1 //===- ScalarEvolution.cpp - Scalar Evolution Analysis ----------*- C++ -*-===//
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 #define DEBUG_TYPE "scalar-evolution"
62 #include "llvm/Analysis/ScalarEvolutionExpressions.h"
63 #include "llvm/Constants.h"
64 #include "llvm/DerivedTypes.h"
65 #include "llvm/GlobalVariable.h"
66 #include "llvm/GlobalAlias.h"
67 #include "llvm/Instructions.h"
68 #include "llvm/LLVMContext.h"
69 #include "llvm/Operator.h"
70 #include "llvm/Analysis/ConstantFolding.h"
71 #include "llvm/Analysis/Dominators.h"
72 #include "llvm/Analysis/LoopInfo.h"
73 #include "llvm/Analysis/ValueTracking.h"
74 #include "llvm/Assembly/Writer.h"
75 #include "llvm/Target/TargetData.h"
76 #include "llvm/Support/CommandLine.h"
77 #include "llvm/Support/ConstantRange.h"
78 #include "llvm/Support/Debug.h"
79 #include "llvm/Support/ErrorHandling.h"
80 #include "llvm/Support/GetElementPtrTypeIterator.h"
81 #include "llvm/Support/InstIterator.h"
82 #include "llvm/Support/MathExtras.h"
83 #include "llvm/Support/raw_ostream.h"
84 #include "llvm/ADT/Statistic.h"
85 #include "llvm/ADT/STLExtras.h"
86 #include "llvm/ADT/SmallPtrSet.h"
90 STATISTIC(NumArrayLenItCounts,
91 "Number of trip counts computed with array length");
92 STATISTIC(NumTripCountsComputed,
93 "Number of loops with predictable loop counts");
94 STATISTIC(NumTripCountsNotComputed,
95 "Number of loops without predictable loop counts");
96 STATISTIC(NumBruteForceTripCountsComputed,
97 "Number of loops with trip counts computed by force");
99 static cl::opt<unsigned>
100 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
101 cl::desc("Maximum number of iterations SCEV will "
102 "symbolically execute a constant "
106 static RegisterPass<ScalarEvolution>
107 R("scalar-evolution", "Scalar Evolution Analysis", false, true);
108 char ScalarEvolution::ID = 0;
110 //===----------------------------------------------------------------------===//
111 // SCEV class definitions
112 //===----------------------------------------------------------------------===//
114 //===----------------------------------------------------------------------===//
115 // Implementation of the SCEV class.
120 void SCEV::dump() const {
125 bool SCEV::isZero() const {
126 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
127 return SC->getValue()->isZero();
131 bool SCEV::isOne() const {
132 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
133 return SC->getValue()->isOne();
137 bool SCEV::isAllOnesValue() const {
138 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
139 return SC->getValue()->isAllOnesValue();
143 SCEVCouldNotCompute::SCEVCouldNotCompute() :
144 SCEV(FoldingSetNodeIDRef(), scCouldNotCompute) {}
146 bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const {
147 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
151 const Type *SCEVCouldNotCompute::getType() const {
152 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
156 bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const {
157 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
161 bool SCEVCouldNotCompute::hasOperand(const SCEV *) const {
162 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
166 void SCEVCouldNotCompute::print(raw_ostream &OS) const {
167 OS << "***COULDNOTCOMPUTE***";
170 bool SCEVCouldNotCompute::classof(const SCEV *S) {
171 return S->getSCEVType() == scCouldNotCompute;
174 const SCEV *ScalarEvolution::getConstant(ConstantInt *V) {
176 ID.AddInteger(scConstant);
179 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
180 SCEV *S = new (SCEVAllocator) SCEVConstant(ID.Intern(SCEVAllocator), V);
181 UniqueSCEVs.InsertNode(S, IP);
185 const SCEV *ScalarEvolution::getConstant(const APInt& Val) {
186 return getConstant(ConstantInt::get(getContext(), Val));
190 ScalarEvolution::getConstant(const Type *Ty, uint64_t V, bool isSigned) {
192 ConstantInt::get(cast<IntegerType>(Ty), V, isSigned));
195 const Type *SCEVConstant::getType() const { return V->getType(); }
197 void SCEVConstant::print(raw_ostream &OS) const {
198 WriteAsOperand(OS, V, false);
201 SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID,
202 unsigned SCEVTy, const SCEV *op, const Type *ty)
203 : SCEV(ID, SCEVTy), Op(op), Ty(ty) {}
205 bool SCEVCastExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
206 return Op->dominates(BB, DT);
209 bool SCEVCastExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const {
210 return Op->properlyDominates(BB, DT);
213 SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID,
214 const SCEV *op, const Type *ty)
215 : SCEVCastExpr(ID, scTruncate, op, ty) {
216 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
217 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
218 "Cannot truncate non-integer value!");
221 void SCEVTruncateExpr::print(raw_ostream &OS) const {
222 OS << "(trunc " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
225 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID,
226 const SCEV *op, const Type *ty)
227 : SCEVCastExpr(ID, scZeroExtend, op, ty) {
228 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
229 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
230 "Cannot zero extend non-integer value!");
233 void SCEVZeroExtendExpr::print(raw_ostream &OS) const {
234 OS << "(zext " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
237 SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID,
238 const SCEV *op, const Type *ty)
239 : SCEVCastExpr(ID, scSignExtend, op, ty) {
240 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
241 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
242 "Cannot sign extend non-integer value!");
245 void SCEVSignExtendExpr::print(raw_ostream &OS) const {
246 OS << "(sext " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
249 void SCEVCommutativeExpr::print(raw_ostream &OS) const {
250 assert(NumOperands > 1 && "This plus expr shouldn't exist!");
251 const char *OpStr = getOperationStr();
252 OS << "(" << *Operands[0];
253 for (unsigned i = 1, e = NumOperands; i != e; ++i)
254 OS << OpStr << *Operands[i];
258 bool SCEVNAryExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
259 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
260 if (!getOperand(i)->dominates(BB, DT))
266 bool SCEVNAryExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const {
267 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
268 if (!getOperand(i)->properlyDominates(BB, DT))
274 bool SCEVUDivExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
275 return LHS->dominates(BB, DT) && RHS->dominates(BB, DT);
278 bool SCEVUDivExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const {
279 return LHS->properlyDominates(BB, DT) && RHS->properlyDominates(BB, DT);
282 void SCEVUDivExpr::print(raw_ostream &OS) const {
283 OS << "(" << *LHS << " /u " << *RHS << ")";
286 const Type *SCEVUDivExpr::getType() const {
287 // In most cases the types of LHS and RHS will be the same, but in some
288 // crazy cases one or the other may be a pointer. ScalarEvolution doesn't
289 // depend on the type for correctness, but handling types carefully can
290 // avoid extra casts in the SCEVExpander. The LHS is more likely to be
291 // a pointer type than the RHS, so use the RHS' type here.
292 return RHS->getType();
295 bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const {
296 // Add recurrences are never invariant in the function-body (null loop).
300 // This recurrence is variant w.r.t. QueryLoop if QueryLoop contains L.
301 if (QueryLoop->contains(L))
304 // This recurrence is variant w.r.t. QueryLoop if any of its operands
306 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
307 if (!getOperand(i)->isLoopInvariant(QueryLoop))
310 // Otherwise it's loop-invariant.
315 SCEVAddRecExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
316 return DT->dominates(L->getHeader(), BB) &&
317 SCEVNAryExpr::dominates(BB, DT);
321 SCEVAddRecExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const {
322 // This uses a "dominates" query instead of "properly dominates" query because
323 // the instruction which produces the addrec's value is a PHI, and a PHI
324 // effectively properly dominates its entire containing block.
325 return DT->dominates(L->getHeader(), BB) &&
326 SCEVNAryExpr::properlyDominates(BB, DT);
329 void SCEVAddRecExpr::print(raw_ostream &OS) const {
330 OS << "{" << *Operands[0];
331 for (unsigned i = 1, e = NumOperands; i != e; ++i)
332 OS << ",+," << *Operands[i];
334 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
338 bool SCEVUnknown::isLoopInvariant(const Loop *L) const {
339 // All non-instruction values are loop invariant. All instructions are loop
340 // invariant if they are not contained in the specified loop.
341 // Instructions are never considered invariant in the function body
342 // (null loop) because they are defined within the "loop".
343 if (Instruction *I = dyn_cast<Instruction>(V))
344 return L && !L->contains(I);
348 bool SCEVUnknown::dominates(BasicBlock *BB, DominatorTree *DT) const {
349 if (Instruction *I = dyn_cast<Instruction>(getValue()))
350 return DT->dominates(I->getParent(), BB);
354 bool SCEVUnknown::properlyDominates(BasicBlock *BB, DominatorTree *DT) const {
355 if (Instruction *I = dyn_cast<Instruction>(getValue()))
356 return DT->properlyDominates(I->getParent(), BB);
360 const Type *SCEVUnknown::getType() const {
364 bool SCEVUnknown::isSizeOf(const Type *&AllocTy) const {
365 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(V))
366 if (VCE->getOpcode() == Instruction::PtrToInt)
367 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
368 if (CE->getOpcode() == Instruction::GetElementPtr &&
369 CE->getOperand(0)->isNullValue() &&
370 CE->getNumOperands() == 2)
371 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1)))
373 AllocTy = cast<PointerType>(CE->getOperand(0)->getType())
381 bool SCEVUnknown::isAlignOf(const Type *&AllocTy) const {
382 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(V))
383 if (VCE->getOpcode() == Instruction::PtrToInt)
384 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
385 if (CE->getOpcode() == Instruction::GetElementPtr &&
386 CE->getOperand(0)->isNullValue()) {
388 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
389 if (const StructType *STy = dyn_cast<StructType>(Ty))
390 if (!STy->isPacked() &&
391 CE->getNumOperands() == 3 &&
392 CE->getOperand(1)->isNullValue()) {
393 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2)))
395 STy->getNumElements() == 2 &&
396 STy->getElementType(0)->isIntegerTy(1)) {
397 AllocTy = STy->getElementType(1);
406 bool SCEVUnknown::isOffsetOf(const Type *&CTy, Constant *&FieldNo) const {
407 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(V))
408 if (VCE->getOpcode() == Instruction::PtrToInt)
409 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
410 if (CE->getOpcode() == Instruction::GetElementPtr &&
411 CE->getNumOperands() == 3 &&
412 CE->getOperand(0)->isNullValue() &&
413 CE->getOperand(1)->isNullValue()) {
415 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
416 // Ignore vector types here so that ScalarEvolutionExpander doesn't
417 // emit getelementptrs that index into vectors.
418 if (Ty->isStructTy() || Ty->isArrayTy()) {
420 FieldNo = CE->getOperand(2);
428 void SCEVUnknown::print(raw_ostream &OS) const {
430 if (isSizeOf(AllocTy)) {
431 OS << "sizeof(" << *AllocTy << ")";
434 if (isAlignOf(AllocTy)) {
435 OS << "alignof(" << *AllocTy << ")";
441 if (isOffsetOf(CTy, FieldNo)) {
442 OS << "offsetof(" << *CTy << ", ";
443 WriteAsOperand(OS, FieldNo, false);
448 // Otherwise just print it normally.
449 WriteAsOperand(OS, V, false);
452 //===----------------------------------------------------------------------===//
454 //===----------------------------------------------------------------------===//
456 static bool CompareTypes(const Type *A, const Type *B) {
457 if (A->getTypeID() != B->getTypeID())
458 return A->getTypeID() < B->getTypeID();
459 if (const IntegerType *AI = dyn_cast<IntegerType>(A)) {
460 const IntegerType *BI = cast<IntegerType>(B);
461 return AI->getBitWidth() < BI->getBitWidth();
463 if (const PointerType *AI = dyn_cast<PointerType>(A)) {
464 const PointerType *BI = cast<PointerType>(B);
465 return CompareTypes(AI->getElementType(), BI->getElementType());
467 if (const ArrayType *AI = dyn_cast<ArrayType>(A)) {
468 const ArrayType *BI = cast<ArrayType>(B);
469 if (AI->getNumElements() != BI->getNumElements())
470 return AI->getNumElements() < BI->getNumElements();
471 return CompareTypes(AI->getElementType(), BI->getElementType());
473 if (const VectorType *AI = dyn_cast<VectorType>(A)) {
474 const VectorType *BI = cast<VectorType>(B);
475 if (AI->getNumElements() != BI->getNumElements())
476 return AI->getNumElements() < BI->getNumElements();
477 return CompareTypes(AI->getElementType(), BI->getElementType());
479 if (const StructType *AI = dyn_cast<StructType>(A)) {
480 const StructType *BI = cast<StructType>(B);
481 if (AI->getNumElements() != BI->getNumElements())
482 return AI->getNumElements() < BI->getNumElements();
483 for (unsigned i = 0, e = AI->getNumElements(); i != e; ++i)
484 if (CompareTypes(AI->getElementType(i), BI->getElementType(i)) ||
485 CompareTypes(BI->getElementType(i), AI->getElementType(i)))
486 return CompareTypes(AI->getElementType(i), BI->getElementType(i));
492 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
493 /// than the complexity of the RHS. This comparator is used to canonicalize
495 class SCEVComplexityCompare {
498 explicit SCEVComplexityCompare(LoopInfo *li) : LI(li) {}
500 bool operator()(const SCEV *LHS, const SCEV *RHS) const {
501 // Fast-path: SCEVs are uniqued so we can do a quick equality check.
505 // Primarily, sort the SCEVs by their getSCEVType().
506 if (LHS->getSCEVType() != RHS->getSCEVType())
507 return LHS->getSCEVType() < RHS->getSCEVType();
509 // Aside from the getSCEVType() ordering, the particular ordering
510 // isn't very important except that it's beneficial to be consistent,
511 // so that (a + b) and (b + a) don't end up as different expressions.
513 // Sort SCEVUnknown values with some loose heuristics. TODO: This is
514 // not as complete as it could be.
515 if (const SCEVUnknown *LU = dyn_cast<SCEVUnknown>(LHS)) {
516 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
518 // Order pointer values after integer values. This helps SCEVExpander
520 if (LU->getType()->isPointerTy() && !RU->getType()->isPointerTy())
522 if (RU->getType()->isPointerTy() && !LU->getType()->isPointerTy())
525 // Compare getValueID values.
526 if (LU->getValue()->getValueID() != RU->getValue()->getValueID())
527 return LU->getValue()->getValueID() < RU->getValue()->getValueID();
529 // Sort arguments by their position.
530 if (const Argument *LA = dyn_cast<Argument>(LU->getValue())) {
531 const Argument *RA = cast<Argument>(RU->getValue());
532 return LA->getArgNo() < RA->getArgNo();
535 // For instructions, compare their loop depth, and their opcode.
536 // This is pretty loose.
537 if (Instruction *LV = dyn_cast<Instruction>(LU->getValue())) {
538 Instruction *RV = cast<Instruction>(RU->getValue());
540 // Compare loop depths.
541 if (LI->getLoopDepth(LV->getParent()) !=
542 LI->getLoopDepth(RV->getParent()))
543 return LI->getLoopDepth(LV->getParent()) <
544 LI->getLoopDepth(RV->getParent());
547 if (LV->getOpcode() != RV->getOpcode())
548 return LV->getOpcode() < RV->getOpcode();
550 // Compare the number of operands.
551 if (LV->getNumOperands() != RV->getNumOperands())
552 return LV->getNumOperands() < RV->getNumOperands();
558 // Compare constant values.
559 if (const SCEVConstant *LC = dyn_cast<SCEVConstant>(LHS)) {
560 const SCEVConstant *RC = cast<SCEVConstant>(RHS);
561 if (LC->getValue()->getBitWidth() != RC->getValue()->getBitWidth())
562 return LC->getValue()->getBitWidth() < RC->getValue()->getBitWidth();
563 return LC->getValue()->getValue().ult(RC->getValue()->getValue());
566 // Compare addrec loop depths.
567 if (const SCEVAddRecExpr *LA = dyn_cast<SCEVAddRecExpr>(LHS)) {
568 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS);
569 if (LA->getLoop()->getLoopDepth() != RA->getLoop()->getLoopDepth())
570 return LA->getLoop()->getLoopDepth() < RA->getLoop()->getLoopDepth();
573 // Lexicographically compare n-ary expressions.
574 if (const SCEVNAryExpr *LC = dyn_cast<SCEVNAryExpr>(LHS)) {
575 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
576 for (unsigned i = 0, e = LC->getNumOperands(); i != e; ++i) {
577 if (i >= RC->getNumOperands())
579 if (operator()(LC->getOperand(i), RC->getOperand(i)))
581 if (operator()(RC->getOperand(i), LC->getOperand(i)))
584 return LC->getNumOperands() < RC->getNumOperands();
587 // Lexicographically compare udiv expressions.
588 if (const SCEVUDivExpr *LC = dyn_cast<SCEVUDivExpr>(LHS)) {
589 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
590 if (operator()(LC->getLHS(), RC->getLHS()))
592 if (operator()(RC->getLHS(), LC->getLHS()))
594 if (operator()(LC->getRHS(), RC->getRHS()))
596 if (operator()(RC->getRHS(), LC->getRHS()))
601 // Compare cast expressions by operand.
602 if (const SCEVCastExpr *LC = dyn_cast<SCEVCastExpr>(LHS)) {
603 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
604 return operator()(LC->getOperand(), RC->getOperand());
607 llvm_unreachable("Unknown SCEV kind!");
613 /// GroupByComplexity - Given a list of SCEV objects, order them by their
614 /// complexity, and group objects of the same complexity together by value.
615 /// When this routine is finished, we know that any duplicates in the vector are
616 /// consecutive and that complexity is monotonically increasing.
618 /// Note that we go take special precautions to ensure that we get deterministic
619 /// results from this routine. In other words, we don't want the results of
620 /// this to depend on where the addresses of various SCEV objects happened to
623 static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops,
625 if (Ops.size() < 2) return; // Noop
626 if (Ops.size() == 2) {
627 // This is the common case, which also happens to be trivially simple.
629 if (SCEVComplexityCompare(LI)(Ops[1], Ops[0]))
630 std::swap(Ops[0], Ops[1]);
634 // Do the rough sort by complexity.
635 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI));
637 // Now that we are sorted by complexity, group elements of the same
638 // complexity. Note that this is, at worst, N^2, but the vector is likely to
639 // be extremely short in practice. Note that we take this approach because we
640 // do not want to depend on the addresses of the objects we are grouping.
641 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
642 const SCEV *S = Ops[i];
643 unsigned Complexity = S->getSCEVType();
645 // If there are any objects of the same complexity and same value as this
647 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
648 if (Ops[j] == S) { // Found a duplicate.
649 // Move it to immediately after i'th element.
650 std::swap(Ops[i+1], Ops[j]);
651 ++i; // no need to rescan it.
652 if (i == e-2) return; // Done!
660 //===----------------------------------------------------------------------===//
661 // Simple SCEV method implementations
662 //===----------------------------------------------------------------------===//
664 /// BinomialCoefficient - Compute BC(It, K). The result has width W.
666 static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K,
668 const Type* ResultTy) {
669 // Handle the simplest case efficiently.
671 return SE.getTruncateOrZeroExtend(It, ResultTy);
673 // We are using the following formula for BC(It, K):
675 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
677 // Suppose, W is the bitwidth of the return value. We must be prepared for
678 // overflow. Hence, we must assure that the result of our computation is
679 // equal to the accurate one modulo 2^W. Unfortunately, division isn't
680 // safe in modular arithmetic.
682 // However, this code doesn't use exactly that formula; the formula it uses
683 // is something like the following, where T is the number of factors of 2 in
684 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
687 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
689 // This formula is trivially equivalent to the previous formula. However,
690 // this formula can be implemented much more efficiently. The trick is that
691 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
692 // arithmetic. To do exact division in modular arithmetic, all we have
693 // to do is multiply by the inverse. Therefore, this step can be done at
696 // The next issue is how to safely do the division by 2^T. The way this
697 // is done is by doing the multiplication step at a width of at least W + T
698 // bits. This way, the bottom W+T bits of the product are accurate. Then,
699 // when we perform the division by 2^T (which is equivalent to a right shift
700 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
701 // truncated out after the division by 2^T.
703 // In comparison to just directly using the first formula, this technique
704 // is much more efficient; using the first formula requires W * K bits,
705 // but this formula less than W + K bits. Also, the first formula requires
706 // a division step, whereas this formula only requires multiplies and shifts.
708 // It doesn't matter whether the subtraction step is done in the calculation
709 // width or the input iteration count's width; if the subtraction overflows,
710 // the result must be zero anyway. We prefer here to do it in the width of
711 // the induction variable because it helps a lot for certain cases; CodeGen
712 // isn't smart enough to ignore the overflow, which leads to much less
713 // efficient code if the width of the subtraction is wider than the native
716 // (It's possible to not widen at all by pulling out factors of 2 before
717 // the multiplication; for example, K=2 can be calculated as
718 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
719 // extra arithmetic, so it's not an obvious win, and it gets
720 // much more complicated for K > 3.)
722 // Protection from insane SCEVs; this bound is conservative,
723 // but it probably doesn't matter.
725 return SE.getCouldNotCompute();
727 unsigned W = SE.getTypeSizeInBits(ResultTy);
729 // Calculate K! / 2^T and T; we divide out the factors of two before
730 // multiplying for calculating K! / 2^T to avoid overflow.
731 // Other overflow doesn't matter because we only care about the bottom
732 // W bits of the result.
733 APInt OddFactorial(W, 1);
735 for (unsigned i = 3; i <= K; ++i) {
737 unsigned TwoFactors = Mult.countTrailingZeros();
739 Mult = Mult.lshr(TwoFactors);
740 OddFactorial *= Mult;
743 // We need at least W + T bits for the multiplication step
744 unsigned CalculationBits = W + T;
746 // Calculate 2^T, at width T+W.
747 APInt DivFactor = APInt(CalculationBits, 1).shl(T);
749 // Calculate the multiplicative inverse of K! / 2^T;
750 // this multiplication factor will perform the exact division by
752 APInt Mod = APInt::getSignedMinValue(W+1);
753 APInt MultiplyFactor = OddFactorial.zext(W+1);
754 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
755 MultiplyFactor = MultiplyFactor.trunc(W);
757 // Calculate the product, at width T+W
758 const IntegerType *CalculationTy = IntegerType::get(SE.getContext(),
760 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
761 for (unsigned i = 1; i != K; ++i) {
762 const SCEV *S = SE.getMinusSCEV(It, SE.getIntegerSCEV(i, It->getType()));
763 Dividend = SE.getMulExpr(Dividend,
764 SE.getTruncateOrZeroExtend(S, CalculationTy));
768 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
770 // Truncate the result, and divide by K! / 2^T.
772 return SE.getMulExpr(SE.getConstant(MultiplyFactor),
773 SE.getTruncateOrZeroExtend(DivResult, ResultTy));
776 /// evaluateAtIteration - Return the value of this chain of recurrences at
777 /// the specified iteration number. We can evaluate this recurrence by
778 /// multiplying each element in the chain by the binomial coefficient
779 /// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
781 /// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
783 /// where BC(It, k) stands for binomial coefficient.
785 const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It,
786 ScalarEvolution &SE) const {
787 const SCEV *Result = getStart();
788 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
789 // The computation is correct in the face of overflow provided that the
790 // multiplication is performed _after_ the evaluation of the binomial
792 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType());
793 if (isa<SCEVCouldNotCompute>(Coeff))
796 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
801 //===----------------------------------------------------------------------===//
802 // SCEV Expression folder implementations
803 //===----------------------------------------------------------------------===//
805 const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op,
807 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
808 "This is not a truncating conversion!");
809 assert(isSCEVable(Ty) &&
810 "This is not a conversion to a SCEVable type!");
811 Ty = getEffectiveSCEVType(Ty);
814 ID.AddInteger(scTruncate);
818 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
820 // Fold if the operand is constant.
821 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
823 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty)));
825 // trunc(trunc(x)) --> trunc(x)
826 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
827 return getTruncateExpr(ST->getOperand(), Ty);
829 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
830 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
831 return getTruncateOrSignExtend(SS->getOperand(), Ty);
833 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
834 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
835 return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
837 // If the input value is a chrec scev, truncate the chrec's operands.
838 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
839 SmallVector<const SCEV *, 4> Operands;
840 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
841 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty));
842 return getAddRecExpr(Operands, AddRec->getLoop());
845 // The cast wasn't folded; create an explicit cast node.
846 // Recompute the insert position, as it may have been invalidated.
847 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
848 SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator),
850 UniqueSCEVs.InsertNode(S, IP);
854 const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op,
856 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
857 "This is not an extending conversion!");
858 assert(isSCEVable(Ty) &&
859 "This is not a conversion to a SCEVable type!");
860 Ty = getEffectiveSCEVType(Ty);
862 // Fold if the operand is constant.
863 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) {
864 const Type *IntTy = getEffectiveSCEVType(Ty);
865 Constant *C = ConstantExpr::getZExt(SC->getValue(), IntTy);
866 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty);
867 return getConstant(cast<ConstantInt>(C));
870 // zext(zext(x)) --> zext(x)
871 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
872 return getZeroExtendExpr(SZ->getOperand(), Ty);
874 // Before doing any expensive analysis, check to see if we've already
875 // computed a SCEV for this Op and Ty.
877 ID.AddInteger(scZeroExtend);
881 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
883 // If the input value is a chrec scev, and we can prove that the value
884 // did not overflow the old, smaller, value, we can zero extend all of the
885 // operands (often constants). This allows analysis of something like
886 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
887 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
888 if (AR->isAffine()) {
889 const SCEV *Start = AR->getStart();
890 const SCEV *Step = AR->getStepRecurrence(*this);
891 unsigned BitWidth = getTypeSizeInBits(AR->getType());
892 const Loop *L = AR->getLoop();
894 // If we have special knowledge that this addrec won't overflow,
895 // we don't need to do any further analysis.
896 if (AR->hasNoUnsignedWrap())
897 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
898 getZeroExtendExpr(Step, Ty),
901 // Check whether the backedge-taken count is SCEVCouldNotCompute.
902 // Note that this serves two purposes: It filters out loops that are
903 // simply not analyzable, and it covers the case where this code is
904 // being called from within backedge-taken count analysis, such that
905 // attempting to ask for the backedge-taken count would likely result
906 // in infinite recursion. In the later case, the analysis code will
907 // cope with a conservative value, and it will take care to purge
908 // that value once it has finished.
909 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
910 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
911 // Manually compute the final value for AR, checking for
914 // Check whether the backedge-taken count can be losslessly casted to
915 // the addrec's type. The count is always unsigned.
916 const SCEV *CastedMaxBECount =
917 getTruncateOrZeroExtend(MaxBECount, Start->getType());
918 const SCEV *RecastedMaxBECount =
919 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
920 if (MaxBECount == RecastedMaxBECount) {
921 const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
922 // Check whether Start+Step*MaxBECount has no unsigned overflow.
923 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step);
924 const SCEV *Add = getAddExpr(Start, ZMul);
925 const SCEV *OperandExtendedAdd =
926 getAddExpr(getZeroExtendExpr(Start, WideTy),
927 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
928 getZeroExtendExpr(Step, WideTy)));
929 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd)
930 // Return the expression with the addrec on the outside.
931 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
932 getZeroExtendExpr(Step, Ty),
935 // Similar to above, only this time treat the step value as signed.
936 // This covers loops that count down.
937 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
938 Add = getAddExpr(Start, SMul);
940 getAddExpr(getZeroExtendExpr(Start, WideTy),
941 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
942 getSignExtendExpr(Step, WideTy)));
943 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd)
944 // Return the expression with the addrec on the outside.
945 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
946 getSignExtendExpr(Step, Ty),
950 // If the backedge is guarded by a comparison with the pre-inc value
951 // the addrec is safe. Also, if the entry is guarded by a comparison
952 // with the start value and the backedge is guarded by a comparison
953 // with the post-inc value, the addrec is safe.
954 if (isKnownPositive(Step)) {
955 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
956 getUnsignedRange(Step).getUnsignedMax());
957 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
958 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) &&
959 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT,
960 AR->getPostIncExpr(*this), N)))
961 // Return the expression with the addrec on the outside.
962 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
963 getZeroExtendExpr(Step, Ty),
965 } else if (isKnownNegative(Step)) {
966 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
967 getSignedRange(Step).getSignedMin());
968 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) &&
969 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) ||
970 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT,
971 AR->getPostIncExpr(*this), N)))
972 // Return the expression with the addrec on the outside.
973 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
974 getSignExtendExpr(Step, Ty),
980 // The cast wasn't folded; create an explicit cast node.
981 // Recompute the insert position, as it may have been invalidated.
982 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
983 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
985 UniqueSCEVs.InsertNode(S, IP);
989 const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op,
991 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
992 "This is not an extending conversion!");
993 assert(isSCEVable(Ty) &&
994 "This is not a conversion to a SCEVable type!");
995 Ty = getEffectiveSCEVType(Ty);
997 // Fold if the operand is constant.
998 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) {
999 const Type *IntTy = getEffectiveSCEVType(Ty);
1000 Constant *C = ConstantExpr::getSExt(SC->getValue(), IntTy);
1001 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty);
1002 return getConstant(cast<ConstantInt>(C));
1005 // sext(sext(x)) --> sext(x)
1006 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1007 return getSignExtendExpr(SS->getOperand(), Ty);
1009 // Before doing any expensive analysis, check to see if we've already
1010 // computed a SCEV for this Op and Ty.
1011 FoldingSetNodeID ID;
1012 ID.AddInteger(scSignExtend);
1016 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1018 // If the input value is a chrec scev, and we can prove that the value
1019 // did not overflow the old, smaller, value, we can sign extend all of the
1020 // operands (often constants). This allows analysis of something like
1021 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
1022 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1023 if (AR->isAffine()) {
1024 const SCEV *Start = AR->getStart();
1025 const SCEV *Step = AR->getStepRecurrence(*this);
1026 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1027 const Loop *L = AR->getLoop();
1029 // If we have special knowledge that this addrec won't overflow,
1030 // we don't need to do any further analysis.
1031 if (AR->hasNoSignedWrap())
1032 return getAddRecExpr(getSignExtendExpr(Start, Ty),
1033 getSignExtendExpr(Step, Ty),
1036 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1037 // Note that this serves two purposes: It filters out loops that are
1038 // simply not analyzable, and it covers the case where this code is
1039 // being called from within backedge-taken count analysis, such that
1040 // attempting to ask for the backedge-taken count would likely result
1041 // in infinite recursion. In the later case, the analysis code will
1042 // cope with a conservative value, and it will take care to purge
1043 // that value once it has finished.
1044 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1045 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1046 // Manually compute the final value for AR, checking for
1049 // Check whether the backedge-taken count can be losslessly casted to
1050 // the addrec's type. The count is always unsigned.
1051 const SCEV *CastedMaxBECount =
1052 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1053 const SCEV *RecastedMaxBECount =
1054 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1055 if (MaxBECount == RecastedMaxBECount) {
1056 const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1057 // Check whether Start+Step*MaxBECount has no signed overflow.
1058 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
1059 const SCEV *Add = getAddExpr(Start, SMul);
1060 const SCEV *OperandExtendedAdd =
1061 getAddExpr(getSignExtendExpr(Start, WideTy),
1062 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
1063 getSignExtendExpr(Step, WideTy)));
1064 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd)
1065 // Return the expression with the addrec on the outside.
1066 return getAddRecExpr(getSignExtendExpr(Start, Ty),
1067 getSignExtendExpr(Step, Ty),
1070 // Similar to above, only this time treat the step value as unsigned.
1071 // This covers loops that count up with an unsigned step.
1072 const SCEV *UMul = getMulExpr(CastedMaxBECount, Step);
1073 Add = getAddExpr(Start, UMul);
1074 OperandExtendedAdd =
1075 getAddExpr(getSignExtendExpr(Start, WideTy),
1076 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
1077 getZeroExtendExpr(Step, WideTy)));
1078 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd)
1079 // Return the expression with the addrec on the outside.
1080 return getAddRecExpr(getSignExtendExpr(Start, Ty),
1081 getZeroExtendExpr(Step, Ty),
1085 // If the backedge is guarded by a comparison with the pre-inc value
1086 // the addrec is safe. Also, if the entry is guarded by a comparison
1087 // with the start value and the backedge is guarded by a comparison
1088 // with the post-inc value, the addrec is safe.
1089 if (isKnownPositive(Step)) {
1090 const SCEV *N = getConstant(APInt::getSignedMinValue(BitWidth) -
1091 getSignedRange(Step).getSignedMax());
1092 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT, AR, N) ||
1093 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_SLT, Start, N) &&
1094 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT,
1095 AR->getPostIncExpr(*this), N)))
1096 // Return the expression with the addrec on the outside.
1097 return getAddRecExpr(getSignExtendExpr(Start, Ty),
1098 getSignExtendExpr(Step, Ty),
1100 } else if (isKnownNegative(Step)) {
1101 const SCEV *N = getConstant(APInt::getSignedMaxValue(BitWidth) -
1102 getSignedRange(Step).getSignedMin());
1103 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT, AR, N) ||
1104 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_SGT, Start, N) &&
1105 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT,
1106 AR->getPostIncExpr(*this), N)))
1107 // Return the expression with the addrec on the outside.
1108 return getAddRecExpr(getSignExtendExpr(Start, Ty),
1109 getSignExtendExpr(Step, Ty),
1115 // The cast wasn't folded; create an explicit cast node.
1116 // Recompute the insert position, as it may have been invalidated.
1117 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1118 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
1120 UniqueSCEVs.InsertNode(S, IP);
1124 /// getAnyExtendExpr - Return a SCEV for the given operand extended with
1125 /// unspecified bits out to the given type.
1127 const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
1129 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1130 "This is not an extending conversion!");
1131 assert(isSCEVable(Ty) &&
1132 "This is not a conversion to a SCEVable type!");
1133 Ty = getEffectiveSCEVType(Ty);
1135 // Sign-extend negative constants.
1136 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1137 if (SC->getValue()->getValue().isNegative())
1138 return getSignExtendExpr(Op, Ty);
1140 // Peel off a truncate cast.
1141 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
1142 const SCEV *NewOp = T->getOperand();
1143 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
1144 return getAnyExtendExpr(NewOp, Ty);
1145 return getTruncateOrNoop(NewOp, Ty);
1148 // Next try a zext cast. If the cast is folded, use it.
1149 const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
1150 if (!isa<SCEVZeroExtendExpr>(ZExt))
1153 // Next try a sext cast. If the cast is folded, use it.
1154 const SCEV *SExt = getSignExtendExpr(Op, Ty);
1155 if (!isa<SCEVSignExtendExpr>(SExt))
1158 // Force the cast to be folded into the operands of an addrec.
1159 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
1160 SmallVector<const SCEV *, 4> Ops;
1161 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
1163 Ops.push_back(getAnyExtendExpr(*I, Ty));
1164 return getAddRecExpr(Ops, AR->getLoop());
1167 // If the expression is obviously signed, use the sext cast value.
1168 if (isa<SCEVSMaxExpr>(Op))
1171 // Absent any other information, use the zext cast value.
1175 /// CollectAddOperandsWithScales - Process the given Ops list, which is
1176 /// a list of operands to be added under the given scale, update the given
1177 /// map. This is a helper function for getAddRecExpr. As an example of
1178 /// what it does, given a sequence of operands that would form an add
1179 /// expression like this:
1181 /// m + n + 13 + (A * (o + p + (B * q + m + 29))) + r + (-1 * r)
1183 /// where A and B are constants, update the map with these values:
1185 /// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
1187 /// and add 13 + A*B*29 to AccumulatedConstant.
1188 /// This will allow getAddRecExpr to produce this:
1190 /// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
1192 /// This form often exposes folding opportunities that are hidden in
1193 /// the original operand list.
1195 /// Return true iff it appears that any interesting folding opportunities
1196 /// may be exposed. This helps getAddRecExpr short-circuit extra work in
1197 /// the common case where no interesting opportunities are present, and
1198 /// is also used as a check to avoid infinite recursion.
1201 CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
1202 SmallVector<const SCEV *, 8> &NewOps,
1203 APInt &AccumulatedConstant,
1204 const SCEV *const *Ops, size_t NumOperands,
1206 ScalarEvolution &SE) {
1207 bool Interesting = false;
1209 // Iterate over the add operands.
1210 for (unsigned i = 0, e = NumOperands; i != e; ++i) {
1211 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
1212 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
1214 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue();
1215 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
1216 // A multiplication of a constant with another add; recurse.
1217 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1));
1219 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1220 Add->op_begin(), Add->getNumOperands(),
1223 // A multiplication of a constant with some other value. Update
1225 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
1226 const SCEV *Key = SE.getMulExpr(MulOps);
1227 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1228 M.insert(std::make_pair(Key, NewScale));
1230 NewOps.push_back(Pair.first->first);
1232 Pair.first->second += NewScale;
1233 // The map already had an entry for this value, which may indicate
1234 // a folding opportunity.
1238 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1239 // Pull a buried constant out to the outside.
1240 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
1242 AccumulatedConstant += Scale * C->getValue()->getValue();
1244 // An ordinary operand. Update the map.
1245 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1246 M.insert(std::make_pair(Ops[i], Scale));
1248 NewOps.push_back(Pair.first->first);
1250 Pair.first->second += Scale;
1251 // The map already had an entry for this value, which may indicate
1252 // a folding opportunity.
1262 struct APIntCompare {
1263 bool operator()(const APInt &LHS, const APInt &RHS) const {
1264 return LHS.ult(RHS);
1269 /// getAddExpr - Get a canonical add expression, or something simpler if
1271 const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
1272 bool HasNUW, bool HasNSW) {
1273 assert(!Ops.empty() && "Cannot get empty add!");
1274 if (Ops.size() == 1) return Ops[0];
1276 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1277 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
1278 getEffectiveSCEVType(Ops[0]->getType()) &&
1279 "SCEVAddExpr operand types don't match!");
1282 // If HasNSW is true and all the operands are non-negative, infer HasNUW.
1283 if (!HasNUW && HasNSW) {
1285 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1286 if (!isKnownNonNegative(Ops[i])) {
1290 if (All) HasNUW = true;
1293 // Sort by complexity, this groups all similar expression types together.
1294 GroupByComplexity(Ops, LI);
1296 // If there are any constants, fold them together.
1298 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1300 assert(Idx < Ops.size());
1301 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1302 // We found two constants, fold them together!
1303 Ops[0] = getConstant(LHSC->getValue()->getValue() +
1304 RHSC->getValue()->getValue());
1305 if (Ops.size() == 2) return Ops[0];
1306 Ops.erase(Ops.begin()+1); // Erase the folded element
1307 LHSC = cast<SCEVConstant>(Ops[0]);
1310 // If we are left with a constant zero being added, strip it off.
1311 if (LHSC->getValue()->isZero()) {
1312 Ops.erase(Ops.begin());
1316 if (Ops.size() == 1) return Ops[0];
1319 // Okay, check to see if the same value occurs in the operand list twice. If
1320 // so, merge them together into an multiply expression. Since we sorted the
1321 // list, these values are required to be adjacent.
1322 const Type *Ty = Ops[0]->getType();
1323 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
1324 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
1325 // Found a match, merge the two values into a multiply, and add any
1326 // remaining values to the result.
1327 const SCEV *Two = getIntegerSCEV(2, Ty);
1328 const SCEV *Mul = getMulExpr(Ops[i], Two);
1329 if (Ops.size() == 2)
1331 Ops.erase(Ops.begin()+i, Ops.begin()+i+2);
1333 return getAddExpr(Ops, HasNUW, HasNSW);
1336 // Check for truncates. If all the operands are truncated from the same
1337 // type, see if factoring out the truncate would permit the result to be
1338 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
1339 // if the contents of the resulting outer trunc fold to something simple.
1340 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
1341 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
1342 const Type *DstType = Trunc->getType();
1343 const Type *SrcType = Trunc->getOperand()->getType();
1344 SmallVector<const SCEV *, 8> LargeOps;
1346 // Check all the operands to see if they can be represented in the
1347 // source type of the truncate.
1348 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1349 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
1350 if (T->getOperand()->getType() != SrcType) {
1354 LargeOps.push_back(T->getOperand());
1355 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1356 // This could be either sign or zero extension, but sign extension
1357 // is much more likely to be foldable here.
1358 LargeOps.push_back(getSignExtendExpr(C, SrcType));
1359 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
1360 SmallVector<const SCEV *, 8> LargeMulOps;
1361 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
1362 if (const SCEVTruncateExpr *T =
1363 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
1364 if (T->getOperand()->getType() != SrcType) {
1368 LargeMulOps.push_back(T->getOperand());
1369 } else if (const SCEVConstant *C =
1370 dyn_cast<SCEVConstant>(M->getOperand(j))) {
1371 // This could be either sign or zero extension, but sign extension
1372 // is much more likely to be foldable here.
1373 LargeMulOps.push_back(getSignExtendExpr(C, SrcType));
1380 LargeOps.push_back(getMulExpr(LargeMulOps));
1387 // Evaluate the expression in the larger type.
1388 const SCEV *Fold = getAddExpr(LargeOps, HasNUW, HasNSW);
1389 // If it folds to something simple, use it. Otherwise, don't.
1390 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
1391 return getTruncateExpr(Fold, DstType);
1395 // Skip past any other cast SCEVs.
1396 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
1399 // If there are add operands they would be next.
1400 if (Idx < Ops.size()) {
1401 bool DeletedAdd = false;
1402 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
1403 // If we have an add, expand the add operands onto the end of the operands
1405 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end());
1406 Ops.erase(Ops.begin()+Idx);
1410 // If we deleted at least one add, we added operands to the end of the list,
1411 // and they are not necessarily sorted. Recurse to resort and resimplify
1412 // any operands we just acquired.
1414 return getAddExpr(Ops);
1417 // Skip over the add expression until we get to a multiply.
1418 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1421 // Check to see if there are any folding opportunities present with
1422 // operands multiplied by constant values.
1423 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
1424 uint64_t BitWidth = getTypeSizeInBits(Ty);
1425 DenseMap<const SCEV *, APInt> M;
1426 SmallVector<const SCEV *, 8> NewOps;
1427 APInt AccumulatedConstant(BitWidth, 0);
1428 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1429 Ops.data(), Ops.size(),
1430 APInt(BitWidth, 1), *this)) {
1431 // Some interesting folding opportunity is present, so its worthwhile to
1432 // re-generate the operands list. Group the operands by constant scale,
1433 // to avoid multiplying by the same constant scale multiple times.
1434 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
1435 for (SmallVector<const SCEV *, 8>::iterator I = NewOps.begin(),
1436 E = NewOps.end(); I != E; ++I)
1437 MulOpLists[M.find(*I)->second].push_back(*I);
1438 // Re-generate the operands list.
1440 if (AccumulatedConstant != 0)
1441 Ops.push_back(getConstant(AccumulatedConstant));
1442 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator
1443 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I)
1445 Ops.push_back(getMulExpr(getConstant(I->first),
1446 getAddExpr(I->second)));
1448 return getIntegerSCEV(0, Ty);
1449 if (Ops.size() == 1)
1451 return getAddExpr(Ops);
1455 // If we are adding something to a multiply expression, make sure the
1456 // something is not already an operand of the multiply. If so, merge it into
1458 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
1459 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
1460 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
1461 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
1462 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
1463 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(Ops[AddOp])) {
1464 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
1465 const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
1466 if (Mul->getNumOperands() != 2) {
1467 // If the multiply has more than two operands, we must get the
1469 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), Mul->op_end());
1470 MulOps.erase(MulOps.begin()+MulOp);
1471 InnerMul = getMulExpr(MulOps);
1473 const SCEV *One = getIntegerSCEV(1, Ty);
1474 const SCEV *AddOne = getAddExpr(InnerMul, One);
1475 const SCEV *OuterMul = getMulExpr(AddOne, Ops[AddOp]);
1476 if (Ops.size() == 2) return OuterMul;
1478 Ops.erase(Ops.begin()+AddOp);
1479 Ops.erase(Ops.begin()+Idx-1);
1481 Ops.erase(Ops.begin()+Idx);
1482 Ops.erase(Ops.begin()+AddOp-1);
1484 Ops.push_back(OuterMul);
1485 return getAddExpr(Ops);
1488 // Check this multiply against other multiplies being added together.
1489 for (unsigned OtherMulIdx = Idx+1;
1490 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
1492 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
1493 // If MulOp occurs in OtherMul, we can fold the two multiplies
1495 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
1496 OMulOp != e; ++OMulOp)
1497 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
1498 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
1499 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
1500 if (Mul->getNumOperands() != 2) {
1501 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
1503 MulOps.erase(MulOps.begin()+MulOp);
1504 InnerMul1 = getMulExpr(MulOps);
1506 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
1507 if (OtherMul->getNumOperands() != 2) {
1508 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
1509 OtherMul->op_end());
1510 MulOps.erase(MulOps.begin()+OMulOp);
1511 InnerMul2 = getMulExpr(MulOps);
1513 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
1514 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
1515 if (Ops.size() == 2) return OuterMul;
1516 Ops.erase(Ops.begin()+Idx);
1517 Ops.erase(Ops.begin()+OtherMulIdx-1);
1518 Ops.push_back(OuterMul);
1519 return getAddExpr(Ops);
1525 // If there are any add recurrences in the operands list, see if any other
1526 // added values are loop invariant. If so, we can fold them into the
1528 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1531 // Scan over all recurrences, trying to fold loop invariants into them.
1532 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1533 // Scan all of the other operands to this add and add them to the vector if
1534 // they are loop invariant w.r.t. the recurrence.
1535 SmallVector<const SCEV *, 8> LIOps;
1536 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1537 const Loop *AddRecLoop = AddRec->getLoop();
1538 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1539 if (Ops[i]->isLoopInvariant(AddRecLoop)) {
1540 LIOps.push_back(Ops[i]);
1541 Ops.erase(Ops.begin()+i);
1545 // If we found some loop invariants, fold them into the recurrence.
1546 if (!LIOps.empty()) {
1547 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
1548 LIOps.push_back(AddRec->getStart());
1550 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
1552 AddRecOps[0] = getAddExpr(LIOps);
1554 // It's tempting to propagate NUW/NSW flags here, but nuw/nsw addition
1555 // is not associative so this isn't necessarily safe.
1556 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop);
1558 // If all of the other operands were loop invariant, we are done.
1559 if (Ops.size() == 1) return NewRec;
1561 // Otherwise, add the folded AddRec by the non-liv parts.
1562 for (unsigned i = 0;; ++i)
1563 if (Ops[i] == AddRec) {
1567 return getAddExpr(Ops);
1570 // Okay, if there weren't any loop invariants to be folded, check to see if
1571 // there are multiple AddRec's with the same loop induction variable being
1572 // added together. If so, we can fold them.
1573 for (unsigned OtherIdx = Idx+1;
1574 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
1575 if (OtherIdx != Idx) {
1576 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
1577 if (AddRecLoop == OtherAddRec->getLoop()) {
1578 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D}
1579 SmallVector<const SCEV *, 4> NewOps(AddRec->op_begin(),
1581 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) {
1582 if (i >= NewOps.size()) {
1583 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i,
1584 OtherAddRec->op_end());
1587 NewOps[i] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i));
1589 const SCEV *NewAddRec = getAddRecExpr(NewOps, AddRecLoop);
1591 if (Ops.size() == 2) return NewAddRec;
1593 Ops.erase(Ops.begin()+Idx);
1594 Ops.erase(Ops.begin()+OtherIdx-1);
1595 Ops.push_back(NewAddRec);
1596 return getAddExpr(Ops);
1600 // Otherwise couldn't fold anything into this recurrence. Move onto the
1604 // Okay, it looks like we really DO need an add expr. Check to see if we
1605 // already have one, otherwise create a new one.
1606 FoldingSetNodeID ID;
1607 ID.AddInteger(scAddExpr);
1608 ID.AddInteger(Ops.size());
1609 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1610 ID.AddPointer(Ops[i]);
1613 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1615 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
1616 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
1617 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator),
1619 UniqueSCEVs.InsertNode(S, IP);
1621 if (HasNUW) S->setHasNoUnsignedWrap(true);
1622 if (HasNSW) S->setHasNoSignedWrap(true);
1626 /// getMulExpr - Get a canonical multiply expression, or something simpler if
1628 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
1629 bool HasNUW, bool HasNSW) {
1630 assert(!Ops.empty() && "Cannot get empty mul!");
1631 if (Ops.size() == 1) return Ops[0];
1633 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1634 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
1635 getEffectiveSCEVType(Ops[0]->getType()) &&
1636 "SCEVMulExpr operand types don't match!");
1639 // If HasNSW is true and all the operands are non-negative, infer HasNUW.
1640 if (!HasNUW && HasNSW) {
1642 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1643 if (!isKnownNonNegative(Ops[i])) {
1647 if (All) HasNUW = true;
1650 // Sort by complexity, this groups all similar expression types together.
1651 GroupByComplexity(Ops, LI);
1653 // If there are any constants, fold them together.
1655 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1657 // C1*(C2+V) -> C1*C2 + C1*V
1658 if (Ops.size() == 2)
1659 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
1660 if (Add->getNumOperands() == 2 &&
1661 isa<SCEVConstant>(Add->getOperand(0)))
1662 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
1663 getMulExpr(LHSC, Add->getOperand(1)));
1666 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1667 // We found two constants, fold them together!
1668 ConstantInt *Fold = ConstantInt::get(getContext(),
1669 LHSC->getValue()->getValue() *
1670 RHSC->getValue()->getValue());
1671 Ops[0] = getConstant(Fold);
1672 Ops.erase(Ops.begin()+1); // Erase the folded element
1673 if (Ops.size() == 1) return Ops[0];
1674 LHSC = cast<SCEVConstant>(Ops[0]);
1677 // If we are left with a constant one being multiplied, strip it off.
1678 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
1679 Ops.erase(Ops.begin());
1681 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
1682 // If we have a multiply of zero, it will always be zero.
1684 } else if (Ops[0]->isAllOnesValue()) {
1685 // If we have a mul by -1 of an add, try distributing the -1 among the
1687 if (Ops.size() == 2)
1688 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
1689 SmallVector<const SCEV *, 4> NewOps;
1690 bool AnyFolded = false;
1691 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(), E = Add->op_end();
1693 const SCEV *Mul = getMulExpr(Ops[0], *I);
1694 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
1695 NewOps.push_back(Mul);
1698 return getAddExpr(NewOps);
1702 if (Ops.size() == 1)
1706 // Skip over the add expression until we get to a multiply.
1707 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1710 // If there are mul operands inline them all into this expression.
1711 if (Idx < Ops.size()) {
1712 bool DeletedMul = false;
1713 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
1714 // If we have an mul, expand the mul operands onto the end of the operands
1716 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end());
1717 Ops.erase(Ops.begin()+Idx);
1721 // If we deleted at least one mul, we added operands to the end of the list,
1722 // and they are not necessarily sorted. Recurse to resort and resimplify
1723 // any operands we just acquired.
1725 return getMulExpr(Ops);
1728 // If there are any add recurrences in the operands list, see if any other
1729 // added values are loop invariant. If so, we can fold them into the
1731 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1734 // Scan over all recurrences, trying to fold loop invariants into them.
1735 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1736 // Scan all of the other operands to this mul and add them to the vector if
1737 // they are loop invariant w.r.t. the recurrence.
1738 SmallVector<const SCEV *, 8> LIOps;
1739 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1740 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1741 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
1742 LIOps.push_back(Ops[i]);
1743 Ops.erase(Ops.begin()+i);
1747 // If we found some loop invariants, fold them into the recurrence.
1748 if (!LIOps.empty()) {
1749 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
1750 SmallVector<const SCEV *, 4> NewOps;
1751 NewOps.reserve(AddRec->getNumOperands());
1752 if (LIOps.size() == 1) {
1753 const SCEV *Scale = LIOps[0];
1754 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
1755 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
1757 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
1758 SmallVector<const SCEV *, 4> MulOps(LIOps.begin(), LIOps.end());
1759 MulOps.push_back(AddRec->getOperand(i));
1760 NewOps.push_back(getMulExpr(MulOps));
1764 // It's tempting to propagate the NSW flag here, but nsw multiplication
1765 // is not associative so this isn't necessarily safe.
1766 const SCEV *NewRec = getAddRecExpr(NewOps, AddRec->getLoop(),
1767 HasNUW && AddRec->hasNoUnsignedWrap(),
1770 // If all of the other operands were loop invariant, we are done.
1771 if (Ops.size() == 1) return NewRec;
1773 // Otherwise, multiply the folded AddRec by the non-liv parts.
1774 for (unsigned i = 0;; ++i)
1775 if (Ops[i] == AddRec) {
1779 return getMulExpr(Ops);
1782 // Okay, if there weren't any loop invariants to be folded, check to see if
1783 // there are multiple AddRec's with the same loop induction variable being
1784 // multiplied together. If so, we can fold them.
1785 for (unsigned OtherIdx = Idx+1;
1786 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
1787 if (OtherIdx != Idx) {
1788 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
1789 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
1790 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D}
1791 const SCEVAddRecExpr *F = AddRec, *G = OtherAddRec;
1792 const SCEV *NewStart = getMulExpr(F->getStart(),
1794 const SCEV *B = F->getStepRecurrence(*this);
1795 const SCEV *D = G->getStepRecurrence(*this);
1796 const SCEV *NewStep = getAddExpr(getMulExpr(F, D),
1799 const SCEV *NewAddRec = getAddRecExpr(NewStart, NewStep,
1801 if (Ops.size() == 2) return NewAddRec;
1803 Ops.erase(Ops.begin()+Idx);
1804 Ops.erase(Ops.begin()+OtherIdx-1);
1805 Ops.push_back(NewAddRec);
1806 return getMulExpr(Ops);
1810 // Otherwise couldn't fold anything into this recurrence. Move onto the
1814 // Okay, it looks like we really DO need an mul expr. Check to see if we
1815 // already have one, otherwise create a new one.
1816 FoldingSetNodeID ID;
1817 ID.AddInteger(scMulExpr);
1818 ID.AddInteger(Ops.size());
1819 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1820 ID.AddPointer(Ops[i]);
1823 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1825 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
1826 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
1827 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
1829 UniqueSCEVs.InsertNode(S, IP);
1831 if (HasNUW) S->setHasNoUnsignedWrap(true);
1832 if (HasNSW) S->setHasNoSignedWrap(true);
1836 /// getUDivExpr - Get a canonical unsigned division expression, or something
1837 /// simpler if possible.
1838 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
1840 assert(getEffectiveSCEVType(LHS->getType()) ==
1841 getEffectiveSCEVType(RHS->getType()) &&
1842 "SCEVUDivExpr operand types don't match!");
1844 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
1845 if (RHSC->getValue()->equalsInt(1))
1846 return LHS; // X udiv 1 --> x
1847 if (RHSC->getValue()->isZero())
1848 return getIntegerSCEV(0, LHS->getType()); // value is undefined
1850 // Determine if the division can be folded into the operands of
1852 // TODO: Generalize this to non-constants by using known-bits information.
1853 const Type *Ty = LHS->getType();
1854 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
1855 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ;
1856 // For non-power-of-two values, effectively round the value up to the
1857 // nearest power of two.
1858 if (!RHSC->getValue()->getValue().isPowerOf2())
1860 const IntegerType *ExtTy =
1861 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
1862 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
1863 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
1864 if (const SCEVConstant *Step =
1865 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this)))
1866 if (!Step->getValue()->getValue()
1867 .urem(RHSC->getValue()->getValue()) &&
1868 getZeroExtendExpr(AR, ExtTy) ==
1869 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
1870 getZeroExtendExpr(Step, ExtTy),
1872 SmallVector<const SCEV *, 4> Operands;
1873 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i)
1874 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS));
1875 return getAddRecExpr(Operands, AR->getLoop());
1877 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
1878 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
1879 SmallVector<const SCEV *, 4> Operands;
1880 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i)
1881 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy));
1882 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
1883 // Find an operand that's safely divisible.
1884 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
1885 const SCEV *Op = M->getOperand(i);
1886 const SCEV *Div = getUDivExpr(Op, RHSC);
1887 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
1888 Operands = SmallVector<const SCEV *, 4>(M->op_begin(), M->op_end());
1890 return getMulExpr(Operands);
1894 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
1895 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(LHS)) {
1896 SmallVector<const SCEV *, 4> Operands;
1897 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i)
1898 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy));
1899 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
1901 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
1902 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
1903 if (isa<SCEVUDivExpr>(Op) || getMulExpr(Op, RHS) != A->getOperand(i))
1905 Operands.push_back(Op);
1907 if (Operands.size() == A->getNumOperands())
1908 return getAddExpr(Operands);
1912 // Fold if both operands are constant.
1913 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
1914 Constant *LHSCV = LHSC->getValue();
1915 Constant *RHSCV = RHSC->getValue();
1916 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
1921 FoldingSetNodeID ID;
1922 ID.AddInteger(scUDivExpr);
1926 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1927 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
1929 UniqueSCEVs.InsertNode(S, IP);
1934 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
1935 /// Simplify the expression as much as possible.
1936 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start,
1937 const SCEV *Step, const Loop *L,
1938 bool HasNUW, bool HasNSW) {
1939 SmallVector<const SCEV *, 4> Operands;
1940 Operands.push_back(Start);
1941 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
1942 if (StepChrec->getLoop() == L) {
1943 Operands.insert(Operands.end(), StepChrec->op_begin(),
1944 StepChrec->op_end());
1945 return getAddRecExpr(Operands, L);
1948 Operands.push_back(Step);
1949 return getAddRecExpr(Operands, L, HasNUW, HasNSW);
1952 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
1953 /// Simplify the expression as much as possible.
1955 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
1957 bool HasNUW, bool HasNSW) {
1958 if (Operands.size() == 1) return Operands[0];
1960 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
1961 assert(getEffectiveSCEVType(Operands[i]->getType()) ==
1962 getEffectiveSCEVType(Operands[0]->getType()) &&
1963 "SCEVAddRecExpr operand types don't match!");
1966 if (Operands.back()->isZero()) {
1967 Operands.pop_back();
1968 return getAddRecExpr(Operands, L, HasNUW, HasNSW); // {X,+,0} --> X
1971 // It's tempting to want to call getMaxBackedgeTakenCount count here and
1972 // use that information to infer NUW and NSW flags. However, computing a
1973 // BE count requires calling getAddRecExpr, so we may not yet have a
1974 // meaningful BE count at this point (and if we don't, we'd be stuck
1975 // with a SCEVCouldNotCompute as the cached BE count).
1977 // If HasNSW is true and all the operands are non-negative, infer HasNUW.
1978 if (!HasNUW && HasNSW) {
1980 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
1981 if (!isKnownNonNegative(Operands[i])) {
1985 if (All) HasNUW = true;
1988 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
1989 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
1990 const Loop *NestedLoop = NestedAR->getLoop();
1991 if (L->contains(NestedLoop->getHeader()) ?
1992 (L->getLoopDepth() < NestedLoop->getLoopDepth()) :
1993 (!NestedLoop->contains(L->getHeader()) &&
1994 DT->dominates(L->getHeader(), NestedLoop->getHeader()))) {
1995 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
1996 NestedAR->op_end());
1997 Operands[0] = NestedAR->getStart();
1998 // AddRecs require their operands be loop-invariant with respect to their
1999 // loops. Don't perform this transformation if it would break this
2001 bool AllInvariant = true;
2002 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2003 if (!Operands[i]->isLoopInvariant(L)) {
2004 AllInvariant = false;
2008 NestedOperands[0] = getAddRecExpr(Operands, L);
2009 AllInvariant = true;
2010 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i)
2011 if (!NestedOperands[i]->isLoopInvariant(NestedLoop)) {
2012 AllInvariant = false;
2016 // Ok, both add recurrences are valid after the transformation.
2017 return getAddRecExpr(NestedOperands, NestedLoop, HasNUW, HasNSW);
2019 // Reset Operands to its original state.
2020 Operands[0] = NestedAR;
2024 // Okay, it looks like we really DO need an addrec expr. Check to see if we
2025 // already have one, otherwise create a new one.
2026 FoldingSetNodeID ID;
2027 ID.AddInteger(scAddRecExpr);
2028 ID.AddInteger(Operands.size());
2029 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2030 ID.AddPointer(Operands[i]);
2034 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2036 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size());
2037 std::uninitialized_copy(Operands.begin(), Operands.end(), O);
2038 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator),
2039 O, Operands.size(), L);
2040 UniqueSCEVs.InsertNode(S, IP);
2042 if (HasNUW) S->setHasNoUnsignedWrap(true);
2043 if (HasNSW) S->setHasNoSignedWrap(true);
2047 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
2049 SmallVector<const SCEV *, 2> Ops;
2052 return getSMaxExpr(Ops);
2056 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2057 assert(!Ops.empty() && "Cannot get empty smax!");
2058 if (Ops.size() == 1) return Ops[0];
2060 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2061 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
2062 getEffectiveSCEVType(Ops[0]->getType()) &&
2063 "SCEVSMaxExpr operand types don't match!");
2066 // Sort by complexity, this groups all similar expression types together.
2067 GroupByComplexity(Ops, LI);
2069 // If there are any constants, fold them together.
2071 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2073 assert(Idx < Ops.size());
2074 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2075 // We found two constants, fold them together!
2076 ConstantInt *Fold = ConstantInt::get(getContext(),
2077 APIntOps::smax(LHSC->getValue()->getValue(),
2078 RHSC->getValue()->getValue()));
2079 Ops[0] = getConstant(Fold);
2080 Ops.erase(Ops.begin()+1); // Erase the folded element
2081 if (Ops.size() == 1) return Ops[0];
2082 LHSC = cast<SCEVConstant>(Ops[0]);
2085 // If we are left with a constant minimum-int, strip it off.
2086 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
2087 Ops.erase(Ops.begin());
2089 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
2090 // If we have an smax with a constant maximum-int, it will always be
2095 if (Ops.size() == 1) return Ops[0];
2098 // Find the first SMax
2099 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
2102 // Check to see if one of the operands is an SMax. If so, expand its operands
2103 // onto our operand list, and recurse to simplify.
2104 if (Idx < Ops.size()) {
2105 bool DeletedSMax = false;
2106 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
2107 Ops.insert(Ops.end(), SMax->op_begin(), SMax->op_end());
2108 Ops.erase(Ops.begin()+Idx);
2113 return getSMaxExpr(Ops);
2116 // Okay, check to see if the same value occurs in the operand list twice. If
2117 // so, delete one. Since we sorted the list, these values are required to
2119 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2120 // X smax Y smax Y --> X smax Y
2121 // X smax Y --> X, if X is always greater than Y
2122 if (Ops[i] == Ops[i+1] ||
2123 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) {
2124 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2126 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) {
2127 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2131 if (Ops.size() == 1) return Ops[0];
2133 assert(!Ops.empty() && "Reduced smax down to nothing!");
2135 // Okay, it looks like we really DO need an smax expr. Check to see if we
2136 // already have one, otherwise create a new one.
2137 FoldingSetNodeID ID;
2138 ID.AddInteger(scSMaxExpr);
2139 ID.AddInteger(Ops.size());
2140 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2141 ID.AddPointer(Ops[i]);
2143 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2144 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2145 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2146 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator),
2148 UniqueSCEVs.InsertNode(S, IP);
2152 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
2154 SmallVector<const SCEV *, 2> Ops;
2157 return getUMaxExpr(Ops);
2161 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2162 assert(!Ops.empty() && "Cannot get empty umax!");
2163 if (Ops.size() == 1) return Ops[0];
2165 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2166 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
2167 getEffectiveSCEVType(Ops[0]->getType()) &&
2168 "SCEVUMaxExpr operand types don't match!");
2171 // Sort by complexity, this groups all similar expression types together.
2172 GroupByComplexity(Ops, LI);
2174 // If there are any constants, fold them together.
2176 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2178 assert(Idx < Ops.size());
2179 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2180 // We found two constants, fold them together!
2181 ConstantInt *Fold = ConstantInt::get(getContext(),
2182 APIntOps::umax(LHSC->getValue()->getValue(),
2183 RHSC->getValue()->getValue()));
2184 Ops[0] = getConstant(Fold);
2185 Ops.erase(Ops.begin()+1); // Erase the folded element
2186 if (Ops.size() == 1) return Ops[0];
2187 LHSC = cast<SCEVConstant>(Ops[0]);
2190 // If we are left with a constant minimum-int, strip it off.
2191 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
2192 Ops.erase(Ops.begin());
2194 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
2195 // If we have an umax with a constant maximum-int, it will always be
2200 if (Ops.size() == 1) return Ops[0];
2203 // Find the first UMax
2204 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
2207 // Check to see if one of the operands is a UMax. If so, expand its operands
2208 // onto our operand list, and recurse to simplify.
2209 if (Idx < Ops.size()) {
2210 bool DeletedUMax = false;
2211 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
2212 Ops.insert(Ops.end(), UMax->op_begin(), UMax->op_end());
2213 Ops.erase(Ops.begin()+Idx);
2218 return getUMaxExpr(Ops);
2221 // Okay, check to see if the same value occurs in the operand list twice. If
2222 // so, delete one. Since we sorted the list, these values are required to
2224 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2225 // X umax Y umax Y --> X umax Y
2226 // X umax Y --> X, if X is always greater than Y
2227 if (Ops[i] == Ops[i+1] ||
2228 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) {
2229 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2231 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) {
2232 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2236 if (Ops.size() == 1) return Ops[0];
2238 assert(!Ops.empty() && "Reduced umax down to nothing!");
2240 // Okay, it looks like we really DO need a umax expr. Check to see if we
2241 // already have one, otherwise create a new one.
2242 FoldingSetNodeID ID;
2243 ID.AddInteger(scUMaxExpr);
2244 ID.AddInteger(Ops.size());
2245 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2246 ID.AddPointer(Ops[i]);
2248 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2249 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2250 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2251 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator),
2253 UniqueSCEVs.InsertNode(S, IP);
2257 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
2259 // ~smax(~x, ~y) == smin(x, y).
2260 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2263 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
2265 // ~umax(~x, ~y) == umin(x, y)
2266 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2269 const SCEV *ScalarEvolution::getSizeOfExpr(const Type *AllocTy) {
2270 // If we have TargetData, we can bypass creating a target-independent
2271 // constant expression and then folding it back into a ConstantInt.
2272 // This is just a compile-time optimization.
2274 return getConstant(TD->getIntPtrType(getContext()),
2275 TD->getTypeAllocSize(AllocTy));
2277 Constant *C = ConstantExpr::getSizeOf(AllocTy);
2278 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2279 C = ConstantFoldConstantExpression(CE, TD);
2280 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2281 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2284 const SCEV *ScalarEvolution::getAlignOfExpr(const Type *AllocTy) {
2285 Constant *C = ConstantExpr::getAlignOf(AllocTy);
2286 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2287 C = ConstantFoldConstantExpression(CE, TD);
2288 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2289 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2292 const SCEV *ScalarEvolution::getOffsetOfExpr(const StructType *STy,
2294 // If we have TargetData, we can bypass creating a target-independent
2295 // constant expression and then folding it back into a ConstantInt.
2296 // This is just a compile-time optimization.
2298 return getConstant(TD->getIntPtrType(getContext()),
2299 TD->getStructLayout(STy)->getElementOffset(FieldNo));
2301 Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo);
2302 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2303 C = ConstantFoldConstantExpression(CE, TD);
2304 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy));
2305 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2308 const SCEV *ScalarEvolution::getOffsetOfExpr(const Type *CTy,
2309 Constant *FieldNo) {
2310 Constant *C = ConstantExpr::getOffsetOf(CTy, FieldNo);
2311 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2312 C = ConstantFoldConstantExpression(CE, TD);
2313 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(CTy));
2314 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2317 const SCEV *ScalarEvolution::getUnknown(Value *V) {
2318 // Don't attempt to do anything other than create a SCEVUnknown object
2319 // here. createSCEV only calls getUnknown after checking for all other
2320 // interesting possibilities, and any other code that calls getUnknown
2321 // is doing so in order to hide a value from SCEV canonicalization.
2323 FoldingSetNodeID ID;
2324 ID.AddInteger(scUnknown);
2327 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2328 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V);
2329 UniqueSCEVs.InsertNode(S, IP);
2333 //===----------------------------------------------------------------------===//
2334 // Basic SCEV Analysis and PHI Idiom Recognition Code
2337 /// isSCEVable - Test if values of the given type are analyzable within
2338 /// the SCEV framework. This primarily includes integer types, and it
2339 /// can optionally include pointer types if the ScalarEvolution class
2340 /// has access to target-specific information.
2341 bool ScalarEvolution::isSCEVable(const Type *Ty) const {
2342 // Integers and pointers are always SCEVable.
2343 return Ty->isIntegerTy() || Ty->isPointerTy();
2346 /// getTypeSizeInBits - Return the size in bits of the specified type,
2347 /// for which isSCEVable must return true.
2348 uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const {
2349 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2351 // If we have a TargetData, use it!
2353 return TD->getTypeSizeInBits(Ty);
2355 // Integer types have fixed sizes.
2356 if (Ty->isIntegerTy())
2357 return Ty->getPrimitiveSizeInBits();
2359 // The only other support type is pointer. Without TargetData, conservatively
2360 // assume pointers are 64-bit.
2361 assert(Ty->isPointerTy() && "isSCEVable permitted a non-SCEVable type!");
2365 /// getEffectiveSCEVType - Return a type with the same bitwidth as
2366 /// the given type and which represents how SCEV will treat the given
2367 /// type, for which isSCEVable must return true. For pointer types,
2368 /// this is the pointer-sized integer type.
2369 const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const {
2370 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2372 if (Ty->isIntegerTy())
2375 // The only other support type is pointer.
2376 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
2377 if (TD) return TD->getIntPtrType(getContext());
2379 // Without TargetData, conservatively assume pointers are 64-bit.
2380 return Type::getInt64Ty(getContext());
2383 const SCEV *ScalarEvolution::getCouldNotCompute() {
2384 return &CouldNotCompute;
2387 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
2388 /// expression and create a new one.
2389 const SCEV *ScalarEvolution::getSCEV(Value *V) {
2390 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
2392 std::map<SCEVCallbackVH, const SCEV *>::iterator I = Scalars.find(V);
2393 if (I != Scalars.end()) return I->second;
2394 const SCEV *S = createSCEV(V);
2395 Scalars.insert(std::make_pair(SCEVCallbackVH(V, this), S));
2399 /// getIntegerSCEV - Given a SCEVable type, create a constant for the
2400 /// specified signed integer value and return a SCEV for the constant.
2401 const SCEV *ScalarEvolution::getIntegerSCEV(int64_t Val, const Type *Ty) {
2402 const IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty));
2403 return getConstant(ConstantInt::get(ITy, Val));
2406 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
2408 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) {
2409 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2411 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
2413 const Type *Ty = V->getType();
2414 Ty = getEffectiveSCEVType(Ty);
2415 return getMulExpr(V,
2416 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))));
2419 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
2420 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
2421 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2423 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
2425 const Type *Ty = V->getType();
2426 Ty = getEffectiveSCEVType(Ty);
2427 const SCEV *AllOnes =
2428 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
2429 return getMinusSCEV(AllOnes, V);
2432 /// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
2434 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS,
2437 return getAddExpr(LHS, getNegativeSCEV(RHS));
2440 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
2441 /// input value to the specified type. If the type must be extended, it is zero
2444 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V,
2446 const Type *SrcTy = V->getType();
2447 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2448 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2449 "Cannot truncate or zero extend with non-integer arguments!");
2450 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2451 return V; // No conversion
2452 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2453 return getTruncateExpr(V, Ty);
2454 return getZeroExtendExpr(V, Ty);
2457 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
2458 /// input value to the specified type. If the type must be extended, it is sign
2461 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
2463 const Type *SrcTy = V->getType();
2464 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2465 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2466 "Cannot truncate or zero extend with non-integer arguments!");
2467 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2468 return V; // No conversion
2469 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2470 return getTruncateExpr(V, Ty);
2471 return getSignExtendExpr(V, Ty);
2474 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
2475 /// input value to the specified type. If the type must be extended, it is zero
2476 /// extended. The conversion must not be narrowing.
2478 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, const Type *Ty) {
2479 const Type *SrcTy = V->getType();
2480 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2481 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2482 "Cannot noop or zero extend with non-integer arguments!");
2483 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2484 "getNoopOrZeroExtend cannot truncate!");
2485 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2486 return V; // No conversion
2487 return getZeroExtendExpr(V, Ty);
2490 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
2491 /// input value to the specified type. If the type must be extended, it is sign
2492 /// extended. The conversion must not be narrowing.
2494 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, const Type *Ty) {
2495 const Type *SrcTy = V->getType();
2496 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2497 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2498 "Cannot noop or sign extend with non-integer arguments!");
2499 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2500 "getNoopOrSignExtend cannot truncate!");
2501 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2502 return V; // No conversion
2503 return getSignExtendExpr(V, Ty);
2506 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
2507 /// the input value to the specified type. If the type must be extended,
2508 /// it is extended with unspecified bits. The conversion must not be
2511 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, const Type *Ty) {
2512 const Type *SrcTy = V->getType();
2513 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2514 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2515 "Cannot noop or any extend with non-integer arguments!");
2516 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2517 "getNoopOrAnyExtend cannot truncate!");
2518 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2519 return V; // No conversion
2520 return getAnyExtendExpr(V, Ty);
2523 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
2524 /// input value to the specified type. The conversion must not be widening.
2526 ScalarEvolution::getTruncateOrNoop(const SCEV *V, const Type *Ty) {
2527 const Type *SrcTy = V->getType();
2528 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2529 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2530 "Cannot truncate or noop with non-integer arguments!");
2531 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
2532 "getTruncateOrNoop cannot extend!");
2533 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2534 return V; // No conversion
2535 return getTruncateExpr(V, Ty);
2538 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
2539 /// the types using zero-extension, and then perform a umax operation
2541 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
2543 const SCEV *PromotedLHS = LHS;
2544 const SCEV *PromotedRHS = RHS;
2546 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2547 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2549 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2551 return getUMaxExpr(PromotedLHS, PromotedRHS);
2554 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
2555 /// the types using zero-extension, and then perform a umin operation
2557 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
2559 const SCEV *PromotedLHS = LHS;
2560 const SCEV *PromotedRHS = RHS;
2562 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2563 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2565 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2567 return getUMinExpr(PromotedLHS, PromotedRHS);
2570 /// PushDefUseChildren - Push users of the given Instruction
2571 /// onto the given Worklist.
2573 PushDefUseChildren(Instruction *I,
2574 SmallVectorImpl<Instruction *> &Worklist) {
2575 // Push the def-use children onto the Worklist stack.
2576 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end();
2578 Worklist.push_back(cast<Instruction>(UI));
2581 /// ForgetSymbolicValue - This looks up computed SCEV values for all
2582 /// instructions that depend on the given instruction and removes them from
2583 /// the Scalars map if they reference SymName. This is used during PHI
2586 ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) {
2587 SmallVector<Instruction *, 16> Worklist;
2588 PushDefUseChildren(PN, Worklist);
2590 SmallPtrSet<Instruction *, 8> Visited;
2592 while (!Worklist.empty()) {
2593 Instruction *I = Worklist.pop_back_val();
2594 if (!Visited.insert(I)) continue;
2596 std::map<SCEVCallbackVH, const SCEV *>::iterator It =
2597 Scalars.find(static_cast<Value *>(I));
2598 if (It != Scalars.end()) {
2599 // Short-circuit the def-use traversal if the symbolic name
2600 // ceases to appear in expressions.
2601 if (It->second != SymName && !It->second->hasOperand(SymName))
2604 // SCEVUnknown for a PHI either means that it has an unrecognized
2605 // structure, it's a PHI that's in the progress of being computed
2606 // by createNodeForPHI, or it's a single-value PHI. In the first case,
2607 // additional loop trip count information isn't going to change anything.
2608 // In the second case, createNodeForPHI will perform the necessary
2609 // updates on its own when it gets to that point. In the third, we do
2610 // want to forget the SCEVUnknown.
2611 if (!isa<PHINode>(I) ||
2612 !isa<SCEVUnknown>(It->second) ||
2613 (I != PN && It->second == SymName)) {
2614 ValuesAtScopes.erase(It->second);
2619 PushDefUseChildren(I, Worklist);
2623 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
2624 /// a loop header, making it a potential recurrence, or it doesn't.
2626 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
2627 if (const Loop *L = LI->getLoopFor(PN->getParent()))
2628 if (L->getHeader() == PN->getParent()) {
2629 // The loop may have multiple entrances or multiple exits; we can analyze
2630 // this phi as an addrec if it has a unique entry value and a unique
2632 Value *BEValueV = 0, *StartValueV = 0;
2633 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
2634 Value *V = PN->getIncomingValue(i);
2635 if (L->contains(PN->getIncomingBlock(i))) {
2638 } else if (BEValueV != V) {
2642 } else if (!StartValueV) {
2644 } else if (StartValueV != V) {
2649 if (BEValueV && StartValueV) {
2650 // While we are analyzing this PHI node, handle its value symbolically.
2651 const SCEV *SymbolicName = getUnknown(PN);
2652 assert(Scalars.find(PN) == Scalars.end() &&
2653 "PHI node already processed?");
2654 Scalars.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
2656 // Using this symbolic name for the PHI, analyze the value coming around
2658 const SCEV *BEValue = getSCEV(BEValueV);
2660 // NOTE: If BEValue is loop invariant, we know that the PHI node just
2661 // has a special value for the first iteration of the loop.
2663 // If the value coming around the backedge is an add with the symbolic
2664 // value we just inserted, then we found a simple induction variable!
2665 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
2666 // If there is a single occurrence of the symbolic value, replace it
2667 // with a recurrence.
2668 unsigned FoundIndex = Add->getNumOperands();
2669 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
2670 if (Add->getOperand(i) == SymbolicName)
2671 if (FoundIndex == e) {
2676 if (FoundIndex != Add->getNumOperands()) {
2677 // Create an add with everything but the specified operand.
2678 SmallVector<const SCEV *, 8> Ops;
2679 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
2680 if (i != FoundIndex)
2681 Ops.push_back(Add->getOperand(i));
2682 const SCEV *Accum = getAddExpr(Ops);
2684 // This is not a valid addrec if the step amount is varying each
2685 // loop iteration, but is not itself an addrec in this loop.
2686 if (Accum->isLoopInvariant(L) ||
2687 (isa<SCEVAddRecExpr>(Accum) &&
2688 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
2689 bool HasNUW = false;
2690 bool HasNSW = false;
2692 // If the increment doesn't overflow, then neither the addrec nor
2693 // the post-increment will overflow.
2694 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) {
2695 if (OBO->hasNoUnsignedWrap())
2697 if (OBO->hasNoSignedWrap())
2701 const SCEV *StartVal = getSCEV(StartValueV);
2702 const SCEV *PHISCEV =
2703 getAddRecExpr(StartVal, Accum, L, HasNUW, HasNSW);
2705 // Since the no-wrap flags are on the increment, they apply to the
2706 // post-incremented value as well.
2707 if (Accum->isLoopInvariant(L))
2708 (void)getAddRecExpr(getAddExpr(StartVal, Accum),
2709 Accum, L, HasNUW, HasNSW);
2711 // Okay, for the entire analysis of this edge we assumed the PHI
2712 // to be symbolic. We now need to go back and purge all of the
2713 // entries for the scalars that use the symbolic expression.
2714 ForgetSymbolicName(PN, SymbolicName);
2715 Scalars[SCEVCallbackVH(PN, this)] = PHISCEV;
2719 } else if (const SCEVAddRecExpr *AddRec =
2720 dyn_cast<SCEVAddRecExpr>(BEValue)) {
2721 // Otherwise, this could be a loop like this:
2722 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
2723 // In this case, j = {1,+,1} and BEValue is j.
2724 // Because the other in-value of i (0) fits the evolution of BEValue
2725 // i really is an addrec evolution.
2726 if (AddRec->getLoop() == L && AddRec->isAffine()) {
2727 const SCEV *StartVal = getSCEV(StartValueV);
2729 // If StartVal = j.start - j.stride, we can use StartVal as the
2730 // initial step of the addrec evolution.
2731 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
2732 AddRec->getOperand(1))) {
2733 const SCEV *PHISCEV =
2734 getAddRecExpr(StartVal, AddRec->getOperand(1), L);
2736 // Okay, for the entire analysis of this edge we assumed the PHI
2737 // to be symbolic. We now need to go back and purge all of the
2738 // entries for the scalars that use the symbolic expression.
2739 ForgetSymbolicName(PN, SymbolicName);
2740 Scalars[SCEVCallbackVH(PN, this)] = PHISCEV;
2748 // If the PHI has a single incoming value, follow that value, unless the
2749 // PHI's incoming blocks are in a different loop, in which case doing so
2750 // risks breaking LCSSA form. Instcombine would normally zap these, but
2751 // it doesn't have DominatorTree information, so it may miss cases.
2752 if (Value *V = PN->hasConstantValue(DT)) {
2753 bool AllSameLoop = true;
2754 Loop *PNLoop = LI->getLoopFor(PN->getParent());
2755 for (size_t i = 0, e = PN->getNumIncomingValues(); i != e; ++i)
2756 if (LI->getLoopFor(PN->getIncomingBlock(i)) != PNLoop) {
2757 AllSameLoop = false;
2764 // If it's not a loop phi, we can't handle it yet.
2765 return getUnknown(PN);
2768 /// createNodeForGEP - Expand GEP instructions into add and multiply
2769 /// operations. This allows them to be analyzed by regular SCEV code.
2771 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
2773 bool InBounds = GEP->isInBounds();
2774 const Type *IntPtrTy = getEffectiveSCEVType(GEP->getType());
2775 Value *Base = GEP->getOperand(0);
2776 // Don't attempt to analyze GEPs over unsized objects.
2777 if (!cast<PointerType>(Base->getType())->getElementType()->isSized())
2778 return getUnknown(GEP);
2779 const SCEV *TotalOffset = getIntegerSCEV(0, IntPtrTy);
2780 gep_type_iterator GTI = gep_type_begin(GEP);
2781 for (GetElementPtrInst::op_iterator I = next(GEP->op_begin()),
2785 // Compute the (potentially symbolic) offset in bytes for this index.
2786 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) {
2787 // For a struct, add the member offset.
2788 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
2789 TotalOffset = getAddExpr(TotalOffset,
2790 getOffsetOfExpr(STy, FieldNo),
2791 /*HasNUW=*/false, /*HasNSW=*/InBounds);
2793 // For an array, add the element offset, explicitly scaled.
2794 const SCEV *LocalOffset = getSCEV(Index);
2795 // Getelementptr indices are signed.
2796 LocalOffset = getTruncateOrSignExtend(LocalOffset, IntPtrTy);
2797 // Lower "inbounds" GEPs to NSW arithmetic.
2798 LocalOffset = getMulExpr(LocalOffset, getSizeOfExpr(*GTI),
2799 /*HasNUW=*/false, /*HasNSW=*/InBounds);
2800 TotalOffset = getAddExpr(TotalOffset, LocalOffset,
2801 /*HasNUW=*/false, /*HasNSW=*/InBounds);
2804 return getAddExpr(getSCEV(Base), TotalOffset,
2805 /*HasNUW=*/false, /*HasNSW=*/InBounds);
2808 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
2809 /// guaranteed to end in (at every loop iteration). It is, at the same time,
2810 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
2811 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
2813 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
2814 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
2815 return C->getValue()->getValue().countTrailingZeros();
2817 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
2818 return std::min(GetMinTrailingZeros(T->getOperand()),
2819 (uint32_t)getTypeSizeInBits(T->getType()));
2821 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
2822 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
2823 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
2824 getTypeSizeInBits(E->getType()) : OpRes;
2827 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
2828 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
2829 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
2830 getTypeSizeInBits(E->getType()) : OpRes;
2833 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
2834 // The result is the min of all operands results.
2835 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
2836 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
2837 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
2841 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
2842 // The result is the sum of all operands results.
2843 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
2844 uint32_t BitWidth = getTypeSizeInBits(M->getType());
2845 for (unsigned i = 1, e = M->getNumOperands();
2846 SumOpRes != BitWidth && i != e; ++i)
2847 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
2852 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
2853 // The result is the min of all operands results.
2854 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
2855 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
2856 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
2860 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
2861 // The result is the min of all operands results.
2862 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
2863 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
2864 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
2868 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
2869 // The result is the min of all operands results.
2870 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
2871 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
2872 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
2876 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
2877 // For a SCEVUnknown, ask ValueTracking.
2878 unsigned BitWidth = getTypeSizeInBits(U->getType());
2879 APInt Mask = APInt::getAllOnesValue(BitWidth);
2880 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
2881 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones);
2882 return Zeros.countTrailingOnes();
2889 /// getUnsignedRange - Determine the unsigned range for a particular SCEV.
2892 ScalarEvolution::getUnsignedRange(const SCEV *S) {
2894 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
2895 return ConstantRange(C->getValue()->getValue());
2897 unsigned BitWidth = getTypeSizeInBits(S->getType());
2898 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
2900 // If the value has known zeros, the maximum unsigned value will have those
2901 // known zeros as well.
2902 uint32_t TZ = GetMinTrailingZeros(S);
2904 ConservativeResult =
2905 ConstantRange(APInt::getMinValue(BitWidth),
2906 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
2908 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
2909 ConstantRange X = getUnsignedRange(Add->getOperand(0));
2910 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
2911 X = X.add(getUnsignedRange(Add->getOperand(i)));
2912 return ConservativeResult.intersectWith(X);
2915 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
2916 ConstantRange X = getUnsignedRange(Mul->getOperand(0));
2917 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
2918 X = X.multiply(getUnsignedRange(Mul->getOperand(i)));
2919 return ConservativeResult.intersectWith(X);
2922 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
2923 ConstantRange X = getUnsignedRange(SMax->getOperand(0));
2924 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
2925 X = X.smax(getUnsignedRange(SMax->getOperand(i)));
2926 return ConservativeResult.intersectWith(X);
2929 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
2930 ConstantRange X = getUnsignedRange(UMax->getOperand(0));
2931 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
2932 X = X.umax(getUnsignedRange(UMax->getOperand(i)));
2933 return ConservativeResult.intersectWith(X);
2936 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
2937 ConstantRange X = getUnsignedRange(UDiv->getLHS());
2938 ConstantRange Y = getUnsignedRange(UDiv->getRHS());
2939 return ConservativeResult.intersectWith(X.udiv(Y));
2942 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
2943 ConstantRange X = getUnsignedRange(ZExt->getOperand());
2944 return ConservativeResult.intersectWith(X.zeroExtend(BitWidth));
2947 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
2948 ConstantRange X = getUnsignedRange(SExt->getOperand());
2949 return ConservativeResult.intersectWith(X.signExtend(BitWidth));
2952 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
2953 ConstantRange X = getUnsignedRange(Trunc->getOperand());
2954 return ConservativeResult.intersectWith(X.truncate(BitWidth));
2957 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
2958 // If there's no unsigned wrap, the value will never be less than its
2960 if (AddRec->hasNoUnsignedWrap())
2961 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
2962 if (!C->getValue()->isZero())
2963 ConservativeResult =
2964 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0));
2966 // TODO: non-affine addrec
2967 if (AddRec->isAffine()) {
2968 const Type *Ty = AddRec->getType();
2969 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
2970 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
2971 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
2972 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
2974 const SCEV *Start = AddRec->getStart();
2975 const SCEV *Step = AddRec->getStepRecurrence(*this);
2977 ConstantRange StartRange = getUnsignedRange(Start);
2978 ConstantRange StepRange = getSignedRange(Step);
2979 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
2980 ConstantRange EndRange =
2981 StartRange.add(MaxBECountRange.multiply(StepRange));
2983 // Check for overflow. This must be done with ConstantRange arithmetic
2984 // because we could be called from within the ScalarEvolution overflow
2986 ConstantRange ExtStartRange = StartRange.zextOrTrunc(BitWidth*2+1);
2987 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
2988 ConstantRange ExtMaxBECountRange =
2989 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
2990 ConstantRange ExtEndRange = EndRange.zextOrTrunc(BitWidth*2+1);
2991 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
2993 return ConservativeResult;
2995 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(),
2996 EndRange.getUnsignedMin());
2997 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(),
2998 EndRange.getUnsignedMax());
2999 if (Min.isMinValue() && Max.isMaxValue())
3000 return ConservativeResult;
3001 return ConservativeResult.intersectWith(ConstantRange(Min, Max+1));
3005 return ConservativeResult;
3008 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3009 // For a SCEVUnknown, ask ValueTracking.
3010 APInt Mask = APInt::getAllOnesValue(BitWidth);
3011 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3012 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones, TD);
3013 if (Ones == ~Zeros + 1)
3014 return ConservativeResult;
3015 return ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1));
3018 return ConservativeResult;
3021 /// getSignedRange - Determine the signed range for a particular SCEV.
3024 ScalarEvolution::getSignedRange(const SCEV *S) {
3026 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3027 return ConstantRange(C->getValue()->getValue());
3029 unsigned BitWidth = getTypeSizeInBits(S->getType());
3030 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3032 // If the value has known zeros, the maximum signed value will have those
3033 // known zeros as well.
3034 uint32_t TZ = GetMinTrailingZeros(S);
3036 ConservativeResult =
3037 ConstantRange(APInt::getSignedMinValue(BitWidth),
3038 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
3040 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3041 ConstantRange X = getSignedRange(Add->getOperand(0));
3042 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3043 X = X.add(getSignedRange(Add->getOperand(i)));
3044 return ConservativeResult.intersectWith(X);
3047 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3048 ConstantRange X = getSignedRange(Mul->getOperand(0));
3049 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3050 X = X.multiply(getSignedRange(Mul->getOperand(i)));
3051 return ConservativeResult.intersectWith(X);
3054 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3055 ConstantRange X = getSignedRange(SMax->getOperand(0));
3056 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3057 X = X.smax(getSignedRange(SMax->getOperand(i)));
3058 return ConservativeResult.intersectWith(X);
3061 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3062 ConstantRange X = getSignedRange(UMax->getOperand(0));
3063 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3064 X = X.umax(getSignedRange(UMax->getOperand(i)));
3065 return ConservativeResult.intersectWith(X);
3068 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3069 ConstantRange X = getSignedRange(UDiv->getLHS());
3070 ConstantRange Y = getSignedRange(UDiv->getRHS());
3071 return ConservativeResult.intersectWith(X.udiv(Y));
3074 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3075 ConstantRange X = getSignedRange(ZExt->getOperand());
3076 return ConservativeResult.intersectWith(X.zeroExtend(BitWidth));
3079 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3080 ConstantRange X = getSignedRange(SExt->getOperand());
3081 return ConservativeResult.intersectWith(X.signExtend(BitWidth));
3084 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3085 ConstantRange X = getSignedRange(Trunc->getOperand());
3086 return ConservativeResult.intersectWith(X.truncate(BitWidth));
3089 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3090 // If there's no signed wrap, and all the operands have the same sign or
3091 // zero, the value won't ever change sign.
3092 if (AddRec->hasNoSignedWrap()) {
3093 bool AllNonNeg = true;
3094 bool AllNonPos = true;
3095 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
3096 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
3097 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
3100 ConservativeResult = ConservativeResult.intersectWith(
3101 ConstantRange(APInt(BitWidth, 0),
3102 APInt::getSignedMinValue(BitWidth)));
3104 ConservativeResult = ConservativeResult.intersectWith(
3105 ConstantRange(APInt::getSignedMinValue(BitWidth),
3106 APInt(BitWidth, 1)));
3109 // TODO: non-affine addrec
3110 if (AddRec->isAffine()) {
3111 const Type *Ty = AddRec->getType();
3112 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3113 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3114 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3115 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3117 const SCEV *Start = AddRec->getStart();
3118 const SCEV *Step = AddRec->getStepRecurrence(*this);
3120 ConstantRange StartRange = getSignedRange(Start);
3121 ConstantRange StepRange = getSignedRange(Step);
3122 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3123 ConstantRange EndRange =
3124 StartRange.add(MaxBECountRange.multiply(StepRange));
3126 // Check for overflow. This must be done with ConstantRange arithmetic
3127 // because we could be called from within the ScalarEvolution overflow
3129 ConstantRange ExtStartRange = StartRange.sextOrTrunc(BitWidth*2+1);
3130 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3131 ConstantRange ExtMaxBECountRange =
3132 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3133 ConstantRange ExtEndRange = EndRange.sextOrTrunc(BitWidth*2+1);
3134 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3136 return ConservativeResult;
3138 APInt Min = APIntOps::smin(StartRange.getSignedMin(),
3139 EndRange.getSignedMin());
3140 APInt Max = APIntOps::smax(StartRange.getSignedMax(),
3141 EndRange.getSignedMax());
3142 if (Min.isMinSignedValue() && Max.isMaxSignedValue())
3143 return ConservativeResult;
3144 return ConservativeResult.intersectWith(ConstantRange(Min, Max+1));
3148 return ConservativeResult;
3151 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3152 // For a SCEVUnknown, ask ValueTracking.
3153 if (!U->getValue()->getType()->isIntegerTy() && !TD)
3154 return ConservativeResult;
3155 unsigned NS = ComputeNumSignBits(U->getValue(), TD);
3157 return ConservativeResult;
3158 return ConservativeResult.intersectWith(
3159 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
3160 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1));
3163 return ConservativeResult;
3166 /// createSCEV - We know that there is no SCEV for the specified value.
3167 /// Analyze the expression.
3169 const SCEV *ScalarEvolution::createSCEV(Value *V) {
3170 if (!isSCEVable(V->getType()))
3171 return getUnknown(V);
3173 unsigned Opcode = Instruction::UserOp1;
3174 if (Instruction *I = dyn_cast<Instruction>(V)) {
3175 Opcode = I->getOpcode();
3177 // Don't attempt to analyze instructions in blocks that aren't
3178 // reachable. Such instructions don't matter, and they aren't required
3179 // to obey basic rules for definitions dominating uses which this
3180 // analysis depends on.
3181 if (!DT->isReachableFromEntry(I->getParent()))
3182 return getUnknown(V);
3183 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
3184 Opcode = CE->getOpcode();
3185 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
3186 return getConstant(CI);
3187 else if (isa<ConstantPointerNull>(V))
3188 return getIntegerSCEV(0, V->getType());
3189 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
3190 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee());
3192 return getUnknown(V);
3194 Operator *U = cast<Operator>(V);
3196 case Instruction::Add:
3197 // Don't transfer the NSW and NUW bits from the Add instruction to the
3198 // Add expression, because the Instruction may be guarded by control
3199 // flow and the no-overflow bits may not be valid for the expression in
3201 return getAddExpr(getSCEV(U->getOperand(0)),
3202 getSCEV(U->getOperand(1)));
3203 case Instruction::Mul:
3204 // Don't transfer the NSW and NUW bits from the Mul instruction to the
3205 // Mul expression, as with Add.
3206 return getMulExpr(getSCEV(U->getOperand(0)),
3207 getSCEV(U->getOperand(1)));
3208 case Instruction::UDiv:
3209 return getUDivExpr(getSCEV(U->getOperand(0)),
3210 getSCEV(U->getOperand(1)));
3211 case Instruction::Sub:
3212 return getMinusSCEV(getSCEV(U->getOperand(0)),
3213 getSCEV(U->getOperand(1)));
3214 case Instruction::And:
3215 // For an expression like x&255 that merely masks off the high bits,
3216 // use zext(trunc(x)) as the SCEV expression.
3217 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3218 if (CI->isNullValue())
3219 return getSCEV(U->getOperand(1));
3220 if (CI->isAllOnesValue())
3221 return getSCEV(U->getOperand(0));
3222 const APInt &A = CI->getValue();
3224 // Instcombine's ShrinkDemandedConstant may strip bits out of
3225 // constants, obscuring what would otherwise be a low-bits mask.
3226 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant
3227 // knew about to reconstruct a low-bits mask value.
3228 unsigned LZ = A.countLeadingZeros();
3229 unsigned BitWidth = A.getBitWidth();
3230 APInt AllOnes = APInt::getAllOnesValue(BitWidth);
3231 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
3232 ComputeMaskedBits(U->getOperand(0), AllOnes, KnownZero, KnownOne, TD);
3234 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ);
3236 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask))
3238 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)),
3239 IntegerType::get(getContext(), BitWidth - LZ)),
3244 case Instruction::Or:
3245 // If the RHS of the Or is a constant, we may have something like:
3246 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
3247 // optimizations will transparently handle this case.
3249 // In order for this transformation to be safe, the LHS must be of the
3250 // form X*(2^n) and the Or constant must be less than 2^n.
3251 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3252 const SCEV *LHS = getSCEV(U->getOperand(0));
3253 const APInt &CIVal = CI->getValue();
3254 if (GetMinTrailingZeros(LHS) >=
3255 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
3256 // Build a plain add SCEV.
3257 const SCEV *S = getAddExpr(LHS, getSCEV(CI));
3258 // If the LHS of the add was an addrec and it has no-wrap flags,
3259 // transfer the no-wrap flags, since an or won't introduce a wrap.
3260 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
3261 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
3262 if (OldAR->hasNoUnsignedWrap())
3263 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoUnsignedWrap(true);
3264 if (OldAR->hasNoSignedWrap())
3265 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoSignedWrap(true);
3271 case Instruction::Xor:
3272 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3273 // If the RHS of the xor is a signbit, then this is just an add.
3274 // Instcombine turns add of signbit into xor as a strength reduction step.
3275 if (CI->getValue().isSignBit())
3276 return getAddExpr(getSCEV(U->getOperand(0)),
3277 getSCEV(U->getOperand(1)));
3279 // If the RHS of xor is -1, then this is a not operation.
3280 if (CI->isAllOnesValue())
3281 return getNotSCEV(getSCEV(U->getOperand(0)));
3283 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
3284 // This is a variant of the check for xor with -1, and it handles
3285 // the case where instcombine has trimmed non-demanded bits out
3286 // of an xor with -1.
3287 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
3288 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
3289 if (BO->getOpcode() == Instruction::And &&
3290 LCI->getValue() == CI->getValue())
3291 if (const SCEVZeroExtendExpr *Z =
3292 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
3293 const Type *UTy = U->getType();
3294 const SCEV *Z0 = Z->getOperand();
3295 const Type *Z0Ty = Z0->getType();
3296 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
3298 // If C is a low-bits mask, the zero extend is serving to
3299 // mask off the high bits. Complement the operand and
3300 // re-apply the zext.
3301 if (APIntOps::isMask(Z0TySize, CI->getValue()))
3302 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
3304 // If C is a single bit, it may be in the sign-bit position
3305 // before the zero-extend. In this case, represent the xor
3306 // using an add, which is equivalent, and re-apply the zext.
3307 APInt Trunc = APInt(CI->getValue()).trunc(Z0TySize);
3308 if (APInt(Trunc).zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
3310 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
3316 case Instruction::Shl:
3317 // Turn shift left of a constant amount into a multiply.
3318 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3319 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3320 Constant *X = ConstantInt::get(getContext(),
3321 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
3322 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3326 case Instruction::LShr:
3327 // Turn logical shift right of a constant into a unsigned divide.
3328 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3329 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3330 Constant *X = ConstantInt::get(getContext(),
3331 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
3332 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3336 case Instruction::AShr:
3337 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
3338 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
3339 if (Instruction *L = dyn_cast<Instruction>(U->getOperand(0)))
3340 if (L->getOpcode() == Instruction::Shl &&
3341 L->getOperand(1) == U->getOperand(1)) {
3342 unsigned BitWidth = getTypeSizeInBits(U->getType());
3343 uint64_t Amt = BitWidth - CI->getZExtValue();
3344 if (Amt == BitWidth)
3345 return getSCEV(L->getOperand(0)); // shift by zero --> noop
3347 return getIntegerSCEV(0, U->getType()); // value is undefined
3349 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
3350 IntegerType::get(getContext(), Amt)),
3355 case Instruction::Trunc:
3356 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
3358 case Instruction::ZExt:
3359 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3361 case Instruction::SExt:
3362 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3364 case Instruction::BitCast:
3365 // BitCasts are no-op casts so we just eliminate the cast.
3366 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
3367 return getSCEV(U->getOperand(0));
3370 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
3371 // lead to pointer expressions which cannot safely be expanded to GEPs,
3372 // because ScalarEvolution doesn't respect the GEP aliasing rules when
3373 // simplifying integer expressions.
3375 case Instruction::GetElementPtr:
3376 return createNodeForGEP(cast<GEPOperator>(U));
3378 case Instruction::PHI:
3379 return createNodeForPHI(cast<PHINode>(U));
3381 case Instruction::Select:
3382 // This could be a smax or umax that was lowered earlier.
3383 // Try to recover it.
3384 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
3385 Value *LHS = ICI->getOperand(0);
3386 Value *RHS = ICI->getOperand(1);
3387 switch (ICI->getPredicate()) {
3388 case ICmpInst::ICMP_SLT:
3389 case ICmpInst::ICMP_SLE:
3390 std::swap(LHS, RHS);
3392 case ICmpInst::ICMP_SGT:
3393 case ICmpInst::ICMP_SGE:
3394 if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
3395 return getSMaxExpr(getSCEV(LHS), getSCEV(RHS));
3396 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
3397 return getSMinExpr(getSCEV(LHS), getSCEV(RHS));
3399 case ICmpInst::ICMP_ULT:
3400 case ICmpInst::ICMP_ULE:
3401 std::swap(LHS, RHS);
3403 case ICmpInst::ICMP_UGT:
3404 case ICmpInst::ICMP_UGE:
3405 if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
3406 return getUMaxExpr(getSCEV(LHS), getSCEV(RHS));
3407 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
3408 return getUMinExpr(getSCEV(LHS), getSCEV(RHS));
3410 case ICmpInst::ICMP_NE:
3411 // n != 0 ? n : 1 -> umax(n, 1)
3412 if (LHS == U->getOperand(1) &&
3413 isa<ConstantInt>(U->getOperand(2)) &&
3414 cast<ConstantInt>(U->getOperand(2))->isOne() &&
3415 isa<ConstantInt>(RHS) &&
3416 cast<ConstantInt>(RHS)->isZero())
3417 return getUMaxExpr(getSCEV(LHS), getSCEV(U->getOperand(2)));
3419 case ICmpInst::ICMP_EQ:
3420 // n == 0 ? 1 : n -> umax(n, 1)
3421 if (LHS == U->getOperand(2) &&
3422 isa<ConstantInt>(U->getOperand(1)) &&
3423 cast<ConstantInt>(U->getOperand(1))->isOne() &&
3424 isa<ConstantInt>(RHS) &&
3425 cast<ConstantInt>(RHS)->isZero())
3426 return getUMaxExpr(getSCEV(LHS), getSCEV(U->getOperand(1)));
3433 default: // We cannot analyze this expression.
3437 return getUnknown(V);
3442 //===----------------------------------------------------------------------===//
3443 // Iteration Count Computation Code
3446 /// getBackedgeTakenCount - If the specified loop has a predictable
3447 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
3448 /// object. The backedge-taken count is the number of times the loop header
3449 /// will be branched to from within the loop. This is one less than the
3450 /// trip count of the loop, since it doesn't count the first iteration,
3451 /// when the header is branched to from outside the loop.
3453 /// Note that it is not valid to call this method on a loop without a
3454 /// loop-invariant backedge-taken count (see
3455 /// hasLoopInvariantBackedgeTakenCount).
3457 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
3458 return getBackedgeTakenInfo(L).Exact;
3461 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
3462 /// return the least SCEV value that is known never to be less than the
3463 /// actual backedge taken count.
3464 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
3465 return getBackedgeTakenInfo(L).Max;
3468 /// PushLoopPHIs - Push PHI nodes in the header of the given loop
3469 /// onto the given Worklist.
3471 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
3472 BasicBlock *Header = L->getHeader();
3474 // Push all Loop-header PHIs onto the Worklist stack.
3475 for (BasicBlock::iterator I = Header->begin();
3476 PHINode *PN = dyn_cast<PHINode>(I); ++I)
3477 Worklist.push_back(PN);
3480 const ScalarEvolution::BackedgeTakenInfo &
3481 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
3482 // Initially insert a CouldNotCompute for this loop. If the insertion
3483 // succeeds, proceed to actually compute a backedge-taken count and
3484 // update the value. The temporary CouldNotCompute value tells SCEV
3485 // code elsewhere that it shouldn't attempt to request a new
3486 // backedge-taken count, which could result in infinite recursion.
3487 std::pair<std::map<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
3488 BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute()));
3490 BackedgeTakenInfo BECount = ComputeBackedgeTakenCount(L);
3491 if (BECount.Exact != getCouldNotCompute()) {
3492 assert(BECount.Exact->isLoopInvariant(L) &&
3493 BECount.Max->isLoopInvariant(L) &&
3494 "Computed backedge-taken count isn't loop invariant for loop!");
3495 ++NumTripCountsComputed;
3497 // Update the value in the map.
3498 Pair.first->second = BECount;
3500 if (BECount.Max != getCouldNotCompute())
3501 // Update the value in the map.
3502 Pair.first->second = BECount;
3503 if (isa<PHINode>(L->getHeader()->begin()))
3504 // Only count loops that have phi nodes as not being computable.
3505 ++NumTripCountsNotComputed;
3508 // Now that we know more about the trip count for this loop, forget any
3509 // existing SCEV values for PHI nodes in this loop since they are only
3510 // conservative estimates made without the benefit of trip count
3511 // information. This is similar to the code in forgetLoop, except that
3512 // it handles SCEVUnknown PHI nodes specially.
3513 if (BECount.hasAnyInfo()) {
3514 SmallVector<Instruction *, 16> Worklist;
3515 PushLoopPHIs(L, Worklist);
3517 SmallPtrSet<Instruction *, 8> Visited;
3518 while (!Worklist.empty()) {
3519 Instruction *I = Worklist.pop_back_val();
3520 if (!Visited.insert(I)) continue;
3522 std::map<SCEVCallbackVH, const SCEV *>::iterator It =
3523 Scalars.find(static_cast<Value *>(I));
3524 if (It != Scalars.end()) {
3525 // SCEVUnknown for a PHI either means that it has an unrecognized
3526 // structure, or it's a PHI that's in the progress of being computed
3527 // by createNodeForPHI. In the former case, additional loop trip
3528 // count information isn't going to change anything. In the later
3529 // case, createNodeForPHI will perform the necessary updates on its
3530 // own when it gets to that point.
3531 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(It->second)) {
3532 ValuesAtScopes.erase(It->second);
3535 if (PHINode *PN = dyn_cast<PHINode>(I))
3536 ConstantEvolutionLoopExitValue.erase(PN);
3539 PushDefUseChildren(I, Worklist);
3543 return Pair.first->second;
3546 /// forgetLoop - This method should be called by the client when it has
3547 /// changed a loop in a way that may effect ScalarEvolution's ability to
3548 /// compute a trip count, or if the loop is deleted.
3549 void ScalarEvolution::forgetLoop(const Loop *L) {
3550 // Drop any stored trip count value.
3551 BackedgeTakenCounts.erase(L);
3553 // Drop information about expressions based on loop-header PHIs.
3554 SmallVector<Instruction *, 16> Worklist;
3555 PushLoopPHIs(L, Worklist);
3557 SmallPtrSet<Instruction *, 8> Visited;
3558 while (!Worklist.empty()) {
3559 Instruction *I = Worklist.pop_back_val();
3560 if (!Visited.insert(I)) continue;
3562 std::map<SCEVCallbackVH, const SCEV *>::iterator It =
3563 Scalars.find(static_cast<Value *>(I));
3564 if (It != Scalars.end()) {
3565 ValuesAtScopes.erase(It->second);
3567 if (PHINode *PN = dyn_cast<PHINode>(I))
3568 ConstantEvolutionLoopExitValue.erase(PN);
3571 PushDefUseChildren(I, Worklist);
3575 /// forgetValue - This method should be called by the client when it has
3576 /// changed a value in a way that may effect its value, or which may
3577 /// disconnect it from a def-use chain linking it to a loop.
3578 void ScalarEvolution::forgetValue(Value *V) {
3579 Instruction *I = dyn_cast<Instruction>(V);
3582 // Drop information about expressions based on loop-header PHIs.
3583 SmallVector<Instruction *, 16> Worklist;
3584 Worklist.push_back(I);
3586 SmallPtrSet<Instruction *, 8> Visited;
3587 while (!Worklist.empty()) {
3588 I = Worklist.pop_back_val();
3589 if (!Visited.insert(I)) continue;
3591 std::map<SCEVCallbackVH, const SCEV *>::iterator It =
3592 Scalars.find(static_cast<Value *>(I));
3593 if (It != Scalars.end()) {
3594 ValuesAtScopes.erase(It->second);
3596 if (PHINode *PN = dyn_cast<PHINode>(I))
3597 ConstantEvolutionLoopExitValue.erase(PN);
3600 PushDefUseChildren(I, Worklist);
3604 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
3605 /// of the specified loop will execute.
3606 ScalarEvolution::BackedgeTakenInfo
3607 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
3608 SmallVector<BasicBlock *, 8> ExitingBlocks;
3609 L->getExitingBlocks(ExitingBlocks);
3611 // Examine all exits and pick the most conservative values.
3612 const SCEV *BECount = getCouldNotCompute();
3613 const SCEV *MaxBECount = getCouldNotCompute();
3614 bool CouldNotComputeBECount = false;
3615 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
3616 BackedgeTakenInfo NewBTI =
3617 ComputeBackedgeTakenCountFromExit(L, ExitingBlocks[i]);
3619 if (NewBTI.Exact == getCouldNotCompute()) {
3620 // We couldn't compute an exact value for this exit, so
3621 // we won't be able to compute an exact value for the loop.
3622 CouldNotComputeBECount = true;
3623 BECount = getCouldNotCompute();
3624 } else if (!CouldNotComputeBECount) {
3625 if (BECount == getCouldNotCompute())
3626 BECount = NewBTI.Exact;
3628 BECount = getUMinFromMismatchedTypes(BECount, NewBTI.Exact);
3630 if (MaxBECount == getCouldNotCompute())
3631 MaxBECount = NewBTI.Max;
3632 else if (NewBTI.Max != getCouldNotCompute())
3633 MaxBECount = getUMinFromMismatchedTypes(MaxBECount, NewBTI.Max);
3636 return BackedgeTakenInfo(BECount, MaxBECount);
3639 /// ComputeBackedgeTakenCountFromExit - Compute the number of times the backedge
3640 /// of the specified loop will execute if it exits via the specified block.
3641 ScalarEvolution::BackedgeTakenInfo
3642 ScalarEvolution::ComputeBackedgeTakenCountFromExit(const Loop *L,
3643 BasicBlock *ExitingBlock) {
3645 // Okay, we've chosen an exiting block. See what condition causes us to
3646 // exit at this block.
3648 // FIXME: we should be able to handle switch instructions (with a single exit)
3649 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
3650 if (ExitBr == 0) return getCouldNotCompute();
3651 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
3653 // At this point, we know we have a conditional branch that determines whether
3654 // the loop is exited. However, we don't know if the branch is executed each
3655 // time through the loop. If not, then the execution count of the branch will
3656 // not be equal to the trip count of the loop.
3658 // Currently we check for this by checking to see if the Exit branch goes to
3659 // the loop header. If so, we know it will always execute the same number of
3660 // times as the loop. We also handle the case where the exit block *is* the
3661 // loop header. This is common for un-rotated loops.
3663 // If both of those tests fail, walk up the unique predecessor chain to the
3664 // header, stopping if there is an edge that doesn't exit the loop. If the
3665 // header is reached, the execution count of the branch will be equal to the
3666 // trip count of the loop.
3668 // More extensive analysis could be done to handle more cases here.
3670 if (ExitBr->getSuccessor(0) != L->getHeader() &&
3671 ExitBr->getSuccessor(1) != L->getHeader() &&
3672 ExitBr->getParent() != L->getHeader()) {
3673 // The simple checks failed, try climbing the unique predecessor chain
3674 // up to the header.
3676 for (BasicBlock *BB = ExitBr->getParent(); BB; ) {
3677 BasicBlock *Pred = BB->getUniquePredecessor();
3679 return getCouldNotCompute();
3680 TerminatorInst *PredTerm = Pred->getTerminator();
3681 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) {
3682 BasicBlock *PredSucc = PredTerm->getSuccessor(i);
3685 // If the predecessor has a successor that isn't BB and isn't
3686 // outside the loop, assume the worst.
3687 if (L->contains(PredSucc))
3688 return getCouldNotCompute();
3690 if (Pred == L->getHeader()) {
3697 return getCouldNotCompute();
3700 // Proceed to the next level to examine the exit condition expression.
3701 return ComputeBackedgeTakenCountFromExitCond(L, ExitBr->getCondition(),
3702 ExitBr->getSuccessor(0),
3703 ExitBr->getSuccessor(1));
3706 /// ComputeBackedgeTakenCountFromExitCond - Compute the number of times the
3707 /// backedge of the specified loop will execute if its exit condition
3708 /// were a conditional branch of ExitCond, TBB, and FBB.
3709 ScalarEvolution::BackedgeTakenInfo
3710 ScalarEvolution::ComputeBackedgeTakenCountFromExitCond(const Loop *L,
3714 // Check if the controlling expression for this loop is an And or Or.
3715 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
3716 if (BO->getOpcode() == Instruction::And) {
3717 // Recurse on the operands of the and.
3718 BackedgeTakenInfo BTI0 =
3719 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB);
3720 BackedgeTakenInfo BTI1 =
3721 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB);
3722 const SCEV *BECount = getCouldNotCompute();
3723 const SCEV *MaxBECount = getCouldNotCompute();
3724 if (L->contains(TBB)) {
3725 // Both conditions must be true for the loop to continue executing.
3726 // Choose the less conservative count.
3727 if (BTI0.Exact == getCouldNotCompute() ||
3728 BTI1.Exact == getCouldNotCompute())
3729 BECount = getCouldNotCompute();
3731 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3732 if (BTI0.Max == getCouldNotCompute())
3733 MaxBECount = BTI1.Max;
3734 else if (BTI1.Max == getCouldNotCompute())
3735 MaxBECount = BTI0.Max;
3737 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max);
3739 // Both conditions must be true for the loop to exit.
3740 assert(L->contains(FBB) && "Loop block has no successor in loop!");
3741 if (BTI0.Exact != getCouldNotCompute() &&
3742 BTI1.Exact != getCouldNotCompute())
3743 BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3744 if (BTI0.Max != getCouldNotCompute() &&
3745 BTI1.Max != getCouldNotCompute())
3746 MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max);
3749 return BackedgeTakenInfo(BECount, MaxBECount);
3751 if (BO->getOpcode() == Instruction::Or) {
3752 // Recurse on the operands of the or.
3753 BackedgeTakenInfo BTI0 =
3754 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB);
3755 BackedgeTakenInfo BTI1 =
3756 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB);
3757 const SCEV *BECount = getCouldNotCompute();
3758 const SCEV *MaxBECount = getCouldNotCompute();
3759 if (L->contains(FBB)) {
3760 // Both conditions must be false for the loop to continue executing.
3761 // Choose the less conservative count.
3762 if (BTI0.Exact == getCouldNotCompute() ||
3763 BTI1.Exact == getCouldNotCompute())
3764 BECount = getCouldNotCompute();
3766 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3767 if (BTI0.Max == getCouldNotCompute())
3768 MaxBECount = BTI1.Max;
3769 else if (BTI1.Max == getCouldNotCompute())
3770 MaxBECount = BTI0.Max;
3772 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max);
3774 // Both conditions must be false for the loop to exit.
3775 assert(L->contains(TBB) && "Loop block has no successor in loop!");
3776 if (BTI0.Exact != getCouldNotCompute() &&
3777 BTI1.Exact != getCouldNotCompute())
3778 BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3779 if (BTI0.Max != getCouldNotCompute() &&
3780 BTI1.Max != getCouldNotCompute())
3781 MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max);
3784 return BackedgeTakenInfo(BECount, MaxBECount);
3788 // With an icmp, it may be feasible to compute an exact backedge-taken count.
3789 // Proceed to the next level to examine the icmp.
3790 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
3791 return ComputeBackedgeTakenCountFromExitCondICmp(L, ExitCondICmp, TBB, FBB);
3793 // Check for a constant condition. These are normally stripped out by
3794 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
3795 // preserve the CFG and is temporarily leaving constant conditions
3797 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
3798 if (L->contains(FBB) == !CI->getZExtValue())
3799 // The backedge is always taken.
3800 return getCouldNotCompute();
3802 // The backedge is never taken.
3803 return getIntegerSCEV(0, CI->getType());
3806 // If it's not an integer or pointer comparison then compute it the hard way.
3807 return ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB));
3810 /// ComputeBackedgeTakenCountFromExitCondICmp - Compute the number of times the
3811 /// backedge of the specified loop will execute if its exit condition
3812 /// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB.
3813 ScalarEvolution::BackedgeTakenInfo
3814 ScalarEvolution::ComputeBackedgeTakenCountFromExitCondICmp(const Loop *L,
3819 // If the condition was exit on true, convert the condition to exit on false
3820 ICmpInst::Predicate Cond;
3821 if (!L->contains(FBB))
3822 Cond = ExitCond->getPredicate();
3824 Cond = ExitCond->getInversePredicate();
3826 // Handle common loops like: for (X = "string"; *X; ++X)
3827 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
3828 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
3829 BackedgeTakenInfo ItCnt =
3830 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond);
3831 if (ItCnt.hasAnyInfo())
3835 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
3836 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
3838 // Try to evaluate any dependencies out of the loop.
3839 LHS = getSCEVAtScope(LHS, L);
3840 RHS = getSCEVAtScope(RHS, L);
3842 // At this point, we would like to compute how many iterations of the
3843 // loop the predicate will return true for these inputs.
3844 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) {
3845 // If there is a loop-invariant, force it into the RHS.
3846 std::swap(LHS, RHS);
3847 Cond = ICmpInst::getSwappedPredicate(Cond);
3850 // If we have a comparison of a chrec against a constant, try to use value
3851 // ranges to answer this query.
3852 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
3853 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
3854 if (AddRec->getLoop() == L) {
3855 // Form the constant range.
3856 ConstantRange CompRange(
3857 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
3859 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
3860 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
3864 case ICmpInst::ICMP_NE: { // while (X != Y)
3865 // Convert to: while (X-Y != 0)
3866 BackedgeTakenInfo BTI = HowFarToZero(getMinusSCEV(LHS, RHS), L);
3867 if (BTI.hasAnyInfo()) return BTI;
3870 case ICmpInst::ICMP_EQ: { // while (X == Y)
3871 // Convert to: while (X-Y == 0)
3872 BackedgeTakenInfo BTI = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
3873 if (BTI.hasAnyInfo()) return BTI;
3876 case ICmpInst::ICMP_SLT: {
3877 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true);
3878 if (BTI.hasAnyInfo()) return BTI;
3881 case ICmpInst::ICMP_SGT: {
3882 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
3883 getNotSCEV(RHS), L, true);
3884 if (BTI.hasAnyInfo()) return BTI;
3887 case ICmpInst::ICMP_ULT: {
3888 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false);
3889 if (BTI.hasAnyInfo()) return BTI;
3892 case ICmpInst::ICMP_UGT: {
3893 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
3894 getNotSCEV(RHS), L, false);
3895 if (BTI.hasAnyInfo()) return BTI;
3900 dbgs() << "ComputeBackedgeTakenCount ";
3901 if (ExitCond->getOperand(0)->getType()->isUnsigned())
3902 dbgs() << "[unsigned] ";
3903 dbgs() << *LHS << " "
3904 << Instruction::getOpcodeName(Instruction::ICmp)
3905 << " " << *RHS << "\n";
3910 ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB));
3913 static ConstantInt *
3914 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
3915 ScalarEvolution &SE) {
3916 const SCEV *InVal = SE.getConstant(C);
3917 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
3918 assert(isa<SCEVConstant>(Val) &&
3919 "Evaluation of SCEV at constant didn't fold correctly?");
3920 return cast<SCEVConstant>(Val)->getValue();
3923 /// GetAddressedElementFromGlobal - Given a global variable with an initializer
3924 /// and a GEP expression (missing the pointer index) indexing into it, return
3925 /// the addressed element of the initializer or null if the index expression is
3928 GetAddressedElementFromGlobal(GlobalVariable *GV,
3929 const std::vector<ConstantInt*> &Indices) {
3930 Constant *Init = GV->getInitializer();
3931 for (unsigned i = 0, e = Indices.size(); i != e; ++i) {
3932 uint64_t Idx = Indices[i]->getZExtValue();
3933 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) {
3934 assert(Idx < CS->getNumOperands() && "Bad struct index!");
3935 Init = cast<Constant>(CS->getOperand(Idx));
3936 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) {
3937 if (Idx >= CA->getNumOperands()) return 0; // Bogus program
3938 Init = cast<Constant>(CA->getOperand(Idx));
3939 } else if (isa<ConstantAggregateZero>(Init)) {
3940 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) {
3941 assert(Idx < STy->getNumElements() && "Bad struct index!");
3942 Init = Constant::getNullValue(STy->getElementType(Idx));
3943 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) {
3944 if (Idx >= ATy->getNumElements()) return 0; // Bogus program
3945 Init = Constant::getNullValue(ATy->getElementType());
3947 llvm_unreachable("Unknown constant aggregate type!");
3951 return 0; // Unknown initializer type
3957 /// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of
3958 /// 'icmp op load X, cst', try to see if we can compute the backedge
3959 /// execution count.
3960 ScalarEvolution::BackedgeTakenInfo
3961 ScalarEvolution::ComputeLoadConstantCompareBackedgeTakenCount(
3965 ICmpInst::Predicate predicate) {
3966 if (LI->isVolatile()) return getCouldNotCompute();
3968 // Check to see if the loaded pointer is a getelementptr of a global.
3969 // TODO: Use SCEV instead of manually grubbing with GEPs.
3970 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
3971 if (!GEP) return getCouldNotCompute();
3973 // Make sure that it is really a constant global we are gepping, with an
3974 // initializer, and make sure the first IDX is really 0.
3975 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
3976 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
3977 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
3978 !cast<Constant>(GEP->getOperand(1))->isNullValue())
3979 return getCouldNotCompute();
3981 // Okay, we allow one non-constant index into the GEP instruction.
3983 std::vector<ConstantInt*> Indexes;
3984 unsigned VarIdxNum = 0;
3985 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
3986 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
3987 Indexes.push_back(CI);
3988 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
3989 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
3990 VarIdx = GEP->getOperand(i);
3992 Indexes.push_back(0);
3995 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
3996 // Check to see if X is a loop variant variable value now.
3997 const SCEV *Idx = getSCEV(VarIdx);
3998 Idx = getSCEVAtScope(Idx, L);
4000 // We can only recognize very limited forms of loop index expressions, in
4001 // particular, only affine AddRec's like {C1,+,C2}.
4002 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
4003 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) ||
4004 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
4005 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
4006 return getCouldNotCompute();
4008 unsigned MaxSteps = MaxBruteForceIterations;
4009 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
4010 ConstantInt *ItCst = ConstantInt::get(
4011 cast<IntegerType>(IdxExpr->getType()), IterationNum);
4012 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
4014 // Form the GEP offset.
4015 Indexes[VarIdxNum] = Val;
4017 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes);
4018 if (Result == 0) break; // Cannot compute!
4020 // Evaluate the condition for this iteration.
4021 Result = ConstantExpr::getICmp(predicate, Result, RHS);
4022 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
4023 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
4025 dbgs() << "\n***\n*** Computed loop count " << *ItCst
4026 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
4029 ++NumArrayLenItCounts;
4030 return getConstant(ItCst); // Found terminating iteration!
4033 return getCouldNotCompute();
4037 /// CanConstantFold - Return true if we can constant fold an instruction of the
4038 /// specified type, assuming that all operands were constants.
4039 static bool CanConstantFold(const Instruction *I) {
4040 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
4041 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I))
4044 if (const CallInst *CI = dyn_cast<CallInst>(I))
4045 if (const Function *F = CI->getCalledFunction())
4046 return canConstantFoldCallTo(F);
4050 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
4051 /// in the loop that V is derived from. We allow arbitrary operations along the
4052 /// way, but the operands of an operation must either be constants or a value
4053 /// derived from a constant PHI. If this expression does not fit with these
4054 /// constraints, return null.
4055 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
4056 // If this is not an instruction, or if this is an instruction outside of the
4057 // loop, it can't be derived from a loop PHI.
4058 Instruction *I = dyn_cast<Instruction>(V);
4059 if (I == 0 || !L->contains(I)) return 0;
4061 if (PHINode *PN = dyn_cast<PHINode>(I)) {
4062 if (L->getHeader() == I->getParent())
4065 // We don't currently keep track of the control flow needed to evaluate
4066 // PHIs, so we cannot handle PHIs inside of loops.
4070 // If we won't be able to constant fold this expression even if the operands
4071 // are constants, return early.
4072 if (!CanConstantFold(I)) return 0;
4074 // Otherwise, we can evaluate this instruction if all of its operands are
4075 // constant or derived from a PHI node themselves.
4077 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op)
4078 if (!(isa<Constant>(I->getOperand(Op)) ||
4079 isa<GlobalValue>(I->getOperand(Op)))) {
4080 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L);
4081 if (P == 0) return 0; // Not evolving from PHI
4085 return 0; // Evolving from multiple different PHIs.
4088 // This is a expression evolving from a constant PHI!
4092 /// EvaluateExpression - Given an expression that passes the
4093 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
4094 /// in the loop has the value PHIVal. If we can't fold this expression for some
4095 /// reason, return null.
4096 static Constant *EvaluateExpression(Value *V, Constant *PHIVal,
4097 const TargetData *TD) {
4098 if (isa<PHINode>(V)) return PHIVal;
4099 if (Constant *C = dyn_cast<Constant>(V)) return C;
4100 if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) return GV;
4101 Instruction *I = cast<Instruction>(V);
4103 std::vector<Constant*> Operands;
4104 Operands.resize(I->getNumOperands());
4106 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
4107 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal, TD);
4108 if (Operands[i] == 0) return 0;
4111 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
4112 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
4114 return ConstantFoldInstOperands(I->getOpcode(), I->getType(),
4115 &Operands[0], Operands.size(), TD);
4118 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
4119 /// in the header of its containing loop, we know the loop executes a
4120 /// constant number of times, and the PHI node is just a recurrence
4121 /// involving constants, fold it.
4123 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
4126 std::map<PHINode*, Constant*>::iterator I =
4127 ConstantEvolutionLoopExitValue.find(PN);
4128 if (I != ConstantEvolutionLoopExitValue.end())
4131 if (BEs.ugt(MaxBruteForceIterations))
4132 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
4134 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
4136 // Since the loop is canonicalized, the PHI node must have two entries. One
4137 // entry must be a constant (coming in from outside of the loop), and the
4138 // second must be derived from the same PHI.
4139 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
4140 Constant *StartCST =
4141 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
4143 return RetVal = 0; // Must be a constant.
4145 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
4146 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
4148 return RetVal = 0; // Not derived from same PHI.
4150 // Execute the loop symbolically to determine the exit value.
4151 if (BEs.getActiveBits() >= 32)
4152 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
4154 unsigned NumIterations = BEs.getZExtValue(); // must be in range
4155 unsigned IterationNum = 0;
4156 for (Constant *PHIVal = StartCST; ; ++IterationNum) {
4157 if (IterationNum == NumIterations)
4158 return RetVal = PHIVal; // Got exit value!
4160 // Compute the value of the PHI node for the next iteration.
4161 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD);
4162 if (NextPHI == PHIVal)
4163 return RetVal = NextPHI; // Stopped evolving!
4165 return 0; // Couldn't evaluate!
4170 /// ComputeBackedgeTakenCountExhaustively - If the loop is known to execute a
4171 /// constant number of times (the condition evolves only from constants),
4172 /// try to evaluate a few iterations of the loop until we get the exit
4173 /// condition gets a value of ExitWhen (true or false). If we cannot
4174 /// evaluate the trip count of the loop, return getCouldNotCompute().
4176 ScalarEvolution::ComputeBackedgeTakenCountExhaustively(const Loop *L,
4179 PHINode *PN = getConstantEvolvingPHI(Cond, L);
4180 if (PN == 0) return getCouldNotCompute();
4182 // Since the loop is canonicalized, the PHI node must have two entries. One
4183 // entry must be a constant (coming in from outside of the loop), and the
4184 // second must be derived from the same PHI.
4185 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
4186 Constant *StartCST =
4187 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
4188 if (StartCST == 0) return getCouldNotCompute(); // Must be a constant.
4190 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
4191 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
4192 if (PN2 != PN) return getCouldNotCompute(); // Not derived from same PHI.
4194 // Okay, we find a PHI node that defines the trip count of this loop. Execute
4195 // the loop symbolically to determine when the condition gets a value of
4197 unsigned IterationNum = 0;
4198 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
4199 for (Constant *PHIVal = StartCST;
4200 IterationNum != MaxIterations; ++IterationNum) {
4201 ConstantInt *CondVal =
4202 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal, TD));
4204 // Couldn't symbolically evaluate.
4205 if (!CondVal) return getCouldNotCompute();
4207 if (CondVal->getValue() == uint64_t(ExitWhen)) {
4208 ++NumBruteForceTripCountsComputed;
4209 return getConstant(Type::getInt32Ty(getContext()), IterationNum);
4212 // Compute the value of the PHI node for the next iteration.
4213 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD);
4214 if (NextPHI == 0 || NextPHI == PHIVal)
4215 return getCouldNotCompute();// Couldn't evaluate or not making progress...
4219 // Too many iterations were needed to evaluate.
4220 return getCouldNotCompute();
4223 /// getSCEVAtScope - Return a SCEV expression for the specified value
4224 /// at the specified scope in the program. The L value specifies a loop
4225 /// nest to evaluate the expression at, where null is the top-level or a
4226 /// specified loop is immediately inside of the loop.
4228 /// This method can be used to compute the exit value for a variable defined
4229 /// in a loop by querying what the value will hold in the parent loop.
4231 /// In the case that a relevant loop exit value cannot be computed, the
4232 /// original value V is returned.
4233 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
4234 // Check to see if we've folded this expression at this loop before.
4235 std::map<const Loop *, const SCEV *> &Values = ValuesAtScopes[V];
4236 std::pair<std::map<const Loop *, const SCEV *>::iterator, bool> Pair =
4237 Values.insert(std::make_pair(L, static_cast<const SCEV *>(0)));
4239 return Pair.first->second ? Pair.first->second : V;
4241 // Otherwise compute it.
4242 const SCEV *C = computeSCEVAtScope(V, L);
4243 ValuesAtScopes[V][L] = C;
4247 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
4248 if (isa<SCEVConstant>(V)) return V;
4250 // If this instruction is evolved from a constant-evolving PHI, compute the
4251 // exit value from the loop without using SCEVs.
4252 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
4253 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
4254 const Loop *LI = (*this->LI)[I->getParent()];
4255 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
4256 if (PHINode *PN = dyn_cast<PHINode>(I))
4257 if (PN->getParent() == LI->getHeader()) {
4258 // Okay, there is no closed form solution for the PHI node. Check
4259 // to see if the loop that contains it has a known backedge-taken
4260 // count. If so, we may be able to force computation of the exit
4262 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
4263 if (const SCEVConstant *BTCC =
4264 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
4265 // Okay, we know how many times the containing loop executes. If
4266 // this is a constant evolving PHI node, get the final value at
4267 // the specified iteration number.
4268 Constant *RV = getConstantEvolutionLoopExitValue(PN,
4269 BTCC->getValue()->getValue(),
4271 if (RV) return getSCEV(RV);
4275 // Okay, this is an expression that we cannot symbolically evaluate
4276 // into a SCEV. Check to see if it's possible to symbolically evaluate
4277 // the arguments into constants, and if so, try to constant propagate the
4278 // result. This is particularly useful for computing loop exit values.
4279 if (CanConstantFold(I)) {
4280 std::vector<Constant*> Operands;
4281 Operands.reserve(I->getNumOperands());
4282 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
4283 Value *Op = I->getOperand(i);
4284 if (Constant *C = dyn_cast<Constant>(Op)) {
4285 Operands.push_back(C);
4287 // If any of the operands is non-constant and if they are
4288 // non-integer and non-pointer, don't even try to analyze them
4289 // with scev techniques.
4290 if (!isSCEVable(Op->getType()))
4293 const SCEV *OpV = getSCEVAtScope(Op, L);
4294 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) {
4295 Constant *C = SC->getValue();
4296 if (C->getType() != Op->getType())
4297 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
4301 Operands.push_back(C);
4302 } else if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) {
4303 if (Constant *C = dyn_cast<Constant>(SU->getValue())) {
4304 if (C->getType() != Op->getType())
4306 ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
4310 Operands.push_back(C);
4320 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
4321 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
4322 Operands[0], Operands[1], TD);
4324 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
4325 &Operands[0], Operands.size(), TD);
4331 // This is some other type of SCEVUnknown, just return it.
4335 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
4336 // Avoid performing the look-up in the common case where the specified
4337 // expression has no loop-variant portions.
4338 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
4339 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
4340 if (OpAtScope != Comm->getOperand(i)) {
4341 // Okay, at least one of these operands is loop variant but might be
4342 // foldable. Build a new instance of the folded commutative expression.
4343 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
4344 Comm->op_begin()+i);
4345 NewOps.push_back(OpAtScope);
4347 for (++i; i != e; ++i) {
4348 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
4349 NewOps.push_back(OpAtScope);
4351 if (isa<SCEVAddExpr>(Comm))
4352 return getAddExpr(NewOps);
4353 if (isa<SCEVMulExpr>(Comm))
4354 return getMulExpr(NewOps);
4355 if (isa<SCEVSMaxExpr>(Comm))
4356 return getSMaxExpr(NewOps);
4357 if (isa<SCEVUMaxExpr>(Comm))
4358 return getUMaxExpr(NewOps);
4359 llvm_unreachable("Unknown commutative SCEV type!");
4362 // If we got here, all operands are loop invariant.
4366 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
4367 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
4368 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
4369 if (LHS == Div->getLHS() && RHS == Div->getRHS())
4370 return Div; // must be loop invariant
4371 return getUDivExpr(LHS, RHS);
4374 // If this is a loop recurrence for a loop that does not contain L, then we
4375 // are dealing with the final value computed by the loop.
4376 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
4377 if (!L || !AddRec->getLoop()->contains(L)) {
4378 // To evaluate this recurrence, we need to know how many times the AddRec
4379 // loop iterates. Compute this now.
4380 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
4381 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
4383 // Then, evaluate the AddRec.
4384 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
4389 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
4390 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
4391 if (Op == Cast->getOperand())
4392 return Cast; // must be loop invariant
4393 return getZeroExtendExpr(Op, Cast->getType());
4396 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
4397 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
4398 if (Op == Cast->getOperand())
4399 return Cast; // must be loop invariant
4400 return getSignExtendExpr(Op, Cast->getType());
4403 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
4404 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
4405 if (Op == Cast->getOperand())
4406 return Cast; // must be loop invariant
4407 return getTruncateExpr(Op, Cast->getType());
4410 llvm_unreachable("Unknown SCEV type!");
4414 /// getSCEVAtScope - This is a convenience function which does
4415 /// getSCEVAtScope(getSCEV(V), L).
4416 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
4417 return getSCEVAtScope(getSCEV(V), L);
4420 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
4421 /// following equation:
4423 /// A * X = B (mod N)
4425 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
4426 /// A and B isn't important.
4428 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
4429 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
4430 ScalarEvolution &SE) {
4431 uint32_t BW = A.getBitWidth();
4432 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
4433 assert(A != 0 && "A must be non-zero.");
4437 // The gcd of A and N may have only one prime factor: 2. The number of
4438 // trailing zeros in A is its multiplicity
4439 uint32_t Mult2 = A.countTrailingZeros();
4442 // 2. Check if B is divisible by D.
4444 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
4445 // is not less than multiplicity of this prime factor for D.
4446 if (B.countTrailingZeros() < Mult2)
4447 return SE.getCouldNotCompute();
4449 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
4452 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
4453 // bit width during computations.
4454 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
4455 APInt Mod(BW + 1, 0);
4456 Mod.set(BW - Mult2); // Mod = N / D
4457 APInt I = AD.multiplicativeInverse(Mod);
4459 // 4. Compute the minimum unsigned root of the equation:
4460 // I * (B / D) mod (N / D)
4461 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
4463 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
4465 return SE.getConstant(Result.trunc(BW));
4468 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
4469 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
4470 /// might be the same) or two SCEVCouldNotCompute objects.
4472 static std::pair<const SCEV *,const SCEV *>
4473 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
4474 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
4475 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
4476 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
4477 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
4479 // We currently can only solve this if the coefficients are constants.
4480 if (!LC || !MC || !NC) {
4481 const SCEV *CNC = SE.getCouldNotCompute();
4482 return std::make_pair(CNC, CNC);
4485 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
4486 const APInt &L = LC->getValue()->getValue();
4487 const APInt &M = MC->getValue()->getValue();
4488 const APInt &N = NC->getValue()->getValue();
4489 APInt Two(BitWidth, 2);
4490 APInt Four(BitWidth, 4);
4493 using namespace APIntOps;
4495 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
4496 // The B coefficient is M-N/2
4500 // The A coefficient is N/2
4501 APInt A(N.sdiv(Two));
4503 // Compute the B^2-4ac term.
4506 SqrtTerm -= Four * (A * C);
4508 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
4509 // integer value or else APInt::sqrt() will assert.
4510 APInt SqrtVal(SqrtTerm.sqrt());
4512 // Compute the two solutions for the quadratic formula.
4513 // The divisions must be performed as signed divisions.
4515 APInt TwoA( A << 1 );
4516 if (TwoA.isMinValue()) {
4517 const SCEV *CNC = SE.getCouldNotCompute();
4518 return std::make_pair(CNC, CNC);
4521 LLVMContext &Context = SE.getContext();
4523 ConstantInt *Solution1 =
4524 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
4525 ConstantInt *Solution2 =
4526 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
4528 return std::make_pair(SE.getConstant(Solution1),
4529 SE.getConstant(Solution2));
4530 } // end APIntOps namespace
4533 /// HowFarToZero - Return the number of times a backedge comparing the specified
4534 /// value to zero will execute. If not computable, return CouldNotCompute.
4535 ScalarEvolution::BackedgeTakenInfo
4536 ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) {
4537 // If the value is a constant
4538 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
4539 // If the value is already zero, the branch will execute zero times.
4540 if (C->getValue()->isZero()) return C;
4541 return getCouldNotCompute(); // Otherwise it will loop infinitely.
4544 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
4545 if (!AddRec || AddRec->getLoop() != L)
4546 return getCouldNotCompute();
4548 if (AddRec->isAffine()) {
4549 // If this is an affine expression, the execution count of this branch is
4550 // the minimum unsigned root of the following equation:
4552 // Start + Step*N = 0 (mod 2^BW)
4556 // Step*N = -Start (mod 2^BW)
4558 // where BW is the common bit width of Start and Step.
4560 // Get the initial value for the loop.
4561 const SCEV *Start = getSCEVAtScope(AddRec->getStart(),
4562 L->getParentLoop());
4563 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1),
4564 L->getParentLoop());
4566 if (const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) {
4567 // For now we handle only constant steps.
4569 // First, handle unitary steps.
4570 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so:
4571 return getNegativeSCEV(Start); // N = -Start (as unsigned)
4572 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so:
4573 return Start; // N = Start (as unsigned)
4575 // Then, try to solve the above equation provided that Start is constant.
4576 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
4577 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
4578 -StartC->getValue()->getValue(),
4581 } else if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
4582 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
4583 // the quadratic equation to solve it.
4584 std::pair<const SCEV *,const SCEV *> Roots = SolveQuadraticEquation(AddRec,
4586 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
4587 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
4590 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1
4591 << " sol#2: " << *R2 << "\n";
4593 // Pick the smallest positive root value.
4594 if (ConstantInt *CB =
4595 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
4596 R1->getValue(), R2->getValue()))) {
4597 if (CB->getZExtValue() == false)
4598 std::swap(R1, R2); // R1 is the minimum root now.
4600 // We can only use this value if the chrec ends up with an exact zero
4601 // value at this index. When solving for "X*X != 5", for example, we
4602 // should not accept a root of 2.
4603 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
4605 return R1; // We found a quadratic root!
4610 return getCouldNotCompute();
4613 /// HowFarToNonZero - Return the number of times a backedge checking the
4614 /// specified value for nonzero will execute. If not computable, return
4616 ScalarEvolution::BackedgeTakenInfo
4617 ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
4618 // Loops that look like: while (X == 0) are very strange indeed. We don't
4619 // handle them yet except for the trivial case. This could be expanded in the
4620 // future as needed.
4622 // If the value is a constant, check to see if it is known to be non-zero
4623 // already. If so, the backedge will execute zero times.
4624 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
4625 if (!C->getValue()->isNullValue())
4626 return getIntegerSCEV(0, C->getType());
4627 return getCouldNotCompute(); // Otherwise it will loop infinitely.
4630 // We could implement others, but I really doubt anyone writes loops like
4631 // this, and if they did, they would already be constant folded.
4632 return getCouldNotCompute();
4635 /// getLoopPredecessor - If the given loop's header has exactly one unique
4636 /// predecessor outside the loop, return it. Otherwise return null.
4638 BasicBlock *ScalarEvolution::getLoopPredecessor(const Loop *L) {
4639 BasicBlock *Header = L->getHeader();
4640 BasicBlock *Pred = 0;
4641 for (pred_iterator PI = pred_begin(Header), E = pred_end(Header);
4643 if (!L->contains(*PI)) {
4644 if (Pred && Pred != *PI) return 0; // Multiple predecessors.
4650 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
4651 /// (which may not be an immediate predecessor) which has exactly one
4652 /// successor from which BB is reachable, or null if no such block is
4656 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
4657 // If the block has a unique predecessor, then there is no path from the
4658 // predecessor to the block that does not go through the direct edge
4659 // from the predecessor to the block.
4660 if (BasicBlock *Pred = BB->getSinglePredecessor())
4663 // A loop's header is defined to be a block that dominates the loop.
4664 // If the header has a unique predecessor outside the loop, it must be
4665 // a block that has exactly one successor that can reach the loop.
4666 if (Loop *L = LI->getLoopFor(BB))
4667 return getLoopPredecessor(L);
4672 /// HasSameValue - SCEV structural equivalence is usually sufficient for
4673 /// testing whether two expressions are equal, however for the purposes of
4674 /// looking for a condition guarding a loop, it can be useful to be a little
4675 /// more general, since a front-end may have replicated the controlling
4678 static bool HasSameValue(const SCEV *A, const SCEV *B) {
4679 // Quick check to see if they are the same SCEV.
4680 if (A == B) return true;
4682 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
4683 // two different instructions with the same value. Check for this case.
4684 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
4685 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
4686 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
4687 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
4688 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory())
4691 // Otherwise assume they may have a different value.
4695 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
4696 return getSignedRange(S).getSignedMax().isNegative();
4699 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
4700 return getSignedRange(S).getSignedMin().isStrictlyPositive();
4703 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
4704 return !getSignedRange(S).getSignedMin().isNegative();
4707 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
4708 return !getSignedRange(S).getSignedMax().isStrictlyPositive();
4711 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
4712 return isKnownNegative(S) || isKnownPositive(S);
4715 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
4716 const SCEV *LHS, const SCEV *RHS) {
4717 // If LHS or RHS is an addrec, check to see if the condition is true in
4718 // every iteration of the loop.
4719 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
4720 if (isLoopEntryGuardedByCond(
4721 AR->getLoop(), Pred, AR->getStart(), RHS) &&
4722 isLoopBackedgeGuardedByCond(
4723 AR->getLoop(), Pred,
4724 getAddExpr(AR, AR->getStepRecurrence(*this)), RHS))
4726 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS))
4727 if (isLoopEntryGuardedByCond(
4728 AR->getLoop(), Pred, LHS, AR->getStart()) &&
4729 isLoopBackedgeGuardedByCond(
4730 AR->getLoop(), Pred,
4731 LHS, getAddExpr(AR, AR->getStepRecurrence(*this))))
4734 // Otherwise see what can be done with known constant ranges.
4735 return isKnownPredicateWithRanges(Pred, LHS, RHS);
4739 ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred,
4740 const SCEV *LHS, const SCEV *RHS) {
4741 if (HasSameValue(LHS, RHS))
4742 return ICmpInst::isTrueWhenEqual(Pred);
4744 // This code is split out from isKnownPredicate because it is called from
4745 // within isLoopEntryGuardedByCond.
4748 llvm_unreachable("Unexpected ICmpInst::Predicate value!");
4750 case ICmpInst::ICMP_SGT:
4751 Pred = ICmpInst::ICMP_SLT;
4752 std::swap(LHS, RHS);
4753 case ICmpInst::ICMP_SLT: {
4754 ConstantRange LHSRange = getSignedRange(LHS);
4755 ConstantRange RHSRange = getSignedRange(RHS);
4756 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
4758 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
4762 case ICmpInst::ICMP_SGE:
4763 Pred = ICmpInst::ICMP_SLE;
4764 std::swap(LHS, RHS);
4765 case ICmpInst::ICMP_SLE: {
4766 ConstantRange LHSRange = getSignedRange(LHS);
4767 ConstantRange RHSRange = getSignedRange(RHS);
4768 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
4770 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
4774 case ICmpInst::ICMP_UGT:
4775 Pred = ICmpInst::ICMP_ULT;
4776 std::swap(LHS, RHS);
4777 case ICmpInst::ICMP_ULT: {
4778 ConstantRange LHSRange = getUnsignedRange(LHS);
4779 ConstantRange RHSRange = getUnsignedRange(RHS);
4780 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
4782 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
4786 case ICmpInst::ICMP_UGE:
4787 Pred = ICmpInst::ICMP_ULE;
4788 std::swap(LHS, RHS);
4789 case ICmpInst::ICMP_ULE: {
4790 ConstantRange LHSRange = getUnsignedRange(LHS);
4791 ConstantRange RHSRange = getUnsignedRange(RHS);
4792 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
4794 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
4798 case ICmpInst::ICMP_NE: {
4799 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
4801 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
4804 const SCEV *Diff = getMinusSCEV(LHS, RHS);
4805 if (isKnownNonZero(Diff))
4809 case ICmpInst::ICMP_EQ:
4810 // The check at the top of the function catches the case where
4811 // the values are known to be equal.
4817 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
4818 /// protected by a conditional between LHS and RHS. This is used to
4819 /// to eliminate casts.
4821 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
4822 ICmpInst::Predicate Pred,
4823 const SCEV *LHS, const SCEV *RHS) {
4824 // Interpret a null as meaning no loop, where there is obviously no guard
4825 // (interprocedural conditions notwithstanding).
4826 if (!L) return true;
4828 BasicBlock *Latch = L->getLoopLatch();
4832 BranchInst *LoopContinuePredicate =
4833 dyn_cast<BranchInst>(Latch->getTerminator());
4834 if (!LoopContinuePredicate ||
4835 LoopContinuePredicate->isUnconditional())
4838 return isImpliedCond(LoopContinuePredicate->getCondition(), Pred, LHS, RHS,
4839 LoopContinuePredicate->getSuccessor(0) != L->getHeader());
4842 /// isLoopEntryGuardedByCond - Test whether entry to the loop is protected
4843 /// by a conditional between LHS and RHS. This is used to help avoid max
4844 /// expressions in loop trip counts, and to eliminate casts.
4846 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
4847 ICmpInst::Predicate Pred,
4848 const SCEV *LHS, const SCEV *RHS) {
4849 // Interpret a null as meaning no loop, where there is obviously no guard
4850 // (interprocedural conditions notwithstanding).
4851 if (!L) return false;
4853 BasicBlock *Predecessor = getLoopPredecessor(L);
4854 BasicBlock *PredecessorDest = L->getHeader();
4856 // Starting at the loop predecessor, climb up the predecessor chain, as long
4857 // as there are predecessors that can be found that have unique successors
4858 // leading to the original header.
4860 PredecessorDest = Predecessor,
4861 Predecessor = getPredecessorWithUniqueSuccessorForBB(Predecessor)) {
4863 BranchInst *LoopEntryPredicate =
4864 dyn_cast<BranchInst>(Predecessor->getTerminator());
4865 if (!LoopEntryPredicate ||
4866 LoopEntryPredicate->isUnconditional())
4869 if (isImpliedCond(LoopEntryPredicate->getCondition(), Pred, LHS, RHS,
4870 LoopEntryPredicate->getSuccessor(0) != PredecessorDest))
4877 /// isImpliedCond - Test whether the condition described by Pred, LHS,
4878 /// and RHS is true whenever the given Cond value evaluates to true.
4879 bool ScalarEvolution::isImpliedCond(Value *CondValue,
4880 ICmpInst::Predicate Pred,
4881 const SCEV *LHS, const SCEV *RHS,
4883 // Recursively handle And and Or conditions.
4884 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(CondValue)) {
4885 if (BO->getOpcode() == Instruction::And) {
4887 return isImpliedCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) ||
4888 isImpliedCond(BO->getOperand(1), Pred, LHS, RHS, Inverse);
4889 } else if (BO->getOpcode() == Instruction::Or) {
4891 return isImpliedCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) ||
4892 isImpliedCond(BO->getOperand(1), Pred, LHS, RHS, Inverse);
4896 ICmpInst *ICI = dyn_cast<ICmpInst>(CondValue);
4897 if (!ICI) return false;
4899 // Bail if the ICmp's operands' types are wider than the needed type
4900 // before attempting to call getSCEV on them. This avoids infinite
4901 // recursion, since the analysis of widening casts can require loop
4902 // exit condition information for overflow checking, which would
4904 if (getTypeSizeInBits(LHS->getType()) <
4905 getTypeSizeInBits(ICI->getOperand(0)->getType()))
4908 // Now that we found a conditional branch that dominates the loop, check to
4909 // see if it is the comparison we are looking for.
4910 ICmpInst::Predicate FoundPred;
4912 FoundPred = ICI->getInversePredicate();
4914 FoundPred = ICI->getPredicate();
4916 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
4917 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
4919 // Balance the types. The case where FoundLHS' type is wider than
4920 // LHS' type is checked for above.
4921 if (getTypeSizeInBits(LHS->getType()) >
4922 getTypeSizeInBits(FoundLHS->getType())) {
4923 if (CmpInst::isSigned(Pred)) {
4924 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
4925 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
4927 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
4928 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
4932 // Canonicalize the query to match the way instcombine will have
4933 // canonicalized the comparison.
4934 // First, put a constant operand on the right.
4935 if (isa<SCEVConstant>(LHS)) {
4936 std::swap(LHS, RHS);
4937 Pred = ICmpInst::getSwappedPredicate(Pred);
4939 // Then, canonicalize comparisons with boundary cases.
4940 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
4941 const APInt &RA = RC->getValue()->getValue();
4943 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
4944 case ICmpInst::ICMP_EQ:
4945 case ICmpInst::ICMP_NE:
4947 case ICmpInst::ICMP_UGE:
4948 if ((RA - 1).isMinValue()) {
4949 Pred = ICmpInst::ICMP_NE;
4950 RHS = getConstant(RA - 1);
4953 if (RA.isMaxValue()) {
4954 Pred = ICmpInst::ICMP_EQ;
4957 if (RA.isMinValue()) return true;
4959 case ICmpInst::ICMP_ULE:
4960 if ((RA + 1).isMaxValue()) {
4961 Pred = ICmpInst::ICMP_NE;
4962 RHS = getConstant(RA + 1);
4965 if (RA.isMinValue()) {
4966 Pred = ICmpInst::ICMP_EQ;
4969 if (RA.isMaxValue()) return true;
4971 case ICmpInst::ICMP_SGE:
4972 if ((RA - 1).isMinSignedValue()) {
4973 Pred = ICmpInst::ICMP_NE;
4974 RHS = getConstant(RA - 1);
4977 if (RA.isMaxSignedValue()) {
4978 Pred = ICmpInst::ICMP_EQ;
4981 if (RA.isMinSignedValue()) return true;
4983 case ICmpInst::ICMP_SLE:
4984 if ((RA + 1).isMaxSignedValue()) {
4985 Pred = ICmpInst::ICMP_NE;
4986 RHS = getConstant(RA + 1);
4989 if (RA.isMinSignedValue()) {
4990 Pred = ICmpInst::ICMP_EQ;
4993 if (RA.isMaxSignedValue()) return true;
4995 case ICmpInst::ICMP_UGT:
4996 if (RA.isMinValue()) {
4997 Pred = ICmpInst::ICMP_NE;
5000 if ((RA + 1).isMaxValue()) {
5001 Pred = ICmpInst::ICMP_EQ;
5002 RHS = getConstant(RA + 1);
5005 if (RA.isMaxValue()) return false;
5007 case ICmpInst::ICMP_ULT:
5008 if (RA.isMaxValue()) {
5009 Pred = ICmpInst::ICMP_NE;
5012 if ((RA - 1).isMinValue()) {
5013 Pred = ICmpInst::ICMP_EQ;
5014 RHS = getConstant(RA - 1);
5017 if (RA.isMinValue()) return false;
5019 case ICmpInst::ICMP_SGT:
5020 if (RA.isMinSignedValue()) {
5021 Pred = ICmpInst::ICMP_NE;
5024 if ((RA + 1).isMaxSignedValue()) {
5025 Pred = ICmpInst::ICMP_EQ;
5026 RHS = getConstant(RA + 1);
5029 if (RA.isMaxSignedValue()) return false;
5031 case ICmpInst::ICMP_SLT:
5032 if (RA.isMaxSignedValue()) {
5033 Pred = ICmpInst::ICMP_NE;
5036 if ((RA - 1).isMinSignedValue()) {
5037 Pred = ICmpInst::ICMP_EQ;
5038 RHS = getConstant(RA - 1);
5041 if (RA.isMinSignedValue()) return false;
5046 // Check to see if we can make the LHS or RHS match.
5047 if (LHS == FoundRHS || RHS == FoundLHS) {
5048 if (isa<SCEVConstant>(RHS)) {
5049 std::swap(FoundLHS, FoundRHS);
5050 FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
5052 std::swap(LHS, RHS);
5053 Pred = ICmpInst::getSwappedPredicate(Pred);
5057 // Check whether the found predicate is the same as the desired predicate.
5058 if (FoundPred == Pred)
5059 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
5061 // Check whether swapping the found predicate makes it the same as the
5062 // desired predicate.
5063 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
5064 if (isa<SCEVConstant>(RHS))
5065 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
5067 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
5068 RHS, LHS, FoundLHS, FoundRHS);
5071 // Check whether the actual condition is beyond sufficient.
5072 if (FoundPred == ICmpInst::ICMP_EQ)
5073 if (ICmpInst::isTrueWhenEqual(Pred))
5074 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
5076 if (Pred == ICmpInst::ICMP_NE)
5077 if (!ICmpInst::isTrueWhenEqual(FoundPred))
5078 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
5081 // Otherwise assume the worst.
5085 /// isImpliedCondOperands - Test whether the condition described by Pred,
5086 /// LHS, and RHS is true whenever the condition described by Pred, FoundLHS,
5087 /// and FoundRHS is true.
5088 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
5089 const SCEV *LHS, const SCEV *RHS,
5090 const SCEV *FoundLHS,
5091 const SCEV *FoundRHS) {
5092 return isImpliedCondOperandsHelper(Pred, LHS, RHS,
5093 FoundLHS, FoundRHS) ||
5094 // ~x < ~y --> x > y
5095 isImpliedCondOperandsHelper(Pred, LHS, RHS,
5096 getNotSCEV(FoundRHS),
5097 getNotSCEV(FoundLHS));
5100 /// isImpliedCondOperandsHelper - Test whether the condition described by
5101 /// Pred, LHS, and RHS is true whenever the condition described by Pred,
5102 /// FoundLHS, and FoundRHS is true.
5104 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
5105 const SCEV *LHS, const SCEV *RHS,
5106 const SCEV *FoundLHS,
5107 const SCEV *FoundRHS) {
5109 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
5110 case ICmpInst::ICMP_EQ:
5111 case ICmpInst::ICMP_NE:
5112 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
5115 case ICmpInst::ICMP_SLT:
5116 case ICmpInst::ICMP_SLE:
5117 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
5118 isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, RHS, FoundRHS))
5121 case ICmpInst::ICMP_SGT:
5122 case ICmpInst::ICMP_SGE:
5123 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
5124 isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, RHS, FoundRHS))
5127 case ICmpInst::ICMP_ULT:
5128 case ICmpInst::ICMP_ULE:
5129 if (isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
5130 isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, RHS, FoundRHS))
5133 case ICmpInst::ICMP_UGT:
5134 case ICmpInst::ICMP_UGE:
5135 if (isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
5136 isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, RHS, FoundRHS))
5144 /// getBECount - Subtract the end and start values and divide by the step,
5145 /// rounding up, to get the number of times the backedge is executed. Return
5146 /// CouldNotCompute if an intermediate computation overflows.
5147 const SCEV *ScalarEvolution::getBECount(const SCEV *Start,
5151 assert(!isKnownNegative(Step) &&
5152 "This code doesn't handle negative strides yet!");
5154 const Type *Ty = Start->getType();
5155 const SCEV *NegOne = getIntegerSCEV(-1, Ty);
5156 const SCEV *Diff = getMinusSCEV(End, Start);
5157 const SCEV *RoundUp = getAddExpr(Step, NegOne);
5159 // Add an adjustment to the difference between End and Start so that
5160 // the division will effectively round up.
5161 const SCEV *Add = getAddExpr(Diff, RoundUp);
5164 // Check Add for unsigned overflow.
5165 // TODO: More sophisticated things could be done here.
5166 const Type *WideTy = IntegerType::get(getContext(),
5167 getTypeSizeInBits(Ty) + 1);
5168 const SCEV *EDiff = getZeroExtendExpr(Diff, WideTy);
5169 const SCEV *ERoundUp = getZeroExtendExpr(RoundUp, WideTy);
5170 const SCEV *OperandExtendedAdd = getAddExpr(EDiff, ERoundUp);
5171 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd)
5172 return getCouldNotCompute();
5175 return getUDivExpr(Add, Step);
5178 /// HowManyLessThans - Return the number of times a backedge containing the
5179 /// specified less-than comparison will execute. If not computable, return
5180 /// CouldNotCompute.
5181 ScalarEvolution::BackedgeTakenInfo
5182 ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
5183 const Loop *L, bool isSigned) {
5184 // Only handle: "ADDREC < LoopInvariant".
5185 if (!RHS->isLoopInvariant(L)) return getCouldNotCompute();
5187 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
5188 if (!AddRec || AddRec->getLoop() != L)
5189 return getCouldNotCompute();
5191 // Check to see if we have a flag which makes analysis easy.
5192 bool NoWrap = isSigned ? AddRec->hasNoSignedWrap() :
5193 AddRec->hasNoUnsignedWrap();
5195 if (AddRec->isAffine()) {
5196 unsigned BitWidth = getTypeSizeInBits(AddRec->getType());
5197 const SCEV *Step = AddRec->getStepRecurrence(*this);
5200 return getCouldNotCompute();
5201 if (Step->isOne()) {
5202 // With unit stride, the iteration never steps past the limit value.
5203 } else if (isKnownPositive(Step)) {
5204 // Test whether a positive iteration can step past the limit
5205 // value and past the maximum value for its type in a single step.
5206 // Note that it's not sufficient to check NoWrap here, because even
5207 // though the value after a wrap is undefined, it's not undefined
5208 // behavior, so if wrap does occur, the loop could either terminate or
5209 // loop infinitely, but in either case, the loop is guaranteed to
5210 // iterate at least until the iteration where the wrapping occurs.
5211 const SCEV *One = getIntegerSCEV(1, Step->getType());
5213 APInt Max = APInt::getSignedMaxValue(BitWidth);
5214 if ((Max - getSignedRange(getMinusSCEV(Step, One)).getSignedMax())
5215 .slt(getSignedRange(RHS).getSignedMax()))
5216 return getCouldNotCompute();
5218 APInt Max = APInt::getMaxValue(BitWidth);
5219 if ((Max - getUnsignedRange(getMinusSCEV(Step, One)).getUnsignedMax())
5220 .ult(getUnsignedRange(RHS).getUnsignedMax()))
5221 return getCouldNotCompute();
5224 // TODO: Handle negative strides here and below.
5225 return getCouldNotCompute();
5227 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant
5228 // m. So, we count the number of iterations in which {n,+,s} < m is true.
5229 // Note that we cannot simply return max(m-n,0)/s because it's not safe to
5230 // treat m-n as signed nor unsigned due to overflow possibility.
5232 // First, we get the value of the LHS in the first iteration: n
5233 const SCEV *Start = AddRec->getOperand(0);
5235 // Determine the minimum constant start value.
5236 const SCEV *MinStart = getConstant(isSigned ?
5237 getSignedRange(Start).getSignedMin() :
5238 getUnsignedRange(Start).getUnsignedMin());
5240 // If we know that the condition is true in order to enter the loop,
5241 // then we know that it will run exactly (m-n)/s times. Otherwise, we
5242 // only know that it will execute (max(m,n)-n)/s times. In both cases,
5243 // the division must round up.
5244 const SCEV *End = RHS;
5245 if (!isLoopEntryGuardedByCond(L,
5246 isSigned ? ICmpInst::ICMP_SLT :
5248 getMinusSCEV(Start, Step), RHS))
5249 End = isSigned ? getSMaxExpr(RHS, Start)
5250 : getUMaxExpr(RHS, Start);
5252 // Determine the maximum constant end value.
5253 const SCEV *MaxEnd = getConstant(isSigned ?
5254 getSignedRange(End).getSignedMax() :
5255 getUnsignedRange(End).getUnsignedMax());
5257 // If MaxEnd is within a step of the maximum integer value in its type,
5258 // adjust it down to the minimum value which would produce the same effect.
5259 // This allows the subsequent ceiling division of (N+(step-1))/step to
5260 // compute the correct value.
5261 const SCEV *StepMinusOne = getMinusSCEV(Step,
5262 getIntegerSCEV(1, Step->getType()));
5265 getMinusSCEV(getConstant(APInt::getSignedMaxValue(BitWidth)),
5268 getMinusSCEV(getConstant(APInt::getMaxValue(BitWidth)),
5271 // Finally, we subtract these two values and divide, rounding up, to get
5272 // the number of times the backedge is executed.
5273 const SCEV *BECount = getBECount(Start, End, Step, NoWrap);
5275 // The maximum backedge count is similar, except using the minimum start
5276 // value and the maximum end value.
5277 const SCEV *MaxBECount = getBECount(MinStart, MaxEnd, Step, NoWrap);
5279 return BackedgeTakenInfo(BECount, MaxBECount);
5282 return getCouldNotCompute();
5285 /// getNumIterationsInRange - Return the number of iterations of this loop that
5286 /// produce values in the specified constant range. Another way of looking at
5287 /// this is that it returns the first iteration number where the value is not in
5288 /// the condition, thus computing the exit count. If the iteration count can't
5289 /// be computed, an instance of SCEVCouldNotCompute is returned.
5290 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
5291 ScalarEvolution &SE) const {
5292 if (Range.isFullSet()) // Infinite loop.
5293 return SE.getCouldNotCompute();
5295 // If the start is a non-zero constant, shift the range to simplify things.
5296 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
5297 if (!SC->getValue()->isZero()) {
5298 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
5299 Operands[0] = SE.getIntegerSCEV(0, SC->getType());
5300 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop());
5301 if (const SCEVAddRecExpr *ShiftedAddRec =
5302 dyn_cast<SCEVAddRecExpr>(Shifted))
5303 return ShiftedAddRec->getNumIterationsInRange(
5304 Range.subtract(SC->getValue()->getValue()), SE);
5305 // This is strange and shouldn't happen.
5306 return SE.getCouldNotCompute();
5309 // The only time we can solve this is when we have all constant indices.
5310 // Otherwise, we cannot determine the overflow conditions.
5311 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
5312 if (!isa<SCEVConstant>(getOperand(i)))
5313 return SE.getCouldNotCompute();
5316 // Okay at this point we know that all elements of the chrec are constants and
5317 // that the start element is zero.
5319 // First check to see if the range contains zero. If not, the first
5321 unsigned BitWidth = SE.getTypeSizeInBits(getType());
5322 if (!Range.contains(APInt(BitWidth, 0)))
5323 return SE.getIntegerSCEV(0, getType());
5326 // If this is an affine expression then we have this situation:
5327 // Solve {0,+,A} in Range === Ax in Range
5329 // We know that zero is in the range. If A is positive then we know that
5330 // the upper value of the range must be the first possible exit value.
5331 // If A is negative then the lower of the range is the last possible loop
5332 // value. Also note that we already checked for a full range.
5333 APInt One(BitWidth,1);
5334 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
5335 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
5337 // The exit value should be (End+A)/A.
5338 APInt ExitVal = (End + A).udiv(A);
5339 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
5341 // Evaluate at the exit value. If we really did fall out of the valid
5342 // range, then we computed our trip count, otherwise wrap around or other
5343 // things must have happened.
5344 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
5345 if (Range.contains(Val->getValue()))
5346 return SE.getCouldNotCompute(); // Something strange happened
5348 // Ensure that the previous value is in the range. This is a sanity check.
5349 assert(Range.contains(
5350 EvaluateConstantChrecAtConstant(this,
5351 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
5352 "Linear scev computation is off in a bad way!");
5353 return SE.getConstant(ExitValue);
5354 } else if (isQuadratic()) {
5355 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
5356 // quadratic equation to solve it. To do this, we must frame our problem in
5357 // terms of figuring out when zero is crossed, instead of when
5358 // Range.getUpper() is crossed.
5359 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
5360 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
5361 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop());
5363 // Next, solve the constructed addrec
5364 std::pair<const SCEV *,const SCEV *> Roots =
5365 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
5366 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
5367 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
5369 // Pick the smallest positive root value.
5370 if (ConstantInt *CB =
5371 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
5372 R1->getValue(), R2->getValue()))) {
5373 if (CB->getZExtValue() == false)
5374 std::swap(R1, R2); // R1 is the minimum root now.
5376 // Make sure the root is not off by one. The returned iteration should
5377 // not be in the range, but the previous one should be. When solving
5378 // for "X*X < 5", for example, we should not return a root of 2.
5379 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
5382 if (Range.contains(R1Val->getValue())) {
5383 // The next iteration must be out of the range...
5384 ConstantInt *NextVal =
5385 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1);
5387 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
5388 if (!Range.contains(R1Val->getValue()))
5389 return SE.getConstant(NextVal);
5390 return SE.getCouldNotCompute(); // Something strange happened
5393 // If R1 was not in the range, then it is a good return value. Make
5394 // sure that R1-1 WAS in the range though, just in case.
5395 ConstantInt *NextVal =
5396 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1);
5397 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
5398 if (Range.contains(R1Val->getValue()))
5400 return SE.getCouldNotCompute(); // Something strange happened
5405 return SE.getCouldNotCompute();
5410 //===----------------------------------------------------------------------===//
5411 // SCEVCallbackVH Class Implementation
5412 //===----------------------------------------------------------------------===//
5414 void ScalarEvolution::SCEVCallbackVH::deleted() {
5415 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
5416 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
5417 SE->ConstantEvolutionLoopExitValue.erase(PN);
5418 SE->Scalars.erase(getValPtr());
5419 // this now dangles!
5422 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *) {
5423 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
5425 // Forget all the expressions associated with users of the old value,
5426 // so that future queries will recompute the expressions using the new
5428 SmallVector<User *, 16> Worklist;
5429 SmallPtrSet<User *, 8> Visited;
5430 Value *Old = getValPtr();
5431 bool DeleteOld = false;
5432 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end();
5434 Worklist.push_back(*UI);
5435 while (!Worklist.empty()) {
5436 User *U = Worklist.pop_back_val();
5437 // Deleting the Old value will cause this to dangle. Postpone
5438 // that until everything else is done.
5443 if (!Visited.insert(U))
5445 if (PHINode *PN = dyn_cast<PHINode>(U))
5446 SE->ConstantEvolutionLoopExitValue.erase(PN);
5447 SE->Scalars.erase(U);
5448 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end();
5450 Worklist.push_back(*UI);
5452 // Delete the Old value if it (indirectly) references itself.
5454 if (PHINode *PN = dyn_cast<PHINode>(Old))
5455 SE->ConstantEvolutionLoopExitValue.erase(PN);
5456 SE->Scalars.erase(Old);
5457 // this now dangles!
5462 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
5463 : CallbackVH(V), SE(se) {}
5465 //===----------------------------------------------------------------------===//
5466 // ScalarEvolution Class Implementation
5467 //===----------------------------------------------------------------------===//
5469 ScalarEvolution::ScalarEvolution()
5470 : FunctionPass(&ID) {
5473 bool ScalarEvolution::runOnFunction(Function &F) {
5475 LI = &getAnalysis<LoopInfo>();
5476 TD = getAnalysisIfAvailable<TargetData>();
5477 DT = &getAnalysis<DominatorTree>();
5481 void ScalarEvolution::releaseMemory() {
5483 BackedgeTakenCounts.clear();
5484 ConstantEvolutionLoopExitValue.clear();
5485 ValuesAtScopes.clear();
5486 UniqueSCEVs.clear();
5487 SCEVAllocator.Reset();
5490 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
5491 AU.setPreservesAll();
5492 AU.addRequiredTransitive<LoopInfo>();
5493 AU.addRequiredTransitive<DominatorTree>();
5496 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
5497 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
5500 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
5502 // Print all inner loops first
5503 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
5504 PrintLoopInfo(OS, SE, *I);
5507 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
5510 SmallVector<BasicBlock *, 8> ExitBlocks;
5511 L->getExitBlocks(ExitBlocks);
5512 if (ExitBlocks.size() != 1)
5513 OS << "<multiple exits> ";
5515 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
5516 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
5518 OS << "Unpredictable backedge-taken count. ";
5523 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
5526 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
5527 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
5529 OS << "Unpredictable max backedge-taken count. ";
5535 void ScalarEvolution::print(raw_ostream &OS, const Module *) const {
5536 // ScalarEvolution's implementation of the print method is to print
5537 // out SCEV values of all instructions that are interesting. Doing
5538 // this potentially causes it to create new SCEV objects though,
5539 // which technically conflicts with the const qualifier. This isn't
5540 // observable from outside the class though, so casting away the
5541 // const isn't dangerous.
5542 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
5544 OS << "Classifying expressions for: ";
5545 WriteAsOperand(OS, F, /*PrintType=*/false);
5547 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
5548 if (isSCEVable(I->getType())) {
5551 const SCEV *SV = SE.getSCEV(&*I);
5554 const Loop *L = LI->getLoopFor((*I).getParent());
5556 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
5563 OS << "\t\t" "Exits: ";
5564 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
5565 if (!ExitValue->isLoopInvariant(L)) {
5566 OS << "<<Unknown>>";
5575 OS << "Determining loop execution counts for: ";
5576 WriteAsOperand(OS, F, /*PrintType=*/false);
5578 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
5579 PrintLoopInfo(OS, &SE, *I);