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->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 (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
1312 Ops.erase(Ops.begin());
1317 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 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1538 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
1539 LIOps.push_back(Ops[i]);
1540 Ops.erase(Ops.begin()+i);
1544 // If we found some loop invariants, fold them into the recurrence.
1545 if (!LIOps.empty()) {
1546 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
1547 LIOps.push_back(AddRec->getStart());
1549 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
1551 AddRecOps[0] = getAddExpr(LIOps);
1553 // It's tempting to propagate NUW/NSW flags here, but nuw/nsw addition
1554 // is not associative so this isn't necessarily safe.
1555 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRec->getLoop());
1557 // If all of the other operands were loop invariant, we are done.
1558 if (Ops.size() == 1) return NewRec;
1560 // Otherwise, add the folded AddRec by the non-liv parts.
1561 for (unsigned i = 0;; ++i)
1562 if (Ops[i] == AddRec) {
1566 return getAddExpr(Ops);
1569 // Okay, if there weren't any loop invariants to be folded, check to see if
1570 // there are multiple AddRec's with the same loop induction variable being
1571 // added together. If so, we can fold them.
1572 for (unsigned OtherIdx = Idx+1;
1573 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
1574 if (OtherIdx != Idx) {
1575 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
1576 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
1577 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D}
1578 SmallVector<const SCEV *, 4> NewOps(AddRec->op_begin(),
1580 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) {
1581 if (i >= NewOps.size()) {
1582 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i,
1583 OtherAddRec->op_end());
1586 NewOps[i] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i));
1588 const SCEV *NewAddRec = getAddRecExpr(NewOps, AddRec->getLoop());
1590 if (Ops.size() == 2) return NewAddRec;
1592 Ops.erase(Ops.begin()+Idx);
1593 Ops.erase(Ops.begin()+OtherIdx-1);
1594 Ops.push_back(NewAddRec);
1595 return getAddExpr(Ops);
1599 // Otherwise couldn't fold anything into this recurrence. Move onto the
1603 // Okay, it looks like we really DO need an add expr. Check to see if we
1604 // already have one, otherwise create a new one.
1605 FoldingSetNodeID ID;
1606 ID.AddInteger(scAddExpr);
1607 ID.AddInteger(Ops.size());
1608 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1609 ID.AddPointer(Ops[i]);
1612 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1614 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
1615 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
1616 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator),
1618 UniqueSCEVs.InsertNode(S, IP);
1620 if (HasNUW) S->setHasNoUnsignedWrap(true);
1621 if (HasNSW) S->setHasNoSignedWrap(true);
1625 /// getMulExpr - Get a canonical multiply expression, or something simpler if
1627 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
1628 bool HasNUW, bool HasNSW) {
1629 assert(!Ops.empty() && "Cannot get empty mul!");
1630 if (Ops.size() == 1) return Ops[0];
1632 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1633 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
1634 getEffectiveSCEVType(Ops[0]->getType()) &&
1635 "SCEVMulExpr operand types don't match!");
1638 // If HasNSW is true and all the operands are non-negative, infer HasNUW.
1639 if (!HasNUW && HasNSW) {
1641 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1642 if (!isKnownNonNegative(Ops[i])) {
1646 if (All) HasNUW = true;
1649 // Sort by complexity, this groups all similar expression types together.
1650 GroupByComplexity(Ops, LI);
1652 // If there are any constants, fold them together.
1654 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1656 // C1*(C2+V) -> C1*C2 + C1*V
1657 if (Ops.size() == 2)
1658 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
1659 if (Add->getNumOperands() == 2 &&
1660 isa<SCEVConstant>(Add->getOperand(0)))
1661 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
1662 getMulExpr(LHSC, Add->getOperand(1)));
1665 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1666 // We found two constants, fold them together!
1667 ConstantInt *Fold = ConstantInt::get(getContext(),
1668 LHSC->getValue()->getValue() *
1669 RHSC->getValue()->getValue());
1670 Ops[0] = getConstant(Fold);
1671 Ops.erase(Ops.begin()+1); // Erase the folded element
1672 if (Ops.size() == 1) return Ops[0];
1673 LHSC = cast<SCEVConstant>(Ops[0]);
1676 // If we are left with a constant one being multiplied, strip it off.
1677 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
1678 Ops.erase(Ops.begin());
1680 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
1681 // If we have a multiply of zero, it will always be zero.
1683 } else if (Ops[0]->isAllOnesValue()) {
1684 // If we have a mul by -1 of an add, try distributing the -1 among the
1686 if (Ops.size() == 2)
1687 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
1688 SmallVector<const SCEV *, 4> NewOps;
1689 bool AnyFolded = false;
1690 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(), E = Add->op_end();
1692 const SCEV *Mul = getMulExpr(Ops[0], *I);
1693 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
1694 NewOps.push_back(Mul);
1697 return getAddExpr(NewOps);
1702 // Skip over the add expression until we get to a multiply.
1703 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1706 if (Ops.size() == 1)
1709 // If there are mul operands inline them all into this expression.
1710 if (Idx < Ops.size()) {
1711 bool DeletedMul = false;
1712 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
1713 // If we have an mul, expand the mul operands onto the end of the operands
1715 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end());
1716 Ops.erase(Ops.begin()+Idx);
1720 // If we deleted at least one mul, we added operands to the end of the list,
1721 // and they are not necessarily sorted. Recurse to resort and resimplify
1722 // any operands we just acquired.
1724 return getMulExpr(Ops);
1727 // If there are any add recurrences in the operands list, see if any other
1728 // added values are loop invariant. If so, we can fold them into the
1730 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1733 // Scan over all recurrences, trying to fold loop invariants into them.
1734 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1735 // Scan all of the other operands to this mul and add them to the vector if
1736 // they are loop invariant w.r.t. the recurrence.
1737 SmallVector<const SCEV *, 8> LIOps;
1738 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1739 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1740 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
1741 LIOps.push_back(Ops[i]);
1742 Ops.erase(Ops.begin()+i);
1746 // If we found some loop invariants, fold them into the recurrence.
1747 if (!LIOps.empty()) {
1748 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
1749 SmallVector<const SCEV *, 4> NewOps;
1750 NewOps.reserve(AddRec->getNumOperands());
1751 if (LIOps.size() == 1) {
1752 const SCEV *Scale = LIOps[0];
1753 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
1754 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
1756 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
1757 SmallVector<const SCEV *, 4> MulOps(LIOps.begin(), LIOps.end());
1758 MulOps.push_back(AddRec->getOperand(i));
1759 NewOps.push_back(getMulExpr(MulOps));
1763 // It's tempting to propagate the NSW flag here, but nsw multiplication
1764 // is not associative so this isn't necessarily safe.
1765 const SCEV *NewRec = getAddRecExpr(NewOps, AddRec->getLoop(),
1766 HasNUW && AddRec->hasNoUnsignedWrap(),
1769 // If all of the other operands were loop invariant, we are done.
1770 if (Ops.size() == 1) return NewRec;
1772 // Otherwise, multiply the folded AddRec by the non-liv parts.
1773 for (unsigned i = 0;; ++i)
1774 if (Ops[i] == AddRec) {
1778 return getMulExpr(Ops);
1781 // Okay, if there weren't any loop invariants to be folded, check to see if
1782 // there are multiple AddRec's with the same loop induction variable being
1783 // multiplied together. If so, we can fold them.
1784 for (unsigned OtherIdx = Idx+1;
1785 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
1786 if (OtherIdx != Idx) {
1787 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
1788 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
1789 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D}
1790 const SCEVAddRecExpr *F = AddRec, *G = OtherAddRec;
1791 const SCEV *NewStart = getMulExpr(F->getStart(),
1793 const SCEV *B = F->getStepRecurrence(*this);
1794 const SCEV *D = G->getStepRecurrence(*this);
1795 const SCEV *NewStep = getAddExpr(getMulExpr(F, D),
1798 const SCEV *NewAddRec = getAddRecExpr(NewStart, NewStep,
1800 if (Ops.size() == 2) return NewAddRec;
1802 Ops.erase(Ops.begin()+Idx);
1803 Ops.erase(Ops.begin()+OtherIdx-1);
1804 Ops.push_back(NewAddRec);
1805 return getMulExpr(Ops);
1809 // Otherwise couldn't fold anything into this recurrence. Move onto the
1813 // Okay, it looks like we really DO need an mul expr. Check to see if we
1814 // already have one, otherwise create a new one.
1815 FoldingSetNodeID ID;
1816 ID.AddInteger(scMulExpr);
1817 ID.AddInteger(Ops.size());
1818 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1819 ID.AddPointer(Ops[i]);
1822 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1824 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
1825 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
1826 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
1828 UniqueSCEVs.InsertNode(S, IP);
1830 if (HasNUW) S->setHasNoUnsignedWrap(true);
1831 if (HasNSW) S->setHasNoSignedWrap(true);
1835 /// getUDivExpr - Get a canonical unsigned division expression, or something
1836 /// simpler if possible.
1837 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
1839 assert(getEffectiveSCEVType(LHS->getType()) ==
1840 getEffectiveSCEVType(RHS->getType()) &&
1841 "SCEVUDivExpr operand types don't match!");
1843 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
1844 if (RHSC->getValue()->equalsInt(1))
1845 return LHS; // X udiv 1 --> x
1847 return getIntegerSCEV(0, LHS->getType()); // value is undefined
1849 // Determine if the division can be folded into the operands of
1851 // TODO: Generalize this to non-constants by using known-bits information.
1852 const Type *Ty = LHS->getType();
1853 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
1854 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ;
1855 // For non-power-of-two values, effectively round the value up to the
1856 // nearest power of two.
1857 if (!RHSC->getValue()->getValue().isPowerOf2())
1859 const IntegerType *ExtTy =
1860 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
1861 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
1862 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
1863 if (const SCEVConstant *Step =
1864 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this)))
1865 if (!Step->getValue()->getValue()
1866 .urem(RHSC->getValue()->getValue()) &&
1867 getZeroExtendExpr(AR, ExtTy) ==
1868 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
1869 getZeroExtendExpr(Step, ExtTy),
1871 SmallVector<const SCEV *, 4> Operands;
1872 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i)
1873 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS));
1874 return getAddRecExpr(Operands, AR->getLoop());
1876 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
1877 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
1878 SmallVector<const SCEV *, 4> Operands;
1879 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i)
1880 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy));
1881 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
1882 // Find an operand that's safely divisible.
1883 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
1884 const SCEV *Op = M->getOperand(i);
1885 const SCEV *Div = getUDivExpr(Op, RHSC);
1886 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
1887 Operands = SmallVector<const SCEV *, 4>(M->op_begin(), M->op_end());
1889 return getMulExpr(Operands);
1893 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
1894 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(LHS)) {
1895 SmallVector<const SCEV *, 4> Operands;
1896 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i)
1897 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy));
1898 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
1900 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
1901 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
1902 if (isa<SCEVUDivExpr>(Op) || getMulExpr(Op, RHS) != A->getOperand(i))
1904 Operands.push_back(Op);
1906 if (Operands.size() == A->getNumOperands())
1907 return getAddExpr(Operands);
1911 // Fold if both operands are constant.
1912 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
1913 Constant *LHSCV = LHSC->getValue();
1914 Constant *RHSCV = RHSC->getValue();
1915 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
1920 FoldingSetNodeID ID;
1921 ID.AddInteger(scUDivExpr);
1925 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1926 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
1928 UniqueSCEVs.InsertNode(S, IP);
1933 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
1934 /// Simplify the expression as much as possible.
1935 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start,
1936 const SCEV *Step, const Loop *L,
1937 bool HasNUW, bool HasNSW) {
1938 SmallVector<const SCEV *, 4> Operands;
1939 Operands.push_back(Start);
1940 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
1941 if (StepChrec->getLoop() == L) {
1942 Operands.insert(Operands.end(), StepChrec->op_begin(),
1943 StepChrec->op_end());
1944 return getAddRecExpr(Operands, L);
1947 Operands.push_back(Step);
1948 return getAddRecExpr(Operands, L, HasNUW, HasNSW);
1951 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
1952 /// Simplify the expression as much as possible.
1954 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
1956 bool HasNUW, bool HasNSW) {
1957 if (Operands.size() == 1) return Operands[0];
1959 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
1960 assert(getEffectiveSCEVType(Operands[i]->getType()) ==
1961 getEffectiveSCEVType(Operands[0]->getType()) &&
1962 "SCEVAddRecExpr operand types don't match!");
1965 if (Operands.back()->isZero()) {
1966 Operands.pop_back();
1967 return getAddRecExpr(Operands, L, HasNUW, HasNSW); // {X,+,0} --> X
1970 // It's tempting to want to call getMaxBackedgeTakenCount count here and
1971 // use that information to infer NUW and NSW flags. However, computing a
1972 // BE count requires calling getAddRecExpr, so we may not yet have a
1973 // meaningful BE count at this point (and if we don't, we'd be stuck
1974 // with a SCEVCouldNotCompute as the cached BE count).
1976 // If HasNSW is true and all the operands are non-negative, infer HasNUW.
1977 if (!HasNUW && HasNSW) {
1979 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
1980 if (!isKnownNonNegative(Operands[i])) {
1984 if (All) HasNUW = true;
1987 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
1988 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
1989 const Loop *NestedLoop = NestedAR->getLoop();
1990 if (L->contains(NestedLoop->getHeader()) ?
1991 (L->getLoopDepth() < NestedLoop->getLoopDepth()) :
1992 (!NestedLoop->contains(L->getHeader()) &&
1993 DT->dominates(L->getHeader(), NestedLoop->getHeader()))) {
1994 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
1995 NestedAR->op_end());
1996 Operands[0] = NestedAR->getStart();
1997 // AddRecs require their operands be loop-invariant with respect to their
1998 // loops. Don't perform this transformation if it would break this
2000 bool AllInvariant = true;
2001 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2002 if (!Operands[i]->isLoopInvariant(L)) {
2003 AllInvariant = false;
2007 NestedOperands[0] = getAddRecExpr(Operands, L);
2008 AllInvariant = true;
2009 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i)
2010 if (!NestedOperands[i]->isLoopInvariant(NestedLoop)) {
2011 AllInvariant = false;
2015 // Ok, both add recurrences are valid after the transformation.
2016 return getAddRecExpr(NestedOperands, NestedLoop, HasNUW, HasNSW);
2018 // Reset Operands to its original state.
2019 Operands[0] = NestedAR;
2023 // Okay, it looks like we really DO need an addrec expr. Check to see if we
2024 // already have one, otherwise create a new one.
2025 FoldingSetNodeID ID;
2026 ID.AddInteger(scAddRecExpr);
2027 ID.AddInteger(Operands.size());
2028 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2029 ID.AddPointer(Operands[i]);
2033 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2035 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size());
2036 std::uninitialized_copy(Operands.begin(), Operands.end(), O);
2037 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator),
2038 O, Operands.size(), L);
2039 UniqueSCEVs.InsertNode(S, IP);
2041 if (HasNUW) S->setHasNoUnsignedWrap(true);
2042 if (HasNSW) S->setHasNoSignedWrap(true);
2046 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
2048 SmallVector<const SCEV *, 2> Ops;
2051 return getSMaxExpr(Ops);
2055 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2056 assert(!Ops.empty() && "Cannot get empty smax!");
2057 if (Ops.size() == 1) return Ops[0];
2059 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2060 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
2061 getEffectiveSCEVType(Ops[0]->getType()) &&
2062 "SCEVSMaxExpr operand types don't match!");
2065 // Sort by complexity, this groups all similar expression types together.
2066 GroupByComplexity(Ops, LI);
2068 // If there are any constants, fold them together.
2070 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2072 assert(Idx < Ops.size());
2073 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2074 // We found two constants, fold them together!
2075 ConstantInt *Fold = ConstantInt::get(getContext(),
2076 APIntOps::smax(LHSC->getValue()->getValue(),
2077 RHSC->getValue()->getValue()));
2078 Ops[0] = getConstant(Fold);
2079 Ops.erase(Ops.begin()+1); // Erase the folded element
2080 if (Ops.size() == 1) return Ops[0];
2081 LHSC = cast<SCEVConstant>(Ops[0]);
2084 // If we are left with a constant minimum-int, strip it off.
2085 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
2086 Ops.erase(Ops.begin());
2088 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
2089 // If we have an smax with a constant maximum-int, it will always be
2095 if (Ops.size() == 1) return Ops[0];
2097 // Find the first SMax
2098 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
2101 // Check to see if one of the operands is an SMax. If so, expand its operands
2102 // onto our operand list, and recurse to simplify.
2103 if (Idx < Ops.size()) {
2104 bool DeletedSMax = false;
2105 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
2106 Ops.insert(Ops.end(), SMax->op_begin(), SMax->op_end());
2107 Ops.erase(Ops.begin()+Idx);
2112 return getSMaxExpr(Ops);
2115 // Okay, check to see if the same value occurs in the operand list twice. If
2116 // so, delete one. Since we sorted the list, these values are required to
2118 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2119 if (Ops[i] == Ops[i+1]) { // X smax Y smax Y --> X smax Y
2120 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2124 if (Ops.size() == 1) return Ops[0];
2126 assert(!Ops.empty() && "Reduced smax down to nothing!");
2128 // Okay, it looks like we really DO need an smax expr. Check to see if we
2129 // already have one, otherwise create a new one.
2130 FoldingSetNodeID ID;
2131 ID.AddInteger(scSMaxExpr);
2132 ID.AddInteger(Ops.size());
2133 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2134 ID.AddPointer(Ops[i]);
2136 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2137 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2138 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2139 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator),
2141 UniqueSCEVs.InsertNode(S, IP);
2145 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
2147 SmallVector<const SCEV *, 2> Ops;
2150 return getUMaxExpr(Ops);
2154 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2155 assert(!Ops.empty() && "Cannot get empty umax!");
2156 if (Ops.size() == 1) return Ops[0];
2158 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2159 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
2160 getEffectiveSCEVType(Ops[0]->getType()) &&
2161 "SCEVUMaxExpr operand types don't match!");
2164 // Sort by complexity, this groups all similar expression types together.
2165 GroupByComplexity(Ops, LI);
2167 // If there are any constants, fold them together.
2169 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2171 assert(Idx < Ops.size());
2172 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2173 // We found two constants, fold them together!
2174 ConstantInt *Fold = ConstantInt::get(getContext(),
2175 APIntOps::umax(LHSC->getValue()->getValue(),
2176 RHSC->getValue()->getValue()));
2177 Ops[0] = getConstant(Fold);
2178 Ops.erase(Ops.begin()+1); // Erase the folded element
2179 if (Ops.size() == 1) return Ops[0];
2180 LHSC = cast<SCEVConstant>(Ops[0]);
2183 // If we are left with a constant minimum-int, strip it off.
2184 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
2185 Ops.erase(Ops.begin());
2187 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
2188 // If we have an umax with a constant maximum-int, it will always be
2194 if (Ops.size() == 1) return Ops[0];
2196 // Find the first UMax
2197 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
2200 // Check to see if one of the operands is a UMax. If so, expand its operands
2201 // onto our operand list, and recurse to simplify.
2202 if (Idx < Ops.size()) {
2203 bool DeletedUMax = false;
2204 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
2205 Ops.insert(Ops.end(), UMax->op_begin(), UMax->op_end());
2206 Ops.erase(Ops.begin()+Idx);
2211 return getUMaxExpr(Ops);
2214 // Okay, check to see if the same value occurs in the operand list twice. If
2215 // so, delete one. Since we sorted the list, these values are required to
2217 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2218 if (Ops[i] == Ops[i+1]) { // X umax Y umax Y --> X umax Y
2219 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2223 if (Ops.size() == 1) return Ops[0];
2225 assert(!Ops.empty() && "Reduced umax down to nothing!");
2227 // Okay, it looks like we really DO need a umax expr. Check to see if we
2228 // already have one, otherwise create a new one.
2229 FoldingSetNodeID ID;
2230 ID.AddInteger(scUMaxExpr);
2231 ID.AddInteger(Ops.size());
2232 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2233 ID.AddPointer(Ops[i]);
2235 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2236 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2237 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2238 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator),
2240 UniqueSCEVs.InsertNode(S, IP);
2244 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
2246 // ~smax(~x, ~y) == smin(x, y).
2247 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2250 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
2252 // ~umax(~x, ~y) == umin(x, y)
2253 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2256 const SCEV *ScalarEvolution::getSizeOfExpr(const Type *AllocTy) {
2257 // If we have TargetData, we can bypass creating a target-independent
2258 // constant expression and then folding it back into a ConstantInt.
2259 // This is just a compile-time optimization.
2261 return getConstant(TD->getIntPtrType(getContext()),
2262 TD->getTypeAllocSize(AllocTy));
2264 Constant *C = ConstantExpr::getSizeOf(AllocTy);
2265 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2266 C = ConstantFoldConstantExpression(CE, TD);
2267 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2268 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2271 const SCEV *ScalarEvolution::getAlignOfExpr(const Type *AllocTy) {
2272 Constant *C = ConstantExpr::getAlignOf(AllocTy);
2273 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2274 C = ConstantFoldConstantExpression(CE, TD);
2275 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2276 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2279 const SCEV *ScalarEvolution::getOffsetOfExpr(const StructType *STy,
2281 // If we have TargetData, we can bypass creating a target-independent
2282 // constant expression and then folding it back into a ConstantInt.
2283 // This is just a compile-time optimization.
2285 return getConstant(TD->getIntPtrType(getContext()),
2286 TD->getStructLayout(STy)->getElementOffset(FieldNo));
2288 Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo);
2289 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2290 C = ConstantFoldConstantExpression(CE, TD);
2291 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy));
2292 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2295 const SCEV *ScalarEvolution::getOffsetOfExpr(const Type *CTy,
2296 Constant *FieldNo) {
2297 Constant *C = ConstantExpr::getOffsetOf(CTy, FieldNo);
2298 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2299 C = ConstantFoldConstantExpression(CE, TD);
2300 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(CTy));
2301 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2304 const SCEV *ScalarEvolution::getUnknown(Value *V) {
2305 // Don't attempt to do anything other than create a SCEVUnknown object
2306 // here. createSCEV only calls getUnknown after checking for all other
2307 // interesting possibilities, and any other code that calls getUnknown
2308 // is doing so in order to hide a value from SCEV canonicalization.
2310 FoldingSetNodeID ID;
2311 ID.AddInteger(scUnknown);
2314 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2315 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V);
2316 UniqueSCEVs.InsertNode(S, IP);
2320 //===----------------------------------------------------------------------===//
2321 // Basic SCEV Analysis and PHI Idiom Recognition Code
2324 /// isSCEVable - Test if values of the given type are analyzable within
2325 /// the SCEV framework. This primarily includes integer types, and it
2326 /// can optionally include pointer types if the ScalarEvolution class
2327 /// has access to target-specific information.
2328 bool ScalarEvolution::isSCEVable(const Type *Ty) const {
2329 // Integers and pointers are always SCEVable.
2330 return Ty->isIntegerTy() || Ty->isPointerTy();
2333 /// getTypeSizeInBits - Return the size in bits of the specified type,
2334 /// for which isSCEVable must return true.
2335 uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const {
2336 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2338 // If we have a TargetData, use it!
2340 return TD->getTypeSizeInBits(Ty);
2342 // Integer types have fixed sizes.
2343 if (Ty->isIntegerTy())
2344 return Ty->getPrimitiveSizeInBits();
2346 // The only other support type is pointer. Without TargetData, conservatively
2347 // assume pointers are 64-bit.
2348 assert(Ty->isPointerTy() && "isSCEVable permitted a non-SCEVable type!");
2352 /// getEffectiveSCEVType - Return a type with the same bitwidth as
2353 /// the given type and which represents how SCEV will treat the given
2354 /// type, for which isSCEVable must return true. For pointer types,
2355 /// this is the pointer-sized integer type.
2356 const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const {
2357 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2359 if (Ty->isIntegerTy())
2362 // The only other support type is pointer.
2363 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
2364 if (TD) return TD->getIntPtrType(getContext());
2366 // Without TargetData, conservatively assume pointers are 64-bit.
2367 return Type::getInt64Ty(getContext());
2370 const SCEV *ScalarEvolution::getCouldNotCompute() {
2371 return &CouldNotCompute;
2374 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
2375 /// expression and create a new one.
2376 const SCEV *ScalarEvolution::getSCEV(Value *V) {
2377 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
2379 std::map<SCEVCallbackVH, const SCEV *>::iterator I = Scalars.find(V);
2380 if (I != Scalars.end()) return I->second;
2381 const SCEV *S = createSCEV(V);
2382 Scalars.insert(std::make_pair(SCEVCallbackVH(V, this), S));
2386 /// getIntegerSCEV - Given a SCEVable type, create a constant for the
2387 /// specified signed integer value and return a SCEV for the constant.
2388 const SCEV *ScalarEvolution::getIntegerSCEV(int64_t Val, const Type *Ty) {
2389 const IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty));
2390 return getConstant(ConstantInt::get(ITy, Val));
2393 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
2395 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) {
2396 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2398 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
2400 const Type *Ty = V->getType();
2401 Ty = getEffectiveSCEVType(Ty);
2402 return getMulExpr(V,
2403 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))));
2406 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
2407 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
2408 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2410 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
2412 const Type *Ty = V->getType();
2413 Ty = getEffectiveSCEVType(Ty);
2414 const SCEV *AllOnes =
2415 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
2416 return getMinusSCEV(AllOnes, V);
2419 /// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
2421 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS,
2424 return getAddExpr(LHS, getNegativeSCEV(RHS));
2427 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
2428 /// input value to the specified type. If the type must be extended, it is zero
2431 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V,
2433 const Type *SrcTy = V->getType();
2434 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2435 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2436 "Cannot truncate or zero extend with non-integer arguments!");
2437 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2438 return V; // No conversion
2439 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2440 return getTruncateExpr(V, Ty);
2441 return getZeroExtendExpr(V, Ty);
2444 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
2445 /// input value to the specified type. If the type must be extended, it is sign
2448 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
2450 const Type *SrcTy = V->getType();
2451 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2452 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2453 "Cannot truncate or zero extend with non-integer arguments!");
2454 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2455 return V; // No conversion
2456 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2457 return getTruncateExpr(V, Ty);
2458 return getSignExtendExpr(V, Ty);
2461 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
2462 /// input value to the specified type. If the type must be extended, it is zero
2463 /// extended. The conversion must not be narrowing.
2465 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, const Type *Ty) {
2466 const Type *SrcTy = V->getType();
2467 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2468 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2469 "Cannot noop or zero extend with non-integer arguments!");
2470 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2471 "getNoopOrZeroExtend cannot truncate!");
2472 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2473 return V; // No conversion
2474 return getZeroExtendExpr(V, Ty);
2477 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
2478 /// input value to the specified type. If the type must be extended, it is sign
2479 /// extended. The conversion must not be narrowing.
2481 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, const Type *Ty) {
2482 const Type *SrcTy = V->getType();
2483 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2484 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2485 "Cannot noop or sign extend with non-integer arguments!");
2486 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2487 "getNoopOrSignExtend cannot truncate!");
2488 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2489 return V; // No conversion
2490 return getSignExtendExpr(V, Ty);
2493 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
2494 /// the input value to the specified type. If the type must be extended,
2495 /// it is extended with unspecified bits. The conversion must not be
2498 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, const Type *Ty) {
2499 const Type *SrcTy = V->getType();
2500 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2501 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2502 "Cannot noop or any extend with non-integer arguments!");
2503 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2504 "getNoopOrAnyExtend cannot truncate!");
2505 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2506 return V; // No conversion
2507 return getAnyExtendExpr(V, Ty);
2510 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
2511 /// input value to the specified type. The conversion must not be widening.
2513 ScalarEvolution::getTruncateOrNoop(const SCEV *V, const Type *Ty) {
2514 const Type *SrcTy = V->getType();
2515 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2516 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2517 "Cannot truncate or noop with non-integer arguments!");
2518 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
2519 "getTruncateOrNoop cannot extend!");
2520 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2521 return V; // No conversion
2522 return getTruncateExpr(V, Ty);
2525 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
2526 /// the types using zero-extension, and then perform a umax operation
2528 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
2530 const SCEV *PromotedLHS = LHS;
2531 const SCEV *PromotedRHS = RHS;
2533 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2534 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2536 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2538 return getUMaxExpr(PromotedLHS, PromotedRHS);
2541 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
2542 /// the types using zero-extension, and then perform a umin operation
2544 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
2546 const SCEV *PromotedLHS = LHS;
2547 const SCEV *PromotedRHS = RHS;
2549 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2550 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2552 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2554 return getUMinExpr(PromotedLHS, PromotedRHS);
2557 /// PushDefUseChildren - Push users of the given Instruction
2558 /// onto the given Worklist.
2560 PushDefUseChildren(Instruction *I,
2561 SmallVectorImpl<Instruction *> &Worklist) {
2562 // Push the def-use children onto the Worklist stack.
2563 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end();
2565 Worklist.push_back(cast<Instruction>(UI));
2568 /// ForgetSymbolicValue - This looks up computed SCEV values for all
2569 /// instructions that depend on the given instruction and removes them from
2570 /// the Scalars map if they reference SymName. This is used during PHI
2573 ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) {
2574 SmallVector<Instruction *, 16> Worklist;
2575 PushDefUseChildren(PN, Worklist);
2577 SmallPtrSet<Instruction *, 8> Visited;
2579 while (!Worklist.empty()) {
2580 Instruction *I = Worklist.pop_back_val();
2581 if (!Visited.insert(I)) continue;
2583 std::map<SCEVCallbackVH, const SCEV *>::iterator It =
2584 Scalars.find(static_cast<Value *>(I));
2585 if (It != Scalars.end()) {
2586 // Short-circuit the def-use traversal if the symbolic name
2587 // ceases to appear in expressions.
2588 if (It->second != SymName && !It->second->hasOperand(SymName))
2591 // SCEVUnknown for a PHI either means that it has an unrecognized
2592 // structure, it's a PHI that's in the progress of being computed
2593 // by createNodeForPHI, or it's a single-value PHI. In the first case,
2594 // additional loop trip count information isn't going to change anything.
2595 // In the second case, createNodeForPHI will perform the necessary
2596 // updates on its own when it gets to that point. In the third, we do
2597 // want to forget the SCEVUnknown.
2598 if (!isa<PHINode>(I) ||
2599 !isa<SCEVUnknown>(It->second) ||
2600 (I != PN && It->second == SymName)) {
2601 ValuesAtScopes.erase(It->second);
2606 PushDefUseChildren(I, Worklist);
2610 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
2611 /// a loop header, making it a potential recurrence, or it doesn't.
2613 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
2614 if (const Loop *L = LI->getLoopFor(PN->getParent()))
2615 if (L->getHeader() == PN->getParent()) {
2616 // The loop may have multiple entrances or multiple exits; we can analyze
2617 // this phi as an addrec if it has a unique entry value and a unique
2619 Value *BEValueV = 0, *StartValueV = 0;
2620 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
2621 Value *V = PN->getIncomingValue(i);
2622 if (L->contains(PN->getIncomingBlock(i))) {
2625 } else if (BEValueV != V) {
2629 } else if (!StartValueV) {
2631 } else if (StartValueV != V) {
2636 if (BEValueV && StartValueV) {
2637 // While we are analyzing this PHI node, handle its value symbolically.
2638 const SCEV *SymbolicName = getUnknown(PN);
2639 assert(Scalars.find(PN) == Scalars.end() &&
2640 "PHI node already processed?");
2641 Scalars.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
2643 // Using this symbolic name for the PHI, analyze the value coming around
2645 const SCEV *BEValue = getSCEV(BEValueV);
2647 // NOTE: If BEValue is loop invariant, we know that the PHI node just
2648 // has a special value for the first iteration of the loop.
2650 // If the value coming around the backedge is an add with the symbolic
2651 // value we just inserted, then we found a simple induction variable!
2652 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
2653 // If there is a single occurrence of the symbolic value, replace it
2654 // with a recurrence.
2655 unsigned FoundIndex = Add->getNumOperands();
2656 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
2657 if (Add->getOperand(i) == SymbolicName)
2658 if (FoundIndex == e) {
2663 if (FoundIndex != Add->getNumOperands()) {
2664 // Create an add with everything but the specified operand.
2665 SmallVector<const SCEV *, 8> Ops;
2666 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
2667 if (i != FoundIndex)
2668 Ops.push_back(Add->getOperand(i));
2669 const SCEV *Accum = getAddExpr(Ops);
2671 // This is not a valid addrec if the step amount is varying each
2672 // loop iteration, but is not itself an addrec in this loop.
2673 if (Accum->isLoopInvariant(L) ||
2674 (isa<SCEVAddRecExpr>(Accum) &&
2675 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
2676 bool HasNUW = false;
2677 bool HasNSW = false;
2679 // If the increment doesn't overflow, then neither the addrec nor
2680 // the post-increment will overflow.
2681 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) {
2682 if (OBO->hasNoUnsignedWrap())
2684 if (OBO->hasNoSignedWrap())
2688 const SCEV *StartVal = getSCEV(StartValueV);
2689 const SCEV *PHISCEV =
2690 getAddRecExpr(StartVal, Accum, L, HasNUW, HasNSW);
2692 // Since the no-wrap flags are on the increment, they apply to the
2693 // post-incremented value as well.
2694 if (Accum->isLoopInvariant(L))
2695 (void)getAddRecExpr(getAddExpr(StartVal, Accum),
2696 Accum, L, HasNUW, HasNSW);
2698 // Okay, for the entire analysis of this edge we assumed the PHI
2699 // to be symbolic. We now need to go back and purge all of the
2700 // entries for the scalars that use the symbolic expression.
2701 ForgetSymbolicName(PN, SymbolicName);
2702 Scalars[SCEVCallbackVH(PN, this)] = PHISCEV;
2706 } else if (const SCEVAddRecExpr *AddRec =
2707 dyn_cast<SCEVAddRecExpr>(BEValue)) {
2708 // Otherwise, this could be a loop like this:
2709 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
2710 // In this case, j = {1,+,1} and BEValue is j.
2711 // Because the other in-value of i (0) fits the evolution of BEValue
2712 // i really is an addrec evolution.
2713 if (AddRec->getLoop() == L && AddRec->isAffine()) {
2714 const SCEV *StartVal = getSCEV(StartValueV);
2716 // If StartVal = j.start - j.stride, we can use StartVal as the
2717 // initial step of the addrec evolution.
2718 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
2719 AddRec->getOperand(1))) {
2720 const SCEV *PHISCEV =
2721 getAddRecExpr(StartVal, AddRec->getOperand(1), L);
2723 // Okay, for the entire analysis of this edge we assumed the PHI
2724 // to be symbolic. We now need to go back and purge all of the
2725 // entries for the scalars that use the symbolic expression.
2726 ForgetSymbolicName(PN, SymbolicName);
2727 Scalars[SCEVCallbackVH(PN, this)] = PHISCEV;
2735 // If the PHI has a single incoming value, follow that value, unless the
2736 // PHI's incoming blocks are in a different loop, in which case doing so
2737 // risks breaking LCSSA form. Instcombine would normally zap these, but
2738 // it doesn't have DominatorTree information, so it may miss cases.
2739 if (Value *V = PN->hasConstantValue(DT)) {
2740 bool AllSameLoop = true;
2741 Loop *PNLoop = LI->getLoopFor(PN->getParent());
2742 for (size_t i = 0, e = PN->getNumIncomingValues(); i != e; ++i)
2743 if (LI->getLoopFor(PN->getIncomingBlock(i)) != PNLoop) {
2744 AllSameLoop = false;
2751 // If it's not a loop phi, we can't handle it yet.
2752 return getUnknown(PN);
2755 /// createNodeForGEP - Expand GEP instructions into add and multiply
2756 /// operations. This allows them to be analyzed by regular SCEV code.
2758 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
2760 bool InBounds = GEP->isInBounds();
2761 const Type *IntPtrTy = getEffectiveSCEVType(GEP->getType());
2762 Value *Base = GEP->getOperand(0);
2763 // Don't attempt to analyze GEPs over unsized objects.
2764 if (!cast<PointerType>(Base->getType())->getElementType()->isSized())
2765 return getUnknown(GEP);
2766 const SCEV *TotalOffset = getIntegerSCEV(0, IntPtrTy);
2767 gep_type_iterator GTI = gep_type_begin(GEP);
2768 for (GetElementPtrInst::op_iterator I = next(GEP->op_begin()),
2772 // Compute the (potentially symbolic) offset in bytes for this index.
2773 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) {
2774 // For a struct, add the member offset.
2775 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
2776 TotalOffset = getAddExpr(TotalOffset,
2777 getOffsetOfExpr(STy, FieldNo),
2778 /*HasNUW=*/false, /*HasNSW=*/InBounds);
2780 // For an array, add the element offset, explicitly scaled.
2781 const SCEV *LocalOffset = getSCEV(Index);
2782 // Getelementptr indices are signed.
2783 LocalOffset = getTruncateOrSignExtend(LocalOffset, IntPtrTy);
2784 // Lower "inbounds" GEPs to NSW arithmetic.
2785 LocalOffset = getMulExpr(LocalOffset, getSizeOfExpr(*GTI),
2786 /*HasNUW=*/false, /*HasNSW=*/InBounds);
2787 TotalOffset = getAddExpr(TotalOffset, LocalOffset,
2788 /*HasNUW=*/false, /*HasNSW=*/InBounds);
2791 return getAddExpr(getSCEV(Base), TotalOffset,
2792 /*HasNUW=*/false, /*HasNSW=*/InBounds);
2795 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
2796 /// guaranteed to end in (at every loop iteration). It is, at the same time,
2797 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
2798 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
2800 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
2801 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
2802 return C->getValue()->getValue().countTrailingZeros();
2804 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
2805 return std::min(GetMinTrailingZeros(T->getOperand()),
2806 (uint32_t)getTypeSizeInBits(T->getType()));
2808 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
2809 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
2810 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
2811 getTypeSizeInBits(E->getType()) : OpRes;
2814 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
2815 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
2816 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
2817 getTypeSizeInBits(E->getType()) : OpRes;
2820 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
2821 // The result is the min of all operands results.
2822 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
2823 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
2824 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
2828 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
2829 // The result is the sum of all operands results.
2830 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
2831 uint32_t BitWidth = getTypeSizeInBits(M->getType());
2832 for (unsigned i = 1, e = M->getNumOperands();
2833 SumOpRes != BitWidth && i != e; ++i)
2834 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
2839 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
2840 // The result is the min of all operands results.
2841 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
2842 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
2843 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
2847 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
2848 // The result is the min of all operands results.
2849 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
2850 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
2851 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
2855 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
2856 // The result is the min of all operands results.
2857 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
2858 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
2859 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
2863 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
2864 // For a SCEVUnknown, ask ValueTracking.
2865 unsigned BitWidth = getTypeSizeInBits(U->getType());
2866 APInt Mask = APInt::getAllOnesValue(BitWidth);
2867 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
2868 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones);
2869 return Zeros.countTrailingOnes();
2876 /// getUnsignedRange - Determine the unsigned range for a particular SCEV.
2879 ScalarEvolution::getUnsignedRange(const SCEV *S) {
2881 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
2882 return ConstantRange(C->getValue()->getValue());
2884 unsigned BitWidth = getTypeSizeInBits(S->getType());
2885 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
2887 // If the value has known zeros, the maximum unsigned value will have those
2888 // known zeros as well.
2889 uint32_t TZ = GetMinTrailingZeros(S);
2891 ConservativeResult =
2892 ConstantRange(APInt::getMinValue(BitWidth),
2893 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
2895 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
2896 ConstantRange X = getUnsignedRange(Add->getOperand(0));
2897 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
2898 X = X.add(getUnsignedRange(Add->getOperand(i)));
2899 return ConservativeResult.intersectWith(X);
2902 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
2903 ConstantRange X = getUnsignedRange(Mul->getOperand(0));
2904 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
2905 X = X.multiply(getUnsignedRange(Mul->getOperand(i)));
2906 return ConservativeResult.intersectWith(X);
2909 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
2910 ConstantRange X = getUnsignedRange(SMax->getOperand(0));
2911 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
2912 X = X.smax(getUnsignedRange(SMax->getOperand(i)));
2913 return ConservativeResult.intersectWith(X);
2916 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
2917 ConstantRange X = getUnsignedRange(UMax->getOperand(0));
2918 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
2919 X = X.umax(getUnsignedRange(UMax->getOperand(i)));
2920 return ConservativeResult.intersectWith(X);
2923 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
2924 ConstantRange X = getUnsignedRange(UDiv->getLHS());
2925 ConstantRange Y = getUnsignedRange(UDiv->getRHS());
2926 return ConservativeResult.intersectWith(X.udiv(Y));
2929 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
2930 ConstantRange X = getUnsignedRange(ZExt->getOperand());
2931 return ConservativeResult.intersectWith(X.zeroExtend(BitWidth));
2934 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
2935 ConstantRange X = getUnsignedRange(SExt->getOperand());
2936 return ConservativeResult.intersectWith(X.signExtend(BitWidth));
2939 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
2940 ConstantRange X = getUnsignedRange(Trunc->getOperand());
2941 return ConservativeResult.intersectWith(X.truncate(BitWidth));
2944 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
2945 // If there's no unsigned wrap, the value will never be less than its
2947 if (AddRec->hasNoUnsignedWrap())
2948 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
2950 ConservativeResult =
2951 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0));
2953 // TODO: non-affine addrec
2954 if (AddRec->isAffine()) {
2955 const Type *Ty = AddRec->getType();
2956 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
2957 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
2958 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
2959 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
2961 const SCEV *Start = AddRec->getStart();
2962 const SCEV *Step = AddRec->getStepRecurrence(*this);
2964 ConstantRange StartRange = getUnsignedRange(Start);
2965 ConstantRange StepRange = getSignedRange(Step);
2966 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
2967 ConstantRange EndRange =
2968 StartRange.add(MaxBECountRange.multiply(StepRange));
2970 // Check for overflow. This must be done with ConstantRange arithmetic
2971 // because we could be called from within the ScalarEvolution overflow
2973 ConstantRange ExtStartRange = StartRange.zextOrTrunc(BitWidth*2+1);
2974 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
2975 ConstantRange ExtMaxBECountRange =
2976 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
2977 ConstantRange ExtEndRange = EndRange.zextOrTrunc(BitWidth*2+1);
2978 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
2980 return ConservativeResult;
2982 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(),
2983 EndRange.getUnsignedMin());
2984 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(),
2985 EndRange.getUnsignedMax());
2986 if (Min.isMinValue() && Max.isMaxValue())
2987 return ConservativeResult;
2988 return ConservativeResult.intersectWith(ConstantRange(Min, Max+1));
2992 return ConservativeResult;
2995 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
2996 // For a SCEVUnknown, ask ValueTracking.
2997 APInt Mask = APInt::getAllOnesValue(BitWidth);
2998 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
2999 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones, TD);
3000 if (Ones == ~Zeros + 1)
3001 return ConservativeResult;
3002 return ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1));
3005 return ConservativeResult;
3008 /// getSignedRange - Determine the signed range for a particular SCEV.
3011 ScalarEvolution::getSignedRange(const SCEV *S) {
3013 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3014 return ConstantRange(C->getValue()->getValue());
3016 unsigned BitWidth = getTypeSizeInBits(S->getType());
3017 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3019 // If the value has known zeros, the maximum signed value will have those
3020 // known zeros as well.
3021 uint32_t TZ = GetMinTrailingZeros(S);
3023 ConservativeResult =
3024 ConstantRange(APInt::getSignedMinValue(BitWidth),
3025 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
3027 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3028 ConstantRange X = getSignedRange(Add->getOperand(0));
3029 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3030 X = X.add(getSignedRange(Add->getOperand(i)));
3031 return ConservativeResult.intersectWith(X);
3034 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3035 ConstantRange X = getSignedRange(Mul->getOperand(0));
3036 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3037 X = X.multiply(getSignedRange(Mul->getOperand(i)));
3038 return ConservativeResult.intersectWith(X);
3041 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3042 ConstantRange X = getSignedRange(SMax->getOperand(0));
3043 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3044 X = X.smax(getSignedRange(SMax->getOperand(i)));
3045 return ConservativeResult.intersectWith(X);
3048 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3049 ConstantRange X = getSignedRange(UMax->getOperand(0));
3050 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3051 X = X.umax(getSignedRange(UMax->getOperand(i)));
3052 return ConservativeResult.intersectWith(X);
3055 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3056 ConstantRange X = getSignedRange(UDiv->getLHS());
3057 ConstantRange Y = getSignedRange(UDiv->getRHS());
3058 return ConservativeResult.intersectWith(X.udiv(Y));
3061 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3062 ConstantRange X = getSignedRange(ZExt->getOperand());
3063 return ConservativeResult.intersectWith(X.zeroExtend(BitWidth));
3066 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3067 ConstantRange X = getSignedRange(SExt->getOperand());
3068 return ConservativeResult.intersectWith(X.signExtend(BitWidth));
3071 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3072 ConstantRange X = getSignedRange(Trunc->getOperand());
3073 return ConservativeResult.intersectWith(X.truncate(BitWidth));
3076 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3077 // If there's no signed wrap, and all the operands have the same sign or
3078 // zero, the value won't ever change sign.
3079 if (AddRec->hasNoSignedWrap()) {
3080 bool AllNonNeg = true;
3081 bool AllNonPos = true;
3082 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
3083 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
3084 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
3087 ConservativeResult = ConservativeResult.intersectWith(
3088 ConstantRange(APInt(BitWidth, 0),
3089 APInt::getSignedMinValue(BitWidth)));
3091 ConservativeResult = ConservativeResult.intersectWith(
3092 ConstantRange(APInt::getSignedMinValue(BitWidth),
3093 APInt(BitWidth, 1)));
3096 // TODO: non-affine addrec
3097 if (AddRec->isAffine()) {
3098 const Type *Ty = AddRec->getType();
3099 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3100 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3101 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3102 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3104 const SCEV *Start = AddRec->getStart();
3105 const SCEV *Step = AddRec->getStepRecurrence(*this);
3107 ConstantRange StartRange = getSignedRange(Start);
3108 ConstantRange StepRange = getSignedRange(Step);
3109 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3110 ConstantRange EndRange =
3111 StartRange.add(MaxBECountRange.multiply(StepRange));
3113 // Check for overflow. This must be done with ConstantRange arithmetic
3114 // because we could be called from within the ScalarEvolution overflow
3116 ConstantRange ExtStartRange = StartRange.sextOrTrunc(BitWidth*2+1);
3117 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3118 ConstantRange ExtMaxBECountRange =
3119 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3120 ConstantRange ExtEndRange = EndRange.sextOrTrunc(BitWidth*2+1);
3121 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3123 return ConservativeResult;
3125 APInt Min = APIntOps::smin(StartRange.getSignedMin(),
3126 EndRange.getSignedMin());
3127 APInt Max = APIntOps::smax(StartRange.getSignedMax(),
3128 EndRange.getSignedMax());
3129 if (Min.isMinSignedValue() && Max.isMaxSignedValue())
3130 return ConservativeResult;
3131 return ConservativeResult.intersectWith(ConstantRange(Min, Max+1));
3135 return ConservativeResult;
3138 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3139 // For a SCEVUnknown, ask ValueTracking.
3140 if (!U->getValue()->getType()->isIntegerTy() && !TD)
3141 return ConservativeResult;
3142 unsigned NS = ComputeNumSignBits(U->getValue(), TD);
3144 return ConservativeResult;
3145 return ConservativeResult.intersectWith(
3146 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
3147 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1));
3150 return ConservativeResult;
3153 /// createSCEV - We know that there is no SCEV for the specified value.
3154 /// Analyze the expression.
3156 const SCEV *ScalarEvolution::createSCEV(Value *V) {
3157 if (!isSCEVable(V->getType()))
3158 return getUnknown(V);
3160 unsigned Opcode = Instruction::UserOp1;
3161 if (Instruction *I = dyn_cast<Instruction>(V)) {
3162 Opcode = I->getOpcode();
3164 // Don't attempt to analyze instructions in blocks that aren't
3165 // reachable. Such instructions don't matter, and they aren't required
3166 // to obey basic rules for definitions dominating uses which this
3167 // analysis depends on.
3168 if (!DT->isReachableFromEntry(I->getParent()))
3169 return getUnknown(V);
3170 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
3171 Opcode = CE->getOpcode();
3172 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
3173 return getConstant(CI);
3174 else if (isa<ConstantPointerNull>(V))
3175 return getIntegerSCEV(0, V->getType());
3176 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
3177 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee());
3179 return getUnknown(V);
3181 Operator *U = cast<Operator>(V);
3183 case Instruction::Add:
3184 // Don't transfer the NSW and NUW bits from the Add instruction to the
3185 // Add expression, because the Instruction may be guarded by control
3186 // flow and the no-overflow bits may not be valid for the expression in
3188 return getAddExpr(getSCEV(U->getOperand(0)),
3189 getSCEV(U->getOperand(1)));
3190 case Instruction::Mul:
3191 // Don't transfer the NSW and NUW bits from the Mul instruction to the
3192 // Mul expression, as with Add.
3193 return getMulExpr(getSCEV(U->getOperand(0)),
3194 getSCEV(U->getOperand(1)));
3195 case Instruction::UDiv:
3196 return getUDivExpr(getSCEV(U->getOperand(0)),
3197 getSCEV(U->getOperand(1)));
3198 case Instruction::Sub:
3199 return getMinusSCEV(getSCEV(U->getOperand(0)),
3200 getSCEV(U->getOperand(1)));
3201 case Instruction::And:
3202 // For an expression like x&255 that merely masks off the high bits,
3203 // use zext(trunc(x)) as the SCEV expression.
3204 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3205 if (CI->isNullValue())
3206 return getSCEV(U->getOperand(1));
3207 if (CI->isAllOnesValue())
3208 return getSCEV(U->getOperand(0));
3209 const APInt &A = CI->getValue();
3211 // Instcombine's ShrinkDemandedConstant may strip bits out of
3212 // constants, obscuring what would otherwise be a low-bits mask.
3213 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant
3214 // knew about to reconstruct a low-bits mask value.
3215 unsigned LZ = A.countLeadingZeros();
3216 unsigned BitWidth = A.getBitWidth();
3217 APInt AllOnes = APInt::getAllOnesValue(BitWidth);
3218 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
3219 ComputeMaskedBits(U->getOperand(0), AllOnes, KnownZero, KnownOne, TD);
3221 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ);
3223 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask))
3225 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)),
3226 IntegerType::get(getContext(), BitWidth - LZ)),
3231 case Instruction::Or:
3232 // If the RHS of the Or is a constant, we may have something like:
3233 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
3234 // optimizations will transparently handle this case.
3236 // In order for this transformation to be safe, the LHS must be of the
3237 // form X*(2^n) and the Or constant must be less than 2^n.
3238 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3239 const SCEV *LHS = getSCEV(U->getOperand(0));
3240 const APInt &CIVal = CI->getValue();
3241 if (GetMinTrailingZeros(LHS) >=
3242 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
3243 // Build a plain add SCEV.
3244 const SCEV *S = getAddExpr(LHS, getSCEV(CI));
3245 // If the LHS of the add was an addrec and it has no-wrap flags,
3246 // transfer the no-wrap flags, since an or won't introduce a wrap.
3247 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
3248 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
3249 if (OldAR->hasNoUnsignedWrap())
3250 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoUnsignedWrap(true);
3251 if (OldAR->hasNoSignedWrap())
3252 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoSignedWrap(true);
3258 case Instruction::Xor:
3259 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3260 // If the RHS of the xor is a signbit, then this is just an add.
3261 // Instcombine turns add of signbit into xor as a strength reduction step.
3262 if (CI->getValue().isSignBit())
3263 return getAddExpr(getSCEV(U->getOperand(0)),
3264 getSCEV(U->getOperand(1)));
3266 // If the RHS of xor is -1, then this is a not operation.
3267 if (CI->isAllOnesValue())
3268 return getNotSCEV(getSCEV(U->getOperand(0)));
3270 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
3271 // This is a variant of the check for xor with -1, and it handles
3272 // the case where instcombine has trimmed non-demanded bits out
3273 // of an xor with -1.
3274 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
3275 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
3276 if (BO->getOpcode() == Instruction::And &&
3277 LCI->getValue() == CI->getValue())
3278 if (const SCEVZeroExtendExpr *Z =
3279 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
3280 const Type *UTy = U->getType();
3281 const SCEV *Z0 = Z->getOperand();
3282 const Type *Z0Ty = Z0->getType();
3283 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
3285 // If C is a low-bits mask, the zero extend is serving to
3286 // mask off the high bits. Complement the operand and
3287 // re-apply the zext.
3288 if (APIntOps::isMask(Z0TySize, CI->getValue()))
3289 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
3291 // If C is a single bit, it may be in the sign-bit position
3292 // before the zero-extend. In this case, represent the xor
3293 // using an add, which is equivalent, and re-apply the zext.
3294 APInt Trunc = APInt(CI->getValue()).trunc(Z0TySize);
3295 if (APInt(Trunc).zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
3297 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
3303 case Instruction::Shl:
3304 // Turn shift left of a constant amount into a multiply.
3305 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3306 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3307 Constant *X = ConstantInt::get(getContext(),
3308 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
3309 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3313 case Instruction::LShr:
3314 // Turn logical shift right of a constant into a unsigned divide.
3315 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3316 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3317 Constant *X = ConstantInt::get(getContext(),
3318 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
3319 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3323 case Instruction::AShr:
3324 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
3325 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
3326 if (Instruction *L = dyn_cast<Instruction>(U->getOperand(0)))
3327 if (L->getOpcode() == Instruction::Shl &&
3328 L->getOperand(1) == U->getOperand(1)) {
3329 unsigned BitWidth = getTypeSizeInBits(U->getType());
3330 uint64_t Amt = BitWidth - CI->getZExtValue();
3331 if (Amt == BitWidth)
3332 return getSCEV(L->getOperand(0)); // shift by zero --> noop
3334 return getIntegerSCEV(0, U->getType()); // value is undefined
3336 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
3337 IntegerType::get(getContext(), Amt)),
3342 case Instruction::Trunc:
3343 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
3345 case Instruction::ZExt:
3346 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3348 case Instruction::SExt:
3349 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3351 case Instruction::BitCast:
3352 // BitCasts are no-op casts so we just eliminate the cast.
3353 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
3354 return getSCEV(U->getOperand(0));
3357 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
3358 // lead to pointer expressions which cannot safely be expanded to GEPs,
3359 // because ScalarEvolution doesn't respect the GEP aliasing rules when
3360 // simplifying integer expressions.
3362 case Instruction::GetElementPtr:
3363 return createNodeForGEP(cast<GEPOperator>(U));
3365 case Instruction::PHI:
3366 return createNodeForPHI(cast<PHINode>(U));
3368 case Instruction::Select:
3369 // This could be a smax or umax that was lowered earlier.
3370 // Try to recover it.
3371 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
3372 Value *LHS = ICI->getOperand(0);
3373 Value *RHS = ICI->getOperand(1);
3374 switch (ICI->getPredicate()) {
3375 case ICmpInst::ICMP_SLT:
3376 case ICmpInst::ICMP_SLE:
3377 std::swap(LHS, RHS);
3379 case ICmpInst::ICMP_SGT:
3380 case ICmpInst::ICMP_SGE:
3381 if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
3382 return getSMaxExpr(getSCEV(LHS), getSCEV(RHS));
3383 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
3384 return getSMinExpr(getSCEV(LHS), getSCEV(RHS));
3386 case ICmpInst::ICMP_ULT:
3387 case ICmpInst::ICMP_ULE:
3388 std::swap(LHS, RHS);
3390 case ICmpInst::ICMP_UGT:
3391 case ICmpInst::ICMP_UGE:
3392 if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
3393 return getUMaxExpr(getSCEV(LHS), getSCEV(RHS));
3394 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
3395 return getUMinExpr(getSCEV(LHS), getSCEV(RHS));
3397 case ICmpInst::ICMP_NE:
3398 // n != 0 ? n : 1 -> umax(n, 1)
3399 if (LHS == U->getOperand(1) &&
3400 isa<ConstantInt>(U->getOperand(2)) &&
3401 cast<ConstantInt>(U->getOperand(2))->isOne() &&
3402 isa<ConstantInt>(RHS) &&
3403 cast<ConstantInt>(RHS)->isZero())
3404 return getUMaxExpr(getSCEV(LHS), getSCEV(U->getOperand(2)));
3406 case ICmpInst::ICMP_EQ:
3407 // n == 0 ? 1 : n -> umax(n, 1)
3408 if (LHS == U->getOperand(2) &&
3409 isa<ConstantInt>(U->getOperand(1)) &&
3410 cast<ConstantInt>(U->getOperand(1))->isOne() &&
3411 isa<ConstantInt>(RHS) &&
3412 cast<ConstantInt>(RHS)->isZero())
3413 return getUMaxExpr(getSCEV(LHS), getSCEV(U->getOperand(1)));
3420 default: // We cannot analyze this expression.
3424 return getUnknown(V);
3429 //===----------------------------------------------------------------------===//
3430 // Iteration Count Computation Code
3433 /// getBackedgeTakenCount - If the specified loop has a predictable
3434 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
3435 /// object. The backedge-taken count is the number of times the loop header
3436 /// will be branched to from within the loop. This is one less than the
3437 /// trip count of the loop, since it doesn't count the first iteration,
3438 /// when the header is branched to from outside the loop.
3440 /// Note that it is not valid to call this method on a loop without a
3441 /// loop-invariant backedge-taken count (see
3442 /// hasLoopInvariantBackedgeTakenCount).
3444 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
3445 return getBackedgeTakenInfo(L).Exact;
3448 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
3449 /// return the least SCEV value that is known never to be less than the
3450 /// actual backedge taken count.
3451 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
3452 return getBackedgeTakenInfo(L).Max;
3455 /// PushLoopPHIs - Push PHI nodes in the header of the given loop
3456 /// onto the given Worklist.
3458 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
3459 BasicBlock *Header = L->getHeader();
3461 // Push all Loop-header PHIs onto the Worklist stack.
3462 for (BasicBlock::iterator I = Header->begin();
3463 PHINode *PN = dyn_cast<PHINode>(I); ++I)
3464 Worklist.push_back(PN);
3467 const ScalarEvolution::BackedgeTakenInfo &
3468 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
3469 // Initially insert a CouldNotCompute for this loop. If the insertion
3470 // succeeds, proceed to actually compute a backedge-taken count and
3471 // update the value. The temporary CouldNotCompute value tells SCEV
3472 // code elsewhere that it shouldn't attempt to request a new
3473 // backedge-taken count, which could result in infinite recursion.
3474 std::pair<std::map<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
3475 BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute()));
3477 BackedgeTakenInfo BECount = ComputeBackedgeTakenCount(L);
3478 if (BECount.Exact != getCouldNotCompute()) {
3479 assert(BECount.Exact->isLoopInvariant(L) &&
3480 BECount.Max->isLoopInvariant(L) &&
3481 "Computed backedge-taken count isn't loop invariant for loop!");
3482 ++NumTripCountsComputed;
3484 // Update the value in the map.
3485 Pair.first->second = BECount;
3487 if (BECount.Max != getCouldNotCompute())
3488 // Update the value in the map.
3489 Pair.first->second = BECount;
3490 if (isa<PHINode>(L->getHeader()->begin()))
3491 // Only count loops that have phi nodes as not being computable.
3492 ++NumTripCountsNotComputed;
3495 // Now that we know more about the trip count for this loop, forget any
3496 // existing SCEV values for PHI nodes in this loop since they are only
3497 // conservative estimates made without the benefit of trip count
3498 // information. This is similar to the code in forgetLoop, except that
3499 // it handles SCEVUnknown PHI nodes specially.
3500 if (BECount.hasAnyInfo()) {
3501 SmallVector<Instruction *, 16> Worklist;
3502 PushLoopPHIs(L, Worklist);
3504 SmallPtrSet<Instruction *, 8> Visited;
3505 while (!Worklist.empty()) {
3506 Instruction *I = Worklist.pop_back_val();
3507 if (!Visited.insert(I)) continue;
3509 std::map<SCEVCallbackVH, const SCEV *>::iterator It =
3510 Scalars.find(static_cast<Value *>(I));
3511 if (It != Scalars.end()) {
3512 // SCEVUnknown for a PHI either means that it has an unrecognized
3513 // structure, or it's a PHI that's in the progress of being computed
3514 // by createNodeForPHI. In the former case, additional loop trip
3515 // count information isn't going to change anything. In the later
3516 // case, createNodeForPHI will perform the necessary updates on its
3517 // own when it gets to that point.
3518 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(It->second)) {
3519 ValuesAtScopes.erase(It->second);
3522 if (PHINode *PN = dyn_cast<PHINode>(I))
3523 ConstantEvolutionLoopExitValue.erase(PN);
3526 PushDefUseChildren(I, Worklist);
3530 return Pair.first->second;
3533 /// forgetLoop - This method should be called by the client when it has
3534 /// changed a loop in a way that may effect ScalarEvolution's ability to
3535 /// compute a trip count, or if the loop is deleted.
3536 void ScalarEvolution::forgetLoop(const Loop *L) {
3537 // Drop any stored trip count value.
3538 BackedgeTakenCounts.erase(L);
3540 // Drop information about expressions based on loop-header PHIs.
3541 SmallVector<Instruction *, 16> Worklist;
3542 PushLoopPHIs(L, Worklist);
3544 SmallPtrSet<Instruction *, 8> Visited;
3545 while (!Worklist.empty()) {
3546 Instruction *I = Worklist.pop_back_val();
3547 if (!Visited.insert(I)) continue;
3549 std::map<SCEVCallbackVH, const SCEV *>::iterator It =
3550 Scalars.find(static_cast<Value *>(I));
3551 if (It != Scalars.end()) {
3552 ValuesAtScopes.erase(It->second);
3554 if (PHINode *PN = dyn_cast<PHINode>(I))
3555 ConstantEvolutionLoopExitValue.erase(PN);
3558 PushDefUseChildren(I, Worklist);
3562 /// forgetValue - This method should be called by the client when it has
3563 /// changed a value in a way that may effect its value, or which may
3564 /// disconnect it from a def-use chain linking it to a loop.
3565 void ScalarEvolution::forgetValue(Value *V) {
3566 Instruction *I = dyn_cast<Instruction>(V);
3569 // Drop information about expressions based on loop-header PHIs.
3570 SmallVector<Instruction *, 16> Worklist;
3571 Worklist.push_back(I);
3573 SmallPtrSet<Instruction *, 8> Visited;
3574 while (!Worklist.empty()) {
3575 I = Worklist.pop_back_val();
3576 if (!Visited.insert(I)) continue;
3578 std::map<SCEVCallbackVH, const SCEV *>::iterator It =
3579 Scalars.find(static_cast<Value *>(I));
3580 if (It != Scalars.end()) {
3581 ValuesAtScopes.erase(It->second);
3583 if (PHINode *PN = dyn_cast<PHINode>(I))
3584 ConstantEvolutionLoopExitValue.erase(PN);
3587 PushDefUseChildren(I, Worklist);
3591 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
3592 /// of the specified loop will execute.
3593 ScalarEvolution::BackedgeTakenInfo
3594 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
3595 SmallVector<BasicBlock *, 8> ExitingBlocks;
3596 L->getExitingBlocks(ExitingBlocks);
3598 // Examine all exits and pick the most conservative values.
3599 const SCEV *BECount = getCouldNotCompute();
3600 const SCEV *MaxBECount = getCouldNotCompute();
3601 bool CouldNotComputeBECount = false;
3602 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
3603 BackedgeTakenInfo NewBTI =
3604 ComputeBackedgeTakenCountFromExit(L, ExitingBlocks[i]);
3606 if (NewBTI.Exact == getCouldNotCompute()) {
3607 // We couldn't compute an exact value for this exit, so
3608 // we won't be able to compute an exact value for the loop.
3609 CouldNotComputeBECount = true;
3610 BECount = getCouldNotCompute();
3611 } else if (!CouldNotComputeBECount) {
3612 if (BECount == getCouldNotCompute())
3613 BECount = NewBTI.Exact;
3615 BECount = getUMinFromMismatchedTypes(BECount, NewBTI.Exact);
3617 if (MaxBECount == getCouldNotCompute())
3618 MaxBECount = NewBTI.Max;
3619 else if (NewBTI.Max != getCouldNotCompute())
3620 MaxBECount = getUMinFromMismatchedTypes(MaxBECount, NewBTI.Max);
3623 return BackedgeTakenInfo(BECount, MaxBECount);
3626 /// ComputeBackedgeTakenCountFromExit - Compute the number of times the backedge
3627 /// of the specified loop will execute if it exits via the specified block.
3628 ScalarEvolution::BackedgeTakenInfo
3629 ScalarEvolution::ComputeBackedgeTakenCountFromExit(const Loop *L,
3630 BasicBlock *ExitingBlock) {
3632 // Okay, we've chosen an exiting block. See what condition causes us to
3633 // exit at this block.
3635 // FIXME: we should be able to handle switch instructions (with a single exit)
3636 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
3637 if (ExitBr == 0) return getCouldNotCompute();
3638 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
3640 // At this point, we know we have a conditional branch that determines whether
3641 // the loop is exited. However, we don't know if the branch is executed each
3642 // time through the loop. If not, then the execution count of the branch will
3643 // not be equal to the trip count of the loop.
3645 // Currently we check for this by checking to see if the Exit branch goes to
3646 // the loop header. If so, we know it will always execute the same number of
3647 // times as the loop. We also handle the case where the exit block *is* the
3648 // loop header. This is common for un-rotated loops.
3650 // If both of those tests fail, walk up the unique predecessor chain to the
3651 // header, stopping if there is an edge that doesn't exit the loop. If the
3652 // header is reached, the execution count of the branch will be equal to the
3653 // trip count of the loop.
3655 // More extensive analysis could be done to handle more cases here.
3657 if (ExitBr->getSuccessor(0) != L->getHeader() &&
3658 ExitBr->getSuccessor(1) != L->getHeader() &&
3659 ExitBr->getParent() != L->getHeader()) {
3660 // The simple checks failed, try climbing the unique predecessor chain
3661 // up to the header.
3663 for (BasicBlock *BB = ExitBr->getParent(); BB; ) {
3664 BasicBlock *Pred = BB->getUniquePredecessor();
3666 return getCouldNotCompute();
3667 TerminatorInst *PredTerm = Pred->getTerminator();
3668 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) {
3669 BasicBlock *PredSucc = PredTerm->getSuccessor(i);
3672 // If the predecessor has a successor that isn't BB and isn't
3673 // outside the loop, assume the worst.
3674 if (L->contains(PredSucc))
3675 return getCouldNotCompute();
3677 if (Pred == L->getHeader()) {
3684 return getCouldNotCompute();
3687 // Proceed to the next level to examine the exit condition expression.
3688 return ComputeBackedgeTakenCountFromExitCond(L, ExitBr->getCondition(),
3689 ExitBr->getSuccessor(0),
3690 ExitBr->getSuccessor(1));
3693 /// ComputeBackedgeTakenCountFromExitCond - Compute the number of times the
3694 /// backedge of the specified loop will execute if its exit condition
3695 /// were a conditional branch of ExitCond, TBB, and FBB.
3696 ScalarEvolution::BackedgeTakenInfo
3697 ScalarEvolution::ComputeBackedgeTakenCountFromExitCond(const Loop *L,
3701 // Check if the controlling expression for this loop is an And or Or.
3702 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
3703 if (BO->getOpcode() == Instruction::And) {
3704 // Recurse on the operands of the and.
3705 BackedgeTakenInfo BTI0 =
3706 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB);
3707 BackedgeTakenInfo BTI1 =
3708 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB);
3709 const SCEV *BECount = getCouldNotCompute();
3710 const SCEV *MaxBECount = getCouldNotCompute();
3711 if (L->contains(TBB)) {
3712 // Both conditions must be true for the loop to continue executing.
3713 // Choose the less conservative count.
3714 if (BTI0.Exact == getCouldNotCompute() ||
3715 BTI1.Exact == getCouldNotCompute())
3716 BECount = getCouldNotCompute();
3718 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3719 if (BTI0.Max == getCouldNotCompute())
3720 MaxBECount = BTI1.Max;
3721 else if (BTI1.Max == getCouldNotCompute())
3722 MaxBECount = BTI0.Max;
3724 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max);
3726 // Both conditions must be true for the loop to exit.
3727 assert(L->contains(FBB) && "Loop block has no successor in loop!");
3728 if (BTI0.Exact != getCouldNotCompute() &&
3729 BTI1.Exact != getCouldNotCompute())
3730 BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3731 if (BTI0.Max != getCouldNotCompute() &&
3732 BTI1.Max != getCouldNotCompute())
3733 MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max);
3736 return BackedgeTakenInfo(BECount, MaxBECount);
3738 if (BO->getOpcode() == Instruction::Or) {
3739 // Recurse on the operands of the or.
3740 BackedgeTakenInfo BTI0 =
3741 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB);
3742 BackedgeTakenInfo BTI1 =
3743 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB);
3744 const SCEV *BECount = getCouldNotCompute();
3745 const SCEV *MaxBECount = getCouldNotCompute();
3746 if (L->contains(FBB)) {
3747 // Both conditions must be false for the loop to continue executing.
3748 // Choose the less conservative count.
3749 if (BTI0.Exact == getCouldNotCompute() ||
3750 BTI1.Exact == getCouldNotCompute())
3751 BECount = getCouldNotCompute();
3753 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3754 if (BTI0.Max == getCouldNotCompute())
3755 MaxBECount = BTI1.Max;
3756 else if (BTI1.Max == getCouldNotCompute())
3757 MaxBECount = BTI0.Max;
3759 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max);
3761 // Both conditions must be false for the loop to exit.
3762 assert(L->contains(TBB) && "Loop block has no successor in loop!");
3763 if (BTI0.Exact != getCouldNotCompute() &&
3764 BTI1.Exact != getCouldNotCompute())
3765 BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3766 if (BTI0.Max != getCouldNotCompute() &&
3767 BTI1.Max != getCouldNotCompute())
3768 MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max);
3771 return BackedgeTakenInfo(BECount, MaxBECount);
3775 // With an icmp, it may be feasible to compute an exact backedge-taken count.
3776 // Proceed to the next level to examine the icmp.
3777 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
3778 return ComputeBackedgeTakenCountFromExitCondICmp(L, ExitCondICmp, TBB, FBB);
3780 // Check for a constant condition. These are normally stripped out by
3781 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
3782 // preserve the CFG and is temporarily leaving constant conditions
3784 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
3785 if (L->contains(FBB) == !CI->getZExtValue())
3786 // The backedge is always taken.
3787 return getCouldNotCompute();
3789 // The backedge is never taken.
3790 return getIntegerSCEV(0, CI->getType());
3793 // If it's not an integer or pointer comparison then compute it the hard way.
3794 return ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB));
3797 /// ComputeBackedgeTakenCountFromExitCondICmp - Compute the number of times the
3798 /// backedge of the specified loop will execute if its exit condition
3799 /// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB.
3800 ScalarEvolution::BackedgeTakenInfo
3801 ScalarEvolution::ComputeBackedgeTakenCountFromExitCondICmp(const Loop *L,
3806 // If the condition was exit on true, convert the condition to exit on false
3807 ICmpInst::Predicate Cond;
3808 if (!L->contains(FBB))
3809 Cond = ExitCond->getPredicate();
3811 Cond = ExitCond->getInversePredicate();
3813 // Handle common loops like: for (X = "string"; *X; ++X)
3814 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
3815 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
3816 BackedgeTakenInfo ItCnt =
3817 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond);
3818 if (ItCnt.hasAnyInfo())
3822 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
3823 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
3825 // Try to evaluate any dependencies out of the loop.
3826 LHS = getSCEVAtScope(LHS, L);
3827 RHS = getSCEVAtScope(RHS, L);
3829 // At this point, we would like to compute how many iterations of the
3830 // loop the predicate will return true for these inputs.
3831 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) {
3832 // If there is a loop-invariant, force it into the RHS.
3833 std::swap(LHS, RHS);
3834 Cond = ICmpInst::getSwappedPredicate(Cond);
3837 // If we have a comparison of a chrec against a constant, try to use value
3838 // ranges to answer this query.
3839 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
3840 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
3841 if (AddRec->getLoop() == L) {
3842 // Form the constant range.
3843 ConstantRange CompRange(
3844 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
3846 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
3847 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
3851 case ICmpInst::ICMP_NE: { // while (X != Y)
3852 // Convert to: while (X-Y != 0)
3853 BackedgeTakenInfo BTI = HowFarToZero(getMinusSCEV(LHS, RHS), L);
3854 if (BTI.hasAnyInfo()) return BTI;
3857 case ICmpInst::ICMP_EQ: { // while (X == Y)
3858 // Convert to: while (X-Y == 0)
3859 BackedgeTakenInfo BTI = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
3860 if (BTI.hasAnyInfo()) return BTI;
3863 case ICmpInst::ICMP_SLT: {
3864 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true);
3865 if (BTI.hasAnyInfo()) return BTI;
3868 case ICmpInst::ICMP_SGT: {
3869 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
3870 getNotSCEV(RHS), L, true);
3871 if (BTI.hasAnyInfo()) return BTI;
3874 case ICmpInst::ICMP_ULT: {
3875 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false);
3876 if (BTI.hasAnyInfo()) return BTI;
3879 case ICmpInst::ICMP_UGT: {
3880 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
3881 getNotSCEV(RHS), L, false);
3882 if (BTI.hasAnyInfo()) return BTI;
3887 dbgs() << "ComputeBackedgeTakenCount ";
3888 if (ExitCond->getOperand(0)->getType()->isUnsigned())
3889 dbgs() << "[unsigned] ";
3890 dbgs() << *LHS << " "
3891 << Instruction::getOpcodeName(Instruction::ICmp)
3892 << " " << *RHS << "\n";
3897 ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB));
3900 static ConstantInt *
3901 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
3902 ScalarEvolution &SE) {
3903 const SCEV *InVal = SE.getConstant(C);
3904 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
3905 assert(isa<SCEVConstant>(Val) &&
3906 "Evaluation of SCEV at constant didn't fold correctly?");
3907 return cast<SCEVConstant>(Val)->getValue();
3910 /// GetAddressedElementFromGlobal - Given a global variable with an initializer
3911 /// and a GEP expression (missing the pointer index) indexing into it, return
3912 /// the addressed element of the initializer or null if the index expression is
3915 GetAddressedElementFromGlobal(GlobalVariable *GV,
3916 const std::vector<ConstantInt*> &Indices) {
3917 Constant *Init = GV->getInitializer();
3918 for (unsigned i = 0, e = Indices.size(); i != e; ++i) {
3919 uint64_t Idx = Indices[i]->getZExtValue();
3920 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) {
3921 assert(Idx < CS->getNumOperands() && "Bad struct index!");
3922 Init = cast<Constant>(CS->getOperand(Idx));
3923 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) {
3924 if (Idx >= CA->getNumOperands()) return 0; // Bogus program
3925 Init = cast<Constant>(CA->getOperand(Idx));
3926 } else if (isa<ConstantAggregateZero>(Init)) {
3927 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) {
3928 assert(Idx < STy->getNumElements() && "Bad struct index!");
3929 Init = Constant::getNullValue(STy->getElementType(Idx));
3930 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) {
3931 if (Idx >= ATy->getNumElements()) return 0; // Bogus program
3932 Init = Constant::getNullValue(ATy->getElementType());
3934 llvm_unreachable("Unknown constant aggregate type!");
3938 return 0; // Unknown initializer type
3944 /// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of
3945 /// 'icmp op load X, cst', try to see if we can compute the backedge
3946 /// execution count.
3947 ScalarEvolution::BackedgeTakenInfo
3948 ScalarEvolution::ComputeLoadConstantCompareBackedgeTakenCount(
3952 ICmpInst::Predicate predicate) {
3953 if (LI->isVolatile()) return getCouldNotCompute();
3955 // Check to see if the loaded pointer is a getelementptr of a global.
3956 // TODO: Use SCEV instead of manually grubbing with GEPs.
3957 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
3958 if (!GEP) return getCouldNotCompute();
3960 // Make sure that it is really a constant global we are gepping, with an
3961 // initializer, and make sure the first IDX is really 0.
3962 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
3963 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
3964 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
3965 !cast<Constant>(GEP->getOperand(1))->isNullValue())
3966 return getCouldNotCompute();
3968 // Okay, we allow one non-constant index into the GEP instruction.
3970 std::vector<ConstantInt*> Indexes;
3971 unsigned VarIdxNum = 0;
3972 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
3973 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
3974 Indexes.push_back(CI);
3975 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
3976 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
3977 VarIdx = GEP->getOperand(i);
3979 Indexes.push_back(0);
3982 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
3983 // Check to see if X is a loop variant variable value now.
3984 const SCEV *Idx = getSCEV(VarIdx);
3985 Idx = getSCEVAtScope(Idx, L);
3987 // We can only recognize very limited forms of loop index expressions, in
3988 // particular, only affine AddRec's like {C1,+,C2}.
3989 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
3990 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) ||
3991 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
3992 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
3993 return getCouldNotCompute();
3995 unsigned MaxSteps = MaxBruteForceIterations;
3996 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
3997 ConstantInt *ItCst = ConstantInt::get(
3998 cast<IntegerType>(IdxExpr->getType()), IterationNum);
3999 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
4001 // Form the GEP offset.
4002 Indexes[VarIdxNum] = Val;
4004 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes);
4005 if (Result == 0) break; // Cannot compute!
4007 // Evaluate the condition for this iteration.
4008 Result = ConstantExpr::getICmp(predicate, Result, RHS);
4009 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
4010 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
4012 dbgs() << "\n***\n*** Computed loop count " << *ItCst
4013 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
4016 ++NumArrayLenItCounts;
4017 return getConstant(ItCst); // Found terminating iteration!
4020 return getCouldNotCompute();
4024 /// CanConstantFold - Return true if we can constant fold an instruction of the
4025 /// specified type, assuming that all operands were constants.
4026 static bool CanConstantFold(const Instruction *I) {
4027 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
4028 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I))
4031 if (const CallInst *CI = dyn_cast<CallInst>(I))
4032 if (const Function *F = CI->getCalledFunction())
4033 return canConstantFoldCallTo(F);
4037 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
4038 /// in the loop that V is derived from. We allow arbitrary operations along the
4039 /// way, but the operands of an operation must either be constants or a value
4040 /// derived from a constant PHI. If this expression does not fit with these
4041 /// constraints, return null.
4042 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
4043 // If this is not an instruction, or if this is an instruction outside of the
4044 // loop, it can't be derived from a loop PHI.
4045 Instruction *I = dyn_cast<Instruction>(V);
4046 if (I == 0 || !L->contains(I)) return 0;
4048 if (PHINode *PN = dyn_cast<PHINode>(I)) {
4049 if (L->getHeader() == I->getParent())
4052 // We don't currently keep track of the control flow needed to evaluate
4053 // PHIs, so we cannot handle PHIs inside of loops.
4057 // If we won't be able to constant fold this expression even if the operands
4058 // are constants, return early.
4059 if (!CanConstantFold(I)) return 0;
4061 // Otherwise, we can evaluate this instruction if all of its operands are
4062 // constant or derived from a PHI node themselves.
4064 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op)
4065 if (!(isa<Constant>(I->getOperand(Op)) ||
4066 isa<GlobalValue>(I->getOperand(Op)))) {
4067 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L);
4068 if (P == 0) return 0; // Not evolving from PHI
4072 return 0; // Evolving from multiple different PHIs.
4075 // This is a expression evolving from a constant PHI!
4079 /// EvaluateExpression - Given an expression that passes the
4080 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
4081 /// in the loop has the value PHIVal. If we can't fold this expression for some
4082 /// reason, return null.
4083 static Constant *EvaluateExpression(Value *V, Constant *PHIVal,
4084 const TargetData *TD) {
4085 if (isa<PHINode>(V)) return PHIVal;
4086 if (Constant *C = dyn_cast<Constant>(V)) return C;
4087 if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) return GV;
4088 Instruction *I = cast<Instruction>(V);
4090 std::vector<Constant*> Operands;
4091 Operands.resize(I->getNumOperands());
4093 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
4094 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal, TD);
4095 if (Operands[i] == 0) return 0;
4098 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
4099 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
4101 return ConstantFoldInstOperands(I->getOpcode(), I->getType(),
4102 &Operands[0], Operands.size(), TD);
4105 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
4106 /// in the header of its containing loop, we know the loop executes a
4107 /// constant number of times, and the PHI node is just a recurrence
4108 /// involving constants, fold it.
4110 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
4113 std::map<PHINode*, Constant*>::iterator I =
4114 ConstantEvolutionLoopExitValue.find(PN);
4115 if (I != ConstantEvolutionLoopExitValue.end())
4118 if (BEs.ugt(MaxBruteForceIterations))
4119 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
4121 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
4123 // Since the loop is canonicalized, the PHI node must have two entries. One
4124 // entry must be a constant (coming in from outside of the loop), and the
4125 // second must be derived from the same PHI.
4126 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
4127 Constant *StartCST =
4128 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
4130 return RetVal = 0; // Must be a constant.
4132 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
4133 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
4135 return RetVal = 0; // Not derived from same PHI.
4137 // Execute the loop symbolically to determine the exit value.
4138 if (BEs.getActiveBits() >= 32)
4139 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
4141 unsigned NumIterations = BEs.getZExtValue(); // must be in range
4142 unsigned IterationNum = 0;
4143 for (Constant *PHIVal = StartCST; ; ++IterationNum) {
4144 if (IterationNum == NumIterations)
4145 return RetVal = PHIVal; // Got exit value!
4147 // Compute the value of the PHI node for the next iteration.
4148 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD);
4149 if (NextPHI == PHIVal)
4150 return RetVal = NextPHI; // Stopped evolving!
4152 return 0; // Couldn't evaluate!
4157 /// ComputeBackedgeTakenCountExhaustively - If the loop is known to execute a
4158 /// constant number of times (the condition evolves only from constants),
4159 /// try to evaluate a few iterations of the loop until we get the exit
4160 /// condition gets a value of ExitWhen (true or false). If we cannot
4161 /// evaluate the trip count of the loop, return getCouldNotCompute().
4163 ScalarEvolution::ComputeBackedgeTakenCountExhaustively(const Loop *L,
4166 PHINode *PN = getConstantEvolvingPHI(Cond, L);
4167 if (PN == 0) return getCouldNotCompute();
4169 // Since the loop is canonicalized, the PHI node must have two entries. One
4170 // entry must be a constant (coming in from outside of the loop), and the
4171 // second must be derived from the same PHI.
4172 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
4173 Constant *StartCST =
4174 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
4175 if (StartCST == 0) return getCouldNotCompute(); // Must be a constant.
4177 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
4178 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
4179 if (PN2 != PN) return getCouldNotCompute(); // Not derived from same PHI.
4181 // Okay, we find a PHI node that defines the trip count of this loop. Execute
4182 // the loop symbolically to determine when the condition gets a value of
4184 unsigned IterationNum = 0;
4185 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
4186 for (Constant *PHIVal = StartCST;
4187 IterationNum != MaxIterations; ++IterationNum) {
4188 ConstantInt *CondVal =
4189 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal, TD));
4191 // Couldn't symbolically evaluate.
4192 if (!CondVal) return getCouldNotCompute();
4194 if (CondVal->getValue() == uint64_t(ExitWhen)) {
4195 ++NumBruteForceTripCountsComputed;
4196 return getConstant(Type::getInt32Ty(getContext()), IterationNum);
4199 // Compute the value of the PHI node for the next iteration.
4200 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD);
4201 if (NextPHI == 0 || NextPHI == PHIVal)
4202 return getCouldNotCompute();// Couldn't evaluate or not making progress...
4206 // Too many iterations were needed to evaluate.
4207 return getCouldNotCompute();
4210 /// getSCEVAtScope - Return a SCEV expression for the specified value
4211 /// at the specified scope in the program. The L value specifies a loop
4212 /// nest to evaluate the expression at, where null is the top-level or a
4213 /// specified loop is immediately inside of the loop.
4215 /// This method can be used to compute the exit value for a variable defined
4216 /// in a loop by querying what the value will hold in the parent loop.
4218 /// In the case that a relevant loop exit value cannot be computed, the
4219 /// original value V is returned.
4220 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
4221 // Check to see if we've folded this expression at this loop before.
4222 std::map<const Loop *, const SCEV *> &Values = ValuesAtScopes[V];
4223 std::pair<std::map<const Loop *, const SCEV *>::iterator, bool> Pair =
4224 Values.insert(std::make_pair(L, static_cast<const SCEV *>(0)));
4226 return Pair.first->second ? Pair.first->second : V;
4228 // Otherwise compute it.
4229 const SCEV *C = computeSCEVAtScope(V, L);
4230 ValuesAtScopes[V][L] = C;
4234 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
4235 if (isa<SCEVConstant>(V)) return V;
4237 // If this instruction is evolved from a constant-evolving PHI, compute the
4238 // exit value from the loop without using SCEVs.
4239 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
4240 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
4241 const Loop *LI = (*this->LI)[I->getParent()];
4242 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
4243 if (PHINode *PN = dyn_cast<PHINode>(I))
4244 if (PN->getParent() == LI->getHeader()) {
4245 // Okay, there is no closed form solution for the PHI node. Check
4246 // to see if the loop that contains it has a known backedge-taken
4247 // count. If so, we may be able to force computation of the exit
4249 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
4250 if (const SCEVConstant *BTCC =
4251 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
4252 // Okay, we know how many times the containing loop executes. If
4253 // this is a constant evolving PHI node, get the final value at
4254 // the specified iteration number.
4255 Constant *RV = getConstantEvolutionLoopExitValue(PN,
4256 BTCC->getValue()->getValue(),
4258 if (RV) return getSCEV(RV);
4262 // Okay, this is an expression that we cannot symbolically evaluate
4263 // into a SCEV. Check to see if it's possible to symbolically evaluate
4264 // the arguments into constants, and if so, try to constant propagate the
4265 // result. This is particularly useful for computing loop exit values.
4266 if (CanConstantFold(I)) {
4267 std::vector<Constant*> Operands;
4268 Operands.reserve(I->getNumOperands());
4269 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
4270 Value *Op = I->getOperand(i);
4271 if (Constant *C = dyn_cast<Constant>(Op)) {
4272 Operands.push_back(C);
4274 // If any of the operands is non-constant and if they are
4275 // non-integer and non-pointer, don't even try to analyze them
4276 // with scev techniques.
4277 if (!isSCEVable(Op->getType()))
4280 const SCEV *OpV = getSCEVAtScope(Op, L);
4281 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) {
4282 Constant *C = SC->getValue();
4283 if (C->getType() != Op->getType())
4284 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
4288 Operands.push_back(C);
4289 } else if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) {
4290 if (Constant *C = dyn_cast<Constant>(SU->getValue())) {
4291 if (C->getType() != Op->getType())
4293 ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
4297 Operands.push_back(C);
4307 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
4308 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
4309 Operands[0], Operands[1], TD);
4311 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
4312 &Operands[0], Operands.size(), TD);
4318 // This is some other type of SCEVUnknown, just return it.
4322 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
4323 // Avoid performing the look-up in the common case where the specified
4324 // expression has no loop-variant portions.
4325 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
4326 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
4327 if (OpAtScope != Comm->getOperand(i)) {
4328 // Okay, at least one of these operands is loop variant but might be
4329 // foldable. Build a new instance of the folded commutative expression.
4330 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
4331 Comm->op_begin()+i);
4332 NewOps.push_back(OpAtScope);
4334 for (++i; i != e; ++i) {
4335 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
4336 NewOps.push_back(OpAtScope);
4338 if (isa<SCEVAddExpr>(Comm))
4339 return getAddExpr(NewOps);
4340 if (isa<SCEVMulExpr>(Comm))
4341 return getMulExpr(NewOps);
4342 if (isa<SCEVSMaxExpr>(Comm))
4343 return getSMaxExpr(NewOps);
4344 if (isa<SCEVUMaxExpr>(Comm))
4345 return getUMaxExpr(NewOps);
4346 llvm_unreachable("Unknown commutative SCEV type!");
4349 // If we got here, all operands are loop invariant.
4353 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
4354 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
4355 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
4356 if (LHS == Div->getLHS() && RHS == Div->getRHS())
4357 return Div; // must be loop invariant
4358 return getUDivExpr(LHS, RHS);
4361 // If this is a loop recurrence for a loop that does not contain L, then we
4362 // are dealing with the final value computed by the loop.
4363 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
4364 if (!L || !AddRec->getLoop()->contains(L)) {
4365 // To evaluate this recurrence, we need to know how many times the AddRec
4366 // loop iterates. Compute this now.
4367 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
4368 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
4370 // Then, evaluate the AddRec.
4371 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
4376 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
4377 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
4378 if (Op == Cast->getOperand())
4379 return Cast; // must be loop invariant
4380 return getZeroExtendExpr(Op, Cast->getType());
4383 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
4384 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
4385 if (Op == Cast->getOperand())
4386 return Cast; // must be loop invariant
4387 return getSignExtendExpr(Op, Cast->getType());
4390 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
4391 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
4392 if (Op == Cast->getOperand())
4393 return Cast; // must be loop invariant
4394 return getTruncateExpr(Op, Cast->getType());
4397 llvm_unreachable("Unknown SCEV type!");
4401 /// getSCEVAtScope - This is a convenience function which does
4402 /// getSCEVAtScope(getSCEV(V), L).
4403 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
4404 return getSCEVAtScope(getSCEV(V), L);
4407 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
4408 /// following equation:
4410 /// A * X = B (mod N)
4412 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
4413 /// A and B isn't important.
4415 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
4416 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
4417 ScalarEvolution &SE) {
4418 uint32_t BW = A.getBitWidth();
4419 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
4420 assert(A != 0 && "A must be non-zero.");
4424 // The gcd of A and N may have only one prime factor: 2. The number of
4425 // trailing zeros in A is its multiplicity
4426 uint32_t Mult2 = A.countTrailingZeros();
4429 // 2. Check if B is divisible by D.
4431 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
4432 // is not less than multiplicity of this prime factor for D.
4433 if (B.countTrailingZeros() < Mult2)
4434 return SE.getCouldNotCompute();
4436 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
4439 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
4440 // bit width during computations.
4441 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
4442 APInt Mod(BW + 1, 0);
4443 Mod.set(BW - Mult2); // Mod = N / D
4444 APInt I = AD.multiplicativeInverse(Mod);
4446 // 4. Compute the minimum unsigned root of the equation:
4447 // I * (B / D) mod (N / D)
4448 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
4450 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
4452 return SE.getConstant(Result.trunc(BW));
4455 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
4456 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
4457 /// might be the same) or two SCEVCouldNotCompute objects.
4459 static std::pair<const SCEV *,const SCEV *>
4460 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
4461 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
4462 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
4463 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
4464 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
4466 // We currently can only solve this if the coefficients are constants.
4467 if (!LC || !MC || !NC) {
4468 const SCEV *CNC = SE.getCouldNotCompute();
4469 return std::make_pair(CNC, CNC);
4472 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
4473 const APInt &L = LC->getValue()->getValue();
4474 const APInt &M = MC->getValue()->getValue();
4475 const APInt &N = NC->getValue()->getValue();
4476 APInt Two(BitWidth, 2);
4477 APInt Four(BitWidth, 4);
4480 using namespace APIntOps;
4482 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
4483 // The B coefficient is M-N/2
4487 // The A coefficient is N/2
4488 APInt A(N.sdiv(Two));
4490 // Compute the B^2-4ac term.
4493 SqrtTerm -= Four * (A * C);
4495 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
4496 // integer value or else APInt::sqrt() will assert.
4497 APInt SqrtVal(SqrtTerm.sqrt());
4499 // Compute the two solutions for the quadratic formula.
4500 // The divisions must be performed as signed divisions.
4502 APInt TwoA( A << 1 );
4503 if (TwoA.isMinValue()) {
4504 const SCEV *CNC = SE.getCouldNotCompute();
4505 return std::make_pair(CNC, CNC);
4508 LLVMContext &Context = SE.getContext();
4510 ConstantInt *Solution1 =
4511 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
4512 ConstantInt *Solution2 =
4513 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
4515 return std::make_pair(SE.getConstant(Solution1),
4516 SE.getConstant(Solution2));
4517 } // end APIntOps namespace
4520 /// HowFarToZero - Return the number of times a backedge comparing the specified
4521 /// value to zero will execute. If not computable, return CouldNotCompute.
4522 ScalarEvolution::BackedgeTakenInfo
4523 ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) {
4524 // If the value is a constant
4525 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
4526 // If the value is already zero, the branch will execute zero times.
4527 if (C->getValue()->isZero()) return C;
4528 return getCouldNotCompute(); // Otherwise it will loop infinitely.
4531 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
4532 if (!AddRec || AddRec->getLoop() != L)
4533 return getCouldNotCompute();
4535 if (AddRec->isAffine()) {
4536 // If this is an affine expression, the execution count of this branch is
4537 // the minimum unsigned root of the following equation:
4539 // Start + Step*N = 0 (mod 2^BW)
4543 // Step*N = -Start (mod 2^BW)
4545 // where BW is the common bit width of Start and Step.
4547 // Get the initial value for the loop.
4548 const SCEV *Start = getSCEVAtScope(AddRec->getStart(),
4549 L->getParentLoop());
4550 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1),
4551 L->getParentLoop());
4553 if (const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) {
4554 // For now we handle only constant steps.
4556 // First, handle unitary steps.
4557 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so:
4558 return getNegativeSCEV(Start); // N = -Start (as unsigned)
4559 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so:
4560 return Start; // N = Start (as unsigned)
4562 // Then, try to solve the above equation provided that Start is constant.
4563 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
4564 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
4565 -StartC->getValue()->getValue(),
4568 } else if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
4569 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
4570 // the quadratic equation to solve it.
4571 std::pair<const SCEV *,const SCEV *> Roots = SolveQuadraticEquation(AddRec,
4573 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
4574 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
4577 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1
4578 << " sol#2: " << *R2 << "\n";
4580 // Pick the smallest positive root value.
4581 if (ConstantInt *CB =
4582 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
4583 R1->getValue(), R2->getValue()))) {
4584 if (CB->getZExtValue() == false)
4585 std::swap(R1, R2); // R1 is the minimum root now.
4587 // We can only use this value if the chrec ends up with an exact zero
4588 // value at this index. When solving for "X*X != 5", for example, we
4589 // should not accept a root of 2.
4590 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
4592 return R1; // We found a quadratic root!
4597 return getCouldNotCompute();
4600 /// HowFarToNonZero - Return the number of times a backedge checking the
4601 /// specified value for nonzero will execute. If not computable, return
4603 ScalarEvolution::BackedgeTakenInfo
4604 ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
4605 // Loops that look like: while (X == 0) are very strange indeed. We don't
4606 // handle them yet except for the trivial case. This could be expanded in the
4607 // future as needed.
4609 // If the value is a constant, check to see if it is known to be non-zero
4610 // already. If so, the backedge will execute zero times.
4611 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
4612 if (!C->getValue()->isNullValue())
4613 return getIntegerSCEV(0, C->getType());
4614 return getCouldNotCompute(); // Otherwise it will loop infinitely.
4617 // We could implement others, but I really doubt anyone writes loops like
4618 // this, and if they did, they would already be constant folded.
4619 return getCouldNotCompute();
4622 /// getLoopPredecessor - If the given loop's header has exactly one unique
4623 /// predecessor outside the loop, return it. Otherwise return null.
4625 BasicBlock *ScalarEvolution::getLoopPredecessor(const Loop *L) {
4626 BasicBlock *Header = L->getHeader();
4627 BasicBlock *Pred = 0;
4628 for (pred_iterator PI = pred_begin(Header), E = pred_end(Header);
4630 if (!L->contains(*PI)) {
4631 if (Pred && Pred != *PI) return 0; // Multiple predecessors.
4637 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
4638 /// (which may not be an immediate predecessor) which has exactly one
4639 /// successor from which BB is reachable, or null if no such block is
4643 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
4644 // If the block has a unique predecessor, then there is no path from the
4645 // predecessor to the block that does not go through the direct edge
4646 // from the predecessor to the block.
4647 if (BasicBlock *Pred = BB->getSinglePredecessor())
4650 // A loop's header is defined to be a block that dominates the loop.
4651 // If the header has a unique predecessor outside the loop, it must be
4652 // a block that has exactly one successor that can reach the loop.
4653 if (Loop *L = LI->getLoopFor(BB))
4654 return getLoopPredecessor(L);
4659 /// HasSameValue - SCEV structural equivalence is usually sufficient for
4660 /// testing whether two expressions are equal, however for the purposes of
4661 /// looking for a condition guarding a loop, it can be useful to be a little
4662 /// more general, since a front-end may have replicated the controlling
4665 static bool HasSameValue(const SCEV *A, const SCEV *B) {
4666 // Quick check to see if they are the same SCEV.
4667 if (A == B) return true;
4669 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
4670 // two different instructions with the same value. Check for this case.
4671 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
4672 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
4673 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
4674 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
4675 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory())
4678 // Otherwise assume they may have a different value.
4682 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
4683 return getSignedRange(S).getSignedMax().isNegative();
4686 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
4687 return getSignedRange(S).getSignedMin().isStrictlyPositive();
4690 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
4691 return !getSignedRange(S).getSignedMin().isNegative();
4694 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
4695 return !getSignedRange(S).getSignedMax().isStrictlyPositive();
4698 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
4699 return isKnownNegative(S) || isKnownPositive(S);
4702 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
4703 const SCEV *LHS, const SCEV *RHS) {
4704 // If LHS or RHS is an addrec, check to see if the condition is true in
4705 // every iteration of the loop.
4706 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
4707 if (isLoopEntryGuardedByCond(
4708 AR->getLoop(), Pred, AR->getStart(), RHS) &&
4709 isLoopBackedgeGuardedByCond(
4710 AR->getLoop(), Pred,
4711 getAddExpr(AR, AR->getStepRecurrence(*this)), RHS))
4713 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS))
4714 if (isLoopEntryGuardedByCond(
4715 AR->getLoop(), Pred, LHS, AR->getStart()) &&
4716 isLoopBackedgeGuardedByCond(
4717 AR->getLoop(), Pred,
4718 LHS, getAddExpr(AR, AR->getStepRecurrence(*this))))
4721 // Otherwise see what can be done with known constant ranges.
4722 return isKnownPredicateWithRanges(Pred, LHS, RHS);
4726 ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred,
4727 const SCEV *LHS, const SCEV *RHS) {
4728 if (HasSameValue(LHS, RHS))
4729 return ICmpInst::isTrueWhenEqual(Pred);
4731 // This code is split out from isKnownPredicate because it is called from
4732 // within isLoopEntryGuardedByCond.
4735 llvm_unreachable("Unexpected ICmpInst::Predicate value!");
4737 case ICmpInst::ICMP_SGT:
4738 Pred = ICmpInst::ICMP_SLT;
4739 std::swap(LHS, RHS);
4740 case ICmpInst::ICMP_SLT: {
4741 ConstantRange LHSRange = getSignedRange(LHS);
4742 ConstantRange RHSRange = getSignedRange(RHS);
4743 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
4745 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
4749 case ICmpInst::ICMP_SGE:
4750 Pred = ICmpInst::ICMP_SLE;
4751 std::swap(LHS, RHS);
4752 case ICmpInst::ICMP_SLE: {
4753 ConstantRange LHSRange = getSignedRange(LHS);
4754 ConstantRange RHSRange = getSignedRange(RHS);
4755 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
4757 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
4761 case ICmpInst::ICMP_UGT:
4762 Pred = ICmpInst::ICMP_ULT;
4763 std::swap(LHS, RHS);
4764 case ICmpInst::ICMP_ULT: {
4765 ConstantRange LHSRange = getUnsignedRange(LHS);
4766 ConstantRange RHSRange = getUnsignedRange(RHS);
4767 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
4769 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
4773 case ICmpInst::ICMP_UGE:
4774 Pred = ICmpInst::ICMP_ULE;
4775 std::swap(LHS, RHS);
4776 case ICmpInst::ICMP_ULE: {
4777 ConstantRange LHSRange = getUnsignedRange(LHS);
4778 ConstantRange RHSRange = getUnsignedRange(RHS);
4779 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
4781 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
4785 case ICmpInst::ICMP_NE: {
4786 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
4788 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
4791 const SCEV *Diff = getMinusSCEV(LHS, RHS);
4792 if (isKnownNonZero(Diff))
4796 case ICmpInst::ICMP_EQ:
4797 // The check at the top of the function catches the case where
4798 // the values are known to be equal.
4804 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
4805 /// protected by a conditional between LHS and RHS. This is used to
4806 /// to eliminate casts.
4808 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
4809 ICmpInst::Predicate Pred,
4810 const SCEV *LHS, const SCEV *RHS) {
4811 // Interpret a null as meaning no loop, where there is obviously no guard
4812 // (interprocedural conditions notwithstanding).
4813 if (!L) return true;
4815 BasicBlock *Latch = L->getLoopLatch();
4819 BranchInst *LoopContinuePredicate =
4820 dyn_cast<BranchInst>(Latch->getTerminator());
4821 if (!LoopContinuePredicate ||
4822 LoopContinuePredicate->isUnconditional())
4825 return isImpliedCond(LoopContinuePredicate->getCondition(), Pred, LHS, RHS,
4826 LoopContinuePredicate->getSuccessor(0) != L->getHeader());
4829 /// isLoopEntryGuardedByCond - Test whether entry to the loop is protected
4830 /// by a conditional between LHS and RHS. This is used to help avoid max
4831 /// expressions in loop trip counts, and to eliminate casts.
4833 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
4834 ICmpInst::Predicate Pred,
4835 const SCEV *LHS, const SCEV *RHS) {
4836 // Interpret a null as meaning no loop, where there is obviously no guard
4837 // (interprocedural conditions notwithstanding).
4838 if (!L) return false;
4840 BasicBlock *Predecessor = getLoopPredecessor(L);
4841 BasicBlock *PredecessorDest = L->getHeader();
4843 // Starting at the loop predecessor, climb up the predecessor chain, as long
4844 // as there are predecessors that can be found that have unique successors
4845 // leading to the original header.
4847 PredecessorDest = Predecessor,
4848 Predecessor = getPredecessorWithUniqueSuccessorForBB(Predecessor)) {
4850 BranchInst *LoopEntryPredicate =
4851 dyn_cast<BranchInst>(Predecessor->getTerminator());
4852 if (!LoopEntryPredicate ||
4853 LoopEntryPredicate->isUnconditional())
4856 if (isImpliedCond(LoopEntryPredicate->getCondition(), Pred, LHS, RHS,
4857 LoopEntryPredicate->getSuccessor(0) != PredecessorDest))
4864 /// isImpliedCond - Test whether the condition described by Pred, LHS,
4865 /// and RHS is true whenever the given Cond value evaluates to true.
4866 bool ScalarEvolution::isImpliedCond(Value *CondValue,
4867 ICmpInst::Predicate Pred,
4868 const SCEV *LHS, const SCEV *RHS,
4870 // Recursively handle And and Or conditions.
4871 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(CondValue)) {
4872 if (BO->getOpcode() == Instruction::And) {
4874 return isImpliedCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) ||
4875 isImpliedCond(BO->getOperand(1), Pred, LHS, RHS, Inverse);
4876 } else if (BO->getOpcode() == Instruction::Or) {
4878 return isImpliedCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) ||
4879 isImpliedCond(BO->getOperand(1), Pred, LHS, RHS, Inverse);
4883 ICmpInst *ICI = dyn_cast<ICmpInst>(CondValue);
4884 if (!ICI) return false;
4886 // Bail if the ICmp's operands' types are wider than the needed type
4887 // before attempting to call getSCEV on them. This avoids infinite
4888 // recursion, since the analysis of widening casts can require loop
4889 // exit condition information for overflow checking, which would
4891 if (getTypeSizeInBits(LHS->getType()) <
4892 getTypeSizeInBits(ICI->getOperand(0)->getType()))
4895 // Now that we found a conditional branch that dominates the loop, check to
4896 // see if it is the comparison we are looking for.
4897 ICmpInst::Predicate FoundPred;
4899 FoundPred = ICI->getInversePredicate();
4901 FoundPred = ICI->getPredicate();
4903 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
4904 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
4906 // Balance the types. The case where FoundLHS' type is wider than
4907 // LHS' type is checked for above.
4908 if (getTypeSizeInBits(LHS->getType()) >
4909 getTypeSizeInBits(FoundLHS->getType())) {
4910 if (CmpInst::isSigned(Pred)) {
4911 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
4912 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
4914 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
4915 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
4919 // Canonicalize the query to match the way instcombine will have
4920 // canonicalized the comparison.
4921 // First, put a constant operand on the right.
4922 if (isa<SCEVConstant>(LHS)) {
4923 std::swap(LHS, RHS);
4924 Pred = ICmpInst::getSwappedPredicate(Pred);
4926 // Then, canonicalize comparisons with boundary cases.
4927 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
4928 const APInt &RA = RC->getValue()->getValue();
4930 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
4931 case ICmpInst::ICMP_EQ:
4932 case ICmpInst::ICMP_NE:
4934 case ICmpInst::ICMP_UGE:
4935 if ((RA - 1).isMinValue()) {
4936 Pred = ICmpInst::ICMP_NE;
4937 RHS = getConstant(RA - 1);
4940 if (RA.isMaxValue()) {
4941 Pred = ICmpInst::ICMP_EQ;
4944 if (RA.isMinValue()) return true;
4946 case ICmpInst::ICMP_ULE:
4947 if ((RA + 1).isMaxValue()) {
4948 Pred = ICmpInst::ICMP_NE;
4949 RHS = getConstant(RA + 1);
4952 if (RA.isMinValue()) {
4953 Pred = ICmpInst::ICMP_EQ;
4956 if (RA.isMaxValue()) return true;
4958 case ICmpInst::ICMP_SGE:
4959 if ((RA - 1).isMinSignedValue()) {
4960 Pred = ICmpInst::ICMP_NE;
4961 RHS = getConstant(RA - 1);
4964 if (RA.isMaxSignedValue()) {
4965 Pred = ICmpInst::ICMP_EQ;
4968 if (RA.isMinSignedValue()) return true;
4970 case ICmpInst::ICMP_SLE:
4971 if ((RA + 1).isMaxSignedValue()) {
4972 Pred = ICmpInst::ICMP_NE;
4973 RHS = getConstant(RA + 1);
4976 if (RA.isMinSignedValue()) {
4977 Pred = ICmpInst::ICMP_EQ;
4980 if (RA.isMaxSignedValue()) return true;
4982 case ICmpInst::ICMP_UGT:
4983 if (RA.isMinValue()) {
4984 Pred = ICmpInst::ICMP_NE;
4987 if ((RA + 1).isMaxValue()) {
4988 Pred = ICmpInst::ICMP_EQ;
4989 RHS = getConstant(RA + 1);
4992 if (RA.isMaxValue()) return false;
4994 case ICmpInst::ICMP_ULT:
4995 if (RA.isMaxValue()) {
4996 Pred = ICmpInst::ICMP_NE;
4999 if ((RA - 1).isMinValue()) {
5000 Pred = ICmpInst::ICMP_EQ;
5001 RHS = getConstant(RA - 1);
5004 if (RA.isMinValue()) return false;
5006 case ICmpInst::ICMP_SGT:
5007 if (RA.isMinSignedValue()) {
5008 Pred = ICmpInst::ICMP_NE;
5011 if ((RA + 1).isMaxSignedValue()) {
5012 Pred = ICmpInst::ICMP_EQ;
5013 RHS = getConstant(RA + 1);
5016 if (RA.isMaxSignedValue()) return false;
5018 case ICmpInst::ICMP_SLT:
5019 if (RA.isMaxSignedValue()) {
5020 Pred = ICmpInst::ICMP_NE;
5023 if ((RA - 1).isMinSignedValue()) {
5024 Pred = ICmpInst::ICMP_EQ;
5025 RHS = getConstant(RA - 1);
5028 if (RA.isMinSignedValue()) return false;
5033 // Check to see if we can make the LHS or RHS match.
5034 if (LHS == FoundRHS || RHS == FoundLHS) {
5035 if (isa<SCEVConstant>(RHS)) {
5036 std::swap(FoundLHS, FoundRHS);
5037 FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
5039 std::swap(LHS, RHS);
5040 Pred = ICmpInst::getSwappedPredicate(Pred);
5044 // Check whether the found predicate is the same as the desired predicate.
5045 if (FoundPred == Pred)
5046 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
5048 // Check whether swapping the found predicate makes it the same as the
5049 // desired predicate.
5050 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
5051 if (isa<SCEVConstant>(RHS))
5052 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
5054 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
5055 RHS, LHS, FoundLHS, FoundRHS);
5058 // Check whether the actual condition is beyond sufficient.
5059 if (FoundPred == ICmpInst::ICMP_EQ)
5060 if (ICmpInst::isTrueWhenEqual(Pred))
5061 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
5063 if (Pred == ICmpInst::ICMP_NE)
5064 if (!ICmpInst::isTrueWhenEqual(FoundPred))
5065 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
5068 // Otherwise assume the worst.
5072 /// isImpliedCondOperands - Test whether the condition described by Pred,
5073 /// LHS, and RHS is true whenever the condition described by Pred, FoundLHS,
5074 /// and FoundRHS is true.
5075 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
5076 const SCEV *LHS, const SCEV *RHS,
5077 const SCEV *FoundLHS,
5078 const SCEV *FoundRHS) {
5079 return isImpliedCondOperandsHelper(Pred, LHS, RHS,
5080 FoundLHS, FoundRHS) ||
5081 // ~x < ~y --> x > y
5082 isImpliedCondOperandsHelper(Pred, LHS, RHS,
5083 getNotSCEV(FoundRHS),
5084 getNotSCEV(FoundLHS));
5087 /// isImpliedCondOperandsHelper - Test whether the condition described by
5088 /// Pred, LHS, and RHS is true whenever the condition described by Pred,
5089 /// FoundLHS, and FoundRHS is true.
5091 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
5092 const SCEV *LHS, const SCEV *RHS,
5093 const SCEV *FoundLHS,
5094 const SCEV *FoundRHS) {
5096 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
5097 case ICmpInst::ICMP_EQ:
5098 case ICmpInst::ICMP_NE:
5099 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
5102 case ICmpInst::ICMP_SLT:
5103 case ICmpInst::ICMP_SLE:
5104 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
5105 isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, RHS, FoundRHS))
5108 case ICmpInst::ICMP_SGT:
5109 case ICmpInst::ICMP_SGE:
5110 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
5111 isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, RHS, FoundRHS))
5114 case ICmpInst::ICMP_ULT:
5115 case ICmpInst::ICMP_ULE:
5116 if (isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
5117 isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, RHS, FoundRHS))
5120 case ICmpInst::ICMP_UGT:
5121 case ICmpInst::ICMP_UGE:
5122 if (isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
5123 isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, RHS, FoundRHS))
5131 /// getBECount - Subtract the end and start values and divide by the step,
5132 /// rounding up, to get the number of times the backedge is executed. Return
5133 /// CouldNotCompute if an intermediate computation overflows.
5134 const SCEV *ScalarEvolution::getBECount(const SCEV *Start,
5138 assert(!isKnownNegative(Step) &&
5139 "This code doesn't handle negative strides yet!");
5141 const Type *Ty = Start->getType();
5142 const SCEV *NegOne = getIntegerSCEV(-1, Ty);
5143 const SCEV *Diff = getMinusSCEV(End, Start);
5144 const SCEV *RoundUp = getAddExpr(Step, NegOne);
5146 // Add an adjustment to the difference between End and Start so that
5147 // the division will effectively round up.
5148 const SCEV *Add = getAddExpr(Diff, RoundUp);
5151 // Check Add for unsigned overflow.
5152 // TODO: More sophisticated things could be done here.
5153 const Type *WideTy = IntegerType::get(getContext(),
5154 getTypeSizeInBits(Ty) + 1);
5155 const SCEV *EDiff = getZeroExtendExpr(Diff, WideTy);
5156 const SCEV *ERoundUp = getZeroExtendExpr(RoundUp, WideTy);
5157 const SCEV *OperandExtendedAdd = getAddExpr(EDiff, ERoundUp);
5158 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd)
5159 return getCouldNotCompute();
5162 return getUDivExpr(Add, Step);
5165 /// HowManyLessThans - Return the number of times a backedge containing the
5166 /// specified less-than comparison will execute. If not computable, return
5167 /// CouldNotCompute.
5168 ScalarEvolution::BackedgeTakenInfo
5169 ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
5170 const Loop *L, bool isSigned) {
5171 // Only handle: "ADDREC < LoopInvariant".
5172 if (!RHS->isLoopInvariant(L)) return getCouldNotCompute();
5174 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
5175 if (!AddRec || AddRec->getLoop() != L)
5176 return getCouldNotCompute();
5178 // Check to see if we have a flag which makes analysis easy.
5179 bool NoWrap = isSigned ? AddRec->hasNoSignedWrap() :
5180 AddRec->hasNoUnsignedWrap();
5182 if (AddRec->isAffine()) {
5183 unsigned BitWidth = getTypeSizeInBits(AddRec->getType());
5184 const SCEV *Step = AddRec->getStepRecurrence(*this);
5187 return getCouldNotCompute();
5188 if (Step->isOne()) {
5189 // With unit stride, the iteration never steps past the limit value.
5190 } else if (isKnownPositive(Step)) {
5191 // Test whether a positive iteration can step past the limit
5192 // value and past the maximum value for its type in a single step.
5193 // Note that it's not sufficient to check NoWrap here, because even
5194 // though the value after a wrap is undefined, it's not undefined
5195 // behavior, so if wrap does occur, the loop could either terminate or
5196 // loop infinitely, but in either case, the loop is guaranteed to
5197 // iterate at least until the iteration where the wrapping occurs.
5198 const SCEV *One = getIntegerSCEV(1, Step->getType());
5200 APInt Max = APInt::getSignedMaxValue(BitWidth);
5201 if ((Max - getSignedRange(getMinusSCEV(Step, One)).getSignedMax())
5202 .slt(getSignedRange(RHS).getSignedMax()))
5203 return getCouldNotCompute();
5205 APInt Max = APInt::getMaxValue(BitWidth);
5206 if ((Max - getUnsignedRange(getMinusSCEV(Step, One)).getUnsignedMax())
5207 .ult(getUnsignedRange(RHS).getUnsignedMax()))
5208 return getCouldNotCompute();
5211 // TODO: Handle negative strides here and below.
5212 return getCouldNotCompute();
5214 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant
5215 // m. So, we count the number of iterations in which {n,+,s} < m is true.
5216 // Note that we cannot simply return max(m-n,0)/s because it's not safe to
5217 // treat m-n as signed nor unsigned due to overflow possibility.
5219 // First, we get the value of the LHS in the first iteration: n
5220 const SCEV *Start = AddRec->getOperand(0);
5222 // Determine the minimum constant start value.
5223 const SCEV *MinStart = getConstant(isSigned ?
5224 getSignedRange(Start).getSignedMin() :
5225 getUnsignedRange(Start).getUnsignedMin());
5227 // If we know that the condition is true in order to enter the loop,
5228 // then we know that it will run exactly (m-n)/s times. Otherwise, we
5229 // only know that it will execute (max(m,n)-n)/s times. In both cases,
5230 // the division must round up.
5231 const SCEV *End = RHS;
5232 if (!isLoopEntryGuardedByCond(L,
5233 isSigned ? ICmpInst::ICMP_SLT :
5235 getMinusSCEV(Start, Step), RHS))
5236 End = isSigned ? getSMaxExpr(RHS, Start)
5237 : getUMaxExpr(RHS, Start);
5239 // Determine the maximum constant end value.
5240 const SCEV *MaxEnd = getConstant(isSigned ?
5241 getSignedRange(End).getSignedMax() :
5242 getUnsignedRange(End).getUnsignedMax());
5244 // If MaxEnd is within a step of the maximum integer value in its type,
5245 // adjust it down to the minimum value which would produce the same effect.
5246 // This allows the subsequent ceiling division of (N+(step-1))/step to
5247 // compute the correct value.
5248 const SCEV *StepMinusOne = getMinusSCEV(Step,
5249 getIntegerSCEV(1, Step->getType()));
5252 getMinusSCEV(getConstant(APInt::getSignedMaxValue(BitWidth)),
5255 getMinusSCEV(getConstant(APInt::getMaxValue(BitWidth)),
5258 // Finally, we subtract these two values and divide, rounding up, to get
5259 // the number of times the backedge is executed.
5260 const SCEV *BECount = getBECount(Start, End, Step, NoWrap);
5262 // The maximum backedge count is similar, except using the minimum start
5263 // value and the maximum end value.
5264 const SCEV *MaxBECount = getBECount(MinStart, MaxEnd, Step, NoWrap);
5266 return BackedgeTakenInfo(BECount, MaxBECount);
5269 return getCouldNotCompute();
5272 /// getNumIterationsInRange - Return the number of iterations of this loop that
5273 /// produce values in the specified constant range. Another way of looking at
5274 /// this is that it returns the first iteration number where the value is not in
5275 /// the condition, thus computing the exit count. If the iteration count can't
5276 /// be computed, an instance of SCEVCouldNotCompute is returned.
5277 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
5278 ScalarEvolution &SE) const {
5279 if (Range.isFullSet()) // Infinite loop.
5280 return SE.getCouldNotCompute();
5282 // If the start is a non-zero constant, shift the range to simplify things.
5283 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
5284 if (!SC->getValue()->isZero()) {
5285 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
5286 Operands[0] = SE.getIntegerSCEV(0, SC->getType());
5287 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop());
5288 if (const SCEVAddRecExpr *ShiftedAddRec =
5289 dyn_cast<SCEVAddRecExpr>(Shifted))
5290 return ShiftedAddRec->getNumIterationsInRange(
5291 Range.subtract(SC->getValue()->getValue()), SE);
5292 // This is strange and shouldn't happen.
5293 return SE.getCouldNotCompute();
5296 // The only time we can solve this is when we have all constant indices.
5297 // Otherwise, we cannot determine the overflow conditions.
5298 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
5299 if (!isa<SCEVConstant>(getOperand(i)))
5300 return SE.getCouldNotCompute();
5303 // Okay at this point we know that all elements of the chrec are constants and
5304 // that the start element is zero.
5306 // First check to see if the range contains zero. If not, the first
5308 unsigned BitWidth = SE.getTypeSizeInBits(getType());
5309 if (!Range.contains(APInt(BitWidth, 0)))
5310 return SE.getIntegerSCEV(0, getType());
5313 // If this is an affine expression then we have this situation:
5314 // Solve {0,+,A} in Range === Ax in Range
5316 // We know that zero is in the range. If A is positive then we know that
5317 // the upper value of the range must be the first possible exit value.
5318 // If A is negative then the lower of the range is the last possible loop
5319 // value. Also note that we already checked for a full range.
5320 APInt One(BitWidth,1);
5321 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
5322 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
5324 // The exit value should be (End+A)/A.
5325 APInt ExitVal = (End + A).udiv(A);
5326 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
5328 // Evaluate at the exit value. If we really did fall out of the valid
5329 // range, then we computed our trip count, otherwise wrap around or other
5330 // things must have happened.
5331 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
5332 if (Range.contains(Val->getValue()))
5333 return SE.getCouldNotCompute(); // Something strange happened
5335 // Ensure that the previous value is in the range. This is a sanity check.
5336 assert(Range.contains(
5337 EvaluateConstantChrecAtConstant(this,
5338 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
5339 "Linear scev computation is off in a bad way!");
5340 return SE.getConstant(ExitValue);
5341 } else if (isQuadratic()) {
5342 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
5343 // quadratic equation to solve it. To do this, we must frame our problem in
5344 // terms of figuring out when zero is crossed, instead of when
5345 // Range.getUpper() is crossed.
5346 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
5347 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
5348 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop());
5350 // Next, solve the constructed addrec
5351 std::pair<const SCEV *,const SCEV *> Roots =
5352 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
5353 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
5354 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
5356 // Pick the smallest positive root value.
5357 if (ConstantInt *CB =
5358 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
5359 R1->getValue(), R2->getValue()))) {
5360 if (CB->getZExtValue() == false)
5361 std::swap(R1, R2); // R1 is the minimum root now.
5363 // Make sure the root is not off by one. The returned iteration should
5364 // not be in the range, but the previous one should be. When solving
5365 // for "X*X < 5", for example, we should not return a root of 2.
5366 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
5369 if (Range.contains(R1Val->getValue())) {
5370 // The next iteration must be out of the range...
5371 ConstantInt *NextVal =
5372 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1);
5374 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
5375 if (!Range.contains(R1Val->getValue()))
5376 return SE.getConstant(NextVal);
5377 return SE.getCouldNotCompute(); // Something strange happened
5380 // If R1 was not in the range, then it is a good return value. Make
5381 // sure that R1-1 WAS in the range though, just in case.
5382 ConstantInt *NextVal =
5383 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1);
5384 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
5385 if (Range.contains(R1Val->getValue()))
5387 return SE.getCouldNotCompute(); // Something strange happened
5392 return SE.getCouldNotCompute();
5397 //===----------------------------------------------------------------------===//
5398 // SCEVCallbackVH Class Implementation
5399 //===----------------------------------------------------------------------===//
5401 void ScalarEvolution::SCEVCallbackVH::deleted() {
5402 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
5403 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
5404 SE->ConstantEvolutionLoopExitValue.erase(PN);
5405 SE->Scalars.erase(getValPtr());
5406 // this now dangles!
5409 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *) {
5410 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
5412 // Forget all the expressions associated with users of the old value,
5413 // so that future queries will recompute the expressions using the new
5415 SmallVector<User *, 16> Worklist;
5416 SmallPtrSet<User *, 8> Visited;
5417 Value *Old = getValPtr();
5418 bool DeleteOld = false;
5419 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end();
5421 Worklist.push_back(*UI);
5422 while (!Worklist.empty()) {
5423 User *U = Worklist.pop_back_val();
5424 // Deleting the Old value will cause this to dangle. Postpone
5425 // that until everything else is done.
5430 if (!Visited.insert(U))
5432 if (PHINode *PN = dyn_cast<PHINode>(U))
5433 SE->ConstantEvolutionLoopExitValue.erase(PN);
5434 SE->Scalars.erase(U);
5435 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end();
5437 Worklist.push_back(*UI);
5439 // Delete the Old value if it (indirectly) references itself.
5441 if (PHINode *PN = dyn_cast<PHINode>(Old))
5442 SE->ConstantEvolutionLoopExitValue.erase(PN);
5443 SE->Scalars.erase(Old);
5444 // this now dangles!
5449 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
5450 : CallbackVH(V), SE(se) {}
5452 //===----------------------------------------------------------------------===//
5453 // ScalarEvolution Class Implementation
5454 //===----------------------------------------------------------------------===//
5456 ScalarEvolution::ScalarEvolution()
5457 : FunctionPass(&ID) {
5460 bool ScalarEvolution::runOnFunction(Function &F) {
5462 LI = &getAnalysis<LoopInfo>();
5463 TD = getAnalysisIfAvailable<TargetData>();
5464 DT = &getAnalysis<DominatorTree>();
5468 void ScalarEvolution::releaseMemory() {
5470 BackedgeTakenCounts.clear();
5471 ConstantEvolutionLoopExitValue.clear();
5472 ValuesAtScopes.clear();
5473 UniqueSCEVs.clear();
5474 SCEVAllocator.Reset();
5477 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
5478 AU.setPreservesAll();
5479 AU.addRequiredTransitive<LoopInfo>();
5480 AU.addRequiredTransitive<DominatorTree>();
5483 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
5484 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
5487 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
5489 // Print all inner loops first
5490 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
5491 PrintLoopInfo(OS, SE, *I);
5494 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
5497 SmallVector<BasicBlock *, 8> ExitBlocks;
5498 L->getExitBlocks(ExitBlocks);
5499 if (ExitBlocks.size() != 1)
5500 OS << "<multiple exits> ";
5502 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
5503 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
5505 OS << "Unpredictable backedge-taken count. ";
5510 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
5513 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
5514 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
5516 OS << "Unpredictable max backedge-taken count. ";
5522 void ScalarEvolution::print(raw_ostream &OS, const Module *) const {
5523 // ScalarEvolution's implementation of the print method is to print
5524 // out SCEV values of all instructions that are interesting. Doing
5525 // this potentially causes it to create new SCEV objects though,
5526 // which technically conflicts with the const qualifier. This isn't
5527 // observable from outside the class though, so casting away the
5528 // const isn't dangerous.
5529 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
5531 OS << "Classifying expressions for: ";
5532 WriteAsOperand(OS, F, /*PrintType=*/false);
5534 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
5535 if (isSCEVable(I->getType())) {
5538 const SCEV *SV = SE.getSCEV(&*I);
5541 const Loop *L = LI->getLoopFor((*I).getParent());
5543 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
5550 OS << "\t\t" "Exits: ";
5551 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
5552 if (!ExitValue->isLoopInvariant(L)) {
5553 OS << "<<Unknown>>";
5562 OS << "Determining loop execution counts for: ";
5563 WriteAsOperand(OS, F, /*PrintType=*/false);
5565 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
5566 PrintLoopInfo(OS, &SE, *I);