1 //===- ScalarEvolution.cpp - Scalar Evolution Analysis ----------*- C++ -*-===//
3 // The LLVM Compiler Infrastructure
5 // This file is distributed under the University of Illinois Open Source
6 // License. See LICENSE.TXT for details.
8 //===----------------------------------------------------------------------===//
10 // This file contains the implementation of the scalar evolution analysis
11 // engine, which is used primarily to analyze expressions involving induction
12 // variables in loops.
14 // There are several aspects to this library. First is the representation of
15 // scalar expressions, which are represented as subclasses of the SCEV class.
16 // These classes are used to represent certain types of subexpressions that we
17 // can handle. We only create one SCEV of a particular shape, so
18 // pointer-comparisons for equality are legal.
20 // One important aspect of the SCEV objects is that they are never cyclic, even
21 // if there is a cycle in the dataflow for an expression (ie, a PHI node). If
22 // the PHI node is one of the idioms that we can represent (e.g., a polynomial
23 // recurrence) then we represent it directly as a recurrence node, otherwise we
24 // represent it as a SCEVUnknown node.
26 // In addition to being able to represent expressions of various types, we also
27 // have folders that are used to build the *canonical* representation for a
28 // particular expression. These folders are capable of using a variety of
29 // rewrite rules to simplify the expressions.
31 // Once the folders are defined, we can implement the more interesting
32 // higher-level code, such as the code that recognizes PHI nodes of various
33 // types, computes the execution count of a loop, etc.
35 // TODO: We should use these routines and value representations to implement
36 // dependence analysis!
38 //===----------------------------------------------------------------------===//
40 // There are several good references for the techniques used in this analysis.
42 // Chains of recurrences -- a method to expedite the evaluation
43 // of closed-form functions
44 // Olaf Bachmann, Paul S. Wang, Eugene V. Zima
46 // On computational properties of chains of recurrences
49 // Symbolic Evaluation of Chains of Recurrences for Loop Optimization
50 // Robert A. van Engelen
52 // Efficient Symbolic Analysis for Optimizing Compilers
53 // Robert A. van Engelen
55 // Using the chains of recurrences algebra for data dependence testing and
56 // induction variable substitution
57 // MS Thesis, Johnie Birch
59 //===----------------------------------------------------------------------===//
61 #define DEBUG_TYPE "scalar-evolution"
62 #include "llvm/Analysis/ScalarEvolutionExpressions.h"
63 #include "llvm/Constants.h"
64 #include "llvm/DerivedTypes.h"
65 #include "llvm/GlobalVariable.h"
66 #include "llvm/GlobalAlias.h"
67 #include "llvm/Instructions.h"
68 #include "llvm/LLVMContext.h"
69 #include "llvm/Operator.h"
70 #include "llvm/Analysis/ConstantFolding.h"
71 #include "llvm/Analysis/Dominators.h"
72 #include "llvm/Analysis/LoopInfo.h"
73 #include "llvm/Analysis/ValueTracking.h"
74 #include "llvm/Assembly/Writer.h"
75 #include "llvm/Target/TargetData.h"
76 #include "llvm/Support/CommandLine.h"
77 #include "llvm/Support/ConstantRange.h"
78 #include "llvm/Support/Debug.h"
79 #include "llvm/Support/ErrorHandling.h"
80 #include "llvm/Support/GetElementPtrTypeIterator.h"
81 #include "llvm/Support/InstIterator.h"
82 #include "llvm/Support/MathExtras.h"
83 #include "llvm/Support/raw_ostream.h"
84 #include "llvm/ADT/Statistic.h"
85 #include "llvm/ADT/STLExtras.h"
86 #include "llvm/ADT/SmallPtrSet.h"
90 STATISTIC(NumArrayLenItCounts,
91 "Number of trip counts computed with array length");
92 STATISTIC(NumTripCountsComputed,
93 "Number of loops with predictable loop counts");
94 STATISTIC(NumTripCountsNotComputed,
95 "Number of loops without predictable loop counts");
96 STATISTIC(NumBruteForceTripCountsComputed,
97 "Number of loops with trip counts computed by force");
99 static cl::opt<unsigned>
100 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
101 cl::desc("Maximum number of iterations SCEV will "
102 "symbolically execute a constant "
106 static RegisterPass<ScalarEvolution>
107 R("scalar-evolution", "Scalar Evolution Analysis", false, true);
108 char ScalarEvolution::ID = 0;
110 //===----------------------------------------------------------------------===//
111 // SCEV class definitions
112 //===----------------------------------------------------------------------===//
114 //===----------------------------------------------------------------------===//
115 // Implementation of the SCEV class.
120 void SCEV::dump() const {
125 bool SCEV::isZero() const {
126 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
127 return SC->getValue()->isZero();
131 bool SCEV::isOne() const {
132 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
133 return SC->getValue()->isOne();
137 bool SCEV::isAllOnesValue() const {
138 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
139 return SC->getValue()->isAllOnesValue();
143 SCEVCouldNotCompute::SCEVCouldNotCompute() :
144 SCEV(FoldingSetNodeIDRef(), scCouldNotCompute) {}
146 bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const {
147 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
151 const Type *SCEVCouldNotCompute::getType() const {
152 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
156 bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const {
157 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
161 bool SCEVCouldNotCompute::hasOperand(const SCEV *) const {
162 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
166 void SCEVCouldNotCompute::print(raw_ostream &OS) const {
167 OS << "***COULDNOTCOMPUTE***";
170 bool SCEVCouldNotCompute::classof(const SCEV *S) {
171 return S->getSCEVType() == scCouldNotCompute;
174 const SCEV *ScalarEvolution::getConstant(ConstantInt *V) {
176 ID.AddInteger(scConstant);
179 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
180 SCEV *S = new (SCEVAllocator) SCEVConstant(ID.Intern(SCEVAllocator), V);
181 UniqueSCEVs.InsertNode(S, IP);
185 const SCEV *ScalarEvolution::getConstant(const APInt& Val) {
186 return getConstant(ConstantInt::get(getContext(), Val));
190 ScalarEvolution::getConstant(const Type *Ty, uint64_t V, bool isSigned) {
191 const IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty));
192 return getConstant(ConstantInt::get(ITy, V, isSigned));
195 const Type *SCEVConstant::getType() const { return V->getType(); }
197 void SCEVConstant::print(raw_ostream &OS) const {
198 WriteAsOperand(OS, V, false);
201 SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID,
202 unsigned SCEVTy, const SCEV *op, const Type *ty)
203 : SCEV(ID, SCEVTy), Op(op), Ty(ty) {}
205 bool SCEVCastExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
206 return Op->dominates(BB, DT);
209 bool SCEVCastExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const {
210 return Op->properlyDominates(BB, DT);
213 SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID,
214 const SCEV *op, const Type *ty)
215 : SCEVCastExpr(ID, scTruncate, op, ty) {
216 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
217 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
218 "Cannot truncate non-integer value!");
221 void SCEVTruncateExpr::print(raw_ostream &OS) const {
222 OS << "(trunc " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
225 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID,
226 const SCEV *op, const Type *ty)
227 : SCEVCastExpr(ID, scZeroExtend, op, ty) {
228 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
229 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
230 "Cannot zero extend non-integer value!");
233 void SCEVZeroExtendExpr::print(raw_ostream &OS) const {
234 OS << "(zext " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
237 SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID,
238 const SCEV *op, const Type *ty)
239 : SCEVCastExpr(ID, scSignExtend, op, ty) {
240 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
241 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
242 "Cannot sign extend non-integer value!");
245 void SCEVSignExtendExpr::print(raw_ostream &OS) const {
246 OS << "(sext " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
249 void SCEVCommutativeExpr::print(raw_ostream &OS) const {
250 const char *OpStr = getOperationStr();
252 for (op_iterator I = op_begin(), E = op_end(); I != E; ++I) {
260 bool SCEVNAryExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
261 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
262 if (!getOperand(i)->dominates(BB, DT))
268 bool SCEVNAryExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const {
269 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
270 if (!getOperand(i)->properlyDominates(BB, DT))
276 bool SCEVUDivExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
277 return LHS->dominates(BB, DT) && RHS->dominates(BB, DT);
280 bool SCEVUDivExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const {
281 return LHS->properlyDominates(BB, DT) && RHS->properlyDominates(BB, DT);
284 void SCEVUDivExpr::print(raw_ostream &OS) const {
285 OS << "(" << *LHS << " /u " << *RHS << ")";
288 const Type *SCEVUDivExpr::getType() const {
289 // In most cases the types of LHS and RHS will be the same, but in some
290 // crazy cases one or the other may be a pointer. ScalarEvolution doesn't
291 // depend on the type for correctness, but handling types carefully can
292 // avoid extra casts in the SCEVExpander. The LHS is more likely to be
293 // a pointer type than the RHS, so use the RHS' type here.
294 return RHS->getType();
297 bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const {
298 // Add recurrences are never invariant in the function-body (null loop).
302 // This recurrence is variant w.r.t. QueryLoop if QueryLoop contains L.
303 if (QueryLoop->contains(L))
306 // This recurrence is variant w.r.t. QueryLoop if any of its operands
308 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
309 if (!getOperand(i)->isLoopInvariant(QueryLoop))
312 // Otherwise it's loop-invariant.
317 SCEVAddRecExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
318 return DT->dominates(L->getHeader(), BB) &&
319 SCEVNAryExpr::dominates(BB, DT);
323 SCEVAddRecExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const {
324 // This uses a "dominates" query instead of "properly dominates" query because
325 // the instruction which produces the addrec's value is a PHI, and a PHI
326 // effectively properly dominates its entire containing block.
327 return DT->dominates(L->getHeader(), BB) &&
328 SCEVNAryExpr::properlyDominates(BB, DT);
331 void SCEVAddRecExpr::print(raw_ostream &OS) const {
332 OS << "{" << *Operands[0];
333 for (unsigned i = 1, e = NumOperands; i != e; ++i)
334 OS << ",+," << *Operands[i];
336 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
340 bool SCEVUnknown::isLoopInvariant(const Loop *L) const {
341 // All non-instruction values are loop invariant. All instructions are loop
342 // invariant if they are not contained in the specified loop.
343 // Instructions are never considered invariant in the function body
344 // (null loop) because they are defined within the "loop".
345 if (Instruction *I = dyn_cast<Instruction>(V))
346 return L && !L->contains(I);
350 bool SCEVUnknown::dominates(BasicBlock *BB, DominatorTree *DT) const {
351 if (Instruction *I = dyn_cast<Instruction>(getValue()))
352 return DT->dominates(I->getParent(), BB);
356 bool SCEVUnknown::properlyDominates(BasicBlock *BB, DominatorTree *DT) const {
357 if (Instruction *I = dyn_cast<Instruction>(getValue()))
358 return DT->properlyDominates(I->getParent(), BB);
362 const Type *SCEVUnknown::getType() const {
366 bool SCEVUnknown::isSizeOf(const Type *&AllocTy) const {
367 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(V))
368 if (VCE->getOpcode() == Instruction::PtrToInt)
369 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
370 if (CE->getOpcode() == Instruction::GetElementPtr &&
371 CE->getOperand(0)->isNullValue() &&
372 CE->getNumOperands() == 2)
373 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1)))
375 AllocTy = cast<PointerType>(CE->getOperand(0)->getType())
383 bool SCEVUnknown::isAlignOf(const Type *&AllocTy) const {
384 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(V))
385 if (VCE->getOpcode() == Instruction::PtrToInt)
386 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
387 if (CE->getOpcode() == Instruction::GetElementPtr &&
388 CE->getOperand(0)->isNullValue()) {
390 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
391 if (const StructType *STy = dyn_cast<StructType>(Ty))
392 if (!STy->isPacked() &&
393 CE->getNumOperands() == 3 &&
394 CE->getOperand(1)->isNullValue()) {
395 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2)))
397 STy->getNumElements() == 2 &&
398 STy->getElementType(0)->isIntegerTy(1)) {
399 AllocTy = STy->getElementType(1);
408 bool SCEVUnknown::isOffsetOf(const Type *&CTy, Constant *&FieldNo) const {
409 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(V))
410 if (VCE->getOpcode() == Instruction::PtrToInt)
411 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
412 if (CE->getOpcode() == Instruction::GetElementPtr &&
413 CE->getNumOperands() == 3 &&
414 CE->getOperand(0)->isNullValue() &&
415 CE->getOperand(1)->isNullValue()) {
417 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
418 // Ignore vector types here so that ScalarEvolutionExpander doesn't
419 // emit getelementptrs that index into vectors.
420 if (Ty->isStructTy() || Ty->isArrayTy()) {
422 FieldNo = CE->getOperand(2);
430 void SCEVUnknown::print(raw_ostream &OS) const {
432 if (isSizeOf(AllocTy)) {
433 OS << "sizeof(" << *AllocTy << ")";
436 if (isAlignOf(AllocTy)) {
437 OS << "alignof(" << *AllocTy << ")";
443 if (isOffsetOf(CTy, FieldNo)) {
444 OS << "offsetof(" << *CTy << ", ";
445 WriteAsOperand(OS, FieldNo, false);
450 // Otherwise just print it normally.
451 WriteAsOperand(OS, V, false);
454 //===----------------------------------------------------------------------===//
456 //===----------------------------------------------------------------------===//
458 static bool CompareTypes(const Type *A, const Type *B) {
459 if (A->getTypeID() != B->getTypeID())
460 return A->getTypeID() < B->getTypeID();
461 if (const IntegerType *AI = dyn_cast<IntegerType>(A)) {
462 const IntegerType *BI = cast<IntegerType>(B);
463 return AI->getBitWidth() < BI->getBitWidth();
465 if (const PointerType *AI = dyn_cast<PointerType>(A)) {
466 const PointerType *BI = cast<PointerType>(B);
467 return CompareTypes(AI->getElementType(), BI->getElementType());
469 if (const ArrayType *AI = dyn_cast<ArrayType>(A)) {
470 const ArrayType *BI = cast<ArrayType>(B);
471 if (AI->getNumElements() != BI->getNumElements())
472 return AI->getNumElements() < BI->getNumElements();
473 return CompareTypes(AI->getElementType(), BI->getElementType());
475 if (const VectorType *AI = dyn_cast<VectorType>(A)) {
476 const VectorType *BI = cast<VectorType>(B);
477 if (AI->getNumElements() != BI->getNumElements())
478 return AI->getNumElements() < BI->getNumElements();
479 return CompareTypes(AI->getElementType(), BI->getElementType());
481 if (const StructType *AI = dyn_cast<StructType>(A)) {
482 const StructType *BI = cast<StructType>(B);
483 if (AI->getNumElements() != BI->getNumElements())
484 return AI->getNumElements() < BI->getNumElements();
485 for (unsigned i = 0, e = AI->getNumElements(); i != e; ++i)
486 if (CompareTypes(AI->getElementType(i), BI->getElementType(i)) ||
487 CompareTypes(BI->getElementType(i), AI->getElementType(i)))
488 return CompareTypes(AI->getElementType(i), BI->getElementType(i));
494 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
495 /// than the complexity of the RHS. This comparator is used to canonicalize
497 class SCEVComplexityCompare {
500 explicit SCEVComplexityCompare(LoopInfo *li) : LI(li) {}
502 bool operator()(const SCEV *LHS, const SCEV *RHS) const {
503 // Fast-path: SCEVs are uniqued so we can do a quick equality check.
507 // Primarily, sort the SCEVs by their getSCEVType().
508 if (LHS->getSCEVType() != RHS->getSCEVType())
509 return LHS->getSCEVType() < RHS->getSCEVType();
511 // Aside from the getSCEVType() ordering, the particular ordering
512 // isn't very important except that it's beneficial to be consistent,
513 // so that (a + b) and (b + a) don't end up as different expressions.
515 // Sort SCEVUnknown values with some loose heuristics. TODO: This is
516 // not as complete as it could be.
517 if (const SCEVUnknown *LU = dyn_cast<SCEVUnknown>(LHS)) {
518 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
520 // Order pointer values after integer values. This helps SCEVExpander
522 if (LU->getType()->isPointerTy() && !RU->getType()->isPointerTy())
524 if (RU->getType()->isPointerTy() && !LU->getType()->isPointerTy())
527 // Compare getValueID values.
528 if (LU->getValue()->getValueID() != RU->getValue()->getValueID())
529 return LU->getValue()->getValueID() < RU->getValue()->getValueID();
531 // Sort arguments by their position.
532 if (const Argument *LA = dyn_cast<Argument>(LU->getValue())) {
533 const Argument *RA = cast<Argument>(RU->getValue());
534 return LA->getArgNo() < RA->getArgNo();
537 // For instructions, compare their loop depth, and their opcode.
538 // This is pretty loose.
539 if (Instruction *LV = dyn_cast<Instruction>(LU->getValue())) {
540 Instruction *RV = cast<Instruction>(RU->getValue());
542 // Compare loop depths.
543 if (LI->getLoopDepth(LV->getParent()) !=
544 LI->getLoopDepth(RV->getParent()))
545 return LI->getLoopDepth(LV->getParent()) <
546 LI->getLoopDepth(RV->getParent());
549 if (LV->getOpcode() != RV->getOpcode())
550 return LV->getOpcode() < RV->getOpcode();
552 // Compare the number of operands.
553 if (LV->getNumOperands() != RV->getNumOperands())
554 return LV->getNumOperands() < RV->getNumOperands();
560 // Compare constant values.
561 if (const SCEVConstant *LC = dyn_cast<SCEVConstant>(LHS)) {
562 const SCEVConstant *RC = cast<SCEVConstant>(RHS);
563 if (LC->getValue()->getBitWidth() != RC->getValue()->getBitWidth())
564 return LC->getValue()->getBitWidth() < RC->getValue()->getBitWidth();
565 return LC->getValue()->getValue().ult(RC->getValue()->getValue());
568 // Compare addrec loop depths.
569 if (const SCEVAddRecExpr *LA = dyn_cast<SCEVAddRecExpr>(LHS)) {
570 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS);
571 if (LA->getLoop()->getLoopDepth() != RA->getLoop()->getLoopDepth())
572 return LA->getLoop()->getLoopDepth() < RA->getLoop()->getLoopDepth();
575 // Lexicographically compare n-ary expressions.
576 if (const SCEVNAryExpr *LC = dyn_cast<SCEVNAryExpr>(LHS)) {
577 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
578 for (unsigned i = 0, e = LC->getNumOperands(); i != e; ++i) {
579 if (i >= RC->getNumOperands())
581 if (operator()(LC->getOperand(i), RC->getOperand(i)))
583 if (operator()(RC->getOperand(i), LC->getOperand(i)))
586 return LC->getNumOperands() < RC->getNumOperands();
589 // Lexicographically compare udiv expressions.
590 if (const SCEVUDivExpr *LC = dyn_cast<SCEVUDivExpr>(LHS)) {
591 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
592 if (operator()(LC->getLHS(), RC->getLHS()))
594 if (operator()(RC->getLHS(), LC->getLHS()))
596 if (operator()(LC->getRHS(), RC->getRHS()))
598 if (operator()(RC->getRHS(), LC->getRHS()))
603 // Compare cast expressions by operand.
604 if (const SCEVCastExpr *LC = dyn_cast<SCEVCastExpr>(LHS)) {
605 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
606 return operator()(LC->getOperand(), RC->getOperand());
609 llvm_unreachable("Unknown SCEV kind!");
615 /// GroupByComplexity - Given a list of SCEV objects, order them by their
616 /// complexity, and group objects of the same complexity together by value.
617 /// When this routine is finished, we know that any duplicates in the vector are
618 /// consecutive and that complexity is monotonically increasing.
620 /// Note that we go take special precautions to ensure that we get deterministic
621 /// results from this routine. In other words, we don't want the results of
622 /// this to depend on where the addresses of various SCEV objects happened to
625 static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops,
627 if (Ops.size() < 2) return; // Noop
628 if (Ops.size() == 2) {
629 // This is the common case, which also happens to be trivially simple.
631 if (SCEVComplexityCompare(LI)(Ops[1], Ops[0]))
632 std::swap(Ops[0], Ops[1]);
636 // Do the rough sort by complexity.
637 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI));
639 // Now that we are sorted by complexity, group elements of the same
640 // complexity. Note that this is, at worst, N^2, but the vector is likely to
641 // be extremely short in practice. Note that we take this approach because we
642 // do not want to depend on the addresses of the objects we are grouping.
643 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
644 const SCEV *S = Ops[i];
645 unsigned Complexity = S->getSCEVType();
647 // If there are any objects of the same complexity and same value as this
649 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
650 if (Ops[j] == S) { // Found a duplicate.
651 // Move it to immediately after i'th element.
652 std::swap(Ops[i+1], Ops[j]);
653 ++i; // no need to rescan it.
654 if (i == e-2) return; // Done!
662 //===----------------------------------------------------------------------===//
663 // Simple SCEV method implementations
664 //===----------------------------------------------------------------------===//
666 /// BinomialCoefficient - Compute BC(It, K). The result has width W.
668 static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K,
670 const Type* ResultTy) {
671 // Handle the simplest case efficiently.
673 return SE.getTruncateOrZeroExtend(It, ResultTy);
675 // We are using the following formula for BC(It, K):
677 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
679 // Suppose, W is the bitwidth of the return value. We must be prepared for
680 // overflow. Hence, we must assure that the result of our computation is
681 // equal to the accurate one modulo 2^W. Unfortunately, division isn't
682 // safe in modular arithmetic.
684 // However, this code doesn't use exactly that formula; the formula it uses
685 // is something like the following, where T is the number of factors of 2 in
686 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
689 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
691 // This formula is trivially equivalent to the previous formula. However,
692 // this formula can be implemented much more efficiently. The trick is that
693 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
694 // arithmetic. To do exact division in modular arithmetic, all we have
695 // to do is multiply by the inverse. Therefore, this step can be done at
698 // The next issue is how to safely do the division by 2^T. The way this
699 // is done is by doing the multiplication step at a width of at least W + T
700 // bits. This way, the bottom W+T bits of the product are accurate. Then,
701 // when we perform the division by 2^T (which is equivalent to a right shift
702 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
703 // truncated out after the division by 2^T.
705 // In comparison to just directly using the first formula, this technique
706 // is much more efficient; using the first formula requires W * K bits,
707 // but this formula less than W + K bits. Also, the first formula requires
708 // a division step, whereas this formula only requires multiplies and shifts.
710 // It doesn't matter whether the subtraction step is done in the calculation
711 // width or the input iteration count's width; if the subtraction overflows,
712 // the result must be zero anyway. We prefer here to do it in the width of
713 // the induction variable because it helps a lot for certain cases; CodeGen
714 // isn't smart enough to ignore the overflow, which leads to much less
715 // efficient code if the width of the subtraction is wider than the native
718 // (It's possible to not widen at all by pulling out factors of 2 before
719 // the multiplication; for example, K=2 can be calculated as
720 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
721 // extra arithmetic, so it's not an obvious win, and it gets
722 // much more complicated for K > 3.)
724 // Protection from insane SCEVs; this bound is conservative,
725 // but it probably doesn't matter.
727 return SE.getCouldNotCompute();
729 unsigned W = SE.getTypeSizeInBits(ResultTy);
731 // Calculate K! / 2^T and T; we divide out the factors of two before
732 // multiplying for calculating K! / 2^T to avoid overflow.
733 // Other overflow doesn't matter because we only care about the bottom
734 // W bits of the result.
735 APInt OddFactorial(W, 1);
737 for (unsigned i = 3; i <= K; ++i) {
739 unsigned TwoFactors = Mult.countTrailingZeros();
741 Mult = Mult.lshr(TwoFactors);
742 OddFactorial *= Mult;
745 // We need at least W + T bits for the multiplication step
746 unsigned CalculationBits = W + T;
748 // Calculate 2^T, at width T+W.
749 APInt DivFactor = APInt(CalculationBits, 1).shl(T);
751 // Calculate the multiplicative inverse of K! / 2^T;
752 // this multiplication factor will perform the exact division by
754 APInt Mod = APInt::getSignedMinValue(W+1);
755 APInt MultiplyFactor = OddFactorial.zext(W+1);
756 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
757 MultiplyFactor = MultiplyFactor.trunc(W);
759 // Calculate the product, at width T+W
760 const IntegerType *CalculationTy = IntegerType::get(SE.getContext(),
762 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
763 for (unsigned i = 1; i != K; ++i) {
764 const SCEV *S = SE.getMinusSCEV(It, SE.getIntegerSCEV(i, It->getType()));
765 Dividend = SE.getMulExpr(Dividend,
766 SE.getTruncateOrZeroExtend(S, CalculationTy));
770 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
772 // Truncate the result, and divide by K! / 2^T.
774 return SE.getMulExpr(SE.getConstant(MultiplyFactor),
775 SE.getTruncateOrZeroExtend(DivResult, ResultTy));
778 /// evaluateAtIteration - Return the value of this chain of recurrences at
779 /// the specified iteration number. We can evaluate this recurrence by
780 /// multiplying each element in the chain by the binomial coefficient
781 /// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
783 /// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
785 /// where BC(It, k) stands for binomial coefficient.
787 const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It,
788 ScalarEvolution &SE) const {
789 const SCEV *Result = getStart();
790 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
791 // The computation is correct in the face of overflow provided that the
792 // multiplication is performed _after_ the evaluation of the binomial
794 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType());
795 if (isa<SCEVCouldNotCompute>(Coeff))
798 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
803 //===----------------------------------------------------------------------===//
804 // SCEV Expression folder implementations
805 //===----------------------------------------------------------------------===//
807 const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op,
809 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
810 "This is not a truncating conversion!");
811 assert(isSCEVable(Ty) &&
812 "This is not a conversion to a SCEVable type!");
813 Ty = getEffectiveSCEVType(Ty);
816 ID.AddInteger(scTruncate);
820 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
822 // Fold if the operand is constant.
823 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
825 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty)));
827 // trunc(trunc(x)) --> trunc(x)
828 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
829 return getTruncateExpr(ST->getOperand(), Ty);
831 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
832 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
833 return getTruncateOrSignExtend(SS->getOperand(), Ty);
835 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
836 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
837 return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
839 // If the input value is a chrec scev, truncate the chrec's operands.
840 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
841 SmallVector<const SCEV *, 4> Operands;
842 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
843 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty));
844 return getAddRecExpr(Operands, AddRec->getLoop());
847 // The cast wasn't folded; create an explicit cast node.
848 // Recompute the insert position, as it may have been invalidated.
849 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
850 SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator),
852 UniqueSCEVs.InsertNode(S, IP);
856 const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op,
858 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
859 "This is not an extending conversion!");
860 assert(isSCEVable(Ty) &&
861 "This is not a conversion to a SCEVable type!");
862 Ty = getEffectiveSCEVType(Ty);
864 // Fold if the operand is constant.
865 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) {
866 const Type *IntTy = getEffectiveSCEVType(Ty);
867 Constant *C = ConstantExpr::getZExt(SC->getValue(), IntTy);
868 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty);
869 return getConstant(cast<ConstantInt>(C));
872 // zext(zext(x)) --> zext(x)
873 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
874 return getZeroExtendExpr(SZ->getOperand(), Ty);
876 // Before doing any expensive analysis, check to see if we've already
877 // computed a SCEV for this Op and Ty.
879 ID.AddInteger(scZeroExtend);
883 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
885 // If the input value is a chrec scev, and we can prove that the value
886 // did not overflow the old, smaller, value, we can zero extend all of the
887 // operands (often constants). This allows analysis of something like
888 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
889 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
890 if (AR->isAffine()) {
891 const SCEV *Start = AR->getStart();
892 const SCEV *Step = AR->getStepRecurrence(*this);
893 unsigned BitWidth = getTypeSizeInBits(AR->getType());
894 const Loop *L = AR->getLoop();
896 // If we have special knowledge that this addrec won't overflow,
897 // we don't need to do any further analysis.
898 if (AR->hasNoUnsignedWrap())
899 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
900 getZeroExtendExpr(Step, Ty),
903 // Check whether the backedge-taken count is SCEVCouldNotCompute.
904 // Note that this serves two purposes: It filters out loops that are
905 // simply not analyzable, and it covers the case where this code is
906 // being called from within backedge-taken count analysis, such that
907 // attempting to ask for the backedge-taken count would likely result
908 // in infinite recursion. In the later case, the analysis code will
909 // cope with a conservative value, and it will take care to purge
910 // that value once it has finished.
911 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
912 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
913 // Manually compute the final value for AR, checking for
916 // Check whether the backedge-taken count can be losslessly casted to
917 // the addrec's type. The count is always unsigned.
918 const SCEV *CastedMaxBECount =
919 getTruncateOrZeroExtend(MaxBECount, Start->getType());
920 const SCEV *RecastedMaxBECount =
921 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
922 if (MaxBECount == RecastedMaxBECount) {
923 const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
924 // Check whether Start+Step*MaxBECount has no unsigned overflow.
925 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step);
926 const SCEV *Add = getAddExpr(Start, ZMul);
927 const SCEV *OperandExtendedAdd =
928 getAddExpr(getZeroExtendExpr(Start, WideTy),
929 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
930 getZeroExtendExpr(Step, WideTy)));
931 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd)
932 // Return the expression with the addrec on the outside.
933 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
934 getZeroExtendExpr(Step, Ty),
937 // Similar to above, only this time treat the step value as signed.
938 // This covers loops that count down.
939 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
940 Add = getAddExpr(Start, SMul);
942 getAddExpr(getZeroExtendExpr(Start, WideTy),
943 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
944 getSignExtendExpr(Step, WideTy)));
945 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd)
946 // Return the expression with the addrec on the outside.
947 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
948 getSignExtendExpr(Step, Ty),
952 // If the backedge is guarded by a comparison with the pre-inc value
953 // the addrec is safe. Also, if the entry is guarded by a comparison
954 // with the start value and the backedge is guarded by a comparison
955 // with the post-inc value, the addrec is safe.
956 if (isKnownPositive(Step)) {
957 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
958 getUnsignedRange(Step).getUnsignedMax());
959 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
960 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) &&
961 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT,
962 AR->getPostIncExpr(*this), N)))
963 // Return the expression with the addrec on the outside.
964 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
965 getZeroExtendExpr(Step, Ty),
967 } else if (isKnownNegative(Step)) {
968 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
969 getSignedRange(Step).getSignedMin());
970 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) &&
971 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) ||
972 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT,
973 AR->getPostIncExpr(*this), N)))
974 // Return the expression with the addrec on the outside.
975 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
976 getSignExtendExpr(Step, Ty),
982 // The cast wasn't folded; create an explicit cast node.
983 // Recompute the insert position, as it may have been invalidated.
984 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
985 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
987 UniqueSCEVs.InsertNode(S, IP);
991 const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op,
993 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
994 "This is not an extending conversion!");
995 assert(isSCEVable(Ty) &&
996 "This is not a conversion to a SCEVable type!");
997 Ty = getEffectiveSCEVType(Ty);
999 // Fold if the operand is constant.
1000 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) {
1001 const Type *IntTy = getEffectiveSCEVType(Ty);
1002 Constant *C = ConstantExpr::getSExt(SC->getValue(), IntTy);
1003 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty);
1004 return getConstant(cast<ConstantInt>(C));
1007 // sext(sext(x)) --> sext(x)
1008 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1009 return getSignExtendExpr(SS->getOperand(), Ty);
1011 // Before doing any expensive analysis, check to see if we've already
1012 // computed a SCEV for this Op and Ty.
1013 FoldingSetNodeID ID;
1014 ID.AddInteger(scSignExtend);
1018 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1020 // If the input value is a chrec scev, and we can prove that the value
1021 // did not overflow the old, smaller, value, we can sign extend all of the
1022 // operands (often constants). This allows analysis of something like
1023 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
1024 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1025 if (AR->isAffine()) {
1026 const SCEV *Start = AR->getStart();
1027 const SCEV *Step = AR->getStepRecurrence(*this);
1028 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1029 const Loop *L = AR->getLoop();
1031 // If we have special knowledge that this addrec won't overflow,
1032 // we don't need to do any further analysis.
1033 if (AR->hasNoSignedWrap())
1034 return getAddRecExpr(getSignExtendExpr(Start, Ty),
1035 getSignExtendExpr(Step, Ty),
1038 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1039 // Note that this serves two purposes: It filters out loops that are
1040 // simply not analyzable, and it covers the case where this code is
1041 // being called from within backedge-taken count analysis, such that
1042 // attempting to ask for the backedge-taken count would likely result
1043 // in infinite recursion. In the later case, the analysis code will
1044 // cope with a conservative value, and it will take care to purge
1045 // that value once it has finished.
1046 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1047 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1048 // Manually compute the final value for AR, checking for
1051 // Check whether the backedge-taken count can be losslessly casted to
1052 // the addrec's type. The count is always unsigned.
1053 const SCEV *CastedMaxBECount =
1054 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1055 const SCEV *RecastedMaxBECount =
1056 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1057 if (MaxBECount == RecastedMaxBECount) {
1058 const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1059 // Check whether Start+Step*MaxBECount has no signed overflow.
1060 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
1061 const SCEV *Add = getAddExpr(Start, SMul);
1062 const SCEV *OperandExtendedAdd =
1063 getAddExpr(getSignExtendExpr(Start, WideTy),
1064 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
1065 getSignExtendExpr(Step, WideTy)));
1066 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd)
1067 // Return the expression with the addrec on the outside.
1068 return getAddRecExpr(getSignExtendExpr(Start, Ty),
1069 getSignExtendExpr(Step, Ty),
1072 // Similar to above, only this time treat the step value as unsigned.
1073 // This covers loops that count up with an unsigned step.
1074 const SCEV *UMul = getMulExpr(CastedMaxBECount, Step);
1075 Add = getAddExpr(Start, UMul);
1076 OperandExtendedAdd =
1077 getAddExpr(getSignExtendExpr(Start, WideTy),
1078 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
1079 getZeroExtendExpr(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 getZeroExtendExpr(Step, Ty),
1087 // If the backedge is guarded by a comparison with the pre-inc value
1088 // the addrec is safe. Also, if the entry is guarded by a comparison
1089 // with the start value and the backedge is guarded by a comparison
1090 // with the post-inc value, the addrec is safe.
1091 if (isKnownPositive(Step)) {
1092 const SCEV *N = getConstant(APInt::getSignedMinValue(BitWidth) -
1093 getSignedRange(Step).getSignedMax());
1094 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT, AR, N) ||
1095 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_SLT, Start, N) &&
1096 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT,
1097 AR->getPostIncExpr(*this), N)))
1098 // Return the expression with the addrec on the outside.
1099 return getAddRecExpr(getSignExtendExpr(Start, Ty),
1100 getSignExtendExpr(Step, Ty),
1102 } else if (isKnownNegative(Step)) {
1103 const SCEV *N = getConstant(APInt::getSignedMaxValue(BitWidth) -
1104 getSignedRange(Step).getSignedMin());
1105 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT, AR, N) ||
1106 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_SGT, Start, N) &&
1107 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT,
1108 AR->getPostIncExpr(*this), N)))
1109 // Return the expression with the addrec on the outside.
1110 return getAddRecExpr(getSignExtendExpr(Start, Ty),
1111 getSignExtendExpr(Step, Ty),
1117 // The cast wasn't folded; create an explicit cast node.
1118 // Recompute the insert position, as it may have been invalidated.
1119 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1120 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
1122 UniqueSCEVs.InsertNode(S, IP);
1126 /// getAnyExtendExpr - Return a SCEV for the given operand extended with
1127 /// unspecified bits out to the given type.
1129 const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
1131 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1132 "This is not an extending conversion!");
1133 assert(isSCEVable(Ty) &&
1134 "This is not a conversion to a SCEVable type!");
1135 Ty = getEffectiveSCEVType(Ty);
1137 // Sign-extend negative constants.
1138 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1139 if (SC->getValue()->getValue().isNegative())
1140 return getSignExtendExpr(Op, Ty);
1142 // Peel off a truncate cast.
1143 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
1144 const SCEV *NewOp = T->getOperand();
1145 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
1146 return getAnyExtendExpr(NewOp, Ty);
1147 return getTruncateOrNoop(NewOp, Ty);
1150 // Next try a zext cast. If the cast is folded, use it.
1151 const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
1152 if (!isa<SCEVZeroExtendExpr>(ZExt))
1155 // Next try a sext cast. If the cast is folded, use it.
1156 const SCEV *SExt = getSignExtendExpr(Op, Ty);
1157 if (!isa<SCEVSignExtendExpr>(SExt))
1160 // Force the cast to be folded into the operands of an addrec.
1161 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
1162 SmallVector<const SCEV *, 4> Ops;
1163 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
1165 Ops.push_back(getAnyExtendExpr(*I, Ty));
1166 return getAddRecExpr(Ops, AR->getLoop());
1169 // If the expression is obviously signed, use the sext cast value.
1170 if (isa<SCEVSMaxExpr>(Op))
1173 // Absent any other information, use the zext cast value.
1177 /// CollectAddOperandsWithScales - Process the given Ops list, which is
1178 /// a list of operands to be added under the given scale, update the given
1179 /// map. This is a helper function for getAddRecExpr. As an example of
1180 /// what it does, given a sequence of operands that would form an add
1181 /// expression like this:
1183 /// m + n + 13 + (A * (o + p + (B * q + m + 29))) + r + (-1 * r)
1185 /// where A and B are constants, update the map with these values:
1187 /// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
1189 /// and add 13 + A*B*29 to AccumulatedConstant.
1190 /// This will allow getAddRecExpr to produce this:
1192 /// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
1194 /// This form often exposes folding opportunities that are hidden in
1195 /// the original operand list.
1197 /// Return true iff it appears that any interesting folding opportunities
1198 /// may be exposed. This helps getAddRecExpr short-circuit extra work in
1199 /// the common case where no interesting opportunities are present, and
1200 /// is also used as a check to avoid infinite recursion.
1203 CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
1204 SmallVector<const SCEV *, 8> &NewOps,
1205 APInt &AccumulatedConstant,
1206 const SCEV *const *Ops, size_t NumOperands,
1208 ScalarEvolution &SE) {
1209 bool Interesting = false;
1211 // Iterate over the add operands.
1212 for (unsigned i = 0, e = NumOperands; i != e; ++i) {
1213 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
1214 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
1216 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue();
1217 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
1218 // A multiplication of a constant with another add; recurse.
1219 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1));
1221 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1222 Add->op_begin(), Add->getNumOperands(),
1225 // A multiplication of a constant with some other value. Update
1227 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
1228 const SCEV *Key = SE.getMulExpr(MulOps);
1229 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1230 M.insert(std::make_pair(Key, NewScale));
1232 NewOps.push_back(Pair.first->first);
1234 Pair.first->second += NewScale;
1235 // The map already had an entry for this value, which may indicate
1236 // a folding opportunity.
1240 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1241 // Pull a buried constant out to the outside.
1242 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
1244 AccumulatedConstant += Scale * C->getValue()->getValue();
1246 // An ordinary operand. Update the map.
1247 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1248 M.insert(std::make_pair(Ops[i], Scale));
1250 NewOps.push_back(Pair.first->first);
1252 Pair.first->second += Scale;
1253 // The map already had an entry for this value, which may indicate
1254 // a folding opportunity.
1264 struct APIntCompare {
1265 bool operator()(const APInt &LHS, const APInt &RHS) const {
1266 return LHS.ult(RHS);
1271 /// getAddExpr - Get a canonical add expression, or something simpler if
1273 const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
1274 bool HasNUW, bool HasNSW) {
1275 assert(!Ops.empty() && "Cannot get empty add!");
1276 if (Ops.size() == 1) return Ops[0];
1278 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1279 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
1280 getEffectiveSCEVType(Ops[0]->getType()) &&
1281 "SCEVAddExpr operand types don't match!");
1284 // If HasNSW is true and all the operands are non-negative, infer HasNUW.
1285 if (!HasNUW && HasNSW) {
1287 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1288 if (!isKnownNonNegative(Ops[i])) {
1292 if (All) HasNUW = true;
1295 // Sort by complexity, this groups all similar expression types together.
1296 GroupByComplexity(Ops, LI);
1298 // If there are any constants, fold them together.
1300 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1302 assert(Idx < Ops.size());
1303 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1304 // We found two constants, fold them together!
1305 Ops[0] = getConstant(LHSC->getValue()->getValue() +
1306 RHSC->getValue()->getValue());
1307 if (Ops.size() == 2) return Ops[0];
1308 Ops.erase(Ops.begin()+1); // Erase the folded element
1309 LHSC = cast<SCEVConstant>(Ops[0]);
1312 // If we are left with a constant zero being added, strip it off.
1313 if (LHSC->getValue()->isZero()) {
1314 Ops.erase(Ops.begin());
1318 if (Ops.size() == 1) return Ops[0];
1321 // Okay, check to see if the same value occurs in the operand list twice. If
1322 // so, merge them together into an multiply expression. Since we sorted the
1323 // list, these values are required to be adjacent.
1324 const Type *Ty = Ops[0]->getType();
1325 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
1326 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
1327 // Found a match, merge the two values into a multiply, and add any
1328 // remaining values to the result.
1329 const SCEV *Two = getIntegerSCEV(2, Ty);
1330 const SCEV *Mul = getMulExpr(Ops[i], Two);
1331 if (Ops.size() == 2)
1333 Ops.erase(Ops.begin()+i, Ops.begin()+i+2);
1335 return getAddExpr(Ops, HasNUW, HasNSW);
1338 // Check for truncates. If all the operands are truncated from the same
1339 // type, see if factoring out the truncate would permit the result to be
1340 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
1341 // if the contents of the resulting outer trunc fold to something simple.
1342 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
1343 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
1344 const Type *DstType = Trunc->getType();
1345 const Type *SrcType = Trunc->getOperand()->getType();
1346 SmallVector<const SCEV *, 8> LargeOps;
1348 // Check all the operands to see if they can be represented in the
1349 // source type of the truncate.
1350 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1351 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
1352 if (T->getOperand()->getType() != SrcType) {
1356 LargeOps.push_back(T->getOperand());
1357 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1358 // This could be either sign or zero extension, but sign extension
1359 // is much more likely to be foldable here.
1360 LargeOps.push_back(getSignExtendExpr(C, SrcType));
1361 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
1362 SmallVector<const SCEV *, 8> LargeMulOps;
1363 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
1364 if (const SCEVTruncateExpr *T =
1365 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
1366 if (T->getOperand()->getType() != SrcType) {
1370 LargeMulOps.push_back(T->getOperand());
1371 } else if (const SCEVConstant *C =
1372 dyn_cast<SCEVConstant>(M->getOperand(j))) {
1373 // This could be either sign or zero extension, but sign extension
1374 // is much more likely to be foldable here.
1375 LargeMulOps.push_back(getSignExtendExpr(C, SrcType));
1382 LargeOps.push_back(getMulExpr(LargeMulOps));
1389 // Evaluate the expression in the larger type.
1390 const SCEV *Fold = getAddExpr(LargeOps, HasNUW, HasNSW);
1391 // If it folds to something simple, use it. Otherwise, don't.
1392 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
1393 return getTruncateExpr(Fold, DstType);
1397 // Skip past any other cast SCEVs.
1398 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
1401 // If there are add operands they would be next.
1402 if (Idx < Ops.size()) {
1403 bool DeletedAdd = false;
1404 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
1405 // If we have an add, expand the add operands onto the end of the operands
1407 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end());
1408 Ops.erase(Ops.begin()+Idx);
1412 // If we deleted at least one add, we added operands to the end of the list,
1413 // and they are not necessarily sorted. Recurse to resort and resimplify
1414 // any operands we just acquired.
1416 return getAddExpr(Ops);
1419 // Skip over the add expression until we get to a multiply.
1420 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1423 // Check to see if there are any folding opportunities present with
1424 // operands multiplied by constant values.
1425 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
1426 uint64_t BitWidth = getTypeSizeInBits(Ty);
1427 DenseMap<const SCEV *, APInt> M;
1428 SmallVector<const SCEV *, 8> NewOps;
1429 APInt AccumulatedConstant(BitWidth, 0);
1430 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1431 Ops.data(), Ops.size(),
1432 APInt(BitWidth, 1), *this)) {
1433 // Some interesting folding opportunity is present, so its worthwhile to
1434 // re-generate the operands list. Group the operands by constant scale,
1435 // to avoid multiplying by the same constant scale multiple times.
1436 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
1437 for (SmallVector<const SCEV *, 8>::iterator I = NewOps.begin(),
1438 E = NewOps.end(); I != E; ++I)
1439 MulOpLists[M.find(*I)->second].push_back(*I);
1440 // Re-generate the operands list.
1442 if (AccumulatedConstant != 0)
1443 Ops.push_back(getConstant(AccumulatedConstant));
1444 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator
1445 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I)
1447 Ops.push_back(getMulExpr(getConstant(I->first),
1448 getAddExpr(I->second)));
1450 return getIntegerSCEV(0, Ty);
1451 if (Ops.size() == 1)
1453 return getAddExpr(Ops);
1457 // If we are adding something to a multiply expression, make sure the
1458 // something is not already an operand of the multiply. If so, merge it into
1460 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
1461 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
1462 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
1463 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
1464 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
1465 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(Ops[AddOp])) {
1466 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
1467 const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
1468 if (Mul->getNumOperands() != 2) {
1469 // If the multiply has more than two operands, we must get the
1471 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), Mul->op_end());
1472 MulOps.erase(MulOps.begin()+MulOp);
1473 InnerMul = getMulExpr(MulOps);
1475 const SCEV *One = getIntegerSCEV(1, Ty);
1476 const SCEV *AddOne = getAddExpr(InnerMul, One);
1477 const SCEV *OuterMul = getMulExpr(AddOne, Ops[AddOp]);
1478 if (Ops.size() == 2) return OuterMul;
1480 Ops.erase(Ops.begin()+AddOp);
1481 Ops.erase(Ops.begin()+Idx-1);
1483 Ops.erase(Ops.begin()+Idx);
1484 Ops.erase(Ops.begin()+AddOp-1);
1486 Ops.push_back(OuterMul);
1487 return getAddExpr(Ops);
1490 // Check this multiply against other multiplies being added together.
1491 for (unsigned OtherMulIdx = Idx+1;
1492 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
1494 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
1495 // If MulOp occurs in OtherMul, we can fold the two multiplies
1497 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
1498 OMulOp != e; ++OMulOp)
1499 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
1500 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
1501 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
1502 if (Mul->getNumOperands() != 2) {
1503 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
1505 MulOps.erase(MulOps.begin()+MulOp);
1506 InnerMul1 = getMulExpr(MulOps);
1508 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
1509 if (OtherMul->getNumOperands() != 2) {
1510 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
1511 OtherMul->op_end());
1512 MulOps.erase(MulOps.begin()+OMulOp);
1513 InnerMul2 = getMulExpr(MulOps);
1515 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
1516 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
1517 if (Ops.size() == 2) return OuterMul;
1518 Ops.erase(Ops.begin()+Idx);
1519 Ops.erase(Ops.begin()+OtherMulIdx-1);
1520 Ops.push_back(OuterMul);
1521 return getAddExpr(Ops);
1527 // If there are any add recurrences in the operands list, see if any other
1528 // added values are loop invariant. If so, we can fold them into the
1530 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1533 // Scan over all recurrences, trying to fold loop invariants into them.
1534 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1535 // Scan all of the other operands to this add and add them to the vector if
1536 // they are loop invariant w.r.t. the recurrence.
1537 SmallVector<const SCEV *, 8> LIOps;
1538 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1539 const Loop *AddRecLoop = AddRec->getLoop();
1540 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1541 if (Ops[i]->isLoopInvariant(AddRecLoop)) {
1542 LIOps.push_back(Ops[i]);
1543 Ops.erase(Ops.begin()+i);
1547 // If we found some loop invariants, fold them into the recurrence.
1548 if (!LIOps.empty()) {
1549 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
1550 LIOps.push_back(AddRec->getStart());
1552 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
1554 AddRecOps[0] = getAddExpr(LIOps);
1556 // It's tempting to propagate NUW/NSW flags here, but nuw/nsw addition
1557 // is not associative so this isn't necessarily safe.
1558 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop);
1560 // If all of the other operands were loop invariant, we are done.
1561 if (Ops.size() == 1) return NewRec;
1563 // Otherwise, add the folded AddRec by the non-liv parts.
1564 for (unsigned i = 0;; ++i)
1565 if (Ops[i] == AddRec) {
1569 return getAddExpr(Ops);
1572 // Okay, if there weren't any loop invariants to be folded, check to see if
1573 // there are multiple AddRec's with the same loop induction variable being
1574 // added together. If so, we can fold them.
1575 for (unsigned OtherIdx = Idx+1;
1576 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
1577 if (OtherIdx != Idx) {
1578 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
1579 if (AddRecLoop == OtherAddRec->getLoop()) {
1580 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D}
1581 SmallVector<const SCEV *, 4> NewOps(AddRec->op_begin(),
1583 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) {
1584 if (i >= NewOps.size()) {
1585 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i,
1586 OtherAddRec->op_end());
1589 NewOps[i] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i));
1591 const SCEV *NewAddRec = getAddRecExpr(NewOps, AddRecLoop);
1593 if (Ops.size() == 2) return NewAddRec;
1595 Ops.erase(Ops.begin()+Idx);
1596 Ops.erase(Ops.begin()+OtherIdx-1);
1597 Ops.push_back(NewAddRec);
1598 return getAddExpr(Ops);
1602 // Otherwise couldn't fold anything into this recurrence. Move onto the
1606 // Okay, it looks like we really DO need an add expr. Check to see if we
1607 // already have one, otherwise create a new one.
1608 FoldingSetNodeID ID;
1609 ID.AddInteger(scAddExpr);
1610 ID.AddInteger(Ops.size());
1611 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1612 ID.AddPointer(Ops[i]);
1615 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1617 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
1618 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
1619 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator),
1621 UniqueSCEVs.InsertNode(S, IP);
1623 if (HasNUW) S->setHasNoUnsignedWrap(true);
1624 if (HasNSW) S->setHasNoSignedWrap(true);
1628 /// getMulExpr - Get a canonical multiply expression, or something simpler if
1630 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
1631 bool HasNUW, bool HasNSW) {
1632 assert(!Ops.empty() && "Cannot get empty mul!");
1633 if (Ops.size() == 1) return Ops[0];
1635 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1636 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
1637 getEffectiveSCEVType(Ops[0]->getType()) &&
1638 "SCEVMulExpr operand types don't match!");
1641 // If HasNSW is true and all the operands are non-negative, infer HasNUW.
1642 if (!HasNUW && HasNSW) {
1644 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1645 if (!isKnownNonNegative(Ops[i])) {
1649 if (All) HasNUW = true;
1652 // Sort by complexity, this groups all similar expression types together.
1653 GroupByComplexity(Ops, LI);
1655 // If there are any constants, fold them together.
1657 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1659 // C1*(C2+V) -> C1*C2 + C1*V
1660 if (Ops.size() == 2)
1661 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
1662 if (Add->getNumOperands() == 2 &&
1663 isa<SCEVConstant>(Add->getOperand(0)))
1664 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
1665 getMulExpr(LHSC, Add->getOperand(1)));
1668 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1669 // We found two constants, fold them together!
1670 ConstantInt *Fold = ConstantInt::get(getContext(),
1671 LHSC->getValue()->getValue() *
1672 RHSC->getValue()->getValue());
1673 Ops[0] = getConstant(Fold);
1674 Ops.erase(Ops.begin()+1); // Erase the folded element
1675 if (Ops.size() == 1) return Ops[0];
1676 LHSC = cast<SCEVConstant>(Ops[0]);
1679 // If we are left with a constant one being multiplied, strip it off.
1680 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
1681 Ops.erase(Ops.begin());
1683 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
1684 // If we have a multiply of zero, it will always be zero.
1686 } else if (Ops[0]->isAllOnesValue()) {
1687 // If we have a mul by -1 of an add, try distributing the -1 among the
1689 if (Ops.size() == 2)
1690 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
1691 SmallVector<const SCEV *, 4> NewOps;
1692 bool AnyFolded = false;
1693 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(), E = Add->op_end();
1695 const SCEV *Mul = getMulExpr(Ops[0], *I);
1696 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
1697 NewOps.push_back(Mul);
1700 return getAddExpr(NewOps);
1704 if (Ops.size() == 1)
1708 // Skip over the add expression until we get to a multiply.
1709 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1712 // If there are mul operands inline them all into this expression.
1713 if (Idx < Ops.size()) {
1714 bool DeletedMul = false;
1715 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
1716 // If we have an mul, expand the mul operands onto the end of the operands
1718 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end());
1719 Ops.erase(Ops.begin()+Idx);
1723 // If we deleted at least one mul, we added operands to the end of the list,
1724 // and they are not necessarily sorted. Recurse to resort and resimplify
1725 // any operands we just acquired.
1727 return getMulExpr(Ops);
1730 // If there are any add recurrences in the operands list, see if any other
1731 // added values are loop invariant. If so, we can fold them into the
1733 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1736 // Scan over all recurrences, trying to fold loop invariants into them.
1737 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1738 // Scan all of the other operands to this mul and add them to the vector if
1739 // they are loop invariant w.r.t. the recurrence.
1740 SmallVector<const SCEV *, 8> LIOps;
1741 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1742 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1743 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
1744 LIOps.push_back(Ops[i]);
1745 Ops.erase(Ops.begin()+i);
1749 // If we found some loop invariants, fold them into the recurrence.
1750 if (!LIOps.empty()) {
1751 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
1752 SmallVector<const SCEV *, 4> NewOps;
1753 NewOps.reserve(AddRec->getNumOperands());
1754 if (LIOps.size() == 1) {
1755 const SCEV *Scale = LIOps[0];
1756 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
1757 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
1759 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
1760 SmallVector<const SCEV *, 4> MulOps(LIOps.begin(), LIOps.end());
1761 MulOps.push_back(AddRec->getOperand(i));
1762 NewOps.push_back(getMulExpr(MulOps));
1766 // It's tempting to propagate the NSW flag here, but nsw multiplication
1767 // is not associative so this isn't necessarily safe.
1768 const SCEV *NewRec = getAddRecExpr(NewOps, AddRec->getLoop(),
1769 HasNUW && AddRec->hasNoUnsignedWrap(),
1772 // If all of the other operands were loop invariant, we are done.
1773 if (Ops.size() == 1) return NewRec;
1775 // Otherwise, multiply the folded AddRec by the non-liv parts.
1776 for (unsigned i = 0;; ++i)
1777 if (Ops[i] == AddRec) {
1781 return getMulExpr(Ops);
1784 // Okay, if there weren't any loop invariants to be folded, check to see if
1785 // there are multiple AddRec's with the same loop induction variable being
1786 // multiplied together. If so, we can fold them.
1787 for (unsigned OtherIdx = Idx+1;
1788 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
1789 if (OtherIdx != Idx) {
1790 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
1791 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
1792 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D}
1793 const SCEVAddRecExpr *F = AddRec, *G = OtherAddRec;
1794 const SCEV *NewStart = getMulExpr(F->getStart(),
1796 const SCEV *B = F->getStepRecurrence(*this);
1797 const SCEV *D = G->getStepRecurrence(*this);
1798 const SCEV *NewStep = getAddExpr(getMulExpr(F, D),
1801 const SCEV *NewAddRec = getAddRecExpr(NewStart, NewStep,
1803 if (Ops.size() == 2) return NewAddRec;
1805 Ops.erase(Ops.begin()+Idx);
1806 Ops.erase(Ops.begin()+OtherIdx-1);
1807 Ops.push_back(NewAddRec);
1808 return getMulExpr(Ops);
1812 // Otherwise couldn't fold anything into this recurrence. Move onto the
1816 // Okay, it looks like we really DO need an mul expr. Check to see if we
1817 // already have one, otherwise create a new one.
1818 FoldingSetNodeID ID;
1819 ID.AddInteger(scMulExpr);
1820 ID.AddInteger(Ops.size());
1821 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1822 ID.AddPointer(Ops[i]);
1825 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1827 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
1828 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
1829 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
1831 UniqueSCEVs.InsertNode(S, IP);
1833 if (HasNUW) S->setHasNoUnsignedWrap(true);
1834 if (HasNSW) S->setHasNoSignedWrap(true);
1838 /// getUDivExpr - Get a canonical unsigned division expression, or something
1839 /// simpler if possible.
1840 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
1842 assert(getEffectiveSCEVType(LHS->getType()) ==
1843 getEffectiveSCEVType(RHS->getType()) &&
1844 "SCEVUDivExpr operand types don't match!");
1846 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
1847 if (RHSC->getValue()->equalsInt(1))
1848 return LHS; // X udiv 1 --> x
1849 // If the denominator is zero, the result of the udiv is undefined. Don't
1850 // try to analyze it, because the resolution chosen here may differ from
1851 // the resolution chosen in other parts of the compiler.
1852 if (!RHSC->getValue()->isZero()) {
1853 // Determine if the division can be folded into the operands of
1855 // TODO: Generalize this to non-constants by using known-bits information.
1856 const Type *Ty = LHS->getType();
1857 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
1858 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ;
1859 // For non-power-of-two values, effectively round the value up to the
1860 // nearest power of two.
1861 if (!RHSC->getValue()->getValue().isPowerOf2())
1863 const IntegerType *ExtTy =
1864 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
1865 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
1866 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
1867 if (const SCEVConstant *Step =
1868 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this)))
1869 if (!Step->getValue()->getValue()
1870 .urem(RHSC->getValue()->getValue()) &&
1871 getZeroExtendExpr(AR, ExtTy) ==
1872 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
1873 getZeroExtendExpr(Step, ExtTy),
1875 SmallVector<const SCEV *, 4> Operands;
1876 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i)
1877 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS));
1878 return getAddRecExpr(Operands, AR->getLoop());
1880 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
1881 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
1882 SmallVector<const SCEV *, 4> Operands;
1883 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i)
1884 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy));
1885 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
1886 // Find an operand that's safely divisible.
1887 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
1888 const SCEV *Op = M->getOperand(i);
1889 const SCEV *Div = getUDivExpr(Op, RHSC);
1890 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
1891 Operands = SmallVector<const SCEV *, 4>(M->op_begin(),
1894 return getMulExpr(Operands);
1898 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
1899 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(LHS)) {
1900 SmallVector<const SCEV *, 4> Operands;
1901 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i)
1902 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy));
1903 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
1905 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
1906 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
1907 if (isa<SCEVUDivExpr>(Op) ||
1908 getMulExpr(Op, RHS) != A->getOperand(i))
1910 Operands.push_back(Op);
1912 if (Operands.size() == A->getNumOperands())
1913 return getAddExpr(Operands);
1917 // Fold if both operands are constant.
1918 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
1919 Constant *LHSCV = LHSC->getValue();
1920 Constant *RHSCV = RHSC->getValue();
1921 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
1927 FoldingSetNodeID ID;
1928 ID.AddInteger(scUDivExpr);
1932 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1933 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
1935 UniqueSCEVs.InsertNode(S, IP);
1940 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
1941 /// Simplify the expression as much as possible.
1942 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start,
1943 const SCEV *Step, const Loop *L,
1944 bool HasNUW, bool HasNSW) {
1945 SmallVector<const SCEV *, 4> Operands;
1946 Operands.push_back(Start);
1947 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
1948 if (StepChrec->getLoop() == L) {
1949 Operands.insert(Operands.end(), StepChrec->op_begin(),
1950 StepChrec->op_end());
1951 return getAddRecExpr(Operands, L);
1954 Operands.push_back(Step);
1955 return getAddRecExpr(Operands, L, HasNUW, HasNSW);
1958 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
1959 /// Simplify the expression as much as possible.
1961 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
1963 bool HasNUW, bool HasNSW) {
1964 if (Operands.size() == 1) return Operands[0];
1966 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
1967 assert(getEffectiveSCEVType(Operands[i]->getType()) ==
1968 getEffectiveSCEVType(Operands[0]->getType()) &&
1969 "SCEVAddRecExpr operand types don't match!");
1972 if (Operands.back()->isZero()) {
1973 Operands.pop_back();
1974 return getAddRecExpr(Operands, L, HasNUW, HasNSW); // {X,+,0} --> X
1977 // It's tempting to want to call getMaxBackedgeTakenCount count here and
1978 // use that information to infer NUW and NSW flags. However, computing a
1979 // BE count requires calling getAddRecExpr, so we may not yet have a
1980 // meaningful BE count at this point (and if we don't, we'd be stuck
1981 // with a SCEVCouldNotCompute as the cached BE count).
1983 // If HasNSW is true and all the operands are non-negative, infer HasNUW.
1984 if (!HasNUW && HasNSW) {
1986 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
1987 if (!isKnownNonNegative(Operands[i])) {
1991 if (All) HasNUW = true;
1994 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
1995 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
1996 const Loop *NestedLoop = NestedAR->getLoop();
1997 if (L->contains(NestedLoop->getHeader()) ?
1998 (L->getLoopDepth() < NestedLoop->getLoopDepth()) :
1999 (!NestedLoop->contains(L->getHeader()) &&
2000 DT->dominates(L->getHeader(), NestedLoop->getHeader()))) {
2001 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
2002 NestedAR->op_end());
2003 Operands[0] = NestedAR->getStart();
2004 // AddRecs require their operands be loop-invariant with respect to their
2005 // loops. Don't perform this transformation if it would break this
2007 bool AllInvariant = true;
2008 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2009 if (!Operands[i]->isLoopInvariant(L)) {
2010 AllInvariant = false;
2014 NestedOperands[0] = getAddRecExpr(Operands, L);
2015 AllInvariant = true;
2016 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i)
2017 if (!NestedOperands[i]->isLoopInvariant(NestedLoop)) {
2018 AllInvariant = false;
2022 // Ok, both add recurrences are valid after the transformation.
2023 return getAddRecExpr(NestedOperands, NestedLoop, HasNUW, HasNSW);
2025 // Reset Operands to its original state.
2026 Operands[0] = NestedAR;
2030 // Okay, it looks like we really DO need an addrec expr. Check to see if we
2031 // already have one, otherwise create a new one.
2032 FoldingSetNodeID ID;
2033 ID.AddInteger(scAddRecExpr);
2034 ID.AddInteger(Operands.size());
2035 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2036 ID.AddPointer(Operands[i]);
2040 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2042 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size());
2043 std::uninitialized_copy(Operands.begin(), Operands.end(), O);
2044 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator),
2045 O, Operands.size(), L);
2046 UniqueSCEVs.InsertNode(S, IP);
2048 if (HasNUW) S->setHasNoUnsignedWrap(true);
2049 if (HasNSW) S->setHasNoSignedWrap(true);
2053 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
2055 SmallVector<const SCEV *, 2> Ops;
2058 return getSMaxExpr(Ops);
2062 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2063 assert(!Ops.empty() && "Cannot get empty smax!");
2064 if (Ops.size() == 1) return Ops[0];
2066 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2067 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
2068 getEffectiveSCEVType(Ops[0]->getType()) &&
2069 "SCEVSMaxExpr operand types don't match!");
2072 // Sort by complexity, this groups all similar expression types together.
2073 GroupByComplexity(Ops, LI);
2075 // If there are any constants, fold them together.
2077 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2079 assert(Idx < Ops.size());
2080 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2081 // We found two constants, fold them together!
2082 ConstantInt *Fold = ConstantInt::get(getContext(),
2083 APIntOps::smax(LHSC->getValue()->getValue(),
2084 RHSC->getValue()->getValue()));
2085 Ops[0] = getConstant(Fold);
2086 Ops.erase(Ops.begin()+1); // Erase the folded element
2087 if (Ops.size() == 1) return Ops[0];
2088 LHSC = cast<SCEVConstant>(Ops[0]);
2091 // If we are left with a constant minimum-int, strip it off.
2092 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
2093 Ops.erase(Ops.begin());
2095 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
2096 // If we have an smax with a constant maximum-int, it will always be
2101 if (Ops.size() == 1) return Ops[0];
2104 // Find the first SMax
2105 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
2108 // Check to see if one of the operands is an SMax. If so, expand its operands
2109 // onto our operand list, and recurse to simplify.
2110 if (Idx < Ops.size()) {
2111 bool DeletedSMax = false;
2112 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
2113 Ops.insert(Ops.end(), SMax->op_begin(), SMax->op_end());
2114 Ops.erase(Ops.begin()+Idx);
2119 return getSMaxExpr(Ops);
2122 // Okay, check to see if the same value occurs in the operand list twice. If
2123 // so, delete one. Since we sorted the list, these values are required to
2125 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2126 // X smax Y smax Y --> X smax Y
2127 // X smax Y --> X, if X is always greater than Y
2128 if (Ops[i] == Ops[i+1] ||
2129 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) {
2130 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2132 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) {
2133 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2137 if (Ops.size() == 1) return Ops[0];
2139 assert(!Ops.empty() && "Reduced smax down to nothing!");
2141 // Okay, it looks like we really DO need an smax expr. Check to see if we
2142 // already have one, otherwise create a new one.
2143 FoldingSetNodeID ID;
2144 ID.AddInteger(scSMaxExpr);
2145 ID.AddInteger(Ops.size());
2146 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2147 ID.AddPointer(Ops[i]);
2149 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2150 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2151 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2152 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator),
2154 UniqueSCEVs.InsertNode(S, IP);
2158 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
2160 SmallVector<const SCEV *, 2> Ops;
2163 return getUMaxExpr(Ops);
2167 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2168 assert(!Ops.empty() && "Cannot get empty umax!");
2169 if (Ops.size() == 1) return Ops[0];
2171 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2172 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
2173 getEffectiveSCEVType(Ops[0]->getType()) &&
2174 "SCEVUMaxExpr operand types don't match!");
2177 // Sort by complexity, this groups all similar expression types together.
2178 GroupByComplexity(Ops, LI);
2180 // If there are any constants, fold them together.
2182 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2184 assert(Idx < Ops.size());
2185 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2186 // We found two constants, fold them together!
2187 ConstantInt *Fold = ConstantInt::get(getContext(),
2188 APIntOps::umax(LHSC->getValue()->getValue(),
2189 RHSC->getValue()->getValue()));
2190 Ops[0] = getConstant(Fold);
2191 Ops.erase(Ops.begin()+1); // Erase the folded element
2192 if (Ops.size() == 1) return Ops[0];
2193 LHSC = cast<SCEVConstant>(Ops[0]);
2196 // If we are left with a constant minimum-int, strip it off.
2197 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
2198 Ops.erase(Ops.begin());
2200 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
2201 // If we have an umax with a constant maximum-int, it will always be
2206 if (Ops.size() == 1) return Ops[0];
2209 // Find the first UMax
2210 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
2213 // Check to see if one of the operands is a UMax. If so, expand its operands
2214 // onto our operand list, and recurse to simplify.
2215 if (Idx < Ops.size()) {
2216 bool DeletedUMax = false;
2217 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
2218 Ops.insert(Ops.end(), UMax->op_begin(), UMax->op_end());
2219 Ops.erase(Ops.begin()+Idx);
2224 return getUMaxExpr(Ops);
2227 // Okay, check to see if the same value occurs in the operand list twice. If
2228 // so, delete one. Since we sorted the list, these values are required to
2230 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2231 // X umax Y umax Y --> X umax Y
2232 // X umax Y --> X, if X is always greater than Y
2233 if (Ops[i] == Ops[i+1] ||
2234 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) {
2235 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2237 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) {
2238 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2242 if (Ops.size() == 1) return Ops[0];
2244 assert(!Ops.empty() && "Reduced umax down to nothing!");
2246 // Okay, it looks like we really DO need a umax expr. Check to see if we
2247 // already have one, otherwise create a new one.
2248 FoldingSetNodeID ID;
2249 ID.AddInteger(scUMaxExpr);
2250 ID.AddInteger(Ops.size());
2251 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2252 ID.AddPointer(Ops[i]);
2254 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2255 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2256 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2257 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator),
2259 UniqueSCEVs.InsertNode(S, IP);
2263 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
2265 // ~smax(~x, ~y) == smin(x, y).
2266 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2269 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
2271 // ~umax(~x, ~y) == umin(x, y)
2272 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2275 const SCEV *ScalarEvolution::getSizeOfExpr(const Type *AllocTy) {
2276 // If we have TargetData, we can bypass creating a target-independent
2277 // constant expression and then folding it back into a ConstantInt.
2278 // This is just a compile-time optimization.
2280 return getConstant(TD->getIntPtrType(getContext()),
2281 TD->getTypeAllocSize(AllocTy));
2283 Constant *C = ConstantExpr::getSizeOf(AllocTy);
2284 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2285 C = ConstantFoldConstantExpression(CE, TD);
2286 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2287 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2290 const SCEV *ScalarEvolution::getAlignOfExpr(const Type *AllocTy) {
2291 Constant *C = ConstantExpr::getAlignOf(AllocTy);
2292 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2293 C = ConstantFoldConstantExpression(CE, TD);
2294 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2295 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2298 const SCEV *ScalarEvolution::getOffsetOfExpr(const StructType *STy,
2300 // If we have TargetData, we can bypass creating a target-independent
2301 // constant expression and then folding it back into a ConstantInt.
2302 // This is just a compile-time optimization.
2304 return getConstant(TD->getIntPtrType(getContext()),
2305 TD->getStructLayout(STy)->getElementOffset(FieldNo));
2307 Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo);
2308 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2309 C = ConstantFoldConstantExpression(CE, TD);
2310 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy));
2311 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2314 const SCEV *ScalarEvolution::getOffsetOfExpr(const Type *CTy,
2315 Constant *FieldNo) {
2316 Constant *C = ConstantExpr::getOffsetOf(CTy, FieldNo);
2317 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2318 C = ConstantFoldConstantExpression(CE, TD);
2319 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(CTy));
2320 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2323 const SCEV *ScalarEvolution::getUnknown(Value *V) {
2324 // Don't attempt to do anything other than create a SCEVUnknown object
2325 // here. createSCEV only calls getUnknown after checking for all other
2326 // interesting possibilities, and any other code that calls getUnknown
2327 // is doing so in order to hide a value from SCEV canonicalization.
2329 FoldingSetNodeID ID;
2330 ID.AddInteger(scUnknown);
2333 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2334 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V);
2335 UniqueSCEVs.InsertNode(S, IP);
2339 //===----------------------------------------------------------------------===//
2340 // Basic SCEV Analysis and PHI Idiom Recognition Code
2343 /// isSCEVable - Test if values of the given type are analyzable within
2344 /// the SCEV framework. This primarily includes integer types, and it
2345 /// can optionally include pointer types if the ScalarEvolution class
2346 /// has access to target-specific information.
2347 bool ScalarEvolution::isSCEVable(const Type *Ty) const {
2348 // Integers and pointers are always SCEVable.
2349 return Ty->isIntegerTy() || Ty->isPointerTy();
2352 /// getTypeSizeInBits - Return the size in bits of the specified type,
2353 /// for which isSCEVable must return true.
2354 uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const {
2355 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2357 // If we have a TargetData, use it!
2359 return TD->getTypeSizeInBits(Ty);
2361 // Integer types have fixed sizes.
2362 if (Ty->isIntegerTy())
2363 return Ty->getPrimitiveSizeInBits();
2365 // The only other support type is pointer. Without TargetData, conservatively
2366 // assume pointers are 64-bit.
2367 assert(Ty->isPointerTy() && "isSCEVable permitted a non-SCEVable type!");
2371 /// getEffectiveSCEVType - Return a type with the same bitwidth as
2372 /// the given type and which represents how SCEV will treat the given
2373 /// type, for which isSCEVable must return true. For pointer types,
2374 /// this is the pointer-sized integer type.
2375 const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const {
2376 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2378 if (Ty->isIntegerTy())
2381 // The only other support type is pointer.
2382 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
2383 if (TD) return TD->getIntPtrType(getContext());
2385 // Without TargetData, conservatively assume pointers are 64-bit.
2386 return Type::getInt64Ty(getContext());
2389 const SCEV *ScalarEvolution::getCouldNotCompute() {
2390 return &CouldNotCompute;
2393 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
2394 /// expression and create a new one.
2395 const SCEV *ScalarEvolution::getSCEV(Value *V) {
2396 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
2398 std::map<SCEVCallbackVH, const SCEV *>::iterator I = Scalars.find(V);
2399 if (I != Scalars.end()) return I->second;
2400 const SCEV *S = createSCEV(V);
2401 Scalars.insert(std::make_pair(SCEVCallbackVH(V, this), S));
2405 /// getIntegerSCEV - Given a SCEVable type, create a constant for the
2406 /// specified signed integer value and return a SCEV for the constant.
2407 const SCEV *ScalarEvolution::getIntegerSCEV(int64_t Val, const Type *Ty) {
2408 const IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty));
2409 return getConstant(ConstantInt::get(ITy, Val));
2412 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
2414 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) {
2415 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2417 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
2419 const Type *Ty = V->getType();
2420 Ty = getEffectiveSCEVType(Ty);
2421 return getMulExpr(V,
2422 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))));
2425 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
2426 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
2427 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2429 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
2431 const Type *Ty = V->getType();
2432 Ty = getEffectiveSCEVType(Ty);
2433 const SCEV *AllOnes =
2434 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
2435 return getMinusSCEV(AllOnes, V);
2438 /// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
2440 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS,
2443 return getAddExpr(LHS, getNegativeSCEV(RHS));
2446 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
2447 /// input value to the specified type. If the type must be extended, it is zero
2450 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V,
2452 const Type *SrcTy = V->getType();
2453 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2454 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2455 "Cannot truncate or zero extend with non-integer arguments!");
2456 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2457 return V; // No conversion
2458 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2459 return getTruncateExpr(V, Ty);
2460 return getZeroExtendExpr(V, Ty);
2463 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
2464 /// input value to the specified type. If the type must be extended, it is sign
2467 ScalarEvolution::getTruncateOrSignExtend(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 getSignExtendExpr(V, Ty);
2480 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
2481 /// input value to the specified type. If the type must be extended, it is zero
2482 /// extended. The conversion must not be narrowing.
2484 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, const Type *Ty) {
2485 const Type *SrcTy = V->getType();
2486 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2487 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2488 "Cannot noop or zero extend with non-integer arguments!");
2489 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2490 "getNoopOrZeroExtend cannot truncate!");
2491 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2492 return V; // No conversion
2493 return getZeroExtendExpr(V, Ty);
2496 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
2497 /// input value to the specified type. If the type must be extended, it is sign
2498 /// extended. The conversion must not be narrowing.
2500 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, const Type *Ty) {
2501 const Type *SrcTy = V->getType();
2502 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2503 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2504 "Cannot noop or sign extend with non-integer arguments!");
2505 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2506 "getNoopOrSignExtend cannot truncate!");
2507 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2508 return V; // No conversion
2509 return getSignExtendExpr(V, Ty);
2512 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
2513 /// the input value to the specified type. If the type must be extended,
2514 /// it is extended with unspecified bits. The conversion must not be
2517 ScalarEvolution::getNoopOrAnyExtend(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 any extend with non-integer arguments!");
2522 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2523 "getNoopOrAnyExtend cannot truncate!");
2524 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2525 return V; // No conversion
2526 return getAnyExtendExpr(V, Ty);
2529 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
2530 /// input value to the specified type. The conversion must not be widening.
2532 ScalarEvolution::getTruncateOrNoop(const SCEV *V, const Type *Ty) {
2533 const Type *SrcTy = V->getType();
2534 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2535 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2536 "Cannot truncate or noop with non-integer arguments!");
2537 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
2538 "getTruncateOrNoop cannot extend!");
2539 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2540 return V; // No conversion
2541 return getTruncateExpr(V, Ty);
2544 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
2545 /// the types using zero-extension, and then perform a umax operation
2547 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
2549 const SCEV *PromotedLHS = LHS;
2550 const SCEV *PromotedRHS = RHS;
2552 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2553 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2555 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2557 return getUMaxExpr(PromotedLHS, PromotedRHS);
2560 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
2561 /// the types using zero-extension, and then perform a umin operation
2563 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
2565 const SCEV *PromotedLHS = LHS;
2566 const SCEV *PromotedRHS = RHS;
2568 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2569 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2571 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2573 return getUMinExpr(PromotedLHS, PromotedRHS);
2576 /// PushDefUseChildren - Push users of the given Instruction
2577 /// onto the given Worklist.
2579 PushDefUseChildren(Instruction *I,
2580 SmallVectorImpl<Instruction *> &Worklist) {
2581 // Push the def-use children onto the Worklist stack.
2582 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end();
2584 Worklist.push_back(cast<Instruction>(UI));
2587 /// ForgetSymbolicValue - This looks up computed SCEV values for all
2588 /// instructions that depend on the given instruction and removes them from
2589 /// the Scalars map if they reference SymName. This is used during PHI
2592 ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) {
2593 SmallVector<Instruction *, 16> Worklist;
2594 PushDefUseChildren(PN, Worklist);
2596 SmallPtrSet<Instruction *, 8> Visited;
2598 while (!Worklist.empty()) {
2599 Instruction *I = Worklist.pop_back_val();
2600 if (!Visited.insert(I)) continue;
2602 std::map<SCEVCallbackVH, const SCEV *>::iterator It =
2603 Scalars.find(static_cast<Value *>(I));
2604 if (It != Scalars.end()) {
2605 // Short-circuit the def-use traversal if the symbolic name
2606 // ceases to appear in expressions.
2607 if (It->second != SymName && !It->second->hasOperand(SymName))
2610 // SCEVUnknown for a PHI either means that it has an unrecognized
2611 // structure, it's a PHI that's in the progress of being computed
2612 // by createNodeForPHI, or it's a single-value PHI. In the first case,
2613 // additional loop trip count information isn't going to change anything.
2614 // In the second case, createNodeForPHI will perform the necessary
2615 // updates on its own when it gets to that point. In the third, we do
2616 // want to forget the SCEVUnknown.
2617 if (!isa<PHINode>(I) ||
2618 !isa<SCEVUnknown>(It->second) ||
2619 (I != PN && It->second == SymName)) {
2620 ValuesAtScopes.erase(It->second);
2625 PushDefUseChildren(I, Worklist);
2629 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
2630 /// a loop header, making it a potential recurrence, or it doesn't.
2632 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
2633 if (const Loop *L = LI->getLoopFor(PN->getParent()))
2634 if (L->getHeader() == PN->getParent()) {
2635 // The loop may have multiple entrances or multiple exits; we can analyze
2636 // this phi as an addrec if it has a unique entry value and a unique
2638 Value *BEValueV = 0, *StartValueV = 0;
2639 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
2640 Value *V = PN->getIncomingValue(i);
2641 if (L->contains(PN->getIncomingBlock(i))) {
2644 } else if (BEValueV != V) {
2648 } else if (!StartValueV) {
2650 } else if (StartValueV != V) {
2655 if (BEValueV && StartValueV) {
2656 // While we are analyzing this PHI node, handle its value symbolically.
2657 const SCEV *SymbolicName = getUnknown(PN);
2658 assert(Scalars.find(PN) == Scalars.end() &&
2659 "PHI node already processed?");
2660 Scalars.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
2662 // Using this symbolic name for the PHI, analyze the value coming around
2664 const SCEV *BEValue = getSCEV(BEValueV);
2666 // NOTE: If BEValue is loop invariant, we know that the PHI node just
2667 // has a special value for the first iteration of the loop.
2669 // If the value coming around the backedge is an add with the symbolic
2670 // value we just inserted, then we found a simple induction variable!
2671 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
2672 // If there is a single occurrence of the symbolic value, replace it
2673 // with a recurrence.
2674 unsigned FoundIndex = Add->getNumOperands();
2675 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
2676 if (Add->getOperand(i) == SymbolicName)
2677 if (FoundIndex == e) {
2682 if (FoundIndex != Add->getNumOperands()) {
2683 // Create an add with everything but the specified operand.
2684 SmallVector<const SCEV *, 8> Ops;
2685 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
2686 if (i != FoundIndex)
2687 Ops.push_back(Add->getOperand(i));
2688 const SCEV *Accum = getAddExpr(Ops);
2690 // This is not a valid addrec if the step amount is varying each
2691 // loop iteration, but is not itself an addrec in this loop.
2692 if (Accum->isLoopInvariant(L) ||
2693 (isa<SCEVAddRecExpr>(Accum) &&
2694 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
2695 bool HasNUW = false;
2696 bool HasNSW = false;
2698 // If the increment doesn't overflow, then neither the addrec nor
2699 // the post-increment will overflow.
2700 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) {
2701 if (OBO->hasNoUnsignedWrap())
2703 if (OBO->hasNoSignedWrap())
2707 const SCEV *StartVal = getSCEV(StartValueV);
2708 const SCEV *PHISCEV =
2709 getAddRecExpr(StartVal, Accum, L, HasNUW, HasNSW);
2711 // Since the no-wrap flags are on the increment, they apply to the
2712 // post-incremented value as well.
2713 if (Accum->isLoopInvariant(L))
2714 (void)getAddRecExpr(getAddExpr(StartVal, Accum),
2715 Accum, L, HasNUW, HasNSW);
2717 // Okay, for the entire analysis of this edge we assumed the PHI
2718 // to be symbolic. We now need to go back and purge all of the
2719 // entries for the scalars that use the symbolic expression.
2720 ForgetSymbolicName(PN, SymbolicName);
2721 Scalars[SCEVCallbackVH(PN, this)] = PHISCEV;
2725 } else if (const SCEVAddRecExpr *AddRec =
2726 dyn_cast<SCEVAddRecExpr>(BEValue)) {
2727 // Otherwise, this could be a loop like this:
2728 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
2729 // In this case, j = {1,+,1} and BEValue is j.
2730 // Because the other in-value of i (0) fits the evolution of BEValue
2731 // i really is an addrec evolution.
2732 if (AddRec->getLoop() == L && AddRec->isAffine()) {
2733 const SCEV *StartVal = getSCEV(StartValueV);
2735 // If StartVal = j.start - j.stride, we can use StartVal as the
2736 // initial step of the addrec evolution.
2737 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
2738 AddRec->getOperand(1))) {
2739 const SCEV *PHISCEV =
2740 getAddRecExpr(StartVal, AddRec->getOperand(1), L);
2742 // Okay, for the entire analysis of this edge we assumed the PHI
2743 // to be symbolic. We now need to go back and purge all of the
2744 // entries for the scalars that use the symbolic expression.
2745 ForgetSymbolicName(PN, SymbolicName);
2746 Scalars[SCEVCallbackVH(PN, this)] = PHISCEV;
2754 // If the PHI has a single incoming value, follow that value, unless the
2755 // PHI's incoming blocks are in a different loop, in which case doing so
2756 // risks breaking LCSSA form. Instcombine would normally zap these, but
2757 // it doesn't have DominatorTree information, so it may miss cases.
2758 if (Value *V = PN->hasConstantValue(DT)) {
2759 bool AllSameLoop = true;
2760 Loop *PNLoop = LI->getLoopFor(PN->getParent());
2761 for (size_t i = 0, e = PN->getNumIncomingValues(); i != e; ++i)
2762 if (LI->getLoopFor(PN->getIncomingBlock(i)) != PNLoop) {
2763 AllSameLoop = false;
2770 // If it's not a loop phi, we can't handle it yet.
2771 return getUnknown(PN);
2774 /// createNodeForGEP - Expand GEP instructions into add and multiply
2775 /// operations. This allows them to be analyzed by regular SCEV code.
2777 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
2779 bool InBounds = GEP->isInBounds();
2780 const Type *IntPtrTy = getEffectiveSCEVType(GEP->getType());
2781 Value *Base = GEP->getOperand(0);
2782 // Don't attempt to analyze GEPs over unsized objects.
2783 if (!cast<PointerType>(Base->getType())->getElementType()->isSized())
2784 return getUnknown(GEP);
2785 const SCEV *TotalOffset = getIntegerSCEV(0, IntPtrTy);
2786 gep_type_iterator GTI = gep_type_begin(GEP);
2787 for (GetElementPtrInst::op_iterator I = next(GEP->op_begin()),
2791 // Compute the (potentially symbolic) offset in bytes for this index.
2792 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) {
2793 // For a struct, add the member offset.
2794 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
2795 TotalOffset = getAddExpr(TotalOffset,
2796 getOffsetOfExpr(STy, FieldNo),
2797 /*HasNUW=*/false, /*HasNSW=*/InBounds);
2799 // For an array, add the element offset, explicitly scaled.
2800 const SCEV *LocalOffset = getSCEV(Index);
2801 // Getelementptr indices are signed.
2802 LocalOffset = getTruncateOrSignExtend(LocalOffset, IntPtrTy);
2803 // Lower "inbounds" GEPs to NSW arithmetic.
2804 LocalOffset = getMulExpr(LocalOffset, getSizeOfExpr(*GTI),
2805 /*HasNUW=*/false, /*HasNSW=*/InBounds);
2806 TotalOffset = getAddExpr(TotalOffset, LocalOffset,
2807 /*HasNUW=*/false, /*HasNSW=*/InBounds);
2810 return getAddExpr(getSCEV(Base), TotalOffset,
2811 /*HasNUW=*/false, /*HasNSW=*/InBounds);
2814 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
2815 /// guaranteed to end in (at every loop iteration). It is, at the same time,
2816 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
2817 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
2819 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
2820 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
2821 return C->getValue()->getValue().countTrailingZeros();
2823 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
2824 return std::min(GetMinTrailingZeros(T->getOperand()),
2825 (uint32_t)getTypeSizeInBits(T->getType()));
2827 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
2828 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
2829 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
2830 getTypeSizeInBits(E->getType()) : OpRes;
2833 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
2834 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
2835 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
2836 getTypeSizeInBits(E->getType()) : OpRes;
2839 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
2840 // The result is the min of all operands results.
2841 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
2842 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
2843 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
2847 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
2848 // The result is the sum of all operands results.
2849 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
2850 uint32_t BitWidth = getTypeSizeInBits(M->getType());
2851 for (unsigned i = 1, e = M->getNumOperands();
2852 SumOpRes != BitWidth && i != e; ++i)
2853 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
2858 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
2859 // The result is the min of all operands results.
2860 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
2861 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
2862 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
2866 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
2867 // The result is the min of all operands results.
2868 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
2869 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
2870 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
2874 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
2875 // The result is the min of all operands results.
2876 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
2877 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
2878 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
2882 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
2883 // For a SCEVUnknown, ask ValueTracking.
2884 unsigned BitWidth = getTypeSizeInBits(U->getType());
2885 APInt Mask = APInt::getAllOnesValue(BitWidth);
2886 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
2887 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones);
2888 return Zeros.countTrailingOnes();
2895 /// getUnsignedRange - Determine the unsigned range for a particular SCEV.
2898 ScalarEvolution::getUnsignedRange(const SCEV *S) {
2900 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
2901 return ConstantRange(C->getValue()->getValue());
2903 unsigned BitWidth = getTypeSizeInBits(S->getType());
2904 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
2906 // If the value has known zeros, the maximum unsigned value will have those
2907 // known zeros as well.
2908 uint32_t TZ = GetMinTrailingZeros(S);
2910 ConservativeResult =
2911 ConstantRange(APInt::getMinValue(BitWidth),
2912 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
2914 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
2915 ConstantRange X = getUnsignedRange(Add->getOperand(0));
2916 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
2917 X = X.add(getUnsignedRange(Add->getOperand(i)));
2918 return ConservativeResult.intersectWith(X);
2921 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
2922 ConstantRange X = getUnsignedRange(Mul->getOperand(0));
2923 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
2924 X = X.multiply(getUnsignedRange(Mul->getOperand(i)));
2925 return ConservativeResult.intersectWith(X);
2928 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
2929 ConstantRange X = getUnsignedRange(SMax->getOperand(0));
2930 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
2931 X = X.smax(getUnsignedRange(SMax->getOperand(i)));
2932 return ConservativeResult.intersectWith(X);
2935 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
2936 ConstantRange X = getUnsignedRange(UMax->getOperand(0));
2937 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
2938 X = X.umax(getUnsignedRange(UMax->getOperand(i)));
2939 return ConservativeResult.intersectWith(X);
2942 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
2943 ConstantRange X = getUnsignedRange(UDiv->getLHS());
2944 ConstantRange Y = getUnsignedRange(UDiv->getRHS());
2945 return ConservativeResult.intersectWith(X.udiv(Y));
2948 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
2949 ConstantRange X = getUnsignedRange(ZExt->getOperand());
2950 return ConservativeResult.intersectWith(X.zeroExtend(BitWidth));
2953 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
2954 ConstantRange X = getUnsignedRange(SExt->getOperand());
2955 return ConservativeResult.intersectWith(X.signExtend(BitWidth));
2958 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
2959 ConstantRange X = getUnsignedRange(Trunc->getOperand());
2960 return ConservativeResult.intersectWith(X.truncate(BitWidth));
2963 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
2964 // If there's no unsigned wrap, the value will never be less than its
2966 if (AddRec->hasNoUnsignedWrap())
2967 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
2968 if (!C->getValue()->isZero())
2969 ConservativeResult =
2970 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0));
2972 // TODO: non-affine addrec
2973 if (AddRec->isAffine()) {
2974 const Type *Ty = AddRec->getType();
2975 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
2976 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
2977 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
2978 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
2980 const SCEV *Start = AddRec->getStart();
2981 const SCEV *Step = AddRec->getStepRecurrence(*this);
2983 ConstantRange StartRange = getUnsignedRange(Start);
2984 ConstantRange StepRange = getSignedRange(Step);
2985 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
2986 ConstantRange EndRange =
2987 StartRange.add(MaxBECountRange.multiply(StepRange));
2989 // Check for overflow. This must be done with ConstantRange arithmetic
2990 // because we could be called from within the ScalarEvolution overflow
2992 ConstantRange ExtStartRange = StartRange.zextOrTrunc(BitWidth*2+1);
2993 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
2994 ConstantRange ExtMaxBECountRange =
2995 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
2996 ConstantRange ExtEndRange = EndRange.zextOrTrunc(BitWidth*2+1);
2997 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
2999 return ConservativeResult;
3001 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(),
3002 EndRange.getUnsignedMin());
3003 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(),
3004 EndRange.getUnsignedMax());
3005 if (Min.isMinValue() && Max.isMaxValue())
3006 return ConservativeResult;
3007 return ConservativeResult.intersectWith(ConstantRange(Min, Max+1));
3011 return ConservativeResult;
3014 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3015 // For a SCEVUnknown, ask ValueTracking.
3016 APInt Mask = APInt::getAllOnesValue(BitWidth);
3017 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3018 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones, TD);
3019 if (Ones == ~Zeros + 1)
3020 return ConservativeResult;
3021 return ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1));
3024 return ConservativeResult;
3027 /// getSignedRange - Determine the signed range for a particular SCEV.
3030 ScalarEvolution::getSignedRange(const SCEV *S) {
3032 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3033 return ConstantRange(C->getValue()->getValue());
3035 unsigned BitWidth = getTypeSizeInBits(S->getType());
3036 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3038 // If the value has known zeros, the maximum signed value will have those
3039 // known zeros as well.
3040 uint32_t TZ = GetMinTrailingZeros(S);
3042 ConservativeResult =
3043 ConstantRange(APInt::getSignedMinValue(BitWidth),
3044 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
3046 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3047 ConstantRange X = getSignedRange(Add->getOperand(0));
3048 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3049 X = X.add(getSignedRange(Add->getOperand(i)));
3050 return ConservativeResult.intersectWith(X);
3053 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3054 ConstantRange X = getSignedRange(Mul->getOperand(0));
3055 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3056 X = X.multiply(getSignedRange(Mul->getOperand(i)));
3057 return ConservativeResult.intersectWith(X);
3060 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3061 ConstantRange X = getSignedRange(SMax->getOperand(0));
3062 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3063 X = X.smax(getSignedRange(SMax->getOperand(i)));
3064 return ConservativeResult.intersectWith(X);
3067 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3068 ConstantRange X = getSignedRange(UMax->getOperand(0));
3069 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3070 X = X.umax(getSignedRange(UMax->getOperand(i)));
3071 return ConservativeResult.intersectWith(X);
3074 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3075 ConstantRange X = getSignedRange(UDiv->getLHS());
3076 ConstantRange Y = getSignedRange(UDiv->getRHS());
3077 return ConservativeResult.intersectWith(X.udiv(Y));
3080 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3081 ConstantRange X = getSignedRange(ZExt->getOperand());
3082 return ConservativeResult.intersectWith(X.zeroExtend(BitWidth));
3085 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3086 ConstantRange X = getSignedRange(SExt->getOperand());
3087 return ConservativeResult.intersectWith(X.signExtend(BitWidth));
3090 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3091 ConstantRange X = getSignedRange(Trunc->getOperand());
3092 return ConservativeResult.intersectWith(X.truncate(BitWidth));
3095 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3096 // If there's no signed wrap, and all the operands have the same sign or
3097 // zero, the value won't ever change sign.
3098 if (AddRec->hasNoSignedWrap()) {
3099 bool AllNonNeg = true;
3100 bool AllNonPos = true;
3101 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
3102 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
3103 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
3106 ConservativeResult = ConservativeResult.intersectWith(
3107 ConstantRange(APInt(BitWidth, 0),
3108 APInt::getSignedMinValue(BitWidth)));
3110 ConservativeResult = ConservativeResult.intersectWith(
3111 ConstantRange(APInt::getSignedMinValue(BitWidth),
3112 APInt(BitWidth, 1)));
3115 // TODO: non-affine addrec
3116 if (AddRec->isAffine()) {
3117 const Type *Ty = AddRec->getType();
3118 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3119 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3120 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3121 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3123 const SCEV *Start = AddRec->getStart();
3124 const SCEV *Step = AddRec->getStepRecurrence(*this);
3126 ConstantRange StartRange = getSignedRange(Start);
3127 ConstantRange StepRange = getSignedRange(Step);
3128 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3129 ConstantRange EndRange =
3130 StartRange.add(MaxBECountRange.multiply(StepRange));
3132 // Check for overflow. This must be done with ConstantRange arithmetic
3133 // because we could be called from within the ScalarEvolution overflow
3135 ConstantRange ExtStartRange = StartRange.sextOrTrunc(BitWidth*2+1);
3136 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3137 ConstantRange ExtMaxBECountRange =
3138 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3139 ConstantRange ExtEndRange = EndRange.sextOrTrunc(BitWidth*2+1);
3140 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3142 return ConservativeResult;
3144 APInt Min = APIntOps::smin(StartRange.getSignedMin(),
3145 EndRange.getSignedMin());
3146 APInt Max = APIntOps::smax(StartRange.getSignedMax(),
3147 EndRange.getSignedMax());
3148 if (Min.isMinSignedValue() && Max.isMaxSignedValue())
3149 return ConservativeResult;
3150 return ConservativeResult.intersectWith(ConstantRange(Min, Max+1));
3154 return ConservativeResult;
3157 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3158 // For a SCEVUnknown, ask ValueTracking.
3159 if (!U->getValue()->getType()->isIntegerTy() && !TD)
3160 return ConservativeResult;
3161 unsigned NS = ComputeNumSignBits(U->getValue(), TD);
3163 return ConservativeResult;
3164 return ConservativeResult.intersectWith(
3165 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
3166 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1));
3169 return ConservativeResult;
3172 /// createSCEV - We know that there is no SCEV for the specified value.
3173 /// Analyze the expression.
3175 const SCEV *ScalarEvolution::createSCEV(Value *V) {
3176 if (!isSCEVable(V->getType()))
3177 return getUnknown(V);
3179 unsigned Opcode = Instruction::UserOp1;
3180 if (Instruction *I = dyn_cast<Instruction>(V)) {
3181 Opcode = I->getOpcode();
3183 // Don't attempt to analyze instructions in blocks that aren't
3184 // reachable. Such instructions don't matter, and they aren't required
3185 // to obey basic rules for definitions dominating uses which this
3186 // analysis depends on.
3187 if (!DT->isReachableFromEntry(I->getParent()))
3188 return getUnknown(V);
3189 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
3190 Opcode = CE->getOpcode();
3191 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
3192 return getConstant(CI);
3193 else if (isa<ConstantPointerNull>(V))
3194 return getIntegerSCEV(0, V->getType());
3195 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
3196 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee());
3198 return getUnknown(V);
3200 Operator *U = cast<Operator>(V);
3202 case Instruction::Add:
3203 // Don't transfer the NSW and NUW bits from the Add instruction to the
3204 // Add expression, because the Instruction may be guarded by control
3205 // flow and the no-overflow bits may not be valid for the expression in
3207 return getAddExpr(getSCEV(U->getOperand(0)),
3208 getSCEV(U->getOperand(1)));
3209 case Instruction::Mul:
3210 // Don't transfer the NSW and NUW bits from the Mul instruction to the
3211 // Mul expression, as with Add.
3212 return getMulExpr(getSCEV(U->getOperand(0)),
3213 getSCEV(U->getOperand(1)));
3214 case Instruction::UDiv:
3215 return getUDivExpr(getSCEV(U->getOperand(0)),
3216 getSCEV(U->getOperand(1)));
3217 case Instruction::Sub:
3218 return getMinusSCEV(getSCEV(U->getOperand(0)),
3219 getSCEV(U->getOperand(1)));
3220 case Instruction::And:
3221 // For an expression like x&255 that merely masks off the high bits,
3222 // use zext(trunc(x)) as the SCEV expression.
3223 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3224 if (CI->isNullValue())
3225 return getSCEV(U->getOperand(1));
3226 if (CI->isAllOnesValue())
3227 return getSCEV(U->getOperand(0));
3228 const APInt &A = CI->getValue();
3230 // Instcombine's ShrinkDemandedConstant may strip bits out of
3231 // constants, obscuring what would otherwise be a low-bits mask.
3232 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant
3233 // knew about to reconstruct a low-bits mask value.
3234 unsigned LZ = A.countLeadingZeros();
3235 unsigned BitWidth = A.getBitWidth();
3236 APInt AllOnes = APInt::getAllOnesValue(BitWidth);
3237 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
3238 ComputeMaskedBits(U->getOperand(0), AllOnes, KnownZero, KnownOne, TD);
3240 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ);
3242 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask))
3244 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)),
3245 IntegerType::get(getContext(), BitWidth - LZ)),
3250 case Instruction::Or:
3251 // If the RHS of the Or is a constant, we may have something like:
3252 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
3253 // optimizations will transparently handle this case.
3255 // In order for this transformation to be safe, the LHS must be of the
3256 // form X*(2^n) and the Or constant must be less than 2^n.
3257 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3258 const SCEV *LHS = getSCEV(U->getOperand(0));
3259 const APInt &CIVal = CI->getValue();
3260 if (GetMinTrailingZeros(LHS) >=
3261 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
3262 // Build a plain add SCEV.
3263 const SCEV *S = getAddExpr(LHS, getSCEV(CI));
3264 // If the LHS of the add was an addrec and it has no-wrap flags,
3265 // transfer the no-wrap flags, since an or won't introduce a wrap.
3266 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
3267 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
3268 if (OldAR->hasNoUnsignedWrap())
3269 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoUnsignedWrap(true);
3270 if (OldAR->hasNoSignedWrap())
3271 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoSignedWrap(true);
3277 case Instruction::Xor:
3278 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3279 // If the RHS of the xor is a signbit, then this is just an add.
3280 // Instcombine turns add of signbit into xor as a strength reduction step.
3281 if (CI->getValue().isSignBit())
3282 return getAddExpr(getSCEV(U->getOperand(0)),
3283 getSCEV(U->getOperand(1)));
3285 // If the RHS of xor is -1, then this is a not operation.
3286 if (CI->isAllOnesValue())
3287 return getNotSCEV(getSCEV(U->getOperand(0)));
3289 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
3290 // This is a variant of the check for xor with -1, and it handles
3291 // the case where instcombine has trimmed non-demanded bits out
3292 // of an xor with -1.
3293 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
3294 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
3295 if (BO->getOpcode() == Instruction::And &&
3296 LCI->getValue() == CI->getValue())
3297 if (const SCEVZeroExtendExpr *Z =
3298 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
3299 const Type *UTy = U->getType();
3300 const SCEV *Z0 = Z->getOperand();
3301 const Type *Z0Ty = Z0->getType();
3302 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
3304 // If C is a low-bits mask, the zero extend is serving to
3305 // mask off the high bits. Complement the operand and
3306 // re-apply the zext.
3307 if (APIntOps::isMask(Z0TySize, CI->getValue()))
3308 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
3310 // If C is a single bit, it may be in the sign-bit position
3311 // before the zero-extend. In this case, represent the xor
3312 // using an add, which is equivalent, and re-apply the zext.
3313 APInt Trunc = APInt(CI->getValue()).trunc(Z0TySize);
3314 if (APInt(Trunc).zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
3316 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
3322 case Instruction::Shl:
3323 // Turn shift left of a constant amount into a multiply.
3324 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3325 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3327 // If the shift count is not less than the bitwidth, the result of
3328 // the shift is undefined. Don't try to analyze it, because the
3329 // resolution chosen here may differ from the resolution chosen in
3330 // other parts of the compiler.
3331 if (SA->getValue().uge(BitWidth))
3334 Constant *X = ConstantInt::get(getContext(),
3335 APInt(BitWidth, 1).shl(SA->getZExtValue()));
3336 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3340 case Instruction::LShr:
3341 // Turn logical shift right of a constant into a unsigned divide.
3342 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3343 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3345 // If the shift count is not less than the bitwidth, the result of
3346 // the shift is undefined. Don't try to analyze it, because the
3347 // resolution chosen here may differ from the resolution chosen in
3348 // other parts of the compiler.
3349 if (SA->getValue().uge(BitWidth))
3352 Constant *X = ConstantInt::get(getContext(),
3353 APInt(BitWidth, 1).shl(SA->getZExtValue()));
3354 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3358 case Instruction::AShr:
3359 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
3360 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
3361 if (Operator *L = dyn_cast<Operator>(U->getOperand(0)))
3362 if (L->getOpcode() == Instruction::Shl &&
3363 L->getOperand(1) == U->getOperand(1)) {
3364 uint64_t BitWidth = getTypeSizeInBits(U->getType());
3366 // If the shift count is not less than the bitwidth, the result of
3367 // the shift is undefined. Don't try to analyze it, because the
3368 // resolution chosen here may differ from the resolution chosen in
3369 // other parts of the compiler.
3370 if (CI->getValue().uge(BitWidth))
3373 uint64_t Amt = BitWidth - CI->getZExtValue();
3374 if (Amt == BitWidth)
3375 return getSCEV(L->getOperand(0)); // shift by zero --> noop
3377 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
3378 IntegerType::get(getContext(),
3384 case Instruction::Trunc:
3385 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
3387 case Instruction::ZExt:
3388 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3390 case Instruction::SExt:
3391 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3393 case Instruction::BitCast:
3394 // BitCasts are no-op casts so we just eliminate the cast.
3395 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
3396 return getSCEV(U->getOperand(0));
3399 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
3400 // lead to pointer expressions which cannot safely be expanded to GEPs,
3401 // because ScalarEvolution doesn't respect the GEP aliasing rules when
3402 // simplifying integer expressions.
3404 case Instruction::GetElementPtr:
3405 return createNodeForGEP(cast<GEPOperator>(U));
3407 case Instruction::PHI:
3408 return createNodeForPHI(cast<PHINode>(U));
3410 case Instruction::Select:
3411 // This could be a smax or umax that was lowered earlier.
3412 // Try to recover it.
3413 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
3414 Value *LHS = ICI->getOperand(0);
3415 Value *RHS = ICI->getOperand(1);
3416 switch (ICI->getPredicate()) {
3417 case ICmpInst::ICMP_SLT:
3418 case ICmpInst::ICMP_SLE:
3419 std::swap(LHS, RHS);
3421 case ICmpInst::ICMP_SGT:
3422 case ICmpInst::ICMP_SGE:
3423 if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
3424 return getSMaxExpr(getSCEV(LHS), getSCEV(RHS));
3425 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
3426 return getSMinExpr(getSCEV(LHS), getSCEV(RHS));
3428 case ICmpInst::ICMP_ULT:
3429 case ICmpInst::ICMP_ULE:
3430 std::swap(LHS, RHS);
3432 case ICmpInst::ICMP_UGT:
3433 case ICmpInst::ICMP_UGE:
3434 if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
3435 return getUMaxExpr(getSCEV(LHS), getSCEV(RHS));
3436 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
3437 return getUMinExpr(getSCEV(LHS), getSCEV(RHS));
3439 case ICmpInst::ICMP_NE:
3440 // n != 0 ? n : 1 -> umax(n, 1)
3441 if (LHS == U->getOperand(1) &&
3442 isa<ConstantInt>(U->getOperand(2)) &&
3443 cast<ConstantInt>(U->getOperand(2))->isOne() &&
3444 isa<ConstantInt>(RHS) &&
3445 cast<ConstantInt>(RHS)->isZero())
3446 return getUMaxExpr(getSCEV(LHS), getSCEV(U->getOperand(2)));
3448 case ICmpInst::ICMP_EQ:
3449 // n == 0 ? 1 : n -> umax(n, 1)
3450 if (LHS == U->getOperand(2) &&
3451 isa<ConstantInt>(U->getOperand(1)) &&
3452 cast<ConstantInt>(U->getOperand(1))->isOne() &&
3453 isa<ConstantInt>(RHS) &&
3454 cast<ConstantInt>(RHS)->isZero())
3455 return getUMaxExpr(getSCEV(LHS), getSCEV(U->getOperand(1)));
3462 default: // We cannot analyze this expression.
3466 return getUnknown(V);
3471 //===----------------------------------------------------------------------===//
3472 // Iteration Count Computation Code
3475 /// getBackedgeTakenCount - If the specified loop has a predictable
3476 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
3477 /// object. The backedge-taken count is the number of times the loop header
3478 /// will be branched to from within the loop. This is one less than the
3479 /// trip count of the loop, since it doesn't count the first iteration,
3480 /// when the header is branched to from outside the loop.
3482 /// Note that it is not valid to call this method on a loop without a
3483 /// loop-invariant backedge-taken count (see
3484 /// hasLoopInvariantBackedgeTakenCount).
3486 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
3487 return getBackedgeTakenInfo(L).Exact;
3490 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
3491 /// return the least SCEV value that is known never to be less than the
3492 /// actual backedge taken count.
3493 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
3494 return getBackedgeTakenInfo(L).Max;
3497 /// PushLoopPHIs - Push PHI nodes in the header of the given loop
3498 /// onto the given Worklist.
3500 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
3501 BasicBlock *Header = L->getHeader();
3503 // Push all Loop-header PHIs onto the Worklist stack.
3504 for (BasicBlock::iterator I = Header->begin();
3505 PHINode *PN = dyn_cast<PHINode>(I); ++I)
3506 Worklist.push_back(PN);
3509 const ScalarEvolution::BackedgeTakenInfo &
3510 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
3511 // Initially insert a CouldNotCompute for this loop. If the insertion
3512 // succeeds, proceed to actually compute a backedge-taken count and
3513 // update the value. The temporary CouldNotCompute value tells SCEV
3514 // code elsewhere that it shouldn't attempt to request a new
3515 // backedge-taken count, which could result in infinite recursion.
3516 std::pair<std::map<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
3517 BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute()));
3519 BackedgeTakenInfo BECount = ComputeBackedgeTakenCount(L);
3520 if (BECount.Exact != getCouldNotCompute()) {
3521 assert(BECount.Exact->isLoopInvariant(L) &&
3522 BECount.Max->isLoopInvariant(L) &&
3523 "Computed backedge-taken count isn't loop invariant for loop!");
3524 ++NumTripCountsComputed;
3526 // Update the value in the map.
3527 Pair.first->second = BECount;
3529 if (BECount.Max != getCouldNotCompute())
3530 // Update the value in the map.
3531 Pair.first->second = BECount;
3532 if (isa<PHINode>(L->getHeader()->begin()))
3533 // Only count loops that have phi nodes as not being computable.
3534 ++NumTripCountsNotComputed;
3537 // Now that we know more about the trip count for this loop, forget any
3538 // existing SCEV values for PHI nodes in this loop since they are only
3539 // conservative estimates made without the benefit of trip count
3540 // information. This is similar to the code in forgetLoop, except that
3541 // it handles SCEVUnknown PHI nodes specially.
3542 if (BECount.hasAnyInfo()) {
3543 SmallVector<Instruction *, 16> Worklist;
3544 PushLoopPHIs(L, Worklist);
3546 SmallPtrSet<Instruction *, 8> Visited;
3547 while (!Worklist.empty()) {
3548 Instruction *I = Worklist.pop_back_val();
3549 if (!Visited.insert(I)) continue;
3551 std::map<SCEVCallbackVH, const SCEV *>::iterator It =
3552 Scalars.find(static_cast<Value *>(I));
3553 if (It != Scalars.end()) {
3554 // SCEVUnknown for a PHI either means that it has an unrecognized
3555 // structure, or it's a PHI that's in the progress of being computed
3556 // by createNodeForPHI. In the former case, additional loop trip
3557 // count information isn't going to change anything. In the later
3558 // case, createNodeForPHI will perform the necessary updates on its
3559 // own when it gets to that point.
3560 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(It->second)) {
3561 ValuesAtScopes.erase(It->second);
3564 if (PHINode *PN = dyn_cast<PHINode>(I))
3565 ConstantEvolutionLoopExitValue.erase(PN);
3568 PushDefUseChildren(I, Worklist);
3572 return Pair.first->second;
3575 /// forgetLoop - This method should be called by the client when it has
3576 /// changed a loop in a way that may effect ScalarEvolution's ability to
3577 /// compute a trip count, or if the loop is deleted.
3578 void ScalarEvolution::forgetLoop(const Loop *L) {
3579 // Drop any stored trip count value.
3580 BackedgeTakenCounts.erase(L);
3582 // Drop information about expressions based on loop-header PHIs.
3583 SmallVector<Instruction *, 16> Worklist;
3584 PushLoopPHIs(L, Worklist);
3586 SmallPtrSet<Instruction *, 8> Visited;
3587 while (!Worklist.empty()) {
3588 Instruction *I = Worklist.pop_back_val();
3589 if (!Visited.insert(I)) continue;
3591 std::map<SCEVCallbackVH, const SCEV *>::iterator It =
3592 Scalars.find(static_cast<Value *>(I));
3593 if (It != Scalars.end()) {
3594 ValuesAtScopes.erase(It->second);
3596 if (PHINode *PN = dyn_cast<PHINode>(I))
3597 ConstantEvolutionLoopExitValue.erase(PN);
3600 PushDefUseChildren(I, Worklist);
3604 /// forgetValue - This method should be called by the client when it has
3605 /// changed a value in a way that may effect its value, or which may
3606 /// disconnect it from a def-use chain linking it to a loop.
3607 void ScalarEvolution::forgetValue(Value *V) {
3608 Instruction *I = dyn_cast<Instruction>(V);
3611 // Drop information about expressions based on loop-header PHIs.
3612 SmallVector<Instruction *, 16> Worklist;
3613 Worklist.push_back(I);
3615 SmallPtrSet<Instruction *, 8> Visited;
3616 while (!Worklist.empty()) {
3617 I = Worklist.pop_back_val();
3618 if (!Visited.insert(I)) continue;
3620 std::map<SCEVCallbackVH, const SCEV *>::iterator It =
3621 Scalars.find(static_cast<Value *>(I));
3622 if (It != Scalars.end()) {
3623 ValuesAtScopes.erase(It->second);
3625 if (PHINode *PN = dyn_cast<PHINode>(I))
3626 ConstantEvolutionLoopExitValue.erase(PN);
3629 PushDefUseChildren(I, Worklist);
3633 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
3634 /// of the specified loop will execute.
3635 ScalarEvolution::BackedgeTakenInfo
3636 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
3637 SmallVector<BasicBlock *, 8> ExitingBlocks;
3638 L->getExitingBlocks(ExitingBlocks);
3640 // Examine all exits and pick the most conservative values.
3641 const SCEV *BECount = getCouldNotCompute();
3642 const SCEV *MaxBECount = getCouldNotCompute();
3643 bool CouldNotComputeBECount = false;
3644 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
3645 BackedgeTakenInfo NewBTI =
3646 ComputeBackedgeTakenCountFromExit(L, ExitingBlocks[i]);
3648 if (NewBTI.Exact == getCouldNotCompute()) {
3649 // We couldn't compute an exact value for this exit, so
3650 // we won't be able to compute an exact value for the loop.
3651 CouldNotComputeBECount = true;
3652 BECount = getCouldNotCompute();
3653 } else if (!CouldNotComputeBECount) {
3654 if (BECount == getCouldNotCompute())
3655 BECount = NewBTI.Exact;
3657 BECount = getUMinFromMismatchedTypes(BECount, NewBTI.Exact);
3659 if (MaxBECount == getCouldNotCompute())
3660 MaxBECount = NewBTI.Max;
3661 else if (NewBTI.Max != getCouldNotCompute())
3662 MaxBECount = getUMinFromMismatchedTypes(MaxBECount, NewBTI.Max);
3665 return BackedgeTakenInfo(BECount, MaxBECount);
3668 /// ComputeBackedgeTakenCountFromExit - Compute the number of times the backedge
3669 /// of the specified loop will execute if it exits via the specified block.
3670 ScalarEvolution::BackedgeTakenInfo
3671 ScalarEvolution::ComputeBackedgeTakenCountFromExit(const Loop *L,
3672 BasicBlock *ExitingBlock) {
3674 // Okay, we've chosen an exiting block. See what condition causes us to
3675 // exit at this block.
3677 // FIXME: we should be able to handle switch instructions (with a single exit)
3678 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
3679 if (ExitBr == 0) return getCouldNotCompute();
3680 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
3682 // At this point, we know we have a conditional branch that determines whether
3683 // the loop is exited. However, we don't know if the branch is executed each
3684 // time through the loop. If not, then the execution count of the branch will
3685 // not be equal to the trip count of the loop.
3687 // Currently we check for this by checking to see if the Exit branch goes to
3688 // the loop header. If so, we know it will always execute the same number of
3689 // times as the loop. We also handle the case where the exit block *is* the
3690 // loop header. This is common for un-rotated loops.
3692 // If both of those tests fail, walk up the unique predecessor chain to the
3693 // header, stopping if there is an edge that doesn't exit the loop. If the
3694 // header is reached, the execution count of the branch will be equal to the
3695 // trip count of the loop.
3697 // More extensive analysis could be done to handle more cases here.
3699 if (ExitBr->getSuccessor(0) != L->getHeader() &&
3700 ExitBr->getSuccessor(1) != L->getHeader() &&
3701 ExitBr->getParent() != L->getHeader()) {
3702 // The simple checks failed, try climbing the unique predecessor chain
3703 // up to the header.
3705 for (BasicBlock *BB = ExitBr->getParent(); BB; ) {
3706 BasicBlock *Pred = BB->getUniquePredecessor();
3708 return getCouldNotCompute();
3709 TerminatorInst *PredTerm = Pred->getTerminator();
3710 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) {
3711 BasicBlock *PredSucc = PredTerm->getSuccessor(i);
3714 // If the predecessor has a successor that isn't BB and isn't
3715 // outside the loop, assume the worst.
3716 if (L->contains(PredSucc))
3717 return getCouldNotCompute();
3719 if (Pred == L->getHeader()) {
3726 return getCouldNotCompute();
3729 // Proceed to the next level to examine the exit condition expression.
3730 return ComputeBackedgeTakenCountFromExitCond(L, ExitBr->getCondition(),
3731 ExitBr->getSuccessor(0),
3732 ExitBr->getSuccessor(1));
3735 /// ComputeBackedgeTakenCountFromExitCond - Compute the number of times the
3736 /// backedge of the specified loop will execute if its exit condition
3737 /// were a conditional branch of ExitCond, TBB, and FBB.
3738 ScalarEvolution::BackedgeTakenInfo
3739 ScalarEvolution::ComputeBackedgeTakenCountFromExitCond(const Loop *L,
3743 // Check if the controlling expression for this loop is an And or Or.
3744 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
3745 if (BO->getOpcode() == Instruction::And) {
3746 // Recurse on the operands of the and.
3747 BackedgeTakenInfo BTI0 =
3748 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB);
3749 BackedgeTakenInfo BTI1 =
3750 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB);
3751 const SCEV *BECount = getCouldNotCompute();
3752 const SCEV *MaxBECount = getCouldNotCompute();
3753 if (L->contains(TBB)) {
3754 // Both conditions must be true for the loop to continue executing.
3755 // Choose the less conservative count.
3756 if (BTI0.Exact == getCouldNotCompute() ||
3757 BTI1.Exact == getCouldNotCompute())
3758 BECount = getCouldNotCompute();
3760 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3761 if (BTI0.Max == getCouldNotCompute())
3762 MaxBECount = BTI1.Max;
3763 else if (BTI1.Max == getCouldNotCompute())
3764 MaxBECount = BTI0.Max;
3766 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max);
3768 // Both conditions must be true for the loop to exit.
3769 assert(L->contains(FBB) && "Loop block has no successor in loop!");
3770 if (BTI0.Exact != getCouldNotCompute() &&
3771 BTI1.Exact != getCouldNotCompute())
3772 BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3773 if (BTI0.Max != getCouldNotCompute() &&
3774 BTI1.Max != getCouldNotCompute())
3775 MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max);
3778 return BackedgeTakenInfo(BECount, MaxBECount);
3780 if (BO->getOpcode() == Instruction::Or) {
3781 // Recurse on the operands of the or.
3782 BackedgeTakenInfo BTI0 =
3783 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB);
3784 BackedgeTakenInfo BTI1 =
3785 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB);
3786 const SCEV *BECount = getCouldNotCompute();
3787 const SCEV *MaxBECount = getCouldNotCompute();
3788 if (L->contains(FBB)) {
3789 // Both conditions must be false for the loop to continue executing.
3790 // Choose the less conservative count.
3791 if (BTI0.Exact == getCouldNotCompute() ||
3792 BTI1.Exact == getCouldNotCompute())
3793 BECount = getCouldNotCompute();
3795 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3796 if (BTI0.Max == getCouldNotCompute())
3797 MaxBECount = BTI1.Max;
3798 else if (BTI1.Max == getCouldNotCompute())
3799 MaxBECount = BTI0.Max;
3801 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max);
3803 // Both conditions must be false for the loop to exit.
3804 assert(L->contains(TBB) && "Loop block has no successor in loop!");
3805 if (BTI0.Exact != getCouldNotCompute() &&
3806 BTI1.Exact != getCouldNotCompute())
3807 BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3808 if (BTI0.Max != getCouldNotCompute() &&
3809 BTI1.Max != getCouldNotCompute())
3810 MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max);
3813 return BackedgeTakenInfo(BECount, MaxBECount);
3817 // With an icmp, it may be feasible to compute an exact backedge-taken count.
3818 // Proceed to the next level to examine the icmp.
3819 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
3820 return ComputeBackedgeTakenCountFromExitCondICmp(L, ExitCondICmp, TBB, FBB);
3822 // Check for a constant condition. These are normally stripped out by
3823 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
3824 // preserve the CFG and is temporarily leaving constant conditions
3826 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
3827 if (L->contains(FBB) == !CI->getZExtValue())
3828 // The backedge is always taken.
3829 return getCouldNotCompute();
3831 // The backedge is never taken.
3832 return getIntegerSCEV(0, CI->getType());
3835 // If it's not an integer or pointer comparison then compute it the hard way.
3836 return ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB));
3839 /// ComputeBackedgeTakenCountFromExitCondICmp - Compute the number of times the
3840 /// backedge of the specified loop will execute if its exit condition
3841 /// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB.
3842 ScalarEvolution::BackedgeTakenInfo
3843 ScalarEvolution::ComputeBackedgeTakenCountFromExitCondICmp(const Loop *L,
3848 // If the condition was exit on true, convert the condition to exit on false
3849 ICmpInst::Predicate Cond;
3850 if (!L->contains(FBB))
3851 Cond = ExitCond->getPredicate();
3853 Cond = ExitCond->getInversePredicate();
3855 // Handle common loops like: for (X = "string"; *X; ++X)
3856 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
3857 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
3858 BackedgeTakenInfo ItCnt =
3859 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond);
3860 if (ItCnt.hasAnyInfo())
3864 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
3865 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
3867 // Try to evaluate any dependencies out of the loop.
3868 LHS = getSCEVAtScope(LHS, L);
3869 RHS = getSCEVAtScope(RHS, L);
3871 // At this point, we would like to compute how many iterations of the
3872 // loop the predicate will return true for these inputs.
3873 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) {
3874 // If there is a loop-invariant, force it into the RHS.
3875 std::swap(LHS, RHS);
3876 Cond = ICmpInst::getSwappedPredicate(Cond);
3879 // If we have a comparison of a chrec against a constant, try to use value
3880 // ranges to answer this query.
3881 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
3882 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
3883 if (AddRec->getLoop() == L) {
3884 // Form the constant range.
3885 ConstantRange CompRange(
3886 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
3888 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
3889 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
3893 case ICmpInst::ICMP_NE: { // while (X != Y)
3894 // Convert to: while (X-Y != 0)
3895 BackedgeTakenInfo BTI = HowFarToZero(getMinusSCEV(LHS, RHS), L);
3896 if (BTI.hasAnyInfo()) return BTI;
3899 case ICmpInst::ICMP_EQ: { // while (X == Y)
3900 // Convert to: while (X-Y == 0)
3901 BackedgeTakenInfo BTI = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
3902 if (BTI.hasAnyInfo()) return BTI;
3905 case ICmpInst::ICMP_SLT: {
3906 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true);
3907 if (BTI.hasAnyInfo()) return BTI;
3910 case ICmpInst::ICMP_SGT: {
3911 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
3912 getNotSCEV(RHS), L, true);
3913 if (BTI.hasAnyInfo()) return BTI;
3916 case ICmpInst::ICMP_ULT: {
3917 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false);
3918 if (BTI.hasAnyInfo()) return BTI;
3921 case ICmpInst::ICMP_UGT: {
3922 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
3923 getNotSCEV(RHS), L, false);
3924 if (BTI.hasAnyInfo()) return BTI;
3929 dbgs() << "ComputeBackedgeTakenCount ";
3930 if (ExitCond->getOperand(0)->getType()->isUnsigned())
3931 dbgs() << "[unsigned] ";
3932 dbgs() << *LHS << " "
3933 << Instruction::getOpcodeName(Instruction::ICmp)
3934 << " " << *RHS << "\n";
3939 ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB));
3942 static ConstantInt *
3943 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
3944 ScalarEvolution &SE) {
3945 const SCEV *InVal = SE.getConstant(C);
3946 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
3947 assert(isa<SCEVConstant>(Val) &&
3948 "Evaluation of SCEV at constant didn't fold correctly?");
3949 return cast<SCEVConstant>(Val)->getValue();
3952 /// GetAddressedElementFromGlobal - Given a global variable with an initializer
3953 /// and a GEP expression (missing the pointer index) indexing into it, return
3954 /// the addressed element of the initializer or null if the index expression is
3957 GetAddressedElementFromGlobal(GlobalVariable *GV,
3958 const std::vector<ConstantInt*> &Indices) {
3959 Constant *Init = GV->getInitializer();
3960 for (unsigned i = 0, e = Indices.size(); i != e; ++i) {
3961 uint64_t Idx = Indices[i]->getZExtValue();
3962 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) {
3963 assert(Idx < CS->getNumOperands() && "Bad struct index!");
3964 Init = cast<Constant>(CS->getOperand(Idx));
3965 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) {
3966 if (Idx >= CA->getNumOperands()) return 0; // Bogus program
3967 Init = cast<Constant>(CA->getOperand(Idx));
3968 } else if (isa<ConstantAggregateZero>(Init)) {
3969 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) {
3970 assert(Idx < STy->getNumElements() && "Bad struct index!");
3971 Init = Constant::getNullValue(STy->getElementType(Idx));
3972 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) {
3973 if (Idx >= ATy->getNumElements()) return 0; // Bogus program
3974 Init = Constant::getNullValue(ATy->getElementType());
3976 llvm_unreachable("Unknown constant aggregate type!");
3980 return 0; // Unknown initializer type
3986 /// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of
3987 /// 'icmp op load X, cst', try to see if we can compute the backedge
3988 /// execution count.
3989 ScalarEvolution::BackedgeTakenInfo
3990 ScalarEvolution::ComputeLoadConstantCompareBackedgeTakenCount(
3994 ICmpInst::Predicate predicate) {
3995 if (LI->isVolatile()) return getCouldNotCompute();
3997 // Check to see if the loaded pointer is a getelementptr of a global.
3998 // TODO: Use SCEV instead of manually grubbing with GEPs.
3999 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
4000 if (!GEP) return getCouldNotCompute();
4002 // Make sure that it is really a constant global we are gepping, with an
4003 // initializer, and make sure the first IDX is really 0.
4004 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
4005 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
4006 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
4007 !cast<Constant>(GEP->getOperand(1))->isNullValue())
4008 return getCouldNotCompute();
4010 // Okay, we allow one non-constant index into the GEP instruction.
4012 std::vector<ConstantInt*> Indexes;
4013 unsigned VarIdxNum = 0;
4014 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
4015 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
4016 Indexes.push_back(CI);
4017 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
4018 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
4019 VarIdx = GEP->getOperand(i);
4021 Indexes.push_back(0);
4024 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
4025 // Check to see if X is a loop variant variable value now.
4026 const SCEV *Idx = getSCEV(VarIdx);
4027 Idx = getSCEVAtScope(Idx, L);
4029 // We can only recognize very limited forms of loop index expressions, in
4030 // particular, only affine AddRec's like {C1,+,C2}.
4031 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
4032 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) ||
4033 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
4034 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
4035 return getCouldNotCompute();
4037 unsigned MaxSteps = MaxBruteForceIterations;
4038 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
4039 ConstantInt *ItCst = ConstantInt::get(
4040 cast<IntegerType>(IdxExpr->getType()), IterationNum);
4041 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
4043 // Form the GEP offset.
4044 Indexes[VarIdxNum] = Val;
4046 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes);
4047 if (Result == 0) break; // Cannot compute!
4049 // Evaluate the condition for this iteration.
4050 Result = ConstantExpr::getICmp(predicate, Result, RHS);
4051 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
4052 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
4054 dbgs() << "\n***\n*** Computed loop count " << *ItCst
4055 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
4058 ++NumArrayLenItCounts;
4059 return getConstant(ItCst); // Found terminating iteration!
4062 return getCouldNotCompute();
4066 /// CanConstantFold - Return true if we can constant fold an instruction of the
4067 /// specified type, assuming that all operands were constants.
4068 static bool CanConstantFold(const Instruction *I) {
4069 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
4070 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I))
4073 if (const CallInst *CI = dyn_cast<CallInst>(I))
4074 if (const Function *F = CI->getCalledFunction())
4075 return canConstantFoldCallTo(F);
4079 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
4080 /// in the loop that V is derived from. We allow arbitrary operations along the
4081 /// way, but the operands of an operation must either be constants or a value
4082 /// derived from a constant PHI. If this expression does not fit with these
4083 /// constraints, return null.
4084 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
4085 // If this is not an instruction, or if this is an instruction outside of the
4086 // loop, it can't be derived from a loop PHI.
4087 Instruction *I = dyn_cast<Instruction>(V);
4088 if (I == 0 || !L->contains(I)) return 0;
4090 if (PHINode *PN = dyn_cast<PHINode>(I)) {
4091 if (L->getHeader() == I->getParent())
4094 // We don't currently keep track of the control flow needed to evaluate
4095 // PHIs, so we cannot handle PHIs inside of loops.
4099 // If we won't be able to constant fold this expression even if the operands
4100 // are constants, return early.
4101 if (!CanConstantFold(I)) return 0;
4103 // Otherwise, we can evaluate this instruction if all of its operands are
4104 // constant or derived from a PHI node themselves.
4106 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op)
4107 if (!(isa<Constant>(I->getOperand(Op)) ||
4108 isa<GlobalValue>(I->getOperand(Op)))) {
4109 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L);
4110 if (P == 0) return 0; // Not evolving from PHI
4114 return 0; // Evolving from multiple different PHIs.
4117 // This is a expression evolving from a constant PHI!
4121 /// EvaluateExpression - Given an expression that passes the
4122 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
4123 /// in the loop has the value PHIVal. If we can't fold this expression for some
4124 /// reason, return null.
4125 static Constant *EvaluateExpression(Value *V, Constant *PHIVal,
4126 const TargetData *TD) {
4127 if (isa<PHINode>(V)) return PHIVal;
4128 if (Constant *C = dyn_cast<Constant>(V)) return C;
4129 if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) return GV;
4130 Instruction *I = cast<Instruction>(V);
4132 std::vector<Constant*> Operands;
4133 Operands.resize(I->getNumOperands());
4135 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
4136 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal, TD);
4137 if (Operands[i] == 0) return 0;
4140 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
4141 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
4143 return ConstantFoldInstOperands(I->getOpcode(), I->getType(),
4144 &Operands[0], Operands.size(), TD);
4147 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
4148 /// in the header of its containing loop, we know the loop executes a
4149 /// constant number of times, and the PHI node is just a recurrence
4150 /// involving constants, fold it.
4152 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
4155 std::map<PHINode*, Constant*>::iterator I =
4156 ConstantEvolutionLoopExitValue.find(PN);
4157 if (I != ConstantEvolutionLoopExitValue.end())
4160 if (BEs.ugt(MaxBruteForceIterations))
4161 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
4163 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
4165 // Since the loop is canonicalized, the PHI node must have two entries. One
4166 // entry must be a constant (coming in from outside of the loop), and the
4167 // second must be derived from the same PHI.
4168 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
4169 Constant *StartCST =
4170 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
4172 return RetVal = 0; // Must be a constant.
4174 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
4175 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
4177 return RetVal = 0; // Not derived from same PHI.
4179 // Execute the loop symbolically to determine the exit value.
4180 if (BEs.getActiveBits() >= 32)
4181 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
4183 unsigned NumIterations = BEs.getZExtValue(); // must be in range
4184 unsigned IterationNum = 0;
4185 for (Constant *PHIVal = StartCST; ; ++IterationNum) {
4186 if (IterationNum == NumIterations)
4187 return RetVal = PHIVal; // Got exit value!
4189 // Compute the value of the PHI node for the next iteration.
4190 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD);
4191 if (NextPHI == PHIVal)
4192 return RetVal = NextPHI; // Stopped evolving!
4194 return 0; // Couldn't evaluate!
4199 /// ComputeBackedgeTakenCountExhaustively - If the loop is known to execute a
4200 /// constant number of times (the condition evolves only from constants),
4201 /// try to evaluate a few iterations of the loop until we get the exit
4202 /// condition gets a value of ExitWhen (true or false). If we cannot
4203 /// evaluate the trip count of the loop, return getCouldNotCompute().
4205 ScalarEvolution::ComputeBackedgeTakenCountExhaustively(const Loop *L,
4208 PHINode *PN = getConstantEvolvingPHI(Cond, L);
4209 if (PN == 0) return getCouldNotCompute();
4211 // Since the loop is canonicalized, the PHI node must have two entries. One
4212 // entry must be a constant (coming in from outside of the loop), and the
4213 // second must be derived from the same PHI.
4214 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
4215 Constant *StartCST =
4216 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
4217 if (StartCST == 0) return getCouldNotCompute(); // Must be a constant.
4219 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
4220 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
4221 if (PN2 != PN) return getCouldNotCompute(); // Not derived from same PHI.
4223 // Okay, we find a PHI node that defines the trip count of this loop. Execute
4224 // the loop symbolically to determine when the condition gets a value of
4226 unsigned IterationNum = 0;
4227 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
4228 for (Constant *PHIVal = StartCST;
4229 IterationNum != MaxIterations; ++IterationNum) {
4230 ConstantInt *CondVal =
4231 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal, TD));
4233 // Couldn't symbolically evaluate.
4234 if (!CondVal) return getCouldNotCompute();
4236 if (CondVal->getValue() == uint64_t(ExitWhen)) {
4237 ++NumBruteForceTripCountsComputed;
4238 return getConstant(Type::getInt32Ty(getContext()), IterationNum);
4241 // Compute the value of the PHI node for the next iteration.
4242 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD);
4243 if (NextPHI == 0 || NextPHI == PHIVal)
4244 return getCouldNotCompute();// Couldn't evaluate or not making progress...
4248 // Too many iterations were needed to evaluate.
4249 return getCouldNotCompute();
4252 /// getSCEVAtScope - Return a SCEV expression for the specified value
4253 /// at the specified scope in the program. The L value specifies a loop
4254 /// nest to evaluate the expression at, where null is the top-level or a
4255 /// specified loop is immediately inside of the loop.
4257 /// This method can be used to compute the exit value for a variable defined
4258 /// in a loop by querying what the value will hold in the parent loop.
4260 /// In the case that a relevant loop exit value cannot be computed, the
4261 /// original value V is returned.
4262 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
4263 // Check to see if we've folded this expression at this loop before.
4264 std::map<const Loop *, const SCEV *> &Values = ValuesAtScopes[V];
4265 std::pair<std::map<const Loop *, const SCEV *>::iterator, bool> Pair =
4266 Values.insert(std::make_pair(L, static_cast<const SCEV *>(0)));
4268 return Pair.first->second ? Pair.first->second : V;
4270 // Otherwise compute it.
4271 const SCEV *C = computeSCEVAtScope(V, L);
4272 ValuesAtScopes[V][L] = C;
4276 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
4277 if (isa<SCEVConstant>(V)) return V;
4279 // If this instruction is evolved from a constant-evolving PHI, compute the
4280 // exit value from the loop without using SCEVs.
4281 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
4282 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
4283 const Loop *LI = (*this->LI)[I->getParent()];
4284 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
4285 if (PHINode *PN = dyn_cast<PHINode>(I))
4286 if (PN->getParent() == LI->getHeader()) {
4287 // Okay, there is no closed form solution for the PHI node. Check
4288 // to see if the loop that contains it has a known backedge-taken
4289 // count. If so, we may be able to force computation of the exit
4291 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
4292 if (const SCEVConstant *BTCC =
4293 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
4294 // Okay, we know how many times the containing loop executes. If
4295 // this is a constant evolving PHI node, get the final value at
4296 // the specified iteration number.
4297 Constant *RV = getConstantEvolutionLoopExitValue(PN,
4298 BTCC->getValue()->getValue(),
4300 if (RV) return getSCEV(RV);
4304 // Okay, this is an expression that we cannot symbolically evaluate
4305 // into a SCEV. Check to see if it's possible to symbolically evaluate
4306 // the arguments into constants, and if so, try to constant propagate the
4307 // result. This is particularly useful for computing loop exit values.
4308 if (CanConstantFold(I)) {
4309 std::vector<Constant*> Operands;
4310 Operands.reserve(I->getNumOperands());
4311 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
4312 Value *Op = I->getOperand(i);
4313 if (Constant *C = dyn_cast<Constant>(Op)) {
4314 Operands.push_back(C);
4316 // If any of the operands is non-constant and if they are
4317 // non-integer and non-pointer, don't even try to analyze them
4318 // with scev techniques.
4319 if (!isSCEVable(Op->getType()))
4322 const SCEV *OpV = getSCEVAtScope(Op, L);
4323 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) {
4324 Constant *C = SC->getValue();
4325 if (C->getType() != Op->getType())
4326 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
4330 Operands.push_back(C);
4331 } else if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) {
4332 if (Constant *C = dyn_cast<Constant>(SU->getValue())) {
4333 if (C->getType() != Op->getType())
4335 ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
4339 Operands.push_back(C);
4349 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
4350 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
4351 Operands[0], Operands[1], TD);
4353 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
4354 &Operands[0], Operands.size(), TD);
4360 // This is some other type of SCEVUnknown, just return it.
4364 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
4365 // Avoid performing the look-up in the common case where the specified
4366 // expression has no loop-variant portions.
4367 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
4368 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
4369 if (OpAtScope != Comm->getOperand(i)) {
4370 // Okay, at least one of these operands is loop variant but might be
4371 // foldable. Build a new instance of the folded commutative expression.
4372 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
4373 Comm->op_begin()+i);
4374 NewOps.push_back(OpAtScope);
4376 for (++i; i != e; ++i) {
4377 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
4378 NewOps.push_back(OpAtScope);
4380 if (isa<SCEVAddExpr>(Comm))
4381 return getAddExpr(NewOps);
4382 if (isa<SCEVMulExpr>(Comm))
4383 return getMulExpr(NewOps);
4384 if (isa<SCEVSMaxExpr>(Comm))
4385 return getSMaxExpr(NewOps);
4386 if (isa<SCEVUMaxExpr>(Comm))
4387 return getUMaxExpr(NewOps);
4388 llvm_unreachable("Unknown commutative SCEV type!");
4391 // If we got here, all operands are loop invariant.
4395 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
4396 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
4397 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
4398 if (LHS == Div->getLHS() && RHS == Div->getRHS())
4399 return Div; // must be loop invariant
4400 return getUDivExpr(LHS, RHS);
4403 // If this is a loop recurrence for a loop that does not contain L, then we
4404 // are dealing with the final value computed by the loop.
4405 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
4406 if (!L || !AddRec->getLoop()->contains(L)) {
4407 // To evaluate this recurrence, we need to know how many times the AddRec
4408 // loop iterates. Compute this now.
4409 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
4410 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
4412 // Then, evaluate the AddRec.
4413 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
4418 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
4419 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
4420 if (Op == Cast->getOperand())
4421 return Cast; // must be loop invariant
4422 return getZeroExtendExpr(Op, Cast->getType());
4425 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
4426 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
4427 if (Op == Cast->getOperand())
4428 return Cast; // must be loop invariant
4429 return getSignExtendExpr(Op, Cast->getType());
4432 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
4433 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
4434 if (Op == Cast->getOperand())
4435 return Cast; // must be loop invariant
4436 return getTruncateExpr(Op, Cast->getType());
4439 llvm_unreachable("Unknown SCEV type!");
4443 /// getSCEVAtScope - This is a convenience function which does
4444 /// getSCEVAtScope(getSCEV(V), L).
4445 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
4446 return getSCEVAtScope(getSCEV(V), L);
4449 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
4450 /// following equation:
4452 /// A * X = B (mod N)
4454 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
4455 /// A and B isn't important.
4457 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
4458 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
4459 ScalarEvolution &SE) {
4460 uint32_t BW = A.getBitWidth();
4461 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
4462 assert(A != 0 && "A must be non-zero.");
4466 // The gcd of A and N may have only one prime factor: 2. The number of
4467 // trailing zeros in A is its multiplicity
4468 uint32_t Mult2 = A.countTrailingZeros();
4471 // 2. Check if B is divisible by D.
4473 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
4474 // is not less than multiplicity of this prime factor for D.
4475 if (B.countTrailingZeros() < Mult2)
4476 return SE.getCouldNotCompute();
4478 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
4481 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
4482 // bit width during computations.
4483 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
4484 APInt Mod(BW + 1, 0);
4485 Mod.set(BW - Mult2); // Mod = N / D
4486 APInt I = AD.multiplicativeInverse(Mod);
4488 // 4. Compute the minimum unsigned root of the equation:
4489 // I * (B / D) mod (N / D)
4490 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
4492 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
4494 return SE.getConstant(Result.trunc(BW));
4497 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
4498 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
4499 /// might be the same) or two SCEVCouldNotCompute objects.
4501 static std::pair<const SCEV *,const SCEV *>
4502 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
4503 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
4504 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
4505 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
4506 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
4508 // We currently can only solve this if the coefficients are constants.
4509 if (!LC || !MC || !NC) {
4510 const SCEV *CNC = SE.getCouldNotCompute();
4511 return std::make_pair(CNC, CNC);
4514 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
4515 const APInt &L = LC->getValue()->getValue();
4516 const APInt &M = MC->getValue()->getValue();
4517 const APInt &N = NC->getValue()->getValue();
4518 APInt Two(BitWidth, 2);
4519 APInt Four(BitWidth, 4);
4522 using namespace APIntOps;
4524 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
4525 // The B coefficient is M-N/2
4529 // The A coefficient is N/2
4530 APInt A(N.sdiv(Two));
4532 // Compute the B^2-4ac term.
4535 SqrtTerm -= Four * (A * C);
4537 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
4538 // integer value or else APInt::sqrt() will assert.
4539 APInt SqrtVal(SqrtTerm.sqrt());
4541 // Compute the two solutions for the quadratic formula.
4542 // The divisions must be performed as signed divisions.
4544 APInt TwoA( A << 1 );
4545 if (TwoA.isMinValue()) {
4546 const SCEV *CNC = SE.getCouldNotCompute();
4547 return std::make_pair(CNC, CNC);
4550 LLVMContext &Context = SE.getContext();
4552 ConstantInt *Solution1 =
4553 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
4554 ConstantInt *Solution2 =
4555 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
4557 return std::make_pair(SE.getConstant(Solution1),
4558 SE.getConstant(Solution2));
4559 } // end APIntOps namespace
4562 /// HowFarToZero - Return the number of times a backedge comparing the specified
4563 /// value to zero will execute. If not computable, return CouldNotCompute.
4564 ScalarEvolution::BackedgeTakenInfo
4565 ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) {
4566 // If the value is a constant
4567 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
4568 // If the value is already zero, the branch will execute zero times.
4569 if (C->getValue()->isZero()) return C;
4570 return getCouldNotCompute(); // Otherwise it will loop infinitely.
4573 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
4574 if (!AddRec || AddRec->getLoop() != L)
4575 return getCouldNotCompute();
4577 if (AddRec->isAffine()) {
4578 // If this is an affine expression, the execution count of this branch is
4579 // the minimum unsigned root of the following equation:
4581 // Start + Step*N = 0 (mod 2^BW)
4585 // Step*N = -Start (mod 2^BW)
4587 // where BW is the common bit width of Start and Step.
4589 // Get the initial value for the loop.
4590 const SCEV *Start = getSCEVAtScope(AddRec->getStart(),
4591 L->getParentLoop());
4592 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1),
4593 L->getParentLoop());
4595 if (const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) {
4596 // For now we handle only constant steps.
4598 // First, handle unitary steps.
4599 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so:
4600 return getNegativeSCEV(Start); // N = -Start (as unsigned)
4601 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so:
4602 return Start; // N = Start (as unsigned)
4604 // Then, try to solve the above equation provided that Start is constant.
4605 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
4606 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
4607 -StartC->getValue()->getValue(),
4610 } else if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
4611 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
4612 // the quadratic equation to solve it.
4613 std::pair<const SCEV *,const SCEV *> Roots = SolveQuadraticEquation(AddRec,
4615 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
4616 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
4619 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1
4620 << " sol#2: " << *R2 << "\n";
4622 // Pick the smallest positive root value.
4623 if (ConstantInt *CB =
4624 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
4625 R1->getValue(), R2->getValue()))) {
4626 if (CB->getZExtValue() == false)
4627 std::swap(R1, R2); // R1 is the minimum root now.
4629 // We can only use this value if the chrec ends up with an exact zero
4630 // value at this index. When solving for "X*X != 5", for example, we
4631 // should not accept a root of 2.
4632 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
4634 return R1; // We found a quadratic root!
4639 return getCouldNotCompute();
4642 /// HowFarToNonZero - Return the number of times a backedge checking the
4643 /// specified value for nonzero will execute. If not computable, return
4645 ScalarEvolution::BackedgeTakenInfo
4646 ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
4647 // Loops that look like: while (X == 0) are very strange indeed. We don't
4648 // handle them yet except for the trivial case. This could be expanded in the
4649 // future as needed.
4651 // If the value is a constant, check to see if it is known to be non-zero
4652 // already. If so, the backedge will execute zero times.
4653 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
4654 if (!C->getValue()->isNullValue())
4655 return getIntegerSCEV(0, C->getType());
4656 return getCouldNotCompute(); // Otherwise it will loop infinitely.
4659 // We could implement others, but I really doubt anyone writes loops like
4660 // this, and if they did, they would already be constant folded.
4661 return getCouldNotCompute();
4664 /// getLoopPredecessor - If the given loop's header has exactly one unique
4665 /// predecessor outside the loop, return it. Otherwise return null.
4666 /// This is less strict that the loop "preheader" concept, which requires
4667 /// the predecessor to have only one single successor.
4669 BasicBlock *ScalarEvolution::getLoopPredecessor(const Loop *L) {
4670 BasicBlock *Header = L->getHeader();
4671 BasicBlock *Pred = 0;
4672 for (pred_iterator PI = pred_begin(Header), E = pred_end(Header);
4674 if (!L->contains(*PI)) {
4675 if (Pred && Pred != *PI) return 0; // Multiple predecessors.
4681 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
4682 /// (which may not be an immediate predecessor) which has exactly one
4683 /// successor from which BB is reachable, or null if no such block is
4686 std::pair<BasicBlock *, BasicBlock *>
4687 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
4688 // If the block has a unique predecessor, then there is no path from the
4689 // predecessor to the block that does not go through the direct edge
4690 // from the predecessor to the block.
4691 if (BasicBlock *Pred = BB->getSinglePredecessor())
4692 return std::make_pair(Pred, BB);
4694 // A loop's header is defined to be a block that dominates the loop.
4695 // If the header has a unique predecessor outside the loop, it must be
4696 // a block that has exactly one successor that can reach the loop.
4697 if (Loop *L = LI->getLoopFor(BB))
4698 return std::make_pair(getLoopPredecessor(L), L->getHeader());
4700 return std::pair<BasicBlock *, BasicBlock *>();
4703 /// HasSameValue - SCEV structural equivalence is usually sufficient for
4704 /// testing whether two expressions are equal, however for the purposes of
4705 /// looking for a condition guarding a loop, it can be useful to be a little
4706 /// more general, since a front-end may have replicated the controlling
4709 static bool HasSameValue(const SCEV *A, const SCEV *B) {
4710 // Quick check to see if they are the same SCEV.
4711 if (A == B) return true;
4713 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
4714 // two different instructions with the same value. Check for this case.
4715 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
4716 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
4717 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
4718 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
4719 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory())
4722 // Otherwise assume they may have a different value.
4726 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
4727 return getSignedRange(S).getSignedMax().isNegative();
4730 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
4731 return getSignedRange(S).getSignedMin().isStrictlyPositive();
4734 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
4735 return !getSignedRange(S).getSignedMin().isNegative();
4738 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
4739 return !getSignedRange(S).getSignedMax().isStrictlyPositive();
4742 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
4743 return isKnownNegative(S) || isKnownPositive(S);
4746 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
4747 const SCEV *LHS, const SCEV *RHS) {
4748 // If LHS or RHS is an addrec, check to see if the condition is true in
4749 // every iteration of the loop.
4750 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
4751 if (isLoopEntryGuardedByCond(
4752 AR->getLoop(), Pred, AR->getStart(), RHS) &&
4753 isLoopBackedgeGuardedByCond(
4754 AR->getLoop(), Pred,
4755 getAddExpr(AR, AR->getStepRecurrence(*this)), RHS))
4757 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS))
4758 if (isLoopEntryGuardedByCond(
4759 AR->getLoop(), Pred, LHS, AR->getStart()) &&
4760 isLoopBackedgeGuardedByCond(
4761 AR->getLoop(), Pred,
4762 LHS, getAddExpr(AR, AR->getStepRecurrence(*this))))
4765 // Otherwise see what can be done with known constant ranges.
4766 return isKnownPredicateWithRanges(Pred, LHS, RHS);
4770 ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred,
4771 const SCEV *LHS, const SCEV *RHS) {
4772 if (HasSameValue(LHS, RHS))
4773 return ICmpInst::isTrueWhenEqual(Pred);
4775 // This code is split out from isKnownPredicate because it is called from
4776 // within isLoopEntryGuardedByCond.
4779 llvm_unreachable("Unexpected ICmpInst::Predicate value!");
4781 case ICmpInst::ICMP_SGT:
4782 Pred = ICmpInst::ICMP_SLT;
4783 std::swap(LHS, RHS);
4784 case ICmpInst::ICMP_SLT: {
4785 ConstantRange LHSRange = getSignedRange(LHS);
4786 ConstantRange RHSRange = getSignedRange(RHS);
4787 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
4789 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
4793 case ICmpInst::ICMP_SGE:
4794 Pred = ICmpInst::ICMP_SLE;
4795 std::swap(LHS, RHS);
4796 case ICmpInst::ICMP_SLE: {
4797 ConstantRange LHSRange = getSignedRange(LHS);
4798 ConstantRange RHSRange = getSignedRange(RHS);
4799 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
4801 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
4805 case ICmpInst::ICMP_UGT:
4806 Pred = ICmpInst::ICMP_ULT;
4807 std::swap(LHS, RHS);
4808 case ICmpInst::ICMP_ULT: {
4809 ConstantRange LHSRange = getUnsignedRange(LHS);
4810 ConstantRange RHSRange = getUnsignedRange(RHS);
4811 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
4813 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
4817 case ICmpInst::ICMP_UGE:
4818 Pred = ICmpInst::ICMP_ULE;
4819 std::swap(LHS, RHS);
4820 case ICmpInst::ICMP_ULE: {
4821 ConstantRange LHSRange = getUnsignedRange(LHS);
4822 ConstantRange RHSRange = getUnsignedRange(RHS);
4823 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
4825 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
4829 case ICmpInst::ICMP_NE: {
4830 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
4832 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
4835 const SCEV *Diff = getMinusSCEV(LHS, RHS);
4836 if (isKnownNonZero(Diff))
4840 case ICmpInst::ICMP_EQ:
4841 // The check at the top of the function catches the case where
4842 // the values are known to be equal.
4848 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
4849 /// protected by a conditional between LHS and RHS. This is used to
4850 /// to eliminate casts.
4852 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
4853 ICmpInst::Predicate Pred,
4854 const SCEV *LHS, const SCEV *RHS) {
4855 // Interpret a null as meaning no loop, where there is obviously no guard
4856 // (interprocedural conditions notwithstanding).
4857 if (!L) return true;
4859 BasicBlock *Latch = L->getLoopLatch();
4863 BranchInst *LoopContinuePredicate =
4864 dyn_cast<BranchInst>(Latch->getTerminator());
4865 if (!LoopContinuePredicate ||
4866 LoopContinuePredicate->isUnconditional())
4869 return isImpliedCond(LoopContinuePredicate->getCondition(), Pred, LHS, RHS,
4870 LoopContinuePredicate->getSuccessor(0) != L->getHeader());
4873 /// isLoopEntryGuardedByCond - Test whether entry to the loop is protected
4874 /// by a conditional between LHS and RHS. This is used to help avoid max
4875 /// expressions in loop trip counts, and to eliminate casts.
4877 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
4878 ICmpInst::Predicate Pred,
4879 const SCEV *LHS, const SCEV *RHS) {
4880 // Interpret a null as meaning no loop, where there is obviously no guard
4881 // (interprocedural conditions notwithstanding).
4882 if (!L) return false;
4884 // Starting at the loop predecessor, climb up the predecessor chain, as long
4885 // as there are predecessors that can be found that have unique successors
4886 // leading to the original header.
4887 for (std::pair<BasicBlock *, BasicBlock *>
4888 Pair(getLoopPredecessor(L), L->getHeader());
4890 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
4892 BranchInst *LoopEntryPredicate =
4893 dyn_cast<BranchInst>(Pair.first->getTerminator());
4894 if (!LoopEntryPredicate ||
4895 LoopEntryPredicate->isUnconditional())
4898 if (isImpliedCond(LoopEntryPredicate->getCondition(), Pred, LHS, RHS,
4899 LoopEntryPredicate->getSuccessor(0) != Pair.second))
4906 /// isImpliedCond - Test whether the condition described by Pred, LHS,
4907 /// and RHS is true whenever the given Cond value evaluates to true.
4908 bool ScalarEvolution::isImpliedCond(Value *CondValue,
4909 ICmpInst::Predicate Pred,
4910 const SCEV *LHS, const SCEV *RHS,
4912 // Recursively handle And and Or conditions.
4913 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(CondValue)) {
4914 if (BO->getOpcode() == Instruction::And) {
4916 return isImpliedCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) ||
4917 isImpliedCond(BO->getOperand(1), Pred, LHS, RHS, Inverse);
4918 } else if (BO->getOpcode() == Instruction::Or) {
4920 return isImpliedCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) ||
4921 isImpliedCond(BO->getOperand(1), Pred, LHS, RHS, Inverse);
4925 ICmpInst *ICI = dyn_cast<ICmpInst>(CondValue);
4926 if (!ICI) return false;
4928 // Bail if the ICmp's operands' types are wider than the needed type
4929 // before attempting to call getSCEV on them. This avoids infinite
4930 // recursion, since the analysis of widening casts can require loop
4931 // exit condition information for overflow checking, which would
4933 if (getTypeSizeInBits(LHS->getType()) <
4934 getTypeSizeInBits(ICI->getOperand(0)->getType()))
4937 // Now that we found a conditional branch that dominates the loop, check to
4938 // see if it is the comparison we are looking for.
4939 ICmpInst::Predicate FoundPred;
4941 FoundPred = ICI->getInversePredicate();
4943 FoundPred = ICI->getPredicate();
4945 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
4946 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
4948 // Balance the types. The case where FoundLHS' type is wider than
4949 // LHS' type is checked for above.
4950 if (getTypeSizeInBits(LHS->getType()) >
4951 getTypeSizeInBits(FoundLHS->getType())) {
4952 if (CmpInst::isSigned(Pred)) {
4953 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
4954 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
4956 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
4957 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
4961 // Canonicalize the query to match the way instcombine will have
4962 // canonicalized the comparison.
4963 // First, put a constant operand on the right.
4964 if (isa<SCEVConstant>(LHS)) {
4965 std::swap(LHS, RHS);
4966 Pred = ICmpInst::getSwappedPredicate(Pred);
4968 // Then, canonicalize comparisons with boundary cases.
4969 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
4970 const APInt &RA = RC->getValue()->getValue();
4972 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
4973 case ICmpInst::ICMP_EQ:
4974 case ICmpInst::ICMP_NE:
4976 case ICmpInst::ICMP_UGE:
4977 if ((RA - 1).isMinValue()) {
4978 Pred = ICmpInst::ICMP_NE;
4979 RHS = getConstant(RA - 1);
4982 if (RA.isMaxValue()) {
4983 Pred = ICmpInst::ICMP_EQ;
4986 if (RA.isMinValue()) return true;
4988 case ICmpInst::ICMP_ULE:
4989 if ((RA + 1).isMaxValue()) {
4990 Pred = ICmpInst::ICMP_NE;
4991 RHS = getConstant(RA + 1);
4994 if (RA.isMinValue()) {
4995 Pred = ICmpInst::ICMP_EQ;
4998 if (RA.isMaxValue()) return true;
5000 case ICmpInst::ICMP_SGE:
5001 if ((RA - 1).isMinSignedValue()) {
5002 Pred = ICmpInst::ICMP_NE;
5003 RHS = getConstant(RA - 1);
5006 if (RA.isMaxSignedValue()) {
5007 Pred = ICmpInst::ICMP_EQ;
5010 if (RA.isMinSignedValue()) return true;
5012 case ICmpInst::ICMP_SLE:
5013 if ((RA + 1).isMaxSignedValue()) {
5014 Pred = ICmpInst::ICMP_NE;
5015 RHS = getConstant(RA + 1);
5018 if (RA.isMinSignedValue()) {
5019 Pred = ICmpInst::ICMP_EQ;
5022 if (RA.isMaxSignedValue()) return true;
5024 case ICmpInst::ICMP_UGT:
5025 if (RA.isMinValue()) {
5026 Pred = ICmpInst::ICMP_NE;
5029 if ((RA + 1).isMaxValue()) {
5030 Pred = ICmpInst::ICMP_EQ;
5031 RHS = getConstant(RA + 1);
5034 if (RA.isMaxValue()) return false;
5036 case ICmpInst::ICMP_ULT:
5037 if (RA.isMaxValue()) {
5038 Pred = ICmpInst::ICMP_NE;
5041 if ((RA - 1).isMinValue()) {
5042 Pred = ICmpInst::ICMP_EQ;
5043 RHS = getConstant(RA - 1);
5046 if (RA.isMinValue()) return false;
5048 case ICmpInst::ICMP_SGT:
5049 if (RA.isMinSignedValue()) {
5050 Pred = ICmpInst::ICMP_NE;
5053 if ((RA + 1).isMaxSignedValue()) {
5054 Pred = ICmpInst::ICMP_EQ;
5055 RHS = getConstant(RA + 1);
5058 if (RA.isMaxSignedValue()) return false;
5060 case ICmpInst::ICMP_SLT:
5061 if (RA.isMaxSignedValue()) {
5062 Pred = ICmpInst::ICMP_NE;
5065 if ((RA - 1).isMinSignedValue()) {
5066 Pred = ICmpInst::ICMP_EQ;
5067 RHS = getConstant(RA - 1);
5070 if (RA.isMinSignedValue()) return false;
5075 // Check to see if we can make the LHS or RHS match.
5076 if (LHS == FoundRHS || RHS == FoundLHS) {
5077 if (isa<SCEVConstant>(RHS)) {
5078 std::swap(FoundLHS, FoundRHS);
5079 FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
5081 std::swap(LHS, RHS);
5082 Pred = ICmpInst::getSwappedPredicate(Pred);
5086 // Check whether the found predicate is the same as the desired predicate.
5087 if (FoundPred == Pred)
5088 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
5090 // Check whether swapping the found predicate makes it the same as the
5091 // desired predicate.
5092 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
5093 if (isa<SCEVConstant>(RHS))
5094 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
5096 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
5097 RHS, LHS, FoundLHS, FoundRHS);
5100 // Check whether the actual condition is beyond sufficient.
5101 if (FoundPred == ICmpInst::ICMP_EQ)
5102 if (ICmpInst::isTrueWhenEqual(Pred))
5103 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
5105 if (Pred == ICmpInst::ICMP_NE)
5106 if (!ICmpInst::isTrueWhenEqual(FoundPred))
5107 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
5110 // Otherwise assume the worst.
5114 /// isImpliedCondOperands - Test whether the condition described by Pred,
5115 /// LHS, and RHS is true whenever the condition described by Pred, FoundLHS,
5116 /// and FoundRHS is true.
5117 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
5118 const SCEV *LHS, const SCEV *RHS,
5119 const SCEV *FoundLHS,
5120 const SCEV *FoundRHS) {
5121 return isImpliedCondOperandsHelper(Pred, LHS, RHS,
5122 FoundLHS, FoundRHS) ||
5123 // ~x < ~y --> x > y
5124 isImpliedCondOperandsHelper(Pred, LHS, RHS,
5125 getNotSCEV(FoundRHS),
5126 getNotSCEV(FoundLHS));
5129 /// isImpliedCondOperandsHelper - Test whether the condition described by
5130 /// Pred, LHS, and RHS is true whenever the condition described by Pred,
5131 /// FoundLHS, and FoundRHS is true.
5133 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
5134 const SCEV *LHS, const SCEV *RHS,
5135 const SCEV *FoundLHS,
5136 const SCEV *FoundRHS) {
5138 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
5139 case ICmpInst::ICMP_EQ:
5140 case ICmpInst::ICMP_NE:
5141 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
5144 case ICmpInst::ICMP_SLT:
5145 case ICmpInst::ICMP_SLE:
5146 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
5147 isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, RHS, FoundRHS))
5150 case ICmpInst::ICMP_SGT:
5151 case ICmpInst::ICMP_SGE:
5152 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
5153 isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, RHS, FoundRHS))
5156 case ICmpInst::ICMP_ULT:
5157 case ICmpInst::ICMP_ULE:
5158 if (isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
5159 isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, RHS, FoundRHS))
5162 case ICmpInst::ICMP_UGT:
5163 case ICmpInst::ICMP_UGE:
5164 if (isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
5165 isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, RHS, FoundRHS))
5173 /// getBECount - Subtract the end and start values and divide by the step,
5174 /// rounding up, to get the number of times the backedge is executed. Return
5175 /// CouldNotCompute if an intermediate computation overflows.
5176 const SCEV *ScalarEvolution::getBECount(const SCEV *Start,
5180 assert(!isKnownNegative(Step) &&
5181 "This code doesn't handle negative strides yet!");
5183 const Type *Ty = Start->getType();
5184 const SCEV *NegOne = getIntegerSCEV(-1, Ty);
5185 const SCEV *Diff = getMinusSCEV(End, Start);
5186 const SCEV *RoundUp = getAddExpr(Step, NegOne);
5188 // Add an adjustment to the difference between End and Start so that
5189 // the division will effectively round up.
5190 const SCEV *Add = getAddExpr(Diff, RoundUp);
5193 // Check Add for unsigned overflow.
5194 // TODO: More sophisticated things could be done here.
5195 const Type *WideTy = IntegerType::get(getContext(),
5196 getTypeSizeInBits(Ty) + 1);
5197 const SCEV *EDiff = getZeroExtendExpr(Diff, WideTy);
5198 const SCEV *ERoundUp = getZeroExtendExpr(RoundUp, WideTy);
5199 const SCEV *OperandExtendedAdd = getAddExpr(EDiff, ERoundUp);
5200 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd)
5201 return getCouldNotCompute();
5204 return getUDivExpr(Add, Step);
5207 /// HowManyLessThans - Return the number of times a backedge containing the
5208 /// specified less-than comparison will execute. If not computable, return
5209 /// CouldNotCompute.
5210 ScalarEvolution::BackedgeTakenInfo
5211 ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
5212 const Loop *L, bool isSigned) {
5213 // Only handle: "ADDREC < LoopInvariant".
5214 if (!RHS->isLoopInvariant(L)) return getCouldNotCompute();
5216 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
5217 if (!AddRec || AddRec->getLoop() != L)
5218 return getCouldNotCompute();
5220 // Check to see if we have a flag which makes analysis easy.
5221 bool NoWrap = isSigned ? AddRec->hasNoSignedWrap() :
5222 AddRec->hasNoUnsignedWrap();
5224 if (AddRec->isAffine()) {
5225 unsigned BitWidth = getTypeSizeInBits(AddRec->getType());
5226 const SCEV *Step = AddRec->getStepRecurrence(*this);
5229 return getCouldNotCompute();
5230 if (Step->isOne()) {
5231 // With unit stride, the iteration never steps past the limit value.
5232 } else if (isKnownPositive(Step)) {
5233 // Test whether a positive iteration can step past the limit
5234 // value and past the maximum value for its type in a single step.
5235 // Note that it's not sufficient to check NoWrap here, because even
5236 // though the value after a wrap is undefined, it's not undefined
5237 // behavior, so if wrap does occur, the loop could either terminate or
5238 // loop infinitely, but in either case, the loop is guaranteed to
5239 // iterate at least until the iteration where the wrapping occurs.
5240 const SCEV *One = getIntegerSCEV(1, Step->getType());
5242 APInt Max = APInt::getSignedMaxValue(BitWidth);
5243 if ((Max - getSignedRange(getMinusSCEV(Step, One)).getSignedMax())
5244 .slt(getSignedRange(RHS).getSignedMax()))
5245 return getCouldNotCompute();
5247 APInt Max = APInt::getMaxValue(BitWidth);
5248 if ((Max - getUnsignedRange(getMinusSCEV(Step, One)).getUnsignedMax())
5249 .ult(getUnsignedRange(RHS).getUnsignedMax()))
5250 return getCouldNotCompute();
5253 // TODO: Handle negative strides here and below.
5254 return getCouldNotCompute();
5256 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant
5257 // m. So, we count the number of iterations in which {n,+,s} < m is true.
5258 // Note that we cannot simply return max(m-n,0)/s because it's not safe to
5259 // treat m-n as signed nor unsigned due to overflow possibility.
5261 // First, we get the value of the LHS in the first iteration: n
5262 const SCEV *Start = AddRec->getOperand(0);
5264 // Determine the minimum constant start value.
5265 const SCEV *MinStart = getConstant(isSigned ?
5266 getSignedRange(Start).getSignedMin() :
5267 getUnsignedRange(Start).getUnsignedMin());
5269 // If we know that the condition is true in order to enter the loop,
5270 // then we know that it will run exactly (m-n)/s times. Otherwise, we
5271 // only know that it will execute (max(m,n)-n)/s times. In both cases,
5272 // the division must round up.
5273 const SCEV *End = RHS;
5274 if (!isLoopEntryGuardedByCond(L,
5275 isSigned ? ICmpInst::ICMP_SLT :
5277 getMinusSCEV(Start, Step), RHS))
5278 End = isSigned ? getSMaxExpr(RHS, Start)
5279 : getUMaxExpr(RHS, Start);
5281 // Determine the maximum constant end value.
5282 const SCEV *MaxEnd = getConstant(isSigned ?
5283 getSignedRange(End).getSignedMax() :
5284 getUnsignedRange(End).getUnsignedMax());
5286 // If MaxEnd is within a step of the maximum integer value in its type,
5287 // adjust it down to the minimum value which would produce the same effect.
5288 // This allows the subsequent ceiling division of (N+(step-1))/step to
5289 // compute the correct value.
5290 const SCEV *StepMinusOne = getMinusSCEV(Step,
5291 getIntegerSCEV(1, Step->getType()));
5294 getMinusSCEV(getConstant(APInt::getSignedMaxValue(BitWidth)),
5297 getMinusSCEV(getConstant(APInt::getMaxValue(BitWidth)),
5300 // Finally, we subtract these two values and divide, rounding up, to get
5301 // the number of times the backedge is executed.
5302 const SCEV *BECount = getBECount(Start, End, Step, NoWrap);
5304 // The maximum backedge count is similar, except using the minimum start
5305 // value and the maximum end value.
5306 const SCEV *MaxBECount = getBECount(MinStart, MaxEnd, Step, NoWrap);
5308 return BackedgeTakenInfo(BECount, MaxBECount);
5311 return getCouldNotCompute();
5314 /// getNumIterationsInRange - Return the number of iterations of this loop that
5315 /// produce values in the specified constant range. Another way of looking at
5316 /// this is that it returns the first iteration number where the value is not in
5317 /// the condition, thus computing the exit count. If the iteration count can't
5318 /// be computed, an instance of SCEVCouldNotCompute is returned.
5319 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
5320 ScalarEvolution &SE) const {
5321 if (Range.isFullSet()) // Infinite loop.
5322 return SE.getCouldNotCompute();
5324 // If the start is a non-zero constant, shift the range to simplify things.
5325 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
5326 if (!SC->getValue()->isZero()) {
5327 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
5328 Operands[0] = SE.getIntegerSCEV(0, SC->getType());
5329 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop());
5330 if (const SCEVAddRecExpr *ShiftedAddRec =
5331 dyn_cast<SCEVAddRecExpr>(Shifted))
5332 return ShiftedAddRec->getNumIterationsInRange(
5333 Range.subtract(SC->getValue()->getValue()), SE);
5334 // This is strange and shouldn't happen.
5335 return SE.getCouldNotCompute();
5338 // The only time we can solve this is when we have all constant indices.
5339 // Otherwise, we cannot determine the overflow conditions.
5340 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
5341 if (!isa<SCEVConstant>(getOperand(i)))
5342 return SE.getCouldNotCompute();
5345 // Okay at this point we know that all elements of the chrec are constants and
5346 // that the start element is zero.
5348 // First check to see if the range contains zero. If not, the first
5350 unsigned BitWidth = SE.getTypeSizeInBits(getType());
5351 if (!Range.contains(APInt(BitWidth, 0)))
5352 return SE.getIntegerSCEV(0, getType());
5355 // If this is an affine expression then we have this situation:
5356 // Solve {0,+,A} in Range === Ax in Range
5358 // We know that zero is in the range. If A is positive then we know that
5359 // the upper value of the range must be the first possible exit value.
5360 // If A is negative then the lower of the range is the last possible loop
5361 // value. Also note that we already checked for a full range.
5362 APInt One(BitWidth,1);
5363 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
5364 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
5366 // The exit value should be (End+A)/A.
5367 APInt ExitVal = (End + A).udiv(A);
5368 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
5370 // Evaluate at the exit value. If we really did fall out of the valid
5371 // range, then we computed our trip count, otherwise wrap around or other
5372 // things must have happened.
5373 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
5374 if (Range.contains(Val->getValue()))
5375 return SE.getCouldNotCompute(); // Something strange happened
5377 // Ensure that the previous value is in the range. This is a sanity check.
5378 assert(Range.contains(
5379 EvaluateConstantChrecAtConstant(this,
5380 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
5381 "Linear scev computation is off in a bad way!");
5382 return SE.getConstant(ExitValue);
5383 } else if (isQuadratic()) {
5384 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
5385 // quadratic equation to solve it. To do this, we must frame our problem in
5386 // terms of figuring out when zero is crossed, instead of when
5387 // Range.getUpper() is crossed.
5388 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
5389 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
5390 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop());
5392 // Next, solve the constructed addrec
5393 std::pair<const SCEV *,const SCEV *> Roots =
5394 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
5395 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
5396 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
5398 // Pick the smallest positive root value.
5399 if (ConstantInt *CB =
5400 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
5401 R1->getValue(), R2->getValue()))) {
5402 if (CB->getZExtValue() == false)
5403 std::swap(R1, R2); // R1 is the minimum root now.
5405 // Make sure the root is not off by one. The returned iteration should
5406 // not be in the range, but the previous one should be. When solving
5407 // for "X*X < 5", for example, we should not return a root of 2.
5408 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
5411 if (Range.contains(R1Val->getValue())) {
5412 // The next iteration must be out of the range...
5413 ConstantInt *NextVal =
5414 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1);
5416 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
5417 if (!Range.contains(R1Val->getValue()))
5418 return SE.getConstant(NextVal);
5419 return SE.getCouldNotCompute(); // Something strange happened
5422 // If R1 was not in the range, then it is a good return value. Make
5423 // sure that R1-1 WAS in the range though, just in case.
5424 ConstantInt *NextVal =
5425 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1);
5426 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
5427 if (Range.contains(R1Val->getValue()))
5429 return SE.getCouldNotCompute(); // Something strange happened
5434 return SE.getCouldNotCompute();
5439 //===----------------------------------------------------------------------===//
5440 // SCEVCallbackVH Class Implementation
5441 //===----------------------------------------------------------------------===//
5443 void ScalarEvolution::SCEVCallbackVH::deleted() {
5444 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
5445 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
5446 SE->ConstantEvolutionLoopExitValue.erase(PN);
5447 SE->Scalars.erase(getValPtr());
5448 // this now dangles!
5451 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *) {
5452 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
5454 // Forget all the expressions associated with users of the old value,
5455 // so that future queries will recompute the expressions using the new
5457 SmallVector<User *, 16> Worklist;
5458 SmallPtrSet<User *, 8> Visited;
5459 Value *Old = getValPtr();
5460 bool DeleteOld = false;
5461 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end();
5463 Worklist.push_back(*UI);
5464 while (!Worklist.empty()) {
5465 User *U = Worklist.pop_back_val();
5466 // Deleting the Old value will cause this to dangle. Postpone
5467 // that until everything else is done.
5472 if (!Visited.insert(U))
5474 if (PHINode *PN = dyn_cast<PHINode>(U))
5475 SE->ConstantEvolutionLoopExitValue.erase(PN);
5476 SE->Scalars.erase(U);
5477 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end();
5479 Worklist.push_back(*UI);
5481 // Delete the Old value if it (indirectly) references itself.
5483 if (PHINode *PN = dyn_cast<PHINode>(Old))
5484 SE->ConstantEvolutionLoopExitValue.erase(PN);
5485 SE->Scalars.erase(Old);
5486 // this now dangles!
5491 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
5492 : CallbackVH(V), SE(se) {}
5494 //===----------------------------------------------------------------------===//
5495 // ScalarEvolution Class Implementation
5496 //===----------------------------------------------------------------------===//
5498 ScalarEvolution::ScalarEvolution()
5499 : FunctionPass(&ID) {
5502 bool ScalarEvolution::runOnFunction(Function &F) {
5504 LI = &getAnalysis<LoopInfo>();
5505 TD = getAnalysisIfAvailable<TargetData>();
5506 DT = &getAnalysis<DominatorTree>();
5510 void ScalarEvolution::releaseMemory() {
5512 BackedgeTakenCounts.clear();
5513 ConstantEvolutionLoopExitValue.clear();
5514 ValuesAtScopes.clear();
5515 UniqueSCEVs.clear();
5516 SCEVAllocator.Reset();
5519 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
5520 AU.setPreservesAll();
5521 AU.addRequiredTransitive<LoopInfo>();
5522 AU.addRequiredTransitive<DominatorTree>();
5525 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
5526 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
5529 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
5531 // Print all inner loops first
5532 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
5533 PrintLoopInfo(OS, SE, *I);
5536 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
5539 SmallVector<BasicBlock *, 8> ExitBlocks;
5540 L->getExitBlocks(ExitBlocks);
5541 if (ExitBlocks.size() != 1)
5542 OS << "<multiple exits> ";
5544 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
5545 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
5547 OS << "Unpredictable backedge-taken count. ";
5552 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
5555 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
5556 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
5558 OS << "Unpredictable max backedge-taken count. ";
5564 void ScalarEvolution::print(raw_ostream &OS, const Module *) const {
5565 // ScalarEvolution's implementation of the print method is to print
5566 // out SCEV values of all instructions that are interesting. Doing
5567 // this potentially causes it to create new SCEV objects though,
5568 // which technically conflicts with the const qualifier. This isn't
5569 // observable from outside the class though, so casting away the
5570 // const isn't dangerous.
5571 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
5573 OS << "Classifying expressions for: ";
5574 WriteAsOperand(OS, F, /*PrintType=*/false);
5576 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
5577 if (isSCEVable(I->getType())) {
5580 const SCEV *SV = SE.getSCEV(&*I);
5583 const Loop *L = LI->getLoopFor((*I).getParent());
5585 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
5592 OS << "\t\t" "Exits: ";
5593 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
5594 if (!ExitValue->isLoopInvariant(L)) {
5595 OS << "<<Unknown>>";
5604 OS << "Determining loop execution counts for: ";
5605 WriteAsOperand(OS, F, /*PrintType=*/false);
5607 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
5608 PrintLoopInfo(OS, &SE, *I);