1 //===- ScalarEvolution.cpp - Scalar Evolution Analysis --------------------===//
3 // The LLVM Compiler Infrastructure
5 // This file is distributed under the University of Illinois Open Source
6 // License. See LICENSE.TXT for details.
8 //===----------------------------------------------------------------------===//
10 // This file contains the implementation of the scalar evolution analysis
11 // engine, which is used primarily to analyze expressions involving induction
12 // variables in loops.
14 // There are several aspects to this library. First is the representation of
15 // scalar expressions, which are represented as subclasses of the SCEV class.
16 // These classes are used to represent certain types of subexpressions that we
17 // can handle. We only create one SCEV of a particular shape, so
18 // pointer-comparisons for equality are legal.
20 // One important aspect of the SCEV objects is that they are never cyclic, even
21 // if there is a cycle in the dataflow for an expression (ie, a PHI node). If
22 // the PHI node is one of the idioms that we can represent (e.g., a polynomial
23 // recurrence) then we represent it directly as a recurrence node, otherwise we
24 // represent it as a SCEVUnknown node.
26 // In addition to being able to represent expressions of various types, we also
27 // have folders that are used to build the *canonical* representation for a
28 // particular expression. These folders are capable of using a variety of
29 // rewrite rules to simplify the expressions.
31 // Once the folders are defined, we can implement the more interesting
32 // higher-level code, such as the code that recognizes PHI nodes of various
33 // types, computes the execution count of a loop, etc.
35 // TODO: We should use these routines and value representations to implement
36 // dependence analysis!
38 //===----------------------------------------------------------------------===//
40 // There are several good references for the techniques used in this analysis.
42 // Chains of recurrences -- a method to expedite the evaluation
43 // of closed-form functions
44 // Olaf Bachmann, Paul S. Wang, Eugene V. Zima
46 // On computational properties of chains of recurrences
49 // Symbolic Evaluation of Chains of Recurrences for Loop Optimization
50 // Robert A. van Engelen
52 // Efficient Symbolic Analysis for Optimizing Compilers
53 // Robert A. van Engelen
55 // Using the chains of recurrences algebra for data dependence testing and
56 // induction variable substitution
57 // MS Thesis, Johnie Birch
59 //===----------------------------------------------------------------------===//
61 #include "llvm/Analysis/ScalarEvolution.h"
62 #include "llvm/ADT/Optional.h"
63 #include "llvm/ADT/STLExtras.h"
64 #include "llvm/ADT/SmallPtrSet.h"
65 #include "llvm/ADT/Statistic.h"
66 #include "llvm/Analysis/AssumptionCache.h"
67 #include "llvm/Analysis/ConstantFolding.h"
68 #include "llvm/Analysis/InstructionSimplify.h"
69 #include "llvm/Analysis/LoopInfo.h"
70 #include "llvm/Analysis/ScalarEvolutionExpressions.h"
71 #include "llvm/Analysis/TargetLibraryInfo.h"
72 #include "llvm/Analysis/ValueTracking.h"
73 #include "llvm/IR/ConstantRange.h"
74 #include "llvm/IR/Constants.h"
75 #include "llvm/IR/DataLayout.h"
76 #include "llvm/IR/DerivedTypes.h"
77 #include "llvm/IR/Dominators.h"
78 #include "llvm/IR/GetElementPtrTypeIterator.h"
79 #include "llvm/IR/GlobalAlias.h"
80 #include "llvm/IR/GlobalVariable.h"
81 #include "llvm/IR/InstIterator.h"
82 #include "llvm/IR/Instructions.h"
83 #include "llvm/IR/LLVMContext.h"
84 #include "llvm/IR/Metadata.h"
85 #include "llvm/IR/Operator.h"
86 #include "llvm/Support/CommandLine.h"
87 #include "llvm/Support/Debug.h"
88 #include "llvm/Support/ErrorHandling.h"
89 #include "llvm/Support/MathExtras.h"
90 #include "llvm/Support/raw_ostream.h"
94 #define DEBUG_TYPE "scalar-evolution"
96 STATISTIC(NumArrayLenItCounts,
97 "Number of trip counts computed with array length");
98 STATISTIC(NumTripCountsComputed,
99 "Number of loops with predictable loop counts");
100 STATISTIC(NumTripCountsNotComputed,
101 "Number of loops without predictable loop counts");
102 STATISTIC(NumBruteForceTripCountsComputed,
103 "Number of loops with trip counts computed by force");
105 static cl::opt<unsigned>
106 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
107 cl::desc("Maximum number of iterations SCEV will "
108 "symbolically execute a constant "
112 // FIXME: Enable this with XDEBUG when the test suite is clean.
114 VerifySCEV("verify-scev",
115 cl::desc("Verify ScalarEvolution's backedge taken counts (slow)"));
117 INITIALIZE_PASS_BEGIN(ScalarEvolution, "scalar-evolution",
118 "Scalar Evolution Analysis", false, true)
119 INITIALIZE_PASS_DEPENDENCY(AssumptionCacheTracker)
120 INITIALIZE_PASS_DEPENDENCY(LoopInfoWrapperPass)
121 INITIALIZE_PASS_DEPENDENCY(DominatorTreeWrapperPass)
122 INITIALIZE_PASS_DEPENDENCY(TargetLibraryInfoWrapperPass)
123 INITIALIZE_PASS_END(ScalarEvolution, "scalar-evolution",
124 "Scalar Evolution Analysis", false, true)
125 char ScalarEvolution::ID = 0;
127 //===----------------------------------------------------------------------===//
128 // SCEV class definitions
129 //===----------------------------------------------------------------------===//
131 //===----------------------------------------------------------------------===//
132 // Implementation of the SCEV class.
135 #if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP)
136 void SCEV::dump() const {
142 void SCEV::print(raw_ostream &OS) const {
143 switch (static_cast<SCEVTypes>(getSCEVType())) {
145 cast<SCEVConstant>(this)->getValue()->printAsOperand(OS, false);
148 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(this);
149 const SCEV *Op = Trunc->getOperand();
150 OS << "(trunc " << *Op->getType() << " " << *Op << " to "
151 << *Trunc->getType() << ")";
155 const SCEVZeroExtendExpr *ZExt = cast<SCEVZeroExtendExpr>(this);
156 const SCEV *Op = ZExt->getOperand();
157 OS << "(zext " << *Op->getType() << " " << *Op << " to "
158 << *ZExt->getType() << ")";
162 const SCEVSignExtendExpr *SExt = cast<SCEVSignExtendExpr>(this);
163 const SCEV *Op = SExt->getOperand();
164 OS << "(sext " << *Op->getType() << " " << *Op << " to "
165 << *SExt->getType() << ")";
169 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(this);
170 OS << "{" << *AR->getOperand(0);
171 for (unsigned i = 1, e = AR->getNumOperands(); i != e; ++i)
172 OS << ",+," << *AR->getOperand(i);
174 if (AR->getNoWrapFlags(FlagNUW))
176 if (AR->getNoWrapFlags(FlagNSW))
178 if (AR->getNoWrapFlags(FlagNW) &&
179 !AR->getNoWrapFlags((NoWrapFlags)(FlagNUW | FlagNSW)))
181 AR->getLoop()->getHeader()->printAsOperand(OS, /*PrintType=*/false);
189 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(this);
190 const char *OpStr = nullptr;
191 switch (NAry->getSCEVType()) {
192 case scAddExpr: OpStr = " + "; break;
193 case scMulExpr: OpStr = " * "; break;
194 case scUMaxExpr: OpStr = " umax "; break;
195 case scSMaxExpr: OpStr = " smax "; break;
198 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
201 if (std::next(I) != E)
205 switch (NAry->getSCEVType()) {
208 if (NAry->getNoWrapFlags(FlagNUW))
210 if (NAry->getNoWrapFlags(FlagNSW))
216 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(this);
217 OS << "(" << *UDiv->getLHS() << " /u " << *UDiv->getRHS() << ")";
221 const SCEVUnknown *U = cast<SCEVUnknown>(this);
223 if (U->isSizeOf(AllocTy)) {
224 OS << "sizeof(" << *AllocTy << ")";
227 if (U->isAlignOf(AllocTy)) {
228 OS << "alignof(" << *AllocTy << ")";
234 if (U->isOffsetOf(CTy, FieldNo)) {
235 OS << "offsetof(" << *CTy << ", ";
236 FieldNo->printAsOperand(OS, false);
241 // Otherwise just print it normally.
242 U->getValue()->printAsOperand(OS, false);
245 case scCouldNotCompute:
246 OS << "***COULDNOTCOMPUTE***";
249 llvm_unreachable("Unknown SCEV kind!");
252 Type *SCEV::getType() const {
253 switch (static_cast<SCEVTypes>(getSCEVType())) {
255 return cast<SCEVConstant>(this)->getType();
259 return cast<SCEVCastExpr>(this)->getType();
264 return cast<SCEVNAryExpr>(this)->getType();
266 return cast<SCEVAddExpr>(this)->getType();
268 return cast<SCEVUDivExpr>(this)->getType();
270 return cast<SCEVUnknown>(this)->getType();
271 case scCouldNotCompute:
272 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
274 llvm_unreachable("Unknown SCEV kind!");
277 bool SCEV::isZero() const {
278 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
279 return SC->getValue()->isZero();
283 bool SCEV::isOne() const {
284 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
285 return SC->getValue()->isOne();
289 bool SCEV::isAllOnesValue() const {
290 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
291 return SC->getValue()->isAllOnesValue();
295 /// isNonConstantNegative - Return true if the specified scev is negated, but
297 bool SCEV::isNonConstantNegative() const {
298 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(this);
299 if (!Mul) return false;
301 // If there is a constant factor, it will be first.
302 const SCEVConstant *SC = dyn_cast<SCEVConstant>(Mul->getOperand(0));
303 if (!SC) return false;
305 // Return true if the value is negative, this matches things like (-42 * V).
306 return SC->getValue()->getValue().isNegative();
309 SCEVCouldNotCompute::SCEVCouldNotCompute() :
310 SCEV(FoldingSetNodeIDRef(), scCouldNotCompute) {}
312 bool SCEVCouldNotCompute::classof(const SCEV *S) {
313 return S->getSCEVType() == scCouldNotCompute;
316 const SCEV *ScalarEvolution::getConstant(ConstantInt *V) {
318 ID.AddInteger(scConstant);
321 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
322 SCEV *S = new (SCEVAllocator) SCEVConstant(ID.Intern(SCEVAllocator), V);
323 UniqueSCEVs.InsertNode(S, IP);
327 const SCEV *ScalarEvolution::getConstant(const APInt &Val) {
328 return getConstant(ConstantInt::get(getContext(), Val));
332 ScalarEvolution::getConstant(Type *Ty, uint64_t V, bool isSigned) {
333 IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty));
334 return getConstant(ConstantInt::get(ITy, V, isSigned));
337 SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID,
338 unsigned SCEVTy, const SCEV *op, Type *ty)
339 : SCEV(ID, SCEVTy), Op(op), Ty(ty) {}
341 SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID,
342 const SCEV *op, Type *ty)
343 : SCEVCastExpr(ID, scTruncate, op, ty) {
344 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
345 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
346 "Cannot truncate non-integer value!");
349 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID,
350 const SCEV *op, Type *ty)
351 : SCEVCastExpr(ID, scZeroExtend, op, ty) {
352 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
353 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
354 "Cannot zero extend non-integer value!");
357 SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID,
358 const SCEV *op, Type *ty)
359 : SCEVCastExpr(ID, scSignExtend, op, ty) {
360 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
361 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
362 "Cannot sign extend non-integer value!");
365 void SCEVUnknown::deleted() {
366 // Clear this SCEVUnknown from various maps.
367 SE->forgetMemoizedResults(this);
369 // Remove this SCEVUnknown from the uniquing map.
370 SE->UniqueSCEVs.RemoveNode(this);
372 // Release the value.
376 void SCEVUnknown::allUsesReplacedWith(Value *New) {
377 // Clear this SCEVUnknown from various maps.
378 SE->forgetMemoizedResults(this);
380 // Remove this SCEVUnknown from the uniquing map.
381 SE->UniqueSCEVs.RemoveNode(this);
383 // Update this SCEVUnknown to point to the new value. This is needed
384 // because there may still be outstanding SCEVs which still point to
389 bool SCEVUnknown::isSizeOf(Type *&AllocTy) const {
390 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
391 if (VCE->getOpcode() == Instruction::PtrToInt)
392 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
393 if (CE->getOpcode() == Instruction::GetElementPtr &&
394 CE->getOperand(0)->isNullValue() &&
395 CE->getNumOperands() == 2)
396 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1)))
398 AllocTy = cast<PointerType>(CE->getOperand(0)->getType())
406 bool SCEVUnknown::isAlignOf(Type *&AllocTy) const {
407 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
408 if (VCE->getOpcode() == Instruction::PtrToInt)
409 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
410 if (CE->getOpcode() == Instruction::GetElementPtr &&
411 CE->getOperand(0)->isNullValue()) {
413 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
414 if (StructType *STy = dyn_cast<StructType>(Ty))
415 if (!STy->isPacked() &&
416 CE->getNumOperands() == 3 &&
417 CE->getOperand(1)->isNullValue()) {
418 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2)))
420 STy->getNumElements() == 2 &&
421 STy->getElementType(0)->isIntegerTy(1)) {
422 AllocTy = STy->getElementType(1);
431 bool SCEVUnknown::isOffsetOf(Type *&CTy, Constant *&FieldNo) const {
432 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
433 if (VCE->getOpcode() == Instruction::PtrToInt)
434 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
435 if (CE->getOpcode() == Instruction::GetElementPtr &&
436 CE->getNumOperands() == 3 &&
437 CE->getOperand(0)->isNullValue() &&
438 CE->getOperand(1)->isNullValue()) {
440 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
441 // Ignore vector types here so that ScalarEvolutionExpander doesn't
442 // emit getelementptrs that index into vectors.
443 if (Ty->isStructTy() || Ty->isArrayTy()) {
445 FieldNo = CE->getOperand(2);
453 //===----------------------------------------------------------------------===//
455 //===----------------------------------------------------------------------===//
458 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
459 /// than the complexity of the RHS. This comparator is used to canonicalize
461 class SCEVComplexityCompare {
462 const LoopInfo *const LI;
464 explicit SCEVComplexityCompare(const LoopInfo *li) : LI(li) {}
466 // Return true or false if LHS is less than, or at least RHS, respectively.
467 bool operator()(const SCEV *LHS, const SCEV *RHS) const {
468 return compare(LHS, RHS) < 0;
471 // Return negative, zero, or positive, if LHS is less than, equal to, or
472 // greater than RHS, respectively. A three-way result allows recursive
473 // comparisons to be more efficient.
474 int compare(const SCEV *LHS, const SCEV *RHS) const {
475 // Fast-path: SCEVs are uniqued so we can do a quick equality check.
479 // Primarily, sort the SCEVs by their getSCEVType().
480 unsigned LType = LHS->getSCEVType(), RType = RHS->getSCEVType();
482 return (int)LType - (int)RType;
484 // Aside from the getSCEVType() ordering, the particular ordering
485 // isn't very important except that it's beneficial to be consistent,
486 // so that (a + b) and (b + a) don't end up as different expressions.
487 switch (static_cast<SCEVTypes>(LType)) {
489 const SCEVUnknown *LU = cast<SCEVUnknown>(LHS);
490 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
492 // Sort SCEVUnknown values with some loose heuristics. TODO: This is
493 // not as complete as it could be.
494 const Value *LV = LU->getValue(), *RV = RU->getValue();
496 // Order pointer values after integer values. This helps SCEVExpander
498 bool LIsPointer = LV->getType()->isPointerTy(),
499 RIsPointer = RV->getType()->isPointerTy();
500 if (LIsPointer != RIsPointer)
501 return (int)LIsPointer - (int)RIsPointer;
503 // Compare getValueID values.
504 unsigned LID = LV->getValueID(),
505 RID = RV->getValueID();
507 return (int)LID - (int)RID;
509 // Sort arguments by their position.
510 if (const Argument *LA = dyn_cast<Argument>(LV)) {
511 const Argument *RA = cast<Argument>(RV);
512 unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo();
513 return (int)LArgNo - (int)RArgNo;
516 // For instructions, compare their loop depth, and their operand
517 // count. This is pretty loose.
518 if (const Instruction *LInst = dyn_cast<Instruction>(LV)) {
519 const Instruction *RInst = cast<Instruction>(RV);
521 // Compare loop depths.
522 const BasicBlock *LParent = LInst->getParent(),
523 *RParent = RInst->getParent();
524 if (LParent != RParent) {
525 unsigned LDepth = LI->getLoopDepth(LParent),
526 RDepth = LI->getLoopDepth(RParent);
527 if (LDepth != RDepth)
528 return (int)LDepth - (int)RDepth;
531 // Compare the number of operands.
532 unsigned LNumOps = LInst->getNumOperands(),
533 RNumOps = RInst->getNumOperands();
534 return (int)LNumOps - (int)RNumOps;
541 const SCEVConstant *LC = cast<SCEVConstant>(LHS);
542 const SCEVConstant *RC = cast<SCEVConstant>(RHS);
544 // Compare constant values.
545 const APInt &LA = LC->getValue()->getValue();
546 const APInt &RA = RC->getValue()->getValue();
547 unsigned LBitWidth = LA.getBitWidth(), RBitWidth = RA.getBitWidth();
548 if (LBitWidth != RBitWidth)
549 return (int)LBitWidth - (int)RBitWidth;
550 return LA.ult(RA) ? -1 : 1;
554 const SCEVAddRecExpr *LA = cast<SCEVAddRecExpr>(LHS);
555 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS);
557 // Compare addrec loop depths.
558 const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop();
559 if (LLoop != RLoop) {
560 unsigned LDepth = LLoop->getLoopDepth(),
561 RDepth = RLoop->getLoopDepth();
562 if (LDepth != RDepth)
563 return (int)LDepth - (int)RDepth;
566 // Addrec complexity grows with operand count.
567 unsigned LNumOps = LA->getNumOperands(), RNumOps = RA->getNumOperands();
568 if (LNumOps != RNumOps)
569 return (int)LNumOps - (int)RNumOps;
571 // Lexicographically compare.
572 for (unsigned i = 0; i != LNumOps; ++i) {
573 long X = compare(LA->getOperand(i), RA->getOperand(i));
585 const SCEVNAryExpr *LC = cast<SCEVNAryExpr>(LHS);
586 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
588 // Lexicographically compare n-ary expressions.
589 unsigned LNumOps = LC->getNumOperands(), RNumOps = RC->getNumOperands();
590 if (LNumOps != RNumOps)
591 return (int)LNumOps - (int)RNumOps;
593 for (unsigned i = 0; i != LNumOps; ++i) {
596 long X = compare(LC->getOperand(i), RC->getOperand(i));
600 return (int)LNumOps - (int)RNumOps;
604 const SCEVUDivExpr *LC = cast<SCEVUDivExpr>(LHS);
605 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
607 // Lexicographically compare udiv expressions.
608 long X = compare(LC->getLHS(), RC->getLHS());
611 return compare(LC->getRHS(), RC->getRHS());
617 const SCEVCastExpr *LC = cast<SCEVCastExpr>(LHS);
618 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
620 // Compare cast expressions by operand.
621 return compare(LC->getOperand(), RC->getOperand());
624 case scCouldNotCompute:
625 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
627 llvm_unreachable("Unknown SCEV kind!");
632 /// GroupByComplexity - Given a list of SCEV objects, order them by their
633 /// complexity, and group objects of the same complexity together by value.
634 /// When this routine is finished, we know that any duplicates in the vector are
635 /// consecutive and that complexity is monotonically increasing.
637 /// Note that we go take special precautions to ensure that we get deterministic
638 /// results from this routine. In other words, we don't want the results of
639 /// this to depend on where the addresses of various SCEV objects happened to
642 static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops,
644 if (Ops.size() < 2) return; // Noop
645 if (Ops.size() == 2) {
646 // This is the common case, which also happens to be trivially simple.
648 const SCEV *&LHS = Ops[0], *&RHS = Ops[1];
649 if (SCEVComplexityCompare(LI)(RHS, LHS))
654 // Do the rough sort by complexity.
655 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI));
657 // Now that we are sorted by complexity, group elements of the same
658 // complexity. Note that this is, at worst, N^2, but the vector is likely to
659 // be extremely short in practice. Note that we take this approach because we
660 // do not want to depend on the addresses of the objects we are grouping.
661 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
662 const SCEV *S = Ops[i];
663 unsigned Complexity = S->getSCEVType();
665 // If there are any objects of the same complexity and same value as this
667 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
668 if (Ops[j] == S) { // Found a duplicate.
669 // Move it to immediately after i'th element.
670 std::swap(Ops[i+1], Ops[j]);
671 ++i; // no need to rescan it.
672 if (i == e-2) return; // Done!
679 struct FindSCEVSize {
681 FindSCEVSize() : Size(0) {}
683 bool follow(const SCEV *S) {
685 // Keep looking at all operands of S.
688 bool isDone() const {
694 // Returns the size of the SCEV S.
695 static inline int sizeOfSCEV(const SCEV *S) {
697 SCEVTraversal<FindSCEVSize> ST(F);
704 struct SCEVDivision : public SCEVVisitor<SCEVDivision, void> {
706 // Computes the Quotient and Remainder of the division of Numerator by
708 static void divide(ScalarEvolution &SE, const SCEV *Numerator,
709 const SCEV *Denominator, const SCEV **Quotient,
710 const SCEV **Remainder) {
711 assert(Numerator && Denominator && "Uninitialized SCEV");
713 SCEVDivision D(SE, Numerator, Denominator);
715 // Check for the trivial case here to avoid having to check for it in the
717 if (Numerator == Denominator) {
723 if (Numerator->isZero()) {
729 // Split the Denominator when it is a product.
730 if (const SCEVMulExpr *T = dyn_cast<const SCEVMulExpr>(Denominator)) {
732 *Quotient = Numerator;
733 for (const SCEV *Op : T->operands()) {
734 divide(SE, *Quotient, Op, &Q, &R);
737 // Bail out when the Numerator is not divisible by one of the terms of
741 *Remainder = Numerator;
750 *Quotient = D.Quotient;
751 *Remainder = D.Remainder;
754 // Except in the trivial case described above, we do not know how to divide
755 // Expr by Denominator for the following functions with empty implementation.
756 void visitTruncateExpr(const SCEVTruncateExpr *Numerator) {}
757 void visitZeroExtendExpr(const SCEVZeroExtendExpr *Numerator) {}
758 void visitSignExtendExpr(const SCEVSignExtendExpr *Numerator) {}
759 void visitUDivExpr(const SCEVUDivExpr *Numerator) {}
760 void visitSMaxExpr(const SCEVSMaxExpr *Numerator) {}
761 void visitUMaxExpr(const SCEVUMaxExpr *Numerator) {}
762 void visitUnknown(const SCEVUnknown *Numerator) {}
763 void visitCouldNotCompute(const SCEVCouldNotCompute *Numerator) {}
765 void visitConstant(const SCEVConstant *Numerator) {
766 if (const SCEVConstant *D = dyn_cast<SCEVConstant>(Denominator)) {
767 APInt NumeratorVal = Numerator->getValue()->getValue();
768 APInt DenominatorVal = D->getValue()->getValue();
769 uint32_t NumeratorBW = NumeratorVal.getBitWidth();
770 uint32_t DenominatorBW = DenominatorVal.getBitWidth();
772 if (NumeratorBW > DenominatorBW)
773 DenominatorVal = DenominatorVal.sext(NumeratorBW);
774 else if (NumeratorBW < DenominatorBW)
775 NumeratorVal = NumeratorVal.sext(DenominatorBW);
777 APInt QuotientVal(NumeratorVal.getBitWidth(), 0);
778 APInt RemainderVal(NumeratorVal.getBitWidth(), 0);
779 APInt::sdivrem(NumeratorVal, DenominatorVal, QuotientVal, RemainderVal);
780 Quotient = SE.getConstant(QuotientVal);
781 Remainder = SE.getConstant(RemainderVal);
786 void visitAddRecExpr(const SCEVAddRecExpr *Numerator) {
787 const SCEV *StartQ, *StartR, *StepQ, *StepR;
788 assert(Numerator->isAffine() && "Numerator should be affine");
789 divide(SE, Numerator->getStart(), Denominator, &StartQ, &StartR);
790 divide(SE, Numerator->getStepRecurrence(SE), Denominator, &StepQ, &StepR);
791 Quotient = SE.getAddRecExpr(StartQ, StepQ, Numerator->getLoop(),
792 Numerator->getNoWrapFlags());
793 Remainder = SE.getAddRecExpr(StartR, StepR, Numerator->getLoop(),
794 Numerator->getNoWrapFlags());
797 void visitAddExpr(const SCEVAddExpr *Numerator) {
798 SmallVector<const SCEV *, 2> Qs, Rs;
799 Type *Ty = Denominator->getType();
801 for (const SCEV *Op : Numerator->operands()) {
803 divide(SE, Op, Denominator, &Q, &R);
805 // Bail out if types do not match.
806 if (Ty != Q->getType() || Ty != R->getType()) {
808 Remainder = Numerator;
816 if (Qs.size() == 1) {
822 Quotient = SE.getAddExpr(Qs);
823 Remainder = SE.getAddExpr(Rs);
826 void visitMulExpr(const SCEVMulExpr *Numerator) {
827 SmallVector<const SCEV *, 2> Qs;
828 Type *Ty = Denominator->getType();
830 bool FoundDenominatorTerm = false;
831 for (const SCEV *Op : Numerator->operands()) {
832 // Bail out if types do not match.
833 if (Ty != Op->getType()) {
835 Remainder = Numerator;
839 if (FoundDenominatorTerm) {
844 // Check whether Denominator divides one of the product operands.
846 divide(SE, Op, Denominator, &Q, &R);
852 // Bail out if types do not match.
853 if (Ty != Q->getType()) {
855 Remainder = Numerator;
859 FoundDenominatorTerm = true;
863 if (FoundDenominatorTerm) {
868 Quotient = SE.getMulExpr(Qs);
872 if (!isa<SCEVUnknown>(Denominator)) {
874 Remainder = Numerator;
878 // The Remainder is obtained by replacing Denominator by 0 in Numerator.
879 ValueToValueMap RewriteMap;
880 RewriteMap[cast<SCEVUnknown>(Denominator)->getValue()] =
881 cast<SCEVConstant>(Zero)->getValue();
882 Remainder = SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true);
884 if (Remainder->isZero()) {
885 // The Quotient is obtained by replacing Denominator by 1 in Numerator.
886 RewriteMap[cast<SCEVUnknown>(Denominator)->getValue()] =
887 cast<SCEVConstant>(One)->getValue();
889 SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true);
893 // Quotient is (Numerator - Remainder) divided by Denominator.
895 const SCEV *Diff = SE.getMinusSCEV(Numerator, Remainder);
896 if (sizeOfSCEV(Diff) > sizeOfSCEV(Numerator)) {
897 // This SCEV does not seem to simplify: fail the division here.
899 Remainder = Numerator;
902 divide(SE, Diff, Denominator, &Q, &R);
904 "(Numerator - Remainder) should evenly divide Denominator");
909 SCEVDivision(ScalarEvolution &S, const SCEV *Numerator,
910 const SCEV *Denominator)
911 : SE(S), Denominator(Denominator) {
912 Zero = SE.getConstant(Denominator->getType(), 0);
913 One = SE.getConstant(Denominator->getType(), 1);
915 // By default, we don't know how to divide Expr by Denominator.
916 // Providing the default here simplifies the rest of the code.
918 Remainder = Numerator;
922 const SCEV *Denominator, *Quotient, *Remainder, *Zero, *One;
927 //===----------------------------------------------------------------------===//
928 // Simple SCEV method implementations
929 //===----------------------------------------------------------------------===//
931 /// BinomialCoefficient - Compute BC(It, K). The result has width W.
933 static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K,
936 // Handle the simplest case efficiently.
938 return SE.getTruncateOrZeroExtend(It, ResultTy);
940 // We are using the following formula for BC(It, K):
942 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
944 // Suppose, W is the bitwidth of the return value. We must be prepared for
945 // overflow. Hence, we must assure that the result of our computation is
946 // equal to the accurate one modulo 2^W. Unfortunately, division isn't
947 // safe in modular arithmetic.
949 // However, this code doesn't use exactly that formula; the formula it uses
950 // is something like the following, where T is the number of factors of 2 in
951 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
954 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
956 // This formula is trivially equivalent to the previous formula. However,
957 // this formula can be implemented much more efficiently. The trick is that
958 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
959 // arithmetic. To do exact division in modular arithmetic, all we have
960 // to do is multiply by the inverse. Therefore, this step can be done at
963 // The next issue is how to safely do the division by 2^T. The way this
964 // is done is by doing the multiplication step at a width of at least W + T
965 // bits. This way, the bottom W+T bits of the product are accurate. Then,
966 // when we perform the division by 2^T (which is equivalent to a right shift
967 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
968 // truncated out after the division by 2^T.
970 // In comparison to just directly using the first formula, this technique
971 // is much more efficient; using the first formula requires W * K bits,
972 // but this formula less than W + K bits. Also, the first formula requires
973 // a division step, whereas this formula only requires multiplies and shifts.
975 // It doesn't matter whether the subtraction step is done in the calculation
976 // width or the input iteration count's width; if the subtraction overflows,
977 // the result must be zero anyway. We prefer here to do it in the width of
978 // the induction variable because it helps a lot for certain cases; CodeGen
979 // isn't smart enough to ignore the overflow, which leads to much less
980 // efficient code if the width of the subtraction is wider than the native
983 // (It's possible to not widen at all by pulling out factors of 2 before
984 // the multiplication; for example, K=2 can be calculated as
985 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
986 // extra arithmetic, so it's not an obvious win, and it gets
987 // much more complicated for K > 3.)
989 // Protection from insane SCEVs; this bound is conservative,
990 // but it probably doesn't matter.
992 return SE.getCouldNotCompute();
994 unsigned W = SE.getTypeSizeInBits(ResultTy);
996 // Calculate K! / 2^T and T; we divide out the factors of two before
997 // multiplying for calculating K! / 2^T to avoid overflow.
998 // Other overflow doesn't matter because we only care about the bottom
999 // W bits of the result.
1000 APInt OddFactorial(W, 1);
1002 for (unsigned i = 3; i <= K; ++i) {
1004 unsigned TwoFactors = Mult.countTrailingZeros();
1006 Mult = Mult.lshr(TwoFactors);
1007 OddFactorial *= Mult;
1010 // We need at least W + T bits for the multiplication step
1011 unsigned CalculationBits = W + T;
1013 // Calculate 2^T, at width T+W.
1014 APInt DivFactor = APInt::getOneBitSet(CalculationBits, T);
1016 // Calculate the multiplicative inverse of K! / 2^T;
1017 // this multiplication factor will perform the exact division by
1019 APInt Mod = APInt::getSignedMinValue(W+1);
1020 APInt MultiplyFactor = OddFactorial.zext(W+1);
1021 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
1022 MultiplyFactor = MultiplyFactor.trunc(W);
1024 // Calculate the product, at width T+W
1025 IntegerType *CalculationTy = IntegerType::get(SE.getContext(),
1027 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
1028 for (unsigned i = 1; i != K; ++i) {
1029 const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i));
1030 Dividend = SE.getMulExpr(Dividend,
1031 SE.getTruncateOrZeroExtend(S, CalculationTy));
1035 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
1037 // Truncate the result, and divide by K! / 2^T.
1039 return SE.getMulExpr(SE.getConstant(MultiplyFactor),
1040 SE.getTruncateOrZeroExtend(DivResult, ResultTy));
1043 /// evaluateAtIteration - Return the value of this chain of recurrences at
1044 /// the specified iteration number. We can evaluate this recurrence by
1045 /// multiplying each element in the chain by the binomial coefficient
1046 /// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
1048 /// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
1050 /// where BC(It, k) stands for binomial coefficient.
1052 const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It,
1053 ScalarEvolution &SE) const {
1054 const SCEV *Result = getStart();
1055 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
1056 // The computation is correct in the face of overflow provided that the
1057 // multiplication is performed _after_ the evaluation of the binomial
1059 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType());
1060 if (isa<SCEVCouldNotCompute>(Coeff))
1063 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
1068 //===----------------------------------------------------------------------===//
1069 // SCEV Expression folder implementations
1070 //===----------------------------------------------------------------------===//
1072 const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op,
1074 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
1075 "This is not a truncating conversion!");
1076 assert(isSCEVable(Ty) &&
1077 "This is not a conversion to a SCEVable type!");
1078 Ty = getEffectiveSCEVType(Ty);
1080 FoldingSetNodeID ID;
1081 ID.AddInteger(scTruncate);
1085 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1087 // Fold if the operand is constant.
1088 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1090 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty)));
1092 // trunc(trunc(x)) --> trunc(x)
1093 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
1094 return getTruncateExpr(ST->getOperand(), Ty);
1096 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
1097 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1098 return getTruncateOrSignExtend(SS->getOperand(), Ty);
1100 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
1101 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1102 return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
1104 // trunc(x1+x2+...+xN) --> trunc(x1)+trunc(x2)+...+trunc(xN) if we can
1105 // eliminate all the truncates.
1106 if (const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Op)) {
1107 SmallVector<const SCEV *, 4> Operands;
1108 bool hasTrunc = false;
1109 for (unsigned i = 0, e = SA->getNumOperands(); i != e && !hasTrunc; ++i) {
1110 const SCEV *S = getTruncateExpr(SA->getOperand(i), Ty);
1111 hasTrunc = isa<SCEVTruncateExpr>(S);
1112 Operands.push_back(S);
1115 return getAddExpr(Operands);
1116 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL.
1119 // trunc(x1*x2*...*xN) --> trunc(x1)*trunc(x2)*...*trunc(xN) if we can
1120 // eliminate all the truncates.
1121 if (const SCEVMulExpr *SM = dyn_cast<SCEVMulExpr>(Op)) {
1122 SmallVector<const SCEV *, 4> Operands;
1123 bool hasTrunc = false;
1124 for (unsigned i = 0, e = SM->getNumOperands(); i != e && !hasTrunc; ++i) {
1125 const SCEV *S = getTruncateExpr(SM->getOperand(i), Ty);
1126 hasTrunc = isa<SCEVTruncateExpr>(S);
1127 Operands.push_back(S);
1130 return getMulExpr(Operands);
1131 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL.
1134 // If the input value is a chrec scev, truncate the chrec's operands.
1135 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
1136 SmallVector<const SCEV *, 4> Operands;
1137 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
1138 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty));
1139 return getAddRecExpr(Operands, AddRec->getLoop(), SCEV::FlagAnyWrap);
1142 // The cast wasn't folded; create an explicit cast node. We can reuse
1143 // the existing insert position since if we get here, we won't have
1144 // made any changes which would invalidate it.
1145 SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator),
1147 UniqueSCEVs.InsertNode(S, IP);
1151 const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op,
1153 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1154 "This is not an extending conversion!");
1155 assert(isSCEVable(Ty) &&
1156 "This is not a conversion to a SCEVable type!");
1157 Ty = getEffectiveSCEVType(Ty);
1159 // Fold if the operand is constant.
1160 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1162 cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(), Ty)));
1164 // zext(zext(x)) --> zext(x)
1165 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1166 return getZeroExtendExpr(SZ->getOperand(), Ty);
1168 // Before doing any expensive analysis, check to see if we've already
1169 // computed a SCEV for this Op and Ty.
1170 FoldingSetNodeID ID;
1171 ID.AddInteger(scZeroExtend);
1175 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1177 // zext(trunc(x)) --> zext(x) or x or trunc(x)
1178 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1179 // It's possible the bits taken off by the truncate were all zero bits. If
1180 // so, we should be able to simplify this further.
1181 const SCEV *X = ST->getOperand();
1182 ConstantRange CR = getUnsignedRange(X);
1183 unsigned TruncBits = getTypeSizeInBits(ST->getType());
1184 unsigned NewBits = getTypeSizeInBits(Ty);
1185 if (CR.truncate(TruncBits).zeroExtend(NewBits).contains(
1186 CR.zextOrTrunc(NewBits)))
1187 return getTruncateOrZeroExtend(X, Ty);
1190 // If the input value is a chrec scev, and we can prove that the value
1191 // did not overflow the old, smaller, value, we can zero extend all of the
1192 // operands (often constants). This allows analysis of something like
1193 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
1194 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1195 if (AR->isAffine()) {
1196 const SCEV *Start = AR->getStart();
1197 const SCEV *Step = AR->getStepRecurrence(*this);
1198 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1199 const Loop *L = AR->getLoop();
1201 // If we have special knowledge that this addrec won't overflow,
1202 // we don't need to do any further analysis.
1203 if (AR->getNoWrapFlags(SCEV::FlagNUW))
1204 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1205 getZeroExtendExpr(Step, Ty),
1206 L, AR->getNoWrapFlags());
1208 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1209 // Note that this serves two purposes: It filters out loops that are
1210 // simply not analyzable, and it covers the case where this code is
1211 // being called from within backedge-taken count analysis, such that
1212 // attempting to ask for the backedge-taken count would likely result
1213 // in infinite recursion. In the later case, the analysis code will
1214 // cope with a conservative value, and it will take care to purge
1215 // that value once it has finished.
1216 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1217 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1218 // Manually compute the final value for AR, checking for
1221 // Check whether the backedge-taken count can be losslessly casted to
1222 // the addrec's type. The count is always unsigned.
1223 const SCEV *CastedMaxBECount =
1224 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1225 const SCEV *RecastedMaxBECount =
1226 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1227 if (MaxBECount == RecastedMaxBECount) {
1228 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1229 // Check whether Start+Step*MaxBECount has no unsigned overflow.
1230 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step);
1231 const SCEV *ZAdd = getZeroExtendExpr(getAddExpr(Start, ZMul), WideTy);
1232 const SCEV *WideStart = getZeroExtendExpr(Start, WideTy);
1233 const SCEV *WideMaxBECount =
1234 getZeroExtendExpr(CastedMaxBECount, WideTy);
1235 const SCEV *OperandExtendedAdd =
1236 getAddExpr(WideStart,
1237 getMulExpr(WideMaxBECount,
1238 getZeroExtendExpr(Step, WideTy)));
1239 if (ZAdd == OperandExtendedAdd) {
1240 // Cache knowledge of AR NUW, which is propagated to this AddRec.
1241 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1242 // Return the expression with the addrec on the outside.
1243 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1244 getZeroExtendExpr(Step, Ty),
1245 L, AR->getNoWrapFlags());
1247 // Similar to above, only this time treat the step value as signed.
1248 // This covers loops that count down.
1249 OperandExtendedAdd =
1250 getAddExpr(WideStart,
1251 getMulExpr(WideMaxBECount,
1252 getSignExtendExpr(Step, WideTy)));
1253 if (ZAdd == OperandExtendedAdd) {
1254 // Cache knowledge of AR NW, which is propagated to this AddRec.
1255 // Negative step causes unsigned wrap, but it still can't self-wrap.
1256 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1257 // Return the expression with the addrec on the outside.
1258 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1259 getSignExtendExpr(Step, Ty),
1260 L, AR->getNoWrapFlags());
1264 // If the backedge is guarded by a comparison with the pre-inc value
1265 // the addrec is safe. Also, if the entry is guarded by a comparison
1266 // with the start value and the backedge is guarded by a comparison
1267 // with the post-inc value, the addrec is safe.
1268 if (isKnownPositive(Step)) {
1269 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
1270 getUnsignedRange(Step).getUnsignedMax());
1271 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
1272 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) &&
1273 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT,
1274 AR->getPostIncExpr(*this), N))) {
1275 // Cache knowledge of AR NUW, which is propagated to this AddRec.
1276 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1277 // Return the expression with the addrec on the outside.
1278 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1279 getZeroExtendExpr(Step, Ty),
1280 L, AR->getNoWrapFlags());
1282 } else if (isKnownNegative(Step)) {
1283 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
1284 getSignedRange(Step).getSignedMin());
1285 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) ||
1286 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) &&
1287 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT,
1288 AR->getPostIncExpr(*this), N))) {
1289 // Cache knowledge of AR NW, which is propagated to this AddRec.
1290 // Negative step causes unsigned wrap, but it still can't self-wrap.
1291 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1292 // Return the expression with the addrec on the outside.
1293 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1294 getSignExtendExpr(Step, Ty),
1295 L, AR->getNoWrapFlags());
1301 // The cast wasn't folded; create an explicit cast node.
1302 // Recompute the insert position, as it may have been invalidated.
1303 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1304 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
1306 UniqueSCEVs.InsertNode(S, IP);
1310 // Get the limit of a recurrence such that incrementing by Step cannot cause
1311 // signed overflow as long as the value of the recurrence within the loop does
1312 // not exceed this limit before incrementing.
1313 static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1314 ICmpInst::Predicate *Pred,
1315 ScalarEvolution *SE) {
1316 unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
1317 if (SE->isKnownPositive(Step)) {
1318 *Pred = ICmpInst::ICMP_SLT;
1319 return SE->getConstant(APInt::getSignedMinValue(BitWidth) -
1320 SE->getSignedRange(Step).getSignedMax());
1322 if (SE->isKnownNegative(Step)) {
1323 *Pred = ICmpInst::ICMP_SGT;
1324 return SE->getConstant(APInt::getSignedMaxValue(BitWidth) -
1325 SE->getSignedRange(Step).getSignedMin());
1330 // The recurrence AR has been shown to have no signed wrap. Typically, if we can
1331 // prove NSW for AR, then we can just as easily prove NSW for its preincrement
1332 // or postincrement sibling. This allows normalizing a sign extended AddRec as
1333 // such: {sext(Step + Start),+,Step} => {(Step + sext(Start),+,Step} As a
1334 // result, the expression "Step + sext(PreIncAR)" is congruent with
1335 // "sext(PostIncAR)"
1336 static const SCEV *getPreStartForSignExtend(const SCEVAddRecExpr *AR,
1338 ScalarEvolution *SE) {
1339 const Loop *L = AR->getLoop();
1340 const SCEV *Start = AR->getStart();
1341 const SCEV *Step = AR->getStepRecurrence(*SE);
1343 // Check for a simple looking step prior to loop entry.
1344 const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Start);
1348 // Create an AddExpr for "PreStart" after subtracting Step. Full SCEV
1349 // subtraction is expensive. For this purpose, perform a quick and dirty
1350 // difference, by checking for Step in the operand list.
1351 SmallVector<const SCEV *, 4> DiffOps;
1352 for (const SCEV *Op : SA->operands())
1354 DiffOps.push_back(Op);
1356 if (DiffOps.size() == SA->getNumOperands())
1359 // This is a postinc AR. Check for overflow on the preinc recurrence using the
1360 // same three conditions that getSignExtendedExpr checks.
1362 // 1. NSW flags on the step increment.
1363 const SCEV *PreStart = SE->getAddExpr(DiffOps, SA->getNoWrapFlags());
1364 const SCEVAddRecExpr *PreAR = dyn_cast<SCEVAddRecExpr>(
1365 SE->getAddRecExpr(PreStart, Step, L, SCEV::FlagAnyWrap));
1367 // WARNING: FIXME: the optimization below assumes that a sign-overflowing nsw
1368 // operation is undefined behavior. This is strictly more aggressive than the
1369 // interpretation of nsw in other parts of LLVM (for instance, they may
1370 // unconditionally hoist nsw arithmetic through control flow). This logic
1371 // needs to be revisited once we have a consistent semantics for poison
1374 // "{S,+,X} is <nsw>" and "{S,+,X} is evaluated at least once" implies "S+X
1375 // does not sign-overflow" (we'd have undefined behavior if it did). If
1376 // `L->getExitingBlock() == L->getLoopLatch()` then `PreAR` (= {S,+,X}<nsw>)
1377 // is evaluated every-time `AR` (= {S+X,+,X}) is evaluated, and hence within
1378 // `AR` we are safe to assume that "S+X" will not sign-overflow.
1381 BasicBlock *ExitingBlock = L->getExitingBlock();
1382 BasicBlock *LatchBlock = L->getLoopLatch();
1383 if (PreAR && PreAR->getNoWrapFlags(SCEV::FlagNSW) &&
1384 ExitingBlock != nullptr && ExitingBlock == LatchBlock)
1387 // 2. Direct overflow check on the step operation's expression.
1388 unsigned BitWidth = SE->getTypeSizeInBits(AR->getType());
1389 Type *WideTy = IntegerType::get(SE->getContext(), BitWidth * 2);
1390 const SCEV *OperandExtendedStart =
1391 SE->getAddExpr(SE->getSignExtendExpr(PreStart, WideTy),
1392 SE->getSignExtendExpr(Step, WideTy));
1393 if (SE->getSignExtendExpr(Start, WideTy) == OperandExtendedStart) {
1394 // Cache knowledge of PreAR NSW.
1396 const_cast<SCEVAddRecExpr *>(PreAR)->setNoWrapFlags(SCEV::FlagNSW);
1397 // FIXME: this optimization needs a unit test
1398 DEBUG(dbgs() << "SCEV: untested prestart overflow check\n");
1402 // 3. Loop precondition.
1403 ICmpInst::Predicate Pred;
1404 const SCEV *OverflowLimit = getOverflowLimitForStep(Step, &Pred, SE);
1406 if (OverflowLimit &&
1407 SE->isLoopEntryGuardedByCond(L, Pred, PreStart, OverflowLimit)) {
1413 // Get the normalized sign-extended expression for this AddRec's Start.
1414 static const SCEV *getSignExtendAddRecStart(const SCEVAddRecExpr *AR,
1416 ScalarEvolution *SE) {
1417 const SCEV *PreStart = getPreStartForSignExtend(AR, Ty, SE);
1419 return SE->getSignExtendExpr(AR->getStart(), Ty);
1421 return SE->getAddExpr(SE->getSignExtendExpr(AR->getStepRecurrence(*SE), Ty),
1422 SE->getSignExtendExpr(PreStart, Ty));
1425 const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op,
1427 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1428 "This is not an extending conversion!");
1429 assert(isSCEVable(Ty) &&
1430 "This is not a conversion to a SCEVable type!");
1431 Ty = getEffectiveSCEVType(Ty);
1433 // Fold if the operand is constant.
1434 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1436 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), Ty)));
1438 // sext(sext(x)) --> sext(x)
1439 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1440 return getSignExtendExpr(SS->getOperand(), Ty);
1442 // sext(zext(x)) --> zext(x)
1443 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1444 return getZeroExtendExpr(SZ->getOperand(), Ty);
1446 // Before doing any expensive analysis, check to see if we've already
1447 // computed a SCEV for this Op and Ty.
1448 FoldingSetNodeID ID;
1449 ID.AddInteger(scSignExtend);
1453 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1455 // If the input value is provably positive, build a zext instead.
1456 if (isKnownNonNegative(Op))
1457 return getZeroExtendExpr(Op, Ty);
1459 // sext(trunc(x)) --> sext(x) or x or trunc(x)
1460 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1461 // It's possible the bits taken off by the truncate were all sign bits. If
1462 // so, we should be able to simplify this further.
1463 const SCEV *X = ST->getOperand();
1464 ConstantRange CR = getSignedRange(X);
1465 unsigned TruncBits = getTypeSizeInBits(ST->getType());
1466 unsigned NewBits = getTypeSizeInBits(Ty);
1467 if (CR.truncate(TruncBits).signExtend(NewBits).contains(
1468 CR.sextOrTrunc(NewBits)))
1469 return getTruncateOrSignExtend(X, Ty);
1472 // sext(C1 + (C2 * x)) --> C1 + sext(C2 * x) if C1 < C2
1473 if (auto SA = dyn_cast<SCEVAddExpr>(Op)) {
1474 if (SA->getNumOperands() == 2) {
1475 auto SC1 = dyn_cast<SCEVConstant>(SA->getOperand(0));
1476 auto SMul = dyn_cast<SCEVMulExpr>(SA->getOperand(1));
1478 if (auto SC2 = dyn_cast<SCEVConstant>(SMul->getOperand(0))) {
1479 const APInt &C1 = SC1->getValue()->getValue();
1480 const APInt &C2 = SC2->getValue()->getValue();
1481 if (C1.isStrictlyPositive() && C2.isStrictlyPositive() &&
1482 C2.ugt(C1) && C2.isPowerOf2())
1483 return getAddExpr(getSignExtendExpr(SC1, Ty),
1484 getSignExtendExpr(SMul, Ty));
1489 // If the input value is a chrec scev, and we can prove that the value
1490 // did not overflow the old, smaller, value, we can sign extend all of the
1491 // operands (often constants). This allows analysis of something like
1492 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
1493 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1494 if (AR->isAffine()) {
1495 const SCEV *Start = AR->getStart();
1496 const SCEV *Step = AR->getStepRecurrence(*this);
1497 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1498 const Loop *L = AR->getLoop();
1500 // If we have special knowledge that this addrec won't overflow,
1501 // we don't need to do any further analysis.
1502 if (AR->getNoWrapFlags(SCEV::FlagNSW))
1503 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1504 getSignExtendExpr(Step, Ty),
1507 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1508 // Note that this serves two purposes: It filters out loops that are
1509 // simply not analyzable, and it covers the case where this code is
1510 // being called from within backedge-taken count analysis, such that
1511 // attempting to ask for the backedge-taken count would likely result
1512 // in infinite recursion. In the later case, the analysis code will
1513 // cope with a conservative value, and it will take care to purge
1514 // that value once it has finished.
1515 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1516 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1517 // Manually compute the final value for AR, checking for
1520 // Check whether the backedge-taken count can be losslessly casted to
1521 // the addrec's type. The count is always unsigned.
1522 const SCEV *CastedMaxBECount =
1523 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1524 const SCEV *RecastedMaxBECount =
1525 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1526 if (MaxBECount == RecastedMaxBECount) {
1527 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1528 // Check whether Start+Step*MaxBECount has no signed overflow.
1529 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
1530 const SCEV *SAdd = getSignExtendExpr(getAddExpr(Start, SMul), WideTy);
1531 const SCEV *WideStart = getSignExtendExpr(Start, WideTy);
1532 const SCEV *WideMaxBECount =
1533 getZeroExtendExpr(CastedMaxBECount, WideTy);
1534 const SCEV *OperandExtendedAdd =
1535 getAddExpr(WideStart,
1536 getMulExpr(WideMaxBECount,
1537 getSignExtendExpr(Step, WideTy)));
1538 if (SAdd == OperandExtendedAdd) {
1539 // Cache knowledge of AR NSW, which is propagated to this AddRec.
1540 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1541 // Return the expression with the addrec on the outside.
1542 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1543 getSignExtendExpr(Step, Ty),
1544 L, AR->getNoWrapFlags());
1546 // Similar to above, only this time treat the step value as unsigned.
1547 // This covers loops that count up with an unsigned step.
1548 OperandExtendedAdd =
1549 getAddExpr(WideStart,
1550 getMulExpr(WideMaxBECount,
1551 getZeroExtendExpr(Step, WideTy)));
1552 if (SAdd == OperandExtendedAdd) {
1553 // If AR wraps around then
1555 // abs(Step) * MaxBECount > unsigned-max(AR->getType())
1556 // => SAdd != OperandExtendedAdd
1558 // Thus (AR is not NW => SAdd != OperandExtendedAdd) <=>
1559 // (SAdd == OperandExtendedAdd => AR is NW)
1561 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1563 // Return the expression with the addrec on the outside.
1564 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1565 getZeroExtendExpr(Step, Ty),
1566 L, AR->getNoWrapFlags());
1570 // If the backedge is guarded by a comparison with the pre-inc value
1571 // the addrec is safe. Also, if the entry is guarded by a comparison
1572 // with the start value and the backedge is guarded by a comparison
1573 // with the post-inc value, the addrec is safe.
1574 ICmpInst::Predicate Pred;
1575 const SCEV *OverflowLimit = getOverflowLimitForStep(Step, &Pred, this);
1576 if (OverflowLimit &&
1577 (isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) ||
1578 (isLoopEntryGuardedByCond(L, Pred, Start, OverflowLimit) &&
1579 isLoopBackedgeGuardedByCond(L, Pred, AR->getPostIncExpr(*this),
1581 // Cache knowledge of AR NSW, then propagate NSW to the wide AddRec.
1582 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1583 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1584 getSignExtendExpr(Step, Ty),
1585 L, AR->getNoWrapFlags());
1588 // If Start and Step are constants, check if we can apply this
1590 // sext{C1,+,C2} --> C1 + sext{0,+,C2} if C1 < C2
1591 auto SC1 = dyn_cast<SCEVConstant>(Start);
1592 auto SC2 = dyn_cast<SCEVConstant>(Step);
1594 const APInt &C1 = SC1->getValue()->getValue();
1595 const APInt &C2 = SC2->getValue()->getValue();
1596 if (C1.isStrictlyPositive() && C2.isStrictlyPositive() && C2.ugt(C1) &&
1598 Start = getSignExtendExpr(Start, Ty);
1599 const SCEV *NewAR = getAddRecExpr(getConstant(AR->getType(), 0), Step,
1600 L, AR->getNoWrapFlags());
1601 return getAddExpr(Start, getSignExtendExpr(NewAR, Ty));
1606 // The cast wasn't folded; create an explicit cast node.
1607 // Recompute the insert position, as it may have been invalidated.
1608 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1609 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
1611 UniqueSCEVs.InsertNode(S, IP);
1615 /// getAnyExtendExpr - Return a SCEV for the given operand extended with
1616 /// unspecified bits out to the given type.
1618 const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
1620 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1621 "This is not an extending conversion!");
1622 assert(isSCEVable(Ty) &&
1623 "This is not a conversion to a SCEVable type!");
1624 Ty = getEffectiveSCEVType(Ty);
1626 // Sign-extend negative constants.
1627 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1628 if (SC->getValue()->getValue().isNegative())
1629 return getSignExtendExpr(Op, Ty);
1631 // Peel off a truncate cast.
1632 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
1633 const SCEV *NewOp = T->getOperand();
1634 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
1635 return getAnyExtendExpr(NewOp, Ty);
1636 return getTruncateOrNoop(NewOp, Ty);
1639 // Next try a zext cast. If the cast is folded, use it.
1640 const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
1641 if (!isa<SCEVZeroExtendExpr>(ZExt))
1644 // Next try a sext cast. If the cast is folded, use it.
1645 const SCEV *SExt = getSignExtendExpr(Op, Ty);
1646 if (!isa<SCEVSignExtendExpr>(SExt))
1649 // Force the cast to be folded into the operands of an addrec.
1650 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
1651 SmallVector<const SCEV *, 4> Ops;
1652 for (const SCEV *Op : AR->operands())
1653 Ops.push_back(getAnyExtendExpr(Op, Ty));
1654 return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW);
1657 // If the expression is obviously signed, use the sext cast value.
1658 if (isa<SCEVSMaxExpr>(Op))
1661 // Absent any other information, use the zext cast value.
1665 /// CollectAddOperandsWithScales - Process the given Ops list, which is
1666 /// a list of operands to be added under the given scale, update the given
1667 /// map. This is a helper function for getAddRecExpr. As an example of
1668 /// what it does, given a sequence of operands that would form an add
1669 /// expression like this:
1671 /// m + n + 13 + (A * (o + p + (B * (q + m + 29)))) + r + (-1 * r)
1673 /// where A and B are constants, update the map with these values:
1675 /// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
1677 /// and add 13 + A*B*29 to AccumulatedConstant.
1678 /// This will allow getAddRecExpr to produce this:
1680 /// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
1682 /// This form often exposes folding opportunities that are hidden in
1683 /// the original operand list.
1685 /// Return true iff it appears that any interesting folding opportunities
1686 /// may be exposed. This helps getAddRecExpr short-circuit extra work in
1687 /// the common case where no interesting opportunities are present, and
1688 /// is also used as a check to avoid infinite recursion.
1691 CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
1692 SmallVectorImpl<const SCEV *> &NewOps,
1693 APInt &AccumulatedConstant,
1694 const SCEV *const *Ops, size_t NumOperands,
1696 ScalarEvolution &SE) {
1697 bool Interesting = false;
1699 // Iterate over the add operands. They are sorted, with constants first.
1701 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1703 // Pull a buried constant out to the outside.
1704 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
1706 AccumulatedConstant += Scale * C->getValue()->getValue();
1709 // Next comes everything else. We're especially interested in multiplies
1710 // here, but they're in the middle, so just visit the rest with one loop.
1711 for (; i != NumOperands; ++i) {
1712 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
1713 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
1715 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue();
1716 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
1717 // A multiplication of a constant with another add; recurse.
1718 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1));
1720 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1721 Add->op_begin(), Add->getNumOperands(),
1724 // A multiplication of a constant with some other value. Update
1726 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
1727 const SCEV *Key = SE.getMulExpr(MulOps);
1728 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1729 M.insert(std::make_pair(Key, NewScale));
1731 NewOps.push_back(Pair.first->first);
1733 Pair.first->second += NewScale;
1734 // The map already had an entry for this value, which may indicate
1735 // a folding opportunity.
1740 // An ordinary operand. Update the map.
1741 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1742 M.insert(std::make_pair(Ops[i], Scale));
1744 NewOps.push_back(Pair.first->first);
1746 Pair.first->second += Scale;
1747 // The map already had an entry for this value, which may indicate
1748 // a folding opportunity.
1758 struct APIntCompare {
1759 bool operator()(const APInt &LHS, const APInt &RHS) const {
1760 return LHS.ult(RHS);
1765 // We're trying to construct a SCEV of type `Type' with `Ops' as operands and
1766 // `OldFlags' as can't-wrap behavior. Infer a more aggressive set of
1767 // can't-overflow flags for the operation if possible.
1768 static SCEV::NoWrapFlags
1769 StrengthenNoWrapFlags(ScalarEvolution *SE, SCEVTypes Type,
1770 const SmallVectorImpl<const SCEV *> &Ops,
1771 SCEV::NoWrapFlags OldFlags) {
1772 using namespace std::placeholders;
1775 Type == scAddExpr || Type == scAddRecExpr || Type == scMulExpr;
1777 assert(CanAnalyze && "don't call from other places!");
1779 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
1780 SCEV::NoWrapFlags SignOrUnsignWrap =
1781 ScalarEvolution::maskFlags(OldFlags, SignOrUnsignMask);
1783 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
1784 auto IsKnownNonNegative =
1785 std::bind(std::mem_fn(&ScalarEvolution::isKnownNonNegative), SE, _1);
1787 if (SignOrUnsignWrap == SCEV::FlagNSW &&
1788 std::all_of(Ops.begin(), Ops.end(), IsKnownNonNegative))
1789 return ScalarEvolution::setFlags(OldFlags,
1790 (SCEV::NoWrapFlags)SignOrUnsignMask);
1795 /// getAddExpr - Get a canonical add expression, or something simpler if
1797 const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
1798 SCEV::NoWrapFlags Flags) {
1799 assert(!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) &&
1800 "only nuw or nsw allowed");
1801 assert(!Ops.empty() && "Cannot get empty add!");
1802 if (Ops.size() == 1) return Ops[0];
1804 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
1805 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1806 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
1807 "SCEVAddExpr operand types don't match!");
1810 Flags = StrengthenNoWrapFlags(this, scAddExpr, Ops, Flags);
1812 // Sort by complexity, this groups all similar expression types together.
1813 GroupByComplexity(Ops, LI);
1815 // If there are any constants, fold them together.
1817 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1819 assert(Idx < Ops.size());
1820 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1821 // We found two constants, fold them together!
1822 Ops[0] = getConstant(LHSC->getValue()->getValue() +
1823 RHSC->getValue()->getValue());
1824 if (Ops.size() == 2) return Ops[0];
1825 Ops.erase(Ops.begin()+1); // Erase the folded element
1826 LHSC = cast<SCEVConstant>(Ops[0]);
1829 // If we are left with a constant zero being added, strip it off.
1830 if (LHSC->getValue()->isZero()) {
1831 Ops.erase(Ops.begin());
1835 if (Ops.size() == 1) return Ops[0];
1838 // Okay, check to see if the same value occurs in the operand list more than
1839 // once. If so, merge them together into an multiply expression. Since we
1840 // sorted the list, these values are required to be adjacent.
1841 Type *Ty = Ops[0]->getType();
1842 bool FoundMatch = false;
1843 for (unsigned i = 0, e = Ops.size(); i != e-1; ++i)
1844 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
1845 // Scan ahead to count how many equal operands there are.
1847 while (i+Count != e && Ops[i+Count] == Ops[i])
1849 // Merge the values into a multiply.
1850 const SCEV *Scale = getConstant(Ty, Count);
1851 const SCEV *Mul = getMulExpr(Scale, Ops[i]);
1852 if (Ops.size() == Count)
1855 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count);
1856 --i; e -= Count - 1;
1860 return getAddExpr(Ops, Flags);
1862 // Check for truncates. If all the operands are truncated from the same
1863 // type, see if factoring out the truncate would permit the result to be
1864 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
1865 // if the contents of the resulting outer trunc fold to something simple.
1866 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
1867 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
1868 Type *DstType = Trunc->getType();
1869 Type *SrcType = Trunc->getOperand()->getType();
1870 SmallVector<const SCEV *, 8> LargeOps;
1872 // Check all the operands to see if they can be represented in the
1873 // source type of the truncate.
1874 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1875 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
1876 if (T->getOperand()->getType() != SrcType) {
1880 LargeOps.push_back(T->getOperand());
1881 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1882 LargeOps.push_back(getAnyExtendExpr(C, SrcType));
1883 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
1884 SmallVector<const SCEV *, 8> LargeMulOps;
1885 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
1886 if (const SCEVTruncateExpr *T =
1887 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
1888 if (T->getOperand()->getType() != SrcType) {
1892 LargeMulOps.push_back(T->getOperand());
1893 } else if (const SCEVConstant *C =
1894 dyn_cast<SCEVConstant>(M->getOperand(j))) {
1895 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType));
1902 LargeOps.push_back(getMulExpr(LargeMulOps));
1909 // Evaluate the expression in the larger type.
1910 const SCEV *Fold = getAddExpr(LargeOps, Flags);
1911 // If it folds to something simple, use it. Otherwise, don't.
1912 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
1913 return getTruncateExpr(Fold, DstType);
1917 // Skip past any other cast SCEVs.
1918 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
1921 // If there are add operands they would be next.
1922 if (Idx < Ops.size()) {
1923 bool DeletedAdd = false;
1924 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
1925 // If we have an add, expand the add operands onto the end of the operands
1927 Ops.erase(Ops.begin()+Idx);
1928 Ops.append(Add->op_begin(), Add->op_end());
1932 // If we deleted at least one add, we added operands to the end of the list,
1933 // and they are not necessarily sorted. Recurse to resort and resimplify
1934 // any operands we just acquired.
1936 return getAddExpr(Ops);
1939 // Skip over the add expression until we get to a multiply.
1940 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1943 // Check to see if there are any folding opportunities present with
1944 // operands multiplied by constant values.
1945 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
1946 uint64_t BitWidth = getTypeSizeInBits(Ty);
1947 DenseMap<const SCEV *, APInt> M;
1948 SmallVector<const SCEV *, 8> NewOps;
1949 APInt AccumulatedConstant(BitWidth, 0);
1950 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1951 Ops.data(), Ops.size(),
1952 APInt(BitWidth, 1), *this)) {
1953 // Some interesting folding opportunity is present, so its worthwhile to
1954 // re-generate the operands list. Group the operands by constant scale,
1955 // to avoid multiplying by the same constant scale multiple times.
1956 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
1957 for (SmallVectorImpl<const SCEV *>::const_iterator I = NewOps.begin(),
1958 E = NewOps.end(); I != E; ++I)
1959 MulOpLists[M.find(*I)->second].push_back(*I);
1960 // Re-generate the operands list.
1962 if (AccumulatedConstant != 0)
1963 Ops.push_back(getConstant(AccumulatedConstant));
1964 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator
1965 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I)
1967 Ops.push_back(getMulExpr(getConstant(I->first),
1968 getAddExpr(I->second)));
1970 return getConstant(Ty, 0);
1971 if (Ops.size() == 1)
1973 return getAddExpr(Ops);
1977 // If we are adding something to a multiply expression, make sure the
1978 // something is not already an operand of the multiply. If so, merge it into
1980 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
1981 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
1982 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
1983 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
1984 if (isa<SCEVConstant>(MulOpSCEV))
1986 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
1987 if (MulOpSCEV == Ops[AddOp]) {
1988 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
1989 const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
1990 if (Mul->getNumOperands() != 2) {
1991 // If the multiply has more than two operands, we must get the
1993 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
1994 Mul->op_begin()+MulOp);
1995 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
1996 InnerMul = getMulExpr(MulOps);
1998 const SCEV *One = getConstant(Ty, 1);
1999 const SCEV *AddOne = getAddExpr(One, InnerMul);
2000 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV);
2001 if (Ops.size() == 2) return OuterMul;
2003 Ops.erase(Ops.begin()+AddOp);
2004 Ops.erase(Ops.begin()+Idx-1);
2006 Ops.erase(Ops.begin()+Idx);
2007 Ops.erase(Ops.begin()+AddOp-1);
2009 Ops.push_back(OuterMul);
2010 return getAddExpr(Ops);
2013 // Check this multiply against other multiplies being added together.
2014 for (unsigned OtherMulIdx = Idx+1;
2015 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
2017 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
2018 // If MulOp occurs in OtherMul, we can fold the two multiplies
2020 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
2021 OMulOp != e; ++OMulOp)
2022 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
2023 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
2024 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
2025 if (Mul->getNumOperands() != 2) {
2026 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
2027 Mul->op_begin()+MulOp);
2028 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
2029 InnerMul1 = getMulExpr(MulOps);
2031 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
2032 if (OtherMul->getNumOperands() != 2) {
2033 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
2034 OtherMul->op_begin()+OMulOp);
2035 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end());
2036 InnerMul2 = getMulExpr(MulOps);
2038 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
2039 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
2040 if (Ops.size() == 2) return OuterMul;
2041 Ops.erase(Ops.begin()+Idx);
2042 Ops.erase(Ops.begin()+OtherMulIdx-1);
2043 Ops.push_back(OuterMul);
2044 return getAddExpr(Ops);
2050 // If there are any add recurrences in the operands list, see if any other
2051 // added values are loop invariant. If so, we can fold them into the
2053 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2056 // Scan over all recurrences, trying to fold loop invariants into them.
2057 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
2058 // Scan all of the other operands to this add and add them to the vector if
2059 // they are loop invariant w.r.t. the recurrence.
2060 SmallVector<const SCEV *, 8> LIOps;
2061 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2062 const Loop *AddRecLoop = AddRec->getLoop();
2063 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2064 if (isLoopInvariant(Ops[i], AddRecLoop)) {
2065 LIOps.push_back(Ops[i]);
2066 Ops.erase(Ops.begin()+i);
2070 // If we found some loop invariants, fold them into the recurrence.
2071 if (!LIOps.empty()) {
2072 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
2073 LIOps.push_back(AddRec->getStart());
2075 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
2077 AddRecOps[0] = getAddExpr(LIOps);
2079 // Build the new addrec. Propagate the NUW and NSW flags if both the
2080 // outer add and the inner addrec are guaranteed to have no overflow.
2081 // Always propagate NW.
2082 Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW));
2083 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags);
2085 // If all of the other operands were loop invariant, we are done.
2086 if (Ops.size() == 1) return NewRec;
2088 // Otherwise, add the folded AddRec by the non-invariant parts.
2089 for (unsigned i = 0;; ++i)
2090 if (Ops[i] == AddRec) {
2094 return getAddExpr(Ops);
2097 // Okay, if there weren't any loop invariants to be folded, check to see if
2098 // there are multiple AddRec's with the same loop induction variable being
2099 // added together. If so, we can fold them.
2100 for (unsigned OtherIdx = Idx+1;
2101 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2103 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
2104 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L>
2105 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
2107 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2109 if (const SCEVAddRecExpr *OtherAddRec =
2110 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]))
2111 if (OtherAddRec->getLoop() == AddRecLoop) {
2112 for (unsigned i = 0, e = OtherAddRec->getNumOperands();
2114 if (i >= AddRecOps.size()) {
2115 AddRecOps.append(OtherAddRec->op_begin()+i,
2116 OtherAddRec->op_end());
2119 AddRecOps[i] = getAddExpr(AddRecOps[i],
2120 OtherAddRec->getOperand(i));
2122 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2124 // Step size has changed, so we cannot guarantee no self-wraparound.
2125 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap);
2126 return getAddExpr(Ops);
2129 // Otherwise couldn't fold anything into this recurrence. Move onto the
2133 // Okay, it looks like we really DO need an add expr. Check to see if we
2134 // already have one, otherwise create a new one.
2135 FoldingSetNodeID ID;
2136 ID.AddInteger(scAddExpr);
2137 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2138 ID.AddPointer(Ops[i]);
2141 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2143 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2144 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2145 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator),
2147 UniqueSCEVs.InsertNode(S, IP);
2149 S->setNoWrapFlags(Flags);
2153 static uint64_t umul_ov(uint64_t i, uint64_t j, bool &Overflow) {
2155 if (j > 1 && k / j != i) Overflow = true;
2159 /// Compute the result of "n choose k", the binomial coefficient. If an
2160 /// intermediate computation overflows, Overflow will be set and the return will
2161 /// be garbage. Overflow is not cleared on absence of overflow.
2162 static uint64_t Choose(uint64_t n, uint64_t k, bool &Overflow) {
2163 // We use the multiplicative formula:
2164 // n(n-1)(n-2)...(n-(k-1)) / k(k-1)(k-2)...1 .
2165 // At each iteration, we take the n-th term of the numeral and divide by the
2166 // (k-n)th term of the denominator. This division will always produce an
2167 // integral result, and helps reduce the chance of overflow in the
2168 // intermediate computations. However, we can still overflow even when the
2169 // final result would fit.
2171 if (n == 0 || n == k) return 1;
2172 if (k > n) return 0;
2178 for (uint64_t i = 1; i <= k; ++i) {
2179 r = umul_ov(r, n-(i-1), Overflow);
2185 /// Determine if any of the operands in this SCEV are a constant or if
2186 /// any of the add or multiply expressions in this SCEV contain a constant.
2187 static bool containsConstantSomewhere(const SCEV *StartExpr) {
2188 SmallVector<const SCEV *, 4> Ops;
2189 Ops.push_back(StartExpr);
2190 while (!Ops.empty()) {
2191 const SCEV *CurrentExpr = Ops.pop_back_val();
2192 if (isa<SCEVConstant>(*CurrentExpr))
2195 if (isa<SCEVAddExpr>(*CurrentExpr) || isa<SCEVMulExpr>(*CurrentExpr)) {
2196 const auto *CurrentNAry = cast<SCEVNAryExpr>(CurrentExpr);
2197 Ops.append(CurrentNAry->op_begin(), CurrentNAry->op_end());
2203 /// getMulExpr - Get a canonical multiply expression, or something simpler if
2205 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
2206 SCEV::NoWrapFlags Flags) {
2207 assert(Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) &&
2208 "only nuw or nsw allowed");
2209 assert(!Ops.empty() && "Cannot get empty mul!");
2210 if (Ops.size() == 1) return Ops[0];
2212 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2213 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2214 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2215 "SCEVMulExpr operand types don't match!");
2218 Flags = StrengthenNoWrapFlags(this, scMulExpr, Ops, Flags);
2220 // Sort by complexity, this groups all similar expression types together.
2221 GroupByComplexity(Ops, LI);
2223 // If there are any constants, fold them together.
2225 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2227 // C1*(C2+V) -> C1*C2 + C1*V
2228 if (Ops.size() == 2)
2229 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
2230 // If any of Add's ops are Adds or Muls with a constant,
2231 // apply this transformation as well.
2232 if (Add->getNumOperands() == 2)
2233 if (containsConstantSomewhere(Add))
2234 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
2235 getMulExpr(LHSC, Add->getOperand(1)));
2238 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2239 // We found two constants, fold them together!
2240 ConstantInt *Fold = ConstantInt::get(getContext(),
2241 LHSC->getValue()->getValue() *
2242 RHSC->getValue()->getValue());
2243 Ops[0] = getConstant(Fold);
2244 Ops.erase(Ops.begin()+1); // Erase the folded element
2245 if (Ops.size() == 1) return Ops[0];
2246 LHSC = cast<SCEVConstant>(Ops[0]);
2249 // If we are left with a constant one being multiplied, strip it off.
2250 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
2251 Ops.erase(Ops.begin());
2253 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
2254 // If we have a multiply of zero, it will always be zero.
2256 } else if (Ops[0]->isAllOnesValue()) {
2257 // If we have a mul by -1 of an add, try distributing the -1 among the
2259 if (Ops.size() == 2) {
2260 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
2261 SmallVector<const SCEV *, 4> NewOps;
2262 bool AnyFolded = false;
2263 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(),
2264 E = Add->op_end(); I != E; ++I) {
2265 const SCEV *Mul = getMulExpr(Ops[0], *I);
2266 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
2267 NewOps.push_back(Mul);
2270 return getAddExpr(NewOps);
2272 else if (const SCEVAddRecExpr *
2273 AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) {
2274 // Negation preserves a recurrence's no self-wrap property.
2275 SmallVector<const SCEV *, 4> Operands;
2276 for (SCEVAddRecExpr::op_iterator I = AddRec->op_begin(),
2277 E = AddRec->op_end(); I != E; ++I) {
2278 Operands.push_back(getMulExpr(Ops[0], *I));
2280 return getAddRecExpr(Operands, AddRec->getLoop(),
2281 AddRec->getNoWrapFlags(SCEV::FlagNW));
2286 if (Ops.size() == 1)
2290 // Skip over the add expression until we get to a multiply.
2291 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
2294 // If there are mul operands inline them all into this expression.
2295 if (Idx < Ops.size()) {
2296 bool DeletedMul = false;
2297 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
2298 // If we have an mul, expand the mul operands onto the end of the operands
2300 Ops.erase(Ops.begin()+Idx);
2301 Ops.append(Mul->op_begin(), Mul->op_end());
2305 // If we deleted at least one mul, we added operands to the end of the list,
2306 // and they are not necessarily sorted. Recurse to resort and resimplify
2307 // any operands we just acquired.
2309 return getMulExpr(Ops);
2312 // If there are any add recurrences in the operands list, see if any other
2313 // added values are loop invariant. If so, we can fold them into the
2315 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2318 // Scan over all recurrences, trying to fold loop invariants into them.
2319 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
2320 // Scan all of the other operands to this mul and add them to the vector if
2321 // they are loop invariant w.r.t. the recurrence.
2322 SmallVector<const SCEV *, 8> LIOps;
2323 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2324 const Loop *AddRecLoop = AddRec->getLoop();
2325 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2326 if (isLoopInvariant(Ops[i], AddRecLoop)) {
2327 LIOps.push_back(Ops[i]);
2328 Ops.erase(Ops.begin()+i);
2332 // If we found some loop invariants, fold them into the recurrence.
2333 if (!LIOps.empty()) {
2334 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
2335 SmallVector<const SCEV *, 4> NewOps;
2336 NewOps.reserve(AddRec->getNumOperands());
2337 const SCEV *Scale = getMulExpr(LIOps);
2338 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
2339 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
2341 // Build the new addrec. Propagate the NUW and NSW flags if both the
2342 // outer mul and the inner addrec are guaranteed to have no overflow.
2344 // No self-wrap cannot be guaranteed after changing the step size, but
2345 // will be inferred if either NUW or NSW is true.
2346 Flags = AddRec->getNoWrapFlags(clearFlags(Flags, SCEV::FlagNW));
2347 const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, Flags);
2349 // If all of the other operands were loop invariant, we are done.
2350 if (Ops.size() == 1) return NewRec;
2352 // Otherwise, multiply the folded AddRec by the non-invariant parts.
2353 for (unsigned i = 0;; ++i)
2354 if (Ops[i] == AddRec) {
2358 return getMulExpr(Ops);
2361 // Okay, if there weren't any loop invariants to be folded, check to see if
2362 // there are multiple AddRec's with the same loop induction variable being
2363 // multiplied together. If so, we can fold them.
2365 // {A1,+,A2,+,...,+,An}<L> * {B1,+,B2,+,...,+,Bn}<L>
2366 // = {x=1 in [ sum y=x..2x [ sum z=max(y-x, y-n)..min(x,n) [
2367 // choose(x, 2x)*choose(2x-y, x-z)*A_{y-z}*B_z
2368 // ]]],+,...up to x=2n}.
2369 // Note that the arguments to choose() are always integers with values
2370 // known at compile time, never SCEV objects.
2372 // The implementation avoids pointless extra computations when the two
2373 // addrec's are of different length (mathematically, it's equivalent to
2374 // an infinite stream of zeros on the right).
2375 bool OpsModified = false;
2376 for (unsigned OtherIdx = Idx+1;
2377 OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2379 const SCEVAddRecExpr *OtherAddRec =
2380 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]);
2381 if (!OtherAddRec || OtherAddRec->getLoop() != AddRecLoop)
2384 bool Overflow = false;
2385 Type *Ty = AddRec->getType();
2386 bool LargerThan64Bits = getTypeSizeInBits(Ty) > 64;
2387 SmallVector<const SCEV*, 7> AddRecOps;
2388 for (int x = 0, xe = AddRec->getNumOperands() +
2389 OtherAddRec->getNumOperands() - 1; x != xe && !Overflow; ++x) {
2390 const SCEV *Term = getConstant(Ty, 0);
2391 for (int y = x, ye = 2*x+1; y != ye && !Overflow; ++y) {
2392 uint64_t Coeff1 = Choose(x, 2*x - y, Overflow);
2393 for (int z = std::max(y-x, y-(int)AddRec->getNumOperands()+1),
2394 ze = std::min(x+1, (int)OtherAddRec->getNumOperands());
2395 z < ze && !Overflow; ++z) {
2396 uint64_t Coeff2 = Choose(2*x - y, x-z, Overflow);
2398 if (LargerThan64Bits)
2399 Coeff = umul_ov(Coeff1, Coeff2, Overflow);
2401 Coeff = Coeff1*Coeff2;
2402 const SCEV *CoeffTerm = getConstant(Ty, Coeff);
2403 const SCEV *Term1 = AddRec->getOperand(y-z);
2404 const SCEV *Term2 = OtherAddRec->getOperand(z);
2405 Term = getAddExpr(Term, getMulExpr(CoeffTerm, Term1,Term2));
2408 AddRecOps.push_back(Term);
2411 const SCEV *NewAddRec = getAddRecExpr(AddRecOps, AddRec->getLoop(),
2413 if (Ops.size() == 2) return NewAddRec;
2414 Ops[Idx] = NewAddRec;
2415 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2417 AddRec = dyn_cast<SCEVAddRecExpr>(NewAddRec);
2423 return getMulExpr(Ops);
2425 // Otherwise couldn't fold anything into this recurrence. Move onto the
2429 // Okay, it looks like we really DO need an mul expr. Check to see if we
2430 // already have one, otherwise create a new one.
2431 FoldingSetNodeID ID;
2432 ID.AddInteger(scMulExpr);
2433 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2434 ID.AddPointer(Ops[i]);
2437 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2439 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2440 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2441 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
2443 UniqueSCEVs.InsertNode(S, IP);
2445 S->setNoWrapFlags(Flags);
2449 /// getUDivExpr - Get a canonical unsigned division expression, or something
2450 /// simpler if possible.
2451 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
2453 assert(getEffectiveSCEVType(LHS->getType()) ==
2454 getEffectiveSCEVType(RHS->getType()) &&
2455 "SCEVUDivExpr operand types don't match!");
2457 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
2458 if (RHSC->getValue()->equalsInt(1))
2459 return LHS; // X udiv 1 --> x
2460 // If the denominator is zero, the result of the udiv is undefined. Don't
2461 // try to analyze it, because the resolution chosen here may differ from
2462 // the resolution chosen in other parts of the compiler.
2463 if (!RHSC->getValue()->isZero()) {
2464 // Determine if the division can be folded into the operands of
2466 // TODO: Generalize this to non-constants by using known-bits information.
2467 Type *Ty = LHS->getType();
2468 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
2469 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1;
2470 // For non-power-of-two values, effectively round the value up to the
2471 // nearest power of two.
2472 if (!RHSC->getValue()->getValue().isPowerOf2())
2474 IntegerType *ExtTy =
2475 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
2476 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
2477 if (const SCEVConstant *Step =
2478 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) {
2479 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
2480 const APInt &StepInt = Step->getValue()->getValue();
2481 const APInt &DivInt = RHSC->getValue()->getValue();
2482 if (!StepInt.urem(DivInt) &&
2483 getZeroExtendExpr(AR, ExtTy) ==
2484 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2485 getZeroExtendExpr(Step, ExtTy),
2486 AR->getLoop(), SCEV::FlagAnyWrap)) {
2487 SmallVector<const SCEV *, 4> Operands;
2488 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i)
2489 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS));
2490 return getAddRecExpr(Operands, AR->getLoop(),
2493 /// Get a canonical UDivExpr for a recurrence.
2494 /// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0.
2495 // We can currently only fold X%N if X is constant.
2496 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(AR->getStart());
2497 if (StartC && !DivInt.urem(StepInt) &&
2498 getZeroExtendExpr(AR, ExtTy) ==
2499 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2500 getZeroExtendExpr(Step, ExtTy),
2501 AR->getLoop(), SCEV::FlagAnyWrap)) {
2502 const APInt &StartInt = StartC->getValue()->getValue();
2503 const APInt &StartRem = StartInt.urem(StepInt);
2505 LHS = getAddRecExpr(getConstant(StartInt - StartRem), Step,
2506 AR->getLoop(), SCEV::FlagNW);
2509 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
2510 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
2511 SmallVector<const SCEV *, 4> Operands;
2512 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i)
2513 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy));
2514 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
2515 // Find an operand that's safely divisible.
2516 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
2517 const SCEV *Op = M->getOperand(i);
2518 const SCEV *Div = getUDivExpr(Op, RHSC);
2519 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
2520 Operands = SmallVector<const SCEV *, 4>(M->op_begin(),
2523 return getMulExpr(Operands);
2527 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
2528 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) {
2529 SmallVector<const SCEV *, 4> Operands;
2530 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i)
2531 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy));
2532 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
2534 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
2535 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
2536 if (isa<SCEVUDivExpr>(Op) ||
2537 getMulExpr(Op, RHS) != A->getOperand(i))
2539 Operands.push_back(Op);
2541 if (Operands.size() == A->getNumOperands())
2542 return getAddExpr(Operands);
2546 // Fold if both operands are constant.
2547 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
2548 Constant *LHSCV = LHSC->getValue();
2549 Constant *RHSCV = RHSC->getValue();
2550 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
2556 FoldingSetNodeID ID;
2557 ID.AddInteger(scUDivExpr);
2561 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2562 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
2564 UniqueSCEVs.InsertNode(S, IP);
2568 static const APInt gcd(const SCEVConstant *C1, const SCEVConstant *C2) {
2569 APInt A = C1->getValue()->getValue().abs();
2570 APInt B = C2->getValue()->getValue().abs();
2571 uint32_t ABW = A.getBitWidth();
2572 uint32_t BBW = B.getBitWidth();
2579 return APIntOps::GreatestCommonDivisor(A, B);
2582 /// getUDivExactExpr - Get a canonical unsigned division expression, or
2583 /// something simpler if possible. There is no representation for an exact udiv
2584 /// in SCEV IR, but we can attempt to remove factors from the LHS and RHS.
2585 /// We can't do this when it's not exact because the udiv may be clearing bits.
2586 const SCEV *ScalarEvolution::getUDivExactExpr(const SCEV *LHS,
2588 // TODO: we could try to find factors in all sorts of things, but for now we
2589 // just deal with u/exact (multiply, constant). See SCEVDivision towards the
2590 // end of this file for inspiration.
2592 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(LHS);
2594 return getUDivExpr(LHS, RHS);
2596 if (const SCEVConstant *RHSCst = dyn_cast<SCEVConstant>(RHS)) {
2597 // If the mulexpr multiplies by a constant, then that constant must be the
2598 // first element of the mulexpr.
2599 if (const SCEVConstant *LHSCst =
2600 dyn_cast<SCEVConstant>(Mul->getOperand(0))) {
2601 if (LHSCst == RHSCst) {
2602 SmallVector<const SCEV *, 2> Operands;
2603 Operands.append(Mul->op_begin() + 1, Mul->op_end());
2604 return getMulExpr(Operands);
2607 // We can't just assume that LHSCst divides RHSCst cleanly, it could be
2608 // that there's a factor provided by one of the other terms. We need to
2610 APInt Factor = gcd(LHSCst, RHSCst);
2611 if (!Factor.isIntN(1)) {
2612 LHSCst = cast<SCEVConstant>(
2613 getConstant(LHSCst->getValue()->getValue().udiv(Factor)));
2614 RHSCst = cast<SCEVConstant>(
2615 getConstant(RHSCst->getValue()->getValue().udiv(Factor)));
2616 SmallVector<const SCEV *, 2> Operands;
2617 Operands.push_back(LHSCst);
2618 Operands.append(Mul->op_begin() + 1, Mul->op_end());
2619 LHS = getMulExpr(Operands);
2621 Mul = dyn_cast<SCEVMulExpr>(LHS);
2623 return getUDivExactExpr(LHS, RHS);
2628 for (int i = 0, e = Mul->getNumOperands(); i != e; ++i) {
2629 if (Mul->getOperand(i) == RHS) {
2630 SmallVector<const SCEV *, 2> Operands;
2631 Operands.append(Mul->op_begin(), Mul->op_begin() + i);
2632 Operands.append(Mul->op_begin() + i + 1, Mul->op_end());
2633 return getMulExpr(Operands);
2637 return getUDivExpr(LHS, RHS);
2640 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2641 /// Simplify the expression as much as possible.
2642 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step,
2644 SCEV::NoWrapFlags Flags) {
2645 SmallVector<const SCEV *, 4> Operands;
2646 Operands.push_back(Start);
2647 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
2648 if (StepChrec->getLoop() == L) {
2649 Operands.append(StepChrec->op_begin(), StepChrec->op_end());
2650 return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW));
2653 Operands.push_back(Step);
2654 return getAddRecExpr(Operands, L, Flags);
2657 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2658 /// Simplify the expression as much as possible.
2660 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
2661 const Loop *L, SCEV::NoWrapFlags Flags) {
2662 if (Operands.size() == 1) return Operands[0];
2664 Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
2665 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
2666 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy &&
2667 "SCEVAddRecExpr operand types don't match!");
2668 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2669 assert(isLoopInvariant(Operands[i], L) &&
2670 "SCEVAddRecExpr operand is not loop-invariant!");
2673 if (Operands.back()->isZero()) {
2674 Operands.pop_back();
2675 return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0} --> X
2678 // It's tempting to want to call getMaxBackedgeTakenCount count here and
2679 // use that information to infer NUW and NSW flags. However, computing a
2680 // BE count requires calling getAddRecExpr, so we may not yet have a
2681 // meaningful BE count at this point (and if we don't, we'd be stuck
2682 // with a SCEVCouldNotCompute as the cached BE count).
2684 Flags = StrengthenNoWrapFlags(this, scAddRecExpr, Operands, Flags);
2686 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
2687 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
2688 const Loop *NestedLoop = NestedAR->getLoop();
2689 if (L->contains(NestedLoop) ?
2690 (L->getLoopDepth() < NestedLoop->getLoopDepth()) :
2691 (!NestedLoop->contains(L) &&
2692 DT->dominates(L->getHeader(), NestedLoop->getHeader()))) {
2693 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
2694 NestedAR->op_end());
2695 Operands[0] = NestedAR->getStart();
2696 // AddRecs require their operands be loop-invariant with respect to their
2697 // loops. Don't perform this transformation if it would break this
2699 bool AllInvariant = true;
2700 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2701 if (!isLoopInvariant(Operands[i], L)) {
2702 AllInvariant = false;
2706 // Create a recurrence for the outer loop with the same step size.
2708 // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the
2709 // inner recurrence has the same property.
2710 SCEV::NoWrapFlags OuterFlags =
2711 maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags());
2713 NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags);
2714 AllInvariant = true;
2715 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i)
2716 if (!isLoopInvariant(NestedOperands[i], NestedLoop)) {
2717 AllInvariant = false;
2721 // Ok, both add recurrences are valid after the transformation.
2723 // The inner recurrence keeps its NW flag but only keeps NUW/NSW if
2724 // the outer recurrence has the same property.
2725 SCEV::NoWrapFlags InnerFlags =
2726 maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags);
2727 return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags);
2730 // Reset Operands to its original state.
2731 Operands[0] = NestedAR;
2735 // Okay, it looks like we really DO need an addrec expr. Check to see if we
2736 // already have one, otherwise create a new one.
2737 FoldingSetNodeID ID;
2738 ID.AddInteger(scAddRecExpr);
2739 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2740 ID.AddPointer(Operands[i]);
2744 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2746 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size());
2747 std::uninitialized_copy(Operands.begin(), Operands.end(), O);
2748 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator),
2749 O, Operands.size(), L);
2750 UniqueSCEVs.InsertNode(S, IP);
2752 S->setNoWrapFlags(Flags);
2756 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
2758 SmallVector<const SCEV *, 2> Ops;
2761 return getSMaxExpr(Ops);
2765 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2766 assert(!Ops.empty() && "Cannot get empty smax!");
2767 if (Ops.size() == 1) return Ops[0];
2769 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2770 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2771 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2772 "SCEVSMaxExpr operand types don't match!");
2775 // Sort by complexity, this groups all similar expression types together.
2776 GroupByComplexity(Ops, LI);
2778 // If there are any constants, fold them together.
2780 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2782 assert(Idx < Ops.size());
2783 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2784 // We found two constants, fold them together!
2785 ConstantInt *Fold = ConstantInt::get(getContext(),
2786 APIntOps::smax(LHSC->getValue()->getValue(),
2787 RHSC->getValue()->getValue()));
2788 Ops[0] = getConstant(Fold);
2789 Ops.erase(Ops.begin()+1); // Erase the folded element
2790 if (Ops.size() == 1) return Ops[0];
2791 LHSC = cast<SCEVConstant>(Ops[0]);
2794 // If we are left with a constant minimum-int, strip it off.
2795 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
2796 Ops.erase(Ops.begin());
2798 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
2799 // If we have an smax with a constant maximum-int, it will always be
2804 if (Ops.size() == 1) return Ops[0];
2807 // Find the first SMax
2808 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
2811 // Check to see if one of the operands is an SMax. If so, expand its operands
2812 // onto our operand list, and recurse to simplify.
2813 if (Idx < Ops.size()) {
2814 bool DeletedSMax = false;
2815 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
2816 Ops.erase(Ops.begin()+Idx);
2817 Ops.append(SMax->op_begin(), SMax->op_end());
2822 return getSMaxExpr(Ops);
2825 // Okay, check to see if the same value occurs in the operand list twice. If
2826 // so, delete one. Since we sorted the list, these values are required to
2828 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2829 // X smax Y smax Y --> X smax Y
2830 // X smax Y --> X, if X is always greater than Y
2831 if (Ops[i] == Ops[i+1] ||
2832 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) {
2833 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2835 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) {
2836 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2840 if (Ops.size() == 1) return Ops[0];
2842 assert(!Ops.empty() && "Reduced smax down to nothing!");
2844 // Okay, it looks like we really DO need an smax expr. Check to see if we
2845 // already have one, otherwise create a new one.
2846 FoldingSetNodeID ID;
2847 ID.AddInteger(scSMaxExpr);
2848 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2849 ID.AddPointer(Ops[i]);
2851 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2852 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2853 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2854 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator),
2856 UniqueSCEVs.InsertNode(S, IP);
2860 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
2862 SmallVector<const SCEV *, 2> Ops;
2865 return getUMaxExpr(Ops);
2869 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2870 assert(!Ops.empty() && "Cannot get empty umax!");
2871 if (Ops.size() == 1) return Ops[0];
2873 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2874 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2875 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2876 "SCEVUMaxExpr operand types don't match!");
2879 // Sort by complexity, this groups all similar expression types together.
2880 GroupByComplexity(Ops, LI);
2882 // If there are any constants, fold them together.
2884 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2886 assert(Idx < Ops.size());
2887 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2888 // We found two constants, fold them together!
2889 ConstantInt *Fold = ConstantInt::get(getContext(),
2890 APIntOps::umax(LHSC->getValue()->getValue(),
2891 RHSC->getValue()->getValue()));
2892 Ops[0] = getConstant(Fold);
2893 Ops.erase(Ops.begin()+1); // Erase the folded element
2894 if (Ops.size() == 1) return Ops[0];
2895 LHSC = cast<SCEVConstant>(Ops[0]);
2898 // If we are left with a constant minimum-int, strip it off.
2899 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
2900 Ops.erase(Ops.begin());
2902 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
2903 // If we have an umax with a constant maximum-int, it will always be
2908 if (Ops.size() == 1) return Ops[0];
2911 // Find the first UMax
2912 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
2915 // Check to see if one of the operands is a UMax. If so, expand its operands
2916 // onto our operand list, and recurse to simplify.
2917 if (Idx < Ops.size()) {
2918 bool DeletedUMax = false;
2919 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
2920 Ops.erase(Ops.begin()+Idx);
2921 Ops.append(UMax->op_begin(), UMax->op_end());
2926 return getUMaxExpr(Ops);
2929 // Okay, check to see if the same value occurs in the operand list twice. If
2930 // so, delete one. Since we sorted the list, these values are required to
2932 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2933 // X umax Y umax Y --> X umax Y
2934 // X umax Y --> X, if X is always greater than Y
2935 if (Ops[i] == Ops[i+1] ||
2936 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) {
2937 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2939 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) {
2940 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2944 if (Ops.size() == 1) return Ops[0];
2946 assert(!Ops.empty() && "Reduced umax down to nothing!");
2948 // Okay, it looks like we really DO need a umax expr. Check to see if we
2949 // already have one, otherwise create a new one.
2950 FoldingSetNodeID ID;
2951 ID.AddInteger(scUMaxExpr);
2952 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2953 ID.AddPointer(Ops[i]);
2955 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2956 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2957 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2958 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator),
2960 UniqueSCEVs.InsertNode(S, IP);
2964 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
2966 // ~smax(~x, ~y) == smin(x, y).
2967 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2970 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
2972 // ~umax(~x, ~y) == umin(x, y)
2973 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2976 const SCEV *ScalarEvolution::getSizeOfExpr(Type *IntTy, Type *AllocTy) {
2977 // If we have DataLayout, we can bypass creating a target-independent
2978 // constant expression and then folding it back into a ConstantInt.
2979 // This is just a compile-time optimization.
2981 return getConstant(IntTy, DL->getTypeAllocSize(AllocTy));
2983 Constant *C = ConstantExpr::getSizeOf(AllocTy);
2984 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2985 if (Constant *Folded = ConstantFoldConstantExpression(CE, DL, TLI))
2987 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2988 assert(Ty == IntTy && "Effective SCEV type doesn't match");
2989 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2992 const SCEV *ScalarEvolution::getOffsetOfExpr(Type *IntTy,
2995 // If we have DataLayout, we can bypass creating a target-independent
2996 // constant expression and then folding it back into a ConstantInt.
2997 // This is just a compile-time optimization.
2999 return getConstant(IntTy,
3000 DL->getStructLayout(STy)->getElementOffset(FieldNo));
3003 Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo);
3004 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
3005 if (Constant *Folded = ConstantFoldConstantExpression(CE, DL, TLI))
3008 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy));
3009 return getTruncateOrZeroExtend(getSCEV(C), Ty);
3012 const SCEV *ScalarEvolution::getUnknown(Value *V) {
3013 // Don't attempt to do anything other than create a SCEVUnknown object
3014 // here. createSCEV only calls getUnknown after checking for all other
3015 // interesting possibilities, and any other code that calls getUnknown
3016 // is doing so in order to hide a value from SCEV canonicalization.
3018 FoldingSetNodeID ID;
3019 ID.AddInteger(scUnknown);
3022 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
3023 assert(cast<SCEVUnknown>(S)->getValue() == V &&
3024 "Stale SCEVUnknown in uniquing map!");
3027 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
3029 FirstUnknown = cast<SCEVUnknown>(S);
3030 UniqueSCEVs.InsertNode(S, IP);
3034 //===----------------------------------------------------------------------===//
3035 // Basic SCEV Analysis and PHI Idiom Recognition Code
3038 /// isSCEVable - Test if values of the given type are analyzable within
3039 /// the SCEV framework. This primarily includes integer types, and it
3040 /// can optionally include pointer types if the ScalarEvolution class
3041 /// has access to target-specific information.
3042 bool ScalarEvolution::isSCEVable(Type *Ty) const {
3043 // Integers and pointers are always SCEVable.
3044 return Ty->isIntegerTy() || Ty->isPointerTy();
3047 /// getTypeSizeInBits - Return the size in bits of the specified type,
3048 /// for which isSCEVable must return true.
3049 uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const {
3050 assert(isSCEVable(Ty) && "Type is not SCEVable!");
3052 // If we have a DataLayout, use it!
3054 return DL->getTypeSizeInBits(Ty);
3056 // Integer types have fixed sizes.
3057 if (Ty->isIntegerTy())
3058 return Ty->getPrimitiveSizeInBits();
3060 // The only other support type is pointer. Without DataLayout, conservatively
3061 // assume pointers are 64-bit.
3062 assert(Ty->isPointerTy() && "isSCEVable permitted a non-SCEVable type!");
3066 /// getEffectiveSCEVType - Return a type with the same bitwidth as
3067 /// the given type and which represents how SCEV will treat the given
3068 /// type, for which isSCEVable must return true. For pointer types,
3069 /// this is the pointer-sized integer type.
3070 Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const {
3071 assert(isSCEVable(Ty) && "Type is not SCEVable!");
3073 if (Ty->isIntegerTy()) {
3077 // The only other support type is pointer.
3078 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
3081 return DL->getIntPtrType(Ty);
3083 // Without DataLayout, conservatively assume pointers are 64-bit.
3084 return Type::getInt64Ty(getContext());
3087 const SCEV *ScalarEvolution::getCouldNotCompute() {
3088 return &CouldNotCompute;
3092 // Helper class working with SCEVTraversal to figure out if a SCEV contains
3093 // a SCEVUnknown with null value-pointer. FindInvalidSCEVUnknown::FindOne
3094 // is set iff if find such SCEVUnknown.
3096 struct FindInvalidSCEVUnknown {
3098 FindInvalidSCEVUnknown() { FindOne = false; }
3099 bool follow(const SCEV *S) {
3100 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
3104 if (!cast<SCEVUnknown>(S)->getValue())
3111 bool isDone() const { return FindOne; }
3115 bool ScalarEvolution::checkValidity(const SCEV *S) const {
3116 FindInvalidSCEVUnknown F;
3117 SCEVTraversal<FindInvalidSCEVUnknown> ST(F);
3123 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
3124 /// expression and create a new one.
3125 const SCEV *ScalarEvolution::getSCEV(Value *V) {
3126 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
3128 ValueExprMapType::iterator I = ValueExprMap.find_as(V);
3129 if (I != ValueExprMap.end()) {
3130 const SCEV *S = I->second;
3131 if (checkValidity(S))
3134 ValueExprMap.erase(I);
3136 const SCEV *S = createSCEV(V);
3138 // The process of creating a SCEV for V may have caused other SCEVs
3139 // to have been created, so it's necessary to insert the new entry
3140 // from scratch, rather than trying to remember the insert position
3142 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(V, this), S));
3146 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
3148 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) {
3149 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
3151 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
3153 Type *Ty = V->getType();
3154 Ty = getEffectiveSCEVType(Ty);
3155 return getMulExpr(V,
3156 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))));
3159 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
3160 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
3161 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
3163 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
3165 Type *Ty = V->getType();
3166 Ty = getEffectiveSCEVType(Ty);
3167 const SCEV *AllOnes =
3168 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
3169 return getMinusSCEV(AllOnes, V);
3172 /// getMinusSCEV - Return LHS-RHS. Minus is represented in SCEV as A+B*-1.
3173 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
3174 SCEV::NoWrapFlags Flags) {
3175 assert(!maskFlags(Flags, SCEV::FlagNUW) && "subtraction does not have NUW");
3177 // Fast path: X - X --> 0.
3179 return getConstant(LHS->getType(), 0);
3181 // X - Y --> X + -Y.
3182 // X -(nsw || nuw) Y --> X + -Y.
3183 return getAddExpr(LHS, getNegativeSCEV(RHS));
3186 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
3187 /// input value to the specified type. If the type must be extended, it is zero
3190 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty) {
3191 Type *SrcTy = V->getType();
3192 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3193 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3194 "Cannot truncate or zero extend with non-integer arguments!");
3195 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3196 return V; // No conversion
3197 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
3198 return getTruncateExpr(V, Ty);
3199 return getZeroExtendExpr(V, Ty);
3202 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
3203 /// input value to the specified type. If the type must be extended, it is sign
3206 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
3208 Type *SrcTy = V->getType();
3209 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3210 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3211 "Cannot truncate or zero extend with non-integer arguments!");
3212 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3213 return V; // No conversion
3214 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
3215 return getTruncateExpr(V, Ty);
3216 return getSignExtendExpr(V, Ty);
3219 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
3220 /// input value to the specified type. If the type must be extended, it is zero
3221 /// extended. The conversion must not be narrowing.
3223 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) {
3224 Type *SrcTy = V->getType();
3225 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3226 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3227 "Cannot noop or zero extend with non-integer arguments!");
3228 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3229 "getNoopOrZeroExtend cannot truncate!");
3230 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3231 return V; // No conversion
3232 return getZeroExtendExpr(V, Ty);
3235 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
3236 /// input value to the specified type. If the type must be extended, it is sign
3237 /// extended. The conversion must not be narrowing.
3239 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) {
3240 Type *SrcTy = V->getType();
3241 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3242 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3243 "Cannot noop or sign extend with non-integer arguments!");
3244 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3245 "getNoopOrSignExtend cannot truncate!");
3246 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3247 return V; // No conversion
3248 return getSignExtendExpr(V, Ty);
3251 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
3252 /// the input value to the specified type. If the type must be extended,
3253 /// it is extended with unspecified bits. The conversion must not be
3256 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) {
3257 Type *SrcTy = V->getType();
3258 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3259 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3260 "Cannot noop or any extend with non-integer arguments!");
3261 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3262 "getNoopOrAnyExtend cannot truncate!");
3263 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3264 return V; // No conversion
3265 return getAnyExtendExpr(V, Ty);
3268 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
3269 /// input value to the specified type. The conversion must not be widening.
3271 ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) {
3272 Type *SrcTy = V->getType();
3273 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3274 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3275 "Cannot truncate or noop with non-integer arguments!");
3276 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
3277 "getTruncateOrNoop cannot extend!");
3278 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3279 return V; // No conversion
3280 return getTruncateExpr(V, Ty);
3283 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
3284 /// the types using zero-extension, and then perform a umax operation
3286 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
3288 const SCEV *PromotedLHS = LHS;
3289 const SCEV *PromotedRHS = RHS;
3291 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
3292 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
3294 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
3296 return getUMaxExpr(PromotedLHS, PromotedRHS);
3299 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
3300 /// the types using zero-extension, and then perform a umin operation
3302 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
3304 const SCEV *PromotedLHS = LHS;
3305 const SCEV *PromotedRHS = RHS;
3307 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
3308 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
3310 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
3312 return getUMinExpr(PromotedLHS, PromotedRHS);
3315 /// getPointerBase - Transitively follow the chain of pointer-type operands
3316 /// until reaching a SCEV that does not have a single pointer operand. This
3317 /// returns a SCEVUnknown pointer for well-formed pointer-type expressions,
3318 /// but corner cases do exist.
3319 const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) {
3320 // A pointer operand may evaluate to a nonpointer expression, such as null.
3321 if (!V->getType()->isPointerTy())
3324 if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) {
3325 return getPointerBase(Cast->getOperand());
3327 else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) {
3328 const SCEV *PtrOp = nullptr;
3329 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
3331 if ((*I)->getType()->isPointerTy()) {
3332 // Cannot find the base of an expression with multiple pointer operands.
3340 return getPointerBase(PtrOp);
3345 /// PushDefUseChildren - Push users of the given Instruction
3346 /// onto the given Worklist.
3348 PushDefUseChildren(Instruction *I,
3349 SmallVectorImpl<Instruction *> &Worklist) {
3350 // Push the def-use children onto the Worklist stack.
3351 for (User *U : I->users())
3352 Worklist.push_back(cast<Instruction>(U));
3355 /// ForgetSymbolicValue - This looks up computed SCEV values for all
3356 /// instructions that depend on the given instruction and removes them from
3357 /// the ValueExprMapType map if they reference SymName. This is used during PHI
3360 ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) {
3361 SmallVector<Instruction *, 16> Worklist;
3362 PushDefUseChildren(PN, Worklist);
3364 SmallPtrSet<Instruction *, 8> Visited;
3366 while (!Worklist.empty()) {
3367 Instruction *I = Worklist.pop_back_val();
3368 if (!Visited.insert(I).second)
3371 ValueExprMapType::iterator It =
3372 ValueExprMap.find_as(static_cast<Value *>(I));
3373 if (It != ValueExprMap.end()) {
3374 const SCEV *Old = It->second;
3376 // Short-circuit the def-use traversal if the symbolic name
3377 // ceases to appear in expressions.
3378 if (Old != SymName && !hasOperand(Old, SymName))
3381 // SCEVUnknown for a PHI either means that it has an unrecognized
3382 // structure, it's a PHI that's in the progress of being computed
3383 // by createNodeForPHI, or it's a single-value PHI. In the first case,
3384 // additional loop trip count information isn't going to change anything.
3385 // In the second case, createNodeForPHI will perform the necessary
3386 // updates on its own when it gets to that point. In the third, we do
3387 // want to forget the SCEVUnknown.
3388 if (!isa<PHINode>(I) ||
3389 !isa<SCEVUnknown>(Old) ||
3390 (I != PN && Old == SymName)) {
3391 forgetMemoizedResults(Old);
3392 ValueExprMap.erase(It);
3396 PushDefUseChildren(I, Worklist);
3400 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
3401 /// a loop header, making it a potential recurrence, or it doesn't.
3403 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
3404 if (const Loop *L = LI->getLoopFor(PN->getParent()))
3405 if (L->getHeader() == PN->getParent()) {
3406 // The loop may have multiple entrances or multiple exits; we can analyze
3407 // this phi as an addrec if it has a unique entry value and a unique
3409 Value *BEValueV = nullptr, *StartValueV = nullptr;
3410 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
3411 Value *V = PN->getIncomingValue(i);
3412 if (L->contains(PN->getIncomingBlock(i))) {
3415 } else if (BEValueV != V) {
3419 } else if (!StartValueV) {
3421 } else if (StartValueV != V) {
3422 StartValueV = nullptr;
3426 if (BEValueV && StartValueV) {
3427 // While we are analyzing this PHI node, handle its value symbolically.
3428 const SCEV *SymbolicName = getUnknown(PN);
3429 assert(ValueExprMap.find_as(PN) == ValueExprMap.end() &&
3430 "PHI node already processed?");
3431 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
3433 // Using this symbolic name for the PHI, analyze the value coming around
3435 const SCEV *BEValue = getSCEV(BEValueV);
3437 // NOTE: If BEValue is loop invariant, we know that the PHI node just
3438 // has a special value for the first iteration of the loop.
3440 // If the value coming around the backedge is an add with the symbolic
3441 // value we just inserted, then we found a simple induction variable!
3442 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
3443 // If there is a single occurrence of the symbolic value, replace it
3444 // with a recurrence.
3445 unsigned FoundIndex = Add->getNumOperands();
3446 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3447 if (Add->getOperand(i) == SymbolicName)
3448 if (FoundIndex == e) {
3453 if (FoundIndex != Add->getNumOperands()) {
3454 // Create an add with everything but the specified operand.
3455 SmallVector<const SCEV *, 8> Ops;
3456 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3457 if (i != FoundIndex)
3458 Ops.push_back(Add->getOperand(i));
3459 const SCEV *Accum = getAddExpr(Ops);
3461 // This is not a valid addrec if the step amount is varying each
3462 // loop iteration, but is not itself an addrec in this loop.
3463 if (isLoopInvariant(Accum, L) ||
3464 (isa<SCEVAddRecExpr>(Accum) &&
3465 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
3466 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
3468 // If the increment doesn't overflow, then neither the addrec nor
3469 // the post-increment will overflow.
3470 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) {
3471 if (OBO->hasNoUnsignedWrap())
3472 Flags = setFlags(Flags, SCEV::FlagNUW);
3473 if (OBO->hasNoSignedWrap())
3474 Flags = setFlags(Flags, SCEV::FlagNSW);
3475 } else if (GEPOperator *GEP = dyn_cast<GEPOperator>(BEValueV)) {
3476 // If the increment is an inbounds GEP, then we know the address
3477 // space cannot be wrapped around. We cannot make any guarantee
3478 // about signed or unsigned overflow because pointers are
3479 // unsigned but we may have a negative index from the base
3480 // pointer. We can guarantee that no unsigned wrap occurs if the
3481 // indices form a positive value.
3482 if (GEP->isInBounds()) {
3483 Flags = setFlags(Flags, SCEV::FlagNW);
3485 const SCEV *Ptr = getSCEV(GEP->getPointerOperand());
3486 if (isKnownPositive(getMinusSCEV(getSCEV(GEP), Ptr)))
3487 Flags = setFlags(Flags, SCEV::FlagNUW);
3490 // We cannot transfer nuw and nsw flags from subtraction
3491 // operations -- sub nuw X, Y is not the same as add nuw X, -Y
3495 const SCEV *StartVal = getSCEV(StartValueV);
3496 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
3498 // Since the no-wrap flags are on the increment, they apply to the
3499 // post-incremented value as well.
3500 if (isLoopInvariant(Accum, L))
3501 (void)getAddRecExpr(getAddExpr(StartVal, Accum),
3504 // Okay, for the entire analysis of this edge we assumed the PHI
3505 // to be symbolic. We now need to go back and purge all of the
3506 // entries for the scalars that use the symbolic expression.
3507 ForgetSymbolicName(PN, SymbolicName);
3508 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3512 } else if (const SCEVAddRecExpr *AddRec =
3513 dyn_cast<SCEVAddRecExpr>(BEValue)) {
3514 // Otherwise, this could be a loop like this:
3515 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
3516 // In this case, j = {1,+,1} and BEValue is j.
3517 // Because the other in-value of i (0) fits the evolution of BEValue
3518 // i really is an addrec evolution.
3519 if (AddRec->getLoop() == L && AddRec->isAffine()) {
3520 const SCEV *StartVal = getSCEV(StartValueV);
3522 // If StartVal = j.start - j.stride, we can use StartVal as the
3523 // initial step of the addrec evolution.
3524 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
3525 AddRec->getOperand(1))) {
3526 // FIXME: For constant StartVal, we should be able to infer
3528 const SCEV *PHISCEV =
3529 getAddRecExpr(StartVal, AddRec->getOperand(1), L,
3532 // Okay, for the entire analysis of this edge we assumed the PHI
3533 // to be symbolic. We now need to go back and purge all of the
3534 // entries for the scalars that use the symbolic expression.
3535 ForgetSymbolicName(PN, SymbolicName);
3536 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3544 // If the PHI has a single incoming value, follow that value, unless the
3545 // PHI's incoming blocks are in a different loop, in which case doing so
3546 // risks breaking LCSSA form. Instcombine would normally zap these, but
3547 // it doesn't have DominatorTree information, so it may miss cases.
3548 if (Value *V = SimplifyInstruction(PN, DL, TLI, DT, AC))
3549 if (LI->replacementPreservesLCSSAForm(PN, V))
3552 // If it's not a loop phi, we can't handle it yet.
3553 return getUnknown(PN);
3556 /// createNodeForGEP - Expand GEP instructions into add and multiply
3557 /// operations. This allows them to be analyzed by regular SCEV code.
3559 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
3560 Type *IntPtrTy = getEffectiveSCEVType(GEP->getType());
3561 Value *Base = GEP->getOperand(0);
3562 // Don't attempt to analyze GEPs over unsized objects.
3563 if (!Base->getType()->getPointerElementType()->isSized())
3564 return getUnknown(GEP);
3566 // Don't blindly transfer the inbounds flag from the GEP instruction to the
3567 // Add expression, because the Instruction may be guarded by control flow
3568 // and the no-overflow bits may not be valid for the expression in any
3570 SCEV::NoWrapFlags Wrap = GEP->isInBounds() ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
3572 const SCEV *TotalOffset = getConstant(IntPtrTy, 0);
3573 gep_type_iterator GTI = gep_type_begin(GEP);
3574 for (GetElementPtrInst::op_iterator I = std::next(GEP->op_begin()),
3578 // Compute the (potentially symbolic) offset in bytes for this index.
3579 if (StructType *STy = dyn_cast<StructType>(*GTI++)) {
3580 // For a struct, add the member offset.
3581 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
3582 const SCEV *FieldOffset = getOffsetOfExpr(IntPtrTy, STy, FieldNo);
3584 // Add the field offset to the running total offset.
3585 TotalOffset = getAddExpr(TotalOffset, FieldOffset);
3587 // For an array, add the element offset, explicitly scaled.
3588 const SCEV *ElementSize = getSizeOfExpr(IntPtrTy, *GTI);
3589 const SCEV *IndexS = getSCEV(Index);
3590 // Getelementptr indices are signed.
3591 IndexS = getTruncateOrSignExtend(IndexS, IntPtrTy);
3593 // Multiply the index by the element size to compute the element offset.
3594 const SCEV *LocalOffset = getMulExpr(IndexS, ElementSize, Wrap);
3596 // Add the element offset to the running total offset.
3597 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
3601 // Get the SCEV for the GEP base.
3602 const SCEV *BaseS = getSCEV(Base);
3604 // Add the total offset from all the GEP indices to the base.
3605 return getAddExpr(BaseS, TotalOffset, Wrap);
3608 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
3609 /// guaranteed to end in (at every loop iteration). It is, at the same time,
3610 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
3611 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
3613 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
3614 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3615 return C->getValue()->getValue().countTrailingZeros();
3617 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
3618 return std::min(GetMinTrailingZeros(T->getOperand()),
3619 (uint32_t)getTypeSizeInBits(T->getType()));
3621 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
3622 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3623 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3624 getTypeSizeInBits(E->getType()) : OpRes;
3627 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
3628 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3629 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3630 getTypeSizeInBits(E->getType()) : OpRes;
3633 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
3634 // The result is the min of all operands results.
3635 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3636 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3637 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3641 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
3642 // The result is the sum of all operands results.
3643 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
3644 uint32_t BitWidth = getTypeSizeInBits(M->getType());
3645 for (unsigned i = 1, e = M->getNumOperands();
3646 SumOpRes != BitWidth && i != e; ++i)
3647 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
3652 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
3653 // The result is the min of all operands results.
3654 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3655 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3656 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3660 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
3661 // The result is the min of all operands results.
3662 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3663 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3664 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3668 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
3669 // The result is the min of all operands results.
3670 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3671 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3672 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3676 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3677 // For a SCEVUnknown, ask ValueTracking.
3678 unsigned BitWidth = getTypeSizeInBits(U->getType());
3679 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3680 computeKnownBits(U->getValue(), Zeros, Ones, DL, 0, AC, nullptr, DT);
3681 return Zeros.countTrailingOnes();
3688 /// GetRangeFromMetadata - Helper method to assign a range to V from
3689 /// metadata present in the IR.
3690 static Optional<ConstantRange> GetRangeFromMetadata(Value *V) {
3691 if (Instruction *I = dyn_cast<Instruction>(V)) {
3692 if (MDNode *MD = I->getMetadata(LLVMContext::MD_range)) {
3693 ConstantRange TotalRange(
3694 cast<IntegerType>(I->getType())->getBitWidth(), false);
3696 unsigned NumRanges = MD->getNumOperands() / 2;
3697 assert(NumRanges >= 1);
3699 for (unsigned i = 0; i < NumRanges; ++i) {
3700 ConstantInt *Lower =
3701 mdconst::extract<ConstantInt>(MD->getOperand(2 * i + 0));
3702 ConstantInt *Upper =
3703 mdconst::extract<ConstantInt>(MD->getOperand(2 * i + 1));
3704 ConstantRange Range(Lower->getValue(), Upper->getValue());
3705 TotalRange = TotalRange.unionWith(Range);
3715 /// getUnsignedRange - Determine the unsigned range for a particular SCEV.
3718 ScalarEvolution::getUnsignedRange(const SCEV *S) {
3719 // See if we've computed this range already.
3720 DenseMap<const SCEV *, ConstantRange>::iterator I = UnsignedRanges.find(S);
3721 if (I != UnsignedRanges.end())
3724 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3725 return setUnsignedRange(C, ConstantRange(C->getValue()->getValue()));
3727 unsigned BitWidth = getTypeSizeInBits(S->getType());
3728 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3730 // If the value has known zeros, the maximum unsigned value will have those
3731 // known zeros as well.
3732 uint32_t TZ = GetMinTrailingZeros(S);
3734 ConservativeResult =
3735 ConstantRange(APInt::getMinValue(BitWidth),
3736 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
3738 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3739 ConstantRange X = getUnsignedRange(Add->getOperand(0));
3740 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3741 X = X.add(getUnsignedRange(Add->getOperand(i)));
3742 return setUnsignedRange(Add, ConservativeResult.intersectWith(X));
3745 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3746 ConstantRange X = getUnsignedRange(Mul->getOperand(0));
3747 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3748 X = X.multiply(getUnsignedRange(Mul->getOperand(i)));
3749 return setUnsignedRange(Mul, ConservativeResult.intersectWith(X));
3752 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3753 ConstantRange X = getUnsignedRange(SMax->getOperand(0));
3754 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3755 X = X.smax(getUnsignedRange(SMax->getOperand(i)));
3756 return setUnsignedRange(SMax, ConservativeResult.intersectWith(X));
3759 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3760 ConstantRange X = getUnsignedRange(UMax->getOperand(0));
3761 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3762 X = X.umax(getUnsignedRange(UMax->getOperand(i)));
3763 return setUnsignedRange(UMax, ConservativeResult.intersectWith(X));
3766 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3767 ConstantRange X = getUnsignedRange(UDiv->getLHS());
3768 ConstantRange Y = getUnsignedRange(UDiv->getRHS());
3769 return setUnsignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y)));
3772 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3773 ConstantRange X = getUnsignedRange(ZExt->getOperand());
3774 return setUnsignedRange(ZExt,
3775 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3778 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3779 ConstantRange X = getUnsignedRange(SExt->getOperand());
3780 return setUnsignedRange(SExt,
3781 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3784 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3785 ConstantRange X = getUnsignedRange(Trunc->getOperand());
3786 return setUnsignedRange(Trunc,
3787 ConservativeResult.intersectWith(X.truncate(BitWidth)));
3790 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3791 // If there's no unsigned wrap, the value will never be less than its
3793 if (AddRec->getNoWrapFlags(SCEV::FlagNUW))
3794 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
3795 if (!C->getValue()->isZero())
3796 ConservativeResult =
3797 ConservativeResult.intersectWith(
3798 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0)));
3800 // TODO: non-affine addrec
3801 if (AddRec->isAffine()) {
3802 Type *Ty = AddRec->getType();
3803 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3804 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3805 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3806 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3808 const SCEV *Start = AddRec->getStart();
3809 const SCEV *Step = AddRec->getStepRecurrence(*this);
3811 ConstantRange StartRange = getUnsignedRange(Start);
3812 ConstantRange StepRange = getSignedRange(Step);
3813 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3814 ConstantRange EndRange =
3815 StartRange.add(MaxBECountRange.multiply(StepRange));
3817 // Check for overflow. This must be done with ConstantRange arithmetic
3818 // because we could be called from within the ScalarEvolution overflow
3820 ConstantRange ExtStartRange = StartRange.zextOrTrunc(BitWidth*2+1);
3821 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3822 ConstantRange ExtMaxBECountRange =
3823 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3824 ConstantRange ExtEndRange = EndRange.zextOrTrunc(BitWidth*2+1);
3825 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3827 return setUnsignedRange(AddRec, ConservativeResult);
3829 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(),
3830 EndRange.getUnsignedMin());
3831 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(),
3832 EndRange.getUnsignedMax());
3833 if (Min.isMinValue() && Max.isMaxValue())
3834 return setUnsignedRange(AddRec, ConservativeResult);
3835 return setUnsignedRange(AddRec,
3836 ConservativeResult.intersectWith(ConstantRange(Min, Max+1)));
3840 return setUnsignedRange(AddRec, ConservativeResult);
3843 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3844 // Check if the IR explicitly contains !range metadata.
3845 Optional<ConstantRange> MDRange = GetRangeFromMetadata(U->getValue());
3846 if (MDRange.hasValue())
3847 ConservativeResult = ConservativeResult.intersectWith(MDRange.getValue());
3849 // For a SCEVUnknown, ask ValueTracking.
3850 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3851 computeKnownBits(U->getValue(), Zeros, Ones, DL, 0, AC, nullptr, DT);
3852 if (Ones == ~Zeros + 1)
3853 return setUnsignedRange(U, ConservativeResult);
3854 return setUnsignedRange(U,
3855 ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1)));
3858 return setUnsignedRange(S, ConservativeResult);
3861 /// getSignedRange - Determine the signed range for a particular SCEV.
3864 ScalarEvolution::getSignedRange(const SCEV *S) {
3865 // See if we've computed this range already.
3866 DenseMap<const SCEV *, ConstantRange>::iterator I = SignedRanges.find(S);
3867 if (I != SignedRanges.end())
3870 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3871 return setSignedRange(C, ConstantRange(C->getValue()->getValue()));
3873 unsigned BitWidth = getTypeSizeInBits(S->getType());
3874 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3876 // If the value has known zeros, the maximum signed value will have those
3877 // known zeros as well.
3878 uint32_t TZ = GetMinTrailingZeros(S);
3880 ConservativeResult =
3881 ConstantRange(APInt::getSignedMinValue(BitWidth),
3882 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
3884 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3885 ConstantRange X = getSignedRange(Add->getOperand(0));
3886 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3887 X = X.add(getSignedRange(Add->getOperand(i)));
3888 return setSignedRange(Add, ConservativeResult.intersectWith(X));
3891 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3892 ConstantRange X = getSignedRange(Mul->getOperand(0));
3893 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3894 X = X.multiply(getSignedRange(Mul->getOperand(i)));
3895 return setSignedRange(Mul, ConservativeResult.intersectWith(X));
3898 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3899 ConstantRange X = getSignedRange(SMax->getOperand(0));
3900 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3901 X = X.smax(getSignedRange(SMax->getOperand(i)));
3902 return setSignedRange(SMax, ConservativeResult.intersectWith(X));
3905 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3906 ConstantRange X = getSignedRange(UMax->getOperand(0));
3907 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3908 X = X.umax(getSignedRange(UMax->getOperand(i)));
3909 return setSignedRange(UMax, ConservativeResult.intersectWith(X));
3912 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3913 ConstantRange X = getSignedRange(UDiv->getLHS());
3914 ConstantRange Y = getSignedRange(UDiv->getRHS());
3915 return setSignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y)));
3918 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3919 ConstantRange X = getSignedRange(ZExt->getOperand());
3920 return setSignedRange(ZExt,
3921 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3924 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3925 ConstantRange X = getSignedRange(SExt->getOperand());
3926 return setSignedRange(SExt,
3927 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3930 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3931 ConstantRange X = getSignedRange(Trunc->getOperand());
3932 return setSignedRange(Trunc,
3933 ConservativeResult.intersectWith(X.truncate(BitWidth)));
3936 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3937 // If there's no signed wrap, and all the operands have the same sign or
3938 // zero, the value won't ever change sign.
3939 if (AddRec->getNoWrapFlags(SCEV::FlagNSW)) {
3940 bool AllNonNeg = true;
3941 bool AllNonPos = true;
3942 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
3943 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
3944 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
3947 ConservativeResult = ConservativeResult.intersectWith(
3948 ConstantRange(APInt(BitWidth, 0),
3949 APInt::getSignedMinValue(BitWidth)));
3951 ConservativeResult = ConservativeResult.intersectWith(
3952 ConstantRange(APInt::getSignedMinValue(BitWidth),
3953 APInt(BitWidth, 1)));
3956 // TODO: non-affine addrec
3957 if (AddRec->isAffine()) {
3958 Type *Ty = AddRec->getType();
3959 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3960 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3961 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3962 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3964 const SCEV *Start = AddRec->getStart();
3965 const SCEV *Step = AddRec->getStepRecurrence(*this);
3967 ConstantRange StartRange = getSignedRange(Start);
3968 ConstantRange StepRange = getSignedRange(Step);
3969 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3970 ConstantRange EndRange =
3971 StartRange.add(MaxBECountRange.multiply(StepRange));
3973 // Check for overflow. This must be done with ConstantRange arithmetic
3974 // because we could be called from within the ScalarEvolution overflow
3976 ConstantRange ExtStartRange = StartRange.sextOrTrunc(BitWidth*2+1);
3977 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3978 ConstantRange ExtMaxBECountRange =
3979 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3980 ConstantRange ExtEndRange = EndRange.sextOrTrunc(BitWidth*2+1);
3981 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3983 return setSignedRange(AddRec, ConservativeResult);
3985 APInt Min = APIntOps::smin(StartRange.getSignedMin(),
3986 EndRange.getSignedMin());
3987 APInt Max = APIntOps::smax(StartRange.getSignedMax(),
3988 EndRange.getSignedMax());
3989 if (Min.isMinSignedValue() && Max.isMaxSignedValue())
3990 return setSignedRange(AddRec, ConservativeResult);
3991 return setSignedRange(AddRec,
3992 ConservativeResult.intersectWith(ConstantRange(Min, Max+1)));
3996 return setSignedRange(AddRec, ConservativeResult);
3999 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
4000 // Check if the IR explicitly contains !range metadata.
4001 Optional<ConstantRange> MDRange = GetRangeFromMetadata(U->getValue());
4002 if (MDRange.hasValue())
4003 ConservativeResult = ConservativeResult.intersectWith(MDRange.getValue());
4005 // For a SCEVUnknown, ask ValueTracking.
4006 if (!U->getValue()->getType()->isIntegerTy() && !DL)
4007 return setSignedRange(U, ConservativeResult);
4008 unsigned NS = ComputeNumSignBits(U->getValue(), DL, 0, AC, nullptr, DT);
4010 return setSignedRange(U, ConservativeResult);
4011 return setSignedRange(U, ConservativeResult.intersectWith(
4012 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
4013 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1)));
4016 return setSignedRange(S, ConservativeResult);
4019 /// createSCEV - We know that there is no SCEV for the specified value.
4020 /// Analyze the expression.
4022 const SCEV *ScalarEvolution::createSCEV(Value *V) {
4023 if (!isSCEVable(V->getType()))
4024 return getUnknown(V);
4026 unsigned Opcode = Instruction::UserOp1;
4027 if (Instruction *I = dyn_cast<Instruction>(V)) {
4028 Opcode = I->getOpcode();
4030 // Don't attempt to analyze instructions in blocks that aren't
4031 // reachable. Such instructions don't matter, and they aren't required
4032 // to obey basic rules for definitions dominating uses which this
4033 // analysis depends on.
4034 if (!DT->isReachableFromEntry(I->getParent()))
4035 return getUnknown(V);
4036 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
4037 Opcode = CE->getOpcode();
4038 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
4039 return getConstant(CI);
4040 else if (isa<ConstantPointerNull>(V))
4041 return getConstant(V->getType(), 0);
4042 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
4043 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee());
4045 return getUnknown(V);
4047 Operator *U = cast<Operator>(V);
4049 case Instruction::Add: {
4050 // The simple thing to do would be to just call getSCEV on both operands
4051 // and call getAddExpr with the result. However if we're looking at a
4052 // bunch of things all added together, this can be quite inefficient,
4053 // because it leads to N-1 getAddExpr calls for N ultimate operands.
4054 // Instead, gather up all the operands and make a single getAddExpr call.
4055 // LLVM IR canonical form means we need only traverse the left operands.
4057 // Don't apply this instruction's NSW or NUW flags to the new
4058 // expression. The instruction may be guarded by control flow that the
4059 // no-wrap behavior depends on. Non-control-equivalent instructions can be
4060 // mapped to the same SCEV expression, and it would be incorrect to transfer
4061 // NSW/NUW semantics to those operations.
4062 SmallVector<const SCEV *, 4> AddOps;
4063 AddOps.push_back(getSCEV(U->getOperand(1)));
4064 for (Value *Op = U->getOperand(0); ; Op = U->getOperand(0)) {
4065 unsigned Opcode = Op->getValueID() - Value::InstructionVal;
4066 if (Opcode != Instruction::Add && Opcode != Instruction::Sub)
4068 U = cast<Operator>(Op);
4069 const SCEV *Op1 = getSCEV(U->getOperand(1));
4070 if (Opcode == Instruction::Sub)
4071 AddOps.push_back(getNegativeSCEV(Op1));
4073 AddOps.push_back(Op1);
4075 AddOps.push_back(getSCEV(U->getOperand(0)));
4076 return getAddExpr(AddOps);
4078 case Instruction::Mul: {
4079 // Don't transfer NSW/NUW for the same reason as AddExpr.
4080 SmallVector<const SCEV *, 4> MulOps;
4081 MulOps.push_back(getSCEV(U->getOperand(1)));
4082 for (Value *Op = U->getOperand(0);
4083 Op->getValueID() == Instruction::Mul + Value::InstructionVal;
4084 Op = U->getOperand(0)) {
4085 U = cast<Operator>(Op);
4086 MulOps.push_back(getSCEV(U->getOperand(1)));
4088 MulOps.push_back(getSCEV(U->getOperand(0)));
4089 return getMulExpr(MulOps);
4091 case Instruction::UDiv:
4092 return getUDivExpr(getSCEV(U->getOperand(0)),
4093 getSCEV(U->getOperand(1)));
4094 case Instruction::Sub:
4095 return getMinusSCEV(getSCEV(U->getOperand(0)),
4096 getSCEV(U->getOperand(1)));
4097 case Instruction::And:
4098 // For an expression like x&255 that merely masks off the high bits,
4099 // use zext(trunc(x)) as the SCEV expression.
4100 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
4101 if (CI->isNullValue())
4102 return getSCEV(U->getOperand(1));
4103 if (CI->isAllOnesValue())
4104 return getSCEV(U->getOperand(0));
4105 const APInt &A = CI->getValue();
4107 // Instcombine's ShrinkDemandedConstant may strip bits out of
4108 // constants, obscuring what would otherwise be a low-bits mask.
4109 // Use computeKnownBits to compute what ShrinkDemandedConstant
4110 // knew about to reconstruct a low-bits mask value.
4111 unsigned LZ = A.countLeadingZeros();
4112 unsigned TZ = A.countTrailingZeros();
4113 unsigned BitWidth = A.getBitWidth();
4114 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
4115 computeKnownBits(U->getOperand(0), KnownZero, KnownOne, DL, 0, AC,
4118 APInt EffectiveMask =
4119 APInt::getLowBitsSet(BitWidth, BitWidth - LZ - TZ).shl(TZ);
4120 if ((LZ != 0 || TZ != 0) && !((~A & ~KnownZero) & EffectiveMask)) {
4121 const SCEV *MulCount = getConstant(
4122 ConstantInt::get(getContext(), APInt::getOneBitSet(BitWidth, TZ)));
4126 getUDivExactExpr(getSCEV(U->getOperand(0)), MulCount),
4127 IntegerType::get(getContext(), BitWidth - LZ - TZ)),
4134 case Instruction::Or:
4135 // If the RHS of the Or is a constant, we may have something like:
4136 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
4137 // optimizations will transparently handle this case.
4139 // In order for this transformation to be safe, the LHS must be of the
4140 // form X*(2^n) and the Or constant must be less than 2^n.
4141 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
4142 const SCEV *LHS = getSCEV(U->getOperand(0));
4143 const APInt &CIVal = CI->getValue();
4144 if (GetMinTrailingZeros(LHS) >=
4145 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
4146 // Build a plain add SCEV.
4147 const SCEV *S = getAddExpr(LHS, getSCEV(CI));
4148 // If the LHS of the add was an addrec and it has no-wrap flags,
4149 // transfer the no-wrap flags, since an or won't introduce a wrap.
4150 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
4151 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
4152 const_cast<SCEVAddRecExpr *>(NewAR)->setNoWrapFlags(
4153 OldAR->getNoWrapFlags());
4159 case Instruction::Xor:
4160 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
4161 // If the RHS of the xor is a signbit, then this is just an add.
4162 // Instcombine turns add of signbit into xor as a strength reduction step.
4163 if (CI->getValue().isSignBit())
4164 return getAddExpr(getSCEV(U->getOperand(0)),
4165 getSCEV(U->getOperand(1)));
4167 // If the RHS of xor is -1, then this is a not operation.
4168 if (CI->isAllOnesValue())
4169 return getNotSCEV(getSCEV(U->getOperand(0)));
4171 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
4172 // This is a variant of the check for xor with -1, and it handles
4173 // the case where instcombine has trimmed non-demanded bits out
4174 // of an xor with -1.
4175 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
4176 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
4177 if (BO->getOpcode() == Instruction::And &&
4178 LCI->getValue() == CI->getValue())
4179 if (const SCEVZeroExtendExpr *Z =
4180 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
4181 Type *UTy = U->getType();
4182 const SCEV *Z0 = Z->getOperand();
4183 Type *Z0Ty = Z0->getType();
4184 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
4186 // If C is a low-bits mask, the zero extend is serving to
4187 // mask off the high bits. Complement the operand and
4188 // re-apply the zext.
4189 if (APIntOps::isMask(Z0TySize, CI->getValue()))
4190 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
4192 // If C is a single bit, it may be in the sign-bit position
4193 // before the zero-extend. In this case, represent the xor
4194 // using an add, which is equivalent, and re-apply the zext.
4195 APInt Trunc = CI->getValue().trunc(Z0TySize);
4196 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
4198 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
4204 case Instruction::Shl:
4205 // Turn shift left of a constant amount into a multiply.
4206 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
4207 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
4209 // If the shift count is not less than the bitwidth, the result of
4210 // the shift is undefined. Don't try to analyze it, because the
4211 // resolution chosen here may differ from the resolution chosen in
4212 // other parts of the compiler.
4213 if (SA->getValue().uge(BitWidth))
4216 Constant *X = ConstantInt::get(getContext(),
4217 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
4218 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
4222 case Instruction::LShr:
4223 // Turn logical shift right of a constant into a unsigned divide.
4224 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
4225 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
4227 // If the shift count is not less than the bitwidth, the result of
4228 // the shift is undefined. Don't try to analyze it, because the
4229 // resolution chosen here may differ from the resolution chosen in
4230 // other parts of the compiler.
4231 if (SA->getValue().uge(BitWidth))
4234 Constant *X = ConstantInt::get(getContext(),
4235 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
4236 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
4240 case Instruction::AShr:
4241 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
4242 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
4243 if (Operator *L = dyn_cast<Operator>(U->getOperand(0)))
4244 if (L->getOpcode() == Instruction::Shl &&
4245 L->getOperand(1) == U->getOperand(1)) {
4246 uint64_t BitWidth = getTypeSizeInBits(U->getType());
4248 // If the shift count is not less than the bitwidth, the result of
4249 // the shift is undefined. Don't try to analyze it, because the
4250 // resolution chosen here may differ from the resolution chosen in
4251 // other parts of the compiler.
4252 if (CI->getValue().uge(BitWidth))
4255 uint64_t Amt = BitWidth - CI->getZExtValue();
4256 if (Amt == BitWidth)
4257 return getSCEV(L->getOperand(0)); // shift by zero --> noop
4259 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
4260 IntegerType::get(getContext(),
4266 case Instruction::Trunc:
4267 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
4269 case Instruction::ZExt:
4270 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
4272 case Instruction::SExt:
4273 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
4275 case Instruction::BitCast:
4276 // BitCasts are no-op casts so we just eliminate the cast.
4277 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
4278 return getSCEV(U->getOperand(0));
4281 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
4282 // lead to pointer expressions which cannot safely be expanded to GEPs,
4283 // because ScalarEvolution doesn't respect the GEP aliasing rules when
4284 // simplifying integer expressions.
4286 case Instruction::GetElementPtr:
4287 return createNodeForGEP(cast<GEPOperator>(U));
4289 case Instruction::PHI:
4290 return createNodeForPHI(cast<PHINode>(U));
4292 case Instruction::Select:
4293 // This could be a smax or umax that was lowered earlier.
4294 // Try to recover it.
4295 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
4296 Value *LHS = ICI->getOperand(0);
4297 Value *RHS = ICI->getOperand(1);
4298 switch (ICI->getPredicate()) {
4299 case ICmpInst::ICMP_SLT:
4300 case ICmpInst::ICMP_SLE:
4301 std::swap(LHS, RHS);
4303 case ICmpInst::ICMP_SGT:
4304 case ICmpInst::ICMP_SGE:
4305 // a >s b ? a+x : b+x -> smax(a, b)+x
4306 // a >s b ? b+x : a+x -> smin(a, b)+x
4307 if (getTypeSizeInBits(LHS->getType()) <=
4308 getTypeSizeInBits(U->getType())) {
4309 const SCEV *LS = getNoopOrSignExtend(getSCEV(LHS), U->getType());
4310 const SCEV *RS = getNoopOrSignExtend(getSCEV(RHS), U->getType());
4311 const SCEV *LA = getSCEV(U->getOperand(1));
4312 const SCEV *RA = getSCEV(U->getOperand(2));
4313 const SCEV *LDiff = getMinusSCEV(LA, LS);
4314 const SCEV *RDiff = getMinusSCEV(RA, RS);
4316 return getAddExpr(getSMaxExpr(LS, RS), LDiff);
4317 LDiff = getMinusSCEV(LA, RS);
4318 RDiff = getMinusSCEV(RA, LS);
4320 return getAddExpr(getSMinExpr(LS, RS), LDiff);
4323 case ICmpInst::ICMP_ULT:
4324 case ICmpInst::ICMP_ULE:
4325 std::swap(LHS, RHS);
4327 case ICmpInst::ICMP_UGT:
4328 case ICmpInst::ICMP_UGE:
4329 // a >u b ? a+x : b+x -> umax(a, b)+x
4330 // a >u b ? b+x : a+x -> umin(a, b)+x
4331 if (getTypeSizeInBits(LHS->getType()) <=
4332 getTypeSizeInBits(U->getType())) {
4333 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), U->getType());
4334 const SCEV *RS = getNoopOrZeroExtend(getSCEV(RHS), U->getType());
4335 const SCEV *LA = getSCEV(U->getOperand(1));
4336 const SCEV *RA = getSCEV(U->getOperand(2));
4337 const SCEV *LDiff = getMinusSCEV(LA, LS);
4338 const SCEV *RDiff = getMinusSCEV(RA, RS);
4340 return getAddExpr(getUMaxExpr(LS, RS), LDiff);
4341 LDiff = getMinusSCEV(LA, RS);
4342 RDiff = getMinusSCEV(RA, LS);
4344 return getAddExpr(getUMinExpr(LS, RS), LDiff);
4347 case ICmpInst::ICMP_NE:
4348 // n != 0 ? n+x : 1+x -> umax(n, 1)+x
4349 if (getTypeSizeInBits(LHS->getType()) <=
4350 getTypeSizeInBits(U->getType()) &&
4351 isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
4352 const SCEV *One = getConstant(U->getType(), 1);
4353 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), U->getType());
4354 const SCEV *LA = getSCEV(U->getOperand(1));
4355 const SCEV *RA = getSCEV(U->getOperand(2));
4356 const SCEV *LDiff = getMinusSCEV(LA, LS);
4357 const SCEV *RDiff = getMinusSCEV(RA, One);
4359 return getAddExpr(getUMaxExpr(One, LS), LDiff);
4362 case ICmpInst::ICMP_EQ:
4363 // n == 0 ? 1+x : n+x -> umax(n, 1)+x
4364 if (getTypeSizeInBits(LHS->getType()) <=
4365 getTypeSizeInBits(U->getType()) &&
4366 isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
4367 const SCEV *One = getConstant(U->getType(), 1);
4368 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), U->getType());
4369 const SCEV *LA = getSCEV(U->getOperand(1));
4370 const SCEV *RA = getSCEV(U->getOperand(2));
4371 const SCEV *LDiff = getMinusSCEV(LA, One);
4372 const SCEV *RDiff = getMinusSCEV(RA, LS);
4374 return getAddExpr(getUMaxExpr(One, LS), LDiff);
4382 default: // We cannot analyze this expression.
4386 return getUnknown(V);
4391 //===----------------------------------------------------------------------===//
4392 // Iteration Count Computation Code
4395 unsigned ScalarEvolution::getSmallConstantTripCount(Loop *L) {
4396 if (BasicBlock *ExitingBB = L->getExitingBlock())
4397 return getSmallConstantTripCount(L, ExitingBB);
4399 // No trip count information for multiple exits.
4403 /// getSmallConstantTripCount - Returns the maximum trip count of this loop as a
4404 /// normal unsigned value. Returns 0 if the trip count is unknown or not
4405 /// constant. Will also return 0 if the maximum trip count is very large (>=
4408 /// This "trip count" assumes that control exits via ExitingBlock. More
4409 /// precisely, it is the number of times that control may reach ExitingBlock
4410 /// before taking the branch. For loops with multiple exits, it may not be the
4411 /// number times that the loop header executes because the loop may exit
4412 /// prematurely via another branch.
4413 unsigned ScalarEvolution::getSmallConstantTripCount(Loop *L,
4414 BasicBlock *ExitingBlock) {
4415 assert(ExitingBlock && "Must pass a non-null exiting block!");
4416 assert(L->isLoopExiting(ExitingBlock) &&
4417 "Exiting block must actually branch out of the loop!");
4418 const SCEVConstant *ExitCount =
4419 dyn_cast<SCEVConstant>(getExitCount(L, ExitingBlock));
4423 ConstantInt *ExitConst = ExitCount->getValue();
4425 // Guard against huge trip counts.
4426 if (ExitConst->getValue().getActiveBits() > 32)
4429 // In case of integer overflow, this returns 0, which is correct.
4430 return ((unsigned)ExitConst->getZExtValue()) + 1;
4433 unsigned ScalarEvolution::getSmallConstantTripMultiple(Loop *L) {
4434 if (BasicBlock *ExitingBB = L->getExitingBlock())
4435 return getSmallConstantTripMultiple(L, ExitingBB);
4437 // No trip multiple information for multiple exits.
4441 /// getSmallConstantTripMultiple - Returns the largest constant divisor of the
4442 /// trip count of this loop as a normal unsigned value, if possible. This
4443 /// means that the actual trip count is always a multiple of the returned
4444 /// value (don't forget the trip count could very well be zero as well!).
4446 /// Returns 1 if the trip count is unknown or not guaranteed to be the
4447 /// multiple of a constant (which is also the case if the trip count is simply
4448 /// constant, use getSmallConstantTripCount for that case), Will also return 1
4449 /// if the trip count is very large (>= 2^32).
4451 /// As explained in the comments for getSmallConstantTripCount, this assumes
4452 /// that control exits the loop via ExitingBlock.
4454 ScalarEvolution::getSmallConstantTripMultiple(Loop *L,
4455 BasicBlock *ExitingBlock) {
4456 assert(ExitingBlock && "Must pass a non-null exiting block!");
4457 assert(L->isLoopExiting(ExitingBlock) &&
4458 "Exiting block must actually branch out of the loop!");
4459 const SCEV *ExitCount = getExitCount(L, ExitingBlock);
4460 if (ExitCount == getCouldNotCompute())
4463 // Get the trip count from the BE count by adding 1.
4464 const SCEV *TCMul = getAddExpr(ExitCount,
4465 getConstant(ExitCount->getType(), 1));
4466 // FIXME: SCEV distributes multiplication as V1*C1 + V2*C1. We could attempt
4467 // to factor simple cases.
4468 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(TCMul))
4469 TCMul = Mul->getOperand(0);
4471 const SCEVConstant *MulC = dyn_cast<SCEVConstant>(TCMul);
4475 ConstantInt *Result = MulC->getValue();
4477 // Guard against huge trip counts (this requires checking
4478 // for zero to handle the case where the trip count == -1 and the
4480 if (!Result || Result->getValue().getActiveBits() > 32 ||
4481 Result->getValue().getActiveBits() == 0)
4484 return (unsigned)Result->getZExtValue();
4487 // getExitCount - Get the expression for the number of loop iterations for which
4488 // this loop is guaranteed not to exit via ExitingBlock. Otherwise return
4489 // SCEVCouldNotCompute.
4490 const SCEV *ScalarEvolution::getExitCount(Loop *L, BasicBlock *ExitingBlock) {
4491 return getBackedgeTakenInfo(L).getExact(ExitingBlock, this);
4494 /// getBackedgeTakenCount - If the specified loop has a predictable
4495 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
4496 /// object. The backedge-taken count is the number of times the loop header
4497 /// will be branched to from within the loop. This is one less than the
4498 /// trip count of the loop, since it doesn't count the first iteration,
4499 /// when the header is branched to from outside the loop.
4501 /// Note that it is not valid to call this method on a loop without a
4502 /// loop-invariant backedge-taken count (see
4503 /// hasLoopInvariantBackedgeTakenCount).
4505 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
4506 return getBackedgeTakenInfo(L).getExact(this);
4509 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
4510 /// return the least SCEV value that is known never to be less than the
4511 /// actual backedge taken count.
4512 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
4513 return getBackedgeTakenInfo(L).getMax(this);
4516 /// PushLoopPHIs - Push PHI nodes in the header of the given loop
4517 /// onto the given Worklist.
4519 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
4520 BasicBlock *Header = L->getHeader();
4522 // Push all Loop-header PHIs onto the Worklist stack.
4523 for (BasicBlock::iterator I = Header->begin();
4524 PHINode *PN = dyn_cast<PHINode>(I); ++I)
4525 Worklist.push_back(PN);
4528 const ScalarEvolution::BackedgeTakenInfo &
4529 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
4530 // Initially insert an invalid entry for this loop. If the insertion
4531 // succeeds, proceed to actually compute a backedge-taken count and
4532 // update the value. The temporary CouldNotCompute value tells SCEV
4533 // code elsewhere that it shouldn't attempt to request a new
4534 // backedge-taken count, which could result in infinite recursion.
4535 std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
4536 BackedgeTakenCounts.insert(std::make_pair(L, BackedgeTakenInfo()));
4538 return Pair.first->second;
4540 // ComputeBackedgeTakenCount may allocate memory for its result. Inserting it
4541 // into the BackedgeTakenCounts map transfers ownership. Otherwise, the result
4542 // must be cleared in this scope.
4543 BackedgeTakenInfo Result = ComputeBackedgeTakenCount(L);
4545 if (Result.getExact(this) != getCouldNotCompute()) {
4546 assert(isLoopInvariant(Result.getExact(this), L) &&
4547 isLoopInvariant(Result.getMax(this), L) &&
4548 "Computed backedge-taken count isn't loop invariant for loop!");
4549 ++NumTripCountsComputed;
4551 else if (Result.getMax(this) == getCouldNotCompute() &&
4552 isa<PHINode>(L->getHeader()->begin())) {
4553 // Only count loops that have phi nodes as not being computable.
4554 ++NumTripCountsNotComputed;
4557 // Now that we know more about the trip count for this loop, forget any
4558 // existing SCEV values for PHI nodes in this loop since they are only
4559 // conservative estimates made without the benefit of trip count
4560 // information. This is similar to the code in forgetLoop, except that
4561 // it handles SCEVUnknown PHI nodes specially.
4562 if (Result.hasAnyInfo()) {
4563 SmallVector<Instruction *, 16> Worklist;
4564 PushLoopPHIs(L, Worklist);
4566 SmallPtrSet<Instruction *, 8> Visited;
4567 while (!Worklist.empty()) {
4568 Instruction *I = Worklist.pop_back_val();
4569 if (!Visited.insert(I).second)
4572 ValueExprMapType::iterator It =
4573 ValueExprMap.find_as(static_cast<Value *>(I));
4574 if (It != ValueExprMap.end()) {
4575 const SCEV *Old = It->second;
4577 // SCEVUnknown for a PHI either means that it has an unrecognized
4578 // structure, or it's a PHI that's in the progress of being computed
4579 // by createNodeForPHI. In the former case, additional loop trip
4580 // count information isn't going to change anything. In the later
4581 // case, createNodeForPHI will perform the necessary updates on its
4582 // own when it gets to that point.
4583 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) {
4584 forgetMemoizedResults(Old);
4585 ValueExprMap.erase(It);
4587 if (PHINode *PN = dyn_cast<PHINode>(I))
4588 ConstantEvolutionLoopExitValue.erase(PN);
4591 PushDefUseChildren(I, Worklist);
4595 // Re-lookup the insert position, since the call to
4596 // ComputeBackedgeTakenCount above could result in a
4597 // recusive call to getBackedgeTakenInfo (on a different
4598 // loop), which would invalidate the iterator computed
4600 return BackedgeTakenCounts.find(L)->second = Result;
4603 /// forgetLoop - This method should be called by the client when it has
4604 /// changed a loop in a way that may effect ScalarEvolution's ability to
4605 /// compute a trip count, or if the loop is deleted.
4606 void ScalarEvolution::forgetLoop(const Loop *L) {
4607 // Drop any stored trip count value.
4608 DenseMap<const Loop*, BackedgeTakenInfo>::iterator BTCPos =
4609 BackedgeTakenCounts.find(L);
4610 if (BTCPos != BackedgeTakenCounts.end()) {
4611 BTCPos->second.clear();
4612 BackedgeTakenCounts.erase(BTCPos);
4615 // Drop information about expressions based on loop-header PHIs.
4616 SmallVector<Instruction *, 16> Worklist;
4617 PushLoopPHIs(L, Worklist);
4619 SmallPtrSet<Instruction *, 8> Visited;
4620 while (!Worklist.empty()) {
4621 Instruction *I = Worklist.pop_back_val();
4622 if (!Visited.insert(I).second)
4625 ValueExprMapType::iterator It =
4626 ValueExprMap.find_as(static_cast<Value *>(I));
4627 if (It != ValueExprMap.end()) {
4628 forgetMemoizedResults(It->second);
4629 ValueExprMap.erase(It);
4630 if (PHINode *PN = dyn_cast<PHINode>(I))
4631 ConstantEvolutionLoopExitValue.erase(PN);
4634 PushDefUseChildren(I, Worklist);
4637 // Forget all contained loops too, to avoid dangling entries in the
4638 // ValuesAtScopes map.
4639 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
4643 /// forgetValue - This method should be called by the client when it has
4644 /// changed a value in a way that may effect its value, or which may
4645 /// disconnect it from a def-use chain linking it to a loop.
4646 void ScalarEvolution::forgetValue(Value *V) {
4647 Instruction *I = dyn_cast<Instruction>(V);
4650 // Drop information about expressions based on loop-header PHIs.
4651 SmallVector<Instruction *, 16> Worklist;
4652 Worklist.push_back(I);
4654 SmallPtrSet<Instruction *, 8> Visited;
4655 while (!Worklist.empty()) {
4656 I = Worklist.pop_back_val();
4657 if (!Visited.insert(I).second)
4660 ValueExprMapType::iterator It =
4661 ValueExprMap.find_as(static_cast<Value *>(I));
4662 if (It != ValueExprMap.end()) {
4663 forgetMemoizedResults(It->second);
4664 ValueExprMap.erase(It);
4665 if (PHINode *PN = dyn_cast<PHINode>(I))
4666 ConstantEvolutionLoopExitValue.erase(PN);
4669 PushDefUseChildren(I, Worklist);
4673 /// getExact - Get the exact loop backedge taken count considering all loop
4674 /// exits. A computable result can only be return for loops with a single exit.
4675 /// Returning the minimum taken count among all exits is incorrect because one
4676 /// of the loop's exit limit's may have been skipped. HowFarToZero assumes that
4677 /// the limit of each loop test is never skipped. This is a valid assumption as
4678 /// long as the loop exits via that test. For precise results, it is the
4679 /// caller's responsibility to specify the relevant loop exit using
4680 /// getExact(ExitingBlock, SE).
4682 ScalarEvolution::BackedgeTakenInfo::getExact(ScalarEvolution *SE) const {
4683 // If any exits were not computable, the loop is not computable.
4684 if (!ExitNotTaken.isCompleteList()) return SE->getCouldNotCompute();
4686 // We need exactly one computable exit.
4687 if (!ExitNotTaken.ExitingBlock) return SE->getCouldNotCompute();
4688 assert(ExitNotTaken.ExactNotTaken && "uninitialized not-taken info");
4690 const SCEV *BECount = nullptr;
4691 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4692 ENT != nullptr; ENT = ENT->getNextExit()) {
4694 assert(ENT->ExactNotTaken != SE->getCouldNotCompute() && "bad exit SCEV");
4697 BECount = ENT->ExactNotTaken;
4698 else if (BECount != ENT->ExactNotTaken)
4699 return SE->getCouldNotCompute();
4701 assert(BECount && "Invalid not taken count for loop exit");
4705 /// getExact - Get the exact not taken count for this loop exit.
4707 ScalarEvolution::BackedgeTakenInfo::getExact(BasicBlock *ExitingBlock,
4708 ScalarEvolution *SE) const {
4709 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4710 ENT != nullptr; ENT = ENT->getNextExit()) {
4712 if (ENT->ExitingBlock == ExitingBlock)
4713 return ENT->ExactNotTaken;
4715 return SE->getCouldNotCompute();
4718 /// getMax - Get the max backedge taken count for the loop.
4720 ScalarEvolution::BackedgeTakenInfo::getMax(ScalarEvolution *SE) const {
4721 return Max ? Max : SE->getCouldNotCompute();
4724 bool ScalarEvolution::BackedgeTakenInfo::hasOperand(const SCEV *S,
4725 ScalarEvolution *SE) const {
4726 if (Max && Max != SE->getCouldNotCompute() && SE->hasOperand(Max, S))
4729 if (!ExitNotTaken.ExitingBlock)
4732 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4733 ENT != nullptr; ENT = ENT->getNextExit()) {
4735 if (ENT->ExactNotTaken != SE->getCouldNotCompute()
4736 && SE->hasOperand(ENT->ExactNotTaken, S)) {
4743 /// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each
4744 /// computable exit into a persistent ExitNotTakenInfo array.
4745 ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo(
4746 SmallVectorImpl< std::pair<BasicBlock *, const SCEV *> > &ExitCounts,
4747 bool Complete, const SCEV *MaxCount) : Max(MaxCount) {
4750 ExitNotTaken.setIncomplete();
4752 unsigned NumExits = ExitCounts.size();
4753 if (NumExits == 0) return;
4755 ExitNotTaken.ExitingBlock = ExitCounts[0].first;
4756 ExitNotTaken.ExactNotTaken = ExitCounts[0].second;
4757 if (NumExits == 1) return;
4759 // Handle the rare case of multiple computable exits.
4760 ExitNotTakenInfo *ENT = new ExitNotTakenInfo[NumExits-1];
4762 ExitNotTakenInfo *PrevENT = &ExitNotTaken;
4763 for (unsigned i = 1; i < NumExits; ++i, PrevENT = ENT, ++ENT) {
4764 PrevENT->setNextExit(ENT);
4765 ENT->ExitingBlock = ExitCounts[i].first;
4766 ENT->ExactNotTaken = ExitCounts[i].second;
4770 /// clear - Invalidate this result and free the ExitNotTakenInfo array.
4771 void ScalarEvolution::BackedgeTakenInfo::clear() {
4772 ExitNotTaken.ExitingBlock = nullptr;
4773 ExitNotTaken.ExactNotTaken = nullptr;
4774 delete[] ExitNotTaken.getNextExit();
4777 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
4778 /// of the specified loop will execute.
4779 ScalarEvolution::BackedgeTakenInfo
4780 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
4781 SmallVector<BasicBlock *, 8> ExitingBlocks;
4782 L->getExitingBlocks(ExitingBlocks);
4784 SmallVector<std::pair<BasicBlock *, const SCEV *>, 4> ExitCounts;
4785 bool CouldComputeBECount = true;
4786 BasicBlock *Latch = L->getLoopLatch(); // may be NULL.
4787 const SCEV *MustExitMaxBECount = nullptr;
4788 const SCEV *MayExitMaxBECount = nullptr;
4790 // Compute the ExitLimit for each loop exit. Use this to populate ExitCounts
4791 // and compute maxBECount.
4792 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
4793 BasicBlock *ExitBB = ExitingBlocks[i];
4794 ExitLimit EL = ComputeExitLimit(L, ExitBB);
4796 // 1. For each exit that can be computed, add an entry to ExitCounts.
4797 // CouldComputeBECount is true only if all exits can be computed.
4798 if (EL.Exact == getCouldNotCompute())
4799 // We couldn't compute an exact value for this exit, so
4800 // we won't be able to compute an exact value for the loop.
4801 CouldComputeBECount = false;
4803 ExitCounts.push_back(std::make_pair(ExitBB, EL.Exact));
4805 // 2. Derive the loop's MaxBECount from each exit's max number of
4806 // non-exiting iterations. Partition the loop exits into two kinds:
4807 // LoopMustExits and LoopMayExits.
4809 // If the exit dominates the loop latch, it is a LoopMustExit otherwise it
4810 // is a LoopMayExit. If any computable LoopMustExit is found, then
4811 // MaxBECount is the minimum EL.Max of computable LoopMustExits. Otherwise,
4812 // MaxBECount is conservatively the maximum EL.Max, where CouldNotCompute is
4813 // considered greater than any computable EL.Max.
4814 if (EL.Max != getCouldNotCompute() && Latch &&
4815 DT->dominates(ExitBB, Latch)) {
4816 if (!MustExitMaxBECount)
4817 MustExitMaxBECount = EL.Max;
4819 MustExitMaxBECount =
4820 getUMinFromMismatchedTypes(MustExitMaxBECount, EL.Max);
4822 } else if (MayExitMaxBECount != getCouldNotCompute()) {
4823 if (!MayExitMaxBECount || EL.Max == getCouldNotCompute())
4824 MayExitMaxBECount = EL.Max;
4827 getUMaxFromMismatchedTypes(MayExitMaxBECount, EL.Max);
4831 const SCEV *MaxBECount = MustExitMaxBECount ? MustExitMaxBECount :
4832 (MayExitMaxBECount ? MayExitMaxBECount : getCouldNotCompute());
4833 return BackedgeTakenInfo(ExitCounts, CouldComputeBECount, MaxBECount);
4836 /// ComputeExitLimit - Compute the number of times the backedge of the specified
4837 /// loop will execute if it exits via the specified block.
4838 ScalarEvolution::ExitLimit
4839 ScalarEvolution::ComputeExitLimit(const Loop *L, BasicBlock *ExitingBlock) {
4841 // Okay, we've chosen an exiting block. See what condition causes us to
4842 // exit at this block and remember the exit block and whether all other targets
4843 // lead to the loop header.
4844 bool MustExecuteLoopHeader = true;
4845 BasicBlock *Exit = nullptr;
4846 for (succ_iterator SI = succ_begin(ExitingBlock), SE = succ_end(ExitingBlock);
4848 if (!L->contains(*SI)) {
4849 if (Exit) // Multiple exit successors.
4850 return getCouldNotCompute();
4852 } else if (*SI != L->getHeader()) {
4853 MustExecuteLoopHeader = false;
4856 // At this point, we know we have a conditional branch that determines whether
4857 // the loop is exited. However, we don't know if the branch is executed each
4858 // time through the loop. If not, then the execution count of the branch will
4859 // not be equal to the trip count of the loop.
4861 // Currently we check for this by checking to see if the Exit branch goes to
4862 // the loop header. If so, we know it will always execute the same number of
4863 // times as the loop. We also handle the case where the exit block *is* the
4864 // loop header. This is common for un-rotated loops.
4866 // If both of those tests fail, walk up the unique predecessor chain to the
4867 // header, stopping if there is an edge that doesn't exit the loop. If the
4868 // header is reached, the execution count of the branch will be equal to the
4869 // trip count of the loop.
4871 // More extensive analysis could be done to handle more cases here.
4873 if (!MustExecuteLoopHeader && ExitingBlock != L->getHeader()) {
4874 // The simple checks failed, try climbing the unique predecessor chain
4875 // up to the header.
4877 for (BasicBlock *BB = ExitingBlock; BB; ) {
4878 BasicBlock *Pred = BB->getUniquePredecessor();
4880 return getCouldNotCompute();
4881 TerminatorInst *PredTerm = Pred->getTerminator();
4882 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) {
4883 BasicBlock *PredSucc = PredTerm->getSuccessor(i);
4886 // If the predecessor has a successor that isn't BB and isn't
4887 // outside the loop, assume the worst.
4888 if (L->contains(PredSucc))
4889 return getCouldNotCompute();
4891 if (Pred == L->getHeader()) {
4898 return getCouldNotCompute();
4901 bool IsOnlyExit = (L->getExitingBlock() != nullptr);
4902 TerminatorInst *Term = ExitingBlock->getTerminator();
4903 if (BranchInst *BI = dyn_cast<BranchInst>(Term)) {
4904 assert(BI->isConditional() && "If unconditional, it can't be in loop!");
4905 // Proceed to the next level to examine the exit condition expression.
4906 return ComputeExitLimitFromCond(L, BI->getCondition(), BI->getSuccessor(0),
4907 BI->getSuccessor(1),
4908 /*ControlsExit=*/IsOnlyExit);
4911 if (SwitchInst *SI = dyn_cast<SwitchInst>(Term))
4912 return ComputeExitLimitFromSingleExitSwitch(L, SI, Exit,
4913 /*ControlsExit=*/IsOnlyExit);
4915 return getCouldNotCompute();
4918 /// ComputeExitLimitFromCond - Compute the number of times the
4919 /// backedge of the specified loop will execute if its exit condition
4920 /// were a conditional branch of ExitCond, TBB, and FBB.
4922 /// @param ControlsExit is true if ExitCond directly controls the exit
4923 /// branch. In this case, we can assume that the loop exits only if the
4924 /// condition is true and can infer that failing to meet the condition prior to
4925 /// integer wraparound results in undefined behavior.
4926 ScalarEvolution::ExitLimit
4927 ScalarEvolution::ComputeExitLimitFromCond(const Loop *L,
4931 bool ControlsExit) {
4932 // Check if the controlling expression for this loop is an And or Or.
4933 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
4934 if (BO->getOpcode() == Instruction::And) {
4935 // Recurse on the operands of the and.
4936 bool EitherMayExit = L->contains(TBB);
4937 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
4938 ControlsExit && !EitherMayExit);
4939 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
4940 ControlsExit && !EitherMayExit);
4941 const SCEV *BECount = getCouldNotCompute();
4942 const SCEV *MaxBECount = getCouldNotCompute();
4943 if (EitherMayExit) {
4944 // Both conditions must be true for the loop to continue executing.
4945 // Choose the less conservative count.
4946 if (EL0.Exact == getCouldNotCompute() ||
4947 EL1.Exact == getCouldNotCompute())
4948 BECount = getCouldNotCompute();
4950 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
4951 if (EL0.Max == getCouldNotCompute())
4952 MaxBECount = EL1.Max;
4953 else if (EL1.Max == getCouldNotCompute())
4954 MaxBECount = EL0.Max;
4956 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
4958 // Both conditions must be true at the same time for the loop to exit.
4959 // For now, be conservative.
4960 assert(L->contains(FBB) && "Loop block has no successor in loop!");
4961 if (EL0.Max == EL1.Max)
4962 MaxBECount = EL0.Max;
4963 if (EL0.Exact == EL1.Exact)
4964 BECount = EL0.Exact;
4967 return ExitLimit(BECount, MaxBECount);
4969 if (BO->getOpcode() == Instruction::Or) {
4970 // Recurse on the operands of the or.
4971 bool EitherMayExit = L->contains(FBB);
4972 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
4973 ControlsExit && !EitherMayExit);
4974 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
4975 ControlsExit && !EitherMayExit);
4976 const SCEV *BECount = getCouldNotCompute();
4977 const SCEV *MaxBECount = getCouldNotCompute();
4978 if (EitherMayExit) {
4979 // Both conditions must be false for the loop to continue executing.
4980 // Choose the less conservative count.
4981 if (EL0.Exact == getCouldNotCompute() ||
4982 EL1.Exact == getCouldNotCompute())
4983 BECount = getCouldNotCompute();
4985 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
4986 if (EL0.Max == getCouldNotCompute())
4987 MaxBECount = EL1.Max;
4988 else if (EL1.Max == getCouldNotCompute())
4989 MaxBECount = EL0.Max;
4991 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
4993 // Both conditions must be false at the same time for the loop to exit.
4994 // For now, be conservative.
4995 assert(L->contains(TBB) && "Loop block has no successor in loop!");
4996 if (EL0.Max == EL1.Max)
4997 MaxBECount = EL0.Max;
4998 if (EL0.Exact == EL1.Exact)
4999 BECount = EL0.Exact;
5002 return ExitLimit(BECount, MaxBECount);
5006 // With an icmp, it may be feasible to compute an exact backedge-taken count.
5007 // Proceed to the next level to examine the icmp.
5008 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
5009 return ComputeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB, ControlsExit);
5011 // Check for a constant condition. These are normally stripped out by
5012 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
5013 // preserve the CFG and is temporarily leaving constant conditions
5015 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
5016 if (L->contains(FBB) == !CI->getZExtValue())
5017 // The backedge is always taken.
5018 return getCouldNotCompute();
5020 // The backedge is never taken.
5021 return getConstant(CI->getType(), 0);
5024 // If it's not an integer or pointer comparison then compute it the hard way.
5025 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
5028 /// ComputeExitLimitFromICmp - Compute the number of times the
5029 /// backedge of the specified loop will execute if its exit condition
5030 /// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB.
5031 ScalarEvolution::ExitLimit
5032 ScalarEvolution::ComputeExitLimitFromICmp(const Loop *L,
5036 bool ControlsExit) {
5038 // If the condition was exit on true, convert the condition to exit on false
5039 ICmpInst::Predicate Cond;
5040 if (!L->contains(FBB))
5041 Cond = ExitCond->getPredicate();
5043 Cond = ExitCond->getInversePredicate();
5045 // Handle common loops like: for (X = "string"; *X; ++X)
5046 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
5047 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
5049 ComputeLoadConstantCompareExitLimit(LI, RHS, L, Cond);
5050 if (ItCnt.hasAnyInfo())
5054 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
5055 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
5057 // Try to evaluate any dependencies out of the loop.
5058 LHS = getSCEVAtScope(LHS, L);
5059 RHS = getSCEVAtScope(RHS, L);
5061 // At this point, we would like to compute how many iterations of the
5062 // loop the predicate will return true for these inputs.
5063 if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) {
5064 // If there is a loop-invariant, force it into the RHS.
5065 std::swap(LHS, RHS);
5066 Cond = ICmpInst::getSwappedPredicate(Cond);
5069 // Simplify the operands before analyzing them.
5070 (void)SimplifyICmpOperands(Cond, LHS, RHS);
5072 // If we have a comparison of a chrec against a constant, try to use value
5073 // ranges to answer this query.
5074 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
5075 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
5076 if (AddRec->getLoop() == L) {
5077 // Form the constant range.
5078 ConstantRange CompRange(
5079 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
5081 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
5082 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
5086 case ICmpInst::ICMP_NE: { // while (X != Y)
5087 // Convert to: while (X-Y != 0)
5088 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit);
5089 if (EL.hasAnyInfo()) return EL;
5092 case ICmpInst::ICMP_EQ: { // while (X == Y)
5093 // Convert to: while (X-Y == 0)
5094 ExitLimit EL = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
5095 if (EL.hasAnyInfo()) return EL;
5098 case ICmpInst::ICMP_SLT:
5099 case ICmpInst::ICMP_ULT: { // while (X < Y)
5100 bool IsSigned = Cond == ICmpInst::ICMP_SLT;
5101 ExitLimit EL = HowManyLessThans(LHS, RHS, L, IsSigned, ControlsExit);
5102 if (EL.hasAnyInfo()) return EL;
5105 case ICmpInst::ICMP_SGT:
5106 case ICmpInst::ICMP_UGT: { // while (X > Y)
5107 bool IsSigned = Cond == ICmpInst::ICMP_SGT;
5108 ExitLimit EL = HowManyGreaterThans(LHS, RHS, L, IsSigned, ControlsExit);
5109 if (EL.hasAnyInfo()) return EL;
5114 dbgs() << "ComputeBackedgeTakenCount ";
5115 if (ExitCond->getOperand(0)->getType()->isUnsigned())
5116 dbgs() << "[unsigned] ";
5117 dbgs() << *LHS << " "
5118 << Instruction::getOpcodeName(Instruction::ICmp)
5119 << " " << *RHS << "\n";
5123 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
5126 ScalarEvolution::ExitLimit
5127 ScalarEvolution::ComputeExitLimitFromSingleExitSwitch(const Loop *L,
5129 BasicBlock *ExitingBlock,
5130 bool ControlsExit) {
5131 assert(!L->contains(ExitingBlock) && "Not an exiting block!");
5133 // Give up if the exit is the default dest of a switch.
5134 if (Switch->getDefaultDest() == ExitingBlock)
5135 return getCouldNotCompute();
5137 assert(L->contains(Switch->getDefaultDest()) &&
5138 "Default case must not exit the loop!");
5139 const SCEV *LHS = getSCEVAtScope(Switch->getCondition(), L);
5140 const SCEV *RHS = getConstant(Switch->findCaseDest(ExitingBlock));
5142 // while (X != Y) --> while (X-Y != 0)
5143 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit);
5144 if (EL.hasAnyInfo())
5147 return getCouldNotCompute();
5150 static ConstantInt *
5151 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
5152 ScalarEvolution &SE) {
5153 const SCEV *InVal = SE.getConstant(C);
5154 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
5155 assert(isa<SCEVConstant>(Val) &&
5156 "Evaluation of SCEV at constant didn't fold correctly?");
5157 return cast<SCEVConstant>(Val)->getValue();
5160 /// ComputeLoadConstantCompareExitLimit - Given an exit condition of
5161 /// 'icmp op load X, cst', try to see if we can compute the backedge
5162 /// execution count.
5163 ScalarEvolution::ExitLimit
5164 ScalarEvolution::ComputeLoadConstantCompareExitLimit(
5168 ICmpInst::Predicate predicate) {
5170 if (LI->isVolatile()) return getCouldNotCompute();
5172 // Check to see if the loaded pointer is a getelementptr of a global.
5173 // TODO: Use SCEV instead of manually grubbing with GEPs.
5174 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
5175 if (!GEP) return getCouldNotCompute();
5177 // Make sure that it is really a constant global we are gepping, with an
5178 // initializer, and make sure the first IDX is really 0.
5179 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
5180 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
5181 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
5182 !cast<Constant>(GEP->getOperand(1))->isNullValue())
5183 return getCouldNotCompute();
5185 // Okay, we allow one non-constant index into the GEP instruction.
5186 Value *VarIdx = nullptr;
5187 std::vector<Constant*> Indexes;
5188 unsigned VarIdxNum = 0;
5189 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
5190 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
5191 Indexes.push_back(CI);
5192 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
5193 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
5194 VarIdx = GEP->getOperand(i);
5196 Indexes.push_back(nullptr);
5199 // Loop-invariant loads may be a byproduct of loop optimization. Skip them.
5201 return getCouldNotCompute();
5203 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
5204 // Check to see if X is a loop variant variable value now.
5205 const SCEV *Idx = getSCEV(VarIdx);
5206 Idx = getSCEVAtScope(Idx, L);
5208 // We can only recognize very limited forms of loop index expressions, in
5209 // particular, only affine AddRec's like {C1,+,C2}.
5210 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
5211 if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) ||
5212 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
5213 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
5214 return getCouldNotCompute();
5216 unsigned MaxSteps = MaxBruteForceIterations;
5217 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
5218 ConstantInt *ItCst = ConstantInt::get(
5219 cast<IntegerType>(IdxExpr->getType()), IterationNum);
5220 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
5222 // Form the GEP offset.
5223 Indexes[VarIdxNum] = Val;
5225 Constant *Result = ConstantFoldLoadThroughGEPIndices(GV->getInitializer(),
5227 if (!Result) break; // Cannot compute!
5229 // Evaluate the condition for this iteration.
5230 Result = ConstantExpr::getICmp(predicate, Result, RHS);
5231 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
5232 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
5234 dbgs() << "\n***\n*** Computed loop count " << *ItCst
5235 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
5238 ++NumArrayLenItCounts;
5239 return getConstant(ItCst); // Found terminating iteration!
5242 return getCouldNotCompute();
5246 /// CanConstantFold - Return true if we can constant fold an instruction of the
5247 /// specified type, assuming that all operands were constants.
5248 static bool CanConstantFold(const Instruction *I) {
5249 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
5250 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I) ||
5254 if (const CallInst *CI = dyn_cast<CallInst>(I))
5255 if (const Function *F = CI->getCalledFunction())
5256 return canConstantFoldCallTo(F);
5260 /// Determine whether this instruction can constant evolve within this loop
5261 /// assuming its operands can all constant evolve.
5262 static bool canConstantEvolve(Instruction *I, const Loop *L) {
5263 // An instruction outside of the loop can't be derived from a loop PHI.
5264 if (!L->contains(I)) return false;
5266 if (isa<PHINode>(I)) {
5267 if (L->getHeader() == I->getParent())
5270 // We don't currently keep track of the control flow needed to evaluate
5271 // PHIs, so we cannot handle PHIs inside of loops.
5275 // If we won't be able to constant fold this expression even if the operands
5276 // are constants, bail early.
5277 return CanConstantFold(I);
5280 /// getConstantEvolvingPHIOperands - Implement getConstantEvolvingPHI by
5281 /// recursing through each instruction operand until reaching a loop header phi.
5283 getConstantEvolvingPHIOperands(Instruction *UseInst, const Loop *L,
5284 DenseMap<Instruction *, PHINode *> &PHIMap) {
5286 // Otherwise, we can evaluate this instruction if all of its operands are
5287 // constant or derived from a PHI node themselves.
5288 PHINode *PHI = nullptr;
5289 for (Instruction::op_iterator OpI = UseInst->op_begin(),
5290 OpE = UseInst->op_end(); OpI != OpE; ++OpI) {
5292 if (isa<Constant>(*OpI)) continue;
5294 Instruction *OpInst = dyn_cast<Instruction>(*OpI);
5295 if (!OpInst || !canConstantEvolve(OpInst, L)) return nullptr;
5297 PHINode *P = dyn_cast<PHINode>(OpInst);
5299 // If this operand is already visited, reuse the prior result.
5300 // We may have P != PHI if this is the deepest point at which the
5301 // inconsistent paths meet.
5302 P = PHIMap.lookup(OpInst);
5304 // Recurse and memoize the results, whether a phi is found or not.
5305 // This recursive call invalidates pointers into PHIMap.
5306 P = getConstantEvolvingPHIOperands(OpInst, L, PHIMap);
5310 return nullptr; // Not evolving from PHI
5311 if (PHI && PHI != P)
5312 return nullptr; // Evolving from multiple different PHIs.
5315 // This is a expression evolving from a constant PHI!
5319 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
5320 /// in the loop that V is derived from. We allow arbitrary operations along the
5321 /// way, but the operands of an operation must either be constants or a value
5322 /// derived from a constant PHI. If this expression does not fit with these
5323 /// constraints, return null.
5324 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
5325 Instruction *I = dyn_cast<Instruction>(V);
5326 if (!I || !canConstantEvolve(I, L)) return nullptr;
5328 if (PHINode *PN = dyn_cast<PHINode>(I)) {
5332 // Record non-constant instructions contained by the loop.
5333 DenseMap<Instruction *, PHINode *> PHIMap;
5334 return getConstantEvolvingPHIOperands(I, L, PHIMap);
5337 /// EvaluateExpression - Given an expression that passes the
5338 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
5339 /// in the loop has the value PHIVal. If we can't fold this expression for some
5340 /// reason, return null.
5341 static Constant *EvaluateExpression(Value *V, const Loop *L,
5342 DenseMap<Instruction *, Constant *> &Vals,
5343 const DataLayout *DL,
5344 const TargetLibraryInfo *TLI) {
5345 // Convenient constant check, but redundant for recursive calls.
5346 if (Constant *C = dyn_cast<Constant>(V)) return C;
5347 Instruction *I = dyn_cast<Instruction>(V);
5348 if (!I) return nullptr;
5350 if (Constant *C = Vals.lookup(I)) return C;
5352 // An instruction inside the loop depends on a value outside the loop that we
5353 // weren't given a mapping for, or a value such as a call inside the loop.
5354 if (!canConstantEvolve(I, L)) return nullptr;
5356 // An unmapped PHI can be due to a branch or another loop inside this loop,
5357 // or due to this not being the initial iteration through a loop where we
5358 // couldn't compute the evolution of this particular PHI last time.
5359 if (isa<PHINode>(I)) return nullptr;
5361 std::vector<Constant*> Operands(I->getNumOperands());
5363 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
5364 Instruction *Operand = dyn_cast<Instruction>(I->getOperand(i));
5366 Operands[i] = dyn_cast<Constant>(I->getOperand(i));
5367 if (!Operands[i]) return nullptr;
5370 Constant *C = EvaluateExpression(Operand, L, Vals, DL, TLI);
5372 if (!C) return nullptr;
5376 if (CmpInst *CI = dyn_cast<CmpInst>(I))
5377 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
5378 Operands[1], DL, TLI);
5379 if (LoadInst *LI = dyn_cast<LoadInst>(I)) {
5380 if (!LI->isVolatile())
5381 return ConstantFoldLoadFromConstPtr(Operands[0], DL);
5383 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), Operands, DL,
5387 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
5388 /// in the header of its containing loop, we know the loop executes a
5389 /// constant number of times, and the PHI node is just a recurrence
5390 /// involving constants, fold it.
5392 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
5395 DenseMap<PHINode*, Constant*>::const_iterator I =
5396 ConstantEvolutionLoopExitValue.find(PN);
5397 if (I != ConstantEvolutionLoopExitValue.end())
5400 if (BEs.ugt(MaxBruteForceIterations))
5401 return ConstantEvolutionLoopExitValue[PN] = nullptr; // Not going to evaluate it.
5403 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
5405 DenseMap<Instruction *, Constant *> CurrentIterVals;
5406 BasicBlock *Header = L->getHeader();
5407 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
5409 // Since the loop is canonicalized, the PHI node must have two entries. One
5410 // entry must be a constant (coming in from outside of the loop), and the
5411 // second must be derived from the same PHI.
5412 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
5413 PHINode *PHI = nullptr;
5414 for (BasicBlock::iterator I = Header->begin();
5415 (PHI = dyn_cast<PHINode>(I)); ++I) {
5416 Constant *StartCST =
5417 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
5418 if (!StartCST) continue;
5419 CurrentIterVals[PHI] = StartCST;
5421 if (!CurrentIterVals.count(PN))
5422 return RetVal = nullptr;
5424 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
5426 // Execute the loop symbolically to determine the exit value.
5427 if (BEs.getActiveBits() >= 32)
5428 return RetVal = nullptr; // More than 2^32-1 iterations?? Not doing it!
5430 unsigned NumIterations = BEs.getZExtValue(); // must be in range
5431 unsigned IterationNum = 0;
5432 for (; ; ++IterationNum) {
5433 if (IterationNum == NumIterations)
5434 return RetVal = CurrentIterVals[PN]; // Got exit value!
5436 // Compute the value of the PHIs for the next iteration.
5437 // EvaluateExpression adds non-phi values to the CurrentIterVals map.
5438 DenseMap<Instruction *, Constant *> NextIterVals;
5439 Constant *NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL,
5442 return nullptr; // Couldn't evaluate!
5443 NextIterVals[PN] = NextPHI;
5445 bool StoppedEvolving = NextPHI == CurrentIterVals[PN];
5447 // Also evaluate the other PHI nodes. However, we don't get to stop if we
5448 // cease to be able to evaluate one of them or if they stop evolving,
5449 // because that doesn't necessarily prevent us from computing PN.
5450 SmallVector<std::pair<PHINode *, Constant *>, 8> PHIsToCompute;
5451 for (DenseMap<Instruction *, Constant *>::const_iterator
5452 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
5453 PHINode *PHI = dyn_cast<PHINode>(I->first);
5454 if (!PHI || PHI == PN || PHI->getParent() != Header) continue;
5455 PHIsToCompute.push_back(std::make_pair(PHI, I->second));
5457 // We use two distinct loops because EvaluateExpression may invalidate any
5458 // iterators into CurrentIterVals.
5459 for (SmallVectorImpl<std::pair<PHINode *, Constant*> >::const_iterator
5460 I = PHIsToCompute.begin(), E = PHIsToCompute.end(); I != E; ++I) {
5461 PHINode *PHI = I->first;
5462 Constant *&NextPHI = NextIterVals[PHI];
5463 if (!NextPHI) { // Not already computed.
5464 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
5465 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, TLI);
5467 if (NextPHI != I->second)
5468 StoppedEvolving = false;
5471 // If all entries in CurrentIterVals == NextIterVals then we can stop
5472 // iterating, the loop can't continue to change.
5473 if (StoppedEvolving)
5474 return RetVal = CurrentIterVals[PN];
5476 CurrentIterVals.swap(NextIterVals);
5480 /// ComputeExitCountExhaustively - If the loop is known to execute a
5481 /// constant number of times (the condition evolves only from constants),
5482 /// try to evaluate a few iterations of the loop until we get the exit
5483 /// condition gets a value of ExitWhen (true or false). If we cannot
5484 /// evaluate the trip count of the loop, return getCouldNotCompute().
5485 const SCEV *ScalarEvolution::ComputeExitCountExhaustively(const Loop *L,
5488 PHINode *PN = getConstantEvolvingPHI(Cond, L);
5489 if (!PN) return getCouldNotCompute();
5491 // If the loop is canonicalized, the PHI will have exactly two entries.
5492 // That's the only form we support here.
5493 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
5495 DenseMap<Instruction *, Constant *> CurrentIterVals;
5496 BasicBlock *Header = L->getHeader();
5497 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
5499 // One entry must be a constant (coming in from outside of the loop), and the
5500 // second must be derived from the same PHI.
5501 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
5502 PHINode *PHI = nullptr;
5503 for (BasicBlock::iterator I = Header->begin();
5504 (PHI = dyn_cast<PHINode>(I)); ++I) {
5505 Constant *StartCST =
5506 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
5507 if (!StartCST) continue;
5508 CurrentIterVals[PHI] = StartCST;
5510 if (!CurrentIterVals.count(PN))
5511 return getCouldNotCompute();
5513 // Okay, we find a PHI node that defines the trip count of this loop. Execute
5514 // the loop symbolically to determine when the condition gets a value of
5517 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
5518 for (unsigned IterationNum = 0; IterationNum != MaxIterations;++IterationNum){
5519 ConstantInt *CondVal =
5520 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, L, CurrentIterVals,
5523 // Couldn't symbolically evaluate.
5524 if (!CondVal) return getCouldNotCompute();
5526 if (CondVal->getValue() == uint64_t(ExitWhen)) {
5527 ++NumBruteForceTripCountsComputed;
5528 return getConstant(Type::getInt32Ty(getContext()), IterationNum);
5531 // Update all the PHI nodes for the next iteration.
5532 DenseMap<Instruction *, Constant *> NextIterVals;
5534 // Create a list of which PHIs we need to compute. We want to do this before
5535 // calling EvaluateExpression on them because that may invalidate iterators
5536 // into CurrentIterVals.
5537 SmallVector<PHINode *, 8> PHIsToCompute;
5538 for (DenseMap<Instruction *, Constant *>::const_iterator
5539 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
5540 PHINode *PHI = dyn_cast<PHINode>(I->first);
5541 if (!PHI || PHI->getParent() != Header) continue;
5542 PHIsToCompute.push_back(PHI);
5544 for (SmallVectorImpl<PHINode *>::const_iterator I = PHIsToCompute.begin(),
5545 E = PHIsToCompute.end(); I != E; ++I) {
5547 Constant *&NextPHI = NextIterVals[PHI];
5548 if (NextPHI) continue; // Already computed!
5550 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
5551 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, TLI);
5553 CurrentIterVals.swap(NextIterVals);
5556 // Too many iterations were needed to evaluate.
5557 return getCouldNotCompute();
5560 /// getSCEVAtScope - Return a SCEV expression for the specified value
5561 /// at the specified scope in the program. The L value specifies a loop
5562 /// nest to evaluate the expression at, where null is the top-level or a
5563 /// specified loop is immediately inside of the loop.
5565 /// This method can be used to compute the exit value for a variable defined
5566 /// in a loop by querying what the value will hold in the parent loop.
5568 /// In the case that a relevant loop exit value cannot be computed, the
5569 /// original value V is returned.
5570 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
5571 // Check to see if we've folded this expression at this loop before.
5572 SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values = ValuesAtScopes[V];
5573 for (unsigned u = 0; u < Values.size(); u++) {
5574 if (Values[u].first == L)
5575 return Values[u].second ? Values[u].second : V;
5577 Values.push_back(std::make_pair(L, static_cast<const SCEV *>(nullptr)));
5578 // Otherwise compute it.
5579 const SCEV *C = computeSCEVAtScope(V, L);
5580 SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values2 = ValuesAtScopes[V];
5581 for (unsigned u = Values2.size(); u > 0; u--) {
5582 if (Values2[u - 1].first == L) {
5583 Values2[u - 1].second = C;
5590 /// This builds up a Constant using the ConstantExpr interface. That way, we
5591 /// will return Constants for objects which aren't represented by a
5592 /// SCEVConstant, because SCEVConstant is restricted to ConstantInt.
5593 /// Returns NULL if the SCEV isn't representable as a Constant.
5594 static Constant *BuildConstantFromSCEV(const SCEV *V) {
5595 switch (static_cast<SCEVTypes>(V->getSCEVType())) {
5596 case scCouldNotCompute:
5600 return cast<SCEVConstant>(V)->getValue();
5602 return dyn_cast<Constant>(cast<SCEVUnknown>(V)->getValue());
5603 case scSignExtend: {
5604 const SCEVSignExtendExpr *SS = cast<SCEVSignExtendExpr>(V);
5605 if (Constant *CastOp = BuildConstantFromSCEV(SS->getOperand()))
5606 return ConstantExpr::getSExt(CastOp, SS->getType());
5609 case scZeroExtend: {
5610 const SCEVZeroExtendExpr *SZ = cast<SCEVZeroExtendExpr>(V);
5611 if (Constant *CastOp = BuildConstantFromSCEV(SZ->getOperand()))
5612 return ConstantExpr::getZExt(CastOp, SZ->getType());
5616 const SCEVTruncateExpr *ST = cast<SCEVTruncateExpr>(V);
5617 if (Constant *CastOp = BuildConstantFromSCEV(ST->getOperand()))
5618 return ConstantExpr::getTrunc(CastOp, ST->getType());
5622 const SCEVAddExpr *SA = cast<SCEVAddExpr>(V);
5623 if (Constant *C = BuildConstantFromSCEV(SA->getOperand(0))) {
5624 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
5625 unsigned AS = PTy->getAddressSpace();
5626 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
5627 C = ConstantExpr::getBitCast(C, DestPtrTy);
5629 for (unsigned i = 1, e = SA->getNumOperands(); i != e; ++i) {
5630 Constant *C2 = BuildConstantFromSCEV(SA->getOperand(i));
5631 if (!C2) return nullptr;
5634 if (!C->getType()->isPointerTy() && C2->getType()->isPointerTy()) {
5635 unsigned AS = C2->getType()->getPointerAddressSpace();
5637 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
5638 // The offsets have been converted to bytes. We can add bytes to an
5639 // i8* by GEP with the byte count in the first index.
5640 C = ConstantExpr::getBitCast(C, DestPtrTy);
5643 // Don't bother trying to sum two pointers. We probably can't
5644 // statically compute a load that results from it anyway.
5645 if (C2->getType()->isPointerTy())
5648 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
5649 if (PTy->getElementType()->isStructTy())
5650 C2 = ConstantExpr::getIntegerCast(
5651 C2, Type::getInt32Ty(C->getContext()), true);
5652 C = ConstantExpr::getGetElementPtr(C, C2);
5654 C = ConstantExpr::getAdd(C, C2);
5661 const SCEVMulExpr *SM = cast<SCEVMulExpr>(V);
5662 if (Constant *C = BuildConstantFromSCEV(SM->getOperand(0))) {
5663 // Don't bother with pointers at all.
5664 if (C->getType()->isPointerTy()) return nullptr;
5665 for (unsigned i = 1, e = SM->getNumOperands(); i != e; ++i) {
5666 Constant *C2 = BuildConstantFromSCEV(SM->getOperand(i));
5667 if (!C2 || C2->getType()->isPointerTy()) return nullptr;
5668 C = ConstantExpr::getMul(C, C2);
5675 const SCEVUDivExpr *SU = cast<SCEVUDivExpr>(V);
5676 if (Constant *LHS = BuildConstantFromSCEV(SU->getLHS()))
5677 if (Constant *RHS = BuildConstantFromSCEV(SU->getRHS()))
5678 if (LHS->getType() == RHS->getType())
5679 return ConstantExpr::getUDiv(LHS, RHS);
5684 break; // TODO: smax, umax.
5689 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
5690 if (isa<SCEVConstant>(V)) return V;
5692 // If this instruction is evolved from a constant-evolving PHI, compute the
5693 // exit value from the loop without using SCEVs.
5694 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
5695 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
5696 const Loop *LI = (*this->LI)[I->getParent()];
5697 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
5698 if (PHINode *PN = dyn_cast<PHINode>(I))
5699 if (PN->getParent() == LI->getHeader()) {
5700 // Okay, there is no closed form solution for the PHI node. Check
5701 // to see if the loop that contains it has a known backedge-taken
5702 // count. If so, we may be able to force computation of the exit
5704 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
5705 if (const SCEVConstant *BTCC =
5706 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
5707 // Okay, we know how many times the containing loop executes. If
5708 // this is a constant evolving PHI node, get the final value at
5709 // the specified iteration number.
5710 Constant *RV = getConstantEvolutionLoopExitValue(PN,
5711 BTCC->getValue()->getValue(),
5713 if (RV) return getSCEV(RV);
5717 // Okay, this is an expression that we cannot symbolically evaluate
5718 // into a SCEV. Check to see if it's possible to symbolically evaluate
5719 // the arguments into constants, and if so, try to constant propagate the
5720 // result. This is particularly useful for computing loop exit values.
5721 if (CanConstantFold(I)) {
5722 SmallVector<Constant *, 4> Operands;
5723 bool MadeImprovement = false;
5724 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
5725 Value *Op = I->getOperand(i);
5726 if (Constant *C = dyn_cast<Constant>(Op)) {
5727 Operands.push_back(C);
5731 // If any of the operands is non-constant and if they are
5732 // non-integer and non-pointer, don't even try to analyze them
5733 // with scev techniques.
5734 if (!isSCEVable(Op->getType()))
5737 const SCEV *OrigV = getSCEV(Op);
5738 const SCEV *OpV = getSCEVAtScope(OrigV, L);
5739 MadeImprovement |= OrigV != OpV;
5741 Constant *C = BuildConstantFromSCEV(OpV);
5743 if (C->getType() != Op->getType())
5744 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
5748 Operands.push_back(C);
5751 // Check to see if getSCEVAtScope actually made an improvement.
5752 if (MadeImprovement) {
5753 Constant *C = nullptr;
5754 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
5755 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
5756 Operands[0], Operands[1], DL,
5758 else if (const LoadInst *LI = dyn_cast<LoadInst>(I)) {
5759 if (!LI->isVolatile())
5760 C = ConstantFoldLoadFromConstPtr(Operands[0], DL);
5762 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
5770 // This is some other type of SCEVUnknown, just return it.
5774 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
5775 // Avoid performing the look-up in the common case where the specified
5776 // expression has no loop-variant portions.
5777 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
5778 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
5779 if (OpAtScope != Comm->getOperand(i)) {
5780 // Okay, at least one of these operands is loop variant but might be
5781 // foldable. Build a new instance of the folded commutative expression.
5782 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
5783 Comm->op_begin()+i);
5784 NewOps.push_back(OpAtScope);
5786 for (++i; i != e; ++i) {
5787 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
5788 NewOps.push_back(OpAtScope);
5790 if (isa<SCEVAddExpr>(Comm))
5791 return getAddExpr(NewOps);
5792 if (isa<SCEVMulExpr>(Comm))
5793 return getMulExpr(NewOps);
5794 if (isa<SCEVSMaxExpr>(Comm))
5795 return getSMaxExpr(NewOps);
5796 if (isa<SCEVUMaxExpr>(Comm))
5797 return getUMaxExpr(NewOps);
5798 llvm_unreachable("Unknown commutative SCEV type!");
5801 // If we got here, all operands are loop invariant.
5805 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
5806 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
5807 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
5808 if (LHS == Div->getLHS() && RHS == Div->getRHS())
5809 return Div; // must be loop invariant
5810 return getUDivExpr(LHS, RHS);
5813 // If this is a loop recurrence for a loop that does not contain L, then we
5814 // are dealing with the final value computed by the loop.
5815 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
5816 // First, attempt to evaluate each operand.
5817 // Avoid performing the look-up in the common case where the specified
5818 // expression has no loop-variant portions.
5819 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
5820 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
5821 if (OpAtScope == AddRec->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(AddRec->op_begin(),
5827 AddRec->op_begin()+i);
5828 NewOps.push_back(OpAtScope);
5829 for (++i; i != e; ++i)
5830 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
5832 const SCEV *FoldedRec =
5833 getAddRecExpr(NewOps, AddRec->getLoop(),
5834 AddRec->getNoWrapFlags(SCEV::FlagNW));
5835 AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec);
5836 // The addrec may be folded to a nonrecurrence, for example, if the
5837 // induction variable is multiplied by zero after constant folding. Go
5838 // ahead and return the folded value.
5844 // If the scope is outside the addrec's loop, evaluate it by using the
5845 // loop exit value of the addrec.
5846 if (!AddRec->getLoop()->contains(L)) {
5847 // To evaluate this recurrence, we need to know how many times the AddRec
5848 // loop iterates. Compute this now.
5849 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
5850 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
5852 // Then, evaluate the AddRec.
5853 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
5859 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
5860 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5861 if (Op == Cast->getOperand())
5862 return Cast; // must be loop invariant
5863 return getZeroExtendExpr(Op, Cast->getType());
5866 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
5867 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5868 if (Op == Cast->getOperand())
5869 return Cast; // must be loop invariant
5870 return getSignExtendExpr(Op, Cast->getType());
5873 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
5874 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5875 if (Op == Cast->getOperand())
5876 return Cast; // must be loop invariant
5877 return getTruncateExpr(Op, Cast->getType());
5880 llvm_unreachable("Unknown SCEV type!");
5883 /// getSCEVAtScope - This is a convenience function which does
5884 /// getSCEVAtScope(getSCEV(V), L).
5885 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
5886 return getSCEVAtScope(getSCEV(V), L);
5889 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
5890 /// following equation:
5892 /// A * X = B (mod N)
5894 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
5895 /// A and B isn't important.
5897 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
5898 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
5899 ScalarEvolution &SE) {
5900 uint32_t BW = A.getBitWidth();
5901 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
5902 assert(A != 0 && "A must be non-zero.");
5906 // The gcd of A and N may have only one prime factor: 2. The number of
5907 // trailing zeros in A is its multiplicity
5908 uint32_t Mult2 = A.countTrailingZeros();
5911 // 2. Check if B is divisible by D.
5913 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
5914 // is not less than multiplicity of this prime factor for D.
5915 if (B.countTrailingZeros() < Mult2)
5916 return SE.getCouldNotCompute();
5918 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
5921 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
5922 // bit width during computations.
5923 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
5924 APInt Mod(BW + 1, 0);
5925 Mod.setBit(BW - Mult2); // Mod = N / D
5926 APInt I = AD.multiplicativeInverse(Mod);
5928 // 4. Compute the minimum unsigned root of the equation:
5929 // I * (B / D) mod (N / D)
5930 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
5932 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
5934 return SE.getConstant(Result.trunc(BW));
5937 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
5938 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
5939 /// might be the same) or two SCEVCouldNotCompute objects.
5941 static std::pair<const SCEV *,const SCEV *>
5942 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
5943 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
5944 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
5945 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
5946 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
5948 // We currently can only solve this if the coefficients are constants.
5949 if (!LC || !MC || !NC) {
5950 const SCEV *CNC = SE.getCouldNotCompute();
5951 return std::make_pair(CNC, CNC);
5954 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
5955 const APInt &L = LC->getValue()->getValue();
5956 const APInt &M = MC->getValue()->getValue();
5957 const APInt &N = NC->getValue()->getValue();
5958 APInt Two(BitWidth, 2);
5959 APInt Four(BitWidth, 4);
5962 using namespace APIntOps;
5964 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
5965 // The B coefficient is M-N/2
5969 // The A coefficient is N/2
5970 APInt A(N.sdiv(Two));
5972 // Compute the B^2-4ac term.
5975 SqrtTerm -= Four * (A * C);
5977 if (SqrtTerm.isNegative()) {
5978 // The loop is provably infinite.
5979 const SCEV *CNC = SE.getCouldNotCompute();
5980 return std::make_pair(CNC, CNC);
5983 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
5984 // integer value or else APInt::sqrt() will assert.
5985 APInt SqrtVal(SqrtTerm.sqrt());
5987 // Compute the two solutions for the quadratic formula.
5988 // The divisions must be performed as signed divisions.
5991 if (TwoA.isMinValue()) {
5992 const SCEV *CNC = SE.getCouldNotCompute();
5993 return std::make_pair(CNC, CNC);
5996 LLVMContext &Context = SE.getContext();
5998 ConstantInt *Solution1 =
5999 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
6000 ConstantInt *Solution2 =
6001 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
6003 return std::make_pair(SE.getConstant(Solution1),
6004 SE.getConstant(Solution2));
6005 } // end APIntOps namespace
6008 /// HowFarToZero - Return the number of times a backedge comparing the specified
6009 /// value to zero will execute. If not computable, return CouldNotCompute.
6011 /// This is only used for loops with a "x != y" exit test. The exit condition is
6012 /// now expressed as a single expression, V = x-y. So the exit test is
6013 /// effectively V != 0. We know and take advantage of the fact that this
6014 /// expression only being used in a comparison by zero context.
6015 ScalarEvolution::ExitLimit
6016 ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L, bool ControlsExit) {
6017 // If the value is a constant
6018 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
6019 // If the value is already zero, the branch will execute zero times.
6020 if (C->getValue()->isZero()) return C;
6021 return getCouldNotCompute(); // Otherwise it will loop infinitely.
6024 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
6025 if (!AddRec || AddRec->getLoop() != L)
6026 return getCouldNotCompute();
6028 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
6029 // the quadratic equation to solve it.
6030 if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
6031 std::pair<const SCEV *,const SCEV *> Roots =
6032 SolveQuadraticEquation(AddRec, *this);
6033 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
6034 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
6037 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1
6038 << " sol#2: " << *R2 << "\n";
6040 // Pick the smallest positive root value.
6041 if (ConstantInt *CB =
6042 dyn_cast<ConstantInt>(ConstantExpr::getICmp(CmpInst::ICMP_ULT,
6045 if (CB->getZExtValue() == false)
6046 std::swap(R1, R2); // R1 is the minimum root now.
6048 // We can only use this value if the chrec ends up with an exact zero
6049 // value at this index. When solving for "X*X != 5", for example, we
6050 // should not accept a root of 2.
6051 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
6053 return R1; // We found a quadratic root!
6056 return getCouldNotCompute();
6059 // Otherwise we can only handle this if it is affine.
6060 if (!AddRec->isAffine())
6061 return getCouldNotCompute();
6063 // If this is an affine expression, the execution count of this branch is
6064 // the minimum unsigned root of the following equation:
6066 // Start + Step*N = 0 (mod 2^BW)
6070 // Step*N = -Start (mod 2^BW)
6072 // where BW is the common bit width of Start and Step.
6074 // Get the initial value for the loop.
6075 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
6076 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
6078 // For now we handle only constant steps.
6080 // TODO: Handle a nonconstant Step given AddRec<NUW>. If the
6081 // AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap
6082 // to 0, it must be counting down to equal 0. Consequently, N = Start / -Step.
6083 // We have not yet seen any such cases.
6084 const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step);
6085 if (!StepC || StepC->getValue()->equalsInt(0))
6086 return getCouldNotCompute();
6088 // For positive steps (counting up until unsigned overflow):
6089 // N = -Start/Step (as unsigned)
6090 // For negative steps (counting down to zero):
6092 // First compute the unsigned distance from zero in the direction of Step.
6093 bool CountDown = StepC->getValue()->getValue().isNegative();
6094 const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start);
6096 // Handle unitary steps, which cannot wraparound.
6097 // 1*N = -Start; -1*N = Start (mod 2^BW), so:
6098 // N = Distance (as unsigned)
6099 if (StepC->getValue()->equalsInt(1) || StepC->getValue()->isAllOnesValue()) {
6100 ConstantRange CR = getUnsignedRange(Start);
6101 const SCEV *MaxBECount;
6102 if (!CountDown && CR.getUnsignedMin().isMinValue())
6103 // When counting up, the worst starting value is 1, not 0.
6104 MaxBECount = CR.getUnsignedMax().isMinValue()
6105 ? getConstant(APInt::getMinValue(CR.getBitWidth()))
6106 : getConstant(APInt::getMaxValue(CR.getBitWidth()));
6108 MaxBECount = getConstant(CountDown ? CR.getUnsignedMax()
6109 : -CR.getUnsignedMin());
6110 return ExitLimit(Distance, MaxBECount);
6113 // As a special case, handle the instance where Step is a positive power of
6114 // two. In this case, determining whether Step divides Distance evenly can be
6115 // done by counting and comparing the number of trailing zeros of Step and
6118 const APInt &StepV = StepC->getValue()->getValue();
6119 // StepV.isPowerOf2() returns true if StepV is an positive power of two. It
6120 // also returns true if StepV is maximally negative (eg, INT_MIN), but that
6121 // case is not handled as this code is guarded by !CountDown.
6122 if (StepV.isPowerOf2() &&
6123 GetMinTrailingZeros(Distance) >= StepV.countTrailingZeros())
6124 return getUDivExactExpr(Distance, Step);
6127 // If the condition controls loop exit (the loop exits only if the expression
6128 // is true) and the addition is no-wrap we can use unsigned divide to
6129 // compute the backedge count. In this case, the step may not divide the
6130 // distance, but we don't care because if the condition is "missed" the loop
6131 // will have undefined behavior due to wrapping.
6132 if (ControlsExit && AddRec->getNoWrapFlags(SCEV::FlagNW)) {
6134 getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
6135 return ExitLimit(Exact, Exact);
6138 // Then, try to solve the above equation provided that Start is constant.
6139 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
6140 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
6141 -StartC->getValue()->getValue(),
6143 return getCouldNotCompute();
6146 /// HowFarToNonZero - Return the number of times a backedge checking the
6147 /// specified value for nonzero will execute. If not computable, return
6149 ScalarEvolution::ExitLimit
6150 ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
6151 // Loops that look like: while (X == 0) are very strange indeed. We don't
6152 // handle them yet except for the trivial case. This could be expanded in the
6153 // future as needed.
6155 // If the value is a constant, check to see if it is known to be non-zero
6156 // already. If so, the backedge will execute zero times.
6157 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
6158 if (!C->getValue()->isNullValue())
6159 return getConstant(C->getType(), 0);
6160 return getCouldNotCompute(); // Otherwise it will loop infinitely.
6163 // We could implement others, but I really doubt anyone writes loops like
6164 // this, and if they did, they would already be constant folded.
6165 return getCouldNotCompute();
6168 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
6169 /// (which may not be an immediate predecessor) which has exactly one
6170 /// successor from which BB is reachable, or null if no such block is
6173 std::pair<BasicBlock *, BasicBlock *>
6174 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
6175 // If the block has a unique predecessor, then there is no path from the
6176 // predecessor to the block that does not go through the direct edge
6177 // from the predecessor to the block.
6178 if (BasicBlock *Pred = BB->getSinglePredecessor())
6179 return std::make_pair(Pred, BB);
6181 // A loop's header is defined to be a block that dominates the loop.
6182 // If the header has a unique predecessor outside the loop, it must be
6183 // a block that has exactly one successor that can reach the loop.
6184 if (Loop *L = LI->getLoopFor(BB))
6185 return std::make_pair(L->getLoopPredecessor(), L->getHeader());
6187 return std::pair<BasicBlock *, BasicBlock *>();
6190 /// HasSameValue - SCEV structural equivalence is usually sufficient for
6191 /// testing whether two expressions are equal, however for the purposes of
6192 /// looking for a condition guarding a loop, it can be useful to be a little
6193 /// more general, since a front-end may have replicated the controlling
6196 static bool HasSameValue(const SCEV *A, const SCEV *B) {
6197 // Quick check to see if they are the same SCEV.
6198 if (A == B) return true;
6200 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
6201 // two different instructions with the same value. Check for this case.
6202 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
6203 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
6204 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
6205 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
6206 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory())
6209 // Otherwise assume they may have a different value.
6213 /// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with
6214 /// predicate Pred. Return true iff any changes were made.
6216 bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
6217 const SCEV *&LHS, const SCEV *&RHS,
6219 bool Changed = false;
6221 // If we hit the max recursion limit bail out.
6225 // Canonicalize a constant to the right side.
6226 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
6227 // Check for both operands constant.
6228 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
6229 if (ConstantExpr::getICmp(Pred,
6231 RHSC->getValue())->isNullValue())
6232 goto trivially_false;
6234 goto trivially_true;
6236 // Otherwise swap the operands to put the constant on the right.
6237 std::swap(LHS, RHS);
6238 Pred = ICmpInst::getSwappedPredicate(Pred);
6242 // If we're comparing an addrec with a value which is loop-invariant in the
6243 // addrec's loop, put the addrec on the left. Also make a dominance check,
6244 // as both operands could be addrecs loop-invariant in each other's loop.
6245 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
6246 const Loop *L = AR->getLoop();
6247 if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) {
6248 std::swap(LHS, RHS);
6249 Pred = ICmpInst::getSwappedPredicate(Pred);
6254 // If there's a constant operand, canonicalize comparisons with boundary
6255 // cases, and canonicalize *-or-equal comparisons to regular comparisons.
6256 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
6257 const APInt &RA = RC->getValue()->getValue();
6259 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6260 case ICmpInst::ICMP_EQ:
6261 case ICmpInst::ICMP_NE:
6262 // Fold ((-1) * %a) + %b == 0 (equivalent to %b-%a == 0) into %a == %b.
6264 if (const SCEVAddExpr *AE = dyn_cast<SCEVAddExpr>(LHS))
6265 if (const SCEVMulExpr *ME = dyn_cast<SCEVMulExpr>(AE->getOperand(0)))
6266 if (AE->getNumOperands() == 2 && ME->getNumOperands() == 2 &&
6267 ME->getOperand(0)->isAllOnesValue()) {
6268 RHS = AE->getOperand(1);
6269 LHS = ME->getOperand(1);
6273 case ICmpInst::ICMP_UGE:
6274 if ((RA - 1).isMinValue()) {
6275 Pred = ICmpInst::ICMP_NE;
6276 RHS = getConstant(RA - 1);
6280 if (RA.isMaxValue()) {
6281 Pred = ICmpInst::ICMP_EQ;
6285 if (RA.isMinValue()) goto trivially_true;
6287 Pred = ICmpInst::ICMP_UGT;
6288 RHS = getConstant(RA - 1);
6291 case ICmpInst::ICMP_ULE:
6292 if ((RA + 1).isMaxValue()) {
6293 Pred = ICmpInst::ICMP_NE;
6294 RHS = getConstant(RA + 1);
6298 if (RA.isMinValue()) {
6299 Pred = ICmpInst::ICMP_EQ;
6303 if (RA.isMaxValue()) goto trivially_true;
6305 Pred = ICmpInst::ICMP_ULT;
6306 RHS = getConstant(RA + 1);
6309 case ICmpInst::ICMP_SGE:
6310 if ((RA - 1).isMinSignedValue()) {
6311 Pred = ICmpInst::ICMP_NE;
6312 RHS = getConstant(RA - 1);
6316 if (RA.isMaxSignedValue()) {
6317 Pred = ICmpInst::ICMP_EQ;
6321 if (RA.isMinSignedValue()) goto trivially_true;
6323 Pred = ICmpInst::ICMP_SGT;
6324 RHS = getConstant(RA - 1);
6327 case ICmpInst::ICMP_SLE:
6328 if ((RA + 1).isMaxSignedValue()) {
6329 Pred = ICmpInst::ICMP_NE;
6330 RHS = getConstant(RA + 1);
6334 if (RA.isMinSignedValue()) {
6335 Pred = ICmpInst::ICMP_EQ;
6339 if (RA.isMaxSignedValue()) goto trivially_true;
6341 Pred = ICmpInst::ICMP_SLT;
6342 RHS = getConstant(RA + 1);
6345 case ICmpInst::ICMP_UGT:
6346 if (RA.isMinValue()) {
6347 Pred = ICmpInst::ICMP_NE;
6351 if ((RA + 1).isMaxValue()) {
6352 Pred = ICmpInst::ICMP_EQ;
6353 RHS = getConstant(RA + 1);
6357 if (RA.isMaxValue()) goto trivially_false;
6359 case ICmpInst::ICMP_ULT:
6360 if (RA.isMaxValue()) {
6361 Pred = ICmpInst::ICMP_NE;
6365 if ((RA - 1).isMinValue()) {
6366 Pred = ICmpInst::ICMP_EQ;
6367 RHS = getConstant(RA - 1);
6371 if (RA.isMinValue()) goto trivially_false;
6373 case ICmpInst::ICMP_SGT:
6374 if (RA.isMinSignedValue()) {
6375 Pred = ICmpInst::ICMP_NE;
6379 if ((RA + 1).isMaxSignedValue()) {
6380 Pred = ICmpInst::ICMP_EQ;
6381 RHS = getConstant(RA + 1);
6385 if (RA.isMaxSignedValue()) goto trivially_false;
6387 case ICmpInst::ICMP_SLT:
6388 if (RA.isMaxSignedValue()) {
6389 Pred = ICmpInst::ICMP_NE;
6393 if ((RA - 1).isMinSignedValue()) {
6394 Pred = ICmpInst::ICMP_EQ;
6395 RHS = getConstant(RA - 1);
6399 if (RA.isMinSignedValue()) goto trivially_false;
6404 // Check for obvious equality.
6405 if (HasSameValue(LHS, RHS)) {
6406 if (ICmpInst::isTrueWhenEqual(Pred))
6407 goto trivially_true;
6408 if (ICmpInst::isFalseWhenEqual(Pred))
6409 goto trivially_false;
6412 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
6413 // adding or subtracting 1 from one of the operands.
6415 case ICmpInst::ICMP_SLE:
6416 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) {
6417 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
6419 Pred = ICmpInst::ICMP_SLT;
6421 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) {
6422 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
6424 Pred = ICmpInst::ICMP_SLT;
6428 case ICmpInst::ICMP_SGE:
6429 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) {
6430 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
6432 Pred = ICmpInst::ICMP_SGT;
6434 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) {
6435 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
6437 Pred = ICmpInst::ICMP_SGT;
6441 case ICmpInst::ICMP_ULE:
6442 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) {
6443 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
6445 Pred = ICmpInst::ICMP_ULT;
6447 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) {
6448 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
6450 Pred = ICmpInst::ICMP_ULT;
6454 case ICmpInst::ICMP_UGE:
6455 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) {
6456 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
6458 Pred = ICmpInst::ICMP_UGT;
6460 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) {
6461 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
6463 Pred = ICmpInst::ICMP_UGT;
6471 // TODO: More simplifications are possible here.
6473 // Recursively simplify until we either hit a recursion limit or nothing
6476 return SimplifyICmpOperands(Pred, LHS, RHS, Depth+1);
6482 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
6483 Pred = ICmpInst::ICMP_EQ;
6488 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
6489 Pred = ICmpInst::ICMP_NE;
6493 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
6494 return getSignedRange(S).getSignedMax().isNegative();
6497 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
6498 return getSignedRange(S).getSignedMin().isStrictlyPositive();
6501 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
6502 return !getSignedRange(S).getSignedMin().isNegative();
6505 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
6506 return !getSignedRange(S).getSignedMax().isStrictlyPositive();
6509 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
6510 return isKnownNegative(S) || isKnownPositive(S);
6513 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
6514 const SCEV *LHS, const SCEV *RHS) {
6515 // Canonicalize the inputs first.
6516 (void)SimplifyICmpOperands(Pred, LHS, RHS);
6518 // If LHS or RHS is an addrec, check to see if the condition is true in
6519 // every iteration of the loop.
6520 // If LHS and RHS are both addrec, both conditions must be true in
6521 // every iteration of the loop.
6522 const SCEVAddRecExpr *LAR = dyn_cast<SCEVAddRecExpr>(LHS);
6523 const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS);
6524 bool LeftGuarded = false;
6525 bool RightGuarded = false;
6527 const Loop *L = LAR->getLoop();
6528 if (isLoopEntryGuardedByCond(L, Pred, LAR->getStart(), RHS) &&
6529 isLoopBackedgeGuardedByCond(L, Pred, LAR->getPostIncExpr(*this), RHS)) {
6530 if (!RAR) return true;
6535 const Loop *L = RAR->getLoop();
6536 if (isLoopEntryGuardedByCond(L, Pred, LHS, RAR->getStart()) &&
6537 isLoopBackedgeGuardedByCond(L, Pred, LHS, RAR->getPostIncExpr(*this))) {
6538 if (!LAR) return true;
6539 RightGuarded = true;
6542 if (LeftGuarded && RightGuarded)
6545 // Otherwise see what can be done with known constant ranges.
6546 return isKnownPredicateWithRanges(Pred, LHS, RHS);
6550 ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred,
6551 const SCEV *LHS, const SCEV *RHS) {
6552 if (HasSameValue(LHS, RHS))
6553 return ICmpInst::isTrueWhenEqual(Pred);
6555 // This code is split out from isKnownPredicate because it is called from
6556 // within isLoopEntryGuardedByCond.
6559 llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6560 case ICmpInst::ICMP_SGT:
6561 std::swap(LHS, RHS);
6562 case ICmpInst::ICMP_SLT: {
6563 ConstantRange LHSRange = getSignedRange(LHS);
6564 ConstantRange RHSRange = getSignedRange(RHS);
6565 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
6567 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
6571 case ICmpInst::ICMP_SGE:
6572 std::swap(LHS, RHS);
6573 case ICmpInst::ICMP_SLE: {
6574 ConstantRange LHSRange = getSignedRange(LHS);
6575 ConstantRange RHSRange = getSignedRange(RHS);
6576 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
6578 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
6582 case ICmpInst::ICMP_UGT:
6583 std::swap(LHS, RHS);
6584 case ICmpInst::ICMP_ULT: {
6585 ConstantRange LHSRange = getUnsignedRange(LHS);
6586 ConstantRange RHSRange = getUnsignedRange(RHS);
6587 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
6589 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
6593 case ICmpInst::ICMP_UGE:
6594 std::swap(LHS, RHS);
6595 case ICmpInst::ICMP_ULE: {
6596 ConstantRange LHSRange = getUnsignedRange(LHS);
6597 ConstantRange RHSRange = getUnsignedRange(RHS);
6598 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
6600 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
6604 case ICmpInst::ICMP_NE: {
6605 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
6607 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
6610 const SCEV *Diff = getMinusSCEV(LHS, RHS);
6611 if (isKnownNonZero(Diff))
6615 case ICmpInst::ICMP_EQ:
6616 // The check at the top of the function catches the case where
6617 // the values are known to be equal.
6623 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
6624 /// protected by a conditional between LHS and RHS. This is used to
6625 /// to eliminate casts.
6627 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
6628 ICmpInst::Predicate Pred,
6629 const SCEV *LHS, const SCEV *RHS) {
6630 // Interpret a null as meaning no loop, where there is obviously no guard
6631 // (interprocedural conditions notwithstanding).
6632 if (!L) return true;
6634 if (isKnownPredicateWithRanges(Pred, LHS, RHS)) return true;
6636 BasicBlock *Latch = L->getLoopLatch();
6640 BranchInst *LoopContinuePredicate =
6641 dyn_cast<BranchInst>(Latch->getTerminator());
6642 if (LoopContinuePredicate && LoopContinuePredicate->isConditional() &&
6643 isImpliedCond(Pred, LHS, RHS,
6644 LoopContinuePredicate->getCondition(),
6645 LoopContinuePredicate->getSuccessor(0) != L->getHeader()))
6648 // Check conditions due to any @llvm.assume intrinsics.
6649 for (auto &AssumeVH : AC->assumptions()) {
6652 auto *CI = cast<CallInst>(AssumeVH);
6653 if (!DT->dominates(CI, Latch->getTerminator()))
6656 if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false))
6663 /// isLoopEntryGuardedByCond - Test whether entry to the loop is protected
6664 /// by a conditional between LHS and RHS. This is used to help avoid max
6665 /// expressions in loop trip counts, and to eliminate casts.
6667 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
6668 ICmpInst::Predicate Pred,
6669 const SCEV *LHS, const SCEV *RHS) {
6670 // Interpret a null as meaning no loop, where there is obviously no guard
6671 // (interprocedural conditions notwithstanding).
6672 if (!L) return false;
6674 if (isKnownPredicateWithRanges(Pred, LHS, RHS)) return true;
6676 // Starting at the loop predecessor, climb up the predecessor chain, as long
6677 // as there are predecessors that can be found that have unique successors
6678 // leading to the original header.
6679 for (std::pair<BasicBlock *, BasicBlock *>
6680 Pair(L->getLoopPredecessor(), L->getHeader());
6682 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
6684 BranchInst *LoopEntryPredicate =
6685 dyn_cast<BranchInst>(Pair.first->getTerminator());
6686 if (!LoopEntryPredicate ||
6687 LoopEntryPredicate->isUnconditional())
6690 if (isImpliedCond(Pred, LHS, RHS,
6691 LoopEntryPredicate->getCondition(),
6692 LoopEntryPredicate->getSuccessor(0) != Pair.second))
6696 // Check conditions due to any @llvm.assume intrinsics.
6697 for (auto &AssumeVH : AC->assumptions()) {
6700 auto *CI = cast<CallInst>(AssumeVH);
6701 if (!DT->dominates(CI, L->getHeader()))
6704 if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false))
6711 /// RAII wrapper to prevent recursive application of isImpliedCond.
6712 /// ScalarEvolution's PendingLoopPredicates set must be empty unless we are
6713 /// currently evaluating isImpliedCond.
6714 struct MarkPendingLoopPredicate {
6716 DenseSet<Value*> &LoopPreds;
6719 MarkPendingLoopPredicate(Value *C, DenseSet<Value*> &LP)
6720 : Cond(C), LoopPreds(LP) {
6721 Pending = !LoopPreds.insert(Cond).second;
6723 ~MarkPendingLoopPredicate() {
6725 LoopPreds.erase(Cond);
6729 /// isImpliedCond - Test whether the condition described by Pred, LHS,
6730 /// and RHS is true whenever the given Cond value evaluates to true.
6731 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred,
6732 const SCEV *LHS, const SCEV *RHS,
6733 Value *FoundCondValue,
6735 MarkPendingLoopPredicate Mark(FoundCondValue, PendingLoopPredicates);
6739 // Recursively handle And and Or conditions.
6740 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) {
6741 if (BO->getOpcode() == Instruction::And) {
6743 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
6744 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
6745 } else if (BO->getOpcode() == Instruction::Or) {
6747 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
6748 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
6752 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue);
6753 if (!ICI) return false;
6755 // Bail if the ICmp's operands' types are wider than the needed type
6756 // before attempting to call getSCEV on them. This avoids infinite
6757 // recursion, since the analysis of widening casts can require loop
6758 // exit condition information for overflow checking, which would
6760 if (getTypeSizeInBits(LHS->getType()) <
6761 getTypeSizeInBits(ICI->getOperand(0)->getType()))
6764 // Now that we found a conditional branch that dominates the loop or controls
6765 // the loop latch. Check to see if it is the comparison we are looking for.
6766 ICmpInst::Predicate FoundPred;
6768 FoundPred = ICI->getInversePredicate();
6770 FoundPred = ICI->getPredicate();
6772 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
6773 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
6775 // Balance the types. The case where FoundLHS' type is wider than
6776 // LHS' type is checked for above.
6777 if (getTypeSizeInBits(LHS->getType()) >
6778 getTypeSizeInBits(FoundLHS->getType())) {
6779 if (CmpInst::isSigned(FoundPred)) {
6780 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
6781 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
6783 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
6784 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
6788 // Canonicalize the query to match the way instcombine will have
6789 // canonicalized the comparison.
6790 if (SimplifyICmpOperands(Pred, LHS, RHS))
6792 return CmpInst::isTrueWhenEqual(Pred);
6793 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
6794 if (FoundLHS == FoundRHS)
6795 return CmpInst::isFalseWhenEqual(FoundPred);
6797 // Check to see if we can make the LHS or RHS match.
6798 if (LHS == FoundRHS || RHS == FoundLHS) {
6799 if (isa<SCEVConstant>(RHS)) {
6800 std::swap(FoundLHS, FoundRHS);
6801 FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
6803 std::swap(LHS, RHS);
6804 Pred = ICmpInst::getSwappedPredicate(Pred);
6808 // Check whether the found predicate is the same as the desired predicate.
6809 if (FoundPred == Pred)
6810 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
6812 // Check whether swapping the found predicate makes it the same as the
6813 // desired predicate.
6814 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
6815 if (isa<SCEVConstant>(RHS))
6816 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
6818 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
6819 RHS, LHS, FoundLHS, FoundRHS);
6822 // Check if we can make progress by sharpening ranges.
6823 if (FoundPred == ICmpInst::ICMP_NE &&
6824 (isa<SCEVConstant>(FoundLHS) || isa<SCEVConstant>(FoundRHS))) {
6826 const SCEVConstant *C = nullptr;
6827 const SCEV *V = nullptr;
6829 if (isa<SCEVConstant>(FoundLHS)) {
6830 C = cast<SCEVConstant>(FoundLHS);
6833 C = cast<SCEVConstant>(FoundRHS);
6837 // The guarding predicate tells us that C != V. If the known range
6838 // of V is [C, t), we can sharpen the range to [C + 1, t). The
6839 // range we consider has to correspond to same signedness as the
6840 // predicate we're interested in folding.
6842 APInt Min = ICmpInst::isSigned(Pred) ?
6843 getSignedRange(V).getSignedMin() : getUnsignedRange(V).getUnsignedMin();
6845 if (Min == C->getValue()->getValue()) {
6846 // Given (V >= Min && V != Min) we conclude V >= (Min + 1).
6847 // This is true even if (Min + 1) wraps around -- in case of
6848 // wraparound, (Min + 1) < Min, so (V >= Min => V >= (Min + 1)).
6850 APInt SharperMin = Min + 1;
6853 case ICmpInst::ICMP_SGE:
6854 case ICmpInst::ICMP_UGE:
6855 // We know V `Pred` SharperMin. If this implies LHS `Pred`
6857 if (isImpliedCondOperands(Pred, LHS, RHS, V,
6858 getConstant(SharperMin)))
6861 case ICmpInst::ICMP_SGT:
6862 case ICmpInst::ICMP_UGT:
6863 // We know from the range information that (V `Pred` Min ||
6864 // V == Min). We know from the guarding condition that !(V
6865 // == Min). This gives us
6867 // V `Pred` Min || V == Min && !(V == Min)
6870 // If V `Pred` Min implies LHS `Pred` RHS, we're done.
6872 if (isImpliedCondOperands(Pred, LHS, RHS, V, getConstant(Min)))
6882 // Check whether the actual condition is beyond sufficient.
6883 if (FoundPred == ICmpInst::ICMP_EQ)
6884 if (ICmpInst::isTrueWhenEqual(Pred))
6885 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
6887 if (Pred == ICmpInst::ICMP_NE)
6888 if (!ICmpInst::isTrueWhenEqual(FoundPred))
6889 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
6892 // Otherwise assume the worst.
6896 /// isImpliedCondOperands - Test whether the condition described by Pred,
6897 /// LHS, and RHS is true whenever the condition described by Pred, FoundLHS,
6898 /// and FoundRHS is true.
6899 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
6900 const SCEV *LHS, const SCEV *RHS,
6901 const SCEV *FoundLHS,
6902 const SCEV *FoundRHS) {
6903 return isImpliedCondOperandsHelper(Pred, LHS, RHS,
6904 FoundLHS, FoundRHS) ||
6905 // ~x < ~y --> x > y
6906 isImpliedCondOperandsHelper(Pred, LHS, RHS,
6907 getNotSCEV(FoundRHS),
6908 getNotSCEV(FoundLHS));
6912 /// If Expr computes ~A, return A else return nullptr
6913 static const SCEV *MatchNotExpr(const SCEV *Expr) {
6914 const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Expr);
6915 if (!Add || Add->getNumOperands() != 2) return nullptr;
6917 const SCEVConstant *AddLHS = dyn_cast<SCEVConstant>(Add->getOperand(0));
6918 if (!(AddLHS && AddLHS->getValue()->getValue().isAllOnesValue()))
6921 const SCEVMulExpr *AddRHS = dyn_cast<SCEVMulExpr>(Add->getOperand(1));
6922 if (!AddRHS || AddRHS->getNumOperands() != 2) return nullptr;
6924 const SCEVConstant *MulLHS = dyn_cast<SCEVConstant>(AddRHS->getOperand(0));
6925 if (!(MulLHS && MulLHS->getValue()->getValue().isAllOnesValue()))
6928 return AddRHS->getOperand(1);
6932 /// Is MaybeMaxExpr an SMax or UMax of Candidate and some other values?
6933 template<typename MaxExprType>
6934 static bool IsMaxConsistingOf(const SCEV *MaybeMaxExpr,
6935 const SCEV *Candidate) {
6936 const MaxExprType *MaxExpr = dyn_cast<MaxExprType>(MaybeMaxExpr);
6937 if (!MaxExpr) return false;
6939 auto It = std::find(MaxExpr->op_begin(), MaxExpr->op_end(), Candidate);
6940 return It != MaxExpr->op_end();
6944 /// Is MaybeMinExpr an SMin or UMin of Candidate and some other values?
6945 template<typename MaxExprType>
6946 static bool IsMinConsistingOf(ScalarEvolution &SE,
6947 const SCEV *MaybeMinExpr,
6948 const SCEV *Candidate) {
6949 const SCEV *MaybeMaxExpr = MatchNotExpr(MaybeMinExpr);
6953 return IsMaxConsistingOf<MaxExprType>(MaybeMaxExpr, SE.getNotSCEV(Candidate));
6957 /// Is LHS `Pred` RHS true on the virtue of LHS or RHS being a Min or Max
6959 static bool IsKnownPredicateViaMinOrMax(ScalarEvolution &SE,
6960 ICmpInst::Predicate Pred,
6961 const SCEV *LHS, const SCEV *RHS) {
6966 case ICmpInst::ICMP_SGE:
6967 std::swap(LHS, RHS);
6969 case ICmpInst::ICMP_SLE:
6972 IsMinConsistingOf<SCEVSMaxExpr>(SE, LHS, RHS) ||
6974 IsMaxConsistingOf<SCEVSMaxExpr>(RHS, LHS);
6976 case ICmpInst::ICMP_UGE:
6977 std::swap(LHS, RHS);
6979 case ICmpInst::ICMP_ULE:
6982 IsMinConsistingOf<SCEVUMaxExpr>(SE, LHS, RHS) ||
6984 IsMaxConsistingOf<SCEVUMaxExpr>(RHS, LHS);
6987 llvm_unreachable("covered switch fell through?!");
6990 /// isImpliedCondOperandsHelper - Test whether the condition described by
6991 /// Pred, LHS, and RHS is true whenever the condition described by Pred,
6992 /// FoundLHS, and FoundRHS is true.
6994 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
6995 const SCEV *LHS, const SCEV *RHS,
6996 const SCEV *FoundLHS,
6997 const SCEV *FoundRHS) {
6998 auto IsKnownPredicateFull =
6999 [this](ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS) {
7000 return isKnownPredicateWithRanges(Pred, LHS, RHS) ||
7001 IsKnownPredicateViaMinOrMax(*this, Pred, LHS, RHS);
7005 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
7006 case ICmpInst::ICMP_EQ:
7007 case ICmpInst::ICMP_NE:
7008 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
7011 case ICmpInst::ICMP_SLT:
7012 case ICmpInst::ICMP_SLE:
7013 if (IsKnownPredicateFull(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
7014 IsKnownPredicateFull(ICmpInst::ICMP_SGE, RHS, FoundRHS))
7017 case ICmpInst::ICMP_SGT:
7018 case ICmpInst::ICMP_SGE:
7019 if (IsKnownPredicateFull(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
7020 IsKnownPredicateFull(ICmpInst::ICMP_SLE, RHS, FoundRHS))
7023 case ICmpInst::ICMP_ULT:
7024 case ICmpInst::ICMP_ULE:
7025 if (IsKnownPredicateFull(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
7026 IsKnownPredicateFull(ICmpInst::ICMP_UGE, RHS, FoundRHS))
7029 case ICmpInst::ICMP_UGT:
7030 case ICmpInst::ICMP_UGE:
7031 if (IsKnownPredicateFull(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
7032 IsKnownPredicateFull(ICmpInst::ICMP_ULE, RHS, FoundRHS))
7040 // Verify if an linear IV with positive stride can overflow when in a
7041 // less-than comparison, knowing the invariant term of the comparison, the
7042 // stride and the knowledge of NSW/NUW flags on the recurrence.
7043 bool ScalarEvolution::doesIVOverflowOnLT(const SCEV *RHS, const SCEV *Stride,
7044 bool IsSigned, bool NoWrap) {
7045 if (NoWrap) return false;
7047 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
7048 const SCEV *One = getConstant(Stride->getType(), 1);
7051 APInt MaxRHS = getSignedRange(RHS).getSignedMax();
7052 APInt MaxValue = APInt::getSignedMaxValue(BitWidth);
7053 APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
7056 // SMaxRHS + SMaxStrideMinusOne > SMaxValue => overflow!
7057 return (MaxValue - MaxStrideMinusOne).slt(MaxRHS);
7060 APInt MaxRHS = getUnsignedRange(RHS).getUnsignedMax();
7061 APInt MaxValue = APInt::getMaxValue(BitWidth);
7062 APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
7065 // UMaxRHS + UMaxStrideMinusOne > UMaxValue => overflow!
7066 return (MaxValue - MaxStrideMinusOne).ult(MaxRHS);
7069 // Verify if an linear IV with negative stride can overflow when in a
7070 // greater-than comparison, knowing the invariant term of the comparison,
7071 // the stride and the knowledge of NSW/NUW flags on the recurrence.
7072 bool ScalarEvolution::doesIVOverflowOnGT(const SCEV *RHS, const SCEV *Stride,
7073 bool IsSigned, bool NoWrap) {
7074 if (NoWrap) return false;
7076 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
7077 const SCEV *One = getConstant(Stride->getType(), 1);
7080 APInt MinRHS = getSignedRange(RHS).getSignedMin();
7081 APInt MinValue = APInt::getSignedMinValue(BitWidth);
7082 APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
7085 // SMinRHS - SMaxStrideMinusOne < SMinValue => overflow!
7086 return (MinValue + MaxStrideMinusOne).sgt(MinRHS);
7089 APInt MinRHS = getUnsignedRange(RHS).getUnsignedMin();
7090 APInt MinValue = APInt::getMinValue(BitWidth);
7091 APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
7094 // UMinRHS - UMaxStrideMinusOne < UMinValue => overflow!
7095 return (MinValue + MaxStrideMinusOne).ugt(MinRHS);
7098 // Compute the backedge taken count knowing the interval difference, the
7099 // stride and presence of the equality in the comparison.
7100 const SCEV *ScalarEvolution::computeBECount(const SCEV *Delta, const SCEV *Step,
7102 const SCEV *One = getConstant(Step->getType(), 1);
7103 Delta = Equality ? getAddExpr(Delta, Step)
7104 : getAddExpr(Delta, getMinusSCEV(Step, One));
7105 return getUDivExpr(Delta, Step);
7108 /// HowManyLessThans - Return the number of times a backedge containing the
7109 /// specified less-than comparison will execute. If not computable, return
7110 /// CouldNotCompute.
7112 /// @param ControlsExit is true when the LHS < RHS condition directly controls
7113 /// the branch (loops exits only if condition is true). In this case, we can use
7114 /// NoWrapFlags to skip overflow checks.
7115 ScalarEvolution::ExitLimit
7116 ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
7117 const Loop *L, bool IsSigned,
7118 bool ControlsExit) {
7119 // We handle only IV < Invariant
7120 if (!isLoopInvariant(RHS, L))
7121 return getCouldNotCompute();
7123 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
7125 // Avoid weird loops
7126 if (!IV || IV->getLoop() != L || !IV->isAffine())
7127 return getCouldNotCompute();
7129 bool NoWrap = ControlsExit &&
7130 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
7132 const SCEV *Stride = IV->getStepRecurrence(*this);
7134 // Avoid negative or zero stride values
7135 if (!isKnownPositive(Stride))
7136 return getCouldNotCompute();
7138 // Avoid proven overflow cases: this will ensure that the backedge taken count
7139 // will not generate any unsigned overflow. Relaxed no-overflow conditions
7140 // exploit NoWrapFlags, allowing to optimize in presence of undefined
7141 // behaviors like the case of C language.
7142 if (!Stride->isOne() && doesIVOverflowOnLT(RHS, Stride, IsSigned, NoWrap))
7143 return getCouldNotCompute();
7145 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SLT
7146 : ICmpInst::ICMP_ULT;
7147 const SCEV *Start = IV->getStart();
7148 const SCEV *End = RHS;
7149 if (!isLoopEntryGuardedByCond(L, Cond, getMinusSCEV(Start, Stride), RHS)) {
7150 const SCEV *Diff = getMinusSCEV(RHS, Start);
7151 // If we have NoWrap set, then we can assume that the increment won't
7152 // overflow, in which case if RHS - Start is a constant, we don't need to
7153 // do a max operation since we can just figure it out statically
7154 if (NoWrap && isa<SCEVConstant>(Diff)) {
7155 APInt D = dyn_cast<const SCEVConstant>(Diff)->getValue()->getValue();
7159 End = IsSigned ? getSMaxExpr(RHS, Start)
7160 : getUMaxExpr(RHS, Start);
7163 const SCEV *BECount = computeBECount(getMinusSCEV(End, Start), Stride, false);
7165 APInt MinStart = IsSigned ? getSignedRange(Start).getSignedMin()
7166 : getUnsignedRange(Start).getUnsignedMin();
7168 APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
7169 : getUnsignedRange(Stride).getUnsignedMin();
7171 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
7172 APInt Limit = IsSigned ? APInt::getSignedMaxValue(BitWidth) - (MinStride - 1)
7173 : APInt::getMaxValue(BitWidth) - (MinStride - 1);
7175 // Although End can be a MAX expression we estimate MaxEnd considering only
7176 // the case End = RHS. This is safe because in the other case (End - Start)
7177 // is zero, leading to a zero maximum backedge taken count.
7179 IsSigned ? APIntOps::smin(getSignedRange(RHS).getSignedMax(), Limit)
7180 : APIntOps::umin(getUnsignedRange(RHS).getUnsignedMax(), Limit);
7182 const SCEV *MaxBECount;
7183 if (isa<SCEVConstant>(BECount))
7184 MaxBECount = BECount;
7186 MaxBECount = computeBECount(getConstant(MaxEnd - MinStart),
7187 getConstant(MinStride), false);
7189 if (isa<SCEVCouldNotCompute>(MaxBECount))
7190 MaxBECount = BECount;
7192 return ExitLimit(BECount, MaxBECount);
7195 ScalarEvolution::ExitLimit
7196 ScalarEvolution::HowManyGreaterThans(const SCEV *LHS, const SCEV *RHS,
7197 const Loop *L, bool IsSigned,
7198 bool ControlsExit) {
7199 // We handle only IV > Invariant
7200 if (!isLoopInvariant(RHS, L))
7201 return getCouldNotCompute();
7203 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
7205 // Avoid weird loops
7206 if (!IV || IV->getLoop() != L || !IV->isAffine())
7207 return getCouldNotCompute();
7209 bool NoWrap = ControlsExit &&
7210 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
7212 const SCEV *Stride = getNegativeSCEV(IV->getStepRecurrence(*this));
7214 // Avoid negative or zero stride values
7215 if (!isKnownPositive(Stride))
7216 return getCouldNotCompute();
7218 // Avoid proven overflow cases: this will ensure that the backedge taken count
7219 // will not generate any unsigned overflow. Relaxed no-overflow conditions
7220 // exploit NoWrapFlags, allowing to optimize in presence of undefined
7221 // behaviors like the case of C language.
7222 if (!Stride->isOne() && doesIVOverflowOnGT(RHS, Stride, IsSigned, NoWrap))
7223 return getCouldNotCompute();
7225 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SGT
7226 : ICmpInst::ICMP_UGT;
7228 const SCEV *Start = IV->getStart();
7229 const SCEV *End = RHS;
7230 if (!isLoopEntryGuardedByCond(L, Cond, getAddExpr(Start, Stride), RHS)) {
7231 const SCEV *Diff = getMinusSCEV(RHS, Start);
7232 // If we have NoWrap set, then we can assume that the increment won't
7233 // overflow, in which case if RHS - Start is a constant, we don't need to
7234 // do a max operation since we can just figure it out statically
7235 if (NoWrap && isa<SCEVConstant>(Diff)) {
7236 APInt D = dyn_cast<const SCEVConstant>(Diff)->getValue()->getValue();
7237 if (!D.isNegative())
7240 End = IsSigned ? getSMinExpr(RHS, Start)
7241 : getUMinExpr(RHS, Start);
7244 const SCEV *BECount = computeBECount(getMinusSCEV(Start, End), Stride, false);
7246 APInt MaxStart = IsSigned ? getSignedRange(Start).getSignedMax()
7247 : getUnsignedRange(Start).getUnsignedMax();
7249 APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
7250 : getUnsignedRange(Stride).getUnsignedMin();
7252 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
7253 APInt Limit = IsSigned ? APInt::getSignedMinValue(BitWidth) + (MinStride - 1)
7254 : APInt::getMinValue(BitWidth) + (MinStride - 1);
7256 // Although End can be a MIN expression we estimate MinEnd considering only
7257 // the case End = RHS. This is safe because in the other case (Start - End)
7258 // is zero, leading to a zero maximum backedge taken count.
7260 IsSigned ? APIntOps::smax(getSignedRange(RHS).getSignedMin(), Limit)
7261 : APIntOps::umax(getUnsignedRange(RHS).getUnsignedMin(), Limit);
7264 const SCEV *MaxBECount = getCouldNotCompute();
7265 if (isa<SCEVConstant>(BECount))
7266 MaxBECount = BECount;
7268 MaxBECount = computeBECount(getConstant(MaxStart - MinEnd),
7269 getConstant(MinStride), false);
7271 if (isa<SCEVCouldNotCompute>(MaxBECount))
7272 MaxBECount = BECount;
7274 return ExitLimit(BECount, MaxBECount);
7277 /// getNumIterationsInRange - Return the number of iterations of this loop that
7278 /// produce values in the specified constant range. Another way of looking at
7279 /// this is that it returns the first iteration number where the value is not in
7280 /// the condition, thus computing the exit count. If the iteration count can't
7281 /// be computed, an instance of SCEVCouldNotCompute is returned.
7282 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
7283 ScalarEvolution &SE) const {
7284 if (Range.isFullSet()) // Infinite loop.
7285 return SE.getCouldNotCompute();
7287 // If the start is a non-zero constant, shift the range to simplify things.
7288 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
7289 if (!SC->getValue()->isZero()) {
7290 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
7291 Operands[0] = SE.getConstant(SC->getType(), 0);
7292 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(),
7293 getNoWrapFlags(FlagNW));
7294 if (const SCEVAddRecExpr *ShiftedAddRec =
7295 dyn_cast<SCEVAddRecExpr>(Shifted))
7296 return ShiftedAddRec->getNumIterationsInRange(
7297 Range.subtract(SC->getValue()->getValue()), SE);
7298 // This is strange and shouldn't happen.
7299 return SE.getCouldNotCompute();
7302 // The only time we can solve this is when we have all constant indices.
7303 // Otherwise, we cannot determine the overflow conditions.
7304 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
7305 if (!isa<SCEVConstant>(getOperand(i)))
7306 return SE.getCouldNotCompute();
7309 // Okay at this point we know that all elements of the chrec are constants and
7310 // that the start element is zero.
7312 // First check to see if the range contains zero. If not, the first
7314 unsigned BitWidth = SE.getTypeSizeInBits(getType());
7315 if (!Range.contains(APInt(BitWidth, 0)))
7316 return SE.getConstant(getType(), 0);
7319 // If this is an affine expression then we have this situation:
7320 // Solve {0,+,A} in Range === Ax in Range
7322 // We know that zero is in the range. If A is positive then we know that
7323 // the upper value of the range must be the first possible exit value.
7324 // If A is negative then the lower of the range is the last possible loop
7325 // value. Also note that we already checked for a full range.
7326 APInt One(BitWidth,1);
7327 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
7328 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
7330 // The exit value should be (End+A)/A.
7331 APInt ExitVal = (End + A).udiv(A);
7332 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
7334 // Evaluate at the exit value. If we really did fall out of the valid
7335 // range, then we computed our trip count, otherwise wrap around or other
7336 // things must have happened.
7337 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
7338 if (Range.contains(Val->getValue()))
7339 return SE.getCouldNotCompute(); // Something strange happened
7341 // Ensure that the previous value is in the range. This is a sanity check.
7342 assert(Range.contains(
7343 EvaluateConstantChrecAtConstant(this,
7344 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
7345 "Linear scev computation is off in a bad way!");
7346 return SE.getConstant(ExitValue);
7347 } else if (isQuadratic()) {
7348 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
7349 // quadratic equation to solve it. To do this, we must frame our problem in
7350 // terms of figuring out when zero is crossed, instead of when
7351 // Range.getUpper() is crossed.
7352 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
7353 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
7354 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop(),
7355 // getNoWrapFlags(FlagNW)
7358 // Next, solve the constructed addrec
7359 std::pair<const SCEV *,const SCEV *> Roots =
7360 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
7361 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
7362 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
7364 // Pick the smallest positive root value.
7365 if (ConstantInt *CB =
7366 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
7367 R1->getValue(), R2->getValue()))) {
7368 if (CB->getZExtValue() == false)
7369 std::swap(R1, R2); // R1 is the minimum root now.
7371 // Make sure the root is not off by one. The returned iteration should
7372 // not be in the range, but the previous one should be. When solving
7373 // for "X*X < 5", for example, we should not return a root of 2.
7374 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
7377 if (Range.contains(R1Val->getValue())) {
7378 // The next iteration must be out of the range...
7379 ConstantInt *NextVal =
7380 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1);
7382 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
7383 if (!Range.contains(R1Val->getValue()))
7384 return SE.getConstant(NextVal);
7385 return SE.getCouldNotCompute(); // Something strange happened
7388 // If R1 was not in the range, then it is a good return value. Make
7389 // sure that R1-1 WAS in the range though, just in case.
7390 ConstantInt *NextVal =
7391 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1);
7392 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
7393 if (Range.contains(R1Val->getValue()))
7395 return SE.getCouldNotCompute(); // Something strange happened
7400 return SE.getCouldNotCompute();
7406 FindUndefs() : Found(false) {}
7408 bool follow(const SCEV *S) {
7409 if (const SCEVUnknown *C = dyn_cast<SCEVUnknown>(S)) {
7410 if (isa<UndefValue>(C->getValue()))
7412 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) {
7413 if (isa<UndefValue>(C->getValue()))
7417 // Keep looking if we haven't found it yet.
7420 bool isDone() const {
7421 // Stop recursion if we have found an undef.
7427 // Return true when S contains at least an undef value.
7429 containsUndefs(const SCEV *S) {
7431 SCEVTraversal<FindUndefs> ST(F);
7438 // Collect all steps of SCEV expressions.
7439 struct SCEVCollectStrides {
7440 ScalarEvolution &SE;
7441 SmallVectorImpl<const SCEV *> &Strides;
7443 SCEVCollectStrides(ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &S)
7444 : SE(SE), Strides(S) {}
7446 bool follow(const SCEV *S) {
7447 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(S))
7448 Strides.push_back(AR->getStepRecurrence(SE));
7451 bool isDone() const { return false; }
7454 // Collect all SCEVUnknown and SCEVMulExpr expressions.
7455 struct SCEVCollectTerms {
7456 SmallVectorImpl<const SCEV *> &Terms;
7458 SCEVCollectTerms(SmallVectorImpl<const SCEV *> &T)
7461 bool follow(const SCEV *S) {
7462 if (isa<SCEVUnknown>(S) || isa<SCEVMulExpr>(S)) {
7463 if (!containsUndefs(S))
7466 // Stop recursion: once we collected a term, do not walk its operands.
7473 bool isDone() const { return false; }
7477 /// Find parametric terms in this SCEVAddRecExpr.
7478 void SCEVAddRecExpr::collectParametricTerms(
7479 ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &Terms) const {
7480 SmallVector<const SCEV *, 4> Strides;
7481 SCEVCollectStrides StrideCollector(SE, Strides);
7482 visitAll(this, StrideCollector);
7485 dbgs() << "Strides:\n";
7486 for (const SCEV *S : Strides)
7487 dbgs() << *S << "\n";
7490 for (const SCEV *S : Strides) {
7491 SCEVCollectTerms TermCollector(Terms);
7492 visitAll(S, TermCollector);
7496 dbgs() << "Terms:\n";
7497 for (const SCEV *T : Terms)
7498 dbgs() << *T << "\n";
7502 static bool findArrayDimensionsRec(ScalarEvolution &SE,
7503 SmallVectorImpl<const SCEV *> &Terms,
7504 SmallVectorImpl<const SCEV *> &Sizes) {
7505 int Last = Terms.size() - 1;
7506 const SCEV *Step = Terms[Last];
7508 // End of recursion.
7510 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Step)) {
7511 SmallVector<const SCEV *, 2> Qs;
7512 for (const SCEV *Op : M->operands())
7513 if (!isa<SCEVConstant>(Op))
7516 Step = SE.getMulExpr(Qs);
7519 Sizes.push_back(Step);
7523 for (const SCEV *&Term : Terms) {
7524 // Normalize the terms before the next call to findArrayDimensionsRec.
7526 SCEVDivision::divide(SE, Term, Step, &Q, &R);
7528 // Bail out when GCD does not evenly divide one of the terms.
7535 // Remove all SCEVConstants.
7536 Terms.erase(std::remove_if(Terms.begin(), Terms.end(), [](const SCEV *E) {
7537 return isa<SCEVConstant>(E);
7541 if (Terms.size() > 0)
7542 if (!findArrayDimensionsRec(SE, Terms, Sizes))
7545 Sizes.push_back(Step);
7550 struct FindParameter {
7551 bool FoundParameter;
7552 FindParameter() : FoundParameter(false) {}
7554 bool follow(const SCEV *S) {
7555 if (isa<SCEVUnknown>(S)) {
7556 FoundParameter = true;
7557 // Stop recursion: we found a parameter.
7563 bool isDone() const {
7564 // Stop recursion if we have found a parameter.
7565 return FoundParameter;
7570 // Returns true when S contains at least a SCEVUnknown parameter.
7572 containsParameters(const SCEV *S) {
7574 SCEVTraversal<FindParameter> ST(F);
7577 return F.FoundParameter;
7580 // Returns true when one of the SCEVs of Terms contains a SCEVUnknown parameter.
7582 containsParameters(SmallVectorImpl<const SCEV *> &Terms) {
7583 for (const SCEV *T : Terms)
7584 if (containsParameters(T))
7589 // Return the number of product terms in S.
7590 static inline int numberOfTerms(const SCEV *S) {
7591 if (const SCEVMulExpr *Expr = dyn_cast<SCEVMulExpr>(S))
7592 return Expr->getNumOperands();
7596 static const SCEV *removeConstantFactors(ScalarEvolution &SE, const SCEV *T) {
7597 if (isa<SCEVConstant>(T))
7600 if (isa<SCEVUnknown>(T))
7603 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(T)) {
7604 SmallVector<const SCEV *, 2> Factors;
7605 for (const SCEV *Op : M->operands())
7606 if (!isa<SCEVConstant>(Op))
7607 Factors.push_back(Op);
7609 return SE.getMulExpr(Factors);
7615 /// Return the size of an element read or written by Inst.
7616 const SCEV *ScalarEvolution::getElementSize(Instruction *Inst) {
7618 if (StoreInst *Store = dyn_cast<StoreInst>(Inst))
7619 Ty = Store->getValueOperand()->getType();
7620 else if (LoadInst *Load = dyn_cast<LoadInst>(Inst))
7621 Ty = Load->getType();
7625 Type *ETy = getEffectiveSCEVType(PointerType::getUnqual(Ty));
7626 return getSizeOfExpr(ETy, Ty);
7629 /// Second step of delinearization: compute the array dimensions Sizes from the
7630 /// set of Terms extracted from the memory access function of this SCEVAddRec.
7631 void ScalarEvolution::findArrayDimensions(SmallVectorImpl<const SCEV *> &Terms,
7632 SmallVectorImpl<const SCEV *> &Sizes,
7633 const SCEV *ElementSize) const {
7635 if (Terms.size() < 1 || !ElementSize)
7638 // Early return when Terms do not contain parameters: we do not delinearize
7639 // non parametric SCEVs.
7640 if (!containsParameters(Terms))
7644 dbgs() << "Terms:\n";
7645 for (const SCEV *T : Terms)
7646 dbgs() << *T << "\n";
7649 // Remove duplicates.
7650 std::sort(Terms.begin(), Terms.end());
7651 Terms.erase(std::unique(Terms.begin(), Terms.end()), Terms.end());
7653 // Put larger terms first.
7654 std::sort(Terms.begin(), Terms.end(), [](const SCEV *LHS, const SCEV *RHS) {
7655 return numberOfTerms(LHS) > numberOfTerms(RHS);
7658 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
7660 // Divide all terms by the element size.
7661 for (const SCEV *&Term : Terms) {
7663 SCEVDivision::divide(SE, Term, ElementSize, &Q, &R);
7667 SmallVector<const SCEV *, 4> NewTerms;
7669 // Remove constant factors.
7670 for (const SCEV *T : Terms)
7671 if (const SCEV *NewT = removeConstantFactors(SE, T))
7672 NewTerms.push_back(NewT);
7675 dbgs() << "Terms after sorting:\n";
7676 for (const SCEV *T : NewTerms)
7677 dbgs() << *T << "\n";
7680 if (NewTerms.empty() ||
7681 !findArrayDimensionsRec(SE, NewTerms, Sizes)) {
7686 // The last element to be pushed into Sizes is the size of an element.
7687 Sizes.push_back(ElementSize);
7690 dbgs() << "Sizes:\n";
7691 for (const SCEV *S : Sizes)
7692 dbgs() << *S << "\n";
7696 /// Third step of delinearization: compute the access functions for the
7697 /// Subscripts based on the dimensions in Sizes.
7698 void SCEVAddRecExpr::computeAccessFunctions(
7699 ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &Subscripts,
7700 SmallVectorImpl<const SCEV *> &Sizes) const {
7702 // Early exit in case this SCEV is not an affine multivariate function.
7703 if (Sizes.empty() || !this->isAffine())
7706 const SCEV *Res = this;
7707 int Last = Sizes.size() - 1;
7708 for (int i = Last; i >= 0; i--) {
7710 SCEVDivision::divide(SE, Res, Sizes[i], &Q, &R);
7713 dbgs() << "Res: " << *Res << "\n";
7714 dbgs() << "Sizes[i]: " << *Sizes[i] << "\n";
7715 dbgs() << "Res divided by Sizes[i]:\n";
7716 dbgs() << "Quotient: " << *Q << "\n";
7717 dbgs() << "Remainder: " << *R << "\n";
7722 // Do not record the last subscript corresponding to the size of elements in
7726 // Bail out if the remainder is too complex.
7727 if (isa<SCEVAddRecExpr>(R)) {
7736 // Record the access function for the current subscript.
7737 Subscripts.push_back(R);
7740 // Also push in last position the remainder of the last division: it will be
7741 // the access function of the innermost dimension.
7742 Subscripts.push_back(Res);
7744 std::reverse(Subscripts.begin(), Subscripts.end());
7747 dbgs() << "Subscripts:\n";
7748 for (const SCEV *S : Subscripts)
7749 dbgs() << *S << "\n";
7753 /// Splits the SCEV into two vectors of SCEVs representing the subscripts and
7754 /// sizes of an array access. Returns the remainder of the delinearization that
7755 /// is the offset start of the array. The SCEV->delinearize algorithm computes
7756 /// the multiples of SCEV coefficients: that is a pattern matching of sub
7757 /// expressions in the stride and base of a SCEV corresponding to the
7758 /// computation of a GCD (greatest common divisor) of base and stride. When
7759 /// SCEV->delinearize fails, it returns the SCEV unchanged.
7761 /// For example: when analyzing the memory access A[i][j][k] in this loop nest
7763 /// void foo(long n, long m, long o, double A[n][m][o]) {
7765 /// for (long i = 0; i < n; i++)
7766 /// for (long j = 0; j < m; j++)
7767 /// for (long k = 0; k < o; k++)
7768 /// A[i][j][k] = 1.0;
7771 /// the delinearization input is the following AddRec SCEV:
7773 /// AddRec: {{{%A,+,(8 * %m * %o)}<%for.i>,+,(8 * %o)}<%for.j>,+,8}<%for.k>
7775 /// From this SCEV, we are able to say that the base offset of the access is %A
7776 /// because it appears as an offset that does not divide any of the strides in
7779 /// CHECK: Base offset: %A
7781 /// and then SCEV->delinearize determines the size of some of the dimensions of
7782 /// the array as these are the multiples by which the strides are happening:
7784 /// CHECK: ArrayDecl[UnknownSize][%m][%o] with elements of sizeof(double) bytes.
7786 /// Note that the outermost dimension remains of UnknownSize because there are
7787 /// no strides that would help identifying the size of the last dimension: when
7788 /// the array has been statically allocated, one could compute the size of that
7789 /// dimension by dividing the overall size of the array by the size of the known
7790 /// dimensions: %m * %o * 8.
7792 /// Finally delinearize provides the access functions for the array reference
7793 /// that does correspond to A[i][j][k] of the above C testcase:
7795 /// CHECK: ArrayRef[{0,+,1}<%for.i>][{0,+,1}<%for.j>][{0,+,1}<%for.k>]
7797 /// The testcases are checking the output of a function pass:
7798 /// DelinearizationPass that walks through all loads and stores of a function
7799 /// asking for the SCEV of the memory access with respect to all enclosing
7800 /// loops, calling SCEV->delinearize on that and printing the results.
7802 void SCEVAddRecExpr::delinearize(ScalarEvolution &SE,
7803 SmallVectorImpl<const SCEV *> &Subscripts,
7804 SmallVectorImpl<const SCEV *> &Sizes,
7805 const SCEV *ElementSize) const {
7806 // First step: collect parametric terms.
7807 SmallVector<const SCEV *, 4> Terms;
7808 collectParametricTerms(SE, Terms);
7813 // Second step: find subscript sizes.
7814 SE.findArrayDimensions(Terms, Sizes, ElementSize);
7819 // Third step: compute the access functions for each subscript.
7820 computeAccessFunctions(SE, Subscripts, Sizes);
7822 if (Subscripts.empty())
7826 dbgs() << "succeeded to delinearize " << *this << "\n";
7827 dbgs() << "ArrayDecl[UnknownSize]";
7828 for (const SCEV *S : Sizes)
7829 dbgs() << "[" << *S << "]";
7831 dbgs() << "\nArrayRef";
7832 for (const SCEV *S : Subscripts)
7833 dbgs() << "[" << *S << "]";
7838 //===----------------------------------------------------------------------===//
7839 // SCEVCallbackVH Class Implementation
7840 //===----------------------------------------------------------------------===//
7842 void ScalarEvolution::SCEVCallbackVH::deleted() {
7843 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
7844 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
7845 SE->ConstantEvolutionLoopExitValue.erase(PN);
7846 SE->ValueExprMap.erase(getValPtr());
7847 // this now dangles!
7850 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) {
7851 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
7853 // Forget all the expressions associated with users of the old value,
7854 // so that future queries will recompute the expressions using the new
7856 Value *Old = getValPtr();
7857 SmallVector<User *, 16> Worklist(Old->user_begin(), Old->user_end());
7858 SmallPtrSet<User *, 8> Visited;
7859 while (!Worklist.empty()) {
7860 User *U = Worklist.pop_back_val();
7861 // Deleting the Old value will cause this to dangle. Postpone
7862 // that until everything else is done.
7865 if (!Visited.insert(U).second)
7867 if (PHINode *PN = dyn_cast<PHINode>(U))
7868 SE->ConstantEvolutionLoopExitValue.erase(PN);
7869 SE->ValueExprMap.erase(U);
7870 Worklist.insert(Worklist.end(), U->user_begin(), U->user_end());
7872 // Delete the Old value.
7873 if (PHINode *PN = dyn_cast<PHINode>(Old))
7874 SE->ConstantEvolutionLoopExitValue.erase(PN);
7875 SE->ValueExprMap.erase(Old);
7876 // this now dangles!
7879 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
7880 : CallbackVH(V), SE(se) {}
7882 //===----------------------------------------------------------------------===//
7883 // ScalarEvolution Class Implementation
7884 //===----------------------------------------------------------------------===//
7886 ScalarEvolution::ScalarEvolution()
7887 : FunctionPass(ID), ValuesAtScopes(64), LoopDispositions(64),
7888 BlockDispositions(64), FirstUnknown(nullptr) {
7889 initializeScalarEvolutionPass(*PassRegistry::getPassRegistry());
7892 bool ScalarEvolution::runOnFunction(Function &F) {
7894 AC = &getAnalysis<AssumptionCacheTracker>().getAssumptionCache(F);
7895 LI = &getAnalysis<LoopInfoWrapperPass>().getLoopInfo();
7896 DataLayoutPass *DLP = getAnalysisIfAvailable<DataLayoutPass>();
7897 DL = DLP ? &DLP->getDataLayout() : nullptr;
7898 TLI = &getAnalysis<TargetLibraryInfoWrapperPass>().getTLI();
7899 DT = &getAnalysis<DominatorTreeWrapperPass>().getDomTree();
7903 void ScalarEvolution::releaseMemory() {
7904 // Iterate through all the SCEVUnknown instances and call their
7905 // destructors, so that they release their references to their values.
7906 for (SCEVUnknown *U = FirstUnknown; U; U = U->Next)
7908 FirstUnknown = nullptr;
7910 ValueExprMap.clear();
7912 // Free any extra memory created for ExitNotTakenInfo in the unlikely event
7913 // that a loop had multiple computable exits.
7914 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
7915 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end();
7920 assert(PendingLoopPredicates.empty() && "isImpliedCond garbage");
7922 BackedgeTakenCounts.clear();
7923 ConstantEvolutionLoopExitValue.clear();
7924 ValuesAtScopes.clear();
7925 LoopDispositions.clear();
7926 BlockDispositions.clear();
7927 UnsignedRanges.clear();
7928 SignedRanges.clear();
7929 UniqueSCEVs.clear();
7930 SCEVAllocator.Reset();
7933 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
7934 AU.setPreservesAll();
7935 AU.addRequired<AssumptionCacheTracker>();
7936 AU.addRequiredTransitive<LoopInfoWrapperPass>();
7937 AU.addRequiredTransitive<DominatorTreeWrapperPass>();
7938 AU.addRequired<TargetLibraryInfoWrapperPass>();
7941 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
7942 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
7945 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
7947 // Print all inner loops first
7948 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
7949 PrintLoopInfo(OS, SE, *I);
7952 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
7955 SmallVector<BasicBlock *, 8> ExitBlocks;
7956 L->getExitBlocks(ExitBlocks);
7957 if (ExitBlocks.size() != 1)
7958 OS << "<multiple exits> ";
7960 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
7961 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
7963 OS << "Unpredictable backedge-taken count. ";
7968 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
7971 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
7972 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
7974 OS << "Unpredictable max backedge-taken count. ";
7980 void ScalarEvolution::print(raw_ostream &OS, const Module *) const {
7981 // ScalarEvolution's implementation of the print method is to print
7982 // out SCEV values of all instructions that are interesting. Doing
7983 // this potentially causes it to create new SCEV objects though,
7984 // which technically conflicts with the const qualifier. This isn't
7985 // observable from outside the class though, so casting away the
7986 // const isn't dangerous.
7987 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
7989 OS << "Classifying expressions for: ";
7990 F->printAsOperand(OS, /*PrintType=*/false);
7992 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
7993 if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) {
7996 const SCEV *SV = SE.getSCEV(&*I);
7999 const Loop *L = LI->getLoopFor((*I).getParent());
8001 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
8008 OS << "\t\t" "Exits: ";
8009 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
8010 if (!SE.isLoopInvariant(ExitValue, L)) {
8011 OS << "<<Unknown>>";
8020 OS << "Determining loop execution counts for: ";
8021 F->printAsOperand(OS, /*PrintType=*/false);
8023 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
8024 PrintLoopInfo(OS, &SE, *I);
8027 ScalarEvolution::LoopDisposition
8028 ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) {
8029 auto &Values = LoopDispositions[S];
8030 for (auto &V : Values) {
8031 if (V.getPointer() == L)
8034 Values.emplace_back(L, LoopVariant);
8035 LoopDisposition D = computeLoopDisposition(S, L);
8036 auto &Values2 = LoopDispositions[S];
8037 for (auto &V : make_range(Values2.rbegin(), Values2.rend())) {
8038 if (V.getPointer() == L) {
8046 ScalarEvolution::LoopDisposition
8047 ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) {
8048 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
8050 return LoopInvariant;
8054 return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L);
8055 case scAddRecExpr: {
8056 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
8058 // If L is the addrec's loop, it's computable.
8059 if (AR->getLoop() == L)
8060 return LoopComputable;
8062 // Add recurrences are never invariant in the function-body (null loop).
8066 // This recurrence is variant w.r.t. L if L contains AR's loop.
8067 if (L->contains(AR->getLoop()))
8070 // This recurrence is invariant w.r.t. L if AR's loop contains L.
8071 if (AR->getLoop()->contains(L))
8072 return LoopInvariant;
8074 // This recurrence is variant w.r.t. L if any of its operands
8076 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
8078 if (!isLoopInvariant(*I, L))
8081 // Otherwise it's loop-invariant.
8082 return LoopInvariant;
8088 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
8089 bool HasVarying = false;
8090 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
8092 LoopDisposition D = getLoopDisposition(*I, L);
8093 if (D == LoopVariant)
8095 if (D == LoopComputable)
8098 return HasVarying ? LoopComputable : LoopInvariant;
8101 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
8102 LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L);
8103 if (LD == LoopVariant)
8105 LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L);
8106 if (RD == LoopVariant)
8108 return (LD == LoopInvariant && RD == LoopInvariant) ?
8109 LoopInvariant : LoopComputable;
8112 // All non-instruction values are loop invariant. All instructions are loop
8113 // invariant if they are not contained in the specified loop.
8114 // Instructions are never considered invariant in the function body
8115 // (null loop) because they are defined within the "loop".
8116 if (Instruction *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue()))
8117 return (L && !L->contains(I)) ? LoopInvariant : LoopVariant;
8118 return LoopInvariant;
8119 case scCouldNotCompute:
8120 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
8122 llvm_unreachable("Unknown SCEV kind!");
8125 bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) {
8126 return getLoopDisposition(S, L) == LoopInvariant;
8129 bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) {
8130 return getLoopDisposition(S, L) == LoopComputable;
8133 ScalarEvolution::BlockDisposition
8134 ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) {
8135 auto &Values = BlockDispositions[S];
8136 for (auto &V : Values) {
8137 if (V.getPointer() == BB)
8140 Values.emplace_back(BB, DoesNotDominateBlock);
8141 BlockDisposition D = computeBlockDisposition(S, BB);
8142 auto &Values2 = BlockDispositions[S];
8143 for (auto &V : make_range(Values2.rbegin(), Values2.rend())) {
8144 if (V.getPointer() == BB) {
8152 ScalarEvolution::BlockDisposition
8153 ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) {
8154 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
8156 return ProperlyDominatesBlock;
8160 return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB);
8161 case scAddRecExpr: {
8162 // This uses a "dominates" query instead of "properly dominates" query
8163 // to test for proper dominance too, because the instruction which
8164 // produces the addrec's value is a PHI, and a PHI effectively properly
8165 // dominates its entire containing block.
8166 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
8167 if (!DT->dominates(AR->getLoop()->getHeader(), BB))
8168 return DoesNotDominateBlock;
8170 // FALL THROUGH into SCEVNAryExpr handling.
8175 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
8177 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
8179 BlockDisposition D = getBlockDisposition(*I, BB);
8180 if (D == DoesNotDominateBlock)
8181 return DoesNotDominateBlock;
8182 if (D == DominatesBlock)
8185 return Proper ? ProperlyDominatesBlock : DominatesBlock;
8188 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
8189 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
8190 BlockDisposition LD = getBlockDisposition(LHS, BB);
8191 if (LD == DoesNotDominateBlock)
8192 return DoesNotDominateBlock;
8193 BlockDisposition RD = getBlockDisposition(RHS, BB);
8194 if (RD == DoesNotDominateBlock)
8195 return DoesNotDominateBlock;
8196 return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ?
8197 ProperlyDominatesBlock : DominatesBlock;
8200 if (Instruction *I =
8201 dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) {
8202 if (I->getParent() == BB)
8203 return DominatesBlock;
8204 if (DT->properlyDominates(I->getParent(), BB))
8205 return ProperlyDominatesBlock;
8206 return DoesNotDominateBlock;
8208 return ProperlyDominatesBlock;
8209 case scCouldNotCompute:
8210 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
8212 llvm_unreachable("Unknown SCEV kind!");
8215 bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) {
8216 return getBlockDisposition(S, BB) >= DominatesBlock;
8219 bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) {
8220 return getBlockDisposition(S, BB) == ProperlyDominatesBlock;
8224 // Search for a SCEV expression node within an expression tree.
8225 // Implements SCEVTraversal::Visitor.
8230 SCEVSearch(const SCEV *N): Node(N), IsFound(false) {}
8232 bool follow(const SCEV *S) {
8233 IsFound |= (S == Node);
8236 bool isDone() const { return IsFound; }
8240 bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const {
8241 SCEVSearch Search(Op);
8242 visitAll(S, Search);
8243 return Search.IsFound;
8246 void ScalarEvolution::forgetMemoizedResults(const SCEV *S) {
8247 ValuesAtScopes.erase(S);
8248 LoopDispositions.erase(S);
8249 BlockDispositions.erase(S);
8250 UnsignedRanges.erase(S);
8251 SignedRanges.erase(S);
8253 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
8254 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end(); I != E; ) {
8255 BackedgeTakenInfo &BEInfo = I->second;
8256 if (BEInfo.hasOperand(S, this)) {
8258 BackedgeTakenCounts.erase(I++);
8265 typedef DenseMap<const Loop *, std::string> VerifyMap;
8267 /// replaceSubString - Replaces all occurrences of From in Str with To.
8268 static void replaceSubString(std::string &Str, StringRef From, StringRef To) {
8270 while ((Pos = Str.find(From, Pos)) != std::string::npos) {
8271 Str.replace(Pos, From.size(), To.data(), To.size());
8276 /// getLoopBackedgeTakenCounts - Helper method for verifyAnalysis.
8278 getLoopBackedgeTakenCounts(Loop *L, VerifyMap &Map, ScalarEvolution &SE) {
8279 for (Loop::reverse_iterator I = L->rbegin(), E = L->rend(); I != E; ++I) {
8280 getLoopBackedgeTakenCounts(*I, Map, SE); // recurse.
8282 std::string &S = Map[L];
8284 raw_string_ostream OS(S);
8285 SE.getBackedgeTakenCount(L)->print(OS);
8287 // false and 0 are semantically equivalent. This can happen in dead loops.
8288 replaceSubString(OS.str(), "false", "0");
8289 // Remove wrap flags, their use in SCEV is highly fragile.
8290 // FIXME: Remove this when SCEV gets smarter about them.
8291 replaceSubString(OS.str(), "<nw>", "");
8292 replaceSubString(OS.str(), "<nsw>", "");
8293 replaceSubString(OS.str(), "<nuw>", "");
8298 void ScalarEvolution::verifyAnalysis() const {
8302 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
8304 // Gather stringified backedge taken counts for all loops using SCEV's caches.
8305 // FIXME: It would be much better to store actual values instead of strings,
8306 // but SCEV pointers will change if we drop the caches.
8307 VerifyMap BackedgeDumpsOld, BackedgeDumpsNew;
8308 for (LoopInfo::reverse_iterator I = LI->rbegin(), E = LI->rend(); I != E; ++I)
8309 getLoopBackedgeTakenCounts(*I, BackedgeDumpsOld, SE);
8311 // Gather stringified backedge taken counts for all loops without using
8314 for (LoopInfo::reverse_iterator I = LI->rbegin(), E = LI->rend(); I != E; ++I)
8315 getLoopBackedgeTakenCounts(*I, BackedgeDumpsNew, SE);
8317 // Now compare whether they're the same with and without caches. This allows
8318 // verifying that no pass changed the cache.
8319 assert(BackedgeDumpsOld.size() == BackedgeDumpsNew.size() &&
8320 "New loops suddenly appeared!");
8322 for (VerifyMap::iterator OldI = BackedgeDumpsOld.begin(),
8323 OldE = BackedgeDumpsOld.end(),
8324 NewI = BackedgeDumpsNew.begin();
8325 OldI != OldE; ++OldI, ++NewI) {
8326 assert(OldI->first == NewI->first && "Loop order changed!");
8328 // Compare the stringified SCEVs. We don't care if undef backedgetaken count
8330 // FIXME: We currently ignore SCEV changes from/to CouldNotCompute. This
8331 // means that a pass is buggy or SCEV has to learn a new pattern but is
8332 // usually not harmful.
8333 if (OldI->second != NewI->second &&
8334 OldI->second.find("undef") == std::string::npos &&
8335 NewI->second.find("undef") == std::string::npos &&
8336 OldI->second != "***COULDNOTCOMPUTE***" &&
8337 NewI->second != "***COULDNOTCOMPUTE***") {
8338 dbgs() << "SCEVValidator: SCEV for loop '"
8339 << OldI->first->getHeader()->getName()
8340 << "' changed from '" << OldI->second
8341 << "' to '" << NewI->second << "'!\n";
8346 // TODO: Verify more things.