1 //===- ScalarEvolution.cpp - Scalar Evolution Analysis ----------*- C++ -*-===//
3 // The LLVM Compiler Infrastructure
5 // This file is distributed under the University of Illinois Open Source
6 // License. See LICENSE.TXT for details.
8 //===----------------------------------------------------------------------===//
10 // This file contains the implementation of the scalar evolution analysis
11 // engine, which is used primarily to analyze expressions involving induction
12 // variables in loops.
14 // There are several aspects to this library. First is the representation of
15 // scalar expressions, which are represented as subclasses of the SCEV class.
16 // These classes are used to represent certain types of subexpressions that we
17 // can handle. We only create one SCEV of a particular shape, so
18 // pointer-comparisons for equality are legal.
20 // One important aspect of the SCEV objects is that they are never cyclic, even
21 // if there is a cycle in the dataflow for an expression (ie, a PHI node). If
22 // the PHI node is one of the idioms that we can represent (e.g., a polynomial
23 // recurrence) then we represent it directly as a recurrence node, otherwise we
24 // represent it as a SCEVUnknown node.
26 // In addition to being able to represent expressions of various types, we also
27 // have folders that are used to build the *canonical* representation for a
28 // particular expression. These folders are capable of using a variety of
29 // rewrite rules to simplify the expressions.
31 // Once the folders are defined, we can implement the more interesting
32 // higher-level code, such as the code that recognizes PHI nodes of various
33 // types, computes the execution count of a loop, etc.
35 // TODO: We should use these routines and value representations to implement
36 // dependence analysis!
38 //===----------------------------------------------------------------------===//
40 // There are several good references for the techniques used in this analysis.
42 // Chains of recurrences -- a method to expedite the evaluation
43 // of closed-form functions
44 // Olaf Bachmann, Paul S. Wang, Eugene V. Zima
46 // On computational properties of chains of recurrences
49 // Symbolic Evaluation of Chains of Recurrences for Loop Optimization
50 // Robert A. van Engelen
52 // Efficient Symbolic Analysis for Optimizing Compilers
53 // Robert A. van Engelen
55 // Using the chains of recurrences algebra for data dependence testing and
56 // induction variable substitution
57 // MS Thesis, Johnie Birch
59 //===----------------------------------------------------------------------===//
61 #define DEBUG_TYPE "scalar-evolution"
62 #include "llvm/Analysis/ScalarEvolutionExpressions.h"
63 #include "llvm/Constants.h"
64 #include "llvm/DerivedTypes.h"
65 #include "llvm/GlobalVariable.h"
66 #include "llvm/GlobalAlias.h"
67 #include "llvm/Instructions.h"
68 #include "llvm/LLVMContext.h"
69 #include "llvm/Operator.h"
70 #include "llvm/Analysis/ConstantFolding.h"
71 #include "llvm/Analysis/Dominators.h"
72 #include "llvm/Analysis/LoopInfo.h"
73 #include "llvm/Analysis/ValueTracking.h"
74 #include "llvm/Assembly/Writer.h"
75 #include "llvm/Target/TargetData.h"
76 #include "llvm/Support/CommandLine.h"
77 #include "llvm/Support/ConstantRange.h"
78 #include "llvm/Support/Debug.h"
79 #include "llvm/Support/ErrorHandling.h"
80 #include "llvm/Support/GetElementPtrTypeIterator.h"
81 #include "llvm/Support/InstIterator.h"
82 #include "llvm/Support/MathExtras.h"
83 #include "llvm/Support/raw_ostream.h"
84 #include "llvm/ADT/Statistic.h"
85 #include "llvm/ADT/STLExtras.h"
86 #include "llvm/ADT/SmallPtrSet.h"
90 STATISTIC(NumArrayLenItCounts,
91 "Number of trip counts computed with array length");
92 STATISTIC(NumTripCountsComputed,
93 "Number of loops with predictable loop counts");
94 STATISTIC(NumTripCountsNotComputed,
95 "Number of loops without predictable loop counts");
96 STATISTIC(NumBruteForceTripCountsComputed,
97 "Number of loops with trip counts computed by force");
99 static cl::opt<unsigned>
100 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
101 cl::desc("Maximum number of iterations SCEV will "
102 "symbolically execute a constant "
106 INITIALIZE_PASS(ScalarEvolution, "scalar-evolution",
107 "Scalar Evolution Analysis", false, true);
108 char ScalarEvolution::ID = 0;
110 //===----------------------------------------------------------------------===//
111 // SCEV class definitions
112 //===----------------------------------------------------------------------===//
114 //===----------------------------------------------------------------------===//
115 // Implementation of the SCEV class.
120 void SCEV::dump() const {
125 bool SCEV::isZero() const {
126 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
127 return SC->getValue()->isZero();
131 bool SCEV::isOne() const {
132 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
133 return SC->getValue()->isOne();
137 bool SCEV::isAllOnesValue() const {
138 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
139 return SC->getValue()->isAllOnesValue();
143 SCEVCouldNotCompute::SCEVCouldNotCompute() :
144 SCEV(FoldingSetNodeIDRef(), scCouldNotCompute) {}
146 bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const {
147 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
151 const Type *SCEVCouldNotCompute::getType() const {
152 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
156 bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const {
157 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
161 bool SCEVCouldNotCompute::hasOperand(const SCEV *) const {
162 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
166 void SCEVCouldNotCompute::print(raw_ostream &OS) const {
167 OS << "***COULDNOTCOMPUTE***";
170 bool SCEVCouldNotCompute::classof(const SCEV *S) {
171 return S->getSCEVType() == scCouldNotCompute;
174 const SCEV *ScalarEvolution::getConstant(ConstantInt *V) {
176 ID.AddInteger(scConstant);
179 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
180 SCEV *S = new (SCEVAllocator) SCEVConstant(ID.Intern(SCEVAllocator), V);
181 UniqueSCEVs.InsertNode(S, IP);
185 const SCEV *ScalarEvolution::getConstant(const APInt& Val) {
186 return getConstant(ConstantInt::get(getContext(), Val));
190 ScalarEvolution::getConstant(const Type *Ty, uint64_t V, bool isSigned) {
191 const IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty));
192 return getConstant(ConstantInt::get(ITy, V, isSigned));
195 const Type *SCEVConstant::getType() const { return V->getType(); }
197 void SCEVConstant::print(raw_ostream &OS) const {
198 WriteAsOperand(OS, V, false);
201 SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID,
202 unsigned SCEVTy, const SCEV *op, const Type *ty)
203 : SCEV(ID, SCEVTy), Op(op), Ty(ty) {}
205 bool SCEVCastExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
206 return Op->dominates(BB, DT);
209 bool SCEVCastExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const {
210 return Op->properlyDominates(BB, DT);
213 SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID,
214 const SCEV *op, const Type *ty)
215 : SCEVCastExpr(ID, scTruncate, op, ty) {
216 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
217 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
218 "Cannot truncate non-integer value!");
221 void SCEVTruncateExpr::print(raw_ostream &OS) const {
222 OS << "(trunc " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
225 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID,
226 const SCEV *op, const Type *ty)
227 : SCEVCastExpr(ID, scZeroExtend, op, ty) {
228 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
229 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
230 "Cannot zero extend non-integer value!");
233 void SCEVZeroExtendExpr::print(raw_ostream &OS) const {
234 OS << "(zext " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
237 SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID,
238 const SCEV *op, const Type *ty)
239 : SCEVCastExpr(ID, scSignExtend, op, ty) {
240 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
241 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
242 "Cannot sign extend non-integer value!");
245 void SCEVSignExtendExpr::print(raw_ostream &OS) const {
246 OS << "(sext " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
249 void SCEVCommutativeExpr::print(raw_ostream &OS) const {
250 const char *OpStr = getOperationStr();
252 for (op_iterator I = op_begin(), E = op_end(); I != E; ++I) {
260 bool SCEVNAryExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
261 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
262 if (!getOperand(i)->dominates(BB, DT))
268 bool SCEVNAryExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const {
269 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
270 if (!getOperand(i)->properlyDominates(BB, DT))
276 bool SCEVUDivExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
277 return LHS->dominates(BB, DT) && RHS->dominates(BB, DT);
280 bool SCEVUDivExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const {
281 return LHS->properlyDominates(BB, DT) && RHS->properlyDominates(BB, DT);
284 void SCEVUDivExpr::print(raw_ostream &OS) const {
285 OS << "(" << *LHS << " /u " << *RHS << ")";
288 const Type *SCEVUDivExpr::getType() const {
289 // In most cases the types of LHS and RHS will be the same, but in some
290 // crazy cases one or the other may be a pointer. ScalarEvolution doesn't
291 // depend on the type for correctness, but handling types carefully can
292 // avoid extra casts in the SCEVExpander. The LHS is more likely to be
293 // a pointer type than the RHS, so use the RHS' type here.
294 return RHS->getType();
297 bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const {
298 // Add recurrences are never invariant in the function-body (null loop).
302 // This recurrence is variant w.r.t. QueryLoop if QueryLoop contains L.
303 if (QueryLoop->contains(L))
306 // This recurrence is variant w.r.t. QueryLoop if any of its operands
308 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
309 if (!getOperand(i)->isLoopInvariant(QueryLoop))
312 // Otherwise it's loop-invariant.
317 SCEVAddRecExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
318 return DT->dominates(L->getHeader(), BB) &&
319 SCEVNAryExpr::dominates(BB, DT);
323 SCEVAddRecExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const {
324 // This uses a "dominates" query instead of "properly dominates" query because
325 // the instruction which produces the addrec's value is a PHI, and a PHI
326 // effectively properly dominates its entire containing block.
327 return DT->dominates(L->getHeader(), BB) &&
328 SCEVNAryExpr::properlyDominates(BB, DT);
331 void SCEVAddRecExpr::print(raw_ostream &OS) const {
332 OS << "{" << *Operands[0];
333 for (unsigned i = 1, e = NumOperands; i != e; ++i)
334 OS << ",+," << *Operands[i];
336 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
340 bool SCEVUnknown::isLoopInvariant(const Loop *L) const {
341 // All non-instruction values are loop invariant. All instructions are loop
342 // invariant if they are not contained in the specified loop.
343 // Instructions are never considered invariant in the function body
344 // (null loop) because they are defined within the "loop".
345 if (Instruction *I = dyn_cast<Instruction>(V))
346 return L && !L->contains(I);
350 bool SCEVUnknown::dominates(BasicBlock *BB, DominatorTree *DT) const {
351 if (Instruction *I = dyn_cast<Instruction>(getValue()))
352 return DT->dominates(I->getParent(), BB);
356 bool SCEVUnknown::properlyDominates(BasicBlock *BB, DominatorTree *DT) const {
357 if (Instruction *I = dyn_cast<Instruction>(getValue()))
358 return DT->properlyDominates(I->getParent(), BB);
362 const Type *SCEVUnknown::getType() const {
366 bool SCEVUnknown::isSizeOf(const Type *&AllocTy) const {
367 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(V))
368 if (VCE->getOpcode() == Instruction::PtrToInt)
369 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
370 if (CE->getOpcode() == Instruction::GetElementPtr &&
371 CE->getOperand(0)->isNullValue() &&
372 CE->getNumOperands() == 2)
373 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1)))
375 AllocTy = cast<PointerType>(CE->getOperand(0)->getType())
383 bool SCEVUnknown::isAlignOf(const Type *&AllocTy) const {
384 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(V))
385 if (VCE->getOpcode() == Instruction::PtrToInt)
386 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
387 if (CE->getOpcode() == Instruction::GetElementPtr &&
388 CE->getOperand(0)->isNullValue()) {
390 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
391 if (const StructType *STy = dyn_cast<StructType>(Ty))
392 if (!STy->isPacked() &&
393 CE->getNumOperands() == 3 &&
394 CE->getOperand(1)->isNullValue()) {
395 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2)))
397 STy->getNumElements() == 2 &&
398 STy->getElementType(0)->isIntegerTy(1)) {
399 AllocTy = STy->getElementType(1);
408 bool SCEVUnknown::isOffsetOf(const Type *&CTy, Constant *&FieldNo) const {
409 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(V))
410 if (VCE->getOpcode() == Instruction::PtrToInt)
411 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
412 if (CE->getOpcode() == Instruction::GetElementPtr &&
413 CE->getNumOperands() == 3 &&
414 CE->getOperand(0)->isNullValue() &&
415 CE->getOperand(1)->isNullValue()) {
417 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
418 // Ignore vector types here so that ScalarEvolutionExpander doesn't
419 // emit getelementptrs that index into vectors.
420 if (Ty->isStructTy() || Ty->isArrayTy()) {
422 FieldNo = CE->getOperand(2);
430 void SCEVUnknown::print(raw_ostream &OS) const {
432 if (isSizeOf(AllocTy)) {
433 OS << "sizeof(" << *AllocTy << ")";
436 if (isAlignOf(AllocTy)) {
437 OS << "alignof(" << *AllocTy << ")";
443 if (isOffsetOf(CTy, FieldNo)) {
444 OS << "offsetof(" << *CTy << ", ";
445 WriteAsOperand(OS, FieldNo, false);
450 // Otherwise just print it normally.
451 WriteAsOperand(OS, V, false);
454 //===----------------------------------------------------------------------===//
456 //===----------------------------------------------------------------------===//
458 static bool CompareTypes(const Type *A, const Type *B) {
459 if (A->getTypeID() != B->getTypeID())
460 return A->getTypeID() < B->getTypeID();
461 if (const IntegerType *AI = dyn_cast<IntegerType>(A)) {
462 const IntegerType *BI = cast<IntegerType>(B);
463 return AI->getBitWidth() < BI->getBitWidth();
465 if (const PointerType *AI = dyn_cast<PointerType>(A)) {
466 const PointerType *BI = cast<PointerType>(B);
467 return CompareTypes(AI->getElementType(), BI->getElementType());
469 if (const ArrayType *AI = dyn_cast<ArrayType>(A)) {
470 const ArrayType *BI = cast<ArrayType>(B);
471 if (AI->getNumElements() != BI->getNumElements())
472 return AI->getNumElements() < BI->getNumElements();
473 return CompareTypes(AI->getElementType(), BI->getElementType());
475 if (const VectorType *AI = dyn_cast<VectorType>(A)) {
476 const VectorType *BI = cast<VectorType>(B);
477 if (AI->getNumElements() != BI->getNumElements())
478 return AI->getNumElements() < BI->getNumElements();
479 return CompareTypes(AI->getElementType(), BI->getElementType());
481 if (const StructType *AI = dyn_cast<StructType>(A)) {
482 const StructType *BI = cast<StructType>(B);
483 if (AI->getNumElements() != BI->getNumElements())
484 return AI->getNumElements() < BI->getNumElements();
485 for (unsigned i = 0, e = AI->getNumElements(); i != e; ++i)
486 if (CompareTypes(AI->getElementType(i), BI->getElementType(i)) ||
487 CompareTypes(BI->getElementType(i), AI->getElementType(i)))
488 return CompareTypes(AI->getElementType(i), BI->getElementType(i));
494 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
495 /// than the complexity of the RHS. This comparator is used to canonicalize
497 class SCEVComplexityCompare {
500 explicit SCEVComplexityCompare(const LoopInfo *li) : LI(li) {}
502 bool operator()(const SCEV *LHS, const SCEV *RHS) const {
503 // Fast-path: SCEVs are uniqued so we can do a quick equality check.
507 // Primarily, sort the SCEVs by their getSCEVType().
508 if (LHS->getSCEVType() != RHS->getSCEVType())
509 return LHS->getSCEVType() < RHS->getSCEVType();
511 // Aside from the getSCEVType() ordering, the particular ordering
512 // isn't very important except that it's beneficial to be consistent,
513 // so that (a + b) and (b + a) don't end up as different expressions.
515 // Sort SCEVUnknown values with some loose heuristics. TODO: This is
516 // not as complete as it could be.
517 if (const SCEVUnknown *LU = dyn_cast<SCEVUnknown>(LHS)) {
518 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
520 // Order pointer values after integer values. This helps SCEVExpander
522 if (LU->getType()->isPointerTy() && !RU->getType()->isPointerTy())
524 if (RU->getType()->isPointerTy() && !LU->getType()->isPointerTy())
527 // Compare getValueID values.
528 if (LU->getValue()->getValueID() != RU->getValue()->getValueID())
529 return LU->getValue()->getValueID() < RU->getValue()->getValueID();
531 // Sort arguments by their position.
532 if (const Argument *LA = dyn_cast<Argument>(LU->getValue())) {
533 const Argument *RA = cast<Argument>(RU->getValue());
534 return LA->getArgNo() < RA->getArgNo();
537 // For instructions, compare their loop depth, and their opcode.
538 // This is pretty loose.
539 if (Instruction *LV = dyn_cast<Instruction>(LU->getValue())) {
540 Instruction *RV = cast<Instruction>(RU->getValue());
542 // Compare loop depths.
543 if (LI->getLoopDepth(LV->getParent()) !=
544 LI->getLoopDepth(RV->getParent()))
545 return LI->getLoopDepth(LV->getParent()) <
546 LI->getLoopDepth(RV->getParent());
549 if (LV->getOpcode() != RV->getOpcode())
550 return LV->getOpcode() < RV->getOpcode();
552 // Compare the number of operands.
553 if (LV->getNumOperands() != RV->getNumOperands())
554 return LV->getNumOperands() < RV->getNumOperands();
560 // Compare constant values.
561 if (const SCEVConstant *LC = dyn_cast<SCEVConstant>(LHS)) {
562 const SCEVConstant *RC = cast<SCEVConstant>(RHS);
563 if (LC->getValue()->getBitWidth() != RC->getValue()->getBitWidth())
564 return LC->getValue()->getBitWidth() < RC->getValue()->getBitWidth();
565 return LC->getValue()->getValue().ult(RC->getValue()->getValue());
568 // Compare addrec loop depths.
569 if (const SCEVAddRecExpr *LA = dyn_cast<SCEVAddRecExpr>(LHS)) {
570 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS);
571 if (LA->getLoop()->getLoopDepth() != RA->getLoop()->getLoopDepth())
572 return LA->getLoop()->getLoopDepth() < RA->getLoop()->getLoopDepth();
575 // Lexicographically compare n-ary expressions.
576 if (const SCEVNAryExpr *LC = dyn_cast<SCEVNAryExpr>(LHS)) {
577 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
578 for (unsigned i = 0, e = LC->getNumOperands(); i != e; ++i) {
579 if (i >= RC->getNumOperands())
581 if (operator()(LC->getOperand(i), RC->getOperand(i)))
583 if (operator()(RC->getOperand(i), LC->getOperand(i)))
586 return LC->getNumOperands() < RC->getNumOperands();
589 // Lexicographically compare udiv expressions.
590 if (const SCEVUDivExpr *LC = dyn_cast<SCEVUDivExpr>(LHS)) {
591 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
592 if (operator()(LC->getLHS(), RC->getLHS()))
594 if (operator()(RC->getLHS(), LC->getLHS()))
596 if (operator()(LC->getRHS(), RC->getRHS()))
598 if (operator()(RC->getRHS(), LC->getRHS()))
603 // Compare cast expressions by operand.
604 if (const SCEVCastExpr *LC = dyn_cast<SCEVCastExpr>(LHS)) {
605 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
606 return operator()(LC->getOperand(), RC->getOperand());
609 llvm_unreachable("Unknown SCEV kind!");
615 /// GroupByComplexity - Given a list of SCEV objects, order them by their
616 /// complexity, and group objects of the same complexity together by value.
617 /// When this routine is finished, we know that any duplicates in the vector are
618 /// consecutive and that complexity is monotonically increasing.
620 /// Note that we go take special precautions to ensure that we get deterministic
621 /// results from this routine. In other words, we don't want the results of
622 /// this to depend on where the addresses of various SCEV objects happened to
625 static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops,
627 if (Ops.size() < 2) return; // Noop
628 if (Ops.size() == 2) {
629 // This is the common case, which also happens to be trivially simple.
631 if (SCEVComplexityCompare(LI)(Ops[1], Ops[0]))
632 std::swap(Ops[0], Ops[1]);
636 // Do the rough sort by complexity.
637 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI));
639 // Now that we are sorted by complexity, group elements of the same
640 // complexity. Note that this is, at worst, N^2, but the vector is likely to
641 // be extremely short in practice. Note that we take this approach because we
642 // do not want to depend on the addresses of the objects we are grouping.
643 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
644 const SCEV *S = Ops[i];
645 unsigned Complexity = S->getSCEVType();
647 // If there are any objects of the same complexity and same value as this
649 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
650 if (Ops[j] == S) { // Found a duplicate.
651 // Move it to immediately after i'th element.
652 std::swap(Ops[i+1], Ops[j]);
653 ++i; // no need to rescan it.
654 if (i == e-2) return; // Done!
662 //===----------------------------------------------------------------------===//
663 // Simple SCEV method implementations
664 //===----------------------------------------------------------------------===//
666 /// BinomialCoefficient - Compute BC(It, K). The result has width W.
668 static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K,
670 const Type* ResultTy) {
671 // Handle the simplest case efficiently.
673 return SE.getTruncateOrZeroExtend(It, ResultTy);
675 // We are using the following formula for BC(It, K):
677 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
679 // Suppose, W is the bitwidth of the return value. We must be prepared for
680 // overflow. Hence, we must assure that the result of our computation is
681 // equal to the accurate one modulo 2^W. Unfortunately, division isn't
682 // safe in modular arithmetic.
684 // However, this code doesn't use exactly that formula; the formula it uses
685 // is something like the following, where T is the number of factors of 2 in
686 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
689 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
691 // This formula is trivially equivalent to the previous formula. However,
692 // this formula can be implemented much more efficiently. The trick is that
693 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
694 // arithmetic. To do exact division in modular arithmetic, all we have
695 // to do is multiply by the inverse. Therefore, this step can be done at
698 // The next issue is how to safely do the division by 2^T. The way this
699 // is done is by doing the multiplication step at a width of at least W + T
700 // bits. This way, the bottom W+T bits of the product are accurate. Then,
701 // when we perform the division by 2^T (which is equivalent to a right shift
702 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
703 // truncated out after the division by 2^T.
705 // In comparison to just directly using the first formula, this technique
706 // is much more efficient; using the first formula requires W * K bits,
707 // but this formula less than W + K bits. Also, the first formula requires
708 // a division step, whereas this formula only requires multiplies and shifts.
710 // It doesn't matter whether the subtraction step is done in the calculation
711 // width or the input iteration count's width; if the subtraction overflows,
712 // the result must be zero anyway. We prefer here to do it in the width of
713 // the induction variable because it helps a lot for certain cases; CodeGen
714 // isn't smart enough to ignore the overflow, which leads to much less
715 // efficient code if the width of the subtraction is wider than the native
718 // (It's possible to not widen at all by pulling out factors of 2 before
719 // the multiplication; for example, K=2 can be calculated as
720 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
721 // extra arithmetic, so it's not an obvious win, and it gets
722 // much more complicated for K > 3.)
724 // Protection from insane SCEVs; this bound is conservative,
725 // but it probably doesn't matter.
727 return SE.getCouldNotCompute();
729 unsigned W = SE.getTypeSizeInBits(ResultTy);
731 // Calculate K! / 2^T and T; we divide out the factors of two before
732 // multiplying for calculating K! / 2^T to avoid overflow.
733 // Other overflow doesn't matter because we only care about the bottom
734 // W bits of the result.
735 APInt OddFactorial(W, 1);
737 for (unsigned i = 3; i <= K; ++i) {
739 unsigned TwoFactors = Mult.countTrailingZeros();
741 Mult = Mult.lshr(TwoFactors);
742 OddFactorial *= Mult;
745 // We need at least W + T bits for the multiplication step
746 unsigned CalculationBits = W + T;
748 // Calculate 2^T, at width T+W.
749 APInt DivFactor = APInt(CalculationBits, 1).shl(T);
751 // Calculate the multiplicative inverse of K! / 2^T;
752 // this multiplication factor will perform the exact division by
754 APInt Mod = APInt::getSignedMinValue(W+1);
755 APInt MultiplyFactor = OddFactorial.zext(W+1);
756 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
757 MultiplyFactor = MultiplyFactor.trunc(W);
759 // Calculate the product, at width T+W
760 const IntegerType *CalculationTy = IntegerType::get(SE.getContext(),
762 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
763 for (unsigned i = 1; i != K; ++i) {
764 const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i));
765 Dividend = SE.getMulExpr(Dividend,
766 SE.getTruncateOrZeroExtend(S, CalculationTy));
770 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
772 // Truncate the result, and divide by K! / 2^T.
774 return SE.getMulExpr(SE.getConstant(MultiplyFactor),
775 SE.getTruncateOrZeroExtend(DivResult, ResultTy));
778 /// evaluateAtIteration - Return the value of this chain of recurrences at
779 /// the specified iteration number. We can evaluate this recurrence by
780 /// multiplying each element in the chain by the binomial coefficient
781 /// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
783 /// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
785 /// where BC(It, k) stands for binomial coefficient.
787 const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It,
788 ScalarEvolution &SE) const {
789 const SCEV *Result = getStart();
790 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
791 // The computation is correct in the face of overflow provided that the
792 // multiplication is performed _after_ the evaluation of the binomial
794 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType());
795 if (isa<SCEVCouldNotCompute>(Coeff))
798 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
803 //===----------------------------------------------------------------------===//
804 // SCEV Expression folder implementations
805 //===----------------------------------------------------------------------===//
807 const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op,
809 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
810 "This is not a truncating conversion!");
811 assert(isSCEVable(Ty) &&
812 "This is not a conversion to a SCEVable type!");
813 Ty = getEffectiveSCEVType(Ty);
816 ID.AddInteger(scTruncate);
820 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
822 // Fold if the operand is constant.
823 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
825 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(),
826 getEffectiveSCEVType(Ty))));
828 // trunc(trunc(x)) --> trunc(x)
829 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
830 return getTruncateExpr(ST->getOperand(), Ty);
832 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
833 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
834 return getTruncateOrSignExtend(SS->getOperand(), Ty);
836 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
837 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
838 return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
840 // If the input value is a chrec scev, truncate the chrec's operands.
841 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
842 SmallVector<const SCEV *, 4> Operands;
843 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
844 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty));
845 return getAddRecExpr(Operands, AddRec->getLoop());
848 // As a special case, fold trunc(undef) to undef. We don't want to
849 // know too much about SCEVUnknowns, but this special case is handy
851 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(Op))
852 if (isa<UndefValue>(U->getValue()))
853 return getSCEV(UndefValue::get(Ty));
855 // The cast wasn't folded; create an explicit cast node. We can reuse
856 // the existing insert position since if we get here, we won't have
857 // made any changes which would invalidate it.
858 SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator),
860 UniqueSCEVs.InsertNode(S, IP);
864 const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op,
866 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
867 "This is not an extending conversion!");
868 assert(isSCEVable(Ty) &&
869 "This is not a conversion to a SCEVable type!");
870 Ty = getEffectiveSCEVType(Ty);
872 // Fold if the operand is constant.
873 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
875 cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(),
876 getEffectiveSCEVType(Ty))));
878 // zext(zext(x)) --> zext(x)
879 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
880 return getZeroExtendExpr(SZ->getOperand(), Ty);
882 // Before doing any expensive analysis, check to see if we've already
883 // computed a SCEV for this Op and Ty.
885 ID.AddInteger(scZeroExtend);
889 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
891 // If the input value is a chrec scev, and we can prove that the value
892 // did not overflow the old, smaller, value, we can zero extend all of the
893 // operands (often constants). This allows analysis of something like
894 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
895 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
896 if (AR->isAffine()) {
897 const SCEV *Start = AR->getStart();
898 const SCEV *Step = AR->getStepRecurrence(*this);
899 unsigned BitWidth = getTypeSizeInBits(AR->getType());
900 const Loop *L = AR->getLoop();
902 // If we have special knowledge that this addrec won't overflow,
903 // we don't need to do any further analysis.
904 if (AR->hasNoUnsignedWrap())
905 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
906 getZeroExtendExpr(Step, Ty),
909 // Check whether the backedge-taken count is SCEVCouldNotCompute.
910 // Note that this serves two purposes: It filters out loops that are
911 // simply not analyzable, and it covers the case where this code is
912 // being called from within backedge-taken count analysis, such that
913 // attempting to ask for the backedge-taken count would likely result
914 // in infinite recursion. In the later case, the analysis code will
915 // cope with a conservative value, and it will take care to purge
916 // that value once it has finished.
917 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
918 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
919 // Manually compute the final value for AR, checking for
922 // Check whether the backedge-taken count can be losslessly casted to
923 // the addrec's type. The count is always unsigned.
924 const SCEV *CastedMaxBECount =
925 getTruncateOrZeroExtend(MaxBECount, Start->getType());
926 const SCEV *RecastedMaxBECount =
927 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
928 if (MaxBECount == RecastedMaxBECount) {
929 const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
930 // Check whether Start+Step*MaxBECount has no unsigned overflow.
931 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step);
932 const SCEV *Add = getAddExpr(Start, ZMul);
933 const SCEV *OperandExtendedAdd =
934 getAddExpr(getZeroExtendExpr(Start, WideTy),
935 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
936 getZeroExtendExpr(Step, WideTy)));
937 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd)
938 // Return the expression with the addrec on the outside.
939 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
940 getZeroExtendExpr(Step, Ty),
943 // Similar to above, only this time treat the step value as signed.
944 // This covers loops that count down.
945 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
946 Add = getAddExpr(Start, SMul);
948 getAddExpr(getZeroExtendExpr(Start, WideTy),
949 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
950 getSignExtendExpr(Step, WideTy)));
951 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd)
952 // Return the expression with the addrec on the outside.
953 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
954 getSignExtendExpr(Step, Ty),
958 // If the backedge is guarded by a comparison with the pre-inc value
959 // the addrec is safe. Also, if the entry is guarded by a comparison
960 // with the start value and the backedge is guarded by a comparison
961 // with the post-inc value, the addrec is safe.
962 if (isKnownPositive(Step)) {
963 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
964 getUnsignedRange(Step).getUnsignedMax());
965 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
966 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) &&
967 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT,
968 AR->getPostIncExpr(*this), N)))
969 // Return the expression with the addrec on the outside.
970 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
971 getZeroExtendExpr(Step, Ty),
973 } else if (isKnownNegative(Step)) {
974 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
975 getSignedRange(Step).getSignedMin());
976 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) ||
977 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) &&
978 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT,
979 AR->getPostIncExpr(*this), N)))
980 // Return the expression with the addrec on the outside.
981 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
982 getSignExtendExpr(Step, Ty),
988 // The cast wasn't folded; create an explicit cast node.
989 // Recompute the insert position, as it may have been invalidated.
990 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
991 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
993 UniqueSCEVs.InsertNode(S, IP);
997 const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op,
999 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1000 "This is not an extending conversion!");
1001 assert(isSCEVable(Ty) &&
1002 "This is not a conversion to a SCEVable type!");
1003 Ty = getEffectiveSCEVType(Ty);
1005 // Fold if the operand is constant.
1006 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1008 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(),
1009 getEffectiveSCEVType(Ty))));
1011 // sext(sext(x)) --> sext(x)
1012 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1013 return getSignExtendExpr(SS->getOperand(), Ty);
1015 // Before doing any expensive analysis, check to see if we've already
1016 // computed a SCEV for this Op and Ty.
1017 FoldingSetNodeID ID;
1018 ID.AddInteger(scSignExtend);
1022 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1024 // If the input value is a chrec scev, and we can prove that the value
1025 // did not overflow the old, smaller, value, we can sign extend all of the
1026 // operands (often constants). This allows analysis of something like
1027 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
1028 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1029 if (AR->isAffine()) {
1030 const SCEV *Start = AR->getStart();
1031 const SCEV *Step = AR->getStepRecurrence(*this);
1032 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1033 const Loop *L = AR->getLoop();
1035 // If we have special knowledge that this addrec won't overflow,
1036 // we don't need to do any further analysis.
1037 if (AR->hasNoSignedWrap())
1038 return getAddRecExpr(getSignExtendExpr(Start, Ty),
1039 getSignExtendExpr(Step, Ty),
1042 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1043 // Note that this serves two purposes: It filters out loops that are
1044 // simply not analyzable, and it covers the case where this code is
1045 // being called from within backedge-taken count analysis, such that
1046 // attempting to ask for the backedge-taken count would likely result
1047 // in infinite recursion. In the later case, the analysis code will
1048 // cope with a conservative value, and it will take care to purge
1049 // that value once it has finished.
1050 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1051 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1052 // Manually compute the final value for AR, checking for
1055 // Check whether the backedge-taken count can be losslessly casted to
1056 // the addrec's type. The count is always unsigned.
1057 const SCEV *CastedMaxBECount =
1058 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1059 const SCEV *RecastedMaxBECount =
1060 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1061 if (MaxBECount == RecastedMaxBECount) {
1062 const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1063 // Check whether Start+Step*MaxBECount has no signed overflow.
1064 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
1065 const SCEV *Add = getAddExpr(Start, SMul);
1066 const SCEV *OperandExtendedAdd =
1067 getAddExpr(getSignExtendExpr(Start, WideTy),
1068 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
1069 getSignExtendExpr(Step, WideTy)));
1070 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd)
1071 // Return the expression with the addrec on the outside.
1072 return getAddRecExpr(getSignExtendExpr(Start, Ty),
1073 getSignExtendExpr(Step, Ty),
1076 // Similar to above, only this time treat the step value as unsigned.
1077 // This covers loops that count up with an unsigned step.
1078 const SCEV *UMul = getMulExpr(CastedMaxBECount, Step);
1079 Add = getAddExpr(Start, UMul);
1080 OperandExtendedAdd =
1081 getAddExpr(getSignExtendExpr(Start, WideTy),
1082 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
1083 getZeroExtendExpr(Step, WideTy)));
1084 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd)
1085 // Return the expression with the addrec on the outside.
1086 return getAddRecExpr(getSignExtendExpr(Start, Ty),
1087 getZeroExtendExpr(Step, Ty),
1091 // If the backedge is guarded by a comparison with the pre-inc value
1092 // the addrec is safe. Also, if the entry is guarded by a comparison
1093 // with the start value and the backedge is guarded by a comparison
1094 // with the post-inc value, the addrec is safe.
1095 if (isKnownPositive(Step)) {
1096 const SCEV *N = getConstant(APInt::getSignedMinValue(BitWidth) -
1097 getSignedRange(Step).getSignedMax());
1098 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT, AR, N) ||
1099 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_SLT, Start, N) &&
1100 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT,
1101 AR->getPostIncExpr(*this), N)))
1102 // Return the expression with the addrec on the outside.
1103 return getAddRecExpr(getSignExtendExpr(Start, Ty),
1104 getSignExtendExpr(Step, Ty),
1106 } else if (isKnownNegative(Step)) {
1107 const SCEV *N = getConstant(APInt::getSignedMaxValue(BitWidth) -
1108 getSignedRange(Step).getSignedMin());
1109 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT, AR, N) ||
1110 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_SGT, Start, N) &&
1111 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT,
1112 AR->getPostIncExpr(*this), N)))
1113 // Return the expression with the addrec on the outside.
1114 return getAddRecExpr(getSignExtendExpr(Start, Ty),
1115 getSignExtendExpr(Step, Ty),
1121 // The cast wasn't folded; create an explicit cast node.
1122 // Recompute the insert position, as it may have been invalidated.
1123 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1124 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
1126 UniqueSCEVs.InsertNode(S, IP);
1130 /// getAnyExtendExpr - Return a SCEV for the given operand extended with
1131 /// unspecified bits out to the given type.
1133 const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
1135 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1136 "This is not an extending conversion!");
1137 assert(isSCEVable(Ty) &&
1138 "This is not a conversion to a SCEVable type!");
1139 Ty = getEffectiveSCEVType(Ty);
1141 // Sign-extend negative constants.
1142 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1143 if (SC->getValue()->getValue().isNegative())
1144 return getSignExtendExpr(Op, Ty);
1146 // Peel off a truncate cast.
1147 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
1148 const SCEV *NewOp = T->getOperand();
1149 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
1150 return getAnyExtendExpr(NewOp, Ty);
1151 return getTruncateOrNoop(NewOp, Ty);
1154 // Next try a zext cast. If the cast is folded, use it.
1155 const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
1156 if (!isa<SCEVZeroExtendExpr>(ZExt))
1159 // Next try a sext cast. If the cast is folded, use it.
1160 const SCEV *SExt = getSignExtendExpr(Op, Ty);
1161 if (!isa<SCEVSignExtendExpr>(SExt))
1164 // Force the cast to be folded into the operands of an addrec.
1165 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
1166 SmallVector<const SCEV *, 4> Ops;
1167 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
1169 Ops.push_back(getAnyExtendExpr(*I, Ty));
1170 return getAddRecExpr(Ops, AR->getLoop());
1173 // As a special case, fold anyext(undef) to undef. We don't want to
1174 // know too much about SCEVUnknowns, but this special case is handy
1176 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(Op))
1177 if (isa<UndefValue>(U->getValue()))
1178 return getSCEV(UndefValue::get(Ty));
1180 // If the expression is obviously signed, use the sext cast value.
1181 if (isa<SCEVSMaxExpr>(Op))
1184 // Absent any other information, use the zext cast value.
1188 /// CollectAddOperandsWithScales - Process the given Ops list, which is
1189 /// a list of operands to be added under the given scale, update the given
1190 /// map. This is a helper function for getAddRecExpr. As an example of
1191 /// what it does, given a sequence of operands that would form an add
1192 /// expression like this:
1194 /// m + n + 13 + (A * (o + p + (B * q + m + 29))) + r + (-1 * r)
1196 /// where A and B are constants, update the map with these values:
1198 /// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
1200 /// and add 13 + A*B*29 to AccumulatedConstant.
1201 /// This will allow getAddRecExpr to produce this:
1203 /// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
1205 /// This form often exposes folding opportunities that are hidden in
1206 /// the original operand list.
1208 /// Return true iff it appears that any interesting folding opportunities
1209 /// may be exposed. This helps getAddRecExpr short-circuit extra work in
1210 /// the common case where no interesting opportunities are present, and
1211 /// is also used as a check to avoid infinite recursion.
1214 CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
1215 SmallVector<const SCEV *, 8> &NewOps,
1216 APInt &AccumulatedConstant,
1217 const SCEV *const *Ops, size_t NumOperands,
1219 ScalarEvolution &SE) {
1220 bool Interesting = false;
1222 // Iterate over the add operands. They are sorted, with constants first.
1224 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1226 // Pull a buried constant out to the outside.
1227 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
1229 AccumulatedConstant += Scale * C->getValue()->getValue();
1232 // Next comes everything else. We're especially interested in multiplies
1233 // here, but they're in the middle, so just visit the rest with one loop.
1234 for (; i != NumOperands; ++i) {
1235 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
1236 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
1238 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue();
1239 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
1240 // A multiplication of a constant with another add; recurse.
1241 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1));
1243 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1244 Add->op_begin(), Add->getNumOperands(),
1247 // A multiplication of a constant with some other value. Update
1249 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
1250 const SCEV *Key = SE.getMulExpr(MulOps);
1251 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1252 M.insert(std::make_pair(Key, NewScale));
1254 NewOps.push_back(Pair.first->first);
1256 Pair.first->second += NewScale;
1257 // The map already had an entry for this value, which may indicate
1258 // a folding opportunity.
1263 // An ordinary operand. Update the map.
1264 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1265 M.insert(std::make_pair(Ops[i], Scale));
1267 NewOps.push_back(Pair.first->first);
1269 Pair.first->second += Scale;
1270 // The map already had an entry for this value, which may indicate
1271 // a folding opportunity.
1281 struct APIntCompare {
1282 bool operator()(const APInt &LHS, const APInt &RHS) const {
1283 return LHS.ult(RHS);
1288 /// getAddExpr - Get a canonical add expression, or something simpler if
1290 const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
1291 bool HasNUW, bool HasNSW) {
1292 assert(!Ops.empty() && "Cannot get empty add!");
1293 if (Ops.size() == 1) return Ops[0];
1295 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
1296 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1297 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
1298 "SCEVAddExpr operand types don't match!");
1301 // If HasNSW is true and all the operands are non-negative, infer HasNUW.
1302 if (!HasNUW && HasNSW) {
1304 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1305 if (!isKnownNonNegative(Ops[i])) {
1309 if (All) HasNUW = true;
1312 // Sort by complexity, this groups all similar expression types together.
1313 GroupByComplexity(Ops, LI);
1315 // If there are any constants, fold them together.
1317 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1319 assert(Idx < Ops.size());
1320 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1321 // We found two constants, fold them together!
1322 Ops[0] = getConstant(LHSC->getValue()->getValue() +
1323 RHSC->getValue()->getValue());
1324 if (Ops.size() == 2) return Ops[0];
1325 Ops.erase(Ops.begin()+1); // Erase the folded element
1326 LHSC = cast<SCEVConstant>(Ops[0]);
1329 // If we are left with a constant zero being added, strip it off.
1330 if (LHSC->getValue()->isZero()) {
1331 Ops.erase(Ops.begin());
1335 if (Ops.size() == 1) return Ops[0];
1338 // Okay, check to see if the same value occurs in the operand list twice. If
1339 // so, merge them together into an multiply expression. Since we sorted the
1340 // list, these values are required to be adjacent.
1341 const Type *Ty = Ops[0]->getType();
1342 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
1343 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
1344 // Found a match, merge the two values into a multiply, and add any
1345 // remaining values to the result.
1346 const SCEV *Two = getConstant(Ty, 2);
1347 const SCEV *Mul = getMulExpr(Ops[i], Two);
1348 if (Ops.size() == 2)
1350 Ops.erase(Ops.begin()+i, Ops.begin()+i+2);
1352 return getAddExpr(Ops, HasNUW, HasNSW);
1355 // Check for truncates. If all the operands are truncated from the same
1356 // type, see if factoring out the truncate would permit the result to be
1357 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
1358 // if the contents of the resulting outer trunc fold to something simple.
1359 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
1360 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
1361 const Type *DstType = Trunc->getType();
1362 const Type *SrcType = Trunc->getOperand()->getType();
1363 SmallVector<const SCEV *, 8> LargeOps;
1365 // Check all the operands to see if they can be represented in the
1366 // source type of the truncate.
1367 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1368 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
1369 if (T->getOperand()->getType() != SrcType) {
1373 LargeOps.push_back(T->getOperand());
1374 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1375 LargeOps.push_back(getAnyExtendExpr(C, SrcType));
1376 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
1377 SmallVector<const SCEV *, 8> LargeMulOps;
1378 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
1379 if (const SCEVTruncateExpr *T =
1380 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
1381 if (T->getOperand()->getType() != SrcType) {
1385 LargeMulOps.push_back(T->getOperand());
1386 } else if (const SCEVConstant *C =
1387 dyn_cast<SCEVConstant>(M->getOperand(j))) {
1388 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType));
1395 LargeOps.push_back(getMulExpr(LargeMulOps));
1402 // Evaluate the expression in the larger type.
1403 const SCEV *Fold = getAddExpr(LargeOps, HasNUW, HasNSW);
1404 // If it folds to something simple, use it. Otherwise, don't.
1405 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
1406 return getTruncateExpr(Fold, DstType);
1410 // Skip past any other cast SCEVs.
1411 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
1414 // If there are add operands they would be next.
1415 if (Idx < Ops.size()) {
1416 bool DeletedAdd = false;
1417 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
1418 // If we have an add, expand the add operands onto the end of the operands
1420 Ops.erase(Ops.begin()+Idx);
1421 Ops.append(Add->op_begin(), Add->op_end());
1425 // If we deleted at least one add, we added operands to the end of the list,
1426 // and they are not necessarily sorted. Recurse to resort and resimplify
1427 // any operands we just acquired.
1429 return getAddExpr(Ops);
1432 // Skip over the add expression until we get to a multiply.
1433 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1436 // Check to see if there are any folding opportunities present with
1437 // operands multiplied by constant values.
1438 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
1439 uint64_t BitWidth = getTypeSizeInBits(Ty);
1440 DenseMap<const SCEV *, APInt> M;
1441 SmallVector<const SCEV *, 8> NewOps;
1442 APInt AccumulatedConstant(BitWidth, 0);
1443 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1444 Ops.data(), Ops.size(),
1445 APInt(BitWidth, 1), *this)) {
1446 // Some interesting folding opportunity is present, so its worthwhile to
1447 // re-generate the operands list. Group the operands by constant scale,
1448 // to avoid multiplying by the same constant scale multiple times.
1449 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
1450 for (SmallVector<const SCEV *, 8>::iterator I = NewOps.begin(),
1451 E = NewOps.end(); I != E; ++I)
1452 MulOpLists[M.find(*I)->second].push_back(*I);
1453 // Re-generate the operands list.
1455 if (AccumulatedConstant != 0)
1456 Ops.push_back(getConstant(AccumulatedConstant));
1457 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator
1458 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I)
1460 Ops.push_back(getMulExpr(getConstant(I->first),
1461 getAddExpr(I->second)));
1463 return getConstant(Ty, 0);
1464 if (Ops.size() == 1)
1466 return getAddExpr(Ops);
1470 // If we are adding something to a multiply expression, make sure the
1471 // something is not already an operand of the multiply. If so, merge it into
1473 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
1474 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
1475 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
1476 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
1477 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
1478 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(Ops[AddOp])) {
1479 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
1480 const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
1481 if (Mul->getNumOperands() != 2) {
1482 // If the multiply has more than two operands, we must get the
1484 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), Mul->op_end());
1485 MulOps.erase(MulOps.begin()+MulOp);
1486 InnerMul = getMulExpr(MulOps);
1488 const SCEV *One = getConstant(Ty, 1);
1489 const SCEV *AddOne = getAddExpr(InnerMul, One);
1490 const SCEV *OuterMul = getMulExpr(AddOne, Ops[AddOp]);
1491 if (Ops.size() == 2) return OuterMul;
1493 Ops.erase(Ops.begin()+AddOp);
1494 Ops.erase(Ops.begin()+Idx-1);
1496 Ops.erase(Ops.begin()+Idx);
1497 Ops.erase(Ops.begin()+AddOp-1);
1499 Ops.push_back(OuterMul);
1500 return getAddExpr(Ops);
1503 // Check this multiply against other multiplies being added together.
1504 for (unsigned OtherMulIdx = Idx+1;
1505 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
1507 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
1508 // If MulOp occurs in OtherMul, we can fold the two multiplies
1510 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
1511 OMulOp != e; ++OMulOp)
1512 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
1513 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
1514 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
1515 if (Mul->getNumOperands() != 2) {
1516 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
1518 MulOps.erase(MulOps.begin()+MulOp);
1519 InnerMul1 = getMulExpr(MulOps);
1521 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
1522 if (OtherMul->getNumOperands() != 2) {
1523 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
1524 OtherMul->op_end());
1525 MulOps.erase(MulOps.begin()+OMulOp);
1526 InnerMul2 = getMulExpr(MulOps);
1528 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
1529 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
1530 if (Ops.size() == 2) return OuterMul;
1531 Ops.erase(Ops.begin()+Idx);
1532 Ops.erase(Ops.begin()+OtherMulIdx-1);
1533 Ops.push_back(OuterMul);
1534 return getAddExpr(Ops);
1540 // If there are any add recurrences in the operands list, see if any other
1541 // added values are loop invariant. If so, we can fold them into the
1543 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1546 // Scan over all recurrences, trying to fold loop invariants into them.
1547 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1548 // Scan all of the other operands to this add and add them to the vector if
1549 // they are loop invariant w.r.t. the recurrence.
1550 SmallVector<const SCEV *, 8> LIOps;
1551 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1552 const Loop *AddRecLoop = AddRec->getLoop();
1553 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1554 if (Ops[i]->isLoopInvariant(AddRecLoop)) {
1555 LIOps.push_back(Ops[i]);
1556 Ops.erase(Ops.begin()+i);
1560 // If we found some loop invariants, fold them into the recurrence.
1561 if (!LIOps.empty()) {
1562 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
1563 LIOps.push_back(AddRec->getStart());
1565 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
1567 AddRecOps[0] = getAddExpr(LIOps);
1569 // Build the new addrec. Propagate the NUW and NSW flags if both the
1570 // outer add and the inner addrec are guaranteed to have no overflow.
1571 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop,
1572 HasNUW && AddRec->hasNoUnsignedWrap(),
1573 HasNSW && AddRec->hasNoSignedWrap());
1575 // If all of the other operands were loop invariant, we are done.
1576 if (Ops.size() == 1) return NewRec;
1578 // Otherwise, add the folded AddRec by the non-liv parts.
1579 for (unsigned i = 0;; ++i)
1580 if (Ops[i] == AddRec) {
1584 return getAddExpr(Ops);
1587 // Okay, if there weren't any loop invariants to be folded, check to see if
1588 // there are multiple AddRec's with the same loop induction variable being
1589 // added together. If so, we can fold them.
1590 for (unsigned OtherIdx = Idx+1;
1591 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
1592 if (OtherIdx != Idx) {
1593 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
1594 if (AddRecLoop == OtherAddRec->getLoop()) {
1595 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D}
1596 SmallVector<const SCEV *, 4> NewOps(AddRec->op_begin(),
1598 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) {
1599 if (i >= NewOps.size()) {
1600 NewOps.append(OtherAddRec->op_begin()+i,
1601 OtherAddRec->op_end());
1604 NewOps[i] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i));
1606 const SCEV *NewAddRec = getAddRecExpr(NewOps, AddRecLoop);
1608 if (Ops.size() == 2) return NewAddRec;
1610 Ops.erase(Ops.begin()+Idx);
1611 Ops.erase(Ops.begin()+OtherIdx-1);
1612 Ops.push_back(NewAddRec);
1613 return getAddExpr(Ops);
1617 // Otherwise couldn't fold anything into this recurrence. Move onto the
1621 // Okay, it looks like we really DO need an add expr. Check to see if we
1622 // already have one, otherwise create a new one.
1623 FoldingSetNodeID ID;
1624 ID.AddInteger(scAddExpr);
1625 ID.AddInteger(Ops.size());
1626 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1627 ID.AddPointer(Ops[i]);
1630 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1632 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
1633 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
1634 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator),
1636 UniqueSCEVs.InsertNode(S, IP);
1638 if (HasNUW) S->setHasNoUnsignedWrap(true);
1639 if (HasNSW) S->setHasNoSignedWrap(true);
1643 /// getMulExpr - Get a canonical multiply expression, or something simpler if
1645 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
1646 bool HasNUW, bool HasNSW) {
1647 assert(!Ops.empty() && "Cannot get empty mul!");
1648 if (Ops.size() == 1) return Ops[0];
1650 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1651 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
1652 getEffectiveSCEVType(Ops[0]->getType()) &&
1653 "SCEVMulExpr operand types don't match!");
1656 // If HasNSW is true and all the operands are non-negative, infer HasNUW.
1657 if (!HasNUW && HasNSW) {
1659 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1660 if (!isKnownNonNegative(Ops[i])) {
1664 if (All) HasNUW = true;
1667 // Sort by complexity, this groups all similar expression types together.
1668 GroupByComplexity(Ops, LI);
1670 // If there are any constants, fold them together.
1672 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1674 // C1*(C2+V) -> C1*C2 + C1*V
1675 if (Ops.size() == 2)
1676 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
1677 if (Add->getNumOperands() == 2 &&
1678 isa<SCEVConstant>(Add->getOperand(0)))
1679 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
1680 getMulExpr(LHSC, Add->getOperand(1)));
1683 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1684 // We found two constants, fold them together!
1685 ConstantInt *Fold = ConstantInt::get(getContext(),
1686 LHSC->getValue()->getValue() *
1687 RHSC->getValue()->getValue());
1688 Ops[0] = getConstant(Fold);
1689 Ops.erase(Ops.begin()+1); // Erase the folded element
1690 if (Ops.size() == 1) return Ops[0];
1691 LHSC = cast<SCEVConstant>(Ops[0]);
1694 // If we are left with a constant one being multiplied, strip it off.
1695 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
1696 Ops.erase(Ops.begin());
1698 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
1699 // If we have a multiply of zero, it will always be zero.
1701 } else if (Ops[0]->isAllOnesValue()) {
1702 // If we have a mul by -1 of an add, try distributing the -1 among the
1704 if (Ops.size() == 2)
1705 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
1706 SmallVector<const SCEV *, 4> NewOps;
1707 bool AnyFolded = false;
1708 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(), E = Add->op_end();
1710 const SCEV *Mul = getMulExpr(Ops[0], *I);
1711 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
1712 NewOps.push_back(Mul);
1715 return getAddExpr(NewOps);
1719 if (Ops.size() == 1)
1723 // Skip over the add expression until we get to a multiply.
1724 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1727 // If there are mul operands inline them all into this expression.
1728 if (Idx < Ops.size()) {
1729 bool DeletedMul = false;
1730 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
1731 // If we have an mul, expand the mul operands onto the end of the operands
1733 Ops.erase(Ops.begin()+Idx);
1734 Ops.append(Mul->op_begin(), Mul->op_end());
1738 // If we deleted at least one mul, we added operands to the end of the list,
1739 // and they are not necessarily sorted. Recurse to resort and resimplify
1740 // any operands we just acquired.
1742 return getMulExpr(Ops);
1745 // If there are any add recurrences in the operands list, see if any other
1746 // added values are loop invariant. If so, we can fold them into the
1748 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1751 // Scan over all recurrences, trying to fold loop invariants into them.
1752 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1753 // Scan all of the other operands to this mul and add them to the vector if
1754 // they are loop invariant w.r.t. the recurrence.
1755 SmallVector<const SCEV *, 8> LIOps;
1756 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1757 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1758 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
1759 LIOps.push_back(Ops[i]);
1760 Ops.erase(Ops.begin()+i);
1764 // If we found some loop invariants, fold them into the recurrence.
1765 if (!LIOps.empty()) {
1766 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
1767 SmallVector<const SCEV *, 4> NewOps;
1768 NewOps.reserve(AddRec->getNumOperands());
1769 const SCEV *Scale = getMulExpr(LIOps);
1770 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
1771 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
1773 // Build the new addrec. Propagate the NUW and NSW flags if both the
1774 // outer mul and the inner addrec are guaranteed to have no overflow.
1775 const SCEV *NewRec = getAddRecExpr(NewOps, AddRec->getLoop(),
1776 HasNUW && AddRec->hasNoUnsignedWrap(),
1777 HasNSW && AddRec->hasNoSignedWrap());
1779 // If all of the other operands were loop invariant, we are done.
1780 if (Ops.size() == 1) return NewRec;
1782 // Otherwise, multiply the folded AddRec by the non-liv parts.
1783 for (unsigned i = 0;; ++i)
1784 if (Ops[i] == AddRec) {
1788 return getMulExpr(Ops);
1791 // Okay, if there weren't any loop invariants to be folded, check to see if
1792 // there are multiple AddRec's with the same loop induction variable being
1793 // multiplied together. If so, we can fold them.
1794 for (unsigned OtherIdx = Idx+1;
1795 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
1796 if (OtherIdx != Idx) {
1797 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
1798 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
1799 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D}
1800 const SCEVAddRecExpr *F = AddRec, *G = OtherAddRec;
1801 const SCEV *NewStart = getMulExpr(F->getStart(),
1803 const SCEV *B = F->getStepRecurrence(*this);
1804 const SCEV *D = G->getStepRecurrence(*this);
1805 const SCEV *NewStep = getAddExpr(getMulExpr(F, D),
1808 const SCEV *NewAddRec = getAddRecExpr(NewStart, NewStep,
1810 if (Ops.size() == 2) return NewAddRec;
1812 Ops.erase(Ops.begin()+Idx);
1813 Ops.erase(Ops.begin()+OtherIdx-1);
1814 Ops.push_back(NewAddRec);
1815 return getMulExpr(Ops);
1819 // Otherwise couldn't fold anything into this recurrence. Move onto the
1823 // Okay, it looks like we really DO need an mul expr. Check to see if we
1824 // already have one, otherwise create a new one.
1825 FoldingSetNodeID ID;
1826 ID.AddInteger(scMulExpr);
1827 ID.AddInteger(Ops.size());
1828 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1829 ID.AddPointer(Ops[i]);
1832 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1834 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
1835 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
1836 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
1838 UniqueSCEVs.InsertNode(S, IP);
1840 if (HasNUW) S->setHasNoUnsignedWrap(true);
1841 if (HasNSW) S->setHasNoSignedWrap(true);
1845 /// getUDivExpr - Get a canonical unsigned division expression, or something
1846 /// simpler if possible.
1847 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
1849 assert(getEffectiveSCEVType(LHS->getType()) ==
1850 getEffectiveSCEVType(RHS->getType()) &&
1851 "SCEVUDivExpr operand types don't match!");
1853 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
1854 if (RHSC->getValue()->equalsInt(1))
1855 return LHS; // X udiv 1 --> x
1856 // If the denominator is zero, the result of the udiv is undefined. Don't
1857 // try to analyze it, because the resolution chosen here may differ from
1858 // the resolution chosen in other parts of the compiler.
1859 if (!RHSC->getValue()->isZero()) {
1860 // Determine if the division can be folded into the operands of
1862 // TODO: Generalize this to non-constants by using known-bits information.
1863 const Type *Ty = LHS->getType();
1864 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
1865 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ;
1866 // For non-power-of-two values, effectively round the value up to the
1867 // nearest power of two.
1868 if (!RHSC->getValue()->getValue().isPowerOf2())
1870 const IntegerType *ExtTy =
1871 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
1872 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
1873 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
1874 if (const SCEVConstant *Step =
1875 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this)))
1876 if (!Step->getValue()->getValue()
1877 .urem(RHSC->getValue()->getValue()) &&
1878 getZeroExtendExpr(AR, ExtTy) ==
1879 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
1880 getZeroExtendExpr(Step, ExtTy),
1882 SmallVector<const SCEV *, 4> Operands;
1883 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i)
1884 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS));
1885 return getAddRecExpr(Operands, AR->getLoop());
1887 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
1888 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
1889 SmallVector<const SCEV *, 4> Operands;
1890 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i)
1891 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy));
1892 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
1893 // Find an operand that's safely divisible.
1894 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
1895 const SCEV *Op = M->getOperand(i);
1896 const SCEV *Div = getUDivExpr(Op, RHSC);
1897 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
1898 Operands = SmallVector<const SCEV *, 4>(M->op_begin(),
1901 return getMulExpr(Operands);
1905 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
1906 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(LHS)) {
1907 SmallVector<const SCEV *, 4> Operands;
1908 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i)
1909 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy));
1910 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
1912 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
1913 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
1914 if (isa<SCEVUDivExpr>(Op) ||
1915 getMulExpr(Op, RHS) != A->getOperand(i))
1917 Operands.push_back(Op);
1919 if (Operands.size() == A->getNumOperands())
1920 return getAddExpr(Operands);
1924 // Fold if both operands are constant.
1925 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
1926 Constant *LHSCV = LHSC->getValue();
1927 Constant *RHSCV = RHSC->getValue();
1928 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
1934 FoldingSetNodeID ID;
1935 ID.AddInteger(scUDivExpr);
1939 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1940 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
1942 UniqueSCEVs.InsertNode(S, IP);
1947 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
1948 /// Simplify the expression as much as possible.
1949 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start,
1950 const SCEV *Step, const Loop *L,
1951 bool HasNUW, bool HasNSW) {
1952 SmallVector<const SCEV *, 4> Operands;
1953 Operands.push_back(Start);
1954 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
1955 if (StepChrec->getLoop() == L) {
1956 Operands.append(StepChrec->op_begin(), StepChrec->op_end());
1957 return getAddRecExpr(Operands, L);
1960 Operands.push_back(Step);
1961 return getAddRecExpr(Operands, L, HasNUW, HasNSW);
1964 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
1965 /// Simplify the expression as much as possible.
1967 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
1969 bool HasNUW, bool HasNSW) {
1970 if (Operands.size() == 1) return Operands[0];
1972 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
1973 assert(getEffectiveSCEVType(Operands[i]->getType()) ==
1974 getEffectiveSCEVType(Operands[0]->getType()) &&
1975 "SCEVAddRecExpr operand types don't match!");
1978 if (Operands.back()->isZero()) {
1979 Operands.pop_back();
1980 return getAddRecExpr(Operands, L, HasNUW, HasNSW); // {X,+,0} --> X
1983 // It's tempting to want to call getMaxBackedgeTakenCount count here and
1984 // use that information to infer NUW and NSW flags. However, computing a
1985 // BE count requires calling getAddRecExpr, so we may not yet have a
1986 // meaningful BE count at this point (and if we don't, we'd be stuck
1987 // with a SCEVCouldNotCompute as the cached BE count).
1989 // If HasNSW is true and all the operands are non-negative, infer HasNUW.
1990 if (!HasNUW && HasNSW) {
1992 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
1993 if (!isKnownNonNegative(Operands[i])) {
1997 if (All) HasNUW = true;
2000 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
2001 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
2002 const Loop *NestedLoop = NestedAR->getLoop();
2003 if (L->contains(NestedLoop->getHeader()) ?
2004 (L->getLoopDepth() < NestedLoop->getLoopDepth()) :
2005 (!NestedLoop->contains(L->getHeader()) &&
2006 DT->dominates(L->getHeader(), NestedLoop->getHeader()))) {
2007 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
2008 NestedAR->op_end());
2009 Operands[0] = NestedAR->getStart();
2010 // AddRecs require their operands be loop-invariant with respect to their
2011 // loops. Don't perform this transformation if it would break this
2013 bool AllInvariant = true;
2014 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2015 if (!Operands[i]->isLoopInvariant(L)) {
2016 AllInvariant = false;
2020 NestedOperands[0] = getAddRecExpr(Operands, L);
2021 AllInvariant = true;
2022 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i)
2023 if (!NestedOperands[i]->isLoopInvariant(NestedLoop)) {
2024 AllInvariant = false;
2028 // Ok, both add recurrences are valid after the transformation.
2029 return getAddRecExpr(NestedOperands, NestedLoop, HasNUW, HasNSW);
2031 // Reset Operands to its original state.
2032 Operands[0] = NestedAR;
2036 // Okay, it looks like we really DO need an addrec expr. Check to see if we
2037 // already have one, otherwise create a new one.
2038 FoldingSetNodeID ID;
2039 ID.AddInteger(scAddRecExpr);
2040 ID.AddInteger(Operands.size());
2041 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2042 ID.AddPointer(Operands[i]);
2046 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2048 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size());
2049 std::uninitialized_copy(Operands.begin(), Operands.end(), O);
2050 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator),
2051 O, Operands.size(), L);
2052 UniqueSCEVs.InsertNode(S, IP);
2054 if (HasNUW) S->setHasNoUnsignedWrap(true);
2055 if (HasNSW) S->setHasNoSignedWrap(true);
2059 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
2061 SmallVector<const SCEV *, 2> Ops;
2064 return getSMaxExpr(Ops);
2068 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2069 assert(!Ops.empty() && "Cannot get empty smax!");
2070 if (Ops.size() == 1) return Ops[0];
2072 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2073 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
2074 getEffectiveSCEVType(Ops[0]->getType()) &&
2075 "SCEVSMaxExpr operand types don't match!");
2078 // Sort by complexity, this groups all similar expression types together.
2079 GroupByComplexity(Ops, LI);
2081 // If there are any constants, fold them together.
2083 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2085 assert(Idx < Ops.size());
2086 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2087 // We found two constants, fold them together!
2088 ConstantInt *Fold = ConstantInt::get(getContext(),
2089 APIntOps::smax(LHSC->getValue()->getValue(),
2090 RHSC->getValue()->getValue()));
2091 Ops[0] = getConstant(Fold);
2092 Ops.erase(Ops.begin()+1); // Erase the folded element
2093 if (Ops.size() == 1) return Ops[0];
2094 LHSC = cast<SCEVConstant>(Ops[0]);
2097 // If we are left with a constant minimum-int, strip it off.
2098 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
2099 Ops.erase(Ops.begin());
2101 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
2102 // If we have an smax with a constant maximum-int, it will always be
2107 if (Ops.size() == 1) return Ops[0];
2110 // Find the first SMax
2111 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
2114 // Check to see if one of the operands is an SMax. If so, expand its operands
2115 // onto our operand list, and recurse to simplify.
2116 if (Idx < Ops.size()) {
2117 bool DeletedSMax = false;
2118 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
2119 Ops.erase(Ops.begin()+Idx);
2120 Ops.append(SMax->op_begin(), SMax->op_end());
2125 return getSMaxExpr(Ops);
2128 // Okay, check to see if the same value occurs in the operand list twice. If
2129 // so, delete one. Since we sorted the list, these values are required to
2131 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2132 // X smax Y smax Y --> X smax Y
2133 // X smax Y --> X, if X is always greater than Y
2134 if (Ops[i] == Ops[i+1] ||
2135 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) {
2136 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2138 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) {
2139 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2143 if (Ops.size() == 1) return Ops[0];
2145 assert(!Ops.empty() && "Reduced smax down to nothing!");
2147 // Okay, it looks like we really DO need an smax expr. Check to see if we
2148 // already have one, otherwise create a new one.
2149 FoldingSetNodeID ID;
2150 ID.AddInteger(scSMaxExpr);
2151 ID.AddInteger(Ops.size());
2152 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2153 ID.AddPointer(Ops[i]);
2155 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2156 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2157 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2158 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator),
2160 UniqueSCEVs.InsertNode(S, IP);
2164 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
2166 SmallVector<const SCEV *, 2> Ops;
2169 return getUMaxExpr(Ops);
2173 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2174 assert(!Ops.empty() && "Cannot get empty umax!");
2175 if (Ops.size() == 1) return Ops[0];
2177 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2178 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
2179 getEffectiveSCEVType(Ops[0]->getType()) &&
2180 "SCEVUMaxExpr operand types don't match!");
2183 // Sort by complexity, this groups all similar expression types together.
2184 GroupByComplexity(Ops, LI);
2186 // If there are any constants, fold them together.
2188 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2190 assert(Idx < Ops.size());
2191 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2192 // We found two constants, fold them together!
2193 ConstantInt *Fold = ConstantInt::get(getContext(),
2194 APIntOps::umax(LHSC->getValue()->getValue(),
2195 RHSC->getValue()->getValue()));
2196 Ops[0] = getConstant(Fold);
2197 Ops.erase(Ops.begin()+1); // Erase the folded element
2198 if (Ops.size() == 1) return Ops[0];
2199 LHSC = cast<SCEVConstant>(Ops[0]);
2202 // If we are left with a constant minimum-int, strip it off.
2203 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
2204 Ops.erase(Ops.begin());
2206 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
2207 // If we have an umax with a constant maximum-int, it will always be
2212 if (Ops.size() == 1) return Ops[0];
2215 // Find the first UMax
2216 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
2219 // Check to see if one of the operands is a UMax. If so, expand its operands
2220 // onto our operand list, and recurse to simplify.
2221 if (Idx < Ops.size()) {
2222 bool DeletedUMax = false;
2223 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
2224 Ops.erase(Ops.begin()+Idx);
2225 Ops.append(UMax->op_begin(), UMax->op_end());
2230 return getUMaxExpr(Ops);
2233 // Okay, check to see if the same value occurs in the operand list twice. If
2234 // so, delete one. Since we sorted the list, these values are required to
2236 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2237 // X umax Y umax Y --> X umax Y
2238 // X umax Y --> X, if X is always greater than Y
2239 if (Ops[i] == Ops[i+1] ||
2240 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) {
2241 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2243 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) {
2244 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2248 if (Ops.size() == 1) return Ops[0];
2250 assert(!Ops.empty() && "Reduced umax down to nothing!");
2252 // Okay, it looks like we really DO need a umax expr. Check to see if we
2253 // already have one, otherwise create a new one.
2254 FoldingSetNodeID ID;
2255 ID.AddInteger(scUMaxExpr);
2256 ID.AddInteger(Ops.size());
2257 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2258 ID.AddPointer(Ops[i]);
2260 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2261 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2262 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2263 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator),
2265 UniqueSCEVs.InsertNode(S, IP);
2269 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
2271 // ~smax(~x, ~y) == smin(x, y).
2272 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2275 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
2277 // ~umax(~x, ~y) == umin(x, y)
2278 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2281 const SCEV *ScalarEvolution::getSizeOfExpr(const Type *AllocTy) {
2282 // If we have TargetData, we can bypass creating a target-independent
2283 // constant expression and then folding it back into a ConstantInt.
2284 // This is just a compile-time optimization.
2286 return getConstant(TD->getIntPtrType(getContext()),
2287 TD->getTypeAllocSize(AllocTy));
2289 Constant *C = ConstantExpr::getSizeOf(AllocTy);
2290 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2291 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD))
2293 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2294 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2297 const SCEV *ScalarEvolution::getAlignOfExpr(const Type *AllocTy) {
2298 Constant *C = ConstantExpr::getAlignOf(AllocTy);
2299 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2300 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD))
2302 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2303 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2306 const SCEV *ScalarEvolution::getOffsetOfExpr(const StructType *STy,
2308 // If we have TargetData, we can bypass creating a target-independent
2309 // constant expression and then folding it back into a ConstantInt.
2310 // This is just a compile-time optimization.
2312 return getConstant(TD->getIntPtrType(getContext()),
2313 TD->getStructLayout(STy)->getElementOffset(FieldNo));
2315 Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo);
2316 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2317 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD))
2319 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy));
2320 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2323 const SCEV *ScalarEvolution::getOffsetOfExpr(const Type *CTy,
2324 Constant *FieldNo) {
2325 Constant *C = ConstantExpr::getOffsetOf(CTy, FieldNo);
2326 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2327 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD))
2329 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(CTy));
2330 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2333 const SCEV *ScalarEvolution::getUnknown(Value *V) {
2334 // Don't attempt to do anything other than create a SCEVUnknown object
2335 // here. createSCEV only calls getUnknown after checking for all other
2336 // interesting possibilities, and any other code that calls getUnknown
2337 // is doing so in order to hide a value from SCEV canonicalization.
2339 FoldingSetNodeID ID;
2340 ID.AddInteger(scUnknown);
2343 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2344 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V);
2345 UniqueSCEVs.InsertNode(S, IP);
2349 //===----------------------------------------------------------------------===//
2350 // Basic SCEV Analysis and PHI Idiom Recognition Code
2353 /// isSCEVable - Test if values of the given type are analyzable within
2354 /// the SCEV framework. This primarily includes integer types, and it
2355 /// can optionally include pointer types if the ScalarEvolution class
2356 /// has access to target-specific information.
2357 bool ScalarEvolution::isSCEVable(const Type *Ty) const {
2358 // Integers and pointers are always SCEVable.
2359 return Ty->isIntegerTy() || Ty->isPointerTy();
2362 /// getTypeSizeInBits - Return the size in bits of the specified type,
2363 /// for which isSCEVable must return true.
2364 uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const {
2365 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2367 // If we have a TargetData, use it!
2369 return TD->getTypeSizeInBits(Ty);
2371 // Integer types have fixed sizes.
2372 if (Ty->isIntegerTy())
2373 return Ty->getPrimitiveSizeInBits();
2375 // The only other support type is pointer. Without TargetData, conservatively
2376 // assume pointers are 64-bit.
2377 assert(Ty->isPointerTy() && "isSCEVable permitted a non-SCEVable type!");
2381 /// getEffectiveSCEVType - Return a type with the same bitwidth as
2382 /// the given type and which represents how SCEV will treat the given
2383 /// type, for which isSCEVable must return true. For pointer types,
2384 /// this is the pointer-sized integer type.
2385 const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const {
2386 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2388 if (Ty->isIntegerTy())
2391 // The only other support type is pointer.
2392 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
2393 if (TD) return TD->getIntPtrType(getContext());
2395 // Without TargetData, conservatively assume pointers are 64-bit.
2396 return Type::getInt64Ty(getContext());
2399 const SCEV *ScalarEvolution::getCouldNotCompute() {
2400 return &CouldNotCompute;
2403 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
2404 /// expression and create a new one.
2405 const SCEV *ScalarEvolution::getSCEV(Value *V) {
2406 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
2408 std::map<SCEVCallbackVH, const SCEV *>::iterator I = Scalars.find(V);
2409 if (I != Scalars.end()) return I->second;
2410 const SCEV *S = createSCEV(V);
2411 Scalars.insert(std::make_pair(SCEVCallbackVH(V, this), S));
2415 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
2417 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) {
2418 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2420 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
2422 const Type *Ty = V->getType();
2423 Ty = getEffectiveSCEVType(Ty);
2424 return getMulExpr(V,
2425 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))));
2428 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
2429 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
2430 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2432 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
2434 const Type *Ty = V->getType();
2435 Ty = getEffectiveSCEVType(Ty);
2436 const SCEV *AllOnes =
2437 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
2438 return getMinusSCEV(AllOnes, V);
2441 /// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
2443 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS,
2445 // Fast path: X - X --> 0.
2447 return getConstant(LHS->getType(), 0);
2450 return getAddExpr(LHS, getNegativeSCEV(RHS));
2453 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
2454 /// input value to the specified type. If the type must be extended, it is zero
2457 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V,
2459 const Type *SrcTy = V->getType();
2460 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2461 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2462 "Cannot truncate or zero extend with non-integer arguments!");
2463 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2464 return V; // No conversion
2465 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2466 return getTruncateExpr(V, Ty);
2467 return getZeroExtendExpr(V, Ty);
2470 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
2471 /// input value to the specified type. If the type must be extended, it is sign
2474 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
2476 const Type *SrcTy = V->getType();
2477 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2478 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2479 "Cannot truncate or zero extend with non-integer arguments!");
2480 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2481 return V; // No conversion
2482 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2483 return getTruncateExpr(V, Ty);
2484 return getSignExtendExpr(V, Ty);
2487 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
2488 /// input value to the specified type. If the type must be extended, it is zero
2489 /// extended. The conversion must not be narrowing.
2491 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, const Type *Ty) {
2492 const Type *SrcTy = V->getType();
2493 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2494 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2495 "Cannot noop or zero extend with non-integer arguments!");
2496 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2497 "getNoopOrZeroExtend cannot truncate!");
2498 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2499 return V; // No conversion
2500 return getZeroExtendExpr(V, Ty);
2503 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
2504 /// input value to the specified type. If the type must be extended, it is sign
2505 /// extended. The conversion must not be narrowing.
2507 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, const Type *Ty) {
2508 const Type *SrcTy = V->getType();
2509 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2510 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2511 "Cannot noop or sign extend with non-integer arguments!");
2512 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2513 "getNoopOrSignExtend cannot truncate!");
2514 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2515 return V; // No conversion
2516 return getSignExtendExpr(V, Ty);
2519 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
2520 /// the input value to the specified type. If the type must be extended,
2521 /// it is extended with unspecified bits. The conversion must not be
2524 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, const Type *Ty) {
2525 const Type *SrcTy = V->getType();
2526 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2527 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2528 "Cannot noop or any extend with non-integer arguments!");
2529 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2530 "getNoopOrAnyExtend cannot truncate!");
2531 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2532 return V; // No conversion
2533 return getAnyExtendExpr(V, Ty);
2536 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
2537 /// input value to the specified type. The conversion must not be widening.
2539 ScalarEvolution::getTruncateOrNoop(const SCEV *V, const Type *Ty) {
2540 const Type *SrcTy = V->getType();
2541 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2542 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2543 "Cannot truncate or noop with non-integer arguments!");
2544 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
2545 "getTruncateOrNoop cannot extend!");
2546 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2547 return V; // No conversion
2548 return getTruncateExpr(V, Ty);
2551 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
2552 /// the types using zero-extension, and then perform a umax operation
2554 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
2556 const SCEV *PromotedLHS = LHS;
2557 const SCEV *PromotedRHS = RHS;
2559 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2560 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2562 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2564 return getUMaxExpr(PromotedLHS, PromotedRHS);
2567 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
2568 /// the types using zero-extension, and then perform a umin operation
2570 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
2572 const SCEV *PromotedLHS = LHS;
2573 const SCEV *PromotedRHS = RHS;
2575 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2576 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2578 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2580 return getUMinExpr(PromotedLHS, PromotedRHS);
2583 /// PushDefUseChildren - Push users of the given Instruction
2584 /// onto the given Worklist.
2586 PushDefUseChildren(Instruction *I,
2587 SmallVectorImpl<Instruction *> &Worklist) {
2588 // Push the def-use children onto the Worklist stack.
2589 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end();
2591 Worklist.push_back(cast<Instruction>(*UI));
2594 /// ForgetSymbolicValue - This looks up computed SCEV values for all
2595 /// instructions that depend on the given instruction and removes them from
2596 /// the Scalars map if they reference SymName. This is used during PHI
2599 ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) {
2600 SmallVector<Instruction *, 16> Worklist;
2601 PushDefUseChildren(PN, Worklist);
2603 SmallPtrSet<Instruction *, 8> Visited;
2605 while (!Worklist.empty()) {
2606 Instruction *I = Worklist.pop_back_val();
2607 if (!Visited.insert(I)) continue;
2609 std::map<SCEVCallbackVH, const SCEV *>::iterator It =
2610 Scalars.find(static_cast<Value *>(I));
2611 if (It != Scalars.end()) {
2612 // Short-circuit the def-use traversal if the symbolic name
2613 // ceases to appear in expressions.
2614 if (It->second != SymName && !It->second->hasOperand(SymName))
2617 // SCEVUnknown for a PHI either means that it has an unrecognized
2618 // structure, it's a PHI that's in the progress of being computed
2619 // by createNodeForPHI, or it's a single-value PHI. In the first case,
2620 // additional loop trip count information isn't going to change anything.
2621 // In the second case, createNodeForPHI will perform the necessary
2622 // updates on its own when it gets to that point. In the third, we do
2623 // want to forget the SCEVUnknown.
2624 if (!isa<PHINode>(I) ||
2625 !isa<SCEVUnknown>(It->second) ||
2626 (I != PN && It->second == SymName)) {
2627 ValuesAtScopes.erase(It->second);
2632 PushDefUseChildren(I, Worklist);
2636 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
2637 /// a loop header, making it a potential recurrence, or it doesn't.
2639 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
2640 if (const Loop *L = LI->getLoopFor(PN->getParent()))
2641 if (L->getHeader() == PN->getParent()) {
2642 // The loop may have multiple entrances or multiple exits; we can analyze
2643 // this phi as an addrec if it has a unique entry value and a unique
2645 Value *BEValueV = 0, *StartValueV = 0;
2646 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
2647 Value *V = PN->getIncomingValue(i);
2648 if (L->contains(PN->getIncomingBlock(i))) {
2651 } else if (BEValueV != V) {
2655 } else if (!StartValueV) {
2657 } else if (StartValueV != V) {
2662 if (BEValueV && StartValueV) {
2663 // While we are analyzing this PHI node, handle its value symbolically.
2664 const SCEV *SymbolicName = getUnknown(PN);
2665 assert(Scalars.find(PN) == Scalars.end() &&
2666 "PHI node already processed?");
2667 Scalars.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
2669 // Using this symbolic name for the PHI, analyze the value coming around
2671 const SCEV *BEValue = getSCEV(BEValueV);
2673 // NOTE: If BEValue is loop invariant, we know that the PHI node just
2674 // has a special value for the first iteration of the loop.
2676 // If the value coming around the backedge is an add with the symbolic
2677 // value we just inserted, then we found a simple induction variable!
2678 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
2679 // If there is a single occurrence of the symbolic value, replace it
2680 // with a recurrence.
2681 unsigned FoundIndex = Add->getNumOperands();
2682 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
2683 if (Add->getOperand(i) == SymbolicName)
2684 if (FoundIndex == e) {
2689 if (FoundIndex != Add->getNumOperands()) {
2690 // Create an add with everything but the specified operand.
2691 SmallVector<const SCEV *, 8> Ops;
2692 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
2693 if (i != FoundIndex)
2694 Ops.push_back(Add->getOperand(i));
2695 const SCEV *Accum = getAddExpr(Ops);
2697 // This is not a valid addrec if the step amount is varying each
2698 // loop iteration, but is not itself an addrec in this loop.
2699 if (Accum->isLoopInvariant(L) ||
2700 (isa<SCEVAddRecExpr>(Accum) &&
2701 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
2702 bool HasNUW = false;
2703 bool HasNSW = false;
2705 // If the increment doesn't overflow, then neither the addrec nor
2706 // the post-increment will overflow.
2707 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) {
2708 if (OBO->hasNoUnsignedWrap())
2710 if (OBO->hasNoSignedWrap())
2714 const SCEV *StartVal = getSCEV(StartValueV);
2715 const SCEV *PHISCEV =
2716 getAddRecExpr(StartVal, Accum, L, HasNUW, HasNSW);
2718 // Since the no-wrap flags are on the increment, they apply to the
2719 // post-incremented value as well.
2720 if (Accum->isLoopInvariant(L))
2721 (void)getAddRecExpr(getAddExpr(StartVal, Accum),
2722 Accum, L, HasNUW, HasNSW);
2724 // Okay, for the entire analysis of this edge we assumed the PHI
2725 // to be symbolic. We now need to go back and purge all of the
2726 // entries for the scalars that use the symbolic expression.
2727 ForgetSymbolicName(PN, SymbolicName);
2728 Scalars[SCEVCallbackVH(PN, this)] = PHISCEV;
2732 } else if (const SCEVAddRecExpr *AddRec =
2733 dyn_cast<SCEVAddRecExpr>(BEValue)) {
2734 // Otherwise, this could be a loop like this:
2735 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
2736 // In this case, j = {1,+,1} and BEValue is j.
2737 // Because the other in-value of i (0) fits the evolution of BEValue
2738 // i really is an addrec evolution.
2739 if (AddRec->getLoop() == L && AddRec->isAffine()) {
2740 const SCEV *StartVal = getSCEV(StartValueV);
2742 // If StartVal = j.start - j.stride, we can use StartVal as the
2743 // initial step of the addrec evolution.
2744 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
2745 AddRec->getOperand(1))) {
2746 const SCEV *PHISCEV =
2747 getAddRecExpr(StartVal, AddRec->getOperand(1), L);
2749 // Okay, for the entire analysis of this edge we assumed the PHI
2750 // to be symbolic. We now need to go back and purge all of the
2751 // entries for the scalars that use the symbolic expression.
2752 ForgetSymbolicName(PN, SymbolicName);
2753 Scalars[SCEVCallbackVH(PN, this)] = PHISCEV;
2761 // If the PHI has a single incoming value, follow that value, unless the
2762 // PHI's incoming blocks are in a different loop, in which case doing so
2763 // risks breaking LCSSA form. Instcombine would normally zap these, but
2764 // it doesn't have DominatorTree information, so it may miss cases.
2765 if (Value *V = PN->hasConstantValue(DT)) {
2766 bool AllSameLoop = true;
2767 Loop *PNLoop = LI->getLoopFor(PN->getParent());
2768 for (size_t i = 0, e = PN->getNumIncomingValues(); i != e; ++i)
2769 if (LI->getLoopFor(PN->getIncomingBlock(i)) != PNLoop) {
2770 AllSameLoop = false;
2777 // If it's not a loop phi, we can't handle it yet.
2778 return getUnknown(PN);
2781 /// createNodeForGEP - Expand GEP instructions into add and multiply
2782 /// operations. This allows them to be analyzed by regular SCEV code.
2784 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
2786 // Don't blindly transfer the inbounds flag from the GEP instruction to the
2787 // Add expression, because the Instruction may be guarded by control flow
2788 // and the no-overflow bits may not be valid for the expression in any
2791 const Type *IntPtrTy = getEffectiveSCEVType(GEP->getType());
2792 Value *Base = GEP->getOperand(0);
2793 // Don't attempt to analyze GEPs over unsized objects.
2794 if (!cast<PointerType>(Base->getType())->getElementType()->isSized())
2795 return getUnknown(GEP);
2796 const SCEV *TotalOffset = getConstant(IntPtrTy, 0);
2797 gep_type_iterator GTI = gep_type_begin(GEP);
2798 for (GetElementPtrInst::op_iterator I = next(GEP->op_begin()),
2802 // Compute the (potentially symbolic) offset in bytes for this index.
2803 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) {
2804 // For a struct, add the member offset.
2805 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
2806 const SCEV *FieldOffset = getOffsetOfExpr(STy, FieldNo);
2808 // Add the field offset to the running total offset.
2809 TotalOffset = getAddExpr(TotalOffset, FieldOffset);
2811 // For an array, add the element offset, explicitly scaled.
2812 const SCEV *ElementSize = getSizeOfExpr(*GTI);
2813 const SCEV *IndexS = getSCEV(Index);
2814 // Getelementptr indices are signed.
2815 IndexS = getTruncateOrSignExtend(IndexS, IntPtrTy);
2817 // Multiply the index by the element size to compute the element offset.
2818 const SCEV *LocalOffset = getMulExpr(IndexS, ElementSize);
2820 // Add the element offset to the running total offset.
2821 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
2825 // Get the SCEV for the GEP base.
2826 const SCEV *BaseS = getSCEV(Base);
2828 // Add the total offset from all the GEP indices to the base.
2829 return getAddExpr(BaseS, TotalOffset);
2832 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
2833 /// guaranteed to end in (at every loop iteration). It is, at the same time,
2834 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
2835 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
2837 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
2838 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
2839 return C->getValue()->getValue().countTrailingZeros();
2841 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
2842 return std::min(GetMinTrailingZeros(T->getOperand()),
2843 (uint32_t)getTypeSizeInBits(T->getType()));
2845 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
2846 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
2847 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
2848 getTypeSizeInBits(E->getType()) : OpRes;
2851 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
2852 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
2853 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
2854 getTypeSizeInBits(E->getType()) : OpRes;
2857 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
2858 // The result is the min of all operands results.
2859 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
2860 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
2861 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
2865 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
2866 // The result is the sum of all operands results.
2867 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
2868 uint32_t BitWidth = getTypeSizeInBits(M->getType());
2869 for (unsigned i = 1, e = M->getNumOperands();
2870 SumOpRes != BitWidth && i != e; ++i)
2871 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
2876 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
2877 // The result is the min of all operands results.
2878 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
2879 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
2880 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
2884 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
2885 // The result is the min of all operands results.
2886 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
2887 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
2888 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
2892 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
2893 // The result is the min of all operands results.
2894 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
2895 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
2896 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
2900 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
2901 // For a SCEVUnknown, ask ValueTracking.
2902 unsigned BitWidth = getTypeSizeInBits(U->getType());
2903 APInt Mask = APInt::getAllOnesValue(BitWidth);
2904 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
2905 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones);
2906 return Zeros.countTrailingOnes();
2913 /// getUnsignedRange - Determine the unsigned range for a particular SCEV.
2916 ScalarEvolution::getUnsignedRange(const SCEV *S) {
2918 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
2919 return ConstantRange(C->getValue()->getValue());
2921 unsigned BitWidth = getTypeSizeInBits(S->getType());
2922 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
2924 // If the value has known zeros, the maximum unsigned value will have those
2925 // known zeros as well.
2926 uint32_t TZ = GetMinTrailingZeros(S);
2928 ConservativeResult =
2929 ConstantRange(APInt::getMinValue(BitWidth),
2930 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
2932 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
2933 ConstantRange X = getUnsignedRange(Add->getOperand(0));
2934 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
2935 X = X.add(getUnsignedRange(Add->getOperand(i)));
2936 return ConservativeResult.intersectWith(X);
2939 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
2940 ConstantRange X = getUnsignedRange(Mul->getOperand(0));
2941 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
2942 X = X.multiply(getUnsignedRange(Mul->getOperand(i)));
2943 return ConservativeResult.intersectWith(X);
2946 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
2947 ConstantRange X = getUnsignedRange(SMax->getOperand(0));
2948 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
2949 X = X.smax(getUnsignedRange(SMax->getOperand(i)));
2950 return ConservativeResult.intersectWith(X);
2953 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
2954 ConstantRange X = getUnsignedRange(UMax->getOperand(0));
2955 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
2956 X = X.umax(getUnsignedRange(UMax->getOperand(i)));
2957 return ConservativeResult.intersectWith(X);
2960 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
2961 ConstantRange X = getUnsignedRange(UDiv->getLHS());
2962 ConstantRange Y = getUnsignedRange(UDiv->getRHS());
2963 return ConservativeResult.intersectWith(X.udiv(Y));
2966 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
2967 ConstantRange X = getUnsignedRange(ZExt->getOperand());
2968 return ConservativeResult.intersectWith(X.zeroExtend(BitWidth));
2971 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
2972 ConstantRange X = getUnsignedRange(SExt->getOperand());
2973 return ConservativeResult.intersectWith(X.signExtend(BitWidth));
2976 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
2977 ConstantRange X = getUnsignedRange(Trunc->getOperand());
2978 return ConservativeResult.intersectWith(X.truncate(BitWidth));
2981 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
2982 // If there's no unsigned wrap, the value will never be less than its
2984 if (AddRec->hasNoUnsignedWrap())
2985 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
2986 if (!C->getValue()->isZero())
2987 ConservativeResult =
2988 ConservativeResult.intersectWith(
2989 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0)));
2991 // TODO: non-affine addrec
2992 if (AddRec->isAffine()) {
2993 const Type *Ty = AddRec->getType();
2994 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
2995 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
2996 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
2997 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
2999 const SCEV *Start = AddRec->getStart();
3000 const SCEV *Step = AddRec->getStepRecurrence(*this);
3002 ConstantRange StartRange = getUnsignedRange(Start);
3003 ConstantRange StepRange = getSignedRange(Step);
3004 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3005 ConstantRange EndRange =
3006 StartRange.add(MaxBECountRange.multiply(StepRange));
3008 // Check for overflow. This must be done with ConstantRange arithmetic
3009 // because we could be called from within the ScalarEvolution overflow
3011 ConstantRange ExtStartRange = StartRange.zextOrTrunc(BitWidth*2+1);
3012 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3013 ConstantRange ExtMaxBECountRange =
3014 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3015 ConstantRange ExtEndRange = EndRange.zextOrTrunc(BitWidth*2+1);
3016 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3018 return ConservativeResult;
3020 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(),
3021 EndRange.getUnsignedMin());
3022 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(),
3023 EndRange.getUnsignedMax());
3024 if (Min.isMinValue() && Max.isMaxValue())
3025 return ConservativeResult;
3026 return ConservativeResult.intersectWith(ConstantRange(Min, Max+1));
3030 return ConservativeResult;
3033 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3034 // For a SCEVUnknown, ask ValueTracking.
3035 APInt Mask = APInt::getAllOnesValue(BitWidth);
3036 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3037 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones, TD);
3038 if (Ones == ~Zeros + 1)
3039 return ConservativeResult;
3040 return ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1));
3043 return ConservativeResult;
3046 /// getSignedRange - Determine the signed range for a particular SCEV.
3049 ScalarEvolution::getSignedRange(const SCEV *S) {
3051 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3052 return ConstantRange(C->getValue()->getValue());
3054 unsigned BitWidth = getTypeSizeInBits(S->getType());
3055 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3057 // If the value has known zeros, the maximum signed value will have those
3058 // known zeros as well.
3059 uint32_t TZ = GetMinTrailingZeros(S);
3061 ConservativeResult =
3062 ConstantRange(APInt::getSignedMinValue(BitWidth),
3063 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
3065 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3066 ConstantRange X = getSignedRange(Add->getOperand(0));
3067 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3068 X = X.add(getSignedRange(Add->getOperand(i)));
3069 return ConservativeResult.intersectWith(X);
3072 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3073 ConstantRange X = getSignedRange(Mul->getOperand(0));
3074 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3075 X = X.multiply(getSignedRange(Mul->getOperand(i)));
3076 return ConservativeResult.intersectWith(X);
3079 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3080 ConstantRange X = getSignedRange(SMax->getOperand(0));
3081 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3082 X = X.smax(getSignedRange(SMax->getOperand(i)));
3083 return ConservativeResult.intersectWith(X);
3086 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3087 ConstantRange X = getSignedRange(UMax->getOperand(0));
3088 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3089 X = X.umax(getSignedRange(UMax->getOperand(i)));
3090 return ConservativeResult.intersectWith(X);
3093 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3094 ConstantRange X = getSignedRange(UDiv->getLHS());
3095 ConstantRange Y = getSignedRange(UDiv->getRHS());
3096 return ConservativeResult.intersectWith(X.udiv(Y));
3099 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3100 ConstantRange X = getSignedRange(ZExt->getOperand());
3101 return ConservativeResult.intersectWith(X.zeroExtend(BitWidth));
3104 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3105 ConstantRange X = getSignedRange(SExt->getOperand());
3106 return ConservativeResult.intersectWith(X.signExtend(BitWidth));
3109 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3110 ConstantRange X = getSignedRange(Trunc->getOperand());
3111 return ConservativeResult.intersectWith(X.truncate(BitWidth));
3114 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3115 // If there's no signed wrap, and all the operands have the same sign or
3116 // zero, the value won't ever change sign.
3117 if (AddRec->hasNoSignedWrap()) {
3118 bool AllNonNeg = true;
3119 bool AllNonPos = true;
3120 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
3121 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
3122 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
3125 ConservativeResult = ConservativeResult.intersectWith(
3126 ConstantRange(APInt(BitWidth, 0),
3127 APInt::getSignedMinValue(BitWidth)));
3129 ConservativeResult = ConservativeResult.intersectWith(
3130 ConstantRange(APInt::getSignedMinValue(BitWidth),
3131 APInt(BitWidth, 1)));
3134 // TODO: non-affine addrec
3135 if (AddRec->isAffine()) {
3136 const Type *Ty = AddRec->getType();
3137 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3138 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3139 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3140 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3142 const SCEV *Start = AddRec->getStart();
3143 const SCEV *Step = AddRec->getStepRecurrence(*this);
3145 ConstantRange StartRange = getSignedRange(Start);
3146 ConstantRange StepRange = getSignedRange(Step);
3147 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3148 ConstantRange EndRange =
3149 StartRange.add(MaxBECountRange.multiply(StepRange));
3151 // Check for overflow. This must be done with ConstantRange arithmetic
3152 // because we could be called from within the ScalarEvolution overflow
3154 ConstantRange ExtStartRange = StartRange.sextOrTrunc(BitWidth*2+1);
3155 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3156 ConstantRange ExtMaxBECountRange =
3157 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3158 ConstantRange ExtEndRange = EndRange.sextOrTrunc(BitWidth*2+1);
3159 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3161 return ConservativeResult;
3163 APInt Min = APIntOps::smin(StartRange.getSignedMin(),
3164 EndRange.getSignedMin());
3165 APInt Max = APIntOps::smax(StartRange.getSignedMax(),
3166 EndRange.getSignedMax());
3167 if (Min.isMinSignedValue() && Max.isMaxSignedValue())
3168 return ConservativeResult;
3169 return ConservativeResult.intersectWith(ConstantRange(Min, Max+1));
3173 return ConservativeResult;
3176 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3177 // For a SCEVUnknown, ask ValueTracking.
3178 if (!U->getValue()->getType()->isIntegerTy() && !TD)
3179 return ConservativeResult;
3180 unsigned NS = ComputeNumSignBits(U->getValue(), TD);
3182 return ConservativeResult;
3183 return ConservativeResult.intersectWith(
3184 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
3185 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1));
3188 return ConservativeResult;
3191 /// createSCEV - We know that there is no SCEV for the specified value.
3192 /// Analyze the expression.
3194 const SCEV *ScalarEvolution::createSCEV(Value *V) {
3195 if (!isSCEVable(V->getType()))
3196 return getUnknown(V);
3198 unsigned Opcode = Instruction::UserOp1;
3199 if (Instruction *I = dyn_cast<Instruction>(V)) {
3200 Opcode = I->getOpcode();
3202 // Don't attempt to analyze instructions in blocks that aren't
3203 // reachable. Such instructions don't matter, and they aren't required
3204 // to obey basic rules for definitions dominating uses which this
3205 // analysis depends on.
3206 if (!DT->isReachableFromEntry(I->getParent()))
3207 return getUnknown(V);
3208 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
3209 Opcode = CE->getOpcode();
3210 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
3211 return getConstant(CI);
3212 else if (isa<ConstantPointerNull>(V))
3213 return getConstant(V->getType(), 0);
3214 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
3215 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee());
3217 return getUnknown(V);
3219 Operator *U = cast<Operator>(V);
3221 case Instruction::Add:
3222 return getAddExpr(getSCEV(U->getOperand(0)),
3223 getSCEV(U->getOperand(1)));
3224 case Instruction::Mul:
3225 return getMulExpr(getSCEV(U->getOperand(0)),
3226 getSCEV(U->getOperand(1)));
3227 case Instruction::UDiv:
3228 return getUDivExpr(getSCEV(U->getOperand(0)),
3229 getSCEV(U->getOperand(1)));
3230 case Instruction::Sub:
3231 return getMinusSCEV(getSCEV(U->getOperand(0)),
3232 getSCEV(U->getOperand(1)));
3233 case Instruction::And:
3234 // For an expression like x&255 that merely masks off the high bits,
3235 // use zext(trunc(x)) as the SCEV expression.
3236 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3237 if (CI->isNullValue())
3238 return getSCEV(U->getOperand(1));
3239 if (CI->isAllOnesValue())
3240 return getSCEV(U->getOperand(0));
3241 const APInt &A = CI->getValue();
3243 // Instcombine's ShrinkDemandedConstant may strip bits out of
3244 // constants, obscuring what would otherwise be a low-bits mask.
3245 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant
3246 // knew about to reconstruct a low-bits mask value.
3247 unsigned LZ = A.countLeadingZeros();
3248 unsigned BitWidth = A.getBitWidth();
3249 APInt AllOnes = APInt::getAllOnesValue(BitWidth);
3250 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
3251 ComputeMaskedBits(U->getOperand(0), AllOnes, KnownZero, KnownOne, TD);
3253 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ);
3255 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask))
3257 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)),
3258 IntegerType::get(getContext(), BitWidth - LZ)),
3263 case Instruction::Or:
3264 // If the RHS of the Or is a constant, we may have something like:
3265 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
3266 // optimizations will transparently handle this case.
3268 // In order for this transformation to be safe, the LHS must be of the
3269 // form X*(2^n) and the Or constant must be less than 2^n.
3270 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3271 const SCEV *LHS = getSCEV(U->getOperand(0));
3272 const APInt &CIVal = CI->getValue();
3273 if (GetMinTrailingZeros(LHS) >=
3274 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
3275 // Build a plain add SCEV.
3276 const SCEV *S = getAddExpr(LHS, getSCEV(CI));
3277 // If the LHS of the add was an addrec and it has no-wrap flags,
3278 // transfer the no-wrap flags, since an or won't introduce a wrap.
3279 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
3280 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
3281 if (OldAR->hasNoUnsignedWrap())
3282 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoUnsignedWrap(true);
3283 if (OldAR->hasNoSignedWrap())
3284 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoSignedWrap(true);
3290 case Instruction::Xor:
3291 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3292 // If the RHS of the xor is a signbit, then this is just an add.
3293 // Instcombine turns add of signbit into xor as a strength reduction step.
3294 if (CI->getValue().isSignBit())
3295 return getAddExpr(getSCEV(U->getOperand(0)),
3296 getSCEV(U->getOperand(1)));
3298 // If the RHS of xor is -1, then this is a not operation.
3299 if (CI->isAllOnesValue())
3300 return getNotSCEV(getSCEV(U->getOperand(0)));
3302 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
3303 // This is a variant of the check for xor with -1, and it handles
3304 // the case where instcombine has trimmed non-demanded bits out
3305 // of an xor with -1.
3306 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
3307 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
3308 if (BO->getOpcode() == Instruction::And &&
3309 LCI->getValue() == CI->getValue())
3310 if (const SCEVZeroExtendExpr *Z =
3311 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
3312 const Type *UTy = U->getType();
3313 const SCEV *Z0 = Z->getOperand();
3314 const Type *Z0Ty = Z0->getType();
3315 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
3317 // If C is a low-bits mask, the zero extend is serving to
3318 // mask off the high bits. Complement the operand and
3319 // re-apply the zext.
3320 if (APIntOps::isMask(Z0TySize, CI->getValue()))
3321 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
3323 // If C is a single bit, it may be in the sign-bit position
3324 // before the zero-extend. In this case, represent the xor
3325 // using an add, which is equivalent, and re-apply the zext.
3326 APInt Trunc = APInt(CI->getValue()).trunc(Z0TySize);
3327 if (APInt(Trunc).zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
3329 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
3335 case Instruction::Shl:
3336 // Turn shift left of a constant amount into a multiply.
3337 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3338 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3340 // If the shift count is not less than the bitwidth, the result of
3341 // the shift is undefined. Don't try to analyze it, because the
3342 // resolution chosen here may differ from the resolution chosen in
3343 // other parts of the compiler.
3344 if (SA->getValue().uge(BitWidth))
3347 Constant *X = ConstantInt::get(getContext(),
3348 APInt(BitWidth, 1).shl(SA->getZExtValue()));
3349 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3353 case Instruction::LShr:
3354 // Turn logical shift right of a constant into a unsigned divide.
3355 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3356 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3358 // If the shift count is not less than the bitwidth, the result of
3359 // the shift is undefined. Don't try to analyze it, because the
3360 // resolution chosen here may differ from the resolution chosen in
3361 // other parts of the compiler.
3362 if (SA->getValue().uge(BitWidth))
3365 Constant *X = ConstantInt::get(getContext(),
3366 APInt(BitWidth, 1).shl(SA->getZExtValue()));
3367 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3371 case Instruction::AShr:
3372 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
3373 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
3374 if (Operator *L = dyn_cast<Operator>(U->getOperand(0)))
3375 if (L->getOpcode() == Instruction::Shl &&
3376 L->getOperand(1) == U->getOperand(1)) {
3377 uint64_t BitWidth = getTypeSizeInBits(U->getType());
3379 // If the shift count is not less than the bitwidth, the result of
3380 // the shift is undefined. Don't try to analyze it, because the
3381 // resolution chosen here may differ from the resolution chosen in
3382 // other parts of the compiler.
3383 if (CI->getValue().uge(BitWidth))
3386 uint64_t Amt = BitWidth - CI->getZExtValue();
3387 if (Amt == BitWidth)
3388 return getSCEV(L->getOperand(0)); // shift by zero --> noop
3390 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
3391 IntegerType::get(getContext(),
3397 case Instruction::Trunc:
3398 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
3400 case Instruction::ZExt:
3401 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3403 case Instruction::SExt:
3404 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3406 case Instruction::BitCast:
3407 // BitCasts are no-op casts so we just eliminate the cast.
3408 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
3409 return getSCEV(U->getOperand(0));
3412 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
3413 // lead to pointer expressions which cannot safely be expanded to GEPs,
3414 // because ScalarEvolution doesn't respect the GEP aliasing rules when
3415 // simplifying integer expressions.
3417 case Instruction::GetElementPtr:
3418 return createNodeForGEP(cast<GEPOperator>(U));
3420 case Instruction::PHI:
3421 return createNodeForPHI(cast<PHINode>(U));
3423 case Instruction::Select:
3424 // This could be a smax or umax that was lowered earlier.
3425 // Try to recover it.
3426 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
3427 Value *LHS = ICI->getOperand(0);
3428 Value *RHS = ICI->getOperand(1);
3429 switch (ICI->getPredicate()) {
3430 case ICmpInst::ICMP_SLT:
3431 case ICmpInst::ICMP_SLE:
3432 std::swap(LHS, RHS);
3434 case ICmpInst::ICMP_SGT:
3435 case ICmpInst::ICMP_SGE:
3436 // a >s b ? a+x : b+x -> smax(a, b)+x
3437 // a >s b ? b+x : a+x -> smin(a, b)+x
3438 if (LHS->getType() == U->getType()) {
3439 const SCEV *LS = getSCEV(LHS);
3440 const SCEV *RS = getSCEV(RHS);
3441 const SCEV *LA = getSCEV(U->getOperand(1));
3442 const SCEV *RA = getSCEV(U->getOperand(2));
3443 const SCEV *LDiff = getMinusSCEV(LA, LS);
3444 const SCEV *RDiff = getMinusSCEV(RA, RS);
3446 return getAddExpr(getSMaxExpr(LS, RS), LDiff);
3447 LDiff = getMinusSCEV(LA, RS);
3448 RDiff = getMinusSCEV(RA, LS);
3450 return getAddExpr(getSMinExpr(LS, RS), LDiff);
3453 case ICmpInst::ICMP_ULT:
3454 case ICmpInst::ICMP_ULE:
3455 std::swap(LHS, RHS);
3457 case ICmpInst::ICMP_UGT:
3458 case ICmpInst::ICMP_UGE:
3459 // a >u b ? a+x : b+x -> umax(a, b)+x
3460 // a >u b ? b+x : a+x -> umin(a, b)+x
3461 if (LHS->getType() == U->getType()) {
3462 const SCEV *LS = getSCEV(LHS);
3463 const SCEV *RS = getSCEV(RHS);
3464 const SCEV *LA = getSCEV(U->getOperand(1));
3465 const SCEV *RA = getSCEV(U->getOperand(2));
3466 const SCEV *LDiff = getMinusSCEV(LA, LS);
3467 const SCEV *RDiff = getMinusSCEV(RA, RS);
3469 return getAddExpr(getUMaxExpr(LS, RS), LDiff);
3470 LDiff = getMinusSCEV(LA, RS);
3471 RDiff = getMinusSCEV(RA, LS);
3473 return getAddExpr(getUMinExpr(LS, RS), LDiff);
3476 case ICmpInst::ICMP_NE:
3477 // n != 0 ? n+x : 1+x -> umax(n, 1)+x
3478 if (LHS->getType() == U->getType() &&
3479 isa<ConstantInt>(RHS) &&
3480 cast<ConstantInt>(RHS)->isZero()) {
3481 const SCEV *One = getConstant(LHS->getType(), 1);
3482 const SCEV *LS = getSCEV(LHS);
3483 const SCEV *LA = getSCEV(U->getOperand(1));
3484 const SCEV *RA = getSCEV(U->getOperand(2));
3485 const SCEV *LDiff = getMinusSCEV(LA, LS);
3486 const SCEV *RDiff = getMinusSCEV(RA, One);
3488 return getAddExpr(getUMaxExpr(LS, One), LDiff);
3491 case ICmpInst::ICMP_EQ:
3492 // n == 0 ? 1+x : n+x -> umax(n, 1)+x
3493 if (LHS->getType() == U->getType() &&
3494 isa<ConstantInt>(RHS) &&
3495 cast<ConstantInt>(RHS)->isZero()) {
3496 const SCEV *One = getConstant(LHS->getType(), 1);
3497 const SCEV *LS = getSCEV(LHS);
3498 const SCEV *LA = getSCEV(U->getOperand(1));
3499 const SCEV *RA = getSCEV(U->getOperand(2));
3500 const SCEV *LDiff = getMinusSCEV(LA, One);
3501 const SCEV *RDiff = getMinusSCEV(RA, LS);
3503 return getAddExpr(getUMaxExpr(LS, One), LDiff);
3511 default: // We cannot analyze this expression.
3515 return getUnknown(V);
3520 //===----------------------------------------------------------------------===//
3521 // Iteration Count Computation Code
3524 /// getBackedgeTakenCount - If the specified loop has a predictable
3525 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
3526 /// object. The backedge-taken count is the number of times the loop header
3527 /// will be branched to from within the loop. This is one less than the
3528 /// trip count of the loop, since it doesn't count the first iteration,
3529 /// when the header is branched to from outside the loop.
3531 /// Note that it is not valid to call this method on a loop without a
3532 /// loop-invariant backedge-taken count (see
3533 /// hasLoopInvariantBackedgeTakenCount).
3535 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
3536 return getBackedgeTakenInfo(L).Exact;
3539 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
3540 /// return the least SCEV value that is known never to be less than the
3541 /// actual backedge taken count.
3542 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
3543 return getBackedgeTakenInfo(L).Max;
3546 /// PushLoopPHIs - Push PHI nodes in the header of the given loop
3547 /// onto the given Worklist.
3549 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
3550 BasicBlock *Header = L->getHeader();
3552 // Push all Loop-header PHIs onto the Worklist stack.
3553 for (BasicBlock::iterator I = Header->begin();
3554 PHINode *PN = dyn_cast<PHINode>(I); ++I)
3555 Worklist.push_back(PN);
3558 const ScalarEvolution::BackedgeTakenInfo &
3559 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
3560 // Initially insert a CouldNotCompute for this loop. If the insertion
3561 // succeeds, proceed to actually compute a backedge-taken count and
3562 // update the value. The temporary CouldNotCompute value tells SCEV
3563 // code elsewhere that it shouldn't attempt to request a new
3564 // backedge-taken count, which could result in infinite recursion.
3565 std::pair<std::map<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
3566 BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute()));
3568 BackedgeTakenInfo BECount = ComputeBackedgeTakenCount(L);
3569 if (BECount.Exact != getCouldNotCompute()) {
3570 assert(BECount.Exact->isLoopInvariant(L) &&
3571 BECount.Max->isLoopInvariant(L) &&
3572 "Computed backedge-taken count isn't loop invariant for loop!");
3573 ++NumTripCountsComputed;
3575 // Update the value in the map.
3576 Pair.first->second = BECount;
3578 if (BECount.Max != getCouldNotCompute())
3579 // Update the value in the map.
3580 Pair.first->second = BECount;
3581 if (isa<PHINode>(L->getHeader()->begin()))
3582 // Only count loops that have phi nodes as not being computable.
3583 ++NumTripCountsNotComputed;
3586 // Now that we know more about the trip count for this loop, forget any
3587 // existing SCEV values for PHI nodes in this loop since they are only
3588 // conservative estimates made without the benefit of trip count
3589 // information. This is similar to the code in forgetLoop, except that
3590 // it handles SCEVUnknown PHI nodes specially.
3591 if (BECount.hasAnyInfo()) {
3592 SmallVector<Instruction *, 16> Worklist;
3593 PushLoopPHIs(L, Worklist);
3595 SmallPtrSet<Instruction *, 8> Visited;
3596 while (!Worklist.empty()) {
3597 Instruction *I = Worklist.pop_back_val();
3598 if (!Visited.insert(I)) continue;
3600 std::map<SCEVCallbackVH, const SCEV *>::iterator It =
3601 Scalars.find(static_cast<Value *>(I));
3602 if (It != Scalars.end()) {
3603 // SCEVUnknown for a PHI either means that it has an unrecognized
3604 // structure, or it's a PHI that's in the progress of being computed
3605 // by createNodeForPHI. In the former case, additional loop trip
3606 // count information isn't going to change anything. In the later
3607 // case, createNodeForPHI will perform the necessary updates on its
3608 // own when it gets to that point.
3609 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(It->second)) {
3610 ValuesAtScopes.erase(It->second);
3613 if (PHINode *PN = dyn_cast<PHINode>(I))
3614 ConstantEvolutionLoopExitValue.erase(PN);
3617 PushDefUseChildren(I, Worklist);
3621 return Pair.first->second;
3624 /// forgetLoop - This method should be called by the client when it has
3625 /// changed a loop in a way that may effect ScalarEvolution's ability to
3626 /// compute a trip count, or if the loop is deleted.
3627 void ScalarEvolution::forgetLoop(const Loop *L) {
3628 // Drop any stored trip count value.
3629 BackedgeTakenCounts.erase(L);
3631 // Drop information about expressions based on loop-header PHIs.
3632 SmallVector<Instruction *, 16> Worklist;
3633 PushLoopPHIs(L, Worklist);
3635 SmallPtrSet<Instruction *, 8> Visited;
3636 while (!Worklist.empty()) {
3637 Instruction *I = Worklist.pop_back_val();
3638 if (!Visited.insert(I)) continue;
3640 std::map<SCEVCallbackVH, const SCEV *>::iterator It =
3641 Scalars.find(static_cast<Value *>(I));
3642 if (It != Scalars.end()) {
3643 ValuesAtScopes.erase(It->second);
3645 if (PHINode *PN = dyn_cast<PHINode>(I))
3646 ConstantEvolutionLoopExitValue.erase(PN);
3649 PushDefUseChildren(I, Worklist);
3653 /// forgetValue - This method should be called by the client when it has
3654 /// changed a value in a way that may effect its value, or which may
3655 /// disconnect it from a def-use chain linking it to a loop.
3656 void ScalarEvolution::forgetValue(Value *V) {
3657 Instruction *I = dyn_cast<Instruction>(V);
3660 // Drop information about expressions based on loop-header PHIs.
3661 SmallVector<Instruction *, 16> Worklist;
3662 Worklist.push_back(I);
3664 SmallPtrSet<Instruction *, 8> Visited;
3665 while (!Worklist.empty()) {
3666 I = Worklist.pop_back_val();
3667 if (!Visited.insert(I)) continue;
3669 std::map<SCEVCallbackVH, const SCEV *>::iterator It =
3670 Scalars.find(static_cast<Value *>(I));
3671 if (It != Scalars.end()) {
3672 ValuesAtScopes.erase(It->second);
3674 if (PHINode *PN = dyn_cast<PHINode>(I))
3675 ConstantEvolutionLoopExitValue.erase(PN);
3678 // If there's a SCEVUnknown tying this value into the SCEV
3679 // space, remove it from the folding set map. The SCEVUnknown
3680 // object and any other SCEV objects which reference it
3681 // (transitively) remain allocated, effectively leaked until
3682 // the underlying BumpPtrAllocator is freed.
3684 // This permits SCEV pointers to be used as keys in maps
3685 // such as the ValuesAtScopes map.
3686 FoldingSetNodeID ID;
3687 ID.AddInteger(scUnknown);
3690 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
3691 UniqueSCEVs.RemoveNode(S);
3693 // This isn't necessary, but we might as well remove the
3694 // value from the ValuesAtScopes map too.
3695 ValuesAtScopes.erase(S);
3698 PushDefUseChildren(I, Worklist);
3702 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
3703 /// of the specified loop will execute.
3704 ScalarEvolution::BackedgeTakenInfo
3705 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
3706 SmallVector<BasicBlock *, 8> ExitingBlocks;
3707 L->getExitingBlocks(ExitingBlocks);
3709 // Examine all exits and pick the most conservative values.
3710 const SCEV *BECount = getCouldNotCompute();
3711 const SCEV *MaxBECount = getCouldNotCompute();
3712 bool CouldNotComputeBECount = false;
3713 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
3714 BackedgeTakenInfo NewBTI =
3715 ComputeBackedgeTakenCountFromExit(L, ExitingBlocks[i]);
3717 if (NewBTI.Exact == getCouldNotCompute()) {
3718 // We couldn't compute an exact value for this exit, so
3719 // we won't be able to compute an exact value for the loop.
3720 CouldNotComputeBECount = true;
3721 BECount = getCouldNotCompute();
3722 } else if (!CouldNotComputeBECount) {
3723 if (BECount == getCouldNotCompute())
3724 BECount = NewBTI.Exact;
3726 BECount = getUMinFromMismatchedTypes(BECount, NewBTI.Exact);
3728 if (MaxBECount == getCouldNotCompute())
3729 MaxBECount = NewBTI.Max;
3730 else if (NewBTI.Max != getCouldNotCompute())
3731 MaxBECount = getUMinFromMismatchedTypes(MaxBECount, NewBTI.Max);
3734 return BackedgeTakenInfo(BECount, MaxBECount);
3737 /// ComputeBackedgeTakenCountFromExit - Compute the number of times the backedge
3738 /// of the specified loop will execute if it exits via the specified block.
3739 ScalarEvolution::BackedgeTakenInfo
3740 ScalarEvolution::ComputeBackedgeTakenCountFromExit(const Loop *L,
3741 BasicBlock *ExitingBlock) {
3743 // Okay, we've chosen an exiting block. See what condition causes us to
3744 // exit at this block.
3746 // FIXME: we should be able to handle switch instructions (with a single exit)
3747 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
3748 if (ExitBr == 0) return getCouldNotCompute();
3749 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
3751 // At this point, we know we have a conditional branch that determines whether
3752 // the loop is exited. However, we don't know if the branch is executed each
3753 // time through the loop. If not, then the execution count of the branch will
3754 // not be equal to the trip count of the loop.
3756 // Currently we check for this by checking to see if the Exit branch goes to
3757 // the loop header. If so, we know it will always execute the same number of
3758 // times as the loop. We also handle the case where the exit block *is* the
3759 // loop header. This is common for un-rotated loops.
3761 // If both of those tests fail, walk up the unique predecessor chain to the
3762 // header, stopping if there is an edge that doesn't exit the loop. If the
3763 // header is reached, the execution count of the branch will be equal to the
3764 // trip count of the loop.
3766 // More extensive analysis could be done to handle more cases here.
3768 if (ExitBr->getSuccessor(0) != L->getHeader() &&
3769 ExitBr->getSuccessor(1) != L->getHeader() &&
3770 ExitBr->getParent() != L->getHeader()) {
3771 // The simple checks failed, try climbing the unique predecessor chain
3772 // up to the header.
3774 for (BasicBlock *BB = ExitBr->getParent(); BB; ) {
3775 BasicBlock *Pred = BB->getUniquePredecessor();
3777 return getCouldNotCompute();
3778 TerminatorInst *PredTerm = Pred->getTerminator();
3779 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) {
3780 BasicBlock *PredSucc = PredTerm->getSuccessor(i);
3783 // If the predecessor has a successor that isn't BB and isn't
3784 // outside the loop, assume the worst.
3785 if (L->contains(PredSucc))
3786 return getCouldNotCompute();
3788 if (Pred == L->getHeader()) {
3795 return getCouldNotCompute();
3798 // Proceed to the next level to examine the exit condition expression.
3799 return ComputeBackedgeTakenCountFromExitCond(L, ExitBr->getCondition(),
3800 ExitBr->getSuccessor(0),
3801 ExitBr->getSuccessor(1));
3804 /// ComputeBackedgeTakenCountFromExitCond - Compute the number of times the
3805 /// backedge of the specified loop will execute if its exit condition
3806 /// were a conditional branch of ExitCond, TBB, and FBB.
3807 ScalarEvolution::BackedgeTakenInfo
3808 ScalarEvolution::ComputeBackedgeTakenCountFromExitCond(const Loop *L,
3812 // Check if the controlling expression for this loop is an And or Or.
3813 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
3814 if (BO->getOpcode() == Instruction::And) {
3815 // Recurse on the operands of the and.
3816 BackedgeTakenInfo BTI0 =
3817 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB);
3818 BackedgeTakenInfo BTI1 =
3819 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB);
3820 const SCEV *BECount = getCouldNotCompute();
3821 const SCEV *MaxBECount = getCouldNotCompute();
3822 if (L->contains(TBB)) {
3823 // Both conditions must be true for the loop to continue executing.
3824 // Choose the less conservative count.
3825 if (BTI0.Exact == getCouldNotCompute() ||
3826 BTI1.Exact == getCouldNotCompute())
3827 BECount = getCouldNotCompute();
3829 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3830 if (BTI0.Max == getCouldNotCompute())
3831 MaxBECount = BTI1.Max;
3832 else if (BTI1.Max == getCouldNotCompute())
3833 MaxBECount = BTI0.Max;
3835 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max);
3837 // Both conditions must be true for the loop to exit.
3838 assert(L->contains(FBB) && "Loop block has no successor in loop!");
3839 if (BTI0.Exact != getCouldNotCompute() &&
3840 BTI1.Exact != getCouldNotCompute())
3841 BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3842 if (BTI0.Max != getCouldNotCompute() &&
3843 BTI1.Max != getCouldNotCompute())
3844 MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max);
3847 return BackedgeTakenInfo(BECount, MaxBECount);
3849 if (BO->getOpcode() == Instruction::Or) {
3850 // Recurse on the operands of the or.
3851 BackedgeTakenInfo BTI0 =
3852 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB);
3853 BackedgeTakenInfo BTI1 =
3854 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB);
3855 const SCEV *BECount = getCouldNotCompute();
3856 const SCEV *MaxBECount = getCouldNotCompute();
3857 if (L->contains(FBB)) {
3858 // Both conditions must be false for the loop to continue executing.
3859 // Choose the less conservative count.
3860 if (BTI0.Exact == getCouldNotCompute() ||
3861 BTI1.Exact == getCouldNotCompute())
3862 BECount = getCouldNotCompute();
3864 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3865 if (BTI0.Max == getCouldNotCompute())
3866 MaxBECount = BTI1.Max;
3867 else if (BTI1.Max == getCouldNotCompute())
3868 MaxBECount = BTI0.Max;
3870 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max);
3872 // Both conditions must be false for the loop to exit.
3873 assert(L->contains(TBB) && "Loop block has no successor in loop!");
3874 if (BTI0.Exact != getCouldNotCompute() &&
3875 BTI1.Exact != getCouldNotCompute())
3876 BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3877 if (BTI0.Max != getCouldNotCompute() &&
3878 BTI1.Max != getCouldNotCompute())
3879 MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max);
3882 return BackedgeTakenInfo(BECount, MaxBECount);
3886 // With an icmp, it may be feasible to compute an exact backedge-taken count.
3887 // Proceed to the next level to examine the icmp.
3888 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
3889 return ComputeBackedgeTakenCountFromExitCondICmp(L, ExitCondICmp, TBB, FBB);
3891 // Check for a constant condition. These are normally stripped out by
3892 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
3893 // preserve the CFG and is temporarily leaving constant conditions
3895 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
3896 if (L->contains(FBB) == !CI->getZExtValue())
3897 // The backedge is always taken.
3898 return getCouldNotCompute();
3900 // The backedge is never taken.
3901 return getConstant(CI->getType(), 0);
3904 // If it's not an integer or pointer comparison then compute it the hard way.
3905 return ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB));
3908 /// ComputeBackedgeTakenCountFromExitCondICmp - Compute the number of times the
3909 /// backedge of the specified loop will execute if its exit condition
3910 /// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB.
3911 ScalarEvolution::BackedgeTakenInfo
3912 ScalarEvolution::ComputeBackedgeTakenCountFromExitCondICmp(const Loop *L,
3917 // If the condition was exit on true, convert the condition to exit on false
3918 ICmpInst::Predicate Cond;
3919 if (!L->contains(FBB))
3920 Cond = ExitCond->getPredicate();
3922 Cond = ExitCond->getInversePredicate();
3924 // Handle common loops like: for (X = "string"; *X; ++X)
3925 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
3926 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
3927 BackedgeTakenInfo ItCnt =
3928 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond);
3929 if (ItCnt.hasAnyInfo())
3933 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
3934 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
3936 // Try to evaluate any dependencies out of the loop.
3937 LHS = getSCEVAtScope(LHS, L);
3938 RHS = getSCEVAtScope(RHS, L);
3940 // At this point, we would like to compute how many iterations of the
3941 // loop the predicate will return true for these inputs.
3942 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) {
3943 // If there is a loop-invariant, force it into the RHS.
3944 std::swap(LHS, RHS);
3945 Cond = ICmpInst::getSwappedPredicate(Cond);
3948 // Simplify the operands before analyzing them.
3949 (void)SimplifyICmpOperands(Cond, LHS, RHS);
3951 // If we have a comparison of a chrec against a constant, try to use value
3952 // ranges to answer this query.
3953 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
3954 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
3955 if (AddRec->getLoop() == L) {
3956 // Form the constant range.
3957 ConstantRange CompRange(
3958 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
3960 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
3961 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
3965 case ICmpInst::ICMP_NE: { // while (X != Y)
3966 // Convert to: while (X-Y != 0)
3967 BackedgeTakenInfo BTI = HowFarToZero(getMinusSCEV(LHS, RHS), L);
3968 if (BTI.hasAnyInfo()) return BTI;
3971 case ICmpInst::ICMP_EQ: { // while (X == Y)
3972 // Convert to: while (X-Y == 0)
3973 BackedgeTakenInfo BTI = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
3974 if (BTI.hasAnyInfo()) return BTI;
3977 case ICmpInst::ICMP_SLT: {
3978 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true);
3979 if (BTI.hasAnyInfo()) return BTI;
3982 case ICmpInst::ICMP_SGT: {
3983 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
3984 getNotSCEV(RHS), L, true);
3985 if (BTI.hasAnyInfo()) return BTI;
3988 case ICmpInst::ICMP_ULT: {
3989 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false);
3990 if (BTI.hasAnyInfo()) return BTI;
3993 case ICmpInst::ICMP_UGT: {
3994 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
3995 getNotSCEV(RHS), L, false);
3996 if (BTI.hasAnyInfo()) return BTI;
4001 dbgs() << "ComputeBackedgeTakenCount ";
4002 if (ExitCond->getOperand(0)->getType()->isUnsigned())
4003 dbgs() << "[unsigned] ";
4004 dbgs() << *LHS << " "
4005 << Instruction::getOpcodeName(Instruction::ICmp)
4006 << " " << *RHS << "\n";
4011 ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB));
4014 static ConstantInt *
4015 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
4016 ScalarEvolution &SE) {
4017 const SCEV *InVal = SE.getConstant(C);
4018 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
4019 assert(isa<SCEVConstant>(Val) &&
4020 "Evaluation of SCEV at constant didn't fold correctly?");
4021 return cast<SCEVConstant>(Val)->getValue();
4024 /// GetAddressedElementFromGlobal - Given a global variable with an initializer
4025 /// and a GEP expression (missing the pointer index) indexing into it, return
4026 /// the addressed element of the initializer or null if the index expression is
4029 GetAddressedElementFromGlobal(GlobalVariable *GV,
4030 const std::vector<ConstantInt*> &Indices) {
4031 Constant *Init = GV->getInitializer();
4032 for (unsigned i = 0, e = Indices.size(); i != e; ++i) {
4033 uint64_t Idx = Indices[i]->getZExtValue();
4034 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) {
4035 assert(Idx < CS->getNumOperands() && "Bad struct index!");
4036 Init = cast<Constant>(CS->getOperand(Idx));
4037 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) {
4038 if (Idx >= CA->getNumOperands()) return 0; // Bogus program
4039 Init = cast<Constant>(CA->getOperand(Idx));
4040 } else if (isa<ConstantAggregateZero>(Init)) {
4041 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) {
4042 assert(Idx < STy->getNumElements() && "Bad struct index!");
4043 Init = Constant::getNullValue(STy->getElementType(Idx));
4044 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) {
4045 if (Idx >= ATy->getNumElements()) return 0; // Bogus program
4046 Init = Constant::getNullValue(ATy->getElementType());
4048 llvm_unreachable("Unknown constant aggregate type!");
4052 return 0; // Unknown initializer type
4058 /// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of
4059 /// 'icmp op load X, cst', try to see if we can compute the backedge
4060 /// execution count.
4061 ScalarEvolution::BackedgeTakenInfo
4062 ScalarEvolution::ComputeLoadConstantCompareBackedgeTakenCount(
4066 ICmpInst::Predicate predicate) {
4067 if (LI->isVolatile()) return getCouldNotCompute();
4069 // Check to see if the loaded pointer is a getelementptr of a global.
4070 // TODO: Use SCEV instead of manually grubbing with GEPs.
4071 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
4072 if (!GEP) return getCouldNotCompute();
4074 // Make sure that it is really a constant global we are gepping, with an
4075 // initializer, and make sure the first IDX is really 0.
4076 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
4077 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
4078 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
4079 !cast<Constant>(GEP->getOperand(1))->isNullValue())
4080 return getCouldNotCompute();
4082 // Okay, we allow one non-constant index into the GEP instruction.
4084 std::vector<ConstantInt*> Indexes;
4085 unsigned VarIdxNum = 0;
4086 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
4087 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
4088 Indexes.push_back(CI);
4089 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
4090 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
4091 VarIdx = GEP->getOperand(i);
4093 Indexes.push_back(0);
4096 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
4097 // Check to see if X is a loop variant variable value now.
4098 const SCEV *Idx = getSCEV(VarIdx);
4099 Idx = getSCEVAtScope(Idx, L);
4101 // We can only recognize very limited forms of loop index expressions, in
4102 // particular, only affine AddRec's like {C1,+,C2}.
4103 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
4104 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) ||
4105 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
4106 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
4107 return getCouldNotCompute();
4109 unsigned MaxSteps = MaxBruteForceIterations;
4110 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
4111 ConstantInt *ItCst = ConstantInt::get(
4112 cast<IntegerType>(IdxExpr->getType()), IterationNum);
4113 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
4115 // Form the GEP offset.
4116 Indexes[VarIdxNum] = Val;
4118 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes);
4119 if (Result == 0) break; // Cannot compute!
4121 // Evaluate the condition for this iteration.
4122 Result = ConstantExpr::getICmp(predicate, Result, RHS);
4123 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
4124 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
4126 dbgs() << "\n***\n*** Computed loop count " << *ItCst
4127 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
4130 ++NumArrayLenItCounts;
4131 return getConstant(ItCst); // Found terminating iteration!
4134 return getCouldNotCompute();
4138 /// CanConstantFold - Return true if we can constant fold an instruction of the
4139 /// specified type, assuming that all operands were constants.
4140 static bool CanConstantFold(const Instruction *I) {
4141 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
4142 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I))
4145 if (const CallInst *CI = dyn_cast<CallInst>(I))
4146 if (const Function *F = CI->getCalledFunction())
4147 return canConstantFoldCallTo(F);
4151 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
4152 /// in the loop that V is derived from. We allow arbitrary operations along the
4153 /// way, but the operands of an operation must either be constants or a value
4154 /// derived from a constant PHI. If this expression does not fit with these
4155 /// constraints, return null.
4156 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
4157 // If this is not an instruction, or if this is an instruction outside of the
4158 // loop, it can't be derived from a loop PHI.
4159 Instruction *I = dyn_cast<Instruction>(V);
4160 if (I == 0 || !L->contains(I)) return 0;
4162 if (PHINode *PN = dyn_cast<PHINode>(I)) {
4163 if (L->getHeader() == I->getParent())
4166 // We don't currently keep track of the control flow needed to evaluate
4167 // PHIs, so we cannot handle PHIs inside of loops.
4171 // If we won't be able to constant fold this expression even if the operands
4172 // are constants, return early.
4173 if (!CanConstantFold(I)) return 0;
4175 // Otherwise, we can evaluate this instruction if all of its operands are
4176 // constant or derived from a PHI node themselves.
4178 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op)
4179 if (!isa<Constant>(I->getOperand(Op))) {
4180 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L);
4181 if (P == 0) return 0; // Not evolving from PHI
4185 return 0; // Evolving from multiple different PHIs.
4188 // This is a expression evolving from a constant PHI!
4192 /// EvaluateExpression - Given an expression that passes the
4193 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
4194 /// in the loop has the value PHIVal. If we can't fold this expression for some
4195 /// reason, return null.
4196 static Constant *EvaluateExpression(Value *V, Constant *PHIVal,
4197 const TargetData *TD) {
4198 if (isa<PHINode>(V)) return PHIVal;
4199 if (Constant *C = dyn_cast<Constant>(V)) return C;
4200 Instruction *I = cast<Instruction>(V);
4202 std::vector<Constant*> Operands(I->getNumOperands());
4204 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
4205 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal, TD);
4206 if (Operands[i] == 0) return 0;
4209 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
4210 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
4212 return ConstantFoldInstOperands(I->getOpcode(), I->getType(),
4213 &Operands[0], Operands.size(), TD);
4216 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
4217 /// in the header of its containing loop, we know the loop executes a
4218 /// constant number of times, and the PHI node is just a recurrence
4219 /// involving constants, fold it.
4221 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
4224 std::map<PHINode*, Constant*>::iterator I =
4225 ConstantEvolutionLoopExitValue.find(PN);
4226 if (I != ConstantEvolutionLoopExitValue.end())
4229 if (BEs.ugt(MaxBruteForceIterations))
4230 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
4232 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
4234 // Since the loop is canonicalized, the PHI node must have two entries. One
4235 // entry must be a constant (coming in from outside of the loop), and the
4236 // second must be derived from the same PHI.
4237 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
4238 Constant *StartCST =
4239 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
4241 return RetVal = 0; // Must be a constant.
4243 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
4244 if (getConstantEvolvingPHI(BEValue, L) != PN &&
4245 !isa<Constant>(BEValue))
4246 return RetVal = 0; // Not derived from same PHI.
4248 // Execute the loop symbolically to determine the exit value.
4249 if (BEs.getActiveBits() >= 32)
4250 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
4252 unsigned NumIterations = BEs.getZExtValue(); // must be in range
4253 unsigned IterationNum = 0;
4254 for (Constant *PHIVal = StartCST; ; ++IterationNum) {
4255 if (IterationNum == NumIterations)
4256 return RetVal = PHIVal; // Got exit value!
4258 // Compute the value of the PHI node for the next iteration.
4259 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD);
4260 if (NextPHI == PHIVal)
4261 return RetVal = NextPHI; // Stopped evolving!
4263 return 0; // Couldn't evaluate!
4268 /// ComputeBackedgeTakenCountExhaustively - If the loop is known to execute a
4269 /// constant number of times (the condition evolves only from constants),
4270 /// try to evaluate a few iterations of the loop until we get the exit
4271 /// condition gets a value of ExitWhen (true or false). If we cannot
4272 /// evaluate the trip count of the loop, return getCouldNotCompute().
4274 ScalarEvolution::ComputeBackedgeTakenCountExhaustively(const Loop *L,
4277 PHINode *PN = getConstantEvolvingPHI(Cond, L);
4278 if (PN == 0) return getCouldNotCompute();
4280 // If the loop is canonicalized, the PHI will have exactly two entries.
4281 // That's the only form we support here.
4282 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
4284 // One entry must be a constant (coming in from outside of the loop), and the
4285 // second must be derived from the same PHI.
4286 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
4287 Constant *StartCST =
4288 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
4289 if (StartCST == 0) return getCouldNotCompute(); // Must be a constant.
4291 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
4292 if (getConstantEvolvingPHI(BEValue, L) != PN &&
4293 !isa<Constant>(BEValue))
4294 return getCouldNotCompute(); // Not derived from same PHI.
4296 // Okay, we find a PHI node that defines the trip count of this loop. Execute
4297 // the loop symbolically to determine when the condition gets a value of
4299 unsigned IterationNum = 0;
4300 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
4301 for (Constant *PHIVal = StartCST;
4302 IterationNum != MaxIterations; ++IterationNum) {
4303 ConstantInt *CondVal =
4304 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal, TD));
4306 // Couldn't symbolically evaluate.
4307 if (!CondVal) return getCouldNotCompute();
4309 if (CondVal->getValue() == uint64_t(ExitWhen)) {
4310 ++NumBruteForceTripCountsComputed;
4311 return getConstant(Type::getInt32Ty(getContext()), IterationNum);
4314 // Compute the value of the PHI node for the next iteration.
4315 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD);
4316 if (NextPHI == 0 || NextPHI == PHIVal)
4317 return getCouldNotCompute();// Couldn't evaluate or not making progress...
4321 // Too many iterations were needed to evaluate.
4322 return getCouldNotCompute();
4325 /// getSCEVAtScope - Return a SCEV expression for the specified value
4326 /// at the specified scope in the program. The L value specifies a loop
4327 /// nest to evaluate the expression at, where null is the top-level or a
4328 /// specified loop is immediately inside of the loop.
4330 /// This method can be used to compute the exit value for a variable defined
4331 /// in a loop by querying what the value will hold in the parent loop.
4333 /// In the case that a relevant loop exit value cannot be computed, the
4334 /// original value V is returned.
4335 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
4336 // Check to see if we've folded this expression at this loop before.
4337 std::map<const Loop *, const SCEV *> &Values = ValuesAtScopes[V];
4338 std::pair<std::map<const Loop *, const SCEV *>::iterator, bool> Pair =
4339 Values.insert(std::make_pair(L, static_cast<const SCEV *>(0)));
4341 return Pair.first->second ? Pair.first->second : V;
4343 // Otherwise compute it.
4344 const SCEV *C = computeSCEVAtScope(V, L);
4345 ValuesAtScopes[V][L] = C;
4349 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
4350 if (isa<SCEVConstant>(V)) return V;
4352 // If this instruction is evolved from a constant-evolving PHI, compute the
4353 // exit value from the loop without using SCEVs.
4354 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
4355 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
4356 const Loop *LI = (*this->LI)[I->getParent()];
4357 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
4358 if (PHINode *PN = dyn_cast<PHINode>(I))
4359 if (PN->getParent() == LI->getHeader()) {
4360 // Okay, there is no closed form solution for the PHI node. Check
4361 // to see if the loop that contains it has a known backedge-taken
4362 // count. If so, we may be able to force computation of the exit
4364 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
4365 if (const SCEVConstant *BTCC =
4366 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
4367 // Okay, we know how many times the containing loop executes. If
4368 // this is a constant evolving PHI node, get the final value at
4369 // the specified iteration number.
4370 Constant *RV = getConstantEvolutionLoopExitValue(PN,
4371 BTCC->getValue()->getValue(),
4373 if (RV) return getSCEV(RV);
4377 // Okay, this is an expression that we cannot symbolically evaluate
4378 // into a SCEV. Check to see if it's possible to symbolically evaluate
4379 // the arguments into constants, and if so, try to constant propagate the
4380 // result. This is particularly useful for computing loop exit values.
4381 if (CanConstantFold(I)) {
4382 SmallVector<Constant *, 4> Operands;
4383 bool MadeImprovement = false;
4384 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
4385 Value *Op = I->getOperand(i);
4386 if (Constant *C = dyn_cast<Constant>(Op)) {
4387 Operands.push_back(C);
4391 // If any of the operands is non-constant and if they are
4392 // non-integer and non-pointer, don't even try to analyze them
4393 // with scev techniques.
4394 if (!isSCEVable(Op->getType()))
4397 const SCEV *OrigV = getSCEV(Op);
4398 const SCEV *OpV = getSCEVAtScope(OrigV, L);
4399 MadeImprovement |= OrigV != OpV;
4402 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV))
4404 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV))
4405 C = dyn_cast<Constant>(SU->getValue());
4407 if (C->getType() != Op->getType())
4408 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
4412 Operands.push_back(C);
4415 // Check to see if getSCEVAtScope actually made an improvement.
4416 if (MadeImprovement) {
4418 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
4419 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
4420 Operands[0], Operands[1], TD);
4422 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
4423 &Operands[0], Operands.size(), TD);
4430 // This is some other type of SCEVUnknown, just return it.
4434 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
4435 // Avoid performing the look-up in the common case where the specified
4436 // expression has no loop-variant portions.
4437 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
4438 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
4439 if (OpAtScope != Comm->getOperand(i)) {
4440 // Okay, at least one of these operands is loop variant but might be
4441 // foldable. Build a new instance of the folded commutative expression.
4442 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
4443 Comm->op_begin()+i);
4444 NewOps.push_back(OpAtScope);
4446 for (++i; i != e; ++i) {
4447 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
4448 NewOps.push_back(OpAtScope);
4450 if (isa<SCEVAddExpr>(Comm))
4451 return getAddExpr(NewOps);
4452 if (isa<SCEVMulExpr>(Comm))
4453 return getMulExpr(NewOps);
4454 if (isa<SCEVSMaxExpr>(Comm))
4455 return getSMaxExpr(NewOps);
4456 if (isa<SCEVUMaxExpr>(Comm))
4457 return getUMaxExpr(NewOps);
4458 llvm_unreachable("Unknown commutative SCEV type!");
4461 // If we got here, all operands are loop invariant.
4465 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
4466 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
4467 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
4468 if (LHS == Div->getLHS() && RHS == Div->getRHS())
4469 return Div; // must be loop invariant
4470 return getUDivExpr(LHS, RHS);
4473 // If this is a loop recurrence for a loop that does not contain L, then we
4474 // are dealing with the final value computed by the loop.
4475 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
4476 // First, attempt to evaluate each operand.
4477 // Avoid performing the look-up in the common case where the specified
4478 // expression has no loop-variant portions.
4479 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
4480 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
4481 if (OpAtScope == AddRec->getOperand(i))
4484 // Okay, at least one of these operands is loop variant but might be
4485 // foldable. Build a new instance of the folded commutative expression.
4486 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(),
4487 AddRec->op_begin()+i);
4488 NewOps.push_back(OpAtScope);
4489 for (++i; i != e; ++i)
4490 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
4492 AddRec = cast<SCEVAddRecExpr>(getAddRecExpr(NewOps, AddRec->getLoop()));
4496 // If the scope is outside the addrec's loop, evaluate it by using the
4497 // loop exit value of the addrec.
4498 if (!AddRec->getLoop()->contains(L)) {
4499 // To evaluate this recurrence, we need to know how many times the AddRec
4500 // loop iterates. Compute this now.
4501 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
4502 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
4504 // Then, evaluate the AddRec.
4505 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
4511 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
4512 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
4513 if (Op == Cast->getOperand())
4514 return Cast; // must be loop invariant
4515 return getZeroExtendExpr(Op, Cast->getType());
4518 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
4519 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
4520 if (Op == Cast->getOperand())
4521 return Cast; // must be loop invariant
4522 return getSignExtendExpr(Op, Cast->getType());
4525 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
4526 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
4527 if (Op == Cast->getOperand())
4528 return Cast; // must be loop invariant
4529 return getTruncateExpr(Op, Cast->getType());
4532 llvm_unreachable("Unknown SCEV type!");
4536 /// getSCEVAtScope - This is a convenience function which does
4537 /// getSCEVAtScope(getSCEV(V), L).
4538 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
4539 return getSCEVAtScope(getSCEV(V), L);
4542 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
4543 /// following equation:
4545 /// A * X = B (mod N)
4547 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
4548 /// A and B isn't important.
4550 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
4551 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
4552 ScalarEvolution &SE) {
4553 uint32_t BW = A.getBitWidth();
4554 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
4555 assert(A != 0 && "A must be non-zero.");
4559 // The gcd of A and N may have only one prime factor: 2. The number of
4560 // trailing zeros in A is its multiplicity
4561 uint32_t Mult2 = A.countTrailingZeros();
4564 // 2. Check if B is divisible by D.
4566 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
4567 // is not less than multiplicity of this prime factor for D.
4568 if (B.countTrailingZeros() < Mult2)
4569 return SE.getCouldNotCompute();
4571 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
4574 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
4575 // bit width during computations.
4576 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
4577 APInt Mod(BW + 1, 0);
4578 Mod.set(BW - Mult2); // Mod = N / D
4579 APInt I = AD.multiplicativeInverse(Mod);
4581 // 4. Compute the minimum unsigned root of the equation:
4582 // I * (B / D) mod (N / D)
4583 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
4585 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
4587 return SE.getConstant(Result.trunc(BW));
4590 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
4591 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
4592 /// might be the same) or two SCEVCouldNotCompute objects.
4594 static std::pair<const SCEV *,const SCEV *>
4595 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
4596 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
4597 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
4598 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
4599 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
4601 // We currently can only solve this if the coefficients are constants.
4602 if (!LC || !MC || !NC) {
4603 const SCEV *CNC = SE.getCouldNotCompute();
4604 return std::make_pair(CNC, CNC);
4607 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
4608 const APInt &L = LC->getValue()->getValue();
4609 const APInt &M = MC->getValue()->getValue();
4610 const APInt &N = NC->getValue()->getValue();
4611 APInt Two(BitWidth, 2);
4612 APInt Four(BitWidth, 4);
4615 using namespace APIntOps;
4617 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
4618 // The B coefficient is M-N/2
4622 // The A coefficient is N/2
4623 APInt A(N.sdiv(Two));
4625 // Compute the B^2-4ac term.
4628 SqrtTerm -= Four * (A * C);
4630 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
4631 // integer value or else APInt::sqrt() will assert.
4632 APInt SqrtVal(SqrtTerm.sqrt());
4634 // Compute the two solutions for the quadratic formula.
4635 // The divisions must be performed as signed divisions.
4637 APInt TwoA( A << 1 );
4638 if (TwoA.isMinValue()) {
4639 const SCEV *CNC = SE.getCouldNotCompute();
4640 return std::make_pair(CNC, CNC);
4643 LLVMContext &Context = SE.getContext();
4645 ConstantInt *Solution1 =
4646 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
4647 ConstantInt *Solution2 =
4648 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
4650 return std::make_pair(SE.getConstant(Solution1),
4651 SE.getConstant(Solution2));
4652 } // end APIntOps namespace
4655 /// HowFarToZero - Return the number of times a backedge comparing the specified
4656 /// value to zero will execute. If not computable, return CouldNotCompute.
4657 ScalarEvolution::BackedgeTakenInfo
4658 ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) {
4659 // If the value is a constant
4660 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
4661 // If the value is already zero, the branch will execute zero times.
4662 if (C->getValue()->isZero()) return C;
4663 return getCouldNotCompute(); // Otherwise it will loop infinitely.
4666 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
4667 if (!AddRec || AddRec->getLoop() != L)
4668 return getCouldNotCompute();
4670 if (AddRec->isAffine()) {
4671 // If this is an affine expression, the execution count of this branch is
4672 // the minimum unsigned root of the following equation:
4674 // Start + Step*N = 0 (mod 2^BW)
4678 // Step*N = -Start (mod 2^BW)
4680 // where BW is the common bit width of Start and Step.
4682 // Get the initial value for the loop.
4683 const SCEV *Start = getSCEVAtScope(AddRec->getStart(),
4684 L->getParentLoop());
4685 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1),
4686 L->getParentLoop());
4688 if (const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) {
4689 // For now we handle only constant steps.
4691 // First, handle unitary steps.
4692 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so:
4693 return getNegativeSCEV(Start); // N = -Start (as unsigned)
4694 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so:
4695 return Start; // N = Start (as unsigned)
4697 // Then, try to solve the above equation provided that Start is constant.
4698 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
4699 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
4700 -StartC->getValue()->getValue(),
4703 } else if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
4704 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
4705 // the quadratic equation to solve it.
4706 std::pair<const SCEV *,const SCEV *> Roots = SolveQuadraticEquation(AddRec,
4708 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
4709 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
4712 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1
4713 << " sol#2: " << *R2 << "\n";
4715 // Pick the smallest positive root value.
4716 if (ConstantInt *CB =
4717 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
4718 R1->getValue(), R2->getValue()))) {
4719 if (CB->getZExtValue() == false)
4720 std::swap(R1, R2); // R1 is the minimum root now.
4722 // We can only use this value if the chrec ends up with an exact zero
4723 // value at this index. When solving for "X*X != 5", for example, we
4724 // should not accept a root of 2.
4725 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
4727 return R1; // We found a quadratic root!
4732 return getCouldNotCompute();
4735 /// HowFarToNonZero - Return the number of times a backedge checking the
4736 /// specified value for nonzero will execute. If not computable, return
4738 ScalarEvolution::BackedgeTakenInfo
4739 ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
4740 // Loops that look like: while (X == 0) are very strange indeed. We don't
4741 // handle them yet except for the trivial case. This could be expanded in the
4742 // future as needed.
4744 // If the value is a constant, check to see if it is known to be non-zero
4745 // already. If so, the backedge will execute zero times.
4746 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
4747 if (!C->getValue()->isNullValue())
4748 return getConstant(C->getType(), 0);
4749 return getCouldNotCompute(); // Otherwise it will loop infinitely.
4752 // We could implement others, but I really doubt anyone writes loops like
4753 // this, and if they did, they would already be constant folded.
4754 return getCouldNotCompute();
4757 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
4758 /// (which may not be an immediate predecessor) which has exactly one
4759 /// successor from which BB is reachable, or null if no such block is
4762 std::pair<BasicBlock *, BasicBlock *>
4763 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
4764 // If the block has a unique predecessor, then there is no path from the
4765 // predecessor to the block that does not go through the direct edge
4766 // from the predecessor to the block.
4767 if (BasicBlock *Pred = BB->getSinglePredecessor())
4768 return std::make_pair(Pred, BB);
4770 // A loop's header is defined to be a block that dominates the loop.
4771 // If the header has a unique predecessor outside the loop, it must be
4772 // a block that has exactly one successor that can reach the loop.
4773 if (Loop *L = LI->getLoopFor(BB))
4774 return std::make_pair(L->getLoopPredecessor(), L->getHeader());
4776 return std::pair<BasicBlock *, BasicBlock *>();
4779 /// HasSameValue - SCEV structural equivalence is usually sufficient for
4780 /// testing whether two expressions are equal, however for the purposes of
4781 /// looking for a condition guarding a loop, it can be useful to be a little
4782 /// more general, since a front-end may have replicated the controlling
4785 static bool HasSameValue(const SCEV *A, const SCEV *B) {
4786 // Quick check to see if they are the same SCEV.
4787 if (A == B) return true;
4789 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
4790 // two different instructions with the same value. Check for this case.
4791 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
4792 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
4793 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
4794 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
4795 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory())
4798 // Otherwise assume they may have a different value.
4802 /// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with
4803 /// predicate Pred. Return true iff any changes were made.
4805 bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
4806 const SCEV *&LHS, const SCEV *&RHS) {
4807 bool Changed = false;
4809 // Canonicalize a constant to the right side.
4810 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
4811 // Check for both operands constant.
4812 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
4813 if (ConstantExpr::getICmp(Pred,
4815 RHSC->getValue())->isNullValue())
4816 goto trivially_false;
4818 goto trivially_true;
4820 // Otherwise swap the operands to put the constant on the right.
4821 std::swap(LHS, RHS);
4822 Pred = ICmpInst::getSwappedPredicate(Pred);
4826 // If we're comparing an addrec with a value which is loop-invariant in the
4827 // addrec's loop, put the addrec on the left. Also make a dominance check,
4828 // as both operands could be addrecs loop-invariant in each other's loop.
4829 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
4830 const Loop *L = AR->getLoop();
4831 if (LHS->isLoopInvariant(L) && LHS->properlyDominates(L->getHeader(), DT)) {
4832 std::swap(LHS, RHS);
4833 Pred = ICmpInst::getSwappedPredicate(Pred);
4838 // If there's a constant operand, canonicalize comparisons with boundary
4839 // cases, and canonicalize *-or-equal comparisons to regular comparisons.
4840 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
4841 const APInt &RA = RC->getValue()->getValue();
4843 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
4844 case ICmpInst::ICMP_EQ:
4845 case ICmpInst::ICMP_NE:
4847 case ICmpInst::ICMP_UGE:
4848 if ((RA - 1).isMinValue()) {
4849 Pred = ICmpInst::ICMP_NE;
4850 RHS = getConstant(RA - 1);
4854 if (RA.isMaxValue()) {
4855 Pred = ICmpInst::ICMP_EQ;
4859 if (RA.isMinValue()) goto trivially_true;
4861 Pred = ICmpInst::ICMP_UGT;
4862 RHS = getConstant(RA - 1);
4865 case ICmpInst::ICMP_ULE:
4866 if ((RA + 1).isMaxValue()) {
4867 Pred = ICmpInst::ICMP_NE;
4868 RHS = getConstant(RA + 1);
4872 if (RA.isMinValue()) {
4873 Pred = ICmpInst::ICMP_EQ;
4877 if (RA.isMaxValue()) goto trivially_true;
4879 Pred = ICmpInst::ICMP_ULT;
4880 RHS = getConstant(RA + 1);
4883 case ICmpInst::ICMP_SGE:
4884 if ((RA - 1).isMinSignedValue()) {
4885 Pred = ICmpInst::ICMP_NE;
4886 RHS = getConstant(RA - 1);
4890 if (RA.isMaxSignedValue()) {
4891 Pred = ICmpInst::ICMP_EQ;
4895 if (RA.isMinSignedValue()) goto trivially_true;
4897 Pred = ICmpInst::ICMP_SGT;
4898 RHS = getConstant(RA - 1);
4901 case ICmpInst::ICMP_SLE:
4902 if ((RA + 1).isMaxSignedValue()) {
4903 Pred = ICmpInst::ICMP_NE;
4904 RHS = getConstant(RA + 1);
4908 if (RA.isMinSignedValue()) {
4909 Pred = ICmpInst::ICMP_EQ;
4913 if (RA.isMaxSignedValue()) goto trivially_true;
4915 Pred = ICmpInst::ICMP_SLT;
4916 RHS = getConstant(RA + 1);
4919 case ICmpInst::ICMP_UGT:
4920 if (RA.isMinValue()) {
4921 Pred = ICmpInst::ICMP_NE;
4925 if ((RA + 1).isMaxValue()) {
4926 Pred = ICmpInst::ICMP_EQ;
4927 RHS = getConstant(RA + 1);
4931 if (RA.isMaxValue()) goto trivially_false;
4933 case ICmpInst::ICMP_ULT:
4934 if (RA.isMaxValue()) {
4935 Pred = ICmpInst::ICMP_NE;
4939 if ((RA - 1).isMinValue()) {
4940 Pred = ICmpInst::ICMP_EQ;
4941 RHS = getConstant(RA - 1);
4945 if (RA.isMinValue()) goto trivially_false;
4947 case ICmpInst::ICMP_SGT:
4948 if (RA.isMinSignedValue()) {
4949 Pred = ICmpInst::ICMP_NE;
4953 if ((RA + 1).isMaxSignedValue()) {
4954 Pred = ICmpInst::ICMP_EQ;
4955 RHS = getConstant(RA + 1);
4959 if (RA.isMaxSignedValue()) goto trivially_false;
4961 case ICmpInst::ICMP_SLT:
4962 if (RA.isMaxSignedValue()) {
4963 Pred = ICmpInst::ICMP_NE;
4967 if ((RA - 1).isMinSignedValue()) {
4968 Pred = ICmpInst::ICMP_EQ;
4969 RHS = getConstant(RA - 1);
4973 if (RA.isMinSignedValue()) goto trivially_false;
4978 // Check for obvious equality.
4979 if (HasSameValue(LHS, RHS)) {
4980 if (ICmpInst::isTrueWhenEqual(Pred))
4981 goto trivially_true;
4982 if (ICmpInst::isFalseWhenEqual(Pred))
4983 goto trivially_false;
4986 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
4987 // adding or subtracting 1 from one of the operands.
4989 case ICmpInst::ICMP_SLE:
4990 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) {
4991 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
4992 /*HasNUW=*/false, /*HasNSW=*/true);
4993 Pred = ICmpInst::ICMP_SLT;
4995 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) {
4996 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
4997 /*HasNUW=*/false, /*HasNSW=*/true);
4998 Pred = ICmpInst::ICMP_SLT;
5002 case ICmpInst::ICMP_SGE:
5003 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) {
5004 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
5005 /*HasNUW=*/false, /*HasNSW=*/true);
5006 Pred = ICmpInst::ICMP_SGT;
5008 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) {
5009 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
5010 /*HasNUW=*/false, /*HasNSW=*/true);
5011 Pred = ICmpInst::ICMP_SGT;
5015 case ICmpInst::ICMP_ULE:
5016 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) {
5017 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
5018 /*HasNUW=*/true, /*HasNSW=*/false);
5019 Pred = ICmpInst::ICMP_ULT;
5021 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) {
5022 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
5023 /*HasNUW=*/true, /*HasNSW=*/false);
5024 Pred = ICmpInst::ICMP_ULT;
5028 case ICmpInst::ICMP_UGE:
5029 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) {
5030 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
5031 /*HasNUW=*/true, /*HasNSW=*/false);
5032 Pred = ICmpInst::ICMP_UGT;
5034 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) {
5035 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
5036 /*HasNUW=*/true, /*HasNSW=*/false);
5037 Pred = ICmpInst::ICMP_UGT;
5045 // TODO: More simplifications are possible here.
5051 LHS = RHS = getConstant(Type::getInt1Ty(getContext()), 0);
5052 Pred = ICmpInst::ICMP_EQ;
5057 LHS = RHS = getConstant(Type::getInt1Ty(getContext()), 0);
5058 Pred = ICmpInst::ICMP_NE;
5062 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
5063 return getSignedRange(S).getSignedMax().isNegative();
5066 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
5067 return getSignedRange(S).getSignedMin().isStrictlyPositive();
5070 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
5071 return !getSignedRange(S).getSignedMin().isNegative();
5074 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
5075 return !getSignedRange(S).getSignedMax().isStrictlyPositive();
5078 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
5079 return isKnownNegative(S) || isKnownPositive(S);
5082 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
5083 const SCEV *LHS, const SCEV *RHS) {
5084 // Canonicalize the inputs first.
5085 (void)SimplifyICmpOperands(Pred, LHS, RHS);
5087 // If LHS or RHS is an addrec, check to see if the condition is true in
5088 // every iteration of the loop.
5089 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
5090 if (isLoopEntryGuardedByCond(
5091 AR->getLoop(), Pred, AR->getStart(), RHS) &&
5092 isLoopBackedgeGuardedByCond(
5093 AR->getLoop(), Pred, AR->getPostIncExpr(*this), RHS))
5095 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS))
5096 if (isLoopEntryGuardedByCond(
5097 AR->getLoop(), Pred, LHS, AR->getStart()) &&
5098 isLoopBackedgeGuardedByCond(
5099 AR->getLoop(), Pred, LHS, AR->getPostIncExpr(*this)))
5102 // Otherwise see what can be done with known constant ranges.
5103 return isKnownPredicateWithRanges(Pred, LHS, RHS);
5107 ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred,
5108 const SCEV *LHS, const SCEV *RHS) {
5109 if (HasSameValue(LHS, RHS))
5110 return ICmpInst::isTrueWhenEqual(Pred);
5112 // This code is split out from isKnownPredicate because it is called from
5113 // within isLoopEntryGuardedByCond.
5116 llvm_unreachable("Unexpected ICmpInst::Predicate value!");
5118 case ICmpInst::ICMP_SGT:
5119 Pred = ICmpInst::ICMP_SLT;
5120 std::swap(LHS, RHS);
5121 case ICmpInst::ICMP_SLT: {
5122 ConstantRange LHSRange = getSignedRange(LHS);
5123 ConstantRange RHSRange = getSignedRange(RHS);
5124 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
5126 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
5130 case ICmpInst::ICMP_SGE:
5131 Pred = ICmpInst::ICMP_SLE;
5132 std::swap(LHS, RHS);
5133 case ICmpInst::ICMP_SLE: {
5134 ConstantRange LHSRange = getSignedRange(LHS);
5135 ConstantRange RHSRange = getSignedRange(RHS);
5136 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
5138 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
5142 case ICmpInst::ICMP_UGT:
5143 Pred = ICmpInst::ICMP_ULT;
5144 std::swap(LHS, RHS);
5145 case ICmpInst::ICMP_ULT: {
5146 ConstantRange LHSRange = getUnsignedRange(LHS);
5147 ConstantRange RHSRange = getUnsignedRange(RHS);
5148 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
5150 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
5154 case ICmpInst::ICMP_UGE:
5155 Pred = ICmpInst::ICMP_ULE;
5156 std::swap(LHS, RHS);
5157 case ICmpInst::ICMP_ULE: {
5158 ConstantRange LHSRange = getUnsignedRange(LHS);
5159 ConstantRange RHSRange = getUnsignedRange(RHS);
5160 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
5162 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
5166 case ICmpInst::ICMP_NE: {
5167 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
5169 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
5172 const SCEV *Diff = getMinusSCEV(LHS, RHS);
5173 if (isKnownNonZero(Diff))
5177 case ICmpInst::ICMP_EQ:
5178 // The check at the top of the function catches the case where
5179 // the values are known to be equal.
5185 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
5186 /// protected by a conditional between LHS and RHS. This is used to
5187 /// to eliminate casts.
5189 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
5190 ICmpInst::Predicate Pred,
5191 const SCEV *LHS, const SCEV *RHS) {
5192 // Interpret a null as meaning no loop, where there is obviously no guard
5193 // (interprocedural conditions notwithstanding).
5194 if (!L) return true;
5196 BasicBlock *Latch = L->getLoopLatch();
5200 BranchInst *LoopContinuePredicate =
5201 dyn_cast<BranchInst>(Latch->getTerminator());
5202 if (!LoopContinuePredicate ||
5203 LoopContinuePredicate->isUnconditional())
5206 return isImpliedCond(LoopContinuePredicate->getCondition(), Pred, LHS, RHS,
5207 LoopContinuePredicate->getSuccessor(0) != L->getHeader());
5210 /// isLoopEntryGuardedByCond - Test whether entry to the loop is protected
5211 /// by a conditional between LHS and RHS. This is used to help avoid max
5212 /// expressions in loop trip counts, and to eliminate casts.
5214 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
5215 ICmpInst::Predicate Pred,
5216 const SCEV *LHS, const SCEV *RHS) {
5217 // Interpret a null as meaning no loop, where there is obviously no guard
5218 // (interprocedural conditions notwithstanding).
5219 if (!L) return false;
5221 // Starting at the loop predecessor, climb up the predecessor chain, as long
5222 // as there are predecessors that can be found that have unique successors
5223 // leading to the original header.
5224 for (std::pair<BasicBlock *, BasicBlock *>
5225 Pair(L->getLoopPredecessor(), L->getHeader());
5227 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
5229 BranchInst *LoopEntryPredicate =
5230 dyn_cast<BranchInst>(Pair.first->getTerminator());
5231 if (!LoopEntryPredicate ||
5232 LoopEntryPredicate->isUnconditional())
5235 if (isImpliedCond(LoopEntryPredicate->getCondition(), Pred, LHS, RHS,
5236 LoopEntryPredicate->getSuccessor(0) != Pair.second))
5243 /// isImpliedCond - Test whether the condition described by Pred, LHS,
5244 /// and RHS is true whenever the given Cond value evaluates to true.
5245 bool ScalarEvolution::isImpliedCond(Value *CondValue,
5246 ICmpInst::Predicate Pred,
5247 const SCEV *LHS, const SCEV *RHS,
5249 // Recursively handle And and Or conditions.
5250 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(CondValue)) {
5251 if (BO->getOpcode() == Instruction::And) {
5253 return isImpliedCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) ||
5254 isImpliedCond(BO->getOperand(1), Pred, LHS, RHS, Inverse);
5255 } else if (BO->getOpcode() == Instruction::Or) {
5257 return isImpliedCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) ||
5258 isImpliedCond(BO->getOperand(1), Pred, LHS, RHS, Inverse);
5262 ICmpInst *ICI = dyn_cast<ICmpInst>(CondValue);
5263 if (!ICI) return false;
5265 // Bail if the ICmp's operands' types are wider than the needed type
5266 // before attempting to call getSCEV on them. This avoids infinite
5267 // recursion, since the analysis of widening casts can require loop
5268 // exit condition information for overflow checking, which would
5270 if (getTypeSizeInBits(LHS->getType()) <
5271 getTypeSizeInBits(ICI->getOperand(0)->getType()))
5274 // Now that we found a conditional branch that dominates the loop, check to
5275 // see if it is the comparison we are looking for.
5276 ICmpInst::Predicate FoundPred;
5278 FoundPred = ICI->getInversePredicate();
5280 FoundPred = ICI->getPredicate();
5282 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
5283 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
5285 // Balance the types. The case where FoundLHS' type is wider than
5286 // LHS' type is checked for above.
5287 if (getTypeSizeInBits(LHS->getType()) >
5288 getTypeSizeInBits(FoundLHS->getType())) {
5289 if (CmpInst::isSigned(Pred)) {
5290 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
5291 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
5293 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
5294 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
5298 // Canonicalize the query to match the way instcombine will have
5299 // canonicalized the comparison.
5300 if (SimplifyICmpOperands(Pred, LHS, RHS))
5302 return CmpInst::isTrueWhenEqual(Pred);
5303 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
5304 if (FoundLHS == FoundRHS)
5305 return CmpInst::isFalseWhenEqual(Pred);
5307 // Check to see if we can make the LHS or RHS match.
5308 if (LHS == FoundRHS || RHS == FoundLHS) {
5309 if (isa<SCEVConstant>(RHS)) {
5310 std::swap(FoundLHS, FoundRHS);
5311 FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
5313 std::swap(LHS, RHS);
5314 Pred = ICmpInst::getSwappedPredicate(Pred);
5318 // Check whether the found predicate is the same as the desired predicate.
5319 if (FoundPred == Pred)
5320 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
5322 // Check whether swapping the found predicate makes it the same as the
5323 // desired predicate.
5324 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
5325 if (isa<SCEVConstant>(RHS))
5326 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
5328 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
5329 RHS, LHS, FoundLHS, FoundRHS);
5332 // Check whether the actual condition is beyond sufficient.
5333 if (FoundPred == ICmpInst::ICMP_EQ)
5334 if (ICmpInst::isTrueWhenEqual(Pred))
5335 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
5337 if (Pred == ICmpInst::ICMP_NE)
5338 if (!ICmpInst::isTrueWhenEqual(FoundPred))
5339 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
5342 // Otherwise assume the worst.
5346 /// isImpliedCondOperands - Test whether the condition described by Pred,
5347 /// LHS, and RHS is true whenever the condition described by Pred, FoundLHS,
5348 /// and FoundRHS is true.
5349 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
5350 const SCEV *LHS, const SCEV *RHS,
5351 const SCEV *FoundLHS,
5352 const SCEV *FoundRHS) {
5353 return isImpliedCondOperandsHelper(Pred, LHS, RHS,
5354 FoundLHS, FoundRHS) ||
5355 // ~x < ~y --> x > y
5356 isImpliedCondOperandsHelper(Pred, LHS, RHS,
5357 getNotSCEV(FoundRHS),
5358 getNotSCEV(FoundLHS));
5361 /// isImpliedCondOperandsHelper - Test whether the condition described by
5362 /// Pred, LHS, and RHS is true whenever the condition described by Pred,
5363 /// FoundLHS, and FoundRHS is true.
5365 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
5366 const SCEV *LHS, const SCEV *RHS,
5367 const SCEV *FoundLHS,
5368 const SCEV *FoundRHS) {
5370 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
5371 case ICmpInst::ICMP_EQ:
5372 case ICmpInst::ICMP_NE:
5373 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
5376 case ICmpInst::ICMP_SLT:
5377 case ICmpInst::ICMP_SLE:
5378 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
5379 isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, RHS, FoundRHS))
5382 case ICmpInst::ICMP_SGT:
5383 case ICmpInst::ICMP_SGE:
5384 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
5385 isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, RHS, FoundRHS))
5388 case ICmpInst::ICMP_ULT:
5389 case ICmpInst::ICMP_ULE:
5390 if (isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
5391 isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, RHS, FoundRHS))
5394 case ICmpInst::ICMP_UGT:
5395 case ICmpInst::ICMP_UGE:
5396 if (isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
5397 isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, RHS, FoundRHS))
5405 /// getBECount - Subtract the end and start values and divide by the step,
5406 /// rounding up, to get the number of times the backedge is executed. Return
5407 /// CouldNotCompute if an intermediate computation overflows.
5408 const SCEV *ScalarEvolution::getBECount(const SCEV *Start,
5412 assert(!isKnownNegative(Step) &&
5413 "This code doesn't handle negative strides yet!");
5415 const Type *Ty = Start->getType();
5416 const SCEV *NegOne = getConstant(Ty, (uint64_t)-1);
5417 const SCEV *Diff = getMinusSCEV(End, Start);
5418 const SCEV *RoundUp = getAddExpr(Step, NegOne);
5420 // Add an adjustment to the difference between End and Start so that
5421 // the division will effectively round up.
5422 const SCEV *Add = getAddExpr(Diff, RoundUp);
5425 // Check Add for unsigned overflow.
5426 // TODO: More sophisticated things could be done here.
5427 const Type *WideTy = IntegerType::get(getContext(),
5428 getTypeSizeInBits(Ty) + 1);
5429 const SCEV *EDiff = getZeroExtendExpr(Diff, WideTy);
5430 const SCEV *ERoundUp = getZeroExtendExpr(RoundUp, WideTy);
5431 const SCEV *OperandExtendedAdd = getAddExpr(EDiff, ERoundUp);
5432 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd)
5433 return getCouldNotCompute();
5436 return getUDivExpr(Add, Step);
5439 /// HowManyLessThans - Return the number of times a backedge containing the
5440 /// specified less-than comparison will execute. If not computable, return
5441 /// CouldNotCompute.
5442 ScalarEvolution::BackedgeTakenInfo
5443 ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
5444 const Loop *L, bool isSigned) {
5445 // Only handle: "ADDREC < LoopInvariant".
5446 if (!RHS->isLoopInvariant(L)) return getCouldNotCompute();
5448 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
5449 if (!AddRec || AddRec->getLoop() != L)
5450 return getCouldNotCompute();
5452 // Check to see if we have a flag which makes analysis easy.
5453 bool NoWrap = isSigned ? AddRec->hasNoSignedWrap() :
5454 AddRec->hasNoUnsignedWrap();
5456 if (AddRec->isAffine()) {
5457 unsigned BitWidth = getTypeSizeInBits(AddRec->getType());
5458 const SCEV *Step = AddRec->getStepRecurrence(*this);
5461 return getCouldNotCompute();
5462 if (Step->isOne()) {
5463 // With unit stride, the iteration never steps past the limit value.
5464 } else if (isKnownPositive(Step)) {
5465 // Test whether a positive iteration can step past the limit
5466 // value and past the maximum value for its type in a single step.
5467 // Note that it's not sufficient to check NoWrap here, because even
5468 // though the value after a wrap is undefined, it's not undefined
5469 // behavior, so if wrap does occur, the loop could either terminate or
5470 // loop infinitely, but in either case, the loop is guaranteed to
5471 // iterate at least until the iteration where the wrapping occurs.
5472 const SCEV *One = getConstant(Step->getType(), 1);
5474 APInt Max = APInt::getSignedMaxValue(BitWidth);
5475 if ((Max - getSignedRange(getMinusSCEV(Step, One)).getSignedMax())
5476 .slt(getSignedRange(RHS).getSignedMax()))
5477 return getCouldNotCompute();
5479 APInt Max = APInt::getMaxValue(BitWidth);
5480 if ((Max - getUnsignedRange(getMinusSCEV(Step, One)).getUnsignedMax())
5481 .ult(getUnsignedRange(RHS).getUnsignedMax()))
5482 return getCouldNotCompute();
5485 // TODO: Handle negative strides here and below.
5486 return getCouldNotCompute();
5488 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant
5489 // m. So, we count the number of iterations in which {n,+,s} < m is true.
5490 // Note that we cannot simply return max(m-n,0)/s because it's not safe to
5491 // treat m-n as signed nor unsigned due to overflow possibility.
5493 // First, we get the value of the LHS in the first iteration: n
5494 const SCEV *Start = AddRec->getOperand(0);
5496 // Determine the minimum constant start value.
5497 const SCEV *MinStart = getConstant(isSigned ?
5498 getSignedRange(Start).getSignedMin() :
5499 getUnsignedRange(Start).getUnsignedMin());
5501 // If we know that the condition is true in order to enter the loop,
5502 // then we know that it will run exactly (m-n)/s times. Otherwise, we
5503 // only know that it will execute (max(m,n)-n)/s times. In both cases,
5504 // the division must round up.
5505 const SCEV *End = RHS;
5506 if (!isLoopEntryGuardedByCond(L,
5507 isSigned ? ICmpInst::ICMP_SLT :
5509 getMinusSCEV(Start, Step), RHS))
5510 End = isSigned ? getSMaxExpr(RHS, Start)
5511 : getUMaxExpr(RHS, Start);
5513 // Determine the maximum constant end value.
5514 const SCEV *MaxEnd = getConstant(isSigned ?
5515 getSignedRange(End).getSignedMax() :
5516 getUnsignedRange(End).getUnsignedMax());
5518 // If MaxEnd is within a step of the maximum integer value in its type,
5519 // adjust it down to the minimum value which would produce the same effect.
5520 // This allows the subsequent ceiling division of (N+(step-1))/step to
5521 // compute the correct value.
5522 const SCEV *StepMinusOne = getMinusSCEV(Step,
5523 getConstant(Step->getType(), 1));
5526 getMinusSCEV(getConstant(APInt::getSignedMaxValue(BitWidth)),
5529 getMinusSCEV(getConstant(APInt::getMaxValue(BitWidth)),
5532 // Finally, we subtract these two values and divide, rounding up, to get
5533 // the number of times the backedge is executed.
5534 const SCEV *BECount = getBECount(Start, End, Step, NoWrap);
5536 // The maximum backedge count is similar, except using the minimum start
5537 // value and the maximum end value.
5538 const SCEV *MaxBECount = getBECount(MinStart, MaxEnd, Step, NoWrap);
5540 return BackedgeTakenInfo(BECount, MaxBECount);
5543 return getCouldNotCompute();
5546 /// getNumIterationsInRange - Return the number of iterations of this loop that
5547 /// produce values in the specified constant range. Another way of looking at
5548 /// this is that it returns the first iteration number where the value is not in
5549 /// the condition, thus computing the exit count. If the iteration count can't
5550 /// be computed, an instance of SCEVCouldNotCompute is returned.
5551 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
5552 ScalarEvolution &SE) const {
5553 if (Range.isFullSet()) // Infinite loop.
5554 return SE.getCouldNotCompute();
5556 // If the start is a non-zero constant, shift the range to simplify things.
5557 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
5558 if (!SC->getValue()->isZero()) {
5559 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
5560 Operands[0] = SE.getConstant(SC->getType(), 0);
5561 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop());
5562 if (const SCEVAddRecExpr *ShiftedAddRec =
5563 dyn_cast<SCEVAddRecExpr>(Shifted))
5564 return ShiftedAddRec->getNumIterationsInRange(
5565 Range.subtract(SC->getValue()->getValue()), SE);
5566 // This is strange and shouldn't happen.
5567 return SE.getCouldNotCompute();
5570 // The only time we can solve this is when we have all constant indices.
5571 // Otherwise, we cannot determine the overflow conditions.
5572 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
5573 if (!isa<SCEVConstant>(getOperand(i)))
5574 return SE.getCouldNotCompute();
5577 // Okay at this point we know that all elements of the chrec are constants and
5578 // that the start element is zero.
5580 // First check to see if the range contains zero. If not, the first
5582 unsigned BitWidth = SE.getTypeSizeInBits(getType());
5583 if (!Range.contains(APInt(BitWidth, 0)))
5584 return SE.getConstant(getType(), 0);
5587 // If this is an affine expression then we have this situation:
5588 // Solve {0,+,A} in Range === Ax in Range
5590 // We know that zero is in the range. If A is positive then we know that
5591 // the upper value of the range must be the first possible exit value.
5592 // If A is negative then the lower of the range is the last possible loop
5593 // value. Also note that we already checked for a full range.
5594 APInt One(BitWidth,1);
5595 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
5596 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
5598 // The exit value should be (End+A)/A.
5599 APInt ExitVal = (End + A).udiv(A);
5600 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
5602 // Evaluate at the exit value. If we really did fall out of the valid
5603 // range, then we computed our trip count, otherwise wrap around or other
5604 // things must have happened.
5605 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
5606 if (Range.contains(Val->getValue()))
5607 return SE.getCouldNotCompute(); // Something strange happened
5609 // Ensure that the previous value is in the range. This is a sanity check.
5610 assert(Range.contains(
5611 EvaluateConstantChrecAtConstant(this,
5612 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
5613 "Linear scev computation is off in a bad way!");
5614 return SE.getConstant(ExitValue);
5615 } else if (isQuadratic()) {
5616 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
5617 // quadratic equation to solve it. To do this, we must frame our problem in
5618 // terms of figuring out when zero is crossed, instead of when
5619 // Range.getUpper() is crossed.
5620 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
5621 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
5622 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop());
5624 // Next, solve the constructed addrec
5625 std::pair<const SCEV *,const SCEV *> Roots =
5626 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
5627 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
5628 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
5630 // Pick the smallest positive root value.
5631 if (ConstantInt *CB =
5632 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
5633 R1->getValue(), R2->getValue()))) {
5634 if (CB->getZExtValue() == false)
5635 std::swap(R1, R2); // R1 is the minimum root now.
5637 // Make sure the root is not off by one. The returned iteration should
5638 // not be in the range, but the previous one should be. When solving
5639 // for "X*X < 5", for example, we should not return a root of 2.
5640 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
5643 if (Range.contains(R1Val->getValue())) {
5644 // The next iteration must be out of the range...
5645 ConstantInt *NextVal =
5646 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1);
5648 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
5649 if (!Range.contains(R1Val->getValue()))
5650 return SE.getConstant(NextVal);
5651 return SE.getCouldNotCompute(); // Something strange happened
5654 // If R1 was not in the range, then it is a good return value. Make
5655 // sure that R1-1 WAS in the range though, just in case.
5656 ConstantInt *NextVal =
5657 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1);
5658 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
5659 if (Range.contains(R1Val->getValue()))
5661 return SE.getCouldNotCompute(); // Something strange happened
5666 return SE.getCouldNotCompute();
5671 //===----------------------------------------------------------------------===//
5672 // SCEVCallbackVH Class Implementation
5673 //===----------------------------------------------------------------------===//
5675 void ScalarEvolution::SCEVCallbackVH::deleted() {
5676 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
5677 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
5678 SE->ConstantEvolutionLoopExitValue.erase(PN);
5679 SE->Scalars.erase(getValPtr());
5680 // this now dangles!
5683 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *) {
5684 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
5686 // Forget all the expressions associated with users of the old value,
5687 // so that future queries will recompute the expressions using the new
5689 SmallVector<User *, 16> Worklist;
5690 SmallPtrSet<User *, 8> Visited;
5691 Value *Old = getValPtr();
5692 bool DeleteOld = false;
5693 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end();
5695 Worklist.push_back(*UI);
5696 while (!Worklist.empty()) {
5697 User *U = Worklist.pop_back_val();
5698 // Deleting the Old value will cause this to dangle. Postpone
5699 // that until everything else is done.
5704 if (!Visited.insert(U))
5706 if (PHINode *PN = dyn_cast<PHINode>(U))
5707 SE->ConstantEvolutionLoopExitValue.erase(PN);
5708 SE->Scalars.erase(U);
5709 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end();
5711 Worklist.push_back(*UI);
5713 // Delete the Old value if it (indirectly) references itself.
5715 if (PHINode *PN = dyn_cast<PHINode>(Old))
5716 SE->ConstantEvolutionLoopExitValue.erase(PN);
5717 SE->Scalars.erase(Old);
5718 // this now dangles!
5723 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
5724 : CallbackVH(V), SE(se) {}
5726 //===----------------------------------------------------------------------===//
5727 // ScalarEvolution Class Implementation
5728 //===----------------------------------------------------------------------===//
5730 ScalarEvolution::ScalarEvolution()
5731 : FunctionPass(&ID) {
5734 bool ScalarEvolution::runOnFunction(Function &F) {
5736 LI = &getAnalysis<LoopInfo>();
5737 TD = getAnalysisIfAvailable<TargetData>();
5738 DT = &getAnalysis<DominatorTree>();
5742 void ScalarEvolution::releaseMemory() {
5744 BackedgeTakenCounts.clear();
5745 ConstantEvolutionLoopExitValue.clear();
5746 ValuesAtScopes.clear();
5747 UniqueSCEVs.clear();
5748 SCEVAllocator.Reset();
5751 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
5752 AU.setPreservesAll();
5753 AU.addRequiredTransitive<LoopInfo>();
5754 AU.addRequiredTransitive<DominatorTree>();
5757 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
5758 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
5761 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
5763 // Print all inner loops first
5764 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
5765 PrintLoopInfo(OS, SE, *I);
5768 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
5771 SmallVector<BasicBlock *, 8> ExitBlocks;
5772 L->getExitBlocks(ExitBlocks);
5773 if (ExitBlocks.size() != 1)
5774 OS << "<multiple exits> ";
5776 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
5777 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
5779 OS << "Unpredictable backedge-taken count. ";
5784 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
5787 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
5788 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
5790 OS << "Unpredictable max backedge-taken count. ";
5796 void ScalarEvolution::print(raw_ostream &OS, const Module *) const {
5797 // ScalarEvolution's implementation of the print method is to print
5798 // out SCEV values of all instructions that are interesting. Doing
5799 // this potentially causes it to create new SCEV objects though,
5800 // which technically conflicts with the const qualifier. This isn't
5801 // observable from outside the class though, so casting away the
5802 // const isn't dangerous.
5803 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
5805 OS << "Classifying expressions for: ";
5806 WriteAsOperand(OS, F, /*PrintType=*/false);
5808 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
5809 if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) {
5812 const SCEV *SV = SE.getSCEV(&*I);
5815 const Loop *L = LI->getLoopFor((*I).getParent());
5817 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
5824 OS << "\t\t" "Exits: ";
5825 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
5826 if (!ExitValue->isLoopInvariant(L)) {
5827 OS << "<<Unknown>>";
5836 OS << "Determining loop execution counts for: ";
5837 WriteAsOperand(OS, F, /*PrintType=*/false);
5839 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
5840 PrintLoopInfo(OS, &SE, *I);