1 //===- ScalarEvolution.cpp - Scalar Evolution Analysis --------------------===//
3 // The LLVM Compiler Infrastructure
5 // This file is distributed under the University of Illinois Open Source
6 // License. See LICENSE.TXT for details.
8 //===----------------------------------------------------------------------===//
10 // This file contains the implementation of the scalar evolution analysis
11 // engine, which is used primarily to analyze expressions involving induction
12 // variables in loops.
14 // There are several aspects to this library. First is the representation of
15 // scalar expressions, which are represented as subclasses of the SCEV class.
16 // These classes are used to represent certain types of subexpressions that we
17 // can handle. We only create one SCEV of a particular shape, so
18 // pointer-comparisons for equality are legal.
20 // One important aspect of the SCEV objects is that they are never cyclic, even
21 // if there is a cycle in the dataflow for an expression (ie, a PHI node). If
22 // the PHI node is one of the idioms that we can represent (e.g., a polynomial
23 // recurrence) then we represent it directly as a recurrence node, otherwise we
24 // represent it as a SCEVUnknown node.
26 // In addition to being able to represent expressions of various types, we also
27 // have folders that are used to build the *canonical* representation for a
28 // particular expression. These folders are capable of using a variety of
29 // rewrite rules to simplify the expressions.
31 // Once the folders are defined, we can implement the more interesting
32 // higher-level code, such as the code that recognizes PHI nodes of various
33 // types, computes the execution count of a loop, etc.
35 // TODO: We should use these routines and value representations to implement
36 // dependence analysis!
38 //===----------------------------------------------------------------------===//
40 // There are several good references for the techniques used in this analysis.
42 // Chains of recurrences -- a method to expedite the evaluation
43 // of closed-form functions
44 // Olaf Bachmann, Paul S. Wang, Eugene V. Zima
46 // On computational properties of chains of recurrences
49 // Symbolic Evaluation of Chains of Recurrences for Loop Optimization
50 // Robert A. van Engelen
52 // Efficient Symbolic Analysis for Optimizing Compilers
53 // Robert A. van Engelen
55 // Using the chains of recurrences algebra for data dependence testing and
56 // induction variable substitution
57 // MS Thesis, Johnie Birch
59 //===----------------------------------------------------------------------===//
61 #include "llvm/Analysis/ScalarEvolution.h"
62 #include "llvm/ADT/Optional.h"
63 #include "llvm/ADT/STLExtras.h"
64 #include "llvm/ADT/SmallPtrSet.h"
65 #include "llvm/ADT/Statistic.h"
66 #include "llvm/Analysis/AssumptionCache.h"
67 #include "llvm/Analysis/ConstantFolding.h"
68 #include "llvm/Analysis/InstructionSimplify.h"
69 #include "llvm/Analysis/LoopInfo.h"
70 #include "llvm/Analysis/ScalarEvolutionExpressions.h"
71 #include "llvm/Analysis/TargetLibraryInfo.h"
72 #include "llvm/Analysis/ValueTracking.h"
73 #include "llvm/IR/ConstantRange.h"
74 #include "llvm/IR/Constants.h"
75 #include "llvm/IR/DataLayout.h"
76 #include "llvm/IR/DerivedTypes.h"
77 #include "llvm/IR/Dominators.h"
78 #include "llvm/IR/GetElementPtrTypeIterator.h"
79 #include "llvm/IR/GlobalAlias.h"
80 #include "llvm/IR/GlobalVariable.h"
81 #include "llvm/IR/InstIterator.h"
82 #include "llvm/IR/Instructions.h"
83 #include "llvm/IR/LLVMContext.h"
84 #include "llvm/IR/Metadata.h"
85 #include "llvm/IR/Operator.h"
86 #include "llvm/Support/CommandLine.h"
87 #include "llvm/Support/Debug.h"
88 #include "llvm/Support/ErrorHandling.h"
89 #include "llvm/Support/MathExtras.h"
90 #include "llvm/Support/raw_ostream.h"
94 #define DEBUG_TYPE "scalar-evolution"
96 STATISTIC(NumArrayLenItCounts,
97 "Number of trip counts computed with array length");
98 STATISTIC(NumTripCountsComputed,
99 "Number of loops with predictable loop counts");
100 STATISTIC(NumTripCountsNotComputed,
101 "Number of loops without predictable loop counts");
102 STATISTIC(NumBruteForceTripCountsComputed,
103 "Number of loops with trip counts computed by force");
105 static cl::opt<unsigned>
106 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
107 cl::desc("Maximum number of iterations SCEV will "
108 "symbolically execute a constant "
112 // FIXME: Enable this with XDEBUG when the test suite is clean.
114 VerifySCEV("verify-scev",
115 cl::desc("Verify ScalarEvolution's backedge taken counts (slow)"));
117 INITIALIZE_PASS_BEGIN(ScalarEvolution, "scalar-evolution",
118 "Scalar Evolution Analysis", false, true)
119 INITIALIZE_PASS_DEPENDENCY(AssumptionCacheTracker)
120 INITIALIZE_PASS_DEPENDENCY(LoopInfoWrapperPass)
121 INITIALIZE_PASS_DEPENDENCY(DominatorTreeWrapperPass)
122 INITIALIZE_PASS_DEPENDENCY(TargetLibraryInfoWrapperPass)
123 INITIALIZE_PASS_END(ScalarEvolution, "scalar-evolution",
124 "Scalar Evolution Analysis", false, true)
125 char ScalarEvolution::ID = 0;
127 //===----------------------------------------------------------------------===//
128 // SCEV class definitions
129 //===----------------------------------------------------------------------===//
131 //===----------------------------------------------------------------------===//
132 // Implementation of the SCEV class.
135 #if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP)
136 void SCEV::dump() const {
142 void SCEV::print(raw_ostream &OS) const {
143 switch (static_cast<SCEVTypes>(getSCEVType())) {
145 cast<SCEVConstant>(this)->getValue()->printAsOperand(OS, false);
148 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(this);
149 const SCEV *Op = Trunc->getOperand();
150 OS << "(trunc " << *Op->getType() << " " << *Op << " to "
151 << *Trunc->getType() << ")";
155 const SCEVZeroExtendExpr *ZExt = cast<SCEVZeroExtendExpr>(this);
156 const SCEV *Op = ZExt->getOperand();
157 OS << "(zext " << *Op->getType() << " " << *Op << " to "
158 << *ZExt->getType() << ")";
162 const SCEVSignExtendExpr *SExt = cast<SCEVSignExtendExpr>(this);
163 const SCEV *Op = SExt->getOperand();
164 OS << "(sext " << *Op->getType() << " " << *Op << " to "
165 << *SExt->getType() << ")";
169 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(this);
170 OS << "{" << *AR->getOperand(0);
171 for (unsigned i = 1, e = AR->getNumOperands(); i != e; ++i)
172 OS << ",+," << *AR->getOperand(i);
174 if (AR->getNoWrapFlags(FlagNUW))
176 if (AR->getNoWrapFlags(FlagNSW))
178 if (AR->getNoWrapFlags(FlagNW) &&
179 !AR->getNoWrapFlags((NoWrapFlags)(FlagNUW | FlagNSW)))
181 AR->getLoop()->getHeader()->printAsOperand(OS, /*PrintType=*/false);
189 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(this);
190 const char *OpStr = nullptr;
191 switch (NAry->getSCEVType()) {
192 case scAddExpr: OpStr = " + "; break;
193 case scMulExpr: OpStr = " * "; break;
194 case scUMaxExpr: OpStr = " umax "; break;
195 case scSMaxExpr: OpStr = " smax "; break;
198 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
201 if (std::next(I) != E)
205 switch (NAry->getSCEVType()) {
208 if (NAry->getNoWrapFlags(FlagNUW))
210 if (NAry->getNoWrapFlags(FlagNSW))
216 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(this);
217 OS << "(" << *UDiv->getLHS() << " /u " << *UDiv->getRHS() << ")";
221 const SCEVUnknown *U = cast<SCEVUnknown>(this);
223 if (U->isSizeOf(AllocTy)) {
224 OS << "sizeof(" << *AllocTy << ")";
227 if (U->isAlignOf(AllocTy)) {
228 OS << "alignof(" << *AllocTy << ")";
234 if (U->isOffsetOf(CTy, FieldNo)) {
235 OS << "offsetof(" << *CTy << ", ";
236 FieldNo->printAsOperand(OS, false);
241 // Otherwise just print it normally.
242 U->getValue()->printAsOperand(OS, false);
245 case scCouldNotCompute:
246 OS << "***COULDNOTCOMPUTE***";
249 llvm_unreachable("Unknown SCEV kind!");
252 Type *SCEV::getType() const {
253 switch (static_cast<SCEVTypes>(getSCEVType())) {
255 return cast<SCEVConstant>(this)->getType();
259 return cast<SCEVCastExpr>(this)->getType();
264 return cast<SCEVNAryExpr>(this)->getType();
266 return cast<SCEVAddExpr>(this)->getType();
268 return cast<SCEVUDivExpr>(this)->getType();
270 return cast<SCEVUnknown>(this)->getType();
271 case scCouldNotCompute:
272 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
274 llvm_unreachable("Unknown SCEV kind!");
277 bool SCEV::isZero() const {
278 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
279 return SC->getValue()->isZero();
283 bool SCEV::isOne() const {
284 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
285 return SC->getValue()->isOne();
289 bool SCEV::isAllOnesValue() const {
290 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
291 return SC->getValue()->isAllOnesValue();
295 /// isNonConstantNegative - Return true if the specified scev is negated, but
297 bool SCEV::isNonConstantNegative() const {
298 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(this);
299 if (!Mul) return false;
301 // If there is a constant factor, it will be first.
302 const SCEVConstant *SC = dyn_cast<SCEVConstant>(Mul->getOperand(0));
303 if (!SC) return false;
305 // Return true if the value is negative, this matches things like (-42 * V).
306 return SC->getValue()->getValue().isNegative();
309 SCEVCouldNotCompute::SCEVCouldNotCompute() :
310 SCEV(FoldingSetNodeIDRef(), scCouldNotCompute) {}
312 bool SCEVCouldNotCompute::classof(const SCEV *S) {
313 return S->getSCEVType() == scCouldNotCompute;
316 const SCEV *ScalarEvolution::getConstant(ConstantInt *V) {
318 ID.AddInteger(scConstant);
321 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
322 SCEV *S = new (SCEVAllocator) SCEVConstant(ID.Intern(SCEVAllocator), V);
323 UniqueSCEVs.InsertNode(S, IP);
327 const SCEV *ScalarEvolution::getConstant(const APInt &Val) {
328 return getConstant(ConstantInt::get(getContext(), Val));
332 ScalarEvolution::getConstant(Type *Ty, uint64_t V, bool isSigned) {
333 IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty));
334 return getConstant(ConstantInt::get(ITy, V, isSigned));
337 SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID,
338 unsigned SCEVTy, const SCEV *op, Type *ty)
339 : SCEV(ID, SCEVTy), Op(op), Ty(ty) {}
341 SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID,
342 const SCEV *op, Type *ty)
343 : SCEVCastExpr(ID, scTruncate, op, ty) {
344 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
345 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
346 "Cannot truncate non-integer value!");
349 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID,
350 const SCEV *op, Type *ty)
351 : SCEVCastExpr(ID, scZeroExtend, op, ty) {
352 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
353 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
354 "Cannot zero extend non-integer value!");
357 SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID,
358 const SCEV *op, Type *ty)
359 : SCEVCastExpr(ID, scSignExtend, op, ty) {
360 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
361 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
362 "Cannot sign extend non-integer value!");
365 void SCEVUnknown::deleted() {
366 // Clear this SCEVUnknown from various maps.
367 SE->forgetMemoizedResults(this);
369 // Remove this SCEVUnknown from the uniquing map.
370 SE->UniqueSCEVs.RemoveNode(this);
372 // Release the value.
376 void SCEVUnknown::allUsesReplacedWith(Value *New) {
377 // Clear this SCEVUnknown from various maps.
378 SE->forgetMemoizedResults(this);
380 // Remove this SCEVUnknown from the uniquing map.
381 SE->UniqueSCEVs.RemoveNode(this);
383 // Update this SCEVUnknown to point to the new value. This is needed
384 // because there may still be outstanding SCEVs which still point to
389 bool SCEVUnknown::isSizeOf(Type *&AllocTy) const {
390 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
391 if (VCE->getOpcode() == Instruction::PtrToInt)
392 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
393 if (CE->getOpcode() == Instruction::GetElementPtr &&
394 CE->getOperand(0)->isNullValue() &&
395 CE->getNumOperands() == 2)
396 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1)))
398 AllocTy = cast<PointerType>(CE->getOperand(0)->getType())
406 bool SCEVUnknown::isAlignOf(Type *&AllocTy) const {
407 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
408 if (VCE->getOpcode() == Instruction::PtrToInt)
409 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
410 if (CE->getOpcode() == Instruction::GetElementPtr &&
411 CE->getOperand(0)->isNullValue()) {
413 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
414 if (StructType *STy = dyn_cast<StructType>(Ty))
415 if (!STy->isPacked() &&
416 CE->getNumOperands() == 3 &&
417 CE->getOperand(1)->isNullValue()) {
418 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2)))
420 STy->getNumElements() == 2 &&
421 STy->getElementType(0)->isIntegerTy(1)) {
422 AllocTy = STy->getElementType(1);
431 bool SCEVUnknown::isOffsetOf(Type *&CTy, Constant *&FieldNo) const {
432 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
433 if (VCE->getOpcode() == Instruction::PtrToInt)
434 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
435 if (CE->getOpcode() == Instruction::GetElementPtr &&
436 CE->getNumOperands() == 3 &&
437 CE->getOperand(0)->isNullValue() &&
438 CE->getOperand(1)->isNullValue()) {
440 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
441 // Ignore vector types here so that ScalarEvolutionExpander doesn't
442 // emit getelementptrs that index into vectors.
443 if (Ty->isStructTy() || Ty->isArrayTy()) {
445 FieldNo = CE->getOperand(2);
453 //===----------------------------------------------------------------------===//
455 //===----------------------------------------------------------------------===//
458 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
459 /// than the complexity of the RHS. This comparator is used to canonicalize
461 class SCEVComplexityCompare {
462 const LoopInfo *const LI;
464 explicit SCEVComplexityCompare(const LoopInfo *li) : LI(li) {}
466 // Return true or false if LHS is less than, or at least RHS, respectively.
467 bool operator()(const SCEV *LHS, const SCEV *RHS) const {
468 return compare(LHS, RHS) < 0;
471 // Return negative, zero, or positive, if LHS is less than, equal to, or
472 // greater than RHS, respectively. A three-way result allows recursive
473 // comparisons to be more efficient.
474 int compare(const SCEV *LHS, const SCEV *RHS) const {
475 // Fast-path: SCEVs are uniqued so we can do a quick equality check.
479 // Primarily, sort the SCEVs by their getSCEVType().
480 unsigned LType = LHS->getSCEVType(), RType = RHS->getSCEVType();
482 return (int)LType - (int)RType;
484 // Aside from the getSCEVType() ordering, the particular ordering
485 // isn't very important except that it's beneficial to be consistent,
486 // so that (a + b) and (b + a) don't end up as different expressions.
487 switch (static_cast<SCEVTypes>(LType)) {
489 const SCEVUnknown *LU = cast<SCEVUnknown>(LHS);
490 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
492 // Sort SCEVUnknown values with some loose heuristics. TODO: This is
493 // not as complete as it could be.
494 const Value *LV = LU->getValue(), *RV = RU->getValue();
496 // Order pointer values after integer values. This helps SCEVExpander
498 bool LIsPointer = LV->getType()->isPointerTy(),
499 RIsPointer = RV->getType()->isPointerTy();
500 if (LIsPointer != RIsPointer)
501 return (int)LIsPointer - (int)RIsPointer;
503 // Compare getValueID values.
504 unsigned LID = LV->getValueID(),
505 RID = RV->getValueID();
507 return (int)LID - (int)RID;
509 // Sort arguments by their position.
510 if (const Argument *LA = dyn_cast<Argument>(LV)) {
511 const Argument *RA = cast<Argument>(RV);
512 unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo();
513 return (int)LArgNo - (int)RArgNo;
516 // For instructions, compare their loop depth, and their operand
517 // count. This is pretty loose.
518 if (const Instruction *LInst = dyn_cast<Instruction>(LV)) {
519 const Instruction *RInst = cast<Instruction>(RV);
521 // Compare loop depths.
522 const BasicBlock *LParent = LInst->getParent(),
523 *RParent = RInst->getParent();
524 if (LParent != RParent) {
525 unsigned LDepth = LI->getLoopDepth(LParent),
526 RDepth = LI->getLoopDepth(RParent);
527 if (LDepth != RDepth)
528 return (int)LDepth - (int)RDepth;
531 // Compare the number of operands.
532 unsigned LNumOps = LInst->getNumOperands(),
533 RNumOps = RInst->getNumOperands();
534 return (int)LNumOps - (int)RNumOps;
541 const SCEVConstant *LC = cast<SCEVConstant>(LHS);
542 const SCEVConstant *RC = cast<SCEVConstant>(RHS);
544 // Compare constant values.
545 const APInt &LA = LC->getValue()->getValue();
546 const APInt &RA = RC->getValue()->getValue();
547 unsigned LBitWidth = LA.getBitWidth(), RBitWidth = RA.getBitWidth();
548 if (LBitWidth != RBitWidth)
549 return (int)LBitWidth - (int)RBitWidth;
550 return LA.ult(RA) ? -1 : 1;
554 const SCEVAddRecExpr *LA = cast<SCEVAddRecExpr>(LHS);
555 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS);
557 // Compare addrec loop depths.
558 const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop();
559 if (LLoop != RLoop) {
560 unsigned LDepth = LLoop->getLoopDepth(),
561 RDepth = RLoop->getLoopDepth();
562 if (LDepth != RDepth)
563 return (int)LDepth - (int)RDepth;
566 // Addrec complexity grows with operand count.
567 unsigned LNumOps = LA->getNumOperands(), RNumOps = RA->getNumOperands();
568 if (LNumOps != RNumOps)
569 return (int)LNumOps - (int)RNumOps;
571 // Lexicographically compare.
572 for (unsigned i = 0; i != LNumOps; ++i) {
573 long X = compare(LA->getOperand(i), RA->getOperand(i));
585 const SCEVNAryExpr *LC = cast<SCEVNAryExpr>(LHS);
586 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
588 // Lexicographically compare n-ary expressions.
589 unsigned LNumOps = LC->getNumOperands(), RNumOps = RC->getNumOperands();
590 if (LNumOps != RNumOps)
591 return (int)LNumOps - (int)RNumOps;
593 for (unsigned i = 0; i != LNumOps; ++i) {
596 long X = compare(LC->getOperand(i), RC->getOperand(i));
600 return (int)LNumOps - (int)RNumOps;
604 const SCEVUDivExpr *LC = cast<SCEVUDivExpr>(LHS);
605 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
607 // Lexicographically compare udiv expressions.
608 long X = compare(LC->getLHS(), RC->getLHS());
611 return compare(LC->getRHS(), RC->getRHS());
617 const SCEVCastExpr *LC = cast<SCEVCastExpr>(LHS);
618 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
620 // Compare cast expressions by operand.
621 return compare(LC->getOperand(), RC->getOperand());
624 case scCouldNotCompute:
625 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
627 llvm_unreachable("Unknown SCEV kind!");
632 /// GroupByComplexity - Given a list of SCEV objects, order them by their
633 /// complexity, and group objects of the same complexity together by value.
634 /// When this routine is finished, we know that any duplicates in the vector are
635 /// consecutive and that complexity is monotonically increasing.
637 /// Note that we go take special precautions to ensure that we get deterministic
638 /// results from this routine. In other words, we don't want the results of
639 /// this to depend on where the addresses of various SCEV objects happened to
642 static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops,
644 if (Ops.size() < 2) return; // Noop
645 if (Ops.size() == 2) {
646 // This is the common case, which also happens to be trivially simple.
648 const SCEV *&LHS = Ops[0], *&RHS = Ops[1];
649 if (SCEVComplexityCompare(LI)(RHS, LHS))
654 // Do the rough sort by complexity.
655 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI));
657 // Now that we are sorted by complexity, group elements of the same
658 // complexity. Note that this is, at worst, N^2, but the vector is likely to
659 // be extremely short in practice. Note that we take this approach because we
660 // do not want to depend on the addresses of the objects we are grouping.
661 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
662 const SCEV *S = Ops[i];
663 unsigned Complexity = S->getSCEVType();
665 // If there are any objects of the same complexity and same value as this
667 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
668 if (Ops[j] == S) { // Found a duplicate.
669 // Move it to immediately after i'th element.
670 std::swap(Ops[i+1], Ops[j]);
671 ++i; // no need to rescan it.
672 if (i == e-2) return; // Done!
679 struct FindSCEVSize {
681 FindSCEVSize() : Size(0) {}
683 bool follow(const SCEV *S) {
685 // Keep looking at all operands of S.
688 bool isDone() const {
694 // Returns the size of the SCEV S.
695 static inline int sizeOfSCEV(const SCEV *S) {
697 SCEVTraversal<FindSCEVSize> ST(F);
704 struct SCEVDivision : public SCEVVisitor<SCEVDivision, void> {
706 // Computes the Quotient and Remainder of the division of Numerator by
708 static void divide(ScalarEvolution &SE, const SCEV *Numerator,
709 const SCEV *Denominator, const SCEV **Quotient,
710 const SCEV **Remainder) {
711 assert(Numerator && Denominator && "Uninitialized SCEV");
713 SCEVDivision D(SE, Numerator, Denominator);
715 // Check for the trivial case here to avoid having to check for it in the
717 if (Numerator == Denominator) {
723 if (Numerator->isZero()) {
729 // A simple case when N/1. The quotient is N.
730 if (Denominator->isOne()) {
731 *Quotient = Numerator;
736 // Split the Denominator when it is a product.
737 if (const SCEVMulExpr *T = dyn_cast<const SCEVMulExpr>(Denominator)) {
739 *Quotient = Numerator;
740 for (const SCEV *Op : T->operands()) {
741 divide(SE, *Quotient, Op, &Q, &R);
744 // Bail out when the Numerator is not divisible by one of the terms of
748 *Remainder = Numerator;
757 *Quotient = D.Quotient;
758 *Remainder = D.Remainder;
761 // Except in the trivial case described above, we do not know how to divide
762 // Expr by Denominator for the following functions with empty implementation.
763 void visitTruncateExpr(const SCEVTruncateExpr *Numerator) {}
764 void visitZeroExtendExpr(const SCEVZeroExtendExpr *Numerator) {}
765 void visitSignExtendExpr(const SCEVSignExtendExpr *Numerator) {}
766 void visitUDivExpr(const SCEVUDivExpr *Numerator) {}
767 void visitSMaxExpr(const SCEVSMaxExpr *Numerator) {}
768 void visitUMaxExpr(const SCEVUMaxExpr *Numerator) {}
769 void visitUnknown(const SCEVUnknown *Numerator) {}
770 void visitCouldNotCompute(const SCEVCouldNotCompute *Numerator) {}
772 void visitConstant(const SCEVConstant *Numerator) {
773 if (const SCEVConstant *D = dyn_cast<SCEVConstant>(Denominator)) {
774 APInt NumeratorVal = Numerator->getValue()->getValue();
775 APInt DenominatorVal = D->getValue()->getValue();
776 uint32_t NumeratorBW = NumeratorVal.getBitWidth();
777 uint32_t DenominatorBW = DenominatorVal.getBitWidth();
779 if (NumeratorBW > DenominatorBW)
780 DenominatorVal = DenominatorVal.sext(NumeratorBW);
781 else if (NumeratorBW < DenominatorBW)
782 NumeratorVal = NumeratorVal.sext(DenominatorBW);
784 APInt QuotientVal(NumeratorVal.getBitWidth(), 0);
785 APInt RemainderVal(NumeratorVal.getBitWidth(), 0);
786 APInt::sdivrem(NumeratorVal, DenominatorVal, QuotientVal, RemainderVal);
787 Quotient = SE.getConstant(QuotientVal);
788 Remainder = SE.getConstant(RemainderVal);
793 void visitAddRecExpr(const SCEVAddRecExpr *Numerator) {
794 const SCEV *StartQ, *StartR, *StepQ, *StepR;
795 assert(Numerator->isAffine() && "Numerator should be affine");
796 divide(SE, Numerator->getStart(), Denominator, &StartQ, &StartR);
797 divide(SE, Numerator->getStepRecurrence(SE), Denominator, &StepQ, &StepR);
798 // Bail out if the types do not match.
799 Type *Ty = Denominator->getType();
800 if (Ty != StartQ->getType() || Ty != StartR->getType() ||
801 Ty != StepQ->getType() || Ty != StepR->getType()) {
803 Remainder = Numerator;
806 Quotient = SE.getAddRecExpr(StartQ, StepQ, Numerator->getLoop(),
807 Numerator->getNoWrapFlags());
808 Remainder = SE.getAddRecExpr(StartR, StepR, Numerator->getLoop(),
809 Numerator->getNoWrapFlags());
812 void visitAddExpr(const SCEVAddExpr *Numerator) {
813 SmallVector<const SCEV *, 2> Qs, Rs;
814 Type *Ty = Denominator->getType();
816 for (const SCEV *Op : Numerator->operands()) {
818 divide(SE, Op, Denominator, &Q, &R);
820 // Bail out if types do not match.
821 if (Ty != Q->getType() || Ty != R->getType()) {
823 Remainder = Numerator;
831 if (Qs.size() == 1) {
837 Quotient = SE.getAddExpr(Qs);
838 Remainder = SE.getAddExpr(Rs);
841 void visitMulExpr(const SCEVMulExpr *Numerator) {
842 SmallVector<const SCEV *, 2> Qs;
843 Type *Ty = Denominator->getType();
845 bool FoundDenominatorTerm = false;
846 for (const SCEV *Op : Numerator->operands()) {
847 // Bail out if types do not match.
848 if (Ty != Op->getType()) {
850 Remainder = Numerator;
854 if (FoundDenominatorTerm) {
859 // Check whether Denominator divides one of the product operands.
861 divide(SE, Op, Denominator, &Q, &R);
867 // Bail out if types do not match.
868 if (Ty != Q->getType()) {
870 Remainder = Numerator;
874 FoundDenominatorTerm = true;
878 if (FoundDenominatorTerm) {
883 Quotient = SE.getMulExpr(Qs);
887 if (!isa<SCEVUnknown>(Denominator)) {
889 Remainder = Numerator;
893 // The Remainder is obtained by replacing Denominator by 0 in Numerator.
894 ValueToValueMap RewriteMap;
895 RewriteMap[cast<SCEVUnknown>(Denominator)->getValue()] =
896 cast<SCEVConstant>(Zero)->getValue();
897 Remainder = SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true);
899 if (Remainder->isZero()) {
900 // The Quotient is obtained by replacing Denominator by 1 in Numerator.
901 RewriteMap[cast<SCEVUnknown>(Denominator)->getValue()] =
902 cast<SCEVConstant>(One)->getValue();
904 SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true);
908 // Quotient is (Numerator - Remainder) divided by Denominator.
910 const SCEV *Diff = SE.getMinusSCEV(Numerator, Remainder);
911 if (sizeOfSCEV(Diff) > sizeOfSCEV(Numerator)) {
912 // This SCEV does not seem to simplify: fail the division here.
914 Remainder = Numerator;
917 divide(SE, Diff, Denominator, &Q, &R);
919 "(Numerator - Remainder) should evenly divide Denominator");
924 SCEVDivision(ScalarEvolution &S, const SCEV *Numerator,
925 const SCEV *Denominator)
926 : SE(S), Denominator(Denominator) {
927 Zero = SE.getConstant(Denominator->getType(), 0);
928 One = SE.getConstant(Denominator->getType(), 1);
930 // By default, we don't know how to divide Expr by Denominator.
931 // Providing the default here simplifies the rest of the code.
933 Remainder = Numerator;
937 const SCEV *Denominator, *Quotient, *Remainder, *Zero, *One;
942 //===----------------------------------------------------------------------===//
943 // Simple SCEV method implementations
944 //===----------------------------------------------------------------------===//
946 /// BinomialCoefficient - Compute BC(It, K). The result has width W.
948 static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K,
951 // Handle the simplest case efficiently.
953 return SE.getTruncateOrZeroExtend(It, ResultTy);
955 // We are using the following formula for BC(It, K):
957 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
959 // Suppose, W is the bitwidth of the return value. We must be prepared for
960 // overflow. Hence, we must assure that the result of our computation is
961 // equal to the accurate one modulo 2^W. Unfortunately, division isn't
962 // safe in modular arithmetic.
964 // However, this code doesn't use exactly that formula; the formula it uses
965 // is something like the following, where T is the number of factors of 2 in
966 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
969 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
971 // This formula is trivially equivalent to the previous formula. However,
972 // this formula can be implemented much more efficiently. The trick is that
973 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
974 // arithmetic. To do exact division in modular arithmetic, all we have
975 // to do is multiply by the inverse. Therefore, this step can be done at
978 // The next issue is how to safely do the division by 2^T. The way this
979 // is done is by doing the multiplication step at a width of at least W + T
980 // bits. This way, the bottom W+T bits of the product are accurate. Then,
981 // when we perform the division by 2^T (which is equivalent to a right shift
982 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
983 // truncated out after the division by 2^T.
985 // In comparison to just directly using the first formula, this technique
986 // is much more efficient; using the first formula requires W * K bits,
987 // but this formula less than W + K bits. Also, the first formula requires
988 // a division step, whereas this formula only requires multiplies and shifts.
990 // It doesn't matter whether the subtraction step is done in the calculation
991 // width or the input iteration count's width; if the subtraction overflows,
992 // the result must be zero anyway. We prefer here to do it in the width of
993 // the induction variable because it helps a lot for certain cases; CodeGen
994 // isn't smart enough to ignore the overflow, which leads to much less
995 // efficient code if the width of the subtraction is wider than the native
998 // (It's possible to not widen at all by pulling out factors of 2 before
999 // the multiplication; for example, K=2 can be calculated as
1000 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
1001 // extra arithmetic, so it's not an obvious win, and it gets
1002 // much more complicated for K > 3.)
1004 // Protection from insane SCEVs; this bound is conservative,
1005 // but it probably doesn't matter.
1007 return SE.getCouldNotCompute();
1009 unsigned W = SE.getTypeSizeInBits(ResultTy);
1011 // Calculate K! / 2^T and T; we divide out the factors of two before
1012 // multiplying for calculating K! / 2^T to avoid overflow.
1013 // Other overflow doesn't matter because we only care about the bottom
1014 // W bits of the result.
1015 APInt OddFactorial(W, 1);
1017 for (unsigned i = 3; i <= K; ++i) {
1019 unsigned TwoFactors = Mult.countTrailingZeros();
1021 Mult = Mult.lshr(TwoFactors);
1022 OddFactorial *= Mult;
1025 // We need at least W + T bits for the multiplication step
1026 unsigned CalculationBits = W + T;
1028 // Calculate 2^T, at width T+W.
1029 APInt DivFactor = APInt::getOneBitSet(CalculationBits, T);
1031 // Calculate the multiplicative inverse of K! / 2^T;
1032 // this multiplication factor will perform the exact division by
1034 APInt Mod = APInt::getSignedMinValue(W+1);
1035 APInt MultiplyFactor = OddFactorial.zext(W+1);
1036 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
1037 MultiplyFactor = MultiplyFactor.trunc(W);
1039 // Calculate the product, at width T+W
1040 IntegerType *CalculationTy = IntegerType::get(SE.getContext(),
1042 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
1043 for (unsigned i = 1; i != K; ++i) {
1044 const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i));
1045 Dividend = SE.getMulExpr(Dividend,
1046 SE.getTruncateOrZeroExtend(S, CalculationTy));
1050 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
1052 // Truncate the result, and divide by K! / 2^T.
1054 return SE.getMulExpr(SE.getConstant(MultiplyFactor),
1055 SE.getTruncateOrZeroExtend(DivResult, ResultTy));
1058 /// evaluateAtIteration - Return the value of this chain of recurrences at
1059 /// the specified iteration number. We can evaluate this recurrence by
1060 /// multiplying each element in the chain by the binomial coefficient
1061 /// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
1063 /// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
1065 /// where BC(It, k) stands for binomial coefficient.
1067 const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It,
1068 ScalarEvolution &SE) const {
1069 const SCEV *Result = getStart();
1070 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
1071 // The computation is correct in the face of overflow provided that the
1072 // multiplication is performed _after_ the evaluation of the binomial
1074 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType());
1075 if (isa<SCEVCouldNotCompute>(Coeff))
1078 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
1083 //===----------------------------------------------------------------------===//
1084 // SCEV Expression folder implementations
1085 //===----------------------------------------------------------------------===//
1087 const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op,
1089 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
1090 "This is not a truncating conversion!");
1091 assert(isSCEVable(Ty) &&
1092 "This is not a conversion to a SCEVable type!");
1093 Ty = getEffectiveSCEVType(Ty);
1095 FoldingSetNodeID ID;
1096 ID.AddInteger(scTruncate);
1100 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1102 // Fold if the operand is constant.
1103 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1105 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty)));
1107 // trunc(trunc(x)) --> trunc(x)
1108 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
1109 return getTruncateExpr(ST->getOperand(), Ty);
1111 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
1112 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1113 return getTruncateOrSignExtend(SS->getOperand(), Ty);
1115 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
1116 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1117 return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
1119 // trunc(x1+x2+...+xN) --> trunc(x1)+trunc(x2)+...+trunc(xN) if we can
1120 // eliminate all the truncates, or we replace other casts with truncates.
1121 if (const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Op)) {
1122 SmallVector<const SCEV *, 4> Operands;
1123 bool hasTrunc = false;
1124 for (unsigned i = 0, e = SA->getNumOperands(); i != e && !hasTrunc; ++i) {
1125 const SCEV *S = getTruncateExpr(SA->getOperand(i), Ty);
1126 if (!isa<SCEVCastExpr>(SA->getOperand(i)))
1127 hasTrunc = isa<SCEVTruncateExpr>(S);
1128 Operands.push_back(S);
1131 return getAddExpr(Operands);
1132 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL.
1135 // trunc(x1*x2*...*xN) --> trunc(x1)*trunc(x2)*...*trunc(xN) if we can
1136 // eliminate all the truncates, or we replace other casts with truncates.
1137 if (const SCEVMulExpr *SM = dyn_cast<SCEVMulExpr>(Op)) {
1138 SmallVector<const SCEV *, 4> Operands;
1139 bool hasTrunc = false;
1140 for (unsigned i = 0, e = SM->getNumOperands(); i != e && !hasTrunc; ++i) {
1141 const SCEV *S = getTruncateExpr(SM->getOperand(i), Ty);
1142 if (!isa<SCEVCastExpr>(SM->getOperand(i)))
1143 hasTrunc = isa<SCEVTruncateExpr>(S);
1144 Operands.push_back(S);
1147 return getMulExpr(Operands);
1148 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL.
1151 // If the input value is a chrec scev, truncate the chrec's operands.
1152 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
1153 SmallVector<const SCEV *, 4> Operands;
1154 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
1155 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty));
1156 return getAddRecExpr(Operands, AddRec->getLoop(), SCEV::FlagAnyWrap);
1159 // The cast wasn't folded; create an explicit cast node. We can reuse
1160 // the existing insert position since if we get here, we won't have
1161 // made any changes which would invalidate it.
1162 SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator),
1164 UniqueSCEVs.InsertNode(S, IP);
1168 // Get the limit of a recurrence such that incrementing by Step cannot cause
1169 // signed overflow as long as the value of the recurrence within the
1170 // loop does not exceed this limit before incrementing.
1171 static const SCEV *getSignedOverflowLimitForStep(const SCEV *Step,
1172 ICmpInst::Predicate *Pred,
1173 ScalarEvolution *SE) {
1174 unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
1175 if (SE->isKnownPositive(Step)) {
1176 *Pred = ICmpInst::ICMP_SLT;
1177 return SE->getConstant(APInt::getSignedMinValue(BitWidth) -
1178 SE->getSignedRange(Step).getSignedMax());
1180 if (SE->isKnownNegative(Step)) {
1181 *Pred = ICmpInst::ICMP_SGT;
1182 return SE->getConstant(APInt::getSignedMaxValue(BitWidth) -
1183 SE->getSignedRange(Step).getSignedMin());
1188 // Get the limit of a recurrence such that incrementing by Step cannot cause
1189 // unsigned overflow as long as the value of the recurrence within the loop does
1190 // not exceed this limit before incrementing.
1191 static const SCEV *getUnsignedOverflowLimitForStep(const SCEV *Step,
1192 ICmpInst::Predicate *Pred,
1193 ScalarEvolution *SE) {
1194 unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
1195 *Pred = ICmpInst::ICMP_ULT;
1197 return SE->getConstant(APInt::getMinValue(BitWidth) -
1198 SE->getUnsignedRange(Step).getUnsignedMax());
1203 struct ExtendOpTraitsBase {
1204 typedef const SCEV *(ScalarEvolution::*GetExtendExprTy)(const SCEV *, Type *);
1207 // Used to make code generic over signed and unsigned overflow.
1208 template <typename ExtendOp> struct ExtendOpTraits {
1211 // static const SCEV::NoWrapFlags WrapType;
1213 // static const ExtendOpTraitsBase::GetExtendExprTy GetExtendExpr;
1215 // static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1216 // ICmpInst::Predicate *Pred,
1217 // ScalarEvolution *SE);
1221 struct ExtendOpTraits<SCEVSignExtendExpr> : public ExtendOpTraitsBase {
1222 static const SCEV::NoWrapFlags WrapType = SCEV::FlagNSW;
1224 static const GetExtendExprTy GetExtendExpr;
1226 static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1227 ICmpInst::Predicate *Pred,
1228 ScalarEvolution *SE) {
1229 return getSignedOverflowLimitForStep(Step, Pred, SE);
1233 const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits<
1234 SCEVSignExtendExpr>::GetExtendExpr = &ScalarEvolution::getSignExtendExpr;
1237 struct ExtendOpTraits<SCEVZeroExtendExpr> : public ExtendOpTraitsBase {
1238 static const SCEV::NoWrapFlags WrapType = SCEV::FlagNUW;
1240 static const GetExtendExprTy GetExtendExpr;
1242 static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1243 ICmpInst::Predicate *Pred,
1244 ScalarEvolution *SE) {
1245 return getUnsignedOverflowLimitForStep(Step, Pred, SE);
1249 const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits<
1250 SCEVZeroExtendExpr>::GetExtendExpr = &ScalarEvolution::getZeroExtendExpr;
1253 // The recurrence AR has been shown to have no signed/unsigned wrap or something
1254 // close to it. Typically, if we can prove NSW/NUW for AR, then we can just as
1255 // easily prove NSW/NUW for its preincrement or postincrement sibling. This
1256 // allows normalizing a sign/zero extended AddRec as such: {sext/zext(Step +
1257 // Start),+,Step} => {(Step + sext/zext(Start),+,Step} As a result, the
1258 // expression "Step + sext/zext(PreIncAR)" is congruent with
1259 // "sext/zext(PostIncAR)"
1260 template <typename ExtendOpTy>
1261 static const SCEV *getPreStartForExtend(const SCEVAddRecExpr *AR, Type *Ty,
1262 ScalarEvolution *SE) {
1263 auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType;
1264 auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr;
1266 const Loop *L = AR->getLoop();
1267 const SCEV *Start = AR->getStart();
1268 const SCEV *Step = AR->getStepRecurrence(*SE);
1270 // Check for a simple looking step prior to loop entry.
1271 const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Start);
1275 // Create an AddExpr for "PreStart" after subtracting Step. Full SCEV
1276 // subtraction is expensive. For this purpose, perform a quick and dirty
1277 // difference, by checking for Step in the operand list.
1278 SmallVector<const SCEV *, 4> DiffOps;
1279 for (const SCEV *Op : SA->operands())
1281 DiffOps.push_back(Op);
1283 if (DiffOps.size() == SA->getNumOperands())
1286 // Try to prove `WrapType` (SCEV::FlagNSW or SCEV::FlagNUW) on `PreStart` +
1289 // 1. NSW/NUW flags on the step increment.
1290 const SCEV *PreStart = SE->getAddExpr(DiffOps, SA->getNoWrapFlags());
1291 const SCEVAddRecExpr *PreAR = dyn_cast<SCEVAddRecExpr>(
1292 SE->getAddRecExpr(PreStart, Step, L, SCEV::FlagAnyWrap));
1294 // "{S,+,X} is <nsw>/<nuw>" and "the backedge is taken at least once" implies
1295 // "S+X does not sign/unsign-overflow".
1298 const SCEV *BECount = SE->getBackedgeTakenCount(L);
1299 if (PreAR && PreAR->getNoWrapFlags(WrapType) &&
1300 !isa<SCEVCouldNotCompute>(BECount) && SE->isKnownPositive(BECount))
1303 // 2. Direct overflow check on the step operation's expression.
1304 unsigned BitWidth = SE->getTypeSizeInBits(AR->getType());
1305 Type *WideTy = IntegerType::get(SE->getContext(), BitWidth * 2);
1306 const SCEV *OperandExtendedStart =
1307 SE->getAddExpr((SE->*GetExtendExpr)(PreStart, WideTy),
1308 (SE->*GetExtendExpr)(Step, WideTy));
1309 if ((SE->*GetExtendExpr)(Start, WideTy) == OperandExtendedStart) {
1310 if (PreAR && AR->getNoWrapFlags(WrapType)) {
1311 // If we know `AR` == {`PreStart`+`Step`,+,`Step`} is `WrapType` (FlagNSW
1312 // or FlagNUW) and that `PreStart` + `Step` is `WrapType` too, then
1313 // `PreAR` == {`PreStart`,+,`Step`} is also `WrapType`. Cache this fact.
1314 const_cast<SCEVAddRecExpr *>(PreAR)->setNoWrapFlags(WrapType);
1319 // 3. Loop precondition.
1320 ICmpInst::Predicate Pred;
1321 const SCEV *OverflowLimit =
1322 ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep(Step, &Pred, SE);
1324 if (OverflowLimit &&
1325 SE->isLoopEntryGuardedByCond(L, Pred, PreStart, OverflowLimit)) {
1331 // Get the normalized zero or sign extended expression for this AddRec's Start.
1332 template <typename ExtendOpTy>
1333 static const SCEV *getExtendAddRecStart(const SCEVAddRecExpr *AR, Type *Ty,
1334 ScalarEvolution *SE) {
1335 auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr;
1337 const SCEV *PreStart = getPreStartForExtend<ExtendOpTy>(AR, Ty, SE);
1339 return (SE->*GetExtendExpr)(AR->getStart(), Ty);
1341 return SE->getAddExpr((SE->*GetExtendExpr)(AR->getStepRecurrence(*SE), Ty),
1342 (SE->*GetExtendExpr)(PreStart, Ty));
1345 // Try to prove away overflow by looking at "nearby" add recurrences. A
1346 // motivating example for this rule: if we know `{0,+,4}` is `ult` `-1` and it
1347 // does not itself wrap then we can conclude that `{1,+,4}` is `nuw`.
1351 // {S,+,X} == {S-T,+,X} + T
1352 // => Ext({S,+,X}) == Ext({S-T,+,X} + T)
1354 // If ({S-T,+,X} + T) does not overflow ... (1)
1356 // RHS == Ext({S-T,+,X} + T) == Ext({S-T,+,X}) + Ext(T)
1358 // If {S-T,+,X} does not overflow ... (2)
1360 // RHS == Ext({S-T,+,X}) + Ext(T) == {Ext(S-T),+,Ext(X)} + Ext(T)
1361 // == {Ext(S-T)+Ext(T),+,Ext(X)}
1363 // If (S-T)+T does not overflow ... (3)
1365 // RHS == {Ext(S-T)+Ext(T),+,Ext(X)} == {Ext(S-T+T),+,Ext(X)}
1366 // == {Ext(S),+,Ext(X)} == LHS
1368 // Thus, if (1), (2) and (3) are true for some T, then
1369 // Ext({S,+,X}) == {Ext(S),+,Ext(X)}
1371 // (3) is implied by (1) -- "(S-T)+T does not overflow" is simply "({S-T,+,X}+T)
1372 // does not overflow" restricted to the 0th iteration. Therefore we only need
1373 // to check for (1) and (2).
1375 // In the current context, S is `Start`, X is `Step`, Ext is `ExtendOpTy` and T
1376 // is `Delta` (defined below).
1378 template <typename ExtendOpTy>
1379 bool ScalarEvolution::proveNoWrapByVaryingStart(const SCEV *Start,
1382 auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType;
1384 // We restrict `Start` to a constant to prevent SCEV from spending too much
1385 // time here. It is correct (but more expensive) to continue with a
1386 // non-constant `Start` and do a general SCEV subtraction to compute
1387 // `PreStart` below.
1389 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start);
1393 APInt StartAI = StartC->getValue()->getValue();
1395 for (unsigned Delta : {-2, -1, 1, 2}) {
1396 const SCEV *PreStart = getConstant(StartAI - Delta);
1398 // Give up if we don't already have the add recurrence we need because
1399 // actually constructing an add recurrence is relatively expensive.
1400 const SCEVAddRecExpr *PreAR = [&]() {
1401 FoldingSetNodeID ID;
1402 ID.AddInteger(scAddRecExpr);
1403 ID.AddPointer(PreStart);
1404 ID.AddPointer(Step);
1407 return static_cast<SCEVAddRecExpr *>(
1408 this->UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1411 if (PreAR && PreAR->getNoWrapFlags(WrapType)) { // proves (2)
1412 const SCEV *DeltaS = getConstant(StartC->getType(), Delta);
1413 ICmpInst::Predicate Pred = ICmpInst::BAD_ICMP_PREDICATE;
1414 const SCEV *Limit = ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep(
1415 DeltaS, &Pred, this);
1416 if (Limit && isKnownPredicate(Pred, PreAR, Limit)) // proves (1)
1424 const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op,
1426 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1427 "This is not an extending conversion!");
1428 assert(isSCEVable(Ty) &&
1429 "This is not a conversion to a SCEVable type!");
1430 Ty = getEffectiveSCEVType(Ty);
1432 // Fold if the operand is constant.
1433 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1435 cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(), Ty)));
1437 // zext(zext(x)) --> zext(x)
1438 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1439 return getZeroExtendExpr(SZ->getOperand(), Ty);
1441 // Before doing any expensive analysis, check to see if we've already
1442 // computed a SCEV for this Op and Ty.
1443 FoldingSetNodeID ID;
1444 ID.AddInteger(scZeroExtend);
1448 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1450 // zext(trunc(x)) --> zext(x) or x or trunc(x)
1451 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1452 // It's possible the bits taken off by the truncate were all zero bits. If
1453 // so, we should be able to simplify this further.
1454 const SCEV *X = ST->getOperand();
1455 ConstantRange CR = getUnsignedRange(X);
1456 unsigned TruncBits = getTypeSizeInBits(ST->getType());
1457 unsigned NewBits = getTypeSizeInBits(Ty);
1458 if (CR.truncate(TruncBits).zeroExtend(NewBits).contains(
1459 CR.zextOrTrunc(NewBits)))
1460 return getTruncateOrZeroExtend(X, Ty);
1463 // If the input value is a chrec scev, and we can prove that the value
1464 // did not overflow the old, smaller, value, we can zero extend all of the
1465 // operands (often constants). This allows analysis of something like
1466 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
1467 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1468 if (AR->isAffine()) {
1469 const SCEV *Start = AR->getStart();
1470 const SCEV *Step = AR->getStepRecurrence(*this);
1471 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1472 const Loop *L = AR->getLoop();
1474 // If we have special knowledge that this addrec won't overflow,
1475 // we don't need to do any further analysis.
1476 if (AR->getNoWrapFlags(SCEV::FlagNUW))
1477 return getAddRecExpr(
1478 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1479 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1481 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1482 // Note that this serves two purposes: It filters out loops that are
1483 // simply not analyzable, and it covers the case where this code is
1484 // being called from within backedge-taken count analysis, such that
1485 // attempting to ask for the backedge-taken count would likely result
1486 // in infinite recursion. In the later case, the analysis code will
1487 // cope with a conservative value, and it will take care to purge
1488 // that value once it has finished.
1489 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1490 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1491 // Manually compute the final value for AR, checking for
1494 // Check whether the backedge-taken count can be losslessly casted to
1495 // the addrec's type. The count is always unsigned.
1496 const SCEV *CastedMaxBECount =
1497 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1498 const SCEV *RecastedMaxBECount =
1499 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1500 if (MaxBECount == RecastedMaxBECount) {
1501 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1502 // Check whether Start+Step*MaxBECount has no unsigned overflow.
1503 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step);
1504 const SCEV *ZAdd = getZeroExtendExpr(getAddExpr(Start, ZMul), WideTy);
1505 const SCEV *WideStart = getZeroExtendExpr(Start, WideTy);
1506 const SCEV *WideMaxBECount =
1507 getZeroExtendExpr(CastedMaxBECount, WideTy);
1508 const SCEV *OperandExtendedAdd =
1509 getAddExpr(WideStart,
1510 getMulExpr(WideMaxBECount,
1511 getZeroExtendExpr(Step, WideTy)));
1512 if (ZAdd == OperandExtendedAdd) {
1513 // Cache knowledge of AR NUW, which is propagated to this AddRec.
1514 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1515 // Return the expression with the addrec on the outside.
1516 return getAddRecExpr(
1517 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1518 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1520 // Similar to above, only this time treat the step value as signed.
1521 // This covers loops that count down.
1522 OperandExtendedAdd =
1523 getAddExpr(WideStart,
1524 getMulExpr(WideMaxBECount,
1525 getSignExtendExpr(Step, WideTy)));
1526 if (ZAdd == OperandExtendedAdd) {
1527 // Cache knowledge of AR NW, which is propagated to this AddRec.
1528 // Negative step causes unsigned wrap, but it still can't self-wrap.
1529 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1530 // Return the expression with the addrec on the outside.
1531 return getAddRecExpr(
1532 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1533 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1537 // If the backedge is guarded by a comparison with the pre-inc value
1538 // the addrec is safe. Also, if the entry is guarded by a comparison
1539 // with the start value and the backedge is guarded by a comparison
1540 // with the post-inc value, the addrec is safe.
1541 if (isKnownPositive(Step)) {
1542 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
1543 getUnsignedRange(Step).getUnsignedMax());
1544 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
1545 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) &&
1546 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT,
1547 AR->getPostIncExpr(*this), N))) {
1548 // Cache knowledge of AR NUW, which is propagated to this AddRec.
1549 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1550 // Return the expression with the addrec on the outside.
1551 return getAddRecExpr(
1552 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1553 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1555 } else if (isKnownNegative(Step)) {
1556 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
1557 getSignedRange(Step).getSignedMin());
1558 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) ||
1559 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) &&
1560 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT,
1561 AR->getPostIncExpr(*this), N))) {
1562 // Cache knowledge of AR NW, which is propagated to this AddRec.
1563 // Negative step causes unsigned wrap, but it still can't self-wrap.
1564 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1565 // Return the expression with the addrec on the outside.
1566 return getAddRecExpr(
1567 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1568 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1573 if (proveNoWrapByVaryingStart<SCEVZeroExtendExpr>(Start, Step, L)) {
1574 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1575 return getAddRecExpr(
1576 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1577 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1581 // The cast wasn't folded; create an explicit cast node.
1582 // Recompute the insert position, as it may have been invalidated.
1583 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1584 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
1586 UniqueSCEVs.InsertNode(S, IP);
1590 const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op,
1592 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1593 "This is not an extending conversion!");
1594 assert(isSCEVable(Ty) &&
1595 "This is not a conversion to a SCEVable type!");
1596 Ty = getEffectiveSCEVType(Ty);
1598 // Fold if the operand is constant.
1599 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1601 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), Ty)));
1603 // sext(sext(x)) --> sext(x)
1604 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1605 return getSignExtendExpr(SS->getOperand(), Ty);
1607 // sext(zext(x)) --> zext(x)
1608 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1609 return getZeroExtendExpr(SZ->getOperand(), Ty);
1611 // Before doing any expensive analysis, check to see if we've already
1612 // computed a SCEV for this Op and Ty.
1613 FoldingSetNodeID ID;
1614 ID.AddInteger(scSignExtend);
1618 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1620 // If the input value is provably positive, build a zext instead.
1621 if (isKnownNonNegative(Op))
1622 return getZeroExtendExpr(Op, Ty);
1624 // sext(trunc(x)) --> sext(x) or x or trunc(x)
1625 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1626 // It's possible the bits taken off by the truncate were all sign bits. If
1627 // so, we should be able to simplify this further.
1628 const SCEV *X = ST->getOperand();
1629 ConstantRange CR = getSignedRange(X);
1630 unsigned TruncBits = getTypeSizeInBits(ST->getType());
1631 unsigned NewBits = getTypeSizeInBits(Ty);
1632 if (CR.truncate(TruncBits).signExtend(NewBits).contains(
1633 CR.sextOrTrunc(NewBits)))
1634 return getTruncateOrSignExtend(X, Ty);
1637 // sext(C1 + (C2 * x)) --> C1 + sext(C2 * x) if C1 < C2
1638 if (auto SA = dyn_cast<SCEVAddExpr>(Op)) {
1639 if (SA->getNumOperands() == 2) {
1640 auto SC1 = dyn_cast<SCEVConstant>(SA->getOperand(0));
1641 auto SMul = dyn_cast<SCEVMulExpr>(SA->getOperand(1));
1643 if (auto SC2 = dyn_cast<SCEVConstant>(SMul->getOperand(0))) {
1644 const APInt &C1 = SC1->getValue()->getValue();
1645 const APInt &C2 = SC2->getValue()->getValue();
1646 if (C1.isStrictlyPositive() && C2.isStrictlyPositive() &&
1647 C2.ugt(C1) && C2.isPowerOf2())
1648 return getAddExpr(getSignExtendExpr(SC1, Ty),
1649 getSignExtendExpr(SMul, Ty));
1654 // If the input value is a chrec scev, and we can prove that the value
1655 // did not overflow the old, smaller, value, we can sign extend all of the
1656 // operands (often constants). This allows analysis of something like
1657 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
1658 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1659 if (AR->isAffine()) {
1660 const SCEV *Start = AR->getStart();
1661 const SCEV *Step = AR->getStepRecurrence(*this);
1662 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1663 const Loop *L = AR->getLoop();
1665 // If we have special knowledge that this addrec won't overflow,
1666 // we don't need to do any further analysis.
1667 if (AR->getNoWrapFlags(SCEV::FlagNSW))
1668 return getAddRecExpr(
1669 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1670 getSignExtendExpr(Step, Ty), L, SCEV::FlagNSW);
1672 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1673 // Note that this serves two purposes: It filters out loops that are
1674 // simply not analyzable, and it covers the case where this code is
1675 // being called from within backedge-taken count analysis, such that
1676 // attempting to ask for the backedge-taken count would likely result
1677 // in infinite recursion. In the later case, the analysis code will
1678 // cope with a conservative value, and it will take care to purge
1679 // that value once it has finished.
1680 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1681 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1682 // Manually compute the final value for AR, checking for
1685 // Check whether the backedge-taken count can be losslessly casted to
1686 // the addrec's type. The count is always unsigned.
1687 const SCEV *CastedMaxBECount =
1688 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1689 const SCEV *RecastedMaxBECount =
1690 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1691 if (MaxBECount == RecastedMaxBECount) {
1692 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1693 // Check whether Start+Step*MaxBECount has no signed overflow.
1694 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
1695 const SCEV *SAdd = getSignExtendExpr(getAddExpr(Start, SMul), WideTy);
1696 const SCEV *WideStart = getSignExtendExpr(Start, WideTy);
1697 const SCEV *WideMaxBECount =
1698 getZeroExtendExpr(CastedMaxBECount, WideTy);
1699 const SCEV *OperandExtendedAdd =
1700 getAddExpr(WideStart,
1701 getMulExpr(WideMaxBECount,
1702 getSignExtendExpr(Step, WideTy)));
1703 if (SAdd == OperandExtendedAdd) {
1704 // Cache knowledge of AR NSW, which is propagated to this AddRec.
1705 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1706 // Return the expression with the addrec on the outside.
1707 return getAddRecExpr(
1708 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1709 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1711 // Similar to above, only this time treat the step value as unsigned.
1712 // This covers loops that count up with an unsigned step.
1713 OperandExtendedAdd =
1714 getAddExpr(WideStart,
1715 getMulExpr(WideMaxBECount,
1716 getZeroExtendExpr(Step, WideTy)));
1717 if (SAdd == OperandExtendedAdd) {
1718 // If AR wraps around then
1720 // abs(Step) * MaxBECount > unsigned-max(AR->getType())
1721 // => SAdd != OperandExtendedAdd
1723 // Thus (AR is not NW => SAdd != OperandExtendedAdd) <=>
1724 // (SAdd == OperandExtendedAdd => AR is NW)
1726 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1728 // Return the expression with the addrec on the outside.
1729 return getAddRecExpr(
1730 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1731 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1735 // If the backedge is guarded by a comparison with the pre-inc value
1736 // the addrec is safe. Also, if the entry is guarded by a comparison
1737 // with the start value and the backedge is guarded by a comparison
1738 // with the post-inc value, the addrec is safe.
1739 ICmpInst::Predicate Pred;
1740 const SCEV *OverflowLimit =
1741 getSignedOverflowLimitForStep(Step, &Pred, this);
1742 if (OverflowLimit &&
1743 (isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) ||
1744 (isLoopEntryGuardedByCond(L, Pred, Start, OverflowLimit) &&
1745 isLoopBackedgeGuardedByCond(L, Pred, AR->getPostIncExpr(*this),
1747 // Cache knowledge of AR NSW, then propagate NSW to the wide AddRec.
1748 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1749 return getAddRecExpr(
1750 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1751 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1754 // If Start and Step are constants, check if we can apply this
1756 // sext{C1,+,C2} --> C1 + sext{0,+,C2} if C1 < C2
1757 auto SC1 = dyn_cast<SCEVConstant>(Start);
1758 auto SC2 = dyn_cast<SCEVConstant>(Step);
1760 const APInt &C1 = SC1->getValue()->getValue();
1761 const APInt &C2 = SC2->getValue()->getValue();
1762 if (C1.isStrictlyPositive() && C2.isStrictlyPositive() && C2.ugt(C1) &&
1764 Start = getSignExtendExpr(Start, Ty);
1765 const SCEV *NewAR = getAddRecExpr(getConstant(AR->getType(), 0), Step,
1766 L, AR->getNoWrapFlags());
1767 return getAddExpr(Start, getSignExtendExpr(NewAR, Ty));
1771 if (proveNoWrapByVaryingStart<SCEVSignExtendExpr>(Start, Step, L)) {
1772 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1773 return getAddRecExpr(
1774 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1775 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1779 // The cast wasn't folded; create an explicit cast node.
1780 // Recompute the insert position, as it may have been invalidated.
1781 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1782 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
1784 UniqueSCEVs.InsertNode(S, IP);
1788 /// getAnyExtendExpr - Return a SCEV for the given operand extended with
1789 /// unspecified bits out to the given type.
1791 const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
1793 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1794 "This is not an extending conversion!");
1795 assert(isSCEVable(Ty) &&
1796 "This is not a conversion to a SCEVable type!");
1797 Ty = getEffectiveSCEVType(Ty);
1799 // Sign-extend negative constants.
1800 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1801 if (SC->getValue()->getValue().isNegative())
1802 return getSignExtendExpr(Op, Ty);
1804 // Peel off a truncate cast.
1805 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
1806 const SCEV *NewOp = T->getOperand();
1807 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
1808 return getAnyExtendExpr(NewOp, Ty);
1809 return getTruncateOrNoop(NewOp, Ty);
1812 // Next try a zext cast. If the cast is folded, use it.
1813 const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
1814 if (!isa<SCEVZeroExtendExpr>(ZExt))
1817 // Next try a sext cast. If the cast is folded, use it.
1818 const SCEV *SExt = getSignExtendExpr(Op, Ty);
1819 if (!isa<SCEVSignExtendExpr>(SExt))
1822 // Force the cast to be folded into the operands of an addrec.
1823 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
1824 SmallVector<const SCEV *, 4> Ops;
1825 for (const SCEV *Op : AR->operands())
1826 Ops.push_back(getAnyExtendExpr(Op, Ty));
1827 return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW);
1830 // If the expression is obviously signed, use the sext cast value.
1831 if (isa<SCEVSMaxExpr>(Op))
1834 // Absent any other information, use the zext cast value.
1838 /// CollectAddOperandsWithScales - Process the given Ops list, which is
1839 /// a list of operands to be added under the given scale, update the given
1840 /// map. This is a helper function for getAddRecExpr. As an example of
1841 /// what it does, given a sequence of operands that would form an add
1842 /// expression like this:
1844 /// m + n + 13 + (A * (o + p + (B * (q + m + 29)))) + r + (-1 * r)
1846 /// where A and B are constants, update the map with these values:
1848 /// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
1850 /// and add 13 + A*B*29 to AccumulatedConstant.
1851 /// This will allow getAddRecExpr to produce this:
1853 /// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
1855 /// This form often exposes folding opportunities that are hidden in
1856 /// the original operand list.
1858 /// Return true iff it appears that any interesting folding opportunities
1859 /// may be exposed. This helps getAddRecExpr short-circuit extra work in
1860 /// the common case where no interesting opportunities are present, and
1861 /// is also used as a check to avoid infinite recursion.
1864 CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
1865 SmallVectorImpl<const SCEV *> &NewOps,
1866 APInt &AccumulatedConstant,
1867 const SCEV *const *Ops, size_t NumOperands,
1869 ScalarEvolution &SE) {
1870 bool Interesting = false;
1872 // Iterate over the add operands. They are sorted, with constants first.
1874 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1876 // Pull a buried constant out to the outside.
1877 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
1879 AccumulatedConstant += Scale * C->getValue()->getValue();
1882 // Next comes everything else. We're especially interested in multiplies
1883 // here, but they're in the middle, so just visit the rest with one loop.
1884 for (; i != NumOperands; ++i) {
1885 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
1886 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
1888 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue();
1889 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
1890 // A multiplication of a constant with another add; recurse.
1891 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1));
1893 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1894 Add->op_begin(), Add->getNumOperands(),
1897 // A multiplication of a constant with some other value. Update
1899 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
1900 const SCEV *Key = SE.getMulExpr(MulOps);
1901 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1902 M.insert(std::make_pair(Key, NewScale));
1904 NewOps.push_back(Pair.first->first);
1906 Pair.first->second += NewScale;
1907 // The map already had an entry for this value, which may indicate
1908 // a folding opportunity.
1913 // An ordinary operand. Update the map.
1914 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1915 M.insert(std::make_pair(Ops[i], Scale));
1917 NewOps.push_back(Pair.first->first);
1919 Pair.first->second += Scale;
1920 // The map already had an entry for this value, which may indicate
1921 // a folding opportunity.
1931 struct APIntCompare {
1932 bool operator()(const APInt &LHS, const APInt &RHS) const {
1933 return LHS.ult(RHS);
1938 // We're trying to construct a SCEV of type `Type' with `Ops' as operands and
1939 // `OldFlags' as can't-wrap behavior. Infer a more aggressive set of
1940 // can't-overflow flags for the operation if possible.
1941 static SCEV::NoWrapFlags
1942 StrengthenNoWrapFlags(ScalarEvolution *SE, SCEVTypes Type,
1943 const SmallVectorImpl<const SCEV *> &Ops,
1944 SCEV::NoWrapFlags OldFlags) {
1945 using namespace std::placeholders;
1948 Type == scAddExpr || Type == scAddRecExpr || Type == scMulExpr;
1950 assert(CanAnalyze && "don't call from other places!");
1952 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
1953 SCEV::NoWrapFlags SignOrUnsignWrap =
1954 ScalarEvolution::maskFlags(OldFlags, SignOrUnsignMask);
1956 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
1957 auto IsKnownNonNegative =
1958 std::bind(std::mem_fn(&ScalarEvolution::isKnownNonNegative), SE, _1);
1960 if (SignOrUnsignWrap == SCEV::FlagNSW &&
1961 std::all_of(Ops.begin(), Ops.end(), IsKnownNonNegative))
1962 return ScalarEvolution::setFlags(OldFlags,
1963 (SCEV::NoWrapFlags)SignOrUnsignMask);
1968 /// getAddExpr - Get a canonical add expression, or something simpler if
1970 const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
1971 SCEV::NoWrapFlags Flags) {
1972 assert(!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) &&
1973 "only nuw or nsw allowed");
1974 assert(!Ops.empty() && "Cannot get empty add!");
1975 if (Ops.size() == 1) return Ops[0];
1977 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
1978 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1979 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
1980 "SCEVAddExpr operand types don't match!");
1983 Flags = StrengthenNoWrapFlags(this, scAddExpr, Ops, Flags);
1985 // Sort by complexity, this groups all similar expression types together.
1986 GroupByComplexity(Ops, LI);
1988 // If there are any constants, fold them together.
1990 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1992 assert(Idx < Ops.size());
1993 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1994 // We found two constants, fold them together!
1995 Ops[0] = getConstant(LHSC->getValue()->getValue() +
1996 RHSC->getValue()->getValue());
1997 if (Ops.size() == 2) return Ops[0];
1998 Ops.erase(Ops.begin()+1); // Erase the folded element
1999 LHSC = cast<SCEVConstant>(Ops[0]);
2002 // If we are left with a constant zero being added, strip it off.
2003 if (LHSC->getValue()->isZero()) {
2004 Ops.erase(Ops.begin());
2008 if (Ops.size() == 1) return Ops[0];
2011 // Okay, check to see if the same value occurs in the operand list more than
2012 // once. If so, merge them together into an multiply expression. Since we
2013 // sorted the list, these values are required to be adjacent.
2014 Type *Ty = Ops[0]->getType();
2015 bool FoundMatch = false;
2016 for (unsigned i = 0, e = Ops.size(); i != e-1; ++i)
2017 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
2018 // Scan ahead to count how many equal operands there are.
2020 while (i+Count != e && Ops[i+Count] == Ops[i])
2022 // Merge the values into a multiply.
2023 const SCEV *Scale = getConstant(Ty, Count);
2024 const SCEV *Mul = getMulExpr(Scale, Ops[i]);
2025 if (Ops.size() == Count)
2028 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count);
2029 --i; e -= Count - 1;
2033 return getAddExpr(Ops, Flags);
2035 // Check for truncates. If all the operands are truncated from the same
2036 // type, see if factoring out the truncate would permit the result to be
2037 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
2038 // if the contents of the resulting outer trunc fold to something simple.
2039 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
2040 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
2041 Type *DstType = Trunc->getType();
2042 Type *SrcType = Trunc->getOperand()->getType();
2043 SmallVector<const SCEV *, 8> LargeOps;
2045 // Check all the operands to see if they can be represented in the
2046 // source type of the truncate.
2047 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
2048 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
2049 if (T->getOperand()->getType() != SrcType) {
2053 LargeOps.push_back(T->getOperand());
2054 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
2055 LargeOps.push_back(getAnyExtendExpr(C, SrcType));
2056 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
2057 SmallVector<const SCEV *, 8> LargeMulOps;
2058 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
2059 if (const SCEVTruncateExpr *T =
2060 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
2061 if (T->getOperand()->getType() != SrcType) {
2065 LargeMulOps.push_back(T->getOperand());
2066 } else if (const SCEVConstant *C =
2067 dyn_cast<SCEVConstant>(M->getOperand(j))) {
2068 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType));
2075 LargeOps.push_back(getMulExpr(LargeMulOps));
2082 // Evaluate the expression in the larger type.
2083 const SCEV *Fold = getAddExpr(LargeOps, Flags);
2084 // If it folds to something simple, use it. Otherwise, don't.
2085 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
2086 return getTruncateExpr(Fold, DstType);
2090 // Skip past any other cast SCEVs.
2091 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
2094 // If there are add operands they would be next.
2095 if (Idx < Ops.size()) {
2096 bool DeletedAdd = false;
2097 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
2098 // If we have an add, expand the add operands onto the end of the operands
2100 Ops.erase(Ops.begin()+Idx);
2101 Ops.append(Add->op_begin(), Add->op_end());
2105 // If we deleted at least one add, we added operands to the end of the list,
2106 // and they are not necessarily sorted. Recurse to resort and resimplify
2107 // any operands we just acquired.
2109 return getAddExpr(Ops);
2112 // Skip over the add expression until we get to a multiply.
2113 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
2116 // Check to see if there are any folding opportunities present with
2117 // operands multiplied by constant values.
2118 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
2119 uint64_t BitWidth = getTypeSizeInBits(Ty);
2120 DenseMap<const SCEV *, APInt> M;
2121 SmallVector<const SCEV *, 8> NewOps;
2122 APInt AccumulatedConstant(BitWidth, 0);
2123 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
2124 Ops.data(), Ops.size(),
2125 APInt(BitWidth, 1), *this)) {
2126 // Some interesting folding opportunity is present, so its worthwhile to
2127 // re-generate the operands list. Group the operands by constant scale,
2128 // to avoid multiplying by the same constant scale multiple times.
2129 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
2130 for (SmallVectorImpl<const SCEV *>::const_iterator I = NewOps.begin(),
2131 E = NewOps.end(); I != E; ++I)
2132 MulOpLists[M.find(*I)->second].push_back(*I);
2133 // Re-generate the operands list.
2135 if (AccumulatedConstant != 0)
2136 Ops.push_back(getConstant(AccumulatedConstant));
2137 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator
2138 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I)
2140 Ops.push_back(getMulExpr(getConstant(I->first),
2141 getAddExpr(I->second)));
2143 return getConstant(Ty, 0);
2144 if (Ops.size() == 1)
2146 return getAddExpr(Ops);
2150 // If we are adding something to a multiply expression, make sure the
2151 // something is not already an operand of the multiply. If so, merge it into
2153 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
2154 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
2155 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
2156 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
2157 if (isa<SCEVConstant>(MulOpSCEV))
2159 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
2160 if (MulOpSCEV == Ops[AddOp]) {
2161 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
2162 const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
2163 if (Mul->getNumOperands() != 2) {
2164 // If the multiply has more than two operands, we must get the
2166 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
2167 Mul->op_begin()+MulOp);
2168 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
2169 InnerMul = getMulExpr(MulOps);
2171 const SCEV *One = getConstant(Ty, 1);
2172 const SCEV *AddOne = getAddExpr(One, InnerMul);
2173 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV);
2174 if (Ops.size() == 2) return OuterMul;
2176 Ops.erase(Ops.begin()+AddOp);
2177 Ops.erase(Ops.begin()+Idx-1);
2179 Ops.erase(Ops.begin()+Idx);
2180 Ops.erase(Ops.begin()+AddOp-1);
2182 Ops.push_back(OuterMul);
2183 return getAddExpr(Ops);
2186 // Check this multiply against other multiplies being added together.
2187 for (unsigned OtherMulIdx = Idx+1;
2188 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
2190 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
2191 // If MulOp occurs in OtherMul, we can fold the two multiplies
2193 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
2194 OMulOp != e; ++OMulOp)
2195 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
2196 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
2197 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
2198 if (Mul->getNumOperands() != 2) {
2199 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
2200 Mul->op_begin()+MulOp);
2201 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
2202 InnerMul1 = getMulExpr(MulOps);
2204 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
2205 if (OtherMul->getNumOperands() != 2) {
2206 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
2207 OtherMul->op_begin()+OMulOp);
2208 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end());
2209 InnerMul2 = getMulExpr(MulOps);
2211 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
2212 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
2213 if (Ops.size() == 2) return OuterMul;
2214 Ops.erase(Ops.begin()+Idx);
2215 Ops.erase(Ops.begin()+OtherMulIdx-1);
2216 Ops.push_back(OuterMul);
2217 return getAddExpr(Ops);
2223 // If there are any add recurrences in the operands list, see if any other
2224 // added values are loop invariant. If so, we can fold them into the
2226 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2229 // Scan over all recurrences, trying to fold loop invariants into them.
2230 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
2231 // Scan all of the other operands to this add and add them to the vector if
2232 // they are loop invariant w.r.t. the recurrence.
2233 SmallVector<const SCEV *, 8> LIOps;
2234 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2235 const Loop *AddRecLoop = AddRec->getLoop();
2236 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2237 if (isLoopInvariant(Ops[i], AddRecLoop)) {
2238 LIOps.push_back(Ops[i]);
2239 Ops.erase(Ops.begin()+i);
2243 // If we found some loop invariants, fold them into the recurrence.
2244 if (!LIOps.empty()) {
2245 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
2246 LIOps.push_back(AddRec->getStart());
2248 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
2250 AddRecOps[0] = getAddExpr(LIOps);
2252 // Build the new addrec. Propagate the NUW and NSW flags if both the
2253 // outer add and the inner addrec are guaranteed to have no overflow.
2254 // Always propagate NW.
2255 Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW));
2256 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags);
2258 // If all of the other operands were loop invariant, we are done.
2259 if (Ops.size() == 1) return NewRec;
2261 // Otherwise, add the folded AddRec by the non-invariant parts.
2262 for (unsigned i = 0;; ++i)
2263 if (Ops[i] == AddRec) {
2267 return getAddExpr(Ops);
2270 // Okay, if there weren't any loop invariants to be folded, check to see if
2271 // there are multiple AddRec's with the same loop induction variable being
2272 // added together. If so, we can fold them.
2273 for (unsigned OtherIdx = Idx+1;
2274 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2276 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
2277 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L>
2278 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
2280 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2282 if (const SCEVAddRecExpr *OtherAddRec =
2283 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]))
2284 if (OtherAddRec->getLoop() == AddRecLoop) {
2285 for (unsigned i = 0, e = OtherAddRec->getNumOperands();
2287 if (i >= AddRecOps.size()) {
2288 AddRecOps.append(OtherAddRec->op_begin()+i,
2289 OtherAddRec->op_end());
2292 AddRecOps[i] = getAddExpr(AddRecOps[i],
2293 OtherAddRec->getOperand(i));
2295 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2297 // Step size has changed, so we cannot guarantee no self-wraparound.
2298 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap);
2299 return getAddExpr(Ops);
2302 // Otherwise couldn't fold anything into this recurrence. Move onto the
2306 // Okay, it looks like we really DO need an add expr. Check to see if we
2307 // already have one, otherwise create a new one.
2308 FoldingSetNodeID ID;
2309 ID.AddInteger(scAddExpr);
2310 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2311 ID.AddPointer(Ops[i]);
2314 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2316 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2317 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2318 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator),
2320 UniqueSCEVs.InsertNode(S, IP);
2322 S->setNoWrapFlags(Flags);
2326 static uint64_t umul_ov(uint64_t i, uint64_t j, bool &Overflow) {
2328 if (j > 1 && k / j != i) Overflow = true;
2332 /// Compute the result of "n choose k", the binomial coefficient. If an
2333 /// intermediate computation overflows, Overflow will be set and the return will
2334 /// be garbage. Overflow is not cleared on absence of overflow.
2335 static uint64_t Choose(uint64_t n, uint64_t k, bool &Overflow) {
2336 // We use the multiplicative formula:
2337 // n(n-1)(n-2)...(n-(k-1)) / k(k-1)(k-2)...1 .
2338 // At each iteration, we take the n-th term of the numeral and divide by the
2339 // (k-n)th term of the denominator. This division will always produce an
2340 // integral result, and helps reduce the chance of overflow in the
2341 // intermediate computations. However, we can still overflow even when the
2342 // final result would fit.
2344 if (n == 0 || n == k) return 1;
2345 if (k > n) return 0;
2351 for (uint64_t i = 1; i <= k; ++i) {
2352 r = umul_ov(r, n-(i-1), Overflow);
2358 /// Determine if any of the operands in this SCEV are a constant or if
2359 /// any of the add or multiply expressions in this SCEV contain a constant.
2360 static bool containsConstantSomewhere(const SCEV *StartExpr) {
2361 SmallVector<const SCEV *, 4> Ops;
2362 Ops.push_back(StartExpr);
2363 while (!Ops.empty()) {
2364 const SCEV *CurrentExpr = Ops.pop_back_val();
2365 if (isa<SCEVConstant>(*CurrentExpr))
2368 if (isa<SCEVAddExpr>(*CurrentExpr) || isa<SCEVMulExpr>(*CurrentExpr)) {
2369 const auto *CurrentNAry = cast<SCEVNAryExpr>(CurrentExpr);
2370 Ops.append(CurrentNAry->op_begin(), CurrentNAry->op_end());
2376 /// getMulExpr - Get a canonical multiply expression, or something simpler if
2378 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
2379 SCEV::NoWrapFlags Flags) {
2380 assert(Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) &&
2381 "only nuw or nsw allowed");
2382 assert(!Ops.empty() && "Cannot get empty mul!");
2383 if (Ops.size() == 1) return Ops[0];
2385 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2386 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2387 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2388 "SCEVMulExpr operand types don't match!");
2391 Flags = StrengthenNoWrapFlags(this, scMulExpr, Ops, Flags);
2393 // Sort by complexity, this groups all similar expression types together.
2394 GroupByComplexity(Ops, LI);
2396 // If there are any constants, fold them together.
2398 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2400 // C1*(C2+V) -> C1*C2 + C1*V
2401 if (Ops.size() == 2)
2402 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
2403 // If any of Add's ops are Adds or Muls with a constant,
2404 // apply this transformation as well.
2405 if (Add->getNumOperands() == 2)
2406 if (containsConstantSomewhere(Add))
2407 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
2408 getMulExpr(LHSC, Add->getOperand(1)));
2411 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2412 // We found two constants, fold them together!
2413 ConstantInt *Fold = ConstantInt::get(getContext(),
2414 LHSC->getValue()->getValue() *
2415 RHSC->getValue()->getValue());
2416 Ops[0] = getConstant(Fold);
2417 Ops.erase(Ops.begin()+1); // Erase the folded element
2418 if (Ops.size() == 1) return Ops[0];
2419 LHSC = cast<SCEVConstant>(Ops[0]);
2422 // If we are left with a constant one being multiplied, strip it off.
2423 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
2424 Ops.erase(Ops.begin());
2426 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
2427 // If we have a multiply of zero, it will always be zero.
2429 } else if (Ops[0]->isAllOnesValue()) {
2430 // If we have a mul by -1 of an add, try distributing the -1 among the
2432 if (Ops.size() == 2) {
2433 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
2434 SmallVector<const SCEV *, 4> NewOps;
2435 bool AnyFolded = false;
2436 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(),
2437 E = Add->op_end(); I != E; ++I) {
2438 const SCEV *Mul = getMulExpr(Ops[0], *I);
2439 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
2440 NewOps.push_back(Mul);
2443 return getAddExpr(NewOps);
2445 else if (const SCEVAddRecExpr *
2446 AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) {
2447 // Negation preserves a recurrence's no self-wrap property.
2448 SmallVector<const SCEV *, 4> Operands;
2449 for (SCEVAddRecExpr::op_iterator I = AddRec->op_begin(),
2450 E = AddRec->op_end(); I != E; ++I) {
2451 Operands.push_back(getMulExpr(Ops[0], *I));
2453 return getAddRecExpr(Operands, AddRec->getLoop(),
2454 AddRec->getNoWrapFlags(SCEV::FlagNW));
2459 if (Ops.size() == 1)
2463 // Skip over the add expression until we get to a multiply.
2464 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
2467 // If there are mul operands inline them all into this expression.
2468 if (Idx < Ops.size()) {
2469 bool DeletedMul = false;
2470 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
2471 // If we have an mul, expand the mul operands onto the end of the operands
2473 Ops.erase(Ops.begin()+Idx);
2474 Ops.append(Mul->op_begin(), Mul->op_end());
2478 // If we deleted at least one mul, we added operands to the end of the list,
2479 // and they are not necessarily sorted. Recurse to resort and resimplify
2480 // any operands we just acquired.
2482 return getMulExpr(Ops);
2485 // If there are any add recurrences in the operands list, see if any other
2486 // added values are loop invariant. If so, we can fold them into the
2488 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2491 // Scan over all recurrences, trying to fold loop invariants into them.
2492 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
2493 // Scan all of the other operands to this mul and add them to the vector if
2494 // they are loop invariant w.r.t. the recurrence.
2495 SmallVector<const SCEV *, 8> LIOps;
2496 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2497 const Loop *AddRecLoop = AddRec->getLoop();
2498 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2499 if (isLoopInvariant(Ops[i], AddRecLoop)) {
2500 LIOps.push_back(Ops[i]);
2501 Ops.erase(Ops.begin()+i);
2505 // If we found some loop invariants, fold them into the recurrence.
2506 if (!LIOps.empty()) {
2507 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
2508 SmallVector<const SCEV *, 4> NewOps;
2509 NewOps.reserve(AddRec->getNumOperands());
2510 const SCEV *Scale = getMulExpr(LIOps);
2511 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
2512 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
2514 // Build the new addrec. Propagate the NUW and NSW flags if both the
2515 // outer mul and the inner addrec are guaranteed to have no overflow.
2517 // No self-wrap cannot be guaranteed after changing the step size, but
2518 // will be inferred if either NUW or NSW is true.
2519 Flags = AddRec->getNoWrapFlags(clearFlags(Flags, SCEV::FlagNW));
2520 const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, Flags);
2522 // If all of the other operands were loop invariant, we are done.
2523 if (Ops.size() == 1) return NewRec;
2525 // Otherwise, multiply the folded AddRec by the non-invariant parts.
2526 for (unsigned i = 0;; ++i)
2527 if (Ops[i] == AddRec) {
2531 return getMulExpr(Ops);
2534 // Okay, if there weren't any loop invariants to be folded, check to see if
2535 // there are multiple AddRec's with the same loop induction variable being
2536 // multiplied together. If so, we can fold them.
2538 // {A1,+,A2,+,...,+,An}<L> * {B1,+,B2,+,...,+,Bn}<L>
2539 // = {x=1 in [ sum y=x..2x [ sum z=max(y-x, y-n)..min(x,n) [
2540 // choose(x, 2x)*choose(2x-y, x-z)*A_{y-z}*B_z
2541 // ]]],+,...up to x=2n}.
2542 // Note that the arguments to choose() are always integers with values
2543 // known at compile time, never SCEV objects.
2545 // The implementation avoids pointless extra computations when the two
2546 // addrec's are of different length (mathematically, it's equivalent to
2547 // an infinite stream of zeros on the right).
2548 bool OpsModified = false;
2549 for (unsigned OtherIdx = Idx+1;
2550 OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2552 const SCEVAddRecExpr *OtherAddRec =
2553 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]);
2554 if (!OtherAddRec || OtherAddRec->getLoop() != AddRecLoop)
2557 bool Overflow = false;
2558 Type *Ty = AddRec->getType();
2559 bool LargerThan64Bits = getTypeSizeInBits(Ty) > 64;
2560 SmallVector<const SCEV*, 7> AddRecOps;
2561 for (int x = 0, xe = AddRec->getNumOperands() +
2562 OtherAddRec->getNumOperands() - 1; x != xe && !Overflow; ++x) {
2563 const SCEV *Term = getConstant(Ty, 0);
2564 for (int y = x, ye = 2*x+1; y != ye && !Overflow; ++y) {
2565 uint64_t Coeff1 = Choose(x, 2*x - y, Overflow);
2566 for (int z = std::max(y-x, y-(int)AddRec->getNumOperands()+1),
2567 ze = std::min(x+1, (int)OtherAddRec->getNumOperands());
2568 z < ze && !Overflow; ++z) {
2569 uint64_t Coeff2 = Choose(2*x - y, x-z, Overflow);
2571 if (LargerThan64Bits)
2572 Coeff = umul_ov(Coeff1, Coeff2, Overflow);
2574 Coeff = Coeff1*Coeff2;
2575 const SCEV *CoeffTerm = getConstant(Ty, Coeff);
2576 const SCEV *Term1 = AddRec->getOperand(y-z);
2577 const SCEV *Term2 = OtherAddRec->getOperand(z);
2578 Term = getAddExpr(Term, getMulExpr(CoeffTerm, Term1,Term2));
2581 AddRecOps.push_back(Term);
2584 const SCEV *NewAddRec = getAddRecExpr(AddRecOps, AddRec->getLoop(),
2586 if (Ops.size() == 2) return NewAddRec;
2587 Ops[Idx] = NewAddRec;
2588 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2590 AddRec = dyn_cast<SCEVAddRecExpr>(NewAddRec);
2596 return getMulExpr(Ops);
2598 // Otherwise couldn't fold anything into this recurrence. Move onto the
2602 // Okay, it looks like we really DO need an mul expr. Check to see if we
2603 // already have one, otherwise create a new one.
2604 FoldingSetNodeID ID;
2605 ID.AddInteger(scMulExpr);
2606 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2607 ID.AddPointer(Ops[i]);
2610 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2612 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2613 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2614 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
2616 UniqueSCEVs.InsertNode(S, IP);
2618 S->setNoWrapFlags(Flags);
2622 /// getUDivExpr - Get a canonical unsigned division expression, or something
2623 /// simpler if possible.
2624 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
2626 assert(getEffectiveSCEVType(LHS->getType()) ==
2627 getEffectiveSCEVType(RHS->getType()) &&
2628 "SCEVUDivExpr operand types don't match!");
2630 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
2631 if (RHSC->getValue()->equalsInt(1))
2632 return LHS; // X udiv 1 --> x
2633 // If the denominator is zero, the result of the udiv is undefined. Don't
2634 // try to analyze it, because the resolution chosen here may differ from
2635 // the resolution chosen in other parts of the compiler.
2636 if (!RHSC->getValue()->isZero()) {
2637 // Determine if the division can be folded into the operands of
2639 // TODO: Generalize this to non-constants by using known-bits information.
2640 Type *Ty = LHS->getType();
2641 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
2642 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1;
2643 // For non-power-of-two values, effectively round the value up to the
2644 // nearest power of two.
2645 if (!RHSC->getValue()->getValue().isPowerOf2())
2647 IntegerType *ExtTy =
2648 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
2649 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
2650 if (const SCEVConstant *Step =
2651 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) {
2652 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
2653 const APInt &StepInt = Step->getValue()->getValue();
2654 const APInt &DivInt = RHSC->getValue()->getValue();
2655 if (!StepInt.urem(DivInt) &&
2656 getZeroExtendExpr(AR, ExtTy) ==
2657 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2658 getZeroExtendExpr(Step, ExtTy),
2659 AR->getLoop(), SCEV::FlagAnyWrap)) {
2660 SmallVector<const SCEV *, 4> Operands;
2661 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i)
2662 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS));
2663 return getAddRecExpr(Operands, AR->getLoop(),
2666 /// Get a canonical UDivExpr for a recurrence.
2667 /// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0.
2668 // We can currently only fold X%N if X is constant.
2669 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(AR->getStart());
2670 if (StartC && !DivInt.urem(StepInt) &&
2671 getZeroExtendExpr(AR, ExtTy) ==
2672 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2673 getZeroExtendExpr(Step, ExtTy),
2674 AR->getLoop(), SCEV::FlagAnyWrap)) {
2675 const APInt &StartInt = StartC->getValue()->getValue();
2676 const APInt &StartRem = StartInt.urem(StepInt);
2678 LHS = getAddRecExpr(getConstant(StartInt - StartRem), Step,
2679 AR->getLoop(), SCEV::FlagNW);
2682 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
2683 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
2684 SmallVector<const SCEV *, 4> Operands;
2685 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i)
2686 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy));
2687 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
2688 // Find an operand that's safely divisible.
2689 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
2690 const SCEV *Op = M->getOperand(i);
2691 const SCEV *Div = getUDivExpr(Op, RHSC);
2692 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
2693 Operands = SmallVector<const SCEV *, 4>(M->op_begin(),
2696 return getMulExpr(Operands);
2700 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
2701 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) {
2702 SmallVector<const SCEV *, 4> Operands;
2703 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i)
2704 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy));
2705 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
2707 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
2708 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
2709 if (isa<SCEVUDivExpr>(Op) ||
2710 getMulExpr(Op, RHS) != A->getOperand(i))
2712 Operands.push_back(Op);
2714 if (Operands.size() == A->getNumOperands())
2715 return getAddExpr(Operands);
2719 // Fold if both operands are constant.
2720 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
2721 Constant *LHSCV = LHSC->getValue();
2722 Constant *RHSCV = RHSC->getValue();
2723 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
2729 FoldingSetNodeID ID;
2730 ID.AddInteger(scUDivExpr);
2734 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2735 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
2737 UniqueSCEVs.InsertNode(S, IP);
2741 static const APInt gcd(const SCEVConstant *C1, const SCEVConstant *C2) {
2742 APInt A = C1->getValue()->getValue().abs();
2743 APInt B = C2->getValue()->getValue().abs();
2744 uint32_t ABW = A.getBitWidth();
2745 uint32_t BBW = B.getBitWidth();
2752 return APIntOps::GreatestCommonDivisor(A, B);
2755 /// getUDivExactExpr - Get a canonical unsigned division expression, or
2756 /// something simpler if possible. There is no representation for an exact udiv
2757 /// in SCEV IR, but we can attempt to remove factors from the LHS and RHS.
2758 /// We can't do this when it's not exact because the udiv may be clearing bits.
2759 const SCEV *ScalarEvolution::getUDivExactExpr(const SCEV *LHS,
2761 // TODO: we could try to find factors in all sorts of things, but for now we
2762 // just deal with u/exact (multiply, constant). See SCEVDivision towards the
2763 // end of this file for inspiration.
2765 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(LHS);
2767 return getUDivExpr(LHS, RHS);
2769 if (const SCEVConstant *RHSCst = dyn_cast<SCEVConstant>(RHS)) {
2770 // If the mulexpr multiplies by a constant, then that constant must be the
2771 // first element of the mulexpr.
2772 if (const SCEVConstant *LHSCst =
2773 dyn_cast<SCEVConstant>(Mul->getOperand(0))) {
2774 if (LHSCst == RHSCst) {
2775 SmallVector<const SCEV *, 2> Operands;
2776 Operands.append(Mul->op_begin() + 1, Mul->op_end());
2777 return getMulExpr(Operands);
2780 // We can't just assume that LHSCst divides RHSCst cleanly, it could be
2781 // that there's a factor provided by one of the other terms. We need to
2783 APInt Factor = gcd(LHSCst, RHSCst);
2784 if (!Factor.isIntN(1)) {
2785 LHSCst = cast<SCEVConstant>(
2786 getConstant(LHSCst->getValue()->getValue().udiv(Factor)));
2787 RHSCst = cast<SCEVConstant>(
2788 getConstant(RHSCst->getValue()->getValue().udiv(Factor)));
2789 SmallVector<const SCEV *, 2> Operands;
2790 Operands.push_back(LHSCst);
2791 Operands.append(Mul->op_begin() + 1, Mul->op_end());
2792 LHS = getMulExpr(Operands);
2794 Mul = dyn_cast<SCEVMulExpr>(LHS);
2796 return getUDivExactExpr(LHS, RHS);
2801 for (int i = 0, e = Mul->getNumOperands(); i != e; ++i) {
2802 if (Mul->getOperand(i) == RHS) {
2803 SmallVector<const SCEV *, 2> Operands;
2804 Operands.append(Mul->op_begin(), Mul->op_begin() + i);
2805 Operands.append(Mul->op_begin() + i + 1, Mul->op_end());
2806 return getMulExpr(Operands);
2810 return getUDivExpr(LHS, RHS);
2813 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2814 /// Simplify the expression as much as possible.
2815 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step,
2817 SCEV::NoWrapFlags Flags) {
2818 SmallVector<const SCEV *, 4> Operands;
2819 Operands.push_back(Start);
2820 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
2821 if (StepChrec->getLoop() == L) {
2822 Operands.append(StepChrec->op_begin(), StepChrec->op_end());
2823 return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW));
2826 Operands.push_back(Step);
2827 return getAddRecExpr(Operands, L, Flags);
2830 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2831 /// Simplify the expression as much as possible.
2833 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
2834 const Loop *L, SCEV::NoWrapFlags Flags) {
2835 if (Operands.size() == 1) return Operands[0];
2837 Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
2838 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
2839 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy &&
2840 "SCEVAddRecExpr operand types don't match!");
2841 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2842 assert(isLoopInvariant(Operands[i], L) &&
2843 "SCEVAddRecExpr operand is not loop-invariant!");
2846 if (Operands.back()->isZero()) {
2847 Operands.pop_back();
2848 return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0} --> X
2851 // It's tempting to want to call getMaxBackedgeTakenCount count here and
2852 // use that information to infer NUW and NSW flags. However, computing a
2853 // BE count requires calling getAddRecExpr, so we may not yet have a
2854 // meaningful BE count at this point (and if we don't, we'd be stuck
2855 // with a SCEVCouldNotCompute as the cached BE count).
2857 Flags = StrengthenNoWrapFlags(this, scAddRecExpr, Operands, Flags);
2859 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
2860 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
2861 const Loop *NestedLoop = NestedAR->getLoop();
2862 if (L->contains(NestedLoop) ?
2863 (L->getLoopDepth() < NestedLoop->getLoopDepth()) :
2864 (!NestedLoop->contains(L) &&
2865 DT->dominates(L->getHeader(), NestedLoop->getHeader()))) {
2866 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
2867 NestedAR->op_end());
2868 Operands[0] = NestedAR->getStart();
2869 // AddRecs require their operands be loop-invariant with respect to their
2870 // loops. Don't perform this transformation if it would break this
2872 bool AllInvariant = true;
2873 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2874 if (!isLoopInvariant(Operands[i], L)) {
2875 AllInvariant = false;
2879 // Create a recurrence for the outer loop with the same step size.
2881 // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the
2882 // inner recurrence has the same property.
2883 SCEV::NoWrapFlags OuterFlags =
2884 maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags());
2886 NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags);
2887 AllInvariant = true;
2888 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i)
2889 if (!isLoopInvariant(NestedOperands[i], NestedLoop)) {
2890 AllInvariant = false;
2894 // Ok, both add recurrences are valid after the transformation.
2896 // The inner recurrence keeps its NW flag but only keeps NUW/NSW if
2897 // the outer recurrence has the same property.
2898 SCEV::NoWrapFlags InnerFlags =
2899 maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags);
2900 return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags);
2903 // Reset Operands to its original state.
2904 Operands[0] = NestedAR;
2908 // Okay, it looks like we really DO need an addrec expr. Check to see if we
2909 // already have one, otherwise create a new one.
2910 FoldingSetNodeID ID;
2911 ID.AddInteger(scAddRecExpr);
2912 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2913 ID.AddPointer(Operands[i]);
2917 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2919 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size());
2920 std::uninitialized_copy(Operands.begin(), Operands.end(), O);
2921 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator),
2922 O, Operands.size(), L);
2923 UniqueSCEVs.InsertNode(S, IP);
2925 S->setNoWrapFlags(Flags);
2930 ScalarEvolution::getGEPExpr(Type *PointeeType, const SCEV *BaseExpr,
2931 const SmallVectorImpl<const SCEV *> &IndexExprs,
2933 // getSCEV(Base)->getType() has the same address space as Base->getType()
2934 // because SCEV::getType() preserves the address space.
2935 Type *IntPtrTy = getEffectiveSCEVType(BaseExpr->getType());
2936 // FIXME(PR23527): Don't blindly transfer the inbounds flag from the GEP
2937 // instruction to its SCEV, because the Instruction may be guarded by control
2938 // flow and the no-overflow bits may not be valid for the expression in any
2939 // context. This can be fixed similarly to how these flags are handled for
2941 SCEV::NoWrapFlags Wrap = InBounds ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
2943 const SCEV *TotalOffset = getConstant(IntPtrTy, 0);
2944 // The address space is unimportant. The first thing we do on CurTy is getting
2945 // its element type.
2946 Type *CurTy = PointerType::getUnqual(PointeeType);
2947 for (const SCEV *IndexExpr : IndexExprs) {
2948 // Compute the (potentially symbolic) offset in bytes for this index.
2949 if (StructType *STy = dyn_cast<StructType>(CurTy)) {
2950 // For a struct, add the member offset.
2951 ConstantInt *Index = cast<SCEVConstant>(IndexExpr)->getValue();
2952 unsigned FieldNo = Index->getZExtValue();
2953 const SCEV *FieldOffset = getOffsetOfExpr(IntPtrTy, STy, FieldNo);
2955 // Add the field offset to the running total offset.
2956 TotalOffset = getAddExpr(TotalOffset, FieldOffset);
2958 // Update CurTy to the type of the field at Index.
2959 CurTy = STy->getTypeAtIndex(Index);
2961 // Update CurTy to its element type.
2962 CurTy = cast<SequentialType>(CurTy)->getElementType();
2963 // For an array, add the element offset, explicitly scaled.
2964 const SCEV *ElementSize = getSizeOfExpr(IntPtrTy, CurTy);
2965 // Getelementptr indices are signed.
2966 IndexExpr = getTruncateOrSignExtend(IndexExpr, IntPtrTy);
2968 // Multiply the index by the element size to compute the element offset.
2969 const SCEV *LocalOffset = getMulExpr(IndexExpr, ElementSize, Wrap);
2971 // Add the element offset to the running total offset.
2972 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
2976 // Add the total offset from all the GEP indices to the base.
2977 return getAddExpr(BaseExpr, TotalOffset, Wrap);
2980 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
2982 SmallVector<const SCEV *, 2> Ops;
2985 return getSMaxExpr(Ops);
2989 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2990 assert(!Ops.empty() && "Cannot get empty smax!");
2991 if (Ops.size() == 1) return Ops[0];
2993 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2994 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2995 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2996 "SCEVSMaxExpr operand types don't match!");
2999 // Sort by complexity, this groups all similar expression types together.
3000 GroupByComplexity(Ops, LI);
3002 // If there are any constants, fold them together.
3004 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
3006 assert(Idx < Ops.size());
3007 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
3008 // We found two constants, fold them together!
3009 ConstantInt *Fold = ConstantInt::get(getContext(),
3010 APIntOps::smax(LHSC->getValue()->getValue(),
3011 RHSC->getValue()->getValue()));
3012 Ops[0] = getConstant(Fold);
3013 Ops.erase(Ops.begin()+1); // Erase the folded element
3014 if (Ops.size() == 1) return Ops[0];
3015 LHSC = cast<SCEVConstant>(Ops[0]);
3018 // If we are left with a constant minimum-int, strip it off.
3019 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
3020 Ops.erase(Ops.begin());
3022 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
3023 // If we have an smax with a constant maximum-int, it will always be
3028 if (Ops.size() == 1) return Ops[0];
3031 // Find the first SMax
3032 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
3035 // Check to see if one of the operands is an SMax. If so, expand its operands
3036 // onto our operand list, and recurse to simplify.
3037 if (Idx < Ops.size()) {
3038 bool DeletedSMax = false;
3039 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
3040 Ops.erase(Ops.begin()+Idx);
3041 Ops.append(SMax->op_begin(), SMax->op_end());
3046 return getSMaxExpr(Ops);
3049 // Okay, check to see if the same value occurs in the operand list twice. If
3050 // so, delete one. Since we sorted the list, these values are required to
3052 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
3053 // X smax Y smax Y --> X smax Y
3054 // X smax Y --> X, if X is always greater than Y
3055 if (Ops[i] == Ops[i+1] ||
3056 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) {
3057 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
3059 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) {
3060 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
3064 if (Ops.size() == 1) return Ops[0];
3066 assert(!Ops.empty() && "Reduced smax down to nothing!");
3068 // Okay, it looks like we really DO need an smax expr. Check to see if we
3069 // already have one, otherwise create a new one.
3070 FoldingSetNodeID ID;
3071 ID.AddInteger(scSMaxExpr);
3072 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
3073 ID.AddPointer(Ops[i]);
3075 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
3076 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
3077 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
3078 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator),
3080 UniqueSCEVs.InsertNode(S, IP);
3084 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
3086 SmallVector<const SCEV *, 2> Ops;
3089 return getUMaxExpr(Ops);
3093 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
3094 assert(!Ops.empty() && "Cannot get empty umax!");
3095 if (Ops.size() == 1) return Ops[0];
3097 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
3098 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
3099 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
3100 "SCEVUMaxExpr operand types don't match!");
3103 // Sort by complexity, this groups all similar expression types together.
3104 GroupByComplexity(Ops, LI);
3106 // If there are any constants, fold them together.
3108 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
3110 assert(Idx < Ops.size());
3111 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
3112 // We found two constants, fold them together!
3113 ConstantInt *Fold = ConstantInt::get(getContext(),
3114 APIntOps::umax(LHSC->getValue()->getValue(),
3115 RHSC->getValue()->getValue()));
3116 Ops[0] = getConstant(Fold);
3117 Ops.erase(Ops.begin()+1); // Erase the folded element
3118 if (Ops.size() == 1) return Ops[0];
3119 LHSC = cast<SCEVConstant>(Ops[0]);
3122 // If we are left with a constant minimum-int, strip it off.
3123 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
3124 Ops.erase(Ops.begin());
3126 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
3127 // If we have an umax with a constant maximum-int, it will always be
3132 if (Ops.size() == 1) return Ops[0];
3135 // Find the first UMax
3136 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
3139 // Check to see if one of the operands is a UMax. If so, expand its operands
3140 // onto our operand list, and recurse to simplify.
3141 if (Idx < Ops.size()) {
3142 bool DeletedUMax = false;
3143 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
3144 Ops.erase(Ops.begin()+Idx);
3145 Ops.append(UMax->op_begin(), UMax->op_end());
3150 return getUMaxExpr(Ops);
3153 // Okay, check to see if the same value occurs in the operand list twice. If
3154 // so, delete one. Since we sorted the list, these values are required to
3156 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
3157 // X umax Y umax Y --> X umax Y
3158 // X umax Y --> X, if X is always greater than Y
3159 if (Ops[i] == Ops[i+1] ||
3160 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) {
3161 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
3163 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) {
3164 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
3168 if (Ops.size() == 1) return Ops[0];
3170 assert(!Ops.empty() && "Reduced umax down to nothing!");
3172 // Okay, it looks like we really DO need a umax expr. Check to see if we
3173 // already have one, otherwise create a new one.
3174 FoldingSetNodeID ID;
3175 ID.AddInteger(scUMaxExpr);
3176 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
3177 ID.AddPointer(Ops[i]);
3179 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
3180 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
3181 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
3182 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator),
3184 UniqueSCEVs.InsertNode(S, IP);
3188 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
3190 // ~smax(~x, ~y) == smin(x, y).
3191 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
3194 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
3196 // ~umax(~x, ~y) == umin(x, y)
3197 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
3200 const SCEV *ScalarEvolution::getSizeOfExpr(Type *IntTy, Type *AllocTy) {
3201 // We can bypass creating a target-independent
3202 // constant expression and then folding it back into a ConstantInt.
3203 // This is just a compile-time optimization.
3204 return getConstant(IntTy,
3205 F->getParent()->getDataLayout().getTypeAllocSize(AllocTy));
3208 const SCEV *ScalarEvolution::getOffsetOfExpr(Type *IntTy,
3211 // We can bypass creating a target-independent
3212 // constant expression and then folding it back into a ConstantInt.
3213 // This is just a compile-time optimization.
3216 F->getParent()->getDataLayout().getStructLayout(STy)->getElementOffset(
3220 const SCEV *ScalarEvolution::getUnknown(Value *V) {
3221 // Don't attempt to do anything other than create a SCEVUnknown object
3222 // here. createSCEV only calls getUnknown after checking for all other
3223 // interesting possibilities, and any other code that calls getUnknown
3224 // is doing so in order to hide a value from SCEV canonicalization.
3226 FoldingSetNodeID ID;
3227 ID.AddInteger(scUnknown);
3230 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
3231 assert(cast<SCEVUnknown>(S)->getValue() == V &&
3232 "Stale SCEVUnknown in uniquing map!");
3235 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
3237 FirstUnknown = cast<SCEVUnknown>(S);
3238 UniqueSCEVs.InsertNode(S, IP);
3242 //===----------------------------------------------------------------------===//
3243 // Basic SCEV Analysis and PHI Idiom Recognition Code
3246 /// isSCEVable - Test if values of the given type are analyzable within
3247 /// the SCEV framework. This primarily includes integer types, and it
3248 /// can optionally include pointer types if the ScalarEvolution class
3249 /// has access to target-specific information.
3250 bool ScalarEvolution::isSCEVable(Type *Ty) const {
3251 // Integers and pointers are always SCEVable.
3252 return Ty->isIntegerTy() || Ty->isPointerTy();
3255 /// getTypeSizeInBits - Return the size in bits of the specified type,
3256 /// for which isSCEVable must return true.
3257 uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const {
3258 assert(isSCEVable(Ty) && "Type is not SCEVable!");
3259 return F->getParent()->getDataLayout().getTypeSizeInBits(Ty);
3262 /// getEffectiveSCEVType - Return a type with the same bitwidth as
3263 /// the given type and which represents how SCEV will treat the given
3264 /// type, for which isSCEVable must return true. For pointer types,
3265 /// this is the pointer-sized integer type.
3266 Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const {
3267 assert(isSCEVable(Ty) && "Type is not SCEVable!");
3269 if (Ty->isIntegerTy()) {
3273 // The only other support type is pointer.
3274 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
3275 return F->getParent()->getDataLayout().getIntPtrType(Ty);
3278 const SCEV *ScalarEvolution::getCouldNotCompute() {
3279 return &CouldNotCompute;
3283 // Helper class working with SCEVTraversal to figure out if a SCEV contains
3284 // a SCEVUnknown with null value-pointer. FindInvalidSCEVUnknown::FindOne
3285 // is set iff if find such SCEVUnknown.
3287 struct FindInvalidSCEVUnknown {
3289 FindInvalidSCEVUnknown() { FindOne = false; }
3290 bool follow(const SCEV *S) {
3291 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
3295 if (!cast<SCEVUnknown>(S)->getValue())
3302 bool isDone() const { return FindOne; }
3306 bool ScalarEvolution::checkValidity(const SCEV *S) const {
3307 FindInvalidSCEVUnknown F;
3308 SCEVTraversal<FindInvalidSCEVUnknown> ST(F);
3314 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
3315 /// expression and create a new one.
3316 const SCEV *ScalarEvolution::getSCEV(Value *V) {
3317 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
3319 const SCEV *S = getExistingSCEV(V);
3322 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(V, this), S));
3327 const SCEV *ScalarEvolution::getExistingSCEV(Value *V) {
3328 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
3330 ValueExprMapType::iterator I = ValueExprMap.find_as(V);
3331 if (I != ValueExprMap.end()) {
3332 const SCEV *S = I->second;
3333 if (checkValidity(S))
3335 ValueExprMap.erase(I);
3340 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
3342 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) {
3343 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
3345 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
3347 Type *Ty = V->getType();
3348 Ty = getEffectiveSCEVType(Ty);
3349 return getMulExpr(V,
3350 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))));
3353 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
3354 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
3355 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
3357 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
3359 Type *Ty = V->getType();
3360 Ty = getEffectiveSCEVType(Ty);
3361 const SCEV *AllOnes =
3362 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
3363 return getMinusSCEV(AllOnes, V);
3366 /// getMinusSCEV - Return LHS-RHS. Minus is represented in SCEV as A+B*-1.
3367 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
3368 SCEV::NoWrapFlags Flags) {
3369 assert(!maskFlags(Flags, SCEV::FlagNUW) && "subtraction does not have NUW");
3371 // Fast path: X - X --> 0.
3373 return getConstant(LHS->getType(), 0);
3375 // X - Y --> X + -Y.
3376 // X -(nsw || nuw) Y --> X + -Y.
3377 return getAddExpr(LHS, getNegativeSCEV(RHS));
3380 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
3381 /// input value to the specified type. If the type must be extended, it is zero
3384 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty) {
3385 Type *SrcTy = V->getType();
3386 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3387 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3388 "Cannot truncate or zero extend with non-integer arguments!");
3389 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3390 return V; // No conversion
3391 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
3392 return getTruncateExpr(V, Ty);
3393 return getZeroExtendExpr(V, Ty);
3396 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
3397 /// input value to the specified type. If the type must be extended, it is sign
3400 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
3402 Type *SrcTy = V->getType();
3403 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3404 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3405 "Cannot truncate or zero extend with non-integer arguments!");
3406 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3407 return V; // No conversion
3408 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
3409 return getTruncateExpr(V, Ty);
3410 return getSignExtendExpr(V, Ty);
3413 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
3414 /// input value to the specified type. If the type must be extended, it is zero
3415 /// extended. The conversion must not be narrowing.
3417 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) {
3418 Type *SrcTy = V->getType();
3419 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3420 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3421 "Cannot noop or zero extend with non-integer arguments!");
3422 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3423 "getNoopOrZeroExtend cannot truncate!");
3424 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3425 return V; // No conversion
3426 return getZeroExtendExpr(V, Ty);
3429 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
3430 /// input value to the specified type. If the type must be extended, it is sign
3431 /// extended. The conversion must not be narrowing.
3433 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) {
3434 Type *SrcTy = V->getType();
3435 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3436 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3437 "Cannot noop or sign extend with non-integer arguments!");
3438 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3439 "getNoopOrSignExtend cannot truncate!");
3440 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3441 return V; // No conversion
3442 return getSignExtendExpr(V, Ty);
3445 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
3446 /// the input value to the specified type. If the type must be extended,
3447 /// it is extended with unspecified bits. The conversion must not be
3450 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) {
3451 Type *SrcTy = V->getType();
3452 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3453 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3454 "Cannot noop or any extend with non-integer arguments!");
3455 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3456 "getNoopOrAnyExtend cannot truncate!");
3457 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3458 return V; // No conversion
3459 return getAnyExtendExpr(V, Ty);
3462 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
3463 /// input value to the specified type. The conversion must not be widening.
3465 ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) {
3466 Type *SrcTy = V->getType();
3467 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3468 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3469 "Cannot truncate or noop with non-integer arguments!");
3470 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
3471 "getTruncateOrNoop cannot extend!");
3472 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3473 return V; // No conversion
3474 return getTruncateExpr(V, Ty);
3477 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
3478 /// the types using zero-extension, and then perform a umax operation
3480 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
3482 const SCEV *PromotedLHS = LHS;
3483 const SCEV *PromotedRHS = RHS;
3485 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
3486 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
3488 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
3490 return getUMaxExpr(PromotedLHS, PromotedRHS);
3493 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
3494 /// the types using zero-extension, and then perform a umin operation
3496 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
3498 const SCEV *PromotedLHS = LHS;
3499 const SCEV *PromotedRHS = RHS;
3501 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
3502 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
3504 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
3506 return getUMinExpr(PromotedLHS, PromotedRHS);
3509 /// getPointerBase - Transitively follow the chain of pointer-type operands
3510 /// until reaching a SCEV that does not have a single pointer operand. This
3511 /// returns a SCEVUnknown pointer for well-formed pointer-type expressions,
3512 /// but corner cases do exist.
3513 const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) {
3514 // A pointer operand may evaluate to a nonpointer expression, such as null.
3515 if (!V->getType()->isPointerTy())
3518 if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) {
3519 return getPointerBase(Cast->getOperand());
3521 else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) {
3522 const SCEV *PtrOp = nullptr;
3523 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
3525 if ((*I)->getType()->isPointerTy()) {
3526 // Cannot find the base of an expression with multiple pointer operands.
3534 return getPointerBase(PtrOp);
3539 /// PushDefUseChildren - Push users of the given Instruction
3540 /// onto the given Worklist.
3542 PushDefUseChildren(Instruction *I,
3543 SmallVectorImpl<Instruction *> &Worklist) {
3544 // Push the def-use children onto the Worklist stack.
3545 for (User *U : I->users())
3546 Worklist.push_back(cast<Instruction>(U));
3549 /// ForgetSymbolicValue - This looks up computed SCEV values for all
3550 /// instructions that depend on the given instruction and removes them from
3551 /// the ValueExprMapType map if they reference SymName. This is used during PHI
3554 ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) {
3555 SmallVector<Instruction *, 16> Worklist;
3556 PushDefUseChildren(PN, Worklist);
3558 SmallPtrSet<Instruction *, 8> Visited;
3560 while (!Worklist.empty()) {
3561 Instruction *I = Worklist.pop_back_val();
3562 if (!Visited.insert(I).second)
3565 ValueExprMapType::iterator It =
3566 ValueExprMap.find_as(static_cast<Value *>(I));
3567 if (It != ValueExprMap.end()) {
3568 const SCEV *Old = It->second;
3570 // Short-circuit the def-use traversal if the symbolic name
3571 // ceases to appear in expressions.
3572 if (Old != SymName && !hasOperand(Old, SymName))
3575 // SCEVUnknown for a PHI either means that it has an unrecognized
3576 // structure, it's a PHI that's in the progress of being computed
3577 // by createNodeForPHI, or it's a single-value PHI. In the first case,
3578 // additional loop trip count information isn't going to change anything.
3579 // In the second case, createNodeForPHI will perform the necessary
3580 // updates on its own when it gets to that point. In the third, we do
3581 // want to forget the SCEVUnknown.
3582 if (!isa<PHINode>(I) ||
3583 !isa<SCEVUnknown>(Old) ||
3584 (I != PN && Old == SymName)) {
3585 forgetMemoizedResults(Old);
3586 ValueExprMap.erase(It);
3590 PushDefUseChildren(I, Worklist);
3594 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
3595 /// a loop header, making it a potential recurrence, or it doesn't.
3597 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
3598 if (const Loop *L = LI->getLoopFor(PN->getParent()))
3599 if (L->getHeader() == PN->getParent()) {
3600 // The loop may have multiple entrances or multiple exits; we can analyze
3601 // this phi as an addrec if it has a unique entry value and a unique
3603 Value *BEValueV = nullptr, *StartValueV = nullptr;
3604 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
3605 Value *V = PN->getIncomingValue(i);
3606 if (L->contains(PN->getIncomingBlock(i))) {
3609 } else if (BEValueV != V) {
3613 } else if (!StartValueV) {
3615 } else if (StartValueV != V) {
3616 StartValueV = nullptr;
3620 if (BEValueV && StartValueV) {
3621 // While we are analyzing this PHI node, handle its value symbolically.
3622 const SCEV *SymbolicName = getUnknown(PN);
3623 assert(ValueExprMap.find_as(PN) == ValueExprMap.end() &&
3624 "PHI node already processed?");
3625 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
3627 // Using this symbolic name for the PHI, analyze the value coming around
3629 const SCEV *BEValue = getSCEV(BEValueV);
3631 // NOTE: If BEValue is loop invariant, we know that the PHI node just
3632 // has a special value for the first iteration of the loop.
3634 // If the value coming around the backedge is an add with the symbolic
3635 // value we just inserted, then we found a simple induction variable!
3636 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
3637 // If there is a single occurrence of the symbolic value, replace it
3638 // with a recurrence.
3639 unsigned FoundIndex = Add->getNumOperands();
3640 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3641 if (Add->getOperand(i) == SymbolicName)
3642 if (FoundIndex == e) {
3647 if (FoundIndex != Add->getNumOperands()) {
3648 // Create an add with everything but the specified operand.
3649 SmallVector<const SCEV *, 8> Ops;
3650 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3651 if (i != FoundIndex)
3652 Ops.push_back(Add->getOperand(i));
3653 const SCEV *Accum = getAddExpr(Ops);
3655 // This is not a valid addrec if the step amount is varying each
3656 // loop iteration, but is not itself an addrec in this loop.
3657 if (isLoopInvariant(Accum, L) ||
3658 (isa<SCEVAddRecExpr>(Accum) &&
3659 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
3660 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
3662 // If the increment doesn't overflow, then neither the addrec nor
3663 // the post-increment will overflow.
3664 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) {
3665 if (OBO->getOperand(0) == PN) {
3666 if (OBO->hasNoUnsignedWrap())
3667 Flags = setFlags(Flags, SCEV::FlagNUW);
3668 if (OBO->hasNoSignedWrap())
3669 Flags = setFlags(Flags, SCEV::FlagNSW);
3671 } else if (GEPOperator *GEP = dyn_cast<GEPOperator>(BEValueV)) {
3672 // If the increment is an inbounds GEP, then we know the address
3673 // space cannot be wrapped around. We cannot make any guarantee
3674 // about signed or unsigned overflow because pointers are
3675 // unsigned but we may have a negative index from the base
3676 // pointer. We can guarantee that no unsigned wrap occurs if the
3677 // indices form a positive value.
3678 if (GEP->isInBounds() && GEP->getOperand(0) == PN) {
3679 Flags = setFlags(Flags, SCEV::FlagNW);
3681 const SCEV *Ptr = getSCEV(GEP->getPointerOperand());
3682 if (isKnownPositive(getMinusSCEV(getSCEV(GEP), Ptr)))
3683 Flags = setFlags(Flags, SCEV::FlagNUW);
3686 // We cannot transfer nuw and nsw flags from subtraction
3687 // operations -- sub nuw X, Y is not the same as add nuw X, -Y
3691 const SCEV *StartVal = getSCEV(StartValueV);
3692 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
3694 // Since the no-wrap flags are on the increment, they apply to the
3695 // post-incremented value as well.
3696 if (isLoopInvariant(Accum, L))
3697 (void)getAddRecExpr(getAddExpr(StartVal, Accum),
3700 // Okay, for the entire analysis of this edge we assumed the PHI
3701 // to be symbolic. We now need to go back and purge all of the
3702 // entries for the scalars that use the symbolic expression.
3703 ForgetSymbolicName(PN, SymbolicName);
3704 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3708 } else if (const SCEVAddRecExpr *AddRec =
3709 dyn_cast<SCEVAddRecExpr>(BEValue)) {
3710 // Otherwise, this could be a loop like this:
3711 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
3712 // In this case, j = {1,+,1} and BEValue is j.
3713 // Because the other in-value of i (0) fits the evolution of BEValue
3714 // i really is an addrec evolution.
3715 if (AddRec->getLoop() == L && AddRec->isAffine()) {
3716 const SCEV *StartVal = getSCEV(StartValueV);
3718 // If StartVal = j.start - j.stride, we can use StartVal as the
3719 // initial step of the addrec evolution.
3720 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
3721 AddRec->getOperand(1))) {
3722 // FIXME: For constant StartVal, we should be able to infer
3724 const SCEV *PHISCEV =
3725 getAddRecExpr(StartVal, AddRec->getOperand(1), L,
3728 // Okay, for the entire analysis of this edge we assumed the PHI
3729 // to be symbolic. We now need to go back and purge all of the
3730 // entries for the scalars that use the symbolic expression.
3731 ForgetSymbolicName(PN, SymbolicName);
3732 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3740 // If the PHI has a single incoming value, follow that value, unless the
3741 // PHI's incoming blocks are in a different loop, in which case doing so
3742 // risks breaking LCSSA form. Instcombine would normally zap these, but
3743 // it doesn't have DominatorTree information, so it may miss cases.
3745 SimplifyInstruction(PN, F->getParent()->getDataLayout(), TLI, DT, AC))
3746 if (LI->replacementPreservesLCSSAForm(PN, V))
3749 // If it's not a loop phi, we can't handle it yet.
3750 return getUnknown(PN);
3753 /// createNodeForGEP - Expand GEP instructions into add and multiply
3754 /// operations. This allows them to be analyzed by regular SCEV code.
3756 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
3757 Value *Base = GEP->getOperand(0);
3758 // Don't attempt to analyze GEPs over unsized objects.
3759 if (!Base->getType()->getPointerElementType()->isSized())
3760 return getUnknown(GEP);
3762 SmallVector<const SCEV *, 4> IndexExprs;
3763 for (auto Index = GEP->idx_begin(); Index != GEP->idx_end(); ++Index)
3764 IndexExprs.push_back(getSCEV(*Index));
3765 return getGEPExpr(GEP->getSourceElementType(), getSCEV(Base), IndexExprs,
3769 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
3770 /// guaranteed to end in (at every loop iteration). It is, at the same time,
3771 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
3772 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
3774 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
3775 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3776 return C->getValue()->getValue().countTrailingZeros();
3778 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
3779 return std::min(GetMinTrailingZeros(T->getOperand()),
3780 (uint32_t)getTypeSizeInBits(T->getType()));
3782 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
3783 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3784 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3785 getTypeSizeInBits(E->getType()) : OpRes;
3788 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
3789 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3790 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3791 getTypeSizeInBits(E->getType()) : OpRes;
3794 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
3795 // The result is the min of all operands results.
3796 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3797 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3798 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3802 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
3803 // The result is the sum of all operands results.
3804 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
3805 uint32_t BitWidth = getTypeSizeInBits(M->getType());
3806 for (unsigned i = 1, e = M->getNumOperands();
3807 SumOpRes != BitWidth && i != e; ++i)
3808 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
3813 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
3814 // The result is the min of all operands results.
3815 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3816 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3817 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3821 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
3822 // The result is the min of all operands results.
3823 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3824 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3825 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3829 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
3830 // The result is the min of all operands results.
3831 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3832 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3833 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3837 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3838 // For a SCEVUnknown, ask ValueTracking.
3839 unsigned BitWidth = getTypeSizeInBits(U->getType());
3840 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3841 computeKnownBits(U->getValue(), Zeros, Ones,
3842 F->getParent()->getDataLayout(), 0, AC, nullptr, DT);
3843 return Zeros.countTrailingOnes();
3850 /// GetRangeFromMetadata - Helper method to assign a range to V from
3851 /// metadata present in the IR.
3852 static Optional<ConstantRange> GetRangeFromMetadata(Value *V) {
3853 if (Instruction *I = dyn_cast<Instruction>(V)) {
3854 if (MDNode *MD = I->getMetadata(LLVMContext::MD_range)) {
3855 ConstantRange TotalRange(
3856 cast<IntegerType>(I->getType())->getBitWidth(), false);
3858 unsigned NumRanges = MD->getNumOperands() / 2;
3859 assert(NumRanges >= 1);
3861 for (unsigned i = 0; i < NumRanges; ++i) {
3862 ConstantInt *Lower =
3863 mdconst::extract<ConstantInt>(MD->getOperand(2 * i + 0));
3864 ConstantInt *Upper =
3865 mdconst::extract<ConstantInt>(MD->getOperand(2 * i + 1));
3866 ConstantRange Range(Lower->getValue(), Upper->getValue());
3867 TotalRange = TotalRange.unionWith(Range);
3877 /// getRange - Determine the range for a particular SCEV. If SignHint is
3878 /// HINT_RANGE_UNSIGNED (resp. HINT_RANGE_SIGNED) then getRange prefers ranges
3879 /// with a "cleaner" unsigned (resp. signed) representation.
3882 ScalarEvolution::getRange(const SCEV *S,
3883 ScalarEvolution::RangeSignHint SignHint) {
3884 DenseMap<const SCEV *, ConstantRange> &Cache =
3885 SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED ? UnsignedRanges
3888 // See if we've computed this range already.
3889 DenseMap<const SCEV *, ConstantRange>::iterator I = Cache.find(S);
3890 if (I != Cache.end())
3893 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3894 return setRange(C, SignHint, ConstantRange(C->getValue()->getValue()));
3896 unsigned BitWidth = getTypeSizeInBits(S->getType());
3897 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3899 // If the value has known zeros, the maximum value will have those known zeros
3901 uint32_t TZ = GetMinTrailingZeros(S);
3903 if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED)
3904 ConservativeResult =
3905 ConstantRange(APInt::getMinValue(BitWidth),
3906 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
3908 ConservativeResult = ConstantRange(
3909 APInt::getSignedMinValue(BitWidth),
3910 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
3913 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3914 ConstantRange X = getRange(Add->getOperand(0), SignHint);
3915 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3916 X = X.add(getRange(Add->getOperand(i), SignHint));
3917 return setRange(Add, SignHint, ConservativeResult.intersectWith(X));
3920 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3921 ConstantRange X = getRange(Mul->getOperand(0), SignHint);
3922 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3923 X = X.multiply(getRange(Mul->getOperand(i), SignHint));
3924 return setRange(Mul, SignHint, ConservativeResult.intersectWith(X));
3927 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3928 ConstantRange X = getRange(SMax->getOperand(0), SignHint);
3929 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3930 X = X.smax(getRange(SMax->getOperand(i), SignHint));
3931 return setRange(SMax, SignHint, ConservativeResult.intersectWith(X));
3934 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3935 ConstantRange X = getRange(UMax->getOperand(0), SignHint);
3936 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3937 X = X.umax(getRange(UMax->getOperand(i), SignHint));
3938 return setRange(UMax, SignHint, ConservativeResult.intersectWith(X));
3941 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3942 ConstantRange X = getRange(UDiv->getLHS(), SignHint);
3943 ConstantRange Y = getRange(UDiv->getRHS(), SignHint);
3944 return setRange(UDiv, SignHint,
3945 ConservativeResult.intersectWith(X.udiv(Y)));
3948 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3949 ConstantRange X = getRange(ZExt->getOperand(), SignHint);
3950 return setRange(ZExt, SignHint,
3951 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3954 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3955 ConstantRange X = getRange(SExt->getOperand(), SignHint);
3956 return setRange(SExt, SignHint,
3957 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3960 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3961 ConstantRange X = getRange(Trunc->getOperand(), SignHint);
3962 return setRange(Trunc, SignHint,
3963 ConservativeResult.intersectWith(X.truncate(BitWidth)));
3966 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3967 // If there's no unsigned wrap, the value will never be less than its
3969 if (AddRec->getNoWrapFlags(SCEV::FlagNUW))
3970 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
3971 if (!C->getValue()->isZero())
3972 ConservativeResult =
3973 ConservativeResult.intersectWith(
3974 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0)));
3976 // If there's no signed wrap, and all the operands have the same sign or
3977 // zero, the value won't ever change sign.
3978 if (AddRec->getNoWrapFlags(SCEV::FlagNSW)) {
3979 bool AllNonNeg = true;
3980 bool AllNonPos = true;
3981 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
3982 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
3983 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
3986 ConservativeResult = ConservativeResult.intersectWith(
3987 ConstantRange(APInt(BitWidth, 0),
3988 APInt::getSignedMinValue(BitWidth)));
3990 ConservativeResult = ConservativeResult.intersectWith(
3991 ConstantRange(APInt::getSignedMinValue(BitWidth),
3992 APInt(BitWidth, 1)));
3995 // TODO: non-affine addrec
3996 if (AddRec->isAffine()) {
3997 Type *Ty = AddRec->getType();
3998 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3999 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
4000 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
4002 // Check for overflow. This must be done with ConstantRange arithmetic
4003 // because we could be called from within the ScalarEvolution overflow
4006 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
4007 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
4008 ConstantRange ZExtMaxBECountRange =
4009 MaxBECountRange.zextOrTrunc(BitWidth * 2 + 1);
4011 const SCEV *Start = AddRec->getStart();
4012 const SCEV *Step = AddRec->getStepRecurrence(*this);
4013 ConstantRange StepSRange = getSignedRange(Step);
4014 ConstantRange SExtStepSRange = StepSRange.sextOrTrunc(BitWidth * 2 + 1);
4016 ConstantRange StartURange = getUnsignedRange(Start);
4017 ConstantRange EndURange =
4018 StartURange.add(MaxBECountRange.multiply(StepSRange));
4020 // Check for unsigned overflow.
4021 ConstantRange ZExtStartURange =
4022 StartURange.zextOrTrunc(BitWidth * 2 + 1);
4023 ConstantRange ZExtEndURange = EndURange.zextOrTrunc(BitWidth * 2 + 1);
4024 if (ZExtStartURange.add(ZExtMaxBECountRange.multiply(SExtStepSRange)) ==
4026 APInt Min = APIntOps::umin(StartURange.getUnsignedMin(),
4027 EndURange.getUnsignedMin());
4028 APInt Max = APIntOps::umax(StartURange.getUnsignedMax(),
4029 EndURange.getUnsignedMax());
4030 bool IsFullRange = Min.isMinValue() && Max.isMaxValue();
4032 ConservativeResult =
4033 ConservativeResult.intersectWith(ConstantRange(Min, Max + 1));
4036 ConstantRange StartSRange = getSignedRange(Start);
4037 ConstantRange EndSRange =
4038 StartSRange.add(MaxBECountRange.multiply(StepSRange));
4040 // Check for signed overflow. This must be done with ConstantRange
4041 // arithmetic because we could be called from within the ScalarEvolution
4042 // overflow checking code.
4043 ConstantRange SExtStartSRange =
4044 StartSRange.sextOrTrunc(BitWidth * 2 + 1);
4045 ConstantRange SExtEndSRange = EndSRange.sextOrTrunc(BitWidth * 2 + 1);
4046 if (SExtStartSRange.add(ZExtMaxBECountRange.multiply(SExtStepSRange)) ==
4048 APInt Min = APIntOps::smin(StartSRange.getSignedMin(),
4049 EndSRange.getSignedMin());
4050 APInt Max = APIntOps::smax(StartSRange.getSignedMax(),
4051 EndSRange.getSignedMax());
4052 bool IsFullRange = Min.isMinSignedValue() && Max.isMaxSignedValue();
4054 ConservativeResult =
4055 ConservativeResult.intersectWith(ConstantRange(Min, Max + 1));
4060 return setRange(AddRec, SignHint, ConservativeResult);
4063 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
4064 // Check if the IR explicitly contains !range metadata.
4065 Optional<ConstantRange> MDRange = GetRangeFromMetadata(U->getValue());
4066 if (MDRange.hasValue())
4067 ConservativeResult = ConservativeResult.intersectWith(MDRange.getValue());
4069 // Split here to avoid paying the compile-time cost of calling both
4070 // computeKnownBits and ComputeNumSignBits. This restriction can be lifted
4072 const DataLayout &DL = F->getParent()->getDataLayout();
4073 if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED) {
4074 // For a SCEVUnknown, ask ValueTracking.
4075 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
4076 computeKnownBits(U->getValue(), Zeros, Ones, DL, 0, AC, nullptr, DT);
4077 if (Ones != ~Zeros + 1)
4078 ConservativeResult =
4079 ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1));
4081 assert(SignHint == ScalarEvolution::HINT_RANGE_SIGNED &&
4082 "generalize as needed!");
4083 unsigned NS = ComputeNumSignBits(U->getValue(), DL, 0, AC, nullptr, DT);
4085 ConservativeResult = ConservativeResult.intersectWith(
4086 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
4087 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1) + 1));
4090 return setRange(U, SignHint, ConservativeResult);
4093 return setRange(S, SignHint, ConservativeResult);
4096 SCEV::NoWrapFlags ScalarEvolution::getNoWrapFlagsFromUB(const Value *V) {
4097 const BinaryOperator *BinOp = cast<BinaryOperator>(V);
4099 // Return early if there are no flags to propagate to the SCEV.
4100 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
4101 if (BinOp->hasNoUnsignedWrap())
4102 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNUW);
4103 if (BinOp->hasNoSignedWrap())
4104 Flags = ScalarEvolution::setFlags(Flags, SCEV::FlagNSW);
4105 if (Flags == SCEV::FlagAnyWrap) {
4106 return SCEV::FlagAnyWrap;
4109 // Here we check that BinOp is in the header of the innermost loop
4110 // containing BinOp, since we only deal with instructions in the loop
4111 // header. The actual loop we need to check later will come from an add
4112 // recurrence, but getting that requires computing the SCEV of the operands,
4113 // which can be expensive. This check we can do cheaply to rule out some
4115 Loop *innermostContainingLoop = LI->getLoopFor(BinOp->getParent());
4116 if (innermostContainingLoop == nullptr ||
4117 innermostContainingLoop->getHeader() != BinOp->getParent())
4118 return SCEV::FlagAnyWrap;
4120 // Only proceed if we can prove that BinOp does not yield poison.
4121 if (!isKnownNotFullPoison(BinOp)) return SCEV::FlagAnyWrap;
4123 // At this point we know that if V is executed, then it does not wrap
4124 // according to at least one of NSW or NUW. If V is not executed, then we do
4125 // not know if the calculation that V represents would wrap. Multiple
4126 // instructions can map to the same SCEV. If we apply NSW or NUW from V to
4127 // the SCEV, we must guarantee no wrapping for that SCEV also when it is
4128 // derived from other instructions that map to the same SCEV. We cannot make
4129 // that guarantee for cases where V is not executed. So we need to find the
4130 // loop that V is considered in relation to and prove that V is executed for
4131 // every iteration of that loop. That implies that the value that V
4132 // calculates does not wrap anywhere in the loop, so then we can apply the
4133 // flags to the SCEV.
4135 // We check isLoopInvariant to disambiguate in case we are adding two
4136 // recurrences from different loops, so that we know which loop to prove
4137 // that V is executed in.
4138 for (int OpIndex = 0; OpIndex < 2; ++OpIndex) {
4139 const SCEV *Op = getSCEV(BinOp->getOperand(OpIndex));
4140 if (auto *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
4141 const int OtherOpIndex = 1 - OpIndex;
4142 const SCEV *OtherOp = getSCEV(BinOp->getOperand(OtherOpIndex));
4143 if (isLoopInvariant(OtherOp, AddRec->getLoop()) &&
4144 isGuaranteedToExecuteForEveryIteration(BinOp, AddRec->getLoop()))
4148 return SCEV::FlagAnyWrap;
4151 /// createSCEV - We know that there is no SCEV for the specified value. Analyze
4154 const SCEV *ScalarEvolution::createSCEV(Value *V) {
4155 if (!isSCEVable(V->getType()))
4156 return getUnknown(V);
4158 unsigned Opcode = Instruction::UserOp1;
4159 if (Instruction *I = dyn_cast<Instruction>(V)) {
4160 Opcode = I->getOpcode();
4162 // Don't attempt to analyze instructions in blocks that aren't
4163 // reachable. Such instructions don't matter, and they aren't required
4164 // to obey basic rules for definitions dominating uses which this
4165 // analysis depends on.
4166 if (!DT->isReachableFromEntry(I->getParent()))
4167 return getUnknown(V);
4168 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
4169 Opcode = CE->getOpcode();
4170 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
4171 return getConstant(CI);
4172 else if (isa<ConstantPointerNull>(V))
4173 return getConstant(V->getType(), 0);
4174 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
4175 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee());
4177 return getUnknown(V);
4179 Operator *U = cast<Operator>(V);
4181 case Instruction::Add: {
4182 // The simple thing to do would be to just call getSCEV on both operands
4183 // and call getAddExpr with the result. However if we're looking at a
4184 // bunch of things all added together, this can be quite inefficient,
4185 // because it leads to N-1 getAddExpr calls for N ultimate operands.
4186 // Instead, gather up all the operands and make a single getAddExpr call.
4187 // LLVM IR canonical form means we need only traverse the left operands.
4189 // FIXME: Expand this handling of NSW and NUW to other instructions, like
4191 SmallVector<const SCEV *, 4> AddOps;
4192 for (Value *Op = U;; Op = U->getOperand(0)) {
4193 U = dyn_cast<Operator>(Op);
4194 unsigned Opcode = U ? U->getOpcode() : 0;
4195 if (!U || (Opcode != Instruction::Add && Opcode != Instruction::Sub)) {
4196 assert(Op != V && "V should be an add");
4197 AddOps.push_back(getSCEV(Op));
4201 if (auto *OpSCEV = getExistingSCEV(Op)) {
4202 AddOps.push_back(OpSCEV);
4206 // If a NUW or NSW flag can be applied to the SCEV for this
4207 // addition, then compute the SCEV for this addition by itself
4208 // with a separate call to getAddExpr. We need to do that
4209 // instead of pushing the operands of the addition onto AddOps,
4210 // since the flags are only known to apply to this particular
4211 // addition - they may not apply to other additions that can be
4212 // formed with operands from AddOps.
4214 // FIXME: Expand this to sub instructions.
4215 if (Opcode == Instruction::Add && isa<BinaryOperator>(U)) {
4216 SCEV::NoWrapFlags Flags = getNoWrapFlagsFromUB(U);
4217 if (Flags != SCEV::FlagAnyWrap) {
4218 AddOps.push_back(getAddExpr(getSCEV(U->getOperand(0)),
4219 getSCEV(U->getOperand(1)), Flags));
4224 const SCEV *Op1 = getSCEV(U->getOperand(1));
4225 if (Opcode == Instruction::Sub)
4226 AddOps.push_back(getNegativeSCEV(Op1));
4228 AddOps.push_back(Op1);
4230 return getAddExpr(AddOps);
4233 case Instruction::Mul: {
4234 // FIXME: Transfer NSW/NUW as in AddExpr.
4235 SmallVector<const SCEV *, 4> MulOps;
4236 MulOps.push_back(getSCEV(U->getOperand(1)));
4237 for (Value *Op = U->getOperand(0);
4238 Op->getValueID() == Instruction::Mul + Value::InstructionVal;
4239 Op = U->getOperand(0)) {
4240 U = cast<Operator>(Op);
4241 MulOps.push_back(getSCEV(U->getOperand(1)));
4243 MulOps.push_back(getSCEV(U->getOperand(0)));
4244 return getMulExpr(MulOps);
4246 case Instruction::UDiv:
4247 return getUDivExpr(getSCEV(U->getOperand(0)),
4248 getSCEV(U->getOperand(1)));
4249 case Instruction::Sub:
4250 return getMinusSCEV(getSCEV(U->getOperand(0)),
4251 getSCEV(U->getOperand(1)));
4252 case Instruction::And:
4253 // For an expression like x&255 that merely masks off the high bits,
4254 // use zext(trunc(x)) as the SCEV expression.
4255 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
4256 if (CI->isNullValue())
4257 return getSCEV(U->getOperand(1));
4258 if (CI->isAllOnesValue())
4259 return getSCEV(U->getOperand(0));
4260 const APInt &A = CI->getValue();
4262 // Instcombine's ShrinkDemandedConstant may strip bits out of
4263 // constants, obscuring what would otherwise be a low-bits mask.
4264 // Use computeKnownBits to compute what ShrinkDemandedConstant
4265 // knew about to reconstruct a low-bits mask value.
4266 unsigned LZ = A.countLeadingZeros();
4267 unsigned TZ = A.countTrailingZeros();
4268 unsigned BitWidth = A.getBitWidth();
4269 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
4270 computeKnownBits(U->getOperand(0), KnownZero, KnownOne,
4271 F->getParent()->getDataLayout(), 0, AC, nullptr, DT);
4273 APInt EffectiveMask =
4274 APInt::getLowBitsSet(BitWidth, BitWidth - LZ - TZ).shl(TZ);
4275 if ((LZ != 0 || TZ != 0) && !((~A & ~KnownZero) & EffectiveMask)) {
4276 const SCEV *MulCount = getConstant(
4277 ConstantInt::get(getContext(), APInt::getOneBitSet(BitWidth, TZ)));
4281 getUDivExactExpr(getSCEV(U->getOperand(0)), MulCount),
4282 IntegerType::get(getContext(), BitWidth - LZ - TZ)),
4289 case Instruction::Or:
4290 // If the RHS of the Or is a constant, we may have something like:
4291 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
4292 // optimizations will transparently handle this case.
4294 // In order for this transformation to be safe, the LHS must be of the
4295 // form X*(2^n) and the Or constant must be less than 2^n.
4296 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
4297 const SCEV *LHS = getSCEV(U->getOperand(0));
4298 const APInt &CIVal = CI->getValue();
4299 if (GetMinTrailingZeros(LHS) >=
4300 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
4301 // Build a plain add SCEV.
4302 const SCEV *S = getAddExpr(LHS, getSCEV(CI));
4303 // If the LHS of the add was an addrec and it has no-wrap flags,
4304 // transfer the no-wrap flags, since an or won't introduce a wrap.
4305 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
4306 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
4307 const_cast<SCEVAddRecExpr *>(NewAR)->setNoWrapFlags(
4308 OldAR->getNoWrapFlags());
4314 case Instruction::Xor:
4315 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
4316 // If the RHS of the xor is a signbit, then this is just an add.
4317 // Instcombine turns add of signbit into xor as a strength reduction step.
4318 if (CI->getValue().isSignBit())
4319 return getAddExpr(getSCEV(U->getOperand(0)),
4320 getSCEV(U->getOperand(1)));
4322 // If the RHS of xor is -1, then this is a not operation.
4323 if (CI->isAllOnesValue())
4324 return getNotSCEV(getSCEV(U->getOperand(0)));
4326 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
4327 // This is a variant of the check for xor with -1, and it handles
4328 // the case where instcombine has trimmed non-demanded bits out
4329 // of an xor with -1.
4330 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
4331 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
4332 if (BO->getOpcode() == Instruction::And &&
4333 LCI->getValue() == CI->getValue())
4334 if (const SCEVZeroExtendExpr *Z =
4335 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
4336 Type *UTy = U->getType();
4337 const SCEV *Z0 = Z->getOperand();
4338 Type *Z0Ty = Z0->getType();
4339 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
4341 // If C is a low-bits mask, the zero extend is serving to
4342 // mask off the high bits. Complement the operand and
4343 // re-apply the zext.
4344 if (APIntOps::isMask(Z0TySize, CI->getValue()))
4345 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
4347 // If C is a single bit, it may be in the sign-bit position
4348 // before the zero-extend. In this case, represent the xor
4349 // using an add, which is equivalent, and re-apply the zext.
4350 APInt Trunc = CI->getValue().trunc(Z0TySize);
4351 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
4353 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
4359 case Instruction::Shl:
4360 // Turn shift left of a constant amount into a multiply.
4361 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
4362 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
4364 // If the shift count is not less than the bitwidth, the result of
4365 // the shift is undefined. Don't try to analyze it, because the
4366 // resolution chosen here may differ from the resolution chosen in
4367 // other parts of the compiler.
4368 if (SA->getValue().uge(BitWidth))
4371 Constant *X = ConstantInt::get(getContext(),
4372 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
4373 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
4377 case Instruction::LShr:
4378 // Turn logical shift right of a constant into a unsigned divide.
4379 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
4380 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
4382 // If the shift count is not less than the bitwidth, the result of
4383 // the shift is undefined. Don't try to analyze it, because the
4384 // resolution chosen here may differ from the resolution chosen in
4385 // other parts of the compiler.
4386 if (SA->getValue().uge(BitWidth))
4389 Constant *X = ConstantInt::get(getContext(),
4390 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
4391 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
4395 case Instruction::AShr:
4396 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
4397 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
4398 if (Operator *L = dyn_cast<Operator>(U->getOperand(0)))
4399 if (L->getOpcode() == Instruction::Shl &&
4400 L->getOperand(1) == U->getOperand(1)) {
4401 uint64_t BitWidth = getTypeSizeInBits(U->getType());
4403 // If the shift count is not less than the bitwidth, the result of
4404 // the shift is undefined. Don't try to analyze it, because the
4405 // resolution chosen here may differ from the resolution chosen in
4406 // other parts of the compiler.
4407 if (CI->getValue().uge(BitWidth))
4410 uint64_t Amt = BitWidth - CI->getZExtValue();
4411 if (Amt == BitWidth)
4412 return getSCEV(L->getOperand(0)); // shift by zero --> noop
4414 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
4415 IntegerType::get(getContext(),
4421 case Instruction::Trunc:
4422 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
4424 case Instruction::ZExt:
4425 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
4427 case Instruction::SExt:
4428 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
4430 case Instruction::BitCast:
4431 // BitCasts are no-op casts so we just eliminate the cast.
4432 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
4433 return getSCEV(U->getOperand(0));
4436 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
4437 // lead to pointer expressions which cannot safely be expanded to GEPs,
4438 // because ScalarEvolution doesn't respect the GEP aliasing rules when
4439 // simplifying integer expressions.
4441 case Instruction::GetElementPtr:
4442 return createNodeForGEP(cast<GEPOperator>(U));
4444 case Instruction::PHI:
4445 return createNodeForPHI(cast<PHINode>(U));
4447 case Instruction::Select:
4448 // This could be a smax or umax that was lowered earlier.
4449 // Try to recover it.
4450 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
4451 Value *LHS = ICI->getOperand(0);
4452 Value *RHS = ICI->getOperand(1);
4453 switch (ICI->getPredicate()) {
4454 case ICmpInst::ICMP_SLT:
4455 case ICmpInst::ICMP_SLE:
4456 std::swap(LHS, RHS);
4458 case ICmpInst::ICMP_SGT:
4459 case ICmpInst::ICMP_SGE:
4460 // a >s b ? a+x : b+x -> smax(a, b)+x
4461 // a >s b ? b+x : a+x -> smin(a, b)+x
4462 if (getTypeSizeInBits(LHS->getType()) <=
4463 getTypeSizeInBits(U->getType())) {
4464 const SCEV *LS = getNoopOrSignExtend(getSCEV(LHS), U->getType());
4465 const SCEV *RS = getNoopOrSignExtend(getSCEV(RHS), U->getType());
4466 const SCEV *LA = getSCEV(U->getOperand(1));
4467 const SCEV *RA = getSCEV(U->getOperand(2));
4468 const SCEV *LDiff = getMinusSCEV(LA, LS);
4469 const SCEV *RDiff = getMinusSCEV(RA, RS);
4471 return getAddExpr(getSMaxExpr(LS, RS), LDiff);
4472 LDiff = getMinusSCEV(LA, RS);
4473 RDiff = getMinusSCEV(RA, LS);
4475 return getAddExpr(getSMinExpr(LS, RS), LDiff);
4478 case ICmpInst::ICMP_ULT:
4479 case ICmpInst::ICMP_ULE:
4480 std::swap(LHS, RHS);
4482 case ICmpInst::ICMP_UGT:
4483 case ICmpInst::ICMP_UGE:
4484 // a >u b ? a+x : b+x -> umax(a, b)+x
4485 // a >u b ? b+x : a+x -> umin(a, b)+x
4486 if (getTypeSizeInBits(LHS->getType()) <=
4487 getTypeSizeInBits(U->getType())) {
4488 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), U->getType());
4489 const SCEV *RS = getNoopOrZeroExtend(getSCEV(RHS), U->getType());
4490 const SCEV *LA = getSCEV(U->getOperand(1));
4491 const SCEV *RA = getSCEV(U->getOperand(2));
4492 const SCEV *LDiff = getMinusSCEV(LA, LS);
4493 const SCEV *RDiff = getMinusSCEV(RA, RS);
4495 return getAddExpr(getUMaxExpr(LS, RS), LDiff);
4496 LDiff = getMinusSCEV(LA, RS);
4497 RDiff = getMinusSCEV(RA, LS);
4499 return getAddExpr(getUMinExpr(LS, RS), LDiff);
4502 case ICmpInst::ICMP_NE:
4503 // n != 0 ? n+x : 1+x -> umax(n, 1)+x
4504 if (getTypeSizeInBits(LHS->getType()) <=
4505 getTypeSizeInBits(U->getType()) &&
4506 isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
4507 const SCEV *One = getConstant(U->getType(), 1);
4508 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), U->getType());
4509 const SCEV *LA = getSCEV(U->getOperand(1));
4510 const SCEV *RA = getSCEV(U->getOperand(2));
4511 const SCEV *LDiff = getMinusSCEV(LA, LS);
4512 const SCEV *RDiff = getMinusSCEV(RA, One);
4514 return getAddExpr(getUMaxExpr(One, LS), LDiff);
4517 case ICmpInst::ICMP_EQ:
4518 // n == 0 ? 1+x : n+x -> umax(n, 1)+x
4519 if (getTypeSizeInBits(LHS->getType()) <=
4520 getTypeSizeInBits(U->getType()) &&
4521 isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
4522 const SCEV *One = getConstant(U->getType(), 1);
4523 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), U->getType());
4524 const SCEV *LA = getSCEV(U->getOperand(1));
4525 const SCEV *RA = getSCEV(U->getOperand(2));
4526 const SCEV *LDiff = getMinusSCEV(LA, One);
4527 const SCEV *RDiff = getMinusSCEV(RA, LS);
4529 return getAddExpr(getUMaxExpr(One, LS), LDiff);
4537 default: // We cannot analyze this expression.
4541 return getUnknown(V);
4546 //===----------------------------------------------------------------------===//
4547 // Iteration Count Computation Code
4550 unsigned ScalarEvolution::getSmallConstantTripCount(Loop *L) {
4551 if (BasicBlock *ExitingBB = L->getExitingBlock())
4552 return getSmallConstantTripCount(L, ExitingBB);
4554 // No trip count information for multiple exits.
4558 /// getSmallConstantTripCount - Returns the maximum trip count of this loop as a
4559 /// normal unsigned value. Returns 0 if the trip count is unknown or not
4560 /// constant. Will also return 0 if the maximum trip count is very large (>=
4563 /// This "trip count" assumes that control exits via ExitingBlock. More
4564 /// precisely, it is the number of times that control may reach ExitingBlock
4565 /// before taking the branch. For loops with multiple exits, it may not be the
4566 /// number times that the loop header executes because the loop may exit
4567 /// prematurely via another branch.
4568 unsigned ScalarEvolution::getSmallConstantTripCount(Loop *L,
4569 BasicBlock *ExitingBlock) {
4570 assert(ExitingBlock && "Must pass a non-null exiting block!");
4571 assert(L->isLoopExiting(ExitingBlock) &&
4572 "Exiting block must actually branch out of the loop!");
4573 const SCEVConstant *ExitCount =
4574 dyn_cast<SCEVConstant>(getExitCount(L, ExitingBlock));
4578 ConstantInt *ExitConst = ExitCount->getValue();
4580 // Guard against huge trip counts.
4581 if (ExitConst->getValue().getActiveBits() > 32)
4584 // In case of integer overflow, this returns 0, which is correct.
4585 return ((unsigned)ExitConst->getZExtValue()) + 1;
4588 unsigned ScalarEvolution::getSmallConstantTripMultiple(Loop *L) {
4589 if (BasicBlock *ExitingBB = L->getExitingBlock())
4590 return getSmallConstantTripMultiple(L, ExitingBB);
4592 // No trip multiple information for multiple exits.
4596 /// getSmallConstantTripMultiple - Returns the largest constant divisor of the
4597 /// trip count of this loop as a normal unsigned value, if possible. This
4598 /// means that the actual trip count is always a multiple of the returned
4599 /// value (don't forget the trip count could very well be zero as well!).
4601 /// Returns 1 if the trip count is unknown or not guaranteed to be the
4602 /// multiple of a constant (which is also the case if the trip count is simply
4603 /// constant, use getSmallConstantTripCount for that case), Will also return 1
4604 /// if the trip count is very large (>= 2^32).
4606 /// As explained in the comments for getSmallConstantTripCount, this assumes
4607 /// that control exits the loop via ExitingBlock.
4609 ScalarEvolution::getSmallConstantTripMultiple(Loop *L,
4610 BasicBlock *ExitingBlock) {
4611 assert(ExitingBlock && "Must pass a non-null exiting block!");
4612 assert(L->isLoopExiting(ExitingBlock) &&
4613 "Exiting block must actually branch out of the loop!");
4614 const SCEV *ExitCount = getExitCount(L, ExitingBlock);
4615 if (ExitCount == getCouldNotCompute())
4618 // Get the trip count from the BE count by adding 1.
4619 const SCEV *TCMul = getAddExpr(ExitCount,
4620 getConstant(ExitCount->getType(), 1));
4621 // FIXME: SCEV distributes multiplication as V1*C1 + V2*C1. We could attempt
4622 // to factor simple cases.
4623 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(TCMul))
4624 TCMul = Mul->getOperand(0);
4626 const SCEVConstant *MulC = dyn_cast<SCEVConstant>(TCMul);
4630 ConstantInt *Result = MulC->getValue();
4632 // Guard against huge trip counts (this requires checking
4633 // for zero to handle the case where the trip count == -1 and the
4635 if (!Result || Result->getValue().getActiveBits() > 32 ||
4636 Result->getValue().getActiveBits() == 0)
4639 return (unsigned)Result->getZExtValue();
4642 // getExitCount - Get the expression for the number of loop iterations for which
4643 // this loop is guaranteed not to exit via ExitingBlock. Otherwise return
4644 // SCEVCouldNotCompute.
4645 const SCEV *ScalarEvolution::getExitCount(Loop *L, BasicBlock *ExitingBlock) {
4646 return getBackedgeTakenInfo(L).getExact(ExitingBlock, this);
4649 /// getBackedgeTakenCount - If the specified loop has a predictable
4650 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
4651 /// object. The backedge-taken count is the number of times the loop header
4652 /// will be branched to from within the loop. This is one less than the
4653 /// trip count of the loop, since it doesn't count the first iteration,
4654 /// when the header is branched to from outside the loop.
4656 /// Note that it is not valid to call this method on a loop without a
4657 /// loop-invariant backedge-taken count (see
4658 /// hasLoopInvariantBackedgeTakenCount).
4660 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
4661 return getBackedgeTakenInfo(L).getExact(this);
4664 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
4665 /// return the least SCEV value that is known never to be less than the
4666 /// actual backedge taken count.
4667 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
4668 return getBackedgeTakenInfo(L).getMax(this);
4671 /// PushLoopPHIs - Push PHI nodes in the header of the given loop
4672 /// onto the given Worklist.
4674 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
4675 BasicBlock *Header = L->getHeader();
4677 // Push all Loop-header PHIs onto the Worklist stack.
4678 for (BasicBlock::iterator I = Header->begin();
4679 PHINode *PN = dyn_cast<PHINode>(I); ++I)
4680 Worklist.push_back(PN);
4683 const ScalarEvolution::BackedgeTakenInfo &
4684 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
4685 // Initially insert an invalid entry for this loop. If the insertion
4686 // succeeds, proceed to actually compute a backedge-taken count and
4687 // update the value. The temporary CouldNotCompute value tells SCEV
4688 // code elsewhere that it shouldn't attempt to request a new
4689 // backedge-taken count, which could result in infinite recursion.
4690 std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
4691 BackedgeTakenCounts.insert(std::make_pair(L, BackedgeTakenInfo()));
4693 return Pair.first->second;
4695 // ComputeBackedgeTakenCount may allocate memory for its result. Inserting it
4696 // into the BackedgeTakenCounts map transfers ownership. Otherwise, the result
4697 // must be cleared in this scope.
4698 BackedgeTakenInfo Result = ComputeBackedgeTakenCount(L);
4700 if (Result.getExact(this) != getCouldNotCompute()) {
4701 assert(isLoopInvariant(Result.getExact(this), L) &&
4702 isLoopInvariant(Result.getMax(this), L) &&
4703 "Computed backedge-taken count isn't loop invariant for loop!");
4704 ++NumTripCountsComputed;
4706 else if (Result.getMax(this) == getCouldNotCompute() &&
4707 isa<PHINode>(L->getHeader()->begin())) {
4708 // Only count loops that have phi nodes as not being computable.
4709 ++NumTripCountsNotComputed;
4712 // Now that we know more about the trip count for this loop, forget any
4713 // existing SCEV values for PHI nodes in this loop since they are only
4714 // conservative estimates made without the benefit of trip count
4715 // information. This is similar to the code in forgetLoop, except that
4716 // it handles SCEVUnknown PHI nodes specially.
4717 if (Result.hasAnyInfo()) {
4718 SmallVector<Instruction *, 16> Worklist;
4719 PushLoopPHIs(L, Worklist);
4721 SmallPtrSet<Instruction *, 8> Visited;
4722 while (!Worklist.empty()) {
4723 Instruction *I = Worklist.pop_back_val();
4724 if (!Visited.insert(I).second)
4727 ValueExprMapType::iterator It =
4728 ValueExprMap.find_as(static_cast<Value *>(I));
4729 if (It != ValueExprMap.end()) {
4730 const SCEV *Old = It->second;
4732 // SCEVUnknown for a PHI either means that it has an unrecognized
4733 // structure, or it's a PHI that's in the progress of being computed
4734 // by createNodeForPHI. In the former case, additional loop trip
4735 // count information isn't going to change anything. In the later
4736 // case, createNodeForPHI will perform the necessary updates on its
4737 // own when it gets to that point.
4738 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) {
4739 forgetMemoizedResults(Old);
4740 ValueExprMap.erase(It);
4742 if (PHINode *PN = dyn_cast<PHINode>(I))
4743 ConstantEvolutionLoopExitValue.erase(PN);
4746 PushDefUseChildren(I, Worklist);
4750 // Re-lookup the insert position, since the call to
4751 // ComputeBackedgeTakenCount above could result in a
4752 // recusive call to getBackedgeTakenInfo (on a different
4753 // loop), which would invalidate the iterator computed
4755 return BackedgeTakenCounts.find(L)->second = Result;
4758 /// forgetLoop - This method should be called by the client when it has
4759 /// changed a loop in a way that may effect ScalarEvolution's ability to
4760 /// compute a trip count, or if the loop is deleted.
4761 void ScalarEvolution::forgetLoop(const Loop *L) {
4762 // Drop any stored trip count value.
4763 DenseMap<const Loop*, BackedgeTakenInfo>::iterator BTCPos =
4764 BackedgeTakenCounts.find(L);
4765 if (BTCPos != BackedgeTakenCounts.end()) {
4766 BTCPos->second.clear();
4767 BackedgeTakenCounts.erase(BTCPos);
4770 // Drop information about expressions based on loop-header PHIs.
4771 SmallVector<Instruction *, 16> Worklist;
4772 PushLoopPHIs(L, Worklist);
4774 SmallPtrSet<Instruction *, 8> Visited;
4775 while (!Worklist.empty()) {
4776 Instruction *I = Worklist.pop_back_val();
4777 if (!Visited.insert(I).second)
4780 ValueExprMapType::iterator It =
4781 ValueExprMap.find_as(static_cast<Value *>(I));
4782 if (It != ValueExprMap.end()) {
4783 forgetMemoizedResults(It->second);
4784 ValueExprMap.erase(It);
4785 if (PHINode *PN = dyn_cast<PHINode>(I))
4786 ConstantEvolutionLoopExitValue.erase(PN);
4789 PushDefUseChildren(I, Worklist);
4792 // Forget all contained loops too, to avoid dangling entries in the
4793 // ValuesAtScopes map.
4794 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
4798 /// forgetValue - This method should be called by the client when it has
4799 /// changed a value in a way that may effect its value, or which may
4800 /// disconnect it from a def-use chain linking it to a loop.
4801 void ScalarEvolution::forgetValue(Value *V) {
4802 Instruction *I = dyn_cast<Instruction>(V);
4805 // Drop information about expressions based on loop-header PHIs.
4806 SmallVector<Instruction *, 16> Worklist;
4807 Worklist.push_back(I);
4809 SmallPtrSet<Instruction *, 8> Visited;
4810 while (!Worklist.empty()) {
4811 I = Worklist.pop_back_val();
4812 if (!Visited.insert(I).second)
4815 ValueExprMapType::iterator It =
4816 ValueExprMap.find_as(static_cast<Value *>(I));
4817 if (It != ValueExprMap.end()) {
4818 forgetMemoizedResults(It->second);
4819 ValueExprMap.erase(It);
4820 if (PHINode *PN = dyn_cast<PHINode>(I))
4821 ConstantEvolutionLoopExitValue.erase(PN);
4824 PushDefUseChildren(I, Worklist);
4828 /// getExact - Get the exact loop backedge taken count considering all loop
4829 /// exits. A computable result can only be returned for loops with a single
4830 /// exit. Returning the minimum taken count among all exits is incorrect
4831 /// because one of the loop's exit limit's may have been skipped. HowFarToZero
4832 /// assumes that the limit of each loop test is never skipped. This is a valid
4833 /// assumption as long as the loop exits via that test. For precise results, it
4834 /// is the caller's responsibility to specify the relevant loop exit using
4835 /// getExact(ExitingBlock, SE).
4837 ScalarEvolution::BackedgeTakenInfo::getExact(ScalarEvolution *SE) const {
4838 // If any exits were not computable, the loop is not computable.
4839 if (!ExitNotTaken.isCompleteList()) return SE->getCouldNotCompute();
4841 // We need exactly one computable exit.
4842 if (!ExitNotTaken.ExitingBlock) return SE->getCouldNotCompute();
4843 assert(ExitNotTaken.ExactNotTaken && "uninitialized not-taken info");
4845 const SCEV *BECount = nullptr;
4846 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4847 ENT != nullptr; ENT = ENT->getNextExit()) {
4849 assert(ENT->ExactNotTaken != SE->getCouldNotCompute() && "bad exit SCEV");
4852 BECount = ENT->ExactNotTaken;
4853 else if (BECount != ENT->ExactNotTaken)
4854 return SE->getCouldNotCompute();
4856 assert(BECount && "Invalid not taken count for loop exit");
4860 /// getExact - Get the exact not taken count for this loop exit.
4862 ScalarEvolution::BackedgeTakenInfo::getExact(BasicBlock *ExitingBlock,
4863 ScalarEvolution *SE) const {
4864 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4865 ENT != nullptr; ENT = ENT->getNextExit()) {
4867 if (ENT->ExitingBlock == ExitingBlock)
4868 return ENT->ExactNotTaken;
4870 return SE->getCouldNotCompute();
4873 /// getMax - Get the max backedge taken count for the loop.
4875 ScalarEvolution::BackedgeTakenInfo::getMax(ScalarEvolution *SE) const {
4876 return Max ? Max : SE->getCouldNotCompute();
4879 bool ScalarEvolution::BackedgeTakenInfo::hasOperand(const SCEV *S,
4880 ScalarEvolution *SE) const {
4881 if (Max && Max != SE->getCouldNotCompute() && SE->hasOperand(Max, S))
4884 if (!ExitNotTaken.ExitingBlock)
4887 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4888 ENT != nullptr; ENT = ENT->getNextExit()) {
4890 if (ENT->ExactNotTaken != SE->getCouldNotCompute()
4891 && SE->hasOperand(ENT->ExactNotTaken, S)) {
4898 /// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each
4899 /// computable exit into a persistent ExitNotTakenInfo array.
4900 ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo(
4901 SmallVectorImpl< std::pair<BasicBlock *, const SCEV *> > &ExitCounts,
4902 bool Complete, const SCEV *MaxCount) : Max(MaxCount) {
4905 ExitNotTaken.setIncomplete();
4907 unsigned NumExits = ExitCounts.size();
4908 if (NumExits == 0) return;
4910 ExitNotTaken.ExitingBlock = ExitCounts[0].first;
4911 ExitNotTaken.ExactNotTaken = ExitCounts[0].second;
4912 if (NumExits == 1) return;
4914 // Handle the rare case of multiple computable exits.
4915 ExitNotTakenInfo *ENT = new ExitNotTakenInfo[NumExits-1];
4917 ExitNotTakenInfo *PrevENT = &ExitNotTaken;
4918 for (unsigned i = 1; i < NumExits; ++i, PrevENT = ENT, ++ENT) {
4919 PrevENT->setNextExit(ENT);
4920 ENT->ExitingBlock = ExitCounts[i].first;
4921 ENT->ExactNotTaken = ExitCounts[i].second;
4925 /// clear - Invalidate this result and free the ExitNotTakenInfo array.
4926 void ScalarEvolution::BackedgeTakenInfo::clear() {
4927 ExitNotTaken.ExitingBlock = nullptr;
4928 ExitNotTaken.ExactNotTaken = nullptr;
4929 delete[] ExitNotTaken.getNextExit();
4932 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
4933 /// of the specified loop will execute.
4934 ScalarEvolution::BackedgeTakenInfo
4935 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
4936 SmallVector<BasicBlock *, 8> ExitingBlocks;
4937 L->getExitingBlocks(ExitingBlocks);
4939 SmallVector<std::pair<BasicBlock *, const SCEV *>, 4> ExitCounts;
4940 bool CouldComputeBECount = true;
4941 BasicBlock *Latch = L->getLoopLatch(); // may be NULL.
4942 const SCEV *MustExitMaxBECount = nullptr;
4943 const SCEV *MayExitMaxBECount = nullptr;
4945 // Compute the ExitLimit for each loop exit. Use this to populate ExitCounts
4946 // and compute maxBECount.
4947 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
4948 BasicBlock *ExitBB = ExitingBlocks[i];
4949 ExitLimit EL = ComputeExitLimit(L, ExitBB);
4951 // 1. For each exit that can be computed, add an entry to ExitCounts.
4952 // CouldComputeBECount is true only if all exits can be computed.
4953 if (EL.Exact == getCouldNotCompute())
4954 // We couldn't compute an exact value for this exit, so
4955 // we won't be able to compute an exact value for the loop.
4956 CouldComputeBECount = false;
4958 ExitCounts.push_back(std::make_pair(ExitBB, EL.Exact));
4960 // 2. Derive the loop's MaxBECount from each exit's max number of
4961 // non-exiting iterations. Partition the loop exits into two kinds:
4962 // LoopMustExits and LoopMayExits.
4964 // If the exit dominates the loop latch, it is a LoopMustExit otherwise it
4965 // is a LoopMayExit. If any computable LoopMustExit is found, then
4966 // MaxBECount is the minimum EL.Max of computable LoopMustExits. Otherwise,
4967 // MaxBECount is conservatively the maximum EL.Max, where CouldNotCompute is
4968 // considered greater than any computable EL.Max.
4969 if (EL.Max != getCouldNotCompute() && Latch &&
4970 DT->dominates(ExitBB, Latch)) {
4971 if (!MustExitMaxBECount)
4972 MustExitMaxBECount = EL.Max;
4974 MustExitMaxBECount =
4975 getUMinFromMismatchedTypes(MustExitMaxBECount, EL.Max);
4977 } else if (MayExitMaxBECount != getCouldNotCompute()) {
4978 if (!MayExitMaxBECount || EL.Max == getCouldNotCompute())
4979 MayExitMaxBECount = EL.Max;
4982 getUMaxFromMismatchedTypes(MayExitMaxBECount, EL.Max);
4986 const SCEV *MaxBECount = MustExitMaxBECount ? MustExitMaxBECount :
4987 (MayExitMaxBECount ? MayExitMaxBECount : getCouldNotCompute());
4988 return BackedgeTakenInfo(ExitCounts, CouldComputeBECount, MaxBECount);
4991 /// ComputeExitLimit - Compute the number of times the backedge of the specified
4992 /// loop will execute if it exits via the specified block.
4993 ScalarEvolution::ExitLimit
4994 ScalarEvolution::ComputeExitLimit(const Loop *L, BasicBlock *ExitingBlock) {
4996 // Okay, we've chosen an exiting block. See what condition causes us to
4997 // exit at this block and remember the exit block and whether all other targets
4998 // lead to the loop header.
4999 bool MustExecuteLoopHeader = true;
5000 BasicBlock *Exit = nullptr;
5001 for (succ_iterator SI = succ_begin(ExitingBlock), SE = succ_end(ExitingBlock);
5003 if (!L->contains(*SI)) {
5004 if (Exit) // Multiple exit successors.
5005 return getCouldNotCompute();
5007 } else if (*SI != L->getHeader()) {
5008 MustExecuteLoopHeader = false;
5011 // At this point, we know we have a conditional branch that determines whether
5012 // the loop is exited. However, we don't know if the branch is executed each
5013 // time through the loop. If not, then the execution count of the branch will
5014 // not be equal to the trip count of the loop.
5016 // Currently we check for this by checking to see if the Exit branch goes to
5017 // the loop header. If so, we know it will always execute the same number of
5018 // times as the loop. We also handle the case where the exit block *is* the
5019 // loop header. This is common for un-rotated loops.
5021 // If both of those tests fail, walk up the unique predecessor chain to the
5022 // header, stopping if there is an edge that doesn't exit the loop. If the
5023 // header is reached, the execution count of the branch will be equal to the
5024 // trip count of the loop.
5026 // More extensive analysis could be done to handle more cases here.
5028 if (!MustExecuteLoopHeader && ExitingBlock != L->getHeader()) {
5029 // The simple checks failed, try climbing the unique predecessor chain
5030 // up to the header.
5032 for (BasicBlock *BB = ExitingBlock; BB; ) {
5033 BasicBlock *Pred = BB->getUniquePredecessor();
5035 return getCouldNotCompute();
5036 TerminatorInst *PredTerm = Pred->getTerminator();
5037 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) {
5038 BasicBlock *PredSucc = PredTerm->getSuccessor(i);
5041 // If the predecessor has a successor that isn't BB and isn't
5042 // outside the loop, assume the worst.
5043 if (L->contains(PredSucc))
5044 return getCouldNotCompute();
5046 if (Pred == L->getHeader()) {
5053 return getCouldNotCompute();
5056 bool IsOnlyExit = (L->getExitingBlock() != nullptr);
5057 TerminatorInst *Term = ExitingBlock->getTerminator();
5058 if (BranchInst *BI = dyn_cast<BranchInst>(Term)) {
5059 assert(BI->isConditional() && "If unconditional, it can't be in loop!");
5060 // Proceed to the next level to examine the exit condition expression.
5061 return ComputeExitLimitFromCond(L, BI->getCondition(), BI->getSuccessor(0),
5062 BI->getSuccessor(1),
5063 /*ControlsExit=*/IsOnlyExit);
5066 if (SwitchInst *SI = dyn_cast<SwitchInst>(Term))
5067 return ComputeExitLimitFromSingleExitSwitch(L, SI, Exit,
5068 /*ControlsExit=*/IsOnlyExit);
5070 return getCouldNotCompute();
5073 /// ComputeExitLimitFromCond - Compute the number of times the
5074 /// backedge of the specified loop will execute if its exit condition
5075 /// were a conditional branch of ExitCond, TBB, and FBB.
5077 /// @param ControlsExit is true if ExitCond directly controls the exit
5078 /// branch. In this case, we can assume that the loop exits only if the
5079 /// condition is true and can infer that failing to meet the condition prior to
5080 /// integer wraparound results in undefined behavior.
5081 ScalarEvolution::ExitLimit
5082 ScalarEvolution::ComputeExitLimitFromCond(const Loop *L,
5086 bool ControlsExit) {
5087 // Check if the controlling expression for this loop is an And or Or.
5088 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
5089 if (BO->getOpcode() == Instruction::And) {
5090 // Recurse on the operands of the and.
5091 bool EitherMayExit = L->contains(TBB);
5092 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
5093 ControlsExit && !EitherMayExit);
5094 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
5095 ControlsExit && !EitherMayExit);
5096 const SCEV *BECount = getCouldNotCompute();
5097 const SCEV *MaxBECount = getCouldNotCompute();
5098 if (EitherMayExit) {
5099 // Both conditions must be true for the loop to continue executing.
5100 // Choose the less conservative count.
5101 if (EL0.Exact == getCouldNotCompute() ||
5102 EL1.Exact == getCouldNotCompute())
5103 BECount = getCouldNotCompute();
5105 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
5106 if (EL0.Max == getCouldNotCompute())
5107 MaxBECount = EL1.Max;
5108 else if (EL1.Max == getCouldNotCompute())
5109 MaxBECount = EL0.Max;
5111 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
5113 // Both conditions must be true at the same time for the loop to exit.
5114 // For now, be conservative.
5115 assert(L->contains(FBB) && "Loop block has no successor in loop!");
5116 if (EL0.Max == EL1.Max)
5117 MaxBECount = EL0.Max;
5118 if (EL0.Exact == EL1.Exact)
5119 BECount = EL0.Exact;
5122 return ExitLimit(BECount, MaxBECount);
5124 if (BO->getOpcode() == Instruction::Or) {
5125 // Recurse on the operands of the or.
5126 bool EitherMayExit = L->contains(FBB);
5127 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
5128 ControlsExit && !EitherMayExit);
5129 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
5130 ControlsExit && !EitherMayExit);
5131 const SCEV *BECount = getCouldNotCompute();
5132 const SCEV *MaxBECount = getCouldNotCompute();
5133 if (EitherMayExit) {
5134 // Both conditions must be false for the loop to continue executing.
5135 // Choose the less conservative count.
5136 if (EL0.Exact == getCouldNotCompute() ||
5137 EL1.Exact == getCouldNotCompute())
5138 BECount = getCouldNotCompute();
5140 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
5141 if (EL0.Max == getCouldNotCompute())
5142 MaxBECount = EL1.Max;
5143 else if (EL1.Max == getCouldNotCompute())
5144 MaxBECount = EL0.Max;
5146 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
5148 // Both conditions must be false at the same time for the loop to exit.
5149 // For now, be conservative.
5150 assert(L->contains(TBB) && "Loop block has no successor in loop!");
5151 if (EL0.Max == EL1.Max)
5152 MaxBECount = EL0.Max;
5153 if (EL0.Exact == EL1.Exact)
5154 BECount = EL0.Exact;
5157 return ExitLimit(BECount, MaxBECount);
5161 // With an icmp, it may be feasible to compute an exact backedge-taken count.
5162 // Proceed to the next level to examine the icmp.
5163 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
5164 return ComputeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB, ControlsExit);
5166 // Check for a constant condition. These are normally stripped out by
5167 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
5168 // preserve the CFG and is temporarily leaving constant conditions
5170 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
5171 if (L->contains(FBB) == !CI->getZExtValue())
5172 // The backedge is always taken.
5173 return getCouldNotCompute();
5175 // The backedge is never taken.
5176 return getConstant(CI->getType(), 0);
5179 // If it's not an integer or pointer comparison then compute it the hard way.
5180 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
5183 /// ComputeExitLimitFromICmp - Compute the number of times the
5184 /// backedge of the specified loop will execute if its exit condition
5185 /// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB.
5186 ScalarEvolution::ExitLimit
5187 ScalarEvolution::ComputeExitLimitFromICmp(const Loop *L,
5191 bool ControlsExit) {
5193 // If the condition was exit on true, convert the condition to exit on false
5194 ICmpInst::Predicate Cond;
5195 if (!L->contains(FBB))
5196 Cond = ExitCond->getPredicate();
5198 Cond = ExitCond->getInversePredicate();
5200 // Handle common loops like: for (X = "string"; *X; ++X)
5201 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
5202 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
5204 ComputeLoadConstantCompareExitLimit(LI, RHS, L, Cond);
5205 if (ItCnt.hasAnyInfo())
5209 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
5210 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
5212 // Try to evaluate any dependencies out of the loop.
5213 LHS = getSCEVAtScope(LHS, L);
5214 RHS = getSCEVAtScope(RHS, L);
5216 // At this point, we would like to compute how many iterations of the
5217 // loop the predicate will return true for these inputs.
5218 if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) {
5219 // If there is a loop-invariant, force it into the RHS.
5220 std::swap(LHS, RHS);
5221 Cond = ICmpInst::getSwappedPredicate(Cond);
5224 // Simplify the operands before analyzing them.
5225 (void)SimplifyICmpOperands(Cond, LHS, RHS);
5227 // If we have a comparison of a chrec against a constant, try to use value
5228 // ranges to answer this query.
5229 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
5230 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
5231 if (AddRec->getLoop() == L) {
5232 // Form the constant range.
5233 ConstantRange CompRange(
5234 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
5236 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
5237 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
5241 case ICmpInst::ICMP_NE: { // while (X != Y)
5242 // Convert to: while (X-Y != 0)
5243 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit);
5244 if (EL.hasAnyInfo()) return EL;
5247 case ICmpInst::ICMP_EQ: { // while (X == Y)
5248 // Convert to: while (X-Y == 0)
5249 ExitLimit EL = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
5250 if (EL.hasAnyInfo()) return EL;
5253 case ICmpInst::ICMP_SLT:
5254 case ICmpInst::ICMP_ULT: { // while (X < Y)
5255 bool IsSigned = Cond == ICmpInst::ICMP_SLT;
5256 ExitLimit EL = HowManyLessThans(LHS, RHS, L, IsSigned, ControlsExit);
5257 if (EL.hasAnyInfo()) return EL;
5260 case ICmpInst::ICMP_SGT:
5261 case ICmpInst::ICMP_UGT: { // while (X > Y)
5262 bool IsSigned = Cond == ICmpInst::ICMP_SGT;
5263 ExitLimit EL = HowManyGreaterThans(LHS, RHS, L, IsSigned, ControlsExit);
5264 if (EL.hasAnyInfo()) return EL;
5269 dbgs() << "ComputeBackedgeTakenCount ";
5270 if (ExitCond->getOperand(0)->getType()->isUnsigned())
5271 dbgs() << "[unsigned] ";
5272 dbgs() << *LHS << " "
5273 << Instruction::getOpcodeName(Instruction::ICmp)
5274 << " " << *RHS << "\n";
5278 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
5281 ScalarEvolution::ExitLimit
5282 ScalarEvolution::ComputeExitLimitFromSingleExitSwitch(const Loop *L,
5284 BasicBlock *ExitingBlock,
5285 bool ControlsExit) {
5286 assert(!L->contains(ExitingBlock) && "Not an exiting block!");
5288 // Give up if the exit is the default dest of a switch.
5289 if (Switch->getDefaultDest() == ExitingBlock)
5290 return getCouldNotCompute();
5292 assert(L->contains(Switch->getDefaultDest()) &&
5293 "Default case must not exit the loop!");
5294 const SCEV *LHS = getSCEVAtScope(Switch->getCondition(), L);
5295 const SCEV *RHS = getConstant(Switch->findCaseDest(ExitingBlock));
5297 // while (X != Y) --> while (X-Y != 0)
5298 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit);
5299 if (EL.hasAnyInfo())
5302 return getCouldNotCompute();
5305 static ConstantInt *
5306 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
5307 ScalarEvolution &SE) {
5308 const SCEV *InVal = SE.getConstant(C);
5309 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
5310 assert(isa<SCEVConstant>(Val) &&
5311 "Evaluation of SCEV at constant didn't fold correctly?");
5312 return cast<SCEVConstant>(Val)->getValue();
5315 /// ComputeLoadConstantCompareExitLimit - Given an exit condition of
5316 /// 'icmp op load X, cst', try to see if we can compute the backedge
5317 /// execution count.
5318 ScalarEvolution::ExitLimit
5319 ScalarEvolution::ComputeLoadConstantCompareExitLimit(
5323 ICmpInst::Predicate predicate) {
5325 if (LI->isVolatile()) return getCouldNotCompute();
5327 // Check to see if the loaded pointer is a getelementptr of a global.
5328 // TODO: Use SCEV instead of manually grubbing with GEPs.
5329 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
5330 if (!GEP) return getCouldNotCompute();
5332 // Make sure that it is really a constant global we are gepping, with an
5333 // initializer, and make sure the first IDX is really 0.
5334 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
5335 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
5336 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
5337 !cast<Constant>(GEP->getOperand(1))->isNullValue())
5338 return getCouldNotCompute();
5340 // Okay, we allow one non-constant index into the GEP instruction.
5341 Value *VarIdx = nullptr;
5342 std::vector<Constant*> Indexes;
5343 unsigned VarIdxNum = 0;
5344 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
5345 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
5346 Indexes.push_back(CI);
5347 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
5348 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
5349 VarIdx = GEP->getOperand(i);
5351 Indexes.push_back(nullptr);
5354 // Loop-invariant loads may be a byproduct of loop optimization. Skip them.
5356 return getCouldNotCompute();
5358 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
5359 // Check to see if X is a loop variant variable value now.
5360 const SCEV *Idx = getSCEV(VarIdx);
5361 Idx = getSCEVAtScope(Idx, L);
5363 // We can only recognize very limited forms of loop index expressions, in
5364 // particular, only affine AddRec's like {C1,+,C2}.
5365 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
5366 if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) ||
5367 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
5368 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
5369 return getCouldNotCompute();
5371 unsigned MaxSteps = MaxBruteForceIterations;
5372 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
5373 ConstantInt *ItCst = ConstantInt::get(
5374 cast<IntegerType>(IdxExpr->getType()), IterationNum);
5375 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
5377 // Form the GEP offset.
5378 Indexes[VarIdxNum] = Val;
5380 Constant *Result = ConstantFoldLoadThroughGEPIndices(GV->getInitializer(),
5382 if (!Result) break; // Cannot compute!
5384 // Evaluate the condition for this iteration.
5385 Result = ConstantExpr::getICmp(predicate, Result, RHS);
5386 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
5387 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
5389 dbgs() << "\n***\n*** Computed loop count " << *ItCst
5390 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
5393 ++NumArrayLenItCounts;
5394 return getConstant(ItCst); // Found terminating iteration!
5397 return getCouldNotCompute();
5401 /// CanConstantFold - Return true if we can constant fold an instruction of the
5402 /// specified type, assuming that all operands were constants.
5403 static bool CanConstantFold(const Instruction *I) {
5404 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
5405 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I) ||
5409 if (const CallInst *CI = dyn_cast<CallInst>(I))
5410 if (const Function *F = CI->getCalledFunction())
5411 return canConstantFoldCallTo(F);
5415 /// Determine whether this instruction can constant evolve within this loop
5416 /// assuming its operands can all constant evolve.
5417 static bool canConstantEvolve(Instruction *I, const Loop *L) {
5418 // An instruction outside of the loop can't be derived from a loop PHI.
5419 if (!L->contains(I)) return false;
5421 if (isa<PHINode>(I)) {
5422 // We don't currently keep track of the control flow needed to evaluate
5423 // PHIs, so we cannot handle PHIs inside of loops.
5424 return L->getHeader() == I->getParent();
5427 // If we won't be able to constant fold this expression even if the operands
5428 // are constants, bail early.
5429 return CanConstantFold(I);
5432 /// getConstantEvolvingPHIOperands - Implement getConstantEvolvingPHI by
5433 /// recursing through each instruction operand until reaching a loop header phi.
5435 getConstantEvolvingPHIOperands(Instruction *UseInst, const Loop *L,
5436 DenseMap<Instruction *, PHINode *> &PHIMap) {
5438 // Otherwise, we can evaluate this instruction if all of its operands are
5439 // constant or derived from a PHI node themselves.
5440 PHINode *PHI = nullptr;
5441 for (Instruction::op_iterator OpI = UseInst->op_begin(),
5442 OpE = UseInst->op_end(); OpI != OpE; ++OpI) {
5444 if (isa<Constant>(*OpI)) continue;
5446 Instruction *OpInst = dyn_cast<Instruction>(*OpI);
5447 if (!OpInst || !canConstantEvolve(OpInst, L)) return nullptr;
5449 PHINode *P = dyn_cast<PHINode>(OpInst);
5451 // If this operand is already visited, reuse the prior result.
5452 // We may have P != PHI if this is the deepest point at which the
5453 // inconsistent paths meet.
5454 P = PHIMap.lookup(OpInst);
5456 // Recurse and memoize the results, whether a phi is found or not.
5457 // This recursive call invalidates pointers into PHIMap.
5458 P = getConstantEvolvingPHIOperands(OpInst, L, PHIMap);
5462 return nullptr; // Not evolving from PHI
5463 if (PHI && PHI != P)
5464 return nullptr; // Evolving from multiple different PHIs.
5467 // This is a expression evolving from a constant PHI!
5471 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
5472 /// in the loop that V is derived from. We allow arbitrary operations along the
5473 /// way, but the operands of an operation must either be constants or a value
5474 /// derived from a constant PHI. If this expression does not fit with these
5475 /// constraints, return null.
5476 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
5477 Instruction *I = dyn_cast<Instruction>(V);
5478 if (!I || !canConstantEvolve(I, L)) return nullptr;
5480 if (PHINode *PN = dyn_cast<PHINode>(I)) {
5484 // Record non-constant instructions contained by the loop.
5485 DenseMap<Instruction *, PHINode *> PHIMap;
5486 return getConstantEvolvingPHIOperands(I, L, PHIMap);
5489 /// EvaluateExpression - Given an expression that passes the
5490 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
5491 /// in the loop has the value PHIVal. If we can't fold this expression for some
5492 /// reason, return null.
5493 static Constant *EvaluateExpression(Value *V, const Loop *L,
5494 DenseMap<Instruction *, Constant *> &Vals,
5495 const DataLayout &DL,
5496 const TargetLibraryInfo *TLI) {
5497 // Convenient constant check, but redundant for recursive calls.
5498 if (Constant *C = dyn_cast<Constant>(V)) return C;
5499 Instruction *I = dyn_cast<Instruction>(V);
5500 if (!I) return nullptr;
5502 if (Constant *C = Vals.lookup(I)) return C;
5504 // An instruction inside the loop depends on a value outside the loop that we
5505 // weren't given a mapping for, or a value such as a call inside the loop.
5506 if (!canConstantEvolve(I, L)) return nullptr;
5508 // An unmapped PHI can be due to a branch or another loop inside this loop,
5509 // or due to this not being the initial iteration through a loop where we
5510 // couldn't compute the evolution of this particular PHI last time.
5511 if (isa<PHINode>(I)) return nullptr;
5513 std::vector<Constant*> Operands(I->getNumOperands());
5515 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
5516 Instruction *Operand = dyn_cast<Instruction>(I->getOperand(i));
5518 Operands[i] = dyn_cast<Constant>(I->getOperand(i));
5519 if (!Operands[i]) return nullptr;
5522 Constant *C = EvaluateExpression(Operand, L, Vals, DL, TLI);
5524 if (!C) return nullptr;
5528 if (CmpInst *CI = dyn_cast<CmpInst>(I))
5529 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
5530 Operands[1], DL, TLI);
5531 if (LoadInst *LI = dyn_cast<LoadInst>(I)) {
5532 if (!LI->isVolatile())
5533 return ConstantFoldLoadFromConstPtr(Operands[0], DL);
5535 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), Operands, DL,
5539 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
5540 /// in the header of its containing loop, we know the loop executes a
5541 /// constant number of times, and the PHI node is just a recurrence
5542 /// involving constants, fold it.
5544 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
5547 DenseMap<PHINode*, Constant*>::const_iterator I =
5548 ConstantEvolutionLoopExitValue.find(PN);
5549 if (I != ConstantEvolutionLoopExitValue.end())
5552 if (BEs.ugt(MaxBruteForceIterations))
5553 return ConstantEvolutionLoopExitValue[PN] = nullptr; // Not going to evaluate it.
5555 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
5557 DenseMap<Instruction *, Constant *> CurrentIterVals;
5558 BasicBlock *Header = L->getHeader();
5559 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
5561 // Since the loop is canonicalized, the PHI node must have two entries. One
5562 // entry must be a constant (coming in from outside of the loop), and the
5563 // second must be derived from the same PHI.
5564 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
5565 PHINode *PHI = nullptr;
5566 for (BasicBlock::iterator I = Header->begin();
5567 (PHI = dyn_cast<PHINode>(I)); ++I) {
5568 Constant *StartCST =
5569 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
5570 if (!StartCST) continue;
5571 CurrentIterVals[PHI] = StartCST;
5573 if (!CurrentIterVals.count(PN))
5574 return RetVal = nullptr;
5576 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
5578 // Execute the loop symbolically to determine the exit value.
5579 if (BEs.getActiveBits() >= 32)
5580 return RetVal = nullptr; // More than 2^32-1 iterations?? Not doing it!
5582 unsigned NumIterations = BEs.getZExtValue(); // must be in range
5583 unsigned IterationNum = 0;
5584 const DataLayout &DL = F->getParent()->getDataLayout();
5585 for (; ; ++IterationNum) {
5586 if (IterationNum == NumIterations)
5587 return RetVal = CurrentIterVals[PN]; // Got exit value!
5589 // Compute the value of the PHIs for the next iteration.
5590 // EvaluateExpression adds non-phi values to the CurrentIterVals map.
5591 DenseMap<Instruction *, Constant *> NextIterVals;
5593 EvaluateExpression(BEValue, L, CurrentIterVals, DL, TLI);
5595 return nullptr; // Couldn't evaluate!
5596 NextIterVals[PN] = NextPHI;
5598 bool StoppedEvolving = NextPHI == CurrentIterVals[PN];
5600 // Also evaluate the other PHI nodes. However, we don't get to stop if we
5601 // cease to be able to evaluate one of them or if they stop evolving,
5602 // because that doesn't necessarily prevent us from computing PN.
5603 SmallVector<std::pair<PHINode *, Constant *>, 8> PHIsToCompute;
5604 for (DenseMap<Instruction *, Constant *>::const_iterator
5605 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
5606 PHINode *PHI = dyn_cast<PHINode>(I->first);
5607 if (!PHI || PHI == PN || PHI->getParent() != Header) continue;
5608 PHIsToCompute.push_back(std::make_pair(PHI, I->second));
5610 // We use two distinct loops because EvaluateExpression may invalidate any
5611 // iterators into CurrentIterVals.
5612 for (SmallVectorImpl<std::pair<PHINode *, Constant*> >::const_iterator
5613 I = PHIsToCompute.begin(), E = PHIsToCompute.end(); I != E; ++I) {
5614 PHINode *PHI = I->first;
5615 Constant *&NextPHI = NextIterVals[PHI];
5616 if (!NextPHI) { // Not already computed.
5617 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
5618 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, TLI);
5620 if (NextPHI != I->second)
5621 StoppedEvolving = false;
5624 // If all entries in CurrentIterVals == NextIterVals then we can stop
5625 // iterating, the loop can't continue to change.
5626 if (StoppedEvolving)
5627 return RetVal = CurrentIterVals[PN];
5629 CurrentIterVals.swap(NextIterVals);
5633 /// ComputeExitCountExhaustively - If the loop is known to execute a
5634 /// constant number of times (the condition evolves only from constants),
5635 /// try to evaluate a few iterations of the loop until we get the exit
5636 /// condition gets a value of ExitWhen (true or false). If we cannot
5637 /// evaluate the trip count of the loop, return getCouldNotCompute().
5638 const SCEV *ScalarEvolution::ComputeExitCountExhaustively(const Loop *L,
5641 PHINode *PN = getConstantEvolvingPHI(Cond, L);
5642 if (!PN) return getCouldNotCompute();
5644 // If the loop is canonicalized, the PHI will have exactly two entries.
5645 // That's the only form we support here.
5646 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
5648 DenseMap<Instruction *, Constant *> CurrentIterVals;
5649 BasicBlock *Header = L->getHeader();
5650 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
5652 // One entry must be a constant (coming in from outside of the loop), and the
5653 // second must be derived from the same PHI.
5654 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
5655 PHINode *PHI = nullptr;
5656 for (BasicBlock::iterator I = Header->begin();
5657 (PHI = dyn_cast<PHINode>(I)); ++I) {
5658 Constant *StartCST =
5659 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
5660 if (!StartCST) continue;
5661 CurrentIterVals[PHI] = StartCST;
5663 if (!CurrentIterVals.count(PN))
5664 return getCouldNotCompute();
5666 // Okay, we find a PHI node that defines the trip count of this loop. Execute
5667 // the loop symbolically to determine when the condition gets a value of
5669 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
5670 const DataLayout &DL = F->getParent()->getDataLayout();
5671 for (unsigned IterationNum = 0; IterationNum != MaxIterations;++IterationNum){
5672 ConstantInt *CondVal = dyn_cast_or_null<ConstantInt>(
5673 EvaluateExpression(Cond, L, CurrentIterVals, DL, TLI));
5675 // Couldn't symbolically evaluate.
5676 if (!CondVal) return getCouldNotCompute();
5678 if (CondVal->getValue() == uint64_t(ExitWhen)) {
5679 ++NumBruteForceTripCountsComputed;
5680 return getConstant(Type::getInt32Ty(getContext()), IterationNum);
5683 // Update all the PHI nodes for the next iteration.
5684 DenseMap<Instruction *, Constant *> NextIterVals;
5686 // Create a list of which PHIs we need to compute. We want to do this before
5687 // calling EvaluateExpression on them because that may invalidate iterators
5688 // into CurrentIterVals.
5689 SmallVector<PHINode *, 8> PHIsToCompute;
5690 for (DenseMap<Instruction *, Constant *>::const_iterator
5691 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
5692 PHINode *PHI = dyn_cast<PHINode>(I->first);
5693 if (!PHI || PHI->getParent() != Header) continue;
5694 PHIsToCompute.push_back(PHI);
5696 for (SmallVectorImpl<PHINode *>::const_iterator I = PHIsToCompute.begin(),
5697 E = PHIsToCompute.end(); I != E; ++I) {
5699 Constant *&NextPHI = NextIterVals[PHI];
5700 if (NextPHI) continue; // Already computed!
5702 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
5703 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, TLI);
5705 CurrentIterVals.swap(NextIterVals);
5708 // Too many iterations were needed to evaluate.
5709 return getCouldNotCompute();
5712 /// getSCEVAtScope - Return a SCEV expression for the specified value
5713 /// at the specified scope in the program. The L value specifies a loop
5714 /// nest to evaluate the expression at, where null is the top-level or a
5715 /// specified loop is immediately inside of the loop.
5717 /// This method can be used to compute the exit value for a variable defined
5718 /// in a loop by querying what the value will hold in the parent loop.
5720 /// In the case that a relevant loop exit value cannot be computed, the
5721 /// original value V is returned.
5722 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
5723 // Check to see if we've folded this expression at this loop before.
5724 SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values = ValuesAtScopes[V];
5725 for (unsigned u = 0; u < Values.size(); u++) {
5726 if (Values[u].first == L)
5727 return Values[u].second ? Values[u].second : V;
5729 Values.push_back(std::make_pair(L, static_cast<const SCEV *>(nullptr)));
5730 // Otherwise compute it.
5731 const SCEV *C = computeSCEVAtScope(V, L);
5732 SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values2 = ValuesAtScopes[V];
5733 for (unsigned u = Values2.size(); u > 0; u--) {
5734 if (Values2[u - 1].first == L) {
5735 Values2[u - 1].second = C;
5742 /// This builds up a Constant using the ConstantExpr interface. That way, we
5743 /// will return Constants for objects which aren't represented by a
5744 /// SCEVConstant, because SCEVConstant is restricted to ConstantInt.
5745 /// Returns NULL if the SCEV isn't representable as a Constant.
5746 static Constant *BuildConstantFromSCEV(const SCEV *V) {
5747 switch (static_cast<SCEVTypes>(V->getSCEVType())) {
5748 case scCouldNotCompute:
5752 return cast<SCEVConstant>(V)->getValue();
5754 return dyn_cast<Constant>(cast<SCEVUnknown>(V)->getValue());
5755 case scSignExtend: {
5756 const SCEVSignExtendExpr *SS = cast<SCEVSignExtendExpr>(V);
5757 if (Constant *CastOp = BuildConstantFromSCEV(SS->getOperand()))
5758 return ConstantExpr::getSExt(CastOp, SS->getType());
5761 case scZeroExtend: {
5762 const SCEVZeroExtendExpr *SZ = cast<SCEVZeroExtendExpr>(V);
5763 if (Constant *CastOp = BuildConstantFromSCEV(SZ->getOperand()))
5764 return ConstantExpr::getZExt(CastOp, SZ->getType());
5768 const SCEVTruncateExpr *ST = cast<SCEVTruncateExpr>(V);
5769 if (Constant *CastOp = BuildConstantFromSCEV(ST->getOperand()))
5770 return ConstantExpr::getTrunc(CastOp, ST->getType());
5774 const SCEVAddExpr *SA = cast<SCEVAddExpr>(V);
5775 if (Constant *C = BuildConstantFromSCEV(SA->getOperand(0))) {
5776 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
5777 unsigned AS = PTy->getAddressSpace();
5778 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
5779 C = ConstantExpr::getBitCast(C, DestPtrTy);
5781 for (unsigned i = 1, e = SA->getNumOperands(); i != e; ++i) {
5782 Constant *C2 = BuildConstantFromSCEV(SA->getOperand(i));
5783 if (!C2) return nullptr;
5786 if (!C->getType()->isPointerTy() && C2->getType()->isPointerTy()) {
5787 unsigned AS = C2->getType()->getPointerAddressSpace();
5789 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
5790 // The offsets have been converted to bytes. We can add bytes to an
5791 // i8* by GEP with the byte count in the first index.
5792 C = ConstantExpr::getBitCast(C, DestPtrTy);
5795 // Don't bother trying to sum two pointers. We probably can't
5796 // statically compute a load that results from it anyway.
5797 if (C2->getType()->isPointerTy())
5800 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
5801 if (PTy->getElementType()->isStructTy())
5802 C2 = ConstantExpr::getIntegerCast(
5803 C2, Type::getInt32Ty(C->getContext()), true);
5804 C = ConstantExpr::getGetElementPtr(PTy->getElementType(), C, C2);
5806 C = ConstantExpr::getAdd(C, C2);
5813 const SCEVMulExpr *SM = cast<SCEVMulExpr>(V);
5814 if (Constant *C = BuildConstantFromSCEV(SM->getOperand(0))) {
5815 // Don't bother with pointers at all.
5816 if (C->getType()->isPointerTy()) return nullptr;
5817 for (unsigned i = 1, e = SM->getNumOperands(); i != e; ++i) {
5818 Constant *C2 = BuildConstantFromSCEV(SM->getOperand(i));
5819 if (!C2 || C2->getType()->isPointerTy()) return nullptr;
5820 C = ConstantExpr::getMul(C, C2);
5827 const SCEVUDivExpr *SU = cast<SCEVUDivExpr>(V);
5828 if (Constant *LHS = BuildConstantFromSCEV(SU->getLHS()))
5829 if (Constant *RHS = BuildConstantFromSCEV(SU->getRHS()))
5830 if (LHS->getType() == RHS->getType())
5831 return ConstantExpr::getUDiv(LHS, RHS);
5836 break; // TODO: smax, umax.
5841 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
5842 if (isa<SCEVConstant>(V)) return V;
5844 // If this instruction is evolved from a constant-evolving PHI, compute the
5845 // exit value from the loop without using SCEVs.
5846 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
5847 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
5848 const Loop *LI = (*this->LI)[I->getParent()];
5849 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
5850 if (PHINode *PN = dyn_cast<PHINode>(I))
5851 if (PN->getParent() == LI->getHeader()) {
5852 // Okay, there is no closed form solution for the PHI node. Check
5853 // to see if the loop that contains it has a known backedge-taken
5854 // count. If so, we may be able to force computation of the exit
5856 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
5857 if (const SCEVConstant *BTCC =
5858 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
5859 // Okay, we know how many times the containing loop executes. If
5860 // this is a constant evolving PHI node, get the final value at
5861 // the specified iteration number.
5862 Constant *RV = getConstantEvolutionLoopExitValue(PN,
5863 BTCC->getValue()->getValue(),
5865 if (RV) return getSCEV(RV);
5869 // Okay, this is an expression that we cannot symbolically evaluate
5870 // into a SCEV. Check to see if it's possible to symbolically evaluate
5871 // the arguments into constants, and if so, try to constant propagate the
5872 // result. This is particularly useful for computing loop exit values.
5873 if (CanConstantFold(I)) {
5874 SmallVector<Constant *, 4> Operands;
5875 bool MadeImprovement = false;
5876 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
5877 Value *Op = I->getOperand(i);
5878 if (Constant *C = dyn_cast<Constant>(Op)) {
5879 Operands.push_back(C);
5883 // If any of the operands is non-constant and if they are
5884 // non-integer and non-pointer, don't even try to analyze them
5885 // with scev techniques.
5886 if (!isSCEVable(Op->getType()))
5889 const SCEV *OrigV = getSCEV(Op);
5890 const SCEV *OpV = getSCEVAtScope(OrigV, L);
5891 MadeImprovement |= OrigV != OpV;
5893 Constant *C = BuildConstantFromSCEV(OpV);
5895 if (C->getType() != Op->getType())
5896 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
5900 Operands.push_back(C);
5903 // Check to see if getSCEVAtScope actually made an improvement.
5904 if (MadeImprovement) {
5905 Constant *C = nullptr;
5906 const DataLayout &DL = F->getParent()->getDataLayout();
5907 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
5908 C = ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
5909 Operands[1], DL, TLI);
5910 else if (const LoadInst *LI = dyn_cast<LoadInst>(I)) {
5911 if (!LI->isVolatile())
5912 C = ConstantFoldLoadFromConstPtr(Operands[0], DL);
5914 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(), Operands,
5922 // This is some other type of SCEVUnknown, just return it.
5926 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
5927 // Avoid performing the look-up in the common case where the specified
5928 // expression has no loop-variant portions.
5929 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
5930 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
5931 if (OpAtScope != Comm->getOperand(i)) {
5932 // Okay, at least one of these operands is loop variant but might be
5933 // foldable. Build a new instance of the folded commutative expression.
5934 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
5935 Comm->op_begin()+i);
5936 NewOps.push_back(OpAtScope);
5938 for (++i; i != e; ++i) {
5939 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
5940 NewOps.push_back(OpAtScope);
5942 if (isa<SCEVAddExpr>(Comm))
5943 return getAddExpr(NewOps);
5944 if (isa<SCEVMulExpr>(Comm))
5945 return getMulExpr(NewOps);
5946 if (isa<SCEVSMaxExpr>(Comm))
5947 return getSMaxExpr(NewOps);
5948 if (isa<SCEVUMaxExpr>(Comm))
5949 return getUMaxExpr(NewOps);
5950 llvm_unreachable("Unknown commutative SCEV type!");
5953 // If we got here, all operands are loop invariant.
5957 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
5958 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
5959 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
5960 if (LHS == Div->getLHS() && RHS == Div->getRHS())
5961 return Div; // must be loop invariant
5962 return getUDivExpr(LHS, RHS);
5965 // If this is a loop recurrence for a loop that does not contain L, then we
5966 // are dealing with the final value computed by the loop.
5967 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
5968 // First, attempt to evaluate each operand.
5969 // Avoid performing the look-up in the common case where the specified
5970 // expression has no loop-variant portions.
5971 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
5972 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
5973 if (OpAtScope == AddRec->getOperand(i))
5976 // Okay, at least one of these operands is loop variant but might be
5977 // foldable. Build a new instance of the folded commutative expression.
5978 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(),
5979 AddRec->op_begin()+i);
5980 NewOps.push_back(OpAtScope);
5981 for (++i; i != e; ++i)
5982 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
5984 const SCEV *FoldedRec =
5985 getAddRecExpr(NewOps, AddRec->getLoop(),
5986 AddRec->getNoWrapFlags(SCEV::FlagNW));
5987 AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec);
5988 // The addrec may be folded to a nonrecurrence, for example, if the
5989 // induction variable is multiplied by zero after constant folding. Go
5990 // ahead and return the folded value.
5996 // If the scope is outside the addrec's loop, evaluate it by using the
5997 // loop exit value of the addrec.
5998 if (!AddRec->getLoop()->contains(L)) {
5999 // To evaluate this recurrence, we need to know how many times the AddRec
6000 // loop iterates. Compute this now.
6001 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
6002 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
6004 // Then, evaluate the AddRec.
6005 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
6011 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
6012 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
6013 if (Op == Cast->getOperand())
6014 return Cast; // must be loop invariant
6015 return getZeroExtendExpr(Op, Cast->getType());
6018 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
6019 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
6020 if (Op == Cast->getOperand())
6021 return Cast; // must be loop invariant
6022 return getSignExtendExpr(Op, Cast->getType());
6025 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
6026 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
6027 if (Op == Cast->getOperand())
6028 return Cast; // must be loop invariant
6029 return getTruncateExpr(Op, Cast->getType());
6032 llvm_unreachable("Unknown SCEV type!");
6035 /// getSCEVAtScope - This is a convenience function which does
6036 /// getSCEVAtScope(getSCEV(V), L).
6037 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
6038 return getSCEVAtScope(getSCEV(V), L);
6041 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
6042 /// following equation:
6044 /// A * X = B (mod N)
6046 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
6047 /// A and B isn't important.
6049 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
6050 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
6051 ScalarEvolution &SE) {
6052 uint32_t BW = A.getBitWidth();
6053 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
6054 assert(A != 0 && "A must be non-zero.");
6058 // The gcd of A and N may have only one prime factor: 2. The number of
6059 // trailing zeros in A is its multiplicity
6060 uint32_t Mult2 = A.countTrailingZeros();
6063 // 2. Check if B is divisible by D.
6065 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
6066 // is not less than multiplicity of this prime factor for D.
6067 if (B.countTrailingZeros() < Mult2)
6068 return SE.getCouldNotCompute();
6070 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
6073 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
6074 // bit width during computations.
6075 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
6076 APInt Mod(BW + 1, 0);
6077 Mod.setBit(BW - Mult2); // Mod = N / D
6078 APInt I = AD.multiplicativeInverse(Mod);
6080 // 4. Compute the minimum unsigned root of the equation:
6081 // I * (B / D) mod (N / D)
6082 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
6084 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
6086 return SE.getConstant(Result.trunc(BW));
6089 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
6090 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
6091 /// might be the same) or two SCEVCouldNotCompute objects.
6093 static std::pair<const SCEV *,const SCEV *>
6094 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
6095 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
6096 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
6097 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
6098 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
6100 // We currently can only solve this if the coefficients are constants.
6101 if (!LC || !MC || !NC) {
6102 const SCEV *CNC = SE.getCouldNotCompute();
6103 return std::make_pair(CNC, CNC);
6106 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
6107 const APInt &L = LC->getValue()->getValue();
6108 const APInt &M = MC->getValue()->getValue();
6109 const APInt &N = NC->getValue()->getValue();
6110 APInt Two(BitWidth, 2);
6111 APInt Four(BitWidth, 4);
6114 using namespace APIntOps;
6116 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
6117 // The B coefficient is M-N/2
6121 // The A coefficient is N/2
6122 APInt A(N.sdiv(Two));
6124 // Compute the B^2-4ac term.
6127 SqrtTerm -= Four * (A * C);
6129 if (SqrtTerm.isNegative()) {
6130 // The loop is provably infinite.
6131 const SCEV *CNC = SE.getCouldNotCompute();
6132 return std::make_pair(CNC, CNC);
6135 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
6136 // integer value or else APInt::sqrt() will assert.
6137 APInt SqrtVal(SqrtTerm.sqrt());
6139 // Compute the two solutions for the quadratic formula.
6140 // The divisions must be performed as signed divisions.
6143 if (TwoA.isMinValue()) {
6144 const SCEV *CNC = SE.getCouldNotCompute();
6145 return std::make_pair(CNC, CNC);
6148 LLVMContext &Context = SE.getContext();
6150 ConstantInt *Solution1 =
6151 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
6152 ConstantInt *Solution2 =
6153 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
6155 return std::make_pair(SE.getConstant(Solution1),
6156 SE.getConstant(Solution2));
6157 } // end APIntOps namespace
6160 /// HowFarToZero - Return the number of times a backedge comparing the specified
6161 /// value to zero will execute. If not computable, return CouldNotCompute.
6163 /// This is only used for loops with a "x != y" exit test. The exit condition is
6164 /// now expressed as a single expression, V = x-y. So the exit test is
6165 /// effectively V != 0. We know and take advantage of the fact that this
6166 /// expression only being used in a comparison by zero context.
6167 ScalarEvolution::ExitLimit
6168 ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L, bool ControlsExit) {
6169 // If the value is a constant
6170 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
6171 // If the value is already zero, the branch will execute zero times.
6172 if (C->getValue()->isZero()) return C;
6173 return getCouldNotCompute(); // Otherwise it will loop infinitely.
6176 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
6177 if (!AddRec || AddRec->getLoop() != L)
6178 return getCouldNotCompute();
6180 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
6181 // the quadratic equation to solve it.
6182 if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
6183 std::pair<const SCEV *,const SCEV *> Roots =
6184 SolveQuadraticEquation(AddRec, *this);
6185 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
6186 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
6189 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1
6190 << " sol#2: " << *R2 << "\n";
6192 // Pick the smallest positive root value.
6193 if (ConstantInt *CB =
6194 dyn_cast<ConstantInt>(ConstantExpr::getICmp(CmpInst::ICMP_ULT,
6197 if (!CB->getZExtValue())
6198 std::swap(R1, R2); // R1 is the minimum root now.
6200 // We can only use this value if the chrec ends up with an exact zero
6201 // value at this index. When solving for "X*X != 5", for example, we
6202 // should not accept a root of 2.
6203 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
6205 return R1; // We found a quadratic root!
6208 return getCouldNotCompute();
6211 // Otherwise we can only handle this if it is affine.
6212 if (!AddRec->isAffine())
6213 return getCouldNotCompute();
6215 // If this is an affine expression, the execution count of this branch is
6216 // the minimum unsigned root of the following equation:
6218 // Start + Step*N = 0 (mod 2^BW)
6222 // Step*N = -Start (mod 2^BW)
6224 // where BW is the common bit width of Start and Step.
6226 // Get the initial value for the loop.
6227 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
6228 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
6230 // For now we handle only constant steps.
6232 // TODO: Handle a nonconstant Step given AddRec<NUW>. If the
6233 // AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap
6234 // to 0, it must be counting down to equal 0. Consequently, N = Start / -Step.
6235 // We have not yet seen any such cases.
6236 const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step);
6237 if (!StepC || StepC->getValue()->equalsInt(0))
6238 return getCouldNotCompute();
6240 // For positive steps (counting up until unsigned overflow):
6241 // N = -Start/Step (as unsigned)
6242 // For negative steps (counting down to zero):
6244 // First compute the unsigned distance from zero in the direction of Step.
6245 bool CountDown = StepC->getValue()->getValue().isNegative();
6246 const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start);
6248 // Handle unitary steps, which cannot wraparound.
6249 // 1*N = -Start; -1*N = Start (mod 2^BW), so:
6250 // N = Distance (as unsigned)
6251 if (StepC->getValue()->equalsInt(1) || StepC->getValue()->isAllOnesValue()) {
6252 ConstantRange CR = getUnsignedRange(Start);
6253 const SCEV *MaxBECount;
6254 if (!CountDown && CR.getUnsignedMin().isMinValue())
6255 // When counting up, the worst starting value is 1, not 0.
6256 MaxBECount = CR.getUnsignedMax().isMinValue()
6257 ? getConstant(APInt::getMinValue(CR.getBitWidth()))
6258 : getConstant(APInt::getMaxValue(CR.getBitWidth()));
6260 MaxBECount = getConstant(CountDown ? CR.getUnsignedMax()
6261 : -CR.getUnsignedMin());
6262 return ExitLimit(Distance, MaxBECount);
6265 // As a special case, handle the instance where Step is a positive power of
6266 // two. In this case, determining whether Step divides Distance evenly can be
6267 // done by counting and comparing the number of trailing zeros of Step and
6270 const APInt &StepV = StepC->getValue()->getValue();
6271 // StepV.isPowerOf2() returns true if StepV is an positive power of two. It
6272 // also returns true if StepV is maximally negative (eg, INT_MIN), but that
6273 // case is not handled as this code is guarded by !CountDown.
6274 if (StepV.isPowerOf2() &&
6275 GetMinTrailingZeros(Distance) >= StepV.countTrailingZeros())
6276 return getUDivExactExpr(Distance, Step);
6279 // If the condition controls loop exit (the loop exits only if the expression
6280 // is true) and the addition is no-wrap we can use unsigned divide to
6281 // compute the backedge count. In this case, the step may not divide the
6282 // distance, but we don't care because if the condition is "missed" the loop
6283 // will have undefined behavior due to wrapping.
6284 if (ControlsExit && AddRec->getNoWrapFlags(SCEV::FlagNW)) {
6286 getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
6287 return ExitLimit(Exact, Exact);
6290 // Then, try to solve the above equation provided that Start is constant.
6291 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
6292 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
6293 -StartC->getValue()->getValue(),
6295 return getCouldNotCompute();
6298 /// HowFarToNonZero - Return the number of times a backedge checking the
6299 /// specified value for nonzero will execute. If not computable, return
6301 ScalarEvolution::ExitLimit
6302 ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
6303 // Loops that look like: while (X == 0) are very strange indeed. We don't
6304 // handle them yet except for the trivial case. This could be expanded in the
6305 // future as needed.
6307 // If the value is a constant, check to see if it is known to be non-zero
6308 // already. If so, the backedge will execute zero times.
6309 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
6310 if (!C->getValue()->isNullValue())
6311 return getConstant(C->getType(), 0);
6312 return getCouldNotCompute(); // Otherwise it will loop infinitely.
6315 // We could implement others, but I really doubt anyone writes loops like
6316 // this, and if they did, they would already be constant folded.
6317 return getCouldNotCompute();
6320 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
6321 /// (which may not be an immediate predecessor) which has exactly one
6322 /// successor from which BB is reachable, or null if no such block is
6325 std::pair<BasicBlock *, BasicBlock *>
6326 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
6327 // If the block has a unique predecessor, then there is no path from the
6328 // predecessor to the block that does not go through the direct edge
6329 // from the predecessor to the block.
6330 if (BasicBlock *Pred = BB->getSinglePredecessor())
6331 return std::make_pair(Pred, BB);
6333 // A loop's header is defined to be a block that dominates the loop.
6334 // If the header has a unique predecessor outside the loop, it must be
6335 // a block that has exactly one successor that can reach the loop.
6336 if (Loop *L = LI->getLoopFor(BB))
6337 return std::make_pair(L->getLoopPredecessor(), L->getHeader());
6339 return std::pair<BasicBlock *, BasicBlock *>();
6342 /// HasSameValue - SCEV structural equivalence is usually sufficient for
6343 /// testing whether two expressions are equal, however for the purposes of
6344 /// looking for a condition guarding a loop, it can be useful to be a little
6345 /// more general, since a front-end may have replicated the controlling
6348 static bool HasSameValue(const SCEV *A, const SCEV *B) {
6349 // Quick check to see if they are the same SCEV.
6350 if (A == B) return true;
6352 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
6353 // two different instructions with the same value. Check for this case.
6354 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
6355 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
6356 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
6357 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
6358 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory())
6361 // Otherwise assume they may have a different value.
6365 /// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with
6366 /// predicate Pred. Return true iff any changes were made.
6368 bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
6369 const SCEV *&LHS, const SCEV *&RHS,
6371 bool Changed = false;
6373 // If we hit the max recursion limit bail out.
6377 // Canonicalize a constant to the right side.
6378 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
6379 // Check for both operands constant.
6380 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
6381 if (ConstantExpr::getICmp(Pred,
6383 RHSC->getValue())->isNullValue())
6384 goto trivially_false;
6386 goto trivially_true;
6388 // Otherwise swap the operands to put the constant on the right.
6389 std::swap(LHS, RHS);
6390 Pred = ICmpInst::getSwappedPredicate(Pred);
6394 // If we're comparing an addrec with a value which is loop-invariant in the
6395 // addrec's loop, put the addrec on the left. Also make a dominance check,
6396 // as both operands could be addrecs loop-invariant in each other's loop.
6397 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
6398 const Loop *L = AR->getLoop();
6399 if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) {
6400 std::swap(LHS, RHS);
6401 Pred = ICmpInst::getSwappedPredicate(Pred);
6406 // If there's a constant operand, canonicalize comparisons with boundary
6407 // cases, and canonicalize *-or-equal comparisons to regular comparisons.
6408 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
6409 const APInt &RA = RC->getValue()->getValue();
6411 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6412 case ICmpInst::ICMP_EQ:
6413 case ICmpInst::ICMP_NE:
6414 // Fold ((-1) * %a) + %b == 0 (equivalent to %b-%a == 0) into %a == %b.
6416 if (const SCEVAddExpr *AE = dyn_cast<SCEVAddExpr>(LHS))
6417 if (const SCEVMulExpr *ME = dyn_cast<SCEVMulExpr>(AE->getOperand(0)))
6418 if (AE->getNumOperands() == 2 && ME->getNumOperands() == 2 &&
6419 ME->getOperand(0)->isAllOnesValue()) {
6420 RHS = AE->getOperand(1);
6421 LHS = ME->getOperand(1);
6425 case ICmpInst::ICMP_UGE:
6426 if ((RA - 1).isMinValue()) {
6427 Pred = ICmpInst::ICMP_NE;
6428 RHS = getConstant(RA - 1);
6432 if (RA.isMaxValue()) {
6433 Pred = ICmpInst::ICMP_EQ;
6437 if (RA.isMinValue()) goto trivially_true;
6439 Pred = ICmpInst::ICMP_UGT;
6440 RHS = getConstant(RA - 1);
6443 case ICmpInst::ICMP_ULE:
6444 if ((RA + 1).isMaxValue()) {
6445 Pred = ICmpInst::ICMP_NE;
6446 RHS = getConstant(RA + 1);
6450 if (RA.isMinValue()) {
6451 Pred = ICmpInst::ICMP_EQ;
6455 if (RA.isMaxValue()) goto trivially_true;
6457 Pred = ICmpInst::ICMP_ULT;
6458 RHS = getConstant(RA + 1);
6461 case ICmpInst::ICMP_SGE:
6462 if ((RA - 1).isMinSignedValue()) {
6463 Pred = ICmpInst::ICMP_NE;
6464 RHS = getConstant(RA - 1);
6468 if (RA.isMaxSignedValue()) {
6469 Pred = ICmpInst::ICMP_EQ;
6473 if (RA.isMinSignedValue()) goto trivially_true;
6475 Pred = ICmpInst::ICMP_SGT;
6476 RHS = getConstant(RA - 1);
6479 case ICmpInst::ICMP_SLE:
6480 if ((RA + 1).isMaxSignedValue()) {
6481 Pred = ICmpInst::ICMP_NE;
6482 RHS = getConstant(RA + 1);
6486 if (RA.isMinSignedValue()) {
6487 Pred = ICmpInst::ICMP_EQ;
6491 if (RA.isMaxSignedValue()) goto trivially_true;
6493 Pred = ICmpInst::ICMP_SLT;
6494 RHS = getConstant(RA + 1);
6497 case ICmpInst::ICMP_UGT:
6498 if (RA.isMinValue()) {
6499 Pred = ICmpInst::ICMP_NE;
6503 if ((RA + 1).isMaxValue()) {
6504 Pred = ICmpInst::ICMP_EQ;
6505 RHS = getConstant(RA + 1);
6509 if (RA.isMaxValue()) goto trivially_false;
6511 case ICmpInst::ICMP_ULT:
6512 if (RA.isMaxValue()) {
6513 Pred = ICmpInst::ICMP_NE;
6517 if ((RA - 1).isMinValue()) {
6518 Pred = ICmpInst::ICMP_EQ;
6519 RHS = getConstant(RA - 1);
6523 if (RA.isMinValue()) goto trivially_false;
6525 case ICmpInst::ICMP_SGT:
6526 if (RA.isMinSignedValue()) {
6527 Pred = ICmpInst::ICMP_NE;
6531 if ((RA + 1).isMaxSignedValue()) {
6532 Pred = ICmpInst::ICMP_EQ;
6533 RHS = getConstant(RA + 1);
6537 if (RA.isMaxSignedValue()) goto trivially_false;
6539 case ICmpInst::ICMP_SLT:
6540 if (RA.isMaxSignedValue()) {
6541 Pred = ICmpInst::ICMP_NE;
6545 if ((RA - 1).isMinSignedValue()) {
6546 Pred = ICmpInst::ICMP_EQ;
6547 RHS = getConstant(RA - 1);
6551 if (RA.isMinSignedValue()) goto trivially_false;
6556 // Check for obvious equality.
6557 if (HasSameValue(LHS, RHS)) {
6558 if (ICmpInst::isTrueWhenEqual(Pred))
6559 goto trivially_true;
6560 if (ICmpInst::isFalseWhenEqual(Pred))
6561 goto trivially_false;
6564 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
6565 // adding or subtracting 1 from one of the operands.
6567 case ICmpInst::ICMP_SLE:
6568 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) {
6569 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
6571 Pred = ICmpInst::ICMP_SLT;
6573 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) {
6574 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
6576 Pred = ICmpInst::ICMP_SLT;
6580 case ICmpInst::ICMP_SGE:
6581 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) {
6582 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
6584 Pred = ICmpInst::ICMP_SGT;
6586 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) {
6587 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
6589 Pred = ICmpInst::ICMP_SGT;
6593 case ICmpInst::ICMP_ULE:
6594 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) {
6595 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
6597 Pred = ICmpInst::ICMP_ULT;
6599 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) {
6600 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
6602 Pred = ICmpInst::ICMP_ULT;
6606 case ICmpInst::ICMP_UGE:
6607 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) {
6608 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
6610 Pred = ICmpInst::ICMP_UGT;
6612 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) {
6613 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
6615 Pred = ICmpInst::ICMP_UGT;
6623 // TODO: More simplifications are possible here.
6625 // Recursively simplify until we either hit a recursion limit or nothing
6628 return SimplifyICmpOperands(Pred, LHS, RHS, Depth+1);
6634 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
6635 Pred = ICmpInst::ICMP_EQ;
6640 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
6641 Pred = ICmpInst::ICMP_NE;
6645 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
6646 return getSignedRange(S).getSignedMax().isNegative();
6649 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
6650 return getSignedRange(S).getSignedMin().isStrictlyPositive();
6653 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
6654 return !getSignedRange(S).getSignedMin().isNegative();
6657 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
6658 return !getSignedRange(S).getSignedMax().isStrictlyPositive();
6661 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
6662 return isKnownNegative(S) || isKnownPositive(S);
6665 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
6666 const SCEV *LHS, const SCEV *RHS) {
6667 // Canonicalize the inputs first.
6668 (void)SimplifyICmpOperands(Pred, LHS, RHS);
6670 // If LHS or RHS is an addrec, check to see if the condition is true in
6671 // every iteration of the loop.
6672 // If LHS and RHS are both addrec, both conditions must be true in
6673 // every iteration of the loop.
6674 const SCEVAddRecExpr *LAR = dyn_cast<SCEVAddRecExpr>(LHS);
6675 const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS);
6676 bool LeftGuarded = false;
6677 bool RightGuarded = false;
6679 const Loop *L = LAR->getLoop();
6680 if (isLoopEntryGuardedByCond(L, Pred, LAR->getStart(), RHS) &&
6681 isLoopBackedgeGuardedByCond(L, Pred, LAR->getPostIncExpr(*this), RHS)) {
6682 if (!RAR) return true;
6687 const Loop *L = RAR->getLoop();
6688 if (isLoopEntryGuardedByCond(L, Pred, LHS, RAR->getStart()) &&
6689 isLoopBackedgeGuardedByCond(L, Pred, LHS, RAR->getPostIncExpr(*this))) {
6690 if (!LAR) return true;
6691 RightGuarded = true;
6694 if (LeftGuarded && RightGuarded)
6697 // Otherwise see what can be done with known constant ranges.
6698 return isKnownPredicateWithRanges(Pred, LHS, RHS);
6701 bool ScalarEvolution::isMonotonicPredicate(const SCEVAddRecExpr *LHS,
6702 ICmpInst::Predicate Pred,
6704 bool Result = isMonotonicPredicateImpl(LHS, Pred, Increasing);
6707 // Verify an invariant: inverting the predicate should turn a monotonically
6708 // increasing change to a monotonically decreasing one, and vice versa.
6709 bool IncreasingSwapped;
6710 bool ResultSwapped = isMonotonicPredicateImpl(
6711 LHS, ICmpInst::getSwappedPredicate(Pred), IncreasingSwapped);
6713 assert(Result == ResultSwapped && "should be able to analyze both!");
6715 assert(Increasing == !IncreasingSwapped &&
6716 "monotonicity should flip as we flip the predicate");
6722 bool ScalarEvolution::isMonotonicPredicateImpl(const SCEVAddRecExpr *LHS,
6723 ICmpInst::Predicate Pred,
6725 SCEV::NoWrapFlags FlagsRequired = SCEV::FlagAnyWrap;
6726 bool IncreasingOnNonNegativeStep = false;
6730 return false; // Conservative answer
6732 case ICmpInst::ICMP_UGT:
6733 case ICmpInst::ICMP_UGE:
6734 FlagsRequired = SCEV::FlagNUW;
6735 IncreasingOnNonNegativeStep = true;
6738 case ICmpInst::ICMP_ULT:
6739 case ICmpInst::ICMP_ULE:
6740 FlagsRequired = SCEV::FlagNUW;
6741 IncreasingOnNonNegativeStep = false;
6744 case ICmpInst::ICMP_SGT:
6745 case ICmpInst::ICMP_SGE:
6746 FlagsRequired = SCEV::FlagNSW;
6747 IncreasingOnNonNegativeStep = true;
6750 case ICmpInst::ICMP_SLT:
6751 case ICmpInst::ICMP_SLE:
6752 FlagsRequired = SCEV::FlagNSW;
6753 IncreasingOnNonNegativeStep = false;
6757 if (!LHS->getNoWrapFlags(FlagsRequired))
6760 // A zero step value for LHS means the induction variable is essentially a
6761 // loop invariant value. We don't really depend on the predicate actually
6762 // flipping from false to true (for increasing predicates, and the other way
6763 // around for decreasing predicates), all we care about is that *if* the
6764 // predicate changes then it only changes from false to true.
6766 // A zero step value in itself is not very useful, but there may be places
6767 // where SCEV can prove X >= 0 but not prove X > 0, so it is helpful to be
6768 // as general as possible.
6770 if (isKnownNonNegative(LHS->getStepRecurrence(*this))) {
6771 Increasing = IncreasingOnNonNegativeStep;
6775 if (isKnownNonPositive(LHS->getStepRecurrence(*this))) {
6776 Increasing = !IncreasingOnNonNegativeStep;
6783 bool ScalarEvolution::isLoopInvariantPredicate(
6784 ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS, const Loop *L,
6785 ICmpInst::Predicate &InvariantPred, const SCEV *&InvariantLHS,
6786 const SCEV *&InvariantRHS) {
6788 // If there is a loop-invariant, force it into the RHS, otherwise bail out.
6789 if (!isLoopInvariant(RHS, L)) {
6790 if (!isLoopInvariant(LHS, L))
6793 std::swap(LHS, RHS);
6794 Pred = ICmpInst::getSwappedPredicate(Pred);
6797 const SCEVAddRecExpr *ArLHS = dyn_cast<SCEVAddRecExpr>(LHS);
6798 if (!ArLHS || ArLHS->getLoop() != L)
6802 if (!isMonotonicPredicate(ArLHS, Pred, Increasing))
6805 // If the predicate "ArLHS `Pred` RHS" monotonically increases from false to
6806 // true as the loop iterates, and the backedge is control dependent on
6807 // "ArLHS `Pred` RHS" == true then we can reason as follows:
6809 // * if the predicate was false in the first iteration then the predicate
6810 // is never evaluated again, since the loop exits without taking the
6812 // * if the predicate was true in the first iteration then it will
6813 // continue to be true for all future iterations since it is
6814 // monotonically increasing.
6816 // For both the above possibilities, we can replace the loop varying
6817 // predicate with its value on the first iteration of the loop (which is
6820 // A similar reasoning applies for a monotonically decreasing predicate, by
6821 // replacing true with false and false with true in the above two bullets.
6823 auto P = Increasing ? Pred : ICmpInst::getInversePredicate(Pred);
6825 if (!isLoopBackedgeGuardedByCond(L, P, LHS, RHS))
6828 InvariantPred = Pred;
6829 InvariantLHS = ArLHS->getStart();
6835 ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred,
6836 const SCEV *LHS, const SCEV *RHS) {
6837 if (HasSameValue(LHS, RHS))
6838 return ICmpInst::isTrueWhenEqual(Pred);
6840 // This code is split out from isKnownPredicate because it is called from
6841 // within isLoopEntryGuardedByCond.
6844 llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6845 case ICmpInst::ICMP_SGT:
6846 std::swap(LHS, RHS);
6847 case ICmpInst::ICMP_SLT: {
6848 ConstantRange LHSRange = getSignedRange(LHS);
6849 ConstantRange RHSRange = getSignedRange(RHS);
6850 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
6852 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
6856 case ICmpInst::ICMP_SGE:
6857 std::swap(LHS, RHS);
6858 case ICmpInst::ICMP_SLE: {
6859 ConstantRange LHSRange = getSignedRange(LHS);
6860 ConstantRange RHSRange = getSignedRange(RHS);
6861 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
6863 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
6867 case ICmpInst::ICMP_UGT:
6868 std::swap(LHS, RHS);
6869 case ICmpInst::ICMP_ULT: {
6870 ConstantRange LHSRange = getUnsignedRange(LHS);
6871 ConstantRange RHSRange = getUnsignedRange(RHS);
6872 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
6874 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
6878 case ICmpInst::ICMP_UGE:
6879 std::swap(LHS, RHS);
6880 case ICmpInst::ICMP_ULE: {
6881 ConstantRange LHSRange = getUnsignedRange(LHS);
6882 ConstantRange RHSRange = getUnsignedRange(RHS);
6883 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
6885 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
6889 case ICmpInst::ICMP_NE: {
6890 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
6892 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
6895 const SCEV *Diff = getMinusSCEV(LHS, RHS);
6896 if (isKnownNonZero(Diff))
6900 case ICmpInst::ICMP_EQ:
6901 // The check at the top of the function catches the case where
6902 // the values are known to be equal.
6908 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
6909 /// protected by a conditional between LHS and RHS. This is used to
6910 /// to eliminate casts.
6912 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
6913 ICmpInst::Predicate Pred,
6914 const SCEV *LHS, const SCEV *RHS) {
6915 // Interpret a null as meaning no loop, where there is obviously no guard
6916 // (interprocedural conditions notwithstanding).
6917 if (!L) return true;
6919 if (isKnownPredicateWithRanges(Pred, LHS, RHS)) return true;
6921 BasicBlock *Latch = L->getLoopLatch();
6925 BranchInst *LoopContinuePredicate =
6926 dyn_cast<BranchInst>(Latch->getTerminator());
6927 if (LoopContinuePredicate && LoopContinuePredicate->isConditional() &&
6928 isImpliedCond(Pred, LHS, RHS,
6929 LoopContinuePredicate->getCondition(),
6930 LoopContinuePredicate->getSuccessor(0) != L->getHeader()))
6933 // Check conditions due to any @llvm.assume intrinsics.
6934 for (auto &AssumeVH : AC->assumptions()) {
6937 auto *CI = cast<CallInst>(AssumeVH);
6938 if (!DT->dominates(CI, Latch->getTerminator()))
6941 if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false))
6945 struct ClearWalkingBEDominatingCondsOnExit {
6946 ScalarEvolution &SE;
6948 explicit ClearWalkingBEDominatingCondsOnExit(ScalarEvolution &SE)
6951 ~ClearWalkingBEDominatingCondsOnExit() {
6952 SE.WalkingBEDominatingConds = false;
6956 // We don't want more than one activation of the following loop on the stack
6957 // -- that can lead to O(n!) time complexity.
6958 if (WalkingBEDominatingConds)
6961 WalkingBEDominatingConds = true;
6962 ClearWalkingBEDominatingCondsOnExit ClearOnExit(*this);
6964 // If the loop is not reachable from the entry block, we risk running into an
6965 // infinite loop as we walk up into the dom tree. These loops do not matter
6966 // anyway, so we just return a conservative answer when we see them.
6967 if (!DT->isReachableFromEntry(L->getHeader()))
6970 for (DomTreeNode *DTN = (*DT)[Latch], *HeaderDTN = (*DT)[L->getHeader()];
6972 DTN = DTN->getIDom()) {
6974 assert(DTN && "should reach the loop header before reaching the root!");
6976 BasicBlock *BB = DTN->getBlock();
6977 BasicBlock *PBB = BB->getSinglePredecessor();
6981 BranchInst *ContinuePredicate = dyn_cast<BranchInst>(PBB->getTerminator());
6982 if (!ContinuePredicate || !ContinuePredicate->isConditional())
6985 Value *Condition = ContinuePredicate->getCondition();
6987 // If we have an edge `E` within the loop body that dominates the only
6988 // latch, the condition guarding `E` also guards the backedge. This
6989 // reasoning works only for loops with a single latch.
6991 BasicBlockEdge DominatingEdge(PBB, BB);
6992 if (DominatingEdge.isSingleEdge()) {
6993 // We're constructively (and conservatively) enumerating edges within the
6994 // loop body that dominate the latch. The dominator tree better agree
6996 assert(DT->dominates(DominatingEdge, Latch) && "should be!");
6998 if (isImpliedCond(Pred, LHS, RHS, Condition,
6999 BB != ContinuePredicate->getSuccessor(0)))
7007 /// isLoopEntryGuardedByCond - Test whether entry to the loop is protected
7008 /// by a conditional between LHS and RHS. This is used to help avoid max
7009 /// expressions in loop trip counts, and to eliminate casts.
7011 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
7012 ICmpInst::Predicate Pred,
7013 const SCEV *LHS, const SCEV *RHS) {
7014 // Interpret a null as meaning no loop, where there is obviously no guard
7015 // (interprocedural conditions notwithstanding).
7016 if (!L) return false;
7018 if (isKnownPredicateWithRanges(Pred, LHS, RHS)) return true;
7020 // Starting at the loop predecessor, climb up the predecessor chain, as long
7021 // as there are predecessors that can be found that have unique successors
7022 // leading to the original header.
7023 for (std::pair<BasicBlock *, BasicBlock *>
7024 Pair(L->getLoopPredecessor(), L->getHeader());
7026 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
7028 BranchInst *LoopEntryPredicate =
7029 dyn_cast<BranchInst>(Pair.first->getTerminator());
7030 if (!LoopEntryPredicate ||
7031 LoopEntryPredicate->isUnconditional())
7034 if (isImpliedCond(Pred, LHS, RHS,
7035 LoopEntryPredicate->getCondition(),
7036 LoopEntryPredicate->getSuccessor(0) != Pair.second))
7040 // Check conditions due to any @llvm.assume intrinsics.
7041 for (auto &AssumeVH : AC->assumptions()) {
7044 auto *CI = cast<CallInst>(AssumeVH);
7045 if (!DT->dominates(CI, L->getHeader()))
7048 if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false))
7055 /// RAII wrapper to prevent recursive application of isImpliedCond.
7056 /// ScalarEvolution's PendingLoopPredicates set must be empty unless we are
7057 /// currently evaluating isImpliedCond.
7058 struct MarkPendingLoopPredicate {
7060 DenseSet<Value*> &LoopPreds;
7063 MarkPendingLoopPredicate(Value *C, DenseSet<Value*> &LP)
7064 : Cond(C), LoopPreds(LP) {
7065 Pending = !LoopPreds.insert(Cond).second;
7067 ~MarkPendingLoopPredicate() {
7069 LoopPreds.erase(Cond);
7073 /// isImpliedCond - Test whether the condition described by Pred, LHS,
7074 /// and RHS is true whenever the given Cond value evaluates to true.
7075 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred,
7076 const SCEV *LHS, const SCEV *RHS,
7077 Value *FoundCondValue,
7079 MarkPendingLoopPredicate Mark(FoundCondValue, PendingLoopPredicates);
7083 // Recursively handle And and Or conditions.
7084 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) {
7085 if (BO->getOpcode() == Instruction::And) {
7087 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
7088 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
7089 } else if (BO->getOpcode() == Instruction::Or) {
7091 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
7092 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
7096 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue);
7097 if (!ICI) return false;
7099 // Now that we found a conditional branch that dominates the loop or controls
7100 // the loop latch. Check to see if it is the comparison we are looking for.
7101 ICmpInst::Predicate FoundPred;
7103 FoundPred = ICI->getInversePredicate();
7105 FoundPred = ICI->getPredicate();
7107 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
7108 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
7110 // Balance the types.
7111 if (getTypeSizeInBits(LHS->getType()) <
7112 getTypeSizeInBits(FoundLHS->getType())) {
7113 if (CmpInst::isSigned(Pred)) {
7114 LHS = getSignExtendExpr(LHS, FoundLHS->getType());
7115 RHS = getSignExtendExpr(RHS, FoundLHS->getType());
7117 LHS = getZeroExtendExpr(LHS, FoundLHS->getType());
7118 RHS = getZeroExtendExpr(RHS, FoundLHS->getType());
7120 } else if (getTypeSizeInBits(LHS->getType()) >
7121 getTypeSizeInBits(FoundLHS->getType())) {
7122 if (CmpInst::isSigned(FoundPred)) {
7123 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
7124 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
7126 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
7127 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
7131 // Canonicalize the query to match the way instcombine will have
7132 // canonicalized the comparison.
7133 if (SimplifyICmpOperands(Pred, LHS, RHS))
7135 return CmpInst::isTrueWhenEqual(Pred);
7136 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
7137 if (FoundLHS == FoundRHS)
7138 return CmpInst::isFalseWhenEqual(FoundPred);
7140 // Check to see if we can make the LHS or RHS match.
7141 if (LHS == FoundRHS || RHS == FoundLHS) {
7142 if (isa<SCEVConstant>(RHS)) {
7143 std::swap(FoundLHS, FoundRHS);
7144 FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
7146 std::swap(LHS, RHS);
7147 Pred = ICmpInst::getSwappedPredicate(Pred);
7151 // Check whether the found predicate is the same as the desired predicate.
7152 if (FoundPred == Pred)
7153 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
7155 // Check whether swapping the found predicate makes it the same as the
7156 // desired predicate.
7157 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
7158 if (isa<SCEVConstant>(RHS))
7159 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
7161 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
7162 RHS, LHS, FoundLHS, FoundRHS);
7165 // Check if we can make progress by sharpening ranges.
7166 if (FoundPred == ICmpInst::ICMP_NE &&
7167 (isa<SCEVConstant>(FoundLHS) || isa<SCEVConstant>(FoundRHS))) {
7169 const SCEVConstant *C = nullptr;
7170 const SCEV *V = nullptr;
7172 if (isa<SCEVConstant>(FoundLHS)) {
7173 C = cast<SCEVConstant>(FoundLHS);
7176 C = cast<SCEVConstant>(FoundRHS);
7180 // The guarding predicate tells us that C != V. If the known range
7181 // of V is [C, t), we can sharpen the range to [C + 1, t). The
7182 // range we consider has to correspond to same signedness as the
7183 // predicate we're interested in folding.
7185 APInt Min = ICmpInst::isSigned(Pred) ?
7186 getSignedRange(V).getSignedMin() : getUnsignedRange(V).getUnsignedMin();
7188 if (Min == C->getValue()->getValue()) {
7189 // Given (V >= Min && V != Min) we conclude V >= (Min + 1).
7190 // This is true even if (Min + 1) wraps around -- in case of
7191 // wraparound, (Min + 1) < Min, so (V >= Min => V >= (Min + 1)).
7193 APInt SharperMin = Min + 1;
7196 case ICmpInst::ICMP_SGE:
7197 case ICmpInst::ICMP_UGE:
7198 // We know V `Pred` SharperMin. If this implies LHS `Pred`
7200 if (isImpliedCondOperands(Pred, LHS, RHS, V,
7201 getConstant(SharperMin)))
7204 case ICmpInst::ICMP_SGT:
7205 case ICmpInst::ICMP_UGT:
7206 // We know from the range information that (V `Pred` Min ||
7207 // V == Min). We know from the guarding condition that !(V
7208 // == Min). This gives us
7210 // V `Pred` Min || V == Min && !(V == Min)
7213 // If V `Pred` Min implies LHS `Pred` RHS, we're done.
7215 if (isImpliedCondOperands(Pred, LHS, RHS, V, getConstant(Min)))
7225 // Check whether the actual condition is beyond sufficient.
7226 if (FoundPred == ICmpInst::ICMP_EQ)
7227 if (ICmpInst::isTrueWhenEqual(Pred))
7228 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
7230 if (Pred == ICmpInst::ICMP_NE)
7231 if (!ICmpInst::isTrueWhenEqual(FoundPred))
7232 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
7235 // Otherwise assume the worst.
7239 /// isImpliedCondOperands - Test whether the condition described by Pred,
7240 /// LHS, and RHS is true whenever the condition described by Pred, FoundLHS,
7241 /// and FoundRHS is true.
7242 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
7243 const SCEV *LHS, const SCEV *RHS,
7244 const SCEV *FoundLHS,
7245 const SCEV *FoundRHS) {
7246 if (isImpliedCondOperandsViaRanges(Pred, LHS, RHS, FoundLHS, FoundRHS))
7249 return isImpliedCondOperandsHelper(Pred, LHS, RHS,
7250 FoundLHS, FoundRHS) ||
7251 // ~x < ~y --> x > y
7252 isImpliedCondOperandsHelper(Pred, LHS, RHS,
7253 getNotSCEV(FoundRHS),
7254 getNotSCEV(FoundLHS));
7258 /// If Expr computes ~A, return A else return nullptr
7259 static const SCEV *MatchNotExpr(const SCEV *Expr) {
7260 const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Expr);
7261 if (!Add || Add->getNumOperands() != 2) return nullptr;
7263 const SCEVConstant *AddLHS = dyn_cast<SCEVConstant>(Add->getOperand(0));
7264 if (!(AddLHS && AddLHS->getValue()->getValue().isAllOnesValue()))
7267 const SCEVMulExpr *AddRHS = dyn_cast<SCEVMulExpr>(Add->getOperand(1));
7268 if (!AddRHS || AddRHS->getNumOperands() != 2) return nullptr;
7270 const SCEVConstant *MulLHS = dyn_cast<SCEVConstant>(AddRHS->getOperand(0));
7271 if (!(MulLHS && MulLHS->getValue()->getValue().isAllOnesValue()))
7274 return AddRHS->getOperand(1);
7278 /// Is MaybeMaxExpr an SMax or UMax of Candidate and some other values?
7279 template<typename MaxExprType>
7280 static bool IsMaxConsistingOf(const SCEV *MaybeMaxExpr,
7281 const SCEV *Candidate) {
7282 const MaxExprType *MaxExpr = dyn_cast<MaxExprType>(MaybeMaxExpr);
7283 if (!MaxExpr) return false;
7285 auto It = std::find(MaxExpr->op_begin(), MaxExpr->op_end(), Candidate);
7286 return It != MaxExpr->op_end();
7290 /// Is MaybeMinExpr an SMin or UMin of Candidate and some other values?
7291 template<typename MaxExprType>
7292 static bool IsMinConsistingOf(ScalarEvolution &SE,
7293 const SCEV *MaybeMinExpr,
7294 const SCEV *Candidate) {
7295 const SCEV *MaybeMaxExpr = MatchNotExpr(MaybeMinExpr);
7299 return IsMaxConsistingOf<MaxExprType>(MaybeMaxExpr, SE.getNotSCEV(Candidate));
7303 /// Is LHS `Pred` RHS true on the virtue of LHS or RHS being a Min or Max
7305 static bool IsKnownPredicateViaMinOrMax(ScalarEvolution &SE,
7306 ICmpInst::Predicate Pred,
7307 const SCEV *LHS, const SCEV *RHS) {
7312 case ICmpInst::ICMP_SGE:
7313 std::swap(LHS, RHS);
7315 case ICmpInst::ICMP_SLE:
7318 IsMinConsistingOf<SCEVSMaxExpr>(SE, LHS, RHS) ||
7320 IsMaxConsistingOf<SCEVSMaxExpr>(RHS, LHS);
7322 case ICmpInst::ICMP_UGE:
7323 std::swap(LHS, RHS);
7325 case ICmpInst::ICMP_ULE:
7328 IsMinConsistingOf<SCEVUMaxExpr>(SE, LHS, RHS) ||
7330 IsMaxConsistingOf<SCEVUMaxExpr>(RHS, LHS);
7333 llvm_unreachable("covered switch fell through?!");
7336 /// isImpliedCondOperandsHelper - Test whether the condition described by
7337 /// Pred, LHS, and RHS is true whenever the condition described by Pred,
7338 /// FoundLHS, and FoundRHS is true.
7340 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
7341 const SCEV *LHS, const SCEV *RHS,
7342 const SCEV *FoundLHS,
7343 const SCEV *FoundRHS) {
7344 auto IsKnownPredicateFull =
7345 [this](ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS) {
7346 return isKnownPredicateWithRanges(Pred, LHS, RHS) ||
7347 IsKnownPredicateViaMinOrMax(*this, Pred, LHS, RHS);
7351 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
7352 case ICmpInst::ICMP_EQ:
7353 case ICmpInst::ICMP_NE:
7354 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
7357 case ICmpInst::ICMP_SLT:
7358 case ICmpInst::ICMP_SLE:
7359 if (IsKnownPredicateFull(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
7360 IsKnownPredicateFull(ICmpInst::ICMP_SGE, RHS, FoundRHS))
7363 case ICmpInst::ICMP_SGT:
7364 case ICmpInst::ICMP_SGE:
7365 if (IsKnownPredicateFull(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
7366 IsKnownPredicateFull(ICmpInst::ICMP_SLE, RHS, FoundRHS))
7369 case ICmpInst::ICMP_ULT:
7370 case ICmpInst::ICMP_ULE:
7371 if (IsKnownPredicateFull(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
7372 IsKnownPredicateFull(ICmpInst::ICMP_UGE, RHS, FoundRHS))
7375 case ICmpInst::ICMP_UGT:
7376 case ICmpInst::ICMP_UGE:
7377 if (IsKnownPredicateFull(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
7378 IsKnownPredicateFull(ICmpInst::ICMP_ULE, RHS, FoundRHS))
7386 /// isImpliedCondOperandsViaRanges - helper function for isImpliedCondOperands.
7387 /// Tries to get cases like "X `sgt` 0 => X - 1 `sgt` -1".
7388 bool ScalarEvolution::isImpliedCondOperandsViaRanges(ICmpInst::Predicate Pred,
7391 const SCEV *FoundLHS,
7392 const SCEV *FoundRHS) {
7393 if (!isa<SCEVConstant>(RHS) || !isa<SCEVConstant>(FoundRHS))
7394 // The restriction on `FoundRHS` be lifted easily -- it exists only to
7395 // reduce the compile time impact of this optimization.
7398 const SCEVAddExpr *AddLHS = dyn_cast<SCEVAddExpr>(LHS);
7399 if (!AddLHS || AddLHS->getOperand(1) != FoundLHS ||
7400 !isa<SCEVConstant>(AddLHS->getOperand(0)))
7403 APInt ConstFoundRHS = cast<SCEVConstant>(FoundRHS)->getValue()->getValue();
7405 // `FoundLHSRange` is the range we know `FoundLHS` to be in by virtue of the
7406 // antecedent "`FoundLHS` `Pred` `FoundRHS`".
7407 ConstantRange FoundLHSRange =
7408 ConstantRange::makeAllowedICmpRegion(Pred, ConstFoundRHS);
7410 // Since `LHS` is `FoundLHS` + `AddLHS->getOperand(0)`, we can compute a range
7413 cast<SCEVConstant>(AddLHS->getOperand(0))->getValue()->getValue();
7414 ConstantRange LHSRange = FoundLHSRange.add(ConstantRange(Addend));
7416 // We can also compute the range of values for `LHS` that satisfy the
7417 // consequent, "`LHS` `Pred` `RHS`":
7418 APInt ConstRHS = cast<SCEVConstant>(RHS)->getValue()->getValue();
7419 ConstantRange SatisfyingLHSRange =
7420 ConstantRange::makeSatisfyingICmpRegion(Pred, ConstRHS);
7422 // The antecedent implies the consequent if every value of `LHS` that
7423 // satisfies the antecedent also satisfies the consequent.
7424 return SatisfyingLHSRange.contains(LHSRange);
7427 // Verify if an linear IV with positive stride can overflow when in a
7428 // less-than comparison, knowing the invariant term of the comparison, the
7429 // stride and the knowledge of NSW/NUW flags on the recurrence.
7430 bool ScalarEvolution::doesIVOverflowOnLT(const SCEV *RHS, const SCEV *Stride,
7431 bool IsSigned, bool NoWrap) {
7432 if (NoWrap) return false;
7434 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
7435 const SCEV *One = getConstant(Stride->getType(), 1);
7438 APInt MaxRHS = getSignedRange(RHS).getSignedMax();
7439 APInt MaxValue = APInt::getSignedMaxValue(BitWidth);
7440 APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
7443 // SMaxRHS + SMaxStrideMinusOne > SMaxValue => overflow!
7444 return (MaxValue - MaxStrideMinusOne).slt(MaxRHS);
7447 APInt MaxRHS = getUnsignedRange(RHS).getUnsignedMax();
7448 APInt MaxValue = APInt::getMaxValue(BitWidth);
7449 APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
7452 // UMaxRHS + UMaxStrideMinusOne > UMaxValue => overflow!
7453 return (MaxValue - MaxStrideMinusOne).ult(MaxRHS);
7456 // Verify if an linear IV with negative stride can overflow when in a
7457 // greater-than comparison, knowing the invariant term of the comparison,
7458 // the stride and the knowledge of NSW/NUW flags on the recurrence.
7459 bool ScalarEvolution::doesIVOverflowOnGT(const SCEV *RHS, const SCEV *Stride,
7460 bool IsSigned, bool NoWrap) {
7461 if (NoWrap) return false;
7463 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
7464 const SCEV *One = getConstant(Stride->getType(), 1);
7467 APInt MinRHS = getSignedRange(RHS).getSignedMin();
7468 APInt MinValue = APInt::getSignedMinValue(BitWidth);
7469 APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
7472 // SMinRHS - SMaxStrideMinusOne < SMinValue => overflow!
7473 return (MinValue + MaxStrideMinusOne).sgt(MinRHS);
7476 APInt MinRHS = getUnsignedRange(RHS).getUnsignedMin();
7477 APInt MinValue = APInt::getMinValue(BitWidth);
7478 APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
7481 // UMinRHS - UMaxStrideMinusOne < UMinValue => overflow!
7482 return (MinValue + MaxStrideMinusOne).ugt(MinRHS);
7485 // Compute the backedge taken count knowing the interval difference, the
7486 // stride and presence of the equality in the comparison.
7487 const SCEV *ScalarEvolution::computeBECount(const SCEV *Delta, const SCEV *Step,
7489 const SCEV *One = getConstant(Step->getType(), 1);
7490 Delta = Equality ? getAddExpr(Delta, Step)
7491 : getAddExpr(Delta, getMinusSCEV(Step, One));
7492 return getUDivExpr(Delta, Step);
7495 /// HowManyLessThans - Return the number of times a backedge containing the
7496 /// specified less-than comparison will execute. If not computable, return
7497 /// CouldNotCompute.
7499 /// @param ControlsExit is true when the LHS < RHS condition directly controls
7500 /// the branch (loops exits only if condition is true). In this case, we can use
7501 /// NoWrapFlags to skip overflow checks.
7502 ScalarEvolution::ExitLimit
7503 ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
7504 const Loop *L, bool IsSigned,
7505 bool ControlsExit) {
7506 // We handle only IV < Invariant
7507 if (!isLoopInvariant(RHS, L))
7508 return getCouldNotCompute();
7510 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
7512 // Avoid weird loops
7513 if (!IV || IV->getLoop() != L || !IV->isAffine())
7514 return getCouldNotCompute();
7516 bool NoWrap = ControlsExit &&
7517 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
7519 const SCEV *Stride = IV->getStepRecurrence(*this);
7521 // Avoid negative or zero stride values
7522 if (!isKnownPositive(Stride))
7523 return getCouldNotCompute();
7525 // Avoid proven overflow cases: this will ensure that the backedge taken count
7526 // will not generate any unsigned overflow. Relaxed no-overflow conditions
7527 // exploit NoWrapFlags, allowing to optimize in presence of undefined
7528 // behaviors like the case of C language.
7529 if (!Stride->isOne() && doesIVOverflowOnLT(RHS, Stride, IsSigned, NoWrap))
7530 return getCouldNotCompute();
7532 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SLT
7533 : ICmpInst::ICMP_ULT;
7534 const SCEV *Start = IV->getStart();
7535 const SCEV *End = RHS;
7536 if (!isLoopEntryGuardedByCond(L, Cond, getMinusSCEV(Start, Stride), RHS)) {
7537 const SCEV *Diff = getMinusSCEV(RHS, Start);
7538 // If we have NoWrap set, then we can assume that the increment won't
7539 // overflow, in which case if RHS - Start is a constant, we don't need to
7540 // do a max operation since we can just figure it out statically
7541 if (NoWrap && isa<SCEVConstant>(Diff)) {
7542 APInt D = dyn_cast<const SCEVConstant>(Diff)->getValue()->getValue();
7546 End = IsSigned ? getSMaxExpr(RHS, Start)
7547 : getUMaxExpr(RHS, Start);
7550 const SCEV *BECount = computeBECount(getMinusSCEV(End, Start), Stride, false);
7552 APInt MinStart = IsSigned ? getSignedRange(Start).getSignedMin()
7553 : getUnsignedRange(Start).getUnsignedMin();
7555 APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
7556 : getUnsignedRange(Stride).getUnsignedMin();
7558 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
7559 APInt Limit = IsSigned ? APInt::getSignedMaxValue(BitWidth) - (MinStride - 1)
7560 : APInt::getMaxValue(BitWidth) - (MinStride - 1);
7562 // Although End can be a MAX expression we estimate MaxEnd considering only
7563 // the case End = RHS. This is safe because in the other case (End - Start)
7564 // is zero, leading to a zero maximum backedge taken count.
7566 IsSigned ? APIntOps::smin(getSignedRange(RHS).getSignedMax(), Limit)
7567 : APIntOps::umin(getUnsignedRange(RHS).getUnsignedMax(), Limit);
7569 const SCEV *MaxBECount;
7570 if (isa<SCEVConstant>(BECount))
7571 MaxBECount = BECount;
7573 MaxBECount = computeBECount(getConstant(MaxEnd - MinStart),
7574 getConstant(MinStride), false);
7576 if (isa<SCEVCouldNotCompute>(MaxBECount))
7577 MaxBECount = BECount;
7579 return ExitLimit(BECount, MaxBECount);
7582 ScalarEvolution::ExitLimit
7583 ScalarEvolution::HowManyGreaterThans(const SCEV *LHS, const SCEV *RHS,
7584 const Loop *L, bool IsSigned,
7585 bool ControlsExit) {
7586 // We handle only IV > Invariant
7587 if (!isLoopInvariant(RHS, L))
7588 return getCouldNotCompute();
7590 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
7592 // Avoid weird loops
7593 if (!IV || IV->getLoop() != L || !IV->isAffine())
7594 return getCouldNotCompute();
7596 bool NoWrap = ControlsExit &&
7597 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
7599 const SCEV *Stride = getNegativeSCEV(IV->getStepRecurrence(*this));
7601 // Avoid negative or zero stride values
7602 if (!isKnownPositive(Stride))
7603 return getCouldNotCompute();
7605 // Avoid proven overflow cases: this will ensure that the backedge taken count
7606 // will not generate any unsigned overflow. Relaxed no-overflow conditions
7607 // exploit NoWrapFlags, allowing to optimize in presence of undefined
7608 // behaviors like the case of C language.
7609 if (!Stride->isOne() && doesIVOverflowOnGT(RHS, Stride, IsSigned, NoWrap))
7610 return getCouldNotCompute();
7612 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SGT
7613 : ICmpInst::ICMP_UGT;
7615 const SCEV *Start = IV->getStart();
7616 const SCEV *End = RHS;
7617 if (!isLoopEntryGuardedByCond(L, Cond, getAddExpr(Start, Stride), RHS)) {
7618 const SCEV *Diff = getMinusSCEV(RHS, Start);
7619 // If we have NoWrap set, then we can assume that the increment won't
7620 // overflow, in which case if RHS - Start is a constant, we don't need to
7621 // do a max operation since we can just figure it out statically
7622 if (NoWrap && isa<SCEVConstant>(Diff)) {
7623 APInt D = dyn_cast<const SCEVConstant>(Diff)->getValue()->getValue();
7624 if (!D.isNegative())
7627 End = IsSigned ? getSMinExpr(RHS, Start)
7628 : getUMinExpr(RHS, Start);
7631 const SCEV *BECount = computeBECount(getMinusSCEV(Start, End), Stride, false);
7633 APInt MaxStart = IsSigned ? getSignedRange(Start).getSignedMax()
7634 : getUnsignedRange(Start).getUnsignedMax();
7636 APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
7637 : getUnsignedRange(Stride).getUnsignedMin();
7639 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
7640 APInt Limit = IsSigned ? APInt::getSignedMinValue(BitWidth) + (MinStride - 1)
7641 : APInt::getMinValue(BitWidth) + (MinStride - 1);
7643 // Although End can be a MIN expression we estimate MinEnd considering only
7644 // the case End = RHS. This is safe because in the other case (Start - End)
7645 // is zero, leading to a zero maximum backedge taken count.
7647 IsSigned ? APIntOps::smax(getSignedRange(RHS).getSignedMin(), Limit)
7648 : APIntOps::umax(getUnsignedRange(RHS).getUnsignedMin(), Limit);
7651 const SCEV *MaxBECount = getCouldNotCompute();
7652 if (isa<SCEVConstant>(BECount))
7653 MaxBECount = BECount;
7655 MaxBECount = computeBECount(getConstant(MaxStart - MinEnd),
7656 getConstant(MinStride), false);
7658 if (isa<SCEVCouldNotCompute>(MaxBECount))
7659 MaxBECount = BECount;
7661 return ExitLimit(BECount, MaxBECount);
7664 /// getNumIterationsInRange - Return the number of iterations of this loop that
7665 /// produce values in the specified constant range. Another way of looking at
7666 /// this is that it returns the first iteration number where the value is not in
7667 /// the condition, thus computing the exit count. If the iteration count can't
7668 /// be computed, an instance of SCEVCouldNotCompute is returned.
7669 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
7670 ScalarEvolution &SE) const {
7671 if (Range.isFullSet()) // Infinite loop.
7672 return SE.getCouldNotCompute();
7674 // If the start is a non-zero constant, shift the range to simplify things.
7675 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
7676 if (!SC->getValue()->isZero()) {
7677 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
7678 Operands[0] = SE.getConstant(SC->getType(), 0);
7679 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(),
7680 getNoWrapFlags(FlagNW));
7681 if (const SCEVAddRecExpr *ShiftedAddRec =
7682 dyn_cast<SCEVAddRecExpr>(Shifted))
7683 return ShiftedAddRec->getNumIterationsInRange(
7684 Range.subtract(SC->getValue()->getValue()), SE);
7685 // This is strange and shouldn't happen.
7686 return SE.getCouldNotCompute();
7689 // The only time we can solve this is when we have all constant indices.
7690 // Otherwise, we cannot determine the overflow conditions.
7691 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
7692 if (!isa<SCEVConstant>(getOperand(i)))
7693 return SE.getCouldNotCompute();
7696 // Okay at this point we know that all elements of the chrec are constants and
7697 // that the start element is zero.
7699 // First check to see if the range contains zero. If not, the first
7701 unsigned BitWidth = SE.getTypeSizeInBits(getType());
7702 if (!Range.contains(APInt(BitWidth, 0)))
7703 return SE.getConstant(getType(), 0);
7706 // If this is an affine expression then we have this situation:
7707 // Solve {0,+,A} in Range === Ax in Range
7709 // We know that zero is in the range. If A is positive then we know that
7710 // the upper value of the range must be the first possible exit value.
7711 // If A is negative then the lower of the range is the last possible loop
7712 // value. Also note that we already checked for a full range.
7713 APInt One(BitWidth,1);
7714 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
7715 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
7717 // The exit value should be (End+A)/A.
7718 APInt ExitVal = (End + A).udiv(A);
7719 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
7721 // Evaluate at the exit value. If we really did fall out of the valid
7722 // range, then we computed our trip count, otherwise wrap around or other
7723 // things must have happened.
7724 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
7725 if (Range.contains(Val->getValue()))
7726 return SE.getCouldNotCompute(); // Something strange happened
7728 // Ensure that the previous value is in the range. This is a sanity check.
7729 assert(Range.contains(
7730 EvaluateConstantChrecAtConstant(this,
7731 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
7732 "Linear scev computation is off in a bad way!");
7733 return SE.getConstant(ExitValue);
7734 } else if (isQuadratic()) {
7735 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
7736 // quadratic equation to solve it. To do this, we must frame our problem in
7737 // terms of figuring out when zero is crossed, instead of when
7738 // Range.getUpper() is crossed.
7739 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
7740 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
7741 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop(),
7742 // getNoWrapFlags(FlagNW)
7745 // Next, solve the constructed addrec
7746 std::pair<const SCEV *,const SCEV *> Roots =
7747 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
7748 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
7749 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
7751 // Pick the smallest positive root value.
7752 if (ConstantInt *CB =
7753 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
7754 R1->getValue(), R2->getValue()))) {
7755 if (!CB->getZExtValue())
7756 std::swap(R1, R2); // R1 is the minimum root now.
7758 // Make sure the root is not off by one. The returned iteration should
7759 // not be in the range, but the previous one should be. When solving
7760 // for "X*X < 5", for example, we should not return a root of 2.
7761 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
7764 if (Range.contains(R1Val->getValue())) {
7765 // The next iteration must be out of the range...
7766 ConstantInt *NextVal =
7767 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1);
7769 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
7770 if (!Range.contains(R1Val->getValue()))
7771 return SE.getConstant(NextVal);
7772 return SE.getCouldNotCompute(); // Something strange happened
7775 // If R1 was not in the range, then it is a good return value. Make
7776 // sure that R1-1 WAS in the range though, just in case.
7777 ConstantInt *NextVal =
7778 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1);
7779 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
7780 if (Range.contains(R1Val->getValue()))
7782 return SE.getCouldNotCompute(); // Something strange happened
7787 return SE.getCouldNotCompute();
7793 FindUndefs() : Found(false) {}
7795 bool follow(const SCEV *S) {
7796 if (const SCEVUnknown *C = dyn_cast<SCEVUnknown>(S)) {
7797 if (isa<UndefValue>(C->getValue()))
7799 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) {
7800 if (isa<UndefValue>(C->getValue()))
7804 // Keep looking if we haven't found it yet.
7807 bool isDone() const {
7808 // Stop recursion if we have found an undef.
7814 // Return true when S contains at least an undef value.
7816 containsUndefs(const SCEV *S) {
7818 SCEVTraversal<FindUndefs> ST(F);
7825 // Collect all steps of SCEV expressions.
7826 struct SCEVCollectStrides {
7827 ScalarEvolution &SE;
7828 SmallVectorImpl<const SCEV *> &Strides;
7830 SCEVCollectStrides(ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &S)
7831 : SE(SE), Strides(S) {}
7833 bool follow(const SCEV *S) {
7834 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(S))
7835 Strides.push_back(AR->getStepRecurrence(SE));
7838 bool isDone() const { return false; }
7841 // Collect all SCEVUnknown and SCEVMulExpr expressions.
7842 struct SCEVCollectTerms {
7843 SmallVectorImpl<const SCEV *> &Terms;
7845 SCEVCollectTerms(SmallVectorImpl<const SCEV *> &T)
7848 bool follow(const SCEV *S) {
7849 if (isa<SCEVUnknown>(S) || isa<SCEVMulExpr>(S)) {
7850 if (!containsUndefs(S))
7853 // Stop recursion: once we collected a term, do not walk its operands.
7860 bool isDone() const { return false; }
7864 /// Find parametric terms in this SCEVAddRecExpr.
7865 void ScalarEvolution::collectParametricTerms(const SCEV *Expr,
7866 SmallVectorImpl<const SCEV *> &Terms) {
7867 SmallVector<const SCEV *, 4> Strides;
7868 SCEVCollectStrides StrideCollector(*this, Strides);
7869 visitAll(Expr, StrideCollector);
7872 dbgs() << "Strides:\n";
7873 for (const SCEV *S : Strides)
7874 dbgs() << *S << "\n";
7877 for (const SCEV *S : Strides) {
7878 SCEVCollectTerms TermCollector(Terms);
7879 visitAll(S, TermCollector);
7883 dbgs() << "Terms:\n";
7884 for (const SCEV *T : Terms)
7885 dbgs() << *T << "\n";
7889 static bool findArrayDimensionsRec(ScalarEvolution &SE,
7890 SmallVectorImpl<const SCEV *> &Terms,
7891 SmallVectorImpl<const SCEV *> &Sizes) {
7892 int Last = Terms.size() - 1;
7893 const SCEV *Step = Terms[Last];
7895 // End of recursion.
7897 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Step)) {
7898 SmallVector<const SCEV *, 2> Qs;
7899 for (const SCEV *Op : M->operands())
7900 if (!isa<SCEVConstant>(Op))
7903 Step = SE.getMulExpr(Qs);
7906 Sizes.push_back(Step);
7910 for (const SCEV *&Term : Terms) {
7911 // Normalize the terms before the next call to findArrayDimensionsRec.
7913 SCEVDivision::divide(SE, Term, Step, &Q, &R);
7915 // Bail out when GCD does not evenly divide one of the terms.
7922 // Remove all SCEVConstants.
7923 Terms.erase(std::remove_if(Terms.begin(), Terms.end(), [](const SCEV *E) {
7924 return isa<SCEVConstant>(E);
7928 if (Terms.size() > 0)
7929 if (!findArrayDimensionsRec(SE, Terms, Sizes))
7932 Sizes.push_back(Step);
7937 struct FindParameter {
7938 bool FoundParameter;
7939 FindParameter() : FoundParameter(false) {}
7941 bool follow(const SCEV *S) {
7942 if (isa<SCEVUnknown>(S)) {
7943 FoundParameter = true;
7944 // Stop recursion: we found a parameter.
7950 bool isDone() const {
7951 // Stop recursion if we have found a parameter.
7952 return FoundParameter;
7957 // Returns true when S contains at least a SCEVUnknown parameter.
7959 containsParameters(const SCEV *S) {
7961 SCEVTraversal<FindParameter> ST(F);
7964 return F.FoundParameter;
7967 // Returns true when one of the SCEVs of Terms contains a SCEVUnknown parameter.
7969 containsParameters(SmallVectorImpl<const SCEV *> &Terms) {
7970 for (const SCEV *T : Terms)
7971 if (containsParameters(T))
7976 // Return the number of product terms in S.
7977 static inline int numberOfTerms(const SCEV *S) {
7978 if (const SCEVMulExpr *Expr = dyn_cast<SCEVMulExpr>(S))
7979 return Expr->getNumOperands();
7983 static const SCEV *removeConstantFactors(ScalarEvolution &SE, const SCEV *T) {
7984 if (isa<SCEVConstant>(T))
7987 if (isa<SCEVUnknown>(T))
7990 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(T)) {
7991 SmallVector<const SCEV *, 2> Factors;
7992 for (const SCEV *Op : M->operands())
7993 if (!isa<SCEVConstant>(Op))
7994 Factors.push_back(Op);
7996 return SE.getMulExpr(Factors);
8002 /// Return the size of an element read or written by Inst.
8003 const SCEV *ScalarEvolution::getElementSize(Instruction *Inst) {
8005 if (StoreInst *Store = dyn_cast<StoreInst>(Inst))
8006 Ty = Store->getValueOperand()->getType();
8007 else if (LoadInst *Load = dyn_cast<LoadInst>(Inst))
8008 Ty = Load->getType();
8012 Type *ETy = getEffectiveSCEVType(PointerType::getUnqual(Ty));
8013 return getSizeOfExpr(ETy, Ty);
8016 /// Second step of delinearization: compute the array dimensions Sizes from the
8017 /// set of Terms extracted from the memory access function of this SCEVAddRec.
8018 void ScalarEvolution::findArrayDimensions(SmallVectorImpl<const SCEV *> &Terms,
8019 SmallVectorImpl<const SCEV *> &Sizes,
8020 const SCEV *ElementSize) const {
8022 if (Terms.size() < 1 || !ElementSize)
8025 // Early return when Terms do not contain parameters: we do not delinearize
8026 // non parametric SCEVs.
8027 if (!containsParameters(Terms))
8031 dbgs() << "Terms:\n";
8032 for (const SCEV *T : Terms)
8033 dbgs() << *T << "\n";
8036 // Remove duplicates.
8037 std::sort(Terms.begin(), Terms.end());
8038 Terms.erase(std::unique(Terms.begin(), Terms.end()), Terms.end());
8040 // Put larger terms first.
8041 std::sort(Terms.begin(), Terms.end(), [](const SCEV *LHS, const SCEV *RHS) {
8042 return numberOfTerms(LHS) > numberOfTerms(RHS);
8045 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
8047 // Divide all terms by the element size.
8048 for (const SCEV *&Term : Terms) {
8050 SCEVDivision::divide(SE, Term, ElementSize, &Q, &R);
8054 SmallVector<const SCEV *, 4> NewTerms;
8056 // Remove constant factors.
8057 for (const SCEV *T : Terms)
8058 if (const SCEV *NewT = removeConstantFactors(SE, T))
8059 NewTerms.push_back(NewT);
8062 dbgs() << "Terms after sorting:\n";
8063 for (const SCEV *T : NewTerms)
8064 dbgs() << *T << "\n";
8067 if (NewTerms.empty() ||
8068 !findArrayDimensionsRec(SE, NewTerms, Sizes)) {
8073 // The last element to be pushed into Sizes is the size of an element.
8074 Sizes.push_back(ElementSize);
8077 dbgs() << "Sizes:\n";
8078 for (const SCEV *S : Sizes)
8079 dbgs() << *S << "\n";
8083 /// Third step of delinearization: compute the access functions for the
8084 /// Subscripts based on the dimensions in Sizes.
8085 void ScalarEvolution::computeAccessFunctions(
8086 const SCEV *Expr, SmallVectorImpl<const SCEV *> &Subscripts,
8087 SmallVectorImpl<const SCEV *> &Sizes) {
8089 // Early exit in case this SCEV is not an affine multivariate function.
8093 if (auto AR = dyn_cast<SCEVAddRecExpr>(Expr))
8094 if (!AR->isAffine())
8097 const SCEV *Res = Expr;
8098 int Last = Sizes.size() - 1;
8099 for (int i = Last; i >= 0; i--) {
8101 SCEVDivision::divide(*this, Res, Sizes[i], &Q, &R);
8104 dbgs() << "Res: " << *Res << "\n";
8105 dbgs() << "Sizes[i]: " << *Sizes[i] << "\n";
8106 dbgs() << "Res divided by Sizes[i]:\n";
8107 dbgs() << "Quotient: " << *Q << "\n";
8108 dbgs() << "Remainder: " << *R << "\n";
8113 // Do not record the last subscript corresponding to the size of elements in
8117 // Bail out if the remainder is too complex.
8118 if (isa<SCEVAddRecExpr>(R)) {
8127 // Record the access function for the current subscript.
8128 Subscripts.push_back(R);
8131 // Also push in last position the remainder of the last division: it will be
8132 // the access function of the innermost dimension.
8133 Subscripts.push_back(Res);
8135 std::reverse(Subscripts.begin(), Subscripts.end());
8138 dbgs() << "Subscripts:\n";
8139 for (const SCEV *S : Subscripts)
8140 dbgs() << *S << "\n";
8144 /// Splits the SCEV into two vectors of SCEVs representing the subscripts and
8145 /// sizes of an array access. Returns the remainder of the delinearization that
8146 /// is the offset start of the array. The SCEV->delinearize algorithm computes
8147 /// the multiples of SCEV coefficients: that is a pattern matching of sub
8148 /// expressions in the stride and base of a SCEV corresponding to the
8149 /// computation of a GCD (greatest common divisor) of base and stride. When
8150 /// SCEV->delinearize fails, it returns the SCEV unchanged.
8152 /// For example: when analyzing the memory access A[i][j][k] in this loop nest
8154 /// void foo(long n, long m, long o, double A[n][m][o]) {
8156 /// for (long i = 0; i < n; i++)
8157 /// for (long j = 0; j < m; j++)
8158 /// for (long k = 0; k < o; k++)
8159 /// A[i][j][k] = 1.0;
8162 /// the delinearization input is the following AddRec SCEV:
8164 /// AddRec: {{{%A,+,(8 * %m * %o)}<%for.i>,+,(8 * %o)}<%for.j>,+,8}<%for.k>
8166 /// From this SCEV, we are able to say that the base offset of the access is %A
8167 /// because it appears as an offset that does not divide any of the strides in
8170 /// CHECK: Base offset: %A
8172 /// and then SCEV->delinearize determines the size of some of the dimensions of
8173 /// the array as these are the multiples by which the strides are happening:
8175 /// CHECK: ArrayDecl[UnknownSize][%m][%o] with elements of sizeof(double) bytes.
8177 /// Note that the outermost dimension remains of UnknownSize because there are
8178 /// no strides that would help identifying the size of the last dimension: when
8179 /// the array has been statically allocated, one could compute the size of that
8180 /// dimension by dividing the overall size of the array by the size of the known
8181 /// dimensions: %m * %o * 8.
8183 /// Finally delinearize provides the access functions for the array reference
8184 /// that does correspond to A[i][j][k] of the above C testcase:
8186 /// CHECK: ArrayRef[{0,+,1}<%for.i>][{0,+,1}<%for.j>][{0,+,1}<%for.k>]
8188 /// The testcases are checking the output of a function pass:
8189 /// DelinearizationPass that walks through all loads and stores of a function
8190 /// asking for the SCEV of the memory access with respect to all enclosing
8191 /// loops, calling SCEV->delinearize on that and printing the results.
8193 void ScalarEvolution::delinearize(const SCEV *Expr,
8194 SmallVectorImpl<const SCEV *> &Subscripts,
8195 SmallVectorImpl<const SCEV *> &Sizes,
8196 const SCEV *ElementSize) {
8197 // First step: collect parametric terms.
8198 SmallVector<const SCEV *, 4> Terms;
8199 collectParametricTerms(Expr, Terms);
8204 // Second step: find subscript sizes.
8205 findArrayDimensions(Terms, Sizes, ElementSize);
8210 // Third step: compute the access functions for each subscript.
8211 computeAccessFunctions(Expr, Subscripts, Sizes);
8213 if (Subscripts.empty())
8217 dbgs() << "succeeded to delinearize " << *Expr << "\n";
8218 dbgs() << "ArrayDecl[UnknownSize]";
8219 for (const SCEV *S : Sizes)
8220 dbgs() << "[" << *S << "]";
8222 dbgs() << "\nArrayRef";
8223 for (const SCEV *S : Subscripts)
8224 dbgs() << "[" << *S << "]";
8229 //===----------------------------------------------------------------------===//
8230 // SCEVCallbackVH Class Implementation
8231 //===----------------------------------------------------------------------===//
8233 void ScalarEvolution::SCEVCallbackVH::deleted() {
8234 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
8235 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
8236 SE->ConstantEvolutionLoopExitValue.erase(PN);
8237 SE->ValueExprMap.erase(getValPtr());
8238 // this now dangles!
8241 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) {
8242 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
8244 // Forget all the expressions associated with users of the old value,
8245 // so that future queries will recompute the expressions using the new
8247 Value *Old = getValPtr();
8248 SmallVector<User *, 16> Worklist(Old->user_begin(), Old->user_end());
8249 SmallPtrSet<User *, 8> Visited;
8250 while (!Worklist.empty()) {
8251 User *U = Worklist.pop_back_val();
8252 // Deleting the Old value will cause this to dangle. Postpone
8253 // that until everything else is done.
8256 if (!Visited.insert(U).second)
8258 if (PHINode *PN = dyn_cast<PHINode>(U))
8259 SE->ConstantEvolutionLoopExitValue.erase(PN);
8260 SE->ValueExprMap.erase(U);
8261 Worklist.insert(Worklist.end(), U->user_begin(), U->user_end());
8263 // Delete the Old value.
8264 if (PHINode *PN = dyn_cast<PHINode>(Old))
8265 SE->ConstantEvolutionLoopExitValue.erase(PN);
8266 SE->ValueExprMap.erase(Old);
8267 // this now dangles!
8270 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
8271 : CallbackVH(V), SE(se) {}
8273 //===----------------------------------------------------------------------===//
8274 // ScalarEvolution Class Implementation
8275 //===----------------------------------------------------------------------===//
8277 ScalarEvolution::ScalarEvolution()
8278 : FunctionPass(ID), WalkingBEDominatingConds(false), ValuesAtScopes(64),
8279 LoopDispositions(64), BlockDispositions(64), FirstUnknown(nullptr) {
8280 initializeScalarEvolutionPass(*PassRegistry::getPassRegistry());
8283 bool ScalarEvolution::runOnFunction(Function &F) {
8285 AC = &getAnalysis<AssumptionCacheTracker>().getAssumptionCache(F);
8286 LI = &getAnalysis<LoopInfoWrapperPass>().getLoopInfo();
8287 TLI = &getAnalysis<TargetLibraryInfoWrapperPass>().getTLI();
8288 DT = &getAnalysis<DominatorTreeWrapperPass>().getDomTree();
8292 void ScalarEvolution::releaseMemory() {
8293 // Iterate through all the SCEVUnknown instances and call their
8294 // destructors, so that they release their references to their values.
8295 for (SCEVUnknown *U = FirstUnknown; U; U = U->Next)
8297 FirstUnknown = nullptr;
8299 ValueExprMap.clear();
8301 // Free any extra memory created for ExitNotTakenInfo in the unlikely event
8302 // that a loop had multiple computable exits.
8303 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
8304 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end();
8309 assert(PendingLoopPredicates.empty() && "isImpliedCond garbage");
8310 assert(!WalkingBEDominatingConds && "isLoopBackedgeGuardedByCond garbage!");
8312 BackedgeTakenCounts.clear();
8313 ConstantEvolutionLoopExitValue.clear();
8314 ValuesAtScopes.clear();
8315 LoopDispositions.clear();
8316 BlockDispositions.clear();
8317 UnsignedRanges.clear();
8318 SignedRanges.clear();
8319 UniqueSCEVs.clear();
8320 SCEVAllocator.Reset();
8323 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
8324 AU.setPreservesAll();
8325 AU.addRequiredTransitive<AssumptionCacheTracker>();
8326 AU.addRequiredTransitive<LoopInfoWrapperPass>();
8327 AU.addRequiredTransitive<DominatorTreeWrapperPass>();
8328 AU.addRequiredTransitive<TargetLibraryInfoWrapperPass>();
8331 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
8332 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
8335 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
8337 // Print all inner loops first
8338 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
8339 PrintLoopInfo(OS, SE, *I);
8342 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
8345 SmallVector<BasicBlock *, 8> ExitBlocks;
8346 L->getExitBlocks(ExitBlocks);
8347 if (ExitBlocks.size() != 1)
8348 OS << "<multiple exits> ";
8350 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
8351 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
8353 OS << "Unpredictable backedge-taken count. ";
8358 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
8361 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
8362 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
8364 OS << "Unpredictable max backedge-taken count. ";
8370 void ScalarEvolution::print(raw_ostream &OS, const Module *) const {
8371 // ScalarEvolution's implementation of the print method is to print
8372 // out SCEV values of all instructions that are interesting. Doing
8373 // this potentially causes it to create new SCEV objects though,
8374 // which technically conflicts with the const qualifier. This isn't
8375 // observable from outside the class though, so casting away the
8376 // const isn't dangerous.
8377 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
8379 OS << "Classifying expressions for: ";
8380 F->printAsOperand(OS, /*PrintType=*/false);
8382 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
8383 if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) {
8386 const SCEV *SV = SE.getSCEV(&*I);
8388 if (!isa<SCEVCouldNotCompute>(SV)) {
8390 SE.getUnsignedRange(SV).print(OS);
8392 SE.getSignedRange(SV).print(OS);
8395 const Loop *L = LI->getLoopFor((*I).getParent());
8397 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
8401 if (!isa<SCEVCouldNotCompute>(AtUse)) {
8403 SE.getUnsignedRange(AtUse).print(OS);
8405 SE.getSignedRange(AtUse).print(OS);
8410 OS << "\t\t" "Exits: ";
8411 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
8412 if (!SE.isLoopInvariant(ExitValue, L)) {
8413 OS << "<<Unknown>>";
8422 OS << "Determining loop execution counts for: ";
8423 F->printAsOperand(OS, /*PrintType=*/false);
8425 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
8426 PrintLoopInfo(OS, &SE, *I);
8429 ScalarEvolution::LoopDisposition
8430 ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) {
8431 auto &Values = LoopDispositions[S];
8432 for (auto &V : Values) {
8433 if (V.getPointer() == L)
8436 Values.emplace_back(L, LoopVariant);
8437 LoopDisposition D = computeLoopDisposition(S, L);
8438 auto &Values2 = LoopDispositions[S];
8439 for (auto &V : make_range(Values2.rbegin(), Values2.rend())) {
8440 if (V.getPointer() == L) {
8448 ScalarEvolution::LoopDisposition
8449 ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) {
8450 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
8452 return LoopInvariant;
8456 return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L);
8457 case scAddRecExpr: {
8458 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
8460 // If L is the addrec's loop, it's computable.
8461 if (AR->getLoop() == L)
8462 return LoopComputable;
8464 // Add recurrences are never invariant in the function-body (null loop).
8468 // This recurrence is variant w.r.t. L if L contains AR's loop.
8469 if (L->contains(AR->getLoop()))
8472 // This recurrence is invariant w.r.t. L if AR's loop contains L.
8473 if (AR->getLoop()->contains(L))
8474 return LoopInvariant;
8476 // This recurrence is variant w.r.t. L if any of its operands
8478 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
8480 if (!isLoopInvariant(*I, L))
8483 // Otherwise it's loop-invariant.
8484 return LoopInvariant;
8490 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
8491 bool HasVarying = false;
8492 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
8494 LoopDisposition D = getLoopDisposition(*I, L);
8495 if (D == LoopVariant)
8497 if (D == LoopComputable)
8500 return HasVarying ? LoopComputable : LoopInvariant;
8503 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
8504 LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L);
8505 if (LD == LoopVariant)
8507 LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L);
8508 if (RD == LoopVariant)
8510 return (LD == LoopInvariant && RD == LoopInvariant) ?
8511 LoopInvariant : LoopComputable;
8514 // All non-instruction values are loop invariant. All instructions are loop
8515 // invariant if they are not contained in the specified loop.
8516 // Instructions are never considered invariant in the function body
8517 // (null loop) because they are defined within the "loop".
8518 if (Instruction *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue()))
8519 return (L && !L->contains(I)) ? LoopInvariant : LoopVariant;
8520 return LoopInvariant;
8521 case scCouldNotCompute:
8522 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
8524 llvm_unreachable("Unknown SCEV kind!");
8527 bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) {
8528 return getLoopDisposition(S, L) == LoopInvariant;
8531 bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) {
8532 return getLoopDisposition(S, L) == LoopComputable;
8535 ScalarEvolution::BlockDisposition
8536 ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) {
8537 auto &Values = BlockDispositions[S];
8538 for (auto &V : Values) {
8539 if (V.getPointer() == BB)
8542 Values.emplace_back(BB, DoesNotDominateBlock);
8543 BlockDisposition D = computeBlockDisposition(S, BB);
8544 auto &Values2 = BlockDispositions[S];
8545 for (auto &V : make_range(Values2.rbegin(), Values2.rend())) {
8546 if (V.getPointer() == BB) {
8554 ScalarEvolution::BlockDisposition
8555 ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) {
8556 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
8558 return ProperlyDominatesBlock;
8562 return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB);
8563 case scAddRecExpr: {
8564 // This uses a "dominates" query instead of "properly dominates" query
8565 // to test for proper dominance too, because the instruction which
8566 // produces the addrec's value is a PHI, and a PHI effectively properly
8567 // dominates its entire containing block.
8568 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
8569 if (!DT->dominates(AR->getLoop()->getHeader(), BB))
8570 return DoesNotDominateBlock;
8572 // FALL THROUGH into SCEVNAryExpr handling.
8577 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
8579 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
8581 BlockDisposition D = getBlockDisposition(*I, BB);
8582 if (D == DoesNotDominateBlock)
8583 return DoesNotDominateBlock;
8584 if (D == DominatesBlock)
8587 return Proper ? ProperlyDominatesBlock : DominatesBlock;
8590 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
8591 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
8592 BlockDisposition LD = getBlockDisposition(LHS, BB);
8593 if (LD == DoesNotDominateBlock)
8594 return DoesNotDominateBlock;
8595 BlockDisposition RD = getBlockDisposition(RHS, BB);
8596 if (RD == DoesNotDominateBlock)
8597 return DoesNotDominateBlock;
8598 return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ?
8599 ProperlyDominatesBlock : DominatesBlock;
8602 if (Instruction *I =
8603 dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) {
8604 if (I->getParent() == BB)
8605 return DominatesBlock;
8606 if (DT->properlyDominates(I->getParent(), BB))
8607 return ProperlyDominatesBlock;
8608 return DoesNotDominateBlock;
8610 return ProperlyDominatesBlock;
8611 case scCouldNotCompute:
8612 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
8614 llvm_unreachable("Unknown SCEV kind!");
8617 bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) {
8618 return getBlockDisposition(S, BB) >= DominatesBlock;
8621 bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) {
8622 return getBlockDisposition(S, BB) == ProperlyDominatesBlock;
8626 // Search for a SCEV expression node within an expression tree.
8627 // Implements SCEVTraversal::Visitor.
8632 SCEVSearch(const SCEV *N): Node(N), IsFound(false) {}
8634 bool follow(const SCEV *S) {
8635 IsFound |= (S == Node);
8638 bool isDone() const { return IsFound; }
8642 bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const {
8643 SCEVSearch Search(Op);
8644 visitAll(S, Search);
8645 return Search.IsFound;
8648 void ScalarEvolution::forgetMemoizedResults(const SCEV *S) {
8649 ValuesAtScopes.erase(S);
8650 LoopDispositions.erase(S);
8651 BlockDispositions.erase(S);
8652 UnsignedRanges.erase(S);
8653 SignedRanges.erase(S);
8655 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
8656 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end(); I != E; ) {
8657 BackedgeTakenInfo &BEInfo = I->second;
8658 if (BEInfo.hasOperand(S, this)) {
8660 BackedgeTakenCounts.erase(I++);
8667 typedef DenseMap<const Loop *, std::string> VerifyMap;
8669 /// replaceSubString - Replaces all occurrences of From in Str with To.
8670 static void replaceSubString(std::string &Str, StringRef From, StringRef To) {
8672 while ((Pos = Str.find(From, Pos)) != std::string::npos) {
8673 Str.replace(Pos, From.size(), To.data(), To.size());
8678 /// getLoopBackedgeTakenCounts - Helper method for verifyAnalysis.
8680 getLoopBackedgeTakenCounts(Loop *L, VerifyMap &Map, ScalarEvolution &SE) {
8681 for (Loop::reverse_iterator I = L->rbegin(), E = L->rend(); I != E; ++I) {
8682 getLoopBackedgeTakenCounts(*I, Map, SE); // recurse.
8684 std::string &S = Map[L];
8686 raw_string_ostream OS(S);
8687 SE.getBackedgeTakenCount(L)->print(OS);
8689 // false and 0 are semantically equivalent. This can happen in dead loops.
8690 replaceSubString(OS.str(), "false", "0");
8691 // Remove wrap flags, their use in SCEV is highly fragile.
8692 // FIXME: Remove this when SCEV gets smarter about them.
8693 replaceSubString(OS.str(), "<nw>", "");
8694 replaceSubString(OS.str(), "<nsw>", "");
8695 replaceSubString(OS.str(), "<nuw>", "");
8700 void ScalarEvolution::verifyAnalysis() const {
8704 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
8706 // Gather stringified backedge taken counts for all loops using SCEV's caches.
8707 // FIXME: It would be much better to store actual values instead of strings,
8708 // but SCEV pointers will change if we drop the caches.
8709 VerifyMap BackedgeDumpsOld, BackedgeDumpsNew;
8710 for (LoopInfo::reverse_iterator I = LI->rbegin(), E = LI->rend(); I != E; ++I)
8711 getLoopBackedgeTakenCounts(*I, BackedgeDumpsOld, SE);
8713 // Gather stringified backedge taken counts for all loops without using
8716 for (LoopInfo::reverse_iterator I = LI->rbegin(), E = LI->rend(); I != E; ++I)
8717 getLoopBackedgeTakenCounts(*I, BackedgeDumpsNew, SE);
8719 // Now compare whether they're the same with and without caches. This allows
8720 // verifying that no pass changed the cache.
8721 assert(BackedgeDumpsOld.size() == BackedgeDumpsNew.size() &&
8722 "New loops suddenly appeared!");
8724 for (VerifyMap::iterator OldI = BackedgeDumpsOld.begin(),
8725 OldE = BackedgeDumpsOld.end(),
8726 NewI = BackedgeDumpsNew.begin();
8727 OldI != OldE; ++OldI, ++NewI) {
8728 assert(OldI->first == NewI->first && "Loop order changed!");
8730 // Compare the stringified SCEVs. We don't care if undef backedgetaken count
8732 // FIXME: We currently ignore SCEV changes from/to CouldNotCompute. This
8733 // means that a pass is buggy or SCEV has to learn a new pattern but is
8734 // usually not harmful.
8735 if (OldI->second != NewI->second &&
8736 OldI->second.find("undef") == std::string::npos &&
8737 NewI->second.find("undef") == std::string::npos &&
8738 OldI->second != "***COULDNOTCOMPUTE***" &&
8739 NewI->second != "***COULDNOTCOMPUTE***") {
8740 dbgs() << "SCEVValidator: SCEV for loop '"
8741 << OldI->first->getHeader()->getName()
8742 << "' changed from '" << OldI->second
8743 << "' to '" << NewI->second << "'!\n";
8748 // TODO: Verify more things.