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 const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op,
1330 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1331 "This is not an extending conversion!");
1332 assert(isSCEVable(Ty) &&
1333 "This is not a conversion to a SCEVable type!");
1334 Ty = getEffectiveSCEVType(Ty);
1336 // Fold if the operand is constant.
1337 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1339 cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(), Ty)));
1341 // zext(zext(x)) --> zext(x)
1342 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1343 return getZeroExtendExpr(SZ->getOperand(), Ty);
1345 // Before doing any expensive analysis, check to see if we've already
1346 // computed a SCEV for this Op and Ty.
1347 FoldingSetNodeID ID;
1348 ID.AddInteger(scZeroExtend);
1352 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1354 // zext(trunc(x)) --> zext(x) or x or trunc(x)
1355 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1356 // It's possible the bits taken off by the truncate were all zero bits. If
1357 // so, we should be able to simplify this further.
1358 const SCEV *X = ST->getOperand();
1359 ConstantRange CR = getUnsignedRange(X);
1360 unsigned TruncBits = getTypeSizeInBits(ST->getType());
1361 unsigned NewBits = getTypeSizeInBits(Ty);
1362 if (CR.truncate(TruncBits).zeroExtend(NewBits).contains(
1363 CR.zextOrTrunc(NewBits)))
1364 return getTruncateOrZeroExtend(X, Ty);
1367 // If the input value is a chrec scev, and we can prove that the value
1368 // did not overflow the old, smaller, value, we can zero extend all of the
1369 // operands (often constants). This allows analysis of something like
1370 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
1371 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1372 if (AR->isAffine()) {
1373 const SCEV *Start = AR->getStart();
1374 const SCEV *Step = AR->getStepRecurrence(*this);
1375 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1376 const Loop *L = AR->getLoop();
1378 // If we have special knowledge that this addrec won't overflow,
1379 // we don't need to do any further analysis.
1380 if (AR->getNoWrapFlags(SCEV::FlagNUW))
1381 return getAddRecExpr(
1382 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1383 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1385 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1386 // Note that this serves two purposes: It filters out loops that are
1387 // simply not analyzable, and it covers the case where this code is
1388 // being called from within backedge-taken count analysis, such that
1389 // attempting to ask for the backedge-taken count would likely result
1390 // in infinite recursion. In the later case, the analysis code will
1391 // cope with a conservative value, and it will take care to purge
1392 // that value once it has finished.
1393 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1394 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1395 // Manually compute the final value for AR, checking for
1398 // Check whether the backedge-taken count can be losslessly casted to
1399 // the addrec's type. The count is always unsigned.
1400 const SCEV *CastedMaxBECount =
1401 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1402 const SCEV *RecastedMaxBECount =
1403 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1404 if (MaxBECount == RecastedMaxBECount) {
1405 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1406 // Check whether Start+Step*MaxBECount has no unsigned overflow.
1407 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step);
1408 const SCEV *ZAdd = getZeroExtendExpr(getAddExpr(Start, ZMul), WideTy);
1409 const SCEV *WideStart = getZeroExtendExpr(Start, WideTy);
1410 const SCEV *WideMaxBECount =
1411 getZeroExtendExpr(CastedMaxBECount, WideTy);
1412 const SCEV *OperandExtendedAdd =
1413 getAddExpr(WideStart,
1414 getMulExpr(WideMaxBECount,
1415 getZeroExtendExpr(Step, WideTy)));
1416 if (ZAdd == OperandExtendedAdd) {
1417 // Cache knowledge of AR NUW, which is propagated to this AddRec.
1418 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1419 // Return the expression with the addrec on the outside.
1420 return getAddRecExpr(
1421 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1422 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1424 // Similar to above, only this time treat the step value as signed.
1425 // This covers loops that count down.
1426 OperandExtendedAdd =
1427 getAddExpr(WideStart,
1428 getMulExpr(WideMaxBECount,
1429 getSignExtendExpr(Step, WideTy)));
1430 if (ZAdd == OperandExtendedAdd) {
1431 // Cache knowledge of AR NW, which is propagated to this AddRec.
1432 // Negative step causes unsigned wrap, but it still can't self-wrap.
1433 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1434 // Return the expression with the addrec on the outside.
1435 return getAddRecExpr(
1436 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1437 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1441 // If the backedge is guarded by a comparison with the pre-inc value
1442 // the addrec is safe. Also, if the entry is guarded by a comparison
1443 // with the start value and the backedge is guarded by a comparison
1444 // with the post-inc value, the addrec is safe.
1445 if (isKnownPositive(Step)) {
1446 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
1447 getUnsignedRange(Step).getUnsignedMax());
1448 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
1449 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) &&
1450 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT,
1451 AR->getPostIncExpr(*this), N))) {
1452 // Cache knowledge of AR NUW, which is propagated to this AddRec.
1453 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1454 // Return the expression with the addrec on the outside.
1455 return getAddRecExpr(
1456 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1457 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1459 } else if (isKnownNegative(Step)) {
1460 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
1461 getSignedRange(Step).getSignedMin());
1462 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) ||
1463 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) &&
1464 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT,
1465 AR->getPostIncExpr(*this), N))) {
1466 // Cache knowledge of AR NW, which is propagated to this AddRec.
1467 // Negative step causes unsigned wrap, but it still can't self-wrap.
1468 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1469 // Return the expression with the addrec on the outside.
1470 return getAddRecExpr(
1471 getExtendAddRecStart<SCEVZeroExtendExpr>(AR, Ty, this),
1472 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1478 // The cast wasn't folded; create an explicit cast node.
1479 // Recompute the insert position, as it may have been invalidated.
1480 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1481 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
1483 UniqueSCEVs.InsertNode(S, IP);
1487 const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op,
1489 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1490 "This is not an extending conversion!");
1491 assert(isSCEVable(Ty) &&
1492 "This is not a conversion to a SCEVable type!");
1493 Ty = getEffectiveSCEVType(Ty);
1495 // Fold if the operand is constant.
1496 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1498 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), Ty)));
1500 // sext(sext(x)) --> sext(x)
1501 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1502 return getSignExtendExpr(SS->getOperand(), Ty);
1504 // sext(zext(x)) --> zext(x)
1505 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1506 return getZeroExtendExpr(SZ->getOperand(), Ty);
1508 // Before doing any expensive analysis, check to see if we've already
1509 // computed a SCEV for this Op and Ty.
1510 FoldingSetNodeID ID;
1511 ID.AddInteger(scSignExtend);
1515 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1517 // If the input value is provably positive, build a zext instead.
1518 if (isKnownNonNegative(Op))
1519 return getZeroExtendExpr(Op, Ty);
1521 // sext(trunc(x)) --> sext(x) or x or trunc(x)
1522 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1523 // It's possible the bits taken off by the truncate were all sign bits. If
1524 // so, we should be able to simplify this further.
1525 const SCEV *X = ST->getOperand();
1526 ConstantRange CR = getSignedRange(X);
1527 unsigned TruncBits = getTypeSizeInBits(ST->getType());
1528 unsigned NewBits = getTypeSizeInBits(Ty);
1529 if (CR.truncate(TruncBits).signExtend(NewBits).contains(
1530 CR.sextOrTrunc(NewBits)))
1531 return getTruncateOrSignExtend(X, Ty);
1534 // sext(C1 + (C2 * x)) --> C1 + sext(C2 * x) if C1 < C2
1535 if (auto SA = dyn_cast<SCEVAddExpr>(Op)) {
1536 if (SA->getNumOperands() == 2) {
1537 auto SC1 = dyn_cast<SCEVConstant>(SA->getOperand(0));
1538 auto SMul = dyn_cast<SCEVMulExpr>(SA->getOperand(1));
1540 if (auto SC2 = dyn_cast<SCEVConstant>(SMul->getOperand(0))) {
1541 const APInt &C1 = SC1->getValue()->getValue();
1542 const APInt &C2 = SC2->getValue()->getValue();
1543 if (C1.isStrictlyPositive() && C2.isStrictlyPositive() &&
1544 C2.ugt(C1) && C2.isPowerOf2())
1545 return getAddExpr(getSignExtendExpr(SC1, Ty),
1546 getSignExtendExpr(SMul, Ty));
1551 // If the input value is a chrec scev, and we can prove that the value
1552 // did not overflow the old, smaller, value, we can sign extend all of the
1553 // operands (often constants). This allows analysis of something like
1554 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
1555 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1556 if (AR->isAffine()) {
1557 const SCEV *Start = AR->getStart();
1558 const SCEV *Step = AR->getStepRecurrence(*this);
1559 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1560 const Loop *L = AR->getLoop();
1562 // If we have special knowledge that this addrec won't overflow,
1563 // we don't need to do any further analysis.
1564 if (AR->getNoWrapFlags(SCEV::FlagNSW))
1565 return getAddRecExpr(
1566 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1567 getSignExtendExpr(Step, Ty), L, SCEV::FlagNSW);
1569 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1570 // Note that this serves two purposes: It filters out loops that are
1571 // simply not analyzable, and it covers the case where this code is
1572 // being called from within backedge-taken count analysis, such that
1573 // attempting to ask for the backedge-taken count would likely result
1574 // in infinite recursion. In the later case, the analysis code will
1575 // cope with a conservative value, and it will take care to purge
1576 // that value once it has finished.
1577 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1578 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1579 // Manually compute the final value for AR, checking for
1582 // Check whether the backedge-taken count can be losslessly casted to
1583 // the addrec's type. The count is always unsigned.
1584 const SCEV *CastedMaxBECount =
1585 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1586 const SCEV *RecastedMaxBECount =
1587 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1588 if (MaxBECount == RecastedMaxBECount) {
1589 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1590 // Check whether Start+Step*MaxBECount has no signed overflow.
1591 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
1592 const SCEV *SAdd = getSignExtendExpr(getAddExpr(Start, SMul), WideTy);
1593 const SCEV *WideStart = getSignExtendExpr(Start, WideTy);
1594 const SCEV *WideMaxBECount =
1595 getZeroExtendExpr(CastedMaxBECount, WideTy);
1596 const SCEV *OperandExtendedAdd =
1597 getAddExpr(WideStart,
1598 getMulExpr(WideMaxBECount,
1599 getSignExtendExpr(Step, WideTy)));
1600 if (SAdd == OperandExtendedAdd) {
1601 // Cache knowledge of AR NSW, which is propagated to this AddRec.
1602 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1603 // Return the expression with the addrec on the outside.
1604 return getAddRecExpr(
1605 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1606 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1608 // Similar to above, only this time treat the step value as unsigned.
1609 // This covers loops that count up with an unsigned step.
1610 OperandExtendedAdd =
1611 getAddExpr(WideStart,
1612 getMulExpr(WideMaxBECount,
1613 getZeroExtendExpr(Step, WideTy)));
1614 if (SAdd == OperandExtendedAdd) {
1615 // If AR wraps around then
1617 // abs(Step) * MaxBECount > unsigned-max(AR->getType())
1618 // => SAdd != OperandExtendedAdd
1620 // Thus (AR is not NW => SAdd != OperandExtendedAdd) <=>
1621 // (SAdd == OperandExtendedAdd => AR is NW)
1623 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1625 // Return the expression with the addrec on the outside.
1626 return getAddRecExpr(
1627 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1628 getZeroExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1632 // If the backedge is guarded by a comparison with the pre-inc value
1633 // the addrec is safe. Also, if the entry is guarded by a comparison
1634 // with the start value and the backedge is guarded by a comparison
1635 // with the post-inc value, the addrec is safe.
1636 ICmpInst::Predicate Pred;
1637 const SCEV *OverflowLimit =
1638 getSignedOverflowLimitForStep(Step, &Pred, this);
1639 if (OverflowLimit &&
1640 (isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) ||
1641 (isLoopEntryGuardedByCond(L, Pred, Start, OverflowLimit) &&
1642 isLoopBackedgeGuardedByCond(L, Pred, AR->getPostIncExpr(*this),
1644 // Cache knowledge of AR NSW, then propagate NSW to the wide AddRec.
1645 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1646 return getAddRecExpr(
1647 getExtendAddRecStart<SCEVSignExtendExpr>(AR, Ty, this),
1648 getSignExtendExpr(Step, Ty), L, AR->getNoWrapFlags());
1651 // If Start and Step are constants, check if we can apply this
1653 // sext{C1,+,C2} --> C1 + sext{0,+,C2} if C1 < C2
1654 auto SC1 = dyn_cast<SCEVConstant>(Start);
1655 auto SC2 = dyn_cast<SCEVConstant>(Step);
1657 const APInt &C1 = SC1->getValue()->getValue();
1658 const APInt &C2 = SC2->getValue()->getValue();
1659 if (C1.isStrictlyPositive() && C2.isStrictlyPositive() && C2.ugt(C1) &&
1661 Start = getSignExtendExpr(Start, Ty);
1662 const SCEV *NewAR = getAddRecExpr(getConstant(AR->getType(), 0), Step,
1663 L, AR->getNoWrapFlags());
1664 return getAddExpr(Start, getSignExtendExpr(NewAR, Ty));
1669 // The cast wasn't folded; create an explicit cast node.
1670 // Recompute the insert position, as it may have been invalidated.
1671 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1672 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
1674 UniqueSCEVs.InsertNode(S, IP);
1678 /// getAnyExtendExpr - Return a SCEV for the given operand extended with
1679 /// unspecified bits out to the given type.
1681 const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
1683 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1684 "This is not an extending conversion!");
1685 assert(isSCEVable(Ty) &&
1686 "This is not a conversion to a SCEVable type!");
1687 Ty = getEffectiveSCEVType(Ty);
1689 // Sign-extend negative constants.
1690 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1691 if (SC->getValue()->getValue().isNegative())
1692 return getSignExtendExpr(Op, Ty);
1694 // Peel off a truncate cast.
1695 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
1696 const SCEV *NewOp = T->getOperand();
1697 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
1698 return getAnyExtendExpr(NewOp, Ty);
1699 return getTruncateOrNoop(NewOp, Ty);
1702 // Next try a zext cast. If the cast is folded, use it.
1703 const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
1704 if (!isa<SCEVZeroExtendExpr>(ZExt))
1707 // Next try a sext cast. If the cast is folded, use it.
1708 const SCEV *SExt = getSignExtendExpr(Op, Ty);
1709 if (!isa<SCEVSignExtendExpr>(SExt))
1712 // Force the cast to be folded into the operands of an addrec.
1713 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
1714 SmallVector<const SCEV *, 4> Ops;
1715 for (const SCEV *Op : AR->operands())
1716 Ops.push_back(getAnyExtendExpr(Op, Ty));
1717 return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW);
1720 // If the expression is obviously signed, use the sext cast value.
1721 if (isa<SCEVSMaxExpr>(Op))
1724 // Absent any other information, use the zext cast value.
1728 /// CollectAddOperandsWithScales - Process the given Ops list, which is
1729 /// a list of operands to be added under the given scale, update the given
1730 /// map. This is a helper function for getAddRecExpr. As an example of
1731 /// what it does, given a sequence of operands that would form an add
1732 /// expression like this:
1734 /// m + n + 13 + (A * (o + p + (B * (q + m + 29)))) + r + (-1 * r)
1736 /// where A and B are constants, update the map with these values:
1738 /// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
1740 /// and add 13 + A*B*29 to AccumulatedConstant.
1741 /// This will allow getAddRecExpr to produce this:
1743 /// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
1745 /// This form often exposes folding opportunities that are hidden in
1746 /// the original operand list.
1748 /// Return true iff it appears that any interesting folding opportunities
1749 /// may be exposed. This helps getAddRecExpr short-circuit extra work in
1750 /// the common case where no interesting opportunities are present, and
1751 /// is also used as a check to avoid infinite recursion.
1754 CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
1755 SmallVectorImpl<const SCEV *> &NewOps,
1756 APInt &AccumulatedConstant,
1757 const SCEV *const *Ops, size_t NumOperands,
1759 ScalarEvolution &SE) {
1760 bool Interesting = false;
1762 // Iterate over the add operands. They are sorted, with constants first.
1764 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1766 // Pull a buried constant out to the outside.
1767 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
1769 AccumulatedConstant += Scale * C->getValue()->getValue();
1772 // Next comes everything else. We're especially interested in multiplies
1773 // here, but they're in the middle, so just visit the rest with one loop.
1774 for (; i != NumOperands; ++i) {
1775 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
1776 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
1778 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue();
1779 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
1780 // A multiplication of a constant with another add; recurse.
1781 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1));
1783 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1784 Add->op_begin(), Add->getNumOperands(),
1787 // A multiplication of a constant with some other value. Update
1789 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
1790 const SCEV *Key = SE.getMulExpr(MulOps);
1791 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1792 M.insert(std::make_pair(Key, NewScale));
1794 NewOps.push_back(Pair.first->first);
1796 Pair.first->second += NewScale;
1797 // The map already had an entry for this value, which may indicate
1798 // a folding opportunity.
1803 // An ordinary operand. Update the map.
1804 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1805 M.insert(std::make_pair(Ops[i], Scale));
1807 NewOps.push_back(Pair.first->first);
1809 Pair.first->second += Scale;
1810 // The map already had an entry for this value, which may indicate
1811 // a folding opportunity.
1821 struct APIntCompare {
1822 bool operator()(const APInt &LHS, const APInt &RHS) const {
1823 return LHS.ult(RHS);
1828 // We're trying to construct a SCEV of type `Type' with `Ops' as operands and
1829 // `OldFlags' as can't-wrap behavior. Infer a more aggressive set of
1830 // can't-overflow flags for the operation if possible.
1831 static SCEV::NoWrapFlags
1832 StrengthenNoWrapFlags(ScalarEvolution *SE, SCEVTypes Type,
1833 const SmallVectorImpl<const SCEV *> &Ops,
1834 SCEV::NoWrapFlags OldFlags) {
1835 using namespace std::placeholders;
1838 Type == scAddExpr || Type == scAddRecExpr || Type == scMulExpr;
1840 assert(CanAnalyze && "don't call from other places!");
1842 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
1843 SCEV::NoWrapFlags SignOrUnsignWrap =
1844 ScalarEvolution::maskFlags(OldFlags, SignOrUnsignMask);
1846 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
1847 auto IsKnownNonNegative =
1848 std::bind(std::mem_fn(&ScalarEvolution::isKnownNonNegative), SE, _1);
1850 if (SignOrUnsignWrap == SCEV::FlagNSW &&
1851 std::all_of(Ops.begin(), Ops.end(), IsKnownNonNegative))
1852 return ScalarEvolution::setFlags(OldFlags,
1853 (SCEV::NoWrapFlags)SignOrUnsignMask);
1858 /// getAddExpr - Get a canonical add expression, or something simpler if
1860 const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
1861 SCEV::NoWrapFlags Flags) {
1862 assert(!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) &&
1863 "only nuw or nsw allowed");
1864 assert(!Ops.empty() && "Cannot get empty add!");
1865 if (Ops.size() == 1) return Ops[0];
1867 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
1868 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1869 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
1870 "SCEVAddExpr operand types don't match!");
1873 Flags = StrengthenNoWrapFlags(this, scAddExpr, Ops, Flags);
1875 // Sort by complexity, this groups all similar expression types together.
1876 GroupByComplexity(Ops, LI);
1878 // If there are any constants, fold them together.
1880 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1882 assert(Idx < Ops.size());
1883 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1884 // We found two constants, fold them together!
1885 Ops[0] = getConstant(LHSC->getValue()->getValue() +
1886 RHSC->getValue()->getValue());
1887 if (Ops.size() == 2) return Ops[0];
1888 Ops.erase(Ops.begin()+1); // Erase the folded element
1889 LHSC = cast<SCEVConstant>(Ops[0]);
1892 // If we are left with a constant zero being added, strip it off.
1893 if (LHSC->getValue()->isZero()) {
1894 Ops.erase(Ops.begin());
1898 if (Ops.size() == 1) return Ops[0];
1901 // Okay, check to see if the same value occurs in the operand list more than
1902 // once. If so, merge them together into an multiply expression. Since we
1903 // sorted the list, these values are required to be adjacent.
1904 Type *Ty = Ops[0]->getType();
1905 bool FoundMatch = false;
1906 for (unsigned i = 0, e = Ops.size(); i != e-1; ++i)
1907 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
1908 // Scan ahead to count how many equal operands there are.
1910 while (i+Count != e && Ops[i+Count] == Ops[i])
1912 // Merge the values into a multiply.
1913 const SCEV *Scale = getConstant(Ty, Count);
1914 const SCEV *Mul = getMulExpr(Scale, Ops[i]);
1915 if (Ops.size() == Count)
1918 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count);
1919 --i; e -= Count - 1;
1923 return getAddExpr(Ops, Flags);
1925 // Check for truncates. If all the operands are truncated from the same
1926 // type, see if factoring out the truncate would permit the result to be
1927 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
1928 // if the contents of the resulting outer trunc fold to something simple.
1929 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
1930 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
1931 Type *DstType = Trunc->getType();
1932 Type *SrcType = Trunc->getOperand()->getType();
1933 SmallVector<const SCEV *, 8> LargeOps;
1935 // Check all the operands to see if they can be represented in the
1936 // source type of the truncate.
1937 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1938 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
1939 if (T->getOperand()->getType() != SrcType) {
1943 LargeOps.push_back(T->getOperand());
1944 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1945 LargeOps.push_back(getAnyExtendExpr(C, SrcType));
1946 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
1947 SmallVector<const SCEV *, 8> LargeMulOps;
1948 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
1949 if (const SCEVTruncateExpr *T =
1950 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
1951 if (T->getOperand()->getType() != SrcType) {
1955 LargeMulOps.push_back(T->getOperand());
1956 } else if (const SCEVConstant *C =
1957 dyn_cast<SCEVConstant>(M->getOperand(j))) {
1958 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType));
1965 LargeOps.push_back(getMulExpr(LargeMulOps));
1972 // Evaluate the expression in the larger type.
1973 const SCEV *Fold = getAddExpr(LargeOps, Flags);
1974 // If it folds to something simple, use it. Otherwise, don't.
1975 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
1976 return getTruncateExpr(Fold, DstType);
1980 // Skip past any other cast SCEVs.
1981 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
1984 // If there are add operands they would be next.
1985 if (Idx < Ops.size()) {
1986 bool DeletedAdd = false;
1987 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
1988 // If we have an add, expand the add operands onto the end of the operands
1990 Ops.erase(Ops.begin()+Idx);
1991 Ops.append(Add->op_begin(), Add->op_end());
1995 // If we deleted at least one add, we added operands to the end of the list,
1996 // and they are not necessarily sorted. Recurse to resort and resimplify
1997 // any operands we just acquired.
1999 return getAddExpr(Ops);
2002 // Skip over the add expression until we get to a multiply.
2003 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
2006 // Check to see if there are any folding opportunities present with
2007 // operands multiplied by constant values.
2008 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
2009 uint64_t BitWidth = getTypeSizeInBits(Ty);
2010 DenseMap<const SCEV *, APInt> M;
2011 SmallVector<const SCEV *, 8> NewOps;
2012 APInt AccumulatedConstant(BitWidth, 0);
2013 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
2014 Ops.data(), Ops.size(),
2015 APInt(BitWidth, 1), *this)) {
2016 // Some interesting folding opportunity is present, so its worthwhile to
2017 // re-generate the operands list. Group the operands by constant scale,
2018 // to avoid multiplying by the same constant scale multiple times.
2019 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
2020 for (SmallVectorImpl<const SCEV *>::const_iterator I = NewOps.begin(),
2021 E = NewOps.end(); I != E; ++I)
2022 MulOpLists[M.find(*I)->second].push_back(*I);
2023 // Re-generate the operands list.
2025 if (AccumulatedConstant != 0)
2026 Ops.push_back(getConstant(AccumulatedConstant));
2027 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator
2028 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I)
2030 Ops.push_back(getMulExpr(getConstant(I->first),
2031 getAddExpr(I->second)));
2033 return getConstant(Ty, 0);
2034 if (Ops.size() == 1)
2036 return getAddExpr(Ops);
2040 // If we are adding something to a multiply expression, make sure the
2041 // something is not already an operand of the multiply. If so, merge it into
2043 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
2044 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
2045 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
2046 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
2047 if (isa<SCEVConstant>(MulOpSCEV))
2049 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
2050 if (MulOpSCEV == Ops[AddOp]) {
2051 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
2052 const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
2053 if (Mul->getNumOperands() != 2) {
2054 // If the multiply has more than two operands, we must get the
2056 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
2057 Mul->op_begin()+MulOp);
2058 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
2059 InnerMul = getMulExpr(MulOps);
2061 const SCEV *One = getConstant(Ty, 1);
2062 const SCEV *AddOne = getAddExpr(One, InnerMul);
2063 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV);
2064 if (Ops.size() == 2) return OuterMul;
2066 Ops.erase(Ops.begin()+AddOp);
2067 Ops.erase(Ops.begin()+Idx-1);
2069 Ops.erase(Ops.begin()+Idx);
2070 Ops.erase(Ops.begin()+AddOp-1);
2072 Ops.push_back(OuterMul);
2073 return getAddExpr(Ops);
2076 // Check this multiply against other multiplies being added together.
2077 for (unsigned OtherMulIdx = Idx+1;
2078 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
2080 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
2081 // If MulOp occurs in OtherMul, we can fold the two multiplies
2083 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
2084 OMulOp != e; ++OMulOp)
2085 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
2086 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
2087 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
2088 if (Mul->getNumOperands() != 2) {
2089 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
2090 Mul->op_begin()+MulOp);
2091 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
2092 InnerMul1 = getMulExpr(MulOps);
2094 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
2095 if (OtherMul->getNumOperands() != 2) {
2096 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
2097 OtherMul->op_begin()+OMulOp);
2098 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end());
2099 InnerMul2 = getMulExpr(MulOps);
2101 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
2102 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
2103 if (Ops.size() == 2) return OuterMul;
2104 Ops.erase(Ops.begin()+Idx);
2105 Ops.erase(Ops.begin()+OtherMulIdx-1);
2106 Ops.push_back(OuterMul);
2107 return getAddExpr(Ops);
2113 // If there are any add recurrences in the operands list, see if any other
2114 // added values are loop invariant. If so, we can fold them into the
2116 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2119 // Scan over all recurrences, trying to fold loop invariants into them.
2120 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
2121 // Scan all of the other operands to this add and add them to the vector if
2122 // they are loop invariant w.r.t. the recurrence.
2123 SmallVector<const SCEV *, 8> LIOps;
2124 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2125 const Loop *AddRecLoop = AddRec->getLoop();
2126 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2127 if (isLoopInvariant(Ops[i], AddRecLoop)) {
2128 LIOps.push_back(Ops[i]);
2129 Ops.erase(Ops.begin()+i);
2133 // If we found some loop invariants, fold them into the recurrence.
2134 if (!LIOps.empty()) {
2135 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
2136 LIOps.push_back(AddRec->getStart());
2138 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
2140 AddRecOps[0] = getAddExpr(LIOps);
2142 // Build the new addrec. Propagate the NUW and NSW flags if both the
2143 // outer add and the inner addrec are guaranteed to have no overflow.
2144 // Always propagate NW.
2145 Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW));
2146 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags);
2148 // If all of the other operands were loop invariant, we are done.
2149 if (Ops.size() == 1) return NewRec;
2151 // Otherwise, add the folded AddRec by the non-invariant parts.
2152 for (unsigned i = 0;; ++i)
2153 if (Ops[i] == AddRec) {
2157 return getAddExpr(Ops);
2160 // Okay, if there weren't any loop invariants to be folded, check to see if
2161 // there are multiple AddRec's with the same loop induction variable being
2162 // added together. If so, we can fold them.
2163 for (unsigned OtherIdx = Idx+1;
2164 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2166 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
2167 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L>
2168 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
2170 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2172 if (const SCEVAddRecExpr *OtherAddRec =
2173 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]))
2174 if (OtherAddRec->getLoop() == AddRecLoop) {
2175 for (unsigned i = 0, e = OtherAddRec->getNumOperands();
2177 if (i >= AddRecOps.size()) {
2178 AddRecOps.append(OtherAddRec->op_begin()+i,
2179 OtherAddRec->op_end());
2182 AddRecOps[i] = getAddExpr(AddRecOps[i],
2183 OtherAddRec->getOperand(i));
2185 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2187 // Step size has changed, so we cannot guarantee no self-wraparound.
2188 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap);
2189 return getAddExpr(Ops);
2192 // Otherwise couldn't fold anything into this recurrence. Move onto the
2196 // Okay, it looks like we really DO need an add expr. Check to see if we
2197 // already have one, otherwise create a new one.
2198 FoldingSetNodeID ID;
2199 ID.AddInteger(scAddExpr);
2200 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2201 ID.AddPointer(Ops[i]);
2204 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2206 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2207 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2208 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator),
2210 UniqueSCEVs.InsertNode(S, IP);
2212 S->setNoWrapFlags(Flags);
2216 static uint64_t umul_ov(uint64_t i, uint64_t j, bool &Overflow) {
2218 if (j > 1 && k / j != i) Overflow = true;
2222 /// Compute the result of "n choose k", the binomial coefficient. If an
2223 /// intermediate computation overflows, Overflow will be set and the return will
2224 /// be garbage. Overflow is not cleared on absence of overflow.
2225 static uint64_t Choose(uint64_t n, uint64_t k, bool &Overflow) {
2226 // We use the multiplicative formula:
2227 // n(n-1)(n-2)...(n-(k-1)) / k(k-1)(k-2)...1 .
2228 // At each iteration, we take the n-th term of the numeral and divide by the
2229 // (k-n)th term of the denominator. This division will always produce an
2230 // integral result, and helps reduce the chance of overflow in the
2231 // intermediate computations. However, we can still overflow even when the
2232 // final result would fit.
2234 if (n == 0 || n == k) return 1;
2235 if (k > n) return 0;
2241 for (uint64_t i = 1; i <= k; ++i) {
2242 r = umul_ov(r, n-(i-1), Overflow);
2248 /// Determine if any of the operands in this SCEV are a constant or if
2249 /// any of the add or multiply expressions in this SCEV contain a constant.
2250 static bool containsConstantSomewhere(const SCEV *StartExpr) {
2251 SmallVector<const SCEV *, 4> Ops;
2252 Ops.push_back(StartExpr);
2253 while (!Ops.empty()) {
2254 const SCEV *CurrentExpr = Ops.pop_back_val();
2255 if (isa<SCEVConstant>(*CurrentExpr))
2258 if (isa<SCEVAddExpr>(*CurrentExpr) || isa<SCEVMulExpr>(*CurrentExpr)) {
2259 const auto *CurrentNAry = cast<SCEVNAryExpr>(CurrentExpr);
2260 Ops.append(CurrentNAry->op_begin(), CurrentNAry->op_end());
2266 /// getMulExpr - Get a canonical multiply expression, or something simpler if
2268 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
2269 SCEV::NoWrapFlags Flags) {
2270 assert(Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) &&
2271 "only nuw or nsw allowed");
2272 assert(!Ops.empty() && "Cannot get empty mul!");
2273 if (Ops.size() == 1) return Ops[0];
2275 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2276 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2277 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2278 "SCEVMulExpr operand types don't match!");
2281 Flags = StrengthenNoWrapFlags(this, scMulExpr, Ops, Flags);
2283 // Sort by complexity, this groups all similar expression types together.
2284 GroupByComplexity(Ops, LI);
2286 // If there are any constants, fold them together.
2288 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2290 // C1*(C2+V) -> C1*C2 + C1*V
2291 if (Ops.size() == 2)
2292 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
2293 // If any of Add's ops are Adds or Muls with a constant,
2294 // apply this transformation as well.
2295 if (Add->getNumOperands() == 2)
2296 if (containsConstantSomewhere(Add))
2297 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
2298 getMulExpr(LHSC, Add->getOperand(1)));
2301 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2302 // We found two constants, fold them together!
2303 ConstantInt *Fold = ConstantInt::get(getContext(),
2304 LHSC->getValue()->getValue() *
2305 RHSC->getValue()->getValue());
2306 Ops[0] = getConstant(Fold);
2307 Ops.erase(Ops.begin()+1); // Erase the folded element
2308 if (Ops.size() == 1) return Ops[0];
2309 LHSC = cast<SCEVConstant>(Ops[0]);
2312 // If we are left with a constant one being multiplied, strip it off.
2313 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
2314 Ops.erase(Ops.begin());
2316 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
2317 // If we have a multiply of zero, it will always be zero.
2319 } else if (Ops[0]->isAllOnesValue()) {
2320 // If we have a mul by -1 of an add, try distributing the -1 among the
2322 if (Ops.size() == 2) {
2323 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
2324 SmallVector<const SCEV *, 4> NewOps;
2325 bool AnyFolded = false;
2326 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(),
2327 E = Add->op_end(); I != E; ++I) {
2328 const SCEV *Mul = getMulExpr(Ops[0], *I);
2329 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
2330 NewOps.push_back(Mul);
2333 return getAddExpr(NewOps);
2335 else if (const SCEVAddRecExpr *
2336 AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) {
2337 // Negation preserves a recurrence's no self-wrap property.
2338 SmallVector<const SCEV *, 4> Operands;
2339 for (SCEVAddRecExpr::op_iterator I = AddRec->op_begin(),
2340 E = AddRec->op_end(); I != E; ++I) {
2341 Operands.push_back(getMulExpr(Ops[0], *I));
2343 return getAddRecExpr(Operands, AddRec->getLoop(),
2344 AddRec->getNoWrapFlags(SCEV::FlagNW));
2349 if (Ops.size() == 1)
2353 // Skip over the add expression until we get to a multiply.
2354 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
2357 // If there are mul operands inline them all into this expression.
2358 if (Idx < Ops.size()) {
2359 bool DeletedMul = false;
2360 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
2361 // If we have an mul, expand the mul operands onto the end of the operands
2363 Ops.erase(Ops.begin()+Idx);
2364 Ops.append(Mul->op_begin(), Mul->op_end());
2368 // If we deleted at least one mul, we added operands to the end of the list,
2369 // and they are not necessarily sorted. Recurse to resort and resimplify
2370 // any operands we just acquired.
2372 return getMulExpr(Ops);
2375 // If there are any add recurrences in the operands list, see if any other
2376 // added values are loop invariant. If so, we can fold them into the
2378 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2381 // Scan over all recurrences, trying to fold loop invariants into them.
2382 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
2383 // Scan all of the other operands to this mul and add them to the vector if
2384 // they are loop invariant w.r.t. the recurrence.
2385 SmallVector<const SCEV *, 8> LIOps;
2386 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2387 const Loop *AddRecLoop = AddRec->getLoop();
2388 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2389 if (isLoopInvariant(Ops[i], AddRecLoop)) {
2390 LIOps.push_back(Ops[i]);
2391 Ops.erase(Ops.begin()+i);
2395 // If we found some loop invariants, fold them into the recurrence.
2396 if (!LIOps.empty()) {
2397 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
2398 SmallVector<const SCEV *, 4> NewOps;
2399 NewOps.reserve(AddRec->getNumOperands());
2400 const SCEV *Scale = getMulExpr(LIOps);
2401 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
2402 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
2404 // Build the new addrec. Propagate the NUW and NSW flags if both the
2405 // outer mul and the inner addrec are guaranteed to have no overflow.
2407 // No self-wrap cannot be guaranteed after changing the step size, but
2408 // will be inferred if either NUW or NSW is true.
2409 Flags = AddRec->getNoWrapFlags(clearFlags(Flags, SCEV::FlagNW));
2410 const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, Flags);
2412 // If all of the other operands were loop invariant, we are done.
2413 if (Ops.size() == 1) return NewRec;
2415 // Otherwise, multiply the folded AddRec by the non-invariant parts.
2416 for (unsigned i = 0;; ++i)
2417 if (Ops[i] == AddRec) {
2421 return getMulExpr(Ops);
2424 // Okay, if there weren't any loop invariants to be folded, check to see if
2425 // there are multiple AddRec's with the same loop induction variable being
2426 // multiplied together. If so, we can fold them.
2428 // {A1,+,A2,+,...,+,An}<L> * {B1,+,B2,+,...,+,Bn}<L>
2429 // = {x=1 in [ sum y=x..2x [ sum z=max(y-x, y-n)..min(x,n) [
2430 // choose(x, 2x)*choose(2x-y, x-z)*A_{y-z}*B_z
2431 // ]]],+,...up to x=2n}.
2432 // Note that the arguments to choose() are always integers with values
2433 // known at compile time, never SCEV objects.
2435 // The implementation avoids pointless extra computations when the two
2436 // addrec's are of different length (mathematically, it's equivalent to
2437 // an infinite stream of zeros on the right).
2438 bool OpsModified = false;
2439 for (unsigned OtherIdx = Idx+1;
2440 OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2442 const SCEVAddRecExpr *OtherAddRec =
2443 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]);
2444 if (!OtherAddRec || OtherAddRec->getLoop() != AddRecLoop)
2447 bool Overflow = false;
2448 Type *Ty = AddRec->getType();
2449 bool LargerThan64Bits = getTypeSizeInBits(Ty) > 64;
2450 SmallVector<const SCEV*, 7> AddRecOps;
2451 for (int x = 0, xe = AddRec->getNumOperands() +
2452 OtherAddRec->getNumOperands() - 1; x != xe && !Overflow; ++x) {
2453 const SCEV *Term = getConstant(Ty, 0);
2454 for (int y = x, ye = 2*x+1; y != ye && !Overflow; ++y) {
2455 uint64_t Coeff1 = Choose(x, 2*x - y, Overflow);
2456 for (int z = std::max(y-x, y-(int)AddRec->getNumOperands()+1),
2457 ze = std::min(x+1, (int)OtherAddRec->getNumOperands());
2458 z < ze && !Overflow; ++z) {
2459 uint64_t Coeff2 = Choose(2*x - y, x-z, Overflow);
2461 if (LargerThan64Bits)
2462 Coeff = umul_ov(Coeff1, Coeff2, Overflow);
2464 Coeff = Coeff1*Coeff2;
2465 const SCEV *CoeffTerm = getConstant(Ty, Coeff);
2466 const SCEV *Term1 = AddRec->getOperand(y-z);
2467 const SCEV *Term2 = OtherAddRec->getOperand(z);
2468 Term = getAddExpr(Term, getMulExpr(CoeffTerm, Term1,Term2));
2471 AddRecOps.push_back(Term);
2474 const SCEV *NewAddRec = getAddRecExpr(AddRecOps, AddRec->getLoop(),
2476 if (Ops.size() == 2) return NewAddRec;
2477 Ops[Idx] = NewAddRec;
2478 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2480 AddRec = dyn_cast<SCEVAddRecExpr>(NewAddRec);
2486 return getMulExpr(Ops);
2488 // Otherwise couldn't fold anything into this recurrence. Move onto the
2492 // Okay, it looks like we really DO need an mul expr. Check to see if we
2493 // already have one, otherwise create a new one.
2494 FoldingSetNodeID ID;
2495 ID.AddInteger(scMulExpr);
2496 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2497 ID.AddPointer(Ops[i]);
2500 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2502 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2503 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2504 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
2506 UniqueSCEVs.InsertNode(S, IP);
2508 S->setNoWrapFlags(Flags);
2512 /// getUDivExpr - Get a canonical unsigned division expression, or something
2513 /// simpler if possible.
2514 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
2516 assert(getEffectiveSCEVType(LHS->getType()) ==
2517 getEffectiveSCEVType(RHS->getType()) &&
2518 "SCEVUDivExpr operand types don't match!");
2520 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
2521 if (RHSC->getValue()->equalsInt(1))
2522 return LHS; // X udiv 1 --> x
2523 // If the denominator is zero, the result of the udiv is undefined. Don't
2524 // try to analyze it, because the resolution chosen here may differ from
2525 // the resolution chosen in other parts of the compiler.
2526 if (!RHSC->getValue()->isZero()) {
2527 // Determine if the division can be folded into the operands of
2529 // TODO: Generalize this to non-constants by using known-bits information.
2530 Type *Ty = LHS->getType();
2531 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
2532 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1;
2533 // For non-power-of-two values, effectively round the value up to the
2534 // nearest power of two.
2535 if (!RHSC->getValue()->getValue().isPowerOf2())
2537 IntegerType *ExtTy =
2538 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
2539 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
2540 if (const SCEVConstant *Step =
2541 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) {
2542 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
2543 const APInt &StepInt = Step->getValue()->getValue();
2544 const APInt &DivInt = RHSC->getValue()->getValue();
2545 if (!StepInt.urem(DivInt) &&
2546 getZeroExtendExpr(AR, ExtTy) ==
2547 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2548 getZeroExtendExpr(Step, ExtTy),
2549 AR->getLoop(), SCEV::FlagAnyWrap)) {
2550 SmallVector<const SCEV *, 4> Operands;
2551 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i)
2552 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS));
2553 return getAddRecExpr(Operands, AR->getLoop(),
2556 /// Get a canonical UDivExpr for a recurrence.
2557 /// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0.
2558 // We can currently only fold X%N if X is constant.
2559 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(AR->getStart());
2560 if (StartC && !DivInt.urem(StepInt) &&
2561 getZeroExtendExpr(AR, ExtTy) ==
2562 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2563 getZeroExtendExpr(Step, ExtTy),
2564 AR->getLoop(), SCEV::FlagAnyWrap)) {
2565 const APInt &StartInt = StartC->getValue()->getValue();
2566 const APInt &StartRem = StartInt.urem(StepInt);
2568 LHS = getAddRecExpr(getConstant(StartInt - StartRem), Step,
2569 AR->getLoop(), SCEV::FlagNW);
2572 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
2573 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
2574 SmallVector<const SCEV *, 4> Operands;
2575 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i)
2576 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy));
2577 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
2578 // Find an operand that's safely divisible.
2579 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
2580 const SCEV *Op = M->getOperand(i);
2581 const SCEV *Div = getUDivExpr(Op, RHSC);
2582 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
2583 Operands = SmallVector<const SCEV *, 4>(M->op_begin(),
2586 return getMulExpr(Operands);
2590 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
2591 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) {
2592 SmallVector<const SCEV *, 4> Operands;
2593 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i)
2594 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy));
2595 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
2597 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
2598 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
2599 if (isa<SCEVUDivExpr>(Op) ||
2600 getMulExpr(Op, RHS) != A->getOperand(i))
2602 Operands.push_back(Op);
2604 if (Operands.size() == A->getNumOperands())
2605 return getAddExpr(Operands);
2609 // Fold if both operands are constant.
2610 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
2611 Constant *LHSCV = LHSC->getValue();
2612 Constant *RHSCV = RHSC->getValue();
2613 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
2619 FoldingSetNodeID ID;
2620 ID.AddInteger(scUDivExpr);
2624 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2625 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
2627 UniqueSCEVs.InsertNode(S, IP);
2631 static const APInt gcd(const SCEVConstant *C1, const SCEVConstant *C2) {
2632 APInt A = C1->getValue()->getValue().abs();
2633 APInt B = C2->getValue()->getValue().abs();
2634 uint32_t ABW = A.getBitWidth();
2635 uint32_t BBW = B.getBitWidth();
2642 return APIntOps::GreatestCommonDivisor(A, B);
2645 /// getUDivExactExpr - Get a canonical unsigned division expression, or
2646 /// something simpler if possible. There is no representation for an exact udiv
2647 /// in SCEV IR, but we can attempt to remove factors from the LHS and RHS.
2648 /// We can't do this when it's not exact because the udiv may be clearing bits.
2649 const SCEV *ScalarEvolution::getUDivExactExpr(const SCEV *LHS,
2651 // TODO: we could try to find factors in all sorts of things, but for now we
2652 // just deal with u/exact (multiply, constant). See SCEVDivision towards the
2653 // end of this file for inspiration.
2655 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(LHS);
2657 return getUDivExpr(LHS, RHS);
2659 if (const SCEVConstant *RHSCst = dyn_cast<SCEVConstant>(RHS)) {
2660 // If the mulexpr multiplies by a constant, then that constant must be the
2661 // first element of the mulexpr.
2662 if (const SCEVConstant *LHSCst =
2663 dyn_cast<SCEVConstant>(Mul->getOperand(0))) {
2664 if (LHSCst == RHSCst) {
2665 SmallVector<const SCEV *, 2> Operands;
2666 Operands.append(Mul->op_begin() + 1, Mul->op_end());
2667 return getMulExpr(Operands);
2670 // We can't just assume that LHSCst divides RHSCst cleanly, it could be
2671 // that there's a factor provided by one of the other terms. We need to
2673 APInt Factor = gcd(LHSCst, RHSCst);
2674 if (!Factor.isIntN(1)) {
2675 LHSCst = cast<SCEVConstant>(
2676 getConstant(LHSCst->getValue()->getValue().udiv(Factor)));
2677 RHSCst = cast<SCEVConstant>(
2678 getConstant(RHSCst->getValue()->getValue().udiv(Factor)));
2679 SmallVector<const SCEV *, 2> Operands;
2680 Operands.push_back(LHSCst);
2681 Operands.append(Mul->op_begin() + 1, Mul->op_end());
2682 LHS = getMulExpr(Operands);
2684 Mul = dyn_cast<SCEVMulExpr>(LHS);
2686 return getUDivExactExpr(LHS, RHS);
2691 for (int i = 0, e = Mul->getNumOperands(); i != e; ++i) {
2692 if (Mul->getOperand(i) == RHS) {
2693 SmallVector<const SCEV *, 2> Operands;
2694 Operands.append(Mul->op_begin(), Mul->op_begin() + i);
2695 Operands.append(Mul->op_begin() + i + 1, Mul->op_end());
2696 return getMulExpr(Operands);
2700 return getUDivExpr(LHS, RHS);
2703 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2704 /// Simplify the expression as much as possible.
2705 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step,
2707 SCEV::NoWrapFlags Flags) {
2708 SmallVector<const SCEV *, 4> Operands;
2709 Operands.push_back(Start);
2710 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
2711 if (StepChrec->getLoop() == L) {
2712 Operands.append(StepChrec->op_begin(), StepChrec->op_end());
2713 return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW));
2716 Operands.push_back(Step);
2717 return getAddRecExpr(Operands, L, Flags);
2720 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2721 /// Simplify the expression as much as possible.
2723 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
2724 const Loop *L, SCEV::NoWrapFlags Flags) {
2725 if (Operands.size() == 1) return Operands[0];
2727 Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
2728 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
2729 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy &&
2730 "SCEVAddRecExpr operand types don't match!");
2731 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2732 assert(isLoopInvariant(Operands[i], L) &&
2733 "SCEVAddRecExpr operand is not loop-invariant!");
2736 if (Operands.back()->isZero()) {
2737 Operands.pop_back();
2738 return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0} --> X
2741 // It's tempting to want to call getMaxBackedgeTakenCount count here and
2742 // use that information to infer NUW and NSW flags. However, computing a
2743 // BE count requires calling getAddRecExpr, so we may not yet have a
2744 // meaningful BE count at this point (and if we don't, we'd be stuck
2745 // with a SCEVCouldNotCompute as the cached BE count).
2747 Flags = StrengthenNoWrapFlags(this, scAddRecExpr, Operands, Flags);
2749 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
2750 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
2751 const Loop *NestedLoop = NestedAR->getLoop();
2752 if (L->contains(NestedLoop) ?
2753 (L->getLoopDepth() < NestedLoop->getLoopDepth()) :
2754 (!NestedLoop->contains(L) &&
2755 DT->dominates(L->getHeader(), NestedLoop->getHeader()))) {
2756 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
2757 NestedAR->op_end());
2758 Operands[0] = NestedAR->getStart();
2759 // AddRecs require their operands be loop-invariant with respect to their
2760 // loops. Don't perform this transformation if it would break this
2762 bool AllInvariant = true;
2763 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2764 if (!isLoopInvariant(Operands[i], L)) {
2765 AllInvariant = false;
2769 // Create a recurrence for the outer loop with the same step size.
2771 // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the
2772 // inner recurrence has the same property.
2773 SCEV::NoWrapFlags OuterFlags =
2774 maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags());
2776 NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags);
2777 AllInvariant = true;
2778 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i)
2779 if (!isLoopInvariant(NestedOperands[i], NestedLoop)) {
2780 AllInvariant = false;
2784 // Ok, both add recurrences are valid after the transformation.
2786 // The inner recurrence keeps its NW flag but only keeps NUW/NSW if
2787 // the outer recurrence has the same property.
2788 SCEV::NoWrapFlags InnerFlags =
2789 maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags);
2790 return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags);
2793 // Reset Operands to its original state.
2794 Operands[0] = NestedAR;
2798 // Okay, it looks like we really DO need an addrec expr. Check to see if we
2799 // already have one, otherwise create a new one.
2800 FoldingSetNodeID ID;
2801 ID.AddInteger(scAddRecExpr);
2802 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2803 ID.AddPointer(Operands[i]);
2807 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2809 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size());
2810 std::uninitialized_copy(Operands.begin(), Operands.end(), O);
2811 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator),
2812 O, Operands.size(), L);
2813 UniqueSCEVs.InsertNode(S, IP);
2815 S->setNoWrapFlags(Flags);
2819 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
2821 SmallVector<const SCEV *, 2> Ops;
2824 return getSMaxExpr(Ops);
2828 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2829 assert(!Ops.empty() && "Cannot get empty smax!");
2830 if (Ops.size() == 1) return Ops[0];
2832 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2833 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2834 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2835 "SCEVSMaxExpr operand types don't match!");
2838 // Sort by complexity, this groups all similar expression types together.
2839 GroupByComplexity(Ops, LI);
2841 // If there are any constants, fold them together.
2843 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2845 assert(Idx < Ops.size());
2846 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2847 // We found two constants, fold them together!
2848 ConstantInt *Fold = ConstantInt::get(getContext(),
2849 APIntOps::smax(LHSC->getValue()->getValue(),
2850 RHSC->getValue()->getValue()));
2851 Ops[0] = getConstant(Fold);
2852 Ops.erase(Ops.begin()+1); // Erase the folded element
2853 if (Ops.size() == 1) return Ops[0];
2854 LHSC = cast<SCEVConstant>(Ops[0]);
2857 // If we are left with a constant minimum-int, strip it off.
2858 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
2859 Ops.erase(Ops.begin());
2861 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
2862 // If we have an smax with a constant maximum-int, it will always be
2867 if (Ops.size() == 1) return Ops[0];
2870 // Find the first SMax
2871 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
2874 // Check to see if one of the operands is an SMax. If so, expand its operands
2875 // onto our operand list, and recurse to simplify.
2876 if (Idx < Ops.size()) {
2877 bool DeletedSMax = false;
2878 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
2879 Ops.erase(Ops.begin()+Idx);
2880 Ops.append(SMax->op_begin(), SMax->op_end());
2885 return getSMaxExpr(Ops);
2888 // Okay, check to see if the same value occurs in the operand list twice. If
2889 // so, delete one. Since we sorted the list, these values are required to
2891 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2892 // X smax Y smax Y --> X smax Y
2893 // X smax Y --> X, if X is always greater than Y
2894 if (Ops[i] == Ops[i+1] ||
2895 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) {
2896 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2898 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) {
2899 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2903 if (Ops.size() == 1) return Ops[0];
2905 assert(!Ops.empty() && "Reduced smax down to nothing!");
2907 // Okay, it looks like we really DO need an smax expr. Check to see if we
2908 // already have one, otherwise create a new one.
2909 FoldingSetNodeID ID;
2910 ID.AddInteger(scSMaxExpr);
2911 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2912 ID.AddPointer(Ops[i]);
2914 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2915 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2916 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2917 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator),
2919 UniqueSCEVs.InsertNode(S, IP);
2923 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
2925 SmallVector<const SCEV *, 2> Ops;
2928 return getUMaxExpr(Ops);
2932 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2933 assert(!Ops.empty() && "Cannot get empty umax!");
2934 if (Ops.size() == 1) return Ops[0];
2936 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2937 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2938 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2939 "SCEVUMaxExpr operand types don't match!");
2942 // Sort by complexity, this groups all similar expression types together.
2943 GroupByComplexity(Ops, LI);
2945 // If there are any constants, fold them together.
2947 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2949 assert(Idx < Ops.size());
2950 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2951 // We found two constants, fold them together!
2952 ConstantInt *Fold = ConstantInt::get(getContext(),
2953 APIntOps::umax(LHSC->getValue()->getValue(),
2954 RHSC->getValue()->getValue()));
2955 Ops[0] = getConstant(Fold);
2956 Ops.erase(Ops.begin()+1); // Erase the folded element
2957 if (Ops.size() == 1) return Ops[0];
2958 LHSC = cast<SCEVConstant>(Ops[0]);
2961 // If we are left with a constant minimum-int, strip it off.
2962 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
2963 Ops.erase(Ops.begin());
2965 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
2966 // If we have an umax with a constant maximum-int, it will always be
2971 if (Ops.size() == 1) return Ops[0];
2974 // Find the first UMax
2975 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
2978 // Check to see if one of the operands is a UMax. If so, expand its operands
2979 // onto our operand list, and recurse to simplify.
2980 if (Idx < Ops.size()) {
2981 bool DeletedUMax = false;
2982 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
2983 Ops.erase(Ops.begin()+Idx);
2984 Ops.append(UMax->op_begin(), UMax->op_end());
2989 return getUMaxExpr(Ops);
2992 // Okay, check to see if the same value occurs in the operand list twice. If
2993 // so, delete one. Since we sorted the list, these values are required to
2995 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2996 // X umax Y umax Y --> X umax Y
2997 // X umax Y --> X, if X is always greater than Y
2998 if (Ops[i] == Ops[i+1] ||
2999 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) {
3000 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
3002 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) {
3003 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
3007 if (Ops.size() == 1) return Ops[0];
3009 assert(!Ops.empty() && "Reduced umax down to nothing!");
3011 // Okay, it looks like we really DO need a umax expr. Check to see if we
3012 // already have one, otherwise create a new one.
3013 FoldingSetNodeID ID;
3014 ID.AddInteger(scUMaxExpr);
3015 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
3016 ID.AddPointer(Ops[i]);
3018 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
3019 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
3020 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
3021 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator),
3023 UniqueSCEVs.InsertNode(S, IP);
3027 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
3029 // ~smax(~x, ~y) == smin(x, y).
3030 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
3033 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
3035 // ~umax(~x, ~y) == umin(x, y)
3036 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
3039 const SCEV *ScalarEvolution::getSizeOfExpr(Type *IntTy, Type *AllocTy) {
3040 // If we have DataLayout, we can bypass creating a target-independent
3041 // constant expression and then folding it back into a ConstantInt.
3042 // This is just a compile-time optimization.
3044 return getConstant(IntTy, DL->getTypeAllocSize(AllocTy));
3046 Constant *C = ConstantExpr::getSizeOf(AllocTy);
3047 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
3048 if (Constant *Folded = ConstantFoldConstantExpression(CE, DL, TLI))
3050 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
3051 assert(Ty == IntTy && "Effective SCEV type doesn't match");
3052 return getTruncateOrZeroExtend(getSCEV(C), Ty);
3055 const SCEV *ScalarEvolution::getOffsetOfExpr(Type *IntTy,
3058 // If we have DataLayout, we can bypass creating a target-independent
3059 // constant expression and then folding it back into a ConstantInt.
3060 // This is just a compile-time optimization.
3062 return getConstant(IntTy,
3063 DL->getStructLayout(STy)->getElementOffset(FieldNo));
3066 Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo);
3067 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
3068 if (Constant *Folded = ConstantFoldConstantExpression(CE, DL, TLI))
3071 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy));
3072 return getTruncateOrZeroExtend(getSCEV(C), Ty);
3075 const SCEV *ScalarEvolution::getUnknown(Value *V) {
3076 // Don't attempt to do anything other than create a SCEVUnknown object
3077 // here. createSCEV only calls getUnknown after checking for all other
3078 // interesting possibilities, and any other code that calls getUnknown
3079 // is doing so in order to hide a value from SCEV canonicalization.
3081 FoldingSetNodeID ID;
3082 ID.AddInteger(scUnknown);
3085 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
3086 assert(cast<SCEVUnknown>(S)->getValue() == V &&
3087 "Stale SCEVUnknown in uniquing map!");
3090 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
3092 FirstUnknown = cast<SCEVUnknown>(S);
3093 UniqueSCEVs.InsertNode(S, IP);
3097 //===----------------------------------------------------------------------===//
3098 // Basic SCEV Analysis and PHI Idiom Recognition Code
3101 /// isSCEVable - Test if values of the given type are analyzable within
3102 /// the SCEV framework. This primarily includes integer types, and it
3103 /// can optionally include pointer types if the ScalarEvolution class
3104 /// has access to target-specific information.
3105 bool ScalarEvolution::isSCEVable(Type *Ty) const {
3106 // Integers and pointers are always SCEVable.
3107 return Ty->isIntegerTy() || Ty->isPointerTy();
3110 /// getTypeSizeInBits - Return the size in bits of the specified type,
3111 /// for which isSCEVable must return true.
3112 uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const {
3113 assert(isSCEVable(Ty) && "Type is not SCEVable!");
3115 // If we have a DataLayout, use it!
3117 return DL->getTypeSizeInBits(Ty);
3119 // Integer types have fixed sizes.
3120 if (Ty->isIntegerTy())
3121 return Ty->getPrimitiveSizeInBits();
3123 // The only other support type is pointer. Without DataLayout, conservatively
3124 // assume pointers are 64-bit.
3125 assert(Ty->isPointerTy() && "isSCEVable permitted a non-SCEVable type!");
3129 /// getEffectiveSCEVType - Return a type with the same bitwidth as
3130 /// the given type and which represents how SCEV will treat the given
3131 /// type, for which isSCEVable must return true. For pointer types,
3132 /// this is the pointer-sized integer type.
3133 Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const {
3134 assert(isSCEVable(Ty) && "Type is not SCEVable!");
3136 if (Ty->isIntegerTy()) {
3140 // The only other support type is pointer.
3141 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
3144 return DL->getIntPtrType(Ty);
3146 // Without DataLayout, conservatively assume pointers are 64-bit.
3147 return Type::getInt64Ty(getContext());
3150 const SCEV *ScalarEvolution::getCouldNotCompute() {
3151 return &CouldNotCompute;
3155 // Helper class working with SCEVTraversal to figure out if a SCEV contains
3156 // a SCEVUnknown with null value-pointer. FindInvalidSCEVUnknown::FindOne
3157 // is set iff if find such SCEVUnknown.
3159 struct FindInvalidSCEVUnknown {
3161 FindInvalidSCEVUnknown() { FindOne = false; }
3162 bool follow(const SCEV *S) {
3163 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
3167 if (!cast<SCEVUnknown>(S)->getValue())
3174 bool isDone() const { return FindOne; }
3178 bool ScalarEvolution::checkValidity(const SCEV *S) const {
3179 FindInvalidSCEVUnknown F;
3180 SCEVTraversal<FindInvalidSCEVUnknown> ST(F);
3186 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
3187 /// expression and create a new one.
3188 const SCEV *ScalarEvolution::getSCEV(Value *V) {
3189 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
3191 ValueExprMapType::iterator I = ValueExprMap.find_as(V);
3192 if (I != ValueExprMap.end()) {
3193 const SCEV *S = I->second;
3194 if (checkValidity(S))
3197 ValueExprMap.erase(I);
3199 const SCEV *S = createSCEV(V);
3201 // The process of creating a SCEV for V may have caused other SCEVs
3202 // to have been created, so it's necessary to insert the new entry
3203 // from scratch, rather than trying to remember the insert position
3205 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(V, this), S));
3209 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
3211 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) {
3212 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
3214 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
3216 Type *Ty = V->getType();
3217 Ty = getEffectiveSCEVType(Ty);
3218 return getMulExpr(V,
3219 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))));
3222 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
3223 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
3224 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
3226 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
3228 Type *Ty = V->getType();
3229 Ty = getEffectiveSCEVType(Ty);
3230 const SCEV *AllOnes =
3231 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
3232 return getMinusSCEV(AllOnes, V);
3235 /// getMinusSCEV - Return LHS-RHS. Minus is represented in SCEV as A+B*-1.
3236 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
3237 SCEV::NoWrapFlags Flags) {
3238 assert(!maskFlags(Flags, SCEV::FlagNUW) && "subtraction does not have NUW");
3240 // Fast path: X - X --> 0.
3242 return getConstant(LHS->getType(), 0);
3244 // X - Y --> X + -Y.
3245 // X -(nsw || nuw) Y --> X + -Y.
3246 return getAddExpr(LHS, getNegativeSCEV(RHS));
3249 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
3250 /// input value to the specified type. If the type must be extended, it is zero
3253 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty) {
3254 Type *SrcTy = V->getType();
3255 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3256 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3257 "Cannot truncate or zero extend with non-integer arguments!");
3258 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3259 return V; // No conversion
3260 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
3261 return getTruncateExpr(V, Ty);
3262 return getZeroExtendExpr(V, Ty);
3265 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
3266 /// input value to the specified type. If the type must be extended, it is sign
3269 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
3271 Type *SrcTy = V->getType();
3272 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3273 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3274 "Cannot truncate or zero extend with non-integer arguments!");
3275 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3276 return V; // No conversion
3277 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
3278 return getTruncateExpr(V, Ty);
3279 return getSignExtendExpr(V, Ty);
3282 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
3283 /// input value to the specified type. If the type must be extended, it is zero
3284 /// extended. The conversion must not be narrowing.
3286 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) {
3287 Type *SrcTy = V->getType();
3288 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3289 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3290 "Cannot noop or zero extend with non-integer arguments!");
3291 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3292 "getNoopOrZeroExtend cannot truncate!");
3293 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3294 return V; // No conversion
3295 return getZeroExtendExpr(V, Ty);
3298 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
3299 /// input value to the specified type. If the type must be extended, it is sign
3300 /// extended. The conversion must not be narrowing.
3302 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) {
3303 Type *SrcTy = V->getType();
3304 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3305 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3306 "Cannot noop or sign extend with non-integer arguments!");
3307 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3308 "getNoopOrSignExtend cannot truncate!");
3309 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3310 return V; // No conversion
3311 return getSignExtendExpr(V, Ty);
3314 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
3315 /// the input value to the specified type. If the type must be extended,
3316 /// it is extended with unspecified bits. The conversion must not be
3319 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) {
3320 Type *SrcTy = V->getType();
3321 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3322 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3323 "Cannot noop or any extend with non-integer arguments!");
3324 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3325 "getNoopOrAnyExtend cannot truncate!");
3326 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3327 return V; // No conversion
3328 return getAnyExtendExpr(V, Ty);
3331 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
3332 /// input value to the specified type. The conversion must not be widening.
3334 ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) {
3335 Type *SrcTy = V->getType();
3336 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3337 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3338 "Cannot truncate or noop with non-integer arguments!");
3339 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
3340 "getTruncateOrNoop cannot extend!");
3341 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3342 return V; // No conversion
3343 return getTruncateExpr(V, Ty);
3346 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
3347 /// the types using zero-extension, and then perform a umax operation
3349 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
3351 const SCEV *PromotedLHS = LHS;
3352 const SCEV *PromotedRHS = RHS;
3354 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
3355 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
3357 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
3359 return getUMaxExpr(PromotedLHS, PromotedRHS);
3362 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
3363 /// the types using zero-extension, and then perform a umin operation
3365 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
3367 const SCEV *PromotedLHS = LHS;
3368 const SCEV *PromotedRHS = RHS;
3370 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
3371 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
3373 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
3375 return getUMinExpr(PromotedLHS, PromotedRHS);
3378 /// getPointerBase - Transitively follow the chain of pointer-type operands
3379 /// until reaching a SCEV that does not have a single pointer operand. This
3380 /// returns a SCEVUnknown pointer for well-formed pointer-type expressions,
3381 /// but corner cases do exist.
3382 const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) {
3383 // A pointer operand may evaluate to a nonpointer expression, such as null.
3384 if (!V->getType()->isPointerTy())
3387 if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) {
3388 return getPointerBase(Cast->getOperand());
3390 else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) {
3391 const SCEV *PtrOp = nullptr;
3392 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
3394 if ((*I)->getType()->isPointerTy()) {
3395 // Cannot find the base of an expression with multiple pointer operands.
3403 return getPointerBase(PtrOp);
3408 /// PushDefUseChildren - Push users of the given Instruction
3409 /// onto the given Worklist.
3411 PushDefUseChildren(Instruction *I,
3412 SmallVectorImpl<Instruction *> &Worklist) {
3413 // Push the def-use children onto the Worklist stack.
3414 for (User *U : I->users())
3415 Worklist.push_back(cast<Instruction>(U));
3418 /// ForgetSymbolicValue - This looks up computed SCEV values for all
3419 /// instructions that depend on the given instruction and removes them from
3420 /// the ValueExprMapType map if they reference SymName. This is used during PHI
3423 ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) {
3424 SmallVector<Instruction *, 16> Worklist;
3425 PushDefUseChildren(PN, Worklist);
3427 SmallPtrSet<Instruction *, 8> Visited;
3429 while (!Worklist.empty()) {
3430 Instruction *I = Worklist.pop_back_val();
3431 if (!Visited.insert(I).second)
3434 ValueExprMapType::iterator It =
3435 ValueExprMap.find_as(static_cast<Value *>(I));
3436 if (It != ValueExprMap.end()) {
3437 const SCEV *Old = It->second;
3439 // Short-circuit the def-use traversal if the symbolic name
3440 // ceases to appear in expressions.
3441 if (Old != SymName && !hasOperand(Old, SymName))
3444 // SCEVUnknown for a PHI either means that it has an unrecognized
3445 // structure, it's a PHI that's in the progress of being computed
3446 // by createNodeForPHI, or it's a single-value PHI. In the first case,
3447 // additional loop trip count information isn't going to change anything.
3448 // In the second case, createNodeForPHI will perform the necessary
3449 // updates on its own when it gets to that point. In the third, we do
3450 // want to forget the SCEVUnknown.
3451 if (!isa<PHINode>(I) ||
3452 !isa<SCEVUnknown>(Old) ||
3453 (I != PN && Old == SymName)) {
3454 forgetMemoizedResults(Old);
3455 ValueExprMap.erase(It);
3459 PushDefUseChildren(I, Worklist);
3463 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
3464 /// a loop header, making it a potential recurrence, or it doesn't.
3466 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
3467 if (const Loop *L = LI->getLoopFor(PN->getParent()))
3468 if (L->getHeader() == PN->getParent()) {
3469 // The loop may have multiple entrances or multiple exits; we can analyze
3470 // this phi as an addrec if it has a unique entry value and a unique
3472 Value *BEValueV = nullptr, *StartValueV = nullptr;
3473 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
3474 Value *V = PN->getIncomingValue(i);
3475 if (L->contains(PN->getIncomingBlock(i))) {
3478 } else if (BEValueV != V) {
3482 } else if (!StartValueV) {
3484 } else if (StartValueV != V) {
3485 StartValueV = nullptr;
3489 if (BEValueV && StartValueV) {
3490 // While we are analyzing this PHI node, handle its value symbolically.
3491 const SCEV *SymbolicName = getUnknown(PN);
3492 assert(ValueExprMap.find_as(PN) == ValueExprMap.end() &&
3493 "PHI node already processed?");
3494 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
3496 // Using this symbolic name for the PHI, analyze the value coming around
3498 const SCEV *BEValue = getSCEV(BEValueV);
3500 // NOTE: If BEValue is loop invariant, we know that the PHI node just
3501 // has a special value for the first iteration of the loop.
3503 // If the value coming around the backedge is an add with the symbolic
3504 // value we just inserted, then we found a simple induction variable!
3505 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
3506 // If there is a single occurrence of the symbolic value, replace it
3507 // with a recurrence.
3508 unsigned FoundIndex = Add->getNumOperands();
3509 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3510 if (Add->getOperand(i) == SymbolicName)
3511 if (FoundIndex == e) {
3516 if (FoundIndex != Add->getNumOperands()) {
3517 // Create an add with everything but the specified operand.
3518 SmallVector<const SCEV *, 8> Ops;
3519 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3520 if (i != FoundIndex)
3521 Ops.push_back(Add->getOperand(i));
3522 const SCEV *Accum = getAddExpr(Ops);
3524 // This is not a valid addrec if the step amount is varying each
3525 // loop iteration, but is not itself an addrec in this loop.
3526 if (isLoopInvariant(Accum, L) ||
3527 (isa<SCEVAddRecExpr>(Accum) &&
3528 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
3529 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
3531 // If the increment doesn't overflow, then neither the addrec nor
3532 // the post-increment will overflow.
3533 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) {
3534 if (OBO->hasNoUnsignedWrap())
3535 Flags = setFlags(Flags, SCEV::FlagNUW);
3536 if (OBO->hasNoSignedWrap())
3537 Flags = setFlags(Flags, SCEV::FlagNSW);
3538 } else if (GEPOperator *GEP = dyn_cast<GEPOperator>(BEValueV)) {
3539 // If the increment is an inbounds GEP, then we know the address
3540 // space cannot be wrapped around. We cannot make any guarantee
3541 // about signed or unsigned overflow because pointers are
3542 // unsigned but we may have a negative index from the base
3543 // pointer. We can guarantee that no unsigned wrap occurs if the
3544 // indices form a positive value.
3545 if (GEP->isInBounds()) {
3546 Flags = setFlags(Flags, SCEV::FlagNW);
3548 const SCEV *Ptr = getSCEV(GEP->getPointerOperand());
3549 if (isKnownPositive(getMinusSCEV(getSCEV(GEP), Ptr)))
3550 Flags = setFlags(Flags, SCEV::FlagNUW);
3553 // We cannot transfer nuw and nsw flags from subtraction
3554 // operations -- sub nuw X, Y is not the same as add nuw X, -Y
3558 const SCEV *StartVal = getSCEV(StartValueV);
3559 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
3561 // Since the no-wrap flags are on the increment, they apply to the
3562 // post-incremented value as well.
3563 if (isLoopInvariant(Accum, L))
3564 (void)getAddRecExpr(getAddExpr(StartVal, Accum),
3567 // Okay, for the entire analysis of this edge we assumed the PHI
3568 // to be symbolic. We now need to go back and purge all of the
3569 // entries for the scalars that use the symbolic expression.
3570 ForgetSymbolicName(PN, SymbolicName);
3571 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3575 } else if (const SCEVAddRecExpr *AddRec =
3576 dyn_cast<SCEVAddRecExpr>(BEValue)) {
3577 // Otherwise, this could be a loop like this:
3578 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
3579 // In this case, j = {1,+,1} and BEValue is j.
3580 // Because the other in-value of i (0) fits the evolution of BEValue
3581 // i really is an addrec evolution.
3582 if (AddRec->getLoop() == L && AddRec->isAffine()) {
3583 const SCEV *StartVal = getSCEV(StartValueV);
3585 // If StartVal = j.start - j.stride, we can use StartVal as the
3586 // initial step of the addrec evolution.
3587 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
3588 AddRec->getOperand(1))) {
3589 // FIXME: For constant StartVal, we should be able to infer
3591 const SCEV *PHISCEV =
3592 getAddRecExpr(StartVal, AddRec->getOperand(1), L,
3595 // Okay, for the entire analysis of this edge we assumed the PHI
3596 // to be symbolic. We now need to go back and purge all of the
3597 // entries for the scalars that use the symbolic expression.
3598 ForgetSymbolicName(PN, SymbolicName);
3599 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3607 // If the PHI has a single incoming value, follow that value, unless the
3608 // PHI's incoming blocks are in a different loop, in which case doing so
3609 // risks breaking LCSSA form. Instcombine would normally zap these, but
3610 // it doesn't have DominatorTree information, so it may miss cases.
3611 if (Value *V = SimplifyInstruction(PN, DL, TLI, DT, AC))
3612 if (LI->replacementPreservesLCSSAForm(PN, V))
3615 // If it's not a loop phi, we can't handle it yet.
3616 return getUnknown(PN);
3619 /// createNodeForGEP - Expand GEP instructions into add and multiply
3620 /// operations. This allows them to be analyzed by regular SCEV code.
3622 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
3623 Type *IntPtrTy = getEffectiveSCEVType(GEP->getType());
3624 Value *Base = GEP->getOperand(0);
3625 // Don't attempt to analyze GEPs over unsized objects.
3626 if (!Base->getType()->getPointerElementType()->isSized())
3627 return getUnknown(GEP);
3629 // Don't blindly transfer the inbounds flag from the GEP instruction to the
3630 // Add expression, because the Instruction may be guarded by control flow
3631 // and the no-overflow bits may not be valid for the expression in any
3633 SCEV::NoWrapFlags Wrap = GEP->isInBounds() ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
3635 const SCEV *TotalOffset = getConstant(IntPtrTy, 0);
3636 gep_type_iterator GTI = gep_type_begin(GEP);
3637 for (GetElementPtrInst::op_iterator I = std::next(GEP->op_begin()),
3641 // Compute the (potentially symbolic) offset in bytes for this index.
3642 if (StructType *STy = dyn_cast<StructType>(*GTI++)) {
3643 // For a struct, add the member offset.
3644 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
3645 const SCEV *FieldOffset = getOffsetOfExpr(IntPtrTy, STy, FieldNo);
3647 // Add the field offset to the running total offset.
3648 TotalOffset = getAddExpr(TotalOffset, FieldOffset);
3650 // For an array, add the element offset, explicitly scaled.
3651 const SCEV *ElementSize = getSizeOfExpr(IntPtrTy, *GTI);
3652 const SCEV *IndexS = getSCEV(Index);
3653 // Getelementptr indices are signed.
3654 IndexS = getTruncateOrSignExtend(IndexS, IntPtrTy);
3656 // Multiply the index by the element size to compute the element offset.
3657 const SCEV *LocalOffset = getMulExpr(IndexS, ElementSize, Wrap);
3659 // Add the element offset to the running total offset.
3660 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
3664 // Get the SCEV for the GEP base.
3665 const SCEV *BaseS = getSCEV(Base);
3667 // Add the total offset from all the GEP indices to the base.
3668 return getAddExpr(BaseS, TotalOffset, Wrap);
3671 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
3672 /// guaranteed to end in (at every loop iteration). It is, at the same time,
3673 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
3674 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
3676 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
3677 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3678 return C->getValue()->getValue().countTrailingZeros();
3680 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
3681 return std::min(GetMinTrailingZeros(T->getOperand()),
3682 (uint32_t)getTypeSizeInBits(T->getType()));
3684 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
3685 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3686 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3687 getTypeSizeInBits(E->getType()) : OpRes;
3690 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
3691 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3692 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3693 getTypeSizeInBits(E->getType()) : OpRes;
3696 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
3697 // The result is the min of all operands results.
3698 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3699 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3700 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3704 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
3705 // The result is the sum of all operands results.
3706 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
3707 uint32_t BitWidth = getTypeSizeInBits(M->getType());
3708 for (unsigned i = 1, e = M->getNumOperands();
3709 SumOpRes != BitWidth && i != e; ++i)
3710 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
3715 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
3716 // The result is the min of all operands results.
3717 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3718 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3719 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3723 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
3724 // The result is the min of all operands results.
3725 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3726 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3727 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3731 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
3732 // The result is the min of all operands results.
3733 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3734 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3735 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3739 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3740 // For a SCEVUnknown, ask ValueTracking.
3741 unsigned BitWidth = getTypeSizeInBits(U->getType());
3742 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3743 computeKnownBits(U->getValue(), Zeros, Ones, DL, 0, AC, nullptr, DT);
3744 return Zeros.countTrailingOnes();
3751 /// GetRangeFromMetadata - Helper method to assign a range to V from
3752 /// metadata present in the IR.
3753 static Optional<ConstantRange> GetRangeFromMetadata(Value *V) {
3754 if (Instruction *I = dyn_cast<Instruction>(V)) {
3755 if (MDNode *MD = I->getMetadata(LLVMContext::MD_range)) {
3756 ConstantRange TotalRange(
3757 cast<IntegerType>(I->getType())->getBitWidth(), false);
3759 unsigned NumRanges = MD->getNumOperands() / 2;
3760 assert(NumRanges >= 1);
3762 for (unsigned i = 0; i < NumRanges; ++i) {
3763 ConstantInt *Lower =
3764 mdconst::extract<ConstantInt>(MD->getOperand(2 * i + 0));
3765 ConstantInt *Upper =
3766 mdconst::extract<ConstantInt>(MD->getOperand(2 * i + 1));
3767 ConstantRange Range(Lower->getValue(), Upper->getValue());
3768 TotalRange = TotalRange.unionWith(Range);
3778 /// getUnsignedRange - Determine the unsigned range for a particular SCEV.
3781 ScalarEvolution::getUnsignedRange(const SCEV *S) {
3782 // See if we've computed this range already.
3783 DenseMap<const SCEV *, ConstantRange>::iterator I = UnsignedRanges.find(S);
3784 if (I != UnsignedRanges.end())
3787 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3788 return setUnsignedRange(C, ConstantRange(C->getValue()->getValue()));
3790 unsigned BitWidth = getTypeSizeInBits(S->getType());
3791 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3793 // If the value has known zeros, the maximum unsigned value will have those
3794 // known zeros as well.
3795 uint32_t TZ = GetMinTrailingZeros(S);
3797 ConservativeResult =
3798 ConstantRange(APInt::getMinValue(BitWidth),
3799 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
3801 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3802 ConstantRange X = getUnsignedRange(Add->getOperand(0));
3803 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3804 X = X.add(getUnsignedRange(Add->getOperand(i)));
3805 return setUnsignedRange(Add, ConservativeResult.intersectWith(X));
3808 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3809 ConstantRange X = getUnsignedRange(Mul->getOperand(0));
3810 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3811 X = X.multiply(getUnsignedRange(Mul->getOperand(i)));
3812 return setUnsignedRange(Mul, ConservativeResult.intersectWith(X));
3815 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3816 ConstantRange X = getUnsignedRange(SMax->getOperand(0));
3817 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3818 X = X.smax(getUnsignedRange(SMax->getOperand(i)));
3819 return setUnsignedRange(SMax, ConservativeResult.intersectWith(X));
3822 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3823 ConstantRange X = getUnsignedRange(UMax->getOperand(0));
3824 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3825 X = X.umax(getUnsignedRange(UMax->getOperand(i)));
3826 return setUnsignedRange(UMax, ConservativeResult.intersectWith(X));
3829 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3830 ConstantRange X = getUnsignedRange(UDiv->getLHS());
3831 ConstantRange Y = getUnsignedRange(UDiv->getRHS());
3832 return setUnsignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y)));
3835 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3836 ConstantRange X = getUnsignedRange(ZExt->getOperand());
3837 return setUnsignedRange(ZExt,
3838 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3841 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3842 ConstantRange X = getUnsignedRange(SExt->getOperand());
3843 return setUnsignedRange(SExt,
3844 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3847 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3848 ConstantRange X = getUnsignedRange(Trunc->getOperand());
3849 return setUnsignedRange(Trunc,
3850 ConservativeResult.intersectWith(X.truncate(BitWidth)));
3853 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3854 // If there's no unsigned wrap, the value will never be less than its
3856 if (AddRec->getNoWrapFlags(SCEV::FlagNUW))
3857 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
3858 if (!C->getValue()->isZero())
3859 ConservativeResult =
3860 ConservativeResult.intersectWith(
3861 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0)));
3863 // TODO: non-affine addrec
3864 if (AddRec->isAffine()) {
3865 Type *Ty = AddRec->getType();
3866 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3867 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3868 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3869 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3871 const SCEV *Start = AddRec->getStart();
3872 const SCEV *Step = AddRec->getStepRecurrence(*this);
3874 ConstantRange StartRange = getUnsignedRange(Start);
3875 ConstantRange StepRange = getSignedRange(Step);
3876 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3877 ConstantRange EndRange =
3878 StartRange.add(MaxBECountRange.multiply(StepRange));
3880 // Check for overflow. This must be done with ConstantRange arithmetic
3881 // because we could be called from within the ScalarEvolution overflow
3883 ConstantRange ExtStartRange = StartRange.zextOrTrunc(BitWidth*2+1);
3884 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3885 ConstantRange ExtMaxBECountRange =
3886 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3887 ConstantRange ExtEndRange = EndRange.zextOrTrunc(BitWidth*2+1);
3888 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3890 return setUnsignedRange(AddRec, ConservativeResult);
3892 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(),
3893 EndRange.getUnsignedMin());
3894 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(),
3895 EndRange.getUnsignedMax());
3896 if (Min.isMinValue() && Max.isMaxValue())
3897 return setUnsignedRange(AddRec, ConservativeResult);
3898 return setUnsignedRange(AddRec,
3899 ConservativeResult.intersectWith(ConstantRange(Min, Max+1)));
3903 return setUnsignedRange(AddRec, ConservativeResult);
3906 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3907 // Check if the IR explicitly contains !range metadata.
3908 Optional<ConstantRange> MDRange = GetRangeFromMetadata(U->getValue());
3909 if (MDRange.hasValue())
3910 ConservativeResult = ConservativeResult.intersectWith(MDRange.getValue());
3912 // For a SCEVUnknown, ask ValueTracking.
3913 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3914 computeKnownBits(U->getValue(), Zeros, Ones, DL, 0, AC, nullptr, DT);
3915 if (Ones == ~Zeros + 1)
3916 return setUnsignedRange(U, ConservativeResult);
3917 return setUnsignedRange(U,
3918 ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1)));
3921 return setUnsignedRange(S, ConservativeResult);
3924 /// getSignedRange - Determine the signed range for a particular SCEV.
3927 ScalarEvolution::getSignedRange(const SCEV *S) {
3928 // See if we've computed this range already.
3929 DenseMap<const SCEV *, ConstantRange>::iterator I = SignedRanges.find(S);
3930 if (I != SignedRanges.end())
3933 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3934 return setSignedRange(C, ConstantRange(C->getValue()->getValue()));
3936 unsigned BitWidth = getTypeSizeInBits(S->getType());
3937 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3939 // If the value has known zeros, the maximum signed value will have those
3940 // known zeros as well.
3941 uint32_t TZ = GetMinTrailingZeros(S);
3943 ConservativeResult =
3944 ConstantRange(APInt::getSignedMinValue(BitWidth),
3945 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
3947 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3948 ConstantRange X = getSignedRange(Add->getOperand(0));
3949 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3950 X = X.add(getSignedRange(Add->getOperand(i)));
3951 return setSignedRange(Add, ConservativeResult.intersectWith(X));
3954 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3955 ConstantRange X = getSignedRange(Mul->getOperand(0));
3956 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3957 X = X.multiply(getSignedRange(Mul->getOperand(i)));
3958 return setSignedRange(Mul, ConservativeResult.intersectWith(X));
3961 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3962 ConstantRange X = getSignedRange(SMax->getOperand(0));
3963 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3964 X = X.smax(getSignedRange(SMax->getOperand(i)));
3965 return setSignedRange(SMax, ConservativeResult.intersectWith(X));
3968 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3969 ConstantRange X = getSignedRange(UMax->getOperand(0));
3970 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3971 X = X.umax(getSignedRange(UMax->getOperand(i)));
3972 return setSignedRange(UMax, ConservativeResult.intersectWith(X));
3975 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3976 ConstantRange X = getSignedRange(UDiv->getLHS());
3977 ConstantRange Y = getSignedRange(UDiv->getRHS());
3978 return setSignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y)));
3981 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3982 ConstantRange X = getSignedRange(ZExt->getOperand());
3983 return setSignedRange(ZExt,
3984 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3987 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3988 ConstantRange X = getSignedRange(SExt->getOperand());
3989 return setSignedRange(SExt,
3990 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3993 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3994 ConstantRange X = getSignedRange(Trunc->getOperand());
3995 return setSignedRange(Trunc,
3996 ConservativeResult.intersectWith(X.truncate(BitWidth)));
3999 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
4000 // If there's no signed wrap, and all the operands have the same sign or
4001 // zero, the value won't ever change sign.
4002 if (AddRec->getNoWrapFlags(SCEV::FlagNSW)) {
4003 bool AllNonNeg = true;
4004 bool AllNonPos = true;
4005 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
4006 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
4007 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
4010 ConservativeResult = ConservativeResult.intersectWith(
4011 ConstantRange(APInt(BitWidth, 0),
4012 APInt::getSignedMinValue(BitWidth)));
4014 ConservativeResult = ConservativeResult.intersectWith(
4015 ConstantRange(APInt::getSignedMinValue(BitWidth),
4016 APInt(BitWidth, 1)));
4019 // TODO: non-affine addrec
4020 if (AddRec->isAffine()) {
4021 Type *Ty = AddRec->getType();
4022 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
4023 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
4024 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
4025 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
4027 const SCEV *Start = AddRec->getStart();
4028 const SCEV *Step = AddRec->getStepRecurrence(*this);
4030 ConstantRange StartRange = getSignedRange(Start);
4031 ConstantRange StepRange = getSignedRange(Step);
4032 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
4033 ConstantRange EndRange =
4034 StartRange.add(MaxBECountRange.multiply(StepRange));
4036 // Check for overflow. This must be done with ConstantRange arithmetic
4037 // because we could be called from within the ScalarEvolution overflow
4039 ConstantRange ExtStartRange = StartRange.sextOrTrunc(BitWidth*2+1);
4040 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
4041 ConstantRange ExtMaxBECountRange =
4042 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
4043 ConstantRange ExtEndRange = EndRange.sextOrTrunc(BitWidth*2+1);
4044 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
4046 return setSignedRange(AddRec, ConservativeResult);
4048 APInt Min = APIntOps::smin(StartRange.getSignedMin(),
4049 EndRange.getSignedMin());
4050 APInt Max = APIntOps::smax(StartRange.getSignedMax(),
4051 EndRange.getSignedMax());
4052 if (Min.isMinSignedValue() && Max.isMaxSignedValue())
4053 return setSignedRange(AddRec, ConservativeResult);
4054 return setSignedRange(AddRec,
4055 ConservativeResult.intersectWith(ConstantRange(Min, Max+1)));
4059 return setSignedRange(AddRec, ConservativeResult);
4062 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
4063 // Check if the IR explicitly contains !range metadata.
4064 Optional<ConstantRange> MDRange = GetRangeFromMetadata(U->getValue());
4065 if (MDRange.hasValue())
4066 ConservativeResult = ConservativeResult.intersectWith(MDRange.getValue());
4068 // For a SCEVUnknown, ask ValueTracking.
4069 if (!U->getValue()->getType()->isIntegerTy() && !DL)
4070 return setSignedRange(U, ConservativeResult);
4071 unsigned NS = ComputeNumSignBits(U->getValue(), DL, 0, AC, nullptr, DT);
4073 return setSignedRange(U, ConservativeResult);
4074 return setSignedRange(U, ConservativeResult.intersectWith(
4075 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
4076 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1)));
4079 return setSignedRange(S, ConservativeResult);
4082 /// createSCEV - We know that there is no SCEV for the specified value.
4083 /// Analyze the expression.
4085 const SCEV *ScalarEvolution::createSCEV(Value *V) {
4086 if (!isSCEVable(V->getType()))
4087 return getUnknown(V);
4089 unsigned Opcode = Instruction::UserOp1;
4090 if (Instruction *I = dyn_cast<Instruction>(V)) {
4091 Opcode = I->getOpcode();
4093 // Don't attempt to analyze instructions in blocks that aren't
4094 // reachable. Such instructions don't matter, and they aren't required
4095 // to obey basic rules for definitions dominating uses which this
4096 // analysis depends on.
4097 if (!DT->isReachableFromEntry(I->getParent()))
4098 return getUnknown(V);
4099 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
4100 Opcode = CE->getOpcode();
4101 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
4102 return getConstant(CI);
4103 else if (isa<ConstantPointerNull>(V))
4104 return getConstant(V->getType(), 0);
4105 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
4106 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee());
4108 return getUnknown(V);
4110 Operator *U = cast<Operator>(V);
4112 case Instruction::Add: {
4113 // The simple thing to do would be to just call getSCEV on both operands
4114 // and call getAddExpr with the result. However if we're looking at a
4115 // bunch of things all added together, this can be quite inefficient,
4116 // because it leads to N-1 getAddExpr calls for N ultimate operands.
4117 // Instead, gather up all the operands and make a single getAddExpr call.
4118 // LLVM IR canonical form means we need only traverse the left operands.
4120 // Don't apply this instruction's NSW or NUW flags to the new
4121 // expression. The instruction may be guarded by control flow that the
4122 // no-wrap behavior depends on. Non-control-equivalent instructions can be
4123 // mapped to the same SCEV expression, and it would be incorrect to transfer
4124 // NSW/NUW semantics to those operations.
4125 SmallVector<const SCEV *, 4> AddOps;
4126 AddOps.push_back(getSCEV(U->getOperand(1)));
4127 for (Value *Op = U->getOperand(0); ; Op = U->getOperand(0)) {
4128 unsigned Opcode = Op->getValueID() - Value::InstructionVal;
4129 if (Opcode != Instruction::Add && Opcode != Instruction::Sub)
4131 U = cast<Operator>(Op);
4132 const SCEV *Op1 = getSCEV(U->getOperand(1));
4133 if (Opcode == Instruction::Sub)
4134 AddOps.push_back(getNegativeSCEV(Op1));
4136 AddOps.push_back(Op1);
4138 AddOps.push_back(getSCEV(U->getOperand(0)));
4139 return getAddExpr(AddOps);
4141 case Instruction::Mul: {
4142 // Don't transfer NSW/NUW for the same reason as AddExpr.
4143 SmallVector<const SCEV *, 4> MulOps;
4144 MulOps.push_back(getSCEV(U->getOperand(1)));
4145 for (Value *Op = U->getOperand(0);
4146 Op->getValueID() == Instruction::Mul + Value::InstructionVal;
4147 Op = U->getOperand(0)) {
4148 U = cast<Operator>(Op);
4149 MulOps.push_back(getSCEV(U->getOperand(1)));
4151 MulOps.push_back(getSCEV(U->getOperand(0)));
4152 return getMulExpr(MulOps);
4154 case Instruction::UDiv:
4155 return getUDivExpr(getSCEV(U->getOperand(0)),
4156 getSCEV(U->getOperand(1)));
4157 case Instruction::Sub:
4158 return getMinusSCEV(getSCEV(U->getOperand(0)),
4159 getSCEV(U->getOperand(1)));
4160 case Instruction::And:
4161 // For an expression like x&255 that merely masks off the high bits,
4162 // use zext(trunc(x)) as the SCEV expression.
4163 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
4164 if (CI->isNullValue())
4165 return getSCEV(U->getOperand(1));
4166 if (CI->isAllOnesValue())
4167 return getSCEV(U->getOperand(0));
4168 const APInt &A = CI->getValue();
4170 // Instcombine's ShrinkDemandedConstant may strip bits out of
4171 // constants, obscuring what would otherwise be a low-bits mask.
4172 // Use computeKnownBits to compute what ShrinkDemandedConstant
4173 // knew about to reconstruct a low-bits mask value.
4174 unsigned LZ = A.countLeadingZeros();
4175 unsigned TZ = A.countTrailingZeros();
4176 unsigned BitWidth = A.getBitWidth();
4177 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
4178 computeKnownBits(U->getOperand(0), KnownZero, KnownOne, DL, 0, AC,
4181 APInt EffectiveMask =
4182 APInt::getLowBitsSet(BitWidth, BitWidth - LZ - TZ).shl(TZ);
4183 if ((LZ != 0 || TZ != 0) && !((~A & ~KnownZero) & EffectiveMask)) {
4184 const SCEV *MulCount = getConstant(
4185 ConstantInt::get(getContext(), APInt::getOneBitSet(BitWidth, TZ)));
4189 getUDivExactExpr(getSCEV(U->getOperand(0)), MulCount),
4190 IntegerType::get(getContext(), BitWidth - LZ - TZ)),
4197 case Instruction::Or:
4198 // If the RHS of the Or is a constant, we may have something like:
4199 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
4200 // optimizations will transparently handle this case.
4202 // In order for this transformation to be safe, the LHS must be of the
4203 // form X*(2^n) and the Or constant must be less than 2^n.
4204 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
4205 const SCEV *LHS = getSCEV(U->getOperand(0));
4206 const APInt &CIVal = CI->getValue();
4207 if (GetMinTrailingZeros(LHS) >=
4208 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
4209 // Build a plain add SCEV.
4210 const SCEV *S = getAddExpr(LHS, getSCEV(CI));
4211 // If the LHS of the add was an addrec and it has no-wrap flags,
4212 // transfer the no-wrap flags, since an or won't introduce a wrap.
4213 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
4214 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
4215 const_cast<SCEVAddRecExpr *>(NewAR)->setNoWrapFlags(
4216 OldAR->getNoWrapFlags());
4222 case Instruction::Xor:
4223 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
4224 // If the RHS of the xor is a signbit, then this is just an add.
4225 // Instcombine turns add of signbit into xor as a strength reduction step.
4226 if (CI->getValue().isSignBit())
4227 return getAddExpr(getSCEV(U->getOperand(0)),
4228 getSCEV(U->getOperand(1)));
4230 // If the RHS of xor is -1, then this is a not operation.
4231 if (CI->isAllOnesValue())
4232 return getNotSCEV(getSCEV(U->getOperand(0)));
4234 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
4235 // This is a variant of the check for xor with -1, and it handles
4236 // the case where instcombine has trimmed non-demanded bits out
4237 // of an xor with -1.
4238 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
4239 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
4240 if (BO->getOpcode() == Instruction::And &&
4241 LCI->getValue() == CI->getValue())
4242 if (const SCEVZeroExtendExpr *Z =
4243 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
4244 Type *UTy = U->getType();
4245 const SCEV *Z0 = Z->getOperand();
4246 Type *Z0Ty = Z0->getType();
4247 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
4249 // If C is a low-bits mask, the zero extend is serving to
4250 // mask off the high bits. Complement the operand and
4251 // re-apply the zext.
4252 if (APIntOps::isMask(Z0TySize, CI->getValue()))
4253 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
4255 // If C is a single bit, it may be in the sign-bit position
4256 // before the zero-extend. In this case, represent the xor
4257 // using an add, which is equivalent, and re-apply the zext.
4258 APInt Trunc = CI->getValue().trunc(Z0TySize);
4259 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
4261 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
4267 case Instruction::Shl:
4268 // Turn shift left of a constant amount into a multiply.
4269 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
4270 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
4272 // If the shift count is not less than the bitwidth, the result of
4273 // the shift is undefined. Don't try to analyze it, because the
4274 // resolution chosen here may differ from the resolution chosen in
4275 // other parts of the compiler.
4276 if (SA->getValue().uge(BitWidth))
4279 Constant *X = ConstantInt::get(getContext(),
4280 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
4281 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
4285 case Instruction::LShr:
4286 // Turn logical shift right of a constant into a unsigned divide.
4287 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
4288 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
4290 // If the shift count is not less than the bitwidth, the result of
4291 // the shift is undefined. Don't try to analyze it, because the
4292 // resolution chosen here may differ from the resolution chosen in
4293 // other parts of the compiler.
4294 if (SA->getValue().uge(BitWidth))
4297 Constant *X = ConstantInt::get(getContext(),
4298 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
4299 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
4303 case Instruction::AShr:
4304 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
4305 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
4306 if (Operator *L = dyn_cast<Operator>(U->getOperand(0)))
4307 if (L->getOpcode() == Instruction::Shl &&
4308 L->getOperand(1) == U->getOperand(1)) {
4309 uint64_t BitWidth = getTypeSizeInBits(U->getType());
4311 // If the shift count is not less than the bitwidth, the result of
4312 // the shift is undefined. Don't try to analyze it, because the
4313 // resolution chosen here may differ from the resolution chosen in
4314 // other parts of the compiler.
4315 if (CI->getValue().uge(BitWidth))
4318 uint64_t Amt = BitWidth - CI->getZExtValue();
4319 if (Amt == BitWidth)
4320 return getSCEV(L->getOperand(0)); // shift by zero --> noop
4322 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
4323 IntegerType::get(getContext(),
4329 case Instruction::Trunc:
4330 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
4332 case Instruction::ZExt:
4333 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
4335 case Instruction::SExt:
4336 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
4338 case Instruction::BitCast:
4339 // BitCasts are no-op casts so we just eliminate the cast.
4340 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
4341 return getSCEV(U->getOperand(0));
4344 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
4345 // lead to pointer expressions which cannot safely be expanded to GEPs,
4346 // because ScalarEvolution doesn't respect the GEP aliasing rules when
4347 // simplifying integer expressions.
4349 case Instruction::GetElementPtr:
4350 return createNodeForGEP(cast<GEPOperator>(U));
4352 case Instruction::PHI:
4353 return createNodeForPHI(cast<PHINode>(U));
4355 case Instruction::Select:
4356 // This could be a smax or umax that was lowered earlier.
4357 // Try to recover it.
4358 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
4359 Value *LHS = ICI->getOperand(0);
4360 Value *RHS = ICI->getOperand(1);
4361 switch (ICI->getPredicate()) {
4362 case ICmpInst::ICMP_SLT:
4363 case ICmpInst::ICMP_SLE:
4364 std::swap(LHS, RHS);
4366 case ICmpInst::ICMP_SGT:
4367 case ICmpInst::ICMP_SGE:
4368 // a >s b ? a+x : b+x -> smax(a, b)+x
4369 // a >s b ? b+x : a+x -> smin(a, b)+x
4370 if (getTypeSizeInBits(LHS->getType()) <=
4371 getTypeSizeInBits(U->getType())) {
4372 const SCEV *LS = getNoopOrSignExtend(getSCEV(LHS), U->getType());
4373 const SCEV *RS = getNoopOrSignExtend(getSCEV(RHS), U->getType());
4374 const SCEV *LA = getSCEV(U->getOperand(1));
4375 const SCEV *RA = getSCEV(U->getOperand(2));
4376 const SCEV *LDiff = getMinusSCEV(LA, LS);
4377 const SCEV *RDiff = getMinusSCEV(RA, RS);
4379 return getAddExpr(getSMaxExpr(LS, RS), LDiff);
4380 LDiff = getMinusSCEV(LA, RS);
4381 RDiff = getMinusSCEV(RA, LS);
4383 return getAddExpr(getSMinExpr(LS, RS), LDiff);
4386 case ICmpInst::ICMP_ULT:
4387 case ICmpInst::ICMP_ULE:
4388 std::swap(LHS, RHS);
4390 case ICmpInst::ICMP_UGT:
4391 case ICmpInst::ICMP_UGE:
4392 // a >u b ? a+x : b+x -> umax(a, b)+x
4393 // a >u b ? b+x : a+x -> umin(a, b)+x
4394 if (getTypeSizeInBits(LHS->getType()) <=
4395 getTypeSizeInBits(U->getType())) {
4396 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), U->getType());
4397 const SCEV *RS = getNoopOrZeroExtend(getSCEV(RHS), U->getType());
4398 const SCEV *LA = getSCEV(U->getOperand(1));
4399 const SCEV *RA = getSCEV(U->getOperand(2));
4400 const SCEV *LDiff = getMinusSCEV(LA, LS);
4401 const SCEV *RDiff = getMinusSCEV(RA, RS);
4403 return getAddExpr(getUMaxExpr(LS, RS), LDiff);
4404 LDiff = getMinusSCEV(LA, RS);
4405 RDiff = getMinusSCEV(RA, LS);
4407 return getAddExpr(getUMinExpr(LS, RS), LDiff);
4410 case ICmpInst::ICMP_NE:
4411 // n != 0 ? n+x : 1+x -> umax(n, 1)+x
4412 if (getTypeSizeInBits(LHS->getType()) <=
4413 getTypeSizeInBits(U->getType()) &&
4414 isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
4415 const SCEV *One = getConstant(U->getType(), 1);
4416 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), U->getType());
4417 const SCEV *LA = getSCEV(U->getOperand(1));
4418 const SCEV *RA = getSCEV(U->getOperand(2));
4419 const SCEV *LDiff = getMinusSCEV(LA, LS);
4420 const SCEV *RDiff = getMinusSCEV(RA, One);
4422 return getAddExpr(getUMaxExpr(One, LS), LDiff);
4425 case ICmpInst::ICMP_EQ:
4426 // n == 0 ? 1+x : n+x -> umax(n, 1)+x
4427 if (getTypeSizeInBits(LHS->getType()) <=
4428 getTypeSizeInBits(U->getType()) &&
4429 isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
4430 const SCEV *One = getConstant(U->getType(), 1);
4431 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), U->getType());
4432 const SCEV *LA = getSCEV(U->getOperand(1));
4433 const SCEV *RA = getSCEV(U->getOperand(2));
4434 const SCEV *LDiff = getMinusSCEV(LA, One);
4435 const SCEV *RDiff = getMinusSCEV(RA, LS);
4437 return getAddExpr(getUMaxExpr(One, LS), LDiff);
4445 default: // We cannot analyze this expression.
4449 return getUnknown(V);
4454 //===----------------------------------------------------------------------===//
4455 // Iteration Count Computation Code
4458 unsigned ScalarEvolution::getSmallConstantTripCount(Loop *L) {
4459 if (BasicBlock *ExitingBB = L->getExitingBlock())
4460 return getSmallConstantTripCount(L, ExitingBB);
4462 // No trip count information for multiple exits.
4466 /// getSmallConstantTripCount - Returns the maximum trip count of this loop as a
4467 /// normal unsigned value. Returns 0 if the trip count is unknown or not
4468 /// constant. Will also return 0 if the maximum trip count is very large (>=
4471 /// This "trip count" assumes that control exits via ExitingBlock. More
4472 /// precisely, it is the number of times that control may reach ExitingBlock
4473 /// before taking the branch. For loops with multiple exits, it may not be the
4474 /// number times that the loop header executes because the loop may exit
4475 /// prematurely via another branch.
4476 unsigned ScalarEvolution::getSmallConstantTripCount(Loop *L,
4477 BasicBlock *ExitingBlock) {
4478 assert(ExitingBlock && "Must pass a non-null exiting block!");
4479 assert(L->isLoopExiting(ExitingBlock) &&
4480 "Exiting block must actually branch out of the loop!");
4481 const SCEVConstant *ExitCount =
4482 dyn_cast<SCEVConstant>(getExitCount(L, ExitingBlock));
4486 ConstantInt *ExitConst = ExitCount->getValue();
4488 // Guard against huge trip counts.
4489 if (ExitConst->getValue().getActiveBits() > 32)
4492 // In case of integer overflow, this returns 0, which is correct.
4493 return ((unsigned)ExitConst->getZExtValue()) + 1;
4496 unsigned ScalarEvolution::getSmallConstantTripMultiple(Loop *L) {
4497 if (BasicBlock *ExitingBB = L->getExitingBlock())
4498 return getSmallConstantTripMultiple(L, ExitingBB);
4500 // No trip multiple information for multiple exits.
4504 /// getSmallConstantTripMultiple - Returns the largest constant divisor of the
4505 /// trip count of this loop as a normal unsigned value, if possible. This
4506 /// means that the actual trip count is always a multiple of the returned
4507 /// value (don't forget the trip count could very well be zero as well!).
4509 /// Returns 1 if the trip count is unknown or not guaranteed to be the
4510 /// multiple of a constant (which is also the case if the trip count is simply
4511 /// constant, use getSmallConstantTripCount for that case), Will also return 1
4512 /// if the trip count is very large (>= 2^32).
4514 /// As explained in the comments for getSmallConstantTripCount, this assumes
4515 /// that control exits the loop via ExitingBlock.
4517 ScalarEvolution::getSmallConstantTripMultiple(Loop *L,
4518 BasicBlock *ExitingBlock) {
4519 assert(ExitingBlock && "Must pass a non-null exiting block!");
4520 assert(L->isLoopExiting(ExitingBlock) &&
4521 "Exiting block must actually branch out of the loop!");
4522 const SCEV *ExitCount = getExitCount(L, ExitingBlock);
4523 if (ExitCount == getCouldNotCompute())
4526 // Get the trip count from the BE count by adding 1.
4527 const SCEV *TCMul = getAddExpr(ExitCount,
4528 getConstant(ExitCount->getType(), 1));
4529 // FIXME: SCEV distributes multiplication as V1*C1 + V2*C1. We could attempt
4530 // to factor simple cases.
4531 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(TCMul))
4532 TCMul = Mul->getOperand(0);
4534 const SCEVConstant *MulC = dyn_cast<SCEVConstant>(TCMul);
4538 ConstantInt *Result = MulC->getValue();
4540 // Guard against huge trip counts (this requires checking
4541 // for zero to handle the case where the trip count == -1 and the
4543 if (!Result || Result->getValue().getActiveBits() > 32 ||
4544 Result->getValue().getActiveBits() == 0)
4547 return (unsigned)Result->getZExtValue();
4550 // getExitCount - Get the expression for the number of loop iterations for which
4551 // this loop is guaranteed not to exit via ExitingBlock. Otherwise return
4552 // SCEVCouldNotCompute.
4553 const SCEV *ScalarEvolution::getExitCount(Loop *L, BasicBlock *ExitingBlock) {
4554 return getBackedgeTakenInfo(L).getExact(ExitingBlock, this);
4557 /// getBackedgeTakenCount - If the specified loop has a predictable
4558 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
4559 /// object. The backedge-taken count is the number of times the loop header
4560 /// will be branched to from within the loop. This is one less than the
4561 /// trip count of the loop, since it doesn't count the first iteration,
4562 /// when the header is branched to from outside the loop.
4564 /// Note that it is not valid to call this method on a loop without a
4565 /// loop-invariant backedge-taken count (see
4566 /// hasLoopInvariantBackedgeTakenCount).
4568 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
4569 return getBackedgeTakenInfo(L).getExact(this);
4572 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
4573 /// return the least SCEV value that is known never to be less than the
4574 /// actual backedge taken count.
4575 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
4576 return getBackedgeTakenInfo(L).getMax(this);
4579 /// PushLoopPHIs - Push PHI nodes in the header of the given loop
4580 /// onto the given Worklist.
4582 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
4583 BasicBlock *Header = L->getHeader();
4585 // Push all Loop-header PHIs onto the Worklist stack.
4586 for (BasicBlock::iterator I = Header->begin();
4587 PHINode *PN = dyn_cast<PHINode>(I); ++I)
4588 Worklist.push_back(PN);
4591 const ScalarEvolution::BackedgeTakenInfo &
4592 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
4593 // Initially insert an invalid entry for this loop. If the insertion
4594 // succeeds, proceed to actually compute a backedge-taken count and
4595 // update the value. The temporary CouldNotCompute value tells SCEV
4596 // code elsewhere that it shouldn't attempt to request a new
4597 // backedge-taken count, which could result in infinite recursion.
4598 std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
4599 BackedgeTakenCounts.insert(std::make_pair(L, BackedgeTakenInfo()));
4601 return Pair.first->second;
4603 // ComputeBackedgeTakenCount may allocate memory for its result. Inserting it
4604 // into the BackedgeTakenCounts map transfers ownership. Otherwise, the result
4605 // must be cleared in this scope.
4606 BackedgeTakenInfo Result = ComputeBackedgeTakenCount(L);
4608 if (Result.getExact(this) != getCouldNotCompute()) {
4609 assert(isLoopInvariant(Result.getExact(this), L) &&
4610 isLoopInvariant(Result.getMax(this), L) &&
4611 "Computed backedge-taken count isn't loop invariant for loop!");
4612 ++NumTripCountsComputed;
4614 else if (Result.getMax(this) == getCouldNotCompute() &&
4615 isa<PHINode>(L->getHeader()->begin())) {
4616 // Only count loops that have phi nodes as not being computable.
4617 ++NumTripCountsNotComputed;
4620 // Now that we know more about the trip count for this loop, forget any
4621 // existing SCEV values for PHI nodes in this loop since they are only
4622 // conservative estimates made without the benefit of trip count
4623 // information. This is similar to the code in forgetLoop, except that
4624 // it handles SCEVUnknown PHI nodes specially.
4625 if (Result.hasAnyInfo()) {
4626 SmallVector<Instruction *, 16> Worklist;
4627 PushLoopPHIs(L, Worklist);
4629 SmallPtrSet<Instruction *, 8> Visited;
4630 while (!Worklist.empty()) {
4631 Instruction *I = Worklist.pop_back_val();
4632 if (!Visited.insert(I).second)
4635 ValueExprMapType::iterator It =
4636 ValueExprMap.find_as(static_cast<Value *>(I));
4637 if (It != ValueExprMap.end()) {
4638 const SCEV *Old = It->second;
4640 // SCEVUnknown for a PHI either means that it has an unrecognized
4641 // structure, or it's a PHI that's in the progress of being computed
4642 // by createNodeForPHI. In the former case, additional loop trip
4643 // count information isn't going to change anything. In the later
4644 // case, createNodeForPHI will perform the necessary updates on its
4645 // own when it gets to that point.
4646 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) {
4647 forgetMemoizedResults(Old);
4648 ValueExprMap.erase(It);
4650 if (PHINode *PN = dyn_cast<PHINode>(I))
4651 ConstantEvolutionLoopExitValue.erase(PN);
4654 PushDefUseChildren(I, Worklist);
4658 // Re-lookup the insert position, since the call to
4659 // ComputeBackedgeTakenCount above could result in a
4660 // recusive call to getBackedgeTakenInfo (on a different
4661 // loop), which would invalidate the iterator computed
4663 return BackedgeTakenCounts.find(L)->second = Result;
4666 /// forgetLoop - This method should be called by the client when it has
4667 /// changed a loop in a way that may effect ScalarEvolution's ability to
4668 /// compute a trip count, or if the loop is deleted.
4669 void ScalarEvolution::forgetLoop(const Loop *L) {
4670 // Drop any stored trip count value.
4671 DenseMap<const Loop*, BackedgeTakenInfo>::iterator BTCPos =
4672 BackedgeTakenCounts.find(L);
4673 if (BTCPos != BackedgeTakenCounts.end()) {
4674 BTCPos->second.clear();
4675 BackedgeTakenCounts.erase(BTCPos);
4678 // Drop information about expressions based on loop-header PHIs.
4679 SmallVector<Instruction *, 16> Worklist;
4680 PushLoopPHIs(L, Worklist);
4682 SmallPtrSet<Instruction *, 8> Visited;
4683 while (!Worklist.empty()) {
4684 Instruction *I = Worklist.pop_back_val();
4685 if (!Visited.insert(I).second)
4688 ValueExprMapType::iterator It =
4689 ValueExprMap.find_as(static_cast<Value *>(I));
4690 if (It != ValueExprMap.end()) {
4691 forgetMemoizedResults(It->second);
4692 ValueExprMap.erase(It);
4693 if (PHINode *PN = dyn_cast<PHINode>(I))
4694 ConstantEvolutionLoopExitValue.erase(PN);
4697 PushDefUseChildren(I, Worklist);
4700 // Forget all contained loops too, to avoid dangling entries in the
4701 // ValuesAtScopes map.
4702 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
4706 /// forgetValue - This method should be called by the client when it has
4707 /// changed a value in a way that may effect its value, or which may
4708 /// disconnect it from a def-use chain linking it to a loop.
4709 void ScalarEvolution::forgetValue(Value *V) {
4710 Instruction *I = dyn_cast<Instruction>(V);
4713 // Drop information about expressions based on loop-header PHIs.
4714 SmallVector<Instruction *, 16> Worklist;
4715 Worklist.push_back(I);
4717 SmallPtrSet<Instruction *, 8> Visited;
4718 while (!Worklist.empty()) {
4719 I = Worklist.pop_back_val();
4720 if (!Visited.insert(I).second)
4723 ValueExprMapType::iterator It =
4724 ValueExprMap.find_as(static_cast<Value *>(I));
4725 if (It != ValueExprMap.end()) {
4726 forgetMemoizedResults(It->second);
4727 ValueExprMap.erase(It);
4728 if (PHINode *PN = dyn_cast<PHINode>(I))
4729 ConstantEvolutionLoopExitValue.erase(PN);
4732 PushDefUseChildren(I, Worklist);
4736 /// getExact - Get the exact loop backedge taken count considering all loop
4737 /// exits. A computable result can only be return for loops with a single exit.
4738 /// Returning the minimum taken count among all exits is incorrect because one
4739 /// of the loop's exit limit's may have been skipped. HowFarToZero assumes that
4740 /// the limit of each loop test is never skipped. This is a valid assumption as
4741 /// long as the loop exits via that test. For precise results, it is the
4742 /// caller's responsibility to specify the relevant loop exit using
4743 /// getExact(ExitingBlock, SE).
4745 ScalarEvolution::BackedgeTakenInfo::getExact(ScalarEvolution *SE) const {
4746 // If any exits were not computable, the loop is not computable.
4747 if (!ExitNotTaken.isCompleteList()) return SE->getCouldNotCompute();
4749 // We need exactly one computable exit.
4750 if (!ExitNotTaken.ExitingBlock) return SE->getCouldNotCompute();
4751 assert(ExitNotTaken.ExactNotTaken && "uninitialized not-taken info");
4753 const SCEV *BECount = nullptr;
4754 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4755 ENT != nullptr; ENT = ENT->getNextExit()) {
4757 assert(ENT->ExactNotTaken != SE->getCouldNotCompute() && "bad exit SCEV");
4760 BECount = ENT->ExactNotTaken;
4761 else if (BECount != ENT->ExactNotTaken)
4762 return SE->getCouldNotCompute();
4764 assert(BECount && "Invalid not taken count for loop exit");
4768 /// getExact - Get the exact not taken count for this loop exit.
4770 ScalarEvolution::BackedgeTakenInfo::getExact(BasicBlock *ExitingBlock,
4771 ScalarEvolution *SE) const {
4772 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4773 ENT != nullptr; ENT = ENT->getNextExit()) {
4775 if (ENT->ExitingBlock == ExitingBlock)
4776 return ENT->ExactNotTaken;
4778 return SE->getCouldNotCompute();
4781 /// getMax - Get the max backedge taken count for the loop.
4783 ScalarEvolution::BackedgeTakenInfo::getMax(ScalarEvolution *SE) const {
4784 return Max ? Max : SE->getCouldNotCompute();
4787 bool ScalarEvolution::BackedgeTakenInfo::hasOperand(const SCEV *S,
4788 ScalarEvolution *SE) const {
4789 if (Max && Max != SE->getCouldNotCompute() && SE->hasOperand(Max, S))
4792 if (!ExitNotTaken.ExitingBlock)
4795 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4796 ENT != nullptr; ENT = ENT->getNextExit()) {
4798 if (ENT->ExactNotTaken != SE->getCouldNotCompute()
4799 && SE->hasOperand(ENT->ExactNotTaken, S)) {
4806 /// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each
4807 /// computable exit into a persistent ExitNotTakenInfo array.
4808 ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo(
4809 SmallVectorImpl< std::pair<BasicBlock *, const SCEV *> > &ExitCounts,
4810 bool Complete, const SCEV *MaxCount) : Max(MaxCount) {
4813 ExitNotTaken.setIncomplete();
4815 unsigned NumExits = ExitCounts.size();
4816 if (NumExits == 0) return;
4818 ExitNotTaken.ExitingBlock = ExitCounts[0].first;
4819 ExitNotTaken.ExactNotTaken = ExitCounts[0].second;
4820 if (NumExits == 1) return;
4822 // Handle the rare case of multiple computable exits.
4823 ExitNotTakenInfo *ENT = new ExitNotTakenInfo[NumExits-1];
4825 ExitNotTakenInfo *PrevENT = &ExitNotTaken;
4826 for (unsigned i = 1; i < NumExits; ++i, PrevENT = ENT, ++ENT) {
4827 PrevENT->setNextExit(ENT);
4828 ENT->ExitingBlock = ExitCounts[i].first;
4829 ENT->ExactNotTaken = ExitCounts[i].second;
4833 /// clear - Invalidate this result and free the ExitNotTakenInfo array.
4834 void ScalarEvolution::BackedgeTakenInfo::clear() {
4835 ExitNotTaken.ExitingBlock = nullptr;
4836 ExitNotTaken.ExactNotTaken = nullptr;
4837 delete[] ExitNotTaken.getNextExit();
4840 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
4841 /// of the specified loop will execute.
4842 ScalarEvolution::BackedgeTakenInfo
4843 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
4844 SmallVector<BasicBlock *, 8> ExitingBlocks;
4845 L->getExitingBlocks(ExitingBlocks);
4847 SmallVector<std::pair<BasicBlock *, const SCEV *>, 4> ExitCounts;
4848 bool CouldComputeBECount = true;
4849 BasicBlock *Latch = L->getLoopLatch(); // may be NULL.
4850 const SCEV *MustExitMaxBECount = nullptr;
4851 const SCEV *MayExitMaxBECount = nullptr;
4853 // Compute the ExitLimit for each loop exit. Use this to populate ExitCounts
4854 // and compute maxBECount.
4855 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
4856 BasicBlock *ExitBB = ExitingBlocks[i];
4857 ExitLimit EL = ComputeExitLimit(L, ExitBB);
4859 // 1. For each exit that can be computed, add an entry to ExitCounts.
4860 // CouldComputeBECount is true only if all exits can be computed.
4861 if (EL.Exact == getCouldNotCompute())
4862 // We couldn't compute an exact value for this exit, so
4863 // we won't be able to compute an exact value for the loop.
4864 CouldComputeBECount = false;
4866 ExitCounts.push_back(std::make_pair(ExitBB, EL.Exact));
4868 // 2. Derive the loop's MaxBECount from each exit's max number of
4869 // non-exiting iterations. Partition the loop exits into two kinds:
4870 // LoopMustExits and LoopMayExits.
4872 // If the exit dominates the loop latch, it is a LoopMustExit otherwise it
4873 // is a LoopMayExit. If any computable LoopMustExit is found, then
4874 // MaxBECount is the minimum EL.Max of computable LoopMustExits. Otherwise,
4875 // MaxBECount is conservatively the maximum EL.Max, where CouldNotCompute is
4876 // considered greater than any computable EL.Max.
4877 if (EL.Max != getCouldNotCompute() && Latch &&
4878 DT->dominates(ExitBB, Latch)) {
4879 if (!MustExitMaxBECount)
4880 MustExitMaxBECount = EL.Max;
4882 MustExitMaxBECount =
4883 getUMinFromMismatchedTypes(MustExitMaxBECount, EL.Max);
4885 } else if (MayExitMaxBECount != getCouldNotCompute()) {
4886 if (!MayExitMaxBECount || EL.Max == getCouldNotCompute())
4887 MayExitMaxBECount = EL.Max;
4890 getUMaxFromMismatchedTypes(MayExitMaxBECount, EL.Max);
4894 const SCEV *MaxBECount = MustExitMaxBECount ? MustExitMaxBECount :
4895 (MayExitMaxBECount ? MayExitMaxBECount : getCouldNotCompute());
4896 return BackedgeTakenInfo(ExitCounts, CouldComputeBECount, MaxBECount);
4899 /// ComputeExitLimit - Compute the number of times the backedge of the specified
4900 /// loop will execute if it exits via the specified block.
4901 ScalarEvolution::ExitLimit
4902 ScalarEvolution::ComputeExitLimit(const Loop *L, BasicBlock *ExitingBlock) {
4904 // Okay, we've chosen an exiting block. See what condition causes us to
4905 // exit at this block and remember the exit block and whether all other targets
4906 // lead to the loop header.
4907 bool MustExecuteLoopHeader = true;
4908 BasicBlock *Exit = nullptr;
4909 for (succ_iterator SI = succ_begin(ExitingBlock), SE = succ_end(ExitingBlock);
4911 if (!L->contains(*SI)) {
4912 if (Exit) // Multiple exit successors.
4913 return getCouldNotCompute();
4915 } else if (*SI != L->getHeader()) {
4916 MustExecuteLoopHeader = false;
4919 // At this point, we know we have a conditional branch that determines whether
4920 // the loop is exited. However, we don't know if the branch is executed each
4921 // time through the loop. If not, then the execution count of the branch will
4922 // not be equal to the trip count of the loop.
4924 // Currently we check for this by checking to see if the Exit branch goes to
4925 // the loop header. If so, we know it will always execute the same number of
4926 // times as the loop. We also handle the case where the exit block *is* the
4927 // loop header. This is common for un-rotated loops.
4929 // If both of those tests fail, walk up the unique predecessor chain to the
4930 // header, stopping if there is an edge that doesn't exit the loop. If the
4931 // header is reached, the execution count of the branch will be equal to the
4932 // trip count of the loop.
4934 // More extensive analysis could be done to handle more cases here.
4936 if (!MustExecuteLoopHeader && ExitingBlock != L->getHeader()) {
4937 // The simple checks failed, try climbing the unique predecessor chain
4938 // up to the header.
4940 for (BasicBlock *BB = ExitingBlock; BB; ) {
4941 BasicBlock *Pred = BB->getUniquePredecessor();
4943 return getCouldNotCompute();
4944 TerminatorInst *PredTerm = Pred->getTerminator();
4945 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) {
4946 BasicBlock *PredSucc = PredTerm->getSuccessor(i);
4949 // If the predecessor has a successor that isn't BB and isn't
4950 // outside the loop, assume the worst.
4951 if (L->contains(PredSucc))
4952 return getCouldNotCompute();
4954 if (Pred == L->getHeader()) {
4961 return getCouldNotCompute();
4964 bool IsOnlyExit = (L->getExitingBlock() != nullptr);
4965 TerminatorInst *Term = ExitingBlock->getTerminator();
4966 if (BranchInst *BI = dyn_cast<BranchInst>(Term)) {
4967 assert(BI->isConditional() && "If unconditional, it can't be in loop!");
4968 // Proceed to the next level to examine the exit condition expression.
4969 return ComputeExitLimitFromCond(L, BI->getCondition(), BI->getSuccessor(0),
4970 BI->getSuccessor(1),
4971 /*ControlsExit=*/IsOnlyExit);
4974 if (SwitchInst *SI = dyn_cast<SwitchInst>(Term))
4975 return ComputeExitLimitFromSingleExitSwitch(L, SI, Exit,
4976 /*ControlsExit=*/IsOnlyExit);
4978 return getCouldNotCompute();
4981 /// ComputeExitLimitFromCond - Compute the number of times the
4982 /// backedge of the specified loop will execute if its exit condition
4983 /// were a conditional branch of ExitCond, TBB, and FBB.
4985 /// @param ControlsExit is true if ExitCond directly controls the exit
4986 /// branch. In this case, we can assume that the loop exits only if the
4987 /// condition is true and can infer that failing to meet the condition prior to
4988 /// integer wraparound results in undefined behavior.
4989 ScalarEvolution::ExitLimit
4990 ScalarEvolution::ComputeExitLimitFromCond(const Loop *L,
4994 bool ControlsExit) {
4995 // Check if the controlling expression for this loop is an And or Or.
4996 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
4997 if (BO->getOpcode() == Instruction::And) {
4998 // Recurse on the operands of the and.
4999 bool EitherMayExit = L->contains(TBB);
5000 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
5001 ControlsExit && !EitherMayExit);
5002 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
5003 ControlsExit && !EitherMayExit);
5004 const SCEV *BECount = getCouldNotCompute();
5005 const SCEV *MaxBECount = getCouldNotCompute();
5006 if (EitherMayExit) {
5007 // Both conditions must be true for the loop to continue executing.
5008 // Choose the less conservative count.
5009 if (EL0.Exact == getCouldNotCompute() ||
5010 EL1.Exact == getCouldNotCompute())
5011 BECount = getCouldNotCompute();
5013 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
5014 if (EL0.Max == getCouldNotCompute())
5015 MaxBECount = EL1.Max;
5016 else if (EL1.Max == getCouldNotCompute())
5017 MaxBECount = EL0.Max;
5019 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
5021 // Both conditions must be true at the same time for the loop to exit.
5022 // For now, be conservative.
5023 assert(L->contains(FBB) && "Loop block has no successor in loop!");
5024 if (EL0.Max == EL1.Max)
5025 MaxBECount = EL0.Max;
5026 if (EL0.Exact == EL1.Exact)
5027 BECount = EL0.Exact;
5030 return ExitLimit(BECount, MaxBECount);
5032 if (BO->getOpcode() == Instruction::Or) {
5033 // Recurse on the operands of the or.
5034 bool EitherMayExit = L->contains(FBB);
5035 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
5036 ControlsExit && !EitherMayExit);
5037 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
5038 ControlsExit && !EitherMayExit);
5039 const SCEV *BECount = getCouldNotCompute();
5040 const SCEV *MaxBECount = getCouldNotCompute();
5041 if (EitherMayExit) {
5042 // Both conditions must be false for the loop to continue executing.
5043 // Choose the less conservative count.
5044 if (EL0.Exact == getCouldNotCompute() ||
5045 EL1.Exact == getCouldNotCompute())
5046 BECount = getCouldNotCompute();
5048 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
5049 if (EL0.Max == getCouldNotCompute())
5050 MaxBECount = EL1.Max;
5051 else if (EL1.Max == getCouldNotCompute())
5052 MaxBECount = EL0.Max;
5054 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
5056 // Both conditions must be false at the same time for the loop to exit.
5057 // For now, be conservative.
5058 assert(L->contains(TBB) && "Loop block has no successor in loop!");
5059 if (EL0.Max == EL1.Max)
5060 MaxBECount = EL0.Max;
5061 if (EL0.Exact == EL1.Exact)
5062 BECount = EL0.Exact;
5065 return ExitLimit(BECount, MaxBECount);
5069 // With an icmp, it may be feasible to compute an exact backedge-taken count.
5070 // Proceed to the next level to examine the icmp.
5071 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
5072 return ComputeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB, ControlsExit);
5074 // Check for a constant condition. These are normally stripped out by
5075 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
5076 // preserve the CFG and is temporarily leaving constant conditions
5078 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
5079 if (L->contains(FBB) == !CI->getZExtValue())
5080 // The backedge is always taken.
5081 return getCouldNotCompute();
5083 // The backedge is never taken.
5084 return getConstant(CI->getType(), 0);
5087 // If it's not an integer or pointer comparison then compute it the hard way.
5088 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
5091 /// ComputeExitLimitFromICmp - Compute the number of times the
5092 /// backedge of the specified loop will execute if its exit condition
5093 /// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB.
5094 ScalarEvolution::ExitLimit
5095 ScalarEvolution::ComputeExitLimitFromICmp(const Loop *L,
5099 bool ControlsExit) {
5101 // If the condition was exit on true, convert the condition to exit on false
5102 ICmpInst::Predicate Cond;
5103 if (!L->contains(FBB))
5104 Cond = ExitCond->getPredicate();
5106 Cond = ExitCond->getInversePredicate();
5108 // Handle common loops like: for (X = "string"; *X; ++X)
5109 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
5110 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
5112 ComputeLoadConstantCompareExitLimit(LI, RHS, L, Cond);
5113 if (ItCnt.hasAnyInfo())
5117 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
5118 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
5120 // Try to evaluate any dependencies out of the loop.
5121 LHS = getSCEVAtScope(LHS, L);
5122 RHS = getSCEVAtScope(RHS, L);
5124 // At this point, we would like to compute how many iterations of the
5125 // loop the predicate will return true for these inputs.
5126 if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) {
5127 // If there is a loop-invariant, force it into the RHS.
5128 std::swap(LHS, RHS);
5129 Cond = ICmpInst::getSwappedPredicate(Cond);
5132 // Simplify the operands before analyzing them.
5133 (void)SimplifyICmpOperands(Cond, LHS, RHS);
5135 // If we have a comparison of a chrec against a constant, try to use value
5136 // ranges to answer this query.
5137 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
5138 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
5139 if (AddRec->getLoop() == L) {
5140 // Form the constant range.
5141 ConstantRange CompRange(
5142 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
5144 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
5145 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
5149 case ICmpInst::ICMP_NE: { // while (X != Y)
5150 // Convert to: while (X-Y != 0)
5151 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit);
5152 if (EL.hasAnyInfo()) return EL;
5155 case ICmpInst::ICMP_EQ: { // while (X == Y)
5156 // Convert to: while (X-Y == 0)
5157 ExitLimit EL = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
5158 if (EL.hasAnyInfo()) return EL;
5161 case ICmpInst::ICMP_SLT:
5162 case ICmpInst::ICMP_ULT: { // while (X < Y)
5163 bool IsSigned = Cond == ICmpInst::ICMP_SLT;
5164 ExitLimit EL = HowManyLessThans(LHS, RHS, L, IsSigned, ControlsExit);
5165 if (EL.hasAnyInfo()) return EL;
5168 case ICmpInst::ICMP_SGT:
5169 case ICmpInst::ICMP_UGT: { // while (X > Y)
5170 bool IsSigned = Cond == ICmpInst::ICMP_SGT;
5171 ExitLimit EL = HowManyGreaterThans(LHS, RHS, L, IsSigned, ControlsExit);
5172 if (EL.hasAnyInfo()) return EL;
5177 dbgs() << "ComputeBackedgeTakenCount ";
5178 if (ExitCond->getOperand(0)->getType()->isUnsigned())
5179 dbgs() << "[unsigned] ";
5180 dbgs() << *LHS << " "
5181 << Instruction::getOpcodeName(Instruction::ICmp)
5182 << " " << *RHS << "\n";
5186 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
5189 ScalarEvolution::ExitLimit
5190 ScalarEvolution::ComputeExitLimitFromSingleExitSwitch(const Loop *L,
5192 BasicBlock *ExitingBlock,
5193 bool ControlsExit) {
5194 assert(!L->contains(ExitingBlock) && "Not an exiting block!");
5196 // Give up if the exit is the default dest of a switch.
5197 if (Switch->getDefaultDest() == ExitingBlock)
5198 return getCouldNotCompute();
5200 assert(L->contains(Switch->getDefaultDest()) &&
5201 "Default case must not exit the loop!");
5202 const SCEV *LHS = getSCEVAtScope(Switch->getCondition(), L);
5203 const SCEV *RHS = getConstant(Switch->findCaseDest(ExitingBlock));
5205 // while (X != Y) --> while (X-Y != 0)
5206 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit);
5207 if (EL.hasAnyInfo())
5210 return getCouldNotCompute();
5213 static ConstantInt *
5214 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
5215 ScalarEvolution &SE) {
5216 const SCEV *InVal = SE.getConstant(C);
5217 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
5218 assert(isa<SCEVConstant>(Val) &&
5219 "Evaluation of SCEV at constant didn't fold correctly?");
5220 return cast<SCEVConstant>(Val)->getValue();
5223 /// ComputeLoadConstantCompareExitLimit - Given an exit condition of
5224 /// 'icmp op load X, cst', try to see if we can compute the backedge
5225 /// execution count.
5226 ScalarEvolution::ExitLimit
5227 ScalarEvolution::ComputeLoadConstantCompareExitLimit(
5231 ICmpInst::Predicate predicate) {
5233 if (LI->isVolatile()) return getCouldNotCompute();
5235 // Check to see if the loaded pointer is a getelementptr of a global.
5236 // TODO: Use SCEV instead of manually grubbing with GEPs.
5237 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
5238 if (!GEP) return getCouldNotCompute();
5240 // Make sure that it is really a constant global we are gepping, with an
5241 // initializer, and make sure the first IDX is really 0.
5242 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
5243 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
5244 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
5245 !cast<Constant>(GEP->getOperand(1))->isNullValue())
5246 return getCouldNotCompute();
5248 // Okay, we allow one non-constant index into the GEP instruction.
5249 Value *VarIdx = nullptr;
5250 std::vector<Constant*> Indexes;
5251 unsigned VarIdxNum = 0;
5252 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
5253 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
5254 Indexes.push_back(CI);
5255 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
5256 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
5257 VarIdx = GEP->getOperand(i);
5259 Indexes.push_back(nullptr);
5262 // Loop-invariant loads may be a byproduct of loop optimization. Skip them.
5264 return getCouldNotCompute();
5266 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
5267 // Check to see if X is a loop variant variable value now.
5268 const SCEV *Idx = getSCEV(VarIdx);
5269 Idx = getSCEVAtScope(Idx, L);
5271 // We can only recognize very limited forms of loop index expressions, in
5272 // particular, only affine AddRec's like {C1,+,C2}.
5273 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
5274 if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) ||
5275 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
5276 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
5277 return getCouldNotCompute();
5279 unsigned MaxSteps = MaxBruteForceIterations;
5280 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
5281 ConstantInt *ItCst = ConstantInt::get(
5282 cast<IntegerType>(IdxExpr->getType()), IterationNum);
5283 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
5285 // Form the GEP offset.
5286 Indexes[VarIdxNum] = Val;
5288 Constant *Result = ConstantFoldLoadThroughGEPIndices(GV->getInitializer(),
5290 if (!Result) break; // Cannot compute!
5292 // Evaluate the condition for this iteration.
5293 Result = ConstantExpr::getICmp(predicate, Result, RHS);
5294 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
5295 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
5297 dbgs() << "\n***\n*** Computed loop count " << *ItCst
5298 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
5301 ++NumArrayLenItCounts;
5302 return getConstant(ItCst); // Found terminating iteration!
5305 return getCouldNotCompute();
5309 /// CanConstantFold - Return true if we can constant fold an instruction of the
5310 /// specified type, assuming that all operands were constants.
5311 static bool CanConstantFold(const Instruction *I) {
5312 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
5313 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I) ||
5317 if (const CallInst *CI = dyn_cast<CallInst>(I))
5318 if (const Function *F = CI->getCalledFunction())
5319 return canConstantFoldCallTo(F);
5323 /// Determine whether this instruction can constant evolve within this loop
5324 /// assuming its operands can all constant evolve.
5325 static bool canConstantEvolve(Instruction *I, const Loop *L) {
5326 // An instruction outside of the loop can't be derived from a loop PHI.
5327 if (!L->contains(I)) return false;
5329 if (isa<PHINode>(I)) {
5330 if (L->getHeader() == I->getParent())
5333 // We don't currently keep track of the control flow needed to evaluate
5334 // PHIs, so we cannot handle PHIs inside of loops.
5338 // If we won't be able to constant fold this expression even if the operands
5339 // are constants, bail early.
5340 return CanConstantFold(I);
5343 /// getConstantEvolvingPHIOperands - Implement getConstantEvolvingPHI by
5344 /// recursing through each instruction operand until reaching a loop header phi.
5346 getConstantEvolvingPHIOperands(Instruction *UseInst, const Loop *L,
5347 DenseMap<Instruction *, PHINode *> &PHIMap) {
5349 // Otherwise, we can evaluate this instruction if all of its operands are
5350 // constant or derived from a PHI node themselves.
5351 PHINode *PHI = nullptr;
5352 for (Instruction::op_iterator OpI = UseInst->op_begin(),
5353 OpE = UseInst->op_end(); OpI != OpE; ++OpI) {
5355 if (isa<Constant>(*OpI)) continue;
5357 Instruction *OpInst = dyn_cast<Instruction>(*OpI);
5358 if (!OpInst || !canConstantEvolve(OpInst, L)) return nullptr;
5360 PHINode *P = dyn_cast<PHINode>(OpInst);
5362 // If this operand is already visited, reuse the prior result.
5363 // We may have P != PHI if this is the deepest point at which the
5364 // inconsistent paths meet.
5365 P = PHIMap.lookup(OpInst);
5367 // Recurse and memoize the results, whether a phi is found or not.
5368 // This recursive call invalidates pointers into PHIMap.
5369 P = getConstantEvolvingPHIOperands(OpInst, L, PHIMap);
5373 return nullptr; // Not evolving from PHI
5374 if (PHI && PHI != P)
5375 return nullptr; // Evolving from multiple different PHIs.
5378 // This is a expression evolving from a constant PHI!
5382 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
5383 /// in the loop that V is derived from. We allow arbitrary operations along the
5384 /// way, but the operands of an operation must either be constants or a value
5385 /// derived from a constant PHI. If this expression does not fit with these
5386 /// constraints, return null.
5387 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
5388 Instruction *I = dyn_cast<Instruction>(V);
5389 if (!I || !canConstantEvolve(I, L)) return nullptr;
5391 if (PHINode *PN = dyn_cast<PHINode>(I)) {
5395 // Record non-constant instructions contained by the loop.
5396 DenseMap<Instruction *, PHINode *> PHIMap;
5397 return getConstantEvolvingPHIOperands(I, L, PHIMap);
5400 /// EvaluateExpression - Given an expression that passes the
5401 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
5402 /// in the loop has the value PHIVal. If we can't fold this expression for some
5403 /// reason, return null.
5404 static Constant *EvaluateExpression(Value *V, const Loop *L,
5405 DenseMap<Instruction *, Constant *> &Vals,
5406 const DataLayout *DL,
5407 const TargetLibraryInfo *TLI) {
5408 // Convenient constant check, but redundant for recursive calls.
5409 if (Constant *C = dyn_cast<Constant>(V)) return C;
5410 Instruction *I = dyn_cast<Instruction>(V);
5411 if (!I) return nullptr;
5413 if (Constant *C = Vals.lookup(I)) return C;
5415 // An instruction inside the loop depends on a value outside the loop that we
5416 // weren't given a mapping for, or a value such as a call inside the loop.
5417 if (!canConstantEvolve(I, L)) return nullptr;
5419 // An unmapped PHI can be due to a branch or another loop inside this loop,
5420 // or due to this not being the initial iteration through a loop where we
5421 // couldn't compute the evolution of this particular PHI last time.
5422 if (isa<PHINode>(I)) return nullptr;
5424 std::vector<Constant*> Operands(I->getNumOperands());
5426 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
5427 Instruction *Operand = dyn_cast<Instruction>(I->getOperand(i));
5429 Operands[i] = dyn_cast<Constant>(I->getOperand(i));
5430 if (!Operands[i]) return nullptr;
5433 Constant *C = EvaluateExpression(Operand, L, Vals, DL, TLI);
5435 if (!C) return nullptr;
5439 if (CmpInst *CI = dyn_cast<CmpInst>(I))
5440 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
5441 Operands[1], DL, TLI);
5442 if (LoadInst *LI = dyn_cast<LoadInst>(I)) {
5443 if (!LI->isVolatile())
5444 return ConstantFoldLoadFromConstPtr(Operands[0], DL);
5446 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), Operands, DL,
5450 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
5451 /// in the header of its containing loop, we know the loop executes a
5452 /// constant number of times, and the PHI node is just a recurrence
5453 /// involving constants, fold it.
5455 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
5458 DenseMap<PHINode*, Constant*>::const_iterator I =
5459 ConstantEvolutionLoopExitValue.find(PN);
5460 if (I != ConstantEvolutionLoopExitValue.end())
5463 if (BEs.ugt(MaxBruteForceIterations))
5464 return ConstantEvolutionLoopExitValue[PN] = nullptr; // Not going to evaluate it.
5466 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
5468 DenseMap<Instruction *, Constant *> CurrentIterVals;
5469 BasicBlock *Header = L->getHeader();
5470 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
5472 // Since the loop is canonicalized, the PHI node must have two entries. One
5473 // entry must be a constant (coming in from outside of the loop), and the
5474 // second must be derived from the same PHI.
5475 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
5476 PHINode *PHI = nullptr;
5477 for (BasicBlock::iterator I = Header->begin();
5478 (PHI = dyn_cast<PHINode>(I)); ++I) {
5479 Constant *StartCST =
5480 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
5481 if (!StartCST) continue;
5482 CurrentIterVals[PHI] = StartCST;
5484 if (!CurrentIterVals.count(PN))
5485 return RetVal = nullptr;
5487 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
5489 // Execute the loop symbolically to determine the exit value.
5490 if (BEs.getActiveBits() >= 32)
5491 return RetVal = nullptr; // More than 2^32-1 iterations?? Not doing it!
5493 unsigned NumIterations = BEs.getZExtValue(); // must be in range
5494 unsigned IterationNum = 0;
5495 for (; ; ++IterationNum) {
5496 if (IterationNum == NumIterations)
5497 return RetVal = CurrentIterVals[PN]; // Got exit value!
5499 // Compute the value of the PHIs for the next iteration.
5500 // EvaluateExpression adds non-phi values to the CurrentIterVals map.
5501 DenseMap<Instruction *, Constant *> NextIterVals;
5502 Constant *NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL,
5505 return nullptr; // Couldn't evaluate!
5506 NextIterVals[PN] = NextPHI;
5508 bool StoppedEvolving = NextPHI == CurrentIterVals[PN];
5510 // Also evaluate the other PHI nodes. However, we don't get to stop if we
5511 // cease to be able to evaluate one of them or if they stop evolving,
5512 // because that doesn't necessarily prevent us from computing PN.
5513 SmallVector<std::pair<PHINode *, Constant *>, 8> PHIsToCompute;
5514 for (DenseMap<Instruction *, Constant *>::const_iterator
5515 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
5516 PHINode *PHI = dyn_cast<PHINode>(I->first);
5517 if (!PHI || PHI == PN || PHI->getParent() != Header) continue;
5518 PHIsToCompute.push_back(std::make_pair(PHI, I->second));
5520 // We use two distinct loops because EvaluateExpression may invalidate any
5521 // iterators into CurrentIterVals.
5522 for (SmallVectorImpl<std::pair<PHINode *, Constant*> >::const_iterator
5523 I = PHIsToCompute.begin(), E = PHIsToCompute.end(); I != E; ++I) {
5524 PHINode *PHI = I->first;
5525 Constant *&NextPHI = NextIterVals[PHI];
5526 if (!NextPHI) { // Not already computed.
5527 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
5528 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, TLI);
5530 if (NextPHI != I->second)
5531 StoppedEvolving = false;
5534 // If all entries in CurrentIterVals == NextIterVals then we can stop
5535 // iterating, the loop can't continue to change.
5536 if (StoppedEvolving)
5537 return RetVal = CurrentIterVals[PN];
5539 CurrentIterVals.swap(NextIterVals);
5543 /// ComputeExitCountExhaustively - If the loop is known to execute a
5544 /// constant number of times (the condition evolves only from constants),
5545 /// try to evaluate a few iterations of the loop until we get the exit
5546 /// condition gets a value of ExitWhen (true or false). If we cannot
5547 /// evaluate the trip count of the loop, return getCouldNotCompute().
5548 const SCEV *ScalarEvolution::ComputeExitCountExhaustively(const Loop *L,
5551 PHINode *PN = getConstantEvolvingPHI(Cond, L);
5552 if (!PN) return getCouldNotCompute();
5554 // If the loop is canonicalized, the PHI will have exactly two entries.
5555 // That's the only form we support here.
5556 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
5558 DenseMap<Instruction *, Constant *> CurrentIterVals;
5559 BasicBlock *Header = L->getHeader();
5560 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
5562 // One entry must be a constant (coming in from outside of the loop), and the
5563 // second must be derived from the same PHI.
5564 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
5565 PHINode *PHI = nullptr;
5566 for (BasicBlock::iterator I = Header->begin();
5567 (PHI = dyn_cast<PHINode>(I)); ++I) {
5568 Constant *StartCST =
5569 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
5570 if (!StartCST) continue;
5571 CurrentIterVals[PHI] = StartCST;
5573 if (!CurrentIterVals.count(PN))
5574 return getCouldNotCompute();
5576 // Okay, we find a PHI node that defines the trip count of this loop. Execute
5577 // the loop symbolically to determine when the condition gets a value of
5580 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
5581 for (unsigned IterationNum = 0; IterationNum != MaxIterations;++IterationNum){
5582 ConstantInt *CondVal =
5583 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, L, CurrentIterVals,
5586 // Couldn't symbolically evaluate.
5587 if (!CondVal) return getCouldNotCompute();
5589 if (CondVal->getValue() == uint64_t(ExitWhen)) {
5590 ++NumBruteForceTripCountsComputed;
5591 return getConstant(Type::getInt32Ty(getContext()), IterationNum);
5594 // Update all the PHI nodes for the next iteration.
5595 DenseMap<Instruction *, Constant *> NextIterVals;
5597 // Create a list of which PHIs we need to compute. We want to do this before
5598 // calling EvaluateExpression on them because that may invalidate iterators
5599 // into CurrentIterVals.
5600 SmallVector<PHINode *, 8> PHIsToCompute;
5601 for (DenseMap<Instruction *, Constant *>::const_iterator
5602 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
5603 PHINode *PHI = dyn_cast<PHINode>(I->first);
5604 if (!PHI || PHI->getParent() != Header) continue;
5605 PHIsToCompute.push_back(PHI);
5607 for (SmallVectorImpl<PHINode *>::const_iterator I = PHIsToCompute.begin(),
5608 E = PHIsToCompute.end(); I != E; ++I) {
5610 Constant *&NextPHI = NextIterVals[PHI];
5611 if (NextPHI) continue; // Already computed!
5613 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
5614 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, TLI);
5616 CurrentIterVals.swap(NextIterVals);
5619 // Too many iterations were needed to evaluate.
5620 return getCouldNotCompute();
5623 /// getSCEVAtScope - Return a SCEV expression for the specified value
5624 /// at the specified scope in the program. The L value specifies a loop
5625 /// nest to evaluate the expression at, where null is the top-level or a
5626 /// specified loop is immediately inside of the loop.
5628 /// This method can be used to compute the exit value for a variable defined
5629 /// in a loop by querying what the value will hold in the parent loop.
5631 /// In the case that a relevant loop exit value cannot be computed, the
5632 /// original value V is returned.
5633 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
5634 // Check to see if we've folded this expression at this loop before.
5635 SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values = ValuesAtScopes[V];
5636 for (unsigned u = 0; u < Values.size(); u++) {
5637 if (Values[u].first == L)
5638 return Values[u].second ? Values[u].second : V;
5640 Values.push_back(std::make_pair(L, static_cast<const SCEV *>(nullptr)));
5641 // Otherwise compute it.
5642 const SCEV *C = computeSCEVAtScope(V, L);
5643 SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values2 = ValuesAtScopes[V];
5644 for (unsigned u = Values2.size(); u > 0; u--) {
5645 if (Values2[u - 1].first == L) {
5646 Values2[u - 1].second = C;
5653 /// This builds up a Constant using the ConstantExpr interface. That way, we
5654 /// will return Constants for objects which aren't represented by a
5655 /// SCEVConstant, because SCEVConstant is restricted to ConstantInt.
5656 /// Returns NULL if the SCEV isn't representable as a Constant.
5657 static Constant *BuildConstantFromSCEV(const SCEV *V) {
5658 switch (static_cast<SCEVTypes>(V->getSCEVType())) {
5659 case scCouldNotCompute:
5663 return cast<SCEVConstant>(V)->getValue();
5665 return dyn_cast<Constant>(cast<SCEVUnknown>(V)->getValue());
5666 case scSignExtend: {
5667 const SCEVSignExtendExpr *SS = cast<SCEVSignExtendExpr>(V);
5668 if (Constant *CastOp = BuildConstantFromSCEV(SS->getOperand()))
5669 return ConstantExpr::getSExt(CastOp, SS->getType());
5672 case scZeroExtend: {
5673 const SCEVZeroExtendExpr *SZ = cast<SCEVZeroExtendExpr>(V);
5674 if (Constant *CastOp = BuildConstantFromSCEV(SZ->getOperand()))
5675 return ConstantExpr::getZExt(CastOp, SZ->getType());
5679 const SCEVTruncateExpr *ST = cast<SCEVTruncateExpr>(V);
5680 if (Constant *CastOp = BuildConstantFromSCEV(ST->getOperand()))
5681 return ConstantExpr::getTrunc(CastOp, ST->getType());
5685 const SCEVAddExpr *SA = cast<SCEVAddExpr>(V);
5686 if (Constant *C = BuildConstantFromSCEV(SA->getOperand(0))) {
5687 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
5688 unsigned AS = PTy->getAddressSpace();
5689 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
5690 C = ConstantExpr::getBitCast(C, DestPtrTy);
5692 for (unsigned i = 1, e = SA->getNumOperands(); i != e; ++i) {
5693 Constant *C2 = BuildConstantFromSCEV(SA->getOperand(i));
5694 if (!C2) return nullptr;
5697 if (!C->getType()->isPointerTy() && C2->getType()->isPointerTy()) {
5698 unsigned AS = C2->getType()->getPointerAddressSpace();
5700 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
5701 // The offsets have been converted to bytes. We can add bytes to an
5702 // i8* by GEP with the byte count in the first index.
5703 C = ConstantExpr::getBitCast(C, DestPtrTy);
5706 // Don't bother trying to sum two pointers. We probably can't
5707 // statically compute a load that results from it anyway.
5708 if (C2->getType()->isPointerTy())
5711 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
5712 if (PTy->getElementType()->isStructTy())
5713 C2 = ConstantExpr::getIntegerCast(
5714 C2, Type::getInt32Ty(C->getContext()), true);
5715 C = ConstantExpr::getGetElementPtr(C, C2);
5717 C = ConstantExpr::getAdd(C, C2);
5724 const SCEVMulExpr *SM = cast<SCEVMulExpr>(V);
5725 if (Constant *C = BuildConstantFromSCEV(SM->getOperand(0))) {
5726 // Don't bother with pointers at all.
5727 if (C->getType()->isPointerTy()) return nullptr;
5728 for (unsigned i = 1, e = SM->getNumOperands(); i != e; ++i) {
5729 Constant *C2 = BuildConstantFromSCEV(SM->getOperand(i));
5730 if (!C2 || C2->getType()->isPointerTy()) return nullptr;
5731 C = ConstantExpr::getMul(C, C2);
5738 const SCEVUDivExpr *SU = cast<SCEVUDivExpr>(V);
5739 if (Constant *LHS = BuildConstantFromSCEV(SU->getLHS()))
5740 if (Constant *RHS = BuildConstantFromSCEV(SU->getRHS()))
5741 if (LHS->getType() == RHS->getType())
5742 return ConstantExpr::getUDiv(LHS, RHS);
5747 break; // TODO: smax, umax.
5752 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
5753 if (isa<SCEVConstant>(V)) return V;
5755 // If this instruction is evolved from a constant-evolving PHI, compute the
5756 // exit value from the loop without using SCEVs.
5757 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
5758 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
5759 const Loop *LI = (*this->LI)[I->getParent()];
5760 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
5761 if (PHINode *PN = dyn_cast<PHINode>(I))
5762 if (PN->getParent() == LI->getHeader()) {
5763 // Okay, there is no closed form solution for the PHI node. Check
5764 // to see if the loop that contains it has a known backedge-taken
5765 // count. If so, we may be able to force computation of the exit
5767 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
5768 if (const SCEVConstant *BTCC =
5769 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
5770 // Okay, we know how many times the containing loop executes. If
5771 // this is a constant evolving PHI node, get the final value at
5772 // the specified iteration number.
5773 Constant *RV = getConstantEvolutionLoopExitValue(PN,
5774 BTCC->getValue()->getValue(),
5776 if (RV) return getSCEV(RV);
5780 // Okay, this is an expression that we cannot symbolically evaluate
5781 // into a SCEV. Check to see if it's possible to symbolically evaluate
5782 // the arguments into constants, and if so, try to constant propagate the
5783 // result. This is particularly useful for computing loop exit values.
5784 if (CanConstantFold(I)) {
5785 SmallVector<Constant *, 4> Operands;
5786 bool MadeImprovement = false;
5787 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
5788 Value *Op = I->getOperand(i);
5789 if (Constant *C = dyn_cast<Constant>(Op)) {
5790 Operands.push_back(C);
5794 // If any of the operands is non-constant and if they are
5795 // non-integer and non-pointer, don't even try to analyze them
5796 // with scev techniques.
5797 if (!isSCEVable(Op->getType()))
5800 const SCEV *OrigV = getSCEV(Op);
5801 const SCEV *OpV = getSCEVAtScope(OrigV, L);
5802 MadeImprovement |= OrigV != OpV;
5804 Constant *C = BuildConstantFromSCEV(OpV);
5806 if (C->getType() != Op->getType())
5807 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
5811 Operands.push_back(C);
5814 // Check to see if getSCEVAtScope actually made an improvement.
5815 if (MadeImprovement) {
5816 Constant *C = nullptr;
5817 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
5818 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
5819 Operands[0], Operands[1], DL,
5821 else if (const LoadInst *LI = dyn_cast<LoadInst>(I)) {
5822 if (!LI->isVolatile())
5823 C = ConstantFoldLoadFromConstPtr(Operands[0], DL);
5825 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
5833 // This is some other type of SCEVUnknown, just return it.
5837 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
5838 // Avoid performing the look-up in the common case where the specified
5839 // expression has no loop-variant portions.
5840 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
5841 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
5842 if (OpAtScope != Comm->getOperand(i)) {
5843 // Okay, at least one of these operands is loop variant but might be
5844 // foldable. Build a new instance of the folded commutative expression.
5845 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
5846 Comm->op_begin()+i);
5847 NewOps.push_back(OpAtScope);
5849 for (++i; i != e; ++i) {
5850 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
5851 NewOps.push_back(OpAtScope);
5853 if (isa<SCEVAddExpr>(Comm))
5854 return getAddExpr(NewOps);
5855 if (isa<SCEVMulExpr>(Comm))
5856 return getMulExpr(NewOps);
5857 if (isa<SCEVSMaxExpr>(Comm))
5858 return getSMaxExpr(NewOps);
5859 if (isa<SCEVUMaxExpr>(Comm))
5860 return getUMaxExpr(NewOps);
5861 llvm_unreachable("Unknown commutative SCEV type!");
5864 // If we got here, all operands are loop invariant.
5868 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
5869 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
5870 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
5871 if (LHS == Div->getLHS() && RHS == Div->getRHS())
5872 return Div; // must be loop invariant
5873 return getUDivExpr(LHS, RHS);
5876 // If this is a loop recurrence for a loop that does not contain L, then we
5877 // are dealing with the final value computed by the loop.
5878 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
5879 // First, attempt to evaluate each operand.
5880 // Avoid performing the look-up in the common case where the specified
5881 // expression has no loop-variant portions.
5882 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
5883 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
5884 if (OpAtScope == AddRec->getOperand(i))
5887 // Okay, at least one of these operands is loop variant but might be
5888 // foldable. Build a new instance of the folded commutative expression.
5889 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(),
5890 AddRec->op_begin()+i);
5891 NewOps.push_back(OpAtScope);
5892 for (++i; i != e; ++i)
5893 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
5895 const SCEV *FoldedRec =
5896 getAddRecExpr(NewOps, AddRec->getLoop(),
5897 AddRec->getNoWrapFlags(SCEV::FlagNW));
5898 AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec);
5899 // The addrec may be folded to a nonrecurrence, for example, if the
5900 // induction variable is multiplied by zero after constant folding. Go
5901 // ahead and return the folded value.
5907 // If the scope is outside the addrec's loop, evaluate it by using the
5908 // loop exit value of the addrec.
5909 if (!AddRec->getLoop()->contains(L)) {
5910 // To evaluate this recurrence, we need to know how many times the AddRec
5911 // loop iterates. Compute this now.
5912 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
5913 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
5915 // Then, evaluate the AddRec.
5916 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
5922 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
5923 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5924 if (Op == Cast->getOperand())
5925 return Cast; // must be loop invariant
5926 return getZeroExtendExpr(Op, Cast->getType());
5929 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
5930 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5931 if (Op == Cast->getOperand())
5932 return Cast; // must be loop invariant
5933 return getSignExtendExpr(Op, Cast->getType());
5936 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
5937 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5938 if (Op == Cast->getOperand())
5939 return Cast; // must be loop invariant
5940 return getTruncateExpr(Op, Cast->getType());
5943 llvm_unreachable("Unknown SCEV type!");
5946 /// getSCEVAtScope - This is a convenience function which does
5947 /// getSCEVAtScope(getSCEV(V), L).
5948 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
5949 return getSCEVAtScope(getSCEV(V), L);
5952 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
5953 /// following equation:
5955 /// A * X = B (mod N)
5957 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
5958 /// A and B isn't important.
5960 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
5961 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
5962 ScalarEvolution &SE) {
5963 uint32_t BW = A.getBitWidth();
5964 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
5965 assert(A != 0 && "A must be non-zero.");
5969 // The gcd of A and N may have only one prime factor: 2. The number of
5970 // trailing zeros in A is its multiplicity
5971 uint32_t Mult2 = A.countTrailingZeros();
5974 // 2. Check if B is divisible by D.
5976 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
5977 // is not less than multiplicity of this prime factor for D.
5978 if (B.countTrailingZeros() < Mult2)
5979 return SE.getCouldNotCompute();
5981 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
5984 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
5985 // bit width during computations.
5986 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
5987 APInt Mod(BW + 1, 0);
5988 Mod.setBit(BW - Mult2); // Mod = N / D
5989 APInt I = AD.multiplicativeInverse(Mod);
5991 // 4. Compute the minimum unsigned root of the equation:
5992 // I * (B / D) mod (N / D)
5993 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
5995 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
5997 return SE.getConstant(Result.trunc(BW));
6000 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
6001 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
6002 /// might be the same) or two SCEVCouldNotCompute objects.
6004 static std::pair<const SCEV *,const SCEV *>
6005 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
6006 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
6007 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
6008 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
6009 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
6011 // We currently can only solve this if the coefficients are constants.
6012 if (!LC || !MC || !NC) {
6013 const SCEV *CNC = SE.getCouldNotCompute();
6014 return std::make_pair(CNC, CNC);
6017 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
6018 const APInt &L = LC->getValue()->getValue();
6019 const APInt &M = MC->getValue()->getValue();
6020 const APInt &N = NC->getValue()->getValue();
6021 APInt Two(BitWidth, 2);
6022 APInt Four(BitWidth, 4);
6025 using namespace APIntOps;
6027 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
6028 // The B coefficient is M-N/2
6032 // The A coefficient is N/2
6033 APInt A(N.sdiv(Two));
6035 // Compute the B^2-4ac term.
6038 SqrtTerm -= Four * (A * C);
6040 if (SqrtTerm.isNegative()) {
6041 // The loop is provably infinite.
6042 const SCEV *CNC = SE.getCouldNotCompute();
6043 return std::make_pair(CNC, CNC);
6046 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
6047 // integer value or else APInt::sqrt() will assert.
6048 APInt SqrtVal(SqrtTerm.sqrt());
6050 // Compute the two solutions for the quadratic formula.
6051 // The divisions must be performed as signed divisions.
6054 if (TwoA.isMinValue()) {
6055 const SCEV *CNC = SE.getCouldNotCompute();
6056 return std::make_pair(CNC, CNC);
6059 LLVMContext &Context = SE.getContext();
6061 ConstantInt *Solution1 =
6062 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
6063 ConstantInt *Solution2 =
6064 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
6066 return std::make_pair(SE.getConstant(Solution1),
6067 SE.getConstant(Solution2));
6068 } // end APIntOps namespace
6071 /// HowFarToZero - Return the number of times a backedge comparing the specified
6072 /// value to zero will execute. If not computable, return CouldNotCompute.
6074 /// This is only used for loops with a "x != y" exit test. The exit condition is
6075 /// now expressed as a single expression, V = x-y. So the exit test is
6076 /// effectively V != 0. We know and take advantage of the fact that this
6077 /// expression only being used in a comparison by zero context.
6078 ScalarEvolution::ExitLimit
6079 ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L, bool ControlsExit) {
6080 // If the value is a constant
6081 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
6082 // If the value is already zero, the branch will execute zero times.
6083 if (C->getValue()->isZero()) return C;
6084 return getCouldNotCompute(); // Otherwise it will loop infinitely.
6087 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
6088 if (!AddRec || AddRec->getLoop() != L)
6089 return getCouldNotCompute();
6091 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
6092 // the quadratic equation to solve it.
6093 if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
6094 std::pair<const SCEV *,const SCEV *> Roots =
6095 SolveQuadraticEquation(AddRec, *this);
6096 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
6097 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
6100 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1
6101 << " sol#2: " << *R2 << "\n";
6103 // Pick the smallest positive root value.
6104 if (ConstantInt *CB =
6105 dyn_cast<ConstantInt>(ConstantExpr::getICmp(CmpInst::ICMP_ULT,
6108 if (CB->getZExtValue() == false)
6109 std::swap(R1, R2); // R1 is the minimum root now.
6111 // We can only use this value if the chrec ends up with an exact zero
6112 // value at this index. When solving for "X*X != 5", for example, we
6113 // should not accept a root of 2.
6114 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
6116 return R1; // We found a quadratic root!
6119 return getCouldNotCompute();
6122 // Otherwise we can only handle this if it is affine.
6123 if (!AddRec->isAffine())
6124 return getCouldNotCompute();
6126 // If this is an affine expression, the execution count of this branch is
6127 // the minimum unsigned root of the following equation:
6129 // Start + Step*N = 0 (mod 2^BW)
6133 // Step*N = -Start (mod 2^BW)
6135 // where BW is the common bit width of Start and Step.
6137 // Get the initial value for the loop.
6138 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
6139 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
6141 // For now we handle only constant steps.
6143 // TODO: Handle a nonconstant Step given AddRec<NUW>. If the
6144 // AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap
6145 // to 0, it must be counting down to equal 0. Consequently, N = Start / -Step.
6146 // We have not yet seen any such cases.
6147 const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step);
6148 if (!StepC || StepC->getValue()->equalsInt(0))
6149 return getCouldNotCompute();
6151 // For positive steps (counting up until unsigned overflow):
6152 // N = -Start/Step (as unsigned)
6153 // For negative steps (counting down to zero):
6155 // First compute the unsigned distance from zero in the direction of Step.
6156 bool CountDown = StepC->getValue()->getValue().isNegative();
6157 const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start);
6159 // Handle unitary steps, which cannot wraparound.
6160 // 1*N = -Start; -1*N = Start (mod 2^BW), so:
6161 // N = Distance (as unsigned)
6162 if (StepC->getValue()->equalsInt(1) || StepC->getValue()->isAllOnesValue()) {
6163 ConstantRange CR = getUnsignedRange(Start);
6164 const SCEV *MaxBECount;
6165 if (!CountDown && CR.getUnsignedMin().isMinValue())
6166 // When counting up, the worst starting value is 1, not 0.
6167 MaxBECount = CR.getUnsignedMax().isMinValue()
6168 ? getConstant(APInt::getMinValue(CR.getBitWidth()))
6169 : getConstant(APInt::getMaxValue(CR.getBitWidth()));
6171 MaxBECount = getConstant(CountDown ? CR.getUnsignedMax()
6172 : -CR.getUnsignedMin());
6173 return ExitLimit(Distance, MaxBECount);
6176 // As a special case, handle the instance where Step is a positive power of
6177 // two. In this case, determining whether Step divides Distance evenly can be
6178 // done by counting and comparing the number of trailing zeros of Step and
6181 const APInt &StepV = StepC->getValue()->getValue();
6182 // StepV.isPowerOf2() returns true if StepV is an positive power of two. It
6183 // also returns true if StepV is maximally negative (eg, INT_MIN), but that
6184 // case is not handled as this code is guarded by !CountDown.
6185 if (StepV.isPowerOf2() &&
6186 GetMinTrailingZeros(Distance) >= StepV.countTrailingZeros())
6187 return getUDivExactExpr(Distance, Step);
6190 // If the condition controls loop exit (the loop exits only if the expression
6191 // is true) and the addition is no-wrap we can use unsigned divide to
6192 // compute the backedge count. In this case, the step may not divide the
6193 // distance, but we don't care because if the condition is "missed" the loop
6194 // will have undefined behavior due to wrapping.
6195 if (ControlsExit && AddRec->getNoWrapFlags(SCEV::FlagNW)) {
6197 getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
6198 return ExitLimit(Exact, Exact);
6201 // Then, try to solve the above equation provided that Start is constant.
6202 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
6203 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
6204 -StartC->getValue()->getValue(),
6206 return getCouldNotCompute();
6209 /// HowFarToNonZero - Return the number of times a backedge checking the
6210 /// specified value for nonzero will execute. If not computable, return
6212 ScalarEvolution::ExitLimit
6213 ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
6214 // Loops that look like: while (X == 0) are very strange indeed. We don't
6215 // handle them yet except for the trivial case. This could be expanded in the
6216 // future as needed.
6218 // If the value is a constant, check to see if it is known to be non-zero
6219 // already. If so, the backedge will execute zero times.
6220 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
6221 if (!C->getValue()->isNullValue())
6222 return getConstant(C->getType(), 0);
6223 return getCouldNotCompute(); // Otherwise it will loop infinitely.
6226 // We could implement others, but I really doubt anyone writes loops like
6227 // this, and if they did, they would already be constant folded.
6228 return getCouldNotCompute();
6231 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
6232 /// (which may not be an immediate predecessor) which has exactly one
6233 /// successor from which BB is reachable, or null if no such block is
6236 std::pair<BasicBlock *, BasicBlock *>
6237 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
6238 // If the block has a unique predecessor, then there is no path from the
6239 // predecessor to the block that does not go through the direct edge
6240 // from the predecessor to the block.
6241 if (BasicBlock *Pred = BB->getSinglePredecessor())
6242 return std::make_pair(Pred, BB);
6244 // A loop's header is defined to be a block that dominates the loop.
6245 // If the header has a unique predecessor outside the loop, it must be
6246 // a block that has exactly one successor that can reach the loop.
6247 if (Loop *L = LI->getLoopFor(BB))
6248 return std::make_pair(L->getLoopPredecessor(), L->getHeader());
6250 return std::pair<BasicBlock *, BasicBlock *>();
6253 /// HasSameValue - SCEV structural equivalence is usually sufficient for
6254 /// testing whether two expressions are equal, however for the purposes of
6255 /// looking for a condition guarding a loop, it can be useful to be a little
6256 /// more general, since a front-end may have replicated the controlling
6259 static bool HasSameValue(const SCEV *A, const SCEV *B) {
6260 // Quick check to see if they are the same SCEV.
6261 if (A == B) return true;
6263 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
6264 // two different instructions with the same value. Check for this case.
6265 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
6266 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
6267 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
6268 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
6269 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory())
6272 // Otherwise assume they may have a different value.
6276 /// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with
6277 /// predicate Pred. Return true iff any changes were made.
6279 bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
6280 const SCEV *&LHS, const SCEV *&RHS,
6282 bool Changed = false;
6284 // If we hit the max recursion limit bail out.
6288 // Canonicalize a constant to the right side.
6289 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
6290 // Check for both operands constant.
6291 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
6292 if (ConstantExpr::getICmp(Pred,
6294 RHSC->getValue())->isNullValue())
6295 goto trivially_false;
6297 goto trivially_true;
6299 // Otherwise swap the operands to put the constant on the right.
6300 std::swap(LHS, RHS);
6301 Pred = ICmpInst::getSwappedPredicate(Pred);
6305 // If we're comparing an addrec with a value which is loop-invariant in the
6306 // addrec's loop, put the addrec on the left. Also make a dominance check,
6307 // as both operands could be addrecs loop-invariant in each other's loop.
6308 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
6309 const Loop *L = AR->getLoop();
6310 if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) {
6311 std::swap(LHS, RHS);
6312 Pred = ICmpInst::getSwappedPredicate(Pred);
6317 // If there's a constant operand, canonicalize comparisons with boundary
6318 // cases, and canonicalize *-or-equal comparisons to regular comparisons.
6319 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
6320 const APInt &RA = RC->getValue()->getValue();
6322 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6323 case ICmpInst::ICMP_EQ:
6324 case ICmpInst::ICMP_NE:
6325 // Fold ((-1) * %a) + %b == 0 (equivalent to %b-%a == 0) into %a == %b.
6327 if (const SCEVAddExpr *AE = dyn_cast<SCEVAddExpr>(LHS))
6328 if (const SCEVMulExpr *ME = dyn_cast<SCEVMulExpr>(AE->getOperand(0)))
6329 if (AE->getNumOperands() == 2 && ME->getNumOperands() == 2 &&
6330 ME->getOperand(0)->isAllOnesValue()) {
6331 RHS = AE->getOperand(1);
6332 LHS = ME->getOperand(1);
6336 case ICmpInst::ICMP_UGE:
6337 if ((RA - 1).isMinValue()) {
6338 Pred = ICmpInst::ICMP_NE;
6339 RHS = getConstant(RA - 1);
6343 if (RA.isMaxValue()) {
6344 Pred = ICmpInst::ICMP_EQ;
6348 if (RA.isMinValue()) goto trivially_true;
6350 Pred = ICmpInst::ICMP_UGT;
6351 RHS = getConstant(RA - 1);
6354 case ICmpInst::ICMP_ULE:
6355 if ((RA + 1).isMaxValue()) {
6356 Pred = ICmpInst::ICMP_NE;
6357 RHS = getConstant(RA + 1);
6361 if (RA.isMinValue()) {
6362 Pred = ICmpInst::ICMP_EQ;
6366 if (RA.isMaxValue()) goto trivially_true;
6368 Pred = ICmpInst::ICMP_ULT;
6369 RHS = getConstant(RA + 1);
6372 case ICmpInst::ICMP_SGE:
6373 if ((RA - 1).isMinSignedValue()) {
6374 Pred = ICmpInst::ICMP_NE;
6375 RHS = getConstant(RA - 1);
6379 if (RA.isMaxSignedValue()) {
6380 Pred = ICmpInst::ICMP_EQ;
6384 if (RA.isMinSignedValue()) goto trivially_true;
6386 Pred = ICmpInst::ICMP_SGT;
6387 RHS = getConstant(RA - 1);
6390 case ICmpInst::ICMP_SLE:
6391 if ((RA + 1).isMaxSignedValue()) {
6392 Pred = ICmpInst::ICMP_NE;
6393 RHS = getConstant(RA + 1);
6397 if (RA.isMinSignedValue()) {
6398 Pred = ICmpInst::ICMP_EQ;
6402 if (RA.isMaxSignedValue()) goto trivially_true;
6404 Pred = ICmpInst::ICMP_SLT;
6405 RHS = getConstant(RA + 1);
6408 case ICmpInst::ICMP_UGT:
6409 if (RA.isMinValue()) {
6410 Pred = ICmpInst::ICMP_NE;
6414 if ((RA + 1).isMaxValue()) {
6415 Pred = ICmpInst::ICMP_EQ;
6416 RHS = getConstant(RA + 1);
6420 if (RA.isMaxValue()) goto trivially_false;
6422 case ICmpInst::ICMP_ULT:
6423 if (RA.isMaxValue()) {
6424 Pred = ICmpInst::ICMP_NE;
6428 if ((RA - 1).isMinValue()) {
6429 Pred = ICmpInst::ICMP_EQ;
6430 RHS = getConstant(RA - 1);
6434 if (RA.isMinValue()) goto trivially_false;
6436 case ICmpInst::ICMP_SGT:
6437 if (RA.isMinSignedValue()) {
6438 Pred = ICmpInst::ICMP_NE;
6442 if ((RA + 1).isMaxSignedValue()) {
6443 Pred = ICmpInst::ICMP_EQ;
6444 RHS = getConstant(RA + 1);
6448 if (RA.isMaxSignedValue()) goto trivially_false;
6450 case ICmpInst::ICMP_SLT:
6451 if (RA.isMaxSignedValue()) {
6452 Pred = ICmpInst::ICMP_NE;
6456 if ((RA - 1).isMinSignedValue()) {
6457 Pred = ICmpInst::ICMP_EQ;
6458 RHS = getConstant(RA - 1);
6462 if (RA.isMinSignedValue()) goto trivially_false;
6467 // Check for obvious equality.
6468 if (HasSameValue(LHS, RHS)) {
6469 if (ICmpInst::isTrueWhenEqual(Pred))
6470 goto trivially_true;
6471 if (ICmpInst::isFalseWhenEqual(Pred))
6472 goto trivially_false;
6475 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
6476 // adding or subtracting 1 from one of the operands.
6478 case ICmpInst::ICMP_SLE:
6479 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) {
6480 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
6482 Pred = ICmpInst::ICMP_SLT;
6484 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) {
6485 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
6487 Pred = ICmpInst::ICMP_SLT;
6491 case ICmpInst::ICMP_SGE:
6492 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) {
6493 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
6495 Pred = ICmpInst::ICMP_SGT;
6497 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) {
6498 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
6500 Pred = ICmpInst::ICMP_SGT;
6504 case ICmpInst::ICMP_ULE:
6505 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) {
6506 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
6508 Pred = ICmpInst::ICMP_ULT;
6510 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) {
6511 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
6513 Pred = ICmpInst::ICMP_ULT;
6517 case ICmpInst::ICMP_UGE:
6518 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) {
6519 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
6521 Pred = ICmpInst::ICMP_UGT;
6523 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) {
6524 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
6526 Pred = ICmpInst::ICMP_UGT;
6534 // TODO: More simplifications are possible here.
6536 // Recursively simplify until we either hit a recursion limit or nothing
6539 return SimplifyICmpOperands(Pred, LHS, RHS, Depth+1);
6545 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
6546 Pred = ICmpInst::ICMP_EQ;
6551 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
6552 Pred = ICmpInst::ICMP_NE;
6556 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
6557 return getSignedRange(S).getSignedMax().isNegative();
6560 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
6561 return getSignedRange(S).getSignedMin().isStrictlyPositive();
6564 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
6565 return !getSignedRange(S).getSignedMin().isNegative();
6568 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
6569 return !getSignedRange(S).getSignedMax().isStrictlyPositive();
6572 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
6573 return isKnownNegative(S) || isKnownPositive(S);
6576 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
6577 const SCEV *LHS, const SCEV *RHS) {
6578 // Canonicalize the inputs first.
6579 (void)SimplifyICmpOperands(Pred, LHS, RHS);
6581 // If LHS or RHS is an addrec, check to see if the condition is true in
6582 // every iteration of the loop.
6583 // If LHS and RHS are both addrec, both conditions must be true in
6584 // every iteration of the loop.
6585 const SCEVAddRecExpr *LAR = dyn_cast<SCEVAddRecExpr>(LHS);
6586 const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS);
6587 bool LeftGuarded = false;
6588 bool RightGuarded = false;
6590 const Loop *L = LAR->getLoop();
6591 if (isLoopEntryGuardedByCond(L, Pred, LAR->getStart(), RHS) &&
6592 isLoopBackedgeGuardedByCond(L, Pred, LAR->getPostIncExpr(*this), RHS)) {
6593 if (!RAR) return true;
6598 const Loop *L = RAR->getLoop();
6599 if (isLoopEntryGuardedByCond(L, Pred, LHS, RAR->getStart()) &&
6600 isLoopBackedgeGuardedByCond(L, Pred, LHS, RAR->getPostIncExpr(*this))) {
6601 if (!LAR) return true;
6602 RightGuarded = true;
6605 if (LeftGuarded && RightGuarded)
6608 // Otherwise see what can be done with known constant ranges.
6609 return isKnownPredicateWithRanges(Pred, LHS, RHS);
6613 ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred,
6614 const SCEV *LHS, const SCEV *RHS) {
6615 if (HasSameValue(LHS, RHS))
6616 return ICmpInst::isTrueWhenEqual(Pred);
6618 // This code is split out from isKnownPredicate because it is called from
6619 // within isLoopEntryGuardedByCond.
6622 llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6623 case ICmpInst::ICMP_SGT:
6624 std::swap(LHS, RHS);
6625 case ICmpInst::ICMP_SLT: {
6626 ConstantRange LHSRange = getSignedRange(LHS);
6627 ConstantRange RHSRange = getSignedRange(RHS);
6628 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
6630 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
6634 case ICmpInst::ICMP_SGE:
6635 std::swap(LHS, RHS);
6636 case ICmpInst::ICMP_SLE: {
6637 ConstantRange LHSRange = getSignedRange(LHS);
6638 ConstantRange RHSRange = getSignedRange(RHS);
6639 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
6641 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
6645 case ICmpInst::ICMP_UGT:
6646 std::swap(LHS, RHS);
6647 case ICmpInst::ICMP_ULT: {
6648 ConstantRange LHSRange = getUnsignedRange(LHS);
6649 ConstantRange RHSRange = getUnsignedRange(RHS);
6650 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
6652 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
6656 case ICmpInst::ICMP_UGE:
6657 std::swap(LHS, RHS);
6658 case ICmpInst::ICMP_ULE: {
6659 ConstantRange LHSRange = getUnsignedRange(LHS);
6660 ConstantRange RHSRange = getUnsignedRange(RHS);
6661 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
6663 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
6667 case ICmpInst::ICMP_NE: {
6668 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
6670 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
6673 const SCEV *Diff = getMinusSCEV(LHS, RHS);
6674 if (isKnownNonZero(Diff))
6678 case ICmpInst::ICMP_EQ:
6679 // The check at the top of the function catches the case where
6680 // the values are known to be equal.
6686 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
6687 /// protected by a conditional between LHS and RHS. This is used to
6688 /// to eliminate casts.
6690 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
6691 ICmpInst::Predicate Pred,
6692 const SCEV *LHS, const SCEV *RHS) {
6693 // Interpret a null as meaning no loop, where there is obviously no guard
6694 // (interprocedural conditions notwithstanding).
6695 if (!L) return true;
6697 if (isKnownPredicateWithRanges(Pred, LHS, RHS)) return true;
6699 BasicBlock *Latch = L->getLoopLatch();
6703 BranchInst *LoopContinuePredicate =
6704 dyn_cast<BranchInst>(Latch->getTerminator());
6705 if (LoopContinuePredicate && LoopContinuePredicate->isConditional() &&
6706 isImpliedCond(Pred, LHS, RHS,
6707 LoopContinuePredicate->getCondition(),
6708 LoopContinuePredicate->getSuccessor(0) != L->getHeader()))
6711 // Check conditions due to any @llvm.assume intrinsics.
6712 for (auto &AssumeVH : AC->assumptions()) {
6715 auto *CI = cast<CallInst>(AssumeVH);
6716 if (!DT->dominates(CI, Latch->getTerminator()))
6719 if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false))
6726 /// isLoopEntryGuardedByCond - Test whether entry to the loop is protected
6727 /// by a conditional between LHS and RHS. This is used to help avoid max
6728 /// expressions in loop trip counts, and to eliminate casts.
6730 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
6731 ICmpInst::Predicate Pred,
6732 const SCEV *LHS, const SCEV *RHS) {
6733 // Interpret a null as meaning no loop, where there is obviously no guard
6734 // (interprocedural conditions notwithstanding).
6735 if (!L) return false;
6737 if (isKnownPredicateWithRanges(Pred, LHS, RHS)) return true;
6739 // Starting at the loop predecessor, climb up the predecessor chain, as long
6740 // as there are predecessors that can be found that have unique successors
6741 // leading to the original header.
6742 for (std::pair<BasicBlock *, BasicBlock *>
6743 Pair(L->getLoopPredecessor(), L->getHeader());
6745 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
6747 BranchInst *LoopEntryPredicate =
6748 dyn_cast<BranchInst>(Pair.first->getTerminator());
6749 if (!LoopEntryPredicate ||
6750 LoopEntryPredicate->isUnconditional())
6753 if (isImpliedCond(Pred, LHS, RHS,
6754 LoopEntryPredicate->getCondition(),
6755 LoopEntryPredicate->getSuccessor(0) != Pair.second))
6759 // Check conditions due to any @llvm.assume intrinsics.
6760 for (auto &AssumeVH : AC->assumptions()) {
6763 auto *CI = cast<CallInst>(AssumeVH);
6764 if (!DT->dominates(CI, L->getHeader()))
6767 if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false))
6774 /// RAII wrapper to prevent recursive application of isImpliedCond.
6775 /// ScalarEvolution's PendingLoopPredicates set must be empty unless we are
6776 /// currently evaluating isImpliedCond.
6777 struct MarkPendingLoopPredicate {
6779 DenseSet<Value*> &LoopPreds;
6782 MarkPendingLoopPredicate(Value *C, DenseSet<Value*> &LP)
6783 : Cond(C), LoopPreds(LP) {
6784 Pending = !LoopPreds.insert(Cond).second;
6786 ~MarkPendingLoopPredicate() {
6788 LoopPreds.erase(Cond);
6792 /// isImpliedCond - Test whether the condition described by Pred, LHS,
6793 /// and RHS is true whenever the given Cond value evaluates to true.
6794 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred,
6795 const SCEV *LHS, const SCEV *RHS,
6796 Value *FoundCondValue,
6798 MarkPendingLoopPredicate Mark(FoundCondValue, PendingLoopPredicates);
6802 // Recursively handle And and Or conditions.
6803 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) {
6804 if (BO->getOpcode() == Instruction::And) {
6806 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
6807 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
6808 } else if (BO->getOpcode() == Instruction::Or) {
6810 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
6811 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
6815 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue);
6816 if (!ICI) return false;
6818 // Bail if the ICmp's operands' types are wider than the needed type
6819 // before attempting to call getSCEV on them. This avoids infinite
6820 // recursion, since the analysis of widening casts can require loop
6821 // exit condition information for overflow checking, which would
6823 if (getTypeSizeInBits(LHS->getType()) <
6824 getTypeSizeInBits(ICI->getOperand(0)->getType()))
6827 // Now that we found a conditional branch that dominates the loop or controls
6828 // the loop latch. Check to see if it is the comparison we are looking for.
6829 ICmpInst::Predicate FoundPred;
6831 FoundPred = ICI->getInversePredicate();
6833 FoundPred = ICI->getPredicate();
6835 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
6836 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
6838 // Balance the types. The case where FoundLHS' type is wider than
6839 // LHS' type is checked for above.
6840 if (getTypeSizeInBits(LHS->getType()) >
6841 getTypeSizeInBits(FoundLHS->getType())) {
6842 if (CmpInst::isSigned(FoundPred)) {
6843 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
6844 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
6846 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
6847 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
6851 // Canonicalize the query to match the way instcombine will have
6852 // canonicalized the comparison.
6853 if (SimplifyICmpOperands(Pred, LHS, RHS))
6855 return CmpInst::isTrueWhenEqual(Pred);
6856 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
6857 if (FoundLHS == FoundRHS)
6858 return CmpInst::isFalseWhenEqual(FoundPred);
6860 // Check to see if we can make the LHS or RHS match.
6861 if (LHS == FoundRHS || RHS == FoundLHS) {
6862 if (isa<SCEVConstant>(RHS)) {
6863 std::swap(FoundLHS, FoundRHS);
6864 FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
6866 std::swap(LHS, RHS);
6867 Pred = ICmpInst::getSwappedPredicate(Pred);
6871 // Check whether the found predicate is the same as the desired predicate.
6872 if (FoundPred == Pred)
6873 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
6875 // Check whether swapping the found predicate makes it the same as the
6876 // desired predicate.
6877 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
6878 if (isa<SCEVConstant>(RHS))
6879 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
6881 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
6882 RHS, LHS, FoundLHS, FoundRHS);
6885 // Check if we can make progress by sharpening ranges.
6886 if (FoundPred == ICmpInst::ICMP_NE &&
6887 (isa<SCEVConstant>(FoundLHS) || isa<SCEVConstant>(FoundRHS))) {
6889 const SCEVConstant *C = nullptr;
6890 const SCEV *V = nullptr;
6892 if (isa<SCEVConstant>(FoundLHS)) {
6893 C = cast<SCEVConstant>(FoundLHS);
6896 C = cast<SCEVConstant>(FoundRHS);
6900 // The guarding predicate tells us that C != V. If the known range
6901 // of V is [C, t), we can sharpen the range to [C + 1, t). The
6902 // range we consider has to correspond to same signedness as the
6903 // predicate we're interested in folding.
6905 APInt Min = ICmpInst::isSigned(Pred) ?
6906 getSignedRange(V).getSignedMin() : getUnsignedRange(V).getUnsignedMin();
6908 if (Min == C->getValue()->getValue()) {
6909 // Given (V >= Min && V != Min) we conclude V >= (Min + 1).
6910 // This is true even if (Min + 1) wraps around -- in case of
6911 // wraparound, (Min + 1) < Min, so (V >= Min => V >= (Min + 1)).
6913 APInt SharperMin = Min + 1;
6916 case ICmpInst::ICMP_SGE:
6917 case ICmpInst::ICMP_UGE:
6918 // We know V `Pred` SharperMin. If this implies LHS `Pred`
6920 if (isImpliedCondOperands(Pred, LHS, RHS, V,
6921 getConstant(SharperMin)))
6924 case ICmpInst::ICMP_SGT:
6925 case ICmpInst::ICMP_UGT:
6926 // We know from the range information that (V `Pred` Min ||
6927 // V == Min). We know from the guarding condition that !(V
6928 // == Min). This gives us
6930 // V `Pred` Min || V == Min && !(V == Min)
6933 // If V `Pred` Min implies LHS `Pred` RHS, we're done.
6935 if (isImpliedCondOperands(Pred, LHS, RHS, V, getConstant(Min)))
6945 // Check whether the actual condition is beyond sufficient.
6946 if (FoundPred == ICmpInst::ICMP_EQ)
6947 if (ICmpInst::isTrueWhenEqual(Pred))
6948 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
6950 if (Pred == ICmpInst::ICMP_NE)
6951 if (!ICmpInst::isTrueWhenEqual(FoundPred))
6952 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
6955 // Otherwise assume the worst.
6959 /// isImpliedCondOperands - Test whether the condition described by Pred,
6960 /// LHS, and RHS is true whenever the condition described by Pred, FoundLHS,
6961 /// and FoundRHS is true.
6962 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
6963 const SCEV *LHS, const SCEV *RHS,
6964 const SCEV *FoundLHS,
6965 const SCEV *FoundRHS) {
6966 return isImpliedCondOperandsHelper(Pred, LHS, RHS,
6967 FoundLHS, FoundRHS) ||
6968 // ~x < ~y --> x > y
6969 isImpliedCondOperandsHelper(Pred, LHS, RHS,
6970 getNotSCEV(FoundRHS),
6971 getNotSCEV(FoundLHS));
6975 /// If Expr computes ~A, return A else return nullptr
6976 static const SCEV *MatchNotExpr(const SCEV *Expr) {
6977 const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Expr);
6978 if (!Add || Add->getNumOperands() != 2) return nullptr;
6980 const SCEVConstant *AddLHS = dyn_cast<SCEVConstant>(Add->getOperand(0));
6981 if (!(AddLHS && AddLHS->getValue()->getValue().isAllOnesValue()))
6984 const SCEVMulExpr *AddRHS = dyn_cast<SCEVMulExpr>(Add->getOperand(1));
6985 if (!AddRHS || AddRHS->getNumOperands() != 2) return nullptr;
6987 const SCEVConstant *MulLHS = dyn_cast<SCEVConstant>(AddRHS->getOperand(0));
6988 if (!(MulLHS && MulLHS->getValue()->getValue().isAllOnesValue()))
6991 return AddRHS->getOperand(1);
6995 /// Is MaybeMaxExpr an SMax or UMax of Candidate and some other values?
6996 template<typename MaxExprType>
6997 static bool IsMaxConsistingOf(const SCEV *MaybeMaxExpr,
6998 const SCEV *Candidate) {
6999 const MaxExprType *MaxExpr = dyn_cast<MaxExprType>(MaybeMaxExpr);
7000 if (!MaxExpr) return false;
7002 auto It = std::find(MaxExpr->op_begin(), MaxExpr->op_end(), Candidate);
7003 return It != MaxExpr->op_end();
7007 /// Is MaybeMinExpr an SMin or UMin of Candidate and some other values?
7008 template<typename MaxExprType>
7009 static bool IsMinConsistingOf(ScalarEvolution &SE,
7010 const SCEV *MaybeMinExpr,
7011 const SCEV *Candidate) {
7012 const SCEV *MaybeMaxExpr = MatchNotExpr(MaybeMinExpr);
7016 return IsMaxConsistingOf<MaxExprType>(MaybeMaxExpr, SE.getNotSCEV(Candidate));
7020 /// Is LHS `Pred` RHS true on the virtue of LHS or RHS being a Min or Max
7022 static bool IsKnownPredicateViaMinOrMax(ScalarEvolution &SE,
7023 ICmpInst::Predicate Pred,
7024 const SCEV *LHS, const SCEV *RHS) {
7029 case ICmpInst::ICMP_SGE:
7030 std::swap(LHS, RHS);
7032 case ICmpInst::ICMP_SLE:
7035 IsMinConsistingOf<SCEVSMaxExpr>(SE, LHS, RHS) ||
7037 IsMaxConsistingOf<SCEVSMaxExpr>(RHS, LHS);
7039 case ICmpInst::ICMP_UGE:
7040 std::swap(LHS, RHS);
7042 case ICmpInst::ICMP_ULE:
7045 IsMinConsistingOf<SCEVUMaxExpr>(SE, LHS, RHS) ||
7047 IsMaxConsistingOf<SCEVUMaxExpr>(RHS, LHS);
7050 llvm_unreachable("covered switch fell through?!");
7053 /// isImpliedCondOperandsHelper - Test whether the condition described by
7054 /// Pred, LHS, and RHS is true whenever the condition described by Pred,
7055 /// FoundLHS, and FoundRHS is true.
7057 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
7058 const SCEV *LHS, const SCEV *RHS,
7059 const SCEV *FoundLHS,
7060 const SCEV *FoundRHS) {
7061 auto IsKnownPredicateFull =
7062 [this](ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS) {
7063 return isKnownPredicateWithRanges(Pred, LHS, RHS) ||
7064 IsKnownPredicateViaMinOrMax(*this, Pred, LHS, RHS);
7068 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
7069 case ICmpInst::ICMP_EQ:
7070 case ICmpInst::ICMP_NE:
7071 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
7074 case ICmpInst::ICMP_SLT:
7075 case ICmpInst::ICMP_SLE:
7076 if (IsKnownPredicateFull(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
7077 IsKnownPredicateFull(ICmpInst::ICMP_SGE, RHS, FoundRHS))
7080 case ICmpInst::ICMP_SGT:
7081 case ICmpInst::ICMP_SGE:
7082 if (IsKnownPredicateFull(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
7083 IsKnownPredicateFull(ICmpInst::ICMP_SLE, RHS, FoundRHS))
7086 case ICmpInst::ICMP_ULT:
7087 case ICmpInst::ICMP_ULE:
7088 if (IsKnownPredicateFull(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
7089 IsKnownPredicateFull(ICmpInst::ICMP_UGE, RHS, FoundRHS))
7092 case ICmpInst::ICMP_UGT:
7093 case ICmpInst::ICMP_UGE:
7094 if (IsKnownPredicateFull(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
7095 IsKnownPredicateFull(ICmpInst::ICMP_ULE, RHS, FoundRHS))
7103 // Verify if an linear IV with positive stride can overflow when in a
7104 // less-than comparison, knowing the invariant term of the comparison, the
7105 // stride and the knowledge of NSW/NUW flags on the recurrence.
7106 bool ScalarEvolution::doesIVOverflowOnLT(const SCEV *RHS, const SCEV *Stride,
7107 bool IsSigned, bool NoWrap) {
7108 if (NoWrap) return false;
7110 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
7111 const SCEV *One = getConstant(Stride->getType(), 1);
7114 APInt MaxRHS = getSignedRange(RHS).getSignedMax();
7115 APInt MaxValue = APInt::getSignedMaxValue(BitWidth);
7116 APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
7119 // SMaxRHS + SMaxStrideMinusOne > SMaxValue => overflow!
7120 return (MaxValue - MaxStrideMinusOne).slt(MaxRHS);
7123 APInt MaxRHS = getUnsignedRange(RHS).getUnsignedMax();
7124 APInt MaxValue = APInt::getMaxValue(BitWidth);
7125 APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
7128 // UMaxRHS + UMaxStrideMinusOne > UMaxValue => overflow!
7129 return (MaxValue - MaxStrideMinusOne).ult(MaxRHS);
7132 // Verify if an linear IV with negative stride can overflow when in a
7133 // greater-than comparison, knowing the invariant term of the comparison,
7134 // the stride and the knowledge of NSW/NUW flags on the recurrence.
7135 bool ScalarEvolution::doesIVOverflowOnGT(const SCEV *RHS, const SCEV *Stride,
7136 bool IsSigned, bool NoWrap) {
7137 if (NoWrap) return false;
7139 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
7140 const SCEV *One = getConstant(Stride->getType(), 1);
7143 APInt MinRHS = getSignedRange(RHS).getSignedMin();
7144 APInt MinValue = APInt::getSignedMinValue(BitWidth);
7145 APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
7148 // SMinRHS - SMaxStrideMinusOne < SMinValue => overflow!
7149 return (MinValue + MaxStrideMinusOne).sgt(MinRHS);
7152 APInt MinRHS = getUnsignedRange(RHS).getUnsignedMin();
7153 APInt MinValue = APInt::getMinValue(BitWidth);
7154 APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
7157 // UMinRHS - UMaxStrideMinusOne < UMinValue => overflow!
7158 return (MinValue + MaxStrideMinusOne).ugt(MinRHS);
7161 // Compute the backedge taken count knowing the interval difference, the
7162 // stride and presence of the equality in the comparison.
7163 const SCEV *ScalarEvolution::computeBECount(const SCEV *Delta, const SCEV *Step,
7165 const SCEV *One = getConstant(Step->getType(), 1);
7166 Delta = Equality ? getAddExpr(Delta, Step)
7167 : getAddExpr(Delta, getMinusSCEV(Step, One));
7168 return getUDivExpr(Delta, Step);
7171 /// HowManyLessThans - Return the number of times a backedge containing the
7172 /// specified less-than comparison will execute. If not computable, return
7173 /// CouldNotCompute.
7175 /// @param ControlsExit is true when the LHS < RHS condition directly controls
7176 /// the branch (loops exits only if condition is true). In this case, we can use
7177 /// NoWrapFlags to skip overflow checks.
7178 ScalarEvolution::ExitLimit
7179 ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
7180 const Loop *L, bool IsSigned,
7181 bool ControlsExit) {
7182 // We handle only IV < Invariant
7183 if (!isLoopInvariant(RHS, L))
7184 return getCouldNotCompute();
7186 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
7188 // Avoid weird loops
7189 if (!IV || IV->getLoop() != L || !IV->isAffine())
7190 return getCouldNotCompute();
7192 bool NoWrap = ControlsExit &&
7193 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
7195 const SCEV *Stride = IV->getStepRecurrence(*this);
7197 // Avoid negative or zero stride values
7198 if (!isKnownPositive(Stride))
7199 return getCouldNotCompute();
7201 // Avoid proven overflow cases: this will ensure that the backedge taken count
7202 // will not generate any unsigned overflow. Relaxed no-overflow conditions
7203 // exploit NoWrapFlags, allowing to optimize in presence of undefined
7204 // behaviors like the case of C language.
7205 if (!Stride->isOne() && doesIVOverflowOnLT(RHS, Stride, IsSigned, NoWrap))
7206 return getCouldNotCompute();
7208 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SLT
7209 : ICmpInst::ICMP_ULT;
7210 const SCEV *Start = IV->getStart();
7211 const SCEV *End = RHS;
7212 if (!isLoopEntryGuardedByCond(L, Cond, getMinusSCEV(Start, Stride), RHS)) {
7213 const SCEV *Diff = getMinusSCEV(RHS, Start);
7214 // If we have NoWrap set, then we can assume that the increment won't
7215 // overflow, in which case if RHS - Start is a constant, we don't need to
7216 // do a max operation since we can just figure it out statically
7217 if (NoWrap && isa<SCEVConstant>(Diff)) {
7218 APInt D = dyn_cast<const SCEVConstant>(Diff)->getValue()->getValue();
7222 End = IsSigned ? getSMaxExpr(RHS, Start)
7223 : getUMaxExpr(RHS, Start);
7226 const SCEV *BECount = computeBECount(getMinusSCEV(End, Start), Stride, false);
7228 APInt MinStart = IsSigned ? getSignedRange(Start).getSignedMin()
7229 : getUnsignedRange(Start).getUnsignedMin();
7231 APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
7232 : getUnsignedRange(Stride).getUnsignedMin();
7234 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
7235 APInt Limit = IsSigned ? APInt::getSignedMaxValue(BitWidth) - (MinStride - 1)
7236 : APInt::getMaxValue(BitWidth) - (MinStride - 1);
7238 // Although End can be a MAX expression we estimate MaxEnd considering only
7239 // the case End = RHS. This is safe because in the other case (End - Start)
7240 // is zero, leading to a zero maximum backedge taken count.
7242 IsSigned ? APIntOps::smin(getSignedRange(RHS).getSignedMax(), Limit)
7243 : APIntOps::umin(getUnsignedRange(RHS).getUnsignedMax(), Limit);
7245 const SCEV *MaxBECount;
7246 if (isa<SCEVConstant>(BECount))
7247 MaxBECount = BECount;
7249 MaxBECount = computeBECount(getConstant(MaxEnd - MinStart),
7250 getConstant(MinStride), false);
7252 if (isa<SCEVCouldNotCompute>(MaxBECount))
7253 MaxBECount = BECount;
7255 return ExitLimit(BECount, MaxBECount);
7258 ScalarEvolution::ExitLimit
7259 ScalarEvolution::HowManyGreaterThans(const SCEV *LHS, const SCEV *RHS,
7260 const Loop *L, bool IsSigned,
7261 bool ControlsExit) {
7262 // We handle only IV > Invariant
7263 if (!isLoopInvariant(RHS, L))
7264 return getCouldNotCompute();
7266 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
7268 // Avoid weird loops
7269 if (!IV || IV->getLoop() != L || !IV->isAffine())
7270 return getCouldNotCompute();
7272 bool NoWrap = ControlsExit &&
7273 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
7275 const SCEV *Stride = getNegativeSCEV(IV->getStepRecurrence(*this));
7277 // Avoid negative or zero stride values
7278 if (!isKnownPositive(Stride))
7279 return getCouldNotCompute();
7281 // Avoid proven overflow cases: this will ensure that the backedge taken count
7282 // will not generate any unsigned overflow. Relaxed no-overflow conditions
7283 // exploit NoWrapFlags, allowing to optimize in presence of undefined
7284 // behaviors like the case of C language.
7285 if (!Stride->isOne() && doesIVOverflowOnGT(RHS, Stride, IsSigned, NoWrap))
7286 return getCouldNotCompute();
7288 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SGT
7289 : ICmpInst::ICMP_UGT;
7291 const SCEV *Start = IV->getStart();
7292 const SCEV *End = RHS;
7293 if (!isLoopEntryGuardedByCond(L, Cond, getAddExpr(Start, Stride), RHS)) {
7294 const SCEV *Diff = getMinusSCEV(RHS, Start);
7295 // If we have NoWrap set, then we can assume that the increment won't
7296 // overflow, in which case if RHS - Start is a constant, we don't need to
7297 // do a max operation since we can just figure it out statically
7298 if (NoWrap && isa<SCEVConstant>(Diff)) {
7299 APInt D = dyn_cast<const SCEVConstant>(Diff)->getValue()->getValue();
7300 if (!D.isNegative())
7303 End = IsSigned ? getSMinExpr(RHS, Start)
7304 : getUMinExpr(RHS, Start);
7307 const SCEV *BECount = computeBECount(getMinusSCEV(Start, End), Stride, false);
7309 APInt MaxStart = IsSigned ? getSignedRange(Start).getSignedMax()
7310 : getUnsignedRange(Start).getUnsignedMax();
7312 APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
7313 : getUnsignedRange(Stride).getUnsignedMin();
7315 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
7316 APInt Limit = IsSigned ? APInt::getSignedMinValue(BitWidth) + (MinStride - 1)
7317 : APInt::getMinValue(BitWidth) + (MinStride - 1);
7319 // Although End can be a MIN expression we estimate MinEnd considering only
7320 // the case End = RHS. This is safe because in the other case (Start - End)
7321 // is zero, leading to a zero maximum backedge taken count.
7323 IsSigned ? APIntOps::smax(getSignedRange(RHS).getSignedMin(), Limit)
7324 : APIntOps::umax(getUnsignedRange(RHS).getUnsignedMin(), Limit);
7327 const SCEV *MaxBECount = getCouldNotCompute();
7328 if (isa<SCEVConstant>(BECount))
7329 MaxBECount = BECount;
7331 MaxBECount = computeBECount(getConstant(MaxStart - MinEnd),
7332 getConstant(MinStride), false);
7334 if (isa<SCEVCouldNotCompute>(MaxBECount))
7335 MaxBECount = BECount;
7337 return ExitLimit(BECount, MaxBECount);
7340 /// getNumIterationsInRange - Return the number of iterations of this loop that
7341 /// produce values in the specified constant range. Another way of looking at
7342 /// this is that it returns the first iteration number where the value is not in
7343 /// the condition, thus computing the exit count. If the iteration count can't
7344 /// be computed, an instance of SCEVCouldNotCompute is returned.
7345 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
7346 ScalarEvolution &SE) const {
7347 if (Range.isFullSet()) // Infinite loop.
7348 return SE.getCouldNotCompute();
7350 // If the start is a non-zero constant, shift the range to simplify things.
7351 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
7352 if (!SC->getValue()->isZero()) {
7353 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
7354 Operands[0] = SE.getConstant(SC->getType(), 0);
7355 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(),
7356 getNoWrapFlags(FlagNW));
7357 if (const SCEVAddRecExpr *ShiftedAddRec =
7358 dyn_cast<SCEVAddRecExpr>(Shifted))
7359 return ShiftedAddRec->getNumIterationsInRange(
7360 Range.subtract(SC->getValue()->getValue()), SE);
7361 // This is strange and shouldn't happen.
7362 return SE.getCouldNotCompute();
7365 // The only time we can solve this is when we have all constant indices.
7366 // Otherwise, we cannot determine the overflow conditions.
7367 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
7368 if (!isa<SCEVConstant>(getOperand(i)))
7369 return SE.getCouldNotCompute();
7372 // Okay at this point we know that all elements of the chrec are constants and
7373 // that the start element is zero.
7375 // First check to see if the range contains zero. If not, the first
7377 unsigned BitWidth = SE.getTypeSizeInBits(getType());
7378 if (!Range.contains(APInt(BitWidth, 0)))
7379 return SE.getConstant(getType(), 0);
7382 // If this is an affine expression then we have this situation:
7383 // Solve {0,+,A} in Range === Ax in Range
7385 // We know that zero is in the range. If A is positive then we know that
7386 // the upper value of the range must be the first possible exit value.
7387 // If A is negative then the lower of the range is the last possible loop
7388 // value. Also note that we already checked for a full range.
7389 APInt One(BitWidth,1);
7390 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
7391 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
7393 // The exit value should be (End+A)/A.
7394 APInt ExitVal = (End + A).udiv(A);
7395 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
7397 // Evaluate at the exit value. If we really did fall out of the valid
7398 // range, then we computed our trip count, otherwise wrap around or other
7399 // things must have happened.
7400 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
7401 if (Range.contains(Val->getValue()))
7402 return SE.getCouldNotCompute(); // Something strange happened
7404 // Ensure that the previous value is in the range. This is a sanity check.
7405 assert(Range.contains(
7406 EvaluateConstantChrecAtConstant(this,
7407 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
7408 "Linear scev computation is off in a bad way!");
7409 return SE.getConstant(ExitValue);
7410 } else if (isQuadratic()) {
7411 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
7412 // quadratic equation to solve it. To do this, we must frame our problem in
7413 // terms of figuring out when zero is crossed, instead of when
7414 // Range.getUpper() is crossed.
7415 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
7416 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
7417 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop(),
7418 // getNoWrapFlags(FlagNW)
7421 // Next, solve the constructed addrec
7422 std::pair<const SCEV *,const SCEV *> Roots =
7423 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
7424 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
7425 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
7427 // Pick the smallest positive root value.
7428 if (ConstantInt *CB =
7429 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
7430 R1->getValue(), R2->getValue()))) {
7431 if (CB->getZExtValue() == false)
7432 std::swap(R1, R2); // R1 is the minimum root now.
7434 // Make sure the root is not off by one. The returned iteration should
7435 // not be in the range, but the previous one should be. When solving
7436 // for "X*X < 5", for example, we should not return a root of 2.
7437 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
7440 if (Range.contains(R1Val->getValue())) {
7441 // The next iteration must be out of the range...
7442 ConstantInt *NextVal =
7443 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1);
7445 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
7446 if (!Range.contains(R1Val->getValue()))
7447 return SE.getConstant(NextVal);
7448 return SE.getCouldNotCompute(); // Something strange happened
7451 // If R1 was not in the range, then it is a good return value. Make
7452 // sure that R1-1 WAS in the range though, just in case.
7453 ConstantInt *NextVal =
7454 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1);
7455 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
7456 if (Range.contains(R1Val->getValue()))
7458 return SE.getCouldNotCompute(); // Something strange happened
7463 return SE.getCouldNotCompute();
7469 FindUndefs() : Found(false) {}
7471 bool follow(const SCEV *S) {
7472 if (const SCEVUnknown *C = dyn_cast<SCEVUnknown>(S)) {
7473 if (isa<UndefValue>(C->getValue()))
7475 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) {
7476 if (isa<UndefValue>(C->getValue()))
7480 // Keep looking if we haven't found it yet.
7483 bool isDone() const {
7484 // Stop recursion if we have found an undef.
7490 // Return true when S contains at least an undef value.
7492 containsUndefs(const SCEV *S) {
7494 SCEVTraversal<FindUndefs> ST(F);
7501 // Collect all steps of SCEV expressions.
7502 struct SCEVCollectStrides {
7503 ScalarEvolution &SE;
7504 SmallVectorImpl<const SCEV *> &Strides;
7506 SCEVCollectStrides(ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &S)
7507 : SE(SE), Strides(S) {}
7509 bool follow(const SCEV *S) {
7510 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(S))
7511 Strides.push_back(AR->getStepRecurrence(SE));
7514 bool isDone() const { return false; }
7517 // Collect all SCEVUnknown and SCEVMulExpr expressions.
7518 struct SCEVCollectTerms {
7519 SmallVectorImpl<const SCEV *> &Terms;
7521 SCEVCollectTerms(SmallVectorImpl<const SCEV *> &T)
7524 bool follow(const SCEV *S) {
7525 if (isa<SCEVUnknown>(S) || isa<SCEVMulExpr>(S)) {
7526 if (!containsUndefs(S))
7529 // Stop recursion: once we collected a term, do not walk its operands.
7536 bool isDone() const { return false; }
7540 /// Find parametric terms in this SCEVAddRecExpr.
7541 void SCEVAddRecExpr::collectParametricTerms(
7542 ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &Terms) const {
7543 SmallVector<const SCEV *, 4> Strides;
7544 SCEVCollectStrides StrideCollector(SE, Strides);
7545 visitAll(this, StrideCollector);
7548 dbgs() << "Strides:\n";
7549 for (const SCEV *S : Strides)
7550 dbgs() << *S << "\n";
7553 for (const SCEV *S : Strides) {
7554 SCEVCollectTerms TermCollector(Terms);
7555 visitAll(S, TermCollector);
7559 dbgs() << "Terms:\n";
7560 for (const SCEV *T : Terms)
7561 dbgs() << *T << "\n";
7565 static bool findArrayDimensionsRec(ScalarEvolution &SE,
7566 SmallVectorImpl<const SCEV *> &Terms,
7567 SmallVectorImpl<const SCEV *> &Sizes) {
7568 int Last = Terms.size() - 1;
7569 const SCEV *Step = Terms[Last];
7571 // End of recursion.
7573 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Step)) {
7574 SmallVector<const SCEV *, 2> Qs;
7575 for (const SCEV *Op : M->operands())
7576 if (!isa<SCEVConstant>(Op))
7579 Step = SE.getMulExpr(Qs);
7582 Sizes.push_back(Step);
7586 for (const SCEV *&Term : Terms) {
7587 // Normalize the terms before the next call to findArrayDimensionsRec.
7589 SCEVDivision::divide(SE, Term, Step, &Q, &R);
7591 // Bail out when GCD does not evenly divide one of the terms.
7598 // Remove all SCEVConstants.
7599 Terms.erase(std::remove_if(Terms.begin(), Terms.end(), [](const SCEV *E) {
7600 return isa<SCEVConstant>(E);
7604 if (Terms.size() > 0)
7605 if (!findArrayDimensionsRec(SE, Terms, Sizes))
7608 Sizes.push_back(Step);
7613 struct FindParameter {
7614 bool FoundParameter;
7615 FindParameter() : FoundParameter(false) {}
7617 bool follow(const SCEV *S) {
7618 if (isa<SCEVUnknown>(S)) {
7619 FoundParameter = true;
7620 // Stop recursion: we found a parameter.
7626 bool isDone() const {
7627 // Stop recursion if we have found a parameter.
7628 return FoundParameter;
7633 // Returns true when S contains at least a SCEVUnknown parameter.
7635 containsParameters(const SCEV *S) {
7637 SCEVTraversal<FindParameter> ST(F);
7640 return F.FoundParameter;
7643 // Returns true when one of the SCEVs of Terms contains a SCEVUnknown parameter.
7645 containsParameters(SmallVectorImpl<const SCEV *> &Terms) {
7646 for (const SCEV *T : Terms)
7647 if (containsParameters(T))
7652 // Return the number of product terms in S.
7653 static inline int numberOfTerms(const SCEV *S) {
7654 if (const SCEVMulExpr *Expr = dyn_cast<SCEVMulExpr>(S))
7655 return Expr->getNumOperands();
7659 static const SCEV *removeConstantFactors(ScalarEvolution &SE, const SCEV *T) {
7660 if (isa<SCEVConstant>(T))
7663 if (isa<SCEVUnknown>(T))
7666 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(T)) {
7667 SmallVector<const SCEV *, 2> Factors;
7668 for (const SCEV *Op : M->operands())
7669 if (!isa<SCEVConstant>(Op))
7670 Factors.push_back(Op);
7672 return SE.getMulExpr(Factors);
7678 /// Return the size of an element read or written by Inst.
7679 const SCEV *ScalarEvolution::getElementSize(Instruction *Inst) {
7681 if (StoreInst *Store = dyn_cast<StoreInst>(Inst))
7682 Ty = Store->getValueOperand()->getType();
7683 else if (LoadInst *Load = dyn_cast<LoadInst>(Inst))
7684 Ty = Load->getType();
7688 Type *ETy = getEffectiveSCEVType(PointerType::getUnqual(Ty));
7689 return getSizeOfExpr(ETy, Ty);
7692 /// Second step of delinearization: compute the array dimensions Sizes from the
7693 /// set of Terms extracted from the memory access function of this SCEVAddRec.
7694 void ScalarEvolution::findArrayDimensions(SmallVectorImpl<const SCEV *> &Terms,
7695 SmallVectorImpl<const SCEV *> &Sizes,
7696 const SCEV *ElementSize) const {
7698 if (Terms.size() < 1 || !ElementSize)
7701 // Early return when Terms do not contain parameters: we do not delinearize
7702 // non parametric SCEVs.
7703 if (!containsParameters(Terms))
7707 dbgs() << "Terms:\n";
7708 for (const SCEV *T : Terms)
7709 dbgs() << *T << "\n";
7712 // Remove duplicates.
7713 std::sort(Terms.begin(), Terms.end());
7714 Terms.erase(std::unique(Terms.begin(), Terms.end()), Terms.end());
7716 // Put larger terms first.
7717 std::sort(Terms.begin(), Terms.end(), [](const SCEV *LHS, const SCEV *RHS) {
7718 return numberOfTerms(LHS) > numberOfTerms(RHS);
7721 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
7723 // Divide all terms by the element size.
7724 for (const SCEV *&Term : Terms) {
7726 SCEVDivision::divide(SE, Term, ElementSize, &Q, &R);
7730 SmallVector<const SCEV *, 4> NewTerms;
7732 // Remove constant factors.
7733 for (const SCEV *T : Terms)
7734 if (const SCEV *NewT = removeConstantFactors(SE, T))
7735 NewTerms.push_back(NewT);
7738 dbgs() << "Terms after sorting:\n";
7739 for (const SCEV *T : NewTerms)
7740 dbgs() << *T << "\n";
7743 if (NewTerms.empty() ||
7744 !findArrayDimensionsRec(SE, NewTerms, Sizes)) {
7749 // The last element to be pushed into Sizes is the size of an element.
7750 Sizes.push_back(ElementSize);
7753 dbgs() << "Sizes:\n";
7754 for (const SCEV *S : Sizes)
7755 dbgs() << *S << "\n";
7759 /// Third step of delinearization: compute the access functions for the
7760 /// Subscripts based on the dimensions in Sizes.
7761 void SCEVAddRecExpr::computeAccessFunctions(
7762 ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &Subscripts,
7763 SmallVectorImpl<const SCEV *> &Sizes) const {
7765 // Early exit in case this SCEV is not an affine multivariate function.
7766 if (Sizes.empty() || !this->isAffine())
7769 const SCEV *Res = this;
7770 int Last = Sizes.size() - 1;
7771 for (int i = Last; i >= 0; i--) {
7773 SCEVDivision::divide(SE, Res, Sizes[i], &Q, &R);
7776 dbgs() << "Res: " << *Res << "\n";
7777 dbgs() << "Sizes[i]: " << *Sizes[i] << "\n";
7778 dbgs() << "Res divided by Sizes[i]:\n";
7779 dbgs() << "Quotient: " << *Q << "\n";
7780 dbgs() << "Remainder: " << *R << "\n";
7785 // Do not record the last subscript corresponding to the size of elements in
7789 // Bail out if the remainder is too complex.
7790 if (isa<SCEVAddRecExpr>(R)) {
7799 // Record the access function for the current subscript.
7800 Subscripts.push_back(R);
7803 // Also push in last position the remainder of the last division: it will be
7804 // the access function of the innermost dimension.
7805 Subscripts.push_back(Res);
7807 std::reverse(Subscripts.begin(), Subscripts.end());
7810 dbgs() << "Subscripts:\n";
7811 for (const SCEV *S : Subscripts)
7812 dbgs() << *S << "\n";
7816 /// Splits the SCEV into two vectors of SCEVs representing the subscripts and
7817 /// sizes of an array access. Returns the remainder of the delinearization that
7818 /// is the offset start of the array. The SCEV->delinearize algorithm computes
7819 /// the multiples of SCEV coefficients: that is a pattern matching of sub
7820 /// expressions in the stride and base of a SCEV corresponding to the
7821 /// computation of a GCD (greatest common divisor) of base and stride. When
7822 /// SCEV->delinearize fails, it returns the SCEV unchanged.
7824 /// For example: when analyzing the memory access A[i][j][k] in this loop nest
7826 /// void foo(long n, long m, long o, double A[n][m][o]) {
7828 /// for (long i = 0; i < n; i++)
7829 /// for (long j = 0; j < m; j++)
7830 /// for (long k = 0; k < o; k++)
7831 /// A[i][j][k] = 1.0;
7834 /// the delinearization input is the following AddRec SCEV:
7836 /// AddRec: {{{%A,+,(8 * %m * %o)}<%for.i>,+,(8 * %o)}<%for.j>,+,8}<%for.k>
7838 /// From this SCEV, we are able to say that the base offset of the access is %A
7839 /// because it appears as an offset that does not divide any of the strides in
7842 /// CHECK: Base offset: %A
7844 /// and then SCEV->delinearize determines the size of some of the dimensions of
7845 /// the array as these are the multiples by which the strides are happening:
7847 /// CHECK: ArrayDecl[UnknownSize][%m][%o] with elements of sizeof(double) bytes.
7849 /// Note that the outermost dimension remains of UnknownSize because there are
7850 /// no strides that would help identifying the size of the last dimension: when
7851 /// the array has been statically allocated, one could compute the size of that
7852 /// dimension by dividing the overall size of the array by the size of the known
7853 /// dimensions: %m * %o * 8.
7855 /// Finally delinearize provides the access functions for the array reference
7856 /// that does correspond to A[i][j][k] of the above C testcase:
7858 /// CHECK: ArrayRef[{0,+,1}<%for.i>][{0,+,1}<%for.j>][{0,+,1}<%for.k>]
7860 /// The testcases are checking the output of a function pass:
7861 /// DelinearizationPass that walks through all loads and stores of a function
7862 /// asking for the SCEV of the memory access with respect to all enclosing
7863 /// loops, calling SCEV->delinearize on that and printing the results.
7865 void SCEVAddRecExpr::delinearize(ScalarEvolution &SE,
7866 SmallVectorImpl<const SCEV *> &Subscripts,
7867 SmallVectorImpl<const SCEV *> &Sizes,
7868 const SCEV *ElementSize) const {
7869 // First step: collect parametric terms.
7870 SmallVector<const SCEV *, 4> Terms;
7871 collectParametricTerms(SE, Terms);
7876 // Second step: find subscript sizes.
7877 SE.findArrayDimensions(Terms, Sizes, ElementSize);
7882 // Third step: compute the access functions for each subscript.
7883 computeAccessFunctions(SE, Subscripts, Sizes);
7885 if (Subscripts.empty())
7889 dbgs() << "succeeded to delinearize " << *this << "\n";
7890 dbgs() << "ArrayDecl[UnknownSize]";
7891 for (const SCEV *S : Sizes)
7892 dbgs() << "[" << *S << "]";
7894 dbgs() << "\nArrayRef";
7895 for (const SCEV *S : Subscripts)
7896 dbgs() << "[" << *S << "]";
7901 //===----------------------------------------------------------------------===//
7902 // SCEVCallbackVH Class Implementation
7903 //===----------------------------------------------------------------------===//
7905 void ScalarEvolution::SCEVCallbackVH::deleted() {
7906 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
7907 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
7908 SE->ConstantEvolutionLoopExitValue.erase(PN);
7909 SE->ValueExprMap.erase(getValPtr());
7910 // this now dangles!
7913 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) {
7914 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
7916 // Forget all the expressions associated with users of the old value,
7917 // so that future queries will recompute the expressions using the new
7919 Value *Old = getValPtr();
7920 SmallVector<User *, 16> Worklist(Old->user_begin(), Old->user_end());
7921 SmallPtrSet<User *, 8> Visited;
7922 while (!Worklist.empty()) {
7923 User *U = Worklist.pop_back_val();
7924 // Deleting the Old value will cause this to dangle. Postpone
7925 // that until everything else is done.
7928 if (!Visited.insert(U).second)
7930 if (PHINode *PN = dyn_cast<PHINode>(U))
7931 SE->ConstantEvolutionLoopExitValue.erase(PN);
7932 SE->ValueExprMap.erase(U);
7933 Worklist.insert(Worklist.end(), U->user_begin(), U->user_end());
7935 // Delete the Old value.
7936 if (PHINode *PN = dyn_cast<PHINode>(Old))
7937 SE->ConstantEvolutionLoopExitValue.erase(PN);
7938 SE->ValueExprMap.erase(Old);
7939 // this now dangles!
7942 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
7943 : CallbackVH(V), SE(se) {}
7945 //===----------------------------------------------------------------------===//
7946 // ScalarEvolution Class Implementation
7947 //===----------------------------------------------------------------------===//
7949 ScalarEvolution::ScalarEvolution()
7950 : FunctionPass(ID), ValuesAtScopes(64), LoopDispositions(64),
7951 BlockDispositions(64), FirstUnknown(nullptr) {
7952 initializeScalarEvolutionPass(*PassRegistry::getPassRegistry());
7955 bool ScalarEvolution::runOnFunction(Function &F) {
7957 AC = &getAnalysis<AssumptionCacheTracker>().getAssumptionCache(F);
7958 LI = &getAnalysis<LoopInfoWrapperPass>().getLoopInfo();
7959 DataLayoutPass *DLP = getAnalysisIfAvailable<DataLayoutPass>();
7960 DL = DLP ? &DLP->getDataLayout() : nullptr;
7961 TLI = &getAnalysis<TargetLibraryInfoWrapperPass>().getTLI();
7962 DT = &getAnalysis<DominatorTreeWrapperPass>().getDomTree();
7966 void ScalarEvolution::releaseMemory() {
7967 // Iterate through all the SCEVUnknown instances and call their
7968 // destructors, so that they release their references to their values.
7969 for (SCEVUnknown *U = FirstUnknown; U; U = U->Next)
7971 FirstUnknown = nullptr;
7973 ValueExprMap.clear();
7975 // Free any extra memory created for ExitNotTakenInfo in the unlikely event
7976 // that a loop had multiple computable exits.
7977 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
7978 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end();
7983 assert(PendingLoopPredicates.empty() && "isImpliedCond garbage");
7985 BackedgeTakenCounts.clear();
7986 ConstantEvolutionLoopExitValue.clear();
7987 ValuesAtScopes.clear();
7988 LoopDispositions.clear();
7989 BlockDispositions.clear();
7990 UnsignedRanges.clear();
7991 SignedRanges.clear();
7992 UniqueSCEVs.clear();
7993 SCEVAllocator.Reset();
7996 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
7997 AU.setPreservesAll();
7998 AU.addRequired<AssumptionCacheTracker>();
7999 AU.addRequiredTransitive<LoopInfoWrapperPass>();
8000 AU.addRequiredTransitive<DominatorTreeWrapperPass>();
8001 AU.addRequired<TargetLibraryInfoWrapperPass>();
8004 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
8005 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
8008 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
8010 // Print all inner loops first
8011 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
8012 PrintLoopInfo(OS, SE, *I);
8015 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
8018 SmallVector<BasicBlock *, 8> ExitBlocks;
8019 L->getExitBlocks(ExitBlocks);
8020 if (ExitBlocks.size() != 1)
8021 OS << "<multiple exits> ";
8023 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
8024 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
8026 OS << "Unpredictable backedge-taken count. ";
8031 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
8034 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
8035 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
8037 OS << "Unpredictable max backedge-taken count. ";
8043 void ScalarEvolution::print(raw_ostream &OS, const Module *) const {
8044 // ScalarEvolution's implementation of the print method is to print
8045 // out SCEV values of all instructions that are interesting. Doing
8046 // this potentially causes it to create new SCEV objects though,
8047 // which technically conflicts with the const qualifier. This isn't
8048 // observable from outside the class though, so casting away the
8049 // const isn't dangerous.
8050 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
8052 OS << "Classifying expressions for: ";
8053 F->printAsOperand(OS, /*PrintType=*/false);
8055 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
8056 if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) {
8059 const SCEV *SV = SE.getSCEV(&*I);
8062 const Loop *L = LI->getLoopFor((*I).getParent());
8064 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
8071 OS << "\t\t" "Exits: ";
8072 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
8073 if (!SE.isLoopInvariant(ExitValue, L)) {
8074 OS << "<<Unknown>>";
8083 OS << "Determining loop execution counts for: ";
8084 F->printAsOperand(OS, /*PrintType=*/false);
8086 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
8087 PrintLoopInfo(OS, &SE, *I);
8090 ScalarEvolution::LoopDisposition
8091 ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) {
8092 auto &Values = LoopDispositions[S];
8093 for (auto &V : Values) {
8094 if (V.getPointer() == L)
8097 Values.emplace_back(L, LoopVariant);
8098 LoopDisposition D = computeLoopDisposition(S, L);
8099 auto &Values2 = LoopDispositions[S];
8100 for (auto &V : make_range(Values2.rbegin(), Values2.rend())) {
8101 if (V.getPointer() == L) {
8109 ScalarEvolution::LoopDisposition
8110 ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) {
8111 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
8113 return LoopInvariant;
8117 return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L);
8118 case scAddRecExpr: {
8119 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
8121 // If L is the addrec's loop, it's computable.
8122 if (AR->getLoop() == L)
8123 return LoopComputable;
8125 // Add recurrences are never invariant in the function-body (null loop).
8129 // This recurrence is variant w.r.t. L if L contains AR's loop.
8130 if (L->contains(AR->getLoop()))
8133 // This recurrence is invariant w.r.t. L if AR's loop contains L.
8134 if (AR->getLoop()->contains(L))
8135 return LoopInvariant;
8137 // This recurrence is variant w.r.t. L if any of its operands
8139 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
8141 if (!isLoopInvariant(*I, L))
8144 // Otherwise it's loop-invariant.
8145 return LoopInvariant;
8151 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
8152 bool HasVarying = false;
8153 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
8155 LoopDisposition D = getLoopDisposition(*I, L);
8156 if (D == LoopVariant)
8158 if (D == LoopComputable)
8161 return HasVarying ? LoopComputable : LoopInvariant;
8164 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
8165 LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L);
8166 if (LD == LoopVariant)
8168 LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L);
8169 if (RD == LoopVariant)
8171 return (LD == LoopInvariant && RD == LoopInvariant) ?
8172 LoopInvariant : LoopComputable;
8175 // All non-instruction values are loop invariant. All instructions are loop
8176 // invariant if they are not contained in the specified loop.
8177 // Instructions are never considered invariant in the function body
8178 // (null loop) because they are defined within the "loop".
8179 if (Instruction *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue()))
8180 return (L && !L->contains(I)) ? LoopInvariant : LoopVariant;
8181 return LoopInvariant;
8182 case scCouldNotCompute:
8183 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
8185 llvm_unreachable("Unknown SCEV kind!");
8188 bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) {
8189 return getLoopDisposition(S, L) == LoopInvariant;
8192 bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) {
8193 return getLoopDisposition(S, L) == LoopComputable;
8196 ScalarEvolution::BlockDisposition
8197 ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) {
8198 auto &Values = BlockDispositions[S];
8199 for (auto &V : Values) {
8200 if (V.getPointer() == BB)
8203 Values.emplace_back(BB, DoesNotDominateBlock);
8204 BlockDisposition D = computeBlockDisposition(S, BB);
8205 auto &Values2 = BlockDispositions[S];
8206 for (auto &V : make_range(Values2.rbegin(), Values2.rend())) {
8207 if (V.getPointer() == BB) {
8215 ScalarEvolution::BlockDisposition
8216 ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) {
8217 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
8219 return ProperlyDominatesBlock;
8223 return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB);
8224 case scAddRecExpr: {
8225 // This uses a "dominates" query instead of "properly dominates" query
8226 // to test for proper dominance too, because the instruction which
8227 // produces the addrec's value is a PHI, and a PHI effectively properly
8228 // dominates its entire containing block.
8229 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
8230 if (!DT->dominates(AR->getLoop()->getHeader(), BB))
8231 return DoesNotDominateBlock;
8233 // FALL THROUGH into SCEVNAryExpr handling.
8238 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
8240 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
8242 BlockDisposition D = getBlockDisposition(*I, BB);
8243 if (D == DoesNotDominateBlock)
8244 return DoesNotDominateBlock;
8245 if (D == DominatesBlock)
8248 return Proper ? ProperlyDominatesBlock : DominatesBlock;
8251 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
8252 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
8253 BlockDisposition LD = getBlockDisposition(LHS, BB);
8254 if (LD == DoesNotDominateBlock)
8255 return DoesNotDominateBlock;
8256 BlockDisposition RD = getBlockDisposition(RHS, BB);
8257 if (RD == DoesNotDominateBlock)
8258 return DoesNotDominateBlock;
8259 return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ?
8260 ProperlyDominatesBlock : DominatesBlock;
8263 if (Instruction *I =
8264 dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) {
8265 if (I->getParent() == BB)
8266 return DominatesBlock;
8267 if (DT->properlyDominates(I->getParent(), BB))
8268 return ProperlyDominatesBlock;
8269 return DoesNotDominateBlock;
8271 return ProperlyDominatesBlock;
8272 case scCouldNotCompute:
8273 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
8275 llvm_unreachable("Unknown SCEV kind!");
8278 bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) {
8279 return getBlockDisposition(S, BB) >= DominatesBlock;
8282 bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) {
8283 return getBlockDisposition(S, BB) == ProperlyDominatesBlock;
8287 // Search for a SCEV expression node within an expression tree.
8288 // Implements SCEVTraversal::Visitor.
8293 SCEVSearch(const SCEV *N): Node(N), IsFound(false) {}
8295 bool follow(const SCEV *S) {
8296 IsFound |= (S == Node);
8299 bool isDone() const { return IsFound; }
8303 bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const {
8304 SCEVSearch Search(Op);
8305 visitAll(S, Search);
8306 return Search.IsFound;
8309 void ScalarEvolution::forgetMemoizedResults(const SCEV *S) {
8310 ValuesAtScopes.erase(S);
8311 LoopDispositions.erase(S);
8312 BlockDispositions.erase(S);
8313 UnsignedRanges.erase(S);
8314 SignedRanges.erase(S);
8316 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
8317 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end(); I != E; ) {
8318 BackedgeTakenInfo &BEInfo = I->second;
8319 if (BEInfo.hasOperand(S, this)) {
8321 BackedgeTakenCounts.erase(I++);
8328 typedef DenseMap<const Loop *, std::string> VerifyMap;
8330 /// replaceSubString - Replaces all occurrences of From in Str with To.
8331 static void replaceSubString(std::string &Str, StringRef From, StringRef To) {
8333 while ((Pos = Str.find(From, Pos)) != std::string::npos) {
8334 Str.replace(Pos, From.size(), To.data(), To.size());
8339 /// getLoopBackedgeTakenCounts - Helper method for verifyAnalysis.
8341 getLoopBackedgeTakenCounts(Loop *L, VerifyMap &Map, ScalarEvolution &SE) {
8342 for (Loop::reverse_iterator I = L->rbegin(), E = L->rend(); I != E; ++I) {
8343 getLoopBackedgeTakenCounts(*I, Map, SE); // recurse.
8345 std::string &S = Map[L];
8347 raw_string_ostream OS(S);
8348 SE.getBackedgeTakenCount(L)->print(OS);
8350 // false and 0 are semantically equivalent. This can happen in dead loops.
8351 replaceSubString(OS.str(), "false", "0");
8352 // Remove wrap flags, their use in SCEV is highly fragile.
8353 // FIXME: Remove this when SCEV gets smarter about them.
8354 replaceSubString(OS.str(), "<nw>", "");
8355 replaceSubString(OS.str(), "<nsw>", "");
8356 replaceSubString(OS.str(), "<nuw>", "");
8361 void ScalarEvolution::verifyAnalysis() const {
8365 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
8367 // Gather stringified backedge taken counts for all loops using SCEV's caches.
8368 // FIXME: It would be much better to store actual values instead of strings,
8369 // but SCEV pointers will change if we drop the caches.
8370 VerifyMap BackedgeDumpsOld, BackedgeDumpsNew;
8371 for (LoopInfo::reverse_iterator I = LI->rbegin(), E = LI->rend(); I != E; ++I)
8372 getLoopBackedgeTakenCounts(*I, BackedgeDumpsOld, SE);
8374 // Gather stringified backedge taken counts for all loops without using
8377 for (LoopInfo::reverse_iterator I = LI->rbegin(), E = LI->rend(); I != E; ++I)
8378 getLoopBackedgeTakenCounts(*I, BackedgeDumpsNew, SE);
8380 // Now compare whether they're the same with and without caches. This allows
8381 // verifying that no pass changed the cache.
8382 assert(BackedgeDumpsOld.size() == BackedgeDumpsNew.size() &&
8383 "New loops suddenly appeared!");
8385 for (VerifyMap::iterator OldI = BackedgeDumpsOld.begin(),
8386 OldE = BackedgeDumpsOld.end(),
8387 NewI = BackedgeDumpsNew.begin();
8388 OldI != OldE; ++OldI, ++NewI) {
8389 assert(OldI->first == NewI->first && "Loop order changed!");
8391 // Compare the stringified SCEVs. We don't care if undef backedgetaken count
8393 // FIXME: We currently ignore SCEV changes from/to CouldNotCompute. This
8394 // means that a pass is buggy or SCEV has to learn a new pattern but is
8395 // usually not harmful.
8396 if (OldI->second != NewI->second &&
8397 OldI->second.find("undef") == std::string::npos &&
8398 NewI->second.find("undef") == std::string::npos &&
8399 OldI->second != "***COULDNOTCOMPUTE***" &&
8400 NewI->second != "***COULDNOTCOMPUTE***") {
8401 dbgs() << "SCEVValidator: SCEV for loop '"
8402 << OldI->first->getHeader()->getName()
8403 << "' changed from '" << OldI->second
8404 << "' to '" << NewI->second << "'!\n";
8409 // TODO: Verify more things.