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 more than
1416 // once. If so, merge them together into an multiply expression. Since we
1417 // sorted the 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(); i != e-1; ++i)
1421 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
1422 // Scan ahead to count how many equal operands there are.
1424 while (i+Count != e && Ops[i+Count] == Ops[i])
1426 // Merge the values into a multiply.
1427 const SCEV *Scale = getConstant(Ty, Count);
1428 const SCEV *Mul = getMulExpr(Scale, Ops[i]);
1429 if (Ops.size() == Count)
1432 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count);
1433 --i; e -= Count - 1;
1437 return getAddExpr(Ops, HasNUW, HasNSW);
1439 // Check for truncates. If all the operands are truncated from the same
1440 // type, see if factoring out the truncate would permit the result to be
1441 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
1442 // if the contents of the resulting outer trunc fold to something simple.
1443 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
1444 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
1445 const Type *DstType = Trunc->getType();
1446 const Type *SrcType = Trunc->getOperand()->getType();
1447 SmallVector<const SCEV *, 8> LargeOps;
1449 // Check all the operands to see if they can be represented in the
1450 // source type of the truncate.
1451 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1452 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
1453 if (T->getOperand()->getType() != SrcType) {
1457 LargeOps.push_back(T->getOperand());
1458 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1459 LargeOps.push_back(getAnyExtendExpr(C, SrcType));
1460 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
1461 SmallVector<const SCEV *, 8> LargeMulOps;
1462 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
1463 if (const SCEVTruncateExpr *T =
1464 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
1465 if (T->getOperand()->getType() != SrcType) {
1469 LargeMulOps.push_back(T->getOperand());
1470 } else if (const SCEVConstant *C =
1471 dyn_cast<SCEVConstant>(M->getOperand(j))) {
1472 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType));
1479 LargeOps.push_back(getMulExpr(LargeMulOps));
1486 // Evaluate the expression in the larger type.
1487 const SCEV *Fold = getAddExpr(LargeOps, HasNUW, HasNSW);
1488 // If it folds to something simple, use it. Otherwise, don't.
1489 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
1490 return getTruncateExpr(Fold, DstType);
1494 // Skip past any other cast SCEVs.
1495 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
1498 // If there are add operands they would be next.
1499 if (Idx < Ops.size()) {
1500 bool DeletedAdd = false;
1501 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
1502 // If we have an add, expand the add operands onto the end of the operands
1504 Ops.erase(Ops.begin()+Idx);
1505 Ops.append(Add->op_begin(), Add->op_end());
1509 // If we deleted at least one add, we added operands to the end of the list,
1510 // and they are not necessarily sorted. Recurse to resort and resimplify
1511 // any operands we just acquired.
1513 return getAddExpr(Ops);
1516 // Skip over the add expression until we get to a multiply.
1517 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1520 // Check to see if there are any folding opportunities present with
1521 // operands multiplied by constant values.
1522 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
1523 uint64_t BitWidth = getTypeSizeInBits(Ty);
1524 DenseMap<const SCEV *, APInt> M;
1525 SmallVector<const SCEV *, 8> NewOps;
1526 APInt AccumulatedConstant(BitWidth, 0);
1527 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1528 Ops.data(), Ops.size(),
1529 APInt(BitWidth, 1), *this)) {
1530 // Some interesting folding opportunity is present, so its worthwhile to
1531 // re-generate the operands list. Group the operands by constant scale,
1532 // to avoid multiplying by the same constant scale multiple times.
1533 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
1534 for (SmallVector<const SCEV *, 8>::const_iterator I = NewOps.begin(),
1535 E = NewOps.end(); I != E; ++I)
1536 MulOpLists[M.find(*I)->second].push_back(*I);
1537 // Re-generate the operands list.
1539 if (AccumulatedConstant != 0)
1540 Ops.push_back(getConstant(AccumulatedConstant));
1541 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator
1542 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I)
1544 Ops.push_back(getMulExpr(getConstant(I->first),
1545 getAddExpr(I->second)));
1547 return getConstant(Ty, 0);
1548 if (Ops.size() == 1)
1550 return getAddExpr(Ops);
1554 // If we are adding something to a multiply expression, make sure the
1555 // something is not already an operand of the multiply. If so, merge it into
1557 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
1558 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
1559 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
1560 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
1561 if (isa<SCEVConstant>(MulOpSCEV))
1563 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
1564 if (MulOpSCEV == Ops[AddOp]) {
1565 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
1566 const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
1567 if (Mul->getNumOperands() != 2) {
1568 // If the multiply has more than two operands, we must get the
1570 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
1571 Mul->op_begin()+MulOp);
1572 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
1573 InnerMul = getMulExpr(MulOps);
1575 const SCEV *One = getConstant(Ty, 1);
1576 const SCEV *AddOne = getAddExpr(One, InnerMul);
1577 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV);
1578 if (Ops.size() == 2) return OuterMul;
1580 Ops.erase(Ops.begin()+AddOp);
1581 Ops.erase(Ops.begin()+Idx-1);
1583 Ops.erase(Ops.begin()+Idx);
1584 Ops.erase(Ops.begin()+AddOp-1);
1586 Ops.push_back(OuterMul);
1587 return getAddExpr(Ops);
1590 // Check this multiply against other multiplies being added together.
1591 bool AnyFold = false;
1592 for (unsigned OtherMulIdx = Idx+1;
1593 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
1595 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
1596 // If MulOp occurs in OtherMul, we can fold the two multiplies
1598 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
1599 OMulOp != e; ++OMulOp)
1600 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
1601 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
1602 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
1603 if (Mul->getNumOperands() != 2) {
1604 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
1605 Mul->op_begin()+MulOp);
1606 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
1607 InnerMul1 = getMulExpr(MulOps);
1609 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
1610 if (OtherMul->getNumOperands() != 2) {
1611 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
1612 OtherMul->op_begin()+OMulOp);
1613 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end());
1614 InnerMul2 = getMulExpr(MulOps);
1616 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
1617 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
1618 if (Ops.size() == 2) return OuterMul;
1619 Ops[Idx] = OuterMul;
1620 Ops.erase(Ops.begin()+OtherMulIdx);
1626 return getAddExpr(Ops);
1630 // If there are any add recurrences in the operands list, see if any other
1631 // added values are loop invariant. If so, we can fold them into the
1633 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1636 // Scan over all recurrences, trying to fold loop invariants into them.
1637 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1638 // Scan all of the other operands to this add and add them to the vector if
1639 // they are loop invariant w.r.t. the recurrence.
1640 SmallVector<const SCEV *, 8> LIOps;
1641 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1642 const Loop *AddRecLoop = AddRec->getLoop();
1643 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1644 if (Ops[i]->isLoopInvariant(AddRecLoop)) {
1645 LIOps.push_back(Ops[i]);
1646 Ops.erase(Ops.begin()+i);
1650 // If we found some loop invariants, fold them into the recurrence.
1651 if (!LIOps.empty()) {
1652 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
1653 LIOps.push_back(AddRec->getStart());
1655 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
1657 AddRecOps[0] = getAddExpr(LIOps);
1659 // Build the new addrec. Propagate the NUW and NSW flags if both the
1660 // outer add and the inner addrec are guaranteed to have no overflow.
1661 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop,
1662 HasNUW && AddRec->hasNoUnsignedWrap(),
1663 HasNSW && AddRec->hasNoSignedWrap());
1665 // If all of the other operands were loop invariant, we are done.
1666 if (Ops.size() == 1) return NewRec;
1668 // Otherwise, add the folded AddRec by the non-liv parts.
1669 for (unsigned i = 0;; ++i)
1670 if (Ops[i] == AddRec) {
1674 return getAddExpr(Ops);
1677 // Okay, if there weren't any loop invariants to be folded, check to see if
1678 // there are multiple AddRec's with the same loop induction variable being
1679 // added together. If so, we can fold them.
1680 for (unsigned OtherIdx = Idx+1;
1681 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
1683 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
1684 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L>
1685 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
1687 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
1689 if (const SCEVAddRecExpr *AR =
1690 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]))
1691 if (AR->getLoop() == AddRecLoop) {
1692 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i) {
1693 if (i >= AddRecOps.size()) {
1694 AddRecOps.append(AR->op_begin()+i, AR->op_end());
1697 AddRecOps[i] = getAddExpr(AddRecOps[i], AR->getOperand(i));
1699 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
1701 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop);
1702 return getAddExpr(Ops);
1705 // Otherwise couldn't fold anything into this recurrence. Move onto the
1709 // Okay, it looks like we really DO need an add expr. Check to see if we
1710 // already have one, otherwise create a new one.
1711 FoldingSetNodeID ID;
1712 ID.AddInteger(scAddExpr);
1713 ID.AddInteger(Ops.size());
1714 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1715 ID.AddPointer(Ops[i]);
1718 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1720 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
1721 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
1722 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator),
1724 UniqueSCEVs.InsertNode(S, IP);
1726 if (HasNUW) S->setHasNoUnsignedWrap(true);
1727 if (HasNSW) S->setHasNoSignedWrap(true);
1731 /// getMulExpr - Get a canonical multiply expression, or something simpler if
1733 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
1734 bool HasNUW, bool HasNSW) {
1735 assert(!Ops.empty() && "Cannot get empty mul!");
1736 if (Ops.size() == 1) return Ops[0];
1738 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
1739 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1740 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
1741 "SCEVMulExpr operand types don't match!");
1744 // If HasNSW is true and all the operands are non-negative, infer HasNUW.
1745 if (!HasNUW && HasNSW) {
1747 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(),
1748 E = Ops.end(); I != E; ++I)
1749 if (!isKnownNonNegative(*I)) {
1753 if (All) HasNUW = true;
1756 // Sort by complexity, this groups all similar expression types together.
1757 GroupByComplexity(Ops, LI);
1759 // If there are any constants, fold them together.
1761 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1763 // C1*(C2+V) -> C1*C2 + C1*V
1764 if (Ops.size() == 2)
1765 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
1766 if (Add->getNumOperands() == 2 &&
1767 isa<SCEVConstant>(Add->getOperand(0)))
1768 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
1769 getMulExpr(LHSC, Add->getOperand(1)));
1772 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1773 // We found two constants, fold them together!
1774 ConstantInt *Fold = ConstantInt::get(getContext(),
1775 LHSC->getValue()->getValue() *
1776 RHSC->getValue()->getValue());
1777 Ops[0] = getConstant(Fold);
1778 Ops.erase(Ops.begin()+1); // Erase the folded element
1779 if (Ops.size() == 1) return Ops[0];
1780 LHSC = cast<SCEVConstant>(Ops[0]);
1783 // If we are left with a constant one being multiplied, strip it off.
1784 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
1785 Ops.erase(Ops.begin());
1787 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
1788 // If we have a multiply of zero, it will always be zero.
1790 } else if (Ops[0]->isAllOnesValue()) {
1791 // If we have a mul by -1 of an add, try distributing the -1 among the
1793 if (Ops.size() == 2)
1794 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
1795 SmallVector<const SCEV *, 4> NewOps;
1796 bool AnyFolded = false;
1797 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(), E = Add->op_end();
1799 const SCEV *Mul = getMulExpr(Ops[0], *I);
1800 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
1801 NewOps.push_back(Mul);
1804 return getAddExpr(NewOps);
1808 if (Ops.size() == 1)
1812 // Skip over the add expression until we get to a multiply.
1813 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1816 // If there are mul operands inline them all into this expression.
1817 if (Idx < Ops.size()) {
1818 bool DeletedMul = false;
1819 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
1820 // If we have an mul, expand the mul operands onto the end of the operands
1822 Ops.erase(Ops.begin()+Idx);
1823 Ops.append(Mul->op_begin(), Mul->op_end());
1827 // If we deleted at least one mul, we added operands to the end of the list,
1828 // and they are not necessarily sorted. Recurse to resort and resimplify
1829 // any operands we just acquired.
1831 return getMulExpr(Ops);
1834 // If there are any add recurrences in the operands list, see if any other
1835 // added values are loop invariant. If so, we can fold them into the
1837 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1840 // Scan over all recurrences, trying to fold loop invariants into them.
1841 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1842 // Scan all of the other operands to this mul and add them to the vector if
1843 // they are loop invariant w.r.t. the recurrence.
1844 SmallVector<const SCEV *, 8> LIOps;
1845 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1846 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1847 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
1848 LIOps.push_back(Ops[i]);
1849 Ops.erase(Ops.begin()+i);
1853 // If we found some loop invariants, fold them into the recurrence.
1854 if (!LIOps.empty()) {
1855 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
1856 SmallVector<const SCEV *, 4> NewOps;
1857 NewOps.reserve(AddRec->getNumOperands());
1858 const SCEV *Scale = getMulExpr(LIOps);
1859 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
1860 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
1862 // Build the new addrec. Propagate the NUW and NSW flags if both the
1863 // outer mul and the inner addrec are guaranteed to have no overflow.
1864 const SCEV *NewRec = getAddRecExpr(NewOps, AddRec->getLoop(),
1865 HasNUW && AddRec->hasNoUnsignedWrap(),
1866 HasNSW && AddRec->hasNoSignedWrap());
1868 // If all of the other operands were loop invariant, we are done.
1869 if (Ops.size() == 1) return NewRec;
1871 // Otherwise, multiply the folded AddRec by the non-liv parts.
1872 for (unsigned i = 0;; ++i)
1873 if (Ops[i] == AddRec) {
1877 return getMulExpr(Ops);
1880 // Okay, if there weren't any loop invariants to be folded, check to see if
1881 // there are multiple AddRec's with the same loop induction variable being
1882 // multiplied together. If so, we can fold them.
1883 for (unsigned OtherIdx = Idx+1;
1884 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
1885 if (OtherIdx != Idx) {
1886 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
1887 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
1888 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D}
1889 const SCEVAddRecExpr *F = AddRec, *G = OtherAddRec;
1890 const SCEV *NewStart = getMulExpr(F->getStart(), G->getStart());
1891 const SCEV *B = F->getStepRecurrence(*this);
1892 const SCEV *D = G->getStepRecurrence(*this);
1893 const SCEV *NewStep = getAddExpr(getMulExpr(F, D),
1896 const SCEV *NewAddRec = getAddRecExpr(NewStart, NewStep,
1898 if (Ops.size() == 2) return NewAddRec;
1900 Ops.erase(Ops.begin()+Idx);
1901 Ops.erase(Ops.begin()+OtherIdx-1);
1902 Ops.push_back(NewAddRec);
1903 return getMulExpr(Ops);
1907 // Otherwise couldn't fold anything into this recurrence. Move onto the
1911 // Okay, it looks like we really DO need an mul expr. Check to see if we
1912 // already have one, otherwise create a new one.
1913 FoldingSetNodeID ID;
1914 ID.AddInteger(scMulExpr);
1915 ID.AddInteger(Ops.size());
1916 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1917 ID.AddPointer(Ops[i]);
1920 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1922 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
1923 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
1924 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
1926 UniqueSCEVs.InsertNode(S, IP);
1928 if (HasNUW) S->setHasNoUnsignedWrap(true);
1929 if (HasNSW) S->setHasNoSignedWrap(true);
1933 /// getUDivExpr - Get a canonical unsigned division expression, or something
1934 /// simpler if possible.
1935 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
1937 assert(getEffectiveSCEVType(LHS->getType()) ==
1938 getEffectiveSCEVType(RHS->getType()) &&
1939 "SCEVUDivExpr operand types don't match!");
1941 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
1942 if (RHSC->getValue()->equalsInt(1))
1943 return LHS; // X udiv 1 --> x
1944 // If the denominator is zero, the result of the udiv is undefined. Don't
1945 // try to analyze it, because the resolution chosen here may differ from
1946 // the resolution chosen in other parts of the compiler.
1947 if (!RHSC->getValue()->isZero()) {
1948 // Determine if the division can be folded into the operands of
1950 // TODO: Generalize this to non-constants by using known-bits information.
1951 const Type *Ty = LHS->getType();
1952 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
1953 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1;
1954 // For non-power-of-two values, effectively round the value up to the
1955 // nearest power of two.
1956 if (!RHSC->getValue()->getValue().isPowerOf2())
1958 const IntegerType *ExtTy =
1959 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
1960 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
1961 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
1962 if (const SCEVConstant *Step =
1963 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this)))
1964 if (!Step->getValue()->getValue()
1965 .urem(RHSC->getValue()->getValue()) &&
1966 getZeroExtendExpr(AR, ExtTy) ==
1967 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
1968 getZeroExtendExpr(Step, ExtTy),
1970 SmallVector<const SCEV *, 4> Operands;
1971 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i)
1972 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS));
1973 return getAddRecExpr(Operands, AR->getLoop());
1975 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
1976 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
1977 SmallVector<const SCEV *, 4> Operands;
1978 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i)
1979 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy));
1980 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
1981 // Find an operand that's safely divisible.
1982 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
1983 const SCEV *Op = M->getOperand(i);
1984 const SCEV *Div = getUDivExpr(Op, RHSC);
1985 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
1986 Operands = SmallVector<const SCEV *, 4>(M->op_begin(),
1989 return getMulExpr(Operands);
1993 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
1994 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(LHS)) {
1995 SmallVector<const SCEV *, 4> Operands;
1996 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i)
1997 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy));
1998 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
2000 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
2001 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
2002 if (isa<SCEVUDivExpr>(Op) ||
2003 getMulExpr(Op, RHS) != A->getOperand(i))
2005 Operands.push_back(Op);
2007 if (Operands.size() == A->getNumOperands())
2008 return getAddExpr(Operands);
2012 // Fold if both operands are constant.
2013 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
2014 Constant *LHSCV = LHSC->getValue();
2015 Constant *RHSCV = RHSC->getValue();
2016 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
2022 FoldingSetNodeID ID;
2023 ID.AddInteger(scUDivExpr);
2027 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2028 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
2030 UniqueSCEVs.InsertNode(S, IP);
2035 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2036 /// Simplify the expression as much as possible.
2037 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start,
2038 const SCEV *Step, const Loop *L,
2039 bool HasNUW, bool HasNSW) {
2040 SmallVector<const SCEV *, 4> Operands;
2041 Operands.push_back(Start);
2042 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
2043 if (StepChrec->getLoop() == L) {
2044 Operands.append(StepChrec->op_begin(), StepChrec->op_end());
2045 return getAddRecExpr(Operands, L);
2048 Operands.push_back(Step);
2049 return getAddRecExpr(Operands, L, HasNUW, HasNSW);
2052 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2053 /// Simplify the expression as much as possible.
2055 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
2057 bool HasNUW, bool HasNSW) {
2058 if (Operands.size() == 1) return Operands[0];
2060 const Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
2061 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
2062 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy &&
2063 "SCEVAddRecExpr operand types don't match!");
2066 if (Operands.back()->isZero()) {
2067 Operands.pop_back();
2068 return getAddRecExpr(Operands, L, HasNUW, HasNSW); // {X,+,0} --> X
2071 // It's tempting to want to call getMaxBackedgeTakenCount count here and
2072 // use that information to infer NUW and NSW flags. However, computing a
2073 // BE count requires calling getAddRecExpr, so we may not yet have a
2074 // meaningful BE count at this point (and if we don't, we'd be stuck
2075 // with a SCEVCouldNotCompute as the cached BE count).
2077 // If HasNSW is true and all the operands are non-negative, infer HasNUW.
2078 if (!HasNUW && HasNSW) {
2080 for (SmallVectorImpl<const SCEV *>::const_iterator I = Operands.begin(),
2081 E = Operands.end(); I != E; ++I)
2082 if (!isKnownNonNegative(*I)) {
2086 if (All) HasNUW = true;
2089 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
2090 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
2091 const Loop *NestedLoop = NestedAR->getLoop();
2092 if (L->contains(NestedLoop) ?
2093 (L->getLoopDepth() < NestedLoop->getLoopDepth()) :
2094 (!NestedLoop->contains(L) &&
2095 DT->dominates(L->getHeader(), NestedLoop->getHeader()))) {
2096 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
2097 NestedAR->op_end());
2098 Operands[0] = NestedAR->getStart();
2099 // AddRecs require their operands be loop-invariant with respect to their
2100 // loops. Don't perform this transformation if it would break this
2102 bool AllInvariant = true;
2103 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2104 if (!Operands[i]->isLoopInvariant(L)) {
2105 AllInvariant = false;
2109 NestedOperands[0] = getAddRecExpr(Operands, L);
2110 AllInvariant = true;
2111 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i)
2112 if (!NestedOperands[i]->isLoopInvariant(NestedLoop)) {
2113 AllInvariant = false;
2117 // Ok, both add recurrences are valid after the transformation.
2118 return getAddRecExpr(NestedOperands, NestedLoop, HasNUW, HasNSW);
2120 // Reset Operands to its original state.
2121 Operands[0] = NestedAR;
2125 // Okay, it looks like we really DO need an addrec expr. Check to see if we
2126 // already have one, otherwise create a new one.
2127 FoldingSetNodeID ID;
2128 ID.AddInteger(scAddRecExpr);
2129 ID.AddInteger(Operands.size());
2130 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2131 ID.AddPointer(Operands[i]);
2135 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2137 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size());
2138 std::uninitialized_copy(Operands.begin(), Operands.end(), O);
2139 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator),
2140 O, Operands.size(), L);
2141 UniqueSCEVs.InsertNode(S, IP);
2143 if (HasNUW) S->setHasNoUnsignedWrap(true);
2144 if (HasNSW) S->setHasNoSignedWrap(true);
2148 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
2150 SmallVector<const SCEV *, 2> Ops;
2153 return getSMaxExpr(Ops);
2157 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2158 assert(!Ops.empty() && "Cannot get empty smax!");
2159 if (Ops.size() == 1) return Ops[0];
2161 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2162 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2163 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2164 "SCEVSMaxExpr operand types don't match!");
2167 // Sort by complexity, this groups all similar expression types together.
2168 GroupByComplexity(Ops, LI);
2170 // If there are any constants, fold them together.
2172 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2174 assert(Idx < Ops.size());
2175 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2176 // We found two constants, fold them together!
2177 ConstantInt *Fold = ConstantInt::get(getContext(),
2178 APIntOps::smax(LHSC->getValue()->getValue(),
2179 RHSC->getValue()->getValue()));
2180 Ops[0] = getConstant(Fold);
2181 Ops.erase(Ops.begin()+1); // Erase the folded element
2182 if (Ops.size() == 1) return Ops[0];
2183 LHSC = cast<SCEVConstant>(Ops[0]);
2186 // If we are left with a constant minimum-int, strip it off.
2187 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
2188 Ops.erase(Ops.begin());
2190 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
2191 // If we have an smax with a constant maximum-int, it will always be
2196 if (Ops.size() == 1) return Ops[0];
2199 // Find the first SMax
2200 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
2203 // Check to see if one of the operands is an SMax. If so, expand its operands
2204 // onto our operand list, and recurse to simplify.
2205 if (Idx < Ops.size()) {
2206 bool DeletedSMax = false;
2207 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
2208 Ops.erase(Ops.begin()+Idx);
2209 Ops.append(SMax->op_begin(), SMax->op_end());
2214 return getSMaxExpr(Ops);
2217 // Okay, check to see if the same value occurs in the operand list twice. If
2218 // so, delete one. Since we sorted the list, these values are required to
2220 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2221 // X smax Y smax Y --> X smax Y
2222 // X smax Y --> X, if X is always greater than Y
2223 if (Ops[i] == Ops[i+1] ||
2224 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) {
2225 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2227 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) {
2228 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2232 if (Ops.size() == 1) return Ops[0];
2234 assert(!Ops.empty() && "Reduced smax down to nothing!");
2236 // Okay, it looks like we really DO need an smax expr. Check to see if we
2237 // already have one, otherwise create a new one.
2238 FoldingSetNodeID ID;
2239 ID.AddInteger(scSMaxExpr);
2240 ID.AddInteger(Ops.size());
2241 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2242 ID.AddPointer(Ops[i]);
2244 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2245 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2246 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2247 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator),
2249 UniqueSCEVs.InsertNode(S, IP);
2253 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
2255 SmallVector<const SCEV *, 2> Ops;
2258 return getUMaxExpr(Ops);
2262 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2263 assert(!Ops.empty() && "Cannot get empty umax!");
2264 if (Ops.size() == 1) return Ops[0];
2266 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2267 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2268 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2269 "SCEVUMaxExpr operand types don't match!");
2272 // Sort by complexity, this groups all similar expression types together.
2273 GroupByComplexity(Ops, LI);
2275 // If there are any constants, fold them together.
2277 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2279 assert(Idx < Ops.size());
2280 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2281 // We found two constants, fold them together!
2282 ConstantInt *Fold = ConstantInt::get(getContext(),
2283 APIntOps::umax(LHSC->getValue()->getValue(),
2284 RHSC->getValue()->getValue()));
2285 Ops[0] = getConstant(Fold);
2286 Ops.erase(Ops.begin()+1); // Erase the folded element
2287 if (Ops.size() == 1) return Ops[0];
2288 LHSC = cast<SCEVConstant>(Ops[0]);
2291 // If we are left with a constant minimum-int, strip it off.
2292 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
2293 Ops.erase(Ops.begin());
2295 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
2296 // If we have an umax with a constant maximum-int, it will always be
2301 if (Ops.size() == 1) return Ops[0];
2304 // Find the first UMax
2305 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
2308 // Check to see if one of the operands is a UMax. If so, expand its operands
2309 // onto our operand list, and recurse to simplify.
2310 if (Idx < Ops.size()) {
2311 bool DeletedUMax = false;
2312 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
2313 Ops.erase(Ops.begin()+Idx);
2314 Ops.append(UMax->op_begin(), UMax->op_end());
2319 return getUMaxExpr(Ops);
2322 // Okay, check to see if the same value occurs in the operand list twice. If
2323 // so, delete one. Since we sorted the list, these values are required to
2325 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2326 // X umax Y umax Y --> X umax Y
2327 // X umax Y --> X, if X is always greater than Y
2328 if (Ops[i] == Ops[i+1] ||
2329 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) {
2330 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2332 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) {
2333 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2337 if (Ops.size() == 1) return Ops[0];
2339 assert(!Ops.empty() && "Reduced umax down to nothing!");
2341 // Okay, it looks like we really DO need a umax expr. Check to see if we
2342 // already have one, otherwise create a new one.
2343 FoldingSetNodeID ID;
2344 ID.AddInteger(scUMaxExpr);
2345 ID.AddInteger(Ops.size());
2346 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2347 ID.AddPointer(Ops[i]);
2349 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2350 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2351 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2352 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator),
2354 UniqueSCEVs.InsertNode(S, IP);
2358 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
2360 // ~smax(~x, ~y) == smin(x, y).
2361 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2364 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
2366 // ~umax(~x, ~y) == umin(x, y)
2367 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2370 const SCEV *ScalarEvolution::getSizeOfExpr(const Type *AllocTy) {
2371 // If we have TargetData, we can bypass creating a target-independent
2372 // constant expression and then folding it back into a ConstantInt.
2373 // This is just a compile-time optimization.
2375 return getConstant(TD->getIntPtrType(getContext()),
2376 TD->getTypeAllocSize(AllocTy));
2378 Constant *C = ConstantExpr::getSizeOf(AllocTy);
2379 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2380 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD))
2382 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2383 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2386 const SCEV *ScalarEvolution::getAlignOfExpr(const Type *AllocTy) {
2387 Constant *C = ConstantExpr::getAlignOf(AllocTy);
2388 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2389 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD))
2391 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2392 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2395 const SCEV *ScalarEvolution::getOffsetOfExpr(const StructType *STy,
2397 // If we have TargetData, we can bypass creating a target-independent
2398 // constant expression and then folding it back into a ConstantInt.
2399 // This is just a compile-time optimization.
2401 return getConstant(TD->getIntPtrType(getContext()),
2402 TD->getStructLayout(STy)->getElementOffset(FieldNo));
2404 Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo);
2405 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2406 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD))
2408 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy));
2409 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2412 const SCEV *ScalarEvolution::getOffsetOfExpr(const Type *CTy,
2413 Constant *FieldNo) {
2414 Constant *C = ConstantExpr::getOffsetOf(CTy, FieldNo);
2415 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2416 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD))
2418 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(CTy));
2419 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2422 const SCEV *ScalarEvolution::getUnknown(Value *V) {
2423 // Don't attempt to do anything other than create a SCEVUnknown object
2424 // here. createSCEV only calls getUnknown after checking for all other
2425 // interesting possibilities, and any other code that calls getUnknown
2426 // is doing so in order to hide a value from SCEV canonicalization.
2428 FoldingSetNodeID ID;
2429 ID.AddInteger(scUnknown);
2432 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
2433 assert(cast<SCEVUnknown>(S)->getValue() == V &&
2434 "Stale SCEVUnknown in uniquing map!");
2437 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
2439 FirstUnknown = cast<SCEVUnknown>(S);
2440 UniqueSCEVs.InsertNode(S, IP);
2444 //===----------------------------------------------------------------------===//
2445 // Basic SCEV Analysis and PHI Idiom Recognition Code
2448 /// isSCEVable - Test if values of the given type are analyzable within
2449 /// the SCEV framework. This primarily includes integer types, and it
2450 /// can optionally include pointer types if the ScalarEvolution class
2451 /// has access to target-specific information.
2452 bool ScalarEvolution::isSCEVable(const Type *Ty) const {
2453 // Integers and pointers are always SCEVable.
2454 return Ty->isIntegerTy() || Ty->isPointerTy();
2457 /// getTypeSizeInBits - Return the size in bits of the specified type,
2458 /// for which isSCEVable must return true.
2459 uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const {
2460 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2462 // If we have a TargetData, use it!
2464 return TD->getTypeSizeInBits(Ty);
2466 // Integer types have fixed sizes.
2467 if (Ty->isIntegerTy())
2468 return Ty->getPrimitiveSizeInBits();
2470 // The only other support type is pointer. Without TargetData, conservatively
2471 // assume pointers are 64-bit.
2472 assert(Ty->isPointerTy() && "isSCEVable permitted a non-SCEVable type!");
2476 /// getEffectiveSCEVType - Return a type with the same bitwidth as
2477 /// the given type and which represents how SCEV will treat the given
2478 /// type, for which isSCEVable must return true. For pointer types,
2479 /// this is the pointer-sized integer type.
2480 const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const {
2481 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2483 if (Ty->isIntegerTy())
2486 // The only other support type is pointer.
2487 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
2488 if (TD) return TD->getIntPtrType(getContext());
2490 // Without TargetData, conservatively assume pointers are 64-bit.
2491 return Type::getInt64Ty(getContext());
2494 const SCEV *ScalarEvolution::getCouldNotCompute() {
2495 return &CouldNotCompute;
2498 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
2499 /// expression and create a new one.
2500 const SCEV *ScalarEvolution::getSCEV(Value *V) {
2501 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
2503 ValueExprMapType::const_iterator I = ValueExprMap.find(V);
2504 if (I != ValueExprMap.end()) return I->second;
2505 const SCEV *S = createSCEV(V);
2507 // The process of creating a SCEV for V may have caused other SCEVs
2508 // to have been created, so it's necessary to insert the new entry
2509 // from scratch, rather than trying to remember the insert position
2511 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(V, this), S));
2515 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
2517 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) {
2518 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2520 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
2522 const Type *Ty = V->getType();
2523 Ty = getEffectiveSCEVType(Ty);
2524 return getMulExpr(V,
2525 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))));
2528 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
2529 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
2530 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2532 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
2534 const Type *Ty = V->getType();
2535 Ty = getEffectiveSCEVType(Ty);
2536 const SCEV *AllOnes =
2537 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
2538 return getMinusSCEV(AllOnes, V);
2541 /// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
2543 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS,
2545 // Fast path: X - X --> 0.
2547 return getConstant(LHS->getType(), 0);
2550 return getAddExpr(LHS, getNegativeSCEV(RHS));
2553 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
2554 /// input value to the specified type. If the type must be extended, it is zero
2557 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V,
2559 const Type *SrcTy = V->getType();
2560 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2561 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2562 "Cannot truncate or zero extend with non-integer arguments!");
2563 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2564 return V; // No conversion
2565 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2566 return getTruncateExpr(V, Ty);
2567 return getZeroExtendExpr(V, Ty);
2570 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
2571 /// input value to the specified type. If the type must be extended, it is sign
2574 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
2576 const Type *SrcTy = V->getType();
2577 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2578 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2579 "Cannot truncate or zero extend with non-integer arguments!");
2580 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2581 return V; // No conversion
2582 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2583 return getTruncateExpr(V, Ty);
2584 return getSignExtendExpr(V, Ty);
2587 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
2588 /// input value to the specified type. If the type must be extended, it is zero
2589 /// extended. The conversion must not be narrowing.
2591 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, const Type *Ty) {
2592 const Type *SrcTy = V->getType();
2593 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2594 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2595 "Cannot noop or zero extend with non-integer arguments!");
2596 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2597 "getNoopOrZeroExtend cannot truncate!");
2598 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2599 return V; // No conversion
2600 return getZeroExtendExpr(V, Ty);
2603 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
2604 /// input value to the specified type. If the type must be extended, it is sign
2605 /// extended. The conversion must not be narrowing.
2607 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, const Type *Ty) {
2608 const Type *SrcTy = V->getType();
2609 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2610 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2611 "Cannot noop or sign extend with non-integer arguments!");
2612 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2613 "getNoopOrSignExtend cannot truncate!");
2614 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2615 return V; // No conversion
2616 return getSignExtendExpr(V, Ty);
2619 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
2620 /// the input value to the specified type. If the type must be extended,
2621 /// it is extended with unspecified bits. The conversion must not be
2624 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, const Type *Ty) {
2625 const Type *SrcTy = V->getType();
2626 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2627 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2628 "Cannot noop or any extend with non-integer arguments!");
2629 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2630 "getNoopOrAnyExtend cannot truncate!");
2631 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2632 return V; // No conversion
2633 return getAnyExtendExpr(V, Ty);
2636 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
2637 /// input value to the specified type. The conversion must not be widening.
2639 ScalarEvolution::getTruncateOrNoop(const SCEV *V, const Type *Ty) {
2640 const Type *SrcTy = V->getType();
2641 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2642 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2643 "Cannot truncate or noop with non-integer arguments!");
2644 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
2645 "getTruncateOrNoop cannot extend!");
2646 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2647 return V; // No conversion
2648 return getTruncateExpr(V, Ty);
2651 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
2652 /// the types using zero-extension, and then perform a umax operation
2654 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
2656 const SCEV *PromotedLHS = LHS;
2657 const SCEV *PromotedRHS = RHS;
2659 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2660 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2662 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2664 return getUMaxExpr(PromotedLHS, PromotedRHS);
2667 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
2668 /// the types using zero-extension, and then perform a umin operation
2670 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
2672 const SCEV *PromotedLHS = LHS;
2673 const SCEV *PromotedRHS = RHS;
2675 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2676 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2678 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2680 return getUMinExpr(PromotedLHS, PromotedRHS);
2683 /// PushDefUseChildren - Push users of the given Instruction
2684 /// onto the given Worklist.
2686 PushDefUseChildren(Instruction *I,
2687 SmallVectorImpl<Instruction *> &Worklist) {
2688 // Push the def-use children onto the Worklist stack.
2689 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end();
2691 Worklist.push_back(cast<Instruction>(*UI));
2694 /// ForgetSymbolicValue - This looks up computed SCEV values for all
2695 /// instructions that depend on the given instruction and removes them from
2696 /// the ValueExprMapType map if they reference SymName. This is used during PHI
2699 ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) {
2700 SmallVector<Instruction *, 16> Worklist;
2701 PushDefUseChildren(PN, Worklist);
2703 SmallPtrSet<Instruction *, 8> Visited;
2705 while (!Worklist.empty()) {
2706 Instruction *I = Worklist.pop_back_val();
2707 if (!Visited.insert(I)) continue;
2709 ValueExprMapType::iterator It =
2710 ValueExprMap.find(static_cast<Value *>(I));
2711 if (It != ValueExprMap.end()) {
2712 // Short-circuit the def-use traversal if the symbolic name
2713 // ceases to appear in expressions.
2714 if (It->second != SymName && !It->second->hasOperand(SymName))
2717 // SCEVUnknown for a PHI either means that it has an unrecognized
2718 // structure, it's a PHI that's in the progress of being computed
2719 // by createNodeForPHI, or it's a single-value PHI. In the first case,
2720 // additional loop trip count information isn't going to change anything.
2721 // In the second case, createNodeForPHI will perform the necessary
2722 // updates on its own when it gets to that point. In the third, we do
2723 // want to forget the SCEVUnknown.
2724 if (!isa<PHINode>(I) ||
2725 !isa<SCEVUnknown>(It->second) ||
2726 (I != PN && It->second == SymName)) {
2727 ValuesAtScopes.erase(It->second);
2728 ValueExprMap.erase(It);
2732 PushDefUseChildren(I, Worklist);
2736 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
2737 /// a loop header, making it a potential recurrence, or it doesn't.
2739 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
2740 if (const Loop *L = LI->getLoopFor(PN->getParent()))
2741 if (L->getHeader() == PN->getParent()) {
2742 // The loop may have multiple entrances or multiple exits; we can analyze
2743 // this phi as an addrec if it has a unique entry value and a unique
2745 Value *BEValueV = 0, *StartValueV = 0;
2746 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
2747 Value *V = PN->getIncomingValue(i);
2748 if (L->contains(PN->getIncomingBlock(i))) {
2751 } else if (BEValueV != V) {
2755 } else if (!StartValueV) {
2757 } else if (StartValueV != V) {
2762 if (BEValueV && StartValueV) {
2763 // While we are analyzing this PHI node, handle its value symbolically.
2764 const SCEV *SymbolicName = getUnknown(PN);
2765 assert(ValueExprMap.find(PN) == ValueExprMap.end() &&
2766 "PHI node already processed?");
2767 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
2769 // Using this symbolic name for the PHI, analyze the value coming around
2771 const SCEV *BEValue = getSCEV(BEValueV);
2773 // NOTE: If BEValue is loop invariant, we know that the PHI node just
2774 // has a special value for the first iteration of the loop.
2776 // If the value coming around the backedge is an add with the symbolic
2777 // value we just inserted, then we found a simple induction variable!
2778 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
2779 // If there is a single occurrence of the symbolic value, replace it
2780 // with a recurrence.
2781 unsigned FoundIndex = Add->getNumOperands();
2782 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
2783 if (Add->getOperand(i) == SymbolicName)
2784 if (FoundIndex == e) {
2789 if (FoundIndex != Add->getNumOperands()) {
2790 // Create an add with everything but the specified operand.
2791 SmallVector<const SCEV *, 8> Ops;
2792 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
2793 if (i != FoundIndex)
2794 Ops.push_back(Add->getOperand(i));
2795 const SCEV *Accum = getAddExpr(Ops);
2797 // This is not a valid addrec if the step amount is varying each
2798 // loop iteration, but is not itself an addrec in this loop.
2799 if (Accum->isLoopInvariant(L) ||
2800 (isa<SCEVAddRecExpr>(Accum) &&
2801 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
2802 bool HasNUW = false;
2803 bool HasNSW = false;
2805 // If the increment doesn't overflow, then neither the addrec nor
2806 // the post-increment will overflow.
2807 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) {
2808 if (OBO->hasNoUnsignedWrap())
2810 if (OBO->hasNoSignedWrap())
2814 const SCEV *StartVal = getSCEV(StartValueV);
2815 const SCEV *PHISCEV =
2816 getAddRecExpr(StartVal, Accum, L, HasNUW, HasNSW);
2818 // Since the no-wrap flags are on the increment, they apply to the
2819 // post-incremented value as well.
2820 if (Accum->isLoopInvariant(L))
2821 (void)getAddRecExpr(getAddExpr(StartVal, Accum),
2822 Accum, L, HasNUW, HasNSW);
2824 // Okay, for the entire analysis of this edge we assumed the PHI
2825 // to be symbolic. We now need to go back and purge all of the
2826 // entries for the scalars that use the symbolic expression.
2827 ForgetSymbolicName(PN, SymbolicName);
2828 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
2832 } else if (const SCEVAddRecExpr *AddRec =
2833 dyn_cast<SCEVAddRecExpr>(BEValue)) {
2834 // Otherwise, this could be a loop like this:
2835 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
2836 // In this case, j = {1,+,1} and BEValue is j.
2837 // Because the other in-value of i (0) fits the evolution of BEValue
2838 // i really is an addrec evolution.
2839 if (AddRec->getLoop() == L && AddRec->isAffine()) {
2840 const SCEV *StartVal = getSCEV(StartValueV);
2842 // If StartVal = j.start - j.stride, we can use StartVal as the
2843 // initial step of the addrec evolution.
2844 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
2845 AddRec->getOperand(1))) {
2846 const SCEV *PHISCEV =
2847 getAddRecExpr(StartVal, AddRec->getOperand(1), L);
2849 // Okay, for the entire analysis of this edge we assumed the PHI
2850 // to be symbolic. We now need to go back and purge all of the
2851 // entries for the scalars that use the symbolic expression.
2852 ForgetSymbolicName(PN, SymbolicName);
2853 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
2861 // If the PHI has a single incoming value, follow that value, unless the
2862 // PHI's incoming blocks are in a different loop, in which case doing so
2863 // risks breaking LCSSA form. Instcombine would normally zap these, but
2864 // it doesn't have DominatorTree information, so it may miss cases.
2865 if (Value *V = PN->hasConstantValue(DT)) {
2866 bool AllSameLoop = true;
2867 Loop *PNLoop = LI->getLoopFor(PN->getParent());
2868 for (size_t i = 0, e = PN->getNumIncomingValues(); i != e; ++i)
2869 if (LI->getLoopFor(PN->getIncomingBlock(i)) != PNLoop) {
2870 AllSameLoop = false;
2877 // If it's not a loop phi, we can't handle it yet.
2878 return getUnknown(PN);
2881 /// createNodeForGEP - Expand GEP instructions into add and multiply
2882 /// operations. This allows them to be analyzed by regular SCEV code.
2884 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
2886 // Don't blindly transfer the inbounds flag from the GEP instruction to the
2887 // Add expression, because the Instruction may be guarded by control flow
2888 // and the no-overflow bits may not be valid for the expression in any
2891 const Type *IntPtrTy = getEffectiveSCEVType(GEP->getType());
2892 Value *Base = GEP->getOperand(0);
2893 // Don't attempt to analyze GEPs over unsized objects.
2894 if (!cast<PointerType>(Base->getType())->getElementType()->isSized())
2895 return getUnknown(GEP);
2896 const SCEV *TotalOffset = getConstant(IntPtrTy, 0);
2897 gep_type_iterator GTI = gep_type_begin(GEP);
2898 for (GetElementPtrInst::op_iterator I = llvm::next(GEP->op_begin()),
2902 // Compute the (potentially symbolic) offset in bytes for this index.
2903 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) {
2904 // For a struct, add the member offset.
2905 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
2906 const SCEV *FieldOffset = getOffsetOfExpr(STy, FieldNo);
2908 // Add the field offset to the running total offset.
2909 TotalOffset = getAddExpr(TotalOffset, FieldOffset);
2911 // For an array, add the element offset, explicitly scaled.
2912 const SCEV *ElementSize = getSizeOfExpr(*GTI);
2913 const SCEV *IndexS = getSCEV(Index);
2914 // Getelementptr indices are signed.
2915 IndexS = getTruncateOrSignExtend(IndexS, IntPtrTy);
2917 // Multiply the index by the element size to compute the element offset.
2918 const SCEV *LocalOffset = getMulExpr(IndexS, ElementSize);
2920 // Add the element offset to the running total offset.
2921 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
2925 // Get the SCEV for the GEP base.
2926 const SCEV *BaseS = getSCEV(Base);
2928 // Add the total offset from all the GEP indices to the base.
2929 return getAddExpr(BaseS, TotalOffset);
2932 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
2933 /// guaranteed to end in (at every loop iteration). It is, at the same time,
2934 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
2935 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
2937 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
2938 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
2939 return C->getValue()->getValue().countTrailingZeros();
2941 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
2942 return std::min(GetMinTrailingZeros(T->getOperand()),
2943 (uint32_t)getTypeSizeInBits(T->getType()));
2945 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
2946 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
2947 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
2948 getTypeSizeInBits(E->getType()) : OpRes;
2951 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
2952 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
2953 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
2954 getTypeSizeInBits(E->getType()) : OpRes;
2957 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
2958 // The result is the min of all operands results.
2959 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
2960 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
2961 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
2965 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
2966 // The result is the sum of all operands results.
2967 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
2968 uint32_t BitWidth = getTypeSizeInBits(M->getType());
2969 for (unsigned i = 1, e = M->getNumOperands();
2970 SumOpRes != BitWidth && i != e; ++i)
2971 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
2976 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
2977 // The result is the min of all operands results.
2978 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
2979 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
2980 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
2984 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
2985 // The result is the min of all operands results.
2986 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
2987 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
2988 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
2992 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
2993 // The result is the min of all operands results.
2994 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
2995 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
2996 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3000 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3001 // For a SCEVUnknown, ask ValueTracking.
3002 unsigned BitWidth = getTypeSizeInBits(U->getType());
3003 APInt Mask = APInt::getAllOnesValue(BitWidth);
3004 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3005 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones);
3006 return Zeros.countTrailingOnes();
3013 /// getUnsignedRange - Determine the unsigned range for a particular SCEV.
3016 ScalarEvolution::getUnsignedRange(const SCEV *S) {
3018 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3019 return ConstantRange(C->getValue()->getValue());
3021 unsigned BitWidth = getTypeSizeInBits(S->getType());
3022 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3024 // If the value has known zeros, the maximum unsigned value will have those
3025 // known zeros as well.
3026 uint32_t TZ = GetMinTrailingZeros(S);
3028 ConservativeResult =
3029 ConstantRange(APInt::getMinValue(BitWidth),
3030 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
3032 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3033 ConstantRange X = getUnsignedRange(Add->getOperand(0));
3034 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3035 X = X.add(getUnsignedRange(Add->getOperand(i)));
3036 return ConservativeResult.intersectWith(X);
3039 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3040 ConstantRange X = getUnsignedRange(Mul->getOperand(0));
3041 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3042 X = X.multiply(getUnsignedRange(Mul->getOperand(i)));
3043 return ConservativeResult.intersectWith(X);
3046 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3047 ConstantRange X = getUnsignedRange(SMax->getOperand(0));
3048 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3049 X = X.smax(getUnsignedRange(SMax->getOperand(i)));
3050 return ConservativeResult.intersectWith(X);
3053 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3054 ConstantRange X = getUnsignedRange(UMax->getOperand(0));
3055 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3056 X = X.umax(getUnsignedRange(UMax->getOperand(i)));
3057 return ConservativeResult.intersectWith(X);
3060 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3061 ConstantRange X = getUnsignedRange(UDiv->getLHS());
3062 ConstantRange Y = getUnsignedRange(UDiv->getRHS());
3063 return ConservativeResult.intersectWith(X.udiv(Y));
3066 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3067 ConstantRange X = getUnsignedRange(ZExt->getOperand());
3068 return ConservativeResult.intersectWith(X.zeroExtend(BitWidth));
3071 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3072 ConstantRange X = getUnsignedRange(SExt->getOperand());
3073 return ConservativeResult.intersectWith(X.signExtend(BitWidth));
3076 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3077 ConstantRange X = getUnsignedRange(Trunc->getOperand());
3078 return ConservativeResult.intersectWith(X.truncate(BitWidth));
3081 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3082 // If there's no unsigned wrap, the value will never be less than its
3084 if (AddRec->hasNoUnsignedWrap())
3085 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
3086 if (!C->getValue()->isZero())
3087 ConservativeResult =
3088 ConservativeResult.intersectWith(
3089 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0)));
3091 // TODO: non-affine addrec
3092 if (AddRec->isAffine()) {
3093 const Type *Ty = AddRec->getType();
3094 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3095 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3096 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3097 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3099 const SCEV *Start = AddRec->getStart();
3100 const SCEV *Step = AddRec->getStepRecurrence(*this);
3102 ConstantRange StartRange = getUnsignedRange(Start);
3103 ConstantRange StepRange = getSignedRange(Step);
3104 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3105 ConstantRange EndRange =
3106 StartRange.add(MaxBECountRange.multiply(StepRange));
3108 // Check for overflow. This must be done with ConstantRange arithmetic
3109 // because we could be called from within the ScalarEvolution overflow
3111 ConstantRange ExtStartRange = StartRange.zextOrTrunc(BitWidth*2+1);
3112 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3113 ConstantRange ExtMaxBECountRange =
3114 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3115 ConstantRange ExtEndRange = EndRange.zextOrTrunc(BitWidth*2+1);
3116 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3118 return ConservativeResult;
3120 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(),
3121 EndRange.getUnsignedMin());
3122 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(),
3123 EndRange.getUnsignedMax());
3124 if (Min.isMinValue() && Max.isMaxValue())
3125 return ConservativeResult;
3126 return ConservativeResult.intersectWith(ConstantRange(Min, Max+1));
3130 return ConservativeResult;
3133 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3134 // For a SCEVUnknown, ask ValueTracking.
3135 APInt Mask = APInt::getAllOnesValue(BitWidth);
3136 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3137 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones, TD);
3138 if (Ones == ~Zeros + 1)
3139 return ConservativeResult;
3140 return ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1));
3143 return ConservativeResult;
3146 /// getSignedRange - Determine the signed range for a particular SCEV.
3149 ScalarEvolution::getSignedRange(const SCEV *S) {
3151 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3152 return ConstantRange(C->getValue()->getValue());
3154 unsigned BitWidth = getTypeSizeInBits(S->getType());
3155 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3157 // If the value has known zeros, the maximum signed value will have those
3158 // known zeros as well.
3159 uint32_t TZ = GetMinTrailingZeros(S);
3161 ConservativeResult =
3162 ConstantRange(APInt::getSignedMinValue(BitWidth),
3163 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
3165 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3166 ConstantRange X = getSignedRange(Add->getOperand(0));
3167 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3168 X = X.add(getSignedRange(Add->getOperand(i)));
3169 return ConservativeResult.intersectWith(X);
3172 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3173 ConstantRange X = getSignedRange(Mul->getOperand(0));
3174 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3175 X = X.multiply(getSignedRange(Mul->getOperand(i)));
3176 return ConservativeResult.intersectWith(X);
3179 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3180 ConstantRange X = getSignedRange(SMax->getOperand(0));
3181 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3182 X = X.smax(getSignedRange(SMax->getOperand(i)));
3183 return ConservativeResult.intersectWith(X);
3186 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3187 ConstantRange X = getSignedRange(UMax->getOperand(0));
3188 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3189 X = X.umax(getSignedRange(UMax->getOperand(i)));
3190 return ConservativeResult.intersectWith(X);
3193 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3194 ConstantRange X = getSignedRange(UDiv->getLHS());
3195 ConstantRange Y = getSignedRange(UDiv->getRHS());
3196 return ConservativeResult.intersectWith(X.udiv(Y));
3199 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3200 ConstantRange X = getSignedRange(ZExt->getOperand());
3201 return ConservativeResult.intersectWith(X.zeroExtend(BitWidth));
3204 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3205 ConstantRange X = getSignedRange(SExt->getOperand());
3206 return ConservativeResult.intersectWith(X.signExtend(BitWidth));
3209 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3210 ConstantRange X = getSignedRange(Trunc->getOperand());
3211 return ConservativeResult.intersectWith(X.truncate(BitWidth));
3214 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3215 // If there's no signed wrap, and all the operands have the same sign or
3216 // zero, the value won't ever change sign.
3217 if (AddRec->hasNoSignedWrap()) {
3218 bool AllNonNeg = true;
3219 bool AllNonPos = true;
3220 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
3221 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
3222 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
3225 ConservativeResult = ConservativeResult.intersectWith(
3226 ConstantRange(APInt(BitWidth, 0),
3227 APInt::getSignedMinValue(BitWidth)));
3229 ConservativeResult = ConservativeResult.intersectWith(
3230 ConstantRange(APInt::getSignedMinValue(BitWidth),
3231 APInt(BitWidth, 1)));
3234 // TODO: non-affine addrec
3235 if (AddRec->isAffine()) {
3236 const Type *Ty = AddRec->getType();
3237 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3238 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3239 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3240 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3242 const SCEV *Start = AddRec->getStart();
3243 const SCEV *Step = AddRec->getStepRecurrence(*this);
3245 ConstantRange StartRange = getSignedRange(Start);
3246 ConstantRange StepRange = getSignedRange(Step);
3247 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3248 ConstantRange EndRange =
3249 StartRange.add(MaxBECountRange.multiply(StepRange));
3251 // Check for overflow. This must be done with ConstantRange arithmetic
3252 // because we could be called from within the ScalarEvolution overflow
3254 ConstantRange ExtStartRange = StartRange.sextOrTrunc(BitWidth*2+1);
3255 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3256 ConstantRange ExtMaxBECountRange =
3257 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3258 ConstantRange ExtEndRange = EndRange.sextOrTrunc(BitWidth*2+1);
3259 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3261 return ConservativeResult;
3263 APInt Min = APIntOps::smin(StartRange.getSignedMin(),
3264 EndRange.getSignedMin());
3265 APInt Max = APIntOps::smax(StartRange.getSignedMax(),
3266 EndRange.getSignedMax());
3267 if (Min.isMinSignedValue() && Max.isMaxSignedValue())
3268 return ConservativeResult;
3269 return ConservativeResult.intersectWith(ConstantRange(Min, Max+1));
3273 return ConservativeResult;
3276 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3277 // For a SCEVUnknown, ask ValueTracking.
3278 if (!U->getValue()->getType()->isIntegerTy() && !TD)
3279 return ConservativeResult;
3280 unsigned NS = ComputeNumSignBits(U->getValue(), TD);
3282 return ConservativeResult;
3283 return ConservativeResult.intersectWith(
3284 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
3285 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1));
3288 return ConservativeResult;
3291 /// createSCEV - We know that there is no SCEV for the specified value.
3292 /// Analyze the expression.
3294 const SCEV *ScalarEvolution::createSCEV(Value *V) {
3295 if (!isSCEVable(V->getType()))
3296 return getUnknown(V);
3298 unsigned Opcode = Instruction::UserOp1;
3299 if (Instruction *I = dyn_cast<Instruction>(V)) {
3300 Opcode = I->getOpcode();
3302 // Don't attempt to analyze instructions in blocks that aren't
3303 // reachable. Such instructions don't matter, and they aren't required
3304 // to obey basic rules for definitions dominating uses which this
3305 // analysis depends on.
3306 if (!DT->isReachableFromEntry(I->getParent()))
3307 return getUnknown(V);
3308 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
3309 Opcode = CE->getOpcode();
3310 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
3311 return getConstant(CI);
3312 else if (isa<ConstantPointerNull>(V))
3313 return getConstant(V->getType(), 0);
3314 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
3315 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee());
3317 return getUnknown(V);
3319 Operator *U = cast<Operator>(V);
3321 case Instruction::Add: {
3322 // The simple thing to do would be to just call getSCEV on both operands
3323 // and call getAddExpr with the result. However if we're looking at a
3324 // bunch of things all added together, this can be quite inefficient,
3325 // because it leads to N-1 getAddExpr calls for N ultimate operands.
3326 // Instead, gather up all the operands and make a single getAddExpr call.
3327 // LLVM IR canonical form means we need only traverse the left operands.
3328 SmallVector<const SCEV *, 4> AddOps;
3329 AddOps.push_back(getSCEV(U->getOperand(1)));
3330 for (Value *Op = U->getOperand(0);
3331 Op->getValueID() == Instruction::Add + Value::InstructionVal;
3332 Op = U->getOperand(0)) {
3333 U = cast<Operator>(Op);
3334 AddOps.push_back(getSCEV(U->getOperand(1)));
3336 AddOps.push_back(getSCEV(U->getOperand(0)));
3337 return getAddExpr(AddOps);
3339 case Instruction::Mul: {
3340 // See the Add code above.
3341 SmallVector<const SCEV *, 4> MulOps;
3342 MulOps.push_back(getSCEV(U->getOperand(1)));
3343 for (Value *Op = U->getOperand(0);
3344 Op->getValueID() == Instruction::Mul + Value::InstructionVal;
3345 Op = U->getOperand(0)) {
3346 U = cast<Operator>(Op);
3347 MulOps.push_back(getSCEV(U->getOperand(1)));
3349 MulOps.push_back(getSCEV(U->getOperand(0)));
3350 return getMulExpr(MulOps);
3352 case Instruction::UDiv:
3353 return getUDivExpr(getSCEV(U->getOperand(0)),
3354 getSCEV(U->getOperand(1)));
3355 case Instruction::Sub:
3356 return getMinusSCEV(getSCEV(U->getOperand(0)),
3357 getSCEV(U->getOperand(1)));
3358 case Instruction::And:
3359 // For an expression like x&255 that merely masks off the high bits,
3360 // use zext(trunc(x)) as the SCEV expression.
3361 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3362 if (CI->isNullValue())
3363 return getSCEV(U->getOperand(1));
3364 if (CI->isAllOnesValue())
3365 return getSCEV(U->getOperand(0));
3366 const APInt &A = CI->getValue();
3368 // Instcombine's ShrinkDemandedConstant may strip bits out of
3369 // constants, obscuring what would otherwise be a low-bits mask.
3370 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant
3371 // knew about to reconstruct a low-bits mask value.
3372 unsigned LZ = A.countLeadingZeros();
3373 unsigned BitWidth = A.getBitWidth();
3374 APInt AllOnes = APInt::getAllOnesValue(BitWidth);
3375 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
3376 ComputeMaskedBits(U->getOperand(0), AllOnes, KnownZero, KnownOne, TD);
3378 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ);
3380 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask))
3382 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)),
3383 IntegerType::get(getContext(), BitWidth - LZ)),
3388 case Instruction::Or:
3389 // If the RHS of the Or is a constant, we may have something like:
3390 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
3391 // optimizations will transparently handle this case.
3393 // In order for this transformation to be safe, the LHS must be of the
3394 // form X*(2^n) and the Or constant must be less than 2^n.
3395 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3396 const SCEV *LHS = getSCEV(U->getOperand(0));
3397 const APInt &CIVal = CI->getValue();
3398 if (GetMinTrailingZeros(LHS) >=
3399 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
3400 // Build a plain add SCEV.
3401 const SCEV *S = getAddExpr(LHS, getSCEV(CI));
3402 // If the LHS of the add was an addrec and it has no-wrap flags,
3403 // transfer the no-wrap flags, since an or won't introduce a wrap.
3404 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
3405 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
3406 if (OldAR->hasNoUnsignedWrap())
3407 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoUnsignedWrap(true);
3408 if (OldAR->hasNoSignedWrap())
3409 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoSignedWrap(true);
3415 case Instruction::Xor:
3416 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3417 // If the RHS of the xor is a signbit, then this is just an add.
3418 // Instcombine turns add of signbit into xor as a strength reduction step.
3419 if (CI->getValue().isSignBit())
3420 return getAddExpr(getSCEV(U->getOperand(0)),
3421 getSCEV(U->getOperand(1)));
3423 // If the RHS of xor is -1, then this is a not operation.
3424 if (CI->isAllOnesValue())
3425 return getNotSCEV(getSCEV(U->getOperand(0)));
3427 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
3428 // This is a variant of the check for xor with -1, and it handles
3429 // the case where instcombine has trimmed non-demanded bits out
3430 // of an xor with -1.
3431 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
3432 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
3433 if (BO->getOpcode() == Instruction::And &&
3434 LCI->getValue() == CI->getValue())
3435 if (const SCEVZeroExtendExpr *Z =
3436 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
3437 const Type *UTy = U->getType();
3438 const SCEV *Z0 = Z->getOperand();
3439 const Type *Z0Ty = Z0->getType();
3440 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
3442 // If C is a low-bits mask, the zero extend is serving to
3443 // mask off the high bits. Complement the operand and
3444 // re-apply the zext.
3445 if (APIntOps::isMask(Z0TySize, CI->getValue()))
3446 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
3448 // If C is a single bit, it may be in the sign-bit position
3449 // before the zero-extend. In this case, represent the xor
3450 // using an add, which is equivalent, and re-apply the zext.
3451 APInt Trunc = APInt(CI->getValue()).trunc(Z0TySize);
3452 if (APInt(Trunc).zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
3454 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
3460 case Instruction::Shl:
3461 // Turn shift left of a constant amount into a multiply.
3462 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3463 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3465 // If the shift count is not less than the bitwidth, the result of
3466 // the shift is undefined. Don't try to analyze it, because the
3467 // resolution chosen here may differ from the resolution chosen in
3468 // other parts of the compiler.
3469 if (SA->getValue().uge(BitWidth))
3472 Constant *X = ConstantInt::get(getContext(),
3473 APInt(BitWidth, 1).shl(SA->getZExtValue()));
3474 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3478 case Instruction::LShr:
3479 // Turn logical shift right of a constant into a unsigned divide.
3480 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3481 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3483 // If the shift count is not less than the bitwidth, the result of
3484 // the shift is undefined. Don't try to analyze it, because the
3485 // resolution chosen here may differ from the resolution chosen in
3486 // other parts of the compiler.
3487 if (SA->getValue().uge(BitWidth))
3490 Constant *X = ConstantInt::get(getContext(),
3491 APInt(BitWidth, 1).shl(SA->getZExtValue()));
3492 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3496 case Instruction::AShr:
3497 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
3498 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
3499 if (Operator *L = dyn_cast<Operator>(U->getOperand(0)))
3500 if (L->getOpcode() == Instruction::Shl &&
3501 L->getOperand(1) == U->getOperand(1)) {
3502 uint64_t BitWidth = getTypeSizeInBits(U->getType());
3504 // If the shift count is not less than the bitwidth, the result of
3505 // the shift is undefined. Don't try to analyze it, because the
3506 // resolution chosen here may differ from the resolution chosen in
3507 // other parts of the compiler.
3508 if (CI->getValue().uge(BitWidth))
3511 uint64_t Amt = BitWidth - CI->getZExtValue();
3512 if (Amt == BitWidth)
3513 return getSCEV(L->getOperand(0)); // shift by zero --> noop
3515 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
3516 IntegerType::get(getContext(),
3522 case Instruction::Trunc:
3523 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
3525 case Instruction::ZExt:
3526 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3528 case Instruction::SExt:
3529 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3531 case Instruction::BitCast:
3532 // BitCasts are no-op casts so we just eliminate the cast.
3533 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
3534 return getSCEV(U->getOperand(0));
3537 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
3538 // lead to pointer expressions which cannot safely be expanded to GEPs,
3539 // because ScalarEvolution doesn't respect the GEP aliasing rules when
3540 // simplifying integer expressions.
3542 case Instruction::GetElementPtr:
3543 return createNodeForGEP(cast<GEPOperator>(U));
3545 case Instruction::PHI:
3546 return createNodeForPHI(cast<PHINode>(U));
3548 case Instruction::Select:
3549 // This could be a smax or umax that was lowered earlier.
3550 // Try to recover it.
3551 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
3552 Value *LHS = ICI->getOperand(0);
3553 Value *RHS = ICI->getOperand(1);
3554 switch (ICI->getPredicate()) {
3555 case ICmpInst::ICMP_SLT:
3556 case ICmpInst::ICMP_SLE:
3557 std::swap(LHS, RHS);
3559 case ICmpInst::ICMP_SGT:
3560 case ICmpInst::ICMP_SGE:
3561 // a >s b ? a+x : b+x -> smax(a, b)+x
3562 // a >s b ? b+x : a+x -> smin(a, b)+x
3563 if (LHS->getType() == U->getType()) {
3564 const SCEV *LS = getSCEV(LHS);
3565 const SCEV *RS = getSCEV(RHS);
3566 const SCEV *LA = getSCEV(U->getOperand(1));
3567 const SCEV *RA = getSCEV(U->getOperand(2));
3568 const SCEV *LDiff = getMinusSCEV(LA, LS);
3569 const SCEV *RDiff = getMinusSCEV(RA, RS);
3571 return getAddExpr(getSMaxExpr(LS, RS), LDiff);
3572 LDiff = getMinusSCEV(LA, RS);
3573 RDiff = getMinusSCEV(RA, LS);
3575 return getAddExpr(getSMinExpr(LS, RS), LDiff);
3578 case ICmpInst::ICMP_ULT:
3579 case ICmpInst::ICMP_ULE:
3580 std::swap(LHS, RHS);
3582 case ICmpInst::ICMP_UGT:
3583 case ICmpInst::ICMP_UGE:
3584 // a >u b ? a+x : b+x -> umax(a, b)+x
3585 // a >u b ? b+x : a+x -> umin(a, b)+x
3586 if (LHS->getType() == U->getType()) {
3587 const SCEV *LS = getSCEV(LHS);
3588 const SCEV *RS = getSCEV(RHS);
3589 const SCEV *LA = getSCEV(U->getOperand(1));
3590 const SCEV *RA = getSCEV(U->getOperand(2));
3591 const SCEV *LDiff = getMinusSCEV(LA, LS);
3592 const SCEV *RDiff = getMinusSCEV(RA, RS);
3594 return getAddExpr(getUMaxExpr(LS, RS), LDiff);
3595 LDiff = getMinusSCEV(LA, RS);
3596 RDiff = getMinusSCEV(RA, LS);
3598 return getAddExpr(getUMinExpr(LS, RS), LDiff);
3601 case ICmpInst::ICMP_NE:
3602 // n != 0 ? n+x : 1+x -> umax(n, 1)+x
3603 if (LHS->getType() == U->getType() &&
3604 isa<ConstantInt>(RHS) &&
3605 cast<ConstantInt>(RHS)->isZero()) {
3606 const SCEV *One = getConstant(LHS->getType(), 1);
3607 const SCEV *LS = getSCEV(LHS);
3608 const SCEV *LA = getSCEV(U->getOperand(1));
3609 const SCEV *RA = getSCEV(U->getOperand(2));
3610 const SCEV *LDiff = getMinusSCEV(LA, LS);
3611 const SCEV *RDiff = getMinusSCEV(RA, One);
3613 return getAddExpr(getUMaxExpr(One, LS), LDiff);
3616 case ICmpInst::ICMP_EQ:
3617 // n == 0 ? 1+x : n+x -> umax(n, 1)+x
3618 if (LHS->getType() == U->getType() &&
3619 isa<ConstantInt>(RHS) &&
3620 cast<ConstantInt>(RHS)->isZero()) {
3621 const SCEV *One = getConstant(LHS->getType(), 1);
3622 const SCEV *LS = getSCEV(LHS);
3623 const SCEV *LA = getSCEV(U->getOperand(1));
3624 const SCEV *RA = getSCEV(U->getOperand(2));
3625 const SCEV *LDiff = getMinusSCEV(LA, One);
3626 const SCEV *RDiff = getMinusSCEV(RA, LS);
3628 return getAddExpr(getUMaxExpr(One, LS), LDiff);
3636 default: // We cannot analyze this expression.
3640 return getUnknown(V);
3645 //===----------------------------------------------------------------------===//
3646 // Iteration Count Computation Code
3649 /// getBackedgeTakenCount - If the specified loop has a predictable
3650 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
3651 /// object. The backedge-taken count is the number of times the loop header
3652 /// will be branched to from within the loop. This is one less than the
3653 /// trip count of the loop, since it doesn't count the first iteration,
3654 /// when the header is branched to from outside the loop.
3656 /// Note that it is not valid to call this method on a loop without a
3657 /// loop-invariant backedge-taken count (see
3658 /// hasLoopInvariantBackedgeTakenCount).
3660 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
3661 return getBackedgeTakenInfo(L).Exact;
3664 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
3665 /// return the least SCEV value that is known never to be less than the
3666 /// actual backedge taken count.
3667 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
3668 return getBackedgeTakenInfo(L).Max;
3671 /// PushLoopPHIs - Push PHI nodes in the header of the given loop
3672 /// onto the given Worklist.
3674 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
3675 BasicBlock *Header = L->getHeader();
3677 // Push all Loop-header PHIs onto the Worklist stack.
3678 for (BasicBlock::iterator I = Header->begin();
3679 PHINode *PN = dyn_cast<PHINode>(I); ++I)
3680 Worklist.push_back(PN);
3683 const ScalarEvolution::BackedgeTakenInfo &
3684 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
3685 // Initially insert a CouldNotCompute for this loop. If the insertion
3686 // succeeds, proceed to actually compute a backedge-taken count and
3687 // update the value. The temporary CouldNotCompute value tells SCEV
3688 // code elsewhere that it shouldn't attempt to request a new
3689 // backedge-taken count, which could result in infinite recursion.
3690 std::pair<std::map<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
3691 BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute()));
3693 BackedgeTakenInfo BECount = ComputeBackedgeTakenCount(L);
3694 if (BECount.Exact != getCouldNotCompute()) {
3695 assert(BECount.Exact->isLoopInvariant(L) &&
3696 BECount.Max->isLoopInvariant(L) &&
3697 "Computed backedge-taken count isn't loop invariant for loop!");
3698 ++NumTripCountsComputed;
3700 // Update the value in the map.
3701 Pair.first->second = BECount;
3703 if (BECount.Max != getCouldNotCompute())
3704 // Update the value in the map.
3705 Pair.first->second = BECount;
3706 if (isa<PHINode>(L->getHeader()->begin()))
3707 // Only count loops that have phi nodes as not being computable.
3708 ++NumTripCountsNotComputed;
3711 // Now that we know more about the trip count for this loop, forget any
3712 // existing SCEV values for PHI nodes in this loop since they are only
3713 // conservative estimates made without the benefit of trip count
3714 // information. This is similar to the code in forgetLoop, except that
3715 // it handles SCEVUnknown PHI nodes specially.
3716 if (BECount.hasAnyInfo()) {
3717 SmallVector<Instruction *, 16> Worklist;
3718 PushLoopPHIs(L, Worklist);
3720 SmallPtrSet<Instruction *, 8> Visited;
3721 while (!Worklist.empty()) {
3722 Instruction *I = Worklist.pop_back_val();
3723 if (!Visited.insert(I)) continue;
3725 ValueExprMapType::iterator It =
3726 ValueExprMap.find(static_cast<Value *>(I));
3727 if (It != ValueExprMap.end()) {
3728 // SCEVUnknown for a PHI either means that it has an unrecognized
3729 // structure, or it's a PHI that's in the progress of being computed
3730 // by createNodeForPHI. In the former case, additional loop trip
3731 // count information isn't going to change anything. In the later
3732 // case, createNodeForPHI will perform the necessary updates on its
3733 // own when it gets to that point.
3734 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(It->second)) {
3735 ValuesAtScopes.erase(It->second);
3736 ValueExprMap.erase(It);
3738 if (PHINode *PN = dyn_cast<PHINode>(I))
3739 ConstantEvolutionLoopExitValue.erase(PN);
3742 PushDefUseChildren(I, Worklist);
3746 return Pair.first->second;
3749 /// forgetLoop - This method should be called by the client when it has
3750 /// changed a loop in a way that may effect ScalarEvolution's ability to
3751 /// compute a trip count, or if the loop is deleted.
3752 void ScalarEvolution::forgetLoop(const Loop *L) {
3753 // Drop any stored trip count value.
3754 BackedgeTakenCounts.erase(L);
3756 // Drop information about expressions based on loop-header PHIs.
3757 SmallVector<Instruction *, 16> Worklist;
3758 PushLoopPHIs(L, Worklist);
3760 SmallPtrSet<Instruction *, 8> Visited;
3761 while (!Worklist.empty()) {
3762 Instruction *I = Worklist.pop_back_val();
3763 if (!Visited.insert(I)) continue;
3765 ValueExprMapType::iterator It = ValueExprMap.find(static_cast<Value *>(I));
3766 if (It != ValueExprMap.end()) {
3767 ValuesAtScopes.erase(It->second);
3768 ValueExprMap.erase(It);
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 ValueExprMapType::iterator It = ValueExprMap.find(static_cast<Value *>(I));
3794 if (It != ValueExprMap.end()) {
3795 ValuesAtScopes.erase(It->second);
3796 ValueExprMap.erase(It);
3797 if (PHINode *PN = dyn_cast<PHINode>(I))
3798 ConstantEvolutionLoopExitValue.erase(PN);
3801 PushDefUseChildren(I, Worklist);
3805 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
3806 /// of the specified loop will execute.
3807 ScalarEvolution::BackedgeTakenInfo
3808 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
3809 SmallVector<BasicBlock *, 8> ExitingBlocks;
3810 L->getExitingBlocks(ExitingBlocks);
3812 // Examine all exits and pick the most conservative values.
3813 const SCEV *BECount = getCouldNotCompute();
3814 const SCEV *MaxBECount = getCouldNotCompute();
3815 bool CouldNotComputeBECount = false;
3816 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
3817 BackedgeTakenInfo NewBTI =
3818 ComputeBackedgeTakenCountFromExit(L, ExitingBlocks[i]);
3820 if (NewBTI.Exact == getCouldNotCompute()) {
3821 // We couldn't compute an exact value for this exit, so
3822 // we won't be able to compute an exact value for the loop.
3823 CouldNotComputeBECount = true;
3824 BECount = getCouldNotCompute();
3825 } else if (!CouldNotComputeBECount) {
3826 if (BECount == getCouldNotCompute())
3827 BECount = NewBTI.Exact;
3829 BECount = getUMinFromMismatchedTypes(BECount, NewBTI.Exact);
3831 if (MaxBECount == getCouldNotCompute())
3832 MaxBECount = NewBTI.Max;
3833 else if (NewBTI.Max != getCouldNotCompute())
3834 MaxBECount = getUMinFromMismatchedTypes(MaxBECount, NewBTI.Max);
3837 return BackedgeTakenInfo(BECount, MaxBECount);
3840 /// ComputeBackedgeTakenCountFromExit - Compute the number of times the backedge
3841 /// of the specified loop will execute if it exits via the specified block.
3842 ScalarEvolution::BackedgeTakenInfo
3843 ScalarEvolution::ComputeBackedgeTakenCountFromExit(const Loop *L,
3844 BasicBlock *ExitingBlock) {
3846 // Okay, we've chosen an exiting block. See what condition causes us to
3847 // exit at this block.
3849 // FIXME: we should be able to handle switch instructions (with a single exit)
3850 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
3851 if (ExitBr == 0) return getCouldNotCompute();
3852 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
3854 // At this point, we know we have a conditional branch that determines whether
3855 // the loop is exited. However, we don't know if the branch is executed each
3856 // time through the loop. If not, then the execution count of the branch will
3857 // not be equal to the trip count of the loop.
3859 // Currently we check for this by checking to see if the Exit branch goes to
3860 // the loop header. If so, we know it will always execute the same number of
3861 // times as the loop. We also handle the case where the exit block *is* the
3862 // loop header. This is common for un-rotated loops.
3864 // If both of those tests fail, walk up the unique predecessor chain to the
3865 // header, stopping if there is an edge that doesn't exit the loop. If the
3866 // header is reached, the execution count of the branch will be equal to the
3867 // trip count of the loop.
3869 // More extensive analysis could be done to handle more cases here.
3871 if (ExitBr->getSuccessor(0) != L->getHeader() &&
3872 ExitBr->getSuccessor(1) != L->getHeader() &&
3873 ExitBr->getParent() != L->getHeader()) {
3874 // The simple checks failed, try climbing the unique predecessor chain
3875 // up to the header.
3877 for (BasicBlock *BB = ExitBr->getParent(); BB; ) {
3878 BasicBlock *Pred = BB->getUniquePredecessor();
3880 return getCouldNotCompute();
3881 TerminatorInst *PredTerm = Pred->getTerminator();
3882 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) {
3883 BasicBlock *PredSucc = PredTerm->getSuccessor(i);
3886 // If the predecessor has a successor that isn't BB and isn't
3887 // outside the loop, assume the worst.
3888 if (L->contains(PredSucc))
3889 return getCouldNotCompute();
3891 if (Pred == L->getHeader()) {
3898 return getCouldNotCompute();
3901 // Proceed to the next level to examine the exit condition expression.
3902 return ComputeBackedgeTakenCountFromExitCond(L, ExitBr->getCondition(),
3903 ExitBr->getSuccessor(0),
3904 ExitBr->getSuccessor(1));
3907 /// ComputeBackedgeTakenCountFromExitCond - Compute the number of times the
3908 /// backedge of the specified loop will execute if its exit condition
3909 /// were a conditional branch of ExitCond, TBB, and FBB.
3910 ScalarEvolution::BackedgeTakenInfo
3911 ScalarEvolution::ComputeBackedgeTakenCountFromExitCond(const Loop *L,
3915 // Check if the controlling expression for this loop is an And or Or.
3916 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
3917 if (BO->getOpcode() == Instruction::And) {
3918 // Recurse on the operands of the and.
3919 BackedgeTakenInfo BTI0 =
3920 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB);
3921 BackedgeTakenInfo BTI1 =
3922 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB);
3923 const SCEV *BECount = getCouldNotCompute();
3924 const SCEV *MaxBECount = getCouldNotCompute();
3925 if (L->contains(TBB)) {
3926 // Both conditions must be true for the loop to continue executing.
3927 // Choose the less conservative count.
3928 if (BTI0.Exact == getCouldNotCompute() ||
3929 BTI1.Exact == getCouldNotCompute())
3930 BECount = getCouldNotCompute();
3932 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3933 if (BTI0.Max == getCouldNotCompute())
3934 MaxBECount = BTI1.Max;
3935 else if (BTI1.Max == getCouldNotCompute())
3936 MaxBECount = BTI0.Max;
3938 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max);
3940 // Both conditions must be true at the same time for the loop to exit.
3941 // For now, be conservative.
3942 assert(L->contains(FBB) && "Loop block has no successor in loop!");
3943 if (BTI0.Max == BTI1.Max)
3944 MaxBECount = BTI0.Max;
3945 if (BTI0.Exact == BTI1.Exact)
3946 BECount = BTI0.Exact;
3949 return BackedgeTakenInfo(BECount, MaxBECount);
3951 if (BO->getOpcode() == Instruction::Or) {
3952 // Recurse on the operands of the or.
3953 BackedgeTakenInfo BTI0 =
3954 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB);
3955 BackedgeTakenInfo BTI1 =
3956 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB);
3957 const SCEV *BECount = getCouldNotCompute();
3958 const SCEV *MaxBECount = getCouldNotCompute();
3959 if (L->contains(FBB)) {
3960 // Both conditions must be false for the loop to continue executing.
3961 // Choose the less conservative count.
3962 if (BTI0.Exact == getCouldNotCompute() ||
3963 BTI1.Exact == getCouldNotCompute())
3964 BECount = getCouldNotCompute();
3966 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3967 if (BTI0.Max == getCouldNotCompute())
3968 MaxBECount = BTI1.Max;
3969 else if (BTI1.Max == getCouldNotCompute())
3970 MaxBECount = BTI0.Max;
3972 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max);
3974 // Both conditions must be false at the same time for the loop to exit.
3975 // For now, be conservative.
3976 assert(L->contains(TBB) && "Loop block has no successor in loop!");
3977 if (BTI0.Max == BTI1.Max)
3978 MaxBECount = BTI0.Max;
3979 if (BTI0.Exact == BTI1.Exact)
3980 BECount = BTI0.Exact;
3983 return BackedgeTakenInfo(BECount, MaxBECount);
3987 // With an icmp, it may be feasible to compute an exact backedge-taken count.
3988 // Proceed to the next level to examine the icmp.
3989 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
3990 return ComputeBackedgeTakenCountFromExitCondICmp(L, ExitCondICmp, TBB, FBB);
3992 // Check for a constant condition. These are normally stripped out by
3993 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
3994 // preserve the CFG and is temporarily leaving constant conditions
3996 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
3997 if (L->contains(FBB) == !CI->getZExtValue())
3998 // The backedge is always taken.
3999 return getCouldNotCompute();
4001 // The backedge is never taken.
4002 return getConstant(CI->getType(), 0);
4005 // If it's not an integer or pointer comparison then compute it the hard way.
4006 return ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB));
4009 /// ComputeBackedgeTakenCountFromExitCondICmp - Compute the number of times the
4010 /// backedge of the specified loop will execute if its exit condition
4011 /// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB.
4012 ScalarEvolution::BackedgeTakenInfo
4013 ScalarEvolution::ComputeBackedgeTakenCountFromExitCondICmp(const Loop *L,
4018 // If the condition was exit on true, convert the condition to exit on false
4019 ICmpInst::Predicate Cond;
4020 if (!L->contains(FBB))
4021 Cond = ExitCond->getPredicate();
4023 Cond = ExitCond->getInversePredicate();
4025 // Handle common loops like: for (X = "string"; *X; ++X)
4026 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
4027 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
4028 BackedgeTakenInfo ItCnt =
4029 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond);
4030 if (ItCnt.hasAnyInfo())
4034 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
4035 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
4037 // Try to evaluate any dependencies out of the loop.
4038 LHS = getSCEVAtScope(LHS, L);
4039 RHS = getSCEVAtScope(RHS, L);
4041 // At this point, we would like to compute how many iterations of the
4042 // loop the predicate will return true for these inputs.
4043 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) {
4044 // If there is a loop-invariant, force it into the RHS.
4045 std::swap(LHS, RHS);
4046 Cond = ICmpInst::getSwappedPredicate(Cond);
4049 // Simplify the operands before analyzing them.
4050 (void)SimplifyICmpOperands(Cond, LHS, RHS);
4052 // If we have a comparison of a chrec against a constant, try to use value
4053 // ranges to answer this query.
4054 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
4055 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
4056 if (AddRec->getLoop() == L) {
4057 // Form the constant range.
4058 ConstantRange CompRange(
4059 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
4061 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
4062 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
4066 case ICmpInst::ICMP_NE: { // while (X != Y)
4067 // Convert to: while (X-Y != 0)
4068 BackedgeTakenInfo BTI = HowFarToZero(getMinusSCEV(LHS, RHS), L);
4069 if (BTI.hasAnyInfo()) return BTI;
4072 case ICmpInst::ICMP_EQ: { // while (X == Y)
4073 // Convert to: while (X-Y == 0)
4074 BackedgeTakenInfo BTI = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
4075 if (BTI.hasAnyInfo()) return BTI;
4078 case ICmpInst::ICMP_SLT: {
4079 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true);
4080 if (BTI.hasAnyInfo()) return BTI;
4083 case ICmpInst::ICMP_SGT: {
4084 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
4085 getNotSCEV(RHS), L, true);
4086 if (BTI.hasAnyInfo()) return BTI;
4089 case ICmpInst::ICMP_ULT: {
4090 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false);
4091 if (BTI.hasAnyInfo()) return BTI;
4094 case ICmpInst::ICMP_UGT: {
4095 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
4096 getNotSCEV(RHS), L, false);
4097 if (BTI.hasAnyInfo()) return BTI;
4102 dbgs() << "ComputeBackedgeTakenCount ";
4103 if (ExitCond->getOperand(0)->getType()->isUnsigned())
4104 dbgs() << "[unsigned] ";
4105 dbgs() << *LHS << " "
4106 << Instruction::getOpcodeName(Instruction::ICmp)
4107 << " " << *RHS << "\n";
4112 ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB));
4115 static ConstantInt *
4116 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
4117 ScalarEvolution &SE) {
4118 const SCEV *InVal = SE.getConstant(C);
4119 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
4120 assert(isa<SCEVConstant>(Val) &&
4121 "Evaluation of SCEV at constant didn't fold correctly?");
4122 return cast<SCEVConstant>(Val)->getValue();
4125 /// GetAddressedElementFromGlobal - Given a global variable with an initializer
4126 /// and a GEP expression (missing the pointer index) indexing into it, return
4127 /// the addressed element of the initializer or null if the index expression is
4130 GetAddressedElementFromGlobal(GlobalVariable *GV,
4131 const std::vector<ConstantInt*> &Indices) {
4132 Constant *Init = GV->getInitializer();
4133 for (unsigned i = 0, e = Indices.size(); i != e; ++i) {
4134 uint64_t Idx = Indices[i]->getZExtValue();
4135 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) {
4136 assert(Idx < CS->getNumOperands() && "Bad struct index!");
4137 Init = cast<Constant>(CS->getOperand(Idx));
4138 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) {
4139 if (Idx >= CA->getNumOperands()) return 0; // Bogus program
4140 Init = cast<Constant>(CA->getOperand(Idx));
4141 } else if (isa<ConstantAggregateZero>(Init)) {
4142 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) {
4143 assert(Idx < STy->getNumElements() && "Bad struct index!");
4144 Init = Constant::getNullValue(STy->getElementType(Idx));
4145 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) {
4146 if (Idx >= ATy->getNumElements()) return 0; // Bogus program
4147 Init = Constant::getNullValue(ATy->getElementType());
4149 llvm_unreachable("Unknown constant aggregate type!");
4153 return 0; // Unknown initializer type
4159 /// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of
4160 /// 'icmp op load X, cst', try to see if we can compute the backedge
4161 /// execution count.
4162 ScalarEvolution::BackedgeTakenInfo
4163 ScalarEvolution::ComputeLoadConstantCompareBackedgeTakenCount(
4167 ICmpInst::Predicate predicate) {
4168 if (LI->isVolatile()) return getCouldNotCompute();
4170 // Check to see if the loaded pointer is a getelementptr of a global.
4171 // TODO: Use SCEV instead of manually grubbing with GEPs.
4172 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
4173 if (!GEP) return getCouldNotCompute();
4175 // Make sure that it is really a constant global we are gepping, with an
4176 // initializer, and make sure the first IDX is really 0.
4177 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
4178 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
4179 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
4180 !cast<Constant>(GEP->getOperand(1))->isNullValue())
4181 return getCouldNotCompute();
4183 // Okay, we allow one non-constant index into the GEP instruction.
4185 std::vector<ConstantInt*> Indexes;
4186 unsigned VarIdxNum = 0;
4187 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
4188 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
4189 Indexes.push_back(CI);
4190 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
4191 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
4192 VarIdx = GEP->getOperand(i);
4194 Indexes.push_back(0);
4197 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
4198 // Check to see if X is a loop variant variable value now.
4199 const SCEV *Idx = getSCEV(VarIdx);
4200 Idx = getSCEVAtScope(Idx, L);
4202 // We can only recognize very limited forms of loop index expressions, in
4203 // particular, only affine AddRec's like {C1,+,C2}.
4204 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
4205 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) ||
4206 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
4207 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
4208 return getCouldNotCompute();
4210 unsigned MaxSteps = MaxBruteForceIterations;
4211 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
4212 ConstantInt *ItCst = ConstantInt::get(
4213 cast<IntegerType>(IdxExpr->getType()), IterationNum);
4214 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
4216 // Form the GEP offset.
4217 Indexes[VarIdxNum] = Val;
4219 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes);
4220 if (Result == 0) break; // Cannot compute!
4222 // Evaluate the condition for this iteration.
4223 Result = ConstantExpr::getICmp(predicate, Result, RHS);
4224 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
4225 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
4227 dbgs() << "\n***\n*** Computed loop count " << *ItCst
4228 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
4231 ++NumArrayLenItCounts;
4232 return getConstant(ItCst); // Found terminating iteration!
4235 return getCouldNotCompute();
4239 /// CanConstantFold - Return true if we can constant fold an instruction of the
4240 /// specified type, assuming that all operands were constants.
4241 static bool CanConstantFold(const Instruction *I) {
4242 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
4243 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I))
4246 if (const CallInst *CI = dyn_cast<CallInst>(I))
4247 if (const Function *F = CI->getCalledFunction())
4248 return canConstantFoldCallTo(F);
4252 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
4253 /// in the loop that V is derived from. We allow arbitrary operations along the
4254 /// way, but the operands of an operation must either be constants or a value
4255 /// derived from a constant PHI. If this expression does not fit with these
4256 /// constraints, return null.
4257 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
4258 // If this is not an instruction, or if this is an instruction outside of the
4259 // loop, it can't be derived from a loop PHI.
4260 Instruction *I = dyn_cast<Instruction>(V);
4261 if (I == 0 || !L->contains(I)) return 0;
4263 if (PHINode *PN = dyn_cast<PHINode>(I)) {
4264 if (L->getHeader() == I->getParent())
4267 // We don't currently keep track of the control flow needed to evaluate
4268 // PHIs, so we cannot handle PHIs inside of loops.
4272 // If we won't be able to constant fold this expression even if the operands
4273 // are constants, return early.
4274 if (!CanConstantFold(I)) return 0;
4276 // Otherwise, we can evaluate this instruction if all of its operands are
4277 // constant or derived from a PHI node themselves.
4279 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op)
4280 if (!isa<Constant>(I->getOperand(Op))) {
4281 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L);
4282 if (P == 0) return 0; // Not evolving from PHI
4286 return 0; // Evolving from multiple different PHIs.
4289 // This is a expression evolving from a constant PHI!
4293 /// EvaluateExpression - Given an expression that passes the
4294 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
4295 /// in the loop has the value PHIVal. If we can't fold this expression for some
4296 /// reason, return null.
4297 static Constant *EvaluateExpression(Value *V, Constant *PHIVal,
4298 const TargetData *TD) {
4299 if (isa<PHINode>(V)) return PHIVal;
4300 if (Constant *C = dyn_cast<Constant>(V)) return C;
4301 Instruction *I = cast<Instruction>(V);
4303 std::vector<Constant*> Operands(I->getNumOperands());
4305 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
4306 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal, TD);
4307 if (Operands[i] == 0) return 0;
4310 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
4311 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
4313 return ConstantFoldInstOperands(I->getOpcode(), I->getType(),
4314 &Operands[0], Operands.size(), TD);
4317 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
4318 /// in the header of its containing loop, we know the loop executes a
4319 /// constant number of times, and the PHI node is just a recurrence
4320 /// involving constants, fold it.
4322 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
4325 std::map<PHINode*, Constant*>::const_iterator I =
4326 ConstantEvolutionLoopExitValue.find(PN);
4327 if (I != ConstantEvolutionLoopExitValue.end())
4330 if (BEs.ugt(MaxBruteForceIterations))
4331 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
4333 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
4335 // Since the loop is canonicalized, the PHI node must have two entries. One
4336 // entry must be a constant (coming in from outside of the loop), and the
4337 // second must be derived from the same PHI.
4338 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
4339 Constant *StartCST =
4340 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
4342 return RetVal = 0; // Must be a constant.
4344 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
4345 if (getConstantEvolvingPHI(BEValue, L) != PN &&
4346 !isa<Constant>(BEValue))
4347 return RetVal = 0; // Not derived from same PHI.
4349 // Execute the loop symbolically to determine the exit value.
4350 if (BEs.getActiveBits() >= 32)
4351 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
4353 unsigned NumIterations = BEs.getZExtValue(); // must be in range
4354 unsigned IterationNum = 0;
4355 for (Constant *PHIVal = StartCST; ; ++IterationNum) {
4356 if (IterationNum == NumIterations)
4357 return RetVal = PHIVal; // Got exit value!
4359 // Compute the value of the PHI node for the next iteration.
4360 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD);
4361 if (NextPHI == PHIVal)
4362 return RetVal = NextPHI; // Stopped evolving!
4364 return 0; // Couldn't evaluate!
4369 /// ComputeBackedgeTakenCountExhaustively - If the loop is known to execute a
4370 /// constant number of times (the condition evolves only from constants),
4371 /// try to evaluate a few iterations of the loop until we get the exit
4372 /// condition gets a value of ExitWhen (true or false). If we cannot
4373 /// evaluate the trip count of the loop, return getCouldNotCompute().
4375 ScalarEvolution::ComputeBackedgeTakenCountExhaustively(const Loop *L,
4378 PHINode *PN = getConstantEvolvingPHI(Cond, L);
4379 if (PN == 0) return getCouldNotCompute();
4381 // If the loop is canonicalized, the PHI will have exactly two entries.
4382 // That's the only form we support here.
4383 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
4385 // One entry must be a constant (coming in from outside of the loop), and the
4386 // second must be derived from the same PHI.
4387 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
4388 Constant *StartCST =
4389 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
4390 if (StartCST == 0) return getCouldNotCompute(); // Must be a constant.
4392 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
4393 if (getConstantEvolvingPHI(BEValue, L) != PN &&
4394 !isa<Constant>(BEValue))
4395 return getCouldNotCompute(); // Not derived from same PHI.
4397 // Okay, we find a PHI node that defines the trip count of this loop. Execute
4398 // the loop symbolically to determine when the condition gets a value of
4400 unsigned IterationNum = 0;
4401 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
4402 for (Constant *PHIVal = StartCST;
4403 IterationNum != MaxIterations; ++IterationNum) {
4404 ConstantInt *CondVal =
4405 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal, TD));
4407 // Couldn't symbolically evaluate.
4408 if (!CondVal) return getCouldNotCompute();
4410 if (CondVal->getValue() == uint64_t(ExitWhen)) {
4411 ++NumBruteForceTripCountsComputed;
4412 return getConstant(Type::getInt32Ty(getContext()), IterationNum);
4415 // Compute the value of the PHI node for the next iteration.
4416 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD);
4417 if (NextPHI == 0 || NextPHI == PHIVal)
4418 return getCouldNotCompute();// Couldn't evaluate or not making progress...
4422 // Too many iterations were needed to evaluate.
4423 return getCouldNotCompute();
4426 /// getSCEVAtScope - Return a SCEV expression for the specified value
4427 /// at the specified scope in the program. The L value specifies a loop
4428 /// nest to evaluate the expression at, where null is the top-level or a
4429 /// specified loop is immediately inside of the loop.
4431 /// This method can be used to compute the exit value for a variable defined
4432 /// in a loop by querying what the value will hold in the parent loop.
4434 /// In the case that a relevant loop exit value cannot be computed, the
4435 /// original value V is returned.
4436 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
4437 // Check to see if we've folded this expression at this loop before.
4438 std::map<const Loop *, const SCEV *> &Values = ValuesAtScopes[V];
4439 std::pair<std::map<const Loop *, const SCEV *>::iterator, bool> Pair =
4440 Values.insert(std::make_pair(L, static_cast<const SCEV *>(0)));
4442 return Pair.first->second ? Pair.first->second : V;
4444 // Otherwise compute it.
4445 const SCEV *C = computeSCEVAtScope(V, L);
4446 ValuesAtScopes[V][L] = C;
4450 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
4451 if (isa<SCEVConstant>(V)) return V;
4453 // If this instruction is evolved from a constant-evolving PHI, compute the
4454 // exit value from the loop without using SCEVs.
4455 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
4456 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
4457 const Loop *LI = (*this->LI)[I->getParent()];
4458 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
4459 if (PHINode *PN = dyn_cast<PHINode>(I))
4460 if (PN->getParent() == LI->getHeader()) {
4461 // Okay, there is no closed form solution for the PHI node. Check
4462 // to see if the loop that contains it has a known backedge-taken
4463 // count. If so, we may be able to force computation of the exit
4465 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
4466 if (const SCEVConstant *BTCC =
4467 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
4468 // Okay, we know how many times the containing loop executes. If
4469 // this is a constant evolving PHI node, get the final value at
4470 // the specified iteration number.
4471 Constant *RV = getConstantEvolutionLoopExitValue(PN,
4472 BTCC->getValue()->getValue(),
4474 if (RV) return getSCEV(RV);
4478 // Okay, this is an expression that we cannot symbolically evaluate
4479 // into a SCEV. Check to see if it's possible to symbolically evaluate
4480 // the arguments into constants, and if so, try to constant propagate the
4481 // result. This is particularly useful for computing loop exit values.
4482 if (CanConstantFold(I)) {
4483 SmallVector<Constant *, 4> Operands;
4484 bool MadeImprovement = false;
4485 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
4486 Value *Op = I->getOperand(i);
4487 if (Constant *C = dyn_cast<Constant>(Op)) {
4488 Operands.push_back(C);
4492 // If any of the operands is non-constant and if they are
4493 // non-integer and non-pointer, don't even try to analyze them
4494 // with scev techniques.
4495 if (!isSCEVable(Op->getType()))
4498 const SCEV *OrigV = getSCEV(Op);
4499 const SCEV *OpV = getSCEVAtScope(OrigV, L);
4500 MadeImprovement |= OrigV != OpV;
4503 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV))
4505 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV))
4506 C = dyn_cast<Constant>(SU->getValue());
4508 if (C->getType() != Op->getType())
4509 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
4513 Operands.push_back(C);
4516 // Check to see if getSCEVAtScope actually made an improvement.
4517 if (MadeImprovement) {
4519 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
4520 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
4521 Operands[0], Operands[1], TD);
4523 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
4524 &Operands[0], Operands.size(), TD);
4531 // This is some other type of SCEVUnknown, just return it.
4535 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
4536 // Avoid performing the look-up in the common case where the specified
4537 // expression has no loop-variant portions.
4538 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
4539 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
4540 if (OpAtScope != Comm->getOperand(i)) {
4541 // Okay, at least one of these operands is loop variant but might be
4542 // foldable. Build a new instance of the folded commutative expression.
4543 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
4544 Comm->op_begin()+i);
4545 NewOps.push_back(OpAtScope);
4547 for (++i; i != e; ++i) {
4548 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
4549 NewOps.push_back(OpAtScope);
4551 if (isa<SCEVAddExpr>(Comm))
4552 return getAddExpr(NewOps);
4553 if (isa<SCEVMulExpr>(Comm))
4554 return getMulExpr(NewOps);
4555 if (isa<SCEVSMaxExpr>(Comm))
4556 return getSMaxExpr(NewOps);
4557 if (isa<SCEVUMaxExpr>(Comm))
4558 return getUMaxExpr(NewOps);
4559 llvm_unreachable("Unknown commutative SCEV type!");
4562 // If we got here, all operands are loop invariant.
4566 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
4567 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
4568 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
4569 if (LHS == Div->getLHS() && RHS == Div->getRHS())
4570 return Div; // must be loop invariant
4571 return getUDivExpr(LHS, RHS);
4574 // If this is a loop recurrence for a loop that does not contain L, then we
4575 // are dealing with the final value computed by the loop.
4576 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
4577 // First, attempt to evaluate each operand.
4578 // Avoid performing the look-up in the common case where the specified
4579 // expression has no loop-variant portions.
4580 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
4581 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
4582 if (OpAtScope == AddRec->getOperand(i))
4585 // Okay, at least one of these operands is loop variant but might be
4586 // foldable. Build a new instance of the folded commutative expression.
4587 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(),
4588 AddRec->op_begin()+i);
4589 NewOps.push_back(OpAtScope);
4590 for (++i; i != e; ++i)
4591 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
4593 AddRec = cast<SCEVAddRecExpr>(getAddRecExpr(NewOps, AddRec->getLoop()));
4597 // If the scope is outside the addrec's loop, evaluate it by using the
4598 // loop exit value of the addrec.
4599 if (!AddRec->getLoop()->contains(L)) {
4600 // To evaluate this recurrence, we need to know how many times the AddRec
4601 // loop iterates. Compute this now.
4602 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
4603 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
4605 // Then, evaluate the AddRec.
4606 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
4612 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
4613 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
4614 if (Op == Cast->getOperand())
4615 return Cast; // must be loop invariant
4616 return getZeroExtendExpr(Op, Cast->getType());
4619 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
4620 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
4621 if (Op == Cast->getOperand())
4622 return Cast; // must be loop invariant
4623 return getSignExtendExpr(Op, Cast->getType());
4626 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
4627 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
4628 if (Op == Cast->getOperand())
4629 return Cast; // must be loop invariant
4630 return getTruncateExpr(Op, Cast->getType());
4633 llvm_unreachable("Unknown SCEV type!");
4637 /// getSCEVAtScope - This is a convenience function which does
4638 /// getSCEVAtScope(getSCEV(V), L).
4639 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
4640 return getSCEVAtScope(getSCEV(V), L);
4643 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
4644 /// following equation:
4646 /// A * X = B (mod N)
4648 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
4649 /// A and B isn't important.
4651 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
4652 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
4653 ScalarEvolution &SE) {
4654 uint32_t BW = A.getBitWidth();
4655 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
4656 assert(A != 0 && "A must be non-zero.");
4660 // The gcd of A and N may have only one prime factor: 2. The number of
4661 // trailing zeros in A is its multiplicity
4662 uint32_t Mult2 = A.countTrailingZeros();
4665 // 2. Check if B is divisible by D.
4667 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
4668 // is not less than multiplicity of this prime factor for D.
4669 if (B.countTrailingZeros() < Mult2)
4670 return SE.getCouldNotCompute();
4672 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
4675 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
4676 // bit width during computations.
4677 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
4678 APInt Mod(BW + 1, 0);
4679 Mod.set(BW - Mult2); // Mod = N / D
4680 APInt I = AD.multiplicativeInverse(Mod);
4682 // 4. Compute the minimum unsigned root of the equation:
4683 // I * (B / D) mod (N / D)
4684 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
4686 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
4688 return SE.getConstant(Result.trunc(BW));
4691 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
4692 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
4693 /// might be the same) or two SCEVCouldNotCompute objects.
4695 static std::pair<const SCEV *,const SCEV *>
4696 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
4697 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
4698 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
4699 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
4700 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
4702 // We currently can only solve this if the coefficients are constants.
4703 if (!LC || !MC || !NC) {
4704 const SCEV *CNC = SE.getCouldNotCompute();
4705 return std::make_pair(CNC, CNC);
4708 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
4709 const APInt &L = LC->getValue()->getValue();
4710 const APInt &M = MC->getValue()->getValue();
4711 const APInt &N = NC->getValue()->getValue();
4712 APInt Two(BitWidth, 2);
4713 APInt Four(BitWidth, 4);
4716 using namespace APIntOps;
4718 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
4719 // The B coefficient is M-N/2
4723 // The A coefficient is N/2
4724 APInt A(N.sdiv(Two));
4726 // Compute the B^2-4ac term.
4729 SqrtTerm -= Four * (A * C);
4731 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
4732 // integer value or else APInt::sqrt() will assert.
4733 APInt SqrtVal(SqrtTerm.sqrt());
4735 // Compute the two solutions for the quadratic formula.
4736 // The divisions must be performed as signed divisions.
4738 APInt TwoA( A << 1 );
4739 if (TwoA.isMinValue()) {
4740 const SCEV *CNC = SE.getCouldNotCompute();
4741 return std::make_pair(CNC, CNC);
4744 LLVMContext &Context = SE.getContext();
4746 ConstantInt *Solution1 =
4747 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
4748 ConstantInt *Solution2 =
4749 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
4751 return std::make_pair(SE.getConstant(Solution1),
4752 SE.getConstant(Solution2));
4753 } // end APIntOps namespace
4756 /// HowFarToZero - Return the number of times a backedge comparing the specified
4757 /// value to zero will execute. If not computable, return CouldNotCompute.
4758 ScalarEvolution::BackedgeTakenInfo
4759 ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) {
4760 // If the value is a constant
4761 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
4762 // If the value is already zero, the branch will execute zero times.
4763 if (C->getValue()->isZero()) return C;
4764 return getCouldNotCompute(); // Otherwise it will loop infinitely.
4767 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
4768 if (!AddRec || AddRec->getLoop() != L)
4769 return getCouldNotCompute();
4771 if (AddRec->isAffine()) {
4772 // If this is an affine expression, the execution count of this branch is
4773 // the minimum unsigned root of the following equation:
4775 // Start + Step*N = 0 (mod 2^BW)
4779 // Step*N = -Start (mod 2^BW)
4781 // where BW is the common bit width of Start and Step.
4783 // Get the initial value for the loop.
4784 const SCEV *Start = getSCEVAtScope(AddRec->getStart(),
4785 L->getParentLoop());
4786 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1),
4787 L->getParentLoop());
4789 if (const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) {
4790 // For now we handle only constant steps.
4792 // First, handle unitary steps.
4793 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so:
4794 return getNegativeSCEV(Start); // N = -Start (as unsigned)
4795 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so:
4796 return Start; // N = Start (as unsigned)
4798 // Then, try to solve the above equation provided that Start is constant.
4799 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
4800 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
4801 -StartC->getValue()->getValue(),
4804 } else if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
4805 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
4806 // the quadratic equation to solve it.
4807 std::pair<const SCEV *,const SCEV *> Roots = SolveQuadraticEquation(AddRec,
4809 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
4810 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
4813 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1
4814 << " sol#2: " << *R2 << "\n";
4816 // Pick the smallest positive root value.
4817 if (ConstantInt *CB =
4818 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
4819 R1->getValue(), R2->getValue()))) {
4820 if (CB->getZExtValue() == false)
4821 std::swap(R1, R2); // R1 is the minimum root now.
4823 // We can only use this value if the chrec ends up with an exact zero
4824 // value at this index. When solving for "X*X != 5", for example, we
4825 // should not accept a root of 2.
4826 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
4828 return R1; // We found a quadratic root!
4833 return getCouldNotCompute();
4836 /// HowFarToNonZero - Return the number of times a backedge checking the
4837 /// specified value for nonzero will execute. If not computable, return
4839 ScalarEvolution::BackedgeTakenInfo
4840 ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
4841 // Loops that look like: while (X == 0) are very strange indeed. We don't
4842 // handle them yet except for the trivial case. This could be expanded in the
4843 // future as needed.
4845 // If the value is a constant, check to see if it is known to be non-zero
4846 // already. If so, the backedge will execute zero times.
4847 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
4848 if (!C->getValue()->isNullValue())
4849 return getConstant(C->getType(), 0);
4850 return getCouldNotCompute(); // Otherwise it will loop infinitely.
4853 // We could implement others, but I really doubt anyone writes loops like
4854 // this, and if they did, they would already be constant folded.
4855 return getCouldNotCompute();
4858 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
4859 /// (which may not be an immediate predecessor) which has exactly one
4860 /// successor from which BB is reachable, or null if no such block is
4863 std::pair<BasicBlock *, BasicBlock *>
4864 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
4865 // If the block has a unique predecessor, then there is no path from the
4866 // predecessor to the block that does not go through the direct edge
4867 // from the predecessor to the block.
4868 if (BasicBlock *Pred = BB->getSinglePredecessor())
4869 return std::make_pair(Pred, BB);
4871 // A loop's header is defined to be a block that dominates the loop.
4872 // If the header has a unique predecessor outside the loop, it must be
4873 // a block that has exactly one successor that can reach the loop.
4874 if (Loop *L = LI->getLoopFor(BB))
4875 return std::make_pair(L->getLoopPredecessor(), L->getHeader());
4877 return std::pair<BasicBlock *, BasicBlock *>();
4880 /// HasSameValue - SCEV structural equivalence is usually sufficient for
4881 /// testing whether two expressions are equal, however for the purposes of
4882 /// looking for a condition guarding a loop, it can be useful to be a little
4883 /// more general, since a front-end may have replicated the controlling
4886 static bool HasSameValue(const SCEV *A, const SCEV *B) {
4887 // Quick check to see if they are the same SCEV.
4888 if (A == B) return true;
4890 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
4891 // two different instructions with the same value. Check for this case.
4892 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
4893 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
4894 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
4895 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
4896 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory())
4899 // Otherwise assume they may have a different value.
4903 /// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with
4904 /// predicate Pred. Return true iff any changes were made.
4906 bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
4907 const SCEV *&LHS, const SCEV *&RHS) {
4908 bool Changed = false;
4910 // Canonicalize a constant to the right side.
4911 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
4912 // Check for both operands constant.
4913 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
4914 if (ConstantExpr::getICmp(Pred,
4916 RHSC->getValue())->isNullValue())
4917 goto trivially_false;
4919 goto trivially_true;
4921 // Otherwise swap the operands to put the constant on the right.
4922 std::swap(LHS, RHS);
4923 Pred = ICmpInst::getSwappedPredicate(Pred);
4927 // If we're comparing an addrec with a value which is loop-invariant in the
4928 // addrec's loop, put the addrec on the left. Also make a dominance check,
4929 // as both operands could be addrecs loop-invariant in each other's loop.
4930 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
4931 const Loop *L = AR->getLoop();
4932 if (LHS->isLoopInvariant(L) && LHS->properlyDominates(L->getHeader(), DT)) {
4933 std::swap(LHS, RHS);
4934 Pred = ICmpInst::getSwappedPredicate(Pred);
4939 // If there's a constant operand, canonicalize comparisons with boundary
4940 // cases, and canonicalize *-or-equal comparisons to regular comparisons.
4941 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
4942 const APInt &RA = RC->getValue()->getValue();
4944 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
4945 case ICmpInst::ICMP_EQ:
4946 case ICmpInst::ICMP_NE:
4948 case ICmpInst::ICMP_UGE:
4949 if ((RA - 1).isMinValue()) {
4950 Pred = ICmpInst::ICMP_NE;
4951 RHS = getConstant(RA - 1);
4955 if (RA.isMaxValue()) {
4956 Pred = ICmpInst::ICMP_EQ;
4960 if (RA.isMinValue()) goto trivially_true;
4962 Pred = ICmpInst::ICMP_UGT;
4963 RHS = getConstant(RA - 1);
4966 case ICmpInst::ICMP_ULE:
4967 if ((RA + 1).isMaxValue()) {
4968 Pred = ICmpInst::ICMP_NE;
4969 RHS = getConstant(RA + 1);
4973 if (RA.isMinValue()) {
4974 Pred = ICmpInst::ICMP_EQ;
4978 if (RA.isMaxValue()) goto trivially_true;
4980 Pred = ICmpInst::ICMP_ULT;
4981 RHS = getConstant(RA + 1);
4984 case ICmpInst::ICMP_SGE:
4985 if ((RA - 1).isMinSignedValue()) {
4986 Pred = ICmpInst::ICMP_NE;
4987 RHS = getConstant(RA - 1);
4991 if (RA.isMaxSignedValue()) {
4992 Pred = ICmpInst::ICMP_EQ;
4996 if (RA.isMinSignedValue()) goto trivially_true;
4998 Pred = ICmpInst::ICMP_SGT;
4999 RHS = getConstant(RA - 1);
5002 case ICmpInst::ICMP_SLE:
5003 if ((RA + 1).isMaxSignedValue()) {
5004 Pred = ICmpInst::ICMP_NE;
5005 RHS = getConstant(RA + 1);
5009 if (RA.isMinSignedValue()) {
5010 Pred = ICmpInst::ICMP_EQ;
5014 if (RA.isMaxSignedValue()) goto trivially_true;
5016 Pred = ICmpInst::ICMP_SLT;
5017 RHS = getConstant(RA + 1);
5020 case ICmpInst::ICMP_UGT:
5021 if (RA.isMinValue()) {
5022 Pred = ICmpInst::ICMP_NE;
5026 if ((RA + 1).isMaxValue()) {
5027 Pred = ICmpInst::ICMP_EQ;
5028 RHS = getConstant(RA + 1);
5032 if (RA.isMaxValue()) goto trivially_false;
5034 case ICmpInst::ICMP_ULT:
5035 if (RA.isMaxValue()) {
5036 Pred = ICmpInst::ICMP_NE;
5040 if ((RA - 1).isMinValue()) {
5041 Pred = ICmpInst::ICMP_EQ;
5042 RHS = getConstant(RA - 1);
5046 if (RA.isMinValue()) goto trivially_false;
5048 case ICmpInst::ICMP_SGT:
5049 if (RA.isMinSignedValue()) {
5050 Pred = ICmpInst::ICMP_NE;
5054 if ((RA + 1).isMaxSignedValue()) {
5055 Pred = ICmpInst::ICMP_EQ;
5056 RHS = getConstant(RA + 1);
5060 if (RA.isMaxSignedValue()) goto trivially_false;
5062 case ICmpInst::ICMP_SLT:
5063 if (RA.isMaxSignedValue()) {
5064 Pred = ICmpInst::ICMP_NE;
5068 if ((RA - 1).isMinSignedValue()) {
5069 Pred = ICmpInst::ICMP_EQ;
5070 RHS = getConstant(RA - 1);
5074 if (RA.isMinSignedValue()) goto trivially_false;
5079 // Check for obvious equality.
5080 if (HasSameValue(LHS, RHS)) {
5081 if (ICmpInst::isTrueWhenEqual(Pred))
5082 goto trivially_true;
5083 if (ICmpInst::isFalseWhenEqual(Pred))
5084 goto trivially_false;
5087 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
5088 // adding or subtracting 1 from one of the operands.
5090 case ICmpInst::ICMP_SLE:
5091 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) {
5092 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
5093 /*HasNUW=*/false, /*HasNSW=*/true);
5094 Pred = ICmpInst::ICMP_SLT;
5096 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) {
5097 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
5098 /*HasNUW=*/false, /*HasNSW=*/true);
5099 Pred = ICmpInst::ICMP_SLT;
5103 case ICmpInst::ICMP_SGE:
5104 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) {
5105 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
5106 /*HasNUW=*/false, /*HasNSW=*/true);
5107 Pred = ICmpInst::ICMP_SGT;
5109 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) {
5110 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
5111 /*HasNUW=*/false, /*HasNSW=*/true);
5112 Pred = ICmpInst::ICMP_SGT;
5116 case ICmpInst::ICMP_ULE:
5117 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) {
5118 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
5119 /*HasNUW=*/true, /*HasNSW=*/false);
5120 Pred = ICmpInst::ICMP_ULT;
5122 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) {
5123 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
5124 /*HasNUW=*/true, /*HasNSW=*/false);
5125 Pred = ICmpInst::ICMP_ULT;
5129 case ICmpInst::ICMP_UGE:
5130 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) {
5131 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
5132 /*HasNUW=*/true, /*HasNSW=*/false);
5133 Pred = ICmpInst::ICMP_UGT;
5135 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) {
5136 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
5137 /*HasNUW=*/true, /*HasNSW=*/false);
5138 Pred = ICmpInst::ICMP_UGT;
5146 // TODO: More simplifications are possible here.
5152 LHS = RHS = getConstant(Type::getInt1Ty(getContext()), 0);
5153 Pred = ICmpInst::ICMP_EQ;
5158 LHS = RHS = getConstant(Type::getInt1Ty(getContext()), 0);
5159 Pred = ICmpInst::ICMP_NE;
5163 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
5164 return getSignedRange(S).getSignedMax().isNegative();
5167 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
5168 return getSignedRange(S).getSignedMin().isStrictlyPositive();
5171 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
5172 return !getSignedRange(S).getSignedMin().isNegative();
5175 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
5176 return !getSignedRange(S).getSignedMax().isStrictlyPositive();
5179 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
5180 return isKnownNegative(S) || isKnownPositive(S);
5183 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
5184 const SCEV *LHS, const SCEV *RHS) {
5185 // Canonicalize the inputs first.
5186 (void)SimplifyICmpOperands(Pred, LHS, RHS);
5188 // If LHS or RHS is an addrec, check to see if the condition is true in
5189 // every iteration of the loop.
5190 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
5191 if (isLoopEntryGuardedByCond(
5192 AR->getLoop(), Pred, AR->getStart(), RHS) &&
5193 isLoopBackedgeGuardedByCond(
5194 AR->getLoop(), Pred, AR->getPostIncExpr(*this), RHS))
5196 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS))
5197 if (isLoopEntryGuardedByCond(
5198 AR->getLoop(), Pred, LHS, AR->getStart()) &&
5199 isLoopBackedgeGuardedByCond(
5200 AR->getLoop(), Pred, LHS, AR->getPostIncExpr(*this)))
5203 // Otherwise see what can be done with known constant ranges.
5204 return isKnownPredicateWithRanges(Pred, LHS, RHS);
5208 ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred,
5209 const SCEV *LHS, const SCEV *RHS) {
5210 if (HasSameValue(LHS, RHS))
5211 return ICmpInst::isTrueWhenEqual(Pred);
5213 // This code is split out from isKnownPredicate because it is called from
5214 // within isLoopEntryGuardedByCond.
5217 llvm_unreachable("Unexpected ICmpInst::Predicate value!");
5219 case ICmpInst::ICMP_SGT:
5220 Pred = ICmpInst::ICMP_SLT;
5221 std::swap(LHS, RHS);
5222 case ICmpInst::ICMP_SLT: {
5223 ConstantRange LHSRange = getSignedRange(LHS);
5224 ConstantRange RHSRange = getSignedRange(RHS);
5225 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
5227 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
5231 case ICmpInst::ICMP_SGE:
5232 Pred = ICmpInst::ICMP_SLE;
5233 std::swap(LHS, RHS);
5234 case ICmpInst::ICMP_SLE: {
5235 ConstantRange LHSRange = getSignedRange(LHS);
5236 ConstantRange RHSRange = getSignedRange(RHS);
5237 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
5239 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
5243 case ICmpInst::ICMP_UGT:
5244 Pred = ICmpInst::ICMP_ULT;
5245 std::swap(LHS, RHS);
5246 case ICmpInst::ICMP_ULT: {
5247 ConstantRange LHSRange = getUnsignedRange(LHS);
5248 ConstantRange RHSRange = getUnsignedRange(RHS);
5249 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
5251 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
5255 case ICmpInst::ICMP_UGE:
5256 Pred = ICmpInst::ICMP_ULE;
5257 std::swap(LHS, RHS);
5258 case ICmpInst::ICMP_ULE: {
5259 ConstantRange LHSRange = getUnsignedRange(LHS);
5260 ConstantRange RHSRange = getUnsignedRange(RHS);
5261 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
5263 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
5267 case ICmpInst::ICMP_NE: {
5268 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
5270 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
5273 const SCEV *Diff = getMinusSCEV(LHS, RHS);
5274 if (isKnownNonZero(Diff))
5278 case ICmpInst::ICMP_EQ:
5279 // The check at the top of the function catches the case where
5280 // the values are known to be equal.
5286 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
5287 /// protected by a conditional between LHS and RHS. This is used to
5288 /// to eliminate casts.
5290 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
5291 ICmpInst::Predicate Pred,
5292 const SCEV *LHS, const SCEV *RHS) {
5293 // Interpret a null as meaning no loop, where there is obviously no guard
5294 // (interprocedural conditions notwithstanding).
5295 if (!L) return true;
5297 BasicBlock *Latch = L->getLoopLatch();
5301 BranchInst *LoopContinuePredicate =
5302 dyn_cast<BranchInst>(Latch->getTerminator());
5303 if (!LoopContinuePredicate ||
5304 LoopContinuePredicate->isUnconditional())
5307 return isImpliedCond(Pred, LHS, RHS,
5308 LoopContinuePredicate->getCondition(),
5309 LoopContinuePredicate->getSuccessor(0) != L->getHeader());
5312 /// isLoopEntryGuardedByCond - Test whether entry to the loop is protected
5313 /// by a conditional between LHS and RHS. This is used to help avoid max
5314 /// expressions in loop trip counts, and to eliminate casts.
5316 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
5317 ICmpInst::Predicate Pred,
5318 const SCEV *LHS, const SCEV *RHS) {
5319 // Interpret a null as meaning no loop, where there is obviously no guard
5320 // (interprocedural conditions notwithstanding).
5321 if (!L) return false;
5323 // Starting at the loop predecessor, climb up the predecessor chain, as long
5324 // as there are predecessors that can be found that have unique successors
5325 // leading to the original header.
5326 for (std::pair<BasicBlock *, BasicBlock *>
5327 Pair(L->getLoopPredecessor(), L->getHeader());
5329 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
5331 BranchInst *LoopEntryPredicate =
5332 dyn_cast<BranchInst>(Pair.first->getTerminator());
5333 if (!LoopEntryPredicate ||
5334 LoopEntryPredicate->isUnconditional())
5337 if (isImpliedCond(Pred, LHS, RHS,
5338 LoopEntryPredicate->getCondition(),
5339 LoopEntryPredicate->getSuccessor(0) != Pair.second))
5346 /// isImpliedCond - Test whether the condition described by Pred, LHS,
5347 /// and RHS is true whenever the given Cond value evaluates to true.
5348 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred,
5349 const SCEV *LHS, const SCEV *RHS,
5350 Value *FoundCondValue,
5352 // Recursively handle And and Or conditions.
5353 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) {
5354 if (BO->getOpcode() == Instruction::And) {
5356 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
5357 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
5358 } else if (BO->getOpcode() == Instruction::Or) {
5360 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
5361 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
5365 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue);
5366 if (!ICI) return false;
5368 // Bail if the ICmp's operands' types are wider than the needed type
5369 // before attempting to call getSCEV on them. This avoids infinite
5370 // recursion, since the analysis of widening casts can require loop
5371 // exit condition information for overflow checking, which would
5373 if (getTypeSizeInBits(LHS->getType()) <
5374 getTypeSizeInBits(ICI->getOperand(0)->getType()))
5377 // Now that we found a conditional branch that dominates the loop, check to
5378 // see if it is the comparison we are looking for.
5379 ICmpInst::Predicate FoundPred;
5381 FoundPred = ICI->getInversePredicate();
5383 FoundPred = ICI->getPredicate();
5385 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
5386 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
5388 // Balance the types. The case where FoundLHS' type is wider than
5389 // LHS' type is checked for above.
5390 if (getTypeSizeInBits(LHS->getType()) >
5391 getTypeSizeInBits(FoundLHS->getType())) {
5392 if (CmpInst::isSigned(Pred)) {
5393 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
5394 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
5396 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
5397 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
5401 // Canonicalize the query to match the way instcombine will have
5402 // canonicalized the comparison.
5403 if (SimplifyICmpOperands(Pred, LHS, RHS))
5405 return CmpInst::isTrueWhenEqual(Pred);
5406 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
5407 if (FoundLHS == FoundRHS)
5408 return CmpInst::isFalseWhenEqual(Pred);
5410 // Check to see if we can make the LHS or RHS match.
5411 if (LHS == FoundRHS || RHS == FoundLHS) {
5412 if (isa<SCEVConstant>(RHS)) {
5413 std::swap(FoundLHS, FoundRHS);
5414 FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
5416 std::swap(LHS, RHS);
5417 Pred = ICmpInst::getSwappedPredicate(Pred);
5421 // Check whether the found predicate is the same as the desired predicate.
5422 if (FoundPred == Pred)
5423 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
5425 // Check whether swapping the found predicate makes it the same as the
5426 // desired predicate.
5427 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
5428 if (isa<SCEVConstant>(RHS))
5429 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
5431 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
5432 RHS, LHS, FoundLHS, FoundRHS);
5435 // Check whether the actual condition is beyond sufficient.
5436 if (FoundPred == ICmpInst::ICMP_EQ)
5437 if (ICmpInst::isTrueWhenEqual(Pred))
5438 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
5440 if (Pred == ICmpInst::ICMP_NE)
5441 if (!ICmpInst::isTrueWhenEqual(FoundPred))
5442 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
5445 // Otherwise assume the worst.
5449 /// isImpliedCondOperands - Test whether the condition described by Pred,
5450 /// LHS, and RHS is true whenever the condition described by Pred, FoundLHS,
5451 /// and FoundRHS is true.
5452 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
5453 const SCEV *LHS, const SCEV *RHS,
5454 const SCEV *FoundLHS,
5455 const SCEV *FoundRHS) {
5456 return isImpliedCondOperandsHelper(Pred, LHS, RHS,
5457 FoundLHS, FoundRHS) ||
5458 // ~x < ~y --> x > y
5459 isImpliedCondOperandsHelper(Pred, LHS, RHS,
5460 getNotSCEV(FoundRHS),
5461 getNotSCEV(FoundLHS));
5464 /// isImpliedCondOperandsHelper - Test whether the condition described by
5465 /// Pred, LHS, and RHS is true whenever the condition described by Pred,
5466 /// FoundLHS, and FoundRHS is true.
5468 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
5469 const SCEV *LHS, const SCEV *RHS,
5470 const SCEV *FoundLHS,
5471 const SCEV *FoundRHS) {
5473 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
5474 case ICmpInst::ICMP_EQ:
5475 case ICmpInst::ICMP_NE:
5476 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
5479 case ICmpInst::ICMP_SLT:
5480 case ICmpInst::ICMP_SLE:
5481 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
5482 isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, RHS, FoundRHS))
5485 case ICmpInst::ICMP_SGT:
5486 case ICmpInst::ICMP_SGE:
5487 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
5488 isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, RHS, FoundRHS))
5491 case ICmpInst::ICMP_ULT:
5492 case ICmpInst::ICMP_ULE:
5493 if (isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
5494 isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, RHS, FoundRHS))
5497 case ICmpInst::ICMP_UGT:
5498 case ICmpInst::ICMP_UGE:
5499 if (isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
5500 isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, RHS, FoundRHS))
5508 /// getBECount - Subtract the end and start values and divide by the step,
5509 /// rounding up, to get the number of times the backedge is executed. Return
5510 /// CouldNotCompute if an intermediate computation overflows.
5511 const SCEV *ScalarEvolution::getBECount(const SCEV *Start,
5515 assert(!isKnownNegative(Step) &&
5516 "This code doesn't handle negative strides yet!");
5518 const Type *Ty = Start->getType();
5519 const SCEV *NegOne = getConstant(Ty, (uint64_t)-1);
5520 const SCEV *Diff = getMinusSCEV(End, Start);
5521 const SCEV *RoundUp = getAddExpr(Step, NegOne);
5523 // Add an adjustment to the difference between End and Start so that
5524 // the division will effectively round up.
5525 const SCEV *Add = getAddExpr(Diff, RoundUp);
5528 // Check Add for unsigned overflow.
5529 // TODO: More sophisticated things could be done here.
5530 const Type *WideTy = IntegerType::get(getContext(),
5531 getTypeSizeInBits(Ty) + 1);
5532 const SCEV *EDiff = getZeroExtendExpr(Diff, WideTy);
5533 const SCEV *ERoundUp = getZeroExtendExpr(RoundUp, WideTy);
5534 const SCEV *OperandExtendedAdd = getAddExpr(EDiff, ERoundUp);
5535 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd)
5536 return getCouldNotCompute();
5539 return getUDivExpr(Add, Step);
5542 /// HowManyLessThans - Return the number of times a backedge containing the
5543 /// specified less-than comparison will execute. If not computable, return
5544 /// CouldNotCompute.
5545 ScalarEvolution::BackedgeTakenInfo
5546 ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
5547 const Loop *L, bool isSigned) {
5548 // Only handle: "ADDREC < LoopInvariant".
5549 if (!RHS->isLoopInvariant(L)) return getCouldNotCompute();
5551 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
5552 if (!AddRec || AddRec->getLoop() != L)
5553 return getCouldNotCompute();
5555 // Check to see if we have a flag which makes analysis easy.
5556 bool NoWrap = isSigned ? AddRec->hasNoSignedWrap() :
5557 AddRec->hasNoUnsignedWrap();
5559 if (AddRec->isAffine()) {
5560 unsigned BitWidth = getTypeSizeInBits(AddRec->getType());
5561 const SCEV *Step = AddRec->getStepRecurrence(*this);
5564 return getCouldNotCompute();
5565 if (Step->isOne()) {
5566 // With unit stride, the iteration never steps past the limit value.
5567 } else if (isKnownPositive(Step)) {
5568 // Test whether a positive iteration can step past the limit
5569 // value and past the maximum value for its type in a single step.
5570 // Note that it's not sufficient to check NoWrap here, because even
5571 // though the value after a wrap is undefined, it's not undefined
5572 // behavior, so if wrap does occur, the loop could either terminate or
5573 // loop infinitely, but in either case, the loop is guaranteed to
5574 // iterate at least until the iteration where the wrapping occurs.
5575 const SCEV *One = getConstant(Step->getType(), 1);
5577 APInt Max = APInt::getSignedMaxValue(BitWidth);
5578 if ((Max - getSignedRange(getMinusSCEV(Step, One)).getSignedMax())
5579 .slt(getSignedRange(RHS).getSignedMax()))
5580 return getCouldNotCompute();
5582 APInt Max = APInt::getMaxValue(BitWidth);
5583 if ((Max - getUnsignedRange(getMinusSCEV(Step, One)).getUnsignedMax())
5584 .ult(getUnsignedRange(RHS).getUnsignedMax()))
5585 return getCouldNotCompute();
5588 // TODO: Handle negative strides here and below.
5589 return getCouldNotCompute();
5591 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant
5592 // m. So, we count the number of iterations in which {n,+,s} < m is true.
5593 // Note that we cannot simply return max(m-n,0)/s because it's not safe to
5594 // treat m-n as signed nor unsigned due to overflow possibility.
5596 // First, we get the value of the LHS in the first iteration: n
5597 const SCEV *Start = AddRec->getOperand(0);
5599 // Determine the minimum constant start value.
5600 const SCEV *MinStart = getConstant(isSigned ?
5601 getSignedRange(Start).getSignedMin() :
5602 getUnsignedRange(Start).getUnsignedMin());
5604 // If we know that the condition is true in order to enter the loop,
5605 // then we know that it will run exactly (m-n)/s times. Otherwise, we
5606 // only know that it will execute (max(m,n)-n)/s times. In both cases,
5607 // the division must round up.
5608 const SCEV *End = RHS;
5609 if (!isLoopEntryGuardedByCond(L,
5610 isSigned ? ICmpInst::ICMP_SLT :
5612 getMinusSCEV(Start, Step), RHS))
5613 End = isSigned ? getSMaxExpr(RHS, Start)
5614 : getUMaxExpr(RHS, Start);
5616 // Determine the maximum constant end value.
5617 const SCEV *MaxEnd = getConstant(isSigned ?
5618 getSignedRange(End).getSignedMax() :
5619 getUnsignedRange(End).getUnsignedMax());
5621 // If MaxEnd is within a step of the maximum integer value in its type,
5622 // adjust it down to the minimum value which would produce the same effect.
5623 // This allows the subsequent ceiling division of (N+(step-1))/step to
5624 // compute the correct value.
5625 const SCEV *StepMinusOne = getMinusSCEV(Step,
5626 getConstant(Step->getType(), 1));
5629 getMinusSCEV(getConstant(APInt::getSignedMaxValue(BitWidth)),
5632 getMinusSCEV(getConstant(APInt::getMaxValue(BitWidth)),
5635 // Finally, we subtract these two values and divide, rounding up, to get
5636 // the number of times the backedge is executed.
5637 const SCEV *BECount = getBECount(Start, End, Step, NoWrap);
5639 // The maximum backedge count is similar, except using the minimum start
5640 // value and the maximum end value.
5641 const SCEV *MaxBECount = getBECount(MinStart, MaxEnd, Step, NoWrap);
5643 return BackedgeTakenInfo(BECount, MaxBECount);
5646 return getCouldNotCompute();
5649 /// getNumIterationsInRange - Return the number of iterations of this loop that
5650 /// produce values in the specified constant range. Another way of looking at
5651 /// this is that it returns the first iteration number where the value is not in
5652 /// the condition, thus computing the exit count. If the iteration count can't
5653 /// be computed, an instance of SCEVCouldNotCompute is returned.
5654 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
5655 ScalarEvolution &SE) const {
5656 if (Range.isFullSet()) // Infinite loop.
5657 return SE.getCouldNotCompute();
5659 // If the start is a non-zero constant, shift the range to simplify things.
5660 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
5661 if (!SC->getValue()->isZero()) {
5662 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
5663 Operands[0] = SE.getConstant(SC->getType(), 0);
5664 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop());
5665 if (const SCEVAddRecExpr *ShiftedAddRec =
5666 dyn_cast<SCEVAddRecExpr>(Shifted))
5667 return ShiftedAddRec->getNumIterationsInRange(
5668 Range.subtract(SC->getValue()->getValue()), SE);
5669 // This is strange and shouldn't happen.
5670 return SE.getCouldNotCompute();
5673 // The only time we can solve this is when we have all constant indices.
5674 // Otherwise, we cannot determine the overflow conditions.
5675 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
5676 if (!isa<SCEVConstant>(getOperand(i)))
5677 return SE.getCouldNotCompute();
5680 // Okay at this point we know that all elements of the chrec are constants and
5681 // that the start element is zero.
5683 // First check to see if the range contains zero. If not, the first
5685 unsigned BitWidth = SE.getTypeSizeInBits(getType());
5686 if (!Range.contains(APInt(BitWidth, 0)))
5687 return SE.getConstant(getType(), 0);
5690 // If this is an affine expression then we have this situation:
5691 // Solve {0,+,A} in Range === Ax in Range
5693 // We know that zero is in the range. If A is positive then we know that
5694 // the upper value of the range must be the first possible exit value.
5695 // If A is negative then the lower of the range is the last possible loop
5696 // value. Also note that we already checked for a full range.
5697 APInt One(BitWidth,1);
5698 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
5699 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
5701 // The exit value should be (End+A)/A.
5702 APInt ExitVal = (End + A).udiv(A);
5703 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
5705 // Evaluate at the exit value. If we really did fall out of the valid
5706 // range, then we computed our trip count, otherwise wrap around or other
5707 // things must have happened.
5708 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
5709 if (Range.contains(Val->getValue()))
5710 return SE.getCouldNotCompute(); // Something strange happened
5712 // Ensure that the previous value is in the range. This is a sanity check.
5713 assert(Range.contains(
5714 EvaluateConstantChrecAtConstant(this,
5715 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
5716 "Linear scev computation is off in a bad way!");
5717 return SE.getConstant(ExitValue);
5718 } else if (isQuadratic()) {
5719 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
5720 // quadratic equation to solve it. To do this, we must frame our problem in
5721 // terms of figuring out when zero is crossed, instead of when
5722 // Range.getUpper() is crossed.
5723 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
5724 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
5725 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop());
5727 // Next, solve the constructed addrec
5728 std::pair<const SCEV *,const SCEV *> Roots =
5729 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
5730 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
5731 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
5733 // Pick the smallest positive root value.
5734 if (ConstantInt *CB =
5735 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
5736 R1->getValue(), R2->getValue()))) {
5737 if (CB->getZExtValue() == false)
5738 std::swap(R1, R2); // R1 is the minimum root now.
5740 // Make sure the root is not off by one. The returned iteration should
5741 // not be in the range, but the previous one should be. When solving
5742 // for "X*X < 5", for example, we should not return a root of 2.
5743 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
5746 if (Range.contains(R1Val->getValue())) {
5747 // The next iteration must be out of the range...
5748 ConstantInt *NextVal =
5749 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1);
5751 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
5752 if (!Range.contains(R1Val->getValue()))
5753 return SE.getConstant(NextVal);
5754 return SE.getCouldNotCompute(); // Something strange happened
5757 // If R1 was not in the range, then it is a good return value. Make
5758 // sure that R1-1 WAS in the range though, just in case.
5759 ConstantInt *NextVal =
5760 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1);
5761 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
5762 if (Range.contains(R1Val->getValue()))
5764 return SE.getCouldNotCompute(); // Something strange happened
5769 return SE.getCouldNotCompute();
5774 //===----------------------------------------------------------------------===//
5775 // SCEVCallbackVH Class Implementation
5776 //===----------------------------------------------------------------------===//
5778 void ScalarEvolution::SCEVCallbackVH::deleted() {
5779 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
5780 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
5781 SE->ConstantEvolutionLoopExitValue.erase(PN);
5782 SE->ValueExprMap.erase(getValPtr());
5783 // this now dangles!
5786 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) {
5787 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
5789 // Forget all the expressions associated with users of the old value,
5790 // so that future queries will recompute the expressions using the new
5792 Value *Old = getValPtr();
5793 SmallVector<User *, 16> Worklist;
5794 SmallPtrSet<User *, 8> Visited;
5795 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end();
5797 Worklist.push_back(*UI);
5798 while (!Worklist.empty()) {
5799 User *U = Worklist.pop_back_val();
5800 // Deleting the Old value will cause this to dangle. Postpone
5801 // that until everything else is done.
5804 if (!Visited.insert(U))
5806 if (PHINode *PN = dyn_cast<PHINode>(U))
5807 SE->ConstantEvolutionLoopExitValue.erase(PN);
5808 SE->ValueExprMap.erase(U);
5809 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end();
5811 Worklist.push_back(*UI);
5813 // Delete the Old value.
5814 if (PHINode *PN = dyn_cast<PHINode>(Old))
5815 SE->ConstantEvolutionLoopExitValue.erase(PN);
5816 SE->ValueExprMap.erase(Old);
5817 // this now dangles!
5820 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
5821 : CallbackVH(V), SE(se) {}
5823 //===----------------------------------------------------------------------===//
5824 // ScalarEvolution Class Implementation
5825 //===----------------------------------------------------------------------===//
5827 ScalarEvolution::ScalarEvolution()
5828 : FunctionPass(ID), FirstUnknown(0) {
5831 bool ScalarEvolution::runOnFunction(Function &F) {
5833 LI = &getAnalysis<LoopInfo>();
5834 TD = getAnalysisIfAvailable<TargetData>();
5835 DT = &getAnalysis<DominatorTree>();
5839 void ScalarEvolution::releaseMemory() {
5840 // Iterate through all the SCEVUnknown instances and call their
5841 // destructors, so that they release their references to their values.
5842 for (SCEVUnknown *U = FirstUnknown; U; U = U->Next)
5846 ValueExprMap.clear();
5847 BackedgeTakenCounts.clear();
5848 ConstantEvolutionLoopExitValue.clear();
5849 ValuesAtScopes.clear();
5850 UniqueSCEVs.clear();
5851 SCEVAllocator.Reset();
5854 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
5855 AU.setPreservesAll();
5856 AU.addRequiredTransitive<LoopInfo>();
5857 AU.addRequiredTransitive<DominatorTree>();
5860 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
5861 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
5864 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
5866 // Print all inner loops first
5867 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
5868 PrintLoopInfo(OS, SE, *I);
5871 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
5874 SmallVector<BasicBlock *, 8> ExitBlocks;
5875 L->getExitBlocks(ExitBlocks);
5876 if (ExitBlocks.size() != 1)
5877 OS << "<multiple exits> ";
5879 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
5880 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
5882 OS << "Unpredictable backedge-taken count. ";
5887 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
5890 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
5891 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
5893 OS << "Unpredictable max backedge-taken count. ";
5899 void ScalarEvolution::print(raw_ostream &OS, const Module *) const {
5900 // ScalarEvolution's implementation of the print method is to print
5901 // out SCEV values of all instructions that are interesting. Doing
5902 // this potentially causes it to create new SCEV objects though,
5903 // which technically conflicts with the const qualifier. This isn't
5904 // observable from outside the class though, so casting away the
5905 // const isn't dangerous.
5906 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
5908 OS << "Classifying expressions for: ";
5909 WriteAsOperand(OS, F, /*PrintType=*/false);
5911 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
5912 if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) {
5915 const SCEV *SV = SE.getSCEV(&*I);
5918 const Loop *L = LI->getLoopFor((*I).getParent());
5920 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
5927 OS << "\t\t" "Exits: ";
5928 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
5929 if (!ExitValue->isLoopInvariant(L)) {
5930 OS << "<<Unknown>>";
5939 OS << "Determining loop execution counts for: ";
5940 WriteAsOperand(OS, F, /*PrintType=*/false);
5942 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
5943 PrintLoopInfo(OS, &SE, *I);