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 INITIALIZE_PASS(ScalarEvolution, "scalar-evolution",
107 "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(const 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 unsigned LType = LHS->getSCEVType(), RType = RHS->getSCEVType();
510 return LType < RType;
512 // Aside from the getSCEVType() ordering, the particular ordering
513 // isn't very important except that it's beneficial to be consistent,
514 // so that (a + b) and (b + a) don't end up as different expressions.
516 // Sort SCEVUnknown values with some loose heuristics. TODO: This is
517 // not as complete as it could be.
518 if (const SCEVUnknown *LU = dyn_cast<SCEVUnknown>(LHS)) {
519 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
521 // Order pointer values after integer values. This helps SCEVExpander
523 bool LIsPointer = LU->getType()->isPointerTy(),
524 RIsPointer = RU->getType()->isPointerTy();
525 if (LIsPointer != RIsPointer)
528 // Compare getValueID values.
529 unsigned LID = LU->getValue()->getValueID(),
530 RID = RU->getValue()->getValueID();
534 // Sort arguments by their position.
535 if (const Argument *LA = dyn_cast<Argument>(LU->getValue())) {
536 const Argument *RA = cast<Argument>(RU->getValue());
537 return LA->getArgNo() < RA->getArgNo();
540 // For instructions, compare their loop depth, and their opcode.
541 // This is pretty loose.
542 if (const Instruction *LV = dyn_cast<Instruction>(LU->getValue())) {
543 const Instruction *RV = cast<Instruction>(RU->getValue());
545 // Compare loop depths.
546 unsigned LDepth = LI->getLoopDepth(LV->getParent()),
547 RDepth = LI->getLoopDepth(RV->getParent());
548 if (LDepth != RDepth)
549 return LDepth < RDepth;
551 // Compare the number of operands.
552 unsigned LNumOps = LV->getNumOperands(),
553 RNumOps = RV->getNumOperands();
554 if (LNumOps != RNumOps)
555 return LNumOps < RNumOps;
561 // Compare constant values.
562 if (const SCEVConstant *LC = dyn_cast<SCEVConstant>(LHS)) {
563 const SCEVConstant *RC = cast<SCEVConstant>(RHS);
564 const ConstantInt *LCC = LC->getValue();
565 const ConstantInt *RCC = RC->getValue();
566 unsigned LBitWidth = LCC->getBitWidth(), RBitWidth = RCC->getBitWidth();
567 if (LBitWidth != RBitWidth)
568 return LBitWidth < RBitWidth;
569 return LCC->getValue().ult(RCC->getValue());
572 // Compare addrec loop depths.
573 if (const SCEVAddRecExpr *LA = dyn_cast<SCEVAddRecExpr>(LHS)) {
574 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS);
575 unsigned LDepth = LA->getLoop()->getLoopDepth(),
576 RDepth = RA->getLoop()->getLoopDepth();
577 if (LDepth != RDepth)
578 return LDepth < RDepth;
581 // Lexicographically compare n-ary expressions.
582 if (const SCEVNAryExpr *LC = dyn_cast<SCEVNAryExpr>(LHS)) {
583 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
584 unsigned LNumOps = LC->getNumOperands(), RNumOps = RC->getNumOperands();
585 for (unsigned i = 0; i != LNumOps; ++i) {
588 const SCEV *LOp = LC->getOperand(i), *ROp = RC->getOperand(i);
589 if (operator()(LOp, ROp))
591 if (operator()(ROp, LOp))
594 return LNumOps < RNumOps;
597 // Lexicographically compare udiv expressions.
598 if (const SCEVUDivExpr *LC = dyn_cast<SCEVUDivExpr>(LHS)) {
599 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
600 const SCEV *LL = LC->getLHS(), *LR = LC->getRHS(),
601 *RL = RC->getLHS(), *RR = RC->getRHS();
602 if (operator()(LL, RL))
604 if (operator()(RL, LL))
606 if (operator()(LR, RR))
608 if (operator()(RR, LR))
613 // Compare cast expressions by operand.
614 if (const SCEVCastExpr *LC = dyn_cast<SCEVCastExpr>(LHS)) {
615 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
616 return operator()(LC->getOperand(), RC->getOperand());
619 llvm_unreachable("Unknown SCEV kind!");
625 /// GroupByComplexity - Given a list of SCEV objects, order them by their
626 /// complexity, and group objects of the same complexity together by value.
627 /// When this routine is finished, we know that any duplicates in the vector are
628 /// consecutive and that complexity is monotonically increasing.
630 /// Note that we go take special precautions to ensure that we get deterministic
631 /// results from this routine. In other words, we don't want the results of
632 /// this to depend on where the addresses of various SCEV objects happened to
635 static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops,
637 if (Ops.size() < 2) return; // Noop
638 if (Ops.size() == 2) {
639 // This is the common case, which also happens to be trivially simple.
641 if (SCEVComplexityCompare(LI)(Ops[1], Ops[0]))
642 std::swap(Ops[0], Ops[1]);
646 // Do the rough sort by complexity.
647 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI));
649 // Now that we are sorted by complexity, group elements of the same
650 // complexity. Note that this is, at worst, N^2, but the vector is likely to
651 // be extremely short in practice. Note that we take this approach because we
652 // do not want to depend on the addresses of the objects we are grouping.
653 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
654 const SCEV *S = Ops[i];
655 unsigned Complexity = S->getSCEVType();
657 // If there are any objects of the same complexity and same value as this
659 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
660 if (Ops[j] == S) { // Found a duplicate.
661 // Move it to immediately after i'th element.
662 std::swap(Ops[i+1], Ops[j]);
663 ++i; // no need to rescan it.
664 if (i == e-2) return; // Done!
672 //===----------------------------------------------------------------------===//
673 // Simple SCEV method implementations
674 //===----------------------------------------------------------------------===//
676 /// BinomialCoefficient - Compute BC(It, K). The result has width W.
678 static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K,
680 const Type* ResultTy) {
681 // Handle the simplest case efficiently.
683 return SE.getTruncateOrZeroExtend(It, ResultTy);
685 // We are using the following formula for BC(It, K):
687 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
689 // Suppose, W is the bitwidth of the return value. We must be prepared for
690 // overflow. Hence, we must assure that the result of our computation is
691 // equal to the accurate one modulo 2^W. Unfortunately, division isn't
692 // safe in modular arithmetic.
694 // However, this code doesn't use exactly that formula; the formula it uses
695 // is something like the following, where T is the number of factors of 2 in
696 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
699 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
701 // This formula is trivially equivalent to the previous formula. However,
702 // this formula can be implemented much more efficiently. The trick is that
703 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
704 // arithmetic. To do exact division in modular arithmetic, all we have
705 // to do is multiply by the inverse. Therefore, this step can be done at
708 // The next issue is how to safely do the division by 2^T. The way this
709 // is done is by doing the multiplication step at a width of at least W + T
710 // bits. This way, the bottom W+T bits of the product are accurate. Then,
711 // when we perform the division by 2^T (which is equivalent to a right shift
712 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
713 // truncated out after the division by 2^T.
715 // In comparison to just directly using the first formula, this technique
716 // is much more efficient; using the first formula requires W * K bits,
717 // but this formula less than W + K bits. Also, the first formula requires
718 // a division step, whereas this formula only requires multiplies and shifts.
720 // It doesn't matter whether the subtraction step is done in the calculation
721 // width or the input iteration count's width; if the subtraction overflows,
722 // the result must be zero anyway. We prefer here to do it in the width of
723 // the induction variable because it helps a lot for certain cases; CodeGen
724 // isn't smart enough to ignore the overflow, which leads to much less
725 // efficient code if the width of the subtraction is wider than the native
728 // (It's possible to not widen at all by pulling out factors of 2 before
729 // the multiplication; for example, K=2 can be calculated as
730 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
731 // extra arithmetic, so it's not an obvious win, and it gets
732 // much more complicated for K > 3.)
734 // Protection from insane SCEVs; this bound is conservative,
735 // but it probably doesn't matter.
737 return SE.getCouldNotCompute();
739 unsigned W = SE.getTypeSizeInBits(ResultTy);
741 // Calculate K! / 2^T and T; we divide out the factors of two before
742 // multiplying for calculating K! / 2^T to avoid overflow.
743 // Other overflow doesn't matter because we only care about the bottom
744 // W bits of the result.
745 APInt OddFactorial(W, 1);
747 for (unsigned i = 3; i <= K; ++i) {
749 unsigned TwoFactors = Mult.countTrailingZeros();
751 Mult = Mult.lshr(TwoFactors);
752 OddFactorial *= Mult;
755 // We need at least W + T bits for the multiplication step
756 unsigned CalculationBits = W + T;
758 // Calculate 2^T, at width T+W.
759 APInt DivFactor = APInt(CalculationBits, 1).shl(T);
761 // Calculate the multiplicative inverse of K! / 2^T;
762 // this multiplication factor will perform the exact division by
764 APInt Mod = APInt::getSignedMinValue(W+1);
765 APInt MultiplyFactor = OddFactorial.zext(W+1);
766 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
767 MultiplyFactor = MultiplyFactor.trunc(W);
769 // Calculate the product, at width T+W
770 const IntegerType *CalculationTy = IntegerType::get(SE.getContext(),
772 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
773 for (unsigned i = 1; i != K; ++i) {
774 const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i));
775 Dividend = SE.getMulExpr(Dividend,
776 SE.getTruncateOrZeroExtend(S, CalculationTy));
780 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
782 // Truncate the result, and divide by K! / 2^T.
784 return SE.getMulExpr(SE.getConstant(MultiplyFactor),
785 SE.getTruncateOrZeroExtend(DivResult, ResultTy));
788 /// evaluateAtIteration - Return the value of this chain of recurrences at
789 /// the specified iteration number. We can evaluate this recurrence by
790 /// multiplying each element in the chain by the binomial coefficient
791 /// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
793 /// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
795 /// where BC(It, k) stands for binomial coefficient.
797 const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It,
798 ScalarEvolution &SE) const {
799 const SCEV *Result = getStart();
800 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
801 // The computation is correct in the face of overflow provided that the
802 // multiplication is performed _after_ the evaluation of the binomial
804 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType());
805 if (isa<SCEVCouldNotCompute>(Coeff))
808 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
813 //===----------------------------------------------------------------------===//
814 // SCEV Expression folder implementations
815 //===----------------------------------------------------------------------===//
817 const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op,
819 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
820 "This is not a truncating conversion!");
821 assert(isSCEVable(Ty) &&
822 "This is not a conversion to a SCEVable type!");
823 Ty = getEffectiveSCEVType(Ty);
826 ID.AddInteger(scTruncate);
830 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
832 // Fold if the operand is constant.
833 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
835 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(),
836 getEffectiveSCEVType(Ty))));
838 // trunc(trunc(x)) --> trunc(x)
839 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
840 return getTruncateExpr(ST->getOperand(), Ty);
842 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
843 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
844 return getTruncateOrSignExtend(SS->getOperand(), Ty);
846 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
847 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
848 return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
850 // If the input value is a chrec scev, truncate the chrec's operands.
851 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
852 SmallVector<const SCEV *, 4> Operands;
853 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
854 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty));
855 return getAddRecExpr(Operands, AddRec->getLoop());
858 // As a special case, fold trunc(undef) to undef. We don't want to
859 // know too much about SCEVUnknowns, but this special case is handy
861 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(Op))
862 if (isa<UndefValue>(U->getValue()))
863 return getSCEV(UndefValue::get(Ty));
865 // The cast wasn't folded; create an explicit cast node. We can reuse
866 // the existing insert position since if we get here, we won't have
867 // made any changes which would invalidate it.
868 SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator),
870 UniqueSCEVs.InsertNode(S, IP);
874 const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op,
876 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
877 "This is not an extending conversion!");
878 assert(isSCEVable(Ty) &&
879 "This is not a conversion to a SCEVable type!");
880 Ty = getEffectiveSCEVType(Ty);
882 // Fold if the operand is constant.
883 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
885 cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(),
886 getEffectiveSCEVType(Ty))));
888 // zext(zext(x)) --> zext(x)
889 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
890 return getZeroExtendExpr(SZ->getOperand(), Ty);
892 // Before doing any expensive analysis, check to see if we've already
893 // computed a SCEV for this Op and Ty.
895 ID.AddInteger(scZeroExtend);
899 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
901 // If the input value is a chrec scev, and we can prove that the value
902 // did not overflow the old, smaller, value, we can zero extend all of the
903 // operands (often constants). This allows analysis of something like
904 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
905 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
906 if (AR->isAffine()) {
907 const SCEV *Start = AR->getStart();
908 const SCEV *Step = AR->getStepRecurrence(*this);
909 unsigned BitWidth = getTypeSizeInBits(AR->getType());
910 const Loop *L = AR->getLoop();
912 // If we have special knowledge that this addrec won't overflow,
913 // we don't need to do any further analysis.
914 if (AR->hasNoUnsignedWrap())
915 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
916 getZeroExtendExpr(Step, Ty),
919 // Check whether the backedge-taken count is SCEVCouldNotCompute.
920 // Note that this serves two purposes: It filters out loops that are
921 // simply not analyzable, and it covers the case where this code is
922 // being called from within backedge-taken count analysis, such that
923 // attempting to ask for the backedge-taken count would likely result
924 // in infinite recursion. In the later case, the analysis code will
925 // cope with a conservative value, and it will take care to purge
926 // that value once it has finished.
927 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
928 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
929 // Manually compute the final value for AR, checking for
932 // Check whether the backedge-taken count can be losslessly casted to
933 // the addrec's type. The count is always unsigned.
934 const SCEV *CastedMaxBECount =
935 getTruncateOrZeroExtend(MaxBECount, Start->getType());
936 const SCEV *RecastedMaxBECount =
937 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
938 if (MaxBECount == RecastedMaxBECount) {
939 const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
940 // Check whether Start+Step*MaxBECount has no unsigned overflow.
941 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step);
942 const SCEV *Add = getAddExpr(Start, ZMul);
943 const SCEV *OperandExtendedAdd =
944 getAddExpr(getZeroExtendExpr(Start, WideTy),
945 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
946 getZeroExtendExpr(Step, WideTy)));
947 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd)
948 // Return the expression with the addrec on the outside.
949 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
950 getZeroExtendExpr(Step, Ty),
953 // Similar to above, only this time treat the step value as signed.
954 // This covers loops that count down.
955 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
956 Add = getAddExpr(Start, SMul);
958 getAddExpr(getZeroExtendExpr(Start, WideTy),
959 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
960 getSignExtendExpr(Step, WideTy)));
961 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd)
962 // Return the expression with the addrec on the outside.
963 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
964 getSignExtendExpr(Step, Ty),
968 // If the backedge is guarded by a comparison with the pre-inc value
969 // the addrec is safe. Also, if the entry is guarded by a comparison
970 // with the start value and the backedge is guarded by a comparison
971 // with the post-inc value, the addrec is safe.
972 if (isKnownPositive(Step)) {
973 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
974 getUnsignedRange(Step).getUnsignedMax());
975 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
976 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) &&
977 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT,
978 AR->getPostIncExpr(*this), N)))
979 // Return the expression with the addrec on the outside.
980 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
981 getZeroExtendExpr(Step, Ty),
983 } else if (isKnownNegative(Step)) {
984 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
985 getSignedRange(Step).getSignedMin());
986 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) ||
987 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) &&
988 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT,
989 AR->getPostIncExpr(*this), N)))
990 // Return the expression with the addrec on the outside.
991 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
992 getSignExtendExpr(Step, Ty),
998 // The cast wasn't folded; create an explicit cast node.
999 // Recompute the insert position, as it may have been invalidated.
1000 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1001 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
1003 UniqueSCEVs.InsertNode(S, IP);
1007 const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op,
1009 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1010 "This is not an extending conversion!");
1011 assert(isSCEVable(Ty) &&
1012 "This is not a conversion to a SCEVable type!");
1013 Ty = getEffectiveSCEVType(Ty);
1015 // Fold if the operand is constant.
1016 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1018 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(),
1019 getEffectiveSCEVType(Ty))));
1021 // sext(sext(x)) --> sext(x)
1022 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1023 return getSignExtendExpr(SS->getOperand(), Ty);
1025 // Before doing any expensive analysis, check to see if we've already
1026 // computed a SCEV for this Op and Ty.
1027 FoldingSetNodeID ID;
1028 ID.AddInteger(scSignExtend);
1032 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1034 // If the input value is a chrec scev, and we can prove that the value
1035 // did not overflow the old, smaller, value, we can sign extend all of the
1036 // operands (often constants). This allows analysis of something like
1037 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
1038 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1039 if (AR->isAffine()) {
1040 const SCEV *Start = AR->getStart();
1041 const SCEV *Step = AR->getStepRecurrence(*this);
1042 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1043 const Loop *L = AR->getLoop();
1045 // If we have special knowledge that this addrec won't overflow,
1046 // we don't need to do any further analysis.
1047 if (AR->hasNoSignedWrap())
1048 return getAddRecExpr(getSignExtendExpr(Start, Ty),
1049 getSignExtendExpr(Step, Ty),
1052 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1053 // Note that this serves two purposes: It filters out loops that are
1054 // simply not analyzable, and it covers the case where this code is
1055 // being called from within backedge-taken count analysis, such that
1056 // attempting to ask for the backedge-taken count would likely result
1057 // in infinite recursion. In the later case, the analysis code will
1058 // cope with a conservative value, and it will take care to purge
1059 // that value once it has finished.
1060 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1061 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1062 // Manually compute the final value for AR, checking for
1065 // Check whether the backedge-taken count can be losslessly casted to
1066 // the addrec's type. The count is always unsigned.
1067 const SCEV *CastedMaxBECount =
1068 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1069 const SCEV *RecastedMaxBECount =
1070 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1071 if (MaxBECount == RecastedMaxBECount) {
1072 const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1073 // Check whether Start+Step*MaxBECount has no signed overflow.
1074 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
1075 const SCEV *Add = getAddExpr(Start, SMul);
1076 const SCEV *OperandExtendedAdd =
1077 getAddExpr(getSignExtendExpr(Start, WideTy),
1078 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
1079 getSignExtendExpr(Step, WideTy)));
1080 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd)
1081 // Return the expression with the addrec on the outside.
1082 return getAddRecExpr(getSignExtendExpr(Start, Ty),
1083 getSignExtendExpr(Step, Ty),
1086 // Similar to above, only this time treat the step value as unsigned.
1087 // This covers loops that count up with an unsigned step.
1088 const SCEV *UMul = getMulExpr(CastedMaxBECount, Step);
1089 Add = getAddExpr(Start, UMul);
1090 OperandExtendedAdd =
1091 getAddExpr(getSignExtendExpr(Start, WideTy),
1092 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
1093 getZeroExtendExpr(Step, WideTy)));
1094 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd)
1095 // Return the expression with the addrec on the outside.
1096 return getAddRecExpr(getSignExtendExpr(Start, Ty),
1097 getZeroExtendExpr(Step, Ty),
1101 // If the backedge is guarded by a comparison with the pre-inc value
1102 // the addrec is safe. Also, if the entry is guarded by a comparison
1103 // with the start value and the backedge is guarded by a comparison
1104 // with the post-inc value, the addrec is safe.
1105 if (isKnownPositive(Step)) {
1106 const SCEV *N = getConstant(APInt::getSignedMinValue(BitWidth) -
1107 getSignedRange(Step).getSignedMax());
1108 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT, AR, N) ||
1109 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_SLT, Start, N) &&
1110 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT,
1111 AR->getPostIncExpr(*this), N)))
1112 // Return the expression with the addrec on the outside.
1113 return getAddRecExpr(getSignExtendExpr(Start, Ty),
1114 getSignExtendExpr(Step, Ty),
1116 } else if (isKnownNegative(Step)) {
1117 const SCEV *N = getConstant(APInt::getSignedMaxValue(BitWidth) -
1118 getSignedRange(Step).getSignedMin());
1119 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT, AR, N) ||
1120 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_SGT, Start, N) &&
1121 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT,
1122 AR->getPostIncExpr(*this), N)))
1123 // Return the expression with the addrec on the outside.
1124 return getAddRecExpr(getSignExtendExpr(Start, Ty),
1125 getSignExtendExpr(Step, Ty),
1131 // The cast wasn't folded; create an explicit cast node.
1132 // Recompute the insert position, as it may have been invalidated.
1133 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1134 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
1136 UniqueSCEVs.InsertNode(S, IP);
1140 /// getAnyExtendExpr - Return a SCEV for the given operand extended with
1141 /// unspecified bits out to the given type.
1143 const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
1145 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1146 "This is not an extending conversion!");
1147 assert(isSCEVable(Ty) &&
1148 "This is not a conversion to a SCEVable type!");
1149 Ty = getEffectiveSCEVType(Ty);
1151 // Sign-extend negative constants.
1152 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1153 if (SC->getValue()->getValue().isNegative())
1154 return getSignExtendExpr(Op, Ty);
1156 // Peel off a truncate cast.
1157 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
1158 const SCEV *NewOp = T->getOperand();
1159 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
1160 return getAnyExtendExpr(NewOp, Ty);
1161 return getTruncateOrNoop(NewOp, Ty);
1164 // Next try a zext cast. If the cast is folded, use it.
1165 const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
1166 if (!isa<SCEVZeroExtendExpr>(ZExt))
1169 // Next try a sext cast. If the cast is folded, use it.
1170 const SCEV *SExt = getSignExtendExpr(Op, Ty);
1171 if (!isa<SCEVSignExtendExpr>(SExt))
1174 // Force the cast to be folded into the operands of an addrec.
1175 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
1176 SmallVector<const SCEV *, 4> Ops;
1177 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
1179 Ops.push_back(getAnyExtendExpr(*I, Ty));
1180 return getAddRecExpr(Ops, AR->getLoop());
1183 // As a special case, fold anyext(undef) to undef. We don't want to
1184 // know too much about SCEVUnknowns, but this special case is handy
1186 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(Op))
1187 if (isa<UndefValue>(U->getValue()))
1188 return getSCEV(UndefValue::get(Ty));
1190 // If the expression is obviously signed, use the sext cast value.
1191 if (isa<SCEVSMaxExpr>(Op))
1194 // Absent any other information, use the zext cast value.
1198 /// CollectAddOperandsWithScales - Process the given Ops list, which is
1199 /// a list of operands to be added under the given scale, update the given
1200 /// map. This is a helper function for getAddRecExpr. As an example of
1201 /// what it does, given a sequence of operands that would form an add
1202 /// expression like this:
1204 /// m + n + 13 + (A * (o + p + (B * q + m + 29))) + r + (-1 * r)
1206 /// where A and B are constants, update the map with these values:
1208 /// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
1210 /// and add 13 + A*B*29 to AccumulatedConstant.
1211 /// This will allow getAddRecExpr to produce this:
1213 /// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
1215 /// This form often exposes folding opportunities that are hidden in
1216 /// the original operand list.
1218 /// Return true iff it appears that any interesting folding opportunities
1219 /// may be exposed. This helps getAddRecExpr short-circuit extra work in
1220 /// the common case where no interesting opportunities are present, and
1221 /// is also used as a check to avoid infinite recursion.
1224 CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
1225 SmallVector<const SCEV *, 8> &NewOps,
1226 APInt &AccumulatedConstant,
1227 const SCEV *const *Ops, size_t NumOperands,
1229 ScalarEvolution &SE) {
1230 bool Interesting = false;
1232 // Iterate over the add operands. They are sorted, with constants first.
1234 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1236 // Pull a buried constant out to the outside.
1237 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
1239 AccumulatedConstant += Scale * C->getValue()->getValue();
1242 // Next comes everything else. We're especially interested in multiplies
1243 // here, but they're in the middle, so just visit the rest with one loop.
1244 for (; i != NumOperands; ++i) {
1245 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
1246 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
1248 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue();
1249 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
1250 // A multiplication of a constant with another add; recurse.
1251 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1));
1253 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1254 Add->op_begin(), Add->getNumOperands(),
1257 // A multiplication of a constant with some other value. Update
1259 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
1260 const SCEV *Key = SE.getMulExpr(MulOps);
1261 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1262 M.insert(std::make_pair(Key, NewScale));
1264 NewOps.push_back(Pair.first->first);
1266 Pair.first->second += NewScale;
1267 // The map already had an entry for this value, which may indicate
1268 // a folding opportunity.
1273 // An ordinary operand. Update the map.
1274 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1275 M.insert(std::make_pair(Ops[i], Scale));
1277 NewOps.push_back(Pair.first->first);
1279 Pair.first->second += Scale;
1280 // The map already had an entry for this value, which may indicate
1281 // a folding opportunity.
1291 struct APIntCompare {
1292 bool operator()(const APInt &LHS, const APInt &RHS) const {
1293 return LHS.ult(RHS);
1298 /// getAddExpr - Get a canonical add expression, or something simpler if
1300 const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
1301 bool HasNUW, bool HasNSW) {
1302 assert(!Ops.empty() && "Cannot get empty add!");
1303 if (Ops.size() == 1) return Ops[0];
1305 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
1306 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1307 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
1308 "SCEVAddExpr operand types don't match!");
1311 // If HasNSW is true and all the operands are non-negative, infer HasNUW.
1312 if (!HasNUW && HasNSW) {
1314 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1315 if (!isKnownNonNegative(Ops[i])) {
1319 if (All) HasNUW = true;
1322 // Sort by complexity, this groups all similar expression types together.
1323 GroupByComplexity(Ops, LI);
1325 // If there are any constants, fold them together.
1327 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1329 assert(Idx < Ops.size());
1330 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1331 // We found two constants, fold them together!
1332 Ops[0] = getConstant(LHSC->getValue()->getValue() +
1333 RHSC->getValue()->getValue());
1334 if (Ops.size() == 2) return Ops[0];
1335 Ops.erase(Ops.begin()+1); // Erase the folded element
1336 LHSC = cast<SCEVConstant>(Ops[0]);
1339 // If we are left with a constant zero being added, strip it off.
1340 if (LHSC->getValue()->isZero()) {
1341 Ops.erase(Ops.begin());
1345 if (Ops.size() == 1) return Ops[0];
1348 // Okay, check to see if the same value occurs in the operand list twice. If
1349 // so, merge them together into an multiply expression. Since we sorted the
1350 // list, these values are required to be adjacent.
1351 const Type *Ty = Ops[0]->getType();
1352 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
1353 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
1354 // Found a match, merge the two values into a multiply, and add any
1355 // remaining values to the result.
1356 const SCEV *Two = getConstant(Ty, 2);
1357 const SCEV *Mul = getMulExpr(Ops[i], Two);
1358 if (Ops.size() == 2)
1360 Ops.erase(Ops.begin()+i, Ops.begin()+i+2);
1362 return getAddExpr(Ops, HasNUW, HasNSW);
1365 // Check for truncates. If all the operands are truncated from the same
1366 // type, see if factoring out the truncate would permit the result to be
1367 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
1368 // if the contents of the resulting outer trunc fold to something simple.
1369 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
1370 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
1371 const Type *DstType = Trunc->getType();
1372 const Type *SrcType = Trunc->getOperand()->getType();
1373 SmallVector<const SCEV *, 8> LargeOps;
1375 // Check all the operands to see if they can be represented in the
1376 // source type of the truncate.
1377 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1378 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
1379 if (T->getOperand()->getType() != SrcType) {
1383 LargeOps.push_back(T->getOperand());
1384 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1385 LargeOps.push_back(getAnyExtendExpr(C, SrcType));
1386 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
1387 SmallVector<const SCEV *, 8> LargeMulOps;
1388 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
1389 if (const SCEVTruncateExpr *T =
1390 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
1391 if (T->getOperand()->getType() != SrcType) {
1395 LargeMulOps.push_back(T->getOperand());
1396 } else if (const SCEVConstant *C =
1397 dyn_cast<SCEVConstant>(M->getOperand(j))) {
1398 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType));
1405 LargeOps.push_back(getMulExpr(LargeMulOps));
1412 // Evaluate the expression in the larger type.
1413 const SCEV *Fold = getAddExpr(LargeOps, HasNUW, HasNSW);
1414 // If it folds to something simple, use it. Otherwise, don't.
1415 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
1416 return getTruncateExpr(Fold, DstType);
1420 // Skip past any other cast SCEVs.
1421 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
1424 // If there are add operands they would be next.
1425 if (Idx < Ops.size()) {
1426 bool DeletedAdd = false;
1427 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
1428 // If we have an add, expand the add operands onto the end of the operands
1430 Ops.erase(Ops.begin()+Idx);
1431 Ops.append(Add->op_begin(), Add->op_end());
1435 // If we deleted at least one add, we added operands to the end of the list,
1436 // and they are not necessarily sorted. Recurse to resort and resimplify
1437 // any operands we just acquired.
1439 return getAddExpr(Ops);
1442 // Skip over the add expression until we get to a multiply.
1443 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1446 // Check to see if there are any folding opportunities present with
1447 // operands multiplied by constant values.
1448 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
1449 uint64_t BitWidth = getTypeSizeInBits(Ty);
1450 DenseMap<const SCEV *, APInt> M;
1451 SmallVector<const SCEV *, 8> NewOps;
1452 APInt AccumulatedConstant(BitWidth, 0);
1453 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1454 Ops.data(), Ops.size(),
1455 APInt(BitWidth, 1), *this)) {
1456 // Some interesting folding opportunity is present, so its worthwhile to
1457 // re-generate the operands list. Group the operands by constant scale,
1458 // to avoid multiplying by the same constant scale multiple times.
1459 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
1460 for (SmallVector<const SCEV *, 8>::iterator I = NewOps.begin(),
1461 E = NewOps.end(); I != E; ++I)
1462 MulOpLists[M.find(*I)->second].push_back(*I);
1463 // Re-generate the operands list.
1465 if (AccumulatedConstant != 0)
1466 Ops.push_back(getConstant(AccumulatedConstant));
1467 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator
1468 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I)
1470 Ops.push_back(getMulExpr(getConstant(I->first),
1471 getAddExpr(I->second)));
1473 return getConstant(Ty, 0);
1474 if (Ops.size() == 1)
1476 return getAddExpr(Ops);
1480 // If we are adding something to a multiply expression, make sure the
1481 // something is not already an operand of the multiply. If so, merge it into
1483 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
1484 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
1485 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
1486 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
1487 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
1488 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(Ops[AddOp])) {
1489 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
1490 const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
1491 if (Mul->getNumOperands() != 2) {
1492 // If the multiply has more than two operands, we must get the
1494 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), Mul->op_end());
1495 MulOps.erase(MulOps.begin()+MulOp);
1496 InnerMul = getMulExpr(MulOps);
1498 const SCEV *One = getConstant(Ty, 1);
1499 const SCEV *AddOne = getAddExpr(InnerMul, One);
1500 const SCEV *OuterMul = getMulExpr(AddOne, Ops[AddOp]);
1501 if (Ops.size() == 2) return OuterMul;
1503 Ops.erase(Ops.begin()+AddOp);
1504 Ops.erase(Ops.begin()+Idx-1);
1506 Ops.erase(Ops.begin()+Idx);
1507 Ops.erase(Ops.begin()+AddOp-1);
1509 Ops.push_back(OuterMul);
1510 return getAddExpr(Ops);
1513 // Check this multiply against other multiplies being added together.
1514 for (unsigned OtherMulIdx = Idx+1;
1515 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
1517 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
1518 // If MulOp occurs in OtherMul, we can fold the two multiplies
1520 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
1521 OMulOp != e; ++OMulOp)
1522 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
1523 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
1524 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
1525 if (Mul->getNumOperands() != 2) {
1526 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
1528 MulOps.erase(MulOps.begin()+MulOp);
1529 InnerMul1 = getMulExpr(MulOps);
1531 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
1532 if (OtherMul->getNumOperands() != 2) {
1533 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
1534 OtherMul->op_end());
1535 MulOps.erase(MulOps.begin()+OMulOp);
1536 InnerMul2 = getMulExpr(MulOps);
1538 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
1539 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
1540 if (Ops.size() == 2) return OuterMul;
1541 Ops.erase(Ops.begin()+Idx);
1542 Ops.erase(Ops.begin()+OtherMulIdx-1);
1543 Ops.push_back(OuterMul);
1544 return getAddExpr(Ops);
1550 // If there are any add recurrences in the operands list, see if any other
1551 // added values are loop invariant. If so, we can fold them into the
1553 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1556 // Scan over all recurrences, trying to fold loop invariants into them.
1557 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1558 // Scan all of the other operands to this add and add them to the vector if
1559 // they are loop invariant w.r.t. the recurrence.
1560 SmallVector<const SCEV *, 8> LIOps;
1561 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1562 const Loop *AddRecLoop = AddRec->getLoop();
1563 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1564 if (Ops[i]->isLoopInvariant(AddRecLoop)) {
1565 LIOps.push_back(Ops[i]);
1566 Ops.erase(Ops.begin()+i);
1570 // If we found some loop invariants, fold them into the recurrence.
1571 if (!LIOps.empty()) {
1572 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
1573 LIOps.push_back(AddRec->getStart());
1575 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
1577 AddRecOps[0] = getAddExpr(LIOps);
1579 // Build the new addrec. Propagate the NUW and NSW flags if both the
1580 // outer add and the inner addrec are guaranteed to have no overflow.
1581 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop,
1582 HasNUW && AddRec->hasNoUnsignedWrap(),
1583 HasNSW && AddRec->hasNoSignedWrap());
1585 // If all of the other operands were loop invariant, we are done.
1586 if (Ops.size() == 1) return NewRec;
1588 // Otherwise, add the folded AddRec by the non-liv parts.
1589 for (unsigned i = 0;; ++i)
1590 if (Ops[i] == AddRec) {
1594 return getAddExpr(Ops);
1597 // Okay, if there weren't any loop invariants to be folded, check to see if
1598 // there are multiple AddRec's with the same loop induction variable being
1599 // added together. If so, we can fold them.
1600 for (unsigned OtherIdx = Idx+1;
1601 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
1602 if (OtherIdx != Idx) {
1603 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
1604 if (AddRecLoop == OtherAddRec->getLoop()) {
1605 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D}
1606 SmallVector<const SCEV *, 4> NewOps(AddRec->op_begin(),
1608 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) {
1609 if (i >= NewOps.size()) {
1610 NewOps.append(OtherAddRec->op_begin()+i,
1611 OtherAddRec->op_end());
1614 NewOps[i] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i));
1616 const SCEV *NewAddRec = getAddRecExpr(NewOps, AddRecLoop);
1618 if (Ops.size() == 2) return NewAddRec;
1620 Ops.erase(Ops.begin()+Idx);
1621 Ops.erase(Ops.begin()+OtherIdx-1);
1622 Ops.push_back(NewAddRec);
1623 return getAddExpr(Ops);
1627 // Otherwise couldn't fold anything into this recurrence. Move onto the
1631 // Okay, it looks like we really DO need an add expr. Check to see if we
1632 // already have one, otherwise create a new one.
1633 FoldingSetNodeID ID;
1634 ID.AddInteger(scAddExpr);
1635 ID.AddInteger(Ops.size());
1636 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1637 ID.AddPointer(Ops[i]);
1640 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1642 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
1643 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
1644 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator),
1646 UniqueSCEVs.InsertNode(S, IP);
1648 if (HasNUW) S->setHasNoUnsignedWrap(true);
1649 if (HasNSW) S->setHasNoSignedWrap(true);
1653 /// getMulExpr - Get a canonical multiply expression, or something simpler if
1655 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
1656 bool HasNUW, bool HasNSW) {
1657 assert(!Ops.empty() && "Cannot get empty mul!");
1658 if (Ops.size() == 1) return Ops[0];
1660 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1661 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
1662 getEffectiveSCEVType(Ops[0]->getType()) &&
1663 "SCEVMulExpr operand types don't match!");
1666 // If HasNSW is true and all the operands are non-negative, infer HasNUW.
1667 if (!HasNUW && HasNSW) {
1669 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1670 if (!isKnownNonNegative(Ops[i])) {
1674 if (All) HasNUW = true;
1677 // Sort by complexity, this groups all similar expression types together.
1678 GroupByComplexity(Ops, LI);
1680 // If there are any constants, fold them together.
1682 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1684 // C1*(C2+V) -> C1*C2 + C1*V
1685 if (Ops.size() == 2)
1686 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
1687 if (Add->getNumOperands() == 2 &&
1688 isa<SCEVConstant>(Add->getOperand(0)))
1689 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
1690 getMulExpr(LHSC, Add->getOperand(1)));
1693 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1694 // We found two constants, fold them together!
1695 ConstantInt *Fold = ConstantInt::get(getContext(),
1696 LHSC->getValue()->getValue() *
1697 RHSC->getValue()->getValue());
1698 Ops[0] = getConstant(Fold);
1699 Ops.erase(Ops.begin()+1); // Erase the folded element
1700 if (Ops.size() == 1) return Ops[0];
1701 LHSC = cast<SCEVConstant>(Ops[0]);
1704 // If we are left with a constant one being multiplied, strip it off.
1705 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
1706 Ops.erase(Ops.begin());
1708 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
1709 // If we have a multiply of zero, it will always be zero.
1711 } else if (Ops[0]->isAllOnesValue()) {
1712 // If we have a mul by -1 of an add, try distributing the -1 among the
1714 if (Ops.size() == 2)
1715 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
1716 SmallVector<const SCEV *, 4> NewOps;
1717 bool AnyFolded = false;
1718 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(), E = Add->op_end();
1720 const SCEV *Mul = getMulExpr(Ops[0], *I);
1721 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
1722 NewOps.push_back(Mul);
1725 return getAddExpr(NewOps);
1729 if (Ops.size() == 1)
1733 // Skip over the add expression until we get to a multiply.
1734 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1737 // If there are mul operands inline them all into this expression.
1738 if (Idx < Ops.size()) {
1739 bool DeletedMul = false;
1740 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
1741 // If we have an mul, expand the mul operands onto the end of the operands
1743 Ops.erase(Ops.begin()+Idx);
1744 Ops.append(Mul->op_begin(), Mul->op_end());
1748 // If we deleted at least one mul, we added operands to the end of the list,
1749 // and they are not necessarily sorted. Recurse to resort and resimplify
1750 // any operands we just acquired.
1752 return getMulExpr(Ops);
1755 // If there are any add recurrences in the operands list, see if any other
1756 // added values are loop invariant. If so, we can fold them into the
1758 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1761 // Scan over all recurrences, trying to fold loop invariants into them.
1762 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1763 // Scan all of the other operands to this mul and add them to the vector if
1764 // they are loop invariant w.r.t. the recurrence.
1765 SmallVector<const SCEV *, 8> LIOps;
1766 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1767 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1768 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
1769 LIOps.push_back(Ops[i]);
1770 Ops.erase(Ops.begin()+i);
1774 // If we found some loop invariants, fold them into the recurrence.
1775 if (!LIOps.empty()) {
1776 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
1777 SmallVector<const SCEV *, 4> NewOps;
1778 NewOps.reserve(AddRec->getNumOperands());
1779 const SCEV *Scale = getMulExpr(LIOps);
1780 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
1781 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
1783 // Build the new addrec. Propagate the NUW and NSW flags if both the
1784 // outer mul and the inner addrec are guaranteed to have no overflow.
1785 const SCEV *NewRec = getAddRecExpr(NewOps, AddRec->getLoop(),
1786 HasNUW && AddRec->hasNoUnsignedWrap(),
1787 HasNSW && AddRec->hasNoSignedWrap());
1789 // If all of the other operands were loop invariant, we are done.
1790 if (Ops.size() == 1) return NewRec;
1792 // Otherwise, multiply the folded AddRec by the non-liv parts.
1793 for (unsigned i = 0;; ++i)
1794 if (Ops[i] == AddRec) {
1798 return getMulExpr(Ops);
1801 // Okay, if there weren't any loop invariants to be folded, check to see if
1802 // there are multiple AddRec's with the same loop induction variable being
1803 // multiplied together. If so, we can fold them.
1804 for (unsigned OtherIdx = Idx+1;
1805 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
1806 if (OtherIdx != Idx) {
1807 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
1808 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
1809 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D}
1810 const SCEVAddRecExpr *F = AddRec, *G = OtherAddRec;
1811 const SCEV *NewStart = getMulExpr(F->getStart(),
1813 const SCEV *B = F->getStepRecurrence(*this);
1814 const SCEV *D = G->getStepRecurrence(*this);
1815 const SCEV *NewStep = getAddExpr(getMulExpr(F, D),
1818 const SCEV *NewAddRec = getAddRecExpr(NewStart, NewStep,
1820 if (Ops.size() == 2) return NewAddRec;
1822 Ops.erase(Ops.begin()+Idx);
1823 Ops.erase(Ops.begin()+OtherIdx-1);
1824 Ops.push_back(NewAddRec);
1825 return getMulExpr(Ops);
1829 // Otherwise couldn't fold anything into this recurrence. Move onto the
1833 // Okay, it looks like we really DO need an mul expr. Check to see if we
1834 // already have one, otherwise create a new one.
1835 FoldingSetNodeID ID;
1836 ID.AddInteger(scMulExpr);
1837 ID.AddInteger(Ops.size());
1838 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1839 ID.AddPointer(Ops[i]);
1842 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1844 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
1845 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
1846 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
1848 UniqueSCEVs.InsertNode(S, IP);
1850 if (HasNUW) S->setHasNoUnsignedWrap(true);
1851 if (HasNSW) S->setHasNoSignedWrap(true);
1855 /// getUDivExpr - Get a canonical unsigned division expression, or something
1856 /// simpler if possible.
1857 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
1859 assert(getEffectiveSCEVType(LHS->getType()) ==
1860 getEffectiveSCEVType(RHS->getType()) &&
1861 "SCEVUDivExpr operand types don't match!");
1863 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
1864 if (RHSC->getValue()->equalsInt(1))
1865 return LHS; // X udiv 1 --> x
1866 // If the denominator is zero, the result of the udiv is undefined. Don't
1867 // try to analyze it, because the resolution chosen here may differ from
1868 // the resolution chosen in other parts of the compiler.
1869 if (!RHSC->getValue()->isZero()) {
1870 // Determine if the division can be folded into the operands of
1872 // TODO: Generalize this to non-constants by using known-bits information.
1873 const Type *Ty = LHS->getType();
1874 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
1875 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ;
1876 // For non-power-of-two values, effectively round the value up to the
1877 // nearest power of two.
1878 if (!RHSC->getValue()->getValue().isPowerOf2())
1880 const IntegerType *ExtTy =
1881 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
1882 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
1883 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
1884 if (const SCEVConstant *Step =
1885 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this)))
1886 if (!Step->getValue()->getValue()
1887 .urem(RHSC->getValue()->getValue()) &&
1888 getZeroExtendExpr(AR, ExtTy) ==
1889 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
1890 getZeroExtendExpr(Step, ExtTy),
1892 SmallVector<const SCEV *, 4> Operands;
1893 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i)
1894 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS));
1895 return getAddRecExpr(Operands, AR->getLoop());
1897 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
1898 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
1899 SmallVector<const SCEV *, 4> Operands;
1900 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i)
1901 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy));
1902 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
1903 // Find an operand that's safely divisible.
1904 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
1905 const SCEV *Op = M->getOperand(i);
1906 const SCEV *Div = getUDivExpr(Op, RHSC);
1907 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
1908 Operands = SmallVector<const SCEV *, 4>(M->op_begin(),
1911 return getMulExpr(Operands);
1915 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
1916 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(LHS)) {
1917 SmallVector<const SCEV *, 4> Operands;
1918 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i)
1919 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy));
1920 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
1922 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
1923 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
1924 if (isa<SCEVUDivExpr>(Op) ||
1925 getMulExpr(Op, RHS) != A->getOperand(i))
1927 Operands.push_back(Op);
1929 if (Operands.size() == A->getNumOperands())
1930 return getAddExpr(Operands);
1934 // Fold if both operands are constant.
1935 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
1936 Constant *LHSCV = LHSC->getValue();
1937 Constant *RHSCV = RHSC->getValue();
1938 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
1944 FoldingSetNodeID ID;
1945 ID.AddInteger(scUDivExpr);
1949 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1950 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
1952 UniqueSCEVs.InsertNode(S, IP);
1957 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
1958 /// Simplify the expression as much as possible.
1959 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start,
1960 const SCEV *Step, const Loop *L,
1961 bool HasNUW, bool HasNSW) {
1962 SmallVector<const SCEV *, 4> Operands;
1963 Operands.push_back(Start);
1964 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
1965 if (StepChrec->getLoop() == L) {
1966 Operands.append(StepChrec->op_begin(), StepChrec->op_end());
1967 return getAddRecExpr(Operands, L);
1970 Operands.push_back(Step);
1971 return getAddRecExpr(Operands, L, HasNUW, HasNSW);
1974 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
1975 /// Simplify the expression as much as possible.
1977 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
1979 bool HasNUW, bool HasNSW) {
1980 if (Operands.size() == 1) return Operands[0];
1982 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
1983 assert(getEffectiveSCEVType(Operands[i]->getType()) ==
1984 getEffectiveSCEVType(Operands[0]->getType()) &&
1985 "SCEVAddRecExpr operand types don't match!");
1988 if (Operands.back()->isZero()) {
1989 Operands.pop_back();
1990 return getAddRecExpr(Operands, L, HasNUW, HasNSW); // {X,+,0} --> X
1993 // It's tempting to want to call getMaxBackedgeTakenCount count here and
1994 // use that information to infer NUW and NSW flags. However, computing a
1995 // BE count requires calling getAddRecExpr, so we may not yet have a
1996 // meaningful BE count at this point (and if we don't, we'd be stuck
1997 // with a SCEVCouldNotCompute as the cached BE count).
1999 // If HasNSW is true and all the operands are non-negative, infer HasNUW.
2000 if (!HasNUW && HasNSW) {
2002 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2003 if (!isKnownNonNegative(Operands[i])) {
2007 if (All) HasNUW = true;
2010 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
2011 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
2012 const Loop *NestedLoop = NestedAR->getLoop();
2013 if (L->contains(NestedLoop->getHeader()) ?
2014 (L->getLoopDepth() < NestedLoop->getLoopDepth()) :
2015 (!NestedLoop->contains(L->getHeader()) &&
2016 DT->dominates(L->getHeader(), NestedLoop->getHeader()))) {
2017 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
2018 NestedAR->op_end());
2019 Operands[0] = NestedAR->getStart();
2020 // AddRecs require their operands be loop-invariant with respect to their
2021 // loops. Don't perform this transformation if it would break this
2023 bool AllInvariant = true;
2024 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2025 if (!Operands[i]->isLoopInvariant(L)) {
2026 AllInvariant = false;
2030 NestedOperands[0] = getAddRecExpr(Operands, L);
2031 AllInvariant = true;
2032 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i)
2033 if (!NestedOperands[i]->isLoopInvariant(NestedLoop)) {
2034 AllInvariant = false;
2038 // Ok, both add recurrences are valid after the transformation.
2039 return getAddRecExpr(NestedOperands, NestedLoop, HasNUW, HasNSW);
2041 // Reset Operands to its original state.
2042 Operands[0] = NestedAR;
2046 // Okay, it looks like we really DO need an addrec expr. Check to see if we
2047 // already have one, otherwise create a new one.
2048 FoldingSetNodeID ID;
2049 ID.AddInteger(scAddRecExpr);
2050 ID.AddInteger(Operands.size());
2051 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2052 ID.AddPointer(Operands[i]);
2056 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2058 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size());
2059 std::uninitialized_copy(Operands.begin(), Operands.end(), O);
2060 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator),
2061 O, Operands.size(), L);
2062 UniqueSCEVs.InsertNode(S, IP);
2064 if (HasNUW) S->setHasNoUnsignedWrap(true);
2065 if (HasNSW) S->setHasNoSignedWrap(true);
2069 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
2071 SmallVector<const SCEV *, 2> Ops;
2074 return getSMaxExpr(Ops);
2078 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2079 assert(!Ops.empty() && "Cannot get empty smax!");
2080 if (Ops.size() == 1) return Ops[0];
2082 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2083 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
2084 getEffectiveSCEVType(Ops[0]->getType()) &&
2085 "SCEVSMaxExpr operand types don't match!");
2088 // Sort by complexity, this groups all similar expression types together.
2089 GroupByComplexity(Ops, LI);
2091 // If there are any constants, fold them together.
2093 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2095 assert(Idx < Ops.size());
2096 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2097 // We found two constants, fold them together!
2098 ConstantInt *Fold = ConstantInt::get(getContext(),
2099 APIntOps::smax(LHSC->getValue()->getValue(),
2100 RHSC->getValue()->getValue()));
2101 Ops[0] = getConstant(Fold);
2102 Ops.erase(Ops.begin()+1); // Erase the folded element
2103 if (Ops.size() == 1) return Ops[0];
2104 LHSC = cast<SCEVConstant>(Ops[0]);
2107 // If we are left with a constant minimum-int, strip it off.
2108 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
2109 Ops.erase(Ops.begin());
2111 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
2112 // If we have an smax with a constant maximum-int, it will always be
2117 if (Ops.size() == 1) return Ops[0];
2120 // Find the first SMax
2121 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
2124 // Check to see if one of the operands is an SMax. If so, expand its operands
2125 // onto our operand list, and recurse to simplify.
2126 if (Idx < Ops.size()) {
2127 bool DeletedSMax = false;
2128 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
2129 Ops.erase(Ops.begin()+Idx);
2130 Ops.append(SMax->op_begin(), SMax->op_end());
2135 return getSMaxExpr(Ops);
2138 // Okay, check to see if the same value occurs in the operand list twice. If
2139 // so, delete one. Since we sorted the list, these values are required to
2141 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2142 // X smax Y smax Y --> X smax Y
2143 // X smax Y --> X, if X is always greater than Y
2144 if (Ops[i] == Ops[i+1] ||
2145 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) {
2146 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2148 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) {
2149 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2153 if (Ops.size() == 1) return Ops[0];
2155 assert(!Ops.empty() && "Reduced smax down to nothing!");
2157 // Okay, it looks like we really DO need an smax expr. Check to see if we
2158 // already have one, otherwise create a new one.
2159 FoldingSetNodeID ID;
2160 ID.AddInteger(scSMaxExpr);
2161 ID.AddInteger(Ops.size());
2162 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2163 ID.AddPointer(Ops[i]);
2165 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2166 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2167 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2168 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator),
2170 UniqueSCEVs.InsertNode(S, IP);
2174 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
2176 SmallVector<const SCEV *, 2> Ops;
2179 return getUMaxExpr(Ops);
2183 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2184 assert(!Ops.empty() && "Cannot get empty umax!");
2185 if (Ops.size() == 1) return Ops[0];
2187 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2188 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
2189 getEffectiveSCEVType(Ops[0]->getType()) &&
2190 "SCEVUMaxExpr operand types don't match!");
2193 // Sort by complexity, this groups all similar expression types together.
2194 GroupByComplexity(Ops, LI);
2196 // If there are any constants, fold them together.
2198 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2200 assert(Idx < Ops.size());
2201 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2202 // We found two constants, fold them together!
2203 ConstantInt *Fold = ConstantInt::get(getContext(),
2204 APIntOps::umax(LHSC->getValue()->getValue(),
2205 RHSC->getValue()->getValue()));
2206 Ops[0] = getConstant(Fold);
2207 Ops.erase(Ops.begin()+1); // Erase the folded element
2208 if (Ops.size() == 1) return Ops[0];
2209 LHSC = cast<SCEVConstant>(Ops[0]);
2212 // If we are left with a constant minimum-int, strip it off.
2213 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
2214 Ops.erase(Ops.begin());
2216 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
2217 // If we have an umax with a constant maximum-int, it will always be
2222 if (Ops.size() == 1) return Ops[0];
2225 // Find the first UMax
2226 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
2229 // Check to see if one of the operands is a UMax. If so, expand its operands
2230 // onto our operand list, and recurse to simplify.
2231 if (Idx < Ops.size()) {
2232 bool DeletedUMax = false;
2233 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
2234 Ops.erase(Ops.begin()+Idx);
2235 Ops.append(UMax->op_begin(), UMax->op_end());
2240 return getUMaxExpr(Ops);
2243 // Okay, check to see if the same value occurs in the operand list twice. If
2244 // so, delete one. Since we sorted the list, these values are required to
2246 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2247 // X umax Y umax Y --> X umax Y
2248 // X umax Y --> X, if X is always greater than Y
2249 if (Ops[i] == Ops[i+1] ||
2250 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) {
2251 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2253 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) {
2254 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2258 if (Ops.size() == 1) return Ops[0];
2260 assert(!Ops.empty() && "Reduced umax down to nothing!");
2262 // Okay, it looks like we really DO need a umax expr. Check to see if we
2263 // already have one, otherwise create a new one.
2264 FoldingSetNodeID ID;
2265 ID.AddInteger(scUMaxExpr);
2266 ID.AddInteger(Ops.size());
2267 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2268 ID.AddPointer(Ops[i]);
2270 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2271 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2272 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2273 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator),
2275 UniqueSCEVs.InsertNode(S, IP);
2279 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
2281 // ~smax(~x, ~y) == smin(x, y).
2282 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2285 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
2287 // ~umax(~x, ~y) == umin(x, y)
2288 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2291 const SCEV *ScalarEvolution::getSizeOfExpr(const Type *AllocTy) {
2292 // If we have TargetData, we can bypass creating a target-independent
2293 // constant expression and then folding it back into a ConstantInt.
2294 // This is just a compile-time optimization.
2296 return getConstant(TD->getIntPtrType(getContext()),
2297 TD->getTypeAllocSize(AllocTy));
2299 Constant *C = ConstantExpr::getSizeOf(AllocTy);
2300 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2301 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD))
2303 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2304 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2307 const SCEV *ScalarEvolution::getAlignOfExpr(const Type *AllocTy) {
2308 Constant *C = ConstantExpr::getAlignOf(AllocTy);
2309 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2310 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD))
2312 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2313 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2316 const SCEV *ScalarEvolution::getOffsetOfExpr(const StructType *STy,
2318 // If we have TargetData, we can bypass creating a target-independent
2319 // constant expression and then folding it back into a ConstantInt.
2320 // This is just a compile-time optimization.
2322 return getConstant(TD->getIntPtrType(getContext()),
2323 TD->getStructLayout(STy)->getElementOffset(FieldNo));
2325 Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo);
2326 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2327 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD))
2329 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy));
2330 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2333 const SCEV *ScalarEvolution::getOffsetOfExpr(const Type *CTy,
2334 Constant *FieldNo) {
2335 Constant *C = ConstantExpr::getOffsetOf(CTy, FieldNo);
2336 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2337 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD))
2339 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(CTy));
2340 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2343 const SCEV *ScalarEvolution::getUnknown(Value *V) {
2344 // Don't attempt to do anything other than create a SCEVUnknown object
2345 // here. createSCEV only calls getUnknown after checking for all other
2346 // interesting possibilities, and any other code that calls getUnknown
2347 // is doing so in order to hide a value from SCEV canonicalization.
2349 FoldingSetNodeID ID;
2350 ID.AddInteger(scUnknown);
2353 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2354 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V);
2355 UniqueSCEVs.InsertNode(S, IP);
2359 //===----------------------------------------------------------------------===//
2360 // Basic SCEV Analysis and PHI Idiom Recognition Code
2363 /// isSCEVable - Test if values of the given type are analyzable within
2364 /// the SCEV framework. This primarily includes integer types, and it
2365 /// can optionally include pointer types if the ScalarEvolution class
2366 /// has access to target-specific information.
2367 bool ScalarEvolution::isSCEVable(const Type *Ty) const {
2368 // Integers and pointers are always SCEVable.
2369 return Ty->isIntegerTy() || Ty->isPointerTy();
2372 /// getTypeSizeInBits - Return the size in bits of the specified type,
2373 /// for which isSCEVable must return true.
2374 uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const {
2375 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2377 // If we have a TargetData, use it!
2379 return TD->getTypeSizeInBits(Ty);
2381 // Integer types have fixed sizes.
2382 if (Ty->isIntegerTy())
2383 return Ty->getPrimitiveSizeInBits();
2385 // The only other support type is pointer. Without TargetData, conservatively
2386 // assume pointers are 64-bit.
2387 assert(Ty->isPointerTy() && "isSCEVable permitted a non-SCEVable type!");
2391 /// getEffectiveSCEVType - Return a type with the same bitwidth as
2392 /// the given type and which represents how SCEV will treat the given
2393 /// type, for which isSCEVable must return true. For pointer types,
2394 /// this is the pointer-sized integer type.
2395 const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const {
2396 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2398 if (Ty->isIntegerTy())
2401 // The only other support type is pointer.
2402 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
2403 if (TD) return TD->getIntPtrType(getContext());
2405 // Without TargetData, conservatively assume pointers are 64-bit.
2406 return Type::getInt64Ty(getContext());
2409 const SCEV *ScalarEvolution::getCouldNotCompute() {
2410 return &CouldNotCompute;
2413 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
2414 /// expression and create a new one.
2415 const SCEV *ScalarEvolution::getSCEV(Value *V) {
2416 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
2418 std::map<SCEVCallbackVH, const SCEV *>::iterator I = Scalars.find(V);
2419 if (I != Scalars.end()) return I->second;
2420 const SCEV *S = createSCEV(V);
2421 Scalars.insert(std::make_pair(SCEVCallbackVH(V, this), S));
2425 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
2427 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) {
2428 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2430 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
2432 const Type *Ty = V->getType();
2433 Ty = getEffectiveSCEVType(Ty);
2434 return getMulExpr(V,
2435 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))));
2438 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
2439 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
2440 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2442 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
2444 const Type *Ty = V->getType();
2445 Ty = getEffectiveSCEVType(Ty);
2446 const SCEV *AllOnes =
2447 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
2448 return getMinusSCEV(AllOnes, V);
2451 /// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
2453 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS,
2455 // Fast path: X - X --> 0.
2457 return getConstant(LHS->getType(), 0);
2460 return getAddExpr(LHS, getNegativeSCEV(RHS));
2463 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
2464 /// input value to the specified type. If the type must be extended, it is zero
2467 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V,
2469 const Type *SrcTy = V->getType();
2470 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2471 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2472 "Cannot truncate or zero extend with non-integer arguments!");
2473 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2474 return V; // No conversion
2475 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2476 return getTruncateExpr(V, Ty);
2477 return getZeroExtendExpr(V, Ty);
2480 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
2481 /// input value to the specified type. If the type must be extended, it is sign
2484 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
2486 const Type *SrcTy = V->getType();
2487 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2488 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2489 "Cannot truncate or zero extend with non-integer arguments!");
2490 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2491 return V; // No conversion
2492 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2493 return getTruncateExpr(V, Ty);
2494 return getSignExtendExpr(V, Ty);
2497 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
2498 /// input value to the specified type. If the type must be extended, it is zero
2499 /// extended. The conversion must not be narrowing.
2501 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, const Type *Ty) {
2502 const Type *SrcTy = V->getType();
2503 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2504 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2505 "Cannot noop or zero extend with non-integer arguments!");
2506 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2507 "getNoopOrZeroExtend cannot truncate!");
2508 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2509 return V; // No conversion
2510 return getZeroExtendExpr(V, Ty);
2513 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
2514 /// input value to the specified type. If the type must be extended, it is sign
2515 /// extended. The conversion must not be narrowing.
2517 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, const Type *Ty) {
2518 const Type *SrcTy = V->getType();
2519 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2520 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2521 "Cannot noop or sign extend with non-integer arguments!");
2522 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2523 "getNoopOrSignExtend cannot truncate!");
2524 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2525 return V; // No conversion
2526 return getSignExtendExpr(V, Ty);
2529 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
2530 /// the input value to the specified type. If the type must be extended,
2531 /// it is extended with unspecified bits. The conversion must not be
2534 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, const Type *Ty) {
2535 const Type *SrcTy = V->getType();
2536 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2537 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2538 "Cannot noop or any extend with non-integer arguments!");
2539 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2540 "getNoopOrAnyExtend cannot truncate!");
2541 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2542 return V; // No conversion
2543 return getAnyExtendExpr(V, Ty);
2546 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
2547 /// input value to the specified type. The conversion must not be widening.
2549 ScalarEvolution::getTruncateOrNoop(const SCEV *V, const Type *Ty) {
2550 const Type *SrcTy = V->getType();
2551 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2552 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2553 "Cannot truncate or noop with non-integer arguments!");
2554 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
2555 "getTruncateOrNoop cannot extend!");
2556 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2557 return V; // No conversion
2558 return getTruncateExpr(V, Ty);
2561 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
2562 /// the types using zero-extension, and then perform a umax operation
2564 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
2566 const SCEV *PromotedLHS = LHS;
2567 const SCEV *PromotedRHS = RHS;
2569 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2570 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2572 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2574 return getUMaxExpr(PromotedLHS, PromotedRHS);
2577 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
2578 /// the types using zero-extension, and then perform a umin operation
2580 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
2582 const SCEV *PromotedLHS = LHS;
2583 const SCEV *PromotedRHS = RHS;
2585 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2586 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2588 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2590 return getUMinExpr(PromotedLHS, PromotedRHS);
2593 /// PushDefUseChildren - Push users of the given Instruction
2594 /// onto the given Worklist.
2596 PushDefUseChildren(Instruction *I,
2597 SmallVectorImpl<Instruction *> &Worklist) {
2598 // Push the def-use children onto the Worklist stack.
2599 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end();
2601 Worklist.push_back(cast<Instruction>(*UI));
2604 /// ForgetSymbolicValue - This looks up computed SCEV values for all
2605 /// instructions that depend on the given instruction and removes them from
2606 /// the Scalars map if they reference SymName. This is used during PHI
2609 ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) {
2610 SmallVector<Instruction *, 16> Worklist;
2611 PushDefUseChildren(PN, Worklist);
2613 SmallPtrSet<Instruction *, 8> Visited;
2615 while (!Worklist.empty()) {
2616 Instruction *I = Worklist.pop_back_val();
2617 if (!Visited.insert(I)) continue;
2619 std::map<SCEVCallbackVH, const SCEV *>::iterator It =
2620 Scalars.find(static_cast<Value *>(I));
2621 if (It != Scalars.end()) {
2622 // Short-circuit the def-use traversal if the symbolic name
2623 // ceases to appear in expressions.
2624 if (It->second != SymName && !It->second->hasOperand(SymName))
2627 // SCEVUnknown for a PHI either means that it has an unrecognized
2628 // structure, it's a PHI that's in the progress of being computed
2629 // by createNodeForPHI, or it's a single-value PHI. In the first case,
2630 // additional loop trip count information isn't going to change anything.
2631 // In the second case, createNodeForPHI will perform the necessary
2632 // updates on its own when it gets to that point. In the third, we do
2633 // want to forget the SCEVUnknown.
2634 if (!isa<PHINode>(I) ||
2635 !isa<SCEVUnknown>(It->second) ||
2636 (I != PN && It->second == SymName)) {
2637 ValuesAtScopes.erase(It->second);
2642 PushDefUseChildren(I, Worklist);
2646 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
2647 /// a loop header, making it a potential recurrence, or it doesn't.
2649 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
2650 if (const Loop *L = LI->getLoopFor(PN->getParent()))
2651 if (L->getHeader() == PN->getParent()) {
2652 // The loop may have multiple entrances or multiple exits; we can analyze
2653 // this phi as an addrec if it has a unique entry value and a unique
2655 Value *BEValueV = 0, *StartValueV = 0;
2656 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
2657 Value *V = PN->getIncomingValue(i);
2658 if (L->contains(PN->getIncomingBlock(i))) {
2661 } else if (BEValueV != V) {
2665 } else if (!StartValueV) {
2667 } else if (StartValueV != V) {
2672 if (BEValueV && StartValueV) {
2673 // While we are analyzing this PHI node, handle its value symbolically.
2674 const SCEV *SymbolicName = getUnknown(PN);
2675 assert(Scalars.find(PN) == Scalars.end() &&
2676 "PHI node already processed?");
2677 Scalars.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
2679 // Using this symbolic name for the PHI, analyze the value coming around
2681 const SCEV *BEValue = getSCEV(BEValueV);
2683 // NOTE: If BEValue is loop invariant, we know that the PHI node just
2684 // has a special value for the first iteration of the loop.
2686 // If the value coming around the backedge is an add with the symbolic
2687 // value we just inserted, then we found a simple induction variable!
2688 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
2689 // If there is a single occurrence of the symbolic value, replace it
2690 // with a recurrence.
2691 unsigned FoundIndex = Add->getNumOperands();
2692 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
2693 if (Add->getOperand(i) == SymbolicName)
2694 if (FoundIndex == e) {
2699 if (FoundIndex != Add->getNumOperands()) {
2700 // Create an add with everything but the specified operand.
2701 SmallVector<const SCEV *, 8> Ops;
2702 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
2703 if (i != FoundIndex)
2704 Ops.push_back(Add->getOperand(i));
2705 const SCEV *Accum = getAddExpr(Ops);
2707 // This is not a valid addrec if the step amount is varying each
2708 // loop iteration, but is not itself an addrec in this loop.
2709 if (Accum->isLoopInvariant(L) ||
2710 (isa<SCEVAddRecExpr>(Accum) &&
2711 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
2712 bool HasNUW = false;
2713 bool HasNSW = false;
2715 // If the increment doesn't overflow, then neither the addrec nor
2716 // the post-increment will overflow.
2717 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) {
2718 if (OBO->hasNoUnsignedWrap())
2720 if (OBO->hasNoSignedWrap())
2724 const SCEV *StartVal = getSCEV(StartValueV);
2725 const SCEV *PHISCEV =
2726 getAddRecExpr(StartVal, Accum, L, HasNUW, HasNSW);
2728 // Since the no-wrap flags are on the increment, they apply to the
2729 // post-incremented value as well.
2730 if (Accum->isLoopInvariant(L))
2731 (void)getAddRecExpr(getAddExpr(StartVal, Accum),
2732 Accum, L, HasNUW, HasNSW);
2734 // Okay, for the entire analysis of this edge we assumed the PHI
2735 // to be symbolic. We now need to go back and purge all of the
2736 // entries for the scalars that use the symbolic expression.
2737 ForgetSymbolicName(PN, SymbolicName);
2738 Scalars[SCEVCallbackVH(PN, this)] = PHISCEV;
2742 } else if (const SCEVAddRecExpr *AddRec =
2743 dyn_cast<SCEVAddRecExpr>(BEValue)) {
2744 // Otherwise, this could be a loop like this:
2745 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
2746 // In this case, j = {1,+,1} and BEValue is j.
2747 // Because the other in-value of i (0) fits the evolution of BEValue
2748 // i really is an addrec evolution.
2749 if (AddRec->getLoop() == L && AddRec->isAffine()) {
2750 const SCEV *StartVal = getSCEV(StartValueV);
2752 // If StartVal = j.start - j.stride, we can use StartVal as the
2753 // initial step of the addrec evolution.
2754 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
2755 AddRec->getOperand(1))) {
2756 const SCEV *PHISCEV =
2757 getAddRecExpr(StartVal, AddRec->getOperand(1), L);
2759 // Okay, for the entire analysis of this edge we assumed the PHI
2760 // to be symbolic. We now need to go back and purge all of the
2761 // entries for the scalars that use the symbolic expression.
2762 ForgetSymbolicName(PN, SymbolicName);
2763 Scalars[SCEVCallbackVH(PN, this)] = PHISCEV;
2771 // If the PHI has a single incoming value, follow that value, unless the
2772 // PHI's incoming blocks are in a different loop, in which case doing so
2773 // risks breaking LCSSA form. Instcombine would normally zap these, but
2774 // it doesn't have DominatorTree information, so it may miss cases.
2775 if (Value *V = PN->hasConstantValue(DT)) {
2776 bool AllSameLoop = true;
2777 Loop *PNLoop = LI->getLoopFor(PN->getParent());
2778 for (size_t i = 0, e = PN->getNumIncomingValues(); i != e; ++i)
2779 if (LI->getLoopFor(PN->getIncomingBlock(i)) != PNLoop) {
2780 AllSameLoop = false;
2787 // If it's not a loop phi, we can't handle it yet.
2788 return getUnknown(PN);
2791 /// createNodeForGEP - Expand GEP instructions into add and multiply
2792 /// operations. This allows them to be analyzed by regular SCEV code.
2794 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
2796 // Don't blindly transfer the inbounds flag from the GEP instruction to the
2797 // Add expression, because the Instruction may be guarded by control flow
2798 // and the no-overflow bits may not be valid for the expression in any
2801 const Type *IntPtrTy = getEffectiveSCEVType(GEP->getType());
2802 Value *Base = GEP->getOperand(0);
2803 // Don't attempt to analyze GEPs over unsized objects.
2804 if (!cast<PointerType>(Base->getType())->getElementType()->isSized())
2805 return getUnknown(GEP);
2806 const SCEV *TotalOffset = getConstant(IntPtrTy, 0);
2807 gep_type_iterator GTI = gep_type_begin(GEP);
2808 for (GetElementPtrInst::op_iterator I = next(GEP->op_begin()),
2812 // Compute the (potentially symbolic) offset in bytes for this index.
2813 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) {
2814 // For a struct, add the member offset.
2815 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
2816 const SCEV *FieldOffset = getOffsetOfExpr(STy, FieldNo);
2818 // Add the field offset to the running total offset.
2819 TotalOffset = getAddExpr(TotalOffset, FieldOffset);
2821 // For an array, add the element offset, explicitly scaled.
2822 const SCEV *ElementSize = getSizeOfExpr(*GTI);
2823 const SCEV *IndexS = getSCEV(Index);
2824 // Getelementptr indices are signed.
2825 IndexS = getTruncateOrSignExtend(IndexS, IntPtrTy);
2827 // Multiply the index by the element size to compute the element offset.
2828 const SCEV *LocalOffset = getMulExpr(IndexS, ElementSize);
2830 // Add the element offset to the running total offset.
2831 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
2835 // Get the SCEV for the GEP base.
2836 const SCEV *BaseS = getSCEV(Base);
2838 // Add the total offset from all the GEP indices to the base.
2839 return getAddExpr(BaseS, TotalOffset);
2842 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
2843 /// guaranteed to end in (at every loop iteration). It is, at the same time,
2844 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
2845 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
2847 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
2848 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
2849 return C->getValue()->getValue().countTrailingZeros();
2851 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
2852 return std::min(GetMinTrailingZeros(T->getOperand()),
2853 (uint32_t)getTypeSizeInBits(T->getType()));
2855 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
2856 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
2857 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
2858 getTypeSizeInBits(E->getType()) : OpRes;
2861 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
2862 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
2863 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
2864 getTypeSizeInBits(E->getType()) : OpRes;
2867 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
2868 // The result is the min of all operands results.
2869 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
2870 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
2871 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
2875 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
2876 // The result is the sum of all operands results.
2877 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
2878 uint32_t BitWidth = getTypeSizeInBits(M->getType());
2879 for (unsigned i = 1, e = M->getNumOperands();
2880 SumOpRes != BitWidth && i != e; ++i)
2881 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
2886 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
2887 // The result is the min of all operands results.
2888 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
2889 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
2890 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
2894 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
2895 // The result is the min of all operands results.
2896 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
2897 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
2898 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
2902 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
2903 // The result is the min of all operands results.
2904 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
2905 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
2906 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
2910 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
2911 // For a SCEVUnknown, ask ValueTracking.
2912 unsigned BitWidth = getTypeSizeInBits(U->getType());
2913 APInt Mask = APInt::getAllOnesValue(BitWidth);
2914 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
2915 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones);
2916 return Zeros.countTrailingOnes();
2923 /// getUnsignedRange - Determine the unsigned range for a particular SCEV.
2926 ScalarEvolution::getUnsignedRange(const SCEV *S) {
2928 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
2929 return ConstantRange(C->getValue()->getValue());
2931 unsigned BitWidth = getTypeSizeInBits(S->getType());
2932 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
2934 // If the value has known zeros, the maximum unsigned value will have those
2935 // known zeros as well.
2936 uint32_t TZ = GetMinTrailingZeros(S);
2938 ConservativeResult =
2939 ConstantRange(APInt::getMinValue(BitWidth),
2940 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
2942 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
2943 ConstantRange X = getUnsignedRange(Add->getOperand(0));
2944 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
2945 X = X.add(getUnsignedRange(Add->getOperand(i)));
2946 return ConservativeResult.intersectWith(X);
2949 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
2950 ConstantRange X = getUnsignedRange(Mul->getOperand(0));
2951 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
2952 X = X.multiply(getUnsignedRange(Mul->getOperand(i)));
2953 return ConservativeResult.intersectWith(X);
2956 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
2957 ConstantRange X = getUnsignedRange(SMax->getOperand(0));
2958 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
2959 X = X.smax(getUnsignedRange(SMax->getOperand(i)));
2960 return ConservativeResult.intersectWith(X);
2963 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
2964 ConstantRange X = getUnsignedRange(UMax->getOperand(0));
2965 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
2966 X = X.umax(getUnsignedRange(UMax->getOperand(i)));
2967 return ConservativeResult.intersectWith(X);
2970 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
2971 ConstantRange X = getUnsignedRange(UDiv->getLHS());
2972 ConstantRange Y = getUnsignedRange(UDiv->getRHS());
2973 return ConservativeResult.intersectWith(X.udiv(Y));
2976 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
2977 ConstantRange X = getUnsignedRange(ZExt->getOperand());
2978 return ConservativeResult.intersectWith(X.zeroExtend(BitWidth));
2981 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
2982 ConstantRange X = getUnsignedRange(SExt->getOperand());
2983 return ConservativeResult.intersectWith(X.signExtend(BitWidth));
2986 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
2987 ConstantRange X = getUnsignedRange(Trunc->getOperand());
2988 return ConservativeResult.intersectWith(X.truncate(BitWidth));
2991 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
2992 // If there's no unsigned wrap, the value will never be less than its
2994 if (AddRec->hasNoUnsignedWrap())
2995 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
2996 if (!C->getValue()->isZero())
2997 ConservativeResult =
2998 ConservativeResult.intersectWith(
2999 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0)));
3001 // TODO: non-affine addrec
3002 if (AddRec->isAffine()) {
3003 const Type *Ty = AddRec->getType();
3004 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3005 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3006 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3007 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3009 const SCEV *Start = AddRec->getStart();
3010 const SCEV *Step = AddRec->getStepRecurrence(*this);
3012 ConstantRange StartRange = getUnsignedRange(Start);
3013 ConstantRange StepRange = getSignedRange(Step);
3014 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3015 ConstantRange EndRange =
3016 StartRange.add(MaxBECountRange.multiply(StepRange));
3018 // Check for overflow. This must be done with ConstantRange arithmetic
3019 // because we could be called from within the ScalarEvolution overflow
3021 ConstantRange ExtStartRange = StartRange.zextOrTrunc(BitWidth*2+1);
3022 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3023 ConstantRange ExtMaxBECountRange =
3024 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3025 ConstantRange ExtEndRange = EndRange.zextOrTrunc(BitWidth*2+1);
3026 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3028 return ConservativeResult;
3030 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(),
3031 EndRange.getUnsignedMin());
3032 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(),
3033 EndRange.getUnsignedMax());
3034 if (Min.isMinValue() && Max.isMaxValue())
3035 return ConservativeResult;
3036 return ConservativeResult.intersectWith(ConstantRange(Min, Max+1));
3040 return ConservativeResult;
3043 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3044 // For a SCEVUnknown, ask ValueTracking.
3045 APInt Mask = APInt::getAllOnesValue(BitWidth);
3046 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3047 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones, TD);
3048 if (Ones == ~Zeros + 1)
3049 return ConservativeResult;
3050 return ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1));
3053 return ConservativeResult;
3056 /// getSignedRange - Determine the signed range for a particular SCEV.
3059 ScalarEvolution::getSignedRange(const SCEV *S) {
3061 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3062 return ConstantRange(C->getValue()->getValue());
3064 unsigned BitWidth = getTypeSizeInBits(S->getType());
3065 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3067 // If the value has known zeros, the maximum signed value will have those
3068 // known zeros as well.
3069 uint32_t TZ = GetMinTrailingZeros(S);
3071 ConservativeResult =
3072 ConstantRange(APInt::getSignedMinValue(BitWidth),
3073 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
3075 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3076 ConstantRange X = getSignedRange(Add->getOperand(0));
3077 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3078 X = X.add(getSignedRange(Add->getOperand(i)));
3079 return ConservativeResult.intersectWith(X);
3082 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3083 ConstantRange X = getSignedRange(Mul->getOperand(0));
3084 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3085 X = X.multiply(getSignedRange(Mul->getOperand(i)));
3086 return ConservativeResult.intersectWith(X);
3089 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3090 ConstantRange X = getSignedRange(SMax->getOperand(0));
3091 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3092 X = X.smax(getSignedRange(SMax->getOperand(i)));
3093 return ConservativeResult.intersectWith(X);
3096 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3097 ConstantRange X = getSignedRange(UMax->getOperand(0));
3098 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3099 X = X.umax(getSignedRange(UMax->getOperand(i)));
3100 return ConservativeResult.intersectWith(X);
3103 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3104 ConstantRange X = getSignedRange(UDiv->getLHS());
3105 ConstantRange Y = getSignedRange(UDiv->getRHS());
3106 return ConservativeResult.intersectWith(X.udiv(Y));
3109 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3110 ConstantRange X = getSignedRange(ZExt->getOperand());
3111 return ConservativeResult.intersectWith(X.zeroExtend(BitWidth));
3114 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3115 ConstantRange X = getSignedRange(SExt->getOperand());
3116 return ConservativeResult.intersectWith(X.signExtend(BitWidth));
3119 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3120 ConstantRange X = getSignedRange(Trunc->getOperand());
3121 return ConservativeResult.intersectWith(X.truncate(BitWidth));
3124 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3125 // If there's no signed wrap, and all the operands have the same sign or
3126 // zero, the value won't ever change sign.
3127 if (AddRec->hasNoSignedWrap()) {
3128 bool AllNonNeg = true;
3129 bool AllNonPos = true;
3130 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
3131 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
3132 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
3135 ConservativeResult = ConservativeResult.intersectWith(
3136 ConstantRange(APInt(BitWidth, 0),
3137 APInt::getSignedMinValue(BitWidth)));
3139 ConservativeResult = ConservativeResult.intersectWith(
3140 ConstantRange(APInt::getSignedMinValue(BitWidth),
3141 APInt(BitWidth, 1)));
3144 // TODO: non-affine addrec
3145 if (AddRec->isAffine()) {
3146 const Type *Ty = AddRec->getType();
3147 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3148 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3149 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3150 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3152 const SCEV *Start = AddRec->getStart();
3153 const SCEV *Step = AddRec->getStepRecurrence(*this);
3155 ConstantRange StartRange = getSignedRange(Start);
3156 ConstantRange StepRange = getSignedRange(Step);
3157 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3158 ConstantRange EndRange =
3159 StartRange.add(MaxBECountRange.multiply(StepRange));
3161 // Check for overflow. This must be done with ConstantRange arithmetic
3162 // because we could be called from within the ScalarEvolution overflow
3164 ConstantRange ExtStartRange = StartRange.sextOrTrunc(BitWidth*2+1);
3165 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3166 ConstantRange ExtMaxBECountRange =
3167 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3168 ConstantRange ExtEndRange = EndRange.sextOrTrunc(BitWidth*2+1);
3169 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3171 return ConservativeResult;
3173 APInt Min = APIntOps::smin(StartRange.getSignedMin(),
3174 EndRange.getSignedMin());
3175 APInt Max = APIntOps::smax(StartRange.getSignedMax(),
3176 EndRange.getSignedMax());
3177 if (Min.isMinSignedValue() && Max.isMaxSignedValue())
3178 return ConservativeResult;
3179 return ConservativeResult.intersectWith(ConstantRange(Min, Max+1));
3183 return ConservativeResult;
3186 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3187 // For a SCEVUnknown, ask ValueTracking.
3188 if (!U->getValue()->getType()->isIntegerTy() && !TD)
3189 return ConservativeResult;
3190 unsigned NS = ComputeNumSignBits(U->getValue(), TD);
3192 return ConservativeResult;
3193 return ConservativeResult.intersectWith(
3194 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
3195 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1));
3198 return ConservativeResult;
3201 /// createSCEV - We know that there is no SCEV for the specified value.
3202 /// Analyze the expression.
3204 const SCEV *ScalarEvolution::createSCEV(Value *V) {
3205 if (!isSCEVable(V->getType()))
3206 return getUnknown(V);
3208 unsigned Opcode = Instruction::UserOp1;
3209 if (Instruction *I = dyn_cast<Instruction>(V)) {
3210 Opcode = I->getOpcode();
3212 // Don't attempt to analyze instructions in blocks that aren't
3213 // reachable. Such instructions don't matter, and they aren't required
3214 // to obey basic rules for definitions dominating uses which this
3215 // analysis depends on.
3216 if (!DT->isReachableFromEntry(I->getParent()))
3217 return getUnknown(V);
3218 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
3219 Opcode = CE->getOpcode();
3220 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
3221 return getConstant(CI);
3222 else if (isa<ConstantPointerNull>(V))
3223 return getConstant(V->getType(), 0);
3224 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
3225 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee());
3227 return getUnknown(V);
3229 Operator *U = cast<Operator>(V);
3231 case Instruction::Add:
3232 return getAddExpr(getSCEV(U->getOperand(0)),
3233 getSCEV(U->getOperand(1)));
3234 case Instruction::Mul:
3235 return getMulExpr(getSCEV(U->getOperand(0)),
3236 getSCEV(U->getOperand(1)));
3237 case Instruction::UDiv:
3238 return getUDivExpr(getSCEV(U->getOperand(0)),
3239 getSCEV(U->getOperand(1)));
3240 case Instruction::Sub:
3241 return getMinusSCEV(getSCEV(U->getOperand(0)),
3242 getSCEV(U->getOperand(1)));
3243 case Instruction::And:
3244 // For an expression like x&255 that merely masks off the high bits,
3245 // use zext(trunc(x)) as the SCEV expression.
3246 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3247 if (CI->isNullValue())
3248 return getSCEV(U->getOperand(1));
3249 if (CI->isAllOnesValue())
3250 return getSCEV(U->getOperand(0));
3251 const APInt &A = CI->getValue();
3253 // Instcombine's ShrinkDemandedConstant may strip bits out of
3254 // constants, obscuring what would otherwise be a low-bits mask.
3255 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant
3256 // knew about to reconstruct a low-bits mask value.
3257 unsigned LZ = A.countLeadingZeros();
3258 unsigned BitWidth = A.getBitWidth();
3259 APInt AllOnes = APInt::getAllOnesValue(BitWidth);
3260 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
3261 ComputeMaskedBits(U->getOperand(0), AllOnes, KnownZero, KnownOne, TD);
3263 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ);
3265 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask))
3267 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)),
3268 IntegerType::get(getContext(), BitWidth - LZ)),
3273 case Instruction::Or:
3274 // If the RHS of the Or is a constant, we may have something like:
3275 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
3276 // optimizations will transparently handle this case.
3278 // In order for this transformation to be safe, the LHS must be of the
3279 // form X*(2^n) and the Or constant must be less than 2^n.
3280 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3281 const SCEV *LHS = getSCEV(U->getOperand(0));
3282 const APInt &CIVal = CI->getValue();
3283 if (GetMinTrailingZeros(LHS) >=
3284 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
3285 // Build a plain add SCEV.
3286 const SCEV *S = getAddExpr(LHS, getSCEV(CI));
3287 // If the LHS of the add was an addrec and it has no-wrap flags,
3288 // transfer the no-wrap flags, since an or won't introduce a wrap.
3289 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
3290 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
3291 if (OldAR->hasNoUnsignedWrap())
3292 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoUnsignedWrap(true);
3293 if (OldAR->hasNoSignedWrap())
3294 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoSignedWrap(true);
3300 case Instruction::Xor:
3301 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3302 // If the RHS of the xor is a signbit, then this is just an add.
3303 // Instcombine turns add of signbit into xor as a strength reduction step.
3304 if (CI->getValue().isSignBit())
3305 return getAddExpr(getSCEV(U->getOperand(0)),
3306 getSCEV(U->getOperand(1)));
3308 // If the RHS of xor is -1, then this is a not operation.
3309 if (CI->isAllOnesValue())
3310 return getNotSCEV(getSCEV(U->getOperand(0)));
3312 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
3313 // This is a variant of the check for xor with -1, and it handles
3314 // the case where instcombine has trimmed non-demanded bits out
3315 // of an xor with -1.
3316 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
3317 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
3318 if (BO->getOpcode() == Instruction::And &&
3319 LCI->getValue() == CI->getValue())
3320 if (const SCEVZeroExtendExpr *Z =
3321 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
3322 const Type *UTy = U->getType();
3323 const SCEV *Z0 = Z->getOperand();
3324 const Type *Z0Ty = Z0->getType();
3325 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
3327 // If C is a low-bits mask, the zero extend is serving to
3328 // mask off the high bits. Complement the operand and
3329 // re-apply the zext.
3330 if (APIntOps::isMask(Z0TySize, CI->getValue()))
3331 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
3333 // If C is a single bit, it may be in the sign-bit position
3334 // before the zero-extend. In this case, represent the xor
3335 // using an add, which is equivalent, and re-apply the zext.
3336 APInt Trunc = APInt(CI->getValue()).trunc(Z0TySize);
3337 if (APInt(Trunc).zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
3339 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
3345 case Instruction::Shl:
3346 // Turn shift left of a constant amount into a multiply.
3347 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3348 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3350 // If the shift count is not less than the bitwidth, the result of
3351 // the shift is undefined. Don't try to analyze it, because the
3352 // resolution chosen here may differ from the resolution chosen in
3353 // other parts of the compiler.
3354 if (SA->getValue().uge(BitWidth))
3357 Constant *X = ConstantInt::get(getContext(),
3358 APInt(BitWidth, 1).shl(SA->getZExtValue()));
3359 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3363 case Instruction::LShr:
3364 // Turn logical shift right of a constant into a unsigned divide.
3365 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3366 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3368 // If the shift count is not less than the bitwidth, the result of
3369 // the shift is undefined. Don't try to analyze it, because the
3370 // resolution chosen here may differ from the resolution chosen in
3371 // other parts of the compiler.
3372 if (SA->getValue().uge(BitWidth))
3375 Constant *X = ConstantInt::get(getContext(),
3376 APInt(BitWidth, 1).shl(SA->getZExtValue()));
3377 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3381 case Instruction::AShr:
3382 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
3383 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
3384 if (Operator *L = dyn_cast<Operator>(U->getOperand(0)))
3385 if (L->getOpcode() == Instruction::Shl &&
3386 L->getOperand(1) == U->getOperand(1)) {
3387 uint64_t BitWidth = getTypeSizeInBits(U->getType());
3389 // If the shift count is not less than the bitwidth, the result of
3390 // the shift is undefined. Don't try to analyze it, because the
3391 // resolution chosen here may differ from the resolution chosen in
3392 // other parts of the compiler.
3393 if (CI->getValue().uge(BitWidth))
3396 uint64_t Amt = BitWidth - CI->getZExtValue();
3397 if (Amt == BitWidth)
3398 return getSCEV(L->getOperand(0)); // shift by zero --> noop
3400 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
3401 IntegerType::get(getContext(),
3407 case Instruction::Trunc:
3408 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
3410 case Instruction::ZExt:
3411 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3413 case Instruction::SExt:
3414 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3416 case Instruction::BitCast:
3417 // BitCasts are no-op casts so we just eliminate the cast.
3418 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
3419 return getSCEV(U->getOperand(0));
3422 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
3423 // lead to pointer expressions which cannot safely be expanded to GEPs,
3424 // because ScalarEvolution doesn't respect the GEP aliasing rules when
3425 // simplifying integer expressions.
3427 case Instruction::GetElementPtr:
3428 return createNodeForGEP(cast<GEPOperator>(U));
3430 case Instruction::PHI:
3431 return createNodeForPHI(cast<PHINode>(U));
3433 case Instruction::Select:
3434 // This could be a smax or umax that was lowered earlier.
3435 // Try to recover it.
3436 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
3437 Value *LHS = ICI->getOperand(0);
3438 Value *RHS = ICI->getOperand(1);
3439 switch (ICI->getPredicate()) {
3440 case ICmpInst::ICMP_SLT:
3441 case ICmpInst::ICMP_SLE:
3442 std::swap(LHS, RHS);
3444 case ICmpInst::ICMP_SGT:
3445 case ICmpInst::ICMP_SGE:
3446 // a >s b ? a+x : b+x -> smax(a, b)+x
3447 // a >s b ? b+x : a+x -> smin(a, b)+x
3448 if (LHS->getType() == U->getType()) {
3449 const SCEV *LS = getSCEV(LHS);
3450 const SCEV *RS = getSCEV(RHS);
3451 const SCEV *LA = getSCEV(U->getOperand(1));
3452 const SCEV *RA = getSCEV(U->getOperand(2));
3453 const SCEV *LDiff = getMinusSCEV(LA, LS);
3454 const SCEV *RDiff = getMinusSCEV(RA, RS);
3456 return getAddExpr(getSMaxExpr(LS, RS), LDiff);
3457 LDiff = getMinusSCEV(LA, RS);
3458 RDiff = getMinusSCEV(RA, LS);
3460 return getAddExpr(getSMinExpr(LS, RS), LDiff);
3463 case ICmpInst::ICMP_ULT:
3464 case ICmpInst::ICMP_ULE:
3465 std::swap(LHS, RHS);
3467 case ICmpInst::ICMP_UGT:
3468 case ICmpInst::ICMP_UGE:
3469 // a >u b ? a+x : b+x -> umax(a, b)+x
3470 // a >u b ? b+x : a+x -> umin(a, b)+x
3471 if (LHS->getType() == U->getType()) {
3472 const SCEV *LS = getSCEV(LHS);
3473 const SCEV *RS = getSCEV(RHS);
3474 const SCEV *LA = getSCEV(U->getOperand(1));
3475 const SCEV *RA = getSCEV(U->getOperand(2));
3476 const SCEV *LDiff = getMinusSCEV(LA, LS);
3477 const SCEV *RDiff = getMinusSCEV(RA, RS);
3479 return getAddExpr(getUMaxExpr(LS, RS), LDiff);
3480 LDiff = getMinusSCEV(LA, RS);
3481 RDiff = getMinusSCEV(RA, LS);
3483 return getAddExpr(getUMinExpr(LS, RS), LDiff);
3486 case ICmpInst::ICMP_NE:
3487 // n != 0 ? n+x : 1+x -> umax(n, 1)+x
3488 if (LHS->getType() == U->getType() &&
3489 isa<ConstantInt>(RHS) &&
3490 cast<ConstantInt>(RHS)->isZero()) {
3491 const SCEV *One = getConstant(LHS->getType(), 1);
3492 const SCEV *LS = getSCEV(LHS);
3493 const SCEV *LA = getSCEV(U->getOperand(1));
3494 const SCEV *RA = getSCEV(U->getOperand(2));
3495 const SCEV *LDiff = getMinusSCEV(LA, LS);
3496 const SCEV *RDiff = getMinusSCEV(RA, One);
3498 return getAddExpr(getUMaxExpr(LS, One), LDiff);
3501 case ICmpInst::ICMP_EQ:
3502 // n == 0 ? 1+x : n+x -> umax(n, 1)+x
3503 if (LHS->getType() == U->getType() &&
3504 isa<ConstantInt>(RHS) &&
3505 cast<ConstantInt>(RHS)->isZero()) {
3506 const SCEV *One = getConstant(LHS->getType(), 1);
3507 const SCEV *LS = getSCEV(LHS);
3508 const SCEV *LA = getSCEV(U->getOperand(1));
3509 const SCEV *RA = getSCEV(U->getOperand(2));
3510 const SCEV *LDiff = getMinusSCEV(LA, One);
3511 const SCEV *RDiff = getMinusSCEV(RA, LS);
3513 return getAddExpr(getUMaxExpr(LS, One), LDiff);
3521 default: // We cannot analyze this expression.
3525 return getUnknown(V);
3530 //===----------------------------------------------------------------------===//
3531 // Iteration Count Computation Code
3534 /// getBackedgeTakenCount - If the specified loop has a predictable
3535 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
3536 /// object. The backedge-taken count is the number of times the loop header
3537 /// will be branched to from within the loop. This is one less than the
3538 /// trip count of the loop, since it doesn't count the first iteration,
3539 /// when the header is branched to from outside the loop.
3541 /// Note that it is not valid to call this method on a loop without a
3542 /// loop-invariant backedge-taken count (see
3543 /// hasLoopInvariantBackedgeTakenCount).
3545 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
3546 return getBackedgeTakenInfo(L).Exact;
3549 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
3550 /// return the least SCEV value that is known never to be less than the
3551 /// actual backedge taken count.
3552 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
3553 return getBackedgeTakenInfo(L).Max;
3556 /// PushLoopPHIs - Push PHI nodes in the header of the given loop
3557 /// onto the given Worklist.
3559 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
3560 BasicBlock *Header = L->getHeader();
3562 // Push all Loop-header PHIs onto the Worklist stack.
3563 for (BasicBlock::iterator I = Header->begin();
3564 PHINode *PN = dyn_cast<PHINode>(I); ++I)
3565 Worklist.push_back(PN);
3568 const ScalarEvolution::BackedgeTakenInfo &
3569 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
3570 // Initially insert a CouldNotCompute for this loop. If the insertion
3571 // succeeds, proceed to actually compute a backedge-taken count and
3572 // update the value. The temporary CouldNotCompute value tells SCEV
3573 // code elsewhere that it shouldn't attempt to request a new
3574 // backedge-taken count, which could result in infinite recursion.
3575 std::pair<std::map<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
3576 BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute()));
3578 BackedgeTakenInfo BECount = ComputeBackedgeTakenCount(L);
3579 if (BECount.Exact != getCouldNotCompute()) {
3580 assert(BECount.Exact->isLoopInvariant(L) &&
3581 BECount.Max->isLoopInvariant(L) &&
3582 "Computed backedge-taken count isn't loop invariant for loop!");
3583 ++NumTripCountsComputed;
3585 // Update the value in the map.
3586 Pair.first->second = BECount;
3588 if (BECount.Max != getCouldNotCompute())
3589 // Update the value in the map.
3590 Pair.first->second = BECount;
3591 if (isa<PHINode>(L->getHeader()->begin()))
3592 // Only count loops that have phi nodes as not being computable.
3593 ++NumTripCountsNotComputed;
3596 // Now that we know more about the trip count for this loop, forget any
3597 // existing SCEV values for PHI nodes in this loop since they are only
3598 // conservative estimates made without the benefit of trip count
3599 // information. This is similar to the code in forgetLoop, except that
3600 // it handles SCEVUnknown PHI nodes specially.
3601 if (BECount.hasAnyInfo()) {
3602 SmallVector<Instruction *, 16> Worklist;
3603 PushLoopPHIs(L, Worklist);
3605 SmallPtrSet<Instruction *, 8> Visited;
3606 while (!Worklist.empty()) {
3607 Instruction *I = Worklist.pop_back_val();
3608 if (!Visited.insert(I)) continue;
3610 std::map<SCEVCallbackVH, const SCEV *>::iterator It =
3611 Scalars.find(static_cast<Value *>(I));
3612 if (It != Scalars.end()) {
3613 // SCEVUnknown for a PHI either means that it has an unrecognized
3614 // structure, or it's a PHI that's in the progress of being computed
3615 // by createNodeForPHI. In the former case, additional loop trip
3616 // count information isn't going to change anything. In the later
3617 // case, createNodeForPHI will perform the necessary updates on its
3618 // own when it gets to that point.
3619 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(It->second)) {
3620 ValuesAtScopes.erase(It->second);
3623 if (PHINode *PN = dyn_cast<PHINode>(I))
3624 ConstantEvolutionLoopExitValue.erase(PN);
3627 PushDefUseChildren(I, Worklist);
3631 return Pair.first->second;
3634 /// forgetLoop - This method should be called by the client when it has
3635 /// changed a loop in a way that may effect ScalarEvolution's ability to
3636 /// compute a trip count, or if the loop is deleted.
3637 void ScalarEvolution::forgetLoop(const Loop *L) {
3638 // Drop any stored trip count value.
3639 BackedgeTakenCounts.erase(L);
3641 // Drop information about expressions based on loop-header PHIs.
3642 SmallVector<Instruction *, 16> Worklist;
3643 PushLoopPHIs(L, Worklist);
3645 SmallPtrSet<Instruction *, 8> Visited;
3646 while (!Worklist.empty()) {
3647 Instruction *I = Worklist.pop_back_val();
3648 if (!Visited.insert(I)) continue;
3650 std::map<SCEVCallbackVH, const SCEV *>::iterator It =
3651 Scalars.find(static_cast<Value *>(I));
3652 if (It != Scalars.end()) {
3653 ValuesAtScopes.erase(It->second);
3655 if (PHINode *PN = dyn_cast<PHINode>(I))
3656 ConstantEvolutionLoopExitValue.erase(PN);
3659 PushDefUseChildren(I, Worklist);
3663 /// forgetValue - This method should be called by the client when it has
3664 /// changed a value in a way that may effect its value, or which may
3665 /// disconnect it from a def-use chain linking it to a loop.
3666 void ScalarEvolution::forgetValue(Value *V) {
3667 // If there's a SCEVUnknown tying this value into the SCEV
3668 // space, remove it from the folding set map. The SCEVUnknown
3669 // object and any other SCEV objects which reference it
3670 // (transitively) remain allocated, effectively leaked until
3671 // the underlying BumpPtrAllocator is freed.
3673 // This permits SCEV pointers to be used as keys in maps
3674 // such as the ValuesAtScopes map.
3675 FoldingSetNodeID ID;
3676 ID.AddInteger(scUnknown);
3679 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
3680 UniqueSCEVs.RemoveNode(S);
3682 // This isn't necessary, but we might as well remove the
3683 // value from the ValuesAtScopes map too.
3684 ValuesAtScopes.erase(S);
3687 Instruction *I = dyn_cast<Instruction>(V);
3690 // Drop information about expressions based on loop-header PHIs.
3691 SmallVector<Instruction *, 16> Worklist;
3692 Worklist.push_back(I);
3694 SmallPtrSet<Instruction *, 8> Visited;
3695 while (!Worklist.empty()) {
3696 I = Worklist.pop_back_val();
3697 if (!Visited.insert(I)) continue;
3699 std::map<SCEVCallbackVH, const SCEV *>::iterator It =
3700 Scalars.find(static_cast<Value *>(I));
3701 if (It != Scalars.end()) {
3702 ValuesAtScopes.erase(It->second);
3704 if (PHINode *PN = dyn_cast<PHINode>(I))
3705 ConstantEvolutionLoopExitValue.erase(PN);
3708 PushDefUseChildren(I, Worklist);
3712 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
3713 /// of the specified loop will execute.
3714 ScalarEvolution::BackedgeTakenInfo
3715 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
3716 SmallVector<BasicBlock *, 8> ExitingBlocks;
3717 L->getExitingBlocks(ExitingBlocks);
3719 // Examine all exits and pick the most conservative values.
3720 const SCEV *BECount = getCouldNotCompute();
3721 const SCEV *MaxBECount = getCouldNotCompute();
3722 bool CouldNotComputeBECount = false;
3723 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
3724 BackedgeTakenInfo NewBTI =
3725 ComputeBackedgeTakenCountFromExit(L, ExitingBlocks[i]);
3727 if (NewBTI.Exact == getCouldNotCompute()) {
3728 // We couldn't compute an exact value for this exit, so
3729 // we won't be able to compute an exact value for the loop.
3730 CouldNotComputeBECount = true;
3731 BECount = getCouldNotCompute();
3732 } else if (!CouldNotComputeBECount) {
3733 if (BECount == getCouldNotCompute())
3734 BECount = NewBTI.Exact;
3736 BECount = getUMinFromMismatchedTypes(BECount, NewBTI.Exact);
3738 if (MaxBECount == getCouldNotCompute())
3739 MaxBECount = NewBTI.Max;
3740 else if (NewBTI.Max != getCouldNotCompute())
3741 MaxBECount = getUMinFromMismatchedTypes(MaxBECount, NewBTI.Max);
3744 return BackedgeTakenInfo(BECount, MaxBECount);
3747 /// ComputeBackedgeTakenCountFromExit - Compute the number of times the backedge
3748 /// of the specified loop will execute if it exits via the specified block.
3749 ScalarEvolution::BackedgeTakenInfo
3750 ScalarEvolution::ComputeBackedgeTakenCountFromExit(const Loop *L,
3751 BasicBlock *ExitingBlock) {
3753 // Okay, we've chosen an exiting block. See what condition causes us to
3754 // exit at this block.
3756 // FIXME: we should be able to handle switch instructions (with a single exit)
3757 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
3758 if (ExitBr == 0) return getCouldNotCompute();
3759 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
3761 // At this point, we know we have a conditional branch that determines whether
3762 // the loop is exited. However, we don't know if the branch is executed each
3763 // time through the loop. If not, then the execution count of the branch will
3764 // not be equal to the trip count of the loop.
3766 // Currently we check for this by checking to see if the Exit branch goes to
3767 // the loop header. If so, we know it will always execute the same number of
3768 // times as the loop. We also handle the case where the exit block *is* the
3769 // loop header. This is common for un-rotated loops.
3771 // If both of those tests fail, walk up the unique predecessor chain to the
3772 // header, stopping if there is an edge that doesn't exit the loop. If the
3773 // header is reached, the execution count of the branch will be equal to the
3774 // trip count of the loop.
3776 // More extensive analysis could be done to handle more cases here.
3778 if (ExitBr->getSuccessor(0) != L->getHeader() &&
3779 ExitBr->getSuccessor(1) != L->getHeader() &&
3780 ExitBr->getParent() != L->getHeader()) {
3781 // The simple checks failed, try climbing the unique predecessor chain
3782 // up to the header.
3784 for (BasicBlock *BB = ExitBr->getParent(); BB; ) {
3785 BasicBlock *Pred = BB->getUniquePredecessor();
3787 return getCouldNotCompute();
3788 TerminatorInst *PredTerm = Pred->getTerminator();
3789 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) {
3790 BasicBlock *PredSucc = PredTerm->getSuccessor(i);
3793 // If the predecessor has a successor that isn't BB and isn't
3794 // outside the loop, assume the worst.
3795 if (L->contains(PredSucc))
3796 return getCouldNotCompute();
3798 if (Pred == L->getHeader()) {
3805 return getCouldNotCompute();
3808 // Proceed to the next level to examine the exit condition expression.
3809 return ComputeBackedgeTakenCountFromExitCond(L, ExitBr->getCondition(),
3810 ExitBr->getSuccessor(0),
3811 ExitBr->getSuccessor(1));
3814 /// ComputeBackedgeTakenCountFromExitCond - Compute the number of times the
3815 /// backedge of the specified loop will execute if its exit condition
3816 /// were a conditional branch of ExitCond, TBB, and FBB.
3817 ScalarEvolution::BackedgeTakenInfo
3818 ScalarEvolution::ComputeBackedgeTakenCountFromExitCond(const Loop *L,
3822 // Check if the controlling expression for this loop is an And or Or.
3823 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
3824 if (BO->getOpcode() == Instruction::And) {
3825 // Recurse on the operands of the and.
3826 BackedgeTakenInfo BTI0 =
3827 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB);
3828 BackedgeTakenInfo BTI1 =
3829 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB);
3830 const SCEV *BECount = getCouldNotCompute();
3831 const SCEV *MaxBECount = getCouldNotCompute();
3832 if (L->contains(TBB)) {
3833 // Both conditions must be true for the loop to continue executing.
3834 // Choose the less conservative count.
3835 if (BTI0.Exact == getCouldNotCompute() ||
3836 BTI1.Exact == getCouldNotCompute())
3837 BECount = getCouldNotCompute();
3839 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3840 if (BTI0.Max == getCouldNotCompute())
3841 MaxBECount = BTI1.Max;
3842 else if (BTI1.Max == getCouldNotCompute())
3843 MaxBECount = BTI0.Max;
3845 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max);
3847 // Both conditions must be true for the loop to exit.
3848 assert(L->contains(FBB) && "Loop block has no successor in loop!");
3849 if (BTI0.Exact != getCouldNotCompute() &&
3850 BTI1.Exact != getCouldNotCompute())
3851 BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3852 if (BTI0.Max != getCouldNotCompute() &&
3853 BTI1.Max != getCouldNotCompute())
3854 MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max);
3857 return BackedgeTakenInfo(BECount, MaxBECount);
3859 if (BO->getOpcode() == Instruction::Or) {
3860 // Recurse on the operands of the or.
3861 BackedgeTakenInfo BTI0 =
3862 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB);
3863 BackedgeTakenInfo BTI1 =
3864 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB);
3865 const SCEV *BECount = getCouldNotCompute();
3866 const SCEV *MaxBECount = getCouldNotCompute();
3867 if (L->contains(FBB)) {
3868 // Both conditions must be false for the loop to continue executing.
3869 // Choose the less conservative count.
3870 if (BTI0.Exact == getCouldNotCompute() ||
3871 BTI1.Exact == getCouldNotCompute())
3872 BECount = getCouldNotCompute();
3874 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3875 if (BTI0.Max == getCouldNotCompute())
3876 MaxBECount = BTI1.Max;
3877 else if (BTI1.Max == getCouldNotCompute())
3878 MaxBECount = BTI0.Max;
3880 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max);
3882 // Both conditions must be false for the loop to exit.
3883 assert(L->contains(TBB) && "Loop block has no successor in loop!");
3884 if (BTI0.Exact != getCouldNotCompute() &&
3885 BTI1.Exact != getCouldNotCompute())
3886 BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3887 if (BTI0.Max != getCouldNotCompute() &&
3888 BTI1.Max != getCouldNotCompute())
3889 MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max);
3892 return BackedgeTakenInfo(BECount, MaxBECount);
3896 // With an icmp, it may be feasible to compute an exact backedge-taken count.
3897 // Proceed to the next level to examine the icmp.
3898 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
3899 return ComputeBackedgeTakenCountFromExitCondICmp(L, ExitCondICmp, TBB, FBB);
3901 // Check for a constant condition. These are normally stripped out by
3902 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
3903 // preserve the CFG and is temporarily leaving constant conditions
3905 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
3906 if (L->contains(FBB) == !CI->getZExtValue())
3907 // The backedge is always taken.
3908 return getCouldNotCompute();
3910 // The backedge is never taken.
3911 return getConstant(CI->getType(), 0);
3914 // If it's not an integer or pointer comparison then compute it the hard way.
3915 return ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB));
3918 /// ComputeBackedgeTakenCountFromExitCondICmp - Compute the number of times the
3919 /// backedge of the specified loop will execute if its exit condition
3920 /// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB.
3921 ScalarEvolution::BackedgeTakenInfo
3922 ScalarEvolution::ComputeBackedgeTakenCountFromExitCondICmp(const Loop *L,
3927 // If the condition was exit on true, convert the condition to exit on false
3928 ICmpInst::Predicate Cond;
3929 if (!L->contains(FBB))
3930 Cond = ExitCond->getPredicate();
3932 Cond = ExitCond->getInversePredicate();
3934 // Handle common loops like: for (X = "string"; *X; ++X)
3935 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
3936 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
3937 BackedgeTakenInfo ItCnt =
3938 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond);
3939 if (ItCnt.hasAnyInfo())
3943 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
3944 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
3946 // Try to evaluate any dependencies out of the loop.
3947 LHS = getSCEVAtScope(LHS, L);
3948 RHS = getSCEVAtScope(RHS, L);
3950 // At this point, we would like to compute how many iterations of the
3951 // loop the predicate will return true for these inputs.
3952 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) {
3953 // If there is a loop-invariant, force it into the RHS.
3954 std::swap(LHS, RHS);
3955 Cond = ICmpInst::getSwappedPredicate(Cond);
3958 // Simplify the operands before analyzing them.
3959 (void)SimplifyICmpOperands(Cond, LHS, RHS);
3961 // If we have a comparison of a chrec against a constant, try to use value
3962 // ranges to answer this query.
3963 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
3964 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
3965 if (AddRec->getLoop() == L) {
3966 // Form the constant range.
3967 ConstantRange CompRange(
3968 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
3970 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
3971 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
3975 case ICmpInst::ICMP_NE: { // while (X != Y)
3976 // Convert to: while (X-Y != 0)
3977 BackedgeTakenInfo BTI = HowFarToZero(getMinusSCEV(LHS, RHS), L);
3978 if (BTI.hasAnyInfo()) return BTI;
3981 case ICmpInst::ICMP_EQ: { // while (X == Y)
3982 // Convert to: while (X-Y == 0)
3983 BackedgeTakenInfo BTI = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
3984 if (BTI.hasAnyInfo()) return BTI;
3987 case ICmpInst::ICMP_SLT: {
3988 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true);
3989 if (BTI.hasAnyInfo()) return BTI;
3992 case ICmpInst::ICMP_SGT: {
3993 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
3994 getNotSCEV(RHS), L, true);
3995 if (BTI.hasAnyInfo()) return BTI;
3998 case ICmpInst::ICMP_ULT: {
3999 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false);
4000 if (BTI.hasAnyInfo()) return BTI;
4003 case ICmpInst::ICMP_UGT: {
4004 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
4005 getNotSCEV(RHS), L, false);
4006 if (BTI.hasAnyInfo()) return BTI;
4011 dbgs() << "ComputeBackedgeTakenCount ";
4012 if (ExitCond->getOperand(0)->getType()->isUnsigned())
4013 dbgs() << "[unsigned] ";
4014 dbgs() << *LHS << " "
4015 << Instruction::getOpcodeName(Instruction::ICmp)
4016 << " " << *RHS << "\n";
4021 ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB));
4024 static ConstantInt *
4025 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
4026 ScalarEvolution &SE) {
4027 const SCEV *InVal = SE.getConstant(C);
4028 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
4029 assert(isa<SCEVConstant>(Val) &&
4030 "Evaluation of SCEV at constant didn't fold correctly?");
4031 return cast<SCEVConstant>(Val)->getValue();
4034 /// GetAddressedElementFromGlobal - Given a global variable with an initializer
4035 /// and a GEP expression (missing the pointer index) indexing into it, return
4036 /// the addressed element of the initializer or null if the index expression is
4039 GetAddressedElementFromGlobal(GlobalVariable *GV,
4040 const std::vector<ConstantInt*> &Indices) {
4041 Constant *Init = GV->getInitializer();
4042 for (unsigned i = 0, e = Indices.size(); i != e; ++i) {
4043 uint64_t Idx = Indices[i]->getZExtValue();
4044 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) {
4045 assert(Idx < CS->getNumOperands() && "Bad struct index!");
4046 Init = cast<Constant>(CS->getOperand(Idx));
4047 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) {
4048 if (Idx >= CA->getNumOperands()) return 0; // Bogus program
4049 Init = cast<Constant>(CA->getOperand(Idx));
4050 } else if (isa<ConstantAggregateZero>(Init)) {
4051 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) {
4052 assert(Idx < STy->getNumElements() && "Bad struct index!");
4053 Init = Constant::getNullValue(STy->getElementType(Idx));
4054 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) {
4055 if (Idx >= ATy->getNumElements()) return 0; // Bogus program
4056 Init = Constant::getNullValue(ATy->getElementType());
4058 llvm_unreachable("Unknown constant aggregate type!");
4062 return 0; // Unknown initializer type
4068 /// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of
4069 /// 'icmp op load X, cst', try to see if we can compute the backedge
4070 /// execution count.
4071 ScalarEvolution::BackedgeTakenInfo
4072 ScalarEvolution::ComputeLoadConstantCompareBackedgeTakenCount(
4076 ICmpInst::Predicate predicate) {
4077 if (LI->isVolatile()) return getCouldNotCompute();
4079 // Check to see if the loaded pointer is a getelementptr of a global.
4080 // TODO: Use SCEV instead of manually grubbing with GEPs.
4081 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
4082 if (!GEP) return getCouldNotCompute();
4084 // Make sure that it is really a constant global we are gepping, with an
4085 // initializer, and make sure the first IDX is really 0.
4086 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
4087 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
4088 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
4089 !cast<Constant>(GEP->getOperand(1))->isNullValue())
4090 return getCouldNotCompute();
4092 // Okay, we allow one non-constant index into the GEP instruction.
4094 std::vector<ConstantInt*> Indexes;
4095 unsigned VarIdxNum = 0;
4096 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
4097 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
4098 Indexes.push_back(CI);
4099 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
4100 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
4101 VarIdx = GEP->getOperand(i);
4103 Indexes.push_back(0);
4106 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
4107 // Check to see if X is a loop variant variable value now.
4108 const SCEV *Idx = getSCEV(VarIdx);
4109 Idx = getSCEVAtScope(Idx, L);
4111 // We can only recognize very limited forms of loop index expressions, in
4112 // particular, only affine AddRec's like {C1,+,C2}.
4113 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
4114 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) ||
4115 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
4116 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
4117 return getCouldNotCompute();
4119 unsigned MaxSteps = MaxBruteForceIterations;
4120 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
4121 ConstantInt *ItCst = ConstantInt::get(
4122 cast<IntegerType>(IdxExpr->getType()), IterationNum);
4123 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
4125 // Form the GEP offset.
4126 Indexes[VarIdxNum] = Val;
4128 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes);
4129 if (Result == 0) break; // Cannot compute!
4131 // Evaluate the condition for this iteration.
4132 Result = ConstantExpr::getICmp(predicate, Result, RHS);
4133 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
4134 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
4136 dbgs() << "\n***\n*** Computed loop count " << *ItCst
4137 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
4140 ++NumArrayLenItCounts;
4141 return getConstant(ItCst); // Found terminating iteration!
4144 return getCouldNotCompute();
4148 /// CanConstantFold - Return true if we can constant fold an instruction of the
4149 /// specified type, assuming that all operands were constants.
4150 static bool CanConstantFold(const Instruction *I) {
4151 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
4152 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I))
4155 if (const CallInst *CI = dyn_cast<CallInst>(I))
4156 if (const Function *F = CI->getCalledFunction())
4157 return canConstantFoldCallTo(F);
4161 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
4162 /// in the loop that V is derived from. We allow arbitrary operations along the
4163 /// way, but the operands of an operation must either be constants or a value
4164 /// derived from a constant PHI. If this expression does not fit with these
4165 /// constraints, return null.
4166 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
4167 // If this is not an instruction, or if this is an instruction outside of the
4168 // loop, it can't be derived from a loop PHI.
4169 Instruction *I = dyn_cast<Instruction>(V);
4170 if (I == 0 || !L->contains(I)) return 0;
4172 if (PHINode *PN = dyn_cast<PHINode>(I)) {
4173 if (L->getHeader() == I->getParent())
4176 // We don't currently keep track of the control flow needed to evaluate
4177 // PHIs, so we cannot handle PHIs inside of loops.
4181 // If we won't be able to constant fold this expression even if the operands
4182 // are constants, return early.
4183 if (!CanConstantFold(I)) return 0;
4185 // Otherwise, we can evaluate this instruction if all of its operands are
4186 // constant or derived from a PHI node themselves.
4188 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op)
4189 if (!isa<Constant>(I->getOperand(Op))) {
4190 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L);
4191 if (P == 0) return 0; // Not evolving from PHI
4195 return 0; // Evolving from multiple different PHIs.
4198 // This is a expression evolving from a constant PHI!
4202 /// EvaluateExpression - Given an expression that passes the
4203 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
4204 /// in the loop has the value PHIVal. If we can't fold this expression for some
4205 /// reason, return null.
4206 static Constant *EvaluateExpression(Value *V, Constant *PHIVal,
4207 const TargetData *TD) {
4208 if (isa<PHINode>(V)) return PHIVal;
4209 if (Constant *C = dyn_cast<Constant>(V)) return C;
4210 Instruction *I = cast<Instruction>(V);
4212 std::vector<Constant*> Operands(I->getNumOperands());
4214 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
4215 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal, TD);
4216 if (Operands[i] == 0) return 0;
4219 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
4220 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
4222 return ConstantFoldInstOperands(I->getOpcode(), I->getType(),
4223 &Operands[0], Operands.size(), TD);
4226 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
4227 /// in the header of its containing loop, we know the loop executes a
4228 /// constant number of times, and the PHI node is just a recurrence
4229 /// involving constants, fold it.
4231 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
4234 std::map<PHINode*, Constant*>::iterator I =
4235 ConstantEvolutionLoopExitValue.find(PN);
4236 if (I != ConstantEvolutionLoopExitValue.end())
4239 if (BEs.ugt(MaxBruteForceIterations))
4240 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
4242 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
4244 // Since the loop is canonicalized, the PHI node must have two entries. One
4245 // entry must be a constant (coming in from outside of the loop), and the
4246 // second must be derived from the same PHI.
4247 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
4248 Constant *StartCST =
4249 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
4251 return RetVal = 0; // Must be a constant.
4253 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
4254 if (getConstantEvolvingPHI(BEValue, L) != PN &&
4255 !isa<Constant>(BEValue))
4256 return RetVal = 0; // Not derived from same PHI.
4258 // Execute the loop symbolically to determine the exit value.
4259 if (BEs.getActiveBits() >= 32)
4260 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
4262 unsigned NumIterations = BEs.getZExtValue(); // must be in range
4263 unsigned IterationNum = 0;
4264 for (Constant *PHIVal = StartCST; ; ++IterationNum) {
4265 if (IterationNum == NumIterations)
4266 return RetVal = PHIVal; // Got exit value!
4268 // Compute the value of the PHI node for the next iteration.
4269 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD);
4270 if (NextPHI == PHIVal)
4271 return RetVal = NextPHI; // Stopped evolving!
4273 return 0; // Couldn't evaluate!
4278 /// ComputeBackedgeTakenCountExhaustively - If the loop is known to execute a
4279 /// constant number of times (the condition evolves only from constants),
4280 /// try to evaluate a few iterations of the loop until we get the exit
4281 /// condition gets a value of ExitWhen (true or false). If we cannot
4282 /// evaluate the trip count of the loop, return getCouldNotCompute().
4284 ScalarEvolution::ComputeBackedgeTakenCountExhaustively(const Loop *L,
4287 PHINode *PN = getConstantEvolvingPHI(Cond, L);
4288 if (PN == 0) return getCouldNotCompute();
4290 // If the loop is canonicalized, the PHI will have exactly two entries.
4291 // That's the only form we support here.
4292 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
4294 // One entry must be a constant (coming in from outside of the loop), and the
4295 // second must be derived from the same PHI.
4296 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
4297 Constant *StartCST =
4298 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
4299 if (StartCST == 0) return getCouldNotCompute(); // Must be a constant.
4301 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
4302 if (getConstantEvolvingPHI(BEValue, L) != PN &&
4303 !isa<Constant>(BEValue))
4304 return getCouldNotCompute(); // Not derived from same PHI.
4306 // Okay, we find a PHI node that defines the trip count of this loop. Execute
4307 // the loop symbolically to determine when the condition gets a value of
4309 unsigned IterationNum = 0;
4310 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
4311 for (Constant *PHIVal = StartCST;
4312 IterationNum != MaxIterations; ++IterationNum) {
4313 ConstantInt *CondVal =
4314 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal, TD));
4316 // Couldn't symbolically evaluate.
4317 if (!CondVal) return getCouldNotCompute();
4319 if (CondVal->getValue() == uint64_t(ExitWhen)) {
4320 ++NumBruteForceTripCountsComputed;
4321 return getConstant(Type::getInt32Ty(getContext()), IterationNum);
4324 // Compute the value of the PHI node for the next iteration.
4325 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD);
4326 if (NextPHI == 0 || NextPHI == PHIVal)
4327 return getCouldNotCompute();// Couldn't evaluate or not making progress...
4331 // Too many iterations were needed to evaluate.
4332 return getCouldNotCompute();
4335 /// getSCEVAtScope - Return a SCEV expression for the specified value
4336 /// at the specified scope in the program. The L value specifies a loop
4337 /// nest to evaluate the expression at, where null is the top-level or a
4338 /// specified loop is immediately inside of the loop.
4340 /// This method can be used to compute the exit value for a variable defined
4341 /// in a loop by querying what the value will hold in the parent loop.
4343 /// In the case that a relevant loop exit value cannot be computed, the
4344 /// original value V is returned.
4345 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
4346 // Check to see if we've folded this expression at this loop before.
4347 std::map<const Loop *, const SCEV *> &Values = ValuesAtScopes[V];
4348 std::pair<std::map<const Loop *, const SCEV *>::iterator, bool> Pair =
4349 Values.insert(std::make_pair(L, static_cast<const SCEV *>(0)));
4351 return Pair.first->second ? Pair.first->second : V;
4353 // Otherwise compute it.
4354 const SCEV *C = computeSCEVAtScope(V, L);
4355 ValuesAtScopes[V][L] = C;
4359 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
4360 if (isa<SCEVConstant>(V)) return V;
4362 // If this instruction is evolved from a constant-evolving PHI, compute the
4363 // exit value from the loop without using SCEVs.
4364 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
4365 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
4366 const Loop *LI = (*this->LI)[I->getParent()];
4367 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
4368 if (PHINode *PN = dyn_cast<PHINode>(I))
4369 if (PN->getParent() == LI->getHeader()) {
4370 // Okay, there is no closed form solution for the PHI node. Check
4371 // to see if the loop that contains it has a known backedge-taken
4372 // count. If so, we may be able to force computation of the exit
4374 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
4375 if (const SCEVConstant *BTCC =
4376 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
4377 // Okay, we know how many times the containing loop executes. If
4378 // this is a constant evolving PHI node, get the final value at
4379 // the specified iteration number.
4380 Constant *RV = getConstantEvolutionLoopExitValue(PN,
4381 BTCC->getValue()->getValue(),
4383 if (RV) return getSCEV(RV);
4387 // Okay, this is an expression that we cannot symbolically evaluate
4388 // into a SCEV. Check to see if it's possible to symbolically evaluate
4389 // the arguments into constants, and if so, try to constant propagate the
4390 // result. This is particularly useful for computing loop exit values.
4391 if (CanConstantFold(I)) {
4392 SmallVector<Constant *, 4> Operands;
4393 bool MadeImprovement = false;
4394 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
4395 Value *Op = I->getOperand(i);
4396 if (Constant *C = dyn_cast<Constant>(Op)) {
4397 Operands.push_back(C);
4401 // If any of the operands is non-constant and if they are
4402 // non-integer and non-pointer, don't even try to analyze them
4403 // with scev techniques.
4404 if (!isSCEVable(Op->getType()))
4407 const SCEV *OrigV = getSCEV(Op);
4408 const SCEV *OpV = getSCEVAtScope(OrigV, L);
4409 MadeImprovement |= OrigV != OpV;
4412 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV))
4414 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV))
4415 C = dyn_cast<Constant>(SU->getValue());
4417 if (C->getType() != Op->getType())
4418 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
4422 Operands.push_back(C);
4425 // Check to see if getSCEVAtScope actually made an improvement.
4426 if (MadeImprovement) {
4428 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
4429 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
4430 Operands[0], Operands[1], TD);
4432 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
4433 &Operands[0], Operands.size(), TD);
4440 // This is some other type of SCEVUnknown, just return it.
4444 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
4445 // Avoid performing the look-up in the common case where the specified
4446 // expression has no loop-variant portions.
4447 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
4448 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
4449 if (OpAtScope != Comm->getOperand(i)) {
4450 // Okay, at least one of these operands is loop variant but might be
4451 // foldable. Build a new instance of the folded commutative expression.
4452 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
4453 Comm->op_begin()+i);
4454 NewOps.push_back(OpAtScope);
4456 for (++i; i != e; ++i) {
4457 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
4458 NewOps.push_back(OpAtScope);
4460 if (isa<SCEVAddExpr>(Comm))
4461 return getAddExpr(NewOps);
4462 if (isa<SCEVMulExpr>(Comm))
4463 return getMulExpr(NewOps);
4464 if (isa<SCEVSMaxExpr>(Comm))
4465 return getSMaxExpr(NewOps);
4466 if (isa<SCEVUMaxExpr>(Comm))
4467 return getUMaxExpr(NewOps);
4468 llvm_unreachable("Unknown commutative SCEV type!");
4471 // If we got here, all operands are loop invariant.
4475 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
4476 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
4477 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
4478 if (LHS == Div->getLHS() && RHS == Div->getRHS())
4479 return Div; // must be loop invariant
4480 return getUDivExpr(LHS, RHS);
4483 // If this is a loop recurrence for a loop that does not contain L, then we
4484 // are dealing with the final value computed by the loop.
4485 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
4486 // First, attempt to evaluate each operand.
4487 // Avoid performing the look-up in the common case where the specified
4488 // expression has no loop-variant portions.
4489 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
4490 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
4491 if (OpAtScope == AddRec->getOperand(i))
4494 // Okay, at least one of these operands is loop variant but might be
4495 // foldable. Build a new instance of the folded commutative expression.
4496 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(),
4497 AddRec->op_begin()+i);
4498 NewOps.push_back(OpAtScope);
4499 for (++i; i != e; ++i)
4500 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
4502 AddRec = cast<SCEVAddRecExpr>(getAddRecExpr(NewOps, AddRec->getLoop()));
4506 // If the scope is outside the addrec's loop, evaluate it by using the
4507 // loop exit value of the addrec.
4508 if (!AddRec->getLoop()->contains(L)) {
4509 // To evaluate this recurrence, we need to know how many times the AddRec
4510 // loop iterates. Compute this now.
4511 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
4512 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
4514 // Then, evaluate the AddRec.
4515 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
4521 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
4522 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
4523 if (Op == Cast->getOperand())
4524 return Cast; // must be loop invariant
4525 return getZeroExtendExpr(Op, Cast->getType());
4528 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
4529 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
4530 if (Op == Cast->getOperand())
4531 return Cast; // must be loop invariant
4532 return getSignExtendExpr(Op, Cast->getType());
4535 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
4536 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
4537 if (Op == Cast->getOperand())
4538 return Cast; // must be loop invariant
4539 return getTruncateExpr(Op, Cast->getType());
4542 llvm_unreachable("Unknown SCEV type!");
4546 /// getSCEVAtScope - This is a convenience function which does
4547 /// getSCEVAtScope(getSCEV(V), L).
4548 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
4549 return getSCEVAtScope(getSCEV(V), L);
4552 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
4553 /// following equation:
4555 /// A * X = B (mod N)
4557 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
4558 /// A and B isn't important.
4560 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
4561 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
4562 ScalarEvolution &SE) {
4563 uint32_t BW = A.getBitWidth();
4564 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
4565 assert(A != 0 && "A must be non-zero.");
4569 // The gcd of A and N may have only one prime factor: 2. The number of
4570 // trailing zeros in A is its multiplicity
4571 uint32_t Mult2 = A.countTrailingZeros();
4574 // 2. Check if B is divisible by D.
4576 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
4577 // is not less than multiplicity of this prime factor for D.
4578 if (B.countTrailingZeros() < Mult2)
4579 return SE.getCouldNotCompute();
4581 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
4584 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
4585 // bit width during computations.
4586 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
4587 APInt Mod(BW + 1, 0);
4588 Mod.set(BW - Mult2); // Mod = N / D
4589 APInt I = AD.multiplicativeInverse(Mod);
4591 // 4. Compute the minimum unsigned root of the equation:
4592 // I * (B / D) mod (N / D)
4593 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
4595 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
4597 return SE.getConstant(Result.trunc(BW));
4600 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
4601 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
4602 /// might be the same) or two SCEVCouldNotCompute objects.
4604 static std::pair<const SCEV *,const SCEV *>
4605 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
4606 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
4607 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
4608 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
4609 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
4611 // We currently can only solve this if the coefficients are constants.
4612 if (!LC || !MC || !NC) {
4613 const SCEV *CNC = SE.getCouldNotCompute();
4614 return std::make_pair(CNC, CNC);
4617 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
4618 const APInt &L = LC->getValue()->getValue();
4619 const APInt &M = MC->getValue()->getValue();
4620 const APInt &N = NC->getValue()->getValue();
4621 APInt Two(BitWidth, 2);
4622 APInt Four(BitWidth, 4);
4625 using namespace APIntOps;
4627 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
4628 // The B coefficient is M-N/2
4632 // The A coefficient is N/2
4633 APInt A(N.sdiv(Two));
4635 // Compute the B^2-4ac term.
4638 SqrtTerm -= Four * (A * C);
4640 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
4641 // integer value or else APInt::sqrt() will assert.
4642 APInt SqrtVal(SqrtTerm.sqrt());
4644 // Compute the two solutions for the quadratic formula.
4645 // The divisions must be performed as signed divisions.
4647 APInt TwoA( A << 1 );
4648 if (TwoA.isMinValue()) {
4649 const SCEV *CNC = SE.getCouldNotCompute();
4650 return std::make_pair(CNC, CNC);
4653 LLVMContext &Context = SE.getContext();
4655 ConstantInt *Solution1 =
4656 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
4657 ConstantInt *Solution2 =
4658 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
4660 return std::make_pair(SE.getConstant(Solution1),
4661 SE.getConstant(Solution2));
4662 } // end APIntOps namespace
4665 /// HowFarToZero - Return the number of times a backedge comparing the specified
4666 /// value to zero will execute. If not computable, return CouldNotCompute.
4667 ScalarEvolution::BackedgeTakenInfo
4668 ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) {
4669 // If the value is a constant
4670 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
4671 // If the value is already zero, the branch will execute zero times.
4672 if (C->getValue()->isZero()) return C;
4673 return getCouldNotCompute(); // Otherwise it will loop infinitely.
4676 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
4677 if (!AddRec || AddRec->getLoop() != L)
4678 return getCouldNotCompute();
4680 if (AddRec->isAffine()) {
4681 // If this is an affine expression, the execution count of this branch is
4682 // the minimum unsigned root of the following equation:
4684 // Start + Step*N = 0 (mod 2^BW)
4688 // Step*N = -Start (mod 2^BW)
4690 // where BW is the common bit width of Start and Step.
4692 // Get the initial value for the loop.
4693 const SCEV *Start = getSCEVAtScope(AddRec->getStart(),
4694 L->getParentLoop());
4695 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1),
4696 L->getParentLoop());
4698 if (const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) {
4699 // For now we handle only constant steps.
4701 // First, handle unitary steps.
4702 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so:
4703 return getNegativeSCEV(Start); // N = -Start (as unsigned)
4704 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so:
4705 return Start; // N = Start (as unsigned)
4707 // Then, try to solve the above equation provided that Start is constant.
4708 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
4709 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
4710 -StartC->getValue()->getValue(),
4713 } else if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
4714 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
4715 // the quadratic equation to solve it.
4716 std::pair<const SCEV *,const SCEV *> Roots = SolveQuadraticEquation(AddRec,
4718 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
4719 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
4722 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1
4723 << " sol#2: " << *R2 << "\n";
4725 // Pick the smallest positive root value.
4726 if (ConstantInt *CB =
4727 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
4728 R1->getValue(), R2->getValue()))) {
4729 if (CB->getZExtValue() == false)
4730 std::swap(R1, R2); // R1 is the minimum root now.
4732 // We can only use this value if the chrec ends up with an exact zero
4733 // value at this index. When solving for "X*X != 5", for example, we
4734 // should not accept a root of 2.
4735 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
4737 return R1; // We found a quadratic root!
4742 return getCouldNotCompute();
4745 /// HowFarToNonZero - Return the number of times a backedge checking the
4746 /// specified value for nonzero will execute. If not computable, return
4748 ScalarEvolution::BackedgeTakenInfo
4749 ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
4750 // Loops that look like: while (X == 0) are very strange indeed. We don't
4751 // handle them yet except for the trivial case. This could be expanded in the
4752 // future as needed.
4754 // If the value is a constant, check to see if it is known to be non-zero
4755 // already. If so, the backedge will execute zero times.
4756 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
4757 if (!C->getValue()->isNullValue())
4758 return getConstant(C->getType(), 0);
4759 return getCouldNotCompute(); // Otherwise it will loop infinitely.
4762 // We could implement others, but I really doubt anyone writes loops like
4763 // this, and if they did, they would already be constant folded.
4764 return getCouldNotCompute();
4767 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
4768 /// (which may not be an immediate predecessor) which has exactly one
4769 /// successor from which BB is reachable, or null if no such block is
4772 std::pair<BasicBlock *, BasicBlock *>
4773 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
4774 // If the block has a unique predecessor, then there is no path from the
4775 // predecessor to the block that does not go through the direct edge
4776 // from the predecessor to the block.
4777 if (BasicBlock *Pred = BB->getSinglePredecessor())
4778 return std::make_pair(Pred, BB);
4780 // A loop's header is defined to be a block that dominates the loop.
4781 // If the header has a unique predecessor outside the loop, it must be
4782 // a block that has exactly one successor that can reach the loop.
4783 if (Loop *L = LI->getLoopFor(BB))
4784 return std::make_pair(L->getLoopPredecessor(), L->getHeader());
4786 return std::pair<BasicBlock *, BasicBlock *>();
4789 /// HasSameValue - SCEV structural equivalence is usually sufficient for
4790 /// testing whether two expressions are equal, however for the purposes of
4791 /// looking for a condition guarding a loop, it can be useful to be a little
4792 /// more general, since a front-end may have replicated the controlling
4795 static bool HasSameValue(const SCEV *A, const SCEV *B) {
4796 // Quick check to see if they are the same SCEV.
4797 if (A == B) return true;
4799 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
4800 // two different instructions with the same value. Check for this case.
4801 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
4802 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
4803 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
4804 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
4805 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory())
4808 // Otherwise assume they may have a different value.
4812 /// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with
4813 /// predicate Pred. Return true iff any changes were made.
4815 bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
4816 const SCEV *&LHS, const SCEV *&RHS) {
4817 bool Changed = false;
4819 // Canonicalize a constant to the right side.
4820 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
4821 // Check for both operands constant.
4822 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
4823 if (ConstantExpr::getICmp(Pred,
4825 RHSC->getValue())->isNullValue())
4826 goto trivially_false;
4828 goto trivially_true;
4830 // Otherwise swap the operands to put the constant on the right.
4831 std::swap(LHS, RHS);
4832 Pred = ICmpInst::getSwappedPredicate(Pred);
4836 // If we're comparing an addrec with a value which is loop-invariant in the
4837 // addrec's loop, put the addrec on the left. Also make a dominance check,
4838 // as both operands could be addrecs loop-invariant in each other's loop.
4839 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
4840 const Loop *L = AR->getLoop();
4841 if (LHS->isLoopInvariant(L) && LHS->properlyDominates(L->getHeader(), DT)) {
4842 std::swap(LHS, RHS);
4843 Pred = ICmpInst::getSwappedPredicate(Pred);
4848 // If there's a constant operand, canonicalize comparisons with boundary
4849 // cases, and canonicalize *-or-equal comparisons to regular comparisons.
4850 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
4851 const APInt &RA = RC->getValue()->getValue();
4853 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
4854 case ICmpInst::ICMP_EQ:
4855 case ICmpInst::ICMP_NE:
4857 case ICmpInst::ICMP_UGE:
4858 if ((RA - 1).isMinValue()) {
4859 Pred = ICmpInst::ICMP_NE;
4860 RHS = getConstant(RA - 1);
4864 if (RA.isMaxValue()) {
4865 Pred = ICmpInst::ICMP_EQ;
4869 if (RA.isMinValue()) goto trivially_true;
4871 Pred = ICmpInst::ICMP_UGT;
4872 RHS = getConstant(RA - 1);
4875 case ICmpInst::ICMP_ULE:
4876 if ((RA + 1).isMaxValue()) {
4877 Pred = ICmpInst::ICMP_NE;
4878 RHS = getConstant(RA + 1);
4882 if (RA.isMinValue()) {
4883 Pred = ICmpInst::ICMP_EQ;
4887 if (RA.isMaxValue()) goto trivially_true;
4889 Pred = ICmpInst::ICMP_ULT;
4890 RHS = getConstant(RA + 1);
4893 case ICmpInst::ICMP_SGE:
4894 if ((RA - 1).isMinSignedValue()) {
4895 Pred = ICmpInst::ICMP_NE;
4896 RHS = getConstant(RA - 1);
4900 if (RA.isMaxSignedValue()) {
4901 Pred = ICmpInst::ICMP_EQ;
4905 if (RA.isMinSignedValue()) goto trivially_true;
4907 Pred = ICmpInst::ICMP_SGT;
4908 RHS = getConstant(RA - 1);
4911 case ICmpInst::ICMP_SLE:
4912 if ((RA + 1).isMaxSignedValue()) {
4913 Pred = ICmpInst::ICMP_NE;
4914 RHS = getConstant(RA + 1);
4918 if (RA.isMinSignedValue()) {
4919 Pred = ICmpInst::ICMP_EQ;
4923 if (RA.isMaxSignedValue()) goto trivially_true;
4925 Pred = ICmpInst::ICMP_SLT;
4926 RHS = getConstant(RA + 1);
4929 case ICmpInst::ICMP_UGT:
4930 if (RA.isMinValue()) {
4931 Pred = ICmpInst::ICMP_NE;
4935 if ((RA + 1).isMaxValue()) {
4936 Pred = ICmpInst::ICMP_EQ;
4937 RHS = getConstant(RA + 1);
4941 if (RA.isMaxValue()) goto trivially_false;
4943 case ICmpInst::ICMP_ULT:
4944 if (RA.isMaxValue()) {
4945 Pred = ICmpInst::ICMP_NE;
4949 if ((RA - 1).isMinValue()) {
4950 Pred = ICmpInst::ICMP_EQ;
4951 RHS = getConstant(RA - 1);
4955 if (RA.isMinValue()) goto trivially_false;
4957 case ICmpInst::ICMP_SGT:
4958 if (RA.isMinSignedValue()) {
4959 Pred = ICmpInst::ICMP_NE;
4963 if ((RA + 1).isMaxSignedValue()) {
4964 Pred = ICmpInst::ICMP_EQ;
4965 RHS = getConstant(RA + 1);
4969 if (RA.isMaxSignedValue()) goto trivially_false;
4971 case ICmpInst::ICMP_SLT:
4972 if (RA.isMaxSignedValue()) {
4973 Pred = ICmpInst::ICMP_NE;
4977 if ((RA - 1).isMinSignedValue()) {
4978 Pred = ICmpInst::ICMP_EQ;
4979 RHS = getConstant(RA - 1);
4983 if (RA.isMinSignedValue()) goto trivially_false;
4988 // Check for obvious equality.
4989 if (HasSameValue(LHS, RHS)) {
4990 if (ICmpInst::isTrueWhenEqual(Pred))
4991 goto trivially_true;
4992 if (ICmpInst::isFalseWhenEqual(Pred))
4993 goto trivially_false;
4996 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
4997 // adding or subtracting 1 from one of the operands.
4999 case ICmpInst::ICMP_SLE:
5000 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) {
5001 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
5002 /*HasNUW=*/false, /*HasNSW=*/true);
5003 Pred = ICmpInst::ICMP_SLT;
5005 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) {
5006 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
5007 /*HasNUW=*/false, /*HasNSW=*/true);
5008 Pred = ICmpInst::ICMP_SLT;
5012 case ICmpInst::ICMP_SGE:
5013 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) {
5014 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
5015 /*HasNUW=*/false, /*HasNSW=*/true);
5016 Pred = ICmpInst::ICMP_SGT;
5018 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) {
5019 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
5020 /*HasNUW=*/false, /*HasNSW=*/true);
5021 Pred = ICmpInst::ICMP_SGT;
5025 case ICmpInst::ICMP_ULE:
5026 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) {
5027 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
5028 /*HasNUW=*/true, /*HasNSW=*/false);
5029 Pred = ICmpInst::ICMP_ULT;
5031 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) {
5032 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
5033 /*HasNUW=*/true, /*HasNSW=*/false);
5034 Pred = ICmpInst::ICMP_ULT;
5038 case ICmpInst::ICMP_UGE:
5039 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) {
5040 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
5041 /*HasNUW=*/true, /*HasNSW=*/false);
5042 Pred = ICmpInst::ICMP_UGT;
5044 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) {
5045 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
5046 /*HasNUW=*/true, /*HasNSW=*/false);
5047 Pred = ICmpInst::ICMP_UGT;
5055 // TODO: More simplifications are possible here.
5061 LHS = RHS = getConstant(Type::getInt1Ty(getContext()), 0);
5062 Pred = ICmpInst::ICMP_EQ;
5067 LHS = RHS = getConstant(Type::getInt1Ty(getContext()), 0);
5068 Pred = ICmpInst::ICMP_NE;
5072 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
5073 return getSignedRange(S).getSignedMax().isNegative();
5076 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
5077 return getSignedRange(S).getSignedMin().isStrictlyPositive();
5080 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
5081 return !getSignedRange(S).getSignedMin().isNegative();
5084 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
5085 return !getSignedRange(S).getSignedMax().isStrictlyPositive();
5088 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
5089 return isKnownNegative(S) || isKnownPositive(S);
5092 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
5093 const SCEV *LHS, const SCEV *RHS) {
5094 // Canonicalize the inputs first.
5095 (void)SimplifyICmpOperands(Pred, LHS, RHS);
5097 // If LHS or RHS is an addrec, check to see if the condition is true in
5098 // every iteration of the loop.
5099 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
5100 if (isLoopEntryGuardedByCond(
5101 AR->getLoop(), Pred, AR->getStart(), RHS) &&
5102 isLoopBackedgeGuardedByCond(
5103 AR->getLoop(), Pred, AR->getPostIncExpr(*this), RHS))
5105 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS))
5106 if (isLoopEntryGuardedByCond(
5107 AR->getLoop(), Pred, LHS, AR->getStart()) &&
5108 isLoopBackedgeGuardedByCond(
5109 AR->getLoop(), Pred, LHS, AR->getPostIncExpr(*this)))
5112 // Otherwise see what can be done with known constant ranges.
5113 return isKnownPredicateWithRanges(Pred, LHS, RHS);
5117 ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred,
5118 const SCEV *LHS, const SCEV *RHS) {
5119 if (HasSameValue(LHS, RHS))
5120 return ICmpInst::isTrueWhenEqual(Pred);
5122 // This code is split out from isKnownPredicate because it is called from
5123 // within isLoopEntryGuardedByCond.
5126 llvm_unreachable("Unexpected ICmpInst::Predicate value!");
5128 case ICmpInst::ICMP_SGT:
5129 Pred = ICmpInst::ICMP_SLT;
5130 std::swap(LHS, RHS);
5131 case ICmpInst::ICMP_SLT: {
5132 ConstantRange LHSRange = getSignedRange(LHS);
5133 ConstantRange RHSRange = getSignedRange(RHS);
5134 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
5136 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
5140 case ICmpInst::ICMP_SGE:
5141 Pred = ICmpInst::ICMP_SLE;
5142 std::swap(LHS, RHS);
5143 case ICmpInst::ICMP_SLE: {
5144 ConstantRange LHSRange = getSignedRange(LHS);
5145 ConstantRange RHSRange = getSignedRange(RHS);
5146 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
5148 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
5152 case ICmpInst::ICMP_UGT:
5153 Pred = ICmpInst::ICMP_ULT;
5154 std::swap(LHS, RHS);
5155 case ICmpInst::ICMP_ULT: {
5156 ConstantRange LHSRange = getUnsignedRange(LHS);
5157 ConstantRange RHSRange = getUnsignedRange(RHS);
5158 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
5160 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
5164 case ICmpInst::ICMP_UGE:
5165 Pred = ICmpInst::ICMP_ULE;
5166 std::swap(LHS, RHS);
5167 case ICmpInst::ICMP_ULE: {
5168 ConstantRange LHSRange = getUnsignedRange(LHS);
5169 ConstantRange RHSRange = getUnsignedRange(RHS);
5170 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
5172 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
5176 case ICmpInst::ICMP_NE: {
5177 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
5179 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
5182 const SCEV *Diff = getMinusSCEV(LHS, RHS);
5183 if (isKnownNonZero(Diff))
5187 case ICmpInst::ICMP_EQ:
5188 // The check at the top of the function catches the case where
5189 // the values are known to be equal.
5195 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
5196 /// protected by a conditional between LHS and RHS. This is used to
5197 /// to eliminate casts.
5199 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
5200 ICmpInst::Predicate Pred,
5201 const SCEV *LHS, const SCEV *RHS) {
5202 // Interpret a null as meaning no loop, where there is obviously no guard
5203 // (interprocedural conditions notwithstanding).
5204 if (!L) return true;
5206 BasicBlock *Latch = L->getLoopLatch();
5210 BranchInst *LoopContinuePredicate =
5211 dyn_cast<BranchInst>(Latch->getTerminator());
5212 if (!LoopContinuePredicate ||
5213 LoopContinuePredicate->isUnconditional())
5216 return isImpliedCond(LoopContinuePredicate->getCondition(), Pred, LHS, RHS,
5217 LoopContinuePredicate->getSuccessor(0) != L->getHeader());
5220 /// isLoopEntryGuardedByCond - Test whether entry to the loop is protected
5221 /// by a conditional between LHS and RHS. This is used to help avoid max
5222 /// expressions in loop trip counts, and to eliminate casts.
5224 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
5225 ICmpInst::Predicate Pred,
5226 const SCEV *LHS, const SCEV *RHS) {
5227 // Interpret a null as meaning no loop, where there is obviously no guard
5228 // (interprocedural conditions notwithstanding).
5229 if (!L) return false;
5231 // Starting at the loop predecessor, climb up the predecessor chain, as long
5232 // as there are predecessors that can be found that have unique successors
5233 // leading to the original header.
5234 for (std::pair<BasicBlock *, BasicBlock *>
5235 Pair(L->getLoopPredecessor(), L->getHeader());
5237 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
5239 BranchInst *LoopEntryPredicate =
5240 dyn_cast<BranchInst>(Pair.first->getTerminator());
5241 if (!LoopEntryPredicate ||
5242 LoopEntryPredicate->isUnconditional())
5245 if (isImpliedCond(LoopEntryPredicate->getCondition(), Pred, LHS, RHS,
5246 LoopEntryPredicate->getSuccessor(0) != Pair.second))
5253 /// isImpliedCond - Test whether the condition described by Pred, LHS,
5254 /// and RHS is true whenever the given Cond value evaluates to true.
5255 bool ScalarEvolution::isImpliedCond(Value *CondValue,
5256 ICmpInst::Predicate Pred,
5257 const SCEV *LHS, const SCEV *RHS,
5259 // Recursively handle And and Or conditions.
5260 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(CondValue)) {
5261 if (BO->getOpcode() == Instruction::And) {
5263 return isImpliedCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) ||
5264 isImpliedCond(BO->getOperand(1), Pred, LHS, RHS, Inverse);
5265 } else if (BO->getOpcode() == Instruction::Or) {
5267 return isImpliedCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) ||
5268 isImpliedCond(BO->getOperand(1), Pred, LHS, RHS, Inverse);
5272 ICmpInst *ICI = dyn_cast<ICmpInst>(CondValue);
5273 if (!ICI) return false;
5275 // Bail if the ICmp's operands' types are wider than the needed type
5276 // before attempting to call getSCEV on them. This avoids infinite
5277 // recursion, since the analysis of widening casts can require loop
5278 // exit condition information for overflow checking, which would
5280 if (getTypeSizeInBits(LHS->getType()) <
5281 getTypeSizeInBits(ICI->getOperand(0)->getType()))
5284 // Now that we found a conditional branch that dominates the loop, check to
5285 // see if it is the comparison we are looking for.
5286 ICmpInst::Predicate FoundPred;
5288 FoundPred = ICI->getInversePredicate();
5290 FoundPred = ICI->getPredicate();
5292 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
5293 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
5295 // Balance the types. The case where FoundLHS' type is wider than
5296 // LHS' type is checked for above.
5297 if (getTypeSizeInBits(LHS->getType()) >
5298 getTypeSizeInBits(FoundLHS->getType())) {
5299 if (CmpInst::isSigned(Pred)) {
5300 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
5301 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
5303 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
5304 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
5308 // Canonicalize the query to match the way instcombine will have
5309 // canonicalized the comparison.
5310 if (SimplifyICmpOperands(Pred, LHS, RHS))
5312 return CmpInst::isTrueWhenEqual(Pred);
5313 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
5314 if (FoundLHS == FoundRHS)
5315 return CmpInst::isFalseWhenEqual(Pred);
5317 // Check to see if we can make the LHS or RHS match.
5318 if (LHS == FoundRHS || RHS == FoundLHS) {
5319 if (isa<SCEVConstant>(RHS)) {
5320 std::swap(FoundLHS, FoundRHS);
5321 FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
5323 std::swap(LHS, RHS);
5324 Pred = ICmpInst::getSwappedPredicate(Pred);
5328 // Check whether the found predicate is the same as the desired predicate.
5329 if (FoundPred == Pred)
5330 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
5332 // Check whether swapping the found predicate makes it the same as the
5333 // desired predicate.
5334 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
5335 if (isa<SCEVConstant>(RHS))
5336 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
5338 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
5339 RHS, LHS, FoundLHS, FoundRHS);
5342 // Check whether the actual condition is beyond sufficient.
5343 if (FoundPred == ICmpInst::ICMP_EQ)
5344 if (ICmpInst::isTrueWhenEqual(Pred))
5345 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
5347 if (Pred == ICmpInst::ICMP_NE)
5348 if (!ICmpInst::isTrueWhenEqual(FoundPred))
5349 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
5352 // Otherwise assume the worst.
5356 /// isImpliedCondOperands - Test whether the condition described by Pred,
5357 /// LHS, and RHS is true whenever the condition described by Pred, FoundLHS,
5358 /// and FoundRHS is true.
5359 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
5360 const SCEV *LHS, const SCEV *RHS,
5361 const SCEV *FoundLHS,
5362 const SCEV *FoundRHS) {
5363 return isImpliedCondOperandsHelper(Pred, LHS, RHS,
5364 FoundLHS, FoundRHS) ||
5365 // ~x < ~y --> x > y
5366 isImpliedCondOperandsHelper(Pred, LHS, RHS,
5367 getNotSCEV(FoundRHS),
5368 getNotSCEV(FoundLHS));
5371 /// isImpliedCondOperandsHelper - Test whether the condition described by
5372 /// Pred, LHS, and RHS is true whenever the condition described by Pred,
5373 /// FoundLHS, and FoundRHS is true.
5375 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
5376 const SCEV *LHS, const SCEV *RHS,
5377 const SCEV *FoundLHS,
5378 const SCEV *FoundRHS) {
5380 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
5381 case ICmpInst::ICMP_EQ:
5382 case ICmpInst::ICMP_NE:
5383 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
5386 case ICmpInst::ICMP_SLT:
5387 case ICmpInst::ICMP_SLE:
5388 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
5389 isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, RHS, FoundRHS))
5392 case ICmpInst::ICMP_SGT:
5393 case ICmpInst::ICMP_SGE:
5394 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
5395 isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, RHS, FoundRHS))
5398 case ICmpInst::ICMP_ULT:
5399 case ICmpInst::ICMP_ULE:
5400 if (isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
5401 isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, RHS, FoundRHS))
5404 case ICmpInst::ICMP_UGT:
5405 case ICmpInst::ICMP_UGE:
5406 if (isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
5407 isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, RHS, FoundRHS))
5415 /// getBECount - Subtract the end and start values and divide by the step,
5416 /// rounding up, to get the number of times the backedge is executed. Return
5417 /// CouldNotCompute if an intermediate computation overflows.
5418 const SCEV *ScalarEvolution::getBECount(const SCEV *Start,
5422 assert(!isKnownNegative(Step) &&
5423 "This code doesn't handle negative strides yet!");
5425 const Type *Ty = Start->getType();
5426 const SCEV *NegOne = getConstant(Ty, (uint64_t)-1);
5427 const SCEV *Diff = getMinusSCEV(End, Start);
5428 const SCEV *RoundUp = getAddExpr(Step, NegOne);
5430 // Add an adjustment to the difference between End and Start so that
5431 // the division will effectively round up.
5432 const SCEV *Add = getAddExpr(Diff, RoundUp);
5435 // Check Add for unsigned overflow.
5436 // TODO: More sophisticated things could be done here.
5437 const Type *WideTy = IntegerType::get(getContext(),
5438 getTypeSizeInBits(Ty) + 1);
5439 const SCEV *EDiff = getZeroExtendExpr(Diff, WideTy);
5440 const SCEV *ERoundUp = getZeroExtendExpr(RoundUp, WideTy);
5441 const SCEV *OperandExtendedAdd = getAddExpr(EDiff, ERoundUp);
5442 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd)
5443 return getCouldNotCompute();
5446 return getUDivExpr(Add, Step);
5449 /// HowManyLessThans - Return the number of times a backedge containing the
5450 /// specified less-than comparison will execute. If not computable, return
5451 /// CouldNotCompute.
5452 ScalarEvolution::BackedgeTakenInfo
5453 ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
5454 const Loop *L, bool isSigned) {
5455 // Only handle: "ADDREC < LoopInvariant".
5456 if (!RHS->isLoopInvariant(L)) return getCouldNotCompute();
5458 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
5459 if (!AddRec || AddRec->getLoop() != L)
5460 return getCouldNotCompute();
5462 // Check to see if we have a flag which makes analysis easy.
5463 bool NoWrap = isSigned ? AddRec->hasNoSignedWrap() :
5464 AddRec->hasNoUnsignedWrap();
5466 if (AddRec->isAffine()) {
5467 unsigned BitWidth = getTypeSizeInBits(AddRec->getType());
5468 const SCEV *Step = AddRec->getStepRecurrence(*this);
5471 return getCouldNotCompute();
5472 if (Step->isOne()) {
5473 // With unit stride, the iteration never steps past the limit value.
5474 } else if (isKnownPositive(Step)) {
5475 // Test whether a positive iteration can step past the limit
5476 // value and past the maximum value for its type in a single step.
5477 // Note that it's not sufficient to check NoWrap here, because even
5478 // though the value after a wrap is undefined, it's not undefined
5479 // behavior, so if wrap does occur, the loop could either terminate or
5480 // loop infinitely, but in either case, the loop is guaranteed to
5481 // iterate at least until the iteration where the wrapping occurs.
5482 const SCEV *One = getConstant(Step->getType(), 1);
5484 APInt Max = APInt::getSignedMaxValue(BitWidth);
5485 if ((Max - getSignedRange(getMinusSCEV(Step, One)).getSignedMax())
5486 .slt(getSignedRange(RHS).getSignedMax()))
5487 return getCouldNotCompute();
5489 APInt Max = APInt::getMaxValue(BitWidth);
5490 if ((Max - getUnsignedRange(getMinusSCEV(Step, One)).getUnsignedMax())
5491 .ult(getUnsignedRange(RHS).getUnsignedMax()))
5492 return getCouldNotCompute();
5495 // TODO: Handle negative strides here and below.
5496 return getCouldNotCompute();
5498 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant
5499 // m. So, we count the number of iterations in which {n,+,s} < m is true.
5500 // Note that we cannot simply return max(m-n,0)/s because it's not safe to
5501 // treat m-n as signed nor unsigned due to overflow possibility.
5503 // First, we get the value of the LHS in the first iteration: n
5504 const SCEV *Start = AddRec->getOperand(0);
5506 // Determine the minimum constant start value.
5507 const SCEV *MinStart = getConstant(isSigned ?
5508 getSignedRange(Start).getSignedMin() :
5509 getUnsignedRange(Start).getUnsignedMin());
5511 // If we know that the condition is true in order to enter the loop,
5512 // then we know that it will run exactly (m-n)/s times. Otherwise, we
5513 // only know that it will execute (max(m,n)-n)/s times. In both cases,
5514 // the division must round up.
5515 const SCEV *End = RHS;
5516 if (!isLoopEntryGuardedByCond(L,
5517 isSigned ? ICmpInst::ICMP_SLT :
5519 getMinusSCEV(Start, Step), RHS))
5520 End = isSigned ? getSMaxExpr(RHS, Start)
5521 : getUMaxExpr(RHS, Start);
5523 // Determine the maximum constant end value.
5524 const SCEV *MaxEnd = getConstant(isSigned ?
5525 getSignedRange(End).getSignedMax() :
5526 getUnsignedRange(End).getUnsignedMax());
5528 // If MaxEnd is within a step of the maximum integer value in its type,
5529 // adjust it down to the minimum value which would produce the same effect.
5530 // This allows the subsequent ceiling division of (N+(step-1))/step to
5531 // compute the correct value.
5532 const SCEV *StepMinusOne = getMinusSCEV(Step,
5533 getConstant(Step->getType(), 1));
5536 getMinusSCEV(getConstant(APInt::getSignedMaxValue(BitWidth)),
5539 getMinusSCEV(getConstant(APInt::getMaxValue(BitWidth)),
5542 // Finally, we subtract these two values and divide, rounding up, to get
5543 // the number of times the backedge is executed.
5544 const SCEV *BECount = getBECount(Start, End, Step, NoWrap);
5546 // The maximum backedge count is similar, except using the minimum start
5547 // value and the maximum end value.
5548 const SCEV *MaxBECount = getBECount(MinStart, MaxEnd, Step, NoWrap);
5550 return BackedgeTakenInfo(BECount, MaxBECount);
5553 return getCouldNotCompute();
5556 /// getNumIterationsInRange - Return the number of iterations of this loop that
5557 /// produce values in the specified constant range. Another way of looking at
5558 /// this is that it returns the first iteration number where the value is not in
5559 /// the condition, thus computing the exit count. If the iteration count can't
5560 /// be computed, an instance of SCEVCouldNotCompute is returned.
5561 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
5562 ScalarEvolution &SE) const {
5563 if (Range.isFullSet()) // Infinite loop.
5564 return SE.getCouldNotCompute();
5566 // If the start is a non-zero constant, shift the range to simplify things.
5567 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
5568 if (!SC->getValue()->isZero()) {
5569 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
5570 Operands[0] = SE.getConstant(SC->getType(), 0);
5571 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop());
5572 if (const SCEVAddRecExpr *ShiftedAddRec =
5573 dyn_cast<SCEVAddRecExpr>(Shifted))
5574 return ShiftedAddRec->getNumIterationsInRange(
5575 Range.subtract(SC->getValue()->getValue()), SE);
5576 // This is strange and shouldn't happen.
5577 return SE.getCouldNotCompute();
5580 // The only time we can solve this is when we have all constant indices.
5581 // Otherwise, we cannot determine the overflow conditions.
5582 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
5583 if (!isa<SCEVConstant>(getOperand(i)))
5584 return SE.getCouldNotCompute();
5587 // Okay at this point we know that all elements of the chrec are constants and
5588 // that the start element is zero.
5590 // First check to see if the range contains zero. If not, the first
5592 unsigned BitWidth = SE.getTypeSizeInBits(getType());
5593 if (!Range.contains(APInt(BitWidth, 0)))
5594 return SE.getConstant(getType(), 0);
5597 // If this is an affine expression then we have this situation:
5598 // Solve {0,+,A} in Range === Ax in Range
5600 // We know that zero is in the range. If A is positive then we know that
5601 // the upper value of the range must be the first possible exit value.
5602 // If A is negative then the lower of the range is the last possible loop
5603 // value. Also note that we already checked for a full range.
5604 APInt One(BitWidth,1);
5605 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
5606 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
5608 // The exit value should be (End+A)/A.
5609 APInt ExitVal = (End + A).udiv(A);
5610 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
5612 // Evaluate at the exit value. If we really did fall out of the valid
5613 // range, then we computed our trip count, otherwise wrap around or other
5614 // things must have happened.
5615 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
5616 if (Range.contains(Val->getValue()))
5617 return SE.getCouldNotCompute(); // Something strange happened
5619 // Ensure that the previous value is in the range. This is a sanity check.
5620 assert(Range.contains(
5621 EvaluateConstantChrecAtConstant(this,
5622 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
5623 "Linear scev computation is off in a bad way!");
5624 return SE.getConstant(ExitValue);
5625 } else if (isQuadratic()) {
5626 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
5627 // quadratic equation to solve it. To do this, we must frame our problem in
5628 // terms of figuring out when zero is crossed, instead of when
5629 // Range.getUpper() is crossed.
5630 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
5631 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
5632 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop());
5634 // Next, solve the constructed addrec
5635 std::pair<const SCEV *,const SCEV *> Roots =
5636 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
5637 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
5638 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
5640 // Pick the smallest positive root value.
5641 if (ConstantInt *CB =
5642 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
5643 R1->getValue(), R2->getValue()))) {
5644 if (CB->getZExtValue() == false)
5645 std::swap(R1, R2); // R1 is the minimum root now.
5647 // Make sure the root is not off by one. The returned iteration should
5648 // not be in the range, but the previous one should be. When solving
5649 // for "X*X < 5", for example, we should not return a root of 2.
5650 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
5653 if (Range.contains(R1Val->getValue())) {
5654 // The next iteration must be out of the range...
5655 ConstantInt *NextVal =
5656 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1);
5658 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
5659 if (!Range.contains(R1Val->getValue()))
5660 return SE.getConstant(NextVal);
5661 return SE.getCouldNotCompute(); // Something strange happened
5664 // If R1 was not in the range, then it is a good return value. Make
5665 // sure that R1-1 WAS in the range though, just in case.
5666 ConstantInt *NextVal =
5667 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1);
5668 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
5669 if (Range.contains(R1Val->getValue()))
5671 return SE.getCouldNotCompute(); // Something strange happened
5676 return SE.getCouldNotCompute();
5681 //===----------------------------------------------------------------------===//
5682 // SCEVCallbackVH Class Implementation
5683 //===----------------------------------------------------------------------===//
5685 void ScalarEvolution::SCEVCallbackVH::deleted() {
5686 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
5687 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
5688 SE->ConstantEvolutionLoopExitValue.erase(PN);
5689 SE->Scalars.erase(getValPtr());
5690 // this now dangles!
5693 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) {
5694 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
5696 Value *Old = getValPtr();
5698 // If there's a SCEVUnknown tying this value into the SCEV
5699 // space, replace the SCEVUnknown's value with the new value
5700 // for the benefit of any SCEVs still referencing it, and
5701 // and remove it from the folding set map so that new scevs
5702 // don't reference it.
5703 FoldingSetNodeID ID;
5704 ID.AddInteger(scUnknown);
5707 if (SCEVUnknown *S = cast_or_null<SCEVUnknown>(
5708 SE->UniqueSCEVs.FindNodeOrInsertPos(ID, IP))) {
5710 SE->UniqueSCEVs.RemoveNode(S);
5711 SE->ValuesAtScopes.erase(S);
5714 // Forget all the expressions associated with users of the old value,
5715 // so that future queries will recompute the expressions using the new
5717 SmallVector<User *, 16> Worklist;
5718 SmallPtrSet<User *, 8> Visited;
5719 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end();
5721 Worklist.push_back(*UI);
5722 while (!Worklist.empty()) {
5723 User *U = Worklist.pop_back_val();
5724 // Deleting the Old value will cause this to dangle. Postpone
5725 // that until everything else is done.
5728 if (!Visited.insert(U))
5730 if (PHINode *PN = dyn_cast<PHINode>(U))
5731 SE->ConstantEvolutionLoopExitValue.erase(PN);
5732 SE->Scalars.erase(U);
5733 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end();
5735 Worklist.push_back(*UI);
5737 // Delete the Old value.
5738 if (PHINode *PN = dyn_cast<PHINode>(Old))
5739 SE->ConstantEvolutionLoopExitValue.erase(PN);
5740 SE->Scalars.erase(Old);
5741 // this now dangles!
5744 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
5745 : CallbackVH(V), SE(se) {}
5747 //===----------------------------------------------------------------------===//
5748 // ScalarEvolution Class Implementation
5749 //===----------------------------------------------------------------------===//
5751 ScalarEvolution::ScalarEvolution()
5752 : FunctionPass(&ID) {
5755 bool ScalarEvolution::runOnFunction(Function &F) {
5757 LI = &getAnalysis<LoopInfo>();
5758 TD = getAnalysisIfAvailable<TargetData>();
5759 DT = &getAnalysis<DominatorTree>();
5763 void ScalarEvolution::releaseMemory() {
5765 BackedgeTakenCounts.clear();
5766 ConstantEvolutionLoopExitValue.clear();
5767 ValuesAtScopes.clear();
5768 UniqueSCEVs.clear();
5769 SCEVAllocator.Reset();
5772 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
5773 AU.setPreservesAll();
5774 AU.addRequiredTransitive<LoopInfo>();
5775 AU.addRequiredTransitive<DominatorTree>();
5778 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
5779 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
5782 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
5784 // Print all inner loops first
5785 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
5786 PrintLoopInfo(OS, SE, *I);
5789 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
5792 SmallVector<BasicBlock *, 8> ExitBlocks;
5793 L->getExitBlocks(ExitBlocks);
5794 if (ExitBlocks.size() != 1)
5795 OS << "<multiple exits> ";
5797 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
5798 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
5800 OS << "Unpredictable backedge-taken count. ";
5805 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
5808 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
5809 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
5811 OS << "Unpredictable max backedge-taken count. ";
5817 void ScalarEvolution::print(raw_ostream &OS, const Module *) const {
5818 // ScalarEvolution's implementation of the print method is to print
5819 // out SCEV values of all instructions that are interesting. Doing
5820 // this potentially causes it to create new SCEV objects though,
5821 // which technically conflicts with the const qualifier. This isn't
5822 // observable from outside the class though, so casting away the
5823 // const isn't dangerous.
5824 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
5826 OS << "Classifying expressions for: ";
5827 WriteAsOperand(OS, F, /*PrintType=*/false);
5829 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
5830 if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) {
5833 const SCEV *SV = SE.getSCEV(&*I);
5836 const Loop *L = LI->getLoopFor((*I).getParent());
5838 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
5845 OS << "\t\t" "Exits: ";
5846 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
5847 if (!ExitValue->isLoopInvariant(L)) {
5848 OS << "<<Unknown>>";
5857 OS << "Determining loop execution counts for: ";
5858 WriteAsOperand(OS, F, /*PrintType=*/false);
5860 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
5861 PrintLoopInfo(OS, &SE, *I);