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 Constant *C = ConstantExpr::getSizeOf(AllocTy);
2258 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2259 C = ConstantFoldConstantExpression(CE, TD);
2260 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2261 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2264 const SCEV *ScalarEvolution::getAlignOfExpr(const Type *AllocTy) {
2265 Constant *C = ConstantExpr::getAlignOf(AllocTy);
2266 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2267 C = ConstantFoldConstantExpression(CE, TD);
2268 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2269 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2272 const SCEV *ScalarEvolution::getOffsetOfExpr(const StructType *STy,
2274 Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo);
2275 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2276 C = ConstantFoldConstantExpression(CE, TD);
2277 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy));
2278 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2281 const SCEV *ScalarEvolution::getOffsetOfExpr(const Type *CTy,
2282 Constant *FieldNo) {
2283 Constant *C = ConstantExpr::getOffsetOf(CTy, FieldNo);
2284 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2285 C = ConstantFoldConstantExpression(CE, TD);
2286 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(CTy));
2287 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2290 const SCEV *ScalarEvolution::getUnknown(Value *V) {
2291 // Don't attempt to do anything other than create a SCEVUnknown object
2292 // here. createSCEV only calls getUnknown after checking for all other
2293 // interesting possibilities, and any other code that calls getUnknown
2294 // is doing so in order to hide a value from SCEV canonicalization.
2296 FoldingSetNodeID ID;
2297 ID.AddInteger(scUnknown);
2300 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2301 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V);
2302 UniqueSCEVs.InsertNode(S, IP);
2306 //===----------------------------------------------------------------------===//
2307 // Basic SCEV Analysis and PHI Idiom Recognition Code
2310 /// isSCEVable - Test if values of the given type are analyzable within
2311 /// the SCEV framework. This primarily includes integer types, and it
2312 /// can optionally include pointer types if the ScalarEvolution class
2313 /// has access to target-specific information.
2314 bool ScalarEvolution::isSCEVable(const Type *Ty) const {
2315 // Integers and pointers are always SCEVable.
2316 return Ty->isIntegerTy() || Ty->isPointerTy();
2319 /// getTypeSizeInBits - Return the size in bits of the specified type,
2320 /// for which isSCEVable must return true.
2321 uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const {
2322 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2324 // If we have a TargetData, use it!
2326 return TD->getTypeSizeInBits(Ty);
2328 // Integer types have fixed sizes.
2329 if (Ty->isIntegerTy())
2330 return Ty->getPrimitiveSizeInBits();
2332 // The only other support type is pointer. Without TargetData, conservatively
2333 // assume pointers are 64-bit.
2334 assert(Ty->isPointerTy() && "isSCEVable permitted a non-SCEVable type!");
2338 /// getEffectiveSCEVType - Return a type with the same bitwidth as
2339 /// the given type and which represents how SCEV will treat the given
2340 /// type, for which isSCEVable must return true. For pointer types,
2341 /// this is the pointer-sized integer type.
2342 const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const {
2343 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2345 if (Ty->isIntegerTy())
2348 // The only other support type is pointer.
2349 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
2350 if (TD) return TD->getIntPtrType(getContext());
2352 // Without TargetData, conservatively assume pointers are 64-bit.
2353 return Type::getInt64Ty(getContext());
2356 const SCEV *ScalarEvolution::getCouldNotCompute() {
2357 return &CouldNotCompute;
2360 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
2361 /// expression and create a new one.
2362 const SCEV *ScalarEvolution::getSCEV(Value *V) {
2363 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
2365 std::map<SCEVCallbackVH, const SCEV *>::iterator I = Scalars.find(V);
2366 if (I != Scalars.end()) return I->second;
2367 const SCEV *S = createSCEV(V);
2368 Scalars.insert(std::make_pair(SCEVCallbackVH(V, this), S));
2372 /// getIntegerSCEV - Given a SCEVable type, create a constant for the
2373 /// specified signed integer value and return a SCEV for the constant.
2374 const SCEV *ScalarEvolution::getIntegerSCEV(int64_t Val, const Type *Ty) {
2375 const IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty));
2376 return getConstant(ConstantInt::get(ITy, Val));
2379 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
2381 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) {
2382 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2384 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
2386 const Type *Ty = V->getType();
2387 Ty = getEffectiveSCEVType(Ty);
2388 return getMulExpr(V,
2389 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))));
2392 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
2393 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
2394 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2396 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
2398 const Type *Ty = V->getType();
2399 Ty = getEffectiveSCEVType(Ty);
2400 const SCEV *AllOnes =
2401 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
2402 return getMinusSCEV(AllOnes, V);
2405 /// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
2407 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS,
2410 return getAddExpr(LHS, getNegativeSCEV(RHS));
2413 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
2414 /// input value to the specified type. If the type must be extended, it is zero
2417 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V,
2419 const Type *SrcTy = V->getType();
2420 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2421 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2422 "Cannot truncate or zero extend with non-integer arguments!");
2423 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2424 return V; // No conversion
2425 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2426 return getTruncateExpr(V, Ty);
2427 return getZeroExtendExpr(V, Ty);
2430 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
2431 /// input value to the specified type. If the type must be extended, it is sign
2434 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
2436 const Type *SrcTy = V->getType();
2437 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2438 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2439 "Cannot truncate or zero extend with non-integer arguments!");
2440 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2441 return V; // No conversion
2442 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2443 return getTruncateExpr(V, Ty);
2444 return getSignExtendExpr(V, Ty);
2447 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
2448 /// input value to the specified type. If the type must be extended, it is zero
2449 /// extended. The conversion must not be narrowing.
2451 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, const Type *Ty) {
2452 const Type *SrcTy = V->getType();
2453 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2454 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2455 "Cannot noop or zero extend with non-integer arguments!");
2456 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2457 "getNoopOrZeroExtend cannot truncate!");
2458 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2459 return V; // No conversion
2460 return getZeroExtendExpr(V, Ty);
2463 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
2464 /// input value to the specified type. If the type must be extended, it is sign
2465 /// extended. The conversion must not be narrowing.
2467 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, const Type *Ty) {
2468 const Type *SrcTy = V->getType();
2469 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2470 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2471 "Cannot noop or sign extend with non-integer arguments!");
2472 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2473 "getNoopOrSignExtend cannot truncate!");
2474 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2475 return V; // No conversion
2476 return getSignExtendExpr(V, Ty);
2479 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
2480 /// the input value to the specified type. If the type must be extended,
2481 /// it is extended with unspecified bits. The conversion must not be
2484 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, const Type *Ty) {
2485 const Type *SrcTy = V->getType();
2486 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2487 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2488 "Cannot noop or any extend with non-integer arguments!");
2489 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2490 "getNoopOrAnyExtend cannot truncate!");
2491 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2492 return V; // No conversion
2493 return getAnyExtendExpr(V, Ty);
2496 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
2497 /// input value to the specified type. The conversion must not be widening.
2499 ScalarEvolution::getTruncateOrNoop(const SCEV *V, const Type *Ty) {
2500 const Type *SrcTy = V->getType();
2501 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2502 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2503 "Cannot truncate or noop with non-integer arguments!");
2504 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
2505 "getTruncateOrNoop cannot extend!");
2506 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2507 return V; // No conversion
2508 return getTruncateExpr(V, Ty);
2511 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
2512 /// the types using zero-extension, and then perform a umax operation
2514 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
2516 const SCEV *PromotedLHS = LHS;
2517 const SCEV *PromotedRHS = RHS;
2519 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2520 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2522 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2524 return getUMaxExpr(PromotedLHS, PromotedRHS);
2527 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
2528 /// the types using zero-extension, and then perform a umin operation
2530 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
2532 const SCEV *PromotedLHS = LHS;
2533 const SCEV *PromotedRHS = RHS;
2535 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2536 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2538 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2540 return getUMinExpr(PromotedLHS, PromotedRHS);
2543 /// PushDefUseChildren - Push users of the given Instruction
2544 /// onto the given Worklist.
2546 PushDefUseChildren(Instruction *I,
2547 SmallVectorImpl<Instruction *> &Worklist) {
2548 // Push the def-use children onto the Worklist stack.
2549 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end();
2551 Worklist.push_back(cast<Instruction>(UI));
2554 /// ForgetSymbolicValue - This looks up computed SCEV values for all
2555 /// instructions that depend on the given instruction and removes them from
2556 /// the Scalars map if they reference SymName. This is used during PHI
2559 ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) {
2560 SmallVector<Instruction *, 16> Worklist;
2561 PushDefUseChildren(PN, Worklist);
2563 SmallPtrSet<Instruction *, 8> Visited;
2565 while (!Worklist.empty()) {
2566 Instruction *I = Worklist.pop_back_val();
2567 if (!Visited.insert(I)) continue;
2569 std::map<SCEVCallbackVH, const SCEV *>::iterator It =
2570 Scalars.find(static_cast<Value *>(I));
2571 if (It != Scalars.end()) {
2572 // Short-circuit the def-use traversal if the symbolic name
2573 // ceases to appear in expressions.
2574 if (It->second != SymName && !It->second->hasOperand(SymName))
2577 // SCEVUnknown for a PHI either means that it has an unrecognized
2578 // structure, it's a PHI that's in the progress of being computed
2579 // by createNodeForPHI, or it's a single-value PHI. In the first case,
2580 // additional loop trip count information isn't going to change anything.
2581 // In the second case, createNodeForPHI will perform the necessary
2582 // updates on its own when it gets to that point. In the third, we do
2583 // want to forget the SCEVUnknown.
2584 if (!isa<PHINode>(I) ||
2585 !isa<SCEVUnknown>(It->second) ||
2586 (I != PN && It->second == SymName)) {
2587 ValuesAtScopes.erase(It->second);
2592 PushDefUseChildren(I, Worklist);
2596 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
2597 /// a loop header, making it a potential recurrence, or it doesn't.
2599 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
2600 if (const Loop *L = LI->getLoopFor(PN->getParent()))
2601 if (L->getHeader() == PN->getParent()) {
2602 // The loop may have multiple entrances or multiple exits; we can analyze
2603 // this phi as an addrec if it has a unique entry value and a unique
2605 Value *BEValueV = 0, *StartValueV = 0;
2606 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
2607 Value *V = PN->getIncomingValue(i);
2608 if (L->contains(PN->getIncomingBlock(i))) {
2611 } else if (BEValueV != V) {
2615 } else if (!StartValueV) {
2617 } else if (StartValueV != V) {
2622 if (BEValueV && StartValueV) {
2623 // While we are analyzing this PHI node, handle its value symbolically.
2624 const SCEV *SymbolicName = getUnknown(PN);
2625 assert(Scalars.find(PN) == Scalars.end() &&
2626 "PHI node already processed?");
2627 Scalars.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
2629 // Using this symbolic name for the PHI, analyze the value coming around
2631 const SCEV *BEValue = getSCEV(BEValueV);
2633 // NOTE: If BEValue is loop invariant, we know that the PHI node just
2634 // has a special value for the first iteration of the loop.
2636 // If the value coming around the backedge is an add with the symbolic
2637 // value we just inserted, then we found a simple induction variable!
2638 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
2639 // If there is a single occurrence of the symbolic value, replace it
2640 // with a recurrence.
2641 unsigned FoundIndex = Add->getNumOperands();
2642 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
2643 if (Add->getOperand(i) == SymbolicName)
2644 if (FoundIndex == e) {
2649 if (FoundIndex != Add->getNumOperands()) {
2650 // Create an add with everything but the specified operand.
2651 SmallVector<const SCEV *, 8> Ops;
2652 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
2653 if (i != FoundIndex)
2654 Ops.push_back(Add->getOperand(i));
2655 const SCEV *Accum = getAddExpr(Ops);
2657 // This is not a valid addrec if the step amount is varying each
2658 // loop iteration, but is not itself an addrec in this loop.
2659 if (Accum->isLoopInvariant(L) ||
2660 (isa<SCEVAddRecExpr>(Accum) &&
2661 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
2662 bool HasNUW = false;
2663 bool HasNSW = false;
2665 // If the increment doesn't overflow, then neither the addrec nor
2666 // the post-increment will overflow.
2667 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) {
2668 if (OBO->hasNoUnsignedWrap())
2670 if (OBO->hasNoSignedWrap())
2674 const SCEV *StartVal = getSCEV(StartValueV);
2675 const SCEV *PHISCEV =
2676 getAddRecExpr(StartVal, Accum, L, HasNUW, HasNSW);
2678 // Since the no-wrap flags are on the increment, they apply to the
2679 // post-incremented value as well.
2680 if (Accum->isLoopInvariant(L))
2681 (void)getAddRecExpr(getAddExpr(StartVal, Accum),
2682 Accum, L, HasNUW, HasNSW);
2684 // Okay, for the entire analysis of this edge we assumed the PHI
2685 // to be symbolic. We now need to go back and purge all of the
2686 // entries for the scalars that use the symbolic expression.
2687 ForgetSymbolicName(PN, SymbolicName);
2688 Scalars[SCEVCallbackVH(PN, this)] = PHISCEV;
2692 } else if (const SCEVAddRecExpr *AddRec =
2693 dyn_cast<SCEVAddRecExpr>(BEValue)) {
2694 // Otherwise, this could be a loop like this:
2695 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
2696 // In this case, j = {1,+,1} and BEValue is j.
2697 // Because the other in-value of i (0) fits the evolution of BEValue
2698 // i really is an addrec evolution.
2699 if (AddRec->getLoop() == L && AddRec->isAffine()) {
2700 const SCEV *StartVal = getSCEV(StartValueV);
2702 // If StartVal = j.start - j.stride, we can use StartVal as the
2703 // initial step of the addrec evolution.
2704 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
2705 AddRec->getOperand(1))) {
2706 const SCEV *PHISCEV =
2707 getAddRecExpr(StartVal, AddRec->getOperand(1), L);
2709 // Okay, for the entire analysis of this edge we assumed the PHI
2710 // to be symbolic. We now need to go back and purge all of the
2711 // entries for the scalars that use the symbolic expression.
2712 ForgetSymbolicName(PN, SymbolicName);
2713 Scalars[SCEVCallbackVH(PN, this)] = PHISCEV;
2721 // If the PHI has a single incoming value, follow that value, unless the
2722 // PHI's incoming blocks are in a different loop, in which case doing so
2723 // risks breaking LCSSA form. Instcombine would normally zap these, but
2724 // it doesn't have DominatorTree information, so it may miss cases.
2725 if (Value *V = PN->hasConstantValue(DT)) {
2726 bool AllSameLoop = true;
2727 Loop *PNLoop = LI->getLoopFor(PN->getParent());
2728 for (size_t i = 0, e = PN->getNumIncomingValues(); i != e; ++i)
2729 if (LI->getLoopFor(PN->getIncomingBlock(i)) != PNLoop) {
2730 AllSameLoop = false;
2737 // If it's not a loop phi, we can't handle it yet.
2738 return getUnknown(PN);
2741 /// createNodeForGEP - Expand GEP instructions into add and multiply
2742 /// operations. This allows them to be analyzed by regular SCEV code.
2744 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
2746 bool InBounds = GEP->isInBounds();
2747 const Type *IntPtrTy = getEffectiveSCEVType(GEP->getType());
2748 Value *Base = GEP->getOperand(0);
2749 // Don't attempt to analyze GEPs over unsized objects.
2750 if (!cast<PointerType>(Base->getType())->getElementType()->isSized())
2751 return getUnknown(GEP);
2752 const SCEV *TotalOffset = getIntegerSCEV(0, IntPtrTy);
2753 gep_type_iterator GTI = gep_type_begin(GEP);
2754 for (GetElementPtrInst::op_iterator I = next(GEP->op_begin()),
2758 // Compute the (potentially symbolic) offset in bytes for this index.
2759 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) {
2760 // For a struct, add the member offset.
2761 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
2762 TotalOffset = getAddExpr(TotalOffset,
2763 getOffsetOfExpr(STy, FieldNo),
2764 /*HasNUW=*/false, /*HasNSW=*/InBounds);
2766 // For an array, add the element offset, explicitly scaled.
2767 const SCEV *LocalOffset = getSCEV(Index);
2768 // Getelementptr indices are signed.
2769 LocalOffset = getTruncateOrSignExtend(LocalOffset, IntPtrTy);
2770 // Lower "inbounds" GEPs to NSW arithmetic.
2771 LocalOffset = getMulExpr(LocalOffset, getSizeOfExpr(*GTI),
2772 /*HasNUW=*/false, /*HasNSW=*/InBounds);
2773 TotalOffset = getAddExpr(TotalOffset, LocalOffset,
2774 /*HasNUW=*/false, /*HasNSW=*/InBounds);
2777 return getAddExpr(getSCEV(Base), TotalOffset,
2778 /*HasNUW=*/false, /*HasNSW=*/InBounds);
2781 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
2782 /// guaranteed to end in (at every loop iteration). It is, at the same time,
2783 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
2784 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
2786 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
2787 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
2788 return C->getValue()->getValue().countTrailingZeros();
2790 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
2791 return std::min(GetMinTrailingZeros(T->getOperand()),
2792 (uint32_t)getTypeSizeInBits(T->getType()));
2794 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
2795 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
2796 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
2797 getTypeSizeInBits(E->getType()) : OpRes;
2800 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
2801 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
2802 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
2803 getTypeSizeInBits(E->getType()) : OpRes;
2806 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
2807 // The result is the min of all operands results.
2808 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
2809 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
2810 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
2814 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
2815 // The result is the sum of all operands results.
2816 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
2817 uint32_t BitWidth = getTypeSizeInBits(M->getType());
2818 for (unsigned i = 1, e = M->getNumOperands();
2819 SumOpRes != BitWidth && i != e; ++i)
2820 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
2825 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
2826 // The result is the min of all operands results.
2827 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
2828 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
2829 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
2833 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
2834 // The result is the min of all operands results.
2835 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
2836 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
2837 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
2841 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
2842 // The result is the min of all operands results.
2843 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
2844 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
2845 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
2849 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
2850 // For a SCEVUnknown, ask ValueTracking.
2851 unsigned BitWidth = getTypeSizeInBits(U->getType());
2852 APInt Mask = APInt::getAllOnesValue(BitWidth);
2853 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
2854 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones);
2855 return Zeros.countTrailingOnes();
2862 /// getUnsignedRange - Determine the unsigned range for a particular SCEV.
2865 ScalarEvolution::getUnsignedRange(const SCEV *S) {
2867 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
2868 return ConstantRange(C->getValue()->getValue());
2870 unsigned BitWidth = getTypeSizeInBits(S->getType());
2871 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
2873 // If the value has known zeros, the maximum unsigned value will have those
2874 // known zeros as well.
2875 uint32_t TZ = GetMinTrailingZeros(S);
2877 ConservativeResult =
2878 ConstantRange(APInt::getMinValue(BitWidth),
2879 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
2881 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
2882 ConstantRange X = getUnsignedRange(Add->getOperand(0));
2883 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
2884 X = X.add(getUnsignedRange(Add->getOperand(i)));
2885 return ConservativeResult.intersectWith(X);
2888 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
2889 ConstantRange X = getUnsignedRange(Mul->getOperand(0));
2890 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
2891 X = X.multiply(getUnsignedRange(Mul->getOperand(i)));
2892 return ConservativeResult.intersectWith(X);
2895 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
2896 ConstantRange X = getUnsignedRange(SMax->getOperand(0));
2897 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
2898 X = X.smax(getUnsignedRange(SMax->getOperand(i)));
2899 return ConservativeResult.intersectWith(X);
2902 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
2903 ConstantRange X = getUnsignedRange(UMax->getOperand(0));
2904 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
2905 X = X.umax(getUnsignedRange(UMax->getOperand(i)));
2906 return ConservativeResult.intersectWith(X);
2909 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
2910 ConstantRange X = getUnsignedRange(UDiv->getLHS());
2911 ConstantRange Y = getUnsignedRange(UDiv->getRHS());
2912 return ConservativeResult.intersectWith(X.udiv(Y));
2915 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
2916 ConstantRange X = getUnsignedRange(ZExt->getOperand());
2917 return ConservativeResult.intersectWith(X.zeroExtend(BitWidth));
2920 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
2921 ConstantRange X = getUnsignedRange(SExt->getOperand());
2922 return ConservativeResult.intersectWith(X.signExtend(BitWidth));
2925 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
2926 ConstantRange X = getUnsignedRange(Trunc->getOperand());
2927 return ConservativeResult.intersectWith(X.truncate(BitWidth));
2930 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
2931 // If there's no unsigned wrap, the value will never be less than its
2933 if (AddRec->hasNoUnsignedWrap())
2934 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
2936 ConservativeResult =
2937 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0));
2939 // TODO: non-affine addrec
2940 if (AddRec->isAffine()) {
2941 const Type *Ty = AddRec->getType();
2942 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
2943 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
2944 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
2945 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
2947 const SCEV *Start = AddRec->getStart();
2948 const SCEV *Step = AddRec->getStepRecurrence(*this);
2950 ConstantRange StartRange = getUnsignedRange(Start);
2951 ConstantRange StepRange = getSignedRange(Step);
2952 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
2953 ConstantRange EndRange =
2954 StartRange.add(MaxBECountRange.multiply(StepRange));
2956 // Check for overflow. This must be done with ConstantRange arithmetic
2957 // because we could be called from within the ScalarEvolution overflow
2959 ConstantRange ExtStartRange = StartRange.zextOrTrunc(BitWidth*2+1);
2960 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
2961 ConstantRange ExtMaxBECountRange =
2962 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
2963 ConstantRange ExtEndRange = EndRange.zextOrTrunc(BitWidth*2+1);
2964 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
2966 return ConservativeResult;
2968 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(),
2969 EndRange.getUnsignedMin());
2970 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(),
2971 EndRange.getUnsignedMax());
2972 if (Min.isMinValue() && Max.isMaxValue())
2973 return ConservativeResult;
2974 return ConservativeResult.intersectWith(ConstantRange(Min, Max+1));
2978 return ConservativeResult;
2981 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
2982 // For a SCEVUnknown, ask ValueTracking.
2983 APInt Mask = APInt::getAllOnesValue(BitWidth);
2984 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
2985 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones, TD);
2986 if (Ones == ~Zeros + 1)
2987 return ConservativeResult;
2988 return ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1));
2991 return ConservativeResult;
2994 /// getSignedRange - Determine the signed range for a particular SCEV.
2997 ScalarEvolution::getSignedRange(const SCEV *S) {
2999 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3000 return ConstantRange(C->getValue()->getValue());
3002 unsigned BitWidth = getTypeSizeInBits(S->getType());
3003 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3005 // If the value has known zeros, the maximum signed value will have those
3006 // known zeros as well.
3007 uint32_t TZ = GetMinTrailingZeros(S);
3009 ConservativeResult =
3010 ConstantRange(APInt::getSignedMinValue(BitWidth),
3011 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
3013 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3014 ConstantRange X = getSignedRange(Add->getOperand(0));
3015 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3016 X = X.add(getSignedRange(Add->getOperand(i)));
3017 return ConservativeResult.intersectWith(X);
3020 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3021 ConstantRange X = getSignedRange(Mul->getOperand(0));
3022 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3023 X = X.multiply(getSignedRange(Mul->getOperand(i)));
3024 return ConservativeResult.intersectWith(X);
3027 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3028 ConstantRange X = getSignedRange(SMax->getOperand(0));
3029 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3030 X = X.smax(getSignedRange(SMax->getOperand(i)));
3031 return ConservativeResult.intersectWith(X);
3034 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3035 ConstantRange X = getSignedRange(UMax->getOperand(0));
3036 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3037 X = X.umax(getSignedRange(UMax->getOperand(i)));
3038 return ConservativeResult.intersectWith(X);
3041 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3042 ConstantRange X = getSignedRange(UDiv->getLHS());
3043 ConstantRange Y = getSignedRange(UDiv->getRHS());
3044 return ConservativeResult.intersectWith(X.udiv(Y));
3047 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3048 ConstantRange X = getSignedRange(ZExt->getOperand());
3049 return ConservativeResult.intersectWith(X.zeroExtend(BitWidth));
3052 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3053 ConstantRange X = getSignedRange(SExt->getOperand());
3054 return ConservativeResult.intersectWith(X.signExtend(BitWidth));
3057 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3058 ConstantRange X = getSignedRange(Trunc->getOperand());
3059 return ConservativeResult.intersectWith(X.truncate(BitWidth));
3062 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3063 // If there's no signed wrap, and all the operands have the same sign or
3064 // zero, the value won't ever change sign.
3065 if (AddRec->hasNoSignedWrap()) {
3066 bool AllNonNeg = true;
3067 bool AllNonPos = true;
3068 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
3069 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
3070 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
3073 ConservativeResult = ConservativeResult.intersectWith(
3074 ConstantRange(APInt(BitWidth, 0),
3075 APInt::getSignedMinValue(BitWidth)));
3077 ConservativeResult = ConservativeResult.intersectWith(
3078 ConstantRange(APInt::getSignedMinValue(BitWidth),
3079 APInt(BitWidth, 1)));
3082 // TODO: non-affine addrec
3083 if (AddRec->isAffine()) {
3084 const Type *Ty = AddRec->getType();
3085 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3086 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3087 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3088 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3090 const SCEV *Start = AddRec->getStart();
3091 const SCEV *Step = AddRec->getStepRecurrence(*this);
3093 ConstantRange StartRange = getSignedRange(Start);
3094 ConstantRange StepRange = getSignedRange(Step);
3095 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3096 ConstantRange EndRange =
3097 StartRange.add(MaxBECountRange.multiply(StepRange));
3099 // Check for overflow. This must be done with ConstantRange arithmetic
3100 // because we could be called from within the ScalarEvolution overflow
3102 ConstantRange ExtStartRange = StartRange.sextOrTrunc(BitWidth*2+1);
3103 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3104 ConstantRange ExtMaxBECountRange =
3105 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3106 ConstantRange ExtEndRange = EndRange.sextOrTrunc(BitWidth*2+1);
3107 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3109 return ConservativeResult;
3111 APInt Min = APIntOps::smin(StartRange.getSignedMin(),
3112 EndRange.getSignedMin());
3113 APInt Max = APIntOps::smax(StartRange.getSignedMax(),
3114 EndRange.getSignedMax());
3115 if (Min.isMinSignedValue() && Max.isMaxSignedValue())
3116 return ConservativeResult;
3117 return ConservativeResult.intersectWith(ConstantRange(Min, Max+1));
3121 return ConservativeResult;
3124 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3125 // For a SCEVUnknown, ask ValueTracking.
3126 if (!U->getValue()->getType()->isIntegerTy() && !TD)
3127 return ConservativeResult;
3128 unsigned NS = ComputeNumSignBits(U->getValue(), TD);
3130 return ConservativeResult;
3131 return ConservativeResult.intersectWith(
3132 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
3133 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1));
3136 return ConservativeResult;
3139 /// createSCEV - We know that there is no SCEV for the specified value.
3140 /// Analyze the expression.
3142 const SCEV *ScalarEvolution::createSCEV(Value *V) {
3143 if (!isSCEVable(V->getType()))
3144 return getUnknown(V);
3146 unsigned Opcode = Instruction::UserOp1;
3147 if (Instruction *I = dyn_cast<Instruction>(V)) {
3148 Opcode = I->getOpcode();
3150 // Don't attempt to analyze instructions in blocks that aren't
3151 // reachable. Such instructions don't matter, and they aren't required
3152 // to obey basic rules for definitions dominating uses which this
3153 // analysis depends on.
3154 if (!DT->isReachableFromEntry(I->getParent()))
3155 return getUnknown(V);
3156 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
3157 Opcode = CE->getOpcode();
3158 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
3159 return getConstant(CI);
3160 else if (isa<ConstantPointerNull>(V))
3161 return getIntegerSCEV(0, V->getType());
3162 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
3163 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee());
3165 return getUnknown(V);
3167 Operator *U = cast<Operator>(V);
3169 case Instruction::Add:
3170 // Don't transfer the NSW and NUW bits from the Add instruction to the
3171 // Add expression, because the Instruction may be guarded by control
3172 // flow and the no-overflow bits may not be valid for the expression in
3174 return getAddExpr(getSCEV(U->getOperand(0)),
3175 getSCEV(U->getOperand(1)));
3176 case Instruction::Mul:
3177 // Don't transfer the NSW and NUW bits from the Mul instruction to the
3178 // Mul expression, as with Add.
3179 return getMulExpr(getSCEV(U->getOperand(0)),
3180 getSCEV(U->getOperand(1)));
3181 case Instruction::UDiv:
3182 return getUDivExpr(getSCEV(U->getOperand(0)),
3183 getSCEV(U->getOperand(1)));
3184 case Instruction::Sub:
3185 return getMinusSCEV(getSCEV(U->getOperand(0)),
3186 getSCEV(U->getOperand(1)));
3187 case Instruction::And:
3188 // For an expression like x&255 that merely masks off the high bits,
3189 // use zext(trunc(x)) as the SCEV expression.
3190 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3191 if (CI->isNullValue())
3192 return getSCEV(U->getOperand(1));
3193 if (CI->isAllOnesValue())
3194 return getSCEV(U->getOperand(0));
3195 const APInt &A = CI->getValue();
3197 // Instcombine's ShrinkDemandedConstant may strip bits out of
3198 // constants, obscuring what would otherwise be a low-bits mask.
3199 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant
3200 // knew about to reconstruct a low-bits mask value.
3201 unsigned LZ = A.countLeadingZeros();
3202 unsigned BitWidth = A.getBitWidth();
3203 APInt AllOnes = APInt::getAllOnesValue(BitWidth);
3204 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
3205 ComputeMaskedBits(U->getOperand(0), AllOnes, KnownZero, KnownOne, TD);
3207 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ);
3209 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask))
3211 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)),
3212 IntegerType::get(getContext(), BitWidth - LZ)),
3217 case Instruction::Or:
3218 // If the RHS of the Or is a constant, we may have something like:
3219 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
3220 // optimizations will transparently handle this case.
3222 // In order for this transformation to be safe, the LHS must be of the
3223 // form X*(2^n) and the Or constant must be less than 2^n.
3224 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3225 const SCEV *LHS = getSCEV(U->getOperand(0));
3226 const APInt &CIVal = CI->getValue();
3227 if (GetMinTrailingZeros(LHS) >=
3228 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
3229 // Build a plain add SCEV.
3230 const SCEV *S = getAddExpr(LHS, getSCEV(CI));
3231 // If the LHS of the add was an addrec and it has no-wrap flags,
3232 // transfer the no-wrap flags, since an or won't introduce a wrap.
3233 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
3234 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
3235 if (OldAR->hasNoUnsignedWrap())
3236 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoUnsignedWrap(true);
3237 if (OldAR->hasNoSignedWrap())
3238 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoSignedWrap(true);
3244 case Instruction::Xor:
3245 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3246 // If the RHS of the xor is a signbit, then this is just an add.
3247 // Instcombine turns add of signbit into xor as a strength reduction step.
3248 if (CI->getValue().isSignBit())
3249 return getAddExpr(getSCEV(U->getOperand(0)),
3250 getSCEV(U->getOperand(1)));
3252 // If the RHS of xor is -1, then this is a not operation.
3253 if (CI->isAllOnesValue())
3254 return getNotSCEV(getSCEV(U->getOperand(0)));
3256 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
3257 // This is a variant of the check for xor with -1, and it handles
3258 // the case where instcombine has trimmed non-demanded bits out
3259 // of an xor with -1.
3260 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
3261 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
3262 if (BO->getOpcode() == Instruction::And &&
3263 LCI->getValue() == CI->getValue())
3264 if (const SCEVZeroExtendExpr *Z =
3265 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
3266 const Type *UTy = U->getType();
3267 const SCEV *Z0 = Z->getOperand();
3268 const Type *Z0Ty = Z0->getType();
3269 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
3271 // If C is a low-bits mask, the zero extend is serving to
3272 // mask off the high bits. Complement the operand and
3273 // re-apply the zext.
3274 if (APIntOps::isMask(Z0TySize, CI->getValue()))
3275 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
3277 // If C is a single bit, it may be in the sign-bit position
3278 // before the zero-extend. In this case, represent the xor
3279 // using an add, which is equivalent, and re-apply the zext.
3280 APInt Trunc = APInt(CI->getValue()).trunc(Z0TySize);
3281 if (APInt(Trunc).zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
3283 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
3289 case Instruction::Shl:
3290 // Turn shift left of a constant amount into a multiply.
3291 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3292 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3293 Constant *X = ConstantInt::get(getContext(),
3294 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
3295 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3299 case Instruction::LShr:
3300 // Turn logical shift right of a constant into a unsigned divide.
3301 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3302 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3303 Constant *X = ConstantInt::get(getContext(),
3304 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
3305 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3309 case Instruction::AShr:
3310 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
3311 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
3312 if (Instruction *L = dyn_cast<Instruction>(U->getOperand(0)))
3313 if (L->getOpcode() == Instruction::Shl &&
3314 L->getOperand(1) == U->getOperand(1)) {
3315 unsigned BitWidth = getTypeSizeInBits(U->getType());
3316 uint64_t Amt = BitWidth - CI->getZExtValue();
3317 if (Amt == BitWidth)
3318 return getSCEV(L->getOperand(0)); // shift by zero --> noop
3320 return getIntegerSCEV(0, U->getType()); // value is undefined
3322 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
3323 IntegerType::get(getContext(), Amt)),
3328 case Instruction::Trunc:
3329 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
3331 case Instruction::ZExt:
3332 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3334 case Instruction::SExt:
3335 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3337 case Instruction::BitCast:
3338 // BitCasts are no-op casts so we just eliminate the cast.
3339 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
3340 return getSCEV(U->getOperand(0));
3343 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
3344 // lead to pointer expressions which cannot safely be expanded to GEPs,
3345 // because ScalarEvolution doesn't respect the GEP aliasing rules when
3346 // simplifying integer expressions.
3348 case Instruction::GetElementPtr:
3349 return createNodeForGEP(cast<GEPOperator>(U));
3351 case Instruction::PHI:
3352 return createNodeForPHI(cast<PHINode>(U));
3354 case Instruction::Select:
3355 // This could be a smax or umax that was lowered earlier.
3356 // Try to recover it.
3357 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
3358 Value *LHS = ICI->getOperand(0);
3359 Value *RHS = ICI->getOperand(1);
3360 switch (ICI->getPredicate()) {
3361 case ICmpInst::ICMP_SLT:
3362 case ICmpInst::ICMP_SLE:
3363 std::swap(LHS, RHS);
3365 case ICmpInst::ICMP_SGT:
3366 case ICmpInst::ICMP_SGE:
3367 if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
3368 return getSMaxExpr(getSCEV(LHS), getSCEV(RHS));
3369 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
3370 return getSMinExpr(getSCEV(LHS), getSCEV(RHS));
3372 case ICmpInst::ICMP_ULT:
3373 case ICmpInst::ICMP_ULE:
3374 std::swap(LHS, RHS);
3376 case ICmpInst::ICMP_UGT:
3377 case ICmpInst::ICMP_UGE:
3378 if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
3379 return getUMaxExpr(getSCEV(LHS), getSCEV(RHS));
3380 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
3381 return getUMinExpr(getSCEV(LHS), getSCEV(RHS));
3383 case ICmpInst::ICMP_NE:
3384 // n != 0 ? n : 1 -> umax(n, 1)
3385 if (LHS == U->getOperand(1) &&
3386 isa<ConstantInt>(U->getOperand(2)) &&
3387 cast<ConstantInt>(U->getOperand(2))->isOne() &&
3388 isa<ConstantInt>(RHS) &&
3389 cast<ConstantInt>(RHS)->isZero())
3390 return getUMaxExpr(getSCEV(LHS), getSCEV(U->getOperand(2)));
3392 case ICmpInst::ICMP_EQ:
3393 // n == 0 ? 1 : n -> umax(n, 1)
3394 if (LHS == U->getOperand(2) &&
3395 isa<ConstantInt>(U->getOperand(1)) &&
3396 cast<ConstantInt>(U->getOperand(1))->isOne() &&
3397 isa<ConstantInt>(RHS) &&
3398 cast<ConstantInt>(RHS)->isZero())
3399 return getUMaxExpr(getSCEV(LHS), getSCEV(U->getOperand(1)));
3406 default: // We cannot analyze this expression.
3410 return getUnknown(V);
3415 //===----------------------------------------------------------------------===//
3416 // Iteration Count Computation Code
3419 /// getBackedgeTakenCount - If the specified loop has a predictable
3420 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
3421 /// object. The backedge-taken count is the number of times the loop header
3422 /// will be branched to from within the loop. This is one less than the
3423 /// trip count of the loop, since it doesn't count the first iteration,
3424 /// when the header is branched to from outside the loop.
3426 /// Note that it is not valid to call this method on a loop without a
3427 /// loop-invariant backedge-taken count (see
3428 /// hasLoopInvariantBackedgeTakenCount).
3430 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
3431 return getBackedgeTakenInfo(L).Exact;
3434 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
3435 /// return the least SCEV value that is known never to be less than the
3436 /// actual backedge taken count.
3437 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
3438 return getBackedgeTakenInfo(L).Max;
3441 /// PushLoopPHIs - Push PHI nodes in the header of the given loop
3442 /// onto the given Worklist.
3444 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
3445 BasicBlock *Header = L->getHeader();
3447 // Push all Loop-header PHIs onto the Worklist stack.
3448 for (BasicBlock::iterator I = Header->begin();
3449 PHINode *PN = dyn_cast<PHINode>(I); ++I)
3450 Worklist.push_back(PN);
3453 const ScalarEvolution::BackedgeTakenInfo &
3454 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
3455 // Initially insert a CouldNotCompute for this loop. If the insertion
3456 // succeeds, proceed to actually compute a backedge-taken count and
3457 // update the value. The temporary CouldNotCompute value tells SCEV
3458 // code elsewhere that it shouldn't attempt to request a new
3459 // backedge-taken count, which could result in infinite recursion.
3460 std::pair<std::map<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
3461 BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute()));
3463 BackedgeTakenInfo BECount = ComputeBackedgeTakenCount(L);
3464 if (BECount.Exact != getCouldNotCompute()) {
3465 assert(BECount.Exact->isLoopInvariant(L) &&
3466 BECount.Max->isLoopInvariant(L) &&
3467 "Computed backedge-taken count isn't loop invariant for loop!");
3468 ++NumTripCountsComputed;
3470 // Update the value in the map.
3471 Pair.first->second = BECount;
3473 if (BECount.Max != getCouldNotCompute())
3474 // Update the value in the map.
3475 Pair.first->second = BECount;
3476 if (isa<PHINode>(L->getHeader()->begin()))
3477 // Only count loops that have phi nodes as not being computable.
3478 ++NumTripCountsNotComputed;
3481 // Now that we know more about the trip count for this loop, forget any
3482 // existing SCEV values for PHI nodes in this loop since they are only
3483 // conservative estimates made without the benefit of trip count
3484 // information. This is similar to the code in forgetLoop, except that
3485 // it handles SCEVUnknown PHI nodes specially.
3486 if (BECount.hasAnyInfo()) {
3487 SmallVector<Instruction *, 16> Worklist;
3488 PushLoopPHIs(L, Worklist);
3490 SmallPtrSet<Instruction *, 8> Visited;
3491 while (!Worklist.empty()) {
3492 Instruction *I = Worklist.pop_back_val();
3493 if (!Visited.insert(I)) continue;
3495 std::map<SCEVCallbackVH, const SCEV *>::iterator It =
3496 Scalars.find(static_cast<Value *>(I));
3497 if (It != Scalars.end()) {
3498 // SCEVUnknown for a PHI either means that it has an unrecognized
3499 // structure, or it's a PHI that's in the progress of being computed
3500 // by createNodeForPHI. In the former case, additional loop trip
3501 // count information isn't going to change anything. In the later
3502 // case, createNodeForPHI will perform the necessary updates on its
3503 // own when it gets to that point.
3504 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(It->second)) {
3505 ValuesAtScopes.erase(It->second);
3508 if (PHINode *PN = dyn_cast<PHINode>(I))
3509 ConstantEvolutionLoopExitValue.erase(PN);
3512 PushDefUseChildren(I, Worklist);
3516 return Pair.first->second;
3519 /// forgetLoop - This method should be called by the client when it has
3520 /// changed a loop in a way that may effect ScalarEvolution's ability to
3521 /// compute a trip count, or if the loop is deleted.
3522 void ScalarEvolution::forgetLoop(const Loop *L) {
3523 // Drop any stored trip count value.
3524 BackedgeTakenCounts.erase(L);
3526 // Drop information about expressions based on loop-header PHIs.
3527 SmallVector<Instruction *, 16> Worklist;
3528 PushLoopPHIs(L, Worklist);
3530 SmallPtrSet<Instruction *, 8> Visited;
3531 while (!Worklist.empty()) {
3532 Instruction *I = Worklist.pop_back_val();
3533 if (!Visited.insert(I)) continue;
3535 std::map<SCEVCallbackVH, const SCEV *>::iterator It =
3536 Scalars.find(static_cast<Value *>(I));
3537 if (It != Scalars.end()) {
3538 ValuesAtScopes.erase(It->second);
3540 if (PHINode *PN = dyn_cast<PHINode>(I))
3541 ConstantEvolutionLoopExitValue.erase(PN);
3544 PushDefUseChildren(I, Worklist);
3548 /// forgetValue - This method should be called by the client when it has
3549 /// changed a value in a way that may effect its value, or which may
3550 /// disconnect it from a def-use chain linking it to a loop.
3551 void ScalarEvolution::forgetValue(Value *V) {
3552 Instruction *I = dyn_cast<Instruction>(V);
3555 // Drop information about expressions based on loop-header PHIs.
3556 SmallVector<Instruction *, 16> Worklist;
3557 Worklist.push_back(I);
3559 SmallPtrSet<Instruction *, 8> Visited;
3560 while (!Worklist.empty()) {
3561 I = Worklist.pop_back_val();
3562 if (!Visited.insert(I)) continue;
3564 std::map<SCEVCallbackVH, const SCEV *>::iterator It =
3565 Scalars.find(static_cast<Value *>(I));
3566 if (It != Scalars.end()) {
3567 ValuesAtScopes.erase(It->second);
3569 if (PHINode *PN = dyn_cast<PHINode>(I))
3570 ConstantEvolutionLoopExitValue.erase(PN);
3573 PushDefUseChildren(I, Worklist);
3577 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
3578 /// of the specified loop will execute.
3579 ScalarEvolution::BackedgeTakenInfo
3580 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
3581 SmallVector<BasicBlock *, 8> ExitingBlocks;
3582 L->getExitingBlocks(ExitingBlocks);
3584 // Examine all exits and pick the most conservative values.
3585 const SCEV *BECount = getCouldNotCompute();
3586 const SCEV *MaxBECount = getCouldNotCompute();
3587 bool CouldNotComputeBECount = false;
3588 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
3589 BackedgeTakenInfo NewBTI =
3590 ComputeBackedgeTakenCountFromExit(L, ExitingBlocks[i]);
3592 if (NewBTI.Exact == getCouldNotCompute()) {
3593 // We couldn't compute an exact value for this exit, so
3594 // we won't be able to compute an exact value for the loop.
3595 CouldNotComputeBECount = true;
3596 BECount = getCouldNotCompute();
3597 } else if (!CouldNotComputeBECount) {
3598 if (BECount == getCouldNotCompute())
3599 BECount = NewBTI.Exact;
3601 BECount = getUMinFromMismatchedTypes(BECount, NewBTI.Exact);
3603 if (MaxBECount == getCouldNotCompute())
3604 MaxBECount = NewBTI.Max;
3605 else if (NewBTI.Max != getCouldNotCompute())
3606 MaxBECount = getUMinFromMismatchedTypes(MaxBECount, NewBTI.Max);
3609 return BackedgeTakenInfo(BECount, MaxBECount);
3612 /// ComputeBackedgeTakenCountFromExit - Compute the number of times the backedge
3613 /// of the specified loop will execute if it exits via the specified block.
3614 ScalarEvolution::BackedgeTakenInfo
3615 ScalarEvolution::ComputeBackedgeTakenCountFromExit(const Loop *L,
3616 BasicBlock *ExitingBlock) {
3618 // Okay, we've chosen an exiting block. See what condition causes us to
3619 // exit at this block.
3621 // FIXME: we should be able to handle switch instructions (with a single exit)
3622 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
3623 if (ExitBr == 0) return getCouldNotCompute();
3624 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
3626 // At this point, we know we have a conditional branch that determines whether
3627 // the loop is exited. However, we don't know if the branch is executed each
3628 // time through the loop. If not, then the execution count of the branch will
3629 // not be equal to the trip count of the loop.
3631 // Currently we check for this by checking to see if the Exit branch goes to
3632 // the loop header. If so, we know it will always execute the same number of
3633 // times as the loop. We also handle the case where the exit block *is* the
3634 // loop header. This is common for un-rotated loops.
3636 // If both of those tests fail, walk up the unique predecessor chain to the
3637 // header, stopping if there is an edge that doesn't exit the loop. If the
3638 // header is reached, the execution count of the branch will be equal to the
3639 // trip count of the loop.
3641 // More extensive analysis could be done to handle more cases here.
3643 if (ExitBr->getSuccessor(0) != L->getHeader() &&
3644 ExitBr->getSuccessor(1) != L->getHeader() &&
3645 ExitBr->getParent() != L->getHeader()) {
3646 // The simple checks failed, try climbing the unique predecessor chain
3647 // up to the header.
3649 for (BasicBlock *BB = ExitBr->getParent(); BB; ) {
3650 BasicBlock *Pred = BB->getUniquePredecessor();
3652 return getCouldNotCompute();
3653 TerminatorInst *PredTerm = Pred->getTerminator();
3654 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) {
3655 BasicBlock *PredSucc = PredTerm->getSuccessor(i);
3658 // If the predecessor has a successor that isn't BB and isn't
3659 // outside the loop, assume the worst.
3660 if (L->contains(PredSucc))
3661 return getCouldNotCompute();
3663 if (Pred == L->getHeader()) {
3670 return getCouldNotCompute();
3673 // Proceed to the next level to examine the exit condition expression.
3674 return ComputeBackedgeTakenCountFromExitCond(L, ExitBr->getCondition(),
3675 ExitBr->getSuccessor(0),
3676 ExitBr->getSuccessor(1));
3679 /// ComputeBackedgeTakenCountFromExitCond - Compute the number of times the
3680 /// backedge of the specified loop will execute if its exit condition
3681 /// were a conditional branch of ExitCond, TBB, and FBB.
3682 ScalarEvolution::BackedgeTakenInfo
3683 ScalarEvolution::ComputeBackedgeTakenCountFromExitCond(const Loop *L,
3687 // Check if the controlling expression for this loop is an And or Or.
3688 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
3689 if (BO->getOpcode() == Instruction::And) {
3690 // Recurse on the operands of the and.
3691 BackedgeTakenInfo BTI0 =
3692 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB);
3693 BackedgeTakenInfo BTI1 =
3694 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB);
3695 const SCEV *BECount = getCouldNotCompute();
3696 const SCEV *MaxBECount = getCouldNotCompute();
3697 if (L->contains(TBB)) {
3698 // Both conditions must be true for the loop to continue executing.
3699 // Choose the less conservative count.
3700 if (BTI0.Exact == getCouldNotCompute() ||
3701 BTI1.Exact == getCouldNotCompute())
3702 BECount = getCouldNotCompute();
3704 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3705 if (BTI0.Max == getCouldNotCompute())
3706 MaxBECount = BTI1.Max;
3707 else if (BTI1.Max == getCouldNotCompute())
3708 MaxBECount = BTI0.Max;
3710 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max);
3712 // Both conditions must be true for the loop to exit.
3713 assert(L->contains(FBB) && "Loop block has no successor in loop!");
3714 if (BTI0.Exact != getCouldNotCompute() &&
3715 BTI1.Exact != getCouldNotCompute())
3716 BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3717 if (BTI0.Max != getCouldNotCompute() &&
3718 BTI1.Max != getCouldNotCompute())
3719 MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max);
3722 return BackedgeTakenInfo(BECount, MaxBECount);
3724 if (BO->getOpcode() == Instruction::Or) {
3725 // Recurse on the operands of the or.
3726 BackedgeTakenInfo BTI0 =
3727 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB);
3728 BackedgeTakenInfo BTI1 =
3729 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB);
3730 const SCEV *BECount = getCouldNotCompute();
3731 const SCEV *MaxBECount = getCouldNotCompute();
3732 if (L->contains(FBB)) {
3733 // Both conditions must be false for the loop to continue executing.
3734 // Choose the less conservative count.
3735 if (BTI0.Exact == getCouldNotCompute() ||
3736 BTI1.Exact == getCouldNotCompute())
3737 BECount = getCouldNotCompute();
3739 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3740 if (BTI0.Max == getCouldNotCompute())
3741 MaxBECount = BTI1.Max;
3742 else if (BTI1.Max == getCouldNotCompute())
3743 MaxBECount = BTI0.Max;
3745 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max);
3747 // Both conditions must be false for the loop to exit.
3748 assert(L->contains(TBB) && "Loop block has no successor in loop!");
3749 if (BTI0.Exact != getCouldNotCompute() &&
3750 BTI1.Exact != getCouldNotCompute())
3751 BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3752 if (BTI0.Max != getCouldNotCompute() &&
3753 BTI1.Max != getCouldNotCompute())
3754 MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max);
3757 return BackedgeTakenInfo(BECount, MaxBECount);
3761 // With an icmp, it may be feasible to compute an exact backedge-taken count.
3762 // Proceed to the next level to examine the icmp.
3763 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
3764 return ComputeBackedgeTakenCountFromExitCondICmp(L, ExitCondICmp, TBB, FBB);
3766 // Check for a constant condition. These are normally stripped out by
3767 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
3768 // preserve the CFG and is temporarily leaving constant conditions
3770 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
3771 if (L->contains(FBB) == !CI->getZExtValue())
3772 // The backedge is always taken.
3773 return getCouldNotCompute();
3775 // The backedge is never taken.
3776 return getIntegerSCEV(0, CI->getType());
3779 // If it's not an integer or pointer comparison then compute it the hard way.
3780 return ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB));
3783 /// ComputeBackedgeTakenCountFromExitCondICmp - Compute the number of times the
3784 /// backedge of the specified loop will execute if its exit condition
3785 /// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB.
3786 ScalarEvolution::BackedgeTakenInfo
3787 ScalarEvolution::ComputeBackedgeTakenCountFromExitCondICmp(const Loop *L,
3792 // If the condition was exit on true, convert the condition to exit on false
3793 ICmpInst::Predicate Cond;
3794 if (!L->contains(FBB))
3795 Cond = ExitCond->getPredicate();
3797 Cond = ExitCond->getInversePredicate();
3799 // Handle common loops like: for (X = "string"; *X; ++X)
3800 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
3801 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
3802 BackedgeTakenInfo ItCnt =
3803 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond);
3804 if (ItCnt.hasAnyInfo())
3808 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
3809 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
3811 // Try to evaluate any dependencies out of the loop.
3812 LHS = getSCEVAtScope(LHS, L);
3813 RHS = getSCEVAtScope(RHS, L);
3815 // At this point, we would like to compute how many iterations of the
3816 // loop the predicate will return true for these inputs.
3817 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) {
3818 // If there is a loop-invariant, force it into the RHS.
3819 std::swap(LHS, RHS);
3820 Cond = ICmpInst::getSwappedPredicate(Cond);
3823 // If we have a comparison of a chrec against a constant, try to use value
3824 // ranges to answer this query.
3825 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
3826 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
3827 if (AddRec->getLoop() == L) {
3828 // Form the constant range.
3829 ConstantRange CompRange(
3830 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
3832 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
3833 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
3837 case ICmpInst::ICMP_NE: { // while (X != Y)
3838 // Convert to: while (X-Y != 0)
3839 BackedgeTakenInfo BTI = HowFarToZero(getMinusSCEV(LHS, RHS), L);
3840 if (BTI.hasAnyInfo()) return BTI;
3843 case ICmpInst::ICMP_EQ: { // while (X == Y)
3844 // Convert to: while (X-Y == 0)
3845 BackedgeTakenInfo BTI = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
3846 if (BTI.hasAnyInfo()) return BTI;
3849 case ICmpInst::ICMP_SLT: {
3850 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true);
3851 if (BTI.hasAnyInfo()) return BTI;
3854 case ICmpInst::ICMP_SGT: {
3855 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
3856 getNotSCEV(RHS), L, true);
3857 if (BTI.hasAnyInfo()) return BTI;
3860 case ICmpInst::ICMP_ULT: {
3861 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false);
3862 if (BTI.hasAnyInfo()) return BTI;
3865 case ICmpInst::ICMP_UGT: {
3866 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
3867 getNotSCEV(RHS), L, false);
3868 if (BTI.hasAnyInfo()) return BTI;
3873 dbgs() << "ComputeBackedgeTakenCount ";
3874 if (ExitCond->getOperand(0)->getType()->isUnsigned())
3875 dbgs() << "[unsigned] ";
3876 dbgs() << *LHS << " "
3877 << Instruction::getOpcodeName(Instruction::ICmp)
3878 << " " << *RHS << "\n";
3883 ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB));
3886 static ConstantInt *
3887 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
3888 ScalarEvolution &SE) {
3889 const SCEV *InVal = SE.getConstant(C);
3890 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
3891 assert(isa<SCEVConstant>(Val) &&
3892 "Evaluation of SCEV at constant didn't fold correctly?");
3893 return cast<SCEVConstant>(Val)->getValue();
3896 /// GetAddressedElementFromGlobal - Given a global variable with an initializer
3897 /// and a GEP expression (missing the pointer index) indexing into it, return
3898 /// the addressed element of the initializer or null if the index expression is
3901 GetAddressedElementFromGlobal(GlobalVariable *GV,
3902 const std::vector<ConstantInt*> &Indices) {
3903 Constant *Init = GV->getInitializer();
3904 for (unsigned i = 0, e = Indices.size(); i != e; ++i) {
3905 uint64_t Idx = Indices[i]->getZExtValue();
3906 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) {
3907 assert(Idx < CS->getNumOperands() && "Bad struct index!");
3908 Init = cast<Constant>(CS->getOperand(Idx));
3909 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) {
3910 if (Idx >= CA->getNumOperands()) return 0; // Bogus program
3911 Init = cast<Constant>(CA->getOperand(Idx));
3912 } else if (isa<ConstantAggregateZero>(Init)) {
3913 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) {
3914 assert(Idx < STy->getNumElements() && "Bad struct index!");
3915 Init = Constant::getNullValue(STy->getElementType(Idx));
3916 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) {
3917 if (Idx >= ATy->getNumElements()) return 0; // Bogus program
3918 Init = Constant::getNullValue(ATy->getElementType());
3920 llvm_unreachable("Unknown constant aggregate type!");
3924 return 0; // Unknown initializer type
3930 /// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of
3931 /// 'icmp op load X, cst', try to see if we can compute the backedge
3932 /// execution count.
3933 ScalarEvolution::BackedgeTakenInfo
3934 ScalarEvolution::ComputeLoadConstantCompareBackedgeTakenCount(
3938 ICmpInst::Predicate predicate) {
3939 if (LI->isVolatile()) return getCouldNotCompute();
3941 // Check to see if the loaded pointer is a getelementptr of a global.
3942 // TODO: Use SCEV instead of manually grubbing with GEPs.
3943 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
3944 if (!GEP) return getCouldNotCompute();
3946 // Make sure that it is really a constant global we are gepping, with an
3947 // initializer, and make sure the first IDX is really 0.
3948 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
3949 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
3950 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
3951 !cast<Constant>(GEP->getOperand(1))->isNullValue())
3952 return getCouldNotCompute();
3954 // Okay, we allow one non-constant index into the GEP instruction.
3956 std::vector<ConstantInt*> Indexes;
3957 unsigned VarIdxNum = 0;
3958 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
3959 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
3960 Indexes.push_back(CI);
3961 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
3962 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
3963 VarIdx = GEP->getOperand(i);
3965 Indexes.push_back(0);
3968 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
3969 // Check to see if X is a loop variant variable value now.
3970 const SCEV *Idx = getSCEV(VarIdx);
3971 Idx = getSCEVAtScope(Idx, L);
3973 // We can only recognize very limited forms of loop index expressions, in
3974 // particular, only affine AddRec's like {C1,+,C2}.
3975 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
3976 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) ||
3977 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
3978 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
3979 return getCouldNotCompute();
3981 unsigned MaxSteps = MaxBruteForceIterations;
3982 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
3983 ConstantInt *ItCst = ConstantInt::get(
3984 cast<IntegerType>(IdxExpr->getType()), IterationNum);
3985 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
3987 // Form the GEP offset.
3988 Indexes[VarIdxNum] = Val;
3990 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes);
3991 if (Result == 0) break; // Cannot compute!
3993 // Evaluate the condition for this iteration.
3994 Result = ConstantExpr::getICmp(predicate, Result, RHS);
3995 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
3996 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
3998 dbgs() << "\n***\n*** Computed loop count " << *ItCst
3999 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
4002 ++NumArrayLenItCounts;
4003 return getConstant(ItCst); // Found terminating iteration!
4006 return getCouldNotCompute();
4010 /// CanConstantFold - Return true if we can constant fold an instruction of the
4011 /// specified type, assuming that all operands were constants.
4012 static bool CanConstantFold(const Instruction *I) {
4013 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
4014 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I))
4017 if (const CallInst *CI = dyn_cast<CallInst>(I))
4018 if (const Function *F = CI->getCalledFunction())
4019 return canConstantFoldCallTo(F);
4023 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
4024 /// in the loop that V is derived from. We allow arbitrary operations along the
4025 /// way, but the operands of an operation must either be constants or a value
4026 /// derived from a constant PHI. If this expression does not fit with these
4027 /// constraints, return null.
4028 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
4029 // If this is not an instruction, or if this is an instruction outside of the
4030 // loop, it can't be derived from a loop PHI.
4031 Instruction *I = dyn_cast<Instruction>(V);
4032 if (I == 0 || !L->contains(I)) return 0;
4034 if (PHINode *PN = dyn_cast<PHINode>(I)) {
4035 if (L->getHeader() == I->getParent())
4038 // We don't currently keep track of the control flow needed to evaluate
4039 // PHIs, so we cannot handle PHIs inside of loops.
4043 // If we won't be able to constant fold this expression even if the operands
4044 // are constants, return early.
4045 if (!CanConstantFold(I)) return 0;
4047 // Otherwise, we can evaluate this instruction if all of its operands are
4048 // constant or derived from a PHI node themselves.
4050 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op)
4051 if (!(isa<Constant>(I->getOperand(Op)) ||
4052 isa<GlobalValue>(I->getOperand(Op)))) {
4053 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L);
4054 if (P == 0) return 0; // Not evolving from PHI
4058 return 0; // Evolving from multiple different PHIs.
4061 // This is a expression evolving from a constant PHI!
4065 /// EvaluateExpression - Given an expression that passes the
4066 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
4067 /// in the loop has the value PHIVal. If we can't fold this expression for some
4068 /// reason, return null.
4069 static Constant *EvaluateExpression(Value *V, Constant *PHIVal,
4070 const TargetData *TD) {
4071 if (isa<PHINode>(V)) return PHIVal;
4072 if (Constant *C = dyn_cast<Constant>(V)) return C;
4073 if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) return GV;
4074 Instruction *I = cast<Instruction>(V);
4076 std::vector<Constant*> Operands;
4077 Operands.resize(I->getNumOperands());
4079 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
4080 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal, TD);
4081 if (Operands[i] == 0) return 0;
4084 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
4085 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
4087 return ConstantFoldInstOperands(I->getOpcode(), I->getType(),
4088 &Operands[0], Operands.size(), TD);
4091 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
4092 /// in the header of its containing loop, we know the loop executes a
4093 /// constant number of times, and the PHI node is just a recurrence
4094 /// involving constants, fold it.
4096 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
4099 std::map<PHINode*, Constant*>::iterator I =
4100 ConstantEvolutionLoopExitValue.find(PN);
4101 if (I != ConstantEvolutionLoopExitValue.end())
4104 if (BEs.ugt(MaxBruteForceIterations))
4105 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
4107 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
4109 // Since the loop is canonicalized, the PHI node must have two entries. One
4110 // entry must be a constant (coming in from outside of the loop), and the
4111 // second must be derived from the same PHI.
4112 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
4113 Constant *StartCST =
4114 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
4116 return RetVal = 0; // Must be a constant.
4118 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
4119 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
4121 return RetVal = 0; // Not derived from same PHI.
4123 // Execute the loop symbolically to determine the exit value.
4124 if (BEs.getActiveBits() >= 32)
4125 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
4127 unsigned NumIterations = BEs.getZExtValue(); // must be in range
4128 unsigned IterationNum = 0;
4129 for (Constant *PHIVal = StartCST; ; ++IterationNum) {
4130 if (IterationNum == NumIterations)
4131 return RetVal = PHIVal; // Got exit value!
4133 // Compute the value of the PHI node for the next iteration.
4134 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD);
4135 if (NextPHI == PHIVal)
4136 return RetVal = NextPHI; // Stopped evolving!
4138 return 0; // Couldn't evaluate!
4143 /// ComputeBackedgeTakenCountExhaustively - If the loop is known to execute a
4144 /// constant number of times (the condition evolves only from constants),
4145 /// try to evaluate a few iterations of the loop until we get the exit
4146 /// condition gets a value of ExitWhen (true or false). If we cannot
4147 /// evaluate the trip count of the loop, return getCouldNotCompute().
4149 ScalarEvolution::ComputeBackedgeTakenCountExhaustively(const Loop *L,
4152 PHINode *PN = getConstantEvolvingPHI(Cond, L);
4153 if (PN == 0) return getCouldNotCompute();
4155 // Since the loop is canonicalized, the PHI node must have two entries. One
4156 // entry must be a constant (coming in from outside of the loop), and the
4157 // second must be derived from the same PHI.
4158 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
4159 Constant *StartCST =
4160 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
4161 if (StartCST == 0) return getCouldNotCompute(); // Must be a constant.
4163 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
4164 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
4165 if (PN2 != PN) return getCouldNotCompute(); // Not derived from same PHI.
4167 // Okay, we find a PHI node that defines the trip count of this loop. Execute
4168 // the loop symbolically to determine when the condition gets a value of
4170 unsigned IterationNum = 0;
4171 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
4172 for (Constant *PHIVal = StartCST;
4173 IterationNum != MaxIterations; ++IterationNum) {
4174 ConstantInt *CondVal =
4175 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal, TD));
4177 // Couldn't symbolically evaluate.
4178 if (!CondVal) return getCouldNotCompute();
4180 if (CondVal->getValue() == uint64_t(ExitWhen)) {
4181 ++NumBruteForceTripCountsComputed;
4182 return getConstant(Type::getInt32Ty(getContext()), IterationNum);
4185 // Compute the value of the PHI node for the next iteration.
4186 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD);
4187 if (NextPHI == 0 || NextPHI == PHIVal)
4188 return getCouldNotCompute();// Couldn't evaluate or not making progress...
4192 // Too many iterations were needed to evaluate.
4193 return getCouldNotCompute();
4196 /// getSCEVAtScope - Return a SCEV expression for the specified value
4197 /// at the specified scope in the program. The L value specifies a loop
4198 /// nest to evaluate the expression at, where null is the top-level or a
4199 /// specified loop is immediately inside of the loop.
4201 /// This method can be used to compute the exit value for a variable defined
4202 /// in a loop by querying what the value will hold in the parent loop.
4204 /// In the case that a relevant loop exit value cannot be computed, the
4205 /// original value V is returned.
4206 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
4207 // Check to see if we've folded this expression at this loop before.
4208 std::map<const Loop *, const SCEV *> &Values = ValuesAtScopes[V];
4209 std::pair<std::map<const Loop *, const SCEV *>::iterator, bool> Pair =
4210 Values.insert(std::make_pair(L, static_cast<const SCEV *>(0)));
4212 return Pair.first->second ? Pair.first->second : V;
4214 // Otherwise compute it.
4215 const SCEV *C = computeSCEVAtScope(V, L);
4216 ValuesAtScopes[V][L] = C;
4220 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
4221 if (isa<SCEVConstant>(V)) return V;
4223 // If this instruction is evolved from a constant-evolving PHI, compute the
4224 // exit value from the loop without using SCEVs.
4225 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
4226 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
4227 const Loop *LI = (*this->LI)[I->getParent()];
4228 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
4229 if (PHINode *PN = dyn_cast<PHINode>(I))
4230 if (PN->getParent() == LI->getHeader()) {
4231 // Okay, there is no closed form solution for the PHI node. Check
4232 // to see if the loop that contains it has a known backedge-taken
4233 // count. If so, we may be able to force computation of the exit
4235 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
4236 if (const SCEVConstant *BTCC =
4237 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
4238 // Okay, we know how many times the containing loop executes. If
4239 // this is a constant evolving PHI node, get the final value at
4240 // the specified iteration number.
4241 Constant *RV = getConstantEvolutionLoopExitValue(PN,
4242 BTCC->getValue()->getValue(),
4244 if (RV) return getSCEV(RV);
4248 // Okay, this is an expression that we cannot symbolically evaluate
4249 // into a SCEV. Check to see if it's possible to symbolically evaluate
4250 // the arguments into constants, and if so, try to constant propagate the
4251 // result. This is particularly useful for computing loop exit values.
4252 if (CanConstantFold(I)) {
4253 std::vector<Constant*> Operands;
4254 Operands.reserve(I->getNumOperands());
4255 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
4256 Value *Op = I->getOperand(i);
4257 if (Constant *C = dyn_cast<Constant>(Op)) {
4258 Operands.push_back(C);
4260 // If any of the operands is non-constant and if they are
4261 // non-integer and non-pointer, don't even try to analyze them
4262 // with scev techniques.
4263 if (!isSCEVable(Op->getType()))
4266 const SCEV *OpV = getSCEVAtScope(Op, L);
4267 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) {
4268 Constant *C = SC->getValue();
4269 if (C->getType() != Op->getType())
4270 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
4274 Operands.push_back(C);
4275 } else if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) {
4276 if (Constant *C = dyn_cast<Constant>(SU->getValue())) {
4277 if (C->getType() != Op->getType())
4279 ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
4283 Operands.push_back(C);
4293 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
4294 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
4295 Operands[0], Operands[1], TD);
4297 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
4298 &Operands[0], Operands.size(), TD);
4304 // This is some other type of SCEVUnknown, just return it.
4308 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
4309 // Avoid performing the look-up in the common case where the specified
4310 // expression has no loop-variant portions.
4311 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
4312 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
4313 if (OpAtScope != Comm->getOperand(i)) {
4314 // Okay, at least one of these operands is loop variant but might be
4315 // foldable. Build a new instance of the folded commutative expression.
4316 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
4317 Comm->op_begin()+i);
4318 NewOps.push_back(OpAtScope);
4320 for (++i; i != e; ++i) {
4321 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
4322 NewOps.push_back(OpAtScope);
4324 if (isa<SCEVAddExpr>(Comm))
4325 return getAddExpr(NewOps);
4326 if (isa<SCEVMulExpr>(Comm))
4327 return getMulExpr(NewOps);
4328 if (isa<SCEVSMaxExpr>(Comm))
4329 return getSMaxExpr(NewOps);
4330 if (isa<SCEVUMaxExpr>(Comm))
4331 return getUMaxExpr(NewOps);
4332 llvm_unreachable("Unknown commutative SCEV type!");
4335 // If we got here, all operands are loop invariant.
4339 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
4340 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
4341 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
4342 if (LHS == Div->getLHS() && RHS == Div->getRHS())
4343 return Div; // must be loop invariant
4344 return getUDivExpr(LHS, RHS);
4347 // If this is a loop recurrence for a loop that does not contain L, then we
4348 // are dealing with the final value computed by the loop.
4349 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
4350 if (!L || !AddRec->getLoop()->contains(L)) {
4351 // To evaluate this recurrence, we need to know how many times the AddRec
4352 // loop iterates. Compute this now.
4353 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
4354 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
4356 // Then, evaluate the AddRec.
4357 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
4362 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
4363 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
4364 if (Op == Cast->getOperand())
4365 return Cast; // must be loop invariant
4366 return getZeroExtendExpr(Op, Cast->getType());
4369 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
4370 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
4371 if (Op == Cast->getOperand())
4372 return Cast; // must be loop invariant
4373 return getSignExtendExpr(Op, Cast->getType());
4376 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
4377 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
4378 if (Op == Cast->getOperand())
4379 return Cast; // must be loop invariant
4380 return getTruncateExpr(Op, Cast->getType());
4383 llvm_unreachable("Unknown SCEV type!");
4387 /// getSCEVAtScope - This is a convenience function which does
4388 /// getSCEVAtScope(getSCEV(V), L).
4389 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
4390 return getSCEVAtScope(getSCEV(V), L);
4393 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
4394 /// following equation:
4396 /// A * X = B (mod N)
4398 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
4399 /// A and B isn't important.
4401 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
4402 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
4403 ScalarEvolution &SE) {
4404 uint32_t BW = A.getBitWidth();
4405 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
4406 assert(A != 0 && "A must be non-zero.");
4410 // The gcd of A and N may have only one prime factor: 2. The number of
4411 // trailing zeros in A is its multiplicity
4412 uint32_t Mult2 = A.countTrailingZeros();
4415 // 2. Check if B is divisible by D.
4417 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
4418 // is not less than multiplicity of this prime factor for D.
4419 if (B.countTrailingZeros() < Mult2)
4420 return SE.getCouldNotCompute();
4422 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
4425 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
4426 // bit width during computations.
4427 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
4428 APInt Mod(BW + 1, 0);
4429 Mod.set(BW - Mult2); // Mod = N / D
4430 APInt I = AD.multiplicativeInverse(Mod);
4432 // 4. Compute the minimum unsigned root of the equation:
4433 // I * (B / D) mod (N / D)
4434 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
4436 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
4438 return SE.getConstant(Result.trunc(BW));
4441 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
4442 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
4443 /// might be the same) or two SCEVCouldNotCompute objects.
4445 static std::pair<const SCEV *,const SCEV *>
4446 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
4447 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
4448 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
4449 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
4450 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
4452 // We currently can only solve this if the coefficients are constants.
4453 if (!LC || !MC || !NC) {
4454 const SCEV *CNC = SE.getCouldNotCompute();
4455 return std::make_pair(CNC, CNC);
4458 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
4459 const APInt &L = LC->getValue()->getValue();
4460 const APInt &M = MC->getValue()->getValue();
4461 const APInt &N = NC->getValue()->getValue();
4462 APInt Two(BitWidth, 2);
4463 APInt Four(BitWidth, 4);
4466 using namespace APIntOps;
4468 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
4469 // The B coefficient is M-N/2
4473 // The A coefficient is N/2
4474 APInt A(N.sdiv(Two));
4476 // Compute the B^2-4ac term.
4479 SqrtTerm -= Four * (A * C);
4481 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
4482 // integer value or else APInt::sqrt() will assert.
4483 APInt SqrtVal(SqrtTerm.sqrt());
4485 // Compute the two solutions for the quadratic formula.
4486 // The divisions must be performed as signed divisions.
4488 APInt TwoA( A << 1 );
4489 if (TwoA.isMinValue()) {
4490 const SCEV *CNC = SE.getCouldNotCompute();
4491 return std::make_pair(CNC, CNC);
4494 LLVMContext &Context = SE.getContext();
4496 ConstantInt *Solution1 =
4497 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
4498 ConstantInt *Solution2 =
4499 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
4501 return std::make_pair(SE.getConstant(Solution1),
4502 SE.getConstant(Solution2));
4503 } // end APIntOps namespace
4506 /// HowFarToZero - Return the number of times a backedge comparing the specified
4507 /// value to zero will execute. If not computable, return CouldNotCompute.
4508 ScalarEvolution::BackedgeTakenInfo
4509 ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) {
4510 // If the value is a constant
4511 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
4512 // If the value is already zero, the branch will execute zero times.
4513 if (C->getValue()->isZero()) return C;
4514 return getCouldNotCompute(); // Otherwise it will loop infinitely.
4517 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
4518 if (!AddRec || AddRec->getLoop() != L)
4519 return getCouldNotCompute();
4521 if (AddRec->isAffine()) {
4522 // If this is an affine expression, the execution count of this branch is
4523 // the minimum unsigned root of the following equation:
4525 // Start + Step*N = 0 (mod 2^BW)
4529 // Step*N = -Start (mod 2^BW)
4531 // where BW is the common bit width of Start and Step.
4533 // Get the initial value for the loop.
4534 const SCEV *Start = getSCEVAtScope(AddRec->getStart(),
4535 L->getParentLoop());
4536 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1),
4537 L->getParentLoop());
4539 if (const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) {
4540 // For now we handle only constant steps.
4542 // First, handle unitary steps.
4543 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so:
4544 return getNegativeSCEV(Start); // N = -Start (as unsigned)
4545 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so:
4546 return Start; // N = Start (as unsigned)
4548 // Then, try to solve the above equation provided that Start is constant.
4549 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
4550 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
4551 -StartC->getValue()->getValue(),
4554 } else if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
4555 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
4556 // the quadratic equation to solve it.
4557 std::pair<const SCEV *,const SCEV *> Roots = SolveQuadraticEquation(AddRec,
4559 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
4560 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
4563 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1
4564 << " sol#2: " << *R2 << "\n";
4566 // Pick the smallest positive root value.
4567 if (ConstantInt *CB =
4568 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
4569 R1->getValue(), R2->getValue()))) {
4570 if (CB->getZExtValue() == false)
4571 std::swap(R1, R2); // R1 is the minimum root now.
4573 // We can only use this value if the chrec ends up with an exact zero
4574 // value at this index. When solving for "X*X != 5", for example, we
4575 // should not accept a root of 2.
4576 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
4578 return R1; // We found a quadratic root!
4583 return getCouldNotCompute();
4586 /// HowFarToNonZero - Return the number of times a backedge checking the
4587 /// specified value for nonzero will execute. If not computable, return
4589 ScalarEvolution::BackedgeTakenInfo
4590 ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
4591 // Loops that look like: while (X == 0) are very strange indeed. We don't
4592 // handle them yet except for the trivial case. This could be expanded in the
4593 // future as needed.
4595 // If the value is a constant, check to see if it is known to be non-zero
4596 // already. If so, the backedge will execute zero times.
4597 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
4598 if (!C->getValue()->isNullValue())
4599 return getIntegerSCEV(0, C->getType());
4600 return getCouldNotCompute(); // Otherwise it will loop infinitely.
4603 // We could implement others, but I really doubt anyone writes loops like
4604 // this, and if they did, they would already be constant folded.
4605 return getCouldNotCompute();
4608 /// getLoopPredecessor - If the given loop's header has exactly one unique
4609 /// predecessor outside the loop, return it. Otherwise return null.
4611 BasicBlock *ScalarEvolution::getLoopPredecessor(const Loop *L) {
4612 BasicBlock *Header = L->getHeader();
4613 BasicBlock *Pred = 0;
4614 for (pred_iterator PI = pred_begin(Header), E = pred_end(Header);
4616 if (!L->contains(*PI)) {
4617 if (Pred && Pred != *PI) return 0; // Multiple predecessors.
4623 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
4624 /// (which may not be an immediate predecessor) which has exactly one
4625 /// successor from which BB is reachable, or null if no such block is
4629 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
4630 // If the block has a unique predecessor, then there is no path from the
4631 // predecessor to the block that does not go through the direct edge
4632 // from the predecessor to the block.
4633 if (BasicBlock *Pred = BB->getSinglePredecessor())
4636 // A loop's header is defined to be a block that dominates the loop.
4637 // If the header has a unique predecessor outside the loop, it must be
4638 // a block that has exactly one successor that can reach the loop.
4639 if (Loop *L = LI->getLoopFor(BB))
4640 return getLoopPredecessor(L);
4645 /// HasSameValue - SCEV structural equivalence is usually sufficient for
4646 /// testing whether two expressions are equal, however for the purposes of
4647 /// looking for a condition guarding a loop, it can be useful to be a little
4648 /// more general, since a front-end may have replicated the controlling
4651 static bool HasSameValue(const SCEV *A, const SCEV *B) {
4652 // Quick check to see if they are the same SCEV.
4653 if (A == B) return true;
4655 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
4656 // two different instructions with the same value. Check for this case.
4657 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
4658 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
4659 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
4660 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
4661 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory())
4664 // Otherwise assume they may have a different value.
4668 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
4669 return getSignedRange(S).getSignedMax().isNegative();
4672 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
4673 return getSignedRange(S).getSignedMin().isStrictlyPositive();
4676 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
4677 return !getSignedRange(S).getSignedMin().isNegative();
4680 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
4681 return !getSignedRange(S).getSignedMax().isStrictlyPositive();
4684 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
4685 return isKnownNegative(S) || isKnownPositive(S);
4688 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
4689 const SCEV *LHS, const SCEV *RHS) {
4690 // If LHS or RHS is an addrec, check to see if the condition is true in
4691 // every iteration of the loop.
4692 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
4693 if (isLoopEntryGuardedByCond(
4694 AR->getLoop(), Pred, AR->getStart(), RHS) &&
4695 isLoopBackedgeGuardedByCond(
4696 AR->getLoop(), Pred,
4697 getAddExpr(AR, AR->getStepRecurrence(*this)), RHS))
4699 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS))
4700 if (isLoopEntryGuardedByCond(
4701 AR->getLoop(), Pred, LHS, AR->getStart()) &&
4702 isLoopBackedgeGuardedByCond(
4703 AR->getLoop(), Pred,
4704 LHS, getAddExpr(AR, AR->getStepRecurrence(*this))))
4707 // Otherwise see what can be done with known constant ranges.
4708 return isKnownPredicateWithRanges(Pred, LHS, RHS);
4712 ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred,
4713 const SCEV *LHS, const SCEV *RHS) {
4714 if (HasSameValue(LHS, RHS))
4715 return ICmpInst::isTrueWhenEqual(Pred);
4717 // This code is split out from isKnownPredicate because it is called from
4718 // within isLoopEntryGuardedByCond.
4721 llvm_unreachable("Unexpected ICmpInst::Predicate value!");
4723 case ICmpInst::ICMP_SGT:
4724 Pred = ICmpInst::ICMP_SLT;
4725 std::swap(LHS, RHS);
4726 case ICmpInst::ICMP_SLT: {
4727 ConstantRange LHSRange = getSignedRange(LHS);
4728 ConstantRange RHSRange = getSignedRange(RHS);
4729 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
4731 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
4735 case ICmpInst::ICMP_SGE:
4736 Pred = ICmpInst::ICMP_SLE;
4737 std::swap(LHS, RHS);
4738 case ICmpInst::ICMP_SLE: {
4739 ConstantRange LHSRange = getSignedRange(LHS);
4740 ConstantRange RHSRange = getSignedRange(RHS);
4741 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
4743 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
4747 case ICmpInst::ICMP_UGT:
4748 Pred = ICmpInst::ICMP_ULT;
4749 std::swap(LHS, RHS);
4750 case ICmpInst::ICMP_ULT: {
4751 ConstantRange LHSRange = getUnsignedRange(LHS);
4752 ConstantRange RHSRange = getUnsignedRange(RHS);
4753 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
4755 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
4759 case ICmpInst::ICMP_UGE:
4760 Pred = ICmpInst::ICMP_ULE;
4761 std::swap(LHS, RHS);
4762 case ICmpInst::ICMP_ULE: {
4763 ConstantRange LHSRange = getUnsignedRange(LHS);
4764 ConstantRange RHSRange = getUnsignedRange(RHS);
4765 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
4767 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
4771 case ICmpInst::ICMP_NE: {
4772 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
4774 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
4777 const SCEV *Diff = getMinusSCEV(LHS, RHS);
4778 if (isKnownNonZero(Diff))
4782 case ICmpInst::ICMP_EQ:
4783 // The check at the top of the function catches the case where
4784 // the values are known to be equal.
4790 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
4791 /// protected by a conditional between LHS and RHS. This is used to
4792 /// to eliminate casts.
4794 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
4795 ICmpInst::Predicate Pred,
4796 const SCEV *LHS, const SCEV *RHS) {
4797 // Interpret a null as meaning no loop, where there is obviously no guard
4798 // (interprocedural conditions notwithstanding).
4799 if (!L) return true;
4801 BasicBlock *Latch = L->getLoopLatch();
4805 BranchInst *LoopContinuePredicate =
4806 dyn_cast<BranchInst>(Latch->getTerminator());
4807 if (!LoopContinuePredicate ||
4808 LoopContinuePredicate->isUnconditional())
4811 return isImpliedCond(LoopContinuePredicate->getCondition(), Pred, LHS, RHS,
4812 LoopContinuePredicate->getSuccessor(0) != L->getHeader());
4815 /// isLoopEntryGuardedByCond - Test whether entry to the loop is protected
4816 /// by a conditional between LHS and RHS. This is used to help avoid max
4817 /// expressions in loop trip counts, and to eliminate casts.
4819 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
4820 ICmpInst::Predicate Pred,
4821 const SCEV *LHS, const SCEV *RHS) {
4822 // Interpret a null as meaning no loop, where there is obviously no guard
4823 // (interprocedural conditions notwithstanding).
4824 if (!L) return false;
4826 BasicBlock *Predecessor = getLoopPredecessor(L);
4827 BasicBlock *PredecessorDest = L->getHeader();
4829 // Starting at the loop predecessor, climb up the predecessor chain, as long
4830 // as there are predecessors that can be found that have unique successors
4831 // leading to the original header.
4833 PredecessorDest = Predecessor,
4834 Predecessor = getPredecessorWithUniqueSuccessorForBB(Predecessor)) {
4836 BranchInst *LoopEntryPredicate =
4837 dyn_cast<BranchInst>(Predecessor->getTerminator());
4838 if (!LoopEntryPredicate ||
4839 LoopEntryPredicate->isUnconditional())
4842 if (isImpliedCond(LoopEntryPredicate->getCondition(), Pred, LHS, RHS,
4843 LoopEntryPredicate->getSuccessor(0) != PredecessorDest))
4850 /// isImpliedCond - Test whether the condition described by Pred, LHS,
4851 /// and RHS is true whenever the given Cond value evaluates to true.
4852 bool ScalarEvolution::isImpliedCond(Value *CondValue,
4853 ICmpInst::Predicate Pred,
4854 const SCEV *LHS, const SCEV *RHS,
4856 // Recursively handle And and Or conditions.
4857 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(CondValue)) {
4858 if (BO->getOpcode() == Instruction::And) {
4860 return isImpliedCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) ||
4861 isImpliedCond(BO->getOperand(1), Pred, LHS, RHS, Inverse);
4862 } else if (BO->getOpcode() == Instruction::Or) {
4864 return isImpliedCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) ||
4865 isImpliedCond(BO->getOperand(1), Pred, LHS, RHS, Inverse);
4869 ICmpInst *ICI = dyn_cast<ICmpInst>(CondValue);
4870 if (!ICI) return false;
4872 // Bail if the ICmp's operands' types are wider than the needed type
4873 // before attempting to call getSCEV on them. This avoids infinite
4874 // recursion, since the analysis of widening casts can require loop
4875 // exit condition information for overflow checking, which would
4877 if (getTypeSizeInBits(LHS->getType()) <
4878 getTypeSizeInBits(ICI->getOperand(0)->getType()))
4881 // Now that we found a conditional branch that dominates the loop, check to
4882 // see if it is the comparison we are looking for.
4883 ICmpInst::Predicate FoundPred;
4885 FoundPred = ICI->getInversePredicate();
4887 FoundPred = ICI->getPredicate();
4889 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
4890 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
4892 // Balance the types. The case where FoundLHS' type is wider than
4893 // LHS' type is checked for above.
4894 if (getTypeSizeInBits(LHS->getType()) >
4895 getTypeSizeInBits(FoundLHS->getType())) {
4896 if (CmpInst::isSigned(Pred)) {
4897 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
4898 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
4900 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
4901 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
4905 // Canonicalize the query to match the way instcombine will have
4906 // canonicalized the comparison.
4907 // First, put a constant operand on the right.
4908 if (isa<SCEVConstant>(LHS)) {
4909 std::swap(LHS, RHS);
4910 Pred = ICmpInst::getSwappedPredicate(Pred);
4912 // Then, canonicalize comparisons with boundary cases.
4913 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
4914 const APInt &RA = RC->getValue()->getValue();
4916 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
4917 case ICmpInst::ICMP_EQ:
4918 case ICmpInst::ICMP_NE:
4920 case ICmpInst::ICMP_UGE:
4921 if ((RA - 1).isMinValue()) {
4922 Pred = ICmpInst::ICMP_NE;
4923 RHS = getConstant(RA - 1);
4926 if (RA.isMaxValue()) {
4927 Pred = ICmpInst::ICMP_EQ;
4930 if (RA.isMinValue()) return true;
4932 case ICmpInst::ICMP_ULE:
4933 if ((RA + 1).isMaxValue()) {
4934 Pred = ICmpInst::ICMP_NE;
4935 RHS = getConstant(RA + 1);
4938 if (RA.isMinValue()) {
4939 Pred = ICmpInst::ICMP_EQ;
4942 if (RA.isMaxValue()) return true;
4944 case ICmpInst::ICMP_SGE:
4945 if ((RA - 1).isMinSignedValue()) {
4946 Pred = ICmpInst::ICMP_NE;
4947 RHS = getConstant(RA - 1);
4950 if (RA.isMaxSignedValue()) {
4951 Pred = ICmpInst::ICMP_EQ;
4954 if (RA.isMinSignedValue()) return true;
4956 case ICmpInst::ICMP_SLE:
4957 if ((RA + 1).isMaxSignedValue()) {
4958 Pred = ICmpInst::ICMP_NE;
4959 RHS = getConstant(RA + 1);
4962 if (RA.isMinSignedValue()) {
4963 Pred = ICmpInst::ICMP_EQ;
4966 if (RA.isMaxSignedValue()) return true;
4968 case ICmpInst::ICMP_UGT:
4969 if (RA.isMinValue()) {
4970 Pred = ICmpInst::ICMP_NE;
4973 if ((RA + 1).isMaxValue()) {
4974 Pred = ICmpInst::ICMP_EQ;
4975 RHS = getConstant(RA + 1);
4978 if (RA.isMaxValue()) return false;
4980 case ICmpInst::ICMP_ULT:
4981 if (RA.isMaxValue()) {
4982 Pred = ICmpInst::ICMP_NE;
4985 if ((RA - 1).isMinValue()) {
4986 Pred = ICmpInst::ICMP_EQ;
4987 RHS = getConstant(RA - 1);
4990 if (RA.isMinValue()) return false;
4992 case ICmpInst::ICMP_SGT:
4993 if (RA.isMinSignedValue()) {
4994 Pred = ICmpInst::ICMP_NE;
4997 if ((RA + 1).isMaxSignedValue()) {
4998 Pred = ICmpInst::ICMP_EQ;
4999 RHS = getConstant(RA + 1);
5002 if (RA.isMaxSignedValue()) return false;
5004 case ICmpInst::ICMP_SLT:
5005 if (RA.isMaxSignedValue()) {
5006 Pred = ICmpInst::ICMP_NE;
5009 if ((RA - 1).isMinSignedValue()) {
5010 Pred = ICmpInst::ICMP_EQ;
5011 RHS = getConstant(RA - 1);
5014 if (RA.isMinSignedValue()) return false;
5019 // Check to see if we can make the LHS or RHS match.
5020 if (LHS == FoundRHS || RHS == FoundLHS) {
5021 if (isa<SCEVConstant>(RHS)) {
5022 std::swap(FoundLHS, FoundRHS);
5023 FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
5025 std::swap(LHS, RHS);
5026 Pred = ICmpInst::getSwappedPredicate(Pred);
5030 // Check whether the found predicate is the same as the desired predicate.
5031 if (FoundPred == Pred)
5032 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
5034 // Check whether swapping the found predicate makes it the same as the
5035 // desired predicate.
5036 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
5037 if (isa<SCEVConstant>(RHS))
5038 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
5040 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
5041 RHS, LHS, FoundLHS, FoundRHS);
5044 // Check whether the actual condition is beyond sufficient.
5045 if (FoundPred == ICmpInst::ICMP_EQ)
5046 if (ICmpInst::isTrueWhenEqual(Pred))
5047 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
5049 if (Pred == ICmpInst::ICMP_NE)
5050 if (!ICmpInst::isTrueWhenEqual(FoundPred))
5051 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
5054 // Otherwise assume the worst.
5058 /// isImpliedCondOperands - Test whether the condition described by Pred,
5059 /// LHS, and RHS is true whenever the condition described by Pred, FoundLHS,
5060 /// and FoundRHS is true.
5061 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
5062 const SCEV *LHS, const SCEV *RHS,
5063 const SCEV *FoundLHS,
5064 const SCEV *FoundRHS) {
5065 return isImpliedCondOperandsHelper(Pred, LHS, RHS,
5066 FoundLHS, FoundRHS) ||
5067 // ~x < ~y --> x > y
5068 isImpliedCondOperandsHelper(Pred, LHS, RHS,
5069 getNotSCEV(FoundRHS),
5070 getNotSCEV(FoundLHS));
5073 /// isImpliedCondOperandsHelper - Test whether the condition described by
5074 /// Pred, LHS, and RHS is true whenever the condition described by Pred,
5075 /// FoundLHS, and FoundRHS is true.
5077 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
5078 const SCEV *LHS, const SCEV *RHS,
5079 const SCEV *FoundLHS,
5080 const SCEV *FoundRHS) {
5082 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
5083 case ICmpInst::ICMP_EQ:
5084 case ICmpInst::ICMP_NE:
5085 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
5088 case ICmpInst::ICMP_SLT:
5089 case ICmpInst::ICMP_SLE:
5090 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
5091 isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, RHS, FoundRHS))
5094 case ICmpInst::ICMP_SGT:
5095 case ICmpInst::ICMP_SGE:
5096 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
5097 isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, RHS, FoundRHS))
5100 case ICmpInst::ICMP_ULT:
5101 case ICmpInst::ICMP_ULE:
5102 if (isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
5103 isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, RHS, FoundRHS))
5106 case ICmpInst::ICMP_UGT:
5107 case ICmpInst::ICMP_UGE:
5108 if (isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
5109 isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, RHS, FoundRHS))
5117 /// getBECount - Subtract the end and start values and divide by the step,
5118 /// rounding up, to get the number of times the backedge is executed. Return
5119 /// CouldNotCompute if an intermediate computation overflows.
5120 const SCEV *ScalarEvolution::getBECount(const SCEV *Start,
5124 assert(!isKnownNegative(Step) &&
5125 "This code doesn't handle negative strides yet!");
5127 const Type *Ty = Start->getType();
5128 const SCEV *NegOne = getIntegerSCEV(-1, Ty);
5129 const SCEV *Diff = getMinusSCEV(End, Start);
5130 const SCEV *RoundUp = getAddExpr(Step, NegOne);
5132 // Add an adjustment to the difference between End and Start so that
5133 // the division will effectively round up.
5134 const SCEV *Add = getAddExpr(Diff, RoundUp);
5137 // Check Add for unsigned overflow.
5138 // TODO: More sophisticated things could be done here.
5139 const Type *WideTy = IntegerType::get(getContext(),
5140 getTypeSizeInBits(Ty) + 1);
5141 const SCEV *EDiff = getZeroExtendExpr(Diff, WideTy);
5142 const SCEV *ERoundUp = getZeroExtendExpr(RoundUp, WideTy);
5143 const SCEV *OperandExtendedAdd = getAddExpr(EDiff, ERoundUp);
5144 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd)
5145 return getCouldNotCompute();
5148 return getUDivExpr(Add, Step);
5151 /// HowManyLessThans - Return the number of times a backedge containing the
5152 /// specified less-than comparison will execute. If not computable, return
5153 /// CouldNotCompute.
5154 ScalarEvolution::BackedgeTakenInfo
5155 ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
5156 const Loop *L, bool isSigned) {
5157 // Only handle: "ADDREC < LoopInvariant".
5158 if (!RHS->isLoopInvariant(L)) return getCouldNotCompute();
5160 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
5161 if (!AddRec || AddRec->getLoop() != L)
5162 return getCouldNotCompute();
5164 // Check to see if we have a flag which makes analysis easy.
5165 bool NoWrap = isSigned ? AddRec->hasNoSignedWrap() :
5166 AddRec->hasNoUnsignedWrap();
5168 if (AddRec->isAffine()) {
5169 unsigned BitWidth = getTypeSizeInBits(AddRec->getType());
5170 const SCEV *Step = AddRec->getStepRecurrence(*this);
5173 return getCouldNotCompute();
5174 if (Step->isOne()) {
5175 // With unit stride, the iteration never steps past the limit value.
5176 } else if (isKnownPositive(Step)) {
5177 // Test whether a positive iteration can step past the limit
5178 // value and past the maximum value for its type in a single step.
5179 // Note that it's not sufficient to check NoWrap here, because even
5180 // though the value after a wrap is undefined, it's not undefined
5181 // behavior, so if wrap does occur, the loop could either terminate or
5182 // loop infinitely, but in either case, the loop is guaranteed to
5183 // iterate at least until the iteration where the wrapping occurs.
5184 const SCEV *One = getIntegerSCEV(1, Step->getType());
5186 APInt Max = APInt::getSignedMaxValue(BitWidth);
5187 if ((Max - getSignedRange(getMinusSCEV(Step, One)).getSignedMax())
5188 .slt(getSignedRange(RHS).getSignedMax()))
5189 return getCouldNotCompute();
5191 APInt Max = APInt::getMaxValue(BitWidth);
5192 if ((Max - getUnsignedRange(getMinusSCEV(Step, One)).getUnsignedMax())
5193 .ult(getUnsignedRange(RHS).getUnsignedMax()))
5194 return getCouldNotCompute();
5197 // TODO: Handle negative strides here and below.
5198 return getCouldNotCompute();
5200 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant
5201 // m. So, we count the number of iterations in which {n,+,s} < m is true.
5202 // Note that we cannot simply return max(m-n,0)/s because it's not safe to
5203 // treat m-n as signed nor unsigned due to overflow possibility.
5205 // First, we get the value of the LHS in the first iteration: n
5206 const SCEV *Start = AddRec->getOperand(0);
5208 // Determine the minimum constant start value.
5209 const SCEV *MinStart = getConstant(isSigned ?
5210 getSignedRange(Start).getSignedMin() :
5211 getUnsignedRange(Start).getUnsignedMin());
5213 // If we know that the condition is true in order to enter the loop,
5214 // then we know that it will run exactly (m-n)/s times. Otherwise, we
5215 // only know that it will execute (max(m,n)-n)/s times. In both cases,
5216 // the division must round up.
5217 const SCEV *End = RHS;
5218 if (!isLoopEntryGuardedByCond(L,
5219 isSigned ? ICmpInst::ICMP_SLT :
5221 getMinusSCEV(Start, Step), RHS))
5222 End = isSigned ? getSMaxExpr(RHS, Start)
5223 : getUMaxExpr(RHS, Start);
5225 // Determine the maximum constant end value.
5226 const SCEV *MaxEnd = getConstant(isSigned ?
5227 getSignedRange(End).getSignedMax() :
5228 getUnsignedRange(End).getUnsignedMax());
5230 // If MaxEnd is within a step of the maximum integer value in its type,
5231 // adjust it down to the minimum value which would produce the same effect.
5232 // This allows the subsequent ceiling division of (N+(step-1))/step to
5233 // compute the correct value.
5234 const SCEV *StepMinusOne = getMinusSCEV(Step,
5235 getIntegerSCEV(1, Step->getType()));
5238 getMinusSCEV(getConstant(APInt::getSignedMaxValue(BitWidth)),
5241 getMinusSCEV(getConstant(APInt::getMaxValue(BitWidth)),
5244 // Finally, we subtract these two values and divide, rounding up, to get
5245 // the number of times the backedge is executed.
5246 const SCEV *BECount = getBECount(Start, End, Step, NoWrap);
5248 // The maximum backedge count is similar, except using the minimum start
5249 // value and the maximum end value.
5250 const SCEV *MaxBECount = getBECount(MinStart, MaxEnd, Step, NoWrap);
5252 return BackedgeTakenInfo(BECount, MaxBECount);
5255 return getCouldNotCompute();
5258 /// getNumIterationsInRange - Return the number of iterations of this loop that
5259 /// produce values in the specified constant range. Another way of looking at
5260 /// this is that it returns the first iteration number where the value is not in
5261 /// the condition, thus computing the exit count. If the iteration count can't
5262 /// be computed, an instance of SCEVCouldNotCompute is returned.
5263 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
5264 ScalarEvolution &SE) const {
5265 if (Range.isFullSet()) // Infinite loop.
5266 return SE.getCouldNotCompute();
5268 // If the start is a non-zero constant, shift the range to simplify things.
5269 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
5270 if (!SC->getValue()->isZero()) {
5271 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
5272 Operands[0] = SE.getIntegerSCEV(0, SC->getType());
5273 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop());
5274 if (const SCEVAddRecExpr *ShiftedAddRec =
5275 dyn_cast<SCEVAddRecExpr>(Shifted))
5276 return ShiftedAddRec->getNumIterationsInRange(
5277 Range.subtract(SC->getValue()->getValue()), SE);
5278 // This is strange and shouldn't happen.
5279 return SE.getCouldNotCompute();
5282 // The only time we can solve this is when we have all constant indices.
5283 // Otherwise, we cannot determine the overflow conditions.
5284 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
5285 if (!isa<SCEVConstant>(getOperand(i)))
5286 return SE.getCouldNotCompute();
5289 // Okay at this point we know that all elements of the chrec are constants and
5290 // that the start element is zero.
5292 // First check to see if the range contains zero. If not, the first
5294 unsigned BitWidth = SE.getTypeSizeInBits(getType());
5295 if (!Range.contains(APInt(BitWidth, 0)))
5296 return SE.getIntegerSCEV(0, getType());
5299 // If this is an affine expression then we have this situation:
5300 // Solve {0,+,A} in Range === Ax in Range
5302 // We know that zero is in the range. If A is positive then we know that
5303 // the upper value of the range must be the first possible exit value.
5304 // If A is negative then the lower of the range is the last possible loop
5305 // value. Also note that we already checked for a full range.
5306 APInt One(BitWidth,1);
5307 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
5308 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
5310 // The exit value should be (End+A)/A.
5311 APInt ExitVal = (End + A).udiv(A);
5312 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
5314 // Evaluate at the exit value. If we really did fall out of the valid
5315 // range, then we computed our trip count, otherwise wrap around or other
5316 // things must have happened.
5317 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
5318 if (Range.contains(Val->getValue()))
5319 return SE.getCouldNotCompute(); // Something strange happened
5321 // Ensure that the previous value is in the range. This is a sanity check.
5322 assert(Range.contains(
5323 EvaluateConstantChrecAtConstant(this,
5324 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
5325 "Linear scev computation is off in a bad way!");
5326 return SE.getConstant(ExitValue);
5327 } else if (isQuadratic()) {
5328 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
5329 // quadratic equation to solve it. To do this, we must frame our problem in
5330 // terms of figuring out when zero is crossed, instead of when
5331 // Range.getUpper() is crossed.
5332 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
5333 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
5334 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop());
5336 // Next, solve the constructed addrec
5337 std::pair<const SCEV *,const SCEV *> Roots =
5338 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
5339 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
5340 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
5342 // Pick the smallest positive root value.
5343 if (ConstantInt *CB =
5344 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
5345 R1->getValue(), R2->getValue()))) {
5346 if (CB->getZExtValue() == false)
5347 std::swap(R1, R2); // R1 is the minimum root now.
5349 // Make sure the root is not off by one. The returned iteration should
5350 // not be in the range, but the previous one should be. When solving
5351 // for "X*X < 5", for example, we should not return a root of 2.
5352 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
5355 if (Range.contains(R1Val->getValue())) {
5356 // The next iteration must be out of the range...
5357 ConstantInt *NextVal =
5358 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1);
5360 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
5361 if (!Range.contains(R1Val->getValue()))
5362 return SE.getConstant(NextVal);
5363 return SE.getCouldNotCompute(); // Something strange happened
5366 // If R1 was not in the range, then it is a good return value. Make
5367 // sure that R1-1 WAS in the range though, just in case.
5368 ConstantInt *NextVal =
5369 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1);
5370 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
5371 if (Range.contains(R1Val->getValue()))
5373 return SE.getCouldNotCompute(); // Something strange happened
5378 return SE.getCouldNotCompute();
5383 //===----------------------------------------------------------------------===//
5384 // SCEVCallbackVH Class Implementation
5385 //===----------------------------------------------------------------------===//
5387 void ScalarEvolution::SCEVCallbackVH::deleted() {
5388 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
5389 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
5390 SE->ConstantEvolutionLoopExitValue.erase(PN);
5391 SE->Scalars.erase(getValPtr());
5392 // this now dangles!
5395 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *) {
5396 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
5398 // Forget all the expressions associated with users of the old value,
5399 // so that future queries will recompute the expressions using the new
5401 SmallVector<User *, 16> Worklist;
5402 SmallPtrSet<User *, 8> Visited;
5403 Value *Old = getValPtr();
5404 bool DeleteOld = false;
5405 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end();
5407 Worklist.push_back(*UI);
5408 while (!Worklist.empty()) {
5409 User *U = Worklist.pop_back_val();
5410 // Deleting the Old value will cause this to dangle. Postpone
5411 // that until everything else is done.
5416 if (!Visited.insert(U))
5418 if (PHINode *PN = dyn_cast<PHINode>(U))
5419 SE->ConstantEvolutionLoopExitValue.erase(PN);
5420 SE->Scalars.erase(U);
5421 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end();
5423 Worklist.push_back(*UI);
5425 // Delete the Old value if it (indirectly) references itself.
5427 if (PHINode *PN = dyn_cast<PHINode>(Old))
5428 SE->ConstantEvolutionLoopExitValue.erase(PN);
5429 SE->Scalars.erase(Old);
5430 // this now dangles!
5435 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
5436 : CallbackVH(V), SE(se) {}
5438 //===----------------------------------------------------------------------===//
5439 // ScalarEvolution Class Implementation
5440 //===----------------------------------------------------------------------===//
5442 ScalarEvolution::ScalarEvolution()
5443 : FunctionPass(&ID) {
5446 bool ScalarEvolution::runOnFunction(Function &F) {
5448 LI = &getAnalysis<LoopInfo>();
5449 TD = getAnalysisIfAvailable<TargetData>();
5450 DT = &getAnalysis<DominatorTree>();
5454 void ScalarEvolution::releaseMemory() {
5456 BackedgeTakenCounts.clear();
5457 ConstantEvolutionLoopExitValue.clear();
5458 ValuesAtScopes.clear();
5459 UniqueSCEVs.clear();
5460 SCEVAllocator.Reset();
5463 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
5464 AU.setPreservesAll();
5465 AU.addRequiredTransitive<LoopInfo>();
5466 AU.addRequiredTransitive<DominatorTree>();
5469 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
5470 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
5473 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
5475 // Print all inner loops first
5476 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
5477 PrintLoopInfo(OS, SE, *I);
5480 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
5483 SmallVector<BasicBlock *, 8> ExitBlocks;
5484 L->getExitBlocks(ExitBlocks);
5485 if (ExitBlocks.size() != 1)
5486 OS << "<multiple exits> ";
5488 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
5489 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
5491 OS << "Unpredictable backedge-taken count. ";
5496 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
5499 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
5500 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
5502 OS << "Unpredictable max backedge-taken count. ";
5508 void ScalarEvolution::print(raw_ostream &OS, const Module *) const {
5509 // ScalarEvolution's implementation of the print method is to print
5510 // out SCEV values of all instructions that are interesting. Doing
5511 // this potentially causes it to create new SCEV objects though,
5512 // which technically conflicts with the const qualifier. This isn't
5513 // observable from outside the class though, so casting away the
5514 // const isn't dangerous.
5515 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
5517 OS << "Classifying expressions for: ";
5518 WriteAsOperand(OS, F, /*PrintType=*/false);
5520 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
5521 if (isSCEVable(I->getType())) {
5524 const SCEV *SV = SE.getSCEV(&*I);
5527 const Loop *L = LI->getLoopFor((*I).getParent());
5529 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
5536 OS << "\t\t" "Exits: ";
5537 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
5538 if (!ExitValue->isLoopInvariant(L)) {
5539 OS << "<<Unknown>>";
5548 OS << "Determining loop execution counts for: ";
5549 WriteAsOperand(OS, F, /*PrintType=*/false);
5551 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
5552 PrintLoopInfo(OS, &SE, *I);