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 // Get the limit of a recurrence such that incrementing by Step cannot cause
1152 // signed overflow as long as the value of the recurrence within the
1153 // loop does not exceed this limit before incrementing.
1154 static const SCEV *getSignedOverflowLimitForStep(const SCEV *Step,
1155 ICmpInst::Predicate *Pred,
1156 ScalarEvolution *SE) {
1157 unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
1158 if (SE->isKnownPositive(Step)) {
1159 *Pred = ICmpInst::ICMP_SLT;
1160 return SE->getConstant(APInt::getSignedMinValue(BitWidth) -
1161 SE->getSignedRange(Step).getSignedMax());
1163 if (SE->isKnownNegative(Step)) {
1164 *Pred = ICmpInst::ICMP_SGT;
1165 return SE->getConstant(APInt::getSignedMaxValue(BitWidth) -
1166 SE->getSignedRange(Step).getSignedMin());
1171 // Get the limit of a recurrence such that incrementing by Step cannot cause
1172 // unsigned overflow as long as the value of the recurrence within the loop does
1173 // not exceed this limit before incrementing.
1174 static const SCEV *getUnsignedOverflowLimitForStep(const SCEV *Step,
1175 ICmpInst::Predicate *Pred,
1176 ScalarEvolution *SE) {
1177 unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
1178 *Pred = ICmpInst::ICMP_ULT;
1180 return SE->getConstant(APInt::getMinValue(BitWidth) -
1181 SE->getUnsignedRange(Step).getUnsignedMax());
1186 struct ExtendOpTraitsBase {
1187 typedef const SCEV *(ScalarEvolution::*GetExtendExprTy)(const SCEV *, Type *);
1190 // Used to make code generic over signed and unsigned overflow.
1191 template <typename ExtendOp> struct ExtendOpTraits {
1194 // static const SCEV::NoWrapFlags WrapType;
1196 // static const ExtendOpTraitsBase::GetExtendExprTy GetExtendExpr;
1198 // static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1199 // ICmpInst::Predicate *Pred,
1200 // ScalarEvolution *SE);
1204 struct ExtendOpTraits<SCEVSignExtendExpr> : public ExtendOpTraitsBase {
1205 static const SCEV::NoWrapFlags WrapType = SCEV::FlagNSW;
1207 static const GetExtendExprTy GetExtendExpr;
1209 static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1210 ICmpInst::Predicate *Pred,
1211 ScalarEvolution *SE) {
1212 return getSignedOverflowLimitForStep(Step, Pred, SE);
1216 const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits<
1217 SCEVSignExtendExpr>::GetExtendExpr = &ScalarEvolution::getSignExtendExpr;
1220 struct ExtendOpTraits<SCEVZeroExtendExpr> : public ExtendOpTraitsBase {
1221 static const SCEV::NoWrapFlags WrapType = SCEV::FlagNUW;
1223 static const GetExtendExprTy GetExtendExpr;
1225 static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1226 ICmpInst::Predicate *Pred,
1227 ScalarEvolution *SE) {
1228 return getUnsignedOverflowLimitForStep(Step, Pred, SE);
1232 const ExtendOpTraitsBase::GetExtendExprTy ExtendOpTraits<
1233 SCEVZeroExtendExpr>::GetExtendExpr = &ScalarEvolution::getZeroExtendExpr;
1236 // The recurrence AR has been shown to have no signed/unsigned wrap or something
1237 // close to it. Typically, if we can prove NSW/NUW for AR, then we can just as
1238 // easily prove NSW/NUW for its preincrement or postincrement sibling. This
1239 // allows normalizing a sign/zero extended AddRec as such: {sext/zext(Step +
1240 // Start),+,Step} => {(Step + sext/zext(Start),+,Step} As a result, the
1241 // expression "Step + sext/zext(PreIncAR)" is congruent with
1242 // "sext/zext(PostIncAR)"
1243 template <typename ExtendOpTy>
1244 static const SCEV *getPreStartForExtend(const SCEVAddRecExpr *AR, Type *Ty,
1245 ScalarEvolution *SE) {
1246 auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType;
1247 auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr;
1249 const Loop *L = AR->getLoop();
1250 const SCEV *Start = AR->getStart();
1251 const SCEV *Step = AR->getStepRecurrence(*SE);
1253 // Check for a simple looking step prior to loop entry.
1254 const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Start);
1258 // Create an AddExpr for "PreStart" after subtracting Step. Full SCEV
1259 // subtraction is expensive. For this purpose, perform a quick and dirty
1260 // difference, by checking for Step in the operand list.
1261 SmallVector<const SCEV *, 4> DiffOps;
1262 for (const SCEV *Op : SA->operands())
1264 DiffOps.push_back(Op);
1266 if (DiffOps.size() == SA->getNumOperands())
1269 // Try to prove `WrapType` (SCEV::FlagNSW or SCEV::FlagNUW) on `PreStart` +
1272 // 1. NSW/NUW flags on the step increment.
1273 const SCEV *PreStart = SE->getAddExpr(DiffOps, SA->getNoWrapFlags());
1274 const SCEVAddRecExpr *PreAR = dyn_cast<SCEVAddRecExpr>(
1275 SE->getAddRecExpr(PreStart, Step, L, SCEV::FlagAnyWrap));
1277 // "{S,+,X} is <nsw>/<nuw>" and "the backedge is taken at least once" implies
1278 // "S+X does not sign/unsign-overflow".
1281 const SCEV *BECount = SE->getBackedgeTakenCount(L);
1282 if (PreAR && PreAR->getNoWrapFlags(WrapType) &&
1283 !isa<SCEVCouldNotCompute>(BECount) && SE->isKnownPositive(BECount))
1286 // 2. Direct overflow check on the step operation's expression.
1287 unsigned BitWidth = SE->getTypeSizeInBits(AR->getType());
1288 Type *WideTy = IntegerType::get(SE->getContext(), BitWidth * 2);
1289 const SCEV *OperandExtendedStart =
1290 SE->getAddExpr((SE->*GetExtendExpr)(PreStart, WideTy),
1291 (SE->*GetExtendExpr)(Step, WideTy));
1292 if ((SE->*GetExtendExpr)(Start, WideTy) == OperandExtendedStart) {
1293 if (PreAR && AR->getNoWrapFlags(WrapType)) {
1294 // If we know `AR` == {`PreStart`+`Step`,+,`Step`} is `WrapType` (FlagNSW
1295 // or FlagNUW) and that `PreStart` + `Step` is `WrapType` too, then
1296 // `PreAR` == {`PreStart`,+,`Step`} is also `WrapType`. Cache this fact.
1297 const_cast<SCEVAddRecExpr *>(PreAR)->setNoWrapFlags(WrapType);
1302 // 3. Loop precondition.
1303 ICmpInst::Predicate Pred;
1304 const SCEV *OverflowLimit =
1305 ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep(Step, &Pred, SE);
1307 if (OverflowLimit &&
1308 SE->isLoopEntryGuardedByCond(L, Pred, PreStart, OverflowLimit)) {
1314 // Get the normalized zero or sign extended expression for this AddRec's Start.
1315 template <typename ExtendOpTy>
1316 static const SCEV *getExtendAddRecStart(const SCEVAddRecExpr *AR, Type *Ty,
1317 ScalarEvolution *SE) {
1318 auto GetExtendExpr = ExtendOpTraits<ExtendOpTy>::GetExtendExpr;
1320 const SCEV *PreStart = getPreStartForExtend<ExtendOpTy>(AR, Ty, SE);
1322 return (SE->*GetExtendExpr)(AR->getStart(), Ty);
1324 return SE->getAddExpr((SE->*GetExtendExpr)(AR->getStepRecurrence(*SE), Ty),
1325 (SE->*GetExtendExpr)(PreStart, Ty));
1328 // Try to prove away overflow by looking at "nearby" add recurrences. A
1329 // motivating example for this rule: if we know `{0,+,4}` is `ult` `-1` and it
1330 // does not itself wrap then we can conclude that `{1,+,4}` is `nuw`.
1334 // {S,+,X} == {S-T,+,X} + T
1335 // => Ext({S,+,X}) == Ext({S-T,+,X} + T)
1337 // If ({S-T,+,X} + T) does not overflow ... (1)
1339 // RHS == Ext({S-T,+,X} + T) == Ext({S-T,+,X}) + Ext(T)
1341 // If {S-T,+,X} does not overflow ... (2)
1343 // RHS == Ext({S-T,+,X}) + Ext(T) == {Ext(S-T),+,Ext(X)} + Ext(T)
1344 // == {Ext(S-T)+Ext(T),+,Ext(X)}
1346 // If (S-T)+T does not overflow ... (3)
1348 // RHS == {Ext(S-T)+Ext(T),+,Ext(X)} == {Ext(S-T+T),+,Ext(X)}
1349 // == {Ext(S),+,Ext(X)} == LHS
1351 // Thus, if (1), (2) and (3) are true for some T, then
1352 // Ext({S,+,X}) == {Ext(S),+,Ext(X)}
1354 // (3) is implied by (1) -- "(S-T)+T does not overflow" is simply "({S-T,+,X}+T)
1355 // does not overflow" restricted to the 0th iteration. Therefore we only need
1356 // to check for (1) and (2).
1358 // In the current context, S is `Start`, X is `Step`, Ext is `ExtendOpTy` and T
1359 // is `Delta` (defined below).
1361 template <typename ExtendOpTy>
1362 bool ScalarEvolution::proveNoWrapByVaryingStart(const SCEV *Start,
1365 auto WrapType = ExtendOpTraits<ExtendOpTy>::WrapType;
1367 // We restrict `Start` to a constant to prevent SCEV from spending too much
1368 // time here. It is correct (but more expensive) to continue with a
1369 // non-constant `Start` and do a general SCEV subtraction to compute
1370 // `PreStart` below.
1372 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start);
1376 APInt StartAI = StartC->getValue()->getValue();
1378 for (unsigned Delta : {-2, -1, 1, 2}) {
1379 const SCEV *PreStart = getConstant(StartAI - Delta);
1381 // Give up if we don't already have the add recurrence we need because
1382 // actually constructing an add recurrence is relatively expensive.
1383 const SCEVAddRecExpr *PreAR = [&]() {
1384 FoldingSetNodeID ID;
1385 ID.AddInteger(scAddRecExpr);
1386 ID.AddPointer(PreStart);
1387 ID.AddPointer(Step);
1390 return static_cast<SCEVAddRecExpr *>(
1391 UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1394 if (PreAR && PreAR->getNoWrapFlags(WrapType)) { // proves (2)
1395 const SCEV *DeltaS = getConstant(StartC->getType(), Delta);
1396 ICmpInst::Predicate Pred = ICmpInst::BAD_ICMP_PREDICATE;
1397 const SCEV *Limit = ExtendOpTraits<ExtendOpTy>::getOverflowLimitForStep(
1398 DeltaS, &Pred, this);
1399 if (Limit && isKnownPredicate(Pred, PreAR, Limit)) // proves (1)
1407 const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op,
1409 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1410 "This is not an extending conversion!");
1411 assert(isSCEVable(Ty) &&
1412 "This is not a conversion to a SCEVable type!");
1413 Ty = getEffectiveSCEVType(Ty);
1415 // Fold if the operand is constant.
1416 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1418 cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(), Ty)));
1420 // zext(zext(x)) --> zext(x)
1421 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1422 return getZeroExtendExpr(SZ->getOperand(), Ty);
1424 // Before doing any expensive analysis, check to see if we've already
1425 // computed a SCEV for this Op and Ty.
1426 FoldingSetNodeID ID;
1427 ID.AddInteger(scZeroExtend);
1431 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1433 // zext(trunc(x)) --> zext(x) or x or trunc(x)
1434 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1435 // It's possible the bits taken off by the truncate were all zero bits. If
1436 // so, we should be able to simplify this further.
1437 const SCEV *X = ST->getOperand();
1438 ConstantRange CR = getUnsignedRange(X);
1439 unsigned TruncBits = getTypeSizeInBits(ST->getType());
1440 unsigned NewBits = getTypeSizeInBits(Ty);
1441 if (CR.truncate(TruncBits).zeroExtend(NewBits).contains(
1442 CR.zextOrTrunc(NewBits)))
1443 return getTruncateOrZeroExtend(X, Ty);
1446 // If the input value is a chrec scev, and we can prove that the value
1447 // did not overflow the old, smaller, value, we can zero extend all of the
1448 // operands (often constants). This allows analysis of something like
1449 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
1450 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1451 if (AR->isAffine()) {
1452 const SCEV *Start = AR->getStart();
1453 const SCEV *Step = AR->getStepRecurrence(*this);
1454 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1455 const Loop *L = AR->getLoop();
1457 // If we have special knowledge that this addrec won't overflow,
1458 // we don't need to do any further analysis.
1459 if (AR->getNoWrapFlags(SCEV::FlagNUW))
1460 return getAddRecExpr(
1461 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1462 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1464 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1465 // Note that this serves two purposes: It filters out loops that are
1466 // simply not analyzable, and it covers the case where this code is
1467 // being called from within backedge-taken count analysis, such that
1468 // attempting to ask for the backedge-taken count would likely result
1469 // in infinite recursion. In the later case, the analysis code will
1470 // cope with a conservative value, and it will take care to purge
1471 // that value once it has finished.
1472 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1473 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1474 // Manually compute the final value for AR, checking for
1477 // Check whether the backedge-taken count can be losslessly casted to
1478 // the addrec's type. The count is always unsigned.
1479 const SCEV *CastedMaxBECount =
1480 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1481 const SCEV *RecastedMaxBECount =
1482 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1483 if (MaxBECount == RecastedMaxBECount) {
1484 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1485 // Check whether Start+Step*MaxBECount has no unsigned overflow.
1486 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step);
1487 const SCEV *ZAdd = getZeroExtendExpr(getAddExpr(Start, ZMul), WideTy);
1488 const SCEV *WideStart = getZeroExtendExpr(Start, WideTy);
1489 const SCEV *WideMaxBECount =
1490 getZeroExtendExpr(CastedMaxBECount, WideTy);
1491 const SCEV *OperandExtendedAdd =
1492 getAddExpr(WideStart,
1493 getMulExpr(WideMaxBECount,
1494 getZeroExtendExpr(Step, WideTy)));
1495 if (ZAdd == OperandExtendedAdd) {
1496 // Cache knowledge of AR NUW, which is propagated to this AddRec.
1497 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1498 // Return the expression with the addrec on the outside.
1499 return getAddRecExpr(
1500 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1501 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1503 // Similar to above, only this time treat the step value as signed.
1504 // This covers loops that count down.
1505 OperandExtendedAdd =
1506 getAddExpr(WideStart,
1507 getMulExpr(WideMaxBECount,
1508 getSignExtendExpr(Step, WideTy)));
1509 if (ZAdd == OperandExtendedAdd) {
1510 // Cache knowledge of AR NW, which is propagated to this AddRec.
1511 // Negative step causes unsigned wrap, but it still can't self-wrap.
1512 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1513 // Return the expression with the addrec on the outside.
1514 return getAddRecExpr(
1515 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1516 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1520 // If the backedge is guarded by a comparison with the pre-inc value
1521 // the addrec is safe. Also, if the entry is guarded by a comparison
1522 // with the start value and the backedge is guarded by a comparison
1523 // with the post-inc value, the addrec is safe.
1524 if (isKnownPositive(Step)) {
1525 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
1526 getUnsignedRange(Step).getUnsignedMax());
1527 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
1528 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) &&
1529 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT,
1530 AR->getPostIncExpr(*this), N))) {
1531 // Cache knowledge of AR NUW, which is propagated to this AddRec.
1532 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1533 // Return the expression with the addrec on the outside.
1534 return getAddRecExpr(
1535 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1536 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1538 } else if (isKnownNegative(Step)) {
1539 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
1540 getSignedRange(Step).getSignedMin());
1541 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) ||
1542 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) &&
1543 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT,
1544 AR->getPostIncExpr(*this), N))) {
1545 // Cache knowledge of AR NW, which is propagated to this AddRec.
1546 // Negative step causes unsigned wrap, but it still can't self-wrap.
1547 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1548 // Return the expression with the addrec on the outside.
1549 return getAddRecExpr(
1550 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1551 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1556 if (proveNoWrapByVaryingStart<SCEVZeroExtendExpr>(Start, Step, L)) {
1557 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1558 return getAddRecExpr(
1559 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1560 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1564 // The cast wasn't folded; create an explicit cast node.
1565 // Recompute the insert position, as it may have been invalidated.
1566 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1567 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
1569 UniqueSCEVs.InsertNode(S, IP);
1573 const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op,
1575 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1576 "This is not an extending conversion!");
1577 assert(isSCEVable(Ty) &&
1578 "This is not a conversion to a SCEVable type!");
1579 Ty = getEffectiveSCEVType(Ty);
1581 // Fold if the operand is constant.
1582 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1584 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), Ty)));
1586 // sext(sext(x)) --> sext(x)
1587 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1588 return getSignExtendExpr(SS->getOperand(), Ty);
1590 // sext(zext(x)) --> zext(x)
1591 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1592 return getZeroExtendExpr(SZ->getOperand(), Ty);
1594 // Before doing any expensive analysis, check to see if we've already
1595 // computed a SCEV for this Op and Ty.
1596 FoldingSetNodeID ID;
1597 ID.AddInteger(scSignExtend);
1601 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1603 // If the input value is provably positive, build a zext instead.
1604 if (isKnownNonNegative(Op))
1605 return getZeroExtendExpr(Op, Ty);
1607 // sext(trunc(x)) --> sext(x) or x or trunc(x)
1608 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1609 // It's possible the bits taken off by the truncate were all sign bits. If
1610 // so, we should be able to simplify this further.
1611 const SCEV *X = ST->getOperand();
1612 ConstantRange CR = getSignedRange(X);
1613 unsigned TruncBits = getTypeSizeInBits(ST->getType());
1614 unsigned NewBits = getTypeSizeInBits(Ty);
1615 if (CR.truncate(TruncBits).signExtend(NewBits).contains(
1616 CR.sextOrTrunc(NewBits)))
1617 return getTruncateOrSignExtend(X, Ty);
1620 // sext(C1 + (C2 * x)) --> C1 + sext(C2 * x) if C1 < C2
1621 if (auto SA = dyn_cast<SCEVAddExpr>(Op)) {
1622 if (SA->getNumOperands() == 2) {
1623 auto SC1 = dyn_cast<SCEVConstant>(SA->getOperand(0));
1624 auto SMul = dyn_cast<SCEVMulExpr>(SA->getOperand(1));
1626 if (auto SC2 = dyn_cast<SCEVConstant>(SMul->getOperand(0))) {
1627 const APInt &C1 = SC1->getValue()->getValue();
1628 const APInt &C2 = SC2->getValue()->getValue();
1629 if (C1.isStrictlyPositive() && C2.isStrictlyPositive() &&
1630 C2.ugt(C1) && C2.isPowerOf2())
1631 return getAddExpr(getSignExtendExpr(SC1, Ty),
1632 getSignExtendExpr(SMul, Ty));
1637 // If the input value is a chrec scev, and we can prove that the value
1638 // did not overflow the old, smaller, value, we can sign extend all of the
1639 // operands (often constants). This allows analysis of something like
1640 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
1641 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1642 if (AR->isAffine()) {
1643 const SCEV *Start = AR->getStart();
1644 const SCEV *Step = AR->getStepRecurrence(*this);
1645 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1646 const Loop *L = AR->getLoop();
1648 // If we have special knowledge that this addrec won't overflow,
1649 // we don't need to do any further analysis.
1650 if (AR->getNoWrapFlags(SCEV::FlagNSW))
1651 return getAddRecExpr(
1652 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1653 getSignExtendExpr(Step, Ty), L, SCEV::FlagNSW);
1655 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1656 // Note that this serves two purposes: It filters out loops that are
1657 // simply not analyzable, and it covers the case where this code is
1658 // being called from within backedge-taken count analysis, such that
1659 // attempting to ask for the backedge-taken count would likely result
1660 // in infinite recursion. In the later case, the analysis code will
1661 // cope with a conservative value, and it will take care to purge
1662 // that value once it has finished.
1663 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1664 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1665 // Manually compute the final value for AR, checking for
1668 // Check whether the backedge-taken count can be losslessly casted to
1669 // the addrec's type. The count is always unsigned.
1670 const SCEV *CastedMaxBECount =
1671 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1672 const SCEV *RecastedMaxBECount =
1673 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1674 if (MaxBECount == RecastedMaxBECount) {
1675 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1676 // Check whether Start+Step*MaxBECount has no signed overflow.
1677 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
1678 const SCEV *SAdd = getSignExtendExpr(getAddExpr(Start, SMul), WideTy);
1679 const SCEV *WideStart = getSignExtendExpr(Start, WideTy);
1680 const SCEV *WideMaxBECount =
1681 getZeroExtendExpr(CastedMaxBECount, WideTy);
1682 const SCEV *OperandExtendedAdd =
1683 getAddExpr(WideStart,
1684 getMulExpr(WideMaxBECount,
1685 getSignExtendExpr(Step, WideTy)));
1686 if (SAdd == OperandExtendedAdd) {
1687 // Cache knowledge of AR NSW, which is propagated to this AddRec.
1688 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1689 // Return the expression with the addrec on the outside.
1690 return getAddRecExpr(
1691 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1692 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1694 // Similar to above, only this time treat the step value as unsigned.
1695 // This covers loops that count up with an unsigned step.
1696 OperandExtendedAdd =
1697 getAddExpr(WideStart,
1698 getMulExpr(WideMaxBECount,
1699 getZeroExtendExpr(Step, WideTy)));
1700 if (SAdd == OperandExtendedAdd) {
1701 // If AR wraps around then
1703 // abs(Step) * MaxBECount > unsigned-max(AR->getType())
1704 // => SAdd != OperandExtendedAdd
1706 // Thus (AR is not NW => SAdd != OperandExtendedAdd) <=>
1707 // (SAdd == OperandExtendedAdd => AR is NW)
1709 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1711 // Return the expression with the addrec on the outside.
1712 return getAddRecExpr(
1713 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1714 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1718 // If the backedge is guarded by a comparison with the pre-inc value
1719 // the addrec is safe. Also, if the entry is guarded by a comparison
1720 // with the start value and the backedge is guarded by a comparison
1721 // with the post-inc value, the addrec is safe.
1722 ICmpInst::Predicate Pred;
1723 const SCEV *OverflowLimit =
1724 getSignedOverflowLimitForStep(Step, &Pred, this);
1725 if (OverflowLimit &&
1726 (isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) ||
1727 (isLoopEntryGuardedByCond(L, Pred, Start, OverflowLimit) &&
1728 isLoopBackedgeGuardedByCond(L, Pred, AR->getPostIncExpr(*this),
1730 // Cache knowledge of AR NSW, then propagate NSW to the wide AddRec.
1731 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1732 return getAddRecExpr(
1733 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1734 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1737 // If Start and Step are constants, check if we can apply this
1739 // sext{C1,+,C2} --> C1 + sext{0,+,C2} if C1 < C2
1740 auto SC1 = dyn_cast<SCEVConstant>(Start);
1741 auto SC2 = dyn_cast<SCEVConstant>(Step);
1743 const APInt &C1 = SC1->getValue()->getValue();
1744 const APInt &C2 = SC2->getValue()->getValue();
1745 if (C1.isStrictlyPositive() && C2.isStrictlyPositive() && C2.ugt(C1) &&
1747 Start = getSignExtendExpr(Start, Ty);
1748 const SCEV *NewAR = getAddRecExpr(getConstant(AR->getType(), 0), Step,
1749 L, AR->getNoWrapFlags());
1750 return getAddExpr(Start, getSignExtendExpr(NewAR, Ty));
1754 if (proveNoWrapByVaryingStart<SCEVSignExtendExpr>(Start, Step, L)) {
1755 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1756 return getAddRecExpr(
1757 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1758 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1762 // The cast wasn't folded; create an explicit cast node.
1763 // Recompute the insert position, as it may have been invalidated.
1764 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1765 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
1767 UniqueSCEVs.InsertNode(S, IP);
1771 /// getAnyExtendExpr - Return a SCEV for the given operand extended with
1772 /// unspecified bits out to the given type.
1774 const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
1776 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1777 "This is not an extending conversion!");
1778 assert(isSCEVable(Ty) &&
1779 "This is not a conversion to a SCEVable type!");
1780 Ty = getEffectiveSCEVType(Ty);
1782 // Sign-extend negative constants.
1783 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1784 if (SC->getValue()->getValue().isNegative())
1785 return getSignExtendExpr(Op, Ty);
1787 // Peel off a truncate cast.
1788 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
1789 const SCEV *NewOp = T->getOperand();
1790 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
1791 return getAnyExtendExpr(NewOp, Ty);
1792 return getTruncateOrNoop(NewOp, Ty);
1795 // Next try a zext cast. If the cast is folded, use it.
1796 const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
1797 if (!isa<SCEVZeroExtendExpr>(ZExt))
1800 // Next try a sext cast. If the cast is folded, use it.
1801 const SCEV *SExt = getSignExtendExpr(Op, Ty);
1802 if (!isa<SCEVSignExtendExpr>(SExt))
1805 // Force the cast to be folded into the operands of an addrec.
1806 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
1807 SmallVector<const SCEV *, 4> Ops;
1808 for (const SCEV *Op : AR->operands())
1809 Ops.push_back(getAnyExtendExpr(Op, Ty));
1810 return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW);
1813 // If the expression is obviously signed, use the sext cast value.
1814 if (isa<SCEVSMaxExpr>(Op))
1817 // Absent any other information, use the zext cast value.
1821 /// CollectAddOperandsWithScales - Process the given Ops list, which is
1822 /// a list of operands to be added under the given scale, update the given
1823 /// map. This is a helper function for getAddRecExpr. As an example of
1824 /// what it does, given a sequence of operands that would form an add
1825 /// expression like this:
1827 /// m + n + 13 + (A * (o + p + (B * (q + m + 29)))) + r + (-1 * r)
1829 /// where A and B are constants, update the map with these values:
1831 /// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
1833 /// and add 13 + A*B*29 to AccumulatedConstant.
1834 /// This will allow getAddRecExpr to produce this:
1836 /// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
1838 /// This form often exposes folding opportunities that are hidden in
1839 /// the original operand list.
1841 /// Return true iff it appears that any interesting folding opportunities
1842 /// may be exposed. This helps getAddRecExpr short-circuit extra work in
1843 /// the common case where no interesting opportunities are present, and
1844 /// is also used as a check to avoid infinite recursion.
1847 CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
1848 SmallVectorImpl<const SCEV *> &NewOps,
1849 APInt &AccumulatedConstant,
1850 const SCEV *const *Ops, size_t NumOperands,
1852 ScalarEvolution &SE) {
1853 bool Interesting = false;
1855 // Iterate over the add operands. They are sorted, with constants first.
1857 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1859 // Pull a buried constant out to the outside.
1860 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
1862 AccumulatedConstant += Scale * C->getValue()->getValue();
1865 // Next comes everything else. We're especially interested in multiplies
1866 // here, but they're in the middle, so just visit the rest with one loop.
1867 for (; i != NumOperands; ++i) {
1868 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
1869 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
1871 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue();
1872 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
1873 // A multiplication of a constant with another add; recurse.
1874 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1));
1876 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1877 Add->op_begin(), Add->getNumOperands(),
1880 // A multiplication of a constant with some other value. Update
1882 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
1883 const SCEV *Key = SE.getMulExpr(MulOps);
1884 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1885 M.insert(std::make_pair(Key, NewScale));
1887 NewOps.push_back(Pair.first->first);
1889 Pair.first->second += NewScale;
1890 // The map already had an entry for this value, which may indicate
1891 // a folding opportunity.
1896 // An ordinary operand. Update the map.
1897 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1898 M.insert(std::make_pair(Ops[i], Scale));
1900 NewOps.push_back(Pair.first->first);
1902 Pair.first->second += Scale;
1903 // The map already had an entry for this value, which may indicate
1904 // a folding opportunity.
1914 struct APIntCompare {
1915 bool operator()(const APInt &LHS, const APInt &RHS) const {
1916 return LHS.ult(RHS);
1921 // We're trying to construct a SCEV of type `Type' with `Ops' as operands and
1922 // `OldFlags' as can't-wrap behavior. Infer a more aggressive set of
1923 // can't-overflow flags for the operation if possible.
1924 static SCEV::NoWrapFlags
1925 StrengthenNoWrapFlags(ScalarEvolution *SE, SCEVTypes Type,
1926 const SmallVectorImpl<const SCEV *> &Ops,
1927 SCEV::NoWrapFlags OldFlags) {
1928 using namespace std::placeholders;
1931 Type == scAddExpr || Type == scAddRecExpr || Type == scMulExpr;
1933 assert(CanAnalyze && "don't call from other places!");
1935 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
1936 SCEV::NoWrapFlags SignOrUnsignWrap =
1937 ScalarEvolution::maskFlags(OldFlags, SignOrUnsignMask);
1939 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
1940 auto IsKnownNonNegative =
1941 std::bind(std::mem_fn(&ScalarEvolution::isKnownNonNegative), SE, _1);
1943 if (SignOrUnsignWrap == SCEV::FlagNSW &&
1944 std::all_of(Ops.begin(), Ops.end(), IsKnownNonNegative))
1945 return ScalarEvolution::setFlags(OldFlags,
1946 (SCEV::NoWrapFlags)SignOrUnsignMask);
1951 /// getAddExpr - Get a canonical add expression, or something simpler if
1953 const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
1954 SCEV::NoWrapFlags Flags) {
1955 assert(!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) &&
1956 "only nuw or nsw allowed");
1957 assert(!Ops.empty() && "Cannot get empty add!");
1958 if (Ops.size() == 1) return Ops[0];
1960 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
1961 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1962 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
1963 "SCEVAddExpr operand types don't match!");
1966 Flags = StrengthenNoWrapFlags(this, scAddExpr, Ops, Flags);
1968 // Sort by complexity, this groups all similar expression types together.
1969 GroupByComplexity(Ops, LI);
1971 // If there are any constants, fold them together.
1973 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1975 assert(Idx < Ops.size());
1976 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1977 // We found two constants, fold them together!
1978 Ops[0] = getConstant(LHSC->getValue()->getValue() +
1979 RHSC->getValue()->getValue());
1980 if (Ops.size() == 2) return Ops[0];
1981 Ops.erase(Ops.begin()+1); // Erase the folded element
1982 LHSC = cast<SCEVConstant>(Ops[0]);
1985 // If we are left with a constant zero being added, strip it off.
1986 if (LHSC->getValue()->isZero()) {
1987 Ops.erase(Ops.begin());
1991 if (Ops.size() == 1) return Ops[0];
1994 // Okay, check to see if the same value occurs in the operand list more than
1995 // once. If so, merge them together into an multiply expression. Since we
1996 // sorted the list, these values are required to be adjacent.
1997 Type *Ty = Ops[0]->getType();
1998 bool FoundMatch = false;
1999 for (unsigned i = 0, e = Ops.size(); i != e-1; ++i)
2000 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
2001 // Scan ahead to count how many equal operands there are.
2003 while (i+Count != e && Ops[i+Count] == Ops[i])
2005 // Merge the values into a multiply.
2006 const SCEV *Scale = getConstant(Ty, Count);
2007 const SCEV *Mul = getMulExpr(Scale, Ops[i]);
2008 if (Ops.size() == Count)
2011 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count);
2012 --i; e -= Count - 1;
2016 return getAddExpr(Ops, Flags);
2018 // Check for truncates. If all the operands are truncated from the same
2019 // type, see if factoring out the truncate would permit the result to be
2020 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
2021 // if the contents of the resulting outer trunc fold to something simple.
2022 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
2023 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
2024 Type *DstType = Trunc->getType();
2025 Type *SrcType = Trunc->getOperand()->getType();
2026 SmallVector<const SCEV *, 8> LargeOps;
2028 // Check all the operands to see if they can be represented in the
2029 // source type of the truncate.
2030 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
2031 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
2032 if (T->getOperand()->getType() != SrcType) {
2036 LargeOps.push_back(T->getOperand());
2037 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
2038 LargeOps.push_back(getAnyExtendExpr(C, SrcType));
2039 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
2040 SmallVector<const SCEV *, 8> LargeMulOps;
2041 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
2042 if (const SCEVTruncateExpr *T =
2043 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
2044 if (T->getOperand()->getType() != SrcType) {
2048 LargeMulOps.push_back(T->getOperand());
2049 } else if (const SCEVConstant *C =
2050 dyn_cast<SCEVConstant>(M->getOperand(j))) {
2051 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType));
2058 LargeOps.push_back(getMulExpr(LargeMulOps));
2065 // Evaluate the expression in the larger type.
2066 const SCEV *Fold = getAddExpr(LargeOps, Flags);
2067 // If it folds to something simple, use it. Otherwise, don't.
2068 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
2069 return getTruncateExpr(Fold, DstType);
2073 // Skip past any other cast SCEVs.
2074 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
2077 // If there are add operands they would be next.
2078 if (Idx < Ops.size()) {
2079 bool DeletedAdd = false;
2080 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
2081 // If we have an add, expand the add operands onto the end of the operands
2083 Ops.erase(Ops.begin()+Idx);
2084 Ops.append(Add->op_begin(), Add->op_end());
2088 // If we deleted at least one add, we added operands to the end of the list,
2089 // and they are not necessarily sorted. Recurse to resort and resimplify
2090 // any operands we just acquired.
2092 return getAddExpr(Ops);
2095 // Skip over the add expression until we get to a multiply.
2096 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
2099 // Check to see if there are any folding opportunities present with
2100 // operands multiplied by constant values.
2101 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
2102 uint64_t BitWidth = getTypeSizeInBits(Ty);
2103 DenseMap<const SCEV *, APInt> M;
2104 SmallVector<const SCEV *, 8> NewOps;
2105 APInt AccumulatedConstant(BitWidth, 0);
2106 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
2107 Ops.data(), Ops.size(),
2108 APInt(BitWidth, 1), *this)) {
2109 // Some interesting folding opportunity is present, so its worthwhile to
2110 // re-generate the operands list. Group the operands by constant scale,
2111 // to avoid multiplying by the same constant scale multiple times.
2112 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
2113 for (SmallVectorImpl<const SCEV *>::const_iterator I = NewOps.begin(),
2114 E = NewOps.end(); I != E; ++I)
2115 MulOpLists[M.find(*I)->second].push_back(*I);
2116 // Re-generate the operands list.
2118 if (AccumulatedConstant != 0)
2119 Ops.push_back(getConstant(AccumulatedConstant));
2120 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator
2121 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I)
2123 Ops.push_back(getMulExpr(getConstant(I->first),
2124 getAddExpr(I->second)));
2126 return getConstant(Ty, 0);
2127 if (Ops.size() == 1)
2129 return getAddExpr(Ops);
2133 // If we are adding something to a multiply expression, make sure the
2134 // something is not already an operand of the multiply. If so, merge it into
2136 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
2137 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
2138 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
2139 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
2140 if (isa<SCEVConstant>(MulOpSCEV))
2142 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
2143 if (MulOpSCEV == Ops[AddOp]) {
2144 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
2145 const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
2146 if (Mul->getNumOperands() != 2) {
2147 // If the multiply has more than two operands, we must get the
2149 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
2150 Mul->op_begin()+MulOp);
2151 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
2152 InnerMul = getMulExpr(MulOps);
2154 const SCEV *One = getConstant(Ty, 1);
2155 const SCEV *AddOne = getAddExpr(One, InnerMul);
2156 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV);
2157 if (Ops.size() == 2) return OuterMul;
2159 Ops.erase(Ops.begin()+AddOp);
2160 Ops.erase(Ops.begin()+Idx-1);
2162 Ops.erase(Ops.begin()+Idx);
2163 Ops.erase(Ops.begin()+AddOp-1);
2165 Ops.push_back(OuterMul);
2166 return getAddExpr(Ops);
2169 // Check this multiply against other multiplies being added together.
2170 for (unsigned OtherMulIdx = Idx+1;
2171 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
2173 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
2174 // If MulOp occurs in OtherMul, we can fold the two multiplies
2176 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
2177 OMulOp != e; ++OMulOp)
2178 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
2179 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
2180 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
2181 if (Mul->getNumOperands() != 2) {
2182 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
2183 Mul->op_begin()+MulOp);
2184 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
2185 InnerMul1 = getMulExpr(MulOps);
2187 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
2188 if (OtherMul->getNumOperands() != 2) {
2189 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
2190 OtherMul->op_begin()+OMulOp);
2191 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end());
2192 InnerMul2 = getMulExpr(MulOps);
2194 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
2195 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
2196 if (Ops.size() == 2) return OuterMul;
2197 Ops.erase(Ops.begin()+Idx);
2198 Ops.erase(Ops.begin()+OtherMulIdx-1);
2199 Ops.push_back(OuterMul);
2200 return getAddExpr(Ops);
2206 // If there are any add recurrences in the operands list, see if any other
2207 // added values are loop invariant. If so, we can fold them into the
2209 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2212 // Scan over all recurrences, trying to fold loop invariants into them.
2213 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
2214 // Scan all of the other operands to this add and add them to the vector if
2215 // they are loop invariant w.r.t. the recurrence.
2216 SmallVector<const SCEV *, 8> LIOps;
2217 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2218 const Loop *AddRecLoop = AddRec->getLoop();
2219 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2220 if (isLoopInvariant(Ops[i], AddRecLoop)) {
2221 LIOps.push_back(Ops[i]);
2222 Ops.erase(Ops.begin()+i);
2226 // If we found some loop invariants, fold them into the recurrence.
2227 if (!LIOps.empty()) {
2228 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
2229 LIOps.push_back(AddRec->getStart());
2231 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
2233 AddRecOps[0] = getAddExpr(LIOps);
2235 // Build the new addrec. Propagate the NUW and NSW flags if both the
2236 // outer add and the inner addrec are guaranteed to have no overflow.
2237 // Always propagate NW.
2238 Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW));
2239 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags);
2241 // If all of the other operands were loop invariant, we are done.
2242 if (Ops.size() == 1) return NewRec;
2244 // Otherwise, add the folded AddRec by the non-invariant parts.
2245 for (unsigned i = 0;; ++i)
2246 if (Ops[i] == AddRec) {
2250 return getAddExpr(Ops);
2253 // Okay, if there weren't any loop invariants to be folded, check to see if
2254 // there are multiple AddRec's with the same loop induction variable being
2255 // added together. If so, we can fold them.
2256 for (unsigned OtherIdx = Idx+1;
2257 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2259 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
2260 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L>
2261 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
2263 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2265 if (const SCEVAddRecExpr *OtherAddRec =
2266 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]))
2267 if (OtherAddRec->getLoop() == AddRecLoop) {
2268 for (unsigned i = 0, e = OtherAddRec->getNumOperands();
2270 if (i >= AddRecOps.size()) {
2271 AddRecOps.append(OtherAddRec->op_begin()+i,
2272 OtherAddRec->op_end());
2275 AddRecOps[i] = getAddExpr(AddRecOps[i],
2276 OtherAddRec->getOperand(i));
2278 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2280 // Step size has changed, so we cannot guarantee no self-wraparound.
2281 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap);
2282 return getAddExpr(Ops);
2285 // Otherwise couldn't fold anything into this recurrence. Move onto the
2289 // Okay, it looks like we really DO need an add expr. Check to see if we
2290 // already have one, otherwise create a new one.
2291 FoldingSetNodeID ID;
2292 ID.AddInteger(scAddExpr);
2293 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2294 ID.AddPointer(Ops[i]);
2297 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2299 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2300 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2301 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator),
2303 UniqueSCEVs.InsertNode(S, IP);
2305 S->setNoWrapFlags(Flags);
2309 static uint64_t umul_ov(uint64_t i, uint64_t j, bool &Overflow) {
2311 if (j > 1 && k / j != i) Overflow = true;
2315 /// Compute the result of "n choose k", the binomial coefficient. If an
2316 /// intermediate computation overflows, Overflow will be set and the return will
2317 /// be garbage. Overflow is not cleared on absence of overflow.
2318 static uint64_t Choose(uint64_t n, uint64_t k, bool &Overflow) {
2319 // We use the multiplicative formula:
2320 // n(n-1)(n-2)...(n-(k-1)) / k(k-1)(k-2)...1 .
2321 // At each iteration, we take the n-th term of the numeral and divide by the
2322 // (k-n)th term of the denominator. This division will always produce an
2323 // integral result, and helps reduce the chance of overflow in the
2324 // intermediate computations. However, we can still overflow even when the
2325 // final result would fit.
2327 if (n == 0 || n == k) return 1;
2328 if (k > n) return 0;
2334 for (uint64_t i = 1; i <= k; ++i) {
2335 r = umul_ov(r, n-(i-1), Overflow);
2341 /// Determine if any of the operands in this SCEV are a constant or if
2342 /// any of the add or multiply expressions in this SCEV contain a constant.
2343 static bool containsConstantSomewhere(const SCEV *StartExpr) {
2344 SmallVector<const SCEV *, 4> Ops;
2345 Ops.push_back(StartExpr);
2346 while (!Ops.empty()) {
2347 const SCEV *CurrentExpr = Ops.pop_back_val();
2348 if (isa<SCEVConstant>(*CurrentExpr))
2351 if (isa<SCEVAddExpr>(*CurrentExpr) || isa<SCEVMulExpr>(*CurrentExpr)) {
2352 const auto *CurrentNAry = cast<SCEVNAryExpr>(CurrentExpr);
2353 Ops.append(CurrentNAry->op_begin(), CurrentNAry->op_end());
2359 /// getMulExpr - Get a canonical multiply expression, or something simpler if
2361 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
2362 SCEV::NoWrapFlags Flags) {
2363 assert(Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) &&
2364 "only nuw or nsw allowed");
2365 assert(!Ops.empty() && "Cannot get empty mul!");
2366 if (Ops.size() == 1) return Ops[0];
2368 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2369 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2370 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2371 "SCEVMulExpr operand types don't match!");
2374 Flags = StrengthenNoWrapFlags(this, scMulExpr, Ops, Flags);
2376 // Sort by complexity, this groups all similar expression types together.
2377 GroupByComplexity(Ops, LI);
2379 // If there are any constants, fold them together.
2381 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2383 // C1*(C2+V) -> C1*C2 + C1*V
2384 if (Ops.size() == 2)
2385 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
2386 // If any of Add's ops are Adds or Muls with a constant,
2387 // apply this transformation as well.
2388 if (Add->getNumOperands() == 2)
2389 if (containsConstantSomewhere(Add))
2390 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
2391 getMulExpr(LHSC, Add->getOperand(1)));
2394 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2395 // We found two constants, fold them together!
2396 ConstantInt *Fold = ConstantInt::get(getContext(),
2397 LHSC->getValue()->getValue() *
2398 RHSC->getValue()->getValue());
2399 Ops[0] = getConstant(Fold);
2400 Ops.erase(Ops.begin()+1); // Erase the folded element
2401 if (Ops.size() == 1) return Ops[0];
2402 LHSC = cast<SCEVConstant>(Ops[0]);
2405 // If we are left with a constant one being multiplied, strip it off.
2406 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
2407 Ops.erase(Ops.begin());
2409 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
2410 // If we have a multiply of zero, it will always be zero.
2412 } else if (Ops[0]->isAllOnesValue()) {
2413 // If we have a mul by -1 of an add, try distributing the -1 among the
2415 if (Ops.size() == 2) {
2416 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
2417 SmallVector<const SCEV *, 4> NewOps;
2418 bool AnyFolded = false;
2419 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(),
2420 E = Add->op_end(); I != E; ++I) {
2421 const SCEV *Mul = getMulExpr(Ops[0], *I);
2422 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
2423 NewOps.push_back(Mul);
2426 return getAddExpr(NewOps);
2428 else if (const SCEVAddRecExpr *
2429 AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) {
2430 // Negation preserves a recurrence's no self-wrap property.
2431 SmallVector<const SCEV *, 4> Operands;
2432 for (SCEVAddRecExpr::op_iterator I = AddRec->op_begin(),
2433 E = AddRec->op_end(); I != E; ++I) {
2434 Operands.push_back(getMulExpr(Ops[0], *I));
2436 return getAddRecExpr(Operands, AddRec->getLoop(),
2437 AddRec->getNoWrapFlags(SCEV::FlagNW));
2442 if (Ops.size() == 1)
2446 // Skip over the add expression until we get to a multiply.
2447 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
2450 // If there are mul operands inline them all into this expression.
2451 if (Idx < Ops.size()) {
2452 bool DeletedMul = false;
2453 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
2454 // If we have an mul, expand the mul operands onto the end of the operands
2456 Ops.erase(Ops.begin()+Idx);
2457 Ops.append(Mul->op_begin(), Mul->op_end());
2461 // If we deleted at least one mul, we added operands to the end of the list,
2462 // and they are not necessarily sorted. Recurse to resort and resimplify
2463 // any operands we just acquired.
2465 return getMulExpr(Ops);
2468 // If there are any add recurrences in the operands list, see if any other
2469 // added values are loop invariant. If so, we can fold them into the
2471 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2474 // Scan over all recurrences, trying to fold loop invariants into them.
2475 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
2476 // Scan all of the other operands to this mul and add them to the vector if
2477 // they are loop invariant w.r.t. the recurrence.
2478 SmallVector<const SCEV *, 8> LIOps;
2479 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2480 const Loop *AddRecLoop = AddRec->getLoop();
2481 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2482 if (isLoopInvariant(Ops[i], AddRecLoop)) {
2483 LIOps.push_back(Ops[i]);
2484 Ops.erase(Ops.begin()+i);
2488 // If we found some loop invariants, fold them into the recurrence.
2489 if (!LIOps.empty()) {
2490 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
2491 SmallVector<const SCEV *, 4> NewOps;
2492 NewOps.reserve(AddRec->getNumOperands());
2493 const SCEV *Scale = getMulExpr(LIOps);
2494 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
2495 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
2497 // Build the new addrec. Propagate the NUW and NSW flags if both the
2498 // outer mul and the inner addrec are guaranteed to have no overflow.
2500 // No self-wrap cannot be guaranteed after changing the step size, but
2501 // will be inferred if either NUW or NSW is true.
2502 Flags = AddRec->getNoWrapFlags(clearFlags(Flags, SCEV::FlagNW));
2503 const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, Flags);
2505 // If all of the other operands were loop invariant, we are done.
2506 if (Ops.size() == 1) return NewRec;
2508 // Otherwise, multiply the folded AddRec by the non-invariant parts.
2509 for (unsigned i = 0;; ++i)
2510 if (Ops[i] == AddRec) {
2514 return getMulExpr(Ops);
2517 // Okay, if there weren't any loop invariants to be folded, check to see if
2518 // there are multiple AddRec's with the same loop induction variable being
2519 // multiplied together. If so, we can fold them.
2521 // {A1,+,A2,+,...,+,An}<L> * {B1,+,B2,+,...,+,Bn}<L>
2522 // = {x=1 in [ sum y=x..2x [ sum z=max(y-x, y-n)..min(x,n) [
2523 // choose(x, 2x)*choose(2x-y, x-z)*A_{y-z}*B_z
2524 // ]]],+,...up to x=2n}.
2525 // Note that the arguments to choose() are always integers with values
2526 // known at compile time, never SCEV objects.
2528 // The implementation avoids pointless extra computations when the two
2529 // addrec's are of different length (mathematically, it's equivalent to
2530 // an infinite stream of zeros on the right).
2531 bool OpsModified = false;
2532 for (unsigned OtherIdx = Idx+1;
2533 OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2535 const SCEVAddRecExpr *OtherAddRec =
2536 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]);
2537 if (!OtherAddRec || OtherAddRec->getLoop() != AddRecLoop)
2540 bool Overflow = false;
2541 Type *Ty = AddRec->getType();
2542 bool LargerThan64Bits = getTypeSizeInBits(Ty) > 64;
2543 SmallVector<const SCEV*, 7> AddRecOps;
2544 for (int x = 0, xe = AddRec->getNumOperands() +
2545 OtherAddRec->getNumOperands() - 1; x != xe && !Overflow; ++x) {
2546 const SCEV *Term = getConstant(Ty, 0);
2547 for (int y = x, ye = 2*x+1; y != ye && !Overflow; ++y) {
2548 uint64_t Coeff1 = Choose(x, 2*x - y, Overflow);
2549 for (int z = std::max(y-x, y-(int)AddRec->getNumOperands()+1),
2550 ze = std::min(x+1, (int)OtherAddRec->getNumOperands());
2551 z < ze && !Overflow; ++z) {
2552 uint64_t Coeff2 = Choose(2*x - y, x-z, Overflow);
2554 if (LargerThan64Bits)
2555 Coeff = umul_ov(Coeff1, Coeff2, Overflow);
2557 Coeff = Coeff1*Coeff2;
2558 const SCEV *CoeffTerm = getConstant(Ty, Coeff);
2559 const SCEV *Term1 = AddRec->getOperand(y-z);
2560 const SCEV *Term2 = OtherAddRec->getOperand(z);
2561 Term = getAddExpr(Term, getMulExpr(CoeffTerm, Term1,Term2));
2564 AddRecOps.push_back(Term);
2567 const SCEV *NewAddRec = getAddRecExpr(AddRecOps, AddRec->getLoop(),
2569 if (Ops.size() == 2) return NewAddRec;
2570 Ops[Idx] = NewAddRec;
2571 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2573 AddRec = dyn_cast<SCEVAddRecExpr>(NewAddRec);
2579 return getMulExpr(Ops);
2581 // Otherwise couldn't fold anything into this recurrence. Move onto the
2585 // Okay, it looks like we really DO need an mul expr. Check to see if we
2586 // already have one, otherwise create a new one.
2587 FoldingSetNodeID ID;
2588 ID.AddInteger(scMulExpr);
2589 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2590 ID.AddPointer(Ops[i]);
2593 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2595 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2596 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2597 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
2599 UniqueSCEVs.InsertNode(S, IP);
2601 S->setNoWrapFlags(Flags);
2605 /// getUDivExpr - Get a canonical unsigned division expression, or something
2606 /// simpler if possible.
2607 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
2609 assert(getEffectiveSCEVType(LHS->getType()) ==
2610 getEffectiveSCEVType(RHS->getType()) &&
2611 "SCEVUDivExpr operand types don't match!");
2613 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
2614 if (RHSC->getValue()->equalsInt(1))
2615 return LHS; // X udiv 1 --> x
2616 // If the denominator is zero, the result of the udiv is undefined. Don't
2617 // try to analyze it, because the resolution chosen here may differ from
2618 // the resolution chosen in other parts of the compiler.
2619 if (!RHSC->getValue()->isZero()) {
2620 // Determine if the division can be folded into the operands of
2622 // TODO: Generalize this to non-constants by using known-bits information.
2623 Type *Ty = LHS->getType();
2624 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
2625 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1;
2626 // For non-power-of-two values, effectively round the value up to the
2627 // nearest power of two.
2628 if (!RHSC->getValue()->getValue().isPowerOf2())
2630 IntegerType *ExtTy =
2631 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
2632 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
2633 if (const SCEVConstant *Step =
2634 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) {
2635 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
2636 const APInt &StepInt = Step->getValue()->getValue();
2637 const APInt &DivInt = RHSC->getValue()->getValue();
2638 if (!StepInt.urem(DivInt) &&
2639 getZeroExtendExpr(AR, ExtTy) ==
2640 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2641 getZeroExtendExpr(Step, ExtTy),
2642 AR->getLoop(), SCEV::FlagAnyWrap)) {
2643 SmallVector<const SCEV *, 4> Operands;
2644 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i)
2645 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS));
2646 return getAddRecExpr(Operands, AR->getLoop(),
2649 /// Get a canonical UDivExpr for a recurrence.
2650 /// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0.
2651 // We can currently only fold X%N if X is constant.
2652 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(AR->getStart());
2653 if (StartC && !DivInt.urem(StepInt) &&
2654 getZeroExtendExpr(AR, ExtTy) ==
2655 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2656 getZeroExtendExpr(Step, ExtTy),
2657 AR->getLoop(), SCEV::FlagAnyWrap)) {
2658 const APInt &StartInt = StartC->getValue()->getValue();
2659 const APInt &StartRem = StartInt.urem(StepInt);
2661 LHS = getAddRecExpr(getConstant(StartInt - StartRem), Step,
2662 AR->getLoop(), SCEV::FlagNW);
2665 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
2666 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
2667 SmallVector<const SCEV *, 4> Operands;
2668 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i)
2669 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy));
2670 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
2671 // Find an operand that's safely divisible.
2672 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
2673 const SCEV *Op = M->getOperand(i);
2674 const SCEV *Div = getUDivExpr(Op, RHSC);
2675 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
2676 Operands = SmallVector<const SCEV *, 4>(M->op_begin(),
2679 return getMulExpr(Operands);
2683 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
2684 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) {
2685 SmallVector<const SCEV *, 4> Operands;
2686 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i)
2687 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy));
2688 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
2690 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
2691 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
2692 if (isa<SCEVUDivExpr>(Op) ||
2693 getMulExpr(Op, RHS) != A->getOperand(i))
2695 Operands.push_back(Op);
2697 if (Operands.size() == A->getNumOperands())
2698 return getAddExpr(Operands);
2702 // Fold if both operands are constant.
2703 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
2704 Constant *LHSCV = LHSC->getValue();
2705 Constant *RHSCV = RHSC->getValue();
2706 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
2712 FoldingSetNodeID ID;
2713 ID.AddInteger(scUDivExpr);
2717 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2718 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
2720 UniqueSCEVs.InsertNode(S, IP);
2724 static const APInt gcd(const SCEVConstant *C1, const SCEVConstant *C2) {
2725 APInt A = C1->getValue()->getValue().abs();
2726 APInt B = C2->getValue()->getValue().abs();
2727 uint32_t ABW = A.getBitWidth();
2728 uint32_t BBW = B.getBitWidth();
2735 return APIntOps::GreatestCommonDivisor(A, B);
2738 /// getUDivExactExpr - Get a canonical unsigned division expression, or
2739 /// something simpler if possible. There is no representation for an exact udiv
2740 /// in SCEV IR, but we can attempt to remove factors from the LHS and RHS.
2741 /// We can't do this when it's not exact because the udiv may be clearing bits.
2742 const SCEV *ScalarEvolution::getUDivExactExpr(const SCEV *LHS,
2744 // TODO: we could try to find factors in all sorts of things, but for now we
2745 // just deal with u/exact (multiply, constant). See SCEVDivision towards the
2746 // end of this file for inspiration.
2748 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(LHS);
2750 return getUDivExpr(LHS, RHS);
2752 if (const SCEVConstant *RHSCst = dyn_cast<SCEVConstant>(RHS)) {
2753 // If the mulexpr multiplies by a constant, then that constant must be the
2754 // first element of the mulexpr.
2755 if (const SCEVConstant *LHSCst =
2756 dyn_cast<SCEVConstant>(Mul->getOperand(0))) {
2757 if (LHSCst == RHSCst) {
2758 SmallVector<const SCEV *, 2> Operands;
2759 Operands.append(Mul->op_begin() + 1, Mul->op_end());
2760 return getMulExpr(Operands);
2763 // We can't just assume that LHSCst divides RHSCst cleanly, it could be
2764 // that there's a factor provided by one of the other terms. We need to
2766 APInt Factor = gcd(LHSCst, RHSCst);
2767 if (!Factor.isIntN(1)) {
2768 LHSCst = cast<SCEVConstant>(
2769 getConstant(LHSCst->getValue()->getValue().udiv(Factor)));
2770 RHSCst = cast<SCEVConstant>(
2771 getConstant(RHSCst->getValue()->getValue().udiv(Factor)));
2772 SmallVector<const SCEV *, 2> Operands;
2773 Operands.push_back(LHSCst);
2774 Operands.append(Mul->op_begin() + 1, Mul->op_end());
2775 LHS = getMulExpr(Operands);
2777 Mul = dyn_cast<SCEVMulExpr>(LHS);
2779 return getUDivExactExpr(LHS, RHS);
2784 for (int i = 0, e = Mul->getNumOperands(); i != e; ++i) {
2785 if (Mul->getOperand(i) == RHS) {
2786 SmallVector<const SCEV *, 2> Operands;
2787 Operands.append(Mul->op_begin(), Mul->op_begin() + i);
2788 Operands.append(Mul->op_begin() + i + 1, Mul->op_end());
2789 return getMulExpr(Operands);
2793 return getUDivExpr(LHS, RHS);
2796 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2797 /// Simplify the expression as much as possible.
2798 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step,
2800 SCEV::NoWrapFlags Flags) {
2801 SmallVector<const SCEV *, 4> Operands;
2802 Operands.push_back(Start);
2803 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
2804 if (StepChrec->getLoop() == L) {
2805 Operands.append(StepChrec->op_begin(), StepChrec->op_end());
2806 return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW));
2809 Operands.push_back(Step);
2810 return getAddRecExpr(Operands, L, Flags);
2813 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2814 /// Simplify the expression as much as possible.
2816 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
2817 const Loop *L, SCEV::NoWrapFlags Flags) {
2818 if (Operands.size() == 1) return Operands[0];
2820 Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
2821 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
2822 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy &&
2823 "SCEVAddRecExpr operand types don't match!");
2824 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2825 assert(isLoopInvariant(Operands[i], L) &&
2826 "SCEVAddRecExpr operand is not loop-invariant!");
2829 if (Operands.back()->isZero()) {
2830 Operands.pop_back();
2831 return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0} --> X
2834 // It's tempting to want to call getMaxBackedgeTakenCount count here and
2835 // use that information to infer NUW and NSW flags. However, computing a
2836 // BE count requires calling getAddRecExpr, so we may not yet have a
2837 // meaningful BE count at this point (and if we don't, we'd be stuck
2838 // with a SCEVCouldNotCompute as the cached BE count).
2840 Flags = StrengthenNoWrapFlags(this, scAddRecExpr, Operands, Flags);
2842 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
2843 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
2844 const Loop *NestedLoop = NestedAR->getLoop();
2845 if (L->contains(NestedLoop) ?
2846 (L->getLoopDepth() < NestedLoop->getLoopDepth()) :
2847 (!NestedLoop->contains(L) &&
2848 DT->dominates(L->getHeader(), NestedLoop->getHeader()))) {
2849 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
2850 NestedAR->op_end());
2851 Operands[0] = NestedAR->getStart();
2852 // AddRecs require their operands be loop-invariant with respect to their
2853 // loops. Don't perform this transformation if it would break this
2855 bool AllInvariant = true;
2856 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2857 if (!isLoopInvariant(Operands[i], L)) {
2858 AllInvariant = false;
2862 // Create a recurrence for the outer loop with the same step size.
2864 // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the
2865 // inner recurrence has the same property.
2866 SCEV::NoWrapFlags OuterFlags =
2867 maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags());
2869 NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags);
2870 AllInvariant = true;
2871 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i)
2872 if (!isLoopInvariant(NestedOperands[i], NestedLoop)) {
2873 AllInvariant = false;
2877 // Ok, both add recurrences are valid after the transformation.
2879 // The inner recurrence keeps its NW flag but only keeps NUW/NSW if
2880 // the outer recurrence has the same property.
2881 SCEV::NoWrapFlags InnerFlags =
2882 maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags);
2883 return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags);
2886 // Reset Operands to its original state.
2887 Operands[0] = NestedAR;
2891 // Okay, it looks like we really DO need an addrec expr. Check to see if we
2892 // already have one, otherwise create a new one.
2893 FoldingSetNodeID ID;
2894 ID.AddInteger(scAddRecExpr);
2895 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2896 ID.AddPointer(Operands[i]);
2900 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2902 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size());
2903 std::uninitialized_copy(Operands.begin(), Operands.end(), O);
2904 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator),
2905 O, Operands.size(), L);
2906 UniqueSCEVs.InsertNode(S, IP);
2908 S->setNoWrapFlags(Flags);
2912 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
2914 SmallVector<const SCEV *, 2> Ops;
2917 return getSMaxExpr(Ops);
2921 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2922 assert(!Ops.empty() && "Cannot get empty smax!");
2923 if (Ops.size() == 1) return Ops[0];
2925 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2926 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2927 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2928 "SCEVSMaxExpr operand types don't match!");
2931 // Sort by complexity, this groups all similar expression types together.
2932 GroupByComplexity(Ops, LI);
2934 // If there are any constants, fold them together.
2936 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2938 assert(Idx < Ops.size());
2939 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2940 // We found two constants, fold them together!
2941 ConstantInt *Fold = ConstantInt::get(getContext(),
2942 APIntOps::smax(LHSC->getValue()->getValue(),
2943 RHSC->getValue()->getValue()));
2944 Ops[0] = getConstant(Fold);
2945 Ops.erase(Ops.begin()+1); // Erase the folded element
2946 if (Ops.size() == 1) return Ops[0];
2947 LHSC = cast<SCEVConstant>(Ops[0]);
2950 // If we are left with a constant minimum-int, strip it off.
2951 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
2952 Ops.erase(Ops.begin());
2954 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
2955 // If we have an smax with a constant maximum-int, it will always be
2960 if (Ops.size() == 1) return Ops[0];
2963 // Find the first SMax
2964 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
2967 // Check to see if one of the operands is an SMax. If so, expand its operands
2968 // onto our operand list, and recurse to simplify.
2969 if (Idx < Ops.size()) {
2970 bool DeletedSMax = false;
2971 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
2972 Ops.erase(Ops.begin()+Idx);
2973 Ops.append(SMax->op_begin(), SMax->op_end());
2978 return getSMaxExpr(Ops);
2981 // Okay, check to see if the same value occurs in the operand list twice. If
2982 // so, delete one. Since we sorted the list, these values are required to
2984 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2985 // X smax Y smax Y --> X smax Y
2986 // X smax Y --> X, if X is always greater than Y
2987 if (Ops[i] == Ops[i+1] ||
2988 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) {
2989 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2991 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) {
2992 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2996 if (Ops.size() == 1) return Ops[0];
2998 assert(!Ops.empty() && "Reduced smax down to nothing!");
3000 // Okay, it looks like we really DO need an smax expr. Check to see if we
3001 // already have one, otherwise create a new one.
3002 FoldingSetNodeID ID;
3003 ID.AddInteger(scSMaxExpr);
3004 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
3005 ID.AddPointer(Ops[i]);
3007 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
3008 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
3009 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
3010 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator),
3012 UniqueSCEVs.InsertNode(S, IP);
3016 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
3018 SmallVector<const SCEV *, 2> Ops;
3021 return getUMaxExpr(Ops);
3025 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
3026 assert(!Ops.empty() && "Cannot get empty umax!");
3027 if (Ops.size() == 1) return Ops[0];
3029 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
3030 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
3031 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
3032 "SCEVUMaxExpr operand types don't match!");
3035 // Sort by complexity, this groups all similar expression types together.
3036 GroupByComplexity(Ops, LI);
3038 // If there are any constants, fold them together.
3040 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
3042 assert(Idx < Ops.size());
3043 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
3044 // We found two constants, fold them together!
3045 ConstantInt *Fold = ConstantInt::get(getContext(),
3046 APIntOps::umax(LHSC->getValue()->getValue(),
3047 RHSC->getValue()->getValue()));
3048 Ops[0] = getConstant(Fold);
3049 Ops.erase(Ops.begin()+1); // Erase the folded element
3050 if (Ops.size() == 1) return Ops[0];
3051 LHSC = cast<SCEVConstant>(Ops[0]);
3054 // If we are left with a constant minimum-int, strip it off.
3055 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
3056 Ops.erase(Ops.begin());
3058 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
3059 // If we have an umax with a constant maximum-int, it will always be
3064 if (Ops.size() == 1) return Ops[0];
3067 // Find the first UMax
3068 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
3071 // Check to see if one of the operands is a UMax. If so, expand its operands
3072 // onto our operand list, and recurse to simplify.
3073 if (Idx < Ops.size()) {
3074 bool DeletedUMax = false;
3075 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
3076 Ops.erase(Ops.begin()+Idx);
3077 Ops.append(UMax->op_begin(), UMax->op_end());
3082 return getUMaxExpr(Ops);
3085 // Okay, check to see if the same value occurs in the operand list twice. If
3086 // so, delete one. Since we sorted the list, these values are required to
3088 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
3089 // X umax Y umax Y --> X umax Y
3090 // X umax Y --> X, if X is always greater than Y
3091 if (Ops[i] == Ops[i+1] ||
3092 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) {
3093 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
3095 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) {
3096 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
3100 if (Ops.size() == 1) return Ops[0];
3102 assert(!Ops.empty() && "Reduced umax down to nothing!");
3104 // Okay, it looks like we really DO need a umax expr. Check to see if we
3105 // already have one, otherwise create a new one.
3106 FoldingSetNodeID ID;
3107 ID.AddInteger(scUMaxExpr);
3108 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
3109 ID.AddPointer(Ops[i]);
3111 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
3112 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
3113 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
3114 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator),
3116 UniqueSCEVs.InsertNode(S, IP);
3120 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
3122 // ~smax(~x, ~y) == smin(x, y).
3123 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
3126 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
3128 // ~umax(~x, ~y) == umin(x, y)
3129 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
3132 const SCEV *ScalarEvolution::getSizeOfExpr(Type *IntTy, Type *AllocTy) {
3133 // If we have DataLayout, we can bypass creating a target-independent
3134 // constant expression and then folding it back into a ConstantInt.
3135 // This is just a compile-time optimization.
3137 return getConstant(IntTy, DL->getTypeAllocSize(AllocTy));
3139 Constant *C = ConstantExpr::getSizeOf(AllocTy);
3140 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
3141 if (Constant *Folded = ConstantFoldConstantExpression(CE, DL, TLI))
3143 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
3144 assert(Ty == IntTy && "Effective SCEV type doesn't match");
3145 return getTruncateOrZeroExtend(getSCEV(C), Ty);
3148 const SCEV *ScalarEvolution::getOffsetOfExpr(Type *IntTy,
3151 // If we have DataLayout, we can bypass creating a target-independent
3152 // constant expression and then folding it back into a ConstantInt.
3153 // This is just a compile-time optimization.
3155 return getConstant(IntTy,
3156 DL->getStructLayout(STy)->getElementOffset(FieldNo));
3159 Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo);
3160 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
3161 if (Constant *Folded = ConstantFoldConstantExpression(CE, DL, TLI))
3164 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy));
3165 return getTruncateOrZeroExtend(getSCEV(C), Ty);
3168 const SCEV *ScalarEvolution::getUnknown(Value *V) {
3169 // Don't attempt to do anything other than create a SCEVUnknown object
3170 // here. createSCEV only calls getUnknown after checking for all other
3171 // interesting possibilities, and any other code that calls getUnknown
3172 // is doing so in order to hide a value from SCEV canonicalization.
3174 FoldingSetNodeID ID;
3175 ID.AddInteger(scUnknown);
3178 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
3179 assert(cast<SCEVUnknown>(S)->getValue() == V &&
3180 "Stale SCEVUnknown in uniquing map!");
3183 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
3185 FirstUnknown = cast<SCEVUnknown>(S);
3186 UniqueSCEVs.InsertNode(S, IP);
3190 //===----------------------------------------------------------------------===//
3191 // Basic SCEV Analysis and PHI Idiom Recognition Code
3194 /// isSCEVable - Test if values of the given type are analyzable within
3195 /// the SCEV framework. This primarily includes integer types, and it
3196 /// can optionally include pointer types if the ScalarEvolution class
3197 /// has access to target-specific information.
3198 bool ScalarEvolution::isSCEVable(Type *Ty) const {
3199 // Integers and pointers are always SCEVable.
3200 return Ty->isIntegerTy() || Ty->isPointerTy();
3203 /// getTypeSizeInBits - Return the size in bits of the specified type,
3204 /// for which isSCEVable must return true.
3205 uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const {
3206 assert(isSCEVable(Ty) && "Type is not SCEVable!");
3208 // If we have a DataLayout, use it!
3210 return DL->getTypeSizeInBits(Ty);
3212 // Integer types have fixed sizes.
3213 if (Ty->isIntegerTy())
3214 return Ty->getPrimitiveSizeInBits();
3216 // The only other support type is pointer. Without DataLayout, conservatively
3217 // assume pointers are 64-bit.
3218 assert(Ty->isPointerTy() && "isSCEVable permitted a non-SCEVable type!");
3222 /// getEffectiveSCEVType - Return a type with the same bitwidth as
3223 /// the given type and which represents how SCEV will treat the given
3224 /// type, for which isSCEVable must return true. For pointer types,
3225 /// this is the pointer-sized integer type.
3226 Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const {
3227 assert(isSCEVable(Ty) && "Type is not SCEVable!");
3229 if (Ty->isIntegerTy()) {
3233 // The only other support type is pointer.
3234 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
3237 return DL->getIntPtrType(Ty);
3239 // Without DataLayout, conservatively assume pointers are 64-bit.
3240 return Type::getInt64Ty(getContext());
3243 const SCEV *ScalarEvolution::getCouldNotCompute() {
3244 return &CouldNotCompute;
3248 // Helper class working with SCEVTraversal to figure out if a SCEV contains
3249 // a SCEVUnknown with null value-pointer. FindInvalidSCEVUnknown::FindOne
3250 // is set iff if find such SCEVUnknown.
3252 struct FindInvalidSCEVUnknown {
3254 FindInvalidSCEVUnknown() { FindOne = false; }
3255 bool follow(const SCEV *S) {
3256 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
3260 if (!cast<SCEVUnknown>(S)->getValue())
3267 bool isDone() const { return FindOne; }
3271 bool ScalarEvolution::checkValidity(const SCEV *S) const {
3272 FindInvalidSCEVUnknown F;
3273 SCEVTraversal<FindInvalidSCEVUnknown> ST(F);
3279 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
3280 /// expression and create a new one.
3281 const SCEV *ScalarEvolution::getSCEV(Value *V) {
3282 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
3284 ValueExprMapType::iterator I = ValueExprMap.find_as(V);
3285 if (I != ValueExprMap.end()) {
3286 const SCEV *S = I->second;
3287 if (checkValidity(S))
3290 ValueExprMap.erase(I);
3292 const SCEV *S = createSCEV(V);
3294 // The process of creating a SCEV for V may have caused other SCEVs
3295 // to have been created, so it's necessary to insert the new entry
3296 // from scratch, rather than trying to remember the insert position
3298 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(V, this), S));
3302 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
3304 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) {
3305 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
3307 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
3309 Type *Ty = V->getType();
3310 Ty = getEffectiveSCEVType(Ty);
3311 return getMulExpr(V,
3312 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))));
3315 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
3316 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
3317 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
3319 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
3321 Type *Ty = V->getType();
3322 Ty = getEffectiveSCEVType(Ty);
3323 const SCEV *AllOnes =
3324 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
3325 return getMinusSCEV(AllOnes, V);
3328 /// getMinusSCEV - Return LHS-RHS. Minus is represented in SCEV as A+B*-1.
3329 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
3330 SCEV::NoWrapFlags Flags) {
3331 assert(!maskFlags(Flags, SCEV::FlagNUW) && "subtraction does not have NUW");
3333 // Fast path: X - X --> 0.
3335 return getConstant(LHS->getType(), 0);
3337 // X - Y --> X + -Y.
3338 // X -(nsw || nuw) Y --> X + -Y.
3339 return getAddExpr(LHS, getNegativeSCEV(RHS));
3342 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
3343 /// input value to the specified type. If the type must be extended, it is zero
3346 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty) {
3347 Type *SrcTy = V->getType();
3348 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3349 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3350 "Cannot truncate or zero extend with non-integer arguments!");
3351 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3352 return V; // No conversion
3353 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
3354 return getTruncateExpr(V, Ty);
3355 return getZeroExtendExpr(V, Ty);
3358 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
3359 /// input value to the specified type. If the type must be extended, it is sign
3362 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
3364 Type *SrcTy = V->getType();
3365 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3366 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3367 "Cannot truncate or zero extend with non-integer arguments!");
3368 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3369 return V; // No conversion
3370 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
3371 return getTruncateExpr(V, Ty);
3372 return getSignExtendExpr(V, Ty);
3375 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
3376 /// input value to the specified type. If the type must be extended, it is zero
3377 /// extended. The conversion must not be narrowing.
3379 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) {
3380 Type *SrcTy = V->getType();
3381 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3382 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3383 "Cannot noop or zero extend with non-integer arguments!");
3384 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3385 "getNoopOrZeroExtend cannot truncate!");
3386 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3387 return V; // No conversion
3388 return getZeroExtendExpr(V, Ty);
3391 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
3392 /// input value to the specified type. If the type must be extended, it is sign
3393 /// extended. The conversion must not be narrowing.
3395 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) {
3396 Type *SrcTy = V->getType();
3397 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3398 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3399 "Cannot noop or sign extend with non-integer arguments!");
3400 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3401 "getNoopOrSignExtend cannot truncate!");
3402 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3403 return V; // No conversion
3404 return getSignExtendExpr(V, Ty);
3407 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
3408 /// the input value to the specified type. If the type must be extended,
3409 /// it is extended with unspecified bits. The conversion must not be
3412 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) {
3413 Type *SrcTy = V->getType();
3414 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3415 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3416 "Cannot noop or any extend with non-integer arguments!");
3417 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3418 "getNoopOrAnyExtend cannot truncate!");
3419 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3420 return V; // No conversion
3421 return getAnyExtendExpr(V, Ty);
3424 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
3425 /// input value to the specified type. The conversion must not be widening.
3427 ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) {
3428 Type *SrcTy = V->getType();
3429 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3430 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3431 "Cannot truncate or noop with non-integer arguments!");
3432 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
3433 "getTruncateOrNoop cannot extend!");
3434 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3435 return V; // No conversion
3436 return getTruncateExpr(V, Ty);
3439 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
3440 /// the types using zero-extension, and then perform a umax operation
3442 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
3444 const SCEV *PromotedLHS = LHS;
3445 const SCEV *PromotedRHS = RHS;
3447 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
3448 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
3450 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
3452 return getUMaxExpr(PromotedLHS, PromotedRHS);
3455 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
3456 /// the types using zero-extension, and then perform a umin operation
3458 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
3460 const SCEV *PromotedLHS = LHS;
3461 const SCEV *PromotedRHS = RHS;
3463 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
3464 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
3466 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
3468 return getUMinExpr(PromotedLHS, PromotedRHS);
3471 /// getPointerBase - Transitively follow the chain of pointer-type operands
3472 /// until reaching a SCEV that does not have a single pointer operand. This
3473 /// returns a SCEVUnknown pointer for well-formed pointer-type expressions,
3474 /// but corner cases do exist.
3475 const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) {
3476 // A pointer operand may evaluate to a nonpointer expression, such as null.
3477 if (!V->getType()->isPointerTy())
3480 if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) {
3481 return getPointerBase(Cast->getOperand());
3483 else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) {
3484 const SCEV *PtrOp = nullptr;
3485 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
3487 if ((*I)->getType()->isPointerTy()) {
3488 // Cannot find the base of an expression with multiple pointer operands.
3496 return getPointerBase(PtrOp);
3501 /// PushDefUseChildren - Push users of the given Instruction
3502 /// onto the given Worklist.
3504 PushDefUseChildren(Instruction *I,
3505 SmallVectorImpl<Instruction *> &Worklist) {
3506 // Push the def-use children onto the Worklist stack.
3507 for (User *U : I->users())
3508 Worklist.push_back(cast<Instruction>(U));
3511 /// ForgetSymbolicValue - This looks up computed SCEV values for all
3512 /// instructions that depend on the given instruction and removes them from
3513 /// the ValueExprMapType map if they reference SymName. This is used during PHI
3516 ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) {
3517 SmallVector<Instruction *, 16> Worklist;
3518 PushDefUseChildren(PN, Worklist);
3520 SmallPtrSet<Instruction *, 8> Visited;
3522 while (!Worklist.empty()) {
3523 Instruction *I = Worklist.pop_back_val();
3524 if (!Visited.insert(I).second)
3527 ValueExprMapType::iterator It =
3528 ValueExprMap.find_as(static_cast<Value *>(I));
3529 if (It != ValueExprMap.end()) {
3530 const SCEV *Old = It->second;
3532 // Short-circuit the def-use traversal if the symbolic name
3533 // ceases to appear in expressions.
3534 if (Old != SymName && !hasOperand(Old, SymName))
3537 // SCEVUnknown for a PHI either means that it has an unrecognized
3538 // structure, it's a PHI that's in the progress of being computed
3539 // by createNodeForPHI, or it's a single-value PHI. In the first case,
3540 // additional loop trip count information isn't going to change anything.
3541 // In the second case, createNodeForPHI will perform the necessary
3542 // updates on its own when it gets to that point. In the third, we do
3543 // want to forget the SCEVUnknown.
3544 if (!isa<PHINode>(I) ||
3545 !isa<SCEVUnknown>(Old) ||
3546 (I != PN && Old == SymName)) {
3547 forgetMemoizedResults(Old);
3548 ValueExprMap.erase(It);
3552 PushDefUseChildren(I, Worklist);
3556 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
3557 /// a loop header, making it a potential recurrence, or it doesn't.
3559 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
3560 if (const Loop *L = LI->getLoopFor(PN->getParent()))
3561 if (L->getHeader() == PN->getParent()) {
3562 // The loop may have multiple entrances or multiple exits; we can analyze
3563 // this phi as an addrec if it has a unique entry value and a unique
3565 Value *BEValueV = nullptr, *StartValueV = nullptr;
3566 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
3567 Value *V = PN->getIncomingValue(i);
3568 if (L->contains(PN->getIncomingBlock(i))) {
3571 } else if (BEValueV != V) {
3575 } else if (!StartValueV) {
3577 } else if (StartValueV != V) {
3578 StartValueV = nullptr;
3582 if (BEValueV && StartValueV) {
3583 // While we are analyzing this PHI node, handle its value symbolically.
3584 const SCEV *SymbolicName = getUnknown(PN);
3585 assert(ValueExprMap.find_as(PN) == ValueExprMap.end() &&
3586 "PHI node already processed?");
3587 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
3589 // Using this symbolic name for the PHI, analyze the value coming around
3591 const SCEV *BEValue = getSCEV(BEValueV);
3593 // NOTE: If BEValue is loop invariant, we know that the PHI node just
3594 // has a special value for the first iteration of the loop.
3596 // If the value coming around the backedge is an add with the symbolic
3597 // value we just inserted, then we found a simple induction variable!
3598 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
3599 // If there is a single occurrence of the symbolic value, replace it
3600 // with a recurrence.
3601 unsigned FoundIndex = Add->getNumOperands();
3602 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3603 if (Add->getOperand(i) == SymbolicName)
3604 if (FoundIndex == e) {
3609 if (FoundIndex != Add->getNumOperands()) {
3610 // Create an add with everything but the specified operand.
3611 SmallVector<const SCEV *, 8> Ops;
3612 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3613 if (i != FoundIndex)
3614 Ops.push_back(Add->getOperand(i));
3615 const SCEV *Accum = getAddExpr(Ops);
3617 // This is not a valid addrec if the step amount is varying each
3618 // loop iteration, but is not itself an addrec in this loop.
3619 if (isLoopInvariant(Accum, L) ||
3620 (isa<SCEVAddRecExpr>(Accum) &&
3621 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
3622 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
3624 // If the increment doesn't overflow, then neither the addrec nor
3625 // the post-increment will overflow.
3626 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) {
3627 if (OBO->hasNoUnsignedWrap())
3628 Flags = setFlags(Flags, SCEV::FlagNUW);
3629 if (OBO->hasNoSignedWrap())
3630 Flags = setFlags(Flags, SCEV::FlagNSW);
3631 } else if (GEPOperator *GEP = dyn_cast<GEPOperator>(BEValueV)) {
3632 // If the increment is an inbounds GEP, then we know the address
3633 // space cannot be wrapped around. We cannot make any guarantee
3634 // about signed or unsigned overflow because pointers are
3635 // unsigned but we may have a negative index from the base
3636 // pointer. We can guarantee that no unsigned wrap occurs if the
3637 // indices form a positive value.
3638 if (GEP->isInBounds()) {
3639 Flags = setFlags(Flags, SCEV::FlagNW);
3641 const SCEV *Ptr = getSCEV(GEP->getPointerOperand());
3642 if (isKnownPositive(getMinusSCEV(getSCEV(GEP), Ptr)))
3643 Flags = setFlags(Flags, SCEV::FlagNUW);
3646 // We cannot transfer nuw and nsw flags from subtraction
3647 // operations -- sub nuw X, Y is not the same as add nuw X, -Y
3651 const SCEV *StartVal = getSCEV(StartValueV);
3652 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
3654 // Since the no-wrap flags are on the increment, they apply to the
3655 // post-incremented value as well.
3656 if (isLoopInvariant(Accum, L))
3657 (void)getAddRecExpr(getAddExpr(StartVal, Accum),
3660 // Okay, for the entire analysis of this edge we assumed the PHI
3661 // to be symbolic. We now need to go back and purge all of the
3662 // entries for the scalars that use the symbolic expression.
3663 ForgetSymbolicName(PN, SymbolicName);
3664 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3668 } else if (const SCEVAddRecExpr *AddRec =
3669 dyn_cast<SCEVAddRecExpr>(BEValue)) {
3670 // Otherwise, this could be a loop like this:
3671 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
3672 // In this case, j = {1,+,1} and BEValue is j.
3673 // Because the other in-value of i (0) fits the evolution of BEValue
3674 // i really is an addrec evolution.
3675 if (AddRec->getLoop() == L && AddRec->isAffine()) {
3676 const SCEV *StartVal = getSCEV(StartValueV);
3678 // If StartVal = j.start - j.stride, we can use StartVal as the
3679 // initial step of the addrec evolution.
3680 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
3681 AddRec->getOperand(1))) {
3682 // FIXME: For constant StartVal, we should be able to infer
3684 const SCEV *PHISCEV =
3685 getAddRecExpr(StartVal, AddRec->getOperand(1), L,
3688 // Okay, for the entire analysis of this edge we assumed the PHI
3689 // to be symbolic. We now need to go back and purge all of the
3690 // entries for the scalars that use the symbolic expression.
3691 ForgetSymbolicName(PN, SymbolicName);
3692 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3700 // If the PHI has a single incoming value, follow that value, unless the
3701 // PHI's incoming blocks are in a different loop, in which case doing so
3702 // risks breaking LCSSA form. Instcombine would normally zap these, but
3703 // it doesn't have DominatorTree information, so it may miss cases.
3704 if (Value *V = SimplifyInstruction(PN, DL, TLI, DT, AC))
3705 if (LI->replacementPreservesLCSSAForm(PN, V))
3708 // If it's not a loop phi, we can't handle it yet.
3709 return getUnknown(PN);
3712 /// createNodeForGEP - Expand GEP instructions into add and multiply
3713 /// operations. This allows them to be analyzed by regular SCEV code.
3715 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
3716 Type *IntPtrTy = getEffectiveSCEVType(GEP->getType());
3717 Value *Base = GEP->getOperand(0);
3718 // Don't attempt to analyze GEPs over unsized objects.
3719 if (!Base->getType()->getPointerElementType()->isSized())
3720 return getUnknown(GEP);
3722 // Don't blindly transfer the inbounds flag from the GEP instruction to the
3723 // Add expression, because the Instruction may be guarded by control flow
3724 // and the no-overflow bits may not be valid for the expression in any
3726 SCEV::NoWrapFlags Wrap = GEP->isInBounds() ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
3728 const SCEV *TotalOffset = getConstant(IntPtrTy, 0);
3729 gep_type_iterator GTI = gep_type_begin(GEP);
3730 for (GetElementPtrInst::op_iterator I = std::next(GEP->op_begin()),
3734 // Compute the (potentially symbolic) offset in bytes for this index.
3735 if (StructType *STy = dyn_cast<StructType>(*GTI++)) {
3736 // For a struct, add the member offset.
3737 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
3738 const SCEV *FieldOffset = getOffsetOfExpr(IntPtrTy, STy, FieldNo);
3740 // Add the field offset to the running total offset.
3741 TotalOffset = getAddExpr(TotalOffset, FieldOffset);
3743 // For an array, add the element offset, explicitly scaled.
3744 const SCEV *ElementSize = getSizeOfExpr(IntPtrTy, *GTI);
3745 const SCEV *IndexS = getSCEV(Index);
3746 // Getelementptr indices are signed.
3747 IndexS = getTruncateOrSignExtend(IndexS, IntPtrTy);
3749 // Multiply the index by the element size to compute the element offset.
3750 const SCEV *LocalOffset = getMulExpr(IndexS, ElementSize, Wrap);
3752 // Add the element offset to the running total offset.
3753 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
3757 // Get the SCEV for the GEP base.
3758 const SCEV *BaseS = getSCEV(Base);
3760 // Add the total offset from all the GEP indices to the base.
3761 return getAddExpr(BaseS, TotalOffset, Wrap);
3764 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
3765 /// guaranteed to end in (at every loop iteration). It is, at the same time,
3766 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
3767 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
3769 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
3770 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3771 return C->getValue()->getValue().countTrailingZeros();
3773 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
3774 return std::min(GetMinTrailingZeros(T->getOperand()),
3775 (uint32_t)getTypeSizeInBits(T->getType()));
3777 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
3778 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3779 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3780 getTypeSizeInBits(E->getType()) : OpRes;
3783 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
3784 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3785 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3786 getTypeSizeInBits(E->getType()) : OpRes;
3789 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
3790 // The result is the min of all operands results.
3791 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3792 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3793 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3797 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
3798 // The result is the sum of all operands results.
3799 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
3800 uint32_t BitWidth = getTypeSizeInBits(M->getType());
3801 for (unsigned i = 1, e = M->getNumOperands();
3802 SumOpRes != BitWidth && i != e; ++i)
3803 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
3808 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
3809 // The result is the min of all operands results.
3810 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3811 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3812 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3816 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
3817 // The result is the min of all operands results.
3818 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3819 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3820 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3824 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
3825 // The result is the min of all operands results.
3826 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3827 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3828 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3832 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3833 // For a SCEVUnknown, ask ValueTracking.
3834 unsigned BitWidth = getTypeSizeInBits(U->getType());
3835 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3836 computeKnownBits(U->getValue(), Zeros, Ones, DL, 0, AC, nullptr, DT);
3837 return Zeros.countTrailingOnes();
3844 /// GetRangeFromMetadata - Helper method to assign a range to V from
3845 /// metadata present in the IR.
3846 static Optional<ConstantRange> GetRangeFromMetadata(Value *V) {
3847 if (Instruction *I = dyn_cast<Instruction>(V)) {
3848 if (MDNode *MD = I->getMetadata(LLVMContext::MD_range)) {
3849 ConstantRange TotalRange(
3850 cast<IntegerType>(I->getType())->getBitWidth(), false);
3852 unsigned NumRanges = MD->getNumOperands() / 2;
3853 assert(NumRanges >= 1);
3855 for (unsigned i = 0; i < NumRanges; ++i) {
3856 ConstantInt *Lower =
3857 mdconst::extract<ConstantInt>(MD->getOperand(2 * i + 0));
3858 ConstantInt *Upper =
3859 mdconst::extract<ConstantInt>(MD->getOperand(2 * i + 1));
3860 ConstantRange Range(Lower->getValue(), Upper->getValue());
3861 TotalRange = TotalRange.unionWith(Range);
3871 /// getUnsignedRange - Determine the unsigned range for a particular SCEV.
3874 ScalarEvolution::getUnsignedRange(const SCEV *S) {
3875 // See if we've computed this range already.
3876 DenseMap<const SCEV *, ConstantRange>::iterator I = UnsignedRanges.find(S);
3877 if (I != UnsignedRanges.end())
3880 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3881 return setUnsignedRange(C, ConstantRange(C->getValue()->getValue()));
3883 unsigned BitWidth = getTypeSizeInBits(S->getType());
3884 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3886 // If the value has known zeros, the maximum unsigned value will have those
3887 // known zeros as well.
3888 uint32_t TZ = GetMinTrailingZeros(S);
3890 ConservativeResult =
3891 ConstantRange(APInt::getMinValue(BitWidth),
3892 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
3894 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3895 ConstantRange X = getUnsignedRange(Add->getOperand(0));
3896 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3897 X = X.add(getUnsignedRange(Add->getOperand(i)));
3898 return setUnsignedRange(Add, ConservativeResult.intersectWith(X));
3901 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3902 ConstantRange X = getUnsignedRange(Mul->getOperand(0));
3903 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3904 X = X.multiply(getUnsignedRange(Mul->getOperand(i)));
3905 return setUnsignedRange(Mul, ConservativeResult.intersectWith(X));
3908 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3909 ConstantRange X = getUnsignedRange(SMax->getOperand(0));
3910 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3911 X = X.smax(getUnsignedRange(SMax->getOperand(i)));
3912 return setUnsignedRange(SMax, ConservativeResult.intersectWith(X));
3915 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3916 ConstantRange X = getUnsignedRange(UMax->getOperand(0));
3917 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3918 X = X.umax(getUnsignedRange(UMax->getOperand(i)));
3919 return setUnsignedRange(UMax, ConservativeResult.intersectWith(X));
3922 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3923 ConstantRange X = getUnsignedRange(UDiv->getLHS());
3924 ConstantRange Y = getUnsignedRange(UDiv->getRHS());
3925 return setUnsignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y)));
3928 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3929 ConstantRange X = getUnsignedRange(ZExt->getOperand());
3930 return setUnsignedRange(ZExt,
3931 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3934 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3935 ConstantRange X = getUnsignedRange(SExt->getOperand());
3936 return setUnsignedRange(SExt,
3937 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3940 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3941 ConstantRange X = getUnsignedRange(Trunc->getOperand());
3942 return setUnsignedRange(Trunc,
3943 ConservativeResult.intersectWith(X.truncate(BitWidth)));
3946 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3947 // If there's no unsigned wrap, the value will never be less than its
3949 if (AddRec->getNoWrapFlags(SCEV::FlagNUW))
3950 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
3951 if (!C->getValue()->isZero())
3952 ConservativeResult =
3953 ConservativeResult.intersectWith(
3954 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0)));
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 = getUnsignedRange(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.zextOrTrunc(BitWidth*2+1);
3977 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3978 ConstantRange ExtMaxBECountRange =
3979 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3980 ConstantRange ExtEndRange = EndRange.zextOrTrunc(BitWidth*2+1);
3981 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3983 return setUnsignedRange(AddRec, ConservativeResult);
3985 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(),
3986 EndRange.getUnsignedMin());
3987 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(),
3988 EndRange.getUnsignedMax());
3989 if (Min.isMinValue() && Max.isMaxValue())
3990 return setUnsignedRange(AddRec, ConservativeResult);
3991 return setUnsignedRange(AddRec,
3992 ConservativeResult.intersectWith(ConstantRange(Min, Max+1)));
3996 return setUnsignedRange(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 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
4007 computeKnownBits(U->getValue(), Zeros, Ones, DL, 0, AC, nullptr, DT);
4008 if (Ones == ~Zeros + 1)
4009 return setUnsignedRange(U, ConservativeResult);
4010 return setUnsignedRange(U,
4011 ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1)));
4014 return setUnsignedRange(S, ConservativeResult);
4017 /// getSignedRange - Determine the signed range for a particular SCEV.
4020 ScalarEvolution::getSignedRange(const SCEV *S) {
4021 // See if we've computed this range already.
4022 DenseMap<const SCEV *, ConstantRange>::iterator I = SignedRanges.find(S);
4023 if (I != SignedRanges.end())
4026 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
4027 return setSignedRange(C, ConstantRange(C->getValue()->getValue()));
4029 unsigned BitWidth = getTypeSizeInBits(S->getType());
4030 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
4032 // If the value has known zeros, the maximum signed value will have those
4033 // known zeros as well.
4034 uint32_t TZ = GetMinTrailingZeros(S);
4036 ConservativeResult =
4037 ConstantRange(APInt::getSignedMinValue(BitWidth),
4038 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
4040 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
4041 ConstantRange X = getSignedRange(Add->getOperand(0));
4042 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
4043 X = X.add(getSignedRange(Add->getOperand(i)));
4044 return setSignedRange(Add, ConservativeResult.intersectWith(X));
4047 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
4048 ConstantRange X = getSignedRange(Mul->getOperand(0));
4049 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
4050 X = X.multiply(getSignedRange(Mul->getOperand(i)));
4051 return setSignedRange(Mul, ConservativeResult.intersectWith(X));
4054 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
4055 ConstantRange X = getSignedRange(SMax->getOperand(0));
4056 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
4057 X = X.smax(getSignedRange(SMax->getOperand(i)));
4058 return setSignedRange(SMax, ConservativeResult.intersectWith(X));
4061 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
4062 ConstantRange X = getSignedRange(UMax->getOperand(0));
4063 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
4064 X = X.umax(getSignedRange(UMax->getOperand(i)));
4065 return setSignedRange(UMax, ConservativeResult.intersectWith(X));
4068 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
4069 ConstantRange X = getSignedRange(UDiv->getLHS());
4070 ConstantRange Y = getSignedRange(UDiv->getRHS());
4071 return setSignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y)));
4074 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
4075 ConstantRange X = getSignedRange(ZExt->getOperand());
4076 return setSignedRange(ZExt,
4077 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
4080 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
4081 ConstantRange X = getSignedRange(SExt->getOperand());
4082 return setSignedRange(SExt,
4083 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
4086 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
4087 ConstantRange X = getSignedRange(Trunc->getOperand());
4088 return setSignedRange(Trunc,
4089 ConservativeResult.intersectWith(X.truncate(BitWidth)));
4092 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
4093 // If there's no signed wrap, and all the operands have the same sign or
4094 // zero, the value won't ever change sign.
4095 if (AddRec->getNoWrapFlags(SCEV::FlagNSW)) {
4096 bool AllNonNeg = true;
4097 bool AllNonPos = true;
4098 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
4099 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
4100 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
4103 ConservativeResult = ConservativeResult.intersectWith(
4104 ConstantRange(APInt(BitWidth, 0),
4105 APInt::getSignedMinValue(BitWidth)));
4107 ConservativeResult = ConservativeResult.intersectWith(
4108 ConstantRange(APInt::getSignedMinValue(BitWidth),
4109 APInt(BitWidth, 1)));
4112 // TODO: non-affine addrec
4113 if (AddRec->isAffine()) {
4114 Type *Ty = AddRec->getType();
4115 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
4116 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
4117 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
4118 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
4120 const SCEV *Start = AddRec->getStart();
4121 const SCEV *Step = AddRec->getStepRecurrence(*this);
4123 ConstantRange StartRange = getSignedRange(Start);
4124 ConstantRange StepRange = getSignedRange(Step);
4125 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
4126 ConstantRange EndRange =
4127 StartRange.add(MaxBECountRange.multiply(StepRange));
4129 // Check for overflow. This must be done with ConstantRange arithmetic
4130 // because we could be called from within the ScalarEvolution overflow
4132 ConstantRange ExtStartRange = StartRange.sextOrTrunc(BitWidth*2+1);
4133 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
4134 ConstantRange ExtMaxBECountRange =
4135 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
4136 ConstantRange ExtEndRange = EndRange.sextOrTrunc(BitWidth*2+1);
4137 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
4139 return setSignedRange(AddRec, ConservativeResult);
4141 APInt Min = APIntOps::smin(StartRange.getSignedMin(),
4142 EndRange.getSignedMin());
4143 APInt Max = APIntOps::smax(StartRange.getSignedMax(),
4144 EndRange.getSignedMax());
4145 if (Min.isMinSignedValue() && Max.isMaxSignedValue())
4146 return setSignedRange(AddRec, ConservativeResult);
4147 return setSignedRange(AddRec,
4148 ConservativeResult.intersectWith(ConstantRange(Min, Max+1)));
4152 return setSignedRange(AddRec, ConservativeResult);
4155 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
4156 // Check if the IR explicitly contains !range metadata.
4157 Optional<ConstantRange> MDRange = GetRangeFromMetadata(U->getValue());
4158 if (MDRange.hasValue())
4159 ConservativeResult = ConservativeResult.intersectWith(MDRange.getValue());
4161 // For a SCEVUnknown, ask ValueTracking.
4162 if (!U->getValue()->getType()->isIntegerTy() && !DL)
4163 return setSignedRange(U, ConservativeResult);
4164 unsigned NS = ComputeNumSignBits(U->getValue(), DL, 0, AC, nullptr, DT);
4166 return setSignedRange(U, ConservativeResult);
4167 return setSignedRange(U, ConservativeResult.intersectWith(
4168 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
4169 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1)));
4172 return setSignedRange(S, ConservativeResult);
4175 /// createSCEV - We know that there is no SCEV for the specified value.
4176 /// Analyze the expression.
4178 const SCEV *ScalarEvolution::createSCEV(Value *V) {
4179 if (!isSCEVable(V->getType()))
4180 return getUnknown(V);
4182 unsigned Opcode = Instruction::UserOp1;
4183 if (Instruction *I = dyn_cast<Instruction>(V)) {
4184 Opcode = I->getOpcode();
4186 // Don't attempt to analyze instructions in blocks that aren't
4187 // reachable. Such instructions don't matter, and they aren't required
4188 // to obey basic rules for definitions dominating uses which this
4189 // analysis depends on.
4190 if (!DT->isReachableFromEntry(I->getParent()))
4191 return getUnknown(V);
4192 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
4193 Opcode = CE->getOpcode();
4194 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
4195 return getConstant(CI);
4196 else if (isa<ConstantPointerNull>(V))
4197 return getConstant(V->getType(), 0);
4198 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
4199 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee());
4201 return getUnknown(V);
4203 Operator *U = cast<Operator>(V);
4205 case Instruction::Add: {
4206 // The simple thing to do would be to just call getSCEV on both operands
4207 // and call getAddExpr with the result. However if we're looking at a
4208 // bunch of things all added together, this can be quite inefficient,
4209 // because it leads to N-1 getAddExpr calls for N ultimate operands.
4210 // Instead, gather up all the operands and make a single getAddExpr call.
4211 // LLVM IR canonical form means we need only traverse the left operands.
4213 // Don't apply this instruction's NSW or NUW flags to the new
4214 // expression. The instruction may be guarded by control flow that the
4215 // no-wrap behavior depends on. Non-control-equivalent instructions can be
4216 // mapped to the same SCEV expression, and it would be incorrect to transfer
4217 // NSW/NUW semantics to those operations.
4218 SmallVector<const SCEV *, 4> AddOps;
4219 AddOps.push_back(getSCEV(U->getOperand(1)));
4220 for (Value *Op = U->getOperand(0); ; Op = U->getOperand(0)) {
4221 unsigned Opcode = Op->getValueID() - Value::InstructionVal;
4222 if (Opcode != Instruction::Add && Opcode != Instruction::Sub)
4224 U = cast<Operator>(Op);
4225 const SCEV *Op1 = getSCEV(U->getOperand(1));
4226 if (Opcode == Instruction::Sub)
4227 AddOps.push_back(getNegativeSCEV(Op1));
4229 AddOps.push_back(Op1);
4231 AddOps.push_back(getSCEV(U->getOperand(0)));
4232 return getAddExpr(AddOps);
4234 case Instruction::Mul: {
4235 // Don't transfer NSW/NUW for the same reason as AddExpr.
4236 SmallVector<const SCEV *, 4> MulOps;
4237 MulOps.push_back(getSCEV(U->getOperand(1)));
4238 for (Value *Op = U->getOperand(0);
4239 Op->getValueID() == Instruction::Mul + Value::InstructionVal;
4240 Op = U->getOperand(0)) {
4241 U = cast<Operator>(Op);
4242 MulOps.push_back(getSCEV(U->getOperand(1)));
4244 MulOps.push_back(getSCEV(U->getOperand(0)));
4245 return getMulExpr(MulOps);
4247 case Instruction::UDiv:
4248 return getUDivExpr(getSCEV(U->getOperand(0)),
4249 getSCEV(U->getOperand(1)));
4250 case Instruction::Sub:
4251 return getMinusSCEV(getSCEV(U->getOperand(0)),
4252 getSCEV(U->getOperand(1)));
4253 case Instruction::And:
4254 // For an expression like x&255 that merely masks off the high bits,
4255 // use zext(trunc(x)) as the SCEV expression.
4256 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
4257 if (CI->isNullValue())
4258 return getSCEV(U->getOperand(1));
4259 if (CI->isAllOnesValue())
4260 return getSCEV(U->getOperand(0));
4261 const APInt &A = CI->getValue();
4263 // Instcombine's ShrinkDemandedConstant may strip bits out of
4264 // constants, obscuring what would otherwise be a low-bits mask.
4265 // Use computeKnownBits to compute what ShrinkDemandedConstant
4266 // knew about to reconstruct a low-bits mask value.
4267 unsigned LZ = A.countLeadingZeros();
4268 unsigned TZ = A.countTrailingZeros();
4269 unsigned BitWidth = A.getBitWidth();
4270 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
4271 computeKnownBits(U->getOperand(0), KnownZero, KnownOne, DL, 0, AC,
4274 APInt EffectiveMask =
4275 APInt::getLowBitsSet(BitWidth, BitWidth - LZ - TZ).shl(TZ);
4276 if ((LZ != 0 || TZ != 0) && !((~A & ~KnownZero) & EffectiveMask)) {
4277 const SCEV *MulCount = getConstant(
4278 ConstantInt::get(getContext(), APInt::getOneBitSet(BitWidth, TZ)));
4282 getUDivExactExpr(getSCEV(U->getOperand(0)), MulCount),
4283 IntegerType::get(getContext(), BitWidth - LZ - TZ)),
4290 case Instruction::Or:
4291 // If the RHS of the Or is a constant, we may have something like:
4292 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
4293 // optimizations will transparently handle this case.
4295 // In order for this transformation to be safe, the LHS must be of the
4296 // form X*(2^n) and the Or constant must be less than 2^n.
4297 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
4298 const SCEV *LHS = getSCEV(U->getOperand(0));
4299 const APInt &CIVal = CI->getValue();
4300 if (GetMinTrailingZeros(LHS) >=
4301 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
4302 // Build a plain add SCEV.
4303 const SCEV *S = getAddExpr(LHS, getSCEV(CI));
4304 // If the LHS of the add was an addrec and it has no-wrap flags,
4305 // transfer the no-wrap flags, since an or won't introduce a wrap.
4306 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
4307 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
4308 const_cast<SCEVAddRecExpr *>(NewAR)->setNoWrapFlags(
4309 OldAR->getNoWrapFlags());
4315 case Instruction::Xor:
4316 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
4317 // If the RHS of the xor is a signbit, then this is just an add.
4318 // Instcombine turns add of signbit into xor as a strength reduction step.
4319 if (CI->getValue().isSignBit())
4320 return getAddExpr(getSCEV(U->getOperand(0)),
4321 getSCEV(U->getOperand(1)));
4323 // If the RHS of xor is -1, then this is a not operation.
4324 if (CI->isAllOnesValue())
4325 return getNotSCEV(getSCEV(U->getOperand(0)));
4327 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
4328 // This is a variant of the check for xor with -1, and it handles
4329 // the case where instcombine has trimmed non-demanded bits out
4330 // of an xor with -1.
4331 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
4332 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
4333 if (BO->getOpcode() == Instruction::And &&
4334 LCI->getValue() == CI->getValue())
4335 if (const SCEVZeroExtendExpr *Z =
4336 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
4337 Type *UTy = U->getType();
4338 const SCEV *Z0 = Z->getOperand();
4339 Type *Z0Ty = Z0->getType();
4340 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
4342 // If C is a low-bits mask, the zero extend is serving to
4343 // mask off the high bits. Complement the operand and
4344 // re-apply the zext.
4345 if (APIntOps::isMask(Z0TySize, CI->getValue()))
4346 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
4348 // If C is a single bit, it may be in the sign-bit position
4349 // before the zero-extend. In this case, represent the xor
4350 // using an add, which is equivalent, and re-apply the zext.
4351 APInt Trunc = CI->getValue().trunc(Z0TySize);
4352 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
4354 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
4360 case Instruction::Shl:
4361 // Turn shift left of a constant amount into a multiply.
4362 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
4363 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
4365 // If the shift count is not less than the bitwidth, the result of
4366 // the shift is undefined. Don't try to analyze it, because the
4367 // resolution chosen here may differ from the resolution chosen in
4368 // other parts of the compiler.
4369 if (SA->getValue().uge(BitWidth))
4372 Constant *X = ConstantInt::get(getContext(),
4373 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
4374 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
4378 case Instruction::LShr:
4379 // Turn logical shift right of a constant into a unsigned divide.
4380 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
4381 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
4383 // If the shift count is not less than the bitwidth, the result of
4384 // the shift is undefined. Don't try to analyze it, because the
4385 // resolution chosen here may differ from the resolution chosen in
4386 // other parts of the compiler.
4387 if (SA->getValue().uge(BitWidth))
4390 Constant *X = ConstantInt::get(getContext(),
4391 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
4392 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
4396 case Instruction::AShr:
4397 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
4398 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
4399 if (Operator *L = dyn_cast<Operator>(U->getOperand(0)))
4400 if (L->getOpcode() == Instruction::Shl &&
4401 L->getOperand(1) == U->getOperand(1)) {
4402 uint64_t BitWidth = getTypeSizeInBits(U->getType());
4404 // If the shift count is not less than the bitwidth, the result of
4405 // the shift is undefined. Don't try to analyze it, because the
4406 // resolution chosen here may differ from the resolution chosen in
4407 // other parts of the compiler.
4408 if (CI->getValue().uge(BitWidth))
4411 uint64_t Amt = BitWidth - CI->getZExtValue();
4412 if (Amt == BitWidth)
4413 return getSCEV(L->getOperand(0)); // shift by zero --> noop
4415 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
4416 IntegerType::get(getContext(),
4422 case Instruction::Trunc:
4423 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
4425 case Instruction::ZExt:
4426 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
4428 case Instruction::SExt:
4429 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
4431 case Instruction::BitCast:
4432 // BitCasts are no-op casts so we just eliminate the cast.
4433 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
4434 return getSCEV(U->getOperand(0));
4437 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
4438 // lead to pointer expressions which cannot safely be expanded to GEPs,
4439 // because ScalarEvolution doesn't respect the GEP aliasing rules when
4440 // simplifying integer expressions.
4442 case Instruction::GetElementPtr:
4443 return createNodeForGEP(cast<GEPOperator>(U));
4445 case Instruction::PHI:
4446 return createNodeForPHI(cast<PHINode>(U));
4448 case Instruction::Select:
4449 // This could be a smax or umax that was lowered earlier.
4450 // Try to recover it.
4451 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
4452 Value *LHS = ICI->getOperand(0);
4453 Value *RHS = ICI->getOperand(1);
4454 switch (ICI->getPredicate()) {
4455 case ICmpInst::ICMP_SLT:
4456 case ICmpInst::ICMP_SLE:
4457 std::swap(LHS, RHS);
4459 case ICmpInst::ICMP_SGT:
4460 case ICmpInst::ICMP_SGE:
4461 // a >s b ? a+x : b+x -> smax(a, b)+x
4462 // a >s b ? b+x : a+x -> smin(a, b)+x
4463 if (getTypeSizeInBits(LHS->getType()) <=
4464 getTypeSizeInBits(U->getType())) {
4465 const SCEV *LS = getNoopOrSignExtend(getSCEV(LHS), U->getType());
4466 const SCEV *RS = getNoopOrSignExtend(getSCEV(RHS), U->getType());
4467 const SCEV *LA = getSCEV(U->getOperand(1));
4468 const SCEV *RA = getSCEV(U->getOperand(2));
4469 const SCEV *LDiff = getMinusSCEV(LA, LS);
4470 const SCEV *RDiff = getMinusSCEV(RA, RS);
4472 return getAddExpr(getSMaxExpr(LS, RS), LDiff);
4473 LDiff = getMinusSCEV(LA, RS);
4474 RDiff = getMinusSCEV(RA, LS);
4476 return getAddExpr(getSMinExpr(LS, RS), LDiff);
4479 case ICmpInst::ICMP_ULT:
4480 case ICmpInst::ICMP_ULE:
4481 std::swap(LHS, RHS);
4483 case ICmpInst::ICMP_UGT:
4484 case ICmpInst::ICMP_UGE:
4485 // a >u b ? a+x : b+x -> umax(a, b)+x
4486 // a >u b ? b+x : a+x -> umin(a, b)+x
4487 if (getTypeSizeInBits(LHS->getType()) <=
4488 getTypeSizeInBits(U->getType())) {
4489 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), U->getType());
4490 const SCEV *RS = getNoopOrZeroExtend(getSCEV(RHS), U->getType());
4491 const SCEV *LA = getSCEV(U->getOperand(1));
4492 const SCEV *RA = getSCEV(U->getOperand(2));
4493 const SCEV *LDiff = getMinusSCEV(LA, LS);
4494 const SCEV *RDiff = getMinusSCEV(RA, RS);
4496 return getAddExpr(getUMaxExpr(LS, RS), LDiff);
4497 LDiff = getMinusSCEV(LA, RS);
4498 RDiff = getMinusSCEV(RA, LS);
4500 return getAddExpr(getUMinExpr(LS, RS), LDiff);
4503 case ICmpInst::ICMP_NE:
4504 // n != 0 ? n+x : 1+x -> umax(n, 1)+x
4505 if (getTypeSizeInBits(LHS->getType()) <=
4506 getTypeSizeInBits(U->getType()) &&
4507 isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
4508 const SCEV *One = getConstant(U->getType(), 1);
4509 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), U->getType());
4510 const SCEV *LA = getSCEV(U->getOperand(1));
4511 const SCEV *RA = getSCEV(U->getOperand(2));
4512 const SCEV *LDiff = getMinusSCEV(LA, LS);
4513 const SCEV *RDiff = getMinusSCEV(RA, One);
4515 return getAddExpr(getUMaxExpr(One, LS), LDiff);
4518 case ICmpInst::ICMP_EQ:
4519 // n == 0 ? 1+x : n+x -> umax(n, 1)+x
4520 if (getTypeSizeInBits(LHS->getType()) <=
4521 getTypeSizeInBits(U->getType()) &&
4522 isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
4523 const SCEV *One = getConstant(U->getType(), 1);
4524 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), U->getType());
4525 const SCEV *LA = getSCEV(U->getOperand(1));
4526 const SCEV *RA = getSCEV(U->getOperand(2));
4527 const SCEV *LDiff = getMinusSCEV(LA, One);
4528 const SCEV *RDiff = getMinusSCEV(RA, LS);
4530 return getAddExpr(getUMaxExpr(One, LS), LDiff);
4538 default: // We cannot analyze this expression.
4542 return getUnknown(V);
4547 //===----------------------------------------------------------------------===//
4548 // Iteration Count Computation Code
4551 unsigned ScalarEvolution::getSmallConstantTripCount(Loop *L) {
4552 if (BasicBlock *ExitingBB = L->getExitingBlock())
4553 return getSmallConstantTripCount(L, ExitingBB);
4555 // No trip count information for multiple exits.
4559 /// getSmallConstantTripCount - Returns the maximum trip count of this loop as a
4560 /// normal unsigned value. Returns 0 if the trip count is unknown or not
4561 /// constant. Will also return 0 if the maximum trip count is very large (>=
4564 /// This "trip count" assumes that control exits via ExitingBlock. More
4565 /// precisely, it is the number of times that control may reach ExitingBlock
4566 /// before taking the branch. For loops with multiple exits, it may not be the
4567 /// number times that the loop header executes because the loop may exit
4568 /// prematurely via another branch.
4569 unsigned ScalarEvolution::getSmallConstantTripCount(Loop *L,
4570 BasicBlock *ExitingBlock) {
4571 assert(ExitingBlock && "Must pass a non-null exiting block!");
4572 assert(L->isLoopExiting(ExitingBlock) &&
4573 "Exiting block must actually branch out of the loop!");
4574 const SCEVConstant *ExitCount =
4575 dyn_cast<SCEVConstant>(getExitCount(L, ExitingBlock));
4579 ConstantInt *ExitConst = ExitCount->getValue();
4581 // Guard against huge trip counts.
4582 if (ExitConst->getValue().getActiveBits() > 32)
4585 // In case of integer overflow, this returns 0, which is correct.
4586 return ((unsigned)ExitConst->getZExtValue()) + 1;
4589 unsigned ScalarEvolution::getSmallConstantTripMultiple(Loop *L) {
4590 if (BasicBlock *ExitingBB = L->getExitingBlock())
4591 return getSmallConstantTripMultiple(L, ExitingBB);
4593 // No trip multiple information for multiple exits.
4597 /// getSmallConstantTripMultiple - Returns the largest constant divisor of the
4598 /// trip count of this loop as a normal unsigned value, if possible. This
4599 /// means that the actual trip count is always a multiple of the returned
4600 /// value (don't forget the trip count could very well be zero as well!).
4602 /// Returns 1 if the trip count is unknown or not guaranteed to be the
4603 /// multiple of a constant (which is also the case if the trip count is simply
4604 /// constant, use getSmallConstantTripCount for that case), Will also return 1
4605 /// if the trip count is very large (>= 2^32).
4607 /// As explained in the comments for getSmallConstantTripCount, this assumes
4608 /// that control exits the loop via ExitingBlock.
4610 ScalarEvolution::getSmallConstantTripMultiple(Loop *L,
4611 BasicBlock *ExitingBlock) {
4612 assert(ExitingBlock && "Must pass a non-null exiting block!");
4613 assert(L->isLoopExiting(ExitingBlock) &&
4614 "Exiting block must actually branch out of the loop!");
4615 const SCEV *ExitCount = getExitCount(L, ExitingBlock);
4616 if (ExitCount == getCouldNotCompute())
4619 // Get the trip count from the BE count by adding 1.
4620 const SCEV *TCMul = getAddExpr(ExitCount,
4621 getConstant(ExitCount->getType(), 1));
4622 // FIXME: SCEV distributes multiplication as V1*C1 + V2*C1. We could attempt
4623 // to factor simple cases.
4624 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(TCMul))
4625 TCMul = Mul->getOperand(0);
4627 const SCEVConstant *MulC = dyn_cast<SCEVConstant>(TCMul);
4631 ConstantInt *Result = MulC->getValue();
4633 // Guard against huge trip counts (this requires checking
4634 // for zero to handle the case where the trip count == -1 and the
4636 if (!Result || Result->getValue().getActiveBits() > 32 ||
4637 Result->getValue().getActiveBits() == 0)
4640 return (unsigned)Result->getZExtValue();
4643 // getExitCount - Get the expression for the number of loop iterations for which
4644 // this loop is guaranteed not to exit via ExitingBlock. Otherwise return
4645 // SCEVCouldNotCompute.
4646 const SCEV *ScalarEvolution::getExitCount(Loop *L, BasicBlock *ExitingBlock) {
4647 return getBackedgeTakenInfo(L).getExact(ExitingBlock, this);
4650 /// getBackedgeTakenCount - If the specified loop has a predictable
4651 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
4652 /// object. The backedge-taken count is the number of times the loop header
4653 /// will be branched to from within the loop. This is one less than the
4654 /// trip count of the loop, since it doesn't count the first iteration,
4655 /// when the header is branched to from outside the loop.
4657 /// Note that it is not valid to call this method on a loop without a
4658 /// loop-invariant backedge-taken count (see
4659 /// hasLoopInvariantBackedgeTakenCount).
4661 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
4662 return getBackedgeTakenInfo(L).getExact(this);
4665 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
4666 /// return the least SCEV value that is known never to be less than the
4667 /// actual backedge taken count.
4668 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
4669 return getBackedgeTakenInfo(L).getMax(this);
4672 /// PushLoopPHIs - Push PHI nodes in the header of the given loop
4673 /// onto the given Worklist.
4675 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
4676 BasicBlock *Header = L->getHeader();
4678 // Push all Loop-header PHIs onto the Worklist stack.
4679 for (BasicBlock::iterator I = Header->begin();
4680 PHINode *PN = dyn_cast<PHINode>(I); ++I)
4681 Worklist.push_back(PN);
4684 const ScalarEvolution::BackedgeTakenInfo &
4685 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
4686 // Initially insert an invalid entry for this loop. If the insertion
4687 // succeeds, proceed to actually compute a backedge-taken count and
4688 // update the value. The temporary CouldNotCompute value tells SCEV
4689 // code elsewhere that it shouldn't attempt to request a new
4690 // backedge-taken count, which could result in infinite recursion.
4691 std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
4692 BackedgeTakenCounts.insert(std::make_pair(L, BackedgeTakenInfo()));
4694 return Pair.first->second;
4696 // ComputeBackedgeTakenCount may allocate memory for its result. Inserting it
4697 // into the BackedgeTakenCounts map transfers ownership. Otherwise, the result
4698 // must be cleared in this scope.
4699 BackedgeTakenInfo Result = ComputeBackedgeTakenCount(L);
4701 if (Result.getExact(this) != getCouldNotCompute()) {
4702 assert(isLoopInvariant(Result.getExact(this), L) &&
4703 isLoopInvariant(Result.getMax(this), L) &&
4704 "Computed backedge-taken count isn't loop invariant for loop!");
4705 ++NumTripCountsComputed;
4707 else if (Result.getMax(this) == getCouldNotCompute() &&
4708 isa<PHINode>(L->getHeader()->begin())) {
4709 // Only count loops that have phi nodes as not being computable.
4710 ++NumTripCountsNotComputed;
4713 // Now that we know more about the trip count for this loop, forget any
4714 // existing SCEV values for PHI nodes in this loop since they are only
4715 // conservative estimates made without the benefit of trip count
4716 // information. This is similar to the code in forgetLoop, except that
4717 // it handles SCEVUnknown PHI nodes specially.
4718 if (Result.hasAnyInfo()) {
4719 SmallVector<Instruction *, 16> Worklist;
4720 PushLoopPHIs(L, Worklist);
4722 SmallPtrSet<Instruction *, 8> Visited;
4723 while (!Worklist.empty()) {
4724 Instruction *I = Worklist.pop_back_val();
4725 if (!Visited.insert(I).second)
4728 ValueExprMapType::iterator It =
4729 ValueExprMap.find_as(static_cast<Value *>(I));
4730 if (It != ValueExprMap.end()) {
4731 const SCEV *Old = It->second;
4733 // SCEVUnknown for a PHI either means that it has an unrecognized
4734 // structure, or it's a PHI that's in the progress of being computed
4735 // by createNodeForPHI. In the former case, additional loop trip
4736 // count information isn't going to change anything. In the later
4737 // case, createNodeForPHI will perform the necessary updates on its
4738 // own when it gets to that point.
4739 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) {
4740 forgetMemoizedResults(Old);
4741 ValueExprMap.erase(It);
4743 if (PHINode *PN = dyn_cast<PHINode>(I))
4744 ConstantEvolutionLoopExitValue.erase(PN);
4747 PushDefUseChildren(I, Worklist);
4751 // Re-lookup the insert position, since the call to
4752 // ComputeBackedgeTakenCount above could result in a
4753 // recusive call to getBackedgeTakenInfo (on a different
4754 // loop), which would invalidate the iterator computed
4756 return BackedgeTakenCounts.find(L)->second = Result;
4759 /// forgetLoop - This method should be called by the client when it has
4760 /// changed a loop in a way that may effect ScalarEvolution's ability to
4761 /// compute a trip count, or if the loop is deleted.
4762 void ScalarEvolution::forgetLoop(const Loop *L) {
4763 // Drop any stored trip count value.
4764 DenseMap<const Loop*, BackedgeTakenInfo>::iterator BTCPos =
4765 BackedgeTakenCounts.find(L);
4766 if (BTCPos != BackedgeTakenCounts.end()) {
4767 BTCPos->second.clear();
4768 BackedgeTakenCounts.erase(BTCPos);
4771 // Drop information about expressions based on loop-header PHIs.
4772 SmallVector<Instruction *, 16> Worklist;
4773 PushLoopPHIs(L, Worklist);
4775 SmallPtrSet<Instruction *, 8> Visited;
4776 while (!Worklist.empty()) {
4777 Instruction *I = Worklist.pop_back_val();
4778 if (!Visited.insert(I).second)
4781 ValueExprMapType::iterator It =
4782 ValueExprMap.find_as(static_cast<Value *>(I));
4783 if (It != ValueExprMap.end()) {
4784 forgetMemoizedResults(It->second);
4785 ValueExprMap.erase(It);
4786 if (PHINode *PN = dyn_cast<PHINode>(I))
4787 ConstantEvolutionLoopExitValue.erase(PN);
4790 PushDefUseChildren(I, Worklist);
4793 // Forget all contained loops too, to avoid dangling entries in the
4794 // ValuesAtScopes map.
4795 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
4799 /// forgetValue - This method should be called by the client when it has
4800 /// changed a value in a way that may effect its value, or which may
4801 /// disconnect it from a def-use chain linking it to a loop.
4802 void ScalarEvolution::forgetValue(Value *V) {
4803 Instruction *I = dyn_cast<Instruction>(V);
4806 // Drop information about expressions based on loop-header PHIs.
4807 SmallVector<Instruction *, 16> Worklist;
4808 Worklist.push_back(I);
4810 SmallPtrSet<Instruction *, 8> Visited;
4811 while (!Worklist.empty()) {
4812 I = Worklist.pop_back_val();
4813 if (!Visited.insert(I).second)
4816 ValueExprMapType::iterator It =
4817 ValueExprMap.find_as(static_cast<Value *>(I));
4818 if (It != ValueExprMap.end()) {
4819 forgetMemoizedResults(It->second);
4820 ValueExprMap.erase(It);
4821 if (PHINode *PN = dyn_cast<PHINode>(I))
4822 ConstantEvolutionLoopExitValue.erase(PN);
4825 PushDefUseChildren(I, Worklist);
4829 /// getExact - Get the exact loop backedge taken count considering all loop
4830 /// exits. A computable result can only be return for loops with a single exit.
4831 /// Returning the minimum taken count among all exits is incorrect because one
4832 /// of the loop's exit limit's may have been skipped. HowFarToZero assumes that
4833 /// the limit of each loop test is never skipped. This is a valid assumption as
4834 /// long as the loop exits via that test. For precise results, it is the
4835 /// caller's responsibility to specify the relevant loop exit using
4836 /// getExact(ExitingBlock, SE).
4838 ScalarEvolution::BackedgeTakenInfo::getExact(ScalarEvolution *SE) const {
4839 // If any exits were not computable, the loop is not computable.
4840 if (!ExitNotTaken.isCompleteList()) return SE->getCouldNotCompute();
4842 // We need exactly one computable exit.
4843 if (!ExitNotTaken.ExitingBlock) return SE->getCouldNotCompute();
4844 assert(ExitNotTaken.ExactNotTaken && "uninitialized not-taken info");
4846 const SCEV *BECount = nullptr;
4847 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4848 ENT != nullptr; ENT = ENT->getNextExit()) {
4850 assert(ENT->ExactNotTaken != SE->getCouldNotCompute() && "bad exit SCEV");
4853 BECount = ENT->ExactNotTaken;
4854 else if (BECount != ENT->ExactNotTaken)
4855 return SE->getCouldNotCompute();
4857 assert(BECount && "Invalid not taken count for loop exit");
4861 /// getExact - Get the exact not taken count for this loop exit.
4863 ScalarEvolution::BackedgeTakenInfo::getExact(BasicBlock *ExitingBlock,
4864 ScalarEvolution *SE) const {
4865 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4866 ENT != nullptr; ENT = ENT->getNextExit()) {
4868 if (ENT->ExitingBlock == ExitingBlock)
4869 return ENT->ExactNotTaken;
4871 return SE->getCouldNotCompute();
4874 /// getMax - Get the max backedge taken count for the loop.
4876 ScalarEvolution::BackedgeTakenInfo::getMax(ScalarEvolution *SE) const {
4877 return Max ? Max : SE->getCouldNotCompute();
4880 bool ScalarEvolution::BackedgeTakenInfo::hasOperand(const SCEV *S,
4881 ScalarEvolution *SE) const {
4882 if (Max && Max != SE->getCouldNotCompute() && SE->hasOperand(Max, S))
4885 if (!ExitNotTaken.ExitingBlock)
4888 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4889 ENT != nullptr; ENT = ENT->getNextExit()) {
4891 if (ENT->ExactNotTaken != SE->getCouldNotCompute()
4892 && SE->hasOperand(ENT->ExactNotTaken, S)) {
4899 /// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each
4900 /// computable exit into a persistent ExitNotTakenInfo array.
4901 ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo(
4902 SmallVectorImpl< std::pair<BasicBlock *, const SCEV *> > &ExitCounts,
4903 bool Complete, const SCEV *MaxCount) : Max(MaxCount) {
4906 ExitNotTaken.setIncomplete();
4908 unsigned NumExits = ExitCounts.size();
4909 if (NumExits == 0) return;
4911 ExitNotTaken.ExitingBlock = ExitCounts[0].first;
4912 ExitNotTaken.ExactNotTaken = ExitCounts[0].second;
4913 if (NumExits == 1) return;
4915 // Handle the rare case of multiple computable exits.
4916 ExitNotTakenInfo *ENT = new ExitNotTakenInfo[NumExits-1];
4918 ExitNotTakenInfo *PrevENT = &ExitNotTaken;
4919 for (unsigned i = 1; i < NumExits; ++i, PrevENT = ENT, ++ENT) {
4920 PrevENT->setNextExit(ENT);
4921 ENT->ExitingBlock = ExitCounts[i].first;
4922 ENT->ExactNotTaken = ExitCounts[i].second;
4926 /// clear - Invalidate this result and free the ExitNotTakenInfo array.
4927 void ScalarEvolution::BackedgeTakenInfo::clear() {
4928 ExitNotTaken.ExitingBlock = nullptr;
4929 ExitNotTaken.ExactNotTaken = nullptr;
4930 delete[] ExitNotTaken.getNextExit();
4933 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
4934 /// of the specified loop will execute.
4935 ScalarEvolution::BackedgeTakenInfo
4936 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
4937 SmallVector<BasicBlock *, 8> ExitingBlocks;
4938 L->getExitingBlocks(ExitingBlocks);
4940 SmallVector<std::pair<BasicBlock *, const SCEV *>, 4> ExitCounts;
4941 bool CouldComputeBECount = true;
4942 BasicBlock *Latch = L->getLoopLatch(); // may be NULL.
4943 const SCEV *MustExitMaxBECount = nullptr;
4944 const SCEV *MayExitMaxBECount = nullptr;
4946 // Compute the ExitLimit for each loop exit. Use this to populate ExitCounts
4947 // and compute maxBECount.
4948 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
4949 BasicBlock *ExitBB = ExitingBlocks[i];
4950 ExitLimit EL = ComputeExitLimit(L, ExitBB);
4952 // 1. For each exit that can be computed, add an entry to ExitCounts.
4953 // CouldComputeBECount is true only if all exits can be computed.
4954 if (EL.Exact == getCouldNotCompute())
4955 // We couldn't compute an exact value for this exit, so
4956 // we won't be able to compute an exact value for the loop.
4957 CouldComputeBECount = false;
4959 ExitCounts.push_back(std::make_pair(ExitBB, EL.Exact));
4961 // 2. Derive the loop's MaxBECount from each exit's max number of
4962 // non-exiting iterations. Partition the loop exits into two kinds:
4963 // LoopMustExits and LoopMayExits.
4965 // If the exit dominates the loop latch, it is a LoopMustExit otherwise it
4966 // is a LoopMayExit. If any computable LoopMustExit is found, then
4967 // MaxBECount is the minimum EL.Max of computable LoopMustExits. Otherwise,
4968 // MaxBECount is conservatively the maximum EL.Max, where CouldNotCompute is
4969 // considered greater than any computable EL.Max.
4970 if (EL.Max != getCouldNotCompute() && Latch &&
4971 DT->dominates(ExitBB, Latch)) {
4972 if (!MustExitMaxBECount)
4973 MustExitMaxBECount = EL.Max;
4975 MustExitMaxBECount =
4976 getUMinFromMismatchedTypes(MustExitMaxBECount, EL.Max);
4978 } else if (MayExitMaxBECount != getCouldNotCompute()) {
4979 if (!MayExitMaxBECount || EL.Max == getCouldNotCompute())
4980 MayExitMaxBECount = EL.Max;
4983 getUMaxFromMismatchedTypes(MayExitMaxBECount, EL.Max);
4987 const SCEV *MaxBECount = MustExitMaxBECount ? MustExitMaxBECount :
4988 (MayExitMaxBECount ? MayExitMaxBECount : getCouldNotCompute());
4989 return BackedgeTakenInfo(ExitCounts, CouldComputeBECount, MaxBECount);
4992 /// ComputeExitLimit - Compute the number of times the backedge of the specified
4993 /// loop will execute if it exits via the specified block.
4994 ScalarEvolution::ExitLimit
4995 ScalarEvolution::ComputeExitLimit(const Loop *L, BasicBlock *ExitingBlock) {
4997 // Okay, we've chosen an exiting block. See what condition causes us to
4998 // exit at this block and remember the exit block and whether all other targets
4999 // lead to the loop header.
5000 bool MustExecuteLoopHeader = true;
5001 BasicBlock *Exit = nullptr;
5002 for (succ_iterator SI = succ_begin(ExitingBlock), SE = succ_end(ExitingBlock);
5004 if (!L->contains(*SI)) {
5005 if (Exit) // Multiple exit successors.
5006 return getCouldNotCompute();
5008 } else if (*SI != L->getHeader()) {
5009 MustExecuteLoopHeader = false;
5012 // At this point, we know we have a conditional branch that determines whether
5013 // the loop is exited. However, we don't know if the branch is executed each
5014 // time through the loop. If not, then the execution count of the branch will
5015 // not be equal to the trip count of the loop.
5017 // Currently we check for this by checking to see if the Exit branch goes to
5018 // the loop header. If so, we know it will always execute the same number of
5019 // times as the loop. We also handle the case where the exit block *is* the
5020 // loop header. This is common for un-rotated loops.
5022 // If both of those tests fail, walk up the unique predecessor chain to the
5023 // header, stopping if there is an edge that doesn't exit the loop. If the
5024 // header is reached, the execution count of the branch will be equal to the
5025 // trip count of the loop.
5027 // More extensive analysis could be done to handle more cases here.
5029 if (!MustExecuteLoopHeader && ExitingBlock != L->getHeader()) {
5030 // The simple checks failed, try climbing the unique predecessor chain
5031 // up to the header.
5033 for (BasicBlock *BB = ExitingBlock; BB; ) {
5034 BasicBlock *Pred = BB->getUniquePredecessor();
5036 return getCouldNotCompute();
5037 TerminatorInst *PredTerm = Pred->getTerminator();
5038 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) {
5039 BasicBlock *PredSucc = PredTerm->getSuccessor(i);
5042 // If the predecessor has a successor that isn't BB and isn't
5043 // outside the loop, assume the worst.
5044 if (L->contains(PredSucc))
5045 return getCouldNotCompute();
5047 if (Pred == L->getHeader()) {
5054 return getCouldNotCompute();
5057 bool IsOnlyExit = (L->getExitingBlock() != nullptr);
5058 TerminatorInst *Term = ExitingBlock->getTerminator();
5059 if (BranchInst *BI = dyn_cast<BranchInst>(Term)) {
5060 assert(BI->isConditional() && "If unconditional, it can't be in loop!");
5061 // Proceed to the next level to examine the exit condition expression.
5062 return ComputeExitLimitFromCond(L, BI->getCondition(), BI->getSuccessor(0),
5063 BI->getSuccessor(1),
5064 /*ControlsExit=*/IsOnlyExit);
5067 if (SwitchInst *SI = dyn_cast<SwitchInst>(Term))
5068 return ComputeExitLimitFromSingleExitSwitch(L, SI, Exit,
5069 /*ControlsExit=*/IsOnlyExit);
5071 return getCouldNotCompute();
5074 /// ComputeExitLimitFromCond - Compute the number of times the
5075 /// backedge of the specified loop will execute if its exit condition
5076 /// were a conditional branch of ExitCond, TBB, and FBB.
5078 /// @param ControlsExit is true if ExitCond directly controls the exit
5079 /// branch. In this case, we can assume that the loop exits only if the
5080 /// condition is true and can infer that failing to meet the condition prior to
5081 /// integer wraparound results in undefined behavior.
5082 ScalarEvolution::ExitLimit
5083 ScalarEvolution::ComputeExitLimitFromCond(const Loop *L,
5087 bool ControlsExit) {
5088 // Check if the controlling expression for this loop is an And or Or.
5089 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
5090 if (BO->getOpcode() == Instruction::And) {
5091 // Recurse on the operands of the and.
5092 bool EitherMayExit = L->contains(TBB);
5093 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
5094 ControlsExit && !EitherMayExit);
5095 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
5096 ControlsExit && !EitherMayExit);
5097 const SCEV *BECount = getCouldNotCompute();
5098 const SCEV *MaxBECount = getCouldNotCompute();
5099 if (EitherMayExit) {
5100 // Both conditions must be true for the loop to continue executing.
5101 // Choose the less conservative count.
5102 if (EL0.Exact == getCouldNotCompute() ||
5103 EL1.Exact == getCouldNotCompute())
5104 BECount = getCouldNotCompute();
5106 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
5107 if (EL0.Max == getCouldNotCompute())
5108 MaxBECount = EL1.Max;
5109 else if (EL1.Max == getCouldNotCompute())
5110 MaxBECount = EL0.Max;
5112 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
5114 // Both conditions must be true at the same time for the loop to exit.
5115 // For now, be conservative.
5116 assert(L->contains(FBB) && "Loop block has no successor in loop!");
5117 if (EL0.Max == EL1.Max)
5118 MaxBECount = EL0.Max;
5119 if (EL0.Exact == EL1.Exact)
5120 BECount = EL0.Exact;
5123 return ExitLimit(BECount, MaxBECount);
5125 if (BO->getOpcode() == Instruction::Or) {
5126 // Recurse on the operands of the or.
5127 bool EitherMayExit = L->contains(FBB);
5128 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
5129 ControlsExit && !EitherMayExit);
5130 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
5131 ControlsExit && !EitherMayExit);
5132 const SCEV *BECount = getCouldNotCompute();
5133 const SCEV *MaxBECount = getCouldNotCompute();
5134 if (EitherMayExit) {
5135 // Both conditions must be false for the loop to continue executing.
5136 // Choose the less conservative count.
5137 if (EL0.Exact == getCouldNotCompute() ||
5138 EL1.Exact == getCouldNotCompute())
5139 BECount = getCouldNotCompute();
5141 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
5142 if (EL0.Max == getCouldNotCompute())
5143 MaxBECount = EL1.Max;
5144 else if (EL1.Max == getCouldNotCompute())
5145 MaxBECount = EL0.Max;
5147 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
5149 // Both conditions must be false at the same time for the loop to exit.
5150 // For now, be conservative.
5151 assert(L->contains(TBB) && "Loop block has no successor in loop!");
5152 if (EL0.Max == EL1.Max)
5153 MaxBECount = EL0.Max;
5154 if (EL0.Exact == EL1.Exact)
5155 BECount = EL0.Exact;
5158 return ExitLimit(BECount, MaxBECount);
5162 // With an icmp, it may be feasible to compute an exact backedge-taken count.
5163 // Proceed to the next level to examine the icmp.
5164 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
5165 return ComputeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB, ControlsExit);
5167 // Check for a constant condition. These are normally stripped out by
5168 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
5169 // preserve the CFG and is temporarily leaving constant conditions
5171 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
5172 if (L->contains(FBB) == !CI->getZExtValue())
5173 // The backedge is always taken.
5174 return getCouldNotCompute();
5176 // The backedge is never taken.
5177 return getConstant(CI->getType(), 0);
5180 // If it's not an integer or pointer comparison then compute it the hard way.
5181 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
5184 /// ComputeExitLimitFromICmp - Compute the number of times the
5185 /// backedge of the specified loop will execute if its exit condition
5186 /// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB.
5187 ScalarEvolution::ExitLimit
5188 ScalarEvolution::ComputeExitLimitFromICmp(const Loop *L,
5192 bool ControlsExit) {
5194 // If the condition was exit on true, convert the condition to exit on false
5195 ICmpInst::Predicate Cond;
5196 if (!L->contains(FBB))
5197 Cond = ExitCond->getPredicate();
5199 Cond = ExitCond->getInversePredicate();
5201 // Handle common loops like: for (X = "string"; *X; ++X)
5202 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
5203 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
5205 ComputeLoadConstantCompareExitLimit(LI, RHS, L, Cond);
5206 if (ItCnt.hasAnyInfo())
5210 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
5211 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
5213 // Try to evaluate any dependencies out of the loop.
5214 LHS = getSCEVAtScope(LHS, L);
5215 RHS = getSCEVAtScope(RHS, L);
5217 // At this point, we would like to compute how many iterations of the
5218 // loop the predicate will return true for these inputs.
5219 if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) {
5220 // If there is a loop-invariant, force it into the RHS.
5221 std::swap(LHS, RHS);
5222 Cond = ICmpInst::getSwappedPredicate(Cond);
5225 // Simplify the operands before analyzing them.
5226 (void)SimplifyICmpOperands(Cond, LHS, RHS);
5228 // If we have a comparison of a chrec against a constant, try to use value
5229 // ranges to answer this query.
5230 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
5231 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
5232 if (AddRec->getLoop() == L) {
5233 // Form the constant range.
5234 ConstantRange CompRange(
5235 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
5237 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
5238 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
5242 case ICmpInst::ICMP_NE: { // while (X != Y)
5243 // Convert to: while (X-Y != 0)
5244 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit);
5245 if (EL.hasAnyInfo()) return EL;
5248 case ICmpInst::ICMP_EQ: { // while (X == Y)
5249 // Convert to: while (X-Y == 0)
5250 ExitLimit EL = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
5251 if (EL.hasAnyInfo()) return EL;
5254 case ICmpInst::ICMP_SLT:
5255 case ICmpInst::ICMP_ULT: { // while (X < Y)
5256 bool IsSigned = Cond == ICmpInst::ICMP_SLT;
5257 ExitLimit EL = HowManyLessThans(LHS, RHS, L, IsSigned, ControlsExit);
5258 if (EL.hasAnyInfo()) return EL;
5261 case ICmpInst::ICMP_SGT:
5262 case ICmpInst::ICMP_UGT: { // while (X > Y)
5263 bool IsSigned = Cond == ICmpInst::ICMP_SGT;
5264 ExitLimit EL = HowManyGreaterThans(LHS, RHS, L, IsSigned, ControlsExit);
5265 if (EL.hasAnyInfo()) return EL;
5270 dbgs() << "ComputeBackedgeTakenCount ";
5271 if (ExitCond->getOperand(0)->getType()->isUnsigned())
5272 dbgs() << "[unsigned] ";
5273 dbgs() << *LHS << " "
5274 << Instruction::getOpcodeName(Instruction::ICmp)
5275 << " " << *RHS << "\n";
5279 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
5282 ScalarEvolution::ExitLimit
5283 ScalarEvolution::ComputeExitLimitFromSingleExitSwitch(const Loop *L,
5285 BasicBlock *ExitingBlock,
5286 bool ControlsExit) {
5287 assert(!L->contains(ExitingBlock) && "Not an exiting block!");
5289 // Give up if the exit is the default dest of a switch.
5290 if (Switch->getDefaultDest() == ExitingBlock)
5291 return getCouldNotCompute();
5293 assert(L->contains(Switch->getDefaultDest()) &&
5294 "Default case must not exit the loop!");
5295 const SCEV *LHS = getSCEVAtScope(Switch->getCondition(), L);
5296 const SCEV *RHS = getConstant(Switch->findCaseDest(ExitingBlock));
5298 // while (X != Y) --> while (X-Y != 0)
5299 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit);
5300 if (EL.hasAnyInfo())
5303 return getCouldNotCompute();
5306 static ConstantInt *
5307 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
5308 ScalarEvolution &SE) {
5309 const SCEV *InVal = SE.getConstant(C);
5310 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
5311 assert(isa<SCEVConstant>(Val) &&
5312 "Evaluation of SCEV at constant didn't fold correctly?");
5313 return cast<SCEVConstant>(Val)->getValue();
5316 /// ComputeLoadConstantCompareExitLimit - Given an exit condition of
5317 /// 'icmp op load X, cst', try to see if we can compute the backedge
5318 /// execution count.
5319 ScalarEvolution::ExitLimit
5320 ScalarEvolution::ComputeLoadConstantCompareExitLimit(
5324 ICmpInst::Predicate predicate) {
5326 if (LI->isVolatile()) return getCouldNotCompute();
5328 // Check to see if the loaded pointer is a getelementptr of a global.
5329 // TODO: Use SCEV instead of manually grubbing with GEPs.
5330 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
5331 if (!GEP) return getCouldNotCompute();
5333 // Make sure that it is really a constant global we are gepping, with an
5334 // initializer, and make sure the first IDX is really 0.
5335 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
5336 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
5337 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
5338 !cast<Constant>(GEP->getOperand(1))->isNullValue())
5339 return getCouldNotCompute();
5341 // Okay, we allow one non-constant index into the GEP instruction.
5342 Value *VarIdx = nullptr;
5343 std::vector<Constant*> Indexes;
5344 unsigned VarIdxNum = 0;
5345 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
5346 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
5347 Indexes.push_back(CI);
5348 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
5349 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
5350 VarIdx = GEP->getOperand(i);
5352 Indexes.push_back(nullptr);
5355 // Loop-invariant loads may be a byproduct of loop optimization. Skip them.
5357 return getCouldNotCompute();
5359 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
5360 // Check to see if X is a loop variant variable value now.
5361 const SCEV *Idx = getSCEV(VarIdx);
5362 Idx = getSCEVAtScope(Idx, L);
5364 // We can only recognize very limited forms of loop index expressions, in
5365 // particular, only affine AddRec's like {C1,+,C2}.
5366 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
5367 if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) ||
5368 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
5369 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
5370 return getCouldNotCompute();
5372 unsigned MaxSteps = MaxBruteForceIterations;
5373 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
5374 ConstantInt *ItCst = ConstantInt::get(
5375 cast<IntegerType>(IdxExpr->getType()), IterationNum);
5376 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
5378 // Form the GEP offset.
5379 Indexes[VarIdxNum] = Val;
5381 Constant *Result = ConstantFoldLoadThroughGEPIndices(GV->getInitializer(),
5383 if (!Result) break; // Cannot compute!
5385 // Evaluate the condition for this iteration.
5386 Result = ConstantExpr::getICmp(predicate, Result, RHS);
5387 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
5388 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
5390 dbgs() << "\n***\n*** Computed loop count " << *ItCst
5391 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
5394 ++NumArrayLenItCounts;
5395 return getConstant(ItCst); // Found terminating iteration!
5398 return getCouldNotCompute();
5402 /// CanConstantFold - Return true if we can constant fold an instruction of the
5403 /// specified type, assuming that all operands were constants.
5404 static bool CanConstantFold(const Instruction *I) {
5405 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
5406 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I) ||
5410 if (const CallInst *CI = dyn_cast<CallInst>(I))
5411 if (const Function *F = CI->getCalledFunction())
5412 return canConstantFoldCallTo(F);
5416 /// Determine whether this instruction can constant evolve within this loop
5417 /// assuming its operands can all constant evolve.
5418 static bool canConstantEvolve(Instruction *I, const Loop *L) {
5419 // An instruction outside of the loop can't be derived from a loop PHI.
5420 if (!L->contains(I)) return false;
5422 if (isa<PHINode>(I)) {
5423 if (L->getHeader() == I->getParent())
5426 // We don't currently keep track of the control flow needed to evaluate
5427 // PHIs, so we cannot handle PHIs inside of loops.
5431 // If we won't be able to constant fold this expression even if the operands
5432 // are constants, bail early.
5433 return CanConstantFold(I);
5436 /// getConstantEvolvingPHIOperands - Implement getConstantEvolvingPHI by
5437 /// recursing through each instruction operand until reaching a loop header phi.
5439 getConstantEvolvingPHIOperands(Instruction *UseInst, const Loop *L,
5440 DenseMap<Instruction *, PHINode *> &PHIMap) {
5442 // Otherwise, we can evaluate this instruction if all of its operands are
5443 // constant or derived from a PHI node themselves.
5444 PHINode *PHI = nullptr;
5445 for (Instruction::op_iterator OpI = UseInst->op_begin(),
5446 OpE = UseInst->op_end(); OpI != OpE; ++OpI) {
5448 if (isa<Constant>(*OpI)) continue;
5450 Instruction *OpInst = dyn_cast<Instruction>(*OpI);
5451 if (!OpInst || !canConstantEvolve(OpInst, L)) return nullptr;
5453 PHINode *P = dyn_cast<PHINode>(OpInst);
5455 // If this operand is already visited, reuse the prior result.
5456 // We may have P != PHI if this is the deepest point at which the
5457 // inconsistent paths meet.
5458 P = PHIMap.lookup(OpInst);
5460 // Recurse and memoize the results, whether a phi is found or not.
5461 // This recursive call invalidates pointers into PHIMap.
5462 P = getConstantEvolvingPHIOperands(OpInst, L, PHIMap);
5466 return nullptr; // Not evolving from PHI
5467 if (PHI && PHI != P)
5468 return nullptr; // Evolving from multiple different PHIs.
5471 // This is a expression evolving from a constant PHI!
5475 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
5476 /// in the loop that V is derived from. We allow arbitrary operations along the
5477 /// way, but the operands of an operation must either be constants or a value
5478 /// derived from a constant PHI. If this expression does not fit with these
5479 /// constraints, return null.
5480 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
5481 Instruction *I = dyn_cast<Instruction>(V);
5482 if (!I || !canConstantEvolve(I, L)) return nullptr;
5484 if (PHINode *PN = dyn_cast<PHINode>(I)) {
5488 // Record non-constant instructions contained by the loop.
5489 DenseMap<Instruction *, PHINode *> PHIMap;
5490 return getConstantEvolvingPHIOperands(I, L, PHIMap);
5493 /// EvaluateExpression - Given an expression that passes the
5494 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
5495 /// in the loop has the value PHIVal. If we can't fold this expression for some
5496 /// reason, return null.
5497 static Constant *EvaluateExpression(Value *V, const Loop *L,
5498 DenseMap<Instruction *, Constant *> &Vals,
5499 const DataLayout *DL,
5500 const TargetLibraryInfo *TLI) {
5501 // Convenient constant check, but redundant for recursive calls.
5502 if (Constant *C = dyn_cast<Constant>(V)) return C;
5503 Instruction *I = dyn_cast<Instruction>(V);
5504 if (!I) return nullptr;
5506 if (Constant *C = Vals.lookup(I)) return C;
5508 // An instruction inside the loop depends on a value outside the loop that we
5509 // weren't given a mapping for, or a value such as a call inside the loop.
5510 if (!canConstantEvolve(I, L)) return nullptr;
5512 // An unmapped PHI can be due to a branch or another loop inside this loop,
5513 // or due to this not being the initial iteration through a loop where we
5514 // couldn't compute the evolution of this particular PHI last time.
5515 if (isa<PHINode>(I)) return nullptr;
5517 std::vector<Constant*> Operands(I->getNumOperands());
5519 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
5520 Instruction *Operand = dyn_cast<Instruction>(I->getOperand(i));
5522 Operands[i] = dyn_cast<Constant>(I->getOperand(i));
5523 if (!Operands[i]) return nullptr;
5526 Constant *C = EvaluateExpression(Operand, L, Vals, DL, TLI);
5528 if (!C) return nullptr;
5532 if (CmpInst *CI = dyn_cast<CmpInst>(I))
5533 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
5534 Operands[1], DL, TLI);
5535 if (LoadInst *LI = dyn_cast<LoadInst>(I)) {
5536 if (!LI->isVolatile())
5537 return ConstantFoldLoadFromConstPtr(Operands[0], DL);
5539 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), Operands, DL,
5543 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
5544 /// in the header of its containing loop, we know the loop executes a
5545 /// constant number of times, and the PHI node is just a recurrence
5546 /// involving constants, fold it.
5548 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
5551 DenseMap<PHINode*, Constant*>::const_iterator I =
5552 ConstantEvolutionLoopExitValue.find(PN);
5553 if (I != ConstantEvolutionLoopExitValue.end())
5556 if (BEs.ugt(MaxBruteForceIterations))
5557 return ConstantEvolutionLoopExitValue[PN] = nullptr; // Not going to evaluate it.
5559 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
5561 DenseMap<Instruction *, Constant *> CurrentIterVals;
5562 BasicBlock *Header = L->getHeader();
5563 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
5565 // Since the loop is canonicalized, the PHI node must have two entries. One
5566 // entry must be a constant (coming in from outside of the loop), and the
5567 // second must be derived from the same PHI.
5568 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
5569 PHINode *PHI = nullptr;
5570 for (BasicBlock::iterator I = Header->begin();
5571 (PHI = dyn_cast<PHINode>(I)); ++I) {
5572 Constant *StartCST =
5573 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
5574 if (!StartCST) continue;
5575 CurrentIterVals[PHI] = StartCST;
5577 if (!CurrentIterVals.count(PN))
5578 return RetVal = nullptr;
5580 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
5582 // Execute the loop symbolically to determine the exit value.
5583 if (BEs.getActiveBits() >= 32)
5584 return RetVal = nullptr; // More than 2^32-1 iterations?? Not doing it!
5586 unsigned NumIterations = BEs.getZExtValue(); // must be in range
5587 unsigned IterationNum = 0;
5588 for (; ; ++IterationNum) {
5589 if (IterationNum == NumIterations)
5590 return RetVal = CurrentIterVals[PN]; // Got exit value!
5592 // Compute the value of the PHIs for the next iteration.
5593 // EvaluateExpression adds non-phi values to the CurrentIterVals map.
5594 DenseMap<Instruction *, Constant *> NextIterVals;
5595 Constant *NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL,
5598 return nullptr; // Couldn't evaluate!
5599 NextIterVals[PN] = NextPHI;
5601 bool StoppedEvolving = NextPHI == CurrentIterVals[PN];
5603 // Also evaluate the other PHI nodes. However, we don't get to stop if we
5604 // cease to be able to evaluate one of them or if they stop evolving,
5605 // because that doesn't necessarily prevent us from computing PN.
5606 SmallVector<std::pair<PHINode *, Constant *>, 8> PHIsToCompute;
5607 for (DenseMap<Instruction *, Constant *>::const_iterator
5608 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
5609 PHINode *PHI = dyn_cast<PHINode>(I->first);
5610 if (!PHI || PHI == PN || PHI->getParent() != Header) continue;
5611 PHIsToCompute.push_back(std::make_pair(PHI, I->second));
5613 // We use two distinct loops because EvaluateExpression may invalidate any
5614 // iterators into CurrentIterVals.
5615 for (SmallVectorImpl<std::pair<PHINode *, Constant*> >::const_iterator
5616 I = PHIsToCompute.begin(), E = PHIsToCompute.end(); I != E; ++I) {
5617 PHINode *PHI = I->first;
5618 Constant *&NextPHI = NextIterVals[PHI];
5619 if (!NextPHI) { // Not already computed.
5620 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
5621 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, TLI);
5623 if (NextPHI != I->second)
5624 StoppedEvolving = false;
5627 // If all entries in CurrentIterVals == NextIterVals then we can stop
5628 // iterating, the loop can't continue to change.
5629 if (StoppedEvolving)
5630 return RetVal = CurrentIterVals[PN];
5632 CurrentIterVals.swap(NextIterVals);
5636 /// ComputeExitCountExhaustively - If the loop is known to execute a
5637 /// constant number of times (the condition evolves only from constants),
5638 /// try to evaluate a few iterations of the loop until we get the exit
5639 /// condition gets a value of ExitWhen (true or false). If we cannot
5640 /// evaluate the trip count of the loop, return getCouldNotCompute().
5641 const SCEV *ScalarEvolution::ComputeExitCountExhaustively(const Loop *L,
5644 PHINode *PN = getConstantEvolvingPHI(Cond, L);
5645 if (!PN) return getCouldNotCompute();
5647 // If the loop is canonicalized, the PHI will have exactly two entries.
5648 // That's the only form we support here.
5649 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
5651 DenseMap<Instruction *, Constant *> CurrentIterVals;
5652 BasicBlock *Header = L->getHeader();
5653 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
5655 // One entry must be a constant (coming in from outside of the loop), and the
5656 // second must be derived from the same PHI.
5657 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
5658 PHINode *PHI = nullptr;
5659 for (BasicBlock::iterator I = Header->begin();
5660 (PHI = dyn_cast<PHINode>(I)); ++I) {
5661 Constant *StartCST =
5662 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
5663 if (!StartCST) continue;
5664 CurrentIterVals[PHI] = StartCST;
5666 if (!CurrentIterVals.count(PN))
5667 return getCouldNotCompute();
5669 // Okay, we find a PHI node that defines the trip count of this loop. Execute
5670 // the loop symbolically to determine when the condition gets a value of
5673 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
5674 for (unsigned IterationNum = 0; IterationNum != MaxIterations;++IterationNum){
5675 ConstantInt *CondVal =
5676 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, L, CurrentIterVals,
5679 // Couldn't symbolically evaluate.
5680 if (!CondVal) return getCouldNotCompute();
5682 if (CondVal->getValue() == uint64_t(ExitWhen)) {
5683 ++NumBruteForceTripCountsComputed;
5684 return getConstant(Type::getInt32Ty(getContext()), IterationNum);
5687 // Update all the PHI nodes for the next iteration.
5688 DenseMap<Instruction *, Constant *> NextIterVals;
5690 // Create a list of which PHIs we need to compute. We want to do this before
5691 // calling EvaluateExpression on them because that may invalidate iterators
5692 // into CurrentIterVals.
5693 SmallVector<PHINode *, 8> PHIsToCompute;
5694 for (DenseMap<Instruction *, Constant *>::const_iterator
5695 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
5696 PHINode *PHI = dyn_cast<PHINode>(I->first);
5697 if (!PHI || PHI->getParent() != Header) continue;
5698 PHIsToCompute.push_back(PHI);
5700 for (SmallVectorImpl<PHINode *>::const_iterator I = PHIsToCompute.begin(),
5701 E = PHIsToCompute.end(); I != E; ++I) {
5703 Constant *&NextPHI = NextIterVals[PHI];
5704 if (NextPHI) continue; // Already computed!
5706 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
5707 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, TLI);
5709 CurrentIterVals.swap(NextIterVals);
5712 // Too many iterations were needed to evaluate.
5713 return getCouldNotCompute();
5716 /// getSCEVAtScope - Return a SCEV expression for the specified value
5717 /// at the specified scope in the program. The L value specifies a loop
5718 /// nest to evaluate the expression at, where null is the top-level or a
5719 /// specified loop is immediately inside of the loop.
5721 /// This method can be used to compute the exit value for a variable defined
5722 /// in a loop by querying what the value will hold in the parent loop.
5724 /// In the case that a relevant loop exit value cannot be computed, the
5725 /// original value V is returned.
5726 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
5727 // Check to see if we've folded this expression at this loop before.
5728 SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values = ValuesAtScopes[V];
5729 for (unsigned u = 0; u < Values.size(); u++) {
5730 if (Values[u].first == L)
5731 return Values[u].second ? Values[u].second : V;
5733 Values.push_back(std::make_pair(L, static_cast<const SCEV *>(nullptr)));
5734 // Otherwise compute it.
5735 const SCEV *C = computeSCEVAtScope(V, L);
5736 SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values2 = ValuesAtScopes[V];
5737 for (unsigned u = Values2.size(); u > 0; u--) {
5738 if (Values2[u - 1].first == L) {
5739 Values2[u - 1].second = C;
5746 /// This builds up a Constant using the ConstantExpr interface. That way, we
5747 /// will return Constants for objects which aren't represented by a
5748 /// SCEVConstant, because SCEVConstant is restricted to ConstantInt.
5749 /// Returns NULL if the SCEV isn't representable as a Constant.
5750 static Constant *BuildConstantFromSCEV(const SCEV *V) {
5751 switch (static_cast<SCEVTypes>(V->getSCEVType())) {
5752 case scCouldNotCompute:
5756 return cast<SCEVConstant>(V)->getValue();
5758 return dyn_cast<Constant>(cast<SCEVUnknown>(V)->getValue());
5759 case scSignExtend: {
5760 const SCEVSignExtendExpr *SS = cast<SCEVSignExtendExpr>(V);
5761 if (Constant *CastOp = BuildConstantFromSCEV(SS->getOperand()))
5762 return ConstantExpr::getSExt(CastOp, SS->getType());
5765 case scZeroExtend: {
5766 const SCEVZeroExtendExpr *SZ = cast<SCEVZeroExtendExpr>(V);
5767 if (Constant *CastOp = BuildConstantFromSCEV(SZ->getOperand()))
5768 return ConstantExpr::getZExt(CastOp, SZ->getType());
5772 const SCEVTruncateExpr *ST = cast<SCEVTruncateExpr>(V);
5773 if (Constant *CastOp = BuildConstantFromSCEV(ST->getOperand()))
5774 return ConstantExpr::getTrunc(CastOp, ST->getType());
5778 const SCEVAddExpr *SA = cast<SCEVAddExpr>(V);
5779 if (Constant *C = BuildConstantFromSCEV(SA->getOperand(0))) {
5780 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
5781 unsigned AS = PTy->getAddressSpace();
5782 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
5783 C = ConstantExpr::getBitCast(C, DestPtrTy);
5785 for (unsigned i = 1, e = SA->getNumOperands(); i != e; ++i) {
5786 Constant *C2 = BuildConstantFromSCEV(SA->getOperand(i));
5787 if (!C2) return nullptr;
5790 if (!C->getType()->isPointerTy() && C2->getType()->isPointerTy()) {
5791 unsigned AS = C2->getType()->getPointerAddressSpace();
5793 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
5794 // The offsets have been converted to bytes. We can add bytes to an
5795 // i8* by GEP with the byte count in the first index.
5796 C = ConstantExpr::getBitCast(C, DestPtrTy);
5799 // Don't bother trying to sum two pointers. We probably can't
5800 // statically compute a load that results from it anyway.
5801 if (C2->getType()->isPointerTy())
5804 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
5805 if (PTy->getElementType()->isStructTy())
5806 C2 = ConstantExpr::getIntegerCast(
5807 C2, Type::getInt32Ty(C->getContext()), true);
5808 C = ConstantExpr::getGetElementPtr(C, C2);
5810 C = ConstantExpr::getAdd(C, C2);
5817 const SCEVMulExpr *SM = cast<SCEVMulExpr>(V);
5818 if (Constant *C = BuildConstantFromSCEV(SM->getOperand(0))) {
5819 // Don't bother with pointers at all.
5820 if (C->getType()->isPointerTy()) return nullptr;
5821 for (unsigned i = 1, e = SM->getNumOperands(); i != e; ++i) {
5822 Constant *C2 = BuildConstantFromSCEV(SM->getOperand(i));
5823 if (!C2 || C2->getType()->isPointerTy()) return nullptr;
5824 C = ConstantExpr::getMul(C, C2);
5831 const SCEVUDivExpr *SU = cast<SCEVUDivExpr>(V);
5832 if (Constant *LHS = BuildConstantFromSCEV(SU->getLHS()))
5833 if (Constant *RHS = BuildConstantFromSCEV(SU->getRHS()))
5834 if (LHS->getType() == RHS->getType())
5835 return ConstantExpr::getUDiv(LHS, RHS);
5840 break; // TODO: smax, umax.
5845 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
5846 if (isa<SCEVConstant>(V)) return V;
5848 // If this instruction is evolved from a constant-evolving PHI, compute the
5849 // exit value from the loop without using SCEVs.
5850 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
5851 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
5852 const Loop *LI = (*this->LI)[I->getParent()];
5853 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
5854 if (PHINode *PN = dyn_cast<PHINode>(I))
5855 if (PN->getParent() == LI->getHeader()) {
5856 // Okay, there is no closed form solution for the PHI node. Check
5857 // to see if the loop that contains it has a known backedge-taken
5858 // count. If so, we may be able to force computation of the exit
5860 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
5861 if (const SCEVConstant *BTCC =
5862 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
5863 // Okay, we know how many times the containing loop executes. If
5864 // this is a constant evolving PHI node, get the final value at
5865 // the specified iteration number.
5866 Constant *RV = getConstantEvolutionLoopExitValue(PN,
5867 BTCC->getValue()->getValue(),
5869 if (RV) return getSCEV(RV);
5873 // Okay, this is an expression that we cannot symbolically evaluate
5874 // into a SCEV. Check to see if it's possible to symbolically evaluate
5875 // the arguments into constants, and if so, try to constant propagate the
5876 // result. This is particularly useful for computing loop exit values.
5877 if (CanConstantFold(I)) {
5878 SmallVector<Constant *, 4> Operands;
5879 bool MadeImprovement = false;
5880 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
5881 Value *Op = I->getOperand(i);
5882 if (Constant *C = dyn_cast<Constant>(Op)) {
5883 Operands.push_back(C);
5887 // If any of the operands is non-constant and if they are
5888 // non-integer and non-pointer, don't even try to analyze them
5889 // with scev techniques.
5890 if (!isSCEVable(Op->getType()))
5893 const SCEV *OrigV = getSCEV(Op);
5894 const SCEV *OpV = getSCEVAtScope(OrigV, L);
5895 MadeImprovement |= OrigV != OpV;
5897 Constant *C = BuildConstantFromSCEV(OpV);
5899 if (C->getType() != Op->getType())
5900 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
5904 Operands.push_back(C);
5907 // Check to see if getSCEVAtScope actually made an improvement.
5908 if (MadeImprovement) {
5909 Constant *C = nullptr;
5910 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
5911 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
5912 Operands[0], Operands[1], DL,
5914 else if (const LoadInst *LI = dyn_cast<LoadInst>(I)) {
5915 if (!LI->isVolatile())
5916 C = ConstantFoldLoadFromConstPtr(Operands[0], DL);
5918 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
5926 // This is some other type of SCEVUnknown, just return it.
5930 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
5931 // Avoid performing the look-up in the common case where the specified
5932 // expression has no loop-variant portions.
5933 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
5934 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
5935 if (OpAtScope != Comm->getOperand(i)) {
5936 // Okay, at least one of these operands is loop variant but might be
5937 // foldable. Build a new instance of the folded commutative expression.
5938 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
5939 Comm->op_begin()+i);
5940 NewOps.push_back(OpAtScope);
5942 for (++i; i != e; ++i) {
5943 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
5944 NewOps.push_back(OpAtScope);
5946 if (isa<SCEVAddExpr>(Comm))
5947 return getAddExpr(NewOps);
5948 if (isa<SCEVMulExpr>(Comm))
5949 return getMulExpr(NewOps);
5950 if (isa<SCEVSMaxExpr>(Comm))
5951 return getSMaxExpr(NewOps);
5952 if (isa<SCEVUMaxExpr>(Comm))
5953 return getUMaxExpr(NewOps);
5954 llvm_unreachable("Unknown commutative SCEV type!");
5957 // If we got here, all operands are loop invariant.
5961 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
5962 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
5963 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
5964 if (LHS == Div->getLHS() && RHS == Div->getRHS())
5965 return Div; // must be loop invariant
5966 return getUDivExpr(LHS, RHS);
5969 // If this is a loop recurrence for a loop that does not contain L, then we
5970 // are dealing with the final value computed by the loop.
5971 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
5972 // First, attempt to evaluate each operand.
5973 // Avoid performing the look-up in the common case where the specified
5974 // expression has no loop-variant portions.
5975 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
5976 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
5977 if (OpAtScope == AddRec->getOperand(i))
5980 // Okay, at least one of these operands is loop variant but might be
5981 // foldable. Build a new instance of the folded commutative expression.
5982 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(),
5983 AddRec->op_begin()+i);
5984 NewOps.push_back(OpAtScope);
5985 for (++i; i != e; ++i)
5986 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
5988 const SCEV *FoldedRec =
5989 getAddRecExpr(NewOps, AddRec->getLoop(),
5990 AddRec->getNoWrapFlags(SCEV::FlagNW));
5991 AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec);
5992 // The addrec may be folded to a nonrecurrence, for example, if the
5993 // induction variable is multiplied by zero after constant folding. Go
5994 // ahead and return the folded value.
6000 // If the scope is outside the addrec's loop, evaluate it by using the
6001 // loop exit value of the addrec.
6002 if (!AddRec->getLoop()->contains(L)) {
6003 // To evaluate this recurrence, we need to know how many times the AddRec
6004 // loop iterates. Compute this now.
6005 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
6006 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
6008 // Then, evaluate the AddRec.
6009 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
6015 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
6016 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
6017 if (Op == Cast->getOperand())
6018 return Cast; // must be loop invariant
6019 return getZeroExtendExpr(Op, Cast->getType());
6022 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
6023 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
6024 if (Op == Cast->getOperand())
6025 return Cast; // must be loop invariant
6026 return getSignExtendExpr(Op, Cast->getType());
6029 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
6030 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
6031 if (Op == Cast->getOperand())
6032 return Cast; // must be loop invariant
6033 return getTruncateExpr(Op, Cast->getType());
6036 llvm_unreachable("Unknown SCEV type!");
6039 /// getSCEVAtScope - This is a convenience function which does
6040 /// getSCEVAtScope(getSCEV(V), L).
6041 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
6042 return getSCEVAtScope(getSCEV(V), L);
6045 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
6046 /// following equation:
6048 /// A * X = B (mod N)
6050 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
6051 /// A and B isn't important.
6053 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
6054 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
6055 ScalarEvolution &SE) {
6056 uint32_t BW = A.getBitWidth();
6057 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
6058 assert(A != 0 && "A must be non-zero.");
6062 // The gcd of A and N may have only one prime factor: 2. The number of
6063 // trailing zeros in A is its multiplicity
6064 uint32_t Mult2 = A.countTrailingZeros();
6067 // 2. Check if B is divisible by D.
6069 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
6070 // is not less than multiplicity of this prime factor for D.
6071 if (B.countTrailingZeros() < Mult2)
6072 return SE.getCouldNotCompute();
6074 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
6077 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
6078 // bit width during computations.
6079 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
6080 APInt Mod(BW + 1, 0);
6081 Mod.setBit(BW - Mult2); // Mod = N / D
6082 APInt I = AD.multiplicativeInverse(Mod);
6084 // 4. Compute the minimum unsigned root of the equation:
6085 // I * (B / D) mod (N / D)
6086 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
6088 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
6090 return SE.getConstant(Result.trunc(BW));
6093 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
6094 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
6095 /// might be the same) or two SCEVCouldNotCompute objects.
6097 static std::pair<const SCEV *,const SCEV *>
6098 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
6099 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
6100 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
6101 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
6102 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
6104 // We currently can only solve this if the coefficients are constants.
6105 if (!LC || !MC || !NC) {
6106 const SCEV *CNC = SE.getCouldNotCompute();
6107 return std::make_pair(CNC, CNC);
6110 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
6111 const APInt &L = LC->getValue()->getValue();
6112 const APInt &M = MC->getValue()->getValue();
6113 const APInt &N = NC->getValue()->getValue();
6114 APInt Two(BitWidth, 2);
6115 APInt Four(BitWidth, 4);
6118 using namespace APIntOps;
6120 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
6121 // The B coefficient is M-N/2
6125 // The A coefficient is N/2
6126 APInt A(N.sdiv(Two));
6128 // Compute the B^2-4ac term.
6131 SqrtTerm -= Four * (A * C);
6133 if (SqrtTerm.isNegative()) {
6134 // The loop is provably infinite.
6135 const SCEV *CNC = SE.getCouldNotCompute();
6136 return std::make_pair(CNC, CNC);
6139 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
6140 // integer value or else APInt::sqrt() will assert.
6141 APInt SqrtVal(SqrtTerm.sqrt());
6143 // Compute the two solutions for the quadratic formula.
6144 // The divisions must be performed as signed divisions.
6147 if (TwoA.isMinValue()) {
6148 const SCEV *CNC = SE.getCouldNotCompute();
6149 return std::make_pair(CNC, CNC);
6152 LLVMContext &Context = SE.getContext();
6154 ConstantInt *Solution1 =
6155 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
6156 ConstantInt *Solution2 =
6157 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
6159 return std::make_pair(SE.getConstant(Solution1),
6160 SE.getConstant(Solution2));
6161 } // end APIntOps namespace
6164 /// HowFarToZero - Return the number of times a backedge comparing the specified
6165 /// value to zero will execute. If not computable, return CouldNotCompute.
6167 /// This is only used for loops with a "x != y" exit test. The exit condition is
6168 /// now expressed as a single expression, V = x-y. So the exit test is
6169 /// effectively V != 0. We know and take advantage of the fact that this
6170 /// expression only being used in a comparison by zero context.
6171 ScalarEvolution::ExitLimit
6172 ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L, bool ControlsExit) {
6173 // If the value is a constant
6174 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
6175 // If the value is already zero, the branch will execute zero times.
6176 if (C->getValue()->isZero()) return C;
6177 return getCouldNotCompute(); // Otherwise it will loop infinitely.
6180 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
6181 if (!AddRec || AddRec->getLoop() != L)
6182 return getCouldNotCompute();
6184 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
6185 // the quadratic equation to solve it.
6186 if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
6187 std::pair<const SCEV *,const SCEV *> Roots =
6188 SolveQuadraticEquation(AddRec, *this);
6189 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
6190 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
6193 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1
6194 << " sol#2: " << *R2 << "\n";
6196 // Pick the smallest positive root value.
6197 if (ConstantInt *CB =
6198 dyn_cast<ConstantInt>(ConstantExpr::getICmp(CmpInst::ICMP_ULT,
6201 if (CB->getZExtValue() == false)
6202 std::swap(R1, R2); // R1 is the minimum root now.
6204 // We can only use this value if the chrec ends up with an exact zero
6205 // value at this index. When solving for "X*X != 5", for example, we
6206 // should not accept a root of 2.
6207 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
6209 return R1; // We found a quadratic root!
6212 return getCouldNotCompute();
6215 // Otherwise we can only handle this if it is affine.
6216 if (!AddRec->isAffine())
6217 return getCouldNotCompute();
6219 // If this is an affine expression, the execution count of this branch is
6220 // the minimum unsigned root of the following equation:
6222 // Start + Step*N = 0 (mod 2^BW)
6226 // Step*N = -Start (mod 2^BW)
6228 // where BW is the common bit width of Start and Step.
6230 // Get the initial value for the loop.
6231 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
6232 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
6234 // For now we handle only constant steps.
6236 // TODO: Handle a nonconstant Step given AddRec<NUW>. If the
6237 // AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap
6238 // to 0, it must be counting down to equal 0. Consequently, N = Start / -Step.
6239 // We have not yet seen any such cases.
6240 const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step);
6241 if (!StepC || StepC->getValue()->equalsInt(0))
6242 return getCouldNotCompute();
6244 // For positive steps (counting up until unsigned overflow):
6245 // N = -Start/Step (as unsigned)
6246 // For negative steps (counting down to zero):
6248 // First compute the unsigned distance from zero in the direction of Step.
6249 bool CountDown = StepC->getValue()->getValue().isNegative();
6250 const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start);
6252 // Handle unitary steps, which cannot wraparound.
6253 // 1*N = -Start; -1*N = Start (mod 2^BW), so:
6254 // N = Distance (as unsigned)
6255 if (StepC->getValue()->equalsInt(1) || StepC->getValue()->isAllOnesValue()) {
6256 ConstantRange CR = getUnsignedRange(Start);
6257 const SCEV *MaxBECount;
6258 if (!CountDown && CR.getUnsignedMin().isMinValue())
6259 // When counting up, the worst starting value is 1, not 0.
6260 MaxBECount = CR.getUnsignedMax().isMinValue()
6261 ? getConstant(APInt::getMinValue(CR.getBitWidth()))
6262 : getConstant(APInt::getMaxValue(CR.getBitWidth()));
6264 MaxBECount = getConstant(CountDown ? CR.getUnsignedMax()
6265 : -CR.getUnsignedMin());
6266 return ExitLimit(Distance, MaxBECount);
6269 // As a special case, handle the instance where Step is a positive power of
6270 // two. In this case, determining whether Step divides Distance evenly can be
6271 // done by counting and comparing the number of trailing zeros of Step and
6274 const APInt &StepV = StepC->getValue()->getValue();
6275 // StepV.isPowerOf2() returns true if StepV is an positive power of two. It
6276 // also returns true if StepV is maximally negative (eg, INT_MIN), but that
6277 // case is not handled as this code is guarded by !CountDown.
6278 if (StepV.isPowerOf2() &&
6279 GetMinTrailingZeros(Distance) >= StepV.countTrailingZeros())
6280 return getUDivExactExpr(Distance, Step);
6283 // If the condition controls loop exit (the loop exits only if the expression
6284 // is true) and the addition is no-wrap we can use unsigned divide to
6285 // compute the backedge count. In this case, the step may not divide the
6286 // distance, but we don't care because if the condition is "missed" the loop
6287 // will have undefined behavior due to wrapping.
6288 if (ControlsExit && AddRec->getNoWrapFlags(SCEV::FlagNW)) {
6290 getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
6291 return ExitLimit(Exact, Exact);
6294 // Then, try to solve the above equation provided that Start is constant.
6295 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
6296 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
6297 -StartC->getValue()->getValue(),
6299 return getCouldNotCompute();
6302 /// HowFarToNonZero - Return the number of times a backedge checking the
6303 /// specified value for nonzero will execute. If not computable, return
6305 ScalarEvolution::ExitLimit
6306 ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
6307 // Loops that look like: while (X == 0) are very strange indeed. We don't
6308 // handle them yet except for the trivial case. This could be expanded in the
6309 // future as needed.
6311 // If the value is a constant, check to see if it is known to be non-zero
6312 // already. If so, the backedge will execute zero times.
6313 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
6314 if (!C->getValue()->isNullValue())
6315 return getConstant(C->getType(), 0);
6316 return getCouldNotCompute(); // Otherwise it will loop infinitely.
6319 // We could implement others, but I really doubt anyone writes loops like
6320 // this, and if they did, they would already be constant folded.
6321 return getCouldNotCompute();
6324 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
6325 /// (which may not be an immediate predecessor) which has exactly one
6326 /// successor from which BB is reachable, or null if no such block is
6329 std::pair<BasicBlock *, BasicBlock *>
6330 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
6331 // If the block has a unique predecessor, then there is no path from the
6332 // predecessor to the block that does not go through the direct edge
6333 // from the predecessor to the block.
6334 if (BasicBlock *Pred = BB->getSinglePredecessor())
6335 return std::make_pair(Pred, BB);
6337 // A loop's header is defined to be a block that dominates the loop.
6338 // If the header has a unique predecessor outside the loop, it must be
6339 // a block that has exactly one successor that can reach the loop.
6340 if (Loop *L = LI->getLoopFor(BB))
6341 return std::make_pair(L->getLoopPredecessor(), L->getHeader());
6343 return std::pair<BasicBlock *, BasicBlock *>();
6346 /// HasSameValue - SCEV structural equivalence is usually sufficient for
6347 /// testing whether two expressions are equal, however for the purposes of
6348 /// looking for a condition guarding a loop, it can be useful to be a little
6349 /// more general, since a front-end may have replicated the controlling
6352 static bool HasSameValue(const SCEV *A, const SCEV *B) {
6353 // Quick check to see if they are the same SCEV.
6354 if (A == B) return true;
6356 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
6357 // two different instructions with the same value. Check for this case.
6358 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
6359 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
6360 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
6361 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
6362 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory())
6365 // Otherwise assume they may have a different value.
6369 /// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with
6370 /// predicate Pred. Return true iff any changes were made.
6372 bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
6373 const SCEV *&LHS, const SCEV *&RHS,
6375 bool Changed = false;
6377 // If we hit the max recursion limit bail out.
6381 // Canonicalize a constant to the right side.
6382 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
6383 // Check for both operands constant.
6384 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
6385 if (ConstantExpr::getICmp(Pred,
6387 RHSC->getValue())->isNullValue())
6388 goto trivially_false;
6390 goto trivially_true;
6392 // Otherwise swap the operands to put the constant on the right.
6393 std::swap(LHS, RHS);
6394 Pred = ICmpInst::getSwappedPredicate(Pred);
6398 // If we're comparing an addrec with a value which is loop-invariant in the
6399 // addrec's loop, put the addrec on the left. Also make a dominance check,
6400 // as both operands could be addrecs loop-invariant in each other's loop.
6401 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
6402 const Loop *L = AR->getLoop();
6403 if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) {
6404 std::swap(LHS, RHS);
6405 Pred = ICmpInst::getSwappedPredicate(Pred);
6410 // If there's a constant operand, canonicalize comparisons with boundary
6411 // cases, and canonicalize *-or-equal comparisons to regular comparisons.
6412 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
6413 const APInt &RA = RC->getValue()->getValue();
6415 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6416 case ICmpInst::ICMP_EQ:
6417 case ICmpInst::ICMP_NE:
6418 // Fold ((-1) * %a) + %b == 0 (equivalent to %b-%a == 0) into %a == %b.
6420 if (const SCEVAddExpr *AE = dyn_cast<SCEVAddExpr>(LHS))
6421 if (const SCEVMulExpr *ME = dyn_cast<SCEVMulExpr>(AE->getOperand(0)))
6422 if (AE->getNumOperands() == 2 && ME->getNumOperands() == 2 &&
6423 ME->getOperand(0)->isAllOnesValue()) {
6424 RHS = AE->getOperand(1);
6425 LHS = ME->getOperand(1);
6429 case ICmpInst::ICMP_UGE:
6430 if ((RA - 1).isMinValue()) {
6431 Pred = ICmpInst::ICMP_NE;
6432 RHS = getConstant(RA - 1);
6436 if (RA.isMaxValue()) {
6437 Pred = ICmpInst::ICMP_EQ;
6441 if (RA.isMinValue()) goto trivially_true;
6443 Pred = ICmpInst::ICMP_UGT;
6444 RHS = getConstant(RA - 1);
6447 case ICmpInst::ICMP_ULE:
6448 if ((RA + 1).isMaxValue()) {
6449 Pred = ICmpInst::ICMP_NE;
6450 RHS = getConstant(RA + 1);
6454 if (RA.isMinValue()) {
6455 Pred = ICmpInst::ICMP_EQ;
6459 if (RA.isMaxValue()) goto trivially_true;
6461 Pred = ICmpInst::ICMP_ULT;
6462 RHS = getConstant(RA + 1);
6465 case ICmpInst::ICMP_SGE:
6466 if ((RA - 1).isMinSignedValue()) {
6467 Pred = ICmpInst::ICMP_NE;
6468 RHS = getConstant(RA - 1);
6472 if (RA.isMaxSignedValue()) {
6473 Pred = ICmpInst::ICMP_EQ;
6477 if (RA.isMinSignedValue()) goto trivially_true;
6479 Pred = ICmpInst::ICMP_SGT;
6480 RHS = getConstant(RA - 1);
6483 case ICmpInst::ICMP_SLE:
6484 if ((RA + 1).isMaxSignedValue()) {
6485 Pred = ICmpInst::ICMP_NE;
6486 RHS = getConstant(RA + 1);
6490 if (RA.isMinSignedValue()) {
6491 Pred = ICmpInst::ICMP_EQ;
6495 if (RA.isMaxSignedValue()) goto trivially_true;
6497 Pred = ICmpInst::ICMP_SLT;
6498 RHS = getConstant(RA + 1);
6501 case ICmpInst::ICMP_UGT:
6502 if (RA.isMinValue()) {
6503 Pred = ICmpInst::ICMP_NE;
6507 if ((RA + 1).isMaxValue()) {
6508 Pred = ICmpInst::ICMP_EQ;
6509 RHS = getConstant(RA + 1);
6513 if (RA.isMaxValue()) goto trivially_false;
6515 case ICmpInst::ICMP_ULT:
6516 if (RA.isMaxValue()) {
6517 Pred = ICmpInst::ICMP_NE;
6521 if ((RA - 1).isMinValue()) {
6522 Pred = ICmpInst::ICMP_EQ;
6523 RHS = getConstant(RA - 1);
6527 if (RA.isMinValue()) goto trivially_false;
6529 case ICmpInst::ICMP_SGT:
6530 if (RA.isMinSignedValue()) {
6531 Pred = ICmpInst::ICMP_NE;
6535 if ((RA + 1).isMaxSignedValue()) {
6536 Pred = ICmpInst::ICMP_EQ;
6537 RHS = getConstant(RA + 1);
6541 if (RA.isMaxSignedValue()) goto trivially_false;
6543 case ICmpInst::ICMP_SLT:
6544 if (RA.isMaxSignedValue()) {
6545 Pred = ICmpInst::ICMP_NE;
6549 if ((RA - 1).isMinSignedValue()) {
6550 Pred = ICmpInst::ICMP_EQ;
6551 RHS = getConstant(RA - 1);
6555 if (RA.isMinSignedValue()) goto trivially_false;
6560 // Check for obvious equality.
6561 if (HasSameValue(LHS, RHS)) {
6562 if (ICmpInst::isTrueWhenEqual(Pred))
6563 goto trivially_true;
6564 if (ICmpInst::isFalseWhenEqual(Pred))
6565 goto trivially_false;
6568 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
6569 // adding or subtracting 1 from one of the operands.
6571 case ICmpInst::ICMP_SLE:
6572 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) {
6573 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
6575 Pred = ICmpInst::ICMP_SLT;
6577 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) {
6578 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
6580 Pred = ICmpInst::ICMP_SLT;
6584 case ICmpInst::ICMP_SGE:
6585 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) {
6586 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
6588 Pred = ICmpInst::ICMP_SGT;
6590 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) {
6591 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
6593 Pred = ICmpInst::ICMP_SGT;
6597 case ICmpInst::ICMP_ULE:
6598 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) {
6599 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
6601 Pred = ICmpInst::ICMP_ULT;
6603 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) {
6604 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
6606 Pred = ICmpInst::ICMP_ULT;
6610 case ICmpInst::ICMP_UGE:
6611 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) {
6612 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
6614 Pred = ICmpInst::ICMP_UGT;
6616 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) {
6617 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
6619 Pred = ICmpInst::ICMP_UGT;
6627 // TODO: More simplifications are possible here.
6629 // Recursively simplify until we either hit a recursion limit or nothing
6632 return SimplifyICmpOperands(Pred, LHS, RHS, Depth+1);
6638 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
6639 Pred = ICmpInst::ICMP_EQ;
6644 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
6645 Pred = ICmpInst::ICMP_NE;
6649 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
6650 return getSignedRange(S).getSignedMax().isNegative();
6653 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
6654 return getSignedRange(S).getSignedMin().isStrictlyPositive();
6657 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
6658 return !getSignedRange(S).getSignedMin().isNegative();
6661 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
6662 return !getSignedRange(S).getSignedMax().isStrictlyPositive();
6665 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
6666 return isKnownNegative(S) || isKnownPositive(S);
6669 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
6670 const SCEV *LHS, const SCEV *RHS) {
6671 // Canonicalize the inputs first.
6672 (void)SimplifyICmpOperands(Pred, LHS, RHS);
6674 // If LHS or RHS is an addrec, check to see if the condition is true in
6675 // every iteration of the loop.
6676 // If LHS and RHS are both addrec, both conditions must be true in
6677 // every iteration of the loop.
6678 const SCEVAddRecExpr *LAR = dyn_cast<SCEVAddRecExpr>(LHS);
6679 const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS);
6680 bool LeftGuarded = false;
6681 bool RightGuarded = false;
6683 const Loop *L = LAR->getLoop();
6684 if (isLoopEntryGuardedByCond(L, Pred, LAR->getStart(), RHS) &&
6685 isLoopBackedgeGuardedByCond(L, Pred, LAR->getPostIncExpr(*this), RHS)) {
6686 if (!RAR) return true;
6691 const Loop *L = RAR->getLoop();
6692 if (isLoopEntryGuardedByCond(L, Pred, LHS, RAR->getStart()) &&
6693 isLoopBackedgeGuardedByCond(L, Pred, LHS, RAR->getPostIncExpr(*this))) {
6694 if (!LAR) return true;
6695 RightGuarded = true;
6698 if (LeftGuarded && RightGuarded)
6701 // Otherwise see what can be done with known constant ranges.
6702 return isKnownPredicateWithRanges(Pred, LHS, RHS);
6706 ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred,
6707 const SCEV *LHS, const SCEV *RHS) {
6708 if (HasSameValue(LHS, RHS))
6709 return ICmpInst::isTrueWhenEqual(Pred);
6711 // This code is split out from isKnownPredicate because it is called from
6712 // within isLoopEntryGuardedByCond.
6715 llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6716 case ICmpInst::ICMP_SGT:
6717 std::swap(LHS, RHS);
6718 case ICmpInst::ICMP_SLT: {
6719 ConstantRange LHSRange = getSignedRange(LHS);
6720 ConstantRange RHSRange = getSignedRange(RHS);
6721 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
6723 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
6727 case ICmpInst::ICMP_SGE:
6728 std::swap(LHS, RHS);
6729 case ICmpInst::ICMP_SLE: {
6730 ConstantRange LHSRange = getSignedRange(LHS);
6731 ConstantRange RHSRange = getSignedRange(RHS);
6732 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
6734 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
6738 case ICmpInst::ICMP_UGT:
6739 std::swap(LHS, RHS);
6740 case ICmpInst::ICMP_ULT: {
6741 ConstantRange LHSRange = getUnsignedRange(LHS);
6742 ConstantRange RHSRange = getUnsignedRange(RHS);
6743 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
6745 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
6749 case ICmpInst::ICMP_UGE:
6750 std::swap(LHS, RHS);
6751 case ICmpInst::ICMP_ULE: {
6752 ConstantRange LHSRange = getUnsignedRange(LHS);
6753 ConstantRange RHSRange = getUnsignedRange(RHS);
6754 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
6756 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
6760 case ICmpInst::ICMP_NE: {
6761 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
6763 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
6766 const SCEV *Diff = getMinusSCEV(LHS, RHS);
6767 if (isKnownNonZero(Diff))
6771 case ICmpInst::ICMP_EQ:
6772 // The check at the top of the function catches the case where
6773 // the values are known to be equal.
6779 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
6780 /// protected by a conditional between LHS and RHS. This is used to
6781 /// to eliminate casts.
6783 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
6784 ICmpInst::Predicate Pred,
6785 const SCEV *LHS, const SCEV *RHS) {
6786 // Interpret a null as meaning no loop, where there is obviously no guard
6787 // (interprocedural conditions notwithstanding).
6788 if (!L) return true;
6790 if (isKnownPredicateWithRanges(Pred, LHS, RHS)) return true;
6792 BasicBlock *Latch = L->getLoopLatch();
6796 BranchInst *LoopContinuePredicate =
6797 dyn_cast<BranchInst>(Latch->getTerminator());
6798 if (LoopContinuePredicate && LoopContinuePredicate->isConditional() &&
6799 isImpliedCond(Pred, LHS, RHS,
6800 LoopContinuePredicate->getCondition(),
6801 LoopContinuePredicate->getSuccessor(0) != L->getHeader()))
6804 // Check conditions due to any @llvm.assume intrinsics.
6805 for (auto &AssumeVH : AC->assumptions()) {
6808 auto *CI = cast<CallInst>(AssumeVH);
6809 if (!DT->dominates(CI, Latch->getTerminator()))
6812 if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false))
6819 /// isLoopEntryGuardedByCond - Test whether entry to the loop is protected
6820 /// by a conditional between LHS and RHS. This is used to help avoid max
6821 /// expressions in loop trip counts, and to eliminate casts.
6823 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
6824 ICmpInst::Predicate Pred,
6825 const SCEV *LHS, const SCEV *RHS) {
6826 // Interpret a null as meaning no loop, where there is obviously no guard
6827 // (interprocedural conditions notwithstanding).
6828 if (!L) return false;
6830 if (isKnownPredicateWithRanges(Pred, LHS, RHS)) return true;
6832 // Starting at the loop predecessor, climb up the predecessor chain, as long
6833 // as there are predecessors that can be found that have unique successors
6834 // leading to the original header.
6835 for (std::pair<BasicBlock *, BasicBlock *>
6836 Pair(L->getLoopPredecessor(), L->getHeader());
6838 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
6840 BranchInst *LoopEntryPredicate =
6841 dyn_cast<BranchInst>(Pair.first->getTerminator());
6842 if (!LoopEntryPredicate ||
6843 LoopEntryPredicate->isUnconditional())
6846 if (isImpliedCond(Pred, LHS, RHS,
6847 LoopEntryPredicate->getCondition(),
6848 LoopEntryPredicate->getSuccessor(0) != Pair.second))
6852 // Check conditions due to any @llvm.assume intrinsics.
6853 for (auto &AssumeVH : AC->assumptions()) {
6856 auto *CI = cast<CallInst>(AssumeVH);
6857 if (!DT->dominates(CI, L->getHeader()))
6860 if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false))
6867 /// RAII wrapper to prevent recursive application of isImpliedCond.
6868 /// ScalarEvolution's PendingLoopPredicates set must be empty unless we are
6869 /// currently evaluating isImpliedCond.
6870 struct MarkPendingLoopPredicate {
6872 DenseSet<Value*> &LoopPreds;
6875 MarkPendingLoopPredicate(Value *C, DenseSet<Value*> &LP)
6876 : Cond(C), LoopPreds(LP) {
6877 Pending = !LoopPreds.insert(Cond).second;
6879 ~MarkPendingLoopPredicate() {
6881 LoopPreds.erase(Cond);
6885 /// isImpliedCond - Test whether the condition described by Pred, LHS,
6886 /// and RHS is true whenever the given Cond value evaluates to true.
6887 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred,
6888 const SCEV *LHS, const SCEV *RHS,
6889 Value *FoundCondValue,
6891 MarkPendingLoopPredicate Mark(FoundCondValue, PendingLoopPredicates);
6895 // Recursively handle And and Or conditions.
6896 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) {
6897 if (BO->getOpcode() == Instruction::And) {
6899 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
6900 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
6901 } else if (BO->getOpcode() == Instruction::Or) {
6903 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
6904 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
6908 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue);
6909 if (!ICI) return false;
6911 // Bail if the ICmp's operands' types are wider than the needed type
6912 // before attempting to call getSCEV on them. This avoids infinite
6913 // recursion, since the analysis of widening casts can require loop
6914 // exit condition information for overflow checking, which would
6916 if (getTypeSizeInBits(LHS->getType()) <
6917 getTypeSizeInBits(ICI->getOperand(0)->getType()))
6920 // Now that we found a conditional branch that dominates the loop or controls
6921 // the loop latch. Check to see if it is the comparison we are looking for.
6922 ICmpInst::Predicate FoundPred;
6924 FoundPred = ICI->getInversePredicate();
6926 FoundPred = ICI->getPredicate();
6928 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
6929 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
6931 // Balance the types. The case where FoundLHS' type is wider than
6932 // LHS' type is checked for above.
6933 if (getTypeSizeInBits(LHS->getType()) >
6934 getTypeSizeInBits(FoundLHS->getType())) {
6935 if (CmpInst::isSigned(FoundPred)) {
6936 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
6937 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
6939 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
6940 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
6944 // Canonicalize the query to match the way instcombine will have
6945 // canonicalized the comparison.
6946 if (SimplifyICmpOperands(Pred, LHS, RHS))
6948 return CmpInst::isTrueWhenEqual(Pred);
6949 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
6950 if (FoundLHS == FoundRHS)
6951 return CmpInst::isFalseWhenEqual(FoundPred);
6953 // Check to see if we can make the LHS or RHS match.
6954 if (LHS == FoundRHS || RHS == FoundLHS) {
6955 if (isa<SCEVConstant>(RHS)) {
6956 std::swap(FoundLHS, FoundRHS);
6957 FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
6959 std::swap(LHS, RHS);
6960 Pred = ICmpInst::getSwappedPredicate(Pred);
6964 // Check whether the found predicate is the same as the desired predicate.
6965 if (FoundPred == Pred)
6966 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
6968 // Check whether swapping the found predicate makes it the same as the
6969 // desired predicate.
6970 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
6971 if (isa<SCEVConstant>(RHS))
6972 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
6974 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
6975 RHS, LHS, FoundLHS, FoundRHS);
6978 // Check if we can make progress by sharpening ranges.
6979 if (FoundPred == ICmpInst::ICMP_NE &&
6980 (isa<SCEVConstant>(FoundLHS) || isa<SCEVConstant>(FoundRHS))) {
6982 const SCEVConstant *C = nullptr;
6983 const SCEV *V = nullptr;
6985 if (isa<SCEVConstant>(FoundLHS)) {
6986 C = cast<SCEVConstant>(FoundLHS);
6989 C = cast<SCEVConstant>(FoundRHS);
6993 // The guarding predicate tells us that C != V. If the known range
6994 // of V is [C, t), we can sharpen the range to [C + 1, t). The
6995 // range we consider has to correspond to same signedness as the
6996 // predicate we're interested in folding.
6998 APInt Min = ICmpInst::isSigned(Pred) ?
6999 getSignedRange(V).getSignedMin() : getUnsignedRange(V).getUnsignedMin();
7001 if (Min == C->getValue()->getValue()) {
7002 // Given (V >= Min && V != Min) we conclude V >= (Min + 1).
7003 // This is true even if (Min + 1) wraps around -- in case of
7004 // wraparound, (Min + 1) < Min, so (V >= Min => V >= (Min + 1)).
7006 APInt SharperMin = Min + 1;
7009 case ICmpInst::ICMP_SGE:
7010 case ICmpInst::ICMP_UGE:
7011 // We know V `Pred` SharperMin. If this implies LHS `Pred`
7013 if (isImpliedCondOperands(Pred, LHS, RHS, V,
7014 getConstant(SharperMin)))
7017 case ICmpInst::ICMP_SGT:
7018 case ICmpInst::ICMP_UGT:
7019 // We know from the range information that (V `Pred` Min ||
7020 // V == Min). We know from the guarding condition that !(V
7021 // == Min). This gives us
7023 // V `Pred` Min || V == Min && !(V == Min)
7026 // If V `Pred` Min implies LHS `Pred` RHS, we're done.
7028 if (isImpliedCondOperands(Pred, LHS, RHS, V, getConstant(Min)))
7038 // Check whether the actual condition is beyond sufficient.
7039 if (FoundPred == ICmpInst::ICMP_EQ)
7040 if (ICmpInst::isTrueWhenEqual(Pred))
7041 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
7043 if (Pred == ICmpInst::ICMP_NE)
7044 if (!ICmpInst::isTrueWhenEqual(FoundPred))
7045 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
7048 // Otherwise assume the worst.
7052 /// isImpliedCondOperands - Test whether the condition described by Pred,
7053 /// LHS, and RHS is true whenever the condition described by Pred, FoundLHS,
7054 /// and FoundRHS is true.
7055 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
7056 const SCEV *LHS, const SCEV *RHS,
7057 const SCEV *FoundLHS,
7058 const SCEV *FoundRHS) {
7059 return isImpliedCondOperandsHelper(Pred, LHS, RHS,
7060 FoundLHS, FoundRHS) ||
7061 // ~x < ~y --> x > y
7062 isImpliedCondOperandsHelper(Pred, LHS, RHS,
7063 getNotSCEV(FoundRHS),
7064 getNotSCEV(FoundLHS));
7068 /// If Expr computes ~A, return A else return nullptr
7069 static const SCEV *MatchNotExpr(const SCEV *Expr) {
7070 const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Expr);
7071 if (!Add || Add->getNumOperands() != 2) return nullptr;
7073 const SCEVConstant *AddLHS = dyn_cast<SCEVConstant>(Add->getOperand(0));
7074 if (!(AddLHS && AddLHS->getValue()->getValue().isAllOnesValue()))
7077 const SCEVMulExpr *AddRHS = dyn_cast<SCEVMulExpr>(Add->getOperand(1));
7078 if (!AddRHS || AddRHS->getNumOperands() != 2) return nullptr;
7080 const SCEVConstant *MulLHS = dyn_cast<SCEVConstant>(AddRHS->getOperand(0));
7081 if (!(MulLHS && MulLHS->getValue()->getValue().isAllOnesValue()))
7084 return AddRHS->getOperand(1);
7088 /// Is MaybeMaxExpr an SMax or UMax of Candidate and some other values?
7089 template<typename MaxExprType>
7090 static bool IsMaxConsistingOf(const SCEV *MaybeMaxExpr,
7091 const SCEV *Candidate) {
7092 const MaxExprType *MaxExpr = dyn_cast<MaxExprType>(MaybeMaxExpr);
7093 if (!MaxExpr) return false;
7095 auto It = std::find(MaxExpr->op_begin(), MaxExpr->op_end(), Candidate);
7096 return It != MaxExpr->op_end();
7100 /// Is MaybeMinExpr an SMin or UMin of Candidate and some other values?
7101 template<typename MaxExprType>
7102 static bool IsMinConsistingOf(ScalarEvolution &SE,
7103 const SCEV *MaybeMinExpr,
7104 const SCEV *Candidate) {
7105 const SCEV *MaybeMaxExpr = MatchNotExpr(MaybeMinExpr);
7109 return IsMaxConsistingOf<MaxExprType>(MaybeMaxExpr, SE.getNotSCEV(Candidate));
7113 /// Is LHS `Pred` RHS true on the virtue of LHS or RHS being a Min or Max
7115 static bool IsKnownPredicateViaMinOrMax(ScalarEvolution &SE,
7116 ICmpInst::Predicate Pred,
7117 const SCEV *LHS, const SCEV *RHS) {
7122 case ICmpInst::ICMP_SGE:
7123 std::swap(LHS, RHS);
7125 case ICmpInst::ICMP_SLE:
7128 IsMinConsistingOf<SCEVSMaxExpr>(SE, LHS, RHS) ||
7130 IsMaxConsistingOf<SCEVSMaxExpr>(RHS, LHS);
7132 case ICmpInst::ICMP_UGE:
7133 std::swap(LHS, RHS);
7135 case ICmpInst::ICMP_ULE:
7138 IsMinConsistingOf<SCEVUMaxExpr>(SE, LHS, RHS) ||
7140 IsMaxConsistingOf<SCEVUMaxExpr>(RHS, LHS);
7143 llvm_unreachable("covered switch fell through?!");
7146 /// isImpliedCondOperandsHelper - Test whether the condition described by
7147 /// Pred, LHS, and RHS is true whenever the condition described by Pred,
7148 /// FoundLHS, and FoundRHS is true.
7150 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
7151 const SCEV *LHS, const SCEV *RHS,
7152 const SCEV *FoundLHS,
7153 const SCEV *FoundRHS) {
7154 auto IsKnownPredicateFull =
7155 [this](ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS) {
7156 return isKnownPredicateWithRanges(Pred, LHS, RHS) ||
7157 IsKnownPredicateViaMinOrMax(*this, Pred, LHS, RHS);
7161 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
7162 case ICmpInst::ICMP_EQ:
7163 case ICmpInst::ICMP_NE:
7164 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
7167 case ICmpInst::ICMP_SLT:
7168 case ICmpInst::ICMP_SLE:
7169 if (IsKnownPredicateFull(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
7170 IsKnownPredicateFull(ICmpInst::ICMP_SGE, RHS, FoundRHS))
7173 case ICmpInst::ICMP_SGT:
7174 case ICmpInst::ICMP_SGE:
7175 if (IsKnownPredicateFull(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
7176 IsKnownPredicateFull(ICmpInst::ICMP_SLE, RHS, FoundRHS))
7179 case ICmpInst::ICMP_ULT:
7180 case ICmpInst::ICMP_ULE:
7181 if (IsKnownPredicateFull(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
7182 IsKnownPredicateFull(ICmpInst::ICMP_UGE, RHS, FoundRHS))
7185 case ICmpInst::ICMP_UGT:
7186 case ICmpInst::ICMP_UGE:
7187 if (IsKnownPredicateFull(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
7188 IsKnownPredicateFull(ICmpInst::ICMP_ULE, RHS, FoundRHS))
7196 // Verify if an linear IV with positive stride can overflow when in a
7197 // less-than comparison, knowing the invariant term of the comparison, the
7198 // stride and the knowledge of NSW/NUW flags on the recurrence.
7199 bool ScalarEvolution::doesIVOverflowOnLT(const SCEV *RHS, const SCEV *Stride,
7200 bool IsSigned, bool NoWrap) {
7201 if (NoWrap) return false;
7203 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
7204 const SCEV *One = getConstant(Stride->getType(), 1);
7207 APInt MaxRHS = getSignedRange(RHS).getSignedMax();
7208 APInt MaxValue = APInt::getSignedMaxValue(BitWidth);
7209 APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
7212 // SMaxRHS + SMaxStrideMinusOne > SMaxValue => overflow!
7213 return (MaxValue - MaxStrideMinusOne).slt(MaxRHS);
7216 APInt MaxRHS = getUnsignedRange(RHS).getUnsignedMax();
7217 APInt MaxValue = APInt::getMaxValue(BitWidth);
7218 APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
7221 // UMaxRHS + UMaxStrideMinusOne > UMaxValue => overflow!
7222 return (MaxValue - MaxStrideMinusOne).ult(MaxRHS);
7225 // Verify if an linear IV with negative stride can overflow when in a
7226 // greater-than comparison, knowing the invariant term of the comparison,
7227 // the stride and the knowledge of NSW/NUW flags on the recurrence.
7228 bool ScalarEvolution::doesIVOverflowOnGT(const SCEV *RHS, const SCEV *Stride,
7229 bool IsSigned, bool NoWrap) {
7230 if (NoWrap) return false;
7232 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
7233 const SCEV *One = getConstant(Stride->getType(), 1);
7236 APInt MinRHS = getSignedRange(RHS).getSignedMin();
7237 APInt MinValue = APInt::getSignedMinValue(BitWidth);
7238 APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
7241 // SMinRHS - SMaxStrideMinusOne < SMinValue => overflow!
7242 return (MinValue + MaxStrideMinusOne).sgt(MinRHS);
7245 APInt MinRHS = getUnsignedRange(RHS).getUnsignedMin();
7246 APInt MinValue = APInt::getMinValue(BitWidth);
7247 APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
7250 // UMinRHS - UMaxStrideMinusOne < UMinValue => overflow!
7251 return (MinValue + MaxStrideMinusOne).ugt(MinRHS);
7254 // Compute the backedge taken count knowing the interval difference, the
7255 // stride and presence of the equality in the comparison.
7256 const SCEV *ScalarEvolution::computeBECount(const SCEV *Delta, const SCEV *Step,
7258 const SCEV *One = getConstant(Step->getType(), 1);
7259 Delta = Equality ? getAddExpr(Delta, Step)
7260 : getAddExpr(Delta, getMinusSCEV(Step, One));
7261 return getUDivExpr(Delta, Step);
7264 /// HowManyLessThans - Return the number of times a backedge containing the
7265 /// specified less-than comparison will execute. If not computable, return
7266 /// CouldNotCompute.
7268 /// @param ControlsExit is true when the LHS < RHS condition directly controls
7269 /// the branch (loops exits only if condition is true). In this case, we can use
7270 /// NoWrapFlags to skip overflow checks.
7271 ScalarEvolution::ExitLimit
7272 ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
7273 const Loop *L, bool IsSigned,
7274 bool ControlsExit) {
7275 // We handle only IV < Invariant
7276 if (!isLoopInvariant(RHS, L))
7277 return getCouldNotCompute();
7279 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
7281 // Avoid weird loops
7282 if (!IV || IV->getLoop() != L || !IV->isAffine())
7283 return getCouldNotCompute();
7285 bool NoWrap = ControlsExit &&
7286 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
7288 const SCEV *Stride = IV->getStepRecurrence(*this);
7290 // Avoid negative or zero stride values
7291 if (!isKnownPositive(Stride))
7292 return getCouldNotCompute();
7294 // Avoid proven overflow cases: this will ensure that the backedge taken count
7295 // will not generate any unsigned overflow. Relaxed no-overflow conditions
7296 // exploit NoWrapFlags, allowing to optimize in presence of undefined
7297 // behaviors like the case of C language.
7298 if (!Stride->isOne() && doesIVOverflowOnLT(RHS, Stride, IsSigned, NoWrap))
7299 return getCouldNotCompute();
7301 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SLT
7302 : ICmpInst::ICMP_ULT;
7303 const SCEV *Start = IV->getStart();
7304 const SCEV *End = RHS;
7305 if (!isLoopEntryGuardedByCond(L, Cond, getMinusSCEV(Start, Stride), RHS)) {
7306 const SCEV *Diff = getMinusSCEV(RHS, Start);
7307 // If we have NoWrap set, then we can assume that the increment won't
7308 // overflow, in which case if RHS - Start is a constant, we don't need to
7309 // do a max operation since we can just figure it out statically
7310 if (NoWrap && isa<SCEVConstant>(Diff)) {
7311 APInt D = dyn_cast<const SCEVConstant>(Diff)->getValue()->getValue();
7315 End = IsSigned ? getSMaxExpr(RHS, Start)
7316 : getUMaxExpr(RHS, Start);
7319 const SCEV *BECount = computeBECount(getMinusSCEV(End, Start), Stride, false);
7321 APInt MinStart = IsSigned ? getSignedRange(Start).getSignedMin()
7322 : getUnsignedRange(Start).getUnsignedMin();
7324 APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
7325 : getUnsignedRange(Stride).getUnsignedMin();
7327 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
7328 APInt Limit = IsSigned ? APInt::getSignedMaxValue(BitWidth) - (MinStride - 1)
7329 : APInt::getMaxValue(BitWidth) - (MinStride - 1);
7331 // Although End can be a MAX expression we estimate MaxEnd considering only
7332 // the case End = RHS. This is safe because in the other case (End - Start)
7333 // is zero, leading to a zero maximum backedge taken count.
7335 IsSigned ? APIntOps::smin(getSignedRange(RHS).getSignedMax(), Limit)
7336 : APIntOps::umin(getUnsignedRange(RHS).getUnsignedMax(), Limit);
7338 const SCEV *MaxBECount;
7339 if (isa<SCEVConstant>(BECount))
7340 MaxBECount = BECount;
7342 MaxBECount = computeBECount(getConstant(MaxEnd - MinStart),
7343 getConstant(MinStride), false);
7345 if (isa<SCEVCouldNotCompute>(MaxBECount))
7346 MaxBECount = BECount;
7348 return ExitLimit(BECount, MaxBECount);
7351 ScalarEvolution::ExitLimit
7352 ScalarEvolution::HowManyGreaterThans(const SCEV *LHS, const SCEV *RHS,
7353 const Loop *L, bool IsSigned,
7354 bool ControlsExit) {
7355 // We handle only IV > Invariant
7356 if (!isLoopInvariant(RHS, L))
7357 return getCouldNotCompute();
7359 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
7361 // Avoid weird loops
7362 if (!IV || IV->getLoop() != L || !IV->isAffine())
7363 return getCouldNotCompute();
7365 bool NoWrap = ControlsExit &&
7366 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
7368 const SCEV *Stride = getNegativeSCEV(IV->getStepRecurrence(*this));
7370 // Avoid negative or zero stride values
7371 if (!isKnownPositive(Stride))
7372 return getCouldNotCompute();
7374 // Avoid proven overflow cases: this will ensure that the backedge taken count
7375 // will not generate any unsigned overflow. Relaxed no-overflow conditions
7376 // exploit NoWrapFlags, allowing to optimize in presence of undefined
7377 // behaviors like the case of C language.
7378 if (!Stride->isOne() && doesIVOverflowOnGT(RHS, Stride, IsSigned, NoWrap))
7379 return getCouldNotCompute();
7381 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SGT
7382 : ICmpInst::ICMP_UGT;
7384 const SCEV *Start = IV->getStart();
7385 const SCEV *End = RHS;
7386 if (!isLoopEntryGuardedByCond(L, Cond, getAddExpr(Start, Stride), RHS)) {
7387 const SCEV *Diff = getMinusSCEV(RHS, Start);
7388 // If we have NoWrap set, then we can assume that the increment won't
7389 // overflow, in which case if RHS - Start is a constant, we don't need to
7390 // do a max operation since we can just figure it out statically
7391 if (NoWrap && isa<SCEVConstant>(Diff)) {
7392 APInt D = dyn_cast<const SCEVConstant>(Diff)->getValue()->getValue();
7393 if (!D.isNegative())
7396 End = IsSigned ? getSMinExpr(RHS, Start)
7397 : getUMinExpr(RHS, Start);
7400 const SCEV *BECount = computeBECount(getMinusSCEV(Start, End), Stride, false);
7402 APInt MaxStart = IsSigned ? getSignedRange(Start).getSignedMax()
7403 : getUnsignedRange(Start).getUnsignedMax();
7405 APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
7406 : getUnsignedRange(Stride).getUnsignedMin();
7408 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
7409 APInt Limit = IsSigned ? APInt::getSignedMinValue(BitWidth) + (MinStride - 1)
7410 : APInt::getMinValue(BitWidth) + (MinStride - 1);
7412 // Although End can be a MIN expression we estimate MinEnd considering only
7413 // the case End = RHS. This is safe because in the other case (Start - End)
7414 // is zero, leading to a zero maximum backedge taken count.
7416 IsSigned ? APIntOps::smax(getSignedRange(RHS).getSignedMin(), Limit)
7417 : APIntOps::umax(getUnsignedRange(RHS).getUnsignedMin(), Limit);
7420 const SCEV *MaxBECount = getCouldNotCompute();
7421 if (isa<SCEVConstant>(BECount))
7422 MaxBECount = BECount;
7424 MaxBECount = computeBECount(getConstant(MaxStart - MinEnd),
7425 getConstant(MinStride), false);
7427 if (isa<SCEVCouldNotCompute>(MaxBECount))
7428 MaxBECount = BECount;
7430 return ExitLimit(BECount, MaxBECount);
7433 /// getNumIterationsInRange - Return the number of iterations of this loop that
7434 /// produce values in the specified constant range. Another way of looking at
7435 /// this is that it returns the first iteration number where the value is not in
7436 /// the condition, thus computing the exit count. If the iteration count can't
7437 /// be computed, an instance of SCEVCouldNotCompute is returned.
7438 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
7439 ScalarEvolution &SE) const {
7440 if (Range.isFullSet()) // Infinite loop.
7441 return SE.getCouldNotCompute();
7443 // If the start is a non-zero constant, shift the range to simplify things.
7444 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
7445 if (!SC->getValue()->isZero()) {
7446 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
7447 Operands[0] = SE.getConstant(SC->getType(), 0);
7448 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(),
7449 getNoWrapFlags(FlagNW));
7450 if (const SCEVAddRecExpr *ShiftedAddRec =
7451 dyn_cast<SCEVAddRecExpr>(Shifted))
7452 return ShiftedAddRec->getNumIterationsInRange(
7453 Range.subtract(SC->getValue()->getValue()), SE);
7454 // This is strange and shouldn't happen.
7455 return SE.getCouldNotCompute();
7458 // The only time we can solve this is when we have all constant indices.
7459 // Otherwise, we cannot determine the overflow conditions.
7460 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
7461 if (!isa<SCEVConstant>(getOperand(i)))
7462 return SE.getCouldNotCompute();
7465 // Okay at this point we know that all elements of the chrec are constants and
7466 // that the start element is zero.
7468 // First check to see if the range contains zero. If not, the first
7470 unsigned BitWidth = SE.getTypeSizeInBits(getType());
7471 if (!Range.contains(APInt(BitWidth, 0)))
7472 return SE.getConstant(getType(), 0);
7475 // If this is an affine expression then we have this situation:
7476 // Solve {0,+,A} in Range === Ax in Range
7478 // We know that zero is in the range. If A is positive then we know that
7479 // the upper value of the range must be the first possible exit value.
7480 // If A is negative then the lower of the range is the last possible loop
7481 // value. Also note that we already checked for a full range.
7482 APInt One(BitWidth,1);
7483 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
7484 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
7486 // The exit value should be (End+A)/A.
7487 APInt ExitVal = (End + A).udiv(A);
7488 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
7490 // Evaluate at the exit value. If we really did fall out of the valid
7491 // range, then we computed our trip count, otherwise wrap around or other
7492 // things must have happened.
7493 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
7494 if (Range.contains(Val->getValue()))
7495 return SE.getCouldNotCompute(); // Something strange happened
7497 // Ensure that the previous value is in the range. This is a sanity check.
7498 assert(Range.contains(
7499 EvaluateConstantChrecAtConstant(this,
7500 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
7501 "Linear scev computation is off in a bad way!");
7502 return SE.getConstant(ExitValue);
7503 } else if (isQuadratic()) {
7504 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
7505 // quadratic equation to solve it. To do this, we must frame our problem in
7506 // terms of figuring out when zero is crossed, instead of when
7507 // Range.getUpper() is crossed.
7508 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
7509 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
7510 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop(),
7511 // getNoWrapFlags(FlagNW)
7514 // Next, solve the constructed addrec
7515 std::pair<const SCEV *,const SCEV *> Roots =
7516 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
7517 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
7518 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
7520 // Pick the smallest positive root value.
7521 if (ConstantInt *CB =
7522 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
7523 R1->getValue(), R2->getValue()))) {
7524 if (CB->getZExtValue() == false)
7525 std::swap(R1, R2); // R1 is the minimum root now.
7527 // Make sure the root is not off by one. The returned iteration should
7528 // not be in the range, but the previous one should be. When solving
7529 // for "X*X < 5", for example, we should not return a root of 2.
7530 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
7533 if (Range.contains(R1Val->getValue())) {
7534 // The next iteration must be out of the range...
7535 ConstantInt *NextVal =
7536 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1);
7538 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
7539 if (!Range.contains(R1Val->getValue()))
7540 return SE.getConstant(NextVal);
7541 return SE.getCouldNotCompute(); // Something strange happened
7544 // If R1 was not in the range, then it is a good return value. Make
7545 // sure that R1-1 WAS in the range though, just in case.
7546 ConstantInt *NextVal =
7547 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1);
7548 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
7549 if (Range.contains(R1Val->getValue()))
7551 return SE.getCouldNotCompute(); // Something strange happened
7556 return SE.getCouldNotCompute();
7562 FindUndefs() : Found(false) {}
7564 bool follow(const SCEV *S) {
7565 if (const SCEVUnknown *C = dyn_cast<SCEVUnknown>(S)) {
7566 if (isa<UndefValue>(C->getValue()))
7568 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) {
7569 if (isa<UndefValue>(C->getValue()))
7573 // Keep looking if we haven't found it yet.
7576 bool isDone() const {
7577 // Stop recursion if we have found an undef.
7583 // Return true when S contains at least an undef value.
7585 containsUndefs(const SCEV *S) {
7587 SCEVTraversal<FindUndefs> ST(F);
7594 // Collect all steps of SCEV expressions.
7595 struct SCEVCollectStrides {
7596 ScalarEvolution &SE;
7597 SmallVectorImpl<const SCEV *> &Strides;
7599 SCEVCollectStrides(ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &S)
7600 : SE(SE), Strides(S) {}
7602 bool follow(const SCEV *S) {
7603 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(S))
7604 Strides.push_back(AR->getStepRecurrence(SE));
7607 bool isDone() const { return false; }
7610 // Collect all SCEVUnknown and SCEVMulExpr expressions.
7611 struct SCEVCollectTerms {
7612 SmallVectorImpl<const SCEV *> &Terms;
7614 SCEVCollectTerms(SmallVectorImpl<const SCEV *> &T)
7617 bool follow(const SCEV *S) {
7618 if (isa<SCEVUnknown>(S) || isa<SCEVMulExpr>(S)) {
7619 if (!containsUndefs(S))
7622 // Stop recursion: once we collected a term, do not walk its operands.
7629 bool isDone() const { return false; }
7633 /// Find parametric terms in this SCEVAddRecExpr.
7634 void SCEVAddRecExpr::collectParametricTerms(
7635 ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &Terms) const {
7636 SmallVector<const SCEV *, 4> Strides;
7637 SCEVCollectStrides StrideCollector(SE, Strides);
7638 visitAll(this, StrideCollector);
7641 dbgs() << "Strides:\n";
7642 for (const SCEV *S : Strides)
7643 dbgs() << *S << "\n";
7646 for (const SCEV *S : Strides) {
7647 SCEVCollectTerms TermCollector(Terms);
7648 visitAll(S, TermCollector);
7652 dbgs() << "Terms:\n";
7653 for (const SCEV *T : Terms)
7654 dbgs() << *T << "\n";
7658 static bool findArrayDimensionsRec(ScalarEvolution &SE,
7659 SmallVectorImpl<const SCEV *> &Terms,
7660 SmallVectorImpl<const SCEV *> &Sizes) {
7661 int Last = Terms.size() - 1;
7662 const SCEV *Step = Terms[Last];
7664 // End of recursion.
7666 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Step)) {
7667 SmallVector<const SCEV *, 2> Qs;
7668 for (const SCEV *Op : M->operands())
7669 if (!isa<SCEVConstant>(Op))
7672 Step = SE.getMulExpr(Qs);
7675 Sizes.push_back(Step);
7679 for (const SCEV *&Term : Terms) {
7680 // Normalize the terms before the next call to findArrayDimensionsRec.
7682 SCEVDivision::divide(SE, Term, Step, &Q, &R);
7684 // Bail out when GCD does not evenly divide one of the terms.
7691 // Remove all SCEVConstants.
7692 Terms.erase(std::remove_if(Terms.begin(), Terms.end(), [](const SCEV *E) {
7693 return isa<SCEVConstant>(E);
7697 if (Terms.size() > 0)
7698 if (!findArrayDimensionsRec(SE, Terms, Sizes))
7701 Sizes.push_back(Step);
7706 struct FindParameter {
7707 bool FoundParameter;
7708 FindParameter() : FoundParameter(false) {}
7710 bool follow(const SCEV *S) {
7711 if (isa<SCEVUnknown>(S)) {
7712 FoundParameter = true;
7713 // Stop recursion: we found a parameter.
7719 bool isDone() const {
7720 // Stop recursion if we have found a parameter.
7721 return FoundParameter;
7726 // Returns true when S contains at least a SCEVUnknown parameter.
7728 containsParameters(const SCEV *S) {
7730 SCEVTraversal<FindParameter> ST(F);
7733 return F.FoundParameter;
7736 // Returns true when one of the SCEVs of Terms contains a SCEVUnknown parameter.
7738 containsParameters(SmallVectorImpl<const SCEV *> &Terms) {
7739 for (const SCEV *T : Terms)
7740 if (containsParameters(T))
7745 // Return the number of product terms in S.
7746 static inline int numberOfTerms(const SCEV *S) {
7747 if (const SCEVMulExpr *Expr = dyn_cast<SCEVMulExpr>(S))
7748 return Expr->getNumOperands();
7752 static const SCEV *removeConstantFactors(ScalarEvolution &SE, const SCEV *T) {
7753 if (isa<SCEVConstant>(T))
7756 if (isa<SCEVUnknown>(T))
7759 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(T)) {
7760 SmallVector<const SCEV *, 2> Factors;
7761 for (const SCEV *Op : M->operands())
7762 if (!isa<SCEVConstant>(Op))
7763 Factors.push_back(Op);
7765 return SE.getMulExpr(Factors);
7771 /// Return the size of an element read or written by Inst.
7772 const SCEV *ScalarEvolution::getElementSize(Instruction *Inst) {
7774 if (StoreInst *Store = dyn_cast<StoreInst>(Inst))
7775 Ty = Store->getValueOperand()->getType();
7776 else if (LoadInst *Load = dyn_cast<LoadInst>(Inst))
7777 Ty = Load->getType();
7781 Type *ETy = getEffectiveSCEVType(PointerType::getUnqual(Ty));
7782 return getSizeOfExpr(ETy, Ty);
7785 /// Second step of delinearization: compute the array dimensions Sizes from the
7786 /// set of Terms extracted from the memory access function of this SCEVAddRec.
7787 void ScalarEvolution::findArrayDimensions(SmallVectorImpl<const SCEV *> &Terms,
7788 SmallVectorImpl<const SCEV *> &Sizes,
7789 const SCEV *ElementSize) const {
7791 if (Terms.size() < 1 || !ElementSize)
7794 // Early return when Terms do not contain parameters: we do not delinearize
7795 // non parametric SCEVs.
7796 if (!containsParameters(Terms))
7800 dbgs() << "Terms:\n";
7801 for (const SCEV *T : Terms)
7802 dbgs() << *T << "\n";
7805 // Remove duplicates.
7806 std::sort(Terms.begin(), Terms.end());
7807 Terms.erase(std::unique(Terms.begin(), Terms.end()), Terms.end());
7809 // Put larger terms first.
7810 std::sort(Terms.begin(), Terms.end(), [](const SCEV *LHS, const SCEV *RHS) {
7811 return numberOfTerms(LHS) > numberOfTerms(RHS);
7814 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
7816 // Divide all terms by the element size.
7817 for (const SCEV *&Term : Terms) {
7819 SCEVDivision::divide(SE, Term, ElementSize, &Q, &R);
7823 SmallVector<const SCEV *, 4> NewTerms;
7825 // Remove constant factors.
7826 for (const SCEV *T : Terms)
7827 if (const SCEV *NewT = removeConstantFactors(SE, T))
7828 NewTerms.push_back(NewT);
7831 dbgs() << "Terms after sorting:\n";
7832 for (const SCEV *T : NewTerms)
7833 dbgs() << *T << "\n";
7836 if (NewTerms.empty() ||
7837 !findArrayDimensionsRec(SE, NewTerms, Sizes)) {
7842 // The last element to be pushed into Sizes is the size of an element.
7843 Sizes.push_back(ElementSize);
7846 dbgs() << "Sizes:\n";
7847 for (const SCEV *S : Sizes)
7848 dbgs() << *S << "\n";
7852 /// Third step of delinearization: compute the access functions for the
7853 /// Subscripts based on the dimensions in Sizes.
7854 void SCEVAddRecExpr::computeAccessFunctions(
7855 ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &Subscripts,
7856 SmallVectorImpl<const SCEV *> &Sizes) const {
7858 // Early exit in case this SCEV is not an affine multivariate function.
7859 if (Sizes.empty() || !this->isAffine())
7862 const SCEV *Res = this;
7863 int Last = Sizes.size() - 1;
7864 for (int i = Last; i >= 0; i--) {
7866 SCEVDivision::divide(SE, Res, Sizes[i], &Q, &R);
7869 dbgs() << "Res: " << *Res << "\n";
7870 dbgs() << "Sizes[i]: " << *Sizes[i] << "\n";
7871 dbgs() << "Res divided by Sizes[i]:\n";
7872 dbgs() << "Quotient: " << *Q << "\n";
7873 dbgs() << "Remainder: " << *R << "\n";
7878 // Do not record the last subscript corresponding to the size of elements in
7882 // Bail out if the remainder is too complex.
7883 if (isa<SCEVAddRecExpr>(R)) {
7892 // Record the access function for the current subscript.
7893 Subscripts.push_back(R);
7896 // Also push in last position the remainder of the last division: it will be
7897 // the access function of the innermost dimension.
7898 Subscripts.push_back(Res);
7900 std::reverse(Subscripts.begin(), Subscripts.end());
7903 dbgs() << "Subscripts:\n";
7904 for (const SCEV *S : Subscripts)
7905 dbgs() << *S << "\n";
7909 /// Splits the SCEV into two vectors of SCEVs representing the subscripts and
7910 /// sizes of an array access. Returns the remainder of the delinearization that
7911 /// is the offset start of the array. The SCEV->delinearize algorithm computes
7912 /// the multiples of SCEV coefficients: that is a pattern matching of sub
7913 /// expressions in the stride and base of a SCEV corresponding to the
7914 /// computation of a GCD (greatest common divisor) of base and stride. When
7915 /// SCEV->delinearize fails, it returns the SCEV unchanged.
7917 /// For example: when analyzing the memory access A[i][j][k] in this loop nest
7919 /// void foo(long n, long m, long o, double A[n][m][o]) {
7921 /// for (long i = 0; i < n; i++)
7922 /// for (long j = 0; j < m; j++)
7923 /// for (long k = 0; k < o; k++)
7924 /// A[i][j][k] = 1.0;
7927 /// the delinearization input is the following AddRec SCEV:
7929 /// AddRec: {{{%A,+,(8 * %m * %o)}<%for.i>,+,(8 * %o)}<%for.j>,+,8}<%for.k>
7931 /// From this SCEV, we are able to say that the base offset of the access is %A
7932 /// because it appears as an offset that does not divide any of the strides in
7935 /// CHECK: Base offset: %A
7937 /// and then SCEV->delinearize determines the size of some of the dimensions of
7938 /// the array as these are the multiples by which the strides are happening:
7940 /// CHECK: ArrayDecl[UnknownSize][%m][%o] with elements of sizeof(double) bytes.
7942 /// Note that the outermost dimension remains of UnknownSize because there are
7943 /// no strides that would help identifying the size of the last dimension: when
7944 /// the array has been statically allocated, one could compute the size of that
7945 /// dimension by dividing the overall size of the array by the size of the known
7946 /// dimensions: %m * %o * 8.
7948 /// Finally delinearize provides the access functions for the array reference
7949 /// that does correspond to A[i][j][k] of the above C testcase:
7951 /// CHECK: ArrayRef[{0,+,1}<%for.i>][{0,+,1}<%for.j>][{0,+,1}<%for.k>]
7953 /// The testcases are checking the output of a function pass:
7954 /// DelinearizationPass that walks through all loads and stores of a function
7955 /// asking for the SCEV of the memory access with respect to all enclosing
7956 /// loops, calling SCEV->delinearize on that and printing the results.
7958 void SCEVAddRecExpr::delinearize(ScalarEvolution &SE,
7959 SmallVectorImpl<const SCEV *> &Subscripts,
7960 SmallVectorImpl<const SCEV *> &Sizes,
7961 const SCEV *ElementSize) const {
7962 // First step: collect parametric terms.
7963 SmallVector<const SCEV *, 4> Terms;
7964 collectParametricTerms(SE, Terms);
7969 // Second step: find subscript sizes.
7970 SE.findArrayDimensions(Terms, Sizes, ElementSize);
7975 // Third step: compute the access functions for each subscript.
7976 computeAccessFunctions(SE, Subscripts, Sizes);
7978 if (Subscripts.empty())
7982 dbgs() << "succeeded to delinearize " << *this << "\n";
7983 dbgs() << "ArrayDecl[UnknownSize]";
7984 for (const SCEV *S : Sizes)
7985 dbgs() << "[" << *S << "]";
7987 dbgs() << "\nArrayRef";
7988 for (const SCEV *S : Subscripts)
7989 dbgs() << "[" << *S << "]";
7994 //===----------------------------------------------------------------------===//
7995 // SCEVCallbackVH Class Implementation
7996 //===----------------------------------------------------------------------===//
7998 void ScalarEvolution::SCEVCallbackVH::deleted() {
7999 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
8000 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
8001 SE->ConstantEvolutionLoopExitValue.erase(PN);
8002 SE->ValueExprMap.erase(getValPtr());
8003 // this now dangles!
8006 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) {
8007 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
8009 // Forget all the expressions associated with users of the old value,
8010 // so that future queries will recompute the expressions using the new
8012 Value *Old = getValPtr();
8013 SmallVector<User *, 16> Worklist(Old->user_begin(), Old->user_end());
8014 SmallPtrSet<User *, 8> Visited;
8015 while (!Worklist.empty()) {
8016 User *U = Worklist.pop_back_val();
8017 // Deleting the Old value will cause this to dangle. Postpone
8018 // that until everything else is done.
8021 if (!Visited.insert(U).second)
8023 if (PHINode *PN = dyn_cast<PHINode>(U))
8024 SE->ConstantEvolutionLoopExitValue.erase(PN);
8025 SE->ValueExprMap.erase(U);
8026 Worklist.insert(Worklist.end(), U->user_begin(), U->user_end());
8028 // Delete the Old value.
8029 if (PHINode *PN = dyn_cast<PHINode>(Old))
8030 SE->ConstantEvolutionLoopExitValue.erase(PN);
8031 SE->ValueExprMap.erase(Old);
8032 // this now dangles!
8035 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
8036 : CallbackVH(V), SE(se) {}
8038 //===----------------------------------------------------------------------===//
8039 // ScalarEvolution Class Implementation
8040 //===----------------------------------------------------------------------===//
8042 ScalarEvolution::ScalarEvolution()
8043 : FunctionPass(ID), ValuesAtScopes(64), LoopDispositions(64),
8044 BlockDispositions(64), FirstUnknown(nullptr) {
8045 initializeScalarEvolutionPass(*PassRegistry::getPassRegistry());
8048 bool ScalarEvolution::runOnFunction(Function &F) {
8050 AC = &getAnalysis<AssumptionCacheTracker>().getAssumptionCache(F);
8051 LI = &getAnalysis<LoopInfoWrapperPass>().getLoopInfo();
8052 DL = &F.getParent()->getDataLayout();
8053 TLI = &getAnalysis<TargetLibraryInfoWrapperPass>().getTLI();
8054 DT = &getAnalysis<DominatorTreeWrapperPass>().getDomTree();
8058 void ScalarEvolution::releaseMemory() {
8059 // Iterate through all the SCEVUnknown instances and call their
8060 // destructors, so that they release their references to their values.
8061 for (SCEVUnknown *U = FirstUnknown; U; U = U->Next)
8063 FirstUnknown = nullptr;
8065 ValueExprMap.clear();
8067 // Free any extra memory created for ExitNotTakenInfo in the unlikely event
8068 // that a loop had multiple computable exits.
8069 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
8070 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end();
8075 assert(PendingLoopPredicates.empty() && "isImpliedCond garbage");
8077 BackedgeTakenCounts.clear();
8078 ConstantEvolutionLoopExitValue.clear();
8079 ValuesAtScopes.clear();
8080 LoopDispositions.clear();
8081 BlockDispositions.clear();
8082 UnsignedRanges.clear();
8083 SignedRanges.clear();
8084 UniqueSCEVs.clear();
8085 SCEVAllocator.Reset();
8088 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
8089 AU.setPreservesAll();
8090 AU.addRequired<AssumptionCacheTracker>();
8091 AU.addRequiredTransitive<LoopInfoWrapperPass>();
8092 AU.addRequiredTransitive<DominatorTreeWrapperPass>();
8093 AU.addRequired<TargetLibraryInfoWrapperPass>();
8096 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
8097 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
8100 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
8102 // Print all inner loops first
8103 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
8104 PrintLoopInfo(OS, SE, *I);
8107 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
8110 SmallVector<BasicBlock *, 8> ExitBlocks;
8111 L->getExitBlocks(ExitBlocks);
8112 if (ExitBlocks.size() != 1)
8113 OS << "<multiple exits> ";
8115 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
8116 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
8118 OS << "Unpredictable backedge-taken count. ";
8123 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
8126 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
8127 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
8129 OS << "Unpredictable max backedge-taken count. ";
8135 void ScalarEvolution::print(raw_ostream &OS, const Module *) const {
8136 // ScalarEvolution's implementation of the print method is to print
8137 // out SCEV values of all instructions that are interesting. Doing
8138 // this potentially causes it to create new SCEV objects though,
8139 // which technically conflicts with the const qualifier. This isn't
8140 // observable from outside the class though, so casting away the
8141 // const isn't dangerous.
8142 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
8144 OS << "Classifying expressions for: ";
8145 F->printAsOperand(OS, /*PrintType=*/false);
8147 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
8148 if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) {
8151 const SCEV *SV = SE.getSCEV(&*I);
8154 const Loop *L = LI->getLoopFor((*I).getParent());
8156 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
8163 OS << "\t\t" "Exits: ";
8164 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
8165 if (!SE.isLoopInvariant(ExitValue, L)) {
8166 OS << "<<Unknown>>";
8175 OS << "Determining loop execution counts for: ";
8176 F->printAsOperand(OS, /*PrintType=*/false);
8178 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
8179 PrintLoopInfo(OS, &SE, *I);
8182 ScalarEvolution::LoopDisposition
8183 ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) {
8184 auto &Values = LoopDispositions[S];
8185 for (auto &V : Values) {
8186 if (V.getPointer() == L)
8189 Values.emplace_back(L, LoopVariant);
8190 LoopDisposition D = computeLoopDisposition(S, L);
8191 auto &Values2 = LoopDispositions[S];
8192 for (auto &V : make_range(Values2.rbegin(), Values2.rend())) {
8193 if (V.getPointer() == L) {
8201 ScalarEvolution::LoopDisposition
8202 ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) {
8203 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
8205 return LoopInvariant;
8209 return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L);
8210 case scAddRecExpr: {
8211 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
8213 // If L is the addrec's loop, it's computable.
8214 if (AR->getLoop() == L)
8215 return LoopComputable;
8217 // Add recurrences are never invariant in the function-body (null loop).
8221 // This recurrence is variant w.r.t. L if L contains AR's loop.
8222 if (L->contains(AR->getLoop()))
8225 // This recurrence is invariant w.r.t. L if AR's loop contains L.
8226 if (AR->getLoop()->contains(L))
8227 return LoopInvariant;
8229 // This recurrence is variant w.r.t. L if any of its operands
8231 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
8233 if (!isLoopInvariant(*I, L))
8236 // Otherwise it's loop-invariant.
8237 return LoopInvariant;
8243 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
8244 bool HasVarying = false;
8245 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
8247 LoopDisposition D = getLoopDisposition(*I, L);
8248 if (D == LoopVariant)
8250 if (D == LoopComputable)
8253 return HasVarying ? LoopComputable : LoopInvariant;
8256 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
8257 LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L);
8258 if (LD == LoopVariant)
8260 LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L);
8261 if (RD == LoopVariant)
8263 return (LD == LoopInvariant && RD == LoopInvariant) ?
8264 LoopInvariant : LoopComputable;
8267 // All non-instruction values are loop invariant. All instructions are loop
8268 // invariant if they are not contained in the specified loop.
8269 // Instructions are never considered invariant in the function body
8270 // (null loop) because they are defined within the "loop".
8271 if (Instruction *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue()))
8272 return (L && !L->contains(I)) ? LoopInvariant : LoopVariant;
8273 return LoopInvariant;
8274 case scCouldNotCompute:
8275 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
8277 llvm_unreachable("Unknown SCEV kind!");
8280 bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) {
8281 return getLoopDisposition(S, L) == LoopInvariant;
8284 bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) {
8285 return getLoopDisposition(S, L) == LoopComputable;
8288 ScalarEvolution::BlockDisposition
8289 ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) {
8290 auto &Values = BlockDispositions[S];
8291 for (auto &V : Values) {
8292 if (V.getPointer() == BB)
8295 Values.emplace_back(BB, DoesNotDominateBlock);
8296 BlockDisposition D = computeBlockDisposition(S, BB);
8297 auto &Values2 = BlockDispositions[S];
8298 for (auto &V : make_range(Values2.rbegin(), Values2.rend())) {
8299 if (V.getPointer() == BB) {
8307 ScalarEvolution::BlockDisposition
8308 ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) {
8309 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
8311 return ProperlyDominatesBlock;
8315 return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB);
8316 case scAddRecExpr: {
8317 // This uses a "dominates" query instead of "properly dominates" query
8318 // to test for proper dominance too, because the instruction which
8319 // produces the addrec's value is a PHI, and a PHI effectively properly
8320 // dominates its entire containing block.
8321 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
8322 if (!DT->dominates(AR->getLoop()->getHeader(), BB))
8323 return DoesNotDominateBlock;
8325 // FALL THROUGH into SCEVNAryExpr handling.
8330 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
8332 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
8334 BlockDisposition D = getBlockDisposition(*I, BB);
8335 if (D == DoesNotDominateBlock)
8336 return DoesNotDominateBlock;
8337 if (D == DominatesBlock)
8340 return Proper ? ProperlyDominatesBlock : DominatesBlock;
8343 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
8344 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
8345 BlockDisposition LD = getBlockDisposition(LHS, BB);
8346 if (LD == DoesNotDominateBlock)
8347 return DoesNotDominateBlock;
8348 BlockDisposition RD = getBlockDisposition(RHS, BB);
8349 if (RD == DoesNotDominateBlock)
8350 return DoesNotDominateBlock;
8351 return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ?
8352 ProperlyDominatesBlock : DominatesBlock;
8355 if (Instruction *I =
8356 dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) {
8357 if (I->getParent() == BB)
8358 return DominatesBlock;
8359 if (DT->properlyDominates(I->getParent(), BB))
8360 return ProperlyDominatesBlock;
8361 return DoesNotDominateBlock;
8363 return ProperlyDominatesBlock;
8364 case scCouldNotCompute:
8365 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
8367 llvm_unreachable("Unknown SCEV kind!");
8370 bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) {
8371 return getBlockDisposition(S, BB) >= DominatesBlock;
8374 bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) {
8375 return getBlockDisposition(S, BB) == ProperlyDominatesBlock;
8379 // Search for a SCEV expression node within an expression tree.
8380 // Implements SCEVTraversal::Visitor.
8385 SCEVSearch(const SCEV *N): Node(N), IsFound(false) {}
8387 bool follow(const SCEV *S) {
8388 IsFound |= (S == Node);
8391 bool isDone() const { return IsFound; }
8395 bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const {
8396 SCEVSearch Search(Op);
8397 visitAll(S, Search);
8398 return Search.IsFound;
8401 void ScalarEvolution::forgetMemoizedResults(const SCEV *S) {
8402 ValuesAtScopes.erase(S);
8403 LoopDispositions.erase(S);
8404 BlockDispositions.erase(S);
8405 UnsignedRanges.erase(S);
8406 SignedRanges.erase(S);
8408 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
8409 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end(); I != E; ) {
8410 BackedgeTakenInfo &BEInfo = I->second;
8411 if (BEInfo.hasOperand(S, this)) {
8413 BackedgeTakenCounts.erase(I++);
8420 typedef DenseMap<const Loop *, std::string> VerifyMap;
8422 /// replaceSubString - Replaces all occurrences of From in Str with To.
8423 static void replaceSubString(std::string &Str, StringRef From, StringRef To) {
8425 while ((Pos = Str.find(From, Pos)) != std::string::npos) {
8426 Str.replace(Pos, From.size(), To.data(), To.size());
8431 /// getLoopBackedgeTakenCounts - Helper method for verifyAnalysis.
8433 getLoopBackedgeTakenCounts(Loop *L, VerifyMap &Map, ScalarEvolution &SE) {
8434 for (Loop::reverse_iterator I = L->rbegin(), E = L->rend(); I != E; ++I) {
8435 getLoopBackedgeTakenCounts(*I, Map, SE); // recurse.
8437 std::string &S = Map[L];
8439 raw_string_ostream OS(S);
8440 SE.getBackedgeTakenCount(L)->print(OS);
8442 // false and 0 are semantically equivalent. This can happen in dead loops.
8443 replaceSubString(OS.str(), "false", "0");
8444 // Remove wrap flags, their use in SCEV is highly fragile.
8445 // FIXME: Remove this when SCEV gets smarter about them.
8446 replaceSubString(OS.str(), "<nw>", "");
8447 replaceSubString(OS.str(), "<nsw>", "");
8448 replaceSubString(OS.str(), "<nuw>", "");
8453 void ScalarEvolution::verifyAnalysis() const {
8457 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
8459 // Gather stringified backedge taken counts for all loops using SCEV's caches.
8460 // FIXME: It would be much better to store actual values instead of strings,
8461 // but SCEV pointers will change if we drop the caches.
8462 VerifyMap BackedgeDumpsOld, BackedgeDumpsNew;
8463 for (LoopInfo::reverse_iterator I = LI->rbegin(), E = LI->rend(); I != E; ++I)
8464 getLoopBackedgeTakenCounts(*I, BackedgeDumpsOld, SE);
8466 // Gather stringified backedge taken counts for all loops without using
8469 for (LoopInfo::reverse_iterator I = LI->rbegin(), E = LI->rend(); I != E; ++I)
8470 getLoopBackedgeTakenCounts(*I, BackedgeDumpsNew, SE);
8472 // Now compare whether they're the same with and without caches. This allows
8473 // verifying that no pass changed the cache.
8474 assert(BackedgeDumpsOld.size() == BackedgeDumpsNew.size() &&
8475 "New loops suddenly appeared!");
8477 for (VerifyMap::iterator OldI = BackedgeDumpsOld.begin(),
8478 OldE = BackedgeDumpsOld.end(),
8479 NewI = BackedgeDumpsNew.begin();
8480 OldI != OldE; ++OldI, ++NewI) {
8481 assert(OldI->first == NewI->first && "Loop order changed!");
8483 // Compare the stringified SCEVs. We don't care if undef backedgetaken count
8485 // FIXME: We currently ignore SCEV changes from/to CouldNotCompute. This
8486 // means that a pass is buggy or SCEV has to learn a new pattern but is
8487 // usually not harmful.
8488 if (OldI->second != NewI->second &&
8489 OldI->second.find("undef") == std::string::npos &&
8490 NewI->second.find("undef") == std::string::npos &&
8491 OldI->second != "***COULDNOTCOMPUTE***" &&
8492 NewI->second != "***COULDNOTCOMPUTE***") {
8493 dbgs() << "SCEVValidator: SCEV for loop '"
8494 << OldI->first->getHeader()->getName()
8495 << "' changed from '" << OldI->second
8496 << "' to '" << NewI->second << "'!\n";
8501 // TODO: Verify more things.