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) {
254 if (llvm::next(I) != E)
260 bool SCEVNAryExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
261 for (op_iterator I = op_begin(), E = op_end(); I != E; ++I)
262 if (!(*I)->dominates(BB, DT))
267 bool SCEVNAryExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const {
268 for (op_iterator I = op_begin(), E = op_end(); I != E; ++I)
269 if (!(*I)->properlyDominates(BB, DT))
274 bool SCEVNAryExpr::isLoopInvariant(const Loop *L) const {
275 for (op_iterator I = op_begin(), E = op_end(); I != E; ++I)
276 if (!(*I)->isLoopInvariant(L))
281 // hasComputableLoopEvolution - N-ary expressions have computable loop
282 // evolutions iff they have at least one operand that varies with the loop,
283 // but that all varying operands are computable.
284 bool SCEVNAryExpr::hasComputableLoopEvolution(const Loop *L) const {
285 bool HasVarying = false;
286 for (op_iterator I = op_begin(), E = op_end(); I != E; ++I) {
288 if (!S->isLoopInvariant(L)) {
289 if (S->hasComputableLoopEvolution(L))
298 bool SCEVNAryExpr::hasOperand(const SCEV *O) const {
299 for (op_iterator I = op_begin(), E = op_end(); I != E; ++I) {
301 if (O == S || S->hasOperand(O))
307 bool SCEVUDivExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
308 return LHS->dominates(BB, DT) && RHS->dominates(BB, DT);
311 bool SCEVUDivExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const {
312 return LHS->properlyDominates(BB, DT) && RHS->properlyDominates(BB, DT);
315 void SCEVUDivExpr::print(raw_ostream &OS) const {
316 OS << "(" << *LHS << " /u " << *RHS << ")";
319 const Type *SCEVUDivExpr::getType() const {
320 // In most cases the types of LHS and RHS will be the same, but in some
321 // crazy cases one or the other may be a pointer. ScalarEvolution doesn't
322 // depend on the type for correctness, but handling types carefully can
323 // avoid extra casts in the SCEVExpander. The LHS is more likely to be
324 // a pointer type than the RHS, so use the RHS' type here.
325 return RHS->getType();
328 bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const {
329 // Add recurrences are never invariant in the function-body (null loop).
333 // This recurrence is variant w.r.t. QueryLoop if QueryLoop contains L.
334 if (QueryLoop->contains(L))
337 // This recurrence is invariant w.r.t. QueryLoop if L contains QueryLoop.
338 if (L->contains(QueryLoop))
341 // This recurrence is variant w.r.t. QueryLoop if any of its operands
343 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
344 if (!getOperand(i)->isLoopInvariant(QueryLoop))
347 // Otherwise it's loop-invariant.
352 SCEVAddRecExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
353 return DT->dominates(L->getHeader(), BB) &&
354 SCEVNAryExpr::dominates(BB, DT);
358 SCEVAddRecExpr::properlyDominates(BasicBlock *BB, DominatorTree *DT) const {
359 // This uses a "dominates" query instead of "properly dominates" query because
360 // the instruction which produces the addrec's value is a PHI, and a PHI
361 // effectively properly dominates its entire containing block.
362 return DT->dominates(L->getHeader(), BB) &&
363 SCEVNAryExpr::properlyDominates(BB, DT);
366 void SCEVAddRecExpr::print(raw_ostream &OS) const {
367 OS << "{" << *Operands[0];
368 for (unsigned i = 1, e = NumOperands; i != e; ++i)
369 OS << ",+," << *Operands[i];
371 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
375 void SCEVUnknown::deleted() {
376 // Clear this SCEVUnknown from ValuesAtScopes.
377 SE->ValuesAtScopes.erase(this);
379 // Remove this SCEVUnknown from the uniquing map.
380 SE->UniqueSCEVs.RemoveNode(this);
382 // Release the value.
386 void SCEVUnknown::allUsesReplacedWith(Value *New) {
387 // Clear this SCEVUnknown from ValuesAtScopes.
388 SE->ValuesAtScopes.erase(this);
390 // Remove this SCEVUnknown from the uniquing map.
391 SE->UniqueSCEVs.RemoveNode(this);
393 // Update this SCEVUnknown to point to the new value. This is needed
394 // because there may still be outstanding SCEVs which still point to
399 bool SCEVUnknown::isLoopInvariant(const Loop *L) const {
400 // All non-instruction values are loop invariant. All instructions are loop
401 // invariant if they are not contained in the specified loop.
402 // Instructions are never considered invariant in the function body
403 // (null loop) because they are defined within the "loop".
404 if (Instruction *I = dyn_cast<Instruction>(getValue()))
405 return L && !L->contains(I);
409 bool SCEVUnknown::dominates(BasicBlock *BB, DominatorTree *DT) const {
410 if (Instruction *I = dyn_cast<Instruction>(getValue()))
411 return DT->dominates(I->getParent(), BB);
415 bool SCEVUnknown::properlyDominates(BasicBlock *BB, DominatorTree *DT) const {
416 if (Instruction *I = dyn_cast<Instruction>(getValue()))
417 return DT->properlyDominates(I->getParent(), BB);
421 const Type *SCEVUnknown::getType() const {
422 return getValue()->getType();
425 bool SCEVUnknown::isSizeOf(const Type *&AllocTy) const {
426 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
427 if (VCE->getOpcode() == Instruction::PtrToInt)
428 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
429 if (CE->getOpcode() == Instruction::GetElementPtr &&
430 CE->getOperand(0)->isNullValue() &&
431 CE->getNumOperands() == 2)
432 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1)))
434 AllocTy = cast<PointerType>(CE->getOperand(0)->getType())
442 bool SCEVUnknown::isAlignOf(const Type *&AllocTy) const {
443 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
444 if (VCE->getOpcode() == Instruction::PtrToInt)
445 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
446 if (CE->getOpcode() == Instruction::GetElementPtr &&
447 CE->getOperand(0)->isNullValue()) {
449 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
450 if (const StructType *STy = dyn_cast<StructType>(Ty))
451 if (!STy->isPacked() &&
452 CE->getNumOperands() == 3 &&
453 CE->getOperand(1)->isNullValue()) {
454 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2)))
456 STy->getNumElements() == 2 &&
457 STy->getElementType(0)->isIntegerTy(1)) {
458 AllocTy = STy->getElementType(1);
467 bool SCEVUnknown::isOffsetOf(const Type *&CTy, Constant *&FieldNo) const {
468 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
469 if (VCE->getOpcode() == Instruction::PtrToInt)
470 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
471 if (CE->getOpcode() == Instruction::GetElementPtr &&
472 CE->getNumOperands() == 3 &&
473 CE->getOperand(0)->isNullValue() &&
474 CE->getOperand(1)->isNullValue()) {
476 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
477 // Ignore vector types here so that ScalarEvolutionExpander doesn't
478 // emit getelementptrs that index into vectors.
479 if (Ty->isStructTy() || Ty->isArrayTy()) {
481 FieldNo = CE->getOperand(2);
489 void SCEVUnknown::print(raw_ostream &OS) const {
491 if (isSizeOf(AllocTy)) {
492 OS << "sizeof(" << *AllocTy << ")";
495 if (isAlignOf(AllocTy)) {
496 OS << "alignof(" << *AllocTy << ")";
502 if (isOffsetOf(CTy, FieldNo)) {
503 OS << "offsetof(" << *CTy << ", ";
504 WriteAsOperand(OS, FieldNo, false);
509 // Otherwise just print it normally.
510 WriteAsOperand(OS, getValue(), false);
513 //===----------------------------------------------------------------------===//
515 //===----------------------------------------------------------------------===//
518 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
519 /// than the complexity of the RHS. This comparator is used to canonicalize
521 class SCEVComplexityCompare {
522 const LoopInfo *const LI;
524 explicit SCEVComplexityCompare(const LoopInfo *li) : LI(li) {}
526 // Return true or false if LHS is less than, or at least RHS, respectively.
527 bool operator()(const SCEV *LHS, const SCEV *RHS) const {
528 return compare(LHS, RHS) < 0;
531 // Return negative, zero, or positive, if LHS is less than, equal to, or
532 // greater than RHS, respectively. A three-way result allows recursive
533 // comparisons to be more efficient.
534 int compare(const SCEV *LHS, const SCEV *RHS) const {
535 // Fast-path: SCEVs are uniqued so we can do a quick equality check.
539 // Primarily, sort the SCEVs by their getSCEVType().
540 unsigned LType = LHS->getSCEVType(), RType = RHS->getSCEVType();
542 return (int)LType - (int)RType;
544 // Aside from the getSCEVType() ordering, the particular ordering
545 // isn't very important except that it's beneficial to be consistent,
546 // so that (a + b) and (b + a) don't end up as different expressions.
549 const SCEVUnknown *LU = cast<SCEVUnknown>(LHS);
550 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
552 // Sort SCEVUnknown values with some loose heuristics. TODO: This is
553 // not as complete as it could be.
554 const Value *LV = LU->getValue(), *RV = RU->getValue();
556 // Order pointer values after integer values. This helps SCEVExpander
558 bool LIsPointer = LV->getType()->isPointerTy(),
559 RIsPointer = RV->getType()->isPointerTy();
560 if (LIsPointer != RIsPointer)
561 return (int)LIsPointer - (int)RIsPointer;
563 // Compare getValueID values.
564 unsigned LID = LV->getValueID(),
565 RID = RV->getValueID();
567 return (int)LID - (int)RID;
569 // Sort arguments by their position.
570 if (const Argument *LA = dyn_cast<Argument>(LV)) {
571 const Argument *RA = cast<Argument>(RV);
572 unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo();
573 return (int)LArgNo - (int)RArgNo;
576 // For instructions, compare their loop depth, and their operand
577 // count. This is pretty loose.
578 if (const Instruction *LInst = dyn_cast<Instruction>(LV)) {
579 const Instruction *RInst = cast<Instruction>(RV);
581 // Compare loop depths.
582 const BasicBlock *LParent = LInst->getParent(),
583 *RParent = RInst->getParent();
584 if (LParent != RParent) {
585 unsigned LDepth = LI->getLoopDepth(LParent),
586 RDepth = LI->getLoopDepth(RParent);
587 if (LDepth != RDepth)
588 return (int)LDepth - (int)RDepth;
591 // Compare the number of operands.
592 unsigned LNumOps = LInst->getNumOperands(),
593 RNumOps = RInst->getNumOperands();
594 return (int)LNumOps - (int)RNumOps;
601 const SCEVConstant *LC = cast<SCEVConstant>(LHS);
602 const SCEVConstant *RC = cast<SCEVConstant>(RHS);
604 // Compare constant values.
605 const APInt &LA = LC->getValue()->getValue();
606 const APInt &RA = RC->getValue()->getValue();
607 unsigned LBitWidth = LA.getBitWidth(), RBitWidth = RA.getBitWidth();
608 if (LBitWidth != RBitWidth)
609 return (int)LBitWidth - (int)RBitWidth;
610 return LA.ult(RA) ? -1 : 1;
614 const SCEVAddRecExpr *LA = cast<SCEVAddRecExpr>(LHS);
615 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS);
617 // Compare addrec loop depths.
618 const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop();
619 if (LLoop != RLoop) {
620 unsigned LDepth = LLoop->getLoopDepth(),
621 RDepth = RLoop->getLoopDepth();
622 if (LDepth != RDepth)
623 return (int)LDepth - (int)RDepth;
626 // Addrec complexity grows with operand count.
627 unsigned LNumOps = LA->getNumOperands(), RNumOps = RA->getNumOperands();
628 if (LNumOps != RNumOps)
629 return (int)LNumOps - (int)RNumOps;
631 // Lexicographically compare.
632 for (unsigned i = 0; i != LNumOps; ++i) {
633 long X = compare(LA->getOperand(i), RA->getOperand(i));
645 const SCEVNAryExpr *LC = cast<SCEVNAryExpr>(LHS);
646 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
648 // Lexicographically compare n-ary expressions.
649 unsigned LNumOps = LC->getNumOperands(), RNumOps = RC->getNumOperands();
650 for (unsigned i = 0; i != LNumOps; ++i) {
653 long X = compare(LC->getOperand(i), RC->getOperand(i));
657 return (int)LNumOps - (int)RNumOps;
661 const SCEVUDivExpr *LC = cast<SCEVUDivExpr>(LHS);
662 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
664 // Lexicographically compare udiv expressions.
665 long X = compare(LC->getLHS(), RC->getLHS());
668 return compare(LC->getRHS(), RC->getRHS());
674 const SCEVCastExpr *LC = cast<SCEVCastExpr>(LHS);
675 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
677 // Compare cast expressions by operand.
678 return compare(LC->getOperand(), RC->getOperand());
685 llvm_unreachable("Unknown SCEV kind!");
691 /// GroupByComplexity - Given a list of SCEV objects, order them by their
692 /// complexity, and group objects of the same complexity together by value.
693 /// When this routine is finished, we know that any duplicates in the vector are
694 /// consecutive and that complexity is monotonically increasing.
696 /// Note that we go take special precautions to ensure that we get deterministic
697 /// results from this routine. In other words, we don't want the results of
698 /// this to depend on where the addresses of various SCEV objects happened to
701 static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops,
703 if (Ops.size() < 2) return; // Noop
704 if (Ops.size() == 2) {
705 // This is the common case, which also happens to be trivially simple.
707 if (SCEVComplexityCompare(LI)(Ops[1], Ops[0]))
708 std::swap(Ops[0], Ops[1]);
712 // Do the rough sort by complexity.
713 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI));
715 // Now that we are sorted by complexity, group elements of the same
716 // complexity. Note that this is, at worst, N^2, but the vector is likely to
717 // be extremely short in practice. Note that we take this approach because we
718 // do not want to depend on the addresses of the objects we are grouping.
719 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
720 const SCEV *S = Ops[i];
721 unsigned Complexity = S->getSCEVType();
723 // If there are any objects of the same complexity and same value as this
725 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
726 if (Ops[j] == S) { // Found a duplicate.
727 // Move it to immediately after i'th element.
728 std::swap(Ops[i+1], Ops[j]);
729 ++i; // no need to rescan it.
730 if (i == e-2) return; // Done!
738 //===----------------------------------------------------------------------===//
739 // Simple SCEV method implementations
740 //===----------------------------------------------------------------------===//
742 /// BinomialCoefficient - Compute BC(It, K). The result has width W.
744 static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K,
746 const Type* ResultTy) {
747 // Handle the simplest case efficiently.
749 return SE.getTruncateOrZeroExtend(It, ResultTy);
751 // We are using the following formula for BC(It, K):
753 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
755 // Suppose, W is the bitwidth of the return value. We must be prepared for
756 // overflow. Hence, we must assure that the result of our computation is
757 // equal to the accurate one modulo 2^W. Unfortunately, division isn't
758 // safe in modular arithmetic.
760 // However, this code doesn't use exactly that formula; the formula it uses
761 // is something like the following, where T is the number of factors of 2 in
762 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
765 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
767 // This formula is trivially equivalent to the previous formula. However,
768 // this formula can be implemented much more efficiently. The trick is that
769 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
770 // arithmetic. To do exact division in modular arithmetic, all we have
771 // to do is multiply by the inverse. Therefore, this step can be done at
774 // The next issue is how to safely do the division by 2^T. The way this
775 // is done is by doing the multiplication step at a width of at least W + T
776 // bits. This way, the bottom W+T bits of the product are accurate. Then,
777 // when we perform the division by 2^T (which is equivalent to a right shift
778 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
779 // truncated out after the division by 2^T.
781 // In comparison to just directly using the first formula, this technique
782 // is much more efficient; using the first formula requires W * K bits,
783 // but this formula less than W + K bits. Also, the first formula requires
784 // a division step, whereas this formula only requires multiplies and shifts.
786 // It doesn't matter whether the subtraction step is done in the calculation
787 // width or the input iteration count's width; if the subtraction overflows,
788 // the result must be zero anyway. We prefer here to do it in the width of
789 // the induction variable because it helps a lot for certain cases; CodeGen
790 // isn't smart enough to ignore the overflow, which leads to much less
791 // efficient code if the width of the subtraction is wider than the native
794 // (It's possible to not widen at all by pulling out factors of 2 before
795 // the multiplication; for example, K=2 can be calculated as
796 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
797 // extra arithmetic, so it's not an obvious win, and it gets
798 // much more complicated for K > 3.)
800 // Protection from insane SCEVs; this bound is conservative,
801 // but it probably doesn't matter.
803 return SE.getCouldNotCompute();
805 unsigned W = SE.getTypeSizeInBits(ResultTy);
807 // Calculate K! / 2^T and T; we divide out the factors of two before
808 // multiplying for calculating K! / 2^T to avoid overflow.
809 // Other overflow doesn't matter because we only care about the bottom
810 // W bits of the result.
811 APInt OddFactorial(W, 1);
813 for (unsigned i = 3; i <= K; ++i) {
815 unsigned TwoFactors = Mult.countTrailingZeros();
817 Mult = Mult.lshr(TwoFactors);
818 OddFactorial *= Mult;
821 // We need at least W + T bits for the multiplication step
822 unsigned CalculationBits = W + T;
824 // Calculate 2^T, at width T+W.
825 APInt DivFactor = APInt(CalculationBits, 1).shl(T);
827 // Calculate the multiplicative inverse of K! / 2^T;
828 // this multiplication factor will perform the exact division by
830 APInt Mod = APInt::getSignedMinValue(W+1);
831 APInt MultiplyFactor = OddFactorial.zext(W+1);
832 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
833 MultiplyFactor = MultiplyFactor.trunc(W);
835 // Calculate the product, at width T+W
836 const IntegerType *CalculationTy = IntegerType::get(SE.getContext(),
838 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
839 for (unsigned i = 1; i != K; ++i) {
840 const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i));
841 Dividend = SE.getMulExpr(Dividend,
842 SE.getTruncateOrZeroExtend(S, CalculationTy));
846 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
848 // Truncate the result, and divide by K! / 2^T.
850 return SE.getMulExpr(SE.getConstant(MultiplyFactor),
851 SE.getTruncateOrZeroExtend(DivResult, ResultTy));
854 /// evaluateAtIteration - Return the value of this chain of recurrences at
855 /// the specified iteration number. We can evaluate this recurrence by
856 /// multiplying each element in the chain by the binomial coefficient
857 /// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
859 /// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
861 /// where BC(It, k) stands for binomial coefficient.
863 const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It,
864 ScalarEvolution &SE) const {
865 const SCEV *Result = getStart();
866 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
867 // The computation is correct in the face of overflow provided that the
868 // multiplication is performed _after_ the evaluation of the binomial
870 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType());
871 if (isa<SCEVCouldNotCompute>(Coeff))
874 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
879 //===----------------------------------------------------------------------===//
880 // SCEV Expression folder implementations
881 //===----------------------------------------------------------------------===//
883 const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op,
885 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
886 "This is not a truncating conversion!");
887 assert(isSCEVable(Ty) &&
888 "This is not a conversion to a SCEVable type!");
889 Ty = getEffectiveSCEVType(Ty);
892 ID.AddInteger(scTruncate);
896 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
898 // Fold if the operand is constant.
899 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
901 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(),
902 getEffectiveSCEVType(Ty))));
904 // trunc(trunc(x)) --> trunc(x)
905 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
906 return getTruncateExpr(ST->getOperand(), Ty);
908 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
909 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
910 return getTruncateOrSignExtend(SS->getOperand(), Ty);
912 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
913 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
914 return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
916 // If the input value is a chrec scev, truncate the chrec's operands.
917 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
918 SmallVector<const SCEV *, 4> Operands;
919 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
920 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty));
921 return getAddRecExpr(Operands, AddRec->getLoop());
924 // As a special case, fold trunc(undef) to undef. We don't want to
925 // know too much about SCEVUnknowns, but this special case is handy
927 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(Op))
928 if (isa<UndefValue>(U->getValue()))
929 return getSCEV(UndefValue::get(Ty));
931 // The cast wasn't folded; create an explicit cast node. We can reuse
932 // the existing insert position since if we get here, we won't have
933 // made any changes which would invalidate it.
934 SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator),
936 UniqueSCEVs.InsertNode(S, IP);
940 const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op,
942 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
943 "This is not an extending conversion!");
944 assert(isSCEVable(Ty) &&
945 "This is not a conversion to a SCEVable type!");
946 Ty = getEffectiveSCEVType(Ty);
948 // Fold if the operand is constant.
949 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
951 cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(),
952 getEffectiveSCEVType(Ty))));
954 // zext(zext(x)) --> zext(x)
955 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
956 return getZeroExtendExpr(SZ->getOperand(), Ty);
958 // Before doing any expensive analysis, check to see if we've already
959 // computed a SCEV for this Op and Ty.
961 ID.AddInteger(scZeroExtend);
965 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
967 // If the input value is a chrec scev, and we can prove that the value
968 // did not overflow the old, smaller, value, we can zero extend all of the
969 // operands (often constants). This allows analysis of something like
970 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
971 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
972 if (AR->isAffine()) {
973 const SCEV *Start = AR->getStart();
974 const SCEV *Step = AR->getStepRecurrence(*this);
975 unsigned BitWidth = getTypeSizeInBits(AR->getType());
976 const Loop *L = AR->getLoop();
978 // If we have special knowledge that this addrec won't overflow,
979 // we don't need to do any further analysis.
980 if (AR->hasNoUnsignedWrap())
981 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
982 getZeroExtendExpr(Step, Ty),
985 // Check whether the backedge-taken count is SCEVCouldNotCompute.
986 // Note that this serves two purposes: It filters out loops that are
987 // simply not analyzable, and it covers the case where this code is
988 // being called from within backedge-taken count analysis, such that
989 // attempting to ask for the backedge-taken count would likely result
990 // in infinite recursion. In the later case, the analysis code will
991 // cope with a conservative value, and it will take care to purge
992 // that value once it has finished.
993 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
994 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
995 // Manually compute the final value for AR, checking for
998 // Check whether the backedge-taken count can be losslessly casted to
999 // the addrec's type. The count is always unsigned.
1000 const SCEV *CastedMaxBECount =
1001 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1002 const SCEV *RecastedMaxBECount =
1003 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1004 if (MaxBECount == RecastedMaxBECount) {
1005 const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1006 // Check whether Start+Step*MaxBECount has no unsigned overflow.
1007 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step);
1008 const SCEV *Add = getAddExpr(Start, ZMul);
1009 const SCEV *OperandExtendedAdd =
1010 getAddExpr(getZeroExtendExpr(Start, WideTy),
1011 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
1012 getZeroExtendExpr(Step, WideTy)));
1013 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd)
1014 // Return the expression with the addrec on the outside.
1015 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1016 getZeroExtendExpr(Step, Ty),
1019 // Similar to above, only this time treat the step value as signed.
1020 // This covers loops that count down.
1021 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
1022 Add = getAddExpr(Start, SMul);
1023 OperandExtendedAdd =
1024 getAddExpr(getZeroExtendExpr(Start, WideTy),
1025 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
1026 getSignExtendExpr(Step, WideTy)));
1027 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd)
1028 // Return the expression with the addrec on the outside.
1029 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1030 getSignExtendExpr(Step, Ty),
1034 // If the backedge is guarded by a comparison with the pre-inc value
1035 // the addrec is safe. Also, if the entry is guarded by a comparison
1036 // with the start value and the backedge is guarded by a comparison
1037 // with the post-inc value, the addrec is safe.
1038 if (isKnownPositive(Step)) {
1039 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
1040 getUnsignedRange(Step).getUnsignedMax());
1041 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
1042 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) &&
1043 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT,
1044 AR->getPostIncExpr(*this), N)))
1045 // Return the expression with the addrec on the outside.
1046 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1047 getZeroExtendExpr(Step, Ty),
1049 } else if (isKnownNegative(Step)) {
1050 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
1051 getSignedRange(Step).getSignedMin());
1052 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) ||
1053 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) &&
1054 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT,
1055 AR->getPostIncExpr(*this), N)))
1056 // Return the expression with the addrec on the outside.
1057 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1058 getSignExtendExpr(Step, Ty),
1064 // The cast wasn't folded; create an explicit cast node.
1065 // Recompute the insert position, as it may have been invalidated.
1066 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1067 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
1069 UniqueSCEVs.InsertNode(S, IP);
1073 const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op,
1075 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1076 "This is not an extending conversion!");
1077 assert(isSCEVable(Ty) &&
1078 "This is not a conversion to a SCEVable type!");
1079 Ty = getEffectiveSCEVType(Ty);
1081 // Fold if the operand is constant.
1082 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1084 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(),
1085 getEffectiveSCEVType(Ty))));
1087 // sext(sext(x)) --> sext(x)
1088 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1089 return getSignExtendExpr(SS->getOperand(), Ty);
1091 // Before doing any expensive analysis, check to see if we've already
1092 // computed a SCEV for this Op and Ty.
1093 FoldingSetNodeID ID;
1094 ID.AddInteger(scSignExtend);
1098 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1100 // If the input value is a chrec scev, and we can prove that the value
1101 // did not overflow the old, smaller, value, we can sign extend all of the
1102 // operands (often constants). This allows analysis of something like
1103 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
1104 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1105 if (AR->isAffine()) {
1106 const SCEV *Start = AR->getStart();
1107 const SCEV *Step = AR->getStepRecurrence(*this);
1108 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1109 const Loop *L = AR->getLoop();
1111 // If we have special knowledge that this addrec won't overflow,
1112 // we don't need to do any further analysis.
1113 if (AR->hasNoSignedWrap())
1114 return getAddRecExpr(getSignExtendExpr(Start, Ty),
1115 getSignExtendExpr(Step, Ty),
1118 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1119 // Note that this serves two purposes: It filters out loops that are
1120 // simply not analyzable, and it covers the case where this code is
1121 // being called from within backedge-taken count analysis, such that
1122 // attempting to ask for the backedge-taken count would likely result
1123 // in infinite recursion. In the later case, the analysis code will
1124 // cope with a conservative value, and it will take care to purge
1125 // that value once it has finished.
1126 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1127 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1128 // Manually compute the final value for AR, checking for
1131 // Check whether the backedge-taken count can be losslessly casted to
1132 // the addrec's type. The count is always unsigned.
1133 const SCEV *CastedMaxBECount =
1134 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1135 const SCEV *RecastedMaxBECount =
1136 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1137 if (MaxBECount == RecastedMaxBECount) {
1138 const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1139 // Check whether Start+Step*MaxBECount has no signed overflow.
1140 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
1141 const SCEV *Add = getAddExpr(Start, SMul);
1142 const SCEV *OperandExtendedAdd =
1143 getAddExpr(getSignExtendExpr(Start, WideTy),
1144 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
1145 getSignExtendExpr(Step, WideTy)));
1146 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd)
1147 // Return the expression with the addrec on the outside.
1148 return getAddRecExpr(getSignExtendExpr(Start, Ty),
1149 getSignExtendExpr(Step, Ty),
1152 // Similar to above, only this time treat the step value as unsigned.
1153 // This covers loops that count up with an unsigned step.
1154 const SCEV *UMul = getMulExpr(CastedMaxBECount, Step);
1155 Add = getAddExpr(Start, UMul);
1156 OperandExtendedAdd =
1157 getAddExpr(getSignExtendExpr(Start, WideTy),
1158 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
1159 getZeroExtendExpr(Step, WideTy)));
1160 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd)
1161 // Return the expression with the addrec on the outside.
1162 return getAddRecExpr(getSignExtendExpr(Start, Ty),
1163 getZeroExtendExpr(Step, Ty),
1167 // If the backedge is guarded by a comparison with the pre-inc value
1168 // the addrec is safe. Also, if the entry is guarded by a comparison
1169 // with the start value and the backedge is guarded by a comparison
1170 // with the post-inc value, the addrec is safe.
1171 if (isKnownPositive(Step)) {
1172 const SCEV *N = getConstant(APInt::getSignedMinValue(BitWidth) -
1173 getSignedRange(Step).getSignedMax());
1174 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT, AR, N) ||
1175 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_SLT, Start, N) &&
1176 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT,
1177 AR->getPostIncExpr(*this), N)))
1178 // Return the expression with the addrec on the outside.
1179 return getAddRecExpr(getSignExtendExpr(Start, Ty),
1180 getSignExtendExpr(Step, Ty),
1182 } else if (isKnownNegative(Step)) {
1183 const SCEV *N = getConstant(APInt::getSignedMaxValue(BitWidth) -
1184 getSignedRange(Step).getSignedMin());
1185 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT, AR, N) ||
1186 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_SGT, Start, N) &&
1187 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT,
1188 AR->getPostIncExpr(*this), N)))
1189 // Return the expression with the addrec on the outside.
1190 return getAddRecExpr(getSignExtendExpr(Start, Ty),
1191 getSignExtendExpr(Step, Ty),
1197 // The cast wasn't folded; create an explicit cast node.
1198 // Recompute the insert position, as it may have been invalidated.
1199 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1200 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
1202 UniqueSCEVs.InsertNode(S, IP);
1206 /// getAnyExtendExpr - Return a SCEV for the given operand extended with
1207 /// unspecified bits out to the given type.
1209 const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
1211 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1212 "This is not an extending conversion!");
1213 assert(isSCEVable(Ty) &&
1214 "This is not a conversion to a SCEVable type!");
1215 Ty = getEffectiveSCEVType(Ty);
1217 // Sign-extend negative constants.
1218 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1219 if (SC->getValue()->getValue().isNegative())
1220 return getSignExtendExpr(Op, Ty);
1222 // Peel off a truncate cast.
1223 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
1224 const SCEV *NewOp = T->getOperand();
1225 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
1226 return getAnyExtendExpr(NewOp, Ty);
1227 return getTruncateOrNoop(NewOp, Ty);
1230 // Next try a zext cast. If the cast is folded, use it.
1231 const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
1232 if (!isa<SCEVZeroExtendExpr>(ZExt))
1235 // Next try a sext cast. If the cast is folded, use it.
1236 const SCEV *SExt = getSignExtendExpr(Op, Ty);
1237 if (!isa<SCEVSignExtendExpr>(SExt))
1240 // Force the cast to be folded into the operands of an addrec.
1241 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
1242 SmallVector<const SCEV *, 4> Ops;
1243 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
1245 Ops.push_back(getAnyExtendExpr(*I, Ty));
1246 return getAddRecExpr(Ops, AR->getLoop());
1249 // As a special case, fold anyext(undef) to undef. We don't want to
1250 // know too much about SCEVUnknowns, but this special case is handy
1252 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(Op))
1253 if (isa<UndefValue>(U->getValue()))
1254 return getSCEV(UndefValue::get(Ty));
1256 // If the expression is obviously signed, use the sext cast value.
1257 if (isa<SCEVSMaxExpr>(Op))
1260 // Absent any other information, use the zext cast value.
1264 /// CollectAddOperandsWithScales - Process the given Ops list, which is
1265 /// a list of operands to be added under the given scale, update the given
1266 /// map. This is a helper function for getAddRecExpr. As an example of
1267 /// what it does, given a sequence of operands that would form an add
1268 /// expression like this:
1270 /// m + n + 13 + (A * (o + p + (B * q + m + 29))) + r + (-1 * r)
1272 /// where A and B are constants, update the map with these values:
1274 /// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
1276 /// and add 13 + A*B*29 to AccumulatedConstant.
1277 /// This will allow getAddRecExpr to produce this:
1279 /// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
1281 /// This form often exposes folding opportunities that are hidden in
1282 /// the original operand list.
1284 /// Return true iff it appears that any interesting folding opportunities
1285 /// may be exposed. This helps getAddRecExpr short-circuit extra work in
1286 /// the common case where no interesting opportunities are present, and
1287 /// is also used as a check to avoid infinite recursion.
1290 CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
1291 SmallVector<const SCEV *, 8> &NewOps,
1292 APInt &AccumulatedConstant,
1293 const SCEV *const *Ops, size_t NumOperands,
1295 ScalarEvolution &SE) {
1296 bool Interesting = false;
1298 // Iterate over the add operands. They are sorted, with constants first.
1300 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1302 // Pull a buried constant out to the outside.
1303 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
1305 AccumulatedConstant += Scale * C->getValue()->getValue();
1308 // Next comes everything else. We're especially interested in multiplies
1309 // here, but they're in the middle, so just visit the rest with one loop.
1310 for (; i != NumOperands; ++i) {
1311 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
1312 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
1314 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue();
1315 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
1316 // A multiplication of a constant with another add; recurse.
1317 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1));
1319 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1320 Add->op_begin(), Add->getNumOperands(),
1323 // A multiplication of a constant with some other value. Update
1325 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
1326 const SCEV *Key = SE.getMulExpr(MulOps);
1327 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1328 M.insert(std::make_pair(Key, NewScale));
1330 NewOps.push_back(Pair.first->first);
1332 Pair.first->second += NewScale;
1333 // The map already had an entry for this value, which may indicate
1334 // a folding opportunity.
1339 // An ordinary operand. Update the map.
1340 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1341 M.insert(std::make_pair(Ops[i], Scale));
1343 NewOps.push_back(Pair.first->first);
1345 Pair.first->second += Scale;
1346 // The map already had an entry for this value, which may indicate
1347 // a folding opportunity.
1357 struct APIntCompare {
1358 bool operator()(const APInt &LHS, const APInt &RHS) const {
1359 return LHS.ult(RHS);
1364 /// getAddExpr - Get a canonical add expression, or something simpler if
1366 const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
1367 bool HasNUW, bool HasNSW) {
1368 assert(!Ops.empty() && "Cannot get empty add!");
1369 if (Ops.size() == 1) return Ops[0];
1371 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
1372 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1373 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
1374 "SCEVAddExpr operand types don't match!");
1377 // If HasNSW is true and all the operands are non-negative, infer HasNUW.
1378 if (!HasNUW && HasNSW) {
1380 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(),
1381 E = Ops.end(); I != E; ++I)
1382 if (!isKnownNonNegative(*I)) {
1386 if (All) HasNUW = true;
1389 // Sort by complexity, this groups all similar expression types together.
1390 GroupByComplexity(Ops, LI);
1392 // If there are any constants, fold them together.
1394 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1396 assert(Idx < Ops.size());
1397 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1398 // We found two constants, fold them together!
1399 Ops[0] = getConstant(LHSC->getValue()->getValue() +
1400 RHSC->getValue()->getValue());
1401 if (Ops.size() == 2) return Ops[0];
1402 Ops.erase(Ops.begin()+1); // Erase the folded element
1403 LHSC = cast<SCEVConstant>(Ops[0]);
1406 // If we are left with a constant zero being added, strip it off.
1407 if (LHSC->getValue()->isZero()) {
1408 Ops.erase(Ops.begin());
1412 if (Ops.size() == 1) return Ops[0];
1415 // Okay, check to see if the same value occurs in the operand list twice. If
1416 // so, merge them together into an multiply expression. Since we sorted the
1417 // list, these values are required to be adjacent.
1418 const Type *Ty = Ops[0]->getType();
1419 bool FoundMatch = false;
1420 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
1421 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
1422 // Found a match, merge the two values into a multiply, and add any
1423 // remaining values to the result.
1424 const SCEV *Two = getConstant(Ty, 2);
1425 const SCEV *Mul = getMulExpr(Two, Ops[i]);
1426 if (Ops.size() == 2)
1429 Ops.erase(Ops.begin()+i+1);
1434 return getAddExpr(Ops, HasNUW, HasNSW);
1436 // Check for truncates. If all the operands are truncated from the same
1437 // type, see if factoring out the truncate would permit the result to be
1438 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
1439 // if the contents of the resulting outer trunc fold to something simple.
1440 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
1441 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
1442 const Type *DstType = Trunc->getType();
1443 const Type *SrcType = Trunc->getOperand()->getType();
1444 SmallVector<const SCEV *, 8> LargeOps;
1446 // Check all the operands to see if they can be represented in the
1447 // source type of the truncate.
1448 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1449 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
1450 if (T->getOperand()->getType() != SrcType) {
1454 LargeOps.push_back(T->getOperand());
1455 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1456 LargeOps.push_back(getAnyExtendExpr(C, SrcType));
1457 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
1458 SmallVector<const SCEV *, 8> LargeMulOps;
1459 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
1460 if (const SCEVTruncateExpr *T =
1461 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
1462 if (T->getOperand()->getType() != SrcType) {
1466 LargeMulOps.push_back(T->getOperand());
1467 } else if (const SCEVConstant *C =
1468 dyn_cast<SCEVConstant>(M->getOperand(j))) {
1469 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType));
1476 LargeOps.push_back(getMulExpr(LargeMulOps));
1483 // Evaluate the expression in the larger type.
1484 const SCEV *Fold = getAddExpr(LargeOps, HasNUW, HasNSW);
1485 // If it folds to something simple, use it. Otherwise, don't.
1486 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
1487 return getTruncateExpr(Fold, DstType);
1491 // Skip past any other cast SCEVs.
1492 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
1495 // If there are add operands they would be next.
1496 if (Idx < Ops.size()) {
1497 bool DeletedAdd = false;
1498 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
1499 // If we have an add, expand the add operands onto the end of the operands
1501 Ops.erase(Ops.begin()+Idx);
1502 Ops.append(Add->op_begin(), Add->op_end());
1506 // If we deleted at least one add, we added operands to the end of the list,
1507 // and they are not necessarily sorted. Recurse to resort and resimplify
1508 // any operands we just acquired.
1510 return getAddExpr(Ops);
1513 // Skip over the add expression until we get to a multiply.
1514 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1517 // Check to see if there are any folding opportunities present with
1518 // operands multiplied by constant values.
1519 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
1520 uint64_t BitWidth = getTypeSizeInBits(Ty);
1521 DenseMap<const SCEV *, APInt> M;
1522 SmallVector<const SCEV *, 8> NewOps;
1523 APInt AccumulatedConstant(BitWidth, 0);
1524 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1525 Ops.data(), Ops.size(),
1526 APInt(BitWidth, 1), *this)) {
1527 // Some interesting folding opportunity is present, so its worthwhile to
1528 // re-generate the operands list. Group the operands by constant scale,
1529 // to avoid multiplying by the same constant scale multiple times.
1530 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
1531 for (SmallVector<const SCEV *, 8>::const_iterator I = NewOps.begin(),
1532 E = NewOps.end(); I != E; ++I)
1533 MulOpLists[M.find(*I)->second].push_back(*I);
1534 // Re-generate the operands list.
1536 if (AccumulatedConstant != 0)
1537 Ops.push_back(getConstant(AccumulatedConstant));
1538 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator
1539 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I)
1541 Ops.push_back(getMulExpr(getConstant(I->first),
1542 getAddExpr(I->second)));
1544 return getConstant(Ty, 0);
1545 if (Ops.size() == 1)
1547 return getAddExpr(Ops);
1551 // If we are adding something to a multiply expression, make sure the
1552 // something is not already an operand of the multiply. If so, merge it into
1554 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
1555 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
1556 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
1557 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
1558 if (isa<SCEVConstant>(MulOpSCEV))
1560 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
1561 if (MulOpSCEV == Ops[AddOp]) {
1562 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
1563 const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
1564 if (Mul->getNumOperands() != 2) {
1565 // If the multiply has more than two operands, we must get the
1567 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
1568 Mul->op_begin()+MulOp);
1569 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
1570 InnerMul = getMulExpr(MulOps);
1572 const SCEV *One = getConstant(Ty, 1);
1573 const SCEV *AddOne = getAddExpr(One, InnerMul);
1574 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV);
1575 if (Ops.size() == 2) return OuterMul;
1577 Ops.erase(Ops.begin()+AddOp);
1578 Ops.erase(Ops.begin()+Idx-1);
1580 Ops.erase(Ops.begin()+Idx);
1581 Ops.erase(Ops.begin()+AddOp-1);
1583 Ops.push_back(OuterMul);
1584 return getAddExpr(Ops);
1587 // Check this multiply against other multiplies being added together.
1588 bool AnyFold = false;
1589 for (unsigned OtherMulIdx = Idx+1;
1590 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
1592 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
1593 // If MulOp occurs in OtherMul, we can fold the two multiplies
1595 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
1596 OMulOp != e; ++OMulOp)
1597 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
1598 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
1599 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
1600 if (Mul->getNumOperands() != 2) {
1601 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
1602 Mul->op_begin()+MulOp);
1603 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
1604 InnerMul1 = getMulExpr(MulOps);
1606 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
1607 if (OtherMul->getNumOperands() != 2) {
1608 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
1609 OtherMul->op_begin()+OMulOp);
1610 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end());
1611 InnerMul2 = getMulExpr(MulOps);
1613 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
1614 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
1615 if (Ops.size() == 2) return OuterMul;
1616 Ops[Idx] = OuterMul;
1617 Ops.erase(Ops.begin()+OtherMulIdx);
1623 return getAddExpr(Ops);
1627 // If there are any add recurrences in the operands list, see if any other
1628 // added values are loop invariant. If so, we can fold them into the
1630 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1633 // Scan over all recurrences, trying to fold loop invariants into them.
1634 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1635 // Scan all of the other operands to this add and add them to the vector if
1636 // they are loop invariant w.r.t. the recurrence.
1637 SmallVector<const SCEV *, 8> LIOps;
1638 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1639 const Loop *AddRecLoop = AddRec->getLoop();
1640 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1641 if (Ops[i]->isLoopInvariant(AddRecLoop)) {
1642 LIOps.push_back(Ops[i]);
1643 Ops.erase(Ops.begin()+i);
1647 // If we found some loop invariants, fold them into the recurrence.
1648 if (!LIOps.empty()) {
1649 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
1650 LIOps.push_back(AddRec->getStart());
1652 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
1654 AddRecOps[0] = getAddExpr(LIOps);
1656 // Build the new addrec. Propagate the NUW and NSW flags if both the
1657 // outer add and the inner addrec are guaranteed to have no overflow.
1658 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop,
1659 HasNUW && AddRec->hasNoUnsignedWrap(),
1660 HasNSW && AddRec->hasNoSignedWrap());
1662 // If all of the other operands were loop invariant, we are done.
1663 if (Ops.size() == 1) return NewRec;
1665 // Otherwise, add the folded AddRec by the non-liv parts.
1666 for (unsigned i = 0;; ++i)
1667 if (Ops[i] == AddRec) {
1671 return getAddExpr(Ops);
1674 // Okay, if there weren't any loop invariants to be folded, check to see if
1675 // there are multiple AddRec's with the same loop induction variable being
1676 // added together. If so, we can fold them.
1677 for (unsigned OtherIdx = Idx+1;
1678 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
1679 if (OtherIdx != Idx) {
1680 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
1681 if (AddRecLoop == OtherAddRec->getLoop()) {
1682 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D}
1683 SmallVector<const SCEV *, 4> NewOps(AddRec->op_begin(),
1685 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) {
1686 if (i >= NewOps.size()) {
1687 NewOps.append(OtherAddRec->op_begin()+i,
1688 OtherAddRec->op_end());
1691 NewOps[i] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i));
1693 const SCEV *NewAddRec = getAddRecExpr(NewOps, AddRecLoop);
1695 if (Ops.size() == 2) return NewAddRec;
1697 Ops.erase(Ops.begin()+Idx);
1698 Ops.erase(Ops.begin()+OtherIdx-1);
1699 Ops.push_back(NewAddRec);
1700 return getAddExpr(Ops);
1704 // Otherwise couldn't fold anything into this recurrence. Move onto the
1708 // Okay, it looks like we really DO need an add expr. Check to see if we
1709 // already have one, otherwise create a new one.
1710 FoldingSetNodeID ID;
1711 ID.AddInteger(scAddExpr);
1712 ID.AddInteger(Ops.size());
1713 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1714 ID.AddPointer(Ops[i]);
1717 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1719 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
1720 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
1721 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator),
1723 UniqueSCEVs.InsertNode(S, IP);
1725 if (HasNUW) S->setHasNoUnsignedWrap(true);
1726 if (HasNSW) S->setHasNoSignedWrap(true);
1730 /// getMulExpr - Get a canonical multiply expression, or something simpler if
1732 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
1733 bool HasNUW, bool HasNSW) {
1734 assert(!Ops.empty() && "Cannot get empty mul!");
1735 if (Ops.size() == 1) return Ops[0];
1737 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
1738 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1739 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
1740 "SCEVMulExpr operand types don't match!");
1743 // If HasNSW is true and all the operands are non-negative, infer HasNUW.
1744 if (!HasNUW && HasNSW) {
1746 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(),
1747 E = Ops.end(); I != E; ++I)
1748 if (!isKnownNonNegative(*I)) {
1752 if (All) HasNUW = true;
1755 // Sort by complexity, this groups all similar expression types together.
1756 GroupByComplexity(Ops, LI);
1758 // If there are any constants, fold them together.
1760 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1762 // C1*(C2+V) -> C1*C2 + C1*V
1763 if (Ops.size() == 2)
1764 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
1765 if (Add->getNumOperands() == 2 &&
1766 isa<SCEVConstant>(Add->getOperand(0)))
1767 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
1768 getMulExpr(LHSC, Add->getOperand(1)));
1771 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1772 // We found two constants, fold them together!
1773 ConstantInt *Fold = ConstantInt::get(getContext(),
1774 LHSC->getValue()->getValue() *
1775 RHSC->getValue()->getValue());
1776 Ops[0] = getConstant(Fold);
1777 Ops.erase(Ops.begin()+1); // Erase the folded element
1778 if (Ops.size() == 1) return Ops[0];
1779 LHSC = cast<SCEVConstant>(Ops[0]);
1782 // If we are left with a constant one being multiplied, strip it off.
1783 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
1784 Ops.erase(Ops.begin());
1786 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
1787 // If we have a multiply of zero, it will always be zero.
1789 } else if (Ops[0]->isAllOnesValue()) {
1790 // If we have a mul by -1 of an add, try distributing the -1 among the
1792 if (Ops.size() == 2)
1793 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
1794 SmallVector<const SCEV *, 4> NewOps;
1795 bool AnyFolded = false;
1796 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(), E = Add->op_end();
1798 const SCEV *Mul = getMulExpr(Ops[0], *I);
1799 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
1800 NewOps.push_back(Mul);
1803 return getAddExpr(NewOps);
1807 if (Ops.size() == 1)
1811 // Skip over the add expression until we get to a multiply.
1812 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1815 // If there are mul operands inline them all into this expression.
1816 if (Idx < Ops.size()) {
1817 bool DeletedMul = false;
1818 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
1819 // If we have an mul, expand the mul operands onto the end of the operands
1821 Ops.erase(Ops.begin()+Idx);
1822 Ops.append(Mul->op_begin(), Mul->op_end());
1826 // If we deleted at least one mul, we added operands to the end of the list,
1827 // and they are not necessarily sorted. Recurse to resort and resimplify
1828 // any operands we just acquired.
1830 return getMulExpr(Ops);
1833 // If there are any add recurrences in the operands list, see if any other
1834 // added values are loop invariant. If so, we can fold them into the
1836 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1839 // Scan over all recurrences, trying to fold loop invariants into them.
1840 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1841 // Scan all of the other operands to this mul and add them to the vector if
1842 // they are loop invariant w.r.t. the recurrence.
1843 SmallVector<const SCEV *, 8> LIOps;
1844 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1845 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1846 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
1847 LIOps.push_back(Ops[i]);
1848 Ops.erase(Ops.begin()+i);
1852 // If we found some loop invariants, fold them into the recurrence.
1853 if (!LIOps.empty()) {
1854 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
1855 SmallVector<const SCEV *, 4> NewOps;
1856 NewOps.reserve(AddRec->getNumOperands());
1857 const SCEV *Scale = getMulExpr(LIOps);
1858 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
1859 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
1861 // Build the new addrec. Propagate the NUW and NSW flags if both the
1862 // outer mul and the inner addrec are guaranteed to have no overflow.
1863 const SCEV *NewRec = getAddRecExpr(NewOps, AddRec->getLoop(),
1864 HasNUW && AddRec->hasNoUnsignedWrap(),
1865 HasNSW && AddRec->hasNoSignedWrap());
1867 // If all of the other operands were loop invariant, we are done.
1868 if (Ops.size() == 1) return NewRec;
1870 // Otherwise, multiply the folded AddRec by the non-liv parts.
1871 for (unsigned i = 0;; ++i)
1872 if (Ops[i] == AddRec) {
1876 return getMulExpr(Ops);
1879 // Okay, if there weren't any loop invariants to be folded, check to see if
1880 // there are multiple AddRec's with the same loop induction variable being
1881 // multiplied together. If so, we can fold them.
1882 for (unsigned OtherIdx = Idx+1;
1883 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
1884 if (OtherIdx != Idx) {
1885 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
1886 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
1887 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D}
1888 const SCEVAddRecExpr *F = AddRec, *G = OtherAddRec;
1889 const SCEV *NewStart = getMulExpr(F->getStart(), G->getStart());
1890 const SCEV *B = F->getStepRecurrence(*this);
1891 const SCEV *D = G->getStepRecurrence(*this);
1892 const SCEV *NewStep = getAddExpr(getMulExpr(F, D),
1895 const SCEV *NewAddRec = getAddRecExpr(NewStart, NewStep,
1897 if (Ops.size() == 2) return NewAddRec;
1899 Ops.erase(Ops.begin()+Idx);
1900 Ops.erase(Ops.begin()+OtherIdx-1);
1901 Ops.push_back(NewAddRec);
1902 return getMulExpr(Ops);
1906 // Otherwise couldn't fold anything into this recurrence. Move onto the
1910 // Okay, it looks like we really DO need an mul expr. Check to see if we
1911 // already have one, otherwise create a new one.
1912 FoldingSetNodeID ID;
1913 ID.AddInteger(scMulExpr);
1914 ID.AddInteger(Ops.size());
1915 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1916 ID.AddPointer(Ops[i]);
1919 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1921 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
1922 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
1923 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
1925 UniqueSCEVs.InsertNode(S, IP);
1927 if (HasNUW) S->setHasNoUnsignedWrap(true);
1928 if (HasNSW) S->setHasNoSignedWrap(true);
1932 /// getUDivExpr - Get a canonical unsigned division expression, or something
1933 /// simpler if possible.
1934 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
1936 assert(getEffectiveSCEVType(LHS->getType()) ==
1937 getEffectiveSCEVType(RHS->getType()) &&
1938 "SCEVUDivExpr operand types don't match!");
1940 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
1941 if (RHSC->getValue()->equalsInt(1))
1942 return LHS; // X udiv 1 --> x
1943 // If the denominator is zero, the result of the udiv is undefined. Don't
1944 // try to analyze it, because the resolution chosen here may differ from
1945 // the resolution chosen in other parts of the compiler.
1946 if (!RHSC->getValue()->isZero()) {
1947 // Determine if the division can be folded into the operands of
1949 // TODO: Generalize this to non-constants by using known-bits information.
1950 const Type *Ty = LHS->getType();
1951 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
1952 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1;
1953 // For non-power-of-two values, effectively round the value up to the
1954 // nearest power of two.
1955 if (!RHSC->getValue()->getValue().isPowerOf2())
1957 const IntegerType *ExtTy =
1958 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
1959 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
1960 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
1961 if (const SCEVConstant *Step =
1962 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this)))
1963 if (!Step->getValue()->getValue()
1964 .urem(RHSC->getValue()->getValue()) &&
1965 getZeroExtendExpr(AR, ExtTy) ==
1966 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
1967 getZeroExtendExpr(Step, ExtTy),
1969 SmallVector<const SCEV *, 4> Operands;
1970 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i)
1971 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS));
1972 return getAddRecExpr(Operands, AR->getLoop());
1974 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
1975 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
1976 SmallVector<const SCEV *, 4> Operands;
1977 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i)
1978 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy));
1979 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
1980 // Find an operand that's safely divisible.
1981 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
1982 const SCEV *Op = M->getOperand(i);
1983 const SCEV *Div = getUDivExpr(Op, RHSC);
1984 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
1985 Operands = SmallVector<const SCEV *, 4>(M->op_begin(),
1988 return getMulExpr(Operands);
1992 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
1993 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(LHS)) {
1994 SmallVector<const SCEV *, 4> Operands;
1995 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i)
1996 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy));
1997 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
1999 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
2000 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
2001 if (isa<SCEVUDivExpr>(Op) ||
2002 getMulExpr(Op, RHS) != A->getOperand(i))
2004 Operands.push_back(Op);
2006 if (Operands.size() == A->getNumOperands())
2007 return getAddExpr(Operands);
2011 // Fold if both operands are constant.
2012 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
2013 Constant *LHSCV = LHSC->getValue();
2014 Constant *RHSCV = RHSC->getValue();
2015 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
2021 FoldingSetNodeID ID;
2022 ID.AddInteger(scUDivExpr);
2026 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2027 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
2029 UniqueSCEVs.InsertNode(S, IP);
2034 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2035 /// Simplify the expression as much as possible.
2036 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start,
2037 const SCEV *Step, const Loop *L,
2038 bool HasNUW, bool HasNSW) {
2039 SmallVector<const SCEV *, 4> Operands;
2040 Operands.push_back(Start);
2041 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
2042 if (StepChrec->getLoop() == L) {
2043 Operands.append(StepChrec->op_begin(), StepChrec->op_end());
2044 return getAddRecExpr(Operands, L);
2047 Operands.push_back(Step);
2048 return getAddRecExpr(Operands, L, HasNUW, HasNSW);
2051 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2052 /// Simplify the expression as much as possible.
2054 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
2056 bool HasNUW, bool HasNSW) {
2057 if (Operands.size() == 1) return Operands[0];
2059 const Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
2060 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
2061 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy &&
2062 "SCEVAddRecExpr operand types don't match!");
2065 if (Operands.back()->isZero()) {
2066 Operands.pop_back();
2067 return getAddRecExpr(Operands, L, HasNUW, HasNSW); // {X,+,0} --> X
2070 // It's tempting to want to call getMaxBackedgeTakenCount count here and
2071 // use that information to infer NUW and NSW flags. However, computing a
2072 // BE count requires calling getAddRecExpr, so we may not yet have a
2073 // meaningful BE count at this point (and if we don't, we'd be stuck
2074 // with a SCEVCouldNotCompute as the cached BE count).
2076 // If HasNSW is true and all the operands are non-negative, infer HasNUW.
2077 if (!HasNUW && HasNSW) {
2079 for (SmallVectorImpl<const SCEV *>::const_iterator I = Operands.begin(),
2080 E = Operands.end(); I != E; ++I)
2081 if (!isKnownNonNegative(*I)) {
2085 if (All) HasNUW = true;
2088 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
2089 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
2090 const Loop *NestedLoop = NestedAR->getLoop();
2091 if (L->contains(NestedLoop) ?
2092 (L->getLoopDepth() < NestedLoop->getLoopDepth()) :
2093 (!NestedLoop->contains(L) &&
2094 DT->dominates(L->getHeader(), NestedLoop->getHeader()))) {
2095 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
2096 NestedAR->op_end());
2097 Operands[0] = NestedAR->getStart();
2098 // AddRecs require their operands be loop-invariant with respect to their
2099 // loops. Don't perform this transformation if it would break this
2101 bool AllInvariant = true;
2102 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2103 if (!Operands[i]->isLoopInvariant(L)) {
2104 AllInvariant = false;
2108 NestedOperands[0] = getAddRecExpr(Operands, L);
2109 AllInvariant = true;
2110 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i)
2111 if (!NestedOperands[i]->isLoopInvariant(NestedLoop)) {
2112 AllInvariant = false;
2116 // Ok, both add recurrences are valid after the transformation.
2117 return getAddRecExpr(NestedOperands, NestedLoop, HasNUW, HasNSW);
2119 // Reset Operands to its original state.
2120 Operands[0] = NestedAR;
2124 // Okay, it looks like we really DO need an addrec expr. Check to see if we
2125 // already have one, otherwise create a new one.
2126 FoldingSetNodeID ID;
2127 ID.AddInteger(scAddRecExpr);
2128 ID.AddInteger(Operands.size());
2129 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2130 ID.AddPointer(Operands[i]);
2134 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2136 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size());
2137 std::uninitialized_copy(Operands.begin(), Operands.end(), O);
2138 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator),
2139 O, Operands.size(), L);
2140 UniqueSCEVs.InsertNode(S, IP);
2142 if (HasNUW) S->setHasNoUnsignedWrap(true);
2143 if (HasNSW) S->setHasNoSignedWrap(true);
2147 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
2149 SmallVector<const SCEV *, 2> Ops;
2152 return getSMaxExpr(Ops);
2156 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2157 assert(!Ops.empty() && "Cannot get empty smax!");
2158 if (Ops.size() == 1) return Ops[0];
2160 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2161 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2162 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2163 "SCEVSMaxExpr operand types don't match!");
2166 // Sort by complexity, this groups all similar expression types together.
2167 GroupByComplexity(Ops, LI);
2169 // If there are any constants, fold them together.
2171 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2173 assert(Idx < Ops.size());
2174 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2175 // We found two constants, fold them together!
2176 ConstantInt *Fold = ConstantInt::get(getContext(),
2177 APIntOps::smax(LHSC->getValue()->getValue(),
2178 RHSC->getValue()->getValue()));
2179 Ops[0] = getConstant(Fold);
2180 Ops.erase(Ops.begin()+1); // Erase the folded element
2181 if (Ops.size() == 1) return Ops[0];
2182 LHSC = cast<SCEVConstant>(Ops[0]);
2185 // If we are left with a constant minimum-int, strip it off.
2186 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
2187 Ops.erase(Ops.begin());
2189 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
2190 // If we have an smax with a constant maximum-int, it will always be
2195 if (Ops.size() == 1) return Ops[0];
2198 // Find the first SMax
2199 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
2202 // Check to see if one of the operands is an SMax. If so, expand its operands
2203 // onto our operand list, and recurse to simplify.
2204 if (Idx < Ops.size()) {
2205 bool DeletedSMax = false;
2206 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
2207 Ops.erase(Ops.begin()+Idx);
2208 Ops.append(SMax->op_begin(), SMax->op_end());
2213 return getSMaxExpr(Ops);
2216 // Okay, check to see if the same value occurs in the operand list twice. If
2217 // so, delete one. Since we sorted the list, these values are required to
2219 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2220 // X smax Y smax Y --> X smax Y
2221 // X smax Y --> X, if X is always greater than Y
2222 if (Ops[i] == Ops[i+1] ||
2223 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) {
2224 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2226 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) {
2227 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2231 if (Ops.size() == 1) return Ops[0];
2233 assert(!Ops.empty() && "Reduced smax down to nothing!");
2235 // Okay, it looks like we really DO need an smax expr. Check to see if we
2236 // already have one, otherwise create a new one.
2237 FoldingSetNodeID ID;
2238 ID.AddInteger(scSMaxExpr);
2239 ID.AddInteger(Ops.size());
2240 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2241 ID.AddPointer(Ops[i]);
2243 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2244 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2245 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2246 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator),
2248 UniqueSCEVs.InsertNode(S, IP);
2252 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
2254 SmallVector<const SCEV *, 2> Ops;
2257 return getUMaxExpr(Ops);
2261 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2262 assert(!Ops.empty() && "Cannot get empty umax!");
2263 if (Ops.size() == 1) return Ops[0];
2265 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2266 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2267 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2268 "SCEVUMaxExpr operand types don't match!");
2271 // Sort by complexity, this groups all similar expression types together.
2272 GroupByComplexity(Ops, LI);
2274 // If there are any constants, fold them together.
2276 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2278 assert(Idx < Ops.size());
2279 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2280 // We found two constants, fold them together!
2281 ConstantInt *Fold = ConstantInt::get(getContext(),
2282 APIntOps::umax(LHSC->getValue()->getValue(),
2283 RHSC->getValue()->getValue()));
2284 Ops[0] = getConstant(Fold);
2285 Ops.erase(Ops.begin()+1); // Erase the folded element
2286 if (Ops.size() == 1) return Ops[0];
2287 LHSC = cast<SCEVConstant>(Ops[0]);
2290 // If we are left with a constant minimum-int, strip it off.
2291 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
2292 Ops.erase(Ops.begin());
2294 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
2295 // If we have an umax with a constant maximum-int, it will always be
2300 if (Ops.size() == 1) return Ops[0];
2303 // Find the first UMax
2304 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
2307 // Check to see if one of the operands is a UMax. If so, expand its operands
2308 // onto our operand list, and recurse to simplify.
2309 if (Idx < Ops.size()) {
2310 bool DeletedUMax = false;
2311 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
2312 Ops.erase(Ops.begin()+Idx);
2313 Ops.append(UMax->op_begin(), UMax->op_end());
2318 return getUMaxExpr(Ops);
2321 // Okay, check to see if the same value occurs in the operand list twice. If
2322 // so, delete one. Since we sorted the list, these values are required to
2324 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2325 // X umax Y umax Y --> X umax Y
2326 // X umax Y --> X, if X is always greater than Y
2327 if (Ops[i] == Ops[i+1] ||
2328 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) {
2329 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2331 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) {
2332 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2336 if (Ops.size() == 1) return Ops[0];
2338 assert(!Ops.empty() && "Reduced umax down to nothing!");
2340 // Okay, it looks like we really DO need a umax expr. Check to see if we
2341 // already have one, otherwise create a new one.
2342 FoldingSetNodeID ID;
2343 ID.AddInteger(scUMaxExpr);
2344 ID.AddInteger(Ops.size());
2345 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2346 ID.AddPointer(Ops[i]);
2348 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2349 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2350 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2351 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator),
2353 UniqueSCEVs.InsertNode(S, IP);
2357 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
2359 // ~smax(~x, ~y) == smin(x, y).
2360 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2363 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
2365 // ~umax(~x, ~y) == umin(x, y)
2366 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2369 const SCEV *ScalarEvolution::getSizeOfExpr(const Type *AllocTy) {
2370 // If we have TargetData, we can bypass creating a target-independent
2371 // constant expression and then folding it back into a ConstantInt.
2372 // This is just a compile-time optimization.
2374 return getConstant(TD->getIntPtrType(getContext()),
2375 TD->getTypeAllocSize(AllocTy));
2377 Constant *C = ConstantExpr::getSizeOf(AllocTy);
2378 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2379 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD))
2381 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2382 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2385 const SCEV *ScalarEvolution::getAlignOfExpr(const Type *AllocTy) {
2386 Constant *C = ConstantExpr::getAlignOf(AllocTy);
2387 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2388 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD))
2390 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2391 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2394 const SCEV *ScalarEvolution::getOffsetOfExpr(const StructType *STy,
2396 // If we have TargetData, we can bypass creating a target-independent
2397 // constant expression and then folding it back into a ConstantInt.
2398 // This is just a compile-time optimization.
2400 return getConstant(TD->getIntPtrType(getContext()),
2401 TD->getStructLayout(STy)->getElementOffset(FieldNo));
2403 Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo);
2404 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2405 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD))
2407 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy));
2408 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2411 const SCEV *ScalarEvolution::getOffsetOfExpr(const Type *CTy,
2412 Constant *FieldNo) {
2413 Constant *C = ConstantExpr::getOffsetOf(CTy, FieldNo);
2414 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2415 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD))
2417 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(CTy));
2418 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2421 const SCEV *ScalarEvolution::getUnknown(Value *V) {
2422 // Don't attempt to do anything other than create a SCEVUnknown object
2423 // here. createSCEV only calls getUnknown after checking for all other
2424 // interesting possibilities, and any other code that calls getUnknown
2425 // is doing so in order to hide a value from SCEV canonicalization.
2427 FoldingSetNodeID ID;
2428 ID.AddInteger(scUnknown);
2431 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
2432 assert(cast<SCEVUnknown>(S)->getValue() == V &&
2433 "Stale SCEVUnknown in uniquing map!");
2436 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
2438 FirstUnknown = cast<SCEVUnknown>(S);
2439 UniqueSCEVs.InsertNode(S, IP);
2443 //===----------------------------------------------------------------------===//
2444 // Basic SCEV Analysis and PHI Idiom Recognition Code
2447 /// isSCEVable - Test if values of the given type are analyzable within
2448 /// the SCEV framework. This primarily includes integer types, and it
2449 /// can optionally include pointer types if the ScalarEvolution class
2450 /// has access to target-specific information.
2451 bool ScalarEvolution::isSCEVable(const Type *Ty) const {
2452 // Integers and pointers are always SCEVable.
2453 return Ty->isIntegerTy() || Ty->isPointerTy();
2456 /// getTypeSizeInBits - Return the size in bits of the specified type,
2457 /// for which isSCEVable must return true.
2458 uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const {
2459 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2461 // If we have a TargetData, use it!
2463 return TD->getTypeSizeInBits(Ty);
2465 // Integer types have fixed sizes.
2466 if (Ty->isIntegerTy())
2467 return Ty->getPrimitiveSizeInBits();
2469 // The only other support type is pointer. Without TargetData, conservatively
2470 // assume pointers are 64-bit.
2471 assert(Ty->isPointerTy() && "isSCEVable permitted a non-SCEVable type!");
2475 /// getEffectiveSCEVType - Return a type with the same bitwidth as
2476 /// the given type and which represents how SCEV will treat the given
2477 /// type, for which isSCEVable must return true. For pointer types,
2478 /// this is the pointer-sized integer type.
2479 const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const {
2480 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2482 if (Ty->isIntegerTy())
2485 // The only other support type is pointer.
2486 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
2487 if (TD) return TD->getIntPtrType(getContext());
2489 // Without TargetData, conservatively assume pointers are 64-bit.
2490 return Type::getInt64Ty(getContext());
2493 const SCEV *ScalarEvolution::getCouldNotCompute() {
2494 return &CouldNotCompute;
2497 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
2498 /// expression and create a new one.
2499 const SCEV *ScalarEvolution::getSCEV(Value *V) {
2500 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
2502 std::map<SCEVCallbackVH, const SCEV *>::const_iterator I = Scalars.find(V);
2503 if (I != Scalars.end()) return I->second;
2504 const SCEV *S = createSCEV(V);
2506 // The process of creating a SCEV for V may have caused other SCEVs
2507 // to have been created, so it's necessary to insert the new entry
2508 // from scratch, rather than trying to remember the insert position
2510 Scalars.insert(std::make_pair(SCEVCallbackVH(V, this), S));
2514 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
2516 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) {
2517 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2519 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
2521 const Type *Ty = V->getType();
2522 Ty = getEffectiveSCEVType(Ty);
2523 return getMulExpr(V,
2524 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))));
2527 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
2528 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
2529 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2531 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
2533 const Type *Ty = V->getType();
2534 Ty = getEffectiveSCEVType(Ty);
2535 const SCEV *AllOnes =
2536 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
2537 return getMinusSCEV(AllOnes, V);
2540 /// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
2542 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS,
2544 // Fast path: X - X --> 0.
2546 return getConstant(LHS->getType(), 0);
2549 return getAddExpr(LHS, getNegativeSCEV(RHS));
2552 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
2553 /// input value to the specified type. If the type must be extended, it is zero
2556 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V,
2558 const Type *SrcTy = V->getType();
2559 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2560 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2561 "Cannot truncate or zero extend with non-integer arguments!");
2562 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2563 return V; // No conversion
2564 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2565 return getTruncateExpr(V, Ty);
2566 return getZeroExtendExpr(V, Ty);
2569 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
2570 /// input value to the specified type. If the type must be extended, it is sign
2573 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
2575 const Type *SrcTy = V->getType();
2576 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2577 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2578 "Cannot truncate or zero extend with non-integer arguments!");
2579 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2580 return V; // No conversion
2581 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2582 return getTruncateExpr(V, Ty);
2583 return getSignExtendExpr(V, Ty);
2586 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
2587 /// input value to the specified type. If the type must be extended, it is zero
2588 /// extended. The conversion must not be narrowing.
2590 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, const Type *Ty) {
2591 const Type *SrcTy = V->getType();
2592 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2593 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2594 "Cannot noop or zero extend with non-integer arguments!");
2595 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2596 "getNoopOrZeroExtend cannot truncate!");
2597 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2598 return V; // No conversion
2599 return getZeroExtendExpr(V, Ty);
2602 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
2603 /// input value to the specified type. If the type must be extended, it is sign
2604 /// extended. The conversion must not be narrowing.
2606 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, const Type *Ty) {
2607 const Type *SrcTy = V->getType();
2608 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2609 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2610 "Cannot noop or sign extend with non-integer arguments!");
2611 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2612 "getNoopOrSignExtend cannot truncate!");
2613 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2614 return V; // No conversion
2615 return getSignExtendExpr(V, Ty);
2618 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
2619 /// the input value to the specified type. If the type must be extended,
2620 /// it is extended with unspecified bits. The conversion must not be
2623 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, const Type *Ty) {
2624 const Type *SrcTy = V->getType();
2625 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2626 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2627 "Cannot noop or any extend with non-integer arguments!");
2628 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2629 "getNoopOrAnyExtend cannot truncate!");
2630 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2631 return V; // No conversion
2632 return getAnyExtendExpr(V, Ty);
2635 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
2636 /// input value to the specified type. The conversion must not be widening.
2638 ScalarEvolution::getTruncateOrNoop(const SCEV *V, const Type *Ty) {
2639 const Type *SrcTy = V->getType();
2640 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2641 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2642 "Cannot truncate or noop with non-integer arguments!");
2643 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
2644 "getTruncateOrNoop cannot extend!");
2645 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2646 return V; // No conversion
2647 return getTruncateExpr(V, Ty);
2650 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
2651 /// the types using zero-extension, and then perform a umax operation
2653 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
2655 const SCEV *PromotedLHS = LHS;
2656 const SCEV *PromotedRHS = RHS;
2658 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2659 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2661 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2663 return getUMaxExpr(PromotedLHS, PromotedRHS);
2666 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
2667 /// the types using zero-extension, and then perform a umin operation
2669 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
2671 const SCEV *PromotedLHS = LHS;
2672 const SCEV *PromotedRHS = RHS;
2674 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2675 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2677 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2679 return getUMinExpr(PromotedLHS, PromotedRHS);
2682 /// PushDefUseChildren - Push users of the given Instruction
2683 /// onto the given Worklist.
2685 PushDefUseChildren(Instruction *I,
2686 SmallVectorImpl<Instruction *> &Worklist) {
2687 // Push the def-use children onto the Worklist stack.
2688 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end();
2690 Worklist.push_back(cast<Instruction>(*UI));
2693 /// ForgetSymbolicValue - This looks up computed SCEV values for all
2694 /// instructions that depend on the given instruction and removes them from
2695 /// the Scalars map if they reference SymName. This is used during PHI
2698 ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) {
2699 SmallVector<Instruction *, 16> Worklist;
2700 PushDefUseChildren(PN, Worklist);
2702 SmallPtrSet<Instruction *, 8> Visited;
2704 while (!Worklist.empty()) {
2705 Instruction *I = Worklist.pop_back_val();
2706 if (!Visited.insert(I)) continue;
2708 std::map<SCEVCallbackVH, const SCEV *>::iterator It =
2709 Scalars.find(static_cast<Value *>(I));
2710 if (It != Scalars.end()) {
2711 // Short-circuit the def-use traversal if the symbolic name
2712 // ceases to appear in expressions.
2713 if (It->second != SymName && !It->second->hasOperand(SymName))
2716 // SCEVUnknown for a PHI either means that it has an unrecognized
2717 // structure, it's a PHI that's in the progress of being computed
2718 // by createNodeForPHI, or it's a single-value PHI. In the first case,
2719 // additional loop trip count information isn't going to change anything.
2720 // In the second case, createNodeForPHI will perform the necessary
2721 // updates on its own when it gets to that point. In the third, we do
2722 // want to forget the SCEVUnknown.
2723 if (!isa<PHINode>(I) ||
2724 !isa<SCEVUnknown>(It->second) ||
2725 (I != PN && It->second == SymName)) {
2726 ValuesAtScopes.erase(It->second);
2731 PushDefUseChildren(I, Worklist);
2735 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
2736 /// a loop header, making it a potential recurrence, or it doesn't.
2738 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
2739 if (const Loop *L = LI->getLoopFor(PN->getParent()))
2740 if (L->getHeader() == PN->getParent()) {
2741 // The loop may have multiple entrances or multiple exits; we can analyze
2742 // this phi as an addrec if it has a unique entry value and a unique
2744 Value *BEValueV = 0, *StartValueV = 0;
2745 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
2746 Value *V = PN->getIncomingValue(i);
2747 if (L->contains(PN->getIncomingBlock(i))) {
2750 } else if (BEValueV != V) {
2754 } else if (!StartValueV) {
2756 } else if (StartValueV != V) {
2761 if (BEValueV && StartValueV) {
2762 // While we are analyzing this PHI node, handle its value symbolically.
2763 const SCEV *SymbolicName = getUnknown(PN);
2764 assert(Scalars.find(PN) == Scalars.end() &&
2765 "PHI node already processed?");
2766 Scalars.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
2768 // Using this symbolic name for the PHI, analyze the value coming around
2770 const SCEV *BEValue = getSCEV(BEValueV);
2772 // NOTE: If BEValue is loop invariant, we know that the PHI node just
2773 // has a special value for the first iteration of the loop.
2775 // If the value coming around the backedge is an add with the symbolic
2776 // value we just inserted, then we found a simple induction variable!
2777 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
2778 // If there is a single occurrence of the symbolic value, replace it
2779 // with a recurrence.
2780 unsigned FoundIndex = Add->getNumOperands();
2781 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
2782 if (Add->getOperand(i) == SymbolicName)
2783 if (FoundIndex == e) {
2788 if (FoundIndex != Add->getNumOperands()) {
2789 // Create an add with everything but the specified operand.
2790 SmallVector<const SCEV *, 8> Ops;
2791 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
2792 if (i != FoundIndex)
2793 Ops.push_back(Add->getOperand(i));
2794 const SCEV *Accum = getAddExpr(Ops);
2796 // This is not a valid addrec if the step amount is varying each
2797 // loop iteration, but is not itself an addrec in this loop.
2798 if (Accum->isLoopInvariant(L) ||
2799 (isa<SCEVAddRecExpr>(Accum) &&
2800 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
2801 bool HasNUW = false;
2802 bool HasNSW = false;
2804 // If the increment doesn't overflow, then neither the addrec nor
2805 // the post-increment will overflow.
2806 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) {
2807 if (OBO->hasNoUnsignedWrap())
2809 if (OBO->hasNoSignedWrap())
2813 const SCEV *StartVal = getSCEV(StartValueV);
2814 const SCEV *PHISCEV =
2815 getAddRecExpr(StartVal, Accum, L, HasNUW, HasNSW);
2817 // Since the no-wrap flags are on the increment, they apply to the
2818 // post-incremented value as well.
2819 if (Accum->isLoopInvariant(L))
2820 (void)getAddRecExpr(getAddExpr(StartVal, Accum),
2821 Accum, L, HasNUW, HasNSW);
2823 // Okay, for the entire analysis of this edge we assumed the PHI
2824 // to be symbolic. We now need to go back and purge all of the
2825 // entries for the scalars that use the symbolic expression.
2826 ForgetSymbolicName(PN, SymbolicName);
2827 Scalars[SCEVCallbackVH(PN, this)] = PHISCEV;
2831 } else if (const SCEVAddRecExpr *AddRec =
2832 dyn_cast<SCEVAddRecExpr>(BEValue)) {
2833 // Otherwise, this could be a loop like this:
2834 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
2835 // In this case, j = {1,+,1} and BEValue is j.
2836 // Because the other in-value of i (0) fits the evolution of BEValue
2837 // i really is an addrec evolution.
2838 if (AddRec->getLoop() == L && AddRec->isAffine()) {
2839 const SCEV *StartVal = getSCEV(StartValueV);
2841 // If StartVal = j.start - j.stride, we can use StartVal as the
2842 // initial step of the addrec evolution.
2843 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
2844 AddRec->getOperand(1))) {
2845 const SCEV *PHISCEV =
2846 getAddRecExpr(StartVal, AddRec->getOperand(1), L);
2848 // Okay, for the entire analysis of this edge we assumed the PHI
2849 // to be symbolic. We now need to go back and purge all of the
2850 // entries for the scalars that use the symbolic expression.
2851 ForgetSymbolicName(PN, SymbolicName);
2852 Scalars[SCEVCallbackVH(PN, this)] = PHISCEV;
2860 // If the PHI has a single incoming value, follow that value, unless the
2861 // PHI's incoming blocks are in a different loop, in which case doing so
2862 // risks breaking LCSSA form. Instcombine would normally zap these, but
2863 // it doesn't have DominatorTree information, so it may miss cases.
2864 if (Value *V = PN->hasConstantValue(DT)) {
2865 bool AllSameLoop = true;
2866 Loop *PNLoop = LI->getLoopFor(PN->getParent());
2867 for (size_t i = 0, e = PN->getNumIncomingValues(); i != e; ++i)
2868 if (LI->getLoopFor(PN->getIncomingBlock(i)) != PNLoop) {
2869 AllSameLoop = false;
2876 // If it's not a loop phi, we can't handle it yet.
2877 return getUnknown(PN);
2880 /// createNodeForGEP - Expand GEP instructions into add and multiply
2881 /// operations. This allows them to be analyzed by regular SCEV code.
2883 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
2885 // Don't blindly transfer the inbounds flag from the GEP instruction to the
2886 // Add expression, because the Instruction may be guarded by control flow
2887 // and the no-overflow bits may not be valid for the expression in any
2890 const Type *IntPtrTy = getEffectiveSCEVType(GEP->getType());
2891 Value *Base = GEP->getOperand(0);
2892 // Don't attempt to analyze GEPs over unsized objects.
2893 if (!cast<PointerType>(Base->getType())->getElementType()->isSized())
2894 return getUnknown(GEP);
2895 const SCEV *TotalOffset = getConstant(IntPtrTy, 0);
2896 gep_type_iterator GTI = gep_type_begin(GEP);
2897 for (GetElementPtrInst::op_iterator I = llvm::next(GEP->op_begin()),
2901 // Compute the (potentially symbolic) offset in bytes for this index.
2902 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) {
2903 // For a struct, add the member offset.
2904 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
2905 const SCEV *FieldOffset = getOffsetOfExpr(STy, FieldNo);
2907 // Add the field offset to the running total offset.
2908 TotalOffset = getAddExpr(TotalOffset, FieldOffset);
2910 // For an array, add the element offset, explicitly scaled.
2911 const SCEV *ElementSize = getSizeOfExpr(*GTI);
2912 const SCEV *IndexS = getSCEV(Index);
2913 // Getelementptr indices are signed.
2914 IndexS = getTruncateOrSignExtend(IndexS, IntPtrTy);
2916 // Multiply the index by the element size to compute the element offset.
2917 const SCEV *LocalOffset = getMulExpr(IndexS, ElementSize);
2919 // Add the element offset to the running total offset.
2920 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
2924 // Get the SCEV for the GEP base.
2925 const SCEV *BaseS = getSCEV(Base);
2927 // Add the total offset from all the GEP indices to the base.
2928 return getAddExpr(BaseS, TotalOffset);
2931 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
2932 /// guaranteed to end in (at every loop iteration). It is, at the same time,
2933 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
2934 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
2936 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
2937 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
2938 return C->getValue()->getValue().countTrailingZeros();
2940 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
2941 return std::min(GetMinTrailingZeros(T->getOperand()),
2942 (uint32_t)getTypeSizeInBits(T->getType()));
2944 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
2945 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
2946 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
2947 getTypeSizeInBits(E->getType()) : OpRes;
2950 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
2951 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
2952 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
2953 getTypeSizeInBits(E->getType()) : OpRes;
2956 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
2957 // The result is the min of all operands results.
2958 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
2959 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
2960 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
2964 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
2965 // The result is the sum of all operands results.
2966 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
2967 uint32_t BitWidth = getTypeSizeInBits(M->getType());
2968 for (unsigned i = 1, e = M->getNumOperands();
2969 SumOpRes != BitWidth && i != e; ++i)
2970 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
2975 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
2976 // The result is the min of all operands results.
2977 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
2978 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
2979 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
2983 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
2984 // The result is the min of all operands results.
2985 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
2986 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
2987 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
2991 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
2992 // The result is the min of all operands results.
2993 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
2994 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
2995 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
2999 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3000 // For a SCEVUnknown, ask ValueTracking.
3001 unsigned BitWidth = getTypeSizeInBits(U->getType());
3002 APInt Mask = APInt::getAllOnesValue(BitWidth);
3003 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3004 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones);
3005 return Zeros.countTrailingOnes();
3012 /// getUnsignedRange - Determine the unsigned range for a particular SCEV.
3015 ScalarEvolution::getUnsignedRange(const SCEV *S) {
3017 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3018 return ConstantRange(C->getValue()->getValue());
3020 unsigned BitWidth = getTypeSizeInBits(S->getType());
3021 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3023 // If the value has known zeros, the maximum unsigned value will have those
3024 // known zeros as well.
3025 uint32_t TZ = GetMinTrailingZeros(S);
3027 ConservativeResult =
3028 ConstantRange(APInt::getMinValue(BitWidth),
3029 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
3031 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3032 ConstantRange X = getUnsignedRange(Add->getOperand(0));
3033 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3034 X = X.add(getUnsignedRange(Add->getOperand(i)));
3035 return ConservativeResult.intersectWith(X);
3038 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3039 ConstantRange X = getUnsignedRange(Mul->getOperand(0));
3040 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3041 X = X.multiply(getUnsignedRange(Mul->getOperand(i)));
3042 return ConservativeResult.intersectWith(X);
3045 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3046 ConstantRange X = getUnsignedRange(SMax->getOperand(0));
3047 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3048 X = X.smax(getUnsignedRange(SMax->getOperand(i)));
3049 return ConservativeResult.intersectWith(X);
3052 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3053 ConstantRange X = getUnsignedRange(UMax->getOperand(0));
3054 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3055 X = X.umax(getUnsignedRange(UMax->getOperand(i)));
3056 return ConservativeResult.intersectWith(X);
3059 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3060 ConstantRange X = getUnsignedRange(UDiv->getLHS());
3061 ConstantRange Y = getUnsignedRange(UDiv->getRHS());
3062 return ConservativeResult.intersectWith(X.udiv(Y));
3065 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3066 ConstantRange X = getUnsignedRange(ZExt->getOperand());
3067 return ConservativeResult.intersectWith(X.zeroExtend(BitWidth));
3070 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3071 ConstantRange X = getUnsignedRange(SExt->getOperand());
3072 return ConservativeResult.intersectWith(X.signExtend(BitWidth));
3075 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3076 ConstantRange X = getUnsignedRange(Trunc->getOperand());
3077 return ConservativeResult.intersectWith(X.truncate(BitWidth));
3080 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3081 // If there's no unsigned wrap, the value will never be less than its
3083 if (AddRec->hasNoUnsignedWrap())
3084 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
3085 if (!C->getValue()->isZero())
3086 ConservativeResult =
3087 ConservativeResult.intersectWith(
3088 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0)));
3090 // TODO: non-affine addrec
3091 if (AddRec->isAffine()) {
3092 const Type *Ty = AddRec->getType();
3093 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3094 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3095 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3096 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3098 const SCEV *Start = AddRec->getStart();
3099 const SCEV *Step = AddRec->getStepRecurrence(*this);
3101 ConstantRange StartRange = getUnsignedRange(Start);
3102 ConstantRange StepRange = getSignedRange(Step);
3103 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3104 ConstantRange EndRange =
3105 StartRange.add(MaxBECountRange.multiply(StepRange));
3107 // Check for overflow. This must be done with ConstantRange arithmetic
3108 // because we could be called from within the ScalarEvolution overflow
3110 ConstantRange ExtStartRange = StartRange.zextOrTrunc(BitWidth*2+1);
3111 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3112 ConstantRange ExtMaxBECountRange =
3113 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3114 ConstantRange ExtEndRange = EndRange.zextOrTrunc(BitWidth*2+1);
3115 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3117 return ConservativeResult;
3119 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(),
3120 EndRange.getUnsignedMin());
3121 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(),
3122 EndRange.getUnsignedMax());
3123 if (Min.isMinValue() && Max.isMaxValue())
3124 return ConservativeResult;
3125 return ConservativeResult.intersectWith(ConstantRange(Min, Max+1));
3129 return ConservativeResult;
3132 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3133 // For a SCEVUnknown, ask ValueTracking.
3134 APInt Mask = APInt::getAllOnesValue(BitWidth);
3135 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3136 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones, TD);
3137 if (Ones == ~Zeros + 1)
3138 return ConservativeResult;
3139 return ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1));
3142 return ConservativeResult;
3145 /// getSignedRange - Determine the signed range for a particular SCEV.
3148 ScalarEvolution::getSignedRange(const SCEV *S) {
3150 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3151 return ConstantRange(C->getValue()->getValue());
3153 unsigned BitWidth = getTypeSizeInBits(S->getType());
3154 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3156 // If the value has known zeros, the maximum signed value will have those
3157 // known zeros as well.
3158 uint32_t TZ = GetMinTrailingZeros(S);
3160 ConservativeResult =
3161 ConstantRange(APInt::getSignedMinValue(BitWidth),
3162 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
3164 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3165 ConstantRange X = getSignedRange(Add->getOperand(0));
3166 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3167 X = X.add(getSignedRange(Add->getOperand(i)));
3168 return ConservativeResult.intersectWith(X);
3171 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3172 ConstantRange X = getSignedRange(Mul->getOperand(0));
3173 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3174 X = X.multiply(getSignedRange(Mul->getOperand(i)));
3175 return ConservativeResult.intersectWith(X);
3178 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3179 ConstantRange X = getSignedRange(SMax->getOperand(0));
3180 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3181 X = X.smax(getSignedRange(SMax->getOperand(i)));
3182 return ConservativeResult.intersectWith(X);
3185 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3186 ConstantRange X = getSignedRange(UMax->getOperand(0));
3187 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3188 X = X.umax(getSignedRange(UMax->getOperand(i)));
3189 return ConservativeResult.intersectWith(X);
3192 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3193 ConstantRange X = getSignedRange(UDiv->getLHS());
3194 ConstantRange Y = getSignedRange(UDiv->getRHS());
3195 return ConservativeResult.intersectWith(X.udiv(Y));
3198 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3199 ConstantRange X = getSignedRange(ZExt->getOperand());
3200 return ConservativeResult.intersectWith(X.zeroExtend(BitWidth));
3203 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3204 ConstantRange X = getSignedRange(SExt->getOperand());
3205 return ConservativeResult.intersectWith(X.signExtend(BitWidth));
3208 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3209 ConstantRange X = getSignedRange(Trunc->getOperand());
3210 return ConservativeResult.intersectWith(X.truncate(BitWidth));
3213 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3214 // If there's no signed wrap, and all the operands have the same sign or
3215 // zero, the value won't ever change sign.
3216 if (AddRec->hasNoSignedWrap()) {
3217 bool AllNonNeg = true;
3218 bool AllNonPos = true;
3219 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
3220 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
3221 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
3224 ConservativeResult = ConservativeResult.intersectWith(
3225 ConstantRange(APInt(BitWidth, 0),
3226 APInt::getSignedMinValue(BitWidth)));
3228 ConservativeResult = ConservativeResult.intersectWith(
3229 ConstantRange(APInt::getSignedMinValue(BitWidth),
3230 APInt(BitWidth, 1)));
3233 // TODO: non-affine addrec
3234 if (AddRec->isAffine()) {
3235 const Type *Ty = AddRec->getType();
3236 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3237 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3238 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3239 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3241 const SCEV *Start = AddRec->getStart();
3242 const SCEV *Step = AddRec->getStepRecurrence(*this);
3244 ConstantRange StartRange = getSignedRange(Start);
3245 ConstantRange StepRange = getSignedRange(Step);
3246 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3247 ConstantRange EndRange =
3248 StartRange.add(MaxBECountRange.multiply(StepRange));
3250 // Check for overflow. This must be done with ConstantRange arithmetic
3251 // because we could be called from within the ScalarEvolution overflow
3253 ConstantRange ExtStartRange = StartRange.sextOrTrunc(BitWidth*2+1);
3254 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3255 ConstantRange ExtMaxBECountRange =
3256 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3257 ConstantRange ExtEndRange = EndRange.sextOrTrunc(BitWidth*2+1);
3258 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3260 return ConservativeResult;
3262 APInt Min = APIntOps::smin(StartRange.getSignedMin(),
3263 EndRange.getSignedMin());
3264 APInt Max = APIntOps::smax(StartRange.getSignedMax(),
3265 EndRange.getSignedMax());
3266 if (Min.isMinSignedValue() && Max.isMaxSignedValue())
3267 return ConservativeResult;
3268 return ConservativeResult.intersectWith(ConstantRange(Min, Max+1));
3272 return ConservativeResult;
3275 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3276 // For a SCEVUnknown, ask ValueTracking.
3277 if (!U->getValue()->getType()->isIntegerTy() && !TD)
3278 return ConservativeResult;
3279 unsigned NS = ComputeNumSignBits(U->getValue(), TD);
3281 return ConservativeResult;
3282 return ConservativeResult.intersectWith(
3283 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
3284 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1));
3287 return ConservativeResult;
3290 /// createSCEV - We know that there is no SCEV for the specified value.
3291 /// Analyze the expression.
3293 const SCEV *ScalarEvolution::createSCEV(Value *V) {
3294 if (!isSCEVable(V->getType()))
3295 return getUnknown(V);
3297 unsigned Opcode = Instruction::UserOp1;
3298 if (Instruction *I = dyn_cast<Instruction>(V)) {
3299 Opcode = I->getOpcode();
3301 // Don't attempt to analyze instructions in blocks that aren't
3302 // reachable. Such instructions don't matter, and they aren't required
3303 // to obey basic rules for definitions dominating uses which this
3304 // analysis depends on.
3305 if (!DT->isReachableFromEntry(I->getParent()))
3306 return getUnknown(V);
3307 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
3308 Opcode = CE->getOpcode();
3309 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
3310 return getConstant(CI);
3311 else if (isa<ConstantPointerNull>(V))
3312 return getConstant(V->getType(), 0);
3313 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
3314 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee());
3316 return getUnknown(V);
3318 Operator *U = cast<Operator>(V);
3320 case Instruction::Add: {
3321 // The simple thing to do would be to just call getSCEV on both operands
3322 // and call getAddExpr with the result. However if we're looking at a
3323 // bunch of things all added together, this can be quite inefficient,
3324 // because it leads to N-1 getAddExpr calls for N ultimate operands.
3325 // Instead, gather up all the operands and make a single getAddExpr call.
3326 // LLVM IR canonical form means we need only traverse the left operands.
3327 SmallVector<const SCEV *, 4> AddOps;
3328 AddOps.push_back(getSCEV(U->getOperand(1)));
3329 for (Value *Op = U->getOperand(0);
3330 Op->getValueID() == Instruction::Add + Value::InstructionVal;
3331 Op = U->getOperand(0)) {
3332 U = cast<Operator>(Op);
3333 AddOps.push_back(getSCEV(U->getOperand(1)));
3335 AddOps.push_back(getSCEV(U->getOperand(0)));
3336 return getAddExpr(AddOps);
3338 case Instruction::Mul: {
3339 // See the Add code above.
3340 SmallVector<const SCEV *, 4> MulOps;
3341 MulOps.push_back(getSCEV(U->getOperand(1)));
3342 for (Value *Op = U->getOperand(0);
3343 Op->getValueID() == Instruction::Mul + Value::InstructionVal;
3344 Op = U->getOperand(0)) {
3345 U = cast<Operator>(Op);
3346 MulOps.push_back(getSCEV(U->getOperand(1)));
3348 MulOps.push_back(getSCEV(U->getOperand(0)));
3349 return getMulExpr(MulOps);
3351 case Instruction::UDiv:
3352 return getUDivExpr(getSCEV(U->getOperand(0)),
3353 getSCEV(U->getOperand(1)));
3354 case Instruction::Sub:
3355 return getMinusSCEV(getSCEV(U->getOperand(0)),
3356 getSCEV(U->getOperand(1)));
3357 case Instruction::And:
3358 // For an expression like x&255 that merely masks off the high bits,
3359 // use zext(trunc(x)) as the SCEV expression.
3360 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3361 if (CI->isNullValue())
3362 return getSCEV(U->getOperand(1));
3363 if (CI->isAllOnesValue())
3364 return getSCEV(U->getOperand(0));
3365 const APInt &A = CI->getValue();
3367 // Instcombine's ShrinkDemandedConstant may strip bits out of
3368 // constants, obscuring what would otherwise be a low-bits mask.
3369 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant
3370 // knew about to reconstruct a low-bits mask value.
3371 unsigned LZ = A.countLeadingZeros();
3372 unsigned BitWidth = A.getBitWidth();
3373 APInt AllOnes = APInt::getAllOnesValue(BitWidth);
3374 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
3375 ComputeMaskedBits(U->getOperand(0), AllOnes, KnownZero, KnownOne, TD);
3377 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ);
3379 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask))
3381 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)),
3382 IntegerType::get(getContext(), BitWidth - LZ)),
3387 case Instruction::Or:
3388 // If the RHS of the Or is a constant, we may have something like:
3389 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
3390 // optimizations will transparently handle this case.
3392 // In order for this transformation to be safe, the LHS must be of the
3393 // form X*(2^n) and the Or constant must be less than 2^n.
3394 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3395 const SCEV *LHS = getSCEV(U->getOperand(0));
3396 const APInt &CIVal = CI->getValue();
3397 if (GetMinTrailingZeros(LHS) >=
3398 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
3399 // Build a plain add SCEV.
3400 const SCEV *S = getAddExpr(LHS, getSCEV(CI));
3401 // If the LHS of the add was an addrec and it has no-wrap flags,
3402 // transfer the no-wrap flags, since an or won't introduce a wrap.
3403 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
3404 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
3405 if (OldAR->hasNoUnsignedWrap())
3406 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoUnsignedWrap(true);
3407 if (OldAR->hasNoSignedWrap())
3408 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoSignedWrap(true);
3414 case Instruction::Xor:
3415 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3416 // If the RHS of the xor is a signbit, then this is just an add.
3417 // Instcombine turns add of signbit into xor as a strength reduction step.
3418 if (CI->getValue().isSignBit())
3419 return getAddExpr(getSCEV(U->getOperand(0)),
3420 getSCEV(U->getOperand(1)));
3422 // If the RHS of xor is -1, then this is a not operation.
3423 if (CI->isAllOnesValue())
3424 return getNotSCEV(getSCEV(U->getOperand(0)));
3426 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
3427 // This is a variant of the check for xor with -1, and it handles
3428 // the case where instcombine has trimmed non-demanded bits out
3429 // of an xor with -1.
3430 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
3431 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
3432 if (BO->getOpcode() == Instruction::And &&
3433 LCI->getValue() == CI->getValue())
3434 if (const SCEVZeroExtendExpr *Z =
3435 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
3436 const Type *UTy = U->getType();
3437 const SCEV *Z0 = Z->getOperand();
3438 const Type *Z0Ty = Z0->getType();
3439 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
3441 // If C is a low-bits mask, the zero extend is serving to
3442 // mask off the high bits. Complement the operand and
3443 // re-apply the zext.
3444 if (APIntOps::isMask(Z0TySize, CI->getValue()))
3445 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
3447 // If C is a single bit, it may be in the sign-bit position
3448 // before the zero-extend. In this case, represent the xor
3449 // using an add, which is equivalent, and re-apply the zext.
3450 APInt Trunc = APInt(CI->getValue()).trunc(Z0TySize);
3451 if (APInt(Trunc).zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
3453 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
3459 case Instruction::Shl:
3460 // Turn shift left of a constant amount into a multiply.
3461 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3462 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3464 // If the shift count is not less than the bitwidth, the result of
3465 // the shift is undefined. Don't try to analyze it, because the
3466 // resolution chosen here may differ from the resolution chosen in
3467 // other parts of the compiler.
3468 if (SA->getValue().uge(BitWidth))
3471 Constant *X = ConstantInt::get(getContext(),
3472 APInt(BitWidth, 1).shl(SA->getZExtValue()));
3473 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3477 case Instruction::LShr:
3478 // Turn logical shift right of a constant into a unsigned divide.
3479 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3480 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3482 // If the shift count is not less than the bitwidth, the result of
3483 // the shift is undefined. Don't try to analyze it, because the
3484 // resolution chosen here may differ from the resolution chosen in
3485 // other parts of the compiler.
3486 if (SA->getValue().uge(BitWidth))
3489 Constant *X = ConstantInt::get(getContext(),
3490 APInt(BitWidth, 1).shl(SA->getZExtValue()));
3491 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3495 case Instruction::AShr:
3496 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
3497 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
3498 if (Operator *L = dyn_cast<Operator>(U->getOperand(0)))
3499 if (L->getOpcode() == Instruction::Shl &&
3500 L->getOperand(1) == U->getOperand(1)) {
3501 uint64_t BitWidth = getTypeSizeInBits(U->getType());
3503 // If the shift count is not less than the bitwidth, the result of
3504 // the shift is undefined. Don't try to analyze it, because the
3505 // resolution chosen here may differ from the resolution chosen in
3506 // other parts of the compiler.
3507 if (CI->getValue().uge(BitWidth))
3510 uint64_t Amt = BitWidth - CI->getZExtValue();
3511 if (Amt == BitWidth)
3512 return getSCEV(L->getOperand(0)); // shift by zero --> noop
3514 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
3515 IntegerType::get(getContext(),
3521 case Instruction::Trunc:
3522 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
3524 case Instruction::ZExt:
3525 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3527 case Instruction::SExt:
3528 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3530 case Instruction::BitCast:
3531 // BitCasts are no-op casts so we just eliminate the cast.
3532 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
3533 return getSCEV(U->getOperand(0));
3536 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
3537 // lead to pointer expressions which cannot safely be expanded to GEPs,
3538 // because ScalarEvolution doesn't respect the GEP aliasing rules when
3539 // simplifying integer expressions.
3541 case Instruction::GetElementPtr:
3542 return createNodeForGEP(cast<GEPOperator>(U));
3544 case Instruction::PHI:
3545 return createNodeForPHI(cast<PHINode>(U));
3547 case Instruction::Select:
3548 // This could be a smax or umax that was lowered earlier.
3549 // Try to recover it.
3550 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
3551 Value *LHS = ICI->getOperand(0);
3552 Value *RHS = ICI->getOperand(1);
3553 switch (ICI->getPredicate()) {
3554 case ICmpInst::ICMP_SLT:
3555 case ICmpInst::ICMP_SLE:
3556 std::swap(LHS, RHS);
3558 case ICmpInst::ICMP_SGT:
3559 case ICmpInst::ICMP_SGE:
3560 // a >s b ? a+x : b+x -> smax(a, b)+x
3561 // a >s b ? b+x : a+x -> smin(a, b)+x
3562 if (LHS->getType() == U->getType()) {
3563 const SCEV *LS = getSCEV(LHS);
3564 const SCEV *RS = getSCEV(RHS);
3565 const SCEV *LA = getSCEV(U->getOperand(1));
3566 const SCEV *RA = getSCEV(U->getOperand(2));
3567 const SCEV *LDiff = getMinusSCEV(LA, LS);
3568 const SCEV *RDiff = getMinusSCEV(RA, RS);
3570 return getAddExpr(getSMaxExpr(LS, RS), LDiff);
3571 LDiff = getMinusSCEV(LA, RS);
3572 RDiff = getMinusSCEV(RA, LS);
3574 return getAddExpr(getSMinExpr(LS, RS), LDiff);
3577 case ICmpInst::ICMP_ULT:
3578 case ICmpInst::ICMP_ULE:
3579 std::swap(LHS, RHS);
3581 case ICmpInst::ICMP_UGT:
3582 case ICmpInst::ICMP_UGE:
3583 // a >u b ? a+x : b+x -> umax(a, b)+x
3584 // a >u b ? b+x : a+x -> umin(a, b)+x
3585 if (LHS->getType() == U->getType()) {
3586 const SCEV *LS = getSCEV(LHS);
3587 const SCEV *RS = getSCEV(RHS);
3588 const SCEV *LA = getSCEV(U->getOperand(1));
3589 const SCEV *RA = getSCEV(U->getOperand(2));
3590 const SCEV *LDiff = getMinusSCEV(LA, LS);
3591 const SCEV *RDiff = getMinusSCEV(RA, RS);
3593 return getAddExpr(getUMaxExpr(LS, RS), LDiff);
3594 LDiff = getMinusSCEV(LA, RS);
3595 RDiff = getMinusSCEV(RA, LS);
3597 return getAddExpr(getUMinExpr(LS, RS), LDiff);
3600 case ICmpInst::ICMP_NE:
3601 // n != 0 ? n+x : 1+x -> umax(n, 1)+x
3602 if (LHS->getType() == U->getType() &&
3603 isa<ConstantInt>(RHS) &&
3604 cast<ConstantInt>(RHS)->isZero()) {
3605 const SCEV *One = getConstant(LHS->getType(), 1);
3606 const SCEV *LS = getSCEV(LHS);
3607 const SCEV *LA = getSCEV(U->getOperand(1));
3608 const SCEV *RA = getSCEV(U->getOperand(2));
3609 const SCEV *LDiff = getMinusSCEV(LA, LS);
3610 const SCEV *RDiff = getMinusSCEV(RA, One);
3612 return getAddExpr(getUMaxExpr(One, LS), LDiff);
3615 case ICmpInst::ICMP_EQ:
3616 // n == 0 ? 1+x : n+x -> umax(n, 1)+x
3617 if (LHS->getType() == U->getType() &&
3618 isa<ConstantInt>(RHS) &&
3619 cast<ConstantInt>(RHS)->isZero()) {
3620 const SCEV *One = getConstant(LHS->getType(), 1);
3621 const SCEV *LS = getSCEV(LHS);
3622 const SCEV *LA = getSCEV(U->getOperand(1));
3623 const SCEV *RA = getSCEV(U->getOperand(2));
3624 const SCEV *LDiff = getMinusSCEV(LA, One);
3625 const SCEV *RDiff = getMinusSCEV(RA, LS);
3627 return getAddExpr(getUMaxExpr(One, LS), LDiff);
3635 default: // We cannot analyze this expression.
3639 return getUnknown(V);
3644 //===----------------------------------------------------------------------===//
3645 // Iteration Count Computation Code
3648 /// getBackedgeTakenCount - If the specified loop has a predictable
3649 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
3650 /// object. The backedge-taken count is the number of times the loop header
3651 /// will be branched to from within the loop. This is one less than the
3652 /// trip count of the loop, since it doesn't count the first iteration,
3653 /// when the header is branched to from outside the loop.
3655 /// Note that it is not valid to call this method on a loop without a
3656 /// loop-invariant backedge-taken count (see
3657 /// hasLoopInvariantBackedgeTakenCount).
3659 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
3660 return getBackedgeTakenInfo(L).Exact;
3663 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
3664 /// return the least SCEV value that is known never to be less than the
3665 /// actual backedge taken count.
3666 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
3667 return getBackedgeTakenInfo(L).Max;
3670 /// PushLoopPHIs - Push PHI nodes in the header of the given loop
3671 /// onto the given Worklist.
3673 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
3674 BasicBlock *Header = L->getHeader();
3676 // Push all Loop-header PHIs onto the Worklist stack.
3677 for (BasicBlock::iterator I = Header->begin();
3678 PHINode *PN = dyn_cast<PHINode>(I); ++I)
3679 Worklist.push_back(PN);
3682 const ScalarEvolution::BackedgeTakenInfo &
3683 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
3684 // Initially insert a CouldNotCompute for this loop. If the insertion
3685 // succeeds, proceed to actually compute a backedge-taken count and
3686 // update the value. The temporary CouldNotCompute value tells SCEV
3687 // code elsewhere that it shouldn't attempt to request a new
3688 // backedge-taken count, which could result in infinite recursion.
3689 std::pair<std::map<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
3690 BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute()));
3692 BackedgeTakenInfo BECount = ComputeBackedgeTakenCount(L);
3693 if (BECount.Exact != getCouldNotCompute()) {
3694 assert(BECount.Exact->isLoopInvariant(L) &&
3695 BECount.Max->isLoopInvariant(L) &&
3696 "Computed backedge-taken count isn't loop invariant for loop!");
3697 ++NumTripCountsComputed;
3699 // Update the value in the map.
3700 Pair.first->second = BECount;
3702 if (BECount.Max != getCouldNotCompute())
3703 // Update the value in the map.
3704 Pair.first->second = BECount;
3705 if (isa<PHINode>(L->getHeader()->begin()))
3706 // Only count loops that have phi nodes as not being computable.
3707 ++NumTripCountsNotComputed;
3710 // Now that we know more about the trip count for this loop, forget any
3711 // existing SCEV values for PHI nodes in this loop since they are only
3712 // conservative estimates made without the benefit of trip count
3713 // information. This is similar to the code in forgetLoop, except that
3714 // it handles SCEVUnknown PHI nodes specially.
3715 if (BECount.hasAnyInfo()) {
3716 SmallVector<Instruction *, 16> Worklist;
3717 PushLoopPHIs(L, Worklist);
3719 SmallPtrSet<Instruction *, 8> Visited;
3720 while (!Worklist.empty()) {
3721 Instruction *I = Worklist.pop_back_val();
3722 if (!Visited.insert(I)) continue;
3724 std::map<SCEVCallbackVH, const SCEV *>::iterator It =
3725 Scalars.find(static_cast<Value *>(I));
3726 if (It != Scalars.end()) {
3727 // SCEVUnknown for a PHI either means that it has an unrecognized
3728 // structure, or it's a PHI that's in the progress of being computed
3729 // by createNodeForPHI. In the former case, additional loop trip
3730 // count information isn't going to change anything. In the later
3731 // case, createNodeForPHI will perform the necessary updates on its
3732 // own when it gets to that point.
3733 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(It->second)) {
3734 ValuesAtScopes.erase(It->second);
3737 if (PHINode *PN = dyn_cast<PHINode>(I))
3738 ConstantEvolutionLoopExitValue.erase(PN);
3741 PushDefUseChildren(I, Worklist);
3745 return Pair.first->second;
3748 /// forgetLoop - This method should be called by the client when it has
3749 /// changed a loop in a way that may effect ScalarEvolution's ability to
3750 /// compute a trip count, or if the loop is deleted.
3751 void ScalarEvolution::forgetLoop(const Loop *L) {
3752 // Drop any stored trip count value.
3753 BackedgeTakenCounts.erase(L);
3755 // Drop information about expressions based on loop-header PHIs.
3756 SmallVector<Instruction *, 16> Worklist;
3757 PushLoopPHIs(L, Worklist);
3759 SmallPtrSet<Instruction *, 8> Visited;
3760 while (!Worklist.empty()) {
3761 Instruction *I = Worklist.pop_back_val();
3762 if (!Visited.insert(I)) continue;
3764 std::map<SCEVCallbackVH, const SCEV *>::iterator It =
3765 Scalars.find(static_cast<Value *>(I));
3766 if (It != Scalars.end()) {
3767 ValuesAtScopes.erase(It->second);
3769 if (PHINode *PN = dyn_cast<PHINode>(I))
3770 ConstantEvolutionLoopExitValue.erase(PN);
3773 PushDefUseChildren(I, Worklist);
3777 /// forgetValue - This method should be called by the client when it has
3778 /// changed a value in a way that may effect its value, or which may
3779 /// disconnect it from a def-use chain linking it to a loop.
3780 void ScalarEvolution::forgetValue(Value *V) {
3781 Instruction *I = dyn_cast<Instruction>(V);
3784 // Drop information about expressions based on loop-header PHIs.
3785 SmallVector<Instruction *, 16> Worklist;
3786 Worklist.push_back(I);
3788 SmallPtrSet<Instruction *, 8> Visited;
3789 while (!Worklist.empty()) {
3790 I = Worklist.pop_back_val();
3791 if (!Visited.insert(I)) continue;
3793 std::map<SCEVCallbackVH, const SCEV *>::iterator It =
3794 Scalars.find(static_cast<Value *>(I));
3795 if (It != Scalars.end()) {
3796 ValuesAtScopes.erase(It->second);
3798 if (PHINode *PN = dyn_cast<PHINode>(I))
3799 ConstantEvolutionLoopExitValue.erase(PN);
3802 PushDefUseChildren(I, Worklist);
3806 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
3807 /// of the specified loop will execute.
3808 ScalarEvolution::BackedgeTakenInfo
3809 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
3810 SmallVector<BasicBlock *, 8> ExitingBlocks;
3811 L->getExitingBlocks(ExitingBlocks);
3813 // Examine all exits and pick the most conservative values.
3814 const SCEV *BECount = getCouldNotCompute();
3815 const SCEV *MaxBECount = getCouldNotCompute();
3816 bool CouldNotComputeBECount = false;
3817 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
3818 BackedgeTakenInfo NewBTI =
3819 ComputeBackedgeTakenCountFromExit(L, ExitingBlocks[i]);
3821 if (NewBTI.Exact == getCouldNotCompute()) {
3822 // We couldn't compute an exact value for this exit, so
3823 // we won't be able to compute an exact value for the loop.
3824 CouldNotComputeBECount = true;
3825 BECount = getCouldNotCompute();
3826 } else if (!CouldNotComputeBECount) {
3827 if (BECount == getCouldNotCompute())
3828 BECount = NewBTI.Exact;
3830 BECount = getUMinFromMismatchedTypes(BECount, NewBTI.Exact);
3832 if (MaxBECount == getCouldNotCompute())
3833 MaxBECount = NewBTI.Max;
3834 else if (NewBTI.Max != getCouldNotCompute())
3835 MaxBECount = getUMinFromMismatchedTypes(MaxBECount, NewBTI.Max);
3838 return BackedgeTakenInfo(BECount, MaxBECount);
3841 /// ComputeBackedgeTakenCountFromExit - Compute the number of times the backedge
3842 /// of the specified loop will execute if it exits via the specified block.
3843 ScalarEvolution::BackedgeTakenInfo
3844 ScalarEvolution::ComputeBackedgeTakenCountFromExit(const Loop *L,
3845 BasicBlock *ExitingBlock) {
3847 // Okay, we've chosen an exiting block. See what condition causes us to
3848 // exit at this block.
3850 // FIXME: we should be able to handle switch instructions (with a single exit)
3851 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
3852 if (ExitBr == 0) return getCouldNotCompute();
3853 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
3855 // At this point, we know we have a conditional branch that determines whether
3856 // the loop is exited. However, we don't know if the branch is executed each
3857 // time through the loop. If not, then the execution count of the branch will
3858 // not be equal to the trip count of the loop.
3860 // Currently we check for this by checking to see if the Exit branch goes to
3861 // the loop header. If so, we know it will always execute the same number of
3862 // times as the loop. We also handle the case where the exit block *is* the
3863 // loop header. This is common for un-rotated loops.
3865 // If both of those tests fail, walk up the unique predecessor chain to the
3866 // header, stopping if there is an edge that doesn't exit the loop. If the
3867 // header is reached, the execution count of the branch will be equal to the
3868 // trip count of the loop.
3870 // More extensive analysis could be done to handle more cases here.
3872 if (ExitBr->getSuccessor(0) != L->getHeader() &&
3873 ExitBr->getSuccessor(1) != L->getHeader() &&
3874 ExitBr->getParent() != L->getHeader()) {
3875 // The simple checks failed, try climbing the unique predecessor chain
3876 // up to the header.
3878 for (BasicBlock *BB = ExitBr->getParent(); BB; ) {
3879 BasicBlock *Pred = BB->getUniquePredecessor();
3881 return getCouldNotCompute();
3882 TerminatorInst *PredTerm = Pred->getTerminator();
3883 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) {
3884 BasicBlock *PredSucc = PredTerm->getSuccessor(i);
3887 // If the predecessor has a successor that isn't BB and isn't
3888 // outside the loop, assume the worst.
3889 if (L->contains(PredSucc))
3890 return getCouldNotCompute();
3892 if (Pred == L->getHeader()) {
3899 return getCouldNotCompute();
3902 // Proceed to the next level to examine the exit condition expression.
3903 return ComputeBackedgeTakenCountFromExitCond(L, ExitBr->getCondition(),
3904 ExitBr->getSuccessor(0),
3905 ExitBr->getSuccessor(1));
3908 /// ComputeBackedgeTakenCountFromExitCond - Compute the number of times the
3909 /// backedge of the specified loop will execute if its exit condition
3910 /// were a conditional branch of ExitCond, TBB, and FBB.
3911 ScalarEvolution::BackedgeTakenInfo
3912 ScalarEvolution::ComputeBackedgeTakenCountFromExitCond(const Loop *L,
3916 // Check if the controlling expression for this loop is an And or Or.
3917 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
3918 if (BO->getOpcode() == Instruction::And) {
3919 // Recurse on the operands of the and.
3920 BackedgeTakenInfo BTI0 =
3921 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB);
3922 BackedgeTakenInfo BTI1 =
3923 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB);
3924 const SCEV *BECount = getCouldNotCompute();
3925 const SCEV *MaxBECount = getCouldNotCompute();
3926 if (L->contains(TBB)) {
3927 // Both conditions must be true for the loop to continue executing.
3928 // Choose the less conservative count.
3929 if (BTI0.Exact == getCouldNotCompute() ||
3930 BTI1.Exact == getCouldNotCompute())
3931 BECount = getCouldNotCompute();
3933 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3934 if (BTI0.Max == getCouldNotCompute())
3935 MaxBECount = BTI1.Max;
3936 else if (BTI1.Max == getCouldNotCompute())
3937 MaxBECount = BTI0.Max;
3939 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max);
3941 // Both conditions must be true at the same time for the loop to exit.
3942 // For now, be conservative.
3943 assert(L->contains(FBB) && "Loop block has no successor in loop!");
3944 if (BTI0.Max == BTI1.Max)
3945 MaxBECount = BTI0.Max;
3946 if (BTI0.Exact == BTI1.Exact)
3947 BECount = BTI0.Exact;
3950 return BackedgeTakenInfo(BECount, MaxBECount);
3952 if (BO->getOpcode() == Instruction::Or) {
3953 // Recurse on the operands of the or.
3954 BackedgeTakenInfo BTI0 =
3955 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB);
3956 BackedgeTakenInfo BTI1 =
3957 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB);
3958 const SCEV *BECount = getCouldNotCompute();
3959 const SCEV *MaxBECount = getCouldNotCompute();
3960 if (L->contains(FBB)) {
3961 // Both conditions must be false for the loop to continue executing.
3962 // Choose the less conservative count.
3963 if (BTI0.Exact == getCouldNotCompute() ||
3964 BTI1.Exact == getCouldNotCompute())
3965 BECount = getCouldNotCompute();
3967 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3968 if (BTI0.Max == getCouldNotCompute())
3969 MaxBECount = BTI1.Max;
3970 else if (BTI1.Max == getCouldNotCompute())
3971 MaxBECount = BTI0.Max;
3973 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max);
3975 // Both conditions must be false at the same time for the loop to exit.
3976 // For now, be conservative.
3977 assert(L->contains(TBB) && "Loop block has no successor in loop!");
3978 if (BTI0.Max == BTI1.Max)
3979 MaxBECount = BTI0.Max;
3980 if (BTI0.Exact == BTI1.Exact)
3981 BECount = BTI0.Exact;
3984 return BackedgeTakenInfo(BECount, MaxBECount);
3988 // With an icmp, it may be feasible to compute an exact backedge-taken count.
3989 // Proceed to the next level to examine the icmp.
3990 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
3991 return ComputeBackedgeTakenCountFromExitCondICmp(L, ExitCondICmp, TBB, FBB);
3993 // Check for a constant condition. These are normally stripped out by
3994 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
3995 // preserve the CFG and is temporarily leaving constant conditions
3997 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
3998 if (L->contains(FBB) == !CI->getZExtValue())
3999 // The backedge is always taken.
4000 return getCouldNotCompute();
4002 // The backedge is never taken.
4003 return getConstant(CI->getType(), 0);
4006 // If it's not an integer or pointer comparison then compute it the hard way.
4007 return ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB));
4010 /// ComputeBackedgeTakenCountFromExitCondICmp - Compute the number of times the
4011 /// backedge of the specified loop will execute if its exit condition
4012 /// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB.
4013 ScalarEvolution::BackedgeTakenInfo
4014 ScalarEvolution::ComputeBackedgeTakenCountFromExitCondICmp(const Loop *L,
4019 // If the condition was exit on true, convert the condition to exit on false
4020 ICmpInst::Predicate Cond;
4021 if (!L->contains(FBB))
4022 Cond = ExitCond->getPredicate();
4024 Cond = ExitCond->getInversePredicate();
4026 // Handle common loops like: for (X = "string"; *X; ++X)
4027 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
4028 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
4029 BackedgeTakenInfo ItCnt =
4030 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond);
4031 if (ItCnt.hasAnyInfo())
4035 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
4036 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
4038 // Try to evaluate any dependencies out of the loop.
4039 LHS = getSCEVAtScope(LHS, L);
4040 RHS = getSCEVAtScope(RHS, L);
4042 // At this point, we would like to compute how many iterations of the
4043 // loop the predicate will return true for these inputs.
4044 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) {
4045 // If there is a loop-invariant, force it into the RHS.
4046 std::swap(LHS, RHS);
4047 Cond = ICmpInst::getSwappedPredicate(Cond);
4050 // Simplify the operands before analyzing them.
4051 (void)SimplifyICmpOperands(Cond, LHS, RHS);
4053 // If we have a comparison of a chrec against a constant, try to use value
4054 // ranges to answer this query.
4055 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
4056 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
4057 if (AddRec->getLoop() == L) {
4058 // Form the constant range.
4059 ConstantRange CompRange(
4060 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
4062 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
4063 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
4067 case ICmpInst::ICMP_NE: { // while (X != Y)
4068 // Convert to: while (X-Y != 0)
4069 BackedgeTakenInfo BTI = HowFarToZero(getMinusSCEV(LHS, RHS), L);
4070 if (BTI.hasAnyInfo()) return BTI;
4073 case ICmpInst::ICMP_EQ: { // while (X == Y)
4074 // Convert to: while (X-Y == 0)
4075 BackedgeTakenInfo BTI = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
4076 if (BTI.hasAnyInfo()) return BTI;
4079 case ICmpInst::ICMP_SLT: {
4080 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true);
4081 if (BTI.hasAnyInfo()) return BTI;
4084 case ICmpInst::ICMP_SGT: {
4085 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
4086 getNotSCEV(RHS), L, true);
4087 if (BTI.hasAnyInfo()) return BTI;
4090 case ICmpInst::ICMP_ULT: {
4091 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false);
4092 if (BTI.hasAnyInfo()) return BTI;
4095 case ICmpInst::ICMP_UGT: {
4096 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
4097 getNotSCEV(RHS), L, false);
4098 if (BTI.hasAnyInfo()) return BTI;
4103 dbgs() << "ComputeBackedgeTakenCount ";
4104 if (ExitCond->getOperand(0)->getType()->isUnsigned())
4105 dbgs() << "[unsigned] ";
4106 dbgs() << *LHS << " "
4107 << Instruction::getOpcodeName(Instruction::ICmp)
4108 << " " << *RHS << "\n";
4113 ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB));
4116 static ConstantInt *
4117 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
4118 ScalarEvolution &SE) {
4119 const SCEV *InVal = SE.getConstant(C);
4120 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
4121 assert(isa<SCEVConstant>(Val) &&
4122 "Evaluation of SCEV at constant didn't fold correctly?");
4123 return cast<SCEVConstant>(Val)->getValue();
4126 /// GetAddressedElementFromGlobal - Given a global variable with an initializer
4127 /// and a GEP expression (missing the pointer index) indexing into it, return
4128 /// the addressed element of the initializer or null if the index expression is
4131 GetAddressedElementFromGlobal(GlobalVariable *GV,
4132 const std::vector<ConstantInt*> &Indices) {
4133 Constant *Init = GV->getInitializer();
4134 for (unsigned i = 0, e = Indices.size(); i != e; ++i) {
4135 uint64_t Idx = Indices[i]->getZExtValue();
4136 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) {
4137 assert(Idx < CS->getNumOperands() && "Bad struct index!");
4138 Init = cast<Constant>(CS->getOperand(Idx));
4139 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) {
4140 if (Idx >= CA->getNumOperands()) return 0; // Bogus program
4141 Init = cast<Constant>(CA->getOperand(Idx));
4142 } else if (isa<ConstantAggregateZero>(Init)) {
4143 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) {
4144 assert(Idx < STy->getNumElements() && "Bad struct index!");
4145 Init = Constant::getNullValue(STy->getElementType(Idx));
4146 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) {
4147 if (Idx >= ATy->getNumElements()) return 0; // Bogus program
4148 Init = Constant::getNullValue(ATy->getElementType());
4150 llvm_unreachable("Unknown constant aggregate type!");
4154 return 0; // Unknown initializer type
4160 /// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of
4161 /// 'icmp op load X, cst', try to see if we can compute the backedge
4162 /// execution count.
4163 ScalarEvolution::BackedgeTakenInfo
4164 ScalarEvolution::ComputeLoadConstantCompareBackedgeTakenCount(
4168 ICmpInst::Predicate predicate) {
4169 if (LI->isVolatile()) return getCouldNotCompute();
4171 // Check to see if the loaded pointer is a getelementptr of a global.
4172 // TODO: Use SCEV instead of manually grubbing with GEPs.
4173 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
4174 if (!GEP) return getCouldNotCompute();
4176 // Make sure that it is really a constant global we are gepping, with an
4177 // initializer, and make sure the first IDX is really 0.
4178 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
4179 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
4180 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
4181 !cast<Constant>(GEP->getOperand(1))->isNullValue())
4182 return getCouldNotCompute();
4184 // Okay, we allow one non-constant index into the GEP instruction.
4186 std::vector<ConstantInt*> Indexes;
4187 unsigned VarIdxNum = 0;
4188 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
4189 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
4190 Indexes.push_back(CI);
4191 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
4192 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
4193 VarIdx = GEP->getOperand(i);
4195 Indexes.push_back(0);
4198 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
4199 // Check to see if X is a loop variant variable value now.
4200 const SCEV *Idx = getSCEV(VarIdx);
4201 Idx = getSCEVAtScope(Idx, L);
4203 // We can only recognize very limited forms of loop index expressions, in
4204 // particular, only affine AddRec's like {C1,+,C2}.
4205 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
4206 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) ||
4207 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
4208 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
4209 return getCouldNotCompute();
4211 unsigned MaxSteps = MaxBruteForceIterations;
4212 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
4213 ConstantInt *ItCst = ConstantInt::get(
4214 cast<IntegerType>(IdxExpr->getType()), IterationNum);
4215 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
4217 // Form the GEP offset.
4218 Indexes[VarIdxNum] = Val;
4220 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes);
4221 if (Result == 0) break; // Cannot compute!
4223 // Evaluate the condition for this iteration.
4224 Result = ConstantExpr::getICmp(predicate, Result, RHS);
4225 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
4226 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
4228 dbgs() << "\n***\n*** Computed loop count " << *ItCst
4229 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
4232 ++NumArrayLenItCounts;
4233 return getConstant(ItCst); // Found terminating iteration!
4236 return getCouldNotCompute();
4240 /// CanConstantFold - Return true if we can constant fold an instruction of the
4241 /// specified type, assuming that all operands were constants.
4242 static bool CanConstantFold(const Instruction *I) {
4243 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
4244 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I))
4247 if (const CallInst *CI = dyn_cast<CallInst>(I))
4248 if (const Function *F = CI->getCalledFunction())
4249 return canConstantFoldCallTo(F);
4253 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
4254 /// in the loop that V is derived from. We allow arbitrary operations along the
4255 /// way, but the operands of an operation must either be constants or a value
4256 /// derived from a constant PHI. If this expression does not fit with these
4257 /// constraints, return null.
4258 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
4259 // If this is not an instruction, or if this is an instruction outside of the
4260 // loop, it can't be derived from a loop PHI.
4261 Instruction *I = dyn_cast<Instruction>(V);
4262 if (I == 0 || !L->contains(I)) return 0;
4264 if (PHINode *PN = dyn_cast<PHINode>(I)) {
4265 if (L->getHeader() == I->getParent())
4268 // We don't currently keep track of the control flow needed to evaluate
4269 // PHIs, so we cannot handle PHIs inside of loops.
4273 // If we won't be able to constant fold this expression even if the operands
4274 // are constants, return early.
4275 if (!CanConstantFold(I)) return 0;
4277 // Otherwise, we can evaluate this instruction if all of its operands are
4278 // constant or derived from a PHI node themselves.
4280 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op)
4281 if (!isa<Constant>(I->getOperand(Op))) {
4282 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L);
4283 if (P == 0) return 0; // Not evolving from PHI
4287 return 0; // Evolving from multiple different PHIs.
4290 // This is a expression evolving from a constant PHI!
4294 /// EvaluateExpression - Given an expression that passes the
4295 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
4296 /// in the loop has the value PHIVal. If we can't fold this expression for some
4297 /// reason, return null.
4298 static Constant *EvaluateExpression(Value *V, Constant *PHIVal,
4299 const TargetData *TD) {
4300 if (isa<PHINode>(V)) return PHIVal;
4301 if (Constant *C = dyn_cast<Constant>(V)) return C;
4302 Instruction *I = cast<Instruction>(V);
4304 std::vector<Constant*> Operands(I->getNumOperands());
4306 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
4307 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal, TD);
4308 if (Operands[i] == 0) return 0;
4311 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
4312 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
4314 return ConstantFoldInstOperands(I->getOpcode(), I->getType(),
4315 &Operands[0], Operands.size(), TD);
4318 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
4319 /// in the header of its containing loop, we know the loop executes a
4320 /// constant number of times, and the PHI node is just a recurrence
4321 /// involving constants, fold it.
4323 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
4326 std::map<PHINode*, Constant*>::const_iterator I =
4327 ConstantEvolutionLoopExitValue.find(PN);
4328 if (I != ConstantEvolutionLoopExitValue.end())
4331 if (BEs.ugt(MaxBruteForceIterations))
4332 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
4334 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
4336 // Since the loop is canonicalized, the PHI node must have two entries. One
4337 // entry must be a constant (coming in from outside of the loop), and the
4338 // second must be derived from the same PHI.
4339 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
4340 Constant *StartCST =
4341 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
4343 return RetVal = 0; // Must be a constant.
4345 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
4346 if (getConstantEvolvingPHI(BEValue, L) != PN &&
4347 !isa<Constant>(BEValue))
4348 return RetVal = 0; // Not derived from same PHI.
4350 // Execute the loop symbolically to determine the exit value.
4351 if (BEs.getActiveBits() >= 32)
4352 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
4354 unsigned NumIterations = BEs.getZExtValue(); // must be in range
4355 unsigned IterationNum = 0;
4356 for (Constant *PHIVal = StartCST; ; ++IterationNum) {
4357 if (IterationNum == NumIterations)
4358 return RetVal = PHIVal; // Got exit value!
4360 // Compute the value of the PHI node for the next iteration.
4361 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD);
4362 if (NextPHI == PHIVal)
4363 return RetVal = NextPHI; // Stopped evolving!
4365 return 0; // Couldn't evaluate!
4370 /// ComputeBackedgeTakenCountExhaustively - If the loop is known to execute a
4371 /// constant number of times (the condition evolves only from constants),
4372 /// try to evaluate a few iterations of the loop until we get the exit
4373 /// condition gets a value of ExitWhen (true or false). If we cannot
4374 /// evaluate the trip count of the loop, return getCouldNotCompute().
4376 ScalarEvolution::ComputeBackedgeTakenCountExhaustively(const Loop *L,
4379 PHINode *PN = getConstantEvolvingPHI(Cond, L);
4380 if (PN == 0) return getCouldNotCompute();
4382 // If the loop is canonicalized, the PHI will have exactly two entries.
4383 // That's the only form we support here.
4384 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
4386 // One entry must be a constant (coming in from outside of the loop), and the
4387 // second must be derived from the same PHI.
4388 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
4389 Constant *StartCST =
4390 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
4391 if (StartCST == 0) return getCouldNotCompute(); // Must be a constant.
4393 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
4394 if (getConstantEvolvingPHI(BEValue, L) != PN &&
4395 !isa<Constant>(BEValue))
4396 return getCouldNotCompute(); // Not derived from same PHI.
4398 // Okay, we find a PHI node that defines the trip count of this loop. Execute
4399 // the loop symbolically to determine when the condition gets a value of
4401 unsigned IterationNum = 0;
4402 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
4403 for (Constant *PHIVal = StartCST;
4404 IterationNum != MaxIterations; ++IterationNum) {
4405 ConstantInt *CondVal =
4406 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal, TD));
4408 // Couldn't symbolically evaluate.
4409 if (!CondVal) return getCouldNotCompute();
4411 if (CondVal->getValue() == uint64_t(ExitWhen)) {
4412 ++NumBruteForceTripCountsComputed;
4413 return getConstant(Type::getInt32Ty(getContext()), IterationNum);
4416 // Compute the value of the PHI node for the next iteration.
4417 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD);
4418 if (NextPHI == 0 || NextPHI == PHIVal)
4419 return getCouldNotCompute();// Couldn't evaluate or not making progress...
4423 // Too many iterations were needed to evaluate.
4424 return getCouldNotCompute();
4427 /// getSCEVAtScope - Return a SCEV expression for the specified value
4428 /// at the specified scope in the program. The L value specifies a loop
4429 /// nest to evaluate the expression at, where null is the top-level or a
4430 /// specified loop is immediately inside of the loop.
4432 /// This method can be used to compute the exit value for a variable defined
4433 /// in a loop by querying what the value will hold in the parent loop.
4435 /// In the case that a relevant loop exit value cannot be computed, the
4436 /// original value V is returned.
4437 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
4438 // Check to see if we've folded this expression at this loop before.
4439 std::map<const Loop *, const SCEV *> &Values = ValuesAtScopes[V];
4440 std::pair<std::map<const Loop *, const SCEV *>::iterator, bool> Pair =
4441 Values.insert(std::make_pair(L, static_cast<const SCEV *>(0)));
4443 return Pair.first->second ? Pair.first->second : V;
4445 // Otherwise compute it.
4446 const SCEV *C = computeSCEVAtScope(V, L);
4447 ValuesAtScopes[V][L] = C;
4451 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
4452 if (isa<SCEVConstant>(V)) return V;
4454 // If this instruction is evolved from a constant-evolving PHI, compute the
4455 // exit value from the loop without using SCEVs.
4456 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
4457 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
4458 const Loop *LI = (*this->LI)[I->getParent()];
4459 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
4460 if (PHINode *PN = dyn_cast<PHINode>(I))
4461 if (PN->getParent() == LI->getHeader()) {
4462 // Okay, there is no closed form solution for the PHI node. Check
4463 // to see if the loop that contains it has a known backedge-taken
4464 // count. If so, we may be able to force computation of the exit
4466 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
4467 if (const SCEVConstant *BTCC =
4468 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
4469 // Okay, we know how many times the containing loop executes. If
4470 // this is a constant evolving PHI node, get the final value at
4471 // the specified iteration number.
4472 Constant *RV = getConstantEvolutionLoopExitValue(PN,
4473 BTCC->getValue()->getValue(),
4475 if (RV) return getSCEV(RV);
4479 // Okay, this is an expression that we cannot symbolically evaluate
4480 // into a SCEV. Check to see if it's possible to symbolically evaluate
4481 // the arguments into constants, and if so, try to constant propagate the
4482 // result. This is particularly useful for computing loop exit values.
4483 if (CanConstantFold(I)) {
4484 SmallVector<Constant *, 4> Operands;
4485 bool MadeImprovement = false;
4486 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
4487 Value *Op = I->getOperand(i);
4488 if (Constant *C = dyn_cast<Constant>(Op)) {
4489 Operands.push_back(C);
4493 // If any of the operands is non-constant and if they are
4494 // non-integer and non-pointer, don't even try to analyze them
4495 // with scev techniques.
4496 if (!isSCEVable(Op->getType()))
4499 const SCEV *OrigV = getSCEV(Op);
4500 const SCEV *OpV = getSCEVAtScope(OrigV, L);
4501 MadeImprovement |= OrigV != OpV;
4504 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV))
4506 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV))
4507 C = dyn_cast<Constant>(SU->getValue());
4509 if (C->getType() != Op->getType())
4510 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
4514 Operands.push_back(C);
4517 // Check to see if getSCEVAtScope actually made an improvement.
4518 if (MadeImprovement) {
4520 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
4521 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
4522 Operands[0], Operands[1], TD);
4524 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
4525 &Operands[0], Operands.size(), TD);
4532 // This is some other type of SCEVUnknown, just return it.
4536 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
4537 // Avoid performing the look-up in the common case where the specified
4538 // expression has no loop-variant portions.
4539 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
4540 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
4541 if (OpAtScope != Comm->getOperand(i)) {
4542 // Okay, at least one of these operands is loop variant but might be
4543 // foldable. Build a new instance of the folded commutative expression.
4544 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
4545 Comm->op_begin()+i);
4546 NewOps.push_back(OpAtScope);
4548 for (++i; i != e; ++i) {
4549 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
4550 NewOps.push_back(OpAtScope);
4552 if (isa<SCEVAddExpr>(Comm))
4553 return getAddExpr(NewOps);
4554 if (isa<SCEVMulExpr>(Comm))
4555 return getMulExpr(NewOps);
4556 if (isa<SCEVSMaxExpr>(Comm))
4557 return getSMaxExpr(NewOps);
4558 if (isa<SCEVUMaxExpr>(Comm))
4559 return getUMaxExpr(NewOps);
4560 llvm_unreachable("Unknown commutative SCEV type!");
4563 // If we got here, all operands are loop invariant.
4567 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
4568 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
4569 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
4570 if (LHS == Div->getLHS() && RHS == Div->getRHS())
4571 return Div; // must be loop invariant
4572 return getUDivExpr(LHS, RHS);
4575 // If this is a loop recurrence for a loop that does not contain L, then we
4576 // are dealing with the final value computed by the loop.
4577 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
4578 // First, attempt to evaluate each operand.
4579 // Avoid performing the look-up in the common case where the specified
4580 // expression has no loop-variant portions.
4581 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
4582 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
4583 if (OpAtScope == AddRec->getOperand(i))
4586 // Okay, at least one of these operands is loop variant but might be
4587 // foldable. Build a new instance of the folded commutative expression.
4588 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(),
4589 AddRec->op_begin()+i);
4590 NewOps.push_back(OpAtScope);
4591 for (++i; i != e; ++i)
4592 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
4594 AddRec = cast<SCEVAddRecExpr>(getAddRecExpr(NewOps, AddRec->getLoop()));
4598 // If the scope is outside the addrec's loop, evaluate it by using the
4599 // loop exit value of the addrec.
4600 if (!AddRec->getLoop()->contains(L)) {
4601 // To evaluate this recurrence, we need to know how many times the AddRec
4602 // loop iterates. Compute this now.
4603 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
4604 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
4606 // Then, evaluate the AddRec.
4607 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
4613 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
4614 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
4615 if (Op == Cast->getOperand())
4616 return Cast; // must be loop invariant
4617 return getZeroExtendExpr(Op, Cast->getType());
4620 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
4621 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
4622 if (Op == Cast->getOperand())
4623 return Cast; // must be loop invariant
4624 return getSignExtendExpr(Op, Cast->getType());
4627 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
4628 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
4629 if (Op == Cast->getOperand())
4630 return Cast; // must be loop invariant
4631 return getTruncateExpr(Op, Cast->getType());
4634 llvm_unreachable("Unknown SCEV type!");
4638 /// getSCEVAtScope - This is a convenience function which does
4639 /// getSCEVAtScope(getSCEV(V), L).
4640 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
4641 return getSCEVAtScope(getSCEV(V), L);
4644 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
4645 /// following equation:
4647 /// A * X = B (mod N)
4649 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
4650 /// A and B isn't important.
4652 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
4653 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
4654 ScalarEvolution &SE) {
4655 uint32_t BW = A.getBitWidth();
4656 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
4657 assert(A != 0 && "A must be non-zero.");
4661 // The gcd of A and N may have only one prime factor: 2. The number of
4662 // trailing zeros in A is its multiplicity
4663 uint32_t Mult2 = A.countTrailingZeros();
4666 // 2. Check if B is divisible by D.
4668 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
4669 // is not less than multiplicity of this prime factor for D.
4670 if (B.countTrailingZeros() < Mult2)
4671 return SE.getCouldNotCompute();
4673 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
4676 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
4677 // bit width during computations.
4678 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
4679 APInt Mod(BW + 1, 0);
4680 Mod.set(BW - Mult2); // Mod = N / D
4681 APInt I = AD.multiplicativeInverse(Mod);
4683 // 4. Compute the minimum unsigned root of the equation:
4684 // I * (B / D) mod (N / D)
4685 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
4687 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
4689 return SE.getConstant(Result.trunc(BW));
4692 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
4693 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
4694 /// might be the same) or two SCEVCouldNotCompute objects.
4696 static std::pair<const SCEV *,const SCEV *>
4697 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
4698 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
4699 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
4700 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
4701 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
4703 // We currently can only solve this if the coefficients are constants.
4704 if (!LC || !MC || !NC) {
4705 const SCEV *CNC = SE.getCouldNotCompute();
4706 return std::make_pair(CNC, CNC);
4709 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
4710 const APInt &L = LC->getValue()->getValue();
4711 const APInt &M = MC->getValue()->getValue();
4712 const APInt &N = NC->getValue()->getValue();
4713 APInt Two(BitWidth, 2);
4714 APInt Four(BitWidth, 4);
4717 using namespace APIntOps;
4719 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
4720 // The B coefficient is M-N/2
4724 // The A coefficient is N/2
4725 APInt A(N.sdiv(Two));
4727 // Compute the B^2-4ac term.
4730 SqrtTerm -= Four * (A * C);
4732 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
4733 // integer value or else APInt::sqrt() will assert.
4734 APInt SqrtVal(SqrtTerm.sqrt());
4736 // Compute the two solutions for the quadratic formula.
4737 // The divisions must be performed as signed divisions.
4739 APInt TwoA( A << 1 );
4740 if (TwoA.isMinValue()) {
4741 const SCEV *CNC = SE.getCouldNotCompute();
4742 return std::make_pair(CNC, CNC);
4745 LLVMContext &Context = SE.getContext();
4747 ConstantInt *Solution1 =
4748 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
4749 ConstantInt *Solution2 =
4750 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
4752 return std::make_pair(SE.getConstant(Solution1),
4753 SE.getConstant(Solution2));
4754 } // end APIntOps namespace
4757 /// HowFarToZero - Return the number of times a backedge comparing the specified
4758 /// value to zero will execute. If not computable, return CouldNotCompute.
4759 ScalarEvolution::BackedgeTakenInfo
4760 ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) {
4761 // If the value is a constant
4762 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
4763 // If the value is already zero, the branch will execute zero times.
4764 if (C->getValue()->isZero()) return C;
4765 return getCouldNotCompute(); // Otherwise it will loop infinitely.
4768 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
4769 if (!AddRec || AddRec->getLoop() != L)
4770 return getCouldNotCompute();
4772 if (AddRec->isAffine()) {
4773 // If this is an affine expression, the execution count of this branch is
4774 // the minimum unsigned root of the following equation:
4776 // Start + Step*N = 0 (mod 2^BW)
4780 // Step*N = -Start (mod 2^BW)
4782 // where BW is the common bit width of Start and Step.
4784 // Get the initial value for the loop.
4785 const SCEV *Start = getSCEVAtScope(AddRec->getStart(),
4786 L->getParentLoop());
4787 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1),
4788 L->getParentLoop());
4790 if (const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) {
4791 // For now we handle only constant steps.
4793 // First, handle unitary steps.
4794 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so:
4795 return getNegativeSCEV(Start); // N = -Start (as unsigned)
4796 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so:
4797 return Start; // N = Start (as unsigned)
4799 // Then, try to solve the above equation provided that Start is constant.
4800 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
4801 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
4802 -StartC->getValue()->getValue(),
4805 } else if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
4806 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
4807 // the quadratic equation to solve it.
4808 std::pair<const SCEV *,const SCEV *> Roots = SolveQuadraticEquation(AddRec,
4810 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
4811 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
4814 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1
4815 << " sol#2: " << *R2 << "\n";
4817 // Pick the smallest positive root value.
4818 if (ConstantInt *CB =
4819 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
4820 R1->getValue(), R2->getValue()))) {
4821 if (CB->getZExtValue() == false)
4822 std::swap(R1, R2); // R1 is the minimum root now.
4824 // We can only use this value if the chrec ends up with an exact zero
4825 // value at this index. When solving for "X*X != 5", for example, we
4826 // should not accept a root of 2.
4827 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
4829 return R1; // We found a quadratic root!
4834 return getCouldNotCompute();
4837 /// HowFarToNonZero - Return the number of times a backedge checking the
4838 /// specified value for nonzero will execute. If not computable, return
4840 ScalarEvolution::BackedgeTakenInfo
4841 ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
4842 // Loops that look like: while (X == 0) are very strange indeed. We don't
4843 // handle them yet except for the trivial case. This could be expanded in the
4844 // future as needed.
4846 // If the value is a constant, check to see if it is known to be non-zero
4847 // already. If so, the backedge will execute zero times.
4848 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
4849 if (!C->getValue()->isNullValue())
4850 return getConstant(C->getType(), 0);
4851 return getCouldNotCompute(); // Otherwise it will loop infinitely.
4854 // We could implement others, but I really doubt anyone writes loops like
4855 // this, and if they did, they would already be constant folded.
4856 return getCouldNotCompute();
4859 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
4860 /// (which may not be an immediate predecessor) which has exactly one
4861 /// successor from which BB is reachable, or null if no such block is
4864 std::pair<BasicBlock *, BasicBlock *>
4865 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
4866 // If the block has a unique predecessor, then there is no path from the
4867 // predecessor to the block that does not go through the direct edge
4868 // from the predecessor to the block.
4869 if (BasicBlock *Pred = BB->getSinglePredecessor())
4870 return std::make_pair(Pred, BB);
4872 // A loop's header is defined to be a block that dominates the loop.
4873 // If the header has a unique predecessor outside the loop, it must be
4874 // a block that has exactly one successor that can reach the loop.
4875 if (Loop *L = LI->getLoopFor(BB))
4876 return std::make_pair(L->getLoopPredecessor(), L->getHeader());
4878 return std::pair<BasicBlock *, BasicBlock *>();
4881 /// HasSameValue - SCEV structural equivalence is usually sufficient for
4882 /// testing whether two expressions are equal, however for the purposes of
4883 /// looking for a condition guarding a loop, it can be useful to be a little
4884 /// more general, since a front-end may have replicated the controlling
4887 static bool HasSameValue(const SCEV *A, const SCEV *B) {
4888 // Quick check to see if they are the same SCEV.
4889 if (A == B) return true;
4891 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
4892 // two different instructions with the same value. Check for this case.
4893 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
4894 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
4895 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
4896 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
4897 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory())
4900 // Otherwise assume they may have a different value.
4904 /// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with
4905 /// predicate Pred. Return true iff any changes were made.
4907 bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
4908 const SCEV *&LHS, const SCEV *&RHS) {
4909 bool Changed = false;
4911 // Canonicalize a constant to the right side.
4912 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
4913 // Check for both operands constant.
4914 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
4915 if (ConstantExpr::getICmp(Pred,
4917 RHSC->getValue())->isNullValue())
4918 goto trivially_false;
4920 goto trivially_true;
4922 // Otherwise swap the operands to put the constant on the right.
4923 std::swap(LHS, RHS);
4924 Pred = ICmpInst::getSwappedPredicate(Pred);
4928 // If we're comparing an addrec with a value which is loop-invariant in the
4929 // addrec's loop, put the addrec on the left. Also make a dominance check,
4930 // as both operands could be addrecs loop-invariant in each other's loop.
4931 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
4932 const Loop *L = AR->getLoop();
4933 if (LHS->isLoopInvariant(L) && LHS->properlyDominates(L->getHeader(), DT)) {
4934 std::swap(LHS, RHS);
4935 Pred = ICmpInst::getSwappedPredicate(Pred);
4940 // If there's a constant operand, canonicalize comparisons with boundary
4941 // cases, and canonicalize *-or-equal comparisons to regular comparisons.
4942 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
4943 const APInt &RA = RC->getValue()->getValue();
4945 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
4946 case ICmpInst::ICMP_EQ:
4947 case ICmpInst::ICMP_NE:
4949 case ICmpInst::ICMP_UGE:
4950 if ((RA - 1).isMinValue()) {
4951 Pred = ICmpInst::ICMP_NE;
4952 RHS = getConstant(RA - 1);
4956 if (RA.isMaxValue()) {
4957 Pred = ICmpInst::ICMP_EQ;
4961 if (RA.isMinValue()) goto trivially_true;
4963 Pred = ICmpInst::ICMP_UGT;
4964 RHS = getConstant(RA - 1);
4967 case ICmpInst::ICMP_ULE:
4968 if ((RA + 1).isMaxValue()) {
4969 Pred = ICmpInst::ICMP_NE;
4970 RHS = getConstant(RA + 1);
4974 if (RA.isMinValue()) {
4975 Pred = ICmpInst::ICMP_EQ;
4979 if (RA.isMaxValue()) goto trivially_true;
4981 Pred = ICmpInst::ICMP_ULT;
4982 RHS = getConstant(RA + 1);
4985 case ICmpInst::ICMP_SGE:
4986 if ((RA - 1).isMinSignedValue()) {
4987 Pred = ICmpInst::ICMP_NE;
4988 RHS = getConstant(RA - 1);
4992 if (RA.isMaxSignedValue()) {
4993 Pred = ICmpInst::ICMP_EQ;
4997 if (RA.isMinSignedValue()) goto trivially_true;
4999 Pred = ICmpInst::ICMP_SGT;
5000 RHS = getConstant(RA - 1);
5003 case ICmpInst::ICMP_SLE:
5004 if ((RA + 1).isMaxSignedValue()) {
5005 Pred = ICmpInst::ICMP_NE;
5006 RHS = getConstant(RA + 1);
5010 if (RA.isMinSignedValue()) {
5011 Pred = ICmpInst::ICMP_EQ;
5015 if (RA.isMaxSignedValue()) goto trivially_true;
5017 Pred = ICmpInst::ICMP_SLT;
5018 RHS = getConstant(RA + 1);
5021 case ICmpInst::ICMP_UGT:
5022 if (RA.isMinValue()) {
5023 Pred = ICmpInst::ICMP_NE;
5027 if ((RA + 1).isMaxValue()) {
5028 Pred = ICmpInst::ICMP_EQ;
5029 RHS = getConstant(RA + 1);
5033 if (RA.isMaxValue()) goto trivially_false;
5035 case ICmpInst::ICMP_ULT:
5036 if (RA.isMaxValue()) {
5037 Pred = ICmpInst::ICMP_NE;
5041 if ((RA - 1).isMinValue()) {
5042 Pred = ICmpInst::ICMP_EQ;
5043 RHS = getConstant(RA - 1);
5047 if (RA.isMinValue()) goto trivially_false;
5049 case ICmpInst::ICMP_SGT:
5050 if (RA.isMinSignedValue()) {
5051 Pred = ICmpInst::ICMP_NE;
5055 if ((RA + 1).isMaxSignedValue()) {
5056 Pred = ICmpInst::ICMP_EQ;
5057 RHS = getConstant(RA + 1);
5061 if (RA.isMaxSignedValue()) goto trivially_false;
5063 case ICmpInst::ICMP_SLT:
5064 if (RA.isMaxSignedValue()) {
5065 Pred = ICmpInst::ICMP_NE;
5069 if ((RA - 1).isMinSignedValue()) {
5070 Pred = ICmpInst::ICMP_EQ;
5071 RHS = getConstant(RA - 1);
5075 if (RA.isMinSignedValue()) goto trivially_false;
5080 // Check for obvious equality.
5081 if (HasSameValue(LHS, RHS)) {
5082 if (ICmpInst::isTrueWhenEqual(Pred))
5083 goto trivially_true;
5084 if (ICmpInst::isFalseWhenEqual(Pred))
5085 goto trivially_false;
5088 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
5089 // adding or subtracting 1 from one of the operands.
5091 case ICmpInst::ICMP_SLE:
5092 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) {
5093 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
5094 /*HasNUW=*/false, /*HasNSW=*/true);
5095 Pred = ICmpInst::ICMP_SLT;
5097 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) {
5098 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
5099 /*HasNUW=*/false, /*HasNSW=*/true);
5100 Pred = ICmpInst::ICMP_SLT;
5104 case ICmpInst::ICMP_SGE:
5105 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) {
5106 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
5107 /*HasNUW=*/false, /*HasNSW=*/true);
5108 Pred = ICmpInst::ICMP_SGT;
5110 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) {
5111 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
5112 /*HasNUW=*/false, /*HasNSW=*/true);
5113 Pred = ICmpInst::ICMP_SGT;
5117 case ICmpInst::ICMP_ULE:
5118 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) {
5119 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
5120 /*HasNUW=*/true, /*HasNSW=*/false);
5121 Pred = ICmpInst::ICMP_ULT;
5123 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) {
5124 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
5125 /*HasNUW=*/true, /*HasNSW=*/false);
5126 Pred = ICmpInst::ICMP_ULT;
5130 case ICmpInst::ICMP_UGE:
5131 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) {
5132 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
5133 /*HasNUW=*/true, /*HasNSW=*/false);
5134 Pred = ICmpInst::ICMP_UGT;
5136 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) {
5137 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
5138 /*HasNUW=*/true, /*HasNSW=*/false);
5139 Pred = ICmpInst::ICMP_UGT;
5147 // TODO: More simplifications are possible here.
5153 LHS = RHS = getConstant(Type::getInt1Ty(getContext()), 0);
5154 Pred = ICmpInst::ICMP_EQ;
5159 LHS = RHS = getConstant(Type::getInt1Ty(getContext()), 0);
5160 Pred = ICmpInst::ICMP_NE;
5164 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
5165 return getSignedRange(S).getSignedMax().isNegative();
5168 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
5169 return getSignedRange(S).getSignedMin().isStrictlyPositive();
5172 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
5173 return !getSignedRange(S).getSignedMin().isNegative();
5176 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
5177 return !getSignedRange(S).getSignedMax().isStrictlyPositive();
5180 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
5181 return isKnownNegative(S) || isKnownPositive(S);
5184 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
5185 const SCEV *LHS, const SCEV *RHS) {
5186 // Canonicalize the inputs first.
5187 (void)SimplifyICmpOperands(Pred, LHS, RHS);
5189 // If LHS or RHS is an addrec, check to see if the condition is true in
5190 // every iteration of the loop.
5191 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
5192 if (isLoopEntryGuardedByCond(
5193 AR->getLoop(), Pred, AR->getStart(), RHS) &&
5194 isLoopBackedgeGuardedByCond(
5195 AR->getLoop(), Pred, AR->getPostIncExpr(*this), RHS))
5197 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS))
5198 if (isLoopEntryGuardedByCond(
5199 AR->getLoop(), Pred, LHS, AR->getStart()) &&
5200 isLoopBackedgeGuardedByCond(
5201 AR->getLoop(), Pred, LHS, AR->getPostIncExpr(*this)))
5204 // Otherwise see what can be done with known constant ranges.
5205 return isKnownPredicateWithRanges(Pred, LHS, RHS);
5209 ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred,
5210 const SCEV *LHS, const SCEV *RHS) {
5211 if (HasSameValue(LHS, RHS))
5212 return ICmpInst::isTrueWhenEqual(Pred);
5214 // This code is split out from isKnownPredicate because it is called from
5215 // within isLoopEntryGuardedByCond.
5218 llvm_unreachable("Unexpected ICmpInst::Predicate value!");
5220 case ICmpInst::ICMP_SGT:
5221 Pred = ICmpInst::ICMP_SLT;
5222 std::swap(LHS, RHS);
5223 case ICmpInst::ICMP_SLT: {
5224 ConstantRange LHSRange = getSignedRange(LHS);
5225 ConstantRange RHSRange = getSignedRange(RHS);
5226 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
5228 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
5232 case ICmpInst::ICMP_SGE:
5233 Pred = ICmpInst::ICMP_SLE;
5234 std::swap(LHS, RHS);
5235 case ICmpInst::ICMP_SLE: {
5236 ConstantRange LHSRange = getSignedRange(LHS);
5237 ConstantRange RHSRange = getSignedRange(RHS);
5238 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
5240 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
5244 case ICmpInst::ICMP_UGT:
5245 Pred = ICmpInst::ICMP_ULT;
5246 std::swap(LHS, RHS);
5247 case ICmpInst::ICMP_ULT: {
5248 ConstantRange LHSRange = getUnsignedRange(LHS);
5249 ConstantRange RHSRange = getUnsignedRange(RHS);
5250 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
5252 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
5256 case ICmpInst::ICMP_UGE:
5257 Pred = ICmpInst::ICMP_ULE;
5258 std::swap(LHS, RHS);
5259 case ICmpInst::ICMP_ULE: {
5260 ConstantRange LHSRange = getUnsignedRange(LHS);
5261 ConstantRange RHSRange = getUnsignedRange(RHS);
5262 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
5264 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
5268 case ICmpInst::ICMP_NE: {
5269 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
5271 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
5274 const SCEV *Diff = getMinusSCEV(LHS, RHS);
5275 if (isKnownNonZero(Diff))
5279 case ICmpInst::ICMP_EQ:
5280 // The check at the top of the function catches the case where
5281 // the values are known to be equal.
5287 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
5288 /// protected by a conditional between LHS and RHS. This is used to
5289 /// to eliminate casts.
5291 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
5292 ICmpInst::Predicate Pred,
5293 const SCEV *LHS, const SCEV *RHS) {
5294 // Interpret a null as meaning no loop, where there is obviously no guard
5295 // (interprocedural conditions notwithstanding).
5296 if (!L) return true;
5298 BasicBlock *Latch = L->getLoopLatch();
5302 BranchInst *LoopContinuePredicate =
5303 dyn_cast<BranchInst>(Latch->getTerminator());
5304 if (!LoopContinuePredicate ||
5305 LoopContinuePredicate->isUnconditional())
5308 return isImpliedCond(Pred, LHS, RHS,
5309 LoopContinuePredicate->getCondition(),
5310 LoopContinuePredicate->getSuccessor(0) != L->getHeader());
5313 /// isLoopEntryGuardedByCond - Test whether entry to the loop is protected
5314 /// by a conditional between LHS and RHS. This is used to help avoid max
5315 /// expressions in loop trip counts, and to eliminate casts.
5317 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
5318 ICmpInst::Predicate Pred,
5319 const SCEV *LHS, const SCEV *RHS) {
5320 // Interpret a null as meaning no loop, where there is obviously no guard
5321 // (interprocedural conditions notwithstanding).
5322 if (!L) return false;
5324 // Starting at the loop predecessor, climb up the predecessor chain, as long
5325 // as there are predecessors that can be found that have unique successors
5326 // leading to the original header.
5327 for (std::pair<BasicBlock *, BasicBlock *>
5328 Pair(L->getLoopPredecessor(), L->getHeader());
5330 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
5332 BranchInst *LoopEntryPredicate =
5333 dyn_cast<BranchInst>(Pair.first->getTerminator());
5334 if (!LoopEntryPredicate ||
5335 LoopEntryPredicate->isUnconditional())
5338 if (isImpliedCond(Pred, LHS, RHS,
5339 LoopEntryPredicate->getCondition(),
5340 LoopEntryPredicate->getSuccessor(0) != Pair.second))
5347 /// isImpliedCond - Test whether the condition described by Pred, LHS,
5348 /// and RHS is true whenever the given Cond value evaluates to true.
5349 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred,
5350 const SCEV *LHS, const SCEV *RHS,
5351 Value *FoundCondValue,
5353 // Recursively handle And and Or conditions.
5354 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) {
5355 if (BO->getOpcode() == Instruction::And) {
5357 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
5358 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
5359 } else if (BO->getOpcode() == Instruction::Or) {
5361 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
5362 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
5366 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue);
5367 if (!ICI) return false;
5369 // Bail if the ICmp's operands' types are wider than the needed type
5370 // before attempting to call getSCEV on them. This avoids infinite
5371 // recursion, since the analysis of widening casts can require loop
5372 // exit condition information for overflow checking, which would
5374 if (getTypeSizeInBits(LHS->getType()) <
5375 getTypeSizeInBits(ICI->getOperand(0)->getType()))
5378 // Now that we found a conditional branch that dominates the loop, check to
5379 // see if it is the comparison we are looking for.
5380 ICmpInst::Predicate FoundPred;
5382 FoundPred = ICI->getInversePredicate();
5384 FoundPred = ICI->getPredicate();
5386 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
5387 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
5389 // Balance the types. The case where FoundLHS' type is wider than
5390 // LHS' type is checked for above.
5391 if (getTypeSizeInBits(LHS->getType()) >
5392 getTypeSizeInBits(FoundLHS->getType())) {
5393 if (CmpInst::isSigned(Pred)) {
5394 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
5395 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
5397 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
5398 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
5402 // Canonicalize the query to match the way instcombine will have
5403 // canonicalized the comparison.
5404 if (SimplifyICmpOperands(Pred, LHS, RHS))
5406 return CmpInst::isTrueWhenEqual(Pred);
5407 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
5408 if (FoundLHS == FoundRHS)
5409 return CmpInst::isFalseWhenEqual(Pred);
5411 // Check to see if we can make the LHS or RHS match.
5412 if (LHS == FoundRHS || RHS == FoundLHS) {
5413 if (isa<SCEVConstant>(RHS)) {
5414 std::swap(FoundLHS, FoundRHS);
5415 FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
5417 std::swap(LHS, RHS);
5418 Pred = ICmpInst::getSwappedPredicate(Pred);
5422 // Check whether the found predicate is the same as the desired predicate.
5423 if (FoundPred == Pred)
5424 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
5426 // Check whether swapping the found predicate makes it the same as the
5427 // desired predicate.
5428 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
5429 if (isa<SCEVConstant>(RHS))
5430 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
5432 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
5433 RHS, LHS, FoundLHS, FoundRHS);
5436 // Check whether the actual condition is beyond sufficient.
5437 if (FoundPred == ICmpInst::ICMP_EQ)
5438 if (ICmpInst::isTrueWhenEqual(Pred))
5439 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
5441 if (Pred == ICmpInst::ICMP_NE)
5442 if (!ICmpInst::isTrueWhenEqual(FoundPred))
5443 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
5446 // Otherwise assume the worst.
5450 /// isImpliedCondOperands - Test whether the condition described by Pred,
5451 /// LHS, and RHS is true whenever the condition described by Pred, FoundLHS,
5452 /// and FoundRHS is true.
5453 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
5454 const SCEV *LHS, const SCEV *RHS,
5455 const SCEV *FoundLHS,
5456 const SCEV *FoundRHS) {
5457 return isImpliedCondOperandsHelper(Pred, LHS, RHS,
5458 FoundLHS, FoundRHS) ||
5459 // ~x < ~y --> x > y
5460 isImpliedCondOperandsHelper(Pred, LHS, RHS,
5461 getNotSCEV(FoundRHS),
5462 getNotSCEV(FoundLHS));
5465 /// isImpliedCondOperandsHelper - Test whether the condition described by
5466 /// Pred, LHS, and RHS is true whenever the condition described by Pred,
5467 /// FoundLHS, and FoundRHS is true.
5469 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
5470 const SCEV *LHS, const SCEV *RHS,
5471 const SCEV *FoundLHS,
5472 const SCEV *FoundRHS) {
5474 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
5475 case ICmpInst::ICMP_EQ:
5476 case ICmpInst::ICMP_NE:
5477 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
5480 case ICmpInst::ICMP_SLT:
5481 case ICmpInst::ICMP_SLE:
5482 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
5483 isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, RHS, FoundRHS))
5486 case ICmpInst::ICMP_SGT:
5487 case ICmpInst::ICMP_SGE:
5488 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
5489 isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, RHS, FoundRHS))
5492 case ICmpInst::ICMP_ULT:
5493 case ICmpInst::ICMP_ULE:
5494 if (isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
5495 isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, RHS, FoundRHS))
5498 case ICmpInst::ICMP_UGT:
5499 case ICmpInst::ICMP_UGE:
5500 if (isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
5501 isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, RHS, FoundRHS))
5509 /// getBECount - Subtract the end and start values and divide by the step,
5510 /// rounding up, to get the number of times the backedge is executed. Return
5511 /// CouldNotCompute if an intermediate computation overflows.
5512 const SCEV *ScalarEvolution::getBECount(const SCEV *Start,
5516 assert(!isKnownNegative(Step) &&
5517 "This code doesn't handle negative strides yet!");
5519 const Type *Ty = Start->getType();
5520 const SCEV *NegOne = getConstant(Ty, (uint64_t)-1);
5521 const SCEV *Diff = getMinusSCEV(End, Start);
5522 const SCEV *RoundUp = getAddExpr(Step, NegOne);
5524 // Add an adjustment to the difference between End and Start so that
5525 // the division will effectively round up.
5526 const SCEV *Add = getAddExpr(Diff, RoundUp);
5529 // Check Add for unsigned overflow.
5530 // TODO: More sophisticated things could be done here.
5531 const Type *WideTy = IntegerType::get(getContext(),
5532 getTypeSizeInBits(Ty) + 1);
5533 const SCEV *EDiff = getZeroExtendExpr(Diff, WideTy);
5534 const SCEV *ERoundUp = getZeroExtendExpr(RoundUp, WideTy);
5535 const SCEV *OperandExtendedAdd = getAddExpr(EDiff, ERoundUp);
5536 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd)
5537 return getCouldNotCompute();
5540 return getUDivExpr(Add, Step);
5543 /// HowManyLessThans - Return the number of times a backedge containing the
5544 /// specified less-than comparison will execute. If not computable, return
5545 /// CouldNotCompute.
5546 ScalarEvolution::BackedgeTakenInfo
5547 ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
5548 const Loop *L, bool isSigned) {
5549 // Only handle: "ADDREC < LoopInvariant".
5550 if (!RHS->isLoopInvariant(L)) return getCouldNotCompute();
5552 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
5553 if (!AddRec || AddRec->getLoop() != L)
5554 return getCouldNotCompute();
5556 // Check to see if we have a flag which makes analysis easy.
5557 bool NoWrap = isSigned ? AddRec->hasNoSignedWrap() :
5558 AddRec->hasNoUnsignedWrap();
5560 if (AddRec->isAffine()) {
5561 unsigned BitWidth = getTypeSizeInBits(AddRec->getType());
5562 const SCEV *Step = AddRec->getStepRecurrence(*this);
5565 return getCouldNotCompute();
5566 if (Step->isOne()) {
5567 // With unit stride, the iteration never steps past the limit value.
5568 } else if (isKnownPositive(Step)) {
5569 // Test whether a positive iteration can step past the limit
5570 // value and past the maximum value for its type in a single step.
5571 // Note that it's not sufficient to check NoWrap here, because even
5572 // though the value after a wrap is undefined, it's not undefined
5573 // behavior, so if wrap does occur, the loop could either terminate or
5574 // loop infinitely, but in either case, the loop is guaranteed to
5575 // iterate at least until the iteration where the wrapping occurs.
5576 const SCEV *One = getConstant(Step->getType(), 1);
5578 APInt Max = APInt::getSignedMaxValue(BitWidth);
5579 if ((Max - getSignedRange(getMinusSCEV(Step, One)).getSignedMax())
5580 .slt(getSignedRange(RHS).getSignedMax()))
5581 return getCouldNotCompute();
5583 APInt Max = APInt::getMaxValue(BitWidth);
5584 if ((Max - getUnsignedRange(getMinusSCEV(Step, One)).getUnsignedMax())
5585 .ult(getUnsignedRange(RHS).getUnsignedMax()))
5586 return getCouldNotCompute();
5589 // TODO: Handle negative strides here and below.
5590 return getCouldNotCompute();
5592 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant
5593 // m. So, we count the number of iterations in which {n,+,s} < m is true.
5594 // Note that we cannot simply return max(m-n,0)/s because it's not safe to
5595 // treat m-n as signed nor unsigned due to overflow possibility.
5597 // First, we get the value of the LHS in the first iteration: n
5598 const SCEV *Start = AddRec->getOperand(0);
5600 // Determine the minimum constant start value.
5601 const SCEV *MinStart = getConstant(isSigned ?
5602 getSignedRange(Start).getSignedMin() :
5603 getUnsignedRange(Start).getUnsignedMin());
5605 // If we know that the condition is true in order to enter the loop,
5606 // then we know that it will run exactly (m-n)/s times. Otherwise, we
5607 // only know that it will execute (max(m,n)-n)/s times. In both cases,
5608 // the division must round up.
5609 const SCEV *End = RHS;
5610 if (!isLoopEntryGuardedByCond(L,
5611 isSigned ? ICmpInst::ICMP_SLT :
5613 getMinusSCEV(Start, Step), RHS))
5614 End = isSigned ? getSMaxExpr(RHS, Start)
5615 : getUMaxExpr(RHS, Start);
5617 // Determine the maximum constant end value.
5618 const SCEV *MaxEnd = getConstant(isSigned ?
5619 getSignedRange(End).getSignedMax() :
5620 getUnsignedRange(End).getUnsignedMax());
5622 // If MaxEnd is within a step of the maximum integer value in its type,
5623 // adjust it down to the minimum value which would produce the same effect.
5624 // This allows the subsequent ceiling division of (N+(step-1))/step to
5625 // compute the correct value.
5626 const SCEV *StepMinusOne = getMinusSCEV(Step,
5627 getConstant(Step->getType(), 1));
5630 getMinusSCEV(getConstant(APInt::getSignedMaxValue(BitWidth)),
5633 getMinusSCEV(getConstant(APInt::getMaxValue(BitWidth)),
5636 // Finally, we subtract these two values and divide, rounding up, to get
5637 // the number of times the backedge is executed.
5638 const SCEV *BECount = getBECount(Start, End, Step, NoWrap);
5640 // The maximum backedge count is similar, except using the minimum start
5641 // value and the maximum end value.
5642 const SCEV *MaxBECount = getBECount(MinStart, MaxEnd, Step, NoWrap);
5644 return BackedgeTakenInfo(BECount, MaxBECount);
5647 return getCouldNotCompute();
5650 /// getNumIterationsInRange - Return the number of iterations of this loop that
5651 /// produce values in the specified constant range. Another way of looking at
5652 /// this is that it returns the first iteration number where the value is not in
5653 /// the condition, thus computing the exit count. If the iteration count can't
5654 /// be computed, an instance of SCEVCouldNotCompute is returned.
5655 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
5656 ScalarEvolution &SE) const {
5657 if (Range.isFullSet()) // Infinite loop.
5658 return SE.getCouldNotCompute();
5660 // If the start is a non-zero constant, shift the range to simplify things.
5661 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
5662 if (!SC->getValue()->isZero()) {
5663 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
5664 Operands[0] = SE.getConstant(SC->getType(), 0);
5665 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop());
5666 if (const SCEVAddRecExpr *ShiftedAddRec =
5667 dyn_cast<SCEVAddRecExpr>(Shifted))
5668 return ShiftedAddRec->getNumIterationsInRange(
5669 Range.subtract(SC->getValue()->getValue()), SE);
5670 // This is strange and shouldn't happen.
5671 return SE.getCouldNotCompute();
5674 // The only time we can solve this is when we have all constant indices.
5675 // Otherwise, we cannot determine the overflow conditions.
5676 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
5677 if (!isa<SCEVConstant>(getOperand(i)))
5678 return SE.getCouldNotCompute();
5681 // Okay at this point we know that all elements of the chrec are constants and
5682 // that the start element is zero.
5684 // First check to see if the range contains zero. If not, the first
5686 unsigned BitWidth = SE.getTypeSizeInBits(getType());
5687 if (!Range.contains(APInt(BitWidth, 0)))
5688 return SE.getConstant(getType(), 0);
5691 // If this is an affine expression then we have this situation:
5692 // Solve {0,+,A} in Range === Ax in Range
5694 // We know that zero is in the range. If A is positive then we know that
5695 // the upper value of the range must be the first possible exit value.
5696 // If A is negative then the lower of the range is the last possible loop
5697 // value. Also note that we already checked for a full range.
5698 APInt One(BitWidth,1);
5699 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
5700 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
5702 // The exit value should be (End+A)/A.
5703 APInt ExitVal = (End + A).udiv(A);
5704 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
5706 // Evaluate at the exit value. If we really did fall out of the valid
5707 // range, then we computed our trip count, otherwise wrap around or other
5708 // things must have happened.
5709 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
5710 if (Range.contains(Val->getValue()))
5711 return SE.getCouldNotCompute(); // Something strange happened
5713 // Ensure that the previous value is in the range. This is a sanity check.
5714 assert(Range.contains(
5715 EvaluateConstantChrecAtConstant(this,
5716 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
5717 "Linear scev computation is off in a bad way!");
5718 return SE.getConstant(ExitValue);
5719 } else if (isQuadratic()) {
5720 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
5721 // quadratic equation to solve it. To do this, we must frame our problem in
5722 // terms of figuring out when zero is crossed, instead of when
5723 // Range.getUpper() is crossed.
5724 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
5725 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
5726 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop());
5728 // Next, solve the constructed addrec
5729 std::pair<const SCEV *,const SCEV *> Roots =
5730 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
5731 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
5732 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
5734 // Pick the smallest positive root value.
5735 if (ConstantInt *CB =
5736 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
5737 R1->getValue(), R2->getValue()))) {
5738 if (CB->getZExtValue() == false)
5739 std::swap(R1, R2); // R1 is the minimum root now.
5741 // Make sure the root is not off by one. The returned iteration should
5742 // not be in the range, but the previous one should be. When solving
5743 // for "X*X < 5", for example, we should not return a root of 2.
5744 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
5747 if (Range.contains(R1Val->getValue())) {
5748 // The next iteration must be out of the range...
5749 ConstantInt *NextVal =
5750 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1);
5752 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
5753 if (!Range.contains(R1Val->getValue()))
5754 return SE.getConstant(NextVal);
5755 return SE.getCouldNotCompute(); // Something strange happened
5758 // If R1 was not in the range, then it is a good return value. Make
5759 // sure that R1-1 WAS in the range though, just in case.
5760 ConstantInt *NextVal =
5761 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1);
5762 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
5763 if (Range.contains(R1Val->getValue()))
5765 return SE.getCouldNotCompute(); // Something strange happened
5770 return SE.getCouldNotCompute();
5775 //===----------------------------------------------------------------------===//
5776 // SCEVCallbackVH Class Implementation
5777 //===----------------------------------------------------------------------===//
5779 void ScalarEvolution::SCEVCallbackVH::deleted() {
5780 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
5781 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
5782 SE->ConstantEvolutionLoopExitValue.erase(PN);
5783 SE->Scalars.erase(getValPtr());
5784 // this now dangles!
5787 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) {
5788 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
5790 // Forget all the expressions associated with users of the old value,
5791 // so that future queries will recompute the expressions using the new
5793 Value *Old = getValPtr();
5794 SmallVector<User *, 16> Worklist;
5795 SmallPtrSet<User *, 8> Visited;
5796 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end();
5798 Worklist.push_back(*UI);
5799 while (!Worklist.empty()) {
5800 User *U = Worklist.pop_back_val();
5801 // Deleting the Old value will cause this to dangle. Postpone
5802 // that until everything else is done.
5805 if (!Visited.insert(U))
5807 if (PHINode *PN = dyn_cast<PHINode>(U))
5808 SE->ConstantEvolutionLoopExitValue.erase(PN);
5809 SE->Scalars.erase(U);
5810 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end();
5812 Worklist.push_back(*UI);
5814 // Delete the Old value.
5815 if (PHINode *PN = dyn_cast<PHINode>(Old))
5816 SE->ConstantEvolutionLoopExitValue.erase(PN);
5817 SE->Scalars.erase(Old);
5818 // this now dangles!
5821 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
5822 : CallbackVH(V), SE(se) {}
5824 //===----------------------------------------------------------------------===//
5825 // ScalarEvolution Class Implementation
5826 //===----------------------------------------------------------------------===//
5828 ScalarEvolution::ScalarEvolution()
5829 : FunctionPass(ID), FirstUnknown(0) {
5832 bool ScalarEvolution::runOnFunction(Function &F) {
5834 LI = &getAnalysis<LoopInfo>();
5835 TD = getAnalysisIfAvailable<TargetData>();
5836 DT = &getAnalysis<DominatorTree>();
5840 void ScalarEvolution::releaseMemory() {
5841 // Iterate through all the SCEVUnknown instances and call their
5842 // destructors, so that they release their references to their values.
5843 for (SCEVUnknown *U = FirstUnknown; U; U = U->Next)
5848 BackedgeTakenCounts.clear();
5849 ConstantEvolutionLoopExitValue.clear();
5850 ValuesAtScopes.clear();
5851 UniqueSCEVs.clear();
5852 SCEVAllocator.Reset();
5855 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
5856 AU.setPreservesAll();
5857 AU.addRequiredTransitive<LoopInfo>();
5858 AU.addRequiredTransitive<DominatorTree>();
5861 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
5862 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
5865 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
5867 // Print all inner loops first
5868 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
5869 PrintLoopInfo(OS, SE, *I);
5872 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
5875 SmallVector<BasicBlock *, 8> ExitBlocks;
5876 L->getExitBlocks(ExitBlocks);
5877 if (ExitBlocks.size() != 1)
5878 OS << "<multiple exits> ";
5880 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
5881 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
5883 OS << "Unpredictable backedge-taken count. ";
5888 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
5891 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
5892 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
5894 OS << "Unpredictable max backedge-taken count. ";
5900 void ScalarEvolution::print(raw_ostream &OS, const Module *) const {
5901 // ScalarEvolution's implementation of the print method is to print
5902 // out SCEV values of all instructions that are interesting. Doing
5903 // this potentially causes it to create new SCEV objects though,
5904 // which technically conflicts with the const qualifier. This isn't
5905 // observable from outside the class though, so casting away the
5906 // const isn't dangerous.
5907 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
5909 OS << "Classifying expressions for: ";
5910 WriteAsOperand(OS, F, /*PrintType=*/false);
5912 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
5913 if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) {
5916 const SCEV *SV = SE.getSCEV(&*I);
5919 const Loop *L = LI->getLoopFor((*I).getParent());
5921 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
5928 OS << "\t\t" "Exits: ";
5929 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
5930 if (!ExitValue->isLoopInvariant(L)) {
5931 OS << "<<Unknown>>";
5940 OS << "Determining loop execution counts for: ";
5941 WriteAsOperand(OS, F, /*PrintType=*/false);
5943 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
5944 PrintLoopInfo(OS, &SE, *I);