1 //===- ScalarEvolution.cpp - Scalar Evolution Analysis --------------------===//
3 // The LLVM Compiler Infrastructure
5 // This file is distributed under the University of Illinois Open Source
6 // License. See LICENSE.TXT for details.
8 //===----------------------------------------------------------------------===//
10 // This file contains the implementation of the scalar evolution analysis
11 // engine, which is used primarily to analyze expressions involving induction
12 // variables in loops.
14 // There are several aspects to this library. First is the representation of
15 // scalar expressions, which are represented as subclasses of the SCEV class.
16 // These classes are used to represent certain types of subexpressions that we
17 // can handle. We only create one SCEV of a particular shape, so
18 // pointer-comparisons for equality are legal.
20 // One important aspect of the SCEV objects is that they are never cyclic, even
21 // if there is a cycle in the dataflow for an expression (ie, a PHI node). If
22 // the PHI node is one of the idioms that we can represent (e.g., a polynomial
23 // recurrence) then we represent it directly as a recurrence node, otherwise we
24 // represent it as a SCEVUnknown node.
26 // In addition to being able to represent expressions of various types, we also
27 // have folders that are used to build the *canonical* representation for a
28 // particular expression. These folders are capable of using a variety of
29 // rewrite rules to simplify the expressions.
31 // Once the folders are defined, we can implement the more interesting
32 // higher-level code, such as the code that recognizes PHI nodes of various
33 // types, computes the execution count of a loop, etc.
35 // TODO: We should use these routines and value representations to implement
36 // dependence analysis!
38 //===----------------------------------------------------------------------===//
40 // There are several good references for the techniques used in this analysis.
42 // Chains of recurrences -- a method to expedite the evaluation
43 // of closed-form functions
44 // Olaf Bachmann, Paul S. Wang, Eugene V. Zima
46 // On computational properties of chains of recurrences
49 // Symbolic Evaluation of Chains of Recurrences for Loop Optimization
50 // Robert A. van Engelen
52 // Efficient Symbolic Analysis for Optimizing Compilers
53 // Robert A. van Engelen
55 // Using the chains of recurrences algebra for data dependence testing and
56 // induction variable substitution
57 // MS Thesis, Johnie Birch
59 //===----------------------------------------------------------------------===//
61 #include "llvm/Analysis/ScalarEvolution.h"
62 #include "llvm/ADT/Optional.h"
63 #include "llvm/ADT/STLExtras.h"
64 #include "llvm/ADT/SmallPtrSet.h"
65 #include "llvm/ADT/Statistic.h"
66 #include "llvm/Analysis/AssumptionCache.h"
67 #include "llvm/Analysis/ConstantFolding.h"
68 #include "llvm/Analysis/InstructionSimplify.h"
69 #include "llvm/Analysis/LoopInfo.h"
70 #include "llvm/Analysis/ScalarEvolutionExpressions.h"
71 #include "llvm/Analysis/TargetLibraryInfo.h"
72 #include "llvm/Analysis/ValueTracking.h"
73 #include "llvm/IR/ConstantRange.h"
74 #include "llvm/IR/Constants.h"
75 #include "llvm/IR/DataLayout.h"
76 #include "llvm/IR/DerivedTypes.h"
77 #include "llvm/IR/Dominators.h"
78 #include "llvm/IR/GetElementPtrTypeIterator.h"
79 #include "llvm/IR/GlobalAlias.h"
80 #include "llvm/IR/GlobalVariable.h"
81 #include "llvm/IR/InstIterator.h"
82 #include "llvm/IR/Instructions.h"
83 #include "llvm/IR/LLVMContext.h"
84 #include "llvm/IR/Metadata.h"
85 #include "llvm/IR/Operator.h"
86 #include "llvm/Support/CommandLine.h"
87 #include "llvm/Support/Debug.h"
88 #include "llvm/Support/ErrorHandling.h"
89 #include "llvm/Support/MathExtras.h"
90 #include "llvm/Support/raw_ostream.h"
94 #define DEBUG_TYPE "scalar-evolution"
96 STATISTIC(NumArrayLenItCounts,
97 "Number of trip counts computed with array length");
98 STATISTIC(NumTripCountsComputed,
99 "Number of loops with predictable loop counts");
100 STATISTIC(NumTripCountsNotComputed,
101 "Number of loops without predictable loop counts");
102 STATISTIC(NumBruteForceTripCountsComputed,
103 "Number of loops with trip counts computed by force");
105 static cl::opt<unsigned>
106 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
107 cl::desc("Maximum number of iterations SCEV will "
108 "symbolically execute a constant "
112 // FIXME: Enable this with XDEBUG when the test suite is clean.
114 VerifySCEV("verify-scev",
115 cl::desc("Verify ScalarEvolution's backedge taken counts (slow)"));
117 INITIALIZE_PASS_BEGIN(ScalarEvolution, "scalar-evolution",
118 "Scalar Evolution Analysis", false, true)
119 INITIALIZE_PASS_DEPENDENCY(AssumptionCacheTracker)
120 INITIALIZE_PASS_DEPENDENCY(LoopInfoWrapperPass)
121 INITIALIZE_PASS_DEPENDENCY(DominatorTreeWrapperPass)
122 INITIALIZE_PASS_DEPENDENCY(TargetLibraryInfoWrapperPass)
123 INITIALIZE_PASS_END(ScalarEvolution, "scalar-evolution",
124 "Scalar Evolution Analysis", false, true)
125 char ScalarEvolution::ID = 0;
127 //===----------------------------------------------------------------------===//
128 // SCEV class definitions
129 //===----------------------------------------------------------------------===//
131 //===----------------------------------------------------------------------===//
132 // Implementation of the SCEV class.
135 #if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP)
136 void SCEV::dump() const {
142 void SCEV::print(raw_ostream &OS) const {
143 switch (static_cast<SCEVTypes>(getSCEVType())) {
145 cast<SCEVConstant>(this)->getValue()->printAsOperand(OS, false);
148 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(this);
149 const SCEV *Op = Trunc->getOperand();
150 OS << "(trunc " << *Op->getType() << " " << *Op << " to "
151 << *Trunc->getType() << ")";
155 const SCEVZeroExtendExpr *ZExt = cast<SCEVZeroExtendExpr>(this);
156 const SCEV *Op = ZExt->getOperand();
157 OS << "(zext " << *Op->getType() << " " << *Op << " to "
158 << *ZExt->getType() << ")";
162 const SCEVSignExtendExpr *SExt = cast<SCEVSignExtendExpr>(this);
163 const SCEV *Op = SExt->getOperand();
164 OS << "(sext " << *Op->getType() << " " << *Op << " to "
165 << *SExt->getType() << ")";
169 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(this);
170 OS << "{" << *AR->getOperand(0);
171 for (unsigned i = 1, e = AR->getNumOperands(); i != e; ++i)
172 OS << ",+," << *AR->getOperand(i);
174 if (AR->getNoWrapFlags(FlagNUW))
176 if (AR->getNoWrapFlags(FlagNSW))
178 if (AR->getNoWrapFlags(FlagNW) &&
179 !AR->getNoWrapFlags((NoWrapFlags)(FlagNUW | FlagNSW)))
181 AR->getLoop()->getHeader()->printAsOperand(OS, /*PrintType=*/false);
189 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(this);
190 const char *OpStr = nullptr;
191 switch (NAry->getSCEVType()) {
192 case scAddExpr: OpStr = " + "; break;
193 case scMulExpr: OpStr = " * "; break;
194 case scUMaxExpr: OpStr = " umax "; break;
195 case scSMaxExpr: OpStr = " smax "; break;
198 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
201 if (std::next(I) != E)
205 switch (NAry->getSCEVType()) {
208 if (NAry->getNoWrapFlags(FlagNUW))
210 if (NAry->getNoWrapFlags(FlagNSW))
216 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(this);
217 OS << "(" << *UDiv->getLHS() << " /u " << *UDiv->getRHS() << ")";
221 const SCEVUnknown *U = cast<SCEVUnknown>(this);
223 if (U->isSizeOf(AllocTy)) {
224 OS << "sizeof(" << *AllocTy << ")";
227 if (U->isAlignOf(AllocTy)) {
228 OS << "alignof(" << *AllocTy << ")";
234 if (U->isOffsetOf(CTy, FieldNo)) {
235 OS << "offsetof(" << *CTy << ", ";
236 FieldNo->printAsOperand(OS, false);
241 // Otherwise just print it normally.
242 U->getValue()->printAsOperand(OS, false);
245 case scCouldNotCompute:
246 OS << "***COULDNOTCOMPUTE***";
249 llvm_unreachable("Unknown SCEV kind!");
252 Type *SCEV::getType() const {
253 switch (static_cast<SCEVTypes>(getSCEVType())) {
255 return cast<SCEVConstant>(this)->getType();
259 return cast<SCEVCastExpr>(this)->getType();
264 return cast<SCEVNAryExpr>(this)->getType();
266 return cast<SCEVAddExpr>(this)->getType();
268 return cast<SCEVUDivExpr>(this)->getType();
270 return cast<SCEVUnknown>(this)->getType();
271 case scCouldNotCompute:
272 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
274 llvm_unreachable("Unknown SCEV kind!");
277 bool SCEV::isZero() const {
278 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
279 return SC->getValue()->isZero();
283 bool SCEV::isOne() const {
284 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
285 return SC->getValue()->isOne();
289 bool SCEV::isAllOnesValue() const {
290 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
291 return SC->getValue()->isAllOnesValue();
295 /// isNonConstantNegative - Return true if the specified scev is negated, but
297 bool SCEV::isNonConstantNegative() const {
298 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(this);
299 if (!Mul) return false;
301 // If there is a constant factor, it will be first.
302 const SCEVConstant *SC = dyn_cast<SCEVConstant>(Mul->getOperand(0));
303 if (!SC) return false;
305 // Return true if the value is negative, this matches things like (-42 * V).
306 return SC->getValue()->getValue().isNegative();
309 SCEVCouldNotCompute::SCEVCouldNotCompute() :
310 SCEV(FoldingSetNodeIDRef(), scCouldNotCompute) {}
312 bool SCEVCouldNotCompute::classof(const SCEV *S) {
313 return S->getSCEVType() == scCouldNotCompute;
316 const SCEV *ScalarEvolution::getConstant(ConstantInt *V) {
318 ID.AddInteger(scConstant);
321 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
322 SCEV *S = new (SCEVAllocator) SCEVConstant(ID.Intern(SCEVAllocator), V);
323 UniqueSCEVs.InsertNode(S, IP);
327 const SCEV *ScalarEvolution::getConstant(const APInt &Val) {
328 return getConstant(ConstantInt::get(getContext(), Val));
332 ScalarEvolution::getConstant(Type *Ty, uint64_t V, bool isSigned) {
333 IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty));
334 return getConstant(ConstantInt::get(ITy, V, isSigned));
337 SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID,
338 unsigned SCEVTy, const SCEV *op, Type *ty)
339 : SCEV(ID, SCEVTy), Op(op), Ty(ty) {}
341 SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID,
342 const SCEV *op, Type *ty)
343 : SCEVCastExpr(ID, scTruncate, op, ty) {
344 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
345 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
346 "Cannot truncate non-integer value!");
349 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID,
350 const SCEV *op, Type *ty)
351 : SCEVCastExpr(ID, scZeroExtend, op, ty) {
352 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
353 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
354 "Cannot zero extend non-integer value!");
357 SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID,
358 const SCEV *op, Type *ty)
359 : SCEVCastExpr(ID, scSignExtend, op, ty) {
360 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
361 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
362 "Cannot sign extend non-integer value!");
365 void SCEVUnknown::deleted() {
366 // Clear this SCEVUnknown from various maps.
367 SE->forgetMemoizedResults(this);
369 // Remove this SCEVUnknown from the uniquing map.
370 SE->UniqueSCEVs.RemoveNode(this);
372 // Release the value.
376 void SCEVUnknown::allUsesReplacedWith(Value *New) {
377 // Clear this SCEVUnknown from various maps.
378 SE->forgetMemoizedResults(this);
380 // Remove this SCEVUnknown from the uniquing map.
381 SE->UniqueSCEVs.RemoveNode(this);
383 // Update this SCEVUnknown to point to the new value. This is needed
384 // because there may still be outstanding SCEVs which still point to
389 bool SCEVUnknown::isSizeOf(Type *&AllocTy) const {
390 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
391 if (VCE->getOpcode() == Instruction::PtrToInt)
392 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
393 if (CE->getOpcode() == Instruction::GetElementPtr &&
394 CE->getOperand(0)->isNullValue() &&
395 CE->getNumOperands() == 2)
396 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1)))
398 AllocTy = cast<PointerType>(CE->getOperand(0)->getType())
406 bool SCEVUnknown::isAlignOf(Type *&AllocTy) const {
407 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
408 if (VCE->getOpcode() == Instruction::PtrToInt)
409 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
410 if (CE->getOpcode() == Instruction::GetElementPtr &&
411 CE->getOperand(0)->isNullValue()) {
413 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
414 if (StructType *STy = dyn_cast<StructType>(Ty))
415 if (!STy->isPacked() &&
416 CE->getNumOperands() == 3 &&
417 CE->getOperand(1)->isNullValue()) {
418 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2)))
420 STy->getNumElements() == 2 &&
421 STy->getElementType(0)->isIntegerTy(1)) {
422 AllocTy = STy->getElementType(1);
431 bool SCEVUnknown::isOffsetOf(Type *&CTy, Constant *&FieldNo) const {
432 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
433 if (VCE->getOpcode() == Instruction::PtrToInt)
434 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
435 if (CE->getOpcode() == Instruction::GetElementPtr &&
436 CE->getNumOperands() == 3 &&
437 CE->getOperand(0)->isNullValue() &&
438 CE->getOperand(1)->isNullValue()) {
440 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
441 // Ignore vector types here so that ScalarEvolutionExpander doesn't
442 // emit getelementptrs that index into vectors.
443 if (Ty->isStructTy() || Ty->isArrayTy()) {
445 FieldNo = CE->getOperand(2);
453 //===----------------------------------------------------------------------===//
455 //===----------------------------------------------------------------------===//
458 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
459 /// than the complexity of the RHS. This comparator is used to canonicalize
461 class SCEVComplexityCompare {
462 const LoopInfo *const LI;
464 explicit SCEVComplexityCompare(const LoopInfo *li) : LI(li) {}
466 // Return true or false if LHS is less than, or at least RHS, respectively.
467 bool operator()(const SCEV *LHS, const SCEV *RHS) const {
468 return compare(LHS, RHS) < 0;
471 // Return negative, zero, or positive, if LHS is less than, equal to, or
472 // greater than RHS, respectively. A three-way result allows recursive
473 // comparisons to be more efficient.
474 int compare(const SCEV *LHS, const SCEV *RHS) const {
475 // Fast-path: SCEVs are uniqued so we can do a quick equality check.
479 // Primarily, sort the SCEVs by their getSCEVType().
480 unsigned LType = LHS->getSCEVType(), RType = RHS->getSCEVType();
482 return (int)LType - (int)RType;
484 // Aside from the getSCEVType() ordering, the particular ordering
485 // isn't very important except that it's beneficial to be consistent,
486 // so that (a + b) and (b + a) don't end up as different expressions.
487 switch (static_cast<SCEVTypes>(LType)) {
489 const SCEVUnknown *LU = cast<SCEVUnknown>(LHS);
490 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
492 // Sort SCEVUnknown values with some loose heuristics. TODO: This is
493 // not as complete as it could be.
494 const Value *LV = LU->getValue(), *RV = RU->getValue();
496 // Order pointer values after integer values. This helps SCEVExpander
498 bool LIsPointer = LV->getType()->isPointerTy(),
499 RIsPointer = RV->getType()->isPointerTy();
500 if (LIsPointer != RIsPointer)
501 return (int)LIsPointer - (int)RIsPointer;
503 // Compare getValueID values.
504 unsigned LID = LV->getValueID(),
505 RID = RV->getValueID();
507 return (int)LID - (int)RID;
509 // Sort arguments by their position.
510 if (const Argument *LA = dyn_cast<Argument>(LV)) {
511 const Argument *RA = cast<Argument>(RV);
512 unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo();
513 return (int)LArgNo - (int)RArgNo;
516 // For instructions, compare their loop depth, and their operand
517 // count. This is pretty loose.
518 if (const Instruction *LInst = dyn_cast<Instruction>(LV)) {
519 const Instruction *RInst = cast<Instruction>(RV);
521 // Compare loop depths.
522 const BasicBlock *LParent = LInst->getParent(),
523 *RParent = RInst->getParent();
524 if (LParent != RParent) {
525 unsigned LDepth = LI->getLoopDepth(LParent),
526 RDepth = LI->getLoopDepth(RParent);
527 if (LDepth != RDepth)
528 return (int)LDepth - (int)RDepth;
531 // Compare the number of operands.
532 unsigned LNumOps = LInst->getNumOperands(),
533 RNumOps = RInst->getNumOperands();
534 return (int)LNumOps - (int)RNumOps;
541 const SCEVConstant *LC = cast<SCEVConstant>(LHS);
542 const SCEVConstant *RC = cast<SCEVConstant>(RHS);
544 // Compare constant values.
545 const APInt &LA = LC->getValue()->getValue();
546 const APInt &RA = RC->getValue()->getValue();
547 unsigned LBitWidth = LA.getBitWidth(), RBitWidth = RA.getBitWidth();
548 if (LBitWidth != RBitWidth)
549 return (int)LBitWidth - (int)RBitWidth;
550 return LA.ult(RA) ? -1 : 1;
554 const SCEVAddRecExpr *LA = cast<SCEVAddRecExpr>(LHS);
555 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS);
557 // Compare addrec loop depths.
558 const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop();
559 if (LLoop != RLoop) {
560 unsigned LDepth = LLoop->getLoopDepth(),
561 RDepth = RLoop->getLoopDepth();
562 if (LDepth != RDepth)
563 return (int)LDepth - (int)RDepth;
566 // Addrec complexity grows with operand count.
567 unsigned LNumOps = LA->getNumOperands(), RNumOps = RA->getNumOperands();
568 if (LNumOps != RNumOps)
569 return (int)LNumOps - (int)RNumOps;
571 // Lexicographically compare.
572 for (unsigned i = 0; i != LNumOps; ++i) {
573 long X = compare(LA->getOperand(i), RA->getOperand(i));
585 const SCEVNAryExpr *LC = cast<SCEVNAryExpr>(LHS);
586 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
588 // Lexicographically compare n-ary expressions.
589 unsigned LNumOps = LC->getNumOperands(), RNumOps = RC->getNumOperands();
590 if (LNumOps != RNumOps)
591 return (int)LNumOps - (int)RNumOps;
593 for (unsigned i = 0; i != LNumOps; ++i) {
596 long X = compare(LC->getOperand(i), RC->getOperand(i));
600 return (int)LNumOps - (int)RNumOps;
604 const SCEVUDivExpr *LC = cast<SCEVUDivExpr>(LHS);
605 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
607 // Lexicographically compare udiv expressions.
608 long X = compare(LC->getLHS(), RC->getLHS());
611 return compare(LC->getRHS(), RC->getRHS());
617 const SCEVCastExpr *LC = cast<SCEVCastExpr>(LHS);
618 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
620 // Compare cast expressions by operand.
621 return compare(LC->getOperand(), RC->getOperand());
624 case scCouldNotCompute:
625 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
627 llvm_unreachable("Unknown SCEV kind!");
632 /// GroupByComplexity - Given a list of SCEV objects, order them by their
633 /// complexity, and group objects of the same complexity together by value.
634 /// When this routine is finished, we know that any duplicates in the vector are
635 /// consecutive and that complexity is monotonically increasing.
637 /// Note that we go take special precautions to ensure that we get deterministic
638 /// results from this routine. In other words, we don't want the results of
639 /// this to depend on where the addresses of various SCEV objects happened to
642 static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops,
644 if (Ops.size() < 2) return; // Noop
645 if (Ops.size() == 2) {
646 // This is the common case, which also happens to be trivially simple.
648 const SCEV *&LHS = Ops[0], *&RHS = Ops[1];
649 if (SCEVComplexityCompare(LI)(RHS, LHS))
654 // Do the rough sort by complexity.
655 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI));
657 // Now that we are sorted by complexity, group elements of the same
658 // complexity. Note that this is, at worst, N^2, but the vector is likely to
659 // be extremely short in practice. Note that we take this approach because we
660 // do not want to depend on the addresses of the objects we are grouping.
661 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
662 const SCEV *S = Ops[i];
663 unsigned Complexity = S->getSCEVType();
665 // If there are any objects of the same complexity and same value as this
667 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
668 if (Ops[j] == S) { // Found a duplicate.
669 // Move it to immediately after i'th element.
670 std::swap(Ops[i+1], Ops[j]);
671 ++i; // no need to rescan it.
672 if (i == e-2) return; // Done!
679 struct FindSCEVSize {
681 FindSCEVSize() : Size(0) {}
683 bool follow(const SCEV *S) {
685 // Keep looking at all operands of S.
688 bool isDone() const {
694 // Returns the size of the SCEV S.
695 static inline int sizeOfSCEV(const SCEV *S) {
697 SCEVTraversal<FindSCEVSize> ST(F);
704 struct SCEVDivision : public SCEVVisitor<SCEVDivision, void> {
706 // Computes the Quotient and Remainder of the division of Numerator by
708 static void divide(ScalarEvolution &SE, const SCEV *Numerator,
709 const SCEV *Denominator, const SCEV **Quotient,
710 const SCEV **Remainder) {
711 assert(Numerator && Denominator && "Uninitialized SCEV");
713 SCEVDivision D(SE, Numerator, Denominator);
715 // Check for the trivial case here to avoid having to check for it in the
717 if (Numerator == Denominator) {
723 if (Numerator->isZero()) {
729 // Split the Denominator when it is a product.
730 if (const SCEVMulExpr *T = dyn_cast<const SCEVMulExpr>(Denominator)) {
732 *Quotient = Numerator;
733 for (const SCEV *Op : T->operands()) {
734 divide(SE, *Quotient, Op, &Q, &R);
737 // Bail out when the Numerator is not divisible by one of the terms of
741 *Remainder = Numerator;
750 *Quotient = D.Quotient;
751 *Remainder = D.Remainder;
754 // Except in the trivial case described above, we do not know how to divide
755 // Expr by Denominator for the following functions with empty implementation.
756 void visitTruncateExpr(const SCEVTruncateExpr *Numerator) {}
757 void visitZeroExtendExpr(const SCEVZeroExtendExpr *Numerator) {}
758 void visitSignExtendExpr(const SCEVSignExtendExpr *Numerator) {}
759 void visitUDivExpr(const SCEVUDivExpr *Numerator) {}
760 void visitSMaxExpr(const SCEVSMaxExpr *Numerator) {}
761 void visitUMaxExpr(const SCEVUMaxExpr *Numerator) {}
762 void visitUnknown(const SCEVUnknown *Numerator) {}
763 void visitCouldNotCompute(const SCEVCouldNotCompute *Numerator) {}
765 void visitConstant(const SCEVConstant *Numerator) {
766 if (const SCEVConstant *D = dyn_cast<SCEVConstant>(Denominator)) {
767 APInt NumeratorVal = Numerator->getValue()->getValue();
768 APInt DenominatorVal = D->getValue()->getValue();
769 uint32_t NumeratorBW = NumeratorVal.getBitWidth();
770 uint32_t DenominatorBW = DenominatorVal.getBitWidth();
772 if (NumeratorBW > DenominatorBW)
773 DenominatorVal = DenominatorVal.sext(NumeratorBW);
774 else if (NumeratorBW < DenominatorBW)
775 NumeratorVal = NumeratorVal.sext(DenominatorBW);
777 APInt QuotientVal(NumeratorVal.getBitWidth(), 0);
778 APInt RemainderVal(NumeratorVal.getBitWidth(), 0);
779 APInt::sdivrem(NumeratorVal, DenominatorVal, QuotientVal, RemainderVal);
780 Quotient = SE.getConstant(QuotientVal);
781 Remainder = SE.getConstant(RemainderVal);
786 void visitAddRecExpr(const SCEVAddRecExpr *Numerator) {
787 const SCEV *StartQ, *StartR, *StepQ, *StepR;
788 assert(Numerator->isAffine() && "Numerator should be affine");
789 divide(SE, Numerator->getStart(), Denominator, &StartQ, &StartR);
790 divide(SE, Numerator->getStepRecurrence(SE), Denominator, &StepQ, &StepR);
791 Quotient = SE.getAddRecExpr(StartQ, StepQ, Numerator->getLoop(),
792 Numerator->getNoWrapFlags());
793 Remainder = SE.getAddRecExpr(StartR, StepR, Numerator->getLoop(),
794 Numerator->getNoWrapFlags());
797 void visitAddExpr(const SCEVAddExpr *Numerator) {
798 SmallVector<const SCEV *, 2> Qs, Rs;
799 Type *Ty = Denominator->getType();
801 for (const SCEV *Op : Numerator->operands()) {
803 divide(SE, Op, Denominator, &Q, &R);
805 // Bail out if types do not match.
806 if (Ty != Q->getType() || Ty != R->getType()) {
808 Remainder = Numerator;
816 if (Qs.size() == 1) {
822 Quotient = SE.getAddExpr(Qs);
823 Remainder = SE.getAddExpr(Rs);
826 void visitMulExpr(const SCEVMulExpr *Numerator) {
827 SmallVector<const SCEV *, 2> Qs;
828 Type *Ty = Denominator->getType();
830 bool FoundDenominatorTerm = false;
831 for (const SCEV *Op : Numerator->operands()) {
832 // Bail out if types do not match.
833 if (Ty != Op->getType()) {
835 Remainder = Numerator;
839 if (FoundDenominatorTerm) {
844 // Check whether Denominator divides one of the product operands.
846 divide(SE, Op, Denominator, &Q, &R);
852 // Bail out if types do not match.
853 if (Ty != Q->getType()) {
855 Remainder = Numerator;
859 FoundDenominatorTerm = true;
863 if (FoundDenominatorTerm) {
868 Quotient = SE.getMulExpr(Qs);
872 if (!isa<SCEVUnknown>(Denominator)) {
874 Remainder = Numerator;
878 // The Remainder is obtained by replacing Denominator by 0 in Numerator.
879 ValueToValueMap RewriteMap;
880 RewriteMap[cast<SCEVUnknown>(Denominator)->getValue()] =
881 cast<SCEVConstant>(Zero)->getValue();
882 Remainder = SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true);
884 if (Remainder->isZero()) {
885 // The Quotient is obtained by replacing Denominator by 1 in Numerator.
886 RewriteMap[cast<SCEVUnknown>(Denominator)->getValue()] =
887 cast<SCEVConstant>(One)->getValue();
889 SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true);
893 // Quotient is (Numerator - Remainder) divided by Denominator.
895 const SCEV *Diff = SE.getMinusSCEV(Numerator, Remainder);
896 if (sizeOfSCEV(Diff) > sizeOfSCEV(Numerator)) {
897 // This SCEV does not seem to simplify: fail the division here.
899 Remainder = Numerator;
902 divide(SE, Diff, Denominator, &Q, &R);
904 "(Numerator - Remainder) should evenly divide Denominator");
909 SCEVDivision(ScalarEvolution &S, const SCEV *Numerator,
910 const SCEV *Denominator)
911 : SE(S), Denominator(Denominator) {
912 Zero = SE.getConstant(Denominator->getType(), 0);
913 One = SE.getConstant(Denominator->getType(), 1);
915 // By default, we don't know how to divide Expr by Denominator.
916 // Providing the default here simplifies the rest of the code.
918 Remainder = Numerator;
922 const SCEV *Denominator, *Quotient, *Remainder, *Zero, *One;
927 //===----------------------------------------------------------------------===//
928 // Simple SCEV method implementations
929 //===----------------------------------------------------------------------===//
931 /// BinomialCoefficient - Compute BC(It, K). The result has width W.
933 static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K,
936 // Handle the simplest case efficiently.
938 return SE.getTruncateOrZeroExtend(It, ResultTy);
940 // We are using the following formula for BC(It, K):
942 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
944 // Suppose, W is the bitwidth of the return value. We must be prepared for
945 // overflow. Hence, we must assure that the result of our computation is
946 // equal to the accurate one modulo 2^W. Unfortunately, division isn't
947 // safe in modular arithmetic.
949 // However, this code doesn't use exactly that formula; the formula it uses
950 // is something like the following, where T is the number of factors of 2 in
951 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
954 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
956 // This formula is trivially equivalent to the previous formula. However,
957 // this formula can be implemented much more efficiently. The trick is that
958 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
959 // arithmetic. To do exact division in modular arithmetic, all we have
960 // to do is multiply by the inverse. Therefore, this step can be done at
963 // The next issue is how to safely do the division by 2^T. The way this
964 // is done is by doing the multiplication step at a width of at least W + T
965 // bits. This way, the bottom W+T bits of the product are accurate. Then,
966 // when we perform the division by 2^T (which is equivalent to a right shift
967 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
968 // truncated out after the division by 2^T.
970 // In comparison to just directly using the first formula, this technique
971 // is much more efficient; using the first formula requires W * K bits,
972 // but this formula less than W + K bits. Also, the first formula requires
973 // a division step, whereas this formula only requires multiplies and shifts.
975 // It doesn't matter whether the subtraction step is done in the calculation
976 // width or the input iteration count's width; if the subtraction overflows,
977 // the result must be zero anyway. We prefer here to do it in the width of
978 // the induction variable because it helps a lot for certain cases; CodeGen
979 // isn't smart enough to ignore the overflow, which leads to much less
980 // efficient code if the width of the subtraction is wider than the native
983 // (It's possible to not widen at all by pulling out factors of 2 before
984 // the multiplication; for example, K=2 can be calculated as
985 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
986 // extra arithmetic, so it's not an obvious win, and it gets
987 // much more complicated for K > 3.)
989 // Protection from insane SCEVs; this bound is conservative,
990 // but it probably doesn't matter.
992 return SE.getCouldNotCompute();
994 unsigned W = SE.getTypeSizeInBits(ResultTy);
996 // Calculate K! / 2^T and T; we divide out the factors of two before
997 // multiplying for calculating K! / 2^T to avoid overflow.
998 // Other overflow doesn't matter because we only care about the bottom
999 // W bits of the result.
1000 APInt OddFactorial(W, 1);
1002 for (unsigned i = 3; i <= K; ++i) {
1004 unsigned TwoFactors = Mult.countTrailingZeros();
1006 Mult = Mult.lshr(TwoFactors);
1007 OddFactorial *= Mult;
1010 // We need at least W + T bits for the multiplication step
1011 unsigned CalculationBits = W + T;
1013 // Calculate 2^T, at width T+W.
1014 APInt DivFactor = APInt::getOneBitSet(CalculationBits, T);
1016 // Calculate the multiplicative inverse of K! / 2^T;
1017 // this multiplication factor will perform the exact division by
1019 APInt Mod = APInt::getSignedMinValue(W+1);
1020 APInt MultiplyFactor = OddFactorial.zext(W+1);
1021 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
1022 MultiplyFactor = MultiplyFactor.trunc(W);
1024 // Calculate the product, at width T+W
1025 IntegerType *CalculationTy = IntegerType::get(SE.getContext(),
1027 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
1028 for (unsigned i = 1; i != K; ++i) {
1029 const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i));
1030 Dividend = SE.getMulExpr(Dividend,
1031 SE.getTruncateOrZeroExtend(S, CalculationTy));
1035 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
1037 // Truncate the result, and divide by K! / 2^T.
1039 return SE.getMulExpr(SE.getConstant(MultiplyFactor),
1040 SE.getTruncateOrZeroExtend(DivResult, ResultTy));
1043 /// evaluateAtIteration - Return the value of this chain of recurrences at
1044 /// the specified iteration number. We can evaluate this recurrence by
1045 /// multiplying each element in the chain by the binomial coefficient
1046 /// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
1048 /// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
1050 /// where BC(It, k) stands for binomial coefficient.
1052 const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It,
1053 ScalarEvolution &SE) const {
1054 const SCEV *Result = getStart();
1055 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
1056 // The computation is correct in the face of overflow provided that the
1057 // multiplication is performed _after_ the evaluation of the binomial
1059 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType());
1060 if (isa<SCEVCouldNotCompute>(Coeff))
1063 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
1068 //===----------------------------------------------------------------------===//
1069 // SCEV Expression folder implementations
1070 //===----------------------------------------------------------------------===//
1072 const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op,
1074 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
1075 "This is not a truncating conversion!");
1076 assert(isSCEVable(Ty) &&
1077 "This is not a conversion to a SCEVable type!");
1078 Ty = getEffectiveSCEVType(Ty);
1080 FoldingSetNodeID ID;
1081 ID.AddInteger(scTruncate);
1085 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1087 // Fold if the operand is constant.
1088 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1090 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty)));
1092 // trunc(trunc(x)) --> trunc(x)
1093 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
1094 return getTruncateExpr(ST->getOperand(), Ty);
1096 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
1097 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1098 return getTruncateOrSignExtend(SS->getOperand(), Ty);
1100 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
1101 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1102 return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
1104 // trunc(x1+x2+...+xN) --> trunc(x1)+trunc(x2)+...+trunc(xN) if we can
1105 // eliminate all the truncates.
1106 if (const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Op)) {
1107 SmallVector<const SCEV *, 4> Operands;
1108 bool hasTrunc = false;
1109 for (unsigned i = 0, e = SA->getNumOperands(); i != e && !hasTrunc; ++i) {
1110 const SCEV *S = getTruncateExpr(SA->getOperand(i), Ty);
1111 hasTrunc = isa<SCEVTruncateExpr>(S);
1112 Operands.push_back(S);
1115 return getAddExpr(Operands);
1116 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL.
1119 // trunc(x1*x2*...*xN) --> trunc(x1)*trunc(x2)*...*trunc(xN) if we can
1120 // eliminate all the truncates.
1121 if (const SCEVMulExpr *SM = dyn_cast<SCEVMulExpr>(Op)) {
1122 SmallVector<const SCEV *, 4> Operands;
1123 bool hasTrunc = false;
1124 for (unsigned i = 0, e = SM->getNumOperands(); i != e && !hasTrunc; ++i) {
1125 const SCEV *S = getTruncateExpr(SM->getOperand(i), Ty);
1126 hasTrunc = isa<SCEVTruncateExpr>(S);
1127 Operands.push_back(S);
1130 return getMulExpr(Operands);
1131 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL.
1134 // If the input value is a chrec scev, truncate the chrec's operands.
1135 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
1136 SmallVector<const SCEV *, 4> Operands;
1137 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
1138 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty));
1139 return getAddRecExpr(Operands, AddRec->getLoop(), SCEV::FlagAnyWrap);
1142 // The cast wasn't folded; create an explicit cast node. We can reuse
1143 // the existing insert position since if we get here, we won't have
1144 // made any changes which would invalidate it.
1145 SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator),
1147 UniqueSCEVs.InsertNode(S, IP);
1151 const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op,
1153 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1154 "This is not an extending conversion!");
1155 assert(isSCEVable(Ty) &&
1156 "This is not a conversion to a SCEVable type!");
1157 Ty = getEffectiveSCEVType(Ty);
1159 // Fold if the operand is constant.
1160 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1162 cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(), Ty)));
1164 // zext(zext(x)) --> zext(x)
1165 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1166 return getZeroExtendExpr(SZ->getOperand(), Ty);
1168 // Before doing any expensive analysis, check to see if we've already
1169 // computed a SCEV for this Op and Ty.
1170 FoldingSetNodeID ID;
1171 ID.AddInteger(scZeroExtend);
1175 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1177 // zext(trunc(x)) --> zext(x) or x or trunc(x)
1178 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1179 // It's possible the bits taken off by the truncate were all zero bits. If
1180 // so, we should be able to simplify this further.
1181 const SCEV *X = ST->getOperand();
1182 ConstantRange CR = getUnsignedRange(X);
1183 unsigned TruncBits = getTypeSizeInBits(ST->getType());
1184 unsigned NewBits = getTypeSizeInBits(Ty);
1185 if (CR.truncate(TruncBits).zeroExtend(NewBits).contains(
1186 CR.zextOrTrunc(NewBits)))
1187 return getTruncateOrZeroExtend(X, Ty);
1190 // If the input value is a chrec scev, and we can prove that the value
1191 // did not overflow the old, smaller, value, we can zero extend all of the
1192 // operands (often constants). This allows analysis of something like
1193 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
1194 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1195 if (AR->isAffine()) {
1196 const SCEV *Start = AR->getStart();
1197 const SCEV *Step = AR->getStepRecurrence(*this);
1198 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1199 const Loop *L = AR->getLoop();
1201 // If we have special knowledge that this addrec won't overflow,
1202 // we don't need to do any further analysis.
1203 if (AR->getNoWrapFlags(SCEV::FlagNUW))
1204 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1205 getZeroExtendExpr(Step, Ty),
1206 L, AR->getNoWrapFlags());
1208 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1209 // Note that this serves two purposes: It filters out loops that are
1210 // simply not analyzable, and it covers the case where this code is
1211 // being called from within backedge-taken count analysis, such that
1212 // attempting to ask for the backedge-taken count would likely result
1213 // in infinite recursion. In the later case, the analysis code will
1214 // cope with a conservative value, and it will take care to purge
1215 // that value once it has finished.
1216 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1217 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1218 // Manually compute the final value for AR, checking for
1221 // Check whether the backedge-taken count can be losslessly casted to
1222 // the addrec's type. The count is always unsigned.
1223 const SCEV *CastedMaxBECount =
1224 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1225 const SCEV *RecastedMaxBECount =
1226 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1227 if (MaxBECount == RecastedMaxBECount) {
1228 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1229 // Check whether Start+Step*MaxBECount has no unsigned overflow.
1230 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step);
1231 const SCEV *ZAdd = getZeroExtendExpr(getAddExpr(Start, ZMul), WideTy);
1232 const SCEV *WideStart = getZeroExtendExpr(Start, WideTy);
1233 const SCEV *WideMaxBECount =
1234 getZeroExtendExpr(CastedMaxBECount, WideTy);
1235 const SCEV *OperandExtendedAdd =
1236 getAddExpr(WideStart,
1237 getMulExpr(WideMaxBECount,
1238 getZeroExtendExpr(Step, WideTy)));
1239 if (ZAdd == OperandExtendedAdd) {
1240 // Cache knowledge of AR NUW, which is propagated to this AddRec.
1241 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1242 // Return the expression with the addrec on the outside.
1243 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1244 getZeroExtendExpr(Step, Ty),
1245 L, AR->getNoWrapFlags());
1247 // Similar to above, only this time treat the step value as signed.
1248 // This covers loops that count down.
1249 OperandExtendedAdd =
1250 getAddExpr(WideStart,
1251 getMulExpr(WideMaxBECount,
1252 getSignExtendExpr(Step, WideTy)));
1253 if (ZAdd == OperandExtendedAdd) {
1254 // Cache knowledge of AR NW, which is propagated to this AddRec.
1255 // Negative step causes unsigned wrap, but it still can't self-wrap.
1256 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1257 // Return the expression with the addrec on the outside.
1258 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1259 getSignExtendExpr(Step, Ty),
1260 L, AR->getNoWrapFlags());
1264 // If the backedge is guarded by a comparison with the pre-inc value
1265 // the addrec is safe. Also, if the entry is guarded by a comparison
1266 // with the start value and the backedge is guarded by a comparison
1267 // with the post-inc value, the addrec is safe.
1268 if (isKnownPositive(Step)) {
1269 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
1270 getUnsignedRange(Step).getUnsignedMax());
1271 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
1272 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) &&
1273 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT,
1274 AR->getPostIncExpr(*this), N))) {
1275 // Cache knowledge of AR NUW, which is propagated to this AddRec.
1276 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1277 // Return the expression with the addrec on the outside.
1278 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1279 getZeroExtendExpr(Step, Ty),
1280 L, AR->getNoWrapFlags());
1282 } else if (isKnownNegative(Step)) {
1283 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
1284 getSignedRange(Step).getSignedMin());
1285 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) ||
1286 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) &&
1287 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT,
1288 AR->getPostIncExpr(*this), N))) {
1289 // Cache knowledge of AR NW, which is propagated to this AddRec.
1290 // Negative step causes unsigned wrap, but it still can't self-wrap.
1291 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1292 // Return the expression with the addrec on the outside.
1293 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1294 getSignExtendExpr(Step, Ty),
1295 L, AR->getNoWrapFlags());
1301 // The cast wasn't folded; create an explicit cast node.
1302 // Recompute the insert position, as it may have been invalidated.
1303 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1304 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
1306 UniqueSCEVs.InsertNode(S, IP);
1310 // Get the limit of a recurrence such that incrementing by Step cannot cause
1311 // signed overflow as long as the value of the recurrence within the loop does
1312 // not exceed this limit before incrementing.
1313 static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1314 ICmpInst::Predicate *Pred,
1315 ScalarEvolution *SE) {
1316 unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
1317 if (SE->isKnownPositive(Step)) {
1318 *Pred = ICmpInst::ICMP_SLT;
1319 return SE->getConstant(APInt::getSignedMinValue(BitWidth) -
1320 SE->getSignedRange(Step).getSignedMax());
1322 if (SE->isKnownNegative(Step)) {
1323 *Pred = ICmpInst::ICMP_SGT;
1324 return SE->getConstant(APInt::getSignedMaxValue(BitWidth) -
1325 SE->getSignedRange(Step).getSignedMin());
1330 // The recurrence AR has been shown to have no signed wrap. Typically, if we can
1331 // prove NSW for AR, then we can just as easily prove NSW for its preincrement
1332 // or postincrement sibling. This allows normalizing a sign extended AddRec as
1333 // such: {sext(Step + Start),+,Step} => {(Step + sext(Start),+,Step} As a
1334 // result, the expression "Step + sext(PreIncAR)" is congruent with
1335 // "sext(PostIncAR)"
1336 static const SCEV *getPreStartForSignExtend(const SCEVAddRecExpr *AR,
1338 ScalarEvolution *SE) {
1339 const Loop *L = AR->getLoop();
1340 const SCEV *Start = AR->getStart();
1341 const SCEV *Step = AR->getStepRecurrence(*SE);
1343 // Check for a simple looking step prior to loop entry.
1344 const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Start);
1348 // Create an AddExpr for "PreStart" after subtracting Step. Full SCEV
1349 // subtraction is expensive. For this purpose, perform a quick and dirty
1350 // difference, by checking for Step in the operand list.
1351 SmallVector<const SCEV *, 4> DiffOps;
1352 for (const SCEV *Op : SA->operands())
1354 DiffOps.push_back(Op);
1356 if (DiffOps.size() == SA->getNumOperands())
1359 // This is a postinc AR. Check for overflow on the preinc recurrence using the
1360 // same three conditions that getSignExtendedExpr checks.
1362 // 1. NSW flags on the step increment.
1363 const SCEV *PreStart = SE->getAddExpr(DiffOps, SA->getNoWrapFlags());
1364 const SCEVAddRecExpr *PreAR = dyn_cast<SCEVAddRecExpr>(
1365 SE->getAddRecExpr(PreStart, Step, L, SCEV::FlagAnyWrap));
1367 // WARNING: FIXME: the optimization below assumes that a sign-overflowing nsw
1368 // operation is undefined behavior. This is strictly more aggressive than the
1369 // interpretation of nsw in other parts of LLVM (for instance, they may
1370 // unconditionally hoist nsw arithmetic through control flow). This logic
1371 // needs to be revisited once we have a consistent semantics for poison
1374 // "{S,+,X} is <nsw>" and "{S,+,X} is evaluated at least once" implies "S+X
1375 // does not sign-overflow" (we'd have undefined behavior if it did). If
1376 // `L->getExitingBlock() == L->getLoopLatch()` then `PreAR` (= {S,+,X}<nsw>)
1377 // is evaluated every-time `AR` (= {S+X,+,X}) is evaluated, and hence within
1378 // `AR` we are safe to assume that "S+X" will not sign-overflow.
1381 BasicBlock *ExitingBlock = L->getExitingBlock();
1382 BasicBlock *LatchBlock = L->getLoopLatch();
1383 if (PreAR && PreAR->getNoWrapFlags(SCEV::FlagNSW) &&
1384 ExitingBlock != nullptr && ExitingBlock == LatchBlock)
1387 // 2. Direct overflow check on the step operation's expression.
1388 unsigned BitWidth = SE->getTypeSizeInBits(AR->getType());
1389 Type *WideTy = IntegerType::get(SE->getContext(), BitWidth * 2);
1390 const SCEV *OperandExtendedStart =
1391 SE->getAddExpr(SE->getSignExtendExpr(PreStart, WideTy),
1392 SE->getSignExtendExpr(Step, WideTy));
1393 if (SE->getSignExtendExpr(Start, WideTy) == OperandExtendedStart) {
1394 // Cache knowledge of PreAR NSW.
1396 const_cast<SCEVAddRecExpr *>(PreAR)->setNoWrapFlags(SCEV::FlagNSW);
1397 // FIXME: this optimization needs a unit test
1398 DEBUG(dbgs() << "SCEV: untested prestart overflow check\n");
1402 // 3. Loop precondition.
1403 ICmpInst::Predicate Pred;
1404 const SCEV *OverflowLimit = getOverflowLimitForStep(Step, &Pred, SE);
1406 if (OverflowLimit &&
1407 SE->isLoopEntryGuardedByCond(L, Pred, PreStart, OverflowLimit)) {
1413 // Get the normalized sign-extended expression for this AddRec's Start.
1414 static const SCEV *getSignExtendAddRecStart(const SCEVAddRecExpr *AR,
1416 ScalarEvolution *SE) {
1417 const SCEV *PreStart = getPreStartForSignExtend(AR, Ty, SE);
1419 return SE->getSignExtendExpr(AR->getStart(), Ty);
1421 return SE->getAddExpr(SE->getSignExtendExpr(AR->getStepRecurrence(*SE), Ty),
1422 SE->getSignExtendExpr(PreStart, Ty));
1425 const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op,
1427 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1428 "This is not an extending conversion!");
1429 assert(isSCEVable(Ty) &&
1430 "This is not a conversion to a SCEVable type!");
1431 Ty = getEffectiveSCEVType(Ty);
1433 // Fold if the operand is constant.
1434 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1436 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), Ty)));
1438 // sext(sext(x)) --> sext(x)
1439 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1440 return getSignExtendExpr(SS->getOperand(), Ty);
1442 // sext(zext(x)) --> zext(x)
1443 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1444 return getZeroExtendExpr(SZ->getOperand(), Ty);
1446 // Before doing any expensive analysis, check to see if we've already
1447 // computed a SCEV for this Op and Ty.
1448 FoldingSetNodeID ID;
1449 ID.AddInteger(scSignExtend);
1453 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1455 // If the input value is provably positive, build a zext instead.
1456 if (isKnownNonNegative(Op))
1457 return getZeroExtendExpr(Op, Ty);
1459 // sext(trunc(x)) --> sext(x) or x or trunc(x)
1460 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1461 // It's possible the bits taken off by the truncate were all sign bits. If
1462 // so, we should be able to simplify this further.
1463 const SCEV *X = ST->getOperand();
1464 ConstantRange CR = getSignedRange(X);
1465 unsigned TruncBits = getTypeSizeInBits(ST->getType());
1466 unsigned NewBits = getTypeSizeInBits(Ty);
1467 if (CR.truncate(TruncBits).signExtend(NewBits).contains(
1468 CR.sextOrTrunc(NewBits)))
1469 return getTruncateOrSignExtend(X, Ty);
1472 // sext(C1 + (C2 * x)) --> C1 + sext(C2 * x) if C1 < C2
1473 if (auto SA = dyn_cast<SCEVAddExpr>(Op)) {
1474 if (SA->getNumOperands() == 2) {
1475 auto SC1 = dyn_cast<SCEVConstant>(SA->getOperand(0));
1476 auto SMul = dyn_cast<SCEVMulExpr>(SA->getOperand(1));
1478 if (auto SC2 = dyn_cast<SCEVConstant>(SMul->getOperand(0))) {
1479 const APInt &C1 = SC1->getValue()->getValue();
1480 const APInt &C2 = SC2->getValue()->getValue();
1481 if (C1.isStrictlyPositive() && C2.isStrictlyPositive() &&
1482 C2.ugt(C1) && C2.isPowerOf2())
1483 return getAddExpr(getSignExtendExpr(SC1, Ty),
1484 getSignExtendExpr(SMul, Ty));
1489 // If the input value is a chrec scev, and we can prove that the value
1490 // did not overflow the old, smaller, value, we can sign extend all of the
1491 // operands (often constants). This allows analysis of something like
1492 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
1493 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1494 if (AR->isAffine()) {
1495 const SCEV *Start = AR->getStart();
1496 const SCEV *Step = AR->getStepRecurrence(*this);
1497 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1498 const Loop *L = AR->getLoop();
1500 // If we have special knowledge that this addrec won't overflow,
1501 // we don't need to do any further analysis.
1502 if (AR->getNoWrapFlags(SCEV::FlagNSW))
1503 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1504 getSignExtendExpr(Step, Ty),
1507 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1508 // Note that this serves two purposes: It filters out loops that are
1509 // simply not analyzable, and it covers the case where this code is
1510 // being called from within backedge-taken count analysis, such that
1511 // attempting to ask for the backedge-taken count would likely result
1512 // in infinite recursion. In the later case, the analysis code will
1513 // cope with a conservative value, and it will take care to purge
1514 // that value once it has finished.
1515 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1516 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1517 // Manually compute the final value for AR, checking for
1520 // Check whether the backedge-taken count can be losslessly casted to
1521 // the addrec's type. The count is always unsigned.
1522 const SCEV *CastedMaxBECount =
1523 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1524 const SCEV *RecastedMaxBECount =
1525 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1526 if (MaxBECount == RecastedMaxBECount) {
1527 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1528 // Check whether Start+Step*MaxBECount has no signed overflow.
1529 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
1530 const SCEV *SAdd = getSignExtendExpr(getAddExpr(Start, SMul), WideTy);
1531 const SCEV *WideStart = getSignExtendExpr(Start, WideTy);
1532 const SCEV *WideMaxBECount =
1533 getZeroExtendExpr(CastedMaxBECount, WideTy);
1534 const SCEV *OperandExtendedAdd =
1535 getAddExpr(WideStart,
1536 getMulExpr(WideMaxBECount,
1537 getSignExtendExpr(Step, WideTy)));
1538 if (SAdd == OperandExtendedAdd) {
1539 // Cache knowledge of AR NSW, which is propagated to this AddRec.
1540 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1541 // Return the expression with the addrec on the outside.
1542 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1543 getSignExtendExpr(Step, Ty),
1544 L, AR->getNoWrapFlags());
1546 // Similar to above, only this time treat the step value as unsigned.
1547 // This covers loops that count up with an unsigned step.
1548 OperandExtendedAdd =
1549 getAddExpr(WideStart,
1550 getMulExpr(WideMaxBECount,
1551 getZeroExtendExpr(Step, WideTy)));
1552 if (SAdd == OperandExtendedAdd) {
1553 // Cache knowledge of AR NSW, which is propagated to this AddRec.
1554 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1555 // Return the expression with the addrec on the outside.
1556 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1557 getZeroExtendExpr(Step, Ty),
1558 L, AR->getNoWrapFlags());
1562 // If the backedge is guarded by a comparison with the pre-inc value
1563 // the addrec is safe. Also, if the entry is guarded by a comparison
1564 // with the start value and the backedge is guarded by a comparison
1565 // with the post-inc value, the addrec is safe.
1566 ICmpInst::Predicate Pred;
1567 const SCEV *OverflowLimit = getOverflowLimitForStep(Step, &Pred, this);
1568 if (OverflowLimit &&
1569 (isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) ||
1570 (isLoopEntryGuardedByCond(L, Pred, Start, OverflowLimit) &&
1571 isLoopBackedgeGuardedByCond(L, Pred, AR->getPostIncExpr(*this),
1573 // Cache knowledge of AR NSW, then propagate NSW to the wide AddRec.
1574 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1575 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1576 getSignExtendExpr(Step, Ty),
1577 L, AR->getNoWrapFlags());
1580 // If Start and Step are constants, check if we can apply this
1582 // sext{C1,+,C2} --> C1 + sext{0,+,C2} if C1 < C2
1583 auto SC1 = dyn_cast<SCEVConstant>(Start);
1584 auto SC2 = dyn_cast<SCEVConstant>(Step);
1586 const APInt &C1 = SC1->getValue()->getValue();
1587 const APInt &C2 = SC2->getValue()->getValue();
1588 if (C1.isStrictlyPositive() && C2.isStrictlyPositive() && C2.ugt(C1) &&
1590 Start = getSignExtendExpr(Start, Ty);
1591 const SCEV *NewAR = getAddRecExpr(getConstant(AR->getType(), 0), Step,
1592 L, AR->getNoWrapFlags());
1593 return getAddExpr(Start, getSignExtendExpr(NewAR, Ty));
1598 // The cast wasn't folded; create an explicit cast node.
1599 // Recompute the insert position, as it may have been invalidated.
1600 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1601 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
1603 UniqueSCEVs.InsertNode(S, IP);
1607 /// getAnyExtendExpr - Return a SCEV for the given operand extended with
1608 /// unspecified bits out to the given type.
1610 const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
1612 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1613 "This is not an extending conversion!");
1614 assert(isSCEVable(Ty) &&
1615 "This is not a conversion to a SCEVable type!");
1616 Ty = getEffectiveSCEVType(Ty);
1618 // Sign-extend negative constants.
1619 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1620 if (SC->getValue()->getValue().isNegative())
1621 return getSignExtendExpr(Op, Ty);
1623 // Peel off a truncate cast.
1624 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
1625 const SCEV *NewOp = T->getOperand();
1626 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
1627 return getAnyExtendExpr(NewOp, Ty);
1628 return getTruncateOrNoop(NewOp, Ty);
1631 // Next try a zext cast. If the cast is folded, use it.
1632 const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
1633 if (!isa<SCEVZeroExtendExpr>(ZExt))
1636 // Next try a sext cast. If the cast is folded, use it.
1637 const SCEV *SExt = getSignExtendExpr(Op, Ty);
1638 if (!isa<SCEVSignExtendExpr>(SExt))
1641 // Force the cast to be folded into the operands of an addrec.
1642 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
1643 SmallVector<const SCEV *, 4> Ops;
1644 for (const SCEV *Op : AR->operands())
1645 Ops.push_back(getAnyExtendExpr(Op, Ty));
1646 return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW);
1649 // If the expression is obviously signed, use the sext cast value.
1650 if (isa<SCEVSMaxExpr>(Op))
1653 // Absent any other information, use the zext cast value.
1657 /// CollectAddOperandsWithScales - Process the given Ops list, which is
1658 /// a list of operands to be added under the given scale, update the given
1659 /// map. This is a helper function for getAddRecExpr. As an example of
1660 /// what it does, given a sequence of operands that would form an add
1661 /// expression like this:
1663 /// m + n + 13 + (A * (o + p + (B * (q + m + 29)))) + r + (-1 * r)
1665 /// where A and B are constants, update the map with these values:
1667 /// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
1669 /// and add 13 + A*B*29 to AccumulatedConstant.
1670 /// This will allow getAddRecExpr to produce this:
1672 /// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
1674 /// This form often exposes folding opportunities that are hidden in
1675 /// the original operand list.
1677 /// Return true iff it appears that any interesting folding opportunities
1678 /// may be exposed. This helps getAddRecExpr short-circuit extra work in
1679 /// the common case where no interesting opportunities are present, and
1680 /// is also used as a check to avoid infinite recursion.
1683 CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
1684 SmallVectorImpl<const SCEV *> &NewOps,
1685 APInt &AccumulatedConstant,
1686 const SCEV *const *Ops, size_t NumOperands,
1688 ScalarEvolution &SE) {
1689 bool Interesting = false;
1691 // Iterate over the add operands. They are sorted, with constants first.
1693 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1695 // Pull a buried constant out to the outside.
1696 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
1698 AccumulatedConstant += Scale * C->getValue()->getValue();
1701 // Next comes everything else. We're especially interested in multiplies
1702 // here, but they're in the middle, so just visit the rest with one loop.
1703 for (; i != NumOperands; ++i) {
1704 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
1705 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
1707 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue();
1708 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
1709 // A multiplication of a constant with another add; recurse.
1710 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1));
1712 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1713 Add->op_begin(), Add->getNumOperands(),
1716 // A multiplication of a constant with some other value. Update
1718 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
1719 const SCEV *Key = SE.getMulExpr(MulOps);
1720 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1721 M.insert(std::make_pair(Key, NewScale));
1723 NewOps.push_back(Pair.first->first);
1725 Pair.first->second += NewScale;
1726 // The map already had an entry for this value, which may indicate
1727 // a folding opportunity.
1732 // An ordinary operand. Update the map.
1733 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1734 M.insert(std::make_pair(Ops[i], Scale));
1736 NewOps.push_back(Pair.first->first);
1738 Pair.first->second += Scale;
1739 // The map already had an entry for this value, which may indicate
1740 // a folding opportunity.
1750 struct APIntCompare {
1751 bool operator()(const APInt &LHS, const APInt &RHS) const {
1752 return LHS.ult(RHS);
1757 // We're trying to construct a SCEV of type `Type' with `Ops' as operands and
1758 // `OldFlags' as can't-wrap behavior. Infer a more aggressive set of
1759 // can't-overflow flags for the operation if possible.
1760 static SCEV::NoWrapFlags
1761 StrengthenNoWrapFlags(ScalarEvolution *SE, SCEVTypes Type,
1762 const SmallVectorImpl<const SCEV *> &Ops,
1763 SCEV::NoWrapFlags OldFlags) {
1764 using namespace std::placeholders;
1767 Type == scAddExpr || Type == scAddRecExpr || Type == scMulExpr;
1769 assert(CanAnalyze && "don't call from other places!");
1771 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
1772 SCEV::NoWrapFlags SignOrUnsignWrap =
1773 ScalarEvolution::maskFlags(OldFlags, SignOrUnsignMask);
1775 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
1776 auto IsKnownNonNegative =
1777 std::bind(std::mem_fn(&ScalarEvolution::isKnownNonNegative), SE, _1);
1779 if (SignOrUnsignWrap == SCEV::FlagNSW &&
1780 std::all_of(Ops.begin(), Ops.end(), IsKnownNonNegative))
1781 return ScalarEvolution::setFlags(OldFlags,
1782 (SCEV::NoWrapFlags)SignOrUnsignMask);
1787 /// getAddExpr - Get a canonical add expression, or something simpler if
1789 const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
1790 SCEV::NoWrapFlags Flags) {
1791 assert(!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) &&
1792 "only nuw or nsw allowed");
1793 assert(!Ops.empty() && "Cannot get empty add!");
1794 if (Ops.size() == 1) return Ops[0];
1796 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
1797 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1798 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
1799 "SCEVAddExpr operand types don't match!");
1802 Flags = StrengthenNoWrapFlags(this, scAddExpr, Ops, Flags);
1804 // Sort by complexity, this groups all similar expression types together.
1805 GroupByComplexity(Ops, LI);
1807 // If there are any constants, fold them together.
1809 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1811 assert(Idx < Ops.size());
1812 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1813 // We found two constants, fold them together!
1814 Ops[0] = getConstant(LHSC->getValue()->getValue() +
1815 RHSC->getValue()->getValue());
1816 if (Ops.size() == 2) return Ops[0];
1817 Ops.erase(Ops.begin()+1); // Erase the folded element
1818 LHSC = cast<SCEVConstant>(Ops[0]);
1821 // If we are left with a constant zero being added, strip it off.
1822 if (LHSC->getValue()->isZero()) {
1823 Ops.erase(Ops.begin());
1827 if (Ops.size() == 1) return Ops[0];
1830 // Okay, check to see if the same value occurs in the operand list more than
1831 // once. If so, merge them together into an multiply expression. Since we
1832 // sorted the list, these values are required to be adjacent.
1833 Type *Ty = Ops[0]->getType();
1834 bool FoundMatch = false;
1835 for (unsigned i = 0, e = Ops.size(); i != e-1; ++i)
1836 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
1837 // Scan ahead to count how many equal operands there are.
1839 while (i+Count != e && Ops[i+Count] == Ops[i])
1841 // Merge the values into a multiply.
1842 const SCEV *Scale = getConstant(Ty, Count);
1843 const SCEV *Mul = getMulExpr(Scale, Ops[i]);
1844 if (Ops.size() == Count)
1847 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count);
1848 --i; e -= Count - 1;
1852 return getAddExpr(Ops, Flags);
1854 // Check for truncates. If all the operands are truncated from the same
1855 // type, see if factoring out the truncate would permit the result to be
1856 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
1857 // if the contents of the resulting outer trunc fold to something simple.
1858 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
1859 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
1860 Type *DstType = Trunc->getType();
1861 Type *SrcType = Trunc->getOperand()->getType();
1862 SmallVector<const SCEV *, 8> LargeOps;
1864 // Check all the operands to see if they can be represented in the
1865 // source type of the truncate.
1866 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1867 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
1868 if (T->getOperand()->getType() != SrcType) {
1872 LargeOps.push_back(T->getOperand());
1873 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1874 LargeOps.push_back(getAnyExtendExpr(C, SrcType));
1875 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
1876 SmallVector<const SCEV *, 8> LargeMulOps;
1877 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
1878 if (const SCEVTruncateExpr *T =
1879 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
1880 if (T->getOperand()->getType() != SrcType) {
1884 LargeMulOps.push_back(T->getOperand());
1885 } else if (const SCEVConstant *C =
1886 dyn_cast<SCEVConstant>(M->getOperand(j))) {
1887 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType));
1894 LargeOps.push_back(getMulExpr(LargeMulOps));
1901 // Evaluate the expression in the larger type.
1902 const SCEV *Fold = getAddExpr(LargeOps, Flags);
1903 // If it folds to something simple, use it. Otherwise, don't.
1904 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
1905 return getTruncateExpr(Fold, DstType);
1909 // Skip past any other cast SCEVs.
1910 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
1913 // If there are add operands they would be next.
1914 if (Idx < Ops.size()) {
1915 bool DeletedAdd = false;
1916 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
1917 // If we have an add, expand the add operands onto the end of the operands
1919 Ops.erase(Ops.begin()+Idx);
1920 Ops.append(Add->op_begin(), Add->op_end());
1924 // If we deleted at least one add, we added operands to the end of the list,
1925 // and they are not necessarily sorted. Recurse to resort and resimplify
1926 // any operands we just acquired.
1928 return getAddExpr(Ops);
1931 // Skip over the add expression until we get to a multiply.
1932 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1935 // Check to see if there are any folding opportunities present with
1936 // operands multiplied by constant values.
1937 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
1938 uint64_t BitWidth = getTypeSizeInBits(Ty);
1939 DenseMap<const SCEV *, APInt> M;
1940 SmallVector<const SCEV *, 8> NewOps;
1941 APInt AccumulatedConstant(BitWidth, 0);
1942 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1943 Ops.data(), Ops.size(),
1944 APInt(BitWidth, 1), *this)) {
1945 // Some interesting folding opportunity is present, so its worthwhile to
1946 // re-generate the operands list. Group the operands by constant scale,
1947 // to avoid multiplying by the same constant scale multiple times.
1948 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
1949 for (SmallVectorImpl<const SCEV *>::const_iterator I = NewOps.begin(),
1950 E = NewOps.end(); I != E; ++I)
1951 MulOpLists[M.find(*I)->second].push_back(*I);
1952 // Re-generate the operands list.
1954 if (AccumulatedConstant != 0)
1955 Ops.push_back(getConstant(AccumulatedConstant));
1956 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator
1957 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I)
1959 Ops.push_back(getMulExpr(getConstant(I->first),
1960 getAddExpr(I->second)));
1962 return getConstant(Ty, 0);
1963 if (Ops.size() == 1)
1965 return getAddExpr(Ops);
1969 // If we are adding something to a multiply expression, make sure the
1970 // something is not already an operand of the multiply. If so, merge it into
1972 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
1973 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
1974 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
1975 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
1976 if (isa<SCEVConstant>(MulOpSCEV))
1978 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
1979 if (MulOpSCEV == Ops[AddOp]) {
1980 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
1981 const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
1982 if (Mul->getNumOperands() != 2) {
1983 // If the multiply has more than two operands, we must get the
1985 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
1986 Mul->op_begin()+MulOp);
1987 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
1988 InnerMul = getMulExpr(MulOps);
1990 const SCEV *One = getConstant(Ty, 1);
1991 const SCEV *AddOne = getAddExpr(One, InnerMul);
1992 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV);
1993 if (Ops.size() == 2) return OuterMul;
1995 Ops.erase(Ops.begin()+AddOp);
1996 Ops.erase(Ops.begin()+Idx-1);
1998 Ops.erase(Ops.begin()+Idx);
1999 Ops.erase(Ops.begin()+AddOp-1);
2001 Ops.push_back(OuterMul);
2002 return getAddExpr(Ops);
2005 // Check this multiply against other multiplies being added together.
2006 for (unsigned OtherMulIdx = Idx+1;
2007 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
2009 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
2010 // If MulOp occurs in OtherMul, we can fold the two multiplies
2012 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
2013 OMulOp != e; ++OMulOp)
2014 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
2015 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
2016 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
2017 if (Mul->getNumOperands() != 2) {
2018 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
2019 Mul->op_begin()+MulOp);
2020 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
2021 InnerMul1 = getMulExpr(MulOps);
2023 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
2024 if (OtherMul->getNumOperands() != 2) {
2025 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
2026 OtherMul->op_begin()+OMulOp);
2027 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end());
2028 InnerMul2 = getMulExpr(MulOps);
2030 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
2031 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
2032 if (Ops.size() == 2) return OuterMul;
2033 Ops.erase(Ops.begin()+Idx);
2034 Ops.erase(Ops.begin()+OtherMulIdx-1);
2035 Ops.push_back(OuterMul);
2036 return getAddExpr(Ops);
2042 // If there are any add recurrences in the operands list, see if any other
2043 // added values are loop invariant. If so, we can fold them into the
2045 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2048 // Scan over all recurrences, trying to fold loop invariants into them.
2049 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
2050 // Scan all of the other operands to this add and add them to the vector if
2051 // they are loop invariant w.r.t. the recurrence.
2052 SmallVector<const SCEV *, 8> LIOps;
2053 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2054 const Loop *AddRecLoop = AddRec->getLoop();
2055 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2056 if (isLoopInvariant(Ops[i], AddRecLoop)) {
2057 LIOps.push_back(Ops[i]);
2058 Ops.erase(Ops.begin()+i);
2062 // If we found some loop invariants, fold them into the recurrence.
2063 if (!LIOps.empty()) {
2064 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
2065 LIOps.push_back(AddRec->getStart());
2067 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
2069 AddRecOps[0] = getAddExpr(LIOps);
2071 // Build the new addrec. Propagate the NUW and NSW flags if both the
2072 // outer add and the inner addrec are guaranteed to have no overflow.
2073 // Always propagate NW.
2074 Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW));
2075 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags);
2077 // If all of the other operands were loop invariant, we are done.
2078 if (Ops.size() == 1) return NewRec;
2080 // Otherwise, add the folded AddRec by the non-invariant parts.
2081 for (unsigned i = 0;; ++i)
2082 if (Ops[i] == AddRec) {
2086 return getAddExpr(Ops);
2089 // Okay, if there weren't any loop invariants to be folded, check to see if
2090 // there are multiple AddRec's with the same loop induction variable being
2091 // added together. If so, we can fold them.
2092 for (unsigned OtherIdx = Idx+1;
2093 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2095 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
2096 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L>
2097 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
2099 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2101 if (const SCEVAddRecExpr *OtherAddRec =
2102 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]))
2103 if (OtherAddRec->getLoop() == AddRecLoop) {
2104 for (unsigned i = 0, e = OtherAddRec->getNumOperands();
2106 if (i >= AddRecOps.size()) {
2107 AddRecOps.append(OtherAddRec->op_begin()+i,
2108 OtherAddRec->op_end());
2111 AddRecOps[i] = getAddExpr(AddRecOps[i],
2112 OtherAddRec->getOperand(i));
2114 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2116 // Step size has changed, so we cannot guarantee no self-wraparound.
2117 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap);
2118 return getAddExpr(Ops);
2121 // Otherwise couldn't fold anything into this recurrence. Move onto the
2125 // Okay, it looks like we really DO need an add expr. Check to see if we
2126 // already have one, otherwise create a new one.
2127 FoldingSetNodeID ID;
2128 ID.AddInteger(scAddExpr);
2129 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2130 ID.AddPointer(Ops[i]);
2133 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2135 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2136 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2137 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator),
2139 UniqueSCEVs.InsertNode(S, IP);
2141 S->setNoWrapFlags(Flags);
2145 static uint64_t umul_ov(uint64_t i, uint64_t j, bool &Overflow) {
2147 if (j > 1 && k / j != i) Overflow = true;
2151 /// Compute the result of "n choose k", the binomial coefficient. If an
2152 /// intermediate computation overflows, Overflow will be set and the return will
2153 /// be garbage. Overflow is not cleared on absence of overflow.
2154 static uint64_t Choose(uint64_t n, uint64_t k, bool &Overflow) {
2155 // We use the multiplicative formula:
2156 // n(n-1)(n-2)...(n-(k-1)) / k(k-1)(k-2)...1 .
2157 // At each iteration, we take the n-th term of the numeral and divide by the
2158 // (k-n)th term of the denominator. This division will always produce an
2159 // integral result, and helps reduce the chance of overflow in the
2160 // intermediate computations. However, we can still overflow even when the
2161 // final result would fit.
2163 if (n == 0 || n == k) return 1;
2164 if (k > n) return 0;
2170 for (uint64_t i = 1; i <= k; ++i) {
2171 r = umul_ov(r, n-(i-1), Overflow);
2177 /// Determine if any of the operands in this SCEV are a constant or if
2178 /// any of the add or multiply expressions in this SCEV contain a constant.
2179 static bool containsConstantSomewhere(const SCEV *StartExpr) {
2180 SmallVector<const SCEV *, 4> Ops;
2181 Ops.push_back(StartExpr);
2182 while (!Ops.empty()) {
2183 const SCEV *CurrentExpr = Ops.pop_back_val();
2184 if (isa<SCEVConstant>(*CurrentExpr))
2187 if (isa<SCEVAddExpr>(*CurrentExpr) || isa<SCEVMulExpr>(*CurrentExpr)) {
2188 const auto *CurrentNAry = cast<SCEVNAryExpr>(CurrentExpr);
2189 for (const SCEV *Operand : CurrentNAry->operands())
2190 Ops.push_back(Operand);
2196 /// getMulExpr - Get a canonical multiply expression, or something simpler if
2198 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
2199 SCEV::NoWrapFlags Flags) {
2200 assert(Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) &&
2201 "only nuw or nsw allowed");
2202 assert(!Ops.empty() && "Cannot get empty mul!");
2203 if (Ops.size() == 1) return Ops[0];
2205 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2206 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2207 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2208 "SCEVMulExpr operand types don't match!");
2211 Flags = StrengthenNoWrapFlags(this, scMulExpr, Ops, Flags);
2213 // Sort by complexity, this groups all similar expression types together.
2214 GroupByComplexity(Ops, LI);
2216 // If there are any constants, fold them together.
2218 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2220 // C1*(C2+V) -> C1*C2 + C1*V
2221 if (Ops.size() == 2)
2222 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
2223 // If any of Add's ops are Adds or Muls with a constant,
2224 // apply this transformation as well.
2225 if (Add->getNumOperands() == 2)
2226 if (containsConstantSomewhere(Add))
2227 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
2228 getMulExpr(LHSC, Add->getOperand(1)));
2231 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2232 // We found two constants, fold them together!
2233 ConstantInt *Fold = ConstantInt::get(getContext(),
2234 LHSC->getValue()->getValue() *
2235 RHSC->getValue()->getValue());
2236 Ops[0] = getConstant(Fold);
2237 Ops.erase(Ops.begin()+1); // Erase the folded element
2238 if (Ops.size() == 1) return Ops[0];
2239 LHSC = cast<SCEVConstant>(Ops[0]);
2242 // If we are left with a constant one being multiplied, strip it off.
2243 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
2244 Ops.erase(Ops.begin());
2246 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
2247 // If we have a multiply of zero, it will always be zero.
2249 } else if (Ops[0]->isAllOnesValue()) {
2250 // If we have a mul by -1 of an add, try distributing the -1 among the
2252 if (Ops.size() == 2) {
2253 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
2254 SmallVector<const SCEV *, 4> NewOps;
2255 bool AnyFolded = false;
2256 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(),
2257 E = Add->op_end(); I != E; ++I) {
2258 const SCEV *Mul = getMulExpr(Ops[0], *I);
2259 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
2260 NewOps.push_back(Mul);
2263 return getAddExpr(NewOps);
2265 else if (const SCEVAddRecExpr *
2266 AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) {
2267 // Negation preserves a recurrence's no self-wrap property.
2268 SmallVector<const SCEV *, 4> Operands;
2269 for (SCEVAddRecExpr::op_iterator I = AddRec->op_begin(),
2270 E = AddRec->op_end(); I != E; ++I) {
2271 Operands.push_back(getMulExpr(Ops[0], *I));
2273 return getAddRecExpr(Operands, AddRec->getLoop(),
2274 AddRec->getNoWrapFlags(SCEV::FlagNW));
2279 if (Ops.size() == 1)
2283 // Skip over the add expression until we get to a multiply.
2284 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
2287 // If there are mul operands inline them all into this expression.
2288 if (Idx < Ops.size()) {
2289 bool DeletedMul = false;
2290 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
2291 // If we have an mul, expand the mul operands onto the end of the operands
2293 Ops.erase(Ops.begin()+Idx);
2294 Ops.append(Mul->op_begin(), Mul->op_end());
2298 // If we deleted at least one mul, we added operands to the end of the list,
2299 // and they are not necessarily sorted. Recurse to resort and resimplify
2300 // any operands we just acquired.
2302 return getMulExpr(Ops);
2305 // If there are any add recurrences in the operands list, see if any other
2306 // added values are loop invariant. If so, we can fold them into the
2308 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2311 // Scan over all recurrences, trying to fold loop invariants into them.
2312 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
2313 // Scan all of the other operands to this mul and add them to the vector if
2314 // they are loop invariant w.r.t. the recurrence.
2315 SmallVector<const SCEV *, 8> LIOps;
2316 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2317 const Loop *AddRecLoop = AddRec->getLoop();
2318 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2319 if (isLoopInvariant(Ops[i], AddRecLoop)) {
2320 LIOps.push_back(Ops[i]);
2321 Ops.erase(Ops.begin()+i);
2325 // If we found some loop invariants, fold them into the recurrence.
2326 if (!LIOps.empty()) {
2327 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
2328 SmallVector<const SCEV *, 4> NewOps;
2329 NewOps.reserve(AddRec->getNumOperands());
2330 const SCEV *Scale = getMulExpr(LIOps);
2331 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
2332 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
2334 // Build the new addrec. Propagate the NUW and NSW flags if both the
2335 // outer mul and the inner addrec are guaranteed to have no overflow.
2337 // No self-wrap cannot be guaranteed after changing the step size, but
2338 // will be inferred if either NUW or NSW is true.
2339 Flags = AddRec->getNoWrapFlags(clearFlags(Flags, SCEV::FlagNW));
2340 const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, Flags);
2342 // If all of the other operands were loop invariant, we are done.
2343 if (Ops.size() == 1) return NewRec;
2345 // Otherwise, multiply the folded AddRec by the non-invariant parts.
2346 for (unsigned i = 0;; ++i)
2347 if (Ops[i] == AddRec) {
2351 return getMulExpr(Ops);
2354 // Okay, if there weren't any loop invariants to be folded, check to see if
2355 // there are multiple AddRec's with the same loop induction variable being
2356 // multiplied together. If so, we can fold them.
2358 // {A1,+,A2,+,...,+,An}<L> * {B1,+,B2,+,...,+,Bn}<L>
2359 // = {x=1 in [ sum y=x..2x [ sum z=max(y-x, y-n)..min(x,n) [
2360 // choose(x, 2x)*choose(2x-y, x-z)*A_{y-z}*B_z
2361 // ]]],+,...up to x=2n}.
2362 // Note that the arguments to choose() are always integers with values
2363 // known at compile time, never SCEV objects.
2365 // The implementation avoids pointless extra computations when the two
2366 // addrec's are of different length (mathematically, it's equivalent to
2367 // an infinite stream of zeros on the right).
2368 bool OpsModified = false;
2369 for (unsigned OtherIdx = Idx+1;
2370 OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2372 const SCEVAddRecExpr *OtherAddRec =
2373 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]);
2374 if (!OtherAddRec || OtherAddRec->getLoop() != AddRecLoop)
2377 bool Overflow = false;
2378 Type *Ty = AddRec->getType();
2379 bool LargerThan64Bits = getTypeSizeInBits(Ty) > 64;
2380 SmallVector<const SCEV*, 7> AddRecOps;
2381 for (int x = 0, xe = AddRec->getNumOperands() +
2382 OtherAddRec->getNumOperands() - 1; x != xe && !Overflow; ++x) {
2383 const SCEV *Term = getConstant(Ty, 0);
2384 for (int y = x, ye = 2*x+1; y != ye && !Overflow; ++y) {
2385 uint64_t Coeff1 = Choose(x, 2*x - y, Overflow);
2386 for (int z = std::max(y-x, y-(int)AddRec->getNumOperands()+1),
2387 ze = std::min(x+1, (int)OtherAddRec->getNumOperands());
2388 z < ze && !Overflow; ++z) {
2389 uint64_t Coeff2 = Choose(2*x - y, x-z, Overflow);
2391 if (LargerThan64Bits)
2392 Coeff = umul_ov(Coeff1, Coeff2, Overflow);
2394 Coeff = Coeff1*Coeff2;
2395 const SCEV *CoeffTerm = getConstant(Ty, Coeff);
2396 const SCEV *Term1 = AddRec->getOperand(y-z);
2397 const SCEV *Term2 = OtherAddRec->getOperand(z);
2398 Term = getAddExpr(Term, getMulExpr(CoeffTerm, Term1,Term2));
2401 AddRecOps.push_back(Term);
2404 const SCEV *NewAddRec = getAddRecExpr(AddRecOps, AddRec->getLoop(),
2406 if (Ops.size() == 2) return NewAddRec;
2407 Ops[Idx] = NewAddRec;
2408 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2410 AddRec = dyn_cast<SCEVAddRecExpr>(NewAddRec);
2416 return getMulExpr(Ops);
2418 // Otherwise couldn't fold anything into this recurrence. Move onto the
2422 // Okay, it looks like we really DO need an mul expr. Check to see if we
2423 // already have one, otherwise create a new one.
2424 FoldingSetNodeID ID;
2425 ID.AddInteger(scMulExpr);
2426 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2427 ID.AddPointer(Ops[i]);
2430 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2432 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2433 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2434 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
2436 UniqueSCEVs.InsertNode(S, IP);
2438 S->setNoWrapFlags(Flags);
2442 /// getUDivExpr - Get a canonical unsigned division expression, or something
2443 /// simpler if possible.
2444 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
2446 assert(getEffectiveSCEVType(LHS->getType()) ==
2447 getEffectiveSCEVType(RHS->getType()) &&
2448 "SCEVUDivExpr operand types don't match!");
2450 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
2451 if (RHSC->getValue()->equalsInt(1))
2452 return LHS; // X udiv 1 --> x
2453 // If the denominator is zero, the result of the udiv is undefined. Don't
2454 // try to analyze it, because the resolution chosen here may differ from
2455 // the resolution chosen in other parts of the compiler.
2456 if (!RHSC->getValue()->isZero()) {
2457 // Determine if the division can be folded into the operands of
2459 // TODO: Generalize this to non-constants by using known-bits information.
2460 Type *Ty = LHS->getType();
2461 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
2462 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1;
2463 // For non-power-of-two values, effectively round the value up to the
2464 // nearest power of two.
2465 if (!RHSC->getValue()->getValue().isPowerOf2())
2467 IntegerType *ExtTy =
2468 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
2469 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
2470 if (const SCEVConstant *Step =
2471 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) {
2472 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
2473 const APInt &StepInt = Step->getValue()->getValue();
2474 const APInt &DivInt = RHSC->getValue()->getValue();
2475 if (!StepInt.urem(DivInt) &&
2476 getZeroExtendExpr(AR, ExtTy) ==
2477 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2478 getZeroExtendExpr(Step, ExtTy),
2479 AR->getLoop(), SCEV::FlagAnyWrap)) {
2480 SmallVector<const SCEV *, 4> Operands;
2481 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i)
2482 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS));
2483 return getAddRecExpr(Operands, AR->getLoop(),
2486 /// Get a canonical UDivExpr for a recurrence.
2487 /// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0.
2488 // We can currently only fold X%N if X is constant.
2489 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(AR->getStart());
2490 if (StartC && !DivInt.urem(StepInt) &&
2491 getZeroExtendExpr(AR, ExtTy) ==
2492 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2493 getZeroExtendExpr(Step, ExtTy),
2494 AR->getLoop(), SCEV::FlagAnyWrap)) {
2495 const APInt &StartInt = StartC->getValue()->getValue();
2496 const APInt &StartRem = StartInt.urem(StepInt);
2498 LHS = getAddRecExpr(getConstant(StartInt - StartRem), Step,
2499 AR->getLoop(), SCEV::FlagNW);
2502 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
2503 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
2504 SmallVector<const SCEV *, 4> Operands;
2505 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i)
2506 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy));
2507 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
2508 // Find an operand that's safely divisible.
2509 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
2510 const SCEV *Op = M->getOperand(i);
2511 const SCEV *Div = getUDivExpr(Op, RHSC);
2512 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
2513 Operands = SmallVector<const SCEV *, 4>(M->op_begin(),
2516 return getMulExpr(Operands);
2520 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
2521 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) {
2522 SmallVector<const SCEV *, 4> Operands;
2523 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i)
2524 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy));
2525 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
2527 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
2528 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
2529 if (isa<SCEVUDivExpr>(Op) ||
2530 getMulExpr(Op, RHS) != A->getOperand(i))
2532 Operands.push_back(Op);
2534 if (Operands.size() == A->getNumOperands())
2535 return getAddExpr(Operands);
2539 // Fold if both operands are constant.
2540 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
2541 Constant *LHSCV = LHSC->getValue();
2542 Constant *RHSCV = RHSC->getValue();
2543 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
2549 FoldingSetNodeID ID;
2550 ID.AddInteger(scUDivExpr);
2554 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2555 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
2557 UniqueSCEVs.InsertNode(S, IP);
2561 static const APInt gcd(const SCEVConstant *C1, const SCEVConstant *C2) {
2562 APInt A = C1->getValue()->getValue().abs();
2563 APInt B = C2->getValue()->getValue().abs();
2564 uint32_t ABW = A.getBitWidth();
2565 uint32_t BBW = B.getBitWidth();
2572 return APIntOps::GreatestCommonDivisor(A, B);
2575 /// getUDivExactExpr - Get a canonical unsigned division expression, or
2576 /// something simpler if possible. There is no representation for an exact udiv
2577 /// in SCEV IR, but we can attempt to remove factors from the LHS and RHS.
2578 /// We can't do this when it's not exact because the udiv may be clearing bits.
2579 const SCEV *ScalarEvolution::getUDivExactExpr(const SCEV *LHS,
2581 // TODO: we could try to find factors in all sorts of things, but for now we
2582 // just deal with u/exact (multiply, constant). See SCEVDivision towards the
2583 // end of this file for inspiration.
2585 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(LHS);
2587 return getUDivExpr(LHS, RHS);
2589 if (const SCEVConstant *RHSCst = dyn_cast<SCEVConstant>(RHS)) {
2590 // If the mulexpr multiplies by a constant, then that constant must be the
2591 // first element of the mulexpr.
2592 if (const SCEVConstant *LHSCst =
2593 dyn_cast<SCEVConstant>(Mul->getOperand(0))) {
2594 if (LHSCst == RHSCst) {
2595 SmallVector<const SCEV *, 2> Operands;
2596 Operands.append(Mul->op_begin() + 1, Mul->op_end());
2597 return getMulExpr(Operands);
2600 // We can't just assume that LHSCst divides RHSCst cleanly, it could be
2601 // that there's a factor provided by one of the other terms. We need to
2603 APInt Factor = gcd(LHSCst, RHSCst);
2604 if (!Factor.isIntN(1)) {
2605 LHSCst = cast<SCEVConstant>(
2606 getConstant(LHSCst->getValue()->getValue().udiv(Factor)));
2607 RHSCst = cast<SCEVConstant>(
2608 getConstant(RHSCst->getValue()->getValue().udiv(Factor)));
2609 SmallVector<const SCEV *, 2> Operands;
2610 Operands.push_back(LHSCst);
2611 Operands.append(Mul->op_begin() + 1, Mul->op_end());
2612 LHS = getMulExpr(Operands);
2614 Mul = dyn_cast<SCEVMulExpr>(LHS);
2616 return getUDivExactExpr(LHS, RHS);
2621 for (int i = 0, e = Mul->getNumOperands(); i != e; ++i) {
2622 if (Mul->getOperand(i) == RHS) {
2623 SmallVector<const SCEV *, 2> Operands;
2624 Operands.append(Mul->op_begin(), Mul->op_begin() + i);
2625 Operands.append(Mul->op_begin() + i + 1, Mul->op_end());
2626 return getMulExpr(Operands);
2630 return getUDivExpr(LHS, RHS);
2633 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2634 /// Simplify the expression as much as possible.
2635 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step,
2637 SCEV::NoWrapFlags Flags) {
2638 SmallVector<const SCEV *, 4> Operands;
2639 Operands.push_back(Start);
2640 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
2641 if (StepChrec->getLoop() == L) {
2642 Operands.append(StepChrec->op_begin(), StepChrec->op_end());
2643 return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW));
2646 Operands.push_back(Step);
2647 return getAddRecExpr(Operands, L, Flags);
2650 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2651 /// Simplify the expression as much as possible.
2653 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
2654 const Loop *L, SCEV::NoWrapFlags Flags) {
2655 if (Operands.size() == 1) return Operands[0];
2657 Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
2658 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
2659 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy &&
2660 "SCEVAddRecExpr operand types don't match!");
2661 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2662 assert(isLoopInvariant(Operands[i], L) &&
2663 "SCEVAddRecExpr operand is not loop-invariant!");
2666 if (Operands.back()->isZero()) {
2667 Operands.pop_back();
2668 return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0} --> X
2671 // It's tempting to want to call getMaxBackedgeTakenCount count here and
2672 // use that information to infer NUW and NSW flags. However, computing a
2673 // BE count requires calling getAddRecExpr, so we may not yet have a
2674 // meaningful BE count at this point (and if we don't, we'd be stuck
2675 // with a SCEVCouldNotCompute as the cached BE count).
2677 Flags = StrengthenNoWrapFlags(this, scAddRecExpr, Operands, Flags);
2679 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
2680 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
2681 const Loop *NestedLoop = NestedAR->getLoop();
2682 if (L->contains(NestedLoop) ?
2683 (L->getLoopDepth() < NestedLoop->getLoopDepth()) :
2684 (!NestedLoop->contains(L) &&
2685 DT->dominates(L->getHeader(), NestedLoop->getHeader()))) {
2686 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
2687 NestedAR->op_end());
2688 Operands[0] = NestedAR->getStart();
2689 // AddRecs require their operands be loop-invariant with respect to their
2690 // loops. Don't perform this transformation if it would break this
2692 bool AllInvariant = true;
2693 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2694 if (!isLoopInvariant(Operands[i], L)) {
2695 AllInvariant = false;
2699 // Create a recurrence for the outer loop with the same step size.
2701 // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the
2702 // inner recurrence has the same property.
2703 SCEV::NoWrapFlags OuterFlags =
2704 maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags());
2706 NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags);
2707 AllInvariant = true;
2708 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i)
2709 if (!isLoopInvariant(NestedOperands[i], NestedLoop)) {
2710 AllInvariant = false;
2714 // Ok, both add recurrences are valid after the transformation.
2716 // The inner recurrence keeps its NW flag but only keeps NUW/NSW if
2717 // the outer recurrence has the same property.
2718 SCEV::NoWrapFlags InnerFlags =
2719 maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags);
2720 return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags);
2723 // Reset Operands to its original state.
2724 Operands[0] = NestedAR;
2728 // Okay, it looks like we really DO need an addrec expr. Check to see if we
2729 // already have one, otherwise create a new one.
2730 FoldingSetNodeID ID;
2731 ID.AddInteger(scAddRecExpr);
2732 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2733 ID.AddPointer(Operands[i]);
2737 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2739 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size());
2740 std::uninitialized_copy(Operands.begin(), Operands.end(), O);
2741 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator),
2742 O, Operands.size(), L);
2743 UniqueSCEVs.InsertNode(S, IP);
2745 S->setNoWrapFlags(Flags);
2749 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
2751 SmallVector<const SCEV *, 2> Ops;
2754 return getSMaxExpr(Ops);
2758 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2759 assert(!Ops.empty() && "Cannot get empty smax!");
2760 if (Ops.size() == 1) return Ops[0];
2762 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2763 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2764 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2765 "SCEVSMaxExpr operand types don't match!");
2768 // Sort by complexity, this groups all similar expression types together.
2769 GroupByComplexity(Ops, LI);
2771 // If there are any constants, fold them together.
2773 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2775 assert(Idx < Ops.size());
2776 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2777 // We found two constants, fold them together!
2778 ConstantInt *Fold = ConstantInt::get(getContext(),
2779 APIntOps::smax(LHSC->getValue()->getValue(),
2780 RHSC->getValue()->getValue()));
2781 Ops[0] = getConstant(Fold);
2782 Ops.erase(Ops.begin()+1); // Erase the folded element
2783 if (Ops.size() == 1) return Ops[0];
2784 LHSC = cast<SCEVConstant>(Ops[0]);
2787 // If we are left with a constant minimum-int, strip it off.
2788 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
2789 Ops.erase(Ops.begin());
2791 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
2792 // If we have an smax with a constant maximum-int, it will always be
2797 if (Ops.size() == 1) return Ops[0];
2800 // Find the first SMax
2801 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
2804 // Check to see if one of the operands is an SMax. If so, expand its operands
2805 // onto our operand list, and recurse to simplify.
2806 if (Idx < Ops.size()) {
2807 bool DeletedSMax = false;
2808 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
2809 Ops.erase(Ops.begin()+Idx);
2810 Ops.append(SMax->op_begin(), SMax->op_end());
2815 return getSMaxExpr(Ops);
2818 // Okay, check to see if the same value occurs in the operand list twice. If
2819 // so, delete one. Since we sorted the list, these values are required to
2821 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2822 // X smax Y smax Y --> X smax Y
2823 // X smax Y --> X, if X is always greater than Y
2824 if (Ops[i] == Ops[i+1] ||
2825 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) {
2826 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2828 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) {
2829 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2833 if (Ops.size() == 1) return Ops[0];
2835 assert(!Ops.empty() && "Reduced smax down to nothing!");
2837 // Okay, it looks like we really DO need an smax expr. Check to see if we
2838 // already have one, otherwise create a new one.
2839 FoldingSetNodeID ID;
2840 ID.AddInteger(scSMaxExpr);
2841 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2842 ID.AddPointer(Ops[i]);
2844 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2845 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2846 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2847 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator),
2849 UniqueSCEVs.InsertNode(S, IP);
2853 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
2855 SmallVector<const SCEV *, 2> Ops;
2858 return getUMaxExpr(Ops);
2862 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2863 assert(!Ops.empty() && "Cannot get empty umax!");
2864 if (Ops.size() == 1) return Ops[0];
2866 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2867 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2868 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2869 "SCEVUMaxExpr operand types don't match!");
2872 // Sort by complexity, this groups all similar expression types together.
2873 GroupByComplexity(Ops, LI);
2875 // If there are any constants, fold them together.
2877 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2879 assert(Idx < Ops.size());
2880 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2881 // We found two constants, fold them together!
2882 ConstantInt *Fold = ConstantInt::get(getContext(),
2883 APIntOps::umax(LHSC->getValue()->getValue(),
2884 RHSC->getValue()->getValue()));
2885 Ops[0] = getConstant(Fold);
2886 Ops.erase(Ops.begin()+1); // Erase the folded element
2887 if (Ops.size() == 1) return Ops[0];
2888 LHSC = cast<SCEVConstant>(Ops[0]);
2891 // If we are left with a constant minimum-int, strip it off.
2892 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
2893 Ops.erase(Ops.begin());
2895 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
2896 // If we have an umax with a constant maximum-int, it will always be
2901 if (Ops.size() == 1) return Ops[0];
2904 // Find the first UMax
2905 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
2908 // Check to see if one of the operands is a UMax. If so, expand its operands
2909 // onto our operand list, and recurse to simplify.
2910 if (Idx < Ops.size()) {
2911 bool DeletedUMax = false;
2912 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
2913 Ops.erase(Ops.begin()+Idx);
2914 Ops.append(UMax->op_begin(), UMax->op_end());
2919 return getUMaxExpr(Ops);
2922 // Okay, check to see if the same value occurs in the operand list twice. If
2923 // so, delete one. Since we sorted the list, these values are required to
2925 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2926 // X umax Y umax Y --> X umax Y
2927 // X umax Y --> X, if X is always greater than Y
2928 if (Ops[i] == Ops[i+1] ||
2929 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) {
2930 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2932 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) {
2933 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2937 if (Ops.size() == 1) return Ops[0];
2939 assert(!Ops.empty() && "Reduced umax down to nothing!");
2941 // Okay, it looks like we really DO need a umax expr. Check to see if we
2942 // already have one, otherwise create a new one.
2943 FoldingSetNodeID ID;
2944 ID.AddInteger(scUMaxExpr);
2945 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2946 ID.AddPointer(Ops[i]);
2948 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2949 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2950 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2951 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator),
2953 UniqueSCEVs.InsertNode(S, IP);
2957 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
2959 // ~smax(~x, ~y) == smin(x, y).
2960 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2963 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
2965 // ~umax(~x, ~y) == umin(x, y)
2966 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2969 const SCEV *ScalarEvolution::getSizeOfExpr(Type *IntTy, Type *AllocTy) {
2970 // If we have DataLayout, we can bypass creating a target-independent
2971 // constant expression and then folding it back into a ConstantInt.
2972 // This is just a compile-time optimization.
2974 return getConstant(IntTy, DL->getTypeAllocSize(AllocTy));
2976 Constant *C = ConstantExpr::getSizeOf(AllocTy);
2977 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2978 if (Constant *Folded = ConstantFoldConstantExpression(CE, DL, TLI))
2980 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2981 assert(Ty == IntTy && "Effective SCEV type doesn't match");
2982 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2985 const SCEV *ScalarEvolution::getOffsetOfExpr(Type *IntTy,
2988 // If we have DataLayout, we can bypass creating a target-independent
2989 // constant expression and then folding it back into a ConstantInt.
2990 // This is just a compile-time optimization.
2992 return getConstant(IntTy,
2993 DL->getStructLayout(STy)->getElementOffset(FieldNo));
2996 Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo);
2997 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2998 if (Constant *Folded = ConstantFoldConstantExpression(CE, DL, TLI))
3001 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy));
3002 return getTruncateOrZeroExtend(getSCEV(C), Ty);
3005 const SCEV *ScalarEvolution::getUnknown(Value *V) {
3006 // Don't attempt to do anything other than create a SCEVUnknown object
3007 // here. createSCEV only calls getUnknown after checking for all other
3008 // interesting possibilities, and any other code that calls getUnknown
3009 // is doing so in order to hide a value from SCEV canonicalization.
3011 FoldingSetNodeID ID;
3012 ID.AddInteger(scUnknown);
3015 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
3016 assert(cast<SCEVUnknown>(S)->getValue() == V &&
3017 "Stale SCEVUnknown in uniquing map!");
3020 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
3022 FirstUnknown = cast<SCEVUnknown>(S);
3023 UniqueSCEVs.InsertNode(S, IP);
3027 //===----------------------------------------------------------------------===//
3028 // Basic SCEV Analysis and PHI Idiom Recognition Code
3031 /// isSCEVable - Test if values of the given type are analyzable within
3032 /// the SCEV framework. This primarily includes integer types, and it
3033 /// can optionally include pointer types if the ScalarEvolution class
3034 /// has access to target-specific information.
3035 bool ScalarEvolution::isSCEVable(Type *Ty) const {
3036 // Integers and pointers are always SCEVable.
3037 return Ty->isIntegerTy() || Ty->isPointerTy();
3040 /// getTypeSizeInBits - Return the size in bits of the specified type,
3041 /// for which isSCEVable must return true.
3042 uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const {
3043 assert(isSCEVable(Ty) && "Type is not SCEVable!");
3045 // If we have a DataLayout, use it!
3047 return DL->getTypeSizeInBits(Ty);
3049 // Integer types have fixed sizes.
3050 if (Ty->isIntegerTy())
3051 return Ty->getPrimitiveSizeInBits();
3053 // The only other support type is pointer. Without DataLayout, conservatively
3054 // assume pointers are 64-bit.
3055 assert(Ty->isPointerTy() && "isSCEVable permitted a non-SCEVable type!");
3059 /// getEffectiveSCEVType - Return a type with the same bitwidth as
3060 /// the given type and which represents how SCEV will treat the given
3061 /// type, for which isSCEVable must return true. For pointer types,
3062 /// this is the pointer-sized integer type.
3063 Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const {
3064 assert(isSCEVable(Ty) && "Type is not SCEVable!");
3066 if (Ty->isIntegerTy()) {
3070 // The only other support type is pointer.
3071 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
3074 return DL->getIntPtrType(Ty);
3076 // Without DataLayout, conservatively assume pointers are 64-bit.
3077 return Type::getInt64Ty(getContext());
3080 const SCEV *ScalarEvolution::getCouldNotCompute() {
3081 return &CouldNotCompute;
3085 // Helper class working with SCEVTraversal to figure out if a SCEV contains
3086 // a SCEVUnknown with null value-pointer. FindInvalidSCEVUnknown::FindOne
3087 // is set iff if find such SCEVUnknown.
3089 struct FindInvalidSCEVUnknown {
3091 FindInvalidSCEVUnknown() { FindOne = false; }
3092 bool follow(const SCEV *S) {
3093 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
3097 if (!cast<SCEVUnknown>(S)->getValue())
3104 bool isDone() const { return FindOne; }
3108 bool ScalarEvolution::checkValidity(const SCEV *S) const {
3109 FindInvalidSCEVUnknown F;
3110 SCEVTraversal<FindInvalidSCEVUnknown> ST(F);
3116 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
3117 /// expression and create a new one.
3118 const SCEV *ScalarEvolution::getSCEV(Value *V) {
3119 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
3121 ValueExprMapType::iterator I = ValueExprMap.find_as(V);
3122 if (I != ValueExprMap.end()) {
3123 const SCEV *S = I->second;
3124 if (checkValidity(S))
3127 ValueExprMap.erase(I);
3129 const SCEV *S = createSCEV(V);
3131 // The process of creating a SCEV for V may have caused other SCEVs
3132 // to have been created, so it's necessary to insert the new entry
3133 // from scratch, rather than trying to remember the insert position
3135 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(V, this), S));
3139 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
3141 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) {
3142 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
3144 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
3146 Type *Ty = V->getType();
3147 Ty = getEffectiveSCEVType(Ty);
3148 return getMulExpr(V,
3149 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))));
3152 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
3153 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
3154 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
3156 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
3158 Type *Ty = V->getType();
3159 Ty = getEffectiveSCEVType(Ty);
3160 const SCEV *AllOnes =
3161 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
3162 return getMinusSCEV(AllOnes, V);
3165 /// getMinusSCEV - Return LHS-RHS. Minus is represented in SCEV as A+B*-1.
3166 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
3167 SCEV::NoWrapFlags Flags) {
3168 assert(!maskFlags(Flags, SCEV::FlagNUW) && "subtraction does not have NUW");
3170 // Fast path: X - X --> 0.
3172 return getConstant(LHS->getType(), 0);
3174 // X - Y --> X + -Y.
3175 // X -(nsw || nuw) Y --> X + -Y.
3176 return getAddExpr(LHS, getNegativeSCEV(RHS));
3179 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
3180 /// input value to the specified type. If the type must be extended, it is zero
3183 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty) {
3184 Type *SrcTy = V->getType();
3185 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3186 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3187 "Cannot truncate or zero extend with non-integer arguments!");
3188 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3189 return V; // No conversion
3190 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
3191 return getTruncateExpr(V, Ty);
3192 return getZeroExtendExpr(V, Ty);
3195 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
3196 /// input value to the specified type. If the type must be extended, it is sign
3199 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
3201 Type *SrcTy = V->getType();
3202 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3203 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3204 "Cannot truncate or zero extend with non-integer arguments!");
3205 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3206 return V; // No conversion
3207 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
3208 return getTruncateExpr(V, Ty);
3209 return getSignExtendExpr(V, Ty);
3212 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
3213 /// input value to the specified type. If the type must be extended, it is zero
3214 /// extended. The conversion must not be narrowing.
3216 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) {
3217 Type *SrcTy = V->getType();
3218 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3219 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3220 "Cannot noop or zero extend with non-integer arguments!");
3221 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3222 "getNoopOrZeroExtend cannot truncate!");
3223 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3224 return V; // No conversion
3225 return getZeroExtendExpr(V, Ty);
3228 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
3229 /// input value to the specified type. If the type must be extended, it is sign
3230 /// extended. The conversion must not be narrowing.
3232 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) {
3233 Type *SrcTy = V->getType();
3234 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3235 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3236 "Cannot noop or sign extend with non-integer arguments!");
3237 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3238 "getNoopOrSignExtend cannot truncate!");
3239 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3240 return V; // No conversion
3241 return getSignExtendExpr(V, Ty);
3244 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
3245 /// the input value to the specified type. If the type must be extended,
3246 /// it is extended with unspecified bits. The conversion must not be
3249 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) {
3250 Type *SrcTy = V->getType();
3251 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3252 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3253 "Cannot noop or any extend with non-integer arguments!");
3254 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3255 "getNoopOrAnyExtend cannot truncate!");
3256 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3257 return V; // No conversion
3258 return getAnyExtendExpr(V, Ty);
3261 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
3262 /// input value to the specified type. The conversion must not be widening.
3264 ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) {
3265 Type *SrcTy = V->getType();
3266 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3267 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3268 "Cannot truncate or noop with non-integer arguments!");
3269 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
3270 "getTruncateOrNoop cannot extend!");
3271 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3272 return V; // No conversion
3273 return getTruncateExpr(V, Ty);
3276 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
3277 /// the types using zero-extension, and then perform a umax operation
3279 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
3281 const SCEV *PromotedLHS = LHS;
3282 const SCEV *PromotedRHS = RHS;
3284 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
3285 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
3287 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
3289 return getUMaxExpr(PromotedLHS, PromotedRHS);
3292 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
3293 /// the types using zero-extension, and then perform a umin operation
3295 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
3297 const SCEV *PromotedLHS = LHS;
3298 const SCEV *PromotedRHS = RHS;
3300 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
3301 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
3303 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
3305 return getUMinExpr(PromotedLHS, PromotedRHS);
3308 /// getPointerBase - Transitively follow the chain of pointer-type operands
3309 /// until reaching a SCEV that does not have a single pointer operand. This
3310 /// returns a SCEVUnknown pointer for well-formed pointer-type expressions,
3311 /// but corner cases do exist.
3312 const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) {
3313 // A pointer operand may evaluate to a nonpointer expression, such as null.
3314 if (!V->getType()->isPointerTy())
3317 if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) {
3318 return getPointerBase(Cast->getOperand());
3320 else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) {
3321 const SCEV *PtrOp = nullptr;
3322 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
3324 if ((*I)->getType()->isPointerTy()) {
3325 // Cannot find the base of an expression with multiple pointer operands.
3333 return getPointerBase(PtrOp);
3338 /// PushDefUseChildren - Push users of the given Instruction
3339 /// onto the given Worklist.
3341 PushDefUseChildren(Instruction *I,
3342 SmallVectorImpl<Instruction *> &Worklist) {
3343 // Push the def-use children onto the Worklist stack.
3344 for (User *U : I->users())
3345 Worklist.push_back(cast<Instruction>(U));
3348 /// ForgetSymbolicValue - This looks up computed SCEV values for all
3349 /// instructions that depend on the given instruction and removes them from
3350 /// the ValueExprMapType map if they reference SymName. This is used during PHI
3353 ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) {
3354 SmallVector<Instruction *, 16> Worklist;
3355 PushDefUseChildren(PN, Worklist);
3357 SmallPtrSet<Instruction *, 8> Visited;
3359 while (!Worklist.empty()) {
3360 Instruction *I = Worklist.pop_back_val();
3361 if (!Visited.insert(I).second)
3364 ValueExprMapType::iterator It =
3365 ValueExprMap.find_as(static_cast<Value *>(I));
3366 if (It != ValueExprMap.end()) {
3367 const SCEV *Old = It->second;
3369 // Short-circuit the def-use traversal if the symbolic name
3370 // ceases to appear in expressions.
3371 if (Old != SymName && !hasOperand(Old, SymName))
3374 // SCEVUnknown for a PHI either means that it has an unrecognized
3375 // structure, it's a PHI that's in the progress of being computed
3376 // by createNodeForPHI, or it's a single-value PHI. In the first case,
3377 // additional loop trip count information isn't going to change anything.
3378 // In the second case, createNodeForPHI will perform the necessary
3379 // updates on its own when it gets to that point. In the third, we do
3380 // want to forget the SCEVUnknown.
3381 if (!isa<PHINode>(I) ||
3382 !isa<SCEVUnknown>(Old) ||
3383 (I != PN && Old == SymName)) {
3384 forgetMemoizedResults(Old);
3385 ValueExprMap.erase(It);
3389 PushDefUseChildren(I, Worklist);
3393 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
3394 /// a loop header, making it a potential recurrence, or it doesn't.
3396 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
3397 if (const Loop *L = LI->getLoopFor(PN->getParent()))
3398 if (L->getHeader() == PN->getParent()) {
3399 // The loop may have multiple entrances or multiple exits; we can analyze
3400 // this phi as an addrec if it has a unique entry value and a unique
3402 Value *BEValueV = nullptr, *StartValueV = nullptr;
3403 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
3404 Value *V = PN->getIncomingValue(i);
3405 if (L->contains(PN->getIncomingBlock(i))) {
3408 } else if (BEValueV != V) {
3412 } else if (!StartValueV) {
3414 } else if (StartValueV != V) {
3415 StartValueV = nullptr;
3419 if (BEValueV && StartValueV) {
3420 // While we are analyzing this PHI node, handle its value symbolically.
3421 const SCEV *SymbolicName = getUnknown(PN);
3422 assert(ValueExprMap.find_as(PN) == ValueExprMap.end() &&
3423 "PHI node already processed?");
3424 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
3426 // Using this symbolic name for the PHI, analyze the value coming around
3428 const SCEV *BEValue = getSCEV(BEValueV);
3430 // NOTE: If BEValue is loop invariant, we know that the PHI node just
3431 // has a special value for the first iteration of the loop.
3433 // If the value coming around the backedge is an add with the symbolic
3434 // value we just inserted, then we found a simple induction variable!
3435 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
3436 // If there is a single occurrence of the symbolic value, replace it
3437 // with a recurrence.
3438 unsigned FoundIndex = Add->getNumOperands();
3439 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3440 if (Add->getOperand(i) == SymbolicName)
3441 if (FoundIndex == e) {
3446 if (FoundIndex != Add->getNumOperands()) {
3447 // Create an add with everything but the specified operand.
3448 SmallVector<const SCEV *, 8> Ops;
3449 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3450 if (i != FoundIndex)
3451 Ops.push_back(Add->getOperand(i));
3452 const SCEV *Accum = getAddExpr(Ops);
3454 // This is not a valid addrec if the step amount is varying each
3455 // loop iteration, but is not itself an addrec in this loop.
3456 if (isLoopInvariant(Accum, L) ||
3457 (isa<SCEVAddRecExpr>(Accum) &&
3458 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
3459 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
3461 // If the increment doesn't overflow, then neither the addrec nor
3462 // the post-increment will overflow.
3463 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) {
3464 if (OBO->hasNoUnsignedWrap())
3465 Flags = setFlags(Flags, SCEV::FlagNUW);
3466 if (OBO->hasNoSignedWrap())
3467 Flags = setFlags(Flags, SCEV::FlagNSW);
3468 } else if (GEPOperator *GEP = dyn_cast<GEPOperator>(BEValueV)) {
3469 // If the increment is an inbounds GEP, then we know the address
3470 // space cannot be wrapped around. We cannot make any guarantee
3471 // about signed or unsigned overflow because pointers are
3472 // unsigned but we may have a negative index from the base
3473 // pointer. We can guarantee that no unsigned wrap occurs if the
3474 // indices form a positive value.
3475 if (GEP->isInBounds()) {
3476 Flags = setFlags(Flags, SCEV::FlagNW);
3478 const SCEV *Ptr = getSCEV(GEP->getPointerOperand());
3479 if (isKnownPositive(getMinusSCEV(getSCEV(GEP), Ptr)))
3480 Flags = setFlags(Flags, SCEV::FlagNUW);
3483 // We cannot transfer nuw and nsw flags from subtraction
3484 // operations -- sub nuw X, Y is not the same as add nuw X, -Y
3488 const SCEV *StartVal = getSCEV(StartValueV);
3489 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
3491 // Since the no-wrap flags are on the increment, they apply to the
3492 // post-incremented value as well.
3493 if (isLoopInvariant(Accum, L))
3494 (void)getAddRecExpr(getAddExpr(StartVal, Accum),
3497 // Okay, for the entire analysis of this edge we assumed the PHI
3498 // to be symbolic. We now need to go back and purge all of the
3499 // entries for the scalars that use the symbolic expression.
3500 ForgetSymbolicName(PN, SymbolicName);
3501 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3505 } else if (const SCEVAddRecExpr *AddRec =
3506 dyn_cast<SCEVAddRecExpr>(BEValue)) {
3507 // Otherwise, this could be a loop like this:
3508 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
3509 // In this case, j = {1,+,1} and BEValue is j.
3510 // Because the other in-value of i (0) fits the evolution of BEValue
3511 // i really is an addrec evolution.
3512 if (AddRec->getLoop() == L && AddRec->isAffine()) {
3513 const SCEV *StartVal = getSCEV(StartValueV);
3515 // If StartVal = j.start - j.stride, we can use StartVal as the
3516 // initial step of the addrec evolution.
3517 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
3518 AddRec->getOperand(1))) {
3519 // FIXME: For constant StartVal, we should be able to infer
3521 const SCEV *PHISCEV =
3522 getAddRecExpr(StartVal, AddRec->getOperand(1), L,
3525 // Okay, for the entire analysis of this edge we assumed the PHI
3526 // to be symbolic. We now need to go back and purge all of the
3527 // entries for the scalars that use the symbolic expression.
3528 ForgetSymbolicName(PN, SymbolicName);
3529 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3537 // If the PHI has a single incoming value, follow that value, unless the
3538 // PHI's incoming blocks are in a different loop, in which case doing so
3539 // risks breaking LCSSA form. Instcombine would normally zap these, but
3540 // it doesn't have DominatorTree information, so it may miss cases.
3541 if (Value *V = SimplifyInstruction(PN, DL, TLI, DT, AC))
3542 if (LI->replacementPreservesLCSSAForm(PN, V))
3545 // If it's not a loop phi, we can't handle it yet.
3546 return getUnknown(PN);
3549 /// createNodeForGEP - Expand GEP instructions into add and multiply
3550 /// operations. This allows them to be analyzed by regular SCEV code.
3552 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
3553 Type *IntPtrTy = getEffectiveSCEVType(GEP->getType());
3554 Value *Base = GEP->getOperand(0);
3555 // Don't attempt to analyze GEPs over unsized objects.
3556 if (!Base->getType()->getPointerElementType()->isSized())
3557 return getUnknown(GEP);
3559 // Don't blindly transfer the inbounds flag from the GEP instruction to the
3560 // Add expression, because the Instruction may be guarded by control flow
3561 // and the no-overflow bits may not be valid for the expression in any
3563 SCEV::NoWrapFlags Wrap = GEP->isInBounds() ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
3565 const SCEV *TotalOffset = getConstant(IntPtrTy, 0);
3566 gep_type_iterator GTI = gep_type_begin(GEP);
3567 for (GetElementPtrInst::op_iterator I = std::next(GEP->op_begin()),
3571 // Compute the (potentially symbolic) offset in bytes for this index.
3572 if (StructType *STy = dyn_cast<StructType>(*GTI++)) {
3573 // For a struct, add the member offset.
3574 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
3575 const SCEV *FieldOffset = getOffsetOfExpr(IntPtrTy, STy, FieldNo);
3577 // Add the field offset to the running total offset.
3578 TotalOffset = getAddExpr(TotalOffset, FieldOffset);
3580 // For an array, add the element offset, explicitly scaled.
3581 const SCEV *ElementSize = getSizeOfExpr(IntPtrTy, *GTI);
3582 const SCEV *IndexS = getSCEV(Index);
3583 // Getelementptr indices are signed.
3584 IndexS = getTruncateOrSignExtend(IndexS, IntPtrTy);
3586 // Multiply the index by the element size to compute the element offset.
3587 const SCEV *LocalOffset = getMulExpr(IndexS, ElementSize, Wrap);
3589 // Add the element offset to the running total offset.
3590 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
3594 // Get the SCEV for the GEP base.
3595 const SCEV *BaseS = getSCEV(Base);
3597 // Add the total offset from all the GEP indices to the base.
3598 return getAddExpr(BaseS, TotalOffset, Wrap);
3601 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
3602 /// guaranteed to end in (at every loop iteration). It is, at the same time,
3603 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
3604 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
3606 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
3607 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3608 return C->getValue()->getValue().countTrailingZeros();
3610 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
3611 return std::min(GetMinTrailingZeros(T->getOperand()),
3612 (uint32_t)getTypeSizeInBits(T->getType()));
3614 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
3615 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3616 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3617 getTypeSizeInBits(E->getType()) : OpRes;
3620 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
3621 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3622 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3623 getTypeSizeInBits(E->getType()) : OpRes;
3626 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
3627 // The result is the min of all operands results.
3628 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3629 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3630 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3634 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
3635 // The result is the sum of all operands results.
3636 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
3637 uint32_t BitWidth = getTypeSizeInBits(M->getType());
3638 for (unsigned i = 1, e = M->getNumOperands();
3639 SumOpRes != BitWidth && i != e; ++i)
3640 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
3645 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
3646 // The result is the min of all operands results.
3647 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3648 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3649 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3653 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
3654 // The result is the min of all operands results.
3655 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3656 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3657 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3661 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
3662 // The result is the min of all operands results.
3663 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3664 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3665 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3669 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3670 // For a SCEVUnknown, ask ValueTracking.
3671 unsigned BitWidth = getTypeSizeInBits(U->getType());
3672 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3673 computeKnownBits(U->getValue(), Zeros, Ones, DL, 0, AC, nullptr, DT);
3674 return Zeros.countTrailingOnes();
3681 /// GetRangeFromMetadata - Helper method to assign a range to V from
3682 /// metadata present in the IR.
3683 static Optional<ConstantRange> GetRangeFromMetadata(Value *V) {
3684 if (Instruction *I = dyn_cast<Instruction>(V)) {
3685 if (MDNode *MD = I->getMetadata(LLVMContext::MD_range)) {
3686 ConstantRange TotalRange(
3687 cast<IntegerType>(I->getType())->getBitWidth(), false);
3689 unsigned NumRanges = MD->getNumOperands() / 2;
3690 assert(NumRanges >= 1);
3692 for (unsigned i = 0; i < NumRanges; ++i) {
3693 ConstantInt *Lower =
3694 mdconst::extract<ConstantInt>(MD->getOperand(2 * i + 0));
3695 ConstantInt *Upper =
3696 mdconst::extract<ConstantInt>(MD->getOperand(2 * i + 1));
3697 ConstantRange Range(Lower->getValue(), Upper->getValue());
3698 TotalRange = TotalRange.unionWith(Range);
3708 /// getUnsignedRange - Determine the unsigned range for a particular SCEV.
3711 ScalarEvolution::getUnsignedRange(const SCEV *S) {
3712 // See if we've computed this range already.
3713 DenseMap<const SCEV *, ConstantRange>::iterator I = UnsignedRanges.find(S);
3714 if (I != UnsignedRanges.end())
3717 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3718 return setUnsignedRange(C, ConstantRange(C->getValue()->getValue()));
3720 unsigned BitWidth = getTypeSizeInBits(S->getType());
3721 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3723 // If the value has known zeros, the maximum unsigned value will have those
3724 // known zeros as well.
3725 uint32_t TZ = GetMinTrailingZeros(S);
3727 ConservativeResult =
3728 ConstantRange(APInt::getMinValue(BitWidth),
3729 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
3731 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3732 ConstantRange X = getUnsignedRange(Add->getOperand(0));
3733 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3734 X = X.add(getUnsignedRange(Add->getOperand(i)));
3735 return setUnsignedRange(Add, ConservativeResult.intersectWith(X));
3738 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3739 ConstantRange X = getUnsignedRange(Mul->getOperand(0));
3740 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3741 X = X.multiply(getUnsignedRange(Mul->getOperand(i)));
3742 return setUnsignedRange(Mul, ConservativeResult.intersectWith(X));
3745 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3746 ConstantRange X = getUnsignedRange(SMax->getOperand(0));
3747 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3748 X = X.smax(getUnsignedRange(SMax->getOperand(i)));
3749 return setUnsignedRange(SMax, ConservativeResult.intersectWith(X));
3752 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3753 ConstantRange X = getUnsignedRange(UMax->getOperand(0));
3754 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3755 X = X.umax(getUnsignedRange(UMax->getOperand(i)));
3756 return setUnsignedRange(UMax, ConservativeResult.intersectWith(X));
3759 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3760 ConstantRange X = getUnsignedRange(UDiv->getLHS());
3761 ConstantRange Y = getUnsignedRange(UDiv->getRHS());
3762 return setUnsignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y)));
3765 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3766 ConstantRange X = getUnsignedRange(ZExt->getOperand());
3767 return setUnsignedRange(ZExt,
3768 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3771 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3772 ConstantRange X = getUnsignedRange(SExt->getOperand());
3773 return setUnsignedRange(SExt,
3774 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3777 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3778 ConstantRange X = getUnsignedRange(Trunc->getOperand());
3779 return setUnsignedRange(Trunc,
3780 ConservativeResult.intersectWith(X.truncate(BitWidth)));
3783 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3784 // If there's no unsigned wrap, the value will never be less than its
3786 if (AddRec->getNoWrapFlags(SCEV::FlagNUW))
3787 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
3788 if (!C->getValue()->isZero())
3789 ConservativeResult =
3790 ConservativeResult.intersectWith(
3791 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0)));
3793 // TODO: non-affine addrec
3794 if (AddRec->isAffine()) {
3795 Type *Ty = AddRec->getType();
3796 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3797 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3798 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3799 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3801 const SCEV *Start = AddRec->getStart();
3802 const SCEV *Step = AddRec->getStepRecurrence(*this);
3804 ConstantRange StartRange = getUnsignedRange(Start);
3805 ConstantRange StepRange = getSignedRange(Step);
3806 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3807 ConstantRange EndRange =
3808 StartRange.add(MaxBECountRange.multiply(StepRange));
3810 // Check for overflow. This must be done with ConstantRange arithmetic
3811 // because we could be called from within the ScalarEvolution overflow
3813 ConstantRange ExtStartRange = StartRange.zextOrTrunc(BitWidth*2+1);
3814 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3815 ConstantRange ExtMaxBECountRange =
3816 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3817 ConstantRange ExtEndRange = EndRange.zextOrTrunc(BitWidth*2+1);
3818 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3820 return setUnsignedRange(AddRec, ConservativeResult);
3822 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(),
3823 EndRange.getUnsignedMin());
3824 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(),
3825 EndRange.getUnsignedMax());
3826 if (Min.isMinValue() && Max.isMaxValue())
3827 return setUnsignedRange(AddRec, ConservativeResult);
3828 return setUnsignedRange(AddRec,
3829 ConservativeResult.intersectWith(ConstantRange(Min, Max+1)));
3833 return setUnsignedRange(AddRec, ConservativeResult);
3836 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3837 // Check if the IR explicitly contains !range metadata.
3838 Optional<ConstantRange> MDRange = GetRangeFromMetadata(U->getValue());
3839 if (MDRange.hasValue())
3840 ConservativeResult = ConservativeResult.intersectWith(MDRange.getValue());
3842 // For a SCEVUnknown, ask ValueTracking.
3843 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3844 computeKnownBits(U->getValue(), Zeros, Ones, DL, 0, AC, nullptr, DT);
3845 if (Ones == ~Zeros + 1)
3846 return setUnsignedRange(U, ConservativeResult);
3847 return setUnsignedRange(U,
3848 ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1)));
3851 return setUnsignedRange(S, ConservativeResult);
3854 /// getSignedRange - Determine the signed range for a particular SCEV.
3857 ScalarEvolution::getSignedRange(const SCEV *S) {
3858 // See if we've computed this range already.
3859 DenseMap<const SCEV *, ConstantRange>::iterator I = SignedRanges.find(S);
3860 if (I != SignedRanges.end())
3863 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3864 return setSignedRange(C, ConstantRange(C->getValue()->getValue()));
3866 unsigned BitWidth = getTypeSizeInBits(S->getType());
3867 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3869 // If the value has known zeros, the maximum signed value will have those
3870 // known zeros as well.
3871 uint32_t TZ = GetMinTrailingZeros(S);
3873 ConservativeResult =
3874 ConstantRange(APInt::getSignedMinValue(BitWidth),
3875 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
3877 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3878 ConstantRange X = getSignedRange(Add->getOperand(0));
3879 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3880 X = X.add(getSignedRange(Add->getOperand(i)));
3881 return setSignedRange(Add, ConservativeResult.intersectWith(X));
3884 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3885 ConstantRange X = getSignedRange(Mul->getOperand(0));
3886 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3887 X = X.multiply(getSignedRange(Mul->getOperand(i)));
3888 return setSignedRange(Mul, ConservativeResult.intersectWith(X));
3891 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3892 ConstantRange X = getSignedRange(SMax->getOperand(0));
3893 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3894 X = X.smax(getSignedRange(SMax->getOperand(i)));
3895 return setSignedRange(SMax, ConservativeResult.intersectWith(X));
3898 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3899 ConstantRange X = getSignedRange(UMax->getOperand(0));
3900 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3901 X = X.umax(getSignedRange(UMax->getOperand(i)));
3902 return setSignedRange(UMax, ConservativeResult.intersectWith(X));
3905 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3906 ConstantRange X = getSignedRange(UDiv->getLHS());
3907 ConstantRange Y = getSignedRange(UDiv->getRHS());
3908 return setSignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y)));
3911 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3912 ConstantRange X = getSignedRange(ZExt->getOperand());
3913 return setSignedRange(ZExt,
3914 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3917 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3918 ConstantRange X = getSignedRange(SExt->getOperand());
3919 return setSignedRange(SExt,
3920 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3923 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3924 ConstantRange X = getSignedRange(Trunc->getOperand());
3925 return setSignedRange(Trunc,
3926 ConservativeResult.intersectWith(X.truncate(BitWidth)));
3929 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3930 // If there's no signed wrap, and all the operands have the same sign or
3931 // zero, the value won't ever change sign.
3932 if (AddRec->getNoWrapFlags(SCEV::FlagNSW)) {
3933 bool AllNonNeg = true;
3934 bool AllNonPos = true;
3935 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
3936 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
3937 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
3940 ConservativeResult = ConservativeResult.intersectWith(
3941 ConstantRange(APInt(BitWidth, 0),
3942 APInt::getSignedMinValue(BitWidth)));
3944 ConservativeResult = ConservativeResult.intersectWith(
3945 ConstantRange(APInt::getSignedMinValue(BitWidth),
3946 APInt(BitWidth, 1)));
3949 // TODO: non-affine addrec
3950 if (AddRec->isAffine()) {
3951 Type *Ty = AddRec->getType();
3952 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3953 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3954 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3955 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3957 const SCEV *Start = AddRec->getStart();
3958 const SCEV *Step = AddRec->getStepRecurrence(*this);
3960 ConstantRange StartRange = getSignedRange(Start);
3961 ConstantRange StepRange = getSignedRange(Step);
3962 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3963 ConstantRange EndRange =
3964 StartRange.add(MaxBECountRange.multiply(StepRange));
3966 // Check for overflow. This must be done with ConstantRange arithmetic
3967 // because we could be called from within the ScalarEvolution overflow
3969 ConstantRange ExtStartRange = StartRange.sextOrTrunc(BitWidth*2+1);
3970 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3971 ConstantRange ExtMaxBECountRange =
3972 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3973 ConstantRange ExtEndRange = EndRange.sextOrTrunc(BitWidth*2+1);
3974 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3976 return setSignedRange(AddRec, ConservativeResult);
3978 APInt Min = APIntOps::smin(StartRange.getSignedMin(),
3979 EndRange.getSignedMin());
3980 APInt Max = APIntOps::smax(StartRange.getSignedMax(),
3981 EndRange.getSignedMax());
3982 if (Min.isMinSignedValue() && Max.isMaxSignedValue())
3983 return setSignedRange(AddRec, ConservativeResult);
3984 return setSignedRange(AddRec,
3985 ConservativeResult.intersectWith(ConstantRange(Min, Max+1)));
3989 return setSignedRange(AddRec, ConservativeResult);
3992 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3993 // Check if the IR explicitly contains !range metadata.
3994 Optional<ConstantRange> MDRange = GetRangeFromMetadata(U->getValue());
3995 if (MDRange.hasValue())
3996 ConservativeResult = ConservativeResult.intersectWith(MDRange.getValue());
3998 // For a SCEVUnknown, ask ValueTracking.
3999 if (!U->getValue()->getType()->isIntegerTy() && !DL)
4000 return setSignedRange(U, ConservativeResult);
4001 unsigned NS = ComputeNumSignBits(U->getValue(), DL, 0, AC, nullptr, DT);
4003 return setSignedRange(U, ConservativeResult);
4004 return setSignedRange(U, ConservativeResult.intersectWith(
4005 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
4006 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1)));
4009 return setSignedRange(S, ConservativeResult);
4012 /// createSCEV - We know that there is no SCEV for the specified value.
4013 /// Analyze the expression.
4015 const SCEV *ScalarEvolution::createSCEV(Value *V) {
4016 if (!isSCEVable(V->getType()))
4017 return getUnknown(V);
4019 unsigned Opcode = Instruction::UserOp1;
4020 if (Instruction *I = dyn_cast<Instruction>(V)) {
4021 Opcode = I->getOpcode();
4023 // Don't attempt to analyze instructions in blocks that aren't
4024 // reachable. Such instructions don't matter, and they aren't required
4025 // to obey basic rules for definitions dominating uses which this
4026 // analysis depends on.
4027 if (!DT->isReachableFromEntry(I->getParent()))
4028 return getUnknown(V);
4029 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
4030 Opcode = CE->getOpcode();
4031 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
4032 return getConstant(CI);
4033 else if (isa<ConstantPointerNull>(V))
4034 return getConstant(V->getType(), 0);
4035 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
4036 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee());
4038 return getUnknown(V);
4040 Operator *U = cast<Operator>(V);
4042 case Instruction::Add: {
4043 // The simple thing to do would be to just call getSCEV on both operands
4044 // and call getAddExpr with the result. However if we're looking at a
4045 // bunch of things all added together, this can be quite inefficient,
4046 // because it leads to N-1 getAddExpr calls for N ultimate operands.
4047 // Instead, gather up all the operands and make a single getAddExpr call.
4048 // LLVM IR canonical form means we need only traverse the left operands.
4050 // Don't apply this instruction's NSW or NUW flags to the new
4051 // expression. The instruction may be guarded by control flow that the
4052 // no-wrap behavior depends on. Non-control-equivalent instructions can be
4053 // mapped to the same SCEV expression, and it would be incorrect to transfer
4054 // NSW/NUW semantics to those operations.
4055 SmallVector<const SCEV *, 4> AddOps;
4056 AddOps.push_back(getSCEV(U->getOperand(1)));
4057 for (Value *Op = U->getOperand(0); ; Op = U->getOperand(0)) {
4058 unsigned Opcode = Op->getValueID() - Value::InstructionVal;
4059 if (Opcode != Instruction::Add && Opcode != Instruction::Sub)
4061 U = cast<Operator>(Op);
4062 const SCEV *Op1 = getSCEV(U->getOperand(1));
4063 if (Opcode == Instruction::Sub)
4064 AddOps.push_back(getNegativeSCEV(Op1));
4066 AddOps.push_back(Op1);
4068 AddOps.push_back(getSCEV(U->getOperand(0)));
4069 return getAddExpr(AddOps);
4071 case Instruction::Mul: {
4072 // Don't transfer NSW/NUW for the same reason as AddExpr.
4073 SmallVector<const SCEV *, 4> MulOps;
4074 MulOps.push_back(getSCEV(U->getOperand(1)));
4075 for (Value *Op = U->getOperand(0);
4076 Op->getValueID() == Instruction::Mul + Value::InstructionVal;
4077 Op = U->getOperand(0)) {
4078 U = cast<Operator>(Op);
4079 MulOps.push_back(getSCEV(U->getOperand(1)));
4081 MulOps.push_back(getSCEV(U->getOperand(0)));
4082 return getMulExpr(MulOps);
4084 case Instruction::UDiv:
4085 return getUDivExpr(getSCEV(U->getOperand(0)),
4086 getSCEV(U->getOperand(1)));
4087 case Instruction::Sub:
4088 return getMinusSCEV(getSCEV(U->getOperand(0)),
4089 getSCEV(U->getOperand(1)));
4090 case Instruction::And:
4091 // For an expression like x&255 that merely masks off the high bits,
4092 // use zext(trunc(x)) as the SCEV expression.
4093 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
4094 if (CI->isNullValue())
4095 return getSCEV(U->getOperand(1));
4096 if (CI->isAllOnesValue())
4097 return getSCEV(U->getOperand(0));
4098 const APInt &A = CI->getValue();
4100 // Instcombine's ShrinkDemandedConstant may strip bits out of
4101 // constants, obscuring what would otherwise be a low-bits mask.
4102 // Use computeKnownBits to compute what ShrinkDemandedConstant
4103 // knew about to reconstruct a low-bits mask value.
4104 unsigned LZ = A.countLeadingZeros();
4105 unsigned TZ = A.countTrailingZeros();
4106 unsigned BitWidth = A.getBitWidth();
4107 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
4108 computeKnownBits(U->getOperand(0), KnownZero, KnownOne, DL, 0, AC,
4111 APInt EffectiveMask =
4112 APInt::getLowBitsSet(BitWidth, BitWidth - LZ - TZ).shl(TZ);
4113 if ((LZ != 0 || TZ != 0) && !((~A & ~KnownZero) & EffectiveMask)) {
4114 const SCEV *MulCount = getConstant(
4115 ConstantInt::get(getContext(), APInt::getOneBitSet(BitWidth, TZ)));
4119 getUDivExactExpr(getSCEV(U->getOperand(0)), MulCount),
4120 IntegerType::get(getContext(), BitWidth - LZ - TZ)),
4127 case Instruction::Or:
4128 // If the RHS of the Or is a constant, we may have something like:
4129 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
4130 // optimizations will transparently handle this case.
4132 // In order for this transformation to be safe, the LHS must be of the
4133 // form X*(2^n) and the Or constant must be less than 2^n.
4134 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
4135 const SCEV *LHS = getSCEV(U->getOperand(0));
4136 const APInt &CIVal = CI->getValue();
4137 if (GetMinTrailingZeros(LHS) >=
4138 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
4139 // Build a plain add SCEV.
4140 const SCEV *S = getAddExpr(LHS, getSCEV(CI));
4141 // If the LHS of the add was an addrec and it has no-wrap flags,
4142 // transfer the no-wrap flags, since an or won't introduce a wrap.
4143 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
4144 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
4145 const_cast<SCEVAddRecExpr *>(NewAR)->setNoWrapFlags(
4146 OldAR->getNoWrapFlags());
4152 case Instruction::Xor:
4153 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
4154 // If the RHS of the xor is a signbit, then this is just an add.
4155 // Instcombine turns add of signbit into xor as a strength reduction step.
4156 if (CI->getValue().isSignBit())
4157 return getAddExpr(getSCEV(U->getOperand(0)),
4158 getSCEV(U->getOperand(1)));
4160 // If the RHS of xor is -1, then this is a not operation.
4161 if (CI->isAllOnesValue())
4162 return getNotSCEV(getSCEV(U->getOperand(0)));
4164 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
4165 // This is a variant of the check for xor with -1, and it handles
4166 // the case where instcombine has trimmed non-demanded bits out
4167 // of an xor with -1.
4168 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
4169 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
4170 if (BO->getOpcode() == Instruction::And &&
4171 LCI->getValue() == CI->getValue())
4172 if (const SCEVZeroExtendExpr *Z =
4173 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
4174 Type *UTy = U->getType();
4175 const SCEV *Z0 = Z->getOperand();
4176 Type *Z0Ty = Z0->getType();
4177 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
4179 // If C is a low-bits mask, the zero extend is serving to
4180 // mask off the high bits. Complement the operand and
4181 // re-apply the zext.
4182 if (APIntOps::isMask(Z0TySize, CI->getValue()))
4183 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
4185 // If C is a single bit, it may be in the sign-bit position
4186 // before the zero-extend. In this case, represent the xor
4187 // using an add, which is equivalent, and re-apply the zext.
4188 APInt Trunc = CI->getValue().trunc(Z0TySize);
4189 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
4191 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
4197 case Instruction::Shl:
4198 // Turn shift left of a constant amount into a multiply.
4199 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
4200 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
4202 // If the shift count is not less than the bitwidth, the result of
4203 // the shift is undefined. Don't try to analyze it, because the
4204 // resolution chosen here may differ from the resolution chosen in
4205 // other parts of the compiler.
4206 if (SA->getValue().uge(BitWidth))
4209 Constant *X = ConstantInt::get(getContext(),
4210 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
4211 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
4215 case Instruction::LShr:
4216 // Turn logical shift right of a constant into a unsigned divide.
4217 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
4218 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
4220 // If the shift count is not less than the bitwidth, the result of
4221 // the shift is undefined. Don't try to analyze it, because the
4222 // resolution chosen here may differ from the resolution chosen in
4223 // other parts of the compiler.
4224 if (SA->getValue().uge(BitWidth))
4227 Constant *X = ConstantInt::get(getContext(),
4228 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
4229 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
4233 case Instruction::AShr:
4234 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
4235 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
4236 if (Operator *L = dyn_cast<Operator>(U->getOperand(0)))
4237 if (L->getOpcode() == Instruction::Shl &&
4238 L->getOperand(1) == U->getOperand(1)) {
4239 uint64_t BitWidth = getTypeSizeInBits(U->getType());
4241 // If the shift count is not less than the bitwidth, the result of
4242 // the shift is undefined. Don't try to analyze it, because the
4243 // resolution chosen here may differ from the resolution chosen in
4244 // other parts of the compiler.
4245 if (CI->getValue().uge(BitWidth))
4248 uint64_t Amt = BitWidth - CI->getZExtValue();
4249 if (Amt == BitWidth)
4250 return getSCEV(L->getOperand(0)); // shift by zero --> noop
4252 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
4253 IntegerType::get(getContext(),
4259 case Instruction::Trunc:
4260 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
4262 case Instruction::ZExt:
4263 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
4265 case Instruction::SExt:
4266 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
4268 case Instruction::BitCast:
4269 // BitCasts are no-op casts so we just eliminate the cast.
4270 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
4271 return getSCEV(U->getOperand(0));
4274 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
4275 // lead to pointer expressions which cannot safely be expanded to GEPs,
4276 // because ScalarEvolution doesn't respect the GEP aliasing rules when
4277 // simplifying integer expressions.
4279 case Instruction::GetElementPtr:
4280 return createNodeForGEP(cast<GEPOperator>(U));
4282 case Instruction::PHI:
4283 return createNodeForPHI(cast<PHINode>(U));
4285 case Instruction::Select:
4286 // This could be a smax or umax that was lowered earlier.
4287 // Try to recover it.
4288 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
4289 Value *LHS = ICI->getOperand(0);
4290 Value *RHS = ICI->getOperand(1);
4291 switch (ICI->getPredicate()) {
4292 case ICmpInst::ICMP_SLT:
4293 case ICmpInst::ICMP_SLE:
4294 std::swap(LHS, RHS);
4296 case ICmpInst::ICMP_SGT:
4297 case ICmpInst::ICMP_SGE:
4298 // a >s b ? a+x : b+x -> smax(a, b)+x
4299 // a >s b ? b+x : a+x -> smin(a, b)+x
4300 if (getTypeSizeInBits(LHS->getType()) <=
4301 getTypeSizeInBits(U->getType())) {
4302 const SCEV *LS = getNoopOrSignExtend(getSCEV(LHS), U->getType());
4303 const SCEV *RS = getNoopOrSignExtend(getSCEV(RHS), U->getType());
4304 const SCEV *LA = getSCEV(U->getOperand(1));
4305 const SCEV *RA = getSCEV(U->getOperand(2));
4306 const SCEV *LDiff = getMinusSCEV(LA, LS);
4307 const SCEV *RDiff = getMinusSCEV(RA, RS);
4309 return getAddExpr(getSMaxExpr(LS, RS), LDiff);
4310 LDiff = getMinusSCEV(LA, RS);
4311 RDiff = getMinusSCEV(RA, LS);
4313 return getAddExpr(getSMinExpr(LS, RS), LDiff);
4316 case ICmpInst::ICMP_ULT:
4317 case ICmpInst::ICMP_ULE:
4318 std::swap(LHS, RHS);
4320 case ICmpInst::ICMP_UGT:
4321 case ICmpInst::ICMP_UGE:
4322 // a >u b ? a+x : b+x -> umax(a, b)+x
4323 // a >u b ? b+x : a+x -> umin(a, b)+x
4324 if (getTypeSizeInBits(LHS->getType()) <=
4325 getTypeSizeInBits(U->getType())) {
4326 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), U->getType());
4327 const SCEV *RS = getNoopOrZeroExtend(getSCEV(RHS), U->getType());
4328 const SCEV *LA = getSCEV(U->getOperand(1));
4329 const SCEV *RA = getSCEV(U->getOperand(2));
4330 const SCEV *LDiff = getMinusSCEV(LA, LS);
4331 const SCEV *RDiff = getMinusSCEV(RA, RS);
4333 return getAddExpr(getUMaxExpr(LS, RS), LDiff);
4334 LDiff = getMinusSCEV(LA, RS);
4335 RDiff = getMinusSCEV(RA, LS);
4337 return getAddExpr(getUMinExpr(LS, RS), LDiff);
4340 case ICmpInst::ICMP_NE:
4341 // n != 0 ? n+x : 1+x -> umax(n, 1)+x
4342 if (getTypeSizeInBits(LHS->getType()) <=
4343 getTypeSizeInBits(U->getType()) &&
4344 isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
4345 const SCEV *One = getConstant(U->getType(), 1);
4346 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), U->getType());
4347 const SCEV *LA = getSCEV(U->getOperand(1));
4348 const SCEV *RA = getSCEV(U->getOperand(2));
4349 const SCEV *LDiff = getMinusSCEV(LA, LS);
4350 const SCEV *RDiff = getMinusSCEV(RA, One);
4352 return getAddExpr(getUMaxExpr(One, LS), LDiff);
4355 case ICmpInst::ICMP_EQ:
4356 // n == 0 ? 1+x : n+x -> umax(n, 1)+x
4357 if (getTypeSizeInBits(LHS->getType()) <=
4358 getTypeSizeInBits(U->getType()) &&
4359 isa<ConstantInt>(RHS) && cast<ConstantInt>(RHS)->isZero()) {
4360 const SCEV *One = getConstant(U->getType(), 1);
4361 const SCEV *LS = getNoopOrZeroExtend(getSCEV(LHS), U->getType());
4362 const SCEV *LA = getSCEV(U->getOperand(1));
4363 const SCEV *RA = getSCEV(U->getOperand(2));
4364 const SCEV *LDiff = getMinusSCEV(LA, One);
4365 const SCEV *RDiff = getMinusSCEV(RA, LS);
4367 return getAddExpr(getUMaxExpr(One, LS), LDiff);
4375 default: // We cannot analyze this expression.
4379 return getUnknown(V);
4384 //===----------------------------------------------------------------------===//
4385 // Iteration Count Computation Code
4388 unsigned ScalarEvolution::getSmallConstantTripCount(Loop *L) {
4389 if (BasicBlock *ExitingBB = L->getExitingBlock())
4390 return getSmallConstantTripCount(L, ExitingBB);
4392 // No trip count information for multiple exits.
4396 /// getSmallConstantTripCount - Returns the maximum trip count of this loop as a
4397 /// normal unsigned value. Returns 0 if the trip count is unknown or not
4398 /// constant. Will also return 0 if the maximum trip count is very large (>=
4401 /// This "trip count" assumes that control exits via ExitingBlock. More
4402 /// precisely, it is the number of times that control may reach ExitingBlock
4403 /// before taking the branch. For loops with multiple exits, it may not be the
4404 /// number times that the loop header executes because the loop may exit
4405 /// prematurely via another branch.
4406 unsigned ScalarEvolution::getSmallConstantTripCount(Loop *L,
4407 BasicBlock *ExitingBlock) {
4408 assert(ExitingBlock && "Must pass a non-null exiting block!");
4409 assert(L->isLoopExiting(ExitingBlock) &&
4410 "Exiting block must actually branch out of the loop!");
4411 const SCEVConstant *ExitCount =
4412 dyn_cast<SCEVConstant>(getExitCount(L, ExitingBlock));
4416 ConstantInt *ExitConst = ExitCount->getValue();
4418 // Guard against huge trip counts.
4419 if (ExitConst->getValue().getActiveBits() > 32)
4422 // In case of integer overflow, this returns 0, which is correct.
4423 return ((unsigned)ExitConst->getZExtValue()) + 1;
4426 unsigned ScalarEvolution::getSmallConstantTripMultiple(Loop *L) {
4427 if (BasicBlock *ExitingBB = L->getExitingBlock())
4428 return getSmallConstantTripMultiple(L, ExitingBB);
4430 // No trip multiple information for multiple exits.
4434 /// getSmallConstantTripMultiple - Returns the largest constant divisor of the
4435 /// trip count of this loop as a normal unsigned value, if possible. This
4436 /// means that the actual trip count is always a multiple of the returned
4437 /// value (don't forget the trip count could very well be zero as well!).
4439 /// Returns 1 if the trip count is unknown or not guaranteed to be the
4440 /// multiple of a constant (which is also the case if the trip count is simply
4441 /// constant, use getSmallConstantTripCount for that case), Will also return 1
4442 /// if the trip count is very large (>= 2^32).
4444 /// As explained in the comments for getSmallConstantTripCount, this assumes
4445 /// that control exits the loop via ExitingBlock.
4447 ScalarEvolution::getSmallConstantTripMultiple(Loop *L,
4448 BasicBlock *ExitingBlock) {
4449 assert(ExitingBlock && "Must pass a non-null exiting block!");
4450 assert(L->isLoopExiting(ExitingBlock) &&
4451 "Exiting block must actually branch out of the loop!");
4452 const SCEV *ExitCount = getExitCount(L, ExitingBlock);
4453 if (ExitCount == getCouldNotCompute())
4456 // Get the trip count from the BE count by adding 1.
4457 const SCEV *TCMul = getAddExpr(ExitCount,
4458 getConstant(ExitCount->getType(), 1));
4459 // FIXME: SCEV distributes multiplication as V1*C1 + V2*C1. We could attempt
4460 // to factor simple cases.
4461 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(TCMul))
4462 TCMul = Mul->getOperand(0);
4464 const SCEVConstant *MulC = dyn_cast<SCEVConstant>(TCMul);
4468 ConstantInt *Result = MulC->getValue();
4470 // Guard against huge trip counts (this requires checking
4471 // for zero to handle the case where the trip count == -1 and the
4473 if (!Result || Result->getValue().getActiveBits() > 32 ||
4474 Result->getValue().getActiveBits() == 0)
4477 return (unsigned)Result->getZExtValue();
4480 // getExitCount - Get the expression for the number of loop iterations for which
4481 // this loop is guaranteed not to exit via ExitingBlock. Otherwise return
4482 // SCEVCouldNotCompute.
4483 const SCEV *ScalarEvolution::getExitCount(Loop *L, BasicBlock *ExitingBlock) {
4484 return getBackedgeTakenInfo(L).getExact(ExitingBlock, this);
4487 /// getBackedgeTakenCount - If the specified loop has a predictable
4488 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
4489 /// object. The backedge-taken count is the number of times the loop header
4490 /// will be branched to from within the loop. This is one less than the
4491 /// trip count of the loop, since it doesn't count the first iteration,
4492 /// when the header is branched to from outside the loop.
4494 /// Note that it is not valid to call this method on a loop without a
4495 /// loop-invariant backedge-taken count (see
4496 /// hasLoopInvariantBackedgeTakenCount).
4498 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
4499 return getBackedgeTakenInfo(L).getExact(this);
4502 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
4503 /// return the least SCEV value that is known never to be less than the
4504 /// actual backedge taken count.
4505 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
4506 return getBackedgeTakenInfo(L).getMax(this);
4509 /// PushLoopPHIs - Push PHI nodes in the header of the given loop
4510 /// onto the given Worklist.
4512 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
4513 BasicBlock *Header = L->getHeader();
4515 // Push all Loop-header PHIs onto the Worklist stack.
4516 for (BasicBlock::iterator I = Header->begin();
4517 PHINode *PN = dyn_cast<PHINode>(I); ++I)
4518 Worklist.push_back(PN);
4521 const ScalarEvolution::BackedgeTakenInfo &
4522 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
4523 // Initially insert an invalid entry for this loop. If the insertion
4524 // succeeds, proceed to actually compute a backedge-taken count and
4525 // update the value. The temporary CouldNotCompute value tells SCEV
4526 // code elsewhere that it shouldn't attempt to request a new
4527 // backedge-taken count, which could result in infinite recursion.
4528 std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
4529 BackedgeTakenCounts.insert(std::make_pair(L, BackedgeTakenInfo()));
4531 return Pair.first->second;
4533 // ComputeBackedgeTakenCount may allocate memory for its result. Inserting it
4534 // into the BackedgeTakenCounts map transfers ownership. Otherwise, the result
4535 // must be cleared in this scope.
4536 BackedgeTakenInfo Result = ComputeBackedgeTakenCount(L);
4538 if (Result.getExact(this) != getCouldNotCompute()) {
4539 assert(isLoopInvariant(Result.getExact(this), L) &&
4540 isLoopInvariant(Result.getMax(this), L) &&
4541 "Computed backedge-taken count isn't loop invariant for loop!");
4542 ++NumTripCountsComputed;
4544 else if (Result.getMax(this) == getCouldNotCompute() &&
4545 isa<PHINode>(L->getHeader()->begin())) {
4546 // Only count loops that have phi nodes as not being computable.
4547 ++NumTripCountsNotComputed;
4550 // Now that we know more about the trip count for this loop, forget any
4551 // existing SCEV values for PHI nodes in this loop since they are only
4552 // conservative estimates made without the benefit of trip count
4553 // information. This is similar to the code in forgetLoop, except that
4554 // it handles SCEVUnknown PHI nodes specially.
4555 if (Result.hasAnyInfo()) {
4556 SmallVector<Instruction *, 16> Worklist;
4557 PushLoopPHIs(L, Worklist);
4559 SmallPtrSet<Instruction *, 8> Visited;
4560 while (!Worklist.empty()) {
4561 Instruction *I = Worklist.pop_back_val();
4562 if (!Visited.insert(I).second)
4565 ValueExprMapType::iterator It =
4566 ValueExprMap.find_as(static_cast<Value *>(I));
4567 if (It != ValueExprMap.end()) {
4568 const SCEV *Old = It->second;
4570 // SCEVUnknown for a PHI either means that it has an unrecognized
4571 // structure, or it's a PHI that's in the progress of being computed
4572 // by createNodeForPHI. In the former case, additional loop trip
4573 // count information isn't going to change anything. In the later
4574 // case, createNodeForPHI will perform the necessary updates on its
4575 // own when it gets to that point.
4576 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) {
4577 forgetMemoizedResults(Old);
4578 ValueExprMap.erase(It);
4580 if (PHINode *PN = dyn_cast<PHINode>(I))
4581 ConstantEvolutionLoopExitValue.erase(PN);
4584 PushDefUseChildren(I, Worklist);
4588 // Re-lookup the insert position, since the call to
4589 // ComputeBackedgeTakenCount above could result in a
4590 // recusive call to getBackedgeTakenInfo (on a different
4591 // loop), which would invalidate the iterator computed
4593 return BackedgeTakenCounts.find(L)->second = Result;
4596 /// forgetLoop - This method should be called by the client when it has
4597 /// changed a loop in a way that may effect ScalarEvolution's ability to
4598 /// compute a trip count, or if the loop is deleted.
4599 void ScalarEvolution::forgetLoop(const Loop *L) {
4600 // Drop any stored trip count value.
4601 DenseMap<const Loop*, BackedgeTakenInfo>::iterator BTCPos =
4602 BackedgeTakenCounts.find(L);
4603 if (BTCPos != BackedgeTakenCounts.end()) {
4604 BTCPos->second.clear();
4605 BackedgeTakenCounts.erase(BTCPos);
4608 // Drop information about expressions based on loop-header PHIs.
4609 SmallVector<Instruction *, 16> Worklist;
4610 PushLoopPHIs(L, Worklist);
4612 SmallPtrSet<Instruction *, 8> Visited;
4613 while (!Worklist.empty()) {
4614 Instruction *I = Worklist.pop_back_val();
4615 if (!Visited.insert(I).second)
4618 ValueExprMapType::iterator It =
4619 ValueExprMap.find_as(static_cast<Value *>(I));
4620 if (It != ValueExprMap.end()) {
4621 forgetMemoizedResults(It->second);
4622 ValueExprMap.erase(It);
4623 if (PHINode *PN = dyn_cast<PHINode>(I))
4624 ConstantEvolutionLoopExitValue.erase(PN);
4627 PushDefUseChildren(I, Worklist);
4630 // Forget all contained loops too, to avoid dangling entries in the
4631 // ValuesAtScopes map.
4632 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
4636 /// forgetValue - This method should be called by the client when it has
4637 /// changed a value in a way that may effect its value, or which may
4638 /// disconnect it from a def-use chain linking it to a loop.
4639 void ScalarEvolution::forgetValue(Value *V) {
4640 Instruction *I = dyn_cast<Instruction>(V);
4643 // Drop information about expressions based on loop-header PHIs.
4644 SmallVector<Instruction *, 16> Worklist;
4645 Worklist.push_back(I);
4647 SmallPtrSet<Instruction *, 8> Visited;
4648 while (!Worklist.empty()) {
4649 I = Worklist.pop_back_val();
4650 if (!Visited.insert(I).second)
4653 ValueExprMapType::iterator It =
4654 ValueExprMap.find_as(static_cast<Value *>(I));
4655 if (It != ValueExprMap.end()) {
4656 forgetMemoizedResults(It->second);
4657 ValueExprMap.erase(It);
4658 if (PHINode *PN = dyn_cast<PHINode>(I))
4659 ConstantEvolutionLoopExitValue.erase(PN);
4662 PushDefUseChildren(I, Worklist);
4666 /// getExact - Get the exact loop backedge taken count considering all loop
4667 /// exits. A computable result can only be return for loops with a single exit.
4668 /// Returning the minimum taken count among all exits is incorrect because one
4669 /// of the loop's exit limit's may have been skipped. HowFarToZero assumes that
4670 /// the limit of each loop test is never skipped. This is a valid assumption as
4671 /// long as the loop exits via that test. For precise results, it is the
4672 /// caller's responsibility to specify the relevant loop exit using
4673 /// getExact(ExitingBlock, SE).
4675 ScalarEvolution::BackedgeTakenInfo::getExact(ScalarEvolution *SE) const {
4676 // If any exits were not computable, the loop is not computable.
4677 if (!ExitNotTaken.isCompleteList()) return SE->getCouldNotCompute();
4679 // We need exactly one computable exit.
4680 if (!ExitNotTaken.ExitingBlock) return SE->getCouldNotCompute();
4681 assert(ExitNotTaken.ExactNotTaken && "uninitialized not-taken info");
4683 const SCEV *BECount = nullptr;
4684 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4685 ENT != nullptr; ENT = ENT->getNextExit()) {
4687 assert(ENT->ExactNotTaken != SE->getCouldNotCompute() && "bad exit SCEV");
4690 BECount = ENT->ExactNotTaken;
4691 else if (BECount != ENT->ExactNotTaken)
4692 return SE->getCouldNotCompute();
4694 assert(BECount && "Invalid not taken count for loop exit");
4698 /// getExact - Get the exact not taken count for this loop exit.
4700 ScalarEvolution::BackedgeTakenInfo::getExact(BasicBlock *ExitingBlock,
4701 ScalarEvolution *SE) const {
4702 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4703 ENT != nullptr; ENT = ENT->getNextExit()) {
4705 if (ENT->ExitingBlock == ExitingBlock)
4706 return ENT->ExactNotTaken;
4708 return SE->getCouldNotCompute();
4711 /// getMax - Get the max backedge taken count for the loop.
4713 ScalarEvolution::BackedgeTakenInfo::getMax(ScalarEvolution *SE) const {
4714 return Max ? Max : SE->getCouldNotCompute();
4717 bool ScalarEvolution::BackedgeTakenInfo::hasOperand(const SCEV *S,
4718 ScalarEvolution *SE) const {
4719 if (Max && Max != SE->getCouldNotCompute() && SE->hasOperand(Max, S))
4722 if (!ExitNotTaken.ExitingBlock)
4725 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4726 ENT != nullptr; ENT = ENT->getNextExit()) {
4728 if (ENT->ExactNotTaken != SE->getCouldNotCompute()
4729 && SE->hasOperand(ENT->ExactNotTaken, S)) {
4736 /// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each
4737 /// computable exit into a persistent ExitNotTakenInfo array.
4738 ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo(
4739 SmallVectorImpl< std::pair<BasicBlock *, const SCEV *> > &ExitCounts,
4740 bool Complete, const SCEV *MaxCount) : Max(MaxCount) {
4743 ExitNotTaken.setIncomplete();
4745 unsigned NumExits = ExitCounts.size();
4746 if (NumExits == 0) return;
4748 ExitNotTaken.ExitingBlock = ExitCounts[0].first;
4749 ExitNotTaken.ExactNotTaken = ExitCounts[0].second;
4750 if (NumExits == 1) return;
4752 // Handle the rare case of multiple computable exits.
4753 ExitNotTakenInfo *ENT = new ExitNotTakenInfo[NumExits-1];
4755 ExitNotTakenInfo *PrevENT = &ExitNotTaken;
4756 for (unsigned i = 1; i < NumExits; ++i, PrevENT = ENT, ++ENT) {
4757 PrevENT->setNextExit(ENT);
4758 ENT->ExitingBlock = ExitCounts[i].first;
4759 ENT->ExactNotTaken = ExitCounts[i].second;
4763 /// clear - Invalidate this result and free the ExitNotTakenInfo array.
4764 void ScalarEvolution::BackedgeTakenInfo::clear() {
4765 ExitNotTaken.ExitingBlock = nullptr;
4766 ExitNotTaken.ExactNotTaken = nullptr;
4767 delete[] ExitNotTaken.getNextExit();
4770 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
4771 /// of the specified loop will execute.
4772 ScalarEvolution::BackedgeTakenInfo
4773 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
4774 SmallVector<BasicBlock *, 8> ExitingBlocks;
4775 L->getExitingBlocks(ExitingBlocks);
4777 SmallVector<std::pair<BasicBlock *, const SCEV *>, 4> ExitCounts;
4778 bool CouldComputeBECount = true;
4779 BasicBlock *Latch = L->getLoopLatch(); // may be NULL.
4780 const SCEV *MustExitMaxBECount = nullptr;
4781 const SCEV *MayExitMaxBECount = nullptr;
4783 // Compute the ExitLimit for each loop exit. Use this to populate ExitCounts
4784 // and compute maxBECount.
4785 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
4786 BasicBlock *ExitBB = ExitingBlocks[i];
4787 ExitLimit EL = ComputeExitLimit(L, ExitBB);
4789 // 1. For each exit that can be computed, add an entry to ExitCounts.
4790 // CouldComputeBECount is true only if all exits can be computed.
4791 if (EL.Exact == getCouldNotCompute())
4792 // We couldn't compute an exact value for this exit, so
4793 // we won't be able to compute an exact value for the loop.
4794 CouldComputeBECount = false;
4796 ExitCounts.push_back(std::make_pair(ExitBB, EL.Exact));
4798 // 2. Derive the loop's MaxBECount from each exit's max number of
4799 // non-exiting iterations. Partition the loop exits into two kinds:
4800 // LoopMustExits and LoopMayExits.
4802 // If the exit dominates the loop latch, it is a LoopMustExit otherwise it
4803 // is a LoopMayExit. If any computable LoopMustExit is found, then
4804 // MaxBECount is the minimum EL.Max of computable LoopMustExits. Otherwise,
4805 // MaxBECount is conservatively the maximum EL.Max, where CouldNotCompute is
4806 // considered greater than any computable EL.Max.
4807 if (EL.Max != getCouldNotCompute() && Latch &&
4808 DT->dominates(ExitBB, Latch)) {
4809 if (!MustExitMaxBECount)
4810 MustExitMaxBECount = EL.Max;
4812 MustExitMaxBECount =
4813 getUMinFromMismatchedTypes(MustExitMaxBECount, EL.Max);
4815 } else if (MayExitMaxBECount != getCouldNotCompute()) {
4816 if (!MayExitMaxBECount || EL.Max == getCouldNotCompute())
4817 MayExitMaxBECount = EL.Max;
4820 getUMaxFromMismatchedTypes(MayExitMaxBECount, EL.Max);
4824 const SCEV *MaxBECount = MustExitMaxBECount ? MustExitMaxBECount :
4825 (MayExitMaxBECount ? MayExitMaxBECount : getCouldNotCompute());
4826 return BackedgeTakenInfo(ExitCounts, CouldComputeBECount, MaxBECount);
4829 /// ComputeExitLimit - Compute the number of times the backedge of the specified
4830 /// loop will execute if it exits via the specified block.
4831 ScalarEvolution::ExitLimit
4832 ScalarEvolution::ComputeExitLimit(const Loop *L, BasicBlock *ExitingBlock) {
4834 // Okay, we've chosen an exiting block. See what condition causes us to
4835 // exit at this block and remember the exit block and whether all other targets
4836 // lead to the loop header.
4837 bool MustExecuteLoopHeader = true;
4838 BasicBlock *Exit = nullptr;
4839 for (succ_iterator SI = succ_begin(ExitingBlock), SE = succ_end(ExitingBlock);
4841 if (!L->contains(*SI)) {
4842 if (Exit) // Multiple exit successors.
4843 return getCouldNotCompute();
4845 } else if (*SI != L->getHeader()) {
4846 MustExecuteLoopHeader = false;
4849 // At this point, we know we have a conditional branch that determines whether
4850 // the loop is exited. However, we don't know if the branch is executed each
4851 // time through the loop. If not, then the execution count of the branch will
4852 // not be equal to the trip count of the loop.
4854 // Currently we check for this by checking to see if the Exit branch goes to
4855 // the loop header. If so, we know it will always execute the same number of
4856 // times as the loop. We also handle the case where the exit block *is* the
4857 // loop header. This is common for un-rotated loops.
4859 // If both of those tests fail, walk up the unique predecessor chain to the
4860 // header, stopping if there is an edge that doesn't exit the loop. If the
4861 // header is reached, the execution count of the branch will be equal to the
4862 // trip count of the loop.
4864 // More extensive analysis could be done to handle more cases here.
4866 if (!MustExecuteLoopHeader && ExitingBlock != L->getHeader()) {
4867 // The simple checks failed, try climbing the unique predecessor chain
4868 // up to the header.
4870 for (BasicBlock *BB = ExitingBlock; BB; ) {
4871 BasicBlock *Pred = BB->getUniquePredecessor();
4873 return getCouldNotCompute();
4874 TerminatorInst *PredTerm = Pred->getTerminator();
4875 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) {
4876 BasicBlock *PredSucc = PredTerm->getSuccessor(i);
4879 // If the predecessor has a successor that isn't BB and isn't
4880 // outside the loop, assume the worst.
4881 if (L->contains(PredSucc))
4882 return getCouldNotCompute();
4884 if (Pred == L->getHeader()) {
4891 return getCouldNotCompute();
4894 bool IsOnlyExit = (L->getExitingBlock() != nullptr);
4895 TerminatorInst *Term = ExitingBlock->getTerminator();
4896 if (BranchInst *BI = dyn_cast<BranchInst>(Term)) {
4897 assert(BI->isConditional() && "If unconditional, it can't be in loop!");
4898 // Proceed to the next level to examine the exit condition expression.
4899 return ComputeExitLimitFromCond(L, BI->getCondition(), BI->getSuccessor(0),
4900 BI->getSuccessor(1),
4901 /*ControlsExit=*/IsOnlyExit);
4904 if (SwitchInst *SI = dyn_cast<SwitchInst>(Term))
4905 return ComputeExitLimitFromSingleExitSwitch(L, SI, Exit,
4906 /*ControlsExit=*/IsOnlyExit);
4908 return getCouldNotCompute();
4911 /// ComputeExitLimitFromCond - Compute the number of times the
4912 /// backedge of the specified loop will execute if its exit condition
4913 /// were a conditional branch of ExitCond, TBB, and FBB.
4915 /// @param ControlsExit is true if ExitCond directly controls the exit
4916 /// branch. In this case, we can assume that the loop exits only if the
4917 /// condition is true and can infer that failing to meet the condition prior to
4918 /// integer wraparound results in undefined behavior.
4919 ScalarEvolution::ExitLimit
4920 ScalarEvolution::ComputeExitLimitFromCond(const Loop *L,
4924 bool ControlsExit) {
4925 // Check if the controlling expression for this loop is an And or Or.
4926 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
4927 if (BO->getOpcode() == Instruction::And) {
4928 // Recurse on the operands of the and.
4929 bool EitherMayExit = L->contains(TBB);
4930 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
4931 ControlsExit && !EitherMayExit);
4932 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
4933 ControlsExit && !EitherMayExit);
4934 const SCEV *BECount = getCouldNotCompute();
4935 const SCEV *MaxBECount = getCouldNotCompute();
4936 if (EitherMayExit) {
4937 // Both conditions must be true for the loop to continue executing.
4938 // Choose the less conservative count.
4939 if (EL0.Exact == getCouldNotCompute() ||
4940 EL1.Exact == getCouldNotCompute())
4941 BECount = getCouldNotCompute();
4943 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
4944 if (EL0.Max == getCouldNotCompute())
4945 MaxBECount = EL1.Max;
4946 else if (EL1.Max == getCouldNotCompute())
4947 MaxBECount = EL0.Max;
4949 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
4951 // Both conditions must be true at the same time for the loop to exit.
4952 // For now, be conservative.
4953 assert(L->contains(FBB) && "Loop block has no successor in loop!");
4954 if (EL0.Max == EL1.Max)
4955 MaxBECount = EL0.Max;
4956 if (EL0.Exact == EL1.Exact)
4957 BECount = EL0.Exact;
4960 return ExitLimit(BECount, MaxBECount);
4962 if (BO->getOpcode() == Instruction::Or) {
4963 // Recurse on the operands of the or.
4964 bool EitherMayExit = L->contains(FBB);
4965 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
4966 ControlsExit && !EitherMayExit);
4967 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
4968 ControlsExit && !EitherMayExit);
4969 const SCEV *BECount = getCouldNotCompute();
4970 const SCEV *MaxBECount = getCouldNotCompute();
4971 if (EitherMayExit) {
4972 // Both conditions must be false for the loop to continue executing.
4973 // Choose the less conservative count.
4974 if (EL0.Exact == getCouldNotCompute() ||
4975 EL1.Exact == getCouldNotCompute())
4976 BECount = getCouldNotCompute();
4978 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
4979 if (EL0.Max == getCouldNotCompute())
4980 MaxBECount = EL1.Max;
4981 else if (EL1.Max == getCouldNotCompute())
4982 MaxBECount = EL0.Max;
4984 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
4986 // Both conditions must be false at the same time for the loop to exit.
4987 // For now, be conservative.
4988 assert(L->contains(TBB) && "Loop block has no successor in loop!");
4989 if (EL0.Max == EL1.Max)
4990 MaxBECount = EL0.Max;
4991 if (EL0.Exact == EL1.Exact)
4992 BECount = EL0.Exact;
4995 return ExitLimit(BECount, MaxBECount);
4999 // With an icmp, it may be feasible to compute an exact backedge-taken count.
5000 // Proceed to the next level to examine the icmp.
5001 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
5002 return ComputeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB, ControlsExit);
5004 // Check for a constant condition. These are normally stripped out by
5005 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
5006 // preserve the CFG and is temporarily leaving constant conditions
5008 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
5009 if (L->contains(FBB) == !CI->getZExtValue())
5010 // The backedge is always taken.
5011 return getCouldNotCompute();
5013 // The backedge is never taken.
5014 return getConstant(CI->getType(), 0);
5017 // If it's not an integer or pointer comparison then compute it the hard way.
5018 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
5021 /// ComputeExitLimitFromICmp - Compute the number of times the
5022 /// backedge of the specified loop will execute if its exit condition
5023 /// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB.
5024 ScalarEvolution::ExitLimit
5025 ScalarEvolution::ComputeExitLimitFromICmp(const Loop *L,
5029 bool ControlsExit) {
5031 // If the condition was exit on true, convert the condition to exit on false
5032 ICmpInst::Predicate Cond;
5033 if (!L->contains(FBB))
5034 Cond = ExitCond->getPredicate();
5036 Cond = ExitCond->getInversePredicate();
5038 // Handle common loops like: for (X = "string"; *X; ++X)
5039 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
5040 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
5042 ComputeLoadConstantCompareExitLimit(LI, RHS, L, Cond);
5043 if (ItCnt.hasAnyInfo())
5047 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
5048 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
5050 // Try to evaluate any dependencies out of the loop.
5051 LHS = getSCEVAtScope(LHS, L);
5052 RHS = getSCEVAtScope(RHS, L);
5054 // At this point, we would like to compute how many iterations of the
5055 // loop the predicate will return true for these inputs.
5056 if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) {
5057 // If there is a loop-invariant, force it into the RHS.
5058 std::swap(LHS, RHS);
5059 Cond = ICmpInst::getSwappedPredicate(Cond);
5062 // Simplify the operands before analyzing them.
5063 (void)SimplifyICmpOperands(Cond, LHS, RHS);
5065 // If we have a comparison of a chrec against a constant, try to use value
5066 // ranges to answer this query.
5067 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
5068 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
5069 if (AddRec->getLoop() == L) {
5070 // Form the constant range.
5071 ConstantRange CompRange(
5072 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
5074 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
5075 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
5079 case ICmpInst::ICMP_NE: { // while (X != Y)
5080 // Convert to: while (X-Y != 0)
5081 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit);
5082 if (EL.hasAnyInfo()) return EL;
5085 case ICmpInst::ICMP_EQ: { // while (X == Y)
5086 // Convert to: while (X-Y == 0)
5087 ExitLimit EL = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
5088 if (EL.hasAnyInfo()) return EL;
5091 case ICmpInst::ICMP_SLT:
5092 case ICmpInst::ICMP_ULT: { // while (X < Y)
5093 bool IsSigned = Cond == ICmpInst::ICMP_SLT;
5094 ExitLimit EL = HowManyLessThans(LHS, RHS, L, IsSigned, ControlsExit);
5095 if (EL.hasAnyInfo()) return EL;
5098 case ICmpInst::ICMP_SGT:
5099 case ICmpInst::ICMP_UGT: { // while (X > Y)
5100 bool IsSigned = Cond == ICmpInst::ICMP_SGT;
5101 ExitLimit EL = HowManyGreaterThans(LHS, RHS, L, IsSigned, ControlsExit);
5102 if (EL.hasAnyInfo()) return EL;
5107 dbgs() << "ComputeBackedgeTakenCount ";
5108 if (ExitCond->getOperand(0)->getType()->isUnsigned())
5109 dbgs() << "[unsigned] ";
5110 dbgs() << *LHS << " "
5111 << Instruction::getOpcodeName(Instruction::ICmp)
5112 << " " << *RHS << "\n";
5116 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
5119 ScalarEvolution::ExitLimit
5120 ScalarEvolution::ComputeExitLimitFromSingleExitSwitch(const Loop *L,
5122 BasicBlock *ExitingBlock,
5123 bool ControlsExit) {
5124 assert(!L->contains(ExitingBlock) && "Not an exiting block!");
5126 // Give up if the exit is the default dest of a switch.
5127 if (Switch->getDefaultDest() == ExitingBlock)
5128 return getCouldNotCompute();
5130 assert(L->contains(Switch->getDefaultDest()) &&
5131 "Default case must not exit the loop!");
5132 const SCEV *LHS = getSCEVAtScope(Switch->getCondition(), L);
5133 const SCEV *RHS = getConstant(Switch->findCaseDest(ExitingBlock));
5135 // while (X != Y) --> while (X-Y != 0)
5136 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit);
5137 if (EL.hasAnyInfo())
5140 return getCouldNotCompute();
5143 static ConstantInt *
5144 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
5145 ScalarEvolution &SE) {
5146 const SCEV *InVal = SE.getConstant(C);
5147 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
5148 assert(isa<SCEVConstant>(Val) &&
5149 "Evaluation of SCEV at constant didn't fold correctly?");
5150 return cast<SCEVConstant>(Val)->getValue();
5153 /// ComputeLoadConstantCompareExitLimit - Given an exit condition of
5154 /// 'icmp op load X, cst', try to see if we can compute the backedge
5155 /// execution count.
5156 ScalarEvolution::ExitLimit
5157 ScalarEvolution::ComputeLoadConstantCompareExitLimit(
5161 ICmpInst::Predicate predicate) {
5163 if (LI->isVolatile()) return getCouldNotCompute();
5165 // Check to see if the loaded pointer is a getelementptr of a global.
5166 // TODO: Use SCEV instead of manually grubbing with GEPs.
5167 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
5168 if (!GEP) return getCouldNotCompute();
5170 // Make sure that it is really a constant global we are gepping, with an
5171 // initializer, and make sure the first IDX is really 0.
5172 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
5173 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
5174 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
5175 !cast<Constant>(GEP->getOperand(1))->isNullValue())
5176 return getCouldNotCompute();
5178 // Okay, we allow one non-constant index into the GEP instruction.
5179 Value *VarIdx = nullptr;
5180 std::vector<Constant*> Indexes;
5181 unsigned VarIdxNum = 0;
5182 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
5183 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
5184 Indexes.push_back(CI);
5185 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
5186 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
5187 VarIdx = GEP->getOperand(i);
5189 Indexes.push_back(nullptr);
5192 // Loop-invariant loads may be a byproduct of loop optimization. Skip them.
5194 return getCouldNotCompute();
5196 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
5197 // Check to see if X is a loop variant variable value now.
5198 const SCEV *Idx = getSCEV(VarIdx);
5199 Idx = getSCEVAtScope(Idx, L);
5201 // We can only recognize very limited forms of loop index expressions, in
5202 // particular, only affine AddRec's like {C1,+,C2}.
5203 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
5204 if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) ||
5205 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
5206 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
5207 return getCouldNotCompute();
5209 unsigned MaxSteps = MaxBruteForceIterations;
5210 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
5211 ConstantInt *ItCst = ConstantInt::get(
5212 cast<IntegerType>(IdxExpr->getType()), IterationNum);
5213 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
5215 // Form the GEP offset.
5216 Indexes[VarIdxNum] = Val;
5218 Constant *Result = ConstantFoldLoadThroughGEPIndices(GV->getInitializer(),
5220 if (!Result) break; // Cannot compute!
5222 // Evaluate the condition for this iteration.
5223 Result = ConstantExpr::getICmp(predicate, Result, RHS);
5224 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
5225 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
5227 dbgs() << "\n***\n*** Computed loop count " << *ItCst
5228 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
5231 ++NumArrayLenItCounts;
5232 return getConstant(ItCst); // Found terminating iteration!
5235 return getCouldNotCompute();
5239 /// CanConstantFold - Return true if we can constant fold an instruction of the
5240 /// specified type, assuming that all operands were constants.
5241 static bool CanConstantFold(const Instruction *I) {
5242 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
5243 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I) ||
5247 if (const CallInst *CI = dyn_cast<CallInst>(I))
5248 if (const Function *F = CI->getCalledFunction())
5249 return canConstantFoldCallTo(F);
5253 /// Determine whether this instruction can constant evolve within this loop
5254 /// assuming its operands can all constant evolve.
5255 static bool canConstantEvolve(Instruction *I, const Loop *L) {
5256 // An instruction outside of the loop can't be derived from a loop PHI.
5257 if (!L->contains(I)) return false;
5259 if (isa<PHINode>(I)) {
5260 if (L->getHeader() == I->getParent())
5263 // We don't currently keep track of the control flow needed to evaluate
5264 // PHIs, so we cannot handle PHIs inside of loops.
5268 // If we won't be able to constant fold this expression even if the operands
5269 // are constants, bail early.
5270 return CanConstantFold(I);
5273 /// getConstantEvolvingPHIOperands - Implement getConstantEvolvingPHI by
5274 /// recursing through each instruction operand until reaching a loop header phi.
5276 getConstantEvolvingPHIOperands(Instruction *UseInst, const Loop *L,
5277 DenseMap<Instruction *, PHINode *> &PHIMap) {
5279 // Otherwise, we can evaluate this instruction if all of its operands are
5280 // constant or derived from a PHI node themselves.
5281 PHINode *PHI = nullptr;
5282 for (Instruction::op_iterator OpI = UseInst->op_begin(),
5283 OpE = UseInst->op_end(); OpI != OpE; ++OpI) {
5285 if (isa<Constant>(*OpI)) continue;
5287 Instruction *OpInst = dyn_cast<Instruction>(*OpI);
5288 if (!OpInst || !canConstantEvolve(OpInst, L)) return nullptr;
5290 PHINode *P = dyn_cast<PHINode>(OpInst);
5292 // If this operand is already visited, reuse the prior result.
5293 // We may have P != PHI if this is the deepest point at which the
5294 // inconsistent paths meet.
5295 P = PHIMap.lookup(OpInst);
5297 // Recurse and memoize the results, whether a phi is found or not.
5298 // This recursive call invalidates pointers into PHIMap.
5299 P = getConstantEvolvingPHIOperands(OpInst, L, PHIMap);
5303 return nullptr; // Not evolving from PHI
5304 if (PHI && PHI != P)
5305 return nullptr; // Evolving from multiple different PHIs.
5308 // This is a expression evolving from a constant PHI!
5312 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
5313 /// in the loop that V is derived from. We allow arbitrary operations along the
5314 /// way, but the operands of an operation must either be constants or a value
5315 /// derived from a constant PHI. If this expression does not fit with these
5316 /// constraints, return null.
5317 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
5318 Instruction *I = dyn_cast<Instruction>(V);
5319 if (!I || !canConstantEvolve(I, L)) return nullptr;
5321 if (PHINode *PN = dyn_cast<PHINode>(I)) {
5325 // Record non-constant instructions contained by the loop.
5326 DenseMap<Instruction *, PHINode *> PHIMap;
5327 return getConstantEvolvingPHIOperands(I, L, PHIMap);
5330 /// EvaluateExpression - Given an expression that passes the
5331 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
5332 /// in the loop has the value PHIVal. If we can't fold this expression for some
5333 /// reason, return null.
5334 static Constant *EvaluateExpression(Value *V, const Loop *L,
5335 DenseMap<Instruction *, Constant *> &Vals,
5336 const DataLayout *DL,
5337 const TargetLibraryInfo *TLI) {
5338 // Convenient constant check, but redundant for recursive calls.
5339 if (Constant *C = dyn_cast<Constant>(V)) return C;
5340 Instruction *I = dyn_cast<Instruction>(V);
5341 if (!I) return nullptr;
5343 if (Constant *C = Vals.lookup(I)) return C;
5345 // An instruction inside the loop depends on a value outside the loop that we
5346 // weren't given a mapping for, or a value such as a call inside the loop.
5347 if (!canConstantEvolve(I, L)) return nullptr;
5349 // An unmapped PHI can be due to a branch or another loop inside this loop,
5350 // or due to this not being the initial iteration through a loop where we
5351 // couldn't compute the evolution of this particular PHI last time.
5352 if (isa<PHINode>(I)) return nullptr;
5354 std::vector<Constant*> Operands(I->getNumOperands());
5356 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
5357 Instruction *Operand = dyn_cast<Instruction>(I->getOperand(i));
5359 Operands[i] = dyn_cast<Constant>(I->getOperand(i));
5360 if (!Operands[i]) return nullptr;
5363 Constant *C = EvaluateExpression(Operand, L, Vals, DL, TLI);
5365 if (!C) return nullptr;
5369 if (CmpInst *CI = dyn_cast<CmpInst>(I))
5370 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
5371 Operands[1], DL, TLI);
5372 if (LoadInst *LI = dyn_cast<LoadInst>(I)) {
5373 if (!LI->isVolatile())
5374 return ConstantFoldLoadFromConstPtr(Operands[0], DL);
5376 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), Operands, DL,
5380 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
5381 /// in the header of its containing loop, we know the loop executes a
5382 /// constant number of times, and the PHI node is just a recurrence
5383 /// involving constants, fold it.
5385 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
5388 DenseMap<PHINode*, Constant*>::const_iterator I =
5389 ConstantEvolutionLoopExitValue.find(PN);
5390 if (I != ConstantEvolutionLoopExitValue.end())
5393 if (BEs.ugt(MaxBruteForceIterations))
5394 return ConstantEvolutionLoopExitValue[PN] = nullptr; // Not going to evaluate it.
5396 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
5398 DenseMap<Instruction *, Constant *> CurrentIterVals;
5399 BasicBlock *Header = L->getHeader();
5400 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
5402 // Since the loop is canonicalized, the PHI node must have two entries. One
5403 // entry must be a constant (coming in from outside of the loop), and the
5404 // second must be derived from the same PHI.
5405 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
5406 PHINode *PHI = nullptr;
5407 for (BasicBlock::iterator I = Header->begin();
5408 (PHI = dyn_cast<PHINode>(I)); ++I) {
5409 Constant *StartCST =
5410 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
5411 if (!StartCST) continue;
5412 CurrentIterVals[PHI] = StartCST;
5414 if (!CurrentIterVals.count(PN))
5415 return RetVal = nullptr;
5417 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
5419 // Execute the loop symbolically to determine the exit value.
5420 if (BEs.getActiveBits() >= 32)
5421 return RetVal = nullptr; // More than 2^32-1 iterations?? Not doing it!
5423 unsigned NumIterations = BEs.getZExtValue(); // must be in range
5424 unsigned IterationNum = 0;
5425 for (; ; ++IterationNum) {
5426 if (IterationNum == NumIterations)
5427 return RetVal = CurrentIterVals[PN]; // Got exit value!
5429 // Compute the value of the PHIs for the next iteration.
5430 // EvaluateExpression adds non-phi values to the CurrentIterVals map.
5431 DenseMap<Instruction *, Constant *> NextIterVals;
5432 Constant *NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL,
5435 return nullptr; // Couldn't evaluate!
5436 NextIterVals[PN] = NextPHI;
5438 bool StoppedEvolving = NextPHI == CurrentIterVals[PN];
5440 // Also evaluate the other PHI nodes. However, we don't get to stop if we
5441 // cease to be able to evaluate one of them or if they stop evolving,
5442 // because that doesn't necessarily prevent us from computing PN.
5443 SmallVector<std::pair<PHINode *, Constant *>, 8> PHIsToCompute;
5444 for (DenseMap<Instruction *, Constant *>::const_iterator
5445 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
5446 PHINode *PHI = dyn_cast<PHINode>(I->first);
5447 if (!PHI || PHI == PN || PHI->getParent() != Header) continue;
5448 PHIsToCompute.push_back(std::make_pair(PHI, I->second));
5450 // We use two distinct loops because EvaluateExpression may invalidate any
5451 // iterators into CurrentIterVals.
5452 for (SmallVectorImpl<std::pair<PHINode *, Constant*> >::const_iterator
5453 I = PHIsToCompute.begin(), E = PHIsToCompute.end(); I != E; ++I) {
5454 PHINode *PHI = I->first;
5455 Constant *&NextPHI = NextIterVals[PHI];
5456 if (!NextPHI) { // Not already computed.
5457 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
5458 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, TLI);
5460 if (NextPHI != I->second)
5461 StoppedEvolving = false;
5464 // If all entries in CurrentIterVals == NextIterVals then we can stop
5465 // iterating, the loop can't continue to change.
5466 if (StoppedEvolving)
5467 return RetVal = CurrentIterVals[PN];
5469 CurrentIterVals.swap(NextIterVals);
5473 /// ComputeExitCountExhaustively - If the loop is known to execute a
5474 /// constant number of times (the condition evolves only from constants),
5475 /// try to evaluate a few iterations of the loop until we get the exit
5476 /// condition gets a value of ExitWhen (true or false). If we cannot
5477 /// evaluate the trip count of the loop, return getCouldNotCompute().
5478 const SCEV *ScalarEvolution::ComputeExitCountExhaustively(const Loop *L,
5481 PHINode *PN = getConstantEvolvingPHI(Cond, L);
5482 if (!PN) return getCouldNotCompute();
5484 // If the loop is canonicalized, the PHI will have exactly two entries.
5485 // That's the only form we support here.
5486 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
5488 DenseMap<Instruction *, Constant *> CurrentIterVals;
5489 BasicBlock *Header = L->getHeader();
5490 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
5492 // One entry must be a constant (coming in from outside of the loop), and the
5493 // second must be derived from the same PHI.
5494 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
5495 PHINode *PHI = nullptr;
5496 for (BasicBlock::iterator I = Header->begin();
5497 (PHI = dyn_cast<PHINode>(I)); ++I) {
5498 Constant *StartCST =
5499 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
5500 if (!StartCST) continue;
5501 CurrentIterVals[PHI] = StartCST;
5503 if (!CurrentIterVals.count(PN))
5504 return getCouldNotCompute();
5506 // Okay, we find a PHI node that defines the trip count of this loop. Execute
5507 // the loop symbolically to determine when the condition gets a value of
5510 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
5511 for (unsigned IterationNum = 0; IterationNum != MaxIterations;++IterationNum){
5512 ConstantInt *CondVal =
5513 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, L, CurrentIterVals,
5516 // Couldn't symbolically evaluate.
5517 if (!CondVal) return getCouldNotCompute();
5519 if (CondVal->getValue() == uint64_t(ExitWhen)) {
5520 ++NumBruteForceTripCountsComputed;
5521 return getConstant(Type::getInt32Ty(getContext()), IterationNum);
5524 // Update all the PHI nodes for the next iteration.
5525 DenseMap<Instruction *, Constant *> NextIterVals;
5527 // Create a list of which PHIs we need to compute. We want to do this before
5528 // calling EvaluateExpression on them because that may invalidate iterators
5529 // into CurrentIterVals.
5530 SmallVector<PHINode *, 8> PHIsToCompute;
5531 for (DenseMap<Instruction *, Constant *>::const_iterator
5532 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
5533 PHINode *PHI = dyn_cast<PHINode>(I->first);
5534 if (!PHI || PHI->getParent() != Header) continue;
5535 PHIsToCompute.push_back(PHI);
5537 for (SmallVectorImpl<PHINode *>::const_iterator I = PHIsToCompute.begin(),
5538 E = PHIsToCompute.end(); I != E; ++I) {
5540 Constant *&NextPHI = NextIterVals[PHI];
5541 if (NextPHI) continue; // Already computed!
5543 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
5544 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, TLI);
5546 CurrentIterVals.swap(NextIterVals);
5549 // Too many iterations were needed to evaluate.
5550 return getCouldNotCompute();
5553 /// getSCEVAtScope - Return a SCEV expression for the specified value
5554 /// at the specified scope in the program. The L value specifies a loop
5555 /// nest to evaluate the expression at, where null is the top-level or a
5556 /// specified loop is immediately inside of the loop.
5558 /// This method can be used to compute the exit value for a variable defined
5559 /// in a loop by querying what the value will hold in the parent loop.
5561 /// In the case that a relevant loop exit value cannot be computed, the
5562 /// original value V is returned.
5563 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
5564 // Check to see if we've folded this expression at this loop before.
5565 SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values = ValuesAtScopes[V];
5566 for (unsigned u = 0; u < Values.size(); u++) {
5567 if (Values[u].first == L)
5568 return Values[u].second ? Values[u].second : V;
5570 Values.push_back(std::make_pair(L, static_cast<const SCEV *>(nullptr)));
5571 // Otherwise compute it.
5572 const SCEV *C = computeSCEVAtScope(V, L);
5573 SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values2 = ValuesAtScopes[V];
5574 for (unsigned u = Values2.size(); u > 0; u--) {
5575 if (Values2[u - 1].first == L) {
5576 Values2[u - 1].second = C;
5583 /// This builds up a Constant using the ConstantExpr interface. That way, we
5584 /// will return Constants for objects which aren't represented by a
5585 /// SCEVConstant, because SCEVConstant is restricted to ConstantInt.
5586 /// Returns NULL if the SCEV isn't representable as a Constant.
5587 static Constant *BuildConstantFromSCEV(const SCEV *V) {
5588 switch (static_cast<SCEVTypes>(V->getSCEVType())) {
5589 case scCouldNotCompute:
5593 return cast<SCEVConstant>(V)->getValue();
5595 return dyn_cast<Constant>(cast<SCEVUnknown>(V)->getValue());
5596 case scSignExtend: {
5597 const SCEVSignExtendExpr *SS = cast<SCEVSignExtendExpr>(V);
5598 if (Constant *CastOp = BuildConstantFromSCEV(SS->getOperand()))
5599 return ConstantExpr::getSExt(CastOp, SS->getType());
5602 case scZeroExtend: {
5603 const SCEVZeroExtendExpr *SZ = cast<SCEVZeroExtendExpr>(V);
5604 if (Constant *CastOp = BuildConstantFromSCEV(SZ->getOperand()))
5605 return ConstantExpr::getZExt(CastOp, SZ->getType());
5609 const SCEVTruncateExpr *ST = cast<SCEVTruncateExpr>(V);
5610 if (Constant *CastOp = BuildConstantFromSCEV(ST->getOperand()))
5611 return ConstantExpr::getTrunc(CastOp, ST->getType());
5615 const SCEVAddExpr *SA = cast<SCEVAddExpr>(V);
5616 if (Constant *C = BuildConstantFromSCEV(SA->getOperand(0))) {
5617 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
5618 unsigned AS = PTy->getAddressSpace();
5619 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
5620 C = ConstantExpr::getBitCast(C, DestPtrTy);
5622 for (unsigned i = 1, e = SA->getNumOperands(); i != e; ++i) {
5623 Constant *C2 = BuildConstantFromSCEV(SA->getOperand(i));
5624 if (!C2) return nullptr;
5627 if (!C->getType()->isPointerTy() && C2->getType()->isPointerTy()) {
5628 unsigned AS = C2->getType()->getPointerAddressSpace();
5630 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
5631 // The offsets have been converted to bytes. We can add bytes to an
5632 // i8* by GEP with the byte count in the first index.
5633 C = ConstantExpr::getBitCast(C, DestPtrTy);
5636 // Don't bother trying to sum two pointers. We probably can't
5637 // statically compute a load that results from it anyway.
5638 if (C2->getType()->isPointerTy())
5641 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
5642 if (PTy->getElementType()->isStructTy())
5643 C2 = ConstantExpr::getIntegerCast(
5644 C2, Type::getInt32Ty(C->getContext()), true);
5645 C = ConstantExpr::getGetElementPtr(C, C2);
5647 C = ConstantExpr::getAdd(C, C2);
5654 const SCEVMulExpr *SM = cast<SCEVMulExpr>(V);
5655 if (Constant *C = BuildConstantFromSCEV(SM->getOperand(0))) {
5656 // Don't bother with pointers at all.
5657 if (C->getType()->isPointerTy()) return nullptr;
5658 for (unsigned i = 1, e = SM->getNumOperands(); i != e; ++i) {
5659 Constant *C2 = BuildConstantFromSCEV(SM->getOperand(i));
5660 if (!C2 || C2->getType()->isPointerTy()) return nullptr;
5661 C = ConstantExpr::getMul(C, C2);
5668 const SCEVUDivExpr *SU = cast<SCEVUDivExpr>(V);
5669 if (Constant *LHS = BuildConstantFromSCEV(SU->getLHS()))
5670 if (Constant *RHS = BuildConstantFromSCEV(SU->getRHS()))
5671 if (LHS->getType() == RHS->getType())
5672 return ConstantExpr::getUDiv(LHS, RHS);
5677 break; // TODO: smax, umax.
5682 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
5683 if (isa<SCEVConstant>(V)) return V;
5685 // If this instruction is evolved from a constant-evolving PHI, compute the
5686 // exit value from the loop without using SCEVs.
5687 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
5688 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
5689 const Loop *LI = (*this->LI)[I->getParent()];
5690 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
5691 if (PHINode *PN = dyn_cast<PHINode>(I))
5692 if (PN->getParent() == LI->getHeader()) {
5693 // Okay, there is no closed form solution for the PHI node. Check
5694 // to see if the loop that contains it has a known backedge-taken
5695 // count. If so, we may be able to force computation of the exit
5697 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
5698 if (const SCEVConstant *BTCC =
5699 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
5700 // Okay, we know how many times the containing loop executes. If
5701 // this is a constant evolving PHI node, get the final value at
5702 // the specified iteration number.
5703 Constant *RV = getConstantEvolutionLoopExitValue(PN,
5704 BTCC->getValue()->getValue(),
5706 if (RV) return getSCEV(RV);
5710 // Okay, this is an expression that we cannot symbolically evaluate
5711 // into a SCEV. Check to see if it's possible to symbolically evaluate
5712 // the arguments into constants, and if so, try to constant propagate the
5713 // result. This is particularly useful for computing loop exit values.
5714 if (CanConstantFold(I)) {
5715 SmallVector<Constant *, 4> Operands;
5716 bool MadeImprovement = false;
5717 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
5718 Value *Op = I->getOperand(i);
5719 if (Constant *C = dyn_cast<Constant>(Op)) {
5720 Operands.push_back(C);
5724 // If any of the operands is non-constant and if they are
5725 // non-integer and non-pointer, don't even try to analyze them
5726 // with scev techniques.
5727 if (!isSCEVable(Op->getType()))
5730 const SCEV *OrigV = getSCEV(Op);
5731 const SCEV *OpV = getSCEVAtScope(OrigV, L);
5732 MadeImprovement |= OrigV != OpV;
5734 Constant *C = BuildConstantFromSCEV(OpV);
5736 if (C->getType() != Op->getType())
5737 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
5741 Operands.push_back(C);
5744 // Check to see if getSCEVAtScope actually made an improvement.
5745 if (MadeImprovement) {
5746 Constant *C = nullptr;
5747 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
5748 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
5749 Operands[0], Operands[1], DL,
5751 else if (const LoadInst *LI = dyn_cast<LoadInst>(I)) {
5752 if (!LI->isVolatile())
5753 C = ConstantFoldLoadFromConstPtr(Operands[0], DL);
5755 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
5763 // This is some other type of SCEVUnknown, just return it.
5767 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
5768 // Avoid performing the look-up in the common case where the specified
5769 // expression has no loop-variant portions.
5770 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
5771 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
5772 if (OpAtScope != Comm->getOperand(i)) {
5773 // Okay, at least one of these operands is loop variant but might be
5774 // foldable. Build a new instance of the folded commutative expression.
5775 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
5776 Comm->op_begin()+i);
5777 NewOps.push_back(OpAtScope);
5779 for (++i; i != e; ++i) {
5780 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
5781 NewOps.push_back(OpAtScope);
5783 if (isa<SCEVAddExpr>(Comm))
5784 return getAddExpr(NewOps);
5785 if (isa<SCEVMulExpr>(Comm))
5786 return getMulExpr(NewOps);
5787 if (isa<SCEVSMaxExpr>(Comm))
5788 return getSMaxExpr(NewOps);
5789 if (isa<SCEVUMaxExpr>(Comm))
5790 return getUMaxExpr(NewOps);
5791 llvm_unreachable("Unknown commutative SCEV type!");
5794 // If we got here, all operands are loop invariant.
5798 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
5799 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
5800 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
5801 if (LHS == Div->getLHS() && RHS == Div->getRHS())
5802 return Div; // must be loop invariant
5803 return getUDivExpr(LHS, RHS);
5806 // If this is a loop recurrence for a loop that does not contain L, then we
5807 // are dealing with the final value computed by the loop.
5808 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
5809 // First, attempt to evaluate each operand.
5810 // Avoid performing the look-up in the common case where the specified
5811 // expression has no loop-variant portions.
5812 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
5813 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
5814 if (OpAtScope == AddRec->getOperand(i))
5817 // Okay, at least one of these operands is loop variant but might be
5818 // foldable. Build a new instance of the folded commutative expression.
5819 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(),
5820 AddRec->op_begin()+i);
5821 NewOps.push_back(OpAtScope);
5822 for (++i; i != e; ++i)
5823 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
5825 const SCEV *FoldedRec =
5826 getAddRecExpr(NewOps, AddRec->getLoop(),
5827 AddRec->getNoWrapFlags(SCEV::FlagNW));
5828 AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec);
5829 // The addrec may be folded to a nonrecurrence, for example, if the
5830 // induction variable is multiplied by zero after constant folding. Go
5831 // ahead and return the folded value.
5837 // If the scope is outside the addrec's loop, evaluate it by using the
5838 // loop exit value of the addrec.
5839 if (!AddRec->getLoop()->contains(L)) {
5840 // To evaluate this recurrence, we need to know how many times the AddRec
5841 // loop iterates. Compute this now.
5842 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
5843 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
5845 // Then, evaluate the AddRec.
5846 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
5852 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
5853 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5854 if (Op == Cast->getOperand())
5855 return Cast; // must be loop invariant
5856 return getZeroExtendExpr(Op, Cast->getType());
5859 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
5860 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5861 if (Op == Cast->getOperand())
5862 return Cast; // must be loop invariant
5863 return getSignExtendExpr(Op, Cast->getType());
5866 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
5867 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5868 if (Op == Cast->getOperand())
5869 return Cast; // must be loop invariant
5870 return getTruncateExpr(Op, Cast->getType());
5873 llvm_unreachable("Unknown SCEV type!");
5876 /// getSCEVAtScope - This is a convenience function which does
5877 /// getSCEVAtScope(getSCEV(V), L).
5878 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
5879 return getSCEVAtScope(getSCEV(V), L);
5882 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
5883 /// following equation:
5885 /// A * X = B (mod N)
5887 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
5888 /// A and B isn't important.
5890 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
5891 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
5892 ScalarEvolution &SE) {
5893 uint32_t BW = A.getBitWidth();
5894 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
5895 assert(A != 0 && "A must be non-zero.");
5899 // The gcd of A and N may have only one prime factor: 2. The number of
5900 // trailing zeros in A is its multiplicity
5901 uint32_t Mult2 = A.countTrailingZeros();
5904 // 2. Check if B is divisible by D.
5906 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
5907 // is not less than multiplicity of this prime factor for D.
5908 if (B.countTrailingZeros() < Mult2)
5909 return SE.getCouldNotCompute();
5911 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
5914 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
5915 // bit width during computations.
5916 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
5917 APInt Mod(BW + 1, 0);
5918 Mod.setBit(BW - Mult2); // Mod = N / D
5919 APInt I = AD.multiplicativeInverse(Mod);
5921 // 4. Compute the minimum unsigned root of the equation:
5922 // I * (B / D) mod (N / D)
5923 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
5925 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
5927 return SE.getConstant(Result.trunc(BW));
5930 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
5931 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
5932 /// might be the same) or two SCEVCouldNotCompute objects.
5934 static std::pair<const SCEV *,const SCEV *>
5935 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
5936 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
5937 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
5938 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
5939 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
5941 // We currently can only solve this if the coefficients are constants.
5942 if (!LC || !MC || !NC) {
5943 const SCEV *CNC = SE.getCouldNotCompute();
5944 return std::make_pair(CNC, CNC);
5947 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
5948 const APInt &L = LC->getValue()->getValue();
5949 const APInt &M = MC->getValue()->getValue();
5950 const APInt &N = NC->getValue()->getValue();
5951 APInt Two(BitWidth, 2);
5952 APInt Four(BitWidth, 4);
5955 using namespace APIntOps;
5957 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
5958 // The B coefficient is M-N/2
5962 // The A coefficient is N/2
5963 APInt A(N.sdiv(Two));
5965 // Compute the B^2-4ac term.
5968 SqrtTerm -= Four * (A * C);
5970 if (SqrtTerm.isNegative()) {
5971 // The loop is provably infinite.
5972 const SCEV *CNC = SE.getCouldNotCompute();
5973 return std::make_pair(CNC, CNC);
5976 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
5977 // integer value or else APInt::sqrt() will assert.
5978 APInt SqrtVal(SqrtTerm.sqrt());
5980 // Compute the two solutions for the quadratic formula.
5981 // The divisions must be performed as signed divisions.
5984 if (TwoA.isMinValue()) {
5985 const SCEV *CNC = SE.getCouldNotCompute();
5986 return std::make_pair(CNC, CNC);
5989 LLVMContext &Context = SE.getContext();
5991 ConstantInt *Solution1 =
5992 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
5993 ConstantInt *Solution2 =
5994 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
5996 return std::make_pair(SE.getConstant(Solution1),
5997 SE.getConstant(Solution2));
5998 } // end APIntOps namespace
6001 /// HowFarToZero - Return the number of times a backedge comparing the specified
6002 /// value to zero will execute. If not computable, return CouldNotCompute.
6004 /// This is only used for loops with a "x != y" exit test. The exit condition is
6005 /// now expressed as a single expression, V = x-y. So the exit test is
6006 /// effectively V != 0. We know and take advantage of the fact that this
6007 /// expression only being used in a comparison by zero context.
6008 ScalarEvolution::ExitLimit
6009 ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L, bool ControlsExit) {
6010 // If the value is a constant
6011 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
6012 // If the value is already zero, the branch will execute zero times.
6013 if (C->getValue()->isZero()) return C;
6014 return getCouldNotCompute(); // Otherwise it will loop infinitely.
6017 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
6018 if (!AddRec || AddRec->getLoop() != L)
6019 return getCouldNotCompute();
6021 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
6022 // the quadratic equation to solve it.
6023 if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
6024 std::pair<const SCEV *,const SCEV *> Roots =
6025 SolveQuadraticEquation(AddRec, *this);
6026 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
6027 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
6030 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1
6031 << " sol#2: " << *R2 << "\n";
6033 // Pick the smallest positive root value.
6034 if (ConstantInt *CB =
6035 dyn_cast<ConstantInt>(ConstantExpr::getICmp(CmpInst::ICMP_ULT,
6038 if (CB->getZExtValue() == false)
6039 std::swap(R1, R2); // R1 is the minimum root now.
6041 // We can only use this value if the chrec ends up with an exact zero
6042 // value at this index. When solving for "X*X != 5", for example, we
6043 // should not accept a root of 2.
6044 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
6046 return R1; // We found a quadratic root!
6049 return getCouldNotCompute();
6052 // Otherwise we can only handle this if it is affine.
6053 if (!AddRec->isAffine())
6054 return getCouldNotCompute();
6056 // If this is an affine expression, the execution count of this branch is
6057 // the minimum unsigned root of the following equation:
6059 // Start + Step*N = 0 (mod 2^BW)
6063 // Step*N = -Start (mod 2^BW)
6065 // where BW is the common bit width of Start and Step.
6067 // Get the initial value for the loop.
6068 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
6069 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
6071 // For now we handle only constant steps.
6073 // TODO: Handle a nonconstant Step given AddRec<NUW>. If the
6074 // AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap
6075 // to 0, it must be counting down to equal 0. Consequently, N = Start / -Step.
6076 // We have not yet seen any such cases.
6077 const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step);
6078 if (!StepC || StepC->getValue()->equalsInt(0))
6079 return getCouldNotCompute();
6081 // For positive steps (counting up until unsigned overflow):
6082 // N = -Start/Step (as unsigned)
6083 // For negative steps (counting down to zero):
6085 // First compute the unsigned distance from zero in the direction of Step.
6086 bool CountDown = StepC->getValue()->getValue().isNegative();
6087 const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start);
6089 // Handle unitary steps, which cannot wraparound.
6090 // 1*N = -Start; -1*N = Start (mod 2^BW), so:
6091 // N = Distance (as unsigned)
6092 if (StepC->getValue()->equalsInt(1) || StepC->getValue()->isAllOnesValue()) {
6093 ConstantRange CR = getUnsignedRange(Start);
6094 const SCEV *MaxBECount;
6095 if (!CountDown && CR.getUnsignedMin().isMinValue())
6096 // When counting up, the worst starting value is 1, not 0.
6097 MaxBECount = CR.getUnsignedMax().isMinValue()
6098 ? getConstant(APInt::getMinValue(CR.getBitWidth()))
6099 : getConstant(APInt::getMaxValue(CR.getBitWidth()));
6101 MaxBECount = getConstant(CountDown ? CR.getUnsignedMax()
6102 : -CR.getUnsignedMin());
6103 return ExitLimit(Distance, MaxBECount);
6106 // As a special case, handle the instance where Step is a positive power of
6107 // two. In this case, determining whether Step divides Distance evenly can be
6108 // done by counting and comparing the number of trailing zeros of Step and
6111 const APInt &StepV = StepC->getValue()->getValue();
6112 // StepV.isPowerOf2() returns true if StepV is an positive power of two. It
6113 // also returns true if StepV is maximally negative (eg, INT_MIN), but that
6114 // case is not handled as this code is guarded by !CountDown.
6115 if (StepV.isPowerOf2() &&
6116 GetMinTrailingZeros(Distance) >= StepV.countTrailingZeros())
6117 return getUDivExactExpr(Distance, Step);
6120 // If the condition controls loop exit (the loop exits only if the expression
6121 // is true) and the addition is no-wrap we can use unsigned divide to
6122 // compute the backedge count. In this case, the step may not divide the
6123 // distance, but we don't care because if the condition is "missed" the loop
6124 // will have undefined behavior due to wrapping.
6125 if (ControlsExit && AddRec->getNoWrapFlags(SCEV::FlagNW)) {
6127 getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
6128 return ExitLimit(Exact, Exact);
6131 // Then, try to solve the above equation provided that Start is constant.
6132 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
6133 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
6134 -StartC->getValue()->getValue(),
6136 return getCouldNotCompute();
6139 /// HowFarToNonZero - Return the number of times a backedge checking the
6140 /// specified value for nonzero will execute. If not computable, return
6142 ScalarEvolution::ExitLimit
6143 ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
6144 // Loops that look like: while (X == 0) are very strange indeed. We don't
6145 // handle them yet except for the trivial case. This could be expanded in the
6146 // future as needed.
6148 // If the value is a constant, check to see if it is known to be non-zero
6149 // already. If so, the backedge will execute zero times.
6150 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
6151 if (!C->getValue()->isNullValue())
6152 return getConstant(C->getType(), 0);
6153 return getCouldNotCompute(); // Otherwise it will loop infinitely.
6156 // We could implement others, but I really doubt anyone writes loops like
6157 // this, and if they did, they would already be constant folded.
6158 return getCouldNotCompute();
6161 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
6162 /// (which may not be an immediate predecessor) which has exactly one
6163 /// successor from which BB is reachable, or null if no such block is
6166 std::pair<BasicBlock *, BasicBlock *>
6167 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
6168 // If the block has a unique predecessor, then there is no path from the
6169 // predecessor to the block that does not go through the direct edge
6170 // from the predecessor to the block.
6171 if (BasicBlock *Pred = BB->getSinglePredecessor())
6172 return std::make_pair(Pred, BB);
6174 // A loop's header is defined to be a block that dominates the loop.
6175 // If the header has a unique predecessor outside the loop, it must be
6176 // a block that has exactly one successor that can reach the loop.
6177 if (Loop *L = LI->getLoopFor(BB))
6178 return std::make_pair(L->getLoopPredecessor(), L->getHeader());
6180 return std::pair<BasicBlock *, BasicBlock *>();
6183 /// HasSameValue - SCEV structural equivalence is usually sufficient for
6184 /// testing whether two expressions are equal, however for the purposes of
6185 /// looking for a condition guarding a loop, it can be useful to be a little
6186 /// more general, since a front-end may have replicated the controlling
6189 static bool HasSameValue(const SCEV *A, const SCEV *B) {
6190 // Quick check to see if they are the same SCEV.
6191 if (A == B) return true;
6193 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
6194 // two different instructions with the same value. Check for this case.
6195 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
6196 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
6197 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
6198 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
6199 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory())
6202 // Otherwise assume they may have a different value.
6206 /// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with
6207 /// predicate Pred. Return true iff any changes were made.
6209 bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
6210 const SCEV *&LHS, const SCEV *&RHS,
6212 bool Changed = false;
6214 // If we hit the max recursion limit bail out.
6218 // Canonicalize a constant to the right side.
6219 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
6220 // Check for both operands constant.
6221 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
6222 if (ConstantExpr::getICmp(Pred,
6224 RHSC->getValue())->isNullValue())
6225 goto trivially_false;
6227 goto trivially_true;
6229 // Otherwise swap the operands to put the constant on the right.
6230 std::swap(LHS, RHS);
6231 Pred = ICmpInst::getSwappedPredicate(Pred);
6235 // If we're comparing an addrec with a value which is loop-invariant in the
6236 // addrec's loop, put the addrec on the left. Also make a dominance check,
6237 // as both operands could be addrecs loop-invariant in each other's loop.
6238 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
6239 const Loop *L = AR->getLoop();
6240 if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) {
6241 std::swap(LHS, RHS);
6242 Pred = ICmpInst::getSwappedPredicate(Pred);
6247 // If there's a constant operand, canonicalize comparisons with boundary
6248 // cases, and canonicalize *-or-equal comparisons to regular comparisons.
6249 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
6250 const APInt &RA = RC->getValue()->getValue();
6252 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6253 case ICmpInst::ICMP_EQ:
6254 case ICmpInst::ICMP_NE:
6255 // Fold ((-1) * %a) + %b == 0 (equivalent to %b-%a == 0) into %a == %b.
6257 if (const SCEVAddExpr *AE = dyn_cast<SCEVAddExpr>(LHS))
6258 if (const SCEVMulExpr *ME = dyn_cast<SCEVMulExpr>(AE->getOperand(0)))
6259 if (AE->getNumOperands() == 2 && ME->getNumOperands() == 2 &&
6260 ME->getOperand(0)->isAllOnesValue()) {
6261 RHS = AE->getOperand(1);
6262 LHS = ME->getOperand(1);
6266 case ICmpInst::ICMP_UGE:
6267 if ((RA - 1).isMinValue()) {
6268 Pred = ICmpInst::ICMP_NE;
6269 RHS = getConstant(RA - 1);
6273 if (RA.isMaxValue()) {
6274 Pred = ICmpInst::ICMP_EQ;
6278 if (RA.isMinValue()) goto trivially_true;
6280 Pred = ICmpInst::ICMP_UGT;
6281 RHS = getConstant(RA - 1);
6284 case ICmpInst::ICMP_ULE:
6285 if ((RA + 1).isMaxValue()) {
6286 Pred = ICmpInst::ICMP_NE;
6287 RHS = getConstant(RA + 1);
6291 if (RA.isMinValue()) {
6292 Pred = ICmpInst::ICMP_EQ;
6296 if (RA.isMaxValue()) goto trivially_true;
6298 Pred = ICmpInst::ICMP_ULT;
6299 RHS = getConstant(RA + 1);
6302 case ICmpInst::ICMP_SGE:
6303 if ((RA - 1).isMinSignedValue()) {
6304 Pred = ICmpInst::ICMP_NE;
6305 RHS = getConstant(RA - 1);
6309 if (RA.isMaxSignedValue()) {
6310 Pred = ICmpInst::ICMP_EQ;
6314 if (RA.isMinSignedValue()) goto trivially_true;
6316 Pred = ICmpInst::ICMP_SGT;
6317 RHS = getConstant(RA - 1);
6320 case ICmpInst::ICMP_SLE:
6321 if ((RA + 1).isMaxSignedValue()) {
6322 Pred = ICmpInst::ICMP_NE;
6323 RHS = getConstant(RA + 1);
6327 if (RA.isMinSignedValue()) {
6328 Pred = ICmpInst::ICMP_EQ;
6332 if (RA.isMaxSignedValue()) goto trivially_true;
6334 Pred = ICmpInst::ICMP_SLT;
6335 RHS = getConstant(RA + 1);
6338 case ICmpInst::ICMP_UGT:
6339 if (RA.isMinValue()) {
6340 Pred = ICmpInst::ICMP_NE;
6344 if ((RA + 1).isMaxValue()) {
6345 Pred = ICmpInst::ICMP_EQ;
6346 RHS = getConstant(RA + 1);
6350 if (RA.isMaxValue()) goto trivially_false;
6352 case ICmpInst::ICMP_ULT:
6353 if (RA.isMaxValue()) {
6354 Pred = ICmpInst::ICMP_NE;
6358 if ((RA - 1).isMinValue()) {
6359 Pred = ICmpInst::ICMP_EQ;
6360 RHS = getConstant(RA - 1);
6364 if (RA.isMinValue()) goto trivially_false;
6366 case ICmpInst::ICMP_SGT:
6367 if (RA.isMinSignedValue()) {
6368 Pred = ICmpInst::ICMP_NE;
6372 if ((RA + 1).isMaxSignedValue()) {
6373 Pred = ICmpInst::ICMP_EQ;
6374 RHS = getConstant(RA + 1);
6378 if (RA.isMaxSignedValue()) goto trivially_false;
6380 case ICmpInst::ICMP_SLT:
6381 if (RA.isMaxSignedValue()) {
6382 Pred = ICmpInst::ICMP_NE;
6386 if ((RA - 1).isMinSignedValue()) {
6387 Pred = ICmpInst::ICMP_EQ;
6388 RHS = getConstant(RA - 1);
6392 if (RA.isMinSignedValue()) goto trivially_false;
6397 // Check for obvious equality.
6398 if (HasSameValue(LHS, RHS)) {
6399 if (ICmpInst::isTrueWhenEqual(Pred))
6400 goto trivially_true;
6401 if (ICmpInst::isFalseWhenEqual(Pred))
6402 goto trivially_false;
6405 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
6406 // adding or subtracting 1 from one of the operands.
6408 case ICmpInst::ICMP_SLE:
6409 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) {
6410 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
6412 Pred = ICmpInst::ICMP_SLT;
6414 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) {
6415 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
6417 Pred = ICmpInst::ICMP_SLT;
6421 case ICmpInst::ICMP_SGE:
6422 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) {
6423 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
6425 Pred = ICmpInst::ICMP_SGT;
6427 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) {
6428 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
6430 Pred = ICmpInst::ICMP_SGT;
6434 case ICmpInst::ICMP_ULE:
6435 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) {
6436 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
6438 Pred = ICmpInst::ICMP_ULT;
6440 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) {
6441 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
6443 Pred = ICmpInst::ICMP_ULT;
6447 case ICmpInst::ICMP_UGE:
6448 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) {
6449 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
6451 Pred = ICmpInst::ICMP_UGT;
6453 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) {
6454 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
6456 Pred = ICmpInst::ICMP_UGT;
6464 // TODO: More simplifications are possible here.
6466 // Recursively simplify until we either hit a recursion limit or nothing
6469 return SimplifyICmpOperands(Pred, LHS, RHS, Depth+1);
6475 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
6476 Pred = ICmpInst::ICMP_EQ;
6481 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
6482 Pred = ICmpInst::ICMP_NE;
6486 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
6487 return getSignedRange(S).getSignedMax().isNegative();
6490 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
6491 return getSignedRange(S).getSignedMin().isStrictlyPositive();
6494 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
6495 return !getSignedRange(S).getSignedMin().isNegative();
6498 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
6499 return !getSignedRange(S).getSignedMax().isStrictlyPositive();
6502 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
6503 return isKnownNegative(S) || isKnownPositive(S);
6506 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
6507 const SCEV *LHS, const SCEV *RHS) {
6508 // Canonicalize the inputs first.
6509 (void)SimplifyICmpOperands(Pred, LHS, RHS);
6511 // If LHS or RHS is an addrec, check to see if the condition is true in
6512 // every iteration of the loop.
6513 // If LHS and RHS are both addrec, both conditions must be true in
6514 // every iteration of the loop.
6515 const SCEVAddRecExpr *LAR = dyn_cast<SCEVAddRecExpr>(LHS);
6516 const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS);
6517 bool LeftGuarded = false;
6518 bool RightGuarded = false;
6520 const Loop *L = LAR->getLoop();
6521 if (isLoopEntryGuardedByCond(L, Pred, LAR->getStart(), RHS) &&
6522 isLoopBackedgeGuardedByCond(L, Pred, LAR->getPostIncExpr(*this), RHS)) {
6523 if (!RAR) return true;
6528 const Loop *L = RAR->getLoop();
6529 if (isLoopEntryGuardedByCond(L, Pred, LHS, RAR->getStart()) &&
6530 isLoopBackedgeGuardedByCond(L, Pred, LHS, RAR->getPostIncExpr(*this))) {
6531 if (!LAR) return true;
6532 RightGuarded = true;
6535 if (LeftGuarded && RightGuarded)
6538 // Otherwise see what can be done with known constant ranges.
6539 return isKnownPredicateWithRanges(Pred, LHS, RHS);
6543 ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred,
6544 const SCEV *LHS, const SCEV *RHS) {
6545 if (HasSameValue(LHS, RHS))
6546 return ICmpInst::isTrueWhenEqual(Pred);
6548 // This code is split out from isKnownPredicate because it is called from
6549 // within isLoopEntryGuardedByCond.
6552 llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6553 case ICmpInst::ICMP_SGT:
6554 std::swap(LHS, RHS);
6555 case ICmpInst::ICMP_SLT: {
6556 ConstantRange LHSRange = getSignedRange(LHS);
6557 ConstantRange RHSRange = getSignedRange(RHS);
6558 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
6560 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
6564 case ICmpInst::ICMP_SGE:
6565 std::swap(LHS, RHS);
6566 case ICmpInst::ICMP_SLE: {
6567 ConstantRange LHSRange = getSignedRange(LHS);
6568 ConstantRange RHSRange = getSignedRange(RHS);
6569 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
6571 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
6575 case ICmpInst::ICMP_UGT:
6576 std::swap(LHS, RHS);
6577 case ICmpInst::ICMP_ULT: {
6578 ConstantRange LHSRange = getUnsignedRange(LHS);
6579 ConstantRange RHSRange = getUnsignedRange(RHS);
6580 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
6582 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
6586 case ICmpInst::ICMP_UGE:
6587 std::swap(LHS, RHS);
6588 case ICmpInst::ICMP_ULE: {
6589 ConstantRange LHSRange = getUnsignedRange(LHS);
6590 ConstantRange RHSRange = getUnsignedRange(RHS);
6591 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
6593 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
6597 case ICmpInst::ICMP_NE: {
6598 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
6600 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
6603 const SCEV *Diff = getMinusSCEV(LHS, RHS);
6604 if (isKnownNonZero(Diff))
6608 case ICmpInst::ICMP_EQ:
6609 // The check at the top of the function catches the case where
6610 // the values are known to be equal.
6616 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
6617 /// protected by a conditional between LHS and RHS. This is used to
6618 /// to eliminate casts.
6620 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
6621 ICmpInst::Predicate Pred,
6622 const SCEV *LHS, const SCEV *RHS) {
6623 // Interpret a null as meaning no loop, where there is obviously no guard
6624 // (interprocedural conditions notwithstanding).
6625 if (!L) return true;
6627 if (isKnownPredicateWithRanges(Pred, LHS, RHS)) return true;
6629 BasicBlock *Latch = L->getLoopLatch();
6633 BranchInst *LoopContinuePredicate =
6634 dyn_cast<BranchInst>(Latch->getTerminator());
6635 if (LoopContinuePredicate && LoopContinuePredicate->isConditional() &&
6636 isImpliedCond(Pred, LHS, RHS,
6637 LoopContinuePredicate->getCondition(),
6638 LoopContinuePredicate->getSuccessor(0) != L->getHeader()))
6641 // Check conditions due to any @llvm.assume intrinsics.
6642 for (auto &AssumeVH : AC->assumptions()) {
6645 auto *CI = cast<CallInst>(AssumeVH);
6646 if (!DT->dominates(CI, Latch->getTerminator()))
6649 if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false))
6656 /// isLoopEntryGuardedByCond - Test whether entry to the loop is protected
6657 /// by a conditional between LHS and RHS. This is used to help avoid max
6658 /// expressions in loop trip counts, and to eliminate casts.
6660 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
6661 ICmpInst::Predicate Pred,
6662 const SCEV *LHS, const SCEV *RHS) {
6663 // Interpret a null as meaning no loop, where there is obviously no guard
6664 // (interprocedural conditions notwithstanding).
6665 if (!L) return false;
6667 if (isKnownPredicateWithRanges(Pred, LHS, RHS)) return true;
6669 // Starting at the loop predecessor, climb up the predecessor chain, as long
6670 // as there are predecessors that can be found that have unique successors
6671 // leading to the original header.
6672 for (std::pair<BasicBlock *, BasicBlock *>
6673 Pair(L->getLoopPredecessor(), L->getHeader());
6675 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
6677 BranchInst *LoopEntryPredicate =
6678 dyn_cast<BranchInst>(Pair.first->getTerminator());
6679 if (!LoopEntryPredicate ||
6680 LoopEntryPredicate->isUnconditional())
6683 if (isImpliedCond(Pred, LHS, RHS,
6684 LoopEntryPredicate->getCondition(),
6685 LoopEntryPredicate->getSuccessor(0) != Pair.second))
6689 // Check conditions due to any @llvm.assume intrinsics.
6690 for (auto &AssumeVH : AC->assumptions()) {
6693 auto *CI = cast<CallInst>(AssumeVH);
6694 if (!DT->dominates(CI, L->getHeader()))
6697 if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false))
6704 /// RAII wrapper to prevent recursive application of isImpliedCond.
6705 /// ScalarEvolution's PendingLoopPredicates set must be empty unless we are
6706 /// currently evaluating isImpliedCond.
6707 struct MarkPendingLoopPredicate {
6709 DenseSet<Value*> &LoopPreds;
6712 MarkPendingLoopPredicate(Value *C, DenseSet<Value*> &LP)
6713 : Cond(C), LoopPreds(LP) {
6714 Pending = !LoopPreds.insert(Cond).second;
6716 ~MarkPendingLoopPredicate() {
6718 LoopPreds.erase(Cond);
6722 /// isImpliedCond - Test whether the condition described by Pred, LHS,
6723 /// and RHS is true whenever the given Cond value evaluates to true.
6724 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred,
6725 const SCEV *LHS, const SCEV *RHS,
6726 Value *FoundCondValue,
6728 MarkPendingLoopPredicate Mark(FoundCondValue, PendingLoopPredicates);
6732 // Recursively handle And and Or conditions.
6733 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) {
6734 if (BO->getOpcode() == Instruction::And) {
6736 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
6737 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
6738 } else if (BO->getOpcode() == Instruction::Or) {
6740 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
6741 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
6745 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue);
6746 if (!ICI) return false;
6748 // Bail if the ICmp's operands' types are wider than the needed type
6749 // before attempting to call getSCEV on them. This avoids infinite
6750 // recursion, since the analysis of widening casts can require loop
6751 // exit condition information for overflow checking, which would
6753 if (getTypeSizeInBits(LHS->getType()) <
6754 getTypeSizeInBits(ICI->getOperand(0)->getType()))
6757 // Now that we found a conditional branch that dominates the loop or controls
6758 // the loop latch. Check to see if it is the comparison we are looking for.
6759 ICmpInst::Predicate FoundPred;
6761 FoundPred = ICI->getInversePredicate();
6763 FoundPred = ICI->getPredicate();
6765 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
6766 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
6768 // Balance the types. The case where FoundLHS' type is wider than
6769 // LHS' type is checked for above.
6770 if (getTypeSizeInBits(LHS->getType()) >
6771 getTypeSizeInBits(FoundLHS->getType())) {
6772 if (CmpInst::isSigned(FoundPred)) {
6773 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
6774 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
6776 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
6777 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
6781 // Canonicalize the query to match the way instcombine will have
6782 // canonicalized the comparison.
6783 if (SimplifyICmpOperands(Pred, LHS, RHS))
6785 return CmpInst::isTrueWhenEqual(Pred);
6786 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
6787 if (FoundLHS == FoundRHS)
6788 return CmpInst::isFalseWhenEqual(FoundPred);
6790 // Check to see if we can make the LHS or RHS match.
6791 if (LHS == FoundRHS || RHS == FoundLHS) {
6792 if (isa<SCEVConstant>(RHS)) {
6793 std::swap(FoundLHS, FoundRHS);
6794 FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
6796 std::swap(LHS, RHS);
6797 Pred = ICmpInst::getSwappedPredicate(Pred);
6801 // Check whether the found predicate is the same as the desired predicate.
6802 if (FoundPred == Pred)
6803 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
6805 // Check whether swapping the found predicate makes it the same as the
6806 // desired predicate.
6807 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
6808 if (isa<SCEVConstant>(RHS))
6809 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
6811 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
6812 RHS, LHS, FoundLHS, FoundRHS);
6815 // Check if we can make progress by sharpening ranges.
6816 if (FoundPred == ICmpInst::ICMP_NE &&
6817 (isa<SCEVConstant>(FoundLHS) || isa<SCEVConstant>(FoundRHS))) {
6819 const SCEVConstant *C = nullptr;
6820 const SCEV *V = nullptr;
6822 if (isa<SCEVConstant>(FoundLHS)) {
6823 C = cast<SCEVConstant>(FoundLHS);
6826 C = cast<SCEVConstant>(FoundRHS);
6830 // The guarding predicate tells us that C != V. If the known range
6831 // of V is [C, t), we can sharpen the range to [C + 1, t). The
6832 // range we consider has to correspond to same signedness as the
6833 // predicate we're interested in folding.
6835 APInt Min = ICmpInst::isSigned(Pred) ?
6836 getSignedRange(V).getSignedMin() : getUnsignedRange(V).getUnsignedMin();
6838 if (Min == C->getValue()->getValue()) {
6839 // Given (V >= Min && V != Min) we conclude V >= (Min + 1).
6840 // This is true even if (Min + 1) wraps around -- in case of
6841 // wraparound, (Min + 1) < Min, so (V >= Min => V >= (Min + 1)).
6843 APInt SharperMin = Min + 1;
6846 case ICmpInst::ICMP_SGE:
6847 case ICmpInst::ICMP_UGE:
6848 // We know V `Pred` SharperMin. If this implies LHS `Pred`
6850 if (isImpliedCondOperands(Pred, LHS, RHS, V,
6851 getConstant(SharperMin)))
6854 case ICmpInst::ICMP_SGT:
6855 case ICmpInst::ICMP_UGT:
6856 // We know from the range information that (V `Pred` Min ||
6857 // V == Min). We know from the guarding condition that !(V
6858 // == Min). This gives us
6860 // V `Pred` Min || V == Min && !(V == Min)
6863 // If V `Pred` Min implies LHS `Pred` RHS, we're done.
6865 if (isImpliedCondOperands(Pred, LHS, RHS, V, getConstant(Min)))
6875 // Check whether the actual condition is beyond sufficient.
6876 if (FoundPred == ICmpInst::ICMP_EQ)
6877 if (ICmpInst::isTrueWhenEqual(Pred))
6878 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
6880 if (Pred == ICmpInst::ICMP_NE)
6881 if (!ICmpInst::isTrueWhenEqual(FoundPred))
6882 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
6885 // Otherwise assume the worst.
6889 /// isImpliedCondOperands - Test whether the condition described by Pred,
6890 /// LHS, and RHS is true whenever the condition described by Pred, FoundLHS,
6891 /// and FoundRHS is true.
6892 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
6893 const SCEV *LHS, const SCEV *RHS,
6894 const SCEV *FoundLHS,
6895 const SCEV *FoundRHS) {
6896 return isImpliedCondOperandsHelper(Pred, LHS, RHS,
6897 FoundLHS, FoundRHS) ||
6898 // ~x < ~y --> x > y
6899 isImpliedCondOperandsHelper(Pred, LHS, RHS,
6900 getNotSCEV(FoundRHS),
6901 getNotSCEV(FoundLHS));
6905 /// If Expr computes ~A, return A else return nullptr
6906 static const SCEV *MatchNotExpr(const SCEV *Expr) {
6907 const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Expr);
6908 if (!Add || Add->getNumOperands() != 2) return nullptr;
6910 const SCEVConstant *AddLHS = dyn_cast<SCEVConstant>(Add->getOperand(0));
6911 if (!(AddLHS && AddLHS->getValue()->getValue().isAllOnesValue()))
6914 const SCEVMulExpr *AddRHS = dyn_cast<SCEVMulExpr>(Add->getOperand(1));
6915 if (!AddRHS || AddRHS->getNumOperands() != 2) return nullptr;
6917 const SCEVConstant *MulLHS = dyn_cast<SCEVConstant>(AddRHS->getOperand(0));
6918 if (!(MulLHS && MulLHS->getValue()->getValue().isAllOnesValue()))
6921 return AddRHS->getOperand(1);
6925 /// Is MaybeMaxExpr an SMax or UMax of Candidate and some other values?
6926 template<typename MaxExprType>
6927 static bool IsMaxConsistingOf(const SCEV *MaybeMaxExpr,
6928 const SCEV *Candidate) {
6929 const MaxExprType *MaxExpr = dyn_cast<MaxExprType>(MaybeMaxExpr);
6930 if (!MaxExpr) return false;
6932 auto It = std::find(MaxExpr->op_begin(), MaxExpr->op_end(), Candidate);
6933 return It != MaxExpr->op_end();
6937 /// Is MaybeMinExpr an SMin or UMin of Candidate and some other values?
6938 template<typename MaxExprType>
6939 static bool IsMinConsistingOf(ScalarEvolution &SE,
6940 const SCEV *MaybeMinExpr,
6941 const SCEV *Candidate) {
6942 const SCEV *MaybeMaxExpr = MatchNotExpr(MaybeMinExpr);
6946 return IsMaxConsistingOf<MaxExprType>(MaybeMaxExpr, SE.getNotSCEV(Candidate));
6950 /// Is LHS `Pred` RHS true on the virtue of LHS or RHS being a Min or Max
6952 static bool IsKnownPredicateViaMinOrMax(ScalarEvolution &SE,
6953 ICmpInst::Predicate Pred,
6954 const SCEV *LHS, const SCEV *RHS) {
6959 case ICmpInst::ICMP_SGE:
6960 std::swap(LHS, RHS);
6962 case ICmpInst::ICMP_SLE:
6965 IsMinConsistingOf<SCEVSMaxExpr>(SE, LHS, RHS) ||
6967 IsMaxConsistingOf<SCEVSMaxExpr>(RHS, LHS);
6969 case ICmpInst::ICMP_UGE:
6970 std::swap(LHS, RHS);
6972 case ICmpInst::ICMP_ULE:
6975 IsMinConsistingOf<SCEVUMaxExpr>(SE, LHS, RHS) ||
6977 IsMaxConsistingOf<SCEVUMaxExpr>(RHS, LHS);
6980 llvm_unreachable("covered switch fell through?!");
6983 /// isImpliedCondOperandsHelper - Test whether the condition described by
6984 /// Pred, LHS, and RHS is true whenever the condition described by Pred,
6985 /// FoundLHS, and FoundRHS is true.
6987 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
6988 const SCEV *LHS, const SCEV *RHS,
6989 const SCEV *FoundLHS,
6990 const SCEV *FoundRHS) {
6991 auto IsKnownPredicateFull =
6992 [this](ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS) {
6993 return isKnownPredicateWithRanges(Pred, LHS, RHS) ||
6994 IsKnownPredicateViaMinOrMax(*this, Pred, LHS, RHS);
6998 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6999 case ICmpInst::ICMP_EQ:
7000 case ICmpInst::ICMP_NE:
7001 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
7004 case ICmpInst::ICMP_SLT:
7005 case ICmpInst::ICMP_SLE:
7006 if (IsKnownPredicateFull(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
7007 IsKnownPredicateFull(ICmpInst::ICMP_SGE, RHS, FoundRHS))
7010 case ICmpInst::ICMP_SGT:
7011 case ICmpInst::ICMP_SGE:
7012 if (IsKnownPredicateFull(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
7013 IsKnownPredicateFull(ICmpInst::ICMP_SLE, RHS, FoundRHS))
7016 case ICmpInst::ICMP_ULT:
7017 case ICmpInst::ICMP_ULE:
7018 if (IsKnownPredicateFull(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
7019 IsKnownPredicateFull(ICmpInst::ICMP_UGE, RHS, FoundRHS))
7022 case ICmpInst::ICMP_UGT:
7023 case ICmpInst::ICMP_UGE:
7024 if (IsKnownPredicateFull(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
7025 IsKnownPredicateFull(ICmpInst::ICMP_ULE, RHS, FoundRHS))
7033 // Verify if an linear IV with positive stride can overflow when in a
7034 // less-than comparison, knowing the invariant term of the comparison, the
7035 // stride and the knowledge of NSW/NUW flags on the recurrence.
7036 bool ScalarEvolution::doesIVOverflowOnLT(const SCEV *RHS, const SCEV *Stride,
7037 bool IsSigned, bool NoWrap) {
7038 if (NoWrap) return false;
7040 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
7041 const SCEV *One = getConstant(Stride->getType(), 1);
7044 APInt MaxRHS = getSignedRange(RHS).getSignedMax();
7045 APInt MaxValue = APInt::getSignedMaxValue(BitWidth);
7046 APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
7049 // SMaxRHS + SMaxStrideMinusOne > SMaxValue => overflow!
7050 return (MaxValue - MaxStrideMinusOne).slt(MaxRHS);
7053 APInt MaxRHS = getUnsignedRange(RHS).getUnsignedMax();
7054 APInt MaxValue = APInt::getMaxValue(BitWidth);
7055 APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
7058 // UMaxRHS + UMaxStrideMinusOne > UMaxValue => overflow!
7059 return (MaxValue - MaxStrideMinusOne).ult(MaxRHS);
7062 // Verify if an linear IV with negative stride can overflow when in a
7063 // greater-than comparison, knowing the invariant term of the comparison,
7064 // the stride and the knowledge of NSW/NUW flags on the recurrence.
7065 bool ScalarEvolution::doesIVOverflowOnGT(const SCEV *RHS, const SCEV *Stride,
7066 bool IsSigned, bool NoWrap) {
7067 if (NoWrap) return false;
7069 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
7070 const SCEV *One = getConstant(Stride->getType(), 1);
7073 APInt MinRHS = getSignedRange(RHS).getSignedMin();
7074 APInt MinValue = APInt::getSignedMinValue(BitWidth);
7075 APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
7078 // SMinRHS - SMaxStrideMinusOne < SMinValue => overflow!
7079 return (MinValue + MaxStrideMinusOne).sgt(MinRHS);
7082 APInt MinRHS = getUnsignedRange(RHS).getUnsignedMin();
7083 APInt MinValue = APInt::getMinValue(BitWidth);
7084 APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
7087 // UMinRHS - UMaxStrideMinusOne < UMinValue => overflow!
7088 return (MinValue + MaxStrideMinusOne).ugt(MinRHS);
7091 // Compute the backedge taken count knowing the interval difference, the
7092 // stride and presence of the equality in the comparison.
7093 const SCEV *ScalarEvolution::computeBECount(const SCEV *Delta, const SCEV *Step,
7095 const SCEV *One = getConstant(Step->getType(), 1);
7096 Delta = Equality ? getAddExpr(Delta, Step)
7097 : getAddExpr(Delta, getMinusSCEV(Step, One));
7098 return getUDivExpr(Delta, Step);
7101 /// HowManyLessThans - Return the number of times a backedge containing the
7102 /// specified less-than comparison will execute. If not computable, return
7103 /// CouldNotCompute.
7105 /// @param ControlsExit is true when the LHS < RHS condition directly controls
7106 /// the branch (loops exits only if condition is true). In this case, we can use
7107 /// NoWrapFlags to skip overflow checks.
7108 ScalarEvolution::ExitLimit
7109 ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
7110 const Loop *L, bool IsSigned,
7111 bool ControlsExit) {
7112 // We handle only IV < Invariant
7113 if (!isLoopInvariant(RHS, L))
7114 return getCouldNotCompute();
7116 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
7118 // Avoid weird loops
7119 if (!IV || IV->getLoop() != L || !IV->isAffine())
7120 return getCouldNotCompute();
7122 bool NoWrap = ControlsExit &&
7123 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
7125 const SCEV *Stride = IV->getStepRecurrence(*this);
7127 // Avoid negative or zero stride values
7128 if (!isKnownPositive(Stride))
7129 return getCouldNotCompute();
7131 // Avoid proven overflow cases: this will ensure that the backedge taken count
7132 // will not generate any unsigned overflow. Relaxed no-overflow conditions
7133 // exploit NoWrapFlags, allowing to optimize in presence of undefined
7134 // behaviors like the case of C language.
7135 if (!Stride->isOne() && doesIVOverflowOnLT(RHS, Stride, IsSigned, NoWrap))
7136 return getCouldNotCompute();
7138 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SLT
7139 : ICmpInst::ICMP_ULT;
7140 const SCEV *Start = IV->getStart();
7141 const SCEV *End = RHS;
7142 if (!isLoopEntryGuardedByCond(L, Cond, getMinusSCEV(Start, Stride), RHS)) {
7143 const SCEV *Diff = getMinusSCEV(RHS, Start);
7144 // If we have NoWrap set, then we can assume that the increment won't
7145 // overflow, in which case if RHS - Start is a constant, we don't need to
7146 // do a max operation since we can just figure it out statically
7147 if (NoWrap && isa<SCEVConstant>(Diff)) {
7148 APInt D = dyn_cast<const SCEVConstant>(Diff)->getValue()->getValue();
7152 End = IsSigned ? getSMaxExpr(RHS, Start)
7153 : getUMaxExpr(RHS, Start);
7156 const SCEV *BECount = computeBECount(getMinusSCEV(End, Start), Stride, false);
7158 APInt MinStart = IsSigned ? getSignedRange(Start).getSignedMin()
7159 : getUnsignedRange(Start).getUnsignedMin();
7161 APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
7162 : getUnsignedRange(Stride).getUnsignedMin();
7164 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
7165 APInt Limit = IsSigned ? APInt::getSignedMaxValue(BitWidth) - (MinStride - 1)
7166 : APInt::getMaxValue(BitWidth) - (MinStride - 1);
7168 // Although End can be a MAX expression we estimate MaxEnd considering only
7169 // the case End = RHS. This is safe because in the other case (End - Start)
7170 // is zero, leading to a zero maximum backedge taken count.
7172 IsSigned ? APIntOps::smin(getSignedRange(RHS).getSignedMax(), Limit)
7173 : APIntOps::umin(getUnsignedRange(RHS).getUnsignedMax(), Limit);
7175 const SCEV *MaxBECount;
7176 if (isa<SCEVConstant>(BECount))
7177 MaxBECount = BECount;
7179 MaxBECount = computeBECount(getConstant(MaxEnd - MinStart),
7180 getConstant(MinStride), false);
7182 if (isa<SCEVCouldNotCompute>(MaxBECount))
7183 MaxBECount = BECount;
7185 return ExitLimit(BECount, MaxBECount);
7188 ScalarEvolution::ExitLimit
7189 ScalarEvolution::HowManyGreaterThans(const SCEV *LHS, const SCEV *RHS,
7190 const Loop *L, bool IsSigned,
7191 bool ControlsExit) {
7192 // We handle only IV > Invariant
7193 if (!isLoopInvariant(RHS, L))
7194 return getCouldNotCompute();
7196 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
7198 // Avoid weird loops
7199 if (!IV || IV->getLoop() != L || !IV->isAffine())
7200 return getCouldNotCompute();
7202 bool NoWrap = ControlsExit &&
7203 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
7205 const SCEV *Stride = getNegativeSCEV(IV->getStepRecurrence(*this));
7207 // Avoid negative or zero stride values
7208 if (!isKnownPositive(Stride))
7209 return getCouldNotCompute();
7211 // Avoid proven overflow cases: this will ensure that the backedge taken count
7212 // will not generate any unsigned overflow. Relaxed no-overflow conditions
7213 // exploit NoWrapFlags, allowing to optimize in presence of undefined
7214 // behaviors like the case of C language.
7215 if (!Stride->isOne() && doesIVOverflowOnGT(RHS, Stride, IsSigned, NoWrap))
7216 return getCouldNotCompute();
7218 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SGT
7219 : ICmpInst::ICMP_UGT;
7221 const SCEV *Start = IV->getStart();
7222 const SCEV *End = RHS;
7223 if (!isLoopEntryGuardedByCond(L, Cond, getAddExpr(Start, Stride), RHS)) {
7224 const SCEV *Diff = getMinusSCEV(RHS, Start);
7225 // If we have NoWrap set, then we can assume that the increment won't
7226 // overflow, in which case if RHS - Start is a constant, we don't need to
7227 // do a max operation since we can just figure it out statically
7228 if (NoWrap && isa<SCEVConstant>(Diff)) {
7229 APInt D = dyn_cast<const SCEVConstant>(Diff)->getValue()->getValue();
7230 if (!D.isNegative())
7233 End = IsSigned ? getSMinExpr(RHS, Start)
7234 : getUMinExpr(RHS, Start);
7237 const SCEV *BECount = computeBECount(getMinusSCEV(Start, End), Stride, false);
7239 APInt MaxStart = IsSigned ? getSignedRange(Start).getSignedMax()
7240 : getUnsignedRange(Start).getUnsignedMax();
7242 APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
7243 : getUnsignedRange(Stride).getUnsignedMin();
7245 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
7246 APInt Limit = IsSigned ? APInt::getSignedMinValue(BitWidth) + (MinStride - 1)
7247 : APInt::getMinValue(BitWidth) + (MinStride - 1);
7249 // Although End can be a MIN expression we estimate MinEnd considering only
7250 // the case End = RHS. This is safe because in the other case (Start - End)
7251 // is zero, leading to a zero maximum backedge taken count.
7253 IsSigned ? APIntOps::smax(getSignedRange(RHS).getSignedMin(), Limit)
7254 : APIntOps::umax(getUnsignedRange(RHS).getUnsignedMin(), Limit);
7257 const SCEV *MaxBECount = getCouldNotCompute();
7258 if (isa<SCEVConstant>(BECount))
7259 MaxBECount = BECount;
7261 MaxBECount = computeBECount(getConstant(MaxStart - MinEnd),
7262 getConstant(MinStride), false);
7264 if (isa<SCEVCouldNotCompute>(MaxBECount))
7265 MaxBECount = BECount;
7267 return ExitLimit(BECount, MaxBECount);
7270 /// getNumIterationsInRange - Return the number of iterations of this loop that
7271 /// produce values in the specified constant range. Another way of looking at
7272 /// this is that it returns the first iteration number where the value is not in
7273 /// the condition, thus computing the exit count. If the iteration count can't
7274 /// be computed, an instance of SCEVCouldNotCompute is returned.
7275 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
7276 ScalarEvolution &SE) const {
7277 if (Range.isFullSet()) // Infinite loop.
7278 return SE.getCouldNotCompute();
7280 // If the start is a non-zero constant, shift the range to simplify things.
7281 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
7282 if (!SC->getValue()->isZero()) {
7283 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
7284 Operands[0] = SE.getConstant(SC->getType(), 0);
7285 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(),
7286 getNoWrapFlags(FlagNW));
7287 if (const SCEVAddRecExpr *ShiftedAddRec =
7288 dyn_cast<SCEVAddRecExpr>(Shifted))
7289 return ShiftedAddRec->getNumIterationsInRange(
7290 Range.subtract(SC->getValue()->getValue()), SE);
7291 // This is strange and shouldn't happen.
7292 return SE.getCouldNotCompute();
7295 // The only time we can solve this is when we have all constant indices.
7296 // Otherwise, we cannot determine the overflow conditions.
7297 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
7298 if (!isa<SCEVConstant>(getOperand(i)))
7299 return SE.getCouldNotCompute();
7302 // Okay at this point we know that all elements of the chrec are constants and
7303 // that the start element is zero.
7305 // First check to see if the range contains zero. If not, the first
7307 unsigned BitWidth = SE.getTypeSizeInBits(getType());
7308 if (!Range.contains(APInt(BitWidth, 0)))
7309 return SE.getConstant(getType(), 0);
7312 // If this is an affine expression then we have this situation:
7313 // Solve {0,+,A} in Range === Ax in Range
7315 // We know that zero is in the range. If A is positive then we know that
7316 // the upper value of the range must be the first possible exit value.
7317 // If A is negative then the lower of the range is the last possible loop
7318 // value. Also note that we already checked for a full range.
7319 APInt One(BitWidth,1);
7320 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
7321 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
7323 // The exit value should be (End+A)/A.
7324 APInt ExitVal = (End + A).udiv(A);
7325 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
7327 // Evaluate at the exit value. If we really did fall out of the valid
7328 // range, then we computed our trip count, otherwise wrap around or other
7329 // things must have happened.
7330 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
7331 if (Range.contains(Val->getValue()))
7332 return SE.getCouldNotCompute(); // Something strange happened
7334 // Ensure that the previous value is in the range. This is a sanity check.
7335 assert(Range.contains(
7336 EvaluateConstantChrecAtConstant(this,
7337 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
7338 "Linear scev computation is off in a bad way!");
7339 return SE.getConstant(ExitValue);
7340 } else if (isQuadratic()) {
7341 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
7342 // quadratic equation to solve it. To do this, we must frame our problem in
7343 // terms of figuring out when zero is crossed, instead of when
7344 // Range.getUpper() is crossed.
7345 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
7346 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
7347 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop(),
7348 // getNoWrapFlags(FlagNW)
7351 // Next, solve the constructed addrec
7352 std::pair<const SCEV *,const SCEV *> Roots =
7353 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
7354 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
7355 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
7357 // Pick the smallest positive root value.
7358 if (ConstantInt *CB =
7359 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
7360 R1->getValue(), R2->getValue()))) {
7361 if (CB->getZExtValue() == false)
7362 std::swap(R1, R2); // R1 is the minimum root now.
7364 // Make sure the root is not off by one. The returned iteration should
7365 // not be in the range, but the previous one should be. When solving
7366 // for "X*X < 5", for example, we should not return a root of 2.
7367 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
7370 if (Range.contains(R1Val->getValue())) {
7371 // The next iteration must be out of the range...
7372 ConstantInt *NextVal =
7373 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1);
7375 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
7376 if (!Range.contains(R1Val->getValue()))
7377 return SE.getConstant(NextVal);
7378 return SE.getCouldNotCompute(); // Something strange happened
7381 // If R1 was not in the range, then it is a good return value. Make
7382 // sure that R1-1 WAS in the range though, just in case.
7383 ConstantInt *NextVal =
7384 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1);
7385 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
7386 if (Range.contains(R1Val->getValue()))
7388 return SE.getCouldNotCompute(); // Something strange happened
7393 return SE.getCouldNotCompute();
7399 FindUndefs() : Found(false) {}
7401 bool follow(const SCEV *S) {
7402 if (const SCEVUnknown *C = dyn_cast<SCEVUnknown>(S)) {
7403 if (isa<UndefValue>(C->getValue()))
7405 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) {
7406 if (isa<UndefValue>(C->getValue()))
7410 // Keep looking if we haven't found it yet.
7413 bool isDone() const {
7414 // Stop recursion if we have found an undef.
7420 // Return true when S contains at least an undef value.
7422 containsUndefs(const SCEV *S) {
7424 SCEVTraversal<FindUndefs> ST(F);
7431 // Collect all steps of SCEV expressions.
7432 struct SCEVCollectStrides {
7433 ScalarEvolution &SE;
7434 SmallVectorImpl<const SCEV *> &Strides;
7436 SCEVCollectStrides(ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &S)
7437 : SE(SE), Strides(S) {}
7439 bool follow(const SCEV *S) {
7440 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(S))
7441 Strides.push_back(AR->getStepRecurrence(SE));
7444 bool isDone() const { return false; }
7447 // Collect all SCEVUnknown and SCEVMulExpr expressions.
7448 struct SCEVCollectTerms {
7449 SmallVectorImpl<const SCEV *> &Terms;
7451 SCEVCollectTerms(SmallVectorImpl<const SCEV *> &T)
7454 bool follow(const SCEV *S) {
7455 if (isa<SCEVUnknown>(S) || isa<SCEVMulExpr>(S)) {
7456 if (!containsUndefs(S))
7459 // Stop recursion: once we collected a term, do not walk its operands.
7466 bool isDone() const { return false; }
7470 /// Find parametric terms in this SCEVAddRecExpr.
7471 void SCEVAddRecExpr::collectParametricTerms(
7472 ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &Terms) const {
7473 SmallVector<const SCEV *, 4> Strides;
7474 SCEVCollectStrides StrideCollector(SE, Strides);
7475 visitAll(this, StrideCollector);
7478 dbgs() << "Strides:\n";
7479 for (const SCEV *S : Strides)
7480 dbgs() << *S << "\n";
7483 for (const SCEV *S : Strides) {
7484 SCEVCollectTerms TermCollector(Terms);
7485 visitAll(S, TermCollector);
7489 dbgs() << "Terms:\n";
7490 for (const SCEV *T : Terms)
7491 dbgs() << *T << "\n";
7495 static bool findArrayDimensionsRec(ScalarEvolution &SE,
7496 SmallVectorImpl<const SCEV *> &Terms,
7497 SmallVectorImpl<const SCEV *> &Sizes) {
7498 int Last = Terms.size() - 1;
7499 const SCEV *Step = Terms[Last];
7501 // End of recursion.
7503 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Step)) {
7504 SmallVector<const SCEV *, 2> Qs;
7505 for (const SCEV *Op : M->operands())
7506 if (!isa<SCEVConstant>(Op))
7509 Step = SE.getMulExpr(Qs);
7512 Sizes.push_back(Step);
7516 for (const SCEV *&Term : Terms) {
7517 // Normalize the terms before the next call to findArrayDimensionsRec.
7519 SCEVDivision::divide(SE, Term, Step, &Q, &R);
7521 // Bail out when GCD does not evenly divide one of the terms.
7528 // Remove all SCEVConstants.
7529 Terms.erase(std::remove_if(Terms.begin(), Terms.end(), [](const SCEV *E) {
7530 return isa<SCEVConstant>(E);
7534 if (Terms.size() > 0)
7535 if (!findArrayDimensionsRec(SE, Terms, Sizes))
7538 Sizes.push_back(Step);
7543 struct FindParameter {
7544 bool FoundParameter;
7545 FindParameter() : FoundParameter(false) {}
7547 bool follow(const SCEV *S) {
7548 if (isa<SCEVUnknown>(S)) {
7549 FoundParameter = true;
7550 // Stop recursion: we found a parameter.
7556 bool isDone() const {
7557 // Stop recursion if we have found a parameter.
7558 return FoundParameter;
7563 // Returns true when S contains at least a SCEVUnknown parameter.
7565 containsParameters(const SCEV *S) {
7567 SCEVTraversal<FindParameter> ST(F);
7570 return F.FoundParameter;
7573 // Returns true when one of the SCEVs of Terms contains a SCEVUnknown parameter.
7575 containsParameters(SmallVectorImpl<const SCEV *> &Terms) {
7576 for (const SCEV *T : Terms)
7577 if (containsParameters(T))
7582 // Return the number of product terms in S.
7583 static inline int numberOfTerms(const SCEV *S) {
7584 if (const SCEVMulExpr *Expr = dyn_cast<SCEVMulExpr>(S))
7585 return Expr->getNumOperands();
7589 static const SCEV *removeConstantFactors(ScalarEvolution &SE, const SCEV *T) {
7590 if (isa<SCEVConstant>(T))
7593 if (isa<SCEVUnknown>(T))
7596 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(T)) {
7597 SmallVector<const SCEV *, 2> Factors;
7598 for (const SCEV *Op : M->operands())
7599 if (!isa<SCEVConstant>(Op))
7600 Factors.push_back(Op);
7602 return SE.getMulExpr(Factors);
7608 /// Return the size of an element read or written by Inst.
7609 const SCEV *ScalarEvolution::getElementSize(Instruction *Inst) {
7611 if (StoreInst *Store = dyn_cast<StoreInst>(Inst))
7612 Ty = Store->getValueOperand()->getType();
7613 else if (LoadInst *Load = dyn_cast<LoadInst>(Inst))
7614 Ty = Load->getType();
7618 Type *ETy = getEffectiveSCEVType(PointerType::getUnqual(Ty));
7619 return getSizeOfExpr(ETy, Ty);
7622 /// Second step of delinearization: compute the array dimensions Sizes from the
7623 /// set of Terms extracted from the memory access function of this SCEVAddRec.
7624 void ScalarEvolution::findArrayDimensions(SmallVectorImpl<const SCEV *> &Terms,
7625 SmallVectorImpl<const SCEV *> &Sizes,
7626 const SCEV *ElementSize) const {
7628 if (Terms.size() < 1 || !ElementSize)
7631 // Early return when Terms do not contain parameters: we do not delinearize
7632 // non parametric SCEVs.
7633 if (!containsParameters(Terms))
7637 dbgs() << "Terms:\n";
7638 for (const SCEV *T : Terms)
7639 dbgs() << *T << "\n";
7642 // Remove duplicates.
7643 std::sort(Terms.begin(), Terms.end());
7644 Terms.erase(std::unique(Terms.begin(), Terms.end()), Terms.end());
7646 // Put larger terms first.
7647 std::sort(Terms.begin(), Terms.end(), [](const SCEV *LHS, const SCEV *RHS) {
7648 return numberOfTerms(LHS) > numberOfTerms(RHS);
7651 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
7653 // Divide all terms by the element size.
7654 for (const SCEV *&Term : Terms) {
7656 SCEVDivision::divide(SE, Term, ElementSize, &Q, &R);
7660 SmallVector<const SCEV *, 4> NewTerms;
7662 // Remove constant factors.
7663 for (const SCEV *T : Terms)
7664 if (const SCEV *NewT = removeConstantFactors(SE, T))
7665 NewTerms.push_back(NewT);
7668 dbgs() << "Terms after sorting:\n";
7669 for (const SCEV *T : NewTerms)
7670 dbgs() << *T << "\n";
7673 if (NewTerms.empty() ||
7674 !findArrayDimensionsRec(SE, NewTerms, Sizes)) {
7679 // The last element to be pushed into Sizes is the size of an element.
7680 Sizes.push_back(ElementSize);
7683 dbgs() << "Sizes:\n";
7684 for (const SCEV *S : Sizes)
7685 dbgs() << *S << "\n";
7689 /// Third step of delinearization: compute the access functions for the
7690 /// Subscripts based on the dimensions in Sizes.
7691 void SCEVAddRecExpr::computeAccessFunctions(
7692 ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &Subscripts,
7693 SmallVectorImpl<const SCEV *> &Sizes) const {
7695 // Early exit in case this SCEV is not an affine multivariate function.
7696 if (Sizes.empty() || !this->isAffine())
7699 const SCEV *Res = this;
7700 int Last = Sizes.size() - 1;
7701 for (int i = Last; i >= 0; i--) {
7703 SCEVDivision::divide(SE, Res, Sizes[i], &Q, &R);
7706 dbgs() << "Res: " << *Res << "\n";
7707 dbgs() << "Sizes[i]: " << *Sizes[i] << "\n";
7708 dbgs() << "Res divided by Sizes[i]:\n";
7709 dbgs() << "Quotient: " << *Q << "\n";
7710 dbgs() << "Remainder: " << *R << "\n";
7715 // Do not record the last subscript corresponding to the size of elements in
7719 // Bail out if the remainder is too complex.
7720 if (isa<SCEVAddRecExpr>(R)) {
7729 // Record the access function for the current subscript.
7730 Subscripts.push_back(R);
7733 // Also push in last position the remainder of the last division: it will be
7734 // the access function of the innermost dimension.
7735 Subscripts.push_back(Res);
7737 std::reverse(Subscripts.begin(), Subscripts.end());
7740 dbgs() << "Subscripts:\n";
7741 for (const SCEV *S : Subscripts)
7742 dbgs() << *S << "\n";
7746 /// Splits the SCEV into two vectors of SCEVs representing the subscripts and
7747 /// sizes of an array access. Returns the remainder of the delinearization that
7748 /// is the offset start of the array. The SCEV->delinearize algorithm computes
7749 /// the multiples of SCEV coefficients: that is a pattern matching of sub
7750 /// expressions in the stride and base of a SCEV corresponding to the
7751 /// computation of a GCD (greatest common divisor) of base and stride. When
7752 /// SCEV->delinearize fails, it returns the SCEV unchanged.
7754 /// For example: when analyzing the memory access A[i][j][k] in this loop nest
7756 /// void foo(long n, long m, long o, double A[n][m][o]) {
7758 /// for (long i = 0; i < n; i++)
7759 /// for (long j = 0; j < m; j++)
7760 /// for (long k = 0; k < o; k++)
7761 /// A[i][j][k] = 1.0;
7764 /// the delinearization input is the following AddRec SCEV:
7766 /// AddRec: {{{%A,+,(8 * %m * %o)}<%for.i>,+,(8 * %o)}<%for.j>,+,8}<%for.k>
7768 /// From this SCEV, we are able to say that the base offset of the access is %A
7769 /// because it appears as an offset that does not divide any of the strides in
7772 /// CHECK: Base offset: %A
7774 /// and then SCEV->delinearize determines the size of some of the dimensions of
7775 /// the array as these are the multiples by which the strides are happening:
7777 /// CHECK: ArrayDecl[UnknownSize][%m][%o] with elements of sizeof(double) bytes.
7779 /// Note that the outermost dimension remains of UnknownSize because there are
7780 /// no strides that would help identifying the size of the last dimension: when
7781 /// the array has been statically allocated, one could compute the size of that
7782 /// dimension by dividing the overall size of the array by the size of the known
7783 /// dimensions: %m * %o * 8.
7785 /// Finally delinearize provides the access functions for the array reference
7786 /// that does correspond to A[i][j][k] of the above C testcase:
7788 /// CHECK: ArrayRef[{0,+,1}<%for.i>][{0,+,1}<%for.j>][{0,+,1}<%for.k>]
7790 /// The testcases are checking the output of a function pass:
7791 /// DelinearizationPass that walks through all loads and stores of a function
7792 /// asking for the SCEV of the memory access with respect to all enclosing
7793 /// loops, calling SCEV->delinearize on that and printing the results.
7795 void SCEVAddRecExpr::delinearize(ScalarEvolution &SE,
7796 SmallVectorImpl<const SCEV *> &Subscripts,
7797 SmallVectorImpl<const SCEV *> &Sizes,
7798 const SCEV *ElementSize) const {
7799 // First step: collect parametric terms.
7800 SmallVector<const SCEV *, 4> Terms;
7801 collectParametricTerms(SE, Terms);
7806 // Second step: find subscript sizes.
7807 SE.findArrayDimensions(Terms, Sizes, ElementSize);
7812 // Third step: compute the access functions for each subscript.
7813 computeAccessFunctions(SE, Subscripts, Sizes);
7815 if (Subscripts.empty())
7819 dbgs() << "succeeded to delinearize " << *this << "\n";
7820 dbgs() << "ArrayDecl[UnknownSize]";
7821 for (const SCEV *S : Sizes)
7822 dbgs() << "[" << *S << "]";
7824 dbgs() << "\nArrayRef";
7825 for (const SCEV *S : Subscripts)
7826 dbgs() << "[" << *S << "]";
7831 //===----------------------------------------------------------------------===//
7832 // SCEVCallbackVH Class Implementation
7833 //===----------------------------------------------------------------------===//
7835 void ScalarEvolution::SCEVCallbackVH::deleted() {
7836 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
7837 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
7838 SE->ConstantEvolutionLoopExitValue.erase(PN);
7839 SE->ValueExprMap.erase(getValPtr());
7840 // this now dangles!
7843 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) {
7844 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
7846 // Forget all the expressions associated with users of the old value,
7847 // so that future queries will recompute the expressions using the new
7849 Value *Old = getValPtr();
7850 SmallVector<User *, 16> Worklist(Old->user_begin(), Old->user_end());
7851 SmallPtrSet<User *, 8> Visited;
7852 while (!Worklist.empty()) {
7853 User *U = Worklist.pop_back_val();
7854 // Deleting the Old value will cause this to dangle. Postpone
7855 // that until everything else is done.
7858 if (!Visited.insert(U).second)
7860 if (PHINode *PN = dyn_cast<PHINode>(U))
7861 SE->ConstantEvolutionLoopExitValue.erase(PN);
7862 SE->ValueExprMap.erase(U);
7863 Worklist.insert(Worklist.end(), U->user_begin(), U->user_end());
7865 // Delete the Old value.
7866 if (PHINode *PN = dyn_cast<PHINode>(Old))
7867 SE->ConstantEvolutionLoopExitValue.erase(PN);
7868 SE->ValueExprMap.erase(Old);
7869 // this now dangles!
7872 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
7873 : CallbackVH(V), SE(se) {}
7875 //===----------------------------------------------------------------------===//
7876 // ScalarEvolution Class Implementation
7877 //===----------------------------------------------------------------------===//
7879 ScalarEvolution::ScalarEvolution()
7880 : FunctionPass(ID), ValuesAtScopes(64), LoopDispositions(64),
7881 BlockDispositions(64), FirstUnknown(nullptr) {
7882 initializeScalarEvolutionPass(*PassRegistry::getPassRegistry());
7885 bool ScalarEvolution::runOnFunction(Function &F) {
7887 AC = &getAnalysis<AssumptionCacheTracker>().getAssumptionCache(F);
7888 LI = &getAnalysis<LoopInfoWrapperPass>().getLoopInfo();
7889 DataLayoutPass *DLP = getAnalysisIfAvailable<DataLayoutPass>();
7890 DL = DLP ? &DLP->getDataLayout() : nullptr;
7891 TLI = &getAnalysis<TargetLibraryInfoWrapperPass>().getTLI();
7892 DT = &getAnalysis<DominatorTreeWrapperPass>().getDomTree();
7896 void ScalarEvolution::releaseMemory() {
7897 // Iterate through all the SCEVUnknown instances and call their
7898 // destructors, so that they release their references to their values.
7899 for (SCEVUnknown *U = FirstUnknown; U; U = U->Next)
7901 FirstUnknown = nullptr;
7903 ValueExprMap.clear();
7905 // Free any extra memory created for ExitNotTakenInfo in the unlikely event
7906 // that a loop had multiple computable exits.
7907 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
7908 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end();
7913 assert(PendingLoopPredicates.empty() && "isImpliedCond garbage");
7915 BackedgeTakenCounts.clear();
7916 ConstantEvolutionLoopExitValue.clear();
7917 ValuesAtScopes.clear();
7918 LoopDispositions.clear();
7919 BlockDispositions.clear();
7920 UnsignedRanges.clear();
7921 SignedRanges.clear();
7922 UniqueSCEVs.clear();
7923 SCEVAllocator.Reset();
7926 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
7927 AU.setPreservesAll();
7928 AU.addRequired<AssumptionCacheTracker>();
7929 AU.addRequiredTransitive<LoopInfoWrapperPass>();
7930 AU.addRequiredTransitive<DominatorTreeWrapperPass>();
7931 AU.addRequired<TargetLibraryInfoWrapperPass>();
7934 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
7935 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
7938 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
7940 // Print all inner loops first
7941 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
7942 PrintLoopInfo(OS, SE, *I);
7945 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
7948 SmallVector<BasicBlock *, 8> ExitBlocks;
7949 L->getExitBlocks(ExitBlocks);
7950 if (ExitBlocks.size() != 1)
7951 OS << "<multiple exits> ";
7953 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
7954 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
7956 OS << "Unpredictable backedge-taken count. ";
7961 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
7964 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
7965 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
7967 OS << "Unpredictable max backedge-taken count. ";
7973 void ScalarEvolution::print(raw_ostream &OS, const Module *) const {
7974 // ScalarEvolution's implementation of the print method is to print
7975 // out SCEV values of all instructions that are interesting. Doing
7976 // this potentially causes it to create new SCEV objects though,
7977 // which technically conflicts with the const qualifier. This isn't
7978 // observable from outside the class though, so casting away the
7979 // const isn't dangerous.
7980 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
7982 OS << "Classifying expressions for: ";
7983 F->printAsOperand(OS, /*PrintType=*/false);
7985 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
7986 if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) {
7989 const SCEV *SV = SE.getSCEV(&*I);
7992 const Loop *L = LI->getLoopFor((*I).getParent());
7994 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
8001 OS << "\t\t" "Exits: ";
8002 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
8003 if (!SE.isLoopInvariant(ExitValue, L)) {
8004 OS << "<<Unknown>>";
8013 OS << "Determining loop execution counts for: ";
8014 F->printAsOperand(OS, /*PrintType=*/false);
8016 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
8017 PrintLoopInfo(OS, &SE, *I);
8020 ScalarEvolution::LoopDisposition
8021 ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) {
8022 auto &Values = LoopDispositions[S];
8023 for (auto &V : Values) {
8024 if (V.getPointer() == L)
8027 Values.emplace_back(L, LoopVariant);
8028 LoopDisposition D = computeLoopDisposition(S, L);
8029 auto &Values2 = LoopDispositions[S];
8030 for (auto &V : make_range(Values2.rbegin(), Values2.rend())) {
8031 if (V.getPointer() == L) {
8039 ScalarEvolution::LoopDisposition
8040 ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) {
8041 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
8043 return LoopInvariant;
8047 return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L);
8048 case scAddRecExpr: {
8049 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
8051 // If L is the addrec's loop, it's computable.
8052 if (AR->getLoop() == L)
8053 return LoopComputable;
8055 // Add recurrences are never invariant in the function-body (null loop).
8059 // This recurrence is variant w.r.t. L if L contains AR's loop.
8060 if (L->contains(AR->getLoop()))
8063 // This recurrence is invariant w.r.t. L if AR's loop contains L.
8064 if (AR->getLoop()->contains(L))
8065 return LoopInvariant;
8067 // This recurrence is variant w.r.t. L if any of its operands
8069 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
8071 if (!isLoopInvariant(*I, L))
8074 // Otherwise it's loop-invariant.
8075 return LoopInvariant;
8081 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
8082 bool HasVarying = false;
8083 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
8085 LoopDisposition D = getLoopDisposition(*I, L);
8086 if (D == LoopVariant)
8088 if (D == LoopComputable)
8091 return HasVarying ? LoopComputable : LoopInvariant;
8094 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
8095 LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L);
8096 if (LD == LoopVariant)
8098 LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L);
8099 if (RD == LoopVariant)
8101 return (LD == LoopInvariant && RD == LoopInvariant) ?
8102 LoopInvariant : LoopComputable;
8105 // All non-instruction values are loop invariant. All instructions are loop
8106 // invariant if they are not contained in the specified loop.
8107 // Instructions are never considered invariant in the function body
8108 // (null loop) because they are defined within the "loop".
8109 if (Instruction *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue()))
8110 return (L && !L->contains(I)) ? LoopInvariant : LoopVariant;
8111 return LoopInvariant;
8112 case scCouldNotCompute:
8113 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
8115 llvm_unreachable("Unknown SCEV kind!");
8118 bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) {
8119 return getLoopDisposition(S, L) == LoopInvariant;
8122 bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) {
8123 return getLoopDisposition(S, L) == LoopComputable;
8126 ScalarEvolution::BlockDisposition
8127 ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) {
8128 auto &Values = BlockDispositions[S];
8129 for (auto &V : Values) {
8130 if (V.getPointer() == BB)
8133 Values.emplace_back(BB, DoesNotDominateBlock);
8134 BlockDisposition D = computeBlockDisposition(S, BB);
8135 auto &Values2 = BlockDispositions[S];
8136 for (auto &V : make_range(Values2.rbegin(), Values2.rend())) {
8137 if (V.getPointer() == BB) {
8145 ScalarEvolution::BlockDisposition
8146 ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) {
8147 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
8149 return ProperlyDominatesBlock;
8153 return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB);
8154 case scAddRecExpr: {
8155 // This uses a "dominates" query instead of "properly dominates" query
8156 // to test for proper dominance too, because the instruction which
8157 // produces the addrec's value is a PHI, and a PHI effectively properly
8158 // dominates its entire containing block.
8159 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
8160 if (!DT->dominates(AR->getLoop()->getHeader(), BB))
8161 return DoesNotDominateBlock;
8163 // FALL THROUGH into SCEVNAryExpr handling.
8168 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
8170 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
8172 BlockDisposition D = getBlockDisposition(*I, BB);
8173 if (D == DoesNotDominateBlock)
8174 return DoesNotDominateBlock;
8175 if (D == DominatesBlock)
8178 return Proper ? ProperlyDominatesBlock : DominatesBlock;
8181 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
8182 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
8183 BlockDisposition LD = getBlockDisposition(LHS, BB);
8184 if (LD == DoesNotDominateBlock)
8185 return DoesNotDominateBlock;
8186 BlockDisposition RD = getBlockDisposition(RHS, BB);
8187 if (RD == DoesNotDominateBlock)
8188 return DoesNotDominateBlock;
8189 return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ?
8190 ProperlyDominatesBlock : DominatesBlock;
8193 if (Instruction *I =
8194 dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) {
8195 if (I->getParent() == BB)
8196 return DominatesBlock;
8197 if (DT->properlyDominates(I->getParent(), BB))
8198 return ProperlyDominatesBlock;
8199 return DoesNotDominateBlock;
8201 return ProperlyDominatesBlock;
8202 case scCouldNotCompute:
8203 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
8205 llvm_unreachable("Unknown SCEV kind!");
8208 bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) {
8209 return getBlockDisposition(S, BB) >= DominatesBlock;
8212 bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) {
8213 return getBlockDisposition(S, BB) == ProperlyDominatesBlock;
8217 // Search for a SCEV expression node within an expression tree.
8218 // Implements SCEVTraversal::Visitor.
8223 SCEVSearch(const SCEV *N): Node(N), IsFound(false) {}
8225 bool follow(const SCEV *S) {
8226 IsFound |= (S == Node);
8229 bool isDone() const { return IsFound; }
8233 bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const {
8234 SCEVSearch Search(Op);
8235 visitAll(S, Search);
8236 return Search.IsFound;
8239 void ScalarEvolution::forgetMemoizedResults(const SCEV *S) {
8240 ValuesAtScopes.erase(S);
8241 LoopDispositions.erase(S);
8242 BlockDispositions.erase(S);
8243 UnsignedRanges.erase(S);
8244 SignedRanges.erase(S);
8246 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
8247 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end(); I != E; ) {
8248 BackedgeTakenInfo &BEInfo = I->second;
8249 if (BEInfo.hasOperand(S, this)) {
8251 BackedgeTakenCounts.erase(I++);
8258 typedef DenseMap<const Loop *, std::string> VerifyMap;
8260 /// replaceSubString - Replaces all occurrences of From in Str with To.
8261 static void replaceSubString(std::string &Str, StringRef From, StringRef To) {
8263 while ((Pos = Str.find(From, Pos)) != std::string::npos) {
8264 Str.replace(Pos, From.size(), To.data(), To.size());
8269 /// getLoopBackedgeTakenCounts - Helper method for verifyAnalysis.
8271 getLoopBackedgeTakenCounts(Loop *L, VerifyMap &Map, ScalarEvolution &SE) {
8272 for (Loop::reverse_iterator I = L->rbegin(), E = L->rend(); I != E; ++I) {
8273 getLoopBackedgeTakenCounts(*I, Map, SE); // recurse.
8275 std::string &S = Map[L];
8277 raw_string_ostream OS(S);
8278 SE.getBackedgeTakenCount(L)->print(OS);
8280 // false and 0 are semantically equivalent. This can happen in dead loops.
8281 replaceSubString(OS.str(), "false", "0");
8282 // Remove wrap flags, their use in SCEV is highly fragile.
8283 // FIXME: Remove this when SCEV gets smarter about them.
8284 replaceSubString(OS.str(), "<nw>", "");
8285 replaceSubString(OS.str(), "<nsw>", "");
8286 replaceSubString(OS.str(), "<nuw>", "");
8291 void ScalarEvolution::verifyAnalysis() const {
8295 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
8297 // Gather stringified backedge taken counts for all loops using SCEV's caches.
8298 // FIXME: It would be much better to store actual values instead of strings,
8299 // but SCEV pointers will change if we drop the caches.
8300 VerifyMap BackedgeDumpsOld, BackedgeDumpsNew;
8301 for (LoopInfo::reverse_iterator I = LI->rbegin(), E = LI->rend(); I != E; ++I)
8302 getLoopBackedgeTakenCounts(*I, BackedgeDumpsOld, SE);
8304 // Gather stringified backedge taken counts for all loops without using
8307 for (LoopInfo::reverse_iterator I = LI->rbegin(), E = LI->rend(); I != E; ++I)
8308 getLoopBackedgeTakenCounts(*I, BackedgeDumpsNew, SE);
8310 // Now compare whether they're the same with and without caches. This allows
8311 // verifying that no pass changed the cache.
8312 assert(BackedgeDumpsOld.size() == BackedgeDumpsNew.size() &&
8313 "New loops suddenly appeared!");
8315 for (VerifyMap::iterator OldI = BackedgeDumpsOld.begin(),
8316 OldE = BackedgeDumpsOld.end(),
8317 NewI = BackedgeDumpsNew.begin();
8318 OldI != OldE; ++OldI, ++NewI) {
8319 assert(OldI->first == NewI->first && "Loop order changed!");
8321 // Compare the stringified SCEVs. We don't care if undef backedgetaken count
8323 // FIXME: We currently ignore SCEV changes from/to CouldNotCompute. This
8324 // means that a pass is buggy or SCEV has to learn a new pattern but is
8325 // usually not harmful.
8326 if (OldI->second != NewI->second &&
8327 OldI->second.find("undef") == std::string::npos &&
8328 NewI->second.find("undef") == std::string::npos &&
8329 OldI->second != "***COULDNOTCOMPUTE***" &&
8330 NewI->second != "***COULDNOTCOMPUTE***") {
8331 dbgs() << "SCEVValidator: SCEV for loop '"
8332 << OldI->first->getHeader()->getName()
8333 << "' changed from '" << OldI->second
8334 << "' to '" << NewI->second << "'!\n";
8339 // TODO: Verify more things.