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) {
191 const IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty));
192 return getConstant(ConstantInt::get(ITy, 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 const char *OpStr = getOperationStr();
252 for (op_iterator I = op_begin(), E = op_end(); I != E; ++I) {
260 bool SCEVNAryExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
261 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
262 if (!getOperand(i)->dominates(BB, DT))
268 bool SCEVNAryExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const {
269 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
270 if (!getOperand(i)->properlyDominates(BB, DT))
276 bool SCEVUDivExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
277 return LHS->dominates(BB, DT) && RHS->dominates(BB, DT);
280 bool SCEVUDivExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const {
281 return LHS->properlyDominates(BB, DT) && RHS->properlyDominates(BB, DT);
284 void SCEVUDivExpr::print(raw_ostream &OS) const {
285 OS << "(" << *LHS << " /u " << *RHS << ")";
288 const Type *SCEVUDivExpr::getType() const {
289 // In most cases the types of LHS and RHS will be the same, but in some
290 // crazy cases one or the other may be a pointer. ScalarEvolution doesn't
291 // depend on the type for correctness, but handling types carefully can
292 // avoid extra casts in the SCEVExpander. The LHS is more likely to be
293 // a pointer type than the RHS, so use the RHS' type here.
294 return RHS->getType();
297 bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const {
298 // Add recurrences are never invariant in the function-body (null loop).
302 // This recurrence is variant w.r.t. QueryLoop if QueryLoop contains L.
303 if (QueryLoop->contains(L))
306 // This recurrence is variant w.r.t. QueryLoop if any of its operands
308 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
309 if (!getOperand(i)->isLoopInvariant(QueryLoop))
312 // Otherwise it's loop-invariant.
317 SCEVAddRecExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
318 return DT->dominates(L->getHeader(), BB) &&
319 SCEVNAryExpr::dominates(BB, DT);
323 SCEVAddRecExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const {
324 // This uses a "dominates" query instead of "properly dominates" query because
325 // the instruction which produces the addrec's value is a PHI, and a PHI
326 // effectively properly dominates its entire containing block.
327 return DT->dominates(L->getHeader(), BB) &&
328 SCEVNAryExpr::properlyDominates(BB, DT);
331 void SCEVAddRecExpr::print(raw_ostream &OS) const {
332 OS << "{" << *Operands[0];
333 for (unsigned i = 1, e = NumOperands; i != e; ++i)
334 OS << ",+," << *Operands[i];
336 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
340 bool SCEVUnknown::isLoopInvariant(const Loop *L) const {
341 // All non-instruction values are loop invariant. All instructions are loop
342 // invariant if they are not contained in the specified loop.
343 // Instructions are never considered invariant in the function body
344 // (null loop) because they are defined within the "loop".
345 if (Instruction *I = dyn_cast<Instruction>(V))
346 return L && !L->contains(I);
350 bool SCEVUnknown::dominates(BasicBlock *BB, DominatorTree *DT) const {
351 if (Instruction *I = dyn_cast<Instruction>(getValue()))
352 return DT->dominates(I->getParent(), BB);
356 bool SCEVUnknown::properlyDominates(BasicBlock *BB, DominatorTree *DT) const {
357 if (Instruction *I = dyn_cast<Instruction>(getValue()))
358 return DT->properlyDominates(I->getParent(), BB);
362 const Type *SCEVUnknown::getType() const {
366 bool SCEVUnknown::isSizeOf(const Type *&AllocTy) const {
367 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(V))
368 if (VCE->getOpcode() == Instruction::PtrToInt)
369 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
370 if (CE->getOpcode() == Instruction::GetElementPtr &&
371 CE->getOperand(0)->isNullValue() &&
372 CE->getNumOperands() == 2)
373 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1)))
375 AllocTy = cast<PointerType>(CE->getOperand(0)->getType())
383 bool SCEVUnknown::isAlignOf(const Type *&AllocTy) const {
384 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(V))
385 if (VCE->getOpcode() == Instruction::PtrToInt)
386 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
387 if (CE->getOpcode() == Instruction::GetElementPtr &&
388 CE->getOperand(0)->isNullValue()) {
390 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
391 if (const StructType *STy = dyn_cast<StructType>(Ty))
392 if (!STy->isPacked() &&
393 CE->getNumOperands() == 3 &&
394 CE->getOperand(1)->isNullValue()) {
395 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2)))
397 STy->getNumElements() == 2 &&
398 STy->getElementType(0)->isIntegerTy(1)) {
399 AllocTy = STy->getElementType(1);
408 bool SCEVUnknown::isOffsetOf(const Type *&CTy, Constant *&FieldNo) const {
409 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(V))
410 if (VCE->getOpcode() == Instruction::PtrToInt)
411 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
412 if (CE->getOpcode() == Instruction::GetElementPtr &&
413 CE->getNumOperands() == 3 &&
414 CE->getOperand(0)->isNullValue() &&
415 CE->getOperand(1)->isNullValue()) {
417 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
418 // Ignore vector types here so that ScalarEvolutionExpander doesn't
419 // emit getelementptrs that index into vectors.
420 if (Ty->isStructTy() || Ty->isArrayTy()) {
422 FieldNo = CE->getOperand(2);
430 void SCEVUnknown::print(raw_ostream &OS) const {
432 if (isSizeOf(AllocTy)) {
433 OS << "sizeof(" << *AllocTy << ")";
436 if (isAlignOf(AllocTy)) {
437 OS << "alignof(" << *AllocTy << ")";
443 if (isOffsetOf(CTy, FieldNo)) {
444 OS << "offsetof(" << *CTy << ", ";
445 WriteAsOperand(OS, FieldNo, false);
450 // Otherwise just print it normally.
451 WriteAsOperand(OS, V, false);
454 //===----------------------------------------------------------------------===//
456 //===----------------------------------------------------------------------===//
458 static bool CompareTypes(const Type *A, const Type *B) {
459 if (A->getTypeID() != B->getTypeID())
460 return A->getTypeID() < B->getTypeID();
461 if (const IntegerType *AI = dyn_cast<IntegerType>(A)) {
462 const IntegerType *BI = cast<IntegerType>(B);
463 return AI->getBitWidth() < BI->getBitWidth();
465 if (const PointerType *AI = dyn_cast<PointerType>(A)) {
466 const PointerType *BI = cast<PointerType>(B);
467 return CompareTypes(AI->getElementType(), BI->getElementType());
469 if (const ArrayType *AI = dyn_cast<ArrayType>(A)) {
470 const ArrayType *BI = cast<ArrayType>(B);
471 if (AI->getNumElements() != BI->getNumElements())
472 return AI->getNumElements() < BI->getNumElements();
473 return CompareTypes(AI->getElementType(), BI->getElementType());
475 if (const VectorType *AI = dyn_cast<VectorType>(A)) {
476 const VectorType *BI = cast<VectorType>(B);
477 if (AI->getNumElements() != BI->getNumElements())
478 return AI->getNumElements() < BI->getNumElements();
479 return CompareTypes(AI->getElementType(), BI->getElementType());
481 if (const StructType *AI = dyn_cast<StructType>(A)) {
482 const StructType *BI = cast<StructType>(B);
483 if (AI->getNumElements() != BI->getNumElements())
484 return AI->getNumElements() < BI->getNumElements();
485 for (unsigned i = 0, e = AI->getNumElements(); i != e; ++i)
486 if (CompareTypes(AI->getElementType(i), BI->getElementType(i)) ||
487 CompareTypes(BI->getElementType(i), AI->getElementType(i)))
488 return CompareTypes(AI->getElementType(i), BI->getElementType(i));
494 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
495 /// than the complexity of the RHS. This comparator is used to canonicalize
497 class SCEVComplexityCompare {
500 explicit SCEVComplexityCompare(LoopInfo *li) : LI(li) {}
502 bool operator()(const SCEV *LHS, const SCEV *RHS) const {
503 // Fast-path: SCEVs are uniqued so we can do a quick equality check.
507 // Primarily, sort the SCEVs by their getSCEVType().
508 if (LHS->getSCEVType() != RHS->getSCEVType())
509 return LHS->getSCEVType() < RHS->getSCEVType();
511 // Aside from the getSCEVType() ordering, the particular ordering
512 // isn't very important except that it's beneficial to be consistent,
513 // so that (a + b) and (b + a) don't end up as different expressions.
515 // Sort SCEVUnknown values with some loose heuristics. TODO: This is
516 // not as complete as it could be.
517 if (const SCEVUnknown *LU = dyn_cast<SCEVUnknown>(LHS)) {
518 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
520 // Order pointer values after integer values. This helps SCEVExpander
522 if (LU->getType()->isPointerTy() && !RU->getType()->isPointerTy())
524 if (RU->getType()->isPointerTy() && !LU->getType()->isPointerTy())
527 // Compare getValueID values.
528 if (LU->getValue()->getValueID() != RU->getValue()->getValueID())
529 return LU->getValue()->getValueID() < RU->getValue()->getValueID();
531 // Sort arguments by their position.
532 if (const Argument *LA = dyn_cast<Argument>(LU->getValue())) {
533 const Argument *RA = cast<Argument>(RU->getValue());
534 return LA->getArgNo() < RA->getArgNo();
537 // For instructions, compare their loop depth, and their opcode.
538 // This is pretty loose.
539 if (Instruction *LV = dyn_cast<Instruction>(LU->getValue())) {
540 Instruction *RV = cast<Instruction>(RU->getValue());
542 // Compare loop depths.
543 if (LI->getLoopDepth(LV->getParent()) !=
544 LI->getLoopDepth(RV->getParent()))
545 return LI->getLoopDepth(LV->getParent()) <
546 LI->getLoopDepth(RV->getParent());
549 if (LV->getOpcode() != RV->getOpcode())
550 return LV->getOpcode() < RV->getOpcode();
552 // Compare the number of operands.
553 if (LV->getNumOperands() != RV->getNumOperands())
554 return LV->getNumOperands() < RV->getNumOperands();
560 // Compare constant values.
561 if (const SCEVConstant *LC = dyn_cast<SCEVConstant>(LHS)) {
562 const SCEVConstant *RC = cast<SCEVConstant>(RHS);
563 if (LC->getValue()->getBitWidth() != RC->getValue()->getBitWidth())
564 return LC->getValue()->getBitWidth() < RC->getValue()->getBitWidth();
565 return LC->getValue()->getValue().ult(RC->getValue()->getValue());
568 // Compare addrec loop depths.
569 if (const SCEVAddRecExpr *LA = dyn_cast<SCEVAddRecExpr>(LHS)) {
570 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS);
571 if (LA->getLoop()->getLoopDepth() != RA->getLoop()->getLoopDepth())
572 return LA->getLoop()->getLoopDepth() < RA->getLoop()->getLoopDepth();
575 // Lexicographically compare n-ary expressions.
576 if (const SCEVNAryExpr *LC = dyn_cast<SCEVNAryExpr>(LHS)) {
577 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
578 for (unsigned i = 0, e = LC->getNumOperands(); i != e; ++i) {
579 if (i >= RC->getNumOperands())
581 if (operator()(LC->getOperand(i), RC->getOperand(i)))
583 if (operator()(RC->getOperand(i), LC->getOperand(i)))
586 return LC->getNumOperands() < RC->getNumOperands();
589 // Lexicographically compare udiv expressions.
590 if (const SCEVUDivExpr *LC = dyn_cast<SCEVUDivExpr>(LHS)) {
591 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
592 if (operator()(LC->getLHS(), RC->getLHS()))
594 if (operator()(RC->getLHS(), LC->getLHS()))
596 if (operator()(LC->getRHS(), RC->getRHS()))
598 if (operator()(RC->getRHS(), LC->getRHS()))
603 // Compare cast expressions by operand.
604 if (const SCEVCastExpr *LC = dyn_cast<SCEVCastExpr>(LHS)) {
605 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
606 return operator()(LC->getOperand(), RC->getOperand());
609 llvm_unreachable("Unknown SCEV kind!");
615 /// GroupByComplexity - Given a list of SCEV objects, order them by their
616 /// complexity, and group objects of the same complexity together by value.
617 /// When this routine is finished, we know that any duplicates in the vector are
618 /// consecutive and that complexity is monotonically increasing.
620 /// Note that we go take special precautions to ensure that we get deterministic
621 /// results from this routine. In other words, we don't want the results of
622 /// this to depend on where the addresses of various SCEV objects happened to
625 static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops,
627 if (Ops.size() < 2) return; // Noop
628 if (Ops.size() == 2) {
629 // This is the common case, which also happens to be trivially simple.
631 if (SCEVComplexityCompare(LI)(Ops[1], Ops[0]))
632 std::swap(Ops[0], Ops[1]);
636 // Do the rough sort by complexity.
637 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI));
639 // Now that we are sorted by complexity, group elements of the same
640 // complexity. Note that this is, at worst, N^2, but the vector is likely to
641 // be extremely short in practice. Note that we take this approach because we
642 // do not want to depend on the addresses of the objects we are grouping.
643 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
644 const SCEV *S = Ops[i];
645 unsigned Complexity = S->getSCEVType();
647 // If there are any objects of the same complexity and same value as this
649 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
650 if (Ops[j] == S) { // Found a duplicate.
651 // Move it to immediately after i'th element.
652 std::swap(Ops[i+1], Ops[j]);
653 ++i; // no need to rescan it.
654 if (i == e-2) return; // Done!
662 //===----------------------------------------------------------------------===//
663 // Simple SCEV method implementations
664 //===----------------------------------------------------------------------===//
666 /// BinomialCoefficient - Compute BC(It, K). The result has width W.
668 static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K,
670 const Type* ResultTy) {
671 // Handle the simplest case efficiently.
673 return SE.getTruncateOrZeroExtend(It, ResultTy);
675 // We are using the following formula for BC(It, K):
677 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
679 // Suppose, W is the bitwidth of the return value. We must be prepared for
680 // overflow. Hence, we must assure that the result of our computation is
681 // equal to the accurate one modulo 2^W. Unfortunately, division isn't
682 // safe in modular arithmetic.
684 // However, this code doesn't use exactly that formula; the formula it uses
685 // is something like the following, where T is the number of factors of 2 in
686 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
689 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
691 // This formula is trivially equivalent to the previous formula. However,
692 // this formula can be implemented much more efficiently. The trick is that
693 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
694 // arithmetic. To do exact division in modular arithmetic, all we have
695 // to do is multiply by the inverse. Therefore, this step can be done at
698 // The next issue is how to safely do the division by 2^T. The way this
699 // is done is by doing the multiplication step at a width of at least W + T
700 // bits. This way, the bottom W+T bits of the product are accurate. Then,
701 // when we perform the division by 2^T (which is equivalent to a right shift
702 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
703 // truncated out after the division by 2^T.
705 // In comparison to just directly using the first formula, this technique
706 // is much more efficient; using the first formula requires W * K bits,
707 // but this formula less than W + K bits. Also, the first formula requires
708 // a division step, whereas this formula only requires multiplies and shifts.
710 // It doesn't matter whether the subtraction step is done in the calculation
711 // width or the input iteration count's width; if the subtraction overflows,
712 // the result must be zero anyway. We prefer here to do it in the width of
713 // the induction variable because it helps a lot for certain cases; CodeGen
714 // isn't smart enough to ignore the overflow, which leads to much less
715 // efficient code if the width of the subtraction is wider than the native
718 // (It's possible to not widen at all by pulling out factors of 2 before
719 // the multiplication; for example, K=2 can be calculated as
720 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
721 // extra arithmetic, so it's not an obvious win, and it gets
722 // much more complicated for K > 3.)
724 // Protection from insane SCEVs; this bound is conservative,
725 // but it probably doesn't matter.
727 return SE.getCouldNotCompute();
729 unsigned W = SE.getTypeSizeInBits(ResultTy);
731 // Calculate K! / 2^T and T; we divide out the factors of two before
732 // multiplying for calculating K! / 2^T to avoid overflow.
733 // Other overflow doesn't matter because we only care about the bottom
734 // W bits of the result.
735 APInt OddFactorial(W, 1);
737 for (unsigned i = 3; i <= K; ++i) {
739 unsigned TwoFactors = Mult.countTrailingZeros();
741 Mult = Mult.lshr(TwoFactors);
742 OddFactorial *= Mult;
745 // We need at least W + T bits for the multiplication step
746 unsigned CalculationBits = W + T;
748 // Calculate 2^T, at width T+W.
749 APInt DivFactor = APInt(CalculationBits, 1).shl(T);
751 // Calculate the multiplicative inverse of K! / 2^T;
752 // this multiplication factor will perform the exact division by
754 APInt Mod = APInt::getSignedMinValue(W+1);
755 APInt MultiplyFactor = OddFactorial.zext(W+1);
756 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
757 MultiplyFactor = MultiplyFactor.trunc(W);
759 // Calculate the product, at width T+W
760 const IntegerType *CalculationTy = IntegerType::get(SE.getContext(),
762 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
763 for (unsigned i = 1; i != K; ++i) {
764 const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i));
765 Dividend = SE.getMulExpr(Dividend,
766 SE.getTruncateOrZeroExtend(S, CalculationTy));
770 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
772 // Truncate the result, and divide by K! / 2^T.
774 return SE.getMulExpr(SE.getConstant(MultiplyFactor),
775 SE.getTruncateOrZeroExtend(DivResult, ResultTy));
778 /// evaluateAtIteration - Return the value of this chain of recurrences at
779 /// the specified iteration number. We can evaluate this recurrence by
780 /// multiplying each element in the chain by the binomial coefficient
781 /// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
783 /// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
785 /// where BC(It, k) stands for binomial coefficient.
787 const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It,
788 ScalarEvolution &SE) const {
789 const SCEV *Result = getStart();
790 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
791 // The computation is correct in the face of overflow provided that the
792 // multiplication is performed _after_ the evaluation of the binomial
794 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType());
795 if (isa<SCEVCouldNotCompute>(Coeff))
798 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
803 //===----------------------------------------------------------------------===//
804 // SCEV Expression folder implementations
805 //===----------------------------------------------------------------------===//
807 const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op,
809 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
810 "This is not a truncating conversion!");
811 assert(isSCEVable(Ty) &&
812 "This is not a conversion to a SCEVable type!");
813 Ty = getEffectiveSCEVType(Ty);
816 ID.AddInteger(scTruncate);
820 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
822 // Fold if the operand is constant.
823 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
825 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(),
826 getEffectiveSCEVType(Ty))));
828 // trunc(trunc(x)) --> trunc(x)
829 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
830 return getTruncateExpr(ST->getOperand(), Ty);
832 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
833 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
834 return getTruncateOrSignExtend(SS->getOperand(), Ty);
836 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
837 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
838 return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
840 // If the input value is a chrec scev, truncate the chrec's operands.
841 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
842 SmallVector<const SCEV *, 4> Operands;
843 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
844 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty));
845 return getAddRecExpr(Operands, AddRec->getLoop());
848 // The cast wasn't folded; create an explicit cast node. We can reuse
849 // the existing insert position since if we get here, we won't have
850 // made any changes which would invalidate it.
851 SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator),
853 UniqueSCEVs.InsertNode(S, IP);
857 const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op,
859 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
860 "This is not an extending conversion!");
861 assert(isSCEVable(Ty) &&
862 "This is not a conversion to a SCEVable type!");
863 Ty = getEffectiveSCEVType(Ty);
865 // Fold if the operand is constant.
866 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
868 cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(),
869 getEffectiveSCEVType(Ty))));
871 // zext(zext(x)) --> zext(x)
872 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
873 return getZeroExtendExpr(SZ->getOperand(), Ty);
875 // Before doing any expensive analysis, check to see if we've already
876 // computed a SCEV for this Op and Ty.
878 ID.AddInteger(scZeroExtend);
882 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
884 // If the input value is a chrec scev, and we can prove that the value
885 // did not overflow the old, smaller, value, we can zero extend all of the
886 // operands (often constants). This allows analysis of something like
887 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
888 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
889 if (AR->isAffine()) {
890 const SCEV *Start = AR->getStart();
891 const SCEV *Step = AR->getStepRecurrence(*this);
892 unsigned BitWidth = getTypeSizeInBits(AR->getType());
893 const Loop *L = AR->getLoop();
895 // If we have special knowledge that this addrec won't overflow,
896 // we don't need to do any further analysis.
897 if (AR->hasNoUnsignedWrap())
898 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
899 getZeroExtendExpr(Step, Ty),
902 // Check whether the backedge-taken count is SCEVCouldNotCompute.
903 // Note that this serves two purposes: It filters out loops that are
904 // simply not analyzable, and it covers the case where this code is
905 // being called from within backedge-taken count analysis, such that
906 // attempting to ask for the backedge-taken count would likely result
907 // in infinite recursion. In the later case, the analysis code will
908 // cope with a conservative value, and it will take care to purge
909 // that value once it has finished.
910 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
911 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
912 // Manually compute the final value for AR, checking for
915 // Check whether the backedge-taken count can be losslessly casted to
916 // the addrec's type. The count is always unsigned.
917 const SCEV *CastedMaxBECount =
918 getTruncateOrZeroExtend(MaxBECount, Start->getType());
919 const SCEV *RecastedMaxBECount =
920 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
921 if (MaxBECount == RecastedMaxBECount) {
922 const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
923 // Check whether Start+Step*MaxBECount has no unsigned overflow.
924 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step);
925 const SCEV *Add = getAddExpr(Start, ZMul);
926 const SCEV *OperandExtendedAdd =
927 getAddExpr(getZeroExtendExpr(Start, WideTy),
928 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
929 getZeroExtendExpr(Step, WideTy)));
930 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd)
931 // Return the expression with the addrec on the outside.
932 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
933 getZeroExtendExpr(Step, Ty),
936 // Similar to above, only this time treat the step value as signed.
937 // This covers loops that count down.
938 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
939 Add = getAddExpr(Start, SMul);
941 getAddExpr(getZeroExtendExpr(Start, WideTy),
942 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
943 getSignExtendExpr(Step, WideTy)));
944 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd)
945 // Return the expression with the addrec on the outside.
946 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
947 getSignExtendExpr(Step, Ty),
951 // If the backedge is guarded by a comparison with the pre-inc value
952 // the addrec is safe. Also, if the entry is guarded by a comparison
953 // with the start value and the backedge is guarded by a comparison
954 // with the post-inc value, the addrec is safe.
955 if (isKnownPositive(Step)) {
956 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
957 getUnsignedRange(Step).getUnsignedMax());
958 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
959 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) &&
960 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT,
961 AR->getPostIncExpr(*this), N)))
962 // Return the expression with the addrec on the outside.
963 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
964 getZeroExtendExpr(Step, Ty),
966 } else if (isKnownNegative(Step)) {
967 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
968 getSignedRange(Step).getSignedMin());
969 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) ||
970 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) &&
971 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT,
972 AR->getPostIncExpr(*this), N)))
973 // Return the expression with the addrec on the outside.
974 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
975 getSignExtendExpr(Step, Ty),
981 // The cast wasn't folded; create an explicit cast node.
982 // Recompute the insert position, as it may have been invalidated.
983 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
984 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
986 UniqueSCEVs.InsertNode(S, IP);
990 const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op,
992 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
993 "This is not an extending conversion!");
994 assert(isSCEVable(Ty) &&
995 "This is not a conversion to a SCEVable type!");
996 Ty = getEffectiveSCEVType(Ty);
998 // Fold if the operand is constant.
999 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1001 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(),
1002 getEffectiveSCEVType(Ty))));
1004 // sext(sext(x)) --> sext(x)
1005 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1006 return getSignExtendExpr(SS->getOperand(), Ty);
1008 // Before doing any expensive analysis, check to see if we've already
1009 // computed a SCEV for this Op and Ty.
1010 FoldingSetNodeID ID;
1011 ID.AddInteger(scSignExtend);
1015 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1017 // If the input value is a chrec scev, and we can prove that the value
1018 // did not overflow the old, smaller, value, we can sign extend all of the
1019 // operands (often constants). This allows analysis of something like
1020 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
1021 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1022 if (AR->isAffine()) {
1023 const SCEV *Start = AR->getStart();
1024 const SCEV *Step = AR->getStepRecurrence(*this);
1025 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1026 const Loop *L = AR->getLoop();
1028 // If we have special knowledge that this addrec won't overflow,
1029 // we don't need to do any further analysis.
1030 if (AR->hasNoSignedWrap())
1031 return getAddRecExpr(getSignExtendExpr(Start, Ty),
1032 getSignExtendExpr(Step, Ty),
1035 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1036 // Note that this serves two purposes: It filters out loops that are
1037 // simply not analyzable, and it covers the case where this code is
1038 // being called from within backedge-taken count analysis, such that
1039 // attempting to ask for the backedge-taken count would likely result
1040 // in infinite recursion. In the later case, the analysis code will
1041 // cope with a conservative value, and it will take care to purge
1042 // that value once it has finished.
1043 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1044 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1045 // Manually compute the final value for AR, checking for
1048 // Check whether the backedge-taken count can be losslessly casted to
1049 // the addrec's type. The count is always unsigned.
1050 const SCEV *CastedMaxBECount =
1051 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1052 const SCEV *RecastedMaxBECount =
1053 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1054 if (MaxBECount == RecastedMaxBECount) {
1055 const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1056 // Check whether Start+Step*MaxBECount has no signed overflow.
1057 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
1058 const SCEV *Add = getAddExpr(Start, SMul);
1059 const SCEV *OperandExtendedAdd =
1060 getAddExpr(getSignExtendExpr(Start, WideTy),
1061 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
1062 getSignExtendExpr(Step, WideTy)));
1063 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd)
1064 // Return the expression with the addrec on the outside.
1065 return getAddRecExpr(getSignExtendExpr(Start, Ty),
1066 getSignExtendExpr(Step, Ty),
1069 // Similar to above, only this time treat the step value as unsigned.
1070 // This covers loops that count up with an unsigned step.
1071 const SCEV *UMul = getMulExpr(CastedMaxBECount, Step);
1072 Add = getAddExpr(Start, UMul);
1073 OperandExtendedAdd =
1074 getAddExpr(getSignExtendExpr(Start, WideTy),
1075 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
1076 getZeroExtendExpr(Step, WideTy)));
1077 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd)
1078 // Return the expression with the addrec on the outside.
1079 return getAddRecExpr(getSignExtendExpr(Start, Ty),
1080 getZeroExtendExpr(Step, Ty),
1084 // If the backedge is guarded by a comparison with the pre-inc value
1085 // the addrec is safe. Also, if the entry is guarded by a comparison
1086 // with the start value and the backedge is guarded by a comparison
1087 // with the post-inc value, the addrec is safe.
1088 if (isKnownPositive(Step)) {
1089 const SCEV *N = getConstant(APInt::getSignedMinValue(BitWidth) -
1090 getSignedRange(Step).getSignedMax());
1091 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT, AR, N) ||
1092 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_SLT, Start, N) &&
1093 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT,
1094 AR->getPostIncExpr(*this), N)))
1095 // Return the expression with the addrec on the outside.
1096 return getAddRecExpr(getSignExtendExpr(Start, Ty),
1097 getSignExtendExpr(Step, Ty),
1099 } else if (isKnownNegative(Step)) {
1100 const SCEV *N = getConstant(APInt::getSignedMaxValue(BitWidth) -
1101 getSignedRange(Step).getSignedMin());
1102 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT, AR, N) ||
1103 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_SGT, Start, N) &&
1104 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT,
1105 AR->getPostIncExpr(*this), N)))
1106 // Return the expression with the addrec on the outside.
1107 return getAddRecExpr(getSignExtendExpr(Start, Ty),
1108 getSignExtendExpr(Step, Ty),
1114 // The cast wasn't folded; create an explicit cast node.
1115 // Recompute the insert position, as it may have been invalidated.
1116 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1117 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
1119 UniqueSCEVs.InsertNode(S, IP);
1123 /// getAnyExtendExpr - Return a SCEV for the given operand extended with
1124 /// unspecified bits out to the given type.
1126 const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
1128 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1129 "This is not an extending conversion!");
1130 assert(isSCEVable(Ty) &&
1131 "This is not a conversion to a SCEVable type!");
1132 Ty = getEffectiveSCEVType(Ty);
1134 // Sign-extend negative constants.
1135 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1136 if (SC->getValue()->getValue().isNegative())
1137 return getSignExtendExpr(Op, Ty);
1139 // Peel off a truncate cast.
1140 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
1141 const SCEV *NewOp = T->getOperand();
1142 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
1143 return getAnyExtendExpr(NewOp, Ty);
1144 return getTruncateOrNoop(NewOp, Ty);
1147 // Next try a zext cast. If the cast is folded, use it.
1148 const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
1149 if (!isa<SCEVZeroExtendExpr>(ZExt))
1152 // Next try a sext cast. If the cast is folded, use it.
1153 const SCEV *SExt = getSignExtendExpr(Op, Ty);
1154 if (!isa<SCEVSignExtendExpr>(SExt))
1157 // Force the cast to be folded into the operands of an addrec.
1158 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
1159 SmallVector<const SCEV *, 4> Ops;
1160 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
1162 Ops.push_back(getAnyExtendExpr(*I, Ty));
1163 return getAddRecExpr(Ops, AR->getLoop());
1166 // If the expression is obviously signed, use the sext cast value.
1167 if (isa<SCEVSMaxExpr>(Op))
1170 // Absent any other information, use the zext cast value.
1174 /// CollectAddOperandsWithScales - Process the given Ops list, which is
1175 /// a list of operands to be added under the given scale, update the given
1176 /// map. This is a helper function for getAddRecExpr. As an example of
1177 /// what it does, given a sequence of operands that would form an add
1178 /// expression like this:
1180 /// m + n + 13 + (A * (o + p + (B * q + m + 29))) + r + (-1 * r)
1182 /// where A and B are constants, update the map with these values:
1184 /// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
1186 /// and add 13 + A*B*29 to AccumulatedConstant.
1187 /// This will allow getAddRecExpr to produce this:
1189 /// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
1191 /// This form often exposes folding opportunities that are hidden in
1192 /// the original operand list.
1194 /// Return true iff it appears that any interesting folding opportunities
1195 /// may be exposed. This helps getAddRecExpr short-circuit extra work in
1196 /// the common case where no interesting opportunities are present, and
1197 /// is also used as a check to avoid infinite recursion.
1200 CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
1201 SmallVector<const SCEV *, 8> &NewOps,
1202 APInt &AccumulatedConstant,
1203 const SCEV *const *Ops, size_t NumOperands,
1205 ScalarEvolution &SE) {
1206 bool Interesting = false;
1208 // Iterate over the add operands. They are sorted, with constants first.
1210 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1212 // Pull a buried constant out to the outside.
1213 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
1215 AccumulatedConstant += Scale * C->getValue()->getValue();
1218 // Next comes everything else. We're especially interested in multiplies
1219 // here, but they're in the middle, so just visit the rest with one loop.
1220 for (; i != NumOperands; ++i) {
1221 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
1222 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
1224 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue();
1225 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
1226 // A multiplication of a constant with another add; recurse.
1227 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1));
1229 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1230 Add->op_begin(), Add->getNumOperands(),
1233 // A multiplication of a constant with some other value. Update
1235 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
1236 const SCEV *Key = SE.getMulExpr(MulOps);
1237 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1238 M.insert(std::make_pair(Key, NewScale));
1240 NewOps.push_back(Pair.first->first);
1242 Pair.first->second += NewScale;
1243 // The map already had an entry for this value, which may indicate
1244 // a folding opportunity.
1249 // An ordinary operand. Update the map.
1250 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1251 M.insert(std::make_pair(Ops[i], Scale));
1253 NewOps.push_back(Pair.first->first);
1255 Pair.first->second += Scale;
1256 // The map already had an entry for this value, which may indicate
1257 // a folding opportunity.
1267 struct APIntCompare {
1268 bool operator()(const APInt &LHS, const APInt &RHS) const {
1269 return LHS.ult(RHS);
1274 /// getAddExpr - Get a canonical add expression, or something simpler if
1276 const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
1277 bool HasNUW, bool HasNSW) {
1278 assert(!Ops.empty() && "Cannot get empty add!");
1279 if (Ops.size() == 1) return Ops[0];
1281 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
1282 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1283 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
1284 "SCEVAddExpr operand types don't match!");
1287 // If HasNSW is true and all the operands are non-negative, infer HasNUW.
1288 if (!HasNUW && HasNSW) {
1290 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1291 if (!isKnownNonNegative(Ops[i])) {
1295 if (All) HasNUW = true;
1298 // Sort by complexity, this groups all similar expression types together.
1299 GroupByComplexity(Ops, LI);
1301 // If there are any constants, fold them together.
1303 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1305 assert(Idx < Ops.size());
1306 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1307 // We found two constants, fold them together!
1308 Ops[0] = getConstant(LHSC->getValue()->getValue() +
1309 RHSC->getValue()->getValue());
1310 if (Ops.size() == 2) return Ops[0];
1311 Ops.erase(Ops.begin()+1); // Erase the folded element
1312 LHSC = cast<SCEVConstant>(Ops[0]);
1315 // If we are left with a constant zero being added, strip it off.
1316 if (LHSC->getValue()->isZero()) {
1317 Ops.erase(Ops.begin());
1321 if (Ops.size() == 1) return Ops[0];
1324 // Okay, check to see if the same value occurs in the operand list twice. If
1325 // so, merge them together into an multiply expression. Since we sorted the
1326 // list, these values are required to be adjacent.
1327 const Type *Ty = Ops[0]->getType();
1328 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
1329 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
1330 // Found a match, merge the two values into a multiply, and add any
1331 // remaining values to the result.
1332 const SCEV *Two = getConstant(Ty, 2);
1333 const SCEV *Mul = getMulExpr(Ops[i], Two);
1334 if (Ops.size() == 2)
1336 Ops.erase(Ops.begin()+i, Ops.begin()+i+2);
1338 return getAddExpr(Ops, HasNUW, HasNSW);
1341 // Check for truncates. If all the operands are truncated from the same
1342 // type, see if factoring out the truncate would permit the result to be
1343 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
1344 // if the contents of the resulting outer trunc fold to something simple.
1345 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
1346 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
1347 const Type *DstType = Trunc->getType();
1348 const Type *SrcType = Trunc->getOperand()->getType();
1349 SmallVector<const SCEV *, 8> LargeOps;
1351 // Check all the operands to see if they can be represented in the
1352 // source type of the truncate.
1353 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1354 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
1355 if (T->getOperand()->getType() != SrcType) {
1359 LargeOps.push_back(T->getOperand());
1360 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1361 LargeOps.push_back(getAnyExtendExpr(C, SrcType));
1362 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
1363 SmallVector<const SCEV *, 8> LargeMulOps;
1364 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
1365 if (const SCEVTruncateExpr *T =
1366 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
1367 if (T->getOperand()->getType() != SrcType) {
1371 LargeMulOps.push_back(T->getOperand());
1372 } else if (const SCEVConstant *C =
1373 dyn_cast<SCEVConstant>(M->getOperand(j))) {
1374 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType));
1381 LargeOps.push_back(getMulExpr(LargeMulOps));
1388 // Evaluate the expression in the larger type.
1389 const SCEV *Fold = getAddExpr(LargeOps, HasNUW, HasNSW);
1390 // If it folds to something simple, use it. Otherwise, don't.
1391 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
1392 return getTruncateExpr(Fold, DstType);
1396 // Skip past any other cast SCEVs.
1397 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
1400 // If there are add operands they would be next.
1401 if (Idx < Ops.size()) {
1402 bool DeletedAdd = false;
1403 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
1404 // If we have an add, expand the add operands onto the end of the operands
1406 Ops.erase(Ops.begin()+Idx);
1407 Ops.append(Add->op_begin(), Add->op_end());
1411 // If we deleted at least one add, we added operands to the end of the list,
1412 // and they are not necessarily sorted. Recurse to resort and resimplify
1413 // any operands we just acquired.
1415 return getAddExpr(Ops);
1418 // Skip over the add expression until we get to a multiply.
1419 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1422 // Check to see if there are any folding opportunities present with
1423 // operands multiplied by constant values.
1424 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
1425 uint64_t BitWidth = getTypeSizeInBits(Ty);
1426 DenseMap<const SCEV *, APInt> M;
1427 SmallVector<const SCEV *, 8> NewOps;
1428 APInt AccumulatedConstant(BitWidth, 0);
1429 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1430 Ops.data(), Ops.size(),
1431 APInt(BitWidth, 1), *this)) {
1432 // Some interesting folding opportunity is present, so its worthwhile to
1433 // re-generate the operands list. Group the operands by constant scale,
1434 // to avoid multiplying by the same constant scale multiple times.
1435 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
1436 for (SmallVector<const SCEV *, 8>::iterator I = NewOps.begin(),
1437 E = NewOps.end(); I != E; ++I)
1438 MulOpLists[M.find(*I)->second].push_back(*I);
1439 // Re-generate the operands list.
1441 if (AccumulatedConstant != 0)
1442 Ops.push_back(getConstant(AccumulatedConstant));
1443 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator
1444 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I)
1446 Ops.push_back(getMulExpr(getConstant(I->first),
1447 getAddExpr(I->second)));
1449 return getConstant(Ty, 0);
1450 if (Ops.size() == 1)
1452 return getAddExpr(Ops);
1456 // If we are adding something to a multiply expression, make sure the
1457 // something is not already an operand of the multiply. If so, merge it into
1459 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
1460 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
1461 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
1462 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
1463 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
1464 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(Ops[AddOp])) {
1465 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
1466 const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
1467 if (Mul->getNumOperands() != 2) {
1468 // If the multiply has more than two operands, we must get the
1470 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), Mul->op_end());
1471 MulOps.erase(MulOps.begin()+MulOp);
1472 InnerMul = getMulExpr(MulOps);
1474 const SCEV *One = getConstant(Ty, 1);
1475 const SCEV *AddOne = getAddExpr(InnerMul, One);
1476 const SCEV *OuterMul = getMulExpr(AddOne, Ops[AddOp]);
1477 if (Ops.size() == 2) return OuterMul;
1479 Ops.erase(Ops.begin()+AddOp);
1480 Ops.erase(Ops.begin()+Idx-1);
1482 Ops.erase(Ops.begin()+Idx);
1483 Ops.erase(Ops.begin()+AddOp-1);
1485 Ops.push_back(OuterMul);
1486 return getAddExpr(Ops);
1489 // Check this multiply against other multiplies being added together.
1490 for (unsigned OtherMulIdx = Idx+1;
1491 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
1493 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
1494 // If MulOp occurs in OtherMul, we can fold the two multiplies
1496 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
1497 OMulOp != e; ++OMulOp)
1498 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
1499 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
1500 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
1501 if (Mul->getNumOperands() != 2) {
1502 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
1504 MulOps.erase(MulOps.begin()+MulOp);
1505 InnerMul1 = getMulExpr(MulOps);
1507 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
1508 if (OtherMul->getNumOperands() != 2) {
1509 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
1510 OtherMul->op_end());
1511 MulOps.erase(MulOps.begin()+OMulOp);
1512 InnerMul2 = getMulExpr(MulOps);
1514 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
1515 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
1516 if (Ops.size() == 2) return OuterMul;
1517 Ops.erase(Ops.begin()+Idx);
1518 Ops.erase(Ops.begin()+OtherMulIdx-1);
1519 Ops.push_back(OuterMul);
1520 return getAddExpr(Ops);
1526 // If there are any add recurrences in the operands list, see if any other
1527 // added values are loop invariant. If so, we can fold them into the
1529 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1532 // Scan over all recurrences, trying to fold loop invariants into them.
1533 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1534 // Scan all of the other operands to this add and add them to the vector if
1535 // they are loop invariant w.r.t. the recurrence.
1536 SmallVector<const SCEV *, 8> LIOps;
1537 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1538 const Loop *AddRecLoop = AddRec->getLoop();
1539 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1540 if (Ops[i]->isLoopInvariant(AddRecLoop)) {
1541 LIOps.push_back(Ops[i]);
1542 Ops.erase(Ops.begin()+i);
1546 // If we found some loop invariants, fold them into the recurrence.
1547 if (!LIOps.empty()) {
1548 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
1549 LIOps.push_back(AddRec->getStart());
1551 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
1553 AddRecOps[0] = getAddExpr(LIOps);
1555 // Build the new addrec. Propagate the NUW and NSW flags if both the
1556 // outer add and the inner addrec are guaranteed to have no overflow.
1557 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop,
1558 HasNUW && AddRec->hasNoUnsignedWrap(),
1559 HasNSW && AddRec->hasNoSignedWrap());
1561 // If all of the other operands were loop invariant, we are done.
1562 if (Ops.size() == 1) return NewRec;
1564 // Otherwise, add the folded AddRec by the non-liv parts.
1565 for (unsigned i = 0;; ++i)
1566 if (Ops[i] == AddRec) {
1570 return getAddExpr(Ops);
1573 // Okay, if there weren't any loop invariants to be folded, check to see if
1574 // there are multiple AddRec's with the same loop induction variable being
1575 // added together. If so, we can fold them.
1576 for (unsigned OtherIdx = Idx+1;
1577 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
1578 if (OtherIdx != Idx) {
1579 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
1580 if (AddRecLoop == OtherAddRec->getLoop()) {
1581 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D}
1582 SmallVector<const SCEV *, 4> NewOps(AddRec->op_begin(),
1584 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) {
1585 if (i >= NewOps.size()) {
1586 NewOps.append(OtherAddRec->op_begin()+i,
1587 OtherAddRec->op_end());
1590 NewOps[i] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i));
1592 const SCEV *NewAddRec = getAddRecExpr(NewOps, AddRecLoop);
1594 if (Ops.size() == 2) return NewAddRec;
1596 Ops.erase(Ops.begin()+Idx);
1597 Ops.erase(Ops.begin()+OtherIdx-1);
1598 Ops.push_back(NewAddRec);
1599 return getAddExpr(Ops);
1603 // Otherwise couldn't fold anything into this recurrence. Move onto the
1607 // Okay, it looks like we really DO need an add expr. Check to see if we
1608 // already have one, otherwise create a new one.
1609 FoldingSetNodeID ID;
1610 ID.AddInteger(scAddExpr);
1611 ID.AddInteger(Ops.size());
1612 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1613 ID.AddPointer(Ops[i]);
1616 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1618 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
1619 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
1620 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator),
1622 UniqueSCEVs.InsertNode(S, IP);
1624 if (HasNUW) S->setHasNoUnsignedWrap(true);
1625 if (HasNSW) S->setHasNoSignedWrap(true);
1629 /// getMulExpr - Get a canonical multiply expression, or something simpler if
1631 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
1632 bool HasNUW, bool HasNSW) {
1633 assert(!Ops.empty() && "Cannot get empty mul!");
1634 if (Ops.size() == 1) return Ops[0];
1636 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1637 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
1638 getEffectiveSCEVType(Ops[0]->getType()) &&
1639 "SCEVMulExpr operand types don't match!");
1642 // If HasNSW is true and all the operands are non-negative, infer HasNUW.
1643 if (!HasNUW && HasNSW) {
1645 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1646 if (!isKnownNonNegative(Ops[i])) {
1650 if (All) HasNUW = true;
1653 // Sort by complexity, this groups all similar expression types together.
1654 GroupByComplexity(Ops, LI);
1656 // If there are any constants, fold them together.
1658 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1660 // C1*(C2+V) -> C1*C2 + C1*V
1661 if (Ops.size() == 2)
1662 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
1663 if (Add->getNumOperands() == 2 &&
1664 isa<SCEVConstant>(Add->getOperand(0)))
1665 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
1666 getMulExpr(LHSC, Add->getOperand(1)));
1669 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1670 // We found two constants, fold them together!
1671 ConstantInt *Fold = ConstantInt::get(getContext(),
1672 LHSC->getValue()->getValue() *
1673 RHSC->getValue()->getValue());
1674 Ops[0] = getConstant(Fold);
1675 Ops.erase(Ops.begin()+1); // Erase the folded element
1676 if (Ops.size() == 1) return Ops[0];
1677 LHSC = cast<SCEVConstant>(Ops[0]);
1680 // If we are left with a constant one being multiplied, strip it off.
1681 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
1682 Ops.erase(Ops.begin());
1684 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
1685 // If we have a multiply of zero, it will always be zero.
1687 } else if (Ops[0]->isAllOnesValue()) {
1688 // If we have a mul by -1 of an add, try distributing the -1 among the
1690 if (Ops.size() == 2)
1691 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
1692 SmallVector<const SCEV *, 4> NewOps;
1693 bool AnyFolded = false;
1694 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(), E = Add->op_end();
1696 const SCEV *Mul = getMulExpr(Ops[0], *I);
1697 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
1698 NewOps.push_back(Mul);
1701 return getAddExpr(NewOps);
1705 if (Ops.size() == 1)
1709 // Skip over the add expression until we get to a multiply.
1710 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1713 // If there are mul operands inline them all into this expression.
1714 if (Idx < Ops.size()) {
1715 bool DeletedMul = false;
1716 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
1717 // If we have an mul, expand the mul operands onto the end of the operands
1719 Ops.erase(Ops.begin()+Idx);
1720 Ops.append(Mul->op_begin(), Mul->op_end());
1724 // If we deleted at least one mul, we added operands to the end of the list,
1725 // and they are not necessarily sorted. Recurse to resort and resimplify
1726 // any operands we just acquired.
1728 return getMulExpr(Ops);
1731 // If there are any add recurrences in the operands list, see if any other
1732 // added values are loop invariant. If so, we can fold them into the
1734 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1737 // Scan over all recurrences, trying to fold loop invariants into them.
1738 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1739 // Scan all of the other operands to this mul and add them to the vector if
1740 // they are loop invariant w.r.t. the recurrence.
1741 SmallVector<const SCEV *, 8> LIOps;
1742 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1743 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1744 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
1745 LIOps.push_back(Ops[i]);
1746 Ops.erase(Ops.begin()+i);
1750 // If we found some loop invariants, fold them into the recurrence.
1751 if (!LIOps.empty()) {
1752 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
1753 SmallVector<const SCEV *, 4> NewOps;
1754 NewOps.reserve(AddRec->getNumOperands());
1755 const SCEV *Scale = getMulExpr(LIOps);
1756 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
1757 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
1759 // Build the new addrec. Propagate the NUW and NSW flags if both the
1760 // outer mul and the inner addrec are guaranteed to have no overflow.
1761 const SCEV *NewRec = getAddRecExpr(NewOps, AddRec->getLoop(),
1762 HasNUW && AddRec->hasNoUnsignedWrap(),
1763 HasNSW && AddRec->hasNoSignedWrap());
1765 // If all of the other operands were loop invariant, we are done.
1766 if (Ops.size() == 1) return NewRec;
1768 // Otherwise, multiply the folded AddRec by the non-liv parts.
1769 for (unsigned i = 0;; ++i)
1770 if (Ops[i] == AddRec) {
1774 return getMulExpr(Ops);
1777 // Okay, if there weren't any loop invariants to be folded, check to see if
1778 // there are multiple AddRec's with the same loop induction variable being
1779 // multiplied together. If so, we can fold them.
1780 for (unsigned OtherIdx = Idx+1;
1781 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
1782 if (OtherIdx != Idx) {
1783 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
1784 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
1785 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D}
1786 const SCEVAddRecExpr *F = AddRec, *G = OtherAddRec;
1787 const SCEV *NewStart = getMulExpr(F->getStart(),
1789 const SCEV *B = F->getStepRecurrence(*this);
1790 const SCEV *D = G->getStepRecurrence(*this);
1791 const SCEV *NewStep = getAddExpr(getMulExpr(F, D),
1794 const SCEV *NewAddRec = getAddRecExpr(NewStart, NewStep,
1796 if (Ops.size() == 2) return NewAddRec;
1798 Ops.erase(Ops.begin()+Idx);
1799 Ops.erase(Ops.begin()+OtherIdx-1);
1800 Ops.push_back(NewAddRec);
1801 return getMulExpr(Ops);
1805 // Otherwise couldn't fold anything into this recurrence. Move onto the
1809 // Okay, it looks like we really DO need an mul expr. Check to see if we
1810 // already have one, otherwise create a new one.
1811 FoldingSetNodeID ID;
1812 ID.AddInteger(scMulExpr);
1813 ID.AddInteger(Ops.size());
1814 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1815 ID.AddPointer(Ops[i]);
1818 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1820 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
1821 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
1822 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
1824 UniqueSCEVs.InsertNode(S, IP);
1826 if (HasNUW) S->setHasNoUnsignedWrap(true);
1827 if (HasNSW) S->setHasNoSignedWrap(true);
1831 /// getUDivExpr - Get a canonical unsigned division expression, or something
1832 /// simpler if possible.
1833 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
1835 assert(getEffectiveSCEVType(LHS->getType()) ==
1836 getEffectiveSCEVType(RHS->getType()) &&
1837 "SCEVUDivExpr operand types don't match!");
1839 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
1840 if (RHSC->getValue()->equalsInt(1))
1841 return LHS; // X udiv 1 --> x
1842 // If the denominator is zero, the result of the udiv is undefined. Don't
1843 // try to analyze it, because the resolution chosen here may differ from
1844 // the resolution chosen in other parts of the compiler.
1845 if (!RHSC->getValue()->isZero()) {
1846 // Determine if the division can be folded into the operands of
1848 // TODO: Generalize this to non-constants by using known-bits information.
1849 const Type *Ty = LHS->getType();
1850 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
1851 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ;
1852 // For non-power-of-two values, effectively round the value up to the
1853 // nearest power of two.
1854 if (!RHSC->getValue()->getValue().isPowerOf2())
1856 const IntegerType *ExtTy =
1857 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
1858 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
1859 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
1860 if (const SCEVConstant *Step =
1861 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this)))
1862 if (!Step->getValue()->getValue()
1863 .urem(RHSC->getValue()->getValue()) &&
1864 getZeroExtendExpr(AR, ExtTy) ==
1865 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
1866 getZeroExtendExpr(Step, ExtTy),
1868 SmallVector<const SCEV *, 4> Operands;
1869 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i)
1870 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS));
1871 return getAddRecExpr(Operands, AR->getLoop());
1873 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
1874 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
1875 SmallVector<const SCEV *, 4> Operands;
1876 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i)
1877 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy));
1878 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
1879 // Find an operand that's safely divisible.
1880 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
1881 const SCEV *Op = M->getOperand(i);
1882 const SCEV *Div = getUDivExpr(Op, RHSC);
1883 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
1884 Operands = SmallVector<const SCEV *, 4>(M->op_begin(),
1887 return getMulExpr(Operands);
1891 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
1892 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(LHS)) {
1893 SmallVector<const SCEV *, 4> Operands;
1894 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i)
1895 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy));
1896 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
1898 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
1899 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
1900 if (isa<SCEVUDivExpr>(Op) ||
1901 getMulExpr(Op, RHS) != A->getOperand(i))
1903 Operands.push_back(Op);
1905 if (Operands.size() == A->getNumOperands())
1906 return getAddExpr(Operands);
1910 // Fold if both operands are constant.
1911 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
1912 Constant *LHSCV = LHSC->getValue();
1913 Constant *RHSCV = RHSC->getValue();
1914 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.append(StepChrec->op_begin(), StepChrec->op_end());
1943 return getAddRecExpr(Operands, L);
1946 Operands.push_back(Step);
1947 return getAddRecExpr(Operands, L, HasNUW, HasNSW);
1950 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
1951 /// Simplify the expression as much as possible.
1953 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
1955 bool HasNUW, bool HasNSW) {
1956 if (Operands.size() == 1) return Operands[0];
1958 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
1959 assert(getEffectiveSCEVType(Operands[i]->getType()) ==
1960 getEffectiveSCEVType(Operands[0]->getType()) &&
1961 "SCEVAddRecExpr operand types don't match!");
1964 if (Operands.back()->isZero()) {
1965 Operands.pop_back();
1966 return getAddRecExpr(Operands, L, HasNUW, HasNSW); // {X,+,0} --> X
1969 // It's tempting to want to call getMaxBackedgeTakenCount count here and
1970 // use that information to infer NUW and NSW flags. However, computing a
1971 // BE count requires calling getAddRecExpr, so we may not yet have a
1972 // meaningful BE count at this point (and if we don't, we'd be stuck
1973 // with a SCEVCouldNotCompute as the cached BE count).
1975 // If HasNSW is true and all the operands are non-negative, infer HasNUW.
1976 if (!HasNUW && HasNSW) {
1978 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
1979 if (!isKnownNonNegative(Operands[i])) {
1983 if (All) HasNUW = true;
1986 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
1987 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
1988 const Loop *NestedLoop = NestedAR->getLoop();
1989 if (L->contains(NestedLoop->getHeader()) ?
1990 (L->getLoopDepth() < NestedLoop->getLoopDepth()) :
1991 (!NestedLoop->contains(L->getHeader()) &&
1992 DT->dominates(L->getHeader(), NestedLoop->getHeader()))) {
1993 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
1994 NestedAR->op_end());
1995 Operands[0] = NestedAR->getStart();
1996 // AddRecs require their operands be loop-invariant with respect to their
1997 // loops. Don't perform this transformation if it would break this
1999 bool AllInvariant = true;
2000 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2001 if (!Operands[i]->isLoopInvariant(L)) {
2002 AllInvariant = false;
2006 NestedOperands[0] = getAddRecExpr(Operands, L);
2007 AllInvariant = true;
2008 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i)
2009 if (!NestedOperands[i]->isLoopInvariant(NestedLoop)) {
2010 AllInvariant = false;
2014 // Ok, both add recurrences are valid after the transformation.
2015 return getAddRecExpr(NestedOperands, NestedLoop, HasNUW, HasNSW);
2017 // Reset Operands to its original state.
2018 Operands[0] = NestedAR;
2022 // Okay, it looks like we really DO need an addrec expr. Check to see if we
2023 // already have one, otherwise create a new one.
2024 FoldingSetNodeID ID;
2025 ID.AddInteger(scAddRecExpr);
2026 ID.AddInteger(Operands.size());
2027 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2028 ID.AddPointer(Operands[i]);
2032 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2034 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size());
2035 std::uninitialized_copy(Operands.begin(), Operands.end(), O);
2036 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator),
2037 O, Operands.size(), L);
2038 UniqueSCEVs.InsertNode(S, IP);
2040 if (HasNUW) S->setHasNoUnsignedWrap(true);
2041 if (HasNSW) S->setHasNoSignedWrap(true);
2045 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
2047 SmallVector<const SCEV *, 2> Ops;
2050 return getSMaxExpr(Ops);
2054 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2055 assert(!Ops.empty() && "Cannot get empty smax!");
2056 if (Ops.size() == 1) return Ops[0];
2058 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2059 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
2060 getEffectiveSCEVType(Ops[0]->getType()) &&
2061 "SCEVSMaxExpr operand types don't match!");
2064 // Sort by complexity, this groups all similar expression types together.
2065 GroupByComplexity(Ops, LI);
2067 // If there are any constants, fold them together.
2069 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2071 assert(Idx < Ops.size());
2072 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2073 // We found two constants, fold them together!
2074 ConstantInt *Fold = ConstantInt::get(getContext(),
2075 APIntOps::smax(LHSC->getValue()->getValue(),
2076 RHSC->getValue()->getValue()));
2077 Ops[0] = getConstant(Fold);
2078 Ops.erase(Ops.begin()+1); // Erase the folded element
2079 if (Ops.size() == 1) return Ops[0];
2080 LHSC = cast<SCEVConstant>(Ops[0]);
2083 // If we are left with a constant minimum-int, strip it off.
2084 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
2085 Ops.erase(Ops.begin());
2087 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
2088 // If we have an smax with a constant maximum-int, it will always be
2093 if (Ops.size() == 1) return Ops[0];
2096 // Find the first SMax
2097 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
2100 // Check to see if one of the operands is an SMax. If so, expand its operands
2101 // onto our operand list, and recurse to simplify.
2102 if (Idx < Ops.size()) {
2103 bool DeletedSMax = false;
2104 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
2105 Ops.erase(Ops.begin()+Idx);
2106 Ops.append(SMax->op_begin(), SMax->op_end());
2111 return getSMaxExpr(Ops);
2114 // Okay, check to see if the same value occurs in the operand list twice. If
2115 // so, delete one. Since we sorted the list, these values are required to
2117 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2118 // X smax Y smax Y --> X smax Y
2119 // X smax Y --> X, if X is always greater than Y
2120 if (Ops[i] == Ops[i+1] ||
2121 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) {
2122 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2124 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) {
2125 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2129 if (Ops.size() == 1) return Ops[0];
2131 assert(!Ops.empty() && "Reduced smax down to nothing!");
2133 // Okay, it looks like we really DO need an smax expr. Check to see if we
2134 // already have one, otherwise create a new one.
2135 FoldingSetNodeID ID;
2136 ID.AddInteger(scSMaxExpr);
2137 ID.AddInteger(Ops.size());
2138 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2139 ID.AddPointer(Ops[i]);
2141 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2142 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2143 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2144 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator),
2146 UniqueSCEVs.InsertNode(S, IP);
2150 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
2152 SmallVector<const SCEV *, 2> Ops;
2155 return getUMaxExpr(Ops);
2159 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2160 assert(!Ops.empty() && "Cannot get empty umax!");
2161 if (Ops.size() == 1) return Ops[0];
2163 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2164 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
2165 getEffectiveSCEVType(Ops[0]->getType()) &&
2166 "SCEVUMaxExpr operand types don't match!");
2169 // Sort by complexity, this groups all similar expression types together.
2170 GroupByComplexity(Ops, LI);
2172 // If there are any constants, fold them together.
2174 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2176 assert(Idx < Ops.size());
2177 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2178 // We found two constants, fold them together!
2179 ConstantInt *Fold = ConstantInt::get(getContext(),
2180 APIntOps::umax(LHSC->getValue()->getValue(),
2181 RHSC->getValue()->getValue()));
2182 Ops[0] = getConstant(Fold);
2183 Ops.erase(Ops.begin()+1); // Erase the folded element
2184 if (Ops.size() == 1) return Ops[0];
2185 LHSC = cast<SCEVConstant>(Ops[0]);
2188 // If we are left with a constant minimum-int, strip it off.
2189 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
2190 Ops.erase(Ops.begin());
2192 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
2193 // If we have an umax with a constant maximum-int, it will always be
2198 if (Ops.size() == 1) return Ops[0];
2201 // Find the first UMax
2202 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
2205 // Check to see if one of the operands is a UMax. If so, expand its operands
2206 // onto our operand list, and recurse to simplify.
2207 if (Idx < Ops.size()) {
2208 bool DeletedUMax = false;
2209 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
2210 Ops.erase(Ops.begin()+Idx);
2211 Ops.append(UMax->op_begin(), UMax->op_end());
2216 return getUMaxExpr(Ops);
2219 // Okay, check to see if the same value occurs in the operand list twice. If
2220 // so, delete one. Since we sorted the list, these values are required to
2222 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2223 // X umax Y umax Y --> X umax Y
2224 // X umax Y --> X, if X is always greater than Y
2225 if (Ops[i] == Ops[i+1] ||
2226 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) {
2227 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2229 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) {
2230 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2234 if (Ops.size() == 1) return Ops[0];
2236 assert(!Ops.empty() && "Reduced umax down to nothing!");
2238 // Okay, it looks like we really DO need a umax expr. Check to see if we
2239 // already have one, otherwise create a new one.
2240 FoldingSetNodeID ID;
2241 ID.AddInteger(scUMaxExpr);
2242 ID.AddInteger(Ops.size());
2243 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2244 ID.AddPointer(Ops[i]);
2246 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2247 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2248 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2249 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator),
2251 UniqueSCEVs.InsertNode(S, IP);
2255 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
2257 // ~smax(~x, ~y) == smin(x, y).
2258 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2261 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
2263 // ~umax(~x, ~y) == umin(x, y)
2264 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2267 const SCEV *ScalarEvolution::getSizeOfExpr(const Type *AllocTy) {
2268 // If we have TargetData, we can bypass creating a target-independent
2269 // constant expression and then folding it back into a ConstantInt.
2270 // This is just a compile-time optimization.
2272 return getConstant(TD->getIntPtrType(getContext()),
2273 TD->getTypeAllocSize(AllocTy));
2275 Constant *C = ConstantExpr::getSizeOf(AllocTy);
2276 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2277 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD))
2279 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2280 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2283 const SCEV *ScalarEvolution::getAlignOfExpr(const Type *AllocTy) {
2284 Constant *C = ConstantExpr::getAlignOf(AllocTy);
2285 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2286 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD))
2288 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2289 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2292 const SCEV *ScalarEvolution::getOffsetOfExpr(const StructType *STy,
2294 // If we have TargetData, we can bypass creating a target-independent
2295 // constant expression and then folding it back into a ConstantInt.
2296 // This is just a compile-time optimization.
2298 return getConstant(TD->getIntPtrType(getContext()),
2299 TD->getStructLayout(STy)->getElementOffset(FieldNo));
2301 Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo);
2302 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2303 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD))
2305 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy));
2306 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2309 const SCEV *ScalarEvolution::getOffsetOfExpr(const Type *CTy,
2310 Constant *FieldNo) {
2311 Constant *C = ConstantExpr::getOffsetOf(CTy, FieldNo);
2312 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2313 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD))
2315 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(CTy));
2316 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2319 const SCEV *ScalarEvolution::getUnknown(Value *V) {
2320 // Don't attempt to do anything other than create a SCEVUnknown object
2321 // here. createSCEV only calls getUnknown after checking for all other
2322 // interesting possibilities, and any other code that calls getUnknown
2323 // is doing so in order to hide a value from SCEV canonicalization.
2325 FoldingSetNodeID ID;
2326 ID.AddInteger(scUnknown);
2329 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2330 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V);
2331 UniqueSCEVs.InsertNode(S, IP);
2335 //===----------------------------------------------------------------------===//
2336 // Basic SCEV Analysis and PHI Idiom Recognition Code
2339 /// isSCEVable - Test if values of the given type are analyzable within
2340 /// the SCEV framework. This primarily includes integer types, and it
2341 /// can optionally include pointer types if the ScalarEvolution class
2342 /// has access to target-specific information.
2343 bool ScalarEvolution::isSCEVable(const Type *Ty) const {
2344 // Integers and pointers are always SCEVable.
2345 return Ty->isIntegerTy() || Ty->isPointerTy();
2348 /// getTypeSizeInBits - Return the size in bits of the specified type,
2349 /// for which isSCEVable must return true.
2350 uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const {
2351 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2353 // If we have a TargetData, use it!
2355 return TD->getTypeSizeInBits(Ty);
2357 // Integer types have fixed sizes.
2358 if (Ty->isIntegerTy())
2359 return Ty->getPrimitiveSizeInBits();
2361 // The only other support type is pointer. Without TargetData, conservatively
2362 // assume pointers are 64-bit.
2363 assert(Ty->isPointerTy() && "isSCEVable permitted a non-SCEVable type!");
2367 /// getEffectiveSCEVType - Return a type with the same bitwidth as
2368 /// the given type and which represents how SCEV will treat the given
2369 /// type, for which isSCEVable must return true. For pointer types,
2370 /// this is the pointer-sized integer type.
2371 const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const {
2372 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2374 if (Ty->isIntegerTy())
2377 // The only other support type is pointer.
2378 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
2379 if (TD) return TD->getIntPtrType(getContext());
2381 // Without TargetData, conservatively assume pointers are 64-bit.
2382 return Type::getInt64Ty(getContext());
2385 const SCEV *ScalarEvolution::getCouldNotCompute() {
2386 return &CouldNotCompute;
2389 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
2390 /// expression and create a new one.
2391 const SCEV *ScalarEvolution::getSCEV(Value *V) {
2392 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
2394 std::map<SCEVCallbackVH, const SCEV *>::iterator I = Scalars.find(V);
2395 if (I != Scalars.end()) return I->second;
2396 const SCEV *S = createSCEV(V);
2397 Scalars.insert(std::make_pair(SCEVCallbackVH(V, this), S));
2401 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
2403 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) {
2404 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2406 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
2408 const Type *Ty = V->getType();
2409 Ty = getEffectiveSCEVType(Ty);
2410 return getMulExpr(V,
2411 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))));
2414 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
2415 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
2416 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2418 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
2420 const Type *Ty = V->getType();
2421 Ty = getEffectiveSCEVType(Ty);
2422 const SCEV *AllOnes =
2423 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
2424 return getMinusSCEV(AllOnes, V);
2427 /// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
2429 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS,
2432 return getAddExpr(LHS, getNegativeSCEV(RHS));
2435 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
2436 /// input value to the specified type. If the type must be extended, it is zero
2439 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V,
2441 const Type *SrcTy = V->getType();
2442 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2443 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2444 "Cannot truncate or zero extend with non-integer arguments!");
2445 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2446 return V; // No conversion
2447 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2448 return getTruncateExpr(V, Ty);
2449 return getZeroExtendExpr(V, Ty);
2452 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
2453 /// input value to the specified type. If the type must be extended, it is sign
2456 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
2458 const Type *SrcTy = V->getType();
2459 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2460 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2461 "Cannot truncate or zero extend with non-integer arguments!");
2462 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2463 return V; // No conversion
2464 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2465 return getTruncateExpr(V, Ty);
2466 return getSignExtendExpr(V, Ty);
2469 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
2470 /// input value to the specified type. If the type must be extended, it is zero
2471 /// extended. The conversion must not be narrowing.
2473 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, const Type *Ty) {
2474 const Type *SrcTy = V->getType();
2475 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2476 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2477 "Cannot noop or zero extend with non-integer arguments!");
2478 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2479 "getNoopOrZeroExtend cannot truncate!");
2480 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2481 return V; // No conversion
2482 return getZeroExtendExpr(V, Ty);
2485 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
2486 /// input value to the specified type. If the type must be extended, it is sign
2487 /// extended. The conversion must not be narrowing.
2489 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, const Type *Ty) {
2490 const Type *SrcTy = V->getType();
2491 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2492 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2493 "Cannot noop or sign extend with non-integer arguments!");
2494 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2495 "getNoopOrSignExtend cannot truncate!");
2496 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2497 return V; // No conversion
2498 return getSignExtendExpr(V, Ty);
2501 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
2502 /// the input value to the specified type. If the type must be extended,
2503 /// it is extended with unspecified bits. The conversion must not be
2506 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, const Type *Ty) {
2507 const Type *SrcTy = V->getType();
2508 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2509 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2510 "Cannot noop or any extend with non-integer arguments!");
2511 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2512 "getNoopOrAnyExtend cannot truncate!");
2513 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2514 return V; // No conversion
2515 return getAnyExtendExpr(V, Ty);
2518 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
2519 /// input value to the specified type. The conversion must not be widening.
2521 ScalarEvolution::getTruncateOrNoop(const SCEV *V, const Type *Ty) {
2522 const Type *SrcTy = V->getType();
2523 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2524 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2525 "Cannot truncate or noop with non-integer arguments!");
2526 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
2527 "getTruncateOrNoop cannot extend!");
2528 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2529 return V; // No conversion
2530 return getTruncateExpr(V, Ty);
2533 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
2534 /// the types using zero-extension, and then perform a umax operation
2536 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
2538 const SCEV *PromotedLHS = LHS;
2539 const SCEV *PromotedRHS = RHS;
2541 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2542 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2544 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2546 return getUMaxExpr(PromotedLHS, PromotedRHS);
2549 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
2550 /// the types using zero-extension, and then perform a umin operation
2552 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
2554 const SCEV *PromotedLHS = LHS;
2555 const SCEV *PromotedRHS = RHS;
2557 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2558 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2560 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2562 return getUMinExpr(PromotedLHS, PromotedRHS);
2565 /// PushDefUseChildren - Push users of the given Instruction
2566 /// onto the given Worklist.
2568 PushDefUseChildren(Instruction *I,
2569 SmallVectorImpl<Instruction *> &Worklist) {
2570 // Push the def-use children onto the Worklist stack.
2571 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end();
2573 Worklist.push_back(cast<Instruction>(UI));
2576 /// ForgetSymbolicValue - This looks up computed SCEV values for all
2577 /// instructions that depend on the given instruction and removes them from
2578 /// the Scalars map if they reference SymName. This is used during PHI
2581 ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) {
2582 SmallVector<Instruction *, 16> Worklist;
2583 PushDefUseChildren(PN, Worklist);
2585 SmallPtrSet<Instruction *, 8> Visited;
2587 while (!Worklist.empty()) {
2588 Instruction *I = Worklist.pop_back_val();
2589 if (!Visited.insert(I)) continue;
2591 std::map<SCEVCallbackVH, const SCEV *>::iterator It =
2592 Scalars.find(static_cast<Value *>(I));
2593 if (It != Scalars.end()) {
2594 // Short-circuit the def-use traversal if the symbolic name
2595 // ceases to appear in expressions.
2596 if (It->second != SymName && !It->second->hasOperand(SymName))
2599 // SCEVUnknown for a PHI either means that it has an unrecognized
2600 // structure, it's a PHI that's in the progress of being computed
2601 // by createNodeForPHI, or it's a single-value PHI. In the first case,
2602 // additional loop trip count information isn't going to change anything.
2603 // In the second case, createNodeForPHI will perform the necessary
2604 // updates on its own when it gets to that point. In the third, we do
2605 // want to forget the SCEVUnknown.
2606 if (!isa<PHINode>(I) ||
2607 !isa<SCEVUnknown>(It->second) ||
2608 (I != PN && It->second == SymName)) {
2609 ValuesAtScopes.erase(It->second);
2614 PushDefUseChildren(I, Worklist);
2618 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
2619 /// a loop header, making it a potential recurrence, or it doesn't.
2621 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
2622 if (const Loop *L = LI->getLoopFor(PN->getParent()))
2623 if (L->getHeader() == PN->getParent()) {
2624 // The loop may have multiple entrances or multiple exits; we can analyze
2625 // this phi as an addrec if it has a unique entry value and a unique
2627 Value *BEValueV = 0, *StartValueV = 0;
2628 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
2629 Value *V = PN->getIncomingValue(i);
2630 if (L->contains(PN->getIncomingBlock(i))) {
2633 } else if (BEValueV != V) {
2637 } else if (!StartValueV) {
2639 } else if (StartValueV != V) {
2644 if (BEValueV && StartValueV) {
2645 // While we are analyzing this PHI node, handle its value symbolically.
2646 const SCEV *SymbolicName = getUnknown(PN);
2647 assert(Scalars.find(PN) == Scalars.end() &&
2648 "PHI node already processed?");
2649 Scalars.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
2651 // Using this symbolic name for the PHI, analyze the value coming around
2653 const SCEV *BEValue = getSCEV(BEValueV);
2655 // NOTE: If BEValue is loop invariant, we know that the PHI node just
2656 // has a special value for the first iteration of the loop.
2658 // If the value coming around the backedge is an add with the symbolic
2659 // value we just inserted, then we found a simple induction variable!
2660 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
2661 // If there is a single occurrence of the symbolic value, replace it
2662 // with a recurrence.
2663 unsigned FoundIndex = Add->getNumOperands();
2664 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
2665 if (Add->getOperand(i) == SymbolicName)
2666 if (FoundIndex == e) {
2671 if (FoundIndex != Add->getNumOperands()) {
2672 // Create an add with everything but the specified operand.
2673 SmallVector<const SCEV *, 8> Ops;
2674 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
2675 if (i != FoundIndex)
2676 Ops.push_back(Add->getOperand(i));
2677 const SCEV *Accum = getAddExpr(Ops);
2679 // This is not a valid addrec if the step amount is varying each
2680 // loop iteration, but is not itself an addrec in this loop.
2681 if (Accum->isLoopInvariant(L) ||
2682 (isa<SCEVAddRecExpr>(Accum) &&
2683 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
2684 bool HasNUW = false;
2685 bool HasNSW = false;
2687 // If the increment doesn't overflow, then neither the addrec nor
2688 // the post-increment will overflow.
2689 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) {
2690 if (OBO->hasNoUnsignedWrap())
2692 if (OBO->hasNoSignedWrap())
2696 const SCEV *StartVal = getSCEV(StartValueV);
2697 const SCEV *PHISCEV =
2698 getAddRecExpr(StartVal, Accum, L, HasNUW, HasNSW);
2700 // Since the no-wrap flags are on the increment, they apply to the
2701 // post-incremented value as well.
2702 if (Accum->isLoopInvariant(L))
2703 (void)getAddRecExpr(getAddExpr(StartVal, Accum),
2704 Accum, L, HasNUW, HasNSW);
2706 // Okay, for the entire analysis of this edge we assumed the PHI
2707 // to be symbolic. We now need to go back and purge all of the
2708 // entries for the scalars that use the symbolic expression.
2709 ForgetSymbolicName(PN, SymbolicName);
2710 Scalars[SCEVCallbackVH(PN, this)] = PHISCEV;
2714 } else if (const SCEVAddRecExpr *AddRec =
2715 dyn_cast<SCEVAddRecExpr>(BEValue)) {
2716 // Otherwise, this could be a loop like this:
2717 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
2718 // In this case, j = {1,+,1} and BEValue is j.
2719 // Because the other in-value of i (0) fits the evolution of BEValue
2720 // i really is an addrec evolution.
2721 if (AddRec->getLoop() == L && AddRec->isAffine()) {
2722 const SCEV *StartVal = getSCEV(StartValueV);
2724 // If StartVal = j.start - j.stride, we can use StartVal as the
2725 // initial step of the addrec evolution.
2726 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
2727 AddRec->getOperand(1))) {
2728 const SCEV *PHISCEV =
2729 getAddRecExpr(StartVal, AddRec->getOperand(1), L);
2731 // Okay, for the entire analysis of this edge we assumed the PHI
2732 // to be symbolic. We now need to go back and purge all of the
2733 // entries for the scalars that use the symbolic expression.
2734 ForgetSymbolicName(PN, SymbolicName);
2735 Scalars[SCEVCallbackVH(PN, this)] = PHISCEV;
2743 // If the PHI has a single incoming value, follow that value, unless the
2744 // PHI's incoming blocks are in a different loop, in which case doing so
2745 // risks breaking LCSSA form. Instcombine would normally zap these, but
2746 // it doesn't have DominatorTree information, so it may miss cases.
2747 if (Value *V = PN->hasConstantValue(DT)) {
2748 bool AllSameLoop = true;
2749 Loop *PNLoop = LI->getLoopFor(PN->getParent());
2750 for (size_t i = 0, e = PN->getNumIncomingValues(); i != e; ++i)
2751 if (LI->getLoopFor(PN->getIncomingBlock(i)) != PNLoop) {
2752 AllSameLoop = false;
2759 // If it's not a loop phi, we can't handle it yet.
2760 return getUnknown(PN);
2763 /// UseFlag - When creating an operator with operands L and R based on an
2764 /// LLVM IR instruction in basic block BB where the instruction has
2765 /// nsw, nuw, or inbounds, test whether the corresponding flag can be
2766 /// set for the resulting SCEV.
2768 UseFlag(bool Flag, const SCEV *L, const SCEV *R, const Value *Inst) {
2769 // If the flag is not set, don't use it. This is included here to reduce
2770 // clutter in the callers.
2774 // Determine the block which contains the instruction with the flag.
2775 const Instruction *I = dyn_cast<Instruction>(Inst);
2778 const BasicBlock *BB = I->getParent();
2780 // Handle an easy case: test if exactly one of the operands is an addrec
2781 // and that the instruction is trivially control-equivalent to the addrec's
2783 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(L)) {
2784 if (!isa<SCEVAddRecExpr>(R) &&
2785 AR->getLoop()->getHeader() == BB)
2787 } else if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(R)) {
2788 if (AR->getLoop()->getHeader() == BB)
2795 /// createNodeForGEP - Expand GEP instructions into add and multiply
2796 /// operations. This allows them to be analyzed by regular SCEV code.
2798 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
2800 // Don't blindly transfer the inbounds flag from the GEP instruction to the
2801 // Add expression, because the Instruction may be guarded by control flow
2802 // and the no-overflow bits may not be valid for the expression in any
2803 // context. However, in the special case where the GEP is in the loop header,
2804 // we know it's trivially control-equivalent to any addrecs for that loop.
2805 bool InBounds = GEP->isInBounds();
2807 const Type *IntPtrTy = getEffectiveSCEVType(GEP->getType());
2808 Value *Base = GEP->getOperand(0);
2809 // Don't attempt to analyze GEPs over unsized objects.
2810 if (!cast<PointerType>(Base->getType())->getElementType()->isSized())
2811 return getUnknown(GEP);
2812 const SCEV *TotalOffset = getConstant(IntPtrTy, 0);
2813 gep_type_iterator GTI = gep_type_begin(GEP);
2814 for (GetElementPtrInst::op_iterator I = next(GEP->op_begin()),
2818 // Compute the (potentially symbolic) offset in bytes for this index.
2819 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) {
2820 // For a struct, add the member offset.
2821 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
2822 const SCEV *FieldOffset = getOffsetOfExpr(STy, FieldNo);
2824 // Test if the GEP has the inbounds keyword and is control-equivalent
2826 bool HasNUW = UseFlag(InBounds, TotalOffset, FieldOffset, GEP);
2828 // Add the field offset to the running total offset.
2829 TotalOffset = getAddExpr(TotalOffset, FieldOffset,
2830 HasNUW, /*HasNSW=*/false);
2832 // For an array, add the element offset, explicitly scaled.
2833 const SCEV *ElementSize = getSizeOfExpr(*GTI);
2834 const SCEV *IndexS = getSCEV(Index);
2835 // Getelementptr indices are signed.
2836 IndexS = getTruncateOrSignExtend(IndexS, IntPtrTy);
2838 // Test if the GEP has the inbounds keyword and is control-equivalent
2840 bool HasNUW = UseFlag(InBounds, IndexS, ElementSize, GEP);
2842 // Multiply the index by the element size to compute the element offset.
2843 const SCEV *LocalOffset = getMulExpr(IndexS, ElementSize,
2844 HasNUW, /*HasNSW=*/false);
2846 // Test if the GEP has the inbounds keyword and is control-equivalent
2848 HasNUW = UseFlag(InBounds, TotalOffset, LocalOffset, GEP);
2850 // Add the element offset to the running total offset.
2851 TotalOffset = getAddExpr(TotalOffset, LocalOffset,
2852 HasNUW, /*HasNSW=*/false);
2856 // Get the SCEV for the GEP base.
2857 const SCEV *BaseS = getSCEV(Base);
2859 // Test if the GEP has the inbounds keyword and is control-equivalent
2861 bool HasNUW = UseFlag(InBounds, BaseS, TotalOffset, GEP);
2863 // Add the total offset from all the GEP indices to the base.
2864 return getAddExpr(BaseS, TotalOffset, HasNUW, /*HasNSW=*/false);
2867 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
2868 /// guaranteed to end in (at every loop iteration). It is, at the same time,
2869 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
2870 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
2872 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
2873 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
2874 return C->getValue()->getValue().countTrailingZeros();
2876 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
2877 return std::min(GetMinTrailingZeros(T->getOperand()),
2878 (uint32_t)getTypeSizeInBits(T->getType()));
2880 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
2881 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
2882 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
2883 getTypeSizeInBits(E->getType()) : OpRes;
2886 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
2887 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
2888 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
2889 getTypeSizeInBits(E->getType()) : OpRes;
2892 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
2893 // The result is the min of all operands results.
2894 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
2895 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
2896 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
2900 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
2901 // The result is the sum of all operands results.
2902 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
2903 uint32_t BitWidth = getTypeSizeInBits(M->getType());
2904 for (unsigned i = 1, e = M->getNumOperands();
2905 SumOpRes != BitWidth && i != e; ++i)
2906 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
2911 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
2912 // The result is the min of all operands results.
2913 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
2914 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
2915 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
2919 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
2920 // The result is the min of all operands results.
2921 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
2922 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
2923 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
2927 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
2928 // The result is the min of all operands results.
2929 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
2930 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
2931 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
2935 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
2936 // For a SCEVUnknown, ask ValueTracking.
2937 unsigned BitWidth = getTypeSizeInBits(U->getType());
2938 APInt Mask = APInt::getAllOnesValue(BitWidth);
2939 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
2940 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones);
2941 return Zeros.countTrailingOnes();
2948 /// getUnsignedRange - Determine the unsigned range for a particular SCEV.
2951 ScalarEvolution::getUnsignedRange(const SCEV *S) {
2953 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
2954 return ConstantRange(C->getValue()->getValue());
2956 unsigned BitWidth = getTypeSizeInBits(S->getType());
2957 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
2959 // If the value has known zeros, the maximum unsigned value will have those
2960 // known zeros as well.
2961 uint32_t TZ = GetMinTrailingZeros(S);
2963 ConservativeResult =
2964 ConstantRange(APInt::getMinValue(BitWidth),
2965 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
2967 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
2968 ConstantRange X = getUnsignedRange(Add->getOperand(0));
2969 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
2970 X = X.add(getUnsignedRange(Add->getOperand(i)));
2971 return ConservativeResult.intersectWith(X);
2974 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
2975 ConstantRange X = getUnsignedRange(Mul->getOperand(0));
2976 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
2977 X = X.multiply(getUnsignedRange(Mul->getOperand(i)));
2978 return ConservativeResult.intersectWith(X);
2981 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
2982 ConstantRange X = getUnsignedRange(SMax->getOperand(0));
2983 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
2984 X = X.smax(getUnsignedRange(SMax->getOperand(i)));
2985 return ConservativeResult.intersectWith(X);
2988 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
2989 ConstantRange X = getUnsignedRange(UMax->getOperand(0));
2990 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
2991 X = X.umax(getUnsignedRange(UMax->getOperand(i)));
2992 return ConservativeResult.intersectWith(X);
2995 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
2996 ConstantRange X = getUnsignedRange(UDiv->getLHS());
2997 ConstantRange Y = getUnsignedRange(UDiv->getRHS());
2998 return ConservativeResult.intersectWith(X.udiv(Y));
3001 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3002 ConstantRange X = getUnsignedRange(ZExt->getOperand());
3003 return ConservativeResult.intersectWith(X.zeroExtend(BitWidth));
3006 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3007 ConstantRange X = getUnsignedRange(SExt->getOperand());
3008 return ConservativeResult.intersectWith(X.signExtend(BitWidth));
3011 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3012 ConstantRange X = getUnsignedRange(Trunc->getOperand());
3013 return ConservativeResult.intersectWith(X.truncate(BitWidth));
3016 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3017 // If there's no unsigned wrap, the value will never be less than its
3019 if (AddRec->hasNoUnsignedWrap())
3020 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
3021 if (!C->getValue()->isZero())
3022 ConservativeResult =
3023 ConservativeResult.intersectWith(
3024 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0)));
3026 // TODO: non-affine addrec
3027 if (AddRec->isAffine()) {
3028 const Type *Ty = AddRec->getType();
3029 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3030 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3031 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3032 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3034 const SCEV *Start = AddRec->getStart();
3035 const SCEV *Step = AddRec->getStepRecurrence(*this);
3037 ConstantRange StartRange = getUnsignedRange(Start);
3038 ConstantRange StepRange = getSignedRange(Step);
3039 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3040 ConstantRange EndRange =
3041 StartRange.add(MaxBECountRange.multiply(StepRange));
3043 // Check for overflow. This must be done with ConstantRange arithmetic
3044 // because we could be called from within the ScalarEvolution overflow
3046 ConstantRange ExtStartRange = StartRange.zextOrTrunc(BitWidth*2+1);
3047 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3048 ConstantRange ExtMaxBECountRange =
3049 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3050 ConstantRange ExtEndRange = EndRange.zextOrTrunc(BitWidth*2+1);
3051 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3053 return ConservativeResult;
3055 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(),
3056 EndRange.getUnsignedMin());
3057 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(),
3058 EndRange.getUnsignedMax());
3059 if (Min.isMinValue() && Max.isMaxValue())
3060 return ConservativeResult;
3061 return ConservativeResult.intersectWith(ConstantRange(Min, Max+1));
3065 return ConservativeResult;
3068 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3069 // For a SCEVUnknown, ask ValueTracking.
3070 APInt Mask = APInt::getAllOnesValue(BitWidth);
3071 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3072 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones, TD);
3073 if (Ones == ~Zeros + 1)
3074 return ConservativeResult;
3075 return ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1));
3078 return ConservativeResult;
3081 /// getSignedRange - Determine the signed range for a particular SCEV.
3084 ScalarEvolution::getSignedRange(const SCEV *S) {
3086 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3087 return ConstantRange(C->getValue()->getValue());
3089 unsigned BitWidth = getTypeSizeInBits(S->getType());
3090 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3092 // If the value has known zeros, the maximum signed value will have those
3093 // known zeros as well.
3094 uint32_t TZ = GetMinTrailingZeros(S);
3096 ConservativeResult =
3097 ConstantRange(APInt::getSignedMinValue(BitWidth),
3098 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
3100 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3101 ConstantRange X = getSignedRange(Add->getOperand(0));
3102 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3103 X = X.add(getSignedRange(Add->getOperand(i)));
3104 return ConservativeResult.intersectWith(X);
3107 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3108 ConstantRange X = getSignedRange(Mul->getOperand(0));
3109 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3110 X = X.multiply(getSignedRange(Mul->getOperand(i)));
3111 return ConservativeResult.intersectWith(X);
3114 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3115 ConstantRange X = getSignedRange(SMax->getOperand(0));
3116 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3117 X = X.smax(getSignedRange(SMax->getOperand(i)));
3118 return ConservativeResult.intersectWith(X);
3121 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3122 ConstantRange X = getSignedRange(UMax->getOperand(0));
3123 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3124 X = X.umax(getSignedRange(UMax->getOperand(i)));
3125 return ConservativeResult.intersectWith(X);
3128 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3129 ConstantRange X = getSignedRange(UDiv->getLHS());
3130 ConstantRange Y = getSignedRange(UDiv->getRHS());
3131 return ConservativeResult.intersectWith(X.udiv(Y));
3134 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3135 ConstantRange X = getSignedRange(ZExt->getOperand());
3136 return ConservativeResult.intersectWith(X.zeroExtend(BitWidth));
3139 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3140 ConstantRange X = getSignedRange(SExt->getOperand());
3141 return ConservativeResult.intersectWith(X.signExtend(BitWidth));
3144 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3145 ConstantRange X = getSignedRange(Trunc->getOperand());
3146 return ConservativeResult.intersectWith(X.truncate(BitWidth));
3149 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3150 // If there's no signed wrap, and all the operands have the same sign or
3151 // zero, the value won't ever change sign.
3152 if (AddRec->hasNoSignedWrap()) {
3153 bool AllNonNeg = true;
3154 bool AllNonPos = true;
3155 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
3156 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
3157 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
3160 ConservativeResult = ConservativeResult.intersectWith(
3161 ConstantRange(APInt(BitWidth, 0),
3162 APInt::getSignedMinValue(BitWidth)));
3164 ConservativeResult = ConservativeResult.intersectWith(
3165 ConstantRange(APInt::getSignedMinValue(BitWidth),
3166 APInt(BitWidth, 1)));
3169 // TODO: non-affine addrec
3170 if (AddRec->isAffine()) {
3171 const Type *Ty = AddRec->getType();
3172 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3173 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3174 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3175 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3177 const SCEV *Start = AddRec->getStart();
3178 const SCEV *Step = AddRec->getStepRecurrence(*this);
3180 ConstantRange StartRange = getSignedRange(Start);
3181 ConstantRange StepRange = getSignedRange(Step);
3182 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3183 ConstantRange EndRange =
3184 StartRange.add(MaxBECountRange.multiply(StepRange));
3186 // Check for overflow. This must be done with ConstantRange arithmetic
3187 // because we could be called from within the ScalarEvolution overflow
3189 ConstantRange ExtStartRange = StartRange.sextOrTrunc(BitWidth*2+1);
3190 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3191 ConstantRange ExtMaxBECountRange =
3192 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3193 ConstantRange ExtEndRange = EndRange.sextOrTrunc(BitWidth*2+1);
3194 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3196 return ConservativeResult;
3198 APInt Min = APIntOps::smin(StartRange.getSignedMin(),
3199 EndRange.getSignedMin());
3200 APInt Max = APIntOps::smax(StartRange.getSignedMax(),
3201 EndRange.getSignedMax());
3202 if (Min.isMinSignedValue() && Max.isMaxSignedValue())
3203 return ConservativeResult;
3204 return ConservativeResult.intersectWith(ConstantRange(Min, Max+1));
3208 return ConservativeResult;
3211 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3212 // For a SCEVUnknown, ask ValueTracking.
3213 if (!U->getValue()->getType()->isIntegerTy() && !TD)
3214 return ConservativeResult;
3215 unsigned NS = ComputeNumSignBits(U->getValue(), TD);
3217 return ConservativeResult;
3218 return ConservativeResult.intersectWith(
3219 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
3220 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1));
3223 return ConservativeResult;
3226 /// createSCEV - We know that there is no SCEV for the specified value.
3227 /// Analyze the expression.
3229 const SCEV *ScalarEvolution::createSCEV(Value *V) {
3230 if (!isSCEVable(V->getType()))
3231 return getUnknown(V);
3233 unsigned Opcode = Instruction::UserOp1;
3234 if (Instruction *I = dyn_cast<Instruction>(V)) {
3235 Opcode = I->getOpcode();
3237 // Don't attempt to analyze instructions in blocks that aren't
3238 // reachable. Such instructions don't matter, and they aren't required
3239 // to obey basic rules for definitions dominating uses which this
3240 // analysis depends on.
3241 if (!DT->isReachableFromEntry(I->getParent()))
3242 return getUnknown(V);
3243 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
3244 Opcode = CE->getOpcode();
3245 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
3246 return getConstant(CI);
3247 else if (isa<ConstantPointerNull>(V))
3248 return getConstant(V->getType(), 0);
3249 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
3250 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee());
3252 return getUnknown(V);
3254 Operator *U = cast<Operator>(V);
3256 case Instruction::Add: {
3257 const SCEV *LHS = getSCEV(U->getOperand(0));
3258 const SCEV *RHS = getSCEV(U->getOperand(1));
3260 // Don't transfer the NSW and NUW bits from the Add instruction to the
3261 // Add expression unless we can prove that it's safe.
3262 AddOperator *Add = cast<AddOperator>(U);
3263 bool HasNUW = UseFlag(Add->hasNoUnsignedWrap(), LHS, RHS, Add);
3264 bool HasNSW = UseFlag(Add->hasNoSignedWrap(), LHS, RHS, Add);
3266 return getAddExpr(LHS, RHS, HasNUW, HasNSW);
3268 case Instruction::Mul: {
3269 const SCEV *LHS = getSCEV(U->getOperand(0));
3270 const SCEV *RHS = getSCEV(U->getOperand(1));
3272 // Don't transfer the NSW and NUW bits from the Mul instruction to the
3273 // Mul expression unless we can prove that it's safe.
3274 MulOperator *Mul = cast<MulOperator>(U);
3275 bool HasNUW = UseFlag(Mul->hasNoUnsignedWrap(), LHS, RHS, Mul);
3276 bool HasNSW = UseFlag(Mul->hasNoSignedWrap(), LHS, RHS, Mul);
3278 return getMulExpr(LHS, RHS, HasNUW, HasNSW);
3280 case Instruction::UDiv:
3281 return getUDivExpr(getSCEV(U->getOperand(0)),
3282 getSCEV(U->getOperand(1)));
3283 case Instruction::Sub:
3284 return getMinusSCEV(getSCEV(U->getOperand(0)),
3285 getSCEV(U->getOperand(1)));
3286 case Instruction::And:
3287 // For an expression like x&255 that merely masks off the high bits,
3288 // use zext(trunc(x)) as the SCEV expression.
3289 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3290 if (CI->isNullValue())
3291 return getSCEV(U->getOperand(1));
3292 if (CI->isAllOnesValue())
3293 return getSCEV(U->getOperand(0));
3294 const APInt &A = CI->getValue();
3296 // Instcombine's ShrinkDemandedConstant may strip bits out of
3297 // constants, obscuring what would otherwise be a low-bits mask.
3298 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant
3299 // knew about to reconstruct a low-bits mask value.
3300 unsigned LZ = A.countLeadingZeros();
3301 unsigned BitWidth = A.getBitWidth();
3302 APInt AllOnes = APInt::getAllOnesValue(BitWidth);
3303 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
3304 ComputeMaskedBits(U->getOperand(0), AllOnes, KnownZero, KnownOne, TD);
3306 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ);
3308 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask))
3310 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)),
3311 IntegerType::get(getContext(), BitWidth - LZ)),
3316 case Instruction::Or:
3317 // If the RHS of the Or is a constant, we may have something like:
3318 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
3319 // optimizations will transparently handle this case.
3321 // In order for this transformation to be safe, the LHS must be of the
3322 // form X*(2^n) and the Or constant must be less than 2^n.
3323 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3324 const SCEV *LHS = getSCEV(U->getOperand(0));
3325 const APInt &CIVal = CI->getValue();
3326 if (GetMinTrailingZeros(LHS) >=
3327 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
3328 // Build a plain add SCEV.
3329 const SCEV *S = getAddExpr(LHS, getSCEV(CI));
3330 // If the LHS of the add was an addrec and it has no-wrap flags,
3331 // transfer the no-wrap flags, since an or won't introduce a wrap.
3332 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
3333 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
3334 if (OldAR->hasNoUnsignedWrap())
3335 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoUnsignedWrap(true);
3336 if (OldAR->hasNoSignedWrap())
3337 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoSignedWrap(true);
3343 case Instruction::Xor:
3344 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3345 // If the RHS of the xor is a signbit, then this is just an add.
3346 // Instcombine turns add of signbit into xor as a strength reduction step.
3347 if (CI->getValue().isSignBit())
3348 return getAddExpr(getSCEV(U->getOperand(0)),
3349 getSCEV(U->getOperand(1)));
3351 // If the RHS of xor is -1, then this is a not operation.
3352 if (CI->isAllOnesValue())
3353 return getNotSCEV(getSCEV(U->getOperand(0)));
3355 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
3356 // This is a variant of the check for xor with -1, and it handles
3357 // the case where instcombine has trimmed non-demanded bits out
3358 // of an xor with -1.
3359 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
3360 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
3361 if (BO->getOpcode() == Instruction::And &&
3362 LCI->getValue() == CI->getValue())
3363 if (const SCEVZeroExtendExpr *Z =
3364 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
3365 const Type *UTy = U->getType();
3366 const SCEV *Z0 = Z->getOperand();
3367 const Type *Z0Ty = Z0->getType();
3368 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
3370 // If C is a low-bits mask, the zero extend is serving to
3371 // mask off the high bits. Complement the operand and
3372 // re-apply the zext.
3373 if (APIntOps::isMask(Z0TySize, CI->getValue()))
3374 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
3376 // If C is a single bit, it may be in the sign-bit position
3377 // before the zero-extend. In this case, represent the xor
3378 // using an add, which is equivalent, and re-apply the zext.
3379 APInt Trunc = APInt(CI->getValue()).trunc(Z0TySize);
3380 if (APInt(Trunc).zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
3382 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
3388 case Instruction::Shl:
3389 // Turn shift left of a constant amount into a multiply.
3390 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3391 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3393 // If the shift count is not less than the bitwidth, the result of
3394 // the shift is undefined. Don't try to analyze it, because the
3395 // resolution chosen here may differ from the resolution chosen in
3396 // other parts of the compiler.
3397 if (SA->getValue().uge(BitWidth))
3400 Constant *X = ConstantInt::get(getContext(),
3401 APInt(BitWidth, 1).shl(SA->getZExtValue()));
3402 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3406 case Instruction::LShr:
3407 // Turn logical shift right of a constant into a unsigned divide.
3408 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3409 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3411 // If the shift count is not less than the bitwidth, the result of
3412 // the shift is undefined. Don't try to analyze it, because the
3413 // resolution chosen here may differ from the resolution chosen in
3414 // other parts of the compiler.
3415 if (SA->getValue().uge(BitWidth))
3418 Constant *X = ConstantInt::get(getContext(),
3419 APInt(BitWidth, 1).shl(SA->getZExtValue()));
3420 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3424 case Instruction::AShr:
3425 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
3426 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
3427 if (Operator *L = dyn_cast<Operator>(U->getOperand(0)))
3428 if (L->getOpcode() == Instruction::Shl &&
3429 L->getOperand(1) == U->getOperand(1)) {
3430 uint64_t BitWidth = getTypeSizeInBits(U->getType());
3432 // If the shift count is not less than the bitwidth, the result of
3433 // the shift is undefined. Don't try to analyze it, because the
3434 // resolution chosen here may differ from the resolution chosen in
3435 // other parts of the compiler.
3436 if (CI->getValue().uge(BitWidth))
3439 uint64_t Amt = BitWidth - CI->getZExtValue();
3440 if (Amt == BitWidth)
3441 return getSCEV(L->getOperand(0)); // shift by zero --> noop
3443 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
3444 IntegerType::get(getContext(),
3450 case Instruction::Trunc:
3451 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
3453 case Instruction::ZExt:
3454 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3456 case Instruction::SExt:
3457 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3459 case Instruction::BitCast:
3460 // BitCasts are no-op casts so we just eliminate the cast.
3461 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
3462 return getSCEV(U->getOperand(0));
3465 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
3466 // lead to pointer expressions which cannot safely be expanded to GEPs,
3467 // because ScalarEvolution doesn't respect the GEP aliasing rules when
3468 // simplifying integer expressions.
3470 case Instruction::GetElementPtr:
3471 return createNodeForGEP(cast<GEPOperator>(U));
3473 case Instruction::PHI:
3474 return createNodeForPHI(cast<PHINode>(U));
3476 case Instruction::Select:
3477 // This could be a smax or umax that was lowered earlier.
3478 // Try to recover it.
3479 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
3480 Value *LHS = ICI->getOperand(0);
3481 Value *RHS = ICI->getOperand(1);
3482 switch (ICI->getPredicate()) {
3483 case ICmpInst::ICMP_SLT:
3484 case ICmpInst::ICMP_SLE:
3485 std::swap(LHS, RHS);
3487 case ICmpInst::ICMP_SGT:
3488 case ICmpInst::ICMP_SGE:
3489 // a >s b ? a+x : b+x -> smax(a, b)+x
3490 // a >s b ? b+x : a+x -> smin(a, b)+x
3491 if (LHS->getType() == U->getType()) {
3492 const SCEV *LS = getSCEV(LHS);
3493 const SCEV *RS = getSCEV(RHS);
3494 const SCEV *LA = getSCEV(U->getOperand(1));
3495 const SCEV *RA = getSCEV(U->getOperand(2));
3496 const SCEV *LDiff = getMinusSCEV(LA, LS);
3497 const SCEV *RDiff = getMinusSCEV(RA, RS);
3499 return getAddExpr(getSMaxExpr(LS, RS), LDiff);
3500 LDiff = getMinusSCEV(LA, RS);
3501 RDiff = getMinusSCEV(RA, LS);
3503 return getAddExpr(getSMinExpr(LS, RS), LDiff);
3506 case ICmpInst::ICMP_ULT:
3507 case ICmpInst::ICMP_ULE:
3508 std::swap(LHS, RHS);
3510 case ICmpInst::ICMP_UGT:
3511 case ICmpInst::ICMP_UGE:
3512 // a >u b ? a+x : b+x -> umax(a, b)+x
3513 // a >u b ? b+x : a+x -> umin(a, b)+x
3514 if (LHS->getType() == U->getType()) {
3515 const SCEV *LS = getSCEV(LHS);
3516 const SCEV *RS = getSCEV(RHS);
3517 const SCEV *LA = getSCEV(U->getOperand(1));
3518 const SCEV *RA = getSCEV(U->getOperand(2));
3519 const SCEV *LDiff = getMinusSCEV(LA, LS);
3520 const SCEV *RDiff = getMinusSCEV(RA, RS);
3522 return getAddExpr(getUMaxExpr(LS, RS), LDiff);
3523 LDiff = getMinusSCEV(LA, RS);
3524 RDiff = getMinusSCEV(RA, LS);
3526 return getAddExpr(getUMinExpr(LS, RS), LDiff);
3529 case ICmpInst::ICMP_NE:
3530 // n != 0 ? n+x : 1+x -> umax(n, 1)+x
3531 if (LHS->getType() == U->getType() &&
3532 isa<ConstantInt>(RHS) &&
3533 cast<ConstantInt>(RHS)->isZero()) {
3534 const SCEV *One = getConstant(LHS->getType(), 1);
3535 const SCEV *LS = getSCEV(LHS);
3536 const SCEV *LA = getSCEV(U->getOperand(1));
3537 const SCEV *RA = getSCEV(U->getOperand(2));
3538 const SCEV *LDiff = getMinusSCEV(LA, LS);
3539 const SCEV *RDiff = getMinusSCEV(RA, One);
3541 return getAddExpr(getUMaxExpr(LS, One), LDiff);
3544 case ICmpInst::ICMP_EQ:
3545 // n == 0 ? 1+x : n+x -> umax(n, 1)+x
3546 if (LHS->getType() == U->getType() &&
3547 isa<ConstantInt>(RHS) &&
3548 cast<ConstantInt>(RHS)->isZero()) {
3549 const SCEV *One = getConstant(LHS->getType(), 1);
3550 const SCEV *LS = getSCEV(LHS);
3551 const SCEV *LA = getSCEV(U->getOperand(1));
3552 const SCEV *RA = getSCEV(U->getOperand(2));
3553 const SCEV *LDiff = getMinusSCEV(LA, One);
3554 const SCEV *RDiff = getMinusSCEV(RA, LS);
3556 return getAddExpr(getUMaxExpr(LS, One), LDiff);
3564 default: // We cannot analyze this expression.
3568 return getUnknown(V);
3573 //===----------------------------------------------------------------------===//
3574 // Iteration Count Computation Code
3577 /// getBackedgeTakenCount - If the specified loop has a predictable
3578 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
3579 /// object. The backedge-taken count is the number of times the loop header
3580 /// will be branched to from within the loop. This is one less than the
3581 /// trip count of the loop, since it doesn't count the first iteration,
3582 /// when the header is branched to from outside the loop.
3584 /// Note that it is not valid to call this method on a loop without a
3585 /// loop-invariant backedge-taken count (see
3586 /// hasLoopInvariantBackedgeTakenCount).
3588 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
3589 return getBackedgeTakenInfo(L).Exact;
3592 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
3593 /// return the least SCEV value that is known never to be less than the
3594 /// actual backedge taken count.
3595 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
3596 return getBackedgeTakenInfo(L).Max;
3599 /// PushLoopPHIs - Push PHI nodes in the header of the given loop
3600 /// onto the given Worklist.
3602 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
3603 BasicBlock *Header = L->getHeader();
3605 // Push all Loop-header PHIs onto the Worklist stack.
3606 for (BasicBlock::iterator I = Header->begin();
3607 PHINode *PN = dyn_cast<PHINode>(I); ++I)
3608 Worklist.push_back(PN);
3611 const ScalarEvolution::BackedgeTakenInfo &
3612 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
3613 // Initially insert a CouldNotCompute for this loop. If the insertion
3614 // succeeds, proceed to actually compute a backedge-taken count and
3615 // update the value. The temporary CouldNotCompute value tells SCEV
3616 // code elsewhere that it shouldn't attempt to request a new
3617 // backedge-taken count, which could result in infinite recursion.
3618 std::pair<std::map<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
3619 BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute()));
3621 BackedgeTakenInfo BECount = ComputeBackedgeTakenCount(L);
3622 if (BECount.Exact != getCouldNotCompute()) {
3623 assert(BECount.Exact->isLoopInvariant(L) &&
3624 BECount.Max->isLoopInvariant(L) &&
3625 "Computed backedge-taken count isn't loop invariant for loop!");
3626 ++NumTripCountsComputed;
3628 // Update the value in the map.
3629 Pair.first->second = BECount;
3631 if (BECount.Max != getCouldNotCompute())
3632 // Update the value in the map.
3633 Pair.first->second = BECount;
3634 if (isa<PHINode>(L->getHeader()->begin()))
3635 // Only count loops that have phi nodes as not being computable.
3636 ++NumTripCountsNotComputed;
3639 // Now that we know more about the trip count for this loop, forget any
3640 // existing SCEV values for PHI nodes in this loop since they are only
3641 // conservative estimates made without the benefit of trip count
3642 // information. This is similar to the code in forgetLoop, except that
3643 // it handles SCEVUnknown PHI nodes specially.
3644 if (BECount.hasAnyInfo()) {
3645 SmallVector<Instruction *, 16> Worklist;
3646 PushLoopPHIs(L, Worklist);
3648 SmallPtrSet<Instruction *, 8> Visited;
3649 while (!Worklist.empty()) {
3650 Instruction *I = Worklist.pop_back_val();
3651 if (!Visited.insert(I)) continue;
3653 std::map<SCEVCallbackVH, const SCEV *>::iterator It =
3654 Scalars.find(static_cast<Value *>(I));
3655 if (It != Scalars.end()) {
3656 // SCEVUnknown for a PHI either means that it has an unrecognized
3657 // structure, or it's a PHI that's in the progress of being computed
3658 // by createNodeForPHI. In the former case, additional loop trip
3659 // count information isn't going to change anything. In the later
3660 // case, createNodeForPHI will perform the necessary updates on its
3661 // own when it gets to that point.
3662 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(It->second)) {
3663 ValuesAtScopes.erase(It->second);
3666 if (PHINode *PN = dyn_cast<PHINode>(I))
3667 ConstantEvolutionLoopExitValue.erase(PN);
3670 PushDefUseChildren(I, Worklist);
3674 return Pair.first->second;
3677 /// forgetLoop - This method should be called by the client when it has
3678 /// changed a loop in a way that may effect ScalarEvolution's ability to
3679 /// compute a trip count, or if the loop is deleted.
3680 void ScalarEvolution::forgetLoop(const Loop *L) {
3681 // Drop any stored trip count value.
3682 BackedgeTakenCounts.erase(L);
3684 // Drop information about expressions based on loop-header PHIs.
3685 SmallVector<Instruction *, 16> Worklist;
3686 PushLoopPHIs(L, Worklist);
3688 SmallPtrSet<Instruction *, 8> Visited;
3689 while (!Worklist.empty()) {
3690 Instruction *I = Worklist.pop_back_val();
3691 if (!Visited.insert(I)) continue;
3693 std::map<SCEVCallbackVH, const SCEV *>::iterator It =
3694 Scalars.find(static_cast<Value *>(I));
3695 if (It != Scalars.end()) {
3696 ValuesAtScopes.erase(It->second);
3698 if (PHINode *PN = dyn_cast<PHINode>(I))
3699 ConstantEvolutionLoopExitValue.erase(PN);
3702 PushDefUseChildren(I, Worklist);
3706 /// forgetValue - This method should be called by the client when it has
3707 /// changed a value in a way that may effect its value, or which may
3708 /// disconnect it from a def-use chain linking it to a loop.
3709 void ScalarEvolution::forgetValue(Value *V) {
3710 Instruction *I = dyn_cast<Instruction>(V);
3713 // Drop information about expressions based on loop-header PHIs.
3714 SmallVector<Instruction *, 16> Worklist;
3715 Worklist.push_back(I);
3717 SmallPtrSet<Instruction *, 8> Visited;
3718 while (!Worklist.empty()) {
3719 I = Worklist.pop_back_val();
3720 if (!Visited.insert(I)) continue;
3722 std::map<SCEVCallbackVH, const SCEV *>::iterator It =
3723 Scalars.find(static_cast<Value *>(I));
3724 if (It != Scalars.end()) {
3725 ValuesAtScopes.erase(It->second);
3727 if (PHINode *PN = dyn_cast<PHINode>(I))
3728 ConstantEvolutionLoopExitValue.erase(PN);
3731 PushDefUseChildren(I, Worklist);
3735 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
3736 /// of the specified loop will execute.
3737 ScalarEvolution::BackedgeTakenInfo
3738 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
3739 SmallVector<BasicBlock *, 8> ExitingBlocks;
3740 L->getExitingBlocks(ExitingBlocks);
3742 // Examine all exits and pick the most conservative values.
3743 const SCEV *BECount = getCouldNotCompute();
3744 const SCEV *MaxBECount = getCouldNotCompute();
3745 bool CouldNotComputeBECount = false;
3746 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
3747 BackedgeTakenInfo NewBTI =
3748 ComputeBackedgeTakenCountFromExit(L, ExitingBlocks[i]);
3750 if (NewBTI.Exact == getCouldNotCompute()) {
3751 // We couldn't compute an exact value for this exit, so
3752 // we won't be able to compute an exact value for the loop.
3753 CouldNotComputeBECount = true;
3754 BECount = getCouldNotCompute();
3755 } else if (!CouldNotComputeBECount) {
3756 if (BECount == getCouldNotCompute())
3757 BECount = NewBTI.Exact;
3759 BECount = getUMinFromMismatchedTypes(BECount, NewBTI.Exact);
3761 if (MaxBECount == getCouldNotCompute())
3762 MaxBECount = NewBTI.Max;
3763 else if (NewBTI.Max != getCouldNotCompute())
3764 MaxBECount = getUMinFromMismatchedTypes(MaxBECount, NewBTI.Max);
3767 return BackedgeTakenInfo(BECount, MaxBECount);
3770 /// ComputeBackedgeTakenCountFromExit - Compute the number of times the backedge
3771 /// of the specified loop will execute if it exits via the specified block.
3772 ScalarEvolution::BackedgeTakenInfo
3773 ScalarEvolution::ComputeBackedgeTakenCountFromExit(const Loop *L,
3774 BasicBlock *ExitingBlock) {
3776 // Okay, we've chosen an exiting block. See what condition causes us to
3777 // exit at this block.
3779 // FIXME: we should be able to handle switch instructions (with a single exit)
3780 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
3781 if (ExitBr == 0) return getCouldNotCompute();
3782 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
3784 // At this point, we know we have a conditional branch that determines whether
3785 // the loop is exited. However, we don't know if the branch is executed each
3786 // time through the loop. If not, then the execution count of the branch will
3787 // not be equal to the trip count of the loop.
3789 // Currently we check for this by checking to see if the Exit branch goes to
3790 // the loop header. If so, we know it will always execute the same number of
3791 // times as the loop. We also handle the case where the exit block *is* the
3792 // loop header. This is common for un-rotated loops.
3794 // If both of those tests fail, walk up the unique predecessor chain to the
3795 // header, stopping if there is an edge that doesn't exit the loop. If the
3796 // header is reached, the execution count of the branch will be equal to the
3797 // trip count of the loop.
3799 // More extensive analysis could be done to handle more cases here.
3801 if (ExitBr->getSuccessor(0) != L->getHeader() &&
3802 ExitBr->getSuccessor(1) != L->getHeader() &&
3803 ExitBr->getParent() != L->getHeader()) {
3804 // The simple checks failed, try climbing the unique predecessor chain
3805 // up to the header.
3807 for (BasicBlock *BB = ExitBr->getParent(); BB; ) {
3808 BasicBlock *Pred = BB->getUniquePredecessor();
3810 return getCouldNotCompute();
3811 TerminatorInst *PredTerm = Pred->getTerminator();
3812 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) {
3813 BasicBlock *PredSucc = PredTerm->getSuccessor(i);
3816 // If the predecessor has a successor that isn't BB and isn't
3817 // outside the loop, assume the worst.
3818 if (L->contains(PredSucc))
3819 return getCouldNotCompute();
3821 if (Pred == L->getHeader()) {
3828 return getCouldNotCompute();
3831 // Proceed to the next level to examine the exit condition expression.
3832 return ComputeBackedgeTakenCountFromExitCond(L, ExitBr->getCondition(),
3833 ExitBr->getSuccessor(0),
3834 ExitBr->getSuccessor(1));
3837 /// ComputeBackedgeTakenCountFromExitCond - Compute the number of times the
3838 /// backedge of the specified loop will execute if its exit condition
3839 /// were a conditional branch of ExitCond, TBB, and FBB.
3840 ScalarEvolution::BackedgeTakenInfo
3841 ScalarEvolution::ComputeBackedgeTakenCountFromExitCond(const Loop *L,
3845 // Check if the controlling expression for this loop is an And or Or.
3846 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
3847 if (BO->getOpcode() == Instruction::And) {
3848 // Recurse on the operands of the and.
3849 BackedgeTakenInfo BTI0 =
3850 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB);
3851 BackedgeTakenInfo BTI1 =
3852 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB);
3853 const SCEV *BECount = getCouldNotCompute();
3854 const SCEV *MaxBECount = getCouldNotCompute();
3855 if (L->contains(TBB)) {
3856 // Both conditions must be true for the loop to continue executing.
3857 // Choose the less conservative count.
3858 if (BTI0.Exact == getCouldNotCompute() ||
3859 BTI1.Exact == getCouldNotCompute())
3860 BECount = getCouldNotCompute();
3862 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3863 if (BTI0.Max == getCouldNotCompute())
3864 MaxBECount = BTI1.Max;
3865 else if (BTI1.Max == getCouldNotCompute())
3866 MaxBECount = BTI0.Max;
3868 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max);
3870 // Both conditions must be true for the loop to exit.
3871 assert(L->contains(FBB) && "Loop block has no successor in loop!");
3872 if (BTI0.Exact != getCouldNotCompute() &&
3873 BTI1.Exact != getCouldNotCompute())
3874 BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3875 if (BTI0.Max != getCouldNotCompute() &&
3876 BTI1.Max != getCouldNotCompute())
3877 MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max);
3880 return BackedgeTakenInfo(BECount, MaxBECount);
3882 if (BO->getOpcode() == Instruction::Or) {
3883 // Recurse on the operands of the or.
3884 BackedgeTakenInfo BTI0 =
3885 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB);
3886 BackedgeTakenInfo BTI1 =
3887 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB);
3888 const SCEV *BECount = getCouldNotCompute();
3889 const SCEV *MaxBECount = getCouldNotCompute();
3890 if (L->contains(FBB)) {
3891 // Both conditions must be false for the loop to continue executing.
3892 // Choose the less conservative count.
3893 if (BTI0.Exact == getCouldNotCompute() ||
3894 BTI1.Exact == getCouldNotCompute())
3895 BECount = getCouldNotCompute();
3897 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3898 if (BTI0.Max == getCouldNotCompute())
3899 MaxBECount = BTI1.Max;
3900 else if (BTI1.Max == getCouldNotCompute())
3901 MaxBECount = BTI0.Max;
3903 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max);
3905 // Both conditions must be false for the loop to exit.
3906 assert(L->contains(TBB) && "Loop block has no successor in loop!");
3907 if (BTI0.Exact != getCouldNotCompute() &&
3908 BTI1.Exact != getCouldNotCompute())
3909 BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3910 if (BTI0.Max != getCouldNotCompute() &&
3911 BTI1.Max != getCouldNotCompute())
3912 MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max);
3915 return BackedgeTakenInfo(BECount, MaxBECount);
3919 // With an icmp, it may be feasible to compute an exact backedge-taken count.
3920 // Proceed to the next level to examine the icmp.
3921 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
3922 return ComputeBackedgeTakenCountFromExitCondICmp(L, ExitCondICmp, TBB, FBB);
3924 // Check for a constant condition. These are normally stripped out by
3925 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
3926 // preserve the CFG and is temporarily leaving constant conditions
3928 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
3929 if (L->contains(FBB) == !CI->getZExtValue())
3930 // The backedge is always taken.
3931 return getCouldNotCompute();
3933 // The backedge is never taken.
3934 return getConstant(CI->getType(), 0);
3937 // If it's not an integer or pointer comparison then compute it the hard way.
3938 return ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB));
3941 /// ComputeBackedgeTakenCountFromExitCondICmp - Compute the number of times the
3942 /// backedge of the specified loop will execute if its exit condition
3943 /// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB.
3944 ScalarEvolution::BackedgeTakenInfo
3945 ScalarEvolution::ComputeBackedgeTakenCountFromExitCondICmp(const Loop *L,
3950 // If the condition was exit on true, convert the condition to exit on false
3951 ICmpInst::Predicate Cond;
3952 if (!L->contains(FBB))
3953 Cond = ExitCond->getPredicate();
3955 Cond = ExitCond->getInversePredicate();
3957 // Handle common loops like: for (X = "string"; *X; ++X)
3958 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
3959 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
3960 BackedgeTakenInfo ItCnt =
3961 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond);
3962 if (ItCnt.hasAnyInfo())
3966 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
3967 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
3969 // Try to evaluate any dependencies out of the loop.
3970 LHS = getSCEVAtScope(LHS, L);
3971 RHS = getSCEVAtScope(RHS, L);
3973 // At this point, we would like to compute how many iterations of the
3974 // loop the predicate will return true for these inputs.
3975 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) {
3976 // If there is a loop-invariant, force it into the RHS.
3977 std::swap(LHS, RHS);
3978 Cond = ICmpInst::getSwappedPredicate(Cond);
3981 // Simplify the operands before analyzing them.
3982 (void)SimplifyICmpOperands(Cond, LHS, RHS);
3984 // If we have a comparison of a chrec against a constant, try to use value
3985 // ranges to answer this query.
3986 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
3987 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
3988 if (AddRec->getLoop() == L) {
3989 // Form the constant range.
3990 ConstantRange CompRange(
3991 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
3993 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
3994 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
3998 case ICmpInst::ICMP_NE: { // while (X != Y)
3999 // Convert to: while (X-Y != 0)
4000 BackedgeTakenInfo BTI = HowFarToZero(getMinusSCEV(LHS, RHS), L);
4001 if (BTI.hasAnyInfo()) return BTI;
4004 case ICmpInst::ICMP_EQ: { // while (X == Y)
4005 // Convert to: while (X-Y == 0)
4006 BackedgeTakenInfo BTI = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
4007 if (BTI.hasAnyInfo()) return BTI;
4010 case ICmpInst::ICMP_SLT: {
4011 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true);
4012 if (BTI.hasAnyInfo()) return BTI;
4015 case ICmpInst::ICMP_SGT: {
4016 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
4017 getNotSCEV(RHS), L, true);
4018 if (BTI.hasAnyInfo()) return BTI;
4021 case ICmpInst::ICMP_ULT: {
4022 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false);
4023 if (BTI.hasAnyInfo()) return BTI;
4026 case ICmpInst::ICMP_UGT: {
4027 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
4028 getNotSCEV(RHS), L, false);
4029 if (BTI.hasAnyInfo()) return BTI;
4034 dbgs() << "ComputeBackedgeTakenCount ";
4035 if (ExitCond->getOperand(0)->getType()->isUnsigned())
4036 dbgs() << "[unsigned] ";
4037 dbgs() << *LHS << " "
4038 << Instruction::getOpcodeName(Instruction::ICmp)
4039 << " " << *RHS << "\n";
4044 ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB));
4047 static ConstantInt *
4048 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
4049 ScalarEvolution &SE) {
4050 const SCEV *InVal = SE.getConstant(C);
4051 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
4052 assert(isa<SCEVConstant>(Val) &&
4053 "Evaluation of SCEV at constant didn't fold correctly?");
4054 return cast<SCEVConstant>(Val)->getValue();
4057 /// GetAddressedElementFromGlobal - Given a global variable with an initializer
4058 /// and a GEP expression (missing the pointer index) indexing into it, return
4059 /// the addressed element of the initializer or null if the index expression is
4062 GetAddressedElementFromGlobal(GlobalVariable *GV,
4063 const std::vector<ConstantInt*> &Indices) {
4064 Constant *Init = GV->getInitializer();
4065 for (unsigned i = 0, e = Indices.size(); i != e; ++i) {
4066 uint64_t Idx = Indices[i]->getZExtValue();
4067 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) {
4068 assert(Idx < CS->getNumOperands() && "Bad struct index!");
4069 Init = cast<Constant>(CS->getOperand(Idx));
4070 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) {
4071 if (Idx >= CA->getNumOperands()) return 0; // Bogus program
4072 Init = cast<Constant>(CA->getOperand(Idx));
4073 } else if (isa<ConstantAggregateZero>(Init)) {
4074 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) {
4075 assert(Idx < STy->getNumElements() && "Bad struct index!");
4076 Init = Constant::getNullValue(STy->getElementType(Idx));
4077 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) {
4078 if (Idx >= ATy->getNumElements()) return 0; // Bogus program
4079 Init = Constant::getNullValue(ATy->getElementType());
4081 llvm_unreachable("Unknown constant aggregate type!");
4085 return 0; // Unknown initializer type
4091 /// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of
4092 /// 'icmp op load X, cst', try to see if we can compute the backedge
4093 /// execution count.
4094 ScalarEvolution::BackedgeTakenInfo
4095 ScalarEvolution::ComputeLoadConstantCompareBackedgeTakenCount(
4099 ICmpInst::Predicate predicate) {
4100 if (LI->isVolatile()) return getCouldNotCompute();
4102 // Check to see if the loaded pointer is a getelementptr of a global.
4103 // TODO: Use SCEV instead of manually grubbing with GEPs.
4104 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
4105 if (!GEP) return getCouldNotCompute();
4107 // Make sure that it is really a constant global we are gepping, with an
4108 // initializer, and make sure the first IDX is really 0.
4109 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
4110 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
4111 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
4112 !cast<Constant>(GEP->getOperand(1))->isNullValue())
4113 return getCouldNotCompute();
4115 // Okay, we allow one non-constant index into the GEP instruction.
4117 std::vector<ConstantInt*> Indexes;
4118 unsigned VarIdxNum = 0;
4119 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
4120 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
4121 Indexes.push_back(CI);
4122 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
4123 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
4124 VarIdx = GEP->getOperand(i);
4126 Indexes.push_back(0);
4129 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
4130 // Check to see if X is a loop variant variable value now.
4131 const SCEV *Idx = getSCEV(VarIdx);
4132 Idx = getSCEVAtScope(Idx, L);
4134 // We can only recognize very limited forms of loop index expressions, in
4135 // particular, only affine AddRec's like {C1,+,C2}.
4136 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
4137 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) ||
4138 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
4139 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
4140 return getCouldNotCompute();
4142 unsigned MaxSteps = MaxBruteForceIterations;
4143 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
4144 ConstantInt *ItCst = ConstantInt::get(
4145 cast<IntegerType>(IdxExpr->getType()), IterationNum);
4146 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
4148 // Form the GEP offset.
4149 Indexes[VarIdxNum] = Val;
4151 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes);
4152 if (Result == 0) break; // Cannot compute!
4154 // Evaluate the condition for this iteration.
4155 Result = ConstantExpr::getICmp(predicate, Result, RHS);
4156 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
4157 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
4159 dbgs() << "\n***\n*** Computed loop count " << *ItCst
4160 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
4163 ++NumArrayLenItCounts;
4164 return getConstant(ItCst); // Found terminating iteration!
4167 return getCouldNotCompute();
4171 /// CanConstantFold - Return true if we can constant fold an instruction of the
4172 /// specified type, assuming that all operands were constants.
4173 static bool CanConstantFold(const Instruction *I) {
4174 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
4175 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I))
4178 if (const CallInst *CI = dyn_cast<CallInst>(I))
4179 if (const Function *F = CI->getCalledFunction())
4180 return canConstantFoldCallTo(F);
4184 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
4185 /// in the loop that V is derived from. We allow arbitrary operations along the
4186 /// way, but the operands of an operation must either be constants or a value
4187 /// derived from a constant PHI. If this expression does not fit with these
4188 /// constraints, return null.
4189 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
4190 // If this is not an instruction, or if this is an instruction outside of the
4191 // loop, it can't be derived from a loop PHI.
4192 Instruction *I = dyn_cast<Instruction>(V);
4193 if (I == 0 || !L->contains(I)) return 0;
4195 if (PHINode *PN = dyn_cast<PHINode>(I)) {
4196 if (L->getHeader() == I->getParent())
4199 // We don't currently keep track of the control flow needed to evaluate
4200 // PHIs, so we cannot handle PHIs inside of loops.
4204 // If we won't be able to constant fold this expression even if the operands
4205 // are constants, return early.
4206 if (!CanConstantFold(I)) return 0;
4208 // Otherwise, we can evaluate this instruction if all of its operands are
4209 // constant or derived from a PHI node themselves.
4211 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op)
4212 if (!isa<Constant>(I->getOperand(Op))) {
4213 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L);
4214 if (P == 0) return 0; // Not evolving from PHI
4218 return 0; // Evolving from multiple different PHIs.
4221 // This is a expression evolving from a constant PHI!
4225 /// EvaluateExpression - Given an expression that passes the
4226 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
4227 /// in the loop has the value PHIVal. If we can't fold this expression for some
4228 /// reason, return null.
4229 static Constant *EvaluateExpression(Value *V, Constant *PHIVal,
4230 const TargetData *TD) {
4231 if (isa<PHINode>(V)) return PHIVal;
4232 if (Constant *C = dyn_cast<Constant>(V)) return C;
4233 Instruction *I = cast<Instruction>(V);
4235 std::vector<Constant*> Operands(I->getNumOperands());
4237 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
4238 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal, TD);
4239 if (Operands[i] == 0) return 0;
4242 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
4243 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
4245 return ConstantFoldInstOperands(I->getOpcode(), I->getType(),
4246 &Operands[0], Operands.size(), TD);
4249 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
4250 /// in the header of its containing loop, we know the loop executes a
4251 /// constant number of times, and the PHI node is just a recurrence
4252 /// involving constants, fold it.
4254 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
4257 std::map<PHINode*, Constant*>::iterator I =
4258 ConstantEvolutionLoopExitValue.find(PN);
4259 if (I != ConstantEvolutionLoopExitValue.end())
4262 if (BEs.ugt(MaxBruteForceIterations))
4263 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
4265 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
4267 // Since the loop is canonicalized, the PHI node must have two entries. One
4268 // entry must be a constant (coming in from outside of the loop), and the
4269 // second must be derived from the same PHI.
4270 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
4271 Constant *StartCST =
4272 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
4274 return RetVal = 0; // Must be a constant.
4276 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
4277 if (getConstantEvolvingPHI(BEValue, L) != PN &&
4278 !isa<Constant>(BEValue))
4279 return RetVal = 0; // Not derived from same PHI.
4281 // Execute the loop symbolically to determine the exit value.
4282 if (BEs.getActiveBits() >= 32)
4283 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
4285 unsigned NumIterations = BEs.getZExtValue(); // must be in range
4286 unsigned IterationNum = 0;
4287 for (Constant *PHIVal = StartCST; ; ++IterationNum) {
4288 if (IterationNum == NumIterations)
4289 return RetVal = PHIVal; // Got exit value!
4291 // Compute the value of the PHI node for the next iteration.
4292 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD);
4293 if (NextPHI == PHIVal)
4294 return RetVal = NextPHI; // Stopped evolving!
4296 return 0; // Couldn't evaluate!
4301 /// ComputeBackedgeTakenCountExhaustively - If the loop is known to execute a
4302 /// constant number of times (the condition evolves only from constants),
4303 /// try to evaluate a few iterations of the loop until we get the exit
4304 /// condition gets a value of ExitWhen (true or false). If we cannot
4305 /// evaluate the trip count of the loop, return getCouldNotCompute().
4307 ScalarEvolution::ComputeBackedgeTakenCountExhaustively(const Loop *L,
4310 PHINode *PN = getConstantEvolvingPHI(Cond, L);
4311 if (PN == 0) return getCouldNotCompute();
4313 // If the loop is canonicalized, the PHI will have exactly two entries.
4314 // That's the only form we support here.
4315 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
4317 // One entry must be a constant (coming in from outside of the loop), and the
4318 // second must be derived from the same PHI.
4319 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
4320 Constant *StartCST =
4321 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
4322 if (StartCST == 0) return getCouldNotCompute(); // Must be a constant.
4324 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
4325 if (getConstantEvolvingPHI(BEValue, L) != PN &&
4326 !isa<Constant>(BEValue))
4327 return getCouldNotCompute(); // Not derived from same PHI.
4329 // Okay, we find a PHI node that defines the trip count of this loop. Execute
4330 // the loop symbolically to determine when the condition gets a value of
4332 unsigned IterationNum = 0;
4333 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
4334 for (Constant *PHIVal = StartCST;
4335 IterationNum != MaxIterations; ++IterationNum) {
4336 ConstantInt *CondVal =
4337 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal, TD));
4339 // Couldn't symbolically evaluate.
4340 if (!CondVal) return getCouldNotCompute();
4342 if (CondVal->getValue() == uint64_t(ExitWhen)) {
4343 ++NumBruteForceTripCountsComputed;
4344 return getConstant(Type::getInt32Ty(getContext()), IterationNum);
4347 // Compute the value of the PHI node for the next iteration.
4348 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD);
4349 if (NextPHI == 0 || NextPHI == PHIVal)
4350 return getCouldNotCompute();// Couldn't evaluate or not making progress...
4354 // Too many iterations were needed to evaluate.
4355 return getCouldNotCompute();
4358 /// getSCEVAtScope - Return a SCEV expression for the specified value
4359 /// at the specified scope in the program. The L value specifies a loop
4360 /// nest to evaluate the expression at, where null is the top-level or a
4361 /// specified loop is immediately inside of the loop.
4363 /// This method can be used to compute the exit value for a variable defined
4364 /// in a loop by querying what the value will hold in the parent loop.
4366 /// In the case that a relevant loop exit value cannot be computed, the
4367 /// original value V is returned.
4368 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
4369 // Check to see if we've folded this expression at this loop before.
4370 std::map<const Loop *, const SCEV *> &Values = ValuesAtScopes[V];
4371 std::pair<std::map<const Loop *, const SCEV *>::iterator, bool> Pair =
4372 Values.insert(std::make_pair(L, static_cast<const SCEV *>(0)));
4374 return Pair.first->second ? Pair.first->second : V;
4376 // Otherwise compute it.
4377 const SCEV *C = computeSCEVAtScope(V, L);
4378 ValuesAtScopes[V][L] = C;
4382 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
4383 if (isa<SCEVConstant>(V)) return V;
4385 // If this instruction is evolved from a constant-evolving PHI, compute the
4386 // exit value from the loop without using SCEVs.
4387 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
4388 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
4389 const Loop *LI = (*this->LI)[I->getParent()];
4390 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
4391 if (PHINode *PN = dyn_cast<PHINode>(I))
4392 if (PN->getParent() == LI->getHeader()) {
4393 // Okay, there is no closed form solution for the PHI node. Check
4394 // to see if the loop that contains it has a known backedge-taken
4395 // count. If so, we may be able to force computation of the exit
4397 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
4398 if (const SCEVConstant *BTCC =
4399 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
4400 // Okay, we know how many times the containing loop executes. If
4401 // this is a constant evolving PHI node, get the final value at
4402 // the specified iteration number.
4403 Constant *RV = getConstantEvolutionLoopExitValue(PN,
4404 BTCC->getValue()->getValue(),
4406 if (RV) return getSCEV(RV);
4410 // Okay, this is an expression that we cannot symbolically evaluate
4411 // into a SCEV. Check to see if it's possible to symbolically evaluate
4412 // the arguments into constants, and if so, try to constant propagate the
4413 // result. This is particularly useful for computing loop exit values.
4414 if (CanConstantFold(I)) {
4415 SmallVector<Constant *, 4> Operands;
4416 bool MadeImprovement = false;
4417 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
4418 Value *Op = I->getOperand(i);
4419 if (Constant *C = dyn_cast<Constant>(Op)) {
4420 Operands.push_back(C);
4424 // If any of the operands is non-constant and if they are
4425 // non-integer and non-pointer, don't even try to analyze them
4426 // with scev techniques.
4427 if (!isSCEVable(Op->getType()))
4430 const SCEV *OrigV = getSCEV(Op);
4431 const SCEV *OpV = getSCEVAtScope(OrigV, L);
4432 MadeImprovement |= OrigV != OpV;
4435 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV))
4437 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV))
4438 C = dyn_cast<Constant>(SU->getValue());
4440 if (C->getType() != Op->getType())
4441 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
4445 Operands.push_back(C);
4448 // Check to see if getSCEVAtScope actually made an improvement.
4449 if (MadeImprovement) {
4451 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
4452 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
4453 Operands[0], Operands[1], TD);
4455 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
4456 &Operands[0], Operands.size(), TD);
4463 // This is some other type of SCEVUnknown, just return it.
4467 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
4468 // Avoid performing the look-up in the common case where the specified
4469 // expression has no loop-variant portions.
4470 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
4471 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
4472 if (OpAtScope != Comm->getOperand(i)) {
4473 // Okay, at least one of these operands is loop variant but might be
4474 // foldable. Build a new instance of the folded commutative expression.
4475 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
4476 Comm->op_begin()+i);
4477 NewOps.push_back(OpAtScope);
4479 for (++i; i != e; ++i) {
4480 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
4481 NewOps.push_back(OpAtScope);
4483 if (isa<SCEVAddExpr>(Comm))
4484 return getAddExpr(NewOps);
4485 if (isa<SCEVMulExpr>(Comm))
4486 return getMulExpr(NewOps);
4487 if (isa<SCEVSMaxExpr>(Comm))
4488 return getSMaxExpr(NewOps);
4489 if (isa<SCEVUMaxExpr>(Comm))
4490 return getUMaxExpr(NewOps);
4491 llvm_unreachable("Unknown commutative SCEV type!");
4494 // If we got here, all operands are loop invariant.
4498 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
4499 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
4500 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
4501 if (LHS == Div->getLHS() && RHS == Div->getRHS())
4502 return Div; // must be loop invariant
4503 return getUDivExpr(LHS, RHS);
4506 // If this is a loop recurrence for a loop that does not contain L, then we
4507 // are dealing with the final value computed by the loop.
4508 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
4509 // First, attempt to evaluate each operand.
4510 // Avoid performing the look-up in the common case where the specified
4511 // expression has no loop-variant portions.
4512 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
4513 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
4514 if (OpAtScope == AddRec->getOperand(i))
4517 // Okay, at least one of these operands is loop variant but might be
4518 // foldable. Build a new instance of the folded commutative expression.
4519 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(),
4520 AddRec->op_begin()+i);
4521 NewOps.push_back(OpAtScope);
4522 for (++i; i != e; ++i)
4523 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
4525 AddRec = cast<SCEVAddRecExpr>(getAddRecExpr(NewOps, AddRec->getLoop()));
4529 // If the scope is outside the addrec's loop, evaluate it by using the
4530 // loop exit value of the addrec.
4531 if (!AddRec->getLoop()->contains(L)) {
4532 // To evaluate this recurrence, we need to know how many times the AddRec
4533 // loop iterates. Compute this now.
4534 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
4535 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
4537 // Then, evaluate the AddRec.
4538 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
4544 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
4545 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
4546 if (Op == Cast->getOperand())
4547 return Cast; // must be loop invariant
4548 return getZeroExtendExpr(Op, Cast->getType());
4551 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
4552 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
4553 if (Op == Cast->getOperand())
4554 return Cast; // must be loop invariant
4555 return getSignExtendExpr(Op, Cast->getType());
4558 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
4559 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
4560 if (Op == Cast->getOperand())
4561 return Cast; // must be loop invariant
4562 return getTruncateExpr(Op, Cast->getType());
4565 llvm_unreachable("Unknown SCEV type!");
4569 /// getSCEVAtScope - This is a convenience function which does
4570 /// getSCEVAtScope(getSCEV(V), L).
4571 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
4572 return getSCEVAtScope(getSCEV(V), L);
4575 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
4576 /// following equation:
4578 /// A * X = B (mod N)
4580 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
4581 /// A and B isn't important.
4583 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
4584 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
4585 ScalarEvolution &SE) {
4586 uint32_t BW = A.getBitWidth();
4587 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
4588 assert(A != 0 && "A must be non-zero.");
4592 // The gcd of A and N may have only one prime factor: 2. The number of
4593 // trailing zeros in A is its multiplicity
4594 uint32_t Mult2 = A.countTrailingZeros();
4597 // 2. Check if B is divisible by D.
4599 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
4600 // is not less than multiplicity of this prime factor for D.
4601 if (B.countTrailingZeros() < Mult2)
4602 return SE.getCouldNotCompute();
4604 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
4607 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
4608 // bit width during computations.
4609 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
4610 APInt Mod(BW + 1, 0);
4611 Mod.set(BW - Mult2); // Mod = N / D
4612 APInt I = AD.multiplicativeInverse(Mod);
4614 // 4. Compute the minimum unsigned root of the equation:
4615 // I * (B / D) mod (N / D)
4616 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
4618 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
4620 return SE.getConstant(Result.trunc(BW));
4623 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
4624 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
4625 /// might be the same) or two SCEVCouldNotCompute objects.
4627 static std::pair<const SCEV *,const SCEV *>
4628 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
4629 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
4630 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
4631 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
4632 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
4634 // We currently can only solve this if the coefficients are constants.
4635 if (!LC || !MC || !NC) {
4636 const SCEV *CNC = SE.getCouldNotCompute();
4637 return std::make_pair(CNC, CNC);
4640 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
4641 const APInt &L = LC->getValue()->getValue();
4642 const APInt &M = MC->getValue()->getValue();
4643 const APInt &N = NC->getValue()->getValue();
4644 APInt Two(BitWidth, 2);
4645 APInt Four(BitWidth, 4);
4648 using namespace APIntOps;
4650 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
4651 // The B coefficient is M-N/2
4655 // The A coefficient is N/2
4656 APInt A(N.sdiv(Two));
4658 // Compute the B^2-4ac term.
4661 SqrtTerm -= Four * (A * C);
4663 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
4664 // integer value or else APInt::sqrt() will assert.
4665 APInt SqrtVal(SqrtTerm.sqrt());
4667 // Compute the two solutions for the quadratic formula.
4668 // The divisions must be performed as signed divisions.
4670 APInt TwoA( A << 1 );
4671 if (TwoA.isMinValue()) {
4672 const SCEV *CNC = SE.getCouldNotCompute();
4673 return std::make_pair(CNC, CNC);
4676 LLVMContext &Context = SE.getContext();
4678 ConstantInt *Solution1 =
4679 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
4680 ConstantInt *Solution2 =
4681 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
4683 return std::make_pair(SE.getConstant(Solution1),
4684 SE.getConstant(Solution2));
4685 } // end APIntOps namespace
4688 /// HowFarToZero - Return the number of times a backedge comparing the specified
4689 /// value to zero will execute. If not computable, return CouldNotCompute.
4690 ScalarEvolution::BackedgeTakenInfo
4691 ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) {
4692 // If the value is a constant
4693 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
4694 // If the value is already zero, the branch will execute zero times.
4695 if (C->getValue()->isZero()) return C;
4696 return getCouldNotCompute(); // Otherwise it will loop infinitely.
4699 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
4700 if (!AddRec || AddRec->getLoop() != L)
4701 return getCouldNotCompute();
4703 if (AddRec->isAffine()) {
4704 // If this is an affine expression, the execution count of this branch is
4705 // the minimum unsigned root of the following equation:
4707 // Start + Step*N = 0 (mod 2^BW)
4711 // Step*N = -Start (mod 2^BW)
4713 // where BW is the common bit width of Start and Step.
4715 // Get the initial value for the loop.
4716 const SCEV *Start = getSCEVAtScope(AddRec->getStart(),
4717 L->getParentLoop());
4718 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1),
4719 L->getParentLoop());
4721 if (const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) {
4722 // For now we handle only constant steps.
4724 // First, handle unitary steps.
4725 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so:
4726 return getNegativeSCEV(Start); // N = -Start (as unsigned)
4727 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so:
4728 return Start; // N = Start (as unsigned)
4730 // Then, try to solve the above equation provided that Start is constant.
4731 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
4732 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
4733 -StartC->getValue()->getValue(),
4736 } else if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
4737 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
4738 // the quadratic equation to solve it.
4739 std::pair<const SCEV *,const SCEV *> Roots = SolveQuadraticEquation(AddRec,
4741 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
4742 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
4745 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1
4746 << " sol#2: " << *R2 << "\n";
4748 // Pick the smallest positive root value.
4749 if (ConstantInt *CB =
4750 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
4751 R1->getValue(), R2->getValue()))) {
4752 if (CB->getZExtValue() == false)
4753 std::swap(R1, R2); // R1 is the minimum root now.
4755 // We can only use this value if the chrec ends up with an exact zero
4756 // value at this index. When solving for "X*X != 5", for example, we
4757 // should not accept a root of 2.
4758 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
4760 return R1; // We found a quadratic root!
4765 return getCouldNotCompute();
4768 /// HowFarToNonZero - Return the number of times a backedge checking the
4769 /// specified value for nonzero will execute. If not computable, return
4771 ScalarEvolution::BackedgeTakenInfo
4772 ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
4773 // Loops that look like: while (X == 0) are very strange indeed. We don't
4774 // handle them yet except for the trivial case. This could be expanded in the
4775 // future as needed.
4777 // If the value is a constant, check to see if it is known to be non-zero
4778 // already. If so, the backedge will execute zero times.
4779 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
4780 if (!C->getValue()->isNullValue())
4781 return getConstant(C->getType(), 0);
4782 return getCouldNotCompute(); // Otherwise it will loop infinitely.
4785 // We could implement others, but I really doubt anyone writes loops like
4786 // this, and if they did, they would already be constant folded.
4787 return getCouldNotCompute();
4790 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
4791 /// (which may not be an immediate predecessor) which has exactly one
4792 /// successor from which BB is reachable, or null if no such block is
4795 std::pair<BasicBlock *, BasicBlock *>
4796 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
4797 // If the block has a unique predecessor, then there is no path from the
4798 // predecessor to the block that does not go through the direct edge
4799 // from the predecessor to the block.
4800 if (BasicBlock *Pred = BB->getSinglePredecessor())
4801 return std::make_pair(Pred, BB);
4803 // A loop's header is defined to be a block that dominates the loop.
4804 // If the header has a unique predecessor outside the loop, it must be
4805 // a block that has exactly one successor that can reach the loop.
4806 if (Loop *L = LI->getLoopFor(BB))
4807 return std::make_pair(L->getLoopPredecessor(), L->getHeader());
4809 return std::pair<BasicBlock *, BasicBlock *>();
4812 /// HasSameValue - SCEV structural equivalence is usually sufficient for
4813 /// testing whether two expressions are equal, however for the purposes of
4814 /// looking for a condition guarding a loop, it can be useful to be a little
4815 /// more general, since a front-end may have replicated the controlling
4818 static bool HasSameValue(const SCEV *A, const SCEV *B) {
4819 // Quick check to see if they are the same SCEV.
4820 if (A == B) return true;
4822 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
4823 // two different instructions with the same value. Check for this case.
4824 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
4825 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
4826 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
4827 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
4828 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory())
4831 // Otherwise assume they may have a different value.
4835 /// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with
4836 /// predicate Pred. Return true iff any changes were made.
4838 bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
4839 const SCEV *&LHS, const SCEV *&RHS) {
4840 bool Changed = false;
4842 // Canonicalize a constant to the right side.
4843 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
4844 // Check for both operands constant.
4845 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
4846 if (ConstantExpr::getICmp(Pred,
4848 RHSC->getValue())->isNullValue())
4849 goto trivially_false;
4851 goto trivially_true;
4853 // Otherwise swap the operands to put the constant on the right.
4854 std::swap(LHS, RHS);
4855 Pred = ICmpInst::getSwappedPredicate(Pred);
4859 // If we're comparing an addrec with a value which is loop-invariant in the
4860 // addrec's loop, put the addrec on the left. Also make a dominance check,
4861 // as both operands could be addrecs loop-invariant in each other's loop.
4862 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
4863 const Loop *L = AR->getLoop();
4864 if (LHS->isLoopInvariant(L) && LHS->properlyDominates(L->getHeader(), DT)) {
4865 std::swap(LHS, RHS);
4866 Pred = ICmpInst::getSwappedPredicate(Pred);
4871 // If there's a constant operand, canonicalize comparisons with boundary
4872 // cases, and canonicalize *-or-equal comparisons to regular comparisons.
4873 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
4874 const APInt &RA = RC->getValue()->getValue();
4876 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
4877 case ICmpInst::ICMP_EQ:
4878 case ICmpInst::ICMP_NE:
4880 case ICmpInst::ICMP_UGE:
4881 if ((RA - 1).isMinValue()) {
4882 Pred = ICmpInst::ICMP_NE;
4883 RHS = getConstant(RA - 1);
4887 if (RA.isMaxValue()) {
4888 Pred = ICmpInst::ICMP_EQ;
4892 if (RA.isMinValue()) goto trivially_true;
4894 Pred = ICmpInst::ICMP_UGT;
4895 RHS = getConstant(RA - 1);
4898 case ICmpInst::ICMP_ULE:
4899 if ((RA + 1).isMaxValue()) {
4900 Pred = ICmpInst::ICMP_NE;
4901 RHS = getConstant(RA + 1);
4905 if (RA.isMinValue()) {
4906 Pred = ICmpInst::ICMP_EQ;
4910 if (RA.isMaxValue()) goto trivially_true;
4912 Pred = ICmpInst::ICMP_ULT;
4913 RHS = getConstant(RA + 1);
4916 case ICmpInst::ICMP_SGE:
4917 if ((RA - 1).isMinSignedValue()) {
4918 Pred = ICmpInst::ICMP_NE;
4919 RHS = getConstant(RA - 1);
4923 if (RA.isMaxSignedValue()) {
4924 Pred = ICmpInst::ICMP_EQ;
4928 if (RA.isMinSignedValue()) goto trivially_true;
4930 Pred = ICmpInst::ICMP_SGT;
4931 RHS = getConstant(RA - 1);
4934 case ICmpInst::ICMP_SLE:
4935 if ((RA + 1).isMaxSignedValue()) {
4936 Pred = ICmpInst::ICMP_NE;
4937 RHS = getConstant(RA + 1);
4941 if (RA.isMinSignedValue()) {
4942 Pred = ICmpInst::ICMP_EQ;
4946 if (RA.isMaxSignedValue()) goto trivially_true;
4948 Pred = ICmpInst::ICMP_SLT;
4949 RHS = getConstant(RA + 1);
4952 case ICmpInst::ICMP_UGT:
4953 if (RA.isMinValue()) {
4954 Pred = ICmpInst::ICMP_NE;
4958 if ((RA + 1).isMaxValue()) {
4959 Pred = ICmpInst::ICMP_EQ;
4960 RHS = getConstant(RA + 1);
4964 if (RA.isMaxValue()) goto trivially_false;
4966 case ICmpInst::ICMP_ULT:
4967 if (RA.isMaxValue()) {
4968 Pred = ICmpInst::ICMP_NE;
4972 if ((RA - 1).isMinValue()) {
4973 Pred = ICmpInst::ICMP_EQ;
4974 RHS = getConstant(RA - 1);
4978 if (RA.isMinValue()) goto trivially_false;
4980 case ICmpInst::ICMP_SGT:
4981 if (RA.isMinSignedValue()) {
4982 Pred = ICmpInst::ICMP_NE;
4986 if ((RA + 1).isMaxSignedValue()) {
4987 Pred = ICmpInst::ICMP_EQ;
4988 RHS = getConstant(RA + 1);
4992 if (RA.isMaxSignedValue()) goto trivially_false;
4994 case ICmpInst::ICMP_SLT:
4995 if (RA.isMaxSignedValue()) {
4996 Pred = ICmpInst::ICMP_NE;
5000 if ((RA - 1).isMinSignedValue()) {
5001 Pred = ICmpInst::ICMP_EQ;
5002 RHS = getConstant(RA - 1);
5006 if (RA.isMinSignedValue()) goto trivially_false;
5011 // Check for obvious equality.
5012 if (HasSameValue(LHS, RHS)) {
5013 if (ICmpInst::isTrueWhenEqual(Pred))
5014 goto trivially_true;
5015 if (ICmpInst::isFalseWhenEqual(Pred))
5016 goto trivially_false;
5019 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
5020 // adding or subtracting 1 from one of the operands.
5022 case ICmpInst::ICMP_SLE:
5023 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) {
5024 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
5025 /*HasNUW=*/false, /*HasNSW=*/true);
5026 Pred = ICmpInst::ICMP_SLT;
5028 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) {
5029 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
5030 /*HasNUW=*/false, /*HasNSW=*/true);
5031 Pred = ICmpInst::ICMP_SLT;
5035 case ICmpInst::ICMP_SGE:
5036 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) {
5037 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
5038 /*HasNUW=*/false, /*HasNSW=*/true);
5039 Pred = ICmpInst::ICMP_SGT;
5041 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) {
5042 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
5043 /*HasNUW=*/false, /*HasNSW=*/true);
5044 Pred = ICmpInst::ICMP_SGT;
5048 case ICmpInst::ICMP_ULE:
5049 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) {
5050 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
5051 /*HasNUW=*/true, /*HasNSW=*/false);
5052 Pred = ICmpInst::ICMP_ULT;
5054 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) {
5055 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
5056 /*HasNUW=*/true, /*HasNSW=*/false);
5057 Pred = ICmpInst::ICMP_ULT;
5061 case ICmpInst::ICMP_UGE:
5062 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) {
5063 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
5064 /*HasNUW=*/true, /*HasNSW=*/false);
5065 Pred = ICmpInst::ICMP_UGT;
5067 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) {
5068 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
5069 /*HasNUW=*/true, /*HasNSW=*/false);
5070 Pred = ICmpInst::ICMP_UGT;
5078 // TODO: More simplifications are possible here.
5084 LHS = RHS = getConstant(Type::getInt1Ty(getContext()), 0);
5085 Pred = ICmpInst::ICMP_EQ;
5090 LHS = RHS = getConstant(Type::getInt1Ty(getContext()), 0);
5091 Pred = ICmpInst::ICMP_NE;
5095 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
5096 return getSignedRange(S).getSignedMax().isNegative();
5099 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
5100 return getSignedRange(S).getSignedMin().isStrictlyPositive();
5103 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
5104 return !getSignedRange(S).getSignedMin().isNegative();
5107 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
5108 return !getSignedRange(S).getSignedMax().isStrictlyPositive();
5111 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
5112 return isKnownNegative(S) || isKnownPositive(S);
5115 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
5116 const SCEV *LHS, const SCEV *RHS) {
5117 // Canonicalize the inputs first.
5118 (void)SimplifyICmpOperands(Pred, LHS, RHS);
5120 // If LHS or RHS is an addrec, check to see if the condition is true in
5121 // every iteration of the loop.
5122 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
5123 if (isLoopEntryGuardedByCond(
5124 AR->getLoop(), Pred, AR->getStart(), RHS) &&
5125 isLoopBackedgeGuardedByCond(
5126 AR->getLoop(), Pred, AR->getPostIncExpr(*this), RHS))
5128 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS))
5129 if (isLoopEntryGuardedByCond(
5130 AR->getLoop(), Pred, LHS, AR->getStart()) &&
5131 isLoopBackedgeGuardedByCond(
5132 AR->getLoop(), Pred, LHS, AR->getPostIncExpr(*this)))
5135 // Otherwise see what can be done with known constant ranges.
5136 return isKnownPredicateWithRanges(Pred, LHS, RHS);
5140 ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred,
5141 const SCEV *LHS, const SCEV *RHS) {
5142 if (HasSameValue(LHS, RHS))
5143 return ICmpInst::isTrueWhenEqual(Pred);
5145 // This code is split out from isKnownPredicate because it is called from
5146 // within isLoopEntryGuardedByCond.
5149 llvm_unreachable("Unexpected ICmpInst::Predicate value!");
5151 case ICmpInst::ICMP_SGT:
5152 Pred = ICmpInst::ICMP_SLT;
5153 std::swap(LHS, RHS);
5154 case ICmpInst::ICMP_SLT: {
5155 ConstantRange LHSRange = getSignedRange(LHS);
5156 ConstantRange RHSRange = getSignedRange(RHS);
5157 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
5159 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
5163 case ICmpInst::ICMP_SGE:
5164 Pred = ICmpInst::ICMP_SLE;
5165 std::swap(LHS, RHS);
5166 case ICmpInst::ICMP_SLE: {
5167 ConstantRange LHSRange = getSignedRange(LHS);
5168 ConstantRange RHSRange = getSignedRange(RHS);
5169 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
5171 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
5175 case ICmpInst::ICMP_UGT:
5176 Pred = ICmpInst::ICMP_ULT;
5177 std::swap(LHS, RHS);
5178 case ICmpInst::ICMP_ULT: {
5179 ConstantRange LHSRange = getUnsignedRange(LHS);
5180 ConstantRange RHSRange = getUnsignedRange(RHS);
5181 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
5183 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
5187 case ICmpInst::ICMP_UGE:
5188 Pred = ICmpInst::ICMP_ULE;
5189 std::swap(LHS, RHS);
5190 case ICmpInst::ICMP_ULE: {
5191 ConstantRange LHSRange = getUnsignedRange(LHS);
5192 ConstantRange RHSRange = getUnsignedRange(RHS);
5193 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
5195 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
5199 case ICmpInst::ICMP_NE: {
5200 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
5202 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
5205 const SCEV *Diff = getMinusSCEV(LHS, RHS);
5206 if (isKnownNonZero(Diff))
5210 case ICmpInst::ICMP_EQ:
5211 // The check at the top of the function catches the case where
5212 // the values are known to be equal.
5218 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
5219 /// protected by a conditional between LHS and RHS. This is used to
5220 /// to eliminate casts.
5222 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
5223 ICmpInst::Predicate Pred,
5224 const SCEV *LHS, const SCEV *RHS) {
5225 // Interpret a null as meaning no loop, where there is obviously no guard
5226 // (interprocedural conditions notwithstanding).
5227 if (!L) return true;
5229 BasicBlock *Latch = L->getLoopLatch();
5233 BranchInst *LoopContinuePredicate =
5234 dyn_cast<BranchInst>(Latch->getTerminator());
5235 if (!LoopContinuePredicate ||
5236 LoopContinuePredicate->isUnconditional())
5239 return isImpliedCond(LoopContinuePredicate->getCondition(), Pred, LHS, RHS,
5240 LoopContinuePredicate->getSuccessor(0) != L->getHeader());
5243 /// isLoopEntryGuardedByCond - Test whether entry to the loop is protected
5244 /// by a conditional between LHS and RHS. This is used to help avoid max
5245 /// expressions in loop trip counts, and to eliminate casts.
5247 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
5248 ICmpInst::Predicate Pred,
5249 const SCEV *LHS, const SCEV *RHS) {
5250 // Interpret a null as meaning no loop, where there is obviously no guard
5251 // (interprocedural conditions notwithstanding).
5252 if (!L) return false;
5254 // Starting at the loop predecessor, climb up the predecessor chain, as long
5255 // as there are predecessors that can be found that have unique successors
5256 // leading to the original header.
5257 for (std::pair<BasicBlock *, BasicBlock *>
5258 Pair(L->getLoopPredecessor(), L->getHeader());
5260 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
5262 BranchInst *LoopEntryPredicate =
5263 dyn_cast<BranchInst>(Pair.first->getTerminator());
5264 if (!LoopEntryPredicate ||
5265 LoopEntryPredicate->isUnconditional())
5268 if (isImpliedCond(LoopEntryPredicate->getCondition(), Pred, LHS, RHS,
5269 LoopEntryPredicate->getSuccessor(0) != Pair.second))
5276 /// isImpliedCond - Test whether the condition described by Pred, LHS,
5277 /// and RHS is true whenever the given Cond value evaluates to true.
5278 bool ScalarEvolution::isImpliedCond(Value *CondValue,
5279 ICmpInst::Predicate Pred,
5280 const SCEV *LHS, const SCEV *RHS,
5282 // Recursively handle And and Or conditions.
5283 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(CondValue)) {
5284 if (BO->getOpcode() == Instruction::And) {
5286 return isImpliedCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) ||
5287 isImpliedCond(BO->getOperand(1), Pred, LHS, RHS, Inverse);
5288 } else if (BO->getOpcode() == Instruction::Or) {
5290 return isImpliedCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) ||
5291 isImpliedCond(BO->getOperand(1), Pred, LHS, RHS, Inverse);
5295 ICmpInst *ICI = dyn_cast<ICmpInst>(CondValue);
5296 if (!ICI) return false;
5298 // Bail if the ICmp's operands' types are wider than the needed type
5299 // before attempting to call getSCEV on them. This avoids infinite
5300 // recursion, since the analysis of widening casts can require loop
5301 // exit condition information for overflow checking, which would
5303 if (getTypeSizeInBits(LHS->getType()) <
5304 getTypeSizeInBits(ICI->getOperand(0)->getType()))
5307 // Now that we found a conditional branch that dominates the loop, check to
5308 // see if it is the comparison we are looking for.
5309 ICmpInst::Predicate FoundPred;
5311 FoundPred = ICI->getInversePredicate();
5313 FoundPred = ICI->getPredicate();
5315 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
5316 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
5318 // Balance the types. The case where FoundLHS' type is wider than
5319 // LHS' type is checked for above.
5320 if (getTypeSizeInBits(LHS->getType()) >
5321 getTypeSizeInBits(FoundLHS->getType())) {
5322 if (CmpInst::isSigned(Pred)) {
5323 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
5324 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
5326 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
5327 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
5331 // Canonicalize the query to match the way instcombine will have
5332 // canonicalized the comparison.
5333 if (SimplifyICmpOperands(Pred, LHS, RHS))
5335 return CmpInst::isTrueWhenEqual(Pred);
5336 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
5337 if (FoundLHS == FoundRHS)
5338 return CmpInst::isFalseWhenEqual(Pred);
5340 // Check to see if we can make the LHS or RHS match.
5341 if (LHS == FoundRHS || RHS == FoundLHS) {
5342 if (isa<SCEVConstant>(RHS)) {
5343 std::swap(FoundLHS, FoundRHS);
5344 FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
5346 std::swap(LHS, RHS);
5347 Pred = ICmpInst::getSwappedPredicate(Pred);
5351 // Check whether the found predicate is the same as the desired predicate.
5352 if (FoundPred == Pred)
5353 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
5355 // Check whether swapping the found predicate makes it the same as the
5356 // desired predicate.
5357 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
5358 if (isa<SCEVConstant>(RHS))
5359 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
5361 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
5362 RHS, LHS, FoundLHS, FoundRHS);
5365 // Check whether the actual condition is beyond sufficient.
5366 if (FoundPred == ICmpInst::ICMP_EQ)
5367 if (ICmpInst::isTrueWhenEqual(Pred))
5368 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
5370 if (Pred == ICmpInst::ICMP_NE)
5371 if (!ICmpInst::isTrueWhenEqual(FoundPred))
5372 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
5375 // Otherwise assume the worst.
5379 /// isImpliedCondOperands - Test whether the condition described by Pred,
5380 /// LHS, and RHS is true whenever the condition described by Pred, FoundLHS,
5381 /// and FoundRHS is true.
5382 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
5383 const SCEV *LHS, const SCEV *RHS,
5384 const SCEV *FoundLHS,
5385 const SCEV *FoundRHS) {
5386 return isImpliedCondOperandsHelper(Pred, LHS, RHS,
5387 FoundLHS, FoundRHS) ||
5388 // ~x < ~y --> x > y
5389 isImpliedCondOperandsHelper(Pred, LHS, RHS,
5390 getNotSCEV(FoundRHS),
5391 getNotSCEV(FoundLHS));
5394 /// isImpliedCondOperandsHelper - Test whether the condition described by
5395 /// Pred, LHS, and RHS is true whenever the condition described by Pred,
5396 /// FoundLHS, and FoundRHS is true.
5398 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
5399 const SCEV *LHS, const SCEV *RHS,
5400 const SCEV *FoundLHS,
5401 const SCEV *FoundRHS) {
5403 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
5404 case ICmpInst::ICMP_EQ:
5405 case ICmpInst::ICMP_NE:
5406 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
5409 case ICmpInst::ICMP_SLT:
5410 case ICmpInst::ICMP_SLE:
5411 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
5412 isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, RHS, FoundRHS))
5415 case ICmpInst::ICMP_SGT:
5416 case ICmpInst::ICMP_SGE:
5417 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
5418 isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, RHS, FoundRHS))
5421 case ICmpInst::ICMP_ULT:
5422 case ICmpInst::ICMP_ULE:
5423 if (isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
5424 isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, RHS, FoundRHS))
5427 case ICmpInst::ICMP_UGT:
5428 case ICmpInst::ICMP_UGE:
5429 if (isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
5430 isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, RHS, FoundRHS))
5438 /// getBECount - Subtract the end and start values and divide by the step,
5439 /// rounding up, to get the number of times the backedge is executed. Return
5440 /// CouldNotCompute if an intermediate computation overflows.
5441 const SCEV *ScalarEvolution::getBECount(const SCEV *Start,
5445 assert(!isKnownNegative(Step) &&
5446 "This code doesn't handle negative strides yet!");
5448 const Type *Ty = Start->getType();
5449 const SCEV *NegOne = getConstant(Ty, (uint64_t)-1);
5450 const SCEV *Diff = getMinusSCEV(End, Start);
5451 const SCEV *RoundUp = getAddExpr(Step, NegOne);
5453 // Add an adjustment to the difference between End and Start so that
5454 // the division will effectively round up.
5455 const SCEV *Add = getAddExpr(Diff, RoundUp);
5458 // Check Add for unsigned overflow.
5459 // TODO: More sophisticated things could be done here.
5460 const Type *WideTy = IntegerType::get(getContext(),
5461 getTypeSizeInBits(Ty) + 1);
5462 const SCEV *EDiff = getZeroExtendExpr(Diff, WideTy);
5463 const SCEV *ERoundUp = getZeroExtendExpr(RoundUp, WideTy);
5464 const SCEV *OperandExtendedAdd = getAddExpr(EDiff, ERoundUp);
5465 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd)
5466 return getCouldNotCompute();
5469 return getUDivExpr(Add, Step);
5472 /// HowManyLessThans - Return the number of times a backedge containing the
5473 /// specified less-than comparison will execute. If not computable, return
5474 /// CouldNotCompute.
5475 ScalarEvolution::BackedgeTakenInfo
5476 ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
5477 const Loop *L, bool isSigned) {
5478 // Only handle: "ADDREC < LoopInvariant".
5479 if (!RHS->isLoopInvariant(L)) return getCouldNotCompute();
5481 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
5482 if (!AddRec || AddRec->getLoop() != L)
5483 return getCouldNotCompute();
5485 // Check to see if we have a flag which makes analysis easy.
5486 bool NoWrap = isSigned ? AddRec->hasNoSignedWrap() :
5487 AddRec->hasNoUnsignedWrap();
5489 if (AddRec->isAffine()) {
5490 unsigned BitWidth = getTypeSizeInBits(AddRec->getType());
5491 const SCEV *Step = AddRec->getStepRecurrence(*this);
5494 return getCouldNotCompute();
5495 if (Step->isOne()) {
5496 // With unit stride, the iteration never steps past the limit value.
5497 } else if (isKnownPositive(Step)) {
5498 // Test whether a positive iteration can step past the limit
5499 // value and past the maximum value for its type in a single step.
5500 // Note that it's not sufficient to check NoWrap here, because even
5501 // though the value after a wrap is undefined, it's not undefined
5502 // behavior, so if wrap does occur, the loop could either terminate or
5503 // loop infinitely, but in either case, the loop is guaranteed to
5504 // iterate at least until the iteration where the wrapping occurs.
5505 const SCEV *One = getConstant(Step->getType(), 1);
5507 APInt Max = APInt::getSignedMaxValue(BitWidth);
5508 if ((Max - getSignedRange(getMinusSCEV(Step, One)).getSignedMax())
5509 .slt(getSignedRange(RHS).getSignedMax()))
5510 return getCouldNotCompute();
5512 APInt Max = APInt::getMaxValue(BitWidth);
5513 if ((Max - getUnsignedRange(getMinusSCEV(Step, One)).getUnsignedMax())
5514 .ult(getUnsignedRange(RHS).getUnsignedMax()))
5515 return getCouldNotCompute();
5518 // TODO: Handle negative strides here and below.
5519 return getCouldNotCompute();
5521 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant
5522 // m. So, we count the number of iterations in which {n,+,s} < m is true.
5523 // Note that we cannot simply return max(m-n,0)/s because it's not safe to
5524 // treat m-n as signed nor unsigned due to overflow possibility.
5526 // First, we get the value of the LHS in the first iteration: n
5527 const SCEV *Start = AddRec->getOperand(0);
5529 // Determine the minimum constant start value.
5530 const SCEV *MinStart = getConstant(isSigned ?
5531 getSignedRange(Start).getSignedMin() :
5532 getUnsignedRange(Start).getUnsignedMin());
5534 // If we know that the condition is true in order to enter the loop,
5535 // then we know that it will run exactly (m-n)/s times. Otherwise, we
5536 // only know that it will execute (max(m,n)-n)/s times. In both cases,
5537 // the division must round up.
5538 const SCEV *End = RHS;
5539 if (!isLoopEntryGuardedByCond(L,
5540 isSigned ? ICmpInst::ICMP_SLT :
5542 getMinusSCEV(Start, Step), RHS))
5543 End = isSigned ? getSMaxExpr(RHS, Start)
5544 : getUMaxExpr(RHS, Start);
5546 // Determine the maximum constant end value.
5547 const SCEV *MaxEnd = getConstant(isSigned ?
5548 getSignedRange(End).getSignedMax() :
5549 getUnsignedRange(End).getUnsignedMax());
5551 // If MaxEnd is within a step of the maximum integer value in its type,
5552 // adjust it down to the minimum value which would produce the same effect.
5553 // This allows the subsequent ceiling division of (N+(step-1))/step to
5554 // compute the correct value.
5555 const SCEV *StepMinusOne = getMinusSCEV(Step,
5556 getConstant(Step->getType(), 1));
5559 getMinusSCEV(getConstant(APInt::getSignedMaxValue(BitWidth)),
5562 getMinusSCEV(getConstant(APInt::getMaxValue(BitWidth)),
5565 // Finally, we subtract these two values and divide, rounding up, to get
5566 // the number of times the backedge is executed.
5567 const SCEV *BECount = getBECount(Start, End, Step, NoWrap);
5569 // The maximum backedge count is similar, except using the minimum start
5570 // value and the maximum end value.
5571 const SCEV *MaxBECount = getBECount(MinStart, MaxEnd, Step, NoWrap);
5573 return BackedgeTakenInfo(BECount, MaxBECount);
5576 return getCouldNotCompute();
5579 /// getNumIterationsInRange - Return the number of iterations of this loop that
5580 /// produce values in the specified constant range. Another way of looking at
5581 /// this is that it returns the first iteration number where the value is not in
5582 /// the condition, thus computing the exit count. If the iteration count can't
5583 /// be computed, an instance of SCEVCouldNotCompute is returned.
5584 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
5585 ScalarEvolution &SE) const {
5586 if (Range.isFullSet()) // Infinite loop.
5587 return SE.getCouldNotCompute();
5589 // If the start is a non-zero constant, shift the range to simplify things.
5590 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
5591 if (!SC->getValue()->isZero()) {
5592 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
5593 Operands[0] = SE.getConstant(SC->getType(), 0);
5594 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop());
5595 if (const SCEVAddRecExpr *ShiftedAddRec =
5596 dyn_cast<SCEVAddRecExpr>(Shifted))
5597 return ShiftedAddRec->getNumIterationsInRange(
5598 Range.subtract(SC->getValue()->getValue()), SE);
5599 // This is strange and shouldn't happen.
5600 return SE.getCouldNotCompute();
5603 // The only time we can solve this is when we have all constant indices.
5604 // Otherwise, we cannot determine the overflow conditions.
5605 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
5606 if (!isa<SCEVConstant>(getOperand(i)))
5607 return SE.getCouldNotCompute();
5610 // Okay at this point we know that all elements of the chrec are constants and
5611 // that the start element is zero.
5613 // First check to see if the range contains zero. If not, the first
5615 unsigned BitWidth = SE.getTypeSizeInBits(getType());
5616 if (!Range.contains(APInt(BitWidth, 0)))
5617 return SE.getConstant(getType(), 0);
5620 // If this is an affine expression then we have this situation:
5621 // Solve {0,+,A} in Range === Ax in Range
5623 // We know that zero is in the range. If A is positive then we know that
5624 // the upper value of the range must be the first possible exit value.
5625 // If A is negative then the lower of the range is the last possible loop
5626 // value. Also note that we already checked for a full range.
5627 APInt One(BitWidth,1);
5628 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
5629 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
5631 // The exit value should be (End+A)/A.
5632 APInt ExitVal = (End + A).udiv(A);
5633 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
5635 // Evaluate at the exit value. If we really did fall out of the valid
5636 // range, then we computed our trip count, otherwise wrap around or other
5637 // things must have happened.
5638 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
5639 if (Range.contains(Val->getValue()))
5640 return SE.getCouldNotCompute(); // Something strange happened
5642 // Ensure that the previous value is in the range. This is a sanity check.
5643 assert(Range.contains(
5644 EvaluateConstantChrecAtConstant(this,
5645 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
5646 "Linear scev computation is off in a bad way!");
5647 return SE.getConstant(ExitValue);
5648 } else if (isQuadratic()) {
5649 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
5650 // quadratic equation to solve it. To do this, we must frame our problem in
5651 // terms of figuring out when zero is crossed, instead of when
5652 // Range.getUpper() is crossed.
5653 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
5654 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
5655 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop());
5657 // Next, solve the constructed addrec
5658 std::pair<const SCEV *,const SCEV *> Roots =
5659 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
5660 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
5661 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
5663 // Pick the smallest positive root value.
5664 if (ConstantInt *CB =
5665 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
5666 R1->getValue(), R2->getValue()))) {
5667 if (CB->getZExtValue() == false)
5668 std::swap(R1, R2); // R1 is the minimum root now.
5670 // Make sure the root is not off by one. The returned iteration should
5671 // not be in the range, but the previous one should be. When solving
5672 // for "X*X < 5", for example, we should not return a root of 2.
5673 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
5676 if (Range.contains(R1Val->getValue())) {
5677 // The next iteration must be out of the range...
5678 ConstantInt *NextVal =
5679 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1);
5681 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
5682 if (!Range.contains(R1Val->getValue()))
5683 return SE.getConstant(NextVal);
5684 return SE.getCouldNotCompute(); // Something strange happened
5687 // If R1 was not in the range, then it is a good return value. Make
5688 // sure that R1-1 WAS in the range though, just in case.
5689 ConstantInt *NextVal =
5690 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1);
5691 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
5692 if (Range.contains(R1Val->getValue()))
5694 return SE.getCouldNotCompute(); // Something strange happened
5699 return SE.getCouldNotCompute();
5704 //===----------------------------------------------------------------------===//
5705 // SCEVCallbackVH Class Implementation
5706 //===----------------------------------------------------------------------===//
5708 void ScalarEvolution::SCEVCallbackVH::deleted() {
5709 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
5710 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
5711 SE->ConstantEvolutionLoopExitValue.erase(PN);
5712 SE->Scalars.erase(getValPtr());
5713 // this now dangles!
5716 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *) {
5717 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
5719 // Forget all the expressions associated with users of the old value,
5720 // so that future queries will recompute the expressions using the new
5722 SmallVector<User *, 16> Worklist;
5723 SmallPtrSet<User *, 8> Visited;
5724 Value *Old = getValPtr();
5725 bool DeleteOld = false;
5726 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end();
5728 Worklist.push_back(*UI);
5729 while (!Worklist.empty()) {
5730 User *U = Worklist.pop_back_val();
5731 // Deleting the Old value will cause this to dangle. Postpone
5732 // that until everything else is done.
5737 if (!Visited.insert(U))
5739 if (PHINode *PN = dyn_cast<PHINode>(U))
5740 SE->ConstantEvolutionLoopExitValue.erase(PN);
5741 SE->Scalars.erase(U);
5742 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end();
5744 Worklist.push_back(*UI);
5746 // Delete the Old value if it (indirectly) references itself.
5748 if (PHINode *PN = dyn_cast<PHINode>(Old))
5749 SE->ConstantEvolutionLoopExitValue.erase(PN);
5750 SE->Scalars.erase(Old);
5751 // this now dangles!
5756 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
5757 : CallbackVH(V), SE(se) {}
5759 //===----------------------------------------------------------------------===//
5760 // ScalarEvolution Class Implementation
5761 //===----------------------------------------------------------------------===//
5763 ScalarEvolution::ScalarEvolution()
5764 : FunctionPass(&ID) {
5767 bool ScalarEvolution::runOnFunction(Function &F) {
5769 LI = &getAnalysis<LoopInfo>();
5770 TD = getAnalysisIfAvailable<TargetData>();
5771 DT = &getAnalysis<DominatorTree>();
5775 void ScalarEvolution::releaseMemory() {
5777 BackedgeTakenCounts.clear();
5778 ConstantEvolutionLoopExitValue.clear();
5779 ValuesAtScopes.clear();
5780 UniqueSCEVs.clear();
5781 SCEVAllocator.Reset();
5784 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
5785 AU.setPreservesAll();
5786 AU.addRequiredTransitive<LoopInfo>();
5787 AU.addRequiredTransitive<DominatorTree>();
5790 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
5791 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
5794 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
5796 // Print all inner loops first
5797 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
5798 PrintLoopInfo(OS, SE, *I);
5801 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
5804 SmallVector<BasicBlock *, 8> ExitBlocks;
5805 L->getExitBlocks(ExitBlocks);
5806 if (ExitBlocks.size() != 1)
5807 OS << "<multiple exits> ";
5809 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
5810 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
5812 OS << "Unpredictable backedge-taken count. ";
5817 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
5820 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
5821 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
5823 OS << "Unpredictable max backedge-taken count. ";
5829 void ScalarEvolution::print(raw_ostream &OS, const Module *) const {
5830 // ScalarEvolution's implementation of the print method is to print
5831 // out SCEV values of all instructions that are interesting. Doing
5832 // this potentially causes it to create new SCEV objects though,
5833 // which technically conflicts with the const qualifier. This isn't
5834 // observable from outside the class though, so casting away the
5835 // const isn't dangerous.
5836 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
5838 OS << "Classifying expressions for: ";
5839 WriteAsOperand(OS, F, /*PrintType=*/false);
5841 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
5842 if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) {
5845 const SCEV *SV = SE.getSCEV(&*I);
5848 const Loop *L = LI->getLoopFor((*I).getParent());
5850 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
5857 OS << "\t\t" "Exits: ";
5858 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
5859 if (!ExitValue->isLoopInvariant(L)) {
5860 OS << "<<Unknown>>";
5869 OS << "Determining loop execution counts for: ";
5870 WriteAsOperand(OS, F, /*PrintType=*/false);
5872 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
5873 PrintLoopInfo(OS, &SE, *I);