariant parts.
2354 for (unsigned i = 0;; ++i)
2355 if (Ops[i] == AddRec) {
2359 return getMulExpr(Ops);
2362 // Okay, if there weren't any loop invariants to be folded, check to see if
2363 // there are multiple AddRec's with the same loop induction variable being
2364 // multiplied together. If so, we can fold them.
2366 // {A1,+,A2,+,...,+,An}<L> * {B1,+,B2,+,...,+,Bn}<L>
2367 // = {x=1 in [ sum y=x..2x [ sum z=max(y-x, y-n)..min(x,n) [
2368 // choose(x, 2x)*choose(2x-y, x-z)*A_{y-z}*B_z
2369 // ]]],+,...up to x=2n}.
2370 // Note that the arguments to choose() are always integers with values
2371 // known at compile time, never SCEV objects.
2373 // The implementation avoids pointless extra computations when the two
2374 // addrec's are of different length (mathematically, it's equivalent to
2375 // an infinite stream of zeros on the right).
2376 bool OpsModified = false;
2377 for (unsigned OtherIdx = Idx+1;
2378 OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2380 const SCEVAddRecExpr *OtherAddRec =
2381 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]);
2382 if (!OtherAddRec || OtherAddRec->getLoop() != AddRecLoop)
2385 bool Overflow = false;
2386 Type *Ty = AddRec->getType();
2387 bool LargerThan64Bits = getTypeSizeInBits(Ty) > 64;
2388 SmallVector<const SCEV*, 7> AddRecOps;
2389 for (int x = 0, xe = AddRec->getNumOperands() +
2390 OtherAddRec->getNumOperands() - 1; x != xe && !Overflow; ++x) {
2391 const SCEV *Term = getConstant(Ty, 0);
2392 for (int y = x, ye = 2*x+1; y != ye && !Overflow; ++y) {
2393 uint64_t Coeff1 = Choose(x, 2*x - y, Overflow);
2394 for (int z = std::max(y-x, y-(int)AddRec->getNumOperands()+1),
2395 ze = std::min(x+1, (int)OtherAddRec->getNumOperands());
2396 z < ze && !Overflow; ++z) {
2397 uint64_t Coeff2 = Choose(2*x - y, x-z, Overflow);
2399 if (LargerThan64Bits)
2400 Coeff = umul_ov(Coeff1, Coeff2, Overflow);
2402 Coeff = Coeff1*Coeff2;
2403 const SCEV *CoeffTerm = getConstant(Ty, Coeff);
2404 const SCEV *Term1 = AddRec->getOperand(y-z);
2405 const SCEV *Term2 = OtherAddRec->getOperand(z);
2406 Term = getAddExpr(Term, getMulExpr(CoeffTerm, Term1,Term2));
2409 AddRecOps.push_back(Term);
2412 const SCEV *NewAddRec = getAddRecExpr(AddRecOps, AddRec->getLoop(),
2414 if (Ops.size() == 2) return NewAddRec;
2415 Ops[Idx] = NewAddRec;
2416 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2418 AddRec = dyn_cast<SCEVAddRecExpr>(NewAddRec);
2424 return getMulExpr(Ops);
2426 // Otherwise couldn't fold anything into this recurrence. Move onto the
2430 // Okay, it looks like we really DO need an mul expr. Check to see if we
2431 // already have one, otherwise create a new one.
2432 FoldingSetNodeID ID;
2433 ID.AddInteger(scMulExpr);
2434 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2435 ID.AddPointer(Ops[i]);
2438 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2440 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2441 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2442 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
2444 UniqueSCEVs.InsertNode(S, IP);
2446 S->setNoWrapFlags(Flags);
2450 /// getUDivExpr - Get a canonical unsigned division expression, or something
2451 /// simpler if possible.
2452 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
2454 assert(getEffectiveSCEVType(LHS->getType()) ==
2455 getEffectiveSCEVType(RHS->getType()) &&
2456 "SCEVUDivExpr operand types don't match!");
2458 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
2459 if (RHSC->getValue()->equalsInt(1))
2460 return LHS; // X udiv 1 --> x
2461 // If the denominator is zero, the result of the udiv is undefined. Don't
2462 // try to analyze it, because the resolution chosen here may differ from
2463 // the resolution chosen in other parts of the compiler.
2464 if (!RHSC->getValue()->isZero()) {
2465 // Determine if the division can be folded into the operands of
2467 // TODO: Generalize this to non-constants by using known-bits information.
2468 Type *Ty = LHS->getType();
2469 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
2470 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1;
2471 // For non-power-of-two values, effectively round the value up to the
2472 // nearest power of two.
2473 if (!RHSC->getValue()->getValue().isPowerOf2())
2475 IntegerType *ExtTy =
2476 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
2477 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
2478 if (const SCEVConstant *Step =
2479 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) {
2480 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
2481 const APInt &StepInt = Step->getValue()->getValue();
2482 const APInt &DivInt = RHSC->getValue()->getValue();
2483 if (!StepInt.urem(DivInt) &&
2484 getZeroExtendExpr(AR, ExtTy) ==
2485 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2486 getZeroExtendExpr(Step, ExtTy),
2487 AR->getLoop(), SCEV::FlagAnyWrap)) {
2488 SmallVector<const SCEV *, 4> Operands;
2489 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i)
2490 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS));
2491 return getAddRecExpr(Operands, AR->getLoop(),
2494 /// Get a canonical UDivExpr for a recurrence.
2495 /// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0.
2496 // We can currently only fold X%N if X is constant.
2497 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(AR->getStart());
2498 if (StartC && !DivInt.urem(StepInt) &&
2499 getZeroExtendExpr(AR, ExtTy) ==
2500 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2501 getZeroExtendExpr(Step, ExtTy),
2502 AR->getLoop(), SCEV::FlagAnyWrap)) {
2503 const APInt &StartInt = StartC->getValue()->getValue();
2504 const APInt &StartRem = StartInt.urem(StepInt);
2506 LHS = getAddRecExpr(getConstant(StartInt - StartRem), Step,
2507 AR->getLoop(), SCEV::FlagNW);
2510 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
2511 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
2512 SmallVector<const SCEV *, 4> Operands;
2513 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i)
2514 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy));
2515 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
2516 // Find an operand that's safely divisible.
2517 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
2518 const SCEV *Op = M->getOperand(i);
2519 const SCEV *Div = getUDivExpr(Op, RHSC);
2520 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
2521 Operands = SmallVector<const SCEV *, 4>(M->op_begin(),
2524 return getMulExpr(Operands);
2528 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
2529 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) {
2530 SmallVector<const SCEV *, 4> Operands;
2531 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i)
2532 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy));
2533 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
2535 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
2536 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
2537 if (isa<SCEVUDivExpr>(Op) ||
2538 getMulExpr(Op, RHS) != A->getOperand(i))
2540 Operands.push_back(Op);
2542 if (Operands.size() == A->getNumOperands())
2543 return getAddExpr(Operands);
2547 // Fold if both operands are constant.
2548 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
2549 Constant *LHSCV = LHSC->getValue();
2550 Constant *RHSCV = RHSC->getValue();
2551 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
2557 FoldingSetNodeID ID;
2558 ID.AddInteger(scUDivExpr);
2562 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2563 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
2565 UniqueSCEVs.InsertNode(S, IP);
2569 static const APInt gcd(const SCEVConstant *C1, const SCEVConstant *C2) {
2570 APInt A = C1->getValue()->getValue().abs();
2571 APInt B = C2->getValue()->getValue().abs();
2572 uint32_t ABW = A.getBitWidth();
2573 uint32_t BBW = B.getBitWidth();
2580 return APIntOps::GreatestCommonDivisor(A, B);
2583 /// getUDivExactExpr - Get a canonical unsigned division expression, or
2584 /// something simpler if possible. There is no representation for an exact udiv
2585 /// in SCEV IR, but we can attempt to remove factors from the LHS and RHS.
2586 /// We can't do this when it's not exact because the udiv may be clearing bits.
2587 const SCEV *ScalarEvolution::getUDivExactExpr(const SCEV *LHS,
2589 // TODO: we could try to find factors in all sorts of things, but for now we
2590 // just deal with u/exact (multiply, constant). See SCEVDivision towards the
2591 // end of this file for inspiration.
2593 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(LHS);
2595 return getUDivExpr(LHS, RHS);
2597 if (const SCEVConstant *RHSCst = dyn_cast<SCEVConstant>(RHS)) {
2598 // If the mulexpr multiplies by a constant, then that constant must be the
2599 // first element of the mulexpr.
2600 if (const SCEVConstant *LHSCst =
2601 dyn_cast<SCEVConstant>(Mul->getOperand(0))) {
2602 if (LHSCst == RHSCst) {
2603 SmallVector<const SCEV *, 2> Operands;
2604 Operands.append(Mul->op_begin() + 1, Mul->op_end());
2605 return getMulExpr(Operands);
2608 // We can't just assume that LHSCst divides RHSCst cleanly, it could be
2609 // that there's a factor provided by one of the other terms. We need to
2611 APInt Factor = gcd(LHSCst, RHSCst);
2612 if (!Factor.isIntN(1)) {
2613 LHSCst = cast<SCEVConstant>(
2614 getConstant(LHSCst->getValue()->getValue().udiv(Factor)));
2615 RHSCst = cast<SCEVConstant>(
2616 getConstant(RHSCst->getValue()->getValue().udiv(Factor)));
2617 SmallVector<const SCEV *, 2> Operands;
2618 Operands.push_back(LHSCst);
2619 Operands.append(Mul->op_begin() + 1, Mul->op_end());
2620 LHS = getMulExpr(Operands);
2622 Mul = dyn_cast<SCEVMulExpr>(LHS);
2624 return getUDivExactExpr(LHS, RHS);
2629 for (int i = 0, e = Mul->getNumOperands(); i != e; ++i) {
2630 if (Mul->getOperand(i) == RHS) {
2631 SmallVector<const SCEV *, 2> Operands;
2632 Operands.append(Mul->op_begin(), Mul->op_begin() + i);
2633 Operands.append(Mul->op_begin() + i + 1, Mul->op_end());
2634 return getMulExpr(Operands);
2638 return getUDivExpr(LHS, RHS);
2641 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2642 /// Simplify the expression as much as possible.
2643 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step,
2645 SCEV::NoWrapFlags Flags) {
2646 SmallVector<const SCEV *, 4> Operands;
2647 Operands.push_back(Start);
2648 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
2649 if (StepChrec->getLoop() == L) {
2650 Operands.append(StepChrec->op_begin(), StepChrec->op_end());
2651 return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW));
2654 Operands.push_back(Step);
2655 return getAddRecExpr(Operands, L, Flags);
2658 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2659 /// Simplify the expression as much as possible.
2661 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
2662 const Loop *L, SCEV::NoWrapFlags Flags) {
2663 if (Operands.size() == 1) return Operands[0];
2665 Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
2666 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
2667 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy &&
2668 "SCEVAddRecExpr operand types don't match!");
2669 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2670 assert(isLoopInvariant(Operands[i], L) &&
2671 "SCEVAddRecExpr operand is not loop-invariant!");
2674 if (Operands.back()->isZero()) {
2675 Operands.pop_back();
2676 return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0} --> X
2679 // It's tempting to want to call getMaxBackedgeTakenCount count here and
2680 // use that information to infer NUW and NSW flags. However, computing a
2681 // BE count requires calling getAddRecExpr, so we may not yet have a
2682 // meaningful BE count at this point (and if we don't, we'd be stuck
2683 // with a SCEVCouldNotCompute as the cached BE count).
2685 Flags = StrengthenNoWrapFlags(this, scAddRecExpr, Operands, Flags);
2687 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
2688 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
2689 const Loop *NestedLoop = NestedAR->getLoop();
2690 if (L->contains(NestedLoop) ?
2691 (L->getLoopDepth() < NestedLoop->getLoopDepth()) :
2692 (!NestedLoop->contains(L) &&
2693 DT->dominates(L->getHeader(), NestedLoop->getHeader()))) {
2694 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
2695 NestedAR->op_end());
2696 Operands[0] = NestedAR->getStart();
2697 // AddRecs require their operands be loop-invariant with respect to their
2698 // loops. Don't perform this transformation if it would break this
2700 bool AllInvariant = true;
2701 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2702 if (!isLoopInvariant(Operands[i], L)) {
2703 AllInvariant = false;
2707 // Create a recurrence for the outer loop with the same step size.
2709 // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the
2710 // inner recurrence has the same property.
2711 SCEV::NoWrapFlags OuterFlags =
2712 maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags());
2714 NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags);
2715 AllInvariant = true;
2716 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i)
2717 if (!isLoopInvariant(NestedOperands[i], NestedLoop)) {
2718 AllInvariant = false;
2722 // Ok, both add recurrences are valid after the transformation.
2724 // The inner recurrence keeps its NW flag but only keeps NUW/NSW if
2725 // the outer recurrence has the same property.
2726 SCEV::NoWrapFlags InnerFlags =
2727 maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags);
2728 return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags);
2731 // Reset Operands to its original state.
2732 Operands[0] = NestedAR;
2736 // Okay, it looks like we really DO need an addrec expr. Check to see if we
2737 // already have one, otherwise create a new one.
2738 FoldingSetNodeID ID;
2739 ID.AddInteger(scAddRecExpr);
2740 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2741 ID.AddPointer(Operands[i]);
2745 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2747 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size());
2748 std::uninitialized_copy(Operands.begin(), Operands.end(), O);
2749 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator),
2750 O, Operands.size(), L);
2751 UniqueSCEVs.InsertNode(S, IP);
2753 S->setNoWrapFlags(Flags);
2757 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
2759 SmallVector<const SCEV *, 2> Ops;
2762 return getSMaxExpr(Ops);
2766 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2767 assert(!Ops.empty() && "Cannot get empty smax!");
2768 if (Ops.size() == 1) return Ops[0];
2770 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2771 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2772 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2773 "SCEVSMaxExpr operand types don't match!");
2776 // Sort by complexity, this groups all similar expression types together.
2777 GroupByComplexity(Ops, LI);
2779 // If there are any constants, fold them together.
2781 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2783 assert(Idx < Ops.size());
2784 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2785 // We found two constants, fold them together!
2786 ConstantInt *Fold = ConstantInt::get(getContext(),
2787 APIntOps::smax(LHSC->getValue()->getValue(),
2788 RHSC->getValue()->getValue()));
2789 Ops[0] = getConstant(Fold);
2790 Ops.erase(Ops.begin()+1); // Erase the folded element
2791 if (Ops.size() == 1) return Ops[0];
2792 LHSC = cast<SCEVConstant>(Ops[0]);
2795 // If we are left with a constant minimum-int, strip it off.
2796 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
2797 Ops.erase(Ops.begin());
2799 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
2800 // If we have an smax with a constant maximum-int, it will always be
2805 if (Ops.size() == 1) return Ops[0];
2808 // Find the first SMax
2809 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
2812 // Check to see if one of the operands is an SMax. If so, expand its operands
2813 // onto our operand list, and recurse to simplify.
2814 if (Idx < Ops.size()) {
2815 bool DeletedSMax = false;
2816 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
2817 Ops.erase(Ops.begin()+Idx);
2818 Ops.append(SMax->op_begin(), SMax->op_end());
2823 return getSMaxExpr(Ops);
2826 // Okay, check to see if the same value occurs in the operand list twice. If
2827 // so, delete one. Since we sorted the list, these values are required to
2829 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2830 // X smax Y smax Y --> X smax Y
2831 // X smax Y --> X, if X is always greater than Y
2832 if (Ops[i] == Ops[i+1] ||
2833 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) {
2834 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2836 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) {
2837 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2841 if (Ops.size() == 1) return Ops[0];
2843 assert(!Ops.empty() && "Reduced smax down to nothing!");
2845 // Okay, it looks like we really DO need an smax expr. Check to see if we
2846 // already have one, otherwise create a new one.
2847 FoldingSetNodeID ID;
2848 ID.AddInteger(scSMaxExpr);
2849 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2850 ID.AddPointer(Ops[i]);
2852 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2853 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2854 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2855 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator),
2857 UniqueSCEVs.InsertNode(S, IP);
2861 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
2863 SmallVector<const SCEV *, 2> Ops;
2866 return getUMaxExpr(Ops);
2870 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2871 assert(!Ops.empty() && "Cannot get empty umax!");
2872 if (Ops.size() == 1) return Ops[0];
2874 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2875 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2876 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2877 "SCEVUMaxExpr operand types don't match!");
2880 // Sort by complexity, this groups all similar expression types together.
2881 GroupByComplexity(Ops, LI);
2883 // If there are any constants, fold them together.
2885 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2887 assert(Idx < Ops.size());
2888 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2889 // We found two constants, fold them together!
2890 ConstantInt *Fold = ConstantInt::get(getContext(),
2891 APIntOps::umax(LHSC->getValue()->getValue(),
2892 RHSC->getValue()->getValue()));
2893 Ops[0] = getConstant(Fold);
2894 Ops.erase(Ops.begin()+1); // Erase the folded element
2895 if (Ops.size() == 1) return Ops[0];
2896 LHSC = cast<SCEVConstant>(Ops[0]);
2899 // If we are left with a constant minimum-int, strip it off.
2900 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
2901 Ops.erase(Ops.begin());
2903 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
2904 // If we have an umax with a constant maximum-int, it will always be
2909 if (Ops.size() == 1) return Ops[0];
2912 // Find the first UMax
2913 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
2916 // Check to see if one of the operands is a UMax. If so, expand its operands
2917 // onto our operand list, and recurse to simplify.
2918 if (Idx < Ops.size()) {
2919 bool DeletedUMax = false;
2920 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
2921 Ops.erase(Ops.begin()+Idx);
2922 Ops.append(UMax->op_begin(), UMax->op_end());
2927 return getUMaxExpr(Ops);
2930 // Okay, check to see if the same value occurs in the operand list twice. If
2931 // so, delete one. Since we sorted the list, these values are required to
2933 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2934 // X umax Y umax Y --> X umax Y
2935 // X umax Y --> X, if X is always greater than Y
2936 if (Ops[i] == Ops[i+1] ||
2937 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) {
2938 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2940 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) {
2941 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2945 if (Ops.size() == 1) return Ops[0];
2947 assert(!Ops.empty() && "Reduced umax down to nothing!");
2949 // Okay, it looks like we really DO need a umax expr. Check to see if we
2950 // already have one, otherwise create a new one.
2951 FoldingSetNodeID ID;
2952 ID.AddInteger(scUMaxExpr);
2953 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2954 ID.AddPointer(Ops[i]);
2956 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2957 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2958 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2959 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator),
2961 UniqueSCEVs.InsertNode(S, IP);
2965 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
2967 // ~smax(~x, ~y) == smin(x, y).
2968 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2971 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
2973 // ~umax(~x, ~y) == umin(x, y)
2974 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2977 const SCEV *ScalarEvolution::getSizeOfExpr(Type *IntTy, Type *AllocTy) {
2978 // If we have DataLayout, we can bypass creating a target-independent
2979 // constant expression and then folding it back into a ConstantInt.
2980 // This is just a compile-time optimization.
2982 return getConstant(IntTy, DL->getTypeAllocSize(AllocTy));
2984 Constant *C = ConstantExpr::getSizeOf(AllocTy);
2985 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2986 if (Constant *Folded = ConstantFoldConstantExpression(CE, DL, TLI))
2988 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2989 assert(Ty == IntTy && "Effective SCEV type doesn't match");
2990 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2993 const SCEV *ScalarEvolution::getOffsetOfExpr(Type *IntTy,
2996 // If we have DataLayout, we can bypass creating a target-independent
2997 // constant expression and then folding it back into a ConstantInt.
2998 // This is just a compile-time optimization.
3000 return getConstant(IntTy,
3001 DL->getStructLayout(STy)->getElementOffset(FieldNo));
3004 Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo);
3005 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
3006 if (Constant *Folded = ConstantFoldConstantExpression(CE, DL, TLI))
3009 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy));
3010 return getTruncateOrZeroExtend(getSCEV(C), Ty);
3013 const SCEV *ScalarEvolution::getUnknown(Value *V) {
3014 // Don't attempt to do anything other than create a SCEVUnknown object
3015 // here. createSCEV only calls getUnknown after checking for all other
3016 // interesting possibilities, and any other code that calls getUnknown
3017 // is doing so in order to hide a value from SCEV canonicalization.
3019 FoldingSetNodeID ID;
3020 ID.AddInteger(scUnknown);
3023 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
3024 assert(cast<SCEVUnknown>(S)->getValue() == V &&
3025 "Stale SCEVUnknown in uniquing map!");
3028 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
3030 FirstUnknown = cast<SCEVUnknown>(S);
3031 UniqueSCEVs.InsertNode(S, IP);
3035 //===----------------------------------------------------------------------===//
3036 // Basic SCEV Analysis and PHI Idiom Recognition Code
3039 /// isSCEVable - Test if values of the given type are analyzable within
3040 /// the SCEV framework. This primarily includes integer types, and it
3041 /// can optionally include pointer types if the ScalarEvolution class
3042 /// has access to target-specific information.
3043 bool ScalarEvolution::isSCEVable(Type *Ty) const {
3044 // Integers and pointers are always SCEVable.
3045 return Ty->isIntegerTy() || Ty->isPointerTy();
3048 /// getTypeSizeInBits - Return the size in bits of the specified type,
3049 /// for which isSCEVable must return true.
3050 uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const {
3051 assert(isSCEVable(Ty) && "Type is not SCEVable!");
3053 // If we have a DataLayout, use it!
3055 return DL->getTypeSizeInBits(Ty);
3057 // Integer types have fixed sizes.
3058 if (Ty->isIntegerTy())
3059 return Ty->getPrimitiveSizeInBits();
3061 // The only other support type is pointer. Without DataLayout, conservatively
3062 // assume pointers are 64-bit.
3063 assert(Ty->isPointerTy() && "isSCEVable permitted a non-SCEVable type!");
3067 /// getEffectiveSCEVType - Return a type with the same bitwidth as
3068 /// the given type and which represents how SCEV will treat the given
3069 /// type, for which isSCEVable must return true. For pointer types,
3070 /// this is the pointer-sized integer type.
3071 Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const {
3072 assert(isSCEVable(Ty) && "Type is not SCEVable!");
3074 if (Ty->isIntegerTy()) {
3078 // The only other support type is pointer.
3079 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
3082 return DL->getIntPtrType(Ty);
3084 // Without DataLayout, conservatively assume pointers are 64-bit.
3085 return Type::getInt64Ty(getContext());
3088 const SCEV *ScalarEvolution::getCouldNotCompute() {
3089 return &CouldNotCompute;
3093 // Helper class working with SCEVTraversal to figure out if a SCEV contains
3094 // a SCEVUnknown with null value-pointer. FindInvalidSCEVUnknown::FindOne
3095 // is set iff if find such SCEVUnknown.
3097 struct FindInvalidSCEVUnknown {
3099 FindInvalidSCEVUnknown() { FindOne = false; }
3100 bool follow(const SCEV *S) {
3101 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
3105 if (!cast<SCEVUnknown>(S)->getValue())
3112 bool isDone() const { return FindOne; }
3116 bool ScalarEvolution::checkValidity(const SCEV *S) const {
3117 FindInvalidSCEVUnknown F;
3118 SCEVTraversal<FindInvalidSCEVUnknown> ST(F);
3124 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
3125 /// expression and create a new one.
3126 const SCEV *ScalarEvolution::getSCEV(Value *V) {
3127 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
3129 ValueExprMapType::iterator I = ValueExprMap.find_as(V);
3130 if (I != ValueExprMap.end()) {
3131 const SCEV *S = I->second;
3132 if (checkValidity(S))
3135 ValueExprMap.erase(I);
3137 const SCEV *S = createSCEV(V);
3139 // The process of creating a SCEV for V may have caused other SCEVs
3140 // to have been created, so it's necessary to insert the new entry
3141 // from scratch, rather than trying to remember the insert position
3143 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(V, this), S));
3147 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
3149 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) {
3150 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
3152 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
3154 Type *Ty = V->getType();
3155 Ty = getEffectiveSCEVType(Ty);
3156 return getMulExpr(V,
3157 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))));
3160 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
3161 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
3162 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
3164 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
3166 Type *Ty = V->getType();
3167 Ty = getEffectiveSCEVType(Ty);
3168 const SCEV *AllOnes =
3169 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
3170 return getMinusSCEV(AllOnes, V);
3173 /// getMinusSCEV - Return LHS-RHS. Minus is represented in SCEV as A+B*-1.
3174 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
3175 SCEV::NoWrapFlags Flags) {
3176 assert(!maskFlags(Flags, SCEV::FlagNUW) && "subtraction does not have NUW");
3178 // Fast path: X - X --> 0.
3180 return getConstant(LHS->getType(), 0);
3182 // X - Y --> X + -Y.
3183 // X -(nsw || nuw) Y --> X + -Y.
3184 return getAddExpr(LHS, getNegativeSCEV(RHS));
3187 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
3188 /// input value to the specified type. If the type must be extended, it is zero
3191 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty) {
3192 Type *SrcTy = V->getType();
3193 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3194 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3195 "Cannot truncate or zero extend with non-integer arguments!");
3196 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3197 return V; // No conversion
3198 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
3199 return getTruncateExpr(V, Ty);
3200 return getZeroExtendExpr(V, Ty);
3203 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
3204 /// input value to the specified type. If the type must be extended, it is sign
3207 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
3209 Type *SrcTy = V->getType();
3210 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3211 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3212 "Cannot truncate or zero extend with non-integer arguments!");
3213 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3214 return V; // No conversion
3215 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
3216 return getTruncateExpr(V, Ty);
3217 return getSignExtendExpr(V, Ty);
3220 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
3221 /// input value to the specified type. If the type must be extended, it is zero
3222 /// extended. The conversion must not be narrowing.
3224 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) {
3225 Type *SrcTy = V->getType();
3226 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3227 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3228 "Cannot noop or zero extend with non-integer arguments!");
3229 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3230 "getNoopOrZeroExtend cannot truncate!");
3231 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3232 return V; // No conversion
3233 return getZeroExtendExpr(V, Ty);
3236 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
3237 /// input value to the specified type. If the type must be extended, it is sign
3238 /// extended. The conversion must not be narrowing.
3240 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) {
3241 Type *SrcTy = V->getType();
3242 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3243 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3244 "Cannot noop or sign extend with non-integer arguments!");
3245 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3246 "getNoopOrSignExtend cannot truncate!");
3247 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3248 return V; // No conversion
3249 return getSignExtendExpr(V, Ty);
3252 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
3253 /// the input value to the specified type. If the type must be extended,
3254 /// it is extended with unspecified bits. The conversion must not be
3257 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) {
3258 Type *SrcTy = V->getType();
3259 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3260 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3261 "Cannot noop or any extend with non-integer arguments!");
3262 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3263 "getNoopOrAnyExtend cannot truncate!");
3264 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3265 return V; // No conversion
3266 return getAnyExtendExpr(V, Ty);
3269 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
3270 /// input value to the specified type. The conversion must not be widening.
3272 ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) {
3273 Type *SrcTy = V->getType();
3274 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3275 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3276 "Cannot truncate or noop with non-integer arguments!");
3277 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
3278 "getTruncateOrNoop cannot extend!");
3279 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3280 return V; // No conversion
3281 return getTruncateExpr(V, Ty);
3284 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
3285 /// the types using zero-extension, and then perform a umax operation
3287 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
3289 const SCEV *PromotedLHS = LHS;
3290 const SCEV *PromotedRHS = RHS;
3292 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
3293 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
3295 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
3297 return getUMaxExpr(PromotedLHS, PromotedRHS);
3300 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
3301 /// the types using zero-extension, and then perform a umin operation
3303 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
3305 const SCEV *PromotedLHS = LHS;
3306 const SCEV *PromotedRHS = RHS;
3308 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
3309 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
3311 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
3313 return getUMinExpr(PromotedLHS, PromotedRHS);
3316 /// getPointerBase - Transitively follow the chain of pointer-type operands
3317 /// until reaching a SCEV that does not have a single pointer operand. This
3318 /// returns a SCEVUnknown pointer for well-formed pointer-type expressions,
3319 /// but corner cases do exist.
3320 const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) {
3321 // A pointer operand may evaluate to a nonpointer expression, such as null.
3322 if (!V->getType()->isPointerTy())
3325 if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) {
3326 return getPointerBase(Cast->getOperand());
3328 else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) {
3329 const SCEV *PtrOp = nullptr;
3330 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
3332 if ((*I)->getType()->isPointerTy()) {
3333 // Cannot find the base of an expression with multiple pointer operands.
3341 return getPointerBase(PtrOp);
3346 /// PushDefUseChildren - Push users of the given Instruction
3347 /// onto the given Worklist.
3349 PushDefUseChildren(Instruction *I,
3350 SmallVectorImpl<Instruction *> &Worklist) {
3351 // Push the def-use children onto the Worklist stack.
3352 for (User *U : I->users())
3353 Worklist.push_back(cast<Instruction>(U));
3356 /// ForgetSymbolicValue - This looks up computed SCEV values for all
3357 /// instructions that depend on the given instruction and removes them from
3358 /// the ValueExprMapType map if they reference SymName. This is used during PHI
3361 ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) {
3362 SmallVector<Instruction *, 16> Worklist;
3363 PushDefUseChildren(PN, Worklist);
3365 SmallPtrSet<Instruction *, 8> Visited;
3367 while (!Worklist.empty()) {
3368 Instruction *I = Worklist.pop_back_val();
3369 if (!Visited.insert(I).second)
3372 ValueExprMapType::iterator It =
3373 ValueExprMap.find_as(static_cast<Value *>(I));
3374 if (It != ValueExprMap.end()) {
3375 const SCEV *Old = It->second;
3377 // Short-circuit the def-use traversal if the symbolic name
3378 // ceases to appear in expressions.
3379 if (Old != SymName && !hasOperand(Old, SymName))
3382 // SCEVUnknown for a PHI either means that it has an unrecognized
3383 // structure, it's a PHI that's in the progress of being computed
3384 // by createNodeForPHI, or it's a single-value PHI. In the first case,
3385 // additional loop trip count information isn't going to change anything.
3386 // In the second case, createNodeForPHI will perform the necessary
3387 // updates on its own when it gets to that point. In the third, we do
3388 // want to forget the SCEVUnknown.
3389 if (!isa<PHINode>(I) ||
3390 !isa<SCEVUnknown>(Old) ||
3391 (I != PN && Old == SymName)) {
3392 forgetMemoizedResults(Old);
3393 ValueExprMap.erase(It);
3397 PushDefUseChildren(I, Worklist);
3401 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
3402 /// a loop header, making it a potential recurrence, or it doesn't.
3404 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
3405 if (const Loop *L = LI->getLoopFor(PN->getParent()))
3406 if (L->getHeader() == PN->getParent()) {
3407 // The loop may have multiple entrances or multiple exits; we can analyze
3408 // this phi as an addrec if it has a unique entry value and a unique
3410 Value *BEValueV = nullptr, *StartValueV = nullptr;
3411 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
3412 Value *V = PN->getIncomingValue(i);
3413 if (L->contains(PN->getIncomingBlock(i))) {
3416 } else if (BEValueV != V) {
3420 } else if (!StartValueV) {
3422 } else if (StartValueV != V) {
3423 StartValueV = nullptr;
3427 if (BEValueV && StartValueV) {
3428 // While we are analyzing this PHI node, handle its value symbolically.
3429 const SCEV *SymbolicName = getUnknown(PN);
3430 assert(ValueExprMap.find_as(PN) == ValueExprMap.end() &&
3431 "PHI node already processed?");
3432 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
3434 // Using this symbolic name for the PHI, analyze the value coming around
3436 const SCEV *BEValue = getSCEV(BEValueV);
3438 // NOTE: If BEValue is loop invariant, we know that the PHI node just
3439 // has a special value for the first iteration of the loop.
3441 // If the value coming around the backedge is an add with the symbolic
3442 // value we just inserted, then we found a simple induction variable!
3443 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
3444 // If there is a single occurrence of the symbolic value, replace it
3445 // with a recurrence.
3446 unsigned FoundIndex = Add->getNumOperands();
3447 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3448 if (Add->getOperand(i) == SymbolicName)
3449 if (FoundIndex == e) {
3454 if (FoundIndex != Add->getNumOperands()) {
3455 // Create an add with everything but the specified operand.
3456 SmallVector<const SCEV *, 8> Ops;
3457 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3458 if (i != FoundIndex)
3459 Ops.push_back(Add->getOperand(i));
3460 const SCEV *Accum = getAddExpr(Ops);
3462 // This is not a valid addrec if the step amount is varying each
3463 // loop iteration, but is not itself an addrec in this loop.
3464 if (isLoopInvariant(Accum, L) ||
3465 (isa<SCEVAddRecExpr>(Accum) &&
3466 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
3467 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
3469 // If the increment doesn't overflow, then neither the addrec nor
3470 // the post-increment will overflow.
3471 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) {
3472 if (OBO->hasNoUnsignedWrap())
3473 Flags = setFlags(Flags, SCEV::FlagNUW);
3474 if (OBO->hasNoSignedWrap())
3475 Flags = setFlags(Flags, SCEV::FlagNSW);
3476 } else if (GEPOperator *GEP = dyn_cast<GEPOperator>(BEValueV)) {
3477 // If the increment is an inbounds GEP, then we know the address
3478 // space cannot be wrapped around. We cannot make any guarantee
3479 // about signed or unsigned overflow because pointers are
3480 // unsigned but we may have a negative index from the base
3481 // pointer. We can guarantee that no unsigned wrap occurs if the
3482 // indices form a positive value.
3483 if (GEP->isInBounds()) {
3484 Flags = setFlags(Flags, SCEV::FlagNW);
3486 const SCEV *Ptr = getSCEV(GEP->getPointerOperand());
3487 if (isKnownPositive(getMinusSCEV(getSCEV(GEP), Ptr)))
3488 Flags = setFlags(Flags, SCEV::FlagNUW);
3491 // We cannot transfer nuw and nsw flags from subtraction
3492 // operations -- sub nuw X, Y is not the same as add nuw X, -Y
3496 const SCEV *StartVal = getSCEV(StartValueV);
3497 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
3499 // Since the no-wrap flags are on the increment, they apply to the
3500 // post-incremented value as well.
3501 if (isLoopInvariant(Accum, L))
3502 (void)getAddRecExpr(getAddExpr(StartVal, Accum),
3505 // Okay, for the entire analysis of this edge we assumed the PHI
3506 // to be symbolic. We now need to go back and purge all of the
3507 // entries for the scalars that use the symbolic expression.
3508 ForgetSymbolicName(PN, SymbolicName);
3509 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3513 } else if (const SCEVAddRecExpr *AddRec =
3514 dyn_cast<SCEVAddRecExpr>(BEValue)) {
3515 // Otherwise, this could be a loop like this:
3516 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
3517 // In this case, j = {1,+,1} and BEValue is j.
3518 // Because the other in-value of i (0) fits the evolution of BEValue
3519 // i really is an addrec evolution.
3520 if (AddRec->getLoop() == L && AddRec->isAffine()) {
3521 const SCEV *StartVal = getSCEV(StartValueV);
3523 // If StartVal = j.start - j.stride, we can use StartVal as the
3524 // initial step of the addrec evolution.
3525 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
3526 AddRec->getOperand(1))) {
3527 // FIXME: For constant StartVal, we should be able to infer
3529 const SCEV *PHISCEV =
3530 getAddRecExpr(StartVal, AddRec->getOperand(1), L,
3533 // Okay, for the entire analysis of this edge we assumed the PHI
3534 // to be symbolic. We now need to go back and purge all of the
3535 // entries for the scalars that use the symbolic expression.
3536 ForgetSymbolicName(PN, SymbolicName);
3537 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3545 // If the PHI has a single incoming value, follow that value, unless the
3546 // PHI's incoming blocks are in a different loop, in which case doing so
3547 // risks breaking LCSSA form. Instcombine would normally zap these, but
3548 // it doesn't have DominatorTree information, so it may miss cases.
3549 if (Value *V = SimplifyInstruction(PN, DL, TLI, DT, AC))
3550 if (LI->replacementPreservesLCSSAForm(PN, V))
3553 // If it's not a loop phi, we can't handle it yet.
3554 return getUnknown(PN);
3557 /// createNodeForGEP - Expand GEP instructions into add and multiply
3558 /// operations. This allows them to be analyzed by regular SCEV code.
3560 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
3561 Type *IntPtrTy = getEffectiveSCEVType(GEP->getType());
3562 Value *Base = GEP->getOperand(0);
3563 // Don't attempt to analyze GEPs over unsized objects.
3564 if (!Base->getType()->getPointerElementType()->isSized())
3565 return getUnknown(GEP);
3567 // Don't blindly transfer the inbounds flag from the GEP instruction to the
3568 // Add expression, because the Instruction may be guarded by control flow
3569 // and the no-overflow bits may not be valid for the expression in any
3571 SCEV::NoWrapFlags Wrap = GEP->isInBounds() ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
3573 const SCEV *TotalOffset = getConstant(IntPtrTy, 0);
3574 gep_type_iterator GTI = gep_type_begin(GEP);
3575 for (GetElementPtrInst::op_iterator I = std::next(GEP->op_begin()),
3579 // Compute the (potentially symbolic) offset in bytes for this index.
3580 if (StructType *STy = dyn_cast<StructType>(*GTI++)) {
3581 // For a struct, add the member offset.
3582 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
3583 const SCEV *FieldOffset = getOffsetOfExpr(IntPtrTy, STy, FieldNo);
3585 // Add the field offset to the running total offset.
3586 TotalOffset = getAddExpr(TotalOffset, FieldOffset);
3588 // For an array, add the element offset, explicitly scaled.
3589 const SCEV *ElementSize = getSizeOfExpr(IntPtrTy, *GTI);
3590 const SCEV *IndexS = getSCEV(Index);
3591 // Getelementptr indices are signed.
3592 IndexS = getTruncateOrSignExtend(IndexS, IntPtrTy);
3594 // Multiply the index by the element size to compute the element offset.
3595 const SCEV *LocalOffset = getMulExpr(IndexS, ElementSize, Wrap);
3597 // Add the element offset to the running total offset.
3598 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
3602 // Get the SCEV for the GEP base.
3603 const SCEV *BaseS = getSCEV(Base);
3605 // Add the total offset from all the GEP indices to the base.
3606 return getAddExpr(BaseS, TotalOffset, Wrap);
3609 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
3610 /// guaranteed to end in (at every loop iteration). It is, at the same time,
3611 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
3612 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
3614 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
3615 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3616 return C->getValue()->getValue().countTrailingZeros();
3618 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
3619 return std::min(GetMinTrailingZeros(T->getOperand()),
3620 (uint32_t)getTypeSizeInBits(T->getType()));
3622 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
3623 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3624 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3625 getTypeSizeInBits(E->getType()) : OpRes;
3628 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
3629 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3630 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3631 getTypeSizeInBits(E->getType()) : OpRes;
3634 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
3635 // The result is the min of all operands results.
3636 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3637 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3638 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3642 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
3643 // The result is the sum of all operands results.
3644 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
3645 uint32_t BitWidth = getTypeSizeInBits(M->getType());
3646 for (unsigned i = 1, e = M->getNumOperands();
3647 SumOpRes != BitWidth && i != e; ++i)
3648 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
3653 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
3654 // The result is the min of all operands results.
3655 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3656 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3657 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3661 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
3662 // The result is the min of all operands results.
3663 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3664 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3665 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3669 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
3670 // The result is the min of all operands results.
3671 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3672 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3673 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3677 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3678 // For a SCEVUnknown, ask ValueTracking.
3679 unsigned BitWidth = getTypeSizeInBits(U->getType());
3680 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3681 computeKnownBits(U->getValue(), Zeros, Ones, DL, 0, AC, nullptr, DT);
3682 return Zeros.countTrailingOnes();
3689 /// GetRangeFromMetadata - Helper method to assign a range to V from
3690 /// metadata present in the IR.
3691 static Optional<ConstantRange> GetRangeFromMetadata(Value *V) {
3692 if (Instruction *I = dyn_cast<Instruction>(V)) {
3693 if (MDNode *MD = I->getMetadata(LLVMContext::MD_range)) {
3694 ConstantRange TotalRange(
3695 cast<IntegerType>(I->getType())->getBitWidth(), false);
3697 unsigned NumRanges = MD->getNumOperands() / 2;
3698 assert(NumRanges >= 1);
3700 for (unsigned i = 0; i < NumRanges; ++i) {
3701 ConstantInt *Lower =
3702 mdconst::extract<ConstantInt>(MD->getOperand(2 * i + 0));
3703 ConstantInt *Upper =
3704 mdconst::extract<ConstantInt>(MD->getOperand(2 * i + 1));
3705 ConstantRange Range(Lower->getValue(), Upper->getValue());
3706 TotalRange = TotalRange.unionWith(Range);
3716 /// getUnsignedRange - Determine the unsigned range for a particular SCEV.
3719 ScalarEvolution::getUnsignedRange(const SCEV *S) {
3720 // See if we've computed this range already.
3721 DenseMap<const SCEV *, ConstantRange>::iterator I = UnsignedRanges.find(S);
3722 if (I != UnsignedRanges.end())
3725 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3726 return setUnsignedRange(C, ConstantRange(C->getValue()->getValue()));
3728 unsigned BitWidth = getTypeSizeInBits(S->getType());
3729 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3731 // If the value has known zeros, the maximum unsigned value will have those
3732 // known zeros as well.
3733 uint32_t TZ = GetMinTrailingZeros(S);
3735 ConservativeResult =
3736 ConstantRange(APInt::getMinValue(BitWidth),
3737 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
3739 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3740 ConstantRange X = getUnsignedRange(Add->getOperand(0));
3741 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3742 X = X.add(getUnsignedRange(Add->getOperand(i)));
3743 return setUnsignedRange(Add, ConservativeResult.intersectWith(X));
3746 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3747 ConstantRange X = getUnsignedRange(Mul->getOperand(0));
3748 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3749 X = X.multiply(getUnsignedRange(Mul->getOperand(i)));
3750 return setUnsignedRange(Mul, ConservativeResult.intersectWith(X));
3753 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3754 ConstantRange X = getUnsignedRange(SMax->getOperand(0));
3755 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3756 X = X.smax(getUnsignedRange(SMax->getOperand(i)));
3757 return setUnsignedRange(SMax, ConservativeResult.intersectWith(X));
3760 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3761 ConstantRange X = getUnsignedRange(UMax->getOperand(0));
3762 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3763 X = X.umax(getUnsignedRange(UMax->getOperand(i)));
3764 return setUnsignedRange(UMax, ConservativeResult.intersectWith(X));
3767 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3768 ConstantRange X = getUnsignedRange(UDiv->getLHS());
3769 ConstantRange Y = getUnsignedRange(UDiv->getRHS());
3770 return setUnsignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y)));
3773 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3774 ConstantRange X = getUnsignedRange(ZExt->getOperand());
3775 return setUnsignedRange(ZExt,
3776 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3779 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3780 ConstantRange X = getUnsignedRange(SExt->getOperand());
3781 return setUnsignedRange(SExt,
3782 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3785 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3786 ConstantRange X = getUnsignedRange(Trunc->getOperand());
3787 return setUnsignedRange(Trunc,
3788 ConservativeResult.intersectWith(X.truncate(BitWidth)));
3791 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3792 // If there's no unsigned wrap, the value will never be less than its
3794 if (AddRec->getNoWrapFlags(SCEV::FlagNUW))
3795 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
3796 if (!C->getValue()->isZero())
3797 ConservativeResult =
3798 ConservativeResult.intersectWith(
3799 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0)));
3801 // TODO: non-affine addrec
3802 if (AddRec->isAffine()) {
3803 Type *Ty = AddRec->getType();
3804 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3805 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3806 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3807 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3809 const SCEV *Start = AddRec->getStart();
3810 const SCEV *Step = AddRec->getStepRecurrence(*this);
3812 ConstantRange StartRange = getUnsignedRange(Start);
3813 ConstantRange StepRange = getSignedRange(Step);
3814 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3815 ConstantRange EndRange =
3816 StartRange.add(MaxBECountRange.multiply(StepRange));
3818 // Check for overflow. This must be done with ConstantRange arithmetic
3819 // because we could be called from within the ScalarEvolution overflow
3821 ConstantRange ExtStartRange = StartRange.zextOrTrunc(BitWidth*2+1);
3822 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3823 ConstantRange ExtMaxBECountRange =
3824 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3825 ConstantRange ExtEndRange = EndRange.zextOrTrunc(BitWidth*2+1);
3826 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3828 return setUnsignedRange(AddRec, ConservativeResult);
3830 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(),
3831 EndRange.getUnsignedMin());
3832 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(),
3833 EndRange.getUnsignedMax());
3834 if (Min.isMinValue() && Max.isMaxValue())
3835 return setUnsignedRange(AddRec, ConservativeResult);
3836 return setUnsignedRange(AddRec,
3837 ConservativeResult.intersectWith(ConstantRange(Min, Max+1)));
3841 return setUnsignedRange(AddRec, ConservativeResult);
3844 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3845 // Check if the IR explicitly contains !range metadata.
3846 Optional<ConstantRange> MDRange = GetRangeFromMetadata(U->getValue());
3847 if (MDRange.hasValue())
3848 ConservativeResult = ConservativeResult.intersectWith(MDRange.getValue());
3850 // For a SCEVUnknown, ask ValueTracking.
3851 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3852 computeKnownBits(U->getValue(), Zeros, Ones, DL, 0, AC, nullptr, DT);
3853 if (Ones == ~Zeros + 1)
3854 return setUnsignedRange(U, ConservativeResult);
3855 return setUnsignedRange(U,
3856 ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1)));
3859 return setUnsignedRange(S, ConservativeResult);
3862 /// getSignedRange - Determine the signed range for a particular SCEV.
3865 ScalarEvolution::getSignedRange(const SCEV *S) {
3866 // See if we've computed this range already.
3867 DenseMap<const SCEV *, ConstantRange>::iterator I = SignedRanges.find(S);
3868 if (I != SignedRanges.end())
3871 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3872 return setSignedRange(C, ConstantRange(C->getValue()->getValue()));
3874 unsigned BitWidth = getTypeSizeInBits(S->getType());
3875 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3877 // If the value has known zeros, the maximum signed value will have those
3878 // known zeros as well.
3879 uint32_t TZ = GetMinTrailingZeros(S);
3881 ConservativeResult =
3882 ConstantRange(APInt::getSignedMinValue(BitWidth),
3883 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
3885 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3886 ConstantRange X = getSignedRange(Add->getOperand(0));
3887 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3888 X = X.add(getSignedRange(Add->getOperand(i)));
3889 return setSignedRange(Add, ConservativeResult.intersectWith(X));
3892 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3893 ConstantRange X = getSignedRange(Mul->getOperand(0));
3894 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3895 X = X.multiply(getSignedRange(Mul->getOperand(i)));
3896 return setSignedRange(Mul, ConservativeResult.intersectWith(X));
3899 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3900 ConstantRange X = getSignedRange(SMax->getOperand(0));
3901 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3902 X = X.smax(getSignedRange(SMax->getOperand(i)));
3903 return setSignedRange(SMax, ConservativeResult.intersectWith(X));
3906 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3907 ConstantRange X = getSignedRange(UMax->getOperand(0));
3908 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3909 X = X.umax(getSignedRange(UMax->getOperand(i)));
3910 return setSignedRange(UMax, ConservativeResult.intersectWith(X));
3913 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3914 ConstantRange X = getSignedRange(UDiv->getLHS());
3915 ConstantRange Y = getSignedRange(UDiv->getRHS());
3916 return setSignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y)));
3919 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3920 ConstantRange X = getSignedRange(ZExt->getOperand());
3921 return setSignedRange(ZExt,
3922 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3925 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3926 ConstantRange X = getSignedRange(SExt->getOperand());
3927 return setSignedRange(SExt,
3928 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3931 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3932 ConstantRange X = getSignedRange(Trunc->getOperand());
3933 return setSignedRange(Trunc,
3934 ConservativeResult.intersectWith(X.truncate(BitWidth)));
3937 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3938 // If there's no signed wrap, and all the operands have the same sign or
3939 // zero, the value won't ever change sign.
3940 if (AddRec->getNoWrapFlags(SCEV::FlagNSW)) {
3941 bool AllNonNeg = true;
3942 bool AllNonPos = true;
3943 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
3944 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
3945 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
3948 ConservativeResult = ConservativeResult.intersectWith(
3949 ConstantRange(APInt(BitWidth, 0),
3950 APInt::getSignedMinValue(BitWidth)));
3952 ConservativeResult = ConservativeResult.intersectWith(
3953 ConstantRange(APInt::getSignedMinValue(BitWidth),
3954 APInt(BitWidth, 1)));
3957 // TODO: non-affine addrec
3958 if (AddRec->isAffine()) {
3959 Type *Ty = AddRec->getType();
3960 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3961 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3962 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3963 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3965 const SCEV *Start = AddRec->getStart();
3966 const SCEV *Step = AddRec->getStepRecurrence(*this);
3968 ConstantRange StartRange = getSignedRange(Start);
3969 ConstantRange StepRange = getSignedRange(Step);
3970 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3971 ConstantRange EndRange =
3972 StartRange.add(MaxBECountRange.multiply(StepRange));
3974 // Check for overflow. This must be done with ConstantRange arithmetic
3975 // because we could be called from within the ScalarEvolution overflow
3977 ConstantRange ExtStartRange = StartRange.sextOrTrunc(BitWidth*2+1);
3978 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3979 ConstantRange ExtMaxBECountRange =
3980 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3981 ConstantRange ExtEndRange = EndRange.sextOrTrunc(BitWidth*2+1);
3982 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3984 return setSignedRange(AddRec, ConservativeResult);
3986 APInt Min = APIntOps::smin(StartRange.getSignedMin(),
3987 EndRange.getSignedMin());
3988 APInt Max = APIntOps::smax(StartRange.getSignedMax(),
3989 EndRange.getSignedMax());
3990 if (Min.isMinSignedValue() && Max.isMaxSignedValue())
3991 return setSignedRange(AddRec, ConservativeResult);
3992 return setSignedRange(AddRec,
3993 ConservativeResult.intersectWith(ConstantRange(Min, Max+1)));
3997 return setSignedRange(AddRec, ConservativeResult);
4000 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
4001 // Check if the IR explicitly contains !range metadata.
4002 Optional<ConstantRange> MDRange = GetRangeFromMetadata(U->getValue());
4003 if (MDRange.hasValue())
4004 ConservativeResult = ConservativeResult.intersectWith(MDRange.getValue());
4006 // For a SCEVUnknown, ask ValueTracking.
4007 if (!U->getValue()->getType()->isIntegerTy() && !DL)
4008 return setSignedRange(U, ConservativeResult);
4009 unsigned NS = ComputeNumSignBits(U->getValue(), DL, 0, AC, nullptr, DT);
4011 return setSignedRange(U, ConservativeResult);
4012 return setSignedRange(U, ConservativeResult.intersectWith(
4013 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
4014 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1)));
4017 return setSignedRange(S, ConservativeResult);
4020 /// createSCEV - We know that there is no SCEV for the specified value.
4021 /// Analyze the expression.
4023 const SCEV *ScalarEvolution::createSCEV(Value *V) {
4024 if (!isSCEVable(V->getType()))
4025 return getUnknown(V);
4027 unsigned Opcode = Instruction::UserOp1;
4028 if (Instruction *I = dyn_cast<Instruction>(V)) {
4029 Opcode = I->getOpcode();
4031 // Don't attempt to analyze instructions in blocks that aren't
4032 // reachable. Such instructions don't matter, and they aren't required
4033 // to obey basic rules for definitions dominating uses which this
4034 // analysis depends on.
4035 if (!DT->isReachableFromEntry(I->getParent()))
4036 return getUnknown(V);
4037 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
4038 Opcode = CE->getOpcode();
4039 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
4040 return getConstant(CI);
4041 else if (isa<ConstantPointerNull>(V))
4042 return getConstant(V->getType(), 0);
4043 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
4044 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee());
4046 return getUnknown(V);
4048 Operator *U = cast<Operator>(V);
4050 case Instruction::Add: {
4051 // The simple thing to do would be to just call getSCEV on both operands
4052 // and call getAddExpr with the result. However if we're looking at a
4053 // bunch of things all added together, this can be quite inefficient,
4054 // because it leads to N-1 getAddExpr calls for N ultimate operands.
4055 // Instead, gather up all the operands and make a single getAddExpr call.
4056 // LLVM IR canonical form means we need only traverse the left operands.
4058 // Don't apply this instruction's NSW or NUW flags to the new
4059 // expression. The instruction may be guarded by control flow that the
4060 // no-wrap behavior depends on. Non-control-equivalent instructions can be
4061 // mapped to the same SCEV expression, and it would be incorrect to transfer
4062 // NSW/NUW semantics to those operations.
4063 SmallVector<const SCEV *, 4> AddOps;
4064 AddOps.push_back(getSCEV(U->getOperand(1)));
4065 for (Value *Op = U->getOperand(0); ; Op = U->getOperand(0)) {
4066 unsigned Opcode = Op->getValueID() - Value::InstructionVal;
4067 if (Opcode != Instruction::Add && Opcode != Instruction::Sub)
4069 U = cast<Operator>(Op);
4070 const SCEV *Op1 = getSCEV(U->getOperand(1));
4071 if (Opcode == Instruction::Sub)
4072 AddOps.push_back(getNegativeSCEV(Op1));
4074 AddOps.push_back(Op1);
4076 AddOps.push_back(getSCEV(U->getOperand(0)));
4077 return getAddExpr(AddOps);
4079 case Instruction::Mul: {
4080 // Don't transfer NSW/NUW for the same reason as AddExpr.
4081 SmallVector<const SCEV *, 4> MulOps;
4082 MulOps.push_back(getSCEV(U->getOperand(1)));
4083 for (Value *Op = U->getOperand(0);
4084 Op->getValueID() == Instruction::Mul + Value::InstructionVal;
4085 Op = U->getOperand(0)) {
4086 U = cast<Operator>(Op);
4087 MulOps.push_back(getSCEV(U->getOperand(1)));
4089 MulOps.push_back(getSCEV(U->getOperand(0)));
4090 return getMulExpr(MulOps);
4092 case Instruction::UDiv:
4093 return getUDivExpr(getSCEV(U->getOperand(0)),
4094 getSCEV(U->getOperand(1)));
4095 case Instruction::Sub:
4096 return getMinusSCEV(getSCEV(U->getOperand(0)),
4097 getSCEV(U->getOperand(1)));
4098 case Instruction::And:
4099 // For an expression like x&255 that merely masks off the high bits,
4100 // use zext(trunc(x)) as the SCEV expression.
4101 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
4102 if (CI->isNullValue())
4103 return getSCEV(U->getOperand(1));
4104 if (CI->isAllOnesValue())
4105 return getSCEV(U->getOperand(0));
4106 const APInt &A = CI->getValue();
4108 // Instcombine's ShrinkDemandedConstant may strip bits out of
4109 // constants, obscuring what would otherwise be a low-bits mask.
4110 // Use computeKnownBits to compute what ShrinkDemandedConstant
4111 // knew about to reconstruct a low-bits mask value.
4112 unsigned LZ = A.countLeadingZeros();
4113 unsigned TZ = A.countTrailingZeros();
4114 unsigned BitWidth = A.getBitWidth();
4115 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
4116 computeKnownBits(U->getOperand(0), KnownZero, KnownOne, DL, 0, AC,
4119 APInt EffectiveMask =
4120 APInt::getLowBitsSet(BitWidth, BitWidth - LZ - TZ).shl(TZ);
4121 if ((LZ != 0 || TZ != 0) && !((~A & ~KnownZero) & EffectiveMask)) {
4122 const SCEV *MulCount = getConstant(
4123 ConstantInt::get(getContext(), APInt::getOneBitSet(BitWidth, TZ)));
4127 getUDivExactExpr(getSCEV(U->getOperand(0)), MulCount),
4128 IntegerType::get(getContext(), BitWidth - LZ - TZ)),
4135 case Instruction::Or:
4136 // If the RHS of the Or is a constant, we may have something like:
4137 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
4138 // optimizations will transparently handle this case.
4140 // In order for this transformation to be safe, the LHS must be of the
4141 // form X*(2^n) and the Or constant must be less than 2^n.
4142 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
4143 const SCEV *LHS = getSCEV(U->getOperand(0));
4144 const APInt &CIVal = CI->getValue();
4145 if (GetMinTrailingZeros(LHS) >=
4146 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
4147 // Build a plain add SCEV.
4148 const SCEV *S = getAddExpr(LHS, getSCEV(CI));
4149 // If the LHS of the add was an addrec and it has no-wrap flags,
4150 // transfer the no-wrap flags, since an or won't introduce a wrap.
4151 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
4152 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
4153 const_cast<SCEVAddRecExpr *>(NewAR)->setNoWrapFlags(
4154 OldAR->getNoWrapFlags());
4160 case Instruction::Xor:
4161 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
4162 // If the RHS of the xor is a signbit, then this is just an add.
4163 // Instcombine turns add of signbit into xor as a strength reduction step.
4164 if (CI->getValue().isSignBit())
4165 return getAddExpr(getSCEV(U->getOperand(0)),
4166 getSCEV(U->getOperand(1)));
4168 // If the RHS of xor is -1, then this is a not operation.
4169 if (CI->isAllOnesValue())
4170 return getNotSCEV(getSCEV(U->getOperand(0)));
4172 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
4173 // This is a variant of the check for xor with -1, and it handles
4174 // the case where instcombine has trimmed non-demanded bits out
4175 // of an xor with -1.
4176 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
4177 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
4178 if (BO->getOpcode() == Instruction::And &&
4179 LCI->getValue() == CI->getValue())
4180 if (const SCEVZeroExtendExpr *Z =
4181 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
4182 Type *UTy = U->getType();
4183 const SCEV *Z0 = Z->getOperand();
4184 Type *Z0Ty = Z0->getType();
4185 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
4187 // If C is a low-bits mask, the zero extend is serving to
4188 // mask off the high bits. Complement the operand and
4189 // re-apply the zext.
4190 if (APIntOps::isMask(Z0TySize, CI->getValue()))
4191 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
4193 // If C is a single bit, it may be in the sign-bit position
4194 // before the zero-extend. In this case, represent the xor
4195 // using an add, which is equivalent, and re-apply the zext.
4196 APInt Trunc = CI->getValue().trunc(Z0TySize);
4197 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
4199 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
4205 case Instruction::Shl:
4206 // Turn shift left of a constant amount into a multiply.
4207 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
4208 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
4210 // If the shift count is not less than the bitwidth, the result of
4211 // the shift is undefined. Don't try to analyze it, because the
4212 // resolution chosen here may differ from the resolution chosen in
4213 // other parts of the compiler.
4214 if (SA->getValue().uge(BitWidth))
4217 Constant *X = ConstantInt::get(getContext(),
4218 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
4219 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
4223 case Instruction::LShr:
4224 // Turn logical shift right of a constant into a unsigned divide.
4225 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
4226 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
4228 // If the shift count is not less than the bitwidth, the result of
4229 // the shift is undefined. Don't try to analyze it, because the
4230 // resolution chosen here may differ from the resolution chosen in
4231 // other parts of the compiler.
4232 if (SA->getValue().uge(BitWidth))
4235 Constant *X = ConstantInt::get(getContext(),
4236 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
4237 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
4241 case Instruction::AShr:
4242 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
4243 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
4244 if (Operator *L = dyn_cast<Operator>(U->getOperand(0)))
4245 if (L->getOpcode() == Instruction::Shl &&
4246 L->getOperand(1) == U->getOperand(1)) {
4247 uint64_t BitWidth = getTypeSizeInBits(U->getType());
4249 // If the shift count is not less than the bitwidth, the result of
4250 // the shift is undefined. Don't try to analyze it, because the
4251 // resolution chosen here may differ from the resolution chosen in
4252 // other parts of the compiler.
4253 if (CI->getValue().uge(BitWidth))
4256 uint64_t Amt = BitWidth - CI->getZExtValue();
4257 if (Amt == BitWidth)
4258 return getSCEV(L->getOperand(0)); // shift by zero --> noop
4260 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
4261 IntegerType::get(getContext(),
4267 case Instruction::Trunc:
4268 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
4270 case Instruction::ZExt:
4271 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
4273 case Instruction::SExt:
4274 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
4276 case Instruction::BitCast:
4277 // BitCasts are no-op casts so we just eliminate the cast.
4278 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
4279 return getSCEV(U->getOperand(0));
4282 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
4283 // lead to pointer expressions which cannot safely be expanded to GEPs,
4284 // because ScalarEvolution doesn't respect the GEP aliasing rules when
4285 // simplifying integer expressions.
4287 case Instruction::GetElementPtr:
4288 return createNodeForGEP(cast<GEPOperator>(U));
4290 case Instruction::PHI:
4291 return createNodeForPHI(cast<PHINode>(U));
4293 case Instruction::Select:
4294 // This could be a smax or umax that was lowered earlier.
4295 // Try to recover it.
4296 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
4297 Value *LHS = ICI->getOperand(0);
4298 Value *RHS = ICI->getOperand(1);
4299 switch (ICI->getPredicate()) {
4300 case ICmpInst::ICMP_SLT:
4301 case ICmpInst::ICMP_SLE:
4302 std::swap(LHS, RHS);
4304 case ICmpInst::ICMP_SGT:
4305 case ICmpInst::ICMP_SGE:
4306 // a >s b ? a+x : b+x -> smax(a, b)+x
4307 // a >s b ? b+x : a+x -> smin(a, b)+x
4308 if (getTypeSizeInBits(LHS->getType()) <=
4309 getTypeSizeInBits(U->getType())) {
4310 const SCEV *LS = getNoopOrSignExtend(getSCEV(LHS), U->getType());
4311 const SCEV *RS = getNoopOrSignExtend(getSCEV(RHS), U->getType());
4312 const SCEV *LA = getSCEV(U->getOperand(1));
4313 const SCEV *RA = getSCEV(U->getOperand(2));
4314 const SCEV *LDiff = getMinusSCEV(LA, LS);
4315 const SCEV *RDiff = getMinusSCEV(RA, RS);
4317 return getAddExpr(getSMaxExpr(LS, RS), LDiff);
4318 LDiff = getMinusSCEV(LA, RS);
4319 RDiff = getMinusSCEV(RA, LS);
4321 return getAddExpr(getSMinExpr(LS, RS), LDiff);
4324 case ICmpInst::ICMP_ULT:
4325 case ICmpInst::ICMP_ULE:
4326 std::swap(LHS, RHS);
4328 case ICmpInst::ICMP_UGT:
4329 case ICmpInst::ICMP_UGE:
4330 // a >u b ? a+x : b+x -> umax(a, b)+x
4331 // a >u b ? b+x : a+x -> umin(a, b)+x
4332 if (getTypeSizeInBits(LHS->getType()) <=
4333 getTypeSizeInBits(U->getType())) {
4334 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), U->getType());
4335 const SCEV *RS = getNoopOrZeroExtend(getSCEV(RHS), U->getType());
4336 const SCEV *LA = getSCEV(U->getOperand(1));
4337 const SCEV *RA = getSCEV(U->getOperand(2));
4338 const SCEV *LDiff = getMinusSCEV(LA, LS);
4339 const SCEV *RDiff = getMinusSCEV(RA, RS);
4341 return getAddExpr(getUMaxExpr(LS, RS), LDiff);
4342 LDiff = getMinusSCEV(LA, RS);
4343 RDiff = getMinusSCEV(RA, LS);
4345 return getAddExpr(getUMinExpr(LS, RS), LDiff);
4348 case ICmpInst::ICMP_NE:
4349 // n != 0 ? n+x : 1+x -> umax(n, 1)+x
4350 if (getTypeSizeInBits(LHS->getType()) <=
4351 getTypeSizeInBits(U->getType()) &&
4352 isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
4353 const SCEV *One = getConstant(U->getType(), 1);
4354 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), U->getType());
4355 const SCEV *LA = getSCEV(U->getOperand(1));
4356 const SCEV *RA = getSCEV(U->getOperand(2));
4357 const SCEV *LDiff = getMinusSCEV(LA, LS);
4358 const SCEV *RDiff = getMinusSCEV(RA, One);
4360 return getAddExpr(getUMaxExpr(One, LS), LDiff);
4363 case ICmpInst::ICMP_EQ:
4364 // n == 0 ? 1+x : n+x -> umax(n, 1)+x
4365 if (getTypeSizeInBits(LHS->getType()) <=
4366 getTypeSizeInBits(U->getType()) &&
4367 isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
4368 const SCEV *One = getConstant(U->getType(), 1);
4369 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), U->getType());
4370 const SCEV *LA = getSCEV(U->getOperand(1));
4371 const SCEV *RA = getSCEV(U->getOperand(2));
4372 const SCEV *LDiff = getMinusSCEV(LA, One);
4373 const SCEV *RDiff = getMinusSCEV(RA, LS);
4375 return getAddExpr(getUMaxExpr(One, LS), LDiff);
4383 default: // We cannot analyze this expression.
4387 return getUnknown(V);
4392 //===----------------------------------------------------------------------===//
4393 // Iteration Count Computation Code
4396 unsigned ScalarEvolution::getSmallConstantTripCount(Loop *L) {
4397 if (BasicBlock *ExitingBB = L->getExitingBlock())
4398 return getSmallConstantTripCount(L, ExitingBB);
4400 // No trip count information for multiple exits.
4404 /// getSmallConstantTripCount - Returns the maximum trip count of this loop as a
4405 /// normal unsigned value. Returns 0 if the trip count is unknown or not
4406 /// constant. Will also return 0 if the maximum trip count is very large (>=
4409 /// This "trip count" assumes that control exits via ExitingBlock. More
4410 /// precisely, it is the number of times that control may reach ExitingBlock
4411 /// before taking the branch. For loops with multiple exits, it may not be the
4412 /// number times that the loop header executes because the loop may exit
4413 /// prematurely via another branch.
4414 unsigned ScalarEvolution::getSmallConstantTripCount(Loop *L,
4415 BasicBlock *ExitingBlock) {
4416 assert(ExitingBlock && "Must pass a non-null exiting block!");
4417 assert(L->isLoopExiting(ExitingBlock) &&
4418 "Exiting block must actually branch out of the loop!");
4419 const SCEVConstant *ExitCount =
4420 dyn_cast<SCEVConstant>(getExitCount(L, ExitingBlock));
4424 ConstantInt *ExitConst = ExitCount->getValue();
4426 // Guard against huge trip counts.
4427 if (ExitConst->getValue().getActiveBits() > 32)
4430 // In case of integer overflow, this returns 0, which is correct.
4431 return ((unsigned)ExitConst->getZExtValue()) + 1;
4434 unsigned ScalarEvolution::getSmallConstantTripMultiple(Loop *L) {
4435 if (BasicBlock *ExitingBB = L->getExitingBlock())
4436 return getSmallConstantTripMultiple(L, ExitingBB);
4438 // No trip multiple information for multiple exits.
4442 /// getSmallConstantTripMultiple - Returns the largest constant divisor of the
4443 /// trip count of this loop as a normal unsigned value, if possible. This
4444 /// means that the actual trip count is always a multiple of the returned
4445 /// value (don't forget the trip count could very well be zero as well!).
4447 /// Returns 1 if the trip count is unknown or not guaranteed to be the
4448 /// multiple of a constant (which is also the case if the trip count is simply
4449 /// constant, use getSmallConstantTripCount for that case), Will also return 1
4450 /// if the trip count is very large (>= 2^32).
4452 /// As explained in the comments for getSmallConstantTripCount, this assumes
4453 /// that control exits the loop via ExitingBlock.
4455 ScalarEvolution::getSmallConstantTripMultiple(Loop *L,
4456 BasicBlock *ExitingBlock) {
4457 assert(ExitingBlock && "Must pass a non-null exiting block!");
4458 assert(L->isLoopExiting(ExitingBlock) &&
4459 "Exiting block must actually branch out of the loop!");
4460 const SCEV *ExitCount = getExitCount(L, ExitingBlock);
4461 if (ExitCount == getCouldNotCompute())
4464 // Get the trip count from the BE count by adding 1.
4465 const SCEV *TCMul = getAddExpr(ExitCount,
4466 getConstant(ExitCount->getType(), 1));
4467 // FIXME: SCEV distributes multiplication as V1*C1 + V2*C1. We could attempt
4468 // to factor simple cases.
4469 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(TCMul))
4470 TCMul = Mul->getOperand(0);
4472 const SCEVConstant *MulC = dyn_cast<SCEVConstant>(TCMul);
4476 ConstantInt *Result = MulC->getValue();
4478 // Guard against huge trip counts (this requires checking
4479 // for zero to handle the case where the trip count == -1 and the
4481 if (!Result || Result->getValue().getActiveBits() > 32 ||
4482 Result->getValue().getActiveBits() == 0)
4485 return (unsigned)Result->getZExtValue();
4488 // getExitCount - Get the expression for the number of loop iterations for which
4489 // this loop is guaranteed not to exit via ExitingBlock. Otherwise return
4490 // SCEVCouldNotCompute.
4491 const SCEV *ScalarEvolution::getExitCount(Loop *L, BasicBlock *ExitingBlock) {
4492 return getBackedgeTakenInfo(L).getExact(ExitingBlock, this);
4495 /// getBackedgeTakenCount - If the specified loop has a predictable
4496 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
4497 /// object. The backedge-taken count is the number of times the loop header
4498 /// will be branched to from within the loop. This is one less than the
4499 /// trip count of the loop, since it doesn't count the first iteration,
4500 /// when the header is branched to from outside the loop.
4502 /// Note that it is not valid to call this method on a loop without a
4503 /// loop-invariant backedge-taken count (see
4504 /// hasLoopInvariantBackedgeTakenCount).
4506 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
4507 return getBackedgeTakenInfo(L).getExact(this);
4510 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
4511 /// return the least SCEV value that is known never to be less than the
4512 /// actual backedge taken count.
4513 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
4514 return getBackedgeTakenInfo(L).getMax(this);
4517 /// PushLoopPHIs - Push PHI nodes in the header of the given loop
4518 /// onto the given Worklist.
4520 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
4521 BasicBlock *Header = L->getHeader();
4523 // Push all Loop-header PHIs onto the Worklist stack.
4524 for (BasicBlock::iterator I = Header->begin();
4525 PHINode *PN = dyn_cast<PHINode>(I); ++I)
4526 Worklist.push_back(PN);
4529 const ScalarEvolution::BackedgeTakenInfo &
4530 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
4531 // Initially insert an invalid entry for this loop. If the insertion
4532 // succeeds, proceed to actually compute a backedge-taken count and
4533 // update the value. The temporary CouldNotCompute value tells SCEV
4534 // code elsewhere that it shouldn't attempt to request a new
4535 // backedge-taken count, which could result in infinite recursion.
4536 std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
4537 BackedgeTakenCounts.insert(std::make_pair(L, BackedgeTakenInfo()));
4539 return Pair.first->second;
4541 // ComputeBackedgeTakenCount may allocate memory for its result. Inserting it
4542 // into the BackedgeTakenCounts map transfers ownership. Otherwise, the result
4543 // must be cleared in this scope.
4544 BackedgeTakenInfo Result = ComputeBackedgeTakenCount(L);
4546 if (Result.getExact(this) != getCouldNotCompute()) {
4547 assert(isLoopInvariant(Result.getExact(this), L) &&
4548 isLoopInvariant(Result.getMax(this), L) &&
4549 "Computed backedge-taken count isn't loop invariant for loop!");
4550 ++NumTripCountsComputed;
4552 else if (Result.getMax(this) == getCouldNotCompute() &&
4553 isa<PHINode>(L->getHeader()->begin())) {
4554 // Only count loops that have phi nodes as not being computable.
4555 ++NumTripCountsNotComputed;
4558 // Now that we know more about the trip count for this loop, forget any
4559 // existing SCEV values for PHI nodes in this loop since they are only
4560 // conservative estimates made without the benefit of trip count
4561 // information. This is similar to the code in forgetLoop, except that
4562 // it handles SCEVUnknown PHI nodes specially.
4563 if (Result.hasAnyInfo()) {
4564 SmallVector<Instruction *, 16> Worklist;
4565 PushLoopPHIs(L, Worklist);
4567 SmallPtrSet<Instruction *, 8> Visited;
4568 while (!Worklist.empty()) {
4569 Instruction *I = Worklist.pop_back_val();
4570 if (!Visited.insert(I).second)
4573 ValueExprMapType::iterator It =
4574 ValueExprMap.find_as(static_cast<Value *>(I));
4575 if (It != ValueExprMap.end()) {
4576 const SCEV *Old = It->second;
4578 // SCEVUnknown for a PHI either means that it has an unrecognized
4579 // structure, or it's a PHI that's in the progress of being computed
4580 // by createNodeForPHI. In the former case, additional loop trip
4581 // count information isn't going to change anything. In the later
4582 // case, createNodeForPHI will perform the necessary updates on its
4583 // own when it gets to that point.
4584 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) {
4585 forgetMemoizedResults(Old);
4586 ValueExprMap.erase(It);
4588 if (PHINode *PN = dyn_cast<PHINode>(I))
4589 ConstantEvolutionLoopExitValue.erase(PN);
4592 PushDefUseChildren(I, Worklist);
4596 // Re-lookup the insert position, since the call to
4597 // ComputeBackedgeTakenCount above could result in a
4598 // recusive call to getBackedgeTakenInfo (on a different
4599 // loop), which would invalidate the iterator computed
4601 return BackedgeTakenCounts.find(L)->second = Result;
4604 /// forgetLoop - This method should be called by the client when it has
4605 /// changed a loop in a way that may effect ScalarEvolution's ability to
4606 /// compute a trip count, or if the loop is deleted.
4607 void ScalarEvolution::forgetLoop(const Loop *L) {
4608 // Drop any stored trip count value.
4609 DenseMap<const Loop*, BackedgeTakenInfo>::iterator BTCPos =
4610 BackedgeTakenCounts.find(L);
4611 if (BTCPos != BackedgeTakenCounts.end()) {
4612 BTCPos->second.clear();
4613 BackedgeTakenCounts.erase(BTCPos);
4616 // Drop information about expressions based on loop-header PHIs.
4617 SmallVector<Instruction *, 16> Worklist;
4618 PushLoopPHIs(L, Worklist);
4620 SmallPtrSet<Instruction *, 8> Visited;
4621 while (!Worklist.empty()) {
4622 Instruction *I = Worklist.pop_back_val();
4623 if (!Visited.insert(I).second)
4626 ValueExprMapType::iterator It =
4627 ValueExprMap.find_as(static_cast<Value *>(I));
4628 if (It != ValueExprMap.end()) {
4629 forgetMemoizedResults(It->second);
4630 ValueExprMap.erase(It);
4631 if (PHINode *PN = dyn_cast<PHINode>(I))
4632 ConstantEvolutionLoopExitValue.erase(PN);
4635 PushDefUseChildren(I, Worklist);
4638 // Forget all contained loops too, to avoid dangling entries in the
4639 // ValuesAtScopes map.
4640 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
4644 /// forgetValue - This method should be called by the client when it has
4645 /// changed a value in a way that may effect its value, or which may
4646 /// disconnect it from a def-use chain linking it to a loop.
4647 void ScalarEvolution::forgetValue(Value *V) {
4648 Instruction *I = dyn_cast<Instruction>(V);
4651 // Drop information about expressions based on loop-header PHIs.
4652 SmallVector<Instruction *, 16> Worklist;
4653 Worklist.push_back(I);
4655 SmallPtrSet<Instruction *, 8> Visited;
4656 while (!Worklist.empty()) {
4657 I = Worklist.pop_back_val();
4658 if (!Visited.insert(I).second)
4661 ValueExprMapType::iterator It =
4662 ValueExprMap.find_as(static_cast<Value *>(I));
4663 if (It != ValueExprMap.end()) {
4664 forgetMemoizedResults(It->second);
4665 ValueExprMap.erase(It);
4666 if (PHINode *PN = dyn_cast<PHINode>(I))
4667 ConstantEvolutionLoopExitValue.erase(PN);
4670 PushDefUseChildren(I, Worklist);
4674 /// getExact - Get the exact loop backedge taken count considering all loop
4675 /// exits. A computable result can only be return for loops with a single exit.
4676 /// Returning the minimum taken count among all exits is incorrect because one
4677 /// of the loop's exit limit's may have been skipped. HowFarToZero assumes that
4678 /// the limit of each loop test is never skipped. This is a valid assumption as
4679 /// long as the loop exits via that test. For precise results, it is the
4680 /// caller's responsibility to specify the relevant loop exit using
4681 /// getExact(ExitingBlock, SE).
4683 ScalarEvolution::BackedgeTakenInfo::getExact(ScalarEvolution *SE) const {
4684 // If any exits were not computable, the loop is not computable.
4685 if (!ExitNotTaken.isCompleteList()) return SE->getCouldNotCompute();
4687 // We need exactly one computable exit.
4688 if (!ExitNotTaken.ExitingBlock) return SE->getCouldNotCompute();
4689 assert(ExitNotTaken.ExactNotTaken && "uninitialized not-taken info");
4691 const SCEV *BECount = nullptr;
4692 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4693 ENT != nullptr; ENT = ENT->getNextExit()) {
4695 assert(ENT->ExactNotTaken != SE->getCouldNotCompute() && "bad exit SCEV");
4698 BECount = ENT->ExactNotTaken;
4699 else if (BECount != ENT->ExactNotTaken)
4700 return SE->getCouldNotCompute();
4702 assert(BECount && "Invalid not taken count for loop exit");
4706 /// getExact - Get the exact not taken count for this loop exit.
4708 ScalarEvolution::BackedgeTakenInfo::getExact(BasicBlock *ExitingBlock,
4709 ScalarEvolution *SE) const {
4710 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4711 ENT != nullptr; ENT = ENT->getNextExit()) {
4713 if (ENT->ExitingBlock == ExitingBlock)
4714 return ENT->ExactNotTaken;
4716 return SE->getCouldNotCompute();
4719 /// getMax - Get the max backedge taken count for the loop.
4721 ScalarEvolution::BackedgeTakenInfo::getMax(ScalarEvolution *SE) const {
4722 return Max ? Max : SE->getCouldNotCompute();
4725 bool ScalarEvolution::BackedgeTakenInfo::hasOperand(const SCEV *S,
4726 ScalarEvolution *SE) const {
4727 if (Max && Max != SE->getCouldNotCompute() && SE->hasOperand(Max, S))
4730 if (!ExitNotTaken.ExitingBlock)
4733 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4734 ENT != nullptr; ENT = ENT->getNextExit()) {
4736 if (ENT->ExactNotTaken != SE->getCouldNotCompute()
4737 && SE->hasOperand(ENT->ExactNotTaken, S)) {
4744 /// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each
4745 /// computable exit into a persistent ExitNotTakenInfo array.
4746 ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo(
4747 SmallVectorImpl< std::pair<BasicBlock *, const SCEV *> > &ExitCounts,
4748 bool Complete, const SCEV *MaxCount) : Max(MaxCount) {
4751 ExitNotTaken.setIncomplete();
4753 unsigned NumExits = ExitCounts.size();
4754 if (NumExits == 0) return;
4756 ExitNotTaken.ExitingBlock = ExitCounts[0].first;
4757 ExitNotTaken.ExactNotTaken = ExitCounts[0].second;
4758 if (NumExits == 1) return;
4760 // Handle the rare case of multiple computable exits.
4761 ExitNotTakenInfo *ENT = new ExitNotTakenInfo[NumExits-1];
4763 ExitNotTakenInfo *PrevENT = &ExitNotTaken;
4764 for (unsigned i = 1; i < NumExits; ++i, PrevENT = ENT, ++ENT) {
4765 PrevENT->setNextExit(ENT);
4766 ENT->ExitingBlock = ExitCounts[i].first;
4767 ENT->ExactNotTaken = ExitCounts[i].second;
4771 /// clear - Invalidate this result and free the ExitNotTakenInfo array.
4772 void ScalarEvolution::BackedgeTakenInfo::clear() {
4773 ExitNotTaken.ExitingBlock = nullptr;
4774 ExitNotTaken.ExactNotTaken = nullptr;
4775 delete[] ExitNotTaken.getNextExit();
4778 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
4779 /// of the specified loop will execute.
4780 ScalarEvolution::BackedgeTakenInfo
4781 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
4782 SmallVector<BasicBlock *, 8> ExitingBlocks;
4783 L->getExitingBlocks(ExitingBlocks);
4785 SmallVector<std::pair<BasicBlock *, const SCEV *>, 4> ExitCounts;
4786 bool CouldComputeBECount = true;
4787 BasicBlock *Latch = L->getLoopLatch(); // may be NULL.
4788 const SCEV *MustExitMaxBECount = nullptr;
4789 const SCEV *MayExitMaxBECount = nullptr;
4791 // Compute the ExitLimit for each loop exit. Use this to populate ExitCounts
4792 // and compute maxBECount.
4793 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
4794 BasicBlock *ExitBB = ExitingBlocks[i];
4795 ExitLimit EL = ComputeExitLimit(L, ExitBB);
4797 // 1. For each exit that can be computed, add an entry to ExitCounts.
4798 // CouldComputeBECount is true only if all exits can be computed.
4799 if (EL.Exact == getCouldNotCompute())
4800 // We couldn't compute an exact value for this exit, so
4801 // we won't be able to compute an exact value for the loop.
4802 CouldComputeBECount = false;
4804 ExitCounts.push_back(std::make_pair(ExitBB, EL.Exact));
4806 // 2. Derive the loop's MaxBECount from each exit's max number of
4807 // non-exiting iterations. Partition the loop exits into two kinds:
4808 // LoopMustExits and LoopMayExits.
4810 // If the exit dominates the loop latch, it is a LoopMustExit otherwise it
4811 // is a LoopMayExit. If any computable LoopMustExit is found, then
4812 // MaxBECount is the minimum EL.Max of computable LoopMustExits. Otherwise,
4813 // MaxBECount is conservatively the maximum EL.Max, where CouldNotCompute is
4814 // considered greater than any computable EL.Max.
4815 if (EL.Max != getCouldNotCompute() && Latch &&
4816 DT->dominates(ExitBB, Latch)) {
4817 if (!MustExitMaxBECount)
4818 MustExitMaxBECount = EL.Max;
4820 MustExitMaxBECount =
4821 getUMinFromMismatchedTypes(MustExitMaxBECount, EL.Max);
4823 } else if (MayExitMaxBECount != getCouldNotCompute()) {
4824 if (!MayExitMaxBECount || EL.Max == getCouldNotCompute())
4825 MayExitMaxBECount = EL.Max;
4828 getUMaxFromMismatchedTypes(MayExitMaxBECount, EL.Max);
4832 const SCEV *MaxBECount = MustExitMaxBECount ? MustExitMaxBECount :
4833 (MayExitMaxBECount ? MayExitMaxBECount : getCouldNotCompute());
4834 return BackedgeTakenInfo(ExitCounts, CouldComputeBECount, MaxBECount);
4837 /// ComputeExitLimit - Compute the number of times the backedge of the specified
4838 /// loop will execute if it exits via the specified block.
4839 ScalarEvolution::ExitLimit
4840 ScalarEvolution::ComputeExitLimit(const Loop *L, BasicBlock *ExitingBlock) {
4842 // Okay, we've chosen an exiting block. See what condition causes us to
4843 // exit at this block and remember the exit block and whether all other targets
4844 // lead to the loop header.
4845 bool MustExecuteLoopHeader = true;
4846 BasicBlock *Exit = nullptr;
4847 for (succ_iterator SI = succ_begin(ExitingBlock), SE = succ_end(ExitingBlock);
4849 if (!L->contains(*SI)) {
4850 if (Exit) // Multiple exit successors.
4851 return getCouldNotCompute();
4853 } else if (*SI != L->getHeader()) {
4854 MustExecuteLoopHeader = false;
4857 // At this point, we know we have a conditional branch that determines whether
4858 // the loop is exited. However, we don't know if the branch is executed each
4859 // time through the loop. If not, then the execution count of the branch will
4860 // not be equal to the trip count of the loop.
4862 // Currently we check for this by checking to see if the Exit branch goes to
4863 // the loop header. If so, we know it will always execute the same number of
4864 // times as the loop. We also handle the case where the exit block *is* the
4865 // loop header. This is common for un-rotated loops.
4867 // If both of those tests fail, walk up the unique predecessor chain to the
4868 // header, stopping if there is an edge that doesn't exit the loop. If the
4869 // header is reached, the execution count of the branch will be equal to the
4870 // trip count of the loop.
4872 // More extensive analysis could be done to handle more cases here.
4874 if (!MustExecuteLoopHeader && ExitingBlock != L->getHeader()) {
4875 // The simple checks failed, try climbing the unique predecessor chain
4876 // up to the header.
4878 for (BasicBlock *BB = ExitingBlock; BB; ) {
4879 BasicBlock *Pred = BB->getUniquePredecessor();
4881 return getCouldNotCompute();
4882 TerminatorInst *PredTerm = Pred->getTerminator();
4883 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) {
4884 BasicBlock *PredSucc = PredTerm->getSuccessor(i);
4887 // If the predecessor has a successor that isn't BB and isn't
4888 // outside the loop, assume the worst.
4889 if (L->contains(PredSucc))
4890 return getCouldNotCompute();
4892 if (Pred == L->getHeader()) {
4899 return getCouldNotCompute();
4902 bool IsOnlyExit = (L->getExitingBlock() != nullptr);
4903 TerminatorInst *Term = ExitingBlock->getTerminator();
4904 if (BranchInst *BI = dyn_cast<BranchInst>(Term)) {
4905 assert(BI->isConditional() && "If unconditional, it can't be in loop!");
4906 // Proceed to the next level to examine the exit condition expression.
4907 return ComputeExitLimitFromCond(L, BI->getCondition(), BI->getSuccessor(0),
4908 BI->getSuccessor(1),
4909 /*ControlsExit=*/IsOnlyExit);
4912 if (SwitchInst *SI = dyn_cast<SwitchInst>(Term))
4913 return ComputeExitLimitFromSingleExitSwitch(L, SI, Exit,
4914 /*ControlsExit=*/IsOnlyExit);
4916 return getCouldNotCompute();
4919 /// ComputeExitLimitFromCond - Compute the number of times the
4920 /// backedge of the specified loop will execute if its exit condition
4921 /// were a conditional branch of ExitCond, TBB, and FBB.
4923 /// @param ControlsExit is true if ExitCond directly controls the exit
4924 /// branch. In this case, we can assume that the loop exits only if the
4925 /// condition is true and can infer that failing to meet the condition prior to
4926 /// integer wraparound results in undefined behavior.
4927 ScalarEvolution::ExitLimit
4928 ScalarEvolution::ComputeExitLimitFromCond(const Loop *L,
4932 bool ControlsExit) {
4933 // Check if the controlling expression for this loop is an And or Or.
4934 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
4935 if (BO->getOpcode() == Instruction::And) {
4936 // Recurse on the operands of the and.
4937 bool EitherMayExit = L->contains(TBB);
4938 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
4939 ControlsExit && !EitherMayExit);
4940 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
4941 ControlsExit && !EitherMayExit);
4942 const SCEV *BECount = getCouldNotCompute();
4943 const SCEV *MaxBECount = getCouldNotCompute();
4944 if (EitherMayExit) {
4945 // Both conditions must be true for the loop to continue executing.
4946 // Choose the less conservative count.
4947 if (EL0.Exact == getCouldNotCompute() ||
4948 EL1.Exact == getCouldNotCompute())
4949 BECount = getCouldNotCompute();
4951 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
4952 if (EL0.Max == getCouldNotCompute())
4953 MaxBECount = EL1.Max;
4954 else if (EL1.Max == getCouldNotCompute())
4955 MaxBECount = EL0.Max;
4957 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
4959 // Both conditions must be true at the same time for the loop to exit.
4960 // For now, be conservative.
4961 assert(L->contains(FBB) && "Loop block has no successor in loop!");
4962 if (EL0.Max == EL1.Max)
4963 MaxBECount = EL0.Max;
4964 if (EL0.Exact == EL1.Exact)
4965 BECount = EL0.Exact;
4968 return ExitLimit(BECount, MaxBECount);
4970 if (BO->getOpcode() == Instruction::Or) {
4971 // Recurse on the operands of the or.
4972 bool EitherMayExit = L->contains(FBB);
4973 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
4974 ControlsExit && !EitherMayExit);
4975 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
4976 ControlsExit && !EitherMayExit);
4977 const SCEV *BECount = getCouldNotCompute();
4978 const SCEV *MaxBECount = getCouldNotCompute();
4979 if (EitherMayExit) {
4980 // Both conditions must be false for the loop to continue executing.
4981 // Choose the less conservative count.
4982 if (EL0.Exact == getCouldNotCompute() ||
4983 EL1.Exact == getCouldNotCompute())
4984 BECount = getCouldNotCompute();
4986 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
4987 if (EL0.Max == getCouldNotCompute())
4988 MaxBECount = EL1.Max;
4989 else if (EL1.Max == getCouldNotCompute())
4990 MaxBECount = EL0.Max;
4992 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
4994 // Both conditions must be false at the same time for the loop to exit.
4995 // For now, be conservative.
4996 assert(L->contains(TBB) && "Loop block has no successor in loop!");
4997 if (EL0.Max == EL1.Max)
4998 MaxBECount = EL0.Max;
4999 if (EL0.Exact == EL1.Exact)
5000 BECount = EL0.Exact;
5003 return ExitLimit(BECount, MaxBECount);
5007 // With an icmp, it may be feasible to compute an exact backedge-taken count.
5008 // Proceed to the next level to examine the icmp.
5009 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
5010 return ComputeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB, ControlsExit);
5012 // Check for a constant condition. These are normally stripped out by
5013 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
5014 // preserve the CFG and is temporarily leaving constant conditions
5016 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
5017 if (L->contains(FBB) == !CI->getZExtValue())
5018 // The backedge is always taken.
5019 return getCouldNotCompute();
5021 // The backedge is never taken.
5022 return getConstant(CI->getType(), 0);
5025 // If it's not an integer or pointer comparison then compute it the hard way.
5026 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
5029 /// ComputeExitLimitFromICmp - Compute the number of times the
5030 /// backedge of the specified loop will execute if its exit condition
5031 /// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB.
5032 ScalarEvolution::ExitLimit
5033 ScalarEvolution::ComputeExitLimitFromICmp(const Loop *L,
5037 bool ControlsExit) {
5039 // If the condition was exit on true, convert the condition to exit on false
5040 ICmpInst::Predicate Cond;
5041 if (!L->contains(FBB))
5042 Cond = ExitCond->getPredicate();
5044 Cond = ExitCond->getInversePredicate();
5046 // Handle common loops like: for (X = "string"; *X; ++X)
5047 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
5048 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
5050 ComputeLoadConstantCompareExitLimit(LI, RHS, L, Cond);
5051 if (ItCnt.hasAnyInfo())
5055 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
5056 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
5058 // Try to evaluate any dependencies out of the loop.
5059 LHS = getSCEVAtScope(LHS, L);
5060 RHS = getSCEVAtScope(RHS, L);
5062 // At this point, we would like to compute how many iterations of the
5063 // loop the predicate will return true for these inputs.
5064 if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) {
5065 // If there is a loop-invariant, force it into the RHS.
5066 std::swap(LHS, RHS);
5067 Cond = ICmpInst::getSwappedPredicate(Cond);
5070 // Simplify the operands before analyzing them.
5071 (void)SimplifyICmpOperands(Cond, LHS, RHS);
5073 // If we have a comparison of a chrec against a constant, try to use value
5074 // ranges to answer this query.
5075 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
5076 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
5077 if (AddRec->getLoop() == L) {
5078 // Form the constant range.
5079 ConstantRange CompRange(
5080 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
5082 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
5083 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
5087 case ICmpInst::ICMP_NE: { // while (X != Y)
5088 // Convert to: while (X-Y != 0)
5089 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit);
5090 if (EL.hasAnyInfo()) return EL;
5093 case ICmpInst::ICMP_EQ: { // while (X == Y)
5094 // Convert to: while (X-Y == 0)
5095 ExitLimit EL = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
5096 if (EL.hasAnyInfo()) return EL;
5099 case ICmpInst::ICMP_SLT:
5100 case ICmpInst::ICMP_ULT: { // while (X < Y)
5101 bool IsSigned = Cond == ICmpInst::ICMP_SLT;
5102 ExitLimit EL = HowManyLessThans(LHS, RHS, L, IsSigned, ControlsExit);
5103 if (EL.hasAnyInfo()) return EL;
5106 case ICmpInst::ICMP_SGT:
5107 case ICmpInst::ICMP_UGT: { // while (X > Y)
5108 bool IsSigned = Cond == ICmpInst::ICMP_SGT;
5109 ExitLimit EL = HowManyGreaterThans(LHS, RHS, L, IsSigned, ControlsExit);
5110 if (EL.hasAnyInfo()) return EL;
5115 dbgs() << "ComputeBackedgeTakenCount ";
5116 if (ExitCond->getOperand(0)->getType()->isUnsigned())
5117 dbgs() << "[unsigned] ";
5118 dbgs() << *LHS << " "
5119 << Instruction::getOpcodeName(Instruction::ICmp)
5120 << " " << *RHS << "\n";
5124 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
5127 ScalarEvolution::ExitLimit
5128 ScalarEvolution::ComputeExitLimitFromSingleExitSwitch(const Loop *L,
5130 BasicBlock *ExitingBlock,
5131 bool ControlsExit) {
5132 assert(!L->contains(ExitingBlock) && "Not an exiting block!");
5134 // Give up if the exit is the default dest of a switch.
5135 if (Switch->getDefaultDest() == ExitingBlock)
5136 return getCouldNotCompute();
5138 assert(L->contains(Switch->getDefaultDest()) &&
5139 "Default case must not exit the loop!");
5140 const SCEV *LHS = getSCEVAtScope(Switch->getCondition(), L);
5141 const SCEV *RHS = getConstant(Switch->findCaseDest(ExitingBlock));
5143 // while (X != Y) --> while (X-Y != 0)
5144 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit);
5145 if (EL.hasAnyInfo())
5148 return getCouldNotCompute();
5151 static ConstantInt *
5152 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
5153 ScalarEvolution &SE) {
5154 const SCEV *InVal = SE.getConstant(C);
5155 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
5156 assert(isa<SCEVConstant>(Val) &&
5157 "Evaluation of SCEV at constant didn't fold correctly?");
5158 return cast<SCEVConstant>(Val)->getValue();
5161 /// ComputeLoadConstantCompareExitLimit - Given an exit condition of
5162 /// 'icmp op load X, cst', try to see if we can compute the backedge
5163 /// execution count.
5164 ScalarEvolution::ExitLimit
5165 ScalarEvolution::ComputeLoadConstantCompareExitLimit(
5169 ICmpInst::Predicate predicate) {
5171 if (LI->isVolatile()) return getCouldNotCompute();
5173 // Check to see if the loaded pointer is a getelementptr of a global.
5174 // TODO: Use SCEV instead of manually grubbing with GEPs.
5175 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
5176 if (!GEP) return getCouldNotCompute();
5178 // Make sure that it is really a constant global we are gepping, with an
5179 // initializer, and make sure the first IDX is really 0.
5180 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
5181 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
5182 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
5183 !cast<Constant>(GEP->getOperand(1))->isNullValue())
5184 return getCouldNotCompute();
5186 // Okay, we allow one non-constant index into the GEP instruction.
5187 Value *VarIdx = nullptr;
5188 std::vector<Constant*> Indexes;
5189 unsigned VarIdxNum = 0;
5190 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
5191 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
5192 Indexes.push_back(CI);
5193 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
5194 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
5195 VarIdx = GEP->getOperand(i);
5197 Indexes.push_back(nullptr);
5200 // Loop-invariant loads may be a byproduct of loop optimization. Skip them.
5202 return getCouldNotCompute();
5204 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
5205 // Check to see if X is a loop variant variable value now.
5206 const SCEV *Idx = getSCEV(VarIdx);
5207 Idx = getSCEVAtScope(Idx, L);
5209 // We can only recognize very limited forms of loop index expressions, in
5210 // particular, only affine AddRec's like {C1,+,C2}.
5211 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
5212 if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) ||
5213 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
5214 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
5215 return getCouldNotCompute();
5217 unsigned MaxSteps = MaxBruteForceIterations;
5218 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
5219 ConstantInt *ItCst = ConstantInt::get(
5220 cast<IntegerType>(IdxExpr->getType()), IterationNum);
5221 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
5223 // Form the GEP offset.
5224 Indexes[VarIdxNum] = Val;
5226 Constant *Result = ConstantFoldLoadThroughGEPIndices(GV->getInitializer(),
5228 if (!Result) break; // Cannot compute!
5230 // Evaluate the condition for this iteration.
5231 Result = ConstantExpr::getICmp(predicate, Result, RHS);
5232 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
5233 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
5235 dbgs() << "\n***\n*** Computed loop count " << *ItCst
5236 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
5239 ++NumArrayLenItCounts;
5240 return getConstant(ItCst); // Found terminating iteration!
5243 return getCouldNotCompute();
5247 /// CanConstantFold - Return true if we can constant fold an instruction of the
5248 /// specified type, assuming that all operands were constants.
5249 static bool CanConstantFold(const Instruction *I) {
5250 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
5251 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I) ||
5255 if (const CallInst *CI = dyn_cast<CallInst>(I))
5256 if (const Function *F = CI->getCalledFunction())
5257 return canConstantFoldCallTo(F);
5261 /// Determine whether this instruction can constant evolve within this loop
5262 /// assuming its operands can all constant evolve.
5263 static bool canConstantEvolve(Instruction *I, const Loop *L) {
5264 // An instruction outside of the loop can't be derived from a loop PHI.
5265 if (!L->contains(I)) return false;
5267 if (isa<PHINode>(I)) {
5268 if (L->getHeader() == I->getParent())
5271 // We don't currently keep track of the control flow needed to evaluate
5272 // PHIs, so we cannot handle PHIs inside of loops.
5276 // If we won't be able to constant fold this expression even if the operands
5277 // are constants, bail early.
5278 return CanConstantFold(I);
5281 /// getConstantEvolvingPHIOperands - Implement getConstantEvolvingPHI by
5282 /// recursing through each instruction operand until reaching a loop header phi.
5284 getConstantEvolvingPHIOperands(Instruction *UseInst, const Loop *L,
5285 DenseMap<Instruction *, PHINode *> &PHIMap) {
5287 // Otherwise, we can evaluate this instruction if all of its operands are
5288 // constant or derived from a PHI node themselves.
5289 PHINode *PHI = nullptr;
5290 for (Instruction::op_iterator OpI = UseInst->op_begin(),
5291 OpE = UseInst->op_end(); OpI != OpE; ++OpI) {
5293 if (isa<Constant>(*OpI)) continue;
5295 Instruction *OpInst = dyn_cast<Instruction>(*OpI);
5296 if (!OpInst || !canConstantEvolve(OpInst, L)) return nullptr;
5298 PHINode *P = dyn_cast<PHINode>(OpInst);
5300 // If this operand is already visited, reuse the prior result.
5301 // We may have P != PHI if this is the deepest point at which the
5302 // inconsistent paths meet.
5303 P = PHIMap.lookup(OpInst);
5305 // Recurse and memoize the results, whether a phi is found or not.
5306 // This recursive call invalidates pointers into PHIMap.
5307 P = getConstantEvolvingPHIOperands(OpInst, L, PHIMap);
5311 return nullptr; // Not evolving from PHI
5312 if (PHI && PHI != P)
5313 return nullptr; // Evolving from multiple different PHIs.
5316 // This is a expression evolving from a constant PHI!
5320 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
5321 /// in the loop that V is derived from. We allow arbitrary operations along the
5322 /// way, but the operands of an operation must either be constants or a value
5323 /// derived from a constant PHI. If this expression does not fit with these
5324 /// constraints, return null.
5325 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
5326 Instruction *I = dyn_cast<Instruction>(V);
5327 if (!I || !canConstantEvolve(I, L)) return nullptr;
5329 if (PHINode *PN = dyn_cast<PHINode>(I)) {
5333 // Record non-constant instructions contained by the loop.
5334 DenseMap<Instruction *, PHINode *> PHIMap;
5335 return getConstantEvolvingPHIOperands(I, L, PHIMap);
5338 /// EvaluateExpression - Given an expression that passes the
5339 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
5340 /// in the loop has the value PHIVal. If we can't fold this expression for some
5341 /// reason, return null.
5342 static Constant *EvaluateExpression(Value *V, const Loop *L,
5343 DenseMap<Instruction *, Constant *> &Vals,
5344 const DataLayout *DL,
5345 const TargetLibraryInfo *TLI) {
5346 // Convenient constant check, but redundant for recursive calls.
5347 if (Constant *C = dyn_cast<Constant>(V)) return C;
5348 Instruction *I = dyn_cast<Instruction>(V);
5349 if (!I) return nullptr;
5351 if (Constant *C = Vals.lookup(I)) return C;
5353 // An instruction inside the loop depends on a value outside the loop that we
5354 // weren't given a mapping for, or a value such as a call inside the loop.
5355 if (!canConstantEvolve(I, L)) return nullptr;
5357 // An unmapped PHI can be due to a branch or another loop inside this loop,
5358 // or due to this not being the initial iteration through a loop where we
5359 // couldn't compute the evolution of this particular PHI last time.
5360 if (isa<PHINode>(I)) return nullptr;
5362 std::vector<Constant*> Operands(I->getNumOperands());
5364 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
5365 Instruction *Operand = dyn_cast<Instruction>(I->getOperand(i));
5367 Operands[i] = dyn_cast<Constant>(I->getOperand(i));
5368 if (!Operands[i]) return nullptr;
5371 Constant *C = EvaluateExpression(Operand, L, Vals, DL, TLI);
5373 if (!C) return nullptr;
5377 if (CmpInst *CI = dyn_cast<CmpInst>(I))
5378 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
5379 Operands[1], DL, TLI);
5380 if (LoadInst *LI = dyn_cast<LoadInst>(I)) {
5381 if (!LI->isVolatile())
5382 return ConstantFoldLoadFromConstPtr(Operands[0], DL);
5384 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), Operands, DL,
5388 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
5389 /// in the header of its containing loop, we know the loop executes a
5390 /// constant number of times, and the PHI node is just a recurrence
5391 /// involving constants, fold it.
5393 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
5396 DenseMap<PHINode*, Constant*>::const_iterator I =
5397 ConstantEvolutionLoopExitValue.find(PN);
5398 if (I != ConstantEvolutionLoopExitValue.end())
5401 if (BEs.ugt(MaxBruteForceIterations))
5402 return ConstantEvolutionLoopExitValue[PN] = nullptr; // Not going to evaluate it.
5404 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
5406 DenseMap<Instruction *, Constant *> CurrentIterVals;
5407 BasicBlock *Header = L->getHeader();
5408 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
5410 // Since the loop is canonicalized, the PHI node must have two entries. One
5411 // entry must be a constant (coming in from outside of the loop), and the
5412 // second must be derived from the same PHI.
5413 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
5414 PHINode *PHI = nullptr;
5415 for (BasicBlock::iterator I = Header->begin();
5416 (PHI = dyn_cast<PHINode>(I)); ++I) {
5417 Constant *StartCST =
5418 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
5419 if (!StartCST) continue;
5420 CurrentIterVals[PHI] = StartCST;
5422 if (!CurrentIterVals.count(PN))
5423 return RetVal = nullptr;
5425 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
5427 // Execute the loop symbolically to determine the exit value.
5428 if (BEs.getActiveBits() >= 32)
5429 return RetVal = nullptr; // More than 2^32-1 iterations?? Not doing it!
5431 unsigned NumIterations = BEs.getZExtValue(); // must be in range
5432 unsigned IterationNum = 0;
5433 for (; ; ++IterationNum) {
5434 if (IterationNum == NumIterations)
5435 return RetVal = CurrentIterVals[PN]; // Got exit value!
5437 // Compute the value of the PHIs for the next iteration.
5438 // EvaluateExpression adds non-phi values to the CurrentIterVals map.
5439 DenseMap<Instruction *, Constant *> NextIterVals;
5440 Constant *NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL,
5443 return nullptr; // Couldn't evaluate!
5444 NextIterVals[PN] = NextPHI;
5446 bool StoppedEvolving = NextPHI == CurrentIterVals[PN];
5448 // Also evaluate the other PHI nodes. However, we don't get to stop if we
5449 // cease to be able to evaluate one of them or if they stop evolving,
5450 // because that doesn't necessarily prevent us from computing PN.
5451 SmallVector<std::pair<PHINode *, Constant *>, 8> PHIsToCompute;
5452 for (DenseMap<Instruction *, Constant *>::const_iterator
5453 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
5454 PHINode *PHI = dyn_cast<PHINode>(I->first);
5455 if (!PHI || PHI == PN || PHI->getParent() != Header) continue;
5456 PHIsToCompute.push_back(std::make_pair(PHI, I->second));
5458 // We use two distinct loops because EvaluateExpression may invalidate any
5459 // iterators into CurrentIterVals.
5460 for (SmallVectorImpl<std::pair<PHINode *, Constant*> >::const_iterator
5461 I = PHIsToCompute.begin(), E = PHIsToCompute.end(); I != E; ++I) {
5462 PHINode *PHI = I->first;
5463 Constant *&NextPHI = NextIterVals[PHI];
5464 if (!NextPHI) { // Not already computed.
5465 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
5466 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, TLI);
5468 if (NextPHI != I->second)
5469 StoppedEvolving = false;
5472 // If all entries in CurrentIterVals == NextIterVals then we can stop
5473 // iterating, the loop can't continue to change.
5474 if (StoppedEvolving)
5475 return RetVal = CurrentIterVals[PN];
5477 CurrentIterVals.swap(NextIterVals);
5481 /// ComputeExitCountExhaustively - If the loop is known to execute a
5482 /// constant number of times (the condition evolves only from constants),
5483 /// try to evaluate a few iterations of the loop until we get the exit
5484 /// condition gets a value of ExitWhen (true or false). If we cannot
5485 /// evaluate the trip count of the loop, return getCouldNotCompute().
5486 const SCEV *ScalarEvolution::ComputeExitCountExhaustively(const Loop *L,
5489 PHINode *PN = getConstantEvolvingPHI(Cond, L);
5490 if (!PN) return getCouldNotCompute();
5492 // If the loop is canonicalized, the PHI will have exactly two entries.
5493 // That's the only form we support here.
5494 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
5496 DenseMap<Instruction *, Constant *> CurrentIterVals;
5497 BasicBlock *Header = L->getHeader();
5498 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
5500 // One entry must be a constant (coming in from outside of the loop), and the
5501 // second must be derived from the same PHI.
5502 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
5503 PHINode *PHI = nullptr;
5504 for (BasicBlock::iterator I = Header->begin();
5505 (PHI = dyn_cast<PHINode>(I)); ++I) {
5506 Constant *StartCST =
5507 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
5508 if (!StartCST) continue;
5509 CurrentIterVals[PHI] = StartCST;
5511 if (!CurrentIterVals.count(PN))
5512 return getCouldNotCompute();
5514 // Okay, we find a PHI node that defines the trip count of this loop. Execute
5515 // the loop symbolically to determine when the condition gets a value of
5518 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
5519 for (unsigned IterationNum = 0; IterationNum != MaxIterations;++IterationNum){
5520 ConstantInt *CondVal =
5521 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, L, CurrentIterVals,
5524 // Couldn't symbolically evaluate.
5525 if (!CondVal) return getCouldNotCompute();
5527 if (CondVal->getValue() == uint64_t(ExitWhen)) {
5528 ++NumBruteForceTripCountsComputed;
5529 return getConstant(Type::getInt32Ty(getContext()), IterationNum);
5532 // Update all the PHI nodes for the next iteration.
5533 DenseMap<Instruction *, Constant *> NextIterVals;
5535 // Create a list of which PHIs we need to compute. We want to do this before
5536 // calling EvaluateExpression on them because that may invalidate iterators
5537 // into CurrentIterVals.
5538 SmallVector<PHINode *, 8> PHIsToCompute;
5539 for (DenseMap<Instruction *, Constant *>::const_iterator
5540 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
5541 PHINode *PHI = dyn_cast<PHINode>(I->first);
5542 if (!PHI || PHI->getParent() != Header) continue;
5543 PHIsToCompute.push_back(PHI);
5545 for (SmallVectorImpl<PHINode *>::const_iterator I = PHIsToCompute.begin(),
5546 E = PHIsToCompute.end(); I != E; ++I) {
5548 Constant *&NextPHI = NextIterVals[PHI];
5549 if (NextPHI) continue; // Already computed!
5551 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
5552 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, TLI);
5554 CurrentIterVals.swap(NextIterVals);
5557 // Too many iterations were needed to evaluate.
5558 return getCouldNotCompute();
5561 /// getSCEVAtScope - Return a SCEV expression for the specified value
5562 /// at the specified scope in the program. The L value specifies a loop
5563 /// nest to evaluate the expression at, where null is the top-level or a
5564 /// specified loop is immediately inside of the loop.
5566 /// This method can be used to compute the exit value for a variable defined
5567 /// in a loop by querying what the value will hold in the parent loop.
5569 /// In the case that a relevant loop exit value cannot be computed, the
5570 /// original value V is returned.
5571 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
5572 // Check to see if we've folded this expression at this loop before.
5573 SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values = ValuesAtScopes[V];
5574 for (unsigned u = 0; u < Values.size(); u++) {
5575 if (Values[u].first == L)
5576 return Values[u].second ? Values[u].second : V;
5578 Values.push_back(std::make_pair(L, static_cast<const SCEV *>(nullptr)));
5579 // Otherwise compute it.
5580 const SCEV *C = computeSCEVAtScope(V, L);
5581 SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values2 = ValuesAtScopes[V];
5582 for (unsigned u = Values2.size(); u > 0; u--) {
5583 if (Values2[u - 1].first == L) {
5584 Values2[u - 1].second = C;
5591 /// This builds up a Constant using the ConstantExpr interface. That way, we
5592 /// will return Constants for objects which aren't represented by a
5593 /// SCEVConstant, because SCEVConstant is restricted to ConstantInt.
5594 /// Returns NULL if the SCEV isn't representable as a Constant.
5595 static Constant *BuildConstantFromSCEV(const SCEV *V) {
5596 switch (static_cast<SCEVTypes>(V->getSCEVType())) {
5597 case scCouldNotCompute:
5601 return cast<SCEVConstant>(V)->getValue();
5603 return dyn_cast<Constant>(cast<SCEVUnknown>(V)->getValue());
5604 case scSignExtend: {
5605 const SCEVSignExtendExpr *SS = cast<SCEVSignExtendExpr>(V);
5606 if (Constant *CastOp = BuildConstantFromSCEV(SS->getOperand()))
5607 return ConstantExpr::getSExt(CastOp, SS->getType());
5610 case scZeroExtend: {
5611 const SCEVZeroExtendExpr *SZ = cast<SCEVZeroExtendExpr>(V);
5612 if (Constant *CastOp = BuildConstantFromSCEV(SZ->getOperand()))
5613 return ConstantExpr::getZExt(CastOp, SZ->getType());
5617 const SCEVTruncateExpr *ST = cast<SCEVTruncateExpr>(V);
5618 if (Constant *CastOp = BuildConstantFromSCEV(ST->getOperand()))
5619 return ConstantExpr::getTrunc(CastOp, ST->getType());
5623 const SCEVAddExpr *SA = cast<SCEVAddExpr>(V);
5624 if (Constant *C = BuildConstantFromSCEV(SA->getOperand(0))) {
5625 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
5626 unsigned AS = PTy->getAddressSpace();
5627 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
5628 C = ConstantExpr::getBitCast(C, DestPtrTy);
5630 for (unsigned i = 1, e = SA->getNumOperands(); i != e; ++i) {
5631 Constant *C2 = BuildConstantFromSCEV(SA->getOperand(i));
5632 if (!C2) return nullptr;
5635 if (!C->getType()->isPointerTy() && C2->getType()->isPointerTy()) {
5636 unsigned AS = C2->getType()->getPointerAddressSpace();
5638 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
5639 // The offsets have been converted to bytes. We can add bytes to an
5640 // i8* by GEP with the byte count in the first index.
5641 C = ConstantExpr::getBitCast(C, DestPtrTy);
5644 // Don't bother trying to sum two pointers. We probably can't
5645 // statically compute a load that results from it anyway.
5646 if (C2->getType()->isPointerTy())
5649 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
5650 if (PTy->getElementType()->isStructTy())
5651 C2 = ConstantExpr::getIntegerCast(
5652 C2, Type::getInt32Ty(C->getContext()), true);
5653 C = ConstantExpr::getGetElementPtr(C, C2);
5655 C = ConstantExpr::getAdd(C, C2);
5662 const SCEVMulExpr *SM = cast<SCEVMulExpr>(V);
5663 if (Constant *C = BuildConstantFromSCEV(SM->getOperand(0))) {
5664 // Don't bother with pointers at all.
5665 if (C->getType()->isPointerTy()) return nullptr;
5666 for (unsigned i = 1, e = SM->getNumOperands(); i != e; ++i) {
5667 Constant *C2 = BuildConstantFromSCEV(SM->getOperand(i));
5668 if (!C2 || C2->getType()->isPointerTy()) return nullptr;
5669 C = ConstantExpr::getMul(C, C2);
5676 const SCEVUDivExpr *SU = cast<SCEVUDivExpr>(V);
5677 if (Constant *LHS = BuildConstantFromSCEV(SU->getLHS()))
5678 if (Constant *RHS = BuildConstantFromSCEV(SU->getRHS()))
5679 if (LHS->getType() == RHS->getType())
5680 return ConstantExpr::getUDiv(LHS, RHS);
5685 break; // TODO: smax, umax.
5690 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
5691 if (isa<SCEVConstant>(V)) return V;
5693 // If this instruction is evolved from a constant-evolving PHI, compute the
5694 // exit value from the loop without using SCEVs.
5695 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
5696 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
5697 const Loop *LI = (*this->LI)[I->getParent()];
5698 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
5699 if (PHINode *PN = dyn_cast<PHINode>(I))
5700 if (PN->getParent() == LI->getHeader()) {
5701 // Okay, there is no closed form solution for the PHI node. Check
5702 // to see if the loop that contains it has a known backedge-taken
5703 // count. If so, we may be able to force computation of the exit
5705 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
5706 if (const SCEVConstant *BTCC =
5707 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
5708 // Okay, we know how many times the containing loop executes. If
5709 // this is a constant evolving PHI node, get the final value at
5710 // the specified iteration number.
5711 Constant *RV = getConstantEvolutionLoopExitValue(PN,
5712 BTCC->getValue()->getValue(),
5714 if (RV) return getSCEV(RV);
5718 // Okay, this is an expression that we cannot symbolically evaluate
5719 // into a SCEV. Check to see if it's possible to symbolically evaluate
5720 // the arguments into constants, and if so, try to constant propagate the
5721 // result. This is particularly useful for computing loop exit values.
5722 if (CanConstantFold(I)) {
5723 SmallVector<Constant *, 4> Operands;
5724 bool MadeImprovement = false;
5725 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
5726 Value *Op = I->getOperand(i);
5727 if (Constant *C = dyn_cast<Constant>(Op)) {
5728 Operands.push_back(C);
5732 // If any of the operands is non-constant and if they are
5733 // non-integer and non-pointer, don't even try to analyze them
5734 // with scev techniques.
5735 if (!isSCEVable(Op->getType()))
5738 const SCEV *OrigV = getSCEV(Op);
5739 const SCEV *OpV = getSCEVAtScope(OrigV, L);
5740 MadeImprovement |= OrigV != OpV;
5742 Constant *C = BuildConstantFromSCEV(OpV);
5744 if (C->getType() != Op->getType())
5745 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
5749 Operands.push_back(C);
5752 // Check to see if getSCEVAtScope actually made an improvement.
5753 if (MadeImprovement) {
5754 Constant *C = nullptr;
5755 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
5756 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
5757 Operands[0], Operands[1], DL,
5759 else if (const LoadInst *LI = dyn_cast<LoadInst>(I)) {
5760 if (!LI->isVolatile())
5761 C = ConstantFoldLoadFromConstPtr(Operands[0], DL);
5763 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
5771 // This is some other type of SCEVUnknown, just return it.
5775 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
5776 // Avoid performing the look-up in the common case where the specified
5777 // expression has no loop-variant portions.
5778 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
5779 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
5780 if (OpAtScope != Comm->getOperand(i)) {
5781 // Okay, at least one of these operands is loop variant but might be
5782 // foldable. Build a new instance of the folded commutative expression.
5783 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
5784 Comm->op_begin()+i);
5785 NewOps.push_back(OpAtScope);
5787 for (++i; i != e; ++i) {
5788 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
5789 NewOps.push_back(OpAtScope);
5791 if (isa<SCEVAddExpr>(Comm))
5792 return getAddExpr(NewOps);
5793 if (isa<SCEVMulExpr>(Comm))
5794 return getMulExpr(NewOps);
5795 if (isa<SCEVSMaxExpr>(Comm))
5796 return getSMaxExpr(NewOps);
5797 if (isa<SCEVUMaxExpr>(Comm))
5798 return getUMaxExpr(NewOps);
5799 llvm_unreachable("Unknown commutative SCEV type!");
5802 // If we got here, all operands are loop invariant.
5806 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
5807 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
5808 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
5809 if (LHS == Div->getLHS() && RHS == Div->getRHS())
5810 return Div; // must be loop invariant
5811 return getUDivExpr(LHS, RHS);
5814 // If this is a loop recurrence for a loop that does not contain L, then we
5815 // are dealing with the final value computed by the loop.
5816 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
5817 // First, attempt to evaluate each operand.
5818 // Avoid performing the look-up in the common case where the specified
5819 // expression has no loop-variant portions.
5820 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
5821 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
5822 if (OpAtScope == AddRec->getOperand(i))
5825 // Okay, at least one of these operands is loop variant but might be
5826 // foldable. Build a new instance of the folded commutative expression.
5827 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(),
5828 AddRec->op_begin()+i);
5829 NewOps.push_back(OpAtScope);
5830 for (++i; i != e; ++i)
5831 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
5833 const SCEV *FoldedRec =
5834 getAddRecExpr(NewOps, AddRec->getLoop(),
5835 AddRec->getNoWrapFlags(SCEV::FlagNW));
5836 AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec);
5837 // The addrec may be folded to a nonrecurrence, for example, if the
5838 // induction variable is multiplied by zero after constant folding. Go
5839 // ahead and return the folded value.
5845 // If the scope is outside the addrec's loop, evaluate it by using the
5846 // loop exit value of the addrec.
5847 if (!AddRec->getLoop()->contains(L)) {
5848 // To evaluate this recurrence, we need to know how many times the AddRec
5849 // loop iterates. Compute this now.
5850 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
5851 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
5853 // Then, evaluate the AddRec.
5854 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
5860 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
5861 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5862 if (Op == Cast->getOperand())
5863 return Cast; // must be loop invariant
5864 return getZeroExtendExpr(Op, Cast->getType());
5867 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
5868 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5869 if (Op == Cast->getOperand())
5870 return Cast; // must be loop invariant
5871 return getSignExtendExpr(Op, Cast->getType());
5874 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
5875 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5876 if (Op == Cast->getOperand())
5877 return Cast; // must be loop invariant
5878 return getTruncateExpr(Op, Cast->getType());
5881 llvm_unreachable("Unknown SCEV type!");
5884 /// getSCEVAtScope - This is a convenience function which does
5885 /// getSCEVAtScope(getSCEV(V), L).
5886 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
5887 return getSCEVAtScope(getSCEV(V), L);
5890 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
5891 /// following equation:
5893 /// A * X = B (mod N)
5895 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
5896 /// A and B isn't important.
5898 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
5899 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
5900 ScalarEvolution &SE) {
5901 uint32_t BW = A.getBitWidth();
5902 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
5903 assert(A != 0 && "A must be non-zero.");
5907 // The gcd of A and N may have only one prime factor: 2. The number of
5908 // trailing zeros in A is its multiplicity
5909 uint32_t Mult2 = A.countTrailingZeros();
5912 // 2. Check if B is divisible by D.
5914 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
5915 // is not less than multiplicity of this prime factor for D.
5916 if (B.countTrailingZeros() < Mult2)
5917 return SE.getCouldNotCompute();
5919 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
5922 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
5923 // bit width during computations.
5924 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
5925 APInt Mod(BW + 1, 0);
5926 Mod.setBit(BW - Mult2); // Mod = N / D
5927 APInt I = AD.multiplicativeInverse(Mod);
5929 // 4. Compute the minimum unsigned root of the equation:
5930 // I * (B / D) mod (N / D)
5931 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
5933 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
5935 return SE.getConstant(Result.trunc(BW));
5938 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
5939 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
5940 /// might be the same) or two SCEVCouldNotCompute objects.
5942 static std::pair<const SCEV *,const SCEV *>
5943 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
5944 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
5945 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
5946 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
5947 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
5949 // We currently can only solve this if the coefficients are constants.
5950 if (!LC || !MC || !NC) {
5951 const SCEV *CNC = SE.getCouldNotCompute();
5952 return std::make_pair(CNC, CNC);
5955 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
5956 const APInt &L = LC->getValue()->getValue();
5957 const APInt &M = MC->getValue()->getValue();
5958 const APInt &N = NC->getValue()->getValue();
5959 APInt Two(BitWidth, 2);
5960 APInt Four(BitWidth, 4);
5963 using namespace APIntOps;
5965 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
5966 // The B coefficient is M-N/2
5970 // The A coefficient is N/2
5971 APInt A(N.sdiv(Two));
5973 // Compute the B^2-4ac term.
5976 SqrtTerm -= Four * (A * C);
5978 if (SqrtTerm.isNegative()) {
5979 // The loop is provably infinite.
5980 const SCEV *CNC = SE.getCouldNotCompute();
5981 return std::make_pair(CNC, CNC);
5984 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
5985 // integer value or else APInt::sqrt() will assert.
5986 APInt SqrtVal(SqrtTerm.sqrt());
5988 // Compute the two solutions for the quadratic formula.
5989 // The divisions must be performed as signed divisions.
5992 if (TwoA.isMinValue()) {
5993 const SCEV *CNC = SE.getCouldNotCompute();
5994 return std::make_pair(CNC, CNC);
5997 LLVMContext &Context = SE.getContext();
5999 ConstantInt *Solution1 =
6000 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
6001 ConstantInt *Solution2 =
6002 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
6004 return std::make_pair(SE.getConstant(Solution1),
6005 SE.getConstant(Solution2));
6006 } // end APIntOps namespace
6009 /// HowFarToZero - Return the number of times a backedge comparing the specified
6010 /// value to zero will execute. If not computable, return CouldNotCompute.
6012 /// This is only used for loops with a "x != y" exit test. The exit condition is
6013 /// now expressed as a single expression, V = x-y. So the exit test is
6014 /// effectively V != 0. We know and take advantage of the fact that this
6015 /// expression only being used in a comparison by zero context.
6016 ScalarEvolution::ExitLimit
6017 ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L, bool ControlsExit) {
6018 // If the value is a constant
6019 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
6020 // If the value is already zero, the branch will execute zero times.
6021 if (C->getValue()->isZero()) return C;
6022 return getCouldNotCompute(); // Otherwise it will loop infinitely.
6025 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
6026 if (!AddRec || AddRec->getLoop() != L)
6027 return getCouldNotCompute();
6029 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
6030 // the quadratic equation to solve it.
6031 if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
6032 std::pair<const SCEV *,const SCEV *> Roots =
6033 SolveQuadraticEquation(AddRec, *this);
6034 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
6035 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
6038 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1
6039 << " sol#2: " << *R2 << "\n";
6041 // Pick the smallest positive root value.
6042 if (ConstantInt *CB =
6043 dyn_cast<ConstantInt>(ConstantExpr::getICmp(CmpInst::ICMP_ULT,
6046 if (CB->getZExtValue() == false)
6047 std::swap(R1, R2); // R1 is the minimum root now.
6049 // We can only use this value if the chrec ends up with an exact zero
6050 // value at this index. When solving for "X*X != 5", for example, we
6051 // should not accept a root of 2.
6052 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
6054 return R1; // We found a quadratic root!
6057 return getCouldNotCompute();
6060 // Otherwise we can only handle this if it is affine.
6061 if (!AddRec->isAffine())
6062 return getCouldNotCompute();
6064 // If this is an affine expression, the execution count of this branch is
6065 // the minimum unsigned root of the following equation:
6067 // Start + Step*N = 0 (mod 2^BW)
6071 // Step*N = -Start (mod 2^BW)
6073 // where BW is the common bit width of Start and Step.
6075 // Get the initial value for the loop.
6076 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
6077 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
6079 // For now we handle only constant steps.
6081 // TODO: Handle a nonconstant Step given AddRec<NUW>. If the
6082 // AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap
6083 // to 0, it must be counting down to equal 0. Consequently, N = Start / -Step.
6084 // We have not yet seen any such cases.
6085 const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step);
6086 if (!StepC || StepC->getValue()->equalsInt(0))
6087 return getCouldNotCompute();
6089 // For positive steps (counting up until unsigned overflow):
6090 // N = -Start/Step (as unsigned)
6091 // For negative steps (counting down to zero):
6093 // First compute the unsigned distance from zero in the direction of Step.
6094 bool CountDown = StepC->getValue()->getValue().isNegative();
6095 const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start);
6097 // Handle unitary steps, which cannot wraparound.
6098 // 1*N = -Start; -1*N = Start (mod 2^BW), so:
6099 // N = Distance (as unsigned)
6100 if (StepC->getValue()->equalsInt(1) || StepC->getValue()->isAllOnesValue()) {
6101 ConstantRange CR = getUnsignedRange(Start);
6102 const SCEV *MaxBECount;
6103 if (!CountDown && CR.getUnsignedMin().isMinValue())
6104 // When counting up, the worst starting value is 1, not 0.
6105 MaxBECount = CR.getUnsignedMax().isMinValue()
6106 ? getConstant(APInt::getMinValue(CR.getBitWidth()))
6107 : getConstant(APInt::getMaxValue(CR.getBitWidth()));
6109 MaxBECount = getConstant(CountDown ? CR.getUnsignedMax()
6110 : -CR.getUnsignedMin());
6111 return ExitLimit(Distance, MaxBECount);
6114 // As a special case, handle the instance where Step is a positive power of
6115 // two. In this case, determining whether Step divides Distance evenly can be
6116 // done by counting and comparing the number of trailing zeros of Step and
6119 const APInt &StepV = StepC->getValue()->getValue();
6120 // StepV.isPowerOf2() returns true if StepV is an positive power of two. It
6121 // also returns true if StepV is maximally negative (eg, INT_MIN), but that
6122 // case is not handled as this code is guarded by !CountDown.
6123 if (StepV.isPowerOf2() &&
6124 GetMinTrailingZeros(Distance) >= StepV.countTrailingZeros())
6125 return getUDivExactExpr(Distance, Step);
6128 // If the condition controls loop exit (the loop exits only if the expression
6129 // is true) and the addition is no-wrap we can use unsigned divide to
6130 // compute the backedge count. In this case, the step may not divide the
6131 // distance, but we don't care because if the condition is "missed" the loop
6132 // will have undefined behavior due to wrapping.
6133 if (ControlsExit && AddRec->getNoWrapFlags(SCEV::FlagNW)) {
6135 getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
6136 return ExitLimit(Exact, Exact);
6139 // Then, try to solve the above equation provided that Start is constant.
6140 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
6141 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
6142 -StartC->getValue()->getValue(),
6144 return getCouldNotCompute();
6147 /// HowFarToNonZero - Return the number of times a backedge checking the
6148 /// specified value for nonzero will execute. If not computable, return
6150 ScalarEvolution::ExitLimit
6151 ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
6152 // Loops that look like: while (X == 0) are very strange indeed. We don't
6153 // handle them yet except for the trivial case. This could be expanded in the
6154 // future as needed.
6156 // If the value is a constant, check to see if it is known to be non-zero
6157 // already. If so, the backedge will execute zero times.
6158 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
6159 if (!C->getValue()->isNullValue())
6160 return getConstant(C->getType(), 0);
6161 return getCouldNotCompute(); // Otherwise it will loop infinitely.
6164 // We could implement others, but I really doubt anyone writes loops like
6165 // this, and if they did, they would already be constant folded.
6166 return getCouldNotCompute();
6169 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
6170 /// (which may not be an immediate predecessor) which has exactly one
6171 /// successor from which BB is reachable, or null if no such block is
6174 std::pair<BasicBlock *, BasicBlock *>
6175 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
6176 // If the block has a unique predecessor, then there is no path from the
6177 // predecessor to the block that does not go through the direct edge
6178 // from the predecessor to the block.
6179 if (BasicBlock *Pred = BB->getSinglePredecessor())
6180 return std::make_pair(Pred, BB);
6182 // A loop's header is defined to be a block that dominates the loop.
6183 // If the header has a unique predecessor outside the loop, it must be
6184 // a block that has exactly one successor that can reach the loop.
6185 if (Loop *L = LI->getLoopFor(BB))
6186 return std::make_pair(L->getLoopPredecessor(), L->getHeader());
6188 return std::pair<BasicBlock *, BasicBlock *>();
6191 /// HasSameValue - SCEV structural equivalence is usually sufficient for
6192 /// testing whether two expressions are equal, however for the purposes of
6193 /// looking for a condition guarding a loop, it can be useful to be a little
6194 /// more general, since a front-end may have replicated the controlling
6197 static bool HasSameValue(const SCEV *A, const SCEV *B) {
6198 // Quick check to see if they are the same SCEV.
6199 if (A == B) return true;
6201 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
6202 // two different instructions with the same value. Check for this case.
6203 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
6204 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
6205 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
6206 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
6207 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory())
6210 // Otherwise assume they may have a different value.
6214 /// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with
6215 /// predicate Pred. Return true iff any changes were made.
6217 bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
6218 const SCEV *&LHS, const SCEV *&RHS,
6220 bool Changed = false;
6222 // If we hit the max recursion limit bail out.
6226 // Canonicalize a constant to the right side.
6227 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
6228 // Check for both operands constant.
6229 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
6230 if (ConstantExpr::getICmp(Pred,
6232 RHSC->getValue())->isNullValue())
6233 goto trivially_false;
6235 goto trivially_true;
6237 // Otherwise swap the operands to put the constant on the right.
6238 std::swap(LHS, RHS);
6239 Pred = ICmpInst::getSwappedPredicate(Pred);
6243 // If we're comparing an addrec with a value which is loop-invariant in the
6244 // addrec's loop, put the addrec on the left. Also make a dominance check,
6245 // as both operands could be addrecs loop-invariant in each other's loop.
6246 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
6247 const Loop *L = AR->getLoop();
6248 if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) {
6249 std::swap(LHS, RHS);
6250 Pred = ICmpInst::getSwappedPredicate(Pred);
6255 // If there's a constant operand, canonicalize comparisons with boundary
6256 // cases, and canonicalize *-or-equal comparisons to regular comparisons.
6257 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
6258 const APInt &RA = RC->getValue()->getValue();
6260 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6261 case ICmpInst::ICMP_EQ:
6262 case ICmpInst::ICMP_NE:
6263 // Fold ((-1) * %a) + %b == 0 (equivalent to %b-%a == 0) into %a == %b.
6265 if (const SCEVAddExpr *AE = dyn_cast<SCEVAddExpr>(LHS))
6266 if (const SCEVMulExpr *ME = dyn_cast<SCEVMulExpr>(AE->getOperand(0)))
6267 if (AE->getNumOperands() == 2 && ME->getNumOperands() == 2 &&
6268 ME->getOperand(0)->isAllOnesValue()) {
6269 RHS = AE->getOperand(1);
6270 LHS = ME->getOperand(1);
6274 case ICmpInst::ICMP_UGE:
6275 if ((RA - 1).isMinValue()) {
6276 Pred = ICmpInst::ICMP_NE;
6277 RHS = getConstant(RA - 1);
6281 if (RA.isMaxValue()) {
6282 Pred = ICmpInst::ICMP_EQ;
6286 if (RA.isMinValue()) goto trivially_true;
6288 Pred = ICmpInst::ICMP_UGT;
6289 RHS = getConstant(RA - 1);
6292 case ICmpInst::ICMP_ULE:
6293 if ((RA + 1).isMaxValue()) {
6294 Pred = ICmpInst::ICMP_NE;
6295 RHS = getConstant(RA + 1);
6299 if (RA.isMinValue()) {
6300 Pred = ICmpInst::ICMP_EQ;
6304 if (RA.isMaxValue()) goto trivially_true;
6306 Pred = ICmpInst::ICMP_ULT;
6307 RHS = getConstant(RA + 1);
6310 case ICmpInst::ICMP_SGE:
6311 if ((RA - 1).isMinSignedValue()) {
6312 Pred = ICmpInst::ICMP_NE;
6313 RHS = getConstant(RA - 1);
6317 if (RA.isMaxSignedValue()) {
6318 Pred = ICmpInst::ICMP_EQ;
6322 if (RA.isMinSignedValue()) goto trivially_true;
6324 Pred = ICmpInst::ICMP_SGT;
6325 RHS = getConstant(RA - 1);
6328 case ICmpInst::ICMP_SLE:
6329 if ((RA + 1).isMaxSignedValue()) {
6330 Pred = ICmpInst::ICMP_NE;
6331 RHS = getConstant(RA + 1);
6335 if (RA.isMinSignedValue()) {
6336 Pred = ICmpInst::ICMP_EQ;
6340 if (RA.isMaxSignedValue()) goto trivially_true;
6342 Pred = ICmpInst::ICMP_SLT;
6343 RHS = getConstant(RA + 1);
6346 case ICmpInst::ICMP_UGT:
6347 if (RA.isMinValue()) {
6348 Pred = ICmpInst::ICMP_NE;
6352 if ((RA + 1).isMaxValue()) {
6353 Pred = ICmpInst::ICMP_EQ;
6354 RHS = getConstant(RA + 1);
6358 if (RA.isMaxValue()) goto trivially_false;
6360 case ICmpInst::ICMP_ULT:
6361 if (RA.isMaxValue()) {
6362 Pred = ICmpInst::ICMP_NE;
6366 if ((RA - 1).isMinValue()) {
6367 Pred = ICmpInst::ICMP_EQ;
6368 RHS = getConstant(RA - 1);
6372 if (RA.isMinValue()) goto trivially_false;
6374 case ICmpInst::ICMP_SGT:
6375 if (RA.isMinSignedValue()) {
6376 Pred = ICmpInst::ICMP_NE;
6380 if ((RA + 1).isMaxSignedValue()) {
6381 Pred = ICmpInst::ICMP_EQ;
6382 RHS = getConstant(RA + 1);
6386 if (RA.isMaxSignedValue()) goto trivially_false;
6388 case ICmpInst::ICMP_SLT:
6389 if (RA.isMaxSignedValue()) {
6390 Pred = ICmpInst::ICMP_NE;
6394 if ((RA - 1).isMinSignedValue()) {
6395 Pred = ICmpInst::ICMP_EQ;
6396 RHS = getConstant(RA - 1);
6400 if (RA.isMinSignedValue()) goto trivially_false;
6405 // Check for obvious equality.
6406 if (HasSameValue(LHS, RHS)) {
6407 if (ICmpInst::isTrueWhenEqual(Pred))
6408 goto trivially_true;
6409 if (ICmpInst::isFalseWhenEqual(Pred))
6410 goto trivially_false;
6413 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
6414 // adding or subtracting 1 from one of the operands.
6416 case ICmpInst::ICMP_SLE:
6417 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) {
6418 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
6420 Pred = ICmpInst::ICMP_SLT;
6422 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) {
6423 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
6425 Pred = ICmpInst::ICMP_SLT;
6429 case ICmpInst::ICMP_SGE:
6430 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) {
6431 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
6433 Pred = ICmpInst::ICMP_SGT;
6435 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) {
6436 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
6438 Pred = ICmpInst::ICMP_SGT;
6442 case ICmpInst::ICMP_ULE:
6443 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) {
6444 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
6446 Pred = ICmpInst::ICMP_ULT;
6448 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) {
6449 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
6451 Pred = ICmpInst::ICMP_ULT;
6455 case ICmpInst::ICMP_UGE:
6456 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) {
6457 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
6459 Pred = ICmpInst::ICMP_UGT;
6461 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) {
6462 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
6464 Pred = ICmpInst::ICMP_UGT;
6472 // TODO: More simplifications are possible here.
6474 // Recursively simplify until we either hit a recursion limit or nothing
6477 return SimplifyICmpOperands(Pred, LHS, RHS, Depth+1);
6483 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
6484 Pred = ICmpInst::ICMP_EQ;
6489 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
6490 Pred = ICmpInst::ICMP_NE;
6494 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
6495 return getSignedRange(S).getSignedMax().isNegative();
6498 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
6499 return getSignedRange(S).getSignedMin().isStrictlyPositive();
6502 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
6503 return !getSignedRange(S).getSignedMin().isNegative();
6506 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
6507 return !getSignedRange(S).getSignedMax().isStrictlyPositive();
6510 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
6511 return isKnownNegative(S) || isKnownPositive(S);
6514 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
6515 const SCEV *LHS, const SCEV *RHS) {
6516 // Canonicalize the inputs first.
6517 (void)SimplifyICmpOperands(Pred, LHS, RHS);
6519 // If LHS or RHS is an addrec, check to see if the condition is true in
6520 // every iteration of the loop.
6521 // If LHS and RHS are both addrec, both conditions must be true in
6522 // every iteration of the loop.
6523 const SCEVAddRecExpr *LAR = dyn_cast<SCEVAddRecExpr>(LHS);
6524 const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS);
6525 bool LeftGuarded = false;
6526 bool RightGuarded = false;
6528 const Loop *L = LAR->getLoop();
6529 if (isLoopEntryGuardedByCond(L, Pred, LAR->getStart(), RHS) &&
6530 isLoopBackedgeGuardedByCond(L, Pred, LAR->getPostIncExpr(*this), RHS)) {
6531 if (!RAR) return true;
6536 const Loop *L = RAR->getLoop();
6537 if (isLoopEntryGuardedByCond(L, Pred, LHS, RAR->getStart()) &&
6538 isLoopBackedgeGuardedByCond(L, Pred, LHS, RAR->getPostIncExpr(*this))) {
6539 if (!LAR) return true;
6540 RightGuarded = true;
6543 if (LeftGuarded && RightGuarded)
6546 // Otherwise see what can be done with known constant ranges.
6547 return isKnownPredicateWithRanges(Pred, LHS, RHS);
6551 ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred,
6552 const SCEV *LHS, const SCEV *RHS) {
6553 if (HasSameValue(LHS, RHS))
6554 return ICmpInst::isTrueWhenEqual(Pred);
6556 // This code is split out from isKnownPredicate because it is called from
6557 // within isLoopEntryGuardedByCond.
6560 llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6561 case ICmpInst::ICMP_SGT:
6562 std::swap(LHS, RHS);
6563 case ICmpInst::ICMP_SLT: {
6564 ConstantRange LHSRange = getSignedRange(LHS);
6565 ConstantRange RHSRange = getSignedRange(RHS);
6566 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
6568 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
6572 case ICmpInst::ICMP_SGE:
6573 std::swap(LHS, RHS);
6574 case ICmpInst::ICMP_SLE: {
6575 ConstantRange LHSRange = getSignedRange(LHS);
6576 ConstantRange RHSRange = getSignedRange(RHS);
6577 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
6579 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
6583 case ICmpInst::ICMP_UGT:
6584 std::swap(LHS, RHS);
6585 case ICmpInst::ICMP_ULT: {
6586 ConstantRange LHSRange = getUnsignedRange(LHS);
6587 ConstantRange RHSRange = getUnsignedRange(RHS);
6588 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
6590 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
6594 case ICmpInst::ICMP_UGE:
6595 std::swap(LHS, RHS);
6596 case ICmpInst::ICMP_ULE: {
6597 ConstantRange LHSRange = getUnsignedRange(LHS);
6598 ConstantRange RHSRange = getUnsignedRange(RHS);
6599 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
6601 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
6605 case ICmpInst::ICMP_NE: {
6606 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
6608 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
6611 const SCEV *Diff = getMinusSCEV(LHS, RHS);
6612 if (isKnownNonZero(Diff))
6616 case ICmpInst::ICMP_EQ:
6617 // The check at the top of the function catches the case where
6618 // the values are known to be equal.
6624 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
6625 /// protected by a conditional between LHS and RHS. This is used to
6626 /// to eliminate casts.
6628 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
6629 ICmpInst::Predicate Pred,
6630 const SCEV *LHS, const SCEV *RHS) {
6631 // Interpret a null as meaning no loop, where there is obviously no guard
6632 // (interprocedural conditions notwithstanding).
6633 if (!L) return true;
6635 if (isKnownPredicateWithRanges(Pred, LHS, RHS)) return true;
6637 BasicBlock *Latch = L->getLoopLatch();
6641 BranchInst *LoopContinuePredicate =
6642 dyn_cast<BranchInst>(Latch->getTerminator());
6643 if (LoopContinuePredicate && LoopContinuePredicate->isConditional() &&
6644 isImpliedCond(Pred, LHS, RHS,
6645 LoopContinuePredicate->getCondition(),
6646 LoopContinuePredicate->getSuccessor(0) != L->getHeader()))
6649 // Check conditions due to any @llvm.assume intrinsics.
6650 for (auto &AssumeVH : AC->assumptions()) {
6653 auto *CI = cast<CallInst>(AssumeVH);
6654 if (!DT->dominates(CI, Latch->getTerminator()))
6657 if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false))
6664 /// isLoopEntryGuardedByCond - Test whether entry to the loop is protected
6665 /// by a conditional between LHS and RHS. This is used to help avoid max
6666 /// expressions in loop trip counts, and to eliminate casts.
6668 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
6669 ICmpInst::Predicate Pred,
6670 const SCEV *LHS, const SCEV *RHS) {
6671 // Interpret a null as meaning no loop, where there is obviously no guard
6672 // (interprocedural conditions notwithstanding).
6673 if (!L) return false;
6675 if (isKnownPredicateWithRanges(Pred, LHS, RHS)) return true;
6677 // Starting at the loop predecessor, climb up the predecessor chain, as long
6678 // as there are predecessors that can be found that have unique successors
6679 // leading to the original header.
6680 for (std::pair<BasicBlock *, BasicBlock *>
6681 Pair(L->getLoopPredecessor(), L->getHeader());
6683 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
6685 BranchInst *LoopEntryPredicate =
6686 dyn_cast<BranchInst>(Pair.first->getTerminator());
6687 if (!LoopEntryPredicate ||
6688 LoopEntryPredicate->isUnconditional())
6691 if (isImpliedCond(Pred, LHS, RHS,
6692 LoopEntryPredicate->getCondition(),
6693 LoopEntryPredicate->getSuccessor(0) != Pair.second))
6697 // Check conditions due to any @llvm.assume intrinsics.
6698 for (auto &AssumeVH : AC->assumptions()) {
6701 auto *CI = cast<CallInst>(AssumeVH);
6702 if (!DT->dominates(CI, L->getHeader()))
6705 if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false))
6712 /// RAII wrapper to prevent recursive application of isImpliedCond.
6713 /// ScalarEvolution's PendingLoopPredicates set must be empty unless we are
6714 /// currently evaluating isImpliedCond.
6715 struct MarkPendingLoopPredicate {
6717 DenseSet<Value*> &LoopPreds;
6720 MarkPendingLoopPredicate(Value *C, DenseSet<Value*> &LP)
6721 : Cond(C), LoopPreds(LP) {
6722 Pending = !LoopPreds.insert(Cond).second;
6724 ~MarkPendingLoopPredicate() {
6726 LoopPreds.erase(Cond);
6730 /// isImpliedCond - Test whether the condition described by Pred, LHS,
6731 /// and RHS is true whenever the given Cond value evaluates to true.
6732 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred,
6733 const SCEV *LHS, const SCEV *RHS,
6734 Value *FoundCondValue,
6736 MarkPendingLoopPredicate Mark(FoundCondValue, PendingLoopPredicates);
6740 // Recursively handle And and Or conditions.
6741 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) {
6742 if (BO->getOpcode() == Instruction::And) {
6744 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
6745 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
6746 } else if (BO->getOpcode() == Instruction::Or) {
6748 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
6749 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
6753 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue);
6754 if (!ICI) return false;
6756 // Bail if the ICmp's operands' types are wider than the needed type
6757 // before attempting to call getSCEV on them. This avoids infinite
6758 // recursion, since the analysis of widening casts can require loop
6759 // exit condition information for overflow checking, which would
6761 if (getTypeSizeInBits(LHS->getType()) <
6762 getTypeSizeInBits(ICI->getOperand(0)->getType()))
6765 // Now that we found a conditional branch that dominates the loop or controls
6766 // the loop latch. Check to see if it is the comparison we are looking for.
6767 ICmpInst::Predicate FoundPred;
6769 FoundPred = ICI->getInversePredicate();
6771 FoundPred = ICI->getPredicate();
6773 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
6774 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
6776 // Balance the types. The case where FoundLHS' type is wider than
6777 // LHS' type is checked for above.
6778 if (getTypeSizeInBits(LHS->getType()) >
6779 getTypeSizeInBits(FoundLHS->getType())) {
6780 if (CmpInst::isSigned(FoundPred)) {
6781 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
6782 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
6784 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
6785 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
6789 // Canonicalize the query to match the way instcombine will have
6790 // canonicalized the comparison.
6791 if (SimplifyICmpOperands(Pred, LHS, RHS))
6793 return CmpInst::isTrueWhenEqual(Pred);
6794 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
6795 if (FoundLHS == FoundRHS)
6796 return CmpInst::isFalseWhenEqual(FoundPred);
6798 // Check to see if we can make the LHS or RHS match.
6799 if (LHS == FoundRHS || RHS == FoundLHS) {
6800 if (isa<SCEVConstant>(RHS)) {
6801 std::swap(FoundLHS, FoundRHS);
6802 FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
6804 std::swap(LHS, RHS);
6805 Pred = ICmpInst::getSwappedPredicate(Pred);
6809 // Check whether the found predicate is the same as the desired predicate.
6810 if (FoundPred == Pred)
6811 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
6813 // Check whether swapping the found predicate makes it the same as the
6814 // desired predicate.
6815 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
6816 if (isa<SCEVConstant>(RHS))
6817 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
6819 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
6820 RHS, LHS, FoundLHS, FoundRHS);
6823 // Check if we can make progress by sharpening ranges.
6824 if (FoundPred == ICmpInst::ICMP_NE &&
6825 (isa<SCEVConstant>(FoundLHS) || isa<SCEVConstant>(FoundRHS))) {
6827 const SCEVConstant *C = nullptr;
6828 const SCEV *V = nullptr;
6830 if (isa<SCEVConstant>(FoundLHS)) {
6831 C = cast<SCEVConstant>(FoundLHS);
6834 C = cast<SCEVConstant>(FoundRHS);
6838 // The guarding predicate tells us that C != V. If the known range
6839 // of V is [C, t), we can sharpen the range to [C + 1, t). The
6840 // range we consider has to correspond to same signedness as the
6841 // predicate we're interested in folding.
6843 APInt Min = ICmpInst::isSigned(Pred) ?
6844 getSignedRange(V).getSignedMin() : getUnsignedRange(V).getUnsignedMin();
6846 if (Min == C->getValue()->getValue()) {
6847 // Given (V >= Min && V != Min) we conclude V >= (Min + 1).
6848 // This is true even if (Min + 1) wraps around -- in case of
6849 // wraparound, (Min + 1) < Min, so (V >= Min => V >= (Min + 1)).
6851 APInt SharperMin = Min + 1;
6854 case ICmpInst::ICMP_SGE:
6855 case ICmpInst::ICMP_UGE:
6856 // We know V `Pred` SharperMin. If this implies LHS `Pred`
6858 if (isImpliedCondOperands(Pred, LHS, RHS, V,
6859 getConstant(SharperMin)))
6862 case ICmpInst::ICMP_SGT:
6863 case ICmpInst::ICMP_UGT:
6864 // We know from the range information that (V `Pred` Min ||
6865 // V == Min). We know from the guarding condition that !(V
6866 // == Min). This gives us
6868 // V `Pred` Min || V == Min && !(V == Min)
6871 // If V `Pred` Min implies LHS `Pred` RHS, we're done.
6873 if (isImpliedCondOperands(Pred, LHS, RHS, V, getConstant(Min)))
6883 // Check whether the actual condition is beyond sufficient.
6884 if (FoundPred == ICmpInst::ICMP_EQ)
6885 if (ICmpInst::isTrueWhenEqual(Pred))
6886 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
6888 if (Pred == ICmpInst::ICMP_NE)
6889 if (!ICmpInst::isTrueWhenEqual(FoundPred))
6890 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
6893 // Otherwise assume the worst.
6897 /// isImpliedCondOperands - Test whether the condition described by Pred,
6898 /// LHS, and RHS is true whenever the condition described by Pred, FoundLHS,
6899 /// and FoundRHS is true.
6900 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
6901 const SCEV *LHS, const SCEV *RHS,
6902 const SCEV *FoundLHS,
6903 const SCEV *FoundRHS) {
6904 return isImpliedCondOperandsHelper(Pred, LHS, RHS,
6905 FoundLHS, FoundRHS) ||
6906 // ~x < ~y --> x > y
6907 isImpliedCondOperandsHelper(Pred, LHS, RHS,
6908 getNotSCEV(FoundRHS),
6909 getNotSCEV(FoundLHS));
6913 /// If Expr computes ~A, return A else return nullptr
6914 static const SCEV *MatchNotExpr(const SCEV *Expr) {
6915 const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Expr);
6916 if (!Add || Add->getNumOperands() != 2) return nullptr;
6918 const SCEVConstant *AddLHS = dyn_cast<SCEVConstant>(Add->getOperand(0));
6919 if (!(AddLHS && AddLHS->getValue()->getValue().isAllOnesValue()))
6922 const SCEVMulExpr *AddRHS = dyn_cast<SCEVMulExpr>(Add->getOperand(1));
6923 if (!AddRHS || AddRHS->getNumOperands() != 2) return nullptr;
6925 const SCEVConstant *MulLHS = dyn_cast<SCEVConstant>(AddRHS->getOperand(0));
6926 if (!(MulLHS && MulLHS->getValue()->getValue().isAllOnesValue()))
6929 return AddRHS->getOperand(1);
6933 /// Is MaybeMaxExpr an SMax or UMax of Candidate and some other values?
6934 template<typename MaxExprType>
6935 static bool IsMaxConsistingOf(const SCEV *MaybeMaxExpr,
6936 const SCEV *Candidate) {
6937 const MaxExprType *MaxExpr = dyn_cast<MaxExprType>(MaybeMaxExpr);
6938 if (!MaxExpr) return false;
6940 auto It = std::find(MaxExpr->op_begin(), MaxExpr->op_end(), Candidate);
6941 return It != MaxExpr->op_end();
6945 /// Is MaybeMinExpr an SMin or UMin of Candidate and some other values?
6946 template<typename MaxExprType>
6947 static bool IsMinConsistingOf(ScalarEvolution &SE,
6948 const SCEV *MaybeMinExpr,
6949 const SCEV *Candidate) {
6950 const SCEV *MaybeMaxExpr = MatchNotExpr(MaybeMinExpr);
6954 return IsMaxConsistingOf<MaxExprType>(MaybeMaxExpr, SE.getNotSCEV(Candidate));
6958 /// Is LHS `Pred` RHS true on the virtue of LHS or RHS being a Min or Max
6960 static bool IsKnownPredicateViaMinOrMax(ScalarEvolution &SE,
6961 ICmpInst::Predicate Pred,
6962 const SCEV *LHS, const SCEV *RHS) {
6967 case ICmpInst::ICMP_SGE:
6968 std::swap(LHS, RHS);
6970 case ICmpInst::ICMP_SLE:
6973 IsMinConsistingOf<SCEVSMaxExpr>(SE, LHS, RHS) ||
6975 IsMaxConsistingOf<SCEVSMaxExpr>(RHS, LHS);
6977 case ICmpInst::ICMP_UGE:
6978 std::swap(LHS, RHS);
6980 case ICmpInst::ICMP_ULE:
6983 IsMinConsistingOf<SCEVUMaxExpr>(SE, LHS, RHS) ||
6985 IsMaxConsistingOf<SCEVUMaxExpr>(RHS, LHS);
6988 llvm_unreachable("covered switch fell through?!");
6991 /// isImpliedCondOperandsHelper - Test whether the condition described by
6992 /// Pred, LHS, and RHS is true whenever the condition described by Pred,
6993 /// FoundLHS, and FoundRHS is true.
6995 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
6996 const SCEV *LHS, const SCEV *RHS,
6997 const SCEV *FoundLHS,
6998 const SCEV *FoundRHS) {
6999 auto IsKnownPredicateFull =
7000 [this](ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS) {
7001 return isKnownPredicateWithRanges(Pred, LHS, RHS) ||
7002 IsKnownPredicateViaMinOrMax(*this, Pred, LHS, RHS);
7006 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
7007 case ICmpInst::ICMP_EQ:
7008 case ICmpInst::ICMP_NE:
7009 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
7012 case ICmpInst::ICMP_SLT:
7013 case ICmpInst::ICMP_SLE:
7014 if (IsKnownPredicateFull(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
7015 IsKnownPredicateFull(ICmpInst::ICMP_SGE, RHS, FoundRHS))
7018 case ICmpInst::ICMP_SGT:
7019 case ICmpInst::ICMP_SGE:
7020 if (IsKnownPredicateFull(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
7021 IsKnownPredicateFull(ICmpInst::ICMP_SLE, RHS, FoundRHS))
7024 case ICmpInst::ICMP_ULT:
7025 case ICmpInst::ICMP_ULE:
7026 if (IsKnownPredicateFull(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
7027 IsKnownPredicateFull(ICmpInst::ICMP_UGE, RHS, FoundRHS))
7030 case ICmpInst::ICMP_UGT:
7031 case ICmpInst::ICMP_UGE:
7032 if (IsKnownPredicateFull(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
7033 IsKnownPredicateFull(ICmpInst::ICMP_ULE, RHS, FoundRHS))
7041 // Verify if an linear IV with positive stride can overflow when in a
7042 // less-than comparison, knowing the invariant term of the comparison, the
7043 // stride and the knowledge of NSW/NUW flags on the recurrence.
7044 bool ScalarEvolution::doesIVOverflowOnLT(const SCEV *RHS, const SCEV *Stride,
7045 bool IsSigned, bool NoWrap) {
7046 if (NoWrap) return false;
7048 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
7049 const SCEV *One = getConstant(Stride->getType(), 1);
7052 APInt MaxRHS = getSignedRange(RHS).getSignedMax();
7053 APInt MaxValue = APInt::getSignedMaxValue(BitWidth);
7054 APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
7057 // SMaxRHS + SMaxStrideMinusOne > SMaxValue => overflow!
7058 return (MaxValue - MaxStrideMinusOne).slt(MaxRHS);
7061 APInt MaxRHS = getUnsignedRange(RHS).getUnsignedMax();
7062 APInt MaxValue = APInt::getMaxValue(BitWidth);
7063 APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
7066 // UMaxRHS + UMaxStrideMinusOne > UMaxValue => overflow!
7067 return (MaxValue - MaxStrideMinusOne).ult(MaxRHS);
7070 // Verify if an linear IV with negative stride can overflow when in a
7071 // greater-than comparison, knowing the invariant term of the comparison,
7072 // the stride and the knowledge of NSW/NUW flags on the recurrence.
7073 bool ScalarEvolution::doesIVOverflowOnGT(const SCEV *RHS, const SCEV *Stride,
7074 bool IsSigned, bool NoWrap) {
7075 if (NoWrap) return false;
7077 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
7078 const SCEV *One = getConstant(Stride->getType(), 1);
7081 APInt MinRHS = getSignedRange(RHS).getSignedMin();
7082 APInt MinValue = APInt::getSignedMinValue(BitWidth);
7083 APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
7086 // SMinRHS - SMaxStrideMinusOne < SMinValue => overflow!
7087 return (MinValue + MaxStrideMinusOne).sgt(MinRHS);
7090 APInt MinRHS = getUnsignedRange(RHS).getUnsignedMin();
7091 APInt MinValue = APInt::getMinValue(BitWidth);
7092 APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
7095 // UMinRHS - UMaxStrideMinusOne < UMinValue => overflow!
7096 return (MinValue + MaxStrideMinusOne).ugt(MinRHS);
7099 // Compute the backedge taken count knowing the interval difference, the
7100 // stride and presence of the equality in the comparison.
7101 const SCEV *ScalarEvolution::computeBECount(const SCEV *Delta, const SCEV *Step,
7103 const SCEV *One = getConstant(Step->getType(), 1);
7104 Delta = Equality ? getAddExpr(Delta, Step)
7105 : getAddExpr(Delta, getMinusSCEV(Step, One));
7106 return getUDivExpr(Delta, Step);
7109 /// HowManyLessThans - Return the number of times a backedge containing the
7110 /// specified less-than comparison will execute. If not computable, return
7111 /// CouldNotCompute.
7113 /// @param ControlsExit is true when the LHS < RHS condition directly controls
7114 /// the branch (loops exits only if condition is true). In this case, we can use
7115 /// NoWrapFlags to skip overflow checks.
7116 ScalarEvolution::ExitLimit
7117 ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
7118 const Loop *L, bool IsSigned,
7119 bool ControlsExit) {
7120 // We handle only IV < Invariant
7121 if (!isLoopInvariant(RHS, L))
7122 return getCouldNotCompute();
7124 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
7126 // Avoid weird loops
7127 if (!IV || IV->getLoop() != L || !IV->isAffine())
7128 return getCouldNotCompute();
7130 bool NoWrap = ControlsExit &&
7131 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
7133 const SCEV *Stride = IV->getStepRecurrence(*this);
7135 // Avoid negative or zero stride values
7136 if (!isKnownPositive(Stride))
7137 return getCouldNotCompute();
7139 // Avoid proven overflow cases: this will ensure that the backedge taken count
7140 // will not generate any unsigned overflow. Relaxed no-overflow conditions
7141 // exploit NoWrapFlags, allowing to optimize in presence of undefined
7142 // behaviors like the case of C language.
7143 if (!Stride->isOne() && doesIVOverflowOnLT(RHS, Stride, IsSigned, NoWrap))
7144 return getCouldNotCompute();
7146 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SLT
7147 : ICmpInst::ICMP_ULT;
7148 const SCEV *Start = IV->getStart();
7149 const SCEV *End = RHS;
7150 if (!isLoopEntryGuardedByCond(L, Cond, getMinusSCEV(Start, Stride), RHS)) {
7151 const SCEV *Diff = getMinusSCEV(RHS, Start);
7152 // If we have NoWrap set, then we can assume that the increment won't
7153 // overflow, in which case if RHS - Start is a constant, we don't need to
7154 // do a max operation since we can just figure it out statically
7155 if (NoWrap && isa<SCEVConstant>(Diff)) {
7156 APInt D = dyn_cast<const SCEVConstant>(Diff)->getValue()->getValue();
7160 End = IsSigned ? getSMaxExpr(RHS, Start)
7161 : getUMaxExpr(RHS, Start);
7164 const SCEV *BECount = computeBECount(getMinusSCEV(End, Start), Stride, false);
7166 APInt MinStart = IsSigned ? getSignedRange(Start).getSignedMin()
7167 : getUnsignedRange(Start).getUnsignedMin();
7169 APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
7170 : getUnsignedRange(Stride).getUnsignedMin();
7172 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
7173 APInt Limit = IsSigned ? APInt::getSignedMaxValue(BitWidth) - (MinStride - 1)
7174 : APInt::getMaxValue(BitWidth) - (MinStride - 1);
7176 // Although End can be a MAX expression we estimate MaxEnd considering only
7177 // the case End = RHS. This is safe because in the other case (End - Start)
7178 // is zero, leading to a zero maximum backedge taken count.
7180 IsSigned ? APIntOps::smin(getSignedRange(RHS).getSignedMax(), Limit)
7181 : APIntOps::umin(getUnsignedRange(RHS).getUnsignedMax(), Limit);
7183 const SCEV *MaxBECount;
7184 if (isa<SCEVConstant>(BECount))
7185 MaxBECount = BECount;
7187 MaxBECount = computeBECount(getConstant(MaxEnd - MinStart),
7188 getConstant(MinStride), false);
7190 if (isa<SCEVCouldNotCompute>(MaxBECount))
7191 MaxBECount = BECount;
7193 return ExitLimit(BECount, MaxBECount);
7196 ScalarEvolution::ExitLimit
7197 ScalarEvolution::HowManyGreaterThans(const SCEV *LHS, const SCEV *RHS,
7198 const Loop *L, bool IsSigned,
7199 bool ControlsExit) {
7200 // We handle only IV > Invariant
7201 if (!isLoopInvariant(RHS, L))
7202 return getCouldNotCompute();
7204 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
7206 // Avoid weird loops
7207 if (!IV || IV->getLoop() != L || !IV->isAffine())
7208 return getCouldNotCompute();
7210 bool NoWrap = ControlsExit &&
7211 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
7213 const SCEV *Stride = getNegativeSCEV(IV->getStepRecurrence(*this));
7215 // Avoid negative or zero stride values
7216 if (!isKnownPositive(Stride))
7217 return getCouldNotCompute();
7219 // Avoid proven overflow cases: this will ensure that the backedge taken count
7220 // will not generate any unsigned overflow. Relaxed no-overflow conditions
7221 // exploit NoWrapFlags, allowing to optimize in presence of undefined
7222 // behaviors like the case of C language.
7223 if (!Stride->isOne() && doesIVOverflowOnGT(RHS, Stride, IsSigned, NoWrap))
7224 return getCouldNotCompute();
7226 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SGT
7227 : ICmpInst::ICMP_UGT;
7229 const SCEV *Start = IV->getStart();
7230 const SCEV *End = RHS;
7231 if (!isLoopEntryGuardedByCond(L, Cond, getAddExpr(Start, Stride), RHS)) {
7232 const SCEV *Diff = getMinusSCEV(RHS, Start);
7233 // If we have NoWrap set, then we can assume that the increment won't
7234 // overflow, in which case if RHS - Start is a constant, we don't need to
7235 // do a max operation since we can just figure it out statically
7236 if (NoWrap && isa<SCEVConstant>(Diff)) {
7237 APInt D = dyn_cast<const SCEVConstant>(Diff)->getValue()->getValue();
7238 if (!D.isNegative())
7241 End = IsSigned ? getSMinExpr(RHS, Start)
7242 : getUMinExpr(RHS, Start);
7245 const SCEV *BECount = computeBECount(getMinusSCEV(Start, End), Stride, false);
7247 APInt MaxStart = IsSigned ? getSignedRange(Start).getSignedMax()
7248 : getUnsignedRange(Start).getUnsignedMax();
7250 APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
7251 : getUnsignedRange(Stride).getUnsignedMin();
7253 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
7254 APInt Limit = IsSigned ? APInt::getSignedMinValue(BitWidth) + (MinStride - 1)
7255 : APInt::getMinValue(BitWidth) + (MinStride - 1);
7257 // Although End can be a MIN expression we estimate MinEnd considering only
7258 // the case End = RHS. This is safe because in the other case (Start - End)
7259 // is zero, leading to a zero maximum backedge taken count.
7261 IsSigned ? APIntOps::smax(getSignedRange(RHS).getSignedMin(), Limit)
7262 : APIntOps::umax(getUnsignedRange(RHS).getUnsignedMin(), Limit);
7265 const SCEV *MaxBECount = getCouldNotCompute();
7266 if (isa<SCEVConstant>(BECount))
7267 MaxBECount = BECount;
7269 MaxBECount = computeBECount(getConstant(MaxStart - MinEnd),
7270 getConstant(MinStride), false);
7272 if (isa<SCEVCouldNotCompute>(MaxBECount))
7273 MaxBECount = BECount;
7275 return ExitLimit(BECount, MaxBECount);
7278 /// getNumIterationsInRange - Return the number of iterations of this loop that
7279 /// produce values in the specified constant range. Another way of looking at
7280 /// this is that it returns the first iteration number where the value is not in
7281 /// the condition, thus computing the exit count. If the iteration count can't
7282 /// be computed, an instance of SCEVCouldNotCompute is returned.
7283 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
7284 ScalarEvolution &SE) const {
7285 if (Range.isFullSet()) // Infinite loop.
7286 return SE.getCouldNotCompute();
7288 // If the start is a non-zero constant, shift the range to simplify things.
7289 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
7290 if (!SC->getValue()->isZero()) {
7291 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
7292 Operands[0] = SE.getConstant(SC->getType(), 0);
7293 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(),
7294 getNoWrapFlags(FlagNW));
7295 if (const SCEVAddRecExpr *ShiftedAddRec =
7296 dyn_cast<SCEVAddRecExpr>(Shifted))
7297 return ShiftedAddRec->getNumIterationsInRange(
7298 Range.subtract(SC->getValue()->getValue()), SE);
7299 // This is strange and shouldn't happen.
7300 return SE.getCouldNotCompute();
7303 // The only time we can solve this is when we have all constant indices.
7304 // Otherwise, we cannot determine the overflow conditions.
7305 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
7306 if (!isa<SCEVConstant>(getOperand(i)))
7307 return SE.getCouldNotCompute();
7310 // Okay at this point we know that all elements of the chrec are constants and
7311 // that the start element is zero.
7313 // First check to see if the range contains zero. If not, the first
7315 unsigned BitWidth = SE.getTypeSizeInBits(getType());
7316 if (!Range.contains(APInt(BitWidth, 0)))
7317 return SE.getConstant(getType(), 0);
7320 // If this is an affine expression then we have this situation:
7321 // Solve {0,+,A} in Range === Ax in Range
7323 // We know that zero is in the range. If A is positive then we know that
7324 // the upper value of the range must be the first possible exit value.
7325 // If A is negative then the lower of the range is the last possible loop
7326 // value. Also note that we already checked for a full range.
7327 APInt One(BitWidth,1);
7328 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
7329 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
7331 // The exit value should be (End+A)/A.
7332 APInt ExitVal = (End + A).udiv(A);
7333 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
7335 // Evaluate at the exit value. If we really did fall out of the valid
7336 // range, then we computed our trip count, otherwise wrap around or other
7337 // things must have happened.
7338 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
7339 if (Range.contains(Val->getValue()))
7340 return SE.getCouldNotCompute(); // Something strange happened
7342 // Ensure that the previous value is in the range. This is a sanity check.
7343 assert(Range.contains(
7344 EvaluateConstantChrecAtConstant(this,
7345 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
7346 "Linear scev computation is off in a bad way!");
7347 return SE.getConstant(ExitValue);
7348 } else if (isQuadratic()) {
7349 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
7350 // quadratic equation to solve it. To do this, we must frame our problem in
7351 // terms of figuring out when zero is crossed, instead of when
7352 // Range.getUpper() is crossed.
7353 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
7354 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
7355 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop(),
7356 // getNoWrapFlags(FlagNW)
7359 // Next, solve the constructed addrec
7360 std::pair<const SCEV *,const SCEV *> Roots =
7361 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
7362 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
7363 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
7365 // Pick the smallest positive root value.
7366 if (ConstantInt *CB =
7367 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
7368 R1->getValue(), R2->getValue()))) {
7369 if (CB->getZExtValue() == false)
7370 std::swap(R1, R2); // R1 is the minimum root now.
7372 // Make sure the root is not off by one. The returned iteration should
7373 // not be in the range, but the previous one should be. When solving
7374 // for "X*X < 5", for example, we should not return a root of 2.
7375 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
7378 if (Range.contains(R1Val->getValue())) {
7379 // The next iteration must be out of the range...
7380 ConstantInt *NextVal =
7381 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1);
7383 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
7384 if (!Range.contains(R1Val->getValue()))
7385 return SE.getConstant(NextVal);
7386 return SE.getCouldNotCompute(); // Something strange happened
7389 // If R1 was not in the range, then it is a good return value. Make
7390 // sure that R1-1 WAS in the range though, just in case.
7391 ConstantInt *NextVal =
7392 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1);
7393 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
7394 if (Range.contains(R1Val->getValue()))
7396 return SE.getCouldNotCompute(); // Something strange happened
7401 return SE.getCouldNotCompute();
7407 FindUndefs() : Found(false) {}
7409 bool follow(const SCEV *S) {
7410 if (const SCEVUnknown *C = dyn_cast<SCEVUnknown>(S)) {
7411 if (isa<UndefValue>(C->getValue()))
7413 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) {
7414 if (isa<UndefValue>(C->getValue()))
7418 // Keep looking if we haven't found it yet.
7421 bool isDone() const {
7422 // Stop recursion if we have found an undef.
7428 // Return true when S contains at least an undef value.
7430 containsUndefs(const SCEV *S) {
7432 SCEVTraversal<FindUndefs> ST(F);
7439 // Collect all steps of SCEV expressions.
7440 struct SCEVCollectStrides {
7441 ScalarEvolution &SE;
7442 SmallVectorImpl<const SCEV *> &Strides;
7444 SCEVCollectStrides(ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &S)
7445 : SE(SE), Strides(S) {}
7447 bool follow(const SCEV *S) {
7448 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(S))
7449 Strides.push_back(AR->getStepRecurrence(SE));
7452 bool isDone() const { return false; }
7455 // Collect all SCEVUnknown and SCEVMulExpr expressions.
7456 struct SCEVCollectTerms {
7457 SmallVectorImpl<const SCEV *> &Terms;
7459 SCEVCollectTerms(SmallVectorImpl<const SCEV *> &T)
7462 bool follow(const SCEV *S) {
7463 if (isa<SCEVUnknown>(S) || isa<SCEVMulExpr>(S)) {
7464 if (!containsUndefs(S))
7467 // Stop recursion: once we collected a term, do not walk its operands.
7474 bool isDone() const { return false; }
7478 /// Find parametric terms in this SCEVAddRecExpr.
7479 void SCEVAddRecExpr::collectParametricTerms(
7480 ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &Terms) const {
7481 SmallVector<const SCEV *, 4> Strides;
7482 SCEVCollectStrides StrideCollector(SE, Strides);
7483 visitAll(this, StrideCollector);
7486 dbgs() << "Strides:\n";
7487 for (const SCEV *S : Strides)
7488 dbgs() << *S << "\n";
7491 for (const SCEV *S : Strides) {
7492 SCEVCollectTerms TermCollector(Terms);
7493 visitAll(S, TermCollector);
7497 dbgs() << "Terms:\n";
7498 for (const SCEV *T : Terms)
7499 dbgs() << *T << "\n";
7503 static bool findArrayDimensionsRec(ScalarEvolution &SE,
7504 SmallVectorImpl<const SCEV *> &Terms,
7505 SmallVectorImpl<const SCEV *> &Sizes) {
7506 int Last = Terms.size() - 1;
7507 const SCEV *Step = Terms[Last];
7509 // End of recursion.
7511 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Step)) {
7512 SmallVector<const SCEV *, 2> Qs;
7513 for (const SCEV *Op : M->operands())
7514 if (!isa<SCEVConstant>(Op))
7517 Step = SE.getMulExpr(Qs);
7520 Sizes.push_back(Step);
7524 for (const SCEV *&Term : Terms) {
7525 // Normalize the terms before the next call to findArrayDimensionsRec.
7527 SCEVDivision::divide(SE, Term, Step, &Q, &R);
7529 // Bail out when GCD does not evenly divide one of the terms.
7536 // Remove all SCEVConstants.
7537 Terms.erase(std::remove_if(Terms.begin(), Terms.end(), [](const SCEV *E) {
7538 return isa<SCEVConstant>(E);
7542 if (Terms.size() > 0)
7543 if (!findArrayDimensionsRec(SE, Terms, Sizes))
7546 Sizes.push_back(Step);
7551 struct FindParameter {
7552 bool FoundParameter;
7553 FindParameter() : FoundParameter(false) {}
7555 bool follow(const SCEV *S) {
7556 if (isa<SCEVUnknown>(S)) {
7557 FoundParameter = true;
7558 // Stop recursion: we found a parameter.
7564 bool isDone() const {
7565 // Stop recursion if we have found a parameter.
7566 return FoundParameter;
7571 // Returns true when S contains at least a SCEVUnknown parameter.
7573 containsParameters(const SCEV *S) {
7575 SCEVTraversal<FindParameter> ST(F);
7578 return F.FoundParameter;
7581 // Returns true when one of the SCEVs of Terms contains a SCEVUnknown parameter.
7583 containsParameters(SmallVectorImpl<const SCEV *> &Terms) {
7584 for (const SCEV *T : Terms)
7585 if (containsParameters(T))
7590 // Return the number of product terms in S.
7591 static inline int numberOfTerms(const SCEV *S) {
7592 if (const SCEVMulExpr *Expr = dyn_cast<SCEVMulExpr>(S))
7593 return Expr->getNumOperands();
7597 static const SCEV *removeConstantFactors(ScalarEvolution &SE, const SCEV *T) {
7598 if (isa<SCEVConstant>(T))
7601 if (isa<SCEVUnknown>(T))
7604 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(T)) {
7605 SmallVector<const SCEV *, 2> Factors;
7606 for (const SCEV *Op : M->operands())
7607 if (!isa<SCEVConstant>(Op))
7608 Factors.push_back(Op);
7610 return SE.getMulExpr(Factors);
7616 /// Return the size of an element read or written by Inst.
7617 const SCEV *ScalarEvolution::getElementSize(Instruction *Inst) {
7619 if (StoreInst *Store = dyn_cast<StoreInst>(Inst))
7620 Ty = Store->getValueOperand()->getType();
7621 else if (LoadInst *Load = dyn_cast<LoadInst>(Inst))
7622 Ty = Load->getType();
7626 Type *ETy = getEffectiveSCEVType(PointerType::getUnqual(Ty));
7627 return getSizeOfExpr(ETy, Ty);
7630 /// Second step of delinearization: compute the array dimensions Sizes from the
7631 /// set of Terms extracted from the memory access function of this SCEVAddRec.
7632 void ScalarEvolution::findArrayDimensions(SmallVectorImpl<const SCEV *> &Terms,
7633 SmallVectorImpl<const SCEV *> &Sizes,
7634 const SCEV *ElementSize) const {
7636 if (Terms.size() < 1 || !ElementSize)
7639 // Early return when Terms do not contain parameters: we do not delinearize
7640 // non parametric SCEVs.
7641 if (!containsParameters(Terms))
7645 dbgs() << "Terms:\n";
7646 for (const SCEV *T : Terms)
7647 dbgs() << *T << "\n";
7650 // Remove duplicates.
7651 std::sort(Terms.begin(), Terms.end());
7652 Terms.erase(std::unique(Terms.begin(), Terms.end()), Terms.end());
7654 // Put larger terms first.
7655 std::sort(Terms.begin(), Terms.end(), [](const SCEV *LHS, const SCEV *RHS) {
7656 return numberOfTerms(LHS) > numberOfTerms(RHS);
7659 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
7661 // Divide all terms by the element size.
7662 for (const SCEV *&Term : Terms) {
7664 SCEVDivision::divide(SE, Term, ElementSize, &Q, &R);
7668 SmallVector<const SCEV *, 4> NewTerms;
7670 // Remove constant factors.
7671 for (const SCEV *T : Terms)
7672 if (const SCEV *NewT = removeConstantFactors(SE, T))
7673 NewTerms.push_back(NewT);
7676 dbgs() << "Terms after sorting:\n";
7677 for (const SCEV *T : NewTerms)
7678 dbgs() << *T << "\n";
7681 if (NewTerms.empty() ||
7682 !findArrayDimensionsRec(SE, NewTerms, Sizes)) {
7687 // The last element to be pushed into Sizes is the size of an element.
7688 Sizes.push_back(ElementSize);
7691 dbgs() << "Sizes:\n";
7692 for (const SCEV *S : Sizes)
7693 dbgs() << *S << "\n";
7697 /// Third step of delinearization: compute the access functions for the
7698 /// Subscripts based on the dimensions in Sizes.
7699 void SCEVAddRecExpr::computeAccessFunctions(
7700 ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &Subscripts,
7701 SmallVectorImpl<const SCEV *> &Sizes) const {
7703 // Early exit in case this SCEV is not an affine multivariate function.
7704 if (Sizes.empty() || !this->isAffine())
7707 const SCEV *Res = this;
7708 int Last = Sizes.size() - 1;
7709 for (int i = Last; i >= 0; i--) {
7711 SCEVDivision::divide(SE, Res, Sizes[i], &Q, &R);
7714 dbgs() << "Res: " << *Res << "\n";
7715 dbgs() << "Sizes[i]: " << *Sizes[i] << "\n";
7716 dbgs() << "Res divided by Sizes[i]:\n";
7717 dbgs() << "Quotient: " << *Q << "\n";
7718 dbgs() << "Remainder: " << *R << "\n";
7723 // Do not record the last subscript corresponding to the size of elements in
7727 // Bail out if the remainder is too complex.
7728 if (isa<SCEVAddRecExpr>(R)) {
7737 // Record the access function for the current subscript.
7738 Subscripts.push_back(R);
7741 // Also push in last position the remainder of the last division: it will be
7742 // the access function of the innermost dimension.
7743 Subscripts.push_back(Res);
7745 std::reverse(Subscripts.begin(), Subscripts.end());
7748 dbgs() << "Subscripts:\n";
7749 for (const SCEV *S : Subscripts)
7750 dbgs() << *S << "\n";
7754 /// Splits the SCEV into two vectors of SCEVs representing the subscripts and
7755 /// sizes of an array access. Returns the remainder of the delinearization that
7756 /// is the offset start of the array. The SCEV->delinearize algorithm computes
7757 /// the multiples of SCEV coefficients: that is a pattern matching of sub
7758 /// expressions in the stride and base of a SCEV corresponding to the
7759 /// computation of a GCD (greatest common divisor) of base and stride. When
7760 /// SCEV->delinearize fails, it returns the SCEV unchanged.
7762 /// For example: when analyzing the memory access A[i][j][k] in this loop nest
7764 /// void foo(long n, long m, long o, double A[n][m][o]) {
7766 /// for (long i = 0; i < n; i++)
7767 /// for (long j = 0; j < m; j++)
7768 /// for (long k = 0; k < o; k++)
7769 /// A[i][j][k] = 1.0;
7772 /// the delinearization input is the following AddRec SCEV:
7774 /// AddRec: {{{%A,+,(8 * %m * %o)}<%for.i>,+,(8 * %o)}<%for.j>,+,8}<%for.k>
7776 /// From this SCEV, we are able to say that the base offset of the access is %A
7777 /// because it appears as an offset that does not divide any of the strides in
7780 /// CHECK: Base offset: %A
7782 /// and then SCEV->delinearize determines the size of some of the dimensions of
7783 /// the array as these are the multiples by which the strides are happening:
7785 /// CHECK: ArrayDecl[UnknownSize][%m][%o] with elements of sizeof(double) bytes.
7787 /// Note that the outermost dimension remains of UnknownSize because there are
7788 /// no strides that would help identifying the size of the last dimension: when
7789 /// the array has been statically allocated, one could compute the size of that
7790 /// dimension by dividing the overall size of the array by the size of the known
7791 /// dimensions: %m * %o * 8.
7793 /// Finally delinearize provides the access functions for the array reference
7794 /// that does correspond to A[i][j][k] of the above C testcase:
7796 /// CHECK: ArrayRef[{0,+,1}<%for.i>][{0,+,1}<%for.j>][{0,+,1}<%for.k>]
7798 /// The testcases are checking the output of a function pass:
7799 /// DelinearizationPass that walks through all loads and stores of a function
7800 /// asking for the SCEV of the memory access with respect to all enclosing
7801 /// loops, calling SCEV->delinearize on that and printing the results.
7803 void SCEVAddRecExpr::delinearize(ScalarEvolution &SE,
7804 SmallVectorImpl<const SCEV *> &Subscripts,
7805 SmallVectorImpl<const SCEV *> &Sizes,
7806 const SCEV *ElementSize) const {
7807 // First step: collect parametric terms.
7808 SmallVector<const SCEV *, 4> Terms;
7809 collectParametricTerms(SE, Terms);
7814 // Second step: find subscript sizes.
7815 SE.findArrayDimensions(Terms, Sizes, ElementSize);
7820 // Third step: compute the access functions for each subscript.
7821 computeAccessFunctions(SE, Subscripts, Sizes);
7823 if (Subscripts.empty())
7827 dbgs() << "succeeded to delinearize " << *this << "\n";
7828 dbgs() << "ArrayDecl[UnknownSize]";
7829 for (const SCEV *S : Sizes)
7830 dbgs() << "[" << *S << "]";
7832 dbgs() << "\nArrayRef";
7833 for (const SCEV *S : Subscripts)
7834 dbgs() << "[" << *S << "]";
7839 //===----------------------------------------------------------------------===//
7840 // SCEVCallbackVH Class Implementation
7841 //===----------------------------------------------------------------------===//
7843 void ScalarEvolution::SCEVCallbackVH::deleted() {
7844 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
7845 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
7846 SE->ConstantEvolutionLoopExitValue.erase(PN);
7847 SE->ValueExprMap.erase(getValPtr());
7848 // this now dangles!
7851 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) {
7852 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
7854 // Forget all the expressions associated with users of the old value,
7855 // so that future queries will recompute the expressions using the new
7857 Value *Old = getValPtr();
7858 SmallVector<User *, 16> Worklist(Old->user_begin(), Old->user_end());
7859 SmallPtrSet<User *, 8> Visited;
7860 while (!Worklist.empty()) {
7861 User *U = Worklist.pop_back_val();
7862 // Deleting the Old value will cause this to dangle. Postpone
7863 // that until everything else is done.
7866 if (!Visited.insert(U).second)
7868 if (PHINode *PN = dyn_cast<PHINode>(U))
7869 SE->ConstantEvolutionLoopExitValue.erase(PN);
7870 SE->ValueExprMap.erase(U);
7871 Worklist.insert(Worklist.end(), U->user_begin(), U->user_end());
7873 // Delete the Old value.
7874 if (PHINode *PN = dyn_cast<PHINode>(Old))
7875 SE->ConstantEvolutionLoopExitValue.erase(PN);
7876 SE->ValueExprMap.erase(Old);
7877 // this now dangles!
7880 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
7881 : CallbackVH(V), SE(se) {}
7883 //===----------------------------------------------------------------------===//
7884 // ScalarEvolution Class Implementation
7885 //===----------------------------------------------------------------------===//
7887 ScalarEvolution::ScalarEvolution()
7888 : FunctionPass(ID), ValuesAtScopes(64), LoopDispositions(64),
7889 BlockDispositions(64), FirstUnknown(nullptr) {
7890 initializeScalarEvolutionPass(*PassRegistry::getPassRegistry());
7893 bool ScalarEvolution::runOnFunction(Function &F) {
7895 AC = &getAnalysis<AssumptionCacheTracker>().getAssumptionCache(F);
7896 LI = &getAnalysis<LoopInfoWrapperPass>().getLoopInfo();
7897 DataLayoutPass *DLP = getAnalysisIfAvailable<DataLayoutPass>();
7898 DL = DLP ? &DLP->getDataLayout() : nullptr;
7899 TLI = &getAnalysis<TargetLibraryInfoWrapperPass>().getTLI();
7900 DT = &getAnalysis<DominatorTreeWrapperPass>().getDomTree();
7904 void ScalarEvolution::releaseMemory() {
7905 // Iterate through all the SCEVUnknown instances and call their
7906 // destructors, so that they release their references to their values.
7907 for (SCEVUnknown *U = FirstUnknown; U; U = U->Next)
7909 FirstUnknown = nullptr;
7911 ValueExprMap.clear();
7913 // Free any extra memory created for ExitNotTakenInfo in the unlikely event
7914 // that a loop had multiple computable exits.
7915 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
7916 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end();
7921 assert(PendingLoopPredicates.empty() && "isImpliedCond garbage");
7923 BackedgeTakenCounts.clear();
7924 ConstantEvolutionLoopExitValue.clear();
7925 ValuesAtScopes.clear();
7926 LoopDispositions.clear();
7927 BlockDispositions.clear();
7928 UnsignedRanges.clear();
7929 SignedRanges.clear();
7930 UniqueSCEVs.clear();
7931 SCEVAllocator.Reset();
7934 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
7935 AU.setPreservesAll();
7936 AU.addRequired<AssumptionCacheTracker>();
7937 AU.addRequiredTransitive<LoopInfoWrapperPass>();
7938 AU.addRequiredTransitive<DominatorTreeWrapperPass>();
7939 AU.addRequired<TargetLibraryInfoWrapperPass>();
7942 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
7943 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
7946 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
7948 // Print all inner loops first
7949 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
7950 PrintLoopInfo(OS, SE, *I);
7953 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
7956 SmallVector<BasicBlock *, 8> ExitBlocks;
7957 L->getExitBlocks(ExitBlocks);
7958 if (ExitBlocks.size() != 1)
7959 OS << "<multiple exits> ";
7961 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
7962 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
7964 OS << "Unpredictable backedge-taken count. ";
7969 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
7972 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
7973 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
7975 OS << "Unpredictable max backedge-taken count. ";
7981 void ScalarEvolution::print(raw_ostream &OS, const Module *) const {
7982 // ScalarEvolution's implementation of the print method is to print
7983 // out SCEV values of all instructions that are interesting. Doing
7984 // this potentially causes it to create new SCEV objects though,
7985 // which technically conflicts with the const qualifier. This isn't
7986 // observable from outside the class though, so casting away the
7987 // const isn't dangerous.
7988 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
7990 OS << "Classifying expressions for: ";
7991 F->printAsOperand(OS, /*PrintType=*/false);
7993 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
7994 if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) {
7997 const SCEV *SV = SE.getSCEV(&*I);
8000 const Loop *L = LI->getLoopFor((*I).getParent());
8002 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
8009 OS << "\t\t" "Exits: ";
8010 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
8011 if (!SE.isLoopInvariant(ExitValue, L)) {
8012 OS << "<<Unknown>>";
8021 OS << "Determining loop execution counts for: ";
8022 F->printAsOperand(OS, /*PrintType=*/false);
8024 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
8025 PrintLoopInfo(OS, &SE, *I);
8028 ScalarEvolution::LoopDisposition
8029 ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) {
8030 auto &Values = LoopDispositions[S];
8031 for (auto &V : Values) {
8032 if (V.getPointer() == L)
8035 Values.emplace_back(L, LoopVariant);
8036 LoopDisposition D = computeLoopDisposition(S, L);
8037 auto &Values2 = LoopDispositions[S];
8038 for (auto &V : make_range(Values2.rbegin(), Values2.rend())) {
8039 if (V.getPointer() == L) {
8047 ScalarEvolution::LoopDisposition
8048 ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) {
8049 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
8051 return LoopInvariant;
8055 return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L);
8056 case scAddRecExpr: {
8057 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
8059 // If L is the addrec's loop, it's computable.
8060 if (AR->getLoop() == L)
8061 return LoopComputable;
8063 // Add recurrences are never invariant in the function-body (null loop).
8067 // This recurrence is variant w.r.t. L if L contains AR's loop.
8068 if (L->contains(AR->getLoop()))
8071 // This recurrence is invariant w.r.t. L if AR's loop contains L.
8072 if (AR->getLoop()->contains(L))
8073 return LoopInvariant;
8075 // This recurrence is variant w.r.t. L if any of its operands
8077 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
8079 if (!isLoopInvariant(*I, L))
8082 // Otherwise it's loop-invariant.
8083 return LoopInvariant;
8089 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
8090 bool HasVarying = false;
8091 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
8093 LoopDisposition D = getLoopDisposition(*I, L);
8094 if (D == LoopVariant)
8096 if (D == LoopComputable)
8099 return HasVarying ? LoopComputable : LoopInvariant;
8102 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
8103 LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L);
8104 if (LD == LoopVariant)
8106 LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L);
8107 if (RD == LoopVariant)
8109 return (LD == LoopInvariant && RD == LoopInvariant) ?
8110 LoopInvariant : LoopComputable;
8113 // All non-instruction values are loop invariant. All instructions are loop
8114 // invariant if they are not contained in the specified loop.
8115 // Instructions are never considered invariant in the function body
8116 // (null loop) because they are defined within the "loop".
8117 if (Instruction *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue()))
8118 return (L && !L->contains(I)) ? LoopInvariant : LoopVariant;
8119 return LoopInvariant;
8120 case scCouldNotCompute:
8121 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
8123 llvm_unreachable("Unknown SCEV kind!");
8126 bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) {
8127 return getLoopDisposition(S, L) == LoopInvariant;
8130 bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) {
8131 return getLoopDisposition(S, L) == LoopComputable;
8134 ScalarEvolution::BlockDisposition
8135 ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) {
8136 auto &Values = BlockDispositions[S];
8137 for (auto &V : Values) {
8138 if (V.getPointer() == BB)
8141 Values.emplace_back(BB, DoesNotDominateBlock);
8142 BlockDisposition D = computeBlockDisposition(S, BB);
8143 auto &Values2 = BlockDispositions[S];
8144 for (auto &V : make_range(Values2.rbegin(), Values2.rend())) {
8145 if (V.getPointer() == BB) {
8153 ScalarEvolution::BlockDisposition
8154 ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) {
8155 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
8157 return ProperlyDominatesBlock;
8161 return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB);
8162 case scAddRecExpr: {
8163 // This uses a "dominates" query instead of "properly dominates" query
8164 // to test for proper dominance too, because the instruction which
8165 // produces the addrec's value is a PHI, and a PHI effectively properly
8166 // dominates its entire containing block.
8167 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
8168 if (!DT->dominates(AR->getLoop()->getHeader(), BB))
8169 return DoesNotDominateBlock;
8171 // FALL THROUGH into SCEVNAryExpr handling.
8176 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
8178 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
8180 BlockDisposition D = getBlockDisposition(*I, BB);
8181 if (D == DoesNotDominateBlock)
8182 return DoesNotDominateBlock;
8183 if (D == DominatesBlock)
8186 return Proper ? ProperlyDominatesBlock : DominatesBlock;
8189 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
8190 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
8191 BlockDisposition LD = getBlockDisposition(LHS, BB);
8192 if (LD == DoesNotDominateBlock)
8193 return DoesNotDominateBlock;
8194 BlockDisposition RD = getBlockDisposition(RHS, BB);
8195 if (RD == DoesNotDominateBlock)
8196 return DoesNotDominateBlock;
8197 return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ?
8198 ProperlyDominatesBlock : DominatesBlock;
8201 if (Instruction *I =
8202 dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) {
8203 if (I->getParent() == BB)
8204 return DominatesBlock;
8205 if (DT->properlyDominates(I->getParent(), BB))
8206 return ProperlyDominatesBlock;
8207 return DoesNotDominateBlock;
8209 return ProperlyDominatesBlock;
8210 case scCouldNotCompute:
8211 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
8213 llvm_unreachable("Unknown SCEV kind!");
8216 bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) {
8217 return getBlockDisposition(S, BB) >= DominatesBlock;
8220 bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) {
8221 return getBlockDisposition(S, BB) == ProperlyDominatesBlock;
8225 // Search for a SCEV expression node within an expression tree.
8226 // Implements SCEVTraversal::Visitor.
8231 SCEVSearch(const SCEV *N): Node(N), IsFound(false) {}
8233 bool follow(const SCEV *S) {
8234 IsFound |= (S == Node);
8237 bool isDone() const { return IsFound; }
8241 bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const {
8242 SCEVSearch Search(Op);
8243 visitAll(S, Search);
8244 return Search.IsFound;
8247 void ScalarEvolution::forgetMemoizedResults(const SCEV *S) {
8248 ValuesAtScopes.erase(S);
8249 LoopDispositions.erase(S);
8250 BlockDispositions.erase(S);
8251 UnsignedRanges.erase(S);
8252 SignedRanges.erase(S);
8254 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
8255 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end(); I != E; ) {
8256 BackedgeTakenInfo &BEInfo = I->second;
8257 if (BEInfo.hasOperand(S, this)) {
8259 BackedgeTakenCounts.erase(I++);
8266 typedef DenseMap<const Loop *, std::string> VerifyMap;
8268 /// replaceSubString - Replaces all occurrences of From in Str with To.
8269 static void replaceSubString(std::string &Str, StringRef From, StringRef To) {
8271 while ((Pos = Str.find(From, Pos)) != std::string::npos) {
8272 Str.replace(Pos, From.size(), To.data(), To.size());
8277 /// getLoopBackedgeTakenCounts - Helper method for verifyAnalysis.
8279 getLoopBackedgeTakenCounts(Loop *L, VerifyMap &Map, ScalarEvolution &SE) {
8280 for (Loop::reverse_iterator I = L->rbegin(), E = L->rend(); I != E; ++I) {
8281 getLoopBackedgeTakenCounts(*I, Map, SE); // recurse.
8283 std::string &S = Map[L];
8285 raw_string_ostream OS(S);
8286 SE.getBackedgeTakenCount(L)->print(OS);
8288 // false and 0 are semantically equivalent. This can happen in dead loops.
8289 replaceSubString(OS.str(), "false", "0");
8290 // Remove wrap flags, their use in SCEV is highly fragile.
8291 // FIXME: Remove this when SCEV gets smarter about them.
8292 replaceSubString(OS.str(), "<nw>", "");
8293 replaceSubString(OS.str(), "<nsw>", "");
8294 replaceSubString(OS.str(), "<nuw>", "");
8299 void ScalarEvolution::verifyAnalysis() const {
8303 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
8305 // Gather stringified backedge taken counts for all loops using SCEV's caches.
8306 // FIXME: It would be much better to store actual values instead of strings,
8307 // but SCEV pointers will change if we drop the caches.
8308 VerifyMap BackedgeDumpsOld, BackedgeDumpsNew;
8309 for (LoopInfo::reverse_iterator I = LI->rbegin(), E = LI->rend(); I != E; ++I)
8310 getLoopBackedgeTakenCounts(*I, BackedgeDumpsOld, SE);
8312 // Gather stringified backedge taken counts for all loops without using
8315 for (LoopInfo::reverse_iterator I = LI->rbegin(), E = LI->rend(); I != E; ++I)
8316 getLoopBackedgeTakenCounts(*I, BackedgeDumpsNew, SE);
8318 // Now compare whether they're the same with and without caches. This allows
8319 // verifying that no pass changed the cache.
8320 assert(BackedgeDumpsOld.size() == BackedgeDumpsNew.size() &&
8321 "New loops suddenly appeared!");
8323 for (VerifyMap::iterator OldI = BackedgeDumpsOld.begin(),
8324 OldE = BackedgeDumpsOld.end(),
8325 NewI = BackedgeDumpsNew.begin();
8326 OldI != OldE; ++OldI, ++NewI) {
8327 assert(OldI->first == NewI->first && "Loop order changed!");
8329 // Compare the stringified SCEVs. We don't care if undef backedgetaken count
8331 // FIXME: We currently ignore SCEV changes from/to CouldNotCompute. This
8332 // means that a pass is buggy or SCEV has to learn a new pattern but is
8333 // usually not harmful.
8334 if (OldI->second != NewI->second &&
8335 OldI->second.find("undef") == std::string::npos &&
8336 NewI->second.find("undef") == std::string::npos &&
8337 OldI->second != "***COULDNOTCOMPUTE***" &&
8338 NewI->second != "***COULDNOTCOMPUTE***") {
8339 dbgs() << "SCEVValidator: SCEV for loop '"
8340 << OldI->first->getHeader()->getName()
8341 << "' changed from '" << OldI->second
8342 << "' to '" << NewI->second << "'!\n";
8347 // TODO: Verify more things.