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/ValueTracking.h"
72 #include "llvm/IR/ConstantRange.h"
73 #include "llvm/IR/Constants.h"
74 #include "llvm/IR/DataLayout.h"
75 #include "llvm/IR/DerivedTypes.h"
76 #include "llvm/IR/Dominators.h"
77 #include "llvm/IR/GetElementPtrTypeIterator.h"
78 #include "llvm/IR/GlobalAlias.h"
79 #include "llvm/IR/GlobalVariable.h"
80 #include "llvm/IR/InstIterator.h"
81 #include "llvm/IR/Instructions.h"
82 #include "llvm/IR/LLVMContext.h"
83 #include "llvm/IR/Metadata.h"
84 #include "llvm/IR/Operator.h"
85 #include "llvm/Support/CommandLine.h"
86 #include "llvm/Support/Debug.h"
87 #include "llvm/Support/ErrorHandling.h"
88 #include "llvm/Support/MathExtras.h"
89 #include "llvm/Support/raw_ostream.h"
90 #include "llvm/Target/TargetLibraryInfo.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(LoopInfo)
121 INITIALIZE_PASS_DEPENDENCY(DominatorTreeWrapperPass)
122 INITIALIZE_PASS_DEPENDENCY(TargetLibraryInfo)
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 if (PreAR && PreAR->getNoWrapFlags(SCEV::FlagNSW))
1370 // 2. Direct overflow check on the step operation's expression.
1371 unsigned BitWidth = SE->getTypeSizeInBits(AR->getType());
1372 Type *WideTy = IntegerType::get(SE->getContext(), BitWidth * 2);
1373 const SCEV *OperandExtendedStart =
1374 SE->getAddExpr(SE->getSignExtendExpr(PreStart, WideTy),
1375 SE->getSignExtendExpr(Step, WideTy));
1376 if (SE->getSignExtendExpr(Start, WideTy) == OperandExtendedStart) {
1377 // Cache knowledge of PreAR NSW.
1379 const_cast<SCEVAddRecExpr *>(PreAR)->setNoWrapFlags(SCEV::FlagNSW);
1380 // FIXME: this optimization needs a unit test
1381 DEBUG(dbgs() << "SCEV: untested prestart overflow check\n");
1385 // 3. Loop precondition.
1386 ICmpInst::Predicate Pred;
1387 const SCEV *OverflowLimit = getOverflowLimitForStep(Step, &Pred, SE);
1389 if (OverflowLimit &&
1390 SE->isLoopEntryGuardedByCond(L, Pred, PreStart, OverflowLimit)) {
1396 // Get the normalized sign-extended expression for this AddRec's Start.
1397 static const SCEV *getSignExtendAddRecStart(const SCEVAddRecExpr *AR,
1399 ScalarEvolution *SE) {
1400 const SCEV *PreStart = getPreStartForSignExtend(AR, Ty, SE);
1402 return SE->getSignExtendExpr(AR->getStart(), Ty);
1404 return SE->getAddExpr(SE->getSignExtendExpr(AR->getStepRecurrence(*SE), Ty),
1405 SE->getSignExtendExpr(PreStart, Ty));
1408 const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op,
1410 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1411 "This is not an extending conversion!");
1412 assert(isSCEVable(Ty) &&
1413 "This is not a conversion to a SCEVable type!");
1414 Ty = getEffectiveSCEVType(Ty);
1416 // Fold if the operand is constant.
1417 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1419 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), Ty)));
1421 // sext(sext(x)) --> sext(x)
1422 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1423 return getSignExtendExpr(SS->getOperand(), Ty);
1425 // sext(zext(x)) --> zext(x)
1426 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1427 return getZeroExtendExpr(SZ->getOperand(), Ty);
1429 // Before doing any expensive analysis, check to see if we've already
1430 // computed a SCEV for this Op and Ty.
1431 FoldingSetNodeID ID;
1432 ID.AddInteger(scSignExtend);
1436 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1438 // If the input value is provably positive, build a zext instead.
1439 if (isKnownNonNegative(Op))
1440 return getZeroExtendExpr(Op, Ty);
1442 // sext(trunc(x)) --> sext(x) or x or trunc(x)
1443 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1444 // It's possible the bits taken off by the truncate were all sign bits. If
1445 // so, we should be able to simplify this further.
1446 const SCEV *X = ST->getOperand();
1447 ConstantRange CR = getSignedRange(X);
1448 unsigned TruncBits = getTypeSizeInBits(ST->getType());
1449 unsigned NewBits = getTypeSizeInBits(Ty);
1450 if (CR.truncate(TruncBits).signExtend(NewBits).contains(
1451 CR.sextOrTrunc(NewBits)))
1452 return getTruncateOrSignExtend(X, Ty);
1455 // sext(C1 + (C2 * x)) --> C1 + sext(C2 * x) if C1 < C2
1456 if (auto SA = dyn_cast<SCEVAddExpr>(Op)) {
1457 if (SA->getNumOperands() == 2) {
1458 auto SC1 = dyn_cast<SCEVConstant>(SA->getOperand(0));
1459 auto SMul = dyn_cast<SCEVMulExpr>(SA->getOperand(1));
1461 if (auto SC2 = dyn_cast<SCEVConstant>(SMul->getOperand(0))) {
1462 const APInt &C1 = SC1->getValue()->getValue();
1463 const APInt &C2 = SC2->getValue()->getValue();
1464 if (C1.isStrictlyPositive() && C2.isStrictlyPositive() &&
1465 C2.ugt(C1) && C2.isPowerOf2())
1466 return getAddExpr(getSignExtendExpr(SC1, Ty),
1467 getSignExtendExpr(SMul, Ty));
1472 // If the input value is a chrec scev, and we can prove that the value
1473 // did not overflow the old, smaller, value, we can sign extend all of the
1474 // operands (often constants). This allows analysis of something like
1475 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
1476 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1477 if (AR->isAffine()) {
1478 const SCEV *Start = AR->getStart();
1479 const SCEV *Step = AR->getStepRecurrence(*this);
1480 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1481 const Loop *L = AR->getLoop();
1483 // If we have special knowledge that this addrec won't overflow,
1484 // we don't need to do any further analysis.
1485 if (AR->getNoWrapFlags(SCEV::FlagNSW))
1486 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1487 getSignExtendExpr(Step, Ty),
1490 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1491 // Note that this serves two purposes: It filters out loops that are
1492 // simply not analyzable, and it covers the case where this code is
1493 // being called from within backedge-taken count analysis, such that
1494 // attempting to ask for the backedge-taken count would likely result
1495 // in infinite recursion. In the later case, the analysis code will
1496 // cope with a conservative value, and it will take care to purge
1497 // that value once it has finished.
1498 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1499 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1500 // Manually compute the final value for AR, checking for
1503 // Check whether the backedge-taken count can be losslessly casted to
1504 // the addrec's type. The count is always unsigned.
1505 const SCEV *CastedMaxBECount =
1506 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1507 const SCEV *RecastedMaxBECount =
1508 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1509 if (MaxBECount == RecastedMaxBECount) {
1510 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1511 // Check whether Start+Step*MaxBECount has no signed overflow.
1512 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
1513 const SCEV *SAdd = getSignExtendExpr(getAddExpr(Start, SMul), WideTy);
1514 const SCEV *WideStart = getSignExtendExpr(Start, WideTy);
1515 const SCEV *WideMaxBECount =
1516 getZeroExtendExpr(CastedMaxBECount, WideTy);
1517 const SCEV *OperandExtendedAdd =
1518 getAddExpr(WideStart,
1519 getMulExpr(WideMaxBECount,
1520 getSignExtendExpr(Step, WideTy)));
1521 if (SAdd == OperandExtendedAdd) {
1522 // Cache knowledge of AR NSW, which is propagated to this AddRec.
1523 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1524 // Return the expression with the addrec on the outside.
1525 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1526 getSignExtendExpr(Step, Ty),
1527 L, AR->getNoWrapFlags());
1529 // Similar to above, only this time treat the step value as unsigned.
1530 // This covers loops that count up with an unsigned step.
1531 OperandExtendedAdd =
1532 getAddExpr(WideStart,
1533 getMulExpr(WideMaxBECount,
1534 getZeroExtendExpr(Step, WideTy)));
1535 if (SAdd == OperandExtendedAdd) {
1536 // Cache knowledge of AR NSW, which is propagated to this AddRec.
1537 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1538 // Return the expression with the addrec on the outside.
1539 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1540 getZeroExtendExpr(Step, Ty),
1541 L, AR->getNoWrapFlags());
1545 // If the backedge is guarded by a comparison with the pre-inc value
1546 // the addrec is safe. Also, if the entry is guarded by a comparison
1547 // with the start value and the backedge is guarded by a comparison
1548 // with the post-inc value, the addrec is safe.
1549 ICmpInst::Predicate Pred;
1550 const SCEV *OverflowLimit = getOverflowLimitForStep(Step, &Pred, this);
1551 if (OverflowLimit &&
1552 (isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) ||
1553 (isLoopEntryGuardedByCond(L, Pred, Start, OverflowLimit) &&
1554 isLoopBackedgeGuardedByCond(L, Pred, AR->getPostIncExpr(*this),
1556 // Cache knowledge of AR NSW, then propagate NSW to the wide AddRec.
1557 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1558 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1559 getSignExtendExpr(Step, Ty),
1560 L, AR->getNoWrapFlags());
1563 // If Start and Step are constants, check if we can apply this
1565 // sext{C1,+,C2} --> C1 + sext{0,+,C2} if C1 < C2
1566 auto SC1 = dyn_cast<SCEVConstant>(Start);
1567 auto SC2 = dyn_cast<SCEVConstant>(Step);
1569 const APInt &C1 = SC1->getValue()->getValue();
1570 const APInt &C2 = SC2->getValue()->getValue();
1571 if (C1.isStrictlyPositive() && C2.isStrictlyPositive() && C2.ugt(C1) &&
1573 Start = getSignExtendExpr(Start, Ty);
1574 const SCEV *NewAR = getAddRecExpr(getConstant(AR->getType(), 0), Step,
1575 L, AR->getNoWrapFlags());
1576 return getAddExpr(Start, getSignExtendExpr(NewAR, Ty));
1581 // The cast wasn't folded; create an explicit cast node.
1582 // Recompute the insert position, as it may have been invalidated.
1583 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1584 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
1586 UniqueSCEVs.InsertNode(S, IP);
1590 /// getAnyExtendExpr - Return a SCEV for the given operand extended with
1591 /// unspecified bits out to the given type.
1593 const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
1595 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1596 "This is not an extending conversion!");
1597 assert(isSCEVable(Ty) &&
1598 "This is not a conversion to a SCEVable type!");
1599 Ty = getEffectiveSCEVType(Ty);
1601 // Sign-extend negative constants.
1602 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1603 if (SC->getValue()->getValue().isNegative())
1604 return getSignExtendExpr(Op, Ty);
1606 // Peel off a truncate cast.
1607 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
1608 const SCEV *NewOp = T->getOperand();
1609 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
1610 return getAnyExtendExpr(NewOp, Ty);
1611 return getTruncateOrNoop(NewOp, Ty);
1614 // Next try a zext cast. If the cast is folded, use it.
1615 const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
1616 if (!isa<SCEVZeroExtendExpr>(ZExt))
1619 // Next try a sext cast. If the cast is folded, use it.
1620 const SCEV *SExt = getSignExtendExpr(Op, Ty);
1621 if (!isa<SCEVSignExtendExpr>(SExt))
1624 // Force the cast to be folded into the operands of an addrec.
1625 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
1626 SmallVector<const SCEV *, 4> Ops;
1627 for (const SCEV *Op : AR->operands())
1628 Ops.push_back(getAnyExtendExpr(Op, Ty));
1629 return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW);
1632 // If the expression is obviously signed, use the sext cast value.
1633 if (isa<SCEVSMaxExpr>(Op))
1636 // Absent any other information, use the zext cast value.
1640 /// CollectAddOperandsWithScales - Process the given Ops list, which is
1641 /// a list of operands to be added under the given scale, update the given
1642 /// map. This is a helper function for getAddRecExpr. As an example of
1643 /// what it does, given a sequence of operands that would form an add
1644 /// expression like this:
1646 /// m + n + 13 + (A * (o + p + (B * (q + m + 29)))) + r + (-1 * r)
1648 /// where A and B are constants, update the map with these values:
1650 /// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
1652 /// and add 13 + A*B*29 to AccumulatedConstant.
1653 /// This will allow getAddRecExpr to produce this:
1655 /// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
1657 /// This form often exposes folding opportunities that are hidden in
1658 /// the original operand list.
1660 /// Return true iff it appears that any interesting folding opportunities
1661 /// may be exposed. This helps getAddRecExpr short-circuit extra work in
1662 /// the common case where no interesting opportunities are present, and
1663 /// is also used as a check to avoid infinite recursion.
1666 CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
1667 SmallVectorImpl<const SCEV *> &NewOps,
1668 APInt &AccumulatedConstant,
1669 const SCEV *const *Ops, size_t NumOperands,
1671 ScalarEvolution &SE) {
1672 bool Interesting = false;
1674 // Iterate over the add operands. They are sorted, with constants first.
1676 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1678 // Pull a buried constant out to the outside.
1679 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
1681 AccumulatedConstant += Scale * C->getValue()->getValue();
1684 // Next comes everything else. We're especially interested in multiplies
1685 // here, but they're in the middle, so just visit the rest with one loop.
1686 for (; i != NumOperands; ++i) {
1687 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
1688 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
1690 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue();
1691 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
1692 // A multiplication of a constant with another add; recurse.
1693 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1));
1695 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1696 Add->op_begin(), Add->getNumOperands(),
1699 // A multiplication of a constant with some other value. Update
1701 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
1702 const SCEV *Key = SE.getMulExpr(MulOps);
1703 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1704 M.insert(std::make_pair(Key, NewScale));
1706 NewOps.push_back(Pair.first->first);
1708 Pair.first->second += NewScale;
1709 // The map already had an entry for this value, which may indicate
1710 // a folding opportunity.
1715 // An ordinary operand. Update the map.
1716 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1717 M.insert(std::make_pair(Ops[i], Scale));
1719 NewOps.push_back(Pair.first->first);
1721 Pair.first->second += Scale;
1722 // The map already had an entry for this value, which may indicate
1723 // a folding opportunity.
1733 struct APIntCompare {
1734 bool operator()(const APInt &LHS, const APInt &RHS) const {
1735 return LHS.ult(RHS);
1740 /// getAddExpr - Get a canonical add expression, or something simpler if
1742 const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
1743 SCEV::NoWrapFlags Flags) {
1744 assert(!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) &&
1745 "only nuw or nsw allowed");
1746 assert(!Ops.empty() && "Cannot get empty add!");
1747 if (Ops.size() == 1) return Ops[0];
1749 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
1750 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1751 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
1752 "SCEVAddExpr operand types don't match!");
1755 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
1757 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
1758 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask);
1759 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) {
1761 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(),
1762 E = Ops.end(); I != E; ++I)
1763 if (!isKnownNonNegative(*I)) {
1767 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
1770 // Sort by complexity, this groups all similar expression types together.
1771 GroupByComplexity(Ops, LI);
1773 // If there are any constants, fold them together.
1775 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1777 assert(Idx < Ops.size());
1778 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1779 // We found two constants, fold them together!
1780 Ops[0] = getConstant(LHSC->getValue()->getValue() +
1781 RHSC->getValue()->getValue());
1782 if (Ops.size() == 2) return Ops[0];
1783 Ops.erase(Ops.begin()+1); // Erase the folded element
1784 LHSC = cast<SCEVConstant>(Ops[0]);
1787 // If we are left with a constant zero being added, strip it off.
1788 if (LHSC->getValue()->isZero()) {
1789 Ops.erase(Ops.begin());
1793 if (Ops.size() == 1) return Ops[0];
1796 // Okay, check to see if the same value occurs in the operand list more than
1797 // once. If so, merge them together into an multiply expression. Since we
1798 // sorted the list, these values are required to be adjacent.
1799 Type *Ty = Ops[0]->getType();
1800 bool FoundMatch = false;
1801 for (unsigned i = 0, e = Ops.size(); i != e-1; ++i)
1802 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
1803 // Scan ahead to count how many equal operands there are.
1805 while (i+Count != e && Ops[i+Count] == Ops[i])
1807 // Merge the values into a multiply.
1808 const SCEV *Scale = getConstant(Ty, Count);
1809 const SCEV *Mul = getMulExpr(Scale, Ops[i]);
1810 if (Ops.size() == Count)
1813 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count);
1814 --i; e -= Count - 1;
1818 return getAddExpr(Ops, Flags);
1820 // Check for truncates. If all the operands are truncated from the same
1821 // type, see if factoring out the truncate would permit the result to be
1822 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
1823 // if the contents of the resulting outer trunc fold to something simple.
1824 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
1825 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
1826 Type *DstType = Trunc->getType();
1827 Type *SrcType = Trunc->getOperand()->getType();
1828 SmallVector<const SCEV *, 8> LargeOps;
1830 // Check all the operands to see if they can be represented in the
1831 // source type of the truncate.
1832 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1833 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
1834 if (T->getOperand()->getType() != SrcType) {
1838 LargeOps.push_back(T->getOperand());
1839 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1840 LargeOps.push_back(getAnyExtendExpr(C, SrcType));
1841 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
1842 SmallVector<const SCEV *, 8> LargeMulOps;
1843 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
1844 if (const SCEVTruncateExpr *T =
1845 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
1846 if (T->getOperand()->getType() != SrcType) {
1850 LargeMulOps.push_back(T->getOperand());
1851 } else if (const SCEVConstant *C =
1852 dyn_cast<SCEVConstant>(M->getOperand(j))) {
1853 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType));
1860 LargeOps.push_back(getMulExpr(LargeMulOps));
1867 // Evaluate the expression in the larger type.
1868 const SCEV *Fold = getAddExpr(LargeOps, Flags);
1869 // If it folds to something simple, use it. Otherwise, don't.
1870 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
1871 return getTruncateExpr(Fold, DstType);
1875 // Skip past any other cast SCEVs.
1876 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
1879 // If there are add operands they would be next.
1880 if (Idx < Ops.size()) {
1881 bool DeletedAdd = false;
1882 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
1883 // If we have an add, expand the add operands onto the end of the operands
1885 Ops.erase(Ops.begin()+Idx);
1886 Ops.append(Add->op_begin(), Add->op_end());
1890 // If we deleted at least one add, we added operands to the end of the list,
1891 // and they are not necessarily sorted. Recurse to resort and resimplify
1892 // any operands we just acquired.
1894 return getAddExpr(Ops);
1897 // Skip over the add expression until we get to a multiply.
1898 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1901 // Check to see if there are any folding opportunities present with
1902 // operands multiplied by constant values.
1903 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
1904 uint64_t BitWidth = getTypeSizeInBits(Ty);
1905 DenseMap<const SCEV *, APInt> M;
1906 SmallVector<const SCEV *, 8> NewOps;
1907 APInt AccumulatedConstant(BitWidth, 0);
1908 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1909 Ops.data(), Ops.size(),
1910 APInt(BitWidth, 1), *this)) {
1911 // Some interesting folding opportunity is present, so its worthwhile to
1912 // re-generate the operands list. Group the operands by constant scale,
1913 // to avoid multiplying by the same constant scale multiple times.
1914 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
1915 for (SmallVectorImpl<const SCEV *>::const_iterator I = NewOps.begin(),
1916 E = NewOps.end(); I != E; ++I)
1917 MulOpLists[M.find(*I)->second].push_back(*I);
1918 // Re-generate the operands list.
1920 if (AccumulatedConstant != 0)
1921 Ops.push_back(getConstant(AccumulatedConstant));
1922 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator
1923 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I)
1925 Ops.push_back(getMulExpr(getConstant(I->first),
1926 getAddExpr(I->second)));
1928 return getConstant(Ty, 0);
1929 if (Ops.size() == 1)
1931 return getAddExpr(Ops);
1935 // If we are adding something to a multiply expression, make sure the
1936 // something is not already an operand of the multiply. If so, merge it into
1938 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
1939 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
1940 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
1941 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
1942 if (isa<SCEVConstant>(MulOpSCEV))
1944 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
1945 if (MulOpSCEV == Ops[AddOp]) {
1946 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
1947 const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
1948 if (Mul->getNumOperands() != 2) {
1949 // If the multiply has more than two operands, we must get the
1951 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
1952 Mul->op_begin()+MulOp);
1953 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
1954 InnerMul = getMulExpr(MulOps);
1956 const SCEV *One = getConstant(Ty, 1);
1957 const SCEV *AddOne = getAddExpr(One, InnerMul);
1958 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV);
1959 if (Ops.size() == 2) return OuterMul;
1961 Ops.erase(Ops.begin()+AddOp);
1962 Ops.erase(Ops.begin()+Idx-1);
1964 Ops.erase(Ops.begin()+Idx);
1965 Ops.erase(Ops.begin()+AddOp-1);
1967 Ops.push_back(OuterMul);
1968 return getAddExpr(Ops);
1971 // Check this multiply against other multiplies being added together.
1972 for (unsigned OtherMulIdx = Idx+1;
1973 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
1975 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
1976 // If MulOp occurs in OtherMul, we can fold the two multiplies
1978 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
1979 OMulOp != e; ++OMulOp)
1980 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
1981 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
1982 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
1983 if (Mul->getNumOperands() != 2) {
1984 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
1985 Mul->op_begin()+MulOp);
1986 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
1987 InnerMul1 = getMulExpr(MulOps);
1989 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
1990 if (OtherMul->getNumOperands() != 2) {
1991 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
1992 OtherMul->op_begin()+OMulOp);
1993 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end());
1994 InnerMul2 = getMulExpr(MulOps);
1996 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
1997 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
1998 if (Ops.size() == 2) return OuterMul;
1999 Ops.erase(Ops.begin()+Idx);
2000 Ops.erase(Ops.begin()+OtherMulIdx-1);
2001 Ops.push_back(OuterMul);
2002 return getAddExpr(Ops);
2008 // If there are any add recurrences in the operands list, see if any other
2009 // added values are loop invariant. If so, we can fold them into the
2011 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2014 // Scan over all recurrences, trying to fold loop invariants into them.
2015 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
2016 // Scan all of the other operands to this add and add them to the vector if
2017 // they are loop invariant w.r.t. the recurrence.
2018 SmallVector<const SCEV *, 8> LIOps;
2019 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2020 const Loop *AddRecLoop = AddRec->getLoop();
2021 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2022 if (isLoopInvariant(Ops[i], AddRecLoop)) {
2023 LIOps.push_back(Ops[i]);
2024 Ops.erase(Ops.begin()+i);
2028 // If we found some loop invariants, fold them into the recurrence.
2029 if (!LIOps.empty()) {
2030 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
2031 LIOps.push_back(AddRec->getStart());
2033 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
2035 AddRecOps[0] = getAddExpr(LIOps);
2037 // Build the new addrec. Propagate the NUW and NSW flags if both the
2038 // outer add and the inner addrec are guaranteed to have no overflow.
2039 // Always propagate NW.
2040 Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW));
2041 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags);
2043 // If all of the other operands were loop invariant, we are done.
2044 if (Ops.size() == 1) return NewRec;
2046 // Otherwise, add the folded AddRec by the non-invariant parts.
2047 for (unsigned i = 0;; ++i)
2048 if (Ops[i] == AddRec) {
2052 return getAddExpr(Ops);
2055 // Okay, if there weren't any loop invariants to be folded, check to see if
2056 // there are multiple AddRec's with the same loop induction variable being
2057 // added together. If so, we can fold them.
2058 for (unsigned OtherIdx = Idx+1;
2059 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2061 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
2062 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L>
2063 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
2065 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2067 if (const SCEVAddRecExpr *OtherAddRec =
2068 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]))
2069 if (OtherAddRec->getLoop() == AddRecLoop) {
2070 for (unsigned i = 0, e = OtherAddRec->getNumOperands();
2072 if (i >= AddRecOps.size()) {
2073 AddRecOps.append(OtherAddRec->op_begin()+i,
2074 OtherAddRec->op_end());
2077 AddRecOps[i] = getAddExpr(AddRecOps[i],
2078 OtherAddRec->getOperand(i));
2080 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2082 // Step size has changed, so we cannot guarantee no self-wraparound.
2083 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap);
2084 return getAddExpr(Ops);
2087 // Otherwise couldn't fold anything into this recurrence. Move onto the
2091 // Okay, it looks like we really DO need an add expr. Check to see if we
2092 // already have one, otherwise create a new one.
2093 FoldingSetNodeID ID;
2094 ID.AddInteger(scAddExpr);
2095 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2096 ID.AddPointer(Ops[i]);
2099 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2101 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2102 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2103 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator),
2105 UniqueSCEVs.InsertNode(S, IP);
2107 S->setNoWrapFlags(Flags);
2111 static uint64_t umul_ov(uint64_t i, uint64_t j, bool &Overflow) {
2113 if (j > 1 && k / j != i) Overflow = true;
2117 /// Compute the result of "n choose k", the binomial coefficient. If an
2118 /// intermediate computation overflows, Overflow will be set and the return will
2119 /// be garbage. Overflow is not cleared on absence of overflow.
2120 static uint64_t Choose(uint64_t n, uint64_t k, bool &Overflow) {
2121 // We use the multiplicative formula:
2122 // n(n-1)(n-2)...(n-(k-1)) / k(k-1)(k-2)...1 .
2123 // At each iteration, we take the n-th term of the numeral and divide by the
2124 // (k-n)th term of the denominator. This division will always produce an
2125 // integral result, and helps reduce the chance of overflow in the
2126 // intermediate computations. However, we can still overflow even when the
2127 // final result would fit.
2129 if (n == 0 || n == k) return 1;
2130 if (k > n) return 0;
2136 for (uint64_t i = 1; i <= k; ++i) {
2137 r = umul_ov(r, n-(i-1), Overflow);
2143 /// Determine if any of the operands in this SCEV are a constant or if
2144 /// any of the add or multiply expressions in this SCEV contain a constant.
2145 static bool containsConstantSomewhere(const SCEV *StartExpr) {
2146 SmallVector<const SCEV *, 4> Ops;
2147 Ops.push_back(StartExpr);
2148 while (!Ops.empty()) {
2149 const SCEV *CurrentExpr = Ops.pop_back_val();
2150 if (isa<SCEVConstant>(*CurrentExpr))
2153 if (isa<SCEVAddExpr>(*CurrentExpr) || isa<SCEVMulExpr>(*CurrentExpr)) {
2154 const auto *CurrentNAry = cast<SCEVNAryExpr>(CurrentExpr);
2155 for (const SCEV *Operand : CurrentNAry->operands())
2156 Ops.push_back(Operand);
2162 /// getMulExpr - Get a canonical multiply expression, or something simpler if
2164 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
2165 SCEV::NoWrapFlags Flags) {
2166 assert(Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) &&
2167 "only nuw or nsw allowed");
2168 assert(!Ops.empty() && "Cannot get empty mul!");
2169 if (Ops.size() == 1) return Ops[0];
2171 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2172 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2173 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2174 "SCEVMulExpr operand types don't match!");
2177 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
2179 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
2180 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask);
2181 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) {
2183 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(),
2184 E = Ops.end(); I != E; ++I)
2185 if (!isKnownNonNegative(*I)) {
2189 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
2192 // Sort by complexity, this groups all similar expression types together.
2193 GroupByComplexity(Ops, LI);
2195 // If there are any constants, fold them together.
2197 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2199 // C1*(C2+V) -> C1*C2 + C1*V
2200 if (Ops.size() == 2)
2201 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
2202 // If any of Add's ops are Adds or Muls with a constant,
2203 // apply this transformation as well.
2204 if (Add->getNumOperands() == 2)
2205 if (containsConstantSomewhere(Add))
2206 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
2207 getMulExpr(LHSC, Add->getOperand(1)));
2210 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2211 // We found two constants, fold them together!
2212 ConstantInt *Fold = ConstantInt::get(getContext(),
2213 LHSC->getValue()->getValue() *
2214 RHSC->getValue()->getValue());
2215 Ops[0] = getConstant(Fold);
2216 Ops.erase(Ops.begin()+1); // Erase the folded element
2217 if (Ops.size() == 1) return Ops[0];
2218 LHSC = cast<SCEVConstant>(Ops[0]);
2221 // If we are left with a constant one being multiplied, strip it off.
2222 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
2223 Ops.erase(Ops.begin());
2225 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
2226 // If we have a multiply of zero, it will always be zero.
2228 } else if (Ops[0]->isAllOnesValue()) {
2229 // If we have a mul by -1 of an add, try distributing the -1 among the
2231 if (Ops.size() == 2) {
2232 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
2233 SmallVector<const SCEV *, 4> NewOps;
2234 bool AnyFolded = false;
2235 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(),
2236 E = Add->op_end(); I != E; ++I) {
2237 const SCEV *Mul = getMulExpr(Ops[0], *I);
2238 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
2239 NewOps.push_back(Mul);
2242 return getAddExpr(NewOps);
2244 else if (const SCEVAddRecExpr *
2245 AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) {
2246 // Negation preserves a recurrence's no self-wrap property.
2247 SmallVector<const SCEV *, 4> Operands;
2248 for (SCEVAddRecExpr::op_iterator I = AddRec->op_begin(),
2249 E = AddRec->op_end(); I != E; ++I) {
2250 Operands.push_back(getMulExpr(Ops[0], *I));
2252 return getAddRecExpr(Operands, AddRec->getLoop(),
2253 AddRec->getNoWrapFlags(SCEV::FlagNW));
2258 if (Ops.size() == 1)
2262 // Skip over the add expression until we get to a multiply.
2263 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
2266 // If there are mul operands inline them all into this expression.
2267 if (Idx < Ops.size()) {
2268 bool DeletedMul = false;
2269 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
2270 // If we have an mul, expand the mul operands onto the end of the operands
2272 Ops.erase(Ops.begin()+Idx);
2273 Ops.append(Mul->op_begin(), Mul->op_end());
2277 // If we deleted at least one mul, we added operands to the end of the list,
2278 // and they are not necessarily sorted. Recurse to resort and resimplify
2279 // any operands we just acquired.
2281 return getMulExpr(Ops);
2284 // If there are any add recurrences in the operands list, see if any other
2285 // added values are loop invariant. If so, we can fold them into the
2287 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
2290 // Scan over all recurrences, trying to fold loop invariants into them.
2291 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
2292 // Scan all of the other operands to this mul and add them to the vector if
2293 // they are loop invariant w.r.t. the recurrence.
2294 SmallVector<const SCEV *, 8> LIOps;
2295 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
2296 const Loop *AddRecLoop = AddRec->getLoop();
2297 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2298 if (isLoopInvariant(Ops[i], AddRecLoop)) {
2299 LIOps.push_back(Ops[i]);
2300 Ops.erase(Ops.begin()+i);
2304 // If we found some loop invariants, fold them into the recurrence.
2305 if (!LIOps.empty()) {
2306 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
2307 SmallVector<const SCEV *, 4> NewOps;
2308 NewOps.reserve(AddRec->getNumOperands());
2309 const SCEV *Scale = getMulExpr(LIOps);
2310 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
2311 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
2313 // Build the new addrec. Propagate the NUW and NSW flags if both the
2314 // outer mul and the inner addrec are guaranteed to have no overflow.
2316 // No self-wrap cannot be guaranteed after changing the step size, but
2317 // will be inferred if either NUW or NSW is true.
2318 Flags = AddRec->getNoWrapFlags(clearFlags(Flags, SCEV::FlagNW));
2319 const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, Flags);
2321 // If all of the other operands were loop invariant, we are done.
2322 if (Ops.size() == 1) return NewRec;
2324 // Otherwise, multiply the folded AddRec by the non-invariant parts.
2325 for (unsigned i = 0;; ++i)
2326 if (Ops[i] == AddRec) {
2330 return getMulExpr(Ops);
2333 // Okay, if there weren't any loop invariants to be folded, check to see if
2334 // there are multiple AddRec's with the same loop induction variable being
2335 // multiplied together. If so, we can fold them.
2337 // {A1,+,A2,+,...,+,An}<L> * {B1,+,B2,+,...,+,Bn}<L>
2338 // = {x=1 in [ sum y=x..2x [ sum z=max(y-x, y-n)..min(x,n) [
2339 // choose(x, 2x)*choose(2x-y, x-z)*A_{y-z}*B_z
2340 // ]]],+,...up to x=2n}.
2341 // Note that the arguments to choose() are always integers with values
2342 // known at compile time, never SCEV objects.
2344 // The implementation avoids pointless extra computations when the two
2345 // addrec's are of different length (mathematically, it's equivalent to
2346 // an infinite stream of zeros on the right).
2347 bool OpsModified = false;
2348 for (unsigned OtherIdx = Idx+1;
2349 OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2351 const SCEVAddRecExpr *OtherAddRec =
2352 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]);
2353 if (!OtherAddRec || OtherAddRec->getLoop() != AddRecLoop)
2356 bool Overflow = false;
2357 Type *Ty = AddRec->getType();
2358 bool LargerThan64Bits = getTypeSizeInBits(Ty) > 64;
2359 SmallVector<const SCEV*, 7> AddRecOps;
2360 for (int x = 0, xe = AddRec->getNumOperands() +
2361 OtherAddRec->getNumOperands() - 1; x != xe && !Overflow; ++x) {
2362 const SCEV *Term = getConstant(Ty, 0);
2363 for (int y = x, ye = 2*x+1; y != ye && !Overflow; ++y) {
2364 uint64_t Coeff1 = Choose(x, 2*x - y, Overflow);
2365 for (int z = std::max(y-x, y-(int)AddRec->getNumOperands()+1),
2366 ze = std::min(x+1, (int)OtherAddRec->getNumOperands());
2367 z < ze && !Overflow; ++z) {
2368 uint64_t Coeff2 = Choose(2*x - y, x-z, Overflow);
2370 if (LargerThan64Bits)
2371 Coeff = umul_ov(Coeff1, Coeff2, Overflow);
2373 Coeff = Coeff1*Coeff2;
2374 const SCEV *CoeffTerm = getConstant(Ty, Coeff);
2375 const SCEV *Term1 = AddRec->getOperand(y-z);
2376 const SCEV *Term2 = OtherAddRec->getOperand(z);
2377 Term = getAddExpr(Term, getMulExpr(CoeffTerm, Term1,Term2));
2380 AddRecOps.push_back(Term);
2383 const SCEV *NewAddRec = getAddRecExpr(AddRecOps, AddRec->getLoop(),
2385 if (Ops.size() == 2) return NewAddRec;
2386 Ops[Idx] = NewAddRec;
2387 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2389 AddRec = dyn_cast<SCEVAddRecExpr>(NewAddRec);
2395 return getMulExpr(Ops);
2397 // Otherwise couldn't fold anything into this recurrence. Move onto the
2401 // Okay, it looks like we really DO need an mul expr. Check to see if we
2402 // already have one, otherwise create a new one.
2403 FoldingSetNodeID ID;
2404 ID.AddInteger(scMulExpr);
2405 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2406 ID.AddPointer(Ops[i]);
2409 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2411 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2412 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2413 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
2415 UniqueSCEVs.InsertNode(S, IP);
2417 S->setNoWrapFlags(Flags);
2421 /// getUDivExpr - Get a canonical unsigned division expression, or something
2422 /// simpler if possible.
2423 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
2425 assert(getEffectiveSCEVType(LHS->getType()) ==
2426 getEffectiveSCEVType(RHS->getType()) &&
2427 "SCEVUDivExpr operand types don't match!");
2429 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
2430 if (RHSC->getValue()->equalsInt(1))
2431 return LHS; // X udiv 1 --> x
2432 // If the denominator is zero, the result of the udiv is undefined. Don't
2433 // try to analyze it, because the resolution chosen here may differ from
2434 // the resolution chosen in other parts of the compiler.
2435 if (!RHSC->getValue()->isZero()) {
2436 // Determine if the division can be folded into the operands of
2438 // TODO: Generalize this to non-constants by using known-bits information.
2439 Type *Ty = LHS->getType();
2440 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
2441 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1;
2442 // For non-power-of-two values, effectively round the value up to the
2443 // nearest power of two.
2444 if (!RHSC->getValue()->getValue().isPowerOf2())
2446 IntegerType *ExtTy =
2447 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
2448 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
2449 if (const SCEVConstant *Step =
2450 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) {
2451 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
2452 const APInt &StepInt = Step->getValue()->getValue();
2453 const APInt &DivInt = RHSC->getValue()->getValue();
2454 if (!StepInt.urem(DivInt) &&
2455 getZeroExtendExpr(AR, ExtTy) ==
2456 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2457 getZeroExtendExpr(Step, ExtTy),
2458 AR->getLoop(), SCEV::FlagAnyWrap)) {
2459 SmallVector<const SCEV *, 4> Operands;
2460 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i)
2461 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS));
2462 return getAddRecExpr(Operands, AR->getLoop(),
2465 /// Get a canonical UDivExpr for a recurrence.
2466 /// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0.
2467 // We can currently only fold X%N if X is constant.
2468 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(AR->getStart());
2469 if (StartC && !DivInt.urem(StepInt) &&
2470 getZeroExtendExpr(AR, ExtTy) ==
2471 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2472 getZeroExtendExpr(Step, ExtTy),
2473 AR->getLoop(), SCEV::FlagAnyWrap)) {
2474 const APInt &StartInt = StartC->getValue()->getValue();
2475 const APInt &StartRem = StartInt.urem(StepInt);
2477 LHS = getAddRecExpr(getConstant(StartInt - StartRem), Step,
2478 AR->getLoop(), SCEV::FlagNW);
2481 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
2482 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
2483 SmallVector<const SCEV *, 4> Operands;
2484 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i)
2485 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy));
2486 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
2487 // Find an operand that's safely divisible.
2488 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
2489 const SCEV *Op = M->getOperand(i);
2490 const SCEV *Div = getUDivExpr(Op, RHSC);
2491 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
2492 Operands = SmallVector<const SCEV *, 4>(M->op_begin(),
2495 return getMulExpr(Operands);
2499 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
2500 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) {
2501 SmallVector<const SCEV *, 4> Operands;
2502 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i)
2503 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy));
2504 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
2506 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
2507 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
2508 if (isa<SCEVUDivExpr>(Op) ||
2509 getMulExpr(Op, RHS) != A->getOperand(i))
2511 Operands.push_back(Op);
2513 if (Operands.size() == A->getNumOperands())
2514 return getAddExpr(Operands);
2518 // Fold if both operands are constant.
2519 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
2520 Constant *LHSCV = LHSC->getValue();
2521 Constant *RHSCV = RHSC->getValue();
2522 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
2528 FoldingSetNodeID ID;
2529 ID.AddInteger(scUDivExpr);
2533 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2534 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
2536 UniqueSCEVs.InsertNode(S, IP);
2540 static const APInt gcd(const SCEVConstant *C1, const SCEVConstant *C2) {
2541 APInt A = C1->getValue()->getValue().abs();
2542 APInt B = C2->getValue()->getValue().abs();
2543 uint32_t ABW = A.getBitWidth();
2544 uint32_t BBW = B.getBitWidth();
2551 return APIntOps::GreatestCommonDivisor(A, B);
2554 /// getUDivExactExpr - Get a canonical unsigned division expression, or
2555 /// something simpler if possible. There is no representation for an exact udiv
2556 /// in SCEV IR, but we can attempt to remove factors from the LHS and RHS.
2557 /// We can't do this when it's not exact because the udiv may be clearing bits.
2558 const SCEV *ScalarEvolution::getUDivExactExpr(const SCEV *LHS,
2560 // TODO: we could try to find factors in all sorts of things, but for now we
2561 // just deal with u/exact (multiply, constant). See SCEVDivision towards the
2562 // end of this file for inspiration.
2564 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(LHS);
2566 return getUDivExpr(LHS, RHS);
2568 if (const SCEVConstant *RHSCst = dyn_cast<SCEVConstant>(RHS)) {
2569 // If the mulexpr multiplies by a constant, then that constant must be the
2570 // first element of the mulexpr.
2571 if (const SCEVConstant *LHSCst =
2572 dyn_cast<SCEVConstant>(Mul->getOperand(0))) {
2573 if (LHSCst == RHSCst) {
2574 SmallVector<const SCEV *, 2> Operands;
2575 Operands.append(Mul->op_begin() + 1, Mul->op_end());
2576 return getMulExpr(Operands);
2579 // We can't just assume that LHSCst divides RHSCst cleanly, it could be
2580 // that there's a factor provided by one of the other terms. We need to
2582 APInt Factor = gcd(LHSCst, RHSCst);
2583 if (!Factor.isIntN(1)) {
2584 LHSCst = cast<SCEVConstant>(
2585 getConstant(LHSCst->getValue()->getValue().udiv(Factor)));
2586 RHSCst = cast<SCEVConstant>(
2587 getConstant(RHSCst->getValue()->getValue().udiv(Factor)));
2588 SmallVector<const SCEV *, 2> Operands;
2589 Operands.push_back(LHSCst);
2590 Operands.append(Mul->op_begin() + 1, Mul->op_end());
2591 LHS = getMulExpr(Operands);
2593 Mul = dyn_cast<SCEVMulExpr>(LHS);
2595 return getUDivExactExpr(LHS, RHS);
2600 for (int i = 0, e = Mul->getNumOperands(); i != e; ++i) {
2601 if (Mul->getOperand(i) == RHS) {
2602 SmallVector<const SCEV *, 2> Operands;
2603 Operands.append(Mul->op_begin(), Mul->op_begin() + i);
2604 Operands.append(Mul->op_begin() + i + 1, Mul->op_end());
2605 return getMulExpr(Operands);
2609 return getUDivExpr(LHS, RHS);
2612 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2613 /// Simplify the expression as much as possible.
2614 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step,
2616 SCEV::NoWrapFlags Flags) {
2617 SmallVector<const SCEV *, 4> Operands;
2618 Operands.push_back(Start);
2619 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
2620 if (StepChrec->getLoop() == L) {
2621 Operands.append(StepChrec->op_begin(), StepChrec->op_end());
2622 return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW));
2625 Operands.push_back(Step);
2626 return getAddRecExpr(Operands, L, Flags);
2629 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2630 /// Simplify the expression as much as possible.
2632 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
2633 const Loop *L, SCEV::NoWrapFlags Flags) {
2634 if (Operands.size() == 1) return Operands[0];
2636 Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
2637 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
2638 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy &&
2639 "SCEVAddRecExpr operand types don't match!");
2640 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2641 assert(isLoopInvariant(Operands[i], L) &&
2642 "SCEVAddRecExpr operand is not loop-invariant!");
2645 if (Operands.back()->isZero()) {
2646 Operands.pop_back();
2647 return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0} --> X
2650 // It's tempting to want to call getMaxBackedgeTakenCount count here and
2651 // use that information to infer NUW and NSW flags. However, computing a
2652 // BE count requires calling getAddRecExpr, so we may not yet have a
2653 // meaningful BE count at this point (and if we don't, we'd be stuck
2654 // with a SCEVCouldNotCompute as the cached BE count).
2656 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
2658 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
2659 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask);
2660 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) {
2662 for (SmallVectorImpl<const SCEV *>::const_iterator I = Operands.begin(),
2663 E = Operands.end(); I != E; ++I)
2664 if (!isKnownNonNegative(*I)) {
2668 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
2671 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
2672 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
2673 const Loop *NestedLoop = NestedAR->getLoop();
2674 if (L->contains(NestedLoop) ?
2675 (L->getLoopDepth() < NestedLoop->getLoopDepth()) :
2676 (!NestedLoop->contains(L) &&
2677 DT->dominates(L->getHeader(), NestedLoop->getHeader()))) {
2678 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
2679 NestedAR->op_end());
2680 Operands[0] = NestedAR->getStart();
2681 // AddRecs require their operands be loop-invariant with respect to their
2682 // loops. Don't perform this transformation if it would break this
2684 bool AllInvariant = true;
2685 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2686 if (!isLoopInvariant(Operands[i], L)) {
2687 AllInvariant = false;
2691 // Create a recurrence for the outer loop with the same step size.
2693 // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the
2694 // inner recurrence has the same property.
2695 SCEV::NoWrapFlags OuterFlags =
2696 maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags());
2698 NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags);
2699 AllInvariant = true;
2700 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i)
2701 if (!isLoopInvariant(NestedOperands[i], NestedLoop)) {
2702 AllInvariant = false;
2706 // Ok, both add recurrences are valid after the transformation.
2708 // The inner recurrence keeps its NW flag but only keeps NUW/NSW if
2709 // the outer recurrence has the same property.
2710 SCEV::NoWrapFlags InnerFlags =
2711 maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags);
2712 return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags);
2715 // Reset Operands to its original state.
2716 Operands[0] = NestedAR;
2720 // Okay, it looks like we really DO need an addrec expr. Check to see if we
2721 // already have one, otherwise create a new one.
2722 FoldingSetNodeID ID;
2723 ID.AddInteger(scAddRecExpr);
2724 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2725 ID.AddPointer(Operands[i]);
2729 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2731 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size());
2732 std::uninitialized_copy(Operands.begin(), Operands.end(), O);
2733 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator),
2734 O, Operands.size(), L);
2735 UniqueSCEVs.InsertNode(S, IP);
2737 S->setNoWrapFlags(Flags);
2741 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
2743 SmallVector<const SCEV *, 2> Ops;
2746 return getSMaxExpr(Ops);
2750 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2751 assert(!Ops.empty() && "Cannot get empty smax!");
2752 if (Ops.size() == 1) return Ops[0];
2754 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2755 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2756 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2757 "SCEVSMaxExpr operand types don't match!");
2760 // Sort by complexity, this groups all similar expression types together.
2761 GroupByComplexity(Ops, LI);
2763 // If there are any constants, fold them together.
2765 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2767 assert(Idx < Ops.size());
2768 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2769 // We found two constants, fold them together!
2770 ConstantInt *Fold = ConstantInt::get(getContext(),
2771 APIntOps::smax(LHSC->getValue()->getValue(),
2772 RHSC->getValue()->getValue()));
2773 Ops[0] = getConstant(Fold);
2774 Ops.erase(Ops.begin()+1); // Erase the folded element
2775 if (Ops.size() == 1) return Ops[0];
2776 LHSC = cast<SCEVConstant>(Ops[0]);
2779 // If we are left with a constant minimum-int, strip it off.
2780 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
2781 Ops.erase(Ops.begin());
2783 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
2784 // If we have an smax with a constant maximum-int, it will always be
2789 if (Ops.size() == 1) return Ops[0];
2792 // Find the first SMax
2793 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
2796 // Check to see if one of the operands is an SMax. If so, expand its operands
2797 // onto our operand list, and recurse to simplify.
2798 if (Idx < Ops.size()) {
2799 bool DeletedSMax = false;
2800 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
2801 Ops.erase(Ops.begin()+Idx);
2802 Ops.append(SMax->op_begin(), SMax->op_end());
2807 return getSMaxExpr(Ops);
2810 // Okay, check to see if the same value occurs in the operand list twice. If
2811 // so, delete one. Since we sorted the list, these values are required to
2813 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2814 // X smax Y smax Y --> X smax Y
2815 // X smax Y --> X, if X is always greater than Y
2816 if (Ops[i] == Ops[i+1] ||
2817 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) {
2818 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2820 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) {
2821 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2825 if (Ops.size() == 1) return Ops[0];
2827 assert(!Ops.empty() && "Reduced smax down to nothing!");
2829 // Okay, it looks like we really DO need an smax expr. Check to see if we
2830 // already have one, otherwise create a new one.
2831 FoldingSetNodeID ID;
2832 ID.AddInteger(scSMaxExpr);
2833 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2834 ID.AddPointer(Ops[i]);
2836 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2837 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2838 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2839 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator),
2841 UniqueSCEVs.InsertNode(S, IP);
2845 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
2847 SmallVector<const SCEV *, 2> Ops;
2850 return getUMaxExpr(Ops);
2854 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2855 assert(!Ops.empty() && "Cannot get empty umax!");
2856 if (Ops.size() == 1) return Ops[0];
2858 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2859 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2860 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2861 "SCEVUMaxExpr operand types don't match!");
2864 // Sort by complexity, this groups all similar expression types together.
2865 GroupByComplexity(Ops, LI);
2867 // If there are any constants, fold them together.
2869 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2871 assert(Idx < Ops.size());
2872 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2873 // We found two constants, fold them together!
2874 ConstantInt *Fold = ConstantInt::get(getContext(),
2875 APIntOps::umax(LHSC->getValue()->getValue(),
2876 RHSC->getValue()->getValue()));
2877 Ops[0] = getConstant(Fold);
2878 Ops.erase(Ops.begin()+1); // Erase the folded element
2879 if (Ops.size() == 1) return Ops[0];
2880 LHSC = cast<SCEVConstant>(Ops[0]);
2883 // If we are left with a constant minimum-int, strip it off.
2884 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
2885 Ops.erase(Ops.begin());
2887 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
2888 // If we have an umax with a constant maximum-int, it will always be
2893 if (Ops.size() == 1) return Ops[0];
2896 // Find the first UMax
2897 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
2900 // Check to see if one of the operands is a UMax. If so, expand its operands
2901 // onto our operand list, and recurse to simplify.
2902 if (Idx < Ops.size()) {
2903 bool DeletedUMax = false;
2904 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
2905 Ops.erase(Ops.begin()+Idx);
2906 Ops.append(UMax->op_begin(), UMax->op_end());
2911 return getUMaxExpr(Ops);
2914 // Okay, check to see if the same value occurs in the operand list twice. If
2915 // so, delete one. Since we sorted the list, these values are required to
2917 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2918 // X umax Y umax Y --> X umax Y
2919 // X umax Y --> X, if X is always greater than Y
2920 if (Ops[i] == Ops[i+1] ||
2921 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) {
2922 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2924 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) {
2925 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2929 if (Ops.size() == 1) return Ops[0];
2931 assert(!Ops.empty() && "Reduced umax down to nothing!");
2933 // Okay, it looks like we really DO need a umax expr. Check to see if we
2934 // already have one, otherwise create a new one.
2935 FoldingSetNodeID ID;
2936 ID.AddInteger(scUMaxExpr);
2937 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2938 ID.AddPointer(Ops[i]);
2940 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2941 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2942 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2943 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator),
2945 UniqueSCEVs.InsertNode(S, IP);
2949 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
2951 // ~smax(~x, ~y) == smin(x, y).
2952 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2955 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
2957 // ~umax(~x, ~y) == umin(x, y)
2958 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2961 const SCEV *ScalarEvolution::getSizeOfExpr(Type *IntTy, Type *AllocTy) {
2962 // If we have DataLayout, we can bypass creating a target-independent
2963 // constant expression and then folding it back into a ConstantInt.
2964 // This is just a compile-time optimization.
2966 return getConstant(IntTy, DL->getTypeAllocSize(AllocTy));
2968 Constant *C = ConstantExpr::getSizeOf(AllocTy);
2969 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2970 if (Constant *Folded = ConstantFoldConstantExpression(CE, DL, TLI))
2972 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2973 assert(Ty == IntTy && "Effective SCEV type doesn't match");
2974 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2977 const SCEV *ScalarEvolution::getOffsetOfExpr(Type *IntTy,
2980 // If we have DataLayout, we can bypass creating a target-independent
2981 // constant expression and then folding it back into a ConstantInt.
2982 // This is just a compile-time optimization.
2984 return getConstant(IntTy,
2985 DL->getStructLayout(STy)->getElementOffset(FieldNo));
2988 Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo);
2989 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2990 if (Constant *Folded = ConstantFoldConstantExpression(CE, DL, TLI))
2993 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy));
2994 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2997 const SCEV *ScalarEvolution::getUnknown(Value *V) {
2998 // Don't attempt to do anything other than create a SCEVUnknown object
2999 // here. createSCEV only calls getUnknown after checking for all other
3000 // interesting possibilities, and any other code that calls getUnknown
3001 // is doing so in order to hide a value from SCEV canonicalization.
3003 FoldingSetNodeID ID;
3004 ID.AddInteger(scUnknown);
3007 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
3008 assert(cast<SCEVUnknown>(S)->getValue() == V &&
3009 "Stale SCEVUnknown in uniquing map!");
3012 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
3014 FirstUnknown = cast<SCEVUnknown>(S);
3015 UniqueSCEVs.InsertNode(S, IP);
3019 //===----------------------------------------------------------------------===//
3020 // Basic SCEV Analysis and PHI Idiom Recognition Code
3023 /// isSCEVable - Test if values of the given type are analyzable within
3024 /// the SCEV framework. This primarily includes integer types, and it
3025 /// can optionally include pointer types if the ScalarEvolution class
3026 /// has access to target-specific information.
3027 bool ScalarEvolution::isSCEVable(Type *Ty) const {
3028 // Integers and pointers are always SCEVable.
3029 return Ty->isIntegerTy() || Ty->isPointerTy();
3032 /// getTypeSizeInBits - Return the size in bits of the specified type,
3033 /// for which isSCEVable must return true.
3034 uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const {
3035 assert(isSCEVable(Ty) && "Type is not SCEVable!");
3037 // If we have a DataLayout, use it!
3039 return DL->getTypeSizeInBits(Ty);
3041 // Integer types have fixed sizes.
3042 if (Ty->isIntegerTy())
3043 return Ty->getPrimitiveSizeInBits();
3045 // The only other support type is pointer. Without DataLayout, conservatively
3046 // assume pointers are 64-bit.
3047 assert(Ty->isPointerTy() && "isSCEVable permitted a non-SCEVable type!");
3051 /// getEffectiveSCEVType - Return a type with the same bitwidth as
3052 /// the given type and which represents how SCEV will treat the given
3053 /// type, for which isSCEVable must return true. For pointer types,
3054 /// this is the pointer-sized integer type.
3055 Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const {
3056 assert(isSCEVable(Ty) && "Type is not SCEVable!");
3058 if (Ty->isIntegerTy()) {
3062 // The only other support type is pointer.
3063 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
3066 return DL->getIntPtrType(Ty);
3068 // Without DataLayout, conservatively assume pointers are 64-bit.
3069 return Type::getInt64Ty(getContext());
3072 const SCEV *ScalarEvolution::getCouldNotCompute() {
3073 return &CouldNotCompute;
3077 // Helper class working with SCEVTraversal to figure out if a SCEV contains
3078 // a SCEVUnknown with null value-pointer. FindInvalidSCEVUnknown::FindOne
3079 // is set iff if find such SCEVUnknown.
3081 struct FindInvalidSCEVUnknown {
3083 FindInvalidSCEVUnknown() { FindOne = false; }
3084 bool follow(const SCEV *S) {
3085 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
3089 if (!cast<SCEVUnknown>(S)->getValue())
3096 bool isDone() const { return FindOne; }
3100 bool ScalarEvolution::checkValidity(const SCEV *S) const {
3101 FindInvalidSCEVUnknown F;
3102 SCEVTraversal<FindInvalidSCEVUnknown> ST(F);
3108 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
3109 /// expression and create a new one.
3110 const SCEV *ScalarEvolution::getSCEV(Value *V) {
3111 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
3113 ValueExprMapType::iterator I = ValueExprMap.find_as(V);
3114 if (I != ValueExprMap.end()) {
3115 const SCEV *S = I->second;
3116 if (checkValidity(S))
3119 ValueExprMap.erase(I);
3121 const SCEV *S = createSCEV(V);
3123 // The process of creating a SCEV for V may have caused other SCEVs
3124 // to have been created, so it's necessary to insert the new entry
3125 // from scratch, rather than trying to remember the insert position
3127 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(V, this), S));
3131 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
3133 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) {
3134 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
3136 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
3138 Type *Ty = V->getType();
3139 Ty = getEffectiveSCEVType(Ty);
3140 return getMulExpr(V,
3141 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))));
3144 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
3145 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
3146 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
3148 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
3150 Type *Ty = V->getType();
3151 Ty = getEffectiveSCEVType(Ty);
3152 const SCEV *AllOnes =
3153 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
3154 return getMinusSCEV(AllOnes, V);
3157 /// getMinusSCEV - Return LHS-RHS. Minus is represented in SCEV as A+B*-1.
3158 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
3159 SCEV::NoWrapFlags Flags) {
3160 assert(!maskFlags(Flags, SCEV::FlagNUW) && "subtraction does not have NUW");
3162 // Fast path: X - X --> 0.
3164 return getConstant(LHS->getType(), 0);
3167 return getAddExpr(LHS, getNegativeSCEV(RHS), Flags);
3170 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
3171 /// input value to the specified type. If the type must be extended, it is zero
3174 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty) {
3175 Type *SrcTy = V->getType();
3176 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3177 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3178 "Cannot truncate or zero extend with non-integer arguments!");
3179 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3180 return V; // No conversion
3181 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
3182 return getTruncateExpr(V, Ty);
3183 return getZeroExtendExpr(V, Ty);
3186 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
3187 /// input value to the specified type. If the type must be extended, it is sign
3190 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
3192 Type *SrcTy = V->getType();
3193 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3194 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3195 "Cannot truncate or zero extend with non-integer arguments!");
3196 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3197 return V; // No conversion
3198 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
3199 return getTruncateExpr(V, Ty);
3200 return getSignExtendExpr(V, Ty);
3203 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
3204 /// input value to the specified type. If the type must be extended, it is zero
3205 /// extended. The conversion must not be narrowing.
3207 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) {
3208 Type *SrcTy = V->getType();
3209 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3210 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3211 "Cannot noop or zero extend with non-integer arguments!");
3212 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3213 "getNoopOrZeroExtend cannot truncate!");
3214 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3215 return V; // No conversion
3216 return getZeroExtendExpr(V, Ty);
3219 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
3220 /// input value to the specified type. If the type must be extended, it is sign
3221 /// extended. The conversion must not be narrowing.
3223 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) {
3224 Type *SrcTy = V->getType();
3225 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3226 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3227 "Cannot noop or sign extend with non-integer arguments!");
3228 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3229 "getNoopOrSignExtend cannot truncate!");
3230 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3231 return V; // No conversion
3232 return getSignExtendExpr(V, Ty);
3235 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
3236 /// the input value to the specified type. If the type must be extended,
3237 /// it is extended with unspecified bits. The conversion must not be
3240 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) {
3241 Type *SrcTy = V->getType();
3242 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3243 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3244 "Cannot noop or any extend with non-integer arguments!");
3245 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
3246 "getNoopOrAnyExtend cannot truncate!");
3247 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3248 return V; // No conversion
3249 return getAnyExtendExpr(V, Ty);
3252 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
3253 /// input value to the specified type. The conversion must not be widening.
3255 ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) {
3256 Type *SrcTy = V->getType();
3257 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
3258 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
3259 "Cannot truncate or noop with non-integer arguments!");
3260 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
3261 "getTruncateOrNoop cannot extend!");
3262 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
3263 return V; // No conversion
3264 return getTruncateExpr(V, Ty);
3267 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
3268 /// the types using zero-extension, and then perform a umax operation
3270 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
3272 const SCEV *PromotedLHS = LHS;
3273 const SCEV *PromotedRHS = RHS;
3275 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
3276 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
3278 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
3280 return getUMaxExpr(PromotedLHS, PromotedRHS);
3283 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
3284 /// the types using zero-extension, and then perform a umin operation
3286 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
3288 const SCEV *PromotedLHS = LHS;
3289 const SCEV *PromotedRHS = RHS;
3291 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
3292 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
3294 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
3296 return getUMinExpr(PromotedLHS, PromotedRHS);
3299 /// getPointerBase - Transitively follow the chain of pointer-type operands
3300 /// until reaching a SCEV that does not have a single pointer operand. This
3301 /// returns a SCEVUnknown pointer for well-formed pointer-type expressions,
3302 /// but corner cases do exist.
3303 const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) {
3304 // A pointer operand may evaluate to a nonpointer expression, such as null.
3305 if (!V->getType()->isPointerTy())
3308 if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) {
3309 return getPointerBase(Cast->getOperand());
3311 else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) {
3312 const SCEV *PtrOp = nullptr;
3313 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
3315 if ((*I)->getType()->isPointerTy()) {
3316 // Cannot find the base of an expression with multiple pointer operands.
3324 return getPointerBase(PtrOp);
3329 /// PushDefUseChildren - Push users of the given Instruction
3330 /// onto the given Worklist.
3332 PushDefUseChildren(Instruction *I,
3333 SmallVectorImpl<Instruction *> &Worklist) {
3334 // Push the def-use children onto the Worklist stack.
3335 for (User *U : I->users())
3336 Worklist.push_back(cast<Instruction>(U));
3339 /// ForgetSymbolicValue - This looks up computed SCEV values for all
3340 /// instructions that depend on the given instruction and removes them from
3341 /// the ValueExprMapType map if they reference SymName. This is used during PHI
3344 ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) {
3345 SmallVector<Instruction *, 16> Worklist;
3346 PushDefUseChildren(PN, Worklist);
3348 SmallPtrSet<Instruction *, 8> Visited;
3350 while (!Worklist.empty()) {
3351 Instruction *I = Worklist.pop_back_val();
3352 if (!Visited.insert(I).second)
3355 ValueExprMapType::iterator It =
3356 ValueExprMap.find_as(static_cast<Value *>(I));
3357 if (It != ValueExprMap.end()) {
3358 const SCEV *Old = It->second;
3360 // Short-circuit the def-use traversal if the symbolic name
3361 // ceases to appear in expressions.
3362 if (Old != SymName && !hasOperand(Old, SymName))
3365 // SCEVUnknown for a PHI either means that it has an unrecognized
3366 // structure, it's a PHI that's in the progress of being computed
3367 // by createNodeForPHI, or it's a single-value PHI. In the first case,
3368 // additional loop trip count information isn't going to change anything.
3369 // In the second case, createNodeForPHI will perform the necessary
3370 // updates on its own when it gets to that point. In the third, we do
3371 // want to forget the SCEVUnknown.
3372 if (!isa<PHINode>(I) ||
3373 !isa<SCEVUnknown>(Old) ||
3374 (I != PN && Old == SymName)) {
3375 forgetMemoizedResults(Old);
3376 ValueExprMap.erase(It);
3380 PushDefUseChildren(I, Worklist);
3384 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
3385 /// a loop header, making it a potential recurrence, or it doesn't.
3387 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
3388 if (const Loop *L = LI->getLoopFor(PN->getParent()))
3389 if (L->getHeader() == PN->getParent()) {
3390 // The loop may have multiple entrances or multiple exits; we can analyze
3391 // this phi as an addrec if it has a unique entry value and a unique
3393 Value *BEValueV = nullptr, *StartValueV = nullptr;
3394 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
3395 Value *V = PN->getIncomingValue(i);
3396 if (L->contains(PN->getIncomingBlock(i))) {
3399 } else if (BEValueV != V) {
3403 } else if (!StartValueV) {
3405 } else if (StartValueV != V) {
3406 StartValueV = nullptr;
3410 if (BEValueV && StartValueV) {
3411 // While we are analyzing this PHI node, handle its value symbolically.
3412 const SCEV *SymbolicName = getUnknown(PN);
3413 assert(ValueExprMap.find_as(PN) == ValueExprMap.end() &&
3414 "PHI node already processed?");
3415 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
3417 // Using this symbolic name for the PHI, analyze the value coming around
3419 const SCEV *BEValue = getSCEV(BEValueV);
3421 // NOTE: If BEValue is loop invariant, we know that the PHI node just
3422 // has a special value for the first iteration of the loop.
3424 // If the value coming around the backedge is an add with the symbolic
3425 // value we just inserted, then we found a simple induction variable!
3426 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
3427 // If there is a single occurrence of the symbolic value, replace it
3428 // with a recurrence.
3429 unsigned FoundIndex = Add->getNumOperands();
3430 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3431 if (Add->getOperand(i) == SymbolicName)
3432 if (FoundIndex == e) {
3437 if (FoundIndex != Add->getNumOperands()) {
3438 // Create an add with everything but the specified operand.
3439 SmallVector<const SCEV *, 8> Ops;
3440 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3441 if (i != FoundIndex)
3442 Ops.push_back(Add->getOperand(i));
3443 const SCEV *Accum = getAddExpr(Ops);
3445 // This is not a valid addrec if the step amount is varying each
3446 // loop iteration, but is not itself an addrec in this loop.
3447 if (isLoopInvariant(Accum, L) ||
3448 (isa<SCEVAddRecExpr>(Accum) &&
3449 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
3450 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
3452 // If the increment doesn't overflow, then neither the addrec nor
3453 // the post-increment will overflow.
3454 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) {
3455 if (OBO->hasNoUnsignedWrap())
3456 Flags = setFlags(Flags, SCEV::FlagNUW);
3457 if (OBO->hasNoSignedWrap())
3458 Flags = setFlags(Flags, SCEV::FlagNSW);
3459 } else if (GEPOperator *GEP = dyn_cast<GEPOperator>(BEValueV)) {
3460 // If the increment is an inbounds GEP, then we know the address
3461 // space cannot be wrapped around. We cannot make any guarantee
3462 // about signed or unsigned overflow because pointers are
3463 // unsigned but we may have a negative index from the base
3464 // pointer. We can guarantee that no unsigned wrap occurs if the
3465 // indices form a positive value.
3466 if (GEP->isInBounds()) {
3467 Flags = setFlags(Flags, SCEV::FlagNW);
3469 const SCEV *Ptr = getSCEV(GEP->getPointerOperand());
3470 if (isKnownPositive(getMinusSCEV(getSCEV(GEP), Ptr)))
3471 Flags = setFlags(Flags, SCEV::FlagNUW);
3473 } else if (const SubOperator *OBO =
3474 dyn_cast<SubOperator>(BEValueV)) {
3475 if (OBO->hasNoUnsignedWrap())
3476 Flags = setFlags(Flags, SCEV::FlagNUW);
3477 if (OBO->hasNoSignedWrap())
3478 Flags = setFlags(Flags, SCEV::FlagNSW);
3481 const SCEV *StartVal = getSCEV(StartValueV);
3482 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
3484 // Since the no-wrap flags are on the increment, they apply to the
3485 // post-incremented value as well.
3486 if (isLoopInvariant(Accum, L))
3487 (void)getAddRecExpr(getAddExpr(StartVal, Accum),
3490 // Okay, for the entire analysis of this edge we assumed the PHI
3491 // to be symbolic. We now need to go back and purge all of the
3492 // entries for the scalars that use the symbolic expression.
3493 ForgetSymbolicName(PN, SymbolicName);
3494 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3498 } else if (const SCEVAddRecExpr *AddRec =
3499 dyn_cast<SCEVAddRecExpr>(BEValue)) {
3500 // Otherwise, this could be a loop like this:
3501 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
3502 // In this case, j = {1,+,1} and BEValue is j.
3503 // Because the other in-value of i (0) fits the evolution of BEValue
3504 // i really is an addrec evolution.
3505 if (AddRec->getLoop() == L && AddRec->isAffine()) {
3506 const SCEV *StartVal = getSCEV(StartValueV);
3508 // If StartVal = j.start - j.stride, we can use StartVal as the
3509 // initial step of the addrec evolution.
3510 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
3511 AddRec->getOperand(1))) {
3512 // FIXME: For constant StartVal, we should be able to infer
3514 const SCEV *PHISCEV =
3515 getAddRecExpr(StartVal, AddRec->getOperand(1), L,
3518 // Okay, for the entire analysis of this edge we assumed the PHI
3519 // to be symbolic. We now need to go back and purge all of the
3520 // entries for the scalars that use the symbolic expression.
3521 ForgetSymbolicName(PN, SymbolicName);
3522 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3530 // If the PHI has a single incoming value, follow that value, unless the
3531 // PHI's incoming blocks are in a different loop, in which case doing so
3532 // risks breaking LCSSA form. Instcombine would normally zap these, but
3533 // it doesn't have DominatorTree information, so it may miss cases.
3534 if (Value *V = SimplifyInstruction(PN, DL, TLI, DT, AC))
3535 if (LI->replacementPreservesLCSSAForm(PN, V))
3538 // If it's not a loop phi, we can't handle it yet.
3539 return getUnknown(PN);
3542 /// createNodeForGEP - Expand GEP instructions into add and multiply
3543 /// operations. This allows them to be analyzed by regular SCEV code.
3545 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
3546 Type *IntPtrTy = getEffectiveSCEVType(GEP->getType());
3547 Value *Base = GEP->getOperand(0);
3548 // Don't attempt to analyze GEPs over unsized objects.
3549 if (!Base->getType()->getPointerElementType()->isSized())
3550 return getUnknown(GEP);
3552 // Don't blindly transfer the inbounds flag from the GEP instruction to the
3553 // Add expression, because the Instruction may be guarded by control flow
3554 // and the no-overflow bits may not be valid for the expression in any
3556 SCEV::NoWrapFlags Wrap = GEP->isInBounds() ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
3558 const SCEV *TotalOffset = getConstant(IntPtrTy, 0);
3559 gep_type_iterator GTI = gep_type_begin(GEP);
3560 for (GetElementPtrInst::op_iterator I = std::next(GEP->op_begin()),
3564 // Compute the (potentially symbolic) offset in bytes for this index.
3565 if (StructType *STy = dyn_cast<StructType>(*GTI++)) {
3566 // For a struct, add the member offset.
3567 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
3568 const SCEV *FieldOffset = getOffsetOfExpr(IntPtrTy, STy, FieldNo);
3570 // Add the field offset to the running total offset.
3571 TotalOffset = getAddExpr(TotalOffset, FieldOffset);
3573 // For an array, add the element offset, explicitly scaled.
3574 const SCEV *ElementSize = getSizeOfExpr(IntPtrTy, *GTI);
3575 const SCEV *IndexS = getSCEV(Index);
3576 // Getelementptr indices are signed.
3577 IndexS = getTruncateOrSignExtend(IndexS, IntPtrTy);
3579 // Multiply the index by the element size to compute the element offset.
3580 const SCEV *LocalOffset = getMulExpr(IndexS, ElementSize, Wrap);
3582 // Add the element offset to the running total offset.
3583 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
3587 // Get the SCEV for the GEP base.
3588 const SCEV *BaseS = getSCEV(Base);
3590 // Add the total offset from all the GEP indices to the base.
3591 return getAddExpr(BaseS, TotalOffset, Wrap);
3594 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
3595 /// guaranteed to end in (at every loop iteration). It is, at the same time,
3596 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
3597 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
3599 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
3600 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3601 return C->getValue()->getValue().countTrailingZeros();
3603 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
3604 return std::min(GetMinTrailingZeros(T->getOperand()),
3605 (uint32_t)getTypeSizeInBits(T->getType()));
3607 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
3608 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3609 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3610 getTypeSizeInBits(E->getType()) : OpRes;
3613 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
3614 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3615 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3616 getTypeSizeInBits(E->getType()) : OpRes;
3619 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
3620 // The result is the min of all operands results.
3621 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3622 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3623 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3627 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
3628 // The result is the sum of all operands results.
3629 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
3630 uint32_t BitWidth = getTypeSizeInBits(M->getType());
3631 for (unsigned i = 1, e = M->getNumOperands();
3632 SumOpRes != BitWidth && i != e; ++i)
3633 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
3638 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
3639 // The result is the min of all operands results.
3640 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3641 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3642 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3646 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
3647 // The result is the min of all operands results.
3648 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3649 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3650 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3654 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
3655 // The result is the min of all operands results.
3656 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3657 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3658 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3662 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3663 // For a SCEVUnknown, ask ValueTracking.
3664 unsigned BitWidth = getTypeSizeInBits(U->getType());
3665 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3666 computeKnownBits(U->getValue(), Zeros, Ones, DL, 0, AC, nullptr, DT);
3667 return Zeros.countTrailingOnes();
3674 /// GetRangeFromMetadata - Helper method to assign a range to V from
3675 /// metadata present in the IR.
3676 static Optional<ConstantRange> GetRangeFromMetadata(Value *V) {
3677 if (Instruction *I = dyn_cast<Instruction>(V)) {
3678 if (MDNode *MD = I->getMetadata(LLVMContext::MD_range)) {
3679 ConstantRange TotalRange(
3680 cast<IntegerType>(I->getType())->getBitWidth(), false);
3682 unsigned NumRanges = MD->getNumOperands() / 2;
3683 assert(NumRanges >= 1);
3685 for (unsigned i = 0; i < NumRanges; ++i) {
3686 ConstantInt *Lower =
3687 mdconst::extract<ConstantInt>(MD->getOperand(2 * i + 0));
3688 ConstantInt *Upper =
3689 mdconst::extract<ConstantInt>(MD->getOperand(2 * i + 1));
3690 ConstantRange Range(Lower->getValue(), Upper->getValue());
3691 TotalRange = TotalRange.unionWith(Range);
3701 /// getUnsignedRange - Determine the unsigned range for a particular SCEV.
3704 ScalarEvolution::getUnsignedRange(const SCEV *S) {
3705 // See if we've computed this range already.
3706 DenseMap<const SCEV *, ConstantRange>::iterator I = UnsignedRanges.find(S);
3707 if (I != UnsignedRanges.end())
3710 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3711 return setUnsignedRange(C, ConstantRange(C->getValue()->getValue()));
3713 unsigned BitWidth = getTypeSizeInBits(S->getType());
3714 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3716 // If the value has known zeros, the maximum unsigned value will have those
3717 // known zeros as well.
3718 uint32_t TZ = GetMinTrailingZeros(S);
3720 ConservativeResult =
3721 ConstantRange(APInt::getMinValue(BitWidth),
3722 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
3724 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3725 ConstantRange X = getUnsignedRange(Add->getOperand(0));
3726 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3727 X = X.add(getUnsignedRange(Add->getOperand(i)));
3728 return setUnsignedRange(Add, ConservativeResult.intersectWith(X));
3731 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3732 ConstantRange X = getUnsignedRange(Mul->getOperand(0));
3733 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3734 X = X.multiply(getUnsignedRange(Mul->getOperand(i)));
3735 return setUnsignedRange(Mul, ConservativeResult.intersectWith(X));
3738 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3739 ConstantRange X = getUnsignedRange(SMax->getOperand(0));
3740 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3741 X = X.smax(getUnsignedRange(SMax->getOperand(i)));
3742 return setUnsignedRange(SMax, ConservativeResult.intersectWith(X));
3745 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3746 ConstantRange X = getUnsignedRange(UMax->getOperand(0));
3747 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3748 X = X.umax(getUnsignedRange(UMax->getOperand(i)));
3749 return setUnsignedRange(UMax, ConservativeResult.intersectWith(X));
3752 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3753 ConstantRange X = getUnsignedRange(UDiv->getLHS());
3754 ConstantRange Y = getUnsignedRange(UDiv->getRHS());
3755 return setUnsignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y)));
3758 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3759 ConstantRange X = getUnsignedRange(ZExt->getOperand());
3760 return setUnsignedRange(ZExt,
3761 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3764 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3765 ConstantRange X = getUnsignedRange(SExt->getOperand());
3766 return setUnsignedRange(SExt,
3767 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3770 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3771 ConstantRange X = getUnsignedRange(Trunc->getOperand());
3772 return setUnsignedRange(Trunc,
3773 ConservativeResult.intersectWith(X.truncate(BitWidth)));
3776 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3777 // If there's no unsigned wrap, the value will never be less than its
3779 if (AddRec->getNoWrapFlags(SCEV::FlagNUW))
3780 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
3781 if (!C->getValue()->isZero())
3782 ConservativeResult =
3783 ConservativeResult.intersectWith(
3784 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0)));
3786 // TODO: non-affine addrec
3787 if (AddRec->isAffine()) {
3788 Type *Ty = AddRec->getType();
3789 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3790 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3791 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3792 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3794 const SCEV *Start = AddRec->getStart();
3795 const SCEV *Step = AddRec->getStepRecurrence(*this);
3797 ConstantRange StartRange = getUnsignedRange(Start);
3798 ConstantRange StepRange = getSignedRange(Step);
3799 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3800 ConstantRange EndRange =
3801 StartRange.add(MaxBECountRange.multiply(StepRange));
3803 // Check for overflow. This must be done with ConstantRange arithmetic
3804 // because we could be called from within the ScalarEvolution overflow
3806 ConstantRange ExtStartRange = StartRange.zextOrTrunc(BitWidth*2+1);
3807 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3808 ConstantRange ExtMaxBECountRange =
3809 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3810 ConstantRange ExtEndRange = EndRange.zextOrTrunc(BitWidth*2+1);
3811 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3813 return setUnsignedRange(AddRec, ConservativeResult);
3815 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(),
3816 EndRange.getUnsignedMin());
3817 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(),
3818 EndRange.getUnsignedMax());
3819 if (Min.isMinValue() && Max.isMaxValue())
3820 return setUnsignedRange(AddRec, ConservativeResult);
3821 return setUnsignedRange(AddRec,
3822 ConservativeResult.intersectWith(ConstantRange(Min, Max+1)));
3826 return setUnsignedRange(AddRec, ConservativeResult);
3829 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3830 // Check if the IR explicitly contains !range metadata.
3831 Optional<ConstantRange> MDRange = GetRangeFromMetadata(U->getValue());
3832 if (MDRange.hasValue())
3833 ConservativeResult = ConservativeResult.intersectWith(MDRange.getValue());
3835 // For a SCEVUnknown, ask ValueTracking.
3836 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3837 computeKnownBits(U->getValue(), Zeros, Ones, DL, 0, AC, nullptr, DT);
3838 if (Ones == ~Zeros + 1)
3839 return setUnsignedRange(U, ConservativeResult);
3840 return setUnsignedRange(U,
3841 ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1)));
3844 return setUnsignedRange(S, ConservativeResult);
3847 /// getSignedRange - Determine the signed range for a particular SCEV.
3850 ScalarEvolution::getSignedRange(const SCEV *S) {
3851 // See if we've computed this range already.
3852 DenseMap<const SCEV *, ConstantRange>::iterator I = SignedRanges.find(S);
3853 if (I != SignedRanges.end())
3856 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3857 return setSignedRange(C, ConstantRange(C->getValue()->getValue()));
3859 unsigned BitWidth = getTypeSizeInBits(S->getType());
3860 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3862 // If the value has known zeros, the maximum signed value will have those
3863 // known zeros as well.
3864 uint32_t TZ = GetMinTrailingZeros(S);
3866 ConservativeResult =
3867 ConstantRange(APInt::getSignedMinValue(BitWidth),
3868 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
3870 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3871 ConstantRange X = getSignedRange(Add->getOperand(0));
3872 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3873 X = X.add(getSignedRange(Add->getOperand(i)));
3874 return setSignedRange(Add, ConservativeResult.intersectWith(X));
3877 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3878 ConstantRange X = getSignedRange(Mul->getOperand(0));
3879 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3880 X = X.multiply(getSignedRange(Mul->getOperand(i)));
3881 return setSignedRange(Mul, ConservativeResult.intersectWith(X));
3884 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3885 ConstantRange X = getSignedRange(SMax->getOperand(0));
3886 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3887 X = X.smax(getSignedRange(SMax->getOperand(i)));
3888 return setSignedRange(SMax, ConservativeResult.intersectWith(X));
3891 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3892 ConstantRange X = getSignedRange(UMax->getOperand(0));
3893 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3894 X = X.umax(getSignedRange(UMax->getOperand(i)));
3895 return setSignedRange(UMax, ConservativeResult.intersectWith(X));
3898 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3899 ConstantRange X = getSignedRange(UDiv->getLHS());
3900 ConstantRange Y = getSignedRange(UDiv->getRHS());
3901 return setSignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y)));
3904 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3905 ConstantRange X = getSignedRange(ZExt->getOperand());
3906 return setSignedRange(ZExt,
3907 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3910 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3911 ConstantRange X = getSignedRange(SExt->getOperand());
3912 return setSignedRange(SExt,
3913 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3916 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3917 ConstantRange X = getSignedRange(Trunc->getOperand());
3918 return setSignedRange(Trunc,
3919 ConservativeResult.intersectWith(X.truncate(BitWidth)));
3922 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3923 // If there's no signed wrap, and all the operands have the same sign or
3924 // zero, the value won't ever change sign.
3925 if (AddRec->getNoWrapFlags(SCEV::FlagNSW)) {
3926 bool AllNonNeg = true;
3927 bool AllNonPos = true;
3928 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
3929 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
3930 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
3933 ConservativeResult = ConservativeResult.intersectWith(
3934 ConstantRange(APInt(BitWidth, 0),
3935 APInt::getSignedMinValue(BitWidth)));
3937 ConservativeResult = ConservativeResult.intersectWith(
3938 ConstantRange(APInt::getSignedMinValue(BitWidth),
3939 APInt(BitWidth, 1)));
3942 // TODO: non-affine addrec
3943 if (AddRec->isAffine()) {
3944 Type *Ty = AddRec->getType();
3945 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3946 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3947 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3948 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3950 const SCEV *Start = AddRec->getStart();
3951 const SCEV *Step = AddRec->getStepRecurrence(*this);
3953 ConstantRange StartRange = getSignedRange(Start);
3954 ConstantRange StepRange = getSignedRange(Step);
3955 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3956 ConstantRange EndRange =
3957 StartRange.add(MaxBECountRange.multiply(StepRange));
3959 // Check for overflow. This must be done with ConstantRange arithmetic
3960 // because we could be called from within the ScalarEvolution overflow
3962 ConstantRange ExtStartRange = StartRange.sextOrTrunc(BitWidth*2+1);
3963 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3964 ConstantRange ExtMaxBECountRange =
3965 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3966 ConstantRange ExtEndRange = EndRange.sextOrTrunc(BitWidth*2+1);
3967 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3969 return setSignedRange(AddRec, ConservativeResult);
3971 APInt Min = APIntOps::smin(StartRange.getSignedMin(),
3972 EndRange.getSignedMin());
3973 APInt Max = APIntOps::smax(StartRange.getSignedMax(),
3974 EndRange.getSignedMax());
3975 if (Min.isMinSignedValue() && Max.isMaxSignedValue())
3976 return setSignedRange(AddRec, ConservativeResult);
3977 return setSignedRange(AddRec,
3978 ConservativeResult.intersectWith(ConstantRange(Min, Max+1)));
3982 return setSignedRange(AddRec, ConservativeResult);
3985 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3986 // Check if the IR explicitly contains !range metadata.
3987 Optional<ConstantRange> MDRange = GetRangeFromMetadata(U->getValue());
3988 if (MDRange.hasValue())
3989 ConservativeResult = ConservativeResult.intersectWith(MDRange.getValue());
3991 // For a SCEVUnknown, ask ValueTracking.
3992 if (!U->getValue()->getType()->isIntegerTy() && !DL)
3993 return setSignedRange(U, ConservativeResult);
3994 unsigned NS = ComputeNumSignBits(U->getValue(), DL, 0, AC, nullptr, DT);
3996 return setSignedRange(U, ConservativeResult);
3997 return setSignedRange(U, ConservativeResult.intersectWith(
3998 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
3999 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1)));
4002 return setSignedRange(S, ConservativeResult);
4005 /// createSCEV - We know that there is no SCEV for the specified value.
4006 /// Analyze the expression.
4008 const SCEV *ScalarEvolution::createSCEV(Value *V) {
4009 if (!isSCEVable(V->getType()))
4010 return getUnknown(V);
4012 unsigned Opcode = Instruction::UserOp1;
4013 if (Instruction *I = dyn_cast<Instruction>(V)) {
4014 Opcode = I->getOpcode();
4016 // Don't attempt to analyze instructions in blocks that aren't
4017 // reachable. Such instructions don't matter, and they aren't required
4018 // to obey basic rules for definitions dominating uses which this
4019 // analysis depends on.
4020 if (!DT->isReachableFromEntry(I->getParent()))
4021 return getUnknown(V);
4022 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
4023 Opcode = CE->getOpcode();
4024 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
4025 return getConstant(CI);
4026 else if (isa<ConstantPointerNull>(V))
4027 return getConstant(V->getType(), 0);
4028 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
4029 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee());
4031 return getUnknown(V);
4033 Operator *U = cast<Operator>(V);
4035 case Instruction::Add: {
4036 // The simple thing to do would be to just call getSCEV on both operands
4037 // and call getAddExpr with the result. However if we're looking at a
4038 // bunch of things all added together, this can be quite inefficient,
4039 // because it leads to N-1 getAddExpr calls for N ultimate operands.
4040 // Instead, gather up all the operands and make a single getAddExpr call.
4041 // LLVM IR canonical form means we need only traverse the left operands.
4043 // Don't apply this instruction's NSW or NUW flags to the new
4044 // expression. The instruction may be guarded by control flow that the
4045 // no-wrap behavior depends on. Non-control-equivalent instructions can be
4046 // mapped to the same SCEV expression, and it would be incorrect to transfer
4047 // NSW/NUW semantics to those operations.
4048 SmallVector<const SCEV *, 4> AddOps;
4049 AddOps.push_back(getSCEV(U->getOperand(1)));
4050 for (Value *Op = U->getOperand(0); ; Op = U->getOperand(0)) {
4051 unsigned Opcode = Op->getValueID() - Value::InstructionVal;
4052 if (Opcode != Instruction::Add && Opcode != Instruction::Sub)
4054 U = cast<Operator>(Op);
4055 const SCEV *Op1 = getSCEV(U->getOperand(1));
4056 if (Opcode == Instruction::Sub)
4057 AddOps.push_back(getNegativeSCEV(Op1));
4059 AddOps.push_back(Op1);
4061 AddOps.push_back(getSCEV(U->getOperand(0)));
4062 return getAddExpr(AddOps);
4064 case Instruction::Mul: {
4065 // Don't transfer NSW/NUW for the same reason as AddExpr.
4066 SmallVector<const SCEV *, 4> MulOps;
4067 MulOps.push_back(getSCEV(U->getOperand(1)));
4068 for (Value *Op = U->getOperand(0);
4069 Op->getValueID() == Instruction::Mul + Value::InstructionVal;
4070 Op = U->getOperand(0)) {
4071 U = cast<Operator>(Op);
4072 MulOps.push_back(getSCEV(U->getOperand(1)));
4074 MulOps.push_back(getSCEV(U->getOperand(0)));
4075 return getMulExpr(MulOps);
4077 case Instruction::UDiv:
4078 return getUDivExpr(getSCEV(U->getOperand(0)),
4079 getSCEV(U->getOperand(1)));
4080 case Instruction::Sub:
4081 return getMinusSCEV(getSCEV(U->getOperand(0)),
4082 getSCEV(U->getOperand(1)));
4083 case Instruction::And:
4084 // For an expression like x&255 that merely masks off the high bits,
4085 // use zext(trunc(x)) as the SCEV expression.
4086 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
4087 if (CI->isNullValue())
4088 return getSCEV(U->getOperand(1));
4089 if (CI->isAllOnesValue())
4090 return getSCEV(U->getOperand(0));
4091 const APInt &A = CI->getValue();
4093 // Instcombine's ShrinkDemandedConstant may strip bits out of
4094 // constants, obscuring what would otherwise be a low-bits mask.
4095 // Use computeKnownBits to compute what ShrinkDemandedConstant
4096 // knew about to reconstruct a low-bits mask value.
4097 unsigned LZ = A.countLeadingZeros();
4098 unsigned TZ = A.countTrailingZeros();
4099 unsigned BitWidth = A.getBitWidth();
4100 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
4101 computeKnownBits(U->getOperand(0), KnownZero, KnownOne, DL, 0, AC,
4104 APInt EffectiveMask =
4105 APInt::getLowBitsSet(BitWidth, BitWidth - LZ - TZ).shl(TZ);
4106 if ((LZ != 0 || TZ != 0) && !((~A & ~KnownZero) & EffectiveMask)) {
4107 const SCEV *MulCount = getConstant(
4108 ConstantInt::get(getContext(), APInt::getOneBitSet(BitWidth, TZ)));
4112 getUDivExactExpr(getSCEV(U->getOperand(0)), MulCount),
4113 IntegerType::get(getContext(), BitWidth - LZ - TZ)),
4120 case Instruction::Or:
4121 // If the RHS of the Or is a constant, we may have something like:
4122 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
4123 // optimizations will transparently handle this case.
4125 // In order for this transformation to be safe, the LHS must be of the
4126 // form X*(2^n) and the Or constant must be less than 2^n.
4127 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
4128 const SCEV *LHS = getSCEV(U->getOperand(0));
4129 const APInt &CIVal = CI->getValue();
4130 if (GetMinTrailingZeros(LHS) >=
4131 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
4132 // Build a plain add SCEV.
4133 const SCEV *S = getAddExpr(LHS, getSCEV(CI));
4134 // If the LHS of the add was an addrec and it has no-wrap flags,
4135 // transfer the no-wrap flags, since an or won't introduce a wrap.
4136 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
4137 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
4138 const_cast<SCEVAddRecExpr *>(NewAR)->setNoWrapFlags(
4139 OldAR->getNoWrapFlags());
4145 case Instruction::Xor:
4146 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
4147 // If the RHS of the xor is a signbit, then this is just an add.
4148 // Instcombine turns add of signbit into xor as a strength reduction step.
4149 if (CI->getValue().isSignBit())
4150 return getAddExpr(getSCEV(U->getOperand(0)),
4151 getSCEV(U->getOperand(1)));
4153 // If the RHS of xor is -1, then this is a not operation.
4154 if (CI->isAllOnesValue())
4155 return getNotSCEV(getSCEV(U->getOperand(0)));
4157 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
4158 // This is a variant of the check for xor with -1, and it handles
4159 // the case where instcombine has trimmed non-demanded bits out
4160 // of an xor with -1.
4161 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
4162 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
4163 if (BO->getOpcode() == Instruction::And &&
4164 LCI->getValue() == CI->getValue())
4165 if (const SCEVZeroExtendExpr *Z =
4166 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
4167 Type *UTy = U->getType();
4168 const SCEV *Z0 = Z->getOperand();
4169 Type *Z0Ty = Z0->getType();
4170 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
4172 // If C is a low-bits mask, the zero extend is serving to
4173 // mask off the high bits. Complement the operand and
4174 // re-apply the zext.
4175 if (APIntOps::isMask(Z0TySize, CI->getValue()))
4176 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
4178 // If C is a single bit, it may be in the sign-bit position
4179 // before the zero-extend. In this case, represent the xor
4180 // using an add, which is equivalent, and re-apply the zext.
4181 APInt Trunc = CI->getValue().trunc(Z0TySize);
4182 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
4184 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
4190 case Instruction::Shl:
4191 // Turn shift left of a constant amount into a multiply.
4192 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
4193 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
4195 // If the shift count is not less than the bitwidth, the result of
4196 // the shift is undefined. Don't try to analyze it, because the
4197 // resolution chosen here may differ from the resolution chosen in
4198 // other parts of the compiler.
4199 if (SA->getValue().uge(BitWidth))
4202 Constant *X = ConstantInt::get(getContext(),
4203 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
4204 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
4208 case Instruction::LShr:
4209 // Turn logical shift right of a constant into a unsigned divide.
4210 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
4211 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
4213 // If the shift count is not less than the bitwidth, the result of
4214 // the shift is undefined. Don't try to analyze it, because the
4215 // resolution chosen here may differ from the resolution chosen in
4216 // other parts of the compiler.
4217 if (SA->getValue().uge(BitWidth))
4220 Constant *X = ConstantInt::get(getContext(),
4221 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
4222 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
4226 case Instruction::AShr:
4227 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
4228 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
4229 if (Operator *L = dyn_cast<Operator>(U->getOperand(0)))
4230 if (L->getOpcode() == Instruction::Shl &&
4231 L->getOperand(1) == U->getOperand(1)) {
4232 uint64_t BitWidth = getTypeSizeInBits(U->getType());
4234 // If the shift count is not less than the bitwidth, the result of
4235 // the shift is undefined. Don't try to analyze it, because the
4236 // resolution chosen here may differ from the resolution chosen in
4237 // other parts of the compiler.
4238 if (CI->getValue().uge(BitWidth))
4241 uint64_t Amt = BitWidth - CI->getZExtValue();
4242 if (Amt == BitWidth)
4243 return getSCEV(L->getOperand(0)); // shift by zero --> noop
4245 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
4246 IntegerType::get(getContext(),
4252 case Instruction::Trunc:
4253 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
4255 case Instruction::ZExt:
4256 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
4258 case Instruction::SExt:
4259 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
4261 case Instruction::BitCast:
4262 // BitCasts are no-op casts so we just eliminate the cast.
4263 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
4264 return getSCEV(U->getOperand(0));
4267 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
4268 // lead to pointer expressions which cannot safely be expanded to GEPs,
4269 // because ScalarEvolution doesn't respect the GEP aliasing rules when
4270 // simplifying integer expressions.
4272 case Instruction::GetElementPtr:
4273 return createNodeForGEP(cast<GEPOperator>(U));
4275 case Instruction::PHI:
4276 return createNodeForPHI(cast<PHINode>(U));
4278 case Instruction::Select:
4279 // This could be a smax or umax that was lowered earlier.
4280 // Try to recover it.
4281 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
4282 Value *LHS = ICI->getOperand(0);
4283 Value *RHS = ICI->getOperand(1);
4284 switch (ICI->getPredicate()) {
4285 case ICmpInst::ICMP_SLT:
4286 case ICmpInst::ICMP_SLE:
4287 std::swap(LHS, RHS);
4289 case ICmpInst::ICMP_SGT:
4290 case ICmpInst::ICMP_SGE:
4291 // a >s b ? a+x : b+x -> smax(a, b)+x
4292 // a >s b ? b+x : a+x -> smin(a, b)+x
4293 if (LHS->getType() == U->getType()) {
4294 const SCEV *LS = getSCEV(LHS);
4295 const SCEV *RS = getSCEV(RHS);
4296 const SCEV *LA = getSCEV(U->getOperand(1));
4297 const SCEV *RA = getSCEV(U->getOperand(2));
4298 const SCEV *LDiff = getMinusSCEV(LA, LS);
4299 const SCEV *RDiff = getMinusSCEV(RA, RS);
4301 return getAddExpr(getSMaxExpr(LS, RS), LDiff);
4302 LDiff = getMinusSCEV(LA, RS);
4303 RDiff = getMinusSCEV(RA, LS);
4305 return getAddExpr(getSMinExpr(LS, RS), LDiff);
4308 case ICmpInst::ICMP_ULT:
4309 case ICmpInst::ICMP_ULE:
4310 std::swap(LHS, RHS);
4312 case ICmpInst::ICMP_UGT:
4313 case ICmpInst::ICMP_UGE:
4314 // a >u b ? a+x : b+x -> umax(a, b)+x
4315 // a >u b ? b+x : a+x -> umin(a, b)+x
4316 if (LHS->getType() == U->getType()) {
4317 const SCEV *LS = getSCEV(LHS);
4318 const SCEV *RS = getSCEV(RHS);
4319 const SCEV *LA = getSCEV(U->getOperand(1));
4320 const SCEV *RA = getSCEV(U->getOperand(2));
4321 const SCEV *LDiff = getMinusSCEV(LA, LS);
4322 const SCEV *RDiff = getMinusSCEV(RA, RS);
4324 return getAddExpr(getUMaxExpr(LS, RS), LDiff);
4325 LDiff = getMinusSCEV(LA, RS);
4326 RDiff = getMinusSCEV(RA, LS);
4328 return getAddExpr(getUMinExpr(LS, RS), LDiff);
4331 case ICmpInst::ICMP_NE:
4332 // n != 0 ? n+x : 1+x -> umax(n, 1)+x
4333 if (LHS->getType() == U->getType() &&
4334 isa<ConstantInt>(RHS) &&
4335 cast<ConstantInt>(RHS)->isZero()) {
4336 const SCEV *One = getConstant(LHS->getType(), 1);
4337 const SCEV *LS = getSCEV(LHS);
4338 const SCEV *LA = getSCEV(U->getOperand(1));
4339 const SCEV *RA = getSCEV(U->getOperand(2));
4340 const SCEV *LDiff = getMinusSCEV(LA, LS);
4341 const SCEV *RDiff = getMinusSCEV(RA, One);
4343 return getAddExpr(getUMaxExpr(One, LS), LDiff);
4346 case ICmpInst::ICMP_EQ:
4347 // n == 0 ? 1+x : n+x -> umax(n, 1)+x
4348 if (LHS->getType() == U->getType() &&
4349 isa<ConstantInt>(RHS) &&
4350 cast<ConstantInt>(RHS)->isZero()) {
4351 const SCEV *One = getConstant(LHS->getType(), 1);
4352 const SCEV *LS = getSCEV(LHS);
4353 const SCEV *LA = getSCEV(U->getOperand(1));
4354 const SCEV *RA = getSCEV(U->getOperand(2));
4355 const SCEV *LDiff = getMinusSCEV(LA, One);
4356 const SCEV *RDiff = getMinusSCEV(RA, LS);
4358 return getAddExpr(getUMaxExpr(One, LS), LDiff);
4366 default: // We cannot analyze this expression.
4370 return getUnknown(V);
4375 //===----------------------------------------------------------------------===//
4376 // Iteration Count Computation Code
4379 unsigned ScalarEvolution::getSmallConstantTripCount(Loop *L) {
4380 if (BasicBlock *ExitingBB = L->getExitingBlock())
4381 return getSmallConstantTripCount(L, ExitingBB);
4383 // No trip count information for multiple exits.
4387 /// getSmallConstantTripCount - Returns the maximum trip count of this loop as a
4388 /// normal unsigned value. Returns 0 if the trip count is unknown or not
4389 /// constant. Will also return 0 if the maximum trip count is very large (>=
4392 /// This "trip count" assumes that control exits via ExitingBlock. More
4393 /// precisely, it is the number of times that control may reach ExitingBlock
4394 /// before taking the branch. For loops with multiple exits, it may not be the
4395 /// number times that the loop header executes because the loop may exit
4396 /// prematurely via another branch.
4397 unsigned ScalarEvolution::getSmallConstantTripCount(Loop *L,
4398 BasicBlock *ExitingBlock) {
4399 assert(ExitingBlock && "Must pass a non-null exiting block!");
4400 assert(L->isLoopExiting(ExitingBlock) &&
4401 "Exiting block must actually branch out of the loop!");
4402 const SCEVConstant *ExitCount =
4403 dyn_cast<SCEVConstant>(getExitCount(L, ExitingBlock));
4407 ConstantInt *ExitConst = ExitCount->getValue();
4409 // Guard against huge trip counts.
4410 if (ExitConst->getValue().getActiveBits() > 32)
4413 // In case of integer overflow, this returns 0, which is correct.
4414 return ((unsigned)ExitConst->getZExtValue()) + 1;
4417 unsigned ScalarEvolution::getSmallConstantTripMultiple(Loop *L) {
4418 if (BasicBlock *ExitingBB = L->getExitingBlock())
4419 return getSmallConstantTripMultiple(L, ExitingBB);
4421 // No trip multiple information for multiple exits.
4425 /// getSmallConstantTripMultiple - Returns the largest constant divisor of the
4426 /// trip count of this loop as a normal unsigned value, if possible. This
4427 /// means that the actual trip count is always a multiple of the returned
4428 /// value (don't forget the trip count could very well be zero as well!).
4430 /// Returns 1 if the trip count is unknown or not guaranteed to be the
4431 /// multiple of a constant (which is also the case if the trip count is simply
4432 /// constant, use getSmallConstantTripCount for that case), Will also return 1
4433 /// if the trip count is very large (>= 2^32).
4435 /// As explained in the comments for getSmallConstantTripCount, this assumes
4436 /// that control exits the loop via ExitingBlock.
4438 ScalarEvolution::getSmallConstantTripMultiple(Loop *L,
4439 BasicBlock *ExitingBlock) {
4440 assert(ExitingBlock && "Must pass a non-null exiting block!");
4441 assert(L->isLoopExiting(ExitingBlock) &&
4442 "Exiting block must actually branch out of the loop!");
4443 const SCEV *ExitCount = getExitCount(L, ExitingBlock);
4444 if (ExitCount == getCouldNotCompute())
4447 // Get the trip count from the BE count by adding 1.
4448 const SCEV *TCMul = getAddExpr(ExitCount,
4449 getConstant(ExitCount->getType(), 1));
4450 // FIXME: SCEV distributes multiplication as V1*C1 + V2*C1. We could attempt
4451 // to factor simple cases.
4452 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(TCMul))
4453 TCMul = Mul->getOperand(0);
4455 const SCEVConstant *MulC = dyn_cast<SCEVConstant>(TCMul);
4459 ConstantInt *Result = MulC->getValue();
4461 // Guard against huge trip counts (this requires checking
4462 // for zero to handle the case where the trip count == -1 and the
4464 if (!Result || Result->getValue().getActiveBits() > 32 ||
4465 Result->getValue().getActiveBits() == 0)
4468 return (unsigned)Result->getZExtValue();
4471 // getExitCount - Get the expression for the number of loop iterations for which
4472 // this loop is guaranteed not to exit via ExitingBlock. Otherwise return
4473 // SCEVCouldNotCompute.
4474 const SCEV *ScalarEvolution::getExitCount(Loop *L, BasicBlock *ExitingBlock) {
4475 return getBackedgeTakenInfo(L).getExact(ExitingBlock, this);
4478 /// getBackedgeTakenCount - If the specified loop has a predictable
4479 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
4480 /// object. The backedge-taken count is the number of times the loop header
4481 /// will be branched to from within the loop. This is one less than the
4482 /// trip count of the loop, since it doesn't count the first iteration,
4483 /// when the header is branched to from outside the loop.
4485 /// Note that it is not valid to call this method on a loop without a
4486 /// loop-invariant backedge-taken count (see
4487 /// hasLoopInvariantBackedgeTakenCount).
4489 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
4490 return getBackedgeTakenInfo(L).getExact(this);
4493 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
4494 /// return the least SCEV value that is known never to be less than the
4495 /// actual backedge taken count.
4496 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
4497 return getBackedgeTakenInfo(L).getMax(this);
4500 /// PushLoopPHIs - Push PHI nodes in the header of the given loop
4501 /// onto the given Worklist.
4503 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
4504 BasicBlock *Header = L->getHeader();
4506 // Push all Loop-header PHIs onto the Worklist stack.
4507 for (BasicBlock::iterator I = Header->begin();
4508 PHINode *PN = dyn_cast<PHINode>(I); ++I)
4509 Worklist.push_back(PN);
4512 const ScalarEvolution::BackedgeTakenInfo &
4513 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
4514 // Initially insert an invalid entry for this loop. If the insertion
4515 // succeeds, proceed to actually compute a backedge-taken count and
4516 // update the value. The temporary CouldNotCompute value tells SCEV
4517 // code elsewhere that it shouldn't attempt to request a new
4518 // backedge-taken count, which could result in infinite recursion.
4519 std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
4520 BackedgeTakenCounts.insert(std::make_pair(L, BackedgeTakenInfo()));
4522 return Pair.first->second;
4524 // ComputeBackedgeTakenCount may allocate memory for its result. Inserting it
4525 // into the BackedgeTakenCounts map transfers ownership. Otherwise, the result
4526 // must be cleared in this scope.
4527 BackedgeTakenInfo Result = ComputeBackedgeTakenCount(L);
4529 if (Result.getExact(this) != getCouldNotCompute()) {
4530 assert(isLoopInvariant(Result.getExact(this), L) &&
4531 isLoopInvariant(Result.getMax(this), L) &&
4532 "Computed backedge-taken count isn't loop invariant for loop!");
4533 ++NumTripCountsComputed;
4535 else if (Result.getMax(this) == getCouldNotCompute() &&
4536 isa<PHINode>(L->getHeader()->begin())) {
4537 // Only count loops that have phi nodes as not being computable.
4538 ++NumTripCountsNotComputed;
4541 // Now that we know more about the trip count for this loop, forget any
4542 // existing SCEV values for PHI nodes in this loop since they are only
4543 // conservative estimates made without the benefit of trip count
4544 // information. This is similar to the code in forgetLoop, except that
4545 // it handles SCEVUnknown PHI nodes specially.
4546 if (Result.hasAnyInfo()) {
4547 SmallVector<Instruction *, 16> Worklist;
4548 PushLoopPHIs(L, Worklist);
4550 SmallPtrSet<Instruction *, 8> Visited;
4551 while (!Worklist.empty()) {
4552 Instruction *I = Worklist.pop_back_val();
4553 if (!Visited.insert(I).second)
4556 ValueExprMapType::iterator It =
4557 ValueExprMap.find_as(static_cast<Value *>(I));
4558 if (It != ValueExprMap.end()) {
4559 const SCEV *Old = It->second;
4561 // SCEVUnknown for a PHI either means that it has an unrecognized
4562 // structure, or it's a PHI that's in the progress of being computed
4563 // by createNodeForPHI. In the former case, additional loop trip
4564 // count information isn't going to change anything. In the later
4565 // case, createNodeForPHI will perform the necessary updates on its
4566 // own when it gets to that point.
4567 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) {
4568 forgetMemoizedResults(Old);
4569 ValueExprMap.erase(It);
4571 if (PHINode *PN = dyn_cast<PHINode>(I))
4572 ConstantEvolutionLoopExitValue.erase(PN);
4575 PushDefUseChildren(I, Worklist);
4579 // Re-lookup the insert position, since the call to
4580 // ComputeBackedgeTakenCount above could result in a
4581 // recusive call to getBackedgeTakenInfo (on a different
4582 // loop), which would invalidate the iterator computed
4584 return BackedgeTakenCounts.find(L)->second = Result;
4587 /// forgetLoop - This method should be called by the client when it has
4588 /// changed a loop in a way that may effect ScalarEvolution's ability to
4589 /// compute a trip count, or if the loop is deleted.
4590 void ScalarEvolution::forgetLoop(const Loop *L) {
4591 // Drop any stored trip count value.
4592 DenseMap<const Loop*, BackedgeTakenInfo>::iterator BTCPos =
4593 BackedgeTakenCounts.find(L);
4594 if (BTCPos != BackedgeTakenCounts.end()) {
4595 BTCPos->second.clear();
4596 BackedgeTakenCounts.erase(BTCPos);
4599 // Drop information about expressions based on loop-header PHIs.
4600 SmallVector<Instruction *, 16> Worklist;
4601 PushLoopPHIs(L, Worklist);
4603 SmallPtrSet<Instruction *, 8> Visited;
4604 while (!Worklist.empty()) {
4605 Instruction *I = Worklist.pop_back_val();
4606 if (!Visited.insert(I).second)
4609 ValueExprMapType::iterator It =
4610 ValueExprMap.find_as(static_cast<Value *>(I));
4611 if (It != ValueExprMap.end()) {
4612 forgetMemoizedResults(It->second);
4613 ValueExprMap.erase(It);
4614 if (PHINode *PN = dyn_cast<PHINode>(I))
4615 ConstantEvolutionLoopExitValue.erase(PN);
4618 PushDefUseChildren(I, Worklist);
4621 // Forget all contained loops too, to avoid dangling entries in the
4622 // ValuesAtScopes map.
4623 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
4627 /// forgetValue - This method should be called by the client when it has
4628 /// changed a value in a way that may effect its value, or which may
4629 /// disconnect it from a def-use chain linking it to a loop.
4630 void ScalarEvolution::forgetValue(Value *V) {
4631 Instruction *I = dyn_cast<Instruction>(V);
4634 // Drop information about expressions based on loop-header PHIs.
4635 SmallVector<Instruction *, 16> Worklist;
4636 Worklist.push_back(I);
4638 SmallPtrSet<Instruction *, 8> Visited;
4639 while (!Worklist.empty()) {
4640 I = Worklist.pop_back_val();
4641 if (!Visited.insert(I).second)
4644 ValueExprMapType::iterator It =
4645 ValueExprMap.find_as(static_cast<Value *>(I));
4646 if (It != ValueExprMap.end()) {
4647 forgetMemoizedResults(It->second);
4648 ValueExprMap.erase(It);
4649 if (PHINode *PN = dyn_cast<PHINode>(I))
4650 ConstantEvolutionLoopExitValue.erase(PN);
4653 PushDefUseChildren(I, Worklist);
4657 /// getExact - Get the exact loop backedge taken count considering all loop
4658 /// exits. A computable result can only be return for loops with a single exit.
4659 /// Returning the minimum taken count among all exits is incorrect because one
4660 /// of the loop's exit limit's may have been skipped. HowFarToZero assumes that
4661 /// the limit of each loop test is never skipped. This is a valid assumption as
4662 /// long as the loop exits via that test. For precise results, it is the
4663 /// caller's responsibility to specify the relevant loop exit using
4664 /// getExact(ExitingBlock, SE).
4666 ScalarEvolution::BackedgeTakenInfo::getExact(ScalarEvolution *SE) const {
4667 // If any exits were not computable, the loop is not computable.
4668 if (!ExitNotTaken.isCompleteList()) return SE->getCouldNotCompute();
4670 // We need exactly one computable exit.
4671 if (!ExitNotTaken.ExitingBlock) return SE->getCouldNotCompute();
4672 assert(ExitNotTaken.ExactNotTaken && "uninitialized not-taken info");
4674 const SCEV *BECount = nullptr;
4675 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4676 ENT != nullptr; ENT = ENT->getNextExit()) {
4678 assert(ENT->ExactNotTaken != SE->getCouldNotCompute() && "bad exit SCEV");
4681 BECount = ENT->ExactNotTaken;
4682 else if (BECount != ENT->ExactNotTaken)
4683 return SE->getCouldNotCompute();
4685 assert(BECount && "Invalid not taken count for loop exit");
4689 /// getExact - Get the exact not taken count for this loop exit.
4691 ScalarEvolution::BackedgeTakenInfo::getExact(BasicBlock *ExitingBlock,
4692 ScalarEvolution *SE) const {
4693 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4694 ENT != nullptr; ENT = ENT->getNextExit()) {
4696 if (ENT->ExitingBlock == ExitingBlock)
4697 return ENT->ExactNotTaken;
4699 return SE->getCouldNotCompute();
4702 /// getMax - Get the max backedge taken count for the loop.
4704 ScalarEvolution::BackedgeTakenInfo::getMax(ScalarEvolution *SE) const {
4705 return Max ? Max : SE->getCouldNotCompute();
4708 bool ScalarEvolution::BackedgeTakenInfo::hasOperand(const SCEV *S,
4709 ScalarEvolution *SE) const {
4710 if (Max && Max != SE->getCouldNotCompute() && SE->hasOperand(Max, S))
4713 if (!ExitNotTaken.ExitingBlock)
4716 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4717 ENT != nullptr; ENT = ENT->getNextExit()) {
4719 if (ENT->ExactNotTaken != SE->getCouldNotCompute()
4720 && SE->hasOperand(ENT->ExactNotTaken, S)) {
4727 /// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each
4728 /// computable exit into a persistent ExitNotTakenInfo array.
4729 ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo(
4730 SmallVectorImpl< std::pair<BasicBlock *, const SCEV *> > &ExitCounts,
4731 bool Complete, const SCEV *MaxCount) : Max(MaxCount) {
4734 ExitNotTaken.setIncomplete();
4736 unsigned NumExits = ExitCounts.size();
4737 if (NumExits == 0) return;
4739 ExitNotTaken.ExitingBlock = ExitCounts[0].first;
4740 ExitNotTaken.ExactNotTaken = ExitCounts[0].second;
4741 if (NumExits == 1) return;
4743 // Handle the rare case of multiple computable exits.
4744 ExitNotTakenInfo *ENT = new ExitNotTakenInfo[NumExits-1];
4746 ExitNotTakenInfo *PrevENT = &ExitNotTaken;
4747 for (unsigned i = 1; i < NumExits; ++i, PrevENT = ENT, ++ENT) {
4748 PrevENT->setNextExit(ENT);
4749 ENT->ExitingBlock = ExitCounts[i].first;
4750 ENT->ExactNotTaken = ExitCounts[i].second;
4754 /// clear - Invalidate this result and free the ExitNotTakenInfo array.
4755 void ScalarEvolution::BackedgeTakenInfo::clear() {
4756 ExitNotTaken.ExitingBlock = nullptr;
4757 ExitNotTaken.ExactNotTaken = nullptr;
4758 delete[] ExitNotTaken.getNextExit();
4761 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
4762 /// of the specified loop will execute.
4763 ScalarEvolution::BackedgeTakenInfo
4764 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
4765 SmallVector<BasicBlock *, 8> ExitingBlocks;
4766 L->getExitingBlocks(ExitingBlocks);
4768 SmallVector<std::pair<BasicBlock *, const SCEV *>, 4> ExitCounts;
4769 bool CouldComputeBECount = true;
4770 BasicBlock *Latch = L->getLoopLatch(); // may be NULL.
4771 const SCEV *MustExitMaxBECount = nullptr;
4772 const SCEV *MayExitMaxBECount = nullptr;
4774 // Compute the ExitLimit for each loop exit. Use this to populate ExitCounts
4775 // and compute maxBECount.
4776 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
4777 BasicBlock *ExitBB = ExitingBlocks[i];
4778 ExitLimit EL = ComputeExitLimit(L, ExitBB);
4780 // 1. For each exit that can be computed, add an entry to ExitCounts.
4781 // CouldComputeBECount is true only if all exits can be computed.
4782 if (EL.Exact == getCouldNotCompute())
4783 // We couldn't compute an exact value for this exit, so
4784 // we won't be able to compute an exact value for the loop.
4785 CouldComputeBECount = false;
4787 ExitCounts.push_back(std::make_pair(ExitBB, EL.Exact));
4789 // 2. Derive the loop's MaxBECount from each exit's max number of
4790 // non-exiting iterations. Partition the loop exits into two kinds:
4791 // LoopMustExits and LoopMayExits.
4793 // If the exit dominates the loop latch, it is a LoopMustExit otherwise it
4794 // is a LoopMayExit. If any computable LoopMustExit is found, then
4795 // MaxBECount is the minimum EL.Max of computable LoopMustExits. Otherwise,
4796 // MaxBECount is conservatively the maximum EL.Max, where CouldNotCompute is
4797 // considered greater than any computable EL.Max.
4798 if (EL.Max != getCouldNotCompute() && Latch &&
4799 DT->dominates(ExitBB, Latch)) {
4800 if (!MustExitMaxBECount)
4801 MustExitMaxBECount = EL.Max;
4803 MustExitMaxBECount =
4804 getUMinFromMismatchedTypes(MustExitMaxBECount, EL.Max);
4806 } else if (MayExitMaxBECount != getCouldNotCompute()) {
4807 if (!MayExitMaxBECount || EL.Max == getCouldNotCompute())
4808 MayExitMaxBECount = EL.Max;
4811 getUMaxFromMismatchedTypes(MayExitMaxBECount, EL.Max);
4815 const SCEV *MaxBECount = MustExitMaxBECount ? MustExitMaxBECount :
4816 (MayExitMaxBECount ? MayExitMaxBECount : getCouldNotCompute());
4817 return BackedgeTakenInfo(ExitCounts, CouldComputeBECount, MaxBECount);
4820 /// ComputeExitLimit - Compute the number of times the backedge of the specified
4821 /// loop will execute if it exits via the specified block.
4822 ScalarEvolution::ExitLimit
4823 ScalarEvolution::ComputeExitLimit(const Loop *L, BasicBlock *ExitingBlock) {
4825 // Okay, we've chosen an exiting block. See what condition causes us to
4826 // exit at this block and remember the exit block and whether all other targets
4827 // lead to the loop header.
4828 bool MustExecuteLoopHeader = true;
4829 BasicBlock *Exit = nullptr;
4830 for (succ_iterator SI = succ_begin(ExitingBlock), SE = succ_end(ExitingBlock);
4832 if (!L->contains(*SI)) {
4833 if (Exit) // Multiple exit successors.
4834 return getCouldNotCompute();
4836 } else if (*SI != L->getHeader()) {
4837 MustExecuteLoopHeader = false;
4840 // At this point, we know we have a conditional branch that determines whether
4841 // the loop is exited. However, we don't know if the branch is executed each
4842 // time through the loop. If not, then the execution count of the branch will
4843 // not be equal to the trip count of the loop.
4845 // Currently we check for this by checking to see if the Exit branch goes to
4846 // the loop header. If so, we know it will always execute the same number of
4847 // times as the loop. We also handle the case where the exit block *is* the
4848 // loop header. This is common for un-rotated loops.
4850 // If both of those tests fail, walk up the unique predecessor chain to the
4851 // header, stopping if there is an edge that doesn't exit the loop. If the
4852 // header is reached, the execution count of the branch will be equal to the
4853 // trip count of the loop.
4855 // More extensive analysis could be done to handle more cases here.
4857 if (!MustExecuteLoopHeader && ExitingBlock != L->getHeader()) {
4858 // The simple checks failed, try climbing the unique predecessor chain
4859 // up to the header.
4861 for (BasicBlock *BB = ExitingBlock; BB; ) {
4862 BasicBlock *Pred = BB->getUniquePredecessor();
4864 return getCouldNotCompute();
4865 TerminatorInst *PredTerm = Pred->getTerminator();
4866 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) {
4867 BasicBlock *PredSucc = PredTerm->getSuccessor(i);
4870 // If the predecessor has a successor that isn't BB and isn't
4871 // outside the loop, assume the worst.
4872 if (L->contains(PredSucc))
4873 return getCouldNotCompute();
4875 if (Pred == L->getHeader()) {
4882 return getCouldNotCompute();
4885 bool IsOnlyExit = (L->getExitingBlock() != nullptr);
4886 TerminatorInst *Term = ExitingBlock->getTerminator();
4887 if (BranchInst *BI = dyn_cast<BranchInst>(Term)) {
4888 assert(BI->isConditional() && "If unconditional, it can't be in loop!");
4889 // Proceed to the next level to examine the exit condition expression.
4890 return ComputeExitLimitFromCond(L, BI->getCondition(), BI->getSuccessor(0),
4891 BI->getSuccessor(1),
4892 /*ControlsExit=*/IsOnlyExit);
4895 if (SwitchInst *SI = dyn_cast<SwitchInst>(Term))
4896 return ComputeExitLimitFromSingleExitSwitch(L, SI, Exit,
4897 /*ControlsExit=*/IsOnlyExit);
4899 return getCouldNotCompute();
4902 /// ComputeExitLimitFromCond - Compute the number of times the
4903 /// backedge of the specified loop will execute if its exit condition
4904 /// were a conditional branch of ExitCond, TBB, and FBB.
4906 /// @param ControlsExit is true if ExitCond directly controls the exit
4907 /// branch. In this case, we can assume that the loop exits only if the
4908 /// condition is true and can infer that failing to meet the condition prior to
4909 /// integer wraparound results in undefined behavior.
4910 ScalarEvolution::ExitLimit
4911 ScalarEvolution::ComputeExitLimitFromCond(const Loop *L,
4915 bool ControlsExit) {
4916 // Check if the controlling expression for this loop is an And or Or.
4917 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
4918 if (BO->getOpcode() == Instruction::And) {
4919 // Recurse on the operands of the and.
4920 bool EitherMayExit = L->contains(TBB);
4921 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
4922 ControlsExit && !EitherMayExit);
4923 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
4924 ControlsExit && !EitherMayExit);
4925 const SCEV *BECount = getCouldNotCompute();
4926 const SCEV *MaxBECount = getCouldNotCompute();
4927 if (EitherMayExit) {
4928 // Both conditions must be true for the loop to continue executing.
4929 // Choose the less conservative count.
4930 if (EL0.Exact == getCouldNotCompute() ||
4931 EL1.Exact == getCouldNotCompute())
4932 BECount = getCouldNotCompute();
4934 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
4935 if (EL0.Max == getCouldNotCompute())
4936 MaxBECount = EL1.Max;
4937 else if (EL1.Max == getCouldNotCompute())
4938 MaxBECount = EL0.Max;
4940 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
4942 // Both conditions must be true at the same time for the loop to exit.
4943 // For now, be conservative.
4944 assert(L->contains(FBB) && "Loop block has no successor in loop!");
4945 if (EL0.Max == EL1.Max)
4946 MaxBECount = EL0.Max;
4947 if (EL0.Exact == EL1.Exact)
4948 BECount = EL0.Exact;
4951 return ExitLimit(BECount, MaxBECount);
4953 if (BO->getOpcode() == Instruction::Or) {
4954 // Recurse on the operands of the or.
4955 bool EitherMayExit = L->contains(FBB);
4956 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
4957 ControlsExit && !EitherMayExit);
4958 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
4959 ControlsExit && !EitherMayExit);
4960 const SCEV *BECount = getCouldNotCompute();
4961 const SCEV *MaxBECount = getCouldNotCompute();
4962 if (EitherMayExit) {
4963 // Both conditions must be false for the loop to continue executing.
4964 // Choose the less conservative count.
4965 if (EL0.Exact == getCouldNotCompute() ||
4966 EL1.Exact == getCouldNotCompute())
4967 BECount = getCouldNotCompute();
4969 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
4970 if (EL0.Max == getCouldNotCompute())
4971 MaxBECount = EL1.Max;
4972 else if (EL1.Max == getCouldNotCompute())
4973 MaxBECount = EL0.Max;
4975 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
4977 // Both conditions must be false at the same time for the loop to exit.
4978 // For now, be conservative.
4979 assert(L->contains(TBB) && "Loop block has no successor in loop!");
4980 if (EL0.Max == EL1.Max)
4981 MaxBECount = EL0.Max;
4982 if (EL0.Exact == EL1.Exact)
4983 BECount = EL0.Exact;
4986 return ExitLimit(BECount, MaxBECount);
4990 // With an icmp, it may be feasible to compute an exact backedge-taken count.
4991 // Proceed to the next level to examine the icmp.
4992 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
4993 return ComputeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB, ControlsExit);
4995 // Check for a constant condition. These are normally stripped out by
4996 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
4997 // preserve the CFG and is temporarily leaving constant conditions
4999 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
5000 if (L->contains(FBB) == !CI->getZExtValue())
5001 // The backedge is always taken.
5002 return getCouldNotCompute();
5004 // The backedge is never taken.
5005 return getConstant(CI->getType(), 0);
5008 // If it's not an integer or pointer comparison then compute it the hard way.
5009 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
5012 /// ComputeExitLimitFromICmp - Compute the number of times the
5013 /// backedge of the specified loop will execute if its exit condition
5014 /// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB.
5015 ScalarEvolution::ExitLimit
5016 ScalarEvolution::ComputeExitLimitFromICmp(const Loop *L,
5020 bool ControlsExit) {
5022 // If the condition was exit on true, convert the condition to exit on false
5023 ICmpInst::Predicate Cond;
5024 if (!L->contains(FBB))
5025 Cond = ExitCond->getPredicate();
5027 Cond = ExitCond->getInversePredicate();
5029 // Handle common loops like: for (X = "string"; *X; ++X)
5030 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
5031 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
5033 ComputeLoadConstantCompareExitLimit(LI, RHS, L, Cond);
5034 if (ItCnt.hasAnyInfo())
5038 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
5039 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
5041 // Try to evaluate any dependencies out of the loop.
5042 LHS = getSCEVAtScope(LHS, L);
5043 RHS = getSCEVAtScope(RHS, L);
5045 // At this point, we would like to compute how many iterations of the
5046 // loop the predicate will return true for these inputs.
5047 if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) {
5048 // If there is a loop-invariant, force it into the RHS.
5049 std::swap(LHS, RHS);
5050 Cond = ICmpInst::getSwappedPredicate(Cond);
5053 // Simplify the operands before analyzing them.
5054 (void)SimplifyICmpOperands(Cond, LHS, RHS);
5056 // If we have a comparison of a chrec against a constant, try to use value
5057 // ranges to answer this query.
5058 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
5059 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
5060 if (AddRec->getLoop() == L) {
5061 // Form the constant range.
5062 ConstantRange CompRange(
5063 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
5065 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
5066 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
5070 case ICmpInst::ICMP_NE: { // while (X != Y)
5071 // Convert to: while (X-Y != 0)
5072 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit);
5073 if (EL.hasAnyInfo()) return EL;
5076 case ICmpInst::ICMP_EQ: { // while (X == Y)
5077 // Convert to: while (X-Y == 0)
5078 ExitLimit EL = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
5079 if (EL.hasAnyInfo()) return EL;
5082 case ICmpInst::ICMP_SLT:
5083 case ICmpInst::ICMP_ULT: { // while (X < Y)
5084 bool IsSigned = Cond == ICmpInst::ICMP_SLT;
5085 ExitLimit EL = HowManyLessThans(LHS, RHS, L, IsSigned, ControlsExit);
5086 if (EL.hasAnyInfo()) return EL;
5089 case ICmpInst::ICMP_SGT:
5090 case ICmpInst::ICMP_UGT: { // while (X > Y)
5091 bool IsSigned = Cond == ICmpInst::ICMP_SGT;
5092 ExitLimit EL = HowManyGreaterThans(LHS, RHS, L, IsSigned, ControlsExit);
5093 if (EL.hasAnyInfo()) return EL;
5098 dbgs() << "ComputeBackedgeTakenCount ";
5099 if (ExitCond->getOperand(0)->getType()->isUnsigned())
5100 dbgs() << "[unsigned] ";
5101 dbgs() << *LHS << " "
5102 << Instruction::getOpcodeName(Instruction::ICmp)
5103 << " " << *RHS << "\n";
5107 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
5110 ScalarEvolution::ExitLimit
5111 ScalarEvolution::ComputeExitLimitFromSingleExitSwitch(const Loop *L,
5113 BasicBlock *ExitingBlock,
5114 bool ControlsExit) {
5115 assert(!L->contains(ExitingBlock) && "Not an exiting block!");
5117 // Give up if the exit is the default dest of a switch.
5118 if (Switch->getDefaultDest() == ExitingBlock)
5119 return getCouldNotCompute();
5121 assert(L->contains(Switch->getDefaultDest()) &&
5122 "Default case must not exit the loop!");
5123 const SCEV *LHS = getSCEVAtScope(Switch->getCondition(), L);
5124 const SCEV *RHS = getConstant(Switch->findCaseDest(ExitingBlock));
5126 // while (X != Y) --> while (X-Y != 0)
5127 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, ControlsExit);
5128 if (EL.hasAnyInfo())
5131 return getCouldNotCompute();
5134 static ConstantInt *
5135 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
5136 ScalarEvolution &SE) {
5137 const SCEV *InVal = SE.getConstant(C);
5138 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
5139 assert(isa<SCEVConstant>(Val) &&
5140 "Evaluation of SCEV at constant didn't fold correctly?");
5141 return cast<SCEVConstant>(Val)->getValue();
5144 /// ComputeLoadConstantCompareExitLimit - Given an exit condition of
5145 /// 'icmp op load X, cst', try to see if we can compute the backedge
5146 /// execution count.
5147 ScalarEvolution::ExitLimit
5148 ScalarEvolution::ComputeLoadConstantCompareExitLimit(
5152 ICmpInst::Predicate predicate) {
5154 if (LI->isVolatile()) return getCouldNotCompute();
5156 // Check to see if the loaded pointer is a getelementptr of a global.
5157 // TODO: Use SCEV instead of manually grubbing with GEPs.
5158 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
5159 if (!GEP) return getCouldNotCompute();
5161 // Make sure that it is really a constant global we are gepping, with an
5162 // initializer, and make sure the first IDX is really 0.
5163 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
5164 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
5165 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
5166 !cast<Constant>(GEP->getOperand(1))->isNullValue())
5167 return getCouldNotCompute();
5169 // Okay, we allow one non-constant index into the GEP instruction.
5170 Value *VarIdx = nullptr;
5171 std::vector<Constant*> Indexes;
5172 unsigned VarIdxNum = 0;
5173 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
5174 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
5175 Indexes.push_back(CI);
5176 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
5177 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
5178 VarIdx = GEP->getOperand(i);
5180 Indexes.push_back(nullptr);
5183 // Loop-invariant loads may be a byproduct of loop optimization. Skip them.
5185 return getCouldNotCompute();
5187 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
5188 // Check to see if X is a loop variant variable value now.
5189 const SCEV *Idx = getSCEV(VarIdx);
5190 Idx = getSCEVAtScope(Idx, L);
5192 // We can only recognize very limited forms of loop index expressions, in
5193 // particular, only affine AddRec's like {C1,+,C2}.
5194 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
5195 if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) ||
5196 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
5197 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
5198 return getCouldNotCompute();
5200 unsigned MaxSteps = MaxBruteForceIterations;
5201 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
5202 ConstantInt *ItCst = ConstantInt::get(
5203 cast<IntegerType>(IdxExpr->getType()), IterationNum);
5204 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
5206 // Form the GEP offset.
5207 Indexes[VarIdxNum] = Val;
5209 Constant *Result = ConstantFoldLoadThroughGEPIndices(GV->getInitializer(),
5211 if (!Result) break; // Cannot compute!
5213 // Evaluate the condition for this iteration.
5214 Result = ConstantExpr::getICmp(predicate, Result, RHS);
5215 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
5216 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
5218 dbgs() << "\n***\n*** Computed loop count " << *ItCst
5219 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
5222 ++NumArrayLenItCounts;
5223 return getConstant(ItCst); // Found terminating iteration!
5226 return getCouldNotCompute();
5230 /// CanConstantFold - Return true if we can constant fold an instruction of the
5231 /// specified type, assuming that all operands were constants.
5232 static bool CanConstantFold(const Instruction *I) {
5233 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
5234 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I) ||
5238 if (const CallInst *CI = dyn_cast<CallInst>(I))
5239 if (const Function *F = CI->getCalledFunction())
5240 return canConstantFoldCallTo(F);
5244 /// Determine whether this instruction can constant evolve within this loop
5245 /// assuming its operands can all constant evolve.
5246 static bool canConstantEvolve(Instruction *I, const Loop *L) {
5247 // An instruction outside of the loop can't be derived from a loop PHI.
5248 if (!L->contains(I)) return false;
5250 if (isa<PHINode>(I)) {
5251 if (L->getHeader() == I->getParent())
5254 // We don't currently keep track of the control flow needed to evaluate
5255 // PHIs, so we cannot handle PHIs inside of loops.
5259 // If we won't be able to constant fold this expression even if the operands
5260 // are constants, bail early.
5261 return CanConstantFold(I);
5264 /// getConstantEvolvingPHIOperands - Implement getConstantEvolvingPHI by
5265 /// recursing through each instruction operand until reaching a loop header phi.
5267 getConstantEvolvingPHIOperands(Instruction *UseInst, const Loop *L,
5268 DenseMap<Instruction *, PHINode *> &PHIMap) {
5270 // Otherwise, we can evaluate this instruction if all of its operands are
5271 // constant or derived from a PHI node themselves.
5272 PHINode *PHI = nullptr;
5273 for (Instruction::op_iterator OpI = UseInst->op_begin(),
5274 OpE = UseInst->op_end(); OpI != OpE; ++OpI) {
5276 if (isa<Constant>(*OpI)) continue;
5278 Instruction *OpInst = dyn_cast<Instruction>(*OpI);
5279 if (!OpInst || !canConstantEvolve(OpInst, L)) return nullptr;
5281 PHINode *P = dyn_cast<PHINode>(OpInst);
5283 // If this operand is already visited, reuse the prior result.
5284 // We may have P != PHI if this is the deepest point at which the
5285 // inconsistent paths meet.
5286 P = PHIMap.lookup(OpInst);
5288 // Recurse and memoize the results, whether a phi is found or not.
5289 // This recursive call invalidates pointers into PHIMap.
5290 P = getConstantEvolvingPHIOperands(OpInst, L, PHIMap);
5294 return nullptr; // Not evolving from PHI
5295 if (PHI && PHI != P)
5296 return nullptr; // Evolving from multiple different PHIs.
5299 // This is a expression evolving from a constant PHI!
5303 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
5304 /// in the loop that V is derived from. We allow arbitrary operations along the
5305 /// way, but the operands of an operation must either be constants or a value
5306 /// derived from a constant PHI. If this expression does not fit with these
5307 /// constraints, return null.
5308 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
5309 Instruction *I = dyn_cast<Instruction>(V);
5310 if (!I || !canConstantEvolve(I, L)) return nullptr;
5312 if (PHINode *PN = dyn_cast<PHINode>(I)) {
5316 // Record non-constant instructions contained by the loop.
5317 DenseMap<Instruction *, PHINode *> PHIMap;
5318 return getConstantEvolvingPHIOperands(I, L, PHIMap);
5321 /// EvaluateExpression - Given an expression that passes the
5322 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
5323 /// in the loop has the value PHIVal. If we can't fold this expression for some
5324 /// reason, return null.
5325 static Constant *EvaluateExpression(Value *V, const Loop *L,
5326 DenseMap<Instruction *, Constant *> &Vals,
5327 const DataLayout *DL,
5328 const TargetLibraryInfo *TLI) {
5329 // Convenient constant check, but redundant for recursive calls.
5330 if (Constant *C = dyn_cast<Constant>(V)) return C;
5331 Instruction *I = dyn_cast<Instruction>(V);
5332 if (!I) return nullptr;
5334 if (Constant *C = Vals.lookup(I)) return C;
5336 // An instruction inside the loop depends on a value outside the loop that we
5337 // weren't given a mapping for, or a value such as a call inside the loop.
5338 if (!canConstantEvolve(I, L)) return nullptr;
5340 // An unmapped PHI can be due to a branch or another loop inside this loop,
5341 // or due to this not being the initial iteration through a loop where we
5342 // couldn't compute the evolution of this particular PHI last time.
5343 if (isa<PHINode>(I)) return nullptr;
5345 std::vector<Constant*> Operands(I->getNumOperands());
5347 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
5348 Instruction *Operand = dyn_cast<Instruction>(I->getOperand(i));
5350 Operands[i] = dyn_cast<Constant>(I->getOperand(i));
5351 if (!Operands[i]) return nullptr;
5354 Constant *C = EvaluateExpression(Operand, L, Vals, DL, TLI);
5356 if (!C) return nullptr;
5360 if (CmpInst *CI = dyn_cast<CmpInst>(I))
5361 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
5362 Operands[1], DL, TLI);
5363 if (LoadInst *LI = dyn_cast<LoadInst>(I)) {
5364 if (!LI->isVolatile())
5365 return ConstantFoldLoadFromConstPtr(Operands[0], DL);
5367 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), Operands, DL,
5371 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
5372 /// in the header of its containing loop, we know the loop executes a
5373 /// constant number of times, and the PHI node is just a recurrence
5374 /// involving constants, fold it.
5376 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
5379 DenseMap<PHINode*, Constant*>::const_iterator I =
5380 ConstantEvolutionLoopExitValue.find(PN);
5381 if (I != ConstantEvolutionLoopExitValue.end())
5384 if (BEs.ugt(MaxBruteForceIterations))
5385 return ConstantEvolutionLoopExitValue[PN] = nullptr; // Not going to evaluate it.
5387 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
5389 DenseMap<Instruction *, Constant *> CurrentIterVals;
5390 BasicBlock *Header = L->getHeader();
5391 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
5393 // Since the loop is canonicalized, the PHI node must have two entries. One
5394 // entry must be a constant (coming in from outside of the loop), and the
5395 // second must be derived from the same PHI.
5396 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
5397 PHINode *PHI = nullptr;
5398 for (BasicBlock::iterator I = Header->begin();
5399 (PHI = dyn_cast<PHINode>(I)); ++I) {
5400 Constant *StartCST =
5401 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
5402 if (!StartCST) continue;
5403 CurrentIterVals[PHI] = StartCST;
5405 if (!CurrentIterVals.count(PN))
5406 return RetVal = nullptr;
5408 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
5410 // Execute the loop symbolically to determine the exit value.
5411 if (BEs.getActiveBits() >= 32)
5412 return RetVal = nullptr; // More than 2^32-1 iterations?? Not doing it!
5414 unsigned NumIterations = BEs.getZExtValue(); // must be in range
5415 unsigned IterationNum = 0;
5416 for (; ; ++IterationNum) {
5417 if (IterationNum == NumIterations)
5418 return RetVal = CurrentIterVals[PN]; // Got exit value!
5420 // Compute the value of the PHIs for the next iteration.
5421 // EvaluateExpression adds non-phi values to the CurrentIterVals map.
5422 DenseMap<Instruction *, Constant *> NextIterVals;
5423 Constant *NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL,
5426 return nullptr; // Couldn't evaluate!
5427 NextIterVals[PN] = NextPHI;
5429 bool StoppedEvolving = NextPHI == CurrentIterVals[PN];
5431 // Also evaluate the other PHI nodes. However, we don't get to stop if we
5432 // cease to be able to evaluate one of them or if they stop evolving,
5433 // because that doesn't necessarily prevent us from computing PN.
5434 SmallVector<std::pair<PHINode *, Constant *>, 8> PHIsToCompute;
5435 for (DenseMap<Instruction *, Constant *>::const_iterator
5436 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
5437 PHINode *PHI = dyn_cast<PHINode>(I->first);
5438 if (!PHI || PHI == PN || PHI->getParent() != Header) continue;
5439 PHIsToCompute.push_back(std::make_pair(PHI, I->second));
5441 // We use two distinct loops because EvaluateExpression may invalidate any
5442 // iterators into CurrentIterVals.
5443 for (SmallVectorImpl<std::pair<PHINode *, Constant*> >::const_iterator
5444 I = PHIsToCompute.begin(), E = PHIsToCompute.end(); I != E; ++I) {
5445 PHINode *PHI = I->first;
5446 Constant *&NextPHI = NextIterVals[PHI];
5447 if (!NextPHI) { // Not already computed.
5448 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
5449 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, TLI);
5451 if (NextPHI != I->second)
5452 StoppedEvolving = false;
5455 // If all entries in CurrentIterVals == NextIterVals then we can stop
5456 // iterating, the loop can't continue to change.
5457 if (StoppedEvolving)
5458 return RetVal = CurrentIterVals[PN];
5460 CurrentIterVals.swap(NextIterVals);
5464 /// ComputeExitCountExhaustively - If the loop is known to execute a
5465 /// constant number of times (the condition evolves only from constants),
5466 /// try to evaluate a few iterations of the loop until we get the exit
5467 /// condition gets a value of ExitWhen (true or false). If we cannot
5468 /// evaluate the trip count of the loop, return getCouldNotCompute().
5469 const SCEV *ScalarEvolution::ComputeExitCountExhaustively(const Loop *L,
5472 PHINode *PN = getConstantEvolvingPHI(Cond, L);
5473 if (!PN) return getCouldNotCompute();
5475 // If the loop is canonicalized, the PHI will have exactly two entries.
5476 // That's the only form we support here.
5477 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
5479 DenseMap<Instruction *, Constant *> CurrentIterVals;
5480 BasicBlock *Header = L->getHeader();
5481 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
5483 // One entry must be a constant (coming in from outside of the loop), and the
5484 // second must be derived from the same PHI.
5485 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
5486 PHINode *PHI = nullptr;
5487 for (BasicBlock::iterator I = Header->begin();
5488 (PHI = dyn_cast<PHINode>(I)); ++I) {
5489 Constant *StartCST =
5490 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
5491 if (!StartCST) continue;
5492 CurrentIterVals[PHI] = StartCST;
5494 if (!CurrentIterVals.count(PN))
5495 return getCouldNotCompute();
5497 // Okay, we find a PHI node that defines the trip count of this loop. Execute
5498 // the loop symbolically to determine when the condition gets a value of
5501 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
5502 for (unsigned IterationNum = 0; IterationNum != MaxIterations;++IterationNum){
5503 ConstantInt *CondVal =
5504 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, L, CurrentIterVals,
5507 // Couldn't symbolically evaluate.
5508 if (!CondVal) return getCouldNotCompute();
5510 if (CondVal->getValue() == uint64_t(ExitWhen)) {
5511 ++NumBruteForceTripCountsComputed;
5512 return getConstant(Type::getInt32Ty(getContext()), IterationNum);
5515 // Update all the PHI nodes for the next iteration.
5516 DenseMap<Instruction *, Constant *> NextIterVals;
5518 // Create a list of which PHIs we need to compute. We want to do this before
5519 // calling EvaluateExpression on them because that may invalidate iterators
5520 // into CurrentIterVals.
5521 SmallVector<PHINode *, 8> PHIsToCompute;
5522 for (DenseMap<Instruction *, Constant *>::const_iterator
5523 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
5524 PHINode *PHI = dyn_cast<PHINode>(I->first);
5525 if (!PHI || PHI->getParent() != Header) continue;
5526 PHIsToCompute.push_back(PHI);
5528 for (SmallVectorImpl<PHINode *>::const_iterator I = PHIsToCompute.begin(),
5529 E = PHIsToCompute.end(); I != E; ++I) {
5531 Constant *&NextPHI = NextIterVals[PHI];
5532 if (NextPHI) continue; // Already computed!
5534 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
5535 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, TLI);
5537 CurrentIterVals.swap(NextIterVals);
5540 // Too many iterations were needed to evaluate.
5541 return getCouldNotCompute();
5544 /// getSCEVAtScope - Return a SCEV expression for the specified value
5545 /// at the specified scope in the program. The L value specifies a loop
5546 /// nest to evaluate the expression at, where null is the top-level or a
5547 /// specified loop is immediately inside of the loop.
5549 /// This method can be used to compute the exit value for a variable defined
5550 /// in a loop by querying what the value will hold in the parent loop.
5552 /// In the case that a relevant loop exit value cannot be computed, the
5553 /// original value V is returned.
5554 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
5555 // Check to see if we've folded this expression at this loop before.
5556 SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values = ValuesAtScopes[V];
5557 for (unsigned u = 0; u < Values.size(); u++) {
5558 if (Values[u].first == L)
5559 return Values[u].second ? Values[u].second : V;
5561 Values.push_back(std::make_pair(L, static_cast<const SCEV *>(nullptr)));
5562 // Otherwise compute it.
5563 const SCEV *C = computeSCEVAtScope(V, L);
5564 SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values2 = ValuesAtScopes[V];
5565 for (unsigned u = Values2.size(); u > 0; u--) {
5566 if (Values2[u - 1].first == L) {
5567 Values2[u - 1].second = C;
5574 /// This builds up a Constant using the ConstantExpr interface. That way, we
5575 /// will return Constants for objects which aren't represented by a
5576 /// SCEVConstant, because SCEVConstant is restricted to ConstantInt.
5577 /// Returns NULL if the SCEV isn't representable as a Constant.
5578 static Constant *BuildConstantFromSCEV(const SCEV *V) {
5579 switch (static_cast<SCEVTypes>(V->getSCEVType())) {
5580 case scCouldNotCompute:
5584 return cast<SCEVConstant>(V)->getValue();
5586 return dyn_cast<Constant>(cast<SCEVUnknown>(V)->getValue());
5587 case scSignExtend: {
5588 const SCEVSignExtendExpr *SS = cast<SCEVSignExtendExpr>(V);
5589 if (Constant *CastOp = BuildConstantFromSCEV(SS->getOperand()))
5590 return ConstantExpr::getSExt(CastOp, SS->getType());
5593 case scZeroExtend: {
5594 const SCEVZeroExtendExpr *SZ = cast<SCEVZeroExtendExpr>(V);
5595 if (Constant *CastOp = BuildConstantFromSCEV(SZ->getOperand()))
5596 return ConstantExpr::getZExt(CastOp, SZ->getType());
5600 const SCEVTruncateExpr *ST = cast<SCEVTruncateExpr>(V);
5601 if (Constant *CastOp = BuildConstantFromSCEV(ST->getOperand()))
5602 return ConstantExpr::getTrunc(CastOp, ST->getType());
5606 const SCEVAddExpr *SA = cast<SCEVAddExpr>(V);
5607 if (Constant *C = BuildConstantFromSCEV(SA->getOperand(0))) {
5608 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
5609 unsigned AS = PTy->getAddressSpace();
5610 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
5611 C = ConstantExpr::getBitCast(C, DestPtrTy);
5613 for (unsigned i = 1, e = SA->getNumOperands(); i != e; ++i) {
5614 Constant *C2 = BuildConstantFromSCEV(SA->getOperand(i));
5615 if (!C2) return nullptr;
5618 if (!C->getType()->isPointerTy() && C2->getType()->isPointerTy()) {
5619 unsigned AS = C2->getType()->getPointerAddressSpace();
5621 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
5622 // The offsets have been converted to bytes. We can add bytes to an
5623 // i8* by GEP with the byte count in the first index.
5624 C = ConstantExpr::getBitCast(C, DestPtrTy);
5627 // Don't bother trying to sum two pointers. We probably can't
5628 // statically compute a load that results from it anyway.
5629 if (C2->getType()->isPointerTy())
5632 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
5633 if (PTy->getElementType()->isStructTy())
5634 C2 = ConstantExpr::getIntegerCast(
5635 C2, Type::getInt32Ty(C->getContext()), true);
5636 C = ConstantExpr::getGetElementPtr(C, C2);
5638 C = ConstantExpr::getAdd(C, C2);
5645 const SCEVMulExpr *SM = cast<SCEVMulExpr>(V);
5646 if (Constant *C = BuildConstantFromSCEV(SM->getOperand(0))) {
5647 // Don't bother with pointers at all.
5648 if (C->getType()->isPointerTy()) return nullptr;
5649 for (unsigned i = 1, e = SM->getNumOperands(); i != e; ++i) {
5650 Constant *C2 = BuildConstantFromSCEV(SM->getOperand(i));
5651 if (!C2 || C2->getType()->isPointerTy()) return nullptr;
5652 C = ConstantExpr::getMul(C, C2);
5659 const SCEVUDivExpr *SU = cast<SCEVUDivExpr>(V);
5660 if (Constant *LHS = BuildConstantFromSCEV(SU->getLHS()))
5661 if (Constant *RHS = BuildConstantFromSCEV(SU->getRHS()))
5662 if (LHS->getType() == RHS->getType())
5663 return ConstantExpr::getUDiv(LHS, RHS);
5668 break; // TODO: smax, umax.
5673 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
5674 if (isa<SCEVConstant>(V)) return V;
5676 // If this instruction is evolved from a constant-evolving PHI, compute the
5677 // exit value from the loop without using SCEVs.
5678 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
5679 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
5680 const Loop *LI = (*this->LI)[I->getParent()];
5681 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
5682 if (PHINode *PN = dyn_cast<PHINode>(I))
5683 if (PN->getParent() == LI->getHeader()) {
5684 // Okay, there is no closed form solution for the PHI node. Check
5685 // to see if the loop that contains it has a known backedge-taken
5686 // count. If so, we may be able to force computation of the exit
5688 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
5689 if (const SCEVConstant *BTCC =
5690 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
5691 // Okay, we know how many times the containing loop executes. If
5692 // this is a constant evolving PHI node, get the final value at
5693 // the specified iteration number.
5694 Constant *RV = getConstantEvolutionLoopExitValue(PN,
5695 BTCC->getValue()->getValue(),
5697 if (RV) return getSCEV(RV);
5701 // Okay, this is an expression that we cannot symbolically evaluate
5702 // into a SCEV. Check to see if it's possible to symbolically evaluate
5703 // the arguments into constants, and if so, try to constant propagate the
5704 // result. This is particularly useful for computing loop exit values.
5705 if (CanConstantFold(I)) {
5706 SmallVector<Constant *, 4> Operands;
5707 bool MadeImprovement = false;
5708 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
5709 Value *Op = I->getOperand(i);
5710 if (Constant *C = dyn_cast<Constant>(Op)) {
5711 Operands.push_back(C);
5715 // If any of the operands is non-constant and if they are
5716 // non-integer and non-pointer, don't even try to analyze them
5717 // with scev techniques.
5718 if (!isSCEVable(Op->getType()))
5721 const SCEV *OrigV = getSCEV(Op);
5722 const SCEV *OpV = getSCEVAtScope(OrigV, L);
5723 MadeImprovement |= OrigV != OpV;
5725 Constant *C = BuildConstantFromSCEV(OpV);
5727 if (C->getType() != Op->getType())
5728 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
5732 Operands.push_back(C);
5735 // Check to see if getSCEVAtScope actually made an improvement.
5736 if (MadeImprovement) {
5737 Constant *C = nullptr;
5738 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
5739 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
5740 Operands[0], Operands[1], DL,
5742 else if (const LoadInst *LI = dyn_cast<LoadInst>(I)) {
5743 if (!LI->isVolatile())
5744 C = ConstantFoldLoadFromConstPtr(Operands[0], DL);
5746 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
5754 // This is some other type of SCEVUnknown, just return it.
5758 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
5759 // Avoid performing the look-up in the common case where the specified
5760 // expression has no loop-variant portions.
5761 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
5762 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
5763 if (OpAtScope != Comm->getOperand(i)) {
5764 // Okay, at least one of these operands is loop variant but might be
5765 // foldable. Build a new instance of the folded commutative expression.
5766 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
5767 Comm->op_begin()+i);
5768 NewOps.push_back(OpAtScope);
5770 for (++i; i != e; ++i) {
5771 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
5772 NewOps.push_back(OpAtScope);
5774 if (isa<SCEVAddExpr>(Comm))
5775 return getAddExpr(NewOps);
5776 if (isa<SCEVMulExpr>(Comm))
5777 return getMulExpr(NewOps);
5778 if (isa<SCEVSMaxExpr>(Comm))
5779 return getSMaxExpr(NewOps);
5780 if (isa<SCEVUMaxExpr>(Comm))
5781 return getUMaxExpr(NewOps);
5782 llvm_unreachable("Unknown commutative SCEV type!");
5785 // If we got here, all operands are loop invariant.
5789 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
5790 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
5791 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
5792 if (LHS == Div->getLHS() && RHS == Div->getRHS())
5793 return Div; // must be loop invariant
5794 return getUDivExpr(LHS, RHS);
5797 // If this is a loop recurrence for a loop that does not contain L, then we
5798 // are dealing with the final value computed by the loop.
5799 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
5800 // First, attempt to evaluate each operand.
5801 // Avoid performing the look-up in the common case where the specified
5802 // expression has no loop-variant portions.
5803 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
5804 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
5805 if (OpAtScope == AddRec->getOperand(i))
5808 // Okay, at least one of these operands is loop variant but might be
5809 // foldable. Build a new instance of the folded commutative expression.
5810 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(),
5811 AddRec->op_begin()+i);
5812 NewOps.push_back(OpAtScope);
5813 for (++i; i != e; ++i)
5814 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
5816 const SCEV *FoldedRec =
5817 getAddRecExpr(NewOps, AddRec->getLoop(),
5818 AddRec->getNoWrapFlags(SCEV::FlagNW));
5819 AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec);
5820 // The addrec may be folded to a nonrecurrence, for example, if the
5821 // induction variable is multiplied by zero after constant folding. Go
5822 // ahead and return the folded value.
5828 // If the scope is outside the addrec's loop, evaluate it by using the
5829 // loop exit value of the addrec.
5830 if (!AddRec->getLoop()->contains(L)) {
5831 // To evaluate this recurrence, we need to know how many times the AddRec
5832 // loop iterates. Compute this now.
5833 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
5834 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
5836 // Then, evaluate the AddRec.
5837 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
5843 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
5844 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5845 if (Op == Cast->getOperand())
5846 return Cast; // must be loop invariant
5847 return getZeroExtendExpr(Op, Cast->getType());
5850 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
5851 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5852 if (Op == Cast->getOperand())
5853 return Cast; // must be loop invariant
5854 return getSignExtendExpr(Op, Cast->getType());
5857 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
5858 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5859 if (Op == Cast->getOperand())
5860 return Cast; // must be loop invariant
5861 return getTruncateExpr(Op, Cast->getType());
5864 llvm_unreachable("Unknown SCEV type!");
5867 /// getSCEVAtScope - This is a convenience function which does
5868 /// getSCEVAtScope(getSCEV(V), L).
5869 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
5870 return getSCEVAtScope(getSCEV(V), L);
5873 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
5874 /// following equation:
5876 /// A * X = B (mod N)
5878 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
5879 /// A and B isn't important.
5881 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
5882 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
5883 ScalarEvolution &SE) {
5884 uint32_t BW = A.getBitWidth();
5885 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
5886 assert(A != 0 && "A must be non-zero.");
5890 // The gcd of A and N may have only one prime factor: 2. The number of
5891 // trailing zeros in A is its multiplicity
5892 uint32_t Mult2 = A.countTrailingZeros();
5895 // 2. Check if B is divisible by D.
5897 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
5898 // is not less than multiplicity of this prime factor for D.
5899 if (B.countTrailingZeros() < Mult2)
5900 return SE.getCouldNotCompute();
5902 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
5905 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
5906 // bit width during computations.
5907 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
5908 APInt Mod(BW + 1, 0);
5909 Mod.setBit(BW - Mult2); // Mod = N / D
5910 APInt I = AD.multiplicativeInverse(Mod);
5912 // 4. Compute the minimum unsigned root of the equation:
5913 // I * (B / D) mod (N / D)
5914 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
5916 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
5918 return SE.getConstant(Result.trunc(BW));
5921 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
5922 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
5923 /// might be the same) or two SCEVCouldNotCompute objects.
5925 static std::pair<const SCEV *,const SCEV *>
5926 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
5927 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
5928 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
5929 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
5930 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
5932 // We currently can only solve this if the coefficients are constants.
5933 if (!LC || !MC || !NC) {
5934 const SCEV *CNC = SE.getCouldNotCompute();
5935 return std::make_pair(CNC, CNC);
5938 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
5939 const APInt &L = LC->getValue()->getValue();
5940 const APInt &M = MC->getValue()->getValue();
5941 const APInt &N = NC->getValue()->getValue();
5942 APInt Two(BitWidth, 2);
5943 APInt Four(BitWidth, 4);
5946 using namespace APIntOps;
5948 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
5949 // The B coefficient is M-N/2
5953 // The A coefficient is N/2
5954 APInt A(N.sdiv(Two));
5956 // Compute the B^2-4ac term.
5959 SqrtTerm -= Four * (A * C);
5961 if (SqrtTerm.isNegative()) {
5962 // The loop is provably infinite.
5963 const SCEV *CNC = SE.getCouldNotCompute();
5964 return std::make_pair(CNC, CNC);
5967 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
5968 // integer value or else APInt::sqrt() will assert.
5969 APInt SqrtVal(SqrtTerm.sqrt());
5971 // Compute the two solutions for the quadratic formula.
5972 // The divisions must be performed as signed divisions.
5975 if (TwoA.isMinValue()) {
5976 const SCEV *CNC = SE.getCouldNotCompute();
5977 return std::make_pair(CNC, CNC);
5980 LLVMContext &Context = SE.getContext();
5982 ConstantInt *Solution1 =
5983 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
5984 ConstantInt *Solution2 =
5985 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
5987 return std::make_pair(SE.getConstant(Solution1),
5988 SE.getConstant(Solution2));
5989 } // end APIntOps namespace
5992 /// HowFarToZero - Return the number of times a backedge comparing the specified
5993 /// value to zero will execute. If not computable, return CouldNotCompute.
5995 /// This is only used for loops with a "x != y" exit test. The exit condition is
5996 /// now expressed as a single expression, V = x-y. So the exit test is
5997 /// effectively V != 0. We know and take advantage of the fact that this
5998 /// expression only being used in a comparison by zero context.
5999 ScalarEvolution::ExitLimit
6000 ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L, bool ControlsExit) {
6001 // If the value is a constant
6002 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
6003 // If the value is already zero, the branch will execute zero times.
6004 if (C->getValue()->isZero()) return C;
6005 return getCouldNotCompute(); // Otherwise it will loop infinitely.
6008 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
6009 if (!AddRec || AddRec->getLoop() != L)
6010 return getCouldNotCompute();
6012 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
6013 // the quadratic equation to solve it.
6014 if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
6015 std::pair<const SCEV *,const SCEV *> Roots =
6016 SolveQuadraticEquation(AddRec, *this);
6017 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
6018 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
6021 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1
6022 << " sol#2: " << *R2 << "\n";
6024 // Pick the smallest positive root value.
6025 if (ConstantInt *CB =
6026 dyn_cast<ConstantInt>(ConstantExpr::getICmp(CmpInst::ICMP_ULT,
6029 if (CB->getZExtValue() == false)
6030 std::swap(R1, R2); // R1 is the minimum root now.
6032 // We can only use this value if the chrec ends up with an exact zero
6033 // value at this index. When solving for "X*X != 5", for example, we
6034 // should not accept a root of 2.
6035 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
6037 return R1; // We found a quadratic root!
6040 return getCouldNotCompute();
6043 // Otherwise we can only handle this if it is affine.
6044 if (!AddRec->isAffine())
6045 return getCouldNotCompute();
6047 // If this is an affine expression, the execution count of this branch is
6048 // the minimum unsigned root of the following equation:
6050 // Start + Step*N = 0 (mod 2^BW)
6054 // Step*N = -Start (mod 2^BW)
6056 // where BW is the common bit width of Start and Step.
6058 // Get the initial value for the loop.
6059 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
6060 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
6062 // For now we handle only constant steps.
6064 // TODO: Handle a nonconstant Step given AddRec<NUW>. If the
6065 // AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap
6066 // to 0, it must be counting down to equal 0. Consequently, N = Start / -Step.
6067 // We have not yet seen any such cases.
6068 const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step);
6069 if (!StepC || StepC->getValue()->equalsInt(0))
6070 return getCouldNotCompute();
6072 // For positive steps (counting up until unsigned overflow):
6073 // N = -Start/Step (as unsigned)
6074 // For negative steps (counting down to zero):
6076 // First compute the unsigned distance from zero in the direction of Step.
6077 bool CountDown = StepC->getValue()->getValue().isNegative();
6078 const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start);
6080 // Handle unitary steps, which cannot wraparound.
6081 // 1*N = -Start; -1*N = Start (mod 2^BW), so:
6082 // N = Distance (as unsigned)
6083 if (StepC->getValue()->equalsInt(1) || StepC->getValue()->isAllOnesValue()) {
6084 ConstantRange CR = getUnsignedRange(Start);
6085 const SCEV *MaxBECount;
6086 if (!CountDown && CR.getUnsignedMin().isMinValue())
6087 // When counting up, the worst starting value is 1, not 0.
6088 MaxBECount = CR.getUnsignedMax().isMinValue()
6089 ? getConstant(APInt::getMinValue(CR.getBitWidth()))
6090 : getConstant(APInt::getMaxValue(CR.getBitWidth()));
6092 MaxBECount = getConstant(CountDown ? CR.getUnsignedMax()
6093 : -CR.getUnsignedMin());
6094 return ExitLimit(Distance, MaxBECount);
6097 // As a special case, handle the instance where Step is a positive power of
6098 // two. In this case, determining whether Step divides Distance evenly can be
6099 // done by counting and comparing the number of trailing zeros of Step and
6102 const APInt &StepV = StepC->getValue()->getValue();
6103 // StepV.isPowerOf2() returns true if StepV is an positive power of two. It
6104 // also returns true if StepV is maximally negative (eg, INT_MIN), but that
6105 // case is not handled as this code is guarded by !CountDown.
6106 if (StepV.isPowerOf2() &&
6107 GetMinTrailingZeros(Distance) >= StepV.countTrailingZeros())
6108 return getUDivExactExpr(Distance, Step);
6111 // If the condition controls loop exit (the loop exits only if the expression
6112 // is true) and the addition is no-wrap we can use unsigned divide to
6113 // compute the backedge count. In this case, the step may not divide the
6114 // distance, but we don't care because if the condition is "missed" the loop
6115 // will have undefined behavior due to wrapping.
6116 if (ControlsExit && AddRec->getNoWrapFlags(SCEV::FlagNW)) {
6118 getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
6119 return ExitLimit(Exact, Exact);
6122 // Then, try to solve the above equation provided that Start is constant.
6123 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
6124 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
6125 -StartC->getValue()->getValue(),
6127 return getCouldNotCompute();
6130 /// HowFarToNonZero - Return the number of times a backedge checking the
6131 /// specified value for nonzero will execute. If not computable, return
6133 ScalarEvolution::ExitLimit
6134 ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
6135 // Loops that look like: while (X == 0) are very strange indeed. We don't
6136 // handle them yet except for the trivial case. This could be expanded in the
6137 // future as needed.
6139 // If the value is a constant, check to see if it is known to be non-zero
6140 // already. If so, the backedge will execute zero times.
6141 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
6142 if (!C->getValue()->isNullValue())
6143 return getConstant(C->getType(), 0);
6144 return getCouldNotCompute(); // Otherwise it will loop infinitely.
6147 // We could implement others, but I really doubt anyone writes loops like
6148 // this, and if they did, they would already be constant folded.
6149 return getCouldNotCompute();
6152 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
6153 /// (which may not be an immediate predecessor) which has exactly one
6154 /// successor from which BB is reachable, or null if no such block is
6157 std::pair<BasicBlock *, BasicBlock *>
6158 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
6159 // If the block has a unique predecessor, then there is no path from the
6160 // predecessor to the block that does not go through the direct edge
6161 // from the predecessor to the block.
6162 if (BasicBlock *Pred = BB->getSinglePredecessor())
6163 return std::make_pair(Pred, BB);
6165 // A loop's header is defined to be a block that dominates the loop.
6166 // If the header has a unique predecessor outside the loop, it must be
6167 // a block that has exactly one successor that can reach the loop.
6168 if (Loop *L = LI->getLoopFor(BB))
6169 return std::make_pair(L->getLoopPredecessor(), L->getHeader());
6171 return std::pair<BasicBlock *, BasicBlock *>();
6174 /// HasSameValue - SCEV structural equivalence is usually sufficient for
6175 /// testing whether two expressions are equal, however for the purposes of
6176 /// looking for a condition guarding a loop, it can be useful to be a little
6177 /// more general, since a front-end may have replicated the controlling
6180 static bool HasSameValue(const SCEV *A, const SCEV *B) {
6181 // Quick check to see if they are the same SCEV.
6182 if (A == B) return true;
6184 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
6185 // two different instructions with the same value. Check for this case.
6186 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
6187 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
6188 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
6189 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
6190 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory())
6193 // Otherwise assume they may have a different value.
6197 /// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with
6198 /// predicate Pred. Return true iff any changes were made.
6200 bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
6201 const SCEV *&LHS, const SCEV *&RHS,
6203 bool Changed = false;
6205 // If we hit the max recursion limit bail out.
6209 // Canonicalize a constant to the right side.
6210 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
6211 // Check for both operands constant.
6212 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
6213 if (ConstantExpr::getICmp(Pred,
6215 RHSC->getValue())->isNullValue())
6216 goto trivially_false;
6218 goto trivially_true;
6220 // Otherwise swap the operands to put the constant on the right.
6221 std::swap(LHS, RHS);
6222 Pred = ICmpInst::getSwappedPredicate(Pred);
6226 // If we're comparing an addrec with a value which is loop-invariant in the
6227 // addrec's loop, put the addrec on the left. Also make a dominance check,
6228 // as both operands could be addrecs loop-invariant in each other's loop.
6229 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
6230 const Loop *L = AR->getLoop();
6231 if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) {
6232 std::swap(LHS, RHS);
6233 Pred = ICmpInst::getSwappedPredicate(Pred);
6238 // If there's a constant operand, canonicalize comparisons with boundary
6239 // cases, and canonicalize *-or-equal comparisons to regular comparisons.
6240 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
6241 const APInt &RA = RC->getValue()->getValue();
6243 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6244 case ICmpInst::ICMP_EQ:
6245 case ICmpInst::ICMP_NE:
6246 // Fold ((-1) * %a) + %b == 0 (equivalent to %b-%a == 0) into %a == %b.
6248 if (const SCEVAddExpr *AE = dyn_cast<SCEVAddExpr>(LHS))
6249 if (const SCEVMulExpr *ME = dyn_cast<SCEVMulExpr>(AE->getOperand(0)))
6250 if (AE->getNumOperands() == 2 && ME->getNumOperands() == 2 &&
6251 ME->getOperand(0)->isAllOnesValue()) {
6252 RHS = AE->getOperand(1);
6253 LHS = ME->getOperand(1);
6257 case ICmpInst::ICMP_UGE:
6258 if ((RA - 1).isMinValue()) {
6259 Pred = ICmpInst::ICMP_NE;
6260 RHS = getConstant(RA - 1);
6264 if (RA.isMaxValue()) {
6265 Pred = ICmpInst::ICMP_EQ;
6269 if (RA.isMinValue()) goto trivially_true;
6271 Pred = ICmpInst::ICMP_UGT;
6272 RHS = getConstant(RA - 1);
6275 case ICmpInst::ICMP_ULE:
6276 if ((RA + 1).isMaxValue()) {
6277 Pred = ICmpInst::ICMP_NE;
6278 RHS = getConstant(RA + 1);
6282 if (RA.isMinValue()) {
6283 Pred = ICmpInst::ICMP_EQ;
6287 if (RA.isMaxValue()) goto trivially_true;
6289 Pred = ICmpInst::ICMP_ULT;
6290 RHS = getConstant(RA + 1);
6293 case ICmpInst::ICMP_SGE:
6294 if ((RA - 1).isMinSignedValue()) {
6295 Pred = ICmpInst::ICMP_NE;
6296 RHS = getConstant(RA - 1);
6300 if (RA.isMaxSignedValue()) {
6301 Pred = ICmpInst::ICMP_EQ;
6305 if (RA.isMinSignedValue()) goto trivially_true;
6307 Pred = ICmpInst::ICMP_SGT;
6308 RHS = getConstant(RA - 1);
6311 case ICmpInst::ICMP_SLE:
6312 if ((RA + 1).isMaxSignedValue()) {
6313 Pred = ICmpInst::ICMP_NE;
6314 RHS = getConstant(RA + 1);
6318 if (RA.isMinSignedValue()) {
6319 Pred = ICmpInst::ICMP_EQ;
6323 if (RA.isMaxSignedValue()) goto trivially_true;
6325 Pred = ICmpInst::ICMP_SLT;
6326 RHS = getConstant(RA + 1);
6329 case ICmpInst::ICMP_UGT:
6330 if (RA.isMinValue()) {
6331 Pred = ICmpInst::ICMP_NE;
6335 if ((RA + 1).isMaxValue()) {
6336 Pred = ICmpInst::ICMP_EQ;
6337 RHS = getConstant(RA + 1);
6341 if (RA.isMaxValue()) goto trivially_false;
6343 case ICmpInst::ICMP_ULT:
6344 if (RA.isMaxValue()) {
6345 Pred = ICmpInst::ICMP_NE;
6349 if ((RA - 1).isMinValue()) {
6350 Pred = ICmpInst::ICMP_EQ;
6351 RHS = getConstant(RA - 1);
6355 if (RA.isMinValue()) goto trivially_false;
6357 case ICmpInst::ICMP_SGT:
6358 if (RA.isMinSignedValue()) {
6359 Pred = ICmpInst::ICMP_NE;
6363 if ((RA + 1).isMaxSignedValue()) {
6364 Pred = ICmpInst::ICMP_EQ;
6365 RHS = getConstant(RA + 1);
6369 if (RA.isMaxSignedValue()) goto trivially_false;
6371 case ICmpInst::ICMP_SLT:
6372 if (RA.isMaxSignedValue()) {
6373 Pred = ICmpInst::ICMP_NE;
6377 if ((RA - 1).isMinSignedValue()) {
6378 Pred = ICmpInst::ICMP_EQ;
6379 RHS = getConstant(RA - 1);
6383 if (RA.isMinSignedValue()) goto trivially_false;
6388 // Check for obvious equality.
6389 if (HasSameValue(LHS, RHS)) {
6390 if (ICmpInst::isTrueWhenEqual(Pred))
6391 goto trivially_true;
6392 if (ICmpInst::isFalseWhenEqual(Pred))
6393 goto trivially_false;
6396 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
6397 // adding or subtracting 1 from one of the operands.
6399 case ICmpInst::ICMP_SLE:
6400 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) {
6401 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
6403 Pred = ICmpInst::ICMP_SLT;
6405 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) {
6406 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
6408 Pred = ICmpInst::ICMP_SLT;
6412 case ICmpInst::ICMP_SGE:
6413 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) {
6414 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
6416 Pred = ICmpInst::ICMP_SGT;
6418 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) {
6419 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
6421 Pred = ICmpInst::ICMP_SGT;
6425 case ICmpInst::ICMP_ULE:
6426 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) {
6427 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
6429 Pred = ICmpInst::ICMP_ULT;
6431 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) {
6432 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
6434 Pred = ICmpInst::ICMP_ULT;
6438 case ICmpInst::ICMP_UGE:
6439 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) {
6440 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
6442 Pred = ICmpInst::ICMP_UGT;
6444 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) {
6445 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
6447 Pred = ICmpInst::ICMP_UGT;
6455 // TODO: More simplifications are possible here.
6457 // Recursively simplify until we either hit a recursion limit or nothing
6460 return SimplifyICmpOperands(Pred, LHS, RHS, Depth+1);
6466 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
6467 Pred = ICmpInst::ICMP_EQ;
6472 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
6473 Pred = ICmpInst::ICMP_NE;
6477 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
6478 return getSignedRange(S).getSignedMax().isNegative();
6481 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
6482 return getSignedRange(S).getSignedMin().isStrictlyPositive();
6485 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
6486 return !getSignedRange(S).getSignedMin().isNegative();
6489 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
6490 return !getSignedRange(S).getSignedMax().isStrictlyPositive();
6493 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
6494 return isKnownNegative(S) || isKnownPositive(S);
6497 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
6498 const SCEV *LHS, const SCEV *RHS) {
6499 // Canonicalize the inputs first.
6500 (void)SimplifyICmpOperands(Pred, LHS, RHS);
6502 // If LHS or RHS is an addrec, check to see if the condition is true in
6503 // every iteration of the loop.
6504 // If LHS and RHS are both addrec, both conditions must be true in
6505 // every iteration of the loop.
6506 const SCEVAddRecExpr *LAR = dyn_cast<SCEVAddRecExpr>(LHS);
6507 const SCEVAddRecExpr *RAR = dyn_cast<SCEVAddRecExpr>(RHS);
6508 bool LeftGuarded = false;
6509 bool RightGuarded = false;
6511 const Loop *L = LAR->getLoop();
6512 if (isLoopEntryGuardedByCond(L, Pred, LAR->getStart(), RHS) &&
6513 isLoopBackedgeGuardedByCond(L, Pred, LAR->getPostIncExpr(*this), RHS)) {
6514 if (!RAR) return true;
6519 const Loop *L = RAR->getLoop();
6520 if (isLoopEntryGuardedByCond(L, Pred, LHS, RAR->getStart()) &&
6521 isLoopBackedgeGuardedByCond(L, Pred, LHS, RAR->getPostIncExpr(*this))) {
6522 if (!LAR) return true;
6523 RightGuarded = true;
6526 if (LeftGuarded && RightGuarded)
6529 // Otherwise see what can be done with known constant ranges.
6530 return isKnownPredicateWithRanges(Pred, LHS, RHS);
6534 ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred,
6535 const SCEV *LHS, const SCEV *RHS) {
6536 if (HasSameValue(LHS, RHS))
6537 return ICmpInst::isTrueWhenEqual(Pred);
6539 // This code is split out from isKnownPredicate because it is called from
6540 // within isLoopEntryGuardedByCond.
6543 llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6544 case ICmpInst::ICMP_SGT:
6545 std::swap(LHS, RHS);
6546 case ICmpInst::ICMP_SLT: {
6547 ConstantRange LHSRange = getSignedRange(LHS);
6548 ConstantRange RHSRange = getSignedRange(RHS);
6549 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
6551 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
6555 case ICmpInst::ICMP_SGE:
6556 std::swap(LHS, RHS);
6557 case ICmpInst::ICMP_SLE: {
6558 ConstantRange LHSRange = getSignedRange(LHS);
6559 ConstantRange RHSRange = getSignedRange(RHS);
6560 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
6562 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
6566 case ICmpInst::ICMP_UGT:
6567 std::swap(LHS, RHS);
6568 case ICmpInst::ICMP_ULT: {
6569 ConstantRange LHSRange = getUnsignedRange(LHS);
6570 ConstantRange RHSRange = getUnsignedRange(RHS);
6571 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
6573 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
6577 case ICmpInst::ICMP_UGE:
6578 std::swap(LHS, RHS);
6579 case ICmpInst::ICMP_ULE: {
6580 ConstantRange LHSRange = getUnsignedRange(LHS);
6581 ConstantRange RHSRange = getUnsignedRange(RHS);
6582 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
6584 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
6588 case ICmpInst::ICMP_NE: {
6589 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
6591 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
6594 const SCEV *Diff = getMinusSCEV(LHS, RHS);
6595 if (isKnownNonZero(Diff))
6599 case ICmpInst::ICMP_EQ:
6600 // The check at the top of the function catches the case where
6601 // the values are known to be equal.
6607 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
6608 /// protected by a conditional between LHS and RHS. This is used to
6609 /// to eliminate casts.
6611 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
6612 ICmpInst::Predicate Pred,
6613 const SCEV *LHS, const SCEV *RHS) {
6614 // Interpret a null as meaning no loop, where there is obviously no guard
6615 // (interprocedural conditions notwithstanding).
6616 if (!L) return true;
6618 if (isKnownPredicateWithRanges(Pred, LHS, RHS)) return true;
6620 BasicBlock *Latch = L->getLoopLatch();
6624 BranchInst *LoopContinuePredicate =
6625 dyn_cast<BranchInst>(Latch->getTerminator());
6626 if (LoopContinuePredicate && LoopContinuePredicate->isConditional() &&
6627 isImpliedCond(Pred, LHS, RHS,
6628 LoopContinuePredicate->getCondition(),
6629 LoopContinuePredicate->getSuccessor(0) != L->getHeader()))
6632 // Check conditions due to any @llvm.assume intrinsics.
6633 for (auto &AssumeVH : AC->assumptions()) {
6636 auto *CI = cast<CallInst>(AssumeVH);
6637 if (!DT->dominates(CI, Latch->getTerminator()))
6640 if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false))
6647 /// isLoopEntryGuardedByCond - Test whether entry to the loop is protected
6648 /// by a conditional between LHS and RHS. This is used to help avoid max
6649 /// expressions in loop trip counts, and to eliminate casts.
6651 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
6652 ICmpInst::Predicate Pred,
6653 const SCEV *LHS, const SCEV *RHS) {
6654 // Interpret a null as meaning no loop, where there is obviously no guard
6655 // (interprocedural conditions notwithstanding).
6656 if (!L) return false;
6658 if (isKnownPredicateWithRanges(Pred, LHS, RHS)) return true;
6660 // Starting at the loop predecessor, climb up the predecessor chain, as long
6661 // as there are predecessors that can be found that have unique successors
6662 // leading to the original header.
6663 for (std::pair<BasicBlock *, BasicBlock *>
6664 Pair(L->getLoopPredecessor(), L->getHeader());
6666 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
6668 BranchInst *LoopEntryPredicate =
6669 dyn_cast<BranchInst>(Pair.first->getTerminator());
6670 if (!LoopEntryPredicate ||
6671 LoopEntryPredicate->isUnconditional())
6674 if (isImpliedCond(Pred, LHS, RHS,
6675 LoopEntryPredicate->getCondition(),
6676 LoopEntryPredicate->getSuccessor(0) != Pair.second))
6680 // Check conditions due to any @llvm.assume intrinsics.
6681 for (auto &AssumeVH : AC->assumptions()) {
6684 auto *CI = cast<CallInst>(AssumeVH);
6685 if (!DT->dominates(CI, L->getHeader()))
6688 if (isImpliedCond(Pred, LHS, RHS, CI->getArgOperand(0), false))
6695 /// RAII wrapper to prevent recursive application of isImpliedCond.
6696 /// ScalarEvolution's PendingLoopPredicates set must be empty unless we are
6697 /// currently evaluating isImpliedCond.
6698 struct MarkPendingLoopPredicate {
6700 DenseSet<Value*> &LoopPreds;
6703 MarkPendingLoopPredicate(Value *C, DenseSet<Value*> &LP)
6704 : Cond(C), LoopPreds(LP) {
6705 Pending = !LoopPreds.insert(Cond).second;
6707 ~MarkPendingLoopPredicate() {
6709 LoopPreds.erase(Cond);
6713 /// isImpliedCond - Test whether the condition described by Pred, LHS,
6714 /// and RHS is true whenever the given Cond value evaluates to true.
6715 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred,
6716 const SCEV *LHS, const SCEV *RHS,
6717 Value *FoundCondValue,
6719 MarkPendingLoopPredicate Mark(FoundCondValue, PendingLoopPredicates);
6723 // Recursively handle And and Or conditions.
6724 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) {
6725 if (BO->getOpcode() == Instruction::And) {
6727 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
6728 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
6729 } else if (BO->getOpcode() == Instruction::Or) {
6731 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
6732 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
6736 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue);
6737 if (!ICI) return false;
6739 // Bail if the ICmp's operands' types are wider than the needed type
6740 // before attempting to call getSCEV on them. This avoids infinite
6741 // recursion, since the analysis of widening casts can require loop
6742 // exit condition information for overflow checking, which would
6744 if (getTypeSizeInBits(LHS->getType()) <
6745 getTypeSizeInBits(ICI->getOperand(0)->getType()))
6748 // Now that we found a conditional branch that dominates the loop or controls
6749 // the loop latch. Check to see if it is the comparison we are looking for.
6750 ICmpInst::Predicate FoundPred;
6752 FoundPred = ICI->getInversePredicate();
6754 FoundPred = ICI->getPredicate();
6756 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
6757 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
6759 // Balance the types. The case where FoundLHS' type is wider than
6760 // LHS' type is checked for above.
6761 if (getTypeSizeInBits(LHS->getType()) >
6762 getTypeSizeInBits(FoundLHS->getType())) {
6763 if (CmpInst::isSigned(FoundPred)) {
6764 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
6765 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
6767 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
6768 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
6772 // Canonicalize the query to match the way instcombine will have
6773 // canonicalized the comparison.
6774 if (SimplifyICmpOperands(Pred, LHS, RHS))
6776 return CmpInst::isTrueWhenEqual(Pred);
6777 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
6778 if (FoundLHS == FoundRHS)
6779 return CmpInst::isFalseWhenEqual(FoundPred);
6781 // Check to see if we can make the LHS or RHS match.
6782 if (LHS == FoundRHS || RHS == FoundLHS) {
6783 if (isa<SCEVConstant>(RHS)) {
6784 std::swap(FoundLHS, FoundRHS);
6785 FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
6787 std::swap(LHS, RHS);
6788 Pred = ICmpInst::getSwappedPredicate(Pred);
6792 // Check whether the found predicate is the same as the desired predicate.
6793 if (FoundPred == Pred)
6794 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
6796 // Check whether swapping the found predicate makes it the same as the
6797 // desired predicate.
6798 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
6799 if (isa<SCEVConstant>(RHS))
6800 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
6802 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
6803 RHS, LHS, FoundLHS, FoundRHS);
6806 // Check if we can make progress by sharpening ranges.
6807 if (FoundPred == ICmpInst::ICMP_NE &&
6808 (isa<SCEVConstant>(FoundLHS) || isa<SCEVConstant>(FoundRHS))) {
6810 const SCEVConstant *C = nullptr;
6811 const SCEV *V = nullptr;
6813 if (isa<SCEVConstant>(FoundLHS)) {
6814 C = cast<SCEVConstant>(FoundLHS);
6817 C = cast<SCEVConstant>(FoundRHS);
6821 // The guarding predicate tells us that C != V. If the known range
6822 // of V is [C, t), we can sharpen the range to [C + 1, t). The
6823 // range we consider has to correspond to same signedness as the
6824 // predicate we're interested in folding.
6826 APInt Min = ICmpInst::isSigned(Pred) ?
6827 getSignedRange(V).getSignedMin() : getUnsignedRange(V).getUnsignedMin();
6829 if (Min == C->getValue()->getValue()) {
6830 // Given (V >= Min && V != Min) we conclude V >= (Min + 1).
6831 // This is true even if (Min + 1) wraps around -- in case of
6832 // wraparound, (Min + 1) < Min, so (V >= Min => V >= (Min + 1)).
6834 APInt SharperMin = Min + 1;
6837 case ICmpInst::ICMP_SGE:
6838 case ICmpInst::ICMP_UGE:
6839 // We know V `Pred` SharperMin. If this implies LHS `Pred`
6841 if (isImpliedCondOperands(Pred, LHS, RHS, V,
6842 getConstant(SharperMin)))
6845 case ICmpInst::ICMP_SGT:
6846 case ICmpInst::ICMP_UGT:
6847 // We know from the range information that (V `Pred` Min ||
6848 // V == Min). We know from the guarding condition that !(V
6849 // == Min). This gives us
6851 // V `Pred` Min || V == Min && !(V == Min)
6854 // If V `Pred` Min implies LHS `Pred` RHS, we're done.
6856 if (isImpliedCondOperands(Pred, LHS, RHS, V, getConstant(Min)))
6866 // Check whether the actual condition is beyond sufficient.
6867 if (FoundPred == ICmpInst::ICMP_EQ)
6868 if (ICmpInst::isTrueWhenEqual(Pred))
6869 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
6871 if (Pred == ICmpInst::ICMP_NE)
6872 if (!ICmpInst::isTrueWhenEqual(FoundPred))
6873 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
6876 // Otherwise assume the worst.
6880 /// isImpliedCondOperands - Test whether the condition described by Pred,
6881 /// LHS, and RHS is true whenever the condition described by Pred, FoundLHS,
6882 /// and FoundRHS is true.
6883 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
6884 const SCEV *LHS, const SCEV *RHS,
6885 const SCEV *FoundLHS,
6886 const SCEV *FoundRHS) {
6887 return isImpliedCondOperandsHelper(Pred, LHS, RHS,
6888 FoundLHS, FoundRHS) ||
6889 // ~x < ~y --> x > y
6890 isImpliedCondOperandsHelper(Pred, LHS, RHS,
6891 getNotSCEV(FoundRHS),
6892 getNotSCEV(FoundLHS));
6896 /// If Expr computes ~A, return A else return nullptr
6897 static const SCEV *MatchNotExpr(const SCEV *Expr) {
6898 const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Expr);
6899 if (!Add || Add->getNumOperands() != 2) return nullptr;
6901 const SCEVConstant *AddLHS = dyn_cast<SCEVConstant>(Add->getOperand(0));
6902 if (!(AddLHS && AddLHS->getValue()->getValue().isAllOnesValue()))
6905 const SCEVMulExpr *AddRHS = dyn_cast<SCEVMulExpr>(Add->getOperand(1));
6906 if (!AddRHS || AddRHS->getNumOperands() != 2) return nullptr;
6908 const SCEVConstant *MulLHS = dyn_cast<SCEVConstant>(AddRHS->getOperand(0));
6909 if (!(MulLHS && MulLHS->getValue()->getValue().isAllOnesValue()))
6912 return AddRHS->getOperand(1);
6916 /// Is MaybeMaxExpr an SMax or UMax of Candidate and some other values?
6917 template<typename MaxExprType>
6918 static bool IsMaxConsistingOf(const SCEV *MaybeMaxExpr,
6919 const SCEV *Candidate) {
6920 const MaxExprType *MaxExpr = dyn_cast<MaxExprType>(MaybeMaxExpr);
6921 if (!MaxExpr) return false;
6923 auto It = std::find(MaxExpr->op_begin(), MaxExpr->op_end(), Candidate);
6924 return It != MaxExpr->op_end();
6928 /// Is MaybeMinExpr an SMin or UMin of Candidate and some other values?
6929 template<typename MaxExprType>
6930 static bool IsMinConsistingOf(ScalarEvolution &SE,
6931 const SCEV *MaybeMinExpr,
6932 const SCEV *Candidate) {
6933 const SCEV *MaybeMaxExpr = MatchNotExpr(MaybeMinExpr);
6937 return IsMaxConsistingOf<MaxExprType>(MaybeMaxExpr, SE.getNotSCEV(Candidate));
6941 /// Is LHS `Pred` RHS true on the virtue of LHS or RHS being a Min or Max
6943 static bool IsKnownPredicateViaMinOrMax(ScalarEvolution &SE,
6944 ICmpInst::Predicate Pred,
6945 const SCEV *LHS, const SCEV *RHS) {
6950 case ICmpInst::ICMP_SGE:
6951 std::swap(LHS, RHS);
6953 case ICmpInst::ICMP_SLE:
6956 IsMinConsistingOf<SCEVSMaxExpr>(SE, LHS, RHS) ||
6958 IsMaxConsistingOf<SCEVSMaxExpr>(RHS, LHS);
6960 case ICmpInst::ICMP_UGE:
6961 std::swap(LHS, RHS);
6963 case ICmpInst::ICMP_ULE:
6966 IsMinConsistingOf<SCEVUMaxExpr>(SE, LHS, RHS) ||
6968 IsMaxConsistingOf<SCEVUMaxExpr>(RHS, LHS);
6971 llvm_unreachable("covered switch fell through?!");
6974 /// isImpliedCondOperandsHelper - Test whether the condition described by
6975 /// Pred, LHS, and RHS is true whenever the condition described by Pred,
6976 /// FoundLHS, and FoundRHS is true.
6978 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
6979 const SCEV *LHS, const SCEV *RHS,
6980 const SCEV *FoundLHS,
6981 const SCEV *FoundRHS) {
6982 auto IsKnownPredicateFull =
6983 [this](ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS) {
6984 return isKnownPredicateWithRanges(Pred, LHS, RHS) ||
6985 IsKnownPredicateViaMinOrMax(*this, Pred, LHS, RHS);
6989 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6990 case ICmpInst::ICMP_EQ:
6991 case ICmpInst::ICMP_NE:
6992 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
6995 case ICmpInst::ICMP_SLT:
6996 case ICmpInst::ICMP_SLE:
6997 if (IsKnownPredicateFull(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
6998 IsKnownPredicateFull(ICmpInst::ICMP_SGE, RHS, FoundRHS))
7001 case ICmpInst::ICMP_SGT:
7002 case ICmpInst::ICMP_SGE:
7003 if (IsKnownPredicateFull(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
7004 IsKnownPredicateFull(ICmpInst::ICMP_SLE, RHS, FoundRHS))
7007 case ICmpInst::ICMP_ULT:
7008 case ICmpInst::ICMP_ULE:
7009 if (IsKnownPredicateFull(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
7010 IsKnownPredicateFull(ICmpInst::ICMP_UGE, RHS, FoundRHS))
7013 case ICmpInst::ICMP_UGT:
7014 case ICmpInst::ICMP_UGE:
7015 if (IsKnownPredicateFull(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
7016 IsKnownPredicateFull(ICmpInst::ICMP_ULE, RHS, FoundRHS))
7024 // Verify if an linear IV with positive stride can overflow when in a
7025 // less-than comparison, knowing the invariant term of the comparison, the
7026 // stride and the knowledge of NSW/NUW flags on the recurrence.
7027 bool ScalarEvolution::doesIVOverflowOnLT(const SCEV *RHS, const SCEV *Stride,
7028 bool IsSigned, bool NoWrap) {
7029 if (NoWrap) return false;
7031 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
7032 const SCEV *One = getConstant(Stride->getType(), 1);
7035 APInt MaxRHS = getSignedRange(RHS).getSignedMax();
7036 APInt MaxValue = APInt::getSignedMaxValue(BitWidth);
7037 APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
7040 // SMaxRHS + SMaxStrideMinusOne > SMaxValue => overflow!
7041 return (MaxValue - MaxStrideMinusOne).slt(MaxRHS);
7044 APInt MaxRHS = getUnsignedRange(RHS).getUnsignedMax();
7045 APInt MaxValue = APInt::getMaxValue(BitWidth);
7046 APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
7049 // UMaxRHS + UMaxStrideMinusOne > UMaxValue => overflow!
7050 return (MaxValue - MaxStrideMinusOne).ult(MaxRHS);
7053 // Verify if an linear IV with negative stride can overflow when in a
7054 // greater-than comparison, knowing the invariant term of the comparison,
7055 // the stride and the knowledge of NSW/NUW flags on the recurrence.
7056 bool ScalarEvolution::doesIVOverflowOnGT(const SCEV *RHS, const SCEV *Stride,
7057 bool IsSigned, bool NoWrap) {
7058 if (NoWrap) return false;
7060 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
7061 const SCEV *One = getConstant(Stride->getType(), 1);
7064 APInt MinRHS = getSignedRange(RHS).getSignedMin();
7065 APInt MinValue = APInt::getSignedMinValue(BitWidth);
7066 APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
7069 // SMinRHS - SMaxStrideMinusOne < SMinValue => overflow!
7070 return (MinValue + MaxStrideMinusOne).sgt(MinRHS);
7073 APInt MinRHS = getUnsignedRange(RHS).getUnsignedMin();
7074 APInt MinValue = APInt::getMinValue(BitWidth);
7075 APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
7078 // UMinRHS - UMaxStrideMinusOne < UMinValue => overflow!
7079 return (MinValue + MaxStrideMinusOne).ugt(MinRHS);
7082 // Compute the backedge taken count knowing the interval difference, the
7083 // stride and presence of the equality in the comparison.
7084 const SCEV *ScalarEvolution::computeBECount(const SCEV *Delta, const SCEV *Step,
7086 const SCEV *One = getConstant(Step->getType(), 1);
7087 Delta = Equality ? getAddExpr(Delta, Step)
7088 : getAddExpr(Delta, getMinusSCEV(Step, One));
7089 return getUDivExpr(Delta, Step);
7092 /// HowManyLessThans - Return the number of times a backedge containing the
7093 /// specified less-than comparison will execute. If not computable, return
7094 /// CouldNotCompute.
7096 /// @param ControlsExit is true when the LHS < RHS condition directly controls
7097 /// the branch (loops exits only if condition is true). In this case, we can use
7098 /// NoWrapFlags to skip overflow checks.
7099 ScalarEvolution::ExitLimit
7100 ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
7101 const Loop *L, bool IsSigned,
7102 bool ControlsExit) {
7103 // We handle only IV < Invariant
7104 if (!isLoopInvariant(RHS, L))
7105 return getCouldNotCompute();
7107 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
7109 // Avoid weird loops
7110 if (!IV || IV->getLoop() != L || !IV->isAffine())
7111 return getCouldNotCompute();
7113 bool NoWrap = ControlsExit &&
7114 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
7116 const SCEV *Stride = IV->getStepRecurrence(*this);
7118 // Avoid negative or zero stride values
7119 if (!isKnownPositive(Stride))
7120 return getCouldNotCompute();
7122 // Avoid proven overflow cases: this will ensure that the backedge taken count
7123 // will not generate any unsigned overflow. Relaxed no-overflow conditions
7124 // exploit NoWrapFlags, allowing to optimize in presence of undefined
7125 // behaviors like the case of C language.
7126 if (!Stride->isOne() && doesIVOverflowOnLT(RHS, Stride, IsSigned, NoWrap))
7127 return getCouldNotCompute();
7129 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SLT
7130 : ICmpInst::ICMP_ULT;
7131 const SCEV *Start = IV->getStart();
7132 const SCEV *End = RHS;
7133 if (!isLoopEntryGuardedByCond(L, Cond, getMinusSCEV(Start, Stride), RHS)) {
7134 const SCEV *Diff = getMinusSCEV(RHS, Start);
7135 // If we have NoWrap set, then we can assume that the increment won't
7136 // overflow, in which case if RHS - Start is a constant, we don't need to
7137 // do a max operation since we can just figure it out statically
7138 if (NoWrap && isa<SCEVConstant>(Diff)) {
7139 APInt D = dyn_cast<const SCEVConstant>(Diff)->getValue()->getValue();
7143 End = IsSigned ? getSMaxExpr(RHS, Start)
7144 : getUMaxExpr(RHS, Start);
7147 const SCEV *BECount = computeBECount(getMinusSCEV(End, Start), Stride, false);
7149 APInt MinStart = IsSigned ? getSignedRange(Start).getSignedMin()
7150 : getUnsignedRange(Start).getUnsignedMin();
7152 APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
7153 : getUnsignedRange(Stride).getUnsignedMin();
7155 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
7156 APInt Limit = IsSigned ? APInt::getSignedMaxValue(BitWidth) - (MinStride - 1)
7157 : APInt::getMaxValue(BitWidth) - (MinStride - 1);
7159 // Although End can be a MAX expression we estimate MaxEnd considering only
7160 // the case End = RHS. This is safe because in the other case (End - Start)
7161 // is zero, leading to a zero maximum backedge taken count.
7163 IsSigned ? APIntOps::smin(getSignedRange(RHS).getSignedMax(), Limit)
7164 : APIntOps::umin(getUnsignedRange(RHS).getUnsignedMax(), Limit);
7166 const SCEV *MaxBECount;
7167 if (isa<SCEVConstant>(BECount))
7168 MaxBECount = BECount;
7170 MaxBECount = computeBECount(getConstant(MaxEnd - MinStart),
7171 getConstant(MinStride), false);
7173 if (isa<SCEVCouldNotCompute>(MaxBECount))
7174 MaxBECount = BECount;
7176 return ExitLimit(BECount, MaxBECount);
7179 ScalarEvolution::ExitLimit
7180 ScalarEvolution::HowManyGreaterThans(const SCEV *LHS, const SCEV *RHS,
7181 const Loop *L, bool IsSigned,
7182 bool ControlsExit) {
7183 // We handle only IV > Invariant
7184 if (!isLoopInvariant(RHS, L))
7185 return getCouldNotCompute();
7187 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
7189 // Avoid weird loops
7190 if (!IV || IV->getLoop() != L || !IV->isAffine())
7191 return getCouldNotCompute();
7193 bool NoWrap = ControlsExit &&
7194 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
7196 const SCEV *Stride = getNegativeSCEV(IV->getStepRecurrence(*this));
7198 // Avoid negative or zero stride values
7199 if (!isKnownPositive(Stride))
7200 return getCouldNotCompute();
7202 // Avoid proven overflow cases: this will ensure that the backedge taken count
7203 // will not generate any unsigned overflow. Relaxed no-overflow conditions
7204 // exploit NoWrapFlags, allowing to optimize in presence of undefined
7205 // behaviors like the case of C language.
7206 if (!Stride->isOne() && doesIVOverflowOnGT(RHS, Stride, IsSigned, NoWrap))
7207 return getCouldNotCompute();
7209 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SGT
7210 : ICmpInst::ICMP_UGT;
7212 const SCEV *Start = IV->getStart();
7213 const SCEV *End = RHS;
7214 if (!isLoopEntryGuardedByCond(L, Cond, getAddExpr(Start, Stride), RHS)) {
7215 const SCEV *Diff = getMinusSCEV(RHS, Start);
7216 // If we have NoWrap set, then we can assume that the increment won't
7217 // overflow, in which case if RHS - Start is a constant, we don't need to
7218 // do a max operation since we can just figure it out statically
7219 if (NoWrap && isa<SCEVConstant>(Diff)) {
7220 APInt D = dyn_cast<const SCEVConstant>(Diff)->getValue()->getValue();
7221 if (!D.isNegative())
7224 End = IsSigned ? getSMinExpr(RHS, Start)
7225 : getUMinExpr(RHS, Start);
7228 const SCEV *BECount = computeBECount(getMinusSCEV(Start, End), Stride, false);
7230 APInt MaxStart = IsSigned ? getSignedRange(Start).getSignedMax()
7231 : getUnsignedRange(Start).getUnsignedMax();
7233 APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
7234 : getUnsignedRange(Stride).getUnsignedMin();
7236 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
7237 APInt Limit = IsSigned ? APInt::getSignedMinValue(BitWidth) + (MinStride - 1)
7238 : APInt::getMinValue(BitWidth) + (MinStride - 1);
7240 // Although End can be a MIN expression we estimate MinEnd considering only
7241 // the case End = RHS. This is safe because in the other case (Start - End)
7242 // is zero, leading to a zero maximum backedge taken count.
7244 IsSigned ? APIntOps::smax(getSignedRange(RHS).getSignedMin(), Limit)
7245 : APIntOps::umax(getUnsignedRange(RHS).getUnsignedMin(), Limit);
7248 const SCEV *MaxBECount = getCouldNotCompute();
7249 if (isa<SCEVConstant>(BECount))
7250 MaxBECount = BECount;
7252 MaxBECount = computeBECount(getConstant(MaxStart - MinEnd),
7253 getConstant(MinStride), false);
7255 if (isa<SCEVCouldNotCompute>(MaxBECount))
7256 MaxBECount = BECount;
7258 return ExitLimit(BECount, MaxBECount);
7261 /// getNumIterationsInRange - Return the number of iterations of this loop that
7262 /// produce values in the specified constant range. Another way of looking at
7263 /// this is that it returns the first iteration number where the value is not in
7264 /// the condition, thus computing the exit count. If the iteration count can't
7265 /// be computed, an instance of SCEVCouldNotCompute is returned.
7266 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
7267 ScalarEvolution &SE) const {
7268 if (Range.isFullSet()) // Infinite loop.
7269 return SE.getCouldNotCompute();
7271 // If the start is a non-zero constant, shift the range to simplify things.
7272 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
7273 if (!SC->getValue()->isZero()) {
7274 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
7275 Operands[0] = SE.getConstant(SC->getType(), 0);
7276 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(),
7277 getNoWrapFlags(FlagNW));
7278 if (const SCEVAddRecExpr *ShiftedAddRec =
7279 dyn_cast<SCEVAddRecExpr>(Shifted))
7280 return ShiftedAddRec->getNumIterationsInRange(
7281 Range.subtract(SC->getValue()->getValue()), SE);
7282 // This is strange and shouldn't happen.
7283 return SE.getCouldNotCompute();
7286 // The only time we can solve this is when we have all constant indices.
7287 // Otherwise, we cannot determine the overflow conditions.
7288 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
7289 if (!isa<SCEVConstant>(getOperand(i)))
7290 return SE.getCouldNotCompute();
7293 // Okay at this point we know that all elements of the chrec are constants and
7294 // that the start element is zero.
7296 // First check to see if the range contains zero. If not, the first
7298 unsigned BitWidth = SE.getTypeSizeInBits(getType());
7299 if (!Range.contains(APInt(BitWidth, 0)))
7300 return SE.getConstant(getType(), 0);
7303 // If this is an affine expression then we have this situation:
7304 // Solve {0,+,A} in Range === Ax in Range
7306 // We know that zero is in the range. If A is positive then we know that
7307 // the upper value of the range must be the first possible exit value.
7308 // If A is negative then the lower of the range is the last possible loop
7309 // value. Also note that we already checked for a full range.
7310 APInt One(BitWidth,1);
7311 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
7312 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
7314 // The exit value should be (End+A)/A.
7315 APInt ExitVal = (End + A).udiv(A);
7316 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
7318 // Evaluate at the exit value. If we really did fall out of the valid
7319 // range, then we computed our trip count, otherwise wrap around or other
7320 // things must have happened.
7321 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
7322 if (Range.contains(Val->getValue()))
7323 return SE.getCouldNotCompute(); // Something strange happened
7325 // Ensure that the previous value is in the range. This is a sanity check.
7326 assert(Range.contains(
7327 EvaluateConstantChrecAtConstant(this,
7328 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
7329 "Linear scev computation is off in a bad way!");
7330 return SE.getConstant(ExitValue);
7331 } else if (isQuadratic()) {
7332 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
7333 // quadratic equation to solve it. To do this, we must frame our problem in
7334 // terms of figuring out when zero is crossed, instead of when
7335 // Range.getUpper() is crossed.
7336 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
7337 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
7338 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop(),
7339 // getNoWrapFlags(FlagNW)
7342 // Next, solve the constructed addrec
7343 std::pair<const SCEV *,const SCEV *> Roots =
7344 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
7345 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
7346 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
7348 // Pick the smallest positive root value.
7349 if (ConstantInt *CB =
7350 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
7351 R1->getValue(), R2->getValue()))) {
7352 if (CB->getZExtValue() == false)
7353 std::swap(R1, R2); // R1 is the minimum root now.
7355 // Make sure the root is not off by one. The returned iteration should
7356 // not be in the range, but the previous one should be. When solving
7357 // for "X*X < 5", for example, we should not return a root of 2.
7358 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
7361 if (Range.contains(R1Val->getValue())) {
7362 // The next iteration must be out of the range...
7363 ConstantInt *NextVal =
7364 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1);
7366 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
7367 if (!Range.contains(R1Val->getValue()))
7368 return SE.getConstant(NextVal);
7369 return SE.getCouldNotCompute(); // Something strange happened
7372 // If R1 was not in the range, then it is a good return value. Make
7373 // sure that R1-1 WAS in the range though, just in case.
7374 ConstantInt *NextVal =
7375 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1);
7376 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
7377 if (Range.contains(R1Val->getValue()))
7379 return SE.getCouldNotCompute(); // Something strange happened
7384 return SE.getCouldNotCompute();
7390 FindUndefs() : Found(false) {}
7392 bool follow(const SCEV *S) {
7393 if (const SCEVUnknown *C = dyn_cast<SCEVUnknown>(S)) {
7394 if (isa<UndefValue>(C->getValue()))
7396 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) {
7397 if (isa<UndefValue>(C->getValue()))
7401 // Keep looking if we haven't found it yet.
7404 bool isDone() const {
7405 // Stop recursion if we have found an undef.
7411 // Return true when S contains at least an undef value.
7413 containsUndefs(const SCEV *S) {
7415 SCEVTraversal<FindUndefs> ST(F);
7422 // Collect all steps of SCEV expressions.
7423 struct SCEVCollectStrides {
7424 ScalarEvolution &SE;
7425 SmallVectorImpl<const SCEV *> &Strides;
7427 SCEVCollectStrides(ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &S)
7428 : SE(SE), Strides(S) {}
7430 bool follow(const SCEV *S) {
7431 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(S))
7432 Strides.push_back(AR->getStepRecurrence(SE));
7435 bool isDone() const { return false; }
7438 // Collect all SCEVUnknown and SCEVMulExpr expressions.
7439 struct SCEVCollectTerms {
7440 SmallVectorImpl<const SCEV *> &Terms;
7442 SCEVCollectTerms(SmallVectorImpl<const SCEV *> &T)
7445 bool follow(const SCEV *S) {
7446 if (isa<SCEVUnknown>(S) || isa<SCEVMulExpr>(S)) {
7447 if (!containsUndefs(S))
7450 // Stop recursion: once we collected a term, do not walk its operands.
7457 bool isDone() const { return false; }
7461 /// Find parametric terms in this SCEVAddRecExpr.
7462 void SCEVAddRecExpr::collectParametricTerms(
7463 ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &Terms) const {
7464 SmallVector<const SCEV *, 4> Strides;
7465 SCEVCollectStrides StrideCollector(SE, Strides);
7466 visitAll(this, StrideCollector);
7469 dbgs() << "Strides:\n";
7470 for (const SCEV *S : Strides)
7471 dbgs() << *S << "\n";
7474 for (const SCEV *S : Strides) {
7475 SCEVCollectTerms TermCollector(Terms);
7476 visitAll(S, TermCollector);
7480 dbgs() << "Terms:\n";
7481 for (const SCEV *T : Terms)
7482 dbgs() << *T << "\n";
7486 static bool findArrayDimensionsRec(ScalarEvolution &SE,
7487 SmallVectorImpl<const SCEV *> &Terms,
7488 SmallVectorImpl<const SCEV *> &Sizes) {
7489 int Last = Terms.size() - 1;
7490 const SCEV *Step = Terms[Last];
7492 // End of recursion.
7494 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Step)) {
7495 SmallVector<const SCEV *, 2> Qs;
7496 for (const SCEV *Op : M->operands())
7497 if (!isa<SCEVConstant>(Op))
7500 Step = SE.getMulExpr(Qs);
7503 Sizes.push_back(Step);
7507 for (const SCEV *&Term : Terms) {
7508 // Normalize the terms before the next call to findArrayDimensionsRec.
7510 SCEVDivision::divide(SE, Term, Step, &Q, &R);
7512 // Bail out when GCD does not evenly divide one of the terms.
7519 // Remove all SCEVConstants.
7520 Terms.erase(std::remove_if(Terms.begin(), Terms.end(), [](const SCEV *E) {
7521 return isa<SCEVConstant>(E);
7525 if (Terms.size() > 0)
7526 if (!findArrayDimensionsRec(SE, Terms, Sizes))
7529 Sizes.push_back(Step);
7534 struct FindParameter {
7535 bool FoundParameter;
7536 FindParameter() : FoundParameter(false) {}
7538 bool follow(const SCEV *S) {
7539 if (isa<SCEVUnknown>(S)) {
7540 FoundParameter = true;
7541 // Stop recursion: we found a parameter.
7547 bool isDone() const {
7548 // Stop recursion if we have found a parameter.
7549 return FoundParameter;
7554 // Returns true when S contains at least a SCEVUnknown parameter.
7556 containsParameters(const SCEV *S) {
7558 SCEVTraversal<FindParameter> ST(F);
7561 return F.FoundParameter;
7564 // Returns true when one of the SCEVs of Terms contains a SCEVUnknown parameter.
7566 containsParameters(SmallVectorImpl<const SCEV *> &Terms) {
7567 for (const SCEV *T : Terms)
7568 if (containsParameters(T))
7573 // Return the number of product terms in S.
7574 static inline int numberOfTerms(const SCEV *S) {
7575 if (const SCEVMulExpr *Expr = dyn_cast<SCEVMulExpr>(S))
7576 return Expr->getNumOperands();
7580 static const SCEV *removeConstantFactors(ScalarEvolution &SE, const SCEV *T) {
7581 if (isa<SCEVConstant>(T))
7584 if (isa<SCEVUnknown>(T))
7587 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(T)) {
7588 SmallVector<const SCEV *, 2> Factors;
7589 for (const SCEV *Op : M->operands())
7590 if (!isa<SCEVConstant>(Op))
7591 Factors.push_back(Op);
7593 return SE.getMulExpr(Factors);
7599 /// Return the size of an element read or written by Inst.
7600 const SCEV *ScalarEvolution::getElementSize(Instruction *Inst) {
7602 if (StoreInst *Store = dyn_cast<StoreInst>(Inst))
7603 Ty = Store->getValueOperand()->getType();
7604 else if (LoadInst *Load = dyn_cast<LoadInst>(Inst))
7605 Ty = Load->getType();
7609 Type *ETy = getEffectiveSCEVType(PointerType::getUnqual(Ty));
7610 return getSizeOfExpr(ETy, Ty);
7613 /// Second step of delinearization: compute the array dimensions Sizes from the
7614 /// set of Terms extracted from the memory access function of this SCEVAddRec.
7615 void ScalarEvolution::findArrayDimensions(SmallVectorImpl<const SCEV *> &Terms,
7616 SmallVectorImpl<const SCEV *> &Sizes,
7617 const SCEV *ElementSize) const {
7619 if (Terms.size() < 1 || !ElementSize)
7622 // Early return when Terms do not contain parameters: we do not delinearize
7623 // non parametric SCEVs.
7624 if (!containsParameters(Terms))
7628 dbgs() << "Terms:\n";
7629 for (const SCEV *T : Terms)
7630 dbgs() << *T << "\n";
7633 // Remove duplicates.
7634 std::sort(Terms.begin(), Terms.end());
7635 Terms.erase(std::unique(Terms.begin(), Terms.end()), Terms.end());
7637 // Put larger terms first.
7638 std::sort(Terms.begin(), Terms.end(), [](const SCEV *LHS, const SCEV *RHS) {
7639 return numberOfTerms(LHS) > numberOfTerms(RHS);
7642 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
7644 // Divide all terms by the element size.
7645 for (const SCEV *&Term : Terms) {
7647 SCEVDivision::divide(SE, Term, ElementSize, &Q, &R);
7651 SmallVector<const SCEV *, 4> NewTerms;
7653 // Remove constant factors.
7654 for (const SCEV *T : Terms)
7655 if (const SCEV *NewT = removeConstantFactors(SE, T))
7656 NewTerms.push_back(NewT);
7659 dbgs() << "Terms after sorting:\n";
7660 for (const SCEV *T : NewTerms)
7661 dbgs() << *T << "\n";
7664 if (NewTerms.empty() ||
7665 !findArrayDimensionsRec(SE, NewTerms, Sizes)) {
7670 // The last element to be pushed into Sizes is the size of an element.
7671 Sizes.push_back(ElementSize);
7674 dbgs() << "Sizes:\n";
7675 for (const SCEV *S : Sizes)
7676 dbgs() << *S << "\n";
7680 /// Third step of delinearization: compute the access functions for the
7681 /// Subscripts based on the dimensions in Sizes.
7682 void SCEVAddRecExpr::computeAccessFunctions(
7683 ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &Subscripts,
7684 SmallVectorImpl<const SCEV *> &Sizes) const {
7686 // Early exit in case this SCEV is not an affine multivariate function.
7687 if (Sizes.empty() || !this->isAffine())
7690 const SCEV *Res = this;
7691 int Last = Sizes.size() - 1;
7692 for (int i = Last; i >= 0; i--) {
7694 SCEVDivision::divide(SE, Res, Sizes[i], &Q, &R);
7697 dbgs() << "Res: " << *Res << "\n";
7698 dbgs() << "Sizes[i]: " << *Sizes[i] << "\n";
7699 dbgs() << "Res divided by Sizes[i]:\n";
7700 dbgs() << "Quotient: " << *Q << "\n";
7701 dbgs() << "Remainder: " << *R << "\n";
7706 // Do not record the last subscript corresponding to the size of elements in
7710 // Bail out if the remainder is too complex.
7711 if (isa<SCEVAddRecExpr>(R)) {
7720 // Record the access function for the current subscript.
7721 Subscripts.push_back(R);
7724 // Also push in last position the remainder of the last division: it will be
7725 // the access function of the innermost dimension.
7726 Subscripts.push_back(Res);
7728 std::reverse(Subscripts.begin(), Subscripts.end());
7731 dbgs() << "Subscripts:\n";
7732 for (const SCEV *S : Subscripts)
7733 dbgs() << *S << "\n";
7737 /// Splits the SCEV into two vectors of SCEVs representing the subscripts and
7738 /// sizes of an array access. Returns the remainder of the delinearization that
7739 /// is the offset start of the array. The SCEV->delinearize algorithm computes
7740 /// the multiples of SCEV coefficients: that is a pattern matching of sub
7741 /// expressions in the stride and base of a SCEV corresponding to the
7742 /// computation of a GCD (greatest common divisor) of base and stride. When
7743 /// SCEV->delinearize fails, it returns the SCEV unchanged.
7745 /// For example: when analyzing the memory access A[i][j][k] in this loop nest
7747 /// void foo(long n, long m, long o, double A[n][m][o]) {
7749 /// for (long i = 0; i < n; i++)
7750 /// for (long j = 0; j < m; j++)
7751 /// for (long k = 0; k < o; k++)
7752 /// A[i][j][k] = 1.0;
7755 /// the delinearization input is the following AddRec SCEV:
7757 /// AddRec: {{{%A,+,(8 * %m * %o)}<%for.i>,+,(8 * %o)}<%for.j>,+,8}<%for.k>
7759 /// From this SCEV, we are able to say that the base offset of the access is %A
7760 /// because it appears as an offset that does not divide any of the strides in
7763 /// CHECK: Base offset: %A
7765 /// and then SCEV->delinearize determines the size of some of the dimensions of
7766 /// the array as these are the multiples by which the strides are happening:
7768 /// CHECK: ArrayDecl[UnknownSize][%m][%o] with elements of sizeof(double) bytes.
7770 /// Note that the outermost dimension remains of UnknownSize because there are
7771 /// no strides that would help identifying the size of the last dimension: when
7772 /// the array has been statically allocated, one could compute the size of that
7773 /// dimension by dividing the overall size of the array by the size of the known
7774 /// dimensions: %m * %o * 8.
7776 /// Finally delinearize provides the access functions for the array reference
7777 /// that does correspond to A[i][j][k] of the above C testcase:
7779 /// CHECK: ArrayRef[{0,+,1}<%for.i>][{0,+,1}<%for.j>][{0,+,1}<%for.k>]
7781 /// The testcases are checking the output of a function pass:
7782 /// DelinearizationPass that walks through all loads and stores of a function
7783 /// asking for the SCEV of the memory access with respect to all enclosing
7784 /// loops, calling SCEV->delinearize on that and printing the results.
7786 void SCEVAddRecExpr::delinearize(ScalarEvolution &SE,
7787 SmallVectorImpl<const SCEV *> &Subscripts,
7788 SmallVectorImpl<const SCEV *> &Sizes,
7789 const SCEV *ElementSize) const {
7790 // First step: collect parametric terms.
7791 SmallVector<const SCEV *, 4> Terms;
7792 collectParametricTerms(SE, Terms);
7797 // Second step: find subscript sizes.
7798 SE.findArrayDimensions(Terms, Sizes, ElementSize);
7803 // Third step: compute the access functions for each subscript.
7804 computeAccessFunctions(SE, Subscripts, Sizes);
7806 if (Subscripts.empty())
7810 dbgs() << "succeeded to delinearize " << *this << "\n";
7811 dbgs() << "ArrayDecl[UnknownSize]";
7812 for (const SCEV *S : Sizes)
7813 dbgs() << "[" << *S << "]";
7815 dbgs() << "\nArrayRef";
7816 for (const SCEV *S : Subscripts)
7817 dbgs() << "[" << *S << "]";
7822 //===----------------------------------------------------------------------===//
7823 // SCEVCallbackVH Class Implementation
7824 //===----------------------------------------------------------------------===//
7826 void ScalarEvolution::SCEVCallbackVH::deleted() {
7827 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
7828 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
7829 SE->ConstantEvolutionLoopExitValue.erase(PN);
7830 SE->ValueExprMap.erase(getValPtr());
7831 // this now dangles!
7834 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) {
7835 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
7837 // Forget all the expressions associated with users of the old value,
7838 // so that future queries will recompute the expressions using the new
7840 Value *Old = getValPtr();
7841 SmallVector<User *, 16> Worklist(Old->user_begin(), Old->user_end());
7842 SmallPtrSet<User *, 8> Visited;
7843 while (!Worklist.empty()) {
7844 User *U = Worklist.pop_back_val();
7845 // Deleting the Old value will cause this to dangle. Postpone
7846 // that until everything else is done.
7849 if (!Visited.insert(U).second)
7851 if (PHINode *PN = dyn_cast<PHINode>(U))
7852 SE->ConstantEvolutionLoopExitValue.erase(PN);
7853 SE->ValueExprMap.erase(U);
7854 Worklist.insert(Worklist.end(), U->user_begin(), U->user_end());
7856 // Delete the Old value.
7857 if (PHINode *PN = dyn_cast<PHINode>(Old))
7858 SE->ConstantEvolutionLoopExitValue.erase(PN);
7859 SE->ValueExprMap.erase(Old);
7860 // this now dangles!
7863 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
7864 : CallbackVH(V), SE(se) {}
7866 //===----------------------------------------------------------------------===//
7867 // ScalarEvolution Class Implementation
7868 //===----------------------------------------------------------------------===//
7870 ScalarEvolution::ScalarEvolution()
7871 : FunctionPass(ID), ValuesAtScopes(64), LoopDispositions(64),
7872 BlockDispositions(64), FirstUnknown(nullptr) {
7873 initializeScalarEvolutionPass(*PassRegistry::getPassRegistry());
7876 bool ScalarEvolution::runOnFunction(Function &F) {
7878 AC = &getAnalysis<AssumptionCacheTracker>().getAssumptionCache(F);
7879 LI = &getAnalysis<LoopInfo>();
7880 DataLayoutPass *DLP = getAnalysisIfAvailable<DataLayoutPass>();
7881 DL = DLP ? &DLP->getDataLayout() : nullptr;
7882 TLI = &getAnalysis<TargetLibraryInfo>();
7883 DT = &getAnalysis<DominatorTreeWrapperPass>().getDomTree();
7887 void ScalarEvolution::releaseMemory() {
7888 // Iterate through all the SCEVUnknown instances and call their
7889 // destructors, so that they release their references to their values.
7890 for (SCEVUnknown *U = FirstUnknown; U; U = U->Next)
7892 FirstUnknown = nullptr;
7894 ValueExprMap.clear();
7896 // Free any extra memory created for ExitNotTakenInfo in the unlikely event
7897 // that a loop had multiple computable exits.
7898 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
7899 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end();
7904 assert(PendingLoopPredicates.empty() && "isImpliedCond garbage");
7906 BackedgeTakenCounts.clear();
7907 ConstantEvolutionLoopExitValue.clear();
7908 ValuesAtScopes.clear();
7909 LoopDispositions.clear();
7910 BlockDispositions.clear();
7911 UnsignedRanges.clear();
7912 SignedRanges.clear();
7913 UniqueSCEVs.clear();
7914 SCEVAllocator.Reset();
7917 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
7918 AU.setPreservesAll();
7919 AU.addRequired<AssumptionCacheTracker>();
7920 AU.addRequiredTransitive<LoopInfo>();
7921 AU.addRequiredTransitive<DominatorTreeWrapperPass>();
7922 AU.addRequired<TargetLibraryInfo>();
7925 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
7926 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
7929 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
7931 // Print all inner loops first
7932 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
7933 PrintLoopInfo(OS, SE, *I);
7936 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
7939 SmallVector<BasicBlock *, 8> ExitBlocks;
7940 L->getExitBlocks(ExitBlocks);
7941 if (ExitBlocks.size() != 1)
7942 OS << "<multiple exits> ";
7944 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
7945 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
7947 OS << "Unpredictable backedge-taken count. ";
7952 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
7955 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
7956 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
7958 OS << "Unpredictable max backedge-taken count. ";
7964 void ScalarEvolution::print(raw_ostream &OS, const Module *) const {
7965 // ScalarEvolution's implementation of the print method is to print
7966 // out SCEV values of all instructions that are interesting. Doing
7967 // this potentially causes it to create new SCEV objects though,
7968 // which technically conflicts with the const qualifier. This isn't
7969 // observable from outside the class though, so casting away the
7970 // const isn't dangerous.
7971 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
7973 OS << "Classifying expressions for: ";
7974 F->printAsOperand(OS, /*PrintType=*/false);
7976 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
7977 if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) {
7980 const SCEV *SV = SE.getSCEV(&*I);
7983 const Loop *L = LI->getLoopFor((*I).getParent());
7985 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
7992 OS << "\t\t" "Exits: ";
7993 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
7994 if (!SE.isLoopInvariant(ExitValue, L)) {
7995 OS << "<<Unknown>>";
8004 OS << "Determining loop execution counts for: ";
8005 F->printAsOperand(OS, /*PrintType=*/false);
8007 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
8008 PrintLoopInfo(OS, &SE, *I);
8011 ScalarEvolution::LoopDisposition
8012 ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) {
8013 SmallVector<std::pair<const Loop *, LoopDisposition>, 2> &Values = LoopDispositions[S];
8014 for (unsigned u = 0; u < Values.size(); u++) {
8015 if (Values[u].first == L)
8016 return Values[u].second;
8018 Values.push_back(std::make_pair(L, LoopVariant));
8019 LoopDisposition D = computeLoopDisposition(S, L);
8020 SmallVector<std::pair<const Loop *, LoopDisposition>, 2> &Values2 = LoopDispositions[S];
8021 for (unsigned u = Values2.size(); u > 0; u--) {
8022 if (Values2[u - 1].first == L) {
8023 Values2[u - 1].second = D;
8030 ScalarEvolution::LoopDisposition
8031 ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) {
8032 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
8034 return LoopInvariant;
8038 return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L);
8039 case scAddRecExpr: {
8040 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
8042 // If L is the addrec's loop, it's computable.
8043 if (AR->getLoop() == L)
8044 return LoopComputable;
8046 // Add recurrences are never invariant in the function-body (null loop).
8050 // This recurrence is variant w.r.t. L if L contains AR's loop.
8051 if (L->contains(AR->getLoop()))
8054 // This recurrence is invariant w.r.t. L if AR's loop contains L.
8055 if (AR->getLoop()->contains(L))
8056 return LoopInvariant;
8058 // This recurrence is variant w.r.t. L if any of its operands
8060 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
8062 if (!isLoopInvariant(*I, L))
8065 // Otherwise it's loop-invariant.
8066 return LoopInvariant;
8072 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
8073 bool HasVarying = false;
8074 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
8076 LoopDisposition D = getLoopDisposition(*I, L);
8077 if (D == LoopVariant)
8079 if (D == LoopComputable)
8082 return HasVarying ? LoopComputable : LoopInvariant;
8085 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
8086 LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L);
8087 if (LD == LoopVariant)
8089 LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L);
8090 if (RD == LoopVariant)
8092 return (LD == LoopInvariant && RD == LoopInvariant) ?
8093 LoopInvariant : LoopComputable;
8096 // All non-instruction values are loop invariant. All instructions are loop
8097 // invariant if they are not contained in the specified loop.
8098 // Instructions are never considered invariant in the function body
8099 // (null loop) because they are defined within the "loop".
8100 if (Instruction *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue()))
8101 return (L && !L->contains(I)) ? LoopInvariant : LoopVariant;
8102 return LoopInvariant;
8103 case scCouldNotCompute:
8104 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
8106 llvm_unreachable("Unknown SCEV kind!");
8109 bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) {
8110 return getLoopDisposition(S, L) == LoopInvariant;
8113 bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) {
8114 return getLoopDisposition(S, L) == LoopComputable;
8117 ScalarEvolution::BlockDisposition
8118 ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) {
8119 SmallVector<std::pair<const BasicBlock *, BlockDisposition>, 2> &Values = BlockDispositions[S];
8120 for (unsigned u = 0; u < Values.size(); u++) {
8121 if (Values[u].first == BB)
8122 return Values[u].second;
8124 Values.push_back(std::make_pair(BB, DoesNotDominateBlock));
8125 BlockDisposition D = computeBlockDisposition(S, BB);
8126 SmallVector<std::pair<const BasicBlock *, BlockDisposition>, 2> &Values2 = BlockDispositions[S];
8127 for (unsigned u = Values2.size(); u > 0; u--) {
8128 if (Values2[u - 1].first == BB) {
8129 Values2[u - 1].second = D;
8136 ScalarEvolution::BlockDisposition
8137 ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) {
8138 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
8140 return ProperlyDominatesBlock;
8144 return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB);
8145 case scAddRecExpr: {
8146 // This uses a "dominates" query instead of "properly dominates" query
8147 // to test for proper dominance too, because the instruction which
8148 // produces the addrec's value is a PHI, and a PHI effectively properly
8149 // dominates its entire containing block.
8150 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
8151 if (!DT->dominates(AR->getLoop()->getHeader(), BB))
8152 return DoesNotDominateBlock;
8154 // FALL THROUGH into SCEVNAryExpr handling.
8159 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
8161 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
8163 BlockDisposition D = getBlockDisposition(*I, BB);
8164 if (D == DoesNotDominateBlock)
8165 return DoesNotDominateBlock;
8166 if (D == DominatesBlock)
8169 return Proper ? ProperlyDominatesBlock : DominatesBlock;
8172 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
8173 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
8174 BlockDisposition LD = getBlockDisposition(LHS, BB);
8175 if (LD == DoesNotDominateBlock)
8176 return DoesNotDominateBlock;
8177 BlockDisposition RD = getBlockDisposition(RHS, BB);
8178 if (RD == DoesNotDominateBlock)
8179 return DoesNotDominateBlock;
8180 return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ?
8181 ProperlyDominatesBlock : DominatesBlock;
8184 if (Instruction *I =
8185 dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) {
8186 if (I->getParent() == BB)
8187 return DominatesBlock;
8188 if (DT->properlyDominates(I->getParent(), BB))
8189 return ProperlyDominatesBlock;
8190 return DoesNotDominateBlock;
8192 return ProperlyDominatesBlock;
8193 case scCouldNotCompute:
8194 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
8196 llvm_unreachable("Unknown SCEV kind!");
8199 bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) {
8200 return getBlockDisposition(S, BB) >= DominatesBlock;
8203 bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) {
8204 return getBlockDisposition(S, BB) == ProperlyDominatesBlock;
8208 // Search for a SCEV expression node within an expression tree.
8209 // Implements SCEVTraversal::Visitor.
8214 SCEVSearch(const SCEV *N): Node(N), IsFound(false) {}
8216 bool follow(const SCEV *S) {
8217 IsFound |= (S == Node);
8220 bool isDone() const { return IsFound; }
8224 bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const {
8225 SCEVSearch Search(Op);
8226 visitAll(S, Search);
8227 return Search.IsFound;
8230 void ScalarEvolution::forgetMemoizedResults(const SCEV *S) {
8231 ValuesAtScopes.erase(S);
8232 LoopDispositions.erase(S);
8233 BlockDispositions.erase(S);
8234 UnsignedRanges.erase(S);
8235 SignedRanges.erase(S);
8237 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
8238 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end(); I != E; ) {
8239 BackedgeTakenInfo &BEInfo = I->second;
8240 if (BEInfo.hasOperand(S, this)) {
8242 BackedgeTakenCounts.erase(I++);
8249 typedef DenseMap<const Loop *, std::string> VerifyMap;
8251 /// replaceSubString - Replaces all occurrences of From in Str with To.
8252 static void replaceSubString(std::string &Str, StringRef From, StringRef To) {
8254 while ((Pos = Str.find(From, Pos)) != std::string::npos) {
8255 Str.replace(Pos, From.size(), To.data(), To.size());
8260 /// getLoopBackedgeTakenCounts - Helper method for verifyAnalysis.
8262 getLoopBackedgeTakenCounts(Loop *L, VerifyMap &Map, ScalarEvolution &SE) {
8263 for (Loop::reverse_iterator I = L->rbegin(), E = L->rend(); I != E; ++I) {
8264 getLoopBackedgeTakenCounts(*I, Map, SE); // recurse.
8266 std::string &S = Map[L];
8268 raw_string_ostream OS(S);
8269 SE.getBackedgeTakenCount(L)->print(OS);
8271 // false and 0 are semantically equivalent. This can happen in dead loops.
8272 replaceSubString(OS.str(), "false", "0");
8273 // Remove wrap flags, their use in SCEV is highly fragile.
8274 // FIXME: Remove this when SCEV gets smarter about them.
8275 replaceSubString(OS.str(), "<nw>", "");
8276 replaceSubString(OS.str(), "<nsw>", "");
8277 replaceSubString(OS.str(), "<nuw>", "");
8282 void ScalarEvolution::verifyAnalysis() const {
8286 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
8288 // Gather stringified backedge taken counts for all loops using SCEV's caches.
8289 // FIXME: It would be much better to store actual values instead of strings,
8290 // but SCEV pointers will change if we drop the caches.
8291 VerifyMap BackedgeDumpsOld, BackedgeDumpsNew;
8292 for (LoopInfo::reverse_iterator I = LI->rbegin(), E = LI->rend(); I != E; ++I)
8293 getLoopBackedgeTakenCounts(*I, BackedgeDumpsOld, SE);
8295 // Gather stringified backedge taken counts for all loops without using
8298 for (LoopInfo::reverse_iterator I = LI->rbegin(), E = LI->rend(); I != E; ++I)
8299 getLoopBackedgeTakenCounts(*I, BackedgeDumpsNew, SE);
8301 // Now compare whether they're the same with and without caches. This allows
8302 // verifying that no pass changed the cache.
8303 assert(BackedgeDumpsOld.size() == BackedgeDumpsNew.size() &&
8304 "New loops suddenly appeared!");
8306 for (VerifyMap::iterator OldI = BackedgeDumpsOld.begin(),
8307 OldE = BackedgeDumpsOld.end(),
8308 NewI = BackedgeDumpsNew.begin();
8309 OldI != OldE; ++OldI, ++NewI) {
8310 assert(OldI->first == NewI->first && "Loop order changed!");
8312 // Compare the stringified SCEVs. We don't care if undef backedgetaken count
8314 // FIXME: We currently ignore SCEV changes from/to CouldNotCompute. This
8315 // means that a pass is buggy or SCEV has to learn a new pattern but is
8316 // usually not harmful.
8317 if (OldI->second != NewI->second &&
8318 OldI->second.find("undef") == std::string::npos &&
8319 NewI->second.find("undef") == std::string::npos &&
8320 OldI->second != "***COULDNOTCOMPUTE***" &&
8321 NewI->second != "***COULDNOTCOMPUTE***") {
8322 dbgs() << "SCEVValidator: SCEV for loop '"
8323 << OldI->first->getHeader()->getName()
8324 << "' changed from '" << OldI->second
8325 << "' to '" << NewI->second << "'!\n";
8330 // TODO: Verify more things.