1 //===- ScalarEvolution.cpp - Scalar Evolution Analysis --------------------===//
3 // The LLVM Compiler Infrastructure
5 // This file is distributed under the University of Illinois Open Source
6 // License. See LICENSE.TXT for details.
8 //===----------------------------------------------------------------------===//
10 // This file contains the implementation of the scalar evolution analysis
11 // engine, which is used primarily to analyze expressions involving induction
12 // variables in loops.
14 // There are several aspects to this library. First is the representation of
15 // scalar expressions, which are represented as subclasses of the SCEV class.
16 // These classes are used to represent certain types of subexpressions that we
17 // can handle. We only create one SCEV of a particular shape, so
18 // pointer-comparisons for equality are legal.
20 // One important aspect of the SCEV objects is that they are never cyclic, even
21 // if there is a cycle in the dataflow for an expression (ie, a PHI node). If
22 // the PHI node is one of the idioms that we can represent (e.g., a polynomial
23 // recurrence) then we represent it directly as a recurrence node, otherwise we
24 // represent it as a SCEVUnknown node.
26 // In addition to being able to represent expressions of various types, we also
27 // have folders that are used to build the *canonical* representation for a
28 // particular expression. These folders are capable of using a variety of
29 // rewrite rules to simplify the expressions.
31 // Once the folders are defined, we can implement the more interesting
32 // higher-level code, such as the code that recognizes PHI nodes of various
33 // types, computes the execution count of a loop, etc.
35 // TODO: We should use these routines and value representations to implement
36 // dependence analysis!
38 //===----------------------------------------------------------------------===//
40 // There are several good references for the techniques used in this analysis.
42 // Chains of recurrences -- a method to expedite the evaluation
43 // of closed-form functions
44 // Olaf Bachmann, Paul S. Wang, Eugene V. Zima
46 // On computational properties of chains of recurrences
49 // Symbolic Evaluation of Chains of Recurrences for Loop Optimization
50 // Robert A. van Engelen
52 // Efficient Symbolic Analysis for Optimizing Compilers
53 // Robert A. van Engelen
55 // Using the chains of recurrences algebra for data dependence testing and
56 // induction variable substitution
57 // MS Thesis, Johnie Birch
59 //===----------------------------------------------------------------------===//
61 #include "llvm/Analysis/ScalarEvolution.h"
62 #include "llvm/ADT/Optional.h"
63 #include "llvm/ADT/STLExtras.h"
64 #include "llvm/ADT/SmallPtrSet.h"
65 #include "llvm/ADT/Statistic.h"
66 #include "llvm/Analysis/AssumptionCache.h"
67 #include "llvm/Analysis/ConstantFolding.h"
68 #include "llvm/Analysis/InstructionSimplify.h"
69 #include "llvm/Analysis/LoopInfo.h"
70 #include "llvm/Analysis/ScalarEvolutionExpressions.h"
71 #include "llvm/Analysis/TargetLibraryInfo.h"
72 #include "llvm/Analysis/ValueTracking.h"
73 #include "llvm/IR/ConstantRange.h"
74 #include "llvm/IR/Constants.h"
75 #include "llvm/IR/DataLayout.h"
76 #include "llvm/IR/DerivedTypes.h"
77 #include "llvm/IR/Dominators.h"
78 #include "llvm/IR/GetElementPtrTypeIterator.h"
79 #include "llvm/IR/GlobalAlias.h"
80 #include "llvm/IR/GlobalVariable.h"
81 #include "llvm/IR/InstIterator.h"
82 #include "llvm/IR/Instructions.h"
83 #include "llvm/IR/LLVMContext.h"
84 #include "llvm/IR/Metadata.h"
85 #include "llvm/IR/Operator.h"
86 #include "llvm/Support/CommandLine.h"
87 #include "llvm/Support/Debug.h"
88 #include "llvm/Support/ErrorHandling.h"
89 #include "llvm/Support/MathExtras.h"
90 #include "llvm/Support/raw_ostream.h"
94 #define DEBUG_TYPE "scalar-evolution"
96 STATISTIC(NumArrayLenItCounts,
97 "Number of trip counts computed with array length");
98 STATISTIC(NumTripCountsComputed,
99 "Number of loops with predictable loop counts");
100 STATISTIC(NumTripCountsNotComputed,
101 "Number of loops without predictable loop counts");
102 STATISTIC(NumBruteForceTripCountsComputed,
103 "Number of loops with trip counts computed by force");
105 static cl::opt<unsigned>
106 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
107 cl::desc("Maximum number of iterations SCEV will "
108 "symbolically execute a constant "
112 // FIXME: Enable this with XDEBUG when the test suite is clean.
114 VerifySCEV("verify-scev",
115 cl::desc("Verify ScalarEvolution's backedge taken counts (slow)"));
117 INITIALIZE_PASS_BEGIN(ScalarEvolution, "scalar-evolution",
118 "Scalar Evolution Analysis", false, true)
119 INITIALIZE_PASS_DEPENDENCY(AssumptionCacheTracker)
120 INITIALIZE_PASS_DEPENDENCY(LoopInfoWrapperPass)
121 INITIALIZE_PASS_DEPENDENCY(DominatorTreeWrapperPass)
122 INITIALIZE_PASS_DEPENDENCY(TargetLibraryInfoWrapperPass)
123 INITIALIZE_PASS_END(ScalarEvolution, "scalar-evolution",
124 "Scalar Evolution Analysis", false, true)
125 char ScalarEvolution::ID = 0;
127 //===----------------------------------------------------------------------===//
128 // SCEV class definitions
129 //===----------------------------------------------------------------------===//
131 //===----------------------------------------------------------------------===//
132 // Implementation of the SCEV class.
135 #if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP)
136 void SCEV::dump() const {
142 void SCEV::print(raw_ostream &OS) const {
143 switch (static_cast<SCEVTypes>(getSCEVType())) {
145 cast<SCEVConstant>(this)->getValue()->printAsOperand(OS, false);
148 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(this);
149 const SCEV *Op = Trunc->getOperand();
150 OS << "(trunc " << *Op->getType() << " " << *Op << " to "
151 << *Trunc->getType() << ")";
155 const SCEVZeroExtendExpr *ZExt = cast<SCEVZeroExtendExpr>(this);
156 const SCEV *Op = ZExt->getOperand();
157 OS << "(zext " << *Op->getType() << " " << *Op << " to "
158 << *ZExt->getType() << ")";
162 const SCEVSignExtendExpr *SExt = cast<SCEVSignExtendExpr>(this);
163 const SCEV *Op = SExt->getOperand();
164 OS << "(sext " << *Op->getType() << " " << *Op << " to "
165 << *SExt->getType() << ")";
169 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(this);
170 OS << "{" << *AR->getOperand(0);
171 for (unsigned i = 1, e = AR->getNumOperands(); i != e; ++i)
172 OS << ",+," << *AR->getOperand(i);
174 if (AR->getNoWrapFlags(FlagNUW))
176 if (AR->getNoWrapFlags(FlagNSW))
178 if (AR->getNoWrapFlags(FlagNW) &&
179 !AR->getNoWrapFlags((NoWrapFlags)(FlagNUW | FlagNSW)))
181 AR->getLoop()->getHeader()->printAsOperand(OS, /*PrintType=*/false);
189 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(this);
190 const char *OpStr = nullptr;
191 switch (NAry->getSCEVType()) {
192 case scAddExpr: OpStr = " + "; break;
193 case scMulExpr: OpStr = " * "; break;
194 case scUMaxExpr: OpStr = " umax "; break;
195 case scSMaxExpr: OpStr = " smax "; break;
198 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
201 if (std::next(I) != E)
205 switch (NAry->getSCEVType()) {
208 if (NAry->getNoWrapFlags(FlagNUW))
210 if (NAry->getNoWrapFlags(FlagNSW))
216 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(this);
217 OS << "(" << *UDiv->getLHS() << " /u " << *UDiv->getRHS() << ")";
221 const SCEVUnknown *U = cast<SCEVUnknown>(this);
223 if (U->isSizeOf(AllocTy)) {
224 OS << "sizeof(" << *AllocTy << ")";
227 if (U->isAlignOf(AllocTy)) {
228 OS << "alignof(" << *AllocTy << ")";
234 if (U->isOffsetOf(CTy, FieldNo)) {
235 OS << "offsetof(" << *CTy << ", ";
236 FieldNo->printAsOperand(OS, false);
241 // Otherwise just print it normally.
242 U->getValue()->printAsOperand(OS, false);
245 case scCouldNotCompute:
246 OS << "***COULDNOTCOMPUTE***";
249 llvm_unreachable("Unknown SCEV kind!");
252 Type *SCEV::getType() const {
253 switch (static_cast<SCEVTypes>(getSCEVType())) {
255 return cast<SCEVConstant>(this)->getType();
259 return cast<SCEVCastExpr>(this)->getType();
264 return cast<SCEVNAryExpr>(this)->getType();
266 return cast<SCEVAddExpr>(this)->getType();
268 return cast<SCEVUDivExpr>(this)->getType();
270 return cast<SCEVUnknown>(this)->getType();
271 case scCouldNotCompute:
272 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
274 llvm_unreachable("Unknown SCEV kind!");
277 bool SCEV::isZero() const {
278 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
279 return SC->getValue()->isZero();
283 bool SCEV::isOne() const {
284 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
285 return SC->getValue()->isOne();
289 bool SCEV::isAllOnesValue() const {
290 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
291 return SC->getValue()->isAllOnesValue();
295 /// isNonConstantNegative - Return true if the specified scev is negated, but
297 bool SCEV::isNonConstantNegative() const {
298 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(this);
299 if (!Mul) return false;
301 // If there is a constant factor, it will be first.
302 const SCEVConstant *SC = dyn_cast<SCEVConstant>(Mul->getOperand(0));
303 if (!SC) return false;
305 // Return true if the value is negative, this matches things like (-42 * V).
306 return SC->getValue()->getValue().isNegative();
309 SCEVCouldNotCompute::SCEVCouldNotCompute() :
310 SCEV(FoldingSetNodeIDRef(), scCouldNotCompute) {}
312 bool SCEVCouldNotCompute::classof(const SCEV *S) {
313 return S->getSCEVType() == scCouldNotCompute;
316 const SCEV *ScalarEvolution::getConstant(ConstantInt *V) {
318 ID.AddInteger(scConstant);
321 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
322 SCEV *S = new (SCEVAllocator) SCEVConstant(ID.Intern(SCEVAllocator), V);
323 UniqueSCEVs.InsertNode(S, IP);
327 const SCEV *ScalarEvolution::getConstant(const APInt &Val) {
328 return getConstant(ConstantInt::get(getContext(), Val));
332 ScalarEvolution::getConstant(Type *Ty, uint64_t V, bool isSigned) {
333 IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty));
334 return getConstant(ConstantInt::get(ITy, V, isSigned));
337 SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID,
338 unsigned SCEVTy, const SCEV *op, Type *ty)
339 : SCEV(ID, SCEVTy), Op(op), Ty(ty) {}
341 SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID,
342 const SCEV *op, Type *ty)
343 : SCEVCastExpr(ID, scTruncate, op, ty) {
344 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
345 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
346 "Cannot truncate non-integer value!");
349 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID,
350 const SCEV *op, Type *ty)
351 : SCEVCastExpr(ID, scZeroExtend, op, ty) {
352 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
353 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
354 "Cannot zero extend non-integer value!");
357 SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID,
358 const SCEV *op, Type *ty)
359 : SCEVCastExpr(ID, scSignExtend, op, ty) {
360 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
361 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
362 "Cannot sign extend non-integer value!");
365 void SCEVUnknown::deleted() {
366 // Clear this SCEVUnknown from various maps.
367 SE->forgetMemoizedResults(this);
369 // Remove this SCEVUnknown from the uniquing map.
370 SE->UniqueSCEVs.RemoveNode(this);
372 // Release the value.
376 void SCEVUnknown::allUsesReplacedWith(Value *New) {
377 // Clear this SCEVUnknown from various maps.
378 SE->forgetMemoizedResults(this);
380 // Remove this SCEVUnknown from the uniquing map.
381 SE->UniqueSCEVs.RemoveNode(this);
383 // Update this SCEVUnknown to point to the new value. This is needed
384 // because there may still be outstanding SCEVs which still point to
389 bool SCEVUnknown::isSizeOf(Type *&AllocTy) const {
390 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
391 if (VCE->getOpcode() == Instruction::PtrToInt)
392 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
393 if (CE->getOpcode() == Instruction::GetElementPtr &&
394 CE->getOperand(0)->isNullValue() &&
395 CE->getNumOperands() == 2)
396 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1)))
398 AllocTy = cast<PointerType>(CE->getOperand(0)->getType())
406 bool SCEVUnknown::isAlignOf(Type *&AllocTy) const {
407 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
408 if (VCE->getOpcode() == Instruction::PtrToInt)
409 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
410 if (CE->getOpcode() == Instruction::GetElementPtr &&
411 CE->getOperand(0)->isNullValue()) {
413 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
414 if (StructType *STy = dyn_cast<StructType>(Ty))
415 if (!STy->isPacked() &&
416 CE->getNumOperands() == 3 &&
417 CE->getOperand(1)->isNullValue()) {
418 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2)))
420 STy->getNumElements() == 2 &&
421 STy->getElementType(0)->isIntegerTy(1)) {
422 AllocTy = STy->getElementType(1);
431 bool SCEVUnknown::isOffsetOf(Type *&CTy, Constant *&FieldNo) const {
432 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
433 if (VCE->getOpcode() == Instruction::PtrToInt)
434 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
435 if (CE->getOpcode() == Instruction::GetElementPtr &&
436 CE->getNumOperands() == 3 &&
437 CE->getOperand(0)->isNullValue() &&
438 CE->getOperand(1)->isNullValue()) {
440 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
441 // Ignore vector types here so that ScalarEvolutionExpander doesn't
442 // emit getelementptrs that index into vectors.
443 if (Ty->isStructTy() || Ty->isArrayTy()) {
445 FieldNo = CE->getOperand(2);
453 //===----------------------------------------------------------------------===//
455 //===----------------------------------------------------------------------===//
458 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
459 /// than the complexity of the RHS. This comparator is used to canonicalize
461 class SCEVComplexityCompare {
462 const LoopInfo *const LI;
464 explicit SCEVComplexityCompare(const LoopInfo *li) : LI(li) {}
466 // Return true or false if LHS is less than, or at least RHS, respectively.
467 bool operator()(const SCEV *LHS, const SCEV *RHS) const {
468 return compare(LHS, RHS) < 0;
471 // Return negative, zero, or positive, if LHS is less than, equal to, or
472 // greater than RHS, respectively. A three-way result allows recursive
473 // comparisons to be more efficient.
474 int compare(const SCEV *LHS, const SCEV *RHS) const {
475 // Fast-path: SCEVs are uniqued so we can do a quick equality check.
479 // Primarily, sort the SCEVs by their getSCEVType().
480 unsigned LType = LHS->getSCEVType(), RType = RHS->getSCEVType();
482 return (int)LType - (int)RType;
484 // Aside from the getSCEVType() ordering, the particular ordering
485 // isn't very important except that it's beneficial to be consistent,
486 // so that (a + b) and (b + a) don't end up as different expressions.
487 switch (static_cast<SCEVTypes>(LType)) {
489 const SCEVUnknown *LU = cast<SCEVUnknown>(LHS);
490 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
492 // Sort SCEVUnknown values with some loose heuristics. TODO: This is
493 // not as complete as it could be.
494 const Value *LV = LU->getValue(), *RV = RU->getValue();
496 // Order pointer values after integer values. This helps SCEVExpander
498 bool LIsPointer = LV->getType()->isPointerTy(),
499 RIsPointer = RV->getType()->isPointerTy();
500 if (LIsPointer != RIsPointer)
501 return (int)LIsPointer - (int)RIsPointer;
503 // Compare getValueID values.
504 unsigned LID = LV->getValueID(),
505 RID = RV->getValueID();
507 return (int)LID - (int)RID;
509 // Sort arguments by their position.
510 if (const Argument *LA = dyn_cast<Argument>(LV)) {
511 const Argument *RA = cast<Argument>(RV);
512 unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo();
513 return (int)LArgNo - (int)RArgNo;
516 // For instructions, compare their loop depth, and their operand
517 // count. This is pretty loose.
518 if (const Instruction *LInst = dyn_cast<Instruction>(LV)) {
519 const Instruction *RInst = cast<Instruction>(RV);
521 // Compare loop depths.
522 const BasicBlock *LParent = LInst->getParent(),
523 *RParent = RInst->getParent();
524 if (LParent != RParent) {
525 unsigned LDepth = LI->getLoopDepth(LParent),
526 RDepth = LI->getLoopDepth(RParent);
527 if (LDepth != RDepth)
528 return (int)LDepth - (int)RDepth;
531 // Compare the number of operands.
532 unsigned LNumOps = LInst->getNumOperands(),
533 RNumOps = RInst->getNumOperands();
534 return (int)LNumOps - (int)RNumOps;
541 const SCEVConstant *LC = cast<SCEVConstant>(LHS);
542 const SCEVConstant *RC = cast<SCEVConstant>(RHS);
544 // Compare constant values.
545 const APInt &LA = LC->getValue()->getValue();
546 const APInt &RA = RC->getValue()->getValue();
547 unsigned LBitWidth = LA.getBitWidth(), RBitWidth = RA.getBitWidth();
548 if (LBitWidth != RBitWidth)
549 return (int)LBitWidth - (int)RBitWidth;
550 return LA.ult(RA) ? -1 : 1;
554 const SCEVAddRecExpr *LA = cast<SCEVAddRecExpr>(LHS);
555 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS);
557 // Compare addrec loop depths.
558 const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop();
559 if (LLoop != RLoop) {
560 unsigned LDepth = LLoop->getLoopDepth(),
561 RDepth = RLoop->getLoopDepth();
562 if (LDepth != RDepth)
563 return (int)LDepth - (int)RDepth;
566 // Addrec complexity grows with operand count.
567 unsigned LNumOps = LA->getNumOperands(), RNumOps = RA->getNumOperands();
568 if (LNumOps != RNumOps)
569 return (int)LNumOps - (int)RNumOps;
571 // Lexicographically compare.
572 for (unsigned i = 0; i != LNumOps; ++i) {
573 long X = compare(LA->getOperand(i), RA->getOperand(i));
585 const SCEVNAryExpr *LC = cast<SCEVNAryExpr>(LHS);
586 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
588 // Lexicographically compare n-ary expressions.
589 unsigned LNumOps = LC->getNumOperands(), RNumOps = RC->getNumOperands();
590 if (LNumOps != RNumOps)
591 return (int)LNumOps - (int)RNumOps;
593 for (unsigned i = 0; i != LNumOps; ++i) {
596 long X = compare(LC->getOperand(i), RC->getOperand(i));
600 return (int)LNumOps - (int)RNumOps;
604 const SCEVUDivExpr *LC = cast<SCEVUDivExpr>(LHS);
605 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
607 // Lexicographically compare udiv expressions.
608 long X = compare(LC->getLHS(), RC->getLHS());
611 return compare(LC->getRHS(), RC->getRHS());
617 const SCEVCastExpr *LC = cast<SCEVCastExpr>(LHS);
618 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
620 // Compare cast expressions by operand.
621 return compare(LC->getOperand(), RC->getOperand());
624 case scCouldNotCompute:
625 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
627 llvm_unreachable("Unknown SCEV kind!");
632 /// GroupByComplexity - Given a list of SCEV objects, order them by their
633 /// complexity, and group objects of the same complexity together by value.
634 /// When this routine is finished, we know that any duplicates in the vector are
635 /// consecutive and that complexity is monotonically increasing.
637 /// Note that we go take special precautions to ensure that we get deterministic
638 /// results from this routine. In other words, we don't want the results of
639 /// this to depend on where the addresses of various SCEV objects happened to
642 static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops,
644 if (Ops.size() < 2) return; // Noop
645 if (Ops.size() == 2) {
646 // This is the common case, which also happens to be trivially simple.
648 const SCEV *&LHS = Ops[0], *&RHS = Ops[1];
649 if (SCEVComplexityCompare(LI)(RHS, LHS))
654 // Do the rough sort by complexity.
655 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI));
657 // Now that we are sorted by complexity, group elements of the same
658 // complexity. Note that this is, at worst, N^2, but the vector is likely to
659 // be extremely short in practice. Note that we take this approach because we
660 // do not want to depend on the addresses of the objects we are grouping.
661 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
662 const SCEV *S = Ops[i];
663 unsigned Complexity = S->getSCEVType();
665 // If there are any objects of the same complexity and same value as this
667 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
668 if (Ops[j] == S) { // Found a duplicate.
669 // Move it to immediately after i'th element.
670 std::swap(Ops[i+1], Ops[j]);
671 ++i; // no need to rescan it.
672 if (i == e-2) return; // Done!
679 struct FindSCEVSize {
681 FindSCEVSize() : Size(0) {}
683 bool follow(const SCEV *S) {
685 // Keep looking at all operands of S.
688 bool isDone() const {
694 // Returns the size of the SCEV S.
695 static inline int sizeOfSCEV(const SCEV *S) {
697 SCEVTraversal<FindSCEVSize> ST(F);
704 struct SCEVDivision : public SCEVVisitor<SCEVDivision, void> {
706 // Computes the Quotient and Remainder of the division of Numerator by
708 static void divide(ScalarEvolution &SE, const SCEV *Numerator,
709 const SCEV *Denominator, const SCEV **Quotient,
710 const SCEV **Remainder) {
711 assert(Numerator && Denominator && "Uninitialized SCEV");
713 SCEVDivision D(SE, Numerator, Denominator);
715 // Check for the trivial case here to avoid having to check for it in the
717 if (Numerator == Denominator) {
723 if (Numerator->isZero()) {
729 // Split the Denominator when it is a product.
730 if (const SCEVMulExpr *T = dyn_cast<const SCEVMulExpr>(Denominator)) {
732 *Quotient = Numerator;
733 for (const SCEV *Op : T->operands()) {
734 divide(SE, *Quotient, Op, &Q, &R);
737 // Bail out when the Numerator is not divisible by one of the terms of
741 *Remainder = Numerator;
750 *Quotient = D.Quotient;
751 *Remainder = D.Remainder;
754 // Except in the trivial case described above, we do not know how to divide
755 // Expr by Denominator for the following functions with empty implementation.
756 void visitTruncateExpr(const SCEVTruncateExpr *Numerator) {}
757 void visitZeroExtendExpr(const SCEVZeroExtendExpr *Numerator) {}
758 void visitSignExtendExpr(const SCEVSignExtendExpr *Numerator) {}
759 void visitUDivExpr(const SCEVUDivExpr *Numerator) {}
760 void visitSMaxExpr(const SCEVSMaxExpr *Numerator) {}
761 void visitUMaxExpr(const SCEVUMaxExpr *Numerator) {}
762 void visitUnknown(const SCEVUnknown *Numerator) {}
763 void visitCouldNotCompute(const SCEVCouldNotCompute *Numerator) {}
765 void visitConstant(const SCEVConstant *Numerator) {
766 if (const SCEVConstant *D = dyn_cast<SCEVConstant>(Denominator)) {
767 APInt NumeratorVal = Numerator->getValue()->getValue();
768 APInt DenominatorVal = D->getValue()->getValue();
769 uint32_t NumeratorBW = NumeratorVal.getBitWidth();
770 uint32_t DenominatorBW = DenominatorVal.getBitWidth();
772 if (NumeratorBW > DenominatorBW)
773 DenominatorVal = DenominatorVal.sext(NumeratorBW);
774 else if (NumeratorBW < DenominatorBW)
775 NumeratorVal = NumeratorVal.sext(DenominatorBW);
777 APInt QuotientVal(NumeratorVal.getBitWidth(), 0);
778 APInt RemainderVal(NumeratorVal.getBitWidth(), 0);
779 APInt::sdivrem(NumeratorVal, DenominatorVal, QuotientVal, RemainderVal);
780 Quotient = SE.getConstant(QuotientVal);
781 Remainder = SE.getConstant(RemainderVal);
786 void visitAddRecExpr(const SCEVAddRecExpr *Numerator) {
787 const SCEV *StartQ, *StartR, *StepQ, *StepR;
788 assert(Numerator->isAffine() && "Numerator should be affine");
789 divide(SE, Numerator->getStart(), Denominator, &StartQ, &StartR);
790 divide(SE, Numerator->getStepRecurrence(SE), Denominator, &StepQ, &StepR);
791 Quotient = SE.getAddRecExpr(StartQ, StepQ, Numerator->getLoop(),
792 Numerator->getNoWrapFlags());
793 Remainder = SE.getAddRecExpr(StartR, StepR, Numerator->getLoop(),
794 Numerator->getNoWrapFlags());
797 void visitAddExpr(const SCEVAddExpr *Numerator) {
798 SmallVector<const SCEV *, 2> Qs, Rs;
799 Type *Ty = Denominator->getType();
801 for (const SCEV *Op : Numerator->operands()) {
803 divide(SE, Op, Denominator, &Q, &R);
805 // Bail out if types do not match.
806 if (Ty != Q->getType() || Ty != R->getType()) {
808 Remainder = Numerator;
816 if (Qs.size() == 1) {
822 Quotient = SE.getAddExpr(Qs);
823 Remainder = SE.getAddExpr(Rs);
826 void visitMulExpr(const SCEVMulExpr *Numerator) {
827 SmallVector<const SCEV *, 2> Qs;
828 Type *Ty = Denominator->getType();
830 bool FoundDenominatorTerm = false;
831 for (const SCEV *Op : Numerator->operands()) {
832 // Bail out if types do not match.
833 if (Ty != Op->getType()) {
835 Remainder = Numerator;
839 if (FoundDenominatorTerm) {
844 // Check whether Denominator divides one of the product operands.
846 divide(SE, Op, Denominator, &Q, &R);
852 // Bail out if types do not match.
853 if (Ty != Q->getType()) {
855 Remainder = Numerator;
859 FoundDenominatorTerm = true;
863 if (FoundDenominatorTerm) {
868 Quotient = SE.getMulExpr(Qs);
872 if (!isa<SCEVUnknown>(Denominator)) {
874 Remainder = Numerator;
878 // The Remainder is obtained by replacing Denominator by 0 in Numerator.
879 ValueToValueMap RewriteMap;
880 RewriteMap[cast<SCEVUnknown>(Denominator)->getValue()] =
881 cast<SCEVConstant>(Zero)->getValue();
882 Remainder = SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true);
884 if (Remainder->isZero()) {
885 // The Quotient is obtained by replacing Denominator by 1 in Numerator.
886 RewriteMap[cast<SCEVUnknown>(Denominator)->getValue()] =
887 cast<SCEVConstant>(One)->getValue();
889 SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true);
893 // Quotient is (Numerator - Remainder) divided by Denominator.
895 const SCEV *Diff = SE.getMinusSCEV(Numerator, Remainder);
896 if (sizeOfSCEV(Diff) > sizeOfSCEV(Numerator)) {
897 // This SCEV does not seem to simplify: fail the division here.
899 Remainder = Numerator;
902 divide(SE, Diff, Denominator, &Q, &R);
904 "(Numerator - Remainder) should evenly divide Denominator");
909 SCEVDivision(ScalarEvolution &S, const SCEV *Numerator,
910 const SCEV *Denominator)
911 : SE(S), Denominator(Denominator) {
912 Zero = SE.getConstant(Denominator->getType(), 0);
913 One = SE.getConstant(Denominator->getType(), 1);
915 // By default, we don't know how to divide Expr by Denominator.
916 // Providing the default here simplifies the rest of the code.
918 Remainder = Numerator;
922 const SCEV *Denominator, *Quotient, *Remainder, *Zero, *One;
927 //===----------------------------------------------------------------------===//
928 // Simple SCEV method implementations
929 //===----------------------------------------------------------------------===//
931 /// BinomialCoefficient - Compute BC(It, K). The result has width W.
933 static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K,
936 // Handle the simplest case efficiently.
938 return SE.getTruncateOrZeroExtend(It, ResultTy);
940 // We are using the following formula for BC(It, K):
942 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
944 // Suppose, W is the bitwidth of the return value. We must be prepared for
945 // overflow. Hence, we must assure that the result of our computation is
946 // equal to the accurate one modulo 2^W. Unfortunately, division isn't
947 // safe in modular arithmetic.
949 // However, this code doesn't use exactly that formula; the formula it uses
950 // is something like the following, where T is the number of factors of 2 in
951 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
954 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
956 // This formula is trivially equivalent to the previous formula. However,
957 // this formula can be implemented much more efficiently. The trick is that
958 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
959 // arithmetic. To do exact division in modular arithmetic, all we have
960 // to do is multiply by the inverse. Therefore, this step can be done at
963 // The next issue is how to safely do the division by 2^T. The way this
964 // is done is by doing the multiplication step at a width of at least W + T
965 // bits. This way, the bottom W+T bits of the product are accurate. Then,
966 // when we perform the division by 2^T (which is equivalent to a right shift
967 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
968 // truncated out after the division by 2^T.
970 // In comparison to just directly using the first formula, this technique
971 // is much more efficient; using the first formula requires W * K bits,
972 // but this formula less than W + K bits. Also, the first formula requires
973 // a division step, whereas this formula only requires multiplies and shifts.
975 // It doesn't matter whether the subtraction step is done in the calculation
976 // width or the input iteration count's width; if the subtraction overflows,
977 // the result must be zero anyway. We prefer here to do it in the width of
978 // the induction variable because it helps a lot for certain cases; CodeGen
979 // isn't smart enough to ignore the overflow, which leads to much less
980 // efficient code if the width of the subtraction is wider than the native
983 // (It's possible to not widen at all by pulling out factors of 2 before
984 // the multiplication; for example, K=2 can be calculated as
985 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
986 // extra arithmetic, so it's not an obvious win, and it gets
987 // much more complicated for K > 3.)
989 // Protection from insane SCEVs; this bound is conservative,
990 // but it probably doesn't matter.
992 return SE.getCouldNotCompute();
994 unsigned W = SE.getTypeSizeInBits(ResultTy);
996 // Calculate K! / 2^T and T; we divide out the factors of two before
997 // multiplying for calculating K! / 2^T to avoid overflow.
998 // Other overflow doesn't matter because we only care about the bottom
999 // W bits of the result.
1000 APInt OddFactorial(W, 1);
1002 for (unsigned i = 3; i <= K; ++i) {
1004 unsigned TwoFactors = Mult.countTrailingZeros();
1006 Mult = Mult.lshr(TwoFactors);
1007 OddFactorial *= Mult;
1010 // We need at least W + T bits for the multiplication step
1011 unsigned CalculationBits = W + T;
1013 // Calculate 2^T, at width T+W.
1014 APInt DivFactor = APInt::getOneBitSet(CalculationBits, T);
1016 // Calculate the multiplicative inverse of K! / 2^T;
1017 // this multiplication factor will perform the exact division by
1019 APInt Mod = APInt::getSignedMinValue(W+1);
1020 APInt MultiplyFactor = OddFactorial.zext(W+1);
1021 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
1022 MultiplyFactor = MultiplyFactor.trunc(W);
1024 // Calculate the product, at width T+W
1025 IntegerType *CalculationTy = IntegerType::get(SE.getContext(),
1027 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
1028 for (unsigned i = 1; i != K; ++i) {
1029 const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i));
1030 Dividend = SE.getMulExpr(Dividend,
1031 SE.getTruncateOrZeroExtend(S, CalculationTy));
1035 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
1037 // Truncate the result, and divide by K! / 2^T.
1039 return SE.getMulExpr(SE.getConstant(MultiplyFactor),
1040 SE.getTruncateOrZeroExtend(DivResult, ResultTy));
1043 /// evaluateAtIteration - Return the value of this chain of recurrences at
1044 /// the specified iteration number. We can evaluate this recurrence by
1045 /// multiplying each element in the chain by the binomial coefficient
1046 /// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
1048 /// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
1050 /// where BC(It, k) stands for binomial coefficient.
1052 const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It,
1053 ScalarEvolution &SE) const {
1054 const SCEV *Result = getStart();
1055 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
1056 // The computation is correct in the face of overflow provided that the
1057 // multiplication is performed _after_ the evaluation of the binomial
1059 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType());
1060 if (isa<SCEVCouldNotCompute>(Coeff))
1063 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
1068 //===----------------------------------------------------------------------===//
1069 // SCEV Expression folder implementations
1070 //===----------------------------------------------------------------------===//
1072 const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op,
1074 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
1075 "This is not a truncating conversion!");
1076 assert(isSCEVable(Ty) &&
1077 "This is not a conversion to a SCEVable type!");
1078 Ty = getEffectiveSCEVType(Ty);
1080 FoldingSetNodeID ID;
1081 ID.AddInteger(scTruncate);
1085 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1087 // Fold if the operand is constant.
1088 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1090 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty)));
1092 // trunc(trunc(x)) --> trunc(x)
1093 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
1094 return getTruncateExpr(ST->getOperand(), Ty);
1096 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
1097 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1098 return getTruncateOrSignExtend(SS->getOperand(), Ty);
1100 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
1101 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1102 return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
1104 // trunc(x1+x2+...+xN) --> trunc(x1)+trunc(x2)+...+trunc(xN) if we can
1105 // eliminate all the truncates, or we replace other casts with truncates.
1106 if (const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Op)) {
1107 SmallVector<const SCEV *, 4> Operands;
1108 bool hasTrunc = false;
1109 for (unsigned i = 0, e = SA->getNumOperands(); i != e && !hasTrunc; ++i) {
1110 const SCEV *S = getTruncateExpr(SA->getOperand(i), Ty);
1111 if (!isa<SCEVCastExpr>(SA->getOperand(i)))
1112 hasTrunc = isa<SCEVTruncateExpr>(S);
1113 Operands.push_back(S);
1116 return getAddExpr(Operands);
1117 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL.
1120 // trunc(x1*x2*...*xN) --> trunc(x1)*trunc(x2)*...*trunc(xN) if we can
1121 // eliminate all the truncates, or we replace other casts with truncates.
1122 if (const SCEVMulExpr *SM = dyn_cast<SCEVMulExpr>(Op)) {
1123 SmallVector<const SCEV *, 4> Operands;
1124 bool hasTrunc = false;
1125 for (unsigned i = 0, e = SM->getNumOperands(); i != e && !hasTrunc; ++i) {
1126 const SCEV *S = getTruncateExpr(SM->getOperand(i), Ty);
1127 if (!isa<SCEVCastExpr>(SM->getOperand(i)))
1128 hasTrunc = isa<SCEVTruncateExpr>(S);
1129 Operands.push_back(S);
1132 return getMulExpr(Operands);
1133 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL.
1136 // If the input value is a chrec scev, truncate the chrec's operands.
1137 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
1138 SmallVector<const SCEV *, 4> Operands;
1139 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
1140 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty));
1141 return getAddRecExpr(Operands, AddRec->getLoop(), SCEV::FlagAnyWrap);
1144 // The cast wasn't folded; create an explicit cast node. We can reuse
1145 // the existing insert position since if we get here, we won't have
1146 // made any changes which would invalidate it.
1147 SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator),
1149 UniqueSCEVs.InsertNode(S, IP);
1153 // Get the limit of a recurrence such that incrementing by Step cannot cause
1154 // signed overflow as long as the value of the recurrence within the
1155 // loop does not exceed this limit before incrementing.
1156 static const SCEV *getSignedOverflowLimitForStep(const SCEV *Step,
1157 ICmpInst::Predicate *Pred,
1158 ScalarEvolution *SE) {
1159 unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
1160 if (SE->isKnownPositive(Step)) {
1161 *Pred = ICmpInst::ICMP_SLT;
1162 return SE->getConstant(APInt::getSignedMinValue(BitWidth) -
1163 SE->getSignedRange(Step).getSignedMax());
1165 if (SE->isKnownNegative(Step)) {
1166 *Pred = ICmpInst::ICMP_SGT;
1167 return SE->getConstant(APInt::getSignedMaxValue(BitWidth) -
1168 SE->getSignedRange(Step).getSignedMin());
1173 // Get the limit of a recurrence such that incrementing by Step cannot cause
1174 // unsigned overflow as long as the value of the recurrence within the loop does
1175 // not exceed this limit before incrementing.
1176 static const SCEV *getUnsignedOverflowLimitForStep(const SCEV *Step,
1177 ICmpInst::Predicate *Pred,
1178 ScalarEvolution *SE) {
1179 unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
1180 *Pred = ICmpInst::ICMP_ULT;
1182 return SE->getConstant(APInt::getMinValue(BitWidth) -
1183 SE->getUnsignedRange(Step).getUnsignedMax());
1188 struct ExtendOpTraitsBase {
1189 typedef const SCEV *(ScalarEvolution::*GetExtendExprTy)(const SCEV *, Type *);
1192 // Used to make code generic over signed and unsigned overflow.
1193 template <typename ExtendOp> struct ExtendOpTraits {
1196 // static const SCEV::NoWrapFlags WrapType;
1198 // static const ExtendOpTraitsBase::GetExtendExprTy GetExtendExpr;
1200 // static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1201 // ICmpInst::Predicate *Pred,
1202 // ScalarEvolution *SE);
1206 struct ExtendOpTraits<SCEVSignExtendExpr> : public ExtendOpTraitsBase {
1207 static const SCEV::NoWrapFlags WrapType = SCEV::FlagNSW;
1209 static const GetExtendExprTy GetExtendExpr;
1211 static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1212 ICmpInst::Predicate *Pred,
1213 ScalarEvolution *SE) {
1214 return getSignedOverflowLimitForStep(Step, Pred, SE);
1218 const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits<
1219 SCEVSignExtendExpr>::GetExtendExpr = &ScalarEvolution::getSignExtendExpr;
1222 struct ExtendOpTraits<SCEVZeroExtendExpr> : public ExtendOpTraitsBase {
1223 static const SCEV::NoWrapFlags WrapType = SCEV::FlagNUW;
1225 static const GetExtendExprTy GetExtendExpr;
1227 static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1228 ICmpInst::Predicate *Pred,
1229 ScalarEvolution *SE) {
1230 return getUnsignedOverflowLimitForStep(Step, Pred, SE);
1234 const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits<
1235 SCEVZeroExtendExpr>::GetExtendExpr = &ScalarEvolution::getZeroExtendExpr;
1238 // The recurrence AR has been shown to have no signed/unsigned wrap or something
1239 // close to it. Typically, if we can prove NSW/NUW for AR, then we can just as
1240 // easily prove NSW/NUW for its preincrement or postincrement sibling. This
1241 // allows normalizing a sign/zero extended AddRec as such: {sext/zext(Step +
1242 // Start),+,Step} => {(Step + sext/zext(Start),+,Step} As a result, the
1243 // expression "Step + sext/zext(PreIncAR)" is congruent with
1244 // "sext/zext(PostIncAR)"
1245 template <typename ExtendOpTy>
1246 static const SCEV *getPreStartForExtend(const SCEVAddRecExpr *AR, Type *Ty,
1247 ScalarEvolution *SE) {
1248 auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType;
1249 auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr;
1251 const Loop *L = AR->getLoop();
1252 const SCEV *Start = AR->getStart();
1253 const SCEV *Step = AR->getStepRecurrence(*SE);
1255 // Check for a simple looking step prior to loop entry.
1256 const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Start);
1260 // Create an AddExpr for "PreStart" after subtracting Step. Full SCEV
1261 // subtraction is expensive. For this purpose, perform a quick and dirty
1262 // difference, by checking for Step in the operand list.
1263 SmallVector<const SCEV *, 4> DiffOps;
1264 for (const SCEV *Op : SA->operands())
1266 DiffOps.push_back(Op);
1268 if (DiffOps.size() == SA->getNumOperands())
1271 // Try to prove `WrapType` (SCEV::FlagNSW or SCEV::FlagNUW) on `PreStart` +
1274 // 1. NSW/NUW flags on the step increment.
1275 const SCEV *PreStart = SE->getAddExpr(DiffOps, SA->getNoWrapFlags());
1276 const SCEVAddRecExpr *PreAR = dyn_cast<SCEVAddRecExpr>(
1277 SE->getAddRecExpr(PreStart, Step, L, SCEV::FlagAnyWrap));
1279 // "{S,+,X} is <nsw>/<nuw>" and "the backedge is taken at least once" implies
1280 // "S+X does not sign/unsign-overflow".
1283 const SCEV *BECount = SE->getBackedgeTakenCount(L);
1284 if (PreAR && PreAR->getNoWrapFlags(WrapType) &&
1285 !isa<SCEVCouldNotCompute>(BECount) && SE->isKnownPositive(BECount))
1288 // 2. Direct overflow check on the step operation's expression.
1289 unsigned BitWidth = SE->getTypeSizeInBits(AR->getType());
1290 Type *WideTy = IntegerType::get(SE->getContext(), BitWidth * 2);
1291 const SCEV *OperandExtendedStart =
1292 SE->getAddExpr((SE->*GetExtendExpr)(PreStart, WideTy),
1293 (SE->*GetExtendExpr)(Step, WideTy));
1294 if ((SE->*GetExtendExpr)(Start, WideTy) == OperandExtendedStart) {
1295 if (PreAR && AR->getNoWrapFlags(WrapType)) {
1296 // If we know `AR` == {`PreStart`+`Step`,+,`Step`} is `WrapType` (FlagNSW
1297 // or FlagNUW) and that `PreStart` + `Step` is `WrapType` too, then
1298 // `PreAR` == {`PreStart`,+,`Step`} is also `WrapType`. Cache this fact.
1299 const_cast<SCEVAddRecExpr *>(PreAR)->setNoWrapFlags(WrapType);
1304 // 3. Loop precondition.
1305 ICmpInst::Predicate Pred;
1306 const SCEV *OverflowLimit =
1307 ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep(Step, &Pred, SE);
1309 if (OverflowLimit &&
1310 SE->isLoopEntryGuardedByCond(L, Pred, PreStart, OverflowLimit)) {
1316 // Get the normalized zero or sign extended expression for this AddRec's Start.
1317 template <typename ExtendOpTy>
1318 static const SCEV *getExtendAddRecStart(const SCEVAddRecExpr *AR, Type *Ty,
1319 ScalarEvolution *SE) {
1320 auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr;
1322 const SCEV *PreStart = getPreStartForExtend<ExtendOpTy>(AR, Ty, SE);
1324 return (SE->*GetExtendExpr)(AR->getStart(), Ty);
1326 return SE->getAddExpr((SE->*GetExtendExpr)(AR->getStepRecurrence(*SE), Ty),
1327 (SE->*GetExtendExpr)(PreStart, Ty));
1330 // Try to prove away overflow by looking at "nearby" add recurrences. A
1331 // motivating example for this rule: if we know `{0,+,4}` is `ult` `-1` and it
1332 // does not itself wrap then we can conclude that `{1,+,4}` is `nuw`.
1336 // {S,+,X} == {S-T,+,X} + T
1337 // => Ext({S,+,X}) == Ext({S-T,+,X} + T)
1339 // If ({S-T,+,X} + T) does not overflow ... (1)
1341 // RHS == Ext({S-T,+,X} + T) == Ext({S-T,+,X}) + Ext(T)
1343 // If {S-T,+,X} does not overflow ... (2)
1345 // RHS == Ext({S-T,+,X}) + Ext(T) == {Ext(S-T),+,Ext(X)} + Ext(T)
1346 // == {Ext(S-T)+Ext(T),+,Ext(X)}
1348 // If (S-T)+T does not overflow ... (3)
1350 // RHS == {Ext(S-T)+Ext(T),+,Ext(X)} == {Ext(S-T+T),+,Ext(X)}
1351 // == {Ext(S),+,Ext(X)} == LHS
1353 // Thus, if (1), (2) and (3) are true for some T, then
1354 // Ext({S,+,X}) == {Ext(S),+,Ext(X)}
1356 // (3) is implied by (1) -- "(S-T)+T does not overflow" is simply "({S-T,+,X}+T)
1357 // does not overflow" restricted to the 0th iteration. Therefore we only need
1358 // to check for (1) and (2).
1360 // In the current context, S is `Start`, X is `Step`, Ext is `ExtendOpTy` and T
1361 // is `Delta` (defined below).
1363 template <typename ExtendOpTy>
1364 bool ScalarEvolution::proveNoWrapByVaryingStart(const SCEV *Start,
1367 auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType;
1369 // We restrict `Start` to a constant to prevent SCEV from spending too much
1370 // time here. It is correct (but more expensive) to continue with a
1371 // non-constant `Start` and do a general SCEV subtraction to compute
1372 // `PreStart` below.
1374 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start);
1378 APInt StartAI = StartC->getValue()->getValue();
1380 for (unsigned Delta : {-2, -1, 1, 2}) {
1381 const SCEV *PreStart = getConstant(StartAI - Delta);
1383 // Give up if we don't already have the add recurrence we need because
1384 // actually constructing an add recurrence is relatively expensive.
1385 const SCEVAddRecExpr *PreAR = [&]() {
1386 FoldingSetNodeID ID;
1387 ID.AddInteger(scAddRecExpr);
1388 ID.AddPointer(PreStart);
1389 ID.AddPointer(Step);
1392 return static_cast<SCEVAddRecExpr *>(
1393 this->UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1396 if (PreAR && PreAR->getNoWrapFlags(WrapType)) { // proves (2)
1397 const SCEV *DeltaS = getConstant(StartC->getType(), Delta);
1398 ICmpInst::Predicate Pred = ICmpInst::BAD_ICMP_PREDICATE;
1399 const SCEV *Limit = ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep(
1400 DeltaS, &Pred, this);
1401 if (Limit && isKnownPredicate(Pred, PreAR, Limit)) // proves (1)
1409 const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op,
1411 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1412 "This is not an extending conversion!");
1413 assert(isSCEVable(Ty) &&
1414 "This is not a conversion to a SCEVable type!");
1415 Ty = getEffectiveSCEVType(Ty);
1417 // Fold if the operand is constant.
1418 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1420 cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(), Ty)));
1422 // zext(zext(x)) --> zext(x)
1423 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1424 return getZeroExtendExpr(SZ->getOperand(), Ty);
1426 // Before doing any expensive analysis, check to see if we've already
1427 // computed a SCEV for this Op and Ty.
1428 FoldingSetNodeID ID;
1429 ID.AddInteger(scZeroExtend);
1433 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1435 // zext(trunc(x)) --> zext(x) or x or trunc(x)
1436 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1437 // It's possible the bits taken off by the truncate were all zero bits. If
1438 // so, we should be able to simplify this further.
1439 const SCEV *X = ST->getOperand();
1440 ConstantRange CR = getUnsignedRange(X);
1441 unsigned TruncBits = getTypeSizeInBits(ST->getType());
1442 unsigned NewBits = getTypeSizeInBits(Ty);
1443 if (CR.truncate(TruncBits).zeroExtend(NewBits).contains(
1444 CR.zextOrTrunc(NewBits)))
1445 return getTruncateOrZeroExtend(X, Ty);
1448 // If the input value is a chrec scev, and we can prove that the value
1449 // did not overflow the old, smaller, value, we can zero extend all of the
1450 // operands (often constants). This allows analysis of something like
1451 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
1452 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1453 if (AR->isAffine()) {
1454 const SCEV *Start = AR->getStart();
1455 const SCEV *Step = AR->getStepRecurrence(*this);
1456 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1457 const Loop *L = AR->getLoop();
1459 // If we have special knowledge that this addrec won't overflow,
1460 // we don't need to do any further analysis.
1461 if (AR->getNoWrapFlags(SCEV::FlagNUW))
1462 return getAddRecExpr(
1463 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1464 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1466 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1467 // Note that this serves two purposes: It filters out loops that are
1468 // simply not analyzable, and it covers the case where this code is
1469 // being called from within backedge-taken count analysis, such that
1470 // attempting to ask for the backedge-taken count would likely result
1471 // in infinite recursion. In the later case, the analysis code will
1472 // cope with a conservative value, and it will take care to purge
1473 // that value once it has finished.
1474 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1475 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1476 // Manually compute the final value for AR, checking for
1479 // Check whether the backedge-taken count can be losslessly casted to
1480 // the addrec's type. The count is always unsigned.
1481 const SCEV *CastedMaxBECount =
1482 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1483 const SCEV *RecastedMaxBECount =
1484 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1485 if (MaxBECount == RecastedMaxBECount) {
1486 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1487 // Check whether Start+Step*MaxBECount has no unsigned overflow.
1488 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step);
1489 const SCEV *ZAdd = getZeroExtendExpr(getAddExpr(Start, ZMul), WideTy);
1490 const SCEV *WideStart = getZeroExtendExpr(Start, WideTy);
1491 const SCEV *WideMaxBECount =
1492 getZeroExtendExpr(CastedMaxBECount, WideTy);
1493 const SCEV *OperandExtendedAdd =
1494 getAddExpr(WideStart,
1495 getMulExpr(WideMaxBECount,
1496 getZeroExtendExpr(Step, WideTy)));
1497 if (ZAdd == OperandExtendedAdd) {
1498 // Cache knowledge of AR NUW, which is propagated to this AddRec.
1499 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1500 // Return the expression with the addrec on the outside.
1501 return getAddRecExpr(
1502 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1503 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1505 // Similar to above, only this time treat the step value as signed.
1506 // This covers loops that count down.
1507 OperandExtendedAdd =
1508 getAddExpr(WideStart,
1509 getMulExpr(WideMaxBECount,
1510 getSignExtendExpr(Step, WideTy)));
1511 if (ZAdd == OperandExtendedAdd) {
1512 // Cache knowledge of AR NW, which is propagated to this AddRec.
1513 // Negative step causes unsigned wrap, but it still can't self-wrap.
1514 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1515 // Return the expression with the addrec on the outside.
1516 return getAddRecExpr(
1517 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1518 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1522 // If the backedge is guarded by a comparison with the pre-inc value
1523 // the addrec is safe. Also, if the entry is guarded by a comparison
1524 // with the start value and the backedge is guarded by a comparison
1525 // with the post-inc value, the addrec is safe.
1526 if (isKnownPositive(Step)) {
1527 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
1528 getUnsignedRange(Step).getUnsignedMax());
1529 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
1530 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) &&
1531 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT,
1532 AR->getPostIncExpr(*this), N))) {
1533 // Cache knowledge of AR NUW, which is propagated to this AddRec.
1534 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1535 // Return the expression with the addrec on the outside.
1536 return getAddRecExpr(
1537 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1538 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1540 } else if (isKnownNegative(Step)) {
1541 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
1542 getSignedRange(Step).getSignedMin());
1543 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) ||
1544 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) &&
1545 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT,
1546 AR->getPostIncExpr(*this), N))) {
1547 // Cache knowledge of AR NW, which is propagated to this AddRec.
1548 // Negative step causes unsigned wrap, but it still can't self-wrap.
1549 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1550 // Return the expression with the addrec on the outside.
1551 return getAddRecExpr(
1552 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1553 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1558 if (proveNoWrapByVaryingStart<SCEVZeroExtendExpr>(Start, Step, L)) {
1559 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1560 return getAddRecExpr(
1561 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1562 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1566 // The cast wasn't folded; create an explicit cast node.
1567 // Recompute the insert position, as it may have been invalidated.
1568 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1569 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
1571 UniqueSCEVs.InsertNode(S, IP);
1575 const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op,
1577 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1578 "This is not an extending conversion!");
1579 assert(isSCEVable(Ty) &&
1580 "This is not a conversion to a SCEVable type!");
1581 Ty = getEffectiveSCEVType(Ty);
1583 // Fold if the operand is constant.
1584 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1586 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), Ty)));
1588 // sext(sext(x)) --> sext(x)
1589 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1590 return getSignExtendExpr(SS->getOperand(), Ty);
1592 // sext(zext(x)) --> zext(x)
1593 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1594 return getZeroExtendExpr(SZ->getOperand(), Ty);
1596 // Before doing any expensive analysis, check to see if we've already
1597 // computed a SCEV for this Op and Ty.
1598 FoldingSetNodeID ID;
1599 ID.AddInteger(scSignExtend);
1603 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1605 // If the input value is provably positive, build a zext instead.
1606 if (isKnownNonNegative(Op))
1607 return getZeroExtendExpr(Op, Ty);
1609 // sext(trunc(x)) --> sext(x) or x or trunc(x)
1610 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1611 // It's possible the bits taken off by the truncate were all sign bits. If
1612 // so, we should be able to simplify this further.
1613 const SCEV *X = ST->getOperand();
1614 ConstantRange CR = getSignedRange(X);
1615 unsigned TruncBits = getTypeSizeInBits(ST->getType());
1616 unsigned NewBits = getTypeSizeInBits(Ty);
1617 if (CR.truncate(TruncBits).signExtend(NewBits).contains(
1618 CR.sextOrTrunc(NewBits)))
1619 return getTruncateOrSignExtend(X, Ty);
1622 // sext(C1 + (C2 * x)) --> C1 + sext(C2 * x) if C1 < C2
1623 if (auto SA = dyn_cast<SCEVAddExpr>(Op)) {
1624 if (SA->getNumOperands() == 2) {
1625 auto SC1 = dyn_cast<SCEVConstant>(SA->getOperand(0));
1626 auto SMul = dyn_cast<SCEVMulExpr>(SA->getOperand(1));
1628 if (auto SC2 = dyn_cast<SCEVConstant>(SMul->getOperand(0))) {
1629 const APInt &C1 = SC1->getValue()->getValue();
1630 const APInt &C2 = SC2->getValue()->getValue();
1631 if (C1.isStrictlyPositive() && C2.isStrictlyPositive() &&
1632 C2.ugt(C1) && C2.isPowerOf2())
1633 return getAddExpr(getSignExtendExpr(SC1, Ty),
1634 getSignExtendExpr(SMul, Ty));
1639 // If the input value is a chrec scev, and we can prove that the value
1640 // did not overflow the old, smaller, value, we can sign extend all of the
1641 // operands (often constants). This allows analysis of something like
1642 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
1643 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1644 if (AR->isAffine()) {
1645 const SCEV *Start = AR->getStart();
1646 const SCEV *Step = AR->getStepRecurrence(*this);
1647 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1648 const Loop *L = AR->getLoop();
1650 // If we have special knowledge that this addrec won't overflow,
1651 // we don't need to do any further analysis.
1652 if (AR->getNoWrapFlags(SCEV::FlagNSW))
1653 return getAddRecExpr(
1654 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1655 getSignExtendExpr(Step, Ty), L, SCEV::FlagNSW);
1657 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1658 // Note that this serves two purposes: It filters out loops that are
1659 // simply not analyzable, and it covers the case where this code is
1660 // being called from within backedge-taken count analysis, such that
1661 // attempting to ask for the backedge-taken count would likely result
1662 // in infinite recursion. In the later case, the analysis code will
1663 // cope with a conservative value, and it will take care to purge
1664 // that value once it has finished.
1665 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1666 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1667 // Manually compute the final value for AR, checking for
1670 // Check whether the backedge-taken count can be losslessly casted to
1671 // the addrec's type. The count is always unsigned.
1672 const SCEV *CastedMaxBECount =
1673 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1674 const SCEV *RecastedMaxBECount =
1675 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1676 if (MaxBECount == RecastedMaxBECount) {
1677 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1678 // Check whether Start+Step*MaxBECount has no signed overflow.
1679 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
1680 const SCEV *SAdd = getSignExtendExpr(getAddExpr(Start, SMul), WideTy);
1681 const SCEV *WideStart = getSignExtendExpr(Start, WideTy);
1682 const SCEV *WideMaxBECount =
1683 getZeroExtendExpr(CastedMaxBECount, WideTy);
1684 const SCEV *OperandExtendedAdd =
1685 getAddExpr(WideStart,
1686 getMulExpr(WideMaxBECount,
1687 getSignExtendExpr(Step, WideTy)));
1688 if (SAdd == OperandExtendedAdd) {
1689 // Cache knowledge of AR NSW, which is propagated to this AddRec.
1690 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1691 // Return the expression with the addrec on the outside.
1692 return getAddRecExpr(
1693 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1694 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1696 // Similar to above, only this time treat the step value as unsigned.
1697 // This covers loops that count up with an unsigned step.
1698 OperandExtendedAdd =
1699 getAddExpr(WideStart,
1700 getMulExpr(WideMaxBECount,
1701 getZeroExtendExpr(Step, WideTy)));
1702 if (SAdd == OperandExtendedAdd) {
1703 // If AR wraps around then
1705 // abs(Step) * MaxBECount > unsigned-max(AR->getType())
1706 // => SAdd != OperandExtendedAdd
1708 // Thus (AR is not NW => SAdd != OperandExtendedAdd) <=>
1709 // (SAdd == OperandExtendedAdd => AR is NW)
1711 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1713 // Return the expression with the addrec on the outside.
1714 return getAddRecExpr(
1715 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1716 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1720 // If the backedge is guarded by a comparison with the pre-inc value
1721 // the addrec is safe. Also, if the entry is guarded by a comparison
1722 // with the start value and the backedge is guarded by a comparison
1723 // with the post-inc value, the addrec is safe.
1724 ICmpInst::Predicate Pred;
1725 const SCEV *OverflowLimit =
1726 getSignedOverflowLimitForStep(Step, &Pred, this);
1727 if (OverflowLimit &&
1728 (isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) ||
1729 (isLoopEntryGuardedByCond(L, Pred, Start, OverflowLimit) &&
1730 isLoopBackedgeGuardedByCond(L, Pred, AR->getPostIncExpr(*this),
1732 // Cache knowledge of AR NSW, then propagate NSW to the wide AddRec.
1733 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1734 return getAddRecExpr(
1735 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1736 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1739 // If Start and Step are constants, check if we can apply this
1741 // sext{C1,+,C2} --> C1 + sext{0,+,C2} if C1 < C2
1742 auto SC1 = dyn_cast<SCEVConstant>(Start);
1743 auto SC2 = dyn_cast<SCEVConstant>(Step);
1745 const APInt &C1 = SC1->getValue()->getValue();
1746 const APInt &C2 = SC2->getValue()->getValue();
1747 if (C1.isStrictlyPositive() && C2.isStrictlyPositive() && C2.ugt(C1) &&
1749 Start = getSignExtendExpr(Start, Ty);
1750 const SCEV *NewAR = getAddRecExpr(getConstant(AR->getType(), 0), Step,
1751 L, AR->getNoWrapFlags());
1752 return getAddExpr(Start, getSignExtendExpr(NewAR, Ty));
1756 if (proveNoWrapByVaryingStart<SCEVSignExtendExpr>(Start, Step, L)) {
1757 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1758 return getAddRecExpr(
1759 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1760 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1764 // The cast wasn't folded; create an explicit cast node.
1765 // Recompute the insert position, as it may have been invalidated.
1766 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1767 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
1769 UniqueSCEVs.InsertNode(S, IP);
1773 /// getAnyExtendExpr - Return a SCEV for the given operand extended with
1774 /// unspecified bits out to the given type.
1776 const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
1778 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1779 "This is not an extending conversion!");
1780 assert(isSCEVable(Ty) &&
1781 "This is not a conversion to a SCEVable type!");
1782 Ty = getEffectiveSCEVType(Ty);
1784 // Sign-extend negative constants.
1785 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1786 if (SC->getValue()->getValue().isNegative())
1787 return getSignExtendExpr(Op, Ty);
1789 // Peel off a truncate cast.
1790 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
1791 const SCEV *NewOp = T->getOperand();
1792 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
1793 return getAnyExtendExpr(NewOp, Ty);
1794 return getTruncateOrNoop(NewOp, Ty);
1797 // Next try a zext cast. If the cast is folded, use it.
1798 const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
1799 if (!isa<SCEVZeroExtendExpr>(ZExt))
1802 // Next try a sext cast. If the cast is folded, use it.
1803 const SCEV *SExt = getSignExtendExpr(Op, Ty);
1804 if (!isa<SCEVSignExtendExpr>(SExt))
1807 // Force the cast to be folded into the operands of an addrec.
1808 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
1809 SmallVector<const SCEV *, 4> Ops;
1810 for (const SCEV *Op : AR->operands())
1811 Ops.push_back(getAnyExtendExpr(Op, Ty));
1812 return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW);
1815 // If the expression is obviously signed, use the sext cast value.
1816 if (isa<SCEVSMaxExpr>(Op))
1819 // Absent any other information, use the zext cast value.
1823 /// CollectAddOperandsWithScales - Process the given Ops list, which is
1824 /// a list of operands to be added under the given scale, update the given
1825 /// map. This is a helper function for getAddRecExpr. As an example of
1826 /// what it does, given a sequence of operands that would form an add
1827 /// expression like this:
1829 /// m + n + 13 + (A * (o + p + (B * (q + m + 29)))) + r + (-1 * r)
1831 /// where A and B are constants, update the map with these values:
1833 /// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
1835 /// and add 13 + A*B*29 to AccumulatedConstant.
1836 /// This will allow getAddRecExpr to produce this:
1838 /// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
1840 /// This form often exposes folding opportunities that are hidden in
1841 /// the original operand list.
1843 /// Return true iff it appears that any interesting folding opportunities
1844 /// may be exposed. This helps getAddRecExpr short-circuit extra work in
1845 /// the common case where no interesting opportunities are present, and
1846 /// is also used as a check to avoid infinite recursion.
1849 CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
1850 SmallVectorImpl<const SCEV *> &NewOps,
1851 APInt &AccumulatedConstant,
1852 const SCEV *const *Ops, size_t NumOperands,
1854 ScalarEvolution &SE) {
1855 bool Interesting = false;
1857 // Iterate over the add operands. They are sorted, with constants first.
1859 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1861 // Pull a buried constant out to the outside.
1862 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
1864 AccumulatedConstant += Scale * C->getValue()->getValue();
1867 // Next comes everything else. We're especially interested in multiplies
1868 // here, but they're in the middle, so just visit the rest with one loop.
1869 for (; i != NumOperands; ++i) {
1870 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
1871 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
1873 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue();
1874 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
1875 // A multiplication of a constant with another add; recurse.
1876 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1));
1878 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1879 Add->op_begin(), Add->getNumOperands(),
1882 // A multiplication of a constant with some other value. Update
1884 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
1885 const SCEV *Key = SE.getMulExpr(MulOps);
1886 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1887 M.insert(std::make_pair(Key, NewScale));
1889 NewOps.push_back(Pair.first->first);
1891 Pair.first->second += NewScale;
1892 // The map already had an entry for this value, which may indicate
1893 // a folding opportunity.
1898 // An ordinary operand. Update the map.
1899 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1900 M.insert(std::make_pair(Ops[i], Scale));
1902 NewOps.push_back(Pair.first->first);
1904 Pair.first->second += Scale;
1905 // The map already had an entry for this value, which may indicate
1906 // a folding opportunity.
1916 struct APIntCompare {
1917 bool operator()(const APInt &LHS, const APInt &RHS) const {
1918 return LHS.ult(RHS);
1923 // We're trying to construct a SCEV of type `Type' with `Ops' as operands and
1924 // `OldFlags' as can't-wrap behavior. Infer a more aggressive set of
1925 // can't-overflow flags for the operation if possible.
1926 static SCEV::NoWrapFlags
1927 StrengthenNoWrapFlags(ScalarEvolution *SE, SCEVTypes Type,
1928 const SmallVectorImpl<const SCEV *> &Ops,
1929 SCEV::NoWrapFlags OldFlags) {
1930 using namespace std::placeholders;
1933 Type == scAddExpr || Type == scAddRecExpr || Type == scMulExpr;
1935 assert(CanAnalyze && "don't call from other places!");
1937 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
1938 SCEV::NoWrapFlags SignOrUnsignWrap =
1939 ScalarEvolution::maskFlags(OldFlags, SignOrUnsignMask);
1941 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
1942 auto IsKnownNonNegative =
1943 std::bind(std::mem_fn(&ScalarEvolution::isKnownNonNegative), SE, _1);
1945 if (SignOrUnsignWrap == SCEV::FlagNSW &&
1946 std::all_of(Ops.begin(), Ops.end(), IsKnownNonNegative))
1947 return ScalarEvolution::setFlags(OldFlags,
1948 (SCEV::NoWrapFlags)SignOrUnsignMask);
1953 /// getAddExpr - Get a canonical add expression, or something simpler if
1955 const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
1956 SCEV::NoWrapFlags Flags) {
1957 assert(!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) &&
1958 "only nuw or nsw allowed");
1959 assert(!Ops.empty() && "Cannot get empty add!");
1960 if (Ops.size() == 1) return Ops[0];
1962 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
1963 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1964 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
1965 "SCEVAddExpr operand types don't match!");
1968 Flags = StrengthenNoWrapFlags(this, scAddExpr, Ops, Flags);
1970 // Sort by complexity, this groups all similar expression types together.
1971 GroupByComplexity(Ops, LI);
1973 // If there are any constants, fold them together.
1975 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1977 assert(Idx < Ops.size());
1978 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1979 // We found two constants, fold them together!
1980 Ops[0] = getConstant(LHSC->getValue()->getValue() +
1981 RHSC->getValue()->getValue());
1982 if (Ops.size() == 2) return Ops[0];
1983 Ops.erase(Ops.begin()+1); // Erase the folded element
1984 LHSC = cast<SCEVConstant>(Ops[0]);
1987 // If we are left with a constant zero being added, strip it off.
1988 if (LHSC->getValue()->isZero()) {
1989 Ops.erase(Ops.begin());
1993 if (Ops.size() == 1) return Ops[0];
1996 // Okay, check to see if the same value occurs in the operand list more than
1997 // once. If so, merge them together into an multiply expression. Since we
1998 // sorted the list, these values are required to be adjacent.
1999 Type *Ty = Ops[0]->getType();
2000 bool FoundMatch = false;
2001 for (unsigned i = 0, e = Ops.size(); i != e-1; ++i)
2002 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
2003 // Scan ahead to count how many equal operands there are.
2005 while (i+Count != e && Ops[i+Count] == Ops[i])
2007 // Merge the values into a multiply.
2008 const SCEV *Scale = getConstant(Ty, Count);
2009 const SCEV *Mul = getMulExpr(Scale, Ops[i]);
2010 if (Ops.size() == Count)
2013 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count);
2014 --i; e -= Count - 1;
2018 return getAddExpr(Ops, Flags);
2020 // Check for truncates. If all the operands are truncated from the same
2021 // type, see if factoring out the truncate would permit the result to be
2022 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
2023 // if the contents of the resulting outer trunc fold to something simple.
2024 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
2025 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
2026 Type *DstType = Trunc->getType();
2027 Type *SrcType = Trunc->getOperand()->getType();
2028 SmallVector<const SCEV *, 8> LargeOps;
2030 // Check all the operands to see if they can be represented in the
2031 // source type of the truncate.
2032 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
2033 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
2034 if (T->getOperand()->getType() != SrcType) {
2038 LargeOps.push_back(T->getOperand());
2039 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
2040 LargeOps.push_back(getAnyExtendExpr(C, SrcType));
2041 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
2042 SmallVector<const SCEV *, 8> LargeMulOps;
2043 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
2044 if (const SCEVTruncateExpr *T =
2045 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
2046 if (T->getOperand()->getType() != SrcType) {
2050 LargeMulOps.push_back(T->getOperand());
2051 } else if (const SCEVConstant *C =
2052 dyn_cast<SCEVConstant>(M->getOperand(j))) {
2053 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType));
2060 LargeOps.push_back(getMulExpr(LargeMulOps));
2067 // Evaluate the expression in the larger type.
2068 const SCEV *Fold = getAddExpr(LargeOps, Flags);
2069 // If it folds to something simple, use it. Otherwise, don't.
2070 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
2071 return getTruncateExpr(Fold, DstType);
2075 // Skip past any other cast SCEVs.
2076 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
2079 // If there are add operands they would be next.
2080 if (Idx < Ops.size()) {
2081 bool DeletedAdd = false;
2082 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
2083 // If we have an add, expand the add operands onto the end of the operands
2085 Ops.erase(Ops.begin()+Idx);
2086 Ops.append(Add->op_begin(), Add->op_end());
2090 // If we deleted at least one add, we added operands to the end of the list,
2091 // and they are not necessarily sorted. Recurse to resort and resimplify
2092 // any operands we just acquired.
2094 return getAddExpr(Ops);
2097 // Skip over the add expression until we get to a multiply.
2098 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
2101 // Check to see if there are any folding opportunities present with
2102 // operands multiplied by constant values.
2103 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
2104 uint64_t BitWidth = getTypeSizeInBits(Ty);
2105 DenseMap<const SCEV *, APInt> M;
2106 SmallVector<const SCEV *, 8> NewOps;
2107 APInt AccumulatedConstant(BitWidth, 0);
2108 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
2109 Ops.data(), Ops.size(),
2110 APInt(BitWidth, 1), *this)) {
2111 // Some interesting folding opportunity is present, so its worthwhile to
2112 // re-generate the operands list. Group the operands by constant scale,
2113 // to avoid multiplying by the same constant scale multiple times.
2114 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
2115 for (SmallVectorImpl<const SCEV *>::const_iterator I = NewOps.begin(),
2116 E = NewOps.end(); I != E; ++I)
2117 MulOpLists[M.find(*I)->second].push_back(*I);
2118 // Re-generate the operands list.
2120 if (AccumulatedConstant != 0)
2121 Ops.push_back(getConstant(AccumulatedConstant));
2122 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator
2123 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I)
2125 Ops.push_back(getMulExpr(getConstant(I->first),
2126 getAddExpr(I->second)));
2128 return getConstant(Ty, 0);
2129 if (Ops.size() == 1)
2131 return getAddExpr(Ops);
2135 // If we are adding something to a multiply expression, make sure the
2136 // something is not already an operand of the multiply. If so, merge it into
2138 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
2139 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
2140 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
2141 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
2142 if (isa<SCEVConstant>(MulOpSCEV))
2144 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
2145 if (MulOpSCEV == Ops[AddOp]) {
2146 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
2147 const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
2148 if (Mul->getNumOperands() != 2) {
2149 // If the multiply has more than two operands, we must get the
2151 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
2152 Mul->op_begin()+MulOp);
2153 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
2154 InnerMul = getMulExpr(MulOps);
2156 const SCEV *One = getConstant(Ty, 1);
2157 const SCEV *AddOne = getAddExpr(One, InnerMul);
2158 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV);
2159 if (Ops.size() == 2) return OuterMul;
2161 Ops.erase(Ops.begin()+AddOp);
2162 Ops.erase(Ops.begin()+Idx-1);
2164 Ops.erase(Ops.begin()+Idx);
2165 Ops.erase(Ops.begin()+AddOp-1);
2167 Ops.push_back(OuterMul);
2168 return getAddExpr(Ops);
2171 // Check this multiply against other multiplies being added together.
2172 for (unsigned OtherMulIdx = Idx+1;
2173 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
2175 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
2176 // If MulOp occurs in OtherMul, we can fold the two multiplies
2178 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
2179 OMulOp != e; ++OMulOp)
2180 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
2181 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
2182 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
2183 if (Mul->getNumOperands() != 2) {
2184 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
2185 Mul->op_begin()+MulOp);
2186 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
2187 InnerMul1 = getMulExpr(MulOps);
2189 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
2190 if (OtherMul->getNumOperands() != 2) {
2191 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
2192 OtherMul->op_begin()+OMulOp);
2193 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end());
2194 InnerMul2 = getMulExpr(MulOps);
2196 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
2197 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
2198 if (Ops.size() == 2) return OuterMul;
2199 Ops.erase(Ops.begin()+Idx);
2200 Ops.erase(Ops.begin()+OtherMulIdx-1);
2201 Ops.push_back(OuterMul);
2202 return getAddExpr(Ops);
2208 // If there are any add recurrences in the operands list, see if any other
2209 // added values are loop invariant. If so, we can fold them into the
2211 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2214 // Scan over all recurrences, trying to fold loop invariants into them.
2215 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
2216 // Scan all of the other operands to this add and add them to the vector if
2217 // they are loop invariant w.r.t. the recurrence.
2218 SmallVector<const SCEV *, 8> LIOps;
2219 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2220 const Loop *AddRecLoop = AddRec->getLoop();
2221 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2222 if (isLoopInvariant(Ops[i], AddRecLoop)) {
2223 LIOps.push_back(Ops[i]);
2224 Ops.erase(Ops.begin()+i);
2228 // If we found some loop invariants, fold them into the recurrence.
2229 if (!LIOps.empty()) {
2230 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
2231 LIOps.push_back(AddRec->getStart());
2233 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
2235 AddRecOps[0] = getAddExpr(LIOps);
2237 // Build the new addrec. Propagate the NUW and NSW flags if both the
2238 // outer add and the inner addrec are guaranteed to have no overflow.
2239 // Always propagate NW.
2240 Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW));
2241 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags);
2243 // If all of the other operands were loop invariant, we are done.
2244 if (Ops.size() == 1) return NewRec;
2246 // Otherwise, add the folded AddRec by the non-invariant parts.
2247 for (unsigned i = 0;; ++i)
2248 if (Ops[i] == AddRec) {
2252 return getAddExpr(Ops);
2255 // Okay, if there weren't any loop invariants to be folded, check to see if
2256 // there are multiple AddRec's with the same loop induction variable being
2257 // added together. If so, we can fold them.
2258 for (unsigned OtherIdx = Idx+1;
2259 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2261 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
2262 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L>
2263 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
2265 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2267 if (const SCEVAddRecExpr *OtherAddRec =
2268 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]))
2269 if (OtherAddRec->getLoop() == AddRecLoop) {
2270 for (unsigned i = 0, e = OtherAddRec->getNumOperands();
2272 if (i >= AddRecOps.size()) {
2273 AddRecOps.append(OtherAddRec->op_begin()+i,
2274 OtherAddRec->op_end());
2277 AddRecOps[i] = getAddExpr(AddRecOps[i],
2278 OtherAddRec->getOperand(i));
2280 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2282 // Step size has changed, so we cannot guarantee no self-wraparound.
2283 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap);
2284 return getAddExpr(Ops);
2287 // Otherwise couldn't fold anything into this recurrence. Move onto the
2291 // Okay, it looks like we really DO need an add expr. Check to see if we
2292 // already have one, otherwise create a new one.
2293 FoldingSetNodeID ID;
2294 ID.AddInteger(scAddExpr);
2295 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2296 ID.AddPointer(Ops[i]);
2299 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2301 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2302 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2303 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator),
2305 UniqueSCEVs.InsertNode(S, IP);
2307 S->setNoWrapFlags(Flags);
2311 static uint64_t umul_ov(uint64_t i, uint64_t j, bool &Overflow) {
2313 if (j > 1 && k / j != i) Overflow = true;
2317 /// Compute the result of "n choose k", the binomial coefficient. If an
2318 /// intermediate computation overflows, Overflow will be set and the return will
2319 /// be garbage. Overflow is not cleared on absence of overflow.
2320 static uint64_t Choose(uint64_t n, uint64_t k, bool &Overflow) {
2321 // We use the multiplicative formula:
2322 // n(n-1)(n-2)...(n-(k-1)) / k(k-1)(k-2)...1 .
2323 // At each iteration, we take the n-th term of the numeral and divide by the
2324 // (k-n)th term of the denominator. This division will always produce an
2325 // integral result, and helps reduce the chance of overflow in the
2326 // intermediate computations. However, we can still overflow even when the
2327 // final result would fit.
2329 if (n == 0 || n == k) return 1;
2330 if (k > n) return 0;
2336 for (uint64_t i = 1; i <= k; ++i) {
2337 r = umul_ov(r, n-(i-1), Overflow);
2343 /// Determine if any of the operands in this SCEV are a constant or if
2344 /// any of the add or multiply expressions in this SCEV contain a constant.
2345 static bool containsConstantSomewhere(const SCEV *StartExpr) {
2346 SmallVector<const SCEV *, 4> Ops;
2347 Ops.push_back(StartExpr);
2348 while (!Ops.empty()) {
2349 const SCEV *CurrentExpr = Ops.pop_back_val();
2350 if (isa<SCEVConstant>(*CurrentExpr))
2353 if (isa<SCEVAddExpr>(*CurrentExpr) || isa<SCEVMulExpr>(*CurrentExpr)) {
2354 const auto *CurrentNAry = cast<SCEVNAryExpr>(CurrentExpr);
2355 Ops.append(CurrentNAry->op_begin(), CurrentNAry->op_end());
2361 /// getMulExpr - Get a canonical multiply expression, or something simpler if
2363 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
2364 SCEV::NoWrapFlags Flags) {
2365 assert(Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) &&
2366 "only nuw or nsw allowed");
2367 assert(!Ops.empty() && "Cannot get empty mul!");
2368 if (Ops.size() == 1) return Ops[0];
2370 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2371 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2372 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2373 "SCEVMulExpr operand types don't match!");
2376 Flags = StrengthenNoWrapFlags(this, scMulExpr, Ops, Flags);
2378 // Sort by complexity, this groups all similar expression types together.
2379 GroupByComplexity(Ops, LI);
2381 // If there are any constants, fold them together.
2383 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2385 // C1*(C2+V) -> C1*C2 + C1*V
2386 if (Ops.size() == 2)
2387 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
2388 // If any of Add's ops are Adds or Muls with a constant,
2389 // apply this transformation as well.
2390 if (Add->getNumOperands() == 2)
2391 if (containsConstantSomewhere(Add))
2392 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
2393 getMulExpr(LHSC, Add->getOperand(1)));
2396 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2397 // We found two constants, fold them together!
2398 ConstantInt *Fold = ConstantInt::get(getContext(),
2399 LHSC->getValue()->getValue() *
2400 RHSC->getValue()->getValue());
2401 Ops[0] = getConstant(Fold);
2402 Ops.erase(Ops.begin()+1); // Erase the folded element
2403 if (Ops.size() == 1) return Ops[0];
2404 LHSC = cast<SCEVConstant>(Ops[0]);
2407 // If we are left with a constant one being multiplied, strip it off.
2408 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
2409 Ops.erase(Ops.begin());
2411 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
2412 // If we have a multiply of zero, it will always be zero.
2414 } else if (Ops[0]->isAllOnesValue()) {
2415 // If we have a mul by -1 of an add, try distributing the -1 among the
2417 if (Ops.size() == 2) {
2418 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
2419 SmallVector<const SCEV *, 4> NewOps;
2420 bool AnyFolded = false;
2421 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(),
2422 E = Add->op_end(); I != E; ++I) {
2423 const SCEV *Mul = getMulExpr(Ops[0], *I);
2424 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
2425 NewOps.push_back(Mul);
2428 return getAddExpr(NewOps);
2430 else if (const SCEVAddRecExpr *
2431 AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) {
2432 // Negation preserves a recurrence's no self-wrap property.
2433 SmallVector<const SCEV *, 4> Operands;
2434 for (SCEVAddRecExpr::op_iterator I = AddRec->op_begin(),
2435 E = AddRec->op_end(); I != E; ++I) {
2436 Operands.push_back(getMulExpr(Ops[0], *I));
2438 return getAddRecExpr(Operands, AddRec->getLoop(),
2439 AddRec->getNoWrapFlags(SCEV::FlagNW));
2444 if (Ops.size() == 1)
2448 // Skip over the add expression until we get to a multiply.
2449 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
2452 // If there are mul operands inline them all into this expression.
2453 if (Idx < Ops.size()) {
2454 bool DeletedMul = false;
2455 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
2456 // If we have an mul, expand the mul operands onto the end of the operands
2458 Ops.erase(Ops.begin()+Idx);
2459 Ops.append(Mul->op_begin(), Mul->op_end());
2463 // If we deleted at least one mul, we added operands to the end of the list,
2464 // and they are not necessarily sorted. Recurse to resort and resimplify
2465 // any operands we just acquired.
2467 return getMulExpr(Ops);
2470 // If there are any add recurrences in the operands list, see if any other
2471 // added values are loop invariant. If so, we can fold them into the
2473 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2476 // Scan over all recurrences, trying to fold loop invariants into them.
2477 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
2478 // Scan all of the other operands to this mul and add them to the vector if
2479 // they are loop invariant w.r.t. the recurrence.
2480 SmallVector<const SCEV *, 8> LIOps;
2481 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2482 const Loop *AddRecLoop = AddRec->getLoop();
2483 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2484 if (isLoopInvariant(Ops[i], AddRecLoop)) {
2485 LIOps.push_back(Ops[i]);
2486 Ops.erase(Ops.begin()+i);
2490 // If we found some loop invariants, fold them into the recurrence.
2491 if (!LIOps.empty()) {
2492 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
2493 SmallVector<const SCEV *, 4> NewOps;
2494 NewOps.reserve(AddRec->getNumOperands());
2495 const SCEV *Scale = getMulExpr(LIOps);
2496 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
2497 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
2499 // Build the new addrec. Propagate the NUW and NSW flags if both the
2500 // outer mul and the inner addrec are guaranteed to have no overflow.
2502 // No self-wrap cannot be guaranteed after changing the step size, but
2503 // will be inferred if either NUW or NSW is true.
2504 Flags = AddRec->getNoWrapFlags(clearFlags(Flags, SCEV::FlagNW));
2505 const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, Flags);
2507 // If all of the other operands were loop invariant, we are done.
2508 if (Ops.size() == 1) return NewRec;
2510 // Otherwise, multiply the folded AddRec by the non-invariant parts.
2511 for (unsigned i = 0;; ++i)
2512 if (Ops[i] == AddRec) {
2516 return getMulExpr(Ops);
2519 // Okay, if there weren't any loop invariants to be folded, check to see if
2520 // there are multiple AddRec's with the same loop induction variable being
2521 // multiplied together. If so, we can fold them.
2523 // {A1,+,A2,+,...,+,An}<L> * {B1,+,B2,+,...,+,Bn}<L>
2524 // = {x=1 in [ sum y=x..2x [ sum z=max(y-x, y-n)..min(x,n) [
2525 // choose(x, 2x)*choose(2x-y, x-z)*A_{y-z}*B_z
2526 // ]]],+,...up to x=2n}.
2527 // Note that the arguments to choose() are always integers with values
2528 // known at compile time, never SCEV objects.
2530 // The implementation avoids pointless extra computations when the two
2531 // addrec's are of different length (mathematically, it's equivalent to
2532 // an infinite stream of zeros on the right).
2533 bool OpsModified = false;
2534 for (unsigned OtherIdx = Idx+1;
2535 OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2537 const SCEVAddRecExpr *OtherAddRec =
2538 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]);
2539 if (!OtherAddRec || OtherAddRec->getLoop() != AddRecLoop)
2542 bool Overflow = false;
2543 Type *Ty = AddRec->getType();
2544 bool LargerThan64Bits = getTypeSizeInBits(Ty) > 64;
2545 SmallVector<const SCEV*, 7> AddRecOps;
2546 for (int x = 0, xe = AddRec->getNumOperands() +
2547 OtherAddRec->getNumOperands() - 1; x != xe && !Overflow; ++x) {
2548 const SCEV *Term = getConstant(Ty, 0);
2549 for (int y = x, ye = 2*x+1; y != ye && !Overflow; ++y) {
2550 uint64_t Coeff1 = Choose(x, 2*x - y, Overflow);
2551 for (int z = std::max(y-x, y-(int)AddRec->getNumOperands()+1),
2552 ze = std::min(x+1, (int)OtherAddRec->getNumOperands());
2553 z < ze && !Overflow; ++z) {
2554 uint64_t Coeff2 = Choose(2*x - y, x-z, Overflow);
2556 if (LargerThan64Bits)
2557 Coeff = umul_ov(Coeff1, Coeff2, Overflow);
2559 Coeff = Coeff1*Coeff2;
2560 const SCEV *CoeffTerm = getConstant(Ty, Coeff);
2561 const SCEV *Term1 = AddRec->getOperand(y-z);
2562 const SCEV *Term2 = OtherAddRec->getOperand(z);
2563 Term = getAddExpr(Term, getMulExpr(CoeffTerm, Term1,Term2));
2566 AddRecOps.push_back(Term);
2569 const SCEV *NewAddRec = getAddRecExpr(AddRecOps, AddRec->getLoop(),
2571 if (Ops.size() == 2) return NewAddRec;
2572 Ops[Idx] = NewAddRec;
2573 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2575 AddRec = dyn_cast<SCEVAddRecExpr>(NewAddRec);
2581 return getMulExpr(Ops);
2583 // Otherwise couldn't fold anything into this recurrence. Move onto the
2587 // Okay, it looks like we really DO need an mul expr. Check to see if we
2588 // already have one, otherwise create a new one.
2589 FoldingSetNodeID ID;
2590 ID.AddInteger(scMulExpr);
2591 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2592 ID.AddPointer(Ops[i]);
2595 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2597 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2598 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2599 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
2601 UniqueSCEVs.InsertNode(S, IP);
2603 S->setNoWrapFlags(Flags);
2607 /// getUDivExpr - Get a canonical unsigned division expression, or something
2608 /// simpler if possible.
2609 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
2611 assert(getEffectiveSCEVType(LHS->getType()) ==
2612 getEffectiveSCEVType(RHS->getType()) &&
2613 "SCEVUDivExpr operand types don't match!");
2615 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
2616 if (RHSC->getValue()->equalsInt(1))
2617 return LHS; // X udiv 1 --> x
2618 // If the denominator is zero, the result of the udiv is undefined. Don't
2619 // try to analyze it, because the resolution chosen here may differ from
2620 // the resolution chosen in other parts of the compiler.
2621 if (!RHSC->getValue()->isZero()) {
2622 // Determine if the division can be folded into the operands of
2624 // TODO: Generalize this to non-constants by using known-bits information.
2625 Type *Ty = LHS->getType();
2626 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
2627 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1;
2628 // For non-power-of-two values, effectively round the value up to the
2629 // nearest power of two.
2630 if (!RHSC->getValue()->getValue().isPowerOf2())
2632 IntegerType *ExtTy =
2633 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
2634 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
2635 if (const SCEVConstant *Step =
2636 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) {
2637 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
2638 const APInt &StepInt = Step->getValue()->getValue();
2639 const APInt &DivInt = RHSC->getValue()->getValue();
2640 if (!StepInt.urem(DivInt) &&
2641 getZeroExtendExpr(AR, ExtTy) ==
2642 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2643 getZeroExtendExpr(Step, ExtTy),
2644 AR->getLoop(), SCEV::FlagAnyWrap)) {
2645 SmallVector<const SCEV *, 4> Operands;
2646 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i)
2647 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS));
2648 return getAddRecExpr(Operands, AR->getLoop(),
2651 /// Get a canonical UDivExpr for a recurrence.
2652 /// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0.
2653 // We can currently only fold X%N if X is constant.
2654 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(AR->getStart());
2655 if (StartC && !DivInt.urem(StepInt) &&
2656 getZeroExtendExpr(AR, ExtTy) ==
2657 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2658 getZeroExtendExpr(Step, ExtTy),
2659 AR->getLoop(), SCEV::FlagAnyWrap)) {
2660 const APInt &StartInt = StartC->getValue()->getValue();
2661 const APInt &StartRem = StartInt.urem(StepInt);
2663 LHS = getAddRecExpr(getConstant(StartInt - StartRem), Step,
2664 AR->getLoop(), SCEV::FlagNW);
2667 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
2668 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
2669 SmallVector<const SCEV *, 4> Operands;
2670 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i)
2671 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy));
2672 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
2673 // Find an operand that's safely divisible.
2674 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
2675 const SCEV *Op = M->getOperand(i);
2676 const SCEV *Div = getUDivExpr(Op, RHSC);
2677 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
2678 Operands = SmallVector<const SCEV *, 4>(M->op_begin(),
2681 return getMulExpr(Operands);
2685 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
2686 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) {
2687 SmallVector<const SCEV *, 4> Operands;
2688 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i)
2689 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy));
2690 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
2692 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
2693 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
2694 if (isa<SCEVUDivExpr>(Op) ||
2695 getMulExpr(Op, RHS) != A->getOperand(i))
2697 Operands.push_back(Op);
2699 if (Operands.size() == A->getNumOperands())
2700 return getAddExpr(Operands);
2704 // Fold if both operands are constant.
2705 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
2706 Constant *LHSCV = LHSC->getValue();
2707 Constant *RHSCV = RHSC->getValue();
2708 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
2714 FoldingSetNodeID ID;
2715 ID.AddInteger(scUDivExpr);
2719 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2720 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
2722 UniqueSCEVs.InsertNode(S, IP);
2726 static const APInt gcd(const SCEVConstant *C1, const SCEVConstant *C2) {
2727 APInt A = C1->getValue()->getValue().abs();
2728 APInt B = C2->getValue()->getValue().abs();
2729 uint32_t ABW = A.getBitWidth();
2730 uint32_t BBW = B.getBitWidth();
2737 return APIntOps::GreatestCommonDivisor(A, B);
2740 /// getUDivExactExpr - Get a canonical unsigned division expression, or
2741 /// something simpler if possible. There is no representation for an exact udiv
2742 /// in SCEV IR, but we can attempt to remove factors from the LHS and RHS.
2743 /// We can't do this when it's not exact because the udiv may be clearing bits.
2744 const SCEV *ScalarEvolution::getUDivExactExpr(const SCEV *LHS,
2746 // TODO: we could try to find factors in all sorts of things, but for now we
2747 // just deal with u/exact (multiply, constant). See SCEVDivision towards the
2748 // end of this file for inspiration.
2750 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(LHS);
2752 return getUDivExpr(LHS, RHS);
2754 if (const SCEVConstant *RHSCst = dyn_cast<SCEVConstant>(RHS)) {
2755 // If the mulexpr multiplies by a constant, then that constant must be the
2756 // first element of the mulexpr.
2757 if (const SCEVConstant *LHSCst =
2758 dyn_cast<SCEVConstant>(Mul->getOperand(0))) {
2759 if (LHSCst == RHSCst) {
2760 SmallVector<const SCEV *, 2> Operands;
2761 Operands.append(Mul->op_begin() + 1, Mul->op_end());
2762 return getMulExpr(Operands);
2765 // We can't just assume that LHSCst divides RHSCst cleanly, it could be
2766 // that there's a factor provided by one of the other terms. We need to
2768 APInt Factor = gcd(LHSCst, RHSCst);
2769 if (!Factor.isIntN(1)) {
2770 LHSCst = cast<SCEVConstant>(
2771 getConstant(LHSCst->getValue()->getValue().udiv(Factor)));
2772 RHSCst = cast<SCEVConstant>(
2773 getConstant(RHSCst->getValue()->getValue().udiv(Factor)));
2774 SmallVector<const SCEV *, 2> Operands;
2775 Operands.push_back(LHSCst);
2776 Operands.append(Mul->op_begin() + 1, Mul->op_end());
2777 LHS = getMulExpr(Operands);
2779 Mul = dyn_cast<SCEVMulExpr>(LHS);
2781 return getUDivExactExpr(LHS, RHS);
2786 for (int i = 0, e = Mul->getNumOperands(); i != e; ++i) {
2787 if (Mul->getOperand(i) == RHS) {
2788 SmallVector<const SCEV *, 2> Operands;
2789 Operands.append(Mul->op_begin(), Mul->op_begin() + i);
2790 Operands.append(Mul->op_begin() + i + 1, Mul->op_end());
2791 return getMulExpr(Operands);
2795 return getUDivExpr(LHS, RHS);
2798 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2799 /// Simplify the expression as much as possible.
2800 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step,
2802 SCEV::NoWrapFlags Flags) {
2803 SmallVector<const SCEV *, 4> Operands;
2804 Operands.push_back(Start);
2805 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
2806 if (StepChrec->getLoop() == L) {
2807 Operands.append(StepChrec->op_begin(), StepChrec->op_end());
2808 return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW));
2811 Operands.push_back(Step);
2812 return getAddRecExpr(Operands, L, Flags);
2815 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2816 /// Simplify the expression as much as possible.
2818 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
2819 const Loop *L, SCEV::NoWrapFlags Flags) {
2820 if (Operands.size() == 1) return Operands[0];
2822 Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
2823 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
2824 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy &&
2825 "SCEVAddRecExpr operand types don't match!");
2826 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2827 assert(isLoopInvariant(Operands[i], L) &&
2828 "SCEVAddRecExpr operand is not loop-invariant!");
2831 if (Operands.back()->isZero()) {
2832 Operands.pop_back();
2833 return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0} --> X
2836 // It's tempting to want to call getMaxBackedgeTakenCount count here and
2837 // use that information to infer NUW and NSW flags. However, computing a
2838 // BE count requires calling getAddRecExpr, so we may not yet have a
2839 // meaningful BE count at this point (and if we don't, we'd be stuck
2840 // with a SCEVCouldNotCompute as the cached BE count).
2842 Flags = StrengthenNoWrapFlags(this, scAddRecExpr, Operands, Flags);
2844 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
2845 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
2846 const Loop *NestedLoop = NestedAR->getLoop();
2847 if (L->contains(NestedLoop) ?
2848 (L->getLoopDepth() < NestedLoop->getLoopDepth()) :
2849 (!NestedLoop->contains(L) &&
2850 DT->dominates(L->getHeader(), NestedLoop->getHeader()))) {
2851 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
2852 NestedAR->op_end());
2853 Operands[0] = NestedAR->getStart();
2854 // AddRecs require their operands be loop-invariant with respect to their
2855 // loops. Don't perform this transformation if it would break this
2857 bool AllInvariant = true;
2858 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2859 if (!isLoopInvariant(Operands[i], L)) {
2860 AllInvariant = false;
2864 // Create a recurrence for the outer loop with the same step size.
2866 // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the
2867 // inner recurrence has the same property.
2868 SCEV::NoWrapFlags OuterFlags =
2869 maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags());
2871 NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags);
2872 AllInvariant = true;
2873 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i)
2874 if (!isLoopInvariant(NestedOperands[i], NestedLoop)) {
2875 AllInvariant = false;
2879 // Ok, both add recurrences are valid after the transformation.
2881 // The inner recurrence keeps its NW flag but only keeps NUW/NSW if
2882 // the outer recurrence has the same property.
2883 SCEV::NoWrapFlags InnerFlags =
2884 maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags);
2885 return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags);
2888 // Reset Operands to its original state.
2889 Operands[0] = NestedAR;
2893 // Okay, it looks like we really DO need an addrec expr. Check to see if we
2894 // already have one, otherwise create a new one.
2895 FoldingSetNodeID ID;
2896 ID.AddInteger(scAddRecExpr);
2897 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2898 ID.AddPointer(Operands[i]);
2902 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2904 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size());
2905 std::uninitialized_copy(Operands.begin(), Operands.end(), O);
2906 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator),
2907 O, Operands.size(), L);
2908 UniqueSCEVs.InsertNode(S, IP);
2910 S->setNoWrapFlags(Flags);
2914 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
2916 SmallVector<const SCEV *, 2> Ops;
2919 return getSMaxExpr(Ops);
2923 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2924 assert(!Ops.empty() && "Cannot get empty smax!");
2925 if (Ops.size() == 1) return Ops[0];
2927 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2928 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2929 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2930 "SCEVSMaxExpr operand types don't match!");
2933 // Sort by complexity, this groups all similar expression types together.
2934 GroupByComplexity(Ops, LI);
2936 // If there are any constants, fold them together.
2938 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2940 assert(Idx < Ops.size());
2941 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2942 // We found two constants, fold them together!
2943 ConstantInt *Fold = ConstantInt::get(getContext(),
2944 APIntOps::smax(LHSC->getValue()->getValue(),
2945 RHSC->getValue()->getValue()));
2946 Ops[0] = getConstant(Fold);
2947 Ops.erase(Ops.begin()+1); // Erase the folded element
2948 if (Ops.size() == 1) return Ops[0];
2949 LHSC = cast<SCEVConstant>(Ops[0]);
2952 // If we are left with a constant minimum-int, strip it off.
2953 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
2954 Ops.erase(Ops.begin());
2956 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
2957 // If we have an smax with a constant maximum-int, it will always be
2962 if (Ops.size() == 1) return Ops[0];
2965 // Find the first SMax
2966 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
2969 // Check to see if one of the operands is an SMax. If so, expand its operands
2970 // onto our operand list, and recurse to simplify.
2971 if (Idx < Ops.size()) {
2972 bool DeletedSMax = false;
2973 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
2974 Ops.erase(Ops.begin()+Idx);
2975 Ops.append(SMax->op_begin(), SMax->op_end());
2980 return getSMaxExpr(Ops);
2983 // Okay, check to see if the same value occurs in the operand list twice. If
2984 // so, delete one. Since we sorted the list, these values are required to
2986 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2987 // X smax Y smax Y --> X smax Y
2988 // X smax Y --> X, if X is always greater than Y
2989 if (Ops[i] == Ops[i+1] ||
2990 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) {
2991 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2993 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) {
2994 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2998 if (Ops.size() == 1) return Ops[0];
3000 assert(!Ops.empty() && "Reduced smax down to nothing!");
3002 // Okay, it looks like we really DO need an smax expr. Check to see if we
3003 // already have one, otherwise create a new one.
3004 FoldingSetNodeID ID;
3005 ID.AddInteger(scSMaxExpr);
3006 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
3007 ID.AddPointer(Ops[i]);
3009 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
3010 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
3011 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
3012 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator),
3014 UniqueSCEVs.InsertNode(S, IP);
3018 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
3020 SmallVector<const SCEV *, 2> Ops;
3023 return getUMaxExpr(Ops);
3027 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
3028 assert(!Ops.empty() && "Cannot get empty umax!");
3029 if (Ops.size() == 1) return Ops[0];
3031 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
3032 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
3033 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
3034 "SCEVUMaxExpr operand types don't match!");
3037 // Sort by complexity, this groups all similar expression types together.
3038 GroupByComplexity(Ops, LI);
3040 // If there are any constants, fold them together.
3042 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
3044 assert(Idx < Ops.size());
3045 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
3046 // We found two constants, fold them together!
3047 ConstantInt *Fold = ConstantInt::get(getContext(),
3048 APIntOps::umax(LHSC->getValue()->getValue(),
3049 RHSC->getValue()->getValue()));
3050 Ops[0] = getConstant(Fold);
3051 Ops.erase(Ops.begin()+1); // Erase the folded element
3052 if (Ops.size() == 1) return Ops[0];
3053 LHSC = cast<SCEVConstant>(Ops[0]);
3056 // If we are left with a constant minimum-int, strip it off.
3057 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
3058 Ops.erase(Ops.begin());
3060 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
3061 // If we have an umax with a constant maximum-int, it will always be
3066 if (Ops.size() == 1) return Ops[0];
3069 // Find the first UMax
3070 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
3073 // Check to see if one of the operands is a UMax. If so, expand its operands
3074 // onto our operand list, and recurse to simplify.
3075 if (Idx < Ops.size()) {
3076 bool DeletedUMax = false;
3077 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
3078 Ops.erase(Ops.begin()+Idx);
3079 Ops.append(UMax->op_begin(), UMax->op_end());
3084 return getUMaxExpr(Ops);
3087 // Okay, check to see if the same value occurs in the operand list twice. If
3088 // so, delete one. Since we sorted the list, these values are required to
3090 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
3091 // X umax Y umax Y --> X umax Y
3092 // X umax Y --> X, if X is always greater than Y
3093 if (Ops[i] == Ops[i+1] ||
3094 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) {
3095 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
3097 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) {
3098 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
3102 if (Ops.size() == 1) return Ops[0];
3104 assert(!Ops.empty() && "Reduced umax down to nothing!");
3106 // Okay, it looks like we really DO need a umax expr. Check to see if we
3107 // already have one, otherwise create a new one.
3108 FoldingSetNodeID ID;
3109 ID.AddInteger(scUMaxExpr);
3110 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
3111 ID.AddPointer(Ops[i]);
3113 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
3114 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
3115 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
3116 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator),
3118 UniqueSCEVs.InsertNode(S, IP);
3122 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
3124 // ~smax(~x, ~y) == smin(x, y).
3125 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
3128 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
3130 // ~umax(~x, ~y) == umin(x, y)
3131 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
3134 const SCEV *ScalarEvolution::getSizeOfExpr(Type *IntTy, Type *AllocTy) {
3135 // We can bypass creating a target-independent
3136 // constant expression and then folding it back into a ConstantInt.
3137 // This is just a compile-time optimization.
3138 return getConstant(IntTy,
3139 F->getParent()->getDataLayout().getTypeAllocSize(AllocTy));
3142 const SCEV *ScalarEvolution::getOffsetOfExpr(Type *IntTy,
3145 // We can bypass creating a target-independent
3146 // constant expression and then folding it back into a ConstantInt.
3147 // This is just a compile-time optimization.
3150 F->getParent()->getDataLayout().getStructLayout(STy)->getElementOffset(
3154 const SCEV *ScalarEvolution::getUnknown(Value *V) {
3155 // Don't attempt to do anything other than create a SCEVUnknown object
3156 // here. createSCEV only calls getUnknown after checking for all other
3157 // interesting possibilities, and any other code that calls getUnknown
3158 // is doing so in order to hide a value from SCEV canonicalization.
3160 FoldingSetNodeID ID;
3161 ID.AddInteger(scUnknown);
3164 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
3165 assert(cast<SCEVUnknown>(S)->getValue() == V &&
3166 "Stale SCEVUnknown in uniquing map!");
3169 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
3171 FirstUnknown = cast<SCEVUnknown>(S);
3172 UniqueSCEVs.InsertNode(S, IP);
3176 //===----------------------------------------------------------------------===//
3177 // Basic SCEV Analysis and PHI Idiom Recognition Code
3180 /// isSCEVable - Test if values of the given type are analyzable within
3181 /// the SCEV framework. This primarily includes integer types, and it
3182 /// can optionally include pointer types if the ScalarEvolution class
3183 /// has access to target-specific information.
3184 bool ScalarEvolution::isSCEVable(Type *Ty) const {
3185 // Integers and pointers are always SCEVable.
3186 return Ty->isIntegerTy() || Ty->isPointerTy();
3189 /// getTypeSizeInBits - Return the size in bits of the specified type,
3190 /// for which isSCEVable must return true.
3191 uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const {
3192 assert(isSCEVable(Ty) && "Type is not SCEVable!");
3193 return F->getParent()->getDataLayout().getTypeSizeInBits(Ty);
3196 /// getEffectiveSCEVType - Return a type with the same bitwidth as
3197 /// the given type and which represents how SCEV will treat the given
3198 /// type, for which isSCEVable must return true. For pointer types,
3199 /// this is the pointer-sized integer type.
3200 Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const {
3201 assert(isSCEVable(Ty) && "Type is not SCEVable!");
3203 if (Ty->isIntegerTy()) {
3207 // The only other support type is pointer.
3208 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
3209 return F->getParent()->getDataLayout().getIntPtrType(Ty);
3212 const SCEV *ScalarEvolution::getCouldNotCompute() {
3213 return &CouldNotCompute;
3217 // Helper class working with SCEVTraversal to figure out if a SCEV contains
3218 // a SCEVUnknown with null value-pointer. FindInvalidSCEVUnknown::FindOne
3219 // is set iff if find such SCEVUnknown.
3221 struct FindInvalidSCEVUnknown {
3223 FindInvalidSCEVUnknown() { FindOne = false; }
3224 bool follow(const SCEV *S) {
3225 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
3229 if (!cast<SCEVUnknown>(S)->getValue())
3236 bool isDone() const { return FindOne; }
3240 bool ScalarEvolution::checkValidity(const SCEV *S) const {
3241 FindInvalidSCEVUnknown F;
3242 SCEVTraversal<FindInvalidSCEVUnknown> ST(F);
3248 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
3249 /// expression and create a new one.
3250 const SCEV *ScalarEvolution::getSCEV(Value *V) {
3251 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
3253 ValueExprMapType::iterator I = ValueExprMap.find_as(V);
3254 if (I != ValueExprMap.end()) {
3255 const SCEV *S = I->second;
3256 if (checkValidity(S))
3259 ValueExprMap.erase(I);
3261 const SCEV *S = createSCEV(V);
3263 // The process of creating a SCEV for V may have caused other SCEVs
3264 // to have been created, so it's necessary to insert the new entry
3265 // from scratch, rather than trying to remember the insert position
3267 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(V, this), S));
3271 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
3273 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) {
3274 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
3276 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
3278 Type *Ty = V->getType();
3279 Ty = getEffectiveSCEVType(Ty);
3280 return getMulExpr(V,
3281 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))));
3284 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
3285 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
3286 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
3288 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
3290 Type *Ty = V->getType();
3291 Ty = getEffectiveSCEVType(Ty);
3292 const SCEV *AllOnes =
3293 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
3294 return getMinusSCEV(AllOnes, V);
3297 /// getMinusSCEV - Return LHS-RHS. Minus is represented in SCEV as A+B*-1.
3298 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
3299 SCEV::NoWrapFlags Flags) {
3300 assert(!maskFlags(Flags, SCEV::FlagNUW) && "subtraction does not have NUW");
3302 // Fast path: X - X --> 0.
3304 return getConstant(LHS->getType(), 0);
3306 // X - Y --> X + -Y.
3307 // X -(nsw || nuw) Y --> X + -Y.
3308 return getAddExpr(LHS, getNegativeSCEV(RHS));
3311 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
3312 /// input value to the specified type. If the type must be extended, it is zero
3315 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty) {
3316 Type *SrcTy = V->getType();
3317 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3318 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3319 "Cannot truncate or zero extend with non-integer arguments!");
3320 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3321 return V; // No conversion
3322 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
3323 return getTruncateExpr(V, Ty);
3324 return getZeroExtendExpr(V, Ty);
3327 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
3328 /// input value to the specified type. If the type must be extended, it is sign
3331 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
3333 Type *SrcTy = V->getType();
3334 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3335 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3336 "Cannot truncate or zero extend with non-integer arguments!");
3337 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3338 return V; // No conversion
3339 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
3340 return getTruncateExpr(V, Ty);
3341 return getSignExtendExpr(V, Ty);
3344 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
3345 /// input value to the specified type. If the type must be extended, it is zero
3346 /// extended. The conversion must not be narrowing.
3348 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) {
3349 Type *SrcTy = V->getType();
3350 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3351 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3352 "Cannot noop or zero extend with non-integer arguments!");
3353 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3354 "getNoopOrZeroExtend cannot truncate!");
3355 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3356 return V; // No conversion
3357 return getZeroExtendExpr(V, Ty);
3360 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
3361 /// input value to the specified type. If the type must be extended, it is sign
3362 /// extended. The conversion must not be narrowing.
3364 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) {
3365 Type *SrcTy = V->getType();
3366 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3367 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3368 "Cannot noop or sign extend with non-integer arguments!");
3369 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3370 "getNoopOrSignExtend cannot truncate!");
3371 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3372 return V; // No conversion
3373 return getSignExtendExpr(V, Ty);
3376 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
3377 /// the input value to the specified type. If the type must be extended,
3378 /// it is extended with unspecified bits. The conversion must not be
3381 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) {
3382 Type *SrcTy = V->getType();
3383 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3384 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3385 "Cannot noop or any extend with non-integer arguments!");
3386 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3387 "getNoopOrAnyExtend cannot truncate!");
3388 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3389 return V; // No conversion
3390 return getAnyExtendExpr(V, Ty);
3393 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
3394 /// input value to the specified type. The conversion must not be widening.
3396 ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) {
3397 Type *SrcTy = V->getType();
3398 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3399 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3400 "Cannot truncate or noop with non-integer arguments!");
3401 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
3402 "getTruncateOrNoop cannot extend!");
3403 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3404 return V; // No conversion
3405 return getTruncateExpr(V, Ty);
3408 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
3409 /// the types using zero-extension, and then perform a umax operation
3411 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
3413 const SCEV *PromotedLHS = LHS;
3414 const SCEV *PromotedRHS = RHS;
3416 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
3417 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
3419 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
3421 return getUMaxExpr(PromotedLHS, PromotedRHS);
3424 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
3425 /// the types using zero-extension, and then perform a umin operation
3427 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
3429 const SCEV *PromotedLHS = LHS;
3430 const SCEV *PromotedRHS = RHS;
3432 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
3433 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
3435 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
3437 return getUMinExpr(PromotedLHS, PromotedRHS);
3440 /// getPointerBase - Transitively follow the chain of pointer-type operands
3441 /// until reaching a SCEV that does not have a single pointer operand. This
3442 /// returns a SCEVUnknown pointer for well-formed pointer-type expressions,
3443 /// but corner cases do exist.
3444 const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) {
3445 // A pointer operand may evaluate to a nonpointer expression, such as null.
3446 if (!V->getType()->isPointerTy())
3449 if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) {
3450 return getPointerBase(Cast->getOperand());
3452 else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) {
3453 const SCEV *PtrOp = nullptr;
3454 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
3456 if ((*I)->getType()->isPointerTy()) {
3457 // Cannot find the base of an expression with multiple pointer operands.
3465 return getPointerBase(PtrOp);
3470 /// PushDefUseChildren - Push users of the given Instruction
3471 /// onto the given Worklist.
3473 PushDefUseChildren(Instruction *I,
3474 SmallVectorImpl<Instruction *> &Worklist) {
3475 // Push the def-use children onto the Worklist stack.
3476 for (User *U : I->users())
3477 Worklist.push_back(cast<Instruction>(U));
3480 /// ForgetSymbolicValue - This looks up computed SCEV values for all
3481 /// instructions that depend on the given instruction and removes them from
3482 /// the ValueExprMapType map if they reference SymName. This is used during PHI
3485 ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) {
3486 SmallVector<Instruction *, 16> Worklist;
3487 PushDefUseChildren(PN, Worklist);
3489 SmallPtrSet<Instruction *, 8> Visited;
3491 while (!Worklist.empty()) {
3492 Instruction *I = Worklist.pop_back_val();
3493 if (!Visited.insert(I).second)
3496 ValueExprMapType::iterator It =
3497 ValueExprMap.find_as(static_cast<Value *>(I));
3498 if (It != ValueExprMap.end()) {
3499 const SCEV *Old = It->second;
3501 // Short-circuit the def-use traversal if the symbolic name
3502 // ceases to appear in expressions.
3503 if (Old != SymName && !hasOperand(Old, SymName))
3506 // SCEVUnknown for a PHI either means that it has an unrecognized
3507 // structure, it's a PHI that's in the progress of being computed
3508 // by createNodeForPHI, or it's a single-value PHI. In the first case,
3509 // additional loop trip count information isn't going to change anything.
3510 // In the second case, createNodeForPHI will perform the necessary
3511 // updates on its own when it gets to that point. In the third, we do
3512 // want to forget the SCEVUnknown.
3513 if (!isa<PHINode>(I) ||
3514 !isa<SCEVUnknown>(Old) ||
3515 (I != PN && Old == SymName)) {
3516 forgetMemoizedResults(Old);
3517 ValueExprMap.erase(It);
3521 PushDefUseChildren(I, Worklist);
3525 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
3526 /// a loop header, making it a potential recurrence, or it doesn't.
3528 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
3529 if (const Loop *L = LI->getLoopFor(PN->getParent()))
3530 if (L->getHeader() == PN->getParent()) {
3531 // The loop may have multiple entrances or multiple exits; we can analyze
3532 // this phi as an addrec if it has a unique entry value and a unique
3534 Value *BEValueV = nullptr, *StartValueV = nullptr;
3535 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
3536 Value *V = PN->getIncomingValue(i);
3537 if (L->contains(PN->getIncomingBlock(i))) {
3540 } else if (BEValueV != V) {
3544 } else if (!StartValueV) {
3546 } else if (StartValueV != V) {
3547 StartValueV = nullptr;
3551 if (BEValueV && StartValueV) {
3552 // While we are analyzing this PHI node, handle its value symbolically.
3553 const SCEV *SymbolicName = getUnknown(PN);
3554 assert(ValueExprMap.find_as(PN) == ValueExprMap.end() &&
3555 "PHI node already processed?");
3556 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
3558 // Using this symbolic name for the PHI, analyze the value coming around
3560 const SCEV *BEValue = getSCEV(BEValueV);
3562 // NOTE: If BEValue is loop invariant, we know that the PHI node just
3563 // has a special value for the first iteration of the loop.
3565 // If the value coming around the backedge is an add with the symbolic
3566 // value we just inserted, then we found a simple induction variable!
3567 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
3568 // If there is a single occurrence of the symbolic value, replace it
3569 // with a recurrence.
3570 unsigned FoundIndex = Add->getNumOperands();
3571 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3572 if (Add->getOperand(i) == SymbolicName)
3573 if (FoundIndex == e) {
3578 if (FoundIndex != Add->getNumOperands()) {
3579 // Create an add with everything but the specified operand.
3580 SmallVector<const SCEV *, 8> Ops;
3581 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3582 if (i != FoundIndex)
3583 Ops.push_back(Add->getOperand(i));
3584 const SCEV *Accum = getAddExpr(Ops);
3586 // This is not a valid addrec if the step amount is varying each
3587 // loop iteration, but is not itself an addrec in this loop.
3588 if (isLoopInvariant(Accum, L) ||
3589 (isa<SCEVAddRecExpr>(Accum) &&
3590 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
3591 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
3593 // If the increment doesn't overflow, then neither the addrec nor
3594 // the post-increment will overflow.
3595 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) {
3596 if (OBO->getOperand(0) == PN) {
3597 if (OBO->hasNoUnsignedWrap())
3598 Flags = setFlags(Flags, SCEV::FlagNUW);
3599 if (OBO->hasNoSignedWrap())
3600 Flags = setFlags(Flags, SCEV::FlagNSW);
3602 } else if (GEPOperator *GEP = dyn_cast<GEPOperator>(BEValueV)) {
3603 // If the increment is an inbounds GEP, then we know the address
3604 // space cannot be wrapped around. We cannot make any guarantee
3605 // about signed or unsigned overflow because pointers are
3606 // unsigned but we may have a negative index from the base
3607 // pointer. We can guarantee that no unsigned wrap occurs if the
3608 // indices form a positive value.
3609 if (GEP->isInBounds() && GEP->getOperand(0) == PN) {
3610 Flags = setFlags(Flags, SCEV::FlagNW);
3612 const SCEV *Ptr = getSCEV(GEP->getPointerOperand());
3613 if (isKnownPositive(getMinusSCEV(getSCEV(GEP), Ptr)))
3614 Flags = setFlags(Flags, SCEV::FlagNUW);
3617 // We cannot transfer nuw and nsw flags from subtraction
3618 // operations -- sub nuw X, Y is not the same as add nuw X, -Y
3622 const SCEV *StartVal = getSCEV(StartValueV);
3623 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
3625 // Since the no-wrap flags are on the increment, they apply to the
3626 // post-incremented value as well.
3627 if (isLoopInvariant(Accum, L))
3628 (void)getAddRecExpr(getAddExpr(StartVal, Accum),
3631 // Okay, for the entire analysis of this edge we assumed the PHI
3632 // to be symbolic. We now need to go back and purge all of the
3633 // entries for the scalars that use the symbolic expression.
3634 ForgetSymbolicName(PN, SymbolicName);
3635 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3639 } else if (const SCEVAddRecExpr *AddRec =
3640 dyn_cast<SCEVAddRecExpr>(BEValue)) {
3641 // Otherwise, this could be a loop like this:
3642 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
3643 // In this case, j = {1,+,1} and BEValue is j.
3644 // Because the other in-value of i (0) fits the evolution of BEValue
3645 // i really is an addrec evolution.
3646 if (AddRec->getLoop() == L && AddRec->isAffine()) {
3647 const SCEV *StartVal = getSCEV(StartValueV);
3649 // If StartVal = j.start - j.stride, we can use StartVal as the
3650 // initial step of the addrec evolution.
3651 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
3652 AddRec->getOperand(1))) {
3653 // FIXME: For constant StartVal, we should be able to infer
3655 const SCEV *PHISCEV =
3656 getAddRecExpr(StartVal, AddRec->getOperand(1), L,
3659 // Okay, for the entire analysis of this edge we assumed the PHI
3660 // to be symbolic. We now need to go back and purge all of the
3661 // entries for the scalars that use the symbolic expression.
3662 ForgetSymbolicName(PN, SymbolicName);
3663 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3671 // If the PHI has a single incoming value, follow that value, unless the
3672 // PHI's incoming blocks are in a different loop, in which case doing so
3673 // risks breaking LCSSA form. Instcombine would normally zap these, but
3674 // it doesn't have DominatorTree information, so it may miss cases.
3676 SimplifyInstruction(PN, F->getParent()->getDataLayout(), TLI, DT, AC))
3677 if (LI->replacementPreservesLCSSAForm(PN, V))
3680 // If it's not a loop phi, we can't handle it yet.
3681 return getUnknown(PN);
3684 /// createNodeForGEP - Expand GEP instructions into add and multiply
3685 /// operations. This allows them to be analyzed by regular SCEV code.
3687 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
3688 Type *IntPtrTy = getEffectiveSCEVType(GEP->getType());
3689 Value *Base = GEP->getOperand(0);
3690 // Don't attempt to analyze GEPs over unsized objects.
3691 if (!Base->getType()->getPointerElementType()->isSized())
3692 return getUnknown(GEP);
3694 // Don't blindly transfer the inbounds flag from the GEP instruction to the
3695 // Add expression, because the Instruction may be guarded by control flow
3696 // and the no-overflow bits may not be valid for the expression in any
3698 SCEV::NoWrapFlags Wrap = GEP->isInBounds() ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
3700 const SCEV *TotalOffset = getConstant(IntPtrTy, 0);
3701 gep_type_iterator GTI = gep_type_begin(GEP);
3702 for (GetElementPtrInst::op_iterator I = std::next(GEP->op_begin()),
3706 // Compute the (potentially symbolic) offset in bytes for this index.
3707 if (StructType *STy = dyn_cast<StructType>(*GTI++)) {
3708 // For a struct, add the member offset.
3709 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
3710 const SCEV *FieldOffset = getOffsetOfExpr(IntPtrTy, STy, FieldNo);
3712 // Add the field offset to the running total offset.
3713 TotalOffset = getAddExpr(TotalOffset, FieldOffset);
3715 // For an array, add the element offset, explicitly scaled.
3716 const SCEV *ElementSize = getSizeOfExpr(IntPtrTy, *GTI);
3717 const SCEV *IndexS = getSCEV(Index);
3718 // Getelementptr indices are signed.
3719 IndexS = getTruncateOrSignExtend(IndexS, IntPtrTy);
3721 // Multiply the index by the element size to compute the element offset.
3722 const SCEV *LocalOffset = getMulExpr(IndexS, ElementSize, Wrap);
3724 // Add the element offset to the running total offset.
3725 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
3729 // Get the SCEV for the GEP base.
3730 const SCEV *BaseS = getSCEV(Base);
3732 // Add the total offset from all the GEP indices to the base.
3733 return getAddExpr(BaseS, TotalOffset, Wrap);
3736 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
3737 /// guaranteed to end in (at every loop iteration). It is, at the same time,
3738 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
3739 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
3741 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
3742 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3743 return C->getValue()->getValue().countTrailingZeros();
3745 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
3746 return std::min(GetMinTrailingZeros(T->getOperand()),
3747 (uint32_t)getTypeSizeInBits(T->getType()));
3749 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
3750 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3751 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3752 getTypeSizeInBits(E->getType()) : OpRes;
3755 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
3756 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3757 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3758 getTypeSizeInBits(E->getType()) : OpRes;
3761 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
3762 // The result is the min of all operands results.
3763 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3764 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3765 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3769 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
3770 // The result is the sum of all operands results.
3771 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
3772 uint32_t BitWidth = getTypeSizeInBits(M->getType());
3773 for (unsigned i = 1, e = M->getNumOperands();
3774 SumOpRes != BitWidth && i != e; ++i)
3775 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
3780 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
3781 // The result is the min of all operands results.
3782 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3783 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3784 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3788 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
3789 // The result is the min of all operands results.
3790 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3791 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3792 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3796 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
3797 // The result is the min of all operands results.
3798 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3799 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3800 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3804 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3805 // For a SCEVUnknown, ask ValueTracking.
3806 unsigned BitWidth = getTypeSizeInBits(U->getType());
3807 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3808 computeKnownBits(U->getValue(), Zeros, Ones,
3809 F->getParent()->getDataLayout(), 0, AC, nullptr, DT);
3810 return Zeros.countTrailingOnes();
3817 /// GetRangeFromMetadata - Helper method to assign a range to V from
3818 /// metadata present in the IR.
3819 static Optional<ConstantRange> GetRangeFromMetadata(Value *V) {
3820 if (Instruction *I = dyn_cast<Instruction>(V)) {
3821 if (MDNode *MD = I->getMetadata(LLVMContext::MD_range)) {
3822 ConstantRange TotalRange(
3823 cast<IntegerType>(I->getType())->getBitWidth(), false);
3825 unsigned NumRanges = MD->getNumOperands() / 2;
3826 assert(NumRanges >= 1);
3828 for (unsigned i = 0; i < NumRanges; ++i) {
3829 ConstantInt *Lower =
3830 mdconst::extract<ConstantInt>(MD->getOperand(2 * i + 0));
3831 ConstantInt *Upper =
3832 mdconst::extract<ConstantInt>(MD->getOperand(2 * i + 1));
3833 ConstantRange Range(Lower->getValue(), Upper->getValue());
3834 TotalRange = TotalRange.unionWith(Range);
3844 /// getRange - Determine the range for a particular SCEV. If SignHint is
3845 /// HINT_RANGE_UNSIGNED (resp. HINT_RANGE_SIGNED) then getRange prefers ranges
3846 /// with a "cleaner" unsigned (resp. signed) representation.
3849 ScalarEvolution::getRange(const SCEV *S,
3850 ScalarEvolution::RangeSignHint SignHint) {
3851 DenseMap<const SCEV *, ConstantRange> &Cache =
3852 SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED ? UnsignedRanges
3855 // See if we've computed this range already.
3856 DenseMap<const SCEV *, ConstantRange>::iterator I = Cache.find(S);
3857 if (I != Cache.end())
3860 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3861 return setRange(C, SignHint, ConstantRange(C->getValue()->getValue()));
3863 unsigned BitWidth = getTypeSizeInBits(S->getType());
3864 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3866 // If the value has known zeros, the maximum value will have those known zeros
3868 uint32_t TZ = GetMinTrailingZeros(S);
3870 if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED)
3871 ConservativeResult =
3872 ConstantRange(APInt::getMinValue(BitWidth),
3873 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
3875 ConservativeResult = ConstantRange(
3876 APInt::getSignedMinValue(BitWidth),
3877 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
3880 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3881 ConstantRange X = getRange(Add->getOperand(0), SignHint);
3882 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3883 X = X.add(getRange(Add->getOperand(i), SignHint));
3884 return setRange(Add, SignHint, ConservativeResult.intersectWith(X));
3887 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3888 ConstantRange X = getRange(Mul->getOperand(0), SignHint);
3889 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3890 X = X.multiply(getRange(Mul->getOperand(i), SignHint));
3891 return setRange(Mul, SignHint, ConservativeResult.intersectWith(X));
3894 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3895 ConstantRange X = getRange(SMax->getOperand(0), SignHint);
3896 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3897 X = X.smax(getRange(SMax->getOperand(i), SignHint));
3898 return setRange(SMax, SignHint, ConservativeResult.intersectWith(X));
3901 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3902 ConstantRange X = getRange(UMax->getOperand(0), SignHint);
3903 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3904 X = X.umax(getRange(UMax->getOperand(i), SignHint));
3905 return setRange(UMax, SignHint, ConservativeResult.intersectWith(X));
3908 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3909 ConstantRange X = getRange(UDiv->getLHS(), SignHint);
3910 ConstantRange Y = getRange(UDiv->getRHS(), SignHint);
3911 return setRange(UDiv, SignHint,
3912 ConservativeResult.intersectWith(X.udiv(Y)));
3915 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3916 ConstantRange X = getRange(ZExt->getOperand(), SignHint);
3917 return setRange(ZExt, SignHint,
3918 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3921 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3922 ConstantRange X = getRange(SExt->getOperand(), SignHint);
3923 return setRange(SExt, SignHint,
3924 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3927 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3928 ConstantRange X = getRange(Trunc->getOperand(), SignHint);
3929 return setRange(Trunc, SignHint,
3930 ConservativeResult.intersectWith(X.truncate(BitWidth)));
3933 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3934 // If there's no unsigned wrap, the value will never be less than its
3936 if (AddRec->getNoWrapFlags(SCEV::FlagNUW))
3937 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
3938 if (!C->getValue()->isZero())
3939 ConservativeResult =
3940 ConservativeResult.intersectWith(
3941 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0)));
3943 // If there's no signed wrap, and all the operands have the same sign or
3944 // zero, the value won't ever change sign.
3945 if (AddRec->getNoWrapFlags(SCEV::FlagNSW)) {
3946 bool AllNonNeg = true;
3947 bool AllNonPos = true;
3948 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
3949 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
3950 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
3953 ConservativeResult = ConservativeResult.intersectWith(
3954 ConstantRange(APInt(BitWidth, 0),
3955 APInt::getSignedMinValue(BitWidth)));
3957 ConservativeResult = ConservativeResult.intersectWith(
3958 ConstantRange(APInt::getSignedMinValue(BitWidth),
3959 APInt(BitWidth, 1)));
3962 // TODO: non-affine addrec
3963 if (AddRec->isAffine()) {
3964 Type *Ty = AddRec->getType();
3965 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3966 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3967 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3969 // Check for overflow. This must be done with ConstantRange arithmetic
3970 // because we could be called from within the ScalarEvolution overflow
3973 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3974 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3975 ConstantRange ZExtMaxBECountRange =
3976 MaxBECountRange.zextOrTrunc(BitWidth * 2 + 1);
3978 const SCEV *Start = AddRec->getStart();
3979 const SCEV *Step = AddRec->getStepRecurrence(*this);
3980 ConstantRange StepSRange = getSignedRange(Step);
3981 ConstantRange SExtStepSRange = StepSRange.sextOrTrunc(BitWidth * 2 + 1);
3983 ConstantRange StartURange = getUnsignedRange(Start);
3984 ConstantRange EndURange =
3985 StartURange.add(MaxBECountRange.multiply(StepSRange));
3987 // Check for unsigned overflow.
3988 ConstantRange ZExtStartURange =
3989 StartURange.zextOrTrunc(BitWidth * 2 + 1);
3990 ConstantRange ZExtEndURange = EndURange.zextOrTrunc(BitWidth * 2 + 1);
3991 if (ZExtStartURange.add(ZExtMaxBECountRange.multiply(SExtStepSRange)) ==
3993 APInt Min = APIntOps::umin(StartURange.getUnsignedMin(),
3994 EndURange.getUnsignedMin());
3995 APInt Max = APIntOps::umax(StartURange.getUnsignedMax(),
3996 EndURange.getUnsignedMax());
3997 bool IsFullRange = Min.isMinValue() && Max.isMaxValue();
3999 ConservativeResult =
4000 ConservativeResult.intersectWith(ConstantRange(Min, Max + 1));
4003 ConstantRange StartSRange = getSignedRange(Start);
4004 ConstantRange EndSRange =
4005 StartSRange.add(MaxBECountRange.multiply(StepSRange));
4007 // Check for signed overflow. This must be done with ConstantRange
4008 // arithmetic because we could be called from within the ScalarEvolution
4009 // overflow checking code.
4010 ConstantRange SExtStartSRange =
4011 StartSRange.sextOrTrunc(BitWidth * 2 + 1);
4012 ConstantRange SExtEndSRange = EndSRange.sextOrTrunc(BitWidth * 2 + 1);
4013 if (SExtStartSRange.add(ZExtMaxBECountRange.multiply(SExtStepSRange)) ==
4015 APInt Min = APIntOps::smin(StartSRange.getSignedMin(),
4016 EndSRange.getSignedMin());
4017 APInt Max = APIntOps::smax(StartSRange.getSignedMax(),
4018 EndSRange.getSignedMax());
4019 bool IsFullRange = Min.isMinSignedValue() && Max.isMaxSignedValue();
4021 ConservativeResult =
4022 ConservativeResult.intersectWith(ConstantRange(Min, Max + 1));
4027 return setRange(AddRec, SignHint, ConservativeResult);
4030 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
4031 // Check if the IR explicitly contains !range metadata.
4032 Optional<ConstantRange> MDRange = GetRangeFromMetadata(U->getValue());
4033 if (MDRange.hasValue())
4034 ConservativeResult = ConservativeResult.intersectWith(MDRange.getValue());
4036 // Split here to avoid paying the compile-time cost of calling both
4037 // computeKnownBits and ComputeNumSignBits. This restriction can be lifted
4039 const DataLayout &DL = F->getParent()->getDataLayout();
4040 if (SignHint == ScalarEvolution::HINT_RANGE_UNSIGNED) {
4041 // For a SCEVUnknown, ask ValueTracking.
4042 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
4043 computeKnownBits(U->getValue(), Zeros, Ones, DL, 0, AC, nullptr, DT);
4044 if (Ones != ~Zeros + 1)
4045 ConservativeResult =
4046 ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1));
4048 assert(SignHint == ScalarEvolution::HINT_RANGE_SIGNED &&
4049 "generalize as needed!");
4050 unsigned NS = ComputeNumSignBits(U->getValue(), DL, 0, AC, nullptr, DT);
4052 ConservativeResult = ConservativeResult.intersectWith(
4053 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
4054 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1) + 1));
4057 return setRange(U, SignHint, ConservativeResult);
4060 return setRange(S, SignHint, ConservativeResult);
4063 /// createSCEV - We know that there is no SCEV for the specified value.
4064 /// Analyze the expression.
4066 const SCEV *ScalarEvolution::createSCEV(Value *V) {
4067 if (!isSCEVable(V->getType()))
4068 return getUnknown(V);
4070 unsigned Opcode = Instruction::UserOp1;
4071 if (Instruction *I = dyn_cast<Instruction>(V)) {
4072 Opcode = I->getOpcode();
4074 // Don't attempt to analyze instructions in blocks that aren't
4075 // reachable. Such instructions don't matter, and they aren't required
4076 // to obey basic rules for definitions dominating uses which this
4077 // analysis depends on.
4078 if (!DT->isReachableFromEntry(I->getParent()))
4079 return getUnknown(V);
4080 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
4081 Opcode = CE->getOpcode();
4082 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
4083 return getConstant(CI);
4084 else if (isa<ConstantPointerNull>(V))
4085 return getConstant(V->getType(), 0);
4086 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
4087 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee());
4089 return getUnknown(V);
4091 Operator *U = cast<Operator>(V);
4093 case Instruction::Add: {
4094 // The simple thing to do would be to just call getSCEV on both operands
4095 // and call getAddExpr with the result. However if we're looking at a
4096 // bunch of things all added together, this can be quite inefficient,
4097 // because it leads to N-1 getAddExpr calls for N ultimate operands.
4098 // Instead, gather up all the operands and make a single getAddExpr call.
4099 // LLVM IR canonical form means we need only traverse the left operands.
4101 // Don't apply this instruction's NSW or NUW flags to the new
4102 // expression. The instruction may be guarded by control flow that the
4103 // no-wrap behavior depends on. Non-control-equivalent instructions can be
4104 // mapped to the same SCEV expression, and it would be incorrect to transfer
4105 // NSW/NUW semantics to those operations.
4106 SmallVector<const SCEV *, 4> AddOps;
4107 AddOps.push_back(getSCEV(U->getOperand(1)));
4108 for (Value *Op = U->getOperand(0); ; Op = U->getOperand(0)) {
4109 unsigned Opcode = Op->getValueID() - Value::InstructionVal;
4110 if (Opcode != Instruction::Add && Opcode != Instruction::Sub)
4112 U = cast<Operator>(Op);
4113 const SCEV *Op1 = getSCEV(U->getOperand(1));
4114 if (Opcode == Instruction::Sub)
4115 AddOps.push_back(getNegativeSCEV(Op1));
4117 AddOps.push_back(Op1);
4119 AddOps.push_back(getSCEV(U->getOperand(0)));
4120 return getAddExpr(AddOps);
4122 case Instruction::Mul: {
4123 // Don't transfer NSW/NUW for the same reason as AddExpr.
4124 SmallVector<const SCEV *, 4> MulOps;
4125 MulOps.push_back(getSCEV(U->getOperand(1)));
4126 for (Value *Op = U->getOperand(0);
4127 Op->getValueID() == Instruction::Mul + Value::InstructionVal;
4128 Op = U->getOperand(0)) {
4129 U = cast<Operator>(Op);
4130 MulOps.push_back(getSCEV(U->getOperand(1)));
4132 MulOps.push_back(getSCEV(U->getOperand(0)));
4133 return getMulExpr(MulOps);
4135 case Instruction::UDiv:
4136 return getUDivExpr(getSCEV(U->getOperand(0)),
4137 getSCEV(U->getOperand(1)));
4138 case Instruction::Sub:
4139 return getMinusSCEV(getSCEV(U->getOperand(0)),
4140 getSCEV(U->getOperand(1)));
4141 case Instruction::And:
4142 // For an expression like x&255 that merely masks off the high bits,
4143 // use zext(trunc(x)) as the SCEV expression.
4144 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
4145 if (CI->isNullValue())
4146 return getSCEV(U->getOperand(1));
4147 if (CI->isAllOnesValue())
4148 return getSCEV(U->getOperand(0));
4149 const APInt &A = CI->getValue();
4151 // Instcombine's ShrinkDemandedConstant may strip bits out of
4152 // constants, obscuring what would otherwise be a low-bits mask.
4153 // Use computeKnownBits to compute what ShrinkDemandedConstant
4154 // knew about to reconstruct a low-bits mask value.
4155 unsigned LZ = A.countLeadingZeros();
4156 unsigned TZ = A.countTrailingZeros();
4157 unsigned BitWidth = A.getBitWidth();
4158 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
4159 computeKnownBits(U->getOperand(0), KnownZero, KnownOne,
4160 F->getParent()->getDataLayout(), 0, AC, nullptr, DT);
4162 APInt EffectiveMask =
4163 APInt::getLowBitsSet(BitWidth, BitWidth - LZ - TZ).shl(TZ);
4164 if ((LZ != 0 || TZ != 0) && !((~A & ~KnownZero) & EffectiveMask)) {
4165 const SCEV *MulCount = getConstant(
4166 ConstantInt::get(getContext(), APInt::getOneBitSet(BitWidth, TZ)));
4170 getUDivExactExpr(getSCEV(U->getOperand(0)), MulCount),
4171 IntegerType::get(getContext(), BitWidth - LZ - TZ)),
4178 case Instruction::Or:
4179 // If the RHS of the Or is a constant, we may have something like:
4180 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
4181 // optimizations will transparently handle this case.
4183 // In order for this transformation to be safe, the LHS must be of the
4184 // form X*(2^n) and the Or constant must be less than 2^n.
4185 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
4186 const SCEV *LHS = getSCEV(U->getOperand(0));
4187 const APInt &CIVal = CI->getValue();
4188 if (GetMinTrailingZeros(LHS) >=
4189 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
4190 // Build a plain add SCEV.
4191 const SCEV *S = getAddExpr(LHS, getSCEV(CI));
4192 // If the LHS of the add was an addrec and it has no-wrap flags,
4193 // transfer the no-wrap flags, since an or won't introduce a wrap.
4194 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
4195 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
4196 const_cast<SCEVAddRecExpr *>(NewAR)->setNoWrapFlags(
4197 OldAR->getNoWrapFlags());
4203 case Instruction::Xor:
4204 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
4205 // If the RHS of the xor is a signbit, then this is just an add.
4206 // Instcombine turns add of signbit into xor as a strength reduction step.
4207 if (CI->getValue().isSignBit())
4208 return getAddExpr(getSCEV(U->getOperand(0)),
4209 getSCEV(U->getOperand(1)));
4211 // If the RHS of xor is -1, then this is a not operation.
4212 if (CI->isAllOnesValue())
4213 return getNotSCEV(getSCEV(U->getOperand(0)));
4215 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
4216 // This is a variant of the check for xor with -1, and it handles
4217 // the case where instcombine has trimmed non-demanded bits out
4218 // of an xor with -1.
4219 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
4220 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
4221 if (BO->getOpcode() == Instruction::And &&
4222 LCI->getValue() == CI->getValue())
4223 if (const SCEVZeroExtendExpr *Z =
4224 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
4225 Type *UTy = U->getType();
4226 const SCEV *Z0 = Z->getOperand();
4227 Type *Z0Ty = Z0->getType();
4228 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
4230 // If C is a low-bits mask, the zero extend is serving to
4231 // mask off the high bits. Complement the operand and
4232 // re-apply the zext.
4233 if (APIntOps::isMask(Z0TySize, CI->getValue()))
4234 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
4236 // If C is a single bit, it may be in the sign-bit position
4237 // before the zero-extend. In this case, represent the xor
4238 // using an add, which is equivalent, and re-apply the zext.
4239 APInt Trunc = CI->getValue().trunc(Z0TySize);
4240 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
4242 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
4248 case Instruction::Shl:
4249 // Turn shift left of a constant amount into a multiply.
4250 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
4251 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
4253 // If the shift count is not less than the bitwidth, the result of
4254 // the shift is undefined. Don't try to analyze it, because the
4255 // resolution chosen here may differ from the resolution chosen in
4256 // other parts of the compiler.
4257 if (SA->getValue().uge(BitWidth))
4260 Constant *X = ConstantInt::get(getContext(),
4261 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
4262 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
4266 case Instruction::LShr:
4267 // Turn logical shift right of a constant into a unsigned divide.
4268 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
4269 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
4271 // If the shift count is not less than the bitwidth, the result of
4272 // the shift is undefined. Don't try to analyze it, because the
4273 // resolution chosen here may differ from the resolution chosen in
4274 // other parts of the compiler.
4275 if (SA->getValue().uge(BitWidth))
4278 Constant *X = ConstantInt::get(getContext(),
4279 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
4280 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
4284 case Instruction::AShr:
4285 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
4286 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
4287 if (Operator *L = dyn_cast<Operator>(U->getOperand(0)))
4288 if (L->getOpcode() == Instruction::Shl &&
4289 L->getOperand(1) == U->getOperand(1)) {
4290 uint64_t BitWidth = getTypeSizeInBits(U->getType());
4292 // If the shift count is not less than the bitwidth, the result of
4293 // the shift is undefined. Don't try to analyze it, because the
4294 // resolution chosen here may differ from the resolution chosen in
4295 // other parts of the compiler.
4296 if (CI->getValue().uge(BitWidth))
4299 uint64_t Amt = BitWidth - CI->getZExtValue();
4300 if (Amt == BitWidth)
4301 return getSCEV(L->getOperand(0)); // shift by zero --> noop
4303 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
4304 IntegerType::get(getContext(),
4310 case Instruction::Trunc:
4311 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
4313 case Instruction::ZExt:
4314 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
4316 case Instruction::SExt:
4317 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
4319 case Instruction::BitCast:
4320 // BitCasts are no-op casts so we just eliminate the cast.
4321 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
4322 return getSCEV(U->getOperand(0));
4325 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
4326 // lead to pointer expressions which cannot safely be expanded to GEPs,
4327 // because ScalarEvolution doesn't respect the GEP aliasing rules when
4328 // simplifying integer expressions.
4330 case Instruction::GetElementPtr:
4331 return createNodeForGEP(cast<GEPOperator>(U));
4333 case Instruction::PHI:
4334 return createNodeForPHI(cast<PHINode>(U));
4336 case Instruction::Select:
4337 // This could be a smax or umax that was lowered earlier.
4338 // Try to recover it.
4339 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
4340 Value *LHS = ICI->getOperand(0);
4341 Value *RHS = ICI->getOperand(1);
4342 switch (ICI->getPredicate()) {
4343 case ICmpInst::ICMP_SLT:
4344 case ICmpInst::ICMP_SLE:
4345 std::swap(LHS, RHS);
4347 case ICmpInst::ICMP_SGT:
4348 case ICmpInst::ICMP_SGE:
4349 // a >s b ? a+x : b+x -> smax(a, b)+x
4350 // a >s b ? b+x : a+x -> smin(a, b)+x
4351 if (getTypeSizeInBits(LHS->getType()) <=
4352 getTypeSizeInBits(U->getType())) {
4353 const SCEV *LS = getNoopOrSignExtend(getSCEV(LHS), U->getType());
4354 const SCEV *RS = getNoopOrSignExtend(getSCEV(RHS), U->getType());
4355 const SCEV *LA = getSCEV(U->getOperand(1));
4356 const SCEV *RA = getSCEV(U->getOperand(2));
4357 const SCEV *LDiff = getMinusSCEV(LA, LS);
4358 const SCEV *RDiff = getMinusSCEV(RA, RS);
4360 return getAddExpr(getSMaxExpr(LS, RS), LDiff);
4361 LDiff = getMinusSCEV(LA, RS);
4362 RDiff = getMinusSCEV(RA, LS);
4364 return getAddExpr(getSMinExpr(LS, RS), LDiff);
4367 case ICmpInst::ICMP_ULT:
4368 case ICmpInst::ICMP_ULE:
4369 std::swap(LHS, RHS);
4371 case ICmpInst::ICMP_UGT:
4372 case ICmpInst::ICMP_UGE:
4373 // a >u b ? a+x : b+x -> umax(a, b)+x
4374 // a >u b ? b+x : a+x -> umin(a, b)+x
4375 if (getTypeSizeInBits(LHS->getType()) <=
4376 getTypeSizeInBits(U->getType())) {
4377 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), U->getType());
4378 const SCEV *RS = getNoopOrZeroExtend(getSCEV(RHS), U->getType());
4379 const SCEV *LA = getSCEV(U->getOperand(1));
4380 const SCEV *RA = getSCEV(U->getOperand(2));
4381 const SCEV *LDiff = getMinusSCEV(LA, LS);
4382 const SCEV *RDiff = getMinusSCEV(RA, RS);
4384 return getAddExpr(getUMaxExpr(LS, RS), LDiff);
4385 LDiff = getMinusSCEV(LA, RS);
4386 RDiff = getMinusSCEV(RA, LS);
4388 return getAddExpr(getUMinExpr(LS, RS), LDiff);
4391 case ICmpInst::ICMP_NE:
4392 // n != 0 ? n+x : 1+x -> umax(n, 1)+x
4393 if (getTypeSizeInBits(LHS->getType()) <=
4394 getTypeSizeInBits(U->getType()) &&
4395 isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
4396 const SCEV *One = getConstant(U->getType(), 1);
4397 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), U->getType());
4398 const SCEV *LA = getSCEV(U->getOperand(1));
4399 const SCEV *RA = getSCEV(U->getOperand(2));
4400 const SCEV *LDiff = getMinusSCEV(LA, LS);
4401 const SCEV *RDiff = getMinusSCEV(RA, One);
4403 return getAddExpr(getUMaxExpr(One, LS), LDiff);
4406 case ICmpInst::ICMP_EQ:
4407 // n == 0 ? 1+x : n+x -> umax(n, 1)+x
4408 if (getTypeSizeInBits(LHS->getType()) <=
4409 getTypeSizeInBits(U->getType()) &&
4410 isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
4411 const SCEV *One = getConstant(U->getType(), 1);
4412 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), U->getType());
4413 const SCEV *LA = getSCEV(U->getOperand(1));
4414 const SCEV *RA = getSCEV(U->getOperand(2));
4415 const SCEV *LDiff = getMinusSCEV(LA, One);
4416 const SCEV *RDiff = getMinusSCEV(RA, LS);
4418 return getAddExpr(getUMaxExpr(One, LS), LDiff);
4426 default: // We cannot analyze this expression.
4430 return getUnknown(V);
4435 //===----------------------------------------------------------------------===//
4436 // Iteration Count Computation Code
4439 unsigned ScalarEvolution::getSmallConstantTripCount(Loop *L) {
4440 if (BasicBlock *ExitingBB = L->getExitingBlock())
4441 return getSmallConstantTripCount(L, ExitingBB);
4443 // No trip count information for multiple exits.
4447 /// getSmallConstantTripCount - Returns the maximum trip count of this loop as a
4448 /// normal unsigned value. Returns 0 if the trip count is unknown or not
4449 /// constant. Will also return 0 if the maximum trip count is very large (>=
4452 /// This "trip count" assumes that control exits via ExitingBlock. More
4453 /// precisely, it is the number of times that control may reach ExitingBlock
4454 /// before taking the branch. For loops with multiple exits, it may not be the
4455 /// number times that the loop header executes because the loop may exit
4456 /// prematurely via another branch.
4457 unsigned ScalarEvolution::getSmallConstantTripCount(Loop *L,
4458 BasicBlock *ExitingBlock) {
4459 assert(ExitingBlock && "Must pass a non-null exiting block!");
4460 assert(L->isLoopExiting(ExitingBlock) &&
4461 "Exiting block must actually branch out of the loop!");
4462 const SCEVConstant *ExitCount =
4463 dyn_cast<SCEVConstant>(getExitCount(L, ExitingBlock));
4467 ConstantInt *ExitConst = ExitCount->getValue();
4469 // Guard against huge trip counts.
4470 if (ExitConst->getValue().getActiveBits() > 32)
4473 // In case of integer overflow, this returns 0, which is correct.
4474 return ((unsigned)ExitConst->getZExtValue()) + 1;
4477 unsigned ScalarEvolution::getSmallConstantTripMultiple(Loop *L) {
4478 if (BasicBlock *ExitingBB = L->getExitingBlock())
4479 return getSmallConstantTripMultiple(L, ExitingBB);
4481 // No trip multiple information for multiple exits.
4485 /// getSmallConstantTripMultiple - Returns the largest constant divisor of the
4486 /// trip count of this loop as a normal unsigned value, if possible. This
4487 /// means that the actual trip count is always a multiple of the returned
4488 /// value (don't forget the trip count could very well be zero as well!).
4490 /// Returns 1 if the trip count is unknown or not guaranteed to be the
4491 /// multiple of a constant (which is also the case if the trip count is simply
4492 /// constant, use getSmallConstantTripCount for that case), Will also return 1
4493 /// if the trip count is very large (>= 2^32).
4495 /// As explained in the comments for getSmallConstantTripCount, this assumes
4496 /// that control exits the loop via ExitingBlock.
4498 ScalarEvolution::getSmallConstantTripMultiple(Loop *L,
4499 BasicBlock *ExitingBlock) {
4500 assert(ExitingBlock && "Must pass a non-null exiting block!");
4501 assert(L->isLoopExiting(ExitingBlock) &&
4502 "Exiting block must actually branch out of the loop!");
4503 const SCEV *ExitCount = getExitCount(L, ExitingBlock);
4504 if (ExitCount == getCouldNotCompute())
4507 // Get the trip count from the BE count by adding 1.
4508 const SCEV *TCMul = getAddExpr(ExitCount,
4509 getConstant(ExitCount->getType(), 1));
4510 // FIXME: SCEV distributes multiplication as V1*C1 + V2*C1. We could attempt
4511 // to factor simple cases.
4512 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(TCMul))
4513 TCMul = Mul->getOperand(0);
4515 const SCEVConstant *MulC = dyn_cast<SCEVConstant>(TCMul);
4519 ConstantInt *Result = MulC->getValue();
4521 // Guard against huge trip counts (this requires checking
4522 // for zero to handle the case where the trip count == -1 and the
4524 if (!Result || Result->getValue().getActiveBits() > 32 ||
4525 Result->getValue().getActiveBits() == 0)
4528 return (unsigned)Result->getZExtValue();
4531 // getExitCount - Get the expression for the number of loop iterations for which
4532 // this loop is guaranteed not to exit via ExitingBlock. Otherwise return
4533 // SCEVCouldNotCompute.
4534 const SCEV *ScalarEvolution::getExitCount(Loop *L, BasicBlock *ExitingBlock) {
4535 return getBackedgeTakenInfo(L).getExact(ExitingBlock, this);
4538 /// getBackedgeTakenCount - If the specified loop has a predictable
4539 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
4540 /// object. The backedge-taken count is the number of times the loop header
4541 /// will be branched to from within the loop. This is one less than the
4542 /// trip count of the loop, since it doesn't count the first iteration,
4543 /// when the header is branched to from outside the loop.
4545 /// Note that it is not valid to call this method on a loop without a
4546 /// loop-invariant backedge-taken count (see
4547 /// hasLoopInvariantBackedgeTakenCount).
4549 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
4550 return getBackedgeTakenInfo(L).getExact(this);
4553 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
4554 /// return the least SCEV value that is known never to be less than the
4555 /// actual backedge taken count.
4556 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
4557 return getBackedgeTakenInfo(L).getMax(this);
4560 /// PushLoopPHIs - Push PHI nodes in the header of the given loop
4561 /// onto the given Worklist.
4563 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
4564 BasicBlock *Header = L->getHeader();
4566 // Push all Loop-header PHIs onto the Worklist stack.
4567 for (BasicBlock::iterator I = Header->begin();
4568 PHINode *PN = dyn_cast<PHINode>(I); ++I)
4569 Worklist.push_back(PN);
4572 const ScalarEvolution::BackedgeTakenInfo &
4573 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
4574 // Initially insert an invalid entry for this loop. If the insertion
4575 // succeeds, proceed to actually compute a backedge-taken count and
4576 // update the value. The temporary CouldNotCompute value tells SCEV
4577 // code elsewhere that it shouldn't attempt to request a new
4578 // backedge-taken count, which could result in infinite recursion.
4579 std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
4580 BackedgeTakenCounts.insert(std::make_pair(L, BackedgeTakenInfo()));
4582 return Pair.first->second;
4584 // ComputeBackedgeTakenCount may allocate memory for its result. Inserting it
4585 // into the BackedgeTakenCounts map transfers ownership. Otherwise, the result
4586 // must be cleared in this scope.
4587 BackedgeTakenInfo Result = ComputeBackedgeTakenCount(L);
4589 if (Result.getExact(this) != getCouldNotCompute()) {
4590 assert(isLoopInvariant(Result.getExact(this), L) &&
4591 isLoopInvariant(Result.getMax(this), L) &&
4592 "Computed backedge-taken count isn't loop invariant for loop!");
4593 ++NumTripCountsComputed;
4595 else if (Result.getMax(this) == getCouldNotCompute() &&
4596 isa<PHINode>(L->getHeader()->begin())) {
4597 // Only count loops that have phi nodes as not being computable.
4598 ++NumTripCountsNotComputed;
4601 // Now that we know more about the trip count for this loop, forget any
4602 // existing SCEV values for PHI nodes in this loop since they are only
4603 // conservative estimates made without the benefit of trip count
4604 // information. This is similar to the code in forgetLoop, except that
4605 // it handles SCEVUnknown PHI nodes specially.
4606 if (Result.hasAnyInfo()) {
4607 SmallVector<Instruction *, 16> Worklist;
4608 PushLoopPHIs(L, Worklist);
4610 SmallPtrSet<Instruction *, 8> Visited;
4611 while (!Worklist.empty()) {
4612 Instruction *I = Worklist.pop_back_val();
4613 if (!Visited.insert(I).second)
4616 ValueExprMapType::iterator It =
4617 ValueExprMap.find_as(static_cast<Value *>(I));
4618 if (It != ValueExprMap.end()) {
4619 const SCEV *Old = It->second;
4621 // SCEVUnknown for a PHI either means that it has an unrecognized
4622 // structure, or it's a PHI that's in the progress of being computed
4623 // by createNodeForPHI. In the former case, additional loop trip
4624 // count information isn't going to change anything. In the later
4625 // case, createNodeForPHI will perform the necessary updates on its
4626 // own when it gets to that point.
4627 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) {
4628 forgetMemoizedResults(Old);
4629 ValueExprMap.erase(It);
4631 if (PHINode *PN = dyn_cast<PHINode>(I))
4632 ConstantEvolutionLoopExitValue.erase(PN);
4635 PushDefUseChildren(I, Worklist);
4639 // Re-lookup the insert position, since the call to
4640 // ComputeBackedgeTakenCount above could result in a
4641 // recusive call to getBackedgeTakenInfo (on a different
4642 // loop), which would invalidate the iterator computed
4644 return BackedgeTakenCounts.find(L)->second = Result;
4647 /// forgetLoop - This method should be called by the client when it has
4648 /// changed a loop in a way that may effect ScalarEvolution's ability to
4649 /// compute a trip count, or if the loop is deleted.
4650 void ScalarEvolution::forgetLoop(const Loop *L) {
4651 // Drop any stored trip count value.
4652 DenseMap<const Loop*, BackedgeTakenInfo>::iterator BTCPos =
4653 BackedgeTakenCounts.find(L);
4654 if (BTCPos != BackedgeTakenCounts.end()) {
4655 BTCPos->second.clear();
4656 BackedgeTakenCounts.erase(BTCPos);
4659 // Drop information about expressions based on loop-header PHIs.
4660 SmallVector<Instruction *, 16> Worklist;
4661 PushLoopPHIs(L, Worklist);
4663 SmallPtrSet<Instruction *, 8> Visited;
4664 while (!Worklist.empty()) {
4665 Instruction *I = Worklist.pop_back_val();
4666 if (!Visited.insert(I).second)
4669 ValueExprMapType::iterator It =
4670 ValueExprMap.find_as(static_cast<Value *>(I));
4671 if (It != ValueExprMap.end()) {
4672 forgetMemoizedResults(It->second);
4673 ValueExprMap.erase(It);
4674 if (PHINode *PN = dyn_cast<PHINode>(I))
4675 ConstantEvolutionLoopExitValue.erase(PN);
4678 PushDefUseChildren(I, Worklist);
4681 // Forget all contained loops too, to avoid dangling entries in the
4682 // ValuesAtScopes map.
4683 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
4687 /// forgetValue - This method should be called by the client when it has
4688 /// changed a value in a way that may effect its value, or which may
4689 /// disconnect it from a def-use chain linking it to a loop.
4690 void ScalarEvolution::forgetValue(Value *V) {
4691 Instruction *I = dyn_cast<Instruction>(V);
4694 // Drop information about expressions based on loop-header PHIs.
4695 SmallVector<Instruction *, 16> Worklist;
4696 Worklist.push_back(I);
4698 SmallPtrSet<Instruction *, 8> Visited;
4699 while (!Worklist.empty()) {
4700 I = Worklist.pop_back_val();
4701 if (!Visited.insert(I).second)
4704 ValueExprMapType::iterator It =
4705 ValueExprMap.find_as(static_cast<Value *>(I));
4706 if (It != ValueExprMap.end()) {
4707 forgetMemoizedResults(It->second);
4708 ValueExprMap.erase(It);
4709 if (PHINode *PN = dyn_cast<PHINode>(I))
4710 ConstantEvolutionLoopExitValue.erase(PN);
4713 PushDefUseChildren(I, Worklist);
4717 /// getExact - Get the exact loop backedge taken count considering all loop
4718 /// exits. A computable result can only be return for loops with a single exit.
4719 /// Returning the minimum taken count among all exits is incorrect because one
4720 /// of the loop's exit limit's may have been skipped. HowFarToZero assumes that
4721 /// the limit of each loop test is never skipped. This is a valid assumption as
4722 /// long as the loop exits via that test. For precise results, it is the
4723 /// caller's responsibility to specify the relevant loop exit using
4724 /// getExact(ExitingBlock, SE).
4726 ScalarEvolution::BackedgeTakenInfo::getExact(ScalarEvolution *SE) const {
4727 // If any exits were not computable, the loop is not computable.
4728 if (!ExitNotTaken.isCompleteList()) return SE->getCouldNotCompute();
4730 // We need exactly one computable exit.
4731 if (!ExitNotTaken.ExitingBlock) return SE->getCouldNotCompute();
4732 assert(ExitNotTaken.ExactNotTaken && "uninitialized not-taken info");
4734 const SCEV *BECount = nullptr;
4735 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4736 ENT != nullptr; ENT = ENT->getNextExit()) {
4738 assert(ENT->ExactNotTaken != SE->getCouldNotCompute() && "bad exit SCEV");
4741 BECount = ENT->ExactNotTaken;
4742 else if (BECount != ENT->ExactNotTaken)
4743 return SE->getCouldNotCompute();
4745 assert(BECount && "Invalid not taken count for loop exit");
4749 /// getExact - Get the exact not taken count for this loop exit.
4751 ScalarEvolution::BackedgeTakenInfo::getExact(BasicBlock *ExitingBlock,
4752 ScalarEvolution *SE) const {
4753 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4754 ENT != nullptr; ENT = ENT->getNextExit()) {
4756 if (ENT->ExitingBlock == ExitingBlock)
4757 return ENT->ExactNotTaken;
4759 return SE->getCouldNotCompute();
4762 /// getMax - Get the max backedge taken count for the loop.
4764 ScalarEvolution::BackedgeTakenInfo::getMax(ScalarEvolution *SE) const {
4765 return Max ? Max : SE->getCouldNotCompute();
4768 bool ScalarEvolution::BackedgeTakenInfo::hasOperand(const SCEV *S,
4769 ScalarEvolution *SE) const {
4770 if (Max && Max != SE->getCouldNotCompute() && SE->hasOperand(Max, S))
4773 if (!ExitNotTaken.ExitingBlock)
4776 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4777 ENT != nullptr; ENT = ENT->getNextExit()) {
4779 if (ENT->ExactNotTaken != SE->getCouldNotCompute()
4780 && SE->hasOperand(ENT->ExactNotTaken, S)) {
4787 /// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each
4788 /// computable exit into a persistent ExitNotTakenInfo array.
4789 ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo(
4790 SmallVectorImpl< std::pair<BasicBlock *, const SCEV *> > &ExitCounts,
4791 bool Complete, const SCEV *MaxCount) : Max(MaxCount) {
4794 ExitNotTaken.setIncomplete();
4796 unsigned NumExits = ExitCounts.size();
4797 if (NumExits == 0) return;
4799 ExitNotTaken.ExitingBlock = ExitCounts[0].first;
4800 ExitNotTaken.ExactNotTaken = ExitCounts[0].second;
4801 if (NumExits == 1) return;
4803 // Handle the rare case of multiple computable exits.
4804 ExitNotTakenInfo *ENT = new ExitNotTakenInfo[NumExits-1];
4806 ExitNotTakenInfo *PrevENT = &ExitNotTaken;
4807 for (unsigned i = 1; i < NumExits; ++i, PrevENT = ENT, ++ENT) {
4808 PrevENT->setNextExit(ENT);
4809 ENT->ExitingBlock = ExitCounts[i].first;
4810 ENT->ExactNotTaken = ExitCounts[i].second;
4814 /// clear - Invalidate this result and free the ExitNotTakenInfo array.
4815 void ScalarEvolution::BackedgeTakenInfo::clear() {
4816 ExitNotTaken.ExitingBlock = nullptr;
4817 ExitNotTaken.ExactNotTaken = nullptr;
4818 delete[] ExitNotTaken.getNextExit();
4821 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
4822 /// of the specified loop will execute.
4823 ScalarEvolution::BackedgeTakenInfo
4824 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
4825 SmallVector<BasicBlock *, 8> ExitingBlocks;
4826 L->getExitingBlocks(ExitingBlocks);
4828 SmallVector<std::pair<BasicBlock *, const SCEV *>, 4> ExitCounts;
4829 bool CouldComputeBECount = true;
4830 BasicBlock *Latch = L->getLoopLatch(); // may be NULL.
4831 const SCEV *MustExitMaxBECount = nullptr;
4832 const SCEV *MayExitMaxBECount = nullptr;
4834 // Compute the ExitLimit for each loop exit. Use this to populate ExitCounts
4835 // and compute maxBECount.
4836 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
4837 BasicBlock *ExitBB = ExitingBlocks[i];
4838 ExitLimit EL = ComputeExitLimit(L, ExitBB);
4840 // 1. For each exit that can be computed, add an entry to ExitCounts.
4841 // CouldComputeBECount is true only if all exits can be computed.
4842 if (EL.Exact == getCouldNotCompute())
4843 // We couldn't compute an exact value for this exit, so
4844 // we won't be able to compute an exact value for the loop.
4845 CouldComputeBECount = false;
4847 ExitCounts.push_back(std::make_pair(ExitBB, EL.Exact));
4849 // 2. Derive the loop's MaxBECount from each exit's max number of
4850 // non-exiting iterations. Partition the loop exits into two kinds:
4851 // LoopMustExits and LoopMayExits.
4853 // If the exit dominates the loop latch, it is a LoopMustExit otherwise it
4854 // is a LoopMayExit. If any computable LoopMustExit is found, then
4855 // MaxBECount is the minimum EL.Max of computable LoopMustExits. Otherwise,
4856 // MaxBECount is conservatively the maximum EL.Max, where CouldNotCompute is
4857 // considered greater than any computable EL.Max.
4858 if (EL.Max != getCouldNotCompute() && Latch &&
4859 DT->dominates(ExitBB, Latch)) {
4860 if (!MustExitMaxBECount)
4861 MustExitMaxBECount = EL.Max;
4863 MustExitMaxBECount =
4864 getUMinFromMismatchedTypes(MustExitMaxBECount, EL.Max);
4866 } else if (MayExitMaxBECount != getCouldNotCompute()) {
4867 if (!MayExitMaxBECount || EL.Max == getCouldNotCompute())
4868 MayExitMaxBECount = EL.Max;
4871 getUMaxFromMismatchedTypes(MayExitMaxBECount, EL.Max);
4875 const SCEV *MaxBECount = MustExitMaxBECount ? MustExitMaxBECount :
4876 (MayExitMaxBECount ? MayExitMaxBECount : getCouldNotCompute());
4877 return BackedgeTakenInfo(ExitCounts, CouldComputeBECount, MaxBECount);
4880 /// ComputeExitLimit - Compute the number of times the backedge of the specified
4881 /// loop will execute if it exits via the specified block.
4882 ScalarEvolution::ExitLimit
4883 ScalarEvolution::ComputeExitLimit(const Loop *L, BasicBlock *ExitingBlock) {
4885 // Okay, we've chosen an exiting block. See what condition causes us to
4886 // exit at this block and remember the exit block and whether all other targets
4887 // lead to the loop header.
4888 bool MustExecuteLoopHeader = true;
4889 BasicBlock *Exit = nullptr;
4890 for (succ_iterator SI = succ_begin(ExitingBlock), SE = succ_end(ExitingBlock);
4892 if (!L->contains(*SI)) {
4893 if (Exit) // Multiple exit successors.
4894 return getCouldNotCompute();
4896 } else if (*SI != L->getHeader()) {
4897 MustExecuteLoopHeader = false;
4900 // At this point, we know we have a conditional branch that determines whether
4901 // the loop is exited. However, we don't know if the branch is executed each
4902 // time through the loop. If not, then the execution count of the branch will
4903 // not be equal to the trip count of the loop.
4905 // Currently we check for this by checking to see if the Exit branch goes to
4906 // the loop header. If so, we know it will always execute the same number of
4907 // times as the loop. We also handle the case where the exit block *is* the
4908 // loop header. This is common for un-rotated loops.
4910 // If both of those tests fail, walk up the unique predecessor chain to the
4911 // header, stopping if there is an edge that doesn't exit the loop. If the
4912 // header is reached, the execution count of the branch will be equal to the
4913 // trip count of the loop.
4915 // More extensive analysis could be done to handle more cases here.
4917 if (!MustExecuteLoopHeader && ExitingBlock != L->getHeader()) {
4918 // The simple checks failed, try climbing the unique predecessor chain
4919 // up to the header.
4921 for (BasicBlock *BB = ExitingBlock; BB; ) {
4922 BasicBlock *Pred = BB->getUniquePredecessor();
4924 return getCouldNotCompute();
4925 TerminatorInst *PredTerm = Pred->getTerminator();
4926 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) {
4927 BasicBlock *PredSucc = PredTerm->getSuccessor(i);
4930 // If the predecessor has a successor that isn't BB and isn't
4931 // outside the loop, assume the worst.
4932 if (L->contains(PredSucc))
4933 return getCouldNotCompute();
4935 if (Pred == L->getHeader()) {
4942 return getCouldNotCompute();
4945 bool IsOnlyExit = (L->getExitingBlock() != nullptr);
4946 TerminatorInst *Term = ExitingBlock->getTerminator();
4947 if (BranchInst *BI = dyn_cast<BranchInst>(Term)) {
4948 assert(BI->isConditional() && "If unconditional, it can't be in loop!");
4949 // Proceed to the next level to examine the exit condition expression.
4950 return ComputeExitLimitFromCond(L, BI->getCondition(), BI->getSuccessor(0),
4951 BI->getSuccessor(1),
4952 /*ControlsExit=*/IsOnlyExit);
4955 if (SwitchInst *SI = dyn_cast<SwitchInst>(Term))
4956 return ComputeExitLimitFromSingleExitSwitch(L, SI, Exit,
4957 /*ControlsExit=*/IsOnlyExit);
4959 return getCouldNotCompute();
4962 /// ComputeExitLimitFromCond - Compute the number of times the
4963 /// backedge of the specified loop will execute if its exit condition
4964 /// were a conditional branch of ExitCond, TBB, and FBB.
4966 /// @param ControlsExit is true if ExitCond directly controls the exit
4967 /// branch. In this case, we can assume that the loop exits only if the
4968 /// condition is true and can infer that failing to meet the condition prior to
4969 /// integer wraparound results in undefined behavior.
4970 ScalarEvolution::ExitLimit
4971 ScalarEvolution::ComputeExitLimitFromCond(const Loop *L,
4975 bool ControlsExit) {
4976 // Check if the controlling expression for this loop is an And or Or.
4977 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
4978 if (BO->getOpcode() == Instruction::And) {
4979 // Recurse on the operands of the and.
4980 bool EitherMayExit = L->contains(TBB);
4981 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
4982 ControlsExit && !EitherMayExit);
4983 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
4984 ControlsExit && !EitherMayExit);
4985 const SCEV *BECount = getCouldNotCompute();
4986 const SCEV *MaxBECount = getCouldNotCompute();
4987 if (EitherMayExit) {
4988 // Both conditions must be true for the loop to continue executing.
4989 // Choose the less conservative count.
4990 if (EL0.Exact == getCouldNotCompute() ||
4991 EL1.Exact == getCouldNotCompute())
4992 BECount = getCouldNotCompute();
4994 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
4995 if (EL0.Max == getCouldNotCompute())
4996 MaxBECount = EL1.Max;
4997 else if (EL1.Max == getCouldNotCompute())
4998 MaxBECount = EL0.Max;
5000 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
5002 // Both conditions must be true at the same time for the loop to exit.
5003 // For now, be conservative.
5004 assert(L->contains(FBB) && "Loop block has no successor in loop!");
5005 if (EL0.Max == EL1.Max)
5006 MaxBECount = EL0.Max;
5007 if (EL0.Exact == EL1.Exact)
5008 BECount = EL0.Exact;
5011 return ExitLimit(BECount, MaxBECount);
5013 if (BO->getOpcode() == Instruction::Or) {
5014 // Recurse on the operands of the or.
5015 bool EitherMayExit = L->contains(FBB);
5016 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
5017 ControlsExit && !EitherMayExit);
5018 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
5019 ControlsExit && !EitherMayExit);
5020 const SCEV *BECount = getCouldNotCompute();
5021 const SCEV *MaxBECount = getCouldNotCompute();
5022 if (EitherMayExit) {
5023 // Both conditions must be false for the loop to continue executing.
5024 // Choose the less conservative count.
5025 if (EL0.Exact == getCouldNotCompute() ||
5026 EL1.Exact == getCouldNotCompute())
5027 BECount = getCouldNotCompute();
5029 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
5030 if (EL0.Max == getCouldNotCompute())
5031 MaxBECount = EL1.Max;
5032 else if (EL1.Max == getCouldNotCompute())
5033 MaxBECount = EL0.Max;
5035 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
5037 // Both conditions must be false at the same time for the loop to exit.
5038 // For now, be conservative.
5039 assert(L->contains(TBB) && "Loop block has no successor in loop!");
5040 if (EL0.Max == EL1.Max)
5041 MaxBECount = EL0.Max;
5042 if (EL0.Exact == EL1.Exact)
5043 BECount = EL0.Exact;
5046 return ExitLimit(BECount, MaxBECount);
5050 // With an icmp, it may be feasible to compute an exact backedge-taken count.
5051 // Proceed to the next level to examine the icmp.
5052 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
5053 return ComputeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB, ControlsExit);
5055 // Check for a constant condition. These are normally stripped out by
5056 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
5057 // preserve the CFG and is temporarily leaving constant conditions
5059 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
5060 if (L->contains(FBB) == !CI->getZExtValue())
5061 // The backedge is always taken.
5062 return getCouldNotCompute();
5064 // The backedge is never taken.
5065 return getConstant(CI->getType(), 0);
5068 // If it's not an integer or pointer comparison then compute it the hard way.
5069 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
5072 /// ComputeExitLimitFromICmp - Compute the number of times the
5073 /// backedge of the specified loop will execute if its exit condition
5074 /// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB.
5075 ScalarEvolution::ExitLimit
5076 ScalarEvolution::ComputeExitLimitFromICmp(const Loop *L,
5080 bool ControlsExit) {
5082 // If the condition was exit on true, convert the condition to exit on false
5083 ICmpInst::Predicate Cond;
5084 if (!L->contains(FBB))
5085 Cond = ExitCond->getPredicate();
5087 Cond = ExitCond->getInversePredicate();
5089 // Handle common loops like: for (X = "string"; *X; ++X)
5090 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
5091 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
5093 ComputeLoadConstantCompareExitLimit(LI, RHS, L, Cond);
5094 if (ItCnt.hasAnyInfo())
5098 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
5099 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
5101 // Try to evaluate any dependencies out of the loop.
5102 LHS = getSCEVAtScope(LHS, L);
5103 RHS = getSCEVAtScope(RHS, L);
5105 // At this point, we would like to compute how many iterations of the
5106 // loop the predicate will return true for these inputs.
5107 if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) {
5108 // If there is a loop-invariant, force it into the RHS.
5109 std::swap(LHS, RHS);
5110 Cond = ICmpInst::getSwappedPredicate(Cond);
5113 // Simplify the operands before analyzing them.
5114 (void)SimplifyICmpOperands(Cond, LHS, RHS);
5116 // If we have a comparison of a chrec against a constant, try to use value
5117 // ranges to answer this query.
5118 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
5119 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
5120 if (AddRec->getLoop() == L) {
5121 // Form the constant range.
5122 ConstantRange CompRange(
5123 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
5125 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
5126 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
5130 case ICmpInst::ICMP_NE: { // while (X != Y)
5131 // Convert to: while (X-Y != 0)
5132 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit);
5133 if (EL.hasAnyInfo()) return EL;
5136 case ICmpInst::ICMP_EQ: { // while (X == Y)
5137 // Convert to: while (X-Y == 0)
5138 ExitLimit EL = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
5139 if (EL.hasAnyInfo()) return EL;
5142 case ICmpInst::ICMP_SLT:
5143 case ICmpInst::ICMP_ULT: { // while (X < Y)
5144 bool IsSigned = Cond == ICmpInst::ICMP_SLT;
5145 ExitLimit EL = HowManyLessThans(LHS, RHS, L, IsSigned, ControlsExit);
5146 if (EL.hasAnyInfo()) return EL;
5149 case ICmpInst::ICMP_SGT:
5150 case ICmpInst::ICMP_UGT: { // while (X > Y)
5151 bool IsSigned = Cond == ICmpInst::ICMP_SGT;
5152 ExitLimit EL = HowManyGreaterThans(LHS, RHS, L, IsSigned, ControlsExit);
5153 if (EL.hasAnyInfo()) return EL;
5158 dbgs() << "ComputeBackedgeTakenCount ";
5159 if (ExitCond->getOperand(0)->getType()->isUnsigned())
5160 dbgs() << "[unsigned] ";
5161 dbgs() << *LHS << " "
5162 << Instruction::getOpcodeName(Instruction::ICmp)
5163 << " " << *RHS << "\n";
5167 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
5170 ScalarEvolution::ExitLimit
5171 ScalarEvolution::ComputeExitLimitFromSingleExitSwitch(const Loop *L,
5173 BasicBlock *ExitingBlock,
5174 bool ControlsExit) {
5175 assert(!L->contains(ExitingBlock) && "Not an exiting block!");
5177 // Give up if the exit is the default dest of a switch.
5178 if (Switch->getDefaultDest() == ExitingBlock)
5179 return getCouldNotCompute();
5181 assert(L->contains(Switch->getDefaultDest()) &&
5182 "Default case must not exit the loop!");
5183 const SCEV *LHS = getSCEVAtScope(Switch->getCondition(), L);
5184 const SCEV *RHS = getConstant(Switch->findCaseDest(ExitingBlock));
5186 // while (X != Y) --> while (X-Y != 0)
5187 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit);
5188 if (EL.hasAnyInfo())
5191 return getCouldNotCompute();
5194 static ConstantInt *
5195 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
5196 ScalarEvolution &SE) {
5197 const SCEV *InVal = SE.getConstant(C);
5198 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
5199 assert(isa<SCEVConstant>(Val) &&
5200 "Evaluation of SCEV at constant didn't fold correctly?");
5201 return cast<SCEVConstant>(Val)->getValue();
5204 /// ComputeLoadConstantCompareExitLimit - Given an exit condition of
5205 /// 'icmp op load X, cst', try to see if we can compute the backedge
5206 /// execution count.
5207 ScalarEvolution::ExitLimit
5208 ScalarEvolution::ComputeLoadConstantCompareExitLimit(
5212 ICmpInst::Predicate predicate) {
5214 if (LI->isVolatile()) return getCouldNotCompute();
5216 // Check to see if the loaded pointer is a getelementptr of a global.
5217 // TODO: Use SCEV instead of manually grubbing with GEPs.
5218 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
5219 if (!GEP) return getCouldNotCompute();
5221 // Make sure that it is really a constant global we are gepping, with an
5222 // initializer, and make sure the first IDX is really 0.
5223 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
5224 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
5225 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
5226 !cast<Constant>(GEP->getOperand(1))->isNullValue())
5227 return getCouldNotCompute();
5229 // Okay, we allow one non-constant index into the GEP instruction.
5230 Value *VarIdx = nullptr;
5231 std::vector<Constant*> Indexes;
5232 unsigned VarIdxNum = 0;
5233 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
5234 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
5235 Indexes.push_back(CI);
5236 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
5237 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
5238 VarIdx = GEP->getOperand(i);
5240 Indexes.push_back(nullptr);
5243 // Loop-invariant loads may be a byproduct of loop optimization. Skip them.
5245 return getCouldNotCompute();
5247 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
5248 // Check to see if X is a loop variant variable value now.
5249 const SCEV *Idx = getSCEV(VarIdx);
5250 Idx = getSCEVAtScope(Idx, L);
5252 // We can only recognize very limited forms of loop index expressions, in
5253 // particular, only affine AddRec's like {C1,+,C2}.
5254 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
5255 if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) ||
5256 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
5257 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
5258 return getCouldNotCompute();
5260 unsigned MaxSteps = MaxBruteForceIterations;
5261 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
5262 ConstantInt *ItCst = ConstantInt::get(
5263 cast<IntegerType>(IdxExpr->getType()), IterationNum);
5264 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
5266 // Form the GEP offset.
5267 Indexes[VarIdxNum] = Val;
5269 Constant *Result = ConstantFoldLoadThroughGEPIndices(GV->getInitializer(),
5271 if (!Result) break; // Cannot compute!
5273 // Evaluate the condition for this iteration.
5274 Result = ConstantExpr::getICmp(predicate, Result, RHS);
5275 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
5276 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
5278 dbgs() << "\n***\n*** Computed loop count " << *ItCst
5279 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
5282 ++NumArrayLenItCounts;
5283 return getConstant(ItCst); // Found terminating iteration!
5286 return getCouldNotCompute();
5290 /// CanConstantFold - Return true if we can constant fold an instruction of the
5291 /// specified type, assuming that all operands were constants.
5292 static bool CanConstantFold(const Instruction *I) {
5293 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
5294 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I) ||
5298 if (const CallInst *CI = dyn_cast<CallInst>(I))
5299 if (const Function *F = CI->getCalledFunction())
5300 return canConstantFoldCallTo(F);
5304 /// Determine whether this instruction can constant evolve within this loop
5305 /// assuming its operands can all constant evolve.
5306 static bool canConstantEvolve(Instruction *I, const Loop *L) {
5307 // An instruction outside of the loop can't be derived from a loop PHI.
5308 if (!L->contains(I)) return false;
5310 if (isa<PHINode>(I)) {
5311 if (L->getHeader() == I->getParent())
5314 // We don't currently keep track of the control flow needed to evaluate
5315 // PHIs, so we cannot handle PHIs inside of loops.
5319 // If we won't be able to constant fold this expression even if the operands
5320 // are constants, bail early.
5321 return CanConstantFold(I);
5324 /// getConstantEvolvingPHIOperands - Implement getConstantEvolvingPHI by
5325 /// recursing through each instruction operand until reaching a loop header phi.
5327 getConstantEvolvingPHIOperands(Instruction *UseInst, const Loop *L,
5328 DenseMap<Instruction *, PHINode *> &PHIMap) {
5330 // Otherwise, we can evaluate this instruction if all of its operands are
5331 // constant or derived from a PHI node themselves.
5332 PHINode *PHI = nullptr;
5333 for (Instruction::op_iterator OpI = UseInst->op_begin(),
5334 OpE = UseInst->op_end(); OpI != OpE; ++OpI) {
5336 if (isa<Constant>(*OpI)) continue;
5338 Instruction *OpInst = dyn_cast<Instruction>(*OpI);
5339 if (!OpInst || !canConstantEvolve(OpInst, L)) return nullptr;
5341 PHINode *P = dyn_cast<PHINode>(OpInst);
5343 // If this operand is already visited, reuse the prior result.
5344 // We may have P != PHI if this is the deepest point at which the
5345 // inconsistent paths meet.
5346 P = PHIMap.lookup(OpInst);
5348 // Recurse and memoize the results, whether a phi is found or not.
5349 // This recursive call invalidates pointers into PHIMap.
5350 P = getConstantEvolvingPHIOperands(OpInst, L, PHIMap);
5354 return nullptr; // Not evolving from PHI
5355 if (PHI && PHI != P)
5356 return nullptr; // Evolving from multiple different PHIs.
5359 // This is a expression evolving from a constant PHI!
5363 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
5364 /// in the loop that V is derived from. We allow arbitrary operations along the
5365 /// way, but the operands of an operation must either be constants or a value
5366 /// derived from a constant PHI. If this expression does not fit with these
5367 /// constraints, return null.
5368 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
5369 Instruction *I = dyn_cast<Instruction>(V);
5370 if (!I || !canConstantEvolve(I, L)) return nullptr;
5372 if (PHINode *PN = dyn_cast<PHINode>(I)) {
5376 // Record non-constant instructions contained by the loop.
5377 DenseMap<Instruction *, PHINode *> PHIMap;
5378 return getConstantEvolvingPHIOperands(I, L, PHIMap);
5381 /// EvaluateExpression - Given an expression that passes the
5382 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
5383 /// in the loop has the value PHIVal. If we can't fold this expression for some
5384 /// reason, return null.
5385 static Constant *EvaluateExpression(Value *V, const Loop *L,
5386 DenseMap<Instruction *, Constant *> &Vals,
5387 const DataLayout &DL,
5388 const TargetLibraryInfo *TLI) {
5389 // Convenient constant check, but redundant for recursive calls.
5390 if (Constant *C = dyn_cast<Constant>(V)) return C;
5391 Instruction *I = dyn_cast<Instruction>(V);
5392 if (!I) return nullptr;
5394 if (Constant *C = Vals.lookup(I)) return C;
5396 // An instruction inside the loop depends on a value outside the loop that we
5397 // weren't given a mapping for, or a value such as a call inside the loop.
5398 if (!canConstantEvolve(I, L)) return nullptr;
5400 // An unmapped PHI can be due to a branch or another loop inside this loop,
5401 // or due to this not being the initial iteration through a loop where we
5402 // couldn't compute the evolution of this particular PHI last time.
5403 if (isa<PHINode>(I)) return nullptr;
5405 std::vector<Constant*> Operands(I->getNumOperands());
5407 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
5408 Instruction *Operand = dyn_cast<Instruction>(I->getOperand(i));
5410 Operands[i] = dyn_cast<Constant>(I->getOperand(i));
5411 if (!Operands[i]) return nullptr;
5414 Constant *C = EvaluateExpression(Operand, L, Vals, DL, TLI);
5416 if (!C) return nullptr;
5420 if (CmpInst *CI = dyn_cast<CmpInst>(I))
5421 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
5422 Operands[1], DL, TLI);
5423 if (LoadInst *LI = dyn_cast<LoadInst>(I)) {
5424 if (!LI->isVolatile())
5425 return ConstantFoldLoadFromConstPtr(Operands[0], DL);
5427 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), Operands, DL,
5431 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
5432 /// in the header of its containing loop, we know the loop executes a
5433 /// constant number of times, and the PHI node is just a recurrence
5434 /// involving constants, fold it.
5436 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
5439 DenseMap<PHINode*, Constant*>::const_iterator I =
5440 ConstantEvolutionLoopExitValue.find(PN);
5441 if (I != ConstantEvolutionLoopExitValue.end())
5444 if (BEs.ugt(MaxBruteForceIterations))
5445 return ConstantEvolutionLoopExitValue[PN] = nullptr; // Not going to evaluate it.
5447 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
5449 DenseMap<Instruction *, Constant *> CurrentIterVals;
5450 BasicBlock *Header = L->getHeader();
5451 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
5453 // Since the loop is canonicalized, the PHI node must have two entries. One
5454 // entry must be a constant (coming in from outside of the loop), and the
5455 // second must be derived from the same PHI.
5456 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
5457 PHINode *PHI = nullptr;
5458 for (BasicBlock::iterator I = Header->begin();
5459 (PHI = dyn_cast<PHINode>(I)); ++I) {
5460 Constant *StartCST =
5461 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
5462 if (!StartCST) continue;
5463 CurrentIterVals[PHI] = StartCST;
5465 if (!CurrentIterVals.count(PN))
5466 return RetVal = nullptr;
5468 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
5470 // Execute the loop symbolically to determine the exit value.
5471 if (BEs.getActiveBits() >= 32)
5472 return RetVal = nullptr; // More than 2^32-1 iterations?? Not doing it!
5474 unsigned NumIterations = BEs.getZExtValue(); // must be in range
5475 unsigned IterationNum = 0;
5476 const DataLayout &DL = F->getParent()->getDataLayout();
5477 for (; ; ++IterationNum) {
5478 if (IterationNum == NumIterations)
5479 return RetVal = CurrentIterVals[PN]; // Got exit value!
5481 // Compute the value of the PHIs for the next iteration.
5482 // EvaluateExpression adds non-phi values to the CurrentIterVals map.
5483 DenseMap<Instruction *, Constant *> NextIterVals;
5485 EvaluateExpression(BEValue, L, CurrentIterVals, DL, TLI);
5487 return nullptr; // Couldn't evaluate!
5488 NextIterVals[PN] = NextPHI;
5490 bool StoppedEvolving = NextPHI == CurrentIterVals[PN];
5492 // Also evaluate the other PHI nodes. However, we don't get to stop if we
5493 // cease to be able to evaluate one of them or if they stop evolving,
5494 // because that doesn't necessarily prevent us from computing PN.
5495 SmallVector<std::pair<PHINode *, Constant *>, 8> PHIsToCompute;
5496 for (DenseMap<Instruction *, Constant *>::const_iterator
5497 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
5498 PHINode *PHI = dyn_cast<PHINode>(I->first);
5499 if (!PHI || PHI == PN || PHI->getParent() != Header) continue;
5500 PHIsToCompute.push_back(std::make_pair(PHI, I->second));
5502 // We use two distinct loops because EvaluateExpression may invalidate any
5503 // iterators into CurrentIterVals.
5504 for (SmallVectorImpl<std::pair<PHINode *, Constant*> >::const_iterator
5505 I = PHIsToCompute.begin(), E = PHIsToCompute.end(); I != E; ++I) {
5506 PHINode *PHI = I->first;
5507 Constant *&NextPHI = NextIterVals[PHI];
5508 if (!NextPHI) { // Not already computed.
5509 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
5510 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, TLI);
5512 if (NextPHI != I->second)
5513 StoppedEvolving = false;
5516 // If all entries in CurrentIterVals == NextIterVals then we can stop
5517 // iterating, the loop can't continue to change.
5518 if (StoppedEvolving)
5519 return RetVal = CurrentIterVals[PN];
5521 CurrentIterVals.swap(NextIterVals);
5525 /// ComputeExitCountExhaustively - If the loop is known to execute a
5526 /// constant number of times (the condition evolves only from constants),
5527 /// try to evaluate a few iterations of the loop until we get the exit
5528 /// condition gets a value of ExitWhen (true or false). If we cannot
5529 /// evaluate the trip count of the loop, return getCouldNotCompute().
5530 const SCEV *ScalarEvolution::ComputeExitCountExhaustively(const Loop *L,
5533 PHINode *PN = getConstantEvolvingPHI(Cond, L);
5534 if (!PN) return getCouldNotCompute();
5536 // If the loop is canonicalized, the PHI will have exactly two entries.
5537 // That's the only form we support here.
5538 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
5540 DenseMap<Instruction *, Constant *> CurrentIterVals;
5541 BasicBlock *Header = L->getHeader();
5542 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
5544 // One entry must be a constant (coming in from outside of the loop), and the
5545 // second must be derived from the same PHI.
5546 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
5547 PHINode *PHI = nullptr;
5548 for (BasicBlock::iterator I = Header->begin();
5549 (PHI = dyn_cast<PHINode>(I)); ++I) {
5550 Constant *StartCST =
5551 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
5552 if (!StartCST) continue;
5553 CurrentIterVals[PHI] = StartCST;
5555 if (!CurrentIterVals.count(PN))
5556 return getCouldNotCompute();
5558 // Okay, we find a PHI node that defines the trip count of this loop. Execute
5559 // the loop symbolically to determine when the condition gets a value of
5561 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
5562 const DataLayout &DL = F->getParent()->getDataLayout();
5563 for (unsigned IterationNum = 0; IterationNum != MaxIterations;++IterationNum){
5564 ConstantInt *CondVal = dyn_cast_or_null<ConstantInt>(
5565 EvaluateExpression(Cond, L, CurrentIterVals, DL, TLI));
5567 // Couldn't symbolically evaluate.
5568 if (!CondVal) return getCouldNotCompute();
5570 if (CondVal->getValue() == uint64_t(ExitWhen)) {
5571 ++NumBruteForceTripCountsComputed;
5572 return getConstant(Type::getInt32Ty(getContext()), IterationNum);
5575 // Update all the PHI nodes for the next iteration.
5576 DenseMap<Instruction *, Constant *> NextIterVals;
5578 // Create a list of which PHIs we need to compute. We want to do this before
5579 // calling EvaluateExpression on them because that may invalidate iterators
5580 // into CurrentIterVals.
5581 SmallVector<PHINode *, 8> PHIsToCompute;
5582 for (DenseMap<Instruction *, Constant *>::const_iterator
5583 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
5584 PHINode *PHI = dyn_cast<PHINode>(I->first);
5585 if (!PHI || PHI->getParent() != Header) continue;
5586 PHIsToCompute.push_back(PHI);
5588 for (SmallVectorImpl<PHINode *>::const_iterator I = PHIsToCompute.begin(),
5589 E = PHIsToCompute.end(); I != E; ++I) {
5591 Constant *&NextPHI = NextIterVals[PHI];
5592 if (NextPHI) continue; // Already computed!
5594 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
5595 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, TLI);
5597 CurrentIterVals.swap(NextIterVals);
5600 // Too many iterations were needed to evaluate.
5601 return getCouldNotCompute();
5604 /// getSCEVAtScope - Return a SCEV expression for the specified value
5605 /// at the specified scope in the program. The L value specifies a loop
5606 /// nest to evaluate the expression at, where null is the top-level or a
5607 /// specified loop is immediately inside of the loop.
5609 /// This method can be used to compute the exit value for a variable defined
5610 /// in a loop by querying what the value will hold in the parent loop.
5612 /// In the case that a relevant loop exit value cannot be computed, the
5613 /// original value V is returned.
5614 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
5615 // Check to see if we've folded this expression at this loop before.
5616 SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values = ValuesAtScopes[V];
5617 for (unsigned u = 0; u < Values.size(); u++) {
5618 if (Values[u].first == L)
5619 return Values[u].second ? Values[u].second : V;
5621 Values.push_back(std::make_pair(L, static_cast<const SCEV *>(nullptr)));
5622 // Otherwise compute it.
5623 const SCEV *C = computeSCEVAtScope(V, L);
5624 SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values2 = ValuesAtScopes[V];
5625 for (unsigned u = Values2.size(); u > 0; u--) {
5626 if (Values2[u - 1].first == L) {
5627 Values2[u - 1].second = C;
5634 /// This builds up a Constant using the ConstantExpr interface. That way, we
5635 /// will return Constants for objects which aren't represented by a
5636 /// SCEVConstant, because SCEVConstant is restricted to ConstantInt.
5637 /// Returns NULL if the SCEV isn't representable as a Constant.
5638 static Constant *BuildConstantFromSCEV(const SCEV *V) {
5639 switch (static_cast<SCEVTypes>(V->getSCEVType())) {
5640 case scCouldNotCompute:
5644 return cast<SCEVConstant>(V)->getValue();
5646 return dyn_cast<Constant>(cast<SCEVUnknown>(V)->getValue());
5647 case scSignExtend: {
5648 const SCEVSignExtendExpr *SS = cast<SCEVSignExtendExpr>(V);
5649 if (Constant *CastOp = BuildConstantFromSCEV(SS->getOperand()))
5650 return ConstantExpr::getSExt(CastOp, SS->getType());
5653 case scZeroExtend: {
5654 const SCEVZeroExtendExpr *SZ = cast<SCEVZeroExtendExpr>(V);
5655 if (Constant *CastOp = BuildConstantFromSCEV(SZ->getOperand()))
5656 return ConstantExpr::getZExt(CastOp, SZ->getType());
5660 const SCEVTruncateExpr *ST = cast<SCEVTruncateExpr>(V);
5661 if (Constant *CastOp = BuildConstantFromSCEV(ST->getOperand()))
5662 return ConstantExpr::getTrunc(CastOp, ST->getType());
5666 const SCEVAddExpr *SA = cast<SCEVAddExpr>(V);
5667 if (Constant *C = BuildConstantFromSCEV(SA->getOperand(0))) {
5668 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
5669 unsigned AS = PTy->getAddressSpace();
5670 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
5671 C = ConstantExpr::getBitCast(C, DestPtrTy);
5673 for (unsigned i = 1, e = SA->getNumOperands(); i != e; ++i) {
5674 Constant *C2 = BuildConstantFromSCEV(SA->getOperand(i));
5675 if (!C2) return nullptr;
5678 if (!C->getType()->isPointerTy() && C2->getType()->isPointerTy()) {
5679 unsigned AS = C2->getType()->getPointerAddressSpace();
5681 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
5682 // The offsets have been converted to bytes. We can add bytes to an
5683 // i8* by GEP with the byte count in the first index.
5684 C = ConstantExpr::getBitCast(C, DestPtrTy);
5687 // Don't bother trying to sum two pointers. We probably can't
5688 // statically compute a load that results from it anyway.
5689 if (C2->getType()->isPointerTy())
5692 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
5693 if (PTy->getElementType()->isStructTy())
5694 C2 = ConstantExpr::getIntegerCast(
5695 C2, Type::getInt32Ty(C->getContext()), true);
5696 C = ConstantExpr::getGetElementPtr(C, C2);
5698 C = ConstantExpr::getAdd(C, C2);
5705 const SCEVMulExpr *SM = cast<SCEVMulExpr>(V);
5706 if (Constant *C = BuildConstantFromSCEV(SM->getOperand(0))) {
5707 // Don't bother with pointers at all.
5708 if (C->getType()->isPointerTy()) return nullptr;
5709 for (unsigned i = 1, e = SM->getNumOperands(); i != e; ++i) {
5710 Constant *C2 = BuildConstantFromSCEV(SM->getOperand(i));
5711 if (!C2 || C2->getType()->isPointerTy()) return nullptr;
5712 C = ConstantExpr::getMul(C, C2);
5719 const SCEVUDivExpr *SU = cast<SCEVUDivExpr>(V);
5720 if (Constant *LHS = BuildConstantFromSCEV(SU->getLHS()))
5721 if (Constant *RHS = BuildConstantFromSCEV(SU->getRHS()))
5722 if (LHS->getType() == RHS->getType())
5723 return ConstantExpr::getUDiv(LHS, RHS);
5728 break; // TODO: smax, umax.
5733 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
5734 if (isa<SCEVConstant>(V)) return V;
5736 // If this instruction is evolved from a constant-evolving PHI, compute the
5737 // exit value from the loop without using SCEVs.
5738 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
5739 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
5740 const Loop *LI = (*this->LI)[I->getParent()];
5741 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
5742 if (PHINode *PN = dyn_cast<PHINode>(I))
5743 if (PN->getParent() == LI->getHeader()) {
5744 // Okay, there is no closed form solution for the PHI node. Check
5745 // to see if the loop that contains it has a known backedge-taken
5746 // count. If so, we may be able to force computation of the exit
5748 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
5749 if (const SCEVConstant *BTCC =
5750 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
5751 // Okay, we know how many times the containing loop executes. If
5752 // this is a constant evolving PHI node, get the final value at
5753 // the specified iteration number.
5754 Constant *RV = getConstantEvolutionLoopExitValue(PN,
5755 BTCC->getValue()->getValue(),
5757 if (RV) return getSCEV(RV);
5761 // Okay, this is an expression that we cannot symbolically evaluate
5762 // into a SCEV. Check to see if it's possible to symbolically evaluate
5763 // the arguments into constants, and if so, try to constant propagate the
5764 // result. This is particularly useful for computing loop exit values.
5765 if (CanConstantFold(I)) {
5766 SmallVector<Constant *, 4> Operands;
5767 bool MadeImprovement = false;
5768 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
5769 Value *Op = I->getOperand(i);
5770 if (Constant *C = dyn_cast<Constant>(Op)) {
5771 Operands.push_back(C);
5775 // If any of the operands is non-constant and if they are
5776 // non-integer and non-pointer, don't even try to analyze them
5777 // with scev techniques.
5778 if (!isSCEVable(Op->getType()))
5781 const SCEV *OrigV = getSCEV(Op);
5782 const SCEV *OpV = getSCEVAtScope(OrigV, L);
5783 MadeImprovement |= OrigV != OpV;
5785 Constant *C = BuildConstantFromSCEV(OpV);
5787 if (C->getType() != Op->getType())
5788 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
5792 Operands.push_back(C);
5795 // Check to see if getSCEVAtScope actually made an improvement.
5796 if (MadeImprovement) {
5797 Constant *C = nullptr;
5798 const DataLayout &DL = F->getParent()->getDataLayout();
5799 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
5800 C = ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
5801 Operands[1], DL, TLI);
5802 else if (const LoadInst *LI = dyn_cast<LoadInst>(I)) {
5803 if (!LI->isVolatile())
5804 C = ConstantFoldLoadFromConstPtr(Operands[0], DL);
5806 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(), Operands,
5814 // This is some other type of SCEVUnknown, just return it.
5818 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
5819 // Avoid performing the look-up in the common case where the specified
5820 // expression has no loop-variant portions.
5821 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
5822 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
5823 if (OpAtScope != Comm->getOperand(i)) {
5824 // Okay, at least one of these operands is loop variant but might be
5825 // foldable. Build a new instance of the folded commutative expression.
5826 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
5827 Comm->op_begin()+i);
5828 NewOps.push_back(OpAtScope);
5830 for (++i; i != e; ++i) {
5831 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
5832 NewOps.push_back(OpAtScope);
5834 if (isa<SCEVAddExpr>(Comm))
5835 return getAddExpr(NewOps);
5836 if (isa<SCEVMulExpr>(Comm))
5837 return getMulExpr(NewOps);
5838 if (isa<SCEVSMaxExpr>(Comm))
5839 return getSMaxExpr(NewOps);
5840 if (isa<SCEVUMaxExpr>(Comm))
5841 return getUMaxExpr(NewOps);
5842 llvm_unreachable("Unknown commutative SCEV type!");
5845 // If we got here, all operands are loop invariant.
5849 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
5850 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
5851 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
5852 if (LHS == Div->getLHS() && RHS == Div->getRHS())
5853 return Div; // must be loop invariant
5854 return getUDivExpr(LHS, RHS);
5857 // If this is a loop recurrence for a loop that does not contain L, then we
5858 // are dealing with the final value computed by the loop.
5859 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
5860 // First, attempt to evaluate each operand.
5861 // Avoid performing the look-up in the common case where the specified
5862 // expression has no loop-variant portions.
5863 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
5864 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
5865 if (OpAtScope == AddRec->getOperand(i))
5868 // Okay, at least one of these operands is loop variant but might be
5869 // foldable. Build a new instance of the folded commutative expression.
5870 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(),
5871 AddRec->op_begin()+i);
5872 NewOps.push_back(OpAtScope);
5873 for (++i; i != e; ++i)
5874 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
5876 const SCEV *FoldedRec =
5877 getAddRecExpr(NewOps, AddRec->getLoop(),
5878 AddRec->getNoWrapFlags(SCEV::FlagNW));
5879 AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec);
5880 // The addrec may be folded to a nonrecurrence, for example, if the
5881 // induction variable is multiplied by zero after constant folding. Go
5882 // ahead and return the folded value.
5888 // If the scope is outside the addrec's loop, evaluate it by using the
5889 // loop exit value of the addrec.
5890 if (!AddRec->getLoop()->contains(L)) {
5891 // To evaluate this recurrence, we need to know how many times the AddRec
5892 // loop iterates. Compute this now.
5893 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
5894 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
5896 // Then, evaluate the AddRec.
5897 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
5903 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
5904 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5905 if (Op == Cast->getOperand())
5906 return Cast; // must be loop invariant
5907 return getZeroExtendExpr(Op, Cast->getType());
5910 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
5911 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5912 if (Op == Cast->getOperand())
5913 return Cast; // must be loop invariant
5914 return getSignExtendExpr(Op, Cast->getType());
5917 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
5918 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5919 if (Op == Cast->getOperand())
5920 return Cast; // must be loop invariant
5921 return getTruncateExpr(Op, Cast->getType());
5924 llvm_unreachable("Unknown SCEV type!");
5927 /// getSCEVAtScope - This is a convenience function which does
5928 /// getSCEVAtScope(getSCEV(V), L).
5929 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
5930 return getSCEVAtScope(getSCEV(V), L);
5933 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
5934 /// following equation:
5936 /// A * X = B (mod N)
5938 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
5939 /// A and B isn't important.
5941 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
5942 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
5943 ScalarEvolution &SE) {
5944 uint32_t BW = A.getBitWidth();
5945 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
5946 assert(A != 0 && "A must be non-zero.");
5950 // The gcd of A and N may have only one prime factor: 2. The number of
5951 // trailing zeros in A is its multiplicity
5952 uint32_t Mult2 = A.countTrailingZeros();
5955 // 2. Check if B is divisible by D.
5957 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
5958 // is not less than multiplicity of this prime factor for D.
5959 if (B.countTrailingZeros() < Mult2)
5960 return SE.getCouldNotCompute();
5962 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
5965 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
5966 // bit width during computations.
5967 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
5968 APInt Mod(BW + 1, 0);
5969 Mod.setBit(BW - Mult2); // Mod = N / D
5970 APInt I = AD.multiplicativeInverse(Mod);
5972 // 4. Compute the minimum unsigned root of the equation:
5973 // I * (B / D) mod (N / D)
5974 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
5976 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
5978 return SE.getConstant(Result.trunc(BW));
5981 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
5982 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
5983 /// might be the same) or two SCEVCouldNotCompute objects.
5985 static std::pair<const SCEV *,const SCEV *>
5986 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
5987 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
5988 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
5989 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
5990 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
5992 // We currently can only solve this if the coefficients are constants.
5993 if (!LC || !MC || !NC) {
5994 const SCEV *CNC = SE.getCouldNotCompute();
5995 return std::make_pair(CNC, CNC);
5998 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
5999 const APInt &L = LC->getValue()->getValue();
6000 const APInt &M = MC->getValue()->getValue();
6001 const APInt &N = NC->getValue()->getValue();
6002 APInt Two(BitWidth, 2);
6003 APInt Four(BitWidth, 4);
6006 using namespace APIntOps;
6008 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
6009 // The B coefficient is M-N/2
6013 // The A coefficient is N/2
6014 APInt A(N.sdiv(Two));
6016 // Compute the B^2-4ac term.
6019 SqrtTerm -= Four * (A * C);
6021 if (SqrtTerm.isNegative()) {
6022 // The loop is provably infinite.
6023 const SCEV *CNC = SE.getCouldNotCompute();
6024 return std::make_pair(CNC, CNC);
6027 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
6028 // integer value or else APInt::sqrt() will assert.
6029 APInt SqrtVal(SqrtTerm.sqrt());
6031 // Compute the two solutions for the quadratic formula.
6032 // The divisions must be performed as signed divisions.
6035 if (TwoA.isMinValue()) {
6036 const SCEV *CNC = SE.getCouldNotCompute();
6037 return std::make_pair(CNC, CNC);
6040 LLVMContext &Context = SE.getContext();
6042 ConstantInt *Solution1 =
6043 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
6044 ConstantInt *Solution2 =
6045 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
6047 return std::make_pair(SE.getConstant(Solution1),
6048 SE.getConstant(Solution2));
6049 } // end APIntOps namespace
6052 /// HowFarToZero - Return the number of times a backedge comparing the specified
6053 /// value to zero will execute. If not computable, return CouldNotCompute.
6055 /// This is only used for loops with a "x != y" exit test. The exit condition is
6056 /// now expressed as a single expression, V = x-y. So the exit test is
6057 /// effectively V != 0. We know and take advantage of the fact that this
6058 /// expression only being used in a comparison by zero context.
6059 ScalarEvolution::ExitLimit
6060 ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L, bool ControlsExit) {
6061 // If the value is a constant
6062 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
6063 // If the value is already zero, the branch will execute zero times.
6064 if (C->getValue()->isZero()) return C;
6065 return getCouldNotCompute(); // Otherwise it will loop infinitely.
6068 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
6069 if (!AddRec || AddRec->getLoop() != L)
6070 return getCouldNotCompute();
6072 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
6073 // the quadratic equation to solve it.
6074 if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
6075 std::pair<const SCEV *,const SCEV *> Roots =
6076 SolveQuadraticEquation(AddRec, *this);
6077 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
6078 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
6081 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1
6082 << " sol#2: " << *R2 << "\n";
6084 // Pick the smallest positive root value.
6085 if (ConstantInt *CB =
6086 dyn_cast<ConstantInt>(ConstantExpr::getICmp(CmpInst::ICMP_ULT,
6089 if (!CB->getZExtValue())
6090 std::swap(R1, R2); // R1 is the minimum root now.
6092 // We can only use this value if the chrec ends up with an exact zero
6093 // value at this index. When solving for "X*X != 5", for example, we
6094 // should not accept a root of 2.
6095 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
6097 return R1; // We found a quadratic root!
6100 return getCouldNotCompute();
6103 // Otherwise we can only handle this if it is affine.
6104 if (!AddRec->isAffine())
6105 return getCouldNotCompute();
6107 // If this is an affine expression, the execution count of this branch is
6108 // the minimum unsigned root of the following equation:
6110 // Start + Step*N = 0 (mod 2^BW)
6114 // Step*N = -Start (mod 2^BW)
6116 // where BW is the common bit width of Start and Step.
6118 // Get the initial value for the loop.
6119 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
6120 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
6122 // For now we handle only constant steps.
6124 // TODO: Handle a nonconstant Step given AddRec<NUW>. If the
6125 // AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap
6126 // to 0, it must be counting down to equal 0. Consequently, N = Start / -Step.
6127 // We have not yet seen any such cases.
6128 const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step);
6129 if (!StepC || StepC->getValue()->equalsInt(0))
6130 return getCouldNotCompute();
6132 // For positive steps (counting up until unsigned overflow):
6133 // N = -Start/Step (as unsigned)
6134 // For negative steps (counting down to zero):
6136 // First compute the unsigned distance from zero in the direction of Step.
6137 bool CountDown = StepC->getValue()->getValue().isNegative();
6138 const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start);
6140 // Handle unitary steps, which cannot wraparound.
6141 // 1*N = -Start; -1*N = Start (mod 2^BW), so:
6142 // N = Distance (as unsigned)
6143 if (StepC->getValue()->equalsInt(1) || StepC->getValue()->isAllOnesValue()) {
6144 ConstantRange CR = getUnsignedRange(Start);
6145 const SCEV *MaxBECount;
6146 if (!CountDown && CR.getUnsignedMin().isMinValue())
6147 // When counting up, the worst starting value is 1, not 0.
6148 MaxBECount = CR.getUnsignedMax().isMinValue()
6149 ? getConstant(APInt::getMinValue(CR.getBitWidth()))
6150 : getConstant(APInt::getMaxValue(CR.getBitWidth()));
6152 MaxBECount = getConstant(CountDown ? CR.getUnsignedMax()
6153 : -CR.getUnsignedMin());
6154 return ExitLimit(Distance, MaxBECount);
6157 // As a special case, handle the instance where Step is a positive power of
6158 // two. In this case, determining whether Step divides Distance evenly can be
6159 // done by counting and comparing the number of trailing zeros of Step and
6162 const APInt &StepV = StepC->getValue()->getValue();
6163 // StepV.isPowerOf2() returns true if StepV is an positive power of two. It
6164 // also returns true if StepV is maximally negative (eg, INT_MIN), but that
6165 // case is not handled as this code is guarded by !CountDown.
6166 if (StepV.isPowerOf2() &&
6167 GetMinTrailingZeros(Distance) >= StepV.countTrailingZeros())
6168 return getUDivExactExpr(Distance, Step);
6171 // If the condition controls loop exit (the loop exits only if the expression
6172 // is true) and the addition is no-wrap we can use unsigned divide to
6173 // compute the backedge count. In this case, the step may not divide the
6174 // distance, but we don't care because if the condition is "missed" the loop
6175 // will have undefined behavior due to wrapping.
6176 if (ControlsExit && AddRec->getNoWrapFlags(SCEV::FlagNW)) {
6178 getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
6179 return ExitLimit(Exact, Exact);
6182 // Then, try to solve the above equation provided that Start is constant.
6183 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
6184 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
6185 -StartC->getValue()->getValue(),
6187 return getCouldNotCompute();
6190 /// HowFarToNonZero - Return the number of times a backedge checking the
6191 /// specified value for nonzero will execute. If not computable, return
6193 ScalarEvolution::ExitLimit
6194 ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
6195 // Loops that look like: while (X == 0) are very strange indeed. We don't
6196 // handle them yet except for the trivial case. This could be expanded in the
6197 // future as needed.
6199 // If the value is a constant, check to see if it is known to be non-zero
6200 // already. If so, the backedge will execute zero times.
6201 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
6202 if (!C->getValue()->isNullValue())
6203 return getConstant(C->getType(), 0);
6204 return getCouldNotCompute(); // Otherwise it will loop infinitely.
6207 // We could implement others, but I really doubt anyone writes loops like
6208 // this, and if they did, they would already be constant folded.
6209 return getCouldNotCompute();
6212 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
6213 /// (which may not be an immediate predecessor) which has exactly one
6214 /// successor from which BB is reachable, or null if no such block is
6217 std::pair<BasicBlock *, BasicBlock *>
6218 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
6219 // If the block has a unique predecessor, then there is no path from the
6220 // predecessor to the block that does not go through the direct edge
6221 // from the predecessor to the block.
6222 if (BasicBlock *Pred = BB->getSinglePredecessor())
6223 return std::make_pair(Pred, BB);
6225 // A loop's header is defined to be a block that dominates the loop.
6226 // If the header has a unique predecessor outside the loop, it must be
6227 // a block that has exactly one successor that can reach the loop.
6228 if (Loop *L = LI->getLoopFor(BB))
6229 return std::make_pair(L->getLoopPredecessor(), L->getHeader());
6231 return std::pair<BasicBlock *, BasicBlock *>();
6234 /// HasSameValue - SCEV structural equivalence is usually sufficient for
6235 /// testing whether two expressions are equal, however for the purposes of
6236 /// looking for a condition guarding a loop, it can be useful to be a little
6237 /// more general, since a front-end may have replicated the controlling
6240 static bool HasSameValue(const SCEV *A, const SCEV *B) {
6241 // Quick check to see if they are the same SCEV.
6242 if (A == B) return true;
6244 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
6245 // two different instructions with the same value. Check for this case.
6246 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
6247 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
6248 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
6249 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
6250 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory())
6253 // Otherwise assume they may have a different value.
6257 /// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with
6258 /// predicate Pred. Return true iff any changes were made.
6260 bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
6261 const SCEV *&LHS, const SCEV *&RHS,
6263 bool Changed = false;
6265 // If we hit the max recursion limit bail out.
6269 // Canonicalize a constant to the right side.
6270 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
6271 // Check for both operands constant.
6272 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
6273 if (ConstantExpr::getICmp(Pred,
6275 RHSC->getValue())->isNullValue())
6276 goto trivially_false;
6278 goto trivially_true;
6280 // Otherwise swap the operands to put the constant on the right.
6281 std::swap(LHS, RHS);
6282 Pred = ICmpInst::getSwappedPredicate(Pred);
6286 // If we're comparing an addrec with a value which is loop-invariant in the
6287 // addrec's loop, put the addrec on the left. Also make a dominance check,
6288 // as both operands could be addrecs loop-invariant in each other's loop.
6289 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
6290 const Loop *L = AR->getLoop();
6291 if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) {
6292 std::swap(LHS, RHS);
6293 Pred = ICmpInst::getSwappedPredicate(Pred);
6298 // If there's a constant operand, canonicalize comparisons with boundary
6299 // cases, and canonicalize *-or-equal comparisons to regular comparisons.
6300 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
6301 const APInt &RA = RC->getValue()->getValue();
6303 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6304 case ICmpInst::ICMP_EQ:
6305 case ICmpInst::ICMP_NE:
6306 // Fold ((-1) * %a) + %b == 0 (equivalent to %b-%a == 0) into %a == %b.
6308 if (const SCEVAddExpr *AE = dyn_cast<SCEVAddExpr>(LHS))
6309 if (const SCEVMulExpr *ME = dyn_cast<SCEVMulExpr>(AE->getOperand(0)))
6310 if (AE->getNumOperands() == 2 && ME->getNumOperands() == 2 &&
6311 ME->getOperand(0)->isAllOnesValue()) {
6312 RHS = AE->getOperand(1);
6313 LHS = ME->getOperand(1);
6317 case ICmpInst::ICMP_UGE:
6318 if ((RA - 1).isMinValue()) {
6319 Pred = ICmpInst::ICMP_NE;
6320 RHS = getConstant(RA - 1);
6324 if (RA.isMaxValue()) {
6325 Pred = ICmpInst::ICMP_EQ;
6329 if (RA.isMinValue()) goto trivially_true;
6331 Pred = ICmpInst::ICMP_UGT;
6332 RHS = getConstant(RA - 1);
6335 case ICmpInst::ICMP_ULE:
6336 if ((RA + 1).isMaxValue()) {
6337 Pred = ICmpInst::ICMP_NE;
6338 RHS = getConstant(RA + 1);
6342 if (RA.isMinValue()) {
6343 Pred = ICmpInst::ICMP_EQ;
6347 if (RA.isMaxValue()) goto trivially_true;
6349 Pred = ICmpInst::ICMP_ULT;
6350 RHS = getConstant(RA + 1);
6353 case ICmpInst::ICMP_SGE:
6354 if ((RA - 1).isMinSignedValue()) {
6355 Pred = ICmpInst::ICMP_NE;
6356 RHS = getConstant(RA - 1);
6360 if (RA.isMaxSignedValue()) {
6361 Pred = ICmpInst::ICMP_EQ;
6365 if (RA.isMinSignedValue()) goto trivially_true;
6367 Pred = ICmpInst::ICMP_SGT;
6368 RHS = getConstant(RA - 1);
6371 case ICmpInst::ICMP_SLE:
6372 if ((RA + 1).isMaxSignedValue()) {
6373 Pred = ICmpInst::ICMP_NE;
6374 RHS = getConstant(RA + 1);
6378 if (RA.isMinSignedValue()) {
6379 Pred = ICmpInst::ICMP_EQ;
6383 if (RA.isMaxSignedValue()) goto trivially_true;
6385 Pred = ICmpInst::ICMP_SLT;
6386 RHS = getConstant(RA + 1);
6389 case ICmpInst::ICMP_UGT:
6390 if (RA.isMinValue()) {
6391 Pred = ICmpInst::ICMP_NE;
6395 if ((RA + 1).isMaxValue()) {
6396 Pred = ICmpInst::ICMP_EQ;
6397 RHS = getConstant(RA + 1);
6401 if (RA.isMaxValue()) goto trivially_false;
6403 case ICmpInst::ICMP_ULT:
6404 if (RA.isMaxValue()) {
6405 Pred = ICmpInst::ICMP_NE;
6409 if ((RA - 1).isMinValue()) {
6410 Pred = ICmpInst::ICMP_EQ;
6411 RHS = getConstant(RA - 1);
6415 if (RA.isMinValue()) goto trivially_false;
6417 case ICmpInst::ICMP_SGT:
6418 if (RA.isMinSignedValue()) {
6419 Pred = ICmpInst::ICMP_NE;
6423 if ((RA + 1).isMaxSignedValue()) {
6424 Pred = ICmpInst::ICMP_EQ;
6425 RHS = getConstant(RA + 1);
6429 if (RA.isMaxSignedValue()) goto trivially_false;
6431 case ICmpInst::ICMP_SLT:
6432 if (RA.isMaxSignedValue()) {
6433 Pred = ICmpInst::ICMP_NE;
6437 if ((RA - 1).isMinSignedValue()) {
6438 Pred = ICmpInst::ICMP_EQ;
6439 RHS = getConstant(RA - 1);
6443 if (RA.isMinSignedValue()) goto trivially_false;
6448 // Check for obvious equality.
6449 if (HasSameValue(LHS, RHS)) {
6450 if (ICmpInst::isTrueWhenEqual(Pred))
6451 goto trivially_true;
6452 if (ICmpInst::isFalseWhenEqual(Pred))
6453 goto trivially_false;
6456 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
6457 // adding or subtracting 1 from one of the operands.
6459 case ICmpInst::ICMP_SLE:
6460 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) {
6461 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
6463 Pred = ICmpInst::ICMP_SLT;
6465 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) {
6466 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
6468 Pred = ICmpInst::ICMP_SLT;
6472 case ICmpInst::ICMP_SGE:
6473 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) {
6474 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
6476 Pred = ICmpInst::ICMP_SGT;
6478 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) {
6479 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
6481 Pred = ICmpInst::ICMP_SGT;
6485 case ICmpInst::ICMP_ULE:
6486 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) {
6487 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
6489 Pred = ICmpInst::ICMP_ULT;
6491 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) {
6492 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
6494 Pred = ICmpInst::ICMP_ULT;
6498 case ICmpInst::ICMP_UGE:
6499 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) {
6500 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
6502 Pred = ICmpInst::ICMP_UGT;
6504 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) {
6505 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
6507 Pred = ICmpInst::ICMP_UGT;
6515 // TODO: More simplifications are possible here.
6517 // Recursively simplify until we either hit a recursion limit or nothing
6520 return SimplifyICmpOperands(Pred, LHS, RHS, Depth+1);
6526 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
6527 Pred = ICmpInst::ICMP_EQ;
6532 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
6533 Pred = ICmpInst::ICMP_NE;
6537 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
6538 return getSignedRange(S).getSignedMax().isNegative();
6541 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
6542 return getSignedRange(S).getSignedMin().isStrictlyPositive();
6545 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
6546 return !getSignedRange(S).getSignedMin().isNegative();
6549 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
6550 return !getSignedRange(S).getSignedMax().isStrictlyPositive();
6553 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
6554 return isKnownNegative(S) || isKnownPositive(S);
6557 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
6558 const SCEV *LHS, const SCEV *RHS) {
6559 // Canonicalize the inputs first.
6560 (void)SimplifyICmpOperands(Pred, LHS, RHS);
6562 // If LHS or RHS is an addrec, check to see if the condition is true in
6563 // every iteration of the loop.
6564 // If LHS and RHS are both addrec, both conditions must be true in
6565 // every iteration of the loop.
6566 const SCEVAddRecExpr *LAR = dyn_cast<SCEVAddRecExpr>(LHS);
6567 const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS);
6568 bool LeftGuarded = false;
6569 bool RightGuarded = false;
6571 const Loop *L = LAR->getLoop();
6572 if (isLoopEntryGuardedByCond(L, Pred, LAR->getStart(), RHS) &&
6573 isLoopBackedgeGuardedByCond(L, Pred, LAR->getPostIncExpr(*this), RHS)) {
6574 if (!RAR) return true;
6579 const Loop *L = RAR->getLoop();
6580 if (isLoopEntryGuardedByCond(L, Pred, LHS, RAR->getStart()) &&
6581 isLoopBackedgeGuardedByCond(L, Pred, LHS, RAR->getPostIncExpr(*this))) {
6582 if (!LAR) return true;
6583 RightGuarded = true;
6586 if (LeftGuarded && RightGuarded)
6589 // Otherwise see what can be done with known constant ranges.
6590 return isKnownPredicateWithRanges(Pred, LHS, RHS);
6594 ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred,
6595 const SCEV *LHS, const SCEV *RHS) {
6596 if (HasSameValue(LHS, RHS))
6597 return ICmpInst::isTrueWhenEqual(Pred);
6599 // This code is split out from isKnownPredicate because it is called from
6600 // within isLoopEntryGuardedByCond.
6603 llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6604 case ICmpInst::ICMP_SGT:
6605 std::swap(LHS, RHS);
6606 case ICmpInst::ICMP_SLT: {
6607 ConstantRange LHSRange = getSignedRange(LHS);
6608 ConstantRange RHSRange = getSignedRange(RHS);
6609 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
6611 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
6615 case ICmpInst::ICMP_SGE:
6616 std::swap(LHS, RHS);
6617 case ICmpInst::ICMP_SLE: {
6618 ConstantRange LHSRange = getSignedRange(LHS);
6619 ConstantRange RHSRange = getSignedRange(RHS);
6620 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
6622 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
6626 case ICmpInst::ICMP_UGT:
6627 std::swap(LHS, RHS);
6628 case ICmpInst::ICMP_ULT: {
6629 ConstantRange LHSRange = getUnsignedRange(LHS);
6630 ConstantRange RHSRange = getUnsignedRange(RHS);
6631 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
6633 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
6637 case ICmpInst::ICMP_UGE:
6638 std::swap(LHS, RHS);
6639 case ICmpInst::ICMP_ULE: {
6640 ConstantRange LHSRange = getUnsignedRange(LHS);
6641 ConstantRange RHSRange = getUnsignedRange(RHS);
6642 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
6644 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
6648 case ICmpInst::ICMP_NE: {
6649 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
6651 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
6654 const SCEV *Diff = getMinusSCEV(LHS, RHS);
6655 if (isKnownNonZero(Diff))
6659 case ICmpInst::ICMP_EQ:
6660 // The check at the top of the function catches the case where
6661 // the values are known to be equal.
6667 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
6668 /// protected by a conditional between LHS and RHS. This is used to
6669 /// to eliminate casts.
6671 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
6672 ICmpInst::Predicate Pred,
6673 const SCEV *LHS, const SCEV *RHS) {
6674 // Interpret a null as meaning no loop, where there is obviously no guard
6675 // (interprocedural conditions notwithstanding).
6676 if (!L) return true;
6678 if (isKnownPredicateWithRanges(Pred, LHS, RHS)) return true;
6680 BasicBlock *Latch = L->getLoopLatch();
6684 BranchInst *LoopContinuePredicate =
6685 dyn_cast<BranchInst>(Latch->getTerminator());
6686 if (LoopContinuePredicate && LoopContinuePredicate->isConditional() &&
6687 isImpliedCond(Pred, LHS, RHS,
6688 LoopContinuePredicate->getCondition(),
6689 LoopContinuePredicate->getSuccessor(0) != L->getHeader()))
6692 // Check conditions due to any @llvm.assume intrinsics.
6693 for (auto &AssumeVH : AC->assumptions()) {
6696 auto *CI = cast<CallInst>(AssumeVH);
6697 if (!DT->dominates(CI, Latch->getTerminator()))
6700 if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false))
6707 /// isLoopEntryGuardedByCond - Test whether entry to the loop is protected
6708 /// by a conditional between LHS and RHS. This is used to help avoid max
6709 /// expressions in loop trip counts, and to eliminate casts.
6711 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
6712 ICmpInst::Predicate Pred,
6713 const SCEV *LHS, const SCEV *RHS) {
6714 // Interpret a null as meaning no loop, where there is obviously no guard
6715 // (interprocedural conditions notwithstanding).
6716 if (!L) return false;
6718 if (isKnownPredicateWithRanges(Pred, LHS, RHS)) return true;
6720 // Starting at the loop predecessor, climb up the predecessor chain, as long
6721 // as there are predecessors that can be found that have unique successors
6722 // leading to the original header.
6723 for (std::pair<BasicBlock *, BasicBlock *>
6724 Pair(L->getLoopPredecessor(), L->getHeader());
6726 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
6728 BranchInst *LoopEntryPredicate =
6729 dyn_cast<BranchInst>(Pair.first->getTerminator());
6730 if (!LoopEntryPredicate ||
6731 LoopEntryPredicate->isUnconditional())
6734 if (isImpliedCond(Pred, LHS, RHS,
6735 LoopEntryPredicate->getCondition(),
6736 LoopEntryPredicate->getSuccessor(0) != Pair.second))
6740 // Check conditions due to any @llvm.assume intrinsics.
6741 for (auto &AssumeVH : AC->assumptions()) {
6744 auto *CI = cast<CallInst>(AssumeVH);
6745 if (!DT->dominates(CI, L->getHeader()))
6748 if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false))
6755 /// RAII wrapper to prevent recursive application of isImpliedCond.
6756 /// ScalarEvolution's PendingLoopPredicates set must be empty unless we are
6757 /// currently evaluating isImpliedCond.
6758 struct MarkPendingLoopPredicate {
6760 DenseSet<Value*> &LoopPreds;
6763 MarkPendingLoopPredicate(Value *C, DenseSet<Value*> &LP)
6764 : Cond(C), LoopPreds(LP) {
6765 Pending = !LoopPreds.insert(Cond).second;
6767 ~MarkPendingLoopPredicate() {
6769 LoopPreds.erase(Cond);
6773 /// isImpliedCond - Test whether the condition described by Pred, LHS,
6774 /// and RHS is true whenever the given Cond value evaluates to true.
6775 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred,
6776 const SCEV *LHS, const SCEV *RHS,
6777 Value *FoundCondValue,
6779 MarkPendingLoopPredicate Mark(FoundCondValue, PendingLoopPredicates);
6783 // Recursively handle And and Or conditions.
6784 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) {
6785 if (BO->getOpcode() == Instruction::And) {
6787 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
6788 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
6789 } else if (BO->getOpcode() == Instruction::Or) {
6791 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
6792 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
6796 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue);
6797 if (!ICI) return false;
6799 // Bail if the ICmp's operands' types are wider than the needed type
6800 // before attempting to call getSCEV on them. This avoids infinite
6801 // recursion, since the analysis of widening casts can require loop
6802 // exit condition information for overflow checking, which would
6804 if (getTypeSizeInBits(LHS->getType()) <
6805 getTypeSizeInBits(ICI->getOperand(0)->getType()))
6808 // Now that we found a conditional branch that dominates the loop or controls
6809 // the loop latch. Check to see if it is the comparison we are looking for.
6810 ICmpInst::Predicate FoundPred;
6812 FoundPred = ICI->getInversePredicate();
6814 FoundPred = ICI->getPredicate();
6816 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
6817 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
6819 // Balance the types. The case where FoundLHS' type is wider than
6820 // LHS' type is checked for above.
6821 if (getTypeSizeInBits(LHS->getType()) >
6822 getTypeSizeInBits(FoundLHS->getType())) {
6823 if (CmpInst::isSigned(FoundPred)) {
6824 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
6825 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
6827 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
6828 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
6832 // Canonicalize the query to match the way instcombine will have
6833 // canonicalized the comparison.
6834 if (SimplifyICmpOperands(Pred, LHS, RHS))
6836 return CmpInst::isTrueWhenEqual(Pred);
6837 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
6838 if (FoundLHS == FoundRHS)
6839 return CmpInst::isFalseWhenEqual(FoundPred);
6841 // Check to see if we can make the LHS or RHS match.
6842 if (LHS == FoundRHS || RHS == FoundLHS) {
6843 if (isa<SCEVConstant>(RHS)) {
6844 std::swap(FoundLHS, FoundRHS);
6845 FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
6847 std::swap(LHS, RHS);
6848 Pred = ICmpInst::getSwappedPredicate(Pred);
6852 // Check whether the found predicate is the same as the desired predicate.
6853 if (FoundPred == Pred)
6854 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
6856 // Check whether swapping the found predicate makes it the same as the
6857 // desired predicate.
6858 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
6859 if (isa<SCEVConstant>(RHS))
6860 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
6862 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
6863 RHS, LHS, FoundLHS, FoundRHS);
6866 // Check if we can make progress by sharpening ranges.
6867 if (FoundPred == ICmpInst::ICMP_NE &&
6868 (isa<SCEVConstant>(FoundLHS) || isa<SCEVConstant>(FoundRHS))) {
6870 const SCEVConstant *C = nullptr;
6871 const SCEV *V = nullptr;
6873 if (isa<SCEVConstant>(FoundLHS)) {
6874 C = cast<SCEVConstant>(FoundLHS);
6877 C = cast<SCEVConstant>(FoundRHS);
6881 // The guarding predicate tells us that C != V. If the known range
6882 // of V is [C, t), we can sharpen the range to [C + 1, t). The
6883 // range we consider has to correspond to same signedness as the
6884 // predicate we're interested in folding.
6886 APInt Min = ICmpInst::isSigned(Pred) ?
6887 getSignedRange(V).getSignedMin() : getUnsignedRange(V).getUnsignedMin();
6889 if (Min == C->getValue()->getValue()) {
6890 // Given (V >= Min && V != Min) we conclude V >= (Min + 1).
6891 // This is true even if (Min + 1) wraps around -- in case of
6892 // wraparound, (Min + 1) < Min, so (V >= Min => V >= (Min + 1)).
6894 APInt SharperMin = Min + 1;
6897 case ICmpInst::ICMP_SGE:
6898 case ICmpInst::ICMP_UGE:
6899 // We know V `Pred` SharperMin. If this implies LHS `Pred`
6901 if (isImpliedCondOperands(Pred, LHS, RHS, V,
6902 getConstant(SharperMin)))
6905 case ICmpInst::ICMP_SGT:
6906 case ICmpInst::ICMP_UGT:
6907 // We know from the range information that (V `Pred` Min ||
6908 // V == Min). We know from the guarding condition that !(V
6909 // == Min). This gives us
6911 // V `Pred` Min || V == Min && !(V == Min)
6914 // If V `Pred` Min implies LHS `Pred` RHS, we're done.
6916 if (isImpliedCondOperands(Pred, LHS, RHS, V, getConstant(Min)))
6926 // Check whether the actual condition is beyond sufficient.
6927 if (FoundPred == ICmpInst::ICMP_EQ)
6928 if (ICmpInst::isTrueWhenEqual(Pred))
6929 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
6931 if (Pred == ICmpInst::ICMP_NE)
6932 if (!ICmpInst::isTrueWhenEqual(FoundPred))
6933 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
6936 // Otherwise assume the worst.
6940 /// isImpliedCondOperands - Test whether the condition described by Pred,
6941 /// LHS, and RHS is true whenever the condition described by Pred, FoundLHS,
6942 /// and FoundRHS is true.
6943 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
6944 const SCEV *LHS, const SCEV *RHS,
6945 const SCEV *FoundLHS,
6946 const SCEV *FoundRHS) {
6947 if (isImpliedCondOperandsViaRanges(Pred, LHS, RHS, FoundLHS, FoundRHS))
6950 return isImpliedCondOperandsHelper(Pred, LHS, RHS,
6951 FoundLHS, FoundRHS) ||
6952 // ~x < ~y --> x > y
6953 isImpliedCondOperandsHelper(Pred, LHS, RHS,
6954 getNotSCEV(FoundRHS),
6955 getNotSCEV(FoundLHS));
6959 /// If Expr computes ~A, return A else return nullptr
6960 static const SCEV *MatchNotExpr(const SCEV *Expr) {
6961 const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Expr);
6962 if (!Add || Add->getNumOperands() != 2) return nullptr;
6964 const SCEVConstant *AddLHS = dyn_cast<SCEVConstant>(Add->getOperand(0));
6965 if (!(AddLHS && AddLHS->getValue()->getValue().isAllOnesValue()))
6968 const SCEVMulExpr *AddRHS = dyn_cast<SCEVMulExpr>(Add->getOperand(1));
6969 if (!AddRHS || AddRHS->getNumOperands() != 2) return nullptr;
6971 const SCEVConstant *MulLHS = dyn_cast<SCEVConstant>(AddRHS->getOperand(0));
6972 if (!(MulLHS && MulLHS->getValue()->getValue().isAllOnesValue()))
6975 return AddRHS->getOperand(1);
6979 /// Is MaybeMaxExpr an SMax or UMax of Candidate and some other values?
6980 template<typename MaxExprType>
6981 static bool IsMaxConsistingOf(const SCEV *MaybeMaxExpr,
6982 const SCEV *Candidate) {
6983 const MaxExprType *MaxExpr = dyn_cast<MaxExprType>(MaybeMaxExpr);
6984 if (!MaxExpr) return false;
6986 auto It = std::find(MaxExpr->op_begin(), MaxExpr->op_end(), Candidate);
6987 return It != MaxExpr->op_end();
6991 /// Is MaybeMinExpr an SMin or UMin of Candidate and some other values?
6992 template<typename MaxExprType>
6993 static bool IsMinConsistingOf(ScalarEvolution &SE,
6994 const SCEV *MaybeMinExpr,
6995 const SCEV *Candidate) {
6996 const SCEV *MaybeMaxExpr = MatchNotExpr(MaybeMinExpr);
7000 return IsMaxConsistingOf<MaxExprType>(MaybeMaxExpr, SE.getNotSCEV(Candidate));
7004 /// Is LHS `Pred` RHS true on the virtue of LHS or RHS being a Min or Max
7006 static bool IsKnownPredicateViaMinOrMax(ScalarEvolution &SE,
7007 ICmpInst::Predicate Pred,
7008 const SCEV *LHS, const SCEV *RHS) {
7013 case ICmpInst::ICMP_SGE:
7014 std::swap(LHS, RHS);
7016 case ICmpInst::ICMP_SLE:
7019 IsMinConsistingOf<SCEVSMaxExpr>(SE, LHS, RHS) ||
7021 IsMaxConsistingOf<SCEVSMaxExpr>(RHS, LHS);
7023 case ICmpInst::ICMP_UGE:
7024 std::swap(LHS, RHS);
7026 case ICmpInst::ICMP_ULE:
7029 IsMinConsistingOf<SCEVUMaxExpr>(SE, LHS, RHS) ||
7031 IsMaxConsistingOf<SCEVUMaxExpr>(RHS, LHS);
7034 llvm_unreachable("covered switch fell through?!");
7037 /// isImpliedCondOperandsHelper - Test whether the condition described by
7038 /// Pred, LHS, and RHS is true whenever the condition described by Pred,
7039 /// FoundLHS, and FoundRHS is true.
7041 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
7042 const SCEV *LHS, const SCEV *RHS,
7043 const SCEV *FoundLHS,
7044 const SCEV *FoundRHS) {
7045 auto IsKnownPredicateFull =
7046 [this](ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS) {
7047 return isKnownPredicateWithRanges(Pred, LHS, RHS) ||
7048 IsKnownPredicateViaMinOrMax(*this, Pred, LHS, RHS);
7052 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
7053 case ICmpInst::ICMP_EQ:
7054 case ICmpInst::ICMP_NE:
7055 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
7058 case ICmpInst::ICMP_SLT:
7059 case ICmpInst::ICMP_SLE:
7060 if (IsKnownPredicateFull(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
7061 IsKnownPredicateFull(ICmpInst::ICMP_SGE, RHS, FoundRHS))
7064 case ICmpInst::ICMP_SGT:
7065 case ICmpInst::ICMP_SGE:
7066 if (IsKnownPredicateFull(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
7067 IsKnownPredicateFull(ICmpInst::ICMP_SLE, RHS, FoundRHS))
7070 case ICmpInst::ICMP_ULT:
7071 case ICmpInst::ICMP_ULE:
7072 if (IsKnownPredicateFull(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
7073 IsKnownPredicateFull(ICmpInst::ICMP_UGE, RHS, FoundRHS))
7076 case ICmpInst::ICMP_UGT:
7077 case ICmpInst::ICMP_UGE:
7078 if (IsKnownPredicateFull(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
7079 IsKnownPredicateFull(ICmpInst::ICMP_ULE, RHS, FoundRHS))
7087 /// isImpliedCondOperandsViaRanges - helper function for isImpliedCondOperands.
7088 /// Tries to get cases like "X `sgt` 0 => X - 1 `sgt` -1".
7089 bool ScalarEvolution::isImpliedCondOperandsViaRanges(ICmpInst::Predicate Pred,
7092 const SCEV *FoundLHS,
7093 const SCEV *FoundRHS) {
7094 if (!isa<SCEVConstant>(RHS) || !isa<SCEVConstant>(FoundRHS))
7095 // The restriction on `FoundRHS` be lifted easily -- it exists only to
7096 // reduce the compile time impact of this optimization.
7099 const SCEVAddExpr *AddLHS = dyn_cast<SCEVAddExpr>(LHS);
7100 if (!AddLHS || AddLHS->getOperand(1) != FoundLHS ||
7101 !isa<SCEVConstant>(AddLHS->getOperand(0)))
7104 APInt ConstFoundRHS = cast<SCEVConstant>(FoundRHS)->getValue()->getValue();
7106 // `FoundLHSRange` is the range we know `FoundLHS` to be in by virtue of the
7107 // antecedent "`FoundLHS` `Pred` `FoundRHS`".
7108 ConstantRange FoundLHSRange =
7109 ConstantRange::makeAllowedICmpRegion(Pred, ConstFoundRHS);
7111 // Since `LHS` is `FoundLHS` + `AddLHS->getOperand(0)`, we can compute a range
7114 cast<SCEVConstant>(AddLHS->getOperand(0))->getValue()->getValue();
7115 ConstantRange LHSRange = FoundLHSRange.add(ConstantRange(Addend));
7117 // We can also compute the range of values for `LHS` that satisfy the
7118 // consequent, "`LHS` `Pred` `RHS`":
7119 APInt ConstRHS = cast<SCEVConstant>(RHS)->getValue()->getValue();
7120 ConstantRange SatisfyingLHSRange =
7121 ConstantRange::makeSatisfyingICmpRegion(Pred, ConstRHS);
7123 // The antecedent implies the consequent if every value of `LHS` that
7124 // satisfies the antecedent also satisfies the consequent.
7125 return SatisfyingLHSRange.contains(LHSRange);
7128 // Verify if an linear IV with positive stride can overflow when in a
7129 // less-than comparison, knowing the invariant term of the comparison, the
7130 // stride and the knowledge of NSW/NUW flags on the recurrence.
7131 bool ScalarEvolution::doesIVOverflowOnLT(const SCEV *RHS, const SCEV *Stride,
7132 bool IsSigned, bool NoWrap) {
7133 if (NoWrap) return false;
7135 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
7136 const SCEV *One = getConstant(Stride->getType(), 1);
7139 APInt MaxRHS = getSignedRange(RHS).getSignedMax();
7140 APInt MaxValue = APInt::getSignedMaxValue(BitWidth);
7141 APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
7144 // SMaxRHS + SMaxStrideMinusOne > SMaxValue => overflow!
7145 return (MaxValue - MaxStrideMinusOne).slt(MaxRHS);
7148 APInt MaxRHS = getUnsignedRange(RHS).getUnsignedMax();
7149 APInt MaxValue = APInt::getMaxValue(BitWidth);
7150 APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
7153 // UMaxRHS + UMaxStrideMinusOne > UMaxValue => overflow!
7154 return (MaxValue - MaxStrideMinusOne).ult(MaxRHS);
7157 // Verify if an linear IV with negative stride can overflow when in a
7158 // greater-than comparison, knowing the invariant term of the comparison,
7159 // the stride and the knowledge of NSW/NUW flags on the recurrence.
7160 bool ScalarEvolution::doesIVOverflowOnGT(const SCEV *RHS, const SCEV *Stride,
7161 bool IsSigned, bool NoWrap) {
7162 if (NoWrap) return false;
7164 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
7165 const SCEV *One = getConstant(Stride->getType(), 1);
7168 APInt MinRHS = getSignedRange(RHS).getSignedMin();
7169 APInt MinValue = APInt::getSignedMinValue(BitWidth);
7170 APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
7173 // SMinRHS - SMaxStrideMinusOne < SMinValue => overflow!
7174 return (MinValue + MaxStrideMinusOne).sgt(MinRHS);
7177 APInt MinRHS = getUnsignedRange(RHS).getUnsignedMin();
7178 APInt MinValue = APInt::getMinValue(BitWidth);
7179 APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
7182 // UMinRHS - UMaxStrideMinusOne < UMinValue => overflow!
7183 return (MinValue + MaxStrideMinusOne).ugt(MinRHS);
7186 // Compute the backedge taken count knowing the interval difference, the
7187 // stride and presence of the equality in the comparison.
7188 const SCEV *ScalarEvolution::computeBECount(const SCEV *Delta, const SCEV *Step,
7190 const SCEV *One = getConstant(Step->getType(), 1);
7191 Delta = Equality ? getAddExpr(Delta, Step)
7192 : getAddExpr(Delta, getMinusSCEV(Step, One));
7193 return getUDivExpr(Delta, Step);
7196 /// HowManyLessThans - Return the number of times a backedge containing the
7197 /// specified less-than comparison will execute. If not computable, return
7198 /// CouldNotCompute.
7200 /// @param ControlsExit is true when the LHS < RHS condition directly controls
7201 /// the branch (loops exits only if condition is true). In this case, we can use
7202 /// NoWrapFlags to skip overflow checks.
7203 ScalarEvolution::ExitLimit
7204 ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
7205 const Loop *L, bool IsSigned,
7206 bool ControlsExit) {
7207 // We handle only IV < Invariant
7208 if (!isLoopInvariant(RHS, L))
7209 return getCouldNotCompute();
7211 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
7213 // Avoid weird loops
7214 if (!IV || IV->getLoop() != L || !IV->isAffine())
7215 return getCouldNotCompute();
7217 bool NoWrap = ControlsExit &&
7218 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
7220 const SCEV *Stride = IV->getStepRecurrence(*this);
7222 // Avoid negative or zero stride values
7223 if (!isKnownPositive(Stride))
7224 return getCouldNotCompute();
7226 // Avoid proven overflow cases: this will ensure that the backedge taken count
7227 // will not generate any unsigned overflow. Relaxed no-overflow conditions
7228 // exploit NoWrapFlags, allowing to optimize in presence of undefined
7229 // behaviors like the case of C language.
7230 if (!Stride->isOne() && doesIVOverflowOnLT(RHS, Stride, IsSigned, NoWrap))
7231 return getCouldNotCompute();
7233 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SLT
7234 : ICmpInst::ICMP_ULT;
7235 const SCEV *Start = IV->getStart();
7236 const SCEV *End = RHS;
7237 if (!isLoopEntryGuardedByCond(L, Cond, getMinusSCEV(Start, Stride), RHS)) {
7238 const SCEV *Diff = getMinusSCEV(RHS, Start);
7239 // If we have NoWrap set, then we can assume that the increment won't
7240 // overflow, in which case if RHS - Start is a constant, we don't need to
7241 // do a max operation since we can just figure it out statically
7242 if (NoWrap && isa<SCEVConstant>(Diff)) {
7243 APInt D = dyn_cast<const SCEVConstant>(Diff)->getValue()->getValue();
7247 End = IsSigned ? getSMaxExpr(RHS, Start)
7248 : getUMaxExpr(RHS, Start);
7251 const SCEV *BECount = computeBECount(getMinusSCEV(End, Start), Stride, false);
7253 APInt MinStart = IsSigned ? getSignedRange(Start).getSignedMin()
7254 : getUnsignedRange(Start).getUnsignedMin();
7256 APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
7257 : getUnsignedRange(Stride).getUnsignedMin();
7259 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
7260 APInt Limit = IsSigned ? APInt::getSignedMaxValue(BitWidth) - (MinStride - 1)
7261 : APInt::getMaxValue(BitWidth) - (MinStride - 1);
7263 // Although End can be a MAX expression we estimate MaxEnd considering only
7264 // the case End = RHS. This is safe because in the other case (End - Start)
7265 // is zero, leading to a zero maximum backedge taken count.
7267 IsSigned ? APIntOps::smin(getSignedRange(RHS).getSignedMax(), Limit)
7268 : APIntOps::umin(getUnsignedRange(RHS).getUnsignedMax(), Limit);
7270 const SCEV *MaxBECount;
7271 if (isa<SCEVConstant>(BECount))
7272 MaxBECount = BECount;
7274 MaxBECount = computeBECount(getConstant(MaxEnd - MinStart),
7275 getConstant(MinStride), false);
7277 if (isa<SCEVCouldNotCompute>(MaxBECount))
7278 MaxBECount = BECount;
7280 return ExitLimit(BECount, MaxBECount);
7283 ScalarEvolution::ExitLimit
7284 ScalarEvolution::HowManyGreaterThans(const SCEV *LHS, const SCEV *RHS,
7285 const Loop *L, bool IsSigned,
7286 bool ControlsExit) {
7287 // We handle only IV > Invariant
7288 if (!isLoopInvariant(RHS, L))
7289 return getCouldNotCompute();
7291 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
7293 // Avoid weird loops
7294 if (!IV || IV->getLoop() != L || !IV->isAffine())
7295 return getCouldNotCompute();
7297 bool NoWrap = ControlsExit &&
7298 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
7300 const SCEV *Stride = getNegativeSCEV(IV->getStepRecurrence(*this));
7302 // Avoid negative or zero stride values
7303 if (!isKnownPositive(Stride))
7304 return getCouldNotCompute();
7306 // Avoid proven overflow cases: this will ensure that the backedge taken count
7307 // will not generate any unsigned overflow. Relaxed no-overflow conditions
7308 // exploit NoWrapFlags, allowing to optimize in presence of undefined
7309 // behaviors like the case of C language.
7310 if (!Stride->isOne() && doesIVOverflowOnGT(RHS, Stride, IsSigned, NoWrap))
7311 return getCouldNotCompute();
7313 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SGT
7314 : ICmpInst::ICMP_UGT;
7316 const SCEV *Start = IV->getStart();
7317 const SCEV *End = RHS;
7318 if (!isLoopEntryGuardedByCond(L, Cond, getAddExpr(Start, Stride), RHS)) {
7319 const SCEV *Diff = getMinusSCEV(RHS, Start);
7320 // If we have NoWrap set, then we can assume that the increment won't
7321 // overflow, in which case if RHS - Start is a constant, we don't need to
7322 // do a max operation since we can just figure it out statically
7323 if (NoWrap && isa<SCEVConstant>(Diff)) {
7324 APInt D = dyn_cast<const SCEVConstant>(Diff)->getValue()->getValue();
7325 if (!D.isNegative())
7328 End = IsSigned ? getSMinExpr(RHS, Start)
7329 : getUMinExpr(RHS, Start);
7332 const SCEV *BECount = computeBECount(getMinusSCEV(Start, End), Stride, false);
7334 APInt MaxStart = IsSigned ? getSignedRange(Start).getSignedMax()
7335 : getUnsignedRange(Start).getUnsignedMax();
7337 APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
7338 : getUnsignedRange(Stride).getUnsignedMin();
7340 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
7341 APInt Limit = IsSigned ? APInt::getSignedMinValue(BitWidth) + (MinStride - 1)
7342 : APInt::getMinValue(BitWidth) + (MinStride - 1);
7344 // Although End can be a MIN expression we estimate MinEnd considering only
7345 // the case End = RHS. This is safe because in the other case (Start - End)
7346 // is zero, leading to a zero maximum backedge taken count.
7348 IsSigned ? APIntOps::smax(getSignedRange(RHS).getSignedMin(), Limit)
7349 : APIntOps::umax(getUnsignedRange(RHS).getUnsignedMin(), Limit);
7352 const SCEV *MaxBECount = getCouldNotCompute();
7353 if (isa<SCEVConstant>(BECount))
7354 MaxBECount = BECount;
7356 MaxBECount = computeBECount(getConstant(MaxStart - MinEnd),
7357 getConstant(MinStride), false);
7359 if (isa<SCEVCouldNotCompute>(MaxBECount))
7360 MaxBECount = BECount;
7362 return ExitLimit(BECount, MaxBECount);
7365 /// getNumIterationsInRange - Return the number of iterations of this loop that
7366 /// produce values in the specified constant range. Another way of looking at
7367 /// this is that it returns the first iteration number where the value is not in
7368 /// the condition, thus computing the exit count. If the iteration count can't
7369 /// be computed, an instance of SCEVCouldNotCompute is returned.
7370 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
7371 ScalarEvolution &SE) const {
7372 if (Range.isFullSet()) // Infinite loop.
7373 return SE.getCouldNotCompute();
7375 // If the start is a non-zero constant, shift the range to simplify things.
7376 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
7377 if (!SC->getValue()->isZero()) {
7378 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
7379 Operands[0] = SE.getConstant(SC->getType(), 0);
7380 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(),
7381 getNoWrapFlags(FlagNW));
7382 if (const SCEVAddRecExpr *ShiftedAddRec =
7383 dyn_cast<SCEVAddRecExpr>(Shifted))
7384 return ShiftedAddRec->getNumIterationsInRange(
7385 Range.subtract(SC->getValue()->getValue()), SE);
7386 // This is strange and shouldn't happen.
7387 return SE.getCouldNotCompute();
7390 // The only time we can solve this is when we have all constant indices.
7391 // Otherwise, we cannot determine the overflow conditions.
7392 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
7393 if (!isa<SCEVConstant>(getOperand(i)))
7394 return SE.getCouldNotCompute();
7397 // Okay at this point we know that all elements of the chrec are constants and
7398 // that the start element is zero.
7400 // First check to see if the range contains zero. If not, the first
7402 unsigned BitWidth = SE.getTypeSizeInBits(getType());
7403 if (!Range.contains(APInt(BitWidth, 0)))
7404 return SE.getConstant(getType(), 0);
7407 // If this is an affine expression then we have this situation:
7408 // Solve {0,+,A} in Range === Ax in Range
7410 // We know that zero is in the range. If A is positive then we know that
7411 // the upper value of the range must be the first possible exit value.
7412 // If A is negative then the lower of the range is the last possible loop
7413 // value. Also note that we already checked for a full range.
7414 APInt One(BitWidth,1);
7415 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
7416 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
7418 // The exit value should be (End+A)/A.
7419 APInt ExitVal = (End + A).udiv(A);
7420 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
7422 // Evaluate at the exit value. If we really did fall out of the valid
7423 // range, then we computed our trip count, otherwise wrap around or other
7424 // things must have happened.
7425 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
7426 if (Range.contains(Val->getValue()))
7427 return SE.getCouldNotCompute(); // Something strange happened
7429 // Ensure that the previous value is in the range. This is a sanity check.
7430 assert(Range.contains(
7431 EvaluateConstantChrecAtConstant(this,
7432 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
7433 "Linear scev computation is off in a bad way!");
7434 return SE.getConstant(ExitValue);
7435 } else if (isQuadratic()) {
7436 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
7437 // quadratic equation to solve it. To do this, we must frame our problem in
7438 // terms of figuring out when zero is crossed, instead of when
7439 // Range.getUpper() is crossed.
7440 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
7441 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
7442 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop(),
7443 // getNoWrapFlags(FlagNW)
7446 // Next, solve the constructed addrec
7447 std::pair<const SCEV *,const SCEV *> Roots =
7448 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
7449 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
7450 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
7452 // Pick the smallest positive root value.
7453 if (ConstantInt *CB =
7454 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
7455 R1->getValue(), R2->getValue()))) {
7456 if (!CB->getZExtValue())
7457 std::swap(R1, R2); // R1 is the minimum root now.
7459 // Make sure the root is not off by one. The returned iteration should
7460 // not be in the range, but the previous one should be. When solving
7461 // for "X*X < 5", for example, we should not return a root of 2.
7462 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
7465 if (Range.contains(R1Val->getValue())) {
7466 // The next iteration must be out of the range...
7467 ConstantInt *NextVal =
7468 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1);
7470 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
7471 if (!Range.contains(R1Val->getValue()))
7472 return SE.getConstant(NextVal);
7473 return SE.getCouldNotCompute(); // Something strange happened
7476 // If R1 was not in the range, then it is a good return value. Make
7477 // sure that R1-1 WAS in the range though, just in case.
7478 ConstantInt *NextVal =
7479 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1);
7480 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
7481 if (Range.contains(R1Val->getValue()))
7483 return SE.getCouldNotCompute(); // Something strange happened
7488 return SE.getCouldNotCompute();
7494 FindUndefs() : Found(false) {}
7496 bool follow(const SCEV *S) {
7497 if (const SCEVUnknown *C = dyn_cast<SCEVUnknown>(S)) {
7498 if (isa<UndefValue>(C->getValue()))
7500 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) {
7501 if (isa<UndefValue>(C->getValue()))
7505 // Keep looking if we haven't found it yet.
7508 bool isDone() const {
7509 // Stop recursion if we have found an undef.
7515 // Return true when S contains at least an undef value.
7517 containsUndefs(const SCEV *S) {
7519 SCEVTraversal<FindUndefs> ST(F);
7526 // Collect all steps of SCEV expressions.
7527 struct SCEVCollectStrides {
7528 ScalarEvolution &SE;
7529 SmallVectorImpl<const SCEV *> &Strides;
7531 SCEVCollectStrides(ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &S)
7532 : SE(SE), Strides(S) {}
7534 bool follow(const SCEV *S) {
7535 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(S))
7536 Strides.push_back(AR->getStepRecurrence(SE));
7539 bool isDone() const { return false; }
7542 // Collect all SCEVUnknown and SCEVMulExpr expressions.
7543 struct SCEVCollectTerms {
7544 SmallVectorImpl<const SCEV *> &Terms;
7546 SCEVCollectTerms(SmallVectorImpl<const SCEV *> &T)
7549 bool follow(const SCEV *S) {
7550 if (isa<SCEVUnknown>(S) || isa<SCEVMulExpr>(S)) {
7551 if (!containsUndefs(S))
7554 // Stop recursion: once we collected a term, do not walk its operands.
7561 bool isDone() const { return false; }
7565 /// Find parametric terms in this SCEVAddRecExpr.
7566 void SCEVAddRecExpr::collectParametricTerms(
7567 ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &Terms) const {
7568 SmallVector<const SCEV *, 4> Strides;
7569 SCEVCollectStrides StrideCollector(SE, Strides);
7570 visitAll(this, StrideCollector);
7573 dbgs() << "Strides:\n";
7574 for (const SCEV *S : Strides)
7575 dbgs() << *S << "\n";
7578 for (const SCEV *S : Strides) {
7579 SCEVCollectTerms TermCollector(Terms);
7580 visitAll(S, TermCollector);
7584 dbgs() << "Terms:\n";
7585 for (const SCEV *T : Terms)
7586 dbgs() << *T << "\n";
7590 static bool findArrayDimensionsRec(ScalarEvolution &SE,
7591 SmallVectorImpl<const SCEV *> &Terms,
7592 SmallVectorImpl<const SCEV *> &Sizes) {
7593 int Last = Terms.size() - 1;
7594 const SCEV *Step = Terms[Last];
7596 // End of recursion.
7598 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Step)) {
7599 SmallVector<const SCEV *, 2> Qs;
7600 for (const SCEV *Op : M->operands())
7601 if (!isa<SCEVConstant>(Op))
7604 Step = SE.getMulExpr(Qs);
7607 Sizes.push_back(Step);
7611 for (const SCEV *&Term : Terms) {
7612 // Normalize the terms before the next call to findArrayDimensionsRec.
7614 SCEVDivision::divide(SE, Term, Step, &Q, &R);
7616 // Bail out when GCD does not evenly divide one of the terms.
7623 // Remove all SCEVConstants.
7624 Terms.erase(std::remove_if(Terms.begin(), Terms.end(), [](const SCEV *E) {
7625 return isa<SCEVConstant>(E);
7629 if (Terms.size() > 0)
7630 if (!findArrayDimensionsRec(SE, Terms, Sizes))
7633 Sizes.push_back(Step);
7638 struct FindParameter {
7639 bool FoundParameter;
7640 FindParameter() : FoundParameter(false) {}
7642 bool follow(const SCEV *S) {
7643 if (isa<SCEVUnknown>(S)) {
7644 FoundParameter = true;
7645 // Stop recursion: we found a parameter.
7651 bool isDone() const {
7652 // Stop recursion if we have found a parameter.
7653 return FoundParameter;
7658 // Returns true when S contains at least a SCEVUnknown parameter.
7660 containsParameters(const SCEV *S) {
7662 SCEVTraversal<FindParameter> ST(F);
7665 return F.FoundParameter;
7668 // Returns true when one of the SCEVs of Terms contains a SCEVUnknown parameter.
7670 containsParameters(SmallVectorImpl<const SCEV *> &Terms) {
7671 for (const SCEV *T : Terms)
7672 if (containsParameters(T))
7677 // Return the number of product terms in S.
7678 static inline int numberOfTerms(const SCEV *S) {
7679 if (const SCEVMulExpr *Expr = dyn_cast<SCEVMulExpr>(S))
7680 return Expr->getNumOperands();
7684 static const SCEV *removeConstantFactors(ScalarEvolution &SE, const SCEV *T) {
7685 if (isa<SCEVConstant>(T))
7688 if (isa<SCEVUnknown>(T))
7691 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(T)) {
7692 SmallVector<const SCEV *, 2> Factors;
7693 for (const SCEV *Op : M->operands())
7694 if (!isa<SCEVConstant>(Op))
7695 Factors.push_back(Op);
7697 return SE.getMulExpr(Factors);
7703 /// Return the size of an element read or written by Inst.
7704 const SCEV *ScalarEvolution::getElementSize(Instruction *Inst) {
7706 if (StoreInst *Store = dyn_cast<StoreInst>(Inst))
7707 Ty = Store->getValueOperand()->getType();
7708 else if (LoadInst *Load = dyn_cast<LoadInst>(Inst))
7709 Ty = Load->getType();
7713 Type *ETy = getEffectiveSCEVType(PointerType::getUnqual(Ty));
7714 return getSizeOfExpr(ETy, Ty);
7717 /// Second step of delinearization: compute the array dimensions Sizes from the
7718 /// set of Terms extracted from the memory access function of this SCEVAddRec.
7719 void ScalarEvolution::findArrayDimensions(SmallVectorImpl<const SCEV *> &Terms,
7720 SmallVectorImpl<const SCEV *> &Sizes,
7721 const SCEV *ElementSize) const {
7723 if (Terms.size() < 1 || !ElementSize)
7726 // Early return when Terms do not contain parameters: we do not delinearize
7727 // non parametric SCEVs.
7728 if (!containsParameters(Terms))
7732 dbgs() << "Terms:\n";
7733 for (const SCEV *T : Terms)
7734 dbgs() << *T << "\n";
7737 // Remove duplicates.
7738 std::sort(Terms.begin(), Terms.end());
7739 Terms.erase(std::unique(Terms.begin(), Terms.end()), Terms.end());
7741 // Put larger terms first.
7742 std::sort(Terms.begin(), Terms.end(), [](const SCEV *LHS, const SCEV *RHS) {
7743 return numberOfTerms(LHS) > numberOfTerms(RHS);
7746 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
7748 // Divide all terms by the element size.
7749 for (const SCEV *&Term : Terms) {
7751 SCEVDivision::divide(SE, Term, ElementSize, &Q, &R);
7755 SmallVector<const SCEV *, 4> NewTerms;
7757 // Remove constant factors.
7758 for (const SCEV *T : Terms)
7759 if (const SCEV *NewT = removeConstantFactors(SE, T))
7760 NewTerms.push_back(NewT);
7763 dbgs() << "Terms after sorting:\n";
7764 for (const SCEV *T : NewTerms)
7765 dbgs() << *T << "\n";
7768 if (NewTerms.empty() ||
7769 !findArrayDimensionsRec(SE, NewTerms, Sizes)) {
7774 // The last element to be pushed into Sizes is the size of an element.
7775 Sizes.push_back(ElementSize);
7778 dbgs() << "Sizes:\n";
7779 for (const SCEV *S : Sizes)
7780 dbgs() << *S << "\n";
7784 /// Third step of delinearization: compute the access functions for the
7785 /// Subscripts based on the dimensions in Sizes.
7786 void SCEVAddRecExpr::computeAccessFunctions(
7787 ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &Subscripts,
7788 SmallVectorImpl<const SCEV *> &Sizes) const {
7790 // Early exit in case this SCEV is not an affine multivariate function.
7791 if (Sizes.empty() || !this->isAffine())
7794 const SCEV *Res = this;
7795 int Last = Sizes.size() - 1;
7796 for (int i = Last; i >= 0; i--) {
7798 SCEVDivision::divide(SE, Res, Sizes[i], &Q, &R);
7801 dbgs() << "Res: " << *Res << "\n";
7802 dbgs() << "Sizes[i]: " << *Sizes[i] << "\n";
7803 dbgs() << "Res divided by Sizes[i]:\n";
7804 dbgs() << "Quotient: " << *Q << "\n";
7805 dbgs() << "Remainder: " << *R << "\n";
7810 // Do not record the last subscript corresponding to the size of elements in
7814 // Bail out if the remainder is too complex.
7815 if (isa<SCEVAddRecExpr>(R)) {
7824 // Record the access function for the current subscript.
7825 Subscripts.push_back(R);
7828 // Also push in last position the remainder of the last division: it will be
7829 // the access function of the innermost dimension.
7830 Subscripts.push_back(Res);
7832 std::reverse(Subscripts.begin(), Subscripts.end());
7835 dbgs() << "Subscripts:\n";
7836 for (const SCEV *S : Subscripts)
7837 dbgs() << *S << "\n";
7841 /// Splits the SCEV into two vectors of SCEVs representing the subscripts and
7842 /// sizes of an array access. Returns the remainder of the delinearization that
7843 /// is the offset start of the array. The SCEV->delinearize algorithm computes
7844 /// the multiples of SCEV coefficients: that is a pattern matching of sub
7845 /// expressions in the stride and base of a SCEV corresponding to the
7846 /// computation of a GCD (greatest common divisor) of base and stride. When
7847 /// SCEV->delinearize fails, it returns the SCEV unchanged.
7849 /// For example: when analyzing the memory access A[i][j][k] in this loop nest
7851 /// void foo(long n, long m, long o, double A[n][m][o]) {
7853 /// for (long i = 0; i < n; i++)
7854 /// for (long j = 0; j < m; j++)
7855 /// for (long k = 0; k < o; k++)
7856 /// A[i][j][k] = 1.0;
7859 /// the delinearization input is the following AddRec SCEV:
7861 /// AddRec: {{{%A,+,(8 * %m * %o)}<%for.i>,+,(8 * %o)}<%for.j>,+,8}<%for.k>
7863 /// From this SCEV, we are able to say that the base offset of the access is %A
7864 /// because it appears as an offset that does not divide any of the strides in
7867 /// CHECK: Base offset: %A
7869 /// and then SCEV->delinearize determines the size of some of the dimensions of
7870 /// the array as these are the multiples by which the strides are happening:
7872 /// CHECK: ArrayDecl[UnknownSize][%m][%o] with elements of sizeof(double) bytes.
7874 /// Note that the outermost dimension remains of UnknownSize because there are
7875 /// no strides that would help identifying the size of the last dimension: when
7876 /// the array has been statically allocated, one could compute the size of that
7877 /// dimension by dividing the overall size of the array by the size of the known
7878 /// dimensions: %m * %o * 8.
7880 /// Finally delinearize provides the access functions for the array reference
7881 /// that does correspond to A[i][j][k] of the above C testcase:
7883 /// CHECK: ArrayRef[{0,+,1}<%for.i>][{0,+,1}<%for.j>][{0,+,1}<%for.k>]
7885 /// The testcases are checking the output of a function pass:
7886 /// DelinearizationPass that walks through all loads and stores of a function
7887 /// asking for the SCEV of the memory access with respect to all enclosing
7888 /// loops, calling SCEV->delinearize on that and printing the results.
7890 void SCEVAddRecExpr::delinearize(ScalarEvolution &SE,
7891 SmallVectorImpl<const SCEV *> &Subscripts,
7892 SmallVectorImpl<const SCEV *> &Sizes,
7893 const SCEV *ElementSize) const {
7894 // First step: collect parametric terms.
7895 SmallVector<const SCEV *, 4> Terms;
7896 collectParametricTerms(SE, Terms);
7901 // Second step: find subscript sizes.
7902 SE.findArrayDimensions(Terms, Sizes, ElementSize);
7907 // Third step: compute the access functions for each subscript.
7908 computeAccessFunctions(SE, Subscripts, Sizes);
7910 if (Subscripts.empty())
7914 dbgs() << "succeeded to delinearize " << *this << "\n";
7915 dbgs() << "ArrayDecl[UnknownSize]";
7916 for (const SCEV *S : Sizes)
7917 dbgs() << "[" << *S << "]";
7919 dbgs() << "\nArrayRef";
7920 for (const SCEV *S : Subscripts)
7921 dbgs() << "[" << *S << "]";
7926 //===----------------------------------------------------------------------===//
7927 // SCEVCallbackVH Class Implementation
7928 //===----------------------------------------------------------------------===//
7930 void ScalarEvolution::SCEVCallbackVH::deleted() {
7931 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
7932 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
7933 SE->ConstantEvolutionLoopExitValue.erase(PN);
7934 SE->ValueExprMap.erase(getValPtr());
7935 // this now dangles!
7938 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) {
7939 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
7941 // Forget all the expressions associated with users of the old value,
7942 // so that future queries will recompute the expressions using the new
7944 Value *Old = getValPtr();
7945 SmallVector<User *, 16> Worklist(Old->user_begin(), Old->user_end());
7946 SmallPtrSet<User *, 8> Visited;
7947 while (!Worklist.empty()) {
7948 User *U = Worklist.pop_back_val();
7949 // Deleting the Old value will cause this to dangle. Postpone
7950 // that until everything else is done.
7953 if (!Visited.insert(U).second)
7955 if (PHINode *PN = dyn_cast<PHINode>(U))
7956 SE->ConstantEvolutionLoopExitValue.erase(PN);
7957 SE->ValueExprMap.erase(U);
7958 Worklist.insert(Worklist.end(), U->user_begin(), U->user_end());
7960 // Delete the Old value.
7961 if (PHINode *PN = dyn_cast<PHINode>(Old))
7962 SE->ConstantEvolutionLoopExitValue.erase(PN);
7963 SE->ValueExprMap.erase(Old);
7964 // this now dangles!
7967 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
7968 : CallbackVH(V), SE(se) {}
7970 //===----------------------------------------------------------------------===//
7971 // ScalarEvolution Class Implementation
7972 //===----------------------------------------------------------------------===//
7974 ScalarEvolution::ScalarEvolution()
7975 : FunctionPass(ID), ValuesAtScopes(64), LoopDispositions(64),
7976 BlockDispositions(64), FirstUnknown(nullptr) {
7977 initializeScalarEvolutionPass(*PassRegistry::getPassRegistry());
7980 bool ScalarEvolution::runOnFunction(Function &F) {
7982 AC = &getAnalysis<AssumptionCacheTracker>().getAssumptionCache(F);
7983 LI = &getAnalysis<LoopInfoWrapperPass>().getLoopInfo();
7984 TLI = &getAnalysis<TargetLibraryInfoWrapperPass>().getTLI();
7985 DT = &getAnalysis<DominatorTreeWrapperPass>().getDomTree();
7989 void ScalarEvolution::releaseMemory() {
7990 // Iterate through all the SCEVUnknown instances and call their
7991 // destructors, so that they release their references to their values.
7992 for (SCEVUnknown *U = FirstUnknown; U; U = U->Next)
7994 FirstUnknown = nullptr;
7996 ValueExprMap.clear();
7998 // Free any extra memory created for ExitNotTakenInfo in the unlikely event
7999 // that a loop had multiple computable exits.
8000 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
8001 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end();
8006 assert(PendingLoopPredicates.empty() && "isImpliedCond garbage");
8008 BackedgeTakenCounts.clear();
8009 ConstantEvolutionLoopExitValue.clear();
8010 ValuesAtScopes.clear();
8011 LoopDispositions.clear();
8012 BlockDispositions.clear();
8013 UnsignedRanges.clear();
8014 SignedRanges.clear();
8015 UniqueSCEVs.clear();
8016 SCEVAllocator.Reset();
8019 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
8020 AU.setPreservesAll();
8021 AU.addRequired<AssumptionCacheTracker>();
8022 AU.addRequiredTransitive<LoopInfoWrapperPass>();
8023 AU.addRequiredTransitive<DominatorTreeWrapperPass>();
8024 AU.addRequired<TargetLibraryInfoWrapperPass>();
8027 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
8028 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
8031 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
8033 // Print all inner loops first
8034 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
8035 PrintLoopInfo(OS, SE, *I);
8038 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
8041 SmallVector<BasicBlock *, 8> ExitBlocks;
8042 L->getExitBlocks(ExitBlocks);
8043 if (ExitBlocks.size() != 1)
8044 OS << "<multiple exits> ";
8046 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
8047 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
8049 OS << "Unpredictable backedge-taken count. ";
8054 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
8057 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
8058 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
8060 OS << "Unpredictable max backedge-taken count. ";
8066 void ScalarEvolution::print(raw_ostream &OS, const Module *) const {
8067 // ScalarEvolution's implementation of the print method is to print
8068 // out SCEV values of all instructions that are interesting. Doing
8069 // this potentially causes it to create new SCEV objects though,
8070 // which technically conflicts with the const qualifier. This isn't
8071 // observable from outside the class though, so casting away the
8072 // const isn't dangerous.
8073 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
8075 OS << "Classifying expressions for: ";
8076 F->printAsOperand(OS, /*PrintType=*/false);
8078 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
8079 if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) {
8082 const SCEV *SV = SE.getSCEV(&*I);
8084 if (!isa<SCEVCouldNotCompute>(SV)) {
8086 SE.getUnsignedRange(SV).print(OS);
8088 SE.getSignedRange(SV).print(OS);
8091 const Loop *L = LI->getLoopFor((*I).getParent());
8093 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
8097 if (!isa<SCEVCouldNotCompute>(AtUse)) {
8099 SE.getUnsignedRange(AtUse).print(OS);
8101 SE.getSignedRange(AtUse).print(OS);
8106 OS << "\t\t" "Exits: ";
8107 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
8108 if (!SE.isLoopInvariant(ExitValue, L)) {
8109 OS << "<<Unknown>>";
8118 OS << "Determining loop execution counts for: ";
8119 F->printAsOperand(OS, /*PrintType=*/false);
8121 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
8122 PrintLoopInfo(OS, &SE, *I);
8125 ScalarEvolution::LoopDisposition
8126 ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) {
8127 auto &Values = LoopDispositions[S];
8128 for (auto &V : Values) {
8129 if (V.getPointer() == L)
8132 Values.emplace_back(L, LoopVariant);
8133 LoopDisposition D = computeLoopDisposition(S, L);
8134 auto &Values2 = LoopDispositions[S];
8135 for (auto &V : make_range(Values2.rbegin(), Values2.rend())) {
8136 if (V.getPointer() == L) {
8144 ScalarEvolution::LoopDisposition
8145 ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) {
8146 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
8148 return LoopInvariant;
8152 return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L);
8153 case scAddRecExpr: {
8154 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
8156 // If L is the addrec's loop, it's computable.
8157 if (AR->getLoop() == L)
8158 return LoopComputable;
8160 // Add recurrences are never invariant in the function-body (null loop).
8164 // This recurrence is variant w.r.t. L if L contains AR's loop.
8165 if (L->contains(AR->getLoop()))
8168 // This recurrence is invariant w.r.t. L if AR's loop contains L.
8169 if (AR->getLoop()->contains(L))
8170 return LoopInvariant;
8172 // This recurrence is variant w.r.t. L if any of its operands
8174 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
8176 if (!isLoopInvariant(*I, L))
8179 // Otherwise it's loop-invariant.
8180 return LoopInvariant;
8186 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
8187 bool HasVarying = false;
8188 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
8190 LoopDisposition D = getLoopDisposition(*I, L);
8191 if (D == LoopVariant)
8193 if (D == LoopComputable)
8196 return HasVarying ? LoopComputable : LoopInvariant;
8199 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
8200 LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L);
8201 if (LD == LoopVariant)
8203 LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L);
8204 if (RD == LoopVariant)
8206 return (LD == LoopInvariant && RD == LoopInvariant) ?
8207 LoopInvariant : LoopComputable;
8210 // All non-instruction values are loop invariant. All instructions are loop
8211 // invariant if they are not contained in the specified loop.
8212 // Instructions are never considered invariant in the function body
8213 // (null loop) because they are defined within the "loop".
8214 if (Instruction *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue()))
8215 return (L && !L->contains(I)) ? LoopInvariant : LoopVariant;
8216 return LoopInvariant;
8217 case scCouldNotCompute:
8218 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
8220 llvm_unreachable("Unknown SCEV kind!");
8223 bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) {
8224 return getLoopDisposition(S, L) == LoopInvariant;
8227 bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) {
8228 return getLoopDisposition(S, L) == LoopComputable;
8231 ScalarEvolution::BlockDisposition
8232 ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) {
8233 auto &Values = BlockDispositions[S];
8234 for (auto &V : Values) {
8235 if (V.getPointer() == BB)
8238 Values.emplace_back(BB, DoesNotDominateBlock);
8239 BlockDisposition D = computeBlockDisposition(S, BB);
8240 auto &Values2 = BlockDispositions[S];
8241 for (auto &V : make_range(Values2.rbegin(), Values2.rend())) {
8242 if (V.getPointer() == BB) {
8250 ScalarEvolution::BlockDisposition
8251 ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) {
8252 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
8254 return ProperlyDominatesBlock;
8258 return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB);
8259 case scAddRecExpr: {
8260 // This uses a "dominates" query instead of "properly dominates" query
8261 // to test for proper dominance too, because the instruction which
8262 // produces the addrec's value is a PHI, and a PHI effectively properly
8263 // dominates its entire containing block.
8264 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
8265 if (!DT->dominates(AR->getLoop()->getHeader(), BB))
8266 return DoesNotDominateBlock;
8268 // FALL THROUGH into SCEVNAryExpr handling.
8273 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
8275 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
8277 BlockDisposition D = getBlockDisposition(*I, BB);
8278 if (D == DoesNotDominateBlock)
8279 return DoesNotDominateBlock;
8280 if (D == DominatesBlock)
8283 return Proper ? ProperlyDominatesBlock : DominatesBlock;
8286 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
8287 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
8288 BlockDisposition LD = getBlockDisposition(LHS, BB);
8289 if (LD == DoesNotDominateBlock)
8290 return DoesNotDominateBlock;
8291 BlockDisposition RD = getBlockDisposition(RHS, BB);
8292 if (RD == DoesNotDominateBlock)
8293 return DoesNotDominateBlock;
8294 return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ?
8295 ProperlyDominatesBlock : DominatesBlock;
8298 if (Instruction *I =
8299 dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) {
8300 if (I->getParent() == BB)
8301 return DominatesBlock;
8302 if (DT->properlyDominates(I->getParent(), BB))
8303 return ProperlyDominatesBlock;
8304 return DoesNotDominateBlock;
8306 return ProperlyDominatesBlock;
8307 case scCouldNotCompute:
8308 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
8310 llvm_unreachable("Unknown SCEV kind!");
8313 bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) {
8314 return getBlockDisposition(S, BB) >= DominatesBlock;
8317 bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) {
8318 return getBlockDisposition(S, BB) == ProperlyDominatesBlock;
8322 // Search for a SCEV expression node within an expression tree.
8323 // Implements SCEVTraversal::Visitor.
8328 SCEVSearch(const SCEV *N): Node(N), IsFound(false) {}
8330 bool follow(const SCEV *S) {
8331 IsFound |= (S == Node);
8334 bool isDone() const { return IsFound; }
8338 bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const {
8339 SCEVSearch Search(Op);
8340 visitAll(S, Search);
8341 return Search.IsFound;
8344 void ScalarEvolution::forgetMemoizedResults(const SCEV *S) {
8345 ValuesAtScopes.erase(S);
8346 LoopDispositions.erase(S);
8347 BlockDispositions.erase(S);
8348 UnsignedRanges.erase(S);
8349 SignedRanges.erase(S);
8351 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
8352 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end(); I != E; ) {
8353 BackedgeTakenInfo &BEInfo = I->second;
8354 if (BEInfo.hasOperand(S, this)) {
8356 BackedgeTakenCounts.erase(I++);
8363 typedef DenseMap<const Loop *, std::string> VerifyMap;
8365 /// replaceSubString - Replaces all occurrences of From in Str with To.
8366 static void replaceSubString(std::string &Str, StringRef From, StringRef To) {
8368 while ((Pos = Str.find(From, Pos)) != std::string::npos) {
8369 Str.replace(Pos, From.size(), To.data(), To.size());
8374 /// getLoopBackedgeTakenCounts - Helper method for verifyAnalysis.
8376 getLoopBackedgeTakenCounts(Loop *L, VerifyMap &Map, ScalarEvolution &SE) {
8377 for (Loop::reverse_iterator I = L->rbegin(), E = L->rend(); I != E; ++I) {
8378 getLoopBackedgeTakenCounts(*I, Map, SE); // recurse.
8380 std::string &S = Map[L];
8382 raw_string_ostream OS(S);
8383 SE.getBackedgeTakenCount(L)->print(OS);
8385 // false and 0 are semantically equivalent. This can happen in dead loops.
8386 replaceSubString(OS.str(), "false", "0");
8387 // Remove wrap flags, their use in SCEV is highly fragile.
8388 // FIXME: Remove this when SCEV gets smarter about them.
8389 replaceSubString(OS.str(), "<nw>", "");
8390 replaceSubString(OS.str(), "<nsw>", "");
8391 replaceSubString(OS.str(), "<nuw>", "");
8396 void ScalarEvolution::verifyAnalysis() const {
8400 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
8402 // Gather stringified backedge taken counts for all loops using SCEV's caches.
8403 // FIXME: It would be much better to store actual values instead of strings,
8404 // but SCEV pointers will change if we drop the caches.
8405 VerifyMap BackedgeDumpsOld, BackedgeDumpsNew;
8406 for (LoopInfo::reverse_iterator I = LI->rbegin(), E = LI->rend(); I != E; ++I)
8407 getLoopBackedgeTakenCounts(*I, BackedgeDumpsOld, SE);
8409 // Gather stringified backedge taken counts for all loops without using
8412 for (LoopInfo::reverse_iterator I = LI->rbegin(), E = LI->rend(); I != E; ++I)
8413 getLoopBackedgeTakenCounts(*I, BackedgeDumpsNew, SE);
8415 // Now compare whether they're the same with and without caches. This allows
8416 // verifying that no pass changed the cache.
8417 assert(BackedgeDumpsOld.size() == BackedgeDumpsNew.size() &&
8418 "New loops suddenly appeared!");
8420 for (VerifyMap::iterator OldI = BackedgeDumpsOld.begin(),
8421 OldE = BackedgeDumpsOld.end(),
8422 NewI = BackedgeDumpsNew.begin();
8423 OldI != OldE; ++OldI, ++NewI) {
8424 assert(OldI->first == NewI->first && "Loop order changed!");
8426 // Compare the stringified SCEVs. We don't care if undef backedgetaken count
8428 // FIXME: We currently ignore SCEV changes from/to CouldNotCompute. This
8429 // means that a pass is buggy or SCEV has to learn a new pattern but is
8430 // usually not harmful.
8431 if (OldI->second != NewI->second &&
8432 OldI->second.find("undef") == std::string::npos &&
8433 NewI->second.find("undef") == std::string::npos &&
8434 OldI->second != "***COULDNOTCOMPUTE***" &&
8435 NewI->second != "***COULDNOTCOMPUTE***") {
8436 dbgs() << "SCEVValidator: SCEV for loop '"
8437 << OldI->first->getHeader()->getName()
8438 << "' changed from '" << OldI->second
8439 << "' to '" << NewI->second << "'!\n";
8444 // TODO: Verify more things.